LMFDB - Embedded newform 546.2.z.b.131.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(131,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("546.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.z (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.15
Character	$\chi$	$=$	546.131
Dual form			546.2.z.b.521.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(1.16571 + 1.28106i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.35360 + 2.34450i) q^{5} +(0.369008 + 1.69229i) q^{6} +(-2.61407 + 0.408207i) q^{7} +1.00000i q^{8} +(-0.282226 + 2.98670i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(1.16571 + 1.28106i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.35360 + 2.34450i) q^{5} +(0.369008 + 1.69229i) q^{6} +(-2.61407 + 0.408207i) q^{7} +1.00000i q^{8} +(-0.282226 + 2.98670i) q^{9} +(-2.34450 + 1.35360i) q^{10} +(4.42358 - 2.55396i) q^{11} +(-0.526573 + 1.65007i) q^{12} +1.00000i q^{13} +(-2.46796 - 0.953517i) q^{14} +(-4.58136 + 0.998978i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.20626 - 3.82136i) q^{17} +(-1.73776 + 2.44544i) q^{18} +(-3.03961 - 1.75492i) q^{19} -2.70720 q^{20} +(-3.57019 - 2.87293i) q^{21} +5.10791 q^{22} +(4.85709 + 2.80424i) q^{23} +(-1.28106 + 1.16571i) q^{24} +(-1.16447 - 2.01692i) q^{25} +(-0.500000 + 0.866025i) q^{26} +(-4.15513 + 3.12008i) q^{27} +(-1.66055 - 2.05975i) q^{28} +8.08843i q^{29} +(-4.46706 - 1.42554i) q^{30} +(0.214500 - 0.123842i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(8.42839 + 2.68969i) q^{33} -4.41252i q^{34} +(2.58136 - 6.68125i) q^{35} +(-2.72767 + 1.24893i) q^{36} +(-1.86850 + 3.23633i) q^{37} +(-1.75492 - 3.03961i) q^{38} +(-1.28106 + 1.16571i) q^{39} +(-2.34450 - 1.35360i) q^{40} +1.85627 q^{41} +(-1.65542 - 4.27313i) q^{42} +6.76232 q^{43} +(4.42358 + 2.55396i) q^{44} +(-6.62030 - 4.70447i) q^{45} +(2.80424 + 4.85709i) q^{46} +(5.96046 - 10.3238i) q^{47} +(-1.69229 + 0.369008i) q^{48} +(6.66673 - 2.13417i) q^{49} -2.32894i q^{50} +(2.32352 - 7.28096i) q^{51} +(-0.866025 + 0.500000i) q^{52} +(9.86465 - 5.69536i) q^{53} +(-5.15849 + 0.624507i) q^{54} +13.8281i q^{55} +(-0.408207 - 2.61407i) q^{56} +(-1.29516 - 5.93966i) q^{57} +(-4.04422 + 7.00479i) q^{58} +(5.40336 + 9.35890i) q^{59} +(-3.15582 - 3.46808i) q^{60} +(-0.805829 - 0.465246i) q^{61} +0.247684 q^{62} +(-0.481433 - 7.92264i) q^{63} -1.00000 q^{64} +(-2.34450 - 1.35360i) q^{65} +(5.95436 + 6.54354i) q^{66} +(-0.327719 - 0.567626i) q^{67} +(2.20626 - 3.82136i) q^{68} +(2.06957 + 9.49116i) q^{69} +(5.57615 - 4.49545i) q^{70} +5.11939i q^{71} +(-2.98670 - 0.282226i) q^{72} +(-5.12005 + 2.95606i) q^{73} +(-3.23633 + 1.86850i) q^{74} +(1.22636 - 3.84290i) q^{75} -3.50984i q^{76} +(-10.5210 + 8.48196i) q^{77} +(-1.69229 + 0.369008i) q^{78} +(-0.694353 + 1.20265i) q^{79} +(-1.35360 - 2.34450i) q^{80} +(-8.84070 - 1.68584i) q^{81} +(1.60757 + 0.928133i) q^{82} -5.94147 q^{83} +(0.702930 - 4.52834i) q^{84} +11.9456 q^{85} +(5.85634 + 3.38116i) q^{86} +(-10.3618 + 9.42879i) q^{87} +(2.55396 + 4.42358i) q^{88} +(5.85656 - 10.1439i) q^{89} +(-3.38111 - 7.38434i) q^{90} +(-0.408207 - 2.61407i) q^{91} +5.60848i q^{92} +(0.408695 + 0.130424i) q^{93} +(10.3238 - 5.96046i) q^{94} +(8.22884 - 4.75092i) q^{95} +(-1.65007 - 0.526573i) q^{96} -16.7005i q^{97} +(6.84064 + 1.48512i) q^{98} +(6.37944 + 13.9327i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} + 24 q^{11} - 4 q^{14} - 12 q^{15} - 16 q^{16} - 4 q^{17} - 24 q^{18} + 4 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} - 16 q^{26} + 6 q^{27} - 2 q^{28} - 8 q^{30} - 6 q^{31} + 14 q^{33} - 48 q^{35} + 4 q^{36} - 16 q^{38} - 6 q^{39} + 6 q^{40} - 16 q^{41} + 14 q^{42} + 32 q^{43} + 24 q^{44} + 20 q^{45} + 16 q^{46} - 20 q^{47} - 26 q^{49} - 46 q^{51} + 60 q^{53} + 6 q^{54} - 8 q^{56} - 8 q^{57} - 10 q^{58} - 8 q^{59} - 6 q^{60} + 36 q^{61} - 36 q^{62} + 84 q^{63} - 32 q^{64} + 6 q^{65} + 36 q^{66} + 4 q^{68} + 36 q^{69} - 18 q^{70} - 24 q^{72} - 48 q^{73} + 84 q^{74} - 2 q^{75} - 52 q^{77} + 18 q^{79} - 74 q^{81} - 24 q^{83} + 8 q^{84} - 32 q^{85} + 24 q^{86} + 14 q^{87} - 6 q^{88} + 20 q^{89} + 6 q^{90} - 8 q^{91} - 40 q^{93} + 72 q^{95} - 6 q^{96} - 32 q^{98}+O(q^{100}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 + 24 * q^11 - 4 * q^14 - 12 * q^15 - 16 * q^16 - 4 * q^17 - 24 * q^18 + 4 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 - 16 * q^26 + 6 * q^27 - 2 * q^28 - 8 * q^30 - 6 * q^31 + 14 * q^33 - 48 * q^35 + 4 * q^36 - 16 * q^38 - 6 * q^39 + 6 * q^40 - 16 * q^41 + 14 * q^42 + 32 * q^43 + 24 * q^44 + 20 * q^45 + 16 * q^46 - 20 * q^47 - 26 * q^49 - 46 * q^51 + 60 * q^53 + 6 * q^54 - 8 * q^56 - 8 * q^57 - 10 * q^58 - 8 * q^59 - 6 * q^60 + 36 * q^61 - 36 * q^62 + 84 * q^63 - 32 * q^64 + 6 * q^65 + 36 * q^66 + 4 * q^68 + 36 * q^69 - 18 * q^70 - 24 * q^72 - 48 * q^73 + 84 * q^74 - 2 * q^75 - 52 * q^77 + 18 * q^79 - 74 * q^81 - 24 * q^83 + 8 * q^84 - 32 * q^85 + 24 * q^86 + 14 * q^87 - 6 * q^88 + 20 * q^89 + 6 * q^90 - 8 * q^91 - 40 * q^93 + 72 * q^95 - 6 * q^96 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	1.16571	+	1.28106i	0.673025	+	0.739620i
$3$	1.16571	+	1.28106i	0.673025	+	0.739620i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.35360	+	2.34450i	−0.605348	+	1.04849i	0.386648	+	0.922227i	$0.373633\pi$
$5$	−1.35360	+	2.34450i	−0.605348	+	1.04849i	−0.991996	+	0.126267i	$0.959700\pi$
$6$	0.369008	+	1.69229i	0.150647	+	0.690873i
$7$	−2.61407	+	0.408207i	−0.988026	+	0.154288i
$7$	−2.61407	+	0.408207i	−0.988026	+	0.154288i
$8$			1.00000i			0.353553i
$9$	−0.282226	+	2.98670i	−0.0940752	+	0.995565i
$10$	−2.34450	+	1.35360i	−0.741397	+	0.428046i
$11$	4.42358	−	2.55396i	1.33376	−	0.770047i	0.347886	−	0.937537i	$-0.386900\pi$
$11$	4.42358	−	2.55396i	1.33376	−	0.770047i	0.985874	+	0.167490i	$0.0535663\pi$
$12$	−0.526573	+	1.65007i	−0.152009	+	0.476333i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	−2.46796	−	0.953517i	−0.659589	−	0.254838i
$15$	−4.58136	+	0.998978i	−1.18290	+	0.257935i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.20626	−	3.82136i	−0.535097	−	0.926816i	−0.999159	−	0.0410126i	$-0.986942\pi$
$17$	−2.20626	−	3.82136i	−0.535097	−	0.926816i	0.464061	−	0.885803i	$-0.346392\pi$
$18$	−1.73776	+	2.44544i	−0.409594	+	0.576396i
$19$	−3.03961	−	1.75492i	−0.697335	−	0.402606i	0.109019	−	0.994040i	$-0.465229\pi$
$19$	−3.03961	−	1.75492i	−0.697335	−	0.402606i	−0.806354	+	0.591433i	$0.798562\pi$
$20$	−2.70720			−0.605348
$21$	−3.57019	−	2.87293i	−0.779080	−	0.626924i
$22$	5.10791			1.08901
$23$	4.85709	+	2.80424i	1.01277	+	0.584725i	0.912002	−	0.410185i	$-0.134536\pi$
$23$	4.85709	+	2.80424i	1.01277	+	0.584725i	0.100771	+	0.994910i	$0.467869\pi$
$24$	−1.28106	+	1.16571i	−0.261495	+	0.237950i
$25$	−1.16447	−	2.01692i	−0.232894	−	0.403384i
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$	−4.15513	+	3.12008i	−0.799655	+	0.600460i
$28$	−1.66055	−	2.05975i	−0.313815	−	0.389256i
$29$			8.08843i			1.50198i	0.660311	+	0.750992i	$0.270424\pi$
$29$			8.08843i			1.50198i	−0.660311	+	0.750992i	$0.729576\pi$
$30$	−4.46706	−	1.42554i	−0.815570	−	0.260267i
$31$	0.214500	−	0.123842i	0.0385254	−	0.0222427i	−0.480614	−	0.876932i	$-0.659586\pi$
$31$	0.214500	−	0.123842i	0.0385254	−	0.0222427i	0.519139	+	0.854690i	$0.326253\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	8.42839	+	2.68969i	1.46720	+	0.468215i
$34$		−	4.41252i		−	0.756742i
$35$	2.58136	−	6.68125i	0.436330	−	1.12934i
$36$	−2.72767	+	1.24893i	−0.454611	+	0.208156i
$37$	−1.86850	+	3.23633i	−0.307179	+	0.532050i	−0.977744	−	0.209801i	$-0.932718\pi$
$37$	−1.86850	+	3.23633i	−0.307179	+	0.532050i	0.670565	+	0.741851i	$0.266052\pi$
$38$	−1.75492	−	3.03961i	−0.284686	−	0.493090i
$39$	−1.28106	+	1.16571i	−0.205134	+	0.186663i
$40$	−2.34450	−	1.35360i	−0.370699	−	0.214023i
$41$	1.85627			0.289900			0.144950	−	0.989439i	$-0.453698\pi$
$41$	1.85627			0.289900			0.144950	+	0.989439i	$0.453698\pi$
$42$	−1.65542	−	4.27313i	−0.255436	−	0.659358i
$43$	6.76232			1.03124			0.515622	−	0.856816i	$-0.327561\pi$
$43$	6.76232			1.03124			0.515622	+	0.856816i	$0.327561\pi$
$44$	4.42358	+	2.55396i	0.666880	+	0.385023i
$45$	−6.62030	−	4.70447i	−0.986896	−	0.701301i
$46$	2.80424	+	4.85709i	0.413463	+	0.716139i
$47$	5.96046	−	10.3238i	0.869422	−	1.50588i	0.00683461	−	0.999977i	$-0.497824\pi$
$47$	5.96046	−	10.3238i	0.869422	−	1.50588i	0.862588	−	0.505907i	$-0.168842\pi$
$48$	−1.69229	+	0.369008i	−0.244261	+	0.0532617i
$49$	6.66673	−	2.13417i	0.952390	−	0.304881i
$50$		−	2.32894i		−	0.329361i
$51$	2.32352	−	7.28096i	0.325358	−	1.01954i
$52$	−0.866025	+	0.500000i	−0.120096	+	0.0693375i
$53$	9.86465	−	5.69536i	1.35501	−	0.782318i	0.366067	−	0.930588i	$-0.380704\pi$
$53$	9.86465	−	5.69536i	1.35501	−	0.782318i	0.988947	+	0.148270i	$0.0473706\pi$
$54$	−5.15849	+	0.624507i	−0.701981	+	0.0849846i
$55$			13.8281i			1.86459i
$56$	−0.408207	−	2.61407i	−0.0545490	−	0.349320i
$57$	−1.29516	−	5.93966i	−0.171548	−	0.786727i
$58$	−4.04422	+	7.00479i	−0.531032	+	0.919774i
$59$	5.40336	+	9.35890i	0.703458	+	1.21843i	0.967245	+	0.253844i	$0.0816950\pi$
$59$	5.40336	+	9.35890i	0.703458	+	1.21843i	−0.263787	+	0.964581i	$0.584972\pi$
