LMFDB - Embedded newform 546.2.ch.a.305.37

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(137,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 11]))

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

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

chi := DirichletCharacter("546.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.ch (of order $12$, degree $4$, 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:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			305.37
Character	$\chi$	$=$	546.305
Dual form			546.2.ch.a.401.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(1.63694 - 0.566057i) q^{3} +1.00000i q^{4} +(0.469106 - 1.75073i) q^{5} +(1.55776 + 0.757230i) q^{6} +(0.107711 - 2.64356i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.35916 - 1.85321i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(1.63694 - 0.566057i) q^{3} +1.00000i q^{4} +(0.469106 - 1.75073i) q^{5} +(1.55776 + 0.757230i) q^{6} +(0.107711 - 2.64356i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.35916 - 1.85321i) q^{9} +(1.56966 - 0.906243i) q^{10} +(0.871755 + 0.233586i) q^{11} +(0.566057 + 1.63694i) q^{12} +(-0.922476 - 3.48555i) q^{13} +(1.94544 - 1.79311i) q^{14} +(-0.223113 - 3.13138i) q^{15} -1.00000 q^{16} -6.58628 q^{17} +(2.97859 + 0.357762i) q^{18} +(1.69870 + 6.33965i) q^{19} +(1.75073 + 0.469106i) q^{20} +(-1.32009 - 4.38832i) q^{21} +(0.451253 + 0.781594i) q^{22} -1.37581 q^{23} +(-0.757230 + 1.55776i) q^{24} +(1.48514 + 0.857446i) q^{25} +(1.81236 - 3.11694i) q^{26} +(2.81278 - 4.36901i) q^{27} +(2.64356 + 0.107711i) q^{28} +(5.47519 + 3.16110i) q^{29} +(2.05646 - 2.37199i) q^{30} +(1.22720 + 4.57998i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.55924 - 0.111097i) q^{33} +(-4.65721 - 4.65721i) q^{34} +(-4.57762 - 1.42868i) q^{35} +(1.85321 + 2.35916i) q^{36} +(7.02220 + 7.02220i) q^{37} +(-3.28164 + 5.68397i) q^{38} +(-3.48306 - 5.18346i) q^{39} +(0.906243 + 1.56966i) q^{40} +(-12.1581 + 3.25776i) q^{41} +(2.16957 - 4.03646i) q^{42} +(3.99588 - 2.30702i) q^{43} +(-0.233586 + 0.871755i) q^{44} +(-2.13776 - 4.99959i) q^{45} +(-0.972841 - 0.972841i) q^{46} +(3.58728 + 0.961209i) q^{47} +(-1.63694 + 0.566057i) q^{48} +(-6.97680 - 0.569480i) q^{49} +(0.443847 + 1.65646i) q^{50} +(-10.7814 + 3.72822i) q^{51} +(3.48555 - 0.922476i) q^{52} +(4.00068 + 2.30979i) q^{53} +(5.07829 - 1.10042i) q^{54} +(0.817891 - 1.41663i) q^{55} +(1.79311 + 1.94544i) q^{56} +(6.36928 + 9.41607i) q^{57} +(1.63631 + 6.10678i) q^{58} +(-3.79190 + 3.79190i) q^{59} +(3.13138 - 0.223113i) q^{60} +(-0.159236 + 0.275805i) q^{61} +(-2.37077 + 4.10630i) q^{62} +(-4.64495 - 6.43618i) q^{63} -1.00000i q^{64} +(-6.53498 - 0.0200864i) q^{65} +(1.18110 + 1.02399i) q^{66} +(1.50744 + 0.403918i) q^{67} -6.58628i q^{68} +(-2.25211 + 0.778785i) q^{69} +(-2.22664 - 4.24710i) q^{70} +(0.215183 - 0.803072i) q^{71} +(-0.357762 + 2.97859i) q^{72} +(9.62392 - 2.57872i) q^{73} +9.93089i q^{74} +(2.91645 + 0.562915i) q^{75} +(-6.33965 + 1.69870i) q^{76} +(0.711396 - 2.27937i) q^{77} +(1.20237 - 6.12816i) q^{78} +(-3.91647 - 6.78352i) q^{79} +(-0.469106 + 1.75073i) q^{80} +(2.13125 - 8.74401i) q^{81} +(-10.9007 - 6.29352i) q^{82} +(-7.59633 - 7.59633i) q^{83} +(4.38832 - 1.32009i) q^{84} +(-3.08967 + 11.5308i) q^{85} +(4.45683 + 1.19420i) q^{86} +(10.7519 + 2.07527i) q^{87} +(-0.781594 + 0.451253i) q^{88} +(-9.27381 + 9.27381i) q^{89} +(2.02362 - 5.04687i) q^{90} +(-9.31361 + 2.06319i) q^{91} -1.37581i q^{92} +(4.60139 + 6.80250i) q^{93} +(1.85691 + 3.21627i) q^{94} +11.8959 q^{95} +(-1.55776 - 0.757230i) q^{96} +(8.51978 + 2.28287i) q^{97} +(-4.53066 - 5.33602i) q^{98} +(2.48949 - 1.06448i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 8 q^{7}+O(q^{10}) $ 152 * q + 8 * q^7	$ 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	1.63694	−	0.566057i	0.945089	−	0.326813i
$3$	1.63694	−	0.566057i	0.945089	−	0.326813i
$4$			1.00000i			0.500000i
$5$	0.469106	−	1.75073i	0.209791	−	0.782949i	−0.778145	−	0.628085i	$-0.783839\pi$
$5$	0.469106	−	1.75073i	0.209791	−	0.782949i	0.987936	−	0.154865i	$-0.0494942\pi$
$6$	1.55776	+	0.757230i	0.635951	+	0.309138i
$7$	0.107711	−	2.64356i	0.0407109	−	0.999171i
$7$	0.107711	−	2.64356i	0.0407109	−	0.999171i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.35916	−	1.85321i	0.786386	−	0.617735i
$10$	1.56966	−	0.906243i	0.496370	−	0.286579i
$11$	0.871755	+	0.233586i	0.262844	+	0.0704288i	0.387834	−	0.921729i	$-0.373223\pi$
$11$	0.871755	+	0.233586i	0.262844	+	0.0704288i	−0.124990	+	0.992158i	$0.539890\pi$
$12$	0.566057	+	1.63694i	0.163407	+	0.472544i
$13$	−0.922476	−	3.48555i	−0.255849	−	0.966717i
$13$	−0.922476	−	3.48555i	−0.255849	−	0.966717i
$14$	1.94544	−	1.79311i	0.519941	−	0.479230i
$15$	−0.223113	−	3.13138i	−0.0576076	−	0.808519i
$16$	−1.00000			−0.250000
$17$	−6.58628			−1.59741			−0.798704	−	0.601724i	$-0.794481\pi$
$17$	−6.58628			−1.59741			−0.798704	+	0.601724i	$0.794481\pi$
$18$	2.97859	+	0.357762i	0.702061	+	0.0843252i
$19$	1.69870	+	6.33965i	0.389709	+	1.45441i	0.830608	+	0.556858i	$0.187993\pi$
$19$	1.69870	+	6.33965i	0.389709	+	1.45441i	−0.440899	+	0.897557i	$0.645340\pi$
$20$	1.75073	+	0.469106i	0.391475	+	0.104895i
$21$	−1.32009	−	4.38832i	−0.288067	−	0.957610i
$22$	0.451253	+	0.781594i	0.0962076	+	0.166636i
$23$	−1.37581			−0.286875			−0.143438	−	0.989659i	$-0.545816\pi$
$23$	−1.37581			−0.286875			−0.143438	+	0.989659i	$0.545816\pi$
$24$	−0.757230	+	1.55776i	−0.154569	+	0.317976i
$25$	1.48514	+	0.857446i	0.297028	+	0.171489i
$26$	1.81236	−	3.11694i	0.355434	−	0.611283i
$27$	2.81278	−	4.36901i	0.541320	−	0.840816i
$28$	2.64356	+	0.107711i	0.499585	+	0.0203555i
$29$	5.47519	+	3.16110i	1.01672	+	0.587002i	0.913151	−	0.407621i	$-0.133642\pi$
$29$	5.47519	+	3.16110i	1.01672	+	0.587002i	0.103565	+	0.994623i	$0.466975\pi$
$30$	2.05646	−	2.37199i	0.375456	−	0.433063i
$31$	1.22720	+	4.57998i	0.220412	+	0.822589i	0.984191	+	0.177111i	$0.0566752\pi$
$31$	1.22720	+	4.57998i	0.220412	+	0.822589i	−0.763779	+	0.645478i	$0.776658\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	1.55924	−	0.111097i	0.271428	−	0.0193394i
$34$	−4.65721	−	4.65721i	−0.798704	−	0.798704i
$35$	−4.57762	−	1.42868i	−0.773759	−	0.241491i
$36$	1.85321	+	2.35916i	0.308868	+	0.393193i
$37$	7.02220	+	7.02220i	1.15444	+	1.15444i	0.985652	+	0.168790i	$0.0539860\pi$
$37$	7.02220	+	7.02220i	1.15444	+	1.15444i	0.168790	+	0.985652i	$0.446014\pi$
$38$	−3.28164	+	5.68397i	−0.532353	+	0.922062i
$39$	−3.48306	−	5.18346i	−0.557736	−	0.830018i
$40$	0.906243	+	1.56966i	0.143290	+	0.248185i
$41$	−12.1581	+	3.25776i	−1.89878	+	0.508777i	−0.901708	+	0.432346i	$0.857686\pi$
$41$	−12.1581	+	3.25776i	−1.89878	+	0.508777i	−0.997075	+	0.0764312i	$0.975647\pi$
$42$	2.16957	−	4.03646i	0.334772	−	0.622839i
$43$	3.99588	−	2.30702i	0.609366	−	0.351818i	−0.163351	−	0.986568i	$-0.552230\pi$
$43$	3.99588	−	2.30702i	0.609366	−	0.351818i	0.772717	+	0.634750i	$0.218897\pi$
$44$	−0.233586	+	0.871755i	−0.0352144	+	0.131422i
$45$	−2.13776	−	4.99959i	−0.318679	−	0.745295i
$46$	−0.972841	−	0.972841i	−0.143438	−	0.143438i
$47$	3.58728	+	0.961209i	0.523259	+	0.140207i	0.510774	−	0.859715i	$-0.329359\pi$
$47$	3.58728	+	0.961209i	0.523259	+	0.140207i	0.0124852	+	0.999922i	$0.496026\pi$
$48$	−1.63694	+	0.566057i	−0.236272	+	0.0817034i
$49$	−6.97680	−	0.569480i	−0.996685	−	0.0813544i
$50$	0.443847	+	1.65646i	0.0627694	+	0.234259i
$51$	−10.7814	+	3.72822i	−1.50969	+	0.522055i
$52$	3.48555	−	0.922476i	0.483358	−	0.127924i
$53$	4.00068	+	2.30979i	0.549535	+	0.317274i	0.748935	−	0.662644i	$-0.230566\pi$
$53$	4.00068	+	2.30979i	0.549535	+	0.317274i	−0.199399	+	0.979918i	$0.563899\pi$
$54$	5.07829	−	1.10042i	0.691068	−	0.149748i
$55$	0.817891	−	1.41663i	0.110284	−	0.191018i
$56$	1.79311	+	1.94544i	0.239615	+	0.259970i
$57$	6.36928	+	9.41607i	0.843632	+	1.24719i
$58$	1.63631	+	6.10678i	0.214857	+	0.801859i
$59$	−3.79190	+	3.79190i	−0.493663	+	0.493663i	−0.909458	−	0.415795i	$-0.863503\pi$
$59$	−3.79190	+	3.79190i	−0.493663	+	0.493663i	0.415795	+	0.909458i	$0.363503\pi$
$60$	3.13138	−	0.223113i	0.404260	−	0.0288038i
$61$	−0.159236	+	0.275805i	−0.0203881	+	0.0353132i	−0.876039	−	0.482239i	$-0.839824\pi$
$61$	−0.159236	+	0.275805i	−0.0203881	+	0.0353132i	0.855651	+	0.517553i	$0.173157\pi$
$62$	−2.37077	+	4.10630i	−0.301088	+	0.521501i
$63$	−4.64495	−	6.43618i	−0.585209	−	0.810883i
$64$		−	1.00000i		−	0.125000i
$65$	−6.53498	−	0.0200864i	−0.810565	−	0.00249142i
$66$	1.18110	+	1.02399i	0.145384	+	0.126044i
$67$	1.50744	+	0.403918i	0.184163	+	0.0493464i	0.349722	−	0.936854i	$-0.386276\pi$
$67$	1.50744	+	0.403918i	0.184163	+	0.0493464i	−0.165559	+	0.986200i	$0.552943\pi$
$68$		−	6.58628i		−	0.798704i
$69$	−2.25211	+	0.778785i	−0.271123	+	0.0937547i
$70$	−2.22664	−	4.24710i	−0.266134	−	0.507625i
$71$	0.215183	−	0.803072i	0.0255375	−	0.0953072i	−0.951981	−	0.306157i	$-0.900957\pi$
$71$	0.215183	−	0.803072i	0.0255375	−	0.0953072i	0.977518	+	0.210850i	$0.0676233\pi$
$72$	−0.357762	+	2.97859i	−0.0421626	+	0.351030i
$73$	9.62392	−	2.57872i	1.12639	−	0.301816i	0.352926	−	0.935651i	$-0.385187\pi$
$73$	9.62392	−	2.57872i	1.12639	−	0.301816i	0.773468	+	0.633835i	$0.218520\pi$
