LMFDB - Embedded newform 370.2.m.a.249.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(159,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("370.159");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.m (of order $6$, degree $2$, 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:	$2.95446487479$
Analytic rank:	$1$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			249.1
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	370.249
Dual form			370.2.m.a.159.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-2.18614 + 1.26217i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 1.65831i) q^{5} -2.52434i q^{6} +(-3.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(1.68614 - 2.92048i) q^{9} +(-0.686141 - 2.12819i) q^{10} +(2.18614 + 1.26217i) q^{12} +(0.186141 + 0.322405i) q^{13} -3.46410i q^{14} +(1.18614 - 5.51856i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.686141 - 1.18843i) q^{17} +(1.68614 + 2.92048i) q^{18} +(2.18614 + 0.469882i) q^{20} +(4.37228 - 7.57301i) q^{21} +2.74456 q^{23} +(-2.18614 + 1.26217i) q^{24} +(-0.500000 - 4.97494i) q^{25} -0.372281 q^{26} +0.939764i q^{27} +(3.00000 + 1.73205i) q^{28} -7.72049i q^{29} +(4.18614 + 3.78651i) q^{30} +11.0371i q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.686141 + 1.18843i) q^{34} +(1.62772 - 7.57301i) q^{35} -3.37228 q^{36} +(0.500000 - 6.06218i) q^{37} +(-0.813859 - 0.469882i) q^{39} +(-1.50000 + 1.65831i) q^{40} +(2.87228 + 4.97494i) q^{41} +(4.37228 + 7.57301i) q^{42} -9.11684 q^{43} +(2.31386 + 7.17687i) q^{45} +(-1.37228 + 2.37686i) q^{46} -5.04868i q^{47} -2.52434i q^{48} +(2.50000 - 4.33013i) q^{49} +(4.55842 + 2.05446i) q^{50} +3.46410i q^{51} +(0.186141 - 0.322405i) q^{52} +(0.813859 + 0.469882i) q^{53} +(-0.813859 - 0.469882i) q^{54} +(-3.00000 + 1.73205i) q^{56} +(6.68614 + 3.86025i) q^{58} +(-10.3723 - 5.98844i) q^{59} +(-5.37228 + 1.73205i) q^{60} +(2.05842 - 1.18843i) q^{61} +(-9.55842 - 5.51856i) q^{62} +11.6819i q^{63} +1.00000 q^{64} +(-0.813859 - 0.174928i) q^{65} +(-7.11684 + 4.10891i) q^{67} -1.37228 q^{68} +(-6.00000 + 3.46410i) q^{69} +(5.74456 + 5.19615i) q^{70} +(-1.37228 - 2.37686i) q^{71} +(1.68614 - 2.92048i) q^{72} +6.92820i q^{73} +(5.00000 + 3.46410i) q^{74} +(7.37228 + 10.2448i) q^{75} +(0.813859 - 0.469882i) q^{78} +(-7.11684 + 4.10891i) q^{79} +(-0.686141 - 2.12819i) q^{80} +(3.87228 + 6.70699i) q^{81} -5.74456 q^{82} +(-11.7446 - 6.78073i) q^{83} -8.74456 q^{84} +(0.941578 + 2.92048i) q^{85} +(4.55842 - 7.89542i) q^{86} +(9.74456 + 16.8781i) q^{87} +(-8.31386 - 4.80001i) q^{89} +(-7.37228 - 1.58457i) q^{90} +(-1.11684 - 0.644810i) q^{91} +(-1.37228 - 2.37686i) q^{92} +(-13.9307 - 24.1287i) q^{93} +(4.37228 + 2.52434i) q^{94} +(2.18614 + 1.26217i) q^{96} -12.1168 q^{97} +(2.50000 + 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 6 q^{5} - 12 q^{7} + 4 q^{8} + q^{9} + 3 q^{10} + 3 q^{12} - 5 q^{13} - q^{15} - 2 q^{16} - 3 q^{17} + q^{18} + 3 q^{20} + 6 q^{21} - 12 q^{23} - 3 q^{24} - 2 q^{25}+ \cdots + 10 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 - 6 * q^5 - 12 * q^7 + 4 * q^8 + q^9 + 3 * q^10 + 3 * q^12 - 5 * q^13 - q^15 - 2 * q^16 - 3 * q^17 + q^18 + 3 * q^20 + 6 * q^21 - 12 * q^23 - 3 * q^24 - 2 * q^25 + 10 * q^26 + 12 * q^28 + 11 * q^30 - 2 * q^32 - 3 * q^34 + 18 * q^35 - 2 * q^36 + 2 * q^37 - 9 * q^39 - 6 * q^40 + 6 * q^42 - 2 * q^43 + 15 * q^45 + 6 * q^46 + 10 * q^49 + q^50 - 5 * q^52 + 9 * q^53 - 9 * q^54 - 12 * q^56 + 21 * q^58 - 30 * q^59 - 10 * q^60 - 9 * q^61 - 21 * q^62 + 4 * q^64 - 9 * q^65 + 6 * q^67 + 6 * q^68 - 24 * q^69 + 6 * q^71 + q^72 + 20 * q^74 + 18 * q^75 + 9 * q^78 + 6 * q^79 + 3 * q^80 + 4 * q^81 - 24 * q^83 - 12 * q^84 + 21 * q^85 + q^86 + 16 * q^87 - 39 * q^89 - 18 * q^90 + 30 * q^91 + 6 * q^92 - 27 * q^93 + 6 * q^94 + 3 * q^96 - 14 * q^97 + 10 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−2.18614	+	1.26217i	−1.26217	+	0.728714i	−0.973494	−	0.228714i	$-0.926548\pi$
$3$	−2.18614	+	1.26217i	−1.26217	+	0.728714i	−0.288675	+	0.957427i	$0.593215\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.50000	+	1.65831i	−0.670820	+	0.741620i
$5$	−1.50000	+	1.65831i	−0.670820	+	0.741620i
$6$		−	2.52434i		−	1.03056i
$7$	−3.00000	+	1.73205i	−1.13389	+	0.654654i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−3.00000	+	1.73205i	−1.13389	+	0.654654i	−0.188982	+	0.981981i	$0.560519\pi$
$8$	1.00000			0.353553
$9$	1.68614	−	2.92048i	0.562047	−	0.973494i
$10$	−0.686141	−	2.12819i	−0.216977	−	0.672994i
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$	2.18614	+	1.26217i	0.631084	+	0.364357i
$13$	0.186141	+	0.322405i	0.0516261	+	0.0894191i	0.890684	−	0.454624i	$-0.150226\pi$
$13$	0.186141	+	0.322405i	0.0516261	+	0.0894191i	−0.839057	+	0.544043i	$0.816893\pi$
$14$		−	3.46410i		−	0.925820i
$15$	1.18614	−	5.51856i	0.306260	−	1.42489i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.686141	−	1.18843i	0.166414	−	0.288237i	−0.770743	−	0.637146i	$-0.780115\pi$
$17$	0.686141	−	1.18843i	0.166414	−	0.288237i	0.937156	+	0.348910i	$0.113448\pi$
$18$	1.68614	+	2.92048i	0.397427	+	0.688364i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$	2.18614	+	0.469882i	0.488836	+	0.105069i
$21$	4.37228	−	7.57301i	0.954110	−	1.65257i
$22$		0			0
$23$	2.74456			0.572281			0.286140	−	0.958188i	$-0.407628\pi$
$23$	2.74456			0.572281			0.286140	+	0.958188i	$0.407628\pi$
$24$	−2.18614	+	1.26217i	−0.446244	+	0.257639i
$25$	−0.500000	−	4.97494i	−0.100000	−	0.994987i
$26$	−0.372281			−0.0730104
$27$			0.939764i			0.180858i
$28$	3.00000	+	1.73205i	0.566947	+	0.327327i
$29$		−	7.72049i		−	1.43366i	−0.697248	−	0.716830i	$-0.745593\pi$
$29$		−	7.72049i		−	1.43366i	0.697248	−	0.716830i	$-0.254407\pi$
$30$	4.18614	+	3.78651i	0.764281	+	0.691318i
$31$			11.0371i			1.98232i	0.132656	+	0.991162i	$0.457650\pi$
$31$			11.0371i			1.98232i	−0.132656	+	0.991162i	$0.542350\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	0.686141	+	1.18843i	0.117672	+	0.203814i
$35$	1.62772	−	7.57301i	0.275135	−	1.28007i
$36$	−3.37228			−0.562047
$37$	0.500000	−	6.06218i	0.0821995	−	0.996616i
$37$	0.500000	−	6.06218i	0.0821995	−	0.996616i
$38$		0			0
$39$	−0.813859	−	0.469882i	−0.130322	−	0.0752413i
$40$	−1.50000	+	1.65831i	−0.237171	+	0.262202i
$41$	2.87228	+	4.97494i	0.448575	+	0.776955i	0.998294	−	0.0583953i	$-0.0185984\pi$
$41$	2.87228	+	4.97494i	0.448575	+	0.776955i	−0.549719	+	0.835350i	$0.685265\pi$
$42$	4.37228	+	7.57301i	0.674658	+	1.16854i
$43$	−9.11684			−1.39031			−0.695153	−	0.718862i	$-0.744663\pi$
$43$	−9.11684			−1.39031			−0.695153	+	0.718862i	$0.744663\pi$
$44$		0			0
$45$	2.31386	+	7.17687i	0.344930	+	1.06986i
$46$	−1.37228	+	2.37686i	−0.202332	+	0.350449i
$47$		−	5.04868i		−	0.736425i	−0.929742	−	0.368213i	$-0.879970\pi$
$47$		−	5.04868i		−	0.736425i	0.929742	−	0.368213i	$-0.120030\pi$
$48$		−	2.52434i		−	0.364357i
$49$	2.50000	−	4.33013i	0.357143	−	0.618590i
$50$	4.55842	+	2.05446i	0.644658	+	0.290544i
$51$			3.46410i			0.485071i
$52$	0.186141	−	0.322405i	0.0258131	−	0.0447095i
$53$	0.813859	+	0.469882i	0.111792	+	0.0645432i	0.554854	−	0.831948i	$-0.312774\pi$
$53$	0.813859	+	0.469882i	0.111792	+	0.0645432i	−0.443061	+	0.896491i	$0.646108\pi$
$54$	−0.813859	−	0.469882i	−0.110752	−	0.0639428i
$55$		0			0
$56$	−3.00000	+	1.73205i	−0.400892	+	0.231455i
$57$		0			0
$58$	6.68614	+	3.86025i	0.877933	+	0.506875i
$59$	−10.3723	−	5.98844i	−1.35036	−	0.779628i	−0.362057	−	0.932156i	$-0.617925\pi$
$59$	−10.3723	−	5.98844i	−1.35036	−	0.779628i	−0.988299	+	0.152528i	$0.951259\pi$
$60$	−5.37228	+	1.73205i	−0.693559	+	0.223607i
$61$	2.05842	−	1.18843i	0.263554	−	0.152163i	−0.362401	−	0.932022i	$-0.618043\pi$
$61$	2.05842	−	1.18843i	0.263554	−	0.152163i	0.625955	+	0.779859i	$0.284709\pi$
$62$	−9.55842	−	5.51856i	−1.21392	−	0.700858i
$63$			11.6819i			1.47178i
$64$	1.00000			0.125000
$65$	−0.813859	−	0.174928i	−0.100947	−	0.0216972i
$66$		0			0
$67$	−7.11684	+	4.10891i	−0.869461	+	0.501983i	−0.867169	−	0.498014i	$-0.834063\pi$
$67$	−7.11684	+	4.10891i	−0.869461	+	0.501983i	−0.00229183	+	0.999997i	$0.500730\pi$
$68$	−1.37228			−0.166414
$69$	−6.00000	+	3.46410i	−0.722315	+	0.417029i
