LMFDB - Embedded newform 75.9.k.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,9,Mod(13,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 19]))

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

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

chi := DirichletCharacter("75.13");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	75.k (of order $20$, degree $8$, 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:	$30.5533957546$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$40$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			13.2
Character	$\chi$	$=$	75.13
Dual form			75.9.k.a.52.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-29.6660 + 4.69863i) q^{2} +(21.2310 - 41.6683i) q^{3} +(614.522 - 199.670i) q^{4} +(-583.809 - 223.142i) q^{5} +(-434.056 + 1335.89i) q^{6} +(2556.62 - 2556.62i) q^{7} +(-10441.1 + 5320.03i) q^{8} +(-1285.49 - 1769.32i) q^{9} +O(q^{10})$	\(q+(-29.6660 + 4.69863i) q^{2} +(21.2310 - 41.6683i) q^{3} +(614.522 - 199.670i) q^{4} +(-583.809 - 223.142i) q^{5} +(-434.056 + 1335.89i) q^{6} +(2556.62 - 2556.62i) q^{7} +(-10441.1 + 5320.03i) q^{8} +(-1285.49 - 1769.32i) q^{9} +(18367.7 + 3876.61i) q^{10} +(16161.9 + 11742.3i) q^{11} +(4727.03 - 29845.3i) q^{12} +(35922.6 + 5689.59i) q^{13} +(-63832.1 + 87857.4i) q^{14} +(-21692.8 + 19588.8i) q^{15} +(150927. - 109655. i) q^{16} +(41691.5 + 81824.1i) q^{17} +(46448.6 + 46448.6i) q^{18} +(-174610. - 56734.3i) q^{19} +(-403318. - 20556.2i) q^{20} +(-52250.3 - 160810. i) q^{21} +(-534631. - 272408. i) q^{22} +(12329.3 + 77843.9i) q^{23} +548014. i q^{24} +(291041. + 260544. i) q^{25} -1.09241e6 q^{26} +(-101017. + 15999.5i) q^{27} +(1.06062e6 - 2.08158e6i) q^{28} +(-36424.0 + 11834.9i) q^{29} +(551497. - 683046. i) q^{30} +(-418629. + 1.28841e6i) q^{31} +(-1.84093e6 + 1.84093e6i) q^{32} +(832414. - 424136. i) q^{33} +(-1.62128e6 - 2.23150e6i) q^{34} +(-2.06307e6 + 922090. i) q^{35} +(-1.14324e6 - 830613. i) q^{36} +(-143464. + 905794. i) q^{37} +(5.44656e6 + 862650. i) q^{38} +(999750. - 1.37604e6i) q^{39} +(7.28275e6 - 776026. i) q^{40} +(2.02985e6 - 1.47477e6i) q^{41} +(2.30564e6 + 4.52507e6i) q^{42} +(3.91263e6 + 3.91263e6i) q^{43} +(1.22764e7 + 3.98885e6i) q^{44} +(355669. + 1.31979e6i) q^{45} +(-731519. - 2.25138e6i) q^{46} +(3.07900e6 + 1.56883e6i) q^{47} +(-1.36479e6 - 8.61697e6i) q^{48} -7.30785e6i q^{49} +(-9.85820e6 - 6.36180e6i) q^{50} +4.29462e6 q^{51} +(2.32113e7 - 3.67631e6i) q^{52} +(-1.55334e6 + 3.04859e6i) q^{53} +(2.92158e6 - 949280. i) q^{54} +(-6.81525e6 - 1.04616e7i) q^{55} +(-1.30928e7 + 4.02954e7i) q^{56} +(-6.07118e6 + 6.07118e6i) q^{57} +(1.02495e6 - 522236. i) q^{58} +(-5.19118e6 - 7.14505e6i) q^{59} +(-9.41941e6 + 1.63691e7i) q^{60} +(8.21837e6 + 5.97099e6i) q^{61} +(6.36529e6 - 4.01889e7i) q^{62} +(-7.80999e6 - 1.23698e6i) q^{63} +(1.78913e7 - 2.46253e7i) q^{64} +(-1.97024e7 - 1.13375e7i) q^{65} +(-2.27015e7 + 1.64936e7i) q^{66} +(4.87671e6 + 9.57107e6i) q^{67} +(4.19582e7 + 4.19582e7i) q^{68} +(3.50538e6 + 1.13897e6i) q^{69} +(5.68704e7 - 3.70483e7i) q^{70} +(730369. + 2.24784e6i) q^{71} +(2.28348e7 + 1.16349e7i) q^{72} +(3.37520e6 + 2.13102e7i) q^{73} -2.75453e7i q^{74} +(1.70355e7 - 6.59553e6i) q^{75} -1.18630e8 q^{76} +(7.13405e7 - 1.12992e7i) q^{77} +(-2.31931e7 + 4.55190e7i) q^{78} +(4.55224e7 - 1.47911e7i) q^{79} +(-1.12581e8 + 3.03395e7i) q^{80} +(-1.47802e6 + 4.54887e6i) q^{81} +(-5.32881e7 + 5.32881e7i) q^{82} +(4.94404e7 - 2.51911e7i) q^{83} +(-6.42179e7 - 8.83884e7i) q^{84} +(-6.08148e6 - 5.70727e7i) q^{85} +(-1.34456e8 - 9.76879e7i) q^{86} +(-280181. + 1.76899e6i) q^{87} +(-2.31218e8 - 3.66213e7i) q^{88} +(-5.15493e7 + 7.09516e7i) q^{89} +(-1.67525e7 - 3.74817e7i) q^{90} +(1.06387e8 - 7.72945e7i) q^{91} +(2.31197e7 + 4.53750e7i) q^{92} +(4.47978e7 + 4.47978e7i) q^{93} +(-9.87127e7 - 3.20737e7i) q^{94} +(8.92793e7 + 7.20848e7i) q^{95} +(3.76234e7 + 1.15793e8i) q^{96} +(1.06901e8 + 5.44689e7i) q^{97} +(3.43369e7 + 2.16794e8i) q^{98} -4.36901e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 444 q^{5} - 4540 q^{7} - 17460 q^{8}+O(q^{10}) $ 320 * q + 444 * q^5 - 4540 * q^7 - 17460 * q^8	\( 320 q + 444 q^{5} - 4540 q^{7} - 17460 q^{8} + 25496 q^{10} - 22680 q^{12} - 133420 q^{13} + 59616 q^{15} + 1310720 q^{16} + 168000 q^{17} - 718900 q^{19} - 641844 q^{20} + 2257100 q^{22} + 1089120 q^{23} - 1459756 q^{25} + 1827840 q^{26} + 3260740 q^{28} + 3913800 q^{29} + 3585384 q^{30} - 641460 q^{32} - 1458000 q^{33} - 4121600 q^{34} + 853140 q^{35} - 22394880 q^{36} - 14553460 q^{37} + 17491260 q^{38} + 3203652 q^{40} + 8749440 q^{41} + 9643860 q^{42} - 23946520 q^{43} + 4277700 q^{44} - 2204496 q^{45} + 26491200 q^{47} - 3661200 q^{48} - 47100924 q^{50} - 169691020 q^{52} - 97028940 q^{53} + 27431764 q^{55} - 4714200 q^{57} + 179119320 q^{58} + 95587200 q^{59} + 38705364 q^{60} + 36738240 q^{61} - 296094660 q^{62} - 9928980 q^{63} - 59695100 q^{64} + 24018972 q^{65} - 88558160 q^{67} + 197811840 q^{68} + 220501420 q^{70} + 38185020 q^{72} + 110964400 q^{73} + 51345576 q^{75} - 97175880 q^{77} - 131709240 q^{78} - 138506200 q^{79} - 339741204 q^{80} + 382637520 q^{81} + 217169400 q^{82} + 862340400 q^{83} + 743029200 q^{84} + 619431268 q^{85} - 335756340 q^{87} - 1380992420 q^{88} - 1141686000 q^{89} - 265834224 q^{90} - 407198400 q^{92} + 402028920 q^{93} + 290042200 q^{94} + 1436174256 q^{95} - 165325860 q^{96} + 1057772920 q^{97} + 1077594720 q^{98}+O(q^{100}) \) 320 * q + 444 * q^5 - 4540 * q^7 - 17460 * q^8 + 25496 * q^10 - 22680 * q^12 - 133420 * q^13 + 59616 * q^15 + 1310720 * q^16 + 168000 * q^17 - 718900 * q^19 - 641844 * q^20 + 2257100 * q^22 + 1089120 * q^23 - 1459756 * q^25 + 1827840 * q^26 + 3260740 * q^28 + 3913800 * q^29 + 3585384 * q^30 - 641460 * q^32 - 1458000 * q^33 - 4121600 * q^34 + 853140 * q^35 - 22394880 * q^36 - 14553460 * q^37 + 17491260 * q^38 + 3203652 * q^40 + 8749440 * q^41 + 9643860 * q^42 - 23946520 * q^43 + 4277700 * q^44 - 2204496 * q^45 + 26491200 * q^47 - 3661200 * q^48 - 47100924 * q^50 - 169691020 * q^52 - 97028940 * q^53 + 27431764 * q^55 - 4714200 * q^57 + 179119320 * q^58 + 95587200 * q^59 + 38705364 * q^60 + 36738240 * q^61 - 296094660 * q^62 - 9928980 * q^63 - 59695100 * q^64 + 24018972 * q^65 - 88558160 * q^67 + 197811840 * q^68 + 220501420 * q^70 + 38185020 * q^72 + 110964400 * q^73 + 51345576 * q^75 - 97175880 * q^77 - 131709240 * q^78 - 138506200 * q^79 - 339741204 * q^80 + 382637520 * q^81 + 217169400 * q^82 + 862340400 * q^83 + 743029200 * q^84 + 619431268 * q^85 - 335756340 * q^87 - 1380992420 * q^88 - 1141686000 * q^89 - 265834224 * q^90 - 407198400 * q^92 + 402028920 * q^93 + 290042200 * q^94 + 1436174256 * q^95 - 165325860 * q^96 + 1057772920 * q^97 + 1077594720 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$

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 $

$2$	−29.6660	+	4.69863i	−1.85412	+	0.293664i	−0.981025	−	0.193880i	$-0.937893\pi$
$2$	−29.6660	+	4.69863i	−1.85412	+	0.293664i	−0.873098	+	0.487544i	$0.837893\pi$
$3$	21.2310	−	41.6683i	0.262112	−	0.514423i
$3$	21.2310	−	41.6683i	0.262112	−	0.514423i
$4$	614.522	−	199.670i	2.40048	−	0.779963i
$5$	−583.809	−	223.142i	−0.934094	−	0.357027i
$5$	−583.809	−	223.142i	−0.934094	−	0.357027i
$6$	−434.056	+	1335.89i	−0.334920	+	1.03078i
$7$	2556.62	−	2556.62i	1.06482	−	1.06482i	0.0670677	−	0.997748i	$-0.478636\pi$
$7$	2556.62	−	2556.62i	1.06482	−	1.06482i	0.997748	−	0.0670677i	$-0.0213643\pi$
$8$	−10441.1	+	5320.03i	−2.54911	+	1.29883i
$9$	−1285.49	−	1769.32i	−0.195928	−	0.269672i
$10$	18367.7	+	3876.61i	1.83677	+	0.387661i
$11$	16161.9	+	11742.3i	1.10388	+	0.802014i	0.981689	−	0.190492i	$-0.0610085\pi$
$11$	16161.9	+	11742.3i	1.10388	+	0.802014i	0.122189	+	0.992507i	$0.461008\pi$
$12$	4727.03	−	29845.3i	0.227962	−	1.43930i
$13$	35922.6	+	5689.59i	1.25775	+	0.199208i	0.749502	−	0.662002i	$-0.230293\pi$
$13$	35922.6	+	5689.59i	1.25775	+	0.199208i	0.508249	+	0.861210i	$0.330293\pi$
$14$	−63832.1	+	87857.4i	−1.66160	+	2.28700i
$15$	−21692.8	+	19588.8i	−0.428500	+	0.386939i
$16$	150927.	−	109655.i	2.30297	−	1.67320i
$17$	41691.5	+	81824.1i	0.499173	+	0.979683i	0.993864	+	0.110613i	$0.0352815\pi$
$17$	41691.5	+	81824.1i	0.499173	+	0.979683i	−0.494690	+	0.869069i	$0.664718\pi$
$18$	46448.6	+	46448.6i	0.442469	+	0.442469i
$19$	−174610.	−	56734.3i	−1.33985	−	0.435343i	−0.450582	−	0.892735i	$-0.648784\pi$
$19$	−174610.	−	56734.3i	−1.33985	−	0.435343i	−0.889265	+	0.457392i	$0.848784\pi$
$20$	−403318.	−	20556.2i	−2.52074	−	0.128476i
$21$	−52250.3	−	160810.i	−0.268665	−	0.826866i
$22$	−534631.	−	272408.i	−2.28225	−	1.16286i
$23$	12329.3	+	77843.9i	0.0440581	+	0.278172i	0.999875	−	0.0157897i	$-0.00502622\pi$
$23$	12329.3	+	77843.9i	0.0440581	+	0.278172i	−0.955817	+	0.293962i	$0.905026\pi$
$24$			548014.i			1.65176i
$25$	291041.	+	260544.i	0.745064	+	0.666993i
$26$	−1.09241e6			−2.39053
$27$	−101017.	+	15999.5i	−0.190081	+	0.0301058i
$28$	1.06062e6	−	2.08158e6i	1.72555	−	3.38658i
$29$	−36424.0	+	11834.9i	−0.0514986	+	0.0167329i	−0.334653	−	0.942341i	$-0.608619\pi$
$29$	−36424.0	+	11834.9i	−0.0514986	+	0.0167329i	0.283154	+	0.959074i	$0.408619\pi$
$30$	551497.	−	683046.i	0.680861	−	0.843267i
$31$	−418629.	+	1.28841e6i	−0.453297	+	1.39510i	0.419826	+	0.907604i	$0.362091\pi$
$31$	−418629.	+	1.28841e6i	−0.453297	+	1.39510i	−0.873123	+	0.487500i	$0.837909\pi$
$32$	−1.84093e6	+	1.84093e6i	−1.75564	+	1.75564i
$33$	832414.	−	424136.i	0.701914	−	0.357643i
$34$	−1.62128e6	−	2.23150e6i	−1.21323	−	1.66986i
$35$	−2.06307e6	+	922090.i	−1.37481	+	0.614471i
$36$	−1.14324e6	−	830613.i	−0.680656	−	0.494526i
$37$	−143464.	+	905794.i	−0.0765482	+	0.483306i	0.919396	+	0.393333i	$0.128678\pi$
$37$	−143464.	+	905794.i	−0.0765482	+	0.483306i	−0.995944	+	0.0899731i	$0.971322\pi$
$38$	5.44656e6	+	862650.i	2.61209	+	0.413714i
$39$	999750.	−	1.37604e6i	0.432149	−	0.594801i
$40$	7.28275e6	−	776026.i	2.84482	−	0.303135i
$41$	2.02985e6	−	1.47477e6i	0.718338	−	0.521903i	−0.167515	−	0.985870i	$-0.553574\pi$
$41$	2.02985e6	−	1.47477e6i	0.718338	−	0.521903i	0.885853	+	0.463967i	$0.153574\pi$
$42$	2.30564e6	+	4.52507e6i	0.740959	+	1.45421i
$43$	3.91263e6	+	3.91263e6i	1.14444	+	1.14444i	0.987628	+	0.156816i	$0.0501231\pi$
$43$	3.91263e6	+	3.91263e6i	1.14444	+	1.14444i	0.156816	+	0.987628i	$0.449877\pi$
$44$	1.22764e7	+	3.98885e6i	3.27538	+	1.06423i
$45$	355669.	+	1.31979e6i	0.0867354	+	0.321851i
$46$	−731519.	−	2.25138e6i	−0.163378	−	0.502827i
$47$	3.07900e6	+	1.56883e6i	0.630983	+	0.321502i	0.740069	−	0.672530i	$-0.234793\pi$
