LMFDB - Embedded newform 546.2.z.a.521.4

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			521.4
Character	$\chi$	$=$	546.521
Dual form			546.2.z.a.131.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.526573 + 1.65007i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.35360 + 2.34450i) q^{5} +(-0.369008 - 1.69229i) q^{6} +(-2.61407 - 0.408207i) q^{7} +1.00000i q^{8} +(-2.44544 - 1.73776i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.526573 + 1.65007i) 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} +(-2.44544 - 1.73776i) q^{9} +(-2.34450 - 1.35360i) q^{10} +(-4.42358 - 2.55396i) q^{11} +(1.16571 + 1.28106i) 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} +(2.98670 + 0.282226i) q^{18} +(-3.03961 + 1.75492i) q^{19} +2.70720 q^{20} +(2.05007 - 4.09844i) q^{21} +5.10791 q^{22} +(-4.85709 + 2.80424i) q^{23} +(-1.65007 - 0.526573i) 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} +(3.46808 - 3.15582i) q^{30} +(0.214500 + 0.123842i) q^{31} +(0.866025 + 0.500000i) q^{32} +(6.54354 - 5.95436i) 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} +(1.65007 + 0.526573i) q^{39} +(-2.34450 + 1.35360i) q^{40} -1.85627 q^{41} +(0.273808 + 4.57439i) q^{42} +6.76232 q^{43} +(-4.42358 + 2.55396i) q^{44} +(0.764041 - 8.08558i) 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} +(5.14374 + 5.65271i) q^{51} +(-0.866025 - 0.500000i) q^{52} +(-9.86465 - 5.69536i) q^{53} +(-2.03840 + 4.77963i) 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} +(-1.42554 + 4.46706i) q^{60} +(-0.805829 + 0.465246i) q^{61} -0.247684 q^{62} +(5.68319 + 5.54088i) q^{63} -1.00000 q^{64} +(2.34450 - 1.35360i) q^{65} +(-2.68969 + 8.42839i) 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} +(1.73776 - 2.44544i) q^{72} +(-5.12005 - 2.95606i) q^{73} +(3.23633 + 1.86850i) q^{74} +(-2.71487 - 2.98350i) 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} +(2.96037 + 8.49919i) q^{81} +(1.60757 - 0.928133i) q^{82} +5.94147 q^{83} +(-2.52432 - 3.82463i) q^{84} +11.9456 q^{85} +(-5.85634 + 3.38116i) q^{86} +(-13.3465 - 4.25915i) 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} +(-0.317298 + 0.288728i) q^{93} +(10.3238 + 5.96046i) q^{94} +(-8.22884 - 4.75092i) q^{95} +(-1.28106 + 1.16571i) 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} - 12 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} + 16 q^{26} - 6 q^{27} - 2 q^{28} + 10 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} - 18 q^{42} + 32 q^{43} - 24 q^{44} - 20 q^{45} + 16 q^{46} + 20 q^{47} - 26 q^{49} + 44 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} - 28 q^{63} - 32 q^{64} - 6 q^{65} + 12 q^{66} - 4 q^{68} - 36 q^{69} - 18 q^{70} + 24 q^{72} - 48 q^{73} - 84 q^{74} + 14 q^{75} + 52 q^{77} + 18 q^{79} + 70 q^{81} + 24 q^{83} - 24 q^{84} - 32 q^{85} - 24 q^{86} - 26 q^{87} - 6 q^{88} - 20 q^{89} - 6 q^{90} - 8 q^{91} + 92 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 - 12 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 + 16 * q^26 - 6 * q^27 - 2 * q^28 + 10 * 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 - 18 * q^42 + 32 * q^43 - 24 * q^44 - 20 * q^45 + 16 * q^46 + 20 * q^47 - 26 * q^49 + 44 * 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 - 28 * q^63 - 32 * q^64 - 6 * q^65 + 12 * q^66 - 4 * q^68 - 36 * q^69 - 18 * q^70 + 24 * q^72 - 48 * q^73 - 84 * q^74 + 14 * q^75 + 52 * q^77 + 18 * q^79 + 70 * q^81 + 24 * q^83 - 24 * q^84 - 32 * q^85 - 24 * q^86 - 26 * q^87 - 6 * q^88 - 20 * q^89 - 6 * q^90 - 8 * q^91 + 92 * 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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
$3$	−0.526573	+	1.65007i	−0.304017	+	0.952667i
$3$	−0.526573	+	1.65007i	−0.304017	+	0.952667i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.35360	+	2.34450i	0.605348	+	1.04849i	0.991996	+	0.126267i	$0.0402996\pi$
$5$	1.35360	+	2.34450i	0.605348	+	1.04849i	−0.386648	+	0.922227i	$0.626367\pi$
$6$	−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
$9$	−2.44544	−	1.73776i	−0.815147	−	0.579254i
$10$	−2.34450	−	1.35360i	−0.741397	−	0.428046i
$11$	−4.42358	−	2.55396i	−1.33376	−	0.770047i	−0.347886	−	0.937537i	$-0.613100\pi$
$11$	−4.42358	−	2.55396i	−1.33376	−	0.770047i	−0.985874	+	0.167490i	$0.946434\pi$
$12$	1.16571	+	1.28106i	0.336512	+	0.369810i
$13$		−	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	−0.464061	−	0.885803i	$-0.653608\pi$
$17$	2.20626	−	3.82136i	0.535097	−	0.926816i	0.999159	−	0.0410126i	$-0.0130584\pi$
$18$	2.98670	+	0.282226i	0.703971	+	0.0665212i
$19$	−3.03961	+	1.75492i	−0.697335	+	0.402606i	−0.806354	−	0.591433i	$-0.798562\pi$
$19$	−3.03961	+	1.75492i	−0.697335	+	0.402606i	0.109019	+	0.994040i	$0.465229\pi$
$20$	2.70720			0.605348
$21$	2.05007	−	4.09844i	0.447362	−	0.894353i
$22$	5.10791			1.08901
$23$	−4.85709	+	2.80424i	−1.01277	+	0.584725i	−0.912002	−	0.410185i	$-0.865464\pi$
$23$	−4.85709	+	2.80424i	−1.01277	+	0.584725i	−0.100771	+	0.994910i	$0.532131\pi$
$24$	−1.65007	−	0.526573i	−0.336818	−	0.107486i
$25$	−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	$0.729576\pi$
$30$	3.46808	−	3.15582i	0.633183	−	0.576171i
$31$	0.214500	+	0.123842i	0.0385254	+	0.0222427i	0.519139	−	0.854690i	$-0.326253\pi$
$31$	0.214500	+	0.123842i	0.0385254	+	0.0222427i	−0.480614	+	0.876932i	$0.659586\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	6.54354	−	5.95436i	1.13908	−	1.03652i
$34$			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	0.670565	−	0.741851i	$-0.266052\pi$
$37$	−1.86850	−	3.23633i	−0.307179	−	0.532050i	−0.977744	+	0.209801i	$0.932718\pi$
$38$	1.75492	−	3.03961i	0.284686	−	0.493090i
$39$	1.65007	+	0.526573i	0.264222	+	0.0843192i
$40$	−2.34450	+	1.35360i	−0.370699	+	0.214023i
$41$	−1.85627			−0.289900			−0.144950	−	0.989439i	$-0.546302\pi$
$41$	−1.85627			−0.289900			−0.144950	+	0.989439i	$0.546302\pi$
$42$	0.273808	+	4.57439i	0.0422495	+	0.705843i
$43$	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
$45$	0.764041	−	8.08558i	0.113897	−	1.20533i
$46$	2.80424	−	4.85709i	0.413463	−	0.716139i
$47$	−5.96046	−	10.3238i	−0.869422	−	1.50588i	−0.862588	−	0.505907i	$-0.831158\pi$
$47$	−5.96046	−	10.3238i	−0.869422	−	1.50588i	−0.00683461	−	0.999977i	$-0.502176\pi$
$48$	1.69229	−	0.369008i	0.244261	−	0.0532617i
$49$	6.66673	+	2.13417i	0.952390	+	0.304881i
$50$		−	2.32894i		−	0.329361i
$51$	5.14374	+	5.65271i	0.720267	+	0.791537i
$52$	−0.866025	−	0.500000i	−0.120096	−	0.0693375i
$53$	−9.86465	−	5.69536i	−1.35501	−	0.782318i	−0.366067	−	0.930588i	$-0.619296\pi$
$53$	−9.86465	−	5.69536i	−1.35501	−	0.782318i	−0.988947	+	0.148270i	$0.952629\pi$
$54$	−2.03840	+	4.77963i	−0.277392	+	0.650426i
$55$		−	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	0.263787	+	0.964581i	$0.415028\pi$
$59$	−5.40336	+	9.35890i	−0.703458	+	1.21843i	−0.967245	+	0.253844i	$0.918305\pi$
$60$	−1.42554	+	4.46706i	−0.184036	+	0.576695i
$61$	−0.805829	+	0.465246i	−0.103176	+	0.0595686i	−0.550700	−	0.834703i	$-0.685639\pi$
$61$	−0.805829	+	0.465246i	−0.103176	+	0.0595686i	0.447524	+	0.894272i	$0.352306\pi$
