LMFDB - Embedded newform 210.2.m.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(13,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("210.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.1698758656.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 $ x^8 + 18x^6 + 97x^4 + 176*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.2
Root			$-2.16053i$ of defining polynomial
Character	$\chi$	$=$	210.13
Dual form			210.2.m.a.97.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(2.23483 + 0.0743018i) q^{5} -1.00000i q^{6} +(0.781409 - 2.52773i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(2.23483 + 0.0743018i) q^{5} -1.00000i q^{6} +(0.781409 - 2.52773i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(-1.63280 + 1.52773i) q^{10} +4.90685 q^{11} +(0.707107 + 0.707107i) q^{12} +(-3.41421 + 3.41421i) q^{13} +(1.23483 + 2.33991i) q^{14} +(-1.63280 + 1.52773i) q^{15} -1.00000 q^{16} +(2.74632 + 2.74632i) q^{17} +(0.707107 + 0.707107i) q^{18} +1.26561 q^{19} +(0.0743018 - 2.23483i) q^{20} +(1.23483 + 2.33991i) q^{21} +(-3.46967 + 3.46967i) q^{22} +(-1.05545 - 1.05545i) q^{23} -1.00000 q^{24} +(4.98896 + 0.332104i) q^{25} -4.82843i q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.52773 - 0.781409i) q^{28} +4.76687i q^{29} +(0.0743018 - 2.23483i) q^{30} -7.05545i q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.46967 + 3.46967i) q^{33} -3.88388 q^{34} +(1.93413 - 5.59099i) q^{35} -1.00000 q^{36} +(-4.74632 + 4.74632i) q^{37} +(-0.894921 + 0.894921i) q^{38} -4.82843i q^{39} +(1.52773 + 1.63280i) q^{40} -5.44670i q^{41} +(-2.52773 - 0.781409i) q^{42} +(-7.58667 - 7.58667i) q^{43} -4.90685i q^{44} +(0.0743018 - 2.23483i) q^{45} +1.49264 q^{46} +(0.734390 + 0.734390i) q^{47} +(0.707107 - 0.707107i) q^{48} +(-5.77880 - 3.95037i) q^{49} +(-3.76256 + 3.29289i) q^{50} -3.88388 q^{51} +(3.41421 + 3.41421i) q^{52} +(1.26561 + 1.26561i) q^{53} -1.00000 q^{54} +(10.9660 + 0.364588i) q^{55} +(2.33991 - 1.23483i) q^{56} +(-0.894921 + 0.894921i) q^{57} +(-3.37069 - 3.37069i) q^{58} +1.39735 q^{59} +(1.52773 + 1.63280i) q^{60} -2.29721i q^{61} +(4.98896 + 4.98896i) q^{62} +(-2.52773 - 0.781409i) q^{63} +1.00000i q^{64} +(-7.88388 + 7.37652i) q^{65} -4.90685i q^{66} +(3.05545 - 3.05545i) q^{67} +(2.74632 - 2.74632i) q^{68} +1.49264 q^{69} +(2.58579 + 5.32106i) q^{70} -13.0334 q^{71} +(0.707107 - 0.707107i) q^{72} +(5.04441 - 5.04441i) q^{73} -6.71231i q^{74} +(-3.76256 + 3.29289i) q^{75} -1.26561i q^{76} +(3.83425 - 12.4032i) q^{77} +(3.41421 + 3.41421i) q^{78} +14.8063i q^{79} +(-2.23483 - 0.0743018i) q^{80} -1.00000 q^{81} +(3.85140 + 3.85140i) q^{82} +(-9.29809 + 9.29809i) q^{83} +(2.33991 - 1.23483i) q^{84} +(5.93351 + 6.34162i) q^{85} +10.7292 q^{86} +(-3.37069 - 3.37069i) q^{87} +(3.46967 + 3.46967i) q^{88} -15.3596 q^{89} +(1.52773 + 1.63280i) q^{90} +(5.96230 + 11.2981i) q^{91} +(-1.05545 + 1.05545i) q^{92} +(4.98896 + 4.98896i) q^{93} -1.03858 q^{94} +(2.82843 + 0.0940371i) q^{95} +1.00000i q^{96} +(-8.42614 - 8.42614i) q^{97} +(6.87957 - 1.29289i) q^{98} -4.90685i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{7}+O(q^{10}) $ 8 * q + 4 * q^7	$ 8 q + 4 q^{7} - 4 q^{10} + 8 q^{11} - 16 q^{13} - 8 q^{14} - 4 q^{15} - 8 q^{16} + 12 q^{17} - 8 q^{19} + 4 q^{20} - 8 q^{21} + 8 q^{22} + 16 q^{23} - 8 q^{24} - 4 q^{25} - 8 q^{28} + 4 q^{30} + 8 q^{33} + 16 q^{34} + 8 q^{35} - 8 q^{36} - 28 q^{37} - 4 q^{38} - 8 q^{42} + 4 q^{45} - 8 q^{46} + 24 q^{47} + 4 q^{49} + 16 q^{51} + 16 q^{52} - 8 q^{53} - 8 q^{54} + 28 q^{55} + 4 q^{56} - 4 q^{57} - 12 q^{58} + 8 q^{59} - 4 q^{62} - 8 q^{63} - 16 q^{65} + 12 q^{68} - 8 q^{69} + 32 q^{70} + 8 q^{71} - 28 q^{73} - 44 q^{77} + 16 q^{78} - 8 q^{81} + 24 q^{82} - 16 q^{83} + 4 q^{84} + 28 q^{85} + 8 q^{86} - 12 q^{87} - 8 q^{88} - 64 q^{89} - 8 q^{91} + 16 q^{92} - 4 q^{93} + 8 q^{94} - 28 q^{97}+O(q^{100}) $ 8 * q + 4 * q^7 - 4 * q^10 + 8 * q^11 - 16 * q^13 - 8 * q^14 - 4 * q^15 - 8 * q^16 + 12 * q^17 - 8 * q^19 + 4 * q^20 - 8 * q^21 + 8 * q^22 + 16 * q^23 - 8 * q^24 - 4 * q^25 - 8 * q^28 + 4 * q^30 + 8 * q^33 + 16 * q^34 + 8 * q^35 - 8 * q^36 - 28 * q^37 - 4 * q^38 - 8 * q^42 + 4 * q^45 - 8 * q^46 + 24 * q^47 + 4 * q^49 + 16 * q^51 + 16 * q^52 - 8 * q^53 - 8 * q^54 + 28 * q^55 + 4 * q^56 - 4 * q^57 - 12 * q^58 + 8 * q^59 - 4 * q^62 - 8 * q^63 - 16 * q^65 + 12 * q^68 - 8 * q^69 + 32 * q^70 + 8 * q^71 - 28 * q^73 - 44 * q^77 + 16 * q^78 - 8 * q^81 + 24 * q^82 - 16 * q^83 + 4 * q^84 + 28 * q^85 + 8 * q^86 - 12 * q^87 - 8 * q^88 - 64 * q^89 - 8 * q^91 + 16 * q^92 - 4 * q^93 + 8 * q^94 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	2.23483	+	0.0743018i	0.999448	+	0.0332288i
$5$	2.23483	+	0.0743018i	0.999448	+	0.0332288i
$6$		−	1.00000i		−	0.408248i
$7$	0.781409	−	2.52773i	0.295345	−	0.955391i
$7$	0.781409	−	2.52773i	0.295345	−	0.955391i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$	−1.63280	+	1.52773i	−0.516338	+	0.483109i
$11$	4.90685			1.47947			0.739735	−	0.672898i	$-0.234951\pi$
$11$	4.90685			1.47947			0.739735	+	0.672898i	$0.234951\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	−3.41421	+	3.41421i	−0.946932	+	0.946932i	−0.998661	−	0.0517287i	$-0.983527\pi$
