LMFDB - Embedded newform 38.8.e.a.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,8,Mod(5,38)]

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([16]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	38.e (of order $9$, 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:	$11.8706309684$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			17.3
Character	$\chi$	$=$	38.17
Dual form			38.8.e.a.9.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38919 - 7.87846i) q^{2} +(-9.71662 - 8.15321i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(424.315 - 154.438i) q^{5} +(-77.7330 + 65.2257i) q^{6} +(847.859 + 1468.54i) q^{7} +(-256.000 + 443.405i) q^{8} +(-351.831 - 1995.33i) q^{9} +O(q^{10})$	\(q+(1.38919 - 7.87846i) q^{2} +(-9.71662 - 8.15321i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(424.315 - 154.438i) q^{5} +(-77.7330 + 65.2257i) q^{6} +(847.859 + 1468.54i) q^{7} +(-256.000 + 443.405i) q^{8} +(-351.831 - 1995.33i) q^{9} +(-627.282 - 3557.49i) q^{10} +(-355.352 + 615.488i) q^{11} +(405.893 + 703.027i) q^{12} +(7814.84 - 6557.43i) q^{13} +(12747.6 - 4639.76i) q^{14} +(-5382.07 - 1958.91i) q^{15} +(3137.72 + 2632.86i) q^{16} +(3787.71 - 21481.2i) q^{17} -16208.9 q^{18} +(-28741.5 - 8233.82i) q^{19} -28899.0 q^{20} +(3734.95 - 21182.0i) q^{21} +(4355.45 + 3654.66i) q^{22} +(43010.3 + 15654.5i) q^{23} +(6102.63 - 2221.18i) q^{24} +(96344.8 - 80842.9i) q^{25} +(-40806.2 - 70678.4i) q^{26} +(-26719.9 + 46280.2i) q^{27} +(-18845.3 - 106877. i) q^{28} +(9277.13 + 52613.2i) q^{29} +(-22909.9 + 39681.2i) q^{30} +(-32572.1 - 56416.5i) q^{31} +(25101.7 - 21062.9i) q^{32} +(8471.03 - 3083.20i) q^{33} +(-163977. - 59682.7i) q^{34} +(586557. + 492180. i) q^{35} +(-22517.2 + 127701. i) q^{36} -262965. q^{37} +(-104797. + 215001. i) q^{38} -129398. q^{39} +(-40146.0 + 227679. i) q^{40} +(153856. + 129100. i) q^{41} +(-161693. - 58851.4i) q^{42} +(478934. - 174318. i) q^{43} +(34843.6 - 29237.2i) q^{44} +(-457442. - 792313. i) q^{45} +(183082. - 317108. i) q^{46} +(134281. + 761547. i) q^{47} +(-9021.77 - 51165.0i) q^{48} +(-1.02596e6 + 1.77701e6i) q^{49} +(-503077. - 871354. i) q^{50} +(-211944. + 177842. i) q^{51} +(-613524. + 223305. i) q^{52} +(1.20284e6 + 437799. i) q^{53} +(327498. + 274803. i) q^{54} +(-55726.5 + 316041. i) q^{55} -868208. q^{56} +(212139. + 314341. i) q^{57} +427399. q^{58} +(293665. - 1.66545e6i) q^{59} +(280800. + 235620. i) q^{60} +(-1.49554e6 - 544331. i) q^{61} +(-489724. + 178245. i) q^{62} +(2.63191e6 - 2.20844e6i) q^{63} +(-131072. - 227023. i) q^{64} +(2.30324e6 - 3.98932e6i) q^{65} +(-12523.1 - 71021.8i) q^{66} +(-220292. - 1.24934e6i) q^{67} +(-698002. + 1.20897e6i) q^{68} +(-290281. - 502781. i) q^{69} +(4.69245e6 - 3.93744e6i) q^{70} +(-4.78651e6 + 1.74215e6i) q^{71} +(974808. + 354801. i) q^{72} +(4.18395e6 + 3.51075e6i) q^{73} +(-365308. + 2.07176e6i) q^{74} -1.59527e6 q^{75} +(1.54829e6 + 1.12432e6i) q^{76} -1.20515e6 q^{77} +(-179758. + 1.01946e6i) q^{78} +(-4.40140e6 - 3.69321e6i) q^{79} +(1.73799e6 + 632578. i) q^{80} +(-3.52692e6 + 1.28369e6i) q^{81} +(1.23085e6 - 1.03280e6i) q^{82} +(1.52373e6 + 2.63918e6i) q^{83} +(-688280. + 1.19214e6i) q^{84} +(-1.71033e6 - 9.69975e6i) q^{85} +(-708027. - 4.01542e6i) q^{86} +(338824. - 586861. i) q^{87} +(-181940. - 315130. i) q^{88} +(-6.28700e6 + 5.27542e6i) q^{89} +(-6.87768e6 + 2.50327e6i) q^{90} +(1.62557e7 + 5.91659e6i) q^{91} +(-2.24399e6 - 1.88293e6i) q^{92} +(-143485. + 813745. i) q^{93} +6.18636e6 q^{94} +(-1.34671e7 + 945054. i) q^{95} -415634. q^{96} +(767151. - 4.35073e6i) q^{97} +(1.25749e7 + 1.05516e7i) q^{98} +(1.35313e6 + 492498. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 45 q^{3} + 360 q^{6} + 1806 q^{7} - 7680 q^{8} - 3105 q^{9}+O(q^{10}) $ 30 * q + 45 * q^3 + 360 * q^6 + 1806 * q^7 - 7680 * q^8 - 3105 * q^9	\( 30 q + 45 q^{3} + 360 q^{6} + 1806 q^{7} - 7680 q^{8} - 3105 q^{9} + 9786 q^{11} - 11130 q^{13} + 6144 q^{14} - 1818 q^{15} - 65250 q^{17} + 29040 q^{18} + 105906 q^{19} - 47616 q^{20} + 172854 q^{21} + 102336 q^{22} + 101004 q^{23} + 23040 q^{24} - 132756 q^{25} - 92112 q^{26} + 43659 q^{27} + 96384 q^{28} - 273912 q^{29} + 58710 q^{31} - 406965 q^{33} + 84960 q^{34} + 356100 q^{35} - 198720 q^{36} - 2598852 q^{37} - 219336 q^{38} + 1769844 q^{39} + 43377 q^{41} - 79056 q^{42} + 1126698 q^{43} + 818688 q^{44} - 912546 q^{45} - 530880 q^{46} + 588306 q^{47} - 368640 q^{48} - 2778285 q^{49} + 1665288 q^{50} + 3972045 q^{51} - 430080 q^{52} + 6520866 q^{53} - 486648 q^{54} - 1666818 q^{55} - 1849344 q^{56} - 6947844 q^{57} - 4573152 q^{58} - 970467 q^{59} + 4634496 q^{60} - 4037670 q^{61} + 755952 q^{62} + 7946472 q^{63} - 3932160 q^{64} + 1497690 q^{65} + 6499272 q^{66} - 4817025 q^{67} + 1472064 q^{68} + 10299876 q^{69} + 2848800 q^{70} - 25171290 q^{71} + 3179520 q^{72} + 1347750 q^{73} - 3123936 q^{74} + 8817984 q^{75} + 1583232 q^{76} - 11476764 q^{77} - 930960 q^{78} + 10777986 q^{79} - 5365035 q^{81} + 347016 q^{82} + 9745314 q^{83} + 877056 q^{84} + 29258556 q^{85} - 9338208 q^{86} + 25598802 q^{87} + 5010432 q^{88} - 20353740 q^{89} - 30112128 q^{90} + 19748724 q^{91} - 14097792 q^{92} - 18738174 q^{93} + 12376608 q^{94} - 20427204 q^{95} - 23005029 q^{97} + 14869008 q^{98} - 45819771 q^{99}+O(q^{100}) \) 30 * q + 45 * q^3 + 360 * q^6 + 1806 * q^7 - 7680 * q^8 - 3105 * q^9 + 9786 * q^11 - 11130 * q^13 + 6144 * q^14 - 1818 * q^15 - 65250 * q^17 + 29040 * q^18 + 105906 * q^19 - 47616 * q^20 + 172854 * q^21 + 102336 * q^22 + 101004 * q^23 + 23040 * q^24 - 132756 * q^25 - 92112 * q^26 + 43659 * q^27 + 96384 * q^28 - 273912 * q^29 + 58710 * q^31 - 406965 * q^33 + 84960 * q^34 + 356100 * q^35 - 198720 * q^36 - 2598852 * q^37 - 219336 * q^38 + 1769844 * q^39 + 43377 * q^41 - 79056 * q^42 + 1126698 * q^43 + 818688 * q^44 - 912546 * q^45 - 530880 * q^46 + 588306 * q^47 - 368640 * q^48 - 2778285 * q^49 + 1665288 * q^50 + 3972045 * q^51 - 430080 * q^52 + 6520866 * q^53 - 486648 * q^54 - 1666818 * q^55 - 1849344 * q^56 - 6947844 * q^57 - 4573152 * q^58 - 970467 * q^59 + 4634496 * q^60 - 4037670 * q^61 + 755952 * q^62 + 7946472 * q^63 - 3932160 * q^64 + 1497690 * q^65 + 6499272 * q^66 - 4817025 * q^67 + 1472064 * q^68 + 10299876 * q^69 + 2848800 * q^70 - 25171290 * q^71 + 3179520 * q^72 + 1347750 * q^73 - 3123936 * q^74 + 8817984 * q^75 + 1583232 * q^76 - 11476764 * q^77 - 930960 * q^78 + 10777986 * q^79 - 5365035 * q^81 + 347016 * q^82 + 9745314 * q^83 + 877056 * q^84 + 29258556 * q^85 - 9338208 * q^86 + 25598802 * q^87 + 5010432 * q^88 - 20353740 * q^89 - 30112128 * q^90 + 19748724 * q^91 - 14097792 * q^92 - 18738174 * q^93 + 12376608 * q^94 - 20427204 * q^95 - 23005029 * q^97 + 14869008 * q^98 - 45819771 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	1.38919	−	7.87846i	0.122788	−	0.696364i
$2$	1.38919	−	7.87846i	0.122788	−	0.696364i
$3$	−9.71662	−	8.15321i	−0.207774	−	0.174343i	0.532962	−	0.846139i	$-0.321079\pi$
$3$	−9.71662	−	8.15321i	−0.207774	−	0.174343i	−0.740736	+	0.671796i	$0.765523\pi$
$4$	−60.1403	−	21.8893i	−0.469846	−	0.171010i
$5$	424.315	−	154.438i	1.51807	−	0.552534i	0.557408	−	0.830238i	$-0.311796\pi$
$5$	424.315	−	154.438i	1.51807	−	0.552534i	0.960667	+	0.277704i	$0.0895736\pi$
$6$	−77.7330	+	65.2257i	−0.146918	+	0.123279i
$7$	847.859	+	1468.54i	0.934288	+	1.61823i	0.775899	+	0.630857i	$0.217296\pi$
$7$	847.859	+	1468.54i	0.934288	+	1.61823i	0.158388	+	0.987377i	$0.449370\pi$
$8$	−256.000	+	443.405i	−0.176777	+	0.306186i
$9$	−351.831	−	1995.33i	−0.160874	−	0.912360i
$10$	−627.282	−	3557.49i	−0.198364	−	1.12498i
$11$	−355.352	+	615.488i	−0.0804979	+	0.139426i	−0.903464	−	0.428664i	$-0.858984\pi$
$11$	−355.352	+	615.488i	−0.0804979	+	0.139426i	0.822966	+	0.568091i	$0.192318\pi$
$12$	405.893	+	703.027i	0.0678074	+	0.117446i
$13$	7814.84	−	6557.43i	0.986548	−	0.827812i	0.00148360	−	0.999999i	$-0.499528\pi$
$13$	7814.84	−	6557.43i	0.986548	−	0.827812i	0.985064	+	0.172187i	$0.0550833\pi$
$14$	12747.6	−	4639.76i	1.24160	−	0.451905i
$15$	−5382.07	−	1958.91i	−0.411747	−	0.149864i
$16$	3137.72	+	2632.86i	0.191511	+	0.160697i
$17$	3787.71	−	21481.2i	0.186984	−	1.06044i	−0.736395	−	0.676552i	$-0.763473\pi$
$17$	3787.71	−	21481.2i	0.186984	−	1.06044i	0.923379	−	0.383889i	$-0.125416\pi$
$18$	−16208.9			−0.655088
$19$	−28741.5	−	8233.82i	−0.961330	−	0.275400i
$19$	−28741.5	−	8233.82i	−0.961330	−	0.275400i
$20$	−28899.0			−0.807751
$21$	3734.95	−	21182.0i	0.0880071	−	0.499113i
$22$	4355.45	+	3654.66i	0.0872074	+	0.0731757i
$23$	43010.3	+	15654.5i	0.737098	+	0.268282i	0.683166	−	0.730263i	$-0.260603\pi$
$23$	43010.3	+	15654.5i	0.737098	+	0.268282i	0.0539315	+	0.998545i	$0.482825\pi$
$24$	6102.63	−	2221.18i	0.0901110	−	0.0327977i
$25$	96344.8	−	80842.9i	1.23321	−	1.03479i
$26$	−40806.2	−	70678.4i	−0.455323	−	0.788642i
$27$	−26719.9	+	46280.2i	−0.261253	+	0.452503i
$28$	−18845.3	−	106877.i	−0.162237	−	0.920094i
$29$	9277.13	+	52613.2i	0.0706351	+	0.400592i	0.999542	+	0.0302771i	$0.00963898\pi$
$29$	9277.13	+	52613.2i	0.0706351	+	0.400592i	−0.928906	+	0.370315i	$0.879250\pi$
$30$	−22909.9	+	39681.2i	−0.154917	+	0.268324i
$31$	−32572.1	−	56416.5i	−0.196372	−	0.340126i	0.750977	−	0.660328i	$-0.229583\pi$
$31$	−32572.1	−	56416.5i	−0.196372	−	0.340126i	−0.947349	+	0.320202i	$0.896249\pi$
$32$	25101.7	−	21062.9i	0.135419	−	0.113630i
$33$	8471.03	−	3083.20i	0.0410334	−	0.0149349i
$34$	−163977.	−	59682.7i	−0.715494	−	0.260419i
$35$	586557.	+	492180.i	2.31245	+	1.94037i
$36$	−22517.2	+	127701.i	−0.0804368	+	0.456180i
$37$	−262965.			−0.853479			−0.426739	−	0.904375i	$-0.640338\pi$
$37$	−262965.			−0.853479			−0.426739	+	0.904375i	$0.640338\pi$
$38$	−104797.	+	215001.i	−0.309818	+	0.635620i
$39$	−129398.			−0.349302
$40$	−40146.0	+	227679.i	−0.0991819	+	0.562489i
$41$	153856.	+	129100.i	0.348635	+	0.292539i	0.800242	−	0.599678i	$-0.204705\pi$
$41$	153856.	+	129100.i	0.348635	+	0.292539i	−0.451607	+	0.892217i	$0.649149\pi$
$42$	−161693.	−	58851.4i	−0.336758	−	0.122570i
$43$	478934.	−	174318.i	0.918620	−	0.334350i	0.160930	−	0.986966i	$-0.448551\pi$
$43$	478934.	−	174318.i	0.918620	−	0.334350i	0.757689	+	0.652616i	$0.226328\pi$
$44$	34843.6	−	29237.2i	0.0616650	−	0.0517431i
$45$	−457442.	−	792313.i	−0.748328	−	1.29614i
$46$	183082.	−	317108.i	0.277328	−	0.480347i
$47$	134281.	+	761547.i	0.188657	+	1.06993i	0.921166	+	0.389170i	$0.127238\pi$
