LMFDB - Embedded newform 525.2.bc.c.82.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(82,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("525.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bc (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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			82.5
Character	$\chi$	$=$	525.82
Dual form			525.2.bc.c.493.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32591 - 0.355276i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-0.100242 + 0.0578747i) q^{4} +1.37268i q^{6} +(1.82946 + 1.91130i) q^{7} +(-2.05361 + 2.05361i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(1.32591 - 0.355276i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-0.100242 + 0.0578747i) q^{4} +1.37268i q^{6} +(1.82946 + 1.91130i) q^{7} +(-2.05361 + 2.05361i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(0.557875 + 0.966267i) q^{11} +(-0.0299581 - 0.111805i) q^{12} +(-0.707107 - 0.707107i) q^{13} +(3.10473 + 1.88425i) q^{14} +(-1.87755 + 3.25201i) q^{16} +(3.51535 + 0.941934i) q^{17} +(-1.32591 - 0.355276i) q^{18} +(-3.00449 + 5.20393i) q^{19} +(-2.31968 + 1.27244i) q^{21} +(1.08298 + 1.08298i) q^{22} +(1.31732 + 4.91632i) q^{23} +(-1.45212 - 2.51515i) q^{24} +(-1.18878 - 0.686340i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.294005 - 0.0857135i) q^{28} -2.23150i q^{29} +(-4.40786 + 2.54488i) q^{31} +(0.169252 - 0.631656i) q^{32} +(-1.07773 + 0.288777i) q^{33} +4.99567 q^{34} +0.115749 q^{36} +(7.67091 - 2.05541i) q^{37} +(-2.13484 + 7.96735i) q^{38} +(0.866025 - 0.500000i) q^{39} -9.76765i q^{41} +(-2.62361 + 2.51126i) q^{42} +(6.33202 - 6.33202i) q^{43} +(-0.111845 - 0.0645737i) q^{44} +(3.49330 + 6.05057i) q^{46} +(-1.84169 - 6.87329i) q^{47} +(-2.65526 - 2.65526i) q^{48} +(-0.306171 + 6.99330i) q^{49} +(-1.81968 + 3.15177i) q^{51} +(0.111805 + 0.0299581i) q^{52} +(12.7809 + 3.42463i) q^{53} +(0.686340 - 1.18878i) q^{54} +(-7.68208 - 0.168082i) q^{56} +(-4.24899 - 4.24899i) q^{57} +(-0.792797 - 2.95876i) q^{58} +(0.0470420 + 0.0814792i) q^{59} +(-7.50000 - 4.33013i) q^{61} +(-4.94027 + 4.94027i) q^{62} +(-0.628704 - 2.56997i) q^{63} -8.40786i q^{64} +(-1.32638 + 0.765783i) q^{66} +(-1.84504 + 6.88578i) q^{67} +(-0.406899 + 0.109028i) q^{68} -5.08975 q^{69} +5.04721 q^{71} +(2.80529 - 0.751674i) q^{72} +(2.14269 - 7.99662i) q^{73} +(9.44068 - 5.45058i) q^{74} -0.695536i q^{76} +(-0.826223 + 2.83401i) q^{77} +(0.970631 - 0.970631i) q^{78} +(-3.76483 - 2.17362i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-3.47021 - 12.9510i) q^{82} +(-5.03159 - 5.03159i) q^{83} +(0.158887 - 0.261802i) q^{84} +(6.14605 - 10.6453i) q^{86} +(2.15546 + 0.577554i) q^{87} +(-3.13000 - 0.838680i) q^{88} +(-1.52612 + 2.64332i) q^{89} +(0.0578747 - 2.64512i) q^{91} +(-0.416582 - 0.416582i) q^{92} +(-1.31732 - 4.91632i) q^{93} +(-4.88382 - 8.45903i) q^{94} +(0.566327 + 0.326969i) q^{96} +(-11.8810 + 11.8810i) q^{97} +(2.07860 + 9.38124i) q^{98} -1.11575i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 36 q^{16} + 12 q^{21} + 12 q^{26} - 24 q^{31} - 24 q^{36} - 24 q^{46} + 24 q^{51} - 36 q^{56} - 180 q^{61} - 72 q^{66} - 96 q^{71} + 12 q^{81} + 120 q^{86} - 12 q^{91} - 108 q^{96}+O(q^{100}) $ 24 * q + 36 * q^16 + 12 * q^21 + 12 * q^26 - 24 * q^31 - 24 * q^36 - 24 * q^46 + 24 * q^51 - 36 * q^56 - 180 * q^61 - 72 * q^66 - 96 * q^71 + 12 * q^81 + 120 * q^86 - 12 * q^91 - 108 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.32591	−	0.355276i	0.937558	−	0.251218i	0.242483	−	0.970156i	$-0.422038\pi$
$2$	1.32591	−	0.355276i	0.937558	−	0.251218i	0.695075	+	0.718938i	$0.255371\pi$
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$	−0.100242	+	0.0578747i	−0.0501210	+	0.0289373i
$5$		0			0
$5$		0			0
$6$			1.37268i			0.560394i
$7$	1.82946	+	1.91130i	0.691470	+	0.722405i
$7$	1.82946	+	1.91130i	0.691470	+	0.722405i
$8$	−2.05361	+	2.05361i	−0.726062	+	0.726062i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$		0			0
$11$	0.557875	+	0.966267i	0.168206	+	0.291341i	0.937789	−	0.347206i	$-0.112869\pi$
$11$	0.557875	+	0.966267i	0.168206	+	0.291341i	−0.769583	+	0.638546i	$0.779536\pi$
$12$	−0.0299581	−	0.111805i	−0.00864817	−	0.0322754i
$13$	−0.707107	−	0.707107i	−0.196116	−	0.196116i	0.602217	−	0.798333i	$-0.294284\pi$
$13$	−0.707107	−	0.707107i	−0.196116	−	0.196116i	−0.798333	+	0.602217i	$0.794284\pi$
$14$	3.10473	+	1.88425i	0.829774	+	0.503587i
$15$		0			0
$16$	−1.87755	+	3.25201i	−0.469388	+	0.813004i
$17$	3.51535	+	0.941934i	0.852597	+	0.228453i	0.658547	−	0.752539i	$-0.271171\pi$
$17$	3.51535	+	0.941934i	0.852597	+	0.228453i	0.194049	+	0.980992i	$0.437838\pi$
$18$	−1.32591	−	0.355276i	−0.312519	−	0.0837393i
$19$	−3.00449	+	5.20393i	−0.689277	+	1.19386i	0.282795	+	0.959180i	$0.408738\pi$
$19$	−3.00449	+	5.20393i	−0.689277	+	1.19386i	−0.972072	+	0.234682i	$0.924595\pi$
$20$		0			0
$21$	−2.31968	+	1.27244i	−0.506195	+	0.277669i
$22$	1.08298	+	1.08298i	0.230892	+	0.230892i
$23$	1.31732	+	4.91632i	0.274681	+	1.02512i	0.956055	+	0.293188i	$0.0947163\pi$
$23$	1.31732	+	4.91632i	0.274681	+	1.02512i	−0.681373	+	0.731936i	$0.738617\pi$
$24$	−1.45212	−	2.51515i	−0.296413	−	0.513403i
$25$		0			0
$26$	−1.18878	−	0.686340i	−0.233138	−	0.134602i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−0.294005	−	0.0857135i	−0.0555616	−	0.0161983i
$29$		−	2.23150i		−	0.414379i	−0.978301	−	0.207189i	$-0.933568\pi$
$29$		−	2.23150i		−	0.414379i	0.978301	−	0.207189i	$-0.0664317\pi$
$30$		0			0
$31$	−4.40786	+	2.54488i	−0.791674	+	0.457073i	−0.840552	−	0.541732i	$-0.817769\pi$
$31$	−4.40786	+	2.54488i	−0.791674	+	0.457073i	0.0488774	+	0.998805i	$0.484436\pi$
$32$	0.169252	−	0.631656i	0.0299198	−	0.111662i
$33$	−1.07773	+	0.288777i	−0.187609	+	0.0502697i
$34$	4.99567			0.856750
$35$		0			0
$36$	0.115749			0.0192916
$37$	7.67091	−	2.05541i	1.26109	−	0.337908i	0.434479	−	0.900682i	$-0.356932\pi$
$37$	7.67091	−	2.05541i	1.26109	−	0.337908i	0.826611	+	0.562774i	$0.190266\pi$
$38$	−2.13484	+	7.96735i	−0.346317	+	1.29247i
$39$	0.866025	−	0.500000i	0.138675	−	0.0800641i
$40$		0			0
$41$		−	9.76765i		−	1.52545i	−0.646723	−	0.762725i	$-0.723861\pi$
$41$		−	9.76765i		−	1.52545i	0.646723	−	0.762725i	$-0.276139\pi$
$42$	−2.62361	+	2.51126i	−0.404832	+	0.387496i
$43$	6.33202	−	6.33202i	0.965623	−	0.965623i	−0.0338052	−	0.999428i	$-0.510763\pi$
$43$	6.33202	−	6.33202i	0.965623	−	0.965623i	0.999428	+	0.0338052i	$0.0107626\pi$
$44$	−0.111845	−	0.0645737i	−0.0168612	−	0.00973485i
$45$		0			0
$46$	3.49330	+	6.05057i	0.515059	+	0.892109i
$47$	−1.84169	−	6.87329i	−0.268638	−	1.00257i	−0.959986	−	0.280049i	$-0.909649\pi$
$47$	−1.84169	−	6.87329i	−0.268638	−	1.00257i	0.691347	−	0.722523i	$-0.257017\pi$
$48$	−2.65526	−	2.65526i	−0.383254	−	0.383254i
$49$	−0.306171	+	6.99330i	−0.0437387	+	0.999043i
$50$		0			0
$51$	−1.81968	+	3.15177i	−0.254806	+	0.441336i
$52$	0.111805	+	0.0299581i	0.0155046	+	0.00415445i
$53$	12.7809	+	3.42463i	1.75559	+	0.470409i	0.985805	−	0.167894i	$-0.0536967\pi$
$53$	12.7809	+	3.42463i	1.75559	+	0.470409i	0.769785	+	0.638303i	$0.220363\pi$
$54$	0.686340	−	1.18878i	0.0933990	−	0.161772i
$55$		0			0
$56$	−7.68208	−	0.168082i	−1.02656	−	0.0224610i
$57$	−4.24899	−	4.24899i	−0.562792	−	0.562792i
$58$	−0.792797	−	2.95876i	−0.104099	−	0.388504i
$59$	0.0470420	+	0.0814792i	0.00612435	+	0.0106077i	0.869071	−	0.494687i	$-0.164717\pi$
$59$	0.0470420	+	0.0814792i	0.00612435	+	0.0106077i	−0.862947	+	0.505294i	$0.831384\pi$
$60$		0			0
$61$	−7.50000	−	4.33013i	−0.960277	−	0.554416i	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	−7.50000	−	4.33013i	−0.960277	−	0.554416i	−0.896258	+	0.443533i	$0.853725\pi$
$62$	−4.94027	+	4.94027i	−0.627415	+	0.627415i
$63$	−0.628704	−	2.56997i	−0.0792093	−	0.323785i
$64$		−	8.40786i		−	1.05098i
$65$		0			0
$66$	−1.32638	+	0.765783i	−0.163266	+	0.0942614i
$67$	−1.84504	+	6.88578i	−0.225408	+	0.841232i	0.756833	+	0.653608i	$0.226745\pi$
$67$	−1.84504	+	6.88578i	−0.225408	+	0.841232i	−0.982241	+	0.187624i	$0.939921\pi$
$68$	−0.406899	+	0.109028i	−0.0493438	+	0.0132216i
$69$	−5.08975			−0.612734
$70$		0			0
$71$	5.04721			0.598994			0.299497	−	0.954097i	$-0.403181\pi$
$71$	5.04721			0.598994			0.299497	+	0.954097i	$0.403181\pi$
