LMFDB - Embedded newform 74.8.f.b.7.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,8,Mod(7,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, 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("74.7");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	74.f (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:	$23.1164918858$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			7.4
Character	$\chi$	$=$	74.7
Dual form			74.8.f.b.53.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(7.51754 - 2.73616i) q^{2} +(-36.4042 - 13.2501i) q^{3} +(49.0268 - 41.1384i) q^{4} +(-1.10281 - 6.25436i) q^{5} -309.925 q^{6} +(125.532 + 711.929i) q^{7} +(256.000 - 443.405i) q^{8} +(-525.635 - 441.061i) q^{9} +(-25.4034 - 43.9999i) q^{10} +(435.627 - 754.529i) q^{11} +(-2329.87 + 848.004i) q^{12} +(-8006.36 + 6718.13i) q^{13} +(2891.65 + 5008.48i) q^{14} +(-42.7236 + 242.297i) q^{15} +(711.263 - 4033.77i) q^{16} +(21500.3 + 18040.9i) q^{17} +(-5158.30 - 1877.47i) q^{18} +(565.620 + 205.869i) q^{19} +(-311.362 - 261.263i) q^{20} +(4863.19 - 27580.5i) q^{21} +(1210.33 - 6864.15i) q^{22} +(39917.9 + 69139.8i) q^{23} +(-15194.6 + 12749.8i) q^{24} +(73375.6 - 26706.5i) q^{25} +(-41806.2 + 72410.5i) q^{26} +(55654.1 + 96395.7i) q^{27} +(35442.1 + 29739.4i) q^{28} +(-70292.1 + 121749. i) q^{29} +(341.789 + 1938.38i) q^{30} +150217. q^{31} +(-5690.10 - 32270.2i) q^{32} +(-25856.2 + 21695.9i) q^{33} +(210992. + 76794.8i) q^{34} +(4314.22 - 1570.25i) q^{35} -43914.8 q^{36} +(39761.3 + 305534. i) q^{37} +4815.37 q^{38} +(380481. - 138484. i) q^{39} +(-3055.53 - 1112.12i) q^{40} +(-60819.7 + 51033.8i) q^{41} +(-38905.5 - 220644. i) q^{42} -646286. q^{43} +(-9682.67 - 54913.2i) q^{44} +(-2178.87 + 3773.92i) q^{45} +(489262. + 410539. i) q^{46} +(-413470. - 716151. i) q^{47} +(-79340.7 + 137422. i) q^{48} +(282793. - 102928. i) q^{49} +(478531. - 401535. i) q^{50} +(-543658. - 941644. i) q^{51} +(-116153. + 658738. i) q^{52} +(-217169. + 1.23163e6i) q^{53} +(682136. + 572380. i) q^{54} +(-5199.51 - 1892.47i) q^{55} +(347809. + 126592. i) q^{56} +(-17863.2 - 14989.0i) q^{57} +(-195297. + 1.10759e6i) q^{58} +(-313710. + 1.77914e6i) q^{59} +(7873.13 + 13636.7i) q^{60} +(1.69067e6 - 1.41864e6i) q^{61} +(1.12926e6 - 411018. i) q^{62} +(248019. - 429582. i) q^{63} +(-131072. - 227023. i) q^{64} +(50847.1 + 42665.8i) q^{65} +(-135012. + 233847. i) q^{66} +(600356. + 3.40479e6i) q^{67} +1.79626e6 q^{68} +(-537073. - 3.04589e6i) q^{69} +(28135.9 - 23608.8i) q^{70} +(-3.86522e6 - 1.40682e6i) q^{71} +(-330131. + 120158. i) q^{72} -4.23800e6 q^{73} +(1.13490e6 + 2.18807e6i) q^{74} -3.02504e6 q^{75} +(36199.7 - 13175.6i) q^{76} +(591856. + 215418. i) q^{77} +(2.48137e6 - 2.08211e6i) q^{78} +(-333614. - 1.89202e6i) q^{79} -26013.0 q^{80} +(-488210. - 2.76878e6i) q^{81} +(-317578. + 550061. i) q^{82} +(-2.55806e6 - 2.14647e6i) q^{83} +(-896192. - 1.55225e6i) q^{84} +(89123.3 - 154366. i) q^{85} +(-4.85848e6 + 1.76834e6i) q^{86} +(4.17211e6 - 3.50082e6i) q^{87} +(-223041. - 386319. i) q^{88} +(1.85527e6 - 1.05217e7i) q^{89} +(-6053.72 + 34332.3i) q^{90} +(-5.78789e6 - 4.85661e6i) q^{91} +(4.80135e6 + 1.74755e6i) q^{92} +(-5.46853e6 - 1.99038e6i) q^{93} +(-5.06778e6 - 4.25237e6i) q^{94} +(663.805 - 3764.63i) q^{95} +(-220438. + 1.25017e6i) q^{96} +(-2.14726e6 - 3.71917e6i) q^{97} +(1.84428e6 - 1.54754e6i) q^{98} +(-561774. + 204469. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9} + 4704 q^{10} + 4539 q^{11} - 2496 q^{12} - 10542 q^{13} + 6744 q^{14} - 39894 q^{15} - 78822 q^{17} + 51792 q^{18} + 79461 q^{19} + 29376 q^{20}+ \cdots + 66155463 q^{99}+O(q^{100}) $ 66 * q - 39 * q^3 + 459 * q^5 - 918 * q^7 + 16896 * q^8 + 3237 * q^9 + 4704 * q^10 + 4539 * q^11 - 2496 * q^12 - 10542 * q^13 + 6744 * q^14 - 39894 * q^15 - 78822 * q^17 + 51792 * q^18 + 79461 * q^19 + 29376 * q^20 - 5835 * q^21 + 18168 * q^22 - 199479 * q^23 + 19968 * q^24 + 356301 * q^25 + 186744 * q^26 - 91689 * q^27 - 91584 * q^28 - 38526 * q^29 + 319152 * q^30 + 1917246 * q^31 - 902847 * q^33 - 205776 * q^34 - 1574793 * q^35 + 3079296 * q^36 - 396513 * q^37 - 692880 * q^38 + 2514306 * q^39 + 470016 * q^40 + 2989350 * q^41 + 46680 * q^42 + 6006348 * q^43 - 145344 * q^44 + 1083726 * q^45 - 588744 * q^46 - 894135 * q^47 + 7973742 * q^49 + 2012400 * q^50 - 524880 * q^51 - 2262720 * q^52 + 1457844 * q^53 + 1452312 * q^54 + 2415690 * q^55 - 1202688 * q^56 + 2734338 * q^57 - 3423360 * q^58 + 3099522 * q^59 - 3102912 * q^60 - 10968396 * q^61 - 3067320 * q^62 - 10727970 * q^63 - 8650752 * q^64 - 13497300 * q^65 - 4598712 * q^66 - 1978119 * q^67 + 5026176 * q^68 - 7251108 * q^69 + 435744 * q^70 - 19555002 * q^71 + 3314688 * q^72 - 31332840 * q^73 + 7607472 * q^74 + 44758074 * q^75 + 5085504 * q^76 + 1982007 * q^77 - 22512264 * q^78 + 10522902 * q^79 + 4816896 * q^80 - 7548876 * q^81 - 7150320 * q^82 + 19771926 * q^83 + 3556224 * q^84 - 6684072 * q^85 + 22982496 * q^86 - 67769667 * q^87 - 2323968 * q^88 - 42018963 * q^89 - 25158672 * q^90 + 4847565 * q^91 - 1096704 * q^92 - 14558475 * q^93 + 3175680 * q^94 + 4508415 * q^95 - 2555904 * q^96 - 39286662 * q^97 + 71630904 * q^98 + 66155463 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	7.51754	−	2.73616i	0.664463	−	0.241845i
$2$	7.51754	−	2.73616i	0.664463	−	0.241845i
$3$	−36.4042	−	13.2501i	−0.778444	−	0.283330i	−0.0779204	−	0.996960i	$-0.524828\pi$
$3$	−36.4042	−	13.2501i	−0.778444	−	0.283330i	−0.700524	+	0.713629i	$0.747050\pi$
$4$	49.0268	−	41.1384i	0.383022	−	0.321394i
$5$	−1.10281	−	6.25436i	−0.00394554	−	0.0223763i	0.982771	−	0.184825i	$-0.0591719\pi$
$5$	−1.10281	−	6.25436i	−0.00394554	−	0.0223763i	−0.986717	+	0.162449i	$0.948061\pi$
$6$	−309.925			−0.585769
$7$	125.532	+	711.929i	0.138329	+	0.784501i	0.972484	+	0.232971i	$0.0748447\pi$
$7$	125.532	+	711.929i	0.138329	+	0.784501i	−0.834155	+	0.551530i	$0.814044\pi$
$8$	256.000	−	443.405i	0.176777	−	0.306186i
$9$	−525.635	−	441.061i	−0.240345	−	0.201674i
$10$	−25.4034	−	43.9999i	−0.00803325	−	0.0139140i
$11$	435.627	−	754.529i	0.0986826	−	0.170923i	−0.812457	−	0.583021i	$-0.801870\pi$
$11$	435.627	−	754.529i	0.0986826	−	0.170923i	0.911140	+	0.412098i	$0.135204\pi$
$12$	−2329.87	+	848.004i	−0.389222	+	0.141665i
$13$	−8006.36	+	6718.13i	−1.01073	+	0.848100i	−0.988434	−	0.151652i	$-0.951541\pi$
$13$	−8006.36	+	6718.13i	−1.01073	+	0.848100i	−0.0222919	+	0.999752i	$0.507096\pi$
$14$	2891.65	+	5008.48i	0.281642	+	0.487818i
$15$	−42.7236	+	242.297i	−0.00326850	+	0.0185366i
$16$	711.263	−	4033.77i	0.0434120	−	0.246202i
$17$	21500.3	+	18040.9i	1.06138	+	0.890608i	0.994244	−	0.107136i	$-0.0341680\pi$
$17$	21500.3	+	18040.9i	1.06138	+	0.890608i	0.0671404	+	0.997744i	$0.478612\pi$
$18$	−5158.30	−	1877.47i	−0.208474	−	0.0758785i
$19$	565.620	+	205.869i	0.0189185	+	0.00688578i	0.351462	−	0.936202i	$-0.385685\pi$
$19$	565.620	+	205.869i	0.0189185	+	0.00688578i	−0.332544	+	0.943088i	$0.607907\pi$
$20$	−311.362	−	261.263i	−0.00870282	−	0.00730254i
$21$	4863.19	−	27580.5i	0.114592	−	0.649883i
$22$	1210.33	−	6864.15i	0.0242340	−	0.137438i
$23$	39917.9	+	69139.8i	0.684101	+	1.18490i	0.973719	+	0.227755i	$0.0731384\pi$
$23$	39917.9	+	69139.8i	0.684101	+	1.18490i	−0.289618	+	0.957142i	$0.593528\pi$
$24$	−15194.6	+	12749.8i	−0.224363	+	0.188263i
$25$	73375.6	−	26706.5i	0.939207	−	0.341844i
$26$	−41806.2	+	72410.5i	−0.466481	+	0.807970i
$27$	55654.1	+	96395.7i	0.544157	+	0.942507i
$28$	35442.1	+	29739.4i	0.305117	+	0.256023i
$29$	−70292.1	+	121749.i	−0.535197	+	0.926988i	0.463957	+	0.885858i	$0.346429\pi$
$29$	−70292.1	+	121749.i	−0.535197	+	0.926988i	−0.999154	+	0.0411300i	$0.986904\pi$
$30$	341.789	+	1938.38i	0.00231118	+	0.0131073i
$31$	150217.			0.905635			0.452817	−	0.891603i	$-0.350419\pi$
$31$	150217.			0.905635			0.452817	+	0.891603i	$0.350419\pi$
$32$	−5690.10	−	32270.2i	−0.0306970	−	0.174091i
$33$	−25856.2	+	21695.9i	−0.125247	+	0.105094i
$34$	210992.	+	76794.8i	0.920640	+	0.335085i
$35$	4314.22	−	1570.25i	0.0170084	−	0.00619056i
$36$	−43914.8			−0.156874
$37$	39761.3	+	305534.i	0.129049	+	0.991638i
$37$	39761.3	+	305534.i	0.129049	+	0.991638i
$38$	4815.37			0.0142360
$39$	380481.	−	138484.i	1.02709	−	0.373829i
$40$	−3055.53	−	1112.12i	−0.00754878	−	0.00274753i
$41$	−60819.7	+	51033.8i	−0.137816	+	0.115642i	−0.709090	−	0.705118i	$-0.750894\pi$
$41$	−60819.7	+	51033.8i	−0.137816	+	0.115642i	0.571274	+	0.820760i	$0.306450\pi$
$42$	−38905.5	−	220644.i	−0.0810287	−	0.459536i
$43$	−646286.			−1.23961			−0.619805	−	0.784756i	$-0.712788\pi$
$43$	−646286.			−1.23961			−0.619805	+	0.784756i	$0.712788\pi$
$44$	−9682.67	−	54913.2i	−0.0171361	−	0.0971834i
$45$	−2178.87	+	3773.92i	−0.00356441	+	0.00617375i
$46$	489262.	+	410539.i	0.741121	+	0.621874i
$47$	−413470.	−	716151.i	−0.580900	−	1.00615i	−0.995373	−	0.0960868i	$-0.969367\pi$
$47$	−413470.	−	716151.i	−0.580900	−	1.00615i	0.414473	−	0.910062i	$-0.363966\pi$
$48$	−79340.7	+	137422.i	−0.103550	+	0.179354i
$49$	282793.	−	102928.i	0.343386	−	0.124982i
$50$	478531.	−	401535.i	0.541396	−	0.454285i
$51$	−543658.	−	941644.i	−0.573892	−	0.994011i
$52$	−116153.	+	658738.i	−0.114556	+	0.649682i
$53$	−217169.	+	1.23163e6i	−0.200370	+	1.13635i	0.704192	+	0.710010i	$0.251309\pi$
$53$	−217169.	+	1.23163e6i	−0.200370	+	1.13635i	−0.904562	+	0.426343i	$0.859802\pi$
$54$	682136.	+	572380.i	0.589512	+	0.494660i
$55$	−5199.51	−	1892.47i	−0.00421398	−	0.00153376i
$56$	347809.	+	126592.i	0.264657	+	0.0963271i
$57$	−17863.2	−	14989.0i	−0.0127761	−	0.0107204i
$58$	−195297.	+	1.10759e6i	−0.131431	+	0.745383i
$59$	−313710.	+	1.77914e6i	−0.198859	+	1.12779i	0.707955	+	0.706258i	$0.249618\pi$
$59$	−313710.	+	1.77914e6i	−0.198859	+	1.12779i	−0.906814	+	0.421530i	$0.861493\pi$
$60$	7873.13	+	13636.7i	0.00470563	+	0.00815039i
$61$	1.69067e6	−	1.41864e6i	0.953686	−	0.800237i	−0.0262286	−	0.999656i	$-0.508350\pi$
$61$	1.69067e6	−	1.41864e6i	0.953686	−	0.800237i	0.979914	+	0.199419i	$0.0639053\pi$
$62$	1.12926e6	−	411018.i	0.601761	−	0.219023i
$63$	248019.	−	429582.i	0.124967	−	0.216448i
