LMFDB - Embedded newform 403.2.bp.a.10.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(10,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([25, 14]))

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

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

chi := DirichletCharacter("403.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.bp (of order $30$, degree $8$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$35$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			10.15
Character	$\chi$	$=$	403.10
Dual form			403.2.bp.a.121.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.501537 - 0.0527137i) q^{2} +(-0.192422 + 0.139802i) q^{3} +(-1.70753 - 0.362948i) q^{4} +(0.660141 - 0.381132i) q^{5} +(0.103876 - 0.0599729i) q^{6} +(-1.06122 - 0.955523i) q^{7} +(1.79650 + 0.583717i) q^{8} +(-0.909570 + 2.79937i) q^{9} +O(q^{10})$	\(q+(-0.501537 - 0.0527137i) q^{2} +(-0.192422 + 0.139802i) q^{3} +(-1.70753 - 0.362948i) q^{4} +(0.660141 - 0.381132i) q^{5} +(0.103876 - 0.0599729i) q^{6} +(-1.06122 - 0.955523i) q^{7} +(1.79650 + 0.583717i) q^{8} +(-0.909570 + 2.79937i) q^{9} +(-0.351176 + 0.156354i) q^{10} +(0.794476 - 3.73772i) q^{11} +(0.379307 - 0.168879i) q^{12} +(-2.44401 + 2.65082i) q^{13} +(0.481870 + 0.535171i) q^{14} +(-0.0737420 + 0.165627i) q^{15} +(2.31928 + 1.03261i) q^{16} +(-6.69556 + 1.42319i) q^{17} +(0.603748 - 1.35604i) q^{18} +(-3.49945 - 0.367807i) q^{19} +(-1.26554 + 0.411200i) q^{20} +(0.337785 + 0.0355027i) q^{21} +(-0.595488 + 1.83272i) q^{22} +(-1.25474 + 0.266703i) q^{23} +(-0.427289 + 0.138835i) q^{24} +(-2.20948 + 3.82693i) q^{25} +(1.36549 - 1.20065i) q^{26} +(-0.436833 - 1.34443i) q^{27} +(1.46526 + 2.01675i) q^{28} +(-0.405146 + 3.85471i) q^{29} +(0.0457152 - 0.0791811i) q^{30} +(-5.07412 - 2.29202i) q^{31} +(-4.38052 - 2.52910i) q^{32} +(0.369667 + 0.830287i) q^{33} +(3.43310 - 0.360833i) q^{34} +(-1.06473 - 0.226316i) q^{35} +(2.56915 - 4.44989i) q^{36} +0.446668i q^{37} +(1.73571 + 0.368937i) q^{38} +(0.0996888 - 0.851752i) q^{39} +(1.40841 - 0.299367i) q^{40} +(-1.94497 - 4.36847i) q^{41} +(-0.167540 - 0.0356118i) q^{42} +(-0.505653 + 4.81097i) q^{43} +(-2.71319 + 6.09392i) q^{44} +(0.466486 + 2.19464i) q^{45} +(0.643357 - 0.0676196i) q^{46} +(0.830734 + 1.14341i) q^{47} +(-0.590641 + 0.125545i) q^{48} +(-0.518544 - 4.93362i) q^{49} +(1.30987 - 1.80288i) q^{50} +(1.08941 - 1.20991i) q^{51} +(5.13533 - 3.63932i) q^{52} +(-0.188052 + 0.0399718i) q^{53} +(0.148218 + 0.697311i) q^{54} +(-0.900098 - 2.77022i) q^{55} +(-1.34871 - 2.33604i) q^{56} +(0.724789 - 0.418457i) q^{57} +(0.406392 - 1.91192i) q^{58} +(-1.65300 + 3.71270i) q^{59} +(0.186031 - 0.256050i) q^{60} +(2.76664 - 4.79196i) q^{61} +(2.42404 + 1.41701i) q^{62} +(3.64011 - 2.10162i) q^{63} +(-2.04413 - 1.48515i) q^{64} +(-0.603076 + 2.68140i) q^{65} +(-0.141634 - 0.435906i) q^{66} +(9.60659 + 5.54637i) q^{67} +11.9494 q^{68} +(0.204153 - 0.226735i) q^{69} +(0.522073 + 0.169632i) q^{70} +(9.75650 + 3.17008i) q^{71} +(-3.26807 + 4.49812i) q^{72} +(-8.43897 - 7.59848i) q^{73} +(0.0235455 - 0.224021i) q^{74} +(-0.109863 - 1.04527i) q^{75} +(5.84193 + 1.89816i) q^{76} +(-4.41458 + 3.20738i) q^{77} +(-0.0948967 + 0.421931i) q^{78} +(4.59051 + 5.09828i) q^{79} +(1.92461 - 0.202285i) q^{80} +(-6.87184 - 4.99269i) q^{81} +(0.745196 + 2.29348i) q^{82} +(-2.46434 - 0.259012i) q^{83} +(-0.563894 - 0.183220i) q^{84} +(-3.87759 + 3.49140i) q^{85} +(0.507208 - 2.38622i) q^{86} +(-0.460939 - 0.798369i) q^{87} +(3.60904 - 6.25104i) q^{88} +(6.33024 + 5.69977i) q^{89} +(-0.118272 - 1.12529i) q^{90} +(5.12654 - 0.477785i) q^{91} +2.23931 q^{92} +(1.29680 - 0.268340i) q^{93} +(-0.356371 - 0.617252i) q^{94} +(-2.45031 + 1.09095i) q^{95} +(1.19648 - 0.125755i) q^{96} +(2.58776 - 12.1744i) q^{97} +2.50173i q^{98} +(9.74061 + 5.62374i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 9 q^{2} - 9 q^{3} - 35 q^{4} - 21 q^{6} - 3 q^{7} - 45 q^{8} - 63 q^{9}+O(q^{10}) $ 280 * q - 9 * q^2 - 9 * q^3 - 35 * q^4 - 21 * q^6 - 3 * q^7 - 45 * q^8 - 63 * q^9	\( 280 q - 9 q^{2} - 9 q^{3} - 35 q^{4} - 21 q^{6} - 3 q^{7} - 45 q^{8} - 63 q^{9} - 24 q^{10} - 9 q^{11} - 8 q^{12} - 6 q^{13} + 4 q^{14} + 23 q^{16} - 21 q^{17} - 45 q^{18} - 27 q^{19} - 75 q^{20} + 76 q^{21} - 22 q^{22} - 10 q^{23} - 15 q^{24} + 96 q^{25} - 15 q^{26} - 24 q^{27} + 5 q^{28} + 13 q^{29} + 36 q^{30} - 2 q^{31} - 141 q^{32} - 3 q^{33} + 9 q^{34} + 32 q^{35} + 97 q^{36} - 49 q^{38} + 15 q^{39} - 75 q^{40} - 33 q^{41} - 16 q^{42} + 21 q^{43} - 18 q^{44} - 27 q^{45} + 51 q^{46} - 68 q^{48} - 24 q^{49} + 90 q^{50} + 47 q^{51} + 73 q^{52} + 12 q^{53} - 33 q^{54} - 65 q^{55} + 25 q^{56} + 105 q^{57} - 3 q^{58} + 12 q^{59} - 90 q^{60} - 57 q^{61} + 12 q^{62} + 201 q^{63} + 13 q^{64} + 11 q^{65} + 22 q^{66} - 45 q^{67} + 142 q^{68} - 139 q^{69} - 15 q^{71} - 15 q^{72} - 9 q^{73} + 4 q^{74} - 75 q^{75} - 80 q^{76} - 24 q^{77} - 104 q^{78} + 54 q^{79} - 21 q^{80} - 107 q^{81} + 43 q^{82} - 54 q^{83} - 15 q^{84} - 117 q^{85} - 84 q^{86} - 21 q^{87} + 49 q^{88} - 9 q^{89} + 11 q^{90} - 10 q^{91} + 266 q^{92} - 22 q^{93} + 33 q^{94} + 75 q^{95} - 204 q^{96} - 10 q^{97} + 168 q^{99}+O(q^{100}) \) 280 * q - 9 * q^2 - 9 * q^3 - 35 * q^4 - 21 * q^6 - 3 * q^7 - 45 * q^8 - 63 * q^9 - 24 * q^10 - 9 * q^11 - 8 * q^12 - 6 * q^13 + 4 * q^14 + 23 * q^16 - 21 * q^17 - 45 * q^18 - 27 * q^19 - 75 * q^20 + 76 * q^21 - 22 * q^22 - 10 * q^23 - 15 * q^24 + 96 * q^25 - 15 * q^26 - 24 * q^27 + 5 * q^28 + 13 * q^29 + 36 * q^30 - 2 * q^31 - 141 * q^32 - 3 * q^33 + 9 * q^34 + 32 * q^35 + 97 * q^36 - 49 * q^38 + 15 * q^39 - 75 * q^40 - 33 * q^41 - 16 * q^42 + 21 * q^43 - 18 * q^44 - 27 * q^45 + 51 * q^46 - 68 * q^48 - 24 * q^49 + 90 * q^50 + 47 * q^51 + 73 * q^52 + 12 * q^53 - 33 * q^54 - 65 * q^55 + 25 * q^56 + 105 * q^57 - 3 * q^58 + 12 * q^59 - 90 * q^60 - 57 * q^61 + 12 * q^62 + 201 * q^63 + 13 * q^64 + 11 * q^65 + 22 * q^66 - 45 * q^67 + 142 * q^68 - 139 * q^69 - 15 * q^71 - 15 * q^72 - 9 * q^73 + 4 * q^74 - 75 * q^75 - 80 * q^76 - 24 * q^77 - 104 * q^78 + 54 * q^79 - 21 * q^80 - 107 * q^81 + 43 * q^82 - 54 * q^83 - 15 * q^84 - 117 * q^85 - 84 * q^86 - 21 * q^87 + 49 * q^88 - 9 * q^89 + 11 * q^90 - 10 * q^91 + 266 * q^92 - 22 * q^93 + 33 * q^94 + 75 * q^95 - 204 * q^96 - 10 * q^97 + 168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{15}\right)$

Coefficient data

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

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

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

$2$	−0.501537	−	0.0527137i	−0.354640	−	0.0372742i	−0.0744666	−	0.997224i	$-0.523725\pi$
$2$	−0.501537	−	0.0527137i	−0.354640	−	0.0372742i	−0.280174	+	0.959949i	$0.590392\pi$
$3$	−0.192422	+	0.139802i	−0.111095	+	0.0807150i	−0.641945	−	0.766750i	$-0.721872\pi$
$3$	−0.192422	+	0.139802i	−0.111095	+	0.0807150i	0.530851	+	0.847465i	$0.321872\pi$
$4$	−1.70753	−	0.362948i	−0.853767	−	0.181474i
$5$	0.660141	−	0.381132i	0.295224	−	0.170448i	−0.345071	−	0.938576i	$-0.612145\pi$
$5$	0.660141	−	0.381132i	0.295224	−	0.170448i	0.640295	+	0.768129i	$0.278812\pi$
$6$	0.103876	−	0.0599729i	0.0424072	−	0.0244838i
$7$	−1.06122	−	0.955523i	−0.401102	−	0.361154i	0.443753	−	0.896149i	$-0.353647\pi$
$7$	−1.06122	−	0.955523i	−0.401102	−	0.361154i	−0.844855	+	0.534995i	$0.820313\pi$
$8$	1.79650	+	0.583717i	0.635157	+	0.206375i
$9$	−0.909570	+	2.79937i	−0.303190	+	0.933123i
$10$	−0.351176	+	0.156354i	−0.111052	+	0.0494434i
$11$	0.794476	−	3.73772i	0.239543	−	1.12696i	−0.679766	−	0.733429i	$-0.737919\pi$
$11$	0.794476	−	3.73772i	0.239543	−	1.12696i	0.919310	−	0.393535i	$-0.128748\pi$
$12$	0.379307	−	0.168879i	0.109497	−	0.0487510i
$13$	−2.44401	+	2.65082i	−0.677845	+	0.735204i
$13$	−2.44401	+	2.65082i	−0.677845	+	0.735204i
$14$	0.481870	+	0.535171i	0.128785	+	0.143030i
$15$	−0.0737420	+	0.165627i	−0.0190401	+	0.0427648i
$16$	2.31928	+	1.03261i	0.579820	+	0.258152i
$17$	−6.69556	+	1.42319i	−1.62391	+	0.345173i	−0.927892	−	0.372848i	$-0.878381\pi$
$17$	−6.69556	+	1.42319i	−1.62391	+	0.345173i	−0.696021	+	0.718022i	$0.745048\pi$
$18$	0.603748	−	1.35604i	0.142305	−	0.319622i
$19$	−3.49945	−	0.367807i	−0.802828	−	0.0843806i	−0.305778	−	0.952103i	$-0.598917\pi$
$19$	−3.49945	−	0.367807i	−0.802828	−	0.0843806i	−0.497050	+	0.867722i	$0.665583\pi$
$20$	−1.26554	+	0.411200i	−0.282984	+	0.0919472i
$21$	0.337785	+	0.0355027i	0.0737108	+	0.00774732i
$22$	−0.595488	+	1.83272i	−0.126958	+	0.390738i
$23$	−1.25474	+	0.266703i	−0.261631	+	0.0556114i	−0.336860	−	0.941555i	$-0.609365\pi$
$23$	−1.25474	+	0.266703i	−0.261631	+	0.0556114i	0.0752284	+	0.997166i	$0.476031\pi$
$24$	−0.427289	+	0.138835i	−0.0872201	+	0.0283395i
$25$	−2.20948	+	3.82693i	−0.441895	+	0.765385i
$26$	1.36549	−	1.20065i	0.267796	−	0.235467i
$27$	−0.436833	−	1.34443i	−0.0840686	−	0.258736i
$28$	1.46526	+	2.01675i	0.276908	+	0.381131i
$29$	−0.405146	+	3.85471i	−0.0752338	+	0.715801i	0.890274	+	0.455426i	$0.150513\pi$
$29$	−0.405146	+	3.85471i	−0.0752338	+	0.715801i	−0.965507	+	0.260375i	$0.916154\pi$
$30$	0.0457152	−	0.0791811i	0.00834642	−	0.0144564i
$31$	−5.07412	−	2.29202i	−0.911338	−	0.411659i
$31$	−5.07412	−	2.29202i	−0.911338	−	0.411659i
$32$	−4.38052	−	2.52910i	−0.774375	−	0.447085i
$33$	0.369667	+	0.830287i	0.0643508	+	0.144534i
$34$	3.43310	−	0.360833i	0.588771	−	0.0618823i
$35$	−1.06473	−	0.226316i	−0.179973	−	0.0382544i
$36$	2.56915	−	4.44989i	0.428191	−	0.741648i
$37$			0.446668i			0.0734318i	0.999326	+	0.0367159i	$0.0116897\pi$
$37$			0.446668i			0.0734318i	−0.999326	+	0.0367159i	$0.988310\pi$
$38$	1.73571	+	0.368937i	0.281570	+	0.0598495i
$39$	0.0996888	−	0.851752i	0.0159630	−	0.136390i
$40$	1.40841	−	0.299367i	0.222690	−	0.0473341i
$41$	−1.94497	−	4.36847i	−0.303753	−	0.682241i	0.695591	−	0.718438i	$-0.255142\pi$
$41$	−1.94497	−	4.36847i	−0.303753	−	0.682241i	−0.999345	+	0.0361967i	$0.988476\pi$
$42$	−0.167540	−	0.0356118i	−0.0258520	−	0.00549502i
$43$	−0.505653	+	4.81097i	−0.0771114	+	0.733666i	0.885840	+	0.463991i	$0.153583\pi$
$43$	−0.505653	+	4.81097i	−0.0771114	+	0.733666i	−0.962951	+	0.269675i	$0.913084\pi$
