LMFDB - Embedded newform 176.2.j.a.133.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [176,2,Mod(45,176)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(176, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("176.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 176 = 2^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	176.j (of order $4$, 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:	$1.40536707557$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			133.9
Character	$\chi$	$=$	176.133
Dual form			176.2.j.a.45.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.398671 - 1.35686i) q^{2} +(1.34498 - 1.34498i) q^{3} +(-1.68212 + 1.08188i) q^{4} +(2.40794 + 2.40794i) q^{5} +(-2.36114 - 1.28874i) q^{6} -4.88654i q^{7} +(2.13857 + 1.85109i) q^{8} -0.617917i q^{9} +O(q^{10})$	\(q+(-0.398671 - 1.35686i) q^{2} +(1.34498 - 1.34498i) q^{3} +(-1.68212 + 1.08188i) q^{4} +(2.40794 + 2.40794i) q^{5} +(-2.36114 - 1.28874i) q^{6} -4.88654i q^{7} +(2.13857 + 1.85109i) q^{8} -0.617917i q^{9} +(2.30726 - 4.22721i) q^{10} +(-0.707107 - 0.707107i) q^{11} +(-0.807315 + 3.71751i) q^{12} +(-0.532694 + 0.532694i) q^{13} +(-6.63034 + 1.94812i) q^{14} +6.47725 q^{15} +(1.65908 - 3.63971i) q^{16} -1.53906 q^{17} +(-0.838425 + 0.246345i) q^{18} +(-5.98507 + 5.98507i) q^{19} +(-6.65556 - 1.44536i) q^{20} +(-6.57227 - 6.57227i) q^{21} +(-0.677540 + 1.24135i) q^{22} +0.294585i q^{23} +(5.36599 - 0.386652i) q^{24} +6.59638i q^{25} +(0.935159 + 0.510420i) q^{26} +(3.20384 + 3.20384i) q^{27} +(5.28664 + 8.21976i) q^{28} +(4.94569 - 4.94569i) q^{29} +(-2.58229 - 8.78870i) q^{30} -1.43981 q^{31} +(-5.59999 - 0.800091i) q^{32} -1.90208 q^{33} +(0.613578 + 2.08829i) q^{34} +(11.7665 - 11.7665i) q^{35} +(0.668511 + 1.03941i) q^{36} +(1.66532 + 1.66532i) q^{37} +(10.5070 + 5.73482i) q^{38} +1.43292i q^{39} +(0.692232 + 9.60687i) q^{40} +4.09275i q^{41} +(-6.29747 + 11.5378i) q^{42} +(4.95316 + 4.95316i) q^{43} +(1.95444 + 0.424438i) q^{44} +(1.48791 - 1.48791i) q^{45} +(0.399710 - 0.117442i) q^{46} -0.856661 q^{47} +(-2.66389 - 7.12673i) q^{48} -16.8783 q^{49} +(8.95035 - 2.62978i) q^{50} +(-2.07000 + 2.07000i) q^{51} +(0.319747 - 1.47237i) q^{52} +(-0.0858734 - 0.0858734i) q^{53} +(3.06988 - 5.62444i) q^{54} -3.40535i q^{55} +(9.04542 - 10.4502i) q^{56} +16.0995i q^{57} +(-8.68229 - 4.73889i) q^{58} +(-3.37953 - 3.37953i) q^{59} +(-10.8955 + 7.00759i) q^{60} +(0.868220 - 0.868220i) q^{61} +(0.574010 + 1.95362i) q^{62} -3.01948 q^{63} +(1.14694 + 7.91736i) q^{64} -2.56539 q^{65} +(0.758304 + 2.58085i) q^{66} +(-1.38054 + 1.38054i) q^{67} +(2.58889 - 1.66508i) q^{68} +(0.396210 + 0.396210i) q^{69} +(-20.6564 - 11.2745i) q^{70} +2.83422i q^{71} +(1.14382 - 1.32146i) q^{72} +5.62070i q^{73} +(1.59569 - 2.92351i) q^{74} +(8.87197 + 8.87197i) q^{75} +(3.59251 - 16.5427i) q^{76} +(-3.45530 + 3.45530i) q^{77} +(1.94427 - 0.571263i) q^{78} -10.1538 q^{79} +(12.7592 - 4.76924i) q^{80} +10.4719 q^{81} +(5.55327 - 1.63166i) q^{82} +(5.47789 - 5.47789i) q^{83} +(18.1658 + 3.94498i) q^{84} +(-3.70597 - 3.70597i) q^{85} +(4.74605 - 8.69541i) q^{86} -13.3037i q^{87} +(-0.203278 - 2.82111i) q^{88} -8.20417i q^{89} +(-2.61207 - 1.42570i) q^{90} +(2.60303 + 2.60303i) q^{91} +(-0.318705 - 0.495529i) q^{92} +(-1.93651 + 1.93651i) q^{93} +(0.341525 + 1.16237i) q^{94} -28.8234 q^{95} +(-8.60795 + 6.45574i) q^{96} -7.42322 q^{97} +(6.72887 + 22.9014i) q^{98} +(-0.436933 + 0.436933i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 12 q^{6} - 12 q^{8}+O(q^{10}) $ 40 * q - 12 * q^6 - 12 * q^8	$ 40 q - 12 q^{6} - 12 q^{8} - 4 q^{10} - 12 q^{12} + 8 q^{14} - 16 q^{15} - 8 q^{16} - 20 q^{18} - 16 q^{19} - 20 q^{20} + 28 q^{24} + 24 q^{27} + 20 q^{28} + 12 q^{30} + 24 q^{31} - 20 q^{32} - 40 q^{34} + 24 q^{35} + 20 q^{36} + 48 q^{38} - 8 q^{40} - 8 q^{44} - 52 q^{46} - 40 q^{47} - 40 q^{49} + 64 q^{50} - 24 q^{51} - 36 q^{52} + 32 q^{54} - 8 q^{56} + 40 q^{58} - 8 q^{59} + 12 q^{60} + 32 q^{61} - 24 q^{64} - 16 q^{65} - 20 q^{66} - 24 q^{67} + 4 q^{68} + 32 q^{69} - 8 q^{70} - 20 q^{72} - 56 q^{74} - 56 q^{75} + 4 q^{76} + 64 q^{78} + 32 q^{79} + 32 q^{80} - 40 q^{81} + 24 q^{82} + 40 q^{83} + 76 q^{84} - 32 q^{85} - 16 q^{86} + 20 q^{90} - 16 q^{91} + 12 q^{92} - 48 q^{93} + 16 q^{94} - 48 q^{95} + 36 q^{96} + 72 q^{98}+O(q^{100}) $ 40 * q - 12 * q^6 - 12 * q^8 - 4 * q^10 - 12 * q^12 + 8 * q^14 - 16 * q^15 - 8 * q^16 - 20 * q^18 - 16 * q^19 - 20 * q^20 + 28 * q^24 + 24 * q^27 + 20 * q^28 + 12 * q^30 + 24 * q^31 - 20 * q^32 - 40 * q^34 + 24 * q^35 + 20 * q^36 + 48 * q^38 - 8 * q^40 - 8 * q^44 - 52 * q^46 - 40 * q^47 - 40 * q^49 + 64 * q^50 - 24 * q^51 - 36 * q^52 + 32 * q^54 - 8 * q^56 + 40 * q^58 - 8 * q^59 + 12 * q^60 + 32 * q^61 - 24 * q^64 - 16 * q^65 - 20 * q^66 - 24 * q^67 + 4 * q^68 + 32 * q^69 - 8 * q^70 - 20 * q^72 - 56 * q^74 - 56 * q^75 + 4 * q^76 + 64 * q^78 + 32 * q^79 + 32 * q^80 - 40 * q^81 + 24 * q^82 + 40 * q^83 + 76 * q^84 - 32 * q^85 - 16 * q^86 + 20 * q^90 - 16 * q^91 + 12 * q^92 - 48 * q^93 + 16 * q^94 - 48 * q^95 + 36 * q^96 + 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/176\mathbb{Z}\right)^\times$.

$n$	$111$	$133$	$145$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−0.398671	−	1.35686i	−0.281903	−	0.959443i
$2$	−0.398671	−	1.35686i	−0.281903	−	0.959443i
$3$	1.34498	−	1.34498i	0.776522	−	0.776522i	−0.202716	−	0.979238i	$-0.564977\pi$
$3$	1.34498	−	1.34498i	0.776522	−	0.776522i	0.979238	+	0.202716i	$0.0649768\pi$
$4$	−1.68212	+	1.08188i	−0.841062	+	0.540939i
$5$	2.40794	+	2.40794i	1.07687	+	1.07687i	0.996789	+	0.0800763i	$0.0255164\pi$
$5$	2.40794	+	2.40794i	1.07687	+	1.07687i	0.0800763	+	0.996789i	$0.474484\pi$
$6$	−2.36114	−	1.28874i	−0.963932	−	0.526125i
$7$		−	4.88654i		−	1.84694i	−0.383673	−	0.923469i	$-0.625341\pi$
$7$		−	4.88654i		−	1.84694i	0.383673	−	0.923469i	$-0.374659\pi$
$8$	2.13857	+	1.85109i	0.756098	+	0.654459i
$9$		−	0.617917i		−	0.205972i
$10$	2.30726	−	4.22721i	0.729620	−	1.33676i
$11$	−0.707107	−	0.707107i	−0.213201	−	0.213201i
$11$	−0.707107	−	0.707107i	−0.213201	−	0.213201i
$12$	−0.807315	+	3.71751i	−0.233052	+	1.07315i
$13$	−0.532694	+	0.532694i	−0.147743	+	0.147743i	−0.777109	−	0.629366i	$-0.783315\pi$
$13$	−0.532694	+	0.532694i	−0.147743	+	0.147743i	0.629366	+	0.777109i	$0.283315\pi$
$14$	−6.63034	+	1.94812i	−1.77203	+	0.520657i
$15$	6.47725			1.67242
$16$	1.65908	−	3.63971i	0.414770	−	0.909926i
$17$	−1.53906			−0.373277			−0.186639	−	0.982429i	$-0.559759\pi$
$17$	−1.53906			−0.373277			−0.186639	+	0.982429i	$0.559759\pi$
$18$	−0.838425	+	0.246345i	−0.197619	+	0.0580642i
$19$	−5.98507	+	5.98507i	−1.37307	+	1.37307i	−0.517213	+	0.855857i	$0.673030\pi$
$19$	−5.98507	+	5.98507i	−1.37307	+	1.37307i	−0.855857	+	0.517213i	$0.826970\pi$
$20$	−6.65556	−	1.44536i	−1.48823	−	0.323192i
$21$	−6.57227	−	6.57227i	−1.43419	−	1.43419i
$22$	−0.677540	+	1.24135i	−0.144452	+	0.264656i
$23$			0.294585i			0.0614252i	0.999528	+	0.0307126i	$0.00977767\pi$
$23$			0.294585i			0.0614252i	−0.999528	+	0.0307126i	$0.990222\pi$
$24$	5.36599	−	0.386652i	1.09533	−	0.0789249i
$25$			6.59638i			1.31928i
$26$	0.935159	+	0.510420i	0.183400	+	0.100102i
$27$	3.20384	+	3.20384i	0.616580	+	0.616580i
$28$	5.28664	+	8.21976i	0.999081	+	1.55339i
$29$	4.94569	−	4.94569i	0.918391	−	0.918391i	−0.0785216	−	0.996912i	$-0.525020\pi$
$29$	4.94569	−	4.94569i	0.918391	−	0.918391i	0.996912	+	0.0785216i	$0.0250200\pi$
$30$	−2.58229	−	8.78870i	−0.471459	−	1.60459i
$31$	−1.43981			−0.258598			−0.129299	−	0.991606i	$-0.541273\pi$
$31$	−1.43981			−0.258598			−0.129299	+	0.991606i	$0.541273\pi$
$32$	−5.59999	−	0.800091i	−0.989947	−	0.141437i
$33$	−1.90208			−0.331110
$34$	0.613578	+	2.08829i	0.105228	+	0.358138i
$35$	11.7665	−	11.7665i	1.98890	−	1.98890i
$36$	0.668511	+	1.03941i	0.111418	+	0.173235i
$37$	1.66532	+	1.66532i	0.273777	+	0.273777i	0.830619	−	0.556842i	$-0.187987\pi$
$37$	1.66532	+	1.66532i	0.273777	+	0.273777i	−0.556842	+	0.830619i	$0.687987\pi$
$38$	10.5070	+	5.73482i	1.70445	+	0.930310i
$39$			1.43292i			0.229451i
$40$	0.692232	+	9.60687i	0.109452	+	1.51898i
$41$			4.09275i			0.639179i	0.947556	+	0.319590i	$0.103545\pi$
$41$			4.09275i			0.639179i	−0.947556	+	0.319590i	$0.896455\pi$
$42$	−6.29747	+	11.5378i	−0.971720	+	1.78032i
$43$	4.95316	+	4.95316i	0.755350	+	0.755350i	0.975472	−	0.220122i	$-0.0706456\pi$
$43$	4.95316	+	4.95316i	0.755350	+	0.755350i	−0.220122	+	0.975472i	$0.570646\pi$
$44$	1.95444	+	0.424438i	0.294644	+	0.0639864i
$45$	1.48791	−	1.48791i	0.221804	−	0.221804i
$46$	0.399710	−	0.117442i	0.0589340	−	0.0173159i
$47$	−0.856661			−0.124957			−0.0624784	−	0.998046i	$-0.519900\pi$
$47$	−0.856661			−0.124957			−0.0624784	+	0.998046i	$0.519900\pi$
$48$	−2.66389	−	7.12673i	−0.384500	−	1.02866i
$49$	−16.8783			−2.41118
$50$	8.95035	−	2.62978i	1.26577	−	0.371908i
$51$	−2.07000	+	2.07000i	−0.289858	+	0.289858i
$52$	0.319747	−	1.47237i	0.0443409	−	0.204180i
$53$	−0.0858734	−	0.0858734i	−0.0117956	−	0.0117956i	0.701184	−	0.712980i	$-0.252655\pi$
