LMFDB - Embedded newform 544.2.x.a.77.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [544,2,Mod(77,544)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(544, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 7, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("544.77"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 544 = 2^{5} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	544.x (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.34386186996$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$70$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			77.6
Character	$\chi$	$=$	544.77
Dual form			544.2.x.a.325.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37011 + 0.350422i) q^{2} +(1.88387 - 1.88387i) q^{3} +(1.75441 - 0.960235i) q^{4} +4.17244i q^{5} +(-1.92096 + 3.24126i) q^{6} +(-0.584438 - 0.242082i) q^{7} +(-2.06725 + 1.93041i) q^{8} -4.09791i q^{9} +(-1.46212 - 5.71670i) q^{10} +(2.20846 + 2.20846i) q^{11} +(1.49612 - 5.11403i) q^{12} +(-1.68893 + 4.07744i) q^{13} +(0.885576 + 0.126879i) q^{14} +(7.86032 + 7.86032i) q^{15} +(2.15590 - 3.36929i) q^{16} +(4.03039 + 0.869469i) q^{17} +(1.43600 + 5.61459i) q^{18} +(-5.12951 + 2.12471i) q^{19} +(4.00652 + 7.32016i) q^{20} +(-1.55705 + 0.644953i) q^{21} +(-3.79974 - 2.25195i) q^{22} +(1.07973 + 0.447237i) q^{23} +(-0.257780 + 7.53106i) q^{24} -12.4092 q^{25} +(0.885198 - 6.17839i) q^{26} +(-2.06831 - 2.06831i) q^{27} +(-1.25780 + 0.136487i) q^{28} +(-3.43548 - 3.43548i) q^{29} +(-13.5239 - 8.01508i) q^{30} +(9.82081 + 4.06791i) q^{31} +(-1.77315 + 5.37177i) q^{32} +8.32090 q^{33} +(-5.82676 + 0.221067i) q^{34} +(1.01007 - 2.43853i) q^{35} +(-3.93495 - 7.18940i) q^{36} -3.39593 q^{37} +(6.28345 - 4.70858i) q^{38} +(4.49963 + 10.8631i) q^{39} +(-8.05452 - 8.62546i) q^{40} +(2.12550 - 5.13142i) q^{41} +(1.90733 - 1.42928i) q^{42} +(2.33314 - 5.63270i) q^{43} +(5.99519 + 1.75391i) q^{44} +17.0983 q^{45} +(-1.63607 - 0.234405i) q^{46} +7.96286 q^{47} +(-2.28586 - 10.4087i) q^{48} +(-4.66678 - 4.66678i) q^{49} +(17.0020 - 4.34847i) q^{50} +(9.23068 - 5.95475i) q^{51} +(0.952224 + 8.77527i) q^{52} +(5.02061 + 2.07960i) q^{53} +(3.55860 + 2.10903i) q^{54} +(-9.21468 + 9.21468i) q^{55} +(1.67550 - 0.627763i) q^{56} +(-5.66063 + 13.6660i) q^{57} +(5.91087 + 3.50313i) q^{58} +(-1.91534 - 0.793359i) q^{59} +(21.3380 + 6.24246i) q^{60} -3.64838 q^{61} +(-14.8811 - 2.13206i) q^{62} +(-0.992031 + 2.39497i) q^{63} +(0.547022 - 7.98128i) q^{64} +(-17.0129 - 7.04696i) q^{65} +(-11.4006 + 2.91583i) q^{66} +(0.318322 - 0.768497i) q^{67} +(7.90584 - 2.34471i) q^{68} +(2.87659 - 1.19152i) q^{69} +(-0.529397 + 3.69501i) q^{70} +(2.44157 - 1.01133i) q^{71} +(7.91065 + 8.47139i) q^{72} +(14.4597 - 5.98940i) q^{73} +(4.65280 - 1.19001i) q^{74} +(-23.3774 + 23.3774i) q^{75} +(-6.95903 + 8.65314i) q^{76} +(-0.756081 - 1.82534i) q^{77} +(-9.97166 - 13.3068i) q^{78} +(-1.65822 - 4.00329i) q^{79} +(14.0581 + 8.99536i) q^{80} +4.50088 q^{81} +(-1.11401 + 7.77544i) q^{82} +(-9.61074 + 3.98090i) q^{83} +(-2.11240 + 2.62665i) q^{84} +(-3.62781 + 16.8165i) q^{85} +(-1.22284 + 8.53501i) q^{86} -12.9440 q^{87} +(-8.82869 - 0.302196i) q^{88} +(2.20486 + 2.20486i) q^{89} +(-23.4265 + 5.99161i) q^{90} +(1.97415 - 1.97415i) q^{91} +(2.32373 - 0.252153i) q^{92} +(26.1645 - 10.8377i) q^{93} +(-10.9100 + 2.79036i) q^{94} +(-8.86523 - 21.4026i) q^{95} +(6.77933 + 13.4601i) q^{96} +(-1.60004 + 3.86283i) q^{97} +(8.02936 + 4.75867i) q^{98} +(9.05008 - 9.05008i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 4 q^{2} - 4 q^{3} - 8 q^{4} - 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{10} - 4 q^{11} - 4 q^{12} + 8 q^{14} - 24 q^{16} + 4 q^{18} + 12 q^{19} + 12 q^{20} - 12 q^{21} - 4 q^{22} - 4 q^{23} + 48 q^{24}+ \cdots + 20 q^{99}+O(q^{100}) $ 280 * q - 4 * q^2 - 4 * q^3 - 8 * q^4 - 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^10 - 4 * q^11 - 4 * q^12 + 8 * q^14 - 24 * q^16 + 4 * q^18 + 12 * q^19 + 12 * q^20 - 12 * q^21 - 4 * q^22 - 4 * q^23 + 48 * q^24 - 256 * q^25 - 4 * q^26 + 8 * q^27 + 28 * q^28 - 4 * q^29 + 8 * q^30 - 24 * q^31 - 64 * q^32 + 8 * q^33 - 28 * q^34 + 12 * q^35 + 44 * q^36 - 8 * q^37 - 4 * q^39 + 48 * q^40 - 4 * q^41 + 56 * q^42 - 4 * q^43 - 32 * q^44 + 32 * q^45 + 8 * q^46 - 80 * q^47 - 56 * q^48 + 12 * q^50 - 4 * q^51 - 28 * q^52 - 4 * q^53 + 124 * q^54 - 32 * q^56 - 4 * q^57 + 24 * q^58 - 4 * q^59 + 20 * q^60 - 72 * q^61 - 4 * q^62 - 36 * q^63 - 8 * q^64 + 12 * q^65 + 48 * q^66 - 8 * q^67 - 20 * q^68 + 4 * q^69 + 44 * q^70 + 28 * q^71 + 52 * q^72 - 4 * q^73 - 32 * q^74 + 4 * q^75 - 20 * q^76 - 4 * q^77 - 104 * q^78 + 76 * q^80 - 240 * q^81 - 104 * q^82 - 44 * q^83 + 36 * q^84 + 48 * q^85 + 32 * q^86 + 88 * q^87 + 12 * q^88 + 84 * q^90 - 56 * q^91 - 124 * q^92 - 4 * q^93 - 136 * q^94 + 12 * q^95 - 4 * q^96 - 8 * q^97 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/544\mathbb{Z}\right)^\times$.

$n$	$69$	$511$	$513$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.37011	+	0.350422i	−0.968815	+	0.247786i
$2$	−1.37011	+	0.350422i	−0.968815	+	0.247786i
$3$	1.88387	−	1.88387i	1.08765	−	1.08765i	0.0918809	−	0.995770i	$-0.470712\pi$
$3$	1.88387	−	1.88387i	1.08765	−	1.08765i	0.995770	−	0.0918809i	$-0.0292879\pi$
$4$	1.75441	−	0.960235i	0.877204	−	0.480117i
$5$			4.17244i			1.86597i	0.359913	+	0.932986i	$0.382806\pi$
$5$			4.17244i			1.86597i	−0.359913	+	0.932986i	$0.617194\pi$
$6$	−1.92096	+	3.24126i	−0.784228	+	1.32324i
$7$	−0.584438	−	0.242082i	−0.220897	−	0.0914985i	0.269490	−	0.963003i	$-0.413145\pi$
$7$	−0.584438	−	0.242082i	−0.220897	−	0.0914985i	−0.490387	+	0.871505i	$0.663145\pi$
$8$	−2.06725	+	1.93041i	−0.730882	+	0.682504i
$9$		−	4.09791i		−	1.36597i
$10$	−1.46212	−	5.71670i	−0.462361	−	1.80778i
$11$	2.20846	+	2.20846i	0.665877	+	0.665877i	0.956759	−	0.290882i	$-0.0939487\pi$
$11$	2.20846	+	2.20846i	0.665877	+	0.665877i	−0.290882	+	0.956759i	$0.593949\pi$
$12$	1.49612	−	5.11403i	0.431892	−	1.47629i
$13$	−1.68893	+	4.07744i	−0.468425	+	1.13088i	0.496425	+	0.868079i	$0.334646\pi$
$13$	−1.68893	+	4.07744i	−0.468425	+	1.13088i	−0.964851	+	0.262799i	$0.915354\pi$
$14$	0.885576	+	0.126879i	0.236680	+	0.0339100i
$15$	7.86032	+	7.86032i	2.02953	+	2.02953i
$16$	2.15590	−	3.36929i	0.538975	−	0.842322i
$17$	4.03039	+	0.869469i	0.977513	+	0.210877i
$17$	4.03039	+	0.869469i	0.977513	+	0.210877i
$18$	1.43600	+	5.61459i	0.338468	+	1.32337i
$19$	−5.12951	+	2.12471i	−1.17679	+	0.487442i	−0.883431	−	0.468560i	$-0.844773\pi$
$19$	−5.12951	+	2.12471i	−1.17679	+	0.487442i	−0.293358	+	0.956003i	$0.594773\pi$
$20$	4.00652	+	7.32016i	0.895885	+	1.63684i
$21$	−1.55705	+	0.644953i	−0.339777	+	0.140740i
$22$	−3.79974	−	2.25195i	−0.810106	−	0.480117i
$23$	1.07973	+	0.447237i	0.225138	+	0.0932553i	0.492401	−	0.870368i	$-0.336119\pi$
$23$	1.07973	+	0.447237i	0.225138	+	0.0932553i	−0.267263	+	0.963624i	$0.586119\pi$
$24$	−0.257780	+	7.53106i	−0.0526191	+	1.53727i
$25$	−12.4092			−2.48185
$26$	0.885198	−	6.17839i	0.173602	−	1.21168i
$27$	−2.06831	−	2.06831i	−0.398047	−	0.398047i
$28$	−1.25780	+	0.136487i	−0.237702	+	0.0257935i
$29$	−3.43548	−	3.43548i	−0.637954	−	0.637954i	0.312097	−	0.950050i	$-0.398969\pi$
$29$	−3.43548	−	3.43548i	−0.637954	−	0.637954i	−0.950050	+	0.312097i	$0.898969\pi$
$30$	−13.5239	−	8.01508i	−2.46912	−	1.46335i
$31$	9.82081	+	4.06791i	1.76387	+	0.730619i	0.995933	+	0.0900922i	$0.0287162\pi$
$31$	9.82081	+	4.06791i	1.76387	+	0.730619i	0.767936	+	0.640526i	$0.221284\pi$
$32$	−1.77315	+	5.37177i	−0.313451	+	0.949604i
$33$	8.32090			1.44848
$34$	−5.82676	+	0.221067i	−0.999281	+	0.0379127i
$35$	1.01007	−	2.43853i	0.170734	−	0.412187i
$36$	−3.93495	−	7.18940i	−0.655825	−	1.19823i
$37$	−3.39593			−0.558288			−0.279144	−	0.960249i	$-0.590051\pi$
$37$	−3.39593			−0.558288			−0.279144	+	0.960249i	$0.590051\pi$
$38$	6.28345	−	4.70858i	1.01931	−	0.763833i
$39$	4.49963	+	10.8631i	0.720518	+	1.73948i
$40$	−8.05452	−	8.62546i	−1.27353	−	1.36381i
$41$	2.12550	−	5.13142i	0.331948	−	0.801393i	−0.666490	−	0.745514i	$-0.732204\pi$
$41$	2.12550	−	5.13142i	0.331948	−	0.801393i	0.998438	−	0.0558788i	$-0.0177961\pi$
$42$	1.90733	−	1.42928i	0.294308	−	0.220543i
$43$	2.33314	−	5.63270i	0.355801	−	0.858979i	−0.640080	−	0.768308i	$-0.721099\pi$
$43$	2.33314	−	5.63270i	0.355801	−	0.858979i	0.995881	−	0.0906707i	$-0.0289011\pi$
$44$	5.99519	+	1.75391i	0.903809	+	0.264411i
$45$	17.0983			2.54886
$46$	−1.63607	−	0.234405i	−0.241225	−	0.0345611i
$47$	7.96286			1.16150			0.580752	−	0.814081i	$-0.302759\pi$
$47$	7.96286			1.16150			0.580752	+	0.814081i	$0.302759\pi$
$48$	−2.28586	−	10.4087i	−0.329936	−	1.50237i
$49$	−4.66678	−	4.66678i	−0.666683	−	0.666683i
$50$	17.0020	−	4.34847i	2.40445	−	0.614967i
$51$	9.23068	−	5.95475i	1.29255	−	0.833831i
$52$	0.952224	+	8.77527i	0.132050	+	1.21691i
$53$	5.02061	+	2.07960i	0.689633	+	0.285656i	0.699847	−	0.714292i	$-0.253251\pi$
$53$	5.02061	+	2.07960i	0.689633	+	0.285656i	−0.0102140	+	0.999948i	$0.503251\pi$
$54$	3.55860	+	2.10903i	0.484264	+	0.287003i
$55$	−9.21468	+	9.21468i	−1.24251	+	1.24251i
$56$	1.67550	−	0.627763i	0.223898	−	0.0838883i
$57$	−5.66063	+	13.6660i	−0.749769	+	1.81010i
$58$	5.91087	+	3.50313i	0.776135	+	0.459983i
$59$	−1.91534	−	0.793359i	−0.249356	−	0.103287i	0.254505	−	0.967072i	$-0.418088\pi$