$60$	−3.15582	−	3.46808i	−0.407415	−	0.447728i
$61$	−0.805829	−	0.465246i	−0.103176	−	0.0595686i	0.447524	−	0.894272i	$-0.352306\pi$
$61$	−0.805829	−	0.465246i	−0.103176	−	0.0595686i	−0.550700	+	0.834703i	$0.685639\pi$
$62$	0.247684			0.0314559
$63$	−0.481433	−	7.92264i	−0.0606549	−	0.998159i
$64$	−1.00000			−0.125000
$65$	−2.34450	−	1.35360i	−0.290800	−	0.167893i
$66$	5.95436	+	6.54354i	0.732931	+	0.805454i
$67$	−0.327719	−	0.567626i	−0.0400372	−	0.0693465i	0.845312	−	0.534272i	$-0.179414\pi$
$67$	−0.327719	−	0.567626i	−0.0400372	−	0.0693465i	−0.885350	+	0.464926i	$0.846081\pi$
$68$	2.20626	−	3.82136i	0.267549	−	0.463408i
$69$	2.06957	+	9.49116i	0.249147	+	1.14260i
$70$	5.57615	−	4.49545i	0.666478	−	0.537309i
$71$			5.11939i			0.607560i	0.952742	+	0.303780i	$0.0982488\pi$
$71$			5.11939i			0.607560i	−0.952742	+	0.303780i	$0.901751\pi$
$72$	−2.98670	−	0.282226i	−0.351985	−	0.0332606i
$73$	−5.12005	+	2.95606i	−0.599256	+	0.345981i	−0.768749	−	0.639551i	$-0.779120\pi$
$73$	−5.12005	+	2.95606i	−0.599256	+	0.345981i	0.169493	+	0.985531i	$0.445787\pi$
$74$	−3.23633	+	1.86850i	−0.376216	+	0.217209i
$75$	1.22636	−	3.84290i	0.141607	−	0.443740i
$76$		−	3.50984i		−	0.402606i
$77$	−10.5210	+	8.48196i	−1.19898	+	0.966609i
$78$	−1.69229	+	0.369008i	−0.191614	+	0.0417819i
$79$	−0.694353	+	1.20265i	−0.0781208	+	0.135309i	−0.902439	−	0.430817i	$-0.858225\pi$
$79$	−0.694353	+	1.20265i	−0.0781208	+	0.135309i	0.824318	+	0.566127i	$0.191559\pi$
$80$	−1.35360	−	2.34450i	−0.151337	−	0.262124i
$81$	−8.84070	−	1.68584i	−0.982300	−	0.187316i
$82$	1.60757	+	0.928133i	0.177527	+	0.102495i
$83$	−5.94147			−0.652161			−0.326080	−	0.945342i	$-0.605728\pi$
$83$	−5.94147			−0.652161			−0.326080	+	0.945342i	$0.605728\pi$
$84$	0.702930	−	4.52834i	0.0766960	−	0.494083i
$85$	11.9456			1.29568
$86$	5.85634	+	3.38116i	0.631505	+	0.364600i
$87$	−10.3618	+	9.42879i	−1.11090	+	1.01087i
$88$	2.55396	+	4.42358i	0.272253	+	0.471555i
$89$	5.85656	−	10.1439i	0.620794	−	1.07525i	−0.368544	−	0.929610i	$-0.620144\pi$
$89$	5.85656	−	10.1439i	0.620794	−	1.07525i	0.989338	−	0.145636i	$-0.0465229\pi$
$90$	−3.38111	−	7.38434i	−0.356401	−	0.778378i
$91$	−0.408207	−	2.61407i	−0.0427918	−	0.274029i
$92$			5.60848i			0.584725i
$93$	0.408695	+	0.130424i	0.0423797	+	0.0135243i
$94$	10.3238	−	5.96046i	1.06482	−	0.614775i
$95$	8.22884	−	4.75092i	0.844261	−	0.487434i
$96$	−1.65007	−	0.526573i	−0.168409	−	0.0537432i
$97$		−	16.7005i		−	1.69568i	−0.530250	−	0.847841i	$-0.677902\pi$
$97$		−	16.7005i		−	1.69568i	0.530250	−	0.847841i	$-0.322098\pi$
$98$	6.84064	+	1.48512i	0.691009	+	0.150020i
$99$	6.37944	+	13.9327i	0.641158	+	1.40029i
$100$	1.16447	−	2.01692i	0.116447	−	0.201692i
$101$	5.94181	+	10.2915i	0.591232	+	1.02404i	0.994067	+	0.108771i	$0.0346916\pi$
$101$	5.94181	+	10.2915i	0.591232	+	1.02404i	−0.402835	+	0.915273i	$0.631975\pi$
$102$	5.65271	−	5.14374i	0.559701	−	0.509306i
$103$	−3.50048	−	2.02100i	−0.344913	−	0.199135i	0.317530	−	0.948248i	$-0.397147\pi$
$103$	−3.50048	−	2.02100i	−0.344913	−	0.199135i	−0.662442	+	0.749113i	$0.730480\pi$
$104$	−1.00000			−0.0980581
$105$	11.5682	−	4.48154i	1.12894	−	0.437354i
$106$	11.3907			1.10636
$107$	−0.183649	−	0.106030i	−0.0177540	−	0.0102503i	0.491097	−	0.871105i	$-0.336596\pi$
$107$	−0.183649	−	0.106030i	−0.0177540	−	0.0102503i	−0.508851	+	0.860855i	$0.669929\pi$
$108$	−4.77963	−	2.03840i	−0.459921	−	0.196146i
$109$	−8.61992	−	14.9301i	−0.825639	−	1.43005i	−0.901430	−	0.432924i	$-0.857482\pi$
$109$	−8.61992	−	14.9301i	−0.825639	−	1.43005i	0.0757918	−	0.997124i	$-0.475852\pi$
$110$	−6.91407	+	11.9755i	−0.659231	+	1.14182i
$111$	−6.32407	+	1.37898i	−0.600254	+	0.130887i
$112$	0.953517	−	2.46796i	0.0900989	−	0.233200i
$113$		−	5.08917i		−	0.478749i	−0.970927	−	0.239374i	$-0.923058\pi$
$113$		−	5.08917i		−	0.478749i	0.970927	−	0.239374i	$-0.0769423\pi$
$114$	1.84819	−	5.79147i	0.173099	−	0.542421i
$115$	−13.1491	+	7.59165i	−1.22616	+	0.707925i
$116$	−7.00479	+	4.04422i	−0.650378	+	0.375496i
$117$	−2.98670	−	0.282226i	−0.276120	−	0.0260918i
$118$			10.8067i			0.994840i
$119$	7.32723	+	9.08869i	0.671686	+	0.833159i
$120$	−0.998978	−	4.58136i	−0.0911938	−	0.418219i
$121$	7.54538	−	13.0690i	0.685943	−	1.18809i
$122$	−0.465246	−	0.805829i	−0.0421214	−	0.0729563i
$123$	2.16387	+	2.37799i	0.195110	+	0.214416i
$124$	0.214500	+	0.123842i	0.0192627	+	0.0111213i
$125$	−7.23111			−0.646770
$126$	3.54439	−	7.10192i	0.315759	−	0.632690i
$127$	−16.8047			−1.49118			−0.745590	−	0.666405i	$-0.767832\pi$
$127$	−16.8047			−1.49118			−0.745590	+	0.666405i	$0.767832\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	7.88292	+	8.66293i	0.694053	+	0.762728i
$130$	−1.35360	−	2.34450i	−0.118719	−	0.205627i
$131$	0.892356	−	1.54561i	0.0779655	−	0.135040i	−0.824407	−	0.565998i	$-0.808491\pi$
$131$	0.892356	−	1.54561i	0.0779655	−	0.135040i	0.902372	+	0.430958i	$0.141824\pi$
$132$	1.88486	+	8.64405i	0.164056	+	0.752368i
$133$	8.66213	+	3.34670i	0.751102	+	0.290195i
$134$		−	0.655438i		−	0.0566212i
$135$	−1.69067	−	13.9651i	−0.145509	−	1.20192i
$136$	3.82136	−	2.20626i	0.327679	−	0.189185i
$137$	7.66372	−	4.42465i	0.654756	−	0.378023i	−0.135520	−	0.990775i	$-0.543271\pi$
$137$	7.66372	−	4.42465i	0.654756	−	0.378023i	0.790276	+	0.612751i	$0.209937\pi$
$138$	−2.95328	+	9.25437i	−0.251400	+	0.787785i
$139$			1.90671i			0.161725i	0.996725	+	0.0808625i	$0.0257675\pi$
$139$			1.90671i			0.161725i	−0.996725	+	0.0808625i	$0.974233\pi$
$140$	7.07681	−	1.10510i	0.598100	−	0.0933979i
$141$	20.1736	−	4.39891i	1.69892	−	0.370455i
$142$	−2.55970	+	4.43352i	−0.214805	+	0.372053i
$143$	2.55396	+	4.42358i	0.213572	+	0.369918i
$144$	−2.44544	−	1.73776i	−0.203787	−	0.144814i
$145$	−18.9634	−	10.9485i	−1.57482	−	0.909224i
$146$	−5.91212			−0.489290
$147$	10.5055	+	6.05265i	0.866478	+	0.499215i
$148$	−3.73700			−0.307179
$149$	−9.16625	−	5.29214i	−0.750929	−	0.433549i	0.0751008	−	0.997176i	$-0.476072\pi$
$149$	−9.16625	−	5.29214i	−0.750929	−	0.433549i	−0.826029	+	0.563627i	$0.809405\pi$
$150$	2.98350	−	2.71487i	0.243602	−	0.221668i
$151$	−0.0860331	−	0.149014i	−0.00700128	−	0.0121266i	0.862504	−	0.506051i	$-0.168895\pi$
$151$	−0.0860331	−	0.149014i	−0.00700128	−	0.0121266i	−0.869505	+	0.493924i	$0.835562\pi$
$152$	1.75492	−	3.03961i	0.142343	−	0.246545i
$153$	12.0359	−	5.51095i	0.973045	−	0.445534i
$154$	−13.3524	+	2.08509i	−1.07597	+	0.168021i
$155$			0.670530i			0.0538582i
$156$	−1.65007	−	0.526573i	−0.132111	−	0.0421596i
$157$	12.6256	−	7.28938i	1.00763	−	0.581756i	0.0971338	−	0.995271i	$-0.469033\pi$
$157$	12.6256	−	7.28938i	1.00763	−	0.581756i	0.910497	+	0.413515i	$0.135699\pi$
$158$	−1.20265	+	0.694353i	−0.0956780	+	0.0552397i
$159$	18.7955	+	5.99805i	1.49058	+	0.475676i
$160$		−	2.70720i		−	0.214023i
$161$	−13.8415	−	5.34779i	−1.09086	−	0.421465i
$162$	−6.81335	−	5.88033i	−0.535307	−	0.462003i
$163$	3.66859	−	6.35419i	0.287347	−	0.497699i	−0.685829	−	0.727763i	$-0.740560\pi$
$163$	3.66859	−	6.35419i	0.287347	−	0.497699i	0.973176	+	0.230064i	$0.0738935\pi$
$164$	0.928133	+	1.60757i	0.0724750	+	0.125530i
$165$	−17.7147	+	16.1196i	−1.37908	+	1.25491i
$166$	−5.14546	−	2.97073i	−0.399365	−	0.230574i
$167$	12.5939			0.974543			0.487271	−	0.873251i	$-0.337992\pi$
$167$	12.5939			0.974543			0.487271	+	0.873251i	$0.337992\pi$
$168$	2.87293	−	3.57019i	0.221651	−	0.275447i
$169$	−1.00000			−0.0769231
$170$	10.3452	+	5.97280i	0.793439	+	0.458092i
$171$	6.09927	−	8.58311i	0.466423	−	0.656367i
$172$	3.38116	+	5.85634i	0.257811	+	0.446542i
$173$	−10.5343	+	18.2460i	−0.800912	+	1.38722i	0.118105	+	0.993001i	$0.462318\pi$
$173$	−10.5343	+	18.2460i	−0.800912	+	1.38722i	−0.919017	+	0.394219i	$0.871015\pi$
$174$	−13.6879	+	2.98469i	−1.03768	+	0.226269i
$175$	3.86732	+	4.79702i	0.292342	+	0.362621i
$176$			5.10791i			0.385023i
$177$	−5.69053	+	17.8318i	−0.427727	+	1.34032i
$178$	10.1439	−	5.85656i	0.760314	−	0.438967i
$179$	7.26976	−	4.19720i	0.543367	−	0.313713i	−0.203075	−	0.979163i	$-0.565094\pi$
$179$	7.26976	−	4.19720i	0.543367	−	0.313713i	0.746443	+	0.665450i	$0.231760\pi$
$180$	0.764041	−	8.08558i	0.0569483	−	0.602664i
$181$			22.3401i			1.66053i	0.557369	+	0.830265i	$0.311811\pi$
$181$			22.3401i			1.66053i	−0.557369	+	0.830265i	$0.688189\pi$
$182$	0.953517	−	2.46796i	0.0706794	−	0.182937i
$183$	−0.343358	−	1.57466i	−0.0253818	−	0.116402i
$184$	−2.80424	+	4.85709i	−0.206731	+	0.358069i
$185$	−5.05840	−	8.76141i	−0.371901	−	0.644151i
$186$	0.288728	+	0.317298i	0.0211706	+	0.0232654i
$187$	−19.5192	−	11.2694i	−1.42738	−	0.824100i
$188$	11.9209			0.869422
$189$	9.58816	−	9.85227i	0.697436	−	0.716647i
$190$	9.50185			0.689336
$191$	12.4296	+	7.17622i	0.899372	+	0.519253i	0.876997	−	0.480497i	$-0.159544\pi$
$191$	12.4296	+	7.17622i	0.899372	+	0.519253i	0.0223759	+	0.999750i	$0.492877\pi$
$192$	−1.16571	−	1.28106i	−0.0841281	−	0.0924525i
$193$	−11.1294	−	19.2766i	−0.801109	−	1.38756i	−0.918887	−	0.394521i	$-0.870910\pi$
$193$	−11.1294	−	19.2766i	−0.801109	−	1.38756i	0.117778	−	0.993040i	$-0.462423\pi$
$194$	8.35027	−	14.4631i	0.599514	−	1.03839i
$195$	−0.998978	−	4.58136i	−0.0715383	−	0.328078i
$196$	5.18161	+	4.70648i	0.370115	+	0.336177i