$53$	−0.0858734	−	0.0858734i	−0.0117956	−	0.0117956i	−0.712980	+	0.701184i	$0.752655\pi$
$54$	3.06988	−	5.62444i	0.417758	−	0.765389i
$55$		−	3.40535i		−	0.459177i
$56$	9.04542	−	10.4502i	1.20874	−	1.39647i
$57$			16.0995i			2.13244i
$58$	−8.68229	−	4.73889i	−1.14004	−	0.622247i
$59$	−3.37953	−	3.37953i	−0.439978	−	0.439978i	0.452027	−	0.892004i	$-0.350701\pi$
$59$	−3.37953	−	3.37953i	−0.439978	−	0.439978i	−0.892004	+	0.452027i	$0.850701\pi$
$60$	−10.8955	+	7.00759i	−1.40661	+	0.904676i
$61$	0.868220	−	0.868220i	0.111164	−	0.111164i	−0.649337	−	0.760501i	$-0.724953\pi$
$61$	0.868220	−	0.868220i	0.111164	−	0.111164i	0.760501	+	0.649337i	$0.224953\pi$
$62$	0.574010	+	1.95362i	0.0728994	+	0.248110i
$63$	−3.01948			−0.380418
$64$	1.14694	+	7.91736i	0.143368	+	0.989670i
$65$	−2.56539			−0.318198
$66$	0.758304	+	2.58085i	0.0933408	+	0.317681i
$67$	−1.38054	+	1.38054i	−0.168660	+	0.168660i	−0.786390	−	0.617730i	$-0.788052\pi$
$67$	−1.38054	+	1.38054i	−0.168660	+	0.168660i	0.617730	+	0.786390i	$0.288052\pi$
$68$	2.58889	−	1.66508i	0.313949	−	0.201920i
$69$	0.396210	+	0.396210i	0.0476980	+	0.0476980i
$70$	−20.6564	−	11.2745i	−2.46892	−	1.34756i
$71$			2.83422i			0.336360i	0.985756	+	0.168180i	$0.0537890\pi$
$71$			2.83422i			0.336360i	−0.985756	+	0.168180i	$0.946211\pi$
$72$	1.14382	−	1.32146i	0.134800	−	0.155735i
$73$			5.62070i			0.657854i	0.944355	+	0.328927i	$0.106687\pi$
$73$			5.62070i			0.657854i	−0.944355	+	0.328927i	$0.893313\pi$
$74$	1.59569	−	2.92351i	0.185495	−	0.339852i
$75$	8.87197	+	8.87197i	1.02445	+	1.02445i
$76$	3.59251	−	16.5427i	0.412089	−	1.89758i
$77$	−3.45530	+	3.45530i	−0.393769	+	0.393769i
$78$	1.94427	−	0.571263i	0.220145	−	0.0646828i
$79$	−10.1538			−1.14240			−0.571198	−	0.820812i	$-0.693521\pi$
$79$	−10.1538			−1.14240			−0.571198	+	0.820812i	$0.693521\pi$
$80$	12.7592	−	4.76924i	1.42652	−	0.533217i
$81$	10.4719			1.16355
$82$	5.55327	−	1.63166i	0.613256	−	0.180186i
$83$	5.47789	−	5.47789i	0.601276	−	0.601276i	−0.339375	−	0.940651i	$-0.610216\pi$
$83$	5.47789	−	5.47789i	0.601276	−	0.601276i	0.940651	+	0.339375i	$0.110216\pi$
$84$	18.1658	+	3.94498i	1.98205	+	0.430432i
$85$	−3.70597	−	3.70597i	−0.401969	−	0.401969i
$86$	4.74605	−	8.69541i	0.511780	−	0.937650i
$87$		−	13.3037i		−	1.42630i
$88$	−0.203278	−	2.82111i	−0.0216695	−	0.300732i
$89$		−	8.20417i		−	0.869641i	−0.900517	−	0.434820i	$-0.856812\pi$
$89$		−	8.20417i		−	0.869641i	0.900517	−	0.434820i	$-0.143188\pi$
$90$	−2.61207	−	1.42570i	−0.275336	−	0.150281i
$91$	2.60303	+	2.60303i	0.272872	+	0.272872i
$92$	−0.318705	−	0.495529i	−0.0332273	−	0.0516624i
$93$	−1.93651	+	1.93651i	−0.200807	+	0.200807i
$94$	0.341525	+	1.16237i	0.0352257	+	0.119889i
$95$	−28.8234			−2.95722
$96$	−8.60795	+	6.45574i	−0.878545	+	0.658886i
$97$	−7.42322			−0.753714			−0.376857	−	0.926272i	$-0.622995\pi$
$97$	−7.42322			−0.753714			−0.376857	+	0.926272i	$0.622995\pi$
$98$	6.72887	+	22.9014i	0.679718	+	2.31339i
$99$	−0.436933	+	0.436933i	−0.0439135	+	0.0439135i
$100$	−7.13648	−	11.0959i	−0.713648	−	1.10959i
$101$	−6.39297	−	6.39297i	−0.636125	−	0.636125i	0.313473	−	0.949597i	$-0.398508\pi$
$101$	−6.39297	−	6.39297i	−0.636125	−	0.636125i	−0.949597	+	0.313473i	$0.898508\pi$
$102$	3.63394	+	1.98345i	0.359814	+	0.196390i
$103$		−	9.42991i		−	0.929157i	−0.885532	−	0.464578i	$-0.846206\pi$
$103$		−	9.42991i		−	0.929157i	0.885532	−	0.464578i	$-0.153794\pi$
$104$	−2.12526	+	0.153138i	−0.208399	+	0.0150164i
$105$		−	31.6513i		−	3.08885i
$106$	−0.0822827	+	0.150753i	−0.00799201	+	0.0146424i
$107$	2.34961	+	2.34961i	0.227145	+	0.227145i	0.811499	−	0.584354i	$-0.198652\pi$
$107$	2.34961	+	2.34961i	0.227145	+	0.227145i	−0.584354	+	0.811499i	$0.698652\pi$
$108$	−8.85543	−	1.92309i	−0.852114	−	0.185050i
$109$	9.17318	−	9.17318i	0.878631	−	0.878631i	−0.114762	−	0.993393i	$-0.536610\pi$
$109$	9.17318	−	9.17318i	0.878631	−	0.878631i	0.993393	+	0.114762i	$0.0366105\pi$
$110$	−4.62057	+	1.35761i	−0.440554	+	0.129443i
$111$	4.47963			0.425187
$112$	−17.7856	−	8.10716i	−1.68058	−	0.766054i
$113$	−2.88288			−0.271198			−0.135599	−	0.990764i	$-0.543296\pi$
$113$	−2.88288			−0.271198			−0.135599	+	0.990764i	$0.543296\pi$
$114$	21.8448	−	6.41842i	2.04595	−	0.601140i
$115$	−0.709344	+	0.709344i	−0.0661467	+	0.0661467i
$116$	−2.96863	+	13.6699i	−0.275630	+	1.26922i
$117$	0.329161	+	0.329161i	0.0304309	+	0.0304309i
$118$	−3.23822	+	5.93287i	−0.298103	+	0.546165i
$119$			7.52068i			0.689420i
$120$	13.8520	+	11.9900i	1.26451	+	1.09453i
$121$			1.00000i			0.0909091i
$122$	−1.52418	−	0.831916i	−0.137993	−	0.0753182i
$123$	5.50464	+	5.50464i	0.496337	+	0.496337i
$124$	2.42194	−	1.55770i	0.217497	−	0.139886i
$125$	−3.84400	+	3.84400i	−0.343818	+	0.343818i
$126$	1.20378	+	4.09700i	0.107241	+	0.364990i
$127$	−6.43582			−0.571087			−0.285544	−	0.958366i	$-0.592174\pi$
$127$	−6.43582			−0.571087			−0.285544	+	0.958366i	$0.592174\pi$
$128$	10.2855	−	4.71265i	0.909116	−	0.416544i
$129$	13.3238			1.17309
$130$	1.02275	+	3.48087i	0.0897008	+	0.305293i
$131$	−8.02413	+	8.02413i	−0.701072	+	0.701072i	−0.964641	−	0.263569i	$-0.915100\pi$
$131$	−8.02413	+	8.02413i	−0.701072	+	0.701072i	0.263569	+	0.964641i	$0.415100\pi$
$132$	3.19954	−	2.05782i	0.278484	−	0.179110i
$133$	29.2463	+	29.2463i	2.53597	+	2.53597i
$134$	2.42358	+	1.32282i	0.209365	+	0.114274i
$135$			15.4293i			1.32795i
$136$	−3.29138	−	2.84894i	−0.282234	−	0.244294i
$137$		−	10.5001i		−	0.897081i	−0.893762	−	0.448541i	$-0.851944\pi$
$137$		−	10.5001i		−	0.897081i	0.893762	−	0.448541i	$-0.148056\pi$
$138$	0.379643	−	0.695557i	0.0323173	−	0.0592098i
$139$	−14.1139	−	14.1139i	−1.19712	−	1.19712i	−0.975024	−	0.222100i	$-0.928709\pi$
$139$	−14.1139	−	14.1139i	−1.19712	−	1.19712i	−0.222100	−	0.975024i	$-0.571291\pi$
$140$	−7.06279	+	32.5227i	−0.596915	+	2.74867i
$141$	−1.15219	+	1.15219i	−0.0970317	+	0.0970317i
$142$	3.84564	−	1.12992i	0.322719	−	0.0948209i
$143$	0.753343			0.0629977
$144$	−2.24904	−	1.02517i	−0.187420	−	0.0854311i
$145$	23.8179			1.97797
$146$	7.62649	−	2.24081i	0.631173	−	0.185451i
$147$	−22.7008	+	22.7008i	−1.87233	+	1.87233i
$148$	−4.60295	−	0.999600i	−0.378360	−	0.0821666i
$149$	8.66331	+	8.66331i	0.709726	+	0.709726i	0.966477	−	0.256752i	$-0.0826522\pi$
$149$	8.66331	+	8.66331i	0.709726	+	0.709726i	−0.256752	+	0.966477i	$0.582652\pi$
$150$	8.50101	−	15.5750i	0.694104	−	1.27169i
$151$			8.43652i			0.686554i	0.939234	+	0.343277i	$0.111537\pi$
$151$			8.43652i			0.686554i	−0.939234	+	0.343277i	$0.888463\pi$
$152$	−23.8784	+	1.72058i	−1.93679	+	0.139557i
$153$			0.951012i			0.0768847i
$154$	6.06588	+	3.31083i	0.488803	+	0.266794i
$155$	−3.46698	−	3.46698i	−0.278475	−	0.278475i
$156$	−1.55024	−	2.41035i	−0.124119	−	0.192982i
$157$	0.353693	−	0.353693i	0.0282278	−	0.0282278i	−0.692852	−	0.721080i	$-0.743646\pi$
$157$	0.353693	−	0.353693i	0.0282278	−	0.0282278i	0.721080	+	0.692852i	$0.243646\pi$
$158$	4.04804	+	13.7773i	0.322045	+	1.09606i
$159$	−0.230995			−0.0183191
$160$	−11.5579	−	15.4110i	−0.913731	−	1.21835i
$161$	1.43950			0.113449
$162$	−4.17485	−	14.2089i	−0.328007	−	1.11636i
$163$	7.03184	−	7.03184i	0.550777	−	0.550777i	−0.375888	−	0.926665i	$-0.622662\pi$
$163$	7.03184	−	7.03184i	0.550777	−	0.550777i	0.926665	+	0.375888i	$0.122662\pi$
$164$	−4.42785	−	6.88450i	−0.345757	−	0.537589i
$165$	−4.58011	−	4.58011i	−0.356561	−	0.356561i
$166$	−9.61658	−	5.24884i	−0.746392	−	0.407389i
$167$			4.68704i			0.362694i	0.983419	+	0.181347i	$0.0580457\pi$
$167$			4.68704i			0.362694i	−0.983419	+	0.181347i	$0.941954\pi$
$168$	−1.88939	−	26.2211i	−0.145769	−	2.02300i
$169$			12.4325i			0.956344i
$170$	−3.55101	+	6.50593i	−0.272350	+	0.498982i
$171$	3.69828	+	3.69828i	0.282814	+	0.282814i
$172$	−13.6905	−	2.97311i	−1.04389	−	0.226698i
$173$	11.9586	−	11.9586i	0.909193	−	0.909193i	−0.0870143	−	0.996207i	$-0.527733\pi$
$173$	11.9586	−	11.9586i	0.909193	−	0.909193i	0.996207	+	0.0870143i	$0.0277326\pi$
$174$	−18.0512	+	5.30377i	−1.36845	+	0.402078i
$175$	32.2335			2.43662
$176$	−3.74681	+	1.40051i	−0.282426	+	0.105568i
$177$	−9.09078			−0.683305
$178$	−11.1319	+	3.27076i	−0.834371	+	0.245154i
$179$	14.7068	−	14.7068i	1.09924	−	1.09924i	0.104739	−	0.994500i	$-0.466599\pi$
$179$	14.7068	−	14.7068i	1.09924	−	1.09924i	0.994500	−	0.104739i	$-0.0334008\pi$
$180$	−0.893111	+	4.11258i	−0.0665685	+	0.306534i
$181$	−7.86290	−	7.86290i	−0.584445	−	0.584445i	0.351677	−	0.936121i	$-0.385612\pi$
$181$	−7.86290	−	7.86290i	−0.584445	−	0.584445i	−0.936121	+	0.351677i	$0.885612\pi$
$182$	2.49419	−	4.56969i	0.184881	−	0.338728i
$183$		−	2.33547i		−	0.172643i
$184$	−0.545303	+	0.629990i	−0.0402003	+	0.0464435i
$185$			8.01999i			0.589641i
$186$	3.39960	+	1.85554i	0.249271	+	0.136055i
$187$	1.08828	+	1.08828i	0.0795829	+	0.0795829i
$188$	1.44101	−	0.926803i	0.105096	−	0.0675940i
$189$	15.6557	−	15.6557i	1.13878	−	1.13878i
$190$	11.4911	+	39.1093i	0.833649	+	2.83729i
$191$	19.6689			1.42319			0.711596	−	0.702589i	$-0.247973\pi$
$191$	19.6689			1.42319			0.711596	+	0.702589i	$0.247973\pi$