$74$			9.93089i			1.15444i
$75$	2.91645	+	0.562915i	0.336763	+	0.0649998i
$76$	−6.33965	+	1.69870i	−0.727207	+	0.194855i
$77$	0.711396	−	2.27937i	0.0810711	−	0.259759i
$78$	1.20237	−	6.12816i	0.136141	−	0.693877i
$79$	−3.91647	−	6.78352i	−0.440637	−	0.763206i	0.557100	−	0.830446i	$-0.311914\pi$
$79$	−3.91647	−	6.78352i	−0.440637	−	0.763206i	−0.997737	+	0.0672398i	$0.978581\pi$
$80$	−0.469106	+	1.75073i	−0.0524477	+	0.195737i
$81$	2.13125	−	8.74401i	0.236806	−	0.971557i
$82$	−10.9007	−	6.29352i	−1.20378	−	0.695003i
$83$	−7.59633	−	7.59633i	−0.833806	−	0.833806i	0.154229	−	0.988035i	$-0.450711\pi$
$83$	−7.59633	−	7.59633i	−0.833806	−	0.833806i	−0.988035	+	0.154229i	$0.950711\pi$
$84$	4.38832	−	1.32009i	0.478805	−	0.144034i
$85$	−3.08967	+	11.5308i	−0.335121	+	1.25069i
$86$	4.45683	+	1.19420i	0.480592	+	0.128774i
$87$	10.7519	+	2.07527i	1.15273	+	0.222492i
$88$	−0.781594	+	0.451253i	−0.0833182	+	0.0481038i
$89$	−9.27381	+	9.27381i	−0.983022	+	0.983022i	−0.999858	−	0.0168363i	$-0.994641\pi$
$89$	−9.27381	+	9.27381i	−0.983022	+	0.983022i	0.0168363	+	0.999858i	$0.494641\pi$
$90$	2.02362	−	5.04687i	0.213308	−	0.531987i
$91$	−9.31361	+	2.06319i	−0.976331	+	0.216281i
$92$		−	1.37581i		−	0.143438i
$93$	4.60139	+	6.80250i	0.477142	+	0.705386i
$94$	1.85691	+	3.21627i	0.191526	+	0.331733i
$95$	11.8959			1.22049
$96$	−1.55776	−	0.757230i	−0.158988	−	0.0772844i
$97$	8.51978	+	2.28287i	0.865053	+	0.231790i	0.663947	−	0.747779i	$-0.268880\pi$
$97$	8.51978	+	2.28287i	0.865053	+	0.231790i	0.201106	+	0.979570i	$0.435547\pi$
$98$	−4.53066	−	5.33602i	−0.457665	−	0.539020i
$99$	2.48949	−	1.06448i	0.250203	−	0.106984i
$100$	−0.857446	+	1.48514i	−0.0857446	+	0.148514i
$101$	−4.66466	−	8.07942i	−0.464151	−	0.803933i	0.535012	−	0.844844i	$-0.320307\pi$
$101$	−4.66466	−	8.07942i	−0.464151	−	0.803933i	−0.999163	+	0.0409119i	$0.986974\pi$
$102$	−10.2598	−	4.98733i	−1.01587	−	0.493819i
$103$	−6.49600	+	3.75047i	−0.640070	+	0.369544i	−0.784641	−	0.619950i	$-0.787153\pi$
$103$	−6.49600	+	3.75047i	−0.640070	+	0.369544i	0.144572	+	0.989494i	$0.453820\pi$
$104$	3.11694	+	1.81236i	0.305641	+	0.177717i
$105$	−8.30202	+	0.252528i	−0.810194	+	0.0246442i
$106$	1.19564	+	4.46218i	0.116130	+	0.433405i
$107$		−	5.66955i		−	0.548096i	−0.961716	−	0.274048i	$-0.911637\pi$
$107$		−	5.66955i		−	0.548096i	0.961716	−	0.274048i	$-0.0883627\pi$
$108$	4.36901	+	2.81278i	0.420408	+	0.270660i
$109$	−1.48202	−	5.53098i	−0.141952	−	0.529772i	−0.999872	−	0.0159889i	$-0.994910\pi$
$109$	−1.48202	−	5.53098i	−0.141952	−	0.529772i	0.857920	−	0.513783i	$-0.171756\pi$
$110$	1.58004	−	0.423372i	0.150651	−	0.0403669i
$111$	15.4699	+	7.51996i	1.46834	+	0.713763i
$112$	−0.107711	+	2.64356i	−0.0101777	+	0.249793i
$113$	−8.49197	+	4.90284i	−0.798857	+	0.461221i	−0.843071	−	0.537802i	$-0.819255\pi$
$113$	−8.49197	+	4.90284i	−0.798857	+	0.461221i	0.0442141	+	0.999022i	$0.485922\pi$
$114$	−2.15440	+	11.1619i	−0.201778	+	1.04541i
$115$	−0.645399	+	2.40866i	−0.0601837	+	0.224609i
$116$	−3.16110	+	5.47519i	−0.293501	+	0.508358i
$117$	−8.63571	−	6.51342i	−0.798371	−	0.602166i
$118$	−5.36255			−0.493663
$119$	−0.709415	+	17.4112i	−0.0650320	+	1.59608i
$120$	2.37199	+	2.05646i	0.216532	+	0.187728i
$121$	−8.82089	−	5.09274i	−0.801899	−	0.462976i
$122$	−0.307621	+	0.0824267i	−0.0278507	+	0.00746256i
$123$	−18.0581	+	12.2150i	−1.62824	+	1.10139i
$124$	−4.57998	+	1.22720i	−0.411295	+	0.110206i
$125$	8.60595	−	8.60595i	0.769740	−	0.769740i
$126$	1.26659	−	7.83554i	0.112837	−	0.698046i
$127$	12.3064	+	7.10513i	1.09202	+	0.630478i	0.934114	−	0.356976i	$-0.116192\pi$
$127$	12.3064	+	7.10513i	1.09202	+	0.630478i	0.157907	+	0.987454i	$0.449525\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	5.23512	−	6.03836i	0.460927	−	0.531648i
$130$	−4.60673	−	4.63513i	−0.404037	−	0.406528i
$131$	13.7422	−	7.93405i	1.20066	−	0.693201i	0.239958	−	0.970783i	$-0.422866\pi$
$131$	13.7422	−	7.93405i	1.20066	−	0.693201i	0.960702	+	0.277582i	$0.0895330\pi$
$132$	0.111097	+	1.55924i	0.00966972	+	0.135714i
$133$	16.9422	−	3.80777i	1.46907	−	0.330176i
$134$	0.780310	+	1.35154i	0.0674085	+	0.116755i
$135$	−6.32945	−	6.97395i	−0.544753	−	0.600222i
$136$	4.65721	−	4.65721i	0.399352	−	0.399352i
$137$	−4.71149	+	4.71149i	−0.402530	+	0.402530i	−0.879124	−	0.476594i	$-0.841871\pi$
$137$	−4.71149	+	4.71149i	−0.402530	+	0.402530i	0.476594	+	0.879124i	$0.341871\pi$
$138$	−2.14317	−	1.04180i	−0.182439	−	0.0886840i
$139$	−11.4175	−	19.7757i	−0.968420	−	1.67735i	−0.700133	−	0.714013i	$-0.746876\pi$
$139$	−11.4175	−	19.7757i	−0.968420	−	1.67735i	−0.268287	−	0.963339i	$-0.586458\pi$
$140$	1.42868	−	4.57762i	0.120746	−	0.386880i
$141$	6.41627	−	0.457164i	0.540348	−	0.0385001i
$142$	0.720015	−	0.415701i	0.0604223	−	0.0348848i
$143$	0.0100018	−	3.25402i	0.000836394	−	0.272115i
$144$	−2.35916	+	1.85321i	−0.196596	+	0.154434i
$145$	8.10267	−	8.10267i	0.672890	−	0.672890i
$146$	8.62857	+	4.98171i	0.714105	+	0.412289i
$147$	−11.7430	+	3.01706i	−0.968544	+	0.248843i
$148$	−7.02220	+	7.02220i	−0.577221	+	0.577221i
$149$	−10.0818	+	2.70140i	−0.825930	+	0.221307i	−0.646938	−	0.762543i	$-0.723951\pi$
$149$	−10.0818	+	2.70140i	−0.825930	+	0.221307i	−0.178993	+	0.983850i	$0.557284\pi$
$150$	1.66420	+	2.46028i	0.135881	+	0.200881i
$151$	−10.8111	+	2.89683i	−0.879797	+	0.235741i	−0.670319	−	0.742073i	$-0.733843\pi$
$151$	−10.8111	+	2.89683i	−0.879797	+	0.235741i	−0.209477	+	0.977814i	$0.567176\pi$
$152$	−5.68397	−	3.28164i	−0.461031	−	0.266176i
$153$	−15.5381	+	12.2057i	−1.25618	+	0.986776i
$154$	2.11479	−	1.10873i	0.170415	−	0.0893439i
$155$	8.59399			0.690286
$156$	5.18346	−	3.48306i	0.415009	−	0.278868i
$157$	4.24843	−	7.35849i	0.339061	−	0.587272i	−0.645195	−	0.764018i	$-0.723224\pi$
$157$	4.24843	−	7.35849i	0.339061	−	0.587272i	0.984256	+	0.176746i	$0.0565572\pi$
$158$	2.02731	−	7.56603i	0.161284	−	0.601921i
$159$	7.85635	+	1.51638i	0.623049	+	0.120257i
$160$	−1.56966	+	0.906243i	−0.124092	+	0.0716448i
$161$	−0.148189	+	3.63702i	−0.0116790	+	0.286637i
$162$	7.68997	−	4.67593i	0.604181	−	0.367376i
$163$	−16.2420	+	4.35204i	−1.27218	+	0.340878i	−0.830864	−	0.556476i	$-0.812153\pi$
$163$	−16.2420	+	4.35204i	−1.27218	+	0.340878i	−0.441311	+	0.897354i	$0.645487\pi$
$164$	−3.25776	−	12.1581i	−0.254389	−	0.949391i
$165$	0.536947	−	2.78191i	0.0418013	−	0.216572i
$166$		−	10.7428i		−	0.833806i
$167$	−4.01048	−	14.9673i	−0.310340	−	1.15821i	−0.928250	−	0.371957i	$-0.878687\pi$
$167$	−4.01048	−	14.9673i	−0.310340	−	1.15821i	0.617909	−	0.786249i	$-0.287980\pi$
$168$	4.03646	+	2.16957i	0.311419	+	0.167386i
$169$	−11.2981	+	6.43067i	−0.869083	+	0.494667i
$170$	−10.3382	+	5.96878i	−0.792906	+	0.457784i
$171$	15.7562	+	11.8082i	1.20491	+	0.902994i
$172$	2.30702	+	3.99588i	0.175909	+	0.304683i
$173$	−8.29585	+	14.3688i	−0.630721	+	1.09244i	0.356683	+	0.934225i	$0.383908\pi$
$173$	−8.29585	+	14.3688i	−0.630721	+	1.09244i	−0.987405	+	0.158216i	$0.949426\pi$
$174$	6.13532	+	9.07020i	0.465118	+	0.687610i
$175$	2.42667	−	3.83370i	0.183439	−	0.289800i
$176$	−0.871755	−	0.233586i	−0.0657110	−	0.0176072i
$177$	−4.06068	+	8.35354i	−0.305220	+	0.627891i
$178$	−13.1151			−0.983022
$179$	4.36543	+	7.56115i	0.326288	+	0.565147i	0.981772	−	0.190062i	$-0.0608689\pi$
$179$	4.36543	+	7.56115i	0.326288	+	0.565147i	−0.655485	+	0.755209i	$0.727536\pi$
$180$	4.99959	−	2.13776i	0.372648	−	0.159340i
$181$			12.7095i			0.944688i	0.881414	+	0.472344i	$0.156592\pi$
$181$			12.7095i			0.944688i	−0.881414	+	0.472344i	$0.843408\pi$
$182$	−8.04461	−	5.12682i	−0.596306	−	0.380025i
$183$	−0.104539	+	0.541614i	−0.00772773	+	0.0400373i
$184$	0.972841	−	0.972841i	0.0717188	−	0.0717188i
$185$	15.5881	−	8.99980i	1.14606	−	0.661678i
$186$	−1.55642	+	8.06377i	−0.114122	+	0.591264i
$187$	−5.74162	−	1.53846i	−0.419869	−	0.112504i
$188$	−0.961209	+	3.58728i	−0.0701034	+	0.261629i
$189$	−11.2468	−	7.90635i	−0.818082	−	0.575102i
$190$	8.41165	+	8.41165i	0.610245	+	0.610245i
$191$	4.87773	+	2.81616i	0.352940	+	0.203770i	0.665979	−	0.745970i	$-0.268014\pi$
$191$	4.87773	+	2.81616i	0.352940	+	0.203770i	−0.313039	+	0.949740i	$0.601347\pi$
$192$	−0.566057	−	1.63694i	−0.0408517	−	0.118136i
$193$	1.55380	−	5.79885i	0.111845	−	0.417410i	−0.887187	−	0.461411i	$-0.847344\pi$
$193$	1.55380	−	5.79885i	0.111845	−	0.417410i	0.999032	+	0.0440001i	$0.0140102\pi$
$194$	4.41017	+	7.63863i	0.316631	+	0.548422i
$195$	−10.7088	+	3.66630i	−0.766870	+	0.262549i
$196$	0.569480	−	6.97680i	0.0406772	−	0.498343i
$197$	0.130081	−	0.0348552i	0.00926792	−	0.00248333i	−0.254182	−	0.967156i	$-0.581806\pi$
$197$	0.130081	−	0.0348552i	0.00926792	−	0.00248333i	0.263450	+	0.964673i	$0.415140\pi$
$198$	2.51303	+	1.00764i	0.178593	+	0.0716097i
$199$		−	15.4449i		−	1.09486i	−0.836851	−	0.547431i	$-0.815606\pi$
$199$		−	15.4449i		−	1.09486i	0.836851	−	0.547431i	$-0.184394\pi$
$200$	−1.65646	+	0.443847i	−0.117129	+	0.0313847i
$201$	2.69624	−	0.192109i	0.190178	−	0.0135503i
$202$	2.41460	−	9.01142i	0.169891	−	0.634042i
$203$	8.94629	−	14.1335i	0.627906	−	0.991976i
$204$	−3.72822	−	10.7814i	−0.261027	−	0.754847i
$205$			22.8138i			1.59339i
$206$	−7.24535	−	1.94138i	−0.504807	−	0.135263i
