LMFDB - Embedded newform 525.2.bc.c.157.2

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			157.2
Character	$\chi$	$=$	525.157
Dual form			525.2.bc.c.418.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.355276 + 1.32591i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(0.100242 + 0.0578747i) q^{4} -1.37268i q^{6} +(1.91130 + 1.82946i) q^{7} +(-2.05361 + 2.05361i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.355276 + 1.32591i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(0.100242 + 0.0578747i) q^{4} -1.37268i q^{6} +(1.91130 + 1.82946i) q^{7} +(-2.05361 + 2.05361i) q^{8} +(0.866025 - 0.500000i) q^{9} +(0.557875 - 0.966267i) q^{11} +(-0.111805 - 0.0299581i) q^{12} +(0.707107 + 0.707107i) q^{13} +(-3.10473 + 1.88425i) q^{14} +(-1.87755 - 3.25201i) q^{16} +(0.941934 + 3.51535i) q^{17} +(0.355276 + 1.32591i) q^{18} +(3.00449 + 5.20393i) q^{19} +(-2.31968 - 1.27244i) q^{21} +(1.08298 + 1.08298i) q^{22} +(-4.91632 - 1.31732i) q^{23} +(1.45212 - 2.51515i) q^{24} +(-1.18878 + 0.686340i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.0857135 + 0.294005i) q^{28} -2.23150i q^{29} +(-4.40786 - 2.54488i) q^{31} +(-0.631656 + 0.169252i) q^{32} +(-0.288777 + 1.07773i) q^{33} -4.99567 q^{34} +0.115749 q^{36} +(-2.05541 + 7.67091i) q^{37} +(-7.96735 + 2.13484i) q^{38} +(-0.866025 - 0.500000i) q^{39} +9.76765i q^{41} +(2.51126 - 2.62361i) q^{42} +(6.33202 - 6.33202i) q^{43} +(0.111845 - 0.0645737i) q^{44} +(3.49330 - 6.05057i) q^{46} +(-6.87329 - 1.84169i) q^{47} +(2.65526 + 2.65526i) q^{48} +(0.306171 + 6.99330i) q^{49} +(-1.81968 - 3.15177i) q^{51} +(0.0299581 + 0.111805i) q^{52} +(-3.42463 - 12.7809i) q^{53} +(-0.686340 - 1.18878i) q^{54} +(-7.68208 + 0.168082i) q^{56} +(-4.24899 - 4.24899i) q^{57} +(2.95876 + 0.792797i) q^{58} +(-0.0470420 + 0.0814792i) q^{59} +(-7.50000 + 4.33013i) q^{61} +(4.94027 - 4.94027i) q^{62} +(2.56997 + 0.628704i) q^{63} -8.40786i q^{64} +(-1.32638 - 0.765783i) q^{66} +(6.88578 - 1.84504i) q^{67} +(-0.109028 + 0.406899i) q^{68} +5.08975 q^{69} +5.04721 q^{71} +(-0.751674 + 2.80529i) q^{72} +(7.99662 - 2.14269i) q^{73} +(-9.44068 - 5.45058i) q^{74} +0.695536i q^{76} +(2.83401 - 0.826223i) q^{77} +(0.970631 - 0.970631i) q^{78} +(3.76483 - 2.17362i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-12.9510 - 3.47021i) q^{82} +(5.03159 + 5.03159i) q^{83} +(-0.158887 - 0.261802i) q^{84} +(6.14605 + 10.6453i) q^{86} +(0.577554 + 2.15546i) q^{87} +(0.838680 + 3.13000i) q^{88} +(1.52612 + 2.64332i) q^{89} +(0.0578747 + 2.64512i) q^{91} +(-0.416582 - 0.416582i) q^{92} +(4.91632 + 1.31732i) q^{93} +(4.88382 - 8.45903i) q^{94} +(0.566327 - 0.326969i) q^{96} +(11.8810 - 11.8810i) q^{97} +(-9.38124 - 2.07860i) 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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.355276	+	1.32591i	−0.251218	+	0.937558i	0.718938	+	0.695075i	$0.244629\pi$
$2$	−0.355276	+	1.32591i	−0.251218	+	0.937558i	−0.970156	+	0.242483i	$0.922038\pi$
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	0.100242	+	0.0578747i	0.0501210	+	0.0289373i
$5$		0			0
$5$		0			0
$6$		−	1.37268i		−	0.560394i
$7$	1.91130	+	1.82946i	0.722405	+	0.691470i
$7$	1.91130	+	1.82946i	0.722405	+	0.691470i
$8$	−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	−0.769583	−	0.638546i	$-0.779536\pi$
$11$	0.557875	−	0.966267i	0.168206	−	0.291341i	0.937789	+	0.347206i	$0.112869\pi$
$12$	−0.111805	−	0.0299581i	−0.0322754	−	0.00864817i
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i	0.798333	−	0.602217i	$-0.205716\pi$
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i	−0.602217	+	0.798333i	$0.705716\pi$
$14$	−3.10473	+	1.88425i	−0.829774	+	0.503587i
$15$		0			0
$16$	−1.87755	−	3.25201i	−0.469388	−	0.813004i
$17$	0.941934	+	3.51535i	0.228453	+	0.852597i	0.980992	+	0.194049i	$0.0621621\pi$
$17$	0.941934	+	3.51535i	0.228453	+	0.852597i	−0.752539	+	0.658547i	$0.771171\pi$
$18$	0.355276	+	1.32591i	0.0837393	+	0.312519i
$19$	3.00449	+	5.20393i	0.689277	+	1.19386i	0.972072	+	0.234682i	$0.0754050\pi$
$19$	3.00449	+	5.20393i	0.689277	+	1.19386i	−0.282795	+	0.959180i	$0.591262\pi$
$20$		0			0
$21$	−2.31968	−	1.27244i	−0.506195	−	0.277669i
$22$	1.08298	+	1.08298i	0.230892	+	0.230892i
$23$	−4.91632	−	1.31732i	−1.02512	−	0.274681i	−0.293188	−	0.956055i	$-0.594716\pi$
$23$	−4.91632	−	1.31732i	−1.02512	−	0.274681i	−0.731936	+	0.681373i	$0.761383\pi$
$24$	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
$28$	0.0857135	+	0.294005i	0.0161983	+	0.0555616i
$29$		−	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	0.0488774	−	0.998805i	$-0.484436\pi$
$31$	−4.40786	−	2.54488i	−0.791674	−	0.457073i	−0.840552	+	0.541732i	$0.817769\pi$
$32$	−0.631656	+	0.169252i	−0.111662	+	0.0299198i
$33$	−0.288777	+	1.07773i	−0.0502697	+	0.187609i
$34$	−4.99567			−0.856750
$35$		0			0
$36$	0.115749			0.0192916
$37$	−2.05541	+	7.67091i	−0.337908	+	1.26109i	0.562774	+	0.826611i	$0.309734\pi$
$37$	−2.05541	+	7.67091i	−0.337908	+	1.26109i	−0.900682	+	0.434479i	$0.856932\pi$
$38$	−7.96735	+	2.13484i	−1.29247	+	0.346317i
$39$	−0.866025	−	0.500000i	−0.138675	−	0.0800641i
$40$		0			0
$41$			9.76765i			1.52545i	0.646723	+	0.762725i	$0.276139\pi$
$41$			9.76765i			1.52545i	−0.646723	+	0.762725i	$0.723861\pi$
$42$	2.51126	−	2.62361i	0.387496	−	0.404832i
$43$	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
$47$	−6.87329	−	1.84169i	−1.00257	−	0.268638i	−0.280049	−	0.959986i	$-0.590351\pi$
$47$	−6.87329	−	1.84169i	−1.00257	−	0.268638i	−0.722523	+	0.691347i	$0.757017\pi$
$48$	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
$52$	0.0299581	+	0.111805i	0.00415445	+	0.0155046i
$53$	−3.42463	−	12.7809i	−0.470409	−	1.75559i	−0.638303	−	0.769785i	$-0.720363\pi$
$53$	−3.42463	−	12.7809i	−0.470409	−	1.75559i	0.167894	−	0.985805i	$-0.446303\pi$
$54$	−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
$58$	2.95876	+	0.792797i	0.388504	+	0.104099i
$59$	−0.0470420	+	0.0814792i	−0.00612435	+	0.0106077i	−0.869071	−	0.494687i	$-0.835283\pi$
$59$	−0.0470420	+	0.0814792i	−0.00612435	+	0.0106077i	0.862947	+	0.505294i	$0.168616\pi$
$60$		0			0
$61$	−7.50000	+	4.33013i	−0.960277	+	0.554416i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−7.50000	+	4.33013i	−0.960277	+	0.554416i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	4.94027	−	4.94027i	0.627415	−	0.627415i
$63$	2.56997	+	0.628704i	0.323785	+	0.0792093i
$64$		−	8.40786i		−	1.05098i