$197$		−	16.2007i		−	1.15425i	−0.816654	−	0.577127i	$-0.804174\pi$
$197$		−	16.2007i		−	1.15425i	0.816654	−	0.577127i	$-0.195826\pi$
$198$	−1.44158	+	15.2558i	−0.102449	+	1.08418i
$199$	4.44906	−	2.56866i	0.315385	−	0.182088i	−0.333948	−	0.942591i	$-0.608381\pi$
$199$	4.44906	−	2.56866i	0.315385	−	0.182088i	0.649334	+	0.760504i	$0.275048\pi$
$200$	2.01692	−	1.16447i	0.142618	−	0.0823403i
$201$	0.345136	−	1.08152i	0.0243440	−	0.0762843i
$202$			11.8836i			0.836129i
$203$	−3.30176	−	21.1437i	−0.231738	−	1.48400i
$204$	7.46726	−	1.62826i	0.522812	−	0.114001i
$205$	−2.51264	+	4.35202i	−0.175490	+	0.303958i
$206$	−2.02100	−	3.50048i	−0.140810	−	0.243890i
$207$	−9.74621	+	13.7152i	−0.677409	+	0.953274i
$208$	−0.866025	−	0.500000i	−0.0600481	−	0.0346688i
$209$	−17.9280			−1.24010
$210$	12.2591	+	1.90297i	0.845961	+	0.131318i
$211$	22.9415			1.57936			0.789680	−	0.613518i	$-0.210246\pi$
$211$	22.9415			1.57936			0.789680	+	0.613518i	$0.210246\pi$
$212$	9.86465	+	5.69536i	0.677507	+	0.391159i
$213$	−6.55825	+	5.96774i	−0.449364	+	0.408903i
$214$	−0.106030	−	0.183649i	−0.00724804	−	0.0125540i
$215$	−9.15348	+	15.8543i	−0.624262	+	1.08125i
$216$	−3.12008	−	4.15513i	−0.212295	−	0.282721i
$217$	−0.510166	+	0.411292i	−0.0346323	+	0.0279203i
$218$		−	17.2398i		−	1.16763i
$219$	−9.75539	−	3.11316i	−0.659208	−	0.210368i
$220$	−11.9755	+	6.91407i	−0.807389	+	0.466147i
$221$	3.82136	−	2.20626i	0.257052	−	0.148409i
$222$	−6.16629	−	1.96780i	−0.413855	−	0.132070i
$223$			9.34868i			0.626034i	0.949748	+	0.313017i	$0.101340\pi$
$223$			9.34868i			0.626034i	−0.949748	+	0.313017i	$0.898660\pi$
$224$	2.05975	−	1.66055i	0.137623	−	0.110950i
$225$	6.35256	−	2.90869i	0.423504	−	0.193912i
$226$	2.54458	−	4.40735i	0.169263	−	0.293172i
$227$	0.244306	+	0.423151i	0.0162152	+	0.0280855i	0.874019	−	0.485892i	$-0.161505\pi$
$227$	0.244306	+	0.423151i	0.0162152	+	0.0280855i	−0.857804	+	0.513977i	$0.828172\pi$
$228$	4.49632	−	4.09147i	0.297776	−	0.270964i
$229$	−18.1391	−	10.4726i	−1.19866	−	0.692049i	−0.238407	−	0.971165i	$-0.576625\pi$
$229$	−18.1391	−	10.4726i	−1.19866	−	0.692049i	−0.960257	+	0.279116i	$0.909959\pi$
$230$	−15.1833			−1.00116
$231$	−23.1304	−	3.59051i	−1.52187	−	0.236238i
$232$	−8.08843			−0.531032
$233$	−22.6804	−	13.0946i	−1.48584	−	0.857853i	−0.485974	−	0.873973i	$-0.661535\pi$
$233$	−22.6804	−	13.0946i	−1.48584	−	0.857853i	−0.999870	+	0.0161207i	$0.994868\pi$
$234$	−2.44544	−	1.73776i	−0.159863	−	0.113601i
$235$	16.1362	+	27.9487i	1.05261	+	1.82317i
$236$	−5.40336	+	9.35890i	−0.351729	+	0.609213i
$237$	−2.35009	+	0.512443i	−0.152655	+	0.0332867i
$238$	1.80123	+	11.5347i	0.116756	+	0.747680i
$239$			23.1593i			1.49805i	0.662542	+	0.749025i	$0.269478\pi$
$239$			23.1593i			1.49805i	−0.662542	+	0.749025i	$0.730522\pi$
$240$	1.42554	−	4.46706i	0.0920182	−	0.288348i
$241$	−23.5370	+	13.5891i	−1.51615	+	0.875352i	−0.516333	+	0.856388i	$0.672703\pi$
$241$	−23.5370	+	13.5891i	−1.51615	+	0.875352i	−0.999820	+	0.0189640i	$0.993963\pi$
$242$	13.0690	−	7.54538i	0.840106	−	0.485035i
$243$	−8.14605	−	13.2907i	−0.522569	−	0.852597i
$244$		−	0.930491i		−	0.0595686i
$245$	−4.02053	+	18.5190i	−0.256862	+	1.18314i
$246$	0.684976	+	3.14133i	0.0436725	+	0.200284i
$247$	1.75492	−	3.03961i	0.111663	−	0.193406i
$248$	0.123842	+	0.214500i	0.00786397	+	0.0136208i
$249$	−6.92604	−	7.61137i	−0.438920	−	0.482351i
$250$	−6.26232	−	3.61555i	−0.396064	−	0.228668i
$251$	−5.92128			−0.373748			−0.186874	−	0.982384i	$-0.559836\pi$
$251$	−5.92128			−0.373748			−0.186874	+	0.982384i	$0.559836\pi$
$252$	6.62049	−	4.37825i	0.417052	−	0.275804i
$253$	28.6476			1.80106
$254$	−14.5533	−	8.40237i	−0.913157	−	0.527211i
$255$	13.9251	+	15.3030i	0.872026	+	0.958312i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.85122	−	8.40256i	0.302611	−	0.524137i	−0.674116	−	0.738626i	$-0.735475\pi$
$257$	4.85122	−	8.40256i	0.302611	−	0.524137i	0.976727	+	0.214489i	$0.0688085\pi$
$258$	2.49535	+	11.4438i	0.155353	+	0.712459i
$259$	3.56329	−	9.22274i	0.221412	−	0.573073i
$260$		−	2.70720i		−	0.167893i
$261$	−24.1577	−	2.28276i	−1.49532	−	0.141299i
$262$	1.54561	−	0.892356i	0.0954879	−	0.0551300i
$263$	−8.35227	+	4.82218i	−0.515023	+	0.297349i	−0.734896	−	0.678180i	$-0.762769\pi$
$263$	−8.35227	+	4.82218i	−0.515023	+	0.297349i	0.219873	+	0.975528i	$0.429436\pi$
$264$	−2.68969	+	8.42839i	−0.165539	+	0.518732i
$265$			30.8370i			1.89430i
$266$	5.82828	+	7.22939i	0.357355	+	0.443262i
$267$	19.8219	−	4.32223i	1.21308	−	0.264516i
$268$	0.327719	−	0.567626i	0.0200186	−	0.0346733i
$269$	−3.78210	−	6.55079i	−0.230599	−	0.399409i	0.727386	−	0.686229i	$-0.240735\pi$
$269$	−3.78210	−	6.55079i	−0.230599	−	0.399409i	−0.957984	+	0.286820i	$0.907402\pi$
$270$	5.51837	−	12.9394i	0.335837	−	0.787469i
$271$	−9.15154	−	5.28364i	−0.555917	−	0.320959i	0.195588	−	0.980686i	$-0.437338\pi$
$271$	−9.15154	−	5.28364i	−0.555917	−	0.320959i	−0.751505	+	0.659728i	$0.770672\pi$
$272$	4.41252			0.267549
$273$	2.87293	−	3.57019i	0.173877	−	0.216078i
$274$	8.84930			0.534606
$275$	−10.3022	−	5.94800i	−0.621248	−	0.358678i
$276$	−7.18480	+	6.53788i	−0.432474	+	0.393534i
$277$	−7.69761	−	13.3326i	−0.462504	−	0.801081i	0.536581	−	0.843849i	$-0.319716\pi$
$277$	−7.69761	−	13.3326i	−0.462504	−	0.801081i	−0.999085	+	0.0427680i	$0.986382\pi$
$278$	−0.953355	+	1.65126i	−0.0571784	+	0.0990359i
$279$	0.309340	+	0.675599i	0.0185197	+	0.0404470i
$280$	6.68125	+	2.58136i	0.399281	+	0.154266i
$281$			11.0615i			0.659871i	0.944004	+	0.329935i	$0.107027\pi$
$281$			11.0615i			0.659871i	−0.944004	+	0.329935i	$0.892973\pi$
$282$	19.6703	+	6.27724i	1.17135	+	0.373804i
$283$	−0.521259	+	0.300949i	−0.0309856	+	0.0178896i	−0.515413	−	0.856942i	$-0.672361\pi$
$283$	−0.521259	+	0.300949i	−0.0309856	+	0.0178896i	0.484427	+	0.874832i	$0.339028\pi$
$284$	−4.43352	+	2.55970i	−0.263081	+	0.151890i
$285$	15.6787	+	5.00342i	0.928725	+	0.296377i
$286$			5.10791i			0.302037i
$287$	−4.85241	+	0.757741i	−0.286429	+	0.0447280i
$288$	−1.24893	−	2.72767i	−0.0735941	−	0.160729i
$289$	−1.23519	+	2.13941i	−0.0726581	+	0.125848i
$290$	−10.9485	−	18.9634i	−0.642918	−	1.11357i
$291$	21.3944	−	19.4680i	1.25416	−	1.14124i
$292$	−5.12005	−	2.95606i	−0.299628	−	0.172990i
$293$	26.8380			1.56789			0.783945	−	0.620830i	$-0.213204\pi$
$293$	26.8380			1.56789			0.783945	+	0.620830i	$0.213204\pi$
$294$	6.07170	+	10.4945i	0.354108	+	0.612052i
$295$	−29.2560			−1.70335
$296$	−3.23633	−	1.86850i	−0.188108	−	0.108604i
$297$	−10.4120	+	24.4139i	−0.604165	+	1.41664i
$298$	−5.29214	−	9.16625i	−0.306565	−	0.530987i
$299$	−2.80424	+	4.85709i	−0.162174	+	0.280893i
$300$	3.94123	−	0.859395i	0.227547	−	0.0496172i
$301$	−17.6772	+	2.76043i	−1.01890	+	0.159108i
$302$		−	0.172066i		−	0.00990130i
$303$	−6.25760	+	19.6088i	−0.359490	+	1.12649i
$304$	3.03961	−	1.75492i	0.174334	−	0.100652i
$305$	2.18154	−	1.25951i	0.124915	−	0.0721195i
$306$	13.1789	+	1.24533i	0.753386	+	0.0711906i
$307$			11.4430i			0.653084i	0.945183	+	0.326542i	$0.105883\pi$
$307$			11.4430i			0.653084i	−0.945183	+	0.326542i	$0.894117\pi$
$308$	−12.6061	−	4.87048i	−0.718299	−	0.277521i
$309$	−1.49153	−	6.84023i	−0.0848503	−	0.389127i
$310$	−0.335265	+	0.580696i	−0.0190418	+	0.0329813i
$311$	−8.12797	−	14.0781i	−0.460895	−	0.798294i	0.538111	−	0.842874i	$-0.319138\pi$
$311$	−8.12797	−	14.0781i	−0.460895	−	0.798294i	−0.999006	+	0.0445804i	$0.985805\pi$
$312$	−1.16571	−	1.28106i	−0.0659955	−	0.0725257i
$313$	21.4241	+	12.3692i	1.21096	+	0.699148i	0.962968	−	0.269614i	$-0.0868961\pi$
$313$	21.4241	+	12.3692i	1.21096	+	0.699148i	0.247992	+	0.968762i	$0.420229\pi$
$314$	14.5788			0.822727
$315$	19.2263	+	9.59537i	1.08328	+	0.540638i
$316$	−1.38871			−0.0781208
$317$	−1.61844	−	0.934407i	−0.0909007	−	0.0524816i	0.453861	−	0.891073i	$-0.350046\pi$
$317$	−1.61844	−	0.934407i	−0.0909007	−	0.0524816i	−0.544761	+	0.838591i	$0.683380\pi$
$318$	13.2783	+	14.5922i	0.744611	+	0.818289i
$319$	20.6575	+	35.7798i	1.15660	+	2.00329i
$320$	1.35360	−	2.34450i	0.0756686	−	0.131062i
$321$	−0.0782515	−	0.358865i	−0.00436757	−	0.0200299i
$322$	−9.31319	−	11.5521i	−0.519004	−	0.643771i
$323$			15.4873i			0.861734i
$324$	−2.96037	−	8.49919i	−0.164465	−	0.472177i
$325$	2.01692	−	1.16447i	0.111878	−	0.0645931i
$326$	6.35419	−	3.66859i	0.351926	−	0.203185i
$327$	9.07804	−	28.4469i	0.502017	−	1.57312i
$328$			1.85627i			0.102495i
$329$	−11.3668	+	29.4203i	−0.626672	+	1.62199i
$330$	−23.4012	+	5.10269i	−1.28819	+	0.280894i
$331$	−6.88129	+	11.9187i	−0.378230	+	0.655113i	−0.990805	−	0.135299i	$-0.956800\pi$
$331$	−6.88129	+	11.9187i	−0.378230	+	0.655113i	0.612575	+	0.790412i	$0.290134\pi$
$332$	−2.97073	−	5.14546i	−0.163040	−	0.282394i
$333$	−9.13861	−	6.49401i	−0.500793	−	0.355870i
$334$	10.9066	+	6.29693i	0.596783	+	0.344553i
$335$	1.77440			0.0969459
$336$	4.27313	−	1.65542i	0.233118	−	0.0903103i
$337$	−17.9304			−0.976733			−0.488367	−	0.872639i	$-0.662407\pi$
$337$	−17.9304			−0.976733			−0.488367	+	0.872639i	$0.662407\pi$
$338$	−0.866025	−	0.500000i	−0.0471056	−	0.0271964i
$339$	6.51952	−	5.93251i	0.354092	−	0.322210i
$340$	5.97280	+	10.3452i	0.323920	+	0.561046i
$341$	0.632573	−	1.09565i	0.0342558	−	0.0593327i