$47$	134281.	+	761547.i	0.188657	+	1.06993i	−0.732509	+	0.680757i	$0.761651\pi$
$48$	−9021.77	−	51165.0i	−0.0117746	−	0.0667772i
$49$	−1.02596e6	+	1.77701e6i	−1.24579	+	2.15777i
$50$	−503077.	−	871354.i	−0.569166	−	0.985825i
$51$	−211944.	+	177842.i	−0.223731	+	0.187733i
$52$	−613524.	+	223305.i	−0.605090	+	0.220235i
$53$	1.20284e6	+	437799.i	1.10980	+	0.403933i	0.830919	−	0.556393i	$-0.187815\pi$
$53$	1.20284e6	+	437799.i	1.10980	+	0.403933i	0.278878	+	0.960326i	$0.410037\pi$
$54$	327498.	+	274803.i	0.283029	+	0.237489i
$55$	−55726.5	+	316041.i	−0.0451640	+	0.256138i
$56$	−868208.			−0.660641
$57$	212139.	+	314341.i	0.151725	+	0.224822i
$58$	427399.			0.287631
$59$	293665.	−	1.66545e6i	0.186153	−	1.05572i	−0.738313	−	0.674459i	$-0.764377\pi$
$59$	293665.	−	1.66545e6i	0.186153	−	1.05572i	0.924465	−	0.381266i	$-0.124512\pi$
$60$	280800.	+	235620.i	0.167830	+	0.140826i
$61$	−1.49554e6	−	544331.i	−0.843613	−	0.307050i	−0.116179	−	0.993228i	$-0.537065\pi$
$61$	−1.49554e6	−	544331.i	−0.843613	−	0.307050i	−0.727433	+	0.686178i	$0.759287\pi$
$62$	−489724.	+	178245.i	−0.260964	+	0.0949831i
$63$	2.63191e6	−	2.20844e6i	1.32611	−	1.11274i
$64$	−131072.	−	227023.i	−0.0625000	−	0.108253i
$65$	2.30324e6	−	3.98932e6i	1.04026	−	1.80178i
$66$	−12523.1	−	71021.8i	−0.00536175	−	0.0304080i
$67$	−220292.	−	1.24934e6i	−0.0894824	−	0.507480i	−0.996299	−	0.0859547i	$-0.972606\pi$
$67$	−220292.	−	1.24934e6i	−0.0894824	−	0.507480i	0.906817	−	0.421525i	$-0.138505\pi$
$68$	−698002.	+	1.20897e6i	−0.269200	+	0.466268i
$69$	−290281.	−	502781.i	−0.106377	−	0.184250i
$70$	4.69245e6	−	3.93744e6i	1.63515	−	1.37205i
$71$	−4.78651e6	+	1.74215e6i	−1.58714	+	0.577671i	−0.976741	−	0.214424i	$-0.931212\pi$
$71$	−4.78651e6	+	1.74215e6i	−1.58714	+	0.577671i	−0.610397	+	0.792095i	$0.708990\pi$
$72$	974808.	+	354801.i	0.307791	+	0.112027i
$73$	4.18395e6	+	3.51075e6i	1.25880	+	1.05626i	0.995809	+	0.0914597i	$0.0291533\pi$
$73$	4.18395e6	+	3.51075e6i	1.25880	+	1.05626i	0.262991	+	0.964798i	$0.415291\pi$
$74$	−365308.	+	2.07176e6i	−0.104797	+	0.594332i
$75$	−1.59527e6			−0.436638
$76$	1.54829e6	+	1.12432e6i	0.404581	+	0.293793i
$77$	−1.20515e6			−0.300833
$78$	−179758.	+	1.01946e6i	−0.0428900	+	0.243241i
$79$	−4.40140e6	−	3.69321e6i	−1.00438	−	0.842771i	−0.0167905	−	0.999859i	$-0.505345\pi$
$79$	−4.40140e6	−	3.69321e6i	−1.00438	−	0.842771i	−0.987585	+	0.157088i	$0.949789\pi$
$80$	1.73799e6	+	632578.i	0.379519	+	0.138134i
$81$	−3.52692e6	+	1.28369e6i	−0.737391	+	0.268389i
$82$	1.23085e6	−	1.03280e6i	0.246522	−	0.206857i
$83$	1.52373e6	+	2.63918e6i	0.292506	+	0.506635i	0.974402	−	0.224814i	$-0.0721776\pi$
$83$	1.52373e6	+	2.63918e6i	0.292506	+	0.506635i	−0.681896	+	0.731449i	$0.738844\pi$
$84$	−688280.	+	1.19214e6i	−0.126703	+	0.219456i
$85$	−1.71033e6	−	9.69975e6i	−0.302074	−	1.71314i
$86$	−708027.	−	4.01542e6i	−0.120034	−	0.680748i
$87$	338824.	−	586861.i	0.0551642	−	0.0955472i
$88$	−181940.	−	315130.i	−0.0284603	−	0.0492947i
$89$	−6.28700e6	+	5.27542e6i	−0.945320	+	0.793217i	−0.978503	−	0.206232i	$-0.933880\pi$
$89$	−6.28700e6	+	5.27542e6i	−0.945320	+	0.793217i	0.0331836	+	0.999449i	$0.489435\pi$
$90$	−6.87768e6	+	2.50327e6i	−0.994473	+	0.361959i
$91$	1.62557e7	+	5.91659e6i	2.26131	+	0.823051i
$92$	−2.24399e6	−	1.88293e6i	−0.300444	−	0.252102i
$93$	−143485.	+	813745.i	−0.0184977	+	0.104905i
$94$	6.18636e6			0.768224
$95$	−1.34671e7	+	945054.i	−1.61154	+	0.113090i
$96$	−415634.			−0.0479471
$97$	767151.	−	4.35073e6i	0.0853454	−	0.484018i	−0.911936	−	0.410332i	$-0.865413\pi$
$97$	767151.	−	4.35073e6i	0.0853454	−	0.484018i	0.997282	−	0.0736856i	$-0.0234761\pi$
$98$	1.25749e7	+	1.05516e7i	1.34962	+	1.13247i
$99$	1.35313e6	+	492498.i	0.140157	+	0.0510130i
$100$	−7.56380e6	+	2.75300e6i	−0.756380	+	0.275300i
$101$	−8.73713e6	+	7.33132e6i	−0.843809	+	0.708040i	−0.958417	−	0.285371i	$-0.907883\pi$
$101$	−8.73713e6	+	7.33132e6i	−0.843809	+	0.708040i	0.114608	+	0.993411i	$0.463439\pi$
$102$	1.10669e6	+	1.91685e6i	0.103259	+	0.178850i
$103$	−8.05826e6	+	1.39573e7i	−0.726626	+	1.25855i	0.231676	+	0.972793i	$0.425579\pi$
$103$	−8.05826e6	+	1.39573e7i	−0.726626	+	1.25855i	−0.958301	+	0.285759i	$0.907754\pi$
$104$	906998.	+	5.14384e6i	0.0790659	+	0.448405i
$105$	−1.68651e6	−	9.56465e6i	−0.142176	−	0.806318i
$106$	5.12016e6	−	8.86837e6i	0.417554	−	0.723225i
$107$	5.87265e6	+	1.01717e7i	0.463437	+	0.802696i	0.999129	−	0.0417167i	$-0.0132827\pi$
$107$	5.87265e6	+	1.01717e7i	0.463437	+	0.802696i	−0.535692	+	0.844413i	$0.679949\pi$
$108$	2.61998e6	−	2.19843e6i	0.200131	−	0.167930i
$109$	2.45623e6	−	893994.i	0.181667	−	0.0661213i	−0.249585	−	0.968353i	$-0.580294\pi$
$109$	2.45623e6	−	893994.i	0.181667	−	0.0661213i	0.431252	+	0.902232i	$0.358072\pi$
$110$	2.41250e6	+	878078.i	0.172820	+	0.0629012i
$111$	2.55514e6	+	2.14401e6i	0.177331	+	0.148798i
$112$	−1.20610e6	+	6.84014e6i	−0.0811187	+	0.460047i
$113$	−8.76741e6			−0.571606			−0.285803	−	0.958288i	$-0.592260\pi$
$113$	−8.76741e6			−0.571606			−0.285803	+	0.958288i	$0.592260\pi$
$114$	2.77122e6	−	1.23465e6i	0.175188	−	0.0780506i
$115$	2.06676e7			1.26720
$116$	593736.	−	3.36725e6i	0.0353176	−	0.200296i
$117$	−1.58337e7	−	1.32861e7i	−0.913972	−	0.766914i
$118$	−1.27133e7	−	4.62725e6i	−0.712312	−	0.259260i
$119$	3.47573e7	−	1.26506e7i	1.89074	−	0.688173i
$120$	2.24640e6	−	1.88496e6i	0.118673	−	0.0995788i
$121$	9.49104e6	+	1.64390e7i	0.487040	+	0.843578i
$122$	−6.36607e6	+	1.10264e7i	−0.317404	+	0.549760i
$123$	−442376.	−	2.50884e6i	−0.0214350	−	0.121564i
$124$	723979.	+	4.10589e6i	0.0340997	+	0.193389i
$125$	1.07568e7	−	1.86313e7i	0.492603	−	0.853214i
$126$	−1.37429e7	−	2.38033e7i	−0.612041	−	1.06009i
$127$	−5.20368e6	+	4.36641e6i	−0.225423	+	0.189152i	−0.748503	−	0.663131i	$-0.769227\pi$
$127$	−5.20368e6	+	4.36641e6i	−0.225423	+	0.189152i	0.523081	+	0.852283i	$0.324783\pi$
$128$	−1.97068e6	+	717268.i	−0.0830579	+	0.0302306i
$129$	−6.07487e6	−	2.21107e6i	−0.249157	−	0.0906856i
$130$	−2.82301e7	−	2.36879e7i	−1.12697	−	0.945636i
$131$	−1.68445e6	+	9.55299e6i	−0.0654649	+	0.371270i	0.934421	+	0.356170i	$0.115918\pi$
$131$	−1.68445e6	+	9.55299e6i	−0.0654649	+	0.371270i	−0.999886	+	0.0150996i	$0.995193\pi$
$132$	−576940.			−0.0218334
$133$	−1.22771e7	−	4.91891e7i	−0.452497	−	1.81296i
$134$	−1.01489e7			−0.364378
$135$	−4.19022e6	+	2.37639e7i	−0.146578	+	0.831285i
$136$	8.55520e6	+	7.17867e6i	0.291638	+	0.244713i
$137$	8.99401e6	+	3.27355e6i	0.298835	+	0.108767i	0.487086	−	0.873354i	$-0.338060\pi$
$137$	8.99401e6	+	3.27355e6i	0.298835	+	0.108767i	−0.188251	+	0.982121i	$0.560282\pi$
$138$	−4.36439e6	+	1.58851e6i	−0.141367	+	0.0514533i
$139$	−217852.	+	182800.i	−0.00688034	+	0.00577329i	−0.646221	−	0.763150i	$-0.723652\pi$
$139$	−217852.	+	182800.i	−0.00688034	+	0.00577329i	0.639341	+	0.768923i	$0.279207\pi$
$140$	−2.45023e7	−	4.24392e7i	−0.754672	−	1.30713i
$141$	4.90430e6	−	8.49449e6i	0.147336	−	0.255194i
$142$	7.07609e6	+	4.01305e7i	0.207388	+	1.17616i
$143$	1.25900e6	+	7.14013e6i	0.0360039	+	0.204188i
$144$	4.14948e6	−	7.18711e6i	0.115804	−	0.200579i
$145$	1.20619e7	+	2.08918e7i	0.328570	+	0.569100i
$146$	3.34716e7	−	2.80860e7i	0.890106	−	0.746887i
$147$	2.44572e7	−	8.90170e6i	0.635033	−	0.231133i
$148$	1.58148e7	+	5.75613e6i	0.401004	+	0.145953i
$149$	−1.01595e7	−	8.52487e6i	−0.251607	−	0.211123i	0.508257	−	0.861205i	$-0.330290\pi$
$149$	−1.01595e7	−	8.52487e6i	−0.251607	−	0.211123i	−0.759864	+	0.650082i	$0.774734\pi$
$150$	−2.21613e6	+	1.25683e7i	−0.0536138	+	0.304059i
$151$	3.53117e7			0.834640			0.417320	−	0.908760i	$-0.362969\pi$
$151$	3.53117e7			0.834640			0.417320	+	0.908760i	$0.362969\pi$
$152$	1.10087e7	−	1.06363e7i	0.254264	−	0.245662i
$153$	−4.41947e7			−0.997585
$154$	−1.67418e6	+	9.49476e6i	−0.0369386	+	0.209489i
$155$	−2.25337e7	−	1.89080e7i	−0.486039	−	0.407835i
$156$	7.78203e6	+	2.83243e6i	0.164118	+	0.0597342i
$157$	6.20833e7	−	2.25965e7i	1.28034	−	0.466007i	0.389797	−	0.920901i	$-0.372545\pi$
$157$	6.20833e7	−	2.25965e7i	1.28034	−	0.466007i	0.890546	+	0.454894i	$0.150323\pi$
$158$	−3.52112e7	+	2.95457e7i	−0.710200	+	0.595929i
$159$	−8.11811e6	−	1.40610e7i	−0.160164	−	0.277412i
$160$	7.39814e6	−	1.28139e7i	0.142792	−	0.247322i
$161$	1.34775e7	+	7.64349e7i	0.254519	+	1.44345i
$162$	5.21399e6	+	2.95700e7i	0.0963535	+	0.546448i
$163$	−9.85947e6	+	1.70771e7i	−0.178319	+	0.308857i	−0.941305	−	0.337558i	$-0.890399\pi$
$163$	−9.85947e6	+	1.70771e7i	−0.178319	+	0.308857i	0.762986	+	0.646415i	$0.223732\pi$
$164$	−6.42703e6	−	1.11319e7i	−0.113778	−	0.197069i
$165$	3.11822e6	−	2.61650e6i	0.0540397	−	0.0453447i
$166$	2.29094e7	−	8.33834e6i	0.388719	−	0.141482i
$167$	−1.04113e8	−	3.78940e7i	−1.72981	−	0.629598i	−0.731189	−	0.682175i	$-0.761034\pi$
$167$	−1.04113e8	−	3.78940e7i	−1.72981	−	0.629598i	−0.998617	+	0.0525767i	$0.983257\pi$
$168$	8.43605e6	+	7.07868e6i	0.137264	+	0.115178i
$169$	7.17566e6	−	4.06952e7i	0.114356	−	0.648545i
$170$	−7.87950e7			−1.23006
$171$	−6.31704e6	+	6.02458e7i	−0.0966111	+	0.921383i
$172$	−3.26189e7			−0.488787
$173$	−1.90060e7	+	1.07788e8i	−0.279080	+	1.58274i	0.446617	+	0.894725i	$0.352629\pi$
$173$	−1.90060e7	+	1.07788e8i	−0.279080	+	1.58274i	−0.725697	+	0.688015i	$0.758482\pi$
$174$	−4.15287e6	−	3.48467e6i	−0.0597622	−	0.0501464i
$175$	2.00407e8	+	7.29423e7i	2.82671	+	1.02884i
$176$	−2.73549e6	+	995636.i	−0.0378216	+	0.0137660i
$177$	−1.64322e7	+	1.37883e7i	−0.222736	+	0.186898i
$178$	3.28284e7	+	5.68605e7i	0.436294	+	0.755684i
$179$	7.00887e6	−	1.21397e7i	0.0913402	−	0.158206i	−0.816735	−	0.577013i	$-0.804218\pi$
$179$	7.00887e6	−	1.21397e7i	0.0913402	−	0.158206i	0.908075	+	0.418807i	$0.137552\pi$
$180$	1.01675e7	+	5.76630e7i	0.129946	+	0.736959i
$181$	−1.52026e7	−	8.62180e7i	−0.190564	−	1.08074i	−0.918595	−	0.395200i	$-0.870675\pi$
$181$	−1.52026e7	−	8.62180e7i	−0.190564	−	1.08074i	0.728031	−	0.685544i	$-0.240436\pi$
$182$	6.91958e7	−	1.19851e8i	0.850805	−	1.47364i
$183$	1.00935e7	+	1.74825e7i	0.121749	+	0.210875i
$184$	−1.79519e7	+	1.50634e7i	−0.212446	+	0.178263i
$185$	−1.11580e8	+	4.06119e7i	−1.29564	+	0.471576i
$186$	6.21173e6	+	2.26089e6i	0.0707811	+	0.0257622i
$187$	1.18754e7	+	9.96467e6i	0.132802	+	0.111434i
$188$	8.59400e6	−	4.87390e7i	0.0943285	−	0.534964i
$189$	−9.06188e7			−0.976342
$190$	−1.12627e7	+	1.07413e8i	−0.119125	+	1.13610i
$191$	2.19089e7			0.227512			0.113756	−	0.993509i	$-0.463712\pi$