$65$		0			0
$66$	−1.32638	−	0.765783i	−0.163266	−	0.0942614i
$67$	6.88578	−	1.84504i	0.841232	−	0.225408i	0.187624	−	0.982241i	$-0.439921\pi$
$67$	6.88578	−	1.84504i	0.841232	−	0.225408i	0.653608	+	0.756833i	$0.273255\pi$
$68$	−0.109028	+	0.406899i	−0.0132216	+	0.0493438i
$69$	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	$0.403181\pi$
$72$	−0.751674	+	2.80529i	−0.0885857	+	0.330606i
$73$	7.99662	−	2.14269i	0.935933	−	0.250783i	0.241550	−	0.970388i	$-0.422344\pi$
$73$	7.99662	−	2.14269i	0.935933	−	0.250783i	0.694383	+	0.719606i	$0.255677\pi$
$74$	−9.44068	−	5.45058i	−1.09746	−	0.633617i
$75$		0			0
$76$			0.695536i			0.0797834i
$77$	2.83401	−	0.826223i	0.322966	−	0.0941569i
$78$	0.970631	−	0.970631i	0.109902	−	0.109902i
$79$	3.76483	−	2.17362i	0.423576	−	0.244552i	−0.273030	−	0.962006i	$-0.588026\pi$
$79$	3.76483	−	2.17362i	0.423576	−	0.244552i	0.696606	+	0.717454i	$0.254693\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−12.9510	−	3.47021i	−1.43020	−	0.383220i
$83$	5.03159	+	5.03159i	0.552289	+	0.552289i	0.927101	−	0.374812i	$-0.122293\pi$
$83$	5.03159	+	5.03159i	0.552289	+	0.552289i	−0.374812	+	0.927101i	$0.622293\pi$
$84$	−0.158887	−	0.261802i	−0.0173360	−	0.0285650i
$85$		0			0
$86$	6.14605	+	10.6453i	0.662746	+	1.14791i
$87$	0.577554	+	2.15546i	0.0619203	+	0.231090i
$88$	0.838680	+	3.13000i	0.0894036	+	0.333659i
$89$	1.52612	+	2.64332i	0.161769	+	0.280191i	0.935503	−	0.353319i	$-0.114947\pi$
$89$	1.52612	+	2.64332i	0.161769	+	0.280191i	−0.773734	+	0.633510i	$0.781614\pi$
$90$		0			0
$91$	0.0578747	+	2.64512i	0.00606692	+	0.277284i
$92$	−0.416582	−	0.416582i	−0.0434317	−	0.0434317i
$93$	4.91632	+	1.31732i	0.509799	+	0.136600i
$94$	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	$-0.424776\pi$
$97$	11.8810	−	11.8810i	1.20634	−	1.20634i	0.972205	−	0.234131i	$-0.0752243\pi$
$98$	−9.38124	−	2.07860i	−0.947649	−	0.209970i
$99$		−	1.11575i		−	0.112137i
$100$		0			0
$101$	15.8669	+	9.16075i	1.57881	+	0.911529i	0.995025	+	0.0996233i	$0.0317638\pi$
$101$	15.8669	+	9.16075i	1.57881	+	0.911529i	0.583789	+	0.811905i	$0.301570\pi$
$102$	4.82545	−	1.29297i	0.477790	−	0.128024i
$103$	−0.929716	+	3.46975i	−0.0916076	+	0.341884i	−0.996483	−	0.0837917i	$-0.973297\pi$
$103$	−0.929716	+	3.46975i	−0.0916076	+	0.341884i	0.904876	+	0.425676i	$0.139964\pi$
$104$	−2.90425			−0.284785
$105$		0			0
$106$	18.1630			1.76414
$107$	−4.61101	+	17.2085i	−0.445763	+	1.66361i	0.268152	+	0.963377i	$0.413587\pi$
$107$	−4.61101	+	17.2085i	−0.445763	+	1.66361i	−0.713915	+	0.700233i	$0.753080\pi$
$108$	−0.111805	+	0.0299581i	−0.0107585	+	0.00288272i
$109$	7.42254	+	4.28541i	0.710951	+	0.410468i	0.811413	−	0.584473i	$-0.198699\pi$
$109$	7.42254	+	4.28541i	0.710951	+	0.410468i	−0.100462	+	0.994941i	$0.532032\pi$
$110$		0			0
$111$		−	7.94151i		−	0.753775i
$112$	2.36085	−	9.65049i	0.223079	−	0.911886i
$113$	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
$117$	0.965926	+	0.258819i	0.0892999	+	0.0239278i
$118$	−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
$122$	−3.07678	−	11.4827i	−0.278558	−	1.03959i
$123$	−2.52805	−	9.43482i	−0.227947	−	0.850709i
$124$	−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	$0.954886\pi$
$128$	9.88472	+	2.64860i	0.873694	+	0.234106i
$129$	−4.47741	+	7.75510i	−0.394214	+	0.682799i
$130$		0			0
$131$	9.16296	−	5.29024i	0.800571	−	0.462210i	−0.0430995	−	0.999071i	$-0.513723\pi$
$131$	9.16296	−	5.29024i	0.800571	−	0.462210i	0.843671	+	0.536861i	$0.180390\pi$
$132$	−0.0913209	+	0.0913209i	−0.00794847	+	0.00794847i
$133$	−3.77787	+	15.4429i	−0.327583	+	1.33907i
$134$			9.78541i			0.845330i
$135$		0			0
$136$	−9.15353	−	5.28479i	−0.784908	−	0.453167i
$137$	8.64969	−	2.31768i	0.738993	−	0.198013i	0.130363	−	0.991466i	$-0.458386\pi$
$137$	8.64969	−	2.31768i	0.738993	−	0.198013i	0.608631	+	0.793454i	$0.291719\pi$
$138$	−1.80827	+	6.74854i	−0.153930	+	0.574474i
$139$	−5.69120			−0.482722			−0.241361	−	0.970435i	$-0.577594\pi$
$139$	−5.69120			−0.482722			−0.241361	+	0.970435i	$0.577594\pi$
$140$		0			0
$141$	7.11575			0.599254
$142$	−1.79315	+	6.69213i	−0.150478	+	0.561591i
$143$	1.07773	−	0.288777i	0.0901244	−	0.0241488i
$144$	−3.25201	−	1.87755i	−0.271001	−	0.156463i
$145$		0			0
$146$			11.3640i			0.940493i
$147$	−2.10574	−	6.67577i	−0.173678	−	0.550608i
$148$	−0.649990	+	0.649990i	−0.0534289	+	0.0534289i
$149$	8.34793	−	4.81968i	0.683889	−	0.394843i	−0.117430	−	0.993081i	$-0.537466\pi$
$149$	8.34793	−	4.81968i	0.683889	−	0.394843i	0.801319	+	0.598238i	$0.204132\pi$
$150$		0			0
$151$	10.2208	−	17.7030i	0.831760	−	1.44065i	−0.0648821	−	0.997893i	$-0.520667\pi$
$151$	10.2208	−	17.7030i	0.831760	−	1.44065i	0.896642	−	0.442757i	$-0.146000\pi$
$152$	−16.8569	−	4.51680i	−1.36728	−	0.366360i
$153$	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
$157$	−0.394338	−	1.47169i	−0.0314716	−	0.117454i	0.948403	−	0.317067i	$-0.102698\pi$
$157$	−0.394338	−	1.47169i	−0.0314716	−	0.117454i	−0.979875	+	0.199613i	$0.936031\pi$
$158$	1.54447	+	5.76405i	0.122872	+	0.458563i
$159$	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
$163$	−11.8021	−	3.16236i	−0.924412	−	0.247696i	−0.234942	−	0.972009i	$-0.575490\pi$
$163$	−11.8021	−	3.16236i	−0.924412	−	0.247696i	−0.689470	+	0.724314i	$0.742157\pi$
$164$	−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	$-0.485010\pi$
$167$	13.5169	−	13.5169i	1.04597	−	1.04597i	0.998891	−	0.0470760i	$-0.0149903\pi$
$168$	7.37681	−	2.15062i	0.569134	−	0.165924i
$169$		−	12.0000i		−	0.923077i
$170$		0			0
$171$	5.20393	+	3.00449i	0.397954	+	0.229759i
$172$	1.00120	−	0.268270i	0.0763405	−	0.0204554i
$173$	1.55291	−	5.79555i	0.118066	−	0.440628i	−0.881432	−	0.472311i	$-0.843420\pi$
$173$	1.55291	−	5.79555i	0.118066	−	0.440628i	0.999498	+	0.0316829i	$0.0100867\pi$
$174$	−3.06313			−0.232216
$175$		0			0
$176$	−4.18975			−0.315815
$177$	0.0243507	−	0.0908782i	0.00183031	−	0.00683083i
$178$	−4.04699	+	1.08439i	−0.303335	+	0.0812783i
$179$	−10.3923	−	6.00000i	−0.776757	−	0.448461i	0.0585225	−	0.998286i	$-0.481361\pi$
$179$	−10.3923	−	6.00000i	−0.776757	−	0.448461i	−0.835280	+	0.549825i	$0.814694\pi$
$180$		0			0
$181$			6.39763i			0.475532i	0.971322	+	0.237766i	$0.0764152\pi$
$181$			6.39763i			0.475532i	−0.971322	+	0.237766i	$0.923585\pi$
$182$	−3.52774	−	0.863010i	−0.261494	−	0.0639705i
$183$	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
$187$	3.92225	+	1.05096i	0.286823	+	0.0768540i