$47$	3.07900e6	+	1.56883e6i	0.630983	+	0.321502i	−0.109087	+	0.994032i	$0.534793\pi$
$48$	−1.36479e6	−	8.61697e6i	−0.257100	−	1.62327i
$49$		−	7.30785e6i		−	1.26767i
$50$	−9.85820e6	−	6.36180e6i	−1.57731	−	1.01789i
$51$	4.29462e6			0.634810
$52$	2.32113e7	−	3.67631e6i	3.17458	−	0.502804i
$53$	−1.55334e6	+	3.04859e6i	−0.196862	+	0.386363i	−0.968243	−	0.250010i	$-0.919566\pi$
$53$	−1.55334e6	+	3.04859e6i	−0.196862	+	0.386363i	0.771381	+	0.636373i	$0.219566\pi$
$54$	2.92158e6	−	949280.i	0.343592	−	0.111640i
$55$	−6.81525e6	−	1.04616e7i	−0.744786	−	1.14327i
$56$	−1.30928e7	+	4.02954e7i	−1.33131	+	4.09735i
$57$	−6.07118e6	+	6.07118e6i	−0.575140	+	0.575140i
$58$	1.02495e6	−	522236.i	0.0905709	−	0.0461482i
$59$	−5.19118e6	−	7.14505e6i	−0.428409	−	0.589654i	0.539178	−	0.842192i	$-0.318735\pi$
$59$	−5.19118e6	−	7.14505e6i	−0.428409	−	0.589654i	−0.967587	+	0.252537i	$0.918735\pi$
$60$	−9.41941e6	+	1.63691e7i	−0.726806	+	1.26305i
$61$	8.21837e6	+	5.97099e6i	0.593562	+	0.431248i	0.843588	−	0.536991i	$-0.180439\pi$
$61$	8.21837e6	+	5.97099e6i	0.593562	+	0.431248i	−0.250026	+	0.968239i	$0.580439\pi$
$62$	6.36529e6	−	4.01889e7i	0.430776	−	2.71981i
$63$	−7.80999e6	−	1.23698e6i	−0.495779	−	0.0785237i
$64$	1.78913e7	−	2.46253e7i	1.06641	−	1.46778i
$65$	−1.97024e7	−	1.13375e7i	−1.10374	−	0.635130i
$66$	−2.27015e7	+	1.64936e7i	−1.19641	+	0.869241i
$67$	4.87671e6	+	9.57107e6i	0.242007	+	0.474965i	0.979778	−	0.200085i	$-0.0641220\pi$
$67$	4.87671e6	+	9.57107e6i	0.242007	+	0.474965i	−0.737772	+	0.675050i	$0.764122\pi$
$68$	4.19582e7	+	4.19582e7i	1.96237	+	1.96237i
$69$	3.50538e6	+	1.13897e6i	0.154646	+	0.0502476i
$70$	5.68704e7	−	3.70483e7i	2.36861	−	1.54304i
$71$	730369.	+	2.24784e6i	0.0287415	+	0.0884571i	0.964398	−	0.264454i	$-0.0851918\pi$
$71$	730369.	+	2.24784e6i	0.0287415	+	0.0884571i	−0.935657	+	0.352911i	$0.885192\pi$
$72$	2.28348e7	+	1.16349e7i	0.849702	+	0.432945i
$73$	3.37520e6	+	2.13102e7i	0.118852	+	0.750405i	0.973074	+	0.230495i	$0.0740345\pi$
$73$	3.37520e6	+	2.13102e7i	0.118852	+	0.750405i	−0.854221	+	0.519910i	$0.825965\pi$
$74$		−	2.75453e7i		−	0.918589i
$75$	1.70355e7	−	6.59553e6i	0.538406	−	0.208451i
$76$	−1.18630e8			−3.55583
$77$	7.13405e7	−	1.12992e7i	2.02942	−	0.321429i
$78$	−2.31931e7	+	4.55190e7i	−0.626585	+	1.22974i
$79$	4.55224e7	−	1.47911e7i	1.16874	−	0.379745i	0.340565	−	0.940221i	$-0.389382\pi$
$79$	4.55224e7	−	1.47911e7i	1.16874	−	0.379745i	0.828171	+	0.560475i	$0.189382\pi$
$80$	−1.12581e8	+	3.03395e7i	−2.74857	+	0.740710i
$81$	−1.47802e6	+	4.54887e6i	−0.0343352	+	0.105673i
$82$	−5.32881e7	+	5.32881e7i	−1.17862	+	1.17862i
$83$	4.94404e7	−	2.51911e7i	1.04176	−	0.530806i	0.152550	−	0.988296i	$-0.451251\pi$
$83$	4.94404e7	−	2.51911e7i	1.04176	−	0.530806i	0.889215	+	0.457490i	$0.151251\pi$
$84$	−6.42179e7	−	8.83884e7i	−1.28985	−	1.77533i
$85$	−6.08148e6	−	5.70727e7i	−0.116502	−	1.09333i
$86$	−1.34456e8	−	9.76879e7i	−2.45802	−	1.78586i
$87$	−280181.	+	1.76899e6i	−0.00489059	+	0.0308780i
$88$	−2.31218e8	−	3.66213e7i	−3.85559	−	0.610665i
$89$	−5.15493e7	+	7.09516e7i	−0.821605	+	1.13084i	0.167823	+	0.985817i	$0.446326\pi$
$89$	−5.15493e7	+	7.09516e7i	−0.821605	+	1.13084i	−0.989428	+	0.145025i	$0.953674\pi$
$90$	−1.67525e7	−	3.74817e7i	−0.255334	−	0.571280i
$91$	1.06387e8	−	7.72945e7i	1.55139	−	1.12715i
$92$	2.31197e7	+	4.53750e7i	0.322724	+	0.633382i
$93$	4.47978e7	+	4.47978e7i	0.598859	+	0.598859i
$94$	−9.87127e7	−	3.20737e7i	−1.26433	−	0.410807i
$95$	8.92793e7	+	7.20848e7i	1.09611	+	0.885013i
$96$	3.76234e7	+	1.15793e8i	0.442969	+	1.36332i
$97$	1.06901e8	+	5.44689e7i	1.20752	+	0.615264i	0.937633	−	0.347626i	$-0.113012\pi$
$97$	1.06901e8	+	5.44689e7i	1.20752	+	0.615264i	0.269891	+	0.962891i	$0.413012\pi$
$98$	3.43369e7	+	2.16794e8i	0.372268	+	2.35041i
$99$		−	4.36901e7i		−	0.454823i
$100$	2.30874e8	+	1.01998e8i	2.30874	+	1.01998i
$101$	−7.63619e7			−0.733823			−0.366911	−	0.930256i	$-0.619585\pi$
$101$	−7.63619e7			−0.733823			−0.366911	+	0.930256i	$0.619585\pi$
$102$	−1.27404e8	+	2.01788e7i	−1.17702	+	0.186421i
$103$	7.00172e7	−	1.37416e8i	0.622093	−	1.22093i	−0.337973	−	0.941156i	$-0.609741\pi$
$103$	7.00172e7	−	1.37416e8i	0.622093	−	1.22093i	0.960067	−	0.279771i	$-0.0902587\pi$
$104$	−4.05342e8	+	1.31704e8i	−3.46488	+	1.12581i
$105$	−5.37919e6	+	1.05541e8i	−0.0442547	+	0.868292i
$106$	3.17570e7	−	9.77380e7i	0.251545	−	0.774177i
$107$	1.12350e8	−	1.12350e8i	0.857111	−	0.857111i	−0.133886	−	0.990997i	$-0.542746\pi$
$107$	1.12350e8	−	1.12350e8i	0.857111	−	0.857111i	0.990997	+	0.133886i	$0.0427455\pi$
$108$	−5.88824e7	+	3.00021e7i	−0.432803	+	0.220524i
$109$	−5.20897e7	−	7.16954e7i	−0.369017	−	0.507908i	0.583616	−	0.812029i	$-0.301637\pi$
$109$	−5.20897e7	−	7.16954e7i	−0.369017	−	0.507908i	−0.952633	+	0.304121i	$0.901637\pi$
$110$	2.51337e8	+	2.78332e8i	1.71666	+	1.90105i
$111$	3.46970e7	+	2.52088e7i	0.228560	+	0.166058i
$112$	1.05518e8	−	6.66211e8i	0.670583	−	4.23389i
$113$	−1.23519e8	−	1.95635e7i	−0.757567	−	0.119987i	−0.234310	−	0.972162i	$-0.575283\pi$
$113$	−1.23519e8	−	1.95635e7i	−0.757567	−	0.119987i	−0.523257	+	0.852175i	$0.675283\pi$
$114$	1.51581e8	−	2.08634e8i	0.897482	−	1.23528i
$115$	1.01723e7	−	4.81971e7i	0.0581604	−	0.275569i
$116$	−2.00203e7	+	1.45456e7i	−0.110570	+	0.0803340i
$117$	−3.61114e7	−	7.08725e7i	−0.192708	−	0.378211i
$118$	1.87574e8	+	1.87574e8i	0.967483	+	0.967483i
$119$	3.15783e8	+	1.02604e8i	1.57471	+	0.511654i
$120$	1.22285e8	−	3.19935e8i	0.589722	−	1.54290i
$121$	5.70844e7	+	1.75688e8i	0.266303	+	0.819595i
$122$	−2.71861e8	−	1.38520e8i	−1.22718	−	0.625279i
$123$	−1.83554e7	−	1.15891e8i	−0.0801942	−	0.506326i
$124$			8.75343e8i			3.70247i
$125$	−1.11774e8	−	2.17051e8i	−0.457826	−	0.889042i
$126$	2.37503e8			0.942295
$127$	−4.80557e7	+	7.61127e6i	−0.184727	+	0.0292578i	−0.248112	−	0.968731i	$-0.579810\pi$
$127$	−4.80557e7	+	7.61127e6i	−0.184727	+	0.0292578i	0.0633856	+	0.997989i	$0.479810\pi$
$128$	−1.12480e8	+	2.20755e8i	−0.419022	+	0.822377i
$129$	2.46101e8	−	7.99632e7i	0.888700	−	0.288756i
$130$	6.37761e8	+	2.43763e8i	2.23298	+	0.853482i
$131$	−1.46968e8	+	4.52322e8i	−0.499043	+	1.53590i	0.311516	+	0.950241i	$0.399163\pi$
$131$	−1.46968e8	+	4.52322e8i	−0.499043	+	1.53590i	−0.810560	+	0.585656i	$0.800837\pi$
$132$	4.26850e8	−	4.26850e8i	1.40598	−	1.40598i
$133$	−5.91461e8	+	3.01364e8i	−1.89025	+	0.963131i
$134$	−1.89643e8	−	2.61021e8i	−0.588190	−	0.809575i
$135$	6.25446e7	+	1.32004e7i	0.188302	+	0.0397422i
$136$	−8.70613e8	−	6.32537e8i	−2.54489	−	1.84897i
$137$	3.52575e7	−	2.22607e8i	0.100085	−	0.631912i	−0.885746	−	0.464170i	$-0.846353\pi$
$137$	3.52575e7	−	2.22607e8i	0.100085	−	0.631912i	0.985831	−	0.167742i	$-0.0536474\pi$
$138$	−1.09342e8	−	1.73181e7i	−0.301489	−	0.0477512i
$139$	2.16486e8	−	2.97967e8i	0.579922	−	0.798195i	−0.413765	−	0.910384i	$-0.635786\pi$
$139$	2.16486e8	−	2.97967e8i	0.579922	−	0.798195i	0.993687	+	0.112189i	$0.0357863\pi$
$140$	−1.08369e9	+	9.78579e8i	−2.82093	+	2.54732i
$141$	1.30741e8	−	9.49885e7i	0.330776	−	0.240323i
$142$	−3.22289e7	−	6.32528e7i	−0.0792669	−	0.155570i
$143$	5.13769e8	+	5.13769e8i	1.22864	+	1.22864i
$144$	−3.88030e8	−	1.26079e8i	−0.902434	−	0.293219i
$145$	2.39055e7	+	1.21841e6i	0.0540787	+	0.00275626i
$146$	−2.00257e8	−	6.16328e8i	−0.440734	−	1.35644i
$147$	−3.04505e8	−	1.55153e8i	−0.652117	−	0.332270i
$148$	9.26986e7	+	5.85276e8i	0.193209	+	1.21987i
$149$		−	6.20640e8i		−	1.25920i	−0.776919	−	0.629600i	$-0.783219\pi$
$149$		−	6.20640e8i		−	1.25920i	0.776919	−	0.629600i	$-0.216781\pi$
$150$	−4.74385e8	+	2.75706e8i	−0.937057	+	0.544605i
$151$	−7.25686e8			−1.39586			−0.697928	−	0.716168i	$-0.745895\pi$
$151$	−7.25686e8			−1.39586			−0.697928	+	0.716168i	$0.745895\pi$
$152$	2.12496e9	−	3.36560e8i	3.98085	−	0.630505i
$153$	9.11792e7	−	1.78949e8i	0.166391	−	0.326561i
$154$	−2.06329e9	+	6.70405e8i	−3.66841	+	1.19194i
$155$	5.31897e8	−	6.58770e8i	0.921511	−	1.14132i
$156$	3.39615e8	−	1.04523e9i	0.573440	−	1.76487i
$157$	−2.79780e7	+	2.79780e7i	−0.0460488	+	0.0460488i	−0.729756	−	0.683707i	$-0.760366\pi$
$157$	−2.79780e7	+	2.79780e7i	−0.0460488	+	0.0460488i	0.683707	+	0.729756i	$0.260366\pi$
$158$	−1.28097e9	+	6.52686e8i	−2.05546	+	1.04731i
$159$	9.40506e7	+	1.29450e8i	0.147154	+	0.202541i
$160$	1.48554e9	−	6.63962e8i	2.26675	−	1.01313i
$161$	2.30539e8	+	1.67496e8i	0.343116	+	0.249288i
$162$	2.24734e7	−	1.41891e8i	0.0326294	−	0.206014i
$163$	−1.50250e8	−	2.37973e7i	−0.212845	−	0.0337114i	0.0491010	−	0.998794i	$-0.484364\pi$
$163$	−1.50250e8	−	2.37973e7i	−0.212845	−	0.0337114i	−0.261946	+	0.965082i	$0.584364\pi$
$164$	9.52920e8	−	1.31158e9i	1.31729	−	1.81309i
$165$	−5.80613e8	+	6.18682e7i	−0.783342	+	0.0834703i
$166$	−1.34833e9	+	9.79622e8i	−1.77568	+	1.29011i
$167$	−5.86081e8	−	1.15025e9i	−0.753515	−	1.47886i	−0.873887	−	0.486128i	$-0.838409\pi$
$167$	−5.86081e8	−	1.15025e9i	−0.753515	−	1.47886i	0.120372	−	0.992729i	$-0.461591\pi$
$168$	1.40107e9	+	1.40107e9i	1.75882	+	1.75882i
$169$	4.82259e8	+	1.56695e8i	0.591199	+	0.192092i
$170$	4.48577e8	+	1.66454e9i	0.537082	+	1.99296i
$171$	1.24078e8	+	3.81873e8i	0.145114	+	0.446616i
$172$	3.18563e9	+	1.62316e9i	3.63984	+	1.85459i
$173$	2.94641e7	+	1.86029e8i	0.0328934	+	0.207680i	0.998661	−	0.0517273i	$-0.0164727\pi$
$173$	2.94641e7	+	1.86029e8i	0.0328934	+	0.207680i	−0.965768	+	0.259408i	$0.916473\pi$
$174$		−	5.37953e7i		−	0.0586877i
$175$	1.41019e9	−	7.79680e7i	1.50358	−	0.0831313i
$176$	3.72687e9			3.88413
$177$	−4.07936e8	+	6.46107e7i	−0.415623	+	0.0658281i
$178$	1.19589e9	−	2.34706e9i	1.19127	−	2.33800i
$179$	8.83888e8	−	2.87193e8i	0.860965	−	0.279744i	0.154933	−	0.987925i	$-0.450484\pi$
$179$	8.83888e8	−	2.87193e8i	0.860965	−	0.279744i	0.706031	+	0.708181i	$0.250484\pi$
$180$	4.82090e8	+	7.40024e8i	0.459238	+	0.704946i
$181$	7.14061e7	−	2.19766e8i	0.0665306	−	0.204760i	−0.912265	−	0.409601i	$-0.865668\pi$
$181$	7.14061e7	−	2.19766e8i	0.0665306	−	0.204760i	0.978795	+	0.204841i	$0.0656678\pi$
$182$	−2.79289e9	+	2.79289e9i	−2.54547	+	2.54547i
$183$	4.23285e8	−	2.15675e8i	0.377423	−	0.192307i
$184$	−5.42863e8	−	7.47187e8i	−0.473608	−	0.651866i
$185$	2.85876e8	−	4.96798e8i	0.244056	−	0.424124i
$186$	−1.53946e9	−	1.11848e9i	−1.28622	−	0.934495i
$187$	−2.86990e8	+	1.81198e9i	−0.234693	+	1.48179i
$188$	2.20536e9	+	3.49295e8i	1.76542	+	0.279615i
$189$	−2.17357e8	+	2.99166e8i	−0.170344	+	0.234458i
$190$	−2.98726e9	−	1.71898e9i	−2.29223	−	1.31903i
$191$	1.25608e7	−	9.12593e6i	0.00943806	−	0.00685715i	−0.583056	−	0.812432i	$-0.698143\pi$
$191$	1.25608e7	−	9.12593e6i	0.00943806	−	0.00685715i	0.592494	+	0.805575i	$0.298143\pi$