$191$	2.19089e7			0.227512			0.113756	+	0.993509i	$0.463712\pi$
$192$	−577393.	+	3.27456e6i	−0.00588731	+	0.0333886i
$193$	−1.21321e8	−	1.01800e8i	−1.21475	−	1.01929i	−0.999083	−	0.0428253i	$-0.986364\pi$
$193$	−1.21321e8	−	1.01800e8i	−1.21475	−	1.01929i	−0.215664	−	0.976468i	$-0.569191\pi$
$194$	−3.32114e7	−	1.20879e7i	−0.326573	−	0.118863i
$195$	−5.49055e7	+	1.99840e7i	−0.530267	+	0.193001i
$196$	1.00599e8	−	8.44126e7i	0.954328	−	0.800776i
$197$	−1.07126e8	−	1.85548e8i	−0.998308	−	1.72912i	−0.549510	−	0.835487i	$-0.685185\pi$
$197$	−1.07126e8	−	1.85548e8i	−0.998308	−	1.72912i	−0.448799	−	0.893633i	$-0.648148\pi$
$198$	5.75987e6	−	9.97638e6i	0.0527332	−	0.0913366i
$199$	2.44989e7	+	1.38940e8i	0.220375	+	1.24981i	0.871333	+	0.490693i	$0.163256\pi$
$199$	2.44989e7	+	1.38940e8i	0.220375	+	1.24981i	−0.650958	+	0.759114i	$0.725633\pi$
$200$	1.11819e7	+	6.34155e7i	0.0988347	+	0.560519i
$201$	−8.04564e6	+	1.39355e7i	−0.0698835	+	0.121042i
$202$	4.56221e7	+	7.90197e7i	0.389444	+	0.674537i
$203$	−6.93987e7	+	5.82324e7i	−0.582257	+	0.488572i
$204$	1.66392e7	−	6.05619e6i	0.137223	−	0.0499452i
$205$	8.52214e7	+	3.10180e7i	0.690892	+	0.251464i
$206$	9.87677e7	+	8.28759e7i	0.787190	+	0.660531i
$207$	1.61035e7	−	9.13275e7i	0.126190	−	0.715658i
$208$	4.17855e7			0.321962
$209$	1.52812e7	−	1.47642e7i	0.115783	−	0.111866i
$210$	−7.76976e7			−0.578949
$211$	5.91889e6	−	3.35677e7i	0.0433762	−	0.245999i	−0.955408	−	0.295288i	$-0.904584\pi$
$211$	5.91889e6	−	3.35677e7i	0.0433762	−	0.245999i	0.998785	+	0.0492892i	$0.0156956\pi$
$212$	−6.27563e7	−	5.26588e7i	−0.452357	−	0.379573i
$213$	6.07128e7	+	2.20977e7i	0.430479	+	0.156681i
$214$	8.82957e7	−	3.21370e7i	0.615874	−	0.224160i
$215$	1.76297e8	−	1.47931e8i	1.20979	−	1.01514i
$216$	−1.36806e7	−	2.36955e7i	−0.0923669	−	0.159984i
$217$	5.52331e7	−	9.56665e7i	0.366936	−	0.635552i
$218$	−3.63114e6	−	2.05932e7i	−0.0237381	−	0.134625i
$219$	−1.20300e7	−	6.82253e7i	−0.0773944	−	0.438926i
$220$	1.02693e7	−	1.77870e7i	0.0650222	−	0.112622i
$221$	−1.11261e8	−	1.92709e8i	−0.693377	−	1.20096i
$222$	2.04411e7	−	1.71521e7i	0.125392	−	0.105216i
$223$	−9.20381e7	+	3.34991e7i	−0.555777	+	0.202286i	−0.604611	−	0.796521i	$-0.706672\pi$
$223$	−9.20381e7	+	3.34991e7i	−0.555777	+	0.202286i	0.0488343	+	0.998807i	$0.484449\pi$
$224$	5.22143e7	+	1.90045e7i	0.310400	+	0.112976i
$225$	−1.95205e8	−	1.63797e8i	−1.14249	−	0.958664i
$226$	−1.21796e7	+	6.90737e7i	−0.0701863	+	0.398046i
$227$	1.17072e8			0.664297			0.332149	−	0.943227i	$-0.392226\pi$
$227$	1.17072e8			0.664297			0.332149	+	0.943227i	$0.392226\pi$
$228$	−5.87739e6	−	2.35481e7i	−0.0328407	−	0.131578i
$229$	2.85904e7			0.157324			0.0786621	−	0.996901i	$-0.474935\pi$
$229$	2.85904e7			0.157324			0.0786621	+	0.996901i	$0.474935\pi$
$230$	2.87111e7	−	1.62829e8i	0.155597	−	0.882436i
$231$	1.17100e7	+	9.82588e6i	0.0625052	+	0.0524481i
$232$	−2.57039e7	−	9.35546e6i	−0.135142	−	0.0491878i
$233$	1.81468e8	−	6.60491e7i	0.939842	−	0.342075i	0.173739	−	0.984792i	$-0.444415\pi$
$233$	1.81468e8	−	6.60491e7i	0.939842	−	0.342075i	0.766104	+	0.642717i	$0.222193\pi$
$234$	−1.26670e8	+	1.06289e8i	−0.646276	+	0.542290i
$235$	1.74589e8	+	3.02398e8i	0.877567	+	1.51999i
$236$	−5.41167e7	+	9.37329e7i	−0.268003	+	0.464194i
$237$	1.26552e7	+	7.17711e7i	0.0617517	+	0.350211i
$238$	−5.13831e7	−	2.91408e8i	−0.247059	−	1.40114i
$239$	6.31538e7	−	1.09386e8i	0.299231	−	0.518284i	−0.676729	−	0.736232i	$-0.736603\pi$
$239$	6.31538e7	−	1.09386e8i	0.299231	−	0.518284i	0.975960	+	0.217948i	$0.0699365\pi$
$240$	−1.17299e7	−	2.03168e7i	−0.0547715	−	0.0948670i
$241$	1.61799e8	−	1.35766e8i	0.744589	−	0.624784i	−0.189477	−	0.981885i	$-0.560679\pi$
$241$	1.61799e8	−	1.35766e8i	0.744589	−	0.624784i	0.934066	+	0.357101i	$0.116235\pi$
$242$	1.42698e8	−	5.19380e7i	0.647240	−	0.235576i
$243$	1.54560e8	+	5.62554e7i	0.690997	+	0.251502i
$244$	7.80271e7	+	6.54725e7i	0.343860	+	0.288533i
$245$	−1.60891e8	+	9.12460e8i	−0.698958	+	3.96399i
$246$	−2.03804e7			−0.0872848
$247$	−2.78603e8	+	1.24125e8i	−1.17638	+	0.524105i
$248$	3.33538e7			0.138856
$249$	6.71227e6	−	3.80672e7i	0.0275532	−	0.156262i
$250$	−1.31843e8	−	1.10629e8i	−0.533662	−	0.447795i
$251$	−2.85510e8	−	1.03917e8i	−1.13963	−	0.414790i	−0.297848	−	0.954613i	$-0.596269\pi$
$251$	−2.85510e8	−	1.03917e8i	−1.13963	−	0.414790i	−0.841779	+	0.539823i	$0.818491\pi$
$252$	−2.06625e8	+	7.52054e7i	−0.813357	+	0.296038i
$253$	−2.49189e7	+	2.09095e7i	−0.0967404	+	0.0811748i
$254$	2.71717e7	+	4.70627e7i	0.104040	+	0.180202i
$255$	−6.24655e7	+	1.08193e8i	−0.235912	+	0.408611i
$256$	2.91333e6	+	1.65223e7i	0.0108530	+	0.0615505i
$257$	−4.66050e7	−	2.64310e8i	−0.171264	−	0.971287i	−0.942368	−	0.334578i	$-0.891406\pi$
$257$	−4.66050e7	−	2.64310e8i	−0.171264	−	0.971287i	0.771104	−	0.636709i	$-0.219705\pi$
$258$	−2.58589e7	+	4.47890e7i	−0.0937437	+	0.162369i
$259$	−2.22958e8	−	3.86174e8i	−0.797395	−	1.38113i
$260$	−2.25841e8	+	1.89503e8i	−0.796885	+	0.668666i
$261$	1.01717e8	−	3.70219e7i	0.354120	−	0.128889i
$262$	7.29228e7	+	2.65417e7i	0.250501	+	0.0911748i
$263$	−9.73753e7	−	8.17076e7i	−0.330068	−	0.276960i	0.462659	−	0.886536i	$-0.346895\pi$
$263$	−9.73753e7	−	8.17076e7i	−0.330068	−	0.276960i	−0.792728	+	0.609576i	$0.791340\pi$
$264$	−801476.	+	4.54540e6i	−0.00268088	+	0.0152040i
$265$	5.77997e8			1.90794
$266$	−4.04590e8	+	2.83921e7i	−1.31804	+	0.0924937i
$267$	1.04100e8			0.334705
$268$	−1.40987e7	+	7.99578e7i	−0.0447412	+	0.253740i
$269$	3.00091e8	+	2.51806e8i	0.939982	+	0.788739i	0.977582	−	0.210554i	$-0.0675269\pi$
$269$	3.00091e8	+	2.51806e8i	0.939982	+	0.788739i	−0.0376001	+	0.999293i	$0.511971\pi$
$270$	1.81402e8	+	6.60250e7i	0.560879	+	0.204143i
$271$	−4.55757e7	+	1.65882e7i	−0.139104	+	0.0506299i	−0.410634	−	0.911800i	$-0.634693\pi$
$271$	−4.55757e7	+	1.65882e7i	−0.139104	+	0.0506299i	0.271530	+	0.962430i	$0.412470\pi$
$272$	6.84416e7	−	5.74294e7i	0.206219	−	0.173039i
$273$	−1.09711e8	−	1.90025e8i	−0.326349	−	0.565252i
$274$	3.82849e7	−	6.63114e7i	0.112435	−	0.194743i
$275$	1.55215e7	+	8.80267e7i	0.0450059	+	0.255241i
$276$	6.45206e6	+	3.65914e7i	0.0184721	+	0.104761i
$277$	−1.55678e8	+	2.69642e8i	−0.440097	+	0.762270i	−0.997696	−	0.0678401i	$-0.978389\pi$
$277$	−1.55678e8	+	2.69642e8i	−0.440097	+	0.762270i	0.557599	+	0.830110i	$0.311723\pi$
$278$	1.13754e6	+	1.97028e6i	0.00317549	+	0.00550011i
$279$	−1.01110e8	+	8.48412e7i	−0.278727	+	0.233879i
$280$	−3.68393e8	+	1.34084e8i	−1.00290	+	0.365027i
$281$	4.13820e8	+	1.50618e8i	1.11260	+	0.404954i	0.831947	−	0.554855i	$-0.187226\pi$
$281$	4.13820e8	+	1.50618e8i	1.11260	+	0.404954i	0.280654	+	0.959809i	$0.409449\pi$
$282$	−6.01105e7	−	5.04387e7i	−0.159617	−	0.133934i
$283$	−6.84305e7	+	3.88089e8i	−0.179472	+	1.01784i	0.753382	+	0.657583i	$0.228421\pi$
$283$	−6.84305e7	+	3.88089e8i	−0.179472	+	1.01784i	−0.932854	+	0.360254i	$0.882690\pi$
$284$	3.25997e8			0.844498
$285$	1.38560e8	+	1.00617e8i	0.354552	+	0.257463i
$286$	5.80023e7			0.146610
$287$	−5.91404e7	+	3.35402e8i	−0.147672	+	0.837489i
$288$	−5.08590e7	−	4.26757e7i	−0.125457	−	0.105271i
$289$	−6.15017e7	−	2.23848e7i	−0.149880	−	0.0545520i
$290$	1.81352e8	−	6.60066e7i	0.436645	−	0.158926i
$291$	−4.29266e7	+	3.60197e7i	−0.102118	+	0.0856869i
$292$	−1.74776e8	−	3.02721e8i	−0.410811	−	0.711546i
$293$	−2.63024e8	+	4.55571e8i	−0.610884	+	1.05808i	0.380207	+	0.924901i	$0.375853\pi$
$293$	−2.63024e8	+	4.55571e8i	−0.610884	+	1.05808i	−0.991092	+	0.133181i	$0.957481\pi$
$294$	−3.61561e7	−	2.05051e8i	−0.0829786	−	0.470595i
$295$	−1.32603e8	−	7.52030e8i	−0.300730	−	1.70553i
$296$	6.73192e7	−	1.16600e8i	0.150875	−	0.261323i
$297$	−1.89899e7	−	3.28915e7i	−0.0420606	−	0.0728512i
$298$	−8.12763e7	+	6.81989e7i	−0.177913	+	0.149287i
$299$	4.38771e8	−	1.59700e8i	0.949269	−	0.345506i
$300$	9.59404e7	+	3.49194e7i	0.205153	+	0.0746694i
$301$	6.62060e8	+	5.55534e8i	1.39931	+	1.17416i
$302$	4.90545e7	−	2.78202e8i	0.102484	−	0.581214i
$303$	1.44669e8			0.298763
$304$	−6.85044e7	−	1.01508e8i	−0.139849	−	0.207225i
$305$	−7.18644e8			−1.45032
$306$	−6.13946e7	+	3.48186e8i	−0.122491	+	0.694683i
$307$	−2.82358e8	−	2.36927e8i	−0.556950	−	0.467337i	0.320336	−	0.947304i	$-0.396204\pi$
$307$	−2.82358e8	−	2.36927e8i	−0.556950	−	0.467337i	−0.877286	+	0.479967i	$0.840649\pi$
$308$	7.24784e7	+	2.63800e7i	0.141345	+	0.0514454i
$309$	1.92096e8	−	6.99172e7i	0.370394	−	0.134812i
$310$	−1.80269e8	+	1.51264e8i	−0.343681	+	0.288383i
$311$	−7.94819e7	−	1.37667e8i	−0.149833	−	0.259518i	0.781333	−	0.624115i	$-0.214540\pi$
$311$	−7.94819e7	−	1.37667e8i	−0.149833	−	0.259518i	−0.931166	+	0.364597i	$0.881207\pi$
$312$	3.31259e7	−	5.73757e7i	0.0617485	−	0.106951i
$313$	−3.79921e7	−	2.15464e8i	−0.0700307	−	0.397164i	−0.999594	−	0.0285007i	$-0.990927\pi$
$313$	−3.79921e7	−	2.15464e8i	−0.0700307	−	0.397164i	0.929563	−	0.368663i	$-0.120184\pi$
$314$	−9.17803e7	−	5.20512e8i	−0.167300	−	0.948805i
$315$	7.75693e8	−	1.34354e9i	1.39831	−	2.42194i
$316$	1.83860e8	+	3.18454e8i	0.327780	+	0.567731i
$317$	2.05188e8	−	1.72173e8i	0.361780	−	0.303569i	−0.443720	−	0.896165i	$-0.646342\pi$
$317$	2.05188e8	−	1.72173e8i	0.361780	−	0.303569i	0.805500	+	0.592596i	$0.201897\pi$
$318$	−1.22056e8	+	4.44249e7i	−0.212846	+	0.0774696i
$319$	−3.56795e7	−	1.29863e7i	−0.0615391	−	0.0223984i
$320$	−9.06768e7	−	7.60869e7i	−0.154693	−	0.129803i
$321$	2.58699e7	−	1.46716e8i	0.0436544	−	0.247576i
$322$	6.20912e8			1.03642
$323$	−2.85737e8	+	5.86215e8i	−0.471799	+	0.967938i
$324$	2.40209e8			0.392358
$325$	2.22798e8	−	1.26355e9i	0.360013	−	2.04174i
$326$	1.20845e8	+	1.01401e8i	0.193182	+	0.162099i
$327$	−3.11552e7	−	1.13395e7i	−0.0492734	−	0.0179341i
$328$	−9.66309e7	+	3.51708e7i	−0.151202	+	0.0550330i
$329$	−1.00451e9	+	8.42882e8i	−1.55513	+	1.30491i
$330$	−1.62822e7	−	2.82016e7i	−0.0249410	−	0.0431991i
$331$	3.99452e8	−	6.91871e8i	0.605434	−	1.04864i	−0.386549	−	0.922269i	$-0.626333\pi$
$331$	3.99452e8	−	6.91871e8i	0.605434	−	1.04864i	0.991983	−	0.126373i	$-0.0403336\pi$
$332$	−3.38679e7	−	1.92074e8i	−0.0507931	−	0.288062i
$333$	9.25193e7	+	5.24703e8i	0.137302	+	0.778680i
$334$	−4.43179e8	+	7.67609e8i	−0.650829	+	1.12727i
$335$	−2.86419e8	−	4.96092e8i	−0.416241	−	0.720951i
$336$	6.74884e7	−	5.66295e7i	0.0970603	−	0.0814432i
$337$	−3.58551e8	+	1.30502e8i	−0.510324	+	0.185743i	−0.584332	−	0.811515i	$-0.698643\pi$
$337$	−3.58551e8	+	1.30502e8i	−0.510324	+	0.185743i	0.0740078	+	0.997258i	$0.476421\pi$