$70$	5.74456	+	5.19615i	0.686607	+	0.621059i
$71$	−1.37228	−	2.37686i	−0.162860	−	0.282082i	0.773033	−	0.634365i	$-0.218739\pi$
$71$	−1.37228	−	2.37686i	−0.162860	−	0.282082i	−0.935893	+	0.352284i	$0.885405\pi$
$72$	1.68614	−	2.92048i	0.198714	−	0.344182i
$73$			6.92820i			0.810885i	0.914121	+	0.405442i	$0.132883\pi$
$73$			6.92820i			0.810885i	−0.914121	+	0.405442i	$0.867117\pi$
$74$	5.00000	+	3.46410i	0.581238	+	0.402694i
$75$	7.37228	+	10.2448i	0.851278	+	1.18297i
$76$		0			0
$77$		0			0
$78$	0.813859	−	0.469882i	0.0921514	−	0.0532036i
$79$	−7.11684	+	4.10891i	−0.800708	+	0.462289i	−0.843718	−	0.536786i	$-0.819638\pi$
$79$	−7.11684	+	4.10891i	−0.800708	+	0.462289i	0.0430110	+	0.999075i	$0.486305\pi$
$80$	−0.686141	−	2.12819i	−0.0767129	−	0.237939i
$81$	3.87228	+	6.70699i	0.430253	+	0.745221i
$82$	−5.74456			−0.634381
$83$	−11.7446	−	6.78073i	−1.28913	−	0.744281i	−0.310634	−	0.950530i	$-0.600541\pi$
$83$	−11.7446	−	6.78073i	−1.28913	−	0.744281i	−0.978500	+	0.206248i	$0.933875\pi$
$84$	−8.74456			−0.954110
$85$	0.941578	+	2.92048i	0.102128	+	0.316771i
$86$	4.55842	−	7.89542i	0.491547	−	0.851385i
$87$	9.74456	+	16.8781i	1.04473	+	1.80952i
$88$		0			0
$89$	−8.31386	−	4.80001i	−0.881267	−	0.508800i	−0.0101913	−	0.999948i	$-0.503244\pi$
$89$	−8.31386	−	4.80001i	−0.881267	−	0.508800i	−0.871076	+	0.491148i	$0.836577\pi$
$90$	−7.37228	−	1.58457i	−0.777107	−	0.167029i
$91$	−1.11684	−	0.644810i	−0.117077	−	0.0675945i
$92$	−1.37228	−	2.37686i	−0.143070	−	0.247805i
$93$	−13.9307	−	24.1287i	−1.44455	−	2.50203i
$94$	4.37228	+	2.52434i	0.450966	+	0.260366i
$95$		0			0
$96$	2.18614	+	1.26217i	0.223122	+	0.128820i
$97$	−12.1168			−1.23028			−0.615140	−	0.788418i	$-0.710900\pi$
$97$	−12.1168			−1.23028			−0.615140	+	0.788418i	$0.710900\pi$
$98$	2.50000	+	4.33013i	0.252538	+	0.437409i
$99$		0			0
$100$	−4.05842	+	2.92048i	−0.405842	+	0.292048i
$101$	1.37228			0.136547			0.0682735	−	0.997667i	$-0.478251\pi$
$101$	1.37228			0.136547			0.0682735	+	0.997667i	$0.478251\pi$
$102$	−3.00000	−	1.73205i	−0.297044	−	0.171499i
$103$	15.4891			1.52619			0.763094	−	0.646287i	$-0.223679\pi$
$103$	15.4891			1.52619			0.763094	+	0.646287i	$0.223679\pi$
$104$	0.186141	+	0.322405i	0.0182526	+	0.0316144i
$105$	6.00000	+	18.6101i	0.585540	+	1.81616i
$106$	−0.813859	+	0.469882i	−0.0790490	+	0.0456390i
$107$	3.30298	−	1.90698i	0.319312	−	0.184355i	−0.331774	−	0.943359i	$-0.607647\pi$
$107$	3.30298	−	1.90698i	0.319312	−	0.184355i	0.651086	+	0.759004i	$0.274314\pi$
$108$	0.813859	−	0.469882i	0.0783137	−	0.0452144i
$109$	−2.05842	−	1.18843i	−0.197161	−	0.113831i	0.398170	−	0.917312i	$-0.369646\pi$
$109$	−2.05842	−	1.18843i	−0.197161	−	0.113831i	−0.595331	+	0.803481i	$0.702979\pi$
$110$		0			0
$111$	6.55842	+	13.8839i	0.622498	+	1.31780i
$112$		−	3.46410i		−	0.327327i
$113$	10.1168	−	17.5229i	0.951713	−	1.64841i	0.209995	−	0.977702i	$-0.432655\pi$
$113$	10.1168	−	17.5229i	0.951713	−	1.64841i	0.741718	−	0.670712i	$-0.234011\pi$
$114$		0			0
$115$	−4.11684	+	4.55134i	−0.383898	+	0.424415i
$116$	−6.68614	+	3.86025i	−0.620793	+	0.358415i
$117$	1.25544			0.116065
$118$	10.3723	−	5.98844i	0.954846	−	0.551281i
$119$			4.75372i			0.435773i
$120$	1.18614	−	5.51856i	0.108279	−	0.503773i
$121$	−11.0000			−1.00000
$122$			2.37686i			0.215191i
$123$	−12.5584	−	7.25061i	−1.13235	−	0.653765i
$124$	9.55842	−	5.51856i	0.858372	−	0.495581i
$125$	9.00000	+	6.63325i	0.804984	+	0.593296i
$126$	−10.1168	−	5.84096i	−0.901280	−	0.520354i
$127$	15.0000	+	8.66025i	1.33103	+	0.768473i	0.985458	−	0.169917i	$-0.0543501\pi$
$127$	15.0000	+	8.66025i	1.33103	+	0.768473i	0.345576	+	0.938391i	$0.387683\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	19.9307	−	11.5070i	1.75480	−	1.01313i
$130$	0.558422	−	0.617359i	0.0489768	−	0.0541459i
$131$	5.74456	+	3.31662i	0.501905	+	0.289775i	0.729500	−	0.683981i	$-0.239753\pi$
$131$	5.74456	+	3.31662i	0.501905	+	0.289775i	−0.227595	+	0.973756i	$0.573086\pi$
$132$		0			0
$133$		0			0
$134$		−	8.21782i		−	0.709912i
$135$	−1.55842	−	1.40965i	−0.134128	−	0.121323i
$136$	0.686141	−	1.18843i	0.0588361	−	0.101907i
$137$		−	2.67181i		−	0.228269i	−0.993465	−	0.114134i	$-0.963591\pi$
$137$		−	2.67181i		−	0.228269i	0.993465	−	0.114134i	$-0.0364094\pi$
$138$		−	6.92820i		−	0.589768i
$139$	9.37228	−	16.2333i	0.794947	−	1.37689i	−0.127927	−	0.991784i	$-0.540832\pi$
$139$	9.37228	−	16.2333i	0.794947	−	1.37689i	0.922873	−	0.385104i	$-0.125834\pi$
$140$	−7.37228	+	2.37686i	−0.623071	+	0.200881i
$141$	6.37228	+	11.0371i	0.536643	+	0.929493i
$142$	2.74456			0.230319
$143$		0			0
$144$	1.68614	+	2.92048i	0.140512	+	0.243373i
$145$	12.8030	+	11.5807i	1.06323	+	0.961728i
$146$	−6.00000	−	3.46410i	−0.496564	−	0.286691i
$147$			12.6217i			1.04102i
$148$	−5.50000	+	2.59808i	−0.452097	+	0.213561i
$149$	−10.6277			−0.870657			−0.435328	−	0.900272i	$-0.643368\pi$
$149$	−10.6277			−0.870657			−0.435328	+	0.900272i	$0.643368\pi$
$150$	−12.5584	+	1.26217i	−1.02539	+	0.103056i
$151$	−8.93070	−	15.4684i	−0.726770	−	1.25880i	−0.958241	−	0.285961i	$-0.907687\pi$
$151$	−8.93070	−	15.4684i	−0.726770	−	1.25880i	0.231471	−	0.972842i	$-0.425646\pi$
$152$		0			0
$153$	−2.31386	−	4.00772i	−0.187064	−	0.324005i
$154$		0			0
$155$	−18.3030	−	16.5557i	−1.47013	−	1.32978i
$156$			0.939764i			0.0752413i
$157$	5.61684	+	3.24289i	0.448273	+	0.258811i	0.707101	−	0.707113i	$-0.250003\pi$
$157$	5.61684	+	3.24289i	0.448273	+	0.258811i	−0.258828	+	0.965924i	$0.583336\pi$
$158$		−	8.21782i		−	0.653775i
$159$	−2.37228			−0.188134
$160$	2.18614	+	0.469882i	0.172830	+	0.0371474i
$161$	−8.23369	+	4.75372i	−0.648906	+	0.374646i
$162$	−7.74456			−0.608470
$163$	−8.55842	+	14.8236i	−0.670347	+	1.16108i	0.307458	+	0.951562i	$0.400522\pi$
$163$	−8.55842	+	14.8236i	−0.670347	+	1.16108i	−0.977806	+	0.209514i	$0.932812\pi$
$164$	2.87228	−	4.97494i	0.224287	−	0.388477i
$165$		0			0
$166$	11.7446	−	6.78073i	0.911555	−	0.526286i
$167$	−2.74456	−	4.75372i	−0.212381	−	0.367854i	0.740078	−	0.672521i	$-0.234788\pi$
$167$	−2.74456	−	4.75372i	−0.212381	−	0.367854i	−0.952459	+	0.304666i	$0.901455\pi$
$168$	4.37228	−	7.57301i	0.337329	−	0.584271i
$169$	6.43070	−	11.1383i	0.494669	−	0.856793i
$170$	−3.00000	−	0.644810i	−0.230089	−	0.0494547i
$171$		0			0
$172$	4.55842	+	7.89542i	0.347576	+	0.602020i
$173$	10.5475	+	6.08963i	0.801915	+	0.462986i	0.844140	−	0.536122i	$-0.180111\pi$
$173$	10.5475	+	6.08963i	0.801915	+	0.462986i	−0.0422252	+	0.999108i	$0.513445\pi$
$174$	−19.4891			−1.47747
$175$	10.1168	+	14.0588i	0.764762	+	1.06274i
$176$		0			0
$177$	30.2337			2.27250
$178$	8.31386	−	4.80001i	0.623150	−	0.359776i
$179$			20.1947i			1.50942i	0.656057	+	0.754711i	$0.272223\pi$
$179$			20.1947i			1.50942i	−0.656057	+	0.754711i	$0.727777\pi$
$180$	5.05842	−	5.59230i	0.377033	−	0.416825i
$181$	2.43070	+	4.21010i	0.180673	+	0.312934i	0.942110	−	0.335304i	$-0.108839\pi$
$181$	2.43070	+	4.21010i	0.180673	+	0.312934i	−0.761437	+	0.648239i	$0.775506\pi$
$182$	1.11684	−	0.644810i	0.0827860	−	0.0477965i
$183$	−3.00000	+	5.19615i	−0.221766	+	0.384111i
$184$	2.74456			0.202332
$185$	9.30298	+	9.92242i	0.683969	+	0.729511i
$186$	27.8614			2.04290
$187$		0			0
$188$	−4.37228	+	2.52434i	−0.318881	+	0.184106i
$189$	−1.62772	−	2.81929i	−0.118399	−	0.205073i
$190$		0			0
$191$		−	24.5986i		−	1.77989i	−0.456068	−	0.889945i	$-0.650743\pi$
$191$		−	24.5986i		−	1.77989i	0.456068	−	0.889945i	$-0.349257\pi$
$192$	−2.18614	+	1.26217i	−0.157771	+	0.0910892i
$193$	−6.62772			−0.477074			−0.238537	−	0.971133i	$-0.576668\pi$
$193$	−6.62772			−0.477074			−0.238537	+	0.971133i	$0.576668\pi$
$194$	6.05842	−	10.4935i	0.434969	−	0.753389i
$195$	2.00000	−	0.644810i	0.143223	−	0.0461758i
$196$	−5.00000			−0.357143
$197$	−6.12772	−	3.53784i	−0.436582	−	0.252061i	0.265565	−	0.964093i	$-0.414442\pi$
$197$	−6.12772	−	3.53784i	−0.436582	−	0.252061i	−0.702147	+	0.712032i	$0.747775\pi$
$198$		0			0
$199$			8.86263i			0.628255i	0.949381	+	0.314128i	$0.101712\pi$
$199$			8.86263i			0.628255i	−0.949381	+	0.314128i	$0.898288\pi$
$200$	−0.500000	−	4.97494i	−0.0353553	−	0.351781i
$201$	10.3723	−	17.9653i	0.731604	−	1.26718i
$202$	−0.686141	+	1.18843i	−0.0482767	+	0.0836177i