$44$	−2.71319	+	6.09392i	−0.409029	+	0.918694i
$45$	0.466486	+	2.19464i	0.0695396	+	0.327158i
$46$	0.643357	−	0.0676196i	0.0948578	−	0.00996996i
$47$	0.830734	+	1.14341i	0.121175	+	0.166783i	0.865295	−	0.501263i	$-0.167131\pi$
$47$	0.830734	+	1.14341i	0.121175	+	0.166783i	−0.744120	+	0.668046i	$0.767131\pi$
$48$	−0.590641	+	0.125545i	−0.0852517	+	0.0181208i
$49$	−0.518544	−	4.93362i	−0.0740778	−	0.704803i
$50$	1.30987	−	1.80288i	0.185243	−	0.254965i
$51$	1.08941	−	1.20991i	0.152547	−	0.169421i
$52$	5.13533	−	3.63932i	0.712143	−	0.504682i
$53$	−0.188052	+	0.0399718i	−0.0258310	+	0.00549054i	−0.220809	−	0.975317i	$-0.570870\pi$
$53$	−0.188052	+	0.0399718i	−0.0258310	+	0.00549054i	0.194978	+	0.980808i	$0.437536\pi$
$54$	0.148218	+	0.697311i	0.0201699	+	0.0948920i
$55$	−0.900098	−	2.77022i	−0.121369	−	0.373536i
$56$	−1.34871	−	2.33604i	−0.180230	−	0.312167i
$57$	0.724789	−	0.418457i	0.0960006	−	0.0554260i
$58$	0.406392	−	1.91192i	0.0533619	−	0.251048i
$59$	−1.65300	+	3.71270i	−0.215203	+	0.483353i	−0.988599	−	0.150569i	$-0.951889\pi$
$59$	−1.65300	+	3.71270i	−0.215203	+	0.483353i	0.773397	+	0.633922i	$0.218556\pi$
$60$	0.186031	−	0.256050i	0.0240165	−	0.0330559i
$61$	2.76664	−	4.79196i	0.354232	−	0.613547i	−0.632754	−	0.774352i	$-0.718076\pi$
$61$	2.76664	−	4.79196i	0.354232	−	0.613547i	0.986986	+	0.160805i	$0.0514091\pi$
$62$	2.42404	+	1.41701i	0.307853	+	0.179960i
$63$	3.64011	−	2.10162i	0.458611	−	0.264779i
$64$	−2.04413	−	1.48515i	−0.255517	−	0.185644i
$65$	−0.603076	+	2.68140i	−0.0748024	+	0.332587i
$66$	−0.141634	−	0.435906i	−0.0174340	−	0.0536563i
$67$	9.60659	+	5.54637i	1.17363	+	0.677597i	0.954533	−	0.298106i	$-0.0963548\pi$
$67$	9.60659	+	5.54637i	1.17363	+	0.677597i	0.219099	+	0.975703i	$0.429688\pi$
$68$	11.9494			1.44908
$69$	0.204153	−	0.226735i	0.0245771	−	0.0272957i
$70$	0.522073	+	0.169632i	0.0623997	+	0.0202749i
$71$	9.75650	+	3.17008i	1.15788	+	0.376219i	0.824108	−	0.566433i	$-0.191677\pi$
$71$	9.75650	+	3.17008i	1.15788	+	0.376219i	0.333776	+	0.942652i	$0.391677\pi$
$72$	−3.26807	+	4.49812i	−0.385146	+	0.530108i
$73$	−8.43897	−	7.59848i	−0.987707	−	0.889335i	0.00615293	−	0.999981i	$-0.498041\pi$
$73$	−8.43897	−	7.59848i	−0.987707	−	0.889335i	−0.993860	+	0.110646i	$0.964708\pi$
$74$	0.0235455	−	0.224021i	0.00273711	−	0.0260419i
$75$	−0.109863	−	1.04527i	−0.0126858	−	0.120698i
$76$	5.84193	+	1.89816i	0.670115	+	0.217734i
$77$	−4.41458	+	3.20738i	−0.503088	+	0.365515i
$78$	−0.0948967	+	0.421931i	−0.0107449	+	0.0477742i
$79$	4.59051	+	5.09828i	0.516473	+	0.573601i	0.943809	−	0.330492i	$-0.107215\pi$
$79$	4.59051	+	5.09828i	0.516473	+	0.573601i	−0.427336	+	0.904093i	$0.640548\pi$
$80$	1.92461	−	0.202285i	0.215178	−	0.0226161i
$81$	−6.87184	−	4.99269i	−0.763538	−	0.554743i
$82$	0.745196	+	2.29348i	0.0822932	+	0.253272i
$83$	−2.46434	−	0.259012i	−0.270496	−	0.0284303i	−0.0316908	−	0.999498i	$-0.510089\pi$
$83$	−2.46434	−	0.259012i	−0.270496	−	0.0284303i	−0.238806	+	0.971067i	$0.576756\pi$
$84$	−0.563894	−	0.183220i	−0.0615259	−	0.0199910i
$85$	−3.87759	+	3.49140i	−0.420584	+	0.378695i
$86$	0.507208	−	2.38622i	0.0546936	−	0.257313i
$87$	−0.460939	−	0.798369i	−0.0494178	−	0.0855942i
$88$	3.60904	−	6.25104i	0.384725	−	0.666363i
$89$	6.33024	+	5.69977i	0.671004	+	0.604174i	0.932561	−	0.361014i	$-0.117569\pi$
$89$	6.33024	+	5.69977i	0.671004	+	0.604174i	−0.261557	+	0.965188i	$0.584236\pi$
$90$	−0.118272	−	1.12529i	−0.0124670	−	0.118615i
$91$	5.12654	−	0.477785i	0.537407	−	0.0500854i
$92$	2.23931			0.233464
$93$	1.29680	−	0.268340i	0.134472	−	0.0278255i
$94$	−0.356371	−	0.617252i	−0.0367568	−	0.0636647i
$95$	−2.45031	+	1.09095i	−0.251396	+	0.111929i
$96$	1.19648	−	0.125755i	0.122115	−	0.0128348i
$97$	2.58776	−	12.1744i	0.262747	−	1.23613i	−0.626763	−	0.779210i	$-0.715621\pi$
$97$	2.58776	−	12.1744i	0.262747	−	1.23613i	0.889510	−	0.456916i	$-0.151046\pi$
$98$			2.50173i			0.252713i
$99$	9.74061	+	5.62374i	0.978968	+	0.565207i
$100$	5.16173	−	5.73268i	0.516173	−	0.573268i
$101$	−6.18083	+	1.31378i	−0.615016	+	0.130726i	−0.504878	−	0.863191i	$-0.668463\pi$
$101$	−6.18083	+	1.31378i	−0.615016	+	0.130726i	−0.110138	+	0.993916i	$0.535129\pi$
$102$	−0.610156	+	0.549387i	−0.0604145	+	0.0543974i
$103$	1.87645	−	17.8532i	0.184892	−	1.75913i	−0.371710	−	0.928349i	$-0.621228\pi$
$103$	1.87645	−	17.8532i	0.184892	−	1.75913i	0.556602	−	0.830779i	$-0.312105\pi$
$104$	−5.93797	+	3.33557i	−0.582266	+	0.327080i
$105$	0.236517	−	0.105304i	0.0230817	−	0.0102766i
$106$	0.0964223	−	0.0101344i	0.00936536	−	0.000984339i
$107$	−1.31294	+	4.04081i	−0.126927	+	0.390640i	−0.994247	−	0.107110i	$-0.965840\pi$
$107$	−1.31294	+	4.04081i	−0.126927	+	0.390640i	0.867321	+	0.497750i	$0.165840\pi$
$108$	0.257948	+	2.45421i	0.0248211	+	0.236157i
$109$	−7.97634	−	10.9785i	−0.763995	−	1.05155i	−0.996871	−	0.0790420i	$-0.974814\pi$
$109$	−7.97634	−	10.9785i	−0.763995	−	1.05155i	0.232877	−	0.972506i	$-0.425186\pi$
$110$	0.305404	+	1.43682i	0.0291192	+	0.136995i
$111$	−0.0624453	−	0.0859486i	−0.00592705	−	0.00815788i
$112$	−1.47457	−	3.31195i	−0.139334	−	0.312950i
$113$	1.81645	+	5.59047i	0.170878	+	0.525907i	0.999421	−	0.0340173i	$-0.0108301\pi$
$113$	1.81645	+	5.59047i	0.170878	+	0.525907i	−0.828544	+	0.559924i	$0.810830\pi$
$114$	−0.385567	+	0.171665i	−0.0361117	+	0.0160779i
$115$	−0.726655	+	0.654283i	−0.0677609	+	0.0610122i
$116$	2.09086	−	6.43500i	0.194131	−	0.597475i
$117$	−5.19762	−	9.25278i	−0.480520	−	0.855419i
$118$	1.02475	−	1.77492i	0.0943361	−	0.163395i
$119$	8.46533	+	4.88746i	0.776015	+	0.448033i
$120$	−0.229157	+	0.254504i	−0.0209190	+	0.0232330i
$121$	−3.29032	−	1.46495i	−0.299120	−	0.133177i
$122$	−1.64017	+	2.25751i	−0.148494	+	0.204385i
$123$	0.984977	+	0.568677i	0.0888124	+	0.0512759i
$124$	7.83234	+	5.75534i	0.703365	+	0.516845i
$125$			7.17974i			0.642175i
$126$	−1.93643	+	0.862156i	−0.172511	+	0.0768070i
$127$	−2.87879	+	2.09156i	−0.255451	+	0.185596i	−0.708139	−	0.706073i	$-0.750465\pi$
$127$	−2.87879	+	2.09156i	−0.255451	+	0.185596i	0.452688	+	0.891669i	$0.350465\pi$
$128$	8.46486	+	7.62180i	0.748195	+	0.673678i
$129$	−0.575286	−	0.996425i	−0.0506511	−	0.0877303i
$130$	0.443812	−	1.31303i	0.0389249	−	0.115161i
$131$	10.4001	+	2.21060i	0.908659	+	0.193141i	0.638453	−	0.769661i	$-0.279575\pi$
$131$	10.4001	+	2.21060i	0.908659	+	0.193141i	0.270206	+	0.962803i	$0.412908\pi$
$132$	−0.329869	−	1.55191i	−0.0287114	−	0.135077i
$133$	3.36222	+	3.73412i	0.291541	+	0.323790i
$134$	−4.52570	−	3.28811i	−0.390961	−	0.284049i
$135$	−0.800779	−	0.721024i	−0.0689200	−	0.0620559i
$136$	−12.8593	−	1.35157i	−1.10267	−	0.115896i
$137$	1.85933	+	2.55915i	0.158853	+	0.218643i	0.881023	−	0.473073i	$-0.156855\pi$
$137$	1.85933	+	2.55915i	0.158853	+	0.218643i	−0.722170	+	0.691716i	$0.756855\pi$
$138$	−0.114342	+	0.102954i	−0.00973347	+	0.00876406i
$139$	−0.405503	−	3.85810i	−0.0343943	−	0.327240i	−0.998167	−	0.0605158i	$-0.980725\pi$
$139$	−0.405503	−	3.85810i	−0.0343943	−	0.327240i	0.963773	−	0.266724i	$-0.0859412\pi$
$140$	1.73593	+	0.772884i	0.146713	+	0.0653206i
$141$	−0.319702	−	0.103877i	−0.0269238	−	0.00874806i
$142$	−4.72614	−	2.10421i	−0.396609	−	0.176582i
$143$	7.96630	+	11.2410i	0.666175	+	0.940021i
$144$	−5.00020	+	5.55329i	−0.416683	+	0.462774i
$145$	1.20170	+	2.69906i	0.0997958	+	0.224145i
$146$	3.83191	+	4.25577i	0.317132	+	0.352210i
$147$	0.789511	+	0.876841i	0.0651178	+	0.0723206i
$148$	0.162117	−	0.762702i	0.0133260	−	0.0626937i
$149$	−0.221353	+	0.127798i	−0.0181339	+	0.0104696i	−0.509040	−	0.860743i	$-0.669999\pi$
$149$	−0.221353	+	0.127798i	−0.0181339	+	0.0104696i	0.490906	+	0.871213i	$0.336666\pi$
$150$			0.530035i			0.0432771i
$151$	−6.39601	+	2.07819i	−0.520500	+	0.169121i	−0.557472	−	0.830196i	$-0.688229\pi$
$151$	−6.39601	+	2.07819i	−0.520500	+	0.169121i	0.0369723	+	0.999316i	$0.488229\pi$
$152$	−6.07204	−	2.70345i	−0.492508	−	0.219279i
$153$	2.10606	−	20.0378i	0.170265	−	1.61996i
$154$	2.38315	−	1.37591i	0.192040	−	0.110874i
$155$	−4.22319	+	0.420854i	−0.339215	+	0.0338038i
$156$	−0.479364	+	1.41821i	−0.0383798	+	0.113548i
$157$	6.94318	+	5.04451i	0.554126	+	0.402596i	0.829304	−	0.558797i	$-0.188737\pi$
$157$	6.94318	+	5.04451i	0.554126	+	0.402596i	−0.275178	+	0.961393i	$0.588737\pi$
$158$	−2.03356	−	2.79896i	−0.161782	−	0.222673i
$159$	0.0305972	−	0.0339816i	0.00242651	−	0.00269492i
$160$	−3.85568			−0.304818
$161$	1.58639	+	0.915903i	0.125025	+	0.0721832i
$162$	3.18330	+	2.86626i	0.250104	+	0.225194i
$163$	−8.07453	+	7.27034i	−0.632446	+	0.569457i	−0.921752	−	0.387780i	$-0.873242\pi$
$163$	−8.07453	+	7.27034i	−0.632446	+	0.569457i	0.289306	+	0.957237i	$0.406576\pi$
$164$	1.73558	+	8.16524i	0.135526	+	0.637598i
$165$	0.560482	+	0.407214i	0.0436334	+	0.0317015i
$166$	1.22230	+	0.259809i	0.0948692	+	0.0201651i
$167$	1.24100	−	1.70809i	0.0960312	−	0.132176i	−0.758298	−	0.651909i	$-0.773969\pi$
$167$	1.24100	−	1.70809i	0.0960312	−	0.132176i	0.854329	+	0.519733i	$0.173969\pi$
$168$	0.586106	+	0.260951i	0.0452191	+	0.0201328i
$169$	−1.05366	−	12.9572i	−0.0810511	−	0.996710i
$170$	2.12880	−	1.54666i	0.163272	−	0.118624i
$171$	4.21262	−	9.46169i	0.322147	−	0.723553i
$172$	2.60955	−	8.03137i	0.198976	−	0.612386i
$173$	−19.9219	+	14.4741i	−1.51463	+	1.10044i	−0.550562	+	0.834795i	$0.685586\pi$
$173$	−19.9219	+	14.4741i	−1.51463	+	1.10044i	−0.964070	+	0.265649i	$0.914414\pi$
$174$	0.189093	+	0.424710i	0.0143351	+	0.0321972i
$175$	6.00145	−	1.94999i	0.453667	−	0.147405i
$176$	5.70221	−	7.84842i	0.429821	−	0.591597i
$177$	−0.200972	−	0.945498i	−0.0151060	−	0.0710680i
$178$	−2.87439	−	3.19234i	−0.215445	−	0.239276i
$179$	−3.25184	−	10.0081i	−0.243054	−	0.748043i	−0.995950	−	0.0899041i	$-0.971344\pi$
$179$	−3.25184	−	10.0081i	−0.243054	−	0.748043i	0.752897	−	0.658139i	$-0.228656\pi$
$180$		−	3.91674i		−	0.291936i
$181$	−10.4060	−	18.0237i	−0.773470	−	1.33969i	−0.935651	−	0.352928i	$-0.885186\pi$
$181$	−10.4060	−	18.0237i	−0.773470	−	1.33969i	0.162181	−	0.986761i	$-0.448147\pi$
$182$	−2.59633	−	0.0306118i	−0.192453	−	0.00226910i