$62$	−0.247684			−0.0314559
$63$	5.68319	+	5.54088i	0.716015	+	0.698085i
$64$	−1.00000			−0.125000
$65$	2.34450	−	1.35360i	0.290800	−	0.167893i
$66$	−2.68969	+	8.42839i	−0.331078	+	1.03746i
$67$	−0.327719	+	0.567626i	−0.0400372	+	0.0693465i	−0.885350	−	0.464926i	$-0.846081\pi$
$67$	−0.327719	+	0.567626i	−0.0400372	+	0.0693465i	0.845312	+	0.534272i	$0.179414\pi$
$68$	−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	$0.901751\pi$
$72$	1.73776	−	2.44544i	0.204797	−	0.288198i
$73$	−5.12005	−	2.95606i	−0.599256	−	0.345981i	0.169493	−	0.985531i	$-0.445787\pi$
$73$	−5.12005	−	2.95606i	−0.599256	−	0.345981i	−0.768749	+	0.639551i	$0.779120\pi$
$74$	3.23633	+	1.86850i	0.376216	+	0.217209i
$75$	−2.71487	−	2.98350i	−0.313486	−	0.344505i
$76$			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	0.824318	−	0.566127i	$-0.191559\pi$
$79$	−0.694353	−	1.20265i	−0.0781208	−	0.135309i	−0.902439	+	0.430817i	$0.858225\pi$
$80$	1.35360	−	2.34450i	0.151337	−	0.262124i
$81$	2.96037	+	8.49919i	0.328929	+	0.944354i
$82$	1.60757	−	0.928133i	0.177527	−	0.102495i
$83$	5.94147			0.652161			0.326080	−	0.945342i	$-0.394272\pi$
$83$	5.94147			0.652161			0.326080	+	0.945342i	$0.394272\pi$
$84$	−2.52432	−	3.82463i	−0.275426	−	0.417302i
$85$	11.9456			1.29568
$86$	−5.85634	+	3.38116i	−0.631505	+	0.364600i
$87$	−13.3465	−	4.25915i	−1.43089	−	0.456629i
$88$	2.55396	−	4.42358i	0.272253	−	0.471555i
$89$	−5.85656	−	10.1439i	−0.620794	−	1.07525i	−0.989338	−	0.145636i	$-0.953477\pi$
$89$	−5.85656	−	10.1439i	−0.620794	−	1.07525i	0.368544	−	0.929610i	$-0.379856\pi$
$90$	3.38111	+	7.38434i	0.356401	+	0.778378i
$91$	−0.408207	+	2.61407i	−0.0427918	+	0.274029i
$92$			5.60848i			0.584725i
$93$	−0.317298	+	0.288728i	−0.0329022	+	0.0299397i
$94$	10.3238	+	5.96046i	1.06482	+	0.614775i
$95$	−8.22884	−	4.75092i	−0.844261	−	0.487434i
$96$	−1.28106	+	1.16571i	−0.130748	+	0.118975i
$97$			16.7005i			1.69568i	0.530250	+	0.847841i	$0.322098\pi$
$97$			16.7005i			1.69568i	−0.530250	+	0.847841i	$0.677902\pi$
$98$	−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	0.402835	+	0.915273i	$0.368025\pi$
$101$	−5.94181	+	10.2915i	−0.591232	+	1.02404i	−0.994067	+	0.108771i	$0.965308\pi$
$102$	−7.28096	−	2.32352i	−0.720923	−	0.230063i
$103$	−3.50048	+	2.02100i	−0.344913	+	0.199135i	−0.662442	−	0.749113i	$-0.730480\pi$
$103$	−3.50048	+	2.02100i	−0.344913	+	0.199135i	0.317530	+	0.948248i	$0.397147\pi$
$104$	1.00000			0.0980581
$105$	12.3838	−	0.741254i	1.20853	−	0.0723390i
$106$	11.3907			1.10636
$107$	0.183649	−	0.106030i	0.0177540	−	0.0102503i	−0.491097	−	0.871105i	$-0.663404\pi$
$107$	0.183649	−	0.106030i	0.0177540	−	0.0102503i	0.508851	+	0.860855i	$0.330071\pi$
$108$	−0.624507	−	5.15849i	−0.0600932	−	0.496376i
$109$	−8.61992	+	14.9301i	−0.825639	+	1.43005i	0.0757918	+	0.997124i	$0.475852\pi$
$109$	−8.61992	+	14.9301i	−0.825639	+	1.43005i	−0.901430	+	0.432924i	$0.857482\pi$
$110$	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	$-0.0769423\pi$
$114$	4.09147	+	4.49632i	0.383201	+	0.421118i
$115$	−13.1491	−	7.59165i	−1.22616	−	0.707925i
$116$	7.00479	+	4.04422i	0.650378	+	0.375496i
$117$	−1.73776	+	2.44544i	−0.160656	+	0.226081i
$118$		−	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
$123$	0.977460	−	3.06296i	0.0881346	−	0.276178i
$124$	0.214500	−	0.123842i	0.0192627	−	0.0111213i
$125$	7.23111			0.646770
$126$	−7.69223	−	1.95695i	−0.685278	−	0.174339i
$127$	−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
$129$	−3.56086	+	11.1583i	−0.313516	+	0.982431i
$130$	−1.35360	+	2.34450i	−0.118719	+	0.205627i
$131$	−0.892356	−	1.54561i	−0.0779655	−	0.135040i	0.824407	−	0.565998i	$-0.191509\pi$
$131$	−0.892356	−	1.54561i	−0.0779655	−	0.135040i	−0.902372	+	0.430958i	$0.858176\pi$
$132$	−1.88486	−	8.64405i	−0.164056	−	0.752368i
$133$	8.66213	−	3.34670i	0.751102	−	0.290195i
$134$		−	0.655438i		−	0.0566212i
$135$	12.9394	+	5.51837i	1.11365	+	0.474946i
$136$	3.82136	+	2.20626i	0.327679	+	0.189185i
$137$	−7.66372	−	4.42465i	−0.654756	−	0.378023i	0.135520	−	0.990775i	$-0.456729\pi$
$137$	−7.66372	−	4.42465i	−0.654756	−	0.378023i	−0.790276	+	0.612751i	$0.790063\pi$
$138$	6.53788	+	7.18480i	0.556542	+	0.611611i
$139$		−	1.90671i		−	0.161725i	−0.996725	−	0.0808625i	$-0.974233\pi$
$139$		−	1.90671i		−	0.161725i	0.996725	−	0.0808625i	$-0.0257675\pi$
$140$	−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
$144$	−0.282226	+	2.98670i	−0.0235188	+	0.248891i
$145$	−18.9634	+	10.9485i	−1.57482	+	0.909224i
$146$	5.91212			0.489290
$147$	−7.03204	+	9.87676i	−0.579993	+	0.814622i
$148$	−3.73700			−0.307179
$149$	9.16625	−	5.29214i	0.750929	−	0.433549i	−0.0751008	−	0.997176i	$-0.523928\pi$
$149$	9.16625	−	5.29214i	0.750929	−	0.433549i	0.826029	+	0.563627i	$0.190595\pi$
$150$	3.84290	+	1.22636i	0.313771	+	0.100131i
$151$	−0.0860331	+	0.149014i	−0.00700128	+	0.0121266i	−0.869505	−	0.493924i	$-0.835562\pi$
$151$	−0.0860331	+	0.149014i	−0.00700128	+	0.0121266i	0.862504	+	0.506051i	$0.168895\pi$
$152$	−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
$156$	1.28106	−	1.16571i	0.102567	−	0.0933317i
$157$	12.6256	+	7.28938i	1.00763	+	0.581756i	0.910497	−	0.413515i	$-0.135699\pi$
$157$	12.6256	+	7.28938i	1.00763	+	0.581756i	0.0971338	+	0.995271i	$0.469033\pi$
$158$	1.20265	+	0.694353i	0.0956780	+	0.0552397i
$159$	14.5922	−	13.2783i	1.15724	−	1.05304i
$160$			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	0.973176	−	0.230064i	$-0.0738935\pi$
$163$	3.66859	+	6.35419i	0.287347	+	0.497699i	−0.685829	+	0.727763i	$0.740560\pi$
$164$	−0.928133	+	1.60757i	−0.0724750	+	0.125530i
$165$	22.8174	+	7.28153i	1.77633	+	0.566866i
$166$	−5.14546	+	2.97073i	−0.399365	+	0.230574i
$167$	−12.5939			−0.974543			−0.487271	−	0.873251i	$-0.662008\pi$
$167$	−12.5939			−0.974543			−0.487271	+	0.873251i	$0.662008\pi$
$168$	4.09844	+	2.05007i	0.316202	+	0.158166i
$169$	−1.00000			−0.0769231
$170$	−10.3452	+	5.97280i	−0.793439	+	0.458092i
$171$	10.4828	+	0.990567i	0.801642	+	0.0757506i
$172$	3.38116	−	5.85634i	0.257811	−	0.446542i
$173$	10.5343	+	18.2460i	0.800912	+	1.38722i	0.919017	+	0.394219i	$0.128985\pi$
$173$	10.5343	+	18.2460i	0.800912	+	1.38722i	−0.118105	+	0.993001i	$0.537682\pi$
$174$	13.6879	−	2.98469i	1.03768	−	0.226269i
$175$	3.86732	−	4.79702i	0.292342	−	0.362621i
$176$			5.10791i			0.385023i
$177$	−12.5975	−	13.8441i	−0.946889	−	1.04058i
$178$	10.1439	+	5.85656i	0.760314	+	0.438967i
$179$	−7.26976	−	4.19720i	−0.543367	−	0.313713i	0.203075	−	0.979163i	$-0.434906\pi$
$179$	−7.26976	−	4.19720i	−0.543367	−	0.313713i	−0.746443	+	0.665450i	$0.768240\pi$
$180$	−6.62030	−	4.70447i	−0.493448	−	0.350651i
$181$		−	22.3401i		−	1.66053i	−0.557369	−	0.830265i	$-0.688189\pi$
$181$		−	22.3401i		−	1.66053i	0.557369	−	0.830265i	$-0.311811\pi$
$182$	−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
$186$	0.130424	−	0.408695i	0.00956312	−	0.0299670i
$187$	−19.5192	+	11.2694i	−1.42738	+	0.824100i
$188$	−11.9209			−0.869422
$189$	−12.1354	+	6.45996i	−0.882723	+	0.469893i
$190$	9.50185			0.689336
