LMFDB - Embedded newform 35.8.k.a.12.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,8,Mod(3,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("35.3");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	35.k (of order $12$, degree $4$, 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:	$10.9334758919$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$26$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			12.2
Character	$\chi$	$=$	35.12
Dual form			35.8.k.a.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-20.0589 + 5.37477i) q^{2} +(16.6134 - 62.0019i) q^{3} +(262.620 - 151.624i) q^{4} +(227.634 + 162.196i) q^{5} +1332.98i q^{6} +(431.442 - 798.374i) q^{7} +(-2573.37 + 2573.37i) q^{8} +(-1674.24 - 966.621i) q^{9} +O(q^{10})$	\(q+(-20.0589 + 5.37477i) q^{2} +(16.6134 - 62.0019i) q^{3} +(262.620 - 151.624i) q^{4} +(227.634 + 162.196i) q^{5} +1332.98i q^{6} +(431.442 - 798.374i) q^{7} +(-2573.37 + 2573.37i) q^{8} +(-1674.24 - 966.621i) q^{9} +(-5437.86 - 2030.00i) q^{10} +(3097.07 + 5364.28i) q^{11} +(-5037.97 - 18802.0i) q^{12} +(1829.73 + 1829.73i) q^{13} +(-4363.18 + 18333.4i) q^{14} +(13838.2 - 11419.1i) q^{15} +(18379.8 - 31834.7i) q^{16} +(31128.6 + 8340.89i) q^{17} +(38778.7 + 10390.7i) q^{18} +(325.970 - 564.597i) q^{19} +(84374.3 + 8081.20i) q^{20} +(-42333.0 - 40013.9i) q^{21} +(-90955.5 - 90955.5i) q^{22} +(-22358.8 - 83444.1i) q^{23} +(116801. + 202306. i) q^{24} +(25509.8 + 73842.8i) q^{25} +(-46536.8 - 26868.0i) q^{26} +(11517.7 - 11517.7i) q^{27} +(-7747.13 - 275086. i) q^{28} -34083.5i q^{29} +(-216205. + 303433. i) q^{30} +(17500.4 - 10103.8i) q^{31} +(-77008.8 + 287401. i) q^{32} +(384048. - 102905. i) q^{33} -669236. q^{34} +(227704. - 111759. i) q^{35} -586252. q^{36} +(-124841. + 33451.0i) q^{37} +(-3504.03 + 13077.2i) q^{38} +(143845. - 83048.9i) q^{39} +(-1.00318e6 + 168396. i) q^{40} +200670. i q^{41} +(1.06422e6 + 575105. i) q^{42} +(382962. - 382962. i) q^{43} +(1.62671e6 + 939179. i) q^{44} +(-224332. - 491591. i) q^{45} +(896986. + 1.55362e6i) q^{46} +(-48929.0 - 182606. i) q^{47} +(-1.66846e6 - 1.66846e6i) q^{48} +(-451259. - 688904. i) q^{49} +(-908587. - 1.34410e6i) q^{50} +(1.03430e6 - 1.79146e6i) q^{51} +(757956. + 203094. i) q^{52} +(-762696. - 204364. i) q^{53} +(-169127. + 292937. i) q^{54} +(-165066. + 1.72343e6i) q^{55} +(944250. + 3.16477e6i) q^{56} +(-29590.6 - 29590.6i) q^{57} +(183191. + 683679. i) q^{58} +(706980. + 1.22452e6i) q^{59} +(1.90279e6 - 5.09711e6i) q^{60} +(-2.66460e6 - 1.53841e6i) q^{61} +(-296732. + 296732. i) q^{62} +(-1.49406e6 + 919626. i) q^{63} -1.47363e6i q^{64} +(119734. + 713285. i) q^{65} +(-7.15049e6 + 4.12834e6i) q^{66} +(338384. - 1.26287e6i) q^{67} +(9.43969e6 - 2.52936e6i) q^{68} -5.54515e6 q^{69} +(-3.96682e6 + 3.46562e6i) q^{70} +3.53258e6 q^{71} +(6.79589e6 - 1.82095e6i) q^{72} +(15082.3 - 56287.9i) q^{73} +(2.32438e6 - 1.34198e6i) q^{74} +(5.00220e6 - 354879. i) q^{75} -197700. i q^{76} +(5.61890e6 - 158243. i) q^{77} +(-2.43900e6 + 2.43900e6i) q^{78} +(2.09971e6 + 1.21227e6i) q^{79} +(9.34734e6 - 4.26555e6i) q^{80} +(-2.63677e6 - 4.56702e6i) q^{81} +(-1.07855e6 - 4.02522e6i) q^{82} +(203116. + 203116. i) q^{83} +(-1.71846e7 - 4.08977e6i) q^{84} +(5.73308e6 + 6.94761e6i) q^{85} +(-5.62347e6 + 9.74014e6i) q^{86} +(-2.11325e6 - 566242. i) q^{87} +(-2.17741e7 - 5.83436e6i) q^{88} +(-3.06879e6 + 5.31529e6i) q^{89} +(7.14204e6 + 8.65505e6i) q^{90} +(2.25023e6 - 671387. i) q^{91} +(-1.85240e7 - 1.85240e7i) q^{92} +(-335717. - 1.25291e6i) q^{93} +(1.96293e6 + 3.39989e6i) q^{94} +(165778. - 75650.6i) q^{95} +(1.65400e7 + 9.54939e6i) q^{96} +(-2.79540e6 + 2.79540e6i) q^{97} +(1.27545e7 + 1.13933e7i) q^{98} -1.19748e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 2 q^{2} - 6 q^{3} - 1746 q^{7} - 2524 q^{8}+O(q^{10}) $ 104 * q - 2 * q^2 - 6 * q^3 - 1746 * q^7 - 2524 * q^8	\( 104 q - 2 q^{2} - 6 q^{3} - 1746 q^{7} - 2524 q^{8} - 1254 q^{10} + 8932 q^{11} + 762 q^{12} - 17372 q^{15} + 195652 q^{16} + 81660 q^{17} + 54484 q^{18} - 12132 q^{21} + 94520 q^{22} + 140314 q^{23} - 130652 q^{25} + 339924 q^{26} - 700486 q^{28} - 737132 q^{30} - 123336 q^{31} - 44406 q^{32} + 2042712 q^{33} + 1515352 q^{35} - 3108368 q^{36} - 218688 q^{37} - 1242624 q^{38} - 5761962 q^{40} + 1786598 q^{42} - 2298300 q^{43} + 4974504 q^{45} - 415740 q^{46} + 78144 q^{47} + 7621588 q^{50} - 1243672 q^{51} - 904152 q^{52} + 1874804 q^{53} + 7011076 q^{56} - 8000176 q^{57} + 12000550 q^{58} - 7170466 q^{60} - 15847296 q^{61} - 11024724 q^{63} - 10105824 q^{65} + 8994876 q^{66} - 742846 q^{67} + 39849504 q^{68} + 22127240 q^{70} + 8609784 q^{71} + 29505688 q^{72} - 4371720 q^{73} - 35629446 q^{75} - 10458188 q^{77} - 63694784 q^{78} - 2528844 q^{80} - 3862456 q^{81} + 66431478 q^{82} + 51119608 q^{85} - 43323624 q^{86} - 43958022 q^{87} + 14366540 q^{88} + 43669288 q^{91} - 70081332 q^{92} + 15954004 q^{93} - 17456752 q^{95} - 111927000 q^{96} - 58212822 q^{98}+O(q^{100}) \) 104 * q - 2 * q^2 - 6 * q^3 - 1746 * q^7 - 2524 * q^8 - 1254 * q^10 + 8932 * q^11 + 762 * q^12 - 17372 * q^15 + 195652 * q^16 + 81660 * q^17 + 54484 * q^18 - 12132 * q^21 + 94520 * q^22 + 140314 * q^23 - 130652 * q^25 + 339924 * q^26 - 700486 * q^28 - 737132 * q^30 - 123336 * q^31 - 44406 * q^32 + 2042712 * q^33 + 1515352 * q^35 - 3108368 * q^36 - 218688 * q^37 - 1242624 * q^38 - 5761962 * q^40 + 1786598 * q^42 - 2298300 * q^43 + 4974504 * q^45 - 415740 * q^46 + 78144 * q^47 + 7621588 * q^50 - 1243672 * q^51 - 904152 * q^52 + 1874804 * q^53 + 7011076 * q^56 - 8000176 * q^57 + 12000550 * q^58 - 7170466 * q^60 - 15847296 * q^61 - 11024724 * q^63 - 10105824 * q^65 + 8994876 * q^66 - 742846 * q^67 + 39849504 * q^68 + 22127240 * q^70 + 8609784 * q^71 + 29505688 * q^72 - 4371720 * q^73 - 35629446 * q^75 - 10458188 * q^77 - 63694784 * q^78 - 2528844 * q^80 - 3862456 * q^81 + 66431478 * q^82 + 51119608 * q^85 - 43323624 * q^86 - 43958022 * q^87 + 14366540 * q^88 + 43669288 * q^91 - 70081332 * q^92 + 15954004 * q^93 - 17456752 * q^95 - 111927000 * q^96 - 58212822 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−20.0589	+	5.37477i	−1.77297	+	0.475067i	−0.989274	−	0.146073i	$-0.953337\pi$
$2$	−20.0589	+	5.37477i	−1.77297	+	0.475067i	−0.783700	+	0.621140i	$0.786670\pi$
$3$	16.6134	−	62.0019i	0.355249	−	1.32581i	−0.524921	−	0.851151i	$-0.675905\pi$
$3$	16.6134	−	62.0019i	0.355249	−	1.32581i	0.880171	−	0.474658i	$-0.157428\pi$
$4$	262.620	−	151.624i	2.05172	−	1.18456i
$5$	227.634	+	162.196i	0.814409	+	0.580291i
$5$	227.634	+	162.196i	0.814409	+	0.580291i
$6$			1332.98i			2.51939i
$7$	431.442	−	798.374i	0.475422	−	0.879758i
$7$	431.442	−	798.374i	0.475422	−	0.879758i
$8$	−2573.37	+	2573.37i	−1.77700	+	1.77700i
$9$	−1674.24	−	966.621i	−0.765541	−	0.441985i
$10$	−5437.86	−	2030.00i	−1.71960	−	0.641941i
$11$	3097.07	+	5364.28i	0.701578	+	1.21517i	0.967912	+	0.251288i	$0.0808543\pi$
$11$	3097.07	+	5364.28i	0.701578	+	1.21517i	−0.266334	+	0.963881i	$0.585812\pi$
$12$	−5037.97	−	18802.0i	−0.841630	−	3.14101i
$13$	1829.73	+	1829.73i	0.230986	+	0.230986i	0.813104	−	0.582118i	$-0.197776\pi$
$13$	1829.73	+	1829.73i	0.230986	+	0.230986i	−0.582118	+	0.813104i	$0.697776\pi$
$14$	−4363.18	+	18333.4i	−0.424967	+	1.78564i
$15$	13838.2	−	11419.1i	1.05867	−	0.873603i
$16$	18379.8	−	31834.7i	1.12181	−	1.94304i
$17$	31128.6	+	8340.89i	1.53670	+	0.411757i	0.925197	−	0.379487i	$-0.123899\pi$
$17$	31128.6	+	8340.89i	1.53670	+	0.411757i	0.611501	+	0.791244i	$0.290566\pi$
$18$	38778.7	+	10390.7i	1.56726	+	0.419945i
$19$	325.970	−	564.597i	0.0109029	−	0.0188843i	−0.860522	−	0.509412i	$-0.829863\pi$
$19$	325.970	−	564.597i	0.0109029	−	0.0188843i	0.871425	+	0.490528i	$0.163196\pi$
$20$	84374.3	+	8081.20i	2.35833	+	0.225877i
$21$	−42333.0	−	40013.9i	−0.997497	−	0.942852i
$22$	−90955.5	−	90955.5i	−1.82117	−	1.82117i
$23$	−22358.8	−	83444.1i	−0.383178	−	1.43004i	−0.841019	−	0.541006i	$-0.818044\pi$
$23$	−22358.8	−	83444.1i	−0.383178	−	1.43004i	0.457840	−	0.889034i	$-0.348623\pi$
$24$	116801.	+	202306.i	1.72468	+	2.98723i
$25$	25509.8	+	73842.8i	0.326525	+	0.945188i
$26$	−46536.8	−	26868.0i	−0.519266	−	0.299798i
$27$	11517.7	−	11517.7i	0.112614	−	0.112614i
$28$	−7747.13	−	275086.i	−0.0666941	−	2.36819i
$29$		−	34083.5i		−	0.259509i	−0.991546	−	0.129754i	$-0.958581\pi$
$29$		−	34083.5i		−	0.259509i	0.991546	−	0.129754i	$-0.0414189\pi$
$30$	−216205.	+	303433.i	−1.46198	+	2.05182i
$31$	17500.4	−	10103.8i	0.105507	−	0.0609144i	−0.446318	−	0.894874i	$-0.647265\pi$
$31$	17500.4	−	10103.8i	0.105507	−	0.0609144i	0.551825	+	0.833960i	$0.313932\pi$
$32$	−77008.8	+	287401.i	−0.415447	+	1.55047i
$33$	384048.	−	102905.i	1.86032	−	0.498470i
$34$	−669236.			−2.92014
$35$	227704.	−	111759.i	0.897703	−	0.440600i
$36$	−586252.			−2.09424
$37$	−124841.	+	33451.0i	−0.405183	+	0.108568i	−0.455654	−	0.890157i	$-0.650594\pi$
$37$	−124841.	+	33451.0i	−0.405183	+	0.108568i	0.0504709	+	0.998726i	$0.483928\pi$
$38$	−3504.03	+	13077.2i	−0.0103592	+	0.0386610i
$39$	143845.	−	83048.9i	0.388301	−	0.224186i
$40$	−1.00318e6	+	168396.i	−2.47838	+	0.416028i
$41$			200670.i			0.454714i	0.973811	+	0.227357i	$0.0730085\pi$
$41$			200670.i			0.454714i	−0.973811	+	0.227357i	$0.926992\pi$
$42$	1.06422e6	+	575105.i	2.21645	+	1.19777i
$43$	382962.	−	382962.i	0.734542	−	0.734542i	−0.236974	−	0.971516i	$-0.576156\pi$
$43$	382962.	−	382962.i	0.734542	−	0.734542i	0.971516	+	0.236974i	$0.0761557\pi$
$44$	1.62671e6	+	939179.i	2.87889	+	1.66213i
$45$	−224332.	−	491591.i	−0.366984	−	0.804193i
$46$	896986.	+	1.55362e6i	1.35873	+	2.35339i
$47$	−48929.0	−	182606.i	−0.0687423	−	0.256550i	0.922999	−	0.384802i	$-0.125730\pi$
$47$	−48929.0	−	182606.i	−0.0687423	−	0.256550i	−0.991742	+	0.128252i	$0.959063\pi$
$48$	−1.66846e6	−	1.66846e6i	−2.17757	−	2.17757i
$49$	−451259.	−	688904.i	−0.547948	−	0.836513i
$50$	−908587.	−	1.34410e6i	−1.02795	−	1.52067i
$51$	1.03430e6	−	1.79146e6i	1.09182	−	1.89109i
$52$	757956.	+	203094.i	0.747536	+	0.200302i
$53$	−762696.	−	204364.i	−0.703698	−	0.188555i	−0.110811	−	0.993841i	$-0.535345\pi$
$53$	−762696.	−	204364.i	−0.703698	−	0.188555i	−0.592886	+	0.805286i	$0.702012\pi$
$54$	−169127.	+	292937.i	−0.146162	+	0.253160i