$64$	−131072.	−	227023.i	−0.0625000	−	0.108253i
$65$	50847.1	+	42665.8i	0.0229652	+	0.0192701i
$66$	−135012.	+	233847.i	−0.0578052	+	0.100122i
$67$	600356.	+	3.40479e6i	0.243864	+	1.38302i	0.823117	+	0.567871i	$0.192233\pi$
$67$	600356.	+	3.40479e6i	0.243864	+	1.38302i	−0.579254	+	0.815147i	$0.696656\pi$
$68$	1.79626e6			0.692770
$69$	−537073.	−	3.04589e6i	−0.196817	−	1.11620i
$70$	28135.9	−	23608.8i	0.00980431	−	0.00822679i
$71$	−3.86522e6	−	1.40682e6i	−1.28165	−	0.466483i	−0.390673	−	0.920529i	$-0.627758\pi$
$71$	−3.86522e6	−	1.40682e6i	−1.28165	−	0.466483i	−0.890978	+	0.454047i	$0.849980\pi$
$72$	−330131.	+	120158.i	−0.104237	+	0.0379392i
$73$	−4.23800e6			−1.27506			−0.637531	−	0.770425i	$-0.720044\pi$
$73$	−4.23800e6			−1.27506			−0.637531	+	0.770425i	$0.720044\pi$
$74$	1.13490e6	+	2.18807e6i	0.325571	+	0.627697i
$75$	−3.02504e6			−0.827975
$76$	36199.7	−	13175.6i	0.00945927	−	0.00344289i
$77$	591856.	+	215418.i	0.147740	+	0.0537730i
$78$	2.48137e6	−	2.08211e6i	0.592052	−	0.496791i
$79$	−333614.	−	1.89202e6i	−0.0761288	−	0.431748i	−0.998921	−	0.0464491i	$-0.985209\pi$
$79$	−333614.	−	1.89202e6i	−0.0761288	−	0.431748i	0.922792	−	0.385299i	$-0.125902\pi$
$80$	−26013.0			−0.00568036
$81$	−488210.	−	2.76878e6i	−0.102073	−	0.578883i
$82$	−317578.	+	550061.i	−0.0636066	+	0.110170i
$83$	−2.55806e6	−	2.14647e6i	−0.491063	−	0.412051i	0.363344	−	0.931655i	$-0.381635\pi$
$83$	−2.55806e6	−	2.14647e6i	−0.491063	−	0.412051i	−0.854407	+	0.519604i	$0.826079\pi$
$84$	−896192.	−	1.55225e6i	−0.164977	−	0.285749i
$85$	89123.3	−	154366.i	0.0157407	−	0.0272638i
$86$	−4.85848e6	+	1.76834e6i	−0.823675	+	0.299793i
$87$	4.17211e6	−	3.50082e6i	0.679264	−	0.569971i
$88$	−223041.	−	386319.i	−0.0348896	−	0.0604305i
$89$	1.85527e6	−	1.05217e7i	0.278959	−	1.58206i	−0.447137	−	0.894465i	$-0.647557\pi$
$89$	1.85527e6	−	1.05217e7i	0.278959	−	1.58206i	0.726097	−	0.687592i	$-0.241332\pi$
$90$	−6053.72	+	34332.3i	−0.000875333	+	0.00496426i
$91$	−5.78789e6	−	4.85661e6i	−0.805147	−	0.675599i
$92$	4.80135e6	+	1.74755e6i	0.642844	+	0.233976i
$93$	−5.46853e6	−	1.99038e6i	−0.704986	−	0.256594i
$94$	−5.06778e6	−	4.25237e6i	−0.629318	−	0.528061i
$95$	663.805	−	3764.63i	7.94343e−5	−	0.000450494i
$96$	−220438.	+	1.25017e6i	−0.0254294	+	0.144218i
$97$	−2.14726e6	−	3.71917e6i	−0.238882	−	0.413756i	0.721512	−	0.692402i	$-0.243448\pi$
$97$	−2.14726e6	−	3.71917e6i	−0.238882	−	0.413756i	−0.960394	+	0.278646i	$0.910114\pi$
$98$	1.84428e6	−	1.54754e6i	0.197941	−	0.166092i
$99$	−561774.	+	204469.i	−0.0581887	+	0.0211789i
$100$	2.49871e6	−	4.32789e6i	0.249871	−	0.432789i
$101$	2.17976e6	+	3.77545e6i	0.210515	+	0.364623i	0.951876	−	0.306484i	$-0.0991526\pi$
$101$	2.17976e6	+	3.77545e6i	0.210515	+	0.364623i	−0.741361	+	0.671107i	$0.765819\pi$
$102$	−6.66346e6	−	5.59131e6i	−0.621727	−	0.521691i
$103$	−4.69630e6	+	8.13423e6i	−0.423473	+	0.733476i	−0.996276	−	0.0862164i	$-0.972522\pi$
$103$	−4.69630e6	+	8.13423e6i	−0.423473	+	0.733476i	0.572804	+	0.819692i	$0.305856\pi$
$104$	929226.	+	5.26990e6i	0.0810037	+	0.459395i
$105$	−177862.			−0.0149941
$106$	1.73735e6	+	9.85300e6i	0.141683	+	0.803522i
$107$	−8.09118e6	+	6.78931e6i	−0.638511	+	0.535775i	−0.903561	−	0.428460i	$-0.859056\pi$
$107$	−8.09118e6	+	6.78931e6i	−0.638511	+	0.535775i	0.265049	+	0.964235i	$0.414612\pi$
$108$	6.69411e6	+	2.43646e6i	0.511340	+	0.186113i
$109$	1.06434e7	−	3.87388e6i	0.787205	−	0.286519i	0.0830316	−	0.996547i	$-0.473540\pi$
$109$	1.06434e7	−	3.87388e6i	0.787205	−	0.286519i	0.704174	+	0.710028i	$0.251318\pi$
$110$	−44265.6			−0.00317097
$111$	2.60086e6	−	1.16496e7i	0.180504	−	0.808498i
$112$	2.96104e6			0.199151
$113$	4.00406e6	−	1.45736e6i	0.261051	−	0.0950148i	−0.208179	−	0.978091i	$-0.566754\pi$
$113$	4.00406e6	−	1.45736e6i	0.261051	−	0.0950148i	0.469230	+	0.883076i	$0.344531\pi$
$114$	−175300.	−	63803.9i	−0.0110819	−	0.00403348i
$115$	388403.	−	325909.i	0.0238144	−	0.0199827i
$116$	1.56238e6	+	8.86069e6i	0.0929359	+	0.527066i
$117$	7.17153e6			0.413963
$118$	2.50968e6	+	1.42331e7i	0.140615	+	0.797467i
$119$	−1.01448e7	+	1.75714e7i	−0.551862	+	0.955854i
$120$	96498.6	+	80972.0i	0.00509785	+	0.00427760i
$121$	9.36404e6	+	1.62190e7i	0.480523	+	0.832291i
$122$	8.82807e6	−	1.52907e7i	0.440156	−	0.762372i
$123$	2.89030e6	−	1.05198e6i	0.140047	−	0.0509730i
$124$	7.36466e6	−	6.17969e6i	0.346878	−	0.291065i
$125$	−496031.	−	859152.i	−0.0227156	−	0.0393446i
$126$	689090.	−	3.90802e6i	0.0306887	−	0.174044i
$127$	−5.36091e6	+	3.04032e7i	−0.232234	+	1.31706i	0.616128	+	0.787646i	$0.288701\pi$
$127$	−5.36091e6	+	3.04032e7i	−0.232234	+	1.31706i	−0.848362	+	0.529417i	$0.822411\pi$
$128$	−1.60651e6	−	1.34802e6i	−0.0677094	−	0.0568149i
$129$	2.35275e7	+	8.56332e6i	0.964967	+	0.351219i
$130$	498986.	+	181616.i	0.0199199	+	0.00725024i
$131$	1.75300e7	+	1.47094e7i	0.681291	+	0.571671i	0.916383	−	0.400302i	$-0.131095\pi$
$131$	1.75300e7	+	1.47094e7i	0.681291	+	0.571671i	−0.235092	+	0.971973i	$0.575539\pi$
$132$	−375112.	+	2.12737e6i	−0.0141956	+	0.0805070i
$133$	−75560.4	+	428525.i	−0.00278493	+	0.0157941i
$134$	1.38292e7	+	2.39530e7i	0.496514	+	0.859988i
$135$	541517.	−	454387.i	0.0189428	−	0.0158949i
$136$	1.35035e7	−	4.91487e6i	0.460320	−	0.167543i
$137$	−892863.	+	1.54648e6i	−0.0296663	+	0.0513835i	−0.880477	−	0.474088i	$-0.842778\pi$
$137$	−892863.	+	1.54648e6i	−0.0296663	+	0.0513835i	0.850811	+	0.525472i	$0.176111\pi$
$138$	−1.23715e7	−	2.14281e7i	−0.400725	−	0.694076i
$139$	−4.04872e7	−	3.39728e7i	−1.27869	−	1.07295i	−0.993423	−	0.114503i	$-0.963472\pi$
$139$	−4.04872e7	−	3.39728e7i	−1.27869	−	1.07295i	−0.285270	−	0.958447i	$-0.592083\pi$
$140$	146915.	−	254464.i	0.00452500	−	0.00783752i
$141$	5.56301e6	+	3.15494e7i	0.167126	+	0.947817i
$142$	−3.29062e7			−0.964426
$143$	1.58123e6	+	8.96763e6i	0.0452189	+	0.256449i
$144$	−2.15300e6	+	1.80658e6i	−0.0600864	+	0.0504184i
$145$	838983.	+	305365.i	0.0228542	+	0.00831824i
$146$	−3.18594e7	+	1.15959e7i	−0.847231	+	0.308367i
$147$	−1.16587e7			−0.302718
$148$	1.45185e7	+	1.33436e7i	0.368135	+	0.338344i
$149$	2.51436e7			0.622695			0.311347	−	0.950296i	$-0.399220\pi$
$149$	2.51436e7			0.622695			0.311347	+	0.950296i	$0.399220\pi$
$150$	−2.27409e7	+	8.27701e6i	−0.550159	+	0.200241i
$151$	4.46339e7	+	1.62454e7i	1.05498	+	0.383983i	0.810542	−	0.585681i	$-0.199173\pi$
$151$	4.46339e7	+	1.62454e7i	1.05498	+	0.383983i	0.244442	+	0.969664i	$0.421395\pi$
$152$	236082.	−	198096.i	0.00545269	−	0.00457535i
$153$	−3.34419e6	−	1.89658e7i	−0.0754868	−	0.428107i
$154$	5.03872e6			0.111173
$155$	−165661.	−	939511.i	−0.00357322	−	0.0202647i
$156$	1.29568e7	−	2.24418e7i	0.273251	−	0.473284i
$157$	5.14435e7	+	4.31662e7i	1.06092	+	0.890216i	0.994199	−	0.107556i	$-0.0343024\pi$
$157$	5.14435e7	+	4.31662e7i	1.06092	+	0.890216i	0.0667192	+	0.997772i	$0.478747\pi$
$158$	−7.68482e6	−	1.33105e7i	−0.155001	−	0.268469i
$159$	2.42250e7	−	4.19589e7i	0.477940	−	0.827816i
$160$	−195554.	+	71175.9i	−0.00377439	+	0.00137377i
$161$	−4.42116e7	+	3.70980e7i	−0.834922	+	0.700583i
$162$	−1.12460e7	−	1.94786e7i	−0.207823	−	0.359961i
$163$	2.57229e6	−	1.45882e7i	0.0465225	−	0.263842i	−0.952671	−	0.304004i	$-0.901676\pi$
$163$	2.57229e6	−	1.45882e7i	0.0465225	−	0.263842i	0.999193	+	0.0401619i	$0.0127874\pi$
$164$	−882350.	+	5.00405e6i	−0.0156202	+	0.0885867i
$165$	164209.	+	137787.i	0.00284579	+	0.00238790i
$166$	−2.51034e7	−	9.13689e6i	−0.425946	−	0.155032i
$167$	2.27257e7	+	8.27147e6i	0.377580	+	0.137428i	0.523837	−	0.851819i	$-0.324500\pi$
$167$	2.27257e7	+	8.27147e6i	0.377580	+	0.137428i	−0.146256	+	0.989247i	$0.546722\pi$
$168$	−1.09844e7	−	9.21698e6i	−0.178728	−	0.149971i
$169$	8.07231e6	−	4.57804e7i	0.128645	−	0.729585i
$170$	247618.	−	1.40431e6i	0.00386554	−	0.0219226i
$171$	−206509.	−	357685.i	−0.00315830	−	0.00547034i
$172$	−3.16854e7	+	2.65872e7i	−0.474798	+	0.398403i
$173$	−6.22870e7	+	2.26706e7i	−0.914610	+	0.332891i	−0.756092	−	0.654465i	$-0.772894\pi$
$173$	−6.22870e7	+	2.26706e7i	−0.914610	+	0.332891i	−0.158518	+	0.987356i	$0.550672\pi$
$174$	2.17852e7	−	3.77331e7i	0.313502	−	0.543001i
$175$	2.82241e7	+	4.88857e7i	0.398096	+	0.689522i
$176$	−2.73375e6	−	2.29389e6i	−0.0377976	−	0.0317160i
$177$	3.49940e7	−	6.06115e7i	0.474338	−	0.821577i
$178$	−1.48421e7	−	8.41739e7i	−0.197254	−	1.11868i
$179$	8.10296e7			1.05599			0.527993	−	0.849249i	$-0.322945\pi$
$179$	8.10296e7			1.05599			0.527993	+	0.849249i	$0.322945\pi$
$180$	48429.7	+	274659.i	0.000618954	+	0.00351026i
$181$	7.05063e7	−	5.91618e7i	0.883798	−	0.741594i	−0.0831586	−	0.996536i	$-0.526501\pi$
$181$	7.05063e7	−	5.91618e7i	0.883798	−	0.741594i	0.966956	+	0.254942i	$0.0820564\pi$
$182$	−5.67992e7	−	2.06732e7i	−0.698381	−	0.254190i
$183$	−8.03448e7	+	2.92431e7i	−0.969123	+	0.352732i
$184$	4.08759e7			0.483732
$185$	1.86707e6	−	585628.i	0.0216800	−	0.00680018i
$186$	−4.65559e7			−0.530493
$187$	2.29785e7	−	8.36348e6i	0.256966	−	0.0935279i
$188$	−4.97324e7	−	1.81011e7i	−0.545868	−	0.198680i
$189$	−6.16405e7	+	5.17225e7i	−0.664125	+	0.557267i
$190$	−5310.44	−	30117.0i	−5.61685e−5	−	0.000318548i
$191$	−1.55052e8			−1.61013			−0.805067	−	0.593184i	$-0.797871\pi$
$191$	−1.55052e8			−1.61013			−0.805067	+	0.593184i	$0.797871\pi$
$192$	1.76350e6	+	1.00013e7i	0.0179813	+	0.101977i
$193$	−4.30546e6	+	7.45728e6i	−0.0431092	+	0.0746672i	−0.886775	−	0.462202i	$-0.847060\pi$
$193$	−4.30546e6	+	7.45728e6i	−0.0431092	+	0.0746672i	0.843666	+	0.536869i	$0.180393\pi$
$194$	−2.63184e7	−	2.20837e7i	−0.258793	−	0.217153i
$195$	−1.28573e6	−	2.22694e6i	−0.0124173	−	0.0215074i
$196$	9.63015e6	−	1.66799e7i	0.0913559	−	0.158233i
$197$	1.26723e8	−	4.61232e7i	1.18092	−	0.429821i	0.324396	−	0.945921i	$-0.394839\pi$
$197$	1.26723e8	−	4.61232e7i	1.18092	−	0.429821i	0.856528	+	0.516100i	$0.172617\pi$
$198$	−3.66370e6	+	3.07421e6i	−0.0335422	+	0.0281452i
$199$	−6.91886e7	−	1.19838e8i	−0.622370	−	1.07798i	−0.989043	−	0.147627i	$-0.952836\pi$
$199$	−6.91886e7	−	1.19838e8i	−0.622370	−	1.07798i	0.366673	−	0.930350i	$-0.380497\pi$
$200$	6.94234e6	−	3.93720e7i	0.0613622	−	0.348002i