$203$	13.3723	+	23.1615i	0.938550	+	1.62562i
$204$	3.00000	−	1.73205i	0.210042	−	0.121268i
$205$	−12.5584	−	2.69927i	−0.877118	−	0.188525i
$206$	−7.74456	+	13.4140i	−0.539589	+	0.934596i
$207$	4.62772	−	8.01544i	0.321649	−	0.557112i
$208$	−0.372281			−0.0258131
$209$		0			0
$210$	−19.1168	−	4.10891i	−1.31919	−	0.283542i
$211$	−15.4891			−1.06632			−0.533158	−	0.846016i	$-0.678995\pi$
$211$	−15.4891			−1.06632			−0.533158	+	0.846016i	$0.678995\pi$
$212$		−	0.939764i		−	0.0645432i
$213$	6.00000	+	3.46410i	0.411113	+	0.237356i
$214$			3.81396i			0.260717i
$215$	13.6753	−	15.1186i	0.932645	−	1.03108i
$216$			0.939764i			0.0639428i
$217$	−19.1168	−	33.1113i	−1.29774	−	2.24774i
$218$	2.05842	−	1.18843i	0.139414	−	0.0804907i
$219$	−8.74456	−	15.1460i	−0.590903	−	1.02347i
$220$		0			0
$221$	0.510875			0.0343652
$222$	−15.3030	−	1.26217i	−1.02707	−	0.0847112i
$223$		−	18.6101i		−	1.24623i	−0.782132	−	0.623113i	$-0.785868\pi$
$223$		−	18.6101i		−	1.24623i	0.782132	−	0.623113i	$-0.214132\pi$
$224$	3.00000	+	1.73205i	0.200446	+	0.115728i
$225$	−15.3723	−	6.92820i	−1.02482	−	0.461880i
$226$	10.1168	+	17.5229i	0.672962	+	1.16561i
$227$	5.18614	+	8.98266i	0.344216	+	0.596200i	0.985211	−	0.171345i	$-0.0548113\pi$
$227$	5.18614	+	8.98266i	0.344216	+	0.596200i	−0.640995	+	0.767545i	$0.721478\pi$
$228$		0			0
$229$	−4.43070	−	7.67420i	−0.292789	−	0.507126i	0.681679	−	0.731651i	$-0.261250\pi$
$229$	−4.43070	−	7.67420i	−0.292789	−	0.507126i	−0.974468	+	0.224526i	$0.927917\pi$
$230$	−1.88316	−	5.84096i	−0.124172	−	0.385142i
$231$		0			0
$232$		−	7.72049i		−	0.506875i
$233$			14.6487i			0.959668i	0.877359	+	0.479834i	$0.159303\pi$
$233$			14.6487i			0.959668i	−0.877359	+	0.479834i	$0.840697\pi$
$234$	−0.627719	+	1.08724i	−0.0410353	+	0.0710751i
$235$	8.37228	+	7.57301i	0.546147	+	0.494009i
$236$			11.9769i			0.779628i
$237$	10.3723	−	17.9653i	0.673752	−	1.16697i
$238$	−4.11684	−	2.37686i	−0.266855	−	0.154069i
$239$	−8.48913	−	4.90120i	−0.549116	−	0.317032i	0.199649	−	0.979867i	$-0.436020\pi$
$239$	−8.48913	−	4.90120i	−0.549116	−	0.317032i	−0.748765	+	0.662835i	$0.769353\pi$
$240$	4.18614	+	3.78651i	0.270214	+	0.244418i
$241$	−18.0000	+	10.3923i	−1.15948	+	0.669427i	−0.951180	−	0.308637i	$-0.900127\pi$
$241$	−18.0000	+	10.3923i	−1.15948	+	0.669427i	−0.208302	+	0.978065i	$0.566794\pi$
$242$	5.50000	−	9.52628i	0.353553	−	0.612372i
$243$	−19.3723	−	11.1846i	−1.24273	−	0.717492i
$244$	−2.05842	−	1.18843i	−0.131777	−	0.0760815i
$245$	3.43070	+	10.6410i	0.219180	+	0.679827i
$246$	12.5584	−	7.25061i	0.800696	−	0.462282i
$247$		0			0
$248$			11.0371i			0.700858i
$249$	34.2337			2.16947
$250$	−10.2446	+	4.47760i	−0.647923	+	0.283189i
$251$		−	21.7793i		−	1.37470i	−0.726328	−	0.687348i	$-0.758775\pi$
$251$		−	21.7793i		−	1.37470i	0.726328	−	0.687348i	$-0.241225\pi$
$252$	10.1168	−	5.84096i	0.637301	−	0.367946i
$253$		0			0
$254$	−15.0000	+	8.66025i	−0.941184	+	0.543393i
$255$	−5.74456	−	5.19615i	−0.359738	−	0.325396i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.430703	+	0.746000i	−0.0268665	+	0.0465342i	−0.879146	−	0.476552i	$-0.841886\pi$
$257$	−0.430703	+	0.746000i	−0.0268665	+	0.0465342i	0.852280	+	0.523087i	$0.175220\pi$
$258$			23.0140i			1.43279i
$259$	9.00000	+	19.0526i	0.559233	+	1.18387i
$260$	0.255437	+	0.792287i	0.0158416	+	0.0491356i
$261$	−22.5475	−	13.0178i	−1.39566	−	0.805784i
$262$	−5.74456	+	3.31662i	−0.354900	+	0.204902i
$263$	2.74456	−	1.58457i	0.169237	−	0.0977090i	−0.412989	−	0.910736i	$-0.635515\pi$
$263$	2.74456	−	1.58457i	0.169237	−	0.0977090i	0.582226	+	0.813027i	$0.302182\pi$
$264$		0			0
$265$	−2.00000	+	0.644810i	−0.122859	+	0.0396104i
$266$		0			0
$267$	24.2337			1.48308
$268$	7.11684	+	4.10891i	0.434730	+	0.250992i
$269$	−23.4891			−1.43216			−0.716079	−	0.698020i	$-0.754065\pi$
$269$	−23.4891			−1.43216			−0.716079	+	0.698020i	$0.754065\pi$
$270$	2.00000	−	0.644810i	0.121716	−	0.0392419i
$271$	−9.18614	+	15.9109i	−0.558018	+	0.966516i	0.439644	+	0.898172i	$0.355105\pi$
$271$	−9.18614	+	15.9109i	−0.558018	+	0.966516i	−0.997662	+	0.0683437i	$0.978229\pi$
$272$	0.686141	+	1.18843i	0.0416034	+	0.0720592i
$273$	3.25544			0.197028
$274$	2.31386	+	1.33591i	0.139785	+	0.0807051i
$275$		0			0
$276$	6.00000	+	3.46410i	0.361158	+	0.208514i
$277$	−3.50000	−	6.06218i	−0.210295	−	0.364241i	0.741512	−	0.670940i	$-0.234109\pi$
$277$	−3.50000	−	6.06218i	−0.210295	−	0.364241i	−0.951807	+	0.306699i	$0.900776\pi$
$278$	9.37228	+	16.2333i	0.562112	+	0.973607i
$279$	32.2337	+	18.6101i	1.92978	+	1.11416i
$280$	1.62772	−	7.57301i	0.0972748	−	0.452574i
$281$	6.12772	+	3.53784i	0.365549	+	0.211050i	0.671512	−	0.740994i	$-0.265645\pi$
$281$	6.12772	+	3.53784i	0.365549	+	0.211050i	−0.305963	+	0.952043i	$0.598978\pi$
$282$	−12.7446			−0.758928
$283$	−1.44158	−	2.49689i	−0.0856929	−	0.148424i	0.819993	−	0.572373i	$-0.193977\pi$
$283$	−1.44158	−	2.49689i	−0.0856929	−	0.148424i	−0.905686	+	0.423949i	$0.860644\pi$
$284$	−1.37228	+	2.37686i	−0.0814299	+	0.141041i
$285$		0			0
$286$		0			0
$287$	−17.2337	−	9.94987i	−1.01727	−	0.587323i
$288$	−3.37228			−0.198714
$289$	7.55842	+	13.0916i	0.444613	+	0.770092i
$290$	−16.4307	+	5.29734i	−0.964844	+	0.311071i
$291$	26.4891	−	15.2935i	1.55282	−	0.896521i
$292$	6.00000	−	3.46410i	0.351123	−	0.202721i
$293$	−24.9891	+	14.4275i	−1.45988	+	0.842862i	−0.999005	−	0.0446025i	$-0.985798\pi$
$293$	−24.9891	+	14.4275i	−1.45988	+	0.842862i	−0.460875	+	0.887465i	$0.652465\pi$
$294$	−10.9307	−	6.31084i	−0.637492	−	0.368056i
$295$	25.4891	−	8.21782i	1.48403	−	0.478460i
$296$	0.500000	−	6.06218i	0.0290619	−	0.352357i
$297$		0			0
$298$	5.31386	−	9.20387i	0.307824	−	0.533166i
$299$	0.510875	+	0.884861i	0.0295446	+	0.0511728i
$300$	5.18614	−	11.5070i	0.299422	−	0.664357i
$301$	27.3505	−	15.7908i	1.57646	−	0.910169i
$302$	17.8614			1.02781
$303$	−3.00000	+	1.73205i	−0.172345	+	0.0995037i
$304$		0			0
$305$	−1.11684	+	5.19615i	−0.0639503	+	0.297531i
$306$	4.62772			0.264549
$307$			20.1398i			1.14944i	0.818350	+	0.574720i	$0.194889\pi$
$307$			20.1398i			1.14944i	−0.818350	+	0.574720i	$0.805111\pi$
$308$		0			0
$309$	−33.8614	+	19.5499i	−1.92631	+	1.11215i
$310$	23.4891	−	7.57301i	1.33409	−	0.430118i
$311$	16.4198	+	9.47999i	0.931083	+	0.537561i	0.887154	−	0.461474i	$-0.152679\pi$
$311$	16.4198	+	9.47999i	0.931083	+	0.537561i	0.0439291	+	0.999035i	$0.486012\pi$
$312$	−0.813859	−	0.469882i	−0.0460757	−	0.0266018i
$313$	−14.1753	+	24.5523i	−0.801233	+	1.38778i	0.117571	+	0.993064i	$0.462489\pi$
$313$	−14.1753	+	24.5523i	−0.801233	+	1.38778i	−0.918805	+	0.394713i	$0.870844\pi$
$314$	−5.61684	+	3.24289i	−0.316977	+	0.183007i
$315$	−19.3723	−	17.5229i	−1.09150	−	0.987303i
$316$	7.11684	+	4.10891i	0.400354	+	0.231144i
$317$	−11.3614	−	6.55951i	−0.638120	−	0.368419i	0.145770	−	0.989319i	$-0.453434\pi$
$317$	−11.3614	−	6.55951i	−0.638120	−	0.368419i	−0.783890	+	0.620900i	$0.786767\pi$
$318$	1.18614	−	2.05446i	0.0665155	−	0.115208i
$319$		0			0
$320$	−1.50000	+	1.65831i	−0.0838525	+	0.0927025i
$321$	−4.81386	+	8.33785i	−0.268683	+	0.465373i
$322$		−	9.50744i		−	0.529829i
$323$		0			0
$324$	3.87228	−	6.70699i	0.215127	−	0.372610i
$325$	1.51087	−	1.08724i	0.0838082	−	0.0603093i
$326$	−8.55842	−	14.8236i	−0.474007	−	0.821004i
$327$	6.00000			0.331801
$328$	2.87228	+	4.97494i	0.158595	+	0.274695i
$329$	8.74456	+	15.1460i	0.482103	+	0.835027i
$330$		0			0
$331$	−24.0000	−	13.8564i	−1.31916	−	0.761617i	−0.335566	−	0.942017i	$-0.608928\pi$
$331$	−24.0000	−	13.8564i	−1.31916	−	0.761617i	−0.983593	+	0.180400i	$0.942261\pi$
$332$			13.5615i			0.744281i
$333$	−16.8614	−	11.6819i	−0.923999	−	0.640166i
$334$	5.48913			0.300352
$335$	3.86141	−	17.9653i	0.210971	−	0.981550i
$336$	4.37228	+	7.57301i	0.238528	+	0.413142i
$337$	−0.941578	+	0.543620i	−0.0512910	+	0.0296129i	−0.525426	−	0.850839i	$-0.676094\pi$
$337$	−0.941578	+	0.543620i	−0.0512910	+	0.0296129i	0.474135	+	0.880452i	$0.342761\pi$
$338$	6.43070	+	11.1383i	0.349784	+	0.605844i
$339$			51.0767i			2.77410i
$340$	2.05842	−	2.27567i	0.111634	−	0.123416i
$341$		0			0
$342$		0			0
$343$		−	6.92820i		−	0.374088i
$344$	−9.11684			−0.491547
$345$	3.25544	−	15.1460i	0.175267	−	0.815435i