$192$	12.1913	+	9.10604i	0.879828	+	0.657172i
$193$	−8.82705			−0.635385			−0.317692	−	0.948194i	$-0.602908\pi$
$193$	−8.82705			−0.635385			−0.317692	+	0.948194i	$0.602908\pi$
$194$	2.95942	+	10.0722i	0.212474	+	0.723145i
$195$	−3.45039	+	3.45039i	−0.247088	+	0.247088i
$196$	28.3913	−	18.2602i	2.02795	−	1.30430i
$197$	−15.7396	−	15.7396i	−1.12140	−	1.12140i	−0.991531	−	0.129869i	$-0.958544\pi$
$197$	−15.7396	−	15.7396i	−1.12140	−	1.12140i	−0.129869	−	0.991531i	$-0.541456\pi$
$198$	0.767049	+	0.418664i	0.0545118	+	0.0297531i
$199$		−	21.9510i		−	1.55606i	−0.628225	−	0.778032i	$-0.716218\pi$
$199$		−	21.9510i		−	1.55606i	0.628225	−	0.778032i	$-0.283782\pi$
$200$	−12.2105	+	14.1068i	−0.863412	+	0.997502i
$201$			3.71359i			0.261936i
$202$	−6.12566	+	11.2230i	−0.431000	+	0.789650i
$203$	−24.1673	−	24.1673i	−1.69621	−	1.69621i
$204$	1.24251	−	5.72148i	0.0869929	−	0.400584i
$205$	−9.85510	+	9.85510i	−0.688310	+	0.688310i
$206$	−12.7950	+	3.75943i	−0.891473	+	0.261932i
$207$	0.182029			0.0126519
$208$	1.05507	+	2.82263i	0.0731557	+	0.195714i
$209$	8.46417			0.585479
$210$	−42.9463	+	12.6185i	−2.96358	+	0.870756i
$211$	−5.76721	+	5.76721i	−0.397031	+	0.397031i	−0.877184	−	0.480154i	$-0.840581\pi$
$211$	−5.76721	+	5.76721i	−0.397031	+	0.397031i	0.480154	+	0.877184i	$0.340581\pi$
$212$	0.237354	+	0.0515451i	0.0163016	+	0.00354013i
$213$	3.81196	+	3.81196i	0.261191	+	0.261191i
$214$	2.25136	−	4.12480i	0.153900	−	0.281965i
$215$			23.8539i			1.62682i
$216$	0.921036	+	12.7822i	0.0626686	+	0.869721i
$217$			7.03569i			0.477614i
$218$	−16.1038	−	8.78962i	−1.09068	−	0.595308i
$219$	7.55971	+	7.55971i	0.510838	+	0.510838i
$220$	3.68417	+	5.72821i	0.248387	+	0.386196i
$221$	0.819848	−	0.819848i	0.0551489	−	0.0551489i
$222$	−1.78590	−	6.07821i	−0.119861	−	0.407943i
$223$	5.37001			0.359602			0.179801	−	0.983703i	$-0.442455\pi$
$223$	5.37001			0.359602			0.179801	+	0.983703i	$0.442455\pi$
$224$	−3.90967	+	27.3646i	−0.261226	+	1.82837i
$225$	4.07602			0.271734
$226$	1.14932	+	3.91165i	0.0764515	+	0.260199i
$227$	−1.10438	+	1.10438i	−0.0733002	+	0.0733002i	−0.742806	−	0.669506i	$-0.766506\pi$
$227$	−1.10438	+	1.10438i	−0.0733002	+	0.0733002i	0.669506	+	0.742806i	$0.266506\pi$
$228$	−17.4177	−	27.0814i	−1.15352	−	1.79351i
$229$	17.0029	+	17.0029i	1.12359	+	1.12359i	0.991198	+	0.132388i	$0.0422645\pi$
$229$	17.0029	+	17.0029i	1.12359	+	1.12359i	0.132388	+	0.991198i	$0.457735\pi$
$230$	1.24527	+	0.679684i	0.0821109	+	0.0448171i
$231$			9.29460i			0.611540i
$232$	19.7316	−	1.42178i	1.29544	−	0.0933444i
$233$		−	14.8204i		−	0.970914i	−0.874261	−	0.485457i	$-0.838653\pi$
$233$		−	14.8204i		−	0.970914i	0.874261	−	0.485457i	$-0.161347\pi$
$234$	0.315397	−	0.577850i	0.0206182	−	0.0377753i
$235$	−2.06279	−	2.06279i	−0.134562	−	0.134562i
$236$	9.34104	+	2.02855i	0.608050	+	0.132047i
$237$	−13.6567	+	13.6567i	−0.887096	+	0.887096i
$238$	10.2045	−	2.99827i	0.661459	−	0.194349i
$239$	9.10228			0.588778			0.294389	−	0.955686i	$-0.404884\pi$
$239$	9.10228			0.588778			0.294389	+	0.955686i	$0.404884\pi$
$240$	10.7463	−	23.5753i	0.693669	−	1.52178i
$241$	−9.08731			−0.585365			−0.292683	−	0.956210i	$-0.594548\pi$
$241$	−9.08731			−0.585365			−0.292683	+	0.956210i	$0.594548\pi$
$242$	1.35686	−	0.398671i	0.0872221	−	0.0256275i
$243$	4.47296	−	4.47296i	0.286940	−	0.286940i
$244$	−0.521145	+	2.39976i	−0.0333629	+	0.153629i
$245$	−40.6419	−	40.6419i	−2.59652	−	2.59652i
$246$	5.27447	−	9.66355i	0.336288	−	0.616125i
$247$		−	6.37642i		−	0.405722i
$248$	−3.07913	−	2.66522i	−0.195525	−	0.169242i
$249$		−	14.7352i		−	0.933808i
$250$	6.74825	+	3.68327i	0.426797	+	0.232950i
$251$	16.1734	+	16.1734i	1.02086	+	1.02086i	0.999778	+	0.0210806i	$0.00671066\pi$
$251$	16.1734	+	16.1734i	1.02086	+	1.02086i	0.0210806	+	0.999778i	$0.493289\pi$
$252$	5.07913	−	3.26670i	0.319955	−	0.205783i
$253$	0.208303	−	0.208303i	0.0130959	−	0.0130959i
$254$	2.56577	+	8.73250i	0.160991	+	0.547926i
$255$	−9.96888			−0.624275
$256$	−10.4949	−	12.0771i	−0.655932	−	0.754820i
$257$	12.6407			0.788507			0.394254	−	0.919002i	$-0.371003\pi$
$257$	12.6407			0.788507			0.394254	+	0.919002i	$0.371003\pi$
$258$	−5.31179	−	18.0784i	−0.330698	−	1.12551i
$259$	8.13765	−	8.13765i	0.505649	−	0.505649i
$260$	4.31531	−	2.77544i	0.267624	−	0.172126i
$261$	−3.05602	−	3.05602i	−0.189163	−	0.189163i
$262$	14.0866	+	7.68862i	0.870272	+	0.475004i
$263$			3.27578i			0.201993i	0.994887	+	0.100997i	$0.0322031\pi$
$263$			3.27578i			0.201993i	−0.994887	+	0.100997i	$0.967797\pi$
$264$	−4.06773	−	3.52092i	−0.250352	−	0.216698i
$265$		−	0.413557i		−	0.0254046i
$266$	28.0234	−	51.3427i	1.71823	−	3.14802i
$267$	−11.0344	−	11.0344i	−0.675295	−	0.675295i
$268$	0.828664	−	3.81582i	0.0506187	−	0.233088i
$269$	6.23599	−	6.23599i	0.380215	−	0.380215i	−0.490965	−	0.871179i	$-0.663356\pi$
$269$	6.23599	−	6.23599i	0.380215	−	0.380215i	0.871179	+	0.490965i	$0.163356\pi$
$270$	20.9354	−	6.15122i	1.27409	−	0.374352i
$271$	−5.85546			−0.355694			−0.177847	−	0.984058i	$-0.556913\pi$
$271$	−5.85546			−0.355694			−0.177847	+	0.984058i	$0.556913\pi$
$272$	−2.55342	+	5.60173i	−0.154824	+	0.339655i
$273$	7.00202			0.423781
$274$	−14.2471	+	4.18607i	−0.860698	+	0.252890i
$275$	4.66435	−	4.66435i	0.281271	−	0.281271i
$276$	−1.09512	−	0.237823i	−0.0659187	−	0.0143153i
$277$	7.26327	+	7.26327i	0.436407	+	0.436407i	0.890801	−	0.454394i	$-0.150144\pi$
$277$	7.26327	+	7.26327i	0.436407	+	0.436407i	−0.454394	+	0.890801i	$0.650144\pi$
$278$	−13.5237	+	24.7773i	−0.811100	+	1.48604i
$279$			0.889684i			0.0532640i
$280$	46.9443	−	3.38262i	2.80546	−	0.202150i
$281$			19.4088i			1.15783i	0.815386	+	0.578917i	$0.196525\pi$
$281$			19.4088i			1.15783i	−0.815386	+	0.578917i	$0.803475\pi$
$282$	2.02270	+	1.10401i	0.120450	+	0.0657429i
$283$	−19.3205	−	19.3205i	−1.14848	−	1.14848i	−0.986851	−	0.161633i	$-0.948324\pi$
$283$	−19.3205	−	19.3205i	−1.14848	−	1.14848i	−0.161633	−	0.986851i	$-0.551676\pi$
$284$	−3.06628	−	4.76751i	−0.181950	−	0.282900i
$285$	−38.7668	+	38.7668i	−2.29635	+	2.29635i
$286$	−0.300336	−	1.02218i	−0.0177592	−	0.0604427i
$287$	19.9994			1.18052
$288$	−0.494390	+	3.46033i	−0.0291322	+	0.203902i
$289$	−14.6313			−0.860664
$290$	−9.49548	−	32.3174i	−0.557594	−	1.89775i
$291$	−9.98404	+	9.98404i	−0.585275	+	0.585275i
$292$	−6.08092	−	9.45472i	−0.355859	−	0.553296i
$293$	12.2444	+	12.2444i	0.715327	+	0.715327i	0.967644	−	0.252318i	$-0.0811928\pi$
$293$	12.2444	+	12.2444i	0.715327	+	0.715327i	−0.252318	+	0.967644i	$0.581193\pi$
$294$	39.8520	+	21.7517i	2.32421	+	1.26858i
$295$		−	16.2755i		−	0.947594i
$296$	0.478744	+	6.64405i	0.0278264	+	0.386178i
$297$		−	4.53092i		−	0.262911i
$298$	8.30107	−	15.2087i	0.480868	−	0.881015i
$299$	−0.156924	−	0.156924i	−0.00907513	−	0.00907513i
$300$	−24.5221	−	5.32536i	−1.41579	−	0.307460i
$301$	24.2038	−	24.2038i	1.39508	−	1.39508i
$302$	11.4472	−	3.36339i	0.658710	−	0.193541i
$303$	−17.1968			−0.987929
$304$	11.8542	+	31.7136i	0.679884	+	1.81890i
$305$	4.18125			0.239417
$306$	1.29039	−	0.379140i	0.0737665	−	0.0216740i
$307$	−3.81602	+	3.81602i	−0.217792	+	0.217792i	−0.807567	−	0.589775i	$-0.799216\pi$
$307$	−3.81602	+	3.81602i	−0.217792	+	0.217792i	0.589775	+	0.807567i	$0.299216\pi$
$308$	2.07403	−	9.55047i	0.118179	−	0.544188i
$309$	−12.6830	−	12.6830i	−0.721510	−	0.721510i
$310$	−3.32202	+	6.08639i	−0.188678	+	0.345683i
$311$			2.88098i			0.163365i	0.996658	+	0.0816826i	$0.0260294\pi$
$311$			2.88098i			0.163365i	−0.996658	+	0.0816826i	$0.973971\pi$
$312$	−2.65246	+	3.06440i	−0.150166	+	0.173487i
$313$			5.85067i			0.330700i	0.986235	+	0.165350i	$0.0528753\pi$
$313$			5.85067i			0.330700i	−0.986235	+	0.165350i	$0.947125\pi$
$314$	−0.620919	−	0.338904i	−0.0350405	−	0.0191255i
$315$	−7.27073	−	7.27073i	−0.409659	−	0.409659i
$316$	17.0800	−	10.9852i	0.960826	−	0.617967i
$317$	−13.0696	+	13.0696i	−0.734062	+	0.734062i	−0.971422	−	0.237360i	$-0.923718\pi$
$317$	−13.0696	+	13.0696i	−0.734062	+	0.734062i	0.237360	+	0.971422i	$0.423718\pi$
$318$	0.0920910	+	0.313427i	0.00516421	+	0.0175761i
$319$	−6.99426			−0.391603
$320$	−16.3028	+	21.8263i	−0.911353	+	1.22013i
$321$	6.32032			0.352766
$322$	−0.573887	−	1.95320i	−0.0319815	−	0.108847i
$323$	9.21139	−	9.21139i	0.512535	−	0.512535i
$324$	−17.6151	+	11.3294i	−0.978616	+	0.629408i
$325$	−3.51385	−	3.51385i	−0.194913	−	0.194913i
$326$	−12.3446	−	6.73782i	−0.683704	−	0.373173i
$327$		−	24.6754i		−	1.36455i
$328$	−7.57603	+	8.75261i	−0.418317	+	0.483282i
$329$			4.18611i			0.230788i
$330$	−4.38860	+	8.04050i	−0.241584	+	0.442615i
$331$	6.01896	+	6.01896i	0.330832	+	0.330832i	0.852902	−	0.522071i	$-0.174840\pi$
$331$	6.01896	+	6.01896i	0.330832	+	0.330832i	−0.522071	+	0.852902i	$0.674840\pi$
$332$	−3.28808	+	15.1409i	−0.180457	+	0.830964i
$333$	1.02903	−	1.02903i	0.0563905	−	0.0563905i
$334$	6.35965	−	1.86859i	0.347984	−	0.102244i
$335$	−6.64853			−0.363248
$336$	−34.8251	+	13.0172i	−1.89986	+	0.710147i
$337$	29.3513			1.59887			0.799434	−	0.600754i	$-0.205133\pi$
$337$	29.3513			1.59887			0.799434	+	0.600754i	$0.205133\pi$