$188$	−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	0.833635	−	0.552316i	$-0.186256\pi$
$191$	−0.849980	−	1.47221i	−0.0615024	−	0.106525i	−0.895137	+	0.445791i	$0.852923\pi$
$192$	2.17611	+	8.12136i	0.157047	+	0.586109i
$193$	3.82103	+	14.2603i	0.275044	+	1.02648i	0.955812	+	0.293978i	$0.0949793\pi$
$193$	3.82103	+	14.2603i	0.275044	+	1.02648i	−0.680769	+	0.732499i	$0.738354\pi$
$194$	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	$0.404287\pi$
$198$	1.47938	+	0.396399i	0.105135	+	0.0281708i
$199$	−1.11355	+	1.92873i	−0.0789376	+	0.136724i	−0.902792	−	0.430078i	$-0.858486\pi$
$199$	−1.11355	+	1.92873i	−0.0789376	+	0.136724i	0.823854	+	0.566802i	$0.191819\pi$
$200$		0			0
$201$	−6.17362	+	3.56434i	−0.435454	+	0.251409i
$202$	−17.7834	+	17.7834i	−1.25124	+	1.25124i
$203$	4.08243	−	4.26507i	0.286531	−	0.299350i
$204$		−	0.421253i		−	0.0294936i
$205$		0			0
$206$	−4.27026	−	2.46543i	−0.297523	−	0.171775i
$207$	−4.91632	+	1.31732i	−0.341708	+	0.0915604i
$208$	0.971892	−	3.62715i	0.0673886	−	0.251498i
$209$	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	$0.675567\pi$
$212$	0.396399	−	1.47938i	0.0272248	−	0.101604i
$213$	−4.87523	+	1.30631i	−0.334045	+	0.0895071i
$214$	−21.1787	−	12.2275i	−1.44775	−	0.835857i
$215$		0			0
$216$		−	2.90425i		−	0.197609i
$217$	−3.76901	−	12.9280i	−0.255857	−	0.877611i
$218$	−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
$222$	10.5297	+	2.82143i	0.706708	+	0.189362i
$223$	−17.6103	−	17.6103i	−1.17927	−	1.17927i	−0.979930	−	0.199340i	$-0.936120\pi$
$223$	−17.6103	−	17.6103i	−1.17927	−	1.17927i	−0.199340	−	0.979930i	$-0.563880\pi$
$224$	−1.51693	−	0.832096i	−0.101354	−	0.0555968i
$225$		0			0
$226$	3.49330	+	6.05057i	0.232371	+	0.402478i
$227$	3.19018	+	11.9059i	0.211740	+	0.790224i	0.987289	+	0.158936i	$0.0508065\pi$
$227$	3.19018	+	11.9059i	0.211740	+	0.790224i	−0.775549	+	0.631287i	$0.782527\pi$
$228$	−0.180018	−	0.671836i	−0.0119220	−	0.0444934i
$229$	1.22540	+	2.12245i	0.0809765	+	0.140255i	0.903670	−	0.428230i	$-0.140863\pi$
$229$	1.22540	+	2.12245i	0.0809765	+	0.140255i	−0.822693	+	0.568486i	$0.807529\pi$
$230$		0			0
$231$	−2.52360	+	1.53157i	−0.166041	+	0.100770i
$232$	4.58263	+	4.58263i	0.300865	+	0.300865i
$233$	−2.56094	−	0.686201i	−0.167772	−	0.0449545i	0.173955	−	0.984754i	$-0.444345\pi$
$233$	−2.56094	−	0.686201i	−0.167772	−	0.0449545i	−0.341727	+	0.939799i	$0.611012\pi$
$234$	−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
$238$	−9.54824	−	9.13936i	−0.618921	−	0.592417i
$239$		−	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	0.00242769	−	0.999997i	$-0.499227\pi$
$241$	−13.3878	−	7.72943i	−0.862381	−	0.497896i	−0.864809	+	0.502101i	$0.832561\pi$
$242$	−12.9344	+	3.46575i	−0.831452	+	0.222787i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	−1.00242			−0.0641733
$245$		0			0
$246$	13.4079			0.854854
$247$	−1.55524	+	5.80423i	−0.0989574	+	0.369314i
$248$	14.2782	−	3.82584i	0.906668	−	0.242941i
$249$	−6.16242	−	3.55787i	−0.390527	−	0.225471i
$250$		0			0
$251$		−	27.7823i		−	1.75360i	−0.480854	−	0.876801i	$-0.659673\pi$
$251$		−	27.7823i		−	1.75360i	0.480854	−	0.876801i	$-0.340327\pi$
$252$	0.221232	+	0.211759i	0.0139363	+	0.0133395i
$253$	−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
$257$	−8.74660	−	2.34364i	−0.545598	−	0.146192i	−0.0245163	−	0.999699i	$-0.507805\pi$
$257$	−8.74660	−	2.34364i	−0.545598	−	0.146192i	−0.521081	+	0.853507i	$0.674471\pi$
$258$	−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
$262$	3.75899	+	14.0287i	0.232231	+	0.866698i
$263$	−4.21461	−	15.7291i	−0.259884	−	0.969900i	−0.965308	−	0.261114i	$-0.915910\pi$
$263$	−4.21461	−	15.7291i	−0.259884	−	0.969900i	0.705424	−	0.708785i	$-0.250757\pi$
$264$	−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
$268$	0.797025	+	0.213562i	0.0486861	+	0.0130454i
$269$	−1.32564	+	2.29607i	−0.0808256	+	0.139994i	−0.903605	−	0.428367i	$-0.859089\pi$
$269$	−1.32564	+	2.29607i	−0.0808256	+	0.139994i	0.822779	+	0.568361i	$0.192422\pi$
$270$		0			0
$271$	−19.1327	+	11.0462i	−1.16223	+	0.671012i	−0.951836	−	0.306606i	$-0.900807\pi$
$271$	−19.1327	+	11.0462i	−1.16223	+	0.671012i	−0.210390	+	0.977618i	$0.567473\pi$
$272$	9.66343	−	9.66343i	0.585931	−	0.585931i
$273$	−0.740510	−	2.54001i	−0.0448177	−	0.153728i
$274$			12.2921i			0.742593i
$275$		0			0
$276$	0.510207	+	0.294568i	0.0307108	+	0.0177309i
$277$	19.8484	−	5.31837i	1.19258	−	0.319550i	0.392673	−	0.919678i	$-0.371551\pi$
$277$	19.8484	−	5.31837i	1.19258	−	0.319550i	0.799904	+	0.600128i	$0.204884\pi$
$278$	2.02195	−	7.54601i	0.121268	−	0.452579i
$279$	−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	$0.804204\pi$
$282$	−2.52805	+	9.43482i	−0.150543	+	0.561836i
$283$	17.2490	−	4.62185i	1.02535	−	0.274740i	0.293317	−	0.956015i	$-0.405241\pi$
$283$	17.2490	−	4.62185i	1.02535	−	0.274740i	0.732028	+	0.681275i	$0.238574\pi$
$284$	0.505942	+	0.292106i	0.0300221	+	0.0173333i
$285$		0			0
$286$			1.53157i			0.0905635i
$287$	−17.8695	+	18.6689i	−1.05480	+	1.10199i
$288$	−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
$292$	0.925604	+	0.248015i	0.0541669	+	0.0145140i
$293$	22.1174	+	22.1174i	1.29211	+	1.29211i	0.933479	+	0.358633i	$0.116757\pi$
$293$	22.1174	+	22.1174i	1.29211	+	1.29211i	0.358633	+	0.933479i	$0.383243\pi$
$294$	9.59957	−	0.420275i	0.559858	−	0.0245109i
$295$		0			0
$296$	−11.5321	−	19.9741i	−0.670287	−	1.16097i
$297$	0.288777	+	1.07773i	0.0167566	+	0.0625363i
$298$	3.42463	+	12.7809i	0.198383	+	0.740377i
$299$	−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
$303$	−17.6972	−	4.74195i	−1.01668	−	0.272418i
$304$	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	$0.558822\pi$
$307$	−20.4425	+	20.4425i	−1.16672	+	1.16672i	−0.982974	+	0.183744i	$0.941178\pi$
$308$	0.331904	+	0.0811955i	0.0189120	+	0.00462654i
$309$		−	3.59214i		−	0.204350i
$310$		0			0
$311$	8.28664	+	4.78429i	0.469892	+	0.271292i	0.716195	−	0.697901i	$-0.245882\pi$
$311$	8.28664	+	4.78429i	0.469892	+	0.271292i	−0.246302	+	0.969193i	$0.579216\pi$
$312$	2.80529	−	0.751674i	0.158818	−	0.0425552i
$313$	0.839841	−	3.13433i	0.0474706	−	0.177163i	−0.938120	−	0.346310i	$-0.887435\pi$
$313$	0.839841	−	3.13433i	0.0474706	−	0.177163i	0.985591	+	0.169147i	$0.0541013\pi$
$314$	2.09142			0.118026
$315$		0			0
$316$	0.503191			0.0283067
$317$	4.15953	−	15.5236i	0.233623	−	0.871891i	−0.745142	−	0.666905i	$-0.767619\pi$
$317$	4.15953	−	15.5236i	0.233623	−	0.871891i	0.978765	−	0.204986i	$-0.0657148\pi$
