LMFDB - Embedded newform 38.9.f.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,9,Mod(3,38)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([13]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("38.3");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	38.f (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.4803871823$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	38.13
Dual form			38.9.f.a.3.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.27231 - 8.66680i) q^{2} +(-41.5037 + 114.031i) q^{3} +(-22.2270 + 126.055i) q^{4} +(-20.6862 - 117.317i) q^{5} +(1290.11 - 469.561i) q^{6} +(2332.01 - 4039.17i) q^{7} +(1254.14 - 724.077i) q^{8} +(-6254.38 - 5248.05i) q^{9} +O(q^{10})$	\(q+(-7.27231 - 8.66680i) q^{2} +(-41.5037 + 114.031i) q^{3} +(-22.2270 + 126.055i) q^{4} +(-20.6862 - 117.317i) q^{5} +(1290.11 - 469.561i) q^{6} +(2332.01 - 4039.17i) q^{7} +(1254.14 - 724.077i) q^{8} +(-6254.38 - 5248.05i) q^{9} +(-866.329 + 1032.45i) q^{10} +(6621.83 + 11469.3i) q^{11} +(-13451.7 - 7766.32i) q^{12} +(14386.2 + 39525.7i) q^{13} +(-51965.8 + 9162.97i) q^{14} +(14236.3 + 2510.24i) q^{15} +(-15395.9 - 5603.66i) q^{16} +(9772.70 - 8200.27i) q^{17} +92370.9i q^{18} +(-118377. - 54501.0i) q^{19} +15248.3 q^{20} +(363801. + 433561. i) q^{21} +(51246.6 - 140799. i) q^{22} +(-49555.2 + 281042. i) q^{23} +(30515.5 + 173062. i) q^{24} +(353732. - 128748. i) q^{25} +(237940. - 412125. i) q^{26} +(168515. - 97292.2i) q^{27} +(457325. + 383741. i) q^{28} +(-304613. + 363024. i) q^{29} +(-81775.0 - 141639. i) q^{30} +(943123. + 544512. i) q^{31} +(63398.2 + 174185. i) q^{32} +(-1.58269e6 + 279070. i) q^{33} +(-142140. - 25063.2i) q^{34} +(-522104. - 190030. i) q^{35} +(800561. - 671750. i) q^{36} +1.90549e6i q^{37} +(388528. + 1.42230e6i) q^{38} -5.10421e6 q^{39} +(-110890. - 132154. i) q^{40} +(437817. - 1.20289e6i) q^{41} +(1.11191e6 - 6.30598e6i) q^{42} +(167248. + 948510. i) q^{43} +(-1.59296e6 + 579789. i) q^{44} +(-486307. + 842309. i) q^{45} +(2.79611e6 - 1.61434e6i) q^{46} +(4.84784e6 + 4.06782e6i) q^{47} +(1.27798e6 - 1.52303e6i) q^{48} +(-7.99417e6 - 1.38463e7i) q^{49} +(-3.68828e6 - 2.12943e6i) q^{50} +(529478. + 1.45473e6i) q^{51} +(-5.30218e6 + 934918. i) q^{52} +(6.40058e6 + 1.12860e6i) q^{53} +(-2.06871e6 - 752948. i) q^{54} +(1.20857e6 - 1.01411e6i) q^{55} -6.75423e6i q^{56} +(1.11279e7 - 1.12366e7i) q^{57} +5.36149e6 q^{58} +(1.47919e7 + 1.76282e7i) q^{59} +(-632860. + 1.73877e6i) q^{60} +(-659353. + 3.73938e6i) q^{61} +(-2.13950e6 - 1.21337e7i) q^{62} +(-3.57830e7 + 1.30240e7i) q^{63} +(1.04858e6 - 1.81619e6i) q^{64} +(4.33945e6 - 2.50538e6i) q^{65} +(1.39284e7 + 1.16873e7i) q^{66} +(-1.63178e7 + 1.94468e7i) q^{67} +(816471. + 1.41417e6i) q^{68} +(-2.99906e7 - 1.73151e7i) q^{69} +(2.14995e6 + 5.90694e6i) q^{70} +(-6.75035e6 + 1.19027e6i) q^{71} +(-1.16439e7 - 2.05313e6i) q^{72} +(-409903. - 149193. i) q^{73} +(1.65145e7 - 1.38573e7i) q^{74} +4.56798e7i q^{75} +(9.50131e6 - 1.37107e7i) q^{76} +6.17688e7 q^{77} +(3.71194e7 + 4.42372e7i) q^{78} +(8.08570e6 - 2.22153e7i) q^{79} +(-338923. + 1.92213e6i) q^{80} +(-5.20160e6 - 2.94997e7i) q^{81} +(-1.36092e7 + 4.95334e6i) q^{82} +(1.09019e7 - 1.88826e7i) q^{83} +(-6.27389e7 + 3.62223e7i) q^{84} +(-1.16419e6 - 976874. i) q^{85} +(7.00427e6 - 8.34736e6i) q^{86} +(-2.87532e7 - 4.98020e7i) q^{87} +(1.66094e7 + 9.58944e6i) q^{88} +(3.42710e7 + 9.41587e7i) q^{89} +(1.08367e7 - 1.91080e6i) q^{90} +(1.93199e8 + 3.40663e7i) q^{91} +(-3.43253e7 - 1.24934e7i) q^{92} +(-1.01234e8 + 8.49455e7i) q^{93} -7.15978e7i q^{94} +(-3.94513e6 + 1.50151e7i) q^{95} -2.24937e7 q^{96} +(-9.63387e7 - 1.14812e8i) q^{97} +(-6.18671e7 + 1.69979e8i) q^{98} +(1.87762e7 - 1.06485e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 168 q^{3} - 2688 q^{6} - 6570 q^{7} - 2856 q^{9}+O(q^{10}) $ 84 * q - 168 * q^3 - 2688 * q^6 - 6570 * q^7 - 2856 * q^9	\( 84 q - 168 q^{3} - 2688 q^{6} - 6570 q^{7} - 2856 q^{9} - 20970 q^{11} + 62208 q^{12} - 101310 q^{13} - 142848 q^{14} + 331518 q^{15} + 29178 q^{17} - 319212 q^{19} - 428544 q^{20} - 186138 q^{21} + 1238016 q^{22} + 1989360 q^{23} + 344064 q^{24} - 272916 q^{25} - 695808 q^{26} - 6975648 q^{27} - 489984 q^{28} + 1676430 q^{29} - 3498768 q^{31} + 6273750 q^{33} + 2740224 q^{34} + 10942362 q^{35} + 365568 q^{36} + 5830272 q^{38} - 23638704 q^{39} + 430488 q^{41} + 4230144 q^{42} - 20999118 q^{43} + 700416 q^{44} + 49897728 q^{45} + 12003840 q^{46} - 22431150 q^{47} - 5505024 q^{48} - 59138004 q^{49} - 24993792 q^{50} + 6061860 q^{51} - 2857728 q^{52} + 69029982 q^{53} + 63262080 q^{54} + 20438670 q^{55} - 50408076 q^{57} - 31266816 q^{58} - 85956678 q^{59} - 9106176 q^{60} + 29908896 q^{61} - 39755520 q^{62} - 29288274 q^{63} + 88080384 q^{64} + 199314810 q^{65} + 117652224 q^{66} + 64371642 q^{67} + 25820928 q^{68} - 186304482 q^{69} - 187792896 q^{70} - 168095268 q^{71} + 23396352 q^{72} + 104437176 q^{73} + 33624576 q^{74} + 6617088 q^{76} - 277281288 q^{77} + 30777600 q^{78} + 199146114 q^{79} + 245855040 q^{81} - 69199872 q^{82} - 14372262 q^{83} - 348399360 q^{84} - 386680068 q^{85} - 155904768 q^{86} + 36917496 q^{87} + 292036248 q^{89} + 694869504 q^{90} + 285753588 q^{91} + 95143680 q^{92} + 529006800 q^{93} - 166014666 q^{95} + 251818254 q^{97} - 595464192 q^{98} - 1180902678 q^{99}+O(q^{100}) \) 84 * q - 168 * q^3 - 2688 * q^6 - 6570 * q^7 - 2856 * q^9 - 20970 * q^11 + 62208 * q^12 - 101310 * q^13 - 142848 * q^14 + 331518 * q^15 + 29178 * q^17 - 319212 * q^19 - 428544 * q^20 - 186138 * q^21 + 1238016 * q^22 + 1989360 * q^23 + 344064 * q^24 - 272916 * q^25 - 695808 * q^26 - 6975648 * q^27 - 489984 * q^28 + 1676430 * q^29 - 3498768 * q^31 + 6273750 * q^33 + 2740224 * q^34 + 10942362 * q^35 + 365568 * q^36 + 5830272 * q^38 - 23638704 * q^39 + 430488 * q^41 + 4230144 * q^42 - 20999118 * q^43 + 700416 * q^44 + 49897728 * q^45 + 12003840 * q^46 - 22431150 * q^47 - 5505024 * q^48 - 59138004 * q^49 - 24993792 * q^50 + 6061860 * q^51 - 2857728 * q^52 + 69029982 * q^53 + 63262080 * q^54 + 20438670 * q^55 - 50408076 * q^57 - 31266816 * q^58 - 85956678 * q^59 - 9106176 * q^60 + 29908896 * q^61 - 39755520 * q^62 - 29288274 * q^63 + 88080384 * q^64 + 199314810 * q^65 + 117652224 * q^66 + 64371642 * q^67 + 25820928 * q^68 - 186304482 * q^69 - 187792896 * q^70 - 168095268 * q^71 + 23396352 * q^72 + 104437176 * q^73 + 33624576 * q^74 + 6617088 * q^76 - 277281288 * q^77 + 30777600 * q^78 + 199146114 * q^79 + 245855040 * q^81 - 69199872 * q^82 - 14372262 * q^83 - 348399360 * q^84 - 386680068 * q^85 - 155904768 * q^86 + 36917496 * q^87 + 292036248 * q^89 + 694869504 * q^90 + 285753588 * q^91 + 95143680 * q^92 + 529006800 * q^93 - 166014666 * q^95 + 251818254 * q^97 - 595464192 * q^98 - 1180902678 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{5}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−7.27231	−	8.66680i	−0.454519	−	0.541675i
$2$	−7.27231	−	8.66680i	−0.454519	−	0.541675i
$3$	−41.5037	+	114.031i	−0.512391	+	1.40778i	0.366346	+	0.930479i	$0.380609\pi$
$3$	−41.5037	+	114.031i	−0.512391	+	1.40778i	−0.878738	+	0.477305i	$0.841614\pi$
$4$	−22.2270	+	126.055i	−0.0868241	+	0.492404i
$5$	−20.6862	−	117.317i	−0.0330979	−	0.187708i	0.963776	−	0.266712i	$-0.0859371\pi$
$5$	−20.6862	−	117.317i	−0.0330979	−	0.187708i	−0.996874	+	0.0790040i	$0.974826\pi$
$6$	1290.11	−	469.561i	0.995454	−	0.362315i
$7$	2332.01	−	4039.17i	0.971267	−	1.68228i	0.279528	−	0.960138i	$-0.409822\pi$
$7$	2332.01	−	4039.17i	0.971267	−	1.68228i	0.691740	−	0.722147i	$-0.256844\pi$
$8$	1254.14	−	724.077i	0.306186	−	0.176777i
$9$	−6254.38	−	5248.05i	−0.953266	−	0.799885i
$10$	−866.329	+	1032.45i	−0.0866329	+	0.103245i
$11$	6621.83	+	11469.3i	0.452280	+	0.783372i	0.998527	−	0.0542520i	$-0.0172774\pi$
$11$	6621.83	+	11469.3i	0.452280	+	0.783372i	−0.546247	+	0.837624i	$0.683944\pi$
$12$	−13451.7	−	7766.32i	−0.648710	−	0.374533i
$13$	14386.2	+	39525.7i	0.503699	+	1.38390i	0.887637	+	0.460544i	$0.152346\pi$
$13$	14386.2	+	39525.7i	0.503699	+	1.38390i	−0.383938	+	0.923359i	$0.625432\pi$
$14$	−51965.8	+	9162.97i	−1.35271	+	0.238520i
$15$	14236.3	+	2510.24i	0.281211	+	0.0495851i
$16$	−15395.9	−	5603.66i	−0.234923	−	0.0855050i
$17$	9772.70	−	8200.27i	0.117009	−	0.0981821i	−0.582406	−	0.812898i	$-0.697889\pi$
$17$	9772.70	−	8200.27i	0.117009	−	0.0981821i	0.699415	+	0.714716i	$0.253444\pi$
$18$			92370.9i			0.879924i
$19$	−118377.	−	54501.0i	−0.908352	−	0.418206i
$19$	−118377.	−	54501.0i	−0.908352	−	0.418206i
$20$	15248.3			0.0953017
$21$	363801.	+	433561.i	1.87062	+	2.22932i
$22$	51246.6	−	140799.i	0.218763	−	0.601047i
$23$	−49555.2	+	281042.i	−0.177083	+	1.00429i	0.758628	+	0.651524i	$0.225870\pi$
$23$	−49555.2	+	281042.i	−0.177083	+	1.00429i	−0.935711	+	0.352766i	$0.885241\pi$
$24$	30515.5	+	173062.i	0.0919762	+	0.521623i
$25$	353732.	−	128748.i	0.905554	−	0.329595i
$26$	237940.	−	412125.i	0.520685	−	0.901852i
$27$	168515.	−	97292.2i	0.317091	−	0.183072i
$28$	457325.	+	383741.i	0.744034	+	0.624319i
$29$	−304613.	+	363024.i	−0.430682	+	0.513266i	−0.937119	−	0.349010i	$-0.886518\pi$
$29$	−304613.	+	363024.i	−0.430682	+	0.513266i	0.506437	+	0.862277i	$0.330962\pi$
$30$	−81775.0	−	141639.i	−0.100957	−	0.174862i
$31$	943123.	+	544512.i	1.02123	+	0.589605i	0.914459	−	0.404679i	$-0.132617\pi$
$31$	943123.	+	544512.i	1.02123	+	0.589605i	0.106767	+	0.994284i	$0.465950\pi$
$32$	63398.2	+	174185.i	0.0604612	+	0.166116i
$33$	−1.58269e6	+	279070.i	−1.33456	+	0.235319i
$34$	−142140.	−	25063.2i	−0.106366	−	0.0187551i
$35$	−522104.	−	190030.i	−0.347925	−	0.126634i
$36$	800561.	−	671750.i	0.476633	−	0.399943i
$37$			1.90549e6i			1.01672i	0.861146	+	0.508358i	$0.169747\pi$
$37$			1.90549e6i			1.01672i	−0.861146	+	0.508358i	$0.830253\pi$
$38$	388528.	+	1.42230e6i	0.186332	+	0.682115i
$39$	−5.10421e6			−2.20633
$40$	−110890.	−	132154.i	−0.0433165	−	0.0516226i
$41$	437817.	−	1.20289e6i	0.154938	−	0.425688i	−0.837801	−	0.545975i	$-0.816159\pi$
$41$	437817.	−	1.20289e6i	0.154938	−	0.425688i	0.992739	+	0.120287i	$0.0383815\pi$
$42$	1.11191e6	−	6.30598e6i	0.357334	−	2.02654i
$43$	167248.	+	948510.i	0.0489200	+	0.277439i	0.999449	−	0.0331972i	$-0.0105689\pi$
$43$	167248.	+	948510.i	0.0489200	+	0.277439i	−0.950529	+	0.310636i	$0.899458\pi$
$44$	−1.59296e6	+	579789.i	−0.425004	+	0.154689i
$45$	−486307.	+	842309.i	−0.118594	+	0.205410i
$46$	2.79611e6	−	1.61434e6i	0.624487	−	0.360548i
$47$	4.84784e6	+	4.06782e6i	0.993475	+	0.833625i	0.986067	−	0.166348i	$-0.0531974\pi$
$47$	4.84784e6	+	4.06782e6i	0.993475	+	0.833625i	0.00740832	+	0.999973i	$0.497642\pi$