$346$	−10.5475	+	6.08963i	−0.567040	+	0.327380i
$347$	−2.74456			−0.147336			−0.0736679	−	0.997283i	$-0.523470\pi$
$347$	−2.74456			−0.147336			−0.0736679	+	0.997283i	$0.523470\pi$
$348$	9.74456	−	16.8781i	0.522363	−	0.904760i
$349$	−0.313859	+	0.543620i	−0.0168005	+	0.0290993i	−0.874303	−	0.485380i	$-0.838681\pi$
$349$	−0.313859	+	0.543620i	−0.0168005	+	0.0290993i	0.857503	+	0.514479i	$0.172015\pi$
$350$	−17.2337	+	1.73205i	−0.921179	+	0.0925820i
$351$	−0.302985	+	0.174928i	−0.0161721	+	0.00933698i
$352$		0			0
$353$	−12.1753	+	21.0882i	−0.648024	+	1.12241i	0.335570	+	0.942015i	$0.391071\pi$
$353$	−12.1753	+	21.0882i	−0.648024	+	1.12241i	−0.983594	+	0.180395i	$0.942262\pi$
$354$	−15.1168	+	26.1831i	−0.803451	+	1.39162i
$355$	6.00000	+	1.28962i	0.318447	+	0.0684459i
$356$			9.60002i			0.508800i
$357$	−6.00000	−	10.3923i	−0.317554	−	0.550019i
$358$	−17.4891	−	10.0974i	−0.924329	−	0.533662i
$359$	−10.3723			−0.547428			−0.273714	−	0.961811i	$-0.588252\pi$
$359$	−10.3723			−0.547428			−0.273714	+	0.961811i	$0.588252\pi$
$360$	2.31386	+	7.17687i	0.121951	+	0.378254i
$361$	−9.50000	+	16.4545i	−0.500000	+	0.866025i
$362$	−4.86141			−0.255510
$363$	24.0475	−	13.8839i	1.26217	−	0.728714i
$364$			1.28962i			0.0675945i
$365$	−11.4891	−	10.3923i	−0.601368	−	0.543958i
$366$	−3.00000	−	5.19615i	−0.156813	−	0.271607i
$367$	−19.1168	+	11.0371i	−0.997891	+	0.576133i	−0.907624	−	0.419785i	$-0.862106\pi$
$367$	−19.1168	+	11.0371i	−0.997891	+	0.576133i	−0.0902675	+	0.995918i	$0.528772\pi$
$368$	−1.37228	+	2.37686i	−0.0715351	+	0.123902i
$369$	19.3723			1.00848
$370$	−13.2446	+	3.09541i	−0.688552	+	0.160923i
$371$	−3.25544			−0.169014
$372$	−13.9307	+	24.1287i	−0.722273	+	1.25101i
$373$	−10.5000	+	6.06218i	−0.543669	+	0.313888i	−0.746565	−	0.665313i	$-0.768298\pi$
$373$	−10.5000	+	6.06218i	−0.543669	+	0.313888i	0.202895	+	0.979200i	$0.434965\pi$
$374$		0			0
$375$	−28.0475	−	3.14170i	−1.44837	−	0.162237i
$376$		−	5.04868i		−	0.260366i
$377$	2.48913	−	1.43710i	0.128196	−	0.0740143i
$378$	3.25544			0.167442
$379$	−5.37228	+	9.30506i	−0.275956	+	0.477969i	−0.970376	−	0.241601i	$-0.922328\pi$
$379$	−5.37228	+	9.30506i	−0.275956	+	0.477969i	0.694420	+	0.719570i	$0.255661\pi$
$380$		0			0
$381$	−43.7228			−2.23999
$382$	21.3030	+	12.2993i	1.08996	+	0.629286i
$383$	6.25544	+	10.8347i	0.319638	+	0.553629i	0.980412	−	0.196955i	$-0.0631054\pi$
$383$	6.25544	+	10.8347i	0.319638	+	0.553629i	−0.660775	+	0.750584i	$0.729772\pi$
$384$		−	2.52434i		−	0.128820i
$385$		0			0
$386$	3.31386	−	5.73977i	0.168671	−	0.292147i
$387$	−15.3723	+	26.6256i	−0.781417	+	1.35345i
$388$	6.05842	+	10.4935i	0.307570	+	0.532726i
$389$	7.54755	−	4.35758i	0.382676	−	0.220938i	−0.296306	−	0.955093i	$-0.595755\pi$
$389$	7.54755	−	4.35758i	0.382676	−	0.220938i	0.678982	+	0.734155i	$0.262421\pi$
$390$	−0.441578	+	2.05446i	−0.0223602	+	0.104031i
$391$	1.88316	−	3.26172i	0.0952353	−	0.164952i
$392$	2.50000	−	4.33013i	0.126269	−	0.218704i
$393$	−16.7446			−0.844651
$394$	6.12772	−	3.53784i	0.308710	−	0.178234i
$395$	3.86141	−	17.9653i	0.194288	−	0.903933i
$396$		0			0
$397$		−	16.8781i		−	0.847086i	−0.905876	−	0.423543i	$-0.860786\pi$
$397$		−	16.8781i		−	0.847086i	0.905876	−	0.423543i	$-0.139214\pi$
$398$	−7.67527	−	4.43132i	−0.384726	−	0.222122i
$399$		0			0
$400$	4.55842	+	2.05446i	0.227921	+	0.102723i
$401$			13.2665i			0.662497i	0.943543	+	0.331249i	$0.107470\pi$
$401$			13.2665i			0.662497i	−0.943543	+	0.331249i	$0.892530\pi$
$402$	10.3723	+	17.9653i	0.517322	+	0.896029i
$403$	−3.55842	+	2.05446i	−0.177258	+	0.102340i
$404$	−0.686141	−	1.18843i	−0.0341368	−	0.0591266i
$405$	−16.9307	−	3.63903i	−0.841293	−	0.180825i
$406$	−26.7446			−1.32731
$407$		0			0
$408$			3.46410i			0.171499i
$409$	25.5000	+	14.7224i	1.26089	+	0.727977i	0.973247	−	0.229759i	$-0.0737939\pi$
$409$	25.5000	+	14.7224i	1.26089	+	0.727977i	0.287646	+	0.957737i	$0.407127\pi$
$410$	8.61684	−	9.52628i	0.425556	−	0.470469i
$411$	3.37228	+	5.84096i	0.166342	+	0.288113i
$412$	−7.74456	−	13.4140i	−0.381547	−	0.660859i
$413$	41.4891			2.04155
$414$	4.62772	+	8.01544i	0.227440	+	0.393938i
$415$	28.8614	−	9.30506i	1.41675	−	0.456768i
$416$	0.186141	−	0.322405i	0.00912630	−	0.0158072i
$417$			47.3176i			2.31715i
$418$		0			0
$419$	8.48913	−	14.7036i	0.414721	−	0.718318i	−0.580678	−	0.814133i	$-0.697213\pi$
$419$	8.48913	−	14.7036i	0.414721	−	0.718318i	0.995399	+	0.0958155i	$0.0305459\pi$
$420$	13.1168	−	14.5012i	0.640036	−	0.707587i
$421$			10.5947i			0.516353i	0.966098	+	0.258177i	$0.0831217\pi$
$421$			10.5947i			0.516353i	−0.966098	+	0.258177i	$0.916878\pi$
$422$	7.74456	−	13.4140i	0.376999	−	0.652982i
$423$	−14.7446	−	8.51278i	−0.716905	−	0.413905i
$424$	0.813859	+	0.469882i	0.0395245	+	0.0228195i
$425$	−6.25544	−	2.81929i	−0.303433	−	0.136756i
$426$	−6.00000	+	3.46410i	−0.290701	+	0.167836i
$427$	−4.11684	+	7.13058i	−0.199228	+	0.345073i
$428$	−3.30298	−	1.90698i	−0.159656	−	0.0921773i
$429$		0			0
$430$	6.25544	+	19.4024i	0.301664	+	0.935668i
$431$	27.0475	−	15.6159i	1.30283	−	0.752192i	0.321945	−	0.946758i	$-0.395663\pi$
$431$	27.0475	−	15.6159i	1.30283	−	0.752192i	0.980889	+	0.194566i	$0.0623300\pi$
$432$	−0.813859	−	0.469882i	−0.0391568	−	0.0226072i
$433$		−	20.9870i		−	1.00857i	−0.863537	−	0.504285i	$-0.831756\pi$
$433$		−	20.9870i		−	1.00857i	0.863537	−	0.504285i	$-0.168244\pi$
$434$	38.2337			1.83528
$435$	−42.6060	−	9.15759i	−2.04280	−	0.439073i
$436$			2.37686i			0.113831i
$437$		0			0
$438$	17.4891			0.835663
$439$	−14.4416	+	8.33785i	−0.689259	+	0.397944i	−0.803334	−	0.595528i	$-0.796943\pi$
$439$	−14.4416	+	8.33785i	−0.689259	+	0.397944i	0.114075	+	0.993472i	$0.463609\pi$
$440$		0			0
$441$	−8.43070	−	14.6024i	−0.401462	−	0.695353i
$442$	−0.255437	+	0.442430i	−0.0121499	+	0.0210443i
$443$		−	28.6526i		−	1.36133i	−0.732597	−	0.680663i	$-0.761692\pi$
$443$		−	28.6526i		−	1.36133i	0.732597	−	0.680663i	$-0.238308\pi$
$444$	8.74456	−	12.6217i	0.414999	−	0.598999i
$445$	20.4307	−	6.58696i	0.968508	−	0.312252i
$446$	16.1168	+	9.30506i	0.763155	+	0.440608i
$447$	23.2337	−	13.4140i	1.09892	−	0.634459i
$448$	−3.00000	+	1.73205i	−0.141737	+	0.0818317i
$449$	5.69702	−	3.28917i	0.268859	−	0.155226i	−0.359510	−	0.933141i	$-0.617056\pi$
$449$	5.69702	−	3.28917i	0.268859	−	0.155226i	0.628369	+	0.777915i	$0.283723\pi$
$450$	13.6861	−	9.84868i	0.645171	−	0.464271i
$451$		0			0
$452$	−20.2337			−0.951713
$453$	39.0475	+	22.5441i	1.83461	+	1.05921i
$454$	−10.3723			−0.486795
$455$	2.74456	−	0.884861i	0.128667	−	0.0414829i
$456$		0			0
$457$	−9.80298	−	16.9793i	−0.458564	−	0.794257i	0.540321	−	0.841459i	$-0.318303\pi$
$457$	−9.80298	−	16.9793i	−0.458564	−	0.794257i	−0.998885	+	0.0472023i	$0.984969\pi$
$458$	8.86141			0.414066
$459$	1.11684	+	0.644810i	0.0521298	+	0.0300972i
$460$	6.00000	+	1.28962i	0.279751	+	0.0601289i
$461$	27.8614	+	16.0858i	1.29764	+	0.749190i	0.979995	−	0.199021i	$-0.0637763\pi$
$461$	27.8614	+	16.0858i	1.29764	+	0.749190i	0.317640	+	0.948211i	$0.397110\pi$
$462$		0			0
$463$	−2.25544	−	3.90653i	−0.104819	−	0.181552i	0.808845	−	0.588022i	$-0.200093\pi$
$463$	−2.25544	−	3.90653i	−0.104819	−	0.181552i	−0.913664	+	0.406470i	$0.866760\pi$
$464$	6.68614	+	3.86025i	0.310396	+	0.179207i
$465$	60.9090	+	13.0916i	2.82459	+	0.607107i
$466$	−12.6861	−	7.32435i	−0.587674	−	0.339294i
$467$	−22.3723			−1.03527			−0.517633	−	0.855603i	$-0.673187\pi$
$467$	−22.3723			−1.03527			−0.517633	+	0.855603i	$0.673187\pi$
$468$	−0.627719	−	1.08724i	−0.0290163	−	0.0502577i
$469$	14.2337	−	24.6535i	0.657251	−	1.13839i
$470$	−10.7446	+	3.46410i	−0.495610	+	0.159787i
$471$	−16.3723			−0.754395
$472$	−10.3723	−	5.98844i	−0.477423	−	0.275640i
$473$		0			0
$474$	10.3723	+	17.9653i	0.476415	+	0.825174i
$475$		0			0
$476$	4.11684	−	2.37686i	0.188695	−	0.108943i
$477$	2.74456	−	1.58457i	0.125665	−	0.0725527i
$478$	8.48913	−	4.90120i	0.388284	−	0.224176i
$479$	31.4198	+	18.1402i	1.43561	+	0.828849i	0.997540	−	0.0700928i	$-0.0223295\pi$
$479$	31.4198	+	18.1402i	1.43561	+	0.828849i	0.438068	+	0.898942i	$0.355663\pi$
$480$	−5.37228	+	1.73205i	−0.245210	+	0.0790569i
$481$	2.04755	−	0.967215i	0.0933601	−	0.0441012i
$482$		−	20.7846i		−	0.946713i