$201$	2.32581e7	−	1.31903e8i	0.202017	−	1.14570i
$202$	2.67166e7	+	2.24179e7i	0.228061	+	0.191366i
$203$	−9.55008e7	−	3.47595e7i	−0.801255	−	0.291633i
$204$	−6.53916e7	−	2.38006e7i	−0.539282	−	0.196283i
$205$	386256.	+	324108.i	0.00313139	+	0.00262755i
$206$	−1.30481e7	+	7.39992e7i	−0.103995	+	0.589782i
$207$	9.51258e6	−	5.39485e7i	0.0745422	−	0.422750i
$208$	2.14048e7	+	3.70742e7i	0.164926	+	0.285660i
$209$	401734.	−	337095.i	0.00304387	−	0.00255411i
$210$	−1.33708e6	+	486658.i	−0.00996301	+	0.00362624i
$211$	−2.57966e7	+	4.46811e7i	−0.189049	+	0.327443i	−0.944933	−	0.327262i	$-0.893874\pi$
$211$	−2.57966e7	+	4.46811e7i	−0.189049	+	0.327443i	0.755884	+	0.654705i	$0.227207\pi$
$212$	4.00200e7	+	6.93167e7i	0.288471	+	0.499646i
$213$	1.22070e8	+	1.02429e8i	0.865525	+	0.726262i
$214$	−4.22491e7	+	7.31776e7i	−0.294693	+	0.510423i
$215$	712732.	+	4.04210e6i	0.00489093	+	0.0277379i
$216$	5.69898e7			0.384777
$217$	1.88571e7	+	1.06944e8i	0.125275	+	0.710471i
$218$	6.94127e7	−	5.82442e7i	0.453776	−	0.380763i
$219$	1.54281e8	+	5.61538e7i	0.992564	+	0.361264i
$220$	−332768.	+	121118.i	−0.00210699	+	0.000766882i
$221$	−2.93340e8			−1.82809
$222$	−1.23230e7	−	9.46924e7i	−0.0755928	−	0.580871i
$223$	−2.28141e8			−1.37764			−0.688822	−	0.724931i	$-0.741872\pi$
$223$	−2.28141e8			−1.37764			−0.688822	+	0.724931i	$0.741872\pi$
$224$	2.22598e7	−	8.10190e6i	0.132328	−	0.0481636i
$225$	−5.03480e7	−	1.83252e7i	−0.294675	−	0.107253i
$226$	2.61131e7	−	2.19115e7i	0.150480	−	0.126268i
$227$	1.75489e7	+	9.95246e7i	0.0995769	+	0.564729i	0.993248	+	0.116007i	$0.0370095\pi$
$227$	1.75489e7	+	9.95246e7i	0.0995769	+	0.564729i	−0.893672	+	0.448722i	$0.851879\pi$
$228$	−1.49240e6			−0.00833899
$229$	2.74132e7	+	1.55468e8i	0.150847	+	0.855494i	0.962485	+	0.271334i	$0.0874649\pi$
$229$	2.74132e7	+	1.55468e8i	0.150847	+	0.855494i	−0.811638	+	0.584160i	$0.801424\pi$
$230$	2.02810e6	−	3.51277e6i	0.0109911	−	0.0190371i
$231$	−1.86918e7	−	1.56842e7i	−0.0997719	−	0.0837185i
$232$	3.59895e7	+	6.23357e7i	0.189221	+	0.327740i
$233$	1.37409e8	−	2.37999e8i	0.711655	−	1.23262i	−0.252581	−	0.967576i	$-0.581279\pi$
$233$	1.37409e8	−	2.37999e8i	0.711655	−	1.23262i	0.964236	−	0.265046i	$-0.0853873\pi$
$234$	5.39123e7	−	1.96225e7i	0.275063	−	0.100115i
$235$	−4.02308e6	+	3.37577e6i	−0.0202219	+	0.0169682i
$236$	5.78107e7	+	1.00131e8i	0.286297	+	0.495880i
$237$	−1.29244e7	+	7.32978e7i	−0.0630653	+	0.357661i
$238$	−2.81861e7	+	1.59851e8i	−0.135524	+	0.768594i
$239$	1.04434e8	+	8.76304e7i	0.494821	+	0.415204i	0.855750	−	0.517389i	$-0.173096\pi$
$239$	1.04434e8	+	8.76304e7i	0.494821	+	0.415204i	−0.360929	+	0.932593i	$0.617540\pi$
$240$	946985.	+	344674.i	0.00442185	+	0.00160942i
$241$	−1.74352e8	−	6.34589e7i	−0.802356	−	0.292034i	−0.0918934	−	0.995769i	$-0.529292\pi$
$241$	−1.74352e8	−	6.34589e7i	−0.802356	−	0.292034i	−0.710462	+	0.703735i	$0.751514\pi$
$242$	1.14772e8	+	9.63055e7i	0.520575	+	0.436815i
$243$	2.33578e7	−	1.32469e8i	0.104426	−	0.592231i
$244$	2.45277e7	−	1.39103e8i	0.108092	−	0.613017i
$245$	−955618.	−	1.65518e6i	−0.00415148	−	0.00719058i
$246$	1.88495e7	−	1.58166e7i	0.0807286	−	0.0677394i
$247$	−5.91162e6	+	2.15165e6i	−0.0249613	+	0.00908516i
$248$	3.84555e7	−	6.66070e7i	0.160095	−	0.277293i
$249$	6.46834e7	+	1.12035e8i	0.265519	+	0.459892i
$250$	−6.07971e6	−	5.10149e6i	−0.0246089	−	0.0206494i
$251$	1.01523e8	−	1.75844e8i	0.405236	−	0.701889i	−0.589113	−	0.808051i	$-0.700523\pi$
$251$	1.01523e8	−	1.75844e8i	0.405236	−	0.701889i	0.994349	+	0.106162i	$0.0338561\pi$
$252$	−5.51272e6	−	3.12642e7i	−0.0217002	−	0.123068i
$253$	6.95573e7			0.270035
$254$	4.28873e7	+	2.43226e8i	0.164214	+	0.931305i
$255$	−5.28983e6	+	4.43869e6i	−0.0199779	+	0.0167635i
$256$	−1.57654e7	−	5.73815e6i	−0.0587308	−	0.0213763i
$257$	1.02121e8	−	3.71691e7i	0.375275	−	0.136589i	−0.147495	−	0.989063i	$-0.547121\pi$
$257$	1.02121e8	−	3.71691e7i	0.375275	−	0.136589i	0.522770	+	0.852474i	$0.324899\pi$
$258$	2.00300e8			0.726126
$259$	−2.12527e8	+	6.66615e7i	−0.760090	+	0.238411i
$260$	4.24808e6			0.0149894
$261$	9.06469e7	−	3.29928e7i	0.315581	−	0.114862i
$262$	1.72030e8	+	6.26138e7i	0.590948	+	0.215088i
$263$	1.78512e8	−	1.49789e8i	0.605092	−	0.507732i	−0.287986	−	0.957635i	$-0.592986\pi$
$263$	1.78512e8	−	1.49789e8i	0.605092	−	0.507732i	0.893078	+	0.449902i	$0.148541\pi$
$264$	3.00090e6	+	1.70189e7i	0.0100378	+	0.0569271i
$265$	7.94252e6			0.0262179
$266$	604484.	+	3.42820e6i	0.00196924	+	0.0111681i
$267$	−2.06953e8	+	3.58453e8i	−0.665399	+	1.15251i
$268$	1.69501e8	+	1.42228e8i	0.537899	+	0.451351i
$269$	−5.29204e7	−	9.16608e7i	−0.165764	−	0.287112i	0.771162	−	0.636638i	$-0.219676\pi$
$269$	−5.29204e7	−	9.16608e7i	−0.165764	−	0.287112i	−0.936926	+	0.349527i	$0.886342\pi$
$270$	2.82760e6	−	4.89755e6i	0.00874269	−	0.0151428i
$271$	−1.65272e8	+	6.01542e7i	−0.504438	+	0.183600i	−0.581689	−	0.813411i	$-0.697608\pi$
$271$	−1.65272e8	+	6.01542e7i	−0.504438	+	0.183600i	0.0772510	+	0.997012i	$0.475386\pi$
$272$	8.80651e7	−	7.38954e7i	0.265346	−	0.222652i
$273$	1.46353e8	+	2.53491e8i	0.435344	+	0.754039i
$274$	−2.48070e6	+	1.40688e7i	−0.00728531	+	0.0413170i
$275$	1.18136e7	−	6.69981e7i	0.0342544	−	0.194266i
$276$	−1.51634e8	−	1.27236e8i	−0.434126	−	0.364275i
$277$	3.74534e8	+	1.36319e8i	1.05880	+	0.385370i	0.811976	−	0.583691i	$-0.198392\pi$
$277$	3.74534e8	+	1.36319e8i	1.05880	+	0.385370i	0.246820	+	0.969061i	$0.420614\pi$
$278$	−3.97319e8	−	1.44612e8i	−1.10913	−	0.403691i
$279$	−7.89594e7	−	6.62548e7i	−0.217665	−	0.182643i
$280$	408184.	−	2.31493e6i	0.00111123	−	0.00630209i
$281$	7.70508e7	−	4.36977e8i	0.207160	−	1.17486i	−0.686845	−	0.726804i	$-0.741005\pi$
$281$	7.70508e7	−	4.36977e8i	0.207160	−	1.17486i	0.894005	−	0.448057i	$-0.147884\pi$
$282$	1.28144e8	+	2.21953e8i	0.340273	+	0.589371i
$283$	−1.87057e8	+	1.56960e8i	−0.490594	+	0.411657i	−0.854239	−	0.519880i	$-0.825976\pi$
$283$	−1.87057e8	+	1.56960e8i	−0.490594	+	0.411657i	0.363645	+	0.931537i	$0.381532\pi$
$284$	−2.47374e8	+	9.00368e7i	−0.640826	+	0.233241i
$285$	−74046.8	+	128253.i	−0.000189474	+	0.000328178i
$286$	3.64239e7	+	6.30880e7i	0.0920672	+	0.159465i
$287$	−4.39673e7	−	3.68929e7i	−0.109785	−	0.0921205i
$288$	−1.12422e7	+	1.94720e7i	−0.0277317	+	0.0480328i
$289$	6.55342e7	+	3.71663e8i	0.159708	+	0.905747i
$290$	7.14262e6			0.0171975
$291$	2.88902e7	+	1.63845e8i	0.0687267	+	0.389769i
$292$	−2.07776e8	+	1.74345e8i	−0.488377	+	0.409797i
$293$	−1.42181e8	−	5.17496e7i	−0.330221	−	0.120190i	0.171589	−	0.985169i	$-0.445110\pi$
$293$	−1.42181e8	−	5.17496e7i	−0.330221	−	0.120190i	−0.501810	+	0.864978i	$0.667332\pi$
$294$	−8.76445e7	+	3.19000e7i	−0.201145	+	0.0732108i
$295$	1.14733e7			0.0260203
$296$	1.45654e8	+	6.05863e7i	0.326439	+	0.135786i
$297$	9.69777e7			0.214795
$298$	1.89018e8	−	6.87969e7i	0.413758	−	0.150596i
$299$	−7.84087e8	−	2.85384e8i	−1.69635	−	0.617421i
$300$	−1.48308e8	+	1.24446e8i	−0.317133	+	0.266106i
$301$	−8.11297e7	−	4.60110e8i	−0.171474	−	0.972475i
$302$	3.79987e8			0.793862
$303$	−2.93274e7	−	1.66324e8i	−0.0605654	−	0.343484i
$304$	1.23273e6	−	2.13516e6i	0.00251659	−	0.00435885i
$305$	−1.07372e7	−	9.00958e6i	−0.0216691	−	0.0181826i
$306$	−7.70337e7	−	1.33426e8i	−0.153694	−	0.266205i
$307$	−1.28294e8	+	2.22212e8i	−0.253059	+	0.438312i	−0.964367	−	0.264569i	$-0.914770\pi$
$307$	−1.28294e8	+	2.22212e8i	−0.253059	+	0.438312i	0.711307	+	0.702881i	$0.248103\pi$
$308$	3.78788e7	−	1.37867e7i	0.0738700	−	0.0268865i
$309$	2.78744e8	−	2.33894e8i	0.537466	−	0.450987i
$310$	−3.81602e6	−	6.60953e6i	−0.00727519	−	0.0126010i
$311$	5.50954e7	−	3.12462e8i	0.103861	−	0.589027i	−0.887808	−	0.460215i	$-0.847772\pi$
$311$	5.50954e7	−	3.12462e8i	0.103861	−	0.589027i	0.991669	−	0.128812i	$-0.0411165\pi$
$312$	3.59987e7	−	2.04159e8i	0.0671037	−	0.380564i
$313$	3.60069e8	+	3.02134e8i	0.663714	+	0.556922i	0.911197	−	0.411970i	$-0.135159\pi$
$313$	3.60069e8	+	3.02134e8i	0.663714	+	0.556922i	−0.247483	+	0.968892i	$0.579604\pi$
$314$	5.04839e8	+	1.83746e8i	0.920235	+	0.334938i
$315$	−2.96028e6	−	1.07745e6i	−0.00533637	−	0.00194228i
$316$	−9.41906e7	−	7.90353e7i	−0.167920	−	0.140902i
$317$	−2.18828e7	+	1.24104e8i	−0.0385830	+	0.218815i	−0.998003	−	0.0631658i	$-0.979880\pi$
$317$	−2.18828e7	+	1.24104e8i	−0.0385830	+	0.218815i	0.959420	+	0.281981i	$0.0909914\pi$
$318$	6.73059e7	−	3.81711e8i	0.117370	−	0.665640i
$319$	6.12423e7	+	1.06075e8i	0.105629	+	0.182955i
$320$	−1.27534e6	+	1.07014e6i	−0.00217571	+	0.00182563i
$321$	3.84512e8	−	1.39951e8i	0.648847	−	0.236161i
$322$	−2.30857e8	+	3.99855e8i	−0.385342	+	0.667433i
$323$	8.44694e6	+	1.46305e7i	0.0139473	+	0.0241575i
$324$	−1.37839e8	−	1.15660e8i	−0.225145	−	0.188919i
$325$	−4.08053e8	+	7.06769e8i	−0.659364	+	1.14205i
$326$	−2.05783e7	−	1.16705e8i	−0.0328964	−	0.186565i
$327$	−4.38794e8			−0.693975
$328$	7.05880e6	+	4.00324e7i	0.0110452	+	0.0626402i
$329$	4.57945e8	−	3.84261e8i	0.708969	−	0.594896i
$330$	1.61145e6	+	586522.i	0.00246842	+	0.000898432i
$331$	−8.17383e8	+	2.97503e8i	−1.23888	+	0.450914i	−0.876628	−	0.481168i	$-0.840213\pi$
$331$	−8.17383e8	+	2.97503e8i	−1.23888	+	0.450914i	−0.362247	+	0.932082i	$0.617990\pi$
$332$	−2.13716e8			−0.320519
$333$	1.13859e8	−	1.78137e8i	0.168971	−	0.264361i
$334$	1.93473e8			0.284124
$335$	2.06327e7	−	7.50968e6i	0.0299846	−	0.0109135i
$336$	−1.07795e8	−	3.92340e7i	−0.155028	−	0.0564255i
$337$	7.13584e8	−	5.98768e8i	1.01564	−	0.852224i	0.0265678	−	0.999647i	$-0.491542\pi$
$337$	7.13584e8	−	5.98768e8i	1.01564	−	0.852224i	0.989074	+	0.147423i	$0.0470978\pi$
$338$	−6.45785e7	−	3.66243e8i	−0.0909661	−	0.515894i
$339$	−1.65075e8			−0.230134
$340$	−1.98094e6	−	1.12345e7i	−0.00273335	−	0.0155016i
$341$	6.54386e7	−	1.13343e8i	0.0893704	−	0.154794i
$342$	−2.53113e6	−	2.12387e6i	−0.00342155	−	0.00287102i
$343$	4.06452e8	+	7.03995e8i	0.543850	+	0.941976i
$344$	−1.65449e8	+	2.86566e8i	−0.219134	+	0.379552i
$345$	−1.84578e7	+	6.71810e6i	−0.0241999	+	0.00880804i
$346$	−4.06215e8	+	3.40855e8i	−0.527217	+	0.442387i
$347$	−7.07056e8	−	1.22466e9i	−0.908449	−	1.57348i	−0.816219	−	0.577742i	$-0.803934\pi$