$72$	2.80529	−	0.751674i	0.330606	−	0.0885857i
$73$	2.14269	−	7.99662i	0.250783	−	0.935933i	−0.719606	−	0.694383i	$-0.755677\pi$
$73$	2.14269	−	7.99662i	0.250783	−	0.935933i	0.970388	−	0.241550i	$-0.0776559\pi$
$74$	9.44068	−	5.45058i	1.09746	−	0.633617i
$75$		0			0
$76$		−	0.695536i		−	0.0797834i
$77$	−0.826223	+	2.83401i	−0.0941569	+	0.322966i
$78$	0.970631	−	0.970631i	0.109902	−	0.109902i
$79$	−3.76483	−	2.17362i	−0.423576	−	0.244552i	0.273030	−	0.962006i	$-0.411974\pi$
$79$	−3.76483	−	2.17362i	−0.423576	−	0.244552i	−0.696606	+	0.717454i	$0.745307\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−3.47021	−	12.9510i	−0.383220	−	1.43020i
$83$	−5.03159	−	5.03159i	−0.552289	−	0.552289i	0.374812	−	0.927101i	$-0.377707\pi$
$83$	−5.03159	−	5.03159i	−0.552289	−	0.552289i	−0.927101	+	0.374812i	$0.877707\pi$
$84$	0.158887	−	0.261802i	0.0173360	−	0.0285650i
$85$		0			0
$86$	6.14605	−	10.6453i	0.662746	−	1.14791i
$87$	2.15546	+	0.577554i	0.231090	+	0.0619203i
$88$	−3.13000	−	0.838680i	−0.333659	−	0.0894036i
$89$	−1.52612	+	2.64332i	−0.161769	+	0.280191i	−0.935503	−	0.353319i	$-0.885053\pi$
$89$	−1.52612	+	2.64332i	−0.161769	+	0.280191i	0.773734	+	0.633510i	$0.218386\pi$
$90$		0			0
$91$	0.0578747	−	2.64512i	0.00606692	−	0.277284i
$92$	−0.416582	−	0.416582i	−0.0434317	−	0.0434317i
$93$	−1.31732	−	4.91632i	−0.136600	−	0.509799i
$94$	−4.88382	−	8.45903i	−0.503728	−	0.872482i
$95$		0			0
$96$	0.566327	+	0.326969i	0.0578006	+	0.0333712i
$97$	−11.8810	+	11.8810i	−1.20634	+	1.20634i	−0.234131	+	0.972205i	$0.575224\pi$
$97$	−11.8810	+	11.8810i	−1.20634	+	1.20634i	−0.972205	+	0.234131i	$0.924776\pi$
$98$	2.07860	+	9.38124i	0.209970	+	0.947649i
$99$		−	1.11575i		−	0.112137i
$100$		0			0
$101$	15.8669	−	9.16075i	1.57881	−	0.911529i	0.583789	−	0.811905i	$-0.301570\pi$
$101$	15.8669	−	9.16075i	1.57881	−	0.911529i	0.995025	−	0.0996233i	$-0.0317638\pi$
$102$	−1.29297	+	4.82545i	−0.128024	+	0.477790i
$103$	−3.46975	+	0.929716i	−0.341884	+	0.0916076i	−0.425676	−	0.904876i	$-0.639964\pi$
$103$	−3.46975	+	0.929716i	−0.341884	+	0.0916076i	0.0837917	+	0.996483i	$0.473297\pi$
$104$	2.90425			0.284785
$105$		0			0
$106$	18.1630			1.76414
$107$	17.2085	−	4.61101i	1.66361	−	0.445763i	0.700233	−	0.713915i	$-0.253080\pi$
$107$	17.2085	−	4.61101i	1.66361	−	0.445763i	0.963377	+	0.268152i	$0.0864129\pi$
$108$	−0.0299581	+	0.111805i	−0.00288272	+	0.0107585i
$109$	−7.42254	+	4.28541i	−0.710951	+	0.410468i	−0.811413	−	0.584473i	$-0.801301\pi$
$109$	−7.42254	+	4.28541i	−0.710951	+	0.410468i	0.100462	+	0.994941i	$0.467968\pi$
$110$		0			0
$111$			7.94151i			0.753775i
$112$	−9.65049	+	2.36085i	−0.911886	+	0.223079i
$113$	3.59900	−	3.59900i	0.338565	−	0.338565i	−0.517262	−	0.855827i	$-0.673049\pi$
$113$	3.59900	−	3.59900i	0.338565	−	0.338565i	0.855827	+	0.517262i	$0.173049\pi$
$114$	−7.14333	−	4.12420i	−0.669034	−	0.386267i
$115$		0			0
$116$	0.129147	+	0.223690i	0.0119910	+	0.0207691i
$117$	0.258819	+	0.965926i	0.0239278	+	0.0892999i
$118$	0.0913209	+	0.0913209i	0.00840677	+	0.00840677i
$119$	4.63085	+	8.44213i	0.424510	+	0.773888i
$120$		0			0
$121$	4.87755	−	8.44817i	0.443414	−	0.768015i
$122$	−11.4827	−	3.07678i	−1.03959	−	0.278558i
$123$	9.43482	+	2.52805i	0.850709	+	0.227947i
$124$	0.294568	−	0.510207i	0.0264530	−	0.0458179i
$125$		0			0
$126$	−1.74665	−	3.18417i	−0.155604	−	0.283669i
$127$	−9.56455	−	9.56455i	−0.848717	−	0.848717i	0.141256	−	0.989973i	$-0.454886\pi$
$127$	−9.56455	−	9.56455i	−0.848717	−	0.848717i	−0.989973	+	0.141256i	$0.954886\pi$
$128$	−2.64860	−	9.88472i	−0.234106	−	0.873694i
$129$	4.47741	+	7.75510i	0.394214	+	0.682799i
$130$		0			0
$131$	9.16296	+	5.29024i	0.800571	+	0.462210i	0.843671	−	0.536861i	$-0.180390\pi$
$131$	9.16296	+	5.29024i	0.800571	+	0.462210i	−0.0430995	+	0.999071i	$0.513723\pi$
$132$	0.0913209	−	0.0913209i	0.00794847	−	0.00794847i
$133$	−15.4429	+	3.77787i	−1.33907	+	0.327583i
$134$			9.78541i			0.845330i
$135$		0			0
$136$	−9.15353	+	5.28479i	−0.784908	+	0.453167i
$137$	−2.31768	+	8.64969i	−0.198013	+	0.738993i	0.793454	+	0.608631i	$0.208281\pi$
$137$	−2.31768	+	8.64969i	−0.198013	+	0.738993i	−0.991466	+	0.130363i	$0.958386\pi$
$138$	−6.74854	+	1.80827i	−0.574474	+	0.153930i
$139$	5.69120			0.482722			0.241361	−	0.970435i	$-0.422406\pi$
$139$	5.69120			0.482722			0.241361	+	0.970435i	$0.422406\pi$
$140$		0			0
$141$	7.11575			0.599254
$142$	6.69213	−	1.79315i	0.561591	−	0.150478i
$143$	0.288777	−	1.07773i	0.0241488	−	0.0901244i
$144$	3.25201	−	1.87755i	0.271001	−	0.156463i
$145$		0			0
$146$		−	11.3640i		−	0.940493i
$147$	−6.67577	−	2.10574i	−0.550608	−	0.173678i
$148$	−0.649990	+	0.649990i	−0.0534289	+	0.0534289i
$149$	−8.34793	−	4.81968i	−0.683889	−	0.394843i	0.117430	−	0.993081i	$-0.462534\pi$
$149$	−8.34793	−	4.81968i	−0.683889	−	0.394843i	−0.801319	+	0.598238i	$0.795868\pi$
$150$		0			0
$151$	10.2208	+	17.7030i	0.831760	+	1.44065i	0.896642	+	0.442757i	$0.146000\pi$
$151$	10.2208	+	17.7030i	0.831760	+	1.44065i	−0.0648821	+	0.997893i	$0.520667\pi$
$152$	−4.51680	−	16.8569i	−0.366360	−	1.36728i
$153$	−2.57341	−	2.57341i	−0.208048	−	0.208048i
$154$	−0.0886390	+	4.05118i	−0.00714273	+	0.326453i
$155$		0			0
$156$	−0.0578747	+	0.100242i	−0.00463368	+	0.00802578i
$157$	−1.47169	−	0.394338i	−0.117454	−	0.0314716i	0.199613	−	0.979875i	$-0.436031\pi$
$157$	−1.47169	−	0.394338i	−0.117454	−	0.0314716i	−0.317067	+	0.948403i	$0.602698\pi$
$158$	−5.76405	−	1.54447i	−0.458563	−	0.122872i
$159$	−6.61587	+	11.4590i	−0.524673	+	0.908760i
$160$		0			0
$161$	−6.98660	+	11.5120i	−0.550621	+	0.907274i
$162$	0.970631	+	0.970631i	0.0762600	+	0.0762600i
$163$	3.16236	+	11.8021i	0.247696	+	0.924412i	0.972009	+	0.234942i	$0.0754900\pi$
$163$	3.16236	+	11.8021i	0.247696	+	0.924412i	−0.724314	+	0.689470i	$0.757843\pi$
$164$	0.565300	+	0.979128i	0.0441425	+	0.0764570i
$165$		0			0
$166$	−8.45903	−	4.88382i	−0.656548	−	0.379058i
$167$	−13.5169	+	13.5169i	−1.04597	+	1.04597i	−0.0470760	+	0.998891i	$0.514990\pi$
$167$	−13.5169	+	13.5169i	−1.04597	+	1.04597i	−0.998891	+	0.0470760i	$0.985010\pi$
$168$	2.15062	−	7.37681i	0.165924	−	0.569134i
$169$		−	12.0000i		−	0.923077i
$170$		0			0
$171$	5.20393	−	3.00449i	0.397954	−	0.229759i
$172$	−0.268270	+	1.00120i	−0.0204554	+	0.0763405i
$173$	5.79555	−	1.55291i	0.440628	−	0.118066i	−0.0316829	−	0.999498i	$-0.510087\pi$
$173$	5.79555	−	1.55291i	0.440628	−	0.118066i	0.472311	+	0.881432i	$0.343420\pi$
$174$	3.06313			0.232216
$175$		0			0
$176$	−4.18975			−0.315815
$177$	−0.0908782	+	0.0243507i	−0.00683083	+	0.00183031i
$178$	−1.08439	+	4.04699i	−0.0812783	+	0.303335i
$179$	10.3923	−	6.00000i	0.776757	−	0.448461i	−0.0585225	−	0.998286i	$-0.518639\pi$
$179$	10.3923	−	6.00000i	0.776757	−	0.448461i	0.835280	+	0.549825i	$0.185306\pi$
$180$		0			0
$181$		−	6.39763i		−	0.475532i	−0.971322	−	0.237766i	$-0.923585\pi$
$181$		−	6.39763i		−	0.475532i	0.971322	−	0.237766i	$-0.0764152\pi$
$182$	−0.863010	−	3.52774i	−0.0639705	−	0.261494i
$183$	6.12372	−	6.12372i	0.452679	−	0.452679i
$184$	−12.8015	−	7.39095i	−0.943739	−	0.544868i
$185$		0			0
$186$	−3.49330	−	6.05057i	−0.256141	−	0.443650i
$187$	1.05096	+	3.92225i	0.0768540	+	0.286823i
$188$	0.582404	+	0.582404i	0.0424762	+	0.0424762i
$189$	2.64512	+	0.0578747i	0.192404	+	0.00420976i
$190$		0			0
$191$	−0.849980	+	1.47221i	−0.0615024	+	0.106525i	−0.895137	−	0.445791i	$-0.852923\pi$
$191$	−0.849980	+	1.47221i	−0.0615024	+	0.106525i	0.833635	+	0.552316i	$0.186256\pi$
$192$	8.12136	+	2.17611i	0.586109	+	0.157047i
$193$	−14.2603	−	3.82103i	−1.02648	−	0.275044i	−0.293978	−	0.955812i	$-0.594979\pi$
$193$	−14.2603	−	3.82103i	−1.02648	−	0.275044i	−0.732499	+	0.680769i	$0.761646\pi$
$194$	−11.5321	+	19.9742i	−0.827957	+	1.43406i
$195$		0			0
$196$	−0.374044	−	0.718741i	−0.0267174	−	0.0513387i
$197$	17.5630	+	17.5630i	1.25131	+	1.25131i	0.955132	+	0.296181i	$0.0957131\pi$
$197$	17.5630	+	17.5630i	1.25131	+	1.25131i	0.296181	+	0.955132i	$0.404287\pi$
$198$	−0.396399	−	1.47938i	−0.0281708	−	0.105135i
$199$	1.11355	+	1.92873i	0.0789376	+	0.136724i	0.902792	−	0.430078i	$-0.141514\pi$
$199$	1.11355	+	1.92873i	0.0789376	+	0.136724i	−0.823854	+	0.566802i	$0.808181\pi$
$200$		0			0
$201$	−6.17362	−	3.56434i	−0.435454	−	0.251409i
$202$	17.7834	−	17.7834i	1.25124	−	1.25124i