$13$	−3.41421	+	3.41421i	−0.946932	+	0.946932i	0.0517287	+	0.998661i	$0.483527\pi$
$14$	1.23483	+	2.33991i	0.330023	+	0.625368i
$15$	−1.63280	+	1.52773i	−0.421588	+	0.394457i
$16$	−1.00000			−0.250000
$17$	2.74632	+	2.74632i	0.666080	+	0.666080i	0.956806	−	0.290726i	$-0.0938969\pi$
$17$	2.74632	+	2.74632i	0.666080	+	0.666080i	−0.290726	+	0.956806i	$0.593897\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	1.26561			0.290351			0.145175	−	0.989406i	$-0.453625\pi$
$19$	1.26561			0.290351			0.145175	+	0.989406i	$0.453625\pi$
$20$	0.0743018	−	2.23483i	0.0166144	−	0.499724i
$21$	1.23483	+	2.33991i	0.269463	+	0.510611i
$22$	−3.46967	+	3.46967i	−0.739735	+	0.739735i
$23$	−1.05545	−	1.05545i	−0.220077	−	0.220077i	0.588454	−	0.808531i	$-0.299737\pi$
$23$	−1.05545	−	1.05545i	−0.220077	−	0.220077i	−0.808531	+	0.588454i	$0.799737\pi$
$24$	−1.00000			−0.204124
$25$	4.98896	+	0.332104i	0.997792	+	0.0664208i
$26$		−	4.82843i		−	0.946932i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−2.52773	−	0.781409i	−0.477695	−	0.147672i
$29$			4.76687i			0.885186i	0.896723	+	0.442593i	$0.145941\pi$
$29$			4.76687i			0.885186i	−0.896723	+	0.442593i	$0.854059\pi$
$30$	0.0743018	−	2.23483i	0.0135656	−	0.408023i
$31$		−	7.05545i		−	1.26720i	−0.773662	−	0.633598i	$-0.781577\pi$
$31$		−	7.05545i		−	1.26720i	0.773662	−	0.633598i	$-0.218423\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−3.46967	+	3.46967i	−0.603991	+	0.603991i
$34$	−3.88388			−0.666080
$35$	1.93413	−	5.59099i	0.326928	−	0.945049i
$36$	−1.00000			−0.166667
$37$	−4.74632	+	4.74632i	−0.780290	+	0.780290i	−0.979880	−	0.199590i	$-0.936039\pi$
$37$	−4.74632	+	4.74632i	−0.780290	+	0.780290i	0.199590	+	0.979880i	$0.436039\pi$
$38$	−0.894921	+	0.894921i	−0.145175	+	0.145175i
$39$		−	4.82843i		−	0.773167i
$40$	1.52773	+	1.63280i	0.241555	+	0.258169i
$41$		−	5.44670i		−	0.850631i	−0.905045	−	0.425316i	$-0.860163\pi$
$41$		−	5.44670i		−	0.850631i	0.905045	−	0.425316i	$-0.139837\pi$
$42$	−2.52773	−	0.781409i	−0.390037	−	0.120574i
$43$	−7.58667	−	7.58667i	−1.15696	−	1.15696i	−0.985127	−	0.171830i	$-0.945032\pi$
$43$	−7.58667	−	7.58667i	−1.15696	−	1.15696i	−0.171830	−	0.985127i	$-0.554968\pi$
$44$		−	4.90685i		−	0.739735i
$45$	0.0743018	−	2.23483i	0.0110763	−	0.333149i
$46$	1.49264			0.220077
$47$	0.734390	+	0.734390i	0.107122	+	0.107122i	0.758636	−	0.651514i	$-0.225866\pi$
$47$	0.734390	+	0.734390i	0.107122	+	0.107122i	−0.651514	+	0.758636i	$0.725866\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$	−5.77880	−	3.95037i	−0.825543	−	0.564339i
$50$	−3.76256	+	3.29289i	−0.532106	+	0.465685i
$51$	−3.88388			−0.543852
$52$	3.41421	+	3.41421i	0.473466	+	0.473466i
$53$	1.26561	+	1.26561i	0.173845	+	0.173845i	0.788666	−	0.614821i	$-0.210772\pi$
$53$	1.26561	+	1.26561i	0.173845	+	0.173845i	−0.614821	+	0.788666i	$0.710772\pi$
$54$	−1.00000			−0.136083
$55$	10.9660	+	0.364588i	1.47865	+	0.0491610i
$56$	2.33991	−	1.23483i	0.312684	−	0.165012i
$57$	−0.894921	+	0.894921i	−0.118535	+	0.118535i
$58$	−3.37069	−	3.37069i	−0.442593	−	0.442593i
$59$	1.39735			0.181919			0.0909594	−	0.995855i	$-0.471007\pi$
$59$	1.39735			0.181919			0.0909594	+	0.995855i	$0.471007\pi$
$60$	1.52773	+	1.63280i	0.197229	+	0.210794i
$61$		−	2.29721i		−	0.294127i	−0.989127	−	0.147064i	$-0.953018\pi$
$61$		−	2.29721i		−	0.294127i	0.989127	−	0.147064i	$-0.0469822\pi$
$62$	4.98896	+	4.98896i	0.633598	+	0.633598i
$63$	−2.52773	−	0.781409i	−0.318464	−	0.0984482i
$64$			1.00000i			0.125000i
$65$	−7.88388	+	7.37652i	−0.977875	+	0.914944i
$66$		−	4.90685i		−	0.603991i
$67$	3.05545	−	3.05545i	0.373283	−	0.373283i	−0.495389	−	0.868672i	$-0.664974\pi$
$67$	3.05545	−	3.05545i	0.373283	−	0.373283i	0.868672	+	0.495389i	$0.164974\pi$
$68$	2.74632	−	2.74632i	0.333040	−	0.333040i
$69$	1.49264			0.179692
$70$	2.58579	+	5.32106i	0.309061	+	0.635989i
$71$	−13.0334			−1.54678			−0.773388	−	0.633933i	$-0.781440\pi$
$71$	−13.0334			−1.54678			−0.773388	+	0.633933i	$0.781440\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	5.04441	−	5.04441i	0.590404	−	0.590404i	−0.347337	−	0.937740i	$-0.612914\pi$
$73$	5.04441	−	5.04441i	0.590404	−	0.590404i	0.937740	+	0.347337i	$0.112914\pi$
$74$		−	6.71231i		−	0.780290i
$75$	−3.76256	+	3.29289i	−0.434463	+	0.380231i
$76$		−	1.26561i		−	0.145175i
$77$	3.83425	−	12.4032i	0.436954	−	1.41347i
$78$	3.41421	+	3.41421i	0.386584	+	0.386584i
$79$			14.8063i			1.66584i	0.553391	+	0.832922i	$0.313334\pi$
$79$			14.8063i			1.66584i	−0.553391	+	0.832922i	$0.686666\pi$
$80$	−2.23483	−	0.0743018i	−0.249862	−	0.00830719i
$81$	−1.00000			−0.111111
$82$	3.85140	+	3.85140i	0.425316	+	0.425316i
$83$	−9.29809	+	9.29809i	−1.02060	+	1.02060i	−0.0208150	+	0.999783i	$0.506626\pi$
$83$	−9.29809	+	9.29809i	−1.02060	+	1.02060i	−0.999783	+	0.0208150i	$0.993374\pi$
$84$	2.33991	−	1.23483i	0.255305	−	0.134731i
$85$	5.93351	+	6.34162i	0.643579	+	0.687845i
$86$	10.7292			1.15696
$87$	−3.37069	−	3.37069i	−0.361376	−	0.361376i
$88$	3.46967	+	3.46967i	0.369868	+	0.369868i
$89$	−15.3596			−1.62812			−0.814060	−	0.580781i	$-0.802747\pi$