$338$	−3.10647e8	−	1.13066e8i	−0.437582	−	0.159267i
$339$	8.51896e7	+	7.14826e7i	0.118765	+	0.0996555i
$340$	−1.09461e8	+	6.20784e8i	−0.151037	+	0.856572i
$341$	4.62983e7			0.0632302
$342$	4.65869e8	+	1.33461e8i	0.629756	+	0.180411i
$343$	−2.08298e9			−2.78712
$344$	−4.53137e7	+	2.56987e8i	−0.0600171	+	0.340374i
$345$	−2.00819e8	−	1.68507e8i	−0.263292	−	0.220928i
$346$	8.22802e8	+	2.99475e8i	1.06790	+	0.388682i
$347$	8.04045e8	−	2.92649e8i	1.03306	−	0.376005i	0.230817	−	0.972997i	$-0.425860\pi$
$347$	8.04045e8	−	2.92649e8i	1.03306	−	0.376005i	0.802247	+	0.596992i	$0.203638\pi$
$348$	−3.32230e7	+	2.78774e7i	−0.0422582	+	0.0354589i
$349$	−4.58203e8	−	7.93631e8i	−0.576991	−	0.999377i	−0.995822	−	0.0913131i	$-0.970894\pi$
$349$	−4.58203e8	−	7.93631e8i	−0.576991	−	0.999377i	0.418832	−	0.908064i	$-0.362440\pi$
$350$	8.53076e8	−	1.47757e9i	1.06353	−	1.84209i
$351$	9.46674e7	+	5.36886e8i	0.116849	+	0.662685i
$352$	4.04398e6	+	2.29346e7i	0.00494208	+	0.0280279i
$353$	3.18673e8	−	5.51958e8i	0.385597	−	0.667873i	−0.606255	−	0.795270i	$-0.707329\pi$
$353$	3.18673e8	−	5.51958e8i	0.385597	−	0.667873i	0.991852	+	0.127397i	$0.0406622\pi$
$354$	8.58030e7	+	1.48615e8i	0.102800	+	0.178054i
$355$	−1.76193e9	+	1.47844e9i	−2.09021	+	1.75390i
$356$	4.93578e8	−	1.79648e8i	0.579803	−	0.211031i
$357$	−4.40867e8	−	1.60462e8i	−0.512824	−	0.186653i
$358$	−8.59056e7	−	7.20834e7i	−0.0989535	−	0.0830318i
$359$	−2.03430e6	+	1.15371e7i	−0.00232052	+	0.0131603i	−0.985946	−	0.167064i	$-0.946571\pi$
$359$	−2.03430e6	+	1.15371e7i	−0.00232052	+	0.0131603i	0.983626	+	0.180224i	$0.0576824\pi$
$360$	4.68420e8			0.529148
$361$	7.58280e8	+	4.73305e8i	0.848310	+	0.529500i
$362$	−7.00385e8			−0.775991
$363$	4.18095e7	−	2.37114e8i	0.0458777	−	0.260186i
$364$	−8.48113e8	−	7.11651e8i	−0.921720	−	0.773415i
$365$	2.31751e9	+	8.43503e8i	2.49457	+	0.907949i
$366$	1.51757e8	−	5.52350e7i	0.161795	−	0.0588886i
$367$	5.31463e8	−	4.45950e8i	0.561231	−	0.470929i	−0.317492	−	0.948261i	$-0.602841\pi$
$367$	5.31463e8	−	4.45950e8i	0.561231	−	0.470929i	0.878723	+	0.477332i	$0.158396\pi$
$368$	9.37382e7	+	1.62359e8i	0.0980504	+	0.169828i
$369$	2.03467e8	−	3.52415e8i	0.210815	−	0.365142i
$370$	1.64953e8	+	9.35497e8i	0.169299	+	0.960144i
$371$	3.76918e8	+	2.13761e9i	0.383212	+	2.17330i
$372$	2.64416e7	−	4.57981e7i	0.0266310	−	0.0461262i
$373$	−5.98557e8	−	1.03673e9i	−0.597207	−	1.03439i	−0.993231	−	0.116153i	$-0.962944\pi$
$373$	−5.98557e8	−	1.03673e9i	−0.597207	−	1.03439i	0.396025	−	0.918240i	$-0.370390\pi$
$374$	9.50035e7	−	7.97174e7i	0.0939050	−	0.0787957i
$375$	−2.56424e8	+	9.33308e7i	−0.251102	+	0.0913936i
$376$	−3.72050e8	−	1.35415e8i	−0.360947	−	0.131374i
$377$	4.17507e8	+	3.50330e8i	0.401299	+	0.336730i
$378$	−1.25886e8	+	7.13937e8i	−0.119883	+	0.679889i
$379$	9.05030e8			0.853937			0.426968	−	0.904267i	$-0.359582\pi$
$379$	9.05030e8			0.853937			0.426968	+	0.904267i	$0.359582\pi$
$380$	8.30601e8	+	2.37949e8i	0.776515	+	0.222454i
$381$	8.61624e7			0.0798143
$382$	3.04356e7	−	1.72609e8i	0.0279357	−	0.158431i
$383$	6.91275e7	+	5.80048e7i	0.0628717	+	0.0527556i	0.673682	−	0.739021i	$-0.264712\pi$
$383$	6.91275e7	+	5.80048e7i	0.0628717	+	0.0527556i	−0.610810	+	0.791777i	$0.709156\pi$
$384$	2.49964e7	+	9.09794e6i	0.0225277	+	0.00819943i
$385$	−5.11365e8	+	1.86122e8i	−0.456687	+	0.166220i
$386$	−9.70568e8	+	8.14403e8i	−0.858955	+	0.720749i
$387$	−5.16325e8	−	8.94301e8i	−0.452829	−	0.784324i
$388$	−1.41371e8	+	2.44862e8i	−0.122871	+	0.212819i
$389$	2.12246e8	+	1.20371e9i	0.182817	+	1.03681i	0.928729	+	0.370761i	$0.120903\pi$
$389$	2.12246e8	+	1.20371e9i	0.182817	+	1.03681i	−0.745912	+	0.666045i	$0.767986\pi$
$390$	8.11689e7	+	4.60332e8i	0.0692889	+	0.392957i
$391$	4.99187e8	−	8.64617e8i	0.422323	−	0.731484i
$392$	−5.25291e8	−	9.09831e8i	−0.440452	−	0.762886i
$393$	9.42547e7	−	7.90891e7i	0.0783302	−	0.0657268i
$394$	−1.61065e9	+	5.86230e8i	−1.32668	+	0.482871i
$395$	−2.43795e9	−	8.87342e8i	−1.99038	−	0.724438i
$396$	−7.05970e7	−	5.92379e7i	−0.0571286	−	0.0479366i
$397$	−3.87601e8	+	2.19820e9i	−0.310898	+	1.76319i	0.283452	+	0.958986i	$0.408520\pi$
$397$	−3.87601e8	+	2.19820e9i	−0.310898	+	1.76319i	−0.594351	+	0.804206i	$0.702591\pi$
$398$	1.12867e9			0.897380
$399$	−2.81757e8	+	5.78050e8i	−0.222060	+	0.455575i
$400$	5.15151e8			0.402461
$401$	−2.92801e8	+	1.66056e9i	−0.226760	+	1.28602i	0.632531	+	0.774535i	$0.282016\pi$
$401$	−2.92801e8	+	1.66056e9i	−0.226760	+	1.28602i	−0.859291	+	0.511487i	$0.829095\pi$
$402$	9.86131e7	+	8.27462e7i	0.0757083	+	0.0635268i
$403$	−6.24493e8	−	2.27297e8i	−0.475291	−	0.172992i
$404$	6.85931e8	−	2.49659e8i	0.517542	−	0.188370i
$405$	−1.29827e9	+	1.08938e9i	−0.971122	+	0.814868i
$406$	3.62374e8	+	6.27650e8i	0.268730	+	0.465454i
$407$	9.34453e7	−	1.61852e8i	0.0687032	−	0.118998i
$408$	−2.45985e7	−	1.39505e8i	−0.0179307	−	0.101690i
$409$	−2.79996e8	−	1.58794e9i	−0.202358	−	1.14763i	−0.901543	−	0.432690i	$-0.857565\pi$
$409$	−2.79996e8	−	1.58794e9i	−0.202358	−	1.14763i	0.699185	−	0.714941i	$-0.253546\pi$
$410$	3.62763e8	−	6.28324e8i	0.259944	−	0.450236i
$411$	−6.07014e7	−	1.05138e8i	−0.0431273	−	0.0746987i
$412$	7.90142e8	−	6.63008e8i	0.556628	−	0.467066i
$413$	2.69477e9	−	9.80814e8i	1.88233	−	0.685112i
$414$	−6.97150e8	−	2.53742e8i	−0.482864	−	0.175748i
$415$	1.05413e9	+	8.84520e8i	0.723979	+	0.607491i
$416$	5.80478e7	−	3.29206e8i	0.0395330	−	0.224203i
$417$	3.60719e6			0.00243609
$418$	−9.50905e7	−	1.40902e8i	−0.0636825	−	0.0943629i
$419$	2.01929e8			0.134107			0.0670533	−	0.997749i	$-0.478640\pi$
$419$	2.01929e8			0.134107			0.0670533	+	0.997749i	$0.478640\pi$
$420$	−1.07936e8	+	6.12137e8i	−0.0710878	+	0.403159i
$421$	3.90140e8	+	3.27367e8i	0.254820	+	0.213819i	0.761245	−	0.648465i	$-0.224589\pi$
$421$	3.90140e8	+	3.27367e8i	0.254820	+	0.213819i	−0.506425	+	0.862284i	$0.669033\pi$
$422$	−2.56239e8	−	9.32635e7i	−0.165979	−	0.0604113i
$423$	1.47229e9	−	5.35871e8i	0.945809	−	0.344246i
$424$	−5.02050e8	+	4.21270e8i	−0.319865	+	0.268399i
$425$	−1.37167e9	−	2.37581e9i	−0.866741	−	1.50124i
$426$	2.58437e8	−	4.47626e8i	0.161965	−	0.280531i
$427$	−4.68636e8	−	2.65777e9i	−0.291298	−	1.65204i
$428$	−1.30531e8	−	7.40279e8i	−0.0804750	−	0.456396i
$429$	4.59818e7	−	7.96429e7i	0.0281181	−	0.0487020i
$430$	−9.20560e8	−	1.59446e9i	−0.558357	−	0.967103i
$431$	−1.89330e9	+	1.58867e9i	−1.13907	+	0.955789i	−0.999408	−	0.0344105i	$-0.989045\pi$
$431$	−1.89330e9	+	1.58867e9i	−1.13907	+	0.955789i	−0.139658	+	0.990200i	$0.544600\pi$
$432$	−2.05689e8	+	7.48645e7i	−0.122749	+	0.0446769i
$433$	9.21258e8	+	3.35311e8i	0.545348	+	0.198490i	0.599978	−	0.800016i	$-0.295176\pi$
$433$	9.21258e8	+	3.35311e8i	0.545348	+	0.198490i	−0.0546304	+	0.998507i	$0.517398\pi$
$434$	−6.76976e8	−	5.68050e8i	−0.397520	−	0.333559i
$435$	5.31346e7	−	3.01341e8i	0.0309503	−	0.175528i
$436$	−1.67287e8			−0.0966629
$437$	−1.10729e9	−	8.04072e8i	−0.634709	−	0.460904i
$438$	−5.54222e8			−0.315155
$439$	6.08257e8	−	3.44960e9i	0.343132	−	1.94600i	0.0195182	−	0.999810i	$-0.493787\pi$
$439$	6.08257e8	−	3.44960e9i	0.343132	−	1.94600i	0.323614	−	0.946189i	$-0.395102\pi$
$440$	−1.25868e8	−	1.05616e8i	−0.0704419	−	0.0591078i
$441$	3.90669e9	+	1.42192e9i	2.16907	+	0.789478i
$442$	−1.67282e9	+	6.08855e8i	−0.921447	+	0.335379i
$443$	8.41111e7	−	7.05776e7i	0.0459664	−	0.0385704i	−0.619515	−	0.784985i	$-0.712671\pi$
$443$	8.41111e7	−	7.05776e7i	0.0459664	−	0.0385704i	0.665481	+	0.746414i	$0.268226\pi$
$444$	−1.06736e8	−	1.84872e8i	−0.0578722	−	0.100238i
$445$	−1.85294e9	+	3.20939e9i	−0.996786	+	1.72648i
$446$	1.36064e8	+	7.71655e8i	0.0726223	+	0.411862i
$447$	2.92113e7	+	1.65666e8i	0.0154695	+	0.0877317i
$448$	2.22261e8	−	3.84968e8i	0.116786	−	0.202279i
$449$	−7.20969e8	−	1.24876e9i	−0.375885	−	0.651051i	0.614574	−	0.788859i	$-0.289328\pi$
$449$	−7.20969e8	−	1.24876e9i	−0.375885	−	0.651051i	−0.990459	+	0.137808i	$0.955994\pi$
$450$	−1.56164e9	+	1.31037e9i	−0.807863	+	0.677878i
$451$	−1.34133e8	+	4.88204e7i	−0.0688521	+	0.0250601i
$452$	5.27275e8	+	1.91912e8i	0.268567	+	0.0977504i
$453$	−3.43110e8	−	2.87904e8i	−0.173416	−	0.145514i
$454$	1.62635e8	−	9.22347e8i	0.0815676	−	0.462593i
$455$	7.81128e9			3.88761
$456$	−1.93688e8	+	1.35921e7i	−0.0956589	+	0.00671287i
$457$	1.47968e9			0.725207			0.362604	−	0.931943i	$-0.381888\pi$
$457$	1.47968e9			0.725207			0.362604	+	0.931943i	$0.381888\pi$
$458$	3.97173e7	−	2.25248e8i	0.0193175	−	0.109555i
$459$	8.92945e8	+	7.49270e8i	0.431003	+	0.361655i
$460$	−1.24295e9	−	4.52398e8i	−0.595391	−	0.216705i
$461$	−7.80344e8	+	2.84022e8i	−0.370965	+	0.135020i	−0.520774	−	0.853695i	$-0.674356\pi$
$461$	−7.80344e8	+	2.84022e8i	−0.370965	+	0.135020i	0.149809	+	0.988715i	$0.452134\pi$
$462$	9.36803e7	−	7.86071e7i	0.0441978	−	0.0370864i
$463$	1.79631e9	+	3.11130e9i	0.841101	+	1.45683i	0.888965	+	0.457976i	$0.151425\pi$
$463$	1.79631e9	+	3.11130e9i	0.841101	+	1.45683i	−0.0478636	+	0.998854i	$0.515241\pi$
$464$	−1.09414e8	+	1.89511e8i	−0.0508464	+	0.0880686i
$465$	6.47903e7	+	3.67444e8i	0.0298830	+	0.169475i
$466$	−2.68272e8	−	1.52145e9i	−0.122807	−	0.696475i
$467$	1.31546e8	−	2.27844e8i	0.0597680	−	0.103521i	−0.834593	−	0.550867i	$-0.814297\pi$
$467$	1.31546e8	−	2.27844e8i	0.0597680	−	0.103521i	0.894361	+	0.447346i	$0.147631\pi$
$468$	6.61423e8	+	1.14562e9i	0.298276	+	0.516630i
$469$	1.64792e9	−	1.38277e9i	0.737619	−	0.618936i
$470$	2.62497e9	−	9.55409e8i	1.16622	−	0.424470i
$471$	−7.87474e8	−	2.86617e8i	−0.347267	−	0.126395i
$472$	6.63293e8	+	5.56569e8i	0.290341	+	0.243625i
$473$	−6.28997e7	+	3.56722e8i	−0.0273297	+	0.154994i
$474$	5.83026e8			0.251457
$475$	−3.43474e9	+	1.53026e9i	−1.47051	+	0.655146i
$476$	−2.36723e9			−1.00604
$477$	4.50357e8	−	2.55410e9i	0.189995	−	1.07752i
$478$	−7.74058e8	−	6.49512e8i	−0.324172	−	0.272013i
$479$	−3.68456e9	−	1.34107e9i	−1.53183	−	0.557541i	−0.567762	−	0.823192i	$-0.692191\pi$
$479$	−3.68456e9	−	1.34107e9i	−1.53183	−	0.557541i	−0.964069	+	0.265651i	$0.914413\pi$
$480$	−1.76360e8	+	6.41897e7i	−0.0727872	+	0.0264924i
$481$	−2.05503e9	+	1.72438e9i	−0.841998	+	0.706520i
$482$	−8.44855e8	−	1.46333e9i	−0.343651	−	0.595221i
$483$	4.92234e8	−	8.52575e8i	0.198773	−	0.344284i
$484$	−2.10957e8	−	1.19640e9i	−0.0845736	−	0.479641i
$485$	−3.46404e8	−	1.96456e9i	−0.137876	−	0.781931i
$486$	6.57919e8	−	1.13955e9i	0.259983	−	0.450304i