$192$	−6.46243e8	−	1.26832e9i	−0.475544	−	0.933307i
$193$	7.75263e8	+	7.75263e8i	0.558753	+	0.558753i	0.928952	−	0.370199i	$-0.120711\pi$
$193$	7.75263e8	+	7.75263e8i	0.558753	+	0.558753i	−0.370199	+	0.928952i	$0.620711\pi$
$194$	−3.42726e9	−	1.11358e9i	−2.41958	−	0.786169i
$195$	−8.90714e8	+	5.80257e8i	−0.616027	+	0.401312i
$196$	−1.45916e9	−	4.49084e9i	−0.988733	−	3.04301i
$197$	2.29369e6	+	1.16869e6i	0.00152289	+	0.000775953i	0.454752	−	0.890618i	$-0.349728\pi$
$197$	2.29369e6	+	1.16869e6i	0.00152289	+	0.000775953i	−0.453229	+	0.891394i	$0.649728\pi$
$198$	2.05284e8	+	1.29611e9i	0.133565	+	0.843298i
$199$			2.36563e9i			1.50846i	0.656608	+	0.754232i	$0.271991\pi$
$199$			2.36563e9i			1.50846i	−0.656608	+	0.754232i	$0.728009\pi$
$200$	−4.42490e9	−	1.17203e9i	−2.76556	−	0.732521i
$201$	5.02347e8			0.307765
$202$	2.26535e9	−	3.58796e8i	1.36060	−	0.215497i
$203$	−6.28651e7	+	1.23380e8i	−0.0370191	+	0.0726540i
$204$	2.63914e9	−	8.57509e8i	1.52385	−	0.495128i
$205$	−1.51413e9	+	4.08041e8i	−0.857328	+	0.231041i
$206$	−1.43146e9	+	4.40558e9i	−0.794895	+	2.44644i
$207$	1.21882e8	−	1.21882e8i	0.0663830	−	0.0663830i
$208$	6.04560e9	−	3.08039e9i	3.22988	−	1.64571i
$209$	−2.15584e9	−	2.96726e9i	−1.12988	−	1.55514i
$210$	−3.36321e8	−	3.15626e9i	−0.172933	−	1.62292i
$211$	−1.51261e9	−	1.09897e9i	−0.763126	−	0.554443i	0.136742	−	0.990607i	$-0.456337\pi$
$211$	−1.51261e9	−	1.09897e9i	−0.763126	−	0.554443i	−0.899868	+	0.436163i	$0.856337\pi$
$212$	−3.45846e8	+	2.18358e9i	−0.171214	+	1.08100i
$213$	1.09170e8	+	1.72909e7i	0.0530378	+	0.00840037i
$214$	−2.80508e9	+	3.86085e9i	−1.33749	+	1.84089i
$215$	−1.41116e9	−	3.15730e9i	−0.660422	−	1.47762i
$216$	9.69612e8	−	7.04464e8i	0.445434	−	0.323626i
$217$	2.22370e9	+	4.36425e9i	1.00285	+	1.96821i
$218$	1.88216e9	+	1.88216e9i	0.833357	+	0.833357i
$219$	9.59617e8	+	3.11798e8i	0.417178	+	0.135549i
$220$	−6.27701e9	−	5.06811e9i	−2.67955	−	2.16349i
$221$	1.03212e9	+	3.17654e9i	0.432675	+	1.33164i
$222$	−1.14777e9	−	5.84816e8i	−0.472543	−	0.240773i
$223$	−3.24648e8	−	2.04975e9i	−0.131278	−	0.828859i	−0.962175	−	0.272432i	$-0.912172\pi$
$223$	−3.24648e8	−	2.04975e9i	−0.131278	−	0.828859i	0.830897	−	0.556427i	$-0.187828\pi$
$224$			9.41312e9i			3.73888i
$225$	8.68572e7	−	8.49870e8i	0.0338903	−	0.331606i
$226$	3.75624e9			1.43986
$227$	2.23340e9	−	3.53736e8i	0.841131	−	0.133222i	0.279022	−	0.960285i	$-0.409990\pi$
$227$	2.23340e9	−	3.53736e8i	0.841131	−	0.133222i	0.562110	+	0.827063i	$0.309990\pi$
$228$	−2.51864e9	+	4.94311e9i	−0.932023	+	1.82920i
$229$	3.47138e9	−	1.12792e9i	1.26229	−	0.410144i	0.399982	−	0.916523i	$-0.369016\pi$
$229$	3.47138e9	−	1.12792e9i	1.26229	−	0.410144i	0.862311	+	0.506379i	$0.169016\pi$
$230$	−7.53102e7	+	1.47761e9i	−0.0269118	+	0.528018i
$231$	1.04381e9	−	3.21253e9i	0.366585	−	1.12823i
$232$	3.17346e8	−	3.17346e8i	0.109542	−	0.109542i
$233$	−7.98434e8	+	4.06822e8i	−0.270904	+	0.138032i	−0.584166	−	0.811634i	$-0.698578\pi$
$233$	−7.98434e8	+	4.06822e8i	−0.270904	+	0.138032i	0.313262	+	0.949667i	$0.398578\pi$
$234$	1.40428e9	+	1.93283e9i	0.468372	+	0.644659i
$235$	−1.44747e9	−	1.60295e9i	−0.474613	−	0.525591i
$236$	−4.61676e9	−	3.35427e9i	−1.48829	−	1.08131i
$237$	3.50167e8	−	2.21087e9i	0.110990	−	0.700760i
$238$	−9.85010e9	−	1.56010e9i	−3.06996	−	0.486234i
$239$	−2.39171e9	+	3.29191e9i	−0.733022	+	1.00892i	0.265968	+	0.963982i	$0.414308\pi$
$239$	−2.39171e9	+	3.29191e9i	−0.733022	+	1.00892i	−0.998990	+	0.0449360i	$0.985692\pi$
$240$	−1.12603e9	+	5.33521e9i	−0.339393	+	1.60807i
$241$	−6.74111e7	+	4.89770e7i	−0.0199831	+	0.0145186i	−0.597732	−	0.801696i	$-0.703931\pi$
$241$	−6.74111e7	+	4.89770e7i	−0.0199831	+	0.0145186i	0.577749	+	0.816215i	$0.303931\pi$
$242$	−2.51895e9	−	4.94372e9i	−0.734444	−	1.44143i
$243$	1.58164e8	+	1.58164e8i	0.0453609	+	0.0453609i
$244$	6.24260e9	+	2.02834e9i	1.76119	+	0.572246i
$245$	−1.63068e9	+	4.26639e9i	−0.452591	+	1.18412i
$246$	1.08906e9	+	3.35178e9i	0.297380	+	0.915241i
$247$	−5.94967e9	−	3.03151e9i	−1.59847	−	0.814462i
$248$	−2.48340e9	−	1.56796e10i	−0.656508	−	4.14503i
$249$		−	2.59493e9i		−	0.675038i
$250$	4.33572e9	+	5.91385e9i	1.10995	+	1.51395i
$251$	2.78544e9			0.701777			0.350889	−	0.936417i	$-0.385880\pi$
$251$	2.78544e9			0.701777			0.350889	+	0.936417i	$0.385880\pi$
$252$	−5.04640e9	+	7.99272e8i	−1.25135	+	0.198195i
$253$	−7.14802e8	+	1.40288e9i	−0.174463	+	0.342403i
$254$	1.38986e9	−	4.51592e8i	0.333914	−	0.108495i
$255$	−2.50724e9	−	9.58308e8i	−0.592973	−	0.226644i
$256$	−1.08354e8	+	3.33479e8i	−0.0252281	+	0.0776441i
$257$	1.46267e9	−	1.46267e9i	0.335284	−	0.335284i	−0.519305	−	0.854589i	$-0.673809\pi$
$257$	1.46267e9	−	1.46267e9i	0.335284	−	0.335284i	0.854589	+	0.519305i	$0.173809\pi$
$258$	−6.92512e9	+	3.52853e9i	−1.56296	+	0.796369i
$259$	1.94899e9	+	2.68256e9i	0.433123	+	0.596142i
$260$	−1.43713e10	−	3.03315e9i	−3.14487	−	0.663743i
$261$	6.77622e7	+	4.92321e7i	0.0146024	+	0.0106093i
$262$	2.23466e9	−	1.41091e10i	0.474250	−	2.99429i
$263$	3.96259e9	+	6.27613e8i	0.828240	+	0.131180i	0.556140	−	0.831088i	$-0.312282\pi$
$263$	3.96259e9	+	6.27613e8i	0.828240	+	0.131180i	0.272100	+	0.962269i	$0.412282\pi$
$264$	−6.43494e9	+	8.85693e9i	−1.32473	+	1.82334i
$265$	1.58712e9	−	1.43318e9i	0.321830	−	0.290615i
$266$	1.61303e10	−	1.17193e10i	3.22192	−	2.34086i
$267$	1.86198e9	+	3.65435e9i	0.366379	+	0.719059i
$268$	4.90791e9	+	4.90791e9i	0.951387	+	0.951387i
$269$	3.26059e7	+	1.05943e7i	0.00622711	+	0.00202331i	0.312129	−	0.950040i	$-0.398958\pi$
$269$	3.26059e7	+	1.05943e7i	0.00622711	+	0.00202331i	−0.305902	+	0.952063i	$0.598958\pi$
$270$	−1.91747e9	−	9.77288e7i	−0.360806	−	0.0183894i
$271$	1.47924e9	+	4.55264e9i	0.274260	+	0.844085i	0.989414	+	0.145119i	$0.0463564\pi$
$271$	1.47924e9	+	4.55264e9i	0.274260	+	0.844085i	−0.715154	+	0.698966i	$0.753644\pi$
$272$	1.52648e10	+	7.77781e9i	2.78879	+	1.42096i
$273$	−9.62026e8	−	6.07400e9i	−0.173195	−	1.09351i
$274$			6.76952e9i			1.20103i
$275$	1.64438e9	+	7.62837e9i	0.287522	+	1.33383i
$276$	2.38155e9			0.410416
$277$	−8.05302e9	+	1.27547e9i	−1.36785	+	0.216647i	−0.796789	−	0.604258i	$-0.793470\pi$
$277$	−8.05302e9	+	1.27547e9i	−1.36785	+	0.216647i	−0.571065	+	0.820905i	$0.693470\pi$
$278$	−5.02222e9	+	9.85666e9i	−0.840846	+	1.65025i
$279$	2.81775e9	−	9.15542e8i	0.465035	−	0.151099i
$280$	1.66352e10	−	2.06033e10i	2.70643	−	3.35200i
$281$	1.09037e9	−	3.35583e9i	0.174884	−	0.538238i	−0.824744	−	0.565506i	$-0.808681\pi$
$281$	1.09037e9	−	3.35583e9i	0.174884	−	0.538238i	0.999628	+	0.0272683i	$0.00868083\pi$
$282$	−3.43223e9	+	3.43223e9i	−0.542725	+	0.542725i
$283$	5.05082e9	−	2.57352e9i	0.787437	−	0.401219i	−0.0135445	−	0.999908i	$-0.504311\pi$
$283$	5.05082e9	−	2.57352e9i	0.787437	−	0.401219i	0.800982	+	0.598689i	$0.204311\pi$
$284$	8.97656e8	+	1.23552e9i	0.137987	+	0.189922i
$285$	4.89914e9	−	2.18967e9i	0.742575	−	0.331895i
$286$	−1.76555e10	−	1.28274e10i	−2.63885	−	1.91724i
$287$	1.41913e9	−	8.96000e9i	0.209167	−	1.32063i
$288$	5.62368e9	+	8.90703e8i	0.817430	+	0.129468i
$289$	−8.56756e8	+	1.17922e9i	−0.122819	+	0.169046i
$290$	−7.14905e8	+	7.61779e7i	−0.101078	+	0.0107705i
$291$	4.53925e9	−	3.29796e9i	0.633012	−	0.459910i
$292$	6.32915e9	+	1.24217e10i	0.870591	+	1.70863i
$293$	−1.20363e9	−	1.20363e9i	−0.163313	−	0.163313i	0.620719	−	0.784033i	$-0.286841\pi$
$293$	−1.20363e9	−	1.20363e9i	−0.163313	−	0.163313i	−0.784033	+	0.620719i	$0.786841\pi$
$294$	9.76245e9	+	3.17201e9i	1.30668	+	0.424566i
$295$	1.43630e9	+	5.32971e9i	0.189652	+	0.703746i
$296$	−3.32092e9	−	1.02208e10i	−0.432605	−	1.33142i
$297$	−1.82049e9	−	9.27586e8i	−0.233971	−	0.119214i
$298$	2.91616e9	+	1.84119e10i	0.369782	+	2.33471i
$299$			2.86651e9i			0.358648i
$300$	9.15177e9	−	7.45459e9i	1.12985	−	0.920320i
$301$	2.00062e10			2.43725
$302$	2.15282e10	−	3.40973e9i	2.58809	−	0.409913i
$303$	−1.62124e9	+	3.18187e9i	−0.192343	+	0.377495i
$304$	−3.25747e10	+	1.05842e10i	−3.81405	+	1.23926i
$305$	−3.46558e9	−	5.31978e9i	−0.400476	−	0.614744i
$306$	−1.86410e9	+	5.73712e9i	−0.212610	+	0.654347i
$307$	−5.95932e9	+	5.95932e9i	−0.670877	+	0.670877i	−0.957918	−	0.287041i	$-0.907328\pi$
$307$	−5.95932e9	+	5.95932e9i	−0.670877	+	0.670877i	0.287041	+	0.957918i	$0.407328\pi$
$308$	4.15842e10	−	2.11882e10i	4.62089	−	2.35446i
$309$	−4.23937e9	−	5.83499e9i	−0.465015	−	0.640038i
$310$	−1.26839e10	+	2.20423e10i	−1.37343	+	2.38676i
$311$	4.03063e9	+	2.92842e9i	0.430855	+	0.313035i	0.781991	−	0.623290i	$-0.214204\pi$
$311$	4.03063e9	+	2.92842e9i	0.430855	+	0.313035i	−0.351136	+	0.936325i	$0.614204\pi$
$312$	−3.11797e9	+	1.96861e10i	−0.329044	+	2.07750i
$313$	−5.19220e9	−	8.22364e8i	−0.540971	−	0.0856814i	−0.120031	−	0.992770i	$-0.538300\pi$
$313$	−5.19220e9	−	8.22364e8i	−0.540971	−	0.0856814i	−0.420940	+	0.907089i	$0.638300\pi$
$314$	6.98536e8	−	9.61453e8i	0.0718572	−	0.0989030i
$315$	4.28352e9	+	2.46489e9i	0.435069	+	0.250355i
$316$	2.50212e10	−	1.81789e10i	2.50934	−	1.82314i
$317$	−2.00851e9	−	3.94192e9i	−0.198901	−	0.390365i	0.769915	−	0.638146i	$-0.220299\pi$
$317$	−2.00851e9	−	3.94192e9i	−0.198901	−	0.390365i	−0.968816	+	0.247781i	$0.920299\pi$
$318$	−3.39834e9	−	3.39834e9i	−0.332321	−	0.332321i
$319$	−7.27649e8	−	2.36427e8i	−0.0702682	−	0.0228315i
$320$	−1.59401e10	+	1.03842e10i	−1.52016	+	0.990313i
$321$	−2.29612e9	−	7.06672e9i	−0.216259	−	0.665576i
$322$	−7.62616e9	−	3.88572e9i	−0.709386	−	0.361450i
$323$	−2.63752e9	−	1.66527e10i	−0.242318	−	1.52994i
$324$			3.09050e9i			0.280446i
$325$	8.97256e9	+	1.10153e10i	0.804235	+	0.987334i
$326$	4.56913e9			0.404542
$327$	−4.09334e9	+	6.48321e8i	−0.358003	+	0.0567021i
$328$	−1.33481e10	+	2.61972e10i	−1.15325	+	2.26339i
$329$	1.18827e10	−	3.86093e9i	1.01422	−	0.329540i
$330$	1.69338e10	−	4.56347e9i	1.42790	−	0.384804i
$331$	−6.83233e9	+	2.10277e10i	−0.569189	+	1.75178i	0.0859750	+	0.996297i	$0.472599\pi$
$331$	−6.83233e9	+	2.10277e10i	−0.569189	+	1.75178i	−0.655164	+	0.755487i	$0.727401\pi$
$332$	2.53523e10	−	2.53523e10i	2.08673	−	2.08673i
$333$	1.78706e9	−	9.10552e8i	0.145332	−	0.0740505i
$334$	2.27913e10	+	3.13695e10i	1.83140	+	2.52070i
$335$	−7.11359e8	−	6.67587e9i	−0.0564819	−	0.530065i
$336$	−2.55196e10	−	1.85411e10i	−2.00224	−	1.45472i
$337$	1.79135e9	−	1.13101e10i	0.138887	−	0.876897i	−0.815594	−	0.578625i	$-0.803590\pi$
$337$	1.79135e9	−	1.13101e10i	0.138887	−	0.876897i	0.954481	−	0.298272i	$-0.0964103\pi$
$338$	−1.50429e10	−	2.38257e9i	−1.15257	−	0.182549i
$339$	−3.43762e9	+	4.73148e9i	−0.260291	+	0.358260i
$340$	−1.51329e10	−	3.38582e10i	−1.13242	−	2.53366i
$341$	−2.18947e10	+	1.59074e10i	−1.61928	+	1.17647i