$191$	−12.4296	+	7.17622i	−0.899372	+	0.519253i	−0.876997	−	0.480497i	$-0.840456\pi$
$191$	−12.4296	+	7.17622i	−0.899372	+	0.519253i	−0.0223759	+	0.999750i	$0.507123\pi$
$192$	0.526573	−	1.65007i	0.0380022	−	0.119083i
$193$	−11.1294	+	19.2766i	−0.801109	+	1.38756i	0.117778	+	0.993040i	$0.462423\pi$
$193$	−11.1294	+	19.2766i	−0.801109	+	1.38756i	−0.918887	+	0.394521i	$0.870910\pi$
$194$	−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	$-0.195826\pi$
$198$	−12.4911	−	8.87633i	−0.887704	−	0.630814i
$199$	4.44906	+	2.56866i	0.315385	+	0.182088i	0.649334	−	0.760504i	$-0.275048\pi$
$199$	4.44906	+	2.56866i	0.315385	+	0.182088i	−0.333948	+	0.942591i	$0.608381\pi$
$200$	−2.01692	−	1.16447i	−0.142618	−	0.0823403i
$201$	−0.764052	−	0.839655i	−0.0538921	−	0.0592247i
$202$		−	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
$207$	16.7508	+	1.58286i	1.16426	+	0.110016i
$208$	−0.866025	+	0.500000i	−0.0600481	+	0.0346688i
$209$	17.9280			1.24010
$210$	−10.3540	+	6.83384i	−0.714497	+	0.471580i
$211$	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
$213$	−8.44734	−	2.69574i	−0.578802	−	0.184709i
$214$	−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
$219$	7.57377	−	6.89183i	0.511788	−	0.465707i
$220$	−11.9755	−	6.91407i	−0.807389	−	0.466147i
$221$	−3.82136	−	2.20626i	−0.257052	−	0.148409i
$222$	−4.78731	+	4.35627i	−0.321303	+	0.292373i
$223$		−	9.34868i		−	0.626034i	−0.949748	−	0.313017i	$-0.898660\pi$
$223$		−	9.34868i		−	0.626034i	0.949748	−	0.313017i	$-0.101340\pi$
$224$	−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	$-0.838495\pi$
$227$	−0.244306	+	0.423151i	−0.0162152	+	0.0280855i	0.857804	+	0.513977i	$0.171828\pi$
$228$	−5.79147	−	1.84819i	−0.383550	−	0.122399i
$229$	−18.1391	+	10.4726i	−1.19866	+	0.692049i	−0.960257	−	0.279116i	$-0.909959\pi$
$229$	−18.1391	+	10.4726i	−1.19866	+	0.692049i	−0.238407	+	0.971165i	$0.576625\pi$
$230$	15.1833			1.00116
$231$	−19.5359	+	12.8940i	−1.28537	+	0.848363i
$232$	−8.08843			−0.531032
$233$	22.6804	−	13.0946i	1.48584	−	0.857853i	0.485974	−	0.873973i	$-0.338465\pi$
$233$	22.6804	−	13.0946i	1.48584	−	0.857853i	0.999870	+	0.0161207i	$0.00513160\pi$
$234$	0.282226	−	2.98670i	0.0184497	−	0.195246i
$235$	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	$0.730522\pi$
$240$	3.15582	+	3.46808i	0.203707	+	0.223864i
$241$	−23.5370	−	13.5891i	−1.51615	−	0.875352i	−0.999820	−	0.0189640i	$-0.993963\pi$
$241$	−23.5370	−	13.5891i	−1.51615	−	0.875352i	−0.516333	−	0.856388i	$-0.672703\pi$
$242$	−13.0690	−	7.54538i	−0.840106	−	0.485035i
$243$	−15.5831	+	0.409354i	−0.999655	+	0.0262601i
$244$			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
$249$	−3.12862	+	9.80382i	−0.198268	+	0.621292i
$250$	−6.26232	+	3.61555i	−0.396064	+	0.228668i
$251$	5.92128			0.373748			0.186874	−	0.982384i	$-0.440164\pi$
$251$	5.92128			0.373748			0.186874	+	0.982384i	$0.440164\pi$
$252$	7.64014	−	2.15135i	0.481283	−	0.135522i
$253$	28.6476			1.80106
$254$	14.5533	−	8.40237i	0.913157	−	0.527211i
$255$	−6.29023	+	19.7110i	−0.393909	+	1.23435i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.85122	−	8.40256i	−0.302611	−	0.524137i	0.674116	−	0.738626i	$-0.264525\pi$
$257$	−4.85122	−	8.40256i	−0.302611	−	0.524137i	−0.976727	+	0.214489i	$0.931192\pi$
$258$	−2.49535	−	11.4438i	−0.155353	−	0.712459i
$259$	3.56329	+	9.22274i	0.221412	+	0.573073i
$260$		−	2.70720i		−	0.167893i
$261$	14.0558	−	19.7798i	0.870030	−	1.22434i
$262$	1.54561	+	0.892356i	0.0954879	+	0.0551300i
$263$	8.35227	+	4.82218i	0.515023	+	0.297349i	0.734896	−	0.678180i	$-0.237231\pi$
$263$	8.35227	+	4.82218i	0.515023	+	0.297349i	−0.219873	+	0.975528i	$0.570564\pi$
$264$	5.95436	+	6.54354i	0.366465	+	0.402727i
$265$		−	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	$-0.759265\pi$
$269$	3.78210	−	6.55079i	0.230599	−	0.399409i	0.957984	+	0.286820i	$0.0925982\pi$
$270$	−13.9651	+	1.69067i	−0.849887	+	0.102891i
$271$	−9.15154	+	5.28364i	−0.555917	+	0.320959i	−0.751505	−	0.659728i	$-0.770672\pi$
$271$	−9.15154	+	5.28364i	−0.555917	+	0.320959i	0.195588	+	0.980686i	$0.437338\pi$
$272$	−4.41252			−0.267549
$273$	−4.09844	−	2.05007i	−0.248049	−	0.124076i
$274$	8.84930			0.534606
$275$	10.3022	−	5.94800i	0.621248	−	0.358678i
$276$	−9.25437	−	2.95328i	−0.557048	−	0.177766i
$277$	−7.69761	+	13.3326i	−0.462504	+	0.801081i	−0.999085	−	0.0427680i	$-0.986382\pi$
$277$	−7.69761	+	13.3326i	−0.462504	+	0.801081i	0.536581	+	0.843849i	$0.319716\pi$
$278$	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	$0.892973\pi$
$282$	−15.2714	+	13.8964i	−0.909399	+	0.827517i
$283$	−0.521259	−	0.300949i	−0.0309856	−	0.0178896i	0.484427	−	0.874832i	$-0.339028\pi$
$283$	−0.521259	−	0.300949i	−0.0309856	−	0.0178896i	−0.515413	+	0.856942i	$0.672361\pi$
$284$	4.43352	+	2.55970i	0.263081	+	0.151890i
$285$	12.1724	−	11.0764i	0.721032	−	0.656111i
$286$		−	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
$291$	−27.5570	−	8.79406i	−1.61542	−	0.515517i
$292$	−5.12005	+	2.95606i	−0.299628	+	0.172990i
$293$	−26.8380			−1.56789			−0.783945	−	0.620830i	$-0.786796\pi$
$293$	−26.8380			−1.56789			−0.783945	+	0.620830i	$0.786796\pi$
$294$	1.15154	−	12.0695i	0.0671595	−	0.703910i
$295$	−29.2560			−1.70335
$296$	3.23633	−	1.86850i	0.188108	−	0.108604i
$297$	−26.3491	+	3.18992i	−1.52893	+	0.185098i
$298$	−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
$303$	−13.8529	−	15.2236i	−0.795828	−	0.874574i
$304$	3.03961	+	1.75492i	0.174334	+	0.100652i
$305$	−2.18154	−	1.25951i	−0.124915	−	0.0721195i
$306$	7.66792	−	10.7906i	0.438346	−	0.616856i
$307$		−	11.4430i		−	0.653084i	−0.945183	−	0.326542i	$-0.894117\pi$
$307$		−	11.4430i		−	0.653084i	0.945183	−	0.326542i	$-0.105883\pi$
$308$	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	$-0.680862\pi$
$311$	8.12797	−	14.0781i	0.460895	−	0.798294i	0.999006	+	0.0445804i	$0.0141951\pi$
$312$	−0.526573	+	1.65007i	−0.0298113	+	0.0934166i
$313$	21.4241	−	12.3692i	1.21096	−	0.699148i	0.247992	−	0.968762i	$-0.420229\pi$
$313$	21.4241	−	12.3692i	1.21096	−	0.699148i	0.962968	+	0.269614i	$0.0868961\pi$
$314$	−14.5788			−0.822727
$315$	−5.29785	+	20.8244i	−0.298500	+	1.17332i
$316$	−1.38871			−0.0781208
$317$	1.61844	−	0.934407i	0.0909007	−	0.0524816i	−0.453861	−	0.891073i	$-0.649954\pi$
$317$	1.61844	−	0.934407i	0.0909007	−	0.0524816i	0.544761	+	0.838591i	$0.316620\pi$
$318$	−5.99805	+	18.7955i	−0.336354	+	1.05400i
$319$	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
$324$	8.84070	+	1.68584i	0.491150	+	0.0936580i
$325$	2.01692	+	1.16447i	0.111878	+	0.0645931i
$326$	−6.35419	−	3.66859i	−0.351926	−	0.203185i
$327$	−20.0967	−	22.0853i	−1.11135	−	1.22132i
$328$		−	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	0.612575	−	0.790412i	$-0.290134\pi$
$331$	−6.88129	−	11.9187i	−0.378230	−	0.655113i	−0.990805	+	0.135299i	$0.956800\pi$
$332$	2.97073	−	5.14546i	0.163040	−	0.282394i
$333$	−1.05468	+	11.1613i	−0.0577959	+	0.611634i
$334$	10.9066	−	6.29693i	0.596783	−	0.344553i
$335$	−1.77440			−0.0969459
$336$	−4.57439	+	0.273808i	−0.249553	+	0.0149375i
$337$	−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