$347$	−7.07056e8	−	1.22466e9i	−0.908449	−	1.57348i	−0.0922295	−	0.995738i	$-0.529399\pi$
$348$	6.05275e7	−	3.43268e8i	0.0769884	−	0.436623i
$349$	−1.68121e8	+	9.53461e8i	−0.211706	+	1.20064i	0.674826	+	0.737976i	$0.264218\pi$
$349$	−1.68121e8	+	9.53461e8i	−0.211706	+	1.20064i	−0.886532	+	0.462667i	$0.846893\pi$
$350$	3.45935e8	+	2.90274e8i	0.431277	+	0.361885i
$351$	−1.09319e9	−	3.97887e8i	−1.34933	−	0.491117i
$352$	−2.68275e7	−	9.76442e6i	−0.0327855	−	0.0119329i
$353$	4.43597e8	+	3.72222e8i	0.536756	+	0.450392i	0.870427	−	0.492298i	$-0.163843\pi$
$353$	4.43597e8	+	3.72222e8i	0.536756	+	0.450392i	−0.333671	+	0.942690i	$0.608287\pi$
$354$	9.72264e7	−	5.51398e8i	0.116486	−	0.660624i
$355$	−4.53617e6	+	2.57259e7i	−0.00538134	+	0.0305191i
$356$	−3.41890e8	−	5.92170e8i	−0.401616	−	0.695619i
$357$	6.02137e8	−	5.05253e8i	0.700416	−	0.587719i
$358$	6.09143e8	−	2.21710e8i	0.701663	−	0.255385i
$359$	−1.55797e7	+	2.69848e7i	−0.0177717	+	0.0307814i	−0.874774	−	0.484530i	$-0.838991\pi$
$359$	−1.55797e7	+	2.69848e7i	−0.0177717	+	0.0307814i	0.857003	+	0.515312i	$0.172324\pi$
$360$	1.11558e6	+	1.93225e6i	0.00126021	+	0.00218275i
$361$	−6.84468e8	−	5.74337e8i	−0.765734	−	0.642527i
$362$	3.68158e8	−	6.37668e8i	0.407900	−	0.706504i
$363$	−1.25988e8	−	7.14514e8i	−0.138247	−	0.784039i
$364$	−4.83555e8			−0.525522
$365$	4.67372e6	+	2.65060e7i	0.00503081	+	0.0285311i
$366$	−5.23981e8	+	4.39672e8i	−0.558640	+	0.468755i
$367$	2.86450e6	+	1.04259e6i	0.00302494	+	0.00110099i	0.343532	−	0.939141i	$-0.388377\pi$
$367$	2.86450e6	+	1.04259e6i	0.00302494	+	0.00110099i	−0.340507	+	0.940242i	$0.610599\pi$
$368$	3.07286e8	−	1.11843e8i	0.321422	−	0.116988i
$369$	5.44780e7			0.0564454
$370$	1.24334e7	−	9.51108e6i	0.0127610	−	0.00976166i
$371$	−9.04091e8			−0.919186
$372$	−3.49986e8	+	1.27385e8i	−0.352493	+	0.128297i
$373$	−4.19649e8	−	1.52740e8i	−0.418702	−	0.152395i	0.124073	−	0.992273i	$-0.460404\pi$
$373$	−4.19649e8	−	1.52740e8i	−0.418702	−	0.152395i	−0.542775	+	0.839878i	$0.682626\pi$
$374$	1.49858e8	−	1.25746e8i	0.148125	−	0.124292i
$375$	6.67383e6	+	3.78492e7i	0.00653531	+	0.0370636i
$376$	−4.23393e8			−0.410758
$377$	−2.55145e8	−	1.44700e9i	−0.245241	−	1.39083i
$378$	−3.21864e8	+	5.57484e8i	−0.306514	+	0.530898i
$379$	1.42460e9	+	1.19538e9i	1.34417	+	1.12789i	0.980533	+	0.196353i	$0.0629098\pi$
$379$	1.42460e9	+	1.19538e9i	1.34417	+	1.12789i	0.363638	+	0.931541i	$0.381535\pi$
$380$	−122326.	−	211876.i	−0.000114361	−	0.000198079i
$381$	5.98004e8	−	1.03577e9i	0.553945	−	0.959461i
$382$	−1.16561e9	+	4.24249e8i	−1.06987	+	0.389402i
$383$	5.10819e8	−	4.28628e8i	0.464591	−	0.389839i	−0.380226	−	0.924894i	$-0.624154\pi$
$383$	5.10819e8	−	4.28628e8i	0.464591	−	0.389839i	0.844817	+	0.535055i	$0.179709\pi$
$384$	4.06224e7	+	7.03601e7i	0.0366106	+	0.0634114i
$385$	694595.	−	3.93924e6i	0.000620325	−	0.00351804i
$386$	−1.19622e7	+	6.78409e7i	−0.0105866	+	0.0600393i
$387$	3.39711e8	+	2.85051e8i	0.297935	+	0.249997i
$388$	−2.58274e8	−	9.40041e7i	−0.224476	−	0.0817026i
$389$	1.34630e9	+	4.90013e8i	1.15963	+	0.422070i	0.848964	−	0.528451i	$-0.177227\pi$
$389$	1.34630e9	+	4.90013e8i	1.15963	+	0.422070i	0.310663	+	0.950520i	$0.399449\pi$
$390$	−1.57588e7	−	1.32232e7i	−0.0134523	−	0.0112878i
$391$	−3.89097e8	+	2.20668e9i	−0.329184	+	1.86690i
$392$	2.67561e7	−	1.51742e8i	0.0224348	−	0.127234i
$393$	−4.43266e8	−	7.67759e8i	−0.368375	−	0.638044i
$394$	8.26441e8	−	6.93466e8i	0.680730	−	0.571201i
$395$	−1.14654e7	+	4.17308e6i	−0.00936054	+	0.00340696i
$396$	−1.91305e7	+	3.31349e7i	−0.0154808	+	0.0268135i
$397$	6.46929e8	+	1.12051e9i	0.518907	+	0.898774i	0.999759	+	0.0219718i	$0.00699439\pi$
$397$	6.46929e8	+	1.12051e9i	0.518907	+	0.898774i	−0.480851	+	0.876802i	$0.659672\pi$
$398$	−8.48025e8	−	7.11577e8i	−0.674245	−	0.565759i
$399$	8.42869e6	−	1.45989e7i	0.00664286	−	0.0115058i
$400$	−5.55387e7	−	3.14976e8i	−0.0433896	−	0.246075i
$401$	8.27509e7			0.0640866			0.0320433	−	0.999486i	$-0.489799\pi$
$401$	8.27509e7			0.0640866			0.0320433	+	0.999486i	$0.489799\pi$
$402$	−1.86065e8	−	1.05523e9i	−0.142848	−	0.810130i
$403$	−1.20269e9	+	1.00918e9i	−0.915348	+	0.768068i
$404$	2.62182e8	+	9.54266e7i	0.197819	+	0.0720004i
$405$	−1.67785e7	+	6.10689e6i	−0.0125505	+	0.00456801i
$406$	−8.13039e8			−0.602935
$407$	2.47855e8	+	1.03098e8i	0.182229	+	0.0758000i
$408$	−5.56706e8			−0.405803
$409$	1.95167e9	−	7.10351e8i	1.41051	−	0.513383i	0.479229	−	0.877690i	$-0.340916\pi$
$409$	1.95167e9	−	7.10351e8i	1.41051	−	0.513383i	0.931279	+	0.364307i	$0.118694\pi$
$410$	3.79051e6	+	1.37963e6i	0.00271615	+	0.000988598i
$411$	5.29950e7	−	4.44681e7i	0.0376520	−	0.0315938i
$412$	1.04384e8	+	5.91994e8i	0.0735352	+	0.417039i
$413$	−1.30600e9			−0.912259
$414$	−7.61006e7	−	4.31588e8i	−0.0527093	−	0.298929i
$415$	−1.06037e7	+	1.83662e7i	−0.00728265	+	0.0126139i
$416$	2.62352e8	+	2.20140e8i	0.178673	+	0.149924i
$417$	1.02376e9	+	1.77321e9i	0.691391	+	1.19752i
$418$	2.09770e6	−	3.63333e6i	0.00140484	−	0.00243326i
$419$	4.86676e8	−	1.77136e8i	0.323215	−	0.117641i	−0.175317	−	0.984512i	$-0.556095\pi$
$419$	4.86676e8	−	1.77136e8i	0.323215	−	0.117641i	0.498532	+	0.866871i	$0.333873\pi$
$420$	−8.71999e6	+	7.31694e6i	−0.00574306	+	0.00481900i
$421$	1.25936e9	+	2.18128e9i	0.822551	+	1.42470i	0.903777	+	0.428004i	$0.140783\pi$
$421$	1.25936e9	+	2.18128e9i	0.822551	+	1.42470i	−0.0812264	+	0.996696i	$0.525884\pi$
$422$	−7.16727e7	+	4.06476e8i	−0.0464259	+	0.263294i
$423$	−9.85314e7	+	5.58800e8i	−0.0632971	+	0.358975i
$424$	4.90514e8	+	4.11590e8i	0.312515	+	0.262231i
$425$	2.05940e9	+	7.49562e8i	1.30131	+	0.473638i
$426$	1.19793e9	+	4.36009e8i	0.750752	+	0.273251i
$427$	1.22221e9	+	1.02555e9i	0.759709	+	0.637471i
$428$	−1.17384e8	+	6.65716e8i	−0.0723694	+	0.410427i
$429$	6.12579e7	−	3.47411e8i	0.0374595	−	0.212443i
$430$	1.64178e7	+	2.84365e7i	0.00995810	+	0.0172479i
$431$	−2.71960e8	+	2.28201e8i	−0.163619	+	0.137293i	−0.720921	−	0.693017i	$-0.756281\pi$
$431$	−2.71960e8	+	2.28201e8i	−0.163619	+	0.137293i	0.557302	+	0.830310i	$0.311837\pi$
$432$	4.28423e8	−	1.55933e8i	0.255670	−	0.0930563i
$433$	−5.23718e8	+	9.07105e8i	−0.310020	+	0.536970i	−0.978366	−	0.206880i	$-0.933669\pi$
$433$	−5.23718e8	+	9.07105e8i	−0.310020	+	0.536970i	0.668346	+	0.743850i	$0.267002\pi$
$434$	4.34374e8	+	7.52358e8i	0.255064	+	0.441785i
$435$	−2.64964e7	−	2.22332e7i	−0.0154339	−	0.0129506i
$436$	3.62447e8	−	6.27777e8i	0.209432	−	0.362746i
$437$	8.34463e6	+	4.73247e7i	0.00478324	+	0.0271271i
$438$	1.31346e9			0.746892
$439$	−9.56915e7	−	5.42694e8i	−0.0539818	−	0.306146i	0.945848	−	0.324611i	$-0.105233\pi$
$439$	−9.56915e7	−	5.42694e8i	−0.0539818	−	0.306146i	−0.999830	+	0.0184646i	$0.994122\pi$
$440$	−2.17020e6	+	1.82102e6i	−0.00121455	+	0.00101913i
$441$	−1.94044e8	−	7.06261e7i	−0.107737	−	0.0392130i
$442$	−2.20520e9	+	8.02625e8i	−1.21470	+	0.442115i
$443$	2.96415e9			1.61990			0.809948	−	0.586502i	$-0.199495\pi$
$443$	2.96415e9			1.61990			0.809948	+	0.586502i	$0.199495\pi$
$444$	−3.51732e8	−	6.78137e8i	−0.190709	−	0.367686i
$445$	−6.78527e7			−0.0365012
$446$	−1.71506e9	+	6.24231e8i	−0.915393	+	0.333176i
$447$	−9.15333e8	−	3.33154e8i	−0.484733	−	0.176428i
$448$	1.45171e8	−	1.21813e8i	0.0762792	−	0.0640058i
$449$	2.99521e8	+	1.69867e9i	0.156158	+	0.885618i	0.957719	+	0.287705i	$0.0928923\pi$
$449$	2.99521e8	+	1.69867e9i	0.156158	+	0.885618i	−0.801561	+	0.597913i	$0.795997\pi$
$450$	−4.28634e8			−0.221739
$451$	1.20117e7	+	6.81219e7i	0.00616578	+	0.0349679i
$452$	1.36353e8	−	2.36170e8i	0.0694512	−	0.120293i
$453$	−1.40961e9	−	1.18280e9i	−0.712452	−	0.597818i
$454$	4.04240e8	+	7.00164e8i	0.202742	+	0.351159i
$455$	−2.39921e7	+	4.15555e7i	−0.0119406	+	0.0206818i
$456$	−1.12192e7	+	4.08345e6i	−0.00554095	+	0.00201674i
$457$	1.38846e9	−	1.16506e9i	0.680498	−	0.571006i	−0.235654	−	0.971837i	$-0.575723\pi$
$457$	1.38846e9	−	1.16506e9i	0.680498	−	0.571006i	0.916152	+	0.400831i	$0.131279\pi$
$458$	6.31466e8	+	1.09373e9i	0.307129	+	0.531963i
$459$	−5.42485e8	+	3.07658e9i	−0.261844	+	1.48499i
$460$	5.63480e6	−	3.19566e7i	0.00269915	−	0.0153076i
$461$	1.65509e9	+	1.38878e9i	0.786806	+	0.660209i	0.944953	−	0.327207i	$-0.106107\pi$
$461$	1.65509e9	+	1.38878e9i	0.786806	+	0.660209i	−0.158147	+	0.987416i	$0.550552\pi$
$462$	−1.83431e8	−	6.67633e7i	−0.0865416	−	0.0314986i
$463$	4.43654e8	+	1.61477e8i	0.207736	+	0.0756096i	0.443792	−	0.896130i	$-0.353633\pi$
$463$	4.43654e8	+	1.61477e8i	0.207736	+	0.0756096i	−0.236056	+	0.971739i	$0.575855\pi$
$464$	4.41113e8	+	3.70138e8i	0.204992	+	0.172009i
$465$	−6.41780e6	+	3.63972e7i	−0.00296006	+	0.0167874i
$466$	3.81773e8	−	2.16514e9i	0.174765	−	0.991142i
$467$	−1.45207e9	−	2.51506e9i	−0.659750	−	1.14272i	−0.980680	−	0.195617i	$-0.937329\pi$
$467$	−1.45207e9	−	2.51506e9i	−0.659750	−	1.14272i	0.320931	−	0.947103i	$-0.396004\pi$
$468$	3.51597e8	−	2.95025e8i	0.158557	−	0.133045i
$469$	−2.34860e9	+	8.54821e8i	−1.05125	+	0.382622i
$470$	−2.10071e7	+	3.63853e7i	−0.00933303	+	0.0161653i
$471$	−1.30081e9	−	2.25306e9i	−0.573640	−	0.993574i
$472$	7.08569e8	+	5.94560e8i	0.310159	+	0.260255i
$473$	−2.81540e8	+	4.87641e8i	−0.122328	+	0.211878i
$474$	1.03395e8	+	5.86383e8i	0.0445939	+	0.252905i
$475$	4.70008e7			0.0201223
$476$	2.25489e8	+	1.27881e9i	0.0958299	+	0.543478i
$477$	6.57373e8	−	5.51601e8i	0.277330	−	0.232708i
$478$	1.02486e9	+	3.73017e8i	0.429206	+	0.156218i
$479$	−2.01530e9	+	7.33511e8i	−0.837850	+	0.304953i	−0.725077	−	0.688668i	$-0.758196\pi$
$479$	−2.01530e9	+	7.33511e8i	−0.837850	+	0.304953i	−0.112774	+	0.993621i	$0.535974\pi$
$480$	8.06208e6			0.00332738
$481$	−2.37096e9	−	2.17909e9i	−0.971441	−	0.892828i
$482$	−1.48433e9			−0.603762
$483$	2.10104e9	−	7.64716e8i	0.848436	−	0.308806i
$484$	1.12631e9	+	4.09945e8i	0.451544	+	0.164349i
$485$	−2.08930e7	+	1.75313e7i	−0.00831580	+	0.00697779i
$486$	−1.86862e8	−	1.05975e9i	−0.0738405	−	0.418771i
$487$	1.13768e9			0.446344			0.223172	−	0.974779i	$-0.428359\pi$
$487$	1.13768e9			0.446344			0.223172	+	0.974779i	$0.428359\pi$
$488$	−1.96221e8	−	1.11283e9i	−0.0764322	−	0.433469i