$318$	−17.5441	+	4.70092i	−0.983823	+	0.263614i
$319$	−2.15622	−	1.24490i	−0.120725	−	0.0697008i
$320$		0			0
$321$		−	17.8156i		−	0.994368i
$322$	17.7460	−	5.17365i	0.988948	−	0.288316i
$323$	−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
$327$	−8.27877	−	2.21829i	−0.457817	−	0.122672i
$328$	−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	0.975852	−	0.218432i	$-0.0700943\pi$
$331$	5.43543	+	9.41443i	0.298758	+	0.517464i	−0.677094	+	0.735897i	$0.736761\pi$
$332$	0.213175	+	0.795579i	0.0116995	+	0.0436631i
$333$	2.05541	+	7.67091i	0.112636	+	0.420363i
$334$	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	$0.756232\pi$
$338$	15.9109	+	4.26331i	0.865438	+	0.231893i
$339$	−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
$343$	−12.2088	+	13.9265i	−0.659211	+	0.751958i
$344$			26.0070i			1.40220i
$345$		0			0
$346$	7.13265	+	4.11804i	0.383454	+	0.221387i
$347$	4.43814	−	1.18920i	0.238252	−	0.0638394i	−0.137717	−	0.990472i	$-0.543977\pi$
$347$	4.43814	−	1.18920i	0.238252	−	0.0638394i	0.375969	+	0.926632i	$0.377310\pi$
$348$	−0.0668516	+	0.249493i	−0.00358362	+	0.0133743i
$349$	−2.53256			−0.135565			−0.0677824	−	0.997700i	$-0.521592\pi$
$349$	−2.53256			−0.135565			−0.0677824	+	0.997700i	$0.521592\pi$
$350$		0			0
$351$	−1.00000			−0.0533761
$352$	−0.188843	+	0.704770i	−0.0100653	+	0.0375644i
$353$	6.90595	−	1.85044i	0.367566	−	0.0984891i	−0.0703079	−	0.997525i	$-0.522398\pi$
$353$	6.90595	−	1.85044i	0.367566	−	0.0984891i	0.437874	+	0.899036i	$0.355732\pi$
$354$	0.111845	+	0.0645737i	0.00594449	+	0.00343205i
$355$		0			0
$356$			0.353295i			0.0187246i
$357$	2.28808	−	9.35302i	0.121098	−	0.495014i
$358$	11.6476	−	11.6476i	0.615594	−	0.615594i
$359$	4.00620	−	2.31298i	0.211439	−	0.122074i	−0.390541	−	0.920586i	$-0.627712\pi$
$359$	4.00620	−	2.31298i	0.211439	−	0.122074i	0.601980	+	0.798511i	$0.294379\pi$
$360$		0			0
$361$	−8.55391	+	14.8158i	−0.450206	+	0.779779i
$362$	−8.48266	−	2.27292i	−0.445839	−	0.119462i
$363$	−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
$367$	0.779925	+	2.91072i	0.0407117	+	0.151938i	0.983290	−	0.182048i	$-0.0582727\pi$
$367$	0.779925	+	2.91072i	0.0407117	+	0.151938i	−0.942578	+	0.333986i	$0.891606\pi$
$368$	4.94669	+	18.4613i	0.257864	+	0.962362i
$369$	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
$373$	−6.10065	−	1.63467i	−0.315880	−	0.0846398i	0.0973958	−	0.995246i	$-0.468949\pi$
$373$	−6.10065	−	1.63467i	−0.315880	−	0.0846398i	−0.413276	+	0.910606i	$0.635615\pi$
$374$	−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
$378$	0.863010	−	3.52774i	0.0443884	−	0.181448i
$379$			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
$382$	2.25399	−	0.603955i	0.115324	−	0.0309010i
$383$	−6.69382	+	24.9817i	−0.342038	+	1.27650i	0.553997	+	0.832519i	$0.313102\pi$
$383$	−6.69382	+	24.9817i	−0.342038	+	1.27650i	−0.896035	+	0.443984i	$0.853565\pi$
$384$	−10.2334			−0.522222
$385$		0			0
$386$	−20.2653			−1.03148
$387$	2.31768	−	8.64969i	0.117814	−	0.439689i
$388$	1.87859	−	0.503366i	0.0953709	−	0.0255545i
$389$	7.84198	+	4.52757i	0.397604	+	0.229557i	0.685450	−	0.728120i	$-0.259606\pi$
$389$	7.84198	+	4.52757i	0.397604	+	0.229557i	−0.287845	+	0.957677i	$0.592939\pi$
$390$		0			0
$391$		−	18.5234i		−	0.936769i
$392$	−14.9903	−	13.7328i	−0.757124	−	0.693610i
$393$	−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
$397$	12.2034	+	3.26989i	0.612471	+	0.164111i	0.551703	−	0.834041i	$-0.313978\pi$
$397$	12.2034	+	3.26989i	0.612471	+	0.164111i	0.0607683	+	0.998152i	$0.480645\pi$
$398$	−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	0.877088	+	0.480330i	$0.159483\pi$
$401$	17.1118	+	29.6385i	0.854522	+	1.48007i	−0.0225664	+	0.999745i	$0.507184\pi$
$402$	−2.53265	−	9.45198i	−0.126317	−	0.471422i
$403$	−1.31732	−	4.91632i	−0.0656206	−	0.244900i
$404$	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
$408$	10.2094	+	2.73561i	0.505442	+	0.135433i
$409$	−15.0170	+	26.0102i	−0.742543	+	1.28612i	0.208791	+	0.977960i	$0.433047\pi$
$409$	−15.0170	+	26.0102i	−0.742543	+	1.28612i	−0.951334	+	0.308162i	$0.900286\pi$
$410$		0			0
$411$	−7.75510	+	4.47741i	−0.382531	+	0.220854i
$412$	−0.294007	+	0.294007i	−0.0144847	+	0.0144847i
$413$	−0.238974	+	0.0696702i	−0.0117592	+	0.00342824i
$414$		−	6.98660i		−	0.343373i
$415$		0			0
$416$	−0.566327	−	0.326969i	−0.0277665	−	0.0160310i
$417$	5.49728	−	1.47299i	0.269203	−	0.0721327i
$418$	−2.38195	+	8.88956i	−0.116505	+	0.434803i
$419$	25.9684			1.26864			0.634321	−	0.773070i	$-0.281280\pi$
$419$	25.9684			1.26864			0.634321	+	0.773070i	$0.281280\pi$
$420$		0			0
$421$	1.29211			0.0629734			0.0314867	−	0.999504i	$-0.489976\pi$
$421$	1.29211			0.0629734			0.0314867	+	0.999504i	$0.489976\pi$
$422$	5.40856	−	20.1850i	0.263285	−	0.982592i
$423$	−6.87329	+	1.84169i	−0.334191	+	0.0895461i
$424$	33.2799	+	19.2141i	1.61621	+	0.933121i
$425$		0			0
$426$		−	6.92820i		−	0.335673i
$427$	−22.2566	−	5.44474i	−1.07707	−	0.263489i
$428$	−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	−0.660641	−	0.750702i	$-0.729715\pi$
$431$	6.63935	−	11.4997i	0.319806	−	0.553921i	0.980447	+	0.196781i	$0.0630488\pi$
$432$	3.62715	+	0.971892i	0.174511	+	0.0467602i
$433$	2.29449	+	2.29449i	0.110266	+	0.110266i	0.760087	−	0.649821i	$-0.225156\pi$
$433$	2.29449	+	2.29449i	0.110266	+	0.110266i	−0.649821	+	0.760087i	$0.725156\pi$
$434$	18.4804	−	0.404347i	0.887087	−	0.0194093i
$435$		0			0
$436$	0.496033	+	0.859155i	0.0237557	+	0.0411461i
$437$	−7.91578	−	29.5421i	−0.378663	−	1.41319i
$438$	−2.94122	−	10.9768i	−0.140537	−	0.524492i
$439$	−19.8885	−	34.4479i	−0.949227	−	1.64411i	−0.747059	−	0.664758i	$-0.768535\pi$
$439$	−19.8885	−	34.4479i	−0.949227	−	1.64411i	−0.202168	−	0.979351i	$-0.564799\pi$
$440$		0			0
$441$	3.76180	+	5.90329i	0.179133	+	0.281109i
$442$	−3.53247	−	3.53247i	−0.168023	−	0.168023i
$443$	23.0114	+	6.16588i	1.09330	+	0.292950i	0.760035	−	0.649883i	$-0.225182\pi$
$443$	23.0114	+	6.16588i	1.09330	+	0.292950i	0.333268	+	0.942832i	$0.391849\pi$
$444$	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
$448$	15.3818	−	16.0700i	0.726722	−	0.759235i
$449$		−	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
$452$	0.569061	−	0.152480i	0.0267664	−	0.00717204i
$453$	−5.29069	+	19.7451i	−0.248578	+	0.927707i
$454$	−16.9195			−0.794073
$455$		0			0
$456$	17.4516			0.817244
$457$	0.627937	−	2.34349i	0.0293736	−	0.109624i	−0.949683	−	0.313214i	$-0.898594\pi$