$339$	8.39747	+	2.67982i	0.456088	+	0.145548i
$340$	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
$345$	19.4507	−	17.6994i	1.04719	−	0.952902i
$346$	−18.2460	−	10.5343i	−0.980913	−	0.566330i
$347$	−8.39852	−	4.84889i	−0.450856	−	0.260302i	0.257335	−	0.966322i	$-0.417155\pi$
$347$	−8.39852	−	4.84889i	−0.450856	−	0.260302i	−0.708192	+	0.706020i	$0.750489\pi$
$348$	−10.3618	+	9.42879i	−0.555449	+	0.505436i
$349$			17.7598i			0.950658i	0.879808	+	0.475329i	$0.157671\pi$
$349$			17.7598i			0.950658i	−0.879808	+	0.475329i	$0.842329\pi$
$350$	−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	−0.308867	−	0.951105i	$-0.599950\pi$
$353$	12.5740	−	21.7789i	0.669248	−	1.15917i	0.978115	−	0.208066i	$-0.0667170\pi$
$354$	17.8318	+	5.69053i	0.947751	+	0.302448i
$355$	−12.0024	+	6.92961i	−0.637023	+	0.367786i
$356$	−11.7131			−0.620794
$357$	−11.1386	−	16.8763i	−0.589518	−	0.893188i
$358$	8.39439			0.443658
$359$	−2.89946	+	1.67400i	−0.153028	+	0.0883506i	−0.574559	−	0.818463i	$-0.694826\pi$
$359$	−2.89946	+	1.67400i	−0.153028	+	0.0883506i	0.421531	+	0.906814i	$0.361493\pi$
$360$	8.08558	+	0.764041i	0.426148	+	0.0402685i
$361$	−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
$366$	1.08469	+	1.19201i	0.0566974	+	0.0623076i
$367$	8.58651	+	4.95743i	0.448212	+	0.258776i	0.707075	−	0.707139i	$-0.250014\pi$
$367$	8.58651	+	4.95743i	0.448212	+	0.258776i	−0.258863	+	0.965914i	$0.583348\pi$
$368$	4.85709	+	2.80424i	0.253193	+	0.146181i
$369$	4.53939	+	3.22575i	0.236311	+	0.167926i
$370$			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	0.987080	+	0.160229i	$0.0512234\pi$
$373$	12.2118	+	21.1514i	0.632303	+	1.09518i	−0.354777	+	0.934951i	$0.615443\pi$
$374$	11.2694	−	19.5192i	0.582726	−	1.00931i
$375$	−3.80771	+	11.9318i	−0.196629	+	0.616156i
$376$	10.3238	−	5.96046i	0.532410	−	0.307387i
$377$	8.08843			0.416575
$378$	7.27962	−	11.6622i	0.374423	−	0.599839i
$379$	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
$381$	8.84893	−	27.7289i	0.453344	−	1.42060i
$382$	7.17622	−	12.4296i	0.367167	−	0.635952i
$383$	6.05529	+	10.4881i	0.309411	+	0.535916i	0.978234	−	0.207506i	$-0.0665348\pi$
$383$	6.05529	+	10.4881i	0.309411	+	0.535916i	−0.668823	+	0.743422i	$0.733201\pi$
$384$	0.369008	+	1.69229i	0.0188308	+	0.0863591i
$385$	−5.64475	+	36.1477i	−0.287683	+	1.84226i
$386$		−	22.2587i		−	1.13294i
$387$	−16.5368	−	11.7513i	−0.840615	−	0.597352i
$388$	14.4631	+	8.35027i	0.734252	+	0.423921i
$389$	4.46068	+	2.57537i	0.226165	+	0.130577i	0.608802	−	0.793322i	$-0.291650\pi$
$389$	4.46068	+	2.57537i	0.226165	+	0.130577i	−0.382636	+	0.923899i	$0.624984\pi$
$390$	−3.15582	−	3.46808i	−0.159801	−	0.175613i
$391$			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
$396$	15.2558	+	1.44158i	0.766631	+	0.0724423i
$397$	23.9744	−	13.8416i	1.20324	−	0.694690i	0.241965	−	0.970285i	$-0.422208\pi$
$397$	23.9744	−	13.8416i	1.20324	−	0.694690i	0.961274	+	0.275595i	$0.0888748\pi$
$398$	−5.13733			−0.257511
$399$	0.961024	+	16.0554i	0.0481114	+	0.803774i
$400$	2.32894			0.116447
$401$	12.7601	−	7.36705i	0.637209	−	0.367893i	−0.146330	−	0.989236i	$-0.546746\pi$
$401$	12.7601	−	7.36705i	0.637209	−	0.367893i	0.783539	+	0.621343i	$0.213413\pi$
$402$	1.08152	+	0.345136i	0.0539411	+	0.0172138i
$403$	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
$408$	−5.65271	+	5.14374i	−0.279851	+	0.254653i
$409$	−0.297547	−	0.171789i	−0.0147128	−	0.00849442i	0.492626	−	0.870241i	$-0.336037\pi$
$409$	−0.297547	−	0.171789i	−0.0147128	−	0.00849442i	−0.507338	+	0.861747i	$0.669371\pi$
$410$	4.35202	+	2.51264i	0.214931	+	0.124091i
$411$	11.3365	−	10.3157i	0.559187	−	0.508838i
$412$			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
$417$	3.14620	+	1.00402i	0.154070	+	0.0491672i
$418$	−15.5261	+	8.96398i	−0.759405	+	0.438443i
$419$	−11.7555			−0.574294			−0.287147	−	0.957887i	$-0.592707\pi$
$419$	−11.7555			−0.574294			−0.287147	+	0.957887i	$0.592707\pi$
$420$	5.54995	−	11.0953i	0.270810	−	0.541395i
$421$	−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
$423$	−3.36439	+	35.6042i	−0.163582	+	1.73113i
$424$	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
$429$	−5.95436	−	6.54354i	−0.287479	−	0.315925i
$430$	−15.8543	−	9.15348i	−0.764562	−	0.441420i
$431$	27.1079	+	15.6507i	1.30574	+	0.753869i	0.981382	−	0.192065i	$-0.0615185\pi$
$431$	27.1079	+	15.6507i	1.30574	+	0.753869i	0.324358	+	0.945934i	$0.394852\pi$
$432$	−4.77963	−	2.03840i	−0.229960	−	0.0980728i
$433$		−	27.5102i		−	1.32206i	−0.750360	−	0.661029i	$-0.770120\pi$
$433$		−	27.5102i		−	1.32206i	0.750360	−	0.661029i	$-0.229880\pi$
$434$	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
$438$	−3.11316	+	9.75539i	−0.148753	+	0.466131i
$439$	28.7016	−	16.5709i	1.36985	−	0.790884i	0.378943	−	0.925420i	$-0.376288\pi$
$439$	28.7016	−	16.5709i	1.36985	−	0.790884i	0.990909	+	0.134536i	$0.0429543\pi$
$440$	13.8281			0.659231
$441$	−12.5944	−	16.8042i	−0.599735	−	0.800199i
$442$	4.41252			0.209882
$443$	16.8419	−	9.72365i	0.800181	−	0.461985i	−0.0433534	−	0.999060i	$-0.513804\pi$
$443$	16.8419	−	9.72365i	0.800181	−	0.461985i	0.843534	+	0.537075i	$0.180471\pi$
$444$	1.96780	−	6.16629i	0.0933878	−	0.292639i
$445$	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	$0.789797\pi$
$450$	−4.04714	+	5.69528i	−0.190784	+	0.268478i
$451$	8.21134	+	4.74082i	0.386657	+	0.223236i
$452$	−4.40735	−	2.54458i	−0.207304	−	0.119687i
$453$	−0.200580	−	0.220427i	−0.00942406	−	0.0103566i
$454$		−	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	0.692609	−	0.721313i	$-0.256461\pi$
$457$	−5.95090	−	10.3073i	−0.278371	−	0.482153i	−0.970980	+	0.239160i	$0.923128\pi$
$458$	10.4726	−	18.1391i	0.489353	−	0.847584i
$459$	−2.75565	−	22.7620i	−0.128623	−	1.06244i
$460$	−13.1491	+	7.59165i	−0.613081	+	0.353962i
$461$	20.5943			0.959172			0.479586	−	0.877495i	$-0.340787\pi$
$461$	20.5943			0.959172			0.479586	+	0.877495i	$0.340787\pi$
$462$	10.4716	−	20.9345i	0.487182	−	0.973960i
$463$	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
$465$	−1.10642	−	0.353083i	−0.0513089	−	0.0163738i
$466$	−13.0946	+	22.6804i	−0.606593	+	1.05065i
$467$	−15.5511	−	26.9353i	−0.719619	−	1.24642i	−0.961151	−	0.276024i	$-0.910983\pi$
$467$	−15.5511	−	26.9353i	−0.719619	−	1.24642i	0.241531	−	0.970393i	$-0.422350\pi$
$468$	1.24893	+	2.72767i	0.0577320	+	0.126086i
$469$	1.08839	−	1.35004i	0.0502572	−	0.0623389i
$470$			32.2723i			1.48861i
$471$	−18.6763	+	16.9947i	−0.860557	+	0.783072i
$472$	−9.35890	−	5.40336i	−0.430778	−	0.248710i
$473$	−29.9137	−	17.2707i	−1.37543	−	0.794106i
$474$	−1.77901	+	1.61883i	−0.0817128	+	0.0743554i
$475$		−	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	$-0.814715\pi$
$479$	1.27943	−	2.21604i	0.0584587	−	0.101253i	0.893774	+	0.448518i	$0.148048\pi$
$480$	−4.46706	−	1.42554i	−0.203893	−	0.0650667i
$481$	−3.23633	+	1.86850i	−0.147564	+	0.0851962i
$482$	27.1782			1.23793
$483$	1.53565	+	25.6554i	0.0698745	+	1.16736i
$484$	15.0908			0.685943
$485$	−39.1545	+	22.6059i	−1.77791	+	1.02648i
$486$	13.2907	−	8.14605i	0.602877	−	0.369512i