$207$	−3.24574	+	2.54965i	−0.225595	+	0.177213i
$208$	0.922476	+	3.48555i	0.0639622	+	0.241679i
$209$			5.92341i			0.409731i
$210$	−6.04898	−	5.69185i	−0.417419	−	0.392775i
$211$	8.34474	−	14.4535i	0.574475	−	0.995020i	−0.421623	−	0.906771i	$-0.638539\pi$
$211$	8.34474	−	14.4535i	0.574475	−	0.995020i	0.996098	−	0.0882493i	$-0.0281272\pi$
$212$	−2.30979	+	4.00068i	−0.158637	+	0.274768i
$213$	−0.102344	−	1.43639i	−0.00701248	−	0.0984197i
$214$	4.00898	−	4.00898i	0.274048	−	0.274048i
$215$	−2.16448	−	8.07794i	−0.147616	−	0.550911i
$216$	1.10042	+	5.07829i	0.0748740	+	0.345534i
$217$	12.2396	−	2.75087i	0.830880	−	0.186741i
$218$	2.86305	−	4.95894i	0.193910	−	0.335862i
$219$	14.2941	−	9.66891i	0.965905	−	0.653364i
$220$	1.41663	+	0.817891i	0.0955091	+	0.0551422i
$221$	6.07569	+	22.9568i	0.408695	+	1.54424i
$222$	5.62145	+	16.2563i	0.377287	+	1.09105i
$223$	−4.88471	−	18.2300i	−0.327105	−	1.22077i	−0.912179	−	0.409791i	$-0.865602\pi$
$223$	−4.88471	−	18.2300i	−0.327105	−	1.22077i	0.585075	−	0.810979i	$-0.301065\pi$
$224$	−1.94544	+	1.79311i	−0.129985	+	0.119808i
$225$	5.09270	−	0.729420i	0.339513	−	0.0486280i
$226$	−9.47156	−	2.53790i	−0.630039	−	0.168818i
$227$	4.35833	+	4.35833i	0.289273	+	0.289273i	0.836793	−	0.547520i	$-0.184428\pi$
$227$	4.35833	+	4.35833i	0.289273	+	0.289273i	−0.547520	+	0.836793i	$0.684428\pi$
$228$	−9.41607	+	6.36928i	−0.623595	+	0.421816i
$229$	−7.77816	+	29.0285i	−0.513996	+	1.91826i	−0.142609	+	0.989779i	$0.545549\pi$
$229$	−7.77816	+	29.0285i	−0.513996	+	1.91826i	−0.371386	+	0.928479i	$0.621117\pi$
$230$	−2.15955	+	1.24681i	−0.142396	+	0.0822125i
$231$	−0.125744	−	4.13389i	−0.00827332	−	0.271990i
$232$	−6.10678	+	1.63631i	−0.400930	+	0.107429i
$233$	−2.90989	−	5.04008i	−0.190633	−	0.330187i	0.754827	−	0.655924i	$-0.227721\pi$
$233$	−2.90989	−	5.04008i	−0.190633	−	0.330187i	−0.945460	+	0.325737i	$0.894388\pi$
$234$	−1.50068	−	10.7120i	−0.0981028	−	0.700268i
$235$	3.36563	−	5.82944i	0.219550	−	0.380271i
$236$	−3.79190	−	3.79190i	−0.246831	−	0.246831i
$237$	−10.2509	−	8.88728i	−0.665867	−	0.577291i
$238$	−12.8132	+	11.8100i	−0.830558	+	0.765526i
$239$	−4.35751	−	4.35751i	−0.281864	−	0.281864i	0.551988	−	0.833852i	$-0.313869\pi$
$239$	−4.35751	−	4.35751i	−0.281864	−	0.281864i	−0.833852	+	0.551988i	$0.813869\pi$
$240$	0.223113	+	3.13138i	0.0144019	+	0.202130i
$241$	5.45104	+	5.45104i	0.351132	+	0.351132i	0.860531	−	0.509399i	$-0.170132\pi$
$241$	5.45104	+	5.45104i	0.351132	+	0.351132i	−0.509399	+	0.860531i	$0.670132\pi$
$242$	−2.63620	−	9.83842i	−0.169461	−	0.632438i
$243$	−1.46088	−	15.5199i	−0.0937154	−	0.995599i
$244$	−0.275805	−	0.159236i	−0.0176566	−	0.0101941i
$245$	−4.26986	+	11.9473i	−0.272792	+	0.763287i
$246$	−21.4063	−	4.13170i	−1.36482	−	0.263428i
$247$	20.5301	−	11.7691i	1.30630	−	0.748849i
$248$	−4.10630	−	2.37077i	−0.260750	−	0.150544i
$249$	−16.7347	−	8.13480i	−1.06052	−	0.515522i
$250$	12.1707			0.769740
$251$	−2.45017	−	4.24381i	−0.154653	−	0.267867i	0.778280	−	0.627918i	$-0.216093\pi$
$251$	−2.45017	−	4.24381i	−0.154653	−	0.267867i	−0.932933	+	0.360051i	$0.882759\pi$
$252$	6.43618	−	4.64495i	0.405441	−	0.292604i
$253$	−1.19936	−	0.321369i	−0.0754034	−	0.0202043i
$254$	3.67789	+	13.7261i	0.230771	+	0.861249i
$255$	1.46949	+	20.6242i	0.0920228	+	1.29154i
$256$	1.00000			0.0625000
$257$	22.1351			1.38075			0.690375	−	0.723452i	$-0.257446\pi$
$257$	22.1351			1.38075			0.690375	+	0.723452i	$0.257446\pi$
$258$	7.97156	−	0.567979i	0.496287	−	0.0353608i
$259$	19.3200	−	17.8072i	1.20048	−	1.10649i
$260$	0.0200864	−	6.53498i	0.00124571	−	0.405282i
$261$	18.7750	−	2.68912i	1.16214	−	0.166452i
$262$	15.3274	+	4.10697i	0.946931	+	0.253729i
$263$	14.2409	−	8.22199i	0.878131	−	0.506989i	0.00808956	−	0.999967i	$-0.497425\pi$
$263$	14.2409	−	8.22199i	0.878131	−	0.506989i	0.870042	+	0.492978i	$0.164092\pi$
$264$	−1.02399	+	1.18110i	−0.0630221	+	0.0726919i
$265$	5.92056	−	5.92056i	0.363697	−	0.363697i
$266$	14.6724	+	9.28744i	0.899625	+	0.569449i
$267$	−9.93118	+	20.4302i	−0.607778	+	1.25031i
$268$	−0.403918	+	1.50744i	−0.0246732	+	0.0920817i
$269$			8.80178i			0.536654i	0.963328	+	0.268327i	$0.0864708\pi$
$269$			8.80178i			0.536654i	−0.963328	+	0.268327i	$0.913529\pi$
$270$	0.455725	−	9.40693i	0.0277346	−	0.572487i
$271$	16.4390	+	16.4390i	0.998598	+	0.998598i	0.999999	−	0.00140113i	$-0.000445993\pi$
$271$	16.4390	+	16.4390i	0.998598	+	0.998598i	−0.00140113	+	0.999999i	$0.500446\pi$
$272$	6.58628			0.399352
$273$	−14.0779	+	8.64935i	−0.852036	+	0.523483i
$274$	−6.66305			−0.402530
$275$	1.09439	+	1.09439i	0.0659942	+	0.0659942i
$276$	−0.778785	−	2.25211i	−0.0468773	−	0.135561i
$277$			8.79047i			0.528168i	0.964500	+	0.264084i	$0.0850697\pi$
$277$			8.79047i			0.528168i	−0.964500	+	0.264084i	$0.914930\pi$
$278$	5.91013	−	22.0569i	0.354466	−	1.32289i
$279$	11.3828	+	8.53064i	0.681471	+	0.510716i
$280$	4.24710	−	2.22664i	0.253813	−	0.133067i
$281$	−5.77940	+	5.77940i	−0.344770	+	0.344770i	−0.858157	−	0.513387i	$-0.828391\pi$
$281$	−5.77940	+	5.77940i	−0.344770	+	0.344770i	0.513387	+	0.858157i	$0.328391\pi$
$282$	4.86025	+	4.21373i	0.289424	+	0.250924i
$283$	15.8077	−	9.12659i	0.939671	−	0.542520i	0.0498142	−	0.998759i	$-0.484137\pi$
$283$	15.8077	−	9.12659i	0.939671	−	0.542520i	0.889857	+	0.456239i	$0.150804\pi$
$284$	0.803072	+	0.215183i	0.0476536	+	0.0127687i
$285$	19.4728	−	6.73375i	1.15347	−	0.398873i
$286$	2.30801	−	2.29387i	0.136476	−	0.135639i
$287$	7.30252	+	32.4916i	0.431054	+	1.91792i
$288$	−2.97859	−	0.357762i	−0.175515	−	0.0210813i
$289$	26.3791			1.55171
$290$	11.4589			0.672890
$291$	15.2386	−	1.08576i	0.893304	−	0.0636486i
$292$	2.57872	+	9.62392i	0.150908	+	0.563197i
$293$	3.68965	+	0.988640i	0.215552	+	0.0577570i	0.364979	−	0.931016i	$-0.381076\pi$
$293$	3.68965	+	0.988640i	0.215552	+	0.0577570i	−0.149427	+	0.988773i	$0.547743\pi$
$294$	−10.4369	−	6.17015i	−0.608693	−	0.359850i
$295$	4.85978	+	8.41738i	0.282947	+	0.490079i
$296$	−9.93089			−0.577221
$297$	3.47260	−	3.15168i	0.201501	−	0.182879i
$298$	−9.03906	−	5.21871i	−0.523619	−	0.302312i
$299$	1.26915	+	4.79543i	0.0733967	+	0.277327i
$300$	−0.562915	+	2.91645i	−0.0324999	+	0.168381i
$301$	−5.66835	−	10.8118i	−0.326718	−	0.623184i
$302$	−9.69299	−	5.59625i	−0.557769	−	0.322028i
$303$	−12.2092	−	10.5851i	−0.701400	−	0.608097i
$304$	−1.69870	−	6.33965i	−0.0974273	−	0.363604i
$305$	0.408161	+	0.408161i	0.0233712	+	0.0233712i
$306$	−19.6178	−	2.35632i	−1.12148	−	0.134702i
$307$	11.9104	+	11.9104i	0.679761	+	0.679761i	0.959946	−	0.280185i	$-0.0903959\pi$
$307$	11.9104	+	11.9104i	0.679761	+	0.679761i	−0.280185	+	0.959946i	$0.590396\pi$
$308$	2.27937	+	0.711396i	0.129879	+	0.0405355i
$309$	−8.51059	+	9.81640i	−0.484151	+	0.558436i
$310$	6.07687	+	6.07687i	0.345143	+	0.345143i
$311$	12.1481	−	21.0411i	0.688853	−	1.19313i	−0.283356	−	0.959015i	$-0.591448\pi$
$311$	12.1481	−	21.0411i	0.688853	−	1.19313i	0.972209	−	0.234114i	$-0.0752190\pi$
$312$	6.12816	+	1.20237i	0.346939	+	0.0680706i
$313$	−7.76181	−	13.4438i	−0.438723	−	0.759891i	0.558868	−	0.829257i	$-0.311236\pi$
$313$	−7.76181	−	13.4438i	−0.438723	−	0.759891i	−0.997591	+	0.0693657i	$0.977902\pi$
$314$	8.20733	−	2.19915i	0.463166	−	0.124105i
$315$	−13.4470	+	5.11279i	−0.757651	+	0.288073i
$316$	6.78352	−	3.91647i	0.381603	−	0.220319i
$317$	−6.90434	+	25.7673i	−0.387786	+	1.44724i	0.445941	+	0.895062i	$0.352869\pi$
$317$	−6.90434	+	25.7673i	−0.387786	+	1.44724i	−0.833728	+	0.552176i	$0.813798\pi$
$318$	4.48304	+	6.62752i	0.251396	+	0.371653i
$319$	4.03463	+	4.03463i	0.225896	+	0.225896i
$320$	−1.75073	−	0.469106i	−0.0978687	−	0.0262238i
$321$	−3.20929	−	9.28072i	−0.179125	−	0.517999i
$322$	−2.67655	+	2.46698i	−0.149158	+	0.137479i
$323$	−11.1881	−	41.7547i	−0.622525	−	2.32329i
$324$	8.74401	+	2.13125i	0.485779	+	0.118403i
$325$	1.61866	−	5.96750i	0.0897872	−	0.331017i
$326$	−14.5622	−	8.40750i	−0.806527	−	0.465648i
$327$	−5.55684	−	8.21498i	−0.307294	−	0.454290i
$328$	6.29352	−	10.9007i	0.347501	−	0.601890i
$329$	2.92740	−	9.37965i	0.161393	−	0.517117i
$330$	2.34679	−	1.58743i	0.129186	−	0.0873852i
$331$	3.30758	+	12.3441i	0.181801	+	0.678490i	0.995293	+	0.0969140i	$0.0308972\pi$
$331$	3.30758	+	12.3441i	0.181801	+	0.678490i	−0.813492	+	0.581576i	$0.802436\pi$
$332$	7.59633	−	7.59633i	0.416903	−	0.416903i
$333$	29.5801	+	3.55289i	1.62098	+	0.194697i
$334$	7.74766	−	13.4193i	0.423933	−	0.734273i
$335$	1.41430	−	2.44964i	0.0772715	−	0.133838i
$336$	1.32009	+	4.38832i	0.0720168	+	0.239403i
$337$			6.18136i			0.336720i	0.985726	+	0.168360i	$0.0538471\pi$
$337$			6.18136i			0.336720i	−0.985726	+	0.168360i	$0.946153\pi$
$338$	−12.5361	−	3.44178i	−0.681875	−	0.187208i
$339$	−11.1256	+	12.8326i	−0.604258	+	0.696972i
$340$	−11.5308	−	3.08967i	−0.625345	−	0.167561i
$341$			4.27928i			0.231736i
$342$	2.79166	+	19.4909i	0.150956	+	1.05395i
$343$	−2.25693	+	18.3822i	−0.121863	+	0.992547i
$344$	−1.19420	+	4.45683i	−0.0643871	+	0.240296i
$345$	0.306960	+	4.30817i	0.0165262	+	0.231944i
$346$	−16.0263	+	4.29425i	−0.861582	+	0.230860i
$347$		−	9.99643i		−	0.536637i	−0.963330	−	0.268318i	$-0.913532\pi$
$347$		−	9.99643i		−	0.536637i	0.963330	−	0.268318i	$-0.0864679\pi$
$348$	−2.07527	+	10.7519i	−0.111246	+	0.576364i