$59$	−1.91534	−	0.793359i	−0.249356	−	0.103287i	−0.503861	+	0.863785i	$0.668088\pi$
$60$	21.3380	+	6.24246i	2.75472	+	0.805898i
$61$	−3.64838			−0.467127			−0.233563	−	0.972342i	$-0.575039\pi$
$61$	−3.64838			−0.467127			−0.233563	+	0.972342i	$0.575039\pi$
$62$	−14.8811	−	2.13206i	−1.88990	−	0.270772i
$63$	−0.992031	+	2.39497i	−0.124984	+	0.301738i
$64$	0.547022	−	7.98128i	0.0683777	−	0.997660i
$65$	−17.0129	−	7.04696i	−2.11019	−	0.874068i
$66$	−11.4006	+	2.91583i	−1.40331	+	0.358914i
$67$	0.318322	−	0.768497i	0.0388892	−	0.0938868i	−0.903242	−	0.429133i	$-0.858819\pi$
$67$	0.318322	−	0.768497i	0.0388892	−	0.0938868i	0.942131	+	0.335246i	$0.108819\pi$
$68$	7.90584	−	2.34471i	0.958724	−	0.284338i
$69$	2.87659	−	1.19152i	0.346301	−	0.143443i
$70$	−0.529397	+	3.69501i	−0.0632750	+	0.441639i
$71$	2.44157	−	1.01133i	0.289761	−	0.120023i	−0.233068	−	0.972460i	$-0.574877\pi$
$71$	2.44157	−	1.01133i	0.289761	−	0.120023i	0.522829	+	0.852437i	$0.324877\pi$
$72$	7.91065	+	8.47139i	0.932279	+	0.998362i
$73$	14.4597	−	5.98940i	1.69238	−	0.701006i	0.692586	−	0.721336i	$-0.256471\pi$
$73$	14.4597	−	5.98940i	1.69238	−	0.701006i	0.999793	+	0.0203294i	$0.00647148\pi$
$74$	4.65280	−	1.19001i	0.540878	−	0.138336i
$75$	−23.3774	+	23.3774i	−2.69939	+	2.69939i
$76$	−6.95903	+	8.65314i	−0.798255	+	0.992583i
$77$	−0.756081	−	1.82534i	−0.0861634	−	0.208017i
$78$	−9.97166	−	13.3068i	−1.12907	−	1.50670i
$79$	−1.65822	−	4.00329i	−0.186564	−	0.450405i	0.802730	−	0.596343i	$-0.203380\pi$
$79$	−1.65822	−	4.00329i	−0.186564	−	0.450405i	−0.989294	+	0.145938i	$0.953380\pi$
$80$	14.0581	+	8.99536i	1.57175	+	1.00571i
$81$	4.50088			0.500098
$82$	−1.11401	+	7.77544i	−0.123022	+	0.858654i
$83$	−9.61074	+	3.98090i	−1.05492	+	0.436961i	−0.841644	−	0.540032i	$-0.818412\pi$
$83$	−9.61074	+	3.98090i	−1.05492	+	0.436961i	−0.213272	+	0.976993i	$0.568412\pi$
$84$	−2.11240	+	2.62665i	−0.230482	+	0.286591i
$85$	−3.62781	+	16.8165i	−0.393491	+	1.82401i
$86$	−1.22284	+	8.53501i	−0.131862	+	0.920354i
$87$	−12.9440			−1.38774
$88$	−8.82869	−	0.302196i	−0.941141	−	0.0322143i
$89$	2.20486	+	2.20486i	0.233715	+	0.233715i	0.814241	−	0.580526i	$-0.197153\pi$
$89$	2.20486	+	2.20486i	0.233715	+	0.233715i	−0.580526	+	0.814241i	$0.697153\pi$
$90$	−23.4265	+	5.99161i	−2.46937	+	0.631571i
$91$	1.97415	−	1.97415i	0.206947	−	0.206947i
$92$	2.32373	−	0.252153i	0.242266	−	0.0262888i
$93$	26.1645	−	10.8377i	2.71313	−	1.12382i
$94$	−10.9100	+	2.79036i	−1.12528	+	0.287804i
$95$	−8.86523	−	21.4026i	−0.909553	−	2.19586i
$96$	6.77933	+	13.4601i	0.691912	+	1.37376i
$97$	−1.60004	+	3.86283i	−0.162459	+	0.392211i	−0.984056	−	0.177858i	$-0.943083\pi$
$97$	−1.60004	+	3.86283i	−0.162459	+	0.392211i	0.821597	+	0.570068i	$0.193083\pi$
$98$	8.02936	+	4.75867i	0.811087	+	0.480698i
$99$	9.05008	−	9.05008i	0.909567	−	0.909567i
$100$	−21.7709	+	11.9158i	−2.17709	+	1.19158i
$101$	−2.79760	+	1.15880i	−0.278371	+	0.115305i	−0.517501	−	0.855682i	$-0.673138\pi$
$101$	−2.79760	+	1.15880i	−0.278371	+	0.115305i	0.239130	+	0.970988i	$0.423138\pi$
$102$	−10.5604	+	11.3933i	−1.04563	+	1.12810i
$103$	4.76794	−	4.76794i	0.469799	−	0.469799i	−0.432051	−	0.901849i	$-0.642210\pi$
$103$	4.76794	−	4.76794i	0.469799	−	0.469799i	0.901849	+	0.432051i	$0.142210\pi$
$104$	−4.37970	−	11.6894i	−0.429465	−	1.14624i
$105$	−2.69103	−	6.49672i	−0.262617	−	0.634015i
$106$	−7.60753	−	1.08996i	−0.738908	−	0.105866i
$107$	14.6511			1.41638			0.708188	−	0.706023i	$-0.249513\pi$
$107$	14.6511			1.41638			0.708188	+	0.706023i	$0.249513\pi$
$108$	−5.61472	−	1.64260i	−0.540277	−	0.158059i
$109$		−	2.87165i		−	0.275054i	−0.990498	−	0.137527i	$-0.956085\pi$
$109$		−	2.87165i		−	0.275054i	0.990498	−	0.137527i	$-0.0439154\pi$
$110$	9.39611	−	15.8542i	0.895884	−	1.51164i
$111$	−6.39748	+	6.39748i	−0.607222	+	0.607222i
$112$	−2.07564	+	1.44724i	−0.196129	+	0.136751i
$113$	1.15186	+	2.78084i	0.108358	+	0.261599i	0.968753	−	0.248029i	$-0.0797829\pi$
$113$	1.15186	+	2.78084i	0.108358	+	0.261599i	−0.860395	+	0.509628i	$0.829783\pi$
$114$	2.96683	−	20.7075i	0.277870	−	1.93944i
$115$	−1.86607	+	4.50509i	−0.174012	+	0.420102i
$116$	−9.32612	−	2.72837i	−0.865908	−	0.253323i
$117$	16.7090	+	6.92108i	1.54475	+	0.639854i
$118$	2.90224	+	0.415813i	0.267173	+	0.0382787i
$119$	−2.14503	−	1.48384i	−0.196635	−	0.136023i
$120$	−31.4229	−	1.07557i	−2.86850	−	0.0981858i
$121$		−	1.24537i		−	0.113216i
$122$	4.99868	−	1.27847i	0.452559	−	0.115747i
$123$	−5.66274	−	13.6711i	−0.510593	−	1.23268i
$124$	21.1359	−	2.29350i	1.89806	−	0.205962i
$125$		−	30.9146i		−	2.76509i
$126$	0.519940	−	3.62901i	0.0463200	−	0.323298i
$127$	−5.29157	−	5.29157i	−0.469551	−	0.469551i	0.432218	−	0.901769i	$-0.357731\pi$
$127$	−5.29157	−	5.29157i	−0.469551	−	0.469551i	−0.901769	+	0.432218i	$0.857731\pi$
$128$	2.04734	+	11.1269i	0.180961	+	0.983490i
$129$	−6.21593	−	15.0066i	−0.547282	−	1.32126i
$130$	25.7789	+	3.69343i	2.26096	+	0.323936i
$131$	0.499340	+	0.499340i	0.0436275	+	0.0436275i	0.728584	−	0.684956i	$-0.240179\pi$
$131$	0.499340	+	0.499340i	0.0436275	+	0.0436275i	−0.684956	+	0.728584i	$0.740179\pi$
$132$	14.5983	−	7.99002i	1.27062	−	0.695442i
$133$	3.51224			0.304549
$134$	−0.166838	+	1.16447i	−0.0144126	+	0.100595i
$135$	8.62990	−	8.62990i	0.742743	−	0.742743i
$136$	−10.0102	+	5.98290i	−0.858371	+	0.513029i
$137$	−9.90729	−	9.90729i	−0.846437	−	0.846437i	0.143250	−	0.989687i	$-0.454245\pi$
$137$	−9.90729	−	9.90729i	−0.846437	−	0.846437i	−0.989687	+	0.143250i	$0.954245\pi$
$138$	−3.52372	+	2.64054i	−0.299959	+	0.224778i
$139$		−	14.5059i		−	1.23037i	−0.788382	−	0.615186i	$-0.789081\pi$
$139$		−	14.5059i		−	1.23037i	0.788382	−	0.615186i	$-0.210919\pi$
$140$	−0.569482	−	5.24809i	−0.0481300	−	0.443545i
$141$	15.0010	−	15.0010i	1.26331	−	1.26331i
$142$	−2.99083	+	2.24122i	−0.250985	+	0.188079i
$143$	−12.7348	+	5.27494i	−1.06494	+	0.441112i
$144$	−13.8070	−	8.83467i	−1.15059	−	0.736223i
$145$	14.3344	−	14.3344i	1.19040	−	1.19040i
$146$	−17.7126	+	13.2731i	−1.46590	+	1.09849i
$147$	−17.5832			−1.45024
$148$	−5.95785	+	3.26089i	−0.489733	+	0.268044i
$149$	−19.9028	+	8.24400i	−1.63050	+	0.675375i	−0.995288	−	0.0969639i	$-0.969087\pi$
$149$	−19.9028	+	8.24400i	−1.63050	+	0.675375i	−0.635211	+	0.772339i	$0.719087\pi$
$150$	23.8376	−	40.2215i	1.94634	−	3.28407i
$151$	−23.8038			−1.93712			−0.968561	−	0.248776i	$-0.919972\pi$
$151$	−23.8038			−1.93712			−0.968561	+	0.248776i	$0.919972\pi$
$152$	6.50239	−	14.2944i	0.527414	−	1.15943i
$153$	3.56300	−	16.5162i	0.288052	−	1.33525i
$154$	1.67556	+	2.23597i	0.135020	+	0.180180i
$155$	−16.9731	+	40.9767i	−1.36331	+	3.29133i
$156$	18.3253	+	14.7376i	1.46720	+	1.17995i
$157$	17.0699	+	7.07059i	1.36233	+	0.564295i	0.939697	−	0.342007i	$-0.111107\pi$
$157$	17.0699	+	7.07059i	1.36233	+	0.564295i	0.422631	+	0.906302i	$0.361107\pi$
$158$	3.67478	+	4.90387i	0.292350	+	0.390131i
$159$	13.3759	−	5.54046i	1.06077	−	0.439387i
$160$	−22.4134	−	7.39835i	−1.77193	−	0.584891i
$161$	−0.522765	−	0.522765i	−0.0411996	−	0.0411996i
$162$	−6.16670	+	1.57721i	−0.484502	+	0.123917i
$163$	−1.78972			−0.140181			−0.0700907	−	0.997541i	$-0.522329\pi$
$163$	−1.78972			−0.140181			−0.0700907	+	0.997541i	$0.522329\pi$
$164$	−1.19836	−	11.0436i	−0.0935765	−	0.862359i
$165$			34.7185i			2.70283i
$166$	11.7728	−	8.82209i	0.913746	−	0.684727i
$167$	8.24936	−	3.41700i	0.638354	−	0.264415i	−0.0399436	−	0.999202i	$-0.512718\pi$
$167$	8.24936	−	3.41700i	0.638354	−	0.264415i	0.678298	+	0.734787i	$0.262718\pi$
$168$	1.97379	−	4.33903i	0.152281	−	0.334764i
$169$	−4.58065	−	4.58065i	−0.352357	−	0.352357i
$170$	−0.922390	−	24.3118i	−0.0707441	−	1.86463i
$171$	8.70687	+	21.0202i	0.665831	+	1.60746i
$172$	−1.31543	−	12.1224i	−0.100301	−	0.924326i
$173$	0.673009	+	0.673009i	0.0511679	+	0.0511679i	0.732228	−	0.681060i	$-0.238481\pi$
$173$	0.673009	+	0.673009i	0.0511679	+	0.0511679i	−0.681060	+	0.732228i	$0.738481\pi$
$174$	17.7347	−	4.53586i	1.34446	−	0.343863i
$175$	7.25244	+	3.00406i	0.548233	+	0.227086i
$176$	12.2022	−	2.67972i	0.919774	−	0.201992i
$177$	−5.10283	+	2.11366i	−0.383552	+	0.158872i
$178$	−3.79354	−	2.24827i	−0.284338	−	0.168515i
$179$	4.49778	+	10.8586i	0.336180	+	0.811611i	0.998075	+	0.0620142i	$0.0197524\pi$
$179$	4.49778	+	10.8586i	0.336180	+	0.811611i	−0.661895	+	0.749596i	$0.730248\pi$
$180$	29.9973	−	16.4183i	2.23587	−	1.22375i
$181$	−9.44781	−	9.44781i	−0.702250	−	0.702250i	0.262643	−	0.964893i	$-0.415406\pi$
$181$	−9.44781	−	9.44781i	−0.702250	−	0.702250i	−0.964893	+	0.262643i	$0.915406\pi$
$182$	−2.01302	+	3.39659i	−0.149215	+	0.251772i
$183$	−6.87305	+	6.87305i	−0.508071	+	0.508071i
$184$	−3.09541	+	1.15977i	−0.228197	+	0.0854990i
$185$		−	14.1693i		−	1.04175i
$186$	−32.0505	+	24.0175i	−2.35006	+	1.76105i
$187$	6.98077	+	10.8212i	0.510485	+	0.791321i
$188$	13.9701	−	7.64622i	1.01888	−	0.557658i
$189$	0.708099	+	1.70950i	0.0515066	+	0.124348i
$190$	19.6463	+	26.2173i	1.42529	+	1.90200i
$191$			5.70983i			0.413149i	0.978431	+	0.206575i	$0.0662316\pi$
$191$			5.70983i			0.413149i	−0.978431	+	0.206575i	$0.933768\pi$
$192$	−14.0051	−	16.0662i	−1.01073	−	1.15948i
$193$	−8.68465	+	3.59730i	−0.625135	+	0.258939i	−0.672684	−	0.739930i	$-0.734859\pi$
$193$	−8.68465	+	3.59730i	−0.625135	+	0.258939i	0.0475496	+	0.998869i	$0.484859\pi$