$183$	0.137567	+	1.30886i	0.0101692	+	0.0967536i
$184$	−2.40981	−	0.253281i	−0.177654	−	0.0186721i
$185$	0.170240	+	0.294864i	0.0125163	+	0.0216788i
$186$	−0.664538	+	0.0662233i	−0.0487263	+	0.00485573i
$187$			26.1568i			1.91277i
$188$	−1.00351	−	2.25392i	−0.0731884	−	0.164384i
$189$	−0.821063	+	1.84414i	−0.0597236	+	0.134141i
$190$	1.28643	−	0.417986i	0.0933274	−	0.0303239i
$191$	−14.3762			−1.04023			−0.520113	−	0.854097i	$-0.674110\pi$
$191$	−14.3762			−1.04023			−0.520113	+	0.854097i	$0.674110\pi$
$192$	0.600963			0.0433708
$193$	−7.97287	+	2.59054i	−0.573900	+	0.186471i	−0.581566	−	0.813499i	$-0.697560\pi$
$193$	−7.97287	+	2.59054i	−0.573900	+	0.186471i	0.00766622	+	0.999971i	$0.497560\pi$
$194$	−1.93962	+	5.96952i	−0.139256	+	0.428587i
$195$	−0.258822	−	0.600271i	−0.0185346	−	0.0429863i
$196$	−0.905214	+	8.61253i	−0.0646581	+	0.615181i
$197$	−1.95498	+	9.19747i	−0.139287	+	0.655293i	0.851997	+	0.523547i	$0.175392\pi$
$197$	−1.95498	+	9.19747i	−0.139287	+	0.655293i	−0.991284	+	0.131746i	$0.957942\pi$
$198$	−4.58883	−	3.33398i	−0.326114	−	0.236936i
$199$	−5.46940	+	3.97375i	−0.387715	+	0.281692i	−0.764519	−	0.644602i	$-0.777023\pi$
$199$	−5.46940	+	3.97375i	−0.387715	+	0.281692i	0.376803	+	0.926293i	$0.377023\pi$
$200$	−6.20315	+	5.58534i	−0.438629	+	0.394943i
$201$	−2.62391	+	0.275784i	−0.185076	+	0.0194523i
$202$	3.16917	−	0.333093i	0.222982	−	0.0234364i
$203$	4.11321	−	3.70355i	0.288691	−	0.259938i
$204$	−2.29933	+	1.67056i	−0.160985	+	0.116963i
$205$	−2.94892	−	2.14252i	−0.205962	−	0.149640i
$206$	−1.88222	+	8.85513i	−0.131140	+	0.616966i
$207$	0.394673	−	3.75506i	0.0274317	−	0.260995i
$208$	−8.40560	+	3.62428i	−0.582823	+	0.251299i
$209$	−4.15498	+	12.7877i	−0.287406	+	0.884545i
$210$	−0.124173	+	0.0403463i	−0.00856875	+	0.00278416i
$211$	−15.1436			−1.04253			−0.521264	−	0.853395i	$-0.674539\pi$
$211$	−15.1436			−1.04253			−0.521264	+	0.853395i	$0.674539\pi$
$212$	0.335614			0.0230500
$213$	−2.32055	+	0.753991i	−0.159001	+	0.0516626i
$214$	0.871494	−	1.95741i	0.0595741	−	0.133806i
$215$	1.49981	+	3.36864i	0.102286	+	0.229739i
$216$		−	2.67026i		−	0.181688i
$217$	3.19465	+	7.28076i	0.216867	+	0.494250i
$218$	3.42171	+	5.92658i	0.231748	+	0.401399i
$219$	2.68613	+	0.282323i	0.181512	+	0.0190776i
$220$	0.531505	+	5.05693i	0.0358341	+	0.340938i
$221$	12.5914	−	21.2270i	0.846989	−	1.42788i
$222$	0.0267880	+	0.0463982i	0.00179789	+	0.00311404i
$223$			10.5883i			0.709045i	0.935048	+	0.354522i	$0.115356\pi$
$223$			10.5883i			0.709045i	−0.935048	+	0.354522i	$0.884644\pi$
$224$	2.23207	+	6.86961i	0.149137	+	0.458995i
$225$	−8.70330	−	9.66599i	−0.580220	−	0.644399i
$226$	−0.616325	−	2.89958i	−0.0409973	−	0.192877i
$227$	−0.669648	+	0.921692i	−0.0444461	+	0.0611748i	−0.830662	−	0.556778i	$-0.812038\pi$
$227$	−0.669648	+	0.921692i	−0.0444461	+	0.0611748i	0.786215	+	0.617952i	$0.212038\pi$
$228$	−1.38948	+	0.451469i	−0.0920206	+	0.0298993i
$229$	0.581280	+	1.30558i	0.0384120	+	0.0862749i	0.931732	−	0.363145i	$-0.118297\pi$
$229$	0.581280	+	1.30558i	0.0384120	+	0.0862749i	−0.893320	+	0.449420i	$0.851631\pi$
$230$	0.398934	−	0.289843i	0.0263049	−	0.0191117i
$231$	0.401061	−	1.23434i	0.0263879	−	0.0812135i
$232$	−2.97790	+	6.68847i	−0.195509	+	0.439120i
$233$	−14.3153	+	10.4007i	−0.937829	+	0.681373i	−0.947897	−	0.318576i	$-0.896795\pi$
$233$	−14.3153	+	10.4007i	−0.937829	+	0.681373i	0.0100679	+	0.999949i	$0.496795\pi$
$234$	2.11905	+	4.91460i	0.138527	+	0.321277i
$235$	0.984190	+	0.438190i	0.0642015	+	0.0285843i
$236$	4.17008	−	5.73962i	0.271449	−	0.373617i
$237$	−1.59606	−	0.339254i	−0.103676	−	0.0220369i
$238$	−3.98804	−	2.89748i	−0.258506	−	0.187816i
$239$	3.76905	+	17.7320i	0.243800	+	1.14699i	0.914287	+	0.405067i	$0.132752\pi$
$239$	3.76905	+	17.7320i	0.243800	+	1.14699i	−0.670487	+	0.741921i	$0.733915\pi$
$240$	−0.342057	+	0.307989i	−0.0220797	+	0.0198806i
$241$	12.1030	+	10.8976i	0.779620	+	0.701973i	0.959498	−	0.281716i	$-0.0909035\pi$
$241$	12.1030	+	10.8976i	0.779620	+	0.701973i	−0.179878	+	0.983689i	$0.557570\pi$
$242$	1.57300	+	0.908170i	0.101116	+	0.0583794i
$243$	6.26114			0.401653
$244$	−6.46336	+	7.17829i	−0.413774	+	0.459543i
$245$	−2.22267	−	3.05925i	−0.142001	−	0.195448i
$246$	−0.464026	−	0.337134i	−0.0295852	−	0.0214949i
$247$	9.52766	−	8.37747i	0.606230	−	0.533046i
$248$	−7.77773	−	7.07945i	−0.493887	−	0.449545i
$249$	0.510402	−	0.294681i	0.0323454	−	0.0186746i
$250$	0.378470	−	3.60090i	0.0239366	−	0.227741i
$251$	−23.3956	−	10.4164i	−1.47672	−	0.657477i	−0.498847	−	0.866690i	$-0.666243\pi$
$251$	−23.3956	−	10.4164i	−1.47672	−	0.657477i	−0.977870	+	0.209213i	$0.932910\pi$
$252$	−6.97839	+	2.26742i	−0.439597	+	0.142834i
$253$			4.90175i			0.308170i
$254$	1.55408	−	0.897246i	0.0975113	−	0.0562982i
$255$	0.258026	−	1.21392i	0.0161582	−	0.0760184i
$256$	−0.462300	−	0.513436i	−0.0288937	−	0.0320898i
$257$	18.6334	+	20.6944i	1.16232	+	1.29088i	0.949491	+	0.313794i	$0.101600\pi$
$257$	18.6334	+	20.6944i	1.16232	+	1.29088i	0.212826	+	0.977090i	$0.431733\pi$
$258$	0.236002	+	0.530070i	0.0146929	+	0.0330007i
$259$	0.426802	−	0.474012i	0.0265202	−	0.0294537i
$260$	2.00298	−	4.35970i	0.124220	−	0.270377i
$261$	−10.4222	−	4.64028i	−0.645120	−	0.287226i
$262$	−5.09950	−	1.65693i	−0.315048	−	0.102365i
$263$	−24.8869	−	11.0804i	−1.53459	−	0.683245i	−0.546551	−	0.837426i	$-0.684059\pi$
$263$	−24.8869	−	11.0804i	−1.53459	−	0.683245i	−0.988043	+	0.154181i	$0.950726\pi$
$264$	0.179454	+	1.70739i	0.0110446	+	0.105082i
$265$	−0.108906	+	0.0980598i	−0.00669007	+	0.00602377i
$266$	−1.48944	−	2.05004i	−0.0913234	−	0.125696i
$267$	−2.01492	−	0.211776i	−0.123311	−	0.0129605i
$268$	−14.3905	−	12.9573i	−0.879043	−	0.791494i
$269$	2.47084	+	1.79517i	0.150650	+	0.109453i	0.660557	−	0.750776i	$-0.270320\pi$
$269$	2.47084	+	1.79517i	0.150650	+	0.109453i	−0.509907	+	0.860229i	$0.670320\pi$
$270$	0.363612	+	0.403832i	0.0221287	+	0.0245765i
$271$	−2.15263	−	10.1273i	−0.130763	−	0.615191i	−0.993906	−	0.110232i	$-0.964841\pi$
$271$	−2.15263	−	10.1273i	−0.130763	−	0.615191i	0.863143	−	0.504960i	$-0.168493\pi$
$272$	−16.9985	−	3.61314i	−1.03068	−	0.219079i
$273$	−0.919660	+	0.808638i	−0.0556604	+	0.0489410i
$274$	−0.797622	−	1.38152i	−0.0481861	−	0.0834607i
$275$	12.5486	+	11.2988i	0.756708	+	0.681343i
$276$	−0.430891	+	0.313061i	−0.0259366	+	0.0188440i
$277$	4.05564	−	1.80569i	0.243680	−	0.108493i	−0.281263	−	0.959631i	$-0.590753\pi$
$277$	4.05564	−	1.80569i	0.243680	−	0.108493i	0.524943	+	0.851137i	$0.324087\pi$
$278$			1.95636i			0.117334i
$279$	11.0315	−	12.1196i	0.660437	−	0.725579i
$280$	−1.78068	−	1.02808i	−0.106416	−	0.0614394i
$281$	14.3461	−	19.7457i	0.855818	−	1.17793i	−0.126733	−	0.991937i	$-0.540449\pi$
$281$	14.3461	−	19.7457i	0.855818	−	1.17793i	0.982551	−	0.185995i	$-0.0595508\pi$
$282$	0.154867	+	0.0689511i	0.00922218	+	0.00410598i
$283$	18.5054	−	20.5523i	1.10003	−	1.22171i	0.126790	−	0.991930i	$-0.459533\pi$
$283$	18.5054	−	20.5523i	1.10003	−	1.22171i	0.973243	−	0.229780i	$-0.0738007\pi$
$284$	−15.5090	−	8.95412i	−0.920289	−	0.531329i
$285$	0.318975	−	0.552481i	0.0188945	−	0.0327262i
$286$	−3.40284	−	6.05772i	−0.201214	−	0.358200i
$287$	−2.11014	+	6.49436i	−0.124558	+	0.383350i
$288$	11.0643	−	9.96231i	0.651968	−	0.587035i
$289$	27.2749	−	12.1435i	1.60440	−	0.714326i
$290$	−0.460420	−	1.41703i	−0.0270368	−	0.0832107i
$291$	1.20408	+	2.70440i	0.0705841	+	0.158535i
$292$	11.6520	+	16.0376i	0.681881	+	0.938528i
$293$	2.47758	+	11.6561i	0.144742	+	0.680955i	0.989348	+	0.145568i	$0.0465010\pi$
$293$	2.47758	+	11.6561i	0.144742	+	0.680955i	−0.844607	+	0.535387i	$0.820166\pi$
$294$	−0.349748	−	0.481386i	−0.0203977	−	0.0280750i
$295$	0.323818	+	3.08092i	0.0188534	+	0.179378i
$296$	−0.260728	+	0.802438i	−0.0151545	+	0.0466407i
$297$	−5.37216	+	0.564637i	−0.311725	+	0.0327636i
$298$	0.117753	−	0.0524272i	0.00682128	−	0.00303703i
$299$	2.35961	−	3.97791i	0.136460	−	0.230048i
$300$	−0.191785	+	1.82471i	−0.0110727	+	0.105350i
$301$	5.13360	−	4.62231i	0.295896	−	0.266426i
$302$	3.31739	−	0.705132i	0.190894	−	0.0405758i
$303$	1.00566	−	1.11689i	0.0577734	−	0.0641639i
$304$	−7.73639	−	4.46661i	−0.443713	−	0.256178i
$305$		−	4.21782i		−	0.241512i
$306$	−2.11254	+	9.93870i	−0.120766	+	0.568158i
$307$	20.8722	−	2.19376i	1.19124	−	0.125204i	0.511912	−	0.859038i	$-0.328937\pi$
$307$	20.8722	−	2.19376i	1.19124	−	0.125204i	0.679329	+	0.733834i	$0.262271\pi$
$308$	8.70216	−	3.87445i	0.495852	−	0.220767i
$309$	2.13485	+	3.69767i	0.121448	+	0.210353i
$310$	2.14027	+	0.0115460i	0.121559	+	0.000655769i
$311$	24.0239			1.36227			0.681136	−	0.732157i	$-0.261486\pi$
$311$	24.0239			1.36227			0.681136	+	0.732157i	$0.261486\pi$
$312$	0.676272	−	1.47198i	0.0382864	−	0.0833344i
$313$	2.36630	+	22.5138i	0.133751	+	1.27256i	0.831221	+	0.555943i	$0.187643\pi$
$313$	2.36630	+	22.5138i	0.133751	+	1.27256i	−0.697469	+	0.716615i	$0.745691\pi$
$314$	−3.21635	−	2.89601i	−0.181509	−	0.163431i
$315$	1.60199	−	2.77473i	0.0902619	−	0.156338i
$316$	−5.98805	−	10.3716i	−0.336854	−	0.583448i
$317$	−5.15055	+	24.2314i	−0.289284	+	1.36097i	0.558004	+	0.829838i	$0.311567\pi$
$317$	−5.15055	+	24.2314i	−0.289284	+	1.36097i	−0.847287	+	0.531135i	$0.821766\pi$
$318$	−0.0171369	+	0.0154302i	−0.000960991	+	0.000865280i
$319$	14.0859	+	4.57679i	0.788660	+	0.256251i
$320$	−1.91546	−	0.201323i	−0.107077	−	0.0112543i
$321$	−0.312277	−	0.961091i	−0.0174296	−	0.0536429i
$322$	−0.747353	−	0.542984i	−0.0416483	−	0.0302593i
$323$	23.9542	−	2.51769i	1.33285	−	0.140088i
$324$	9.92182	+	11.0193i	0.551212	+	0.612183i
$325$	−4.74450	−	15.2099i	−0.263178	−	0.843696i
$326$	4.43293	−	3.22071i	0.245517	−	0.178379i
$327$	3.06964	+	0.997386i	0.169751	+	0.0551556i
$328$	−0.944178	−	8.98325i	−0.0521335	−	0.496017i
$329$	0.210964	−	2.00719i	0.0116308	−	0.110660i
$330$	−0.259637	−	0.233778i	−0.0142925	−	0.0128690i
$331$	19.6376	−	27.0289i	1.07938	−	1.48564i	0.219181	−	0.975684i	$-0.429661\pi$
$331$	19.6376	−	27.0289i	1.07938	−	1.48564i	0.860200	−	0.509957i	$-0.170339\pi$
$332$	4.11393	+	1.33670i	0.225781	+	0.0733609i
$333$	−1.25039	−	0.406276i	−0.0685209	−	0.0222638i