$489$	−2.86937e8	+	4.96989e8i	−0.110970	+	0.192205i
$490$	−1.17127e7	−	9.82815e6i	−0.00449751	−	0.00377386i
$491$	−2.39856e9	−	4.15442e9i	−0.914461	−	1.58389i	−0.807689	−	0.589609i	$-0.799282\pi$
$491$	−2.39856e9	−	4.15442e9i	−0.914461	−	1.58389i	−0.106772	−	0.994284i	$-0.534051\pi$
$492$	9.84252e7	−	1.70478e8i	0.0372588	−	0.0645341i
$493$	−3.70777e9	+	1.34952e9i	−1.39363	+	0.507240i
$494$	−3.85535e7	+	3.23503e7i	−0.0143886	+	0.0120735i
$495$	1.89835e6	+	3.28804e6i	0.000703491	+	0.00121848i
$496$	1.06844e8	−	6.05941e8i	0.0393155	−	0.222969i
$497$	5.16349e8	−	2.92836e9i	0.188667	−	1.06998i
$498$	7.92806e8	+	6.65243e8i	0.287650	+	0.241367i
$499$	−1.46323e9	−	5.32570e8i	−0.527180	−	0.191878i	0.0646985	−	0.997905i	$-0.479391\pi$
$499$	−1.46323e9	−	5.32570e8i	−0.527180	−	0.191878i	−0.591879	+	0.806027i	$0.701614\pi$
$500$	−5.96630e7	−	2.17155e7i	−0.0213457	−	0.00776919i
$501$	−7.17714e8	−	6.02233e8i	−0.254988	−	0.213960i
$502$	2.82069e8	−	1.59970e9i	0.0995160	−	0.564383i
$503$	8.52519e8	−	4.83488e9i	0.298687	−	1.69394i	−0.353140	−	0.935570i	$-0.614886\pi$
$503$	8.52519e8	−	4.83488e9i	0.298687	−	1.69394i	0.651827	−	0.758368i	$-0.274003\pi$
$504$	−1.26986e8	−	2.19946e8i	−0.0441823	−	0.0765261i
$505$	2.12091e7	−	1.77966e7i	0.00732830	−	0.00614917i
$506$	5.22900e8	−	1.90320e8i	0.179429	−	0.0653066i
$507$	−9.00459e8	+	1.55964e9i	−0.306857	+	0.531492i
$508$	9.87912e8	+	1.71111e9i	0.334345	+	0.579103i
$509$	−4.13818e9	−	3.47234e9i	−1.39090	−	1.16711i	−0.964973	−	0.262350i	$-0.915502\pi$
$509$	−4.13818e9	−	3.47234e9i	−1.39090	−	1.16711i	−0.425930	−	0.904756i	$-0.640053\pi$
$510$	−2.76215e7	+	4.78418e7i	−0.00922044	+	0.0159703i
$511$	−5.32006e8	−	3.01716e9i	−0.176378	−	1.00029i
$512$	−1.34218e8			−0.0441942
$513$	1.16342e7	+	6.59808e7i	0.00380475	+	0.0215778i
$514$	6.66000e8	−	5.58840e8i	0.216323	−	0.181517i
$515$	5.60535e7	+	2.04018e7i	0.0180833	+	0.00658178i
$516$	1.50576e9	−	5.48053e8i	0.482484	−	0.175610i
$517$	−7.20475e8			−0.229299
$518$	−1.41528e9	+	1.08264e9i	−0.447393	+	0.342239i
$519$	2.56790e9			0.806291
$520$	3.19351e7	−	1.16234e7i	0.00995993	−	0.00362512i
$521$	−4.31186e9	−	1.56939e9i	−1.33577	−	0.486182i	−0.427295	−	0.904112i	$-0.640533\pi$
$521$	−4.31186e9	−	1.56939e9i	−1.33577	−	0.486182i	−0.908479	+	0.417930i	$0.862756\pi$
$522$	5.91168e8	−	4.96049e8i	0.181913	−	0.152643i
$523$	−7.68916e7	−	4.36074e8i	−0.0235030	−	0.133292i	0.970799	−	0.239896i	$-0.0771134\pi$
$523$	−7.68916e7	−	4.36074e8i	−0.0235030	−	0.133292i	−0.994302	+	0.106604i	$0.966002\pi$
$524$	1.46456e9			0.444681
$525$	−3.79741e8	−	2.15362e9i	−0.114533	−	0.649547i
$526$	9.32121e8	−	1.61448e9i	0.279269	−	0.483708i
$527$	3.22971e9	+	2.71005e9i	0.961227	+	0.806565i
$528$	6.91259e7	+	1.19730e8i	0.0204372	+	0.0353983i
$529$	−1.48446e9	+	2.57116e9i	−0.435987	+	0.755152i
$530$	5.97082e7	−	2.17320e7i	0.0174208	−	0.00634066i
$531$	9.49604e8	−	7.96813e8i	0.275240	−	0.230954i
$532$	1.39243e7	+	2.41176e7i	0.00400944	+	0.00694455i
$533$	1.44093e8	−	8.17190e8i	0.0412189	−	0.233764i
$534$	−5.74992e8	+	3.26094e9i	−0.163406	+	0.926721i
$535$	5.13858e7	+	4.31178e7i	0.0145079	+	0.0121736i
$536$	1.66339e9	+	6.05425e8i	0.466571	+	0.169818i
$537$	−2.94982e9	−	1.07365e9i	−0.822026	−	0.299193i
$538$	−6.48630e8	−	5.44265e8i	−0.179580	−	0.150686i
$539$	4.55301e7	−	2.58214e8i	0.0125238	−	0.0710263i
$540$	7.85613e6	−	4.45543e7i	0.00214699	−	0.0121762i
$541$	3.23065e9	+	5.59566e9i	0.877203	+	1.51936i	0.854398	+	0.519620i	$0.173926\pi$
$541$	3.23065e9	+	5.59566e9i	0.877203	+	1.51936i	0.0228052	+	0.999740i	$0.492740\pi$
$542$	−1.07785e9	+	9.04424e8i	−0.290778	+	0.243991i
$543$	−3.35062e9	+	1.21953e9i	−0.898103	+	0.326883i
$544$	4.59843e8	−	7.96472e8i	0.122466	−	0.212117i
$545$	−3.59663e7	−	6.22955e7i	−0.00951719	−	0.0164842i
$546$	1.79381e9	+	1.50518e9i	0.471630	+	0.395745i
$547$	−6.65158e8	+	1.15209e9i	−0.173768	+	0.300975i	−0.939734	−	0.341906i	$-0.888928\pi$
$547$	−6.65158e8	+	1.15209e9i	−0.173768	+	0.300975i	0.765966	+	0.642881i	$0.222261\pi$
$548$	1.98456e7	+	1.12550e8i	0.00515149	+	0.0292156i
$549$	−1.51439e9			−0.390601
$550$	−9.45085e7	−	5.35985e8i	−0.0242215	−	0.137367i
$551$	−6.48231e7	+	5.43930e7i	−0.0165082	+	0.0138520i
$552$	−1.48806e9	−	5.41608e8i	−0.376558	−	0.137056i
$553$	1.30510e9	−	4.75018e8i	0.328176	−	0.119446i
$554$	3.18857e9			0.796731
$555$	−7.57288e7	−	3.41944e6i	−0.0188034	−	0.000849044i
$556$	−3.38255e9			−0.834607
$557$	−3.88091e9	+	1.41254e9i	−0.951569	+	0.346343i	−0.770724	−	0.637169i	$-0.780105\pi$
$557$	−3.88091e9	+	1.41254e9i	−0.951569	+	0.346343i	−0.180845	+	0.983512i	$0.557883\pi$
$558$	−7.74864e8	−	2.82027e8i	−0.188802	−	0.0687182i
$559$	5.17440e9	−	4.34184e9i	1.25291	−	1.05131i
$560$	−3.26548e6	−	1.85194e7i	−0.000785757	−	0.00445625i
$561$	−9.47330e8			−0.226533
$562$	−6.16407e8	−	3.49582e9i	−0.146484	−	0.830752i
$563$	−1.04915e9	+	1.81719e9i	−0.247777	+	0.429162i	−0.962909	−	0.269828i	$-0.913033\pi$
$563$	−1.04915e9	+	1.81719e9i	−0.247777	+	0.429162i	0.715132	+	0.698989i	$0.246367\pi$
$564$	1.57063e9	+	1.31792e9i	0.368635	+	0.309322i
$565$	−1.35306e7	−	2.34356e7i	−0.00315607	−	0.00546647i
$566$	−9.76744e8	+	1.69177e9i	−0.226424	+	0.392178i
$567$	1.90989e9	−	6.95142e8i	0.440014	−	0.160152i
$568$	−1.61329e9	+	1.35371e9i	−0.369397	+	0.309961i
$569$	1.14261e9	+	1.97906e9i	0.260019	+	0.450367i	0.966247	−	0.257618i	$-0.0829377\pi$
$569$	1.14261e9	+	1.97906e9i	0.260019	+	0.450367i	−0.706227	+	0.707985i	$0.749604\pi$
$570$	−205730.	+	1.16675e6i	−4.65302e−5	+	0.000263886i
$571$	−2.99823e8	+	1.70038e9i	−0.0673966	+	0.382225i	0.932388	+	0.361460i	$0.117721\pi$
$571$	−2.99823e8	+	1.70038e9i	−0.0673966	+	0.382225i	−0.999784	+	0.0207656i	$0.993390\pi$
$572$	4.46437e8	+	3.74605e8i	0.0997411	+	0.0836927i
$573$	5.64457e9	+	2.05445e9i	1.25340	+	0.456200i
$574$	−4.31471e8	−	1.57042e8i	−0.0952269	−	0.0346598i
$575$	4.77548e9	+	4.00710e9i	1.04756	+	0.879009i
$576$	−3.12350e7	+	1.77142e8i	−0.00681024	+	0.0386228i
$577$	1.46831e9	−	8.32720e9i	0.318202	−	1.80461i	−0.235475	−	0.971880i	$-0.575665\pi$
$577$	1.46831e9	−	8.32720e9i	0.318202	−	1.80461i	0.553677	−	0.832732i	$-0.313224\pi$
$578$	1.50959e9	+	2.61468e9i	0.325170	+	0.563211i
$579$	2.55547e8	−	2.14429e8i	0.0547136	−	0.0459101i
$580$	5.36949e7	−	1.95434e7i	0.0114271	−	0.00415912i
$581$	1.20701e9	−	2.09061e9i	0.255326	−	0.442238i
$582$	6.65489e8	+	1.15266e9i	0.139930	+	0.242366i
$583$	8.34692e8	+	7.00389e8i	0.174456	+	0.146386i
$584$	−1.08493e9	+	1.87915e9i	−0.225401	+	0.390406i
$585$	−7.90885e6	−	4.48533e7i	−0.00163331	−	0.00926294i
$586$	−1.21045e9			−0.248487
$587$	2.14299e8	+	1.21535e9i	0.0437308	+	0.248010i	0.998835	−	0.0482612i	$-0.0153680\pi$
$587$	2.14299e8	+	1.21535e9i	0.0437308	+	0.248010i	−0.955104	+	0.296271i	$0.904257\pi$
$588$	−5.71588e8	+	4.79619e8i	−0.115948	+	0.0972917i
$589$	8.49658e7	+	3.09250e7i	0.0171333	+	0.00623600i
$590$	8.62512e7	−	3.13929e7i	0.0172895	−	0.00629287i
$591$	−5.22437e9			−1.04106
$592$	1.26073e9	+	5.69270e7i	0.249746	+	0.0112770i
$593$	−8.65489e9			−1.70439			−0.852197	−	0.523221i	$-0.824730\pi$
$593$	−8.65489e9			−1.70439			−0.852197	+	0.523221i	$0.824730\pi$
$594$	7.29034e8	−	2.65347e8i	0.142723	−	0.0519471i
$595$	1.21086e8	+	4.40715e7i	0.0235658	+	0.00857726i
$596$	1.23271e9	−	1.03437e9i	0.238506	−	0.200130i
$597$	9.30895e8	+	5.27937e9i	0.179057	+	1.01548i
$598$	−6.67527e9			−1.27648
$599$	−8.17151e8	−	4.63430e9i	−0.155349	−	0.881028i	−0.958466	−	0.285207i	$-0.907938\pi$
$599$	−8.17151e8	−	4.63430e9i	−0.155349	−	0.881028i	0.803117	−	0.595821i	$-0.203173\pi$
$600$	−7.74411e8	+	1.34132e9i	−0.146367	+	0.253515i
$601$	−3.68345e7	−	3.09078e7i	−0.00692141	−	0.00580775i	0.639320	−	0.768941i	$-0.279216\pi$
$601$	−3.68345e7	−	3.09078e7i	−0.00692141	−	0.00580775i	−0.646242	+	0.763133i	$0.723660\pi$
$602$	−1.86883e9	−	3.23691e9i	−0.349126	−	0.604704i
$603$	1.18615e9	−	2.05447e9i	0.220307	−	0.381583i
$604$	2.85657e9	−	1.03971e9i	0.527492	−	0.191991i
$605$	9.11126e7	−	7.64526e7i	0.0167276	−	0.0140362i
$606$	−6.75560e8	−	1.17010e9i	−0.123313	−	0.213585i
$607$	−6.71139e8	+	3.80622e9i	−0.121801	+	0.690770i	0.861355	+	0.508004i	$0.169616\pi$
$607$	−6.71139e8	+	3.80622e9i	−0.121801	+	0.690770i	−0.983156	+	0.182766i	$0.941495\pi$
$608$	3.42499e6	−	1.94241e7i	0.000618012	−	0.00350492i
$609$	3.01607e9	+	2.53078e9i	0.541104	+	0.454040i
$610$	−1.05369e8	−	3.83512e7i	−0.0187957	−	0.00684107i
$611$	8.12159e9	+	2.95602e9i	1.44044	+	0.524279i
$612$	−9.44180e8	−	7.92261e8i	−0.166504	−	0.139713i
$613$	1.24108e9	−	7.03850e9i	0.217614	−	1.23415i	−0.658698	−	0.752407i	$-0.728892\pi$
$613$	1.24108e9	−	7.03850e9i	0.217614	−	1.23415i	0.876312	−	0.481744i	$-0.159996\pi$
$614$	−3.56449e8	+	2.02152e9i	−0.0621452	+	0.352443i
$615$	−9.76692e6	−	1.69168e7i	−0.00169315	−	0.00293262i
$616$	2.47032e8	−	2.07285e8i	0.0425816	−	0.0357302i
$617$	−4.95444e9	+	1.80327e9i	−0.849174	+	0.309074i	−0.729703	−	0.683764i	$-0.760342\pi$
$617$	−4.95444e9	+	1.80327e9i	−0.849174	+	0.309074i	−0.119470	+	0.992838i	$0.538120\pi$
$618$	1.45550e9	−	2.52100e9i	0.248057	−	0.429648i
$619$	−1.13889e8	−	1.97262e8i	−0.0193003	−	0.0334292i	0.856214	−	0.516621i	$-0.172811\pi$
$619$	−1.13889e8	−	1.97262e8i	−0.0193003	−	0.0334292i	−0.875514	+	0.483192i	$0.839477\pi$
$620$	−4.67718e7	−	3.92462e7i	−0.00788158	−	0.00661343i
$621$	−4.44319e9	+	7.69582e9i	−0.744516	+	1.28954i
$622$	−4.40763e8	−	2.49969e9i	−0.0734411	−	0.416505i
$623$	7.72362e9			1.27971
$624$	−2.87990e8	−	1.63327e9i	−0.0474495	−	0.269099i
$625$	4.66832e9	−	3.91719e9i	0.764858	−	0.641792i
$626$	3.53352e9	+	1.28610e9i	0.575702	+	0.209538i
$627$	−1.90913e7	+	6.94867e6i	−0.00309314	+	0.00112581i
$628$	4.29790e9			0.692465
$629$	−4.65722e9	+	7.28639e9i	−0.746190	+	1.16744i
$630$	−2.52021e7			−0.00401555
$631$	−1.26060e9	+	4.58821e8i	−0.199745	+	0.0727011i	−0.439955	−	0.898020i	$-0.645006\pi$
$631$	−1.26060e9	+	4.58821e8i	−0.199745	+	0.0727011i	0.240211	+	0.970721i	$0.422783\pi$
$632$	−9.24335e8	−	3.36430e8i	−0.145653	−	0.0530134i
$633$	1.53113e9	−	1.28477e9i	0.239939	−	0.201332i