$48$	1.27798e6	−	1.52303e6i	0.240745	−	0.286909i
$49$	−7.99417e6	−	1.38463e7i	−1.38672	−	2.40187i
$50$	−3.68828e6	−	2.12943e6i	−0.590125	−	0.340709i
$51$	529478.	+	1.45473e6i	0.0782649	+	0.215031i
$52$	−5.30218e6	+	934918.i	−0.725172	+	0.127867i
$53$	6.40058e6	+	1.12860e6i	0.811178	+	0.143033i	0.563827	−	0.825893i	$-0.309329\pi$
$53$	6.40058e6	+	1.12860e6i	0.811178	+	0.143033i	0.247351	+	0.968926i	$0.420440\pi$
$54$	−2.06871e6	−	752948.i	−0.243290	−	0.0885502i
$55$	1.20857e6	−	1.01411e6i	0.132075	−	0.110824i
$56$		−	6.75423e6i		−	0.686790i
$57$	1.11279e7	−	1.12366e7i	1.05418	−	1.06448i
$58$	5.36149e6			0.473777
$59$	1.47919e7	+	1.76282e7i	1.22072	+	1.45479i	0.850606	+	0.525804i	$0.176236\pi$
$59$	1.47919e7	+	1.76282e7i	1.22072	+	1.45479i	0.370110	+	0.928988i	$0.379320\pi$
$60$	−632860.	+	1.73877e6i	−0.0488318	+	0.134164i
$61$	−659353.	+	3.73938e6i	−0.0476210	+	0.270072i	−0.999316	−	0.0369718i	$-0.988229\pi$
$61$	−659353.	+	3.73938e6i	−0.0476210	+	0.270072i	0.951695	+	0.307044i	$0.0993399\pi$
$62$	−2.13950e6	−	1.21337e7i	−0.144793	−	0.821159i
$63$	−3.57830e7	+	1.30240e7i	−2.27151	+	0.826763i
$64$	1.04858e6	−	1.81619e6i	0.0625000	−	0.108253i
$65$	4.33945e6	−	2.50538e6i	0.243098	−	0.140353i
$66$	1.39284e7	+	1.16873e7i	0.734052	+	0.615942i
$67$	−1.63178e7	+	1.94468e7i	−0.809770	+	0.965047i	−0.999860	−	0.0167200i	$-0.994678\pi$
$67$	−1.63178e7	+	1.94468e7i	−0.809770	+	0.965047i	0.190090	+	0.981767i	$0.439122\pi$
$68$	816471.	+	1.41417e6i	0.0381861	+	0.0661402i
$69$	−2.99906e7	−	1.73151e7i	−1.32309	−	0.763885i
$70$	2.14995e6	+	5.90694e6i	0.0895439	+	0.246020i
$71$	−6.75035e6	+	1.19027e6i	−0.265640	+	0.0468394i	−0.304881	−	0.952390i	$-0.598617\pi$
$71$	−6.75035e6	+	1.19027e6i	−0.265640	+	0.0468394i	0.0392418	+	0.999230i	$0.487506\pi$
$72$	−1.16439e7	−	2.05313e6i	−0.433278	−	0.0763986i
$73$	−409903.	−	149193.i	−0.0144341	−	0.00525359i	0.334793	−	0.942292i	$-0.391334\pi$
$73$	−409903.	−	149193.i	−0.0144341	−	0.00525359i	−0.349227	+	0.937038i	$0.613556\pi$
$74$	1.65145e7	−	1.38573e7i	0.550730	−	0.462117i
$75$			4.56798e7i			1.44371i
$76$	9.50131e6	−	1.37107e7i	0.284793	−	0.410966i
$77$	6.17688e7			1.75714
$78$	3.71194e7	+	4.42372e7i	1.00282	+	1.19511i
$79$	8.08570e6	−	2.22153e7i	0.207591	−	0.570353i	−0.791579	−	0.611066i	$-0.790741\pi$
$79$	8.08570e6	−	2.22153e7i	0.207591	−	0.570353i	0.999171	+	0.0407134i	$0.0129631\pi$
$80$	−338923.	+	1.92213e6i	−0.00827448	+	0.0469269i
$81$	−5.20160e6	−	2.94997e7i	−0.120836	−	0.685295i
$82$	−1.36092e7	+	4.95334e6i	−0.301007	+	0.109558i
$83$	1.09019e7	−	1.88826e7i	0.229715	−	0.397878i	−0.728009	−	0.685568i	$-0.759554\pi$
$83$	1.09019e7	−	1.88826e7i	0.229715	−	0.397878i	0.957724	+	0.287690i	$0.0928872\pi$
$84$	−6.27389e7	+	3.62223e7i	−1.26014	+	0.727544i
$85$	−1.16419e6	−	976874.i	−0.0223023	−	0.0187138i
$86$	7.00427e6	−	8.34736e6i	0.128047	−	0.152600i
$87$	−2.87532e7	−	4.98020e7i	−0.501891	−	0.869300i
$88$	1.66094e7	+	9.58944e6i	0.276964	+	0.159905i
$89$	3.42710e7	+	9.41587e7i	0.546219	+	1.50072i	0.838777	+	0.544475i	$0.183271\pi$
$89$	3.42710e7	+	9.41587e7i	0.546219	+	1.50072i	−0.292558	+	0.956248i	$0.594507\pi$
$90$	1.08367e7	−	1.91080e6i	0.165169	−	0.0291237i
$91$	1.93199e8	+	3.40663e7i	2.81735	+	0.496774i
$92$	−3.43253e7	−	1.24934e7i	−0.479141	−	0.174393i
$93$	−1.01234e8	+	8.49455e7i	−1.35330	+	1.13556i
$94$		−	7.15978e7i		−	0.917040i
$95$	−3.94513e6	+	1.50151e7i	−0.0484358	+	0.184346i
$96$	−2.24937e7			−0.264835
$97$	−9.63387e7	−	1.14812e8i	−1.08821	−	1.29688i	−0.951965	−	0.306207i	$-0.900940\pi$
$97$	−9.63387e7	−	1.14812e8i	−1.08821	−	1.29688i	−0.136248	−	0.990675i	$-0.543504\pi$
$98$	−6.18671e7	+	1.69979e8i	−0.670742	+	1.84285i
$99$	1.87762e7	−	1.06485e8i	0.195465	−	1.10853i
$100$	8.36698e6	+	4.74515e7i	0.0836698	+	0.474515i
$101$	−1.85641e7	+	6.75680e6i	−0.178398	+	0.0649315i	−0.429675	−	0.902984i	$-0.641372\pi$
$101$	−1.85641e7	+	6.75680e6i	−0.178398	+	0.0649315i	0.251277	+	0.967915i	$0.419150\pi$
$102$	8.75731e6	−	1.51681e7i	0.0809040	−	0.140130i
$103$	5.97464e7	−	3.44946e7i	0.530839	−	0.306480i	−0.210519	−	0.977590i	$-0.567515\pi$
$103$	5.97464e7	−	3.44946e7i	0.530839	−	0.306480i	0.741358	+	0.671110i	$0.234182\pi$
$104$	4.66619e7	+	3.91540e7i	0.398868	+	0.334690i
$105$	4.33385e7	−	5.16489e7i	0.356547	−	0.424916i
$106$	−3.67657e7	−	6.36801e7i	−0.291219	−	0.504406i
$107$	1.82693e7	+	1.05478e7i	0.139376	+	0.0804688i	0.568067	−	0.822983i	$-0.307692\pi$
$107$	1.82693e7	+	1.05478e7i	0.139376	+	0.0804688i	−0.428691	+	0.903451i	$0.641025\pi$
$108$	8.51863e6	+	2.34047e7i	0.0626145	+	0.172032i
$109$	7.94673e7	−	1.40122e7i	0.562966	−	0.0992661i	0.115079	−	0.993356i	$-0.463288\pi$
$109$	7.94673e7	−	1.40122e7i	0.562966	−	0.0992661i	0.447887	+	0.894090i	$0.352177\pi$
$110$	−1.75782e7	−	3.09952e6i	−0.120062	−	0.0211701i
$111$	−2.17284e8	−	7.90849e7i	−1.43132	−	0.520957i
$112$	−5.85376e7	+	4.91189e7i	−0.372017	+	0.312159i
$113$		−	1.05233e8i		−	0.645412i	−0.946499	−	0.322706i	$-0.895407\pi$
$113$		−	1.05233e8i		−	0.645412i	0.946499	−	0.322706i	$-0.104593\pi$
$114$	−1.78311e8	−	1.47267e7i	−1.05575	−	0.0871941i
$115$	3.39962e7			0.194374
$116$	−3.89905e7	−	4.64670e7i	−0.215341	−	0.256633i
$117$	1.17456e8	−	3.22708e8i	0.626804	−	1.72213i
$118$	4.52096e7	−	2.56396e8i	0.233186	−	1.32246i
$119$	−1.03322e7	−	5.85967e7i	−0.0515233	−	0.292203i
$120$	1.96719e7	−	7.15999e6i	0.0948684	−	0.0345293i
$121$	1.94821e7	−	3.37441e7i	0.0908856	−	0.157419i
$122$	3.72035e7	−	2.14794e7i	0.167936	−	0.0969580i
$123$	1.18995e8	+	9.98491e7i	0.519888	+	0.436238i
$124$	−8.96015e7	+	1.06783e8i	−0.378991	+	0.451664i
$125$	−4.56887e7	−	7.91352e7i	−0.187141	−	0.324138i
$126$	3.73101e8	+	2.15410e8i	1.48028	+	0.854642i
$127$	−4.85137e7	−	1.33290e8i	−0.186487	−	0.512370i	0.810853	−	0.585249i	$-0.199003\pi$
$127$	−4.85137e7	−	1.33290e8i	−0.186487	−	0.512370i	−0.997341	+	0.0728795i	$0.976781\pi$
$128$	−2.33661e7	+	4.12008e6i	−0.0870455	+	0.0153485i
$129$	−1.15100e8	−	2.02953e7i	−0.415641	−	0.0732887i
$130$	−5.32715e7	−	1.93892e7i	−0.186518	−	0.0678871i
$131$	−3.76641e8	+	3.16039e8i	−1.27892	+	1.07314i	−0.285525	+	0.958371i	$0.592168\pi$
$131$	−3.76641e8	+	3.16039e8i	−1.27892	+	1.07314i	−0.993392	+	0.114767i	$0.963388\pi$
$132$		−	2.05709e8i		−	0.677575i
$133$	−4.96196e8	+	3.51049e8i	−1.58579	+	1.12192i
$134$	2.87209e8			0.890798
$135$	−1.49000e7	−	1.77571e7i	−0.0448592	−	0.0534611i
$136$	6.31869e6	−	1.73605e7i	0.0184702	−	0.0507465i
$137$	−5.35679e7	+	3.03799e8i	−0.152063	+	0.862391i	0.809359	+	0.587314i	$0.199814\pi$
$137$	−5.35679e7	+	3.03799e8i	−0.152063	+	0.862391i	−0.961422	+	0.275077i	$0.911297\pi$
$138$	6.80346e7	+	3.85843e8i	0.187592	+	1.06388i
$139$	3.40102e8	−	1.23787e8i	0.911066	−	0.331601i	0.156388	−	0.987696i	$-0.450015\pi$
$139$	3.40102e8	−	1.23787e8i	0.911066	−	0.331601i	0.754678	+	0.656095i	$0.227793\pi$
$140$	3.55592e7	−	6.15903e7i	0.0925634	−	0.160325i
$141$	−6.65059e8	+	3.83972e8i	−1.68261	+	0.971457i
$142$	5.94065e7	+	4.98480e7i	0.146110	+	0.122601i
$143$	−3.58071e8	+	4.26732e8i	−0.856297	+	1.02050i
$144$	6.68837e7	+	1.15846e8i	0.155550	+	0.269421i
$145$	4.88902e7	+	2.82268e7i	0.110599	+	0.0638542i
$146$	1.68792e6	+	4.63753e6i	0.00371485	+	0.0102065i
$147$	1.91069e9	−	3.36906e8i	4.09186	−	0.721505i
$148$	−2.40197e8	−	4.23533e7i	−0.500635	−	0.0882755i
$149$	7.58614e8	+	2.76113e8i	1.53913	+	0.560198i	0.965837	−	0.259151i	$-0.0834427\pi$
$149$	7.58614e8	+	2.76113e8i	1.53913	+	0.560198i	0.573295	+	0.819349i	$0.305665\pi$
$150$	3.95897e8	−	3.32197e8i	0.782020	−	0.656192i
$151$			3.50927e8i			0.675008i	0.941324	+	0.337504i	$0.109583\pi$
$151$			3.50927e8i			0.675008i	−0.941324	+	0.337504i	$0.890417\pi$
$152$	−1.87925e8	+	1.73626e7i	−0.352054	+	0.0325268i
$153$	−1.04158e8			−0.190075
$154$	−4.49202e8	−	5.35338e8i	−0.798654	−	0.951799i
$155$	4.43711e7	−	1.21909e8i	0.0768729	−	0.211207i
$156$	1.13451e8	−	6.43413e8i	0.191562	−	1.08640i
$157$	−1.41116e8	−	8.00310e8i	−0.232262	−	1.31722i	−0.848303	−	0.529510i	$-0.822376\pi$
$157$	−1.41116e8	−	8.00310e8i	−0.232262	−	1.31722i	0.616041	−	0.787714i	$-0.288735\pi$
$158$	−2.51337e8	+	9.14793e7i	−0.403300	+	0.146789i
$159$	−3.94342e8	+	6.83021e8i	−0.617000	+	1.06867i
$160$	1.91234e7	−	1.10409e7i	0.0291801	−	0.0168471i
$161$	1.01961e9	+	8.55554e8i	1.51751	+	1.27334i
$162$	−2.17841e8	+	2.59612e8i	−0.316285	+	0.376934i
$163$	−2.02883e8	−	3.51404e8i	−0.287406	−	0.497801i	0.685784	−	0.727805i	$-0.259459\pi$
$163$	−2.02883e8	−	3.51404e8i	−0.287406	−	0.497801i	−0.973190	+	0.230004i	$0.926126\pi$
$164$	1.41900e8	+	8.19259e7i	0.196158	+	0.113252i
$165$	6.54795e7	+	1.79904e8i	0.0883425	+	0.242719i
$166$	−2.42934e8	+	4.28358e7i	−0.319931	+	0.0564124i
$167$	5.79111e8	+	1.02113e8i	0.744554	+	0.131285i	0.533040	−	0.846090i	$-0.321050\pi$
$167$	5.79111e8	+	1.02113e8i	0.744554	+	0.131285i	0.211514	+	0.977375i	$0.432161\pi$
$168$	7.70188e8	+	2.80326e8i	0.966852	+	0.351905i
$169$	−7.30429e8	+	6.12903e8i	−0.895430	+	0.751355i
$170$			1.71940e7i			0.0205864i
$171$	4.54354e8	+	9.62120e8i	0.531385	+	1.12524i
$172$	−1.23282e8			−0.140860
$173$	−1.08699e9	−	1.29543e9i	−1.21351	−	1.44620i	−0.859638	−	0.510903i	$-0.829311\pi$
$173$	−1.08699e9	−	1.29543e9i	−1.21351	−	1.44620i	−0.353867	−	0.935296i	$-0.615133\pi$
$174$	−2.22522e8	+	6.11374e8i	−0.242759	+	0.666976i
$175$	3.04874e8	−	1.72902e9i	0.325063	−	1.84352i
$176$	−3.76789e7	−	2.13688e8i	−0.0392688	−	0.222704i
$177$	−2.62407e9	+	9.55085e8i	−2.67352	+	0.973081i
$178$	5.66826e8	−	9.81771e8i	0.564638	−	0.977981i
$179$	−1.05411e9	+	6.08593e8i	−1.02678	+	0.592809i	−0.916059	−	0.401043i	$-0.868648\pi$
$179$	−1.05411e9	+	6.08593e8i	−1.02678	+	0.592809i	−0.110716	+	0.993852i	$0.535315\pi$
$180$	−9.53685e7	−	8.00237e7i	−0.0908479	−	0.0762304i
$181$	2.50378e8	−	2.98388e8i	0.233282	−	0.278015i	−0.636686	−	0.771123i	$-0.719695\pi$
$181$	2.50378e8	−	2.98388e8i	0.233282	−	0.278015i	0.869968	+	0.493109i	$0.164140\pi$
$182$	−1.10976e9	−	1.92216e9i	−1.01145	−	1.75188i
$183$	−3.99038e8	−	2.30384e8i	−0.355803	−	0.205423i
$184$	1.41347e8	+	3.88347e8i	0.123315	+	0.338804i
$185$	2.23547e8	−	3.94174e7i	0.190845	−	0.0336512i
$186$	1.47241e9	+	2.59626e8i	1.23021	+	0.216918i
$187$	1.58765e8	+	5.77857e7i	0.129834	+	0.0472557i
$188$	−6.20524e8	+	5.20681e8i	−0.496738	+	0.416812i
$189$		−	9.07547e8i		−	0.711249i
$190$	1.58823e8	−	7.50031e7i	0.121871	−	0.0575526i
$191$	−8.09569e8			−0.608304			−0.304152	−	0.952624i	$-0.598373\pi$
$191$	−8.09569e8			−0.608304			−0.304152	+	0.952624i	$0.598373\pi$
$192$	1.63581e8	+	1.94948e8i	0.120373	+	0.143455i