$342$	9.57368	−	4.38356i	0.517685	−	0.237036i
$343$	−16.5561	+	8.30027i	−0.893947	+	0.448173i
$344$			6.76232i			0.364600i
$345$	−25.0534	−	7.99512i	−1.34883	−	0.430443i
$346$	−18.2460	+	10.5343i	−0.980913	+	0.566330i
$347$	8.39852	−	4.84889i	0.450856	−	0.260302i	−0.257335	−	0.966322i	$-0.582845\pi$
$347$	8.39852	−	4.84889i	0.450856	−	0.260302i	0.708192	+	0.706020i	$0.249511\pi$
$348$	−13.3465	−	4.25915i	−0.715445	−	0.228315i
$349$		−	17.7598i		−	0.950658i	−0.879808	−	0.475329i	$-0.842329\pi$
$349$		−	17.7598i		−	0.950658i	0.879808	−	0.475329i	$-0.157671\pi$
$350$	0.950689	+	6.08800i	0.0508165	+	0.325417i
$351$	−3.12008	−	4.15513i	−0.166538	−	0.221784i
$352$	−2.55396	+	4.42358i	−0.136126	+	0.235778i
$353$	−12.5740	−	21.7789i	−0.669248	−	1.15917i	−0.978115	−	0.208066i	$-0.933283\pi$
$353$	−12.5740	−	21.7789i	−0.669248	−	1.15917i	0.308867	−	0.951105i	$-0.400050\pi$
$354$	−13.8441	+	12.5975i	−0.735803	+	0.669552i
$355$	−12.0024	−	6.92961i	−0.637023	−	0.367786i
$356$	11.7131			0.620794
$357$	−3.10170	+	19.9814i	−0.164159	+	1.05753i
$358$	8.39439			0.443658
$359$	2.89946	+	1.67400i	0.153028	+	0.0883506i	0.574559	−	0.818463i	$-0.305174\pi$
$359$	2.89946	+	1.67400i	0.153028	+	0.0883506i	−0.421531	+	0.906814i	$0.638507\pi$
$360$	4.70447	−	6.62030i	0.247947	−	0.348920i
$361$	−3.34051	−	5.78593i	−0.175816	−	0.304522i
$362$	−11.1701	+	19.3471i	−0.587086	+	1.01686i
$363$	25.5379	−	5.56860i	1.34039	−	0.292276i
$364$	2.05975	−	1.66055i	0.107960	−	0.0870366i
$365$		−	16.0053i		−	0.837755i
$366$	0.489972	−	1.53537i	0.0256112	−	0.0802552i
$367$	8.58651	−	4.95743i	0.448212	−	0.258776i	−0.258863	−	0.965914i	$-0.583348\pi$
$367$	8.58651	−	4.95743i	0.448212	−	0.258776i	0.707075	+	0.707139i	$0.250014\pi$
$368$	−4.85709	+	2.80424i	−0.253193	+	0.146181i
$369$	−0.523885	+	5.54410i	−0.0272724	+	0.288614i
$370$		−	10.1168i		−	0.525947i
$371$	−23.4620	+	18.9149i	−1.21809	+	0.982013i
$372$	0.0913972	+	0.419152i	0.00473872	+	0.0217320i
$373$	12.2118	−	21.1514i	0.632303	−	1.09518i	−0.354777	−	0.934951i	$-0.615443\pi$
$373$	12.2118	−	21.1514i	0.632303	−	1.09518i	0.987080	−	0.160229i	$-0.0512234\pi$
$374$	−11.2694	−	19.5192i	−0.582726	−	1.00931i
$375$	−8.42940	−	9.26348i	−0.435292	−	0.478364i
$376$	10.3238	+	5.96046i	0.532410	+	0.307387i
$377$	−8.08843			−0.416575
$378$	13.2297	−	3.73824i	0.680464	−	0.192274i
$379$	14.4628			0.742906			0.371453	−	0.928452i	$-0.378860\pi$
$379$	14.4628			0.742906			0.371453	+	0.928452i	$0.378860\pi$
$380$	8.22884	+	4.75092i	0.422131	+	0.243717i
$381$	−19.5895	−	21.5279i	−1.00360	−	1.10291i
$382$	7.17622	+	12.4296i	0.367167	+	0.635952i
$383$	−6.05529	+	10.4881i	−0.309411	+	0.535916i	−0.978234	−	0.207506i	$-0.933465\pi$
$383$	−6.05529	+	10.4881i	−0.309411	+	0.535916i	0.668823	+	0.743422i	$0.266799\pi$
$384$	−0.369008	−	1.69229i	−0.0188308	−	0.0863591i
$385$	−5.64475	−	36.1477i	−0.287683	−	1.84226i
$386$		−	22.2587i		−	1.13294i
$387$	−1.90850	+	20.1970i	−0.0970145	+	1.02667i
$388$	14.4631	−	8.35027i	0.734252	−	0.423921i
$389$	−4.46068	+	2.57537i	−0.226165	+	0.130577i	−0.608802	−	0.793322i	$-0.708350\pi$
$389$	−4.46068	+	2.57537i	−0.226165	+	0.130577i	0.382636	+	0.923899i	$0.375016\pi$
$390$	1.42554	−	4.46706i	0.0721850	−	0.226198i
$391$		−	24.7476i		−	1.25154i
$392$	2.13417	+	6.66673i	0.107792	+	0.336721i
$393$	3.02024	−	0.658573i	0.152351	−	0.0332206i
$394$	8.10037	−	14.0302i	0.408091	−	0.706834i
$395$	−1.87975	−	3.25583i	−0.0945806	−	0.163818i
$396$	−8.87633	+	12.4911i	−0.446053	+	0.627701i
$397$	23.9744	+	13.8416i	1.20324	+	0.694690i	0.961274	−	0.275595i	$-0.0888748\pi$
$397$	23.9744	+	13.8416i	1.20324	+	0.694690i	0.241965	+	0.970285i	$0.422208\pi$
$398$	5.13733			0.257511
$399$	5.81025	+	14.9980i	0.290876	+	0.750839i
$400$	2.32894			0.116447
$401$	−12.7601	−	7.36705i	−0.637209	−	0.367893i	0.146330	−	0.989236i	$-0.453254\pi$
$401$	−12.7601	−	7.36705i	−0.637209	−	0.367893i	−0.783539	+	0.621343i	$0.786587\pi$
$402$	0.839655	−	0.764052i	0.0418782	−	0.0381075i
$403$	0.123842	+	0.214500i	0.00616900	+	0.0106850i
$404$	−5.94181	+	10.2915i	−0.295616	+	0.512022i
$405$	15.9192	−	18.4451i	0.791033	−	0.916544i
$406$	7.71246	−	19.9619i	0.382763	−	0.990692i
$407$			19.0882i			0.946169i
$408$	7.28096	+	2.32352i	0.360461	+	0.115031i
$409$	−0.297547	+	0.171789i	−0.0147128	+	0.00849442i	−0.507338	−	0.861747i	$-0.669371\pi$
$409$	−0.297547	+	0.171789i	−0.0147128	+	0.00849442i	0.492626	+	0.870241i	$0.336037\pi$
$410$	−4.35202	+	2.51264i	−0.214931	+	0.124091i
$411$	14.6019	+	4.65980i	0.720260	+	0.229851i
$412$		−	4.04201i		−	0.199135i
$413$	−17.9451	−	22.2591i	−0.883023	−	1.09530i
$414$	−15.2981	+	7.00462i	−0.751859	+	0.344258i
$415$	8.04237	−	13.9298i	0.394784	−	0.683787i
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	−2.44261	+	2.22268i	−0.119615	+	0.108845i
$418$	−15.5261	−	8.96398i	−0.759405	−	0.438443i
$419$	11.7555			0.574294			0.287147	−	0.957887i	$-0.407293\pi$
$419$	11.7555			0.574294			0.287147	+	0.957887i	$0.407293\pi$
$420$	9.66523	+	7.77759i	0.471615	+	0.379508i
$421$	−13.9796			−0.681322			−0.340661	−	0.940186i	$-0.610651\pi$
$421$	−13.9796			−0.681322			−0.340661	+	0.940186i	$0.610651\pi$
$422$	19.8680	+	11.4708i	0.967157	+	0.558388i
$423$	29.1519	+	20.7157i	1.41741	+	1.00723i
$424$	5.69536	+	9.86465i	0.276591	+	0.479070i
$425$	−5.13824	+	8.89970i	−0.249241	+	0.431699i
$426$	−8.66348	+	1.88909i	−0.419747	+	0.0915269i
$427$	2.29641	+	0.887240i	0.111131	+	0.0429365i
$428$		−	0.212059i		−	0.0102503i
$429$	−2.68969	+	8.42839i	−0.129859	+	0.406927i
$430$	−15.8543	+	9.15348i	−0.764562	+	0.441420i
$431$	−27.1079	+	15.6507i	−1.30574	+	0.753869i	−0.981382	−	0.192065i	$-0.938481\pi$
$431$	−27.1079	+	15.6507i	−1.30574	+	0.753869i	−0.324358	+	0.945934i	$0.605148\pi$
$432$	−0.624507	−	5.15849i	−0.0300466	−	0.248188i
$433$			27.5102i			1.32206i	0.750360	+	0.661029i	$0.229880\pi$
$433$			27.5102i			1.32206i	−0.750360	+	0.661029i	$0.770120\pi$
$434$	−0.647463	+	0.101106i	−0.0310792	+	0.00485326i
$435$	−8.08016	−	37.0560i	−0.387414	−	1.77670i
$436$	8.61992	−	14.9301i	0.412819	−	0.715024i
$437$	−9.84245	−	17.0476i	−0.470828	−	0.815498i
$438$	−6.89183	−	7.57377i	−0.329305	−	0.361889i
$439$	28.7016	+	16.5709i	1.36985	+	0.790884i	0.990909	−	0.134536i	$-0.0429543\pi$
$439$	28.7016	+	16.5709i	1.36985	+	0.790884i	0.378943	+	0.925420i	$0.376288\pi$
$440$	−13.8281			−0.659231
$441$	4.49258	+	20.5138i	0.213932	+	0.976848i
$442$	4.41252			0.209882
$443$	−16.8419	−	9.72365i	−0.800181	−	0.461985i	0.0433534	−	0.999060i	$-0.486196\pi$
$443$	−16.8419	−	9.72365i	−0.800181	−	0.461985i	−0.843534	+	0.537075i	$0.819529\pi$
$444$	−4.35627	−	4.78731i	−0.206739	−	0.227196i
$445$	15.8549	+	27.4614i	0.751593	+	1.30180i
$446$	−4.67434	+	8.09619i	−0.221336	+	0.383366i
$447$	−3.90568	−	17.9116i	−0.184732	−	0.847191i
$448$	2.61407	−	0.408207i	0.123503	−	0.0192860i
$449$			25.9959i			1.22682i	0.789764	+	0.613410i	$0.210203\pi$
$449$			25.9959i			1.22682i	−0.789764	+	0.613410i	$0.789797\pi$
$450$	6.95582	+	0.657285i	0.327901	+	0.0309847i
$451$	8.21134	−	4.74082i	0.386657	−	0.223236i
$452$	4.40735	−	2.54458i	0.207304	−	0.119687i
$453$	0.0906055	−	0.283921i	0.00425702	−	0.0133398i
$454$			0.488613i			0.0229317i
$455$	6.68125	+	2.58136i	0.313222	+	0.121016i
$456$	5.93966	−	1.29516i	0.278150	−	0.0606513i
$457$	−5.95090	+	10.3073i	−0.278371	+	0.482153i	−0.970980	−	0.239160i	$-0.923128\pi$
$457$	−5.95090	+	10.3073i	−0.278371	+	0.482153i	0.692609	+	0.721313i	$0.256461\pi$
$458$	−10.4726	−	18.1391i	−0.489353	−	0.847584i
$459$	21.0903	+	8.99451i	0.984409	+	0.419828i
$460$	−13.1491	−	7.59165i	−0.613081	−	0.353962i
$461$	−20.5943			−0.959172			−0.479586	−	0.877495i	$-0.659213\pi$
$461$	−20.5943			−0.959172			−0.479586	+	0.877495i	$0.659213\pi$
$462$	−18.2362	−	14.6747i	−0.848427	−	0.682727i
$463$	38.0972			1.77053			0.885263	−	0.465092i	$-0.153979\pi$
$463$	38.0972			1.77053			0.885263	+	0.465092i	$0.153979\pi$
$464$	−7.00479	−	4.04422i	−0.325189	−	0.187748i
$465$	−0.858988	+	0.781645i	−0.0398346	+	0.0362479i
$466$	−13.0946	−	22.6804i	−0.606593	−	1.05065i
$467$	15.5511	−	26.9353i	0.719619	−	1.24642i	−0.241531	−	0.970393i	$-0.577650\pi$
$467$	15.5511	−	26.9353i	0.719619	−	1.24642i	0.961151	−	0.276024i	$-0.0890171\pi$
$468$	−1.24893	−	2.72767i	−0.0577320	−	0.126086i
$469$	1.08839	+	1.35004i	0.0502572	+	0.0623389i
$470$			32.2723i			1.48861i
$471$	24.0559	+	7.67679i	1.10844	+	0.353728i
$472$	−9.35890	+	5.40336i	−0.430778	+	0.248710i
$473$	29.9137	−	17.2707i	1.37543	−	0.794106i
$474$	−2.29146	−	0.731255i	−0.105250	−	0.0335877i
$475$			8.17420i			0.375058i
$476$	−4.20742	+	10.8899i	−0.192847	+	0.499138i
$477$	14.2262	+	31.0701i	0.651375	+	1.42260i
$478$	−11.5796	+	20.0565i	−0.529640	+	0.917364i
$479$	−1.27943	−	2.21604i	−0.0584587	−	0.101253i	0.835315	−	0.549772i	$-0.185285\pi$
$479$	−1.27943	−	2.21604i	−0.0584587	−	0.101253i	−0.893774	+	0.448518i	$0.851952\pi$
$480$	3.46808	−	3.15582i	0.158296	−	0.144043i
$481$	−3.23633	−	1.86850i	−0.147564	−	0.0851962i
$482$	−27.1782			−1.23793
$483$	−9.28437	−	23.9658i	−0.422454	−	1.09048i
$484$	15.0908			0.685943
$485$	39.1545	+	22.6059i	1.77791	+	1.02648i
$486$	−0.409354	−	15.5831i	−0.0185687	−	0.706863i