$55$	−165066.	+	1.72343e6i	−0.133779	+	1.39676i
$56$	944250.	+	3.16477e6i	0.718503	+	2.40815i
$57$	−29590.6	−	29590.6i	−0.0211637	−	0.0211637i
$58$	183191.	+	683679.i	0.123284	+	0.460102i
$59$	706980.	+	1.22452e6i	0.448152	+	0.776221i	0.998266	−	0.0588682i	$-0.0187492\pi$
$59$	706980.	+	1.22452e6i	0.448152	+	0.776221i	−0.550114	+	0.835089i	$0.685416\pi$
$60$	1.90279e6	−	5.09711e6i	1.13726	−	3.04645i
$61$	−2.66460e6	−	1.53841e6i	−1.50306	−	0.867794i	−0.999994	−	0.00354728i	$-0.998871\pi$
$61$	−2.66460e6	−	1.53841e6i	−1.50306	−	0.867794i	−0.503069	−	0.864246i	$-0.667796\pi$
$62$	−296732.	+	296732.i	−0.158123	+	0.158123i
$63$	−1.49406e6	+	919626.i	−0.752795	+	0.463361i
$64$		−	1.47363e6i		−	0.702680i
$65$	119734.	+	713285.i	0.0540781	+	0.322156i
$66$	−7.15049e6	+	4.12834e6i	−3.06149	+	1.76755i
$67$	338384.	−	1.26287e6i	0.137451	−	0.512974i	−0.862525	−	0.506015i	$-0.831118\pi$
$67$	338384.	−	1.26287e6i	0.137451	−	0.512974i	0.999976	−	0.00695922i	$-0.00221521\pi$
$68$	9.43969e6	−	2.52936e6i	3.64063	−	0.975504i
$69$	−5.54515e6			−2.03208
$70$	−3.96682e6	+	3.46562e6i	−1.38229	+	1.20764i
$71$	3.53258e6			1.17135			0.585677	−	0.810545i	$-0.300829\pi$
$71$	3.53258e6			1.17135			0.585677	+	0.810545i	$0.300829\pi$
$72$	6.79589e6	−	1.82095e6i	2.14577	−	0.574957i
$73$	15082.3	−	56287.9i	0.00453772	−	0.0169350i	−0.963620	−	0.267277i	$-0.913876\pi$
$73$	15082.3	−	56287.9i	0.00453772	−	0.0169350i	0.968158	+	0.250342i	$0.0805429\pi$
$74$	2.32438e6	−	1.34198e6i	0.666801	−	0.384978i
$75$	5.00220e6	−	354879.i	1.36914	−	0.0971327i
$76$		−	197700.i		−	0.0516605i
$77$	5.61890e6	−	158243.i	1.40260	−	0.0395008i
$78$	−2.43900e6	+	2.43900e6i	−0.581944	+	0.581944i
$79$	2.09971e6	+	1.21227e6i	0.479142	+	0.276633i	0.720059	−	0.693913i	$-0.244115\pi$
$79$	2.09971e6	+	1.21227e6i	0.479142	+	0.276633i	−0.240917	+	0.970546i	$0.577448\pi$
$80$	9.34734e6	−	4.26555e6i	2.04114	−	0.931450i
$81$	−2.63677e6	−	4.56702e6i	−0.551283	−	0.954851i
$82$	−1.07855e6	−	4.02522e6i	−0.216020	−	0.806196i
$83$	203116.	+	203116.i	0.0389917	+	0.0389917i	0.726334	−	0.687342i	$-0.241223\pi$
$83$	203116.	+	203116.i	0.0389917	+	0.0389917i	−0.687342	+	0.726334i	$0.741223\pi$
$84$	−1.71846e7	−	4.08977e6i	−3.16345	−	0.752873i
$85$	5.73308e6	+	6.94761e6i	1.01256	+	1.22707i
$86$	−5.62347e6	+	9.74014e6i	−0.953367	+	1.65128i
$87$	−2.11325e6	−	566242.i	−0.344059	−	0.0921903i
$88$	−2.17741e7	−	5.83436e6i	−3.40605	−	0.912649i
$89$	−3.06879e6	+	5.31529e6i	−0.461425	+	0.799212i	−0.999032	−	0.0439834i	$-0.985995\pi$
$89$	−3.06879e6	+	5.31529e6i	−0.461425	+	0.799212i	0.537607	+	0.843196i	$0.319328\pi$
$90$	7.14204e6	+	8.65505e6i	1.03270	+	1.25147i
$91$	2.25023e6	−	671387.i	0.313027	−	0.0933959i
$92$	−1.85240e7	−	1.85240e7i	−2.48015	−	2.48015i
$93$	−335717.	−	1.25291e6i	−0.0432796	−	0.161522i
$94$	1.96293e6	+	3.39989e6i	0.243757	+	0.422199i
$95$	165778.	−	75650.6i	0.0198378	−	0.00905273i
$96$	1.65400e7	+	9.54939e6i	1.90804	+	1.10161i
$97$	−2.79540e6	+	2.79540e6i	−0.310987	+	0.310987i	−0.845292	−	0.534305i	$-0.820573\pi$
$97$	−2.79540e6	+	2.79540e6i	−0.310987	+	0.310987i	0.534305	+	0.845292i	$0.320573\pi$
$98$	1.27545e7	+	1.13933e7i	1.36890	+	1.22280i
$99$		−	1.19748e7i		−	1.24035i
$100$	1.78957e7	+	1.55247e7i	1.78957	+	1.55247i
$101$	6.09981e6	−	3.52173e6i	0.589104	−	0.340119i	−0.175639	−	0.984455i	$-0.556199\pi$
$101$	6.09981e6	−	3.52173e6i	0.589104	−	0.340119i	0.764743	+	0.644335i	$0.222866\pi$
$102$	−1.11183e7	+	4.14939e7i	−1.03738	+	3.87154i
$103$	−1.84355e7	+	4.93978e6i	−1.66236	+	0.445428i	−0.963035	−	0.269378i	$-0.913182\pi$
$103$	−1.84355e7	+	4.93978e6i	−1.66236	+	0.445428i	−0.699324	+	0.714805i	$0.746515\pi$
$104$	−9.41713e6			−0.820922
$105$	−3.14634e6	−	1.59748e7i	−0.265243	−	1.34671i
$106$	1.63973e7			1.33721
$107$	−8.87265e6	+	2.37742e6i	−0.700181	+	0.187613i	−0.591311	−	0.806443i	$-0.701390\pi$
$107$	−8.87265e6	+	2.37742e6i	−0.700181	+	0.187613i	−0.108869	+	0.994056i	$0.534723\pi$
$108$	1.27842e6	−	4.77113e6i	0.0976541	−	0.364450i
$109$	1.16648e7	−	6.73466e6i	0.862747	−	0.498107i	−0.00218416	−	0.999998i	$-0.500695\pi$
$109$	1.16648e7	−	6.73466e6i	0.862747	−	0.498107i	0.864931	+	0.501890i	$0.167362\pi$
$110$	−5.95196e6	−	3.54572e7i	−0.426369	−	2.53998i
$111$			8.29611e6i			0.575764i
$112$	−1.74862e7	−	2.84088e7i	−1.17607	−	1.91069i
$113$	−1.01605e7	+	1.01605e7i	−0.662430	+	0.662430i	−0.955952	−	0.293522i	$-0.905172\pi$
$113$	−1.01605e7	+	1.01605e7i	−0.662430	+	0.662430i	0.293522	+	0.955952i	$0.405172\pi$
$114$	752599.	+	434513.i	0.0475769	+	0.0274686i
$115$	8.44469e6	−	2.26213e7i	0.517775	−	1.38699i
$116$	−5.16788e6	−	8.95103e6i	−0.307404	−	0.532440i
$117$	−1.29475e6	−	4.83206e6i	−0.0747368	−	0.278921i
$118$	−2.07628e7	−	2.07628e7i	−1.16332	−	1.16332i
$119$	2.00893e7	−	2.12537e7i	1.09283	−	1.15616i
$120$	−6.22524e6	+	6.49965e7i	−0.328868	+	3.43365i
$121$	−9.44006e6	+	1.63507e7i	−0.484424	+	0.839047i
$122$	6.17175e7	+	1.65371e7i	3.07715	+	0.824520i
$123$	1.24419e7	+	3.33380e6i	0.602864	+	0.161537i
$124$	3.06397e6	−	5.30695e6i	0.144314	−	0.249959i
$125$	−6.17012e6	+	2.09468e7i	−0.282559	+	0.959250i
$126$	2.50265e7	−	2.64769e7i	1.11456	−	1.17915i
$127$	3.56136e6	+	3.56136e6i	0.154278	+	0.154278i	0.780025	−	0.625748i	$-0.215206\pi$
$127$	3.56136e6	+	3.56136e6i	0.154278	+	0.154278i	−0.625748	+	0.780025i	$0.715206\pi$
$128$	−1.93673e6	−	7.22798e6i	−0.0816271	−	0.304636i
$129$	−1.73821e7	−	3.01067e7i	−0.712916	−	1.23481i
$130$	−6.23548e6	−	1.36642e7i	−0.248925	−	0.545484i
$131$	1.72417e7	+	9.95447e6i	0.670084	+	0.386873i	0.796109	−	0.605154i	$-0.206888\pi$
$131$	1.72417e7	+	9.95447e6i	0.670084	+	0.386873i	−0.126024	+	0.992027i	$0.540222\pi$
$132$	8.52560e7	−	8.52560e7i	3.22638	−	3.22638i
$133$	−310122.	−	503837.i	−0.0114302	−	0.0185699i
$134$			2.71504e7i			0.974788i
$135$	4.48994e6	−	753695.i	0.157062	−	0.0263650i
$136$	−1.01569e8	+	5.86411e7i	−3.46240	+	1.99902i
$137$	−1.16763e7	+	4.35765e7i	−0.387956	+	1.44787i	0.445498	+	0.895283i	$0.353027\pi$
$137$	−1.16763e7	+	4.35765e7i	−0.387956	+	1.44787i	−0.833454	+	0.552589i	$0.813640\pi$
$138$	1.11230e8	−	2.98039e7i	3.60283	−	0.965376i
$139$	5.29080e7			1.67097			0.835487	−	0.549510i	$-0.185186\pi$
$139$	5.29080e7			1.67097			0.835487	+	0.549510i	$0.185186\pi$
$140$	4.28544e7	−	6.38756e7i	1.31992	−	1.96737i
$141$	−1.21348e7			−0.364556
$142$	−7.08597e7	+	1.89868e7i	−2.07678	+	0.556471i
$143$	−4.14838e6	+	1.54820e7i	−0.118632	+	0.442742i
$144$	−6.15443e7	+	3.55326e7i	−1.71759	+	0.991650i
$145$	5.52822e6	−	7.75859e6i	0.150590	−	0.211346i
$146$			1.21014e6i			0.0321810i
$147$	−5.02103e7	+	1.65339e7i	−1.30371	+	0.429303i
$148$	−2.77138e7	+	2.77138e7i	−0.702717	+	0.702717i
$149$	4.65666e7	+	2.68852e7i	1.15325	+	0.665828i	0.949677	−	0.313232i	$-0.101412\pi$
$149$	4.65666e7	+	2.68852e7i	1.15325	+	0.665828i	0.203571	+	0.979060i	$0.434745\pi$
$150$	−9.84313e7	+	3.40042e7i	−2.38130	+	0.822645i
$151$	−2.02332e7	−	3.50449e7i	−0.478238	−	0.828333i	0.521450	−	0.853282i	$-0.325391\pi$
$151$	−2.02332e7	−	3.50449e7i	−0.478238	−	0.828333i	−0.999689	+	0.0249484i	$0.992058\pi$
$152$	614074.	+	2.29176e6i	0.0141830	+	0.0529317i
$153$	−4.40542e7	−	4.40542e7i	−0.994414	−	0.994414i
$154$	−1.11859e8	+	3.33745e7i	−2.46801	+	0.736363i
$155$	5.62248e6	+	538511.i	0.121274	+	0.0116154i
$156$	2.51844e7	−	4.36207e7i	0.531123	−	0.919933i
$157$	1.78945e7	+	4.79481e6i	0.369037	+	0.0988831i	0.438571	−	0.898696i	$-0.355485\pi$
$157$	1.78945e7	+	4.79481e6i	0.369037	+	0.0988831i	−0.0695344	+	0.997580i	$0.522151\pi$
$158$	−4.86335e7	−	1.30313e7i	−0.980925	−	0.262838i
$159$	−2.53419e7	+	4.38935e7i	−0.499976	+	0.865984i
$160$	−6.41452e7	+	5.29318e7i	−1.23807	+	1.02164i
$161$	−7.62661e7	−	1.81506e7i	−1.44026	−	0.342769i
$162$	7.74374e7	+	7.74374e7i	1.43103	+	1.43103i
$163$	−709311.	−	2.64719e6i	−0.0128286	−	0.0478771i	0.959215	−	0.282678i	$-0.0912228\pi$
$163$	−709311.	−	2.64719e6i	−0.0128286	−	0.0478771i	−0.972043	+	0.234801i	$0.924556\pi$
$164$	3.04264e7	+	5.27000e7i	0.538637	+	0.932947i
$165$	1.04113e8	+	3.88663e7i	1.80432	+	0.673566i
$166$	−5.16600e6	−	2.98259e6i	−0.0876548	−	0.0506075i
$167$	1.79843e6	−	1.79843e6i	0.0298804	−	0.0298804i	−0.692009	−	0.721889i	$-0.743274\pi$
$167$	1.79843e6	−	1.79843e6i	0.0298804	−	0.0298804i	0.721889	+	0.692009i	$0.243274\pi$
$168$	2.11909e8	−	5.96789e6i	3.44799	−	0.0971042i
$169$		−	5.60527e7i		−	0.893291i
$170$	−1.52341e8	−	1.08548e8i	−2.37819	−	1.69453i
$171$	−1.09150e6	+	630180.i	−0.0166932	+	0.00963780i
$172$	4.25075e7	−	1.58640e8i	0.636965	−	2.37719i
$173$	−4.51708e7	+	1.21035e7i	−0.663279	+	0.177725i	−0.574725	−	0.818346i	$-0.694891\pi$
$173$	−4.51708e7	+	1.21035e7i	−0.663279	+	0.177725i	−0.0885536	+	0.996071i	$0.528224\pi$
$174$	4.54328e7			0.653804
$175$	6.99602e7	+	1.14925e7i	0.986774	+	0.162100i
$176$	2.27694e8			3.14816
$177$	8.76682e7	−	2.34906e7i	1.18833	−	0.318411i
$178$	3.29880e7	−	1.23113e8i	0.438416	−	1.63619i
$179$	−9.27331e7	+	5.35395e7i	−1.20851	+	0.697732i	−0.962433	−	0.271519i	$-0.912474\pi$
$179$	−9.27331e7	+	5.35395e7i	−1.20851	+	0.697732i	−0.246074	+	0.969251i	$0.579141\pi$
$180$	−1.33451e8	−	9.50878e7i	−1.70557	−	1.21527i
$181$			1.55440e7i			0.194845i	0.995243	+	0.0974224i	$0.0310598\pi$
$181$			1.55440e7i			0.194845i	−0.995243	+	0.0974224i	$0.968940\pi$
$182$	−4.15287e7	+	2.55618e7i	−0.510620	+	0.314297i
$183$	−1.39652e8	+	1.39652e8i	−1.68449	+	1.68449i
$184$	2.72270e8	+	1.57195e8i	3.22208	+	1.86027i
$185$	−3.38437e7	−	1.26341e7i	−0.392986	−	0.146705i
$186$	1.34682e7	+	2.33277e7i	0.153467	+	0.265813i
$187$	5.16646e7	+	1.92815e8i	0.577760	+	2.15623i
$188$	−4.05371e7	−	4.05371e7i	−0.444939	−	0.444939i
$189$	−4.22620e6	−	1.41646e7i	−0.0455338	−	0.152612i
$190$	−2.91871e6	+	2.40848e6i	−0.0308712	+	0.0254745i
$191$	−2.24254e6	+	3.88419e6i	−0.0232875	+	0.0403352i	−0.877434	−	0.479697i	$-0.840747\pi$
$191$	−2.24254e6	+	3.88419e6i	−0.0232875	+	0.0403352i	0.854147	+	0.520032i	$0.174080\pi$
$192$	−9.13677e7	−	2.44819e7i	−0.931619	−	0.249627i
$193$	1.39022e8	+	3.72509e7i	1.39198	+	0.372981i	0.875459	−	0.483293i	$-0.160559\pi$
$193$	1.39022e8	+	3.72509e7i	1.39198	+	0.372981i	0.516523	+	0.856273i	$0.327226\pi$
$194$	4.10480e7	−	7.10972e7i	0.403632	−	0.699112i