$203$	4.26507	−	4.08243i	0.299350	−	0.286531i
$204$		−	0.421253i		−	0.0294936i
$205$		0			0
$206$	−4.27026	+	2.46543i	−0.297523	+	0.171775i
$207$	1.31732	−	4.91632i	0.0915604	−	0.341708i
$208$	3.62715	−	0.971892i	0.251498	−	0.0673886i
$209$	−6.70451			−0.463761
$210$		0			0
$211$	−15.2236			−1.04803			−0.524017	−	0.851708i	$-0.675567\pi$
$211$	−15.2236			−1.04803			−0.524017	+	0.851708i	$0.675567\pi$
$212$	−1.47938	+	0.396399i	−0.101604	+	0.0272248i
$213$	−1.30631	+	4.87523i	−0.0895071	+	0.334045i
$214$	21.1787	−	12.2275i	1.44775	−	0.835857i
$215$		0			0
$216$			2.90425i			0.197609i
$217$	−12.9280	−	3.76901i	−0.877611	−	0.255857i
$218$	−8.31910	+	8.31910i	−0.563441	+	0.563441i
$219$	7.16957	+	4.13935i	0.484475	+	0.279712i
$220$		0			0
$221$	−1.81968	−	3.15177i	−0.122405	−	0.212011i
$222$	2.82143	+	10.5297i	0.189362	+	0.706708i
$223$	17.6103	+	17.6103i	1.17927	+	1.17927i	0.979930	+	0.199340i	$0.0638797\pi$
$223$	17.6103	+	17.6103i	1.17927	+	1.17927i	0.199340	+	0.979930i	$0.436120\pi$
$224$	1.51693	−	0.832096i	0.101354	−	0.0555968i
$225$		0			0
$226$	3.49330	−	6.05057i	0.232371	−	0.402478i
$227$	11.9059	+	3.19018i	0.790224	+	0.211740i	0.631287	−	0.775549i	$-0.282527\pi$
$227$	11.9059	+	3.19018i	0.790224	+	0.211740i	0.158936	+	0.987289i	$0.449194\pi$
$228$	0.671836	+	0.180018i	0.0444934	+	0.0119220i
$229$	−1.22540	+	2.12245i	−0.0809765	+	0.140255i	−0.903670	−	0.428230i	$-0.859137\pi$
$229$	−1.22540	+	2.12245i	−0.0809765	+	0.140255i	0.822693	+	0.568486i	$0.192471\pi$
$230$		0			0
$231$	−2.52360	−	1.53157i	−0.166041	−	0.100770i
$232$	4.58263	+	4.58263i	0.300865	+	0.300865i
$233$	0.686201	+	2.56094i	0.0449545	+	0.167772i	0.984754	−	0.173955i	$-0.0556547\pi$
$233$	0.686201	+	2.56094i	0.0449545	+	0.167772i	−0.939799	+	0.341727i	$0.888988\pi$
$234$	0.686340	+	1.18878i	0.0448675	+	0.0777127i
$235$		0			0
$236$	−0.00943117	−	0.00544509i	−0.000613917	−	0.000354445i
$237$	3.07397	−	3.07397i	0.199676	−	0.199676i
$238$	9.13936	+	9.54824i	0.592417	+	0.618921i
$239$		−	22.0944i		−	1.42917i	−0.699549	−	0.714585i	$-0.746616\pi$
$239$		−	22.0944i		−	1.42917i	0.699549	−	0.714585i	$-0.253384\pi$
$240$		0			0
$241$	−13.3878	+	7.72943i	−0.862381	+	0.497896i	−0.864809	−	0.502101i	$-0.832561\pi$
$241$	−13.3878	+	7.72943i	−0.862381	+	0.497896i	0.00242769	+	0.999997i	$0.499227\pi$
$242$	3.46575	−	12.9344i	0.222787	−	0.831452i
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	1.00242			0.0641733
$245$		0			0
$246$	13.4079			0.854854
$247$	5.80423	−	1.55524i	0.369314	−	0.0989574i
$248$	3.82584	−	14.2782i	0.242941	−	0.906668i
$249$	6.16242	−	3.55787i	0.390527	−	0.225471i
$250$		0			0
$251$			27.7823i			1.75360i	0.480854	+	0.876801i	$0.340327\pi$
$251$			27.7823i			1.75360i	−0.480854	+	0.876801i	$0.659673\pi$
$252$	0.211759	+	0.221232i	0.0133395	+	0.0139363i
$253$	−4.01558	+	4.01558i	−0.252457	+	0.252457i
$254$	−16.0798	−	9.28365i	−1.00893	−	0.582508i
$255$		0			0
$256$	1.38425	+	2.39759i	0.0865157	+	0.149850i
$257$	−2.34364	−	8.74660i	−0.146192	−	0.545598i	−0.999699	−	0.0245163i	$-0.992195\pi$
$257$	−2.34364	−	8.74660i	−0.146192	−	0.545598i	0.853507	−	0.521081i	$-0.174471\pi$
$258$	8.69183	+	8.69183i	0.541130	+	0.541130i
$259$	17.9621	+	10.9012i	1.11611	+	0.677365i
$260$		0			0
$261$	−1.11575	+	1.93253i	−0.0690632	+	0.119621i
$262$	14.0287	+	3.75899i	0.866698	+	0.232231i
$263$	15.7291	+	4.21461i	0.969900	+	0.259884i	0.708785	−	0.705424i	$-0.249243\pi$
$263$	15.7291	+	4.21461i	0.969900	+	0.259884i	0.261114	+	0.965308i	$0.415910\pi$
$264$	1.62021	−	2.80628i	0.0997168	−	0.172715i
$265$		0			0
$266$	−19.1336	+	10.4956i	−1.17316	+	0.643526i
$267$	−2.15826	−	2.15826i	−0.132084	−	0.132084i
$268$	−0.213562	−	0.797025i	−0.0130454	−	0.0486861i
$269$	1.32564	+	2.29607i	0.0808256	+	0.139994i	0.903605	−	0.428367i	$-0.140911\pi$
$269$	1.32564	+	2.29607i	0.0808256	+	0.139994i	−0.822779	+	0.568361i	$0.807578\pi$
$270$		0			0
$271$	−19.1327	−	11.0462i	−1.16223	−	0.671012i	−0.210390	−	0.977618i	$-0.567473\pi$
$271$	−19.1327	−	11.0462i	−1.16223	−	0.671012i	−0.951836	+	0.306606i	$0.900807\pi$
$272$	−9.66343	+	9.66343i	−0.585931	+	0.585931i
$273$	2.54001	+	0.740510i	0.153728	+	0.0448177i
$274$			12.2921i			0.742593i
$275$		0			0
$276$	0.510207	−	0.294568i	0.0307108	−	0.0177309i
$277$	−5.31837	+	19.8484i	−0.319550	+	1.19258i	0.600128	+	0.799904i	$0.295116\pi$
$277$	−5.31837	+	19.8484i	−0.319550	+	1.19258i	−0.919678	+	0.392673i	$0.871551\pi$
$278$	7.54601	−	2.02195i	0.452579	−	0.121268i
$279$	5.08975			0.304716
$280$		0			0
$281$	−27.3811			−1.63342			−0.816709	−	0.577050i	$-0.804204\pi$
$281$	−27.3811			−1.63342			−0.816709	+	0.577050i	$0.804204\pi$
$282$	9.43482	−	2.52805i	0.561836	−	0.150543i
$283$	4.62185	−	17.2490i	0.274740	−	1.02535i	−0.681275	−	0.732028i	$-0.738574\pi$
$283$	4.62185	−	17.2490i	0.274740	−	1.02535i	0.956015	−	0.293317i	$-0.0947593\pi$
$284$	−0.505942	+	0.292106i	−0.0300221	+	0.0173333i
$285$		0			0
$286$		−	1.53157i		−	0.0905635i
$287$	18.6689	−	17.8695i	1.10199	−	1.05480i
$288$	−0.462404	+	0.462404i	−0.0272474	+	0.0272474i
$289$	−3.25201	−	1.87755i	−0.191295	−	0.110444i
$290$		0			0
$291$	−8.40116	−	14.5512i	−0.492484	−	0.853008i
$292$	0.248015	+	0.925604i	0.0145140	+	0.0541669i
$293$	−22.1174	−	22.1174i	−1.29211	−	1.29211i	−0.933479	−	0.358633i	$-0.883243\pi$
$293$	−22.1174	−	22.1174i	−1.29211	−	1.29211i	−0.358633	−	0.933479i	$-0.616757\pi$
$294$	−9.59957	−	0.420275i	−0.559858	−	0.0245109i
$295$		0			0
$296$	−11.5321	+	19.9741i	−0.670287	+	1.16097i
$297$	1.07773	+	0.288777i	0.0625363	+	0.0167566i
$298$	−12.7809	−	3.42463i	−0.740377	−	0.198383i
$299$	2.54488	−	4.40786i	0.147174	−	0.254913i
$300$		0			0
$301$	23.6866	+	0.518258i	1.36527	+	0.0298719i
$302$	19.8413	+	19.8413i	1.14174	+	1.14174i
$303$	4.74195	+	17.6972i	0.272418	+	1.01668i
$304$	−11.2822	−	19.5413i	−0.647077	−	1.12077i
$305$		0			0
$306$	−4.32638	−	2.49783i	−0.247322	−	0.142792i
$307$	20.4425	−	20.4425i	1.16672	−	1.16672i	0.183744	−	0.982974i	$-0.441178\pi$
$307$	20.4425	−	20.4425i	1.16672	−	1.16672i	0.982974	−	0.183744i	$-0.0588216\pi$
$308$	−0.0811955	−	0.331904i	−0.00462654	−	0.0189120i
$309$		−	3.59214i		−	0.204350i
$310$		0			0
$311$	8.28664	−	4.78429i	0.469892	−	0.271292i	−0.246302	−	0.969193i	$-0.579216\pi$
$311$	8.28664	−	4.78429i	0.469892	−	0.271292i	0.716195	+	0.697901i	$0.245882\pi$
$312$	−0.751674	+	2.80529i	−0.0425552	+	0.158818i
$313$	3.13433	−	0.839841i	0.177163	−	0.0474706i	−0.169147	−	0.985591i	$-0.554101\pi$
$313$	3.13433	−	0.839841i	0.177163	−	0.0474706i	0.346310	+	0.938120i	$0.387435\pi$
$314$	−2.09142			−0.118026
$315$		0			0
$316$	0.503191			0.0283067
$317$	−15.5236	+	4.15953i	−0.871891	+	0.233623i	−0.666905	−	0.745142i	$-0.732381\pi$
$317$	−15.5236	+	4.15953i	−0.871891	+	0.233623i	−0.204986	+	0.978765i	$0.565715\pi$
$318$	−4.70092	+	17.5441i	−0.263614	+	0.983823i
$319$	2.15622	−	1.24490i	0.120725	−	0.0697008i
$320$		0			0
$321$			17.8156i			0.994368i
$322$	−5.17365	+	17.7460i	−0.288316	+	0.988948i
$323$	−15.4636	+	15.4636i	−0.860416	+	0.860416i
$324$	−0.100242	−	0.0578747i	−0.00556900	−	0.00321526i
$325$		0			0
$326$	8.38600	+	14.5250i	0.464458	+	0.804465i
$327$	−2.21829	−	8.27877i	−0.122672	−	0.457817i
$328$	20.0590	+	20.0590i	1.10757	+	1.10757i
$329$	9.76765	−	16.0944i	0.538508	−	0.887314i
$330$		0			0
$331$	5.43543	−	9.41443i	0.298758	−	0.517464i	−0.677094	−	0.735897i	$-0.736761\pi$
$331$	5.43543	−	9.41443i	0.298758	−	0.517464i	0.975852	+	0.218432i	$0.0700943\pi$
$332$	0.795579	+	0.213175i	0.0436631	+	0.0116995i
$333$	−7.67091	−	2.05541i	−0.420363	−	0.112636i
$334$	−13.1199	+	22.7243i	−0.717889	+	1.24342i
$335$		0			0
$336$	0.217325	−	9.93269i	0.0118561	−	0.541873i
$337$	−0.508227	−	0.508227i	−0.0276849	−	0.0276849i	0.693129	−	0.720814i	$-0.256232\pi$
$337$	−0.508227	−	0.508227i	−0.0276849	−	0.0276849i	−0.720814	+	0.693129i	$0.756232\pi$
$338$	−4.26331	−	15.9109i	−0.231893	−	0.865438i
$339$	2.54488	+	4.40786i	0.138219	+	0.239402i
$340$		0			0
$341$	−4.91806	−	2.83944i	−0.266328	−	0.153765i
$342$	5.83250	−	5.83250i	0.315386	−	0.315386i
$343$	−13.9265	+	12.2088i	−0.751958	+	0.659211i
$344$			26.0070i			1.40220i
$345$		0			0
$346$	7.13265	−	4.11804i	0.383454	−	0.221387i
$347$	−1.18920	+	4.43814i	−0.0638394	+	0.238252i	−0.990472	−	0.137717i	$-0.956023\pi$