$349$	−20.8799	+	5.59475i	−1.11768	+	0.299480i	−0.769943	−	0.638113i	$-0.779715\pi$
$349$	−20.8799	+	5.59475i	−1.11768	+	0.299480i	−0.347733	+	0.937594i	$0.613048\pi$
$350$	4.42675	−	0.994915i	0.236620	−	0.0531805i
$351$	−17.8231	−	5.77378i	−0.951328	−	0.308182i
$352$	−0.451253	−	0.781594i	−0.0240519	−	0.0416591i
$353$	2.78201	−	10.3826i	0.148071	−	0.552609i	−0.851528	−	0.524309i	$-0.824324\pi$
$353$	2.78201	−	10.3826i	0.148071	−	0.552609i	0.999599	−	0.0283006i	$-0.00900957\pi$
$354$	−8.77818	+	3.03551i	−0.466555	+	0.161336i
$355$	−1.30502	−	0.753452i	−0.0692632	−	0.0399891i
$356$	−9.27381	−	9.27381i	−0.491511	−	0.491511i
$357$	8.69448	+	28.9027i	0.460161	+	1.52969i
$358$	−2.25971	+	8.43336i	−0.119430	+	0.445717i
$359$	21.8831	+	5.86355i	1.15494	+	0.309466i	0.784945	−	0.619566i	$-0.212691\pi$
$359$	21.8831	+	5.86355i	1.15494	+	0.309466i	0.369999	+	0.929032i	$0.379358\pi$
$360$	5.04687	+	2.02362i	0.265994	+	0.106654i
$361$	−20.8511	+	12.0384i	−1.09742	+	0.633598i
$362$	−8.98696	+	8.98696i	−0.472344	+	0.472344i
$363$	−17.3221	−	3.34339i	−0.909172	−	0.175483i
$364$	−2.06319	−	9.31361i	−0.108140	−	0.488166i
$365$		−	18.0586i		−	0.945228i
$366$	−0.456899	+	0.309059i	−0.0238825	+	0.0161548i
$367$	1.94294	+	3.36526i	0.101420	+	0.175665i	0.912270	−	0.409589i	$-0.134328\pi$
$367$	1.94294	+	3.36526i	0.101420	+	0.175665i	−0.810850	+	0.585255i	$0.800995\pi$
$368$	1.37581			0.0717188
$369$	−22.6457	+	30.2171i	−1.17889	+	1.57304i
$370$	17.3863	+	4.65864i	0.903870	+	0.242191i
$371$	6.53699	−	10.3272i	0.339383	−	0.536163i
$372$	−6.80250	+	4.60139i	−0.352693	+	0.238571i
$373$	−3.70760	+	6.42175i	−0.191972	+	0.332506i	−0.945904	−	0.324447i	$-0.894822\pi$
$373$	−3.70760	+	6.42175i	−0.191972	+	0.332506i	0.753932	+	0.656953i	$0.228155\pi$
$374$	−2.97208	−	5.14780i	−0.153683	−	0.266186i
$375$	9.21598	−	18.9589i	0.475911	−	0.979034i
$376$	−3.21627	+	1.85691i	−0.165866	+	0.0957630i
$377$	5.96743	−	22.0001i	0.307338	−	1.13306i
$378$	−2.36203	−	13.5433i	−0.121490	−	0.696592i
$379$	−2.47437	−	9.23446i	−0.127100	−	0.474342i	0.872806	−	0.488067i	$-0.162298\pi$
$379$	−2.47437	−	9.23446i	−0.127100	−	0.474342i	−0.999906	+	0.0137247i	$0.995631\pi$
$380$			11.8959i			0.610245i
$381$	24.1668	+	4.66453i	1.23811	+	0.238971i
$382$	1.45775	+	5.44040i	0.0745850	+	0.278355i
$383$	−20.4641	+	5.48334i	−1.04567	+	0.280186i	−0.740460	−	0.672101i	$-0.765392\pi$
$383$	−20.4641	+	5.48334i	−1.04567	+	0.280186i	−0.305207	+	0.952286i	$0.598726\pi$
$384$	0.757230	−	1.55776i	0.0386422	−	0.0794939i
$385$	−3.65684	−	2.31473i	−0.186370	−	0.117970i
$386$	5.19911	−	3.00171i	0.264628	−	0.152783i
$387$	5.15153	−	12.8478i	0.261867	−	0.653092i
$388$	−2.28287	+	8.51978i	−0.115895	+	0.432527i
$389$	15.6838	−	27.1652i	0.795202	−	1.37733i	−0.127509	−	0.991837i	$-0.540698\pi$
$389$	15.6838	−	27.1652i	0.795202	−	1.37733i	0.922711	−	0.385493i	$-0.125969\pi$
$390$	−10.1647	−	4.97977i	−0.514710	−	0.252161i
$391$	9.06144			0.458257
$392$	5.33602	−	4.53066i	0.269510	−	0.228833i
$393$	18.0040	−	20.7665i	0.908183	−	1.04753i
$394$	0.116628	+	0.0673351i	0.00587562	+	0.00339229i
$395$	−13.7133	+	3.67448i	−0.689993	+	0.184883i
$396$	1.06448	+	2.48949i	0.0534919	+	0.125102i
$397$	−25.4057	+	6.80743i	−1.27507	+	0.341655i	−0.831973	−	0.554817i	$-0.812788\pi$
$397$	−25.4057	+	6.80743i	−1.27507	+	0.341655i	−0.443101	+	0.896472i	$0.646122\pi$
$398$	10.9212	−	10.9212i	0.547431	−	0.547431i
$399$	25.5780	−	15.8234i	1.28050	−	0.792159i
$400$	−1.48514	−	0.857446i	−0.0742570	−	0.0428723i
$401$	−4.40472	+	4.40472i	−0.219961	+	0.219961i	−0.808482	−	0.588521i	$-0.799711\pi$
$401$	−4.40472	+	4.40472i	−0.219961	+	0.219961i	0.588521	+	0.808482i	$0.299711\pi$
$402$	2.04237	+	1.77069i	0.101864	+	0.0883138i
$403$	14.8317	−	8.50240i	0.738818	−	0.423535i
$404$	8.07942	−	4.66466i	0.401966	−	0.232075i
$405$	−14.3086	−	7.83311i	−0.711000	−	0.389230i
$406$	16.3199	−	3.66790i	0.809941	−	0.182035i
$407$	4.48135	+	7.76192i	0.222132	+	0.384744i
$408$	4.98733	−	10.2598i	0.246910	−	0.507937i
$409$	−7.84266	+	7.84266i	−0.387794	+	0.387794i	−0.873900	−	0.486106i	$-0.838417\pi$
$409$	−7.84266	+	7.84266i	−0.387794	+	0.387794i	0.486106	+	0.873900i	$0.338417\pi$
$410$	−16.1318	+	16.1318i	−0.796694	+	0.796694i
$411$	−5.04546	+	10.3794i	−0.248874	+	0.511978i
$412$	−3.75047	−	6.49600i	−0.184772	−	0.320035i
$413$	9.61567	+	10.4325i	0.473156	+	0.513351i
$414$	−4.09796	−	0.492210i	−0.201404	−	0.0241908i
$415$	−16.8626	+	9.73563i	−0.827752	+	0.477903i
$416$	−1.81236	+	3.11694i	−0.0888585	+	0.152821i
$417$	−29.8840	−	25.9087i	−1.46342	−	1.26875i
$418$	−4.18848	+	4.18848i	−0.204865	+	0.204865i
$419$	−17.9840	−	10.3830i	−0.878574	−	0.507245i	−0.00838623	−	0.999965i	$-0.502669\pi$
$419$	−17.9840	−	10.3830i	−0.878574	−	0.507245i	−0.870188	+	0.492720i	$0.836003\pi$
$420$	−0.252528	−	8.30202i	−0.0123221	−	0.405097i
$421$	−4.07675	+	4.07675i	−0.198689	+	0.198689i	−0.799438	−	0.600749i	$-0.794869\pi$
$421$	−4.07675	+	4.07675i	−0.198689	+	0.198689i	0.600749	+	0.799438i	$0.294869\pi$
$422$	16.1208	−	4.31955i	0.784748	−	0.210273i
$423$	10.2443	−	4.38033i	0.498094	−	0.212979i
$424$	−4.46218	+	1.19564i	−0.216702	+	0.0580652i
$425$	−9.78155	−	5.64738i	−0.474475	−	0.273938i
$426$	0.943312	−	1.08805i	0.0457036	−	0.0527161i
$427$	0.711955	+	0.450657i	0.0344539	+	0.0218088i
$428$	5.66955			0.274048
$429$	−1.82559	−	5.33230i	−0.0881403	−	0.257446i
$430$	4.18145	−	7.24249i	0.201647	−	0.349264i
$431$	6.27842	−	23.4314i	0.302421	−	1.12865i	−0.632722	−	0.774379i	$-0.718063\pi$
$431$	6.27842	−	23.4314i	0.302421	−	1.12865i	0.935143	−	0.354271i	$-0.115271\pi$
$432$	−2.81278	+	4.36901i	−0.135330	+	0.210204i
$433$	−5.95281	+	3.43686i	−0.286074	+	0.165165i	−0.636170	−	0.771549i	$-0.719482\pi$
$433$	−5.95281	+	3.43686i	−0.286074	+	0.165165i	0.350096	+	0.936714i	$0.386149\pi$
$434$	10.5999	+	6.70957i	0.508811	+	0.322070i
$435$	8.67702	−	17.8502i	0.416031	−	0.855850i
$436$	5.53098	−	1.48202i	0.264886	−	0.0709760i
$437$	−2.33708	−	8.72212i	−0.111798	−	0.417236i
$438$	16.9444	+	3.27050i	0.809635	+	0.156270i
$439$		−	9.75835i		−	0.465741i	−0.972508	−	0.232870i	$-0.925188\pi$
$439$		−	9.75835i		−	0.465741i	0.972508	−	0.232870i	$-0.0748118\pi$
$440$	0.423372	+	1.58004i	0.0201834	+	0.0753256i
$441$	−17.5147	+	11.5860i	−0.834035	+	0.551712i
$442$	−11.9367	+	20.5291i	−0.567773	+	0.976468i
$443$	−34.0695	+	19.6700i	−1.61869	+	0.934552i	−0.631431	+	0.775432i	$0.717532\pi$
$443$	−34.0695	+	19.6700i	−1.61869	+	0.934552i	−0.987259	+	0.159120i	$0.949134\pi$
$444$	−7.51996	+	15.4699i	−0.356882	+	0.734169i
$445$	11.8855	+	20.5863i	0.563428	+	0.975885i
$446$	9.43654	−	16.3446i	0.446833	−	0.773938i
$447$	−14.9741	+	10.1289i	−0.708251	+	0.479080i
$448$	−2.64356	−	0.107711i	−0.124896	−	0.00508887i
$449$	21.0377	+	5.63704i	0.992831	+	0.266028i	0.718439	−	0.695590i	$-0.244857\pi$
$449$	21.0377	+	5.63704i	0.992831	+	0.266028i	0.274392	+	0.961618i	$0.411524\pi$
$450$	4.11686	+	3.08531i	0.194071	+	0.145443i
$451$	−11.3599			−0.534916
$452$	−4.90284	−	8.49197i	−0.230610	−	0.399429i
$453$	−16.0574	+	10.8617i	−0.754443	+	0.510325i
$454$			6.16361i			0.289273i
$455$	−0.756989	+	17.2734i	−0.0354882	+	0.809792i
$456$	−11.1619	−	2.15440i	−0.522705	−	0.100889i
$457$	−6.60616	+	6.60616i	−0.309023	+	0.309023i	−0.844530	−	0.535507i	$-0.820120\pi$
$457$	−6.60616	+	6.60616i	−0.309023	+	0.309023i	0.535507	+	0.844530i	$0.320120\pi$
$458$	−26.0262	+	15.0263i	−1.21613	+	0.702131i
$459$	−18.5258	+	28.7755i	−0.864710	+	1.34313i
$460$	−2.40866	−	0.645399i	−0.112304	−	0.0300919i
$461$	5.29013	−	19.7430i	0.246386	−	0.919524i	−0.726296	−	0.687382i	$-0.758760\pi$
$461$	5.29013	−	19.7430i	0.246386	−	0.919524i	0.972682	−	0.232142i	$-0.0745735\pi$
$462$	2.83419	−	3.01202i	0.131858	−	0.140132i
$463$	−6.55850	−	6.55850i	−0.304799	−	0.304799i	0.538089	−	0.842888i	$-0.319146\pi$
$463$	−6.55850	−	6.55850i	−0.304799	−	0.304799i	−0.842888	+	0.538089i	$0.819146\pi$
$464$	−5.47519	−	3.16110i	−0.254179	−	0.146750i
$465$	14.0679	−	4.86469i	0.652382	−	0.225595i
$466$	1.50627	−	5.62148i	0.0697767	−	0.260410i
$467$	13.9409	+	24.1463i	0.645106	+	1.11736i	0.984277	+	0.176631i	$0.0565201\pi$
$467$	13.9409	+	24.1463i	0.645106	+	1.11736i	−0.339171	+	0.940725i	$0.610147\pi$
$468$	6.51342	−	8.63571i	0.301083	−	0.399186i
$469$	1.23015	−	3.94150i	0.0568030	−	0.182002i
$470$	6.50190	−	1.74218i	0.299910	−	0.0803607i
$471$	2.78910	−	14.4503i	0.128515	−	0.665834i
$472$		−	5.36255i		−	0.246831i
$473$	4.02232	−	1.07778i	0.184946	−	0.0495562i
$474$	−0.964217	−	13.5327i	−0.0442880	−	0.621579i
$475$	−2.91309	+	10.8718i	−0.133662	+	0.498833i
$476$	−17.4112	−	0.709415i	−0.798042	−	0.0325160i
$477$	13.7188	−	1.96492i	0.628139	−	0.0899674i
$478$		−	6.16245i		−	0.281864i
$479$	20.8026	+	5.57403i	0.950494	+	0.254684i	0.700572	−	0.713582i	$-0.252928\pi$
$479$	20.8026	+	5.57403i	0.950494	+	0.254684i	0.249922	+	0.968266i	$0.419595\pi$
$480$	−2.05646	+	2.37199i	−0.0938639	+	0.108266i
$481$	17.9984	−	30.9540i	0.820656	−	1.41138i
$482$			7.70893i			0.351132i
$483$	1.81619	+	6.03748i	0.0826393	+	0.274715i
$484$	5.09274	−	8.82089i	0.231488	−	0.400949i
$485$	7.99337	−	13.8449i	0.362960	−	0.628665i
$486$	9.94120	−	12.0072i	0.450942	−	0.544657i