$457$	0.627937	−	2.34349i	0.0293736	−	0.109624i	0.979056	+	0.203590i	$0.0652610\pi$
$458$	−3.24952	+	0.870707i	−0.151840	+	0.0406855i
$459$	−3.15177	−	1.81968i	−0.147112	−	0.0849352i
$460$		0			0
$461$			15.8830i			0.739746i	0.929082	+	0.369873i	$0.120599\pi$
$461$			15.8830i			0.739746i	−0.929082	+	0.369873i	$0.879401\pi$
$462$	−1.13414	−	3.89019i	−0.0527650	−	0.180988i
$463$	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
$467$	−17.1372	−	4.59189i	−0.793014	−	0.212487i	−0.160499	−	0.987036i	$-0.551310\pi$
$467$	−17.1372	−	4.59189i	−0.793014	−	0.212487i	−0.632514	+	0.774549i	$0.717977\pi$
$468$	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
$472$	−0.0707206	−	0.263933i	−0.00325518	−	0.0121485i
$473$	−2.58595	−	9.65089i	−0.118902	−	0.443748i
$474$	−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
$478$	29.2951	+	7.84961i	1.33993	+	0.359033i
$479$	16.7429	−	28.9995i	0.765002	−	1.32502i	−0.175243	−	0.984525i	$-0.556071\pi$
$479$	16.7429	−	28.9995i	0.765002	−	1.32502i	0.940245	−	0.340498i	$-0.110596\pi$
$480$		0			0
$481$	−6.87755	+	3.97076i	−0.313589	+	0.181051i
$482$	15.0048	−	15.0048i	0.683452	−	0.683452i
$483$	9.72807	+	9.31149i	0.442642	+	0.423687i
$484$			1.12915i			0.0513249i
$485$		0			0
$486$	−1.18878	−	0.686340i	−0.0539240	−	0.0311330i
$487$	−13.1787	+	3.53123i	−0.597184	+	0.160015i	−0.544735	−	0.838608i	$-0.683370\pi$
$487$	−13.1787	+	3.53123i	−0.597184	+	0.160015i	−0.0524498	+	0.998624i	$0.516703\pi$
$488$	6.50969	−	24.2945i	0.294680	−	1.09976i
$489$	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	$0.671354\pi$
$492$	0.292621	−	1.09208i	0.0131924	−	0.0492345i
$493$	7.84449	−	2.10192i	0.353298	−	0.0946659i
$494$	−7.14333	−	4.12420i	−0.321394	−	0.185557i
$495$		0			0
$496$			19.1125i			0.858179i
$497$	9.64675	+	9.23365i	0.432716	+	0.414186i
$498$	6.90677	−	6.90677i	0.309500	−	0.309500i
$499$	5.32568	−	3.07478i	0.238410	−	0.137646i	−0.376036	−	0.926605i	$-0.622713\pi$
$499$	5.32568	−	3.07478i	0.238410	−	0.137646i	0.614446	+	0.788959i	$0.289380\pi$
$500$		0			0
$501$	−9.55787	+	16.5547i	−0.427014	+	0.739611i
$502$	36.8367	+	9.87037i	1.64410	+	0.440536i
$503$	11.6411	+	11.6411i	0.519051	+	0.519051i	0.917284	−	0.398233i	$-0.130377\pi$
$503$	11.6411	+	11.6411i	0.519051	+	0.519051i	−0.398233	+	0.917284i	$0.630377\pi$
$504$	−6.56883	+	3.98660i	−0.292599	+	0.177577i
$505$		0			0
$506$	−3.89765	−	6.75093i	−0.173272	−	0.300115i
$507$	3.10583	+	11.5911i	0.137935	+	0.514779i
$508$	−0.405223	−	1.51231i	−0.0179789	−	0.0670981i
$509$	−12.0071	−	20.7968i	−0.532204	−	0.921804i	−0.999293	−	0.0375939i	$-0.988031\pi$
$509$	−12.0071	−	20.7968i	−0.532204	−	0.921804i	0.467089	−	0.884210i	$-0.345303\pi$
$510$		0			0
$511$	19.2039	+	10.5341i	0.849532	+	0.466003i
$512$	17.1594	+	17.1594i	0.758347	+	0.758347i
$513$	−5.80423	−	1.55524i	−0.256263	−	0.0686654i
$514$	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
$518$	−8.07241	−	27.6890i	−0.354681	−	1.21659i
$519$			6.00000i			0.263371i
$520$		0			0
$521$	6.51021	+	3.75867i	0.285217	+	0.164670i	0.635783	−	0.771868i	$-0.280677\pi$
$521$	6.51021	+	3.75867i	0.285217	+	0.164670i	−0.350566	+	0.936538i	$0.614011\pi$
$522$	2.95876	−	0.792797i	0.129501	−	0.0346998i
$523$	2.91914	−	10.8944i	0.127645	−	0.476379i	−0.872275	−	0.489016i	$-0.837356\pi$
$523$	2.91914	−	10.8944i	0.127645	−	0.476379i	0.999920	+	0.0126373i	$0.00402267\pi$
$524$	1.22468			0.0535005
$525$		0			0
$526$	22.3527			0.974625
$527$	4.79421	−	17.8922i	0.208839	−	0.779398i
$528$	4.04699	−	1.08439i	0.176123	−	0.0471919i
$529$	2.51631	+	1.45279i	0.109405	+	0.0631648i
$530$		0			0
$531$			0.0940841i			0.00408290i
$532$	−1.27245	+	1.32938i	−0.0551678	+	0.0576359i
$533$	−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
$537$	11.5911	+	3.10583i	0.500193	+	0.134026i
$538$	−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	0.995475	−	0.0950254i	$-0.0302932\pi$
$541$	9.66296	+	16.7367i	0.415443	+	0.719568i	−0.580032	+	0.814594i	$0.696960\pi$
$542$	−7.84892	−	29.2926i	−0.337140	−	1.25822i
$543$	−1.65583	−	6.17964i	−0.0710584	−	0.265194i
$544$	−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	$0.842131\pi$
$548$	1.00120	+	0.268270i	0.0427690	+	0.0114599i
$549$	−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
$553$	11.1723	+	2.73313i	0.475094	+	0.116225i
$554$			28.2067i			1.19839i
$555$		0			0
$556$	−0.570497	−	0.329377i	−0.0241945	−	0.0139687i
$557$	−14.7728	+	3.95835i	−0.625942	+	0.167721i	−0.557828	−	0.829957i	$-0.688365\pi$
$557$	−14.7728	+	3.95835i	−0.625942	+	0.167721i	−0.0681144	+	0.997678i	$0.521698\pi$
$558$	1.80827	−	6.74854i	0.0765500	−	0.285688i
$559$	8.95482			0.378749
$560$		0			0
$561$	−4.06061			−0.171439
$562$	9.72783	−	36.3047i	0.410344	−	1.53142i
$563$	−3.48269	+	0.933183i	−0.146778	+	0.0393290i	−0.331460	−	0.943469i	$-0.607541\pi$
$563$	−3.48269	+	0.933183i	−0.146778	+	0.0393290i	0.184682	+	0.982798i	$0.440874\pi$
$564$	0.713296	+	0.411822i	0.0300352	+	0.0173408i
$565$		0			0
$566$			24.5126i			1.03034i
$567$	2.54001	−	0.740510i	0.106670	−	0.0310985i
$568$	−10.3650	+	10.3650i	−0.434906	+	0.434906i
$569$	−10.5041	+	6.06457i	−0.440357	+	0.254240i	−0.703749	−	0.710449i	$-0.748492\pi$
$569$	−10.5041	+	6.06457i	−0.440357	+	0.254240i	0.263392	+	0.964689i	$0.415159\pi$
$570$		0			0
$571$	−4.65002	+	8.05407i	−0.194597	+	0.337052i	−0.946768	−	0.321915i	$-0.895673\pi$
$571$	−4.65002	+	8.05407i	−0.194597	+	0.337052i	0.752171	+	0.658968i	$0.229007\pi$
$572$	0.124747	+	0.0334258i	0.00521592	+	0.00139760i
$573$	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
$577$	−7.15154	−	26.6899i	−0.297722	−	1.11112i	−0.939031	−	0.343832i	$-0.888275\pi$
$577$	−7.15154	−	26.6899i	−0.297722	−	1.11112i	0.641309	−	0.767283i	$-0.278392\pi$
$578$	1.33410	+	4.97892i	0.0554911	+	0.207096i
$579$	−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
$583$	−14.2603	−	3.82103i	−0.590600	−	0.158251i
$584$	−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	−0.901825	−	0.432102i	$-0.857772\pi$
$587$	−11.3805	+	11.3805i	−0.469722	+	0.469722i	0.432102	+	0.901825i	$0.357772\pi$
$588$	0.175275	−	0.791061i	0.00722821	−	0.0326228i
$589$		−	30.5842i		−	1.26020i
$590$		0			0
$591$	−21.5102	−	12.4189i	−0.884812	−	0.510846i
$592$	28.8051	−	7.71829i	1.18388	−	0.317220i
$593$	5.96506	−	22.2619i	0.244956	−	0.914186i	−0.728450	−	0.685099i	$-0.759759\pi$
$593$	5.96506	−	22.2619i	0.244956	−	0.914186i	0.973406	−	0.229088i	$-0.0735743\pi$