$487$	−1.37691e9	−	2.38487e9i	−0.540198	−	0.935650i	−0.998892	−	0.0470559i	$-0.985016\pi$
$487$	−1.37691e9	−	2.38487e9i	−0.540198	−	0.935650i	0.458695	−	0.888594i	$-0.348317\pi$
$488$	6.24217e8	−	5.23780e8i	0.243145	−	0.204023i
$489$	2.35034e8	−	8.55454e7i	0.0908971	−	0.0330838i
$490$	6.96527e9	+	2.53515e9i	2.67456	+	0.973459i
$491$	1.54836e9	+	1.29923e9i	0.590318	+	0.495336i	0.888317	−	0.459231i	$-0.151875\pi$
$491$	1.54836e9	+	1.29923e9i	0.590318	+	0.495336i	−0.297999	+	0.954566i	$0.596319\pi$
$492$	−2.83121e7	+	1.60566e8i	−0.0107175	+	0.0607820i
$493$	1.16533e9			0.438012
$494$	5.90880e8	+	2.36740e9i	0.220523	+	0.883541i
$495$	6.50212e8			0.240955
$496$	4.63346e7	−	2.62777e8i	0.0170498	−	0.0966944i
$497$	−6.61669e9	−	5.55206e9i	−2.41765	−	2.02865i
$498$	−2.90586e8	−	1.05765e8i	−0.105432	−	0.0383741i
$499$	8.07024e7	−	2.93733e7i	0.0290760	−	0.0105828i	−0.327441	−	0.944872i	$-0.606186\pi$
$499$	8.07024e7	−	2.93733e7i	0.0290760	−	0.0105828i	0.356517	+	0.934289i	$0.383964\pi$
$500$	−1.05474e9	+	8.85033e8i	−0.377356	+	0.316639i
$501$	7.02669e8	+	1.21706e9i	0.249643	+	0.432394i
$502$	−1.21533e9	+	2.10502e9i	−0.428777	+	0.742664i
$503$	2.69393e8	+	1.52780e9i	0.0943838	+	0.535277i	0.994934	+	0.100526i	$0.0320526\pi$
$503$	2.69393e8	+	1.52780e9i	0.0943838	+	0.535277i	−0.900551	+	0.434751i	$0.856836\pi$
$504$	3.05462e8	+	1.73236e9i	0.106280	+	0.602742i
$505$	−2.57506e9	+	4.46013e9i	−0.889749	+	1.54109i
$506$	1.30117e8	+	2.25370e8i	0.0446487	+	0.0773338i
$507$	−4.01520e8	+	3.36915e8i	−0.136829	+	0.114813i
$508$	4.08529e8	−	1.48692e8i	0.138261	−	0.0503229i
$509$	1.22881e9	+	4.47249e8i	0.413020	+	0.150327i	0.540169	−	0.841557i	$-0.318360\pi$
$509$	1.22881e9	+	4.47249e8i	0.413020	+	0.150327i	−0.127149	+	0.991884i	$0.540583\pi$
$510$	7.65622e8	+	6.42433e8i	0.255575	+	0.214453i
$511$	−1.60826e9	+	9.12090e9i	−0.533192	+	3.02388i
$512$	1.34218e8			0.0441942
$513$	1.14903e9	−	1.11016e9i	0.375770	−	0.363056i
$514$	−2.14710e9			−0.697398
$515$	−1.26370e9	+	7.16679e9i	−0.407679	+	2.31206i
$516$	3.16946e8	+	2.65949e8i	0.101557	+	0.0852166i
$517$	−5.16440e8	−	1.87969e8i	−0.164363	−	0.0598231i
$518$	−3.35219e9	+	1.22010e9i	−1.05968	+	0.385691i
$519$	1.06349e9	−	8.92377e8i	0.333925	−	0.280196i
$520$	1.17926e9	+	2.04253e9i	0.367787	+	0.637026i
$521$	8.88255e8	−	1.53850e9i	0.275173	−	0.476613i	−0.695006	−	0.719004i	$-0.744598\pi$
$521$	8.88255e8	−	1.53850e9i	0.275173	−	0.476613i	0.970179	+	0.242391i	$0.0779316\pi$
$522$	−1.50372e8	−	8.52802e8i	−0.0462722	−	0.262423i
$523$	−8.31644e8	−	4.71649e9i	−0.254204	−	1.44166i	−0.798109	−	0.602513i	$-0.794166\pi$
$523$	−8.31644e8	−	4.71649e9i	−0.254204	−	1.44166i	0.543905	−	0.839147i	$-0.316945\pi$
$524$	3.10411e8	−	5.37648e8i	0.0942493	−	0.163245i
$525$	−1.35257e9	−	2.34272e9i	−0.407945	−	0.706582i
$526$	−7.79003e8	+	6.53661e8i	−0.233394	+	0.195840i
$527$	−1.33527e9	+	4.85997e8i	−0.397403	+	0.144643i
$528$	3.46973e7	+	1.26288e7i	0.0102583	+	0.00373373i
$529$	−1.00342e9	−	8.41973e8i	−0.294707	−	0.247288i
$530$	8.02945e8	−	4.55373e9i	0.234272	−	1.32862i
$531$	−3.42645e9			−0.993148
$532$	−3.38364e8	+	3.22698e9i	−0.0974300	+	0.929194i
$533$	2.04893e9			0.586113
$534$	1.44614e8	−	8.20148e8i	0.0410976	−	0.233076i
$535$	4.06275e9	+	3.40905e9i	1.14705	+	0.962489i
$536$	6.10359e8	+	2.22152e8i	0.171202	+	0.0623124i
$537$	−1.67080e8	+	6.08122e7i	−0.0465602	+	0.0169465i
$538$	2.40073e9	−	2.01445e9i	0.664668	−	0.557722i
$539$	−7.29154e8	−	1.26293e9i	−0.200566	−	0.347391i
$540$	7.72177e8	−	1.33745e9i	0.211027	−	0.365510i
$541$	−5.50143e6	−	3.12002e7i	−0.00149378	−	0.00847162i	0.984052	−	0.177882i	$-0.0569247\pi$
$541$	−5.50143e6	−	3.12002e7i	−0.00149378	−	0.00847162i	−0.985546	+	0.169411i	$0.945814\pi$
$542$	6.73764e7	+	3.82110e8i	0.0181765	+	0.103084i
$543$	−5.55236e8	+	9.61698e8i	−0.148826	+	0.257774i
$544$	−3.57377e8	−	6.18995e8i	−0.0951766	−	0.164851i
$545$	9.04147e8	−	7.58670e8i	0.239250	−	0.200754i
$546$	−1.64952e9	+	6.00375e8i	−0.433693	+	0.157851i
$547$	2.13328e9	+	7.76451e8i	0.557304	+	0.202842i	0.605289	−	0.796006i	$-0.293058\pi$
$547$	2.13328e9	+	7.76451e8i	0.557304	+	0.202842i	−0.0479846	+	0.998848i	$0.515280\pi$
$548$	−4.69247e8	−	3.93745e8i	−0.121806	−	0.102208i
$549$	−5.59945e8	+	3.17561e9i	−0.144425	+	0.819075i
$550$	7.15078e8			0.183267
$551$	1.66569e8	−	1.58857e9i	0.0424192	−	0.404554i
$552$	2.97247e8			0.0752196
$553$	1.69185e9	−	9.59493e9i	0.425425	−	2.41270i
$554$	1.90810e9	+	1.60109e9i	0.476779	+	0.400065i
$555$	1.41530e9	+	5.15127e8i	0.351417	+	0.127905i
$556$	1.71031e7	−	6.22500e6i	0.00421999	−	0.00153595i
$557$	−2.03162e9	+	1.70473e9i	−0.498136	+	0.417986i	−0.856932	−	0.515430i	$-0.827632\pi$
$557$	−2.03162e9	+	1.70473e9i	−0.498136	+	0.417986i	0.358795	+	0.933416i	$0.383188\pi$
$558$	5.27958e8	+	9.14450e8i	0.128641	+	0.222813i
$559$	2.59971e9	−	4.50284e9i	0.629483	−	1.09030i
$560$	5.44611e8	+	3.08864e9i	0.131047	+	0.743206i
$561$	−3.41450e7	−	1.93646e8i	−0.00816502	−	0.0463061i
$562$	1.76151e9	−	3.05103e9i	0.418609	−	0.725052i
$563$	2.84292e9	+	4.92408e9i	0.671405	+	1.16291i	0.977506	+	0.210909i	$0.0676424\pi$
$563$	2.84292e9	+	4.92408e9i	0.671405	+	1.16291i	−0.306100	+	0.951999i	$0.599024\pi$
$564$	−4.80884e8	+	4.03510e8i	−0.112866	+	0.0947060i
$565$	−3.72014e9	+	1.35402e9i	−0.867741	+	0.315832i
$566$	2.96248e9	+	1.07825e9i	0.686749	+	0.249956i
$567$	−4.87548e9	−	4.09101e9i	−1.12325	−	0.942519i
$568$	4.52870e8	−	2.56835e9i	0.103694	−	0.588079i
$569$	−4.20361e9			−0.956598			−0.478299	−	0.878197i	$-0.658747\pi$
$569$	−4.20361e9			−0.956598			−0.478299	+	0.878197i	$0.658747\pi$
$570$	9.85194e8	−	9.51861e8i	0.222823	−	0.215284i
$571$	5.13828e9			1.15502			0.577512	−	0.816382i	$-0.304023\pi$
$571$	5.13828e9			1.15502			0.577512	+	0.816382i	$0.304023\pi$
$572$	8.05759e7	−	4.56969e8i	0.0180019	−	0.102094i
$573$	−2.12881e8	−	1.78628e8i	−0.0472711	−	0.0396651i
$574$	2.56029e9	+	9.31871e8i	0.565065	+	0.205667i
$575$	5.40937e9	−	1.96885e9i	1.18661	−	0.431892i
$576$	−4.06872e8	+	3.41406e8i	−0.0887113	+	0.0744376i
$577$	−3.11524e9	−	5.39575e9i	−0.675112	−	1.16933i	−0.976436	−	0.215807i	$-0.930762\pi$
$577$	−3.11524e9	−	5.39575e9i	−0.675112	−	1.16933i	0.301324	−	0.953522i	$-0.402571\pi$
$578$	−2.61795e8	+	4.53442e8i	−0.0563915	+	0.0976730i
$579$	3.48830e8	+	1.97831e9i	0.0746859	+	0.423565i
$580$	−2.68100e8	−	1.52047e9i	−0.0570556	−	0.323578i
$581$	−2.58382e9	+	4.47530e9i	−0.546569	+	0.946686i
$582$	2.24147e8	+	3.88233e8i	0.0471305	+	0.0816324i
$583$	−6.96893e8	+	5.84763e8i	−0.145655	+	0.122219i
$584$	−2.62778e9	+	9.56432e8i	−0.545938	+	0.198705i
$585$	−8.77037e9	−	3.19215e9i	−1.81122	−	0.659232i
$586$	3.22381e9	+	2.70510e9i	0.661802	+	0.555318i
$587$	1.92621e8	−	1.09241e9i	0.0393069	−	0.222921i	−0.958826	−	0.283993i	$-0.908341\pi$
$587$	1.92621e8	−	1.09241e9i	0.0393069	−	0.222921i	0.998133	+	0.0610720i	$0.0194519\pi$
$588$	−1.66572e9			−0.337894
$589$	4.71649e8	+	1.88969e9i	0.0951076	+	0.381055i
$590$	−6.10905e9			−1.22459
$591$	−4.71909e8	+	2.67633e9i	−0.0940377	+	0.533314i
$592$	−8.25111e8	−	6.92351e8i	−0.163451	−	0.137151i
$593$	1.48302e9	+	5.39774e8i	0.292048	+	0.106297i	0.483890	−	0.875129i	$-0.339224\pi$
$593$	1.48302e9	+	5.39774e8i	0.292048	+	0.106297i	−0.191841	+	0.981426i	$0.561446\pi$
$594$	−2.85515e8	+	1.03919e8i	−0.0558955	+	0.0203443i
$595$	1.27943e10	−	1.07357e10i	2.49005	−	2.08940i
$596$	4.24395e8	+	7.35073e8i	0.0821123	+	0.142223i
$597$	8.94764e8	−	1.54978e9i	0.172107	−	0.298098i
$598$	−6.48653e8	−	3.67870e9i	−0.124039	−	0.703461i
$599$	−7.23308e8	−	4.10208e9i	−0.137508	−	0.779849i	−0.973080	−	0.230468i	$-0.925974\pi$
$599$	−7.23308e8	−	4.10208e9i	−0.137508	−	0.779849i	0.835572	−	0.549382i	$-0.185137\pi$
$600$	4.08390e8	−	7.07353e8i	0.0771874	−	0.133692i
$601$	−3.96326e9	−	6.86457e9i	−0.744719	−	1.28989i	−0.950326	−	0.311256i	$-0.899250\pi$
$601$	−3.96326e9	−	6.86457e9i	−0.744719	−	1.28989i	0.205607	−	0.978635i	$-0.434083\pi$
$602$	5.29648e9	−	4.44427e9i	0.989463	−	0.830258i
$603$	−2.41534e9	+	8.79113e8i	−0.448609	+	0.163280i
$604$	−2.12366e9	−	7.72948e8i	−0.392153	−	0.142732i
$605$	6.56599e9	+	5.50952e9i	1.20547	+	1.01151i
$606$	2.00972e8	−	1.13977e9i	0.0366845	−	0.208048i
$607$	−5.55604e9			−1.00833			−0.504167	−	0.863606i	$-0.668200\pi$
$607$	−5.55604e9			−1.00833			−0.504167	+	0.863606i	$0.668200\pi$
$608$	−8.94891e8	+	3.98696e8i	−0.161476	+	0.0719415i
$609$	1.14910e9			0.206157
$610$	−9.98330e8	+	5.66181e9i	−0.178082	+	1.00995i
$611$	6.04318e9	+	5.07083e9i	1.07182	+	0.899362i
$612$	2.65788e9	+	9.67390e8i	0.468712	+	0.170597i
$613$	5.66090e9	−	2.06040e9i	0.992599	−	0.361276i	0.205873	−	0.978579i	$-0.433997\pi$
$613$	5.66090e9	−	2.06040e9i	0.992599	−	0.361276i	0.786726	+	0.617302i	$0.211774\pi$
$614$	−2.25887e9	+	1.89541e9i	−0.393823	+	0.330457i
$615$	−5.75167e8	−	9.96219e8i	−0.0997083	−	0.172700i
$616$	3.08520e8	−	5.34372e8i	0.0531802	−	0.0921109i
$617$	4.90835e8	+	2.78366e9i	0.0841273	+	0.477110i	0.997541	+	0.0700784i	$0.0223249\pi$
$617$	4.90835e8	+	2.78366e9i	0.0841273	+	0.477110i	−0.913414	+	0.407031i	$0.866564\pi$
$618$	−2.83983e8	−	1.61055e9i	−0.0483986	−	0.274482i
$619$	2.47923e9	−	4.29414e9i	0.420145	−	0.727712i	−0.575809	−	0.817584i	$-0.695313\pi$
$619$	2.47923e9	−	4.29414e9i	0.420145	−	0.727712i	0.995953	+	0.0898728i	$0.0286460\pi$
$620$	9.41300e8	+	1.63038e9i	0.158620	+	0.274737i
$621$	−1.87372e9	+	1.57224e9i	−0.313967	+	0.263450i
$622$	−1.19502e9	+	4.34951e8i	−0.199117	+	0.0724726i
$623$	−1.30776e10	−	4.75987e9i	−2.16681	−	0.788655i
$624$	−4.06014e8	−	3.40686e8i	−0.0668952	−	0.0561318i
$625$	−1.93355e7	+	1.09657e8i	−0.00316792	+	0.0179662i
$626$	−1.75030e9			−0.285170
$627$	−2.68857e8	+	1.88671e7i	−0.0435597	+	0.00305681i
$628$	−4.22833e9			−0.681256
$629$	−9.96037e8	+	5.64881e9i	−0.159587	+	0.905064i
$630$	−9.50744e9	−	7.97769e9i	−1.51486	−	1.27112i
$631$	4.41760e9	+	1.60788e9i	0.699977	+	0.254771i	0.667401	−	0.744698i	$-0.267407\pi$
$631$	4.41760e9	+	1.60788e9i	0.699977	+	0.254771i	0.0325762	+	0.999469i	$0.489629\pi$
$632$	2.76435e9	−	1.00614e9i	0.435595	−	0.158544i
$633$	−3.31196e8	+	2.77906e8i	−0.0519006	+	0.0435498i
$634$	−1.07141e9	−	1.85574e9i	−0.166973	−	0.289205i
$635$	−1.53366e9	+	2.65638e9i	−0.237696	+	0.411701i
$636$	1.80441e8	+	1.02333e9i	0.0278122	+	0.157731i
$637$	3.63493e9	+	2.06147e10i	0.557196	+	3.16002i
$638$	−1.51877e8	+	2.63059e8i	−0.0231537	+	0.0401034i
$639$	5.16020e9	+	8.93773e9i	0.782373	+	1.35511i