$487$	5.64284	−	5.64284i	0.255702	−	0.255702i	−0.567602	−	0.823303i	$-0.692129\pi$
$487$	5.64284	−	5.64284i	0.255702	−	0.255702i	0.823303	+	0.567602i	$0.192129\pi$
$488$	−0.0824267	−	0.307621i	−0.00373128	−	0.0139253i
$489$	−24.1238	+	16.3180i	−1.09092	+	0.737924i
$490$	−11.4673	+	5.42879i	−0.518039	+	0.245248i
$491$	1.14945	−	1.99091i	0.0518741	−	0.0898485i	−0.838922	−	0.544251i	$-0.816814\pi$
$491$	1.14945	−	1.99091i	0.0518741	−	0.0898485i	0.890796	+	0.454403i	$0.150147\pi$
$492$	−12.2150	−	18.0581i	−0.550694	−	0.814122i
$493$	−36.0611	−	20.8199i	−1.62411	−	0.937681i
$494$	22.8390	+	6.19499i	1.02757	+	0.278726i
$495$	−0.695772	−	4.85777i	−0.0312726	−	0.218341i
$496$	−1.22720	−	4.57998i	−0.0551030	−	0.205647i
$497$	−2.09979	−	0.655347i	−0.0941885	−	0.0293964i
$498$	−6.08106	−	17.5854i	−0.272499	−	0.788021i
$499$	−16.0767	−	4.30774i	−0.719692	−	0.192841i	−0.119658	−	0.992815i	$-0.538180\pi$
$499$	−16.0767	−	4.30774i	−0.719692	−	0.192841i	−0.600034	+	0.799974i	$0.704846\pi$
$500$	8.60595	+	8.60595i	0.384870	+	0.384870i
$501$	−15.0373	−	22.2305i	−0.671817	−	0.993185i
$502$	1.26830	−	4.73336i	0.0566070	−	0.211260i
$503$	−1.59511	+	0.920936i	−0.0711223	+	0.0410625i	−0.535139	−	0.844764i	$-0.679741\pi$
$503$	−1.59511	+	0.920936i	−0.0711223	+	0.0410625i	0.464017	+	0.885826i	$0.346408\pi$
$504$	7.83554	+	1.26659i	0.349023	+	0.0564184i
$505$	−16.3331	+	4.37644i	−0.726813	+	0.194749i
$506$	−0.620837	−	1.07532i	−0.0275996	−	0.0478039i
$507$	−14.8542	+	16.9220i	−0.659697	+	0.751532i
$508$	−7.10513	+	12.3064i	−0.315239	+	0.546010i
$509$	−17.9700	−	17.9700i	−0.796508	−	0.796508i	0.186035	−	0.982543i	$-0.440436\pi$
$509$	−17.9700	−	17.9700i	−0.796508	−	0.796508i	−0.982543	+	0.186035i	$0.940436\pi$
$510$	−13.5444	+	15.6226i	−0.599756	+	0.691779i
$511$	−5.78040	−	25.7191i	−0.255710	−	1.13775i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	32.4761	+	10.4104i	1.43385	+	0.459630i
$514$	15.6519	+	15.6519i	0.690375	+	0.690375i
$515$	3.51873	+	13.1321i	0.155054	+	0.578669i
$516$	6.03836	+	5.23512i	0.265824	+	0.230463i
$517$	2.90271	+	1.67588i	0.127661	+	0.0737050i
$518$	26.2529	+	1.06967i	1.15348	+	0.0469984i
$519$	−5.44624	+	28.2169i	−0.239063	+	1.23858i
$520$	4.63513	−	4.60673i	0.203264	−	0.202018i
$521$	12.5241	+	7.23078i	0.548690	+	0.316786i	0.748593	−	0.663029i	$-0.230730\pi$
$521$	12.5241	+	7.23078i	0.548690	+	0.316786i	−0.199904	+	0.979816i	$0.564063\pi$
$522$	15.1774	+	11.3744i	0.664298	+	0.497846i
$523$	−32.5454			−1.42311			−0.711555	−	0.702630i	$-0.752009\pi$
$523$	−32.5454			−1.42311			−0.711555	+	0.702630i	$0.752009\pi$
$524$	7.93405	+	13.7422i	0.346601	+	0.600330i
$525$	1.80223	−	7.64917i	0.0786558	−	0.333837i
$526$	15.8837	+	4.25601i	0.692560	+	0.185571i
$527$	−8.08270	−	30.1651i	−0.352088	−	1.31401i
$528$	−1.55924	+	0.111097i	−0.0678570	+	0.00483486i
$529$	−21.1072			−0.917703
$530$	8.37294			0.363697
$531$	−1.91852	+	15.9728i	−0.0832565	+	0.693163i
$532$	3.80777	+	16.9422i	0.165088	+	0.734537i
$533$	22.5707	+	39.3726i	0.977645	+	1.70541i
$534$	−21.4687	+	7.42393i	−0.929043	+	0.321265i
$535$	−9.92583	−	2.65962i	−0.429131	−	0.114985i
$536$	−1.35154	+	0.780310i	−0.0583775	+	0.0337042i
$537$	11.4260	+	9.90607i	0.493068	+	0.427479i
$538$	−6.22380	+	6.22380i	−0.268327	+	0.268327i
$539$	−5.94903	−	2.12613i	−0.256243	−	0.0915789i
$540$	6.97395	−	6.32945i	0.300111	−	0.272376i
$541$	7.08807	−	26.4530i	0.304740	−	1.13731i	−0.628429	−	0.777867i	$-0.716302\pi$
$541$	7.08807	−	26.4530i	0.304740	−	1.13731i	0.933169	−	0.359438i	$-0.117032\pi$
$542$			23.2483i			0.998598i
$543$	7.19430	+	20.8047i	0.308737	+	0.892815i
$544$	4.65721	+	4.65721i	0.199676	+	0.199676i
$545$	−10.3785			−0.444565
$546$	−16.0706	−	3.83860i	−0.687760	−	0.164277i
$547$	21.0848			0.901523			0.450761	−	0.892645i	$-0.351153\pi$
$547$	21.0848			0.901523			0.450761	+	0.892645i	$0.351153\pi$
$548$	−4.71149	−	4.71149i	−0.201265	−	0.201265i
$549$	0.135461	+	0.945766i	0.00578132	+	0.0403643i
$550$			1.54770i			0.0659942i
$551$	−10.7395	+	40.0805i	−0.457520	+	1.70749i
$552$	1.04180	−	2.14317i	0.0443420	−	0.0912193i
$553$	−18.3545	+	9.62275i	−0.780512	+	0.409201i
$554$	−6.21580	+	6.21580i	−0.264084	+	0.264084i
$555$	20.4224	−	23.5559i	0.866884	−	0.999893i
$556$	19.7757	−	11.4175i	0.838676	−	0.484210i
$557$	11.5621	+	3.09805i	0.489901	+	0.131268i	0.495309	−	0.868717i	$-0.335055\pi$
$557$	11.5621	+	3.09805i	0.489901	+	0.131268i	−0.00540830	+	0.999985i	$0.501722\pi$
$558$	2.01679	+	14.0809i	0.0853776	+	0.596094i
$559$	−11.7273	−	11.7997i	−0.496014	−	0.499073i
$560$	4.57762	+	1.42868i	0.193440	+	0.0603728i
$561$	−10.2696	+	0.731714i	−0.433581	+	0.0308930i
$562$	−8.17331			−0.344770
$563$	−47.0112			−1.98129			−0.990644	−	0.136475i	$-0.956423\pi$
$563$	−47.0112			−1.98129			−0.990644	+	0.136475i	$0.956423\pi$
$564$	0.457164	+	6.41627i	0.0192501	+	0.270174i
$565$	4.59991	+	17.1671i	0.193520	+	0.722225i
$566$	17.6312	+	4.72427i	0.741096	+	0.198576i
$567$	−22.8857	−	6.57591i	−0.961111	−	0.276162i
$568$	0.415701	+	0.720015i	0.0174424	+	0.0302112i
$569$	4.26338			0.178730			0.0893650	−	0.995999i	$-0.471516\pi$
$569$	4.26338			0.178730			0.0893650	+	0.995999i	$0.471516\pi$
$570$	18.5309	+	9.00791i	0.776172	+	0.377300i
$571$	9.82900	+	5.67478i	0.411331	+	0.237482i	0.691361	−	0.722509i	$-0.257011\pi$
$571$	9.82900	+	5.67478i	0.411331	+	0.237482i	−0.280031	+	0.959991i	$0.590345\pi$
$572$	3.25402	+	0.0100018i	0.136057	+	0.000418197i
$573$	9.57867	+	1.84881i	0.400155	+	0.0772353i
$574$	−17.8114	+	28.1387i	−0.743433	+	1.17449i
$575$	−2.04326	−	1.17968i	−0.0852099	−	0.0491960i
$576$	−1.85321	−	2.35916i	−0.0772169	−	0.0982982i
$577$	5.42876	+	20.2604i	0.226002	+	0.843452i	0.982001	+	0.188878i	$0.0604851\pi$
$577$	5.42876	+	20.2604i	0.226002	+	0.843452i	−0.755998	+	0.654574i	$0.772848\pi$
$578$	18.6529	+	18.6529i	0.775857	+	0.775857i
$579$	−0.739007	−	10.3719i	−0.0307121	−	0.431042i
$580$	8.10267	+	8.10267i	0.336445	+	0.336445i
$581$	−20.8996	+	19.2631i	−0.867060	+	0.799170i
$582$	11.5431	+	10.0076i	0.478476	+	0.414828i
$583$	2.94807	+	2.94807i	0.122097	+	0.122097i
$584$	−4.98171	+	8.62857i	−0.206144	+	0.357053i
$585$	−15.4543	+	12.0633i	−0.638956	+	0.498756i
$586$	1.90991	+	3.30805i	0.0788975	+	0.136654i
$587$	23.1964	−	6.21546i	0.957419	−	0.256540i	0.253911	−	0.967227i	$-0.418283\pi$
$587$	23.1964	−	6.21546i	0.957419	−	0.256540i	0.703508	+	0.710688i	$0.251616\pi$
$588$	−3.01706	−	11.7430i	−0.124422	−	0.484272i
$589$	−26.9508	+	15.5601i	−1.11049	+	0.641141i
$590$	−2.51561	+	9.38837i	−0.103566	+	0.386513i
$591$	0.193206	−	0.130690i	0.00794742	−	0.00537585i
$592$	−7.02220	−	7.02220i	−0.288611	−	0.288611i
$593$	−3.62674	−	0.971782i	−0.148932	−	0.0399063i	0.183583	−	0.983004i	$-0.441231\pi$
$593$	−3.62674	−	0.971782i	−0.148932	−	0.0399063i	−0.332515	+	0.943098i	$0.607897\pi$
$594$	4.68407	+	0.226923i	0.192190	+	0.00931077i
$595$	30.1495	+	9.40970i	1.23601	+	0.385760i
$596$	−2.70140	−	10.0818i	−0.110654	−	0.412965i
$597$	−8.74272	−	25.2825i	−0.357816	−	1.03474i
$598$	−2.49346	+	4.28831i	−0.101965	+	0.175362i
$599$	6.17618	+	3.56582i	0.252352	+	0.145695i	0.620841	−	0.783937i	$-0.286791\pi$
$599$	6.17618	+	3.56582i	0.252352	+	0.145695i	−0.368489	+	0.929632i	$0.620125\pi$
$600$	−2.46028	+	1.66420i	−0.100441	+	0.0679407i
$601$	−19.7330	+	34.1785i	−0.804924	+	1.39417i	0.111418	+	0.993774i	$0.464461\pi$
$601$	−19.7330	+	34.1785i	−0.804924	+	1.39417i	−0.916342	+	0.400396i	$0.868872\pi$
$602$	3.63700	−	11.6533i	0.148233	−	0.474951i
$603$	4.30484	−	1.84070i	0.175307	−	0.0749589i
$604$	−2.89683	−	10.8111i	−0.117870	−	0.439898i
$605$	−13.0539	+	13.0539i	−0.530718	+	0.530718i
$606$	−1.14842	−	16.1180i	−0.0466513	−	0.654748i
$607$	3.08875	−	5.34988i	0.125369	−	0.217145i	−0.796508	−	0.604628i	$-0.793322\pi$
$607$	3.08875	−	5.34988i	0.125369	−	0.217145i	0.921877	+	0.387483i	$0.126655\pi$
$608$	3.28164	−	5.68397i	0.133088	−	0.230516i
$609$	6.64419	−	28.1998i	0.269236	−	1.14271i
$610$			0.577227i			0.0233712i
$611$	0.0411576	−	13.3903i	0.00166506	−	0.541715i
$612$	−12.2057	−	15.5381i	−0.493388	−	0.628090i
$613$	9.44086	+	2.52967i	0.381313	+	0.102172i	0.444384	−	0.895837i	$-0.353423\pi$
$613$	9.44086	+	2.52967i	0.381313	+	0.102172i	−0.0630708	+	0.998009i	$0.520089\pi$
$614$			16.8438i			0.679761i
$615$	12.9139	+	37.3449i	0.520740	+	1.50589i
$616$	1.10873	+	2.11479i	0.0446719	+	0.0852075i
$617$	1.15991	−	4.32885i	0.0466963	−	0.174273i	−0.938639	−	0.344900i	$-0.887913\pi$
$617$	1.15991	−	4.32885i	0.0466963	−	0.174273i	0.985336	+	0.170627i	$0.0545794\pi$
$618$	−12.9591	+	0.923348i	−0.521293	+	0.0371425i
$619$	−42.6846	+	11.4373i	−1.71564	+	0.459704i	−0.976796	−	0.214173i	$-0.931294\pi$
$619$	−42.6846	+	11.4373i	−1.71564	+	0.459704i	−0.738843	+	0.673878i	$0.764628\pi$
$620$			8.59399i			0.345143i
$621$	−3.86984	+	6.01091i	−0.155291	+	0.241209i
$622$	23.4683	−	6.28830i	0.940991	−	0.252138i
$623$	23.5170	+	25.5147i	0.942187	+	1.02223i
$624$	3.48306	+	5.18346i	0.139434	+	0.207505i
$625$	−6.74235	−	11.6781i	−0.269694	−	0.467123i
$626$	4.01781	−	14.9947i	0.160584	−	0.599307i
$627$	3.35299	+	9.69628i	0.133906	+	0.387232i
$628$	7.35849	+	4.24843i	0.293636	+	0.169531i
$629$	−46.2502	−	46.2502i	−1.84412	−	1.84412i