$483$	12.0000	−	20.7846i	0.546019	−	0.945732i
$484$	5.50000	+	9.52628i	0.250000	+	0.433013i
$485$	18.1753	−	20.0935i	0.825296	−	0.912399i
$486$	19.3723	−	11.1846i	0.878745	−	0.507343i
$487$	−2.00000			−0.0906287			−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000			−0.0906287			−0.0453143	+	0.998973i	$0.514429\pi$
$488$	2.05842	−	1.18843i	0.0931804	−	0.0537977i
$489$		−	43.2087i		−	1.95396i
$490$	−10.9307	−	2.34941i	−0.493799	−	0.106136i
$491$	−19.7228			−0.890078			−0.445039	−	0.895511i	$-0.646810\pi$
$491$	−19.7228			−0.890078			−0.445039	+	0.895511i	$0.646810\pi$
$492$			14.5012i			0.653765i
$493$	−9.17527	−	5.29734i	−0.413233	−	0.238580i
$494$		0			0
$495$		0			0
$496$	−9.55842	−	5.51856i	−0.429186	−	0.247791i
$497$	8.23369	+	4.75372i	0.369331	+	0.213234i
$498$	−17.1168	+	29.6472i	−0.767024	+	1.32852i
$499$	12.0000	−	6.92820i	0.537194	−	0.310149i	−0.206747	−	0.978394i	$-0.566288\pi$
$499$	12.0000	−	6.92820i	0.537194	−	0.310149i	0.743941	+	0.668245i	$0.232954\pi$
$500$	1.24456	−	11.1109i	0.0556585	−	0.496892i
$501$	12.0000	+	6.92820i	0.536120	+	0.309529i
$502$	18.8614	+	10.8896i	0.841826	+	0.486028i
$503$	11.4891	−	19.8997i	0.512275	−	0.887286i	−0.487624	−	0.873054i	$-0.662136\pi$
$503$	11.4891	−	19.8997i	0.512275	−	0.887286i	0.999899	−	0.0142322i	$-0.00453039\pi$
$504$			11.6819i			0.520354i
$505$	−2.05842	+	2.27567i	−0.0915986	+	0.101266i
$506$		0			0
$507$			32.4665i			1.44189i
$508$		−	17.3205i		−	0.768473i
$509$	−10.8030	+	18.7113i	−0.478834	+	0.829365i	−0.999705	−	0.0242705i	$-0.992274\pi$
$509$	−10.8030	+	18.7113i	−0.478834	+	0.829365i	0.520872	+	0.853635i	$0.325607\pi$
$510$	7.37228	−	2.37686i	0.326450	−	0.105249i
$511$	−12.0000	−	20.7846i	−0.530849	−	0.919457i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−0.430703	−	0.746000i	−0.0189975	−	0.0329046i
$515$	−23.2337	+	25.6858i	−1.02380	+	1.13185i
$516$	−19.9307	−	11.5070i	−0.877400	−	0.506567i
$517$		0			0
$518$	−21.0000	−	1.73205i	−0.922687	−	0.0761019i
$519$	−30.7446			−1.34954
$520$	−0.813859	−	0.174928i	−0.0356901	−	0.00767111i
$521$	−2.18614	−	3.78651i	−0.0957766	−	0.165890i	0.814156	−	0.580646i	$-0.197200\pi$
$521$	−2.18614	−	3.78651i	−0.0957766	−	0.165890i	−0.909932	+	0.414756i	$0.863867\pi$
$522$	22.5475	−	13.0178i	0.986879	−	0.569775i
$523$	−8.55842	−	14.8236i	−0.374234	−	0.648192i	0.615978	−	0.787763i	$-0.288761\pi$
$523$	−8.55842	−	14.8236i	−0.374234	−	0.648192i	−0.990212	+	0.139571i	$0.955428\pi$
$524$		−	6.63325i		−	0.289775i
$525$	−39.8614	−	17.9653i	−1.73969	−	0.784071i
$526$			3.16915i			0.138181i
$527$	13.1168	+	7.57301i	0.571379	+	0.329886i
$528$		0			0
$529$	−15.4674			−0.672495
$530$	0.441578	−	2.05446i	0.0191809	−	0.0892399i
$531$	−34.9783	+	20.1947i	−1.51793	+	0.876375i
$532$		0			0
$533$	−1.06930	+	1.85208i	−0.0463164	+	0.0802223i
$534$	−12.1168	+	20.9870i	−0.524347	+	0.908196i
$535$	−1.79211	+	8.33785i	−0.0774797	+	0.360477i
$536$	−7.11684	+	4.10891i	−0.307401	+	0.177478i
$537$	−25.4891	−	44.1485i	−1.09994	−	1.90515i
$538$	11.7446	−	20.3422i	0.506344	−	0.877014i
$539$		0			0
$540$	−0.441578	+	2.05446i	−0.0190025	+	0.0884097i
$541$		−	44.3508i		−	1.90679i	−0.301723	−	0.953396i	$-0.597562\pi$
$541$		−	44.3508i		−	1.90679i	0.301723	−	0.953396i	$-0.402438\pi$
$542$	−9.18614	−	15.9109i	−0.394579	−	0.683430i
$543$	−10.6277	−	6.13592i	−0.456079	−	0.263317i
$544$	−1.37228			−0.0588361
$545$	5.05842	−	1.63086i	0.216679	−	0.0698584i
$546$	−1.62772	+	2.81929i	−0.0696599	+	0.120655i
$547$	46.0951			1.97088			0.985442	−	0.170012i	$-0.0543807\pi$
$547$	46.0951			1.97088			0.985442	+	0.170012i	$0.0543807\pi$
$548$	−2.31386	+	1.33591i	−0.0988432	+	0.0570671i
$549$		−	8.01544i		−	0.342091i
$550$		0			0
$551$		0			0
$552$	−6.00000	+	3.46410i	−0.255377	+	0.147442i
$553$	14.2337	−	24.6535i	0.605278	−	1.04837i
$554$	7.00000			0.297402
$555$	−32.8614	−	9.94987i	−1.39489	−	0.422349i
$556$	−18.7446			−0.794947
$557$	−22.2446	+	38.5287i	−0.942532	+	1.63251i	−0.181914	+	0.983314i	$0.558229\pi$
$557$	−22.2446	+	38.5287i	−0.942532	+	1.63251i	−0.760618	+	0.649200i	$0.775104\pi$
$558$	−32.2337	+	18.6101i	−1.36456	+	0.787830i
$559$	−1.69702	−	2.93932i	−0.0717761	−	0.124320i
$560$	5.74456	+	5.19615i	0.242752	+	0.219578i
$561$		0			0
$562$	−6.12772	+	3.53784i	−0.258482	+	0.149235i
$563$	−8.23369			−0.347009			−0.173504	−	0.984833i	$-0.555509\pi$
$563$	−8.23369			−0.347009			−0.173504	+	0.984833i	$0.555509\pi$
$564$	6.37228	−	11.0371i	0.268321	−	0.464746i
$565$	13.8832	+	43.0612i	0.584069	+	1.81160i
$566$	2.88316			0.121188
$567$	−23.2337	−	13.4140i	−0.975723	−	0.563334i
$568$	−1.37228	−	2.37686i	−0.0575796	−	0.0997309i
$569$		−	6.19082i		−	0.259533i	−0.991545	−	0.129766i	$-0.958577\pi$
$569$		−	6.19082i		−	0.259533i	0.991545	−	0.129766i	$-0.0414227\pi$
$570$		0			0
$571$	19.2337	−	33.3137i	0.804905	−	1.39414i	−0.111451	−	0.993770i	$-0.535550\pi$
$571$	19.2337	−	33.3137i	0.804905	−	1.39414i	0.916355	−	0.400366i	$-0.131117\pi$
$572$		0			0
$573$	31.0475	+	53.7759i	1.29703	+	2.24652i
$574$	17.2337	−	9.94987i	0.719320	−	0.415300i
$575$	−1.37228	−	13.6540i	−0.0572281	−	0.569412i
$576$	1.68614	−	2.92048i	0.0702559	−	0.121687i
$577$	−13.2337	+	22.9214i	−0.550926	+	0.954231i	0.447282	+	0.894393i	$0.352392\pi$
$577$	−13.2337	+	22.9214i	−0.550926	+	0.954231i	−0.998208	+	0.0598384i	$0.980941\pi$
$578$	−15.1168			−0.628778
$579$	14.4891	−	8.36530i	0.602147	−	0.347650i
$580$	3.62772	−	16.8781i	0.150633	−	0.700824i
$581$	46.9783			1.94899
$582$			30.5870i			1.26787i
$583$		0			0
$584$			6.92820i			0.286691i
$585$	−1.88316	+	2.08191i	−0.0778589	+	0.0860763i
$586$		−	28.8550i		−	1.19199i
$587$	−15.3030	−	26.5055i	−0.631622	−	1.09400i	−0.987220	−	0.159362i	$-0.949056\pi$
$587$	−15.3030	−	26.5055i	−0.631622	−	1.09400i	0.355598	−	0.934639i	$-0.384277\pi$
$588$	10.9307	−	6.31084i	0.450775	−	0.260255i
$589$		0			0
$590$	−5.62772	+	26.1831i	−0.231690	+	1.07794i
$591$	17.8614			0.734720
$592$	5.00000	+	3.46410i	0.205499	+	0.142374i
$593$		−	10.8896i		−	0.447184i	−0.974683	−	0.223592i	$-0.928222\pi$
$593$		−	10.8896i		−	0.447184i	0.974683	−	0.223592i	$-0.0717783\pi$
$594$		0			0
$595$	−7.88316	−	7.13058i	−0.323178	−	0.292325i
$596$	5.31386	+	9.20387i	0.217664	+	0.377005i
$597$	−11.1861	−	19.3750i	−0.457818	−	0.792964i
$598$	−1.02175			−0.0417824
$599$	6.81386	+	11.8020i	0.278407	+	0.482215i	0.970989	−	0.239124i	$-0.0768603\pi$
$599$	6.81386	+	11.8020i	0.278407	+	0.482215i	−0.692582	+	0.721339i	$0.743527\pi$
$600$	7.37228	+	10.2448i	0.300972	+	0.418243i
$601$	−12.8723	+	22.2954i	−0.525071	+	0.909450i	0.474502	+	0.880254i	$0.342628\pi$
$601$	−12.8723	+	22.2954i	−0.525071	+	0.909450i	−0.999574	+	0.0291960i	$0.990705\pi$
$602$			31.5817i			1.28717i
$603$			27.7128i			1.12855i
$604$	−8.93070	+	15.4684i	−0.363385	+	0.629402i
$605$	16.5000	−	18.2414i	0.670820	−	0.741620i
$606$		−	3.46410i		−	0.140720i
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	−0.773358	−	0.633970i	$-0.781424\pi$
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	0.935713	+	0.352763i	$0.114758\pi$
$608$		0			0
$609$	−58.4674	−	33.7562i	−2.36922	−	1.36787i
$610$	−3.94158	−	3.56529i	−0.159590	−	0.144354i
$611$	1.62772	−	0.939764i	0.0658504	−	0.0380188i
$612$	−2.31386	+	4.00772i	−0.0935322	+	0.162003i
$613$	−30.9416	−	17.8641i	−1.24972	−	0.721525i	−0.278665	−	0.960388i	$-0.589892\pi$
$613$	−30.9416	−	17.8641i	−1.24972	−	0.721525i	−0.971053	+	0.238863i	$0.923225\pi$
$614$	−17.4416	−	10.0699i	−0.703885	−	0.406388i
$615$	30.8614	−	9.94987i	1.24445	−	0.401218i
$616$		0			0
$617$	11.4891	+	6.63325i	0.462535	+	0.267045i	0.713109	−	0.701053i	$-0.247286\pi$
$617$	11.4891	+	6.63325i	0.462535	+	0.267045i	−0.250575	+	0.968097i	$0.580620\pi$
$618$		−	39.0998i		−	1.57282i
$619$	−38.4674			−1.54613			−0.773067	−	0.634324i	$-0.781278\pi$
$619$	−38.4674			−1.54613			−0.773067	+	0.634324i	$0.781278\pi$
$620$	−5.18614	+	24.1287i	−0.208280	+	0.969031i
$621$			2.57924i			0.103501i
$622$	−16.4198	+	9.47999i	−0.658375	+	0.380113i
$623$	33.2554			1.33235
$624$	0.813859	−	0.469882i	0.0325804	−	0.0188103i
$625$	−24.5000	+	4.97494i	−0.980000	+	0.198997i
$626$	−14.1753	−	24.5523i	−0.566558	−	0.981307i
$627$		0			0
$628$		−	6.48577i		−	0.258811i