$193$	3.04041e8	−	8.35346e8i	0.219131	−	0.602057i	−0.780605	−	0.625024i	$-0.785089\pi$
$193$	3.04041e8	−	8.35346e8i	0.219131	−	0.602057i	0.999736	+	0.0229673i	$0.00731137\pi$
$194$	−2.94448e8	+	1.66990e9i	−0.207875	+	1.17892i
$195$	1.05587e8	+	5.98812e8i	0.0730249	+	0.414145i
$196$	1.92309e9	−	6.99947e8i	1.30309	−	0.474286i
$197$	6.58144e8	−	1.13994e9i	0.436975	−	0.756862i	−0.560480	−	0.828168i	$-0.689383\pi$
$197$	6.58144e8	−	1.13994e9i	0.436975	−	0.756862i	0.997454	+	0.0713059i	$0.0227167\pi$
$198$	−1.05943e9	+	6.11665e8i	−0.689308	+	0.397972i
$199$	1.15845e9	+	9.72055e8i	0.738695	+	0.619839i	0.932487	−	0.361204i	$-0.117634\pi$
$199$	1.15845e9	+	9.72055e8i	0.738695	+	0.619839i	−0.193792	+	0.981043i	$0.562079\pi$
$200$	3.50406e8	−	4.17597e8i	0.219003	−	0.260998i
$201$	−1.54028e9	−	2.66784e9i	−0.943658	−	1.63446i
$202$	1.93564e8	+	1.11754e8i	0.116257	+	0.0671210i
$203$	7.55951e8	+	2.07696e9i	0.445153	+	1.22305i
$204$	−1.95145e8	+	3.44093e7i	−0.112677	+	0.0198681i
$205$	−1.50177e8	−	2.64802e7i	−0.0850331	−	0.0149936i
$206$	−7.33452e8	−	2.66955e8i	−0.407289	−	0.148241i
$207$	1.78486e9	−	1.49767e9i	0.972125	−	0.815710i
$208$		−	6.89149e8i		−	0.368180i
$209$	−1.58785e8	−	1.71861e9i	−0.0832191	−	0.900724i
$210$	−7.62802e8			−0.392224
$211$	4.03954e8	+	4.81413e8i	0.203799	+	0.242878i	0.858257	−	0.513220i	$-0.171548\pi$
$211$	4.03954e8	+	4.81413e8i	0.203799	+	0.242878i	−0.654458	+	0.756098i	$0.727103\pi$
$212$	−2.84531e8	+	7.81743e8i	−0.140860	+	0.387009i
$213$	1.44438e8	−	8.19147e8i	0.0701717	−	0.397963i
$214$	−4.14446e7	−	2.35044e8i	−0.0197612	−	0.112071i
$215$	1.07817e8	−	3.92421e7i	0.0504583	−	0.0183653i
$216$	1.40894e8	−	2.44036e8i	0.0647259	−	0.112109i
$217$	4.39875e9	−	2.53962e9i	1.98377	−	1.14533i
$218$	−6.99352e8	−	5.86826e8i	−0.309649	−	0.259826i
$219$	3.40250e7	−	4.05494e7i	0.0147918	−	0.0176282i
$220$	1.00971e8	+	1.74888e8i	0.0431030	+	0.0746567i
$221$	4.64713e8	+	2.68302e8i	0.194812	+	0.112475i
$222$	8.94744e8	+	2.45829e9i	0.368372	+	1.01209i
$223$	5.04001e7	−	8.88689e6i	0.0203803	−	0.00359361i	−0.163449	−	0.986552i	$-0.552262\pi$
$223$	5.04001e7	−	8.88689e6i	0.0203803	−	0.00359361i	0.183829	+	0.982958i	$0.441151\pi$
$224$	8.51407e8	+	1.50126e8i	0.338178	+	0.0596299i
$225$	−2.88805e9	−	1.05116e9i	−1.12687	−	0.410148i
$226$	−9.12032e8	+	7.65285e8i	−0.349604	+	0.293352i
$227$			2.74184e9i			1.03261i	0.856403	+	0.516307i	$0.172694\pi$
$227$			2.74184e9i			1.03261i	−0.856403	+	0.516307i	$0.827306\pi$
$228$	1.16910e9	+	1.65248e9i	0.432626	+	0.611502i
$229$	−3.19581e9			−1.16209			−0.581045	−	0.813872i	$-0.697356\pi$
$229$	−3.19581e9			−1.16209			−0.581045	+	0.813872i	$0.697356\pi$
$230$	−2.47231e8	−	2.94638e8i	−0.0883468	−	0.105288i
$231$	−2.56363e9	+	7.04353e9i	−0.900343	+	2.47367i
$232$	−1.19170e8	+	6.75845e8i	−0.0411352	+	0.233290i
$233$	1.71845e8	+	9.74583e8i	0.0583061	+	0.330670i	0.999983	−	0.00584843i	$-0.00186162\pi$
$233$	1.71845e8	+	9.74583e8i	0.0583061	+	0.330670i	−0.941677	+	0.336519i	$0.890751\pi$
$234$	−3.65102e9	+	1.32886e9i	−1.21773	+	0.443217i
$235$	3.76943e8	−	6.52884e8i	0.123596	−	0.214074i
$236$	−2.55091e9	+	1.47277e9i	−0.822333	+	0.474774i
$237$	2.19763e9	+	1.84403e9i	0.696566	+	0.584488i
$238$	−4.32707e8	+	5.15680e8i	−0.134861	+	0.160721i
$239$	1.77212e9	+	3.06940e9i	0.543128	+	0.940725i	0.998722	+	0.0505372i	$0.0160933\pi$
$239$	1.77212e9	+	3.06940e9i	0.543128	+	0.940725i	−0.455595	+	0.890187i	$0.650573\pi$
$240$	−2.05115e8	−	1.18423e8i	−0.0618232	−	0.0356936i
$241$	−1.24958e9	−	3.43320e9i	−0.370422	−	1.01772i	−0.975199	−	0.221330i	$-0.928960\pi$
$241$	−1.24958e9	−	3.43320e9i	−0.370422	−	1.01772i	0.604777	−	0.796395i	$-0.293262\pi$
$242$	−4.34133e8	+	7.65494e7i	−0.126579	+	0.0223193i
$243$	4.83703e9	+	8.52898e8i	1.38725	+	0.244609i
$244$	−4.56713e8	−	1.66230e8i	−0.128850	−	0.0468976i
$245$	−1.45904e9	+	1.22428e9i	−0.404952	+	0.339795i
$246$		−	1.75744e9i		−	0.479889i
$247$	4.51190e8	−	5.46300e9i	0.121219	−	1.46772i
$248$	1.57708e9			0.416914
$249$	1.70073e9	+	2.02685e9i	0.442422	+	0.527259i
$250$	−3.53587e8	+	9.71471e8i	−0.0905182	+	0.248697i
$251$	6.52955e8	−	3.70309e9i	0.164508	−	0.932974i	−0.785061	−	0.619418i	$-0.787369\pi$
$251$	6.52955e8	−	3.70309e9i	0.164508	−	0.932974i	0.949570	−	0.313556i	$-0.101520\pi$
$252$	−8.46392e8	−	4.80013e9i	−0.209879	−	1.19028i
$253$	−3.55151e9	+	1.29264e9i	−0.866824	+	0.315498i
$254$	−8.02394e8	+	1.38979e9i	−0.192776	+	0.333898i
$255$	1.59712e8	−	9.22097e7i	0.0377726	−	0.0218080i
$256$	2.05633e8	+	1.72547e8i	0.0478778	+	0.0401742i
$257$	5.54112e9	−	6.60365e9i	1.27018	−	1.51374i	0.516888	−	0.856053i	$-0.327090\pi$
$257$	5.54112e9	−	6.60365e9i	1.27018	−	1.51374i	0.753291	−	0.657687i	$-0.228465\pi$
$258$	6.61151e8	+	1.14515e9i	0.149218	+	0.258453i
$259$	7.69659e9	+	4.44363e9i	1.71041	+	0.987503i
$260$	2.19364e8	+	6.02698e8i	0.0480034	+	0.131888i
$261$	3.81033e9	−	6.71864e8i	0.821109	−	0.144784i
$262$	5.47810e9	+	9.65937e8i	1.16259	+	0.204995i
$263$	−2.03314e9	−	7.40003e8i	−0.424957	−	0.154672i	0.120684	−	0.992691i	$-0.461491\pi$
$263$	−2.03314e9	−	7.40003e8i	−0.424957	−	0.154672i	−0.545640	+	0.838019i	$0.683714\pi$
$264$	−1.78284e9	+	1.49598e9i	−0.367026	+	0.307971i
$265$		−	7.74246e8i		−	0.156998i
$266$	6.65096e9	+	1.74750e9i	1.32849	+	0.349052i
$267$	−1.21593e10			−2.39257
$268$	−2.08868e9	−	2.48919e9i	−0.404885	−	0.482523i
$269$	1.25968e9	−	3.46094e9i	0.240575	−	0.660974i	−0.759372	−	0.650657i	$-0.774494\pi$
$269$	1.25968e9	−	3.46094e9i	0.240575	−	0.660974i	0.999947	−	0.0103174i	$-0.00328419\pi$
$270$	−4.55401e7	+	2.58271e8i	−0.00856917	+	0.0485982i
$271$	−5.92934e8	−	3.36270e9i	−0.109933	−	0.623463i	−0.989135	−	0.147012i	$-0.953034\pi$
$271$	−5.92934e8	−	3.36270e9i	−0.109933	−	0.623463i	0.879201	−	0.476450i	$-0.158077\pi$
$272$	−1.96411e8	+	7.14878e7i	−0.0358832	+	0.0130604i
$273$	−1.19031e10	+	2.06167e10i	−2.14293	+	3.71167i
$274$	3.02253e9	−	1.74506e9i	0.536251	−	0.309605i
$275$	3.81901e9	+	3.20453e9i	0.667759	+	0.560316i
$276$	2.84926e9	−	3.39561e9i	0.491016	−	0.585170i
$277$	−2.10522e9	−	3.64634e9i	−0.357584	−	0.619353i	0.629973	−	0.776617i	$-0.283066\pi$
$277$	−2.10522e9	−	3.64634e9i	−0.357584	−	0.619353i	−0.987557	+	0.157264i	$0.949733\pi$
$278$	−3.54616e9	−	2.04738e9i	−0.593717	−	0.342783i
$279$	−3.04102e9	−	8.35514e9i	−0.501884	−	1.37891i
$280$	−7.92388e8	+	1.39719e8i	−0.128916	+	0.0227313i
$281$	−3.12639e9	−	5.51267e8i	−0.501438	−	0.0884171i	−0.0827927	−	0.996567i	$-0.526384\pi$
$281$	−3.12639e9	−	5.51267e8i	−0.501438	−	0.0884171i	−0.418646	+	0.908150i	$0.637495\pi$
$282$	8.16433e9	+	2.97157e9i	1.29099	+	0.469883i
$283$	9.79212e8	−	8.21656e8i	0.152662	−	0.128099i	−0.563258	−	0.826281i	$-0.690452\pi$
$283$	9.79212e8	−	8.21656e8i	0.152662	−	0.128099i	0.715920	+	0.698183i	$0.246008\pi$
$284$		−	8.77374e8i		−	0.134869i
$285$	−1.54845e9	−	1.07305e9i	−0.234702	−	0.162645i
$286$	6.30241e9			0.941981
$287$	−3.83769e9	−	4.57358e9i	−0.565643	−	0.674107i
$288$	5.17615e8	−	1.42214e9i	0.0752380	−	0.206715i
$289$	−1.18307e9	+	6.70950e9i	−0.169597	+	0.961831i
$290$	−1.10909e8	−	6.28996e8i	−0.0156810	−	0.0889316i
$291$	1.70905e10	−	6.22043e9i	2.38332	−	0.867458i
$292$	2.79174e7	−	4.83544e7i	0.00384011	−	0.00665127i
$293$	−8.85818e9	+	5.11427e9i	−1.20192	+	0.693926i	−0.960981	−	0.276615i	$-0.910787\pi$
$293$	−8.85818e9	+	5.11427e9i	−1.20192	+	0.693926i	−0.240935	+	0.970541i	$0.577454\pi$
$294$	−1.68150e10	−	1.41095e10i	−2.25065	−	1.88852i
$295$	1.76211e9	−	2.10000e9i	0.232672	−	0.277288i
$296$	1.37972e9	+	2.38975e9i	0.179732	+	0.311305i
$297$	2.23176e9	+	1.28851e9i	0.286828	+	0.165600i
$298$	−3.12386e9	−	8.58274e9i	−0.396120	−	1.08833i
$299$	−1.18213e10	+	2.08441e9i	−1.47904	+	0.260794i
$300$	−5.75818e9	−	1.01532e9i	−0.710886	−	0.125348i
$301$	4.22121e9	+	1.53640e9i	0.514246	+	0.187170i
$302$	3.04142e9	−	2.55205e9i	0.365635	−	0.306804i
$303$		−	2.39731e9i		−	0.284416i
$304$	1.51712e9	+	1.50244e9i	0.177634	+	0.175915i
$305$	4.52333e8			0.0522708
$306$	7.57467e8	+	9.02713e8i	0.0863928	+	0.102959i
$307$	2.56017e9	−	7.03401e9i	0.288214	−	0.791862i	−0.708102	−	0.706110i	$-0.750448\pi$
$307$	2.56017e9	−	7.03401e9i	0.288214	−	0.791862i	0.996316	−	0.0857522i	$-0.0273293\pi$
$308$	−1.37293e9	+	7.78629e9i	−0.152562	+	0.865222i
$309$	1.45374e9	+	8.24456e9i	0.159460	+	0.904344i
$310$	−1.37924e9	+	5.02002e8i	−0.149346	+	0.0543574i
$311$	−2.22599e9	+	3.85552e9i	−0.237948	+	0.412137i	−0.960125	−	0.279570i	$-0.909808\pi$
$311$	−2.22599e9	+	3.85552e9i	−0.237948	+	0.412137i	0.722178	+	0.691708i	$0.243141\pi$
$312$	−6.40139e9	+	3.69584e9i	−0.675547	+	0.390027i
$313$	−8.42866e9	−	7.07249e9i	−0.878176	−	0.736877i	0.0876276	−	0.996153i	$-0.472071\pi$
$313$	−8.42866e9	−	7.07249e9i	−0.878176	−	0.736877i	−0.965803	+	0.259277i	$0.916516\pi$
$314$	−5.90989e9	+	7.04313e9i	−0.607940	+	0.724515i
$315$	2.26815e9	+	3.92855e9i	0.230372	+	0.399016i
$316$	2.62064e9	+	1.51303e9i	0.262820	+	0.151739i
$317$	−2.88900e9	−	7.93746e9i	−0.286095	−	0.786040i	−0.996603	−	0.0823510i	$-0.973757\pi$
$317$	−2.88900e9	−	7.93746e9i	−0.286095	−	0.786040i	0.710508	−	0.703689i	$-0.248465\pi$
$318$	8.78739e9	−	1.54945e9i	0.859313	−	0.151520i
$319$	−6.18074e9	−	1.08983e9i	−0.596867	−	0.105244i
$320$	−2.34761e8	−	8.54461e7i	−0.0223886	−	0.00814877i
$321$	−1.96102e9	+	1.64549e9i	−0.184698	+	0.154980i
$322$		−	1.50586e10i		−	1.40075i
$323$	−1.60379e9	+	4.38105e8i	−0.147346	+	0.0402502i
$324$	3.83422e9			0.347934
$325$	1.01777e10	+	1.21293e10i	0.912254	+	1.08718i
$326$	−1.57012e9	+	4.31387e9i	−0.139015	+	0.381941i
$327$	−1.70037e9	+	9.64325e9i	−0.148714	+	0.843398i
$328$	−3.21904e8	−	1.82561e9i	−0.0278119	−	0.157729i
$329$	2.77358e10	−	1.00950e10i	2.36732	−	0.861636i
$330$	1.08300e9	−	1.87581e9i	0.0913215	−	0.158174i
$331$	4.83407e9	−	2.79095e9i	0.402718	−	0.232509i	−0.284938	−	0.958546i	$-0.591973\pi$
$331$	4.83407e9	−	2.79095e9i	0.402718	−	0.232509i	0.687656	+	0.726037i	$0.258640\pi$
$332$	2.13794e9	+	1.79395e9i	0.175972	+	0.147658i
$333$	1.00001e10	−	1.19177e10i	0.813257	−	0.969202i
$334$	−3.32648e9	−	5.76164e9i	−0.267300	−	0.462978i
$335$	2.61900e9	+	1.51208e9i	0.207948	+	0.120059i
$336$	−3.17152e9	−	8.71369e9i	−0.248835	−	0.683667i
$337$	−1.72418e9	+	3.04020e8i	−0.133679	+	0.0235713i	−0.240087	−	0.970751i	$-0.577176\pi$
$337$	−1.72418e9	+	3.04020e8i	−0.133679	+	0.0235713i	0.106408	+	0.994323i	$0.466065\pi$
$338$	1.06238e10	+	1.87327e9i	0.813980	+	0.143527i
$339$	1.19997e10	+	4.36755e9i	0.908601	+	0.330704i
$340$	1.49017e8	−	1.25040e8i	0.0111511	−	0.00935692i
$341$			1.44227e10i			1.06667i
$342$	5.03431e9	−	1.09346e10i	0.367989	−	0.799281i