$195$	4.62142e7	+	4.42631e6i	0.446329	+	0.0427485i
$196$	−2.22964e8	−	1.12499e8i	−2.11514	−	1.06721i
$197$	−1.23256e8	−	1.23256e8i	−1.14862	−	1.14862i	−0.986824	−	0.161800i	$-0.948270\pi$
$197$	−1.23256e8	−	1.23256e8i	−1.14862	−	1.14862i	−0.161800	−	0.986824i	$-0.551730\pi$
$198$	6.43616e7	+	2.40201e8i	0.589249	+	2.19911i
$199$	2.60828e7	+	4.51768e7i	0.234622	+	0.406378i	0.959163	−	0.282855i	$-0.0912814\pi$
$199$	2.60828e7	+	4.51768e7i	0.234622	+	0.406378i	−0.724541	+	0.689232i	$0.757948\pi$
$200$	−2.55671e8	−	1.24379e8i	−2.25983	−	1.09936i
$201$	−7.26784e7	−	4.19609e7i	−0.631276	−	0.364467i
$202$	−1.03427e8	+	1.03427e8i	−0.882886	+	0.882886i
$203$	−2.72114e7	−	1.47051e7i	−0.228305	−	0.123376i
$204$		−	6.27300e8i		−	5.17332i
$205$	−3.25479e7	+	4.56793e7i	−0.263866	+	0.370324i
$206$	3.43246e8	−	1.98173e8i	2.73571	−	1.57946i
$207$	−4.32250e7	+	1.61318e8i	−0.338718	+	1.26411i
$208$	9.18791e7	−	2.46189e7i	0.707937	−	0.189691i
$209$	4.03821e6			0.0305968
$210$	1.48973e8	+	3.03526e8i	1.11004	+	2.26167i
$211$	−1.86117e8			−1.36395			−0.681973	−	0.731378i	$-0.738878\pi$
$211$	−1.86117e8			−1.36395			−0.681973	+	0.731378i	$0.738878\pi$
$212$	−2.31286e8	+	6.19729e7i	−1.66715	+	0.446711i
$213$	5.86881e7	−	2.19027e8i	0.416123	−	1.55299i
$214$	1.65198e8	−	9.53769e7i	1.15227	−	0.665265i
$215$	1.49290e8	−	2.50604e7i	1.02447	−	0.171970i
$216$			5.92783e7i			0.400228i
$217$	−516249.	−	1.83310e7i	−0.00342965	−	0.121781i
$218$	−1.97785e8	+	1.97785e8i	−1.29299	+	1.29299i
$219$	−3.23939e6	−	1.87026e6i	−0.0208405	−	0.0120323i
$220$	2.17963e8	+	4.77635e8i	1.38008	+	3.02424i
$221$	4.16954e7	+	7.22186e7i	0.259846	+	0.450066i
$222$	−4.45897e7	−	1.66411e8i	−0.273526	−	1.02081i
$223$	−1.13547e8	−	1.13547e8i	−0.685657	−	0.685657i	0.275612	−	0.961269i	$-0.411119\pi$
$223$	−1.13547e8	−	1.13547e8i	−0.685657	−	0.685657i	−0.961269	+	0.275612i	$0.911119\pi$
$224$	1.96228e8	+	1.85479e8i	1.16652	+	1.10262i
$225$	2.86686e7	−	1.48289e8i	0.167791	−	0.867900i
$226$	1.49198e8	−	2.58418e8i	0.859772	−	1.48917i
$227$	−7.46262e7	−	1.99960e7i	−0.423449	−	0.113463i	0.0408006	−	0.999167i	$-0.487009\pi$
$227$	−7.46262e7	−	1.99960e7i	−0.423449	−	0.113463i	−0.464249	+	0.885705i	$0.653676\pi$
$228$	−1.22578e7	−	3.28446e6i	−0.0684919	−	0.0183523i
$229$	4.54200e7	−	7.86697e7i	0.249932	−	0.432896i	−0.713574	−	0.700579i	$-0.752925\pi$
$229$	4.54200e7	−	7.86697e7i	0.249932	−	0.432896i	0.963507	+	0.267684i	$0.0862583\pi$
$230$	−4.78072e7	+	4.99146e8i	−0.259087	+	2.70508i
$231$	8.35375e7	−	3.51012e8i	0.445902	−	1.87361i
$232$	8.77094e7	+	8.77094e7i	0.461146	+	0.461146i
$233$	2.84671e7	+	1.06241e8i	0.147434	+	0.550232i	0.999635	+	0.0270170i	$0.00860083\pi$
$233$	2.84671e7	+	1.06241e8i	0.147434	+	0.550232i	−0.852201	+	0.523215i	$0.824732\pi$
$234$	5.19424e7	+	8.99669e7i	0.265013	+	0.459015i
$235$	1.84800e7	−	4.95034e7i	0.0928890	−	0.248827i
$236$	3.71335e8	+	2.14390e8i	1.83896	+	1.06173i
$237$	1.10046e8	−	1.10046e8i	0.536977	−	0.536977i
$238$	−2.88737e8	+	5.34301e8i	−1.38830	+	2.56901i
$239$			2.54412e8i			1.20544i	0.797953	+	0.602720i	$0.205916\pi$
$239$			2.54412e8i			1.20544i	−0.797953	+	0.602720i	$0.794084\pi$
$240$	−1.09181e8	−	6.50418e8i	−0.509811	−	3.03706i
$241$	1.03175e7	−	5.95681e6i	0.0474804	−	0.0274128i	−0.476072	−	0.879406i	$-0.657940\pi$
$241$	1.03175e7	−	5.95681e6i	0.0474804	−	0.0274128i	0.523552	+	0.851994i	$0.324606\pi$
$242$	1.01476e8	−	3.78714e8i	0.460268	−	1.71774i
$243$	−2.92561e8	+	7.83914e7i	−1.30796	+	0.350467i
$244$	−9.33037e8			−4.11182
$245$	9.01565e6	−	2.30011e8i	0.0391666	−	0.999233i
$246$	−2.67490e8			−1.14560
$247$	1.62950e6	−	436623.i	0.00688042	−	0.00184360i
$248$	−1.90339e7	+	7.10357e7i	−0.0792406	+	0.295730i
$249$	1.59681e7	−	9.21916e6i	0.0655472	−	0.0378437i
$250$	1.11819e7	−	4.53332e8i	0.0452611	−	1.83496i
$251$			4.07077e7i			0.162487i	0.996694	+	0.0812435i	$0.0258892\pi$
$251$			4.07077e7i			0.162487i	−0.996694	+	0.0812435i	$0.974111\pi$
$252$	−2.52934e8	+	4.68048e8i	−0.995646	+	1.84242i
$253$	3.78371e8	−	3.78371e8i	1.46891	−	1.46891i
$254$	−9.05785e7	−	5.22955e7i	−0.346822	−	0.200238i
$255$	5.26011e8	−	2.40039e8i	1.98657	−	0.906548i
$256$	1.72009e8	+	2.97929e8i	0.640785	+	1.10987i
$257$	−6.26534e7	−	2.33826e8i	−0.230239	−	0.859263i	−0.980238	−	0.197824i	$-0.936613\pi$
$257$	−6.26534e7	−	2.33826e8i	−0.230239	−	0.859263i	0.749999	−	0.661439i	$-0.230054\pi$
$258$	5.10483e8	+	5.10483e8i	1.85060	+	1.85060i
$259$	−2.71552e7	+	1.14102e8i	−0.0971189	+	0.408079i
$260$	1.39596e8	+	1.69169e8i	0.492567	+	0.596916i
$261$	−3.29459e7	+	5.70639e7i	−0.114699	+	0.198664i
$262$	−3.99352e8	−	1.07006e8i	−1.37183	−	0.367581i
$263$	4.70582e8	+	1.26092e8i	1.59511	+	0.427408i	0.943561	−	0.331200i	$-0.107453\pi$
$263$	4.70582e8	+	1.26092e8i	1.59511	+	0.427408i	0.651548	+	0.758608i	$0.274120\pi$
$264$	−7.23483e8	+	1.25311e9i	−2.42000	+	4.19156i
$265$	−1.40469e8	−	1.70227e8i	−0.463681	−	0.561910i
$266$	8.92872e6	+	8.43959e6i	0.0290873	+	0.0274938i
$267$	2.78576e8	+	2.78576e8i	0.895681	+	0.895681i
$268$	−1.02614e8	−	3.82961e8i	−0.325638	−	1.21530i
$269$	−2.02946e8	−	3.51512e8i	−0.635692	−	1.10105i	−0.986368	−	0.164554i	$-0.947382\pi$
$269$	−2.02946e8	−	3.51512e8i	−0.635692	−	1.10105i	0.350676	−	0.936497i	$-0.385952\pi$
$270$	−8.60123e7	+	3.92507e7i	−0.265942	+	0.121360i
$271$	4.30831e6	+	2.48740e6i	0.0131497	+	0.00759195i	0.506560	−	0.862204i	$-0.330917\pi$
$271$	4.30831e6	+	2.48740e6i	0.0131497	+	0.00759195i	−0.493411	+	0.869796i	$0.664250\pi$
$272$	8.37667e8	−	8.37667e8i	2.52395	−	2.52395i
$273$	−4.24333e6	−	1.50673e8i	−0.0126223	−	0.448193i
$274$		−	9.36854e8i		−	2.75134i
$275$	−3.17108e8	+	3.65538e8i	−0.919481	+	1.05991i
$276$	−1.45627e9	+	8.40778e8i	−4.16927	+	2.40713i
$277$	−7.44008e7	+	2.77668e8i	−0.210329	+	0.784957i	0.777430	+	0.628969i	$0.216523\pi$
$277$	−7.44008e7	+	2.77668e8i	−0.210329	+	0.784957i	−0.987759	+	0.155988i	$0.950144\pi$
$278$	−1.06128e9	+	2.84368e8i	−2.96259	+	0.793825i
$279$	−3.90663e7			−0.107693
$280$	−2.98369e8	+	8.73563e8i	−0.812271	+	2.37816i
$281$	−1.89925e8			−0.510634			−0.255317	−	0.966857i	$-0.582180\pi$
$281$	−1.89925e8			−0.510634			−0.255317	+	0.966857i	$0.582180\pi$
$282$	2.43410e8	−	6.52216e7i	0.646349	−	0.173189i
$283$	1.17321e8	−	4.37849e8i	0.307698	−	1.14834i	−0.622900	−	0.782301i	$-0.714046\pi$
$283$	1.17321e8	−	4.37849e8i	0.307698	−	1.14834i	0.930598	−	0.366043i	$-0.119288\pi$
$284$	9.27728e8	−	5.35624e8i	2.40329	−	1.38754i
$285$	−1.93636e6	−	1.15353e7i	−0.00495483	−	0.0295171i
$286$		−	3.32848e8i		−	0.841328i
$287$	1.60210e8	+	8.65774e7i	0.400038	+	0.216181i
$288$	4.06739e8	−	4.06739e8i	1.00333	−	1.00333i
$289$	5.44056e8	+	3.14111e8i	1.32587	+	0.765492i
$290$	−6.91895e7	+	1.85342e8i	−0.166589	+	0.446252i
$291$	1.26879e8	+	2.19761e8i	0.301831	+	0.522787i
$292$	−4.57368e6	−	1.70692e7i	−0.0107504	−	0.0401211i
$293$	2.43776e8	+	2.43776e8i	0.566180	+	0.566180i	0.931056	−	0.364876i	$-0.118889\pi$
$293$	2.43776e8	+	2.43776e8i	0.566180	+	0.566180i	−0.364876	+	0.931056i	$0.618889\pi$
$294$	9.18298e8	−	6.01520e8i	2.10750	−	1.38049i
$295$	−3.76804e7	+	3.93413e8i	−0.0854551	+	0.892220i
$296$	2.35180e8	−	4.07343e8i	0.527083	−	0.912934i
$297$	9.74550e7	+	2.61130e7i	0.215852	+	0.0578374i
$298$	−1.07858e9	−	2.89004e8i	−2.36099	−	0.632626i
$299$	1.11770e8	−	1.93591e8i	0.241810	−	0.418828i
$300$	1.25987e9	−	8.51652e8i	2.69403	−	1.82112i
$301$	−1.40521e8	−	4.70973e8i	−0.297001	−	0.995436i
$302$	5.94213e8	+	5.94213e8i	1.24142	+	1.24142i
$303$	−1.17016e8	−	4.36708e8i	−0.241654	−	0.901866i
$304$	−1.19825e7	−	2.07544e7i	−0.0244619	−	0.0423693i
$305$	−3.57030e8	−	7.82381e8i	−0.720536	−	1.57895i
$306$	1.12046e9	+	6.46898e8i	2.23548	+	1.29066i
$307$	−2.03805e8	+	2.03805e8i	−0.402004	+	0.402004i	−0.878939	−	0.476935i	$-0.841748\pi$
$307$	−2.03805e8	+	2.03805e8i	−0.402004	+	0.402004i	0.476935	+	0.878939i	$0.341748\pi$
$308$	1.45165e9	−	8.93518e8i	2.83096	−	1.74251i
$309$			1.22510e9i			2.36221i
$310$	−1.15675e8	+	1.94176e7i	−0.220534	+	0.0370194i
$311$	−3.71467e8	+	2.14467e8i	−0.700260	+	0.404295i	−0.807444	−	0.589944i	$-0.799150\pi$
$311$	−3.71467e8	+	2.14467e8i	−0.700260	+	0.404295i	0.107184	+	0.994239i	$0.465817\pi$
$312$	−1.56450e8	+	5.83880e8i	−0.291632	+	1.08839i
$313$	−6.28215e8	+	1.68330e8i	−1.15799	+	0.310281i	−0.786161	−	0.618022i	$-0.787934\pi$
$313$	−6.28215e8	+	1.68330e8i	−1.15799	+	0.310281i	−0.371825	+	0.928303i	$0.621268\pi$
$314$	−3.84714e8			−0.701269
$315$	−4.89260e8	−	3.29926e7i	−0.881967	−	0.0594743i
$316$	7.35235e8			1.31075
$317$	−5.98211e8	+	1.60290e8i	−1.05474	+	0.282618i	−0.744211	−	0.667945i	$-0.767174\pi$
$317$	−5.98211e8	+	1.60290e8i	−1.05474	+	0.282618i	−0.310533	+	0.950563i	$0.600508\pi$
$318$	2.72414e8	−	1.01666e9i	0.475044	−	1.77289i
$319$	1.82834e8	−	1.05559e8i	0.315347	−	0.182066i
$320$	2.39017e8	−	3.35448e8i	0.407759	−	0.572269i
$321$			5.89618e8i			0.994955i
$322$	1.62737e9	−	4.58309e7i	2.71638	−	0.0765002i
$323$	1.48562e7	−	1.48562e7i	0.0245301	−	0.0245301i
$324$	−1.38494e9	−	7.99596e8i	−2.26216	−	1.30606i
$325$	−8.84365e7	+	1.81789e8i	−0.142902	+	0.293748i
$326$	2.84560e7	+	4.92873e7i	0.0454896	+	0.0787904i
$327$	−2.23771e8	−	8.35124e8i	−0.353905	−	1.32079i
$328$	−5.16397e8	−	5.16397e8i	−0.808025	−	0.808025i
$329$	−1.66898e8	−	3.97201e7i	−0.258383	−	0.0614928i
$330$	−2.29730e9	−	2.20031e8i	−3.51900	−	0.337043i
$331$	−2.19730e8	+	3.80583e8i	−0.333035	+	0.576834i	−0.983105	−	0.183040i	$-0.941406\pi$
$331$	−2.19730e8	+	3.80583e8i	−0.333035	+	0.576834i	0.650070	+	0.759874i	$0.274740\pi$
$332$	8.41398e7	+	2.25452e7i	0.126188	+	0.0338120i
$333$	2.41348e8	+	6.46690e7i	0.358170	+	0.0959713i
$334$	−2.64084e7	+	4.57407e7i	−0.0387819	+	0.0671723i
$335$	2.81860e8	−	2.32587e8i	0.409615	−	0.338009i
$336$	−2.05190e9	+	6.12213e8i	−2.95100	+	0.880471i
$337$	−2.95727e8	−	2.95727e8i	−0.420907	−	0.420907i	0.464609	−	0.885516i	$-0.346195\pi$
$337$	−2.95727e8	−	2.95727e8i	−0.420907	−	0.420907i	−0.885516	+	0.464609i	$0.846195\pi$
$338$	3.01270e8	+	1.12436e9i	0.424373	+	1.58378i
$339$	4.61170e8	+	7.98769e8i	0.642927	+	1.11358i
$340$	2.55905e9	+	9.55313e8i	3.53104	+	1.31816i
$341$	1.08400e8	+	6.25845e7i	0.148043	+	0.0854725i
$342$	1.85073e7	−	1.85073e7i	0.0250179	−	0.0250179i