$347$	−1.18920	+	4.43814i	−0.0638394	+	0.238252i	0.926632	+	0.375969i	$0.122690\pi$
$348$	−0.249493	+	0.0668516i	−0.0133743	+	0.00358362i
$349$	2.53256			0.135565			0.0677824	−	0.997700i	$-0.478408\pi$
$349$	2.53256			0.135565			0.0677824	+	0.997700i	$0.478408\pi$
$350$		0			0
$351$	−1.00000			−0.0533761
$352$	0.704770	−	0.188843i	0.0375644	−	0.0100653i
$353$	1.85044	−	6.90595i	0.0984891	−	0.367566i	−0.899036	−	0.437874i	$-0.855732\pi$
$353$	1.85044	−	6.90595i	0.0984891	−	0.367566i	0.997525	+	0.0703079i	$0.0223982\pi$
$354$	−0.111845	+	0.0645737i	−0.00594449	+	0.00343205i
$355$		0			0
$356$		−	0.353295i		−	0.0187246i
$357$	−9.35302	+	2.28808i	−0.495014	+	0.121098i
$358$	11.6476	−	11.6476i	0.615594	−	0.615594i
$359$	−4.00620	−	2.31298i	−0.211439	−	0.122074i	0.390541	−	0.920586i	$-0.372288\pi$
$359$	−4.00620	−	2.31298i	−0.211439	−	0.122074i	−0.601980	+	0.798511i	$0.705621\pi$
$360$		0			0
$361$	−8.55391	−	14.8158i	−0.450206	−	0.779779i
$362$	−2.27292	−	8.48266i	−0.119462	−	0.445839i
$363$	6.89790	+	6.89790i	0.362046	+	0.362046i
$364$	0.147284	+	0.268501i	0.00771978	+	0.0140733i
$365$		0			0
$366$	5.94388	−	10.2951i	0.310692	−	0.538134i
$367$	2.91072	+	0.779925i	0.151938	+	0.0407117i	0.333986	−	0.942578i	$-0.391606\pi$
$367$	2.91072	+	0.779925i	0.151938	+	0.0407117i	−0.182048	+	0.983290i	$0.558273\pi$
$368$	−18.4613	−	4.94669i	−0.962362	−	0.257864i
$369$	−4.88382	+	8.45903i	−0.254242	+	0.440360i
$370$		0			0
$371$	16.8366	+	30.6934i	0.874112	+	1.59352i
$372$	0.416582	+	0.416582i	0.0215988	+	0.0215988i
$373$	1.63467	+	6.10065i	0.0846398	+	0.315880i	0.995246	−	0.0973958i	$-0.0310513\pi$
$373$	1.63467	+	6.10065i	0.0846398	+	0.315880i	−0.910606	+	0.413276i	$0.864385\pi$
$374$	2.78696	+	4.82715i	0.144110	+	0.249606i
$375$		0			0
$376$	17.8972	+	10.3329i	0.922977	+	0.532881i
$377$	−1.57791	+	1.57791i	−0.0812664	+	0.0812664i
$378$	3.52774	−	0.863010i	0.181448	−	0.0443884i
$379$			18.4685i			0.948661i	0.880347	+	0.474331i	$0.157310\pi$
$379$			18.4685i			0.948661i	−0.880347	+	0.474331i	$0.842690\pi$
$380$		0			0
$381$	11.7141	−	6.76316i	0.600133	−	0.346487i
$382$	−0.603955	+	2.25399i	−0.0309010	+	0.115324i
$383$	−24.9817	+	6.69382i	−1.27650	+	0.342038i	−0.832519	−	0.553997i	$-0.813102\pi$
$383$	−24.9817	+	6.69382i	−1.27650	+	0.342038i	−0.443984	+	0.896035i	$0.646435\pi$
$384$	10.2334			0.522222
$385$		0			0
$386$	−20.2653			−1.03148
$387$	−8.64969	+	2.31768i	−0.439689	+	0.117814i
$388$	0.503366	−	1.87859i	0.0255545	−	0.0953709i
$389$	−7.84198	+	4.52757i	−0.397604	+	0.229557i	−0.685450	−	0.728120i	$-0.740394\pi$
$389$	−7.84198	+	4.52757i	−0.397604	+	0.229557i	0.287845	+	0.957677i	$0.407061\pi$
$390$		0			0
$391$			18.5234i			0.936769i
$392$	−13.7328	−	14.9903i	−0.693610	−	0.757124i
$393$	−7.48152	+	7.48152i	−0.377393	+	0.377393i
$394$	29.5266	+	17.0472i	1.48753	+	0.858826i
$395$		0			0
$396$	0.0645737	+	0.111845i	0.00324495	+	0.00562042i
$397$	3.26989	+	12.2034i	0.164111	+	0.612471i	0.998152	+	0.0607683i	$0.0193551\pi$
$397$	3.26989	+	12.2034i	0.164111	+	0.612471i	−0.834041	+	0.551703i	$0.813978\pi$
$398$	2.16170	+	2.16170i	0.108356	+	0.108356i
$399$	0.347768	−	15.8945i	0.0174102	−	0.795718i
$400$		0			0
$401$	17.1118	−	29.6385i	0.854522	−	1.48007i	−0.0225664	−	0.999745i	$-0.507184\pi$
$401$	17.1118	−	29.6385i	0.854522	−	1.48007i	0.877088	−	0.480330i	$-0.159483\pi$
$402$	−9.45198	−	2.53265i	−0.471422	−	0.126317i
$403$	4.91632	+	1.31732i	0.244900	+	0.0656206i
$404$	−1.06035	+	1.83658i	−0.0527545	+	0.0913734i
$405$		0			0
$406$	4.20470	−	6.92820i	0.208676	−	0.343841i
$407$	6.26549	+	6.26549i	0.310569	+	0.310569i
$408$	−2.73561	−	10.2094i	−0.135433	−	0.505442i
$409$	15.0170	+	26.0102i	0.742543	+	1.28612i	0.951334	+	0.308162i	$0.0997138\pi$
$409$	15.0170	+	26.0102i	0.742543	+	1.28612i	−0.208791	+	0.977960i	$0.566953\pi$
$410$		0			0
$411$	−7.75510	−	4.47741i	−0.382531	−	0.220854i
$412$	0.294007	−	0.294007i	0.0144847	−	0.0144847i
$413$	−0.0696702	+	0.238974i	−0.00342824	+	0.0117592i
$414$		−	6.98660i		−	0.343373i
$415$		0			0
$416$	−0.566327	+	0.326969i	−0.0277665	+	0.0160310i
$417$	−1.47299	+	5.49728i	−0.0721327	+	0.269203i
$418$	−8.88956	+	2.38195i	−0.434803	+	0.116505i
$419$	−25.9684			−1.26864			−0.634321	−	0.773070i	$-0.718720\pi$
$419$	−25.9684			−1.26864			−0.634321	+	0.773070i	$0.718720\pi$
$420$		0			0
$421$	1.29211			0.0629734			0.0314867	−	0.999504i	$-0.489976\pi$
$421$	1.29211			0.0629734			0.0314867	+	0.999504i	$0.489976\pi$
$422$	−20.1850	+	5.40856i	−0.982592	+	0.263285i
$423$	−1.84169	+	6.87329i	−0.0895461	+	0.334191i
$424$	−33.2799	+	19.2141i	−1.61621	+	0.933121i
$425$		0			0
$426$			6.92820i			0.335673i
$427$	−5.44474	−	22.2566i	−0.263489	−	1.07707i
$428$	−1.45815	+	1.45815i	−0.0704825	+	0.0704825i
$429$	0.966267	+	0.557875i	0.0466518	+	0.0269344i
$430$		0			0
$431$	6.63935	+	11.4997i	0.319806	+	0.553921i	0.980447	−	0.196781i	$-0.0630488\pi$
$431$	6.63935	+	11.4997i	0.319806	+	0.553921i	−0.660641	+	0.750702i	$0.729715\pi$
$432$	0.971892	+	3.62715i	0.0467602	+	0.174511i
$433$	−2.29449	−	2.29449i	−0.110266	−	0.110266i	0.649821	−	0.760087i	$-0.274844\pi$
$433$	−2.29449	−	2.29449i	−0.110266	−	0.110266i	−0.760087	+	0.649821i	$0.774844\pi$
$434$	−18.4804	−	0.404347i	−0.887087	−	0.0194093i
$435$		0			0
$436$	0.496033	−	0.859155i	0.0237557	−	0.0411461i
$437$	−29.5421	−	7.91578i	−1.41319	−	0.378663i
$438$	10.9768	+	2.94122i	0.524492	+	0.140537i
$439$	19.8885	−	34.4479i	0.949227	−	1.64411i	0.202168	−	0.979351i	$-0.435201\pi$
$439$	19.8885	−	34.4479i	0.949227	−	1.64411i	0.747059	−	0.664758i	$-0.231465\pi$
$440$		0			0
$441$	3.76180	−	5.90329i	0.179133	−	0.281109i
$442$	−3.53247	−	3.53247i	−0.168023	−	0.168023i
$443$	−6.16588	−	23.0114i	−0.292950	−	1.09330i	−0.942832	−	0.333268i	$-0.891849\pi$
$443$	−6.16588	−	23.0114i	−0.292950	−	1.09330i	0.649883	−	0.760035i	$-0.274818\pi$
$444$	−0.459613	−	0.796072i	−0.0218123	−	0.0377799i
$445$		0			0
$446$	29.6061	+	17.0931i	1.40189	+	0.809380i
$447$	6.81605	−	6.81605i	0.322388	−	0.322388i
$448$	16.0700	−	15.3818i	0.759235	−	0.726722i
$449$		−	32.4283i		−	1.53038i	−0.643802	−	0.765192i	$-0.722644\pi$
$449$		−	32.4283i		−	1.53038i	0.643802	−	0.765192i	$-0.277356\pi$
$450$		0			0
$451$	9.43816	−	5.44912i	0.444426	−	0.256589i
$452$	−0.152480	+	0.569061i	−0.00717204	+	0.0267664i
$453$	−19.7451	+	5.29069i	−0.927707	+	0.248578i
$454$	16.9195			0.794073
$455$		0			0
$456$	17.4516			0.817244
$457$	−2.34349	+	0.627937i	−0.109624	+	0.0293736i	−0.313214	−	0.949683i	$-0.601406\pi$
$457$	−2.34349	+	0.627937i	−0.109624	+	0.0293736i	0.203590	+	0.979056i	$0.434739\pi$
$458$	−0.870707	+	3.24952i	−0.0406855	+	0.151840i
$459$	3.15177	−	1.81968i	0.147112	−	0.0849352i
$460$		0			0
$461$		−	15.8830i		−	0.739746i	−0.929082	−	0.369873i	$-0.879401\pi$
$461$		−	15.8830i		−	0.739746i	0.929082	−	0.369873i	$-0.120599\pi$
$462$	−3.89019	−	1.13414i	−0.180988	−	0.0527650i
$463$	9.80667	−	9.80667i	0.455754	−	0.455754i	−0.441505	−	0.897259i	$-0.645555\pi$
$463$	9.80667	−	9.80667i	0.455754	−	0.455754i	0.897259	+	0.441505i	$0.145555\pi$
$464$	7.25687	+	4.18975i	0.336892	+	0.194504i
$465$		0			0
$466$	1.81968	+	3.15177i	0.0842949	+	0.146003i
$467$	−4.59189	−	17.1372i	−0.212487	−	0.793014i	−0.987036	−	0.160499i	$-0.948690\pi$
$467$	−4.59189	−	17.1372i	−0.212487	−	0.793014i	0.774549	−	0.632514i	$-0.217977\pi$
$468$	−0.0818472	−	0.0818472i	−0.00378339	−	0.00378339i
$469$	−16.5363	+	9.07081i	−0.763573	+	0.418851i
$470$		0			0
$471$	0.761802	−	1.31948i	0.0351020	−	0.0607984i
$472$	−0.263933	−	0.0707206i	−0.0121485	−	0.00325518i
$473$	9.65089	+	2.58595i	0.443748	+	0.118902i
$474$	2.98369	−	5.16790i	0.137045	−	0.237370i
$475$		0			0
$476$	−0.952791	−	0.578246i	−0.0436711	−	0.0265038i
$477$	−9.35626	−	9.35626i	−0.428394	−	0.428394i
$478$	−7.84961	−	29.2951i	−0.359033	−	1.33993i
$479$	−16.7429	−	28.9995i	−0.765002	−	1.32502i	−0.940245	−	0.340498i	$-0.889404\pi$
$479$	−16.7429	−	28.9995i	−0.765002	−	1.32502i	0.175243	−	0.984525i	$-0.443929\pi$
$480$		0			0
$481$	−6.87755	−	3.97076i	−0.313589	−	0.181051i
$482$	−15.0048	+	15.0048i	−0.683452	+	0.683452i
$483$	−9.31149	−	9.72807i	−0.423687	−	0.442642i
$484$			1.12915i			0.0513249i
$485$		0			0
$486$	−1.18878	+	0.686340i	−0.0539240	+	0.0311330i