$487$	−19.1217	+	33.1198i	−0.866489	+	1.50080i	−0.000927910		1.00000i	$0.500295\pi$
$487$	−19.1217	+	33.1198i	−0.866489	+	1.50080i	−0.865561	+	0.500803i	$0.833038\pi$
$488$	−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	$0.689900\pi$
$492$	−2.16387	−	2.37799i	−0.0975549	−	0.107208i
$493$	30.9088	+	17.8452i	1.39206	+	0.803708i
$494$	−3.03961	−	1.75492i	−0.136759	−	0.0789576i
$495$	−24.0300	+	33.8159i	−1.08007	+	1.51991i
$496$		−	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	0.988500	−	0.151218i	$-0.0483195\pi$
$499$	8.11532	+	14.0561i	0.363292	+	0.629240i	−0.625209	+	0.780458i	$0.714986\pi$
$500$	3.61555	−	6.26232i	0.161692	−	0.280060i
$501$	6.63159	−	20.7807i	0.296278	−	0.928414i
$502$	−5.12798	+	2.96064i	−0.228873	+	0.132140i
$503$	−2.95031			−0.131548			−0.0657739	−	0.997835i	$-0.520952\pi$
$503$	−2.95031			−0.131548			−0.0657739	+	0.997835i	$0.520952\pi$
$504$	−5.54088	+	5.68319i	−0.246810	+	0.253149i
$505$	−32.1713			−1.43161
$506$	−24.8096	+	14.3238i	−1.10292	+	0.636771i
$507$	0.526573	−	1.65007i	0.0233859	−	0.0732820i
$508$	−8.40237	+	14.5533i	−0.372795	+	0.645700i
$509$	−15.2131	−	26.3498i	−0.674308	−	1.16794i	−0.976671	−	0.214743i	$-0.931109\pi$
$509$	−15.2131	−	26.3498i	−0.674308	−	1.16794i	0.302363	−	0.953193i	$-0.402225\pi$
$510$	−4.40801	−	20.2154i	−0.195190	−	0.895151i
$511$	12.1775	+	9.81739i	0.538700	+	0.434296i
$512$		−	1.00000i		−	0.0441942i
$513$	−7.15448	+	16.7758i	−0.315878	+	0.740668i
$514$	8.40256	+	4.85122i	0.370621	+	0.213978i
$515$	−9.47651	−	5.47126i	−0.417585	−	0.241093i
$516$	7.88292	+	8.66293i	0.347026	+	0.381364i
$517$			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	0.201544	+	0.979480i	$0.435404\pi$
$521$	−17.0616	+	29.5516i	−0.747482	+	1.29468i	−0.949026	+	0.315198i	$0.897929\pi$
$522$	−2.28276	+	24.1577i	−0.0999138	+	1.05735i
$523$	8.08604	−	4.66848i	0.353578	−	0.204138i	−0.312682	−	0.949858i	$-0.601227\pi$
$523$	8.08604	−	4.66848i	0.353578	−	0.204138i	0.666260	+	0.745719i	$0.267894\pi$
$524$	−1.78471			−0.0779655
$525$	5.87898	+	8.90732i	0.256580	+	0.388747i
$526$	−9.64437			−0.420514
$527$	0.946488	−	0.546455i	0.0412297	−	0.0238040i
$528$	−8.42839	−	2.68969i	−0.366799	−	0.117054i
$529$	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
$534$	−15.0052	+	13.6541i	−0.649338	+	0.590872i
$535$	0.497174	+	0.287044i	0.0214947	+	0.0124100i
$536$	−0.567626	−	0.327719i	−0.0245177	−	0.0141553i
$537$	10.7537	−	9.78546i	0.464057	−	0.422274i
$538$			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	0.943946	−	0.330100i	$-0.107083\pi$
$541$	4.32852	+	7.49722i	0.186098	+	0.322330i	−0.757848	+	0.652431i	$0.773749\pi$
$542$	5.28364	−	9.15154i	0.226952	−	0.393092i
$543$	36.8627	+	11.7637i	1.58193	+	0.504830i
$544$	3.82136	−	2.20626i	0.163839	−	0.0945927i
$545$	−46.6717			−1.99920
$546$	4.57439	−	0.273808i	0.195766	−	0.0117179i
$547$	−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
$549$	2.77909	+	0.262608i	0.118609	+	0.0112079i
$550$	−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
$555$	11.7933	+	12.9602i	0.500597	+	0.550131i
$556$	−1.65126	−	0.953355i	−0.0700290	−	0.0404312i
$557$	14.0448	+	8.10878i	0.595098	+	0.343580i	0.767111	−	0.641515i	$-0.221694\pi$
$557$	14.0448	+	8.10878i	0.595098	+	0.343580i	−0.172013	+	0.985095i	$0.555027\pi$
$558$	0.605696	+	0.430415i	0.0256412	+	0.0182209i
$559$		−	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	−0.442068	−	0.896982i	$-0.645755\pi$
$563$	13.1872	−	22.8409i	0.555775	−	0.962631i	0.997843	−	0.0656491i	$-0.0209118\pi$
$564$	6.27724	−	19.6703i	0.264319	−	0.828270i
$565$	11.9316	−	6.88870i	0.501965	−	0.289810i
$566$	0.601898			0.0252997
$567$	−4.26917	−	23.4259i	−0.179288	−	0.983797i
$568$	−5.11939			−0.214805
$569$	−18.8109	+	10.8605i	−0.788595	+	0.455296i	−0.839468	−	0.543410i	$-0.817133\pi$
$569$	−18.8109	+	10.8605i	−0.788595	+	0.455296i	0.0508726	+	0.998705i	$0.483800\pi$
$570$	−5.00342	+	15.6787i	−0.209570	+	0.656708i
$571$	−11.8476	+	20.5206i	−0.495805	+	0.858759i	−0.999988	−	0.00483744i	$-0.998460\pi$
$571$	−11.8476	+	20.5206i	−0.495805	+	0.858759i	0.504183	+	0.863597i	$0.331794\pi$
$572$	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
$576$	2.44544	+	1.73776i	0.101893	+	0.0724068i
$577$	−7.89963	−	4.56086i	−0.328866	−	0.189871i	0.326471	−	0.945207i	$-0.394140\pi$
$577$	−7.89963	−	4.56086i	−0.328866	−	0.189871i	−0.655338	+	0.755336i	$0.727474\pi$
$578$	2.13941	+	1.23519i	0.0889876	+	0.0513770i
$579$	−25.9473	−	28.5147i	−1.07833	−	1.18503i
$580$			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
$585$	−8.08558	−	0.764041i	−0.334298	−	0.0315892i
$586$	23.2424	−	13.4190i	0.960133	−	0.554333i
$587$	3.84485			0.158694			0.0793470	−	0.996847i	$-0.474717\pi$
$587$	3.84485			0.158694			0.0793470	+	0.996847i	$0.474717\pi$
$588$	5.03751	+	11.0283i	0.207743	+	0.454800i
$589$	−0.869331			−0.0358201
$590$	25.3364	−	14.6280i	1.04308	−	0.602225i
$591$	26.7323	+	8.53087i	1.09962	+	0.350913i
$592$	−1.86850	+	3.23633i	−0.0767948	+	0.133013i
$593$	−4.74133	−	8.21222i	−0.194703	−	0.337235i	0.752100	−	0.659049i	$-0.229041\pi$
$593$	−4.74133	−	8.21222i	−0.194703	−	0.337235i	−0.946803	+	0.321813i	$0.895708\pi$
$594$	21.2240	−	15.9371i	0.870832	−	0.653907i
$595$	−31.2266	−	4.87628i	−1.28017	−	0.199908i
$596$		−	10.5843i		−	0.433549i
$597$	−6.58122	+	5.98865i	−0.269352	+	0.245099i
$598$	−4.85709	−	2.80424i	−0.198621	−	0.114674i
$599$	−10.9081	−	6.29777i	−0.445691	−	0.257320i	0.260318	−	0.965523i	$-0.416173\pi$
$599$	−10.9081	−	6.29777i	−0.445691	−	0.257320i	−0.706009	+	0.708203i	$0.749506\pi$
$600$	2.98350	−	2.71487i	0.121801	−	0.110834i
$601$			0.957604i			0.0390615i	0.999809	+	0.0195307i	$0.00621722\pi$
$601$			0.957604i			0.0390615i	−0.999809	+	0.0195307i	$0.993783\pi$
$602$	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
$606$	19.6088	+	6.25760i	0.796552	+	0.254197i
$607$	−9.74198	+	5.62453i	−0.395415	+	0.228293i	−0.684504	−	0.729009i	$-0.739981\pi$
$607$	−9.74198	+	5.62453i	−0.395415	+	0.228293i	0.289089	+	0.957302i	$0.406648\pi$
$608$	−3.50984			−0.142343
$609$	33.1500	+	16.5818i	1.34330	+	0.671930i
$610$	2.51903			0.101992
$611$	−10.3238	+	5.96046i	−0.417657	+	0.241134i
$612$	−1.24533	+	13.1789i	−0.0503394	+	0.532724i
$613$	13.2047	−	22.8712i	0.533332	−	0.923758i	−0.465910	−	0.884832i	$-0.654273\pi$
$613$	13.2047	−	22.8712i	0.533332	−	0.923758i	0.999242	−	0.0389262i	$-0.0123937\pi$
$614$	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	$-0.271134\pi$
$618$	4.71182	+	5.17805i	0.189537	+	0.208292i
$619$	−4.65636	−	2.68835i	−0.187155	−	0.108054i	0.403495	−	0.914982i	$-0.367795\pi$
$619$	−4.65636	−	2.68835i	−0.187155	−	0.108054i	−0.590650	+	0.806928i	$0.701129\pi$
$620$	0.580696	+	0.335265i	0.0233213	+	0.0134646i
$621$	−11.4324	+	26.8065i	−0.458765	+	1.07571i
$622$			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
$627$	−9.44038	+	29.5823i	−0.377013	+	1.18140i
$628$	12.6256	−	7.28938i	0.503815	−	0.290878i
$629$	−16.4896			−0.657483
$630$	−5.82413	−	20.6834i	−0.232039	−	0.824046i