$594$	−1.53157			−0.0628410
$595$		0			0
$596$	1.11575			0.0457029
$597$	0.576417	−	2.15122i	0.0235912	−	0.0880434i
$598$	6.74854	−	1.80827i	0.275968	−	0.0739455i
$599$	16.3310	+	9.42873i	0.667268	+	0.385247i	0.795041	−	0.606556i	$-0.207449\pi$
$599$	16.3310	+	9.42873i	0.667268	+	0.385247i	−0.127773	+	0.991803i	$0.540783\pi$
$600$		0			0
$601$		−	41.8392i		−	1.70665i	−0.521375	−	0.853327i	$-0.674581\pi$
$601$		−	41.8392i		−	1.70665i	0.521375	−	0.853327i	$-0.325419\pi$
$602$	−7.72810	+	31.5903i	−0.314974	+	1.28752i
$603$	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
$607$	−13.7519	−	3.68480i	−0.558170	−	0.149561i	−0.0313047	−	0.999510i	$-0.509966\pi$
$607$	−13.7519	−	3.68480i	−0.558170	−	0.149561i	−0.526866	+	0.849949i	$0.676633\pi$
$608$	−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
$612$	0.109028	+	0.406899i	0.00440721	+	0.0164479i
$613$	0.819967	+	3.06016i	0.0331181	+	0.123599i	0.980506	−	0.196489i	$-0.0629542\pi$
$613$	0.819967	+	3.06016i	0.0331181	+	0.123599i	−0.947388	+	0.320088i	$0.896287\pi$
$614$	−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	$0.770847\pi$
$618$	4.76285	+	1.27620i	0.191590	+	0.0513364i
$619$	0.825141	−	1.42919i	0.0331652	−	0.0574439i	−0.848966	−	0.528447i	$-0.822775\pi$
$619$	0.825141	−	1.42919i	0.0331652	−	0.0574439i	0.882132	+	0.471003i	$0.156108\pi$
$620$		0			0
$621$	4.40786	−	2.54488i	0.176881	−	0.102122i
$622$	−9.28757	+	9.28757i	−0.372398	+	0.372398i
$623$	−1.91896	+	7.84417i	−0.0768815	+	0.314270i
$624$			3.75510i			0.150324i
$625$		0			0
$626$	3.85745	+	2.22710i	0.154175	+	0.0890129i
$627$	−6.47606	+	1.73526i	−0.258629	+	0.0692994i
$628$	0.0456444	−	0.170347i	0.00182141	−	0.00679759i
$629$	−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	$0.588952\pi$
$632$	−3.26772	+	12.1953i	−0.129983	+	0.485102i
$633$	14.7048	−	3.94015i	0.584465	−	0.156607i
$634$	19.1050	+	11.0303i	0.758758	+	0.438069i
$635$		0			0
$636$			1.53157i			0.0607306i
$637$	−4.72852	+	5.16151i	−0.187351	+	0.204506i
$638$	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	0.310177	+	0.950679i	$0.399612\pi$
$641$	−16.9181	+	29.3029i	−0.668223	+	1.15740i	−0.978401	+	0.206718i	$0.933722\pi$
$642$	23.6218	+	6.32944i	0.932277	+	0.249803i
$643$	11.9534	+	11.9534i	0.471396	+	0.471396i	0.902366	−	0.430970i	$-0.141829\pi$
$643$	11.9534	+	11.9534i	0.471396	+	0.471396i	−0.430970	+	0.902366i	$0.641829\pi$
$644$	−0.0340961	−	1.55833i	−0.00134357	−	0.0614070i
$645$		0			0
$646$	−15.0094	−	25.9971i	−0.590538	−	1.02284i
$647$	−0.288777	−	1.07773i	−0.0113530	−	0.0423700i	0.960017	−	0.279942i	$-0.0903152\pi$
$647$	−0.288777	−	1.07773i	−0.0113530	−	0.0423700i	−0.971370	+	0.237572i	$0.923648\pi$
$648$	0.751674	+	2.80529i	0.0295286	+	0.110202i
$649$	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
$653$	−22.2262	−	5.95550i	−0.869780	−	0.233057i	−0.203787	−	0.979015i	$-0.565325\pi$
$653$	−22.2262	−	5.95550i	−0.869780	−	0.233057i	−0.665992	+	0.745958i	$0.731992\pi$
$654$	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
$658$	24.8099	−	7.23304i	0.967191	−	0.281973i
$659$			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	0.00160630	−	0.999999i	$-0.499489\pi$
$661$	−22.2035	−	12.8192i	−0.863615	−	0.498608i	−0.865221	+	0.501390i	$0.832822\pi$
$662$	−14.4137	+	3.86215i	−0.560206	+	0.150107i
$663$	0.941934	−	3.51535i	0.0365817	−	0.136525i
$664$	−20.6659			−0.801992
$665$		0			0
$666$	−10.9012			−0.422411
$667$	−2.93961	+	10.9708i	−0.113822	+	0.424790i
$668$	2.13724	−	0.572672i	0.0826924	−	0.0221574i
$669$	21.5681	+	12.4523i	0.833870	+	0.481435i
$670$		0			0
$671$			9.66267i			0.373023i
$672$	1.68060	+	0.411134i	0.0648306	+	0.0158598i
$673$	−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
$677$	24.9817	+	6.69382i	0.960123	+	0.257264i	0.704653	−	0.709553i	$-0.251103\pi$
$677$	24.9817	+	6.69382i	0.960123	+	0.257264i	0.255471	+	0.966817i	$0.417770\pi$
$678$	−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
$682$	−2.01757	−	7.52968i	−0.0772568	−	0.288326i
$683$	−3.66573	−	13.6807i	−0.140265	−	0.523477i	−0.999921	−	0.0126025i	$-0.995988\pi$
$683$	−3.66573	−	13.6807i	−0.140265	−	0.523477i	0.859655	−	0.510874i	$-0.170678\pi$
$684$	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
$688$	−32.4805	−	8.70312i	−1.23831	−	0.331803i
$689$	6.61587	−	11.4590i	0.252045	−	0.436554i
$690$		0			0
$691$	33.4086	−	19.2885i	1.27092	−	0.733768i	0.295762	−	0.955262i	$-0.404426\pi$
$691$	33.4086	−	19.2885i	1.27092	−	0.733768i	0.975162	+	0.221493i	$0.0710930\pi$
$692$	0.491083	−	0.491083i	0.0186682	−	0.0186682i
$693$	2.04122	−	2.13254i	0.0775394	−	0.0810084i
$694$			6.30705i			0.239413i
$695$		0			0
$696$	−5.61256	−	3.24041i	−0.212743	−	0.122827i
$697$	−34.3367	+	9.20048i	−1.30059	+	0.348493i
$698$	0.899757	−	3.35794i	0.0340563	−	0.127100i
$699$	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	$0.640305\pi$
$702$	0.355276	−	1.32591i	0.0134090	−	0.0500431i
$703$	−46.0943	+	12.3509i	−1.73848	+	0.465825i
$704$	−8.12424	−	4.69053i	−0.306194	−	0.176781i
$705$		0			0
$706$			9.81406i			0.369357i
$707$	13.5672	+	46.5368i	0.510249	+	1.75020i
$708$	0.00770052	−	0.00770052i	0.000289403	−	0.000289403i
$709$	−11.2058	+	6.46970i	−0.420844	+	0.242975i	−0.695438	−	0.718586i	$-0.744790\pi$
$709$	−11.2058	+	6.46970i	−0.420844	+	0.242975i	0.274594	+	0.961560i	$0.411456\pi$
$710$		0			0
$711$	2.17362	−	3.76483i	0.0815173	−	0.141192i
$712$	−8.56242	−	2.29429i	−0.320890	−	0.0859823i
$713$	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
$717$	5.71846	+	21.3416i	0.213560	+	0.797015i
$718$	1.64349	+	6.13359i	0.0613345	+	0.228903i
$719$	8.17672	+	14.1625i	0.304940	+	0.528172i	0.977248	−	0.212100i	$-0.0680302\pi$
$719$	8.17672	+	14.1625i	0.304940	+	0.528172i	−0.672308	+	0.740272i	$0.734697\pi$
$720$		0			0
$721$	−8.12472	+	4.93087i	−0.302580	+	0.183635i
$722$	−16.6054	−	16.6054i	−0.617988	−	0.617988i
$723$	14.9321	+	4.00105i	0.555331	+	0.148800i
$724$	−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	−0.402173	−	0.915564i	$-0.631745\pi$
$727$	13.8425	−	13.8425i	0.513391	−	0.513391i	0.915564	+	0.402173i	$0.131745\pi$
$728$	−5.55090	−	5.31320i	−0.205730	−	0.196920i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	28.2236	+	16.2949i	1.04389	+	0.602688i
$732$	0.968263	−	0.259445i	0.0357880	−	0.00958937i
$733$	−6.55483	+	24.4630i	−0.242108	+	0.903560i	0.732707	+	0.680544i	$0.238257\pi$