$89$	−15.3596			−1.62812			−0.814060	+	0.580781i	$0.802747\pi$
$90$	1.52773	+	1.63280i	0.161036	+	0.172113i
$91$	5.96230	+	11.2981i	0.625019	+	1.18436i
$92$	−1.05545	+	1.05545i	−0.110039	+	0.110039i
$93$	4.98896	+	4.98896i	0.517331	+	0.517331i
$94$	−1.03858			−0.107122
$95$	2.82843	+	0.0940371i	0.290191	+	0.00964800i
$96$			1.00000i			0.102062i
$97$	−8.42614	−	8.42614i	−0.855545	−	0.855545i	0.135264	−	0.990810i	$-0.456812\pi$
$97$	−8.42614	−	8.42614i	−0.855545	−	0.855545i	−0.990810	+	0.135264i	$0.956812\pi$
$98$	6.87957	−	1.29289i	0.694941	−	0.130602i
$99$		−	4.90685i		−	0.493157i
$100$	0.332104	−	4.98896i	0.0332104	−	0.498896i
$101$			18.1504i			1.80603i	0.429609	+	0.903015i	$0.358651\pi$
$101$			18.1504i			1.80603i	−0.429609	+	0.903015i	$0.641349\pi$
$102$	2.74632	−	2.74632i	0.271926	−	0.271926i
$103$	8.36459	−	8.36459i	0.824187	−	0.824187i	−0.162518	−	0.986706i	$-0.551962\pi$
$103$	8.36459	−	8.36459i	0.824187	−	0.824187i	0.986706	+	0.162518i	$0.0519616\pi$
$104$	−4.82843			−0.473466
$105$	2.58579	+	5.32106i	0.252347	+	0.519283i
$106$	−1.78984			−0.173845
$107$	3.77297	−	3.77297i	0.364747	−	0.364747i	−0.500810	−	0.865557i	$-0.666964\pi$
$107$	3.77297	−	3.77297i	0.364747	−	0.364747i	0.865557	+	0.500810i	$0.166964\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$		−	0.0870500i		−	0.00833787i	−0.999991	−	0.00416894i	$-0.998673\pi$
$109$		−	0.0870500i		−	0.00833787i	0.999991	−	0.00416894i	$-0.00132702\pi$
$110$	−8.01193	+	7.49632i	−0.763907	+	0.714746i
$111$		−	6.71231i		−	0.637104i
$112$	−0.781409	+	2.52773i	−0.0738362	+	0.238848i
$113$	2.03248	+	2.03248i	0.191200	+	0.191200i	0.796214	−	0.605014i	$-0.206833\pi$
$113$	2.03248	+	2.03248i	0.191200	+	0.191200i	−0.605014	+	0.796214i	$0.706833\pi$
$114$		−	1.26561i		−	0.118535i
$115$	−2.28034	−	2.43718i	−0.212643	−	0.227268i
$116$	4.76687			0.442593
$117$	3.41421	+	3.41421i	0.315644	+	0.315644i
$118$	−0.988072	+	0.988072i	−0.0909594	+	0.0909594i
$119$	9.08794	−	4.79594i	0.833090	−	0.439643i
$120$	−2.23483	−	0.0743018i	−0.204011	−	0.00678279i
$121$	13.0772			1.18883
$122$	1.62437	+	1.62437i	0.147064	+	0.147064i
$123$	3.85140	+	3.85140i	0.347269	+	0.347269i
$124$	−7.05545			−0.633598
$125$	11.1248	+	1.11289i	0.995034	+	0.0995396i
$126$	2.33991	−	1.23483i	0.208456	−	0.110008i
$127$	−11.1761	+	11.1761i	−0.991723	+	0.991723i	−0.999966	−	0.00824340i	$-0.997376\pi$
$127$	−11.1761	+	11.1761i	−0.991723	+	0.991723i	0.00824340	+	0.999966i	$0.497376\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	10.7292			0.944651
$130$	0.358761	−	10.7907i	0.0314654	−	0.946410i
$131$		−	12.8367i		−	1.12154i	−0.827970	−	0.560772i	$-0.810504\pi$
$131$		−	12.8367i		−	1.12154i	0.827970	−	0.560772i	$-0.189496\pi$
$132$	3.46967	+	3.46967i	0.301996	+	0.301996i
$133$	0.988958	−	3.19912i	0.0857536	−	0.277399i
$134$			4.32106i			0.373283i
$135$	1.52773	+	1.63280i	0.131486	+	0.140529i
$136$			3.88388i			0.333040i
$137$	−3.62437	+	3.62437i	−0.309651	+	0.309651i	−0.844774	−	0.535123i	$-0.820265\pi$
$137$	−3.62437	+	3.62437i	−0.309651	+	0.309651i	0.535123	+	0.844774i	$0.320265\pi$
$138$	−1.05545	+	1.05545i	−0.0898461	+	0.0898461i
$139$	3.90596			0.331299			0.165650	−	0.986185i	$-0.447028\pi$
$139$	3.90596			0.331299			0.165650	+	0.986185i	$0.447028\pi$
$140$	−5.59099	−	1.93413i	−0.472525	−	0.163464i
$141$	−1.03858			−0.0874646
$142$	9.21598	−	9.21598i	0.773388	−	0.773388i
$143$	−16.7530	+	16.7530i	−1.40096	+	1.40096i
$144$			1.00000i			0.0833333i
$145$	−0.354187	+	10.6532i	−0.0294137	+	0.884697i
$146$			7.13387i			0.590404i
$147$	6.87957	−	1.29289i	0.567417	−	0.106636i
$148$	4.74632	+	4.74632i	0.390145	+	0.390145i
$149$			5.64124i			0.462148i	0.972936	+	0.231074i	$0.0742240\pi$
$149$			5.64124i			0.462148i	−0.972936	+	0.231074i	$0.925776\pi$
$150$	0.332104	−	4.98896i	0.0271162	−	0.407347i
$151$	−11.7678			−0.957647			−0.478823	−	0.877911i	$-0.658937\pi$
$151$	−11.7678			−0.957647			−0.478823	+	0.877911i	$0.658937\pi$
$152$	0.894921	+	0.894921i	0.0725877	+	0.0725877i
$153$	2.74632	−	2.74632i	0.222027	−	0.222027i
$154$	6.05914	+	11.4816i	0.488259	+	0.925213i
$155$	0.524233	−	15.7678i	0.0421074	−	1.26650i
$156$	−4.82843			−0.386584
$157$	−13.7132	−	13.7132i	−1.09443	−	1.09443i	−0.995049	−	0.0993827i	$-0.968313\pi$
$157$	−13.7132	−	13.7132i	−1.09443	−	1.09443i	−0.0993827	−	0.995049i	$-0.531687\pi$
$158$	−10.4697	−	10.4697i	−0.832922	−	0.832922i
$159$	−1.78984			−0.141944
$160$	1.63280	−	1.52773i	0.129085	−	0.120777i
$161$	−3.49264	+	1.84316i	−0.275258	+	0.145261i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−7.21967	−	7.21967i	−0.565488	−	0.565488i	0.365373	−	0.930861i	$-0.380941\pi$
$163$	−7.21967	−	7.21967i	−0.565488	−	0.565488i	−0.930861	+	0.365373i	$0.880941\pi$
$164$	−5.44670			−0.425316
$165$	−8.01193	+	7.49632i	−0.623728	+	0.583588i
$166$		−	13.1495i		−	1.02060i
$167$	−6.73439	−	6.73439i	−0.521123	−	0.521123i	0.396788	−	0.917910i	$-0.370125\pi$
$167$	−6.73439	−	6.73439i	−0.521123	−	0.521123i	−0.917910	+	0.396788i	$0.870125\pi$
$168$	−0.781409	+	2.52773i	−0.0602870	+	0.195018i
$169$		−	10.3137i		−	0.793362i
$170$	−8.67982	−	0.288579i	−0.665712	−	0.0221330i