$343$	−7.44695e8	+	6.30509e7i	−0.996435	+	0.0843649i
$344$			1.97100e9i			2.61056i
$345$	−1.26227e9	−	8.99402e8i	−1.65495	−	1.17920i
$346$	8.41023e8	−	4.85565e8i	1.09154	−	0.630204i
$347$	−1.97312e8	+	7.36380e8i	−0.253513	+	0.946125i	0.715398	+	0.698717i	$0.246245\pi$
$347$	−1.97312e8	+	7.36380e8i	−0.253513	+	0.946125i	−0.968911	+	0.247408i	$0.920421\pi$
$348$	−6.40837e8	+	1.71712e8i	−0.815118	+	0.218410i
$349$	3.27247e8			0.412085			0.206043	−	0.978543i	$-0.433941\pi$
$349$	3.27247e8			0.412085			0.206043	+	0.978543i	$0.433941\pi$
$350$	−1.46509e9	+	1.45492e8i	−1.82653	+	0.181385i
$351$	4.21485e7			0.0520244
$352$	−1.78020e9	+	4.77003e8i	−2.17555	+	0.582937i
$353$	−6.30748e7	+	2.35398e8i	−0.0763211	+	0.284834i	−0.993530	−	0.113573i	$-0.963770\pi$
$353$	−6.30748e7	+	2.35398e8i	−0.0763211	+	0.284834i	0.917209	+	0.398407i	$0.130437\pi$
$354$	−1.63227e9	+	9.42393e8i	−1.95560	+	1.12907i
$355$	8.04137e8	+	5.72971e8i	0.953961	+	0.679726i
$356$			1.86121e9i			2.18635i
$357$	−9.84016e8	−	1.59867e9i	−1.14463	−	1.85961i
$358$	1.57236e9	−	1.57236e9i	1.81118	−	1.81118i
$359$	2.41189e8	+	1.39251e8i	0.275123	+	0.158842i	0.631213	−	0.775609i	$-0.282557\pi$
$359$	2.41189e8	+	1.39251e8i	0.275123	+	0.158842i	−0.356091	+	0.934451i	$0.615891\pi$
$360$	1.84233e9	+	6.87756e8i	2.08118	+	0.776919i
$361$	4.46723e8	+	7.73748e8i	0.499762	+	0.865614i
$362$	−8.35456e7	−	3.11796e8i	−0.0925643	−	0.345455i
$363$	8.56941e8	+	8.56941e8i	0.940325	+	0.940325i
$364$	4.89159e8	−	5.17509e8i	0.531612	−	0.562423i
$365$	1.25629e7	−	1.03668e7i	0.0135228	−	0.0111588i
$366$	2.05067e9	−	3.55186e9i	2.18631	−	3.78680i
$367$	1.07126e9	+	2.87042e8i	1.13126	+	0.303120i	0.775432	−	0.631432i	$-0.217532\pi$
$367$	1.07126e9	+	2.87042e8i	1.13126	+	0.303120i	0.355828	+	0.934552i	$0.384199\pi$
$368$	−3.06737e9	−	8.21900e8i	−3.20848	−	0.859709i
$369$	1.93972e8	−	3.35969e8i	0.200977	−	0.348102i
$370$	7.46774e8	+	7.15245e7i	0.766448	+	0.0734089i
$371$	−4.92218e8	+	5.20746e8i	−0.500436	+	0.529440i
$372$	−2.78138e8	−	2.78138e8i	−0.280130	−	0.280130i
$373$	9.48592e7	+	3.54020e8i	0.0946452	+	0.353221i	0.996965	−	0.0778456i	$-0.0248041\pi$
$373$	9.48592e7	+	3.54020e8i	0.0946452	+	0.353221i	−0.902320	+	0.431066i	$0.858137\pi$
$374$	−2.07267e9	−	3.58997e9i	−2.04871	−	3.54846i
$375$	1.19623e9	+	7.30556e8i	1.17140	+	0.715392i
$376$	5.95823e8	+	3.43999e8i	0.578043	+	0.333733i
$377$	6.23637e7	−	6.23637e7i	0.0599428	−	0.0599428i
$378$	1.60904e8	+	2.61412e8i	0.153231	+	0.248945i
$379$			9.82490e8i			0.927023i	0.886091	+	0.463512i	$0.153411\pi$
$379$			9.82490e8i			0.927023i	−0.886091	+	0.463512i	$0.846589\pi$
$380$	3.20661e7	−	4.50032e7i	0.0299781	−	0.0420728i
$381$	2.79977e8	−	1.61645e8i	0.259350	−	0.149736i
$382$	2.41063e7	−	8.99658e7i	0.0221263	−	0.0825763i
$383$	4.13306e8	−	1.10745e8i	0.375903	−	0.100723i	−0.0659204	−	0.997825i	$-0.520998\pi$
$383$	4.13306e8	−	1.10745e8i	0.375903	−	0.100723i	0.441824	+	0.897102i	$0.354332\pi$
$384$	−4.80324e8			−0.432887
$385$	1.30472e9	+	8.75343e8i	1.16521	+	0.781746i
$386$	−2.98885e9			−2.64514
$387$	−1.01135e9	+	2.70990e8i	−0.886978	+	0.237665i
$388$	−3.10279e8	+	1.15798e9i	−0.269676	+	1.00644i
$389$	−1.32070e9	+	7.62508e8i	−1.13758	+	0.656782i	−0.945830	−	0.324662i	$-0.894749\pi$
$389$	−1.32070e9	+	7.62508e8i	−1.13758	+	0.656782i	−0.191749	+	0.981444i	$0.561416\pi$
$390$	−9.50798e8	+	1.59604e8i	−0.811637	+	0.136244i
$391$		−	2.78399e9i		−	2.35532i
$392$	2.93405e9	+	6.11549e8i	2.46018	+	0.512778i
$393$	9.03638e8	−	9.03638e8i	0.750967	−	0.750967i
$394$	3.13486e9	+	1.80991e9i	2.58215	+	1.49081i
$395$	2.81341e8	+	6.16518e8i	0.229690	+	0.503334i
$396$	−1.81566e9	−	3.14482e9i	−1.46927	−	2.54485i
$397$	−6.23622e8	−	2.32739e9i	−0.500213	−	1.86682i	−0.498618	−	0.866822i	$-0.666159\pi$
$397$	−6.23622e8	−	2.32739e9i	−0.500213	−	1.86682i	−0.00159449	−	0.999999i	$-0.500508\pi$
$398$	−7.66008e8	−	7.66008e8i	−0.609035	−	0.609035i
$399$	−3.63910e7	+	1.08577e7i	−0.0286807	+	0.00855726i
$400$	2.81963e9	+	5.45118e8i	2.20284	+	0.425874i
$401$	−1.04580e9	+	1.81137e9i	−0.809919	+	1.40282i	0.103001	+	0.994681i	$0.467155\pi$
$401$	−1.04580e9	+	1.81137e9i	−0.809919	+	1.40282i	−0.912920	+	0.408139i	$0.866178\pi$
$402$	1.68338e9	+	4.51060e8i	1.29238	+	0.346293i
$403$	5.05082e7	+	1.35336e7i	0.0384410	+	0.0103002i
$404$	1.06796e9	−	1.84976e9i	0.805785	−	1.39566i
$405$	1.40534e8	−	1.46729e9i	0.105121	−	1.09754i
$406$	6.24868e8	+	1.48713e8i	0.463390	+	0.110283i
$407$	−5.66081e8	−	5.66081e8i	−0.416196	−	0.416196i
$408$	1.94845e9	+	7.27173e9i	1.42030	+	5.30062i
$409$	−1.06607e9	−	1.84648e9i	−0.770464	−	1.33448i	−0.937309	−	0.348500i	$-0.886691\pi$
$409$	−1.06607e9	−	1.84648e9i	−0.770464	−	1.33448i	0.166844	−	0.985983i	$-0.446642\pi$
$410$	4.07359e8	−	1.09122e9i	0.291900	−	0.781928i
$411$	2.50784e9	+	1.44790e9i	1.78178	+	1.02871i
$412$	−4.09255e9	+	4.09255e9i	−2.88306	+	2.88306i
$413$	1.28265e9	−	3.61227e7i	0.895948	−	0.0252322i
$414$		−	3.46818e9i		−	2.40215i
$415$	1.32916e7	+	7.91810e7i	0.00912868	+	0.0543817i
$416$	−6.66772e8	+	3.84961e8i	−0.454099	+	0.262174i
$417$	8.78980e8	−	3.28040e9i	0.593612	−	2.21539i
$418$	−8.10020e7	+	2.17044e7i	−0.0542474	+	0.0145355i
$419$	−9.53657e8			−0.633349			−0.316675	−	0.948534i	$-0.602566\pi$
$419$	−9.53657e8			−0.633349			−0.316675	+	0.948534i	$0.602566\pi$
$420$	−3.24846e9	−	3.71825e9i	−2.13946	−	2.44887i
$421$	1.10840e9			0.723950			0.361975	−	0.932188i	$-0.382103\pi$
$421$	1.10840e9			0.723950			0.361975	+	0.932188i	$0.382103\pi$
$422$	3.73330e9	−	1.00033e9i	2.41824	−	0.647965i
$423$	−9.45917e7	+	3.53021e8i	−0.0607661	+	0.226782i
$424$	2.48860e9	−	1.43679e9i	1.58553	−	0.915406i
$425$	1.78170e8	+	2.51140e9i	0.112583	+	1.58692i
$426$			4.70888e9i			2.95110i
$427$	−2.37784e9	+	1.46361e9i	−1.47804	+	0.909763i
$428$	−1.96967e9	+	1.96967e9i	−1.21434	+	1.21434i
$429$	8.90994e8	+	5.14416e8i	0.544847	+	0.314567i
$430$	−2.85991e9	+	1.30508e9i	−1.73465	+	0.791588i
$431$	−1.08575e9	−	1.88058e9i	−0.653221	−	1.13141i	−0.982337	−	0.187122i	$-0.940084\pi$
$431$	−1.08575e9	−	1.88058e9i	−0.653221	−	1.13141i	0.329116	−	0.944289i	$-0.393249\pi$
$432$	−1.54970e8	−	5.78354e8i	−0.0924812	−	0.345144i
$433$	5.75998e8	+	5.75998e8i	0.340968	+	0.340968i	0.856731	−	0.515763i	$-0.172492\pi$
$433$	5.75998e8	+	5.75998e8i	0.340968	+	0.340968i	−0.515763	+	0.856731i	$0.672492\pi$
$434$	1.08880e8	+	3.64926e8i	0.0639346	+	0.214284i
$435$	−3.89205e8	−	4.71657e8i	−0.226708	−	0.274735i
$436$	2.04227e9	−	3.53732e9i	1.18008	−	2.04396i
$437$	−5.44006e7	−	1.45766e7i	−0.0311831	−	0.00835548i
$438$	7.50309e7	+	2.01045e7i	0.0426659	+	0.0114323i
$439$	−5.89961e8	+	1.02184e9i	−0.332811	+	0.576445i	−0.983062	−	0.183274i	$-0.941330\pi$
$439$	−5.89961e8	+	1.02184e9i	−0.332811	+	0.576445i	0.650251	+	0.759719i	$0.274664\pi$
$440$	−4.01023e9	−	4.85978e9i	−2.24432	−	2.71977i
$441$	8.96046e7	+	1.58959e9i	0.0497502	+	0.882569i
$442$	−1.22452e9	−	1.22452e9i	−0.674511	−	0.674511i
$443$	−6.86066e8	−	2.56043e9i	−0.374933	−	1.39927i	−0.853443	−	0.521186i	$-0.825490\pi$
$443$	−6.86066e8	−	2.56043e9i	−0.374933	−	1.39927i	0.478511	−	0.878082i	$-0.341177\pi$
$444$	1.25789e9	+	2.17873e9i	0.682028	+	1.18131i
$445$	−1.56068e9	+	7.12198e8i	−0.839565	+	0.383125i
$446$	2.88791e9	+	1.66733e9i	1.54138	+	0.889919i
$447$	2.44056e9	−	2.44056e9i	1.29245	−	1.29245i
$448$	−1.17650e9	−	6.35784e8i	−0.618188	−	0.334069i
$449$		−	8.85891e8i		−	0.461868i	−0.972969	−	0.230934i	$-0.925822\pi$
$449$		−	8.85891e8i		−	0.461868i	0.972969	−	0.230934i	$-0.0741782\pi$
$450$	2.21957e8	+	3.12860e9i	0.114822	+	1.61847i
$451$	−1.07645e9	+	6.21488e8i	−0.552555	+	0.319018i
$452$	−1.12778e9	+	4.20892e9i	−0.574432	+	2.14381i
$453$	−2.50899e9	+	6.72282e8i	−1.26811	+	0.339788i
$454$	1.60439e9			0.804666
$455$	6.21127e8	+	2.12148e8i	0.309129	+	0.105584i
$456$	1.52295e8			0.0752158
$457$	3.52328e8	−	9.44061e7i	0.172680	−	0.0462694i	−0.171443	−	0.985194i	$-0.554843\pi$
$457$	3.52328e8	−	9.44061e7i	0.172680	−	0.0462694i	0.344123	+	0.938925i	$0.388176\pi$
$458$	−4.88244e8	+	1.82215e9i	−0.237469	+	0.886247i
$459$	4.54597e8	−	2.62462e8i	0.219423	−	0.126684i
$460$	−1.21218e9	−	7.22122e9i	−0.580649	−	3.45906i
$461$			5.60809e8i			0.266601i	0.991076	+	0.133301i	$0.0425575\pi$
$461$			5.60809e8i			0.266601i	−0.991076	+	0.133301i	$0.957442\pi$
$462$	2.10935e8	+	7.48991e9i	0.0995179	+	3.53370i
$463$	1.16500e9	−	1.16500e9i	0.545499	−	0.545499i	−0.379636	−	0.925136i	$-0.623951\pi$
$463$	1.16500e9	−	1.16500e9i	0.545499	−	0.545499i	0.925136	+	0.379636i	$0.123951\pi$
$464$	−1.08504e9	−	6.26448e8i	−0.504235	−	0.291120i
$465$	1.26797e8	−	3.39658e8i	0.0584822	−	0.156660i
$466$	−1.14204e9	−	1.97807e9i	−0.522794	−	0.905506i
$467$	−2.18879e8	−	8.16866e8i	−0.0994476	−	0.371143i	0.898209	−	0.439569i	$-0.144869\pi$
$467$	−2.18879e8	−	8.16866e8i	−0.0994476	−	0.371143i	−0.997656	+	0.0684261i	$0.978202\pi$
$468$	−1.07268e9	−	1.07268e9i	−0.483739	−	0.483739i
$469$	−8.62246e8	−	8.15010e8i	−0.385946	−	0.364803i
$470$	−1.04619e8	+	1.09231e9i	−0.0464804	+	0.485292i
$471$	5.94574e8	−	1.02983e9i	0.262200	−	0.454144i
$472$	−4.97047e9	−	1.33183e9i	−2.17571	−	0.582979i
$473$	3.24038e9	+	8.68256e8i	1.40793	+	0.377254i
$474$	−1.61593e9	+	2.79888e9i	−0.696946	+	1.20715i
$475$	5.00069e7	+	9.66781e6i	0.0214093	+	0.00413905i
$476$	2.05331e9	−	8.62767e9i	0.872628	−	3.66665i
$477$	1.07939e9	+	1.07939e9i	0.455371	+	0.455371i
$478$	−1.36741e9	−	5.10323e9i	−0.572664	−	2.13721i
$479$	1.72136e9	+	2.98148e9i	0.715644	+	1.23953i	0.962711	+	0.270533i	$0.0872001\pi$
$479$	1.72136e9	+	2.98148e9i	0.715644	+	1.23953i	−0.247066	+	0.968999i	$0.579467\pi$
$480$	2.21620e9	+	4.85650e9i	0.914672	+	2.00438i
$481$	−2.89632e8	−	1.67219e8i	−0.118669	−	0.0685138i
$482$	−1.74941e8	+	1.74941e8i	−0.0711586	+	0.0711586i
$483$	−2.39241e9	+	4.42710e9i	−0.966097	+	1.78774i
$484$			5.72536e9i			2.29532i
$485$	−1.08973e9	+	1.82926e8i	−0.433734	+	0.0728079i
$486$	5.44712e9	−	3.14489e9i	2.15248	−	1.24274i
$487$	−1.13078e9	+	4.22014e9i	−0.443637	+	1.65568i	0.275872	+	0.961194i	$0.411034\pi$
$487$	−1.13078e9	+	4.22014e9i	−0.443637	+	1.65568i	−0.719509	+	0.694483i	$0.755633\pi$
$488$	1.08159e10	−	2.89810e9i	4.21300	−	1.12887i
$489$	−1.75915e8			−0.0680332