$634$	1.75062e8	+	9.92829e8i	0.0272823	+	0.154726i
$635$	1.96065e8			0.0303873
$636$	−5.38447e8	−	3.05369e9i	−0.0829934	−	0.470679i
$637$	−1.57266e9	+	2.72392e9i	−0.241072	+	0.417548i
$638$	7.50629e8	+	6.29852e8i	0.114433	+	0.0960210i
$639$	1.41120e9	+	2.44427e9i	0.213962	+	0.370592i
$640$	−6.65934e6	+	1.15343e7i	−0.00100416	+	0.00173925i
$641$	−5.98527e8	+	2.17846e8i	−0.0897596	+	0.0326698i	−0.386510	−	0.922285i	$-0.626319\pi$
$641$	−5.98527e8	+	2.17846e8i	−0.0897596	+	0.0326698i	0.296750	+	0.954955i	$0.404097\pi$
$642$	2.50765e9	−	2.10417e9i	0.374020	−	0.313840i
$643$	1.64682e9	+	2.85238e9i	0.244291	+	0.423125i	0.961932	−	0.273288i	$-0.0881113\pi$
$643$	1.64682e9	+	2.85238e9i	0.244291	+	0.423125i	−0.717641	+	0.696413i	$0.754778\pi$
$644$	−6.41405e8	+	3.63759e9i	−0.0946307	+	0.536677i
$645$	2.76116e7	−	1.56593e8i	0.00405166	−	0.0229781i
$646$	1.03532e8	+	8.68734e7i	0.0151098	+	0.0126786i
$647$	5.30178e8	+	1.92969e8i	0.0769585	+	0.0280106i	0.380213	−	0.924899i	$-0.375851\pi$
$647$	5.30178e8	+	1.92969e8i	0.0769585	+	0.0280106i	−0.303254	+	0.952910i	$0.598073\pi$
$648$	−1.35267e9	−	4.92332e8i	−0.195290	−	0.0710798i
$649$	1.20575e9	+	1.01174e9i	0.173141	+	0.145283i
$650$	−1.13372e9	+	6.42966e9i	−0.161924	+	0.918315i
$651$	7.30534e8	−	4.14306e9i	0.103778	−	0.588556i
$652$	−4.74023e8	−	8.21033e8i	−0.0669782	−	0.116010i
$653$	−6.63367e8	+	5.56631e8i	−0.0932305	+	0.0782296i	−0.688212	−	0.725510i	$-0.741604\pi$
$653$	−6.63367e8	+	5.56631e8i	−0.0932305	+	0.0782296i	0.594981	+	0.803740i	$0.297159\pi$
$654$	−3.29865e9	+	1.20061e9i	−0.461121	+	0.167834i
$655$	7.26657e7	−	1.25861e8i	0.0101038	−	0.0175003i
$656$	1.62600e8	+	2.81631e8i	0.0224883	+	0.0389509i
$657$	2.22764e9	+	1.86922e9i	0.306455	+	0.257146i
$658$	2.39122e9	−	4.14171e9i	0.327211	−	0.566747i
$659$	1.14716e9	+	6.50585e9i	0.156143	+	0.885533i	0.957733	+	0.287659i	$0.0928768\pi$
$659$	1.14716e9	+	6.50585e9i	0.156143	+	0.885533i	−0.801590	+	0.597875i	$0.796012\pi$
$660$	1.37190e7			0.00185746
$661$	2.23844e8	+	1.26948e9i	0.0301467	+	0.170971i	0.996164	−	0.0875075i	$-0.0278902\pi$
$661$	2.23844e8	+	1.26948e9i	0.0301467	+	0.170971i	−0.966017	+	0.258478i	$0.916779\pi$
$662$	−5.33070e9	+	4.47299e9i	−0.714136	+	0.599231i
$663$	1.06788e10	+	3.88677e9i	1.42307	+	0.517954i
$664$	−1.60662e9	+	5.84761e8i	−0.212973	+	0.0775158i
$665$	2.76347e6			0.000364401
$666$	3.68529e8	−	1.65069e9i	0.0483406	−	0.216523i
$667$	−1.12236e10			−1.46451
$668$	1.45444e9	−	5.29374e8i	0.188790	−	0.0687140i
$669$	8.30531e9	+	3.02288e9i	1.07242	+	0.390328i
$670$	1.34559e8	−	1.12909e8i	0.0172843	−	0.0145033i
$671$	−3.33904e8	−	1.89366e9i	−0.0426670	−	0.241977i
$672$	−9.17700e8			−0.116656
$673$	6.42469e8	+	3.64362e9i	0.0812456	+	0.460766i	0.998104	+	0.0615535i	$0.0196055\pi$
$673$	6.42469e8	+	3.64362e9i	0.0812456	+	0.460766i	−0.916858	+	0.399213i	$0.869283\pi$
$674$	3.72607e9	−	6.45374e9i	0.468750	−	0.811899i
$675$	6.65805e9	+	5.58676e9i	0.833266	+	0.699193i
$676$	−1.48757e9	−	2.57655e9i	−0.185210	−	0.320793i
$677$	5.54053e9	−	9.59649e9i	0.686264	−	1.18864i	−0.286774	−	0.957998i	$-0.592583\pi$
$677$	5.54053e9	−	9.59649e9i	0.686264	−	1.18864i	0.973038	−	0.230646i	$-0.0740839\pi$
$678$	−1.24096e9	+	4.51671e8i	−0.152916	+	0.0556568i
$679$	2.37823e9	−	1.99557e9i	0.291548	−	0.244638i
$680$	−4.56311e7	−	7.90355e7i	−0.00556519	−	0.00963919i
$681$	6.79853e8	−	3.85564e9i	0.0824898	−	0.467823i
$682$	1.81813e8	−	1.03111e9i	0.0219472	−	0.124469i
$683$	−5.83240e9	−	4.89396e9i	−0.700446	−	0.587744i	0.221455	−	0.975171i	$-0.428920\pi$
$683$	−5.83240e9	−	4.89396e9i	−0.700446	−	0.587744i	−0.921901	+	0.387427i	$0.873364\pi$
$684$	−2.48391e7	−	9.04069e6i	−0.00296783	−	0.00108020i
$685$	1.06569e7	+	3.87880e6i	0.00126682	+	0.000461085i
$686$	4.98176e9	+	4.18019e9i	0.589180	+	0.494381i
$687$	1.06200e9	−	6.02292e9i	0.124962	−	0.708694i
$688$	−4.59679e8	+	2.60697e9i	−0.0538140	+	0.305194i
$689$	−6.53549e9	−	1.13198e10i	−0.761221	−	1.31847i
$690$	−1.20376e8	+	1.01007e8i	−0.0139498	+	0.0117052i
$691$	6.20007e9	−	2.25664e9i	0.714864	−	0.260189i	0.0411201	−	0.999154i	$-0.486907\pi$
$691$	6.20007e9	−	2.25664e9i	0.714864	−	0.260189i	0.673744	+	0.738965i	$0.264685\pi$
$692$	−2.12110e9	+	3.67386e9i	−0.243327	+	0.421455i
$693$	−2.16088e8	−	3.74275e8i	−0.0246641	−	0.0427194i
$694$	−8.66618e9	−	7.27179e9i	−0.984169	−	0.825816i
$695$	−1.67828e8	+	2.90687e8i	−0.0189635	+	0.0328457i
$696$	−4.84220e8	−	2.74615e9i	−0.0544390	−	0.308739i
$697$	−2.22834e9			−0.249268
$698$	1.34497e9	+	7.62769e9i	0.149699	+	0.848983i
$699$	−8.15577e9	+	6.84350e9i	−0.903223	+	0.757894i
$700$	3.39482e9	+	1.23561e9i	0.374088	+	0.136157i
$701$	2.38178e9	−	8.66899e8i	0.261150	−	0.0950507i	−0.208127	−	0.978102i	$-0.566737\pi$
$701$	2.38178e9	−	8.66899e8i	0.261150	−	0.0950507i	0.469277	+	0.883051i	$0.344515\pi$
$702$	−9.30675e9			−1.01536
$703$	−4.04102e7	+	1.81002e8i	−0.00438679	+	0.0196489i
$704$	−2.28394e8			−0.0246707
$705$	1.91186e8	−	6.95862e7i	0.0205492	−	0.00747930i
$706$	4.35322e9	+	1.58444e9i	0.465579	+	0.169457i
$707$	−2.41422e9	+	2.02577e9i	−0.256926	+	0.215587i
$708$	−7.77811e8	−	4.41119e9i	−0.0823679	−	0.467131i
$709$	−6.43599e9			−0.678193			−0.339097	−	0.940752i	$-0.610121\pi$
$709$	−6.43599e9			−0.678193			−0.339097	+	0.940752i	$0.610121\pi$
$710$	3.62894e7	+	2.05807e8i	0.00380518	+	0.0215803i
$711$	−6.59135e8	+	1.14166e9i	−0.0687750	+	0.119122i
$712$	−4.19044e9	−	3.51620e9i	−0.435091	−	0.365084i
$713$	5.99634e9	+	1.03860e10i	0.619545	+	1.07308i
$714$	3.14413e9	−	5.44580e9i	0.323264	−	0.559910i
$715$	5.43430e7	−	1.97792e7i	0.00555997	−	0.00202366i
$716$	3.97262e9	−	3.33343e9i	0.404466	−	0.339387i
$717$	−2.64073e9	−	4.57387e9i	−0.267551	−	0.463411i
$718$	−4.32862e7	+	2.45488e8i	−0.00436429	+	0.0247511i
$719$	−2.21042e9	+	1.25359e10i	−0.221780	+	1.25778i	0.646965	+	0.762520i	$0.276038\pi$
$719$	−2.21042e9	+	1.25359e10i	−0.221780	+	1.25778i	−0.868745	+	0.495259i	$0.835073\pi$
$720$	1.36734e7	+	1.14733e7i	0.00136525	+	0.00114558i
$721$	−6.38053e9	−	2.32232e9i	−0.633991	−	0.230754i
$722$	−6.71699e9	−	2.44479e9i	−0.664194	−	0.241747i
$723$	5.50631e9	+	4.62034e9i	0.541847	+	0.454664i
$724$	1.02288e9	−	5.80103e9i	0.100170	−	0.568094i
$725$	−1.90622e9	+	1.08107e10i	−0.185776	+	1.05359i
$726$	−2.90215e9	−	5.02667e9i	−0.281476	−	0.487531i
$727$	1.24976e10	−	1.04867e10i	1.20630	−	1.01221i	0.206876	−	0.978367i	$-0.433670\pi$
$727$	1.24976e10	−	1.04867e10i	1.20630	−	1.01221i	0.999427	−	0.0338416i	$-0.0107742\pi$
$728$	−3.63515e9	+	1.32309e9i	−0.349190	+	0.127095i
$729$	−5.67991e9	+	9.83789e9i	−0.542994	+	0.940493i
$730$	1.07660e8	+	1.86472e8i	0.0102429	+	0.0177412i
$731$	−1.38953e10	−	1.16596e10i	−1.31570	−	1.10401i
$732$	−2.73604e9	+	4.73895e9i	−0.257830	+	0.446574i
$733$	−3.25916e9	−	1.84836e10i	−0.305663	−	1.73350i	−0.620370	−	0.784310i	$-0.713017\pi$
$733$	−3.25916e9	−	1.84836e10i	−0.305663	−	1.73350i	0.314707	−	0.949189i	$-0.398094\pi$
$734$	2.43867e7			0.00227623
$735$	1.28573e7	+	7.29175e7i	0.00119439	+	0.00677370i
$736$	2.00402e9	−	1.68157e9i	0.185280	−	0.155469i
$737$	2.83054e9	+	1.03023e9i	0.260455	+	0.0947980i
$738$	4.09541e8	−	1.49061e8i	0.0375059	−	0.0136510i
$739$	4.55534e9			0.415207			0.207604	−	0.978213i	$-0.433434\pi$
$739$	4.55534e9			0.415207			0.207604	+	0.978213i	$0.433434\pi$
$740$	6.74447e7	−	1.05520e8i	0.00611838	−	0.00957244i
$741$	2.43717e8			0.0220051
$742$	−6.79654e9	+	2.47374e9i	−0.610765	+	0.222300i
$743$	8.39606e9	+	3.05592e9i	0.750957	+	0.273326i	0.689008	−	0.724754i	$-0.258046\pi$
$743$	8.39606e9	+	3.05592e9i	0.750957	+	0.273326i	0.0619483	+	0.998079i	$0.480269\pi$
$744$	−2.28249e9	+	1.91524e9i	−0.203191	+	0.170497i
$745$	−2.77287e7	−	1.57257e8i	−0.00245687	−	0.0139336i
$746$	−3.57265e9			−0.315068
$747$	3.97885e8	+	2.25652e9i	0.0349249	+	0.198069i
$748$	7.82501e8	−	1.35533e9i	0.0683643	−	0.118410i
$749$	−5.84920e9	−	4.90807e9i	−0.508640	−	0.426800i
$750$	1.53732e8	+	2.66272e8i	0.0133061	+	0.0230468i
$751$	7.70174e9	−	1.33398e10i	0.663513	−	1.14924i	−0.316173	−	0.948701i	$-0.602398\pi$
$751$	7.70174e9	−	1.33398e10i	0.663513	−	1.14924i	0.979686	−	0.200536i	$-0.0642685\pi$
$752$	−3.18288e9	+	1.15847e9i	−0.272934	+	0.0993398i
$753$	−6.02581e9	+	5.05626e9i	−0.514320	+	0.431566i
$754$	−5.87729e9	−	1.01798e10i	−0.499319	−	0.864845i
$755$	5.23818e7	−	2.97072e8i	0.00442962	−	0.0251216i
$756$	−8.94257e8	+	5.07158e9i	−0.0752724	+	0.426891i
$757$	−4.32122e9	−	3.62593e9i	−0.362052	−	0.303797i	0.443556	−	0.896247i	$-0.353717\pi$
$757$	−4.32122e9	−	3.62593e9i	−0.362052	−	0.303797i	−0.805608	+	0.592449i	$0.798161\pi$
$758$	1.39802e10	+	5.08838e9i	1.16593	+	0.424363i
$759$	−2.53218e9	−	9.21637e8i	−0.210207	−	0.0765092i
$760$	−1.49932e6	−	1.25808e6i	−0.000123893	−	0.000103959i
$761$	−9.20291e8	+	5.21923e9i	−0.0756970	+	0.429299i	0.923282	+	0.384123i	$0.125496\pi$
$761$	−9.20291e8	+	5.21923e9i	−0.0756970	+	0.429299i	−0.998979	+	0.0451764i	$0.985615\pi$
$762$	1.66148e9	−	9.42271e9i	0.136035	−	0.771495i
$763$	4.09402e9	+	7.09105e9i	0.333668	+	0.577929i
$764$	−7.60173e9	+	6.37861e9i	−0.616717	+	0.517487i
$765$	−1.14931e8	+	4.18315e7i	−0.00928160	+	0.00337823i
$766$	2.66731e9	−	4.61991e9i	0.214423	−	0.371392i
$767$	−9.44081e9	−	1.63520e10i	−0.755484	−	1.30854i
$768$	4.97897e8	+	4.17786e8i	0.0396621	+	0.0332804i
$769$	−5.52746e9	+	9.57385e9i	−0.438312	+	0.759179i	−0.997559	−	0.0698217i	$-0.977757\pi$
$769$	−5.52746e9	+	9.57385e9i	−0.438312	+	0.759179i	0.559247	+	0.829001i	$0.311090\pi$
$770$	−5.55676e6	−	3.15139e7i	−0.000438636	−	0.00248763i
$771$	−4.21014e9			−0.330831
$772$	9.56974e7	+	5.42727e8i	0.00748583	+	0.0424542i
$773$	1.36274e10	−	1.14347e10i	1.06117	−	0.890424i	0.0669426	−	0.997757i	$-0.478676\pi$
$773$	1.36274e10	−	1.14347e10i	1.06117	−	0.890424i	0.994223	+	0.107333i	$0.0342311\pi$
$774$	3.33374e9	+	1.21338e9i	0.258427	+	0.0940597i
$775$	1.10223e10	−	4.01177e9i	0.850579	−	0.309585i
$776$	−2.19880e9			−0.168915
$777$	8.62015e9	+	3.89233e8i	0.659236	+	0.0297671i
$778$	1.14616e10			0.872604
$779$	−4.49072e7	+	1.63449e7i	−0.00340357	+	0.00123880i