$342$	−5.47517e9	−	1.07456e10i	−0.400215	−	0.785466i
$343$	−3.94499e9	−	3.94499e9i	−0.285016	−	0.285016i
$344$	−6.16676e10	−	2.00370e10i	−4.40375	−	1.43087i
$345$	−1.79232e9	−	1.44714e9i	−0.126514	−	0.102149i
$346$	−1.74816e9	−	5.38028e9i	−0.121977	−	0.375406i
$347$	1.19504e10	+	6.08905e9i	0.824263	+	0.419983i	0.814637	−	0.579971i	$-0.196936\pi$
$347$	1.19504e10	+	6.08905e9i	0.824263	+	0.419983i	0.00962569	+	0.999954i	$0.496936\pi$
$348$	1.81038e8	+	1.14303e9i	0.0123439	+	0.0779363i
$349$		−	2.46184e10i		−	1.65943i	−0.558190	−	0.829713i	$-0.688504\pi$
$349$		−	2.46184e10i		−	1.65943i	0.558190	−	0.829713i	$-0.311496\pi$
$350$	−4.14685e10	+	8.93898e9i	−2.76341	+	0.595684i
$351$	−3.71982e9			−0.245072
$352$	−5.13695e10	+	8.13614e9i	−3.34607	+	0.529965i
$353$	−8.80524e9	+	1.72813e10i	−0.567078	+	1.11295i	0.412325	+	0.911037i	$0.364717\pi$
$353$	−8.80524e9	+	1.72813e10i	−0.567078	+	1.11295i	−0.979403	+	0.201916i	$0.935283\pi$
$354$	1.17982e10	−	3.83348e9i	0.751284	−	0.244107i
$355$	7.51918e7	−	1.47529e9i	0.00473432	−	0.0928888i
$356$	−1.75113e10	+	5.38942e10i	−1.09023	+	3.35538i
$357$	1.09797e10	−	1.09797e10i	0.675956	−	0.675956i
$358$	−2.48720e10	+	1.26729e10i	−1.51418	+	0.771515i
$359$	−7.72045e8	−	1.06263e9i	−0.0464799	−	0.0639740i	0.785144	−	0.619313i	$-0.212589\pi$
$359$	−7.72045e8	−	1.06263e9i	−0.0464799	−	0.0639740i	−0.831624	+	0.555339i	$0.812589\pi$
$360$	−1.07349e10	−	1.18879e10i	−0.639129	−	0.707778i
$361$	1.35300e10	+	9.83011e9i	0.796651	+	0.578801i
$362$	−1.08574e9	+	6.85507e9i	−0.0632252	+	0.399188i
$363$	8.53255e9	+	1.35142e9i	0.491420	+	0.0778332i
$364$	4.99436e10	−	6.87415e10i	2.84495	−	3.91574i
$365$	2.78472e9	−	1.31942e10i	0.156895	−	0.743382i
$366$	−1.15438e10	+	8.38706e9i	−0.643316	+	0.467396i
$367$	−7.32449e8	−	1.43751e9i	−0.0403750	−	0.0792405i	0.869938	−	0.493162i	$-0.164159\pi$
$367$	−7.32449e8	−	1.43751e9i	−0.0403750	−	0.0792405i	−0.910313	+	0.413921i	$0.864159\pi$
$368$	1.03968e10	+	1.03968e10i	0.566903	+	0.566903i
$369$	−5.21869e9	−	1.69566e9i	−0.281486	−	0.0914602i
$370$	−6.14651e9	+	1.60812e10i	−0.327961	+	0.858049i
$371$	3.82281e9	+	1.17654e10i	0.201784	+	0.621028i
$372$	3.64740e10	+	1.85844e10i	1.90464	+	0.970461i
$373$	5.64917e9	+	3.56675e10i	0.291843	+	1.84263i	0.501887	+	0.864933i	$0.332639\pi$
$373$	5.64917e9	+	3.56675e10i	0.291843	+	1.84263i	−0.210043	+	0.977692i	$0.567361\pi$
$374$		−	5.51027e10i		−	2.81635i
$375$	−1.14172e10	+	4.91984e7i	−0.577345	+	0.00248786i
$376$	−4.04944e10			−2.02602
$377$	−1.37578e9	+	2.17902e8i	−0.0681058	+	0.0107869i
$378$	5.04244e9	−	9.89634e9i	0.246986	−	0.484738i
$379$	3.05376e8	−	9.92227e7i	0.0148006	−	0.00480900i	−0.301607	−	0.953432i	$-0.597523\pi$
$379$	3.05376e8	−	9.92227e7i	0.0148006	−	0.00480900i	0.316408	+	0.948623i	$0.397523\pi$
$380$	6.92573e10	+	2.64713e10i	3.32148	+	1.26952i
$381$	−7.03123e8	+	2.16399e9i	−0.0333681	+	0.102696i
$382$	−3.29748e8	+	3.29748e8i	−0.0154856	+	0.0154856i
$383$	1.82549e10	−	9.30135e9i	0.848370	−	0.432266i	0.0249432	−	0.999689i	$-0.492060\pi$
$383$	1.82549e10	−	9.30135e9i	0.848370	−	0.432266i	0.823427	+	0.567423i	$0.192060\pi$
$384$	6.81040e9	+	9.37371e9i	0.313219	+	0.431109i
$385$	−4.41705e10	−	9.32244e9i	−2.01043	−	0.424313i
$386$	−2.66416e10	−	1.93563e10i	−1.20008	−	0.871912i
$387$	1.89306e9	−	1.19523e10i	0.0843958	−	0.532854i
$388$	7.65691e10	+	1.21273e10i	3.37852	+	0.535105i
$389$	−5.40610e9	+	7.44086e9i	−0.236095	+	0.324956i	−0.910581	−	0.413331i	$-0.864365\pi$
$389$	−5.40610e9	+	7.44086e9i	−0.236095	+	0.324956i	0.674486	+	0.738287i	$0.264365\pi$
$390$	2.36975e10	−	2.13990e10i	1.02434	−	0.924987i
$391$	−5.85548e9	+	4.25426e9i	−0.250528	+	0.182019i
$392$	3.88779e10	+	7.63023e10i	1.64649	+	3.23142i
$393$	1.57272e10	+	1.57272e10i	0.659296	+	0.659296i
$394$	−7.35358e7	−	2.38932e7i	−0.00305150	−	0.000991494i
$395$	−2.98769e10	−	1.52275e9i	−1.22729	−	0.0625519i
$396$	−8.72362e9	−	2.68485e10i	−0.354745	−	1.09179i
$397$	−2.58618e10	−	1.31773e10i	−1.04111	−	0.530473i	−0.152104	−	0.988365i	$-0.548605\pi$
$397$	−2.58618e10	−	1.31773e10i	−1.04111	−	0.530473i	−0.889008	+	0.457892i	$0.848605\pi$
$398$	−1.11152e10	−	7.01788e10i	−0.442982	−	2.79688i
$399$			3.10434e10i			1.22484i
$400$	7.24960e10	+	7.40914e9i	2.83187	+	0.289419i
$401$	3.53646e10			1.36770			0.683850	−	0.729622i	$-0.260304\pi$
$401$	3.53646e10			1.36770			0.683850	+	0.729622i	$0.260304\pi$
$402$	−1.49026e10	+	2.36034e9i	−0.570635	+	0.0903797i
$403$	−2.23688e10	+	4.39012e10i	−0.848051	+	1.66439i
$404$	−4.69261e10	+	1.52472e10i	−1.76153	+	0.572354i
$405$	1.87792e9	−	2.32587e9i	0.0698004	−	0.0864499i
$406$	1.28524e9	−	3.95556e9i	0.0473020	−	0.145581i
$407$	−1.29547e10	+	1.29547e10i	−0.472118	+	0.472118i
$408$	−4.48407e10	+	2.28475e10i	−1.61820	+	0.824514i
$409$	−1.49949e10	−	2.06387e10i	−0.535859	−	0.737547i	0.452150	−	0.891942i	$-0.350657\pi$
$409$	−1.49949e10	−	2.06387e10i	−0.535859	−	0.737547i	−0.988009	+	0.154395i	$0.950657\pi$
$410$	4.30009e10	−	1.92193e10i	1.52174	−	0.680145i
$411$	−8.52709e9	−	6.19529e9i	−0.298837	−	0.217117i
$412$	1.55891e10	−	9.84258e10i	0.541044	−	3.41602i
$413$	−3.15391e10	−	4.99531e9i	−1.08405	−	0.171697i
$414$	−3.04306e9	+	4.18842e9i	−0.103588	+	0.142577i
$415$	−3.44849e10	+	3.67460e9i	−1.16262	+	0.123885i
$416$	−7.66051e10	+	5.56569e10i	−2.55790	+	1.85843i
$417$	−7.81955e9	−	1.53467e10i	−0.258605	−	0.507541i
$418$	7.78971e10	+	7.78971e10i	2.55162	+	2.55162i
$419$	5.64228e10	+	1.83329e10i	1.83062	+	0.594805i	0.999235	+	0.0391084i	$0.0124518\pi$
$419$	5.64228e10	+	1.83329e10i	1.83062	+	0.594805i	0.831385	+	0.555696i	$0.187548\pi$
$420$	1.77679e10	+	6.59316e10i	0.571003	+	2.11883i
$421$	−7.42501e9	−	2.28518e10i	−0.236357	−	0.727432i	−0.996938	−	0.0781898i	$-0.975086\pi$
$421$	−7.42501e9	−	2.28518e10i	−0.236357	−	0.727432i	0.760581	−	0.649243i	$-0.224914\pi$
$422$	5.00366e10	+	2.54949e10i	1.57775	+	0.803904i
$423$	−1.18225e9	−	7.46443e9i	−0.0369273	−	0.233150i
$424$		−	4.00946e10i		−	1.24057i
$425$	−9.18488e9	+	3.46766e10i	−0.281525	+	1.06287i
$426$	−3.31989e9			−0.100806
$427$	3.62769e10	−	5.74569e9i	1.09123	−	0.172835i
$428$	4.66085e10	−	9.14744e10i	1.38896	−	2.72599i
$429$	3.23157e10	−	1.05000e10i	0.954079	−	0.309999i
$430$	5.66983e10	+	8.70338e10i	1.65843	+	2.54574i
$431$	3.00623e9	−	9.25221e9i	0.0871189	−	0.268125i	−0.898001	−	0.439994i	$-0.854981\pi$
$431$	3.00623e9	−	9.25221e9i	0.0871189	−	0.268125i	0.985120	+	0.171869i	$0.0549807\pi$
$432$	−1.34918e10	+	1.34918e10i	−0.387377	+	0.387377i
$433$	−2.93859e10	+	1.49729e10i	−0.835964	+	0.425945i	−0.818919	−	0.573910i	$-0.805426\pi$
$433$	−2.93859e10	+	1.49729e10i	−0.835964	+	0.425945i	−0.0170457	+	0.999855i	$0.505426\pi$
$434$	−8.64741e10	−	1.19021e11i	−2.43740	−	3.35480i
$435$	5.58307e8	−	9.70232e8i	0.0155925	−	0.0270968i
$436$	−4.63258e10	−	3.36576e10i	−1.28197	−	0.931403i
$437$	2.26361e9	−	1.42918e10i	0.0620690	−	0.391888i
$438$	−2.99330e10	−	4.74092e9i	−0.813306	−	0.128815i
$439$	−7.59754e9	+	1.04571e10i	−0.204557	+	0.281549i	−0.898954	−	0.438044i	$-0.855671\pi$
$439$	−7.59754e9	+	1.04571e10i	−0.204557	+	0.281549i	0.694396	+	0.719593i	$0.255671\pi$
$440$	1.26815e11	+	7.29742e10i	3.38346	+	1.94697i
$441$	−1.29299e10	+	9.39414e9i	−0.341855	+	0.248372i
$442$	−4.55443e10	−	8.93857e10i	−1.19329	−	2.34196i
$443$	−2.48547e10	−	2.48547e10i	−0.645348	−	0.645348i	0.306517	−	0.951865i	$-0.400836\pi$
$443$	−2.48547e10	−	2.48547e10i	−0.645348	−	0.645348i	−0.951865	+	0.306517i	$0.900836\pi$
$444$	2.63555e10	+	8.56343e9i	0.678172	+	0.220351i
$445$	4.59272e10	−	2.99194e10i	1.17120	−	0.762979i
$446$	1.92620e10	+	5.92823e10i	0.486813	+	1.49826i
$447$	−2.58610e10	−	1.31768e10i	−0.647762	−	0.330051i
$448$	−1.72163e10	−	1.08699e11i	−0.427392	−	2.69845i
$449$			9.90440e9i			0.243693i	0.992549	+	0.121846i	$0.0388816\pi$
$449$			9.90440e9i			0.243693i	−0.992549	+	0.121846i	$0.961118\pi$
$450$	1.41652e9	+	2.56203e10i	0.0345440	+	0.624791i
$451$	5.01234e10			1.21153
$452$	−7.98116e10	+	1.26409e10i	−1.91211	+	0.302848i
$453$	−1.54071e10	+	3.02381e10i	−0.365870	+	0.718061i
$454$	−6.45940e10	+	2.09879e10i	−1.52044	+	0.494021i
$455$	−7.93572e10	+	2.13859e10i	−1.85157	+	0.498979i
$456$	3.10912e10	−	9.56889e10i	0.719081	−	2.21310i
$457$	−2.30983e10	+	2.30983e10i	−0.529561	+	0.529561i	−0.920441	−	0.390881i	$-0.872171\pi$
$457$	−2.30983e10	+	2.30983e10i	−0.529561	+	0.529561i	0.390881	+	0.920441i	$0.372171\pi$
$458$	−9.76822e10	+	4.97716e10i	−2.22000	+	1.13115i
$459$	−5.52067e9	−	7.59856e9i	−0.124377	−	0.171191i
$460$	−3.37245e9	−	3.16493e10i	−0.0753206	−	0.706860i
$461$	1.61830e10	+	1.17577e10i	0.358308	+	0.260326i	0.752346	−	0.658768i	$-0.228922\pi$
$461$	1.61830e10	+	1.17577e10i	0.358308	+	0.260326i	−0.394038	+	0.919094i	$0.628922\pi$
$462$	−1.58713e10	+	1.00207e11i	−0.348372	+	2.19954i
$463$	−5.88059e10	−	9.31394e9i	−1.27967	−	0.202679i	−0.520661	−	0.853763i	$-0.674315\pi$
$463$	−5.88059e10	−	9.31394e9i	−1.27967	−	0.202679i	−0.759006	+	0.651084i	$0.774315\pi$
$464$	−4.19962e9	+	5.78028e9i	−0.0906021	+	0.124703i
$465$	−1.61571e10	−	3.61496e10i	−0.345582	−	0.773199i
$466$	2.17748e10	−	1.58203e10i	0.461754	−	0.335484i
$467$	−9.71505e8	−	1.90669e9i	−0.0204257	−	0.0400877i	0.880568	−	0.473919i	$-0.157161\pi$
$467$	−9.71505e8	−	1.90669e9i	−0.0204257	−	0.0400877i	−0.900994	+	0.433832i	$0.857161\pi$
$468$	−3.63424e10	−	3.63424e10i	−0.757583	−	0.757583i
$469$	3.69375e10	+	1.20017e10i	0.763443	+	0.248058i
$470$	5.04724e10	+	4.07518e10i	1.03434	+	0.835133i
$471$	5.71792e8	+	1.75980e9i	0.0116186	+	0.0357585i
$472$	9.22138e10	+	4.69853e10i	1.85792	+	0.946659i
$473$	1.72922e10	+	1.09179e11i	0.345466	+	2.18119i
$474$			6.72329e10i			1.33189i
$475$	−3.60369e10	−	6.20057e10i	−0.707902	−	1.21803i
$476$	2.14543e11			4.17913
$477$	7.39073e9	−	1.17058e9i	0.142762	−	0.0226113i
$478$	5.54849e10	−	1.08895e11i	1.06283	−	2.08592i
$479$	−4.63807e10	+	1.50700e10i	−0.881039	+	0.286267i	−0.714389	−	0.699749i	$-0.753295\pi$
$479$	−4.63807e10	+	1.50700e10i	−0.881039	+	0.286267i	−0.166651	+	0.986016i	$0.553295\pi$
$480$	3.87335e9	−	7.59963e10i	0.0729662	−	1.43162i
$481$	−1.03072e10	+	3.17223e10i	−0.192557	+	0.592630i
$482$	1.76969e9	−	1.76969e9i	0.0327876	−	0.0327876i
$483$	1.18739e10	−	6.05003e9i	0.218174	−	0.111165i
$484$	7.01592e10	+	9.65659e10i	1.27851	+	1.75971i
$485$	−5.02556e10	−	5.56536e10i	−0.908276	−	1.00583i
$486$	−5.43523e9	−	3.94893e9i	−0.0974256	−	0.0707839i
$487$	1.62007e10	−	1.02288e11i	0.288018	−	1.81847i	−0.241760	−	0.970336i	$-0.577725\pi$
$487$	1.62007e10	−	1.02288e11i	0.288018	−	1.81847i	0.529778	−	0.848136i	$-0.322275\pi$