$343$	−4.76828e10			−3.44497
$344$	8.96546e8	+	1.06846e9i	0.0640234	+	0.0763002i
$345$	−1.41097e9	+	3.87660e9i	−0.0995956	+	0.273637i
$346$	−3.32226e9	+	1.88415e10i	−0.231809	+	1.31465i
$347$	4.06985e9	+	2.30812e10i	0.280711	+	1.59199i	0.720214	+	0.693752i	$0.244044\pi$
$347$	4.06985e9	+	2.30812e10i	0.280711	+	1.59199i	−0.439503	+	0.898241i	$0.644845\pi$
$348$	6.91691e9	−	2.51755e9i	0.471623	−	0.171657i
$349$	−2.61865e8	+	4.53564e8i	−0.0176513	+	0.0305729i	−0.874716	−	0.484636i	$-0.838952\pi$
$349$	−2.61865e8	+	4.53564e8i	−0.0176513	+	0.0305729i	0.857065	+	0.515209i	$0.172286\pi$
$350$	−1.72022e10	+	9.93172e9i	−1.14634	+	0.661839i
$351$	6.26982e9	+	5.26101e9i	0.413073	+	0.346609i
$352$	−1.57798e9	+	1.88056e9i	−0.102785	+	0.122494i
$353$	−2.60645e9	−	4.51450e9i	−0.167861	−	0.290744i	0.769807	−	0.638277i	$-0.220353\pi$
$353$	−2.60645e9	−	4.51450e9i	−0.167861	−	0.290744i	−0.937668	+	0.347533i	$0.887019\pi$
$354$	2.73606e10	+	1.57967e10i	1.74226	+	1.00589i
$355$	2.79278e8	+	7.67311e8i	0.0175842	+	0.0483123i
$356$	−1.26310e10	+	2.22718e9i	−0.786387	+	0.138661i
$357$	7.11063e9	+	1.25380e9i	0.437759	+	0.0771888i
$358$	1.29404e10	+	4.70992e9i	0.787800	+	0.286736i
$359$	1.36481e10	−	1.14521e10i	0.821664	−	0.689458i	−0.131697	−	0.991290i	$-0.542043\pi$
$359$	1.36481e10	−	1.14521e10i	0.821664	−	0.689458i	0.953361	+	0.301832i	$0.0975981\pi$
$360$			1.40850e9i			0.0838583i
$361$	1.10429e10	+	1.29034e10i	0.650208	+	0.759756i
$362$	−4.40690e9			−0.256625
$363$	3.03927e9	+	3.62206e9i	0.175042	+	0.208607i
$364$	−8.58847e9	+	2.35966e10i	−0.489227	+	1.34414i
$365$	−9.02353e6	+	5.11750e7i	−0.000508399	+	0.00288328i
$366$	9.05229e8	+	5.13381e9i	0.0504469	+	0.286098i
$367$	−3.04472e10	+	1.10819e10i	−1.67835	+	0.610870i	−0.993082	−	0.117420i	$-0.962538\pi$
$367$	−3.04472e10	+	1.10819e10i	−1.67835	+	0.610870i	−0.685269	+	0.728290i	$0.740315\pi$
$368$	2.33781e9	−	4.04920e9i	0.127473	−	0.220790i
$369$	−9.05112e9	+	5.22567e9i	−0.488199	+	0.281862i
$370$	−1.96733e9	−	1.65078e9i	−0.104971	−	0.0880811i
$371$	1.94848e10	−	2.32211e10i	1.02849	−	1.22571i
$372$	−8.45771e9	−	1.46492e10i	−0.441653	−	0.764966i
$373$	−8.41022e9	−	4.85564e9i	−0.434482	−	0.250848i	0.266772	−	0.963760i	$-0.414043\pi$
$373$	−8.41022e9	−	4.85564e9i	−0.434482	−	0.250848i	−0.701254	+	0.712911i	$0.747376\pi$
$374$	−6.53771e8	−	1.79622e9i	−0.0334148	−	0.0918064i
$375$	1.09201e10	−	1.92551e9i	0.552206	−	0.0973688i
$376$	9.02529e9	+	1.59140e9i	0.451554	+	0.0796211i
$377$	−1.87310e10	−	6.81751e9i	−0.927245	−	0.337490i
$378$	−7.86553e9	+	6.59996e9i	−0.385266	+	0.323277i
$379$		−	2.14977e10i		−	1.04192i	−0.853580	−	0.520962i	$-0.825573\pi$
$379$		−	2.14977e10i		−	1.04192i	0.853580	−	0.520962i	$-0.174427\pi$
$380$	−1.80505e9	−	8.31045e8i	−0.0865675	−	0.0398557i
$381$	1.72127e10			0.816861
$382$	5.88744e9	+	7.01638e9i	0.276486	+	0.329503i
$383$	3.96270e9	−	1.08874e10i	0.184160	−	0.505976i	−0.812917	−	0.582380i	$-0.802122\pi$
$383$	3.96270e9	−	1.08874e10i	0.184160	−	0.505976i	0.997077	+	0.0764039i	$0.0243438\pi$
$384$	4.99966e8	−	2.83545e9i	0.0229940	−	0.130406i
$385$	−1.27776e9	−	7.24655e9i	−0.0581577	−	0.329829i
$386$	−9.45087e9	+	3.43983e9i	−0.425718	+	0.154949i
$387$	3.93179e9	−	6.81007e9i	0.175286	−	0.303604i
$388$	1.66140e10	−	9.59209e9i	0.733073	−	0.423240i
$389$	5.27061e9	+	4.42257e9i	0.230177	+	0.193142i	0.750581	−	0.660779i	$-0.229774\pi$
$389$	5.27061e9	+	4.42257e9i	0.230177	+	0.193142i	−0.520403	+	0.853921i	$0.674218\pi$
$390$	4.42193e9	−	5.26985e9i	0.191141	−	0.227793i
$391$	1.82033e9	+	3.15290e9i	0.0778830	+	0.134897i
$392$	−2.00516e10	−	1.15768e10i	−0.849190	−	0.490280i
$393$	−2.04061e10	−	5.60654e10i	−0.855441	−	2.35031i
$394$	−1.46659e10	+	2.58599e9i	−0.608587	+	0.107310i
$395$	−2.77350e9	−	4.89043e8i	−0.113930	−	0.0200890i
$396$	1.30057e10	+	4.73369e9i	0.528876	+	0.192495i
$397$	−1.93245e10	+	1.62152e10i	−0.777941	+	0.652770i	−0.942729	−	0.333559i	$-0.891750\pi$
$397$	−1.93245e10	+	1.62152e10i	−0.777941	+	0.652770i	0.164788	+	0.986329i	$0.447306\pi$
$398$		−	1.71091e10i		−	0.681861i
$399$	−1.94363e10	−	7.11513e10i	−0.766871	−	2.80732i
$400$	−6.16749e9			−0.240918
$401$	2.91498e10	+	3.47394e10i	1.12735	+	1.34352i	0.931860	+	0.362817i	$0.118185\pi$
$401$	2.91498e10	+	3.47394e10i	1.12735	+	1.34352i	0.195489	+	0.980706i	$0.437371\pi$
$402$	−1.19203e10	+	3.27506e10i	−0.456437	+	1.25405i
$403$	−7.95429e9	+	4.51110e10i	−0.301565	+	1.71026i
$404$	−4.39106e8	−	2.49029e9i	−0.0164833	−	0.0934814i
$405$	−3.35323e9	+	1.22047e9i	−0.124636	+	0.0453637i
$406$	1.25031e10	−	2.16560e10i	0.460164	−	0.797028i
$407$	−2.18547e10	+	1.26178e10i	−0.796467	+	0.459840i
$408$	1.71737e9	+	1.44105e9i	0.0619761	+	0.0520041i
$409$	1.80257e10	−	2.14822e10i	0.644168	−	0.767690i	−0.340854	−	0.940116i	$-0.610716\pi$
$409$	1.80257e10	−	2.14822e10i	0.644168	−	0.767690i	0.985022	+	0.172426i	$0.0551606\pi$
$410$	8.62634e8	+	1.49413e9i	0.0305275	+	0.0528752i
$411$	−3.24191e10	−	1.87172e10i	−1.13614	−	0.655953i
$412$	3.02025e9	+	8.29806e9i	0.104822	+	0.287997i
$413$	1.05698e11	−	1.86374e10i	3.63302	−	0.640599i
$414$	−2.59601e10	−	4.57746e9i	−0.883699	−	0.155820i
$415$	−2.44078e9	−	8.88370e8i	−0.0822879	−	0.0299503i
$416$	−5.97272e9	+	5.01171e9i	−0.199434	+	0.167345i
$417$			4.39196e10i			1.45249i
$418$	−1.37401e10	+	1.38744e10i	−0.450075	+	0.454474i
$419$	−3.61675e10			−1.17344			−0.586722	−	0.809789i	$-0.699582\pi$
$419$	−3.61675e10			−1.17344			−0.586722	+	0.809789i	$0.699582\pi$
$420$	5.54733e9	+	6.61105e9i	0.178274	+	0.212458i
$421$	8.28060e9	−	2.27508e10i	0.263593	−	0.724215i	−0.735325	−	0.677714i	$-0.762971\pi$
$421$	8.28060e9	−	2.27508e10i	0.263593	−	0.724215i	0.998918	−	0.0465011i	$-0.0148071\pi$
$422$	1.23464e9	−	7.00198e9i	0.0389305	−	0.220786i
$423$	−8.97212e9	−	5.08834e10i	−0.280242	−	1.58933i
$424$	8.84441e9	−	3.21910e9i	0.273656	−	0.0996028i
$425$	2.40115e9	−	4.15891e9i	0.0735976	−	0.127475i
$426$	−8.14978e9	+	4.70528e9i	−0.247461	+	0.142872i
$427$	1.35663e10	+	1.13835e10i	0.408086	+	0.342425i
$428$	−1.73568e9	+	2.06850e9i	−0.0517243	+	0.0616426i
$429$	−3.37992e10	−	5.85420e10i	−0.997878	−	1.72838i
$430$	−1.12418e9	−	6.49047e8i	−0.0328823	−	0.0189846i
$431$	1.12005e10	+	3.07730e10i	0.324584	+	0.891787i	0.989457	+	0.144830i	$0.0462635\pi$
$431$	1.12005e10	+	3.07730e10i	0.324584	+	0.891787i	−0.664873	+	0.746957i	$0.731514\pi$
$432$	−3.13964e9	+	5.53603e8i	−0.0901456	+	0.0158951i
$433$	5.43482e9	+	9.58305e8i	0.154608	+	0.0272616i	0.250417	−	0.968138i	$-0.419432\pi$
$433$	5.43482e9	+	9.58305e8i	0.154608	+	0.0272616i	−0.0958081	+	0.995400i	$0.530544\pi$
$434$	−5.39995e10	−	1.96542e10i	−1.52206	−	0.553983i
$435$	−5.24784e9	+	4.40346e9i	−0.146563	+	0.122981i
$436$			1.03287e10i			0.285825i
$437$	2.11833e10	−	3.05682e10i	0.580854	−	0.838192i
$438$	−5.98874e8			−0.0162719
$439$	3.37303e10	+	4.01982e10i	0.908159	+	1.08230i	0.996279	+	0.0861917i	$0.0274698\pi$
$439$	3.37303e10	+	4.01982e10i	0.908159	+	1.08230i	−0.0881197	+	0.996110i	$0.528086\pi$
$440$	7.81421e8	−	2.14694e9i	0.0208485	−	0.0572808i
$441$	−2.26675e10	+	1.28554e11i	−0.599307	+	3.39884i
$442$	−1.05421e9	−	5.97875e9i	−0.0276210	−	0.156647i
$443$	1.43332e10	−	5.21687e9i	0.372160	−	0.135455i	−0.149168	−	0.988812i	$-0.547659\pi$
$443$	1.43332e10	−	5.21687e9i	0.372160	−	0.135455i	0.521327	+	0.853357i	$0.325437\pi$
$444$	1.47986e10	−	2.56320e10i	0.380794	−	0.659554i
$445$	1.03375e10	−	5.96837e9i	0.263619	−	0.152200i
$446$	−4.43546e8	−	3.72179e8i	−0.0112098	−	0.00940617i
$447$	−6.29706e10	+	7.50454e10i	−1.57728	+	1.87972i
$448$	−4.89059e9	−	8.47074e9i	−0.121408	−	0.210286i
$449$	1.47996e10	+	8.54453e9i	0.364136	+	0.210234i	0.670893	−	0.741554i	$-0.265911\pi$
$449$	1.47996e10	+	8.54453e9i	0.364136	+	0.210234i	−0.306758	+	0.951788i	$0.599244\pi$
$450$	1.18926e10	+	3.26746e10i	0.290018	+	0.796819i
$451$	1.66956e10	−	2.94388e9i	0.403547	−	0.0711563i
$452$	1.32652e10	+	2.33901e9i	0.317803	+	0.0560373i
$453$	−4.00164e10	−	1.45648e10i	−0.950266	−	0.345869i
$454$	2.37630e10	−	1.99395e10i	0.559342	−	0.469344i
$455$		−	2.33703e10i		−	0.545280i
$456$	5.81970e9	−	2.21497e10i	0.134599	−	0.512282i
$457$	2.61548e10			0.599635			0.299817	−	0.953997i	$-0.403074\pi$
$457$	2.61548e10			0.599635			0.299817	+	0.953997i	$0.403074\pi$
$458$	2.32410e10	+	2.76975e10i	0.528192	+	0.629475i
$459$	8.49025e8	−	2.33268e9i	0.0191280	−	0.0525538i
$460$	−7.55631e8	+	4.28540e9i	−0.0168764	+	0.0957106i
$461$	−1.20219e10	−	6.81796e10i	−0.266176	−	1.50956i	−0.765664	−	0.643240i	$-0.777590\pi$
$461$	−1.20219e10	−	6.81796e10i	−0.266176	−	1.50956i	0.499488	−	0.866321i	$-0.333521\pi$
$462$	7.96884e10	−	2.90042e10i	1.74915	−	0.636639i
$463$	−1.30570e10	+	2.26154e10i	−0.284132	+	0.492131i	−0.972398	−	0.233327i	$-0.925039\pi$
$463$	−1.30570e10	+	2.26154e10i	−0.284132	+	0.492131i	0.688266	+	0.725458i	$0.258372\pi$
$464$	6.72406e9	−	3.88214e9i	0.145064	−	0.0837527i
$465$	1.20597e10	+	1.01193e10i	0.257944	+	0.216441i
$466$	7.19680e9	−	8.57682e9i	0.152615	−	0.181879i
$467$	−3.37226e10	−	5.84092e10i	−0.709011	−	1.22804i	−0.965224	−	0.261423i	$-0.915808\pi$
$467$	−3.37226e10	−	5.84092e10i	−0.709011	−	1.22804i	0.256213	−	0.966620i	$-0.417525\pi$
$468$	3.80684e10	+	2.19788e10i	0.793562	+	0.458163i
$469$	4.04954e10	+	1.11260e11i	0.836980	+	2.29958i
$470$	−8.39966e9	+	1.48109e9i	−0.172135	+	0.0303521i
$471$	9.71166e10	+	1.71243e10i	1.97338	+	0.347960i
$472$	3.13152e10	+	1.13978e10i	0.630940	+	0.229643i
$473$	−9.77130e9	+	8.19909e9i	−0.195213	+	0.163803i
$474$		−	3.24569e10i		−	0.642973i
$475$	−4.88908e10	−	4.03789e9i	−0.960400	−	0.0793196i
$476$	7.61608e9			0.148356
$477$	−3.41088e10	−	4.06492e10i	−0.658859	−	0.785198i
$478$	1.37145e10	−	3.76803e10i	0.262705	−	0.721776i
$479$	1.43342e10	−	8.12931e10i	0.272289	−	1.54423i	−0.475154	−	0.879903i	$-0.657608\pi$
$479$	1.43342e10	−	8.12931e10i	0.272289	−	1.54423i	0.747443	−	0.664326i	$-0.231281\pi$
$480$	4.65308e8	+	2.63890e9i	0.00876549	+	0.0497115i
$481$	−7.53157e10	+	2.74127e10i	−1.40704	+	0.512119i
$482$	−2.06675e10	+	3.57971e10i	−0.382912	+	0.663224i
$483$	−1.39877e11	+	8.07580e10i	−2.57014	+	1.48387i
$484$	3.82059e9	+	3.20586e9i	0.0696224	+	0.0584201i
$485$	−1.14766e10	+	1.36772e10i	−0.207417	+	0.247190i
$486$	−2.77845e10	−	4.81241e10i	−0.498032	−	0.862616i
$487$	8.85352e10	+	5.11158e10i	1.57398	+	0.908740i	0.995673	+	0.0929232i	$0.0296211\pi$
$487$	8.85352e10	+	5.11158e10i	1.57398	+	0.908740i	0.578311	+	0.815817i	$0.303712\pi$
$488$	1.88068e9	+	5.16712e9i	0.0331616	+	0.0911107i
$489$	4.84912e10	−	8.55030e9i	0.848061	−	0.149536i