$490$	1.05541e9	+	4.66222e9i	0.405261	+	1.79022i
$491$	−4.89237e8			−0.186524			−0.0932618	−	0.995642i	$-0.529729\pi$
$491$	−4.89237e8			−0.186524			−0.0932618	+	0.995642i	$0.529729\pi$
$492$	3.77299e9	−	1.01097e9i	1.42826	−	0.382701i
$493$	2.84287e8	−	1.06097e9i	0.106854	−	0.398786i
$494$	−3.03392e7	+	1.75164e7i	−0.0113230	+	0.00653732i
$495$	1.94226e9	−	2.72587e9i	0.719763	−	1.01015i
$496$		−	7.42825e8i		−	0.273338i
$497$	1.52410e9	−	2.82032e9i	0.556887	−	1.03051i
$498$	−2.70751e8	+	2.70751e8i	−0.0982352	+	0.0982352i
$499$	4.00940e8	+	2.31483e8i	0.144453	+	0.0834002i	0.570485	−	0.821308i	$-0.306755\pi$
$499$	4.00940e8	+	2.31483e8i	0.144453	+	0.0834002i	−0.426031	+	0.904708i	$0.640089\pi$
$500$	1.55563e9	+	6.43659e9i	0.556560	+	2.30282i
$501$	−8.16282e7	−	1.41384e8i	−0.0290007	−	0.0502306i
$502$	−2.18795e8	−	8.16553e8i	−0.0771922	−	0.288085i
$503$	−3.98010e9	−	3.98010e9i	−1.39446	−	1.39446i	−0.814999	−	0.579462i	$-0.803263\pi$
$503$	−3.98010e9	−	3.98010e9i	−1.39446	−	1.39446i	−0.579462	−	0.814999i	$-0.696737\pi$
$504$	1.47823e9	−	6.21130e9i	0.514323	−	2.16110i
$505$	1.95974e9	+	1.87700e8i	0.677140	+	0.0648551i
$506$	−5.55605e9	+	9.62336e9i	−1.90651	+	3.30217i
$507$	−3.47537e9	−	9.31224e8i	−1.18433	−	0.317341i
$508$	1.47527e9	+	3.95298e8i	0.499286	+	0.133783i
$509$	2.69929e8	−	4.67531e8i	0.0907273	−	0.157144i	−0.817090	−	0.576510i	$-0.804414\pi$
$509$	2.69929e8	−	4.67531e8i	0.0907273	−	0.157144i	0.907817	+	0.419366i	$0.137748\pi$
$510$	−9.26106e9	+	7.64211e9i	−3.09147	+	2.55104i
$511$	−3.84317e7	−	3.63263e7i	−0.0127414	−	0.0120434i
$512$	−4.37434e9	−	4.37434e9i	−1.44035	−	1.44035i
$513$	−2.74842e6	−	1.02573e7i	−0.000898821	−	0.00335444i
$514$	2.51352e9	+	4.35354e9i	0.816415	+	1.41407i
$515$	−4.99777e9	−	1.86570e9i	−1.61232	−	0.601891i
$516$	−9.12979e9	−	5.27109e9i	−2.92541	−	1.68899i
$517$	8.28010e8	−	8.28010e8i	0.263523	−	0.263523i
$518$	−6.85677e7	−	2.43471e9i	−0.0216753	−	0.769651i
$519$			3.00175e9i			0.942517i
$520$	−2.14366e9	−	1.52742e9i	−0.668567	−	0.476374i
$521$	−4.15450e9	+	2.39860e9i	−1.28702	+	0.743064i	−0.978122	−	0.208030i	$-0.933295\pi$
$521$	−4.15450e9	+	2.39860e9i	−1.28702	+	0.743064i	−0.308902	+	0.951094i	$0.599961\pi$
$522$	3.54153e8	−	1.32172e9i	0.108979	−	0.406716i
$523$	−1.29833e9	+	3.47888e8i	−0.396854	+	0.106337i	−0.451726	−	0.892157i	$-0.649192\pi$
$523$	−1.29833e9	+	3.47888e8i	−0.396854	+	0.106337i	0.0548721	+	0.998493i	$0.482525\pi$
$524$	6.03735e9			1.83310
$525$	1.87483e9	−	4.14674e9i	0.565465	−	1.25069i
$526$	−1.01171e10			−3.03113
$527$	6.29037e8	−	1.68550e8i	0.187214	−	0.0501639i
$528$	3.78276e9	−	1.41174e10i	1.11838	−	4.17386i
$529$	−3.51434e9	+	2.02901e9i	−1.03217	+	0.595921i
$530$	3.73258e9	+	2.65957e9i	1.08904	+	0.775973i
$531$		−	2.73353e9i		−	0.792305i
$532$	−1.57838e8	−	8.52959e7i	−0.0454487	−	0.0245605i
$533$	−3.67172e8	+	3.67172e8i	−0.105033	+	0.105033i
$534$	−7.08520e9	−	4.09064e9i	−2.01353	−	1.16251i
$535$	−2.40533e9	−	8.97927e8i	−0.679104	−	0.253515i
$536$	2.37903e9	+	4.12060e9i	0.667303	+	1.15580i
$537$	1.77894e9	+	6.63910e9i	0.495737	+	1.85012i
$538$	5.96016e9	+	5.96016e9i	1.65014	+	1.65014i
$539$	2.29789e9	−	4.55426e9i	0.632076	−	1.25273i
$540$	1.06487e9	−	8.78718e8i	0.291017	−	0.240144i
$541$	6.76408e8	−	1.17157e9i	0.183661	−	0.318111i	−0.759463	−	0.650550i	$-0.774538\pi$
$541$	6.76408e8	−	1.17157e9i	0.183661	−	0.318111i	0.943125	+	0.332439i	$0.107872\pi$
$542$	−9.97892e7	−	2.67384e7i	−0.0269207	−	0.00721337i
$543$	9.63760e8	+	2.58239e8i	0.258327	+	0.0692185i
$544$	−4.79436e9	+	8.30407e9i	−1.27683	+	2.21154i
$545$	3.74764e9	+	3.58942e8i	0.991676	+	0.0949808i
$546$	8.94948e8	+	2.99952e9i	0.235301	+	0.788639i
$547$	3.46867e9	+	3.46867e9i	0.906165	+	0.906165i	0.995960	−	0.0897957i	$-0.0286214\pi$
$547$	3.46867e9	+	3.46867e9i	0.906165	+	0.906165i	−0.0897957	+	0.995960i	$0.528621\pi$
$548$	3.54081e9	+	1.32145e10i	0.919117	+	3.43019i
$549$	2.97411e9	+	5.15131e9i	0.767104	+	1.32866i
$550$	4.39616e9	−	9.03667e9i	1.12669	−	2.31600i
$551$	−1.92435e7	−	1.11102e7i	−0.00490064	−	0.00282939i
$552$	1.42697e10	−	1.42697e10i	3.61101	−	3.61101i
$553$	1.87374e9	−	1.15333e9i	0.471164	−	0.290011i
$554$		−	5.96960e9i		−	1.49163i
$555$	−1.34560e9	+	1.88848e9i	−0.334110	+	0.468907i
$556$	1.38947e10	−	8.02212e9i	3.42837	−	1.97937i
$557$	−3.86774e8	+	1.44346e9i	−0.0948340	+	0.353925i	−0.996994	−	0.0774758i	$-0.975314\pi$
$557$	−3.86774e8	+	1.44346e9i	−0.0948340	+	0.353925i	0.902160	+	0.431401i	$0.141981\pi$
$558$	7.83628e8	−	2.09972e8i	0.190937	−	0.0511614i
$559$	1.40144e9			0.339338
$560$	6.27336e8	−	9.30301e9i	0.150953	−	2.23854i
$561$	1.28132e10			3.06399
$562$	3.80968e9	−	1.02080e9i	0.905340	−	0.242585i
$563$	1.66383e9	−	6.20949e9i	0.392942	−	1.46648i	−0.432314	−	0.901723i	$-0.642303\pi$
$563$	1.66383e9	−	6.20949e9i	0.392942	−	1.46648i	0.825257	−	0.564758i	$-0.191030\pi$
$564$	−3.18684e9	+	1.83992e9i	−0.747969	+	0.431840i
$565$	−3.96087e9	+	6.64884e8i	−0.923891	+	0.155087i
$566$			9.41335e9i			2.18216i
$567$	−4.78381e9	+	1.34724e8i	−1.10213	+	0.0310388i
$568$	−9.09062e9	+	9.09062e9i	−2.08149	+	2.08149i
$569$	1.42321e9	+	8.21691e8i	0.323874	+	0.186989i	0.653118	−	0.757256i	$-0.273461\pi$
$569$	1.42321e9	+	8.21691e8i	0.323874	+	0.186989i	−0.329244	+	0.944245i	$0.606794\pi$
$570$	1.00841e8	+	2.20979e8i	0.0228074	+	0.0499791i
$571$	−4.69328e8	−	8.12899e8i	−0.105499	−	0.182730i	0.808443	−	0.588575i	$-0.200311\pi$
$571$	−4.69328e8	−	8.12899e8i	−0.105499	−	0.182730i	−0.913942	+	0.405845i	$0.866977\pi$
$572$	1.25799e9	+	4.69488e9i	0.281055	+	1.04891i
$573$	2.03571e8	+	2.03571e8i	0.0452038	+	0.0452038i
$574$	−3.67896e9	−	8.75559e8i	−0.811958	−	0.193239i
$575$	5.59138e9	−	3.77968e9i	1.22654	−	0.829120i
$576$	−1.42444e9	+	2.46720e9i	−0.310574	+	0.537930i
$577$	−5.17956e9	−	1.38786e9i	−1.12248	−	0.300767i	−0.350592	−	0.936528i	$-0.614020\pi$
$577$	−5.17956e9	−	1.38786e9i	−1.12248	−	0.300767i	−0.771886	+	0.635761i	$0.780686\pi$
$578$	−1.26015e10	−	3.37655e9i	−2.71440	−	0.727320i
$579$	4.61926e9	−	8.00078e9i	0.989002	−	1.71300i
$580$	2.75436e8	−	2.87577e9i	0.0586169	−	0.612008i
$581$	2.49796e8	−	7.45299e7i	0.0528407	−	0.0157657i
$582$	−3.72622e9	−	3.72622e9i	−0.783498	−	0.783498i
$583$	−1.26586e9	−	4.72424e9i	−0.264572	−	0.987398i
$584$	1.06037e8	+	1.83662e8i	0.0220299	+	0.0381569i
$585$	4.89013e8	−	1.30995e9i	0.100989	−	0.270525i
$586$	−6.20012e9	−	3.57964e9i	−1.27279	−	0.734848i
$587$	−3.59447e9	+	3.59447e9i	−0.733503	+	0.733503i	−0.971312	−	0.237809i	$-0.923571\pi$
$587$	−3.59447e9	+	3.59447e9i	−0.733503	+	0.733503i	0.237809	+	0.971312i	$0.423571\pi$
$588$	−1.06793e10	+	1.19552e10i	−2.16632	+	2.42514i
$589$		−	1.31742e7i		−	0.00265657i
$590$	−1.35868e9	−	8.09396e9i	−0.272355	−	1.62248i
$591$	−9.68984e9	+	5.59443e9i	−1.93090	+	1.11481i
$592$	−1.22965e9	+	4.58910e9i	−0.243587	+	0.909079i
$593$	2.46086e9	−	6.59386e8i	0.484614	−	0.129852i	−0.00823643	−	0.999966i	$-0.502622\pi$
$593$	2.46086e9	−	6.59386e8i	0.484614	−	0.129852i	0.492850	+	0.870114i	$0.335955\pi$
$594$	−2.09519e9			−0.410177
$595$	8.02029e9	−	1.57965e9i	1.56092	−	0.307434i
$596$	1.63058e10			3.15486
$597$	3.23437e9	−	8.66647e8i	0.622128	−	0.166699i
$598$	−1.20147e9	+	4.48396e9i	−0.229752	+	0.857447i
$599$	8.15757e9	−	4.70978e9i	1.55084	−	0.895378i	0.552767	−	0.833336i	$-0.313572\pi$
$599$	8.15757e9	−	4.70978e9i	1.55084	−	0.895378i	0.998074	−	0.0620420i	$-0.0197613\pi$
$600$	−1.19593e10	+	1.37857e10i	−2.26035	+	2.60556i
$601$			1.84107e8i			0.0345946i	0.999850	+	0.0172973i	$0.00550618\pi$
$601$			1.84107e8i			0.0345946i	−0.999850	+	0.0172973i	$0.994494\pi$
$602$	5.35007e9	+	8.69194e9i	0.999475	+	1.62379i
$603$	−1.78725e9	+	1.78725e9i	−0.331951	+	0.331951i
$604$	−1.06273e10	−	6.13566e9i	−1.96242	−	1.13301i
$605$	−4.80090e9	+	2.19083e9i	−0.881411	+	0.402221i
$606$	4.69441e9	+	8.13096e9i	0.856893	+	1.48418i
$607$	1.12783e9	+	4.20913e9i	0.204684	+	0.763893i	0.989546	+	0.144221i	$0.0460676\pi$
$607$	1.12783e9	+	4.20913e9i	0.204684	+	0.763893i	−0.784861	+	0.619672i	$0.787266\pi$
$608$	1.37163e8	+	1.37163e8i	0.0247500	+	0.0247500i
$609$	−1.36382e9	+	1.44286e9i	−0.244678	+	0.258859i
$610$	1.13668e10	+	1.37748e10i	2.02760	+	2.45714i
$611$	2.44592e8	−	4.23646e8i	0.0433809	−	0.0751379i
$612$	−1.82492e10	−	4.88986e9i	−3.21821	−	0.862316i
$613$	−8.07390e9	−	2.16340e9i	−1.41570	−	0.379336i	−0.531745	−	0.846905i	$-0.678463\pi$
$613$	−8.07390e9	−	2.16340e9i	−1.41570	−	0.379336i	−0.883957	+	0.467568i	$0.845130\pi$
$614$	2.99270e9	−	5.18350e9i	0.521763	−	0.903721i
$615$	2.29148e9	+	2.77692e9i	0.397240	+	0.481394i
$616$	−1.40523e10	+	1.48667e10i	−2.42222	+	2.56261i
$617$	4.09682e9	+	4.09682e9i	0.702181	+	0.702181i	0.964878	−	0.262697i	$-0.0846120\pi$
$617$	4.09682e9	+	4.09682e9i	0.702181	+	0.702181i	−0.262697	+	0.964878i	$0.584612\pi$
$618$	−6.58464e9	−	2.45742e10i	−1.12221	−	4.18813i
$619$	−5.15266e9	−	8.92466e9i	−0.873200	−	1.51243i	−0.858668	−	0.512533i	$-0.828707\pi$
$619$	−5.15266e9	−	8.92466e9i	−0.873200	−	1.51243i	−0.0145325	−	0.999894i	$-0.504626\pi$
$620$	1.55823e9	−	7.11079e8i	0.262579	−	0.119825i
$621$	−1.21860e9	−	7.03561e8i	−0.204193	−	0.117891i
$622$	6.29852e9	−	6.29852e9i	1.04948	−	1.04948i
$623$	2.91959e9	+	4.74328e9i	0.483741	+	0.785906i
$624$		−	6.10568e9i		−	1.00598i
$625$	−4.80202e9	+	3.76743e9i	−0.786762	+	0.617256i
$626$	1.16966e10	−	6.75302e9i	1.90567	−	1.10024i
$627$	6.70882e7	−	2.50377e8i	0.0108695	−	0.0405655i
$628$	5.42646e9	−	1.45401e9i	0.874294	−	0.234266i
$629$	−4.16514e9			−0.667348
$630$	9.99134e9	−	1.96786e9i	1.59196	−	0.313547i
$631$	−1.09464e10			−1.73447			−0.867237	−	0.497896i	$-0.834106\pi$
$631$	−1.09464e10			−1.73447			−0.867237	+	0.497896i	$0.834106\pi$
$632$	−8.52292e9	+	2.28371e9i	−1.34301	+	0.359858i
$633$	−3.09203e9	+	1.15396e10i	−0.484541	+	1.80833i
$634$	1.11379e10	−	6.43049e9i	1.73577	−	1.00215i
$635$	2.33049e8	+	1.38833e9i	0.0361193	+	0.215171i
$636$			1.53698e10i			2.36901i
$637$	4.34827e8	−	2.08619e9i	0.0666544	−	0.319791i
$638$	−3.10009e9	+	3.10009e9i	−0.472608	+	0.472608i
$639$	−5.91438e9	−	3.41467e9i	−0.896719	−	0.517721i
$640$	7.31484e8	−	1.95947e9i	0.110300	−	0.295466i
$641$	−6.16921e9	−	1.06854e10i	−0.925181	−	1.60246i	−0.791271	−	0.611466i	$-0.790580\pi$