$630$	−13.1237	−	5.89316i	−0.522862	−	0.234789i
$631$	5.66403	−	21.1384i	0.225481	−	0.841508i	−0.756730	−	0.653728i	$-0.773204\pi$
$631$	5.66403	−	21.1384i	0.225481	−	0.841508i	0.982211	−	0.187780i	$-0.0601292\pi$
$632$	7.56603	+	2.02731i	0.300961	+	0.0806422i
$633$	5.47833	−	28.3832i	0.217744	−	1.12813i
$634$	−23.1024	+	13.3382i	−0.917512	+	0.529726i
$635$	18.2122	−	18.2122i	0.722728	−	0.722728i
$636$	−1.51638	+	7.85635i	−0.0601285	+	0.311525i
$637$	4.45098	+	24.8433i	0.176354	+	0.984327i
$638$			5.70583i			0.225896i
$639$	−0.980609	−	2.29335i	−0.0387923	−	0.0907236i
$640$	−0.906243	−	1.56966i	−0.0358224	−	0.0620462i
$641$	−45.5041			−1.79731			−0.898653	−	0.438661i	$-0.855453\pi$
$641$	−45.5041			−1.79731			−0.898653	+	0.438661i	$0.855453\pi$
$642$	4.29315	−	8.83177i	0.169437	−	0.348562i
$643$	18.4734	+	4.94992i	0.728518	+	0.195206i	0.603969	−	0.797008i	$-0.293585\pi$
$643$	18.4734	+	4.94992i	0.728518	+	0.195206i	0.124549	+	0.992213i	$0.460252\pi$
$644$	−3.63702	−	0.148189i	−0.143319	−	0.00583948i
$645$	−8.11571	−	11.9979i	−0.319556	−	0.472417i
$646$	21.6138	−	37.4363i	0.850385	−	1.47291i
$647$	−6.77867	−	11.7410i	−0.266497	−	0.461587i	0.701458	−	0.712711i	$-0.252533\pi$
$647$	−6.77867	−	11.7410i	−0.266497	−	0.461587i	−0.967955	+	0.251124i	$0.919200\pi$
$648$	4.67593	+	7.68997i	0.183688	+	0.302091i
$649$	−4.19134	+	2.41987i	−0.164524	+	0.0949882i
$650$	5.36422	−	3.07509i	0.210402	−	0.120615i
$651$	18.4784	−	11.4313i	0.724226	−	0.448030i
$652$	−4.35204	−	16.2420i	−0.170439	−	0.636088i
$653$			7.89746i			0.309052i	0.987989	+	0.154526i	$0.0493850\pi$
$653$			7.89746i			0.309052i	−0.987989	+	0.154526i	$0.950615\pi$
$654$	1.87959	−	9.73815i	0.0734980	−	0.380792i
$655$	−7.44383	−	27.7807i	−0.290854	−	1.08548i
$656$	12.1581	−	3.25776i	0.474696	−	0.127194i
$657$	17.9254	−	23.9187i	0.699338	−	0.933158i
$658$	8.70240	−	4.56243i	0.339255	−	0.177862i
$659$	−27.0573	+	15.6216i	−1.05400	+	0.608530i	−0.923768	−	0.382953i	$-0.874907\pi$
$659$	−27.0573	+	15.6216i	−1.05400	+	0.608530i	−0.130237	+	0.991483i	$0.541574\pi$
$660$	2.78191	+	0.536947i	0.108286	+	0.0209006i
$661$	10.0623	−	37.5529i	0.391377	−	1.46064i	−0.436488	−	0.899710i	$-0.643778\pi$
$661$	10.0623	−	37.5529i	0.391377	−	1.46064i	0.827865	−	0.560927i	$-0.189555\pi$
$662$	−6.38975	+	11.0674i	−0.248345	+	0.430146i
$663$	22.9404	+	34.1398i	0.890932	+	1.32588i
$664$	10.7428			0.416903
$665$	1.28132	−	31.4474i	0.0496873	−	1.21948i
$666$	18.4040	+	23.4285i	0.713140	+	0.907837i
$667$	−7.53279	−	4.34906i	−0.291671	−	0.168396i
$668$	14.9673	−	4.01048i	0.579103	−	0.155170i
$669$	−18.3152	−	27.0764i	−0.708107	−	1.04683i
$670$	2.73222	−	0.732096i	0.105555	−	0.0282833i
$671$	−0.203239	+	0.203239i	−0.00784596	+	0.00784596i
$672$	−2.16957	+	4.03646i	−0.0836929	+	0.155710i
$673$	−26.8382	−	15.4950i	−1.03453	−	0.597289i	−0.116254	−	0.993219i	$-0.537089\pi$
$673$	−26.8382	−	15.4950i	−1.03453	−	0.597289i	−0.918281	+	0.395930i	$0.870422\pi$
$674$	−4.37088	+	4.37088i	−0.168360	+	0.168360i
$675$	7.92356	−	4.07678i	0.304978	−	0.156915i
$676$	−6.43067	−	11.2981i	−0.247333	−	0.434541i
$677$	11.6126	−	6.70454i	0.446309	−	0.257676i	−0.259961	−	0.965619i	$-0.583710\pi$
$677$	11.6126	−	6.70454i	0.446309	−	0.257676i	0.706270	+	0.707943i	$0.250376\pi$
$678$	−16.9410	+	1.20706i	−0.650615	+	0.0463568i
$679$	6.95257	−	22.2767i	0.266815	−	0.854900i
$680$	−5.96878	−	10.3382i	−0.228892	−	0.396453i
$681$	9.60140	+	4.66727i	0.367927	+	0.178850i
$682$	−3.02591	+	3.02591i	−0.115868	+	0.115868i
$683$	−0.158767	+	0.158767i	−0.00607506	+	0.00607506i	−0.710138	−	0.704063i	$-0.751367\pi$
$683$	−0.158767	+	0.158767i	−0.00607506	+	0.00607506i	0.704063	+	0.710138i	$0.251367\pi$
$684$	−11.8082	+	15.7562i	−0.451497	+	0.602453i
$685$	6.03834	+	10.4587i	0.230713	+	0.399607i
$686$	−14.5941	+	11.4023i	−0.557205	+	0.435342i
$687$	3.69940	+	51.9209i	0.141141	+	1.98090i
$688$	−3.99588	+	2.30702i	−0.152342	+	0.0879545i
$689$	4.36036	−	16.0753i	0.166116	−	0.612419i
$690$	−2.82928	+	3.26339i	−0.107709	+	0.124235i
$691$	24.7594	−	24.7594i	0.941894	−	0.941894i	−0.0565085	−	0.998402i	$-0.517997\pi$
$691$	24.7594	−	24.7594i	0.941894	−	0.941894i	0.998402	+	0.0565085i	$0.0179968\pi$
$692$	−14.3688	−	8.29585i	−0.546221	−	0.315361i
$693$	−2.54586	−	6.69577i	−0.0967091	−	0.254351i
$694$	7.06855	−	7.06855i	0.268318	−	0.268318i
$695$	−39.9779	+	10.7120i	−1.51645	+	0.406331i
$696$	−9.07020	+	6.13532i	−0.343805	+	0.232559i
$697$	80.0770	−	21.4566i	3.03313	−	0.812725i
$698$	−18.7204	−	10.8082i	−0.708578	−	0.409098i
$699$	−7.61630	−	6.60316i	−0.288075	−	0.249754i
$700$	3.83370	+	2.42667i	0.144900	+	0.0917196i
$701$	4.70332			0.177642			0.0888209	−	0.996048i	$-0.471690\pi$
$701$	4.70332			0.177642			0.0888209	+	0.996048i	$0.471690\pi$
$702$	−8.52017	−	16.6855i	−0.321573	−	0.629755i
$703$	−32.5896	+	56.4469i	−1.22914	+	2.12893i
$704$	0.233586	−	0.871755i	0.00880360	−	0.0328555i
$705$	2.20954	−	11.4476i	0.0832162	−	0.431142i
$706$	9.30877	−	5.37442i	0.350340	−	0.202269i
$707$	−21.8609	+	11.4610i	−0.822162	+	0.431037i
$708$	−8.35354	−	4.06068i	−0.313945	−	0.152610i
$709$	34.6183	−	9.27595i	1.30012	−	0.348366i	0.458624	−	0.888631i	$-0.348343\pi$
$709$	34.6183	−	9.27595i	1.30012	−	0.348366i	0.841495	+	0.540265i	$0.181676\pi$
$710$	−0.390016	−	1.45556i	−0.0146370	−	0.0546261i
$711$	−21.8108	−	8.74537i	−0.817970	−	0.327977i
$712$		−	13.1151i		−	0.491511i
$713$	−1.68839	−	6.30116i	−0.0632308	−	0.235980i
$714$	−14.2894	+	26.5852i	−0.534767	+	0.994928i
$715$	−5.69221	−	1.54399i	−0.212877	−	0.0577420i
$716$	−7.56115	+	4.36543i	−0.282573	+	0.163144i
$717$	−9.59959	−	4.66639i	−0.358503	−	0.174269i
$718$	11.3275	+	19.6198i	0.422739	+	0.732205i
$719$	8.67999	−	15.0342i	0.323709	−	0.560681i	−0.657541	−	0.753419i	$-0.728403\pi$
$719$	8.67999	−	15.0342i	0.323709	−	0.560681i	0.981250	+	0.192738i	$0.0617368\pi$
$720$	2.13776	+	4.99959i	0.0796698	+	0.186324i
$721$	9.21489	+	17.5765i	0.343180	+	0.654584i
$722$	−23.2563	−	6.23151i	−0.865511	−	0.231913i
$723$	12.0086	+	5.83743i	0.446606	+	0.217096i
$724$	−12.7095			−0.472344
$725$	5.42094	+	9.38935i	0.201329	+	0.348712i
$726$	−9.88441	−	14.6127i	−0.366845	−	0.542328i
$727$		−	2.82499i		−	0.104773i	−0.998627	−	0.0523865i	$-0.983317\pi$
$727$		−	2.82499i		−	0.104773i	0.998627	−	0.0523865i	$-0.0166828\pi$
$728$	5.12682	−	8.04461i	0.190013	−	0.298153i
$729$	−11.1765	−	24.5782i	−0.413945	−	0.910302i
$730$	12.7693	−	12.7693i	0.472614	−	0.472614i
$731$	−26.3180	+	15.1947i	−0.973407	+	0.561997i
$732$	−0.541614	−	0.104539i	−0.0200186	−	0.00386387i
$733$	−9.70415	−	2.60022i	−0.358431	−	0.0960413i	0.0751097	−	0.997175i	$-0.476069\pi$
$733$	−9.70415	−	2.60022i	−0.358431	−	0.0960413i	−0.433541	+	0.901134i	$0.642736\pi$
$734$	−1.00574	+	3.75346i	−0.0371225	+	0.138543i
$735$	−0.226646	+	21.9741i	−0.00835995	+	0.810526i
$736$	0.972841	+	0.972841i	0.0358594	+	0.0358594i
$737$	1.21977	+	0.704235i	0.0449308	+	0.0259408i
$738$	−37.3796	+	5.35383i	−1.37596	+	0.197077i
$739$	−0.242805	+	0.906159i	−0.00893171	+	0.0333336i	−0.970248	−	0.242114i	$-0.922159\pi$
$739$	−0.242805	+	0.906159i	−0.00893171	+	0.0333336i	0.961316	+	0.275447i	$0.0888260\pi$
$740$	8.99980	+	15.5881i	0.330839	+	0.573030i
$741$	26.9446	−	30.8865i	0.989836	−	1.13465i
$742$	11.9248	−	2.68011i	0.437773	−	0.0983899i
$743$	33.4454	−	8.96168i	1.22699	−	0.328772i	0.413586	−	0.910465i	$-0.364276\pi$
$743$	33.4454	−	8.96168i	1.22699	−	0.328772i	0.813408	+	0.581693i	$0.197610\pi$
$744$	−8.06377	−	1.55642i	−0.295632	−	0.0570610i
$745$			18.9177i			0.693090i
$746$	−7.16253	+	1.91919i	−0.262239	+	0.0702667i
$747$	−31.9985	−	3.84338i	−1.17076	−	0.140622i
$748$	1.53846	−	5.74162i	0.0562518	−	0.209935i
$749$	−14.9878	−	0.610673i	−0.547641	−	0.0223135i
$750$	19.9227	−	6.88929i	0.727472	−	0.251561i
$751$			22.2196i			0.810805i	0.914138	+	0.405403i	$0.132869\pi$
$751$			22.2196i			0.810805i	−0.914138	+	0.405403i	$0.867131\pi$
$752$	−3.58728	−	0.961209i	−0.130815	−	0.0350517i
$753$	−6.41302	−	5.55994i	−0.233703	−	0.202615i
$754$	19.7760	−	11.3368i	0.720200	−	0.412861i
$755$			20.2863i			0.738292i
$756$	7.90635	−	11.2468i	0.287551	−	0.409041i
$757$	19.9696	−	34.5883i	0.725807	−	1.25713i	−0.232834	−	0.972516i	$-0.574800\pi$
$757$	19.9696	−	34.5883i	0.725807	−	1.25713i	0.958641	−	0.284618i	$-0.0918667\pi$
$758$	4.78011	−	8.27939i	0.173621	−	0.300721i
$759$	−2.14520	+	0.152847i	−0.0778660	+	0.00554800i
$760$	−8.41165	+	8.41165i	−0.305123	+	0.305123i
$761$	0.754848	+	2.81713i	0.0273632	+	0.102121i	0.978257	−	0.207397i	$-0.0664991\pi$
$761$	0.754848	+	2.81713i	0.0273632	+	0.102121i	−0.950894	+	0.309518i	$0.899832\pi$
$762$	13.7902	+	20.3869i	0.499567	+	0.738538i
$763$	−14.7811	+	3.32206i	−0.535112	+	0.120267i
$764$	−2.81616	+	4.87773i	−0.101885	+	0.176470i
$765$	14.0799	+	32.9287i	0.509061	+	1.19054i
$766$	−18.3476	−	10.5930i	−0.662926	−	0.382741i
$767$	16.7148	+	9.71890i	0.603535	+	0.350929i
$768$	1.63694	−	0.566057i	0.0590681	−	0.0204258i
$769$	9.05425	+	33.7909i	0.326505	+	1.21853i	0.912791	+	0.408427i	$0.133923\pi$
$769$	9.05425	+	33.7909i	0.326505	+	1.21853i	−0.586286	+	0.810104i	$0.699411\pi$
$770$	−0.949019	−	4.22254i	−0.0342003	−	0.152170i