$338$	16.8691	−	4.95646i	0.917558	−	0.269596i
$339$	−3.87740	+	3.87740i	−0.210591	+	0.210591i
$340$	10.2433	+	2.22449i	0.555521	+	0.120640i
$341$	1.01810	+	1.01810i	0.0551332	+	0.0551332i
$342$	3.54364	−	6.49243i	0.191618	−	0.351070i
$343$			48.2705i			2.60636i
$344$	1.42393	+	19.7614i	0.0767730	+	1.06546i
$345$			1.90810i			0.102729i
$346$	−20.9936	−	11.4585i	−1.12862	−	0.616015i
$347$	12.6001	+	12.6001i	0.676410	+	0.676410i	0.959186	−	0.282776i	$-0.0912552\pi$
$347$	12.6001	+	12.6001i	0.676410	+	0.676410i	−0.282776	+	0.959186i	$0.591255\pi$
$348$	14.3929	+	22.3784i	0.771542	+	1.19961i
$349$	−19.3967	+	19.3967i	−1.03828	+	1.03828i	−0.0390466	+	0.999237i	$0.512432\pi$
$349$	−19.3967	+	19.3967i	−1.03828	+	1.03828i	−0.999237	+	0.0390466i	$0.987568\pi$
$350$	−12.8505	−	43.7362i	−0.686890	−	2.33780i
$351$	−3.41333			−0.182190
$352$	3.39404	+	4.52554i	0.180903	+	0.241212i
$353$	−20.5371			−1.09308			−0.546541	−	0.837433i	$-0.684056\pi$
$353$	−20.5371			−1.09308			−0.546541	+	0.837433i	$0.684056\pi$
$354$	3.62423	+	12.3349i	0.192625	+	0.655592i
$355$	−6.82465	+	6.82465i	−0.362215	+	0.362215i
$356$	8.87591	+	13.8004i	0.470423	+	0.731421i
$357$	10.1151	+	10.1151i	0.535349	+	0.535349i
$358$	−25.8182	−	14.0919i	−1.36454	−	0.744779i
$359$		−	8.90052i		−	0.469751i	−0.972025	−	0.234876i	$-0.924532\pi$
$359$		−	8.90052i		−	0.469751i	0.972025	−	0.234876i	$-0.0754683\pi$
$360$	5.93625	−	0.427742i	0.312868	−	0.0225440i
$361$		−	52.6422i		−	2.77064i
$362$	−7.53413	+	13.8035i	−0.395985	+	0.725498i
$363$	1.34498	+	1.34498i	0.0705929	+	0.0705929i
$364$	−7.19478	−	1.56246i	−0.377109	−	0.0818950i
$365$	−13.5343	+	13.5343i	−0.708420	+	0.708420i
$366$	−3.16890	+	0.931082i	−0.165641	+	0.0486684i
$367$	−32.2561			−1.68375			−0.841877	−	0.539669i	$-0.818549\pi$
$367$	−32.2561			−1.68375			−0.841877	+	0.539669i	$0.818549\pi$
$368$	1.07220	+	0.488740i	0.0558924	+	0.0254773i
$369$	2.52898			0.131653
$370$	10.8820	−	3.19733i	0.565727	−	0.166221i
$371$	−0.419624	+	0.419624i	−0.0217858	+	0.0217858i
$372$	1.16238	−	5.35252i	0.0602667	−	0.277515i
$373$	16.1348	+	16.1348i	0.835426	+	0.835426i	0.988253	−	0.152827i	$-0.0488376\pi$
$373$	16.1348	+	16.1348i	0.835426	+	0.835426i	−0.152827	+	0.988253i	$0.548838\pi$
$374$	1.04278	−	1.91051i	0.0539206	−	0.0987899i
$375$			10.3402i			0.533964i
$376$	−1.83203	−	1.58576i	−0.0944796	−	0.0817791i
$377$			5.26907i			0.271371i
$378$	−27.4840	−	15.0011i	−1.41363	−	0.771573i
$379$	2.56853	+	2.56853i	0.131936	+	0.131936i	0.769991	−	0.638055i	$-0.220261\pi$
$379$	2.56853	+	2.56853i	0.131936	+	0.131936i	−0.638055	+	0.769991i	$0.720261\pi$
$380$	48.4846	−	31.1834i	2.48721	−	1.59968i
$381$	−8.65603	+	8.65603i	−0.443462	+	0.443462i
$382$	−7.84141	−	26.6879i	−0.401201	−	1.36547i
$383$	28.0600			1.43380			0.716900	−	0.697176i	$-0.245560\pi$
$383$	28.0600			1.43380			0.716900	+	0.697176i	$0.245560\pi$
$384$	7.49530	−	20.1721i	0.382493	−	1.02940i
$385$	−16.6404			−0.848071
$386$	3.51908	+	11.9770i	0.179117	+	0.609615i
$387$	3.06064	−	3.06064i	0.155581	−	0.155581i
$388$	12.4868	−	8.03102i	0.633920	−	0.407713i
$389$	−12.5053	−	12.5053i	−0.634044	−	0.634044i	0.315036	−	0.949080i	$-0.397984\pi$
$389$	−12.5053	−	12.5053i	−0.634044	−	0.634044i	−0.949080	+	0.315036i	$0.897984\pi$
$390$	6.05725	+	3.30612i	0.306721	+	0.167412i
$391$		−	0.453384i		−	0.0229286i
$392$	−36.0953	−	31.2432i	−1.82309	−	1.57802i
$393$			21.5845i			1.08879i
$394$	−15.0815	+	27.6313i	−0.759794	+	1.39205i
$395$	−24.4499	−	24.4499i	−1.23021	−	1.23021i
$396$	0.262267	−	1.20768i	0.0131794	−	0.0606884i
$397$	−19.7711	+	19.7711i	−0.992283	+	0.992283i	−0.999970	−	0.00768742i	$-0.997553\pi$
$397$	−19.7711	+	19.7711i	−0.992283	+	0.992283i	0.00768742	+	0.999970i	$0.497553\pi$
$398$	−29.7844	+	8.75121i	−1.49295	+	0.438659i
$399$	78.6711			3.93848
$400$	24.0089	+	10.9439i	1.20044	+	0.547196i
$401$	2.05935			0.102839			0.0514195	−	0.998677i	$-0.483625\pi$
$401$	2.05935			0.102839			0.0514195	+	0.998677i	$0.483625\pi$
$402$	5.03881	−	1.48050i	0.251313	−	0.0738405i
$403$	0.766978	−	0.766978i	0.0382059	−	0.0382059i
$404$	17.6702	+	3.83735i	0.879125	+	0.190915i
$405$	25.2158	+	25.2158i	1.25298	+	1.25298i
$406$	−23.1568	+	42.4263i	−1.14925	+	2.10558i
$407$		−	2.35512i		−	0.116739i
$408$	−8.25858	+	0.595080i	−0.408861	+	0.0294609i
$409$			1.04009i			0.0514289i	0.999669	+	0.0257145i	$0.00818607\pi$
$409$			1.04009i			0.0514289i	−0.999669	+	0.0257145i	$0.991814\pi$
$410$	17.3009	+	9.44303i	0.854431	+	0.466358i
$411$	−14.1223	−	14.1223i	−0.696603	−	0.696603i
$412$	10.2020	+	15.8623i	0.502617	+	0.781478i
$413$	−16.5142	+	16.5142i	−0.812612	+	0.812612i
$414$	−0.0725697	−	0.246988i	−0.00356660	−	0.0121388i
$415$	26.3809			1.29499
$416$	3.40928	−	2.55687i	0.167154	−	0.125361i
$417$	−37.9657			−1.85919
$418$	−3.37442	−	11.4847i	−0.165048	−	0.561734i
$419$	−12.1644	+	12.1644i	−0.594271	+	0.594271i	−0.938782	−	0.344511i	$-0.888045\pi$
$419$	−12.1644	+	12.1644i	−0.594271	+	0.594271i	0.344511	+	0.938782i	$0.388045\pi$
$420$	34.2429	+	53.2414i	1.67088	+	2.59792i
$421$	0.787881	+	0.787881i	0.0383990	+	0.0383990i	0.726046	−	0.687647i	$-0.241356\pi$
$421$	0.787881	+	0.787881i	0.0383990	+	0.0383990i	−0.687647	+	0.726046i	$0.741356\pi$
$422$	10.1245	+	5.52606i	0.492853	+	0.269005i
$423$			0.529345i			0.0257376i
$424$	−0.0246868	−	0.342605i	−0.00119890	−	0.0166384i
$425$		−	10.1522i		−	0.492456i
$426$	3.65257	−	6.69200i	0.176968	−	0.324228i
$427$	−4.24259	−	4.24259i	−0.205313	−	0.205313i
$428$	−6.49431	−	1.41034i	−0.313915	−	0.0681714i
$429$	1.01323	−	1.01323i	0.0489191	−	0.0489191i
$430$	32.3663	−	9.50983i	1.56084	−	0.458605i
$431$	−20.8973			−1.00659			−0.503293	−	0.864116i	$-0.667878\pi$
$431$	−20.8973			−1.00659			−0.503293	+	0.864116i	$0.667878\pi$
$432$	16.9765	−	6.34561i	0.816781	−	0.305303i
$433$	31.9139			1.53368			0.766842	−	0.641836i	$-0.221827\pi$
$433$	31.9139			1.53368			0.766842	+	0.641836i	$0.221827\pi$
$434$	9.54643	−	2.80492i	0.458243	−	0.134641i
$435$	32.0344	−	32.0344i	1.53593	−	1.53593i
$436$	−5.50616	+	25.3547i	−0.263697	+	1.21427i
$437$	−1.76311	−	1.76311i	−0.0843411	−	0.0843411i
$438$	7.24361	−	13.2713i	0.346113	−	0.634126i
$439$		−	0.0658140i		−	0.00314113i	−0.999999	−	0.00157056i	$-0.999500\pi$
$439$		−	0.0658140i		−	0.00314113i	0.999999	−	0.00157056i	$-0.000499926\pi$
$440$	6.30360	−	7.28256i	0.300512	−	0.347183i
$441$			10.4294i			0.496637i
$442$	−1.43927	−	0.785567i	−0.0684589	−	0.0373656i
$443$	17.0350	+	17.0350i	0.809357	+	0.809357i	0.984536	−	0.175180i	$-0.0560506\pi$
$443$	17.0350	+	17.0350i	0.809357	+	0.809357i	−0.175180	+	0.984536i	$0.556051\pi$
$444$	−7.53529	+	4.84641i	−0.357609	+	0.230000i
$445$	19.7552	−	19.7552i	0.936485	−	0.936485i
$446$	−2.14086	−	7.28634i	−0.101373	−	0.345018i
$447$	23.3039			1.10224
$448$	38.6885	−	5.60457i	1.82786	−	0.264791i
$449$	−24.1440			−1.13943			−0.569714	−	0.821843i	$-0.692946\pi$
$449$	−24.1440			−1.13943			−0.569714	+	0.821843i	$0.692946\pi$
$450$	−1.62499	−	5.53057i	−0.0766027	−	0.260714i
$451$	2.89401	−	2.89401i	0.136274	−	0.136274i
$452$	4.84935	−	3.11892i	0.228094	−	0.146702i
$453$	11.3469	+	11.3469i	0.533124	+	0.533124i
$454$	1.93877	+	1.05820i	0.0909909	+	0.0496639i
$455$			12.5359i			0.587692i
$456$	−29.8017	+	34.4300i	−1.39559	+	1.61233i
$457$		−	5.17834i		−	0.242233i	−0.992638	−	0.121116i	$-0.961353\pi$
$457$		−	5.17834i		−	0.242233i	0.992638	−	0.121116i	$-0.0386474\pi$
$458$	16.2920	−	29.8491i	0.761275	−	1.39476i
$459$	−4.93091	−	4.93091i	−0.230155	−	0.230155i
$460$	0.425781	−	1.96063i	0.0198521	−	0.0914148i
$461$	21.5047	−	21.5047i	1.00157	−	1.00157i	0.00157450	−	0.999999i	$-0.499499\pi$
$461$	21.5047	−	21.5047i	1.00157	−	1.00157i	0.999999	−	0.00157450i	$-0.000501180\pi$
$462$	12.6114	−	3.70548i	0.586738	−	0.172395i
$463$	−23.4294			−1.08886			−0.544428	−	0.838808i	$-0.683253\pi$
$463$	−23.4294			−1.08886			−0.544428	+	0.838808i	$0.683253\pi$
$464$	−9.79555	−	26.2061i	−0.454747	−	1.21659i
$465$	−9.32601			−0.432484
$466$	−20.1091	+	5.90844i	−0.931536	+	0.273703i
$467$	−13.2909	+	13.2909i	−0.615030	+	0.615030i	−0.944252	−	0.329222i	$-0.893213\pi$
$467$	−13.2909	+	13.2909i	−0.615030	+	0.615030i	0.329222	+	0.944252i	$0.393213\pi$
$468$	−0.909800	−	0.197577i	−0.0420555	−	0.00913300i
$469$	6.74607	+	6.74607i	0.311505	+	0.311505i
$470$	−1.97654	+	3.62129i	−0.0911709	+	0.167037i
$471$		−	0.951418i		−	0.0438390i
$472$	−0.971544	−	13.4832i	−0.0447189	−	0.620614i
$473$		−	7.00483i		−	0.322082i
$474$	23.9747	+	13.0856i	1.10119	+	0.601043i
$475$	−39.4798	−	39.4798i	−1.81146	−	1.81146i
$476$	−8.13646	−	12.6507i	−0.372934	−	0.579844i
$477$	−0.0530626	+	0.0530626i	−0.00242957	+	0.00242957i
$478$	−3.62881	−	12.3505i	−0.165978	−	0.564899i
$479$	−43.4425			−1.98494			−0.992469	−	0.122495i	$-0.960910\pi$
$479$	−43.4425			−1.98494			−0.992469	+	0.122495i	$0.960910\pi$
$480$	−36.2725	−	5.18239i	−1.65561	−	0.236543i
$481$	−1.77421			−0.0808970
$482$	3.62284	+	12.3302i	0.165016	+	0.561625i
$483$	1.93609	−	1.93609i	0.0880953	−	0.0880953i