$487$	3.53123	−	13.1787i	0.160015	−	0.597184i	−0.838608	−	0.544735i	$-0.816630\pi$
$487$	3.53123	−	13.1787i	0.160015	−	0.597184i	0.998624	−	0.0524498i	$-0.0167030\pi$
$488$	24.2945	−	6.50969i	1.09976	−	0.294680i
$489$	−12.2184			−0.552537
$490$		0			0
$491$	−22.7213			−1.02540			−0.512699	−	0.858569i	$-0.671354\pi$
$491$	−22.7213			−1.02540			−0.512699	+	0.858569i	$0.671354\pi$
$492$	−1.09208	+	0.292621i	−0.0492345	+	0.0131924i
$493$	2.10192	−	7.84449i	0.0946659	−	0.353298i
$494$	7.14333	−	4.12420i	0.321394	−	0.185557i
$495$		0			0
$496$		−	19.1125i		−	0.858179i
$497$	9.23365	+	9.64675i	0.414186	+	0.432716i
$498$	6.90677	−	6.90677i	0.309500	−	0.309500i
$499$	−5.32568	−	3.07478i	−0.238410	−	0.137646i	0.376036	−	0.926605i	$-0.377287\pi$
$499$	−5.32568	−	3.07478i	−0.238410	−	0.137646i	−0.614446	+	0.788959i	$0.710620\pi$
$500$		0			0
$501$	−9.55787	−	16.5547i	−0.427014	−	0.739611i
$502$	9.87037	+	36.8367i	0.440536	+	1.64410i
$503$	−11.6411	−	11.6411i	−0.519051	−	0.519051i	0.398233	−	0.917284i	$-0.369623\pi$
$503$	−11.6411	−	11.6411i	−0.519051	−	0.519051i	−0.917284	+	0.398233i	$0.869623\pi$
$504$	6.56883	+	3.98660i	0.292599	+	0.177577i
$505$		0			0
$506$	−3.89765	+	6.75093i	−0.173272	+	0.300115i
$507$	11.5911	+	3.10583i	0.514779	+	0.137935i
$508$	1.51231	+	0.405223i	0.0670981	+	0.0179789i
$509$	12.0071	−	20.7968i	0.532204	−	0.921804i	−0.467089	−	0.884210i	$-0.654697\pi$
$509$	12.0071	−	20.7968i	0.532204	−	0.921804i	0.999293	−	0.0375939i	$-0.0119693\pi$
$510$		0			0
$511$	19.2039	−	10.5341i	0.849532	−	0.466003i
$512$	17.1594	+	17.1594i	0.758347	+	0.758347i
$513$	1.55524	+	5.80423i	0.0686654	+	0.256263i
$514$	−6.21491	−	10.7645i	−0.274128	−	0.474803i
$515$		0			0
$516$	−0.897649	−	0.518258i	−0.0395168	−	0.0228150i
$517$	5.61400	−	5.61400i	0.246903	−	0.246903i
$518$	27.6890	+	8.07241i	1.21659	+	0.354681i
$519$			6.00000i			0.263371i
$520$		0			0
$521$	6.51021	−	3.75867i	0.285217	−	0.164670i	−0.350566	−	0.936538i	$-0.614011\pi$
$521$	6.51021	−	3.75867i	0.285217	−	0.164670i	0.635783	+	0.771868i	$0.280677\pi$
$522$	−0.792797	+	2.95876i	−0.0346998	+	0.129501i
$523$	10.8944	−	2.91914i	0.476379	−	0.127645i	−0.0126373	−	0.999920i	$-0.504023\pi$
$523$	10.8944	−	2.91914i	0.476379	−	0.127645i	0.489016	+	0.872275i	$0.337356\pi$
$524$	−1.22468			−0.0535005
$525$		0			0
$526$	22.3527			0.974625
$527$	−17.8922	+	4.79421i	−0.779398	+	0.208839i
$528$	1.08439	−	4.04699i	0.0471919	−	0.176123i
$529$	−2.51631	+	1.45279i	−0.109405	+	0.0631648i
$530$		0			0
$531$		−	0.0940841i		−	0.00408290i
$532$	1.32938	−	1.27245i	0.0576359	−	0.0551678i
$533$	−6.90677	+	6.90677i	−0.299165	+	0.299165i
$534$	−3.62843	−	2.09488i	−0.157018	−	0.0906542i
$535$		0			0
$536$	−10.3517	−	17.9297i	−0.447127	−	0.774446i
$537$	3.10583	+	11.5911i	0.134026	+	0.500193i
$538$	2.57341	+	2.57341i	0.110948	+	0.110948i
$539$	−6.92820	+	3.60554i	−0.298419	+	0.155302i
$540$		0			0
$541$	9.66296	−	16.7367i	0.415443	−	0.719568i	−0.580032	−	0.814594i	$-0.696960\pi$
$541$	9.66296	−	16.7367i	0.415443	−	0.719568i	0.995475	+	0.0950254i	$0.0302932\pi$
$542$	−29.2926	−	7.84892i	−1.25822	−	0.337140i
$543$	6.17964	+	1.65583i	0.265194	+	0.0710584i
$544$	1.18996	−	2.06107i	0.0510190	−	0.0883675i
$545$		0			0
$546$	3.63090	+	0.0794434i	0.155388	+	0.00339987i
$547$	−9.44020	−	9.44020i	−0.403634	−	0.403634i	0.475878	−	0.879512i	$-0.342131\pi$
$547$	−9.44020	−	9.44020i	−0.403634	−	0.403634i	−0.879512	+	0.475878i	$0.842131\pi$
$548$	−0.268270	−	1.00120i	−0.0114599	−	0.0427690i
$549$	4.33013	+	7.50000i	0.184805	+	0.320092i
$550$		0			0
$551$	11.6126	+	6.70451i	0.494712	+	0.285622i
$552$	10.4524	−	10.4524i	0.444883	−	0.444883i
$553$	−2.73313	−	11.1723i	−0.116225	−	0.475094i
$554$			28.2067i			1.19839i
$555$		0			0
$556$	−0.570497	+	0.329377i	−0.0241945	+	0.0139687i
$557$	3.95835	−	14.7728i	0.167721	−	0.625942i	−0.829957	−	0.557828i	$-0.811635\pi$
$557$	3.95835	−	14.7728i	0.167721	−	0.625942i	0.997678	−	0.0681144i	$-0.0216983\pi$
$558$	6.74854	−	1.80827i	0.285688	−	0.0765500i
$559$	−8.95482			−0.378749
$560$		0			0
$561$	−4.06061			−0.171439
$562$	−36.3047	+	9.72783i	−1.53142	+	0.410344i
$563$	−0.933183	+	3.48269i	−0.0393290	+	0.146778i	−0.982798	−	0.184682i	$-0.940874\pi$
$563$	−0.933183	+	3.48269i	−0.0393290	+	0.146778i	0.943469	+	0.331460i	$0.107541\pi$
$564$	−0.713296	+	0.411822i	−0.0300352	+	0.0173408i
$565$		0			0
$566$		−	24.5126i		−	1.03034i
$567$	−0.740510	+	2.54001i	−0.0310985	+	0.106670i
$568$	−10.3650	+	10.3650i	−0.434906	+	0.434906i
$569$	10.5041	+	6.06457i	0.440357	+	0.254240i	0.703749	−	0.710449i	$-0.251508\pi$
$569$	10.5041	+	6.06457i	0.440357	+	0.254240i	−0.263392	+	0.964689i	$0.584841\pi$
$570$		0			0
$571$	−4.65002	−	8.05407i	−0.194597	−	0.337052i	0.752171	−	0.658968i	$-0.229007\pi$
$571$	−4.65002	−	8.05407i	−0.194597	−	0.337052i	−0.946768	+	0.321915i	$0.895673\pi$
$572$	0.0334258	+	0.124747i	0.00139760	+	0.00521592i
$573$	−1.20205	−	1.20205i	−0.0502165	−	0.0502165i
$574$	18.4047	−	30.3259i	0.768197	−	1.26578i
$575$		0			0
$576$	−4.20393	+	7.28142i	−0.175164	+	0.303392i
$577$	−26.6899	−	7.15154i	−1.11112	−	0.297722i	−0.343832	−	0.939031i	$-0.611725\pi$
$577$	−26.6899	−	7.15154i	−1.11112	−	0.297722i	−0.767283	+	0.641309i	$0.778392\pi$
$578$	−4.97892	−	1.33410i	−0.207096	−	0.0554911i
$579$	7.38166	−	12.7854i	0.306771	−	0.531343i
$580$		0			0
$581$	0.411822	−	18.8220i	0.0170852	−	0.780868i
$582$	−16.3089	−	16.3089i	−0.676024	−	0.676024i
$583$	3.82103	+	14.2603i	0.158251	+	0.590600i
$584$	12.0217	+	20.8222i	0.497462	+	0.861629i
$585$		0			0
$586$	−37.1834	−	21.4678i	−1.53603	−	0.886828i
$587$	11.3805	−	11.3805i	0.469722	−	0.469722i	−0.432102	−	0.901825i	$-0.642228\pi$
$587$	11.3805	−	11.3805i	0.469722	−	0.469722i	0.901825	+	0.432102i	$0.142228\pi$
$588$	0.791061	−	0.175275i	0.0326228	−	0.00722821i
$589$		−	30.5842i		−	1.26020i
$590$		0			0
$591$	−21.5102	+	12.4189i	−0.884812	+	0.510846i
$592$	−7.71829	+	28.8051i	−0.317220	+	1.18388i
$593$	22.2619	−	5.96506i	0.914186	−	0.244956i	0.229088	−	0.973406i	$-0.426426\pi$
$593$	22.2619	−	5.96506i	0.914186	−	0.244956i	0.685099	+	0.728450i	$0.259759\pi$
$594$	1.53157			0.0628410
$595$		0			0
$596$	1.11575			0.0457029
$597$	−2.15122	+	0.576417i	−0.0880434	+	0.0235912i
$598$	1.80827	−	6.74854i	0.0739455	−	0.275968i
$599$	−16.3310	+	9.42873i	−0.667268	+	0.385247i	−0.795041	−	0.606556i	$-0.792551\pi$
$599$	−16.3310	+	9.42873i	−0.667268	+	0.385247i	0.127773	+	0.991803i	$0.459217\pi$
$600$		0			0
$601$			41.8392i			1.70665i	0.521375	+	0.853327i	$0.325419\pi$
$601$			41.8392i			1.70665i	−0.521375	+	0.853327i	$0.674581\pi$
$602$	31.5903	−	7.72810i	1.28752	−	0.314974i
$603$	5.04074	−	5.04074i	0.205275	−	0.205275i
$604$	−2.04911	−	1.18306i	−0.0833772	−	0.0481378i
$605$		0			0
$606$	12.5748	+	21.7802i	0.510816	+	0.884758i
$607$	−3.68480	−	13.7519i	−0.149561	−	0.558170i	−0.999510	−	0.0313047i	$-0.990034\pi$
$607$	−3.68480	−	13.7519i	−0.149561	−	0.558170i	0.849949	−	0.526866i	$-0.176633\pi$
$608$	2.77858	+	2.77858i	0.112686	+	0.112686i
$609$	2.83944	+	5.17636i	0.115060	+	0.209757i
$610$		0			0
$611$	−3.55787	+	6.16242i	−0.143936	+	0.249305i
$612$	0.406899	+	0.109028i	0.0164479	+	0.00440721i
$613$	−3.06016	−	0.819967i	−0.123599	−	0.0331181i	0.196489	−	0.980506i	$-0.437046\pi$
$613$	−3.06016	−	0.819967i	−0.123599	−	0.0331181i	−0.320088	+	0.947388i	$0.603713\pi$
$614$	19.8422	−	34.3677i	0.800765	−	1.38697i
$615$		0			0
$616$	−4.12322	−	7.51671i	−0.166129	−	0.302857i
$617$	−2.29902	−	2.29902i	−0.0925550	−	0.0925550i	0.659313	−	0.751868i	$-0.270847\pi$
$617$	−2.29902	−	2.29902i	−0.0925550	−	0.0925550i	−0.751868	+	0.659313i	$0.770847\pi$
$618$	−1.27620	−	4.76285i	−0.0513364	−	0.191590i
$619$	−0.825141	−	1.42919i	−0.0331652	−	0.0574439i	0.848966	−	0.528447i	$-0.177225\pi$
$619$	−0.825141	−	1.42919i	−0.0331652	−	0.0574439i	−0.882132	+	0.471003i	$0.843892\pi$
$620$		0			0
$621$	4.40786	+	2.54488i	0.176881	+	0.102122i
$622$	9.28757	−	9.28757i	0.372398	−	0.372398i
$623$	−7.84417	+	1.91896i	−0.314270	+	0.0768815i
$624$			3.75510i			0.150324i
$625$		0			0
$626$	3.85745	−	2.22710i	0.154175	−	0.0890129i
$627$	1.73526	−	6.47606i	0.0692994	−	0.258629i
$628$	0.170347	−	0.0456444i	0.00679759	−	0.00182141i
$629$	28.9020			1.15240
$630$		0			0