$194$	0.838606	−	5.85319i	0.0602084	−	0.420235i
$195$	−45.3255	+	18.7744i	−3.24583	+	1.34447i
$196$	−12.6687	−	3.70624i	−0.904904	−	0.264731i
$197$	−6.40112	−	6.40112i	−0.456061	−	0.456061i	0.441299	−	0.897360i	$-0.354518\pi$
$197$	−6.40112	−	6.40112i	−0.456061	−	0.456061i	−0.897360	+	0.441299i	$0.854518\pi$
$198$	−9.22827	+	15.5710i	−0.655824	+	1.10658i
$199$	−2.66942	−	6.44456i	−0.189230	−	0.456843i	0.800582	−	0.599224i	$-0.204524\pi$
$199$	−2.66942	−	6.44456i	−0.189230	−	0.456843i	−0.989812	+	0.142381i	$0.954524\pi$
$200$	25.6530	−	23.9550i	1.81394	−	1.69387i
$201$	−0.848069	−	2.04742i	−0.0598182	−	0.144414i
$202$	3.42695	−	2.56803i	0.241119	−	0.180686i
$203$	1.17616	+	2.83950i	0.0825502	+	0.199294i
$204$	10.4764	−	19.3107i	0.733496	−	1.35202i
$205$	21.4105	+	8.86853i	1.49538	+	0.619405i
$206$	−4.86181	+	8.20339i	−0.338738	+	0.571557i
$207$	1.83274	−	4.42461i	0.127384	−	0.307532i
$208$	10.0969	+	14.4810i	0.700094	+	1.00408i
$209$	−16.0207	−	6.63598i	−1.10817	−	0.459021i
$210$	5.96360	+	7.95823i	0.411527	+	0.549170i
$211$			11.9092i			0.819866i	0.912116	+	0.409933i	$0.134448\pi$
$211$			11.9092i			0.819866i	−0.912116	+	0.409933i	$0.865552\pi$
$212$	10.8051	−	1.17249i	0.742098	−	0.0805267i
$213$	2.69438	−	6.50480i	0.184616	−	0.445702i
$214$	−20.0737	+	5.13408i	−1.37221	+	0.350958i
$215$	23.5021	+	9.73489i	1.60283	+	0.663914i
$216$	8.26840	+	0.283018i	0.562593	+	0.0192570i
$217$	−4.75489	−	4.75489i	−0.322783	−	0.322783i
$218$	1.00629	+	3.93448i	0.0681545	+	0.266476i
$219$	15.9569	−	38.5234i	1.07827	−	2.60317i
$220$	−7.31806	+	25.0146i	−0.493384	+	1.68648i
$221$	−10.3523	+	14.9652i	−0.696368	+	1.00667i
$222$	6.52344	−	11.0071i	0.437825	−	0.738747i
$223$	−2.73240	+	2.73240i	−0.182975	+	0.182975i	−0.792651	−	0.609676i	$-0.791300\pi$
$223$	−2.73240	+	2.73240i	−0.182975	+	0.182975i	0.609676	+	0.792651i	$0.291300\pi$
$224$	2.33671	−	2.71022i	0.156128	−	0.181084i
$225$			50.8519i			3.39013i
$226$	−2.55264	−	3.40642i	−0.169799	−	0.226592i
$227$		−	11.7055i		−	0.776920i	−0.921466	−	0.388460i	$-0.873007\pi$
$227$		−	11.7055i		−	0.776920i	0.921466	−	0.388460i	$-0.126993\pi$
$228$	3.19148	+	29.4112i	0.211361	+	1.94781i
$229$	−22.3128	−	9.24226i	−1.47447	−	0.610746i	−0.506597	−	0.862183i	$-0.669097\pi$
$229$	−22.3128	−	9.24226i	−1.47447	−	0.610746i	−0.967874	+	0.251438i	$0.919097\pi$
$230$	0.978039	−	6.82638i	0.0644900	−	0.450118i
$231$	−4.86306	−	2.01434i	−0.319966	−	0.132534i
$232$	13.7339	+	0.470097i	0.901674	+	0.0308634i
$233$	−4.36138	+	1.80654i	−0.285724	+	0.118351i	−0.520942	−	0.853592i	$-0.674419\pi$
$233$	−4.36138	+	1.80654i	−0.285724	+	0.118351i	0.235219	+	0.971942i	$0.424419\pi$
$234$	−25.3185	−	3.62746i	−1.65512	−	0.237134i
$235$			33.2246i			2.16733i
$236$	−4.12210	+	0.447298i	−0.268326	+	0.0291166i
$237$	−10.6655	−	4.41780i	−0.692800	−	0.286967i
$238$	3.45890	+	1.28136i	0.224207	+	0.0830579i
$239$			0.503387i			0.0325614i	0.999867	+	0.0162807i	$0.00518254\pi$
$239$			0.503387i			0.0325614i	−0.999867	+	0.0162807i	$0.994817\pi$
$240$	43.4297	−	9.53762i	2.80338	−	0.615651i
$241$	−7.72004	+	18.6378i	−0.497292	+	1.20057i	0.453645	+	0.891183i	$0.350123\pi$
$241$	−7.72004	+	18.6378i	−0.497292	+	1.20057i	−0.950937	+	0.309386i	$0.899877\pi$
$242$	0.436406	+	1.70630i	0.0280532	+	0.109685i
$243$	14.6840	−	14.6840i	0.941978	−	0.941978i
$244$	−6.40074	+	3.50330i	−0.409765	+	0.224276i
$245$	19.4719	−	19.4719i	1.24401	−	1.24401i
$246$	12.5492	+	16.7465i	0.800110	+	1.06772i
$247$		−	24.5037i		−	1.55914i
$248$	−28.1548	+	10.5488i	−1.78783	+	0.669851i
$249$	−10.6059	+	25.6048i	−0.672120	+	1.62264i
$250$	10.8332	+	42.3565i	0.685150	+	2.67886i
$251$	5.34517	+	12.9044i	0.337384	+	0.814518i	0.997965	+	0.0637628i	$0.0203101\pi$
$251$	5.34517	+	12.9044i	0.337384	+	0.814518i	−0.660581	+	0.750755i	$0.729690\pi$
$252$	0.559310	+	5.15435i	0.0352332	+	0.324693i
$253$	1.39683	+	3.37224i	0.0878178	+	0.212011i
$254$	9.10433	+	5.39576i	0.571256	+	0.338560i
$255$	24.8458	+	38.5144i	1.55591	+	2.41187i
$256$	−6.70420	−	14.5277i	−0.419012	−	0.907981i
$257$	15.9683	−	15.9683i	0.996078	−	0.996078i	−0.00391437	−	0.999992i	$-0.501246\pi$
$257$	15.9683	−	15.9683i	0.996078	−	0.996078i	0.999992	+	0.00391437i	$0.00124599\pi$
$258$	13.7752	+	18.3825i	0.857604	+	1.14444i
$259$	1.98471	+	0.822095i	0.123324	+	0.0510825i
$260$	−36.6143	+	3.97310i	−2.27072	+	0.246401i
$261$	−14.0783	+	14.0783i	−0.871425	+	0.871425i
$262$	−0.859131	−	0.509171i	−0.0530773	−	0.0314567i
$263$	10.2845			0.634167			0.317083	−	0.948398i	$-0.397296\pi$
$263$	10.2845			0.634167			0.317083	+	0.948398i	$0.397296\pi$
$264$	−17.2014	+	16.0628i	−1.05867	+	0.988595i
$265$	−8.67702	+	20.9482i	−0.533025	+	1.28684i
$266$	−4.81215	+	1.23077i	−0.295052	+	0.0754630i
$267$	8.30733			0.508400
$268$	−0.179471	−	1.65392i	−0.0109629	−	0.101029i
$269$	−6.89370	−	6.89370i	−0.420316	−	0.420316i	0.464996	−	0.885313i	$-0.346056\pi$
$269$	−6.89370	−	6.89370i	−0.420316	−	0.420316i	−0.885313	+	0.464996i	$0.846056\pi$
$270$	−8.79981	+	14.8480i	−0.535539	+	0.903622i
$271$		−	14.3505i		−	0.871731i	−0.900012	−	0.435865i	$-0.856442\pi$
$271$		−	14.3505i		−	0.871731i	0.900012	−	0.435865i	$-0.143558\pi$
$272$	11.6186	−	11.7050i	0.704481	−	0.709723i
$273$		−	7.43808i		−	0.450173i
$274$	17.0458	+	10.1024i	1.02978	+	0.610306i
$275$	−27.4054	−	27.4054i	−1.65261	−	1.65261i
$276$	3.90258	−	4.85262i	0.234908	−	0.292094i
$277$	−12.4128			−0.745814			−0.372907	−	0.927869i	$-0.621639\pi$
$277$	−12.4128			−0.745814			−0.372907	+	0.927869i	$0.621639\pi$
$278$	5.08318	+	19.8746i	0.304869	+	1.19200i
$279$	16.6699	−	40.2448i	0.998002	−	2.40939i
$280$	2.61930	+	6.99091i	0.156533	+	0.417787i
$281$	23.2135			1.38480			0.692401	−	0.721513i	$-0.256553\pi$
$281$	23.2135			1.38480			0.692401	+	0.721513i	$0.256553\pi$
$282$	−15.2963	+	25.8097i	−0.910883	+	1.53694i
$283$	7.86531	−	7.86531i	0.467544	−	0.467544i	−0.433574	−	0.901118i	$-0.642748\pi$
$283$	7.86531	−	7.86531i	0.467544	−	0.467544i	0.901118	+	0.433574i	$0.142748\pi$
$284$	3.31239	−	4.11877i	0.196554	−	0.244404i
$285$	−57.0205	−	23.6186i	−3.37760	−	1.39905i
$286$	15.5997	−	11.6898i	0.922428	−	0.691233i
$287$	−2.48445	+	2.48445i	−0.146653	+	0.146653i
$288$	22.0130	+	7.26620i	1.29713	+	0.428165i
$289$	15.4880	+	7.00860i	0.911062	+	0.412270i
$290$	−14.6166	+	24.6627i	−0.858315	+	1.44825i
$291$	4.26280	+	10.2913i	0.249890	+	0.603287i
$292$	19.6170	−	24.3926i	1.14800	−	1.42747i
$293$	8.39840	+	20.2755i	0.490640	+	1.18451i	0.954395	+	0.298546i	$0.0965015\pi$
$293$	8.39840	+	20.2755i	0.490640	+	1.18451i	−0.463756	+	0.885963i	$0.653498\pi$
$294$	24.0909	−	6.16154i	1.40501	−	0.359348i
$295$	3.31024	−	7.99164i	0.192730	−	0.465291i
$296$	7.02023	−	6.55555i	0.408043	−	0.381033i
$297$		−	9.13558i		−	0.530100i
$298$	24.3801	−	18.2696i	1.41230	−	1.05833i
$299$	−3.64716	+	3.64716i	−0.210921	+	0.210921i
$300$	−18.5657	+	63.4612i	−1.07189	+	3.66393i
$301$	−2.72715	+	2.72715i	−0.157191	+	0.157191i
$302$	32.6138	−	8.34136i	1.87671	−	0.479991i
$303$	−3.08727	+	7.45333i	−0.177359	+	0.428183i
$304$	−3.89994	+	21.8634i	−0.223677	+	1.25395i
$305$		−	15.2226i		−	0.871645i
$306$	0.905913	+	23.8775i	0.0517876	+	1.36499i
$307$	3.20724	+	1.32848i	0.183047	+	0.0758204i	0.472324	−	0.881425i	$-0.343415\pi$
$307$	3.20724	+	1.32848i	0.183047	+	0.0758204i	−0.289278	+	0.957245i	$0.593415\pi$
$308$	−3.07923	−	2.47638i	−0.175455	−	0.141105i
$309$		−	17.9643i		−	1.02195i
$310$	8.89590	−	62.0904i	0.505253	−	3.52650i
$311$	8.14402	−	3.37337i	0.461805	−	0.191286i	−0.139636	−	0.990203i	$-0.544593\pi$
$311$	8.14402	−	3.37337i	0.461805	−	0.191286i	0.601441	+	0.798917i	$0.294593\pi$
$312$	−30.2721	−	13.7705i	−1.71382	−	0.779602i
$313$	−6.19411	−	2.56569i	−0.350112	−	0.145021i	0.200695	−	0.979654i	$-0.435680\pi$
$313$	−6.19411	−	2.56569i	−0.350112	−	0.145021i	−0.550807	+	0.834633i	$0.685680\pi$
$314$	−25.8654	−	3.70582i	−1.45967	−	0.209131i
$315$	−9.99288	−	4.13919i	−0.563035	−	0.233217i
$316$	−6.75328	−	5.43112i	−0.379902	−	0.305525i
$317$			12.8305i			0.720631i	0.932830	+	0.360316i	$0.117331\pi$
$317$			12.8305i			0.720631i	−0.932830	+	0.360316i	$0.882669\pi$
$318$	−16.3849	+	12.2782i	−0.918820	+	0.688529i
$319$		−	15.1743i		−	0.849597i
$320$	33.3014	+	2.28242i	1.86160	+	0.127591i
$321$	27.6007	−	27.6007i	1.54052	−	1.54052i
$322$	0.899434	+	0.533057i	0.0501235	+	0.0297061i
$323$	−22.5213	+	4.10346i	−1.25312	+	0.228323i
$324$	7.89638	−	4.32190i	0.438688	−	0.240106i
$325$	20.9584	−	50.5980i	1.16256	−	2.80667i
$326$	2.45211	−	0.627156i	0.135810	−	0.0347350i
$327$	−5.40980	−	5.40980i	−0.299163	−	0.299163i
$328$	5.51181	+	14.7110i	0.304339	+	0.812280i
$329$	−4.65380	−	1.92767i	−0.256572	−	0.106276i
$330$	−12.1661	−	47.5682i	−0.669723	−	2.61854i
$331$	8.32238	−	20.0920i	0.457439	−	1.10436i	−0.511991	−	0.858991i	$-0.671092\pi$
$331$	8.32238	−	20.0920i	0.457439	−	1.10436i	0.969431	−	0.245366i	$-0.0789080\pi$
$332$	−13.0386	+	16.2127i	−0.715585	+	0.889787i
$333$			13.9162i			0.762604i
$334$	−10.1051	+	7.57242i	−0.552929	+	0.414344i
$335$	3.20650	+	1.32818i	0.175190	+	0.0725661i
$336$	−1.18382	+	6.63662i	−0.0645827	+	0.362057i
$337$	−13.3466	+	32.2217i	−0.727038	+	1.75523i	−0.0748161	+	0.997197i	$0.523837\pi$
$337$	−13.3466	+	32.2217i	−0.727038	+	1.75523i	−0.652222	+	0.758028i	$0.726163\pi$
$338$	7.88116	+	4.67083i	0.428678	+	0.254060i