$641$	−6.16921e9	−	1.06854e10i	−0.925181	−	1.60246i	−0.133910	−	0.990993i	$-0.542753\pi$
$642$	−3.16906e9	−	1.18271e10i	−0.472670	−	1.76403i
$643$	3.39530e9	+	3.39530e9i	0.503663	+	0.503663i	0.912574	−	0.408911i	$-0.134091\pi$
$643$	3.39530e9	+	3.39530e9i	0.503663	+	0.503663i	−0.408911	+	0.912574i	$0.634091\pi$
$644$	−2.27811e10	+	6.79705e9i	−3.36105	+	1.00281i
$645$	9.26426e8	−	9.67263e9i	0.135941	−	1.41934i
$646$	−2.18151e8	+	3.77849e8i	−0.0318378	+	0.0551448i
$647$	9.62679e9	+	2.57949e9i	1.39739	+	0.374428i	0.877405	−	0.479750i	$-0.159273\pi$
$647$	9.62679e9	+	2.57949e9i	1.39739	+	0.374428i	0.519980	+	0.854178i	$0.325939\pi$
$648$	1.85380e10	+	4.96724e9i	2.67640	+	0.717138i
$649$	−4.37913e9	+	7.58487e9i	−0.628827	+	1.08916i
$650$	7.96867e8	−	4.12181e9i	0.113812	−	0.588696i
$651$	−1.14514e9	−	2.72532e8i	−0.162676	−	0.0387154i
$652$	−5.87656e8	−	5.87656e8i	−0.0830342	−	0.0830342i
$653$	3.14815e9	+	1.17491e10i	0.442445	+	1.65123i	0.722595	+	0.691272i	$0.242949\pi$
$653$	3.14815e9	+	1.17491e10i	0.442445	+	1.65123i	−0.280150	+	0.959956i	$0.590384\pi$
$654$	8.97719e9	+	1.55490e10i	1.25493	+	2.17360i
$655$	2.31021e9	+	5.06251e9i	0.321224	+	0.703917i
$656$	6.38827e9	+	3.68827e9i	0.883527	+	0.510104i
$657$	−7.96605e7	+	7.96605e7i	−0.0109588	+	0.0109588i
$658$	3.56127e9	−	1.00294e8i	0.487320	−	0.0137242i
$659$			2.38207e9i			0.324232i	0.986772	+	0.162116i	$0.0518319\pi$
$659$			2.38207e9i			0.324232i	−0.986772	+	0.162116i	$0.948168\pi$
$660$	3.32354e10	−	5.57900e9i	4.49984	−	0.755357i
$661$	−9.77057e8	+	5.64104e8i	−0.131587	+	0.0759721i	−0.564349	−	0.825537i	$-0.690873\pi$
$661$	−9.77057e8	+	5.64104e8i	−0.131587	+	0.0759721i	0.432761	+	0.901509i	$0.357539\pi$
$662$	2.36199e9	−	8.81507e9i	0.316428	−	1.18093i
$663$	5.17039e9	−	1.38540e9i	0.689011	−	0.184620i
$664$	−1.04539e9			−0.138576
$665$	1.11260e7	−	1.64991e8i	0.00146711	−	0.0217563i
$666$	−5.18876e9			−0.680618
$667$	−2.84407e9	+	7.62067e8i	−0.371108	+	0.0994380i
$668$	1.99619e8	−	7.44990e8i	0.0259111	−	0.0967014i
$669$	−8.92649e9	+	5.15371e9i	−1.15263	+	0.665470i
$670$	−4.40370e9	+	6.18037e9i	−0.565660	+	0.793876i
$671$		−	1.90582e10i		−	2.43530i
$672$	1.47600e10	−	9.08512e9i	1.87627	−	1.15488i
$673$	4.40583e9	−	4.40583e9i	0.557154	−	0.557154i	−0.371342	−	0.928496i	$-0.621102\pi$
$673$	4.40583e9	−	4.40583e9i	0.557154	−	0.557154i	0.928496	+	0.371342i	$0.121102\pi$
$674$	7.52142e9	+	4.34249e9i	0.946215	+	0.546298i
$675$	1.14431e9	+	5.56684e8i	0.143212	+	0.0696700i
$676$	−8.49893e9	−	1.47206e10i	−1.05816	−	1.83278i
$677$	5.16460e8	+	1.92745e9i	0.0639699	+	0.238739i	0.990507	−	0.137466i	$-0.0438956\pi$
$677$	5.16460e8	+	1.92745e9i	0.0639699	+	0.238739i	−0.926537	+	0.376205i	$0.877229\pi$
$678$	−1.35438e10	−	1.35438e10i	−1.66892	−	1.66892i
$679$	1.02572e9	+	3.43782e9i	0.125743	+	0.421443i
$680$	−3.26321e10	−	3.12544e9i	−3.97982	−	0.381179i
$681$	−2.47958e9	+	4.29477e9i	−0.300860	+	0.521104i
$682$	−2.51075e9	−	6.72754e8i	−0.303081	−	0.0812103i
$683$	6.07662e9	+	1.62823e9i	0.729776	+	0.195543i	0.604530	−	0.796583i	$-0.293361\pi$
$683$	6.07662e9	+	1.62823e9i	0.729776	+	0.195543i	0.125247	+	0.992126i	$0.460028\pi$
$684$	−1.91101e8	+	3.30996e8i	−0.0228332	+	0.0395482i
$685$	−9.72586e9	+	8.02566e9i	−1.15614	+	0.954033i
$686$	1.45989e10	−	5.26729e9i	1.72657	−	0.622950i
$687$	−4.12309e9	−	4.12309e9i	−0.485148	−	0.485148i
$688$	−5.15273e9	−	1.92303e10i	−0.603223	−	2.25126i
$689$	−1.02160e9	−	1.76946e9i	−0.118991	−	0.206098i
$690$	3.01538e10	+	1.12566e10i	3.49438	+	1.30448i
$691$	6.97749e9	+	4.02846e9i	0.804500	+	0.464478i	0.845042	−	0.534699i	$-0.179575\pi$
$691$	6.97749e9	+	4.02846e9i	0.804500	+	0.464478i	−0.0405420	+	0.999178i	$0.512908\pi$
$692$	−1.00276e10	+	1.00276e10i	−1.15034	+	1.15034i
$693$	−9.56034e9	−	5.16642e9i	−1.09121	−	0.589689i
$694$		−	1.58315e10i		−	1.79789i
$695$	1.20437e10	+	8.58148e9i	1.36086	+	0.969651i
$696$	6.89530e9	−	3.98100e9i	0.775213	−	0.447569i
$697$	−1.67376e9	+	6.24657e9i	−0.187232	+	0.698758i
$698$	−6.56422e9	+	1.75888e9i	−0.730616	+	0.195768i
$699$	7.06007e9			0.781878
$700$	2.01155e10	−	7.58946e9i	2.21660	−	0.836311i
$701$	8.70961e9			0.954961			0.477480	−	0.878642i	$-0.341550\pi$
$701$	8.70961e9			0.954961			0.477480	+	0.878642i	$0.341550\pi$
$702$	−8.45452e8	+	2.26538e8i	−0.0922379	+	0.0247151i
$703$	−2.18081e7	+	8.13889e7i	−0.00236741	+	0.00883530i
$704$	7.90494e9	−	4.56392e9i	0.853875	−	0.492985i
$705$	−2.76229e9	−	1.96821e9i	−0.296898	−	0.211549i
$706$		−	5.06085e9i		−	0.541261i
$707$	−1.79940e8	−	6.38935e9i	−0.0191497	−	0.679969i
$708$	1.94617e10	−	1.94617e10i	2.06094	−	2.06094i
$709$	1.48739e9	+	8.58746e8i	0.156734	+	0.0904905i	0.576316	−	0.817227i	$-0.304490\pi$
$709$	1.48739e9	+	8.58746e8i	0.156734	+	0.0904905i	−0.419582	+	0.907718i	$0.637823\pi$
$710$	−1.92097e10	−	7.17113e9i	−2.01426	−	0.751940i
$711$	−2.34361e9	−	4.05924e9i	−0.244535	−	0.423547i
$712$	−5.78108e9	−	2.15753e10i	−0.600246	−	2.24015i
$713$	−1.23439e9	−	1.23439e9i	−0.127538	−	0.127538i
$714$	2.83308e10	+	2.67788e10i	2.91283	+	2.75326i
$715$	−3.45543e9	+	2.85138e9i	−0.353534	+	0.291732i
$716$	−1.62357e10	+	2.81211e10i	−1.65301	+	2.86310i
$717$	1.57740e10	+	4.22664e9i	1.59818	+	0.428231i
$718$	−5.58643e9	−	1.49688e9i	−0.563247	−	0.150921i
$719$	−9.90591e8	+	1.71575e9i	−0.0993901	+	0.172149i	−0.911432	−	0.411450i	$-0.865023\pi$
$719$	−9.90591e8	+	1.71575e9i	−0.0993901	+	0.172149i	0.812042	+	0.583599i	$0.198356\pi$
$720$	−1.97728e10	−	1.89380e9i	−1.97426	−	0.189091i
$721$	−4.01006e9	+	1.68496e10i	−0.398453	+	1.67424i
$722$	−1.31195e10	−	1.31195e10i	−1.29729	−	1.29729i
$723$	−1.97925e8	−	7.38667e8i	−0.0194768	−	0.0726883i
$724$	2.35685e9	+	4.08218e9i	0.230806	+	0.399767i
$725$	2.51683e9	−	8.69464e8i	0.245285	−	0.0847362i
$726$	−2.17952e10	−	1.25834e10i	−2.11389	−	1.22045i
$727$	−3.52574e9	+	3.52574e9i	−0.340314	+	0.340314i	−0.856486	−	0.516171i	$-0.827357\pi$
$727$	−3.52574e9	+	3.52574e9i	−0.340314	+	0.340314i	0.516171	+	0.856486i	$0.327357\pi$
$728$	−4.06295e9	+	7.51839e9i	−0.390285	+	0.722213i
$729$			7.90844e9i			0.756040i
$730$	−1.96280e8	+	2.75469e8i	−0.0186744	+	0.0262085i
$731$	1.51153e10	−	8.72684e9i	1.43122	−	0.826316i
$732$	−1.55009e10	+	5.78501e10i	−1.46072	+	5.45149i
$733$	−1.69523e10	+	4.54235e9i	−1.58988	+	0.426007i	−0.941966	−	0.335708i	$-0.891025\pi$
$733$	−1.69523e10	+	4.54235e9i	−1.58988	+	0.426007i	−0.647913	+	0.761714i	$0.724358\pi$
$734$	−2.30310e10			−2.14970
$735$	−1.41113e10	−	4.38024e9i	−1.31088	−	0.406904i
$736$	2.57037e10			2.37642
$737$	7.82236e9	−	2.09599e9i	0.719783	−	0.192865i
$738$	−2.08511e9	+	7.78172e9i	−0.190955	+	0.712654i
$739$	4.62638e9	−	2.67104e9i	0.421683	−	0.243459i	−0.274114	−	0.961697i	$-0.588385\pi$
$739$	4.62638e9	−	2.67104e9i	0.421683	−	0.243459i	0.695797	+	0.718239i	$0.255051\pi$
$740$	−1.08037e10	+	1.81354e9i	−0.980079	+	0.164519i
$741$		−	1.08286e8i		−	0.00977705i
$742$	7.07447e9	−	1.30911e10i	0.635741	−	1.17642i
$743$	−9.56069e9	+	9.56069e9i	−0.855123	+	0.855123i	−0.990759	−	0.135636i	$-0.956692\pi$
$743$	−9.56069e9	+	9.56069e9i	−0.855123	+	0.855123i	0.135636	+	0.990759i	$0.456692\pi$
$744$	4.08813e9	+	2.36028e9i	0.363931	+	0.210116i
$745$	6.23948e9	+	1.36729e10i	0.552842	+	1.21148i
$746$	−3.80555e9	−	6.59140e9i	−0.335607	−	0.581288i
$747$	−1.43728e8	−	5.36402e8i	−0.0126160	−	0.0470834i
$748$	4.28035e10	+	4.28035e10i	3.73959	+	3.73959i
$749$	−1.92996e9	+	8.10941e9i	−0.167827	+	0.705185i
$750$	−2.79217e10	−	8.22467e9i	−2.41673	−	0.711876i
$751$	−1.98793e9	+	3.44320e9i	−0.171262	+	0.296635i	−0.938861	−	0.344295i	$-0.888118\pi$
$751$	−1.98793e9	+	3.44320e9i	−0.171262	+	0.296635i	0.767599	+	0.640930i	$0.221451\pi$
$752$	−6.71250e9	−	1.79861e9i	−0.575602	−	0.154232i
$753$	2.52396e9	+	6.76292e8i	0.215427	+	0.0577234i
$754$	−9.15758e8	+	1.58614e9i	−0.0778002	+	0.134754i
$755$	1.07838e9	−	1.12592e10i	0.0911922	−	0.952120i
$756$	−3.25758e9	−	3.07912e9i	−0.274201	−	0.259180i
$757$	−2.42740e9	−	2.42740e9i	−0.203378	−	0.203378i	0.598067	−	0.801446i	$-0.295936\pi$
$757$	−2.42740e9	−	2.42740e9i	−0.203378	−	0.203378i	−0.801446	+	0.598067i	$0.795936\pi$
$758$	−5.28065e9	−	1.97077e10i	−0.440398	−	1.64359i
$759$	−1.71737e10	−	2.97457e10i	−1.42567	−	2.46933i
$760$	−2.31930e8	+	6.21283e8i	−0.0191650	+	0.0513383i
$761$	−2.79081e9	−	1.61127e9i	−0.229553	−	0.132533i	0.380813	−	0.924652i	$-0.375644\pi$
$761$	−2.79081e9	−	1.61127e9i	−0.229553	−	0.132533i	−0.610366	+	0.792120i	$0.708978\pi$
$762$	−4.74724e9	+	4.74724e9i	−0.388686	+	0.388686i
$763$	−3.44103e8	−	1.22185e10i	−0.0280448	−	0.995820i
$764$			1.36009e9i			0.110342i
$765$	−2.88283e9	−	1.71737e10i	−0.232811	−	1.38691i
$766$	−7.69524e9	+	4.44285e9i	−0.618617	+	0.357158i
$767$	−9.46968e8	+	3.53413e9i	−0.0757795	+	0.282813i
$768$	2.13298e10	−	5.71531e9i	1.69912	−	0.455277i
$769$	9.13050e9			0.724023			0.362011	−	0.932174i	$-0.382090\pi$
$769$	9.13050e9			0.724023			0.362011	+	0.932174i	$0.382090\pi$
$770$	−3.08761e10	−	1.05459e10i	−2.43727	−	0.832461i
$771$	−1.55385e10			−1.22101
$772$	4.21582e10	−	1.12963e10i	3.29778	−	0.883637i
$773$	1.66780e9	−	6.22431e9i	0.129872	−	0.484689i	−0.870094	−	0.492885i	$-0.835942\pi$
$773$	1.66780e9	−	6.22431e9i	0.129872	−	0.484689i	0.999966	+	0.00819604i	$0.00260891\pi$
$774$	1.88301e10	−	1.08715e10i	1.45968	−	0.842748i
$775$	1.19253e9	+	1.03453e9i	0.0920263	+	0.0798338i
$776$		−	1.43872e10i		−	1.10525i
$777$	6.62340e9	+	3.57929e9i	0.506533	+	0.273731i
$778$	2.23936e10	−	2.23936e10i	1.70488	−	1.70488i
$779$	1.13298e8	+	6.54124e7i	0.00858696	+	0.00495768i
$780$	1.28079e10	−	5.84475e9i	0.966380	−	0.440996i
$781$	1.09406e10	+	1.89497e10i	0.821796	+	1.42339i
$782$	1.49633e10	+	5.58438e10i	1.11893	+	4.17592i
$783$	−3.92563e8	−	3.92563e8i	−0.0292242	−	0.0292242i
$784$	−3.02251e10	+	1.70378e9i	−2.24007	+	0.126272i
$785$	3.29569e9	+	3.99388e9i	0.243166	+	0.294680i
$786$	−1.32692e10	+	2.29828e10i	−0.974685	+	1.68820i
$787$	1.65213e10	+	4.42688e9i	1.20818	+	0.323732i	0.806049	−	0.591848i	$-0.201602\pi$
$787$	1.65213e10	+	4.42688e9i	1.20818	+	0.323732i	0.402135	+	0.915580i	$0.368268\pi$
$788$	−5.10583e10	−	1.36810e10i	−3.71727	−	0.996040i
$789$	1.56359e10	−	2.70822e10i	1.13332	−	1.96297i
$790$	−8.95702e9	−	1.08545e10i	−0.646352	−	0.783279i