$629$	−6.86141	−	4.75372i	−0.273582	−	0.189543i
$630$	24.8614	−	8.01544i	0.990502	−	0.319343i
$631$	−10.3247	−	5.96099i	−0.411021	−	0.237303i	0.280207	−	0.959940i	$-0.409597\pi$
$631$	−10.3247	−	5.96099i	−0.411021	−	0.237303i	−0.691228	+	0.722636i	$0.742930\pi$
$632$	−7.11684	+	4.10891i	−0.283093	+	0.163444i
$633$	33.8614	−	19.5499i	1.34587	−	0.777038i
$634$	11.3614	−	6.55951i	0.451219	−	0.260511i
$635$	−36.8614	+	11.8843i	−1.46280	+	0.471614i
$636$	1.18614	+	2.05446i	0.0470335	+	0.0814645i
$637$	1.86141			0.0737516
$638$		0			0
$639$	−9.25544			−0.366139
$640$	−0.686141	−	2.12819i	−0.0271221	−	0.0841243i
$641$	13.5000	−	23.3827i	0.533218	−	0.923561i	−0.466029	−	0.884769i	$-0.654316\pi$
$641$	13.5000	−	23.3827i	0.533218	−	0.923561i	0.999247	−	0.0387913i	$-0.0123508\pi$
$642$	−4.81386	−	8.33785i	−0.189988	−	0.329069i
$643$	7.86141			0.310024			0.155012	−	0.987913i	$-0.450458\pi$
$643$	7.86141			0.310024			0.155012	+	0.987913i	$0.450458\pi$
$644$	8.23369	+	4.75372i	0.324453	+	0.187323i
$645$	−10.8139	+	50.3118i	−0.425795	+	1.98103i
$646$		0			0
$647$	11.7446	+	20.3422i	0.461726	+	0.799734i	0.999047	−	0.0436444i	$-0.0138969\pi$
$647$	11.7446	+	20.3422i	0.461726	+	0.799734i	−0.537321	+	0.843378i	$0.680564\pi$
$648$	3.87228	+	6.70699i	0.152118	+	0.263475i
$649$		0			0
$650$	0.186141	+	1.85208i	0.00730104	+	0.0726444i
$651$	83.5842	+	48.2574i	3.27592	+	1.89136i
$652$	17.1168			0.670347
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	0.999456	+	0.0329874i	$0.0105021\pi$
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	−0.471160	+	0.882048i	$0.656165\pi$
$654$	−3.00000	+	5.19615i	−0.117309	+	0.203186i
$655$	−14.1168	+	4.55134i	−0.551591	+	0.177836i
$656$	−5.74456			−0.224287
$657$	20.2337	+	11.6819i	0.789391	+	0.455755i
$658$	−17.4891			−0.681797
$659$	−0.510875	−	0.884861i	−0.0199009	−	0.0344693i	0.855903	−	0.517136i	$-0.173002\pi$
$659$	−0.510875	−	0.884861i	−0.0199009	−	0.0344693i	−0.875804	+	0.482666i	$0.839668\pi$
$660$		0			0
$661$	43.2921	−	24.9947i	1.68387	−	0.972182i	0.724820	−	0.688939i	$-0.241923\pi$
$661$	43.2921	−	24.9947i	1.68387	−	0.972182i	0.959048	−	0.283243i	$-0.0914103\pi$
$662$	24.0000	−	13.8564i	0.932786	−	0.538545i
$663$	−1.11684	+	0.644810i	−0.0433746	+	0.0250424i
$664$	−11.7446	−	6.78073i	−0.455777	−	0.263143i
$665$		0			0
$666$	18.5475	−	8.76144i	0.718703	−	0.339499i
$667$		−	21.1894i		−	0.820456i
$668$	−2.74456	+	4.75372i	−0.106190	+	0.183927i
$669$	23.4891	+	40.6844i	0.908142	+	1.57295i
$670$	13.6277	+	12.3267i	0.526485	+	0.476223i
$671$		0			0
$672$	−8.74456			−0.337329
$673$	6.00000	−	3.46410i	0.231283	−	0.133531i	−0.379881	−	0.925035i	$-0.624035\pi$
$673$	6.00000	−	3.46410i	0.231283	−	0.133531i	0.611164	+	0.791504i	$0.290702\pi$
$674$		−	1.08724i		−	0.0418789i
$675$	4.67527	−	0.469882i	0.179951	−	0.0180858i
$676$	−12.8614			−0.494669
$677$		−	4.84630i		−	0.186258i	−0.995654	−	0.0931291i	$-0.970313\pi$
$677$		−	4.84630i		−	0.186258i	0.995654	−	0.0931291i	$-0.0296869\pi$
$678$	−44.2337	−	25.5383i	−1.69878	−	0.980794i
$679$	36.3505	−	20.9870i	1.39501	−	0.805407i
$680$	0.941578	+	2.92048i	0.0361079	+	0.111995i
$681$	−22.6753	−	13.0916i	−0.868918	−	0.501670i
$682$		0			0
$683$	5.44158	−	9.42509i	0.208216	−	0.360641i	−0.742936	−	0.669362i	$-0.766568\pi$
$683$	5.44158	−	9.42509i	0.208216	−	0.360641i	0.951153	+	0.308721i	$0.0999009\pi$
$684$		0			0
$685$	4.43070	+	4.00772i	0.169288	+	0.153127i
$686$	6.00000	+	3.46410i	0.229081	+	0.132260i
$687$	19.3723	+	11.1846i	0.739099	+	0.426719i
$688$	4.55842	−	7.89542i	0.173788	−	0.301010i
$689$			0.349857i			0.0133285i
$690$	11.4891	+	10.3923i	0.437384	+	0.395628i
$691$	−6.74456	+	11.6819i	−0.256575	+	0.444401i	−0.965322	−	0.261061i	$-0.915927\pi$
$691$	−6.74456	+	11.6819i	−0.256575	+	0.444401i	0.708747	+	0.705463i	$0.249261\pi$
$692$		−	12.1793i		−	0.462986i
$693$		0			0
$694$	1.37228	−	2.37686i	0.0520911	−	0.0902244i
$695$	12.8614	+	39.8921i	0.487861	+	1.51319i
$696$	9.74456	+	16.8781i	0.369367	+	0.639762i
$697$	7.88316			0.298596
$698$	−0.313859	−	0.543620i	−0.0118798	−	0.0205763i
$699$	−18.4891	−	32.0241i	−0.699323	−	1.21126i
$700$	7.11684	−	15.7908i	0.268991	−	0.596838i
$701$	32.7446	+	18.9051i	1.23675	+	0.714035i	0.968427	−	0.249295i	$-0.0801990\pi$
$701$	32.7446	+	18.9051i	1.23675	+	0.714035i	0.268318	+	0.963331i	$0.413532\pi$
$702$		−	0.349857i		−	0.0132045i
$703$		0			0
$704$		0			0
$705$	−27.8614	−	5.98844i	−1.04932	−	0.225538i
$706$	−12.1753	−	21.0882i	−0.458222	−	0.793664i
$707$	−4.11684	+	2.37686i	−0.154830	+	0.0893911i
$708$	−15.1168	−	26.1831i	−0.568126	−	0.984023i
$709$			22.0742i			0.829015i	0.910046	+	0.414508i	$0.136046\pi$
$709$			22.0742i			0.829015i	−0.910046	+	0.414508i	$0.863954\pi$
$710$	−4.11684	+	4.55134i	−0.154502	+	0.170809i
$711$			27.7128i			1.03931i
$712$	−8.31386	−	4.80001i	−0.311575	−	0.179888i
$713$			30.2921i			1.13445i
$714$	12.0000			0.449089
$715$		0			0
$716$	17.4891	−	10.0974i	0.653599	−	0.377356i
$717$	24.7446			0.924103
$718$	5.18614	−	8.98266i	0.193545	−	0.335230i
$719$	−19.6753	+	34.0786i	−0.733764	+	1.27092i	0.221500	+	0.975160i	$0.428905\pi$
$719$	−19.6753	+	34.0786i	−0.733764	+	1.27092i	−0.955264	+	0.295755i	$0.904429\pi$
$720$	−7.37228	−	1.58457i	−0.274749	−	0.0590536i
$721$	−46.4674	+	26.8280i	−1.73054	+	0.999125i
$722$	−9.50000	−	16.4545i	−0.353553	−	0.612372i
$723$	26.2337	−	45.4381i	0.975641	−	1.68986i
$724$	2.43070	−	4.21010i	0.0903364	−	0.156467i
$725$	−38.4090	+	3.86025i	−1.42647	+	0.143366i
$726$			27.7677i			1.03056i
$727$	4.00000	+	6.92820i	0.148352	+	0.256953i	0.930618	−	0.365991i	$-0.119270\pi$
$727$	4.00000	+	6.92820i	0.148352	+	0.256953i	−0.782267	+	0.622944i	$0.785937\pi$
$728$	−1.11684	−	0.644810i	−0.0413930	−	0.0238983i
$729$	33.2337			1.23088
$730$	14.7446	−	4.75372i	0.545721	−	0.175943i
$731$	−6.25544	+	10.8347i	−0.231366	+	0.400737i
$732$	6.00000			0.221766
$733$	−2.23369	+	1.28962i	−0.0825031	+	0.0476332i	−0.540684	−	0.841226i	$-0.681835\pi$
$733$	−2.23369	+	1.28962i	−0.0825031	+	0.0476332i	0.458181	+	0.888859i	$0.348501\pi$
$734$		−	22.0742i		−	0.814775i
$735$	−20.9307	−	18.9325i	−0.772041	−	0.698337i
$736$	−1.37228	−	2.37686i	−0.0505830	−	0.0876123i
$737$		0			0
$738$	−9.68614	+	16.7769i	−0.356552	+	0.617566i
$739$	−20.9783			−0.771697			−0.385849	−	0.922562i	$-0.626091\pi$
$739$	−20.9783			−0.771697			−0.385849	+	0.922562i	$0.626091\pi$
$740$	3.94158	−	13.0178i	0.144895	−	0.478545i
$741$		0			0
$742$	1.62772	−	2.81929i	0.0597554	−	0.103499i
$743$	−24.6060	+	14.2063i	−0.902705	+	0.521177i	−0.878077	−	0.478519i	$-0.841174\pi$
$743$	−24.6060	+	14.2063i	−0.902705	+	0.521177i	−0.0246285	+	0.999697i	$0.507840\pi$
$744$	−13.9307	−	24.1287i	−0.510724	−	0.884601i
$745$	15.9416	−	17.6241i	0.584054	−	0.645696i
$746$		−	12.1244i		−	0.443904i
$747$	−39.6060	+	22.8665i	−1.44911	+	0.836642i
$748$		0			0
$749$	−6.60597	+	11.4419i	−0.241377	+	0.418077i
$750$	16.7446	−	22.7190i	0.611425	−	0.829582i
$751$	−19.3505			−0.706111			−0.353055	−	0.935602i	$-0.614857\pi$
$751$	−19.3505			−0.706111			−0.353055	+	0.935602i	$0.614857\pi$
$752$	4.37228	+	2.52434i	0.159441	+	0.0920531i
$753$	27.4891	+	47.6126i	1.00176	+	1.73510i
$754$			2.87419i			0.104672i
$755$	39.0475	+	8.39275i	1.42109	+	0.305444i
$756$	−1.62772	+	2.81929i	−0.0591996	+	0.102537i
$757$	−13.6168	+	23.5851i	−0.494913	+	0.857214i	−0.999983	−	0.00586448i	$-0.998133\pi$
$757$	−13.6168	+	23.5851i	−0.494913	+	0.857214i	0.505070	+	0.863078i	$0.331467\pi$
$758$	−5.37228	−	9.30506i	−0.195130	−	0.337975i
$759$		0			0
$760$		0			0
$761$	−24.1753	+	41.8728i	−0.876353	+	1.51789i	−0.0210379	+	0.999779i	$0.506697\pi$
$761$	−24.1753	+	41.8728i	−0.876353	+	1.51789i	−0.855315	+	0.518109i	$0.826636\pi$
$762$	21.8614	−	37.8651i	0.791955	−	1.37171i
$763$	8.23369			0.298080
$764$	−21.3030	+	12.2993i	−0.770715	+	0.444972i
$765$	10.1168	+	2.17448i	0.365775	+	0.0786185i
$766$	−12.5109			−0.452036
$767$		−	4.45877i		−	0.160997i
$768$	2.18614	+	1.26217i	0.0788856	+	0.0455446i
$769$			39.7995i			1.43521i	0.696452	+	0.717603i	$0.254761\pi$
$769$			39.7995i			1.43521i	−0.696452	+	0.717603i	$0.745239\pi$
$770$		0			0
$771$		−	2.17448i		−	0.0783120i
$772$	3.31386	+	5.73977i	0.119268	+	0.206579i