$487$	−19.1217	−	33.1198i	−0.866489	−	1.50080i	−0.865561	−	0.500803i	$-0.833038\pi$
$487$	−19.1217	−	33.1198i	−0.866489	−	1.50080i	−0.000927910	−	1.00000i	$-0.500295\pi$
$488$	0.465246	−	0.805829i	0.0210607	−	0.0364782i
$489$	12.4166	−	2.70748i	0.561499	−	0.122436i
$490$	−12.7414	+	14.0277i	−0.575597	+	0.633705i
$491$			36.6616i			1.65451i	0.561824	+	0.827257i	$0.310100\pi$
$491$			36.6616i			1.65451i	−0.561824	+	0.827257i	$0.689900\pi$
$492$	−0.977460	+	3.06296i	−0.0440673	+	0.138089i
$493$	30.9088	−	17.8452i	1.39206	−	0.803708i
$494$	3.03961	−	1.75492i	0.136759	−	0.0789576i
$495$	−41.3004	−	3.90265i	−1.85632	−	0.175411i
$496$			0.247684i			0.0111213i
$497$	−2.08977	−	13.3825i	−0.0937392	−	0.600285i
$498$	−2.19245	−	10.0547i	−0.0982459	−	0.450560i
$499$	8.11532	−	14.0561i	0.363292	−	0.629240i	−0.625209	−	0.780458i	$-0.714986\pi$
$499$	8.11532	−	14.0561i	0.363292	−	0.629240i	0.988500	+	0.151218i	$0.0483195\pi$
$500$	−3.61555	−	6.26232i	−0.161692	−	0.280060i
$501$	14.6808	+	16.1335i	0.655892	+	0.720791i
$502$	−5.12798	−	2.96064i	−0.228873	−	0.132140i
$503$	2.95031			0.131548			0.0657739	−	0.997835i	$-0.479048\pi$
$503$	2.95031			0.131548			0.0657739	+	0.997835i	$0.479048\pi$
$504$	7.92264	−	0.481433i	0.352902	−	0.0214447i
$505$	−32.1713			−1.43161
$506$	24.8096	+	14.3238i	1.10292	+	0.636771i
$507$	−1.16571	−	1.28106i	−0.0517711	−	0.0568938i
$508$	−8.40237	−	14.5533i	−0.372795	−	0.645700i
$509$	15.2131	−	26.3498i	0.674308	−	1.16794i	−0.302363	−	0.953193i	$-0.597775\pi$
$509$	15.2131	−	26.3498i	0.674308	−	1.16794i	0.976671	−	0.214743i	$-0.0688912\pi$
$510$	4.40801	+	20.2154i	0.195190	+	0.895151i
$511$	12.1775	−	9.81739i	0.538700	−	0.434296i
$512$		−	1.00000i		−	0.0441942i
$513$	18.1055	−	2.19192i	0.799376	−	0.0967756i
$514$	8.40256	−	4.85122i	0.370621	−	0.213978i
$515$	9.47651	−	5.47126i	0.417585	−	0.241093i
$516$	−3.56086	+	11.1583i	−0.156758	+	0.491216i
$517$		−	60.8910i		−	2.67798i
$518$	7.69727	−	6.20548i	0.338199	−	0.272653i
$519$	−35.6543	+	7.77451i	−1.56505	+	0.341263i
$520$	1.35360	−	2.34450i	0.0593593	−	0.102813i
$521$	17.0616	+	29.5516i	0.747482	+	1.29468i	0.949026	+	0.315198i	$0.102071\pi$
$521$	17.0616	+	29.5516i	0.747482	+	1.29468i	−0.201544	+	0.979480i	$0.564596\pi$
$522$	−19.7798	−	14.0558i	−0.865738	−	0.615204i
$523$	8.08604	+	4.66848i	0.353578	+	0.204138i	0.666260	−	0.745719i	$-0.267894\pi$
$523$	8.08604	+	4.66848i	0.353578	+	0.204138i	−0.312682	+	0.949858i	$0.601227\pi$
$524$	1.78471			0.0779655
$525$	−1.63708	+	10.5462i	−0.0714480	+	0.460275i
$526$	−9.64437			−0.420514
$527$	−0.946488	−	0.546455i	−0.0412297	−	0.0238040i
$528$	−6.54354	+	5.95436i	−0.284771	+	0.259130i
$529$	4.22755	+	7.32233i	0.183806	+	0.318362i
$530$	−15.4185	+	26.7056i	−0.669736	+	1.16002i
$531$	−29.4772	+	13.4969i	−1.27920	+	0.585715i
$532$	1.43274	+	9.17497i	0.0621173	+	0.397786i
$533$			1.85627i			0.0804038i
$534$	19.3274	+	6.16781i	0.836379	+	0.266907i
$535$	0.497174	−	0.287044i	0.0214947	−	0.0124100i
$536$	0.567626	−	0.327719i	0.0245177	−	0.0141553i
$537$	13.8513	+	4.42026i	0.597728	+	0.190748i
$538$		−	7.56420i		−	0.326116i
$539$	24.0403	−	26.4672i	1.03549	−	1.14002i
$540$	11.2488	−	8.44669i	0.484070	−	0.363488i
$541$	4.32852	−	7.49722i	0.186098	−	0.322330i	−0.757848	−	0.652431i	$-0.773749\pi$
$541$	4.32852	−	7.49722i	0.186098	−	0.322330i	0.943946	+	0.330100i	$0.107083\pi$
$542$	−5.28364	−	9.15154i	−0.226952	−	0.393092i
$543$	−28.6190	+	26.0422i	−1.22816	+	1.11758i
$544$	3.82136	+	2.20626i	0.163839	+	0.0945927i
$545$	46.6717			1.99920
$546$	4.27313	−	1.65542i	0.182873	−	0.0708453i
$547$	−28.7879			−1.23088			−0.615442	−	0.788182i	$-0.711022\pi$
$547$	−28.7879			−1.23088			−0.615442	+	0.788182i	$0.711022\pi$
$548$	7.66372	+	4.42465i	0.327378	+	0.189012i
$549$	1.61697	−	2.27546i	0.0690107	−	0.0971143i
$550$	−5.94800	−	10.3022i	−0.253624	−	0.439289i
$551$	14.1946	−	24.5857i	0.604709	−	1.04739i
$552$	−9.49116	+	2.06957i	−0.403971	+	0.0880869i
$553$	1.32416	−	3.42726i	0.0563088	−	0.145742i
$554$		−	15.3952i		−	0.654080i
$555$	5.32724	−	16.6934i	0.226129	−	0.708595i
$556$	−1.65126	+	0.953355i	−0.0700290	+	0.0404312i
$557$	−14.0448	+	8.10878i	−0.595098	+	0.343580i	−0.767111	−	0.641515i	$-0.778306\pi$
$557$	−14.0448	+	8.10878i	−0.595098	+	0.343580i	0.172013	+	0.985095i	$0.444973\pi$
$558$	−0.0699027	+	0.739756i	−0.00295922	+	0.0313164i
$559$			6.76232i			0.286016i
$560$	4.49545	+	5.57615i	0.189967	+	0.235635i
$561$	−8.31698	−	38.1421i	−0.351143	−	1.61036i
$562$	−5.53073	+	9.57950i	−0.233300	+	0.404087i
$563$	−13.1872	−	22.8409i	−0.555775	−	0.962631i	−0.997843	−	0.0656491i	$-0.979088\pi$
$563$	−13.1872	−	22.8409i	−0.555775	−	0.962631i	0.442068	−	0.896982i	$-0.354245\pi$
$564$	13.8964	+	15.2714i	0.585143	+	0.643042i
$565$	11.9316	+	6.88870i	0.501965	+	0.289810i
$566$	−0.601898			−0.0252997
$567$	23.7984	+	0.798077i	0.999438	+	0.0335161i
$568$	−5.11939			−0.214805
$569$	18.8109	+	10.8605i	0.788595	+	0.455296i	0.839468	−	0.543410i	$-0.182867\pi$
$569$	18.8109	+	10.8605i	0.788595	+	0.455296i	−0.0508726	+	0.998705i	$0.516200\pi$
$570$	11.0764	+	12.1724i	0.463940	+	0.509847i
$571$	−11.8476	−	20.5206i	−0.495805	−	0.858759i	0.504183	−	0.863597i	$-0.331794\pi$
$571$	−11.8476	−	20.5206i	−0.495805	−	0.858759i	−0.999988	+	0.00483744i	$0.998460\pi$
$572$	−2.55396	+	4.42358i	−0.106786	+	0.184959i
$573$	5.29616	+	24.2884i	0.221250	+	1.01466i
$574$	−4.58118	−	1.76998i	−0.191215	−	0.0738776i
$575$		−	13.0618i		−	0.544715i
$576$	0.282226	−	2.98670i	0.0117594	−	0.124446i
$577$	−7.89963	+	4.56086i	−0.328866	+	0.189871i	−0.655338	−	0.755336i	$-0.727474\pi$
$577$	−7.89963	+	4.56086i	−0.328866	+	0.189871i	0.326471	+	0.945207i	$0.394140\pi$
$578$	−2.13941	+	1.23519i	−0.0889876	+	0.0513770i
$579$	11.7208	−	36.7284i	0.487102	−	1.52638i
$580$		−	21.8970i		−	0.909224i
$581$	15.5314	−	2.42535i	0.644352	−	0.100620i
$582$	28.2621	−	6.16263i	1.17150	−	0.255449i
$583$	29.0914	−	50.3878i	1.20484	−	2.08685i
$584$	−2.95606	−	5.12005i	−0.122323	−	0.211869i
$585$	4.70447	−	6.62030i	0.194506	−	0.273716i
$586$	23.2424	+	13.4190i	0.960133	+	0.554333i
$587$	−3.84485			−0.158694			−0.0793470	−	0.996847i	$-0.525283\pi$
$587$	−3.84485			−0.158694			−0.0793470	+	0.996847i	$0.525283\pi$
$588$	0.0109932	+	12.1244i	0.000453350	+	0.500000i
$589$	−0.869331			−0.0358201
$590$	−25.3364	−	14.6280i	−1.04308	−	0.602225i
$591$	20.7541	−	18.8854i	0.853710	−	0.776842i
$592$	−1.86850	−	3.23633i	−0.0767948	−	0.133013i
$593$	4.74133	−	8.21222i	0.194703	−	0.337235i	−0.752100	−	0.659049i	$-0.770959\pi$
$593$	4.74133	−	8.21222i	0.194703	−	0.337235i	0.946803	+	0.321813i	$0.104292\pi$
$594$	−21.2240	+	15.9371i	−0.870832	+	0.653907i
$595$	−31.2266	+	4.87628i	−1.28017	+	0.199908i
$596$		−	10.5843i		−	0.433549i
$597$	8.47694	+	2.70518i	0.346938	+	0.110716i
$598$	−4.85709	+	2.80424i	−0.198621	+	0.114674i
$599$	10.9081	−	6.29777i	0.445691	−	0.257320i	−0.260318	−	0.965523i	$-0.583827\pi$
$599$	10.9081	−	6.29777i	0.445691	−	0.257320i	0.706009	+	0.708203i	$0.250494\pi$
$600$	3.84290	+	1.22636i	0.156886	+	0.0500657i
$601$		−	0.957604i		−	0.0390615i	−0.999809	−	0.0195307i	$-0.993783\pi$
$601$		−	0.957604i		−	0.0390615i	0.999809	−	0.0195307i	$-0.00621722\pi$
$602$	−16.6891	−	6.44799i	−0.680197	−	0.262800i
$603$	1.78782	−	0.818598i	0.0728055	−	0.0333359i
$604$	0.0860331	−	0.149014i	0.00350064	−	0.00606328i
$605$	20.4268	+	35.3803i	0.830470	+	1.43842i
$606$	−15.2236	+	13.8529i	−0.618417	+	0.562735i
$607$	−9.74198	−	5.62453i	−0.395415	−	0.228293i	0.289089	−	0.957302i	$-0.406648\pi$
$607$	−9.74198	−	5.62453i	−0.395415	−	0.228293i	−0.684504	+	0.729009i	$0.739981\pi$
$608$	3.50984			0.142343
$609$	23.2375	−	28.8773i	0.941630	−	1.17017i
$610$	2.51903			0.101992
$611$	10.3238	+	5.96046i	0.417657	+	0.241134i
$612$	10.7906	+	7.66792i	0.436183	+	0.309957i
$613$	13.2047	+	22.8712i	0.533332	+	0.923758i	0.999242	+	0.0389262i	$0.0123937\pi$
$613$	13.2047	+	22.8712i	0.533332	+	0.923758i	−0.465910	+	0.884832i	$0.654273\pi$
$614$	−5.72148	+	9.90989i	−0.230900	+	0.399931i
$615$	−8.50422	+	1.85437i	−0.342923	+	0.0747753i
$616$	−8.48196	−	10.5210i	−0.341748	−	0.423904i
$617$		−	37.3816i		−	1.50492i	−0.658635	−	0.752462i	$-0.728866\pi$
$617$		−	37.3816i		−	1.50492i	0.658635	−	0.752462i	$-0.271134\pi$
$618$	2.12841	−	6.66958i	0.0856173	−	0.268290i
$619$	−4.65636	+	2.68835i	−0.187155	+	0.108054i	−0.590650	−	0.806928i	$-0.701129\pi$
$619$	−4.65636	+	2.68835i	−0.187155	+	0.108054i	0.403495	+	0.914982i	$0.367795\pi$
$620$	−0.580696	+	0.335265i	−0.0233213	+	0.0134646i
$621$	−28.9313	+	3.50254i	−1.16097	+	0.140552i
$622$		−	16.2559i		−	0.651804i
$623$	−11.1687	+	28.9074i	−0.447463	+	1.15815i
$624$	−0.369008	−	1.69229i	−0.0147721	−	0.0677457i
$625$	15.6104	−	27.0380i	0.624415	−	1.08152i
$626$	12.3692	+	21.4241i	0.494372	+	0.856278i
$627$	−20.8989	−	22.9668i	−0.834620	−	0.917205i
$628$	12.6256	+	7.28938i	0.503815	+	0.290878i
$629$	16.4896			0.657483
$630$	11.8528	+	17.9230i	0.472227	+	0.714069i
$631$	1.95685			0.0779011			0.0389506	−	0.999241i	$-0.487599\pi$
$631$	1.95685			0.0779011			0.0389506	+	0.999241i	$0.487599\pi$
$632$	−1.20265	−	0.694353i	−0.0478390	−	0.0276199i