$339$	7.40868	+	3.06878i	0.402384	+	0.166673i
$340$	9.78317	+	32.9866i	0.530567	+	1.78895i
$341$	12.7051	+	30.6727i	0.688018	+	1.66102i
$342$	−19.2953	−	25.7490i	−1.04337	−	1.39235i
$343$	3.29228	+	7.94826i	0.177766	+	0.429166i
$344$	6.05025	+	16.1481i	0.326208	+	0.870648i
$345$	4.97156	+	12.0024i	0.267660	+	0.646188i
$346$	−1.15793	−	0.686260i	−0.0622509	−	0.0368936i
$347$	22.6738	+	22.6738i	1.21719	+	1.21719i	0.968611	+	0.248582i	$0.0799644\pi$
$347$	22.6738	+	22.6738i	1.21719	+	1.21719i	0.248582	+	0.968611i	$0.420036\pi$
$348$	−22.7090	+	12.4293i	−1.21733	+	0.666279i
$349$	18.3158	−	7.58667i	0.980425	−	0.406105i	0.165842	−	0.986152i	$-0.446966\pi$
$349$	18.3158	−	7.58667i	0.980425	−	0.406105i	0.814583	+	0.580047i	$0.196966\pi$
$350$	−10.9893	−	1.57448i	−0.587405	−	0.0841594i
$351$	11.9266	−	4.94018i	0.636597	−	0.263687i
$352$	−15.7793	+	7.94743i	−0.841040	+	0.423600i
$353$		−	25.2098i		−	1.34178i	−0.741557	−	0.670890i	$-0.765912\pi$
$353$		−	25.2098i		−	1.34178i	0.741557	−	0.670890i	$-0.234088\pi$
$354$	6.25077	−	4.68409i	0.332224	−	0.248957i
$355$	4.21972	+	10.1873i	0.223959	+	0.540686i
$356$	5.98541	+	1.75104i	0.317226	+	0.0928052i
$357$	−6.83630	+	1.24560i	−0.361815	+	0.0659241i
$358$	−9.96756	−	13.3014i	−0.526802	−	0.703000i
$359$		−	6.22565i		−	0.328577i	−0.986412	−	0.164289i	$-0.947467\pi$
$359$		−	6.22565i		−	0.328577i	0.986412	−	0.164289i	$-0.0525329\pi$
$360$	−35.3463	+	33.0067i	−1.86292	+	1.73961i
$361$	8.36241	−	8.36241i	0.440127	−	0.440127i
$362$	16.2553	+	9.63382i	0.854358	+	0.506342i
$363$	−2.34611	−	2.34611i	−0.123139	−	0.123139i
$364$	1.56782	−	5.35912i	0.0821761	−	0.280894i
$365$	24.9904	+	60.3322i	1.30806	+	3.15793i
$366$	7.00838	−	11.8253i	0.366334	−	0.618119i
$367$	24.6516	−	10.2110i	1.28680	−	0.533012i	0.368773	−	0.929520i	$-0.379778\pi$
$367$	24.6516	−	10.2110i	1.28680	−	0.533012i	0.918031	+	0.396508i	$0.129778\pi$
$368$	3.83465	−	2.67371i	0.199895	−	0.139377i
$369$	−21.0281	−	8.71012i	−1.09468	−	0.453431i
$370$	4.96524	+	19.4135i	0.258131	+	1.00926i
$371$	−2.43080	−	2.43080i	−0.126201	−	0.126201i
$372$	35.4965	−	44.1378i	1.84041	−	2.28844i
$373$	−2.13169	−	5.14636i	−0.110375	−	0.266468i	0.859035	−	0.511917i	$-0.171065\pi$
$373$	−2.13169	−	5.14636i	−0.110375	−	0.266468i	−0.969410	+	0.245449i	$0.921065\pi$
$374$	−13.3564	−	12.3800i	−0.690644	−	0.640153i
$375$	−58.2390	−	58.2390i	−3.00745	−	3.00745i
$376$	−16.4612	+	15.3716i	−0.848922	+	0.792730i
$377$	19.8103	−	8.20569i	1.02028	−	0.422614i
$378$	−1.56922	−	2.09407i	−0.0807120	−	0.107707i
$379$		−	24.9049i		−	1.27928i	−0.768675	−	0.639640i	$-0.779083\pi$
$379$		−	24.9049i		−	1.27928i	0.768675	−	0.639640i	$-0.220917\pi$
$380$	−36.1047	−	29.0361i	−1.85213	−	1.48952i
$381$	−19.9372			−1.02142
$382$	−2.00085	−	7.82311i	−0.102372	−	0.400265i
$383$	19.5348	+	19.5348i	0.998184	+	0.998184i	0.999998	−	0.00181452i	$-0.000577580\pi$
$383$	19.5348	+	19.5348i	0.998184	+	0.998184i	−0.00181452	+	0.999998i	$0.500578\pi$
$384$	24.8185	+	17.1047i	1.26652	+	0.872872i
$385$	7.61613	−	3.15470i	0.388154	−	0.160779i
$386$	10.6384	−	7.97199i	0.541478	−	0.405764i
$387$	−23.0823	−	9.56099i	−1.17334	−	0.486013i
$388$	0.902104	+	8.31339i	0.0457974	+	0.422048i
$389$	−0.726874	+	1.75483i	−0.0368540	+	0.0889734i	−0.941235	−	0.337753i	$-0.890333\pi$
$389$	−0.726874	+	1.75483i	−0.0368540	+	0.0889734i	0.904381	+	0.426726i	$0.140333\pi$
$390$	55.5220	−	41.6061i	2.81147	−	2.10681i
$391$	3.96285	+	2.74133i	0.200410	+	0.138635i
$392$	18.6562	+	0.638582i	0.942281	+	0.0322533i
$393$	1.88138			0.0949030
$394$	11.0133	+	6.52715i	0.554844	+	0.328833i
$395$	16.7035	−	6.91880i	0.840443	−	0.348123i
$396$	7.18734	−	24.5677i	0.361177	−	1.23458i
$397$	3.93302			0.197392			0.0986962	−	0.995118i	$-0.468533\pi$
$397$	3.93302			0.197392			0.0986962	+	0.995118i	$0.468533\pi$
$398$	5.91572	+	7.89433i	0.296528	+	0.395707i
$399$	6.61658	−	6.61658i	0.331243	−	0.331243i
$400$	−26.7531	+	41.8103i	−1.33765	+	2.09052i
$401$	17.9451	−	7.43312i	0.896137	−	0.371192i	0.113403	−	0.993549i	$-0.463825\pi$
$401$	17.9451	−	7.43312i	0.896137	−	0.371192i	0.782734	+	0.622357i	$0.213825\pi$
$402$	1.87941	+	2.50801i	0.0937365	+	0.125088i
$403$	−33.1733	+	33.1733i	−1.65248	+	1.65248i
$404$	−3.79541	+	4.71937i	−0.188829	+	0.234797i
$405$			18.7796i			0.933168i
$406$	−2.60649	−	3.47828i	−0.129358	−	0.172624i
$407$	−7.49980	−	7.49980i	−0.371751	−	0.371751i
$408$	−7.58698	+	30.1289i	−0.375611	+	1.49160i
$409$	11.0642	−	11.0642i	0.547091	−	0.547091i	−0.378507	−	0.925598i	$-0.623562\pi$
$409$	11.0642	−	11.0642i	0.547091	−	0.547091i	0.925598	+	0.378507i	$0.123562\pi$
$410$	−32.4425	−	4.64815i	−1.60222	−	0.229556i
$411$	−37.3280			−1.84126
$412$	3.78657	−	12.9432i	0.186551	−	0.637668i
$413$	0.927339	+	0.927339i	0.0456314	+	0.0456314i
$414$	−0.960568	+	6.70444i	−0.0472093	+	0.329505i
$415$	−16.6101	−	40.1002i	−0.815356	−	1.96844i
$416$	−18.9084	−	16.3025i	−0.927059	−	0.799294i
$417$	−27.3271	−	27.3271i	−1.33821	−	1.33821i
$418$	24.2755	+	3.47803i	1.18735	+	0.170116i
$419$			26.3303i			1.28632i	0.765733	+	0.643159i	$0.222376\pi$
$419$			26.3303i			1.28632i	−0.765733	+	0.643159i	$0.777624\pi$
$420$	−10.9595	−	8.81388i	−0.534770	−	0.430073i
$421$	0.533190	+	1.28723i	0.0259861	+	0.0627359i	0.936340	−	0.351095i	$-0.114191\pi$
$421$	0.533190	+	1.28723i	0.0259861	+	0.0627359i	−0.910354	+	0.413831i	$0.864191\pi$
$422$	−4.17326	−	16.3170i	−0.203151	−	0.794298i
$423$		−	32.6311i		−	1.58658i
$424$	−14.3933	+	5.39278i	−0.699002	+	0.261897i
$425$	−50.0141	−	10.7895i	−2.42604	−	0.523366i
$426$	−1.41217	+	9.85647i	−0.0684198	+	0.477548i
$427$	2.13225	+	0.883207i	0.103187	+	0.0427414i
$428$	25.7040	−	14.0685i	1.24245	−	0.680027i
$429$	−14.0534	+	33.9280i	−0.678506	+	1.63806i
$430$	−35.6118	−	5.10222i	−1.71735	−	0.246051i
$431$	1.19810	+	2.89248i	0.0577107	+	0.139326i	0.950105	−	0.311931i	$-0.100976\pi$
$431$	1.19810	+	2.89248i	0.0577107	+	0.139326i	−0.892394	+	0.451257i	$0.850976\pi$
$432$	−11.4278	+	2.50966i	−0.549820	+	0.120746i
$433$	−7.71957	+	7.71957i	−0.370979	+	0.370979i	−0.867834	−	0.496855i	$-0.834488\pi$
$433$	−7.71957	+	7.71957i	−0.370979	+	0.370979i	0.496855	+	0.867834i	$0.334488\pi$
$434$	8.18094	+	4.84851i	0.392698	+	0.232736i
$435$		−	54.0080i		−	2.58949i
$436$	−2.75746	−	5.03805i	−0.132058	−	0.241279i
$437$	−6.48871			−0.310397
$438$	−8.36328	+	58.3729i	−0.399613	+	2.78917i
$439$	−8.42029	−	20.3284i	−0.401879	−	0.970221i	−0.987210	−	0.159426i	$-0.949036\pi$
$439$	−8.42029	−	20.3284i	−0.401879	−	0.970221i	0.585331	−	0.810794i	$-0.300964\pi$
$440$	1.26090	−	36.8372i	0.0601109	−	1.75614i
$441$	−19.1240	+	19.1240i	−0.910669	+	0.910669i
$442$	8.93961	−	24.1316i	0.425214	−	1.14782i
$443$	25.3170	−	10.4866i	1.20284	−	0.498235i	0.310928	−	0.950434i	$-0.399360\pi$
$443$	25.3170	−	10.4866i	1.20284	−	0.498235i	0.891917	+	0.452199i	$0.149360\pi$
$444$	−5.08072	+	17.3669i	−0.241120	+	0.824196i
$445$	−9.19965	+	9.19965i	−0.436105	+	0.436105i
$446$	2.78620	−	4.70119i	0.131930	−	0.222608i
$447$	−21.9636	+	53.0248i	−1.03884	+	2.50799i
$448$	−2.25183	+	4.53214i	−0.106389	+	0.214123i
$449$	−0.452525	−	1.09249i	−0.0213560	−	0.0515578i	0.912842	−	0.408313i	$-0.133883\pi$
$449$	−0.452525	−	1.09249i	−0.0213560	−	0.0515578i	−0.934198	+	0.356756i	$0.883883\pi$
$450$	−17.8196	−	69.6728i	−0.840026	−	3.28441i
$451$	16.0267	−	6.63846i	0.754666	−	0.312593i
$452$	4.69109	+	3.77267i	0.220650	+	0.177451i
$453$	−44.8431	+	44.8431i	−2.10691	+	2.10691i
$454$	4.10186	+	16.0378i	0.192510	+	0.752691i
$455$	8.23703	+	8.23703i	0.386158	+	0.386158i
$456$	−14.6790	−	39.1783i	−0.687409	−	1.83469i
$457$	27.8545			1.30298			0.651489	−	0.758658i	$-0.274144\pi$
$457$	27.8545			1.30298			0.651489	+	0.758658i	$0.274144\pi$
$458$	33.8097	+	4.84403i	1.57982	+	0.226346i
$459$	−6.53776	−	10.1344i	−0.305156	−	0.473034i
$460$	1.05209	+	9.69563i	0.0490542	+	0.452061i
$461$	−30.4511	+	12.6133i	−1.41825	+	0.587458i	−0.954420	−	0.298466i	$-0.903525\pi$
$461$	−30.4511	+	12.6133i	−1.41825	+	0.587458i	−0.463830	+	0.885924i	$0.653525\pi$
$462$	7.36880	+	1.05575i	0.342827	+	0.0491180i
$463$	−35.0899			−1.63077			−0.815384	−	0.578921i	$-0.803474\pi$
$463$	−35.0899			−1.63077			−0.815384	+	0.578921i	$0.803474\pi$
$464$	−18.9817	+	4.16858i	−0.881203	+	0.193521i
$465$	45.2196	+	109.170i	2.09701	+	5.06263i
$466$	5.34253	−	4.00349i	0.247488	−	0.185458i
$467$	1.12698	+	2.72077i	0.0521505	+	0.125902i	0.947808	−	0.318843i	$-0.103294\pi$
$467$	1.12698	+	2.72077i	0.0521505	+	0.125902i	−0.895657	+	0.444745i	$0.853294\pi$
$468$	35.9602	−	3.90212i	1.66226	−	0.180376i
$469$	−0.372079	+	0.372079i	−0.0171810	+	0.0171810i
$470$	−11.6426	−	45.5213i	−0.537034	−	2.09974i
$471$	45.4775	−	18.8374i	2.09549	−	0.867982i
$472$	5.49099	−	2.05732i	0.252743	−	0.0946960i
$473$	17.5923	−	7.28696i	0.808894	−	0.335055i
$474$	16.1610	+	2.31544i	0.742301	+	0.106352i
$475$	63.6533	−	26.3661i	2.92061	−	1.20976i
$476$	−5.18809	−	0.543524i	−0.237796	−	0.0249124i
$477$	8.52202	−	20.5740i	0.390197	−	0.942018i
$478$	−0.176398	−	0.689697i	−0.00806826	−	0.0315460i
$479$	−2.89930	−	1.20093i	−0.132472	−	0.0548719i	0.315462	−	0.948938i	$-0.397840\pi$
$479$	−2.89930	−	1.20093i	−0.132472	−	0.0548719i	−0.447935	+	0.894066i	$0.647840\pi$
$480$	−56.1614	+	28.2863i	−2.56340	+	1.29109i