$484$	−1.08188	−	1.68212i	−0.0491763	−	0.0764602i
$485$	−17.8747	−	17.8747i	−0.811648	−	0.811648i
$486$	−7.85240	−	4.28593i	−0.356192	−	0.194414i
$487$		−	20.5820i		−	0.932661i	−0.884610	−	0.466331i	$-0.845576\pi$
$487$		−	20.5820i		−	0.932661i	0.884610	−	0.466331i	$-0.154424\pi$
$488$	3.46390	−	0.249595i	0.156803	−	0.0112986i
$489$		−	18.9153i		−	0.855380i
$490$	−38.9425	+	71.3480i	−1.75924	+	3.22317i
$491$	19.5086	+	19.5086i	0.880412	+	0.880412i	0.993576	−	0.113164i	$-0.0360986\pi$
$491$	19.5086	+	19.5086i	0.880412	+	0.880412i	−0.113164	+	0.993576i	$0.536099\pi$
$492$	−15.2148	−	3.30414i	−0.685938	−	0.148962i
$493$	−7.61171	+	7.61171i	−0.342814	+	0.342814i
$494$	−8.65189	+	2.54209i	−0.389267	+	0.114374i
$495$	−2.10422			−0.0945777
$496$	−2.38876	+	5.24049i	−0.107259	+	0.235305i
$497$	13.8495			0.621237
$498$	−19.9936	+	5.87451i	−0.895936	+	0.263243i
$499$	20.3380	−	20.3380i	0.910456	−	0.910456i	−0.0858519	−	0.996308i	$-0.527361\pi$
$499$	20.3380	−	20.3380i	0.910456	−	0.910456i	0.996308	+	0.0858519i	$0.0273612\pi$
$500$	2.30734	−	10.6248i	0.103188	−	0.475156i
$501$	6.30395	+	6.30395i	0.281640	+	0.281640i
$502$	15.4972	−	28.3929i	0.691673	−	1.26724i
$503$		−	12.2713i		−	0.547152i	−0.961850	−	0.273576i	$-0.911793\pi$
$503$		−	12.2713i		−	0.547152i	0.961850	−	0.273576i	$-0.0882065\pi$
$504$	−6.45735	−	5.58932i	−0.287633	−	0.248968i
$505$		−	30.7878i		−	1.37004i
$506$	−0.365682	−	0.199593i	−0.0162565	−	0.00887300i
$507$	16.7214	+	16.7214i	0.742622	+	0.742622i
$508$	10.8259	−	6.96278i	0.480320	−	0.308923i
$509$	−17.5441	+	17.5441i	−0.777629	+	0.777629i	−0.979427	−	0.201798i	$-0.935322\pi$
$509$	−17.5441	+	17.5441i	−0.777629	+	0.777629i	0.201798	+	0.979427i	$0.435322\pi$
$510$	3.97430	+	13.5263i	0.175985	+	0.598957i
$511$	27.4658			1.21502
$512$	−12.2029	+	19.0549i	−0.539298	+	0.842115i
$513$	−38.3505			−1.69321
$514$	−5.03949	−	17.1517i	−0.222282	−	0.756528i
$515$	22.7067	−	22.7067i	1.00058	−	1.00058i
$516$	−22.4122	+	14.4147i	−0.986642	+	0.634571i
$517$	0.605751	+	0.605751i	0.0266409	+	0.0266409i
$518$	−14.2859	−	7.79739i	−0.627685	−	0.342598i
$519$		−	32.1679i		−	1.41202i
$520$	−5.48626	−	4.74877i	−0.240589	−	0.208247i
$521$			35.7622i			1.56677i	0.621538	+	0.783384i	$0.286508\pi$
$521$			35.7622i			1.56677i	−0.621538	+	0.783384i	$0.713492\pi$
$522$	−2.92824	+	5.36493i	−0.128166	+	0.234817i
$523$	16.2700	+	16.2700i	0.711437	+	0.711437i	0.966836	−	0.255399i	$-0.0822068\pi$
$523$	16.2700	+	16.2700i	0.711437	+	0.711437i	−0.255399	+	0.966836i	$0.582207\pi$
$524$	4.81645	−	22.1787i	0.210407	−	0.968881i
$525$	43.3532	−	43.3532i	1.89209	−	1.89209i
$526$	4.44477	−	1.30596i	0.193801	−	0.0569424i
$527$	2.21596			0.0965286
$528$	−3.15571	+	6.92302i	−0.137334	+	0.301286i
$529$	22.9132			0.996227
$530$	−0.561137	+	0.164873i	−0.0243742	+	0.00716162i
$531$	−2.08827	+	2.08827i	−0.0906233	+	0.0906233i
$532$	−80.8368	−	17.5550i	−3.50472	−	0.761104i
$533$	−2.18018	−	2.18018i	−0.0944341	−	0.0944341i
$534$	−10.5730	+	19.3712i	−0.457540	+	0.838274i
$535$			11.3154i			0.489209i
$536$	−5.50788	+	0.396876i	−0.237904	+	0.0171424i
$537$		−	39.5606i		−	1.70717i
$538$	−10.9474	−	5.97524i	−0.471978	−	0.257611i
$539$	11.9347	+	11.9347i	0.514065	+	0.514065i
$540$	−16.6927	−	25.9541i	−0.718338	−	1.11689i
$541$	−25.1002	+	25.1002i	−1.07914	+	1.07914i	−0.0825554	+	0.996586i	$0.526308\pi$
$541$	−25.1002	+	25.1002i	−1.07914	+	1.07914i	−0.996586	+	0.0825554i	$0.973692\pi$
$542$	2.33440	+	7.94503i	0.100271	+	0.341268i
$543$	−21.1508			−0.907668
$544$	8.61872	+	1.23139i	0.369525	+	0.0527953i
$545$	44.1770			1.89233
$546$	−2.79150	−	9.50074i	−0.119465	−	0.406594i
$547$	3.89719	−	3.89719i	0.166632	−	0.166632i	−0.618865	−	0.785497i	$-0.712407\pi$
$547$	3.89719	−	3.89719i	0.166632	−	0.166632i	0.785497	+	0.618865i	$0.212407\pi$
$548$	11.3598	+	17.6624i	0.485266	+	0.754501i
$549$	−0.536488	−	0.536488i	−0.0228967	−	0.0228967i
$550$	−8.18839	−	4.46932i	−0.349154	−	0.190572i
$551$			59.2006i			2.52203i
$552$	0.113902	+	1.58074i	0.00484798	+	0.0672808i
$553$			49.6172i			2.10994i
$554$	6.95957	−	12.7509i	0.295684	−	0.541732i
$555$	10.7867	+	10.7867i	0.457869	+	0.457869i
$556$	39.0108	+	8.47180i	1.65443	+	0.359284i
$557$	25.1453	−	25.1453i	1.06544	−	1.06544i	0.0677385	−	0.997703i	$-0.478422\pi$
$557$	25.1453	−	25.1453i	1.06544	−	1.06544i	0.997703	−	0.0677385i	$-0.0215784\pi$
$558$	1.20717	−	0.354691i	0.0511037	−	0.0150153i
$559$	−5.27704			−0.223195
$560$	−23.3051	−	62.3482i	−0.984818	−	2.63469i
$561$	2.92742			0.123596
$562$	26.3350	−	7.73773i	1.11088	−	0.326397i
$563$	−14.1939	+	14.1939i	−0.598200	+	0.598200i	−0.939833	−	0.341633i	$-0.889020\pi$
$563$	−14.1939	+	14.1939i	−0.598200	+	0.598200i	0.341633	+	0.939833i	$0.389020\pi$
$564$	0.691595	−	3.18465i	0.0291214	−	0.134098i
$565$	−6.94180	−	6.94180i	−0.292044	−	0.292044i
$566$	−18.5126	+	33.9177i	−0.778144	+	1.42567i
$567$		−	51.1715i		−	2.14900i
$568$	−5.24640	+	6.06118i	−0.220134	+	0.254321i
$569$		−	18.7864i		−	0.787567i	−0.919203	−	0.393784i	$-0.871166\pi$
$569$		−	18.7864i		−	0.787567i	0.919203	−	0.393784i	$-0.128834\pi$
$570$	68.0562	+	37.1458i	2.85056	+	1.55587i
$571$	28.1583	+	28.1583i	1.17839	+	1.17839i	0.980155	+	0.198234i	$0.0635205\pi$
$571$	28.1583	+	28.1583i	1.17839	+	1.17839i	0.198234	+	0.980155i	$0.436480\pi$
$572$	−1.26722	+	0.815025i	−0.0529849	+	0.0340779i
$573$	26.4542	−	26.4542i	1.10514	−	1.10514i
$574$	−7.97316	−	27.1363i	−0.332793	−	1.13265i
$575$	−1.94320			−0.0810369
$576$	4.89227	−	0.708714i	0.203845	−	0.0295298i
$577$	29.0480			1.20928			0.604642	−	0.796498i	$-0.293316\pi$
$577$	29.0480			1.20928			0.604642	+	0.796498i	$0.293316\pi$
$578$	5.83307	+	19.8526i	0.242624	+	0.825758i
$579$	−11.8722	+	11.8722i	−0.493390	+	0.493390i
$580$	−40.0646	+	25.7680i	−1.66359	+	1.06996i
$581$	−26.7679	−	26.7679i	−1.11052	−	1.11052i
$582$	17.5273	+	9.56658i	0.726529	+	0.396547i
$583$			0.121443i			0.00502967i
$584$	−10.4044	+	12.0203i	−0.430538	+	0.497402i
$585$			1.58520i			0.0655399i
$586$	11.7324	−	21.4954i	0.484663	−	0.887968i
$587$	23.1186	+	23.1186i	0.954206	+	0.954206i	0.998996	−	0.0447900i	$-0.0142619\pi$
$587$	23.1186	+	23.1186i	0.954206	+	0.954206i	−0.0447900	+	0.998996i	$0.514262\pi$
$588$	13.6261	−	62.7452i	0.561930	−	2.58757i
$589$	8.61737	−	8.61737i	0.355073	−	0.355073i
$590$	−22.0835	+	6.48854i	−0.909162	+	0.267129i
$591$	−42.3388			−1.74158
$592$	8.82417	−	3.29837i	0.362671	−	0.135562i
$593$	18.0038			0.739326			0.369663	−	0.929166i	$-0.379473\pi$
$593$	18.0038			0.739326			0.369663	+	0.929166i	$0.379473\pi$
$594$	−6.14781	+	1.80634i	−0.252248	+	0.0741152i
$595$	−18.1094	+	18.1094i	−0.742412	+	0.742412i
$596$	−23.9454	−	5.20011i	−0.980842	−	0.213005i
$597$	−29.5235	−	29.5235i	−1.20832	−	1.20832i
$598$	−0.150362	+	0.275484i	−0.00614877	+	0.0112654i
$599$		−	31.9869i		−	1.30695i	−0.756948	−	0.653475i	$-0.773310\pi$
$599$		−	31.9869i		−	1.30695i	0.756948	−	0.653475i	$-0.226690\pi$
$600$	2.55050	+	35.3961i	0.104124	+	1.44504i
$601$		−	23.8213i		−	0.971689i	−0.874045	−	0.485845i	$-0.838512\pi$
$601$		−	23.8213i		−	0.971689i	0.874045	−	0.485845i	$-0.161488\pi$
$602$	−42.4905	−	23.1918i	−1.73178	−	0.945226i
$603$	0.853060	+	0.853060i	0.0347393	+	0.0347393i
$604$	−9.12728	−	14.1913i	−0.371384	−	0.577434i
$605$	−2.40794	+	2.40794i	−0.0978968	+	0.0978968i
$606$	6.85585	+	23.3336i	0.278500	+	0.947862i
$607$	28.0295			1.13768			0.568842	−	0.822447i	$-0.307392\pi$
$607$	28.0295			1.13768			0.568842	+	0.822447i	$0.307392\pi$
$608$	38.3049	−	28.7277i	1.55347	−	1.16506i
$609$	−65.0088			−2.63429
$610$	−1.66694	−	5.67336i	−0.0674924	−	0.229707i
$611$	0.456338	−	0.456338i	0.0184615	−	0.0184615i
$612$	−1.02888	−	1.59972i	−0.0415900	−	0.0646648i
$613$	18.5453	+	18.5453i	0.749038	+	0.749038i	0.974299	−	0.225260i	$-0.0723232\pi$
$613$	18.5453	+	18.5453i	0.749038	+	0.749038i	−0.225260	+	0.974299i	$0.572323\pi$
$614$	6.69913	+	3.65646i	0.270355	+	0.147563i
$615$			26.5097i			1.06898i
$616$	−13.7855	+	0.993326i	−0.555433	+	0.0400223i
$617$		−	13.6782i		−	0.550664i	−0.961349	−	0.275332i	$-0.911212\pi$
$617$		−	13.6782i		−	0.550664i	0.961349	−	0.275332i	$-0.0887877\pi$
$618$	−12.1527	+	22.2654i	−0.488852	+	0.895644i
$619$	−3.06112	−	3.06112i	−0.123037	−	0.123037i	0.642907	−	0.765944i	$-0.277728\pi$
$619$	−3.06112	−	3.06112i	−0.123037	−	0.123037i	−0.765944	+	0.642907i	$0.777728\pi$
$620$	9.58275	+	2.08104i	0.384852	+	0.0835766i
$621$	−0.943804	+	0.943804i	−0.0378736	+	0.0378736i
$622$	3.90907	−	1.14856i	0.156740	−	0.0460531i
$623$	−40.0900			−1.60617
$624$	5.21541	+	2.37733i	0.208783	+	0.0951693i
$625$	14.4696			0.578786
$626$	7.93853	−	2.33249i	0.317288	−	0.0932251i
$627$	11.3841	−	11.3841i	0.454637	−	0.454637i
$628$	−0.212303	+	0.977609i	−0.00847181	+	0.0390108i
$629$	−2.56303	−	2.56303i	−0.102195	−	0.102195i
$630$	−6.96671	+	12.7640i	−0.277561	+	0.508528i
$631$			16.5679i			0.659556i	0.944059	+	0.329778i	$0.106974\pi$
$631$			16.5679i			0.659556i	−0.944059	+	0.329778i	$0.893026\pi$
$632$	−21.7147	−	18.7957i	−0.863763	−	0.747651i
$633$			15.5135i			0.616606i