$640$	−7.25415e8	+	6.08695e8i	−0.109385	+	0.0917846i
$641$	7.38171e9	−	2.68672e9i	1.10702	−	0.402921i	0.277118	−	0.960836i	$-0.410621\pi$
$641$	7.38171e9	−	2.68672e9i	1.10702	−	0.402921i	0.829898	+	0.557915i	$0.188398\pi$
$642$	−1.11996e9	−	4.07631e8i	−0.167043	−	0.0607987i
$643$	−1.62492e9	−	1.36347e9i	−0.241043	−	0.202259i	0.514261	−	0.857634i	$-0.328066\pi$
$643$	−1.62492e9	−	1.36347e9i	−0.241043	−	0.202259i	−0.755304	+	0.655375i	$0.772511\pi$
$644$	8.62562e8	−	4.89183e9i	0.127259	−	0.721724i
$645$	−2.91913e9			−0.428346
$646$	4.22153e9	+	3.06553e9i	0.616107	+	0.447395i
$647$	−7.07566e9			−1.02707			−0.513537	−	0.858067i	$-0.671665\pi$
$647$	−7.07566e9			−1.02707			−0.513537	+	0.858067i	$0.671665\pi$
$648$	3.33695e8	−	1.89248e9i	0.0481767	−	0.273224i
$649$	9.20713e8	+	7.72570e8i	0.132211	+	0.110938i
$650$	−9.64530e9	−	3.51060e9i	−1.37759	−	0.501401i
$651$	−1.31667e9	+	4.79228e8i	−0.187044	+	0.0680784i
$652$	9.66758e8	−	8.11206e8i	0.136600	−	0.114621i
$653$	−1.96193e9	−	3.39815e9i	−0.275731	−	0.477581i	0.694588	−	0.719408i	$-0.255587\pi$
$653$	−1.96193e9	−	3.39815e9i	−0.275731	−	0.477581i	−0.970319	+	0.241827i	$0.922253\pi$
$654$	−1.32618e8	+	2.29702e8i	−0.0185388	+	0.0321102i
$655$	7.60607e8	+	4.31362e9i	0.105759	+	0.599787i
$656$	1.42853e8	+	8.10162e8i	0.0197573	+	0.112049i
$657$	5.53307e9	−	9.58356e9i	0.761180	−	1.31840i
$658$	5.24516e9	+	9.08489e9i	0.717742	+	1.24317i
$659$	−3.02275e9	+	2.53639e9i	−0.411437	+	0.345236i	−0.824894	−	0.565287i	$-0.808765\pi$
$659$	−3.02275e9	+	2.53639e9i	−0.411437	+	0.345236i	0.413458	+	0.910523i	$0.364321\pi$
$660$	−2.44804e8	+	8.91014e7i	−0.0331448	+	0.0120637i
$661$	1.33826e10	+	4.87088e9i	1.80234	+	0.655998i	0.998095	+	0.0616988i	$0.0196518\pi$
$661$	1.33826e10	+	4.87088e9i	1.80234	+	0.655998i	0.804244	+	0.594299i	$0.202570\pi$
$662$	−4.89597e9	−	4.10820e9i	−0.655897	−	0.550363i
$663$	−4.90122e8	+	2.77962e9i	−0.0653141	+	0.370414i
$664$	−1.56030e9			−0.206833
$665$	−1.28060e10	−	1.89756e10i	−1.68865	−	2.50219i
$666$	4.26238e9			0.559104
$667$	−4.24620e8	+	2.40814e9i	−0.0554064	+	0.314225i
$668$	5.43192e9	+	4.55792e9i	0.705075	+	0.591629i
$669$	1.16743e9	+	4.24908e8i	0.150743	+	0.0548660i
$670$	−4.30633e9	+	1.56738e9i	−0.553154	+	0.201331i
$671$	8.66472e8	−	7.27056e8i	0.110720	−	0.0929051i
$672$	−3.52399e8	−	6.10374e8i	−0.0447963	−	0.0775895i
$673$	−5.53476e9	+	9.58649e9i	−0.699917	+	1.21229i	0.268578	+	0.963258i	$0.413446\pi$
$673$	−5.53476e9	+	9.58649e9i	−0.699917	+	1.21229i	−0.968495	+	0.249034i	$0.919887\pi$
$674$	5.30060e8	+	3.00612e9i	0.0666830	+	0.378178i
$675$	1.16710e9	+	6.61896e9i	0.146065	+	0.828375i
$676$	−1.32234e9	+	2.29035e9i	−0.164637	+	0.285160i
$677$	4.57989e9	+	7.93259e9i	0.567276	+	0.982551i	0.996834	+	0.0795113i	$0.0253360\pi$
$677$	4.57989e9	+	7.93259e9i	0.567276	+	0.982551i	−0.429558	+	0.903039i	$0.641331\pi$
$678$	6.81517e8	−	5.71861e8i	0.0839794	−	0.0704671i
$679$	7.03964e9	−	2.56222e9i	0.862991	−	0.314103i
$680$	4.73876e9	+	1.72477e9i	0.577941	+	0.210353i
$681$	−1.13754e9	−	9.54513e8i	−0.138024	−	0.115816i
$682$	6.43169e7	−	3.64759e8i	0.00776389	−	0.0440312i
$683$	−9.60067e8			−0.115300			−0.0576500	−	0.998337i	$-0.518361\pi$
$683$	−9.60067e8			−0.115300			−0.0576500	+	0.998337i	$0.518361\pi$
$684$	1.69865e9	−	3.48493e9i	0.202958	−	0.416387i
$685$	4.32185e9			0.513751
$686$	−2.89364e9	+	1.64107e10i	−0.342224	+	1.94085i
$687$	−2.77802e8	−	2.33103e8i	−0.0326878	−	0.0274284i
$688$	1.96171e9	+	7.14005e8i	0.229655	+	0.0835875i
$689$	1.22709e10	−	4.46623e9i	1.42925	−	0.520204i
$690$	−1.60655e9	+	1.34806e9i	−0.186175	+	0.156220i
$691$	3.06336e9	+	5.30589e9i	0.353203	+	0.611766i	0.986809	−	0.161890i	$-0.0517591\pi$
$691$	3.06336e9	+	5.30589e9i	0.353203	+	0.611766i	−0.633606	+	0.773656i	$0.718426\pi$
$692$	3.50243e9	−	6.06639e9i	0.401789	−	0.695919i
$693$	4.24010e8	+	2.40468e9i	0.0483961	+	0.274468i
$694$	−1.18865e9	−	6.74118e9i	−0.134988	−	0.765558i
$695$	−6.42067e7	+	1.11209e8i	−0.00725493	+	0.0125659i
$696$	1.73478e8	+	3.00473e8i	0.0195035	+	0.0337810i
$697$	3.35599e9	−	2.81601e9i	0.375410	−	0.315007i
$698$	−6.88912e9	+	2.50743e9i	−0.766778	+	0.279084i
$699$	−2.30177e9	−	8.37776e8i	−0.254913	−	0.0927807i
$700$	−1.04559e10	−	8.77355e9i	−1.15218	−	0.966790i
$701$	1.87922e9	−	1.06576e10i	0.206046	−	1.16854i	−0.689739	−	0.724058i	$-0.742275\pi$
$701$	1.87922e9	−	1.06576e10i	0.206046	−	1.16854i	0.895785	−	0.444487i	$-0.146614\pi$
$702$	4.36134e9			0.475818
$703$	7.55803e9	+	2.16521e9i	0.820474	+	0.235048i
$704$	1.86307e8			0.0201245
$705$	7.69094e8	−	4.36175e9i	0.0826642	−	0.468812i
$706$	−3.90588e9	−	3.27742e9i	−0.417737	−	0.350523i
$707$	−1.81742e10	−	6.61485e9i	−1.93413	−	0.703967i
$708$	1.29006e9	−	4.69542e8i	0.136613	−	0.0497231i
$709$	−5.27787e9	+	4.42866e9i	−0.556156	+	0.466670i	−0.877019	−	0.480455i	$-0.840471\pi$
$709$	−5.27787e9	+	4.42866e9i	−0.556156	+	0.466670i	0.320863	+	0.947126i	$0.396027\pi$
$710$	9.20016e9	+	1.59351e10i	0.964698	+	1.67091i
$711$	−5.82063e9	+	1.00816e10i	−0.607333	+	1.05193i
$712$	−7.29676e8	−	4.13820e9i	−0.0757617	−	0.429666i
$713$	−5.17765e8	−	2.93639e9i	−0.0534957	−	0.303389i
$714$	−1.87664e9	+	3.25044e9i	−0.192947	+	0.334194i
$715$	1.63692e9	+	2.83523e9i	0.167477	+	0.290079i
$716$	−6.87245e8	+	5.76667e8i	−0.0699707	+	0.0587124i
$717$	−1.50549e9	+	5.47952e8i	−0.152532	+	0.0555169i
$718$	8.80686e7	+	3.20544e7i	0.00887944	+	0.00323185i
$719$	−4.66166e9	−	3.91160e9i	−0.467724	−	0.392467i	0.378240	−	0.925708i	$-0.376529\pi$
$719$	−4.66166e9	−	3.91160e9i	−0.467724	−	0.392467i	−0.845963	+	0.533241i	$0.820974\pi$
$720$	6.50723e8	−	3.69043e9i	0.0649729	−	0.368480i
$721$	−2.73291e10			−2.71551
$722$	4.78231e9	−	5.31657e9i	0.472887	−	0.525717i
$723$	−2.67907e9			−0.263633
$724$	−9.72964e8	+	5.51795e9i	−0.0952822	+	0.540372i
$725$	5.14721e9	+	4.31902e9i	0.501636	+	0.420922i
$726$	−1.81001e9	−	6.58789e8i	−0.175551	−	0.0638952i
$727$	−3.19927e9	+	1.16444e9i	−0.308802	+	0.112395i	−0.491773	−	0.870724i	$-0.663651\pi$
$727$	−3.19927e9	+	1.16444e9i	−0.308802	+	0.112395i	0.182971	+	0.983118i	$0.441429\pi$
$728$	−6.78490e9	+	5.69321e9i	−0.651754	+	0.546887i
$729$	3.06106e9	+	5.30191e9i	0.292634	+	0.506857i
$730$	9.86495e9	−	1.70866e10i	0.938566	−	1.62564i
$731$	−1.93048e9	−	1.09483e10i	−0.182791	−	1.03666i
$732$	−2.24349e8	−	1.27234e9i	−0.0211414	−	0.119899i
$733$	5.61319e9	−	9.72233e9i	0.526437	−	0.911815i	−0.473089	−	0.881015i	$-0.656861\pi$
$733$	5.61319e9	−	9.72233e9i	0.526437	−	0.911815i	0.999526	−	0.0308002i	$-0.00980556\pi$
$734$	−2.77510e9	−	4.80662e9i	−0.259026	−	0.448646i
$735$	9.00280e9	−	7.55425e9i	0.836319	−	0.701755i
$736$	1.40936e9	−	5.12966e8i	0.130302	−	0.0474259i
$737$	8.47236e8	+	3.08369e8i	0.0779593	+	0.0283749i
$738$	−2.49384e9	−	2.09258e9i	−0.228387	−	0.191639i
$739$	1.23892e9	−	7.02626e9i	0.112924	−	0.640425i	−0.874833	−	0.484425i	$-0.839029\pi$
$739$	1.23892e9	−	7.02626e9i	0.112924	−	0.640425i	0.987757	−	0.156000i	$-0.0498600\pi$
$740$	7.59943e9			0.689398
$741$	3.71910e9	+	1.06544e9i	0.335794	+	0.0961977i
$742$	1.73647e10			1.56046
$743$	1.62815e8	−	9.23368e8i	0.0145624	−	0.0825874i	−0.976660	−	0.214789i	$-0.931094\pi$
$743$	1.62815e8	−	9.23368e8i	0.0145624	−	0.0825874i	0.991223	+	0.132202i	$0.0422047\pi$
$744$	−3.24087e8	−	2.71941e8i	−0.0288507	−	0.0242086i
$745$	−5.62741e9	−	2.04821e9i	−0.498610	−	0.181479i
$746$	−8.99936e9	+	3.27550e9i	−0.793644	+	0.288863i
$747$	4.72994e9	−	3.96889e9i	0.415177	−	0.348375i
$748$	−4.96073e8	−	8.59223e8i	−0.0433401	−	0.0750672i
$749$	−9.95836e9	+	1.72484e10i	−0.865967	+	1.49990i
$750$	3.79082e8	+	2.14988e9i	0.0328110	+	0.186080i
$751$	−1.99961e9	−	1.13403e10i	−0.172268	−	0.976981i	−0.941250	−	0.337710i	$-0.890348\pi$
$751$	−1.99961e9	−	1.13403e10i	−0.172268	−	0.976981i	0.768982	−	0.639271i	$-0.220764\pi$
$752$	−1.58371e9	+	2.74306e9i	−0.135804	+	0.235220i
$753$	1.92693e9	+	3.33754e9i	0.164469	+	0.284868i
$754$	3.34005e9	−	2.80264e9i	0.283762	−	0.238104i
$755$	1.49833e10	−	5.45347e9i	1.26705	−	0.461167i
$756$	5.44984e9	+	1.98358e9i	0.458731	+	0.166964i
$757$	−3.24335e9	−	2.72150e9i	−0.271743	−	0.228020i	0.496724	−	0.867908i	$-0.334536\pi$
$757$	−3.24335e9	−	2.72150e9i	−0.271743	−	0.228020i	−0.768468	+	0.639889i	$0.778980\pi$
$758$	1.25725e9	−	7.13024e9i	0.104853	−	0.594651i
$759$	4.12607e8			0.0342524
$760$	3.02853e9	−	6.21330e9i	0.250256	−	0.513423i
$761$	1.05189e10			0.865217			0.432608	−	0.901582i	$-0.357593\pi$
$761$	1.05189e10			0.865217			0.432608	+	0.901582i	$0.357593\pi$
$762$	1.19696e8	−	6.78828e8i	0.00980022	−	0.0555798i
$763$	3.39540e9	+	2.84908e9i	0.276729	+	0.232203i
$764$	−1.31761e9	−	4.79571e8i	−0.106896	−	0.0389069i
$765$	−1.87525e10	+	6.82534e9i	−1.51441	+	0.551200i
$766$	5.53020e8	−	4.64039e8i	0.0444570	−	0.0373038i
$767$	−8.62616e9	−	1.49409e10i	−0.690293	−	1.19562i
$768$	1.06402e8	−	1.84294e8i	0.00847592	−	0.0146807i
$769$	−1.75411e9	−	9.94806e9i	−0.139096	−	0.788853i	−0.971919	−	0.235314i	$-0.924388\pi$
$769$	−1.75411e9	−	9.94806e9i	−0.139096	−	0.788853i	0.832823	−	0.553539i	$-0.186723\pi$
$770$	7.55971e8	+	4.28733e9i	0.0596744	+	0.338430i
$771$	−1.70213e9	+	2.94818e9i	−0.133753	+	0.231667i
$772$	5.06795e9	+	8.77794e9i	0.396435	+	0.686645i
$773$	9.00421e9	−	7.55543e9i	0.701160	−	0.588343i	−0.220943	−	0.975287i	$-0.570914\pi$
$773$	9.00421e9	−	7.55543e9i	0.701160	−	0.588343i	0.922104	+	0.386943i	$0.126469\pi$
$774$	−7.76299e9	+	2.82550e9i	−0.601777	+	0.219029i
$775$	−7.69902e9	−	2.80222e9i	−0.594128	−	0.216245i
$776$	1.73275e9	+	1.45395e9i	0.133112	+	0.111695i
$777$	−9.82164e8	+	5.57013e9i	−0.0751122	+	0.425982i
$778$	9.77821e9			0.744442
$779$	−3.35907e9	−	4.97737e9i	−0.254588	−	0.377241i
$780$	3.73947e9			0.282149
$781$	6.28626e8	−	3.56511e9i	0.0472187	−	0.267790i
$782$	−6.11839e9	−	5.13394e9i	−0.457523	−	0.383908i
$783$	−2.68283e9	−	9.76471e8i	−0.199723	−	0.0726931i
$784$	−7.89779e9	+	2.87456e9i	−0.585328	+	0.213042i
$785$	2.28531e10	−	1.91760e10i	1.68617	−	1.41487i
$786$	−4.92163e8	−	8.52452e8i	−0.0361518	−	0.0626168i
$787$	−8.27590e9	+	1.43343e10i	−0.605206	+	1.04825i	0.386813	+	0.922158i	$0.373576\pi$
$787$	−8.27590e9	+	1.43343e10i	−0.605206	+	1.04825i	−0.992019	+	0.126090i	$0.959757\pi$
$788$	2.38109e9	+	1.35039e10i	0.173354	+	0.983142i
$789$	2.79980e8	+	1.58784e9i	0.0202935	+	0.115090i
$790$	−1.03777e10	+	1.79746e10i	−0.748866	+	1.29707i
$791$	−7.43353e9	−	1.28753e10i	−0.534045	−	0.924992i