$481$	5.73550	−	13.8467i	0.261516	−	0.631356i
$482$	4.04621	−	28.2412i	0.184300	−	1.28635i
$483$	−1.96964			−0.0896216
$484$	−1.19585	−	2.18489i	−0.0543568	−	0.0993132i
$485$	−16.1174	−	6.67605i	−0.731854	−	0.303144i
$486$	−14.9731	+	25.2643i	−0.679194	+	1.14601i
$487$	−3.25837	+	7.86639i	−0.147651	+	0.356460i	−0.980350	−	0.197265i	$-0.936794\pi$
$487$	−3.25837	+	7.86639i	−0.147651	+	0.356460i	0.832700	+	0.553725i	$0.186794\pi$
$488$	7.54209	−	7.04287i	0.341415	−	0.318816i
$489$	−3.37159	+	3.37159i	−0.152468	+	0.152468i
$490$	−19.8552	+	33.5020i	−0.896969	+	1.51347i
$491$	9.02326	+	3.73756i	0.407214	+	0.168674i	0.576882	−	0.816828i	$-0.304269\pi$
$491$	9.02326	+	3.73756i	0.407214	+	0.168674i	−0.169668	+	0.985501i	$0.554269\pi$
$492$	−23.0622	−	18.5471i	−1.03972	−	0.836167i
$493$	−10.8593	−	16.8334i	−0.489078	−	0.758138i
$494$	8.58666	+	33.5729i	0.386332	+	1.51051i
$495$	37.7609	+	37.7609i	1.69723	+	1.69723i
$496$	34.8786	−	24.3191i	1.56610	−	1.09196i
$497$	−1.67177			−0.0749892
$498$	5.55872	−	38.7980i	0.249092	−	1.73858i
$499$	18.6506			0.834914			0.417457	−	0.908697i	$-0.362922\pi$
$499$	18.6506			0.834914			0.417457	+	0.908697i	$0.362922\pi$
$500$	−29.6853	−	54.2369i	−1.32757	−	2.42555i
$501$	9.10352	−	21.9779i	0.406715	−	0.981898i
$502$	−11.8455	−	15.8074i	−0.528689	−	0.705518i
$503$	−12.9629	+	31.2953i	−0.577989	+	1.39539i	0.316626	+	0.948550i	$0.397450\pi$
$503$	−12.9629	+	31.2953i	−0.577989	+	1.39539i	−0.894615	+	0.446838i	$0.852550\pi$
$504$	−2.57251	−	6.86603i	−0.114589	−	0.305837i
$505$	−4.83504	−	11.6728i	−0.215156	−	0.519433i
$506$	−3.09552	−	4.13087i	−0.137613	−	0.183639i
$507$	−17.2587			−0.766484
$508$	−14.3647	−	4.20243i	−0.637332	−	0.186453i
$509$	7.99752	−	19.3077i	0.354484	−	0.855800i	−0.641571	−	0.767063i	$-0.721717\pi$
$509$	7.99752	−	19.3077i	0.354484	−	0.855800i	0.996055	−	0.0887362i	$-0.0282828\pi$
$510$	−47.5378	−	44.0625i	−2.10501	−	1.95112i
$511$	−9.90073			−0.437982
$512$	14.2763	+	17.5552i	0.630930	+	0.775840i
$513$	15.0040	+	6.21485i	0.662442	+	0.274392i
$514$	−16.2827	+	27.4741i	−0.718201	+	1.21183i
$515$	19.8939	+	19.8939i	0.876631	+	0.876631i
$516$	−25.3151	−	20.3589i	−1.11444	−	0.896252i
$517$	17.5857	+	17.5857i	0.773418	+	0.773418i
$518$	−3.00736	−	0.430874i	−0.132136	−	0.0189315i
$519$	2.53572			0.111306
$520$	48.7734	−	18.2740i	2.13885	−	0.801369i
$521$	−23.4619	−	9.71822i	−1.02788	−	0.425763i	−0.195935	−	0.980617i	$-0.562774\pi$
$521$	−23.4619	−	9.71822i	−1.02788	−	0.425763i	−0.831948	+	0.554854i	$0.812774\pi$
$522$	14.3555	−	24.2222i	0.628322	−	1.06018i
$523$	21.4038	−	8.86575i	0.935924	−	0.387672i	0.138001	−	0.990432i	$-0.455932\pi$
$523$	21.4038	−	8.86575i	0.935924	−	0.387672i	0.797923	+	0.602760i	$0.205932\pi$
$524$	1.35553	+	0.396563i	0.0592166	+	0.0173239i
$525$	19.3219	−	8.00338i	0.843276	−	0.349296i
$526$	−14.0909	+	3.60390i	−0.614390	+	0.157138i
$527$	36.0447	+	24.9342i	1.57013	+	1.08615i
$528$	17.9390	−	28.0355i	0.780696	−	1.22009i
$529$	−15.2977	−	15.2977i	−0.665116	−	0.665116i
$530$	4.54777	−	31.7419i	0.197543	−	1.37878i
$531$	−3.25111	+	7.84888i	−0.141086	+	0.340612i
$532$	6.16190	−	3.37257i	0.267152	−	0.146219i
$533$	17.3332	+	17.3332i	0.750786	+	0.750786i
$534$	−11.3820	+	2.91107i	−0.492546	+	0.125974i
$535$			61.1309i			2.64292i
$536$	0.825465	+	2.20316i	0.0356547	+	0.0951622i
$537$	28.9294	+	11.9829i	1.24840	+	0.517102i
$538$	11.8608	+	7.02943i	0.511357	+	0.303060i
$539$		−	20.6128i		−	0.887858i
$540$	6.85364	−	23.4271i	0.294934	−	1.00814i
$541$	7.41029	−	7.41029i	0.318593	−	0.318593i	−0.529633	−	0.848227i	$-0.677670\pi$
$541$	7.41029	−	7.41029i	0.318593	−	0.318593i	0.848227	+	0.529633i	$0.177670\pi$
$542$	5.02873	+	19.6618i	0.216003	+	0.844546i
$543$	−35.5968			−1.52761
$544$	−11.8171	+	20.1086i	−0.506653	+	0.862150i
$545$	11.9818			0.513243
$546$	2.60647	+	10.1910i	0.111547	+	0.436134i
$547$	−1.45246	+	1.45246i	−0.0621028	+	0.0621028i	−0.737476	−	0.675373i	$-0.763983\pi$
$547$	−1.45246	+	1.45246i	−0.0621028	+	0.0621028i	0.675373	+	0.737476i	$0.263983\pi$
$548$	−26.8948	−	7.86811i	−1.14889	−	0.336109i
$549$			14.9507i			0.638080i
$550$	47.1519	+	27.9450i	2.01056	+	1.19158i
$551$	24.9218	+	10.3229i	1.06170	+	0.439772i
$552$	−3.64650	+	8.01618i	−0.155205	+	0.341191i
$553$			2.74110i			0.116563i
$554$	17.0069	−	4.34973i	0.722556	−	0.184802i
$555$	−26.6931	−	26.6931i	−1.13306	−	1.13306i
$556$	−13.9290	−	25.4492i	−0.590723	−	1.07929i
$557$	5.76441	−	13.9165i	0.244246	−	0.589662i	−0.753450	−	0.657505i	$-0.771612\pi$
$557$	5.76441	−	13.9165i	0.244246	−	0.589662i	0.997696	+	0.0678434i	$0.0216118\pi$
$558$	−8.73699	+	60.9813i	−0.369866	+	2.58154i
$559$	19.0265	+	19.0265i	0.804735	+	0.804735i
$560$	−6.03850	−	8.66046i	−0.255173	−	0.365971i
$561$	33.5365	+	7.23477i	1.41591	+	0.305452i
$562$	−31.8051	+	8.13453i	−1.34162	+	0.343135i
$563$	−4.61862	+	1.91309i	−0.194652	+	0.0806273i	−0.477880	−	0.878425i	$-0.658595\pi$
$563$	−4.61862	+	1.91309i	−0.194652	+	0.0806273i	0.283228	+	0.959053i	$0.408595\pi$
$564$	11.9134	−	40.7223i	0.501644	−	1.71472i
$565$	−11.6029	+	4.80607i	−0.488137	+	0.202193i
$566$	−8.02016	+	13.5325i	−0.337113	+	0.568814i
$567$	−2.63049	−	1.08958i	−0.110470	−	0.0457582i
$568$	−3.09504	+	6.80390i	−0.129865	+	0.285485i
$569$	−25.0505			−1.05017			−0.525085	−	0.851050i	$-0.675967\pi$
$569$	−25.0505			−1.05017			−0.525085	+	0.851050i	$0.675967\pi$
$570$	86.4009	+	12.3789i	3.61893	+	0.518497i
$571$	−11.7695	−	11.7695i	−0.492537	−	0.492537i	0.416568	−	0.909105i	$-0.363233\pi$
$571$	−11.7695	−	11.7695i	−0.492537	−	0.492537i	−0.909105	+	0.416568i	$0.863233\pi$
$572$	−17.2769	+	21.4828i	−0.722384	+	0.898242i
$573$	10.7566	+	10.7566i	0.449362	+	0.449362i
$574$	2.53337	−	4.27458i	0.105741	−	0.178418i
$575$	−13.3986	−	5.54987i	−0.558759	−	0.231446i
$576$	−32.7065	−	2.24165i	−1.36277	−	0.0934019i
$577$	−47.3468			−1.97107			−0.985536	−	0.169465i	$-0.945796\pi$
$577$	−47.3468			−1.97107			−0.985536	+	0.169465i	$0.945796\pi$
$578$	−23.6763	−	4.17520i	−0.984805	−	0.173666i
$579$	−9.58389	+	23.1376i	−0.398293	+	0.961564i
$580$	11.3840	−	38.9126i	0.472694	−	1.61576i
$581$	6.58059			0.273009
$582$	−9.44681	−	12.6065i	−0.391583	−	0.522554i
$583$	6.49510	+	15.6806i	0.269000	+	0.649423i
$584$	−18.3297	+	40.2947i	−0.758490	+	1.66741i
$585$	−28.8778	+	69.7172i	−1.19395	+	2.88245i
$586$	−18.6117	−	24.8367i	−0.768843	−	1.02600i
$587$	−7.43212	+	17.9427i	−0.306756	+	0.740575i	0.693050	+	0.720890i	$0.256267\pi$
$587$	−7.43212	+	17.9427i	−0.306756	+	0.740575i	−0.999806	+	0.0196858i	$0.993733\pi$
$588$	−30.8481	+	16.8840i	−1.27215	+	0.696284i
$589$	−59.0190			−2.43184
$590$	−1.73496	+	12.1094i	−0.0714270	+	0.498537i
$591$	−24.1177			−0.992070
$592$	−7.32129	+	11.4419i	−0.300903	+	0.470258i
$593$	−15.3202	−	15.3202i	−0.629127	−	0.629127i	0.318722	−	0.947848i	$-0.396746\pi$
$593$	−15.3202	−	15.3202i	−0.629127	−	0.629127i	−0.947848	+	0.318722i	$0.896746\pi$
$594$	3.20131	+	12.5168i	0.131351	+	0.513569i
$595$	6.19122	−	8.95001i	0.253815	−	0.366914i
$596$	−27.0014	+	33.5747i	−1.10602	+	1.37527i
$597$	−17.1695	−	7.11185i	−0.702702	−	0.291069i
$598$	3.71897	−	6.27507i	0.152080	−	0.256607i
$599$	28.9861	−	28.9861i	1.18434	−	1.18434i	0.205733	−	0.978608i	$-0.434042\pi$
$599$	28.9861	−	28.9861i	1.18434	−	1.18434i	0.978608	−	0.205733i	$-0.0659579\pi$
$600$	3.19886	−	93.4547i	0.130593	−	3.81527i
$601$	1.78781	−	4.31616i	0.0729264	−	0.176060i	−0.883213	−	0.468972i	$-0.844624\pi$
$601$	1.78781	−	4.31616i	0.0729264	−	0.176060i	0.956139	+	0.292912i	$0.0946244\pi$
$602$	2.78085	−	4.69216i	0.113339	−	0.191238i
$603$	−3.14923	−	1.30445i	−0.128246	−	0.0531214i
$604$	−41.7615	+	22.8572i	−1.69925	+	0.930046i
$605$	5.19624			0.211257
$606$	1.61809	−	11.2937i	0.0657305	−	0.458777i
$607$	−2.09512	+	5.05806i	−0.0850382	+	0.205300i	−0.960678	−	0.277664i	$-0.910440\pi$
$607$	−2.09512	+	5.05806i	−0.0850382	+	0.205300i	0.875640	+	0.482964i	$0.160440\pi$
$608$	−2.31809	−	31.3220i	−0.0940109	−	1.27027i
$609$	7.56496	+	3.13351i	0.306548	+	0.126976i
$610$	5.33434	+	20.8567i	0.215981	+	0.844462i
$611$	−13.4487	+	32.4681i	−0.544077	+	1.31352i
$612$	−9.60841	−	32.3974i	−0.388397	−	1.30959i
$613$	24.8181	−	10.2800i	1.00239	−	0.415205i	0.179719	−	0.983718i	$-0.442481\pi$
$613$	24.8181	−	10.2800i	1.00239	−	0.415205i	0.822674	+	0.568513i	$0.192481\pi$
$614$	−4.85980	−	0.696280i	−0.196126	−	0.0280996i
$615$	57.0417	−	23.6275i	2.30014	−	0.952751i
$616$	5.08667	+	2.31388i	0.204948	+	0.0932290i
$617$	−27.2142	+	11.2725i	−1.09560	+	0.453814i	−0.855957	−	0.517046i	$-0.827031\pi$
$617$	−27.2142	+	11.2725i	−1.09560	+	0.453814i	−0.239646	+	0.970860i	$0.577031\pi$
$618$	6.29509	+	24.6131i	0.253226	+	0.990084i
$619$	−1.49308	+	1.49308i	−0.0600118	+	0.0600118i	−0.736476	−	0.676464i	$-0.763511\pi$
$619$	−1.49308	+	1.49308i	−0.0600118	+	0.0600118i	0.676464	+	0.736476i	$0.263511\pi$
$620$	9.56949	+	88.1881i	0.384320	+	3.54172i
$621$	−1.30818	−	3.15823i	−0.0524956	−	0.126735i
$622$	−9.97612	+	7.47573i	−0.400006	+	0.299750i
$623$	−0.754848	−	1.82236i	−0.0302423	−	0.0730115i
$624$	46.3016	+	8.25914i	1.85355	+	0.330630i
$625$	66.9432			2.67773
$626$	9.38570	+	1.34472i	0.375128	+	0.0537458i
$627$	−42.6821	+	17.6795i	−1.70456	+	0.706052i
$628$	36.7370	−	3.98642i	1.46597	−	0.159075i
$629$	−13.6869	−	2.95266i	−0.545733	−	0.117730i