$634$	22.9440	+	12.5231i	0.911224	+	0.497356i
$635$	−15.4971	−	15.4971i	−0.614984	−	0.614984i
$636$	0.388562	−	0.249909i	0.0154075	−	0.00990952i
$637$	8.99095	−	8.99095i	0.356234	−	0.356234i
$638$	2.78840	+	9.49021i	0.110394	+	0.375721i
$639$	1.75131			0.0692809
$640$	36.1146	+	13.4190i	1.42756	+	0.530434i
$641$	42.4474			1.67657			0.838285	−	0.545232i	$-0.183558\pi$
$641$	42.4474			1.67657			0.838285	+	0.545232i	$0.183558\pi$
$642$	−2.51973	−	8.57578i	−0.0994457	−	0.338459i
$643$	−24.6339	+	24.6339i	−0.971464	+	0.971464i	−0.999604	−	0.0281396i	$-0.991042\pi$
$643$	−24.6339	+	24.6339i	−0.971464	+	0.971464i	0.0281396	+	0.999604i	$0.491042\pi$
$644$	−2.42142	+	1.55737i	−0.0954173	+	0.0613688i
$645$	32.0829	+	32.0829i	1.26326	+	1.26326i
$646$	−16.1708	−	8.82623i	−0.636234	−	0.347263i
$647$			25.5797i			1.00564i	0.864391	+	0.502820i	$0.167704\pi$
$647$			25.5797i			1.00564i	−0.864391	+	0.502820i	$0.832296\pi$
$648$	22.3949	+	19.3845i	0.879756	+	0.761494i
$649$			4.77938i			0.187607i
$650$	−3.36693	+	6.16866i	−0.132062	+	0.241955i
$651$	9.46283	+	9.46283i	0.370878	+	0.370878i
$652$	−4.22083	+	19.4360i	−0.165301	+	0.761174i
$653$	12.5576	−	12.5576i	0.491416	−	0.491416i	−0.417336	−	0.908752i	$-0.637036\pi$
$653$	12.5576	−	12.5576i	0.491416	−	0.491416i	0.908752	+	0.417336i	$0.137036\pi$
$654$	−33.4810	+	9.83735i	−1.30921	+	0.384671i
$655$	−38.6433			−1.50992
$656$	14.8964	+	6.79019i	0.581606	+	0.265112i
$657$	3.47313			0.135500
$658$	5.67995	−	1.66888i	0.221427	−	0.0650596i
$659$	29.3389	−	29.3389i	1.14288	−	1.14288i	0.154958	−	0.987921i	$-0.450476\pi$
$659$	29.3389	−	29.3389i	1.14288	−	1.14288i	0.987921	−	0.154958i	$-0.0495244\pi$
$660$	12.6594	+	2.74919i	0.492767	+	0.107012i
$661$	−31.6490	−	31.6490i	−1.23100	−	1.23100i	−0.963579	−	0.267426i	$-0.913827\pi$
$661$	−31.6490	−	31.6490i	−1.23100	−	1.23100i	−0.267426	−	0.963579i	$-0.586173\pi$
$662$	5.76728	−	10.5664i	0.224152	−	0.410677i
$663$		−	2.20535i		−	0.0856487i
$664$	21.8549	−	1.57478i	0.848134	−	0.0611131i
$665$			140.847i			5.46180i
$666$	−1.80649	−	0.986002i	−0.0700000	−	0.0382068i
$667$	1.45693	+	1.45693i	0.0564124	+	0.0564124i
$668$	−5.07081	−	7.88418i	−0.196195	−	0.305048i
$669$	7.22253	−	7.22253i	0.279239	−	0.279239i
$670$	2.65057	+	9.02111i	0.102401	+	0.348516i
$671$	−1.22785			−0.0474005
$672$	31.5462	+	42.0631i	1.21692	+	1.62262i
$673$	−18.3424			−0.707048			−0.353524	−	0.935425i	$-0.615017\pi$
$673$	−18.3424			−0.707048			−0.353524	+	0.935425i	$0.615017\pi$
$674$	−11.7015	−	39.8256i	−0.450725	−	1.53402i
$675$	−21.1338	+	21.1338i	−0.813439	+	0.813439i
$676$	−13.4504	−	20.9130i	−0.517324	−	0.804345i
$677$	29.5579	+	29.5579i	1.13600	+	1.13600i	0.989160	+	0.146843i	$0.0469113\pi$
$677$	29.5579	+	29.5579i	1.13600	+	1.13600i	0.146843	+	0.989160i	$0.453089\pi$
$678$	6.80688	+	3.71527i	0.261417	+	0.142684i
$679$			36.2738i			1.39206i
$680$	−1.06539	−	14.7855i	−0.0408557	−	0.567000i
$681$			2.97073i			0.113838i
$682$	0.975530	−	1.78730i	0.0373550	−	0.0684394i
$683$	7.57608	+	7.57608i	0.289891	+	0.289891i	0.837037	−	0.547146i	$-0.184286\pi$
$683$	7.57608	+	7.57608i	0.289891	+	0.289891i	−0.547146	+	0.837037i	$0.684286\pi$
$684$	−10.2220	−	2.21987i	−0.390850	−	0.0848790i
$685$	25.2836	−	25.2836i	0.966035	−	0.966035i
$686$	65.4962	−	19.2440i	2.50066	−	0.734741i
$687$	45.7371			1.74498
$688$	26.2457	−	9.81036i	1.00061	−	0.374016i
$689$	0.0914884			0.00348543
$690$	2.58902	−	0.760704i	0.0985623	−	0.0289595i
$691$	12.8736	−	12.8736i	0.489736	−	0.489736i	−0.418487	−	0.908223i	$-0.637439\pi$
$691$	12.8736	−	12.8736i	0.489736	−	0.489736i	0.908223	+	0.418487i	$0.137439\pi$
$692$	−7.17807	+	33.0535i	−0.272869	+	1.25651i
$693$	2.13509	+	2.13509i	0.0811054	+	0.0811054i
$694$	12.0733	−	22.1199i	0.458295	−	0.839659i
$695$		−	67.9709i		−	2.57828i
$696$	24.6262	−	28.4508i	0.933455	−	1.07842i
$697$		−	6.29898i		−	0.238591i
$698$	34.0515	+	18.5857i	1.28887	+	0.703479i
$699$	−19.9330	−	19.9330i	−0.753936	−	0.753936i
$700$	−54.2207	+	34.8727i	−2.04935	+	1.31806i
$701$	−5.49286	+	5.49286i	−0.207463	+	0.207463i	−0.803188	−	0.595726i	$-0.796865\pi$
$701$	−5.49286	+	5.49286i	−0.207463	+	0.207463i	0.595726	+	0.803188i	$0.296865\pi$
$702$	1.36080	+	4.63141i	0.0513599	+	0.174801i
$703$	−19.9341			−0.751829
$704$	4.78741	−	6.40943i	0.180432	−	0.241564i
$705$	−5.54880			−0.208980
$706$	8.18755	+	27.8660i	0.308142	+	1.04875i
$707$	−31.2395	+	31.2395i	−1.17488	+	1.17488i
$708$	15.2918	−	9.83512i	0.574702	−	0.369626i
$709$	−30.5453	−	30.5453i	−1.14715	−	1.14715i	−0.987110	−	0.160041i	$-0.948837\pi$
$709$	−30.5453	−	30.5453i	−1.14715	−	1.14715i	−0.160041	−	0.987110i	$-0.551163\pi$
$710$	11.9809	+	6.53929i	0.449634	+	0.245415i
$711$			6.27423i			0.235302i
$712$	15.1867	−	17.5452i	0.569144	−	0.657533i
$713$		−	0.424147i		−	0.0158844i
$714$	9.69218	−	17.7574i	0.362721	−	0.664554i
$715$	1.81401	+	1.81401i	0.0678400	+	0.0678400i
$716$	−8.82770	+	40.6497i	−0.329907	+	1.51915i
$717$	12.2423	−	12.2423i	0.457199	−	0.457199i
$718$	−12.0767	+	3.54837i	−0.450700	+	0.132424i
$719$	−17.7339			−0.661364			−0.330682	−	0.943742i	$-0.607279\pi$
$719$	−17.7339			−0.661364			−0.330682	+	0.943742i	$0.607279\pi$
$720$	−2.94699	−	7.88411i	−0.109828	−	0.293823i
$721$	−46.0796			−1.71609
$722$	−71.4279	+	20.9869i	−2.65827	+	0.781051i
$723$	−12.2222	+	12.2222i	−0.454549	+	0.454549i
$724$	21.7331	+	4.71967i	0.807703	+	0.175405i
$725$	32.6236	+	32.6236i	1.21161	+	1.21161i
$726$	1.28874	−	2.36114i	0.0478295	−	0.0876302i
$727$		−	39.2767i		−	1.45669i	−0.685210	−	0.728345i	$-0.740290\pi$
$727$		−	39.2767i		−	1.45669i	0.685210	−	0.728345i	$-0.259710\pi$
$728$	0.748315	+	10.3852i	0.0277344	+	0.384901i
$729$			19.3838i			0.717917i
$730$	23.7599	+	12.9684i	0.879394	+	0.479983i
$731$	−7.62321	−	7.62321i	−0.281955	−	0.281955i
$732$	2.52669	+	3.92855i	0.0933892	+	0.145203i
$733$	0.305033	−	0.305033i	0.0112667	−	0.0112667i	−0.701451	−	0.712718i	$-0.747464\pi$
$733$	0.305033	−	0.305033i	0.0112667	−	0.0112667i	0.712718	+	0.701451i	$0.247464\pi$
$734$	12.8596	+	43.7669i	0.474655	+	1.61547i
$735$	−109.325			−4.03250
$736$	0.235695	−	1.64967i	0.00868783	−	0.0608077i
$737$	1.95238			0.0719168
$738$	−1.00823	−	3.43146i	−0.0371134	−	0.126314i
$739$	−8.16495	+	8.16495i	−0.300353	+	0.300353i	−0.841152	−	0.540799i	$-0.818122\pi$
$739$	−8.16495	+	8.16495i	−0.300353	+	0.300353i	0.540799	+	0.841152i	$0.318122\pi$
$740$	−8.67665	−	13.4906i	−0.318960	−	0.495925i
$741$	−8.57613	−	8.57613i	−0.315052	−	0.315052i
$742$	0.736661	+	0.402078i	0.0270437	+	0.0147607i
$743$			13.2880i			0.487488i	0.969840	+	0.243744i	$0.0783757\pi$
$743$			13.2880i			0.487488i	−0.969840	+	0.243744i	$0.921624\pi$
$744$	−7.72601	+	0.556705i	−0.283249	+	0.0204098i
$745$			41.7215i			1.52856i
$746$	15.4601	−	28.3250i	0.566035	−	1.03705i
$747$	−3.38488	−	3.38488i	−0.123846	−	0.123846i
$748$	−3.00801	−	0.653235i	−0.109984	−	0.0238846i
$749$	11.4814	−	11.4814i	0.419523	−	0.419523i
$750$	14.0301	−	4.12232i	0.512308	−	0.150526i
$751$	19.9332			0.727372			0.363686	−	0.931522i	$-0.381518\pi$
$751$	19.9332			0.727372			0.363686	+	0.931522i	$0.381518\pi$
$752$	−1.42127	+	3.11799i	−0.0518283	+	0.113701i
$753$	43.5057			1.58544
$754$	7.14938	−	2.10062i	0.260365	−	0.0765002i
$755$	−20.3147	+	20.3147i	−0.739326	+	0.739326i
$756$	−9.39726	+	43.2724i	−0.341775	+	1.57380i
$757$	−10.4321	−	10.4321i	−0.379160	−	0.379160i	0.491639	−	0.870799i	$-0.336398\pi$
$757$	−10.4321	−	10.4321i	−0.379160	−	0.379160i	−0.870799	+	0.491639i	$0.836398\pi$
$758$	2.46113	−	4.50912i	0.0893922	−	0.163779i
$759$		−	0.560325i		−	0.0203385i
$760$	−61.6408	−	53.3547i	−2.23595	−	1.93538i
$761$		−	8.05745i		−	0.292082i	−0.989279	−	0.146041i	$-0.953347\pi$
$761$		−	8.05745i		−	0.292082i	0.989279	−	0.146041i	$-0.0466532\pi$
$762$	15.1959	+	8.29409i	0.550489	+	0.300463i
$763$	−44.8251	−	44.8251i	−1.62278	−	1.62278i
$764$	−33.0855	+	21.2793i	−1.19699	+	0.769860i
$765$	−2.28998	+	2.28998i	−0.0827945	+	0.0827945i
$766$	−11.1867	−	38.0734i	−0.404192	−	1.37565i
$767$	3.60051			0.130007
$768$	−30.3588	−	2.12803i	−1.09548	−	0.0767888i
$769$	−47.7768			−1.72287			−0.861437	−	0.507864i	$-0.830435\pi$
$769$	−47.7768			−1.72287			−0.861437	+	0.507864i	$0.830435\pi$
$770$	6.63402	+	22.5786i	0.239074	+	0.813676i
$771$	17.0015	−	17.0015i	0.612293	−	0.612293i
$772$	14.8482	−	9.54979i	0.534398	−	0.343704i
$773$	13.4035	+	13.4035i	0.482091	+	0.482091i	0.905799	−	0.423708i	$-0.139272\pi$
$773$	13.4035	+	13.4035i	0.482091	+	0.482091i	−0.423708	+	0.905799i	$0.639272\pi$
$774$	−5.37304	−	2.93267i	−0.193130	−	0.105413i
$775$		−	9.49754i		−	0.341162i
$776$	−15.8751	−	13.7410i	−0.569881	−	0.493274i
$777$		−	21.8899i		−	0.785295i
$778$	−11.9824	+	21.9534i	−0.429591	+	0.787068i
$779$	−24.4954	−	24.4954i	−0.877638	−	0.877638i
$780$	2.07108	−	9.53688i	0.0741566	−	0.341475i
$781$	2.00410	−	2.00410i	0.0717123	−	0.0717123i
$782$	−0.615178	+	0.180751i	−0.0219987	+	0.00646364i
$783$	31.6904			1.13252
$784$	−28.0024	+	61.4319i	−1.00009	+	2.19400i
$785$	1.70335			0.0607951
$786$	29.2871	−	8.60511i	1.04464	−	0.306934i