$631$	−13.8575			−0.551657			−0.275828	−	0.961207i	$-0.588952\pi$
$631$	−13.8575			−0.551657			−0.275828	+	0.961207i	$0.588952\pi$
$632$	12.1953	−	3.26772i	0.485102	−	0.129983i
$633$	3.94015	−	14.7048i	0.156607	−	0.584465i
$634$	−19.1050	+	11.0303i	−0.758758	+	0.438069i
$635$		0			0
$636$		−	1.53157i		−	0.0607306i
$637$	5.16151	−	4.72852i	0.204506	−	0.187351i
$638$	2.41667	−	2.41667i	0.0956769	−	0.0956769i
$639$	−4.37101	−	2.52360i	−0.172915	−	0.0998323i
$640$		0			0
$641$	−16.9181	−	29.3029i	−0.668223	−	1.15740i	−0.978401	−	0.206718i	$-0.933722\pi$
$641$	−16.9181	−	29.3029i	−0.668223	−	1.15740i	0.310177	−	0.950679i	$-0.399612\pi$
$642$	6.32944	+	23.6218i	0.249803	+	0.932277i
$643$	−11.9534	−	11.9534i	−0.471396	−	0.471396i	0.430970	−	0.902366i	$-0.358171\pi$
$643$	−11.9534	−	11.9534i	−0.471396	−	0.471396i	−0.902366	+	0.430970i	$0.858171\pi$
$644$	0.0340961	−	1.55833i	0.00134357	−	0.0614070i
$645$		0			0
$646$	−15.0094	+	25.9971i	−0.590538	+	1.02284i
$647$	−1.07773	−	0.288777i	−0.0423700	−	0.0113530i	0.237572	−	0.971370i	$-0.423648\pi$
$647$	−1.07773	−	0.288777i	−0.0423700	−	0.0113530i	−0.279942	+	0.960017i	$0.590315\pi$
$648$	−2.80529	−	0.751674i	−0.110202	−	0.0295286i
$649$	−0.0524871	+	0.0909104i	−0.00206030	+	0.00356854i
$650$		0			0
$651$	6.98660	−	11.5120i	0.273827	−	0.451191i
$652$	−1.00004	−	1.00004i	−0.0391648	−	0.0391648i
$653$	5.95550	+	22.2262i	0.233057	+	0.869780i	0.979015	+	0.203787i	$0.0653250\pi$
$653$	5.95550	+	22.2262i	0.233057	+	0.869780i	−0.745958	+	0.665992i	$0.768008\pi$
$654$	−5.88249	−	10.1888i	−0.230024	−	0.398413i
$655$		0			0
$656$	31.7645	+	18.3393i	1.24020	+	0.716028i
$657$	−5.85393	+	5.85393i	−0.228384	+	0.228384i
$658$	7.23304	−	24.8099i	0.281973	−	0.967191i
$659$			46.9519i			1.82899i	0.404603	+	0.914493i	$0.367410\pi$
$659$			46.9519i			1.82899i	−0.404603	+	0.914493i	$0.632590\pi$
$660$		0			0
$661$	−22.2035	+	12.8192i	−0.863615	+	0.498608i	−0.865221	−	0.501390i	$-0.832822\pi$
$661$	−22.2035	+	12.8192i	−0.863615	+	0.498608i	0.00160630	+	0.999999i	$0.499489\pi$
$662$	3.86215	−	14.4137i	0.150107	−	0.560206i
$663$	3.51535	−	0.941934i	0.136525	−	0.0365817i
$664$	20.6659			0.801992
$665$		0			0
$666$	−10.9012			−0.422411
$667$	10.9708	−	2.93961i	0.424790	−	0.113822i
$668$	0.572672	−	2.13724i	0.0221574	−	0.0826924i
$669$	−21.5681	+	12.4523i	−0.833870	+	0.481435i
$670$		0			0
$671$		−	9.66267i		−	0.373023i
$672$	0.411134	+	1.68060i	0.0158598	+	0.0648306i
$673$	−10.2898	+	10.2898i	−0.396642	+	0.396642i	−0.877047	−	0.480405i	$-0.840490\pi$
$673$	−10.2898	+	10.2898i	−0.396642	+	0.396642i	0.480405	+	0.877047i	$0.340490\pi$
$674$	−0.854422	−	0.493301i	−0.0329111	−	0.0190012i
$675$		0			0
$676$	0.694496	+	1.20290i	0.0267114	+	0.0462655i
$677$	6.69382	+	24.9817i	0.257264	+	0.960123i	0.966817	+	0.255471i	$0.0822304\pi$
$677$	6.69382	+	24.9817i	0.257264	+	0.960123i	−0.709553	+	0.704653i	$0.751103\pi$
$678$	4.94027	+	4.94027i	0.189730	+	0.189730i
$679$	−44.4441	−	0.972429i	−1.70561	−	0.0373184i
$680$		0			0
$681$	−6.16296	+	10.6746i	−0.236165	+	0.409050i
$682$	−7.52968	−	2.01757i	−0.288326	−	0.0772568i
$683$	13.6807	+	3.66573i	0.523477	+	0.140265i	0.510874	−	0.859655i	$-0.329322\pi$
$683$	13.6807	+	3.66573i	0.523477	+	0.140265i	0.0126025	+	0.999921i	$0.495988\pi$
$684$	−0.347768	+	0.602351i	−0.0132972	+	0.0230315i
$685$		0			0
$686$	−14.1277	+	21.1354i	−0.539398	+	0.806954i
$687$	−1.73297	−	1.73297i	−0.0661170	−	0.0661170i
$688$	8.70312	+	32.4805i	0.331803	+	1.23831i
$689$	−6.61587	−	11.4590i	−0.252045	−	0.436554i
$690$		0			0
$691$	33.4086	+	19.2885i	1.27092	+	0.733768i	0.975162	−	0.221493i	$-0.0710930\pi$
$691$	33.4086	+	19.2885i	1.27092	+	0.733768i	0.295762	+	0.955262i	$0.404426\pi$
$692$	−0.491083	+	0.491083i	−0.0186682	+	0.0186682i
$693$	2.13254	−	2.04122i	0.0810084	−	0.0775394i
$694$			6.30705i			0.239413i
$695$		0			0
$696$	−5.61256	+	3.24041i	−0.212743	+	0.122827i
$697$	9.20048	−	34.3367i	0.348493	−	1.30059i
$698$	3.35794	−	0.899757i	0.127100	−	0.0340563i
$699$	−2.65128			−0.100280
$700$		0			0
$701$	−22.5921			−0.853294			−0.426647	−	0.904418i	$-0.640305\pi$
$701$	−22.5921			−0.853294			−0.426647	+	0.904418i	$0.640305\pi$
$702$	−1.32591	+	0.355276i	−0.0500431	+	0.0134090i
$703$	−12.3509	+	46.0943i	−0.465825	+	1.73848i
$704$	8.12424	−	4.69053i	0.306194	−	0.176781i
$705$		0			0
$706$		−	9.81406i		−	0.369357i
$707$	46.5368	+	13.5672i	1.75020	+	0.510249i
$708$	0.00770052	−	0.00770052i	0.000289403	−	0.000289403i
$709$	11.2058	+	6.46970i	0.420844	+	0.242975i	0.695438	−	0.718586i	$-0.255210\pi$
$709$	11.2058	+	6.46970i	0.420844	+	0.242975i	−0.274594	+	0.961560i	$0.588544\pi$
$710$		0			0
$711$	2.17362	+	3.76483i	0.0815173	+	0.141192i
$712$	−2.29429	−	8.56242i	−0.0859823	−	0.320890i
$713$	−18.3180	−	18.3180i	−0.686015	−	0.686015i
$714$	−11.5883	+	6.35668i	−0.433683	+	0.237893i
$715$		0			0
$716$	−0.694496	+	1.20290i	−0.0259545	+	0.0449546i
$717$	21.3416	+	5.71846i	0.797015	+	0.213560i
$718$	−6.13359	−	1.64349i	−0.228903	−	0.0613345i
$719$	−8.17672	+	14.1625i	−0.304940	+	0.528172i	−0.977248	−	0.212100i	$-0.931970\pi$
$719$	−8.17672	+	14.1625i	−0.304940	+	0.528172i	0.672308	+	0.740272i	$0.265303\pi$
$720$		0			0
$721$	−8.12472	−	4.93087i	−0.302580	−	0.183635i
$722$	−16.6054	−	16.6054i	−0.617988	−	0.617988i
$723$	−4.00105	−	14.9321i	−0.148800	−	0.555331i
$724$	0.370261	+	0.641311i	0.0137606	+	0.0238341i
$725$		0			0
$726$	11.5966	+	6.69532i	0.430391	+	0.248487i
$727$	−13.8425	+	13.8425i	−0.513391	+	0.513391i	−0.915564	−	0.402173i	$-0.868255\pi$
$727$	−13.8425	+	13.8425i	−0.513391	+	0.513391i	0.402173	+	0.915564i	$0.368255\pi$
$728$	5.31320	+	5.55090i	0.196920	+	0.205730i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	28.2236	−	16.2949i	1.04389	−	0.602688i
$732$	−0.259445	+	0.968263i	−0.00958937	+	0.0357880i
$733$	−24.4630	+	6.55483i	−0.903560	+	0.242108i	−0.680544	−	0.732707i	$-0.738257\pi$
$733$	−24.4630	+	6.55483i	−0.903560	+	0.242108i	−0.223015	+	0.974815i	$0.571590\pi$
$734$	4.13643			0.152678
$735$		0			0
$736$	3.32839			0.122686
$737$	−7.68281	+	2.05860i	−0.283000	+	0.0758296i
$738$	−3.47021	+	12.9510i	−0.127740	+	0.476733i
$739$	14.6106	−	8.43543i	0.537459	−	0.310302i	−0.206589	−	0.978428i	$-0.566236\pi$
$739$	14.6106	−	8.43543i	0.537459	−	0.310302i	0.744049	+	0.668126i	$0.232903\pi$
$740$		0			0
$741$			6.00898i			0.220745i
$742$	33.2284	+	34.7149i	1.21985	+	1.27443i
$743$	−8.63103	+	8.63103i	−0.316642	+	0.316642i	−0.847476	−	0.530834i	$-0.821879\pi$
$743$	−8.63103	+	8.63103i	−0.316642	+	0.316642i	0.530834	+	0.847476i	$0.321879\pi$
$744$	12.8015	+	7.39095i	0.469326	+	0.270965i
$745$		0			0
$746$	4.33483	+	7.50814i	0.158709	+	0.274893i
$747$	1.84169	+	6.87329i	0.0673840	+	0.251480i
$748$	−0.332349	−	0.332349i	−0.0121519	−	0.0121519i
$749$	40.2953	+	24.4551i	1.47236	+	0.893569i
$750$		0			0
$751$	−20.4692	+	35.4538i	−0.746933	+	1.29373i	0.202353	+	0.979313i	$0.435141\pi$
$751$	−20.4692	+	35.4538i	−0.746933	+	1.29373i	−0.949286	+	0.314413i	$0.898192\pi$
$752$	25.8099	+	6.91574i	0.941190	+	0.252191i
$753$	−26.8356	−	7.19058i	−0.977944	−	0.262039i
$754$	−1.53157	+	2.65275i	−0.0557764	+	0.0966075i
$755$		0			0
$756$	−0.268501	+	0.147284i	−0.00976529	+	0.00535667i
$757$	−22.0290	−	22.0290i	−0.800658	−	0.800658i	0.182541	−	0.983198i	$-0.441568\pi$
$757$	−22.0290	−	22.0290i	−0.800658	−	0.800658i	−0.983198	+	0.182541i	$0.941568\pi$
$758$	6.56140	+	24.4875i	0.238321	+	0.889425i
$759$	−2.83944	−	4.91806i	−0.103065	−	0.178514i
$760$		0			0
$761$	−1.02984	−	0.594581i	−0.0373318	−	0.0215535i	0.481218	−	0.876601i	$-0.340195\pi$
$761$	−1.02984	−	0.594581i	−0.0373318	−	0.0215535i	−0.518550	+	0.855047i	$0.673528\pi$
$762$	13.1291	−	13.1291i	0.475616	−	0.475616i
$763$	−21.7699	−	6.34677i	−0.788125	−	0.229769i
$764$		−	0.196769i		−	0.00711887i
$765$		0			0
$766$	−30.7452	+	17.7508i	−1.11087	+	0.641361i
$767$	0.0243507	−	0.0908782i	0.000879255	−	0.00328142i
$768$	−2.67417	+	0.716541i	−0.0964957	+	0.0258559i
$769$	−18.0146			−0.649624			−0.324812	−	0.945779i	$-0.605301\pi$
$769$	−18.0146			−0.649624			−0.324812	+	0.945779i	$0.605301\pi$
$770$		0			0
$771$	9.05514			0.326113
$772$	1.65062	−	0.442282i	0.0594070	−	0.0159181i
$773$	−8.39794	+	31.3415i	−0.302053	+	1.12728i	0.633400	+	0.773825i	$0.281659\pi$