$631$	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
$633$	−12.0804	+	37.8551i	−0.480153	+	1.50460i
$634$	−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
$639$	8.89629	−	12.5192i	0.351932	−	0.495251i
$640$	2.34450	+	1.35360i	0.0926747	+	0.0535058i
$641$	22.7276	+	13.1218i	0.897688	+	0.518281i	0.876449	−	0.481494i	$-0.159906\pi$
$641$	22.7276	+	13.1218i	0.897688	+	0.518281i	0.0212387	+	0.999774i	$0.493239\pi$
$642$	−0.247200	−	0.271661i	−0.00975622	−	0.0107216i
$643$		−	23.1283i		−	0.912090i	−0.889957	−	0.456045i	$-0.849266\pi$
$643$		−	23.1283i		−	0.912090i	0.889957	−	0.456045i	$-0.150734\pi$
$644$	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	−0.468220	−	0.883612i	$-0.655104\pi$
$647$	13.5097	−	23.3995i	0.531121	−	0.919928i	0.999340	−	0.0363159i	$-0.0115622\pi$
$648$	−8.49919	+	2.96037i	−0.333880	+	0.116294i
$649$	47.8044	−	27.5999i	1.87649	−	1.08339i
$650$	−2.32894			−0.0913484
$651$	0.947299	−	0.625233i	0.0371276	−	0.0245048i
$652$	7.33719			0.287347
$653$	13.2266	−	7.63639i	0.517597	−	0.298835i	−0.218354	−	0.975870i	$-0.570069\pi$
$653$	13.2266	−	7.63639i	0.517597	−	0.298835i	0.735951	+	0.677035i	$0.236735\pi$
$654$	28.4469	+	9.07804i	1.11236	+	0.354979i
$655$	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	$-0.147429\pi$
$660$	17.7147	−	16.1196i	0.689542	−	0.627456i
$661$	−18.7330	−	10.8155i	−0.728630	−	0.420675i	0.0892909	−	0.996006i	$-0.471540\pi$
$661$	−18.7330	−	10.8155i	−0.728630	−	0.420675i	−0.817921	+	0.575331i	$0.804873\pi$
$662$	11.9187	+	6.88129i	0.463235	+	0.267449i
$663$	5.65271	−	5.14374i	0.219533	−	0.199766i
$664$			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
$669$	15.4259	+	4.92276i	0.596402	+	0.190325i
$670$	1.53668	−	0.887201i	0.0593670	−	0.0342756i
$671$	4.75287			0.183482
$672$	3.82463	−	2.52432i	0.147538	−	0.0973777i
$673$	−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
$675$	1.45444	+	12.0138i	0.0559813	+	0.462411i
$676$	−0.500000	+	0.866025i	−0.0192308	+	0.0333087i
$677$	4.20080	+	7.27601i	0.161450	+	0.279640i	0.935389	−	0.353621i	$-0.115050\pi$
$677$	4.20080	+	7.27601i	0.161450	+	0.279640i	−0.773939	+	0.633260i	$0.781716\pi$
$678$	−8.61233	+	1.87794i	−0.330754	+	0.0721219i
$679$	6.81728	−	43.6564i	0.261623	−	1.67538i
$680$			11.9456i			0.458092i
$681$	−0.569582	−	0.625942i	−0.0218264	−	0.0239861i
$682$	1.09565	+	0.632573i	0.0419546	+	0.0242225i
$683$	6.24041	+	3.60290i	0.238783	+	0.137861i	0.614617	−	0.788826i	$-0.289311\pi$
$683$	6.24041	+	3.60290i	0.238783	+	0.137861i	−0.375835	+	0.926687i	$0.622644\pi$
$684$	6.09927	−	8.58311i	0.233211	−	0.328183i
$685$		−	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
$690$	−7.99512	+	25.0534i	−0.304369	+	0.953768i
$691$	16.3538	−	9.44187i	0.622128	−	0.359186i	−0.155569	−	0.987825i	$-0.549721\pi$
$691$	16.3538	−	9.44187i	0.622128	−	0.359186i	0.777697	+	0.628639i	$0.216388\pi$
$692$	21.0687			0.800912
$693$	−10.9889	−	39.0251i	−0.417433	−	1.48244i
$694$	9.69778			0.368123
$695$	4.47029	−	2.58092i	0.169568	−	0.0979000i
$696$	4.25915	−	13.3465i	0.161443	−	0.505896i
$697$	−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	$-0.151363\pi$
$702$	4.77963	+	2.03840i	0.180396	+	0.0769346i
$703$	11.3590	+	6.55813i	0.428414	+	0.247345i
$704$	4.42358	+	2.55396i	0.166720	+	0.0962558i
$705$	37.6203	+	41.3428i	1.41686	+	1.55706i
$706$			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	0.901633	−	0.432501i	$-0.142369\pi$
$709$	2.03057	+	3.51705i	0.0762596	+	0.132085i	−0.825374	+	0.564587i	$0.809036\pi$
$710$	6.92961	−	12.0024i	0.260064	−	0.450444i
$711$	−0.391928	+	4.14764i	−0.0146985	+	0.155549i
$712$	10.1439	−	5.85656i	0.380157	−	0.219484i
$713$	−1.38913			−0.0520233
$714$	18.0845	+	9.04598i	0.676794	+	0.338537i
$715$	−13.8281			−0.517143
$716$	−7.26976	+	4.19720i	−0.271684	+	0.156857i
$717$	−38.2144	−	12.1951i	−1.42714	−	0.455433i
$718$	1.67400	−	2.89946i	0.0624733	−	0.108207i
$719$	−3.51698	−	6.09159i	−0.131161	−	0.227178i	0.792963	−	0.609269i	$-0.208537\pi$
$719$	−3.51698	−	6.09159i	−0.131161	−	0.227178i	−0.924124	+	0.382092i	$0.875204\pi$
$720$	−7.38434	+	3.38111i	−0.275198	+	0.126007i
$721$	9.97549	−	3.85412i	0.371507	−	0.143535i
$722$		−	6.68101i		−	0.248642i
$723$	34.8169	−	31.6820i	1.29486	−	1.17827i
$724$	−19.3471	−	11.1701i	−0.719030	−	0.415132i
$725$	−16.3137	−	9.41872i	−0.605876	−	0.349803i
$726$	19.3321	−	17.5915i	0.717483	−	0.652881i
$727$		−	28.4841i		−	1.05642i	−0.849115	−	0.528208i	$-0.822864\pi$
$727$		−	28.4841i		−	1.05642i	0.849115	−	0.528208i	$-0.177136\pi$
$728$	−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
$732$	−1.53537	−	0.489972i	−0.0567490	−	0.0181099i
$733$	9.63371	−	5.56203i	0.355829	−	0.205438i	−0.311420	−	0.950272i	$-0.600805\pi$
$733$	9.63371	−	5.56203i	0.355829	−	0.205438i	0.667250	+	0.744834i	$0.267471\pi$
$734$	−9.91485			−0.365964
$735$	−32.6747	−	3.11746i	−1.20522	−	0.114989i
$736$	−5.60848			−0.206731
$737$	2.89938	−	1.67396i	0.106800	−	0.0616611i
$738$	−5.54410	−	0.523885i	−0.204081	−	0.0192845i
$739$	17.9013	−	31.0060i	0.658511	−	1.14058i	−0.322490	−	0.946573i	$-0.604520\pi$
$739$	17.9013	−	31.0060i	0.658511	−	1.14058i	0.981001	−	0.194002i	$-0.0621469\pi$
$740$	−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	$0.662459\pi$
$744$	−0.288728	−	0.317298i	−0.0105853	−	0.0116327i
$745$	24.8149	+	14.3269i	0.909147	+	0.524896i
$746$	−21.1514	−	12.2118i	−0.774409	−	0.447105i
$747$	−14.5295	−	10.3249i	−0.531607	−	0.377767i
$748$			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	−0.904963	−	0.425490i	$-0.860102\pi$
$751$	−22.4981	−	38.9678i	−0.820967	−	1.42196i	0.0839962	−	0.996466i	$-0.473232\pi$
$752$	−5.96046	+	10.3238i	−0.217356	+	0.376471i
$753$	−3.11799	+	9.77052i	−0.113626	+	0.356057i
$754$	−7.00479	+	4.04422i	−0.255099	+	0.147282i
$755$	−0.465818			−0.0169528
$756$	−0.473228	+	13.7396i	−0.0172111	+	0.499704i
$757$	−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
$759$	−15.0851	+	47.2705i	−0.547554	+	1.71581i
$760$	4.75092	−	8.22884i	0.172334	−	0.298491i
$761$	4.09677	+	7.09582i	0.148508	+	0.257223i	0.930676	−	0.365844i	$-0.119220\pi$
$761$	4.09677	+	7.09582i	0.148508	+	0.257223i	−0.782168	+	0.623067i	$0.785886\pi$
$762$	6.20108	+	28.4384i	0.224641	+	1.03022i
$763$	28.6277	−	35.5097i	1.03639	−	1.28554i
$764$			14.3524i			0.519253i
$765$	−29.2122	−	20.7586i	−1.05617	−	0.750529i
$766$	−10.4881	−	6.05529i	−0.378950	−	0.218787i
$767$	9.35890	+	5.40336i	0.337930	+	0.195104i
$768$	−1.16571	−	1.28106i	−0.0420641	−	0.0462262i
$769$			32.7079i			1.17948i	0.807595	+	0.589738i	$0.200769\pi$
$769$			32.7079i			1.17948i	−0.807595	+	0.589738i	$0.799231\pi$
$770$	−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	$-0.949687\pi$
$773$	−9.93817	+	17.2134i	−0.357451	+	0.619124i	0.630083	+	0.776528i	$0.283021\pi$
$774$	20.1970	+	1.90850i	0.725966	+	0.0685996i
$775$	−0.499558	+	0.288420i	−0.0179446	+	0.0103603i
$776$	−16.7005			−0.599514
$777$	−17.0945	+	1.02322i	−0.613261	+	0.0367078i
$778$	−5.15075			−0.184663
$779$	5.64233	−	3.25760i	0.202157	−	0.116716i
$780$	4.46706	+	1.42554i	0.159946	+	0.0510425i