$792$	−5.64776e8	+	4.73904e8i	−0.0403960	+	0.0338963i
$793$	−1.52568e10	+	5.55302e9i	−1.08644	+	0.395433i
$794$	1.67800e10	+	6.10740e9i	1.18965	+	0.432997i
$795$	−5.61618e9	−	4.71254e9i	−0.396421	−	0.332636i
$796$	1.56793e9	−	8.89218e9i	0.110187	−	0.624903i
$797$	−3.07356e9			−0.215049			−0.107525	−	0.994202i	$-0.534292\pi$
$797$	−3.07356e9			−0.215049			−0.107525	+	0.994202i	$0.534292\pi$
$798$	4.16273e9	+	3.02283e9i	0.289980	+	0.210573i
$799$	1.68675e10			1.16987
$800$	7.15640e8	−	4.05859e9i	0.0494173	−	0.280260i
$801$	1.27382e10	+	1.06886e10i	0.875777	+	0.734864i
$802$	1.26759e10	+	4.61364e9i	0.867697	+	0.315816i
$803$	−3.64760e9	+	1.32762e9i	−0.248601	+	0.0904834i
$804$	7.88905e8	−	6.61970e8i	0.0535339	−	0.0449202i
$805$	1.75232e10	+	3.03510e10i	1.18393	+	2.05063i
$806$	−2.65829e9	+	4.60429e9i	−0.178825	+	0.309735i
$807$	−8.62840e8	−	4.89341e9i	−0.0577927	−	0.327759i
$808$	−1.01404e9	−	5.75091e9i	−0.0676262	−	0.383527i
$809$	−9.51688e9	+	1.64837e10i	−0.631938	+	1.09455i	0.355217	+	0.934784i	$0.384407\pi$
$809$	−9.51688e9	+	1.64837e10i	−0.631938	+	1.09455i	−0.987155	+	0.159765i	$0.948926\pi$
$810$	6.77910e9	+	1.17417e10i	0.448203	+	0.776310i
$811$	−1.20746e10	+	1.01318e10i	−0.794877	+	0.666981i	−0.946947	−	0.321388i	$-0.895850\pi$
$811$	−1.20746e10	+	1.01318e10i	−0.794877	+	0.666981i	0.152070	+	0.988370i	$0.451406\pi$
$812$	5.44832e9	−	1.98303e9i	0.357122	−	0.129982i
$813$	5.78089e8	+	2.10407e8i	0.0377292	+	0.0137323i
$814$	−1.14533e9	−	9.61048e8i	−0.0744297	−	0.0624539i
$815$	−1.54617e9	+	8.76875e9i	−0.100047	+	0.567395i
$816$	−1.13326e9			−0.0730150
$817$	−1.52006e10	+	1.06670e9i	−0.975176	+	0.0684331i
$818$	−1.28995e10			−0.824016
$819$	6.08630e9	−	3.45171e10i	0.387133	−	2.19554i
$820$	−4.44628e9	−	3.73087e9i	−0.281610	−	0.236299i
$821$	5.14232e9	+	1.87165e9i	0.324308	+	0.118039i	0.499044	−	0.866577i	$-0.333685\pi$
$821$	5.14232e9	+	1.87165e9i	0.324308	+	0.118039i	−0.174735	+	0.984615i	$0.555907\pi$
$822$	−9.12651e8	+	3.32178e8i	−0.0573130	+	0.0208602i
$823$	3.61597e9	−	3.03416e9i	0.226113	−	0.189731i	−0.522692	−	0.852521i	$-0.675072\pi$
$823$	3.61597e9	−	3.03416e9i	0.226113	−	0.189731i	0.748805	+	0.662790i	$0.230628\pi$
$824$	−4.12583e9	−	7.14614e9i	−0.256901	−	0.444966i
$825$	5.66884e8	−	9.81873e8i	0.0351484	−	0.0608788i
$826$	−3.98378e9	−	2.25931e10i	−0.245960	−	1.39491i
$827$	3.32061e9	+	1.88321e10i	0.204150	+	1.15779i	0.898772	+	0.438416i	$0.144460\pi$
$827$	3.32061e9	+	1.88321e10i	0.204150	+	1.15779i	−0.694623	+	0.719374i	$0.744429\pi$
$828$	−2.96756e9	+	5.13997e9i	−0.181674	+	0.314669i
$829$	−5.04108e8	−	8.73141e8i	−0.0307314	−	0.0532284i	0.850251	−	0.526378i	$-0.176450\pi$
$829$	−5.04108e8	−	8.73141e8i	−0.0307314	−	0.0532284i	−0.880982	+	0.473150i	$0.843117\pi$
$830$	8.43304e9	−	7.07616e9i	0.511930	−	0.429561i
$831$	3.71112e9	−	1.35074e9i	0.224337	−	0.0816520i
$832$	−2.51300e9	−	9.14655e8i	−0.151273	−	0.0550587i
$833$	3.42863e10	+	2.87696e10i	2.05524	+	1.72455i
$834$	5.01106e6	−	2.84191e7i	0.000299122	−	0.00169640i
$835$	−5.00290e10			−2.97385
$836$	−1.24219e9	+	5.53428e8i	−0.0735304	+	0.0327596i
$837$	3.48129e9			0.205211
$838$	2.80517e8	−	1.59089e9i	0.0164667	−	0.0933871i
$839$	8.91618e9	+	7.48156e9i	0.521209	+	0.437346i	0.865053	−	0.501681i	$-0.167285\pi$
$839$	8.91618e9	+	7.48156e9i	0.521209	+	0.437346i	−0.343844	+	0.939027i	$0.611729\pi$
$840$	4.67276e9	+	1.70074e9i	0.272017	+	0.0990060i
$841$	1.35275e10	−	4.92361e9i	0.784208	−	0.285428i
$842$	3.12112e9	−	2.61893e9i	0.180185	−	0.151193i
$843$	−2.79291e9	−	4.83747e9i	−0.160569	−	0.278113i
$844$	−1.09074e9	+	1.88921e9i	−0.0624484	+	0.108164i
$845$	−3.24015e9	−	1.83758e10i	−0.184742	−	1.04772i
$846$	−2.17655e9	−	1.23438e10i	−0.123587	−	0.700897i
$847$	−1.60941e10	+	2.78758e10i	−0.910071	+	1.57629i
$848$	2.62152e9	+	4.54061e9i	0.147628	+	0.255699i
$849$	3.82908e9	−	3.21298e9i	0.214742	−	0.180190i
$850$	−2.06232e10	+	7.50624e9i	−1.15183	+	0.419234i
$851$	−1.13102e10	−	4.11658e9i	−0.629097	−	0.228973i
$852$	−3.16759e9	−	2.65792e9i	−0.175465	−	0.147232i
$853$	2.01232e9	−	1.14124e10i	0.111013	−	0.629587i	−0.877634	−	0.479331i	$-0.840879\pi$
$853$	2.01232e9	−	1.14124e10i	0.111013	−	0.629587i	0.988647	−	0.150256i	$-0.0480097\pi$
$854$	−2.15901e10			−1.18619
$855$	6.62383e9	+	2.65388e10i	0.362433	+	1.45211i
$856$	−6.01359e9			−0.327699
$857$	9.15282e8	−	5.19082e9i	0.0496732	−	0.281711i	−0.949846	−	0.312718i	$-0.898760\pi$
$857$	9.15282e8	−	5.19082e9i	0.0496732	−	0.281711i	0.999519	+	0.0310075i	$0.00987159\pi$
$858$	−5.63586e8	−	4.72905e8i	−0.0304617	−	0.0255604i
$859$	−2.14535e10	−	7.80844e9i	−1.15484	−	0.420328i	−0.307590	−	0.951519i	$-0.599522\pi$
$859$	−2.14535e10	−	7.80844e9i	−1.15484	−	0.420328i	−0.847252	+	0.531191i	$0.821745\pi$
$860$	−1.38407e10	+	5.03760e9i	−0.742016	+	0.270072i
$861$	3.30925e9	−	2.77679e9i	0.176693	−	0.148263i
$862$	9.88610e9	+	1.71232e10i	0.525714	+	0.910564i
$863$	3.91799e9	−	6.78615e9i	0.207503	−	0.359406i	−0.743424	−	0.668820i	$-0.766800\pi$
$863$	3.91799e9	−	6.78615e9i	0.207503	−	0.359406i	0.950927	+	0.309414i	$0.100133\pi$
$864$	3.04078e8	+	1.72451e9i	0.0160393	+	0.0909636i
$865$	8.58207e9	+	4.86713e10i	0.450854	+	2.55692i
$866$	3.92153e9	−	6.79229e9i	0.205184	−	0.355389i
$867$	4.15081e8	+	7.18941e8i	0.0216305	+	0.0374650i
$868$	−5.41581e9	+	4.54440e9i	−0.281089	+	0.235862i
$869$	3.83717e9	−	1.39662e9i	0.198355	−	0.0721952i
$870$	−2.30029e9	−	8.37238e8i	−0.118431	−	0.0431054i
$871$	−9.91401e9	−	8.31884e9i	−0.508377	−	0.426579i
$872$	−2.32393e8	+	1.31797e9i	−0.0118690	+	0.0673126i
$873$	−8.95106e9			−0.455328
$874$	−7.87308e9	+	7.60670e9i	−0.398891	+	0.385395i
$875$	3.64809e10			1.84093
$876$	−7.69917e8	+	4.36642e9i	−0.0386972	+	0.219463i
$877$	8.35803e9	+	7.01322e9i	0.418413	+	0.351090i	0.827559	−	0.561379i	$-0.189729\pi$
$877$	8.35803e9	+	7.01322e9i	0.418413	+	0.351090i	−0.409146	+	0.912469i	$0.634173\pi$
$878$	−2.63325e10	−	9.58426e9i	−1.31299	−	0.477890i
$879$	6.27008e9	−	2.28212e9i	0.311395	−	0.113339i
$880$	−1.00694e9	+	8.44926e8i	−0.0498099	+	0.0417955i
$881$	1.78272e9	+	3.08776e9i	0.0878348	+	0.152134i	0.906596	−	0.422000i	$-0.138672\pi$
$881$	1.78272e9	+	3.08776e9i	0.0878348	+	0.152134i	−0.818761	+	0.574135i	$0.805339\pi$
$882$	1.66297e10	−	2.88034e10i	0.816100	−	1.41353i
$883$	1.92869e9	+	1.09382e10i	0.0942759	+	0.534665i	0.994967	+	0.100205i	$0.0319498\pi$
$883$	1.92869e9	+	1.09382e10i	0.0942759	+	0.534665i	−0.900691	+	0.434461i	$0.856939\pi$
$884$	2.47299e9	+	1.40250e10i	0.120404	+	0.682843i
$885$	−4.84301e9	+	8.38833e9i	−0.234862	+	0.406794i
$886$	−4.39197e8	−	7.60712e8i	−0.0212149	−	0.0367453i
$887$	1.79494e10	−	1.50613e10i	0.863609	−	0.724654i	−0.0991336	−	0.995074i	$-0.531607\pi$
$887$	1.79494e10	−	1.50613e10i	0.863609	−	0.724654i	0.962742	+	0.270420i	$0.0871627\pi$
$888$	−1.60478e9	+	5.84093e8i	−0.0769078	+	0.0279922i
$889$	−1.08242e10	−	3.93969e9i	−0.516702	−	0.188064i
$890$	2.27110e10	+	1.90568e10i	1.07987	+	0.906118i
$891$	4.63200e8	−	2.62694e9i	0.0219380	−	0.124417i
$892$	6.26848e9			0.295723
$893$	2.41099e9	−	2.29937e10i	0.113296	−	1.08051i
$894$	1.34577e9			0.0629927
$895$	1.09913e9	−	6.23349e9i	0.0512471	−	0.290637i
$896$	−2.72419e9	−	2.28587e9i	−0.126520	−	0.106163i
$897$	−5.56544e9	−	2.02566e9i	−0.257470	−	0.0937113i
$898$	−1.08398e10	+	3.94538e9i	−0.499523	+	0.181811i
$899$	2.66608e9	−	2.23711e9i	0.122381	−	0.102690i
$900$	8.15432e9	+	1.41237e10i	0.372854	+	0.645802i
$901$	1.39605e10	−	2.41802e10i	0.635862	−	1.10135i
$902$	1.98294e8	+	1.12458e9i	0.00899677	+	0.0510232i
$903$	−1.90360e9	−	1.07958e10i	−0.0860335	−	0.487920i
$904$	2.24446e9	−	3.88751e9i	0.101047	−	0.175018i
$905$	−1.97660e10	−	3.42357e10i	−0.886439	−	1.53536i
$906$	−2.74488e9	+	2.30323e9i	−0.122624	+	0.102894i
$907$	3.13215e10	−	1.14001e10i	1.39385	−	0.507321i	0.467505	−	0.883990i	$-0.345153\pi$
$907$	3.13215e10	−	1.14001e10i	1.39385	−	0.507321i	0.926348	+	0.376669i	$0.122931\pi$
$908$	−7.04075e9	−	2.56262e9i	−0.312118	−	0.113602i
$909$	1.77024e10	+	1.48541e10i	0.781733	+	0.655952i
$910$	1.08513e10	−	6.15409e10i	0.477351	−	2.70719i
$911$	−8.50734e9			−0.372803			−0.186401	−	0.982474i	$-0.559683\pi$
$911$	−8.50734e9			−0.372803			−0.186401	+	0.982474i	$0.559683\pi$
$912$	−1.61984e8	+	1.54484e9i	−0.00707114	+	0.0674377i
$913$	−2.16584e9			−0.0941845
$914$	2.05555e9	−	1.16576e10i	0.0890466	−	0.505008i
$915$	6.98280e9	+	5.85926e9i	0.301339	+	0.252854i
$916$	−1.71943e9	−	6.25823e8i	−0.0739182	−	0.0269040i
$917$	−1.54571e10	+	5.62591e9i	−0.661964	+	0.240935i
$918$	7.14356e9	−	5.99416e9i	0.304765	−	0.255728i
$919$	−1.95260e10	−	3.38201e10i	−0.829869	−	1.43737i	−0.898141	−	0.439708i	$-0.855082\pi$
$919$	−1.95260e10	−	3.38201e10i	−0.829869	−	1.43737i	0.0682719	−	0.997667i	$-0.478251\pi$
$920$	−5.29089e9	+	9.16410e9i	−0.224012	+	0.388000i
$921$	8.11854e8	+	4.60426e9i	0.0342428	+	0.194201i
$922$	1.15361e9	+	6.54247e9i	0.0484733	+	0.274905i
$923$	−2.59818e10	+	4.50018e10i	−1.08758	+	1.88375i
$924$	−4.89164e8	−	8.47256e8i	−0.0203987	−	0.0353316i
$925$	−2.53353e10	+	2.12589e10i	−1.05252	+	0.883170i
$926$	2.70077e10	−	9.83000e9i	1.11776	−	0.406832i
$927$	3.06846e10	+	1.11683e10i	1.26515	+	0.460476i
$928$	1.34106e9	+	1.12528e9i	0.0550845	+	0.0462214i
$929$	2.91874e9	−	1.65530e10i	0.119437	−	0.677364i	−0.865020	−	0.501738i	$-0.832694\pi$
$929$	2.91874e9	−	1.65530e10i	0.119437	−	0.677364i	0.984457	−	0.175625i	$-0.0561948\pi$
$930$	2.98490e9			0.121686
$931$	4.41192e10	−	4.26265e10i	1.79186	−	1.73124i
$932$	−1.23593e10			−0.500080
$933$	−3.50131e8	+	1.98569e9i	−0.0141138	+	0.0800434i
$934$	−1.61232e9	−	1.35290e9i	−0.0647496	−	0.0543314i
$935$	6.57785e9	+	2.39414e9i	0.263174	+	0.0957875i
$936$	9.94455e9	−	3.61952e9i	0.396387	−	0.144273i
$937$	6.22954e9	−	5.22721e9i	0.247382	−	0.207578i	−0.510662	−	0.859781i	$-0.670600\pi$
$937$	6.22954e9	−	5.22721e9i	0.247382	−	0.207578i	0.758044	+	0.652204i	$0.226155\pi$
$938$	−8.60485e9	−	1.49040e10i	−0.340434	−	0.589649i
$939$	−1.38757e9	+	2.40334e9i	−0.0546922	+	0.0947296i
$940$	−3.88059e9	−	2.20079e10i	−0.152388	−	0.864235i
$941$	−2.20696e7	−	1.25163e8i	−0.000863438	−	0.00489680i	0.984373	−	0.176096i	$-0.0563469\pi$
$941$	−2.20696e7	−	1.25163e8i	−0.000863438	−	0.00489680i	−0.985236	+	0.171199i	$0.945236\pi$
$942$	−3.35205e9	+	5.80592e9i	−0.130657	+	0.226304i
$943$	4.59639e9	+	7.96118e9i	0.178495	+	0.309162i
$944$	5.30634e9	−	4.45255e9i	0.205302	−	0.172269i