$787$	−19.6451	+	19.6451i	−0.700271	+	0.700271i	−0.964468	−	0.264198i	$-0.914893\pi$
$787$	−19.6451	+	19.6451i	−0.700271	+	0.700271i	0.264198	+	0.964468i	$0.414893\pi$
$788$	43.5043	+	9.44762i	1.54978	+	0.336558i
$789$	4.40584	+	4.40584i	0.156852	+	0.156852i
$790$	−23.4276	+	42.9224i	−0.833515	+	1.52711i
$791$			14.0873i			0.500886i
$792$	−1.74321	+	0.125609i	−0.0619424	+	0.00446332i
$793$			0.924990i			0.0328474i
$794$	34.7087	+	18.9444i	1.23177	+	0.672312i
$795$	−0.556223	−	0.556223i	−0.0197272	−	0.0197272i
$796$	23.7483	+	36.9243i	0.841736	+	1.30875i
$797$	16.4970	−	16.4970i	0.584352	−	0.584352i	−0.351744	−	0.936096i	$-0.614411\pi$
$797$	16.4970	−	16.4970i	0.584352	−	0.584352i	0.936096	+	0.351744i	$0.114411\pi$
$798$	−31.3638	−	106.745i	−1.11027	−	3.77875i
$799$	1.31845			0.0466435
$800$	5.27771	−	36.9397i	0.186595	−	1.30601i
$801$	−5.06950			−0.179122
$802$	−0.821002	−	2.79424i	−0.0289906	−	0.0986681i
$803$	3.97444	−	3.97444i	0.140255	−	0.140255i
$804$	−4.01765	−	6.24671i	−0.141692	−	0.220305i
$805$	3.46624	+	3.46624i	0.122169	+	0.122169i
$806$	−1.34645	−	0.734908i	−0.0474267	−	0.0258860i
$807$		−	16.7745i		−	0.590490i
$808$	−1.83784	−	25.5058i	−0.0646551	−	0.897290i
$809$		−	54.1309i		−	1.90314i	−0.307430	−	0.951571i	$-0.599469\pi$
$809$		−	54.1309i		−	1.90314i	0.307430	−	0.951571i	$-0.400531\pi$
$810$	24.1615	−	44.2671i	0.848947	−	1.55539i
$811$	4.58286	+	4.58286i	0.160926	+	0.160926i	0.782977	−	0.622051i	$-0.213700\pi$
$811$	4.58286	+	4.58286i	0.160926	+	0.160926i	−0.622051	+	0.782977i	$0.713700\pi$
$812$	66.7984	+	14.5063i	2.34417	+	0.509071i
$813$	−7.87545	+	7.87545i	−0.276204	+	0.276204i
$814$	−3.19556	+	0.938916i	−0.112004	+	0.0329090i
$815$	33.8646			1.18622
$816$	4.09989	+	10.9685i	0.143525	+	0.383973i
$817$	−59.2900			−2.07430
$818$	1.41125	−	0.414652i	0.0493431	−	0.0144980i
$819$	1.60846	−	1.60846i	0.0562040	−	0.0562040i
$820$	5.91548	−	27.2395i	0.206577	−	0.951245i
$821$	−13.8584	−	13.8584i	−0.483663	−	0.483663i	0.422636	−	0.906299i	$-0.361105\pi$
$821$	−13.8584	−	13.8584i	−0.483663	−	0.483663i	−0.906299	+	0.422636i	$0.861105\pi$
$822$	−13.5318	+	24.7921i	−0.471977	+	0.864725i
$823$		−	25.4191i		−	0.886052i	−0.896509	−	0.443026i	$-0.853905\pi$
$823$		−	25.4191i		−	0.886052i	0.896509	−	0.443026i	$-0.146095\pi$
$824$	17.4556	−	20.1665i	0.608095	−	0.702533i
$825$		−	12.5469i		−	0.436826i
$826$	28.9912	+	15.8237i	1.00873	+	0.550577i
$827$	29.0520	+	29.0520i	1.01024	+	1.01024i	0.999947	+	0.0102897i	$0.00327538\pi$
$827$	29.0520	+	29.0520i	1.01024	+	1.01024i	0.0102897	+	0.999947i	$0.496725\pi$
$828$	−0.306196	+	0.196933i	−0.0106410	+	0.00684391i
$829$	−2.05453	+	2.05453i	−0.0713568	+	0.0713568i	−0.741884	−	0.670528i	$-0.766068\pi$
$829$	−2.05453	+	2.05453i	−0.0713568	+	0.0713568i	0.670528	+	0.741884i	$0.266068\pi$
$830$	−10.5173	−	35.7951i	−0.365060	−	1.24247i
$831$	19.5378			0.677760
$832$	−4.82849	−	3.60656i	−0.167398	−	0.125035i
$833$	25.9767			0.900038
$834$	15.1358	+	51.5140i	0.524109	+	1.78378i
$835$	−11.2861	+	11.2861i	−0.390573	+	0.390573i
$836$	−14.2378	+	9.15720i	−0.492424	+	0.316708i
$837$	−4.61293	−	4.61293i	−0.159446	−	0.159446i
$838$	21.3550	+	11.6558i	0.737695	+	0.402642i
$839$			47.0571i			1.62459i	0.583246	+	0.812295i	$0.301782\pi$
$839$			47.0571i			1.62459i	−0.583246	+	0.812295i	$0.698218\pi$
$840$	58.5894	−	67.6885i	2.02153	−	2.33548i
$841$		−	19.9196i		−	0.686883i
$842$	0.754937	−	1.38315i	0.0260169	−	0.0476664i
$843$	26.1044	+	26.1044i	0.899084	+	0.899084i
$844$	3.46174	−	15.9406i	0.119158	−	0.548697i
$845$	−29.9367	+	29.9367i	−1.02985	+	1.02985i
$846$	0.718246	−	0.211034i	0.0246938	−	0.00725551i
$847$	4.88654			0.167903
$848$	−0.455025	+	0.170083i	−0.0156256	+	0.00584068i
$849$	−51.9712			−1.78365
$850$	−13.7751	+	4.04740i	−0.472483	+	0.138825i
$851$	−0.490578	+	0.490578i	−0.0168168	+	0.0168168i
$852$	−10.5363	−	2.28811i	−0.360966	−	0.0783894i
$853$	−25.7103	−	25.7103i	−0.880302	−	0.880302i	0.113263	−	0.993565i	$-0.463870\pi$
$853$	−25.7103	−	25.7103i	−0.880302	−	0.880302i	−0.993565	+	0.113263i	$0.963870\pi$
$854$	−4.06519	+	7.44798i	−0.139108	+	0.254865i
$855$			17.8105i			0.609106i
$856$	0.675461	+	9.37412i	0.0230868	+	0.320401i
$857$			20.1931i			0.689784i	0.938642	+	0.344892i	$0.112084\pi$
$857$			20.1931i			0.689784i	−0.938642	+	0.344892i	$0.887916\pi$
$858$	−1.77875	−	0.970861i	−0.0607255	−	0.0331446i
$859$	−14.7908	−	14.7908i	−0.504656	−	0.504656i	0.408225	−	0.912881i	$-0.366148\pi$
$859$	−14.7908	−	14.7908i	−0.504656	−	0.504656i	−0.912881	+	0.408225i	$0.866148\pi$
$860$	−25.8070	−	40.1251i	−0.880010	−	1.36826i
$861$	26.8986	−	26.8986i	0.916703	−	0.916703i
$862$	8.33112	+	28.3546i	0.283759	+	0.965761i
$863$	8.04857			0.273976			0.136988	−	0.990573i	$-0.456258\pi$
$863$	8.04857			0.273976			0.136988	+	0.990573i	$0.456258\pi$
$864$	−15.3781	−	20.5048i	−0.523174	−	0.697589i
$865$	57.5911			1.95816
$866$	−12.7231	−	43.3026i	−0.432350	−	1.47148i
$867$	−19.6787	+	19.6787i	−0.668325	+	0.668325i
$868$	−7.61176	−	11.8349i	−0.258360	−	0.401703i
$869$	7.17985	+	7.17985i	0.243560	+	0.243560i
$870$	−56.2373	−	30.6950i	−1.90662	−	1.04066i
$871$		−	1.47081i		−	0.0498365i
$872$	36.5978	−	2.63709i	1.23936	−	0.0893032i
$873$			4.58693i			0.155244i
$874$	−1.68939	+	3.09519i	−0.0571445	+	0.104696i
$875$	18.7839	+	18.7839i	0.635010	+	0.635010i
$876$	−20.8950	−	4.53768i	−0.705978	−	0.153314i
$877$	9.03375	−	9.03375i	0.305048	−	0.305048i	−0.537937	−	0.842985i	$-0.680796\pi$
$877$	9.03375	−	9.03375i	0.305048	−	0.305048i	0.842985	+	0.537937i	$0.180796\pi$
$878$	−0.0893002	+	0.0262381i	−0.00301373	+	0.000885493i
$879$	32.9369			1.11093
$880$	−12.3945	−	5.64974i	−0.417817	−	0.190453i
$881$	−6.16395			−0.207669			−0.103834	−	0.994595i	$-0.533111\pi$
$881$	−6.16395			−0.207669			−0.103834	+	0.994595i	$0.533111\pi$
$882$	14.1512	−	4.15788i	0.476494	−	0.140003i
$883$	−35.1572	+	35.1572i	−1.18313	+	1.18313i	−0.204206	+	0.978928i	$0.565461\pi$
$883$	−35.1572	+	35.1572i	−1.18313	+	1.18313i	−0.978928	+	0.204206i	$0.934539\pi$
$884$	−0.492110	+	2.26606i	−0.0165514	+	0.0762159i
$885$	−21.8901	−	21.8901i	−0.735827	−	0.735827i
$886$	16.3227	−	29.9054i	0.548372	−	1.00469i
$887$			50.5055i			1.69581i	0.530150	+	0.847904i	$0.322136\pi$
$887$			50.5055i			1.69581i	−0.530150	+	0.847904i	$0.677864\pi$
$888$	9.57998	+	8.29219i	0.321483	+	0.278268i
$889$			31.4489i			1.05476i
$890$	−34.6808	−	18.9292i	−1.16250	−	0.634507i
$891$	−7.40477	−	7.40477i	−0.248069	−	0.248069i
$892$	−9.03302	+	5.80970i	−0.302448	+	0.194523i
$893$	5.12718	−	5.12718i	0.171574	−	0.171574i
$894$	−9.29057	−	31.6200i	−0.310723	−	1.05753i
$895$	70.8264			2.36746
$896$	−23.0286	−	50.2604i	−0.769330	−	1.67908i
$897$	−0.422117			−0.0140941
$898$	9.62552	+	32.7600i	0.321208	+	1.09322i
$899$	−7.12085	+	7.12085i	−0.237494	+	0.237494i
$900$	−6.85637	+	4.40975i	−0.228546	+	0.146992i
$901$	0.132164	+	0.132164i	0.00440303	+	0.00440303i
$902$	−5.08051	−	2.77300i	−0.169163	−	0.0923308i
$903$		−	65.1071i		−	2.16663i
$904$	−6.16523	−	5.33646i	−0.205052	−	0.177488i
$905$		−	37.8668i		−	1.25874i
$906$	10.8725	−	19.9198i	0.361213	−	0.661792i
$907$	38.2155	+	38.2155i	1.26893	+	1.26893i	0.946643	+	0.322283i	$0.104450\pi$
$907$	38.2155	+	38.2155i	1.26893	+	1.26893i	0.322283	+	0.946643i	$0.395550\pi$
$908$	0.662899	−	3.05251i	0.0219991	−	0.101301i
$909$	−3.95033	+	3.95033i	−0.131024	+	0.131024i
$910$	17.0094	−	4.99769i	0.563857	−	0.165672i
$911$	−24.8890			−0.824609			−0.412304	−	0.911046i	$-0.635276\pi$
$911$	−24.8890			−0.824609			−0.412304	+	0.911046i	$0.635276\pi$
$912$	58.5976	+	26.7104i	1.94036	+	0.884471i
$913$	−7.74690			−0.256385
$914$	−7.02627	+	2.06445i	−0.232408	+	0.0682860i
$915$	5.62367	−	5.62367i	0.185913	−	0.185913i
$916$	−46.9962	−	10.2059i	−1.55280	−	0.337214i
$917$	39.2102	+	39.2102i	1.29484	+	1.29484i
$918$	−4.72473	+	8.65635i	−0.155939	+	0.285702i
$919$		−	18.2745i		−	0.602819i	−0.953495	−	0.301410i	$-0.902543\pi$
$919$		−	18.2745i		−	0.602819i	0.953495	−	0.301410i	$-0.0974571\pi$
$920$	−2.83004	+	0.203921i	−0.0933036	+	0.00672309i
$921$			10.2649i			0.338240i
$922$	−37.7521	−	20.6055i	−1.24330	−	0.678606i
$923$	−1.50977	−	1.50977i	−0.0496948	−	0.0496948i
$924$	−10.0556	−	15.6347i	−0.330806	−	0.514343i
$925$	−10.9851	+	10.9851i	−0.361187	+	0.361187i
$926$	9.34061	+	31.7903i	0.306951	+	1.04470i
$927$	−5.82690			−0.191381
$928$	−31.6528	+	23.7388i	−1.03905	+	0.779264i
$929$	−29.4590			−0.966520			−0.483260	−	0.875477i	$-0.660547\pi$
$929$	−29.4590			−0.966520			−0.483260	+	0.875477i	$0.660547\pi$
$930$	3.71801	+	12.6541i	0.121918	+	0.414943i
$931$	101.018	−	101.018i	3.31072	−	3.31072i
$932$	16.0338	+	24.9297i	0.525205	+	0.816599i
$933$	3.87484	+	3.87484i	0.126857	+	0.126857i
$934$	23.3326	+	12.7352i	0.763465	+	0.416708i
$935$			5.24103i			0.171400i
$936$	0.0946266	+	1.31324i	0.00309297	+	0.0429245i
$937$		−	24.0064i		−	0.784254i	−0.919911	−	0.392127i	$-0.871739\pi$
$937$		−	24.0064i		−	0.784254i	0.919911	−	0.392127i	$-0.128261\pi$
$938$	6.46399	−	11.8429i	0.211057	−	0.386685i