$334$	−0.712446	+	0.791251i	−0.0389833	+	0.0432953i
$335$	8.45561			0.461979
$336$	0.746758	+	0.431141i	0.0407390	+	0.0235207i
$337$	6.17813	+	19.0143i	0.336544	+	1.03578i	0.965957	+	0.258705i	$0.0832956\pi$
$337$	6.17813	+	19.0143i	0.336544	+	1.03578i	−0.629413	+	0.777071i	$0.716704\pi$
$338$	−0.154572	+	6.55408i	−0.00840759	+	0.356495i
$339$	−1.13109	−	0.821782i	−0.0614322	−	0.0446331i
$340$	7.88832	−	4.55432i	0.427804	−	0.246993i
$341$	−12.5982	+	17.1446i	−0.682230	+	0.928434i
$342$	−2.61154	+	4.52333i	−0.141216	+	0.244593i
$343$	−10.0394	+	13.8181i	−0.542078	+	0.746107i
$344$	−3.71664	+	8.34772i	−0.200388	+	0.450079i
$345$	0.0483537	−	0.227486i	0.00260328	−	0.0122475i
$346$	10.7545	−	6.20914i	0.578168	−	0.333805i
$347$	−7.67876	−	13.3000i	−0.412217	−	0.713981i	0.582915	−	0.812533i	$-0.301912\pi$
$347$	−7.67876	−	13.3000i	−0.412217	−	0.713981i	−0.995132	+	0.0985521i	$0.968579\pi$
$348$	0.497303	+	1.53054i	0.0266582	+	0.0820455i
$349$	1.25111	+	5.88600i	0.0669703	+	0.315070i	0.998864	−	0.0476623i	$-0.0151771\pi$
$349$	1.25111	+	5.88600i	0.0669703	+	0.315070i	−0.931893	+	0.362733i	$0.881844\pi$
$350$	−3.11274	+	0.661633i	−0.166383	+	0.0353658i
$351$	4.63147	+	2.12784i	0.247210	+	0.113576i
$352$	−12.9333	+	14.3638i	−0.689345	+	0.765595i
$353$	−1.72831	+	2.37882i	−0.0919888	+	0.126612i	−0.852531	−	0.522677i	$-0.824933\pi$
$353$	−1.72831	+	2.37882i	−0.0919888	+	0.126612i	0.760542	+	0.649289i	$0.224933\pi$
$354$	0.0509542	+	0.484796i	0.00270818	+	0.0257666i
$355$	7.64888	−	1.62582i	0.405960	−	0.0862896i
$356$	−8.74038	−	12.0301i	−0.463239	−	0.637594i
$357$	−2.31219	+	0.243021i	−0.122374	+	0.0128620i
$358$	1.10335	+	5.19087i	0.0583140	+	0.274346i
$359$	7.16518	−	16.0933i	0.378164	−	0.849370i	−0.619750	−	0.784800i	$-0.712766\pi$
$359$	7.16518	−	16.0933i	0.378164	−	0.849370i	0.997913	−	0.0645699i	$-0.0205675\pi$
$360$	−0.443010	+	4.21496i	−0.0233487	+	0.222148i
$361$	−6.47397	−	1.37608i	−0.340735	−	0.0724255i
$362$	4.26889	+	9.58808i	0.224368	+	0.503938i
$363$	0.837932	−	0.178108i	0.0439800	−	0.00934824i
$364$	−8.92715	−	1.04483i	−0.467910	−	0.0547640i
$365$	−8.46694	−	1.79970i	−0.443180	−	0.0942008i
$366$		−	0.663693i		−	0.0346918i
$367$	10.9488	−	18.9639i	0.571524	−	0.989909i	−0.424885	−	0.905247i	$-0.639686\pi$
$367$	10.9488	−	18.9639i	0.571524	−	0.989909i	0.996410	−	0.0846619i	$-0.0269810\pi$
$368$	−3.18549	−	0.677097i	−0.166055	−	0.0352961i
$369$	13.9980	−	1.47125i	0.728709	−	0.0765904i
$370$	−0.0698382	−	0.156859i	−0.00363072	−	0.00815472i
$371$	0.237758	+	0.137270i	0.0123438	+	0.00712669i
$372$	−2.31172	−	0.0124709i	−0.119857	−	0.000646587i
$373$	−0.680238	+	1.17821i	−0.0352214	+	0.0610052i	−0.883099	−	0.469187i	$-0.844547\pi$
$373$	−0.680238	+	1.17821i	−0.0352214	+	0.0610052i	0.847877	+	0.530192i	$0.177880\pi$
$374$	1.37882	−	13.1186i	0.0712972	−	0.678347i
$375$	−1.00374	−	1.38154i	−0.0518331	−	0.0713422i
$376$	0.824983	+	2.53904i	0.0425453	+	0.130941i
$377$	−9.22795	−	10.4949i	−0.475264	−	0.540515i
$378$	0.509005	−	0.881623i	0.0261804	−	0.0453458i
$379$	−6.56691	+	2.13372i	−0.337320	+	0.109602i	−0.472779	−	0.881181i	$-0.656749\pi$
$379$	−6.56691	+	2.13372i	−0.337320	+	0.109602i	0.135459	+	0.990783i	$0.456749\pi$
$380$	4.57994	−	0.973497i	0.234946	−	0.0499394i
$381$	0.261536	−	0.804924i	0.0133989	−	0.0412375i
$382$	7.21021	+	0.757823i	0.368906	+	0.0387736i
$383$	−31.2158	+	10.1426i	−1.59505	+	0.518264i	−0.965877	−	0.259001i	$-0.916607\pi$
$383$	−31.2158	+	10.1426i	−1.59505	+	0.518264i	−0.629174	+	0.777264i	$0.716607\pi$
$384$	−2.69437	−	0.283189i	−0.137496	−	0.0144515i
$385$	−1.69181	+	3.79986i	−0.0862226	+	0.193659i
$386$	4.13525	−	0.878974i	0.210479	−	0.0447386i
$387$	−13.0077	−	5.79142i	−0.661220	−	0.294394i
$388$	−8.83736	+	19.8490i	−0.448649	+	1.00768i
$389$	−17.0782	−	18.9672i	−0.865898	−	0.961677i	0.133671	−	0.991026i	$-0.457323\pi$
$389$	−17.0782	−	18.9672i	−0.865898	−	0.961677i	−0.999569	+	0.0293487i	$0.990657\pi$
$390$	0.0981663	+	0.314702i	0.00497084	+	0.0159355i
$391$	8.02162	−	3.57145i	0.405671	−	0.180616i
$392$	1.94827	−	9.16591i	0.0984027	−	0.462948i
$393$	−2.31025	+	1.02859i	−0.116536	+	0.0518854i
$394$	1.46533	−	4.50982i	0.0738222	−	0.227201i
$395$	4.97350	+	1.61599i	0.250244	+	0.0813092i
$396$	−14.5913	−	13.1381i	−0.733240	−	0.660213i
$397$	−24.3520	+	14.0597i	−1.22219	+	0.705634i	−0.965385	−	0.260828i	$-0.916004\pi$
$397$	−24.3520	+	14.0597i	−1.22219	+	0.705634i	−0.256809	+	0.966462i	$0.582671\pi$
$398$	2.95258	−	1.70467i	0.147999	−	0.0854474i
$399$	−1.16900	−	0.248479i	−0.0585233	−	0.0124395i
$400$	−9.07611	+	6.59418i	−0.453806	+	0.329709i
$401$	29.5394	+	3.10471i	1.47513	+	0.155042i	0.807682	−	0.589618i	$-0.200722\pi$
$401$	29.5394	+	3.10471i	1.47513	+	0.155042i	0.667444	+	0.744660i	$0.267388\pi$
$402$	1.33053			0.0663607
$403$	18.4769	−	7.84884i	0.920400	−	0.390979i
$404$	11.0308			0.548804
$405$	−6.43926	−	0.676793i	−0.319969	−	0.0336301i
$406$	−2.25816	+	1.64065i	−0.112070	+	0.0814239i
$407$	1.66952	+	0.354867i	0.0827550	+	0.0175901i
$408$	2.66336	−	1.53769i	0.131856	−	0.0761270i
$409$	5.74616	−	3.31754i	0.284129	−	0.164042i	−0.351162	−	0.936315i	$-0.614213\pi$
$409$	5.74616	−	3.31754i	0.284129	−	0.164042i	0.635291	+	0.772273i	$0.280880\pi$
$410$	1.36605	+	1.23000i	0.0674646	+	0.0607454i
$411$	−0.715551	−	0.232497i	−0.0352955	−	0.0114682i
$412$	−9.68388	+	29.8039i	−0.477090	+	1.46833i
$413$	5.30177	−	2.36050i	0.260883	−	0.116153i
$414$	−0.395886	+	1.86250i	−0.0194567	+	0.0915368i
$415$	−1.72553	+	0.768255i	−0.0847028	+	0.0377121i
$416$	17.4102	−	5.43084i	0.853605	−	0.266269i
$417$	0.617399	+	0.685691i	0.0302342	+	0.0335784i
$418$	2.75797	−	6.19449i	0.134896	−	0.302982i
$419$	15.8340	+	7.04975i	0.773541	+	0.344403i	0.755256	−	0.655430i	$-0.227513\pi$
$419$	15.8340	+	7.04975i	0.773541	+	0.344403i	0.0182852	+	0.999833i	$0.494179\pi$
$420$	−0.442081	+	0.0939672i	−0.0215713	+	0.00458513i
$421$	16.0896	−	36.1377i	0.784157	−	1.76125i	0.149037	−	0.988832i	$-0.452383\pi$
$421$	16.0896	−	36.1377i	0.784157	−	1.76125i	0.635120	−	0.772413i	$-0.280951\pi$
$422$	7.59508	+	0.798275i	0.369722	+	0.0388594i
$423$	−3.95643	+	1.28552i	−0.192368	+	0.0625041i
$424$	−0.361167	−	0.0379602i	−0.0175398	−	0.00184351i
$425$	9.34726	−	28.7679i	0.453409	−	1.39545i
$426$	1.20359	−	0.255830i	0.0583139	−	0.0123950i
$427$	−7.51483	+	2.44172i	−0.363668	+	0.118163i
$428$	3.70849	−	6.42330i	0.179257	−	0.310482i
$429$	−3.10441	−	1.04931i	−0.149882	−	0.0506609i
$430$	−0.574639	−	1.76856i	−0.0277116	−	0.0852874i
$431$	12.2936	+	16.9207i	0.592161	+	0.815040i	0.994963	−	0.100248i	$-0.0319635\pi$
$431$	12.2936	+	16.9207i	0.592161	+	0.815040i	−0.402802	+	0.915287i	$0.631964\pi$
$432$	0.375138	−	3.56920i	0.0180488	−	0.171723i
$433$	−14.5177	+	25.1454i	−0.697675	+	1.20841i	0.271596	+	0.962411i	$0.412449\pi$
$433$	−14.5177	+	25.1454i	−0.697675	+	1.20841i	−0.969271	+	0.245997i	$0.920885\pi$
$434$	−1.21844	−	3.81998i	−0.0584871	−	0.183365i
$435$	−0.608569	−	0.351357i	−0.0291786	−	0.0168463i
$436$	9.63525	+	21.6411i	0.461445	+	1.03642i
$437$	4.48899	−	0.471811i	0.214737	−	0.0225698i
$438$	−1.33231	−	0.283191i	−0.0636602	−	0.0135314i
$439$	1.37565	−	2.38270i	0.0656563	−	0.113720i	−0.831329	−	0.555781i	$-0.812419\pi$
$439$	1.37565	−	2.38270i	0.0656563	−	0.113720i	0.896985	+	0.442061i	$0.145753\pi$
$440$		−	5.50209i		−	0.262302i
$441$	14.2827	+	3.03588i	0.680127	+	0.144565i
$442$	−7.43401	+	9.98239i	−0.353600	+	0.474814i
$443$	37.3822	−	7.94583i	1.77608	−	0.377518i	0.800877	−	0.598828i	$-0.204367\pi$
$443$	37.3822	−	7.94583i	1.77608	−	0.377518i	0.975203	+	0.221311i	$0.0710336\pi$
$444$	0.0754327	+	0.169425i	0.00357988	+	0.00804054i
$445$	6.35121	+	1.34999i	0.301076	+	0.0639958i
$446$	0.558148	−	5.31042i	0.0264291	−	0.251456i
$447$	0.0247266	−	0.0555368i	0.00116953	−	0.00262680i
$448$	0.750172	+	3.52928i	0.0354423	+	0.166743i
$449$	−28.5353	+	2.99918i	−1.34666	+	0.141540i	−0.750259	−	0.661143i	$-0.770071\pi$
$449$	−28.5353	+	2.99918i	−1.34666	+	0.141540i	−0.596405	+	0.802684i	$0.703405\pi$
$450$	3.85550	+	5.30664i	0.181750	+	0.250157i
$451$	−17.8733	+	3.79910i	−0.841623	+	0.178892i
$452$	−1.07261	−	10.2052i	−0.0504513	−	0.480012i
$453$	0.940194	−	1.29407i	0.0441742	−	0.0608005i
$454$	0.384439	−	0.426963i	0.0180426	−	0.0200384i
$455$	3.20214	−	2.26929i	0.150118	−	0.106386i
$456$	1.54634	−	0.328685i	0.0724140	−	0.0153921i
$457$	4.99622	+	23.5054i	0.233713	+	1.09953i	0.925886	+	0.377803i	$0.123320\pi$
$457$	4.99622	+	23.5054i	0.233713	+	1.09953i	−0.692173	+	0.721732i	$0.743346\pi$
$458$	−0.222712	−	0.685436i	−0.0104066	−	0.0320283i
$459$	4.83822	+	8.38005i	0.225829	+	0.391147i
$460$	1.47826	−	0.853473i	0.0689242	−	0.0397934i
$461$	1.62723	−	7.65553i	0.0757878	−	0.356553i	−0.923870	−	0.382706i	$-0.874992\pi$
$461$	1.62723	−	7.65553i	0.0757878	−	0.356553i	0.999658	+	0.0261526i	$0.00832557\pi$
$462$	−0.266214	+	0.597926i	−0.0123854	+	0.0278180i
$463$	−19.1484	+	26.3555i	−0.889900	+	1.22484i	0.0836789	+	0.996493i	$0.473333\pi$
$463$	−19.1484	+	26.3555i	−0.889900	+	1.22484i	−0.973579	+	0.228350i	$0.926667\pi$
$464$	−4.92006	+	8.52179i	−0.228408	+	0.395614i
$465$	0.753797	−	0.671394i	0.0349565	−	0.0311352i
$466$	7.72794	−	4.46173i	0.357990	−	0.206685i
$467$	−5.08368	−	3.69351i	−0.235244	−	0.170915i	0.463918	−	0.885878i	$-0.346443\pi$
$467$	−5.08368	−	3.69351i	−0.235244	−	0.170915i	−0.699162	+	0.714963i	$0.746443\pi$
$468$	5.51684	+	17.6859i	0.255016	+	0.817531i
$469$	−4.89499	−	15.0652i	−0.226029	−	0.695647i
$470$	−0.470509	−	0.271649i	−0.0217030	−	0.0125302i
$471$	−2.04125			−0.0940559
$472$	−5.13678	+	5.70497i	−0.236439	+	0.262593i
$473$	17.5803	+	5.71218i	0.808343	+	0.262647i
$474$	0.782603	+	0.254283i	0.0359461	+	0.0116796i
$475$	9.13951	−	12.5795i	0.419349	−	0.577185i
$476$	−12.6809	−	11.4180i	−0.581230	−	0.523342i
$477$	0.0591511	−	0.562785i	0.00270834	−	0.0257681i
$478$	−0.955602	−	9.09194i	−0.0437082	−	0.415856i
$479$	15.4122	+	5.00772i	0.704201	+	0.228809i	0.639160	−	0.769074i	$-0.279282\pi$
$479$	15.4122	+	5.00772i	0.704201	+	0.228809i	0.0650409	+	0.997883i	$0.479282\pi$