$773$	6.89403	−	3.98027i	0.247961	−	0.143160i	−0.370869	−	0.928685i	$-0.620940\pi$
$773$	6.89403	−	3.98027i	0.247961	−	0.143160i	0.618830	+	0.785525i	$0.287607\pi$
$774$	−15.3723	−	26.6256i	−0.552545	−	0.957036i
$775$	54.9090	−	5.51856i	1.97239	−	0.198232i
$776$	−12.1168			−0.434969
$777$	−43.7228	−	30.2921i	−1.56855	−	1.08672i
$778$			8.71516i			0.312454i
$779$		0			0
$780$	−1.55842	−	1.40965i	−0.0558005	−	0.0504734i
$781$		0			0
$782$	1.88316	+	3.26172i	0.0673415	+	0.116639i
$783$	7.25544			0.259288
$784$	2.50000	+	4.33013i	0.0892857	+	0.154647i
$785$	−13.8030	+	4.45015i	−0.492650	+	0.158833i
$786$	8.37228	−	14.5012i	0.298629	−	0.517241i
$787$		−	20.5446i		−	0.732334i	−0.930549	−	0.366167i	$-0.880670\pi$
$787$		−	20.5446i		−	0.732334i	0.930549	−	0.366167i	$-0.119330\pi$
$788$			7.07568i			0.252061i
$789$	−4.00000	+	6.92820i	−0.142404	+	0.246651i
$790$	13.6277	+	12.3267i	0.484852	+	0.438566i
$791$			70.0916i			2.49217i
$792$		0			0
$793$	0.766312	+	0.442430i	0.0272125	+	0.0157112i
$794$	14.6168	+	8.43904i	0.518732	+	0.299490i
$795$	3.55842	−	3.93398i	0.126204	−	0.139524i
$796$	7.67527	−	4.43132i	0.272043	−	0.157064i
$797$	−3.81386	+	6.60580i	−0.135094	+	0.233989i	−0.925633	−	0.378422i	$-0.876467\pi$
$797$	−3.81386	+	6.60580i	−0.135094	+	0.233989i	0.790539	+	0.612411i	$0.209800\pi$
$798$		0			0
$799$	−6.00000	−	3.46410i	−0.212265	−	0.122551i
$800$	−4.05842	+	2.92048i	−0.143487	+	0.103255i
$801$	−28.0367	+	16.1870i	−0.990627	+	0.571939i
$802$	−11.4891	−	6.63325i	−0.405695	−	0.234228i
$803$		0			0
$804$	−20.7446			−0.731604
$805$	4.46738	−	20.7846i	0.157454	−	0.732561i
$806$		−	4.10891i		−	0.144730i
$807$	51.3505	−	29.6472i	1.80762	−	1.04363i
$808$	1.37228			0.0482767
$809$	−16.0693	+	9.27761i	−0.564966	+	0.326183i	−0.755136	−	0.655568i	$-0.772429\pi$
$809$	−16.0693	+	9.27761i	−0.564966	+	0.326183i	0.190170	+	0.981751i	$0.439096\pi$
$810$	11.6168	−	12.8429i	0.408174	−	0.451254i
$811$	−5.11684	−	8.86263i	−0.179677	−	0.311209i	0.762093	−	0.647467i	$-0.224172\pi$
$811$	−5.11684	−	8.86263i	−0.179677	−	0.311209i	−0.941770	+	0.336258i	$0.890838\pi$
$812$	13.3723	−	23.1615i	0.469275	−	0.812808i
$813$		−	46.3778i		−	1.62654i
$814$		0			0
$815$	−11.7446	−	36.4280i	−0.411394	−	1.27602i
$816$	−3.00000	−	1.73205i	−0.105021	−	0.0606339i
$817$		0			0
$818$	−25.5000	+	14.7224i	−0.891587	+	0.514758i
$819$	−3.76631	+	2.17448i	−0.131606	+	0.0759825i
$820$	3.94158	+	12.2255i	0.137646	+	0.426935i
$821$	16.1168	+	27.9152i	0.562482	+	0.974247i	0.997279	+	0.0737186i	$0.0234867\pi$
$821$	16.1168	+	27.9152i	0.562482	+	0.974247i	−0.434797	+	0.900528i	$0.643180\pi$
$822$	−6.74456			−0.235244
$823$	−4.11684	−	2.37686i	−0.143504	−	0.0828522i	0.426529	−	0.904474i	$-0.359736\pi$
$823$	−4.11684	−	2.37686i	−0.143504	−	0.0828522i	−0.570033	+	0.821622i	$0.693070\pi$
$824$	15.4891			0.539589
$825$		0			0
$826$	−20.7446	+	35.9306i	−0.721796	+	1.25019i
$827$	14.2337	+	24.6535i	0.494954	+	0.857285i	0.999983	−	0.00581705i	$-0.00185164\pi$
$827$	14.2337	+	24.6535i	0.494954	+	0.857285i	−0.505029	+	0.863102i	$0.668518\pi$
$828$	−9.25544			−0.321649
$829$	−2.23369	−	1.28962i	−0.0775792	−	0.0447904i	0.460709	−	0.887551i	$-0.347595\pi$
$829$	−2.23369	−	1.28962i	−0.0775792	−	0.0447904i	−0.538288	+	0.842761i	$0.680929\pi$
$830$	−6.37228	+	29.6472i	−0.221185	+	1.02907i
$831$	15.3030	+	8.83518i	0.530855	+	0.306489i
$832$	0.186141	+	0.322405i	0.00645327	+	0.0111774i
$833$	−3.43070	−	5.94215i	−0.118867	−	0.205883i
$834$	−40.9783	−	23.6588i	−1.41896	−	0.819237i
$835$	12.0000	+	2.57924i	0.415277	+	0.0892583i
$836$		0			0
$837$	−10.3723			−0.358518
$838$	8.48913	+	14.7036i	0.293252	+	0.507927i
$839$	27.3030	−	47.2902i	0.942604	−	1.63264i	0.182124	−	0.983276i	$-0.441703\pi$
$839$	27.3030	−	47.2902i	0.942604	−	1.63264i	0.760479	−	0.649362i	$-0.224964\pi$
$840$	6.00000	+	18.6101i	0.207020	+	0.642110i
$841$	−30.6060			−1.05538
$842$	−9.17527	−	5.29734i	−0.316201	−	0.182558i
$843$	−17.8614			−0.615180
$844$	7.74456	+	13.4140i	0.266579	+	0.461728i
$845$	8.82473	+	27.3716i	0.303580	+	0.941611i
$846$	14.7446	−	8.51278i	0.506929	−	0.292675i
$847$	33.0000	−	19.0526i	1.13389	−	0.654654i
$848$	−0.813859	+	0.469882i	−0.0279480	+	0.0161358i
$849$	6.30298	+	3.63903i	0.216318	+	0.124891i
$850$	5.56930	−	4.00772i	0.191025	−	0.137464i
$851$	1.37228	−	16.6380i	0.0470412	−	0.570344i
$852$		−	6.92820i		−	0.237356i
$853$	0.616844	−	1.06841i	0.0211203	−	0.0365815i	−0.855272	−	0.518179i	$-0.826610\pi$
$853$	0.616844	−	1.06841i	0.0211203	−	0.0365815i	0.876392	+	0.481598i	$0.159943\pi$
$854$	−4.11684	−	7.13058i	−0.140876	−	0.244004i
$855$		0			0
$856$	3.30298	−	1.90698i	0.112894	−	0.0651792i
$857$	18.8614			0.644293			0.322147	−	0.946690i	$-0.395596\pi$
$857$	18.8614			0.644293			0.322147	+	0.946690i	$0.395596\pi$
$858$		0			0
$859$		−	3.46410i		−	0.118194i	−0.998252	−	0.0590968i	$-0.981178\pi$
$859$		−	3.46410i		−	0.118194i	0.998252	−	0.0590968i	$-0.0188221\pi$
$860$	−19.9307	−	4.28384i	−0.679631	−	0.146078i
$861$	50.2337			1.71196
$862$			31.2318i			1.06376i
$863$	6.60597	+	3.81396i	0.224870	+	0.129829i	0.608203	−	0.793781i	$-0.291891\pi$
$863$	6.60597	+	3.81396i	0.224870	+	0.129829i	−0.383333	+	0.923610i	$0.625224\pi$
$864$	0.813859	−	0.469882i	0.0276881	−	0.0159857i
$865$	−25.9198	+	8.35668i	−0.881301	+	0.284136i
$866$	18.1753	+	10.4935i	0.617621	+	0.356583i
$867$	−33.0475	−	19.0800i	−1.12235	−	0.647991i
$868$	−19.1168	+	33.1113i	−0.648868	+	1.12387i
$869$		0			0
$870$	29.2337	−	32.3191i	0.991115	−	1.09572i
$871$	−2.64947	−	1.52967i	−0.0897738	−	0.0518309i
$872$	−2.05842	−	1.18843i	−0.0697070	−	0.0402453i
$873$	−20.4307	+	35.3870i	−0.691475	+	1.19767i
$874$		0			0
$875$	−38.4891	−	4.31129i	−1.30117	−	0.145748i
$876$	−8.74456	+	15.1460i	−0.295451	+	0.511737i
$877$			15.9932i			0.540053i	0.962853	+	0.270026i	$0.0870324\pi$
$877$			15.9932i			0.540053i	−0.962853	+	0.270026i	$0.912968\pi$
$878$		−	16.6757i		−	0.562778i
$879$	36.4198	−	63.0810i	1.22841	−	2.12767i
$880$		0			0
$881$	−8.05842	−	13.9576i	−0.271495	−	0.470243i	0.697750	−	0.716342i	$-0.254185\pi$
$881$	−8.05842	−	13.9576i	−0.271495	−	0.470243i	−0.969245	+	0.246098i	$0.920851\pi$
$882$	16.8614			0.567753
$883$	29.6753	+	51.3991i	0.998652	+	1.72972i	0.544274	+	0.838907i	$0.316805\pi$
$883$	29.6753	+	51.3991i	0.998652	+	1.72972i	0.454378	+	0.890809i	$0.349862\pi$
$884$	−0.255437	−	0.442430i	−0.00859129	−	0.0148805i
$885$	−45.3505	+	50.1369i	−1.52444	+	1.68533i
$886$	24.8139	+	14.3263i	0.833638	+	0.481301i
$887$			21.7793i			0.731277i	0.930757	+	0.365638i	$0.119149\pi$
$887$			21.7793i			0.731277i	−0.930757	+	0.365638i	$0.880851\pi$
$888$	6.55842	+	13.8839i	0.220086	+	0.465912i
$889$	−60.0000			−2.01234
$890$	−4.51087	+	20.9870i	−0.151205	+	0.703485i
$891$		0			0
$892$	−16.1168	+	9.30506i	−0.539632	+	0.311557i
$893$		0			0
$894$			26.8280i			0.897261i
$895$	−33.4891	−	30.2921i	−1.11942	−	1.01255i
$896$		−	3.46410i		−	0.115728i
$897$	−2.23369	−	1.28962i	−0.0745807	−	0.0430592i
$898$			6.57835i			0.219522i
$899$	85.2119			2.84198
$900$	1.68614	+	16.7769i	0.0562047	+	0.559230i
$901$	1.11684	−	0.644810i	0.0372075	−	0.0214817i
$902$		0			0
$903$	−39.8614	+	69.0420i	−1.32650	+	2.29757i
$904$	10.1168	−	17.5229i	0.336481	−	0.582803i
$905$	−10.6277	−	2.28429i	−0.353277	−	0.0759323i
$906$	−39.0475	+	22.5441i	−1.29727	+	0.748978i
$907$	13.2554	+	22.9591i	0.440140	+	0.762344i	0.997699	−	0.0677926i	$-0.0215956\pi$
$907$	13.2554	+	22.9591i	0.440140	+	0.762344i	−0.557560	+	0.830137i	$0.688262\pi$
$908$	5.18614	−	8.98266i	0.172108	−	0.298100i
$909$	2.31386	−	4.00772i	0.0767459	−	0.132928i
$910$	−0.605969	+	2.81929i	−0.0200877	+	0.0934586i
$911$		−	49.2520i		−	1.63179i	−0.578198	−	0.815896i	$-0.696244\pi$
$911$		−	49.2520i		−	1.63179i	0.578198	−	0.815896i	$-0.303756\pi$
$912$		0			0
$913$		0			0
$914$	19.6060			0.648508
$915$	−4.11684	−	12.7692i	−0.136099	−	0.422136i
$916$	−4.43070	+	7.67420i	−0.146395	+	0.253563i
$917$	−22.9783			−0.758809
$918$	−1.11684	+	0.644810i	−0.0368613	+	0.0212819i
$919$		−	3.46410i		−	0.114270i	−0.998366	−	0.0571351i	$-0.981803\pi$
$919$		−	3.46410i		−	0.114270i	0.998366	−	0.0571351i	$-0.0181966\pi$