$633$	26.7433	+	29.3895i	1.06295	+	1.16813i
$634$	−0.934407	−	1.61844i	−0.0371101	−	0.0642765i
$635$	22.7469	−	39.3988i	0.902683	−	1.56349i
$636$	4.20326	+	19.2764i	0.166670	+	0.764357i
$637$	2.13417	+	6.66673i	0.0845587	+	0.264146i
$638$			41.3150i			1.63568i
$639$	−15.2901	−	1.44482i	−0.604866	−	0.0571563i
$640$	2.34450	−	1.35360i	0.0926747	−	0.0535058i
$641$	−22.7276	+	13.1218i	−0.897688	+	0.518281i	−0.876449	−	0.481494i	$-0.840094\pi$
$641$	−22.7276	+	13.1218i	−0.897688	+	0.518281i	−0.0212387	+	0.999774i	$0.506761\pi$
$642$	0.111665	−	0.349912i	0.00440706	−	0.0138099i
$643$			23.1283i			0.912090i	0.889957	+	0.456045i	$0.150734\pi$
$643$			23.1283i			0.912090i	−0.889957	+	0.456045i	$0.849266\pi$
$644$	−2.28942	−	14.6610i	−0.0902160	−	0.577723i
$645$	−30.9806	+	6.75540i	−1.21986	+	0.265994i
$646$	−7.74363	+	13.4124i	−0.304669	+	0.527702i
$647$	−13.5097	−	23.3995i	−0.531121	−	0.919928i	−0.999340	−	0.0363159i	$-0.988438\pi$
$647$	−13.5097	−	23.3995i	−0.531121	−	0.919928i	0.468220	−	0.883612i	$-0.344896\pi$
$648$	1.68584	−	8.84070i	0.0662262	−	0.347295i
$649$	47.8044	+	27.5999i	1.87649	+	1.08339i
$650$	2.32894			0.0913484
$651$	−1.12160	−	0.174104i	−0.0439588	−	0.00682369i
$652$	7.33719			0.287347
$653$	−13.2266	−	7.63639i	−0.517597	−	0.298835i	0.218354	−	0.975870i	$-0.429931\pi$
$653$	−13.2266	−	7.63639i	−0.517597	−	0.298835i	−0.735951	+	0.677035i	$0.763265\pi$
$654$	22.0853	−	20.0967i	0.863602	−	0.785843i
$655$	2.41579	+	4.18427i	0.0943926	+	0.163493i
$656$	−0.928133	+	1.60757i	−0.0362375	+	0.0627652i
$657$	−7.38384	−	16.1263i	−0.288071	−	0.629146i
$658$	−24.5541	+	19.7953i	−0.957218	+	0.771702i
$659$		−	22.9385i		−	0.893556i	−0.894645	−	0.446778i	$-0.852571\pi$
$659$		−	22.9385i		−	0.893556i	0.894645	−	0.446778i	$-0.147429\pi$
$660$	−22.8174	−	7.28153i	−0.888164	−	0.283433i
$661$	−18.7330	+	10.8155i	−0.728630	+	0.420675i	−0.817921	−	0.575331i	$-0.804873\pi$
$661$	−18.7330	+	10.8155i	−0.728630	+	0.420675i	0.0892909	+	0.996006i	$0.471540\pi$
$662$	−11.9187	+	6.88129i	−0.463235	+	0.267449i
$663$	7.28096	+	2.32352i	0.282769	+	0.0902379i
$664$		−	5.94147i		−	0.230574i
$665$	−19.5714	+	15.7783i	−0.758947	+	0.611857i
$666$	−4.66726	−	10.1933i	−0.180853	−	0.394982i
$667$	−22.6819	+	39.2862i	−0.878248	+	1.52117i
$668$	6.29693	+	10.9066i	0.243636	+	0.421989i
$669$	−11.9762	+	10.8979i	−0.463027	+	0.421336i
$670$	1.53668	+	0.887201i	0.0593670	+	0.0342756i
$671$	−4.75287			−0.183482
$672$	4.52834	+	0.702930i	0.174685	+	0.0271161i
$673$	−13.5846			−0.523648			−0.261824	−	0.965116i	$-0.584324\pi$
$673$	−13.5846			−0.523648			−0.261824	+	0.965116i	$0.584324\pi$
$674$	−15.5282	−	8.96522i	−0.598124	−	0.345327i
$675$	11.1315	+	4.74731i	0.428450	+	0.182724i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	−4.20080	+	7.27601i	−0.161450	+	0.279640i	−0.935389	−	0.353621i	$-0.884950\pi$
$677$	−4.20080	+	7.27601i	−0.161450	+	0.279640i	0.773939	+	0.633260i	$0.218284\pi$
$678$	8.61233	−	1.87794i	0.330754	−	0.0721219i
$679$	6.81728	+	43.6564i	0.261623	+	1.67538i
$680$			11.9456i			0.458092i
$681$	−0.257290	+	0.806244i	−0.00985939	+	0.0308953i
$682$	1.09565	−	0.632573i	0.0419546	−	0.0242225i
$683$	−6.24041	+	3.60290i	−0.238783	+	0.137861i	−0.614617	−	0.788826i	$-0.710689\pi$
$683$	−6.24041	+	3.60290i	−0.238783	+	0.137861i	0.375835	+	0.926687i	$0.377356\pi$
$684$	10.4828	+	0.990567i	0.400821	+	0.0378753i
$685$			23.9568i			0.915343i
$686$	−18.4882	−	1.08982i	−0.705881	−	0.0416095i
$687$	−7.72894	−	35.4453i	−0.294878	−	1.35232i
$688$	−3.38116	+	5.85634i	−0.128905	+	0.223271i
$689$	5.69536	+	9.86465i	0.216976	+	0.375813i
$690$	−17.6994	−	19.4507i	−0.673803	−	0.740475i
$691$	16.3538	+	9.44187i	0.622128	+	0.359186i	0.777697	−	0.628639i	$-0.216388\pi$
$691$	16.3538	+	9.44187i	0.622128	+	0.359186i	−0.155569	+	0.987825i	$0.549721\pi$
$692$	−21.0687			−0.800912
$693$	−22.3637	−	33.8169i	−0.849528	−	1.28460i
$694$	9.69778			0.368123
$695$	−4.47029	−	2.58092i	−0.169568	−	0.0979000i
$696$	−9.42879	−	10.3618i	−0.357397	−	0.392762i
$697$	−4.09541	−	7.09345i	−0.155125	−	0.268684i
$698$	8.87988	−	15.3804i	0.336108	−	0.582157i
$699$	−9.66398	−	44.3195i	−0.365525	−	1.67632i
$700$	−2.22068	+	5.74771i	−0.0839339	+	0.217243i
$701$		−	24.2419i		−	0.915605i	−0.889054	−	0.457802i	$-0.848637\pi$
$701$		−	24.2419i		−	0.915605i	0.889054	−	0.457802i	$-0.151363\pi$
$702$	−0.624507	−	5.15849i	−0.0235705	−	0.194695i
$703$	11.3590	−	6.55813i	0.428414	−	0.247345i
$704$	−4.42358	+	2.55396i	−0.166720	+	0.0962558i
$705$	−16.9937	+	53.2515i	−0.640021	+	2.00557i
$706$		−	25.1481i		−	0.946460i
$707$	−19.7334	−	24.4773i	−0.742150	−	0.920562i
$708$	−18.2881	+	3.98776i	−0.687308	+	0.149869i
$709$	2.03057	−	3.51705i	0.0762596	−	0.132085i	−0.825374	−	0.564587i	$-0.809036\pi$
$709$	2.03057	−	3.51705i	0.0762596	−	0.132085i	0.901633	+	0.432501i	$0.142369\pi$
$710$	−6.92961	−	12.0024i	−0.260064	−	0.450444i
$711$	−3.39600	−	2.41324i	−0.127360	−	0.0905036i
$712$	10.1439	+	5.85656i	0.380157	+	0.219484i
$713$	1.38913			0.0520233
$714$	−12.6769	+	15.7536i	−0.474420	+	0.589563i
$715$	−13.8281			−0.517143
$716$	7.26976	+	4.19720i	0.271684	+	0.156857i
$717$	−29.6684	+	26.9971i	−1.10799	+	1.00822i
$718$	1.67400	+	2.89946i	0.0624733	+	0.108207i
$719$	3.51698	−	6.09159i	0.131161	−	0.227178i	−0.792963	−	0.609269i	$-0.791463\pi$
$719$	3.51698	−	6.09159i	0.131161	−	0.227178i	0.924124	+	0.382092i	$0.124796\pi$
$720$	7.38434	−	3.38111i	0.275198	−	0.126007i
$721$	9.97549	+	3.85412i	0.371507	+	0.143535i
$722$		−	6.68101i		−	0.248642i
$723$	−44.8459	−	14.3113i	−1.66784	−	0.532244i
$724$	−19.3471	+	11.1701i	−0.719030	+	0.415132i
$725$	16.3137	−	9.41872i	0.605876	−	0.349803i
$726$	24.9008	+	7.94639i	0.924154	+	0.294918i
$727$			28.4841i			1.05642i	0.849115	+	0.528208i	$0.177136\pi$
$727$			28.4841i			1.05642i	−0.849115	+	0.528208i	$0.822864\pi$
$728$	2.61407	−	0.408207i	0.0968839	−	0.0151292i
$729$	7.53017	−	25.9287i	0.278895	−	0.960322i
$730$	8.00265	−	13.8610i	0.296191	−	0.513018i
$731$	−14.9194	−	25.8412i	−0.551816	−	0.955773i
$732$	1.19201	−	1.08469i	0.0440581	−	0.0400911i
$733$	9.63371	+	5.56203i	0.355829	+	0.205438i	0.667250	−	0.744834i	$-0.267471\pi$
$733$	9.63371	+	5.56203i	0.355829	+	0.205438i	−0.311420	+	0.950272i	$0.600805\pi$
$734$	9.91485			0.365964
$735$	−28.4107	+	16.4373i	−1.04795	+	0.606299i
$736$	−5.60848			−0.206731
$737$	−2.89938	−	1.67396i	−0.106800	−	0.0616611i
$738$	−3.22575	+	4.53939i	−0.118741	+	0.167097i
$739$	17.9013	+	31.0060i	0.658511	+	1.14058i	0.981001	+	0.194002i	$0.0621469\pi$
$739$	17.9013	+	31.0060i	0.658511	+	1.14058i	−0.322490	+	0.946573i	$0.604520\pi$
$740$	5.05840	−	8.76141i	0.185950	−	0.322076i
$741$	5.93966	−	1.29516i	0.218199	−	0.0475788i
$742$	−29.7762	+	4.64978i	−1.09312	+	0.170699i
$743$			47.5685i			1.74512i	0.488508	+	0.872559i	$0.337541\pi$
$743$			47.5685i			1.74512i	−0.488508	+	0.872559i	$0.662459\pi$
$744$	−0.130424	+	0.408695i	−0.00478156	+	0.0149835i
$745$	24.8149	−	14.3269i	0.909147	−	0.524896i
$746$	21.1514	−	12.2118i	0.774409	−	0.447105i
$747$	1.67683	−	17.7453i	0.0613521	−	0.649268i
$748$		−	22.5388i		−	0.824100i
$749$	0.523353	+	0.202202i	0.0191229	+	0.00738831i
$750$	−2.66833	−	12.2371i	−0.0974338	−	0.446836i
$751$	−22.4981	+	38.9678i	−0.820967	+	1.42196i	0.0839962	+	0.996466i	$0.473232\pi$
$751$	−22.4981	+	38.9678i	−0.820967	+	1.42196i	−0.904963	+	0.425490i	$0.860102\pi$
$752$	5.96046	+	10.3238i	0.217356	+	0.376471i
$753$	−6.90252	−	7.58552i	−0.251542	−	0.276432i
$754$	−7.00479	−	4.04422i	−0.255099	−	0.147282i
$755$	0.465818			0.0169528
$756$	13.3264	+	3.37745i	0.484676	+	0.122837i
$757$	−29.8762			−1.08587			−0.542934	−	0.839775i	$-0.682687\pi$
$757$	−29.8762			−1.08587			−0.542934	+	0.839775i	$0.682687\pi$
$758$	12.5252	+	7.23141i	0.454935	+	0.262657i
$759$	33.3949	+	36.6993i	1.21216	+	1.33210i
$760$	4.75092	+	8.22884i	0.172334	+	0.298491i
$761$	−4.09677	+	7.09582i	−0.148508	+	0.257223i	−0.930676	−	0.365844i	$-0.880780\pi$
$761$	−4.09677	+	7.09582i	−0.148508	+	0.257223i	0.782168	+	0.623067i	$0.214114\pi$
$762$	−6.20108	−	28.4384i	−0.224641	−	1.03022i
$763$	28.6277	+	35.5097i	1.03639	+	1.28554i
$764$			14.3524i			0.519253i
$765$	−3.37135	+	35.6778i	−0.121891	+	1.28993i
$766$	−10.4881	+	6.05529i	−0.378950	+	0.218787i
$767$	−9.35890	+	5.40336i	−0.337930	+	0.195104i
$768$	0.526573	−	1.65007i	0.0190011	−	0.0595417i
$769$		−	32.7079i		−	1.17948i	−0.807595	−	0.589738i	$-0.799231\pi$
$769$		−	32.7079i		−	1.17948i	0.807595	−	0.589738i	$-0.200769\pi$
$770$	13.1854	−	34.1272i	0.475168	−	1.22986i
$771$	16.4193	−	3.58027i	0.591327	−	0.128940i
$772$	11.1294	−	19.2766i	0.400554	−	0.693781i
$773$	9.93817	+	17.2134i	0.357451	+	0.619124i	0.987534	−	0.157404i	$-0.0503125\pi$
$773$	9.93817	+	17.2134i	0.357451	+	0.619124i	−0.630083	+	0.776528i	$0.716979\pi$
$774$	−11.7513	+	16.5368i	−0.422392	+	0.594405i
$775$	−0.499558	−	0.288420i	−0.0179446	−	0.0103603i
$776$	16.7005			0.599514
$777$	15.9687	−	6.18628i	0.572872	−	0.221932i
$778$	−5.15075			−0.184663
$779$	−5.64233	−	3.25760i	−0.202157	−	0.116716i
$780$	3.46808	−	3.15582i	0.124177	−	0.112996i
$781$	13.0747	+	22.6460i	0.467850	+	0.810339i
$782$	12.3738	−	21.4320i	0.442486	−	0.766408i