$480$	0.741916	−	0.539034i	0.0338637	−	0.0246034i
$481$	−1.18404	−	1.09166i	−0.0539874	−	0.0497754i
$482$	−5.49563	−	6.10352i	−0.250319	−	0.278008i
$483$	−0.433301	+	0.0455418i	−0.0197159	+	0.00207222i
$484$	5.08664	+	3.69566i	0.231211	+	0.167985i
$485$	−2.93179	−	9.02312i	−0.133126	−	0.409719i
$486$	−3.14020	−	0.330048i	−0.142442	−	0.0149713i
$487$	−16.4999	−	5.36114i	−0.747681	−	0.242936i	−0.0896980	−	0.995969i	$-0.528590\pi$
$487$	−16.4999	−	5.36114i	−0.747681	−	0.242936i	−0.657983	+	0.753033i	$0.728590\pi$
$488$	7.76740	−	6.99380i	0.351614	−	0.316594i
$489$	0.537303	−	2.52781i	0.0242977	−	0.114312i
$490$	0.953490	+	1.65149i	0.0430743	+	0.0746068i
$491$	−19.6738	+	34.0760i	−0.887866	+	1.53783i	−0.0454721	+	0.998966i	$0.514479\pi$
$491$	−19.6738	+	34.0760i	−0.887866	+	1.53783i	−0.842394	+	0.538863i	$0.818854\pi$
$492$	−1.47548	−	1.32853i	−0.0665199	−	0.0598948i
$493$	−2.77329	−	26.3860i	−0.124902	−	1.18837i
$494$	−5.22008	+	3.69937i	−0.234863	+	0.166443i
$495$	8.57356			0.385353
$496$	−9.40153	−	10.5554i	−0.422141	−	0.473952i
$497$	−7.32467	−	12.6867i	−0.328556	−	0.569076i
$498$	−0.271519	+	0.120888i	−0.0121671	+	0.00541713i
$499$	−7.56552	+	0.795168i	−0.338679	+	0.0355966i	−0.272342	−	0.962201i	$-0.587798\pi$
$499$	−7.56552	+	0.795168i	−0.338679	+	0.0355966i	−0.0663375	+	0.997797i	$0.521131\pi$
$500$	2.60587	−	12.2596i	0.116538	−	0.548268i
$501$			0.502167i			0.0224352i
$502$	11.1847	+	6.45748i	0.499197	+	0.288211i
$503$	12.0163	−	13.3454i	0.535780	−	0.595044i	−0.413098	−	0.910686i	$-0.635553\pi$
$503$	12.0163	−	13.3454i	0.535780	−	0.595044i	0.948878	+	0.315643i	$0.102220\pi$
$504$	7.76619	−	1.65075i	0.345934	−	0.0735304i
$505$	−3.57950	+	3.22299i	−0.159285	+	0.143421i
$506$	0.258389	−	2.45841i	0.0114868	−	0.109290i
$507$	2.01420	+	2.34595i	0.0894537	+	0.104187i
$508$	5.67476	−	2.52657i	0.251777	−	0.112098i
$509$	−40.8857	+	4.29726i	−1.81223	+	0.190473i	−0.949198	−	0.314680i	$-0.898103\pi$
$509$	−40.8857	+	4.29726i	−1.81223	+	0.190473i	−0.863030	+	0.505153i	$0.831436\pi$
$510$	−0.193400	+	0.595223i	−0.00856388	+	0.0263569i
$511$	1.69504	+	16.1273i	0.0749843	+	0.713428i
$512$	−13.1857	−	18.1485i	−0.582729	−	0.802058i
$513$	1.03418	+	4.86544i	0.0456602	+	0.214815i
$514$	−8.25445	−	11.3613i	−0.364088	−	0.501124i
$515$	−5.56571	−	12.5008i	−0.245255	−	0.550851i
$516$	0.620671	+	1.91023i	0.0273235	+	0.0840931i
$517$	4.93373	−	2.19664i	0.216985	−	0.0966080i
$518$	−0.239044	+	0.215236i	−0.0105030	+	0.00945694i
$519$	1.80988	−	5.57025i	0.0794451	−	0.244507i
$520$	−2.64860	+	4.46510i	−0.116149	+	0.195808i
$521$	3.46105	−	5.99471i	0.151631	−	0.262633i	−0.780196	−	0.625535i	$-0.784881\pi$
$521$	3.46105	−	5.99471i	0.151631	−	0.262633i	0.931827	+	0.362902i	$0.118214\pi$
$522$	4.98253	+	2.87667i	0.218080	+	0.125908i
$523$	−17.6028	+	19.5499i	−0.769716	+	0.854857i	−0.992780	−	0.119947i	$-0.961728\pi$
$523$	−17.6028	+	19.5499i	−0.769716	+	0.854857i	0.223064	+	0.974804i	$0.428394\pi$
$524$	−16.9562	−	7.54936i	−0.740733	−	0.329796i
$525$	−0.882194	+	1.21424i	−0.0385021	+	0.0529936i
$526$	11.8976	+	6.86910i	0.518761	+	0.299507i
$527$	37.2360	+	8.12496i	1.62203	+	0.353929i
$528$			2.30739i			0.100416i
$529$	−19.5083	+	8.68566i	−0.848187	+	0.377637i
$530$	0.0597898	−	0.0434398i	0.00259710	−	0.00188690i
$531$	−8.88970	−	8.00432i	−0.385780	−	0.347358i
$532$	−4.38581	−	7.59645i	−0.190149	−	0.329348i
$533$	16.3335	+	5.52082i	0.707484	+	0.239133i
$534$	0.999392	+	0.212427i	0.0432479	+	0.00919263i
$535$	0.673359	+	3.16791i	0.0291119	+	0.136961i
$536$	14.0207	+	15.5716i	0.605602	+	0.672589i
$537$	2.02489	+	1.47117i	0.0873802	+	0.0634855i
$538$	−1.14459	−	1.03059i	−0.0493467	−	0.0444320i
$539$	−18.8524	−	1.98147i	−0.812032	−	0.0853480i
$540$	1.10566	+	1.52181i	0.0475802	+	0.0654885i
$541$	−26.6663	+	24.0105i	−1.14647	+	1.03229i	−0.147409	+	0.989076i	$0.547093\pi$
$541$	−26.6663	+	24.0105i	−1.14647	+	1.03229i	−0.999066	+	0.0432149i	$0.986240\pi$
$542$	0.545775	+	5.19270i	0.0234431	+	0.223046i
$543$	4.52209	+	2.01336i	0.194061	+	0.0864016i
$544$	32.9295	+	10.6994i	1.41184	+	0.458734i
$545$	−9.44976	−	4.20730i	−0.404783	−	0.180221i
$546$	0.503870	−	0.357083i	0.0215637	−	0.0152818i
$547$	−4.79219	+	5.32226i	−0.204899	+	0.227564i	−0.836832	−	0.547459i	$-0.815595\pi$
$547$	−4.79219	+	5.32226i	−0.204899	+	0.227564i	0.631933	+	0.775023i	$0.282262\pi$
$548$	−2.24603	−	5.04468i	−0.0959458	−	0.215498i
$549$	10.8980	+	12.1035i	0.465115	+	0.516563i
$550$	−5.69798	−	6.32825i	−0.242963	−	0.269837i
$551$	2.83557	−	13.3403i	0.120800	−	0.568317i
$552$	0.499109	−	0.288161i	0.0212435	−	0.0122649i
$553$		−	9.79671i		−	0.416599i
$554$	−2.12924	+	0.691832i	−0.0904628	+	0.0293931i
$555$	−0.0739805	−	0.0329382i	−0.00314030	−	0.00139815i
$556$	−0.707879	+	6.73501i	−0.0300207	+	0.285628i
$557$	−27.6434	+	15.9599i	−1.17129	+	0.676244i	−0.953983	−	0.299860i	$-0.903060\pi$
$557$	−27.6434	+	15.9599i	−1.17129	+	0.676244i	−0.217305	+	0.976104i	$0.569727\pi$
$558$	−6.17156	+	5.49690i	−0.261263	+	0.232702i
$559$	−11.5172	−	13.0984i	−0.487125	−	0.554005i
$560$	−2.23572	−	1.62434i	−0.0944763	−	0.0686410i
$561$	−3.65678	−	5.03313i	−0.154390	−	0.212499i
$562$	−8.23598	+	9.14698i	−0.347414	+	0.385842i
$563$	25.5182			1.07546			0.537731	−	0.843116i	$-0.319282\pi$
$563$	25.5182			1.07546			0.537731	+	0.843116i	$0.319282\pi$
$564$	0.508200	+	0.293409i	0.0213991	+	0.0123548i
$565$	3.32982	+	2.99819i	0.140087	+	0.126135i
$566$	−10.3645	+	9.33227i	−0.435654	+	0.392265i
$567$	2.52188	+	11.8645i	0.105909	+	0.498263i
$568$	15.6771	+	11.3901i	0.657795	+	0.477916i
$569$	−25.2563	−	5.36840i	−1.05880	−	0.225055i	−0.354572	−	0.935029i	$-0.615374\pi$
$569$	−25.2563	−	5.36840i	−1.05880	−	0.225055i	−0.704228	+	0.709974i	$0.748707\pi$
$570$	−0.189101	+	0.260275i	−0.00792058	+	0.0109017i
$571$	34.4829	+	15.3528i	1.44307	+	0.642494i	0.971002	−	0.239070i	$-0.0768426\pi$
$571$	34.4829	+	15.3528i	1.44307	+	0.642494i	0.472064	+	0.881564i	$0.343509\pi$
$572$	−9.52282	−	22.0858i	−0.398169	−	0.923452i
$573$	2.76629	−	2.00983i	0.115564	−	0.0839619i
$574$	1.40066	−	3.14593i	0.0584623	−	0.131308i
$575$	1.75166	−	5.39107i	0.0730494	−	0.224823i
$576$	6.01677	−	4.37144i	0.250699	−	0.182143i
$577$	−7.59826	−	17.0660i	−0.316320	−	0.710466i	0.683490	−	0.729960i	$-0.260461\pi$
$577$	−7.59826	−	17.0660i	−0.316320	−	0.710466i	−0.999810	+	0.0194940i	$0.993794\pi$
$578$	−14.3195	+	4.65268i	−0.595612	+	0.193526i
$579$	1.17199	−	1.61310i	0.0487061	−	0.0670383i
$580$	−1.07233	−	5.04490i	−0.0445259	−	0.209478i
$581$	2.36770	+	2.62960i	0.0982289	+	0.109094i
$582$	−0.461330	−	1.41983i	−0.0191227	−	0.0588537i
$583$			0.734643i			0.0304258i
$584$	−10.7252	−	18.5766i	−0.443812	−	0.768706i
$585$	−6.95769	−	4.12715i	−0.287665	−	0.170637i
$586$	−0.628162	−	5.97656i	−0.0259491	−	0.246889i
$587$	−40.8552	−	4.29406i	−1.68628	−	0.177235i	−0.787701	−	0.616057i	$-0.788729\pi$
$587$	−40.8552	−	4.29406i	−1.68628	−	0.177235i	−0.898574	+	0.438823i	$0.855396\pi$
$588$	−1.02987	−	1.78379i	−0.0424711	−	0.0735622i
$589$	16.9136	+	9.88709i	0.696911	+	0.407390i
$590$		−	1.56227i		−	0.0643175i
$591$	−0.909648	−	2.04310i	−0.0374179	−	0.0840420i
$592$	−0.461234	+	1.03595i	−0.0189566	+	0.0425772i
$593$	15.5917	−	5.06606i	0.640275	−	0.208038i	0.0291540	−	0.999575i	$-0.490719\pi$
$593$	15.5917	−	5.06606i	0.640275	−	0.208038i	0.611121	+	0.791537i	$0.290719\pi$
$594$	2.72410			0.111771
$595$	7.45108			0.305464
$596$	0.424352	−	0.137880i	0.0173821	−	0.00564780i
$597$	0.496890	−	1.52927i	0.0203363	−	0.0625888i
$598$	−1.39312	+	1.87068i	−0.0569690	+	0.0764980i
$599$	−1.14895	+	10.9315i	−0.0469446	+	0.446648i	0.945651	+	0.325183i	$0.105426\pi$
$599$	−1.14895	+	10.9315i	−0.0469446	+	0.446648i	−0.992596	+	0.121465i	$0.961241\pi$
$600$	0.412776	−	1.94196i	0.0168515	−	0.0792800i
$601$	−32.1180	−	23.3351i	−1.31012	−	0.951857i	−0.999999	−	0.00115962i	$-0.999631\pi$
$601$	−32.1180	−	23.3351i	−1.31012	−	0.951857i	−0.310120	−	0.950698i	$-0.600369\pi$
$602$	−2.81835	+	2.04765i	−0.114867	+	0.0834560i
$603$	−24.2642	+	21.8476i	−0.988114	+	0.889702i
$604$	11.6757	−	1.22716i	0.475077	−	0.0499326i
$605$	−2.73041	+	0.286978i	−0.111007	+	0.0116673i
$606$	−0.563250	+	0.507152i	−0.0228804	+	0.0206016i
$607$	−5.48809	+	3.98733i	−0.222755	+	0.161841i	−0.693566	−	0.720393i	$-0.743961\pi$
$607$	−5.48809	+	3.98733i	−0.222755	+	0.161841i	0.470811	+	0.882234i	$0.343961\pi$
$608$	14.3992	+	10.4616i	0.583964	+	0.424275i
$609$	−0.273705	+	1.28768i	−0.0110911	+	0.0521794i
$610$	−0.222337	+	2.11539i	−0.00900216	+	0.0856498i
$611$	−5.06128	−	0.592371i	−0.204757	−	0.0239647i
$612$	−10.8689	+	33.4509i	−0.439347	+	1.35217i
$613$	−1.90649	+	0.619456i	−0.0770024	+	0.0250196i	−0.347265	−	0.937767i	$-0.612890\pi$
$613$	−1.90649	+	0.619456i	−0.0770024	+	0.0250196i	0.270262	+	0.962787i	$0.412890\pi$
$614$	−10.5838			−0.427129
$615$	0.866965			0.0349594
$616$	−9.80298	+	3.18518i	−0.394973	+	0.128335i
$617$	−7.15616	+	16.0730i	−0.288096	+	0.647074i	−0.998383	−	0.0568375i	$-0.981898\pi$
$617$	−7.15616	+	16.0730i	−0.288096	+	0.647074i	0.710287	+	0.703912i	$0.248565\pi$
$618$	−0.875790	−	1.96706i	−0.0352294	−	0.0791266i
$619$			15.9738i			0.642041i	0.947072	+	0.321021i	$0.104026\pi$
$619$			15.9738i			0.642041i	−0.947072	+	0.321021i	$0.895974\pi$
$620$	7.36399	+	0.814175i	0.295745	+	0.0326980i
$621$	0.906676	+	1.57041i	0.0363837	+	0.0630183i
$622$	−12.0489	−	1.26639i	−0.483117	−	0.0507776i
$623$	−1.27149	−	12.0974i	−0.0509410	−	0.484671i
$624$	1.11073	−	1.87251i	0.0444650	−	0.0749605i
$625$	−8.31095	−	14.3950i	−0.332438	−	0.575800i
$626$		−	11.4163i		−	0.456286i
$627$	−0.988246	−	3.04151i	−0.0394667	−	0.121466i
$628$	−10.0248	−	11.1337i	−0.400034	−	0.444283i
$629$	−0.635692	−	2.99070i	−0.0253467	−	0.119247i
$630$	−0.949724	+	1.30718i	−0.0378379	+	0.0520794i
$631$	5.63870	−	1.83213i	0.224473	−	0.0729357i	−0.194621	−	0.980879i	$-0.562348\pi$
$631$	5.63870	−	1.83213i	0.224473	−	0.0729357i	0.419094	+	0.907943i	$0.362348\pi$
$632$	5.27088	+	11.8386i	0.209664	+	0.470914i
$633$	2.91395	−	2.11711i	0.115819	−	0.0841476i