$773$	−8.39794	+	31.3415i	−0.302053	+	1.12728i	−0.935453	+	0.353452i	$0.885008\pi$
$774$	−10.6453	+	6.14605i	−0.382637	+	0.220915i
$775$		0			0
$776$		−	48.7981i		−	1.75175i
$777$	−15.1786	+	14.5287i	−0.544531	+	0.521213i
$778$	−8.78921	+	8.78921i	−0.315108	+	0.315108i
$779$	50.8301	+	29.3468i	1.82118	+	1.05146i
$780$		0			0
$781$	2.81571	+	4.87695i	0.100754	+	0.174511i
$782$	6.58092	+	24.5603i	0.235333	+	0.878275i
$783$	−1.57791	−	1.57791i	−0.0563898	−	0.0563898i
$784$	−22.1675	−	14.1260i	−0.791695	−	0.504498i
$785$		0			0
$786$	−7.26180	+	12.5778i	−0.259020	+	0.448636i
$787$	27.7806	+	7.44378i	0.990271	+	0.265342i	0.717364	−	0.696698i	$-0.245348\pi$
$787$	27.7806	+	7.44378i	0.990271	+	0.265342i	0.272906	+	0.962041i	$0.412015\pi$
$788$	−2.77700	−	0.744096i	−0.0989267	−	0.0265073i
$789$	−8.14200	+	14.1024i	−0.289863	+	0.502057i
$790$		0			0
$791$	13.4630	+	0.294568i	0.478689	+	0.0104736i
$792$	2.29132	+	2.29132i	0.0814184	+	0.0814184i
$793$	2.24144	+	8.36516i	0.0795958	+	0.297056i
$794$	8.67114	+	15.0189i	0.307727	+	0.532999i
$795$		0			0
$796$	−0.223249	−	0.128893i	−0.00791285	−	0.00456849i
$797$	−4.06000	+	4.06000i	−0.143813	+	0.143813i	−0.775347	−	0.631535i	$-0.782425\pi$
$797$	−4.06000	+	4.06000i	−0.143813	+	0.143813i	0.631535	+	0.775347i	$0.282425\pi$
$798$	−5.18581	−	21.1981i	−0.183576	−	0.750406i
$799$		−	25.8967i		−	0.916160i
$800$		0			0
$801$	2.64332	−	1.52612i	0.0933971	−	0.0539229i
$802$	12.1588	−	45.3773i	0.429342	−	1.60233i
$803$	8.92222	−	2.39070i	0.314858	−	0.0843660i
$804$	0.825141			0.0291005
$805$		0			0
$806$	6.98660			0.246093
$807$	−2.56094	+	0.686201i	−0.0901492	+	0.0241554i
$808$	−13.7718	+	51.3971i	−0.484490	+	1.80814i
$809$	−38.8115	+	22.4079i	−1.36454	+	0.787818i	−0.990225	−	0.139483i	$-0.955456\pi$
$809$	−38.8115	+	22.4079i	−1.36454	+	0.787818i	−0.374317	+	0.927301i	$0.622123\pi$
$810$		0			0
$811$			24.7670i			0.869686i	0.900506	+	0.434843i	$0.143196\pi$
$811$			24.7670i			0.869686i	−0.900506	+	0.434843i	$0.856804\pi$
$812$	−0.191270	+	0.656071i	−0.00671225	+	0.0230236i
$813$	15.6217	−	15.6217i	0.547879	−	0.547879i
$814$	10.5334	+	6.08148i	0.369197	+	0.213156i
$815$		0			0
$816$	−6.83307	−	11.8352i	−0.239205	−	0.414316i
$817$	13.9269	+	51.9758i	0.487240	+	1.81840i
$818$	29.1519	+	29.1519i	1.01927	+	1.01927i
$819$	−1.37268	+	2.26180i	−0.0479653	+	0.0790338i
$820$		0			0
$821$	−1.05118	+	1.82069i	−0.0366863	+	0.0635425i	−0.883786	−	0.467892i	$-0.845014\pi$
$821$	−1.05118	+	1.82069i	−0.0366863	+	0.0635425i	0.847099	+	0.531435i	$0.178347\pi$
$822$	−11.8733	−	3.18143i	−0.414128	−	0.110965i
$823$	8.94474	+	2.39674i	0.311794	+	0.0835450i	0.411323	−	0.911490i	$-0.365067\pi$
$823$	8.94474	+	2.39674i	0.311794	+	0.0835450i	−0.0995288	+	0.995035i	$0.531734\pi$
$824$	5.21624	−	9.03479i	0.181716	−	0.314742i
$825$		0			0
$826$	−0.00747436	+	0.341610i	−0.000260066	+	0.0118861i
$827$	8.91456	+	8.91456i	0.309990	+	0.309990i	0.844905	−	0.534916i	$-0.179657\pi$
$827$	8.91456	+	8.91456i	0.309990	+	0.309990i	−0.534916	+	0.844905i	$0.679657\pi$
$828$	0.152480	+	0.569061i	0.00529903	+	0.0197763i
$829$	12.8315	+	22.2248i	0.445656	+	0.771899i	0.998098	−	0.0616525i	$-0.0196371\pi$
$829$	12.8315	+	22.2248i	0.445656	+	0.771899i	−0.552441	+	0.833552i	$0.686304\pi$
$830$		0			0
$831$	−17.7956	−	10.2743i	−0.617323	−	0.356412i
$832$	−5.94525	+	5.94525i	−0.206115	+	0.206115i
$833$	−7.66353	+	24.2955i	−0.265525	+	0.841788i
$834$			7.81220i			0.270514i
$835$		0			0
$836$	0.672073	−	0.388022i	0.0232441	−	0.0134200i
$837$	−1.31732	+	4.91632i	−0.0455334	+	0.169933i
$838$	−34.4317	+	9.22596i	−1.18943	+	0.318705i
$839$	−29.2921			−1.01127			−0.505637	−	0.862746i	$-0.668742\pi$
$839$	−29.2921			−1.01127			−0.505637	+	0.862746i	$0.668742\pi$
$840$		0			0
$841$	24.0204			0.828290
$842$	1.71321	−	0.459054i	0.0590412	−	0.0158200i
$843$	7.08674	−	26.4481i	0.244080	−	0.910920i
$844$	1.52604	−	0.881059i	0.0525284	−	0.0303273i
$845$		0			0
$846$			9.76765i			0.335819i
$847$	25.0703	−	6.13308i	0.861426	−	0.210735i
$848$	−35.1337	+	35.1337i	−1.20650	+	1.20650i
$849$	15.4650	+	8.92873i	0.530758	+	0.306433i
$850$		0			0
$851$	20.2102	+	35.0050i	0.692796	+	1.19996i
$852$	−0.151205	−	0.564305i	−0.00518020	−	0.0193328i
$853$	−14.2089	−	14.2089i	−0.486503	−	0.486503i	0.420698	−	0.907201i	$-0.361785\pi$
$853$	−14.2089	−	14.2089i	−0.486503	−	0.486503i	−0.907201	+	0.420698i	$0.861785\pi$
$854$	−15.1264	−	27.5758i	−0.517616	−	0.943623i
$855$		0			0
$856$	−25.8704	+	44.8088i	−0.884232	+	1.53153i
$857$	25.5460	+	6.84502i	0.872634	+	0.233821i	0.667226	−	0.744855i	$-0.267481\pi$
$857$	25.5460	+	6.84502i	0.872634	+	0.233821i	0.205407	+	0.978677i	$0.434148\pi$
$858$	1.47938	+	0.396399i	0.0505052	+	0.0135328i
$859$	15.1766	−	26.2866i	0.517819	−	0.896889i	−0.481967	−	0.876189i	$-0.660077\pi$
$859$	15.1766	−	26.2866i	0.517819	−	0.896889i	0.999786	−	0.0206992i	$-0.00658922\pi$
$860$		0			0
$861$	12.4287	+	22.6578i	0.423570	+	0.772175i
$862$	12.8887	+	12.8887i	0.438992	+	0.438992i
$863$	7.87396	+	29.3860i	0.268033	+	1.00031i	0.960368	+	0.278736i	$0.0899154\pi$
$863$	7.87396	+	29.3860i	0.268033	+	1.00031i	−0.692335	+	0.721576i	$0.743418\pi$
$864$	−0.326969	−	0.566327i	−0.0111237	−	0.0192669i
$865$		0			0
$866$	−3.85745	−	2.22710i	−0.131082	−	0.0756800i
$867$	2.65526	−	2.65526i	0.0901773	−	0.0901773i
$868$	1.51406	−	0.370392i	0.0513905	−	0.0125719i
$869$		−	4.85044i		−	0.164540i
$870$		0			0
$871$	6.17362	−	3.56434i	0.209185	−	0.120773i
$872$	6.44246	−	24.0436i	0.218169	−	0.814219i
$873$	16.2298	−	4.34876i	0.549295	−	0.147183i
$874$	−41.9823			−1.42007
$875$		0			0
$876$	−0.958255			−0.0323765
$877$	−4.65558	+	1.24746i	−0.157208	+	0.0421237i	−0.336565	−	0.941660i	$-0.609265\pi$
$877$	−4.65558	+	1.24746i	−0.157208	+	0.0421237i	0.179357	+	0.983784i	$0.442598\pi$
$878$	14.1318	−	52.7406i	0.476925	−	1.77991i
$879$	27.0882	−	15.6394i	0.913661	−	0.527502i
$880$		0			0
$881$		−	32.9661i		−	1.11066i	−0.831631	−	0.555328i	$-0.812593\pi$
$881$		−	32.9661i		−	1.11066i	0.831631	−	0.555328i	$-0.187407\pi$
$882$	2.89050	−	9.16369i	0.0973283	−	0.308558i
$883$	36.2080	−	36.2080i	1.21850	−	1.21850i	0.250337	−	0.968159i	$-0.419458\pi$
$883$	36.2080	−	36.2080i	1.21850	−	1.21850i	0.968159	−	0.250337i	$-0.0805415\pi$
$884$	0.364816	+	0.210627i	0.0122701	+	0.00708414i
$885$		0			0
$886$	−16.3508	−	28.3203i	−0.549314	−	0.951440i
$887$	−5.32065	−	19.8569i	−0.178650	−	0.666731i	−0.995901	−	0.0904490i	$-0.971170\pi$
$887$	−5.32065	−	19.8569i	−0.178650	−	0.666731i	0.817251	−	0.576282i	$-0.195497\pi$
$888$	−16.3088	−	16.3088i	−0.547287	−	0.547287i
$889$	0.782832	−	35.7787i	0.0262553	−	1.19998i
$890$		0			0
$891$	−0.557875	+	0.966267i	−0.0186895	+	0.0323712i
$892$	−2.78447	−	0.746098i	−0.0932311	−	0.0249812i
$893$	41.3014	+	11.0667i	1.38210	+	0.370332i
$894$	6.61587	−	11.4590i	0.221268	−	0.383247i
$895$		0			0
$896$	14.0472	−	23.1460i	0.469284	−	0.773253i
$897$	3.59900	+	3.59900i	0.120167	+	0.120167i
$898$	−11.5210	−	42.9969i	−0.384460	−	1.43482i
$899$	5.67889	+	9.83612i	0.189402	+	0.328053i
$900$		0			0
$901$	41.7035	+	24.0775i	1.38934	+	0.802138i
$902$	10.5782	−	10.5782i	0.352215	−	0.352215i
$903$	−6.63113	+	22.7453i	−0.220670	+	0.756917i
$904$			14.7819i			0.491639i
$905$		0			0
$906$	−24.3006	+	14.0299i	−0.807332	+	0.466113i
$907$	−2.39674	+	8.94474i	−0.0795823	+	0.297005i	−0.994233	−	0.107239i	$-0.965799\pi$
$907$	−2.39674	+	8.94474i	−0.0795823	+	0.297005i	0.914651	+	0.404245i	$0.132466\pi$
$908$	−1.37810	+	0.369262i	−0.0457340	+	0.0122544i
$909$	−18.3215			−0.607686
$910$		0			0
$911$	−12.9528			−0.429145			−0.214573	−	0.976708i	$-0.568836\pi$
$911$	−12.9528			−0.429145			−0.214573	+	0.976708i	$0.568836\pi$
$912$	21.7955	−	5.84008i	0.721720	−	0.193384i
$913$	2.05487	−	7.66886i	0.0680061	−	0.253802i
$914$	−2.88416	+	1.66517i	−0.0953996	+	0.0550790i
$915$		0			0
$916$		−	0.283678i		−	0.00937298i
$917$	6.65199	+	27.1915i	0.219668	+	0.897941i
$918$	3.53247	−	3.53247i	0.116589	−	0.116589i
$919$	16.8146	+	9.70789i	0.554661	+	0.320234i	0.751000	−	0.660302i	$-0.229572\pi$
$919$	16.8146	+	9.70789i	0.554661	+	0.320234i	−0.196339	+	0.980536i	$0.562905\pi$
$920$		0			0
$921$	14.4551	+	25.0369i	0.476311	+	0.824994i
$922$	−5.64285	−	21.0594i	−0.185837	−	0.693555i