$771$	36.2339	−	12.5297i	1.30493	−	0.451248i
$772$	5.79885	+	1.55380i	0.208705	+	0.0559224i
$773$	3.72808	+	3.72808i	0.134090	+	0.134090i	0.770966	−	0.636876i	$-0.219774\pi$
$773$	3.72808	+	3.72808i	0.134090	+	0.134090i	−0.636876	+	0.770966i	$0.719774\pi$
$774$	12.7275	−	5.44211i	0.457479	−	0.195613i
$775$	−2.10452	+	7.85417i	−0.0755965	+	0.282130i
$776$	−7.63863	+	4.41017i	−0.274211	+	0.158316i
$777$	21.5457	−	40.0856i	0.772949	−	1.43806i
$778$	30.2988	−	8.11855i	1.08627	−	0.291064i
$779$	−41.3062	−	71.5444i	−1.47995	−	2.56334i
$780$	−3.66630	−	10.7088i	−0.131274	−	0.383435i
$781$	0.375173	−	0.649819i	0.0134247	−	0.0232523i
$782$	6.40741	+	6.40741i	0.229128	+	0.229128i
$783$	29.2114	−	15.0297i	1.04393	−	0.537116i
$784$	6.97680	+	0.569480i	0.249171	+	0.0203386i
$785$	−10.8898	−	10.8898i	−0.388672	−	0.388672i
$786$	27.4149	−	1.95333i	0.977856	−	0.0696729i
$787$	−3.00075	−	3.00075i	−0.106965	−	0.106965i	0.651599	−	0.758564i	$-0.274099\pi$
$787$	−3.00075	−	3.00075i	−0.106965	−	0.106965i	−0.758564	+	0.651599i	$0.774099\pi$
$788$	0.0348552	+	0.130081i	0.00124167	+	0.00463396i
$789$	18.6574	−	21.5201i	0.664221	−	0.766135i
$790$	−12.2950	−	7.09855i	−0.437438	−	0.252555i
$791$	12.0463	+	22.9771i	0.428316	+	0.816972i
$792$	−1.00764	+	2.51303i	−0.0358048	+	0.0892967i
$793$	1.10822	+	0.300601i	0.0393542	+	0.0106747i
$794$	−22.7781	−	13.1509i	−0.808364	−	0.466709i
$795$	6.34024	−	13.0430i	0.224865	−	0.462587i
$796$	15.4449			0.547431
$797$	5.97249	+	10.3447i	0.211557	+	0.366427i	0.952202	−	0.305470i	$-0.0988134\pi$
$797$	5.97249	+	10.3447i	0.211557	+	0.366427i	−0.740645	+	0.671896i	$0.765480\pi$
$798$	29.2752	+	6.89755i	1.03633	+	0.244171i
$799$	−23.6269	−	6.33080i	−0.835858	−	0.223968i
$800$	−0.443847	−	1.65646i	−0.0156923	−	0.0585646i
$801$	−4.69210	+	39.0647i	−0.165787	+	1.38028i
$802$	−6.22922			−0.219961
$803$	8.99205			0.317323
$804$	0.192109	+	2.69624i	0.00677515	+	0.0950889i
$805$	6.29792	+	1.96559i	0.221972	+	0.0692779i
$806$	16.4997	+	4.47548i	0.581176	+	0.157642i
$807$	4.98232	+	14.4080i	0.175386	+	0.507186i
$808$	9.01142	+	2.41460i	0.317021	+	0.0849455i
$809$	24.1570	−	13.9470i	0.849314	−	0.490352i	−0.0111055	−	0.999938i	$-0.503535\pi$
$809$	24.1570	−	13.9470i	0.849314	−	0.490352i	0.860419	+	0.509587i	$0.170202\pi$
$810$	−4.57886	−	15.6566i	−0.160885	−	0.550115i
$811$	−13.1791	+	13.1791i	−0.462781	+	0.462781i	−0.899566	−	0.436785i	$-0.856117\pi$
$811$	−13.1791	+	13.1791i	−0.462781	+	0.462781i	0.436785	+	0.899566i	$0.356117\pi$
$812$	14.1335	+	8.94629i	0.495988	+	0.313953i
$813$	36.2151	+	17.6043i	1.27012	+	0.617409i
$814$	−2.31972	+	8.65730i	−0.0813060	+	0.303438i
$815$			30.4770i			1.06756i
$816$	10.7814	−	3.72822i	0.377423	−	0.130514i
$817$	21.4135	+	21.4135i	0.749165	+	0.749165i
$818$	−11.0912			−0.387794
$819$	−18.1488	+	22.1274i	−0.634169	+	0.773195i
$820$	−22.8138			−0.796694
$821$	29.3117	+	29.3117i	1.02298	+	1.02298i	0.999730	+	0.0232551i	$0.00740300\pi$
$821$	29.3117	+	29.3117i	1.02298	+	1.02298i	0.0232551	+	0.999730i	$0.492597\pi$
$822$	−10.9070	+	3.77167i	−0.380426	+	0.131552i
$823$		−	17.3698i		−	0.605472i	−0.953075	−	0.302736i	$-0.902100\pi$
$823$		−	17.3698i		−	0.605472i	0.953075	−	0.302736i	$-0.0979000\pi$
$824$	1.94138	−	7.24535i	0.0676313	−	0.252404i
$825$	2.41094	+	1.17197i	0.0839382	+	0.0408026i
$826$	−0.577606	+	14.1762i	−0.0200975	+	0.493254i
$827$	−19.6554	+	19.6554i	−0.683486	+	0.683486i	−0.960784	−	0.277298i	$-0.910561\pi$
$827$	−19.6554	+	19.6554i	−0.683486	+	0.683486i	0.277298	+	0.960784i	$0.410561\pi$
$828$	−2.54965	−	3.24574i	−0.0886065	−	0.112797i
$829$	4.64439	−	2.68144i	0.161306	−	0.0931303i	−0.417174	−	0.908827i	$-0.636979\pi$
$829$	4.64439	−	2.68144i	0.161306	−	0.0931303i	0.578480	+	0.815696i	$0.303646\pi$
$830$	−18.8078	−	5.03953i	−0.652828	−	0.174925i
$831$	4.97591	+	14.3895i	0.172613	+	0.499166i
$832$	−3.48555	+	0.922476i	−0.120840	+	0.0319811i
$833$	45.9512	+	3.75076i	1.59211	+	0.129956i
$834$	−2.81094	−	39.4514i	−0.0973348	−	1.36609i
$835$	−28.0851			−0.971923
$836$	−5.92341			−0.204865
$837$	23.4618	+	7.52084i	0.810960	+	0.259958i
$838$	−5.37466	−	20.0585i	−0.185665	−	0.692910i
$839$	18.8876	+	5.06091i	0.652071	+	0.174722i	0.569665	−	0.821877i	$-0.307073\pi$
$839$	18.8876	+	5.06091i	0.652071	+	0.174722i	0.0824061	+	0.996599i	$0.473740\pi$
$840$	5.69185	−	6.04898i	0.196387	−	0.208710i
$841$	5.48511	+	9.50049i	0.189142	+	0.327603i
$842$	−5.76539			−0.198689
$843$	−6.18907	+	12.7320i	−0.213163	+	0.438514i
$844$	14.4535	+	8.34474i	0.497510	+	0.287238i
$845$	5.95836	+	22.7965i	0.204974	+	0.784224i
$846$	10.3412	+	4.14644i	0.355536	+	0.142558i
$847$	−14.4131	+	22.7700i	−0.495239	+	0.782386i
$848$	−4.00068	−	2.30979i	−0.137384	−	0.0793186i
$849$	20.7101	−	23.8878i	0.710770	−	0.819826i
$850$	−2.92330	−	10.9099i	−0.100268	−	0.374207i
$851$	−9.66118	−	9.66118i	−0.331181	−	0.331181i
$852$	1.43639	−	0.102344i	0.0492099	−	0.00350624i
$853$	23.1719	+	23.1719i	0.793391	+	0.793391i	0.982044	−	0.188653i	$-0.0604120\pi$
$853$	23.1719	+	23.1719i	0.793391	+	0.793391i	−0.188653	+	0.982044i	$0.560412\pi$
$854$	0.184766	+	0.822091i	0.00632255	+	0.0281314i
$855$	28.0642	−	22.0455i	0.959777	−	0.753940i
$856$	4.00898	+	4.00898i	0.137024	+	0.137024i
$857$	11.3306	−	19.6252i	0.387046	−	0.670383i	−0.605005	−	0.796222i	$-0.706829\pi$
$857$	11.3306	−	19.6252i	0.387046	−	0.670383i	0.992051	+	0.125839i	$0.0401622\pi$
$858$	2.47962	−	5.06139i	0.0846529	−	0.172793i
$859$	2.02468	+	3.50686i	0.0690813	+	0.119652i	0.898497	−	0.438979i	$-0.144660\pi$
$859$	2.02468	+	3.50686i	0.0690813	+	0.119652i	−0.829416	+	0.558632i	$0.811327\pi$
$860$	8.07794	−	2.16448i	0.275456	−	0.0738081i
$861$	30.3459	+	49.0533i	1.03419	+	1.67173i
$862$	21.0080	−	12.1290i	0.715535	−	0.413114i
$863$	4.39948	−	16.4191i	0.149760	−	0.558912i	−0.849737	−	0.527207i	$-0.823239\pi$
$863$	4.39948	−	16.4191i	0.149760	−	0.558912i	0.999497	−	0.0317057i	$-0.0100939\pi$
$864$	−5.07829	+	1.10042i	−0.172767	+	0.0374370i
$865$	21.2643	+	21.2643i	0.723007	+	0.723007i
$866$	−6.63950	−	1.77905i	−0.225619	−	0.0604545i
$867$	43.1811	−	14.9321i	1.46651	−	0.507121i
$868$	2.75087	+	12.2396i	0.0933705	+	0.415440i
$869$	−1.82966	−	6.82840i	−0.0620671	−	0.231638i
$870$	18.7576	−	6.48640i	0.635941	−	0.219910i
$871$	0.0172952	−	5.62687i	0.000586025	−	0.190659i
$872$	4.95894	+	2.86305i	0.167931	+	0.0969550i
$873$	24.3301	−	10.4033i	0.823451	−	0.352097i
$874$	4.51490	−	7.82004i	0.152719	−	0.264517i
$875$	−21.8234	−	23.6773i	−0.737765	−	0.800438i
$876$	9.66891	+	14.2941i	0.326682	+	0.482953i
$877$	−11.1425	−	41.5843i	−0.376255	−	1.40420i	−0.851503	−	0.524350i	$-0.824308\pi$
$877$	−11.1425	−	41.5843i	−0.376255	−	1.40420i	0.475248	−	0.879852i	$-0.342358\pi$
$878$	6.90020	−	6.90020i	0.232870	−	0.232870i
$879$	6.59938	−	0.470210i	0.222591	−	0.0158598i
$880$	−0.817891	+	1.41663i	−0.0275711	+	0.0477545i
$881$	−2.80656	+	4.86111i	−0.0945554	+	0.163775i	−0.909423	−	0.415872i	$-0.863476\pi$
$881$	−2.80656	+	4.86111i	−0.0945554	+	0.163775i	0.814868	+	0.579647i	$0.196810\pi$
$882$	−20.5773	−	4.19228i	−0.692873	−	0.141161i
$883$		−	48.7239i		−	1.63969i	−0.572586	−	0.819844i	$-0.694060\pi$
$883$		−	48.7239i		−	1.63969i	0.572586	−	0.819844i	$-0.305940\pi$
$884$	−22.9568	+	6.07569i	−0.772121	+	0.204348i
$885$	12.7199	+	11.0278i	0.427574	+	0.370697i
$886$	−37.9996	−	10.1820i	−1.27662	−	0.342070i
$887$		−	18.0951i		−	0.607573i	−0.952740	−	0.303787i	$-0.901749\pi$
$887$		−	18.0951i		−	0.607573i	0.952740	−	0.303787i	$-0.0982510\pi$
$888$	−16.2563	+	5.62145i	−0.545525	+	0.188644i
$889$	20.1084	−	31.7675i	0.674413	−	1.06545i
$890$	−6.15240	+	22.9611i	−0.206229	+	0.769656i
$891$	3.90041	−	7.12480i	0.130669	−	0.238690i
$892$	18.2300	−	4.88471i	0.610385	−	0.163552i
$893$			24.3749i			0.815675i
$894$	−17.7505	−	3.42609i	−0.593666	−	0.114586i
$895$	15.2854	−	4.09570i	0.510933	−	0.136904i
$896$	−1.79311	−	1.94544i	−0.0599038	−	0.0649926i
$897$	4.79201	+	7.13144i	0.160001	+	0.238112i
$898$	10.8899	+	18.8619i	0.363401	+	0.629430i
$899$	−7.75862	+	28.9556i	−0.258764	+	0.965722i
$900$	0.729420	+	5.09270i	0.0243140	+	0.169757i
$901$	−26.3496	−	15.2129i	−0.877832	−	0.506817i
$902$	−8.03265	−	8.03265i	−0.267458	−	0.267458i
$903$	−15.3989	−	14.4897i	−0.512443	−	0.482188i
$904$	2.53790	−	9.47156i	0.0844092	−	0.315019i
$905$	22.2508	+	5.96210i	0.739643	+	0.198187i
$906$	−19.0347	−	3.67395i	−0.632384	−	0.122059i
$907$	−1.73882	+	1.00391i	−0.0577365	+	0.0333342i	−0.528590	−	0.848877i	$-0.677279\pi$
$907$	−1.73882	+	1.00391i	−0.0577365	+	0.0333342i	0.470854	+	0.882211i	$0.343946\pi$
$908$	−4.35833	+	4.35833i	−0.144636	+	0.144636i
$909$	−25.9775	−	10.4161i	−0.861619	−	0.345479i
$910$	−12.7494	+	11.6789i	−0.422640	+	0.387152i
$911$			39.1948i			1.29858i	0.760540	+	0.649291i	$0.224934\pi$
$911$			39.1948i			1.29858i	−0.760540	+	0.649291i	$0.775066\pi$
$912$	−6.36928	−	9.41607i	−0.210908	−	0.311797i
$913$	−4.84774	−	8.39654i	−0.160437	−	0.277885i
$914$	−9.34252			−0.309023
$915$	0.899179	+	0.437093i	0.0297259	+	0.0144499i
$916$	−29.0285	−	7.77816i	−0.959129	−	0.256998i
$917$	−19.4939	−	37.1828i	−0.643747	−	1.22789i
$918$	−33.4471	+	7.24767i	−1.10392	+	0.239209i
$919$	2.72787	−	4.72481i	0.0899842	−	0.155857i	−0.817520	−	0.575900i	$-0.804652\pi$