$781$	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
$786$	−2.28632	+	2.08046i	−0.0815504	+	0.0742077i
$787$	11.2281	+	6.48252i	0.400237	+	0.231077i	0.686586	−	0.727048i	$-0.259108\pi$
$787$	11.2281	+	6.48252i	0.400237	+	0.231077i	−0.286349	+	0.958125i	$0.592442\pi$
$788$	−14.0302	−	8.10037i	−0.499807	−	0.288564i
$789$	−12.3550	+	11.2426i	−0.439850	+	0.400246i
$790$			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
$795$	50.8831	+	16.2379i	1.80464	+	0.575900i
$796$	4.44906	−	2.56866i	0.157693	−	0.0910439i
$797$	−37.9680			−1.34489			−0.672447	−	0.740145i	$-0.734757\pi$
$797$	−37.9680			−1.34489			−0.672447	+	0.740145i	$0.734757\pi$
$798$	−8.85996	−	13.4239i	−0.313639	−	0.475199i
$799$	−52.6014			−1.86090
$800$	−2.01692	+	1.16447i	−0.0713088	+	0.0411702i
$801$	−3.30574	+	34.9835i	−0.116803	+	1.23608i
$802$	−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
$807$	8.81769	+	9.69019i	0.310397	+	0.341111i
$808$	−10.2915	−	5.94181i	−0.362054	−	0.209032i
$809$	−34.0444	−	19.6555i	−1.19694	−	0.691052i	−0.237066	−	0.971494i	$-0.576186\pi$
$809$	−34.0444	−	19.6555i	−1.19694	−	0.691052i	−0.959871	+	0.280442i	$0.909519\pi$
$810$	4.56392	−	23.9335i	0.160360	−	0.840939i
$811$		−	22.1733i		−	0.778609i	−0.921109	−	0.389304i	$-0.872715\pi$
$811$		−	22.1733i		−	0.778609i	0.921109	−	0.389304i	$-0.127285\pi$
$812$	−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
$816$	2.32352	−	7.28096i	0.0813394	−	0.254885i
$817$	−20.5548	+	11.8673i	−0.719122	+	0.415185i
$818$	0.343578			0.0120129
$819$	5.54088	−	5.68319i	0.193614	−	0.198587i
$820$	−5.02528			−0.175490
$821$	−36.9360	+	21.3250i	−1.28908	+	0.744249i	−0.978490	−	0.206296i	$-0.933859\pi$
$821$	−36.9360	+	21.3250i	−1.28908	+	0.744249i	−0.310587	+	0.950545i	$0.600526\pi$
$822$	−4.65980	+	14.6019i	−0.162529	+	0.509301i
$823$	3.55404	−	6.15578i	0.123886	−	0.214577i	−0.797411	−	0.603437i	$-0.793798\pi$
$823$	3.55404	−	6.15578i	0.123886	−	0.214577i	0.921297	+	0.388860i	$0.127131\pi$
$824$	−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	$-0.304515\pi$
$828$	9.74621	−	13.7152i	0.338704	−	0.476637i
$829$	−0.655437	−	0.378417i	−0.0227643	−	0.0131430i	0.488575	−	0.872522i	$-0.337517\pi$
$829$	−0.655437	−	0.378417i	−0.0227643	−	0.0131430i	−0.511339	+	0.859379i	$0.670850\pi$
$830$	−13.9298	−	8.04237i	−0.483510	−	0.279155i
$831$	−17.9464	−	19.7222i	−0.622554	−	0.684155i
$832$			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
$837$	1.27767	−	0.154680i	0.0441629	−	0.00534653i
$838$	10.1806	−	5.87775i	0.351682	−	0.203043i
$839$	37.6979			1.30148			0.650739	−	0.759302i	$-0.274459\pi$
$839$	37.6979			1.30148			0.650739	+	0.759302i	$0.274459\pi$
$840$	0.741254	+	12.3838i	0.0255757	+	0.427281i
$841$	−36.4227			−1.25596
$842$	12.1067	−	6.98978i	0.417223	−	0.240884i
$843$	−18.2521	−	5.82466i	−0.628637	−	0.200612i
$844$	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
$849$	0.771067	−	0.701640i	0.0264630	−	0.0240802i
$850$	−8.89970	−	5.13824i	−0.305257	−	0.176240i
$851$	18.1509	+	10.4794i	0.622206	+	0.359231i
$852$	−6.55825	+	5.96774i	−0.224682	+	0.204452i
$853$			2.08804i			0.0714933i	0.999361	+	0.0357466i	$0.0113809\pi$
$853$			2.08804i			0.0714933i	−0.999361	+	0.0357466i	$0.988619\pi$
$854$	−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	0.158481	+	0.987362i	$0.449340\pi$
$857$	−22.7124	+	39.3390i	−0.775840	+	1.34379i	−0.934321	+	0.356433i	$0.883993\pi$
$858$	8.42839	+	2.68969i	0.287741	+	0.0918245i
$859$	13.4731	−	7.77872i	0.459697	−	0.265406i	−0.252220	−	0.967670i	$-0.581161\pi$
$859$	13.4731	−	7.77872i	0.459697	−	0.265406i	0.711917	+	0.702264i	$0.247827\pi$
$860$	18.3070			0.624262
$861$	−3.80547	+	7.60779i	−0.129690	+	0.259273i
$862$	−31.3015			−1.06613
$863$	−27.2987	+	15.7609i	−0.929258	+	0.536508i	−0.886577	−	0.462581i	$-0.846923\pi$
$863$	−27.2987	+	15.7609i	−0.929258	+	0.536508i	−0.0426815	+	0.999089i	$0.513590\pi$
$864$	5.15849	−	0.624507i	0.175495	−	0.0212462i
$865$	−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
$870$	25.5256	+	28.0514i	0.865400	+	0.951030i
$871$	0.567626	+	0.327719i	0.0192333	+	0.0111043i
$872$	−14.9301	−	8.61992i	−0.505598	−	0.291907i
$873$	29.0216	−	40.8402i	0.982231	−	1.38223i
$874$			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	0.588555	−	0.808457i	$-0.299697\pi$
$877$	−12.0194	−	20.8182i	−0.405867	−	0.702982i	−0.994422	+	0.105475i	$0.966364\pi$
$878$	−16.5709	+	28.7016i	−0.559240	+	0.968632i
$879$	14.1322	−	44.2844i	0.476666	−	1.49368i
$880$	−11.9755	+	6.91407i	−0.403695	+	0.233073i
$881$	−8.78222			−0.295880			−0.147940	−	0.988996i	$-0.547264\pi$
$881$	−8.78222			−0.295880			−0.147940	+	0.988996i	$0.547264\pi$
$882$	19.3092	+	8.25563i	0.650174	+	0.277981i
$883$	−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
$885$	15.4054	−	48.2743i	0.517847	−	1.62272i
$886$	−9.72365	+	16.8419i	−0.326673	+	0.565813i
$887$	19.5915	+	33.9334i	0.657817	+	1.13937i	0.981180	+	0.193098i	$0.0618534\pi$
$887$	19.5915	+	33.9334i	0.657817	+	1.13937i	−0.323362	+	0.946275i	$0.604813\pi$
$888$	1.37898	+	6.32407i	0.0462755	+	0.212222i
$889$	43.9288	+	6.85982i	1.47332	+	0.230071i
$890$			31.7097i			1.06291i
$891$	8.61114	−	45.1575i	0.288484	−	1.51283i
$892$	−8.09619	−	4.67434i	−0.271081	−	0.156508i
$893$	36.2350	+	20.9203i	1.21256	+	0.700070i
$894$	−12.3382	−	13.5591i	−0.412652	−	0.453484i
$895$		−	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
$900$	0.657285	−	6.95582i	0.0219095	−	0.231861i
$901$	−43.5280	+	25.1309i	−1.45013	+	0.837232i
$902$	−9.48164			−0.315704
$903$	13.8632	−	27.7150i	0.461339	−	0.922296i
$904$	5.08917			0.169263
$905$	52.3766	−	30.2396i	1.74106	−	1.00520i
$906$	0.283921	+	0.0906055i	0.00943264	+	0.00301017i
$907$	14.6243	−	25.3301i	0.485593	−	0.841072i	−0.514270	−	0.857628i	$-0.671937\pi$
$907$	14.6243	−	25.3301i	0.485593	−	0.841072i	0.999863	+	0.0165568i	$0.00527042\pi$
$908$	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	$0.966996\pi$
$912$	−4.49632	+	4.09147i	−0.148888	+	0.135482i
$913$	−26.2826	−	15.1742i	−0.869826	−	0.502194i
$914$	10.3073	+	5.95090i	0.340934	+	0.196838i
$915$	3.22702	−	2.93646i	0.106682	−	0.0970764i
$916$			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	0.994955	+	0.100327i	$0.0319888\pi$
$919$	17.7150	+	30.6832i	0.584363	+	1.01215i	−0.410592	+	0.911819i	$0.634678\pi$
$920$	7.59165	−	13.1491i	0.250289	−	0.433514i
$921$	18.8816	+	6.02555i	0.622171	+	0.198549i
$922$	−17.8352	+	10.2971i	−0.587370	+	0.339118i
$923$	5.11939			0.168507
$924$	1.39859	+	23.3656i	0.0460102	+	0.768671i
$925$	8.70323			0.286160
$926$	−32.9931	+	19.0486i	−1.08422	+	0.625975i
$927$	12.0722	+	1.14076i	0.396505	+	0.0374674i
$928$	−4.04422	+	7.00479i	−0.132758	+	0.229943i
$929$	10.4723	+	18.1385i	0.343584	+	0.595106i	0.985096	−	0.172008i	$-0.0550255\pi$
$929$	10.4723	+	18.1385i	0.343584	+	0.595106i	−0.641511	+	0.767114i	$0.721692\pi$
$930$	1.13473	−	0.247431i	0.0372092	−	0.00811357i
$931$	−24.0096	+	5.21255i	−0.786882	+	0.170835i
$932$		−	26.1891i		−	0.857853i
$933$	18.9498	+	20.8248i	0.620388	+	0.681774i
$934$	26.9353	+	15.5511i	0.881350	+	0.508848i