$630$	15.1418	+	2.16942i	0.603265	+	0.0864317i
$631$	5.12669			0.204090			0.102045	−	0.994780i	$-0.467461\pi$
$631$	5.12669			0.204090			0.102045	+	0.994780i	$0.467461\pi$
$632$	11.1559	+	5.07474i	0.443759	+	0.201862i
$633$	22.4354	+	22.4354i	0.891728	+	0.891728i
$634$	−4.49608	−	17.5792i	−0.178562	−	0.698158i
$635$	22.0788	−	22.0788i	0.876169	−	0.876169i
$636$	18.1466	−	22.5642i	0.719558	−	0.894728i
$637$	26.9104	−	11.1467i	1.06623	−	0.441647i
$638$	5.31741	+	20.7905i	0.210518	+	0.823102i
$639$	−4.14434	−	10.0053i	−0.163948	−	0.395804i
$640$	−46.4264	+	8.54238i	−1.83516	+	0.337667i
$641$	−0.190461	+	0.459814i	−0.00752276	+	0.0181615i	−0.927596	−	0.373584i	$-0.878129\pi$
$641$	−0.190461	+	0.459814i	−0.00752276	+	0.0181615i	0.920074	+	0.391746i	$0.128129\pi$
$642$	−28.1442	+	47.4880i	−1.11076	+	1.87420i
$643$	13.4753	−	13.4753i	0.531413	−	0.531413i	−0.389580	−	0.920993i	$-0.627380\pi$
$643$	13.4753	−	13.4753i	0.531413	−	0.531413i	0.920993	+	0.389580i	$0.127380\pi$
$644$	−1.41912	−	0.415166i	−0.0559212	−	0.0163598i
$645$	62.6141	−	25.9356i	2.46543	−	1.02121i
$646$	29.4187	−	13.5141i	1.15746	−	0.531707i
$647$	−19.4975	+	19.4975i	−0.766525	+	0.766525i	−0.977493	−	0.210968i	$-0.932338\pi$
$647$	−19.4975	+	19.4975i	−0.766525	+	0.766525i	0.210968	+	0.977493i	$0.432338\pi$
$648$	−9.30443	+	8.68855i	−0.365513	+	0.341318i
$649$	−2.47785	−	5.98206i	−0.0972642	−	0.234817i
$650$	−10.9846	+	76.6691i	−0.430853	+	3.00721i
$651$	−17.9152			−0.702150
$652$	−3.13989	+	1.71855i	−0.122968	+	0.0673035i
$653$		−	3.84015i		−	0.150277i	−0.997173	−	0.0751384i	$-0.976060\pi$
$653$		−	3.84015i		−	0.150277i	0.997173	−	0.0751384i	$-0.0239398\pi$
$654$	9.30775	+	5.51632i	0.363962	+	0.215705i
$655$	−2.08346	+	2.08346i	−0.0814077	+	0.0814077i
$656$	−12.7069	−	18.2243i	−0.496119	−	0.711538i
$657$	−24.5440	−	59.2545i	−0.957553	−	2.31174i
$658$	7.05172	+	1.01032i	0.274905	+	0.0393865i
$659$	6.06220	−	14.6354i	0.236150	−	0.570116i	−0.760729	−	0.649070i	$-0.775158\pi$
$659$	6.06220	−	14.6354i	0.236150	−	0.570116i	0.996878	+	0.0789543i	$0.0251581\pi$
$660$	33.3379	+	60.9104i	1.29767	+	2.37093i
$661$	25.0717	+	10.3850i	0.975176	+	0.403931i	0.812637	−	0.582771i	$-0.198031\pi$
$661$	25.0717	+	10.3850i	0.975176	+	0.403931i	0.162540	+	0.986702i	$0.448031\pi$
$662$	−4.36190	+	30.4446i	−0.169530	+	1.18326i
$663$	8.69015	+	47.6947i	0.337498	+	1.85231i
$664$	12.1830	−	26.7822i	0.472792	−	1.03935i
$665$			14.6546i			0.568280i
$666$	−4.87655	−	19.0668i	−0.188962	−	0.738822i
$667$	−2.17290	−	5.24586i	−0.0841352	−	0.203120i
$668$	11.1916	−	13.9161i	0.433017	−	0.538431i
$669$			10.2950i			0.398026i
$670$	−4.85869	−	0.696121i	−0.187708	−	0.0268935i
$671$	−8.05731	−	8.05731i	−0.311049	−	0.311049i
$672$	−0.703653	−	9.50774i	−0.0271440	−	0.366769i
$673$	12.5038	+	30.1869i	0.481987	+	1.16362i	0.958664	+	0.284541i	$0.0918411\pi$
$673$	12.5038	+	30.1869i	0.481987	+	1.16362i	−0.476677	+	0.879078i	$0.658159\pi$
$674$	6.99521	−	48.8242i	0.269445	−	1.88064i
$675$	25.6662	+	25.6662i	0.987891	+	0.987891i
$676$	−12.4348	−	3.63783i	−0.478262	−	0.139917i
$677$	−36.7356			−1.41187			−0.705933	−	0.708279i	$-0.749472\pi$
$677$	−36.7356			−1.41187			−0.705933	+	0.708279i	$0.749472\pi$
$678$	−11.2261	−	1.60840i	−0.431135	−	0.0617701i
$679$	1.87024	−	1.87024i	0.0717734	−	0.0717734i
$680$	−24.9633	−	41.7671i	−0.957298	−	1.60170i
$681$	−22.0516	−	22.0516i	−0.845017	−	0.845017i
$682$	−28.1558	−	37.5729i	−1.07814	−	1.43874i
$683$		−	36.8581i		−	1.41034i	−0.709040	−	0.705168i	$-0.750872\pi$
$683$		−	36.8581i		−	1.41034i	0.709040	−	0.705168i	$-0.249128\pi$
$684$	35.4598	+	28.5175i	1.35584	+	1.09039i
$685$	41.3376	−	41.3376i	1.57943	−	1.57943i
$686$	−7.29603	−	9.73631i	−0.278564	−	0.371734i
$687$	−59.4455	+	24.6231i	−2.26799	+	0.939431i
$688$	−13.9482	−	20.0046i	−0.531769	−	0.762667i
$689$	−16.9589	+	16.9589i	−0.646083	+	0.646083i
$690$	−11.0175	−	14.7025i	−0.419429	−	0.559714i
$691$	17.3485			0.659970			0.329985	−	0.943986i	$-0.392956\pi$
$691$	17.3485			0.659970			0.329985	+	0.943986i	$0.392956\pi$
$692$	1.82698	+	0.534486i	0.0694513	+	0.0203181i
$693$	−7.48008	+	3.09835i	−0.284145	+	0.117697i
$694$	−39.0110	−	23.1202i	−1.48084	−	0.877631i
$695$	60.5248			2.29584
$696$	26.7584	−	24.9872i	1.01428	−	0.947139i
$697$	13.0282	−	18.8335i	0.493479	−	0.713372i
$698$	−22.4362	+	16.8129i	−0.849223	+	0.636376i
$699$	−4.81298	+	11.6196i	−0.182044	+	0.439492i
$700$	15.6083	−	1.69370i	0.589940	−	0.0640157i
$701$	−34.1214	−	14.1335i	−1.28875	−	0.533816i	−0.370135	−	0.928978i	$-0.620689\pi$
$701$	−34.1214	−	14.1335i	−1.28875	−	0.533816i	−0.918612	+	0.395162i	$0.870689\pi$
$702$	−14.6097	+	10.9480i	−0.551407	+	0.413204i
$703$	17.4195	−	7.21538i	0.656987	−	0.272133i
$704$	18.8344	−	16.4183i	0.709850	−	0.618787i
$705$	62.5906	+	62.5906i	2.35730	+	2.35730i
$706$	8.83406	+	34.5402i	0.332474	+	1.29994i
$707$	1.91555			0.0720417
$708$	−6.92283	+	8.60813i	−0.260176	+	0.323514i
$709$		−	7.82169i		−	0.293750i	−0.989155	−	0.146875i	$-0.953079\pi$
$709$		−	7.82169i		−	0.293750i	0.989155	−	0.146875i	$-0.0469215\pi$
$710$	−9.35134	−	12.4790i	−0.350949	−	0.468330i
$711$	−16.4051	+	6.79521i	−0.615239	+	0.254840i
$712$	−8.81429	−	0.301704i	−0.330329	−	0.0113068i
$713$	8.78446	+	8.78446i	0.328980	+	0.328980i
$714$	8.93001	−	4.10220i	0.334197	−	0.153521i
$715$	−22.0094	−	53.1353i	−0.823103	−	1.98715i
$716$	18.3178	+	14.7315i	0.684567	+	0.550542i
$717$	0.948315	+	0.948315i	0.0354155	+	0.0354155i
$718$	2.18161	+	8.52984i	0.0814168	+	0.318331i
$719$	−41.5358	−	17.2047i	−1.54903	−	0.641627i	−0.565886	−	0.824484i	$-0.691466\pi$
$719$	−41.5358	−	17.2047i	−1.54903	−	0.641627i	−0.983140	+	0.182856i	$0.941466\pi$
$720$	36.8621	−	57.6090i	1.37377	−	2.14696i
$721$	−3.94080	+	1.63233i	−0.146763	+	0.0607912i
$722$	−8.52706	+	14.3878i	−0.317344	+	0.535459i
$723$	20.5677	+	49.6547i	0.764919	+	1.84668i
$724$	−25.6474	−	7.50320i	−0.953179	−	0.278854i
$725$	42.6318	+	42.6318i	1.58330	+	1.58330i
$726$	4.03657	+	2.39231i	0.149811	+	0.0887868i
$727$	14.2705	−	14.2705i	0.529265	−	0.529265i	−0.391088	−	0.920353i	$-0.627901\pi$
$727$	14.2705	−	14.2705i	0.529265	−	0.529265i	0.920353	+	0.391088i	$0.127901\pi$
$728$	−0.270134	+	7.89199i	−0.0100118	+	0.292497i
$729$		−	41.8227i		−	1.54899i
$730$	−55.3814	−	73.9046i	−2.04976	−	2.73533i
$731$	14.3009	−	20.6734i	0.528939	−	0.764632i
$732$	−5.45840	+	18.6579i	−0.201748	+	0.689615i
$733$	10.4213	+	25.1594i	0.384921	+	0.929282i	0.990998	+	0.133876i	$0.0427423\pi$
$733$	10.4213	+	25.1594i	0.384921	+	0.929282i	−0.606077	+	0.795406i	$0.707258\pi$
$734$	−30.1973	+	22.6287i	−1.11460	+	0.835241i
$735$		−	73.3648i		−	2.70610i
$736$	−4.31697	+	5.00702i	−0.159126	+	0.184561i
$737$	2.40020	−	0.994195i	0.0884125	−	0.0366216i
$738$	31.8630	+	4.56512i	1.17289	+	0.168044i
$739$	19.9321	−	8.25613i	0.733212	−	0.303706i	0.0153410	−	0.999882i	$-0.495117\pi$
$739$	19.9321	−	8.25613i	0.733212	−	0.303706i	0.717871	+	0.696176i	$0.245117\pi$
$740$	−13.6059	−	24.8588i	−0.500162	−	0.913827i
$741$	−46.1618	−	46.1618i	−1.69580	−	1.69580i
$742$	4.18227	+	2.47866i	0.153536	+	0.0909945i
$743$	−10.7147	−	25.8675i	−0.393083	−	0.948986i	−0.989264	−	0.146136i	$-0.953316\pi$
$743$	−10.7147	−	25.8675i	−0.393083	−	0.948986i	0.596182	−	0.802850i	$-0.296684\pi$
$744$	−33.1673	+	72.9124i	−1.21597	+	2.67310i
$745$	−34.3976	−	83.0431i	−1.26023	−	3.04246i
$746$	4.72405	+	6.30409i	0.172960	+	0.230809i
$747$	16.3134	+	39.3839i	0.596875	+	1.44098i
$748$	22.6380	+	12.2816i	0.827727	+	0.449058i
$749$	−8.56267	−	3.54678i	−0.312873	−	0.129596i
$750$	100.202	+	59.3857i	3.65887	+	2.16846i
$751$	−12.6302	+	30.4920i	−0.460883	+	1.11267i	0.507153	+	0.861856i	$0.330698\pi$
$751$	−12.6302	+	30.4920i	−0.460883	+	1.11267i	−0.968035	+	0.250813i	$0.919302\pi$
$752$	17.1671	−	26.8292i	0.626021	−	0.978359i
$753$	34.3797	+	14.2406i	1.25287	+	0.518955i
$754$	−24.2668	+	18.1847i	−0.883746	+	0.662247i
$755$		−	99.3197i		−	3.61461i
$756$	2.88382	+	2.31922i	0.104883	+	0.0843493i
$757$	10.2289	−	24.6947i	0.371775	−	0.897545i	−0.621674	−	0.783276i	$-0.713547\pi$
$757$	10.2289	−	24.6947i	0.371775	−	0.897545i	0.993450	−	0.114269i	$-0.0364527\pi$
$758$	8.72724	+	34.1225i	0.316988	+	1.23939i
$759$	8.98429	+	3.72142i	0.326109	+	0.135079i
$760$	59.6424	+	27.1308i	2.16346	+	0.984139i
$761$	−2.80739	−	2.80739i	−0.101768	−	0.101768i	0.654390	−	0.756158i	$-0.272926\pi$
$761$	−2.80739	−	2.80739i	−0.101768	−	0.101768i	−0.756158	+	0.654390i	$0.772926\pi$
$762$	27.3162	−	6.98645i	0.989563	−	0.253092i
$763$	−0.695175	+	1.67830i	−0.0251670	+	0.0607586i
$764$	5.48278	+	10.0174i	0.198360	+	0.362416i
$765$	68.9126	+	14.8664i	2.49154	+	0.537497i
$766$	−33.6103	−	19.9195i	−1.21439	−	0.719719i
$767$	6.46975	−	6.46975i	0.233609	−	0.233609i
$768$	−39.9980	−	14.7384i	−1.44330	−	0.531827i
$769$			17.3835i			0.626867i	0.949610	+	0.313433i	$0.101479\pi$
$769$			17.3835i			0.626867i	−0.949610	+	0.313433i	$0.898521\pi$
$770$	−9.32946	+	6.99115i	−0.336210	+	0.251944i
$771$		−	60.1645i		−	2.16677i
$772$	−11.7822	+	14.6504i	−0.424050	+	0.527281i
$773$	43.2680	+	17.9222i	1.55624	+	0.644616i	0.984431	−	0.175770i	$-0.0562416\pi$
$773$	43.2680	+	17.9222i	1.55624	+	0.644616i	0.571810	+	0.820386i	$0.306242\pi$
$774$	34.9757	+	5.01108i	1.25717	+	0.180120i
$775$	−121.869	−	50.4797i	−4.37766	−	1.81329i