$945$	−3.84509e10	+	1.39950e10i	−1.48216	+	0.539462i
$946$	2.72304e9	+	9.91106e8i	0.104577	+	0.0380628i
$947$	2.72029e9	+	2.28259e9i	0.104085	+	0.0873381i	0.693345	−	0.720606i	$-0.256136\pi$
$947$	2.72029e9	+	2.28259e9i	0.104085	+	0.0873381i	−0.589260	+	0.807944i	$0.700581\pi$
$948$	8.09932e8	−	4.59335e9i	0.0308759	−	0.175106i
$949$	5.57184e10			2.11625
$950$	7.28462e9	+	2.91863e10i	0.275661	+	1.10445i
$951$	−3.39749e9			−0.128093
$952$	−3.28852e9	+	1.86501e10i	−0.123530	+	0.700571i
$953$	1.17781e10	+	9.88302e9i	0.440809	+	0.369883i	0.836012	−	0.548711i	$-0.184881\pi$
$953$	1.17781e10	+	9.88302e9i	0.440809	+	0.369883i	−0.395203	+	0.918594i	$0.629326\pi$
$954$	−1.94968e10	−	7.09624e9i	−0.727015	−	0.264612i
$955$	9.29629e9	−	3.38357e9i	0.345381	−	0.125708i
$956$	−6.19246e9	+	5.19609e9i	−0.229224	+	0.192342i
$957$	2.40804e8	+	4.17085e8i	0.00888121	+	0.0153827i
$958$	−1.56841e10	+	2.71657e10i	−0.576342	+	0.998253i
$959$	2.81833e9	+	1.59835e10i	0.103187	+	0.585204i
$960$	2.60720e8	+	1.47862e9i	0.00951097	+	0.0539394i
$961$	1.16344e10	−	2.01514e10i	0.422876	−	0.732443i
$962$	1.07306e10	+	1.85860e10i	0.388608	+	0.673089i
$963$	1.82298e10	−	1.52966e10i	0.657793	−	0.551954i
$964$	−1.27025e10	+	4.62332e9i	−0.456687	+	0.166220i
$965$	−6.72002e10	−	2.44589e10i	−2.40727	−	0.876175i
$966$	−6.03317e9	−	5.06243e9i	−0.215341	−	0.180692i
$967$	−6.82720e9	+	3.87190e10i	−0.242801	+	1.37699i	0.582744	+	0.812656i	$0.301979\pi$
$967$	−6.82720e9	+	3.87190e10i	−0.242801	+	1.37699i	−0.825545	+	0.564336i	$0.809132\pi$
$968$	−9.71882e9			−0.344389
$969$	7.55593e9	−	3.36635e9i	0.266781	−	0.118857i
$970$	−1.59589e10			−0.561439
$971$	−3.51780e9	+	1.99504e10i	−0.123312	+	0.699335i	0.858985	+	0.512001i	$0.171096\pi$
$971$	−3.51780e9	+	1.99504e10i	−0.123312	+	0.699335i	−0.982296	+	0.187334i	$0.940015\pi$
$972$	−8.06392e9	−	6.76644e9i	−0.281653	−	0.236335i
$973$	−4.53156e8	−	1.64935e8i	−0.0157708	−	0.00574009i
$974$	−2.07019e10	+	7.53487e9i	−0.717883	+	0.261288i
$975$	−1.24668e10	+	1.04609e10i	−0.430764	+	0.361454i
$976$	−3.25943e9	−	5.64550e9i	−0.112219	−	0.194369i
$977$	1.28868e10	−	2.23206e10i	0.442093	−	0.765727i	−0.555752	−	0.831348i	$-0.687570\pi$
$977$	1.28868e10	−	2.23206e10i	0.442093	−	0.765727i	0.997845	+	0.0656212i	$0.0209029\pi$
$978$	−3.47460e8	−	1.97055e9i	−0.0118773	−	0.0673597i
$979$	−1.01286e9	−	5.74421e9i	−0.0344992	−	0.195655i
$980$	2.96492e10	−	5.13539e10i	1.00629	−	1.74294i
$981$	−2.64799e9	−	4.58645e9i	−0.0895519	−	0.155108i
$982$	1.23869e10	−	1.03938e10i	0.417418	−	0.350255i
$983$	2.48711e9	−	9.05234e8i	0.0835137	−	0.0303965i	−0.299925	−	0.953963i	$-0.596962\pi$
$983$	2.48711e9	−	9.05234e8i	0.0835137	−	0.0303965i	0.383439	+	0.923566i	$0.374740\pi$
$984$	1.22568e9	+	4.46111e8i	0.0410105	+	0.0149266i
$985$	−7.41110e10	−	6.21865e10i	−2.47090	−	2.07334i
$986$	1.61886e9	−	9.18103e9i	0.0537825	−	0.305016i
$987$	1.66326e10			0.550618
$988$	1.94723e10	−	1.36647e9i	0.642344	−	0.0450766i
$989$	2.33279e10			0.766812
$990$	9.03265e8	−	5.12267e9i	0.0295864	−	0.167793i
$991$	−1.31129e10	−	1.10030e10i	−0.427997	−	0.359132i	0.403199	−	0.915113i	$-0.367898\pi$
$991$	−1.31129e10	−	1.10030e10i	−0.427997	−	0.359132i	−0.831195	+	0.555981i	$0.812343\pi$
$992$	−2.00591e9	−	7.30092e8i	−0.0652410	−	0.0237458i
$993$	−9.52229e9	+	3.46583e9i	−0.308617	+	0.112327i
$994$	−5.29335e10	+	4.44165e10i	−1.70954	+	1.43447i
$995$	3.18529e10	+	5.51709e10i	1.02511	+	1.77553i
$996$	−1.23694e9	+	2.14245e9i	−0.0396681	+	0.0687072i
$997$	−6.22741e9	−	3.53174e10i	−0.199010	−	1.12864i	−0.906592	−	0.422009i	$-0.861325\pi$
$997$	−6.22741e9	−	3.53174e10i	−0.199010	−	1.12864i	0.707582	−	0.706631i	$-0.249786\pi$
$998$	−1.19306e8	−	6.76615e8i	−0.00379930	−	0.0215469i
$999$	7.02640e9	−	1.21701e10i	0.222974	−	0.386202i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.8.e.a.17.3	yes	30
19.9	even	9	inner	38.8.e.a.9.3	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.8.e.a.9.3	✓	30	19.9	even	9	inner
38.8.e.a.17.3	yes	30	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38919 - 7.87846i) q^{2} +(-9.71662 - 8.15321i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(424.315 - 154.438i) q^{5} +(-77.7330 + 65.2257i) q^{6} +(847.859 + 1468.54i) q^{7} +(-256.000 + 443.405i) q^{8} +(-351.831 - 1995.33i) q^{9} +O(q^{10})\)	\(q+(1.38919 - 7.87846i) q^{2} +(-9.71662 - 8.15321i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(424.315 - 154.438i) q^{5} +(-77.7330 + 65.2257i) q^{6} +(847.859 + 1468.54i) q^{7} +(-256.000 + 443.405i) q^{8} +(-351.831 - 1995.33i) q^{9} +(-627.282 - 3557.49i) q^{10} +(-355.352 + 615.488i) q^{11} +(405.893 + 703.027i) q^{12} +(7814.84 - 6557.43i) q^{13} +(12747.6 - 4639.76i) q^{14} +(-5382.07 - 1958.91i) q^{15} +(3137.72 + 2632.86i) q^{16} +(3787.71 - 21481.2i) q^{17} -16208.9 q^{18} +(-28741.5 - 8233.82i) q^{19} -28899.0 q^{20} +(3734.95 - 21182.0i) q^{21} +(4355.45 + 3654.66i) q^{22} +(43010.3 + 15654.5i) q^{23} +(6102.63 - 2221.18i) q^{24} +(96344.8 - 80842.9i) q^{25} +(-40806.2 - 70678.4i) q^{26} +(-26719.9 + 46280.2i) q^{27} +(-18845.3 - 106877. i) q^{28} +(9277.13 + 52613.2i) q^{29} +(-22909.9 + 39681.2i) q^{30} +(-32572.1 - 56416.5i) q^{31} +(25101.7 - 21062.9i) q^{32} +(8471.03 - 3083.20i) q^{33} +(-163977. - 59682.7i) q^{34} +(586557. + 492180. i) q^{35} +(-22517.2 + 127701. i) q^{36} -262965. q^{37} +(-104797. + 215001. i) q^{38} -129398. q^{39} +(-40146.0 + 227679. i) q^{40} +(153856. + 129100. i) q^{41} +(-161693. - 58851.4i) q^{42} +(478934. - 174318. i) q^{43} +(34843.6 - 29237.2i) q^{44} +(-457442. - 792313. i) q^{45} +(183082. - 317108. i) q^{46} +(134281. + 761547. i) q^{47} +(-9021.77 - 51165.0i) q^{48} +(-1.02596e6 + 1.77701e6i) q^{49} +(-503077. - 871354. i) q^{50} +(-211944. + 177842. i) q^{51} +(-613524. + 223305. i) q^{52} +(1.20284e6 + 437799. i) q^{53} +(327498. + 274803. i) q^{54} +(-55726.5 + 316041. i) q^{55} -868208. q^{56} +(212139. + 314341. i) q^{57} +427399. q^{58} +(293665. - 1.66545e6i) q^{59} +(280800. + 235620. i) q^{60} +(-1.49554e6 - 544331. i) q^{61} +(-489724. + 178245. i) q^{62} +(2.63191e6 - 2.20844e6i) q^{63} +(-131072. - 227023. i) q^{64} +(2.30324e6 - 3.98932e6i) q^{65} +(-12523.1 - 71021.8i) q^{66} +(-220292. - 1.24934e6i) q^{67} +(-698002. + 1.20897e6i) q^{68} +(-290281. - 502781. i) q^{69} +(4.69245e6 - 3.93744e6i) q^{70} +(-4.78651e6 + 1.74215e6i) q^{71} +(974808. + 354801. i) q^{72} +(4.18395e6 + 3.51075e6i) q^{73} +(-365308. + 2.07176e6i) q^{74} -1.59527e6 q^{75} +(1.54829e6 + 1.12432e6i) q^{76} -1.20515e6 q^{77} +(-179758. + 1.01946e6i) q^{78} +(-4.40140e6 - 3.69321e6i) q^{79} +(1.73799e6 + 632578. i) q^{80} +(-3.52692e6 + 1.28369e6i) q^{81} +(1.23085e6 - 1.03280e6i) q^{82} +(1.52373e6 + 2.63918e6i) q^{83} +(-688280. + 1.19214e6i) q^{84} +(-1.71033e6 - 9.69975e6i) q^{85} +(-708027. - 4.01542e6i) q^{86} +(338824. - 586861. i) q^{87} +(-181940. - 315130. i) q^{88} +(-6.28700e6 + 5.27542e6i) q^{89} +(-6.87768e6 + 2.50327e6i) q^{90} +(1.62557e7 + 5.91659e6i) q^{91} +(-2.24399e6 - 1.88293e6i) q^{92} +(-143485. + 813745. i) q^{93} +6.18636e6 q^{94} +(-1.34671e7 + 945054. i) q^{95} -415634. q^{96} +(767151. - 4.35073e6i) q^{97} +(1.25749e7 + 1.05516e7i) q^{98} +(1.35313e6 + 492498. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 45 q^{3} + 360 q^{6} + 1806 q^{7} - 7680 q^{8} - 3105 q^{9}+O(q^{10}) \) 30 * q + 45 * q^3 + 360 * q^6 + 1806 * q^7 - 7680 * q^8 - 3105 * q^9	\( 30 q + 45 q^{3} + 360 q^{6} + 1806 q^{7} - 7680 q^{8} - 3105 q^{9} + 9786 q^{11} - 11130 q^{13} + 6144 q^{14} - 1818 q^{15} - 65250 q^{17} + 29040 q^{18} + 105906 q^{19} - 47616 q^{20} + 172854 q^{21} + 102336 q^{22} + 101004 q^{23} + 23040 q^{24} - 132756 q^{25} - 92112 q^{26} + 43659 q^{27} + 96384 q^{28} - 273912 q^{29} + 58710 q^{31} - 406965 q^{33} + 84960 q^{34} + 356100 q^{35} - 198720 q^{36} - 2598852 q^{37} - 219336 q^{38} + 1769844 q^{39} + 43377 q^{41} - 79056 q^{42} + 1126698 q^{43} + 818688 q^{44} - 912546 q^{45} - 530880 q^{46} + 588306 q^{47} - 368640 q^{48} - 2778285 q^{49} + 1665288 q^{50} + 3972045 q^{51} - 430080 q^{52} + 6520866 q^{53} - 486648 q^{54} - 1666818 q^{55} - 1849344 q^{56} - 6947844 q^{57} - 4573152 q^{58} - 970467 q^{59} + 4634496 q^{60} - 4037670 q^{61} + 755952 q^{62} + 7946472 q^{63} - 3932160 q^{64} + 1497690 q^{65} + 6499272 q^{66} - 4817025 q^{67} + 1472064 q^{68} + 10299876 q^{69} + 2848800 q^{70} - 25171290 q^{71} + 3179520 q^{72} + 1347750 q^{73} - 3123936 q^{74} + 8817984 q^{75} + 1583232 q^{76} - 11476764 q^{77} - 930960 q^{78} + 10777986 q^{79} - 5365035 q^{81} + 347016 q^{82} + 9745314 q^{83} + 877056 q^{84} + 29258556 q^{85} - 9338208 q^{86} + 25598802 q^{87} + 5010432 q^{88} - 20353740 q^{89} - 30112128 q^{90} + 19748724 q^{91} - 14097792 q^{92} - 18738174 q^{93} + 12376608 q^{94} - 20427204 q^{95} - 23005029 q^{97} + 14869008 q^{98} - 45819771 q^{99}+O(q^{100}) \) 30 * q + 45 * q^3 + 360 * q^6 + 1806 * q^7 - 7680 * q^8 - 3105 * q^9 + 9786 * q^11 - 11130 * q^13 + 6144 * q^14 - 1818 * q^15 - 65250 * q^17 + 29040 * q^18 + 105906 * q^19 - 47616 * q^20 + 172854 * q^21 + 102336 * q^22 + 101004 * q^23 + 23040 * q^24 - 132756 * q^25 - 92112 * q^26 + 43659 * q^27 + 96384 * q^28 - 273912 * q^29 + 58710 * q^31 - 406965 * q^33 + 84960 * q^34 + 356100 * q^35 - 198720 * q^36 - 2598852 * q^37 - 219336 * q^38 + 1769844 * q^39 + 43377 * q^41 - 79056 * q^42 + 1126698 * q^43 + 818688 * q^44 - 912546 * q^45 - 530880 * q^46 + 588306 * q^47 - 368640 * q^48 - 2778285 * q^49 + 1665288 * q^50 + 3972045 * q^51 - 430080 * q^52 + 6520866 * q^53 - 486648 * q^54 - 1666818 * q^55 - 1849344 * q^56 - 6947844 * q^57 - 4573152 * q^58 - 970467 * q^59 + 4634496 * q^60 - 4037670 * q^61 + 755952 * q^62 + 7946472 * q^63 - 3932160 * q^64 + 1497690 * q^65 + 6499272 * q^66 - 4817025 * q^67 + 1472064 * q^68 + 10299876 * q^69 + 2848800 * q^70 - 25171290 * q^71 + 3179520 * q^72 + 1347750 * q^73 - 3123936 * q^74 + 8817984 * q^75 + 1583232 * q^76 - 11476764 * q^77 - 930960 * q^78 + 10777986 * q^79 - 5365035 * q^81 + 347016 * q^82 + 9745314 * q^83 + 877056 * q^84 + 29258556 * q^85 - 9338208 * q^86 + 25598802 * q^87 + 5010432 * q^88 - 20353740 * q^89 - 30112128 * q^90 + 19748724 * q^91 - 14097792 * q^92 - 18738174 * q^93 + 12376608 * q^94 - 20427204 * q^95 - 23005029 * q^97 + 14869008 * q^98 - 45819771 * q^99

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