$171$		−	1.26561i		−	0.0967836i
$172$	−7.58667	+	7.58667i	−0.578478	+	0.578478i
$173$	14.1605	−	14.1605i	1.07661	−	1.07661i	0.0797939	−	0.996811i	$-0.474574\pi$
$173$	14.1605	−	14.1605i	1.07661	−	1.07661i	0.996811	−	0.0797939i	$-0.0254262\pi$
$174$	4.76687			0.361376
$175$	4.73788	−	12.3512i	0.358150	−	0.933664i
$176$	−4.90685			−0.369868
$177$	−0.988072	+	0.988072i	−0.0742681	+	0.0742681i
$178$	10.8609	−	10.8609i	0.814060	−	0.814060i
$179$		−	3.28123i		−	0.245250i	−0.992453	−	0.122625i	$-0.960869\pi$
$179$		−	3.28123i		−	0.245250i	0.992453	−	0.122625i	$-0.0391313\pi$
$180$	−2.23483	−	0.0743018i	−0.166575	−	0.00553813i
$181$			19.3934i			1.44150i	0.693196	+	0.720749i	$0.256202\pi$
$181$			19.3934i			1.44150i	−0.693196	+	0.720749i	$0.743798\pi$
$182$	−12.2049	−	3.77297i	−0.904691	−	0.279671i
$183$	1.62437	+	1.62437i	0.120077	+	0.120077i
$184$		−	1.49264i		−	0.110039i
$185$	−10.9599	+	10.2546i	−0.805787	+	0.753931i
$186$	−7.05545			−0.517331
$187$	13.4758	+	13.4758i	0.985446	+	0.985446i
$188$	0.734390	−	0.734390i	0.0535609	−	0.0535609i
$189$	2.33991	−	1.23483i	0.170204	−	0.0898209i
$190$	−2.06649	+	1.93351i	−0.149919	+	0.140271i
$191$	−16.8453			−1.21888			−0.609441	−	0.792831i	$-0.708606\pi$
$191$	−16.8453			−1.21888			−0.609441	+	0.792831i	$0.708606\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	−4.81370	−	4.81370i	−0.346498	−	0.346498i	0.512306	−	0.858803i	$-0.328792\pi$
$193$	−4.81370	−	4.81370i	−0.346498	−	0.346498i	−0.858803	+	0.512306i	$0.828792\pi$
$194$	11.9164			0.855545
$195$	0.358761	−	10.7907i	0.0256914	−	0.772740i
$196$	−3.95037	+	5.77880i	−0.282170	+	0.412772i
$197$	13.0334	−	13.0334i	0.928589	−	0.928589i	−0.0690257	−	0.997615i	$-0.521989\pi$
$197$	13.0334	−	13.0334i	0.928589	−	0.928589i	0.997615	+	0.0690257i	$0.0219891\pi$
$198$	3.46967	+	3.46967i	0.246578	+	0.246578i
$199$	11.7509			0.832999			0.416499	−	0.909136i	$-0.363257\pi$
$199$	11.7509			0.832999			0.416499	+	0.909136i	$0.363257\pi$
$200$	3.29289	+	3.76256i	0.232843	+	0.266053i
$201$			4.32106i			0.304784i
$202$	−12.8343	−	12.8343i	−0.903015	−	0.903015i
$203$	12.0494	+	3.72488i	0.845699	+	0.261435i
$204$			3.88388i			0.271926i
$205$	0.404699	−	12.1725i	0.0282654	−	0.850161i
$206$			11.8293i			0.824187i
$207$	−1.05545	+	1.05545i	−0.0733590	+	0.0733590i
$208$	3.41421	−	3.41421i	0.236733	−	0.236733i
$209$	6.21016			0.429566
$210$	−5.59099	−	1.93413i	−0.385815	−	0.133468i
$211$	16.5502			1.13937			0.569683	−	0.821864i	$-0.307066\pi$
$211$	16.5502			1.13937			0.569683	+	0.821864i	$0.307066\pi$
$212$	1.26561	−	1.26561i	0.0869224	−	0.0869224i
$213$	9.21598	−	9.21598i	0.631469	−	0.631469i
$214$			5.33579i			0.364747i
$215$	−16.3912	−	17.5187i	−1.11787	−	1.19476i
$216$			1.00000i			0.0680414i
$217$	−17.8343	−	5.51319i	−1.21067	−	0.374260i
$218$	0.0615536	+	0.0615536i	0.00416894	+	0.00416894i
$219$			7.13387i			0.482063i
$220$	0.364588	−	10.9660i	0.0245805	−	0.739327i
$221$	−18.7530			−1.26147
$222$	4.74632	+	4.74632i	0.318552	+	0.318552i
$223$	−8.26067	+	8.26067i	−0.553175	+	0.553175i	−0.927356	−	0.374181i	$-0.877924\pi$
$223$	−8.26067	+	8.26067i	−0.553175	+	0.553175i	0.374181	+	0.927356i	$0.377924\pi$
$224$	−1.23483	−	2.33991i	−0.0825058	−	0.156342i
$225$	0.332104	−	4.98896i	0.0221403	−	0.332597i
$226$	−2.87437			−0.191200
$227$	5.91295	+	5.91295i	0.392456	+	0.392456i	0.875562	−	0.483106i	$-0.160491\pi$
$227$	5.91295	+	5.91295i	0.392456	+	0.392456i	−0.483106	+	0.875562i	$0.660491\pi$
$228$	0.894921	+	0.894921i	0.0592676	+	0.0592676i
$229$	−9.31371			−0.615467			−0.307734	−	0.951473i	$-0.599571\pi$
$229$	−9.31371			−0.615467			−0.307734	+	0.951473i	$0.599571\pi$
$230$	3.33579	+	0.110906i	0.219956	+	0.00731289i
$231$	6.05914	+	11.4816i	0.398662	+	0.755433i
$232$	−3.37069	+	3.37069i	−0.221297	+	0.221297i
$233$	16.0563	+	16.0563i	1.05189	+	1.05189i	0.998578	+	0.0533076i	$0.0169764\pi$
$233$	16.0563	+	16.0563i	1.05189	+	1.05189i	0.0533076	+	0.998578i	$0.483024\pi$
$234$	−4.82843			−0.315644
$235$	1.58667	+	1.69581i	0.103503	+	0.110622i
$236$		−	1.39735i		−	0.0909594i
$237$	−10.4697	−	10.4697i	−0.680078	−	0.680078i
$238$	−3.03490	+	9.81739i	−0.196723	+	0.636367i
$239$			1.68592i			0.109053i	0.998512	+	0.0545267i	$0.0173650\pi$
$239$			1.68592i			0.109053i	−0.998512	+	0.0545267i	$0.982635\pi$
$240$	1.63280	−	1.52773i	0.105397	−	0.0986143i
$241$		−	3.61574i		−	0.232910i	−0.993196	−	0.116455i	$-0.962847\pi$
$241$		−	3.61574i		−	0.232910i	0.993196	−	0.116455i	$-0.0371532\pi$
$242$	−9.24695	+	9.24695i	−0.594417	+	0.594417i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−2.29721			−0.147064
$245$	−12.6211	−	9.25780i	−0.806335	−	0.591459i
$246$	−5.44670			−0.347269
$247$	−4.32106	+	4.32106i	−0.274943	+	0.274943i
$248$	4.98896	−	4.98896i	0.316799	−	0.316799i
$249$		−	13.1495i		−	0.833315i
$250$	−8.65336	+	7.07950i	−0.547287	+	0.447747i
$251$			4.78896i			0.302276i	0.988513	+	0.151138i	$0.0482938\pi$
$251$			4.78896i			0.302276i	−0.988513	+	0.151138i	$0.951706\pi$
$252$	−0.781409	+	2.52773i	−0.0492241	+	0.159232i
$253$	−5.17895	−	5.17895i	−0.325598	−	0.325598i
$254$		−	15.8055i		−	0.991723i