$776$	−4.14918	−	11.0741i	−0.148947	−	0.397539i
$777$	5.28765	−	2.19022i	0.189693	−	0.0785736i
$778$	0.380967	−	2.65902i	0.0136583	−	0.0953306i
$779$			30.8377i			1.10488i
$780$	−61.4916	+	76.4612i	−2.20175	+	2.73775i
$781$	7.62561	+	3.15863i	0.272866	+	0.113025i
$782$	−6.39017	−	2.36725i	−0.228512	−	0.0846527i
$783$			14.2113i			0.507870i
$784$	−25.7848	+	5.66262i	−0.920887	+	0.202236i
$785$	−29.5016	+	71.2232i	−1.05296	+	2.54206i
$786$	−2.57770	+	0.659277i	−0.0919435	+	0.0235156i
$787$	−17.6277	+	17.6277i	−0.628360	+	0.628360i	−0.947655	−	0.319295i	$-0.896554\pi$
$787$	−17.6277	+	17.6277i	−0.628360	+	0.628360i	0.319295	+	0.947655i	$0.396554\pi$
$788$	−17.3768	−	5.08360i	−0.619021	−	0.181096i
$789$	19.3745	−	19.3745i	0.689752	−	0.689752i
$790$	−20.4611	+	15.3328i	−0.727973	+	0.545516i
$791$		−	1.90407i		−	0.0677010i
$792$	−1.23837	+	36.1791i	−0.0440037	+	1.28557i
$793$	6.16186	−	14.8760i	0.218814	−	0.528263i
$794$	−5.38867	+	1.37822i	−0.191237	+	0.0489111i
$795$	23.1172	+	55.8099i	0.819883	+	1.97937i
$796$	−10.8715	−	8.74311i	−0.385332	−	0.309891i
$797$	9.05763	+	21.8670i	0.320838	+	0.774570i	0.999206	+	0.0398482i	$0.0126875\pi$
$797$	9.05763	+	21.8670i	0.320838	+	0.774570i	−0.678368	+	0.734722i	$0.737313\pi$
$798$	−6.74686	+	11.3841i	−0.238836	+	0.402991i
$799$	32.0934	+	6.92347i	1.13538	+	0.244935i
$800$	22.0034	−	66.6597i	0.777939	−	2.35677i
$801$	9.03532	−	9.03532i	0.319247	−	0.319247i
$802$	−21.9821	+	16.4726i	−0.776215	+	0.581667i
$803$	45.1611	+	18.7063i	1.59370	+	0.660132i
$804$	−3.45386	−	2.77767i	−0.121808	−	0.0979608i
$805$	2.18120	−	2.18120i	0.0768773	−	0.0768773i
$806$	33.8265	−	57.0758i	1.19149	−	2.01041i
$807$	−25.9736			−0.914315
$808$	3.54636	−	7.79605i	0.124761	−	0.274264i
$809$	4.43227	−	10.7004i	0.155830	−	0.376207i	−0.826613	−	0.562771i	$-0.809735\pi$
$809$	4.43227	−	10.7004i	0.155830	−	0.376207i	0.982443	+	0.186564i	$0.0597351\pi$
$810$	−6.58080	−	25.7302i	−0.231226	−	0.904067i
$811$	−40.1570			−1.41010			−0.705051	−	0.709157i	$-0.749076\pi$
$811$	−40.1570			−1.41010			−0.705051	+	0.709157i	$0.749076\pi$
$812$	4.79005	+	3.85225i	0.168098	+	0.135188i
$813$	−27.0344	−	27.0344i	−0.948139	−	0.948139i
$814$	12.9036	+	7.64746i	0.452273	+	0.268043i
$815$		−	7.46748i		−	0.261574i
$816$	−0.162848	−	43.9386i	−0.00570084	−	1.53816i
$817$			33.8502i			1.18427i
$818$	−11.2821	+	19.0364i	−0.394469	+	0.665592i
$819$	−8.08989	−	8.08989i	−0.282684	−	0.282684i
$820$	46.0787	−	5.00010i	1.60914	−	0.174611i
$821$	−46.3183			−1.61652			−0.808261	−	0.588825i	$-0.799591\pi$
$821$	−46.3183			−1.61652			−0.808261	+	0.588825i	$0.799591\pi$
$822$	51.1435	−	13.0806i	1.78384	−	0.456237i
$823$	−18.7374	+	45.2360i	−0.653144	+	1.57683i	0.155047	+	0.987907i	$0.450447\pi$
$823$	−18.7374	+	45.2360i	−0.653144	+	1.57683i	−0.808190	+	0.588921i	$0.799553\pi$
$824$	−0.652423	+	19.0606i	−0.0227282	+	0.664007i
$825$	−103.256			−3.59492
$826$	−1.59552	−	0.945598i	−0.0555152	−	0.0329016i
$827$	−1.47544	+	1.47544i	−0.0513062	+	0.0513062i	−0.732294	−	0.680988i	$-0.761550\pi$
$827$	−1.47544	+	1.47544i	−0.0513062	+	0.0513062i	0.680988	+	0.732294i	$0.261550\pi$
$828$	−1.03330	−	9.52244i	−0.0359097	−	0.330928i
$829$	−13.2206	−	5.47615i	−0.459171	−	0.190195i	0.141094	−	0.989996i	$-0.454938\pi$
$829$	−13.2206	−	5.47615i	−0.459171	−	0.190195i	−0.600265	+	0.799802i	$0.704938\pi$
$830$	36.8096	+	49.1213i	1.27768	+	1.70502i
$831$	−23.3841	+	23.3841i	−0.811185	+	0.811185i
$832$	31.6193	+	15.7103i	1.09620	+	0.544656i
$833$	−14.7513	−	22.8666i	−0.511103	−	0.792280i
$834$	47.0172	+	27.8652i	1.62807	+	0.964892i
$835$	14.2572	+	34.4199i	0.493391	+	1.19115i
$836$	−34.4789	+	3.74138i	−1.19248	+	0.129398i
$837$	−11.8988	−	28.7262i	−0.411282	−	0.992922i
$838$	−9.22671	−	36.0754i	−0.318731	−	1.24620i
$839$	−13.3354	+	32.1946i	−0.460390	+	1.11148i	0.507847	+	0.861447i	$0.330441\pi$
$839$	−13.3354	+	32.1946i	−0.460390	+	1.11148i	−0.968237	+	0.250033i	$0.919559\pi$
$840$	18.1044	+	8.23553i	0.624660	+	0.284153i
$841$		−	5.39489i		−	0.186031i
$842$	−1.18160	−	1.57681i	−0.0407208	−	0.0543405i
$843$	43.7312	−	43.7312i	1.50618	−	1.50618i
$844$	11.4357	+	20.8937i	0.393632	+	0.719190i
$845$	19.1125	−	19.1125i	0.657489	−	0.657489i
$846$	11.4347	+	44.7082i	0.393131	+	1.53710i
$847$	−0.301482	+	0.727843i	−0.0103591	+	0.0250090i
$848$	17.8307	−	12.4325i	0.612309	−	0.426932i
$849$		−	29.6344i		−	1.01705i
$850$	72.3057	−	2.74328i	2.48007	−	0.0940937i
$851$	−3.66667	−	1.51879i	−0.125692	−	0.0520633i
$852$	−1.51910	−	13.9993i	−0.0520434	−	0.479609i
$853$		−	9.56931i		−	0.327647i	−0.986490	−	0.163823i	$-0.947617\pi$
$853$		−	9.56931i		−	0.327647i	0.986490	−	0.163823i	$-0.0523827\pi$
$854$	−3.23092	−	0.462904i	−0.110560	−	0.0158402i
$855$	−87.7057	+	36.3289i	−2.99947	+	1.24242i
$856$	−30.2875	+	28.2827i	−1.03520	+	0.966682i
$857$	−35.7460	−	14.8065i	−1.22106	−	0.505779i	−0.323313	−	0.946292i	$-0.604797\pi$
$857$	−35.7460	−	14.8065i	−1.22106	−	0.505779i	−0.897746	+	0.440513i	$0.854797\pi$
$858$	7.36565	−	51.4098i	0.251459	−	1.75510i
$859$	27.2759	+	11.2980i	0.930641	+	0.385484i	0.795922	−	0.605399i	$-0.206987\pi$
$859$	27.2759	+	11.2980i	0.930641	+	0.385484i	0.134720	+	0.990884i	$0.456987\pi$
$860$	50.5801	−	5.48856i	1.72477	−	0.187158i
$861$			9.36075i			0.319014i
$862$	−2.65513	−	3.54318i	−0.0904340	−	0.120681i
$863$			28.5614i			0.972242i	0.873892	+	0.486121i	$0.161588\pi$
$863$			28.5614i			0.972242i	−0.873892	+	0.486121i	$0.838412\pi$
$864$	14.7779	−	7.44307i	0.502755	−	0.253218i
$865$	−2.80809	+	2.80809i	−0.0954779	+	0.0954779i
$866$	7.87156	−	13.2818i	0.267487	−	0.451333i
$867$	42.3807	−	15.9741i	1.43932	−	0.542511i
$868$	−12.9078	−	3.77621i	−0.438120	−	0.128173i
$869$	5.17900	−	12.5032i	0.175686	−	0.424143i
$870$	18.9256	+	73.9970i	0.641638	+	2.50873i
$871$	2.59588	+	2.59588i	0.0879579	+	0.0879579i
$872$	5.54346	+	5.93641i	0.187725	+	0.201032i
$873$	15.8295	+	6.55680i	0.535748	+	0.221914i
$874$	8.89025	−	2.27379i	0.300717	−	0.0769120i
$875$	−7.48388	+	18.0677i	−0.253001	+	0.610800i
$876$	−8.99654	−	82.9081i	−0.303965	−	2.80120i
$877$		−	15.8505i		−	0.535234i	−0.963525	−	0.267617i	$-0.913764\pi$
$877$		−	15.8505i		−	0.535234i	0.963525	−	0.267617i	$-0.0862363\pi$
$878$	18.6603	+	24.9015i	0.629753	+	0.840384i
$879$	54.0178	+	22.3749i	1.82198	+	0.754687i
$880$	11.1810	+	50.9128i	0.376911	+	1.71627i
$881$	1.10217	−	2.66086i	0.0371329	−	0.0896468i	−0.904225	−	0.427056i	$-0.859551\pi$
$881$	1.10217	−	2.66086i	0.0371329	−	0.0896468i	0.941358	+	0.337409i	$0.109551\pi$
$882$	19.5006	−	32.9036i	0.656618	−	1.10792i
$883$	−25.7324	−	10.6587i	−0.865965	−	0.358695i	−0.0949277	−	0.995484i	$-0.530262\pi$
$883$	−25.7324	−	10.6587i	−0.865965	−	0.358695i	−0.771038	+	0.636790i	$0.780262\pi$
$884$	−3.79200	+	36.1957i	−0.127539	+	1.21739i
$885$	−8.81912	−	21.2912i	−0.296451	−	0.715697i
$886$	−31.0123	+	23.2395i	−1.04188	+	0.780745i
$887$	19.8839	+	48.0041i	0.667637	+	1.61182i	0.785553	+	0.618795i	$0.212379\pi$
$887$	19.8839	+	48.0041i	0.667637	+	1.61182i	−0.117915	+	0.993024i	$0.537621\pi$
$888$	0.875403	−	25.5750i	0.0293766	−	0.858239i
$889$	1.81160	+	4.37359i	0.0607592	+	0.146686i
$890$	9.38078	−	15.8283i	0.314445	−	0.530566i
$891$	9.94003	+	9.94003i	0.333004	+	0.333004i
$892$	−2.17000	+	7.41750i	−0.0726571	+	0.248356i
$893$	−40.8456	+	16.9188i	−1.36684	+	0.566166i
$894$	11.5115	−	80.3463i	0.385002	−	2.68718i
$895$	−45.3069	+	18.7667i	−1.51444	+	0.627303i
$896$	1.49709	−	6.99862i	0.0500143	−	0.233808i
$897$			13.7415i			0.458817i
$898$	1.00284	+	1.33826i	0.0334653	+	0.0446583i
$899$	−19.7640	−	47.7145i	−0.659166	−	1.59137i
$900$	48.8298	+	89.2151i	1.62766	+	2.97384i
$901$	18.4268	+	12.7469i	0.613887	+	0.424660i
$902$	−19.6320	+	14.7115i	−0.653675	+	0.489840i
$903$			10.2752i			0.341937i
$904$	−7.74934	−	3.52511i	−0.257739	−	0.117244i
$905$	39.4204	−	39.4204i	1.31038	−	1.31038i
$906$	45.7260	−	77.1540i	1.51914	−	2.56327i
$907$	38.7052	+	38.7052i	1.28519	+	1.28519i	0.937676	+	0.347511i	$0.112973\pi$
$907$	38.7052	+	38.7052i	1.28519	+	1.28519i	0.347511	+	0.937676i	$0.387027\pi$
$908$	−11.2400	−	20.5362i	−0.373013	−	0.681517i
$909$	4.74867	+	11.4643i	0.157503	+	0.380247i
$910$	−14.1721	−	8.39921i	−0.469800	−	0.278431i
$911$	−2.05537	+	0.851362i	−0.0680974	+	0.0282069i	−0.416472	−	0.909148i	$-0.636734\pi$
$911$	−2.05537	+	0.851362i	−0.0680974	+	0.0282069i	0.348375	+	0.937355i	$0.386734\pi$
$912$	33.8409	+	48.5348i	1.12058	+	1.60715i
$913$	−30.0167	−	12.4333i	−0.993406	−	0.411482i
$914$	−38.1638	+	9.76084i	−1.26235	+	0.322860i
$915$	−28.6774	−	28.6774i	−0.948045	−	0.948045i
$916$	−48.0205	+	5.21081i	−1.58664	+	0.172170i
$917$	−0.170952	−	0.412715i	−0.00564533	−	0.0136290i
$918$	12.5088	+	11.5943i	0.412851	+	0.382669i
$919$	20.6442	+	20.6442i	0.680990	+	0.680990i	0.960223	−	0.279233i	$-0.0900802\pi$
$919$	20.6442	+	20.6442i	0.680990	+	0.680990i	−0.279233	+	0.960223i	$0.590080\pi$
$920$	−4.83905	−	12.9154i	−0.159539	−	0.425809i
$921$	8.54469	−	3.53933i	0.281557	−	0.116625i
$922$	37.3014	−	27.9523i	1.22846	−	0.920561i
$923$			11.6634i			0.383906i
$924$	−10.4660	+	1.13569i	−0.344307	+	0.0373615i
$925$	42.1410			1.38559
$926$	48.0771	−	12.2963i	1.57991	−	0.404081i
$927$	−19.5386	−	19.5386i	−0.641730	−	0.641730i
$928$	24.5463	−	12.3630i	0.805771	−	0.405836i