$791$	3.72820e9	+	1.24955e10i	0.267844	+	0.897711i
$792$	3.08154e10	+	3.08154e10i	2.20409	+	2.20409i
$793$	−2.06063e9	−	7.69036e9i	−0.146738	−	0.547634i
$794$	2.50184e10	+	4.33331e10i	1.77373	+	3.07219i
$795$	−1.28880e10	+	5.88130e9i	−0.909708	+	0.415134i
$796$	1.36998e10	+	7.90957e9i	0.962759	+	0.555849i
$797$	8.82401e9	−	8.82401e9i	0.617393	−	0.617393i	−0.327469	−	0.944862i	$-0.606196\pi$
$797$	8.82401e9	−	8.82401e9i	0.617393	−	0.617393i	0.944862	+	0.327469i	$0.106196\pi$
$798$	6.71607e8	−	4.13388e8i	0.0467848	−	0.0287970i
$799$		−	6.09237e9i		−	0.422545i
$800$	−2.31870e10	+	1.64499e9i	−1.60114	+	0.113592i
$801$	1.02758e10	−	5.93271e9i	0.706480	−	0.407886i
$802$	1.12418e10	−	4.19550e10i	0.769531	−	2.87193i
$803$	3.48655e8	−	9.34218e7i	0.0237625	−	0.00636713i
$804$	−2.54491e10			−1.72694
$805$	−1.44168e10	−	1.65018e10i	−0.974056	−	1.11492i
$806$	−1.08588e9			−0.0730482
$807$	−2.51660e10	+	6.74322e9i	−1.68561	+	0.451658i
$808$	−6.63435e9	+	2.47597e10i	−0.442445	+	1.65123i
$809$	2.36917e10	−	1.36784e10i	1.57317	−	0.908270i	0.577393	−	0.816466i	$-0.304070\pi$
$809$	2.36917e10	−	1.36784e10i	1.57317	−	0.908270i	0.995777	−	0.0918037i	$-0.0292632\pi$
$810$	5.06737e9	+	3.01875e10i	0.335031	+	1.99586i
$811$		−	1.38312e10i		−	0.910514i	−0.890360	−	0.455257i	$-0.849547\pi$
$811$		−	1.38312e10i		−	0.910514i	0.890360	−	0.455257i	$-0.150453\pi$
$812$	−9.37591e9	+	2.64050e8i	−0.614565	+	0.0173077i
$813$	2.25799e8	−	2.25799e8i	0.0147369	−	0.0147369i
$814$	1.43975e10	+	8.31242e9i	0.935627	+	0.540184i
$815$	2.67900e8	−	7.17638e8i	0.0173349	−	0.0464359i
$816$	−3.80205e10	−	6.58535e10i	−2.44964	−	4.24290i
$817$	−9.13851e7	−	3.41054e8i	−0.00586270	−	0.0218799i
$818$	3.13085e10	+	3.13085e10i	1.99998	+	1.99998i
$819$	−4.41640e9	−	1.05106e9i	−0.280915	−	0.0668551i
$820$	−1.62165e9	+	1.69314e10i	−0.102709	+	1.07237i
$821$	1.03374e10	−	1.79049e10i	0.651946	−	1.12920i	−0.330705	−	0.943734i	$-0.607286\pi$
$821$	1.03374e10	−	1.79049e10i	0.651946	−	1.12920i	0.982650	−	0.185469i	$-0.0593803\pi$
$822$	−5.80868e10	−	1.55643e10i	−3.64776	−	0.977413i
$823$	8.29368e9	+	2.22229e9i	0.518618	+	0.138963i	0.508627	−	0.860987i	$-0.330153\pi$
$823$	8.29368e9	+	2.22229e9i	0.518618	+	0.138963i	0.00999099	+	0.999950i	$0.496820\pi$
$824$	3.47294e10	−	6.01531e10i	2.16248	−	3.74553i
$825$	1.73958e10	+	2.57341e10i	1.07859	+	1.59559i
$826$	−2.55344e10	+	7.61852e9i	−1.57651	+	0.470371i
$827$	−1.44700e10	−	1.44700e10i	−0.889609	−	0.889609i	0.104876	−	0.994485i	$-0.466555\pi$
$827$	−1.44700e10	−	1.44700e10i	−0.889609	−	0.889609i	−0.994485	+	0.104876i	$0.966555\pi$
$828$	1.31079e10	+	4.89193e10i	0.802465	+	2.99484i
$829$	−2.85579e9	−	4.94637e9i	−0.174095	−	0.301541i	0.765753	−	0.643135i	$-0.222367\pi$
$829$	−2.85579e9	−	4.94637e9i	−0.174095	−	0.301541i	−0.939848	+	0.341594i	$0.889033\pi$
$830$	−6.92194e8	−	1.51684e9i	−0.0420198	−	0.0920805i
$831$	1.59799e10	+	9.22599e9i	0.965984	+	0.557711i
$832$	2.69634e9	−	2.69634e9i	0.162309	−	0.162309i
$833$	−8.30098e9	−	2.52085e10i	−0.497590	−	1.51109i
$834$			7.05255e10i			4.20984i
$835$	7.01083e8	−	1.17686e8i	0.0416742	−	0.00699555i
$836$	1.06052e9	−	6.12289e8i	0.0627762	−	0.0362439i
$837$	8.51907e7	−	3.17936e8i	0.00502172	−	0.0187413i
$838$	1.91293e10	−	5.12569e9i	1.12291	−	0.300883i
$839$	−2.23562e10			−1.30686			−0.653432	−	0.756985i	$-0.726671\pi$
$839$	−2.23562e10			−1.30686			−0.653432	+	0.756985i	$0.726671\pi$
$840$	4.92057e10	+	3.30123e10i	2.86443	+	1.92176i
$841$	1.60882e10			0.932655
$842$	−2.22333e10	+	5.95739e9i	−1.28354	+	0.343925i
$843$	−3.15529e9	+	1.17757e10i	−0.181402	+	0.677003i
$844$	−4.88781e10	+	2.82198e10i	−2.79844	+	1.61568i
$845$	9.09153e9	−	1.27595e10i	0.518368	−	0.727505i
$846$		−	7.58962e9i		−	0.430947i
$847$	8.98110e9	+	1.45911e10i	0.507853	+	0.825078i
$848$	−2.05241e10	+	2.05241e10i	−1.15579	+	1.15579i
$849$	−2.51984e10	−	1.45483e10i	−1.41318	−	0.815897i
$850$	−1.70721e10	−	4.94183e10i	−0.953499	−	2.76008i
$851$	5.58258e9	+	9.66932e9i	0.310514	+	0.537827i
$852$	−1.77970e10	−	6.64195e10i	−0.985846	−	3.67923i
$853$	7.33839e9	+	7.33839e9i	0.404836	+	0.404836i	0.879933	−	0.475097i	$-0.157587\pi$
$853$	7.33839e9	+	7.33839e9i	0.404836	+	0.404836i	−0.475097	+	0.879933i	$0.657587\pi$
$854$	3.98303e10	−	4.21388e10i	2.18832	−	2.31515i
$855$	−3.50676e8	−	3.35871e7i	−0.0191878	−	0.00183777i
$856$	1.67146e10	−	2.89505e10i	0.910831	−	1.57761i
$857$	−3.35796e10	−	8.99762e9i	−1.82239	−	0.488309i	−0.825314	−	0.564673i	$-0.809002\pi$
$857$	−3.35796e10	−	8.99762e9i	−1.82239	−	0.488309i	−0.997080	+	0.0763643i	$0.975669\pi$
$858$	−2.06372e10	−	5.52973e9i	−1.11544	−	0.298881i
$859$	−9.97433e9	+	1.72760e10i	−0.536918	+	0.929969i	0.462150	+	0.886802i	$0.347078\pi$
$859$	−9.97433e9	+	1.72760e10i	−0.536918	+	0.929969i	−0.999068	+	0.0431670i	$0.986255\pi$
$860$	3.54070e10	−	2.92174e10i	1.89821	−	1.56638i
$861$	8.02958e9	−	8.49496e9i	0.428728	−	0.453576i
$862$	3.18866e10	+	3.18866e10i	1.69564	+	1.69564i
$863$	6.95209e9	+	2.59456e10i	0.368195	+	1.37412i	0.863038	+	0.505139i	$0.168559\pi$
$863$	6.95209e9	+	2.59456e10i	0.368195	+	1.37412i	−0.494843	+	0.868982i	$0.664774\pi$
$864$	2.42323e9	+	4.19715e9i	0.127819	+	0.221389i
$865$	−1.22456e10	−	4.57136e9i	−0.643313	−	0.240154i
$866$	−1.46497e10	−	8.45803e9i	−0.766509	−	0.442544i
$867$	2.85141e10	−	2.85141e10i	1.48591	−	1.48591i
$868$	−2.91500e9	−	4.73583e9i	−0.151293	−	0.245797i
$869$			1.50179e10i			0.776318i
$870$	1.03421e10	+	7.36903e9i	0.532464	+	0.379396i
$871$	2.92986e9	−	1.69155e9i	0.150239	−	0.0867405i
$872$	−1.26870e10	+	4.73485e10i	−0.647964	+	2.41823i
$873$	7.38225e9	−	1.97807e9i	0.375525	−	0.100622i
$874$	1.16956e9			0.0592562
$875$	1.40613e10	+	1.39634e10i	0.709573	+	0.704632i
$876$	−1.13431e9			−0.0570120
$877$	−2.16534e10	+	5.80200e9i	−1.08399	+	0.290455i	−0.756231	−	0.654305i	$-0.772961\pi$
$877$	−2.16534e10	+	5.80200e9i	−1.08399	+	0.290455i	−0.327763	+	0.944760i	$0.606295\pi$
$878$	6.34181e9	−	2.36679e10i	0.316215	−	1.18013i
$879$	1.91645e10	−	1.10646e10i	0.951781	−	0.549511i
$880$	5.18309e10	+	3.69311e10i	2.56389	+	1.82685i
$881$			2.01372e10i			0.992162i	0.868276	+	0.496081i	$0.165228\pi$
$881$			2.01372e10i			0.992162i	−0.868276	+	0.496081i	$0.834772\pi$
$882$	−1.03410e10	−	3.14037e10i	−0.507485	−	1.54114i
$883$	−2.53893e9	+	2.53893e9i	−0.124105	+	0.124105i	−0.766431	−	0.642326i	$-0.777969\pi$
$883$	−2.53893e9	+	2.53893e9i	−0.124105	+	0.124105i	0.642326	+	0.766431i	$0.277969\pi$
$884$	2.19001e10	+	1.26440e10i	1.06626	+	0.615607i
$885$	2.37664e10	+	8.87217e9i	1.15256	+	0.430258i
$886$	2.75235e10	+	4.76721e10i	1.32949	+	2.30275i
$887$	4.52245e8	+	1.68780e9i	0.0217591	+	0.0812061i	0.975952	−	0.217987i	$-0.0699491\pi$
$887$	4.52245e8	+	1.68780e9i	0.0217591	+	0.0812061i	−0.954193	+	0.299193i	$0.903282\pi$
$888$	−2.13489e10	−	2.13489e10i	−1.02313	−	1.02313i
$889$	4.37982e9	−	1.30678e9i	0.209074	−	0.0623800i
$890$	2.74777e10	−	2.26742e10i	1.30652	−	1.07812i
$891$	1.63325e10	−	2.82887e10i	0.773537	−	1.33981i
$892$	−4.70360e10	−	1.26033e10i	−2.21898	−	0.594574i
$893$	−1.19048e8	−	3.18988e7i	−0.00559425	−	0.00149897i
$894$	−3.58376e10	+	6.20725e10i	−1.67748	+	2.90548i
$895$	−2.97931e10	−	2.85353e9i	−1.38911	−	0.133046i
$896$	−6.60621e9	−	1.57222e9i	−0.306814	−	0.0730188i
$897$	−1.01461e10	−	1.01461e10i	−0.469383	−	0.469383i
$898$	4.76146e9	+	1.77700e10i	0.219418	+	0.818881i
$899$	−3.44374e8	−	5.96474e8i	−0.0158078	−	0.0273799i
$900$	−1.49552e10	−	4.32905e10i	−0.683821	−	1.97945i
$901$	−2.20371e10	−	1.27231e10i	−1.00373	−	0.579505i
$902$	1.82520e10	−	1.82520e10i	0.828110	−	0.828110i
$903$	−3.15358e10	+	8.88127e8i	−1.42527	+	0.0401391i
$904$		−	5.22933e10i		−	2.35427i
$905$	−2.52118e9	+	3.53836e9i	−0.113067	+	0.158683i
$906$	4.67142e10	−	2.69705e10i	2.08690	−	1.20487i
$907$	5.85814e9	−	2.18629e10i	0.260696	−	0.972931i	−0.704136	−	0.710065i	$-0.748666\pi$
$907$	5.85814e9	−	2.18629e10i	0.260696	−	0.972931i	0.964832	−	0.262866i	$-0.0846677\pi$
$908$	−2.26302e10	+	6.06376e9i	−1.00320	+	0.268807i
$909$	−1.36167e10			−0.601311
$910$	−1.35994e10	−	9.17055e8i	−0.598238	−	0.0403414i
$911$	4.69726e9			0.205840			0.102920	−	0.994690i	$-0.467181\pi$
$911$	4.69726e9			0.205840			0.102920	+	0.994690i	$0.467181\pi$
$912$	−1.48588e9	+	3.98140e8i	−0.0648637	+	0.0173802i
$913$	−4.60508e8	+	1.71864e9i	−0.0200258	+	0.0747372i
$914$	−6.55991e9	+	3.78737e9i	−0.284175	+	0.164069i
$915$	−5.44406e10	+	9.13857e9i	−2.34936	+	0.394371i
$916$		−	2.75470e10i		−	1.18424i
$917$	1.53862e10	−	9.47051e9i	0.658928	−	0.405584i
$918$	−7.70804e9	+	7.70804e9i	−0.328848	+	0.328848i
$919$	5.31859e9	+	3.07069e9i	0.226044	+	0.130506i	0.608746	−	0.793366i	$-0.291673\pi$
$919$	5.31859e9	+	3.07069e9i	0.226044	+	0.130506i	−0.382702	+	0.923872i	$0.625006\pi$
$920$	3.64815e10	+	7.99440e10i	1.54460	+	3.38477i
$921$	9.25040e9	+	1.60222e10i	0.390168	+	0.675791i
$922$	−3.01422e9	−	1.12492e10i	−0.126653	−	0.472677i
$923$	6.46368e9	+	6.46368e9i	0.270566	+	0.270566i
$924$	−3.12831e10	−	1.04849e11i	−1.30454	−	4.37233i
$925$	−5.65479e9	−	8.36528e9i	−0.234920	−	0.347524i
$926$	−1.71071e10	+	2.96304e10i	−0.708007	+	1.22630i
$927$	3.56403e10	+	9.54979e9i	1.46948	+	0.393745i
$928$	9.79564e9	+	2.62473e9i	0.402360	+	0.107812i
$929$	1.19342e10	−	2.06706e10i	0.488356	−	0.845857i	−0.511554	−	0.859251i	$-0.670930\pi$
$929$	1.19342e10	−	2.06706e10i	0.488356	−	0.845857i	0.999910	+	0.0133936i	$0.00426344\pi$
$930$	−7.17826e8	+	7.49468e9i	−0.0292637	+	0.305536i
$931$	−5.36050e8	+	3.02170e7i	−0.0217712	+	0.00122724i
$932$	2.35847e10	+	2.35847e10i	0.954278	+	0.954278i
$933$	7.12603e9	+	2.65947e10i	0.287251	+	1.07204i
$934$	8.78093e9	+	1.52090e10i	0.352636	+	0.610783i
$935$	−1.95132e10	+	5.22711e10i	−0.780706	+	2.09132i
$936$	1.57665e10	+	9.10280e9i	0.628449	+	0.362835i
$937$	−7.82268e9	+	7.82268e9i	−0.310647	+	0.310647i	−0.845160	−	0.534513i	$-0.820495\pi$
$937$	−7.82268e9	+	7.82268e9i	−0.310647	+	0.310647i	0.534513	+	0.845160i	$0.320495\pi$
$938$	2.16762e10	+	1.17138e10i	0.857577	+	0.463436i
$939$			4.17471e10i			1.64549i
$940$	−2.65268e9	−	1.58026e10i	−0.104169	−	0.620557i
$941$	2.53176e9	−	1.46171e9i	0.0990510	−	0.0571871i	−0.449656	−	0.893202i	$-0.648454\pi$