$490$	2.12212e10	+	3.74187e9i	0.368117	+	0.0649090i
$491$	3.36353e10	+	1.22422e10i	0.578721	+	0.210637i	0.614761	−	0.788713i	$-0.289252\pi$
$491$	3.36353e10	+	1.22422e10i	0.578721	+	0.210637i	−0.0360406	+	0.999350i	$0.511475\pi$
$492$	−1.52314e10	+	1.27807e10i	−0.259944	+	0.218119i
$493$			6.04563e9i			0.102342i
$494$	−5.06280e10	+	3.58183e10i	−0.850125	+	0.601447i
$495$	−1.28810e10			−0.214550
$496$	−1.14690e10	−	1.36682e10i	−0.189495	−	0.225832i
$497$	−1.09342e10	+	3.00415e10i	−0.179210	+	0.492375i
$498$	5.19807e9	−	2.94797e10i	0.0845133	−	0.479299i
$499$	3.23519e9	+	1.83477e10i	0.0521792	+	0.295923i	0.999719	−	0.0237157i	$-0.00754964\pi$
$499$	3.23519e9	+	1.83477e10i	0.0521792	+	0.295923i	−0.947540	+	0.319638i	$0.896439\pi$
$500$	1.09909e10	−	4.00038e9i	0.175855	−	0.0640060i
$501$	−3.56793e10	+	6.17983e10i	−0.566324	+	0.980902i
$502$	−3.68425e10	+	2.12710e10i	−0.580141	+	0.334945i
$503$	4.68516e10	+	3.93131e10i	0.731901	+	0.614137i	0.930649	−	0.365913i	$-0.119243\pi$
$503$	4.68516e10	+	3.93131e10i	0.731901	+	0.614137i	−0.198749	+	0.980051i	$0.563688\pi$
$504$	−3.54465e10	+	4.22435e10i	−0.549353	+	0.654694i
$505$	1.17671e9	+	2.03812e9i	0.0180927	+	0.0313375i
$506$	3.70308e10	+	2.13797e10i	0.564886	+	0.326137i
$507$	−3.95741e10	−	1.08729e11i	−0.598935	−	1.64556i
$508$	1.78803e10	−	3.15277e9i	0.268484	−	0.0473411i
$509$	−6.99522e10	−	1.23345e10i	−1.04215	−	0.183759i	−0.373725	−	0.927539i	$-0.621920\pi$
$509$	−6.99522e10	−	1.23345e10i	−1.04215	−	0.183759i	−0.668424	+	0.743780i	$0.733031\pi$
$510$	−1.96064e9	−	7.13614e8i	−0.0289812	−	0.0105483i
$511$	−1.55851e9	+	1.30775e9i	−0.0228574	+	0.0191796i
$512$		−	3.03700e9i		−	0.0441942i
$513$	−2.52509e10	+	2.33297e9i	−0.364592	+	0.0336852i
$514$	−9.75293e10			−1.39728
$515$	−5.28274e9	−	6.29572e9i	−0.0750983	−	0.0894986i
$516$	5.11667e9	−	1.40579e10i	0.0721753	−	0.198300i
$517$	−1.45537e10	+	8.25380e10i	−0.203709	+	1.15529i
$518$	−1.74599e10	−	9.90203e10i	−0.242507	−	1.37532i
$519$	1.92832e11	−	7.01852e10i	2.65773	−	0.967333i
$520$	3.62818e9	−	6.28419e9i	0.0496221	−	0.0859480i
$521$	−5.14570e10	+	2.97087e10i	−0.698383	+	0.403212i	−0.806745	−	0.590900i	$-0.798773\pi$
$521$	−5.14570e10	+	2.97087e10i	−0.698383	+	0.403212i	0.108362	+	0.994112i	$0.465439\pi$
$522$	−3.35328e10	−	2.81374e10i	−0.451636	−	0.378967i
$523$	−8.46690e10	+	1.00905e11i	−1.13166	+	1.34867i	−0.202377	+	0.979308i	$0.564867\pi$
$523$	−8.46690e10	+	1.00905e11i	−1.13166	+	1.34867i	−0.929287	+	0.369358i	$0.879578\pi$
$524$	−3.14669e10	−	5.45022e10i	−0.417377	−	0.722918i
$525$	1.84508e11	+	1.06526e11i	2.42872	+	1.40222i
$526$	8.37218e9	+	2.30024e10i	0.109369	+	0.300490i
$527$	1.36820e10	−	2.41251e9i	0.177381	−	0.0312771i
$528$	2.59307e10	+	4.57229e9i	0.333641	+	0.0588299i
$529$	−2.94041e9	−	1.07022e9i	−0.0375478	−	0.0136663i
$530$	−6.71023e9	+	5.63056e9i	−0.0850422	+	0.0713588i
$531$		−	1.87882e11i		−	2.36324i
$532$	−3.32227e10	−	7.03509e10i	−0.414752	−	0.878261i
$533$	5.38436e10			0.667153
$534$	8.84265e10	+	1.05383e11i	1.08747	+	1.29600i
$535$	8.59517e8	−	2.36150e9i	0.0104915	−	0.0288253i
$536$	−6.38379e9	+	3.62043e10i	−0.0773427	+	0.438633i
$537$	−2.56485e10	−	1.45460e11i	−0.308436	−	1.74923i
$538$	−3.91560e10	+	1.42516e10i	−0.467379	+	0.170112i
$539$	1.05872e11	−	1.83376e11i	1.25437	−	2.17264i
$540$	2.56956e9	−	1.48354e9i	0.0302193	−	0.0174471i
$541$	−2.73151e10	−	2.29201e10i	−0.318870	−	0.267564i	0.469277	−	0.883051i	$-0.344515\pi$
$541$	−2.73151e10	−	2.29201e10i	−0.318870	−	0.267564i	−0.788147	+	0.615488i	$0.788959\pi$
$542$	−2.48318e10	+	2.95934e10i	−0.287748	+	0.342924i
$543$	2.36338e10	+	4.09349e10i	0.271853	+	0.470863i
$544$	2.04793e9	+	1.18238e9i	0.0233841	+	0.0135008i
$545$	−3.28775e9	−	9.03303e9i	−0.0372660	−	0.102388i
$546$	2.65244e11	−	4.67697e10i	2.98453	−	0.526252i
$547$	−1.26464e11	−	2.22989e10i	−1.41259	−	0.249078i	−0.585284	−	0.810829i	$-0.699017\pi$
$547$	−1.26464e11	−	2.22989e10i	−1.41259	−	0.249078i	−0.827306	+	0.561751i	$0.810128\pi$
$548$	−3.71048e10	−	1.35051e10i	−0.411442	−	0.149753i
$549$	2.37483e10	−	1.99272e10i	0.261422	−	0.219359i
$550$		−	5.64029e10i		−	0.616383i
$551$	5.58444e10	−	2.63721e10i	0.605862	−	0.286113i
$552$	−5.01498e10			−0.540148
$553$	−7.08753e10	−	8.44658e10i	−0.757869	−	0.903193i
$554$	−1.62923e10	+	4.47628e10i	−0.172959	+	0.475202i
$555$	−4.78325e9	+	2.71271e10i	−0.0504140	+	0.285912i
$556$	8.04458e9	+	4.56231e10i	0.0841791	+	0.477403i
$557$	9.32509e10	−	3.39406e10i	0.968796	−	0.352613i	0.191322	−	0.981527i	$-0.438723\pi$
$557$	9.32509e10	−	3.39406e10i	0.968796	−	0.352613i	0.777475	+	0.628914i	$0.216500\pi$
$558$	−5.02971e10	+	8.71172e10i	−0.518808	+	0.898601i
$559$	−3.50844e10	+	2.02560e10i	−0.359308	+	0.207447i
$560$	6.97341e9	+	5.85139e9i	0.0709077	+	0.0594986i
$561$	−1.31787e10	+	1.57057e10i	−0.133052	+	0.158565i
$562$	1.79583e10	+	3.11048e10i	0.180020	+	0.311804i
$563$	−1.35612e11	−	7.82958e10i	−1.34979	−	0.779300i	−0.361569	−	0.932345i	$-0.617759\pi$
$563$	−1.35612e11	−	7.82958e10i	−1.34979	−	0.779300i	−0.988219	+	0.153045i	$0.951092\pi$
$564$	−3.36195e10	−	9.23689e10i	−0.332258	−	0.912871i
$565$	−1.23456e10	+	2.17687e9i	−0.121149	+	0.0213618i
$566$	−1.42423e10	−	2.51130e9i	−0.138776	−	0.0244699i
$567$	−1.31284e11	−	4.77836e10i	−1.27023	−	0.462324i
$568$	−7.60403e9	+	6.38054e9i	−0.0730551	+	0.0613005i
$569$			7.94991e10i			0.758426i	0.925309	+	0.379213i	$0.123805\pi$
$569$			7.94991e10i			0.758426i	−0.925309	+	0.379213i	$0.876195\pi$
$570$	1.96088e9	+	2.12236e10i	0.0185760	+	0.201057i
$571$	1.77926e10			0.167377			0.0836885	−	0.996492i	$-0.473330\pi$
$571$	1.77926e10			0.167377			0.0836885	+	0.996492i	$0.473330\pi$
$572$	−4.58331e10	−	5.46217e10i	−0.428149	−	0.510248i
$573$	3.36001e10	−	9.23156e10i	0.311690	−	0.856360i
$574$	−1.17294e10	+	6.65210e10i	−0.108051	+	0.612789i
$575$	1.86543e10	+	1.05794e11i	0.170650	+	0.967805i
$576$	−1.60896e10	+	5.85615e9i	−0.146169	+	0.0532013i
$577$	5.02444e10	−	8.70259e10i	0.453299	−	0.785137i	−0.545290	−	0.838248i	$-0.683580\pi$
$577$	5.02444e10	−	8.70259e10i	0.453299	−	0.785137i	0.998589	+	0.0531110i	$0.0169137\pi$
$578$	6.67536e10	−	3.85402e10i	0.598085	−	0.345305i
$579$	8.26361e10	+	6.93400e10i	0.735285	+	0.616977i
$580$	−4.64482e9	+	5.53548e9i	−0.0410447	+	0.0489152i
$581$	−5.08467e10	−	8.80691e10i	−0.446229	−	0.772892i
$582$	−1.78199e11	−	1.02883e11i	−1.55315	−	0.896709i
$583$	2.94393e10	+	8.08839e10i	0.254832	+	0.700145i
$584$	−6.22103e8	+	1.09693e8i	−0.00534824	+	0.000943038i
$585$	−4.02889e10	−	7.10402e9i	−0.344003	−	0.0606570i
$586$	1.08744e11	+	3.95795e10i	0.922177	+	0.335645i
$587$	−7.19538e10	+	6.03764e10i	−0.606040	+	0.508528i	−0.893381	−	0.449300i	$-0.851673\pi$
$587$	−7.19538e10	+	6.03764e10i	−0.606040	+	0.508528i	0.287340	+	0.957829i	$0.407229\pi$
$588$			2.48341e11i			2.07749i
$589$	−8.19680e10	−	1.15859e11i	−0.681057	−	0.962651i
$590$	−3.10149e10			−0.255954
$591$	1.02672e11	+	1.22360e11i	0.841596	+	1.00298i
$592$	1.06777e10	−	2.93368e10i	0.0869344	−	0.238850i
$593$	−1.54390e10	+	8.75589e10i	−0.124853	+	0.708079i	0.856541	+	0.516078i	$0.172609\pi$
$593$	−1.54390e10	+	8.75589e10i	−0.124853	+	0.708079i	−0.981395	+	0.192001i	$0.938502\pi$
$594$	−5.06281e9	−	2.87126e10i	−0.0406673	−	0.230636i
$595$	−6.66067e9	+	2.42429e9i	−0.0531435	+	0.0193427i
$596$	−5.16672e10	+	8.94902e10i	−0.409478	+	0.709236i
$597$	−1.58924e11	+	9.17548e10i	−1.25110	+	0.722323i
$598$	1.04033e11	+	8.72941e10i	0.813517	+	0.682622i
$599$	−2.27078e10	+	2.70622e10i	−0.176388	+	0.210211i	−0.846994	−	0.531603i	$-0.821590\pi$
$599$	−2.27078e10	+	2.70622e10i	−0.176388	+	0.210211i	0.670606	+	0.741814i	$0.266034\pi$
$600$	3.30757e10	+	5.72888e10i	0.255214	+	0.442043i
$601$	1.07880e11	+	6.22847e10i	0.826883	+	0.477401i	0.852784	−	0.522263i	$-0.174912\pi$
$601$	1.07880e11	+	6.22847e10i	0.826883	+	0.477401i	−0.0259012	+	0.999665i	$0.508246\pi$
$602$	−1.73823e10	−	4.77575e10i	−0.132349	−	0.363627i
$603$	2.04115e11	−	3.59910e10i	1.54385	−	0.272223i
$604$	−4.42363e10	−	7.80005e9i	−0.332377	−	0.0586070i
$605$	−4.36177e9	−	1.58756e9i	−0.0325568	−	0.0118497i
$606$	−2.07770e10	+	1.74340e10i	−0.154061	+	0.129273i
$607$		−	1.36035e11i		−	1.00207i	−0.865428	−	0.501033i	$-0.832954\pi$
$607$		−	1.36035e11i		−	1.00207i	0.865428	−	0.501033i	$-0.167046\pi$
$608$	1.98834e9	−	2.40748e10i	0.0145505	−	0.176177i
$609$	−2.68211e11			−1.94988
$610$	−3.28951e9	−	3.92028e9i	−0.0237581	−	0.0283138i
$611$	−9.10415e10	+	2.50135e11i	−0.653243	+	1.79477i
$612$	2.31511e9	−	1.31296e10i	0.0165031	−	0.0935937i
$613$	−2.53928e10	−	1.44009e11i	−0.179832	−	1.01988i	−0.932417	−	0.361384i	$-0.882304\pi$
$613$	−2.53928e10	−	1.44009e11i	−0.179832	−	1.01988i	0.752585	−	0.658496i	$-0.228807\pi$
$614$	−7.95807e10	+	2.89650e10i	−0.559931	+	0.203798i
$615$	9.25246e9	−	1.60257e10i	0.0646780	−	0.112026i
$616$	7.74666e10	−	4.47254e10i	0.538012	−	0.310621i
$617$	−1.08072e11	−	9.06836e10i	−0.745718	−	0.625731i	0.188649	−	0.982045i	$-0.439589\pi$
$617$	−1.08072e11	−	9.06836e10i	−0.745718	−	0.625731i	−0.934367	+	0.356313i	$0.884034\pi$
$618$	6.08819e10	−	7.25563e10i	0.417383	−	0.497418i
$619$	−9.68436e10	−	1.67738e11i	−0.659642	−	1.14253i	−0.980708	−	0.195477i	$-0.937375\pi$
$619$	−9.68436e10	−	1.67738e11i	−0.659642	−	1.14253i	0.321066	−	0.947057i	$-0.395959\pi$
$620$	1.43810e10	+	8.30287e9i	0.0973245	+	0.0561903i
$621$	1.89924e10	+	5.21811e10i	0.127706	+	0.350870i
$622$	4.96031e10	−	8.74637e9i	0.331396	−	0.0584341i
$623$	4.60243e11	+	8.11533e10i	3.05517	+	0.538708i
$624$	7.85840e10	+	2.86022e10i	0.518317	+	0.188652i
$625$	1.04304e11	−	8.75212e10i	0.683565	−	0.573579i
$626$			1.24483e11i			0.810611i
$627$	2.02564e11	+	5.32223e10i	1.31067	+	0.344369i
$628$	1.04020e11			0.668772
$629$	1.56255e10	+	1.86218e10i	0.0998234	+	0.118965i
$630$	1.75533e10	−	4.82273e10i	0.111429	−	0.306147i
$631$	−4.71062e10	+	2.67153e11i	−0.297140	+	1.68516i	0.361236	+	0.932474i	$0.382355\pi$
$631$	−4.71062e10	+	2.67153e11i	−0.297140	+	1.68516i	−0.658376	+	0.752689i	$0.728756\pi$
$632$	−5.94499e9	−	3.37157e10i	−0.0372635	−	0.211332i
$633$	−7.16614e10	+	2.60826e10i	−0.446345	+	0.162456i
$634$	−4.77827e10	+	8.27621e10i	−0.295743	+	0.512241i
$635$	−1.46337e10	+	8.44876e9i	−0.0900034	+	0.0519635i
$636$	−7.73334e10	−	6.48905e10i	−0.472649	−	0.396600i
$637$	4.32279e11	−	5.15170e11i	2.62547	−	3.12891i
$638$	3.55029e10	+	6.14928e10i	0.214280	+	0.371144i
$639$	4.84659e10	+	2.79818e10i	0.290692	+	0.167831i
$640$	9.66712e8	+	2.65602e9i	0.00576205	+	0.0158311i
$641$	−5.54559e10	+	9.77837e9i	−0.328485	+	0.0579208i	−0.335459	−	0.942055i	$-0.608891\pi$