$255$	−8.67982	−	0.288579i	−0.543552	−	0.0180715i
$256$	1.00000			0.0625000
$257$	20.8113	+	20.8113i	1.29817	+	1.29817i	0.929599	+	0.368574i	$0.120154\pi$
$257$	20.8113	+	20.8113i	1.29817	+	1.29817i	0.368574	+	0.929599i	$0.379846\pi$
$258$	−7.58667	+	7.58667i	−0.472326	+	0.472326i
$259$	8.28858	+	15.7062i	0.515027	+	0.975936i
$260$	7.37652	+	7.88388i	0.457472	+	0.488937i
$261$	4.76687			0.295062
$262$	9.07689	+	9.07689i	0.560772	+	0.560772i
$263$	6.61827	+	6.61827i	0.408100	+	0.408100i	0.881076	−	0.472976i	$-0.156820\pi$
$263$	6.61827	+	6.61827i	0.408100	+	0.408100i	−0.472976	+	0.881076i	$0.656820\pi$
$264$	−4.90685			−0.301996
$265$	2.73439	+	2.92246i	0.167972	+	0.179526i
$266$	1.56282	+	2.96142i	0.0958225	+	0.181576i
$267$	10.8609	−	10.8609i	0.664677	−	0.664677i
$268$	−3.05545	−	3.05545i	−0.186641	−	0.186641i
$269$	13.1192			0.799890			0.399945	−	0.916539i	$-0.369029\pi$
$269$	13.1192			0.799890			0.399945	+	0.916539i	$0.369029\pi$
$270$	−2.23483	−	0.0743018i	−0.136008	−	0.00452186i
$271$			18.0836i			1.09850i	0.835658	+	0.549250i	$0.185087\pi$
$271$			18.0836i			1.09850i	−0.835658	+	0.549250i	$0.814913\pi$
$272$	−2.74632	−	2.74632i	−0.166520	−	0.166520i
$273$	−12.2049	−	3.77297i	−0.738677	−	0.228351i
$274$		−	5.12563i		−	0.309651i
$275$	24.4801	+	1.62959i	1.47620	+	0.0982677i
$276$		−	1.49264i		−	0.0898461i
$277$	2.63541	−	2.63541i	0.158347	−	0.158347i	−0.623487	−	0.781834i	$-0.714285\pi$
$277$	2.63541	−	2.63541i	0.158347	−	0.158347i	0.781834	+	0.623487i	$0.214285\pi$
$278$	−2.76193	+	2.76193i	−0.165650	+	0.165650i
$279$	−7.05545			−0.422399
$280$	5.32106	−	2.58579i	0.317994	−	0.154530i
$281$	20.4558			1.22029			0.610146	−	0.792289i	$-0.291111\pi$
$281$	20.4558			1.22029			0.610146	+	0.792289i	$0.291111\pi$
$282$	0.734390	−	0.734390i	0.0437323	−	0.0437323i
$283$	10.7751	−	10.7751i	0.640514	−	0.640514i	−0.310168	−	0.950682i	$-0.600385\pi$
$283$	10.7751	−	10.7751i	0.640514	−	0.640514i	0.950682	+	0.310168i	$0.100385\pi$
$284$			13.0334i			0.773388i
$285$	−2.06649	+	1.93351i	−0.122409	+	0.114531i
$286$		−	23.6924i		−	1.40096i
$287$	−13.7678	−	4.25610i	−0.812685	−	0.251229i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$		−	1.91548i		−	0.112675i
$290$	−7.28248	−	7.78337i	−0.427642	−	0.457056i
$291$	11.9164			0.698550
$292$	−5.04441	−	5.04441i	−0.295202	−	0.295202i
$293$	−3.15965	+	3.15965i	−0.184588	+	0.184588i	−0.793352	−	0.608763i	$-0.791666\pi$
$293$	−3.15965	+	3.15965i	−0.184588	+	0.184588i	0.608763	+	0.793352i	$0.291666\pi$
$294$	−3.95037	+	5.77880i	−0.230390	+	0.337027i
$295$	3.12283	+	0.103825i	0.181818	+	0.00604494i
$296$	−6.71231			−0.390145
$297$	3.46967	+	3.46967i	0.201330	+	0.201330i
$298$	−3.98896	−	3.98896i	−0.231074	−	0.231074i
$299$	7.20708			0.416796
$300$	3.29289	+	3.76256i	0.190115	+	0.217231i
$301$	−25.1053	+	13.2487i	−1.44705	+	0.763645i
$302$	8.32106	−	8.32106i	0.478823	−	0.478823i
$303$	−12.8343	−	12.8343i	−0.737309	−	0.737309i
$304$	−1.26561			−0.0725877
$305$	0.170687	−	5.13387i	0.00977349	−	0.293965i
$306$			3.88388i			0.222027i
$307$	20.8011	+	20.8011i	1.18718	+	1.18718i	0.977843	+	0.209340i	$0.0671316\pi$
$307$	20.8011	+	20.8011i	1.18718	+	1.18718i	0.209340	+	0.977843i	$0.432868\pi$
$308$	−12.4032	−	3.83425i	−0.706736	−	0.218477i
$309$			11.8293i			0.672946i
$310$	10.7788	+	11.5202i	0.612195	+	0.654302i
$311$		−	11.4706i		−	0.650435i	−0.945639	−	0.325218i	$-0.894562\pi$
$311$		−	11.4706i		−	0.650435i	0.945639	−	0.325218i	$-0.105438\pi$
$312$	3.41421	−	3.41421i	0.193292	−	0.193292i
$313$	0.612443	−	0.612443i	0.0346173	−	0.0346173i	−0.689586	−	0.724204i	$-0.742208\pi$
$313$	0.612443	−	0.612443i	0.0346173	−	0.0346173i	0.724204	+	0.689586i	$0.242208\pi$
$314$	19.3934			1.09443
$315$	−5.59099	−	1.93413i	−0.315016	−	0.108976i
$316$	14.8063			0.832922
$317$	7.03984	−	7.03984i	0.395397	−	0.395397i	−0.481209	−	0.876606i	$-0.659802\pi$
$317$	7.03984	−	7.03984i	0.395397	−	0.395397i	0.876606	+	0.481209i	$0.159802\pi$
$318$	1.26561	−	1.26561i	0.0709719	−	0.0709719i
$319$			23.3903i			1.30961i
$320$	−0.0743018	+	2.23483i	−0.00415360	+	0.124931i
$321$			5.33579i			0.297815i
$322$	1.16636	−	3.77297i	0.0649986	−	0.210260i
$323$	3.47577	+	3.47577i	0.193397	+	0.193397i
$324$			1.00000i			0.0555556i
$325$	−18.1672	+	15.8995i	−1.00774	+	0.881945i
$326$	10.2102			0.565488
$327$	0.0615536	+	0.0615536i	0.00340392	+	0.00340392i
$328$	3.85140	−	3.85140i	0.212658	−	0.212658i
$329$	2.43020	−	1.28248i	0.133981	−	0.0707053i
$330$	0.364588	−	10.9660i	0.0200699	−	0.603658i
$331$	10.1759			0.559317			0.279658	−	0.960100i	$-0.409779\pi$
$331$	10.1759			0.559317			0.279658	+	0.960100i	$0.409779\pi$
$332$	9.29809	+	9.29809i	0.510299	+	0.510299i
$333$	4.74632	+	4.74632i	0.260097	+	0.260097i
$334$	9.52387			0.521123
$335$	7.05545	−	6.60140i	0.385481	−	0.360673i
$336$	−1.23483	−	2.33991i	−0.0673657	−	0.127653i
$337$	16.8137	−	16.8137i	0.915901	−	0.915901i	−0.0808276	−	0.996728i	$-0.525756\pi$
$337$	16.8137	−	16.8137i	0.915901	−	0.915901i	0.996728	+	0.0808276i	$0.0257563\pi$
$338$	7.29289	+	7.29289i	0.396681	+	0.396681i
$339$	−2.87437			−0.156114
$340$	6.34162	−	5.93351i	0.343923	−	0.321790i