$780$	−1.54648e8	−	5.62872e7i	−0.0116684	−	0.00424697i
$781$	−2.74528e9	+	2.30357e9i	−0.206209	+	0.173030i
$782$	3.11278e9	+	1.76534e10i	0.232768	+	1.32010i
$783$	−1.56482e10			−1.16492
$784$	−2.14049e8	−	1.21393e9i	−0.0158638	−	0.0899680i
$785$	2.13245e8	−	3.69350e8i	0.0157338	−	0.0272518i
$786$	−5.43298e9	−	4.55881e9i	−0.399079	−	0.334867i
$787$	−4.32543e9	−	7.49186e9i	−0.316313	−	0.547871i	0.663402	−	0.748263i	$-0.269112\pi$
$787$	−4.32543e9	−	7.49186e9i	−0.316313	−	0.547871i	−0.979716	+	0.200392i	$0.935778\pi$
$788$	4.31537e9	−	7.47444e9i	0.314178	−	0.544173i
$789$	−8.48329e9	+	3.08766e9i	−0.614886	+	0.223800i
$790$	−7.47737e7	+	6.27426e7i	−0.00539578	+	0.00452759i
$791$	1.54017e9	+	2.66766e9i	0.110650	+	0.191652i
$792$	−5.31515e7	+	3.01437e8i	−0.00380170	+	0.0215605i
$793$	−4.00550e9	+	2.27163e10i	−0.285234	+	1.61764i
$794$	7.92922e9	+	6.65341e9i	0.562159	+	0.471707i
$795$	−2.89141e8	−	1.05239e8i	−0.0204092	−	0.00742833i
$796$	−8.32205e9	−	3.02898e9i	−0.584837	−	0.212863i
$797$	1.85410e9	+	1.55577e9i	0.129726	+	0.108853i	0.705342	−	0.708867i	$-0.250793\pi$
$797$	1.85410e9	+	1.55577e9i	0.129726	+	0.108853i	−0.575616	+	0.817720i	$0.695238\pi$
$798$	2.34180e7	−	1.32810e8i	0.00163132	−	0.00925170i
$799$	4.03027e9	−	2.28568e10i	0.279525	−	1.58526i
$800$	−1.27934e9	−	2.21588e9i	−0.0883427	−	0.153014i
$801$	−5.61591e9	+	4.71231e9i	−0.386106	+	0.323982i
$802$	6.22083e8	−	2.26420e8i	0.0425832	−	0.0154990i
$803$	−1.84619e9	+	3.19769e9i	−0.125826	+	0.217938i
$804$	−4.28602e9	−	7.42361e9i	−0.290843	−	0.503754i
$805$	2.80781e8	+	2.35603e8i	0.0189706	+	0.0159183i
$806$	−6.28001e9	+	1.08773e10i	−0.422462	+	0.731725i
$807$	7.12015e8	+	4.03804e9i	0.0476905	+	0.270466i
$808$	2.23207e9			0.148857
$809$	−4.37340e9	−	2.48028e10i	−0.290402	−	1.64695i	−0.685327	−	0.728236i	$-0.740341\pi$
$809$	−4.37340e9	−	2.48028e10i	−0.290402	−	1.64695i	0.394925	−	0.918713i	$-0.370770\pi$
$810$	−1.09424e8	+	9.18175e7i	−0.00723460	+	0.00607055i
$811$	2.23526e10	+	8.13567e9i	1.47148	+	0.535575i	0.948502	−	0.316771i	$-0.102599\pi$
$811$	2.23526e10	+	8.13567e9i	1.47148	+	0.535575i	0.522978	+	0.852346i	$0.324821\pi$
$812$	−6.11205e9	+	2.22461e9i	−0.400628	+	0.145817i
$813$	6.81366e9			0.444696
$814$	2.14535e9	+	9.68709e7i	0.139416	+	0.00629518i
$815$	−9.40765e7			−0.00608737
$816$	−4.18506e9	+	1.52324e9i	−0.269641	+	0.0981414i
$817$	−3.65553e8	−	1.33050e8i	−0.0234516	−	0.00853569i
$818$	1.27282e10	−	1.06802e10i	0.813072	−	0.682248i
$819$	9.00258e8	+	5.10562e9i	0.0572629	+	0.324754i
$820$	3.22702e7			0.00204387
$821$	−3.00372e9	−	1.70349e10i	−0.189434	−	1.07433i	−0.920125	−	0.391625i	$-0.871913\pi$
$821$	−3.00372e9	−	1.70349e10i	−0.189434	−	1.07433i	0.730691	−	0.682709i	$-0.239198\pi$
$822$	2.76720e8	−	4.79293e8i	0.0173776	−	0.0300989i
$823$	1.35850e10	+	1.13992e10i	0.849494	+	0.712810i	0.959678	−	0.281101i	$-0.0906997\pi$
$823$	1.35850e10	+	1.13992e10i	0.849494	+	0.712810i	−0.110184	+	0.993911i	$0.535144\pi$
$824$	2.40450e9	+	4.16472e9i	0.149720	+	0.259323i
$825$	−1.31779e9	+	2.28248e9i	−0.0817068	+	0.141520i
$826$	−9.81791e9	+	3.57343e9i	−0.606162	+	0.220625i
$827$	−4.85053e9	+	4.07008e9i	−0.298208	+	0.250227i	−0.779598	−	0.626280i	$-0.784577\pi$
$827$	−4.85053e9	+	4.07008e9i	−0.298208	+	0.250227i	0.481390	+	0.876507i	$0.340132\pi$
$828$	−1.75298e9	−	3.03626e9i	−0.107318	−	0.185880i
$829$	5.35933e9	−	3.03943e10i	0.326715	−	1.85290i	−0.170620	−	0.985337i	$-0.554577\pi$
$829$	5.35933e9	−	3.03943e10i	0.326715	−	1.85290i	0.497335	−	0.867558i	$-0.334312\pi$
$830$	−2.94610e7	+	1.67082e8i	−0.00178844	+	0.0101428i
$831$	−1.18284e10	−	9.92520e9i	−0.715026	−	0.599978i
$832$	2.57458e9	+	9.37072e8i	0.154980	+	0.0564081i
$833$	7.93705e9	+	2.88885e9i	0.475775	+	0.173168i
$834$	1.25480e10	+	1.05290e10i	0.749019	+	0.628501i
$835$	2.66706e7	−	1.51256e8i	0.00158537	−	0.00899107i
$836$	5.82820e6	−	3.30534e7i	0.000344995	−	0.00195656i
$837$	8.36019e9	+	1.44803e10i	0.492807	+	0.853567i
$838$	3.17394e9	−	2.66325e9i	0.186314	−	0.156336i
$839$	−9.76344e9	+	3.55360e9i	−0.570737	+	0.207731i	−0.611236	−	0.791448i	$-0.709327\pi$
$839$	−9.76344e9	+	3.55360e9i	−0.570737	+	0.207731i	0.0404990	+	0.999180i	$0.487105\pi$
$840$	−4.55326e7	+	7.88647e7i	−0.00265060	+	0.00459098i
$841$	−1.25701e9	−	2.17721e9i	−0.0728707	−	0.126216i
$842$	1.54356e10	+	1.29520e10i	0.891111	+	0.747731i
$843$	−8.59494e9	+	1.48869e10i	−0.494136	+	0.855869i
$844$	5.73381e8	+	3.25181e9i	0.0328280	+	0.186177i
$845$	−2.95229e8			−0.0168330
$846$	7.88252e8	+	4.47040e9i	0.0447578	+	0.253834i
$847$	−1.03713e10	+	8.70254e9i	−0.586463	+	0.492101i
$848$	4.81363e9	+	1.75202e9i	0.271074	+	0.0986628i
$849$	8.88940e9	−	3.23548e9i	0.498535	−	0.181452i
$850$	1.75326e10			0.979219
$851$	−1.95374e10	+	1.49453e10i	−1.08671	+	0.831290i
$852$	1.01984e10			0.564931
$853$	−6.13697e9	+	2.23367e9i	−0.338557	+	0.123225i	−0.505704	−	0.862707i	$-0.668767\pi$
$853$	−6.13697e9	+	2.23367e9i	−0.338557	+	0.123225i	0.167146	+	0.985932i	$0.446545\pi$
$854$	1.19941e10	+	4.36548e9i	0.658968	+	0.239845i
$855$	−2.00935e6	+	1.68604e6i	−0.000109945	+	9.22544e-5i
$856$	9.39070e8	+	5.32573e9i	0.0511729	+	0.290216i
$857$	−1.59086e10			−0.863375			−0.431688	−	0.902023i	$-0.642082\pi$
$857$	−1.59086e10			−0.863375			−0.431688	+	0.902023i	$0.642082\pi$
$858$	−4.90064e8	−	2.77929e9i	−0.0264879	−	0.150220i
$859$	5.91392e8	−	1.02432e9i	0.0318346	−	0.0551392i	−0.849669	−	0.527316i	$-0.823198\pi$
$859$	5.91392e8	−	1.02432e9i	0.0318346	−	0.0551392i	0.881504	+	0.472177i	$0.156532\pi$
$860$	2.01229e8	+	1.68851e8i	0.0107881	+	0.00905230i
$861$	1.11176e9	+	1.92563e9i	0.0593609	+	0.102816i
$862$	−1.42007e9	+	2.45964e9i	−0.0755154	+	0.130796i
$863$	2.15428e10	−	7.84095e9i	1.14095	−	0.415270i	0.298691	−	0.954350i	$-0.403450\pi$
$863$	2.15428e10	−	7.84095e9i	1.14095	−	0.415270i	0.842255	+	0.539080i	$0.181228\pi$
$864$	2.79403e9	−	2.34447e9i	0.147378	−	0.123665i
$865$	2.10481e8	+	3.64564e8i	0.0110575	+	0.0191521i
$866$	−1.45508e9	+	8.25218e9i	−0.0761333	+	0.431773i
$867$	2.53883e9	−	1.43984e10i	0.132302	−	0.750323i
$868$	5.32400e9	+	4.46737e9i	0.276324	+	0.231864i
$869$	−1.57291e9	−	5.72493e8i	−0.0813084	−	0.0295938i
$870$	−2.60022e8	−	9.46401e7i	−0.0133873	−	0.00487257i
$871$	−2.76805e10	−	2.32267e10i	−1.41942	−	1.19103i
$872$	1.00701e9	−	5.71106e9i	0.0514313	−	0.291681i
$873$	−5.11701e8	+	2.90200e9i	−0.0260295	+	0.147621i
$874$	1.92219e8	+	3.32933e8i	0.00973883	+	0.0168681i
$875$	5.49387e8	−	4.60990e8i	0.0277236	−	0.0232629i
$876$	9.87400e9	−	3.59384e9i	0.496282	−	0.180632i
$877$	−4.80678e9	+	8.32558e9i	−0.240633	+	0.416789i	−0.960895	−	0.276914i	$-0.910688\pi$
$877$	−4.80678e9	+	8.32558e9i	−0.240633	+	0.416789i	0.720262	+	0.693703i	$0.244022\pi$
$878$	−2.20426e9	−	3.81789e9i	−0.109909	−	0.190368i
$879$	4.49030e9	+	3.76781e9i	0.223005	+	0.187123i
$880$	−1.13320e7	+	1.96276e7i	−0.000560553	+	0.000970907i
$881$	−4.42257e9	−	2.50816e10i	−0.217901	−	1.23578i	−0.875801	−	0.482672i	$-0.839666\pi$
$881$	−4.42257e9	−	2.50816e10i	−0.217901	−	1.23578i	0.657901	−	0.753105i	$-0.271445\pi$
$882$	−1.65198e9			−0.0810707
$883$	5.70132e9	+	3.23338e10i	0.278684	+	1.58050i	0.727010	+	0.686627i	$0.240910\pi$
$883$	5.70132e9	+	3.23338e10i	0.278684	+	1.58050i	−0.448325	+	0.893871i	$0.647979\pi$
$884$	−1.43815e10	+	1.20675e10i	−0.700200	+	0.587538i
$885$	−4.17678e8	−	1.52022e8i	−0.0202553	−	0.00737234i
$886$	2.22831e10	−	8.11039e9i	1.07636	−	0.391763i
$887$	2.37013e10			1.14036			0.570178	−	0.821521i	$-0.306874\pi$
$887$	2.37013e10			1.14036			0.570178	+	0.821521i	$0.306874\pi$
$888$	−4.49965e9	−	4.13552e9i	−0.215642	−	0.198192i
$889$	−2.23179e10			−1.06536
$890$	−5.10085e8	+	1.85656e8i	−0.0242537	+	0.00882762i
$891$	−2.30180e9	−	8.37787e8i	−0.109017	−	0.0396791i
$892$	−1.11850e10	+	9.38537e9i	−0.527668	+	0.442766i
$893$	−8.64338e7	−	4.90190e8i	−0.00406166	−	0.0230348i
$894$	−7.79262e9			−0.364756
$895$	−8.93604e7	−	5.06788e8i	−0.00416643	−	0.0236290i
$896$	7.58027e8	−	1.31294e9i	0.0352052	−	0.0609772i
$897$	2.47627e10	+	2.07784e10i	1.14558	+	0.961255i
$898$	6.89950e9	+	1.19503e10i	0.317944	+	0.550695i
$899$	−1.05591e10	+	1.82888e10i	−0.484693	+	0.839512i
$900$	−3.22227e9	+	1.17281e9i	−0.147338	+	0.0536265i
$901$	−2.68888e10	+	2.25624e10i	−1.22471	+	1.02766i
$902$	2.76691e8	+	4.79243e8i	0.0125537	+	0.0217437i
$903$	−3.14301e9	+	1.78249e10i	−0.142049	+	0.805601i
$904$	3.78839e8	−	2.14850e9i	0.0170555	−	0.0967267i
$905$	−4.47774e8	−	3.75727e8i	−0.0200812	−	0.0168501i
$906$	−1.38331e10	−	5.03485e9i	−0.617977	−	0.224925i
$907$	−8.38887e9	−	3.05330e9i	−0.373317	−	0.135876i	0.148546	−	0.988905i	$-0.452541\pi$
$907$	−8.38887e9	−	3.05330e9i	−0.373317	−	0.135876i	−0.521863	+	0.853029i	$0.674763\pi$
$908$	4.95465e9	+	4.15744e9i	0.219640	+	0.184300i
$909$	5.19444e8	−	2.94591e9i	0.0229385	−	0.130091i
$910$	−6.66588e7	+	3.78041e8i	−0.00293233	+	0.0166301i
$911$	7.10354e9	+	1.23037e10i	0.311287	+	0.539164i	0.978641	−	0.205576i	$-0.0659067\pi$
$911$	7.10354e9	+	1.23037e10i	0.311287	+	0.539164i	−0.667354	+	0.744740i	$0.732573\pi$
$912$	−7.31677e7	+	6.13950e7i	−0.00319402	+	0.00268010i
$913$	−2.73393e9	+	9.95070e8i	−0.118889	+	0.0432719i
$914$	7.25003e9	−	1.25574e10i	0.314071	−	0.543987i
$915$	2.71502e8	+	4.70255e8i	0.0117165	+	0.0202936i
$916$	7.73970e9	+	6.49438e9i	0.332728	+	0.279192i
$917$	−8.27148e9	+	1.43266e10i	−0.354234	+	0.613552i
$918$	4.33988e9	+	2.46127e10i	0.185152	+	1.05005i
$919$	1.81532e10			0.771521			0.385761	−	0.922599i	$-0.373939\pi$
$919$	1.81532e10			0.771521			0.385761	+	0.922599i	$0.373939\pi$
$920$	−4.50784e7	−	2.55653e8i	−0.00190858	−	0.0108241i
$921$	7.61477e9	−	6.38955e9i	0.321180	−	0.269502i
$922$	1.62421e10	+	5.91165e9i	0.682472	+	0.248399i
$923$	4.03976e10	−	1.47035e10i	1.69102	−	0.615482i
$924$	−1.56162e9			−0.0651215
$925$	1.10773e10	+	2.13568e10i	0.460189	+	0.887240i
$926$	3.77702e9			0.156319
$927$	6.05623e9	−	2.20429e9i	0.249703	−	0.0908843i
$928$	4.32885e9	+	1.57557e9i	0.177809	+	0.0647172i
$929$	1.90125e10	−	1.59534e10i	0.778007	−	0.652826i	−0.164739	−	0.986337i	$-0.552678\pi$