$783$	−25.2366	−	33.6085i	−0.901882	−	1.20107i
$784$	−1.48512	+	6.84064i	−0.0530402	+	0.244309i
$785$			39.4676i			1.40866i
$786$	2.94490	+	0.939782i	0.105041	+	0.0335209i
$787$	11.2281	−	6.48252i	0.400237	−	0.231077i	−0.286349	−	0.958125i	$-0.592442\pi$
$787$	11.2281	−	6.48252i	0.400237	−	0.231077i	0.686586	+	0.727048i	$0.259108\pi$
$788$	14.0302	−	8.10037i	0.499807	−	0.288564i
$789$	−15.9138	−	5.07847i	−0.566548	−	0.180798i
$790$		−	3.75950i		−	0.133757i
$791$	2.07744	+	13.3034i	0.0738651	+	0.473016i
$792$	−13.9327	+	6.37944i	−0.495076	+	0.226683i
$793$	0.465246	−	0.805829i	0.0165214	−	0.0286158i
$794$	13.8416	+	23.9744i	0.491220	+	0.850818i
$795$	−39.5040	+	35.9471i	−1.40106	+	1.27491i
$796$	4.44906	+	2.56866i	0.157693	+	0.0910439i
$797$	37.9680			1.34489			0.672447	−	0.740145i	$-0.265243\pi$
$797$	37.9680			1.34489			0.672447	+	0.740145i	$0.265243\pi$
$798$	−2.46717	+	15.8938i	−0.0873370	+	0.562633i
$799$	−52.6014			−1.86090
$800$	2.01692	+	1.16447i	0.0713088	+	0.0411702i
$801$	28.6437	+	20.3546i	1.01208	+	0.719195i
$802$	−7.36705	−	12.7601i	−0.260139	−	0.450575i
$803$	−15.0993	+	26.1527i	−0.532842	+	0.922910i
$804$	1.10919	−	0.241862i	0.0391181	−	0.00852980i
$805$	31.2738	−	25.2127i	1.10226	−	0.888630i
$806$			0.247684i			0.00872429i
$807$	3.98311	−	12.4814i	0.140212	−	0.439367i
$808$	−10.2915	+	5.94181i	−0.362054	+	0.209032i
$809$	34.0444	−	19.6555i	1.19694	−	0.691052i	0.237066	−	0.971494i	$-0.423814\pi$
$809$	34.0444	−	19.6555i	1.19694	−	0.691052i	0.959871	+	0.280442i	$0.0904810\pi$
$810$	23.0090	−	8.01430i	0.808454	−	0.281594i
$811$			22.1733i			0.778609i	0.921109	+	0.389304i	$0.127285\pi$
$811$			22.1733i			0.778609i	−0.921109	+	0.389304i	$0.872715\pi$
$812$	16.6601	−	13.4313i	0.584656	−	0.471345i
$813$	−3.89941	−	17.8829i	−0.136758	−	0.627180i
$814$	−9.54412	+	16.5309i	−0.334521	+	0.579408i
$815$	9.93162	+	17.2021i	0.347890	+	0.602562i
$816$	5.14374	+	5.65271i	0.180067	+	0.197884i
$817$	−20.5548	−	11.8673i	−0.719122	−	0.415185i
$818$	−0.343578			−0.0120129
$819$	7.92264	−	0.481433i	0.276839	−	0.0168226i
$820$	−5.02528			−0.175490
$821$	36.9360	+	21.3250i	1.28908	+	0.744249i	0.978490	−	0.206296i	$-0.0661411\pi$
$821$	36.9360	+	21.3250i	1.28908	+	0.744249i	0.310587	+	0.950545i	$0.399474\pi$
$822$	10.3157	+	11.3365i	0.359803	+	0.395405i
$823$	3.55404	+	6.15578i	0.123886	+	0.214577i	0.921297	−	0.388860i	$-0.127131\pi$
$823$	3.55404	+	6.15578i	0.123886	+	0.214577i	−0.797411	+	0.603437i	$0.793798\pi$
$824$	2.02100	−	3.50048i	0.0704050	−	0.121945i
$825$	−4.38971	−	20.1314i	−0.152830	−	0.700887i
$826$	−4.41139	−	28.2496i	−0.153492	−	0.982928i
$827$		−	47.0056i		−	1.63455i	−0.576251	−	0.817273i	$-0.695485\pi$
$827$		−	47.0056i		−	1.63455i	0.576251	−	0.817273i	$-0.304515\pi$
$828$	−16.7508	−	1.58286i	−0.582132	−	0.0550081i
$829$	−0.655437	+	0.378417i	−0.0227643	+	0.0131430i	−0.511339	−	0.859379i	$-0.670850\pi$
$829$	−0.655437	+	0.378417i	−0.0227643	+	0.0131430i	0.488575	+	0.872522i	$0.337517\pi$
$830$	13.9298	−	8.04237i	0.483510	−	0.279155i
$831$	8.10671	−	25.4031i	0.281219	−	0.881225i
$832$		−	1.00000i		−	0.0346688i
$833$	−22.8640	−	20.7674i	−0.792190	−	0.719549i
$834$	−3.22670	+	0.703590i	−0.111731	+	0.0243633i
$835$	−17.0471	+	29.5264i	−0.589938	+	1.02180i
$836$	−8.96398	−	15.5261i	−0.310026	−	0.536980i
$837$	−0.504880	+	1.18384i	−0.0174512	+	0.0409194i
$838$	10.1806	+	5.87775i	0.351682	+	0.203043i
$839$	−37.6979			−1.30148			−0.650739	−	0.759302i	$-0.725541\pi$
$839$	−37.6979			−1.30148			−0.650739	+	0.759302i	$0.725541\pi$
$840$	4.48154	+	11.5682i	0.154628	+	0.399141i
$841$	−36.4227			−1.25596
$842$	−12.1067	−	6.98978i	−0.417223	−	0.240884i
$843$	−14.1704	+	12.8945i	−0.488054	+	0.444109i
$844$	11.4708	+	19.8680i	0.394840	+	0.683883i
$845$	1.35360	−	2.34450i	0.0465653	−	0.0806534i
$846$	14.8884	+	32.5163i	0.511875	+	1.11793i
$847$	−14.3893	+	37.2433i	−0.494422	+	1.27970i
$848$			11.3907i			0.391159i
$849$	−0.993172	−	0.316943i	−0.0340856	−	0.0108775i
$850$	−8.89970	+	5.13824i	−0.305257	+	0.176240i
$851$	−18.1509	+	10.4794i	−0.622206	+	0.359231i
$852$	−8.44734	−	2.69574i	−0.289401	−	0.0923544i
$853$		−	2.08804i		−	0.0714933i	−0.999361	−	0.0357466i	$-0.988619\pi$
$853$		−	2.08804i		−	0.0714933i	0.999361	−	0.0357466i	$-0.0113809\pi$
$854$	1.54513	+	1.91658i	0.0528733	+	0.0655839i
$855$	11.8672	+	25.9179i	0.405849	+	0.886372i
$856$	0.106030	−	0.183649i	0.00362402	−	0.00627699i
$857$	22.7124	+	39.3390i	0.775840	+	1.34379i	0.934321	+	0.356433i	$0.116007\pi$
$857$	22.7124	+	39.3390i	0.775840	+	1.34379i	−0.158481	+	0.987362i	$0.550660\pi$
$858$	−6.54354	+	5.95436i	−0.223393	+	0.203278i
$859$	13.4731	+	7.77872i	0.459697	+	0.265406i	0.711917	−	0.702264i	$-0.247827\pi$
$859$	13.4731	+	7.77872i	0.459697	+	0.265406i	−0.252220	+	0.967670i	$0.581161\pi$
$860$	−18.3070			−0.624262
$861$	−6.62723	−	5.33291i	−0.225855	−	0.181745i
$862$	−31.3015			−1.06613
$863$	27.2987	+	15.7609i	0.929258	+	0.536508i	0.886577	−	0.462581i	$-0.153077\pi$
$863$	27.2987	+	15.7609i	0.929258	+	0.536508i	0.0426815	+	0.999089i	$0.486410\pi$
$864$	2.03840	−	4.77963i	0.0693479	−	0.162606i
$865$	−28.5186	−	49.3957i	−0.969661	−	1.67950i
$866$	−13.7551	+	23.8246i	−0.467418	+	0.809592i
$867$	−4.18058	+	0.911587i	−0.141980	+	0.0309591i
$868$	−0.611272	−	0.236171i	−0.0207479	−	0.00801616i
$869$			7.09338i			0.240627i
$870$	11.5304	−	36.1315i	0.390917	−	1.22497i
$871$	0.567626	−	0.327719i	0.0192333	−	0.0111043i
$872$	14.9301	−	8.61992i	0.505598	−	0.291907i
$873$	49.8794	+	4.71332i	1.68816	+	0.159522i
$874$		−	19.6849i		−	0.665851i
$875$	18.9026	−	2.95179i	0.639025	−	0.0997888i
$876$	−2.18162	−	10.0050i	−0.0737100	−	0.338038i
$877$	−12.0194	+	20.8182i	−0.405867	+	0.702982i	−0.994422	−	0.105475i	$-0.966364\pi$
$877$	−12.0194	+	20.8182i	−0.405867	+	0.702982i	0.588555	+	0.808457i	$0.299697\pi$
$878$	16.5709	+	28.7016i	0.559240	+	0.968632i
$879$	31.2854	+	34.3810i	1.05523	+	1.15964i
$880$	−11.9755	−	6.91407i	−0.403695	−	0.233073i
$881$	8.78222			0.295880			0.147940	−	0.988996i	$-0.452736\pi$
$881$	8.78222			0.295880			0.147940	+	0.988996i	$0.452736\pi$
$882$	−6.36622	+	20.0118i	−0.214362	+	0.673832i
$883$	−20.6423			−0.694667			−0.347334	−	0.937742i	$-0.612913\pi$
$883$	−20.6423			−0.694667			−0.347334	+	0.937742i	$0.612913\pi$
$884$	3.82136	+	2.20626i	0.128526	+	0.0742046i
$885$	−34.1041	−	37.4786i	−1.14640	−	1.25983i
$886$	−9.72365	−	16.8419i	−0.326673	−	0.565813i
$887$	−19.5915	+	33.9334i	−0.657817	+	1.13937i	0.323362	+	0.946275i	$0.395187\pi$
$887$	−19.5915	+	33.9334i	−0.657817	+	1.13937i	−0.981180	+	0.193098i	$0.938147\pi$
$888$	−1.37898	−	6.32407i	−0.0462755	−	0.212222i
$889$	43.9288	−	6.85982i	1.47332	−	0.230071i
$890$			31.7097i			1.06291i
$891$	−43.4131	+	15.1213i	−1.45439	+	0.506582i
$892$	−8.09619	+	4.67434i	−0.271081	+	0.156508i
$893$	−36.2350	+	20.9203i	−1.21256	+	0.700070i
$894$	5.57340	−	17.4648i	0.186402	−	0.584109i
$895$			22.7253i			0.759623i
$896$	2.46796	+	0.953517i	0.0824486	+	0.0318548i
$897$	−9.49116	+	2.06957i	−0.316901	+	0.0691010i
$898$	−12.9979	+	22.5131i	−0.433747	+	0.751271i
$899$	1.00169	+	1.73497i	0.0334081	+	0.0578646i
$900$	5.69528	+	4.04714i	0.189843	+	0.134905i
$901$	−43.5280	−	25.1309i	−1.45013	−	0.837232i
$902$	9.48164			0.315704
$903$	−24.1428	−	19.4276i	−0.803422	−	0.646512i
$904$	5.08917			0.169263
$905$	−52.3766	−	30.2396i	−1.74106	−	1.00520i
$906$	0.220427	−	0.200580i	0.00732320	−	0.00666382i
$907$	14.6243	+	25.3301i	0.485593	+	0.841072i	0.999863	−	0.0165568i	$-0.00527042\pi$
$907$	14.6243	+	25.3301i	0.485593	+	0.841072i	−0.514270	+	0.857628i	$0.671937\pi$
$908$	−0.244306	+	0.423151i	−0.00810759	+	0.0140428i
$909$	−32.4146	+	14.8418i	−1.07512	+	0.492273i
$910$	4.49545	+	5.57615i	0.149023	+	0.184848i
$911$			6.24784i			0.207000i	0.994629	+	0.103500i	$0.0330042\pi$
$911$			6.24784i			0.207000i	−0.994629	+	0.103500i	$0.966996\pi$
$912$	5.79147	+	1.84819i	0.191775	+	0.0611996i
$913$	−26.2826	+	15.1742i	−0.869826	+	0.502194i
$914$	−10.3073	+	5.95090i	−0.340934	+	0.196838i
$915$	4.15656	+	1.32645i	0.137412	+	0.0438511i
$916$		−	20.9452i		−	0.692049i
$917$	−1.70175	+	4.40459i	−0.0561969	+	0.145452i
$918$	13.7674	+	18.3346i	0.454393	+	0.605132i
$919$	17.7150	−	30.6832i	0.584363	−	1.01215i	−0.410592	−	0.911819i	$-0.634678\pi$
$919$	17.7150	−	30.6832i	0.584363	−	1.01215i	0.994955	−	0.100327i	$-0.0319888\pi$
$920$	−7.59165	−	13.1491i	−0.250289	−	0.433514i
$921$	−14.6591	+	13.3392i	−0.483034	+	0.439542i
$922$	−17.8352	−	10.2971i	−0.587370	−	0.339118i
$923$	−5.11939			−0.168507
$924$	−8.45572	−	21.8267i	−0.278173	−	0.718047i
$925$	8.70323			0.286160
$926$	32.9931	+	19.0486i	1.08422	+	0.625975i
$927$	7.02405	−	9.88449i	0.230700	−	0.324649i
$928$	−4.04422	−	7.00479i	−0.132758	−	0.229943i
$929$	−10.4723	+	18.1385i	−0.343584	+	0.595106i	−0.985096	−	0.172008i	$-0.944975\pi$
$929$	−10.4723	+	18.1385i	−0.343584	+	0.595106i	0.641511	+	0.767114i	$0.278308\pi$
$930$	−1.13473	+	0.247431i	−0.0372092	+	0.00811357i
$931$	−24.0096	−	5.21255i	−0.786882	−	0.170835i
$932$		−	26.1891i		−	0.857853i
$933$	8.55995	−	26.8234i	0.280240	−	0.878159i
$934$	26.9353	−	15.5511i	0.881350	−	0.508848i