$341$		−	34.6200i		−	1.87478i
$342$	0.894921	+	0.894921i	0.0483918	+	0.0483918i
$343$	−14.5011	+	11.5204i	−0.782984	+	0.622042i
$344$		−	10.7292i		−	0.578478i
$345$	3.33579	+	0.110906i	0.179593	+	0.00597095i
$346$			20.0260i			1.07661i
$347$	−7.83919	+	7.83919i	−0.420830	+	0.420830i	−0.885489	−	0.464659i	$-0.846177\pi$
$347$	−7.83919	+	7.83919i	−0.420830	+	0.420830i	0.464659	+	0.885489i	$0.346177\pi$
$348$	−3.37069	+	3.37069i	−0.180688	+	0.180688i
$349$	−5.10838			−0.273445			−0.136723	−	0.990609i	$-0.543657\pi$
$349$	−5.10838			−0.273445			−0.136723	+	0.990609i	$0.543657\pi$
$350$	5.38344	+	12.0838i	0.287757	+	0.645907i
$351$	−4.82843			−0.257722
$352$	3.46967	−	3.46967i	0.184934	−	0.184934i
$353$	12.0821	−	12.0821i	0.643066	−	0.643066i	−0.308242	−	0.951308i	$-0.599741\pi$
$353$	12.0821	−	12.0821i	0.643066	−	0.643066i	0.951308	+	0.308242i	$0.0997407\pi$
$354$		−	1.39735i		−	0.0742681i
$355$	−29.1274	−	0.968403i	−1.54592	−	0.0513975i
$356$			15.3596i			0.814060i
$357$	−3.03490	+	9.81739i	−0.160624	+	0.519591i
$358$	2.32018	+	2.32018i	0.122625	+	0.122625i
$359$		−	3.90596i		−	0.206149i	−0.994674	−	0.103074i	$-0.967132\pi$
$359$		−	3.90596i		−	0.206149i	0.994674	−	0.103074i	$-0.0328680\pi$
$360$	1.63280	−	1.52773i	0.0860564	−	0.0805182i
$361$	−17.3982			−0.915696
$362$	−13.7132	−	13.7132i	−0.720749	−	0.720749i
$363$	−9.24695	+	9.24695i	−0.485339	+	0.485339i
$364$	11.2981	−	5.96230i	0.592181	−	0.312510i
$365$	11.6482	−	10.8986i	0.609696	−	0.570459i
$366$	−2.29721			−0.120077
$367$	−3.98072	−	3.98072i	−0.207792	−	0.207792i	0.595536	−	0.803328i	$-0.296940\pi$
$367$	−3.98072	−	3.98072i	−0.207792	−	0.207792i	−0.803328	+	0.595536i	$0.796940\pi$
$368$	1.05545	+	1.05545i	0.0550193	+	0.0550193i
$369$	−5.44670			−0.283544
$370$	0.498736	−	15.0009i	0.0259281	−	0.779859i
$371$	4.18807	−	2.21016i	0.217434	−	0.114746i
$372$	4.98896	−	4.98896i	0.258665	−	0.258665i
$373$	−8.95648	−	8.95648i	−0.463749	−	0.463749i	0.436133	−	0.899882i	$-0.356348\pi$
$373$	−8.95648	−	8.95648i	−0.463749	−	0.463749i	−0.899882	+	0.436133i	$0.856348\pi$
$374$	−19.0576			−0.985446
$375$	−8.65336	+	7.07950i	−0.446858	+	0.365584i
$376$			1.03858i			0.0535609i
$377$	−16.2751	−	16.2751i	−0.838212	−	0.838212i
$378$	−0.781409	+	2.52773i	−0.0401913	+	0.130012i
$379$		−	14.0190i		−	0.720109i	−0.932931	−	0.360055i	$-0.882758\pi$
$379$		−	14.0190i		−	0.720109i	0.932931	−	0.360055i	$-0.117242\pi$
$380$	0.0940371	−	2.82843i	0.00482400	−	0.145095i
$381$		−	15.8055i		−	0.809738i
$382$	11.9114	−	11.9114i	0.609441	−	0.609441i
$383$	7.00951	−	7.00951i	0.358169	−	0.358169i	−0.504968	−	0.863138i	$-0.668496\pi$
$383$	7.00951	−	7.00951i	0.358169	−	0.358169i	0.863138	+	0.504968i	$0.168496\pi$
$384$	1.00000			0.0510310
$385$	9.49050	−	27.4341i	0.483680	−	1.39817i
$386$	6.80760			0.346498
$387$	−7.58667	+	7.58667i	−0.385652	+	0.385652i
$388$	−8.42614	+	8.42614i	−0.427773	+	0.427773i
$389$			18.6560i			0.945895i	0.881091	+	0.472948i	$0.156810\pi$
$389$			18.6560i			0.945895i	−0.881091	+	0.472948i	$0.843190\pi$
$390$	7.37652	+	7.88388i	0.373524	+	0.399216i
$391$		−	5.79722i		−	0.293178i
$392$	−1.29289	−	6.87957i	−0.0653010	−	0.347471i
$393$	9.07689	+	9.07689i	0.457869	+	0.457869i
$394$			18.4320i			0.928589i
$395$	−1.10014	+	33.0897i	−0.0553539	+	1.66492i
$396$	−4.90685			−0.246578
$397$	19.3683	+	19.3683i	0.972066	+	0.972066i	0.999620	−	0.0275544i	$-0.00877196\pi$
$397$	19.3683	+	19.3683i	0.972066	+	0.972066i	−0.0275544	+	0.999620i	$0.508772\pi$
$398$	−8.30913	+	8.30913i	−0.416499	+	0.416499i
$399$	1.56282	+	2.96142i	0.0782387	+	0.148256i
$400$	−4.98896	−	0.332104i	−0.249448	−	0.0166052i
$401$	−27.9099			−1.39375			−0.696877	−	0.717191i	$-0.745428\pi$
$401$	−27.9099			−1.39375			−0.696877	+	0.717191i	$0.745428\pi$
$402$	−3.05545	−	3.05545i	−0.152392	−	0.152392i
$403$	24.0888	+	24.0888i	1.19995	+	1.19995i
$404$	18.1504			0.903015
$405$	−2.23483	−	0.0743018i	−0.111050	−	0.00369209i
$406$	−11.1541	+	5.88629i	−0.553567	+	0.292132i
$407$	−23.2895	+	23.2895i	−1.15442	+	1.15442i
$408$	−2.74632	−	2.74632i	−0.135963	−	0.135963i
$409$	−18.3211			−0.905918			−0.452959	−	0.891531i	$-0.649632\pi$
$409$	−18.3211			−0.905918			−0.452959	+	0.891531i	$0.649632\pi$
$410$	8.32106	+	8.89339i	0.410948	+	0.439213i
$411$		−	5.12563i		−	0.252829i
$412$	−8.36459	−	8.36459i	−0.412094	−	0.412094i
$413$	1.09190	−	3.53211i	0.0537288	−	0.173804i
$414$		−	1.49264i		−	0.0733590i
$415$	−21.4706	+	20.0888i	−1.05395	+	0.986122i
$416$			4.82843i			0.236733i
$417$	−2.76193	+	2.76193i	−0.135252	+	0.135252i
$418$	−4.39124	+	4.39124i	−0.214783	+	0.214783i
$419$	−5.49605			−0.268500			−0.134250	−	0.990948i	$-0.542862\pi$
$419$	−5.49605			−0.268500			−0.134250	+	0.990948i	$0.542862\pi$
$420$	5.32106	−	2.58579i	0.259641	−	0.126173i
$421$	24.5863			1.19826			0.599132	−	0.800651i	$-0.295513\pi$
$421$	24.5863			1.19826			0.599132	+	0.800651i	$0.295513\pi$
$422$	−11.7028	+	11.7028i	−0.569683	+	0.569683i
$423$	0.734390	−	0.734390i	0.0357073	−	0.0357073i
$424$			1.78984i			0.0869224i
$425$	12.7892	+	14.6133i	0.620367	+	0.708851i
$426$			13.0334i			0.631469i
$427$	−5.80671	−	1.79506i	−0.281006	−	0.0868689i