$488$	−1.17575e11	−	1.86221e10i	−2.07317	−	0.328359i
$489$	−4.18156e9	+	5.75542e9i	−0.0731312	+	0.100656i
$490$	2.83297e10	−	1.34228e11i	0.491425	−	2.32841i
$491$	−2.66721e10	+	1.93784e10i	−0.458913	+	0.333420i	−0.793105	−	0.609085i	$-0.791537\pi$
$491$	−2.66721e10	+	1.93784e10i	−0.458913	+	0.333420i	0.334191	+	0.942505i	$0.391537\pi$
$492$	−3.44199e10	−	6.75528e10i	−0.587420	−	1.15288i
$493$	−2.48695e9	−	2.48695e9i	−0.0420997	−	0.0420997i
$494$	1.90747e11	+	6.19773e10i	3.20294	+	1.04070i
$495$	−9.74908e9	+	2.55067e10i	−0.162384	+	0.424847i
$496$	7.80980e10	+	2.40361e11i	1.29037	+	3.97134i
$497$	7.61417e9	+	3.87961e9i	0.124795	+	0.0635862i
$498$	1.21926e10	+	7.69811e10i	0.198235	+	1.25160i
$499$		−	1.08865e11i		−	1.75585i	−0.478802	−	0.877923i	$-0.658929\pi$
$499$		−	1.08865e11i		−	1.75585i	0.478802	−	0.877923i	$-0.341071\pi$
$500$	−1.12026e11	−	1.11065e11i	−1.79242	−	1.77704i
$501$	−6.03720e10			−0.958263
$502$	−8.26329e10	+	1.30878e10i	−1.30118	+	0.206087i
$503$	−3.15262e10	+	6.18737e10i	−0.492493	+	0.966572i	0.502304	+	0.864691i	$0.332486\pi$
$503$	−3.15262e10	+	6.18737e10i	−0.492493	+	0.966572i	−0.994797	+	0.101881i	$0.967514\pi$
$504$	8.81260e10	−	2.86339e10i	1.36578	−	0.443770i
$505$	4.45807e10	+	1.70395e10i	0.685459	+	0.261994i
$506$	1.46137e10	−	4.49763e10i	0.222925	−	0.686091i
$507$	1.67681e10	−	1.67681e10i	0.253777	−	0.253777i
$508$	−2.80115e10	+	1.42726e10i	−0.420613	+	0.214313i
$509$	−1.33474e10	−	1.83711e10i	−0.198850	−	0.273693i	0.697934	−	0.716162i	$-0.254103\pi$
$509$	−1.33474e10	−	1.83711e10i	−0.198850	−	0.273693i	−0.896784	+	0.442469i	$0.854103\pi$
$510$	7.88824e10	+	1.66486e10i	1.16600	+	0.246091i
$511$	6.31112e10	+	4.58530e10i	0.925599	+	0.672487i
$512$	1.15696e10	−	7.30475e10i	0.168360	−	1.06298i
$513$	1.85463e10	+	2.93744e9i	0.267786	+	0.0424131i
$514$	−3.65189e10	+	5.02640e10i	−0.523198	+	0.720120i
$515$	−7.15400e10	+	6.46012e10i	−1.01700	+	0.918357i
$516$	1.35269e11	−	9.82784e10i	1.90809	−	1.38631i
$517$	3.13407e10	+	6.15096e10i	0.438679	+	0.860956i
$518$	−7.04231e10	−	7.04231e10i	−0.978128	−	0.978128i
$519$	8.37704e9	+	2.72187e9i	0.115457	+	0.0375144i
$520$	2.66031e11	+	1.35590e10i	3.63847	+	0.185444i
$521$	3.78891e10	+	1.16611e11i	0.514237	+	1.58266i	0.784666	+	0.619919i	$0.212835\pi$
$521$	3.78891e10	+	1.16611e11i	0.514237	+	1.58266i	−0.270429	+	0.962740i	$0.587165\pi$
$522$	−2.24156e9	−	1.14213e9i	−0.0301903	−	0.0153827i
$523$	−1.30340e10	−	8.22934e10i	−0.174209	−	1.09991i	−0.907517	−	0.420016i	$-0.862024\pi$
$523$	−1.30340e10	−	8.22934e10i	−0.174209	−	1.09991i	0.733308	−	0.679897i	$-0.237976\pi$
$524$			3.07307e11i			4.07612i
$525$	2.66911e10	−	6.04157e10i	0.351341	−	0.795266i
$526$	−1.20503e11			−1.57418
$527$	−1.22876e11	+	1.94617e10i	−1.59303	+	0.252312i
$528$	7.91254e10	−	1.55292e11i	1.01808	−	1.99809i
$529$	6.85705e10	−	2.22799e10i	0.875618	−	0.284506i
$530$	−4.03494e10	+	4.99740e10i	−0.511369	+	0.633346i
$531$	−5.96869e9	+	1.83697e10i	−0.0750760	+	0.231060i
$532$	−3.03293e11	+	3.03293e11i	−3.78630	+	3.78630i
$533$	8.13085e10	−	4.14287e10i	1.00746	−	0.513325i
$534$	−7.24080e10	−	9.96610e10i	−0.890474	−	1.22563i
$535$	−9.06607e10	+	4.05209e10i	−1.10663	+	0.494611i
$536$	−1.01837e11	−	7.39887e10i	−1.23380	−	0.896409i
$537$	6.79905e9	−	4.29275e10i	0.0817619	−	0.516224i
$538$	−1.01706e9	−	1.61087e8i	−0.0121400	−	0.00192279i
$539$	8.58109e10	−	1.18109e11i	1.01669	−	1.39935i
$540$	4.10708e10	−	4.37637e9i	0.483012	−	0.0514682i
$541$	−5.09188e10	+	3.69946e10i	−0.594414	+	0.431867i	−0.843892	−	0.536514i	$-0.819741\pi$
$541$	−5.09188e10	+	3.69946e10i	−0.594414	+	0.431867i	0.249478	+	0.968380i	$0.419741\pi$
$542$	−6.52743e10	−	1.28108e11i	−0.756389	−	1.48450i
$543$	−7.64122e9	−	7.64122e9i	−0.0878948	−	0.0878948i
$544$	−2.27383e11	−	7.38812e10i	−2.59635	−	0.843604i
$545$	1.44122e10	+	5.34798e10i	0.163360	+	0.606183i
$546$	5.70789e10	+	1.75671e11i	0.642251	+	1.97665i
$547$	−2.50582e10	−	1.27678e10i	−0.279898	−	0.142615i	0.308406	−	0.951255i	$-0.400204\pi$
$547$	−2.50582e10	−	1.27678e10i	−0.279898	−	0.142615i	−0.588304	+	0.808639i	$0.700204\pi$
$548$	−2.27815e10	−	1.43837e11i	−0.252616	−	1.59495i
$549$		−	2.22166e10i		−	0.244561i
$550$	−8.46249e10	−	2.18577e11i	−0.924799	−	2.38865i
$551$	7.03145e9			0.0762849
$552$	−4.26595e10	+	6.75661e9i	−0.459473	+	0.0727734i
$553$	7.85683e10	−	1.54199e11i	0.840130	−	1.64885i
$554$	2.32908e11	−	7.56763e10i	2.47255	−	0.803380i
$555$	−1.46313e10	−	2.24595e10i	−0.154209	−	0.236716i
$556$	7.35401e10	−	2.26333e11i	0.769529	−	2.36837i
$557$	1.11701e11	−	1.11701e11i	1.16047	−	1.16047i	0.176101	−	0.984372i	$-0.443652\pi$
$557$	1.11701e11	−	1.11701e11i	1.16047	−	1.16047i	0.984372	−	0.176101i	$-0.0563484\pi$
$558$	−7.92895e10	+	4.04000e10i	−0.817859	+	0.416720i
$559$	1.18291e11	+	1.62813e11i	1.21144	+	1.66741i
$560$	−2.10262e11	+	3.65395e11i	−2.13800	+	3.71544i
$561$	6.94091e10	+	5.04287e10i	0.700753	+	0.509127i
$562$	−1.65792e10	+	1.04677e11i	−0.166195	+	1.04932i
$563$	1.81772e11	+	2.87899e10i	1.80923	+	0.286554i	0.967413	−	0.253205i	$-0.0814848\pi$
$563$	1.81772e11	+	2.87899e10i	1.80923	+	0.286554i	0.841819	+	0.539759i	$0.181485\pi$
$564$	6.13766e10	−	8.44776e10i	0.606577	−	0.834882i
$565$	6.77462e10	+	3.89837e10i	0.664800	+	0.382551i
$566$	−1.37745e11	+	1.00078e11i	−1.34218	+	0.975152i
$567$	7.85102e9	+	1.54085e10i	0.0759616	+	0.149083i
$568$	−1.95845e10	−	1.95845e10i	−0.188156	−	0.188156i
$569$	−4.08398e10	−	1.32696e10i	−0.389614	−	0.126593i	0.107658	−	0.994188i	$-0.465665\pi$
$569$	−4.08398e10	−	1.32696e10i	−0.389614	−	0.126593i	−0.497272	+	0.867595i	$0.665665\pi$
$570$	−1.35049e11	+	8.79781e10i	−1.27936	+	0.833441i
$571$	8.14544e9	+	2.50691e10i	0.0766250	+	0.235827i	0.982031	−	0.188719i	$-0.0604336\pi$
$571$	8.14544e9	+	2.50691e10i	0.0766250	+	0.235827i	−0.905406	+	0.424546i	$0.860434\pi$
$572$	4.18307e11	+	2.13138e11i	3.90761	+	1.99102i
$573$	−1.13584e8	−	7.17138e8i	−0.00105365	−	0.00665249i
$574$			2.72475e11i			2.51003i
$575$	−1.66935e10	+	2.58681e10i	−0.152713	+	0.236642i
$576$	−6.65692e10			−0.604760
$577$	1.52423e11	−	2.41414e10i	1.37514	−	0.217801i	0.575264	−	0.817968i	$-0.304899\pi$
$577$	1.52423e11	−	2.41414e10i	1.37514	−	0.217801i	0.799875	+	0.600167i	$0.204899\pi$
$578$	1.98758e10	−	3.90084e10i	0.178079	−	0.349499i
$579$	4.87635e10	−	1.58442e10i	0.433891	−	0.140980i
$580$	1.49337e10	−	4.02448e9i	0.131964	−	0.0355630i
$581$	6.19962e10	−	1.90805e11i	0.544078	−	1.67450i
$582$	−1.19165e11	+	1.19165e11i	−1.03862	+	1.03862i
$583$	−6.09023e10	+	3.10313e10i	−0.527181	+	0.268612i
$584$	−1.48612e11	−	2.04546e11i	−1.27762	−	1.75849i
$585$	5.26752e9	+	4.94340e10i	0.0449762	+	0.422087i
$586$	4.13622e10	+	3.00514e10i	0.350763	+	0.254844i
$587$	−2.34329e10	+	1.47949e11i	−0.197366	+	1.24612i	0.667687	+	0.744442i	$0.267284\pi$
$587$	−2.34329e10	+	1.47949e11i	−0.197366	+	1.24612i	−0.865053	+	0.501680i	$0.832716\pi$
$588$	−2.18105e11	−	3.45444e10i	−1.82455	−	0.288980i
$589$	1.46194e11	−	2.01219e11i	1.21470	−	1.67189i
$590$	−6.76516e10	−	1.51363e11i	−0.558303	−	1.24914i
$591$	9.73948e7	−	7.07615e7i	0.000798336	−	0.000580025i
$592$	7.76724e10	+	1.52441e11i	0.632382	+	1.24112i
$593$	2.54776e10	+	2.54776e10i	0.206035	+	0.206035i	0.802580	−	0.596545i	$-0.203460\pi$
$593$	2.54776e10	+	2.54776e10i	0.206035	+	0.206035i	−0.596545	+	0.802580i	$0.703460\pi$
$594$	5.83650e10	+	1.89639e10i	0.468821	+	0.152329i
$595$	−1.61462e11	−	1.30365e11i	−1.28825	−	1.04015i
$596$	−1.23924e11	−	3.81398e11i	−0.982130	−	3.02268i
$597$	9.85717e10	+	5.02248e10i	0.775988	+	0.395386i
$598$	−1.34687e10	−	8.50377e10i	−0.105322	−	0.664978i
$599$		−	5.38337e10i		−	0.418164i	−0.977898	−	0.209082i	$-0.932952\pi$
$599$		−	5.38337e10i		−	0.418164i	0.977898	−	0.209082i	$-0.0670475\pi$
$600$	−1.42782e11	+	1.59494e11i	−1.10171	+	1.23067i
$601$	−9.97196e10			−0.764333			−0.382167	−	0.924093i	$-0.624822\pi$
$601$	−9.97196e10			−0.764333			−0.382167	+	0.924093i	$0.624822\pi$
$602$	−5.93504e11	+	9.40018e10i	−4.51895	+	0.715732i
$603$	1.06654e10	−	2.09319e10i	0.0806689	−	0.158322i
$604$	−4.45950e11	+	1.44898e11i	−3.35072	+	1.08872i
$605$	5.87686e9	−	1.15306e11i	0.0438656	−	0.860657i
$606$	3.31453e10	−	1.02011e11i	0.245771	−	0.756407i
$607$	−4.63037e10	+	4.63037e10i	−0.341084	+	0.341084i	−0.856775	−	0.515691i	$-0.827535\pi$
$607$	−4.63037e10	+	4.63037e10i	−0.341084	+	0.341084i	0.515691	+	0.856775i	$0.327535\pi$
$608$	4.25889e11	−	2.17001e11i	3.11660	−	1.58799i
$609$	3.80633e9	+	5.23896e9i	0.0276718	+	0.0380869i
$610$	1.27805e11	+	1.41533e11i	0.923060	+	1.02221i
$611$	1.01680e11	+	7.38746e10i	0.729574	+	0.530066i
$612$	2.03008e10	−	1.28174e11i	0.144713	−	0.913681i
$613$	1.85861e11	+	2.94375e10i	1.31628	+	0.208478i	0.774783	−	0.632228i	$-0.217859\pi$
$613$	1.85861e11	+	2.94375e10i	1.31628	+	0.208478i	0.541493	+	0.840705i	$0.317859\pi$
$614$	1.48788e11	−	2.04790e11i	1.04688	−	1.44090i
$615$	−1.51441e10	+	7.17542e10i	−0.105863	+	0.501588i
$616$	−6.84764e11	+	4.97510e11i	−4.75574	+	3.45525i
$617$	−5.13182e10	−	1.00718e11i	−0.354104	−	0.694968i	0.643404	−	0.765527i	$-0.277522\pi$
$617$	−5.13182e10	−	1.00718e11i	−0.354104	−	0.694968i	−0.997508	+	0.0705593i	$0.977522\pi$
$618$	1.53181e11	+	1.53181e11i	1.05015	+	1.05015i
$619$	−2.11156e11	−	6.86088e10i	−1.43827	−	0.467323i	−0.516913	−	0.856038i	$-0.672919\pi$
$619$	−2.11156e11	−	6.86088e10i	−1.43827	−	0.467323i	−0.921358	+	0.388715i	$0.872919\pi$
$620$	1.95326e11	−	5.11033e11i	1.32188	−	3.45846i
$621$	−2.49092e9	−	7.66627e9i	−0.0167492	−	0.0515487i
$622$	−1.33332e11	−	6.79361e10i	−0.890785	−	0.453878i
$623$	4.96042e10	+	3.13189e11i	0.329281	+	2.07900i
$624$		−	3.17310e11i		−	2.09288i
$625$	1.68214e10	+	1.51658e11i	0.110241	+	0.993905i
$626$	1.57896e11			1.02819
$627$	−1.69411e11	+	2.68321e10i	−1.09615	+	0.173614i
$628$	−1.16067e10	+	2.27795e10i	−0.0746227	+	0.146455i
$629$	−8.00969e10	+	2.60251e10i	−0.511698	+	0.166261i
$630$	−1.38656e11	−	5.29968e10i	−0.880193	−	0.336425i
$631$	4.29212e10	−	1.32098e11i	0.270741	−	0.833255i	−0.719574	−	0.694416i	$-0.755663\pi$
$631$	4.29212e10	−	1.32098e11i	0.270741	−	0.833255i	0.990315	−	0.138839i	$-0.0443372\pi$
$632$	−3.96616e11	+	3.96616e11i	−2.48601	+	2.48601i
$633$	−7.79065e10	+	3.96953e10i	−0.485243	+	0.247243i
$634$	7.81060e10	+	1.07504e11i	0.483423	+	0.665375i
$635$	2.97537e10	+	6.27969e9i	0.182998	+	0.0386228i
$636$	8.36435e10	+	6.07705e10i	0.511215	+	0.371419i
$637$	4.15786e10	−	2.62517e11i	0.252530	−	1.59441i
$638$	2.26973e10	+	3.59490e9i	0.136991	+	0.0216972i
$639$	3.03828e9	−	4.18183e9i	0.0182232	−	0.0250820i
$640$	1.14927e11	−	1.03780e11i	0.685016	−	0.618575i