$941$	2.53176e9	−	1.46171e9i	0.0990510	−	0.0571871i	0.548707	+	0.836015i	$0.315120\pi$
$942$	−6.39140e9	+	2.38530e10i	−0.249125	+	0.929748i
$943$	1.67447e10	−	4.48673e9i	0.650260	−	0.174237i
$944$	5.19766e10			2.01097
$945$	1.33542e9	−	3.90983e9i	0.0514761	−	0.150711i
$946$	−6.96651e10			−2.67545
$947$	1.60318e10	−	4.29571e9i	0.613420	−	0.164365i	0.0612852	−	0.998120i	$-0.480480\pi$
$947$	1.60318e10	−	4.29571e9i	0.613420	−	0.164365i	0.552135	+	0.833755i	$0.313813\pi$
$948$	1.22147e10	−	4.55860e10i	0.465644	−	1.73781i
$949$	1.30588e8	−	7.53952e7i	0.00495990	−	0.00286360i
$950$	−1.05505e9	+	7.48497e7i	−0.0399244	+	0.00283242i
$951$			3.97532e10i			1.49879i
$952$	2.99623e9	+	1.06391e11i	0.112550	+	3.99645i
$953$	−1.90214e10	+	1.90214e10i	−0.711896	+	0.711896i	−0.966932	−	0.255035i	$-0.917913\pi$
$953$	−1.90214e10	+	1.90214e10i	−0.711896	+	0.711896i	0.255035	+	0.966932i	$0.417913\pi$
$954$	−2.74529e10	−	1.58499e10i	−1.02369	−	0.591029i
$955$	−1.14048e9	+	5.20444e8i	−0.0423717	+	0.0193358i
$956$	3.85750e10	+	6.68138e10i	1.42792	+	2.47323i
$957$	−3.50738e9	−	1.30897e10i	−0.129357	−	0.482768i
$958$	−5.05533e10	−	5.05533e10i	−1.85768	−	1.85768i
$959$	2.97527e10	+	2.81228e10i	1.08933	+	1.02966i
$960$	−1.68276e10	−	2.03924e10i	−0.613863	−	0.743908i
$961$	−1.35521e10	+	2.34730e10i	−0.492579	+	0.853172i
$962$	6.70846e9	+	1.79753e9i	0.242946	+	0.0650972i
$963$	1.71530e10	+	4.59613e9i	0.618939	+	0.165844i
$964$	1.80639e9	−	3.12876e9i	0.0649444	−	0.112487i
$965$	2.56043e10	+	3.10285e10i	0.917206	+	1.11151i
$966$	2.41945e10	−	1.01662e11i	0.863568	−	3.62858i
$967$	−1.95043e9	−	1.95043e9i	−0.0693645	−	0.0693645i	0.671573	−	0.740938i	$-0.265619\pi$
$967$	−1.95043e9	−	1.95043e9i	−0.0693645	−	0.0693645i	−0.740938	+	0.671573i	$0.765619\pi$
$968$	−1.77835e10	−	6.63689e10i	−0.630164	−	2.35180i
$969$	−6.74303e8	−	1.16793e9i	−0.0238080	−	0.0412366i
$970$	2.08756e10	−	9.52634e9i	0.734410	−	0.335139i
$971$	−1.15930e10	−	6.69324e9i	−0.406377	−	0.234622i	0.282855	−	0.959163i	$-0.408719\pi$
$971$	−1.15930e10	−	6.69324e9i	−0.406377	−	0.234622i	−0.689232	+	0.724541i	$0.742052\pi$
$972$	−6.49464e10	+	6.49464e10i	−2.26842	+	2.26842i
$973$	2.28267e10	−	4.22404e10i	0.794418	−	1.47005i
$974$		−	9.07292e10i		−	3.14623i
$975$	9.80202e9	+	8.50335e9i	0.338688	+	0.293815i
$976$	−9.79495e10	+	5.65511e10i	−3.37231	+	1.94700i
$977$	−4.81559e9	+	1.79720e10i	−0.165203	+	0.616546i	0.832811	+	0.553557i	$0.186730\pi$
$977$	−4.81559e9	+	1.79720e10i	−0.165203	+	0.616546i	−0.998014	+	0.0629891i	$0.979937\pi$
$978$	3.52866e9	−	9.45501e8i	0.120621	−	0.0323203i
$979$	−3.80169e10			−1.29490
$980$	−3.25074e10	−	6.17725e10i	−1.10329	−	2.09654i
$981$	−2.60395e10			−0.880624
$982$	9.81355e9	−	2.62953e9i	0.330701	−	0.0886112i
$983$	1.23573e10	−	4.61179e10i	0.414940	−	1.54858i	−0.370017	−	0.929025i	$-0.620648\pi$
$983$	1.23573e10	−	4.61179e10i	0.414940	−	1.54858i	0.784957	−	0.619551i	$-0.212685\pi$
$984$	−4.05967e10	+	2.34385e10i	−1.35834	+	0.784237i
$985$	−8.06568e9	−	4.80491e10i	−0.268914	−	1.60199i
$986$			2.28099e10i			0.757801i
$987$	−5.23545e9	+	9.68809e9i	−0.173318	+	0.320721i
$988$	3.61737e8	−	3.61737e8i	0.0119328	−	0.0119328i
$989$	−4.05185e10	−	2.33934e10i	−1.33188	−	0.768964i
$990$	−2.43087e10	+	6.51171e10i	−0.796231	+	2.13291i
$991$	−1.08033e10	−	1.87118e10i	−0.352613	−	0.610743i	0.634094	−	0.773256i	$-0.281373\pi$
$991$	−1.08033e10	−	1.87118e10i	−0.352613	−	0.610743i	−0.986706	+	0.162513i	$0.948040\pi$
$992$	1.55617e9	+	5.80770e9i	0.0506134	+	0.188892i
$993$	1.99464e10	+	1.99464e10i	0.646461	+	0.646461i
$994$	−1.54133e10	+	6.47643e10i	−0.497787	+	2.09162i
$995$	−1.39015e9	+	1.45143e10i	−0.0447386	+	0.467107i
$996$	2.79569e9	−	4.84228e9i	0.0896565	−	0.155290i
$997$	1.12788e10	+	3.02214e9i	0.360436	+	0.0965786i	0.434492	−	0.900675i	$-0.356928\pi$
$997$	1.12788e10	+	3.02214e9i	0.360436	+	0.0965786i	−0.0740563	+	0.997254i	$0.523594\pi$
$998$	−9.28660e9	−	2.48834e9i	−0.295733	−	0.0792414i
$999$	−1.05260e9	+	1.82315e9i	−0.0334029	+	0.0578555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.8.k.a.12.2	yes	104
5.3	odd	4	inner	35.8.k.a.33.25	yes	104
7.3	odd	6	inner	35.8.k.a.17.25	yes	104
35.3	even	12	inner	35.8.k.a.3.2	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.8.k.a.3.2	✓	104	35.3	even	12	inner
35.8.k.a.12.2	yes	104	1.1	even	1	trivial
35.8.k.a.17.25	yes	104	7.3	odd	6	inner
35.8.k.a.33.25	yes	104	5.3	odd	4	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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	35.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-20.0589 + 5.37477i) q^{2} +(16.6134 - 62.0019i) q^{3} +(262.620 - 151.624i) q^{4} +(227.634 + 162.196i) q^{5} +1332.98i q^{6} +(431.442 - 798.374i) q^{7} +(-2573.37 + 2573.37i) q^{8} +(-1674.24 - 966.621i) q^{9} +O(q^{10})\)	\(q+(-20.0589 + 5.37477i) q^{2} +(16.6134 - 62.0019i) q^{3} +(262.620 - 151.624i) q^{4} +(227.634 + 162.196i) q^{5} +1332.98i q^{6} +(431.442 - 798.374i) q^{7} +(-2573.37 + 2573.37i) q^{8} +(-1674.24 - 966.621i) q^{9} +(-5437.86 - 2030.00i) q^{10} +(3097.07 + 5364.28i) q^{11} +(-5037.97 - 18802.0i) q^{12} +(1829.73 + 1829.73i) q^{13} +(-4363.18 + 18333.4i) q^{14} +(13838.2 - 11419.1i) q^{15} +(18379.8 - 31834.7i) q^{16} +(31128.6 + 8340.89i) q^{17} +(38778.7 + 10390.7i) q^{18} +(325.970 - 564.597i) q^{19} +(84374.3 + 8081.20i) q^{20} +(-42333.0 - 40013.9i) q^{21} +(-90955.5 - 90955.5i) q^{22} +(-22358.8 - 83444.1i) q^{23} +(116801. + 202306. i) q^{24} +(25509.8 + 73842.8i) q^{25} +(-46536.8 - 26868.0i) q^{26} +(11517.7 - 11517.7i) q^{27} +(-7747.13 - 275086. i) q^{28} -34083.5i q^{29} +(-216205. + 303433. i) q^{30} +(17500.4 - 10103.8i) q^{31} +(-77008.8 + 287401. i) q^{32} +(384048. - 102905. i) q^{33} -669236. q^{34} +(227704. - 111759. i) q^{35} -586252. q^{36} +(-124841. + 33451.0i) q^{37} +(-3504.03 + 13077.2i) q^{38} +(143845. - 83048.9i) q^{39} +(-1.00318e6 + 168396. i) q^{40} +200670. i q^{41} +(1.06422e6 + 575105. i) q^{42} +(382962. - 382962. i) q^{43} +(1.62671e6 + 939179. i) q^{44} +(-224332. - 491591. i) q^{45} +(896986. + 1.55362e6i) q^{46} +(-48929.0 - 182606. i) q^{47} +(-1.66846e6 - 1.66846e6i) q^{48} +(-451259. - 688904. i) q^{49} +(-908587. - 1.34410e6i) q^{50} +(1.03430e6 - 1.79146e6i) q^{51} +(757956. + 203094. i) q^{52} +(-762696. - 204364. i) q^{53} +(-169127. + 292937. i) q^{54} +(-165066. + 1.72343e6i) q^{55} +(944250. + 3.16477e6i) q^{56} +(-29590.6 - 29590.6i) q^{57} +(183191. + 683679. i) q^{58} +(706980. + 1.22452e6i) q^{59} +(1.90279e6 - 5.09711e6i) q^{60} +(-2.66460e6 - 1.53841e6i) q^{61} +(-296732. + 296732. i) q^{62} +(-1.49406e6 + 919626. i) q^{63} -1.47363e6i q^{64} +(119734. + 713285. i) q^{65} +(-7.15049e6 + 4.12834e6i) q^{66} +(338384. - 1.26287e6i) q^{67} +(9.43969e6 - 2.52936e6i) q^{68} -5.54515e6 q^{69} +(-3.96682e6 + 3.46562e6i) q^{70} +3.53258e6 q^{71} +(6.79589e6 - 1.82095e6i) q^{72} +(15082.3 - 56287.9i) q^{73} +(2.32438e6 - 1.34198e6i) q^{74} +(5.00220e6 - 354879. i) q^{75} -197700. i q^{76} +(5.61890e6 - 158243. i) q^{77} +(-2.43900e6 + 2.43900e6i) q^{78} +(2.09971e6 + 1.21227e6i) q^{79} +(9.34734e6 - 4.26555e6i) q^{80} +(-2.63677e6 - 4.56702e6i) q^{81} +(-1.07855e6 - 4.02522e6i) q^{82} +(203116. + 203116. i) q^{83} +(-1.71846e7 - 4.08977e6i) q^{84} +(5.73308e6 + 6.94761e6i) q^{85} +(-5.62347e6 + 9.74014e6i) q^{86} +(-2.11325e6 - 566242. i) q^{87} +(-2.17741e7 - 5.83436e6i) q^{88} +(-3.06879e6 + 5.31529e6i) q^{89} +(7.14204e6 + 8.65505e6i) q^{90} +(2.25023e6 - 671387. i) q^{91} +(-1.85240e7 - 1.85240e7i) q^{92} +(-335717. - 1.25291e6i) q^{93} +(1.96293e6 + 3.39989e6i) q^{94} +(165778. - 75650.6i) q^{95} +(1.65400e7 + 9.54939e6i) q^{96} +(-2.79540e6 + 2.79540e6i) q^{97} +(1.27545e7 + 1.13933e7i) q^{98} -1.19748e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 2 q^{2} - 6 q^{3} - 1746 q^{7} - 2524 q^{8}+O(q^{10}) \) 104 * q - 2 * q^2 - 6 * q^3 - 1746 * q^7 - 2524 * q^8	\( 104 q - 2 q^{2} - 6 q^{3} - 1746 q^{7} - 2524 q^{8} - 1254 q^{10} + 8932 q^{11} + 762 q^{12} - 17372 q^{15} + 195652 q^{16} + 81660 q^{17} + 54484 q^{18} - 12132 q^{21} + 94520 q^{22} + 140314 q^{23} - 130652 q^{25} + 339924 q^{26} - 700486 q^{28} - 737132 q^{30} - 123336 q^{31} - 44406 q^{32} + 2042712 q^{33} + 1515352 q^{35} - 3108368 q^{36} - 218688 q^{37} - 1242624 q^{38} - 5761962 q^{40} + 1786598 q^{42} - 2298300 q^{43} + 4974504 q^{45} - 415740 q^{46} + 78144 q^{47} + 7621588 q^{50} - 1243672 q^{51} - 904152 q^{52} + 1874804 q^{53} + 7011076 q^{56} - 8000176 q^{57} + 12000550 q^{58} - 7170466 q^{60} - 15847296 q^{61} - 11024724 q^{63} - 10105824 q^{65} + 8994876 q^{66} - 742846 q^{67} + 39849504 q^{68} + 22127240 q^{70} + 8609784 q^{71} + 29505688 q^{72} - 4371720 q^{73} - 35629446 q^{75} - 10458188 q^{77} - 63694784 q^{78} - 2528844 q^{80} - 3862456 q^{81} + 66431478 q^{82} + 51119608 q^{85} - 43323624 q^{86} - 43958022 q^{87} + 14366540 q^{88} + 43669288 q^{91} - 70081332 q^{92} + 15954004 q^{93} - 17456752 q^{95} - 111927000 q^{96} - 58212822 q^{98}+O(q^{100}) \) 104 * q - 2 * q^2 - 6 * q^3 - 1746 * q^7 - 2524 * q^8 - 1254 * q^10 + 8932 * q^11 + 762 * q^12 - 17372 * q^15 + 195652 * q^16 + 81660 * q^17 + 54484 * q^18 - 12132 * q^21 + 94520 * q^22 + 140314 * q^23 - 130652 * q^25 + 339924 * q^26 - 700486 * q^28 - 737132 * q^30 - 123336 * q^31 - 44406 * q^32 + 2042712 * q^33 + 1515352 * q^35 - 3108368 * q^36 - 218688 * q^37 - 1242624 * q^38 - 5761962 * q^40 + 1786598 * q^42 - 2298300 * q^43 + 4974504 * q^45 - 415740 * q^46 + 78144 * q^47 + 7621588 * q^50 - 1243672 * q^51 - 904152 * q^52 + 1874804 * q^53 + 7011076 * q^56 - 8000176 * q^57 + 12000550 * q^58 - 7170466 * q^60 - 15847296 * q^61 - 11024724 * q^63 - 10105824 * q^65 + 8994876 * q^66 - 742846 * q^67 + 39849504 * q^68 + 22127240 * q^70 + 8609784 * q^71 + 29505688 * q^72 - 4371720 * q^73 - 35629446 * q^75 - 10458188 * q^77 - 63694784 * q^78 - 2528844 * q^80 - 3862456 * q^81 + 66431478 * q^82 + 51119608 * q^85 - 43323624 * q^86 - 43958022 * q^87 + 14366540 * q^88 + 43669288 * q^91 - 70081332 * q^92 + 15954004 * q^93 - 17456752 * q^95 - 111927000 * q^96 - 58212822 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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