$428$	−3.77297	−	3.77297i	−0.182374	−	0.182374i
$429$		−	23.6924i		−	1.14388i
$430$	23.9779	+	0.797197i	1.15632	+	0.0384443i
$431$	22.8133			1.09888			0.549440	−	0.835533i	$-0.314841\pi$
$431$	22.8133			1.09888			0.549440	+	0.835533i	$0.314841\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	17.1216	−	17.1216i	0.822811	−	0.822811i	−0.163700	−	0.986510i	$-0.552343\pi$
$433$	17.1216	−	17.1216i	0.822811	−	0.822811i	0.986510	+	0.163700i	$0.0523428\pi$
$434$	16.5091	−	8.71231i	0.792464	−	0.418204i
$435$	−7.28248	−	7.78337i	−0.349168	−	0.373184i
$436$	−0.0870500			−0.00416894
$437$	−1.33579	−	1.33579i	−0.0638996	−	0.0638996i
$438$	−5.04441	−	5.04441i	−0.241031	−	0.241031i
$439$	−35.8323			−1.71018			−0.855092	−	0.518476i	$-0.826500\pi$
$439$	−35.8323			−1.71018			−0.855092	+	0.518476i	$0.826500\pi$
$440$	7.49632	+	8.01193i	0.357373	+	0.381954i
$441$	−3.95037	+	5.77880i	−0.188113	+	0.275181i
$442$	13.2604	−	13.2604i	0.630733	−	0.630733i
$443$	2.93109	+	2.93109i	0.139260	+	0.139260i	0.773300	−	0.634040i	$-0.218605\pi$
$443$	2.93109	+	2.93109i	0.139260	+	0.139260i	−0.634040	+	0.773300i	$0.718605\pi$
$444$	−6.71231			−0.318552
$445$	−34.3262	−	1.14125i	−1.62722	−	0.0541004i
$446$		−	11.6824i		−	0.553175i
$447$	−3.98896	−	3.98896i	−0.188671	−	0.188671i
$448$	2.52773	+	0.781409i	0.119424	+	0.0369181i
$449$		−	1.70279i		−	0.0803598i	−0.999192	−	0.0401799i	$-0.987207\pi$
$449$		−	1.70279i		−	0.0803598i	0.999192	−	0.0401799i	$-0.0127931\pi$
$450$	3.29289	+	3.76256i	0.155228	+	0.177369i
$451$		−	26.7261i		−	1.25848i
$452$	2.03248	−	2.03248i	0.0956000	−	0.0956000i
$453$	8.32106	−	8.32106i	0.390958	−	0.390958i
$454$	−8.36217			−0.392456
$455$	12.4853	+	25.6924i	0.585319	+	1.20448i
$456$	−1.26561			−0.0592676
$457$	−5.34315	+	5.34315i	−0.249942	+	0.249942i	−0.820947	−	0.571005i	$-0.806554\pi$
$457$	−5.34315	+	5.34315i	−0.249942	+	0.249942i	0.571005	+	0.820947i	$0.306554\pi$
$458$	6.58579	−	6.58579i	0.307734	−	0.307734i
$459$			3.88388i			0.181284i
$460$	−2.43718	+	2.28034i	−0.113634	+	0.106321i
$461$		−	0.858751i		−	0.0399960i	−0.999800	−	0.0199980i	$-0.993634\pi$
$461$		−	0.858751i		−	0.0399960i	0.999800	−	0.0199980i	$-0.00636599\pi$
$462$	−12.4032	−	3.83425i	−0.577048	−	0.178386i
$463$	−20.3594	−	20.3594i	−0.946180	−	0.946180i	0.0524436	−	0.998624i	$-0.483299\pi$
$463$	−20.3594	−	20.3594i	−0.946180	−	0.946180i	−0.998624	+	0.0524436i	$0.983299\pi$
$464$		−	4.76687i		−	0.221297i
$465$	10.7788	+	11.5202i	0.499855	+	0.534235i
$466$	−22.7071			−1.05189
$467$	8.77908	+	8.77908i	0.406247	+	0.406247i	0.880428	−	0.474181i	$-0.157256\pi$
$467$	8.77908	+	8.77908i	0.406247	+	0.406247i	−0.474181	+	0.880428i	$0.657256\pi$
$468$	3.41421	−	3.41421i	0.157822	−	0.157822i
$469$	−5.33579	−	10.1109i	−0.246384	−	0.466878i
$470$	−2.32106	−	0.0771687i	−0.107063	−	0.00355953i
$471$	19.3934			0.893600
$472$	0.988072	+	0.988072i	0.0454797	+	0.0454797i
$473$	−37.2267	−	37.2267i	−1.71168	−	1.71168i
$474$	14.8063			0.680078
$475$	6.31408	+	0.420314i	0.289710	+	0.0192853i
$476$	−4.79594	−	9.08794i	−0.219822	−	0.416545i
$477$	1.26561	−	1.26561i	0.0579483	−	0.0579483i
$478$	−1.19213	−	1.19213i	−0.0545267	−	0.0545267i
$479$	−1.17157			−0.0535305			−0.0267653	−	0.999642i	$-0.508521\pi$
$479$	−1.17157			−0.0535305			−0.0267653	+	0.999642i	$0.508521\pi$
$480$	−0.0743018	+	2.23483i	−0.00339140	+	0.102006i
$481$		−	32.4099i		−	1.47776i
$482$	2.55672	+	2.55672i	0.116455	+	0.116455i
$483$	1.16636	−	3.77297i	0.0530711	−	0.171676i
$484$		−	13.0772i		−	0.594417i
$485$	−18.2049	−	19.4571i	−0.826644	−	0.883501i
$486$			1.00000i			0.0453609i
$487$	9.70737	−	9.70737i	0.439883	−	0.439883i	−0.452090	−	0.891972i	$-0.649321\pi$
$487$	9.70737	−	9.70737i	0.439883	−	0.439883i	0.891972	+	0.452090i	$0.149321\pi$
$488$	1.62437	−	1.62437i	0.0735318	−	0.0735318i
$489$	10.2102			0.461719
$490$	15.4707	−	2.37824i	0.698897	−	0.107438i
$491$	−16.9381			−0.764405			−0.382202	−	0.924079i	$-0.624834\pi$
$491$	−16.9381			−0.764405			−0.382202	+	0.924079i	$0.624834\pi$
$492$	3.85140	−	3.85140i	0.173634	−	0.173634i
$493$	−13.0913	+	13.0913i	−0.589605	+	0.589605i
$494$		−	6.11091i		−	0.274943i
$495$	0.364588	−	10.9660i	0.0163870	−	0.492885i
$496$			7.05545i			0.316799i
$497$	−10.1844	+	32.9448i	−0.456832	+	1.47778i
$498$	9.29809	+	9.29809i	0.416658	+	0.416658i
$499$		−	30.4117i		−	1.36141i	−0.732556	−	0.680706i	$-0.761673\pi$
$499$		−	30.4117i		−	1.36141i	0.732556	−	0.680706i	$-0.238327\pi$
$500$	1.11289	−	11.1248i	0.0497698	−	0.497517i
$501$	9.52387			0.425495
$502$	−3.38630	−	3.38630i	−0.151138	−	0.151138i
$503$	−4.75825	+	4.75825i	−0.212160	+	0.212160i	−0.805184	−	0.593025i	$-0.797934\pi$
$503$	−4.75825	+	4.75825i	−0.212160	+	0.212160i	0.593025	+	0.805184i	$0.297934\pi$
$504$	−1.23483	−	2.33991i	−0.0550038	−	0.104228i
$505$	−1.34861	+	40.5631i	−0.0600122	+	1.80503i
$506$	7.32414			0.325598
$507$	7.29289	+	7.29289i	0.323889	+	0.323889i
$508$	11.1761	+	11.1761i	0.495861	+	0.495861i
$509$	−40.3501			−1.78849			−0.894243	−	0.447581i	$-0.852286\pi$
$509$	−40.3501			−1.78849			−0.894243	+	0.447581i	$0.852286\pi$