$641$	−9.07784e10	+	6.59544e10i	−0.537713	+	0.390671i	−0.823235	−	0.567701i	$-0.807833\pi$
$641$	−9.07784e10	+	6.59544e10i	−0.537713	+	0.390671i	0.285522	+	0.958372i	$0.407833\pi$
$642$	1.01320e11	+	1.98853e11i	0.596426	+	1.17055i
$643$	−6.39012e10	−	6.39012e10i	−0.373822	−	0.373822i	0.495045	−	0.868867i	$-0.335151\pi$
$643$	−6.39012e10	−	6.39012e10i	−0.373822	−	0.373822i	−0.868867	+	0.495045i	$0.835151\pi$
$644$	1.75115e11	+	5.68984e10i	1.01808	+	0.330793i
$645$	−1.61519e11	−	8.23225e9i	−0.933223	−	0.0475641i
$646$	1.56489e11	+	4.81625e11i	0.898576	+	2.76553i
$647$	2.22754e11	+	1.13499e11i	1.27118	+	0.647701i	0.953756	−	0.300582i	$-0.0971808\pi$
$647$	2.22754e11	+	1.13499e11i	1.27118	+	0.647701i	0.317428	+	0.948282i	$0.397181\pi$
$648$	−8.76793e9	−	5.53585e10i	−0.0497276	−	0.313967i
$649$		−	1.76434e11i		−	0.994496i
$650$	−3.17937e11	−	2.84622e11i	−1.78110	−	1.59446i
$651$	2.29062e11			1.27535
$652$	−9.70837e10	+	1.53765e10i	−0.537224	+	0.0850880i
$653$	−8.10253e10	+	1.59021e11i	−0.445623	+	0.874585i	0.553505	+	0.832846i	$0.313290\pi$
$653$	−8.10253e10	+	1.59021e11i	−0.445623	+	0.874585i	−0.999129	+	0.0417392i	$0.986710\pi$
$654$	1.18387e11	−	3.84662e10i	0.647131	−	0.210265i
$655$	1.86733e11	−	2.31275e11i	1.01451	−	1.25650i
$656$	1.44644e11	−	4.45167e11i	0.781059	−	2.40385i
$657$	3.33658e10	−	3.33658e10i	0.179077	−	0.179077i
$658$	−3.34372e11	+	1.70371e11i	−1.78372	+	0.908849i
$659$	8.85549e10	+	1.21885e11i	0.469538	+	0.646264i	0.976452	−	0.215733i	$-0.0692140\pi$
$659$	8.85549e10	+	1.21885e11i	0.469538	+	0.646264i	−0.506914	+	0.861996i	$0.669214\pi$
$660$	−3.44447e11	+	1.53951e11i	−1.81529	+	0.811346i
$661$	3.36016e10	+	2.44130e10i	0.176017	+	0.127884i	0.672305	−	0.740274i	$-0.265304\pi$
$661$	3.36016e10	+	2.44130e10i	0.176017	+	0.127884i	−0.496289	+	0.868158i	$0.665304\pi$
$662$	1.03886e11	−	6.55911e11i	0.540910	−	3.41517i
$663$	1.54274e11	+	2.44346e10i	0.798434	+	0.126459i
$664$	−3.82197e11	+	5.26049e11i	−1.96614	+	2.70616i
$665$	4.12547e11	−	4.39597e10i	2.10954	−	0.224785i
$666$	−4.87365e10	+	3.54092e10i	−0.247718	+	0.179978i
$667$	−1.37035e9	−	2.68947e9i	−0.00692356	−	0.0135882i
$668$	−5.89831e11	−	5.89831e11i	−2.96225	−	2.96225i
$669$	−9.23020e10	−	2.99907e10i	−0.460794	−	0.149721i
$670$	5.24706e10	+	1.94704e11i	0.260386	+	0.966219i
$671$	6.27111e10	+	1.93005e11i	0.309353	+	0.952091i
$672$	3.92228e11	+	1.99850e11i	1.92336	+	0.980003i
$673$	−1.44988e9	−	9.15421e9i	−0.00706762	−	0.0446232i	0.983902	−	0.178706i	$-0.0571911\pi$
$673$	−1.44988e9	−	9.15421e9i	−0.00706762	−	0.0446232i	−0.990970	+	0.134083i	$0.957191\pi$
$674$			3.43943e11i			1.66666i
$675$	−3.35685e10	−	2.16628e10i	−0.161703	−	0.104352i
$676$	3.27646e11			1.56898
$677$	2.37411e11	−	3.76023e10i	1.13018	−	0.179003i	0.436788	−	0.899565i	$-0.356116\pi$
$677$	2.37411e11	−	3.76023e10i	1.13018	−	0.179003i	0.693390	+	0.720562i	$0.256116\pi$
$678$	7.97489e10	−	1.56516e11i	0.377403	−	0.740696i
$679$	4.12563e11	−	1.34050e11i	1.94093	−	0.630648i
$680$	3.67126e11	+	5.63551e11i	1.71704	+	2.63571i
$681$	3.26779e10	−	1.00572e11i	0.151938	−	0.467616i
$682$	5.74784e11	−	5.74784e11i	2.65685	−	2.65685i
$683$	−2.28795e11	+	1.16577e11i	−1.05139	+	0.535711i	−0.892248	−	0.451545i	$-0.850873\pi$
$683$	−2.28795e11	+	1.16577e11i	−1.05139	+	0.535711i	−0.159143	+	0.987256i	$0.550873\pi$
$684$	1.52497e11	+	2.09895e11i	0.696687	+	0.958908i
$685$	−7.02565e10	+	1.22093e11i	−0.319098	+	0.554532i
$686$	1.35568e11	+	9.84958e10i	0.612153	+	0.444755i
$687$	2.67026e10	−	1.68593e11i	0.119874	−	0.756856i
$688$	1.01956e12	+	1.61483e11i	4.55051	+	0.720730i
$689$	−7.31452e10	+	1.00676e11i	−0.324570	+	0.446733i
$690$	5.99705e10	+	3.45093e10i	0.264571	+	0.152244i
$691$	1.23127e11	−	8.94567e10i	0.540057	−	0.392374i	−0.284049	−	0.958810i	$-0.591678\pi$
$691$	1.23127e11	−	8.94567e10i	0.540057	−	0.392374i	0.824106	+	0.566435i	$0.191678\pi$
$692$	5.52508e10	+	1.08436e11i	0.240943	+	0.472877i
$693$	−1.11699e11	−	1.11699e11i	−0.484303	−	0.484303i
$694$	−3.83131e11	−	1.24487e11i	−1.65162	−	0.536644i
$695$	−1.92875e11	+	1.25649e11i	−0.826679	+	0.538541i
$696$	−6.48567e9	−	1.99609e10i	−0.0276387	−	0.0850633i
$697$	2.05299e11	+	1.04605e11i	0.869874	+	0.443223i
$698$	1.15673e11	+	7.30329e11i	0.487314	+	3.07678i
$699$			4.19066e10i			0.175539i
$700$	8.51028e11	−	3.29487e11i	3.54447	−	1.37229i
$701$	−5.65326e10			−0.234114			−0.117057	−	0.993125i	$-0.537346\pi$
$701$	−5.65326e10			−0.234114			−0.117057	+	0.993125i	$0.537346\pi$
$702$	1.10352e11	−	1.74780e10i	0.454393	−	0.0719688i
$703$	7.64398e10	−	1.50022e11i	0.312967	−	0.614232i
$704$	5.78316e11	−	1.87906e11i	2.35437	−	0.764980i
$705$	−9.75234e10	+	2.62815e10i	−0.394777	+	0.106388i
$706$	1.80018e11	−	5.54038e11i	0.724597	−	2.23008i
$707$	−1.95229e11	+	1.95229e11i	−0.781386	+	0.781386i
$708$	−2.37785e11	+	1.21158e11i	−0.946349	+	0.482189i
$709$	3.31353e10	+	4.56068e10i	0.131131	+	0.180487i	0.869534	−	0.493874i	$-0.164419\pi$
$709$	3.31353e10	+	4.56068e10i	0.131131	+	0.180487i	−0.738402	+	0.674360i	$0.764419\pi$
$710$	4.70119e9	+	4.41191e10i	0.0185001	+	0.173618i
$711$	−8.46886e10	−	6.15299e10i	−0.331395	−	0.240773i
$712$	1.60770e11	−	1.01506e12i	0.625582	−	3.94977i
$713$	−1.05456e11	−	1.67026e10i	−0.408050	−	0.0646288i
$714$	−2.74135e11	+	3.77314e11i	−1.05480	+	1.45181i
$715$	−1.85300e11	−	4.14586e11i	−0.709006	−	1.58632i
$716$	4.85825e11	−	3.52973e11i	1.84854	−	1.34304i
$717$	8.63895e10	+	1.69549e11i	0.326877	+	0.641532i
$718$	2.78964e10	+	2.78964e10i	0.104966	+	0.104966i
$719$	−2.63743e11	−	8.56952e10i	−0.986882	−	0.320657i	−0.229270	−	0.973363i	$-0.573634\pi$
$719$	−2.63743e11	−	8.56952e10i	−0.986882	−	0.320657i	−0.757612	+	0.652706i	$0.773634\pi$
$720$	1.98402e11	+	1.60191e11i	0.738272	+	0.596087i
$721$	−1.72315e11	−	5.30330e11i	−0.637648	−	1.96248i
$722$	−4.47568e11	−	2.28047e11i	−1.64706	−	0.839221i
$723$	6.09580e8	+	3.84873e9i	0.00223089	+	0.0140853i
$724$		−	1.49309e11i		−	0.543413i
$725$	−1.36844e10	−	6.04563e9i	−0.0495305	−	0.0218821i
$726$	−2.59476e11			−0.934010
$727$	1.23978e10	−	1.96362e9i	0.0443820	−	0.00702942i	−0.134204	−	0.990954i	$-0.542848\pi$
$727$	1.23978e10	−	1.96362e9i	0.0443820	−	0.00702942i	0.178586	+	0.983924i	$0.442848\pi$
$728$	−6.99591e11	+	1.37302e12i	−2.49068	+	4.88824i
$729$	9.94839e9	−	3.23243e9i	0.0352243	−	0.0114451i
$730$	−2.06166e10	+	4.04504e11i	−0.0725981	+	1.42440i
$731$	−1.57024e11	+	4.83270e11i	−0.549916	+	1.69247i
$732$	2.17055e11	−	2.17055e11i	0.756005	−	0.756005i
$733$	1.86593e11	−	9.50737e10i	0.646366	−	0.329340i	−0.0998905	−	0.994998i	$-0.531849\pi$
$733$	1.86593e11	−	9.50737e10i	0.646366	−	0.329340i	0.746256	+	0.665659i	$0.231849\pi$
$734$	2.84831e10	+	3.92037e10i	0.0981304	+	0.135065i
$735$	1.43152e11	+	1.58528e11i	0.490509	+	0.543195i
$736$	−1.66002e11	−	1.20608e11i	−0.565722	−	0.411021i
$737$	−3.35696e10	+	2.11950e11i	−0.113783	+	0.718396i
$738$	1.62785e11	+	2.57826e10i	0.548768	+	0.0869162i
$739$	−2.97081e11	+	4.08897e11i	−0.996087	+	1.37100i	−0.0683910	+	0.997659i	$0.521787\pi$
$739$	−2.97081e11	+	4.08897e11i	−0.996087	+	1.37100i	−0.927696	+	0.373337i	$0.878213\pi$
$740$	7.64812e10	−	3.62374e11i	0.255051	−	1.20845i
$741$	−2.52635e11	+	1.83550e11i	−0.837956	+	0.608811i
$742$	−1.68689e11	−	3.31070e11i	−0.556506	−	1.09221i
$743$	−3.70353e11	−	3.70353e11i	−1.21524	−	1.21524i	−0.969281	−	0.245954i	$-0.920899\pi$
$743$	−3.70353e11	−	3.70353e11i	−1.21524	−	1.21524i	−0.245954	−	0.969281i	$-0.579101\pi$
$744$	−7.06065e11	−	2.29415e11i	−2.30438	−	0.748737i
$745$	−1.38491e11	+	3.62335e11i	−0.449568	+	1.17621i
$746$	−3.35176e11	−	1.03157e12i	−1.08223	−	3.33075i
$747$	−1.08126e11	−	5.50930e10i	−0.347255	−	0.176935i
$748$	1.85438e11	+	1.17081e12i	0.592368	+	3.74007i
$749$		−	5.74472e11i		−	1.82533i
$750$	3.38472e11	−	5.51048e10i	1.06974	−	0.174158i
$751$	−1.59812e11			−0.502401			−0.251200	−	0.967935i	$-0.580825\pi$
$751$	−1.59812e11			−0.502401			−0.251200	+	0.967935i	$0.580825\pi$
$752$	6.36734e11	−	1.00849e11i	1.99107	−	0.315355i
$753$	5.91378e10	−	1.16065e11i	0.183944	−	0.361010i
$754$	3.97901e10	−	1.29286e10i	0.123109	−	0.0400005i
$755$	4.23662e11	+	1.61931e11i	1.30386	+	0.498358i
$756$	−7.38361e10	+	2.27244e11i	−0.226038	+	0.695674i
$757$	−6.58831e10	+	6.58831e10i	−0.200628	+	0.200628i	−0.800269	−	0.599641i	$-0.795310\pi$
$757$	−6.58831e10	+	6.58831e10i	−0.200628	+	0.200628i	0.599641	+	0.800269i	$0.295310\pi$
$758$	−8.59307e9	+	4.37839e9i	−0.0260298	+	0.0132629i
$759$	4.32795e10	+	5.95691e10i	0.130411	+	0.179496i
$760$	−1.31567e12	−	2.77680e11i	−3.94360	−	0.832319i
$761$	1.61379e11	+	1.17248e11i	0.481180	+	0.349598i	0.801782	−	0.597616i	$-0.203885\pi$
$761$	1.61379e11	+	1.17248e11i	0.481180	+	0.349598i	−0.320602	+	0.947214i	$0.603885\pi$
$762$	1.06910e10	−	6.75006e10i	0.0317103	−	0.200211i
$763$	−3.16472e11	−	5.01242e10i	−0.933764	−	0.147894i
$764$	5.89670e9	−	8.11611e9i	0.0173075	−	0.0238218i
$765$	−9.31623e10	+	8.41263e10i	−0.272016	+	0.245633i
$766$	−4.97847e11	+	3.61707e11i	−1.44604	+	1.05061i
$767$	−1.45829e11	−	2.86205e11i	−0.421368	−	0.826981i
$768$	1.15950e10	+	1.15950e10i	0.0333293	+	0.0333293i
$769$	−4.09352e11	−	1.33006e11i	−1.17055	−	0.380336i	−0.341704	−	0.939808i	$-0.611004\pi$
$769$	−4.09352e11	−	1.33006e11i	−1.17055	−	0.380336i	−0.828849	+	0.559472i	$0.811004\pi$
$770$	1.35416e12	+	6.90185e10i	3.85220	+	0.196337i
$771$	−2.98929e10	−	9.20008e10i	−0.0845961	−	0.260360i
$772$	6.31214e11	+	3.21620e11i	1.77708	+	0.905468i
$773$	−8.08240e10	−	5.10302e11i	−0.226372	−	1.42925i	−0.794975	−	0.606643i	$-0.792516\pi$
$773$	−8.08240e10	−	5.10302e11i	−0.226372	−	1.42925i	0.568603	−	0.822612i	$-0.307484\pi$
$774$			3.63472e11i			1.01276i
$775$	−4.57525e11	+	2.65908e11i	−1.26826	+	0.737096i
$776$	−1.40595e12			−3.87724
$777$	1.53157e11	−	2.42576e10i	0.420195	−	0.0665524i
$778$	1.25415e11	−	2.46142e11i	0.342320	−	0.671842i
$779$	−4.38103e11	+	1.42348e11i	−1.18967	+	0.386547i
$780$	−4.31504e11	+	5.34430e11i	−1.16575	+	1.44382i
$781$	−1.45907e10	+	4.49056e10i	−0.0392168	+	0.120697i
$782$	1.53719e11	−	1.53719e11i	0.411057	−	0.411057i
$783$	3.49008e9	−	1.77828e9i	0.00928513	−	0.00473101i
$784$	−8.01343e11	−	1.10295e12i	−2.12107	−	2.91940i
$785$	2.25769e10	−	1.00907e10i	0.0594545	−	0.0265733i
$786$	−5.40458e11	−	3.92665e11i	−1.41603	−	1.02880i
$787$	−9.20270e10	+	5.81036e11i	−0.239892	+	1.51462i	0.514096	+	0.857733i	$0.328128\pi$
$787$	−9.20270e10	+	5.81036e11i	−0.239892	+	1.51462i	−0.753988	+	0.656888i	$0.771872\pi$
$788$	1.64288e9	+	2.60206e8i	0.00426089	+	0.000674859i
$789$	1.10281e11	−	1.51789e11i	0.284574	−	0.391682i