$929$	−11.7289	+	4.85827i	−0.384813	+	0.159395i	−0.566699	−	0.823925i	$-0.691780\pi$
$929$	−11.7289	+	4.85827i	−0.384813	+	0.159395i	0.181886	+	0.983320i	$0.441780\pi$
$930$	−100.211	−	133.729i	−3.28606	−	4.38514i
$931$	33.8539	+	14.0227i	1.10952	+	0.459576i
$932$	−5.91694	+	7.35737i	−0.193816	+	0.240999i
$933$	8.98728	−	21.6972i	0.294231	−	0.710335i
$934$	−2.49751	−	3.33284i	−0.0817209	−	0.109054i
$935$	−45.1506	+	29.1269i	−1.47658	+	0.952550i
$936$	−47.9021	+	17.9476i	−1.56573	+	0.586636i
$937$	47.1541			1.54046			0.770228	−	0.637769i	$-0.220142\pi$
$937$	47.1541			1.54046			0.770228	+	0.637769i	$0.220142\pi$
$938$	0.379405	−	0.640174i	0.0123880	−	0.0209024i
$939$	−16.5023	+	6.83547i	−0.538532	+	0.223067i
$940$	31.9034	+	58.2895i	1.04057	+	1.90119i
$941$	−15.7909			−0.514767			−0.257384	−	0.966309i	$-0.582860\pi$
$941$	−15.7909			−0.514767			−0.257384	+	0.966309i	$0.582860\pi$
$942$	−55.7082	+	41.7457i	−1.81507	+	1.36015i
$943$	4.58992	−	4.58992i	0.149468	−	0.149468i
$944$	−6.80233	+	4.74293i	−0.221397	+	0.154369i
$945$	−7.13279	+	2.95450i	−0.232030	+	0.0961098i
$946$	−21.5499	+	16.1487i	−0.700646	+	0.525038i
$947$	−7.27552	+	7.27552i	−0.236423	+	0.236423i	−0.815367	−	0.578944i	$-0.803465\pi$
$947$	−7.27552	+	7.27552i	−0.236423	+	0.236423i	0.578944	+	0.815367i	$0.303465\pi$
$948$	−22.9538	+	2.49077i	−0.745505	+	0.0808964i
$949$			69.0742i			2.24224i
$950$	−77.9728	+	58.4300i	−2.52977	+	1.89572i
$951$	24.1709	+	24.1709i	0.783795	+	0.783795i
$952$	7.29872	−	1.07333i	0.236553	−	0.0347869i
$953$	−35.8878	+	35.8878i	−1.16252	+	1.16252i	−0.178596	+	0.983922i	$0.557156\pi$
$953$	−35.8878	+	35.8878i	−1.16252	+	1.16252i	−0.983922	+	0.178596i	$0.942844\pi$
$954$	−4.46654	+	31.1749i	−0.144610	+	1.00933i
$955$	−23.8239			−0.770924
$956$	0.483370	+	0.883147i	0.0156333	+	0.0285630i
$957$	−28.5863	−	28.5863i	−0.924065	−	0.924065i
$958$	4.39320	+	0.629428i	0.141938	+	0.0203359i
$959$	3.39182	+	8.18858i	0.109528	+	0.264423i
$960$	67.0351	−	58.4356i	2.16355	−	1.88600i
$961$	57.9801	+	57.9801i	1.87033	+	1.87033i
$962$	−3.00607	+	20.9814i	−0.0969197	+	0.676467i
$963$		−	60.0389i		−	1.93473i
$964$	4.35258	+	40.1114i	0.140187	+	1.29190i
$965$	−15.0095	−	36.2362i	−0.483173	−	1.16648i
$966$	2.69862	−	0.690205i	0.0868268	−	0.0222070i
$967$		−	43.3400i		−	1.39372i	−0.717208	−	0.696859i	$-0.754580\pi$
$967$		−	43.3400i		−	1.39372i	0.717208	−	0.696859i	$-0.245420\pi$
$968$	2.40408	+	2.57449i	0.0772700	+	0.0827473i
$969$	−34.6967	+	50.1574i	−1.11462	+	1.61129i
$970$	24.4221	+	3.49903i	0.784146	+	0.112347i
$971$	−45.1614	−	18.7065i	−1.44930	−	0.600319i	−0.487265	−	0.873254i	$-0.662005\pi$
$971$	−45.1614	−	18.7065i	−1.44930	−	0.600319i	−0.962032	+	0.272935i	$0.912005\pi$
$972$	11.6616	−	39.8618i	0.374047	−	1.27857i
$973$	−3.51161	+	8.47779i	−0.112577	+	0.271785i
$974$	1.70777	−	11.9196i	0.0547203	−	0.381930i
$975$	−55.8371	−	134.803i	−1.78822	−	4.31714i
$976$	−7.86553	+	12.2924i	−0.251769	+	0.393471i
$977$	−2.36640	+	2.36640i	−0.0757080	+	0.0757080i	−0.743947	−	0.668239i	$-0.767048\pi$
$977$	−2.36640	+	2.36640i	−0.0757080	+	0.0757080i	0.668239	+	0.743947i	$0.267048\pi$
$978$	3.43797	−	5.80093i	0.109934	−	0.185493i
$979$			9.73872i			0.311251i
$980$	15.4641	−	52.8592i	0.493981	−	1.68852i
$981$	−11.7677			−0.375715
$982$	−13.6726	−	1.95892i	−0.436310	−	0.0625115i
$983$	−1.11969	−	2.70318i	−0.0357127	−	0.0862180i	0.905017	−	0.425376i	$-0.139858\pi$
$983$	−1.11969	−	2.70318i	−0.0357127	−	0.0862180i	−0.940730	+	0.339158i	$0.889858\pi$
$984$	38.0971	+	17.3301i	1.21449	+	0.552462i
$985$	26.7083	−	26.7083i	0.850997	−	0.850997i
$986$	20.7772	+	19.2583i	0.661681	+	0.613308i
$987$	−12.3986	+	5.13567i	−0.394652	+	0.163470i
$988$	−23.5293	−	42.9896i	−0.748568	−	1.36768i
$989$	5.03830	−	5.03830i	0.160209	−	0.160209i
$990$	−64.9689	−	38.5044i	−2.06485	−	1.22375i
$991$	−2.36969	+	5.72093i	−0.0752756	+	0.181731i	−0.957038	−	0.289962i	$-0.906357\pi$
$991$	−2.36969	+	5.72093i	−0.0752756	+	0.181731i	0.881762	+	0.471694i	$0.156357\pi$
$992$	−39.2657	+	45.5421i	−1.24669	+	1.44596i
$993$	−22.1724	−	53.5289i	−0.703620	−	1.69869i
$994$	2.29051	−	0.585826i	0.0726507	−	0.0185813i
$995$	26.8895	−	11.1380i	0.852455	−	0.353098i
$996$	5.97962	+	55.1055i	0.189472	+	1.74608i
$997$	1.17156	−	1.17156i	0.0371038	−	0.0371038i	−0.688311	−	0.725415i	$-0.741648\pi$
$997$	1.17156	−	1.17156i	0.0371038	−	0.0371038i	0.725415	+	0.688311i	$0.241648\pi$
$998$	−25.5533	+	6.53557i	−0.808877	+	0.206880i
$999$	7.02384	+	7.02384i	0.222225	+	0.222225i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	544.2.x.a.77.6	yes	280
17.2	even	8		544.2.v.a.461.31	✓	280
32.5	even	8		544.2.v.a.485.31	yes	280
544.325	even	8	inner	544.2.x.a.325.6	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
544.2.v.a.461.31	✓	280	17.2	even	8
544.2.v.a.485.31	yes	280	32.5	even	8
544.2.x.a.77.6	yes	280	1.1	even	1	trivial
544.2.x.a.325.6	yes	280	544.325	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 544 = 2^{5} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	544.x (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37011 + 0.350422i) q^{2} +(1.88387 - 1.88387i) q^{3} +(1.75441 - 0.960235i) q^{4} +4.17244i q^{5} +(-1.92096 + 3.24126i) q^{6} +(-0.584438 - 0.242082i) q^{7} +(-2.06725 + 1.93041i) q^{8} -4.09791i q^{9} +(-1.46212 - 5.71670i) q^{10} +(2.20846 + 2.20846i) q^{11} +(1.49612 - 5.11403i) q^{12} +(-1.68893 + 4.07744i) q^{13} +(0.885576 + 0.126879i) q^{14} +(7.86032 + 7.86032i) q^{15} +(2.15590 - 3.36929i) q^{16} +(4.03039 + 0.869469i) q^{17} +(1.43600 + 5.61459i) q^{18} +(-5.12951 + 2.12471i) q^{19} +(4.00652 + 7.32016i) q^{20} +(-1.55705 + 0.644953i) q^{21} +(-3.79974 - 2.25195i) q^{22} +(1.07973 + 0.447237i) q^{23} +(-0.257780 + 7.53106i) q^{24} -12.4092 q^{25} +(0.885198 - 6.17839i) q^{26} +(-2.06831 - 2.06831i) q^{27} +(-1.25780 + 0.136487i) q^{28} +(-3.43548 - 3.43548i) q^{29} +(-13.5239 - 8.01508i) q^{30} +(9.82081 + 4.06791i) q^{31} +(-1.77315 + 5.37177i) q^{32} +8.32090 q^{33} +(-5.82676 + 0.221067i) q^{34} +(1.01007 - 2.43853i) q^{35} +(-3.93495 - 7.18940i) q^{36} -3.39593 q^{37} +(6.28345 - 4.70858i) q^{38} +(4.49963 + 10.8631i) q^{39} +(-8.05452 - 8.62546i) q^{40} +(2.12550 - 5.13142i) q^{41} +(1.90733 - 1.42928i) q^{42} +(2.33314 - 5.63270i) q^{43} +(5.99519 + 1.75391i) q^{44} +17.0983 q^{45} +(-1.63607 - 0.234405i) q^{46} +7.96286 q^{47} +(-2.28586 - 10.4087i) q^{48} +(-4.66678 - 4.66678i) q^{49} +(17.0020 - 4.34847i) q^{50} +(9.23068 - 5.95475i) q^{51} +(0.952224 + 8.77527i) q^{52} +(5.02061 + 2.07960i) q^{53} +(3.55860 + 2.10903i) q^{54} +(-9.21468 + 9.21468i) q^{55} +(1.67550 - 0.627763i) q^{56} +(-5.66063 + 13.6660i) q^{57} +(5.91087 + 3.50313i) q^{58} +(-1.91534 - 0.793359i) q^{59} +(21.3380 + 6.24246i) q^{60} -3.64838 q^{61} +(-14.8811 - 2.13206i) q^{62} +(-0.992031 + 2.39497i) q^{63} +(0.547022 - 7.98128i) q^{64} +(-17.0129 - 7.04696i) q^{65} +(-11.4006 + 2.91583i) q^{66} +(0.318322 - 0.768497i) q^{67} +(7.90584 - 2.34471i) q^{68} +(2.87659 - 1.19152i) q^{69} +(-0.529397 + 3.69501i) q^{70} +(2.44157 - 1.01133i) q^{71} +(7.91065 + 8.47139i) q^{72} +(14.4597 - 5.98940i) q^{73} +(4.65280 - 1.19001i) q^{74} +(-23.3774 + 23.3774i) q^{75} +(-6.95903 + 8.65314i) q^{76} +(-0.756081 - 1.82534i) q^{77} +(-9.97166 - 13.3068i) q^{78} +(-1.65822 - 4.00329i) q^{79} +(14.0581 + 8.99536i) q^{80} +4.50088 q^{81} +(-1.11401 + 7.77544i) q^{82} +(-9.61074 + 3.98090i) q^{83} +(-2.11240 + 2.62665i) q^{84} +(-3.62781 + 16.8165i) q^{85} +(-1.22284 + 8.53501i) q^{86} -12.9440 q^{87} +(-8.82869 - 0.302196i) q^{88} +(2.20486 + 2.20486i) q^{89} +(-23.4265 + 5.99161i) q^{90} +(1.97415 - 1.97415i) q^{91} +(2.32373 - 0.252153i) q^{92} +(26.1645 - 10.8377i) q^{93} +(-10.9100 + 2.79036i) q^{94} +(-8.86523 - 21.4026i) q^{95} +(6.77933 + 13.4601i) q^{96} +(-1.60004 + 3.86283i) q^{97} +(8.02936 + 4.75867i) q^{98} +(9.05008 - 9.05008i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 4 q^{2} - 4 q^{3} - 8 q^{4} - 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{10} - 4 q^{11} - 4 q^{12} + 8 q^{14} - 24 q^{16} + 4 q^{18} + 12 q^{19} + 12 q^{20} - 12 q^{21} - 4 q^{22} - 4 q^{23} + 48 q^{24}+ \cdots + 20 q^{99}+O(q^{100}) \) 280 * q - 4 * q^2 - 4 * q^3 - 8 * q^4 - 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^10 - 4 * q^11 - 4 * q^12 + 8 * q^14 - 24 * q^16 + 4 * q^18 + 12 * q^19 + 12 * q^20 - 12 * q^21 - 4 * q^22 - 4 * q^23 + 48 * q^24 - 256 * q^25 - 4 * q^26 + 8 * q^27 + 28 * q^28 - 4 * q^29 + 8 * q^30 - 24 * q^31 - 64 * q^32 + 8 * q^33 - 28 * q^34 + 12 * q^35 + 44 * q^36 - 8 * q^37 - 4 * q^39 + 48 * q^40 - 4 * q^41 + 56 * q^42 - 4 * q^43 - 32 * q^44 + 32 * q^45 + 8 * q^46 - 80 * q^47 - 56 * q^48 + 12 * q^50 - 4 * q^51 - 28 * q^52 - 4 * q^53 + 124 * q^54 - 32 * q^56 - 4 * q^57 + 24 * q^58 - 4 * q^59 + 20 * q^60 - 72 * q^61 - 4 * q^62 - 36 * q^63 - 8 * q^64 + 12 * q^65 + 48 * q^66 - 8 * q^67 - 20 * q^68 + 4 * q^69 + 44 * q^70 + 28 * q^71 + 52 * q^72 - 4 * q^73 - 32 * q^74 + 4 * q^75 - 20 * q^76 - 4 * q^77 - 104 * q^78 + 76 * q^80 - 240 * q^81 - 104 * q^82 - 44 * q^83 + 36 * q^84 + 48 * q^85 + 32 * q^86 + 88 * q^87 + 12 * q^88 + 84 * q^90 - 56 * q^91 - 124 * q^92 - 4 * q^93 - 136 * q^94 + 12 * q^95 - 4 * q^96 - 8 * q^97 + 20 * q^99

Introduction

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