$733$	−6.55483	+	24.4630i	−0.242108	+	0.903560i	−0.974815	+	0.223015i	$0.928410\pi$
$734$	−4.13643			−0.152678
$735$		0			0
$736$	3.32839			0.122686
$737$	2.05860	−	7.68281i	0.0758296	−	0.283000i
$738$	−12.9510	+	3.47021i	−0.476733	+	0.127740i
$739$	−14.6106	−	8.43543i	−0.537459	−	0.310302i	0.206589	−	0.978428i	$-0.433764\pi$
$739$	−14.6106	−	8.43543i	−0.537459	−	0.310302i	−0.744049	+	0.668126i	$0.767097\pi$
$740$		0			0
$741$		−	6.00898i		−	0.220745i
$742$	34.7149	+	33.2284i	1.27443	+	1.21985i
$743$	−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
$747$	6.87329	+	1.84169i	0.251480	+	0.0673840i
$748$	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	−0.949286	−	0.314413i	$-0.898192\pi$
$751$	−20.4692	−	35.4538i	−0.746933	−	1.29373i	0.202353	−	0.979313i	$-0.435141\pi$
$752$	6.91574	+	25.8099i	0.252191	+	0.941190i
$753$	7.19058	+	26.8356i	0.262039	+	0.977944i
$754$	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	$0.941568\pi$
$758$	−24.4875	−	6.56140i	−0.889425	−	0.238321i
$759$	2.83944	−	4.91806i	0.103065	−	0.178514i
$760$		0			0
$761$	−1.02984	+	0.594581i	−0.0373318	+	0.0215535i	−0.518550	−	0.855047i	$-0.673528\pi$
$761$	−1.02984	+	0.594581i	−0.0373318	+	0.0215535i	0.481218	+	0.876601i	$0.340195\pi$
$762$	−13.1291	+	13.1291i	−0.475616	+	0.475616i
$763$	6.34677	+	21.7699i	0.229769	+	0.788125i
$764$		−	0.196769i		−	0.00711887i
$765$		0			0
$766$	−30.7452	−	17.7508i	−1.11087	−	0.641361i
$767$	−0.0908782	+	0.0243507i	−0.00328142	+	0.000879255i
$768$	−0.716541	+	2.67417i	−0.0258559	+	0.0964957i
$769$	18.0146			0.649624			0.324812	−	0.945779i	$-0.394699\pi$
$769$	18.0146			0.649624			0.324812	+	0.945779i	$0.394699\pi$
$770$		0			0
$771$	9.05514			0.326113
$772$	−0.442282	+	1.65062i	−0.0159181	+	0.0594070i
$773$	−31.3415	+	8.39794i	−1.12728	+	0.302053i	−0.773825	−	0.633400i	$-0.781659\pi$
$773$	−31.3415	+	8.39794i	−1.12728	+	0.302053i	−0.353452	+	0.935453i	$0.614992\pi$
$774$	10.6453	+	6.14605i	0.382637	+	0.220915i
$775$		0			0
$776$			48.7981i			1.75175i
$777$	14.5287	−	15.1786i	0.521213	−	0.544531i
$778$	−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
$782$	24.5603	+	6.58092i	0.878275	+	0.235333i
$783$	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
$787$	7.44378	+	27.7806i	0.265342	+	0.990271i	0.962041	+	0.272906i	$0.0879849\pi$
$787$	7.44378	+	27.7806i	0.265342	+	0.990271i	−0.696698	+	0.717364i	$0.745348\pi$
$788$	0.744096	+	2.77700i	0.0265073	+	0.0989267i
$789$	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
$793$	−8.36516	−	2.24144i	−0.297056	−	0.0795958i
$794$	−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	−0.631535	−	0.775347i	$-0.717575\pi$
$797$	4.06000	−	4.06000i	0.143813	−	0.143813i	0.775347	+	0.631535i	$0.217575\pi$
$798$	21.1981	+	5.18581i	0.750406	+	0.183576i
$799$		−	25.8967i		−	0.916160i
$800$		0			0
$801$	2.64332	+	1.52612i	0.0933971	+	0.0539229i
$802$	−45.3773	+	12.1588i	−1.60233	+	0.429342i
$803$	2.39070	−	8.92222i	0.0843660	−	0.314858i
$804$	−0.825141			−0.0291005
$805$		0			0
$806$	6.98660			0.246093
$807$	0.686201	−	2.56094i	0.0241554	−	0.0901492i
$808$	−51.3971	+	13.7718i	−1.80814	+	0.484490i
$809$	38.8115	+	22.4079i	1.36454	+	0.787818i	0.990225	−	0.139483i	$-0.0445440\pi$
$809$	38.8115	+	22.4079i	1.36454	+	0.787818i	0.374317	+	0.927301i	$0.377877\pi$
$810$		0			0
$811$		−	24.7670i		−	0.869686i	−0.900506	−	0.434843i	$-0.856804\pi$
$811$		−	24.7670i		−	0.869686i	0.900506	−	0.434843i	$-0.143196\pi$
$812$	0.656071	−	0.191270i	0.0230236	−	0.00671225i
$813$	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
$817$	51.9758	+	13.9269i	1.81840	+	0.487240i
$818$	−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	0.847099	−	0.531435i	$-0.178347\pi$
$821$	−1.05118	−	1.82069i	−0.0366863	−	0.0635425i	−0.883786	+	0.467892i	$0.845014\pi$
$822$	−3.18143	−	11.8733i	−0.110965	−	0.414128i
$823$	−2.39674	−	8.94474i	−0.0835450	−	0.311794i	0.911490	−	0.411323i	$-0.134933\pi$
$823$	−2.39674	−	8.94474i	−0.0835450	−	0.311794i	−0.995035	+	0.0995288i	$0.968266\pi$
$824$	−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	$0.679657\pi$
$828$	−0.569061	−	0.152480i	−0.0197763	−	0.00529903i
$829$	−12.8315	+	22.2248i	−0.445656	+	0.771899i	−0.998098	−	0.0616525i	$-0.980363\pi$
$829$	−12.8315	+	22.2248i	−0.445656	+	0.771899i	0.552441	+	0.833552i	$0.313696\pi$
$830$		0			0
$831$	−17.7956	+	10.2743i	−0.617323	+	0.356412i
$832$	5.94525	−	5.94525i	0.206115	−	0.206115i
$833$	−24.2955	+	7.66353i	−0.841788	+	0.265525i
$834$			7.81220i			0.270514i
$835$		0			0
$836$	0.672073	+	0.388022i	0.0232441	+	0.0134200i
$837$	4.91632	−	1.31732i	0.169933	−	0.0455334i
$838$	−9.22596	+	34.4317i	−0.318705	+	1.18943i
$839$	29.2921			1.01127			0.505637	−	0.862746i	$-0.331258\pi$
$839$	29.2921			1.01127			0.505637	+	0.862746i	$0.331258\pi$
$840$		0			0
$841$	24.0204			0.828290
$842$	−0.459054	+	1.71321i	−0.0158200	+	0.0590412i
$843$	26.4481	−	7.08674i	0.910920	−	0.244080i
$844$	−1.52604	−	0.881059i	−0.0525284	−	0.0303273i
$845$		0			0
$846$		−	9.76765i		−	0.335819i
$847$	−6.13308	+	25.0703i	−0.210735	+	0.861426i
$848$	−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
$852$	−0.564305	−	0.151205i	−0.0193328	−	0.00518020i
$853$	14.2089	+	14.2089i	0.486503	+	0.486503i	0.907201	−	0.420698i	$-0.138215\pi$
$853$	14.2089	+	14.2089i	0.486503	+	0.486503i	−0.420698	+	0.907201i	$0.638215\pi$
$854$	15.1264	−	27.5758i	0.517616	−	0.943623i
$855$		0			0
$856$	−25.8704	−	44.8088i	−0.884232	−	1.53153i
$857$	6.84502	+	25.5460i	0.233821	+	0.872634i	0.978677	+	0.205407i	$0.0658519\pi$
$857$	6.84502	+	25.5460i	0.233821	+	0.872634i	−0.744855	+	0.667226i	$0.767481\pi$
$858$	−0.396399	−	1.47938i	−0.0135328	−	0.0505052i
$859$	−15.1766	−	26.2866i	−0.517819	−	0.896889i	−0.999786	−	0.0206992i	$-0.993411\pi$
$859$	−15.1766	−	26.2866i	−0.517819	−	0.896889i	0.481967	−	0.876189i	$-0.339923\pi$
$860$		0			0
$861$	12.4287	−	22.6578i	0.423570	−	0.772175i
$862$	12.8887	+	12.8887i	0.438992	+	0.438992i
$863$	−29.3860	−	7.87396i	−1.00031	−	0.268033i	−0.278736	−	0.960368i	$-0.589915\pi$
$863$	−29.3860	−	7.87396i	−1.00031	−	0.268033i	−0.721576	+	0.692335i	$0.756582\pi$
$864$	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
$868$	0.370392	−	1.51406i	0.0125719	−	0.0513905i
$869$		−	4.85044i		−	0.164540i
$870$		0			0
$871$	6.17362	+	3.56434i	0.209185	+	0.120773i
$872$	−24.0436	+	6.44246i	−0.814219	+	0.218169i
$873$	4.34876	−	16.2298i	0.147183	−	0.549295i
$874$	41.9823			1.42007
$875$		0			0