$641$	−5.54559e10	+	9.77837e9i	−0.328485	+	0.0579208i	0.00697368	+	0.999976i	$0.497780\pi$
$642$	2.85223e10	+	5.02925e9i	0.167897	+	0.0296048i
$643$	2.06518e11	+	7.51662e10i	1.20813	+	0.439723i	0.866054	−	0.499950i	$-0.166648\pi$
$643$	2.06518e11	+	7.51662e10i	1.20813	+	0.439723i	0.342074	+	0.939673i	$0.388871\pi$
$644$	−1.30510e11	+	1.09511e11i	−0.758753	+	0.636670i
$645$			1.39231e10i			0.0804447i
$646$	1.54602e10	+	1.07137e10i	0.0887740	+	0.0615190i
$647$	−1.49086e11			−0.850782			−0.425391	−	0.905010i	$-0.639863\pi$
$647$	−1.49086e11			−0.850782			−0.425391	+	0.905010i	$0.639863\pi$
$648$	−2.78836e10	−	3.32304e10i	−0.158143	−	0.188467i
$649$	−1.04235e11	+	2.86384e11i	−0.587538	+	1.61425i
$650$	3.11069e10	−	1.76416e11i	0.174262	−	0.988291i
$651$	1.07030e11	+	6.06995e11i	0.595909	+	3.37957i
$652$	4.88058e10	−	1.77639e10i	0.270073	−	0.0982986i
$653$	1.17068e11	−	2.02768e11i	0.643853	−	1.11519i	−0.340712	−	0.940168i	$-0.610668\pi$
$653$	1.17068e11	−	2.02768e11i	0.643853	−	1.11519i	0.984565	−	0.175018i	$-0.0559984\pi$
$654$	9.59418e10	−	5.53920e10i	0.524441	−	0.302786i
$655$	4.48681e10	+	3.76488e10i	0.243766	+	0.204544i
$656$	−1.34812e10	+	1.60663e10i	−0.0727970	+	0.0867560i
$657$	1.78072e9	+	3.08430e9i	0.00955728	+	0.0165537i
$658$	−2.89195e11	−	1.66967e11i	−1.54272	−	0.890691i
$659$	−5.15675e10	−	1.41681e11i	−0.273423	−	0.751222i	−0.998070	−	0.0621023i	$-0.980219\pi$
$659$	−5.15675e10	−	1.41681e11i	−0.273423	−	0.751222i	0.724647	−	0.689120i	$-0.242003\pi$
$660$	−2.41332e10	+	4.25534e9i	−0.127186	+	0.0224263i
$661$	1.48469e10	+	2.61791e9i	0.0777732	+	0.0137135i	0.212399	−	0.977183i	$-0.431872\pi$
$661$	1.48469e10	+	2.61791e9i	0.0777732	+	0.0137135i	−0.134626	+	0.990896i	$0.542983\pi$
$662$	−5.93435e10	−	2.15993e10i	−0.308988	−	0.112462i
$663$	−4.98819e10	+	4.18559e10i	−0.258160	+	0.216622i
$664$		−	3.15752e10i		−	0.162433i
$665$	5.14485e10	+	5.09505e10i	0.263079	+	0.260533i
$666$	−1.76012e11			−0.894633
$667$	−8.69296e10	−	1.03599e11i	−0.439202	−	0.523420i
$668$	−2.57438e10	+	7.07304e10i	−0.129290	+	0.355223i
$669$	−1.07841e9	+	6.11598e9i	−0.00538370	+	0.0305325i
$670$	−5.94127e9	−	3.36946e10i	−0.0294836	−	0.167210i
$671$	−4.72544e10	+	1.71992e10i	−0.233105	+	0.0848433i
$672$	−5.24555e10	+	9.08556e10i	−0.257226	+	0.445528i
$673$	−6.85845e10	+	3.95973e10i	−0.334323	+	0.193021i	−0.657759	−	0.753229i	$-0.728495\pi$
$673$	−6.85845e10	+	3.95973e10i	−0.334323	+	0.193021i	0.323436	+	0.946250i	$0.395162\pi$
$674$	1.51737e10	+	1.27322e10i	0.0735278	+	0.0616972i
$675$	4.70830e10	−	5.61113e10i	0.226803	−	0.270293i
$676$	−6.10245e10	−	1.05698e11i	−0.292225	−	0.506149i
$677$	6.06671e10	+	3.50262e10i	0.288801	+	0.166739i	0.637401	−	0.770532i	$-0.280010\pi$
$677$	6.06671e10	+	3.50262e10i	0.288801	+	0.166739i	−0.348600	+	0.937272i	$0.613343\pi$
$678$	−4.94132e10	−	1.35762e11i	−0.233843	−	0.642478i
$679$	−6.88408e11	+	1.21385e11i	−3.23867	+	0.571065i
$680$	−2.16739e9	−	3.82170e8i	−0.0101368	−	0.00178740i
$681$	−3.12653e11	−	1.13796e11i	−1.45370	−	0.529103i
$682$	1.24999e11	−	1.04886e11i	0.577786	−	0.484820i
$683$			1.34437e11i			0.617781i	0.951098	+	0.308890i	$0.0999577\pi$
$683$			1.34437e11i			0.617781i	−0.951098	+	0.308890i	$0.900042\pi$
$684$	−1.31379e11	+	3.58887e10i	−0.600209	+	0.163958i
$685$	3.67490e10			0.166910
$686$	3.46764e11	+	4.13258e11i	1.56581	+	1.86606i
$687$	1.32638e11	−	3.64420e11i	0.595445	−	1.63597i
$688$	2.74019e9	−	1.55404e10i	0.0122300	−	0.0693598i
$689$	4.74714e10	+	2.69223e11i	0.210647	+	1.19464i
$690$	4.38587e10	−	1.59633e10i	0.193490	−	0.0704247i
$691$	3.84497e10	−	6.65968e10i	0.168648	−	0.292106i	−0.769297	−	0.638891i	$-0.779393\pi$
$691$	3.84497e10	−	6.65968e10i	0.168648	−	0.292106i	0.937945	+	0.346785i	$0.112727\pi$
$692$	1.87456e11	−	1.08228e11i	0.817476	−	0.471970i
$693$	−3.86326e11	−	3.24166e11i	−1.67502	−	1.40551i
$694$	1.70443e11	−	2.03127e11i	0.734755	−	0.875646i
$695$	−2.15578e10	−	3.73391e10i	−0.0923984	−	0.160039i
$696$	−7.21210e10	−	4.16391e10i	−0.307344	−	0.177445i
$697$	−5.58539e9	−	1.53457e10i	−0.0236659	−	0.0650214i
$698$	5.83531e9	−	1.02892e9i	0.0245834	−	0.00433472i
$699$	−1.18264e11	−	2.08532e10i	−0.495388	−	0.0873502i
$700$	2.11176e11	+	7.68619e10i	0.879535	+	0.320125i
$701$	2.90045e11	−	2.43376e11i	1.20114	−	1.00787i	0.201541	−	0.979480i	$-0.435405\pi$
$701$	2.90045e11	−	2.43376e11i	1.20114	−	1.00787i	0.999597	−	0.0283939i	$-0.00903929\pi$
$702$		−	9.25990e10i		−	0.381292i
$703$	1.03851e11	−	2.25567e11i	0.425196	−	0.923537i
$704$	2.77740e10			0.113070
$705$	5.88041e10	+	7.00801e10i	0.238041	+	0.283686i
$706$	−2.01714e10	+	5.54204e10i	−0.0811927	+	0.223075i
$707$	−1.60000e10	+	9.07406e10i	−0.0640387	+	0.363182i
$708$	−6.20684e10	−	3.52007e11i	−0.247023	−	1.40094i
$709$	−2.32306e11	+	8.45524e10i	−0.919337	+	0.334611i	−0.757975	−	0.652284i	$-0.773811\pi$
$709$	−2.32306e11	+	8.45524e10i	−0.919337	+	0.334611i	−0.161363	+	0.986895i	$0.551589\pi$
$710$	4.61913e9	−	8.00057e9i	0.0181772	−	0.0314838i
$711$	−1.67158e11	+	9.65087e10i	−0.654107	+	0.377649i
$712$	1.11159e11	+	9.32733e10i	0.432537	+	0.362942i
$713$	−1.99767e11	+	2.38073e11i	−0.772977	+	0.921198i
$714$	−4.08443e10	−	7.07445e10i	−0.157159	−	0.272207i
$715$	5.74702e10	+	3.31804e10i	0.219897	+	0.126957i
$716$	−5.32867e10	−	1.46404e11i	−0.202753	−	0.557058i
$717$	−4.23555e11	+	7.46842e10i	−1.60263	+	0.282587i
$718$	−1.98507e11	−	3.50021e10i	−0.746925	−	0.131703i
$719$	2.63598e10	+	9.59419e9i	0.0986341	+	0.0358999i	0.390866	−	0.920448i	$-0.372176\pi$
$719$	2.63598e10	+	9.59419e9i	0.0986341	+	0.0358999i	−0.292232	+	0.956348i	$0.594398\pi$
$720$	1.22072e10	−	1.02430e10i	0.0454239	−	0.0381152i
$721$		−	3.21767e11i		−	1.19070i
$722$	3.15239e10	−	1.89544e11i	0.116009	−	0.697526i
$723$	4.43351e11			1.62254
$724$	3.20483e10	+	3.81937e10i	0.116641	+	0.139007i
$725$	−6.10128e10	+	1.67631e11i	−0.220836	+	0.606741i
$726$	9.28917e9	−	5.26815e10i	0.0334373	−	0.189632i
$727$	−6.17538e10	−	3.50223e11i	−0.221068	−	1.25374i	−0.870061	−	0.492945i	$-0.835920\pi$
$727$	−6.17538e10	−	3.50223e11i	−0.221068	−	1.25374i	0.648993	−	0.760795i	$-0.275191\pi$
$728$	2.66965e11	−	9.71675e10i	0.950450	−	0.345936i
$729$	−1.99744e11	+	3.45967e11i	−0.707236	+	1.22497i
$730$	5.09145e8	−	2.93955e8i	0.00179288	−	0.00103512i
$731$	9.41250e9	+	7.89802e9i	0.0329637	+	0.0276598i
$732$	3.79106e10	−	4.51801e10i	0.132043	−	0.157363i
$733$	6.30197e10	+	1.09153e11i	0.218304	+	0.378113i	0.954289	−	0.298884i	$-0.0966144\pi$
$733$	6.30197e10	+	1.09153e11i	0.218304	+	0.378113i	−0.735986	+	0.676997i	$0.763281\pi$
$734$	3.17466e11	+	1.83289e11i	1.09374	+	0.631469i
$735$	−7.90498e10	−	2.17188e11i	−0.270864	−	0.744193i
$736$	−5.20949e10	+	9.18574e9i	−0.177535	+	0.0313042i
$737$	−3.31095e11	−	5.83811e10i	−1.12223	−	0.197880i
$738$	1.11112e11	+	4.04416e10i	0.374573	+	0.136334i
$739$	2.48089e11	−	2.08171e11i	0.831821	−	0.697980i	−0.123888	−	0.992296i	$-0.539536\pi$
$739$	2.48089e11	−	2.08171e11i	0.831821	−	0.697980i	0.955708	+	0.294316i	$0.0950918\pi$
$740$			2.90554e10i			0.0968948i
$741$	6.04223e11	+	2.78184e11i	2.00412	+	0.922699i
$742$	−3.42953e11			−1.13141
$743$	−1.42853e11	−	1.70246e11i	−0.468743	−	0.558627i	0.478936	−	0.877850i	$-0.341022\pi$
$743$	−1.42853e11	−	1.70246e11i	−0.468743	−	0.558627i	−0.947680	+	0.319223i	$0.896578\pi$
$744$	−6.54545e10	+	1.79835e11i	−0.213623	+	0.586924i
$745$	1.67000e10	−	9.47103e10i	0.0542114	−	0.307448i
$746$	1.90788e10	+	1.08201e11i	0.0616023	+	0.349364i
$747$	−1.67282e11	+	6.08855e10i	−0.537237	+	0.195538i
$748$	−1.08131e10	+	1.87288e10i	−0.0345416	+	0.0598278i
$749$	8.52087e10	−	4.91953e10i	0.270743	−	0.156313i
$750$	−9.61022e10	−	8.06393e10i	−0.303730	−	0.254860i
$751$	5.68913e10	−	6.78005e10i	0.178849	−	0.213144i	−0.669171	−	0.743109i	$-0.733350\pi$
$751$	5.68913e10	−	6.78005e10i	0.178849	−	0.213144i	0.848020	+	0.529965i	$0.177795\pi$
$752$	−5.18423e10	−	8.97936e10i	−0.162111	−	0.280785i
$753$	3.95165e11	+	2.28149e11i	1.22913	+	0.709640i
$754$	7.71313e10	+	2.11917e11i	0.238641	+	0.655661i
$755$	4.11698e10	−	7.25935e9i	0.126704	−	0.0223414i
$756$	1.14401e11	+	2.01720e10i	0.350222	+	0.0617536i
$757$	3.32876e11	+	1.21157e11i	1.01368	+	0.368948i	0.794844	−	0.606814i	$-0.207553\pi$
$757$	3.32876e11	+	1.21157e11i	1.01368	+	0.368948i	0.218833	+	0.975762i	$0.429775\pi$
$758$	−1.86317e11	+	1.56338e11i	−0.564384	+	0.473574i
$759$		−	4.58630e11i		−	1.38196i
$760$	5.92438e9	+	2.16876e10i	0.0177578	+	0.0650067i
$761$	4.49506e11			1.34029			0.670143	−	0.742232i	$-0.266233\pi$
$761$	4.49506e11			1.34029			0.670143	+	0.742232i	$0.266233\pi$
$762$	−1.25176e11	−	1.49179e11i	−0.371279	−	0.442473i
$763$	1.28721e11	−	3.53658e11i	0.379797	−	1.04348i
$764$	1.79943e10	−	1.02051e11i	0.0528154	−	0.299531i
$765$	2.15463e9	+	1.22195e10i	0.00629109	+	0.0356786i
$766$	−1.23177e11	+	4.48328e10i	−0.357779	+	0.130221i
$767$	−4.83970e11	+	8.38260e11i	−1.39842	+	2.42213i
$768$	−2.82102e10	+	1.62872e10i	−0.0810888	+	0.0468166i
$769$	1.41138e11	+	1.18429e11i	0.403587	+	0.338650i	0.821878	−	0.569663i	$-0.192926\pi$
$769$	1.41138e11	+	1.18429e11i	0.403587	+	0.338650i	−0.418291	+	0.908313i	$0.637371\pi$
$770$	−5.35121e10	+	6.37733e10i	−0.152226	+	0.181416i
$771$	5.23040e11	+	9.05932e11i	1.48019	+	2.56377i
$772$	9.85420e10	+	5.68933e10i	0.277429	+	0.160174i
$773$	−1.86609e11	−	5.12704e11i	−0.522655	−	1.43598i	−0.867554	−	0.497342i	$-0.834309\pi$
$773$	−1.86609e11	−	5.12704e11i	−0.522655	−	1.43598i	0.344900	−	0.938640i	$-0.387913\pi$
$774$	−8.76147e10	+	1.54488e10i	−0.244126	+	0.0430459i
$775$	4.03718e11	+	7.11863e10i	1.11911	+	0.197328i
$776$	−2.03955e11	−	7.42335e10i	−0.562454	−	0.204717i
$777$	−8.26146e11	+	6.93219e11i	−2.26659	+	1.90189i
$778$		−	7.78416e10i		−	0.212468i
$779$	−1.17387e11	+	1.18534e11i	−0.318763	+	0.321879i
$780$	−7.78304e10			−0.210267
$781$	−5.83513e10	−	6.95404e10i	−0.156836	−	0.186910i
$782$	1.40876e10	−	3.87053e10i	0.0376712	−	0.103501i
$783$	−1.60125e10	+	9.08114e10i	−0.0426003	+	0.241598i
$784$	4.54876e10	+	2.57973e11i	0.120401	+	0.682827i
$785$	−9.09711e10	+	3.31108e10i	−0.239566	+	0.0871948i
$786$	−3.37508e11	+	5.84581e11i	−0.884288	+	1.53163i
$787$	4.07006e11	−	2.34985e11i	1.06097	−	0.612549i	0.135267	−	0.990809i	$-0.456811\pi$
$787$	4.07006e11	−	2.34985e11i	1.06097	−	0.612549i	0.925699	+	0.378260i	$0.123477\pi$
$788$	1.29067e11	+	1.08300e11i	0.334742	+	0.280882i
$789$	1.68766e11	−	2.01127e11i	0.435489	−	0.518995i
$790$	1.59313e10	+	2.75939e10i	0.0409019	+	0.0708442i
$791$	−4.25053e11	−	2.45404e11i	−1.08577	−	0.626868i
$792$	−5.35556e10	−	1.47143e11i	−0.136114	−	0.373972i