$920$	−4.11684	+	4.55134i	−0.135728	+	0.150053i
$921$	−25.4198	−	44.0284i	−0.837612	−	1.45079i
$922$	−27.8614	+	16.0858i	−0.917567	+	0.529757i
$923$	0.510875	−	0.884861i	0.0168156	−	0.0291256i
$924$		0			0
$925$	−30.4090	+	0.543620i	−0.999840	+	0.0178741i
$926$	4.51087			0.148237
$927$	26.1168	−	45.2357i	0.857790	−	1.48574i
$928$	−6.68614	+	3.86025i	−0.219483	+	0.126719i
$929$	−18.9891	−	32.8901i	−0.623013	−	1.07909i	−0.988922	−	0.148439i	$-0.952575\pi$
$929$	−18.9891	−	32.8901i	−0.623013	−	1.07909i	0.365909	−	0.930651i	$-0.380758\pi$
$930$	−41.7921	+	46.2029i	−1.37042	+	1.51505i
$931$		0			0
$932$	12.6861	−	7.32435i	0.415548	−	0.239917i
$933$	−47.8614			−1.56691
$934$	11.1861	−	19.3750i	0.366022	−	0.633968i
$935$		0			0
$936$	1.25544			0.0410353
$937$	−42.9416	−	24.7923i	−1.40284	−	0.809930i	−0.408157	−	0.912912i	$-0.633828\pi$
$937$	−42.9416	−	24.7923i	−1.40284	−	0.809930i	−0.994683	+	0.102982i	$0.967162\pi$
$938$	14.2337	+	24.6535i	0.464746	+	0.804964i
$939$		−	71.5663i		−	2.33548i
$940$	2.37228	−	11.0371i	0.0773753	−	0.359991i
$941$	6.43070	−	11.1383i	0.209635	−	0.363098i	−0.741965	−	0.670439i	$-0.766106\pi$
$941$	6.43070	−	11.1383i	0.209635	−	0.363098i	0.951600	+	0.307341i	$0.0994391\pi$
$942$	8.18614	−	14.1788i	0.266719	−	0.461971i
$943$	7.88316	+	13.6540i	0.256711	+	0.444636i
$944$	10.3723	−	5.98844i	0.337589	−	0.194907i
$945$	7.11684	+	1.52967i	0.231511	+	0.0497602i
$946$		0			0
$947$	−19.9307	+	34.5210i	−0.647661	+	1.12178i	0.336019	+	0.941855i	$0.390919\pi$
$947$	−19.9307	+	34.5210i	−0.647661	+	1.12178i	−0.983680	+	0.179926i	$0.942414\pi$
$948$	−20.7446			−0.673752
$949$	−2.23369	+	1.28962i	−0.0725086	+	0.0418628i
$950$		0			0
$951$	33.1168			1.07389
$952$			4.75372i			0.154069i
$953$	11.4891	+	6.63325i	0.372169	+	0.214872i	0.674406	−	0.738361i	$-0.264400\pi$
$953$	11.4891	+	6.63325i	0.372169	+	0.214872i	−0.302236	+	0.953233i	$0.597733\pi$
$954$			3.16915i			0.102605i
$955$	40.7921	+	36.8979i	1.32000	+	1.19399i
$956$			9.80240i			0.317032i
$957$		0			0
$958$	−31.4198	+	18.1402i	−1.01513	+	0.586085i
$959$	4.62772	+	8.01544i	0.149437	+	0.258832i
$960$	1.18614	−	5.51856i	0.0382825	−	0.178111i
$961$	−90.8179			−2.92961
$962$	−0.186141	+	2.25684i	−0.00600142	+	0.0727633i
$963$		−	12.8617i		−	0.414464i
$964$	18.0000	+	10.3923i	0.579741	+	0.334714i
$965$	9.94158	−	10.9908i	0.320031	−	0.353807i
$966$	12.0000	+	20.7846i	0.386094	+	0.668734i
$967$	17.1168	+	29.6472i	0.550441	+	0.953391i	0.998243	+	0.0592584i	$0.0188736\pi$
$967$	17.1168	+	29.6472i	0.550441	+	0.953391i	−0.447802	+	0.894133i	$0.647793\pi$
$968$	−11.0000			−0.353553
$969$		0			0
$970$	8.31386	+	25.7870i	0.266942	+	0.827971i
$971$	8.48913	−	14.7036i	0.272429	−	0.471861i	−0.697054	−	0.717018i	$-0.745506\pi$
$971$	8.48913	−	14.7036i	0.272429	−	0.471861i	0.969483	+	0.245158i	$0.0788397\pi$
$972$			22.3692i			0.717492i
$973$			64.9331i			2.08166i
$974$	1.00000	−	1.73205i	0.0320421	−	0.0554985i
$975$	−1.93070	+	4.28384i	−0.0618320	+	0.137193i
$976$			2.37686i			0.0760815i
$977$	28.1168	−	48.6998i	0.899538	−	1.55804i	0.0714512	−	0.997444i	$-0.477237\pi$
$977$	28.1168	−	48.6998i	0.899538	−	1.55804i	0.828086	−	0.560601i	$-0.189430\pi$
$978$	37.4198	+	21.6043i	1.19655	+	0.690831i
$979$		0			0
$980$	7.50000	−	8.29156i	0.239579	−	0.264864i
$981$	−6.94158	+	4.00772i	−0.221628	+	0.127957i
$982$	9.86141	−	17.0805i	0.314690	−	0.545059i
$983$	−37.6277	−	21.7244i	−1.20014	−	0.692900i	−0.239552	−	0.970884i	$-0.577001\pi$
$983$	−37.6277	−	21.7244i	−1.20014	−	0.692900i	−0.960586	+	0.277984i	$0.910334\pi$
$984$	−12.5584	−	7.25061i	−0.400348	−	0.231141i
$985$	15.0584	−	4.85491i	0.479801	−	0.154690i
$986$	9.17527	−	5.29734i	0.292200	−	0.168702i
$987$	−38.2337	−	22.0742i	−1.21699	−	0.702630i
$988$		0			0
$989$	−25.0217			−0.795645
$990$		0			0
$991$		−	6.28339i		−	0.199599i	−0.995008	−	0.0997993i	$-0.968180\pi$
$991$		−	6.28339i		−	0.199599i	0.995008	−	0.0997993i	$-0.0318201\pi$
$992$	9.55842	−	5.51856i	0.303480	−	0.175214i
$993$	69.9565			2.22000
$994$	−8.23369	+	4.75372i	−0.261157	+	0.150779i
$995$	−14.6970	−	13.2940i	−0.465927	−	0.421447i
$996$	−17.1168	−	29.6472i	−0.542368	−	0.939409i
$997$	16.5584	−	28.6800i	0.524410	−	0.908306i	−0.475186	−	0.879886i	$-0.657619\pi$
$997$	16.5584	−	28.6800i	0.524410	−	0.908306i	0.999596	−	0.0284200i	$-0.00904759\pi$
$998$			13.8564i			0.438617i
$999$	5.69702	+	0.469882i	0.180246	+	0.0148664i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.m.a.249.1	yes	4
5.4	even	2		370.2.m.b.249.2	yes	4
37.11	even	6		370.2.m.b.159.2	yes	4
185.159	even	6	inner	370.2.m.a.159.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.m.a.159.1	✓	4	185.159	even	6	inner
370.2.m.a.249.1	yes	4	1.1	even	1	trivial
370.2.m.b.159.2	yes	4	37.11	even	6
370.2.m.b.249.2	yes	4	5.4	even	2

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-2.18614 + 1.26217i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 1.65831i) q^{5} -2.52434i q^{6} +(-3.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(1.68614 - 2.92048i) q^{9} +(-0.686141 - 2.12819i) q^{10} +(2.18614 + 1.26217i) q^{12} +(0.186141 + 0.322405i) q^{13} -3.46410i q^{14} +(1.18614 - 5.51856i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.686141 - 1.18843i) q^{17} +(1.68614 + 2.92048i) q^{18} +(2.18614 + 0.469882i) q^{20} +(4.37228 - 7.57301i) q^{21} +2.74456 q^{23} +(-2.18614 + 1.26217i) q^{24} +(-0.500000 - 4.97494i) q^{25} -0.372281 q^{26} +0.939764i q^{27} +(3.00000 + 1.73205i) q^{28} -7.72049i q^{29} +(4.18614 + 3.78651i) q^{30} +11.0371i q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.686141 + 1.18843i) q^{34} +(1.62772 - 7.57301i) q^{35} -3.37228 q^{36} +(0.500000 - 6.06218i) q^{37} +(-0.813859 - 0.469882i) q^{39} +(-1.50000 + 1.65831i) q^{40} +(2.87228 + 4.97494i) q^{41} +(4.37228 + 7.57301i) q^{42} -9.11684 q^{43} +(2.31386 + 7.17687i) q^{45} +(-1.37228 + 2.37686i) q^{46} -5.04868i q^{47} -2.52434i q^{48} +(2.50000 - 4.33013i) q^{49} +(4.55842 + 2.05446i) q^{50} +3.46410i q^{51} +(0.186141 - 0.322405i) q^{52} +(0.813859 + 0.469882i) q^{53} +(-0.813859 - 0.469882i) q^{54} +(-3.00000 + 1.73205i) q^{56} +(6.68614 + 3.86025i) q^{58} +(-10.3723 - 5.98844i) q^{59} +(-5.37228 + 1.73205i) q^{60} +(2.05842 - 1.18843i) q^{61} +(-9.55842 - 5.51856i) q^{62} +11.6819i q^{63} +1.00000 q^{64} +(-0.813859 - 0.174928i) q^{65} +(-7.11684 + 4.10891i) q^{67} -1.37228 q^{68} +(-6.00000 + 3.46410i) q^{69} +(5.74456 + 5.19615i) q^{70} +(-1.37228 - 2.37686i) q^{71} +(1.68614 - 2.92048i) q^{72} +6.92820i q^{73} +(5.00000 + 3.46410i) q^{74} +(7.37228 + 10.2448i) q^{75} +(0.813859 - 0.469882i) q^{78} +(-7.11684 + 4.10891i) q^{79} +(-0.686141 - 2.12819i) q^{80} +(3.87228 + 6.70699i) q^{81} -5.74456 q^{82} +(-11.7446 - 6.78073i) q^{83} -8.74456 q^{84} +(0.941578 + 2.92048i) q^{85} +(4.55842 - 7.89542i) q^{86} +(9.74456 + 16.8781i) q^{87} +(-8.31386 - 4.80001i) q^{89} +(-7.37228 - 1.58457i) q^{90} +(-1.11684 - 0.644810i) q^{91} +(-1.37228 - 2.37686i) q^{92} +(-13.9307 - 24.1287i) q^{93} +(4.37228 + 2.52434i) q^{94} +(2.18614 + 1.26217i) q^{96} -12.1168 q^{97} +(2.50000 + 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 6 q^{5} - 12 q^{7} + 4 q^{8} + q^{9} + 3 q^{10} + 3 q^{12} - 5 q^{13} - q^{15} - 2 q^{16} - 3 q^{17} + q^{18} + 3 q^{20} + 6 q^{21} - 12 q^{23} - 3 q^{24} - 2 q^{25}+ \cdots + 10 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 - 6 * q^5 - 12 * q^7 + 4 * q^8 + q^9 + 3 * q^10 + 3 * q^12 - 5 * q^13 - q^15 - 2 * q^16 - 3 * q^17 + q^18 + 3 * q^20 + 6 * q^21 - 12 * q^23 - 3 * q^24 - 2 * q^25 + 10 * q^26 + 12 * q^28 + 11 * q^30 - 2 * q^32 - 3 * q^34 + 18 * q^35 - 2 * q^36 + 2 * q^37 - 9 * q^39 - 6 * q^40 + 6 * q^42 - 2 * q^43 + 15 * q^45 + 6 * q^46 + 10 * q^49 + q^50 - 5 * q^52 + 9 * q^53 - 9 * q^54 - 12 * q^56 + 21 * q^58 - 30 * q^59 - 10 * q^60 - 9 * q^61 - 21 * q^62 + 4 * q^64 - 9 * q^65 + 6 * q^67 + 6 * q^68 - 24 * q^69 + 6 * q^71 + q^72 + 20 * q^74 + 18 * q^75 + 9 * q^78 + 6 * q^79 + 3 * q^80 + 4 * q^81 - 24 * q^83 - 12 * q^84 + 21 * q^85 + q^86 + 16 * q^87 - 39 * q^89 - 18 * q^90 + 30 * q^91 + 6 * q^92 - 27 * q^93 + 6 * q^94 + 3 * q^96 - 14 * q^97 + 10 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more