$876$	−0.958255			−0.0323765
$877$	1.24746	−	4.65558i	0.0421237	−	0.157208i	−0.941660	−	0.336565i	$-0.890735\pi$
$877$	1.24746	−	4.65558i	0.0421237	−	0.157208i	0.983784	+	0.179357i	$0.0574016\pi$
$878$	52.7406	−	14.1318i	1.77991	−	0.476925i
$879$	−27.0882	−	15.6394i	−0.913661	−	0.527502i
$880$		0			0
$881$			32.9661i			1.11066i	0.831631	+	0.555328i	$0.187407\pi$
$881$			32.9661i			1.11066i	−0.831631	+	0.555328i	$0.812593\pi$
$882$	−9.16369	+	2.89050i	−0.308558	+	0.0973283i
$883$	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
$887$	−19.8569	−	5.32065i	−0.666731	−	0.178650i	−0.0904490	−	0.995901i	$-0.528830\pi$
$887$	−19.8569	−	5.32065i	−0.666731	−	0.178650i	−0.576282	+	0.817251i	$0.695497\pi$
$888$	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
$892$	−0.746098	−	2.78447i	−0.0249812	−	0.0932311i
$893$	−11.0667	−	41.3014i	−0.370332	−	1.38210i
$894$	−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
$898$	42.9969	+	11.5210i	1.43482	+	0.384460i
$899$	−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
$903$	−22.7453	+	6.63113i	−0.756917	+	0.220670i
$904$			14.7819i			0.491639i
$905$		0			0
$906$	−24.3006	−	14.0299i	−0.807332	−	0.466113i
$907$	8.94474	−	2.39674i	0.297005	−	0.0795823i	−0.107239	−	0.994233i	$-0.534201\pi$
$907$	8.94474	−	2.39674i	0.297005	−	0.0795823i	0.404245	+	0.914651i	$0.367534\pi$
$908$	−0.369262	+	1.37810i	−0.0122544	+	0.0457340i
$909$	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	$0.568836\pi$
$912$	−5.84008	+	21.7955i	−0.193384	+	0.721720i
$913$	7.66886	−	2.05487i	0.253802	−	0.0680061i
$914$	2.88416	+	1.66517i	0.0953996	+	0.0550790i
$915$		0			0
$916$			0.283678i			0.00937298i
$917$	27.1915	+	6.65199i	0.897941	+	0.219668i
$918$	3.53247	−	3.53247i	0.116589	−	0.116589i
$919$	−16.8146	+	9.70789i	−0.554661	+	0.320234i	−0.751000	−	0.660302i	$-0.770428\pi$
$919$	−16.8146	+	9.70789i	−0.554661	+	0.320234i	0.196339	+	0.980536i	$0.437095\pi$
$920$		0			0
$921$	14.4551	−	25.0369i	0.476311	−	0.824994i
$922$	−21.0594	−	5.64285i	−0.693555	−	0.185837i
$923$	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
$927$	0.929716	+	3.46975i	0.0305359	+	0.113961i
$928$	0.377685	+	1.40954i	0.0123981	+	0.0462704i
$929$	−24.5487	−	42.5196i	−0.805418	−	1.39502i	−0.916009	−	0.401158i	$-0.868608\pi$
$929$	−24.5487	−	42.5196i	−0.805418	−	1.39502i	0.110591	−	0.993866i	$-0.464726\pi$
$930$		0			0
$931$	−35.4727	+	22.6046i	−1.16257	+	0.740835i
$932$	−0.216999	−	0.216999i	−0.00710805	−	0.00710805i
$933$	−9.24255	−	2.47653i	−0.302587	−	0.0810781i
$934$	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	−0.718715	−	0.695305i	$-0.755269\pi$
$937$	−0.716581	+	0.716581i	−0.0234097	+	0.0234097i	0.695305	+	0.718715i	$0.255269\pi$
$938$	−17.9020	+	18.7029i	−0.584521	+	0.610671i
$939$			3.24490i			0.105893i
$940$		0			0
$941$	−50.7755	−	29.3153i	−1.65523	−	0.955650i	−0.974870	−	0.222777i	$-0.928488\pi$
$941$	−50.7755	−	29.3153i	−1.65523	−	0.955650i	−0.680365	−	0.732873i	$-0.738179\pi$
$942$	−2.02016	+	0.541300i	−0.0658203	+	0.0176365i
$943$	12.8672	−	48.0209i	0.419013	−	1.56378i
$944$	0.353295			0.0114988
$945$		0			0
$946$	13.7149			0.445910
$947$	−0.689019	+	2.57146i	−0.0223901	+	0.0835611i	−0.976217	−	0.216796i	$-0.930439\pi$
$947$	−0.689019	+	2.57146i	−0.0223901	+	0.0835611i	0.953827	+	0.300357i	$0.0971059\pi$
$948$	−0.486046	+	0.130236i	−0.0157860	+	0.00422985i
$949$	7.16957	+	4.13935i	0.232734	+	0.134369i
$950$		0			0
$951$			16.0712i			0.521144i
$952$	−7.82688	−	26.8468i	−0.253671	−	0.870111i
$953$	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
$957$	2.40496	+	0.644406i	0.0777412	+	0.0208307i
$958$	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
$962$	−2.82143	−	10.5297i	−0.0909665	−	0.339491i
$963$	4.61101	+	17.2085i	0.148588	+	0.554536i
$964$	−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	$0.891038\pi$
$968$	−27.3659	−	7.33266i	−0.879572	−	0.235681i
$969$	10.9344	−	18.9389i	0.351263	−	0.608406i
$970$		0			0
$971$	−12.4287	+	7.17573i	−0.398857	+	0.230280i	−0.685991	−	0.727610i	$-0.740631\pi$
$971$	−12.4287	+	7.17573i	−0.398857	+	0.230280i	0.287134	+	0.957890i	$0.407298\pi$
$972$	−0.0818472	+	0.0818472i	−0.00262525	+	0.00262525i
$973$	−10.8776	−	10.4118i	−0.348721	−	0.333787i
$974$		−	18.7283i		−	0.600094i
$975$		0			0
$976$	28.1633	+	16.2601i	0.901484	+	0.520472i
$977$	−12.3725	+	3.31521i	−0.395833	+	0.106063i	−0.451244	−	0.892401i	$-0.649020\pi$
$977$	−12.3725	+	3.31521i	−0.395833	+	0.106063i	0.0554114	+	0.998464i	$0.482353\pi$
$978$	−4.34092	+	16.2005i	−0.138807	+	0.518035i
$979$	3.40554			0.108842
$980$		0			0
$981$	8.57081			0.273645
$982$	8.07232	−	30.1263i	0.257598	−	0.961370i
$983$	−25.2456	+	6.76454i	−0.805209	+	0.215755i	−0.637870	−	0.770144i	$-0.720184\pi$
$983$	−25.2456	+	6.76454i	−0.805209	+	0.215755i	−0.167339	+	0.985899i	$0.553518\pi$
$984$	24.5671	+	14.1838i	0.783171	+	0.452164i
$985$		0			0
$986$			11.1478i			0.355019i
$987$	13.6004	+	13.0180i	0.432904	+	0.414366i
$988$	−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	0.210299	+	0.977637i	$0.432556\pi$
$991$	−23.3428	+	40.4310i	−0.741509	+	1.28433i	−0.951808	+	0.306694i	$0.900777\pi$
$992$	3.21497	+	0.861450i	0.102076	+	0.0273511i
$993$	−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
$997$	0.911976	+	3.40354i	0.0288826	+	0.107791i	0.978862	−	0.204520i	$-0.0655634\pi$
$997$	0.911976	+	3.40354i	0.0288826	+	0.107791i	−0.949980	+	0.312311i	$0.898897\pi$
$998$	2.18479	+	8.15375i	0.0691583	+	0.258102i
$999$	−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.157.2	yes	24
5.2	odd	4	inner	525.2.bc.c.493.2	yes	24
5.3	odd	4	inner	525.2.bc.c.493.5	yes	24
5.4	even	2	inner	525.2.bc.c.157.5	yes	24
7.5	odd	6	inner	525.2.bc.c.82.5	yes	24
35.12	even	12	inner	525.2.bc.c.418.5	yes	24
35.19	odd	6	inner	525.2.bc.c.82.2	✓	24
35.33	even	12	inner	525.2.bc.c.418.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bc.c.82.2	✓	24	35.19	odd	6	inner
525.2.bc.c.82.5	yes	24	7.5	odd	6	inner
525.2.bc.c.157.2	yes	24	1.1	even	1	trivial
525.2.bc.c.157.5	yes	24	5.4	even	2	inner
525.2.bc.c.418.2	yes	24	35.33	even	12	inner
525.2.bc.c.418.5	yes	24	35.12	even	12	inner
525.2.bc.c.493.2	yes	24	5.2	odd	4	inner
525.2.bc.c.493.5	yes	24	5.3	odd	4	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)

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

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Database

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