$793$	−1.57287e11	+	2.77339e10i	−0.397741	+	0.0701324i
$794$	2.81068e11	+	4.95598e10i	0.707179	+	0.124695i
$795$	8.82876e10	+	3.21341e10i	0.221020	+	0.0804447i
$796$	−1.48282e11	+	1.24423e11i	−0.369347	+	0.309919i
$797$			5.97927e11i			1.48189i	0.671568	+	0.740943i	$0.265621\pi$
$797$			5.97927e11i			1.48189i	−0.671568	+	0.740943i	$0.734379\pi$
$798$	−4.75308e11	+	6.85885e11i	−1.17210	+	1.69137i
$799$	8.07338e10			0.198093
$800$	4.48519e10	+	5.34524e10i	0.109502	+	0.130499i
$801$	2.79806e11	−	7.68760e11i	0.679715	−	1.86750i
$802$	8.90931e10	−	5.05272e11i	0.215351	−	1.22131i
$803$	−1.00317e9	−	5.68925e9i	−0.00241275	−	0.0136834i
$804$	3.70531e11	−	1.34862e11i	0.886748	−	0.322750i
$805$	7.92795e10	−	1.37316e11i	0.188789	−	0.326993i
$806$	4.48814e11	−	2.59123e11i	1.06347	−	0.613996i
$807$	3.42371e11	+	2.87283e11i	0.807241	+	0.677355i
$808$	−1.83896e10	+	2.19158e10i	−0.0431446	+	0.0514177i
$809$	1.90186e11	+	3.29412e11i	0.444002	+	0.769035i	0.997982	−	0.0634955i	$-0.0202248\pi$
$809$	1.90186e11	+	3.29412e11i	0.444002	+	0.769035i	−0.553980	+	0.832530i	$0.686892\pi$
$810$	3.49633e10	+	2.01861e10i	0.0812218	+	0.0468934i
$811$	1.05781e11	+	2.90631e11i	0.244526	+	0.671830i	0.999864	+	0.0164942i	$0.00525050\pi$
$811$	1.05781e11	+	2.90631e11i	0.244526	+	0.671830i	−0.755338	+	0.655335i	$0.772527\pi$
$812$	−2.78614e11	+	4.91272e10i	−0.640884	+	0.113005i
$813$	4.08059e11	+	7.19518e10i	0.934030	+	0.164695i
$814$	2.68291e11	+	9.76498e10i	0.611094	+	0.222420i
$815$	−3.70289e10	+	3.10709e10i	−0.0839286	+	0.0704245i
$816$		−	2.53639e10i		−	0.0572078i
$817$	3.18963e10	−	1.21397e11i	0.0715900	−	0.272471i
$818$	−3.17271e11			−0.708626
$819$	−1.02956e12	−	1.22698e12i	−2.28832	−	2.72711i
$820$	6.67596e9	−	1.83420e10i	0.0147658	−	0.0405688i
$821$	1.16022e11	−	6.57995e11i	0.255369	−	1.44827i	−0.539753	−	0.841823i	$-0.681482\pi$
$821$	1.16022e11	−	6.57995e11i	0.255369	−	1.44827i	0.795123	−	0.606449i	$-0.207406\pi$
$822$	7.35437e10	+	4.17087e11i	0.161086	+	0.913564i
$823$	−2.67344e11	+	9.73053e10i	−0.582735	+	0.212098i	−0.616531	−	0.787330i	$-0.711463\pi$
$823$	−2.67344e11	+	9.73053e10i	−0.582735	+	0.212098i	0.0337959	+	0.999429i	$0.489240\pi$
$824$	4.99535e10	−	8.65220e10i	0.108357	−	0.187680i
$825$	−5.23917e11	+	3.02484e11i	−1.13096	+	0.652959i
$826$	−9.30197e11	−	7.80528e11i	−1.99827	−	1.67675i
$827$	3.20697e11	−	3.82192e11i	0.685604	−	0.817071i	−0.305213	−	0.952284i	$-0.598728\pi$
$827$	3.20697e11	−	3.82192e11i	0.685604	−	0.817071i	0.990816	+	0.135213i	$0.0431720\pi$
$828$	1.49118e11	+	2.58280e11i	0.317255	+	0.549501i
$829$	−3.96929e10	−	2.29167e10i	−0.0840418	−	0.0485215i	0.457390	−	0.889266i	$-0.348784\pi$
$829$	−3.96929e10	−	2.29167e10i	−0.0840418	−	0.0485215i	−0.541432	+	0.840745i	$0.682118\pi$
$830$	1.00508e10	+	2.76142e10i	0.0211781	+	0.0581863i
$831$	5.03169e11	−	8.87222e10i	1.05514	−	0.186049i
$832$	8.68710e10	+	1.53177e10i	0.181293	+	0.0319669i
$833$	−1.91668e11	−	6.97615e10i	−0.398079	−	0.144889i
$834$	3.80643e11	−	3.19397e11i	0.786780	−	0.660187i
$835$		−	7.00521e10i		−	0.144104i
$836$	2.20169e11	+	1.81838e10i	0.450745	+	0.0372271i
$837$	2.11907e11			0.431762
$838$	2.63021e11	+	3.13456e11i	0.533353	+	0.635625i
$839$	8.53348e10	−	2.34455e11i	0.172218	−	0.473165i	−0.823314	−	0.567585i	$-0.807878\pi$
$839$	8.53348e10	−	2.34455e11i	0.172218	−	0.473165i	0.995532	+	0.0944206i	$0.0300999\pi$
$840$	1.69548e10	−	9.61553e10i	0.0340545	−	0.193133i
$841$	4.78698e10	+	2.71483e11i	0.0956925	+	0.542699i
$842$	−2.57396e11	+	9.36843e10i	−0.512098	+	0.186388i
$843$	1.92618e11	−	3.33624e11i	0.381405	−	0.660613i
$844$	−6.96634e10	+	4.02202e10i	−0.137289	+	0.0792637i
$845$	8.70139e10	+	7.30134e10i	0.170672	+	0.143211i
$846$	−3.75749e11	+	4.47800e11i	−0.733527	+	0.874183i
$847$	−9.08652e10	−	1.57383e11i	−0.176548	−	0.305791i
$848$	−9.22186e10	−	5.32425e10i	−0.178334	−	0.102961i
$849$	5.30530e10	+	1.45762e11i	0.102112	+	0.280552i
$850$	−5.35064e10	+	9.43462e9i	−0.102501	+	0.0180738i
$851$	−5.35522e11	−	9.44270e10i	−1.02108	−	0.180044i
$852$	1.00047e11	+	3.64143e10i	0.189866	+	0.0691056i
$853$	2.28145e11	−	1.91437e11i	0.430939	−	0.361601i	−0.401367	−	0.915917i	$-0.631465\pi$
$853$	2.28145e11	−	1.91437e11i	0.430939	−	0.361601i	0.832306	+	0.554317i	$0.187020\pi$
$854$		−	2.00361e11i		−	0.376689i
$855$	1.03474e11	−	7.32061e10i	0.193628	−	0.136988i
$856$	3.05497e10			0.0569000
$857$	−1.51383e11	−	1.80411e11i	−0.280643	−	0.334457i	0.607247	−	0.794513i	$-0.292274\pi$
$857$	−1.51383e11	−	1.80411e11i	−0.280643	−	0.334457i	−0.887890	+	0.460056i	$0.847829\pi$
$858$	−2.61573e11	+	7.18666e11i	−0.482663	+	1.32611i
$859$	−1.36085e11	+	7.71776e11i	−0.249941	+	1.41749i	0.558791	+	0.829308i	$0.311265\pi$
$859$	−1.36085e11	+	7.71776e11i	−0.249941	+	1.41749i	−0.808732	+	0.588177i	$0.799846\pi$
$860$	2.55024e9	+	1.44631e10i	0.00466216	+	0.0264404i
$861$	6.80806e11	−	2.47793e11i	1.23883	−	0.450896i
$862$	1.85250e11	−	3.20863e11i	0.335529	−	0.581153i
$863$	−4.43213e11	+	2.55889e11i	−0.799042	+	0.461327i	−0.843136	−	0.537700i	$-0.819293\pi$
$863$	−4.43213e11	+	2.55889e11i	−0.799042	+	0.461327i	0.0440941	+	0.999027i	$0.485960\pi$
$864$	2.76304e10	+	2.31846e10i	0.0495829	+	0.0416050i
$865$	−1.29490e11	+	1.54320e11i	−0.231298	+	0.275650i
$866$	−3.12182e10	−	5.40716e10i	−0.0555056	−	0.0961385i
$867$	−7.15986e11	−	4.13375e11i	−1.26715	−	0.731590i
$868$	2.22362e11	+	6.10934e11i	0.391725	+	1.07626i
$869$	3.08337e11	−	5.43681e10i	0.540688	−	0.0953379i
$870$	7.63279e10	+	1.34587e10i	0.133231	+	0.0234923i
$871$	−1.00340e12	−	3.65206e11i	−1.74341	−	0.634550i
$872$	8.95171e10	−	7.51137e10i	0.154825	−	0.129913i
$873$			1.22367e12i			2.10672i
$874$	−4.18980e11	+	3.87101e10i	−0.718037	+	0.0663405i
$875$	−4.26187e11			−0.727056
$876$	4.35520e9	+	5.19033e9i	0.00739591	+	0.00881411i
$877$	−4.92012e10	+	1.35179e11i	−0.0831720	+	0.228513i	−0.974307	−	0.225226i	$-0.927688\pi$
$877$	−4.92012e10	+	1.35179e11i	−0.0831720	+	0.228513i	0.891135	+	0.453739i	$0.149910\pi$
$878$	1.03093e11	−	5.84667e11i	0.173480	−	0.983854i
$879$	−2.15536e11	−	1.22236e12i	−0.361047	−	2.04760i
$880$	−2.42898e10	+	8.84077e9i	−0.0405036	+	0.0147421i
$881$	3.32961e11	−	5.76706e11i	0.552701	−	0.957306i	−0.445378	−	0.895343i	$-0.646931\pi$
$881$	3.32961e11	−	5.76706e11i	0.552701	−	0.957306i	0.998078	−	0.0619630i	$-0.0197361\pi$
$882$	1.27900e12	−	7.38429e11i	2.11346	−	1.22021i
$883$	2.29020e11	+	1.92170e11i	0.376730	+	0.316114i	0.811417	−	0.584468i	$-0.198697\pi$
$883$	2.29020e11	+	1.92170e11i	0.376730	+	0.316114i	−0.434687	+	0.900581i	$0.643141\pi$
$884$	−4.41501e10	+	5.26160e10i	−0.0722973	+	0.0861606i
$885$	1.66330e11	+	2.88092e11i	0.271143	+	0.469633i
$886$	−1.49449e11	−	8.62846e10i	−0.242526	−	0.140023i
$887$	3.13674e11	+	8.61812e11i	0.506739	+	1.39225i	0.884582	+	0.466384i	$0.154443\pi$
$887$	3.13674e11	+	8.61812e11i	0.506739	+	1.39225i	−0.377844	+	0.925869i	$0.623334\pi$
$888$	−3.29768e11	+	5.81470e10i	−0.530343	+	0.0935137i
$889$	−6.51516e11	−	1.14880e11i	−1.04308	−	0.183923i
$890$	−1.26904e11	−	4.61894e10i	−0.202263	−	0.0736177i
$891$	3.03899e11	−	2.55001e11i	0.482190	−	0.404605i
$892$			6.55073e9i			0.0103474i
$893$	−3.52175e11	−	7.45751e11i	−0.553799	−	1.17270i
$894$	1.10835e12			1.73510
$895$	9.32041e10	+	1.11076e11i	0.145259	+	0.173113i
$896$	−3.78484e10	+	1.03988e11i	−0.0587240	+	0.161343i
$897$	2.52940e11	−	1.43450e12i	0.390704	−	2.21579i
$898$	−3.35732e10	−	1.90403e11i	−0.0516283	−	0.292799i
$899$	−4.84958e11	+	1.76510e11i	−0.742447	+	0.270229i
$900$	1.96698e11	−	3.40690e11i	0.299798	−	0.519265i
$901$	7.18058e10	−	4.14571e10i	0.108958	−	0.0629071i
$902$	−1.46929e11	−	1.23288e11i	−0.221964	−	0.186250i
$903$	−3.50392e11	+	4.17581e11i	−0.526991	+	0.628043i
$904$	−7.61967e10	−	1.31976e11i	−0.114094	−	0.197616i
$905$	−4.01855e10	−	2.32011e10i	−0.0599066	−	0.0345871i
$906$	1.64782e11	+	4.52734e11i	0.244566	+	0.671940i
$907$	2.62383e11	−	4.62653e10i	0.387710	−	0.0683638i	0.0236045	−	0.999721i	$-0.492486\pi$
$907$	2.62383e11	−	4.62653e10i	0.387710	−	0.0683638i	0.364106	+	0.931358i	$0.381375\pi$
$908$	−3.45623e11	−	6.09427e10i	−0.508464	−	0.0896558i
$909$	1.51567e11	+	5.51660e10i	0.221998	+	0.0808008i
$910$	−2.02546e11	+	1.69956e11i	−0.295364	+	0.247840i
$911$		−	5.66183e11i		−	0.822022i	−0.911630	−	0.411011i	$-0.865176\pi$
$911$		−	5.66183e11i		−	0.822022i	0.911630	−	0.411011i	$-0.134824\pi$
$912$	−2.34290e11	+	1.10642e11i	−0.338668	+	0.159933i
$913$	2.88762e11			0.415582
$914$	−1.90206e11	−	2.26679e11i	−0.272546	−	0.324807i
$915$	−1.87735e10	+	5.15798e10i	−0.0267831	+	0.0735860i
$916$	7.10332e10	−	4.02850e11i	0.100897	−	0.572217i
$917$	3.98203e11	+	2.25832e12i	0.563154	+	3.19381i
$918$	−2.63912e10	+	9.60562e9i	−0.0371611	+	0.0135255i
$919$	3.48971e11	−	6.04435e11i	0.489246	−	0.847398i	−0.510678	−	0.859772i	$-0.670605\pi$
$919$	3.48971e11	−	6.04435e11i	0.489246	−	0.847398i	0.999923	+	0.0123739i	$0.00393883\pi$
$920$	4.26359e10	−	2.46158e10i	0.0595147	−	0.0343608i
$921$	6.95835e11	+	5.83875e11i	0.967092	+	0.811487i
$922$	−5.03472e11	+	6.00015e11i	−0.696710	+	0.830306i
$923$	−1.44158e11	−	2.49689e11i	−0.198624	−	0.344027i
$924$	−8.30893e11	−	4.79716e11i	−1.13987	−	0.658107i
$925$	2.45328e11	+	6.74033e11i	0.335104	+	0.920692i
$926$	2.90958e11	−	5.13037e10i	0.395718	−	0.0697758i
$927$	−5.54706e11	−	9.78096e10i	−0.751179	−	0.132453i
$928$	−8.25452e10	−	3.00440e10i	−0.111301	−	0.0405103i
$929$	2.71110e11	−	2.27488e11i	0.363984	−	0.305419i	−0.442392	−	0.896822i	$-0.645870\pi$
$929$	2.71110e11	−	2.27488e11i	0.363984	−	0.305419i	0.806376	+	0.591403i	$0.201426\pi$
$930$		−	1.78110e11i		−	0.238099i
$931$	1.91692e11	+	2.07478e12i	0.255155	+	2.76168i
$932$	−1.26671e11			−0.167886
$933$	−3.47261e11	−	4.13849e11i	−0.458278	−	0.546154i
$934$	−2.60980e11	+	7.17037e11i	−0.342941	+	0.942223i
$935$	3.49502e9	−	1.98212e10i	0.00457302	−	0.0259349i
$936$	−8.63592e10	−	4.89768e11i	−0.112514	−	0.638097i
$937$	−1.05250e12	+	3.83079e11i	−1.36541	+	0.496970i	−0.917724	−	0.397219i	$-0.869975\pi$
$937$	−1.05250e12	+	3.83079e11i	−1.36541	+	0.496970i	−0.447690	+	0.894189i	$0.647753\pi$
$938$	6.69776e11	−	1.16009e12i	0.865203	−	1.49858i
$939$	1.15630e12	−	6.67590e11i	1.48733	−	0.858712i
$940$	7.39212e10	+	6.20273e10i	0.0946799	+	0.0794459i
$941$	1.93865e11	−	2.31039e11i	0.247252	−	0.294664i	−0.628117	−	0.778119i	$-0.716174\pi$
$941$	1.93865e11	−	2.31039e11i	0.247252	−	0.294664i	0.875369	+	0.483455i	$0.160618\pi$
$942$	−5.57850e11	−	9.66224e11i	−0.708457	−	1.22708i
$943$	3.16367e11	+	1.82655e11i	0.400078	+	0.230985i
$944$	−1.28952e11	−	3.54292e11i	−0.162382	−	0.446142i