$935$	52.8423	−	30.5085i	1.72813	−	0.997735i
$936$	0.282226	−	2.98670i	0.00922483	−	0.0976232i
$937$			5.81379i			0.189928i	0.995481	+	0.0949641i	$0.0302736\pi$
$937$			5.81379i			0.189928i	−0.995481	+	0.0949641i	$0.969726\pi$
$938$	0.267555	+	1.71336i	0.00873597	+	0.0559432i
$939$	9.12865	+	41.8644i	0.297902	+	1.36619i
$940$	−16.1362	+	27.9487i	−0.526304	+	0.911585i
$941$	−7.42009	−	12.8520i	−0.241888	−	0.418963i	0.719364	−	0.694633i	$-0.244433\pi$
$941$	−7.42009	−	12.8520i	−0.241888	−	0.418963i	−0.961252	+	0.275671i	$0.911100\pi$
$942$	16.9947	+	18.6763i	0.553716	+	0.608505i
$943$	9.01605	+	5.20542i	0.293603	+	0.169512i
$944$	−10.8067			−0.351729
$945$	10.1202	+	35.8155i	0.329209	+	1.16508i
$946$	34.5413			1.12304
$947$	10.9758	+	6.33690i	0.356667	+	0.205922i	0.667618	−	0.744504i	$-0.267314\pi$
$947$	10.9758	+	6.33690i	0.356667	+	0.205922i	−0.310951	+	0.950426i	$0.600647\pi$
$948$	−1.61883	−	1.77901i	−0.0525772	−	0.0577797i
$949$	−2.95606	−	5.12005i	−0.0959577	−	0.166204i
$950$	−4.08710	+	7.07906i	−0.132603	+	0.229675i
$951$	−0.689607	−	3.16257i	−0.0223620	−	0.102553i
$952$	−9.08869	+	7.32723i	−0.294566	+	0.237477i
$953$			10.7336i			0.347695i	0.984773	+	0.173847i	$0.0556199\pi$
$953$			10.7336i			0.347695i	−0.984773	+	0.173847i	$0.944380\pi$
$954$	−3.21475	+	34.0206i	−0.104081	+	1.10146i
$955$	−33.6494	+	19.4275i	−1.08887	+	0.628658i
$956$	−20.0565	+	11.5796i	−0.648674	+	0.374512i
$957$	−21.7554	+	68.1725i	−0.703251	+	2.20370i
$958$		−	2.55886i		−	0.0826731i
$959$	−18.2273	+	14.6947i	−0.588591	+	0.474518i
$960$	4.58136	−	0.998978i	0.147863	−	0.0322419i
$961$	−15.4693	+	26.7937i	−0.499011	+	0.864312i
$962$	−1.86850	−	3.23633i	−0.0602428	−	0.104344i
$963$	0.368509	−	0.518579i	0.0118750	−	0.0167110i
$964$	−23.5370	−	13.5891i	−0.758077	−	0.437676i
$965$	60.2588			1.93980
$966$	3.94237	−	25.3971i	0.126844	−	0.817140i
$967$	−23.6664			−0.761060			−0.380530	−	0.924769i	$-0.624258\pi$
$967$	−23.6664			−0.761060			−0.380530	+	0.924769i	$0.624258\pi$
$968$	13.0690	+	7.54538i	0.420053	+	0.242518i
$969$	−19.8401	+	18.0537i	−0.637356	+	0.579969i
$970$	22.6059	+	39.1545i	0.725830	+	1.25718i
$971$	−2.57010	+	4.45155i	−0.0824785	+	0.142857i	−0.904314	−	0.426868i	$-0.859617\pi$
$971$	−2.57010	+	4.45155i	−0.0824785	+	0.142857i	0.821835	+	0.569725i	$0.192950\pi$
$972$	7.43703	−	13.7000i	0.238543	−	0.439428i
$973$	−0.778333	−	4.98427i	−0.0249522	−	0.159788i
$974$		−	38.2435i		−	1.22540i
$975$	3.84290	+	1.22636i	0.123071	+	0.0392748i
$976$	0.805829	−	0.465246i	0.0257940	−	0.0148921i
$977$	19.0087	−	10.9747i	0.608141	−	0.351110i	−0.164097	−	0.986444i	$-0.552471\pi$
$977$	19.0087	−	10.9747i	0.608141	−	0.351110i	0.772237	+	0.635334i	$0.219138\pi$
$978$	12.1069	+	3.86357i	0.387134	+	0.123543i
$979$		−	59.8295i		−	1.91216i
$980$	−18.0482	+	5.77762i	−0.576528	+	0.184559i
$981$	47.0245	−	21.5314i	1.50138	−	0.687445i
$982$	−18.3308	+	31.7498i	−0.584959	+	1.01318i
$983$	−27.6255	−	47.8487i	−0.881116	−	1.52614i	−0.850101	−	0.526619i	$-0.823459\pi$
$983$	−27.6255	−	47.8487i	−0.881116	−	1.52614i	−0.0310146	−	0.999519i	$-0.509874\pi$
$984$	−2.37799	+	2.16387i	−0.0758074	+	0.0689817i
$985$	37.9827	+	21.9293i	1.21023	+	0.698726i
$986$	35.6904			1.13661
$987$	−50.9396	+	19.7341i	−1.62142	+	0.628143i
$988$	3.50984			0.111663
$989$	32.8452	+	18.9632i	1.04442	+	0.602994i
$990$	−33.8159	−	24.0300i	−1.07474	−	0.763724i
$991$	−29.2472	−	50.6576i	−0.929067	−	1.60919i	−0.784887	−	0.619639i	$-0.787279\pi$
$991$	−29.2472	−	50.6576i	−0.929067	−	1.60919i	−0.144180	−	0.989552i	$-0.546054\pi$
$992$	−0.123842	+	0.214500i	−0.00393198	+	0.00681039i
$993$	−23.2902	+	5.07849i	−0.739093	+	0.161161i
$994$	4.88143	−	12.6344i	0.154830	−	0.400740i
$995$			13.9078i			0.440906i
$996$	3.12862	−	9.80382i	0.0991340	−	0.310646i
$997$	26.1139	−	15.0768i	0.827034	−	0.477488i	−0.0258019	−	0.999667i	$-0.508214\pi$
$997$	26.1139	−	15.0768i	0.827034	−	0.477488i	0.852836	+	0.522179i	$0.174881\pi$
$998$	14.0561	−	8.11532i	0.444940	−	0.256886i
$999$	−2.33378	−	19.2773i	−0.0738375	−	0.609905i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.z.b.131.15	yes	32
3.2	odd	2		546.2.z.a.131.4	✓	32
7.3	odd	6		546.2.z.a.521.4	yes	32
21.17	even	6	inner	546.2.z.b.521.15	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.z.a.131.4	✓	32	3.2	odd	2
546.2.z.a.521.4	yes	32	7.3	odd	6
546.2.z.b.131.15	yes	32	1.1	even	1	trivial
546.2.z.b.521.15	yes	32	21.17	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.16571 + 1.28106i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.35360 + 2.34450i) q^{5} +(0.369008 + 1.69229i) q^{6} +(-2.61407 + 0.408207i) q^{7} +1.00000i q^{8} +(-0.282226 + 2.98670i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.16571 + 1.28106i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.35360 + 2.34450i) q^{5} +(0.369008 + 1.69229i) q^{6} +(-2.61407 + 0.408207i) q^{7} +1.00000i q^{8} +(-0.282226 + 2.98670i) q^{9} +(-2.34450 + 1.35360i) q^{10} +(4.42358 - 2.55396i) q^{11} +(-0.526573 + 1.65007i) q^{12} +1.00000i q^{13} +(-2.46796 - 0.953517i) q^{14} +(-4.58136 + 0.998978i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.20626 - 3.82136i) q^{17} +(-1.73776 + 2.44544i) q^{18} +(-3.03961 - 1.75492i) q^{19} -2.70720 q^{20} +(-3.57019 - 2.87293i) q^{21} +5.10791 q^{22} +(4.85709 + 2.80424i) q^{23} +(-1.28106 + 1.16571i) q^{24} +(-1.16447 - 2.01692i) q^{25} +(-0.500000 + 0.866025i) q^{26} +(-4.15513 + 3.12008i) q^{27} +(-1.66055 - 2.05975i) q^{28} +8.08843i q^{29} +(-4.46706 - 1.42554i) q^{30} +(0.214500 - 0.123842i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(8.42839 + 2.68969i) q^{33} -4.41252i q^{34} +(2.58136 - 6.68125i) q^{35} +(-2.72767 + 1.24893i) q^{36} +(-1.86850 + 3.23633i) q^{37} +(-1.75492 - 3.03961i) q^{38} +(-1.28106 + 1.16571i) q^{39} +(-2.34450 - 1.35360i) q^{40} +1.85627 q^{41} +(-1.65542 - 4.27313i) q^{42} +6.76232 q^{43} +(4.42358 + 2.55396i) q^{44} +(-6.62030 - 4.70447i) q^{45} +(2.80424 + 4.85709i) q^{46} +(5.96046 - 10.3238i) q^{47} +(-1.69229 + 0.369008i) q^{48} +(6.66673 - 2.13417i) q^{49} -2.32894i q^{50} +(2.32352 - 7.28096i) q^{51} +(-0.866025 + 0.500000i) q^{52} +(9.86465 - 5.69536i) q^{53} +(-5.15849 + 0.624507i) q^{54} +13.8281i q^{55} +(-0.408207 - 2.61407i) q^{56} +(-1.29516 - 5.93966i) q^{57} +(-4.04422 + 7.00479i) q^{58} +(5.40336 + 9.35890i) q^{59} +(-3.15582 - 3.46808i) q^{60} +(-0.805829 - 0.465246i) q^{61} +0.247684 q^{62} +(-0.481433 - 7.92264i) q^{63} -1.00000 q^{64} +(-2.34450 - 1.35360i) q^{65} +(5.95436 + 6.54354i) q^{66} +(-0.327719 - 0.567626i) q^{67} +(2.20626 - 3.82136i) q^{68} +(2.06957 + 9.49116i) q^{69} +(5.57615 - 4.49545i) q^{70} +5.11939i q^{71} +(-2.98670 - 0.282226i) q^{72} +(-5.12005 + 2.95606i) q^{73} +(-3.23633 + 1.86850i) q^{74} +(1.22636 - 3.84290i) q^{75} -3.50984i q^{76} +(-10.5210 + 8.48196i) q^{77} +(-1.69229 + 0.369008i) q^{78} +(-0.694353 + 1.20265i) q^{79} +(-1.35360 - 2.34450i) q^{80} +(-8.84070 - 1.68584i) q^{81} +(1.60757 + 0.928133i) q^{82} -5.94147 q^{83} +(0.702930 - 4.52834i) q^{84} +11.9456 q^{85} +(5.85634 + 3.38116i) q^{86} +(-10.3618 + 9.42879i) q^{87} +(2.55396 + 4.42358i) q^{88} +(5.85656 - 10.1439i) q^{89} +(-3.38111 - 7.38434i) q^{90} +(-0.408207 - 2.61407i) q^{91} +5.60848i q^{92} +(0.408695 + 0.130424i) q^{93} +(10.3238 - 5.96046i) q^{94} +(8.22884 - 4.75092i) q^{95} +(-1.65007 - 0.526573i) q^{96} -16.7005i q^{97} +(6.84064 + 1.48512i) q^{98} +(6.37944 + 13.9327i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} + 24 q^{11} - 4 q^{14} - 12 q^{15} - 16 q^{16} - 4 q^{17} - 24 q^{18} + 4 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} - 16 q^{26} + 6 q^{27} - 2 q^{28} - 8 q^{30} - 6 q^{31} + 14 q^{33} - 48 q^{35} + 4 q^{36} - 16 q^{38} - 6 q^{39} + 6 q^{40} - 16 q^{41} + 14 q^{42} + 32 q^{43} + 24 q^{44} + 20 q^{45} + 16 q^{46} - 20 q^{47} - 26 q^{49} - 46 q^{51} + 60 q^{53} + 6 q^{54} - 8 q^{56} - 8 q^{57} - 10 q^{58} - 8 q^{59} - 6 q^{60} + 36 q^{61} - 36 q^{62} + 84 q^{63} - 32 q^{64} + 6 q^{65} + 36 q^{66} + 4 q^{68} + 36 q^{69} - 18 q^{70} - 24 q^{72} - 48 q^{73} + 84 q^{74} - 2 q^{75} - 52 q^{77} + 18 q^{79} - 74 q^{81} - 24 q^{83} + 8 q^{84} - 32 q^{85} + 24 q^{86} + 14 q^{87} - 6 q^{88} + 20 q^{89} + 6 q^{90} - 8 q^{91} - 40 q^{93} + 72 q^{95} - 6 q^{96} - 32 q^{98}+O(q^{100}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 + 24 * q^11 - 4 * q^14 - 12 * q^15 - 16 * q^16 - 4 * q^17 - 24 * q^18 + 4 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 - 16 * q^26 + 6 * q^27 - 2 * q^28 - 8 * q^30 - 6 * q^31 + 14 * q^33 - 48 * q^35 + 4 * q^36 - 16 * q^38 - 6 * q^39 + 6 * q^40 - 16 * q^41 + 14 * q^42 + 32 * q^43 + 24 * q^44 + 20 * q^45 + 16 * q^46 - 20 * q^47 - 26 * q^49 - 46 * q^51 + 60 * q^53 + 6 * q^54 - 8 * q^56 - 8 * q^57 - 10 * q^58 - 8 * q^59 - 6 * q^60 + 36 * q^61 - 36 * q^62 + 84 * q^63 - 32 * q^64 + 6 * q^65 + 36 * q^66 + 4 * q^68 + 36 * q^69 - 18 * q^70 - 24 * q^72 - 48 * q^73 + 84 * q^74 - 2 * q^75 - 52 * q^77 + 18 * q^79 - 74 * q^81 - 24 * q^83 + 8 * q^84 - 32 * q^85 + 24 * q^86 + 14 * q^87 - 6 * q^88 + 20 * q^89 + 6 * q^90 - 8 * q^91 - 40 * q^93 + 72 * q^95 - 6 * q^96 - 32 * q^98

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