$790$	8.93482e11	−	9.52064e10i	2.29391	−	0.244432i
$791$	−3.65809e11	+	2.65776e11i	−0.934433	+	0.678906i
$792$	2.32433e11	+	4.56174e11i	0.590740	+	1.15939i
$793$	2.61253e11	+	2.61253e11i	0.660646	+	0.660646i
$794$	8.29132e11	+	2.69401e11i	2.08613	+	0.677825i
$795$	−2.60220e10	−	9.65604e10i	−0.0651437	−	0.241730i
$796$	4.72347e11	+	1.45373e12i	1.17655	+	3.62103i
$797$	−1.92098e11	−	9.78786e10i	−0.476090	−	0.242580i	0.199444	−	0.979909i	$-0.436087\pi$
$797$	−1.92098e11	−	9.78786e10i	−0.476090	−	0.242580i	−0.675533	+	0.737329i	$0.736087\pi$
$798$	−1.45862e11	−	9.20934e11i	−0.359691	−	2.27100i
$799$			3.17343e11i			0.778648i
$800$	−1.01543e12	+	5.61418e10i	−2.47907	+	0.137065i
$801$	1.91802e11			0.465933
$802$	−1.04912e12	+	1.66165e11i	−2.53589	+	0.401645i
$803$	−1.95681e11	+	3.84045e11i	−0.470637	+	0.923677i
$804$	3.08704e11	−	1.00304e11i	0.738784	−	0.240046i
$805$	−9.72152e10	−	1.49229e11i	−0.231500	−	0.355360i
$806$	4.57316e11	−	1.40747e12i	1.08362	−	3.33503i
$807$	1.13370e9	−	1.13370e9i	0.00267304	−	0.00267304i
$808$	7.97305e11	−	4.06247e11i	1.87059	−	0.953114i
$809$	3.84315e10	+	5.28964e10i	0.0897207	+	0.123490i	0.851518	−	0.524326i	$-0.175683\pi$
$809$	3.84315e10	+	5.28964e10i	0.0897207	+	0.123490i	−0.761797	+	0.647816i	$0.775683\pi$
$810$	−4.47821e10	+	7.78227e10i	−0.104031	+	0.180787i
$811$	3.23162e11	+	2.34791e11i	0.747029	+	0.542748i	0.894905	−	0.446258i	$-0.147243\pi$
$811$	3.23162e11	+	2.34791e11i	0.747029	+	0.542748i	−0.147875	+	0.989006i	$0.547243\pi$
$812$	−1.39967e10	+	8.83719e10i	−0.0321961	+	0.203278i
$813$	2.21106e11	+	3.50198e10i	0.506103	+	0.0801589i
$814$	3.23445e11	−	4.45184e11i	0.736721	−	1.01401i
$815$	8.24072e10	+	4.74201e10i	0.186782	+	0.107481i
$816$	6.48176e11	−	4.70927e11i	1.46195	−	1.06217i
$817$	−4.61205e11	−	9.05165e11i	−1.03516	−	2.03161i
$818$	5.41812e11	+	5.41812e11i	1.21014	+	1.21014i
$819$	−2.73518e11	−	8.88713e10i	−0.607925	−	0.197527i
$820$	−8.48992e11	+	5.53077e11i	−1.87779	+	1.22329i
$821$	9.54781e10	+	2.93851e11i	0.210151	+	0.646778i	0.999462	+	0.0327848i	$0.0104376\pi$
$821$	9.54781e10	+	2.93851e11i	0.210151	+	0.646778i	−0.789312	+	0.613993i	$0.789562\pi$
$822$	2.82074e11	+	1.43724e11i	0.617839	+	0.314805i
$823$	2.39483e10	+	1.51204e11i	0.0522006	+	0.329582i	0.999944	+	0.0105491i	$0.00335793\pi$
$823$	2.39483e10	+	1.51204e11i	0.0522006	+	0.329582i	−0.947744	+	0.319033i	$0.896642\pi$
$824$			1.80728e12i			3.92027i
$825$	3.52773e11	+	9.34398e10i	0.761516	+	0.201705i
$826$	9.59110e11			2.06038
$827$	1.27488e10	−	2.01921e9i	0.0272551	−	0.00431678i	−0.142792	−	0.989753i	$-0.545608\pi$
$827$	1.27488e10	−	2.01921e9i	0.0272551	−	0.00431678i	0.170047	+	0.985436i	$0.445608\pi$
$828$	5.05629e10	−	9.92352e10i	0.107575	−	0.211127i
$829$	3.81156e11	−	1.23845e11i	0.807021	−	0.262217i	0.123685	−	0.992321i	$-0.460529\pi$
$829$	3.81156e11	−	1.23845e11i	0.807021	−	0.262217i	0.683336	+	0.730104i	$0.260529\pi$
$830$	1.00576e12	−	2.71043e11i	2.11926	−	0.571117i
$831$	−1.17827e11	+	3.62635e11i	−0.247082	+	0.760441i
$832$	7.82812e11	−	7.82812e11i	1.63367	−	1.63367i
$833$	5.97958e11	−	3.04675e11i	1.24191	−	0.632785i
$834$	3.04083e11	+	4.18534e11i	0.628533	+	0.865101i
$835$	8.54910e10	+	8.02305e11i	0.175863	+	1.65042i
$836$	−1.91729e12	−	1.39299e12i	−3.92520	−	2.85182i
$837$	2.16747e10	−	1.36849e11i	0.0441622	−	0.278829i
$838$	−1.75998e12	−	2.78753e11i	−3.56887	−	0.565253i
$839$	4.55428e11	−	6.26842e11i	0.919119	−	1.26506i	−0.0448369	−	0.998994i	$-0.514277\pi$
$839$	4.55428e11	−	6.26842e11i	0.919119	−	1.26506i	0.963955	−	0.266064i	$-0.0857232\pi$
$840$	−5.05318e11	−	1.13059e12i	−1.01496	−	2.27085i
$841$	−4.03521e11	+	2.93175e11i	−0.806645	+	0.586062i
$842$	3.27642e11	+	6.43034e11i	0.651856	+	1.27934i
$843$	−1.16682e11	−	1.16682e11i	−0.231043	−	0.231043i
$844$	−1.14896e12	−	3.73321e11i	−2.26431	−	0.735720i
$845$	−2.46582e11	−	1.99092e11i	−0.483653	−	0.390506i
$846$	7.01452e10	+	2.15885e11i	0.136936	+	0.421445i
$847$	5.95110e11	+	3.03224e11i	1.15628	+	0.589155i
$848$	9.98531e10	+	6.30447e11i	0.193098	+	1.21917i
$849$		−	2.65097e11i		−	0.510240i
$850$	1.09546e11	−	1.07187e12i	0.209856	−	2.05337i
$851$	−7.22793e10			−0.137815
$852$	7.05400e10	−	1.11724e10i	0.133868	−	0.0212026i
$853$	−1.70521e10	+	3.34666e10i	−0.0322093	+	0.0632142i	−0.906550	−	0.422098i	$-0.861294\pi$
$853$	−1.70521e10	+	3.34666e10i	−0.0322093	+	0.0632142i	0.874341	+	0.485312i	$0.161294\pi$
$854$	−1.04919e12	+	3.40903e11i	−1.97253	+	0.640913i
$855$	1.27739e10	−	2.50628e11i	0.0239033	−	0.468991i
$856$	−5.75356e11	+	1.77076e12i	−1.07162	+	3.29811i
$857$	1.72084e11	−	1.72084e11i	0.319020	−	0.319020i	−0.529371	−	0.848391i	$-0.677572\pi$
$857$	1.72084e11	−	1.72084e11i	0.319020	−	0.319020i	0.848391	+	0.529371i	$0.177572\pi$
$858$	−9.09340e11	+	4.63332e11i	−1.67794	+	0.854955i
$859$	−6.32466e11	−	8.70515e11i	−1.16162	−	1.59883i	−0.705070	−	0.709138i	$-0.749085\pi$
$859$	−6.32466e11	−	8.70515e11i	−1.16162	−	1.59883i	−0.456551	−	0.889697i	$-0.650915\pi$
$860$	−1.49761e12	−	1.65846e12i	−2.73781	−	3.03188i
$861$	−3.43218e11	−	2.49363e11i	−0.624536	−	0.453752i
$862$	−4.57099e10	+	2.88601e11i	−0.0827907	+	0.522720i
$863$	3.78732e11	+	5.99853e10i	0.682793	+	0.108144i	0.488189	−	0.872738i	$-0.337658\pi$
$863$	3.78732e11	+	5.99853e10i	0.682793	+	0.108144i	0.194604	+	0.980882i	$0.437658\pi$
$864$	1.56510e11	−	2.15418e11i	0.280859	−	0.386569i
$865$	2.43094e10	−	1.15180e11i	0.0434220	−	0.205737i
$866$	8.01410e11	−	5.82258e11i	1.42490	−	1.03525i
$867$	3.09464e10	+	6.07356e10i	0.0547688	+	0.107490i
$868$	2.23792e12	+	2.23792e12i	3.94245	+	3.94245i
$869$	9.09409e11	+	2.95485e11i	1.59470	+	0.518151i
$870$	−1.20040e10	+	3.14062e10i	−0.0209531	+	0.0548199i
$871$	1.20729e11	+	3.71565e11i	0.209767	+	0.645597i
$872$	9.25298e11	+	4.71463e11i	1.60035	+	0.815420i
$873$	−4.10472e10	−	2.59162e11i	−0.0706686	−	0.446184i
$874$			4.34617e11i			0.744837i
$875$	−8.40682e11	−	2.69155e11i	−1.43417	−	0.459166i
$876$	6.51963e11			1.10715
$877$	5.99759e11	−	9.49924e10i	1.01386	−	0.160580i	0.372672	−	0.927963i	$-0.378442\pi$
$877$	5.99759e11	−	9.49924e10i	1.01386	−	0.160580i	0.641188	+	0.767383i	$0.278442\pi$
$878$	1.76254e11	−	3.45918e11i	0.296593	−	0.582097i
$879$	−7.57074e10	+	2.45988e10i	−0.126819	+	0.0412058i
$880$	−2.17578e12	−	8.31620e11i	−3.62814	−	1.38674i
$881$	7.43118e10	−	2.28708e11i	0.123354	−	0.379646i	−0.870243	−	0.492622i	$-0.836038\pi$
$881$	7.43118e10	−	2.28708e11i	0.123354	−	0.379646i	0.993598	+	0.112977i	$0.0360385\pi$
$882$	3.39439e11	−	3.39439e11i	0.560903	−	0.560903i
$883$	−5.43365e10	+	2.76858e10i	−0.0893817	+	0.0455423i	−0.498110	−	0.867114i	$-0.665972\pi$
$883$	−5.43365e10	+	2.76858e10i	−0.0893817	+	0.0455423i	0.408728	+	0.912656i	$0.365972\pi$
$884$	1.26852e12	+	1.74597e12i	2.07725	+	2.85910i
$885$	2.52574e11	+	5.33072e10i	0.411733	+	0.0868986i
$886$	8.54123e11	+	6.20557e11i	1.38607	+	1.00704i
$887$	−1.15702e11	+	7.30511e11i	−0.186915	+	1.18014i	0.698595	+	0.715517i	$0.253809\pi$
$887$	−1.15702e11	+	7.30511e11i	−0.186915	+	1.18014i	−0.885510	+	0.464620i	$0.846191\pi$
$888$	−4.96387e11	−	7.86201e10i	−0.798305	−	0.126439i
$889$	−1.03401e11	+	1.42319e11i	−0.165546	+	0.227854i
$890$	−1.22190e12	+	1.10338e12i	−1.94749	+	1.75860i
$891$	−7.73018e10	+	5.61630e10i	−0.122653	+	0.0891127i
$892$	−6.08777e11	−	1.19479e12i	−0.961610	−	1.88727i
$893$	−4.48618e11	−	4.48618e11i	−0.705457	−	0.705457i
$894$	8.29105e11	+	2.69393e11i	1.29795	+	0.421731i
$895$	−5.80107e11	−	2.95666e10i	−0.904098	−	0.0460797i
$896$	2.76818e11	+	8.51957e11i	0.429499	+	1.32186i
$897$	1.19442e11	+	6.08589e10i	0.184497	+	0.0940058i
$898$	−4.65371e10	−	2.93824e11i	−0.0715639	−	0.451837i
$899$		−	5.18834e10i		−	0.0794309i
$900$	−1.16318e11	−	5.39607e11i	−0.177287	−	0.822446i
$901$	−3.14209e11			−0.476782
$902$	−1.48696e12	+	2.35511e11i	−2.24633	+	0.355783i
$903$	4.24753e11	−	8.33624e11i	0.638830	−	1.25377i
$904$	1.39376e12	−	4.52860e11i	2.08696	−	0.678095i
$905$	−9.07264e10	+	1.12367e11i	−0.135251	+	0.167512i
$906$	3.14988e11	−	9.69434e11i	0.467500	−	1.43882i
$907$	−5.43052e9	+	5.43052e9i	−0.00802439	+	0.00802439i	−0.711108	−	0.703083i	$-0.751806\pi$
$907$	−5.43052e9	+	5.43052e9i	−0.00802439	+	0.00802439i	0.703083	+	0.711108i	$0.251806\pi$
$908$	1.30185e12	−	6.63324e11i	1.91521	−	0.975848i
$909$	9.81621e10	+	1.35109e11i	0.143777	+	0.197892i
$910$	2.25372e12	−	1.00730e12i	3.28651	−	1.46891i
$911$	−6.69762e11	−	4.86611e11i	−0.972405	−	0.706494i	−0.0164066	−	0.999865i	$-0.505223\pi$
$911$	−6.69762e11	−	4.86611e11i	−0.972405	−	0.706494i	−0.955998	+	0.293372i	$0.905223\pi$
$912$	−2.50571e11	+	1.58204e12i	−0.362202	+	2.28686i
$913$	1.09485e12	+	1.73407e11i	1.57570	+	0.249566i
$914$	5.76704e11	−	7.93765e11i	0.826358	−	1.13738i
$915$	−2.95244e11	+	3.14602e10i	−0.421208	+	0.0448825i
$916$	1.90803e12	−	1.38626e12i	2.71021	−	1.96908i
$917$	7.80674e11	+	1.53216e12i	1.10406	+	2.16684i
$918$	1.99479e11	+	1.99479e11i	0.280884	+	0.280884i
$919$	1.12005e12	+	3.63927e11i	1.57028	+	0.510214i	0.959529	−	0.281610i	$-0.0908683\pi$
$919$	1.12005e12	+	3.63927e11i	1.57028	+	0.510214i	0.610749	+	0.791824i	$0.290868\pi$
$920$	1.50200e11	+	5.57350e11i	0.209661	+	0.777995i
$921$	1.21792e11	+	3.74837e11i	0.169270	+	0.520959i
$922$	−5.35331e11	−	2.72765e11i	−0.740795	−	0.377454i
$923$	1.34475e10	+	8.49040e10i	0.0185282	+	0.116983i
$924$		−	2.18259e12i		−	2.99422i
$925$	−2.77753e11	+	2.26244e11i	−0.379395	+	0.309037i
$926$	1.78830e12			2.43218
$927$	−3.33140e11	+	5.27642e10i	−0.451136	+	0.0714529i
$928$	4.52668e10	−	8.88411e10i	0.0610362	−	0.119790i
$929$	−1.24885e12	+	4.05775e11i	−1.67666	+	0.544781i	−0.984260	−	0.176728i	$-0.943449\pi$
$929$	−1.24885e12	+	4.05775e11i	−1.67666	+	0.544781i	−0.692405	+	0.721509i	$0.743449\pi$
$930$	6.49169e11	+	9.96497e11i	0.867813	+	1.33212i
$931$	−4.14606e11	+	1.27603e12i	−0.551870	+	1.69848i
$932$	−4.09425e11	+	4.09425e11i	−0.542639	+	0.542639i
$933$	2.07597e11	−	1.05776e11i	0.273964	−	0.139592i
$934$	3.77794e10	+	5.19989e10i	0.0496441	+	0.0683293i
$935$	5.71876e11	−	9.93813e11i	0.748266	−	1.30034i
$936$	7.54088e11	+	5.47877e11i	0.982468	+	0.713805i
$937$	−1.11062e11	+	7.01218e11i	−0.144081	+	0.909692i	0.804682	+	0.593705i	$0.202336\pi$
$937$	−1.11062e11	+	7.01218e11i	−0.144081	+	0.909692i	−0.948764	+	0.315987i	$0.897664\pi$
$938$	−1.15218e12	−	1.82487e11i	−1.48836	−	0.235733i
$939$	−1.44502e11	+	1.98890e11i	−0.185871	+	0.255830i
$940$	−1.20957e12	−	6.96029e11i	−1.54924	−	0.891489i
$941$	3.91507e11	−	2.84447e11i	0.499323	−	0.362779i	−0.309436	−	0.950920i	$-0.600140\pi$