$945$	−1.06471e11	+	1.87737e10i	−0.133507	+	0.0235409i
$946$	1.42120e11	+	2.50596e10i	0.177456	+	0.0312903i
$947$	−6.92463e11	−	2.52036e11i	−0.860988	−	0.313374i	−0.126476	−	0.991970i	$-0.540367\pi$
$947$	−6.92463e11	−	2.52036e11i	−0.860988	−	0.313374i	−0.734512	+	0.678596i	$0.762589\pi$
$948$	−2.81297e11	+	2.36036e11i	−0.348283	+	0.292244i
$949$		−	1.83480e10i		−	0.0226216i
$950$	3.20553e11	+	4.53091e11i	0.393555	+	0.556277i
$951$	1.02502e12			1.25317
$952$	−5.53865e10	−	6.60071e10i	−0.0674305	−	0.0803605i
$953$	−3.15046e10	+	8.65583e10i	−0.0381947	+	0.104939i	−0.957324	−	0.289017i	$-0.906672\pi$
$953$	−3.15046e10	+	8.65583e10i	−0.0381947	+	0.104939i	0.919129	+	0.393956i	$0.128894\pi$
$954$	−1.04249e11	+	5.91228e11i	−0.125858	+	0.713775i
$955$	1.67469e10	+	9.49765e10i	0.0201336	+	0.114183i
$956$	−4.26304e11	+	1.55162e11i	−0.510373	+	0.185761i
$957$	3.80798e11	−	6.59561e11i	0.453990	−	0.786334i
$958$	−8.08794e11	+	4.66957e11i	−0.960231	+	0.554390i
$959$	1.10217e12	+	9.24833e11i	1.30309	+	1.09342i
$960$	1.94869e10	−	2.32236e10i	0.0229434	−	0.0273429i
$961$	1.66542e11	+	2.88459e11i	0.195268	+	0.338214i
$962$	7.85300e11	+	4.53393e11i	0.916928	+	0.529389i
$963$	−5.89080e10	−	1.61848e11i	−0.0684966	−	0.188193i
$964$	4.60547e11	−	8.12069e10i	0.533293	−	0.0940340i
$965$	−1.04290e11	−	1.83891e10i	−0.120263	−	0.0212057i
$966$	1.71714e12	+	6.24989e11i	1.97196	+	0.717734i
$967$	3.27471e11	−	2.74781e11i	0.374513	−	0.314254i	−0.436031	−	0.899932i	$-0.643616\pi$
$967$	3.27471e11	−	2.74781e11i	0.374513	−	0.314254i	0.810544	+	0.585678i	$0.199172\pi$
$968$		−	5.64263e10i		−	0.0642658i
$969$	1.66059e10	−	2.01064e11i	0.0188351	−	0.228055i
$970$	2.01999e11			0.228172
$971$	−8.29778e11	−	9.88891e11i	−0.933437	−	1.11243i	−0.993454	−	0.114229i	$-0.963560\pi$
$971$	−8.29778e11	−	9.88891e11i	−0.933437	−	1.11243i	0.0600176	−	0.998197i	$-0.480884\pi$
$972$	−2.15025e11	+	5.90776e11i	−0.240893	+	0.661847i
$973$	2.93126e11	−	1.66240e12i	0.327042	−	1.85475i
$974$	−2.00845e11	−	1.13905e12i	−0.223164	−	1.26563i
$975$	−1.80552e12	+	6.57156e11i	−1.99795	+	0.727194i
$976$	3.11056e10	−	5.38764e10i	0.0342798	−	0.0593744i
$977$	−2.69855e11	+	1.55801e11i	−0.296177	+	0.170998i	−0.640724	−	0.767771i	$-0.721366\pi$
$977$	−2.69855e11	+	1.55801e11i	−0.296177	+	0.170998i	0.344547	+	0.938769i	$0.388032\pi$
$978$	−4.26747e11	−	3.58083e11i	−0.466460	−	0.391407i
$979$	−8.53003e11	+	1.01657e12i	−0.928581	+	1.10664i
$980$	−1.21897e11	−	2.11132e11i	−0.132157	−	0.228902i
$981$	−5.70555e11	−	3.29410e11i	−0.616058	−	0.355681i
$982$	−1.38505e11	−	3.80540e11i	−0.148943	−	0.409217i
$983$	−8.52902e11	+	1.50390e11i	−0.913450	+	0.161066i	−0.610570	−	0.791963i	$-0.709059\pi$
$983$	−8.52902e11	+	1.50390e11i	−0.913450	+	0.161066i	−0.302881	+	0.953028i	$0.597948\pi$
$984$	2.21535e11	+	3.90626e10i	0.236299	+	0.0416659i
$985$	−1.47349e11	−	5.36307e10i	−0.156532	−	0.0569729i
$986$	5.23963e10	−	4.39657e10i	0.0554361	−	0.0465164i
$987$			3.58171e12i			3.77418i
$988$	6.78612e11	+	1.78301e11i	0.712187	+	0.187122i
$989$	−2.74859e11			−0.287292
$990$	9.36745e10	+	1.11637e11i	0.0975171	+	0.116216i
$991$	−2.29159e11	+	6.29609e11i	−0.237598	+	0.652794i	0.762386	+	0.647122i	$0.224028\pi$
$991$	−2.29159e11	+	6.29609e11i	−0.237598	+	0.652794i	−0.999984	+	0.00567205i	$0.998195\pi$
$992$	−3.50536e10	+	1.98799e11i	−0.0361981	+	0.205290i
$993$	1.17622e11	+	6.67066e11i	0.120974	+	0.686075i
$994$	3.39881e11	−	1.23707e11i	0.348162	−	0.126721i
$995$	9.00749e10	−	1.56014e11i	0.0918992	−	0.159174i
$996$	−2.93297e11	+	1.69335e11i	−0.298037	+	0.172072i
$997$	8.66351e11	+	7.26955e11i	0.876826	+	0.735744i	0.965524	−	0.260314i	$-0.0838261\pi$
$997$	8.66351e11	+	7.26955e11i	0.876826	+	0.735744i	−0.0886979	+	0.996059i	$0.528271\pi$
$998$	1.35488e11	−	1.61469e11i	0.136578	−	0.162767i
$999$	1.85389e11	+	3.21104e11i	0.186133	+	0.322391i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.9.f.a.13.1	yes	84
19.3	odd	18	inner	38.9.f.a.3.1	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.9.f.a.3.1	✓	84	19.3	odd	18	inner
38.9.f.a.13.1	yes	84	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	38.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.27231 - 8.66680i) q^{2} +(-41.5037 + 114.031i) q^{3} +(-22.2270 + 126.055i) q^{4} +(-20.6862 - 117.317i) q^{5} +(1290.11 - 469.561i) q^{6} +(2332.01 - 4039.17i) q^{7} +(1254.14 - 724.077i) q^{8} +(-6254.38 - 5248.05i) q^{9} +O(q^{10})\)	\(q+(-7.27231 - 8.66680i) q^{2} +(-41.5037 + 114.031i) q^{3} +(-22.2270 + 126.055i) q^{4} +(-20.6862 - 117.317i) q^{5} +(1290.11 - 469.561i) q^{6} +(2332.01 - 4039.17i) q^{7} +(1254.14 - 724.077i) q^{8} +(-6254.38 - 5248.05i) q^{9} +(-866.329 + 1032.45i) q^{10} +(6621.83 + 11469.3i) q^{11} +(-13451.7 - 7766.32i) q^{12} +(14386.2 + 39525.7i) q^{13} +(-51965.8 + 9162.97i) q^{14} +(14236.3 + 2510.24i) q^{15} +(-15395.9 - 5603.66i) q^{16} +(9772.70 - 8200.27i) q^{17} +92370.9i q^{18} +(-118377. - 54501.0i) q^{19} +15248.3 q^{20} +(363801. + 433561. i) q^{21} +(51246.6 - 140799. i) q^{22} +(-49555.2 + 281042. i) q^{23} +(30515.5 + 173062. i) q^{24} +(353732. - 128748. i) q^{25} +(237940. - 412125. i) q^{26} +(168515. - 97292.2i) q^{27} +(457325. + 383741. i) q^{28} +(-304613. + 363024. i) q^{29} +(-81775.0 - 141639. i) q^{30} +(943123. + 544512. i) q^{31} +(63398.2 + 174185. i) q^{32} +(-1.58269e6 + 279070. i) q^{33} +(-142140. - 25063.2i) q^{34} +(-522104. - 190030. i) q^{35} +(800561. - 671750. i) q^{36} +1.90549e6i q^{37} +(388528. + 1.42230e6i) q^{38} -5.10421e6 q^{39} +(-110890. - 132154. i) q^{40} +(437817. - 1.20289e6i) q^{41} +(1.11191e6 - 6.30598e6i) q^{42} +(167248. + 948510. i) q^{43} +(-1.59296e6 + 579789. i) q^{44} +(-486307. + 842309. i) q^{45} +(2.79611e6 - 1.61434e6i) q^{46} +(4.84784e6 + 4.06782e6i) q^{47} +(1.27798e6 - 1.52303e6i) q^{48} +(-7.99417e6 - 1.38463e7i) q^{49} +(-3.68828e6 - 2.12943e6i) q^{50} +(529478. + 1.45473e6i) q^{51} +(-5.30218e6 + 934918. i) q^{52} +(6.40058e6 + 1.12860e6i) q^{53} +(-2.06871e6 - 752948. i) q^{54} +(1.20857e6 - 1.01411e6i) q^{55} -6.75423e6i q^{56} +(1.11279e7 - 1.12366e7i) q^{57} +5.36149e6 q^{58} +(1.47919e7 + 1.76282e7i) q^{59} +(-632860. + 1.73877e6i) q^{60} +(-659353. + 3.73938e6i) q^{61} +(-2.13950e6 - 1.21337e7i) q^{62} +(-3.57830e7 + 1.30240e7i) q^{63} +(1.04858e6 - 1.81619e6i) q^{64} +(4.33945e6 - 2.50538e6i) q^{65} +(1.39284e7 + 1.16873e7i) q^{66} +(-1.63178e7 + 1.94468e7i) q^{67} +(816471. + 1.41417e6i) q^{68} +(-2.99906e7 - 1.73151e7i) q^{69} +(2.14995e6 + 5.90694e6i) q^{70} +(-6.75035e6 + 1.19027e6i) q^{71} +(-1.16439e7 - 2.05313e6i) q^{72} +(-409903. - 149193. i) q^{73} +(1.65145e7 - 1.38573e7i) q^{74} +4.56798e7i q^{75} +(9.50131e6 - 1.37107e7i) q^{76} +6.17688e7 q^{77} +(3.71194e7 + 4.42372e7i) q^{78} +(8.08570e6 - 2.22153e7i) q^{79} +(-338923. + 1.92213e6i) q^{80} +(-5.20160e6 - 2.94997e7i) q^{81} +(-1.36092e7 + 4.95334e6i) q^{82} +(1.09019e7 - 1.88826e7i) q^{83} +(-6.27389e7 + 3.62223e7i) q^{84} +(-1.16419e6 - 976874. i) q^{85} +(7.00427e6 - 8.34736e6i) q^{86} +(-2.87532e7 - 4.98020e7i) q^{87} +(1.66094e7 + 9.58944e6i) q^{88} +(3.42710e7 + 9.41587e7i) q^{89} +(1.08367e7 - 1.91080e6i) q^{90} +(1.93199e8 + 3.40663e7i) q^{91} +(-3.43253e7 - 1.24934e7i) q^{92} +(-1.01234e8 + 8.49455e7i) q^{93} -7.15978e7i q^{94} +(-3.94513e6 + 1.50151e7i) q^{95} -2.24937e7 q^{96} +(-9.63387e7 - 1.14812e8i) q^{97} +(-6.18671e7 + 1.69979e8i) q^{98} +(1.87762e7 - 1.06485e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 168 q^{3} - 2688 q^{6} - 6570 q^{7} - 2856 q^{9}+O(q^{10}) \) 84 * q - 168 * q^3 - 2688 * q^6 - 6570 * q^7 - 2856 * q^9	\( 84 q - 168 q^{3} - 2688 q^{6} - 6570 q^{7} - 2856 q^{9} - 20970 q^{11} + 62208 q^{12} - 101310 q^{13} - 142848 q^{14} + 331518 q^{15} + 29178 q^{17} - 319212 q^{19} - 428544 q^{20} - 186138 q^{21} + 1238016 q^{22} + 1989360 q^{23} + 344064 q^{24} - 272916 q^{25} - 695808 q^{26} - 6975648 q^{27} - 489984 q^{28} + 1676430 q^{29} - 3498768 q^{31} + 6273750 q^{33} + 2740224 q^{34} + 10942362 q^{35} + 365568 q^{36} + 5830272 q^{38} - 23638704 q^{39} + 430488 q^{41} + 4230144 q^{42} - 20999118 q^{43} + 700416 q^{44} + 49897728 q^{45} + 12003840 q^{46} - 22431150 q^{47} - 5505024 q^{48} - 59138004 q^{49} - 24993792 q^{50} + 6061860 q^{51} - 2857728 q^{52} + 69029982 q^{53} + 63262080 q^{54} + 20438670 q^{55} - 50408076 q^{57} - 31266816 q^{58} - 85956678 q^{59} - 9106176 q^{60} + 29908896 q^{61} - 39755520 q^{62} - 29288274 q^{63} + 88080384 q^{64} + 199314810 q^{65} + 117652224 q^{66} + 64371642 q^{67} + 25820928 q^{68} - 186304482 q^{69} - 187792896 q^{70} - 168095268 q^{71} + 23396352 q^{72} + 104437176 q^{73} + 33624576 q^{74} + 6617088 q^{76} - 277281288 q^{77} + 30777600 q^{78} + 199146114 q^{79} + 245855040 q^{81} - 69199872 q^{82} - 14372262 q^{83} - 348399360 q^{84} - 386680068 q^{85} - 155904768 q^{86} + 36917496 q^{87} + 292036248 q^{89} + 694869504 q^{90} + 285753588 q^{91} + 95143680 q^{92} + 529006800 q^{93} - 166014666 q^{95} + 251818254 q^{97} - 595464192 q^{98} - 1180902678 q^{99}+O(q^{100}) \) 84 * q - 168 * q^3 - 2688 * q^6 - 6570 * q^7 - 2856 * q^9 - 20970 * q^11 + 62208 * q^12 - 101310 * q^13 - 142848 * q^14 + 331518 * q^15 + 29178 * q^17 - 319212 * q^19 - 428544 * q^20 - 186138 * q^21 + 1238016 * q^22 + 1989360 * q^23 + 344064 * q^24 - 272916 * q^25 - 695808 * q^26 - 6975648 * q^27 - 489984 * q^28 + 1676430 * q^29 - 3498768 * q^31 + 6273750 * q^33 + 2740224 * q^34 + 10942362 * q^35 + 365568 * q^36 + 5830272 * q^38 - 23638704 * q^39 + 430488 * q^41 + 4230144 * q^42 - 20999118 * q^43 + 700416 * q^44 + 49897728 * q^45 + 12003840 * q^46 - 22431150 * q^47 - 5505024 * q^48 - 59138004 * q^49 - 24993792 * q^50 + 6061860 * q^51 - 2857728 * q^52 + 69029982 * q^53 + 63262080 * q^54 + 20438670 * q^55 - 50408076 * q^57 - 31266816 * q^58 - 85956678 * q^59 - 9106176 * q^60 + 29908896 * q^61 - 39755520 * q^62 - 29288274 * q^63 + 88080384 * q^64 + 199314810 * q^65 + 117652224 * q^66 + 64371642 * q^67 + 25820928 * q^68 - 186304482 * q^69 - 187792896 * q^70 - 168095268 * q^71 + 23396352 * q^72 + 104437176 * q^73 + 33624576 * q^74 + 6617088 * q^76 - 277281288 * q^77 + 30777600 * q^78 + 199146114 * q^79 + 245855040 * q^81 - 69199872 * q^82 - 14372262 * q^83 - 348399360 * q^84 - 386680068 * q^85 - 155904768 * q^86 + 36917496 * q^87 + 292036248 * q^89 + 694869504 * q^90 + 285753588 * q^91 + 95143680 * q^92 + 529006800 * q^93 - 166014666 * q^95 + 251818254 * q^97 - 595464192 * q^98 - 1180902678 * q^99

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