$634$	3.86052	−	11.8815i	0.153321	−	0.471873i
$635$	−1.10324	+	2.47793i	−0.0437809	+	0.0983336i
$636$	−0.0645793	+	0.0469196i	−0.00256073	+	0.00186048i
$637$	14.3455	+	10.6832i	0.568388	+	0.423285i
$638$	−6.82336	−	3.03795i	−0.270139	−	0.120274i
$639$	−17.7484	+	24.4286i	−0.702117	+	0.966381i
$640$	8.49291	+	1.80522i	0.335712	+	0.0713578i
$641$	37.5137	+	27.2553i	1.48170	+	1.07652i	0.977004	+	0.213222i	$0.0683956\pi$
$641$	37.5137	+	27.2553i	1.48170	+	1.07652i	0.504697	+	0.863297i	$0.331604\pi$
$642$	0.105956	+	0.498484i	0.00418175	+	0.0196736i
$643$	4.29968	−	3.87145i	0.169563	−	0.152675i	−0.579981	−	0.814630i	$-0.696940\pi$
$643$	4.29968	−	3.87145i	0.169563	−	0.152675i	0.749543	+	0.661955i	$0.230273\pi$
$644$	−2.37639	−	2.13971i	−0.0936429	−	0.0843164i
$645$	−0.759540	−	0.438521i	−0.0299069	−	0.0172667i
$646$	−12.1466			−0.477904
$647$	−10.2654	+	11.4009i	−0.403576	+	0.448217i	−0.910336	−	0.413871i	$-0.864177\pi$
$647$	−10.2654	+	11.4009i	−0.403576	+	0.448217i	0.506760	+	0.862087i	$0.330843\pi$
$648$	−9.43092	−	12.9805i	−0.370481	−	0.509924i
$649$	12.5638	+	9.12811i	0.493171	+	0.358310i
$650$	1.57777	+	7.87846i	0.0618854	+	0.309018i
$651$	−1.63259	−	0.954355i	−0.0639862	−	0.0374041i
$652$	16.4263	−	9.48373i	0.643303	−	0.371411i
$653$	−3.51073	+	33.4024i	−0.137386	+	1.30714i	0.680922	+	0.732356i	$0.261579\pi$
$653$	−3.51073	+	33.4024i	−0.137386	+	1.30714i	−0.818308	+	0.574781i	$0.805087\pi$
$654$	−1.48696	−	0.662038i	−0.0581448	−	0.0258877i
$655$	7.70804	−	2.50450i	0.301178	−	0.0978587i
$656$		−	12.1401i		−	0.473992i
$657$	28.9468	−	16.7124i	1.12932	−	0.652014i
$658$	−0.211612	+	0.995558i	−0.00824951	+	0.0388109i
$659$	−19.8150	−	22.0068i	−0.771883	−	0.857263i	0.221133	−	0.975244i	$-0.429025\pi$
$659$	−19.8150	−	22.0068i	−0.771883	−	0.857263i	−0.993016	+	0.117980i	$0.962358\pi$
$660$	−0.809244	−	0.898757i	−0.0314998	−	0.0349841i
$661$	−17.9655	−	40.3513i	−0.698778	−	1.56948i	−0.817093	−	0.576506i	$-0.804416\pi$
$661$	−17.9655	−	40.3513i	−0.698778	−	1.56948i	0.118314	−	0.992976i	$-0.462251\pi$
$662$	−11.2738	+	12.5208i	−0.438168	+	0.486635i
$663$	0.544729	+	5.84484i	0.0211555	+	0.226995i
$664$	−4.27598	−	1.90379i	−0.165940	−	0.0738814i
$665$	3.64273	+	1.18360i	0.141259	+	0.0458979i
$666$	0.605700	+	0.269675i	0.0234704	+	0.0104497i
$667$	−0.519710	−	4.94471i	−0.0201232	−	0.191460i
$668$	−2.73899	+	2.46620i	−0.105975	+	0.0954201i
$669$	−1.48027	−	2.03742i	−0.0572305	−	0.0787710i
$670$	−4.24080	−	0.445726i	−0.163836	−	0.0172199i
$671$	−15.7129	−	14.1480i	−0.606592	−	0.546177i
$672$	−1.38989	−	1.00981i	−0.0536160	−	0.0389543i
$673$	4.59467	+	5.10290i	0.177112	+	0.196702i	0.825164	−	0.564894i	$-0.191083\pi$
$673$	4.59467	+	5.10290i	0.177112	+	0.196702i	−0.648052	+	0.761596i	$0.724416\pi$
$674$	−2.09625	−	9.86206i	−0.0807444	−	0.379872i
$675$	6.11022	+	1.29877i	0.235182	+	0.0499896i
$676$	−2.90363	+	22.5073i	−0.111678	+	0.865667i
$677$	−5.73158	−	9.92739i	−0.220283	−	0.381541i	0.734611	−	0.678488i	$-0.237365\pi$
$677$	−5.73158	−	9.92739i	−0.220283	−	0.381541i	−0.954894	+	0.296948i	$0.904031\pi$
$678$	0.523963	+	0.471778i	0.0201227	+	0.0181185i
$679$	−14.3791	+	10.4470i	−0.551820	+	0.400921i
$680$	−9.00406	+	4.00887i	−0.345290	+	0.153733i
$681$		−	0.270972i		−	0.0103837i
$682$	7.22221	−	7.93458i	0.276553	−	0.303831i
$683$	−22.4636	−	12.9693i	−0.859544	−	0.496258i	0.00431542	−	0.999991i	$-0.498626\pi$
$683$	−22.4636	−	12.9693i	−0.859544	−	0.496258i	−0.863860	+	0.503733i	$0.831960\pi$
$684$	−10.6273	+	14.6272i	−0.406344	+	0.559285i
$685$	2.20279	+	0.980747i	0.0841645	+	0.0374724i
$686$	5.76355	−	6.40107i	0.220053	−	0.244394i
$687$	−0.294373	−	0.169957i	−0.0112310	−	0.00648425i
$688$	−6.14060	+	10.6358i	−0.234108	+	0.405487i
$689$	0.353643	−	0.596184i	0.0134727	−	0.0227128i
$690$	−0.0362428	+	0.111544i	−0.00137974	+	0.00424641i
$691$	28.0166	−	25.2263i	1.06580	−	0.959652i	0.0665292	−	0.997784i	$-0.478807\pi$
$691$	28.0166	−	25.2263i	1.06580	−	0.959652i	0.999273	+	0.0381321i	$0.0121408\pi$
$692$	39.2706	−	17.4844i	1.49284	−	0.664657i
$693$	−4.96327	−	15.2754i	−0.188539	−	0.580264i
$694$	3.15009	+	7.07522i	0.119576	+	0.268572i
$695$	−1.73814	−	2.39234i	−0.0659312	−	0.0907466i
$696$	−0.362053	−	1.70332i	−0.0137236	−	0.0645643i
$697$	19.2398	+	26.4813i	0.728760	+	1.00305i
$698$	−0.317205	−	3.01800i	−0.0120064	−	0.114233i
$699$	1.30054	−	4.00264i	0.0491908	−	0.151394i
$700$	−10.9554	+	1.15146i	−0.414076	+	0.0435211i
$701$	−14.5952	+	6.49822i	−0.551255	+	0.245434i	−0.663410	−	0.748256i	$-0.730891\pi$
$701$	−14.5952	+	6.49822i	−0.551255	+	0.245434i	0.112155	+	0.993691i	$0.464225\pi$
$702$	−2.21069	−	1.31133i	−0.0834371	−	0.0494931i
$703$	0.164288	−	1.56309i	0.00619622	−	0.0589531i
$704$	−7.17509	+	6.46048i	−0.270421	+	0.243488i
$705$	−0.250639	+	0.0532750i	−0.00943963	+	0.00200645i
$706$	0.992209	−	1.10196i	0.0373423	−	0.0414728i
$707$	7.81454	+	4.51173i	0.293896	+	0.169681i
$708$			1.68741i			0.0634168i
$709$	−5.81408	+	27.3531i	−0.218352	+	1.02727i	0.723262	+	0.690574i	$0.242642\pi$
$709$	−5.81408	+	27.3531i	−0.218352	+	1.02727i	−0.941614	+	0.336693i	$0.890692\pi$
$710$	−3.92190	+	0.412208i	−0.147186	+	0.0154699i
$711$	−18.4473	+	8.21329i	−0.691829	+	0.308022i
$712$	8.04519	+	13.9347i	0.301506	+	0.522224i
$713$	6.97798	+	1.52260i	0.261327	+	0.0570220i
$714$	1.17246			0.0438782
$715$	9.54319	+	4.38444i	0.356895	+	0.163969i
$716$	1.92020	+	18.2695i	0.0717612	+	0.682762i
$717$	−3.20422	−	2.88510i	−0.119664	−	0.107746i
$718$	−4.44194	+	7.69366i	−0.165772	+	0.287125i
$719$	14.4298	+	24.9931i	0.538140	+	0.932086i	0.999004	+	0.0446151i	$0.0142061\pi$
$719$	14.4298	+	24.9931i	0.538140	+	0.932086i	−0.460864	+	0.887471i	$0.652461\pi$
$720$	−1.18430	+	5.57169i	−0.0441362	+	0.207645i
$721$	−19.0505	+	17.1531i	−0.709476	+	0.638815i
$722$	3.17440	+	1.03142i	0.118139	+	0.0383856i
$723$	−3.85237	−	0.404901i	−0.143271	−	0.0150584i
$724$	11.2269	+	34.5529i	0.417245	+	1.28415i
$725$	−13.8565	−	10.0674i	−0.514618	−	0.373892i
$726$	−0.429643	+	0.0451573i	−0.0159455	+	0.00167594i
$727$	11.6133	+	12.8979i	0.430715	+	0.478358i	0.918961	−	0.394348i	$-0.129030\pi$
$727$	11.6133	+	12.8979i	0.430715	+	0.478358i	−0.488246	+	0.872706i	$0.662363\pi$
$728$	9.48869	+	2.13411i	0.351674	+	0.0790952i
$729$	19.4107	−	14.1027i	0.718917	−	0.522323i
$730$	4.15162	+	1.34894i	0.153658	+	0.0499266i
$731$	−3.46127	−	32.9318i	−0.128020	−	1.21803i
$732$	0.240147	−	2.28485i	0.00887610	−	0.0844505i
$733$	−28.0167	−	25.2264i	−1.03482	−	0.931758i	−0.0371061	−	0.999311i	$-0.511814\pi$
$733$	−28.0167	−	25.2264i	−1.03482	−	0.931758i	−0.997716	+	0.0675537i	$0.978481\pi$
$734$	−6.49090	+	8.93396i	−0.239584	+	0.329759i
$735$	0.855381	+	0.277930i	0.0315512	+	0.0102516i
$736$	6.17093	+	2.00506i	0.227464	+	0.0739074i
$737$	28.3630	−	31.5003i	1.04476	−	1.16033i
$738$	−7.09810			−0.261285
$739$	−31.5276	−	18.2024i	−1.15976	−	0.669588i	−0.208514	−	0.978019i	$-0.566863\pi$
$739$	−31.5276	−	18.2024i	−1.15976	−	0.669588i	−0.951247	+	0.308432i	$0.900196\pi$
$740$	−0.183670	−	0.565279i	−0.00675185	−	0.0207801i
$741$	−0.662136	+	2.94399i	−0.0243242	+	0.108150i
$742$	−0.112009	−	0.0813790i	−0.00411196	−	0.00298752i
$743$	4.43957	−	2.56319i	0.162872	−	0.0940342i	−0.416348	−	0.909205i	$-0.636690\pi$
$743$	4.43957	−	2.56319i	0.162872	−	0.0940342i	0.579220	+	0.815171i	$0.303357\pi$
$744$	2.48633	+	0.274892i	0.0911532	+	0.0100780i
$745$	−0.0974161	+	0.168730i	−0.00356905	+	0.00618177i
$746$	0.403272	−	0.555057i	0.0147648	−	0.0203221i
$747$	2.96656	−	6.66300i	0.108541	−	0.243786i
$748$	9.49355	−	44.6636i	0.347119	−	1.63306i
$749$	5.25440	−	3.03363i	0.191992	−	0.110846i
$750$	0.430589	+	0.745803i	0.0157229	+	0.0272329i
$751$	6.37254	+	19.6127i	0.232537	+	0.715676i	0.997439	+	0.0715285i	$0.0227877\pi$
$751$	6.37254	+	19.6127i	0.232537	+	0.715676i	−0.764901	+	0.644147i	$0.777212\pi$
$752$	0.746011	+	3.50970i	0.0272042	+	0.127986i
$753$	5.95806	−	1.26642i	0.217124	−	0.0461510i
$754$	4.07493	+	5.75002i	0.148400	+	0.209403i
$755$	−3.43020	+	3.80962i	−0.124838	+	0.138646i
$756$	2.07132	−	2.85093i	0.0753332	−	0.103687i
$757$	−1.35337	−	12.8764i	−0.0491890	−	0.468002i	−0.991195	−	0.132407i	$-0.957729\pi$
$757$	−1.35337	−	12.8764i	−0.0491890	−	0.468002i	0.942006	−	0.335595i	$-0.108937\pi$
$758$	3.40603	−	0.723974i	0.123713	−	0.0262959i
$759$	−0.685276	−	0.943201i	−0.0248739	−	0.0342360i
$760$	−5.03877	+	0.529596i	−0.182775	+	0.0192105i
$761$	−5.44325	−	25.6085i	−0.197318	−	0.928306i	−0.959667	−	0.281140i	$-0.909287\pi$
$761$	−5.44325	−	25.6085i	−0.197318	−	0.928306i	0.762349	−	0.647166i	$-0.224046\pi$
$762$	−0.173600	+	0.389913i	−0.00628888	+	0.0141251i
$763$	−2.02558	+	19.2721i	−0.0733310	+	0.697698i
$764$	24.5479	+	5.21781i	0.888111	+	0.188774i
$765$	−6.24677	−	14.0305i	−0.225852	−	0.507273i
$766$	16.1905	−	3.44140i	0.584987	−	0.124343i
$767$	−5.80175	−	13.4557i	−0.209489	−	0.485856i
$768$	0.160736	+	0.0341655i	0.00580006	+	0.00123284i
$769$			19.2256i			0.693294i	0.937996	+	0.346647i	$0.112680\pi$
$769$			19.2256i			0.693294i	−0.937996	+	0.346647i	$0.887320\pi$
$770$	1.04881	−	1.81659i	0.0377965	−	0.0654654i
$771$	−6.47859	−	1.37707i	−0.233321	−	0.0495939i
$772$	14.5542	−	1.52971i	0.523816	−	0.0550553i
$773$	9.94977	+	22.3475i	0.357868	+	0.803785i	0.999329	+	0.0366294i	$0.0116621\pi$
$773$	9.94977	+	22.3475i	0.357868	+	0.803785i	−0.641461	+	0.767156i	$0.721671\pi$
$774$	6.21858	+	3.59030i	0.223522	+	0.129051i
$775$	19.9825	−	14.3541i	0.717793	−	0.515614i
$776$	11.7553	−	20.3608i	0.421991	−	0.730910i
$777$	−0.0158579	+	0.150878i	−0.000568900	+	0.00541272i
$778$	7.56551	+	10.4130i	0.271237	+	0.373325i
$779$	5.19956	+	16.0026i	0.186294	+	0.573353i
$780$	0.224080	+	1.11892i	0.00802336	+	0.0400638i
$781$	19.6002	−	33.9485i	0.701349	−	1.21477i
$782$	−4.21140	+	1.36837i	−0.150600	+	0.0489327i
$783$	5.35938	−	1.13917i	0.191529	−	0.0407107i
$784$	3.89186	−	11.9779i	0.138995	−	0.427782i
$785$	6.50610	+	0.683819i	0.232213	+	0.0244065i
$786$	1.21290	−	0.394093i	0.0432625	−	0.0140568i
$787$	−18.6119	−	1.95619i	−0.663443	−	0.0697307i	−0.233179	−	0.972434i	$-0.574913\pi$