$941$	3.91507e11	−	2.84447e11i	0.499323	−	0.362779i	0.808758	+	0.588141i	$0.200140\pi$
$942$	−2.52314e10	−	4.95194e10i	−0.0320433	−	0.0628886i
$943$	1.39829e11	+	1.39829e11i	0.176827	+	0.176827i
$944$	−1.56698e12	−	5.09144e11i	−1.97322	−	0.641139i
$945$	1.93651e11	−	1.26155e11i	0.242825	−	0.158189i
$946$	−1.02598e12	−	3.15764e12i	−1.28107	−	3.94274i
$947$	8.71180e11	+	4.43888e11i	1.08320	+	0.551917i	0.902091	−	0.431546i	$-0.142032\pi$
$947$	8.71180e11	+	4.43888e11i	1.08320	+	0.551917i	0.181107	+	0.983463i	$0.442032\pi$
$948$	−2.26260e11	−	1.42855e12i	−0.280139	−	1.76873i
$949$			7.84722e11i			0.967499i
$950$	1.36041e12	+	1.67013e12i	1.67023	+	2.05049i
$951$	−2.06896e11			−0.252947
$952$	−3.84299e12	+	6.08670e11i	−4.67866	+	0.741027i
$953$	2.67087e11	−	5.24187e11i	0.323803	−	0.635499i	−0.670521	−	0.741890i	$-0.733930\pi$
$953$	2.67087e11	−	5.24187e11i	0.323803	−	0.635499i	0.994324	+	0.106391i	$0.0339295\pi$
$954$	−2.13753e11	+	6.94526e10i	−0.258059	+	0.0838484i
$955$	−9.36947e9	+	2.52497e9i	−0.0112642	+	0.00303559i
$956$	−8.12463e11	+	2.50050e12i	−0.972684	+	2.99361i
$957$	−2.53002e10	+	2.53002e10i	−0.0301632	+	0.0301632i
$958$	1.30512e12	−	6.64992e11i	1.54949	−	0.789504i
$959$	−4.78982e11	−	6.59262e11i	−0.566298	−	0.779442i
$960$	9.42666e10	+	8.84661e11i	0.110987	+	1.04158i
$961$	−7.94741e11	−	5.77413e11i	−0.931820	−	0.677007i
$962$	1.56722e11	−	9.89501e11i	0.182991	−	1.15536i
$963$	−3.43207e11	−	5.43586e10i	−0.399071	−	0.0632067i
$964$	−3.16464e10	+	4.35575e10i	−0.0366451	+	0.0504376i
$965$	−2.79612e11	−	6.25599e11i	−0.322438	−	0.721418i
$966$	−3.23823e11	+	2.35271e11i	−0.371876	+	0.270184i
$967$	5.47463e11	+	1.07446e12i	0.626108	+	1.22881i	0.958346	+	0.285610i	$0.0921961\pi$
$967$	5.47463e11	+	1.07446e12i	0.626108	+	1.22881i	−0.332238	+	0.943195i	$0.607804\pi$
$968$	−1.53069e12	−	1.53069e12i	−1.74335	−	1.74335i
$969$	−7.49885e11	−	2.43652e11i	−0.850549	−	0.276360i
$970$	1.75238e12	+	1.41488e12i	1.97943	+	1.59821i
$971$	−1.79660e11	−	5.52937e11i	−0.202104	−	0.622011i	−0.999820	−	0.0189783i	$-0.993959\pi$
$971$	−1.79660e11	−	5.52937e11i	−0.202104	−	0.622011i	0.797716	−	0.603033i	$-0.206041\pi$
$972$	1.28776e11	+	6.56146e10i	0.144268	+	0.0735081i
$973$	−2.08317e11	−	1.31526e12i	−0.232420	−	1.46744i
$974$			3.11058e12i			3.45625i
$975$	6.49487e11	−	1.40004e11i	0.718707	−	0.154925i
$976$	1.89513e12			2.08852
$977$	−1.48006e12	+	2.34419e11i	−1.62443	+	0.257285i	−0.901226	−	0.433349i	$-0.857332\pi$
$977$	−1.48006e12	+	2.34419e11i	−1.62443	+	0.257285i	−0.723205	+	0.690633i	$0.757332\pi$
$978$	9.70074e10	−	1.90388e11i	0.106035	−	0.208105i
$979$	−1.66627e12	+	5.41403e11i	−1.81390	+	0.589373i
$980$	−1.50221e11	+	2.94739e12i	−0.162865	+	3.19546i
$981$	−5.98914e10	+	1.84327e11i	−0.0646679	+	0.199027i
$982$	7.00201e11	−	7.00201e11i	0.752969	−	0.752969i
$983$	7.40072e11	−	3.77086e11i	0.792611	−	0.403855i	−0.0103057	−	0.999947i	$-0.503280\pi$
$983$	7.40072e11	−	3.77086e11i	0.792611	−	0.403855i	0.802917	+	0.596092i	$0.203280\pi$
$984$	8.08196e11	+	1.11239e12i	0.862058	+	1.18652i
$985$	−1.07829e9	−	1.19411e9i	−0.00114549	−	0.00126853i
$986$	8.54629e10	+	6.20925e10i	0.0904212	+	0.0656948i
$987$	9.14043e10	−	5.77104e11i	0.0963159	−	0.608115i
$988$	−4.26151e12	−	6.74956e11i	−4.47235	−	0.708350i
$989$	−2.56334e11	+	3.52814e11i	−0.267930	+	0.368774i
$990$	1.69370e11	−	8.02487e11i	0.176317	−	0.835406i
$991$	9.15937e10	−	6.65467e10i	0.0949666	−	0.0689973i	−0.539289	−	0.842121i	$-0.681307\pi$
$991$	9.15937e10	−	6.65467e10i	0.0949666	−	0.0689973i	0.634255	+	0.773124i	$0.281307\pi$
$992$	−1.60120e12	−	3.14253e12i	−1.65348	−	3.24514i
$993$	7.31132e11	+	7.31132e11i	0.751967	+	0.751967i
$994$	−2.44111e11	−	7.93164e10i	−0.250058	−	0.0812489i
$995$	5.27871e11	−	1.38108e12i	0.538562	−	1.40905i
$996$	−5.18131e11	−	1.59464e12i	−0.526504	−	1.62041i
$997$	1.10518e11	+	5.63116e10i	0.111854	+	0.0569924i	0.509022	−	0.860753i	$-0.330007\pi$
$997$	1.10518e11	+	5.63116e10i	0.111854	+	0.0569924i	−0.397168	+	0.917746i	$0.630007\pi$
$998$	5.11517e11	+	3.22959e12i	0.515629	+	3.25556i
$999$		−	9.37956e10i		−	0.0941717i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.k.a.13.2	✓	320
25.2	odd	20	inner	75.9.k.a.52.2	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.9.k.a.13.2	✓	320	1.1	even	1	trivial
75.9.k.a.52.2	yes	320	25.2	odd	20	inner

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	75.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-29.6660 + 4.69863i) q^{2} +(21.2310 - 41.6683i) q^{3} +(614.522 - 199.670i) q^{4} +(-583.809 - 223.142i) q^{5} +(-434.056 + 1335.89i) q^{6} +(2556.62 - 2556.62i) q^{7} +(-10441.1 + 5320.03i) q^{8} +(-1285.49 - 1769.32i) q^{9} +O(q^{10})\)	\(q+(-29.6660 + 4.69863i) q^{2} +(21.2310 - 41.6683i) q^{3} +(614.522 - 199.670i) q^{4} +(-583.809 - 223.142i) q^{5} +(-434.056 + 1335.89i) q^{6} +(2556.62 - 2556.62i) q^{7} +(-10441.1 + 5320.03i) q^{8} +(-1285.49 - 1769.32i) q^{9} +(18367.7 + 3876.61i) q^{10} +(16161.9 + 11742.3i) q^{11} +(4727.03 - 29845.3i) q^{12} +(35922.6 + 5689.59i) q^{13} +(-63832.1 + 87857.4i) q^{14} +(-21692.8 + 19588.8i) q^{15} +(150927. - 109655. i) q^{16} +(41691.5 + 81824.1i) q^{17} +(46448.6 + 46448.6i) q^{18} +(-174610. - 56734.3i) q^{19} +(-403318. - 20556.2i) q^{20} +(-52250.3 - 160810. i) q^{21} +(-534631. - 272408. i) q^{22} +(12329.3 + 77843.9i) q^{23} +548014. i q^{24} +(291041. + 260544. i) q^{25} -1.09241e6 q^{26} +(-101017. + 15999.5i) q^{27} +(1.06062e6 - 2.08158e6i) q^{28} +(-36424.0 + 11834.9i) q^{29} +(551497. - 683046. i) q^{30} +(-418629. + 1.28841e6i) q^{31} +(-1.84093e6 + 1.84093e6i) q^{32} +(832414. - 424136. i) q^{33} +(-1.62128e6 - 2.23150e6i) q^{34} +(-2.06307e6 + 922090. i) q^{35} +(-1.14324e6 - 830613. i) q^{36} +(-143464. + 905794. i) q^{37} +(5.44656e6 + 862650. i) q^{38} +(999750. - 1.37604e6i) q^{39} +(7.28275e6 - 776026. i) q^{40} +(2.02985e6 - 1.47477e6i) q^{41} +(2.30564e6 + 4.52507e6i) q^{42} +(3.91263e6 + 3.91263e6i) q^{43} +(1.22764e7 + 3.98885e6i) q^{44} +(355669. + 1.31979e6i) q^{45} +(-731519. - 2.25138e6i) q^{46} +(3.07900e6 + 1.56883e6i) q^{47} +(-1.36479e6 - 8.61697e6i) q^{48} -7.30785e6i q^{49} +(-9.85820e6 - 6.36180e6i) q^{50} +4.29462e6 q^{51} +(2.32113e7 - 3.67631e6i) q^{52} +(-1.55334e6 + 3.04859e6i) q^{53} +(2.92158e6 - 949280. i) q^{54} +(-6.81525e6 - 1.04616e7i) q^{55} +(-1.30928e7 + 4.02954e7i) q^{56} +(-6.07118e6 + 6.07118e6i) q^{57} +(1.02495e6 - 522236. i) q^{58} +(-5.19118e6 - 7.14505e6i) q^{59} +(-9.41941e6 + 1.63691e7i) q^{60} +(8.21837e6 + 5.97099e6i) q^{61} +(6.36529e6 - 4.01889e7i) q^{62} +(-7.80999e6 - 1.23698e6i) q^{63} +(1.78913e7 - 2.46253e7i) q^{64} +(-1.97024e7 - 1.13375e7i) q^{65} +(-2.27015e7 + 1.64936e7i) q^{66} +(4.87671e6 + 9.57107e6i) q^{67} +(4.19582e7 + 4.19582e7i) q^{68} +(3.50538e6 + 1.13897e6i) q^{69} +(5.68704e7 - 3.70483e7i) q^{70} +(730369. + 2.24784e6i) q^{71} +(2.28348e7 + 1.16349e7i) q^{72} +(3.37520e6 + 2.13102e7i) q^{73} -2.75453e7i q^{74} +(1.70355e7 - 6.59553e6i) q^{75} -1.18630e8 q^{76} +(7.13405e7 - 1.12992e7i) q^{77} +(-2.31931e7 + 4.55190e7i) q^{78} +(4.55224e7 - 1.47911e7i) q^{79} +(-1.12581e8 + 3.03395e7i) q^{80} +(-1.47802e6 + 4.54887e6i) q^{81} +(-5.32881e7 + 5.32881e7i) q^{82} +(4.94404e7 - 2.51911e7i) q^{83} +(-6.42179e7 - 8.83884e7i) q^{84} +(-6.08148e6 - 5.70727e7i) q^{85} +(-1.34456e8 - 9.76879e7i) q^{86} +(-280181. + 1.76899e6i) q^{87} +(-2.31218e8 - 3.66213e7i) q^{88} +(-5.15493e7 + 7.09516e7i) q^{89} +(-1.67525e7 - 3.74817e7i) q^{90} +(1.06387e8 - 7.72945e7i) q^{91} +(2.31197e7 + 4.53750e7i) q^{92} +(4.47978e7 + 4.47978e7i) q^{93} +(-9.87127e7 - 3.20737e7i) q^{94} +(8.92793e7 + 7.20848e7i) q^{95} +(3.76234e7 + 1.15793e8i) q^{96} +(1.06901e8 + 5.44689e7i) q^{97} +(3.43369e7 + 2.16794e8i) q^{98} -4.36901e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 444 q^{5} - 4540 q^{7} - 17460 q^{8}+O(q^{10}) \) 320 * q + 444 * q^5 - 4540 * q^7 - 17460 * q^8	\( 320 q + 444 q^{5} - 4540 q^{7} - 17460 q^{8} + 25496 q^{10} - 22680 q^{12} - 133420 q^{13} + 59616 q^{15} + 1310720 q^{16} + 168000 q^{17} - 718900 q^{19} - 641844 q^{20} + 2257100 q^{22} + 1089120 q^{23} - 1459756 q^{25} + 1827840 q^{26} + 3260740 q^{28} + 3913800 q^{29} + 3585384 q^{30} - 641460 q^{32} - 1458000 q^{33} - 4121600 q^{34} + 853140 q^{35} - 22394880 q^{36} - 14553460 q^{37} + 17491260 q^{38} + 3203652 q^{40} + 8749440 q^{41} + 9643860 q^{42} - 23946520 q^{43} + 4277700 q^{44} - 2204496 q^{45} + 26491200 q^{47} - 3661200 q^{48} - 47100924 q^{50} - 169691020 q^{52} - 97028940 q^{53} + 27431764 q^{55} - 4714200 q^{57} + 179119320 q^{58} + 95587200 q^{59} + 38705364 q^{60} + 36738240 q^{61} - 296094660 q^{62} - 9928980 q^{63} - 59695100 q^{64} + 24018972 q^{65} - 88558160 q^{67} + 197811840 q^{68} + 220501420 q^{70} + 38185020 q^{72} + 110964400 q^{73} + 51345576 q^{75} - 97175880 q^{77} - 131709240 q^{78} - 138506200 q^{79} - 339741204 q^{80} + 382637520 q^{81} + 217169400 q^{82} + 862340400 q^{83} + 743029200 q^{84} + 619431268 q^{85} - 335756340 q^{87} - 1380992420 q^{88} - 1141686000 q^{89} - 265834224 q^{90} - 407198400 q^{92} + 402028920 q^{93} + 290042200 q^{94} + 1436174256 q^{95} - 165325860 q^{96} + 1057772920 q^{97} + 1077594720 q^{98}+O(q^{100}) \) 320 * q + 444 * q^5 - 4540 * q^7 - 17460 * q^8 + 25496 * q^10 - 22680 * q^12 - 133420 * q^13 + 59616 * q^15 + 1310720 * q^16 + 168000 * q^17 - 718900 * q^19 - 641844 * q^20 + 2257100 * q^22 + 1089120 * q^23 - 1459756 * q^25 + 1827840 * q^26 + 3260740 * q^28 + 3913800 * q^29 + 3585384 * q^30 - 641460 * q^32 - 1458000 * q^33 - 4121600 * q^34 + 853140 * q^35 - 22394880 * q^36 - 14553460 * q^37 + 17491260 * q^38 + 3203652 * q^40 + 8749440 * q^41 + 9643860 * q^42 - 23946520 * q^43 + 4277700 * q^44 - 2204496 * q^45 + 26491200 * q^47 - 3661200 * q^48 - 47100924 * q^50 - 169691020 * q^52 - 97028940 * q^53 + 27431764 * q^55 - 4714200 * q^57 + 179119320 * q^58 + 95587200 * q^59 + 38705364 * q^60 + 36738240 * q^61 - 296094660 * q^62 - 9928980 * q^63 - 59695100 * q^64 + 24018972 * q^65 - 88558160 * q^67 + 197811840 * q^68 + 220501420 * q^70 + 38185020 * q^72 + 110964400 * q^73 + 51345576 * q^75 - 97175880 * q^77 - 131709240 * q^78 - 138506200 * q^79 - 339741204 * q^80 + 382637520 * q^81 + 217169400 * q^82 + 862340400 * q^83 + 743029200 * q^84 + 619431268 * q^85 - 335756340 * q^87 - 1380992420 * q^88 - 1141686000 * q^89 - 265834224 * q^90 - 407198400 * q^92 + 402028920 * q^93 + 290042200 * q^94 + 1436174256 * q^95 - 165325860 * q^96 + 1057772920 * q^97 + 1077594720 * q^98

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