$929$	1.90125e10	−	1.59534e10i	0.778007	−	0.652826i	0.942746	+	0.333512i	$0.108234\pi$
$930$	5.13424e7	+	2.91177e8i	0.00209308	+	0.0118705i
$931$	1.81143e8			0.00735696
$932$	−3.05418e9	−	1.73211e10i	−0.123578	−	0.700843i
$933$	−6.14584e9	+	1.06449e10i	−0.247740	+	0.429098i
$934$	−1.77976e10	−	1.49340e10i	−0.714740	−	0.599738i
$935$	−7.76491e7	−	1.34492e8i	−0.00310667	−	0.00538092i
$936$	1.83591e9	−	3.17989e9i	0.0731790	−	0.126750i
$937$	−4.00553e10	+	1.45789e10i	−1.59064	+	0.578945i	−0.977482	−	0.211017i	$-0.932323\pi$
$937$	−4.00553e10	+	1.45789e10i	−1.59064	+	0.578945i	−0.613156	+	0.789962i	$0.710100\pi$
$938$	−1.53168e10	+	1.28523e10i	−0.605979	+	0.508477i
$939$	−9.10475e9	−	1.57699e10i	−0.358871	−	0.621583i
$940$	−5.83654e7	+	3.31007e8i	−0.00229196	+	0.0129984i
$941$	3.23320e8	−	1.83364e9i	0.0126494	−	0.0717381i	−0.977830	−	0.209402i	$-0.932848\pi$
$941$	3.23320e8	−	1.83364e9i	0.0126494	−	0.0717381i	0.990479	+	0.137664i	$0.0439594\pi$
$942$	−1.59436e10	−	1.33783e10i	−0.621453	−	0.521461i
$943$	−5.95626e9	−	2.16790e9i	−0.231304	−	0.0841877i
$944$	6.95351e9	+	2.53087e9i	0.269031	+	0.0979192i
$945$	3.91469e8	+	3.28481e8i	0.0150899	+	0.0126619i
$946$	−7.82222e8	+	4.43620e9i	−0.0300408	+	0.170370i
$947$	4.27683e9	−	2.42551e10i	0.163643	−	0.928064i	−0.786810	−	0.617195i	$-0.788269\pi$
$947$	4.27683e9	−	2.42551e10i	0.163643	−	0.928064i	0.950453	−	0.310869i	$-0.100620\pi$
$948$	2.38171e9	+	4.12525e9i	0.0907947	+	0.157261i
$949$	3.39310e10	−	2.84715e10i	1.28874	−	1.08138i
$950$	3.53330e8	−	1.28602e8i	0.0133705	−	0.00486647i
$951$	2.44101e9	−	4.22795e9i	0.0920316	−	0.159403i
$952$	5.19416e9	+	8.99654e9i	0.195113	+	0.337945i
$953$	3.71469e10	+	3.11699e10i	1.39026	+	1.16657i	0.965233	+	0.261390i	$0.0841809\pi$
$953$	3.71469e10	+	3.11699e10i	1.39026	+	1.16657i	0.425030	+	0.905179i	$0.360264\pi$
$954$	3.43256e9	−	5.94536e9i	0.127997	−	0.221697i
$955$	1.70994e8	+	9.69754e8i	0.00635285	+	0.0360288i
$956$	8.72503e9			0.322972
$957$	−8.23982e8	−	4.67303e9i	−0.0303897	−	0.172348i
$958$	−1.31431e10	+	1.10284e10i	−0.482969	+	0.405259i
$959$	−1.21307e9	−	4.41521e8i	−0.0444141	−	0.0161654i
$960$	6.06070e7	−	2.20592e7i	0.00221092	−	0.000804710i
$961$	−4.94748e9			−0.179826
$962$	−2.37861e10	−	9.89409e9i	−0.861412	−	0.358313i
$963$	7.24750e9			0.261515
$964$	−1.11585e10	+	4.06137e9i	−0.401178	+	0.146017i
$965$	5.13886e7	+	1.87039e7i	0.00184086	+	0.000670019i
$966$	1.37023e10	−	1.14976e10i	0.489072	−	0.410380i
$967$	−7.95901e9	−	4.51378e10i	−0.283052	−	1.60527i	−0.712161	−	0.702016i	$-0.752283\pi$
$967$	−7.95901e9	−	4.51378e10i	−0.283052	−	1.60527i	0.429109	−	0.903253i	$-0.358828\pi$
$968$	9.58878e9			0.339781
$969$	−1.13649e8	−	6.44535e8i	−0.00401266	−	0.0227569i
$970$	−1.09095e8	+	1.88959e8i	−0.00383800	+	0.00664761i
$971$	−3.54778e10	−	2.97694e10i	−1.24362	−	1.04353i	−0.997232	−	0.0743552i	$-0.976310\pi$
$971$	−3.54778e10	−	2.97694e10i	−1.24362	−	1.04353i	−0.246393	−	0.969170i	$-0.579245\pi$
$972$	−4.30439e9	−	7.45542e9i	−0.150342	−	0.260400i
$973$	1.91038e10	−	3.30887e10i	0.664851	−	1.15155i
$974$	8.55258e9	−	3.11289e9i	0.296579	−	0.107946i
$975$	2.42196e10	−	2.03227e10i	0.836856	−	0.702206i
$976$	−4.51997e9	−	7.82882e9i	−0.155619	−	0.269539i
$977$	−4.67790e9	+	2.65297e10i	−0.160480	+	0.910125i	0.793124	+	0.609060i	$0.208453\pi$
$977$	−4.67790e9	+	2.65297e10i	−0.160480	+	0.910125i	−0.953604	+	0.301065i	$0.902658\pi$
$978$	−7.97216e8	+	4.52124e9i	−0.0272515	+	0.154551i
$979$	−7.13074e9	−	5.98341e9i	−0.242882	−	0.203802i
$980$	−1.14942e8	−	4.18356e7i	−0.00390112	−	0.00141989i
$981$	−7.30317e9	−	2.65814e9i	−0.246985	−	0.0898951i
$982$	−2.93984e10	−	2.46682e10i	−0.990681	−	0.831280i
$983$	−1.41378e9	+	8.01794e9i	−0.0474728	+	0.269231i	−0.999300	−	0.0374025i	$-0.988092\pi$
$983$	−1.41378e9	+	8.01794e9i	−0.0474728	+	0.269231i	0.951828	+	0.306634i	$0.0992027\pi$
$984$	2.73462e8	−	1.55088e9i	0.00914985	−	0.0518914i
$985$	−4.28222e8	−	7.41703e8i	−0.0142772	−	0.0247288i
$986$	−2.41808e10	+	2.02901e10i	−0.803343	+	0.674085i
$987$	−2.17626e10	+	7.92094e9i	−0.720445	+	0.262220i
$988$	−2.01312e8	+	3.48683e8i	−0.00664081	+	0.0115022i
$989$	−2.57984e10	−	4.46841e10i	−0.848018	−	1.46881i
$990$	2.32676e7	+	1.95238e7i	0.000762128	+	0.000639501i
$991$	−1.28719e10	+	2.22949e10i	−0.420132	+	0.727691i	−0.995952	−	0.0898860i	$-0.971350\pi$
$991$	−1.28719e10	+	2.22949e10i	−0.420132	+	0.727691i	0.575820	+	0.817577i	$0.304683\pi$
$992$	−8.54750e8	−	4.84753e9i	−0.0278002	−	0.157663i
$993$	3.36981e10			1.09215
$994$	−4.13079e9	−	2.34269e10i	−0.133408	−	0.756593i
$995$	−6.73209e8	+	5.64889e8i	−0.0216655	+	0.0181795i
$996$	7.78016e9	+	2.83175e9i	0.249506	+	0.0908127i
$997$	2.78207e10	−	1.01259e10i	0.889068	−	0.323594i	0.143204	−	0.989693i	$-0.454259\pi$
$997$	2.78207e10	−	1.01259e10i	0.889068	−	0.323594i	0.745863	+	0.666099i	$0.232037\pi$
$998$	−1.24571e10			−0.396697
$999$	−2.72393e10	+	2.08370e10i	−0.864403	+	0.661236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.8.f.b.7.4	✓	66
37.16	even	9	inner	74.8.f.b.53.4	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.8.f.b.7.4	✓	66	1.1	even	1	trivial
74.8.f.b.53.4	yes	66	37.16	even	9	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	74.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(7.51754 - 2.73616i) q^{2} +(-36.4042 - 13.2501i) q^{3} +(49.0268 - 41.1384i) q^{4} +(-1.10281 - 6.25436i) q^{5} -309.925 q^{6} +(125.532 + 711.929i) q^{7} +(256.000 - 443.405i) q^{8} +(-525.635 - 441.061i) q^{9} +(-25.4034 - 43.9999i) q^{10} +(435.627 - 754.529i) q^{11} +(-2329.87 + 848.004i) q^{12} +(-8006.36 + 6718.13i) q^{13} +(2891.65 + 5008.48i) q^{14} +(-42.7236 + 242.297i) q^{15} +(711.263 - 4033.77i) q^{16} +(21500.3 + 18040.9i) q^{17} +(-5158.30 - 1877.47i) q^{18} +(565.620 + 205.869i) q^{19} +(-311.362 - 261.263i) q^{20} +(4863.19 - 27580.5i) q^{21} +(1210.33 - 6864.15i) q^{22} +(39917.9 + 69139.8i) q^{23} +(-15194.6 + 12749.8i) q^{24} +(73375.6 - 26706.5i) q^{25} +(-41806.2 + 72410.5i) q^{26} +(55654.1 + 96395.7i) q^{27} +(35442.1 + 29739.4i) q^{28} +(-70292.1 + 121749. i) q^{29} +(341.789 + 1938.38i) q^{30} +150217. q^{31} +(-5690.10 - 32270.2i) q^{32} +(-25856.2 + 21695.9i) q^{33} +(210992. + 76794.8i) q^{34} +(4314.22 - 1570.25i) q^{35} -43914.8 q^{36} +(39761.3 + 305534. i) q^{37} +4815.37 q^{38} +(380481. - 138484. i) q^{39} +(-3055.53 - 1112.12i) q^{40} +(-60819.7 + 51033.8i) q^{41} +(-38905.5 - 220644. i) q^{42} -646286. q^{43} +(-9682.67 - 54913.2i) q^{44} +(-2178.87 + 3773.92i) q^{45} +(489262. + 410539. i) q^{46} +(-413470. - 716151. i) q^{47} +(-79340.7 + 137422. i) q^{48} +(282793. - 102928. i) q^{49} +(478531. - 401535. i) q^{50} +(-543658. - 941644. i) q^{51} +(-116153. + 658738. i) q^{52} +(-217169. + 1.23163e6i) q^{53} +(682136. + 572380. i) q^{54} +(-5199.51 - 1892.47i) q^{55} +(347809. + 126592. i) q^{56} +(-17863.2 - 14989.0i) q^{57} +(-195297. + 1.10759e6i) q^{58} +(-313710. + 1.77914e6i) q^{59} +(7873.13 + 13636.7i) q^{60} +(1.69067e6 - 1.41864e6i) q^{61} +(1.12926e6 - 411018. i) q^{62} +(248019. - 429582. i) q^{63} +(-131072. - 227023. i) q^{64} +(50847.1 + 42665.8i) q^{65} +(-135012. + 233847. i) q^{66} +(600356. + 3.40479e6i) q^{67} +1.79626e6 q^{68} +(-537073. - 3.04589e6i) q^{69} +(28135.9 - 23608.8i) q^{70} +(-3.86522e6 - 1.40682e6i) q^{71} +(-330131. + 120158. i) q^{72} -4.23800e6 q^{73} +(1.13490e6 + 2.18807e6i) q^{74} -3.02504e6 q^{75} +(36199.7 - 13175.6i) q^{76} +(591856. + 215418. i) q^{77} +(2.48137e6 - 2.08211e6i) q^{78} +(-333614. - 1.89202e6i) q^{79} -26013.0 q^{80} +(-488210. - 2.76878e6i) q^{81} +(-317578. + 550061. i) q^{82} +(-2.55806e6 - 2.14647e6i) q^{83} +(-896192. - 1.55225e6i) q^{84} +(89123.3 - 154366. i) q^{85} +(-4.85848e6 + 1.76834e6i) q^{86} +(4.17211e6 - 3.50082e6i) q^{87} +(-223041. - 386319. i) q^{88} +(1.85527e6 - 1.05217e7i) q^{89} +(-6053.72 + 34332.3i) q^{90} +(-5.78789e6 - 4.85661e6i) q^{91} +(4.80135e6 + 1.74755e6i) q^{92} +(-5.46853e6 - 1.99038e6i) q^{93} +(-5.06778e6 - 4.25237e6i) q^{94} +(663.805 - 3764.63i) q^{95} +(-220438. + 1.25017e6i) q^{96} +(-2.14726e6 - 3.71917e6i) q^{97} +(1.84428e6 - 1.54754e6i) q^{98} +(-561774. + 204469. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9} + 4704 q^{10} + 4539 q^{11} - 2496 q^{12} - 10542 q^{13} + 6744 q^{14} - 39894 q^{15} - 78822 q^{17} + 51792 q^{18} + 79461 q^{19} + 29376 q^{20}+ \cdots + 66155463 q^{99}+O(q^{100}) \) 66 * q - 39 * q^3 + 459 * q^5 - 918 * q^7 + 16896 * q^8 + 3237 * q^9 + 4704 * q^10 + 4539 * q^11 - 2496 * q^12 - 10542 * q^13 + 6744 * q^14 - 39894 * q^15 - 78822 * q^17 + 51792 * q^18 + 79461 * q^19 + 29376 * q^20 - 5835 * q^21 + 18168 * q^22 - 199479 * q^23 + 19968 * q^24 + 356301 * q^25 + 186744 * q^26 - 91689 * q^27 - 91584 * q^28 - 38526 * q^29 + 319152 * q^30 + 1917246 * q^31 - 902847 * q^33 - 205776 * q^34 - 1574793 * q^35 + 3079296 * q^36 - 396513 * q^37 - 692880 * q^38 + 2514306 * q^39 + 470016 * q^40 + 2989350 * q^41 + 46680 * q^42 + 6006348 * q^43 - 145344 * q^44 + 1083726 * q^45 - 588744 * q^46 - 894135 * q^47 + 7973742 * q^49 + 2012400 * q^50 - 524880 * q^51 - 2262720 * q^52 + 1457844 * q^53 + 1452312 * q^54 + 2415690 * q^55 - 1202688 * q^56 + 2734338 * q^57 - 3423360 * q^58 + 3099522 * q^59 - 3102912 * q^60 - 10968396 * q^61 - 3067320 * q^62 - 10727970 * q^63 - 8650752 * q^64 - 13497300 * q^65 - 4598712 * q^66 - 1978119 * q^67 + 5026176 * q^68 - 7251108 * q^69 + 435744 * q^70 - 19555002 * q^71 + 3314688 * q^72 - 31332840 * q^73 + 7607472 * q^74 + 44758074 * q^75 + 5085504 * q^76 + 1982007 * q^77 - 22512264 * q^78 + 10522902 * q^79 + 4816896 * q^80 - 7548876 * q^81 - 7150320 * q^82 + 19771926 * q^83 + 3556224 * q^84 - 6684072 * q^85 + 22982496 * q^86 - 67769667 * q^87 - 2323968 * q^88 - 42018963 * q^89 - 25158672 * q^90 + 4847565 * q^91 - 1096704 * q^92 - 14558475 * q^93 + 3175680 * q^94 + 4508415 * q^95 - 2555904 * q^96 - 39286662 * q^97 + 71630904 * q^98 + 66155463 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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