$923$	−3.56892	−	3.56892i	−0.117472	−	0.117472i
$924$	0.341610	+	0.00747436i	0.0112381	+	0.000245888i
$925$		0			0
$926$	9.51866	−	16.4868i	0.312803	−	0.541790i
$927$	3.46975	+	0.929716i	0.113961	+	0.0305359i
$928$	−1.40954	−	0.377685i	−0.0462704	−	0.0123981i
$929$	24.5487	−	42.5196i	0.805418	−	1.39502i	−0.110591	−	0.993866i	$-0.535274\pi$
$929$	24.5487	−	42.5196i	0.805418	−	1.39502i	0.916009	−	0.401158i	$-0.131392\pi$
$930$		0			0
$931$	−35.4727	−	22.6046i	−1.16257	−	0.740835i
$932$	−0.216999	−	0.216999i	−0.00710805	−	0.00710805i
$933$	2.47653	+	9.24255i	0.0810781	+	0.302587i
$934$	−12.1768	−	21.0909i	−0.398438	−	0.690116i
$935$		0			0
$936$	−2.51515	−	1.45212i	−0.0822103	−	0.0474641i
$937$	0.716581	−	0.716581i	0.0234097	−	0.0234097i	−0.695305	−	0.718715i	$-0.744731\pi$
$937$	0.716581	−	0.716581i	0.0234097	−	0.0234097i	0.718715	+	0.695305i	$0.244731\pi$
$938$	−18.7029	+	17.9020i	−0.610671	+	0.584521i
$939$			3.24490i			0.105893i
$940$		0			0
$941$	−50.7755	+	29.3153i	−1.65523	+	0.955650i	−0.680365	+	0.732873i	$0.738179\pi$
$941$	−50.7755	+	29.3153i	−1.65523	+	0.955650i	−0.974870	+	0.222777i	$0.928488\pi$
$942$	0.541300	−	2.02016i	0.0176365	−	0.0658203i
$943$	48.0209	−	12.8672i	1.56378	−	0.419013i
$944$	−0.353295			−0.0114988
$945$		0			0
$946$	13.7149			0.445910
$947$	2.57146	−	0.689019i	0.0835611	−	0.0223901i	−0.216796	−	0.976217i	$-0.569561\pi$
$947$	2.57146	−	0.689019i	0.0835611	−	0.0223901i	0.300357	+	0.953827i	$0.402894\pi$
$948$	−0.130236	+	0.486046i	−0.00422985	+	0.0157860i
$949$	−7.16957	+	4.13935i	−0.232734	+	0.134369i
$950$		0			0
$951$		−	16.0712i		−	0.521144i
$952$	−26.8468	−	7.82688i	−0.870111	−	0.253671i
$953$	30.7844	−	30.7844i	0.997204	−	0.997204i	−0.00279228	−	0.999996i	$-0.500889\pi$
$953$	30.7844	−	30.7844i	0.997204	−	0.997204i	0.999996	+	0.00279228i	$0.000888811\pi$
$954$	−15.7296	−	9.08148i	−0.509264	−	0.294024i
$955$		0			0
$956$	1.27871	+	2.21479i	0.0413564	+	0.0716313i
$957$	0.644406	+	2.40496i	0.0208307	+	0.0777412i
$958$	−32.5024	−	32.5024i	−1.05010	−	1.05010i
$959$	−20.7723	+	11.3945i	−0.670772	+	0.367946i
$960$		0			0
$961$	−2.54721	+	4.41190i	−0.0821680	+	0.142319i
$962$	−10.5297	−	2.82143i	−0.339491	−	0.0909665i
$963$	−17.2085	−	4.61101i	−0.554536	−	0.148588i
$964$	0.894676	−	1.54962i	0.0288156	−	0.0499101i
$965$		0			0
$966$	−15.8023	−	9.59037i	−0.508431	−	0.308565i
$967$	−18.8543	−	18.8543i	−0.606313	−	0.606313i	0.335668	−	0.941980i	$-0.391038\pi$
$967$	−18.8543	−	18.8543i	−0.606313	−	0.606313i	−0.941980	+	0.335668i	$0.891038\pi$
$968$	7.33266	+	27.3659i	0.235681	+	0.879572i
$969$	−10.9344	−	18.9389i	−0.351263	−	0.608406i
$970$		0			0
$971$	−12.4287	−	7.17573i	−0.398857	−	0.230280i	0.287134	−	0.957890i	$-0.407298\pi$
$971$	−12.4287	−	7.17573i	−0.398857	−	0.230280i	−0.685991	+	0.727610i	$0.740631\pi$
$972$	0.0818472	−	0.0818472i	0.00262525	−	0.00262525i
$973$	10.4118	+	10.8776i	0.333787	+	0.348721i
$974$		−	18.7283i		−	0.600094i
$975$		0			0
$976$	28.1633	−	16.2601i	0.901484	−	0.520472i
$977$	3.31521	−	12.3725i	0.106063	−	0.395833i	−0.892401	−	0.451244i	$-0.850980\pi$
$977$	3.31521	−	12.3725i	0.106063	−	0.395833i	0.998464	+	0.0554114i	$0.0176470\pi$
$978$	−16.2005	+	4.34092i	−0.518035	+	0.138807i
$979$	−3.40554			−0.108842
$980$		0			0
$981$	8.57081			0.273645
$982$	−30.1263	+	8.07232i	−0.961370	+	0.257598i
$983$	−6.76454	+	25.2456i	−0.215755	+	0.805209i	0.770144	+	0.637870i	$0.220184\pi$
$983$	−6.76454	+	25.2456i	−0.215755	+	0.805209i	−0.985899	+	0.167339i	$0.946482\pi$
$984$	−24.5671	+	14.1838i	−0.783171	+	0.452164i
$985$		0			0
$986$		−	11.1478i		−	0.355019i
$987$	13.0180	+	13.6004i	0.414366	+	0.432904i
$988$	−0.491818	+	0.491818i	−0.0156468	+	0.0156468i
$989$	39.4716	+	22.7889i	1.25512	+	0.724645i
$990$		0			0
$991$	−23.3428	−	40.4310i	−0.741509	−	1.28433i	−0.951808	−	0.306694i	$-0.900777\pi$
$991$	−23.3428	−	40.4310i	−0.741509	−	1.28433i	0.210299	−	0.977637i	$-0.432556\pi$
$992$	0.861450	+	3.21497i	0.0273511	+	0.102076i
$993$	7.68685	+	7.68685i	0.243935	+	0.243935i
$994$	15.6702	+	9.51021i	0.497029	+	0.301645i
$995$		0			0
$996$	−0.411822	+	0.713296i	−0.0130491	+	0.0226017i
$997$	3.40354	+	0.911976i	0.107791	+	0.0288826i	0.312311	−	0.949980i	$-0.398897\pi$
$997$	3.40354	+	0.911976i	0.107791	+	0.0288826i	−0.204520	+	0.978862i	$0.565563\pi$
$998$	−8.15375	−	2.18479i	−0.258102	−	0.0691583i
$999$	3.97076	−	6.87755i	0.125629	−	0.217596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bc.c.82.5	yes	24
5.2	odd	4	inner	525.2.bc.c.418.5	yes	24
5.3	odd	4	inner	525.2.bc.c.418.2	yes	24
5.4	even	2	inner	525.2.bc.c.82.2	✓	24
7.3	odd	6	inner	525.2.bc.c.157.2	yes	24
35.3	even	12	inner	525.2.bc.c.493.5	yes	24
35.17	even	12	inner	525.2.bc.c.493.2	yes	24
35.24	odd	6	inner	525.2.bc.c.157.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bc.c.82.2	✓	24	5.4	even	2	inner
525.2.bc.c.82.5	yes	24	1.1	even	1	trivial
525.2.bc.c.157.2	yes	24	7.3	odd	6	inner
525.2.bc.c.157.5	yes	24	35.24	odd	6	inner
525.2.bc.c.418.2	yes	24	5.3	odd	4	inner
525.2.bc.c.418.5	yes	24	5.2	odd	4	inner
525.2.bc.c.493.2	yes	24	35.17	even	12	inner
525.2.bc.c.493.5	yes	24	35.3	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.32591 - 0.355276i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-0.100242 + 0.0578747i) q^{4} +1.37268i q^{6} +(1.82946 + 1.91130i) q^{7} +(-2.05361 + 2.05361i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(1.32591 - 0.355276i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-0.100242 + 0.0578747i) q^{4} +1.37268i q^{6} +(1.82946 + 1.91130i) q^{7} +(-2.05361 + 2.05361i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(0.557875 + 0.966267i) q^{11} +(-0.0299581 - 0.111805i) q^{12} +(-0.707107 - 0.707107i) q^{13} +(3.10473 + 1.88425i) q^{14} +(-1.87755 + 3.25201i) q^{16} +(3.51535 + 0.941934i) q^{17} +(-1.32591 - 0.355276i) q^{18} +(-3.00449 + 5.20393i) q^{19} +(-2.31968 + 1.27244i) q^{21} +(1.08298 + 1.08298i) q^{22} +(1.31732 + 4.91632i) q^{23} +(-1.45212 - 2.51515i) q^{24} +(-1.18878 - 0.686340i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.294005 - 0.0857135i) q^{28} -2.23150i q^{29} +(-4.40786 + 2.54488i) q^{31} +(0.169252 - 0.631656i) q^{32} +(-1.07773 + 0.288777i) q^{33} +4.99567 q^{34} +0.115749 q^{36} +(7.67091 - 2.05541i) q^{37} +(-2.13484 + 7.96735i) q^{38} +(0.866025 - 0.500000i) q^{39} -9.76765i q^{41} +(-2.62361 + 2.51126i) q^{42} +(6.33202 - 6.33202i) q^{43} +(-0.111845 - 0.0645737i) q^{44} +(3.49330 + 6.05057i) q^{46} +(-1.84169 - 6.87329i) q^{47} +(-2.65526 - 2.65526i) q^{48} +(-0.306171 + 6.99330i) q^{49} +(-1.81968 + 3.15177i) q^{51} +(0.111805 + 0.0299581i) q^{52} +(12.7809 + 3.42463i) q^{53} +(0.686340 - 1.18878i) q^{54} +(-7.68208 - 0.168082i) q^{56} +(-4.24899 - 4.24899i) q^{57} +(-0.792797 - 2.95876i) q^{58} +(0.0470420 + 0.0814792i) q^{59} +(-7.50000 - 4.33013i) q^{61} +(-4.94027 + 4.94027i) q^{62} +(-0.628704 - 2.56997i) q^{63} -8.40786i q^{64} +(-1.32638 + 0.765783i) q^{66} +(-1.84504 + 6.88578i) q^{67} +(-0.406899 + 0.109028i) q^{68} -5.08975 q^{69} +5.04721 q^{71} +(2.80529 - 0.751674i) q^{72} +(2.14269 - 7.99662i) q^{73} +(9.44068 - 5.45058i) q^{74} -0.695536i q^{76} +(-0.826223 + 2.83401i) q^{77} +(0.970631 - 0.970631i) q^{78} +(-3.76483 - 2.17362i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-3.47021 - 12.9510i) q^{82} +(-5.03159 - 5.03159i) q^{83} +(0.158887 - 0.261802i) q^{84} +(6.14605 - 10.6453i) q^{86} +(2.15546 + 0.577554i) q^{87} +(-3.13000 - 0.838680i) q^{88} +(-1.52612 + 2.64332i) q^{89} +(0.0578747 - 2.64512i) q^{91} +(-0.416582 - 0.416582i) q^{92} +(-1.31732 - 4.91632i) q^{93} +(-4.88382 - 8.45903i) q^{94} +(0.566327 + 0.326969i) q^{96} +(-11.8810 + 11.8810i) q^{97} +(2.07860 + 9.38124i) q^{98} -1.11575i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 36 q^{16} + 12 q^{21} + 12 q^{26} - 24 q^{31} - 24 q^{36} - 24 q^{46} + 24 q^{51} - 36 q^{56} - 180 q^{61} - 72 q^{66} - 96 q^{71} + 12 q^{81} + 120 q^{86} - 12 q^{91} - 108 q^{96}+O(q^{100}) \) 24 * q + 36 * q^16 + 12 * q^21 + 12 * q^26 - 24 * q^31 - 24 * q^36 - 24 * q^46 + 24 * q^51 - 36 * q^56 - 180 * q^61 - 72 * q^66 - 96 * q^71 + 12 * q^81 + 120 * q^86 - 12 * q^91 - 108 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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