$919$	2.72787	−	4.72481i	0.0899842	−	0.155857i	0.907504	+	0.420043i	$0.137985\pi$
$920$	−1.24681	−	2.15955i	−0.0411063	−	0.0711981i
$921$	26.2385	+	12.7546i	0.864589	+	0.420279i
$922$	17.7011	−	10.2197i	0.582955	−	0.336569i
$923$	−2.99765	−	0.00921381i	−0.0986688	−	0.000303276i
$924$	4.13389	−	0.125744i	0.135995	−	0.00413666i
$925$	4.40779	+	16.4501i	0.144927	+	0.540876i
$926$		−	9.27511i		−	0.304799i
$927$	−8.37470	+	20.8864i	−0.275061	+	0.685998i
$928$	−1.63631	−	6.10678i	−0.0537144	−	0.200465i
$929$	58.2185	−	15.5996i	1.91009	−	0.511807i	0.916305	−	0.400482i	$-0.131157\pi$
$929$	58.2185	−	15.5996i	1.91009	−	0.511807i	0.993784	−	0.111324i	$-0.0355093\pi$
$930$	13.3873	+	6.50762i	0.438988	+	0.213393i
$931$	−8.24120	−	45.1978i	−0.270095	−	1.48130i
$932$	5.04008	−	2.90989i	0.165093	−	0.0953167i
$933$	7.97522	−	41.3195i	0.261097	−	1.35274i
$934$	−7.21632	+	26.9317i	−0.236125	+	0.881231i
$935$	−5.38686	+	9.33032i	−0.176169	+	0.305134i
$936$	10.7120	−	1.50068i	0.350134	−	0.0490514i
$937$	26.9548			0.880575			0.440287	−	0.897857i	$-0.354877\pi$
$937$	26.9548			0.880575			0.440287	+	0.897857i	$0.354877\pi$
$938$	3.65691	−	1.91722i	0.119402	−	0.0625994i
$939$	−20.3156	−	17.6132i	−0.662975	−	0.574784i
$940$	5.82944	+	3.36563i	0.190136	+	0.109775i
$941$	−20.5894	+	5.51692i	−0.671196	+	0.179846i	−0.578294	−	0.815829i	$-0.696281\pi$
$941$	−20.5894	+	5.51692i	−0.671196	+	0.179846i	−0.0929026	+	0.995675i	$0.529615\pi$
$942$	12.1901	−	8.24570i	0.397174	−	0.268659i
$943$	16.7272	−	4.48205i	0.544714	−	0.145956i
$944$	3.79190	−	3.79190i	0.123416	−	0.123416i
$945$	−19.1178	+	15.9811i	−0.621902	+	0.519865i
$946$	3.60631	+	2.08211i	0.117251	+	0.0676951i
$947$	−20.0900	+	20.0900i	−0.652838	+	0.652838i	−0.953675	−	0.300838i	$-0.902734\pi$
$947$	−20.0900	+	20.0900i	−0.652838	+	0.652838i	0.300838	+	0.953675i	$0.402734\pi$
$948$	8.88728	−	10.2509i	0.288646	−	0.332934i
$949$	−17.8661	−	31.1658i	−0.579958	−	1.01169i
$950$	−9.74740	+	5.62766i	−0.316247	+	0.182585i
$951$	3.28380	+	46.0879i	0.106484	+	1.49450i
$952$	−11.8100	−	12.8132i	−0.382763	−	0.415279i
$953$	−2.18676	−	3.78759i	−0.0708363	−	0.122692i	0.828432	−	0.560090i	$-0.189233\pi$
$953$	−2.18676	−	3.78759i	−0.0708363	−	0.122692i	−0.899268	+	0.437398i	$0.855900\pi$
$954$	11.0900	+	8.31122i	0.359053	+	0.269086i
$955$	7.21850	−	7.21850i	0.233585	−	0.233585i
$956$	4.35751	−	4.35751i	0.140932	−	0.140932i
$957$	8.88829	+	4.32062i	0.287318	+	0.139666i
$958$	10.7682	+	18.6511i	0.347905	+	0.602589i
$959$	11.9476	+	12.9626i	0.385808	+	0.418583i
$960$	−3.13138	+	0.223113i	−0.101065	+	0.00720094i
$961$	7.37658	−	4.25887i	0.237954	−	0.137383i
$962$	34.6146	−	9.16101i	1.11602	−	0.295363i
$963$	−10.5068	−	13.3754i	−0.338578	−	0.431015i
$964$	−5.45104	+	5.45104i	−0.175566	+	0.175566i
$965$	−9.42331	−	5.44055i	−0.303347	−	0.175138i
$966$	−2.98490	+	5.55338i	−0.0960377	+	0.178677i
$967$	28.0679	−	28.0679i	0.902603	−	0.902603i	−0.0930581	−	0.995661i	$-0.529664\pi$
$967$	28.0679	−	28.0679i	0.902603	−	0.902603i	0.995661	+	0.0930581i	$0.0296642\pi$
$968$	9.83842	−	2.63620i	0.316219	−	0.0847306i
$969$	−41.9499	−	62.0169i	−1.34763	−	1.99227i
$970$	15.4420	−	4.13767i	0.495813	−	0.132853i
$971$	1.31542	+	0.759459i	0.0422139	+	0.0243722i	0.520958	−	0.853582i	$-0.325575\pi$
$971$	1.31542	+	0.759459i	0.0422139	+	0.0243722i	−0.478745	+	0.877954i	$0.658908\pi$
$972$	15.5199	−	1.46088i	0.497800	−	0.0468577i
$973$	−53.5080	+	28.0528i	−1.71539	+	0.899330i
$974$	7.98018			0.255702
$975$	−0.728292	−	10.6847i	−0.0233240	−	0.342184i
$976$	0.159236	−	0.275805i	0.00509703	−	0.00882831i
$977$	−8.68251	+	32.4036i	−0.277778	+	1.03668i	0.676179	+	0.736738i	$0.263635\pi$
$977$	−8.68251	+	32.4036i	−0.277778	+	1.03668i	−0.953957	+	0.299944i	$0.903032\pi$
$978$	−28.5966	−	5.51954i	−0.914420	−	0.176495i
$979$	−10.2507	+	5.91826i	−0.327614	+	0.189148i
$980$	−11.9473	−	4.26986i	−0.381643	−	0.136396i
$981$	−13.7464	−	10.3020i	−0.438888	−	0.328916i
$982$	2.22057	−	0.595000i	0.0708613	−	0.0189872i
$983$	10.8387	+	40.4506i	0.345701	+	1.29018i	0.891791	+	0.452448i	$0.149449\pi$
$983$	10.8387	+	40.4506i	0.345701	+	1.29018i	−0.546089	+	0.837727i	$0.683884\pi$
$984$	4.13170	−	21.4063i	0.131714	−	0.682408i
$985$		−	0.244088i		−	0.00777729i
$986$	−10.7772	−	40.2210i	−0.343215	−	1.28090i
$987$	−0.517436	−	17.0110i	−0.0164702	−	0.541467i
$988$	11.7691	+	20.5301i	0.374424	+	0.653150i
$989$	−5.49756	+	3.17402i	−0.174812	+	0.100928i
$990$	2.94298	−	3.92695i	0.0935340	−	0.124807i
$991$	19.2586	+	33.3569i	0.611771	+	1.05962i	0.990942	+	0.134291i	$0.0428758\pi$
$991$	19.2586	+	33.3569i	0.611771	+	1.05962i	−0.379171	+	0.925327i	$0.623791\pi$
$992$	2.37077	−	4.10630i	0.0752721	−	0.130375i
$993$	12.4018	+	18.3342i	0.393558	+	0.581819i
$994$	−1.02138	−	1.94818i	−0.0323961	−	0.0617924i
$995$	−27.0399	−	7.24532i	−0.857222	−	0.229692i
$996$	8.13480	−	16.7347i	0.257761	−	0.530260i
$997$	−8.97595			−0.284271			−0.142136	−	0.989847i	$-0.545397\pi$
$997$	−8.97595			−0.284271			−0.142136	+	0.989847i	$0.545397\pi$
$998$	−8.32191	−	14.4140i	−0.263425	−	0.456266i
$999$	50.4320	−	10.9281i	1.59560	−	0.345751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.ch.a.305.37	yes	152
3.2	odd	2	inner	546.2.ch.a.305.5	yes	152
7.2	even	3		546.2.bw.a.149.27	yes	152
13.11	odd	12		546.2.bw.a.11.8	✓	152
21.2	odd	6		546.2.bw.a.149.8	yes	152
39.11	even	12		546.2.bw.a.11.27	yes	152
91.37	odd	12	inner	546.2.ch.a.401.5	yes	152
273.128	even	12	inner	546.2.ch.a.401.37	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.11.8	✓	152	13.11	odd	12
546.2.bw.a.11.27	yes	152	39.11	even	12
546.2.bw.a.149.8	yes	152	21.2	odd	6
546.2.bw.a.149.27	yes	152	7.2	even	3
546.2.ch.a.305.5	yes	152	3.2	odd	2	inner
546.2.ch.a.305.37	yes	152	1.1	even	1	trivial
546.2.ch.a.401.5	yes	152	91.37	odd	12	inner
546.2.ch.a.401.37	yes	152	273.128	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.ch (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.63694 - 0.566057i) q^{3} +1.00000i q^{4} +(0.469106 - 1.75073i) q^{5} +(1.55776 + 0.757230i) q^{6} +(0.107711 - 2.64356i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.35916 - 1.85321i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.63694 - 0.566057i) q^{3} +1.00000i q^{4} +(0.469106 - 1.75073i) q^{5} +(1.55776 + 0.757230i) q^{6} +(0.107711 - 2.64356i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.35916 - 1.85321i) q^{9} +(1.56966 - 0.906243i) q^{10} +(0.871755 + 0.233586i) q^{11} +(0.566057 + 1.63694i) q^{12} +(-0.922476 - 3.48555i) q^{13} +(1.94544 - 1.79311i) q^{14} +(-0.223113 - 3.13138i) q^{15} -1.00000 q^{16} -6.58628 q^{17} +(2.97859 + 0.357762i) q^{18} +(1.69870 + 6.33965i) q^{19} +(1.75073 + 0.469106i) q^{20} +(-1.32009 - 4.38832i) q^{21} +(0.451253 + 0.781594i) q^{22} -1.37581 q^{23} +(-0.757230 + 1.55776i) q^{24} +(1.48514 + 0.857446i) q^{25} +(1.81236 - 3.11694i) q^{26} +(2.81278 - 4.36901i) q^{27} +(2.64356 + 0.107711i) q^{28} +(5.47519 + 3.16110i) q^{29} +(2.05646 - 2.37199i) q^{30} +(1.22720 + 4.57998i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.55924 - 0.111097i) q^{33} +(-4.65721 - 4.65721i) q^{34} +(-4.57762 - 1.42868i) q^{35} +(1.85321 + 2.35916i) q^{36} +(7.02220 + 7.02220i) q^{37} +(-3.28164 + 5.68397i) q^{38} +(-3.48306 - 5.18346i) q^{39} +(0.906243 + 1.56966i) q^{40} +(-12.1581 + 3.25776i) q^{41} +(2.16957 - 4.03646i) q^{42} +(3.99588 - 2.30702i) q^{43} +(-0.233586 + 0.871755i) q^{44} +(-2.13776 - 4.99959i) q^{45} +(-0.972841 - 0.972841i) q^{46} +(3.58728 + 0.961209i) q^{47} +(-1.63694 + 0.566057i) q^{48} +(-6.97680 - 0.569480i) q^{49} +(0.443847 + 1.65646i) q^{50} +(-10.7814 + 3.72822i) q^{51} +(3.48555 - 0.922476i) q^{52} +(4.00068 + 2.30979i) q^{53} +(5.07829 - 1.10042i) q^{54} +(0.817891 - 1.41663i) q^{55} +(1.79311 + 1.94544i) q^{56} +(6.36928 + 9.41607i) q^{57} +(1.63631 + 6.10678i) q^{58} +(-3.79190 + 3.79190i) q^{59} +(3.13138 - 0.223113i) q^{60} +(-0.159236 + 0.275805i) q^{61} +(-2.37077 + 4.10630i) q^{62} +(-4.64495 - 6.43618i) q^{63} -1.00000i q^{64} +(-6.53498 - 0.0200864i) q^{65} +(1.18110 + 1.02399i) q^{66} +(1.50744 + 0.403918i) q^{67} -6.58628i q^{68} +(-2.25211 + 0.778785i) q^{69} +(-2.22664 - 4.24710i) q^{70} +(0.215183 - 0.803072i) q^{71} +(-0.357762 + 2.97859i) q^{72} +(9.62392 - 2.57872i) q^{73} +9.93089i q^{74} +(2.91645 + 0.562915i) q^{75} +(-6.33965 + 1.69870i) q^{76} +(0.711396 - 2.27937i) q^{77} +(1.20237 - 6.12816i) q^{78} +(-3.91647 - 6.78352i) q^{79} +(-0.469106 + 1.75073i) q^{80} +(2.13125 - 8.74401i) q^{81} +(-10.9007 - 6.29352i) q^{82} +(-7.59633 - 7.59633i) q^{83} +(4.38832 - 1.32009i) q^{84} +(-3.08967 + 11.5308i) q^{85} +(4.45683 + 1.19420i) q^{86} +(10.7519 + 2.07527i) q^{87} +(-0.781594 + 0.451253i) q^{88} +(-9.27381 + 9.27381i) q^{89} +(2.02362 - 5.04687i) q^{90} +(-9.31361 + 2.06319i) q^{91} -1.37581i q^{92} +(4.60139 + 6.80250i) q^{93} +(1.85691 + 3.21627i) q^{94} +11.8959 q^{95} +(-1.55776 - 0.757230i) q^{96} +(8.51978 + 2.28287i) q^{97} +(-4.53066 - 5.33602i) q^{98} +(2.48949 - 1.06448i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 8 q^{7}+O(q^{10}) \) 152 * q + 8 * q^7	\( 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more