$787$	−18.6119	−	1.95619i	−0.663443	−	0.0697307i	−0.430264	+	0.902703i	$0.641580\pi$
$788$	6.67640	−	14.9954i	0.237837	−	0.534190i
$789$	6.33784	−	1.34715i	0.225633	−	0.0479598i
$790$	−2.40921	−	1.07265i	−0.0857159	−	0.0381632i
$791$	3.41417	−	7.66836i	0.121394	−	0.272655i
$792$	14.2163	+	15.7888i	0.505154	+	0.561030i
$793$	5.94092	+	19.0454i	0.210968	+	0.676323i
$794$	12.9546	−	5.76776i	0.459741	−	0.204690i
$795$	0.00724695	−	0.0340942i	0.000257023	−	0.00120920i
$796$	10.7814	−	4.80021i	0.382138	−	0.170139i
$797$	11.1498	−	34.3155i	0.394946	−	1.21552i	−0.534058	−	0.845448i	$-0.679334\pi$
$797$	11.1498	−	34.3155i	0.394946	−	1.21552i	0.929004	−	0.370071i	$-0.120666\pi$
$798$	0.573200	+	0.186244i	0.0202911	+	0.00659297i
$799$	−7.18951	−	6.47346i	−0.254347	−	0.229015i
$800$	19.3573	−	11.1760i	0.684385	−	0.395130i
$801$	−21.7135	+	12.5363i	−0.767210	+	0.442949i
$802$	−14.6514	−	3.11426i	−0.517360	−	0.109968i
$803$	−35.1055	+	25.5057i	−1.23885	+	0.900075i
$804$	4.58051	+	0.481431i	0.161542	+	0.0169788i
$805$	1.39632			0.0492138
$806$	−9.68059	+	2.96250i	−0.340984	+	0.104350i
$807$	−0.726412			−0.0255709
$808$	−11.8707	−	1.24766i	−0.417610	−	0.0438926i
$809$	−16.7679	+	12.1826i	−0.589529	+	0.428318i	−0.842147	−	0.539248i	$-0.818709\pi$
$809$	−16.7679	+	12.1826i	−0.589529	+	0.428318i	0.252618	+	0.967566i	$0.418709\pi$
$810$	3.19385	+	0.678874i	0.112220	+	0.0238532i
$811$	38.2341	−	22.0745i	1.34258	−	0.775139i	0.355395	−	0.934716i	$-0.384346\pi$
$811$	38.2341	−	22.0745i	1.34258	−	0.775139i	0.987186	+	0.159577i	$0.0510130\pi$
$812$	−8.36764	+	4.83106i	−0.293647	+	0.169537i
$813$	1.83004	+	1.64777i	0.0641822	+	0.0577899i
$814$	−0.818620	−	0.265986i	−0.0286926	−	0.00932279i
$815$	−2.55936	+	7.87692i	−0.0896506	+	0.275916i
$816$	3.77600	−	1.68118i	0.132186	−	0.0588532i
$817$	3.53901	−	16.6497i	0.123814	−	0.582500i
$818$	−3.05679	+	1.36097i	−0.106878	+	0.0475852i
$819$	−3.32545	+	14.7856i	−0.116200	+	0.516652i
$820$	4.25776	+	4.72872i	0.148687	+	0.165134i
$821$	−16.4158	+	36.8704i	−0.572914	+	1.28679i	0.362087	+	0.932144i	$0.382064\pi$
$821$	−16.4158	+	36.8704i	−0.572914	+	1.28679i	−0.935002	+	0.354643i	$0.884602\pi$
$822$	0.346620	+	0.154325i	0.0120897	+	0.00538270i
$823$	4.18247	−	0.889012i	0.145792	−	0.0309890i	−0.134438	−	0.990922i	$-0.542923\pi$
$823$	4.18247	−	0.889012i	0.145792	−	0.0309890i	0.280229	+	0.959933i	$0.409589\pi$
$824$	13.7922	−	30.9779i	0.480475	−	1.07917i
$825$	−3.99422	−	0.419809i	−0.139061	−	0.0146159i
$826$	−2.78346	+	0.904402i	−0.0968491	+	0.0314682i
$827$	2.37000	+	0.249097i	0.0824130	+	0.00866195i	0.145645	−	0.989337i	$-0.453474\pi$
$827$	2.37000	+	0.249097i	0.0824130	+	0.00866195i	−0.0632322	+	0.997999i	$0.520141\pi$
$828$	−2.03681	+	6.26865i	−0.0707840	+	0.217851i
$829$	−15.4823	+	3.29086i	−0.537722	+	0.114296i	−0.468764	−	0.883323i	$-0.655301\pi$
$829$	−15.4823	+	3.29086i	−0.537722	+	0.114296i	−0.0689576	+	0.997620i	$0.521967\pi$
$830$	0.905914	−	0.294349i	0.0314447	−	0.0102170i
$831$	−0.527953	+	0.914442i	−0.0183145	+	0.0317216i
$832$	8.93274	−	1.78891i	0.309687	−	0.0620193i
$833$	10.4934	+	32.2954i	0.363575	+	1.11897i
$834$	−0.273503	−	0.376445i	−0.00947065	−	0.0130352i
$835$	0.168226	−	1.60056i	0.00582169	−	0.0553897i
$836$	11.7360	−	20.3274i	0.405900	−	0.703039i
$837$	−0.864928	+	7.82304i	−0.0298963	+	0.270404i
$838$	−7.56972	−	4.37038i	−0.261492	−	0.150972i
$839$	−22.7028	−	50.9913i	−0.783787	−	1.76041i	−0.636434	−	0.771331i	$-0.719591\pi$
$839$	−22.7028	−	50.9913i	−0.783787	−	1.76041i	−0.147353	−	0.989084i	$-0.547075\pi$
$840$	0.486369	−	0.0511195i	0.0167813	−	0.00176379i
$841$	13.6716	+	2.90600i	0.471436	+	0.100207i
$842$	−9.97446	+	17.2763i	−0.343743	+	0.595380i
$843$			5.80513i			0.199939i
$844$	25.8582	+	5.49633i	0.890076	+	0.189192i
$845$	−5.63399	−	8.15201i	−0.193815	−	0.280438i
$846$	2.05206	−	0.436179i	0.0705512	−	0.0149961i
$847$	2.09195	+	4.69860i	0.0718803	+	0.161446i
$848$	−0.477421	−	0.101479i	−0.0163947	−	0.00348480i
$849$	−0.687572	+	6.54181i	−0.0235974	+	0.224514i
$850$	−6.20446	+	13.9355i	−0.212811	+	0.477982i
$851$	−0.119128	−	0.560452i	−0.00408365	−	0.0192121i
$852$	4.23607	−	0.445229i	0.145125	−	0.0152533i
$853$	−6.92479	−	9.53116i	−0.237100	−	0.326341i	0.673841	−	0.738876i	$-0.264643\pi$
$853$	−6.92479	−	9.53116i	−0.237100	−	0.326341i	−0.910941	+	0.412536i	$0.864643\pi$
$854$	3.89768	−	0.828477i	0.133376	−	0.0283499i
$855$	−0.825237	−	7.85161i	−0.0282225	−	0.268519i
$856$	−4.71738	+	6.49291i	−0.161237	+	0.221923i
$857$	−13.6064	+	15.1114i	−0.464784	+	0.516195i	−0.929278	−	0.369381i	$-0.879570\pi$
$857$	−13.6064	+	15.1114i	−0.464784	+	0.516195i	0.464494	+	0.885576i	$0.346236\pi$
$858$	1.50166	+	0.689910i	0.0512659	+	0.0235531i
$859$	0.908645	−	0.193139i	0.0310026	−	0.00658980i	−0.192384	−	0.981320i	$-0.561622\pi$
$859$	0.908645	−	0.193139i	0.0310026	−	0.00658980i	0.223387	+	0.974730i	$0.428289\pi$
$860$	−1.33834	−	6.29641i	−0.0456372	−	0.214706i
$861$	−0.501890	−	1.54466i	−0.0171044	−	0.0526418i
$862$	−5.27374	−	9.13438i	−0.179624	−	0.311118i
$863$	49.9839	−	28.8582i	1.70147	−	0.982346i	0.757199	−	0.653184i	$-0.226567\pi$
$863$	49.9839	−	28.8582i	1.70147	−	0.982346i	0.944274	−	0.329162i	$-0.106766\pi$
$864$	−1.48665	+	6.99412i	−0.0505767	+	0.237945i
$865$	−7.63469	+	17.1478i	−0.259587	+	0.583043i
$866$	8.60666	−	11.8460i	0.292466	−	0.402545i
$867$	−3.55057	+	6.14977i	−0.120584	+	0.208857i
$868$	−2.81245	−	13.5916i	−0.0954606	−	0.461330i
$869$	22.7030	−	13.1076i	0.770145	−	0.444644i
$870$	0.286699	+	0.208299i	0.00971999	+	0.00706199i
$871$	−38.1810	+	11.9100i	−1.29371	+	0.403554i
$872$	−7.92112	−	24.3787i	−0.268243	−	0.825567i
$873$	31.7270	+	18.3176i	1.07380	+	0.619956i
$874$	−2.27626			−0.0769958
$875$	6.86040	−	7.61925i	0.231924	−	0.257578i
$876$	−4.48418	−	1.45700i	−0.151507	−	0.0492275i
$877$	22.9967	+	7.47208i	0.776543	+	0.252314i	0.670363	−	0.742033i	$-0.266138\pi$
$877$	22.9967	+	7.47208i	0.776543	+	0.252314i	0.106179	+	0.994347i	$0.466138\pi$
$878$	−0.815542	+	1.12250i	−0.0275232	+	0.0378824i
$879$	−2.10629	−	1.89651i	−0.0710433	−	0.0639677i
$880$	0.772975	−	7.35436i	0.0260570	−	0.247915i
$881$	−0.140846	−	1.34006i	−0.00474523	−	0.0451478i	0.991893	−	0.127075i	$-0.0405590\pi$
$881$	−0.140846	−	1.34006i	−0.00474523	−	0.0451478i	−0.996638	+	0.0819276i	$0.973892\pi$
$882$	−7.00326	−	2.27550i	−0.235812	−	0.0766200i
$883$	−34.0349	+	24.7278i	−1.14537	+	0.832158i	−0.987858	−	0.155360i	$-0.950346\pi$
$883$	−34.0349	+	24.7278i	−1.14537	+	0.832158i	−0.157509	+	0.987518i	$0.550346\pi$
$884$	−29.2045	+	31.6758i	−0.982255	+	1.06537i
$885$	−0.493030	−	0.547565i	−0.0165730	−	0.0184062i
$886$	−19.1674	+	2.01458i	−0.643942	+	0.0676810i
$887$	16.6704	+	12.1118i	0.559738	+	0.406673i	0.831363	−	0.555730i	$-0.187561\pi$
$887$	16.6704	+	12.1118i	0.559738	+	0.406673i	−0.271625	+	0.962403i	$0.587561\pi$
$888$	−0.0620131	−	0.190857i	−0.00208102	−	0.00640473i
$889$	5.05356	+	0.531150i	0.169491	+	0.0178142i
$890$	−3.11421	−	1.01187i	−0.104388	−	0.0339179i
$891$	−24.1207	+	21.7184i	−0.808075	+	0.727594i
$892$	3.84300	−	18.0799i	0.128673	−	0.605359i
$893$	−2.48655	−	4.30684i	−0.0832094	−	0.144123i
$894$	−0.0153289	+	0.0265504i	−0.000512674	+	0.000887977i
$895$	−5.96110	−	5.36739i	−0.199257	−	0.179412i
$896$	−1.70024	−	16.1767i	−0.0568012	−	0.540427i
$897$	0.102081	+	1.09531i	0.00340840	+	0.0365715i
$898$	14.4696			0.482857
$899$	10.8908	−	18.6306i	0.363229	−	0.621366i
$900$	11.3529	+	19.6639i	0.378431	+	0.655462i
$901$	1.20223	−	0.535267i	0.0400521	−	0.0178323i
$902$	9.16441	−	0.963218i	0.305141	−	0.0320717i
$903$	−0.341604	+	1.60712i	−0.0113679	+	0.0534817i
$904$			11.1035i			0.369298i
$905$	−13.7388	−	7.93211i	−0.456693	−	0.263672i
$906$	−0.539757	+	0.599461i	−0.0179322	+	0.0199158i
$907$	16.9443	−	3.60163i	0.562627	−	0.119590i	0.0821858	−	0.996617i	$-0.473810\pi$
$907$	16.9443	−	3.60163i	0.562627	−	0.119590i	0.480441	+	0.877027i	$0.340477\pi$
$908$	1.47797	−	1.33077i	0.0490483	−	0.0441633i
$909$	1.94415	−	18.4974i	0.0644835	−	0.613520i
$910$	−1.72561	+	0.969339i	−0.0572035	+	0.0321333i
$911$	−4.13464	+	1.84086i	−0.136987	+	0.0609904i	−0.474085	−	0.880479i	$-0.657221\pi$
$911$	−4.13464	+	1.84086i	−0.136987	+	0.0609904i	0.337098	+	0.941469i	$0.390554\pi$
$912$	2.11309	−	0.222095i	0.0699714	−	0.00735429i
$913$	−2.92597	+	9.00522i	−0.0968355	+	0.298029i
$914$	−1.26674	−	12.0522i	−0.0418999	−	0.398651i
$915$	0.589662	+	0.811600i	0.0194936	+	0.0268307i
$916$	−0.518700	−	2.44029i	−0.0171383	−	0.0806294i
$917$	−8.92444	−	12.2834i	−0.294711	−	0.405635i
$918$	−1.98481	−	4.45795i	−0.0655084	−	0.147134i
$919$	0.405916	+	1.24928i	0.0133899	+	0.0412099i	0.957528	−	0.288339i	$-0.0931032\pi$
$919$	0.405916	+	1.24928i	0.0133899	+	0.0412099i	−0.944138	+	0.329549i	$0.893103\pi$
$920$	−1.68735	+	0.751256i	−0.0556302	+	0.0247682i
$921$	−3.70957	+	3.34012i	−0.122235	+	0.110061i
$922$	−1.21967	+	3.75375i	−0.0401676	+	0.123623i
$923$	−32.2482	+	18.1150i	−1.06146	+	0.596263i
$924$	−1.13283	+	1.96211i	−0.0372672	+	0.0645487i
$925$	−1.70937	−	0.986903i	−0.0562036	−	0.0324492i
$926$	10.9929	−	12.2089i	0.361250	−	0.401208i
$927$	48.2709	+	21.4916i	1.58542	+	0.705877i
$928$	11.5237	−	15.8610i	0.378283	−	0.520663i
$929$	16.1664	+	9.33366i	0.530401	+	0.306227i	0.741180	−	0.671306i	$-0.234267\pi$
$929$	16.1664	+	9.33366i	0.530401	+	0.306227i	−0.210778	+	0.977534i	$0.567600\pi$
$930$	−0.413449	+	0.296994i	−0.0135575	+	0.00973881i
$931$			17.4557i			0.572086i
$932$	28.2189	−	12.5638i	0.924339	−	0.411542i
$933$	−4.62272	+	3.35860i	−0.151341	+	0.109956i
$934$	2.35495	+	2.12041i	0.0770565	+	0.0693819i
$935$	9.96920	+	17.2672i	0.326028	+	0.564697i
$936$	−3.93650	−	19.6565i	−0.128668	−	0.642493i
$937$	6.58530	+	1.39975i	0.215132	+	0.0457278i	0.314217	−	0.949351i	$-0.398258\pi$
$937$	6.58530	+	1.39975i	0.215132	+	0.0457278i	−0.0990845	+	0.995079i	$0.531591\pi$
$938$	1.66087	+	7.81380i	0.0542295	+	0.255130i
$939$	−3.60282	−	4.00133i	−0.117573	−	0.130579i
$940$	−1.52150	−	1.10543i	−0.0496258	−	0.0360553i
$941$	−13.9492	−	12.5599i	−0.454729	−	0.409440i	0.409680	−	0.912230i	$-0.365641\pi$