$935$	−52.8423	−	30.5085i	−1.72813	−	0.997735i
$936$	−2.44544	−	1.73776i	−0.0799317	−	0.0568005i
$937$		−	5.81379i		−	0.189928i	−0.995481	−	0.0949641i	$-0.969726\pi$
$937$		−	5.81379i		−	0.189928i	0.995481	−	0.0949641i	$-0.0302736\pi$
$938$	−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	$-0.755567\pi$
$941$	7.42009	−	12.8520i	0.241888	−	0.418963i	0.961252	+	0.275671i	$0.0889000\pi$
$942$	7.67679	−	24.0559i	0.250123	−	0.783785i
$943$	9.01605	−	5.20542i	0.293603	−	0.169512i
$944$	10.8067			0.351729
$945$	−31.5719	−	19.7074i	−1.02704	−	0.641081i
$946$	34.5413			1.12304
$947$	−10.9758	+	6.33690i	−0.356667	+	0.205922i	−0.667618	−	0.744504i	$-0.732686\pi$
$947$	−10.9758	+	6.33690i	−0.356667	+	0.205922i	0.310951	+	0.950426i	$0.399353\pi$
$948$	0.731255	−	2.29146i	0.0237501	−	0.0744231i
$949$	−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	$0.944380\pi$
$954$	−27.8553	−	19.7944i	−0.901850	−	0.640866i
$955$	−33.6494	−	19.4275i	−1.08887	−	0.628658i
$956$	20.0565	+	11.5796i	0.648674	+	0.374512i
$957$	48.1614	+	52.9270i	1.55684	+	1.71089i
$958$			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
$963$	−0.633357	−	0.0598486i	−0.0204096	−	0.00192859i
$964$	−23.5370	+	13.5891i	−0.758077	+	0.437676i
$965$	−60.2588			−1.93980
$966$	−14.1576	−	21.4504i	−0.455513	−	0.690155i
$967$	−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
$969$	−25.5550	−	8.15518i	−0.820946	−	0.261982i
$970$	22.6059	−	39.1545i	0.725830	−	1.25718i
$971$	2.57010	+	4.45155i	0.0824785	+	0.142857i	0.904314	−	0.426868i	$-0.140383\pi$
$971$	2.57010	+	4.45155i	0.0824785	+	0.142857i	−0.821835	+	0.569725i	$0.807050\pi$
$972$	−7.43703	+	13.7000i	−0.238543	+	0.439428i
$973$	−0.778333	+	4.98427i	−0.0249522	+	0.159788i
$974$		−	38.2435i		−	1.22540i
$975$	−2.98350	+	2.71487i	−0.0955486	+	0.0869455i
$976$	0.805829	+	0.465246i	0.0257940	+	0.0148921i
$977$	−19.0087	−	10.9747i	−0.608141	−	0.351110i	0.164097	−	0.986444i	$-0.447529\pi$
$977$	−19.0087	−	10.9747i	−0.608141	−	0.351110i	−0.772237	+	0.635334i	$0.780862\pi$
$978$	9.39937	−	8.55306i	0.300559	−	0.273497i
$979$			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	0.0310146	−	0.999519i	$-0.490126\pi$
$983$	27.6255	−	47.8487i	0.881116	−	1.52614i	0.850101	−	0.526619i	$-0.176541\pi$
$984$	3.06296	+	0.977460i	0.0976436	+	0.0311603i
$985$	37.9827	−	21.9293i	1.21023	−	0.698726i
$986$	−35.6904			−1.13661
$987$	−54.5309	+	3.26405i	−1.73574	+	0.103896i
$988$	3.50984			0.111663
$989$	−32.8452	+	18.9632i	−1.04442	+	0.602994i
$990$	3.90265	−	41.3004i	0.124035	−	1.31261i
$991$	−29.2472	+	50.6576i	−0.929067	+	1.60919i	−0.144180	+	0.989552i	$0.546054\pi$
$991$	−29.2472	+	50.6576i	−0.929067	+	1.60919i	−0.784887	+	0.619639i	$0.787279\pi$
$992$	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
$996$	6.92604	+	7.61137i	0.219460	+	0.241175i
$997$	26.1139	+	15.0768i	0.827034	+	0.477488i	0.852836	−	0.522179i	$-0.174881\pi$
$997$	26.1139	+	15.0768i	0.827034	+	0.477488i	−0.0258019	+	0.999667i	$0.508214\pi$
$998$	−14.0561	−	8.11532i	−0.444940	−	0.256886i
$999$	−17.8615	−	7.61751i	−0.565112	−	0.241007i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.z.a.131.4	✓	32	21.5	even	6	inner
546.2.z.a.521.4	yes	32	1.1	even	1	trivial
546.2.z.b.131.15	yes	32	7.5	odd	6
546.2.z.b.521.15	yes	32	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.526573 + 1.65007i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.35360 + 2.34450i) q^{5} +(-0.369008 - 1.69229i) q^{6} +(-2.61407 - 0.408207i) q^{7} +1.00000i q^{8} +(-2.44544 - 1.73776i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.526573 + 1.65007i) 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} +(-2.44544 - 1.73776i) q^{9} +(-2.34450 - 1.35360i) q^{10} +(-4.42358 - 2.55396i) q^{11} +(1.16571 + 1.28106i) 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} +(2.98670 + 0.282226i) q^{18} +(-3.03961 + 1.75492i) q^{19} +2.70720 q^{20} +(2.05007 - 4.09844i) q^{21} +5.10791 q^{22} +(-4.85709 + 2.80424i) q^{23} +(-1.65007 - 0.526573i) 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} +(3.46808 - 3.15582i) q^{30} +(0.214500 + 0.123842i) q^{31} +(0.866025 + 0.500000i) q^{32} +(6.54354 - 5.95436i) 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} +(1.65007 + 0.526573i) q^{39} +(-2.34450 + 1.35360i) q^{40} -1.85627 q^{41} +(0.273808 + 4.57439i) q^{42} +6.76232 q^{43} +(-4.42358 + 2.55396i) q^{44} +(0.764041 - 8.08558i) 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} +(5.14374 + 5.65271i) q^{51} +(-0.866025 - 0.500000i) q^{52} +(-9.86465 - 5.69536i) q^{53} +(-2.03840 + 4.77963i) 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} +(-1.42554 + 4.46706i) q^{60} +(-0.805829 + 0.465246i) q^{61} -0.247684 q^{62} +(5.68319 + 5.54088i) q^{63} -1.00000 q^{64} +(2.34450 - 1.35360i) q^{65} +(-2.68969 + 8.42839i) 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} +(1.73776 - 2.44544i) q^{72} +(-5.12005 - 2.95606i) q^{73} +(3.23633 + 1.86850i) q^{74} +(-2.71487 - 2.98350i) 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} +(2.96037 + 8.49919i) q^{81} +(1.60757 - 0.928133i) q^{82} +5.94147 q^{83} +(-2.52432 - 3.82463i) q^{84} +11.9456 q^{85} +(-5.85634 + 3.38116i) q^{86} +(-13.3465 - 4.25915i) 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} +(-0.317298 + 0.288728i) q^{93} +(10.3238 + 5.96046i) q^{94} +(-8.22884 - 4.75092i) q^{95} +(-1.28106 + 1.16571i) 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	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} - 24 q^{11} + 4 q^{14} - 12 q^{15} - 16 q^{16} + 4 q^{17} + 24 q^{18} - 12 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} + 16 q^{26} - 6 q^{27} - 2 q^{28} + 10 q^{30} - 6 q^{31} - 14 q^{33} + 48 q^{35} + 4 q^{36} + 16 q^{38} + 6 q^{39} + 6 q^{40} + 16 q^{41} - 18 q^{42} + 32 q^{43} - 24 q^{44} - 20 q^{45} + 16 q^{46} + 20 q^{47} - 26 q^{49} + 44 q^{51} - 60 q^{53} - 6 q^{54} + 8 q^{56} - 8 q^{57} - 10 q^{58} + 8 q^{59} - 6 q^{60} + 36 q^{61} + 36 q^{62} - 28 q^{63} - 32 q^{64} - 6 q^{65} + 12 q^{66} - 4 q^{68} - 36 q^{69} - 18 q^{70} + 24 q^{72} - 48 q^{73} - 84 q^{74} + 14 q^{75} + 52 q^{77} + 18 q^{79} + 70 q^{81} + 24 q^{83} - 24 q^{84} - 32 q^{85} - 24 q^{86} - 26 q^{87} - 6 q^{88} - 20 q^{89} - 6 q^{90} - 8 q^{91} + 92 q^{93} - 72 q^{95} - 6 q^{96} + 32 q^{98}+O(q^{100}) \) 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 - 12 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 + 16 * q^26 - 6 * q^27 - 2 * q^28 + 10 * 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 - 18 * q^42 + 32 * q^43 - 24 * q^44 - 20 * q^45 + 16 * q^46 + 20 * q^47 - 26 * q^49 + 44 * 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 - 28 * q^63 - 32 * q^64 - 6 * q^65 + 12 * q^66 - 4 * q^68 - 36 * q^69 - 18 * q^70 + 24 * q^72 - 48 * q^73 - 84 * q^74 + 14 * q^75 + 52 * q^77 + 18 * q^79 + 70 * q^81 + 24 * q^83 - 24 * q^84 - 32 * q^85 - 24 * q^86 - 26 * q^87 - 6 * q^88 - 20 * q^89 - 6 * q^90 - 8 * q^91 + 92 * q^93 - 72 * q^95 - 6 * q^96 + 32 * q^98

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