$939$	7.86901	+	7.86901i	0.256796	+	0.256796i
$940$	5.70156	+	1.23818i	0.185964	+	0.0403850i
$941$	9.66150	−	9.66150i	0.314956	−	0.314956i	−0.531870	−	0.846826i	$-0.678511\pi$
$941$	9.66150	−	9.66150i	0.314956	−	0.314956i	0.846826	+	0.531870i	$0.178511\pi$
$942$	−1.29094	+	0.379302i	−0.0420610	+	0.0123583i
$943$	−1.20566			−0.0392617
$944$	−17.9074	+	6.69359i	−0.582837	+	0.217858i
$945$	75.3961			2.45264
$946$	−9.50455	+	2.79262i	−0.309020	+	0.0907959i
$947$	30.5375	−	30.5375i	0.992335	−	0.992335i	−0.00763605	−	0.999971i	$-0.502431\pi$
$947$	30.5375	−	30.5375i	0.992335	−	0.992335i	0.999971	+	0.00763605i	$0.00243065\pi$
$948$	8.19735	−	37.7471i	0.266238	−	1.22597i
$949$	−2.99411	−	2.99411i	−0.0971930	−	0.0971930i
$950$	−37.8290	+	69.3079i	−1.22734	+	2.24865i
$951$			35.1566i			1.14003i
$952$	−13.9214	+	16.0835i	−0.451197	+	0.521269i
$953$			32.6689i			1.05825i	0.848544	+	0.529124i	$0.177480\pi$
$953$			32.6689i			1.05825i	−0.848544	+	0.529124i	$0.822520\pi$
$954$	0.0931529	+	0.0508439i	0.00301594	+	0.00164613i
$955$	47.3616	+	47.3616i	1.53258	+	1.53258i
$956$	−15.3112	+	9.84756i	−0.495198	+	0.318493i
$957$	−9.40710	+	9.40710i	−0.304088	+	0.304088i
$958$	17.3192	+	58.9453i	0.559559	+	1.90444i
$959$	−51.3090			−1.65685
$960$	7.42902	+	51.2827i	0.239771	+	1.65514i
$961$	−28.9269			−0.933127
$962$	0.707325	+	2.40735i	0.0228051	+	0.0776161i
$963$	1.45186	−	1.45186i	0.0467856	−	0.0467856i
$964$	15.2860	−	9.83137i	0.492328	−	0.316647i
$965$	−21.2550	−	21.2550i	−0.684223	−	0.684223i
$966$	−3.39887	−	1.85514i	−0.109357	−	0.0596881i
$967$		−	14.5873i		−	0.469097i	−0.972104	−	0.234549i	$-0.924639\pi$
$967$		−	14.5873i		−	0.469097i	0.972104	−	0.234549i	$-0.0753612\pi$
$968$	−1.85109	+	2.13857i	−0.0594962	+	0.0687362i
$969$		−	24.7782i		−	0.795990i
$970$	−17.1273	+	31.3795i	−0.549924	+	1.00754i
$971$	−23.5279	−	23.5279i	−0.755045	−	0.755045i	0.220371	−	0.975416i	$-0.429273\pi$
$971$	−23.5279	−	23.5279i	−0.755045	−	0.755045i	−0.975416	+	0.220371i	$0.929273\pi$
$972$	−2.68487	+	12.3633i	−0.0861173	+	0.396552i
$973$	−68.9681	+	68.9681i	−2.21101	+	2.21101i
$974$	−27.9269	+	8.20545i	−0.894835	+	0.262920i
$975$	−9.45209			−0.302709
$976$	−1.71962	−	4.60051i	−0.0550436	−	0.147259i
$977$	−54.7989			−1.75317			−0.876586	−	0.481246i	$-0.840184\pi$
$977$	−54.7989			−1.75317			−0.876586	+	0.481246i	$0.840184\pi$
$978$	−25.6654	+	7.54098i	−0.820688	+	0.241134i
$979$	−5.80123	+	5.80123i	−0.185408	+	0.185408i
$980$	112.334	+	24.3951i	3.58839	+	0.779274i
$981$	−5.66826	−	5.66826i	−0.180974	−	0.180974i
$982$	18.6929	−	34.2479i	0.596515	−	1.09290i
$983$		−	9.00546i		−	0.287229i	−0.989634	−	0.143615i	$-0.954127\pi$
$983$		−	9.00546i		−	0.287229i	0.989634	−	0.143615i	$-0.0458726\pi$
$984$	1.58247	+	21.9616i	0.0504472	+	0.700111i
$985$		−	75.8001i		−	2.41519i
$986$	13.3626	+	7.29344i	0.425551	+	0.232270i
$987$	5.63021	+	5.63021i	0.179212	+	0.179212i
$988$	6.89851	+	10.7259i	0.219471	+	0.341237i
$989$	−1.45913	+	1.45913i	−0.0463976	+	0.0463976i
$990$	0.838891	+	2.85513i	0.0266617	+	0.0907419i
$991$	−52.9389			−1.68166			−0.840831	−	0.541298i	$-0.817933\pi$
$991$	−52.9389			−1.68166			−0.840831	+	0.541298i	$0.817933\pi$
$992$	8.06292	+	1.15198i	0.255998	+	0.0365754i
$993$	16.1907			0.513796
$994$	−5.52140	−	18.7918i	−0.175128	−	0.596041i
$995$	52.8567	−	52.8567i	1.67567	−	1.67567i
$996$	15.9417	+	24.7865i	0.505133	+	0.785390i
$997$	3.97532	+	3.97532i	0.125900	+	0.125900i	0.767249	−	0.641349i	$-0.221625\pi$
$997$	3.97532	+	3.97532i	0.125900	+	0.125900i	−0.641349	+	0.767249i	$0.721625\pi$
$998$	−35.7040	−	19.4876i	−1.13019	−	0.616871i
$999$			10.6708i			0.337611i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	176.2.j.a.133.9	yes	40
4.3	odd	2		704.2.j.a.177.5		40
8.3	odd	2		1408.2.j.b.353.16		40
8.5	even	2		1408.2.j.a.353.5		40
16.3	odd	4		704.2.j.a.529.5		40
16.5	even	4		1408.2.j.a.1057.5		40
16.11	odd	4		1408.2.j.b.1057.16		40
16.13	even	4	inner	176.2.j.a.45.9	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
176.2.j.a.45.9	✓	40	16.13	even	4	inner
176.2.j.a.133.9	yes	40	1.1	even	1	trivial
704.2.j.a.177.5		40	4.3	odd	2
704.2.j.a.529.5		40	16.3	odd	4
1408.2.j.a.353.5		40	8.5	even	2
1408.2.j.a.1057.5		40	16.5	even	4
1408.2.j.b.353.16		40	8.3	odd	2
1408.2.j.b.1057.16		40	16.11	odd	4

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:	\( N \)	\(=\)	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	176.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.398671 - 1.35686i) q^{2} +(1.34498 - 1.34498i) q^{3} +(-1.68212 + 1.08188i) q^{4} +(2.40794 + 2.40794i) q^{5} +(-2.36114 - 1.28874i) q^{6} -4.88654i q^{7} +(2.13857 + 1.85109i) q^{8} -0.617917i q^{9} +O(q^{10})\)	\(q+(-0.398671 - 1.35686i) q^{2} +(1.34498 - 1.34498i) q^{3} +(-1.68212 + 1.08188i) q^{4} +(2.40794 + 2.40794i) q^{5} +(-2.36114 - 1.28874i) q^{6} -4.88654i q^{7} +(2.13857 + 1.85109i) q^{8} -0.617917i q^{9} +(2.30726 - 4.22721i) q^{10} +(-0.707107 - 0.707107i) q^{11} +(-0.807315 + 3.71751i) q^{12} +(-0.532694 + 0.532694i) q^{13} +(-6.63034 + 1.94812i) q^{14} +6.47725 q^{15} +(1.65908 - 3.63971i) q^{16} -1.53906 q^{17} +(-0.838425 + 0.246345i) q^{18} +(-5.98507 + 5.98507i) q^{19} +(-6.65556 - 1.44536i) q^{20} +(-6.57227 - 6.57227i) q^{21} +(-0.677540 + 1.24135i) q^{22} +0.294585i q^{23} +(5.36599 - 0.386652i) q^{24} +6.59638i q^{25} +(0.935159 + 0.510420i) q^{26} +(3.20384 + 3.20384i) q^{27} +(5.28664 + 8.21976i) q^{28} +(4.94569 - 4.94569i) q^{29} +(-2.58229 - 8.78870i) q^{30} -1.43981 q^{31} +(-5.59999 - 0.800091i) q^{32} -1.90208 q^{33} +(0.613578 + 2.08829i) q^{34} +(11.7665 - 11.7665i) q^{35} +(0.668511 + 1.03941i) q^{36} +(1.66532 + 1.66532i) q^{37} +(10.5070 + 5.73482i) q^{38} +1.43292i q^{39} +(0.692232 + 9.60687i) q^{40} +4.09275i q^{41} +(-6.29747 + 11.5378i) q^{42} +(4.95316 + 4.95316i) q^{43} +(1.95444 + 0.424438i) q^{44} +(1.48791 - 1.48791i) q^{45} +(0.399710 - 0.117442i) q^{46} -0.856661 q^{47} +(-2.66389 - 7.12673i) q^{48} -16.8783 q^{49} +(8.95035 - 2.62978i) q^{50} +(-2.07000 + 2.07000i) q^{51} +(0.319747 - 1.47237i) q^{52} +(-0.0858734 - 0.0858734i) q^{53} +(3.06988 - 5.62444i) q^{54} -3.40535i q^{55} +(9.04542 - 10.4502i) q^{56} +16.0995i q^{57} +(-8.68229 - 4.73889i) q^{58} +(-3.37953 - 3.37953i) q^{59} +(-10.8955 + 7.00759i) q^{60} +(0.868220 - 0.868220i) q^{61} +(0.574010 + 1.95362i) q^{62} -3.01948 q^{63} +(1.14694 + 7.91736i) q^{64} -2.56539 q^{65} +(0.758304 + 2.58085i) q^{66} +(-1.38054 + 1.38054i) q^{67} +(2.58889 - 1.66508i) q^{68} +(0.396210 + 0.396210i) q^{69} +(-20.6564 - 11.2745i) q^{70} +2.83422i q^{71} +(1.14382 - 1.32146i) q^{72} +5.62070i q^{73} +(1.59569 - 2.92351i) q^{74} +(8.87197 + 8.87197i) q^{75} +(3.59251 - 16.5427i) q^{76} +(-3.45530 + 3.45530i) q^{77} +(1.94427 - 0.571263i) q^{78} -10.1538 q^{79} +(12.7592 - 4.76924i) q^{80} +10.4719 q^{81} +(5.55327 - 1.63166i) q^{82} +(5.47789 - 5.47789i) q^{83} +(18.1658 + 3.94498i) q^{84} +(-3.70597 - 3.70597i) q^{85} +(4.74605 - 8.69541i) q^{86} -13.3037i q^{87} +(-0.203278 - 2.82111i) q^{88} -8.20417i q^{89} +(-2.61207 - 1.42570i) q^{90} +(2.60303 + 2.60303i) q^{91} +(-0.318705 - 0.495529i) q^{92} +(-1.93651 + 1.93651i) q^{93} +(0.341525 + 1.16237i) q^{94} -28.8234 q^{95} +(-8.60795 + 6.45574i) q^{96} -7.42322 q^{97} +(6.72887 + 22.9014i) q^{98} +(-0.436933 + 0.436933i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{6} - 12 q^{8}+O(q^{10}) \) 40 * q - 12 * q^6 - 12 * q^8	\( 40 q - 12 q^{6} - 12 q^{8} - 4 q^{10} - 12 q^{12} + 8 q^{14} - 16 q^{15} - 8 q^{16} - 20 q^{18} - 16 q^{19} - 20 q^{20} + 28 q^{24} + 24 q^{27} + 20 q^{28} + 12 q^{30} + 24 q^{31} - 20 q^{32} - 40 q^{34} + 24 q^{35} + 20 q^{36} + 48 q^{38} - 8 q^{40} - 8 q^{44} - 52 q^{46} - 40 q^{47} - 40 q^{49} + 64 q^{50} - 24 q^{51} - 36 q^{52} + 32 q^{54} - 8 q^{56} + 40 q^{58} - 8 q^{59} + 12 q^{60} + 32 q^{61} - 24 q^{64} - 16 q^{65} - 20 q^{66} - 24 q^{67} + 4 q^{68} + 32 q^{69} - 8 q^{70} - 20 q^{72} - 56 q^{74} - 56 q^{75} + 4 q^{76} + 64 q^{78} + 32 q^{79} + 32 q^{80} - 40 q^{81} + 24 q^{82} + 40 q^{83} + 76 q^{84} - 32 q^{85} - 16 q^{86} + 20 q^{90} - 16 q^{91} + 12 q^{92} - 48 q^{93} + 16 q^{94} - 48 q^{95} + 36 q^{96} + 72 q^{98}+O(q^{100}) \) 40 * q - 12 * q^6 - 12 * q^8 - 4 * q^10 - 12 * q^12 + 8 * q^14 - 16 * q^15 - 8 * q^16 - 20 * q^18 - 16 * q^19 - 20 * q^20 + 28 * q^24 + 24 * q^27 + 20 * q^28 + 12 * q^30 + 24 * q^31 - 20 * q^32 - 40 * q^34 + 24 * q^35 + 20 * q^36 + 48 * q^38 - 8 * q^40 - 8 * q^44 - 52 * q^46 - 40 * q^47 - 40 * q^49 + 64 * q^50 - 24 * q^51 - 36 * q^52 + 32 * q^54 - 8 * q^56 + 40 * q^58 - 8 * q^59 + 12 * q^60 + 32 * q^61 - 24 * q^64 - 16 * q^65 - 20 * q^66 - 24 * q^67 + 4 * q^68 + 32 * q^69 - 8 * q^70 - 20 * q^72 - 56 * q^74 - 56 * q^75 + 4 * q^76 + 64 * q^78 + 32 * q^79 + 32 * q^80 - 40 * q^81 + 24 * q^82 + 40 * q^83 + 76 * q^84 - 32 * q^85 - 16 * q^86 + 20 * q^90 - 16 * q^91 + 12 * q^92 - 48 * q^93 + 16 * q^94 - 48 * q^95 + 36 * q^96 + 72 * q^98

Introduction

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