$941$	−13.9492	−	12.5599i	−0.454729	−	0.409440i	−0.864409	+	0.502789i	$0.832307\pi$
$942$	1.02376	+	0.107602i	0.0333560	+	0.00350586i
$943$	3.60551	+	4.96256i	0.117412	+	0.161603i
$944$	−7.66755	+	6.90389i	−0.249558	+	0.224703i
$945$	0.160844	+	1.53032i	0.00523224	+	0.0497815i
$946$	−8.51606	−	3.79160i	−0.276881	−	0.123275i
$947$	23.9145	+	7.77029i	0.777117	+	0.252501i	0.670609	−	0.741811i	$-0.266033\pi$
$947$	23.9145	+	7.77029i	0.777117	+	0.252501i	0.106508	+	0.994312i	$0.466033\pi$
$948$	2.60220	+	1.15858i	0.0845157	+	0.0376288i
$949$	40.7671	−	3.79943i	1.32336	−	0.123335i
$950$	−5.24691	+	5.82729i	−0.170232	+	0.189062i
$951$	−2.39654	−	5.38271i	−0.0777130	−	0.174546i
$952$	12.3550	+	13.7216i	0.400429	+	0.444721i
$953$	15.9050	+	17.6643i	0.515212	+	0.572201i	0.943471	−	0.331455i	$-0.107539\pi$
$953$	15.9050	+	17.6643i	0.515212	+	0.572201i	−0.428259	+	0.903656i	$0.640873\pi$
$954$	−0.0593329	+	0.279139i	−0.00192097	+	0.00903747i
$955$	−9.49033	+	5.47924i	−0.307100	+	0.177304i
$956$		−	31.6460i		−	1.02350i
$957$	−3.35028	+	1.08857i	−0.108299	+	0.0351886i
$958$	−7.46581	−	3.32399i	−0.241209	−	0.107393i
$959$	0.472175	−	4.49244i	0.0152473	−	0.145069i
$960$	0.396720	−	0.229047i	0.0128041	−	0.00739245i
$961$	20.4933	+	23.2599i	0.661074	+	0.750321i
$962$	0.536293	+	0.609923i	0.0172908	+	0.0196647i
$963$	−10.1175	−	7.35080i	−0.326032	−	0.236876i
$964$	−16.7110	−	23.0007i	−0.538224	−	0.740802i
$965$	−4.27588	+	4.74884i	−0.137645	+	0.152871i
$966$	0.219717			0.00706929
$967$	−38.1026	−	21.9985i	−1.22530	−	0.707425i	−0.259254	−	0.965809i	$-0.583477\pi$
$967$	−38.1026	−	21.9985i	−1.22530	−	0.707425i	−0.966042	+	0.258384i	$0.916810\pi$
$968$	−5.05593	−	4.55238i	−0.162504	−	0.146319i
$969$	−4.25733	+	3.83332i	−0.136765	+	0.123144i
$970$	0.994759	+	4.67997i	0.0319398	+	0.150265i
$971$	33.6343	+	24.4368i	1.07938	+	0.784213i	0.977574	−	0.210592i	$-0.0675390\pi$
$971$	33.6343	+	24.4368i	1.07938	+	0.784213i	0.101802	+	0.994805i	$0.467539\pi$
$972$	−10.6911	−	2.27247i	−0.342918	−	0.0728894i
$973$	−3.25618	+	4.48174i	−0.104388	+	0.143678i
$974$	7.99270	+	3.55858i	0.256103	+	0.114024i
$975$	3.03933	+	2.26343i	0.0973365	+	0.0724877i
$976$	11.3648	−	8.25703i	0.363779	−	0.264301i
$977$	2.63892	−	5.92712i	0.0844266	−	0.189625i	−0.866399	−	0.499353i	$-0.833571\pi$
$977$	2.63892	−	5.92712i	0.0844266	−	0.189625i	0.950825	+	0.309728i	$0.100238\pi$
$978$	−0.402727	+	1.23947i	−0.0128778	+	0.0396338i
$979$	26.3333	−	19.1323i	0.841617	−	0.611471i
$980$	2.68495	+	6.03049i	0.0857675	+	0.192637i
$981$	37.9879	−	12.3430i	1.21286	−	0.394082i
$982$	11.6634	−	16.0533i	0.372194	−	0.512282i
$983$	−0.0602632	−	0.283516i	−0.00192210	−	0.00904277i	0.977176	−	0.212431i	$-0.0681380\pi$
$983$	−0.0602632	−	0.283516i	−0.00192210	−	0.00904277i	−0.979098	+	0.203388i	$0.934805\pi$
$984$	1.43756	+	1.59657i	0.0458278	+	0.0508969i
$985$	2.21489	+	6.81673i	0.0705723	+	0.217199i
$986$			13.3798i			0.426099i
$987$	0.240016	+	0.415719i	0.00763978	+	0.0132325i
$988$	−19.3094	+	10.8468i	−0.614313	+	0.345082i
$989$	−0.648637	−	6.17137i	−0.0206254	−	0.196238i
$990$	−4.29996	−	0.451944i	−0.136662	−	0.0143637i
$991$	−15.0049	−	25.9893i	−0.476648	−	0.825578i	0.522994	−	0.852336i	$-0.324815\pi$
$991$	−15.0049	−	25.9893i	−0.476648	−	0.825578i	−0.999642	+	0.0267582i	$0.991482\pi$
$992$	16.4305	+	22.8732i	0.521670	+	0.726224i
$993$			7.94632i			0.252169i
$994$	3.00483	+	6.74896i	0.0953075	+	0.214064i
$995$	−2.09605	+	4.70780i	−0.0664491	+	0.149247i
$996$	−0.978483	+	0.317928i	−0.0310044	+	0.0100739i
$997$	−38.9359			−1.23311			−0.616556	−	0.787311i	$-0.711473\pi$
$997$	−38.9359			−1.23311			−0.616556	+	0.787311i	$0.711473\pi$
$998$	3.83630			0.121436
$999$	0.600516	−	0.195120i	0.0189995	−	0.00617331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.bp.a.10.15	✓	280
13.4	even	6		403.2.bt.a.134.15	yes	280
31.28	even	15		403.2.bt.a.400.15	yes	280
403.121	even	30	inner	403.2.bp.a.121.15	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.bp.a.10.15	✓	280	1.1	even	1	trivial
403.2.bp.a.121.15	yes	280	403.121	even	30	inner
403.2.bt.a.134.15	yes	280	13.4	even	6
403.2.bt.a.400.15	yes	280	31.28	even	15

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bp (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.501537 - 0.0527137i) q^{2} +(-0.192422 + 0.139802i) q^{3} +(-1.70753 - 0.362948i) q^{4} +(0.660141 - 0.381132i) q^{5} +(0.103876 - 0.0599729i) q^{6} +(-1.06122 - 0.955523i) q^{7} +(1.79650 + 0.583717i) q^{8} +(-0.909570 + 2.79937i) q^{9} +O(q^{10})\)	\(q+(-0.501537 - 0.0527137i) q^{2} +(-0.192422 + 0.139802i) q^{3} +(-1.70753 - 0.362948i) q^{4} +(0.660141 - 0.381132i) q^{5} +(0.103876 - 0.0599729i) q^{6} +(-1.06122 - 0.955523i) q^{7} +(1.79650 + 0.583717i) q^{8} +(-0.909570 + 2.79937i) q^{9} +(-0.351176 + 0.156354i) q^{10} +(0.794476 - 3.73772i) q^{11} +(0.379307 - 0.168879i) q^{12} +(-2.44401 + 2.65082i) q^{13} +(0.481870 + 0.535171i) q^{14} +(-0.0737420 + 0.165627i) q^{15} +(2.31928 + 1.03261i) q^{16} +(-6.69556 + 1.42319i) q^{17} +(0.603748 - 1.35604i) q^{18} +(-3.49945 - 0.367807i) q^{19} +(-1.26554 + 0.411200i) q^{20} +(0.337785 + 0.0355027i) q^{21} +(-0.595488 + 1.83272i) q^{22} +(-1.25474 + 0.266703i) q^{23} +(-0.427289 + 0.138835i) q^{24} +(-2.20948 + 3.82693i) q^{25} +(1.36549 - 1.20065i) q^{26} +(-0.436833 - 1.34443i) q^{27} +(1.46526 + 2.01675i) q^{28} +(-0.405146 + 3.85471i) q^{29} +(0.0457152 - 0.0791811i) q^{30} +(-5.07412 - 2.29202i) q^{31} +(-4.38052 - 2.52910i) q^{32} +(0.369667 + 0.830287i) q^{33} +(3.43310 - 0.360833i) q^{34} +(-1.06473 - 0.226316i) q^{35} +(2.56915 - 4.44989i) q^{36} +0.446668i q^{37} +(1.73571 + 0.368937i) q^{38} +(0.0996888 - 0.851752i) q^{39} +(1.40841 - 0.299367i) q^{40} +(-1.94497 - 4.36847i) q^{41} +(-0.167540 - 0.0356118i) q^{42} +(-0.505653 + 4.81097i) q^{43} +(-2.71319 + 6.09392i) q^{44} +(0.466486 + 2.19464i) q^{45} +(0.643357 - 0.0676196i) q^{46} +(0.830734 + 1.14341i) q^{47} +(-0.590641 + 0.125545i) q^{48} +(-0.518544 - 4.93362i) q^{49} +(1.30987 - 1.80288i) q^{50} +(1.08941 - 1.20991i) q^{51} +(5.13533 - 3.63932i) q^{52} +(-0.188052 + 0.0399718i) q^{53} +(0.148218 + 0.697311i) q^{54} +(-0.900098 - 2.77022i) q^{55} +(-1.34871 - 2.33604i) q^{56} +(0.724789 - 0.418457i) q^{57} +(0.406392 - 1.91192i) q^{58} +(-1.65300 + 3.71270i) q^{59} +(0.186031 - 0.256050i) q^{60} +(2.76664 - 4.79196i) q^{61} +(2.42404 + 1.41701i) q^{62} +(3.64011 - 2.10162i) q^{63} +(-2.04413 - 1.48515i) q^{64} +(-0.603076 + 2.68140i) q^{65} +(-0.141634 - 0.435906i) q^{66} +(9.60659 + 5.54637i) q^{67} +11.9494 q^{68} +(0.204153 - 0.226735i) q^{69} +(0.522073 + 0.169632i) q^{70} +(9.75650 + 3.17008i) q^{71} +(-3.26807 + 4.49812i) q^{72} +(-8.43897 - 7.59848i) q^{73} +(0.0235455 - 0.224021i) q^{74} +(-0.109863 - 1.04527i) q^{75} +(5.84193 + 1.89816i) q^{76} +(-4.41458 + 3.20738i) q^{77} +(-0.0948967 + 0.421931i) q^{78} +(4.59051 + 5.09828i) q^{79} +(1.92461 - 0.202285i) q^{80} +(-6.87184 - 4.99269i) q^{81} +(0.745196 + 2.29348i) q^{82} +(-2.46434 - 0.259012i) q^{83} +(-0.563894 - 0.183220i) q^{84} +(-3.87759 + 3.49140i) q^{85} +(0.507208 - 2.38622i) q^{86} +(-0.460939 - 0.798369i) q^{87} +(3.60904 - 6.25104i) q^{88} +(6.33024 + 5.69977i) q^{89} +(-0.118272 - 1.12529i) q^{90} +(5.12654 - 0.477785i) q^{91} +2.23931 q^{92} +(1.29680 - 0.268340i) q^{93} +(-0.356371 - 0.617252i) q^{94} +(-2.45031 + 1.09095i) q^{95} +(1.19648 - 0.125755i) q^{96} +(2.58776 - 12.1744i) q^{97} +2.50173i q^{98} +(9.74061 + 5.62374i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 9 q^{2} - 9 q^{3} - 35 q^{4} - 21 q^{6} - 3 q^{7} - 45 q^{8} - 63 q^{9}+O(q^{10}) \) 280 * q - 9 * q^2 - 9 * q^3 - 35 * q^4 - 21 * q^6 - 3 * q^7 - 45 * q^8 - 63 * q^9	\( 280 q - 9 q^{2} - 9 q^{3} - 35 q^{4} - 21 q^{6} - 3 q^{7} - 45 q^{8} - 63 q^{9} - 24 q^{10} - 9 q^{11} - 8 q^{12} - 6 q^{13} + 4 q^{14} + 23 q^{16} - 21 q^{17} - 45 q^{18} - 27 q^{19} - 75 q^{20} + 76 q^{21} - 22 q^{22} - 10 q^{23} - 15 q^{24} + 96 q^{25} - 15 q^{26} - 24 q^{27} + 5 q^{28} + 13 q^{29} + 36 q^{30} - 2 q^{31} - 141 q^{32} - 3 q^{33} + 9 q^{34} + 32 q^{35} + 97 q^{36} - 49 q^{38} + 15 q^{39} - 75 q^{40} - 33 q^{41} - 16 q^{42} + 21 q^{43} - 18 q^{44} - 27 q^{45} + 51 q^{46} - 68 q^{48} - 24 q^{49} + 90 q^{50} + 47 q^{51} + 73 q^{52} + 12 q^{53} - 33 q^{54} - 65 q^{55} + 25 q^{56} + 105 q^{57} - 3 q^{58} + 12 q^{59} - 90 q^{60} - 57 q^{61} + 12 q^{62} + 201 q^{63} + 13 q^{64} + 11 q^{65} + 22 q^{66} - 45 q^{67} + 142 q^{68} - 139 q^{69} - 15 q^{71} - 15 q^{72} - 9 q^{73} + 4 q^{74} - 75 q^{75} - 80 q^{76} - 24 q^{77} - 104 q^{78} + 54 q^{79} - 21 q^{80} - 107 q^{81} + 43 q^{82} - 54 q^{83} - 15 q^{84} - 117 q^{85} - 84 q^{86} - 21 q^{87} + 49 q^{88} - 9 q^{89} + 11 q^{90} - 10 q^{91} + 266 q^{92} - 22 q^{93} + 33 q^{94} + 75 q^{95} - 204 q^{96} - 10 q^{97} + 168 q^{99}+O(q^{100}) \) 280 * q - 9 * q^2 - 9 * q^3 - 35 * q^4 - 21 * q^6 - 3 * q^7 - 45 * q^8 - 63 * q^9 - 24 * q^10 - 9 * q^11 - 8 * q^12 - 6 * q^13 + 4 * q^14 + 23 * q^16 - 21 * q^17 - 45 * q^18 - 27 * q^19 - 75 * q^20 + 76 * q^21 - 22 * q^22 - 10 * q^23 - 15 * q^24 + 96 * q^25 - 15 * q^26 - 24 * q^27 + 5 * q^28 + 13 * q^29 + 36 * q^30 - 2 * q^31 - 141 * q^32 - 3 * q^33 + 9 * q^34 + 32 * q^35 + 97 * q^36 - 49 * q^38 + 15 * q^39 - 75 * q^40 - 33 * q^41 - 16 * q^42 + 21 * q^43 - 18 * q^44 - 27 * q^45 + 51 * q^46 - 68 * q^48 - 24 * q^49 + 90 * q^50 + 47 * q^51 + 73 * q^52 + 12 * q^53 - 33 * q^54 - 65 * q^55 + 25 * q^56 + 105 * q^57 - 3 * q^58 + 12 * q^59 - 90 * q^60 - 57 * q^61 + 12 * q^62 + 201 * q^63 + 13 * q^64 + 11 * q^65 + 22 * q^66 - 45 * q^67 + 142 * q^68 - 139 * q^69 - 15 * q^71 - 15 * q^72 - 9 * q^73 + 4 * q^74 - 75 * q^75 - 80 * q^76 - 24 * q^77 - 104 * q^78 + 54 * q^79 - 21 * q^80 - 107 * q^81 + 43 * q^82 - 54 * q^83 - 15 * q^84 - 117 * q^85 - 84 * q^86 - 21 * q^87 + 49 * q^88 - 9 * q^89 + 11 * q^90 - 10 * q^91 + 266 * q^92 - 22 * q^93 + 33 * q^94 + 75 * q^95 - 204 * q^96 - 10 * q^97 + 168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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