$510$	6.34162	−	5.93351i	0.280812	−	0.262740i
$511$	−8.80915	−	16.6926i	−0.389694	−	0.738439i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	0.894921	+	0.894921i	0.0395117	+	0.0395117i
$514$	−29.4316			−1.29817
$515$	19.3150	−	18.0720i	0.851119	−	0.796345i
$516$		−	10.7292i		−	0.472326i
$517$	3.60354	+	3.60354i	0.158484	+	0.158484i
$518$	−16.9669	−	5.24505i	−0.745482	−	0.230454i
$519$			20.0260i			0.879045i
$520$	−10.7907	−	0.358761i	−0.473205	−	0.0157327i
$521$		−	8.96879i		−	0.392930i	−0.980511	−	0.196465i	$-0.937054\pi$
$521$		−	8.96879i		−	0.392930i	0.980511	−	0.196465i	$-0.0629462\pi$
$522$	−3.37069	+	3.37069i	−0.147531	+	0.147531i
$523$	−8.40290	+	8.40290i	−0.367433	+	0.367433i	−0.866540	−	0.499107i	$-0.833661\pi$
$523$	−8.40290	+	8.40290i	−0.367433	+	0.367433i	0.499107	+	0.866540i	$0.333661\pi$
$524$	−12.8367			−0.560772
$525$	5.38344	+	12.0838i	0.234952	+	0.527381i
$526$	−9.35965			−0.408100
$527$	19.3765	−	19.3765i	0.844054	−	0.844054i
$528$	3.46967	−	3.46967i	0.150998	−	0.150998i
$529$		−	20.7720i		−	0.903132i
$530$	−4.00000	−	0.132989i	−0.173749	−	0.00577665i
$531$		−	1.39735i		−	0.0606396i
$532$	−3.19912	−	0.988958i	−0.138699	−	0.0428768i
$533$	18.5962	+	18.5962i	0.805490	+	0.805490i
$534$			15.3596i			0.664677i
$535$	8.71231	−	8.15163i	0.376666	−	0.352426i
$536$	4.32106			0.186641
$537$	2.32018	+	2.32018i	0.100123	+	0.100123i
$538$	−9.27665	+	9.27665i	−0.399945	+	0.399945i
$539$	−28.3557	−	19.3839i	−1.22137	−	0.834923i
$540$	1.63280	−	1.52773i	0.0702647	−	0.0657429i
$541$	27.1611			1.16775			0.583874	−	0.811844i	$-0.301536\pi$
$541$	27.1611			1.16775			0.583874	+	0.811844i	$0.301536\pi$
$542$	−12.7870	−	12.7870i	−0.549250	−	0.549250i
$543$	−13.7132	−	13.7132i	−0.588489	−	0.588489i
$544$	3.88388			0.166520
$545$	0.00646797	−	0.194542i	0.000277057	−	0.00833327i
$546$	11.2981	−	5.96230i	0.483514	−	0.255163i
$547$	−16.8471	+	16.8471i	−0.720329	+	0.720329i	−0.968672	−	0.248343i	$-0.920114\pi$
$547$	−16.8471	+	16.8471i	−0.720329	+	0.720329i	0.248343	+	0.968672i	$0.420114\pi$
$548$	3.62437	+	3.62437i	0.154825	+	0.154825i
$549$	−2.29721			−0.0980424
$550$	−18.4623	+	16.1577i	−0.787236	+	0.688968i
$551$			6.03300i			0.257015i
$552$	1.05545	+	1.05545i	0.0449231	+	0.0449231i
$553$	37.4264	+	11.5698i	1.59153	+	0.491998i
$554$			3.72704i			0.158347i
$555$	0.498736	−	15.0009i	0.0211702	−	0.636752i
$556$		−	3.90596i		−	0.165650i
$557$	−0.0529257	+	0.0529257i	−0.00224253	+	0.00224253i	−0.708227	−	0.705985i	$-0.750505\pi$
$557$	−0.0529257	+	0.0529257i	−0.00224253	+	0.00224253i	0.705985	+	0.708227i	$0.250505\pi$
$558$	4.98896	−	4.98896i	0.211199	−	0.211199i
$559$	51.8050			2.19112
$560$	−1.93413	+	5.59099i	−0.0817320	+	0.236262i
$561$	−19.0576			−0.804613
$562$	−14.4645	+	14.4645i	−0.610146	+	0.610146i
$563$	−7.84316	+	7.84316i	−0.330550	+	0.330550i	−0.852795	−	0.522246i	$-0.825094\pi$
$563$	−7.84316	+	7.84316i	−0.330550	+	0.330550i	0.522246	+	0.852795i	$0.325094\pi$
$564$			1.03858i			0.0437323i
$565$	4.39124	+	4.69328i	0.184741	+	0.197448i
$566$			15.2383i			0.640514i
$567$	−0.781409	+	2.52773i	−0.0328161	+	0.106155i
$568$	−9.21598	−	9.21598i	−0.386694	−	0.386694i
$569$		−	6.12311i		−	0.256694i	−0.991729	−	0.128347i	$-0.959033\pi$
$569$		−	6.12311i		−	0.256694i	0.991729	−	0.128347i	$-0.0409671\pi$
$570$	0.0940371	−	2.82843i	0.00393878	−	0.118470i
$571$	30.4896			1.27595			0.637974	−	0.770058i	$-0.279773\pi$
$571$	30.4896			1.27595			0.637974	+	0.770058i	$0.279773\pi$
$572$	16.7530	+	16.7530i	0.700479	+	0.700479i
$573$	11.9114	−	11.9114i	0.497607	−	0.497607i
$574$	12.7448	−	6.72576i	0.531957	−	0.280728i
$575$	−4.91509	−	5.61613i	−0.204973	−	0.234209i
$576$	1.00000			0.0416667
$577$	−11.5444	−	11.5444i	−0.480600	−	0.480600i	0.424723	−	0.905323i	$-0.360371\pi$
$577$	−11.5444	−	11.5444i	−0.480600	−	0.480600i	−0.905323	+	0.424723i	$0.860371\pi$
$578$	1.35445	+	1.35445i	0.0563376	+	0.0563376i
$579$	6.80760			0.282914
$580$	10.6532	+	0.354187i	0.442349	+	0.0147068i
$581$	16.2374	+	30.7686i	0.673642	+	1.27650i
$582$	−8.42614	+	8.42614i	−0.349275	+	0.349275i
$583$	6.21016	+	6.21016i	0.257198	+	0.257198i
$584$	7.13387			0.295202
$585$	7.37652	+	7.88388i	0.304981	+	0.325958i
$586$		−	4.46841i		−	0.184588i
$587$	−7.24478	−	7.24478i	−0.299024	−	0.299024i	0.541607	−	0.840632i	$-0.317816\pi$
$587$	−7.24478	−	7.24478i	−0.299024	−	0.299024i	−0.840632	+	0.541607i	$0.817816\pi$
$588$	−1.29289	−	6.87957i	−0.0533180	−	0.283709i
$589$		−	8.92945i		−	0.367932i
$590$	−2.28159	+	2.13476i	−0.0939317	+	0.0878867i
$591$			18.4320i			0.758190i
$592$	4.74632	−	4.74632i	0.195072	−	0.195072i
$593$	−6.67652	+	6.67652i	−0.274172	+	0.274172i	−0.830777	−	0.556605i	$-0.812104\pi$
$593$	−6.67652	+	6.67652i	−0.274172	+	0.274172i	0.556605	+	0.830777i	$0.312104\pi$
$594$	−4.90685			−0.201330
$595$	20.6664	−	10.0429i	0.847239	−	0.411718i
$596$	5.64124			0.231074
$597$	−8.30913	+	8.30913i	−0.340070	+	0.340070i
$598$	−5.09618	+	5.09618i	−0.208398	+	0.208398i
$599$			2.62526i			0.107265i	0.998561	+	0.0536325i	$0.0170800\pi$
$599$			2.62526i			0.107265i	−0.998561	+	0.0536325i	$0.982920\pi$
$600$	−4.98896	−	0.332104i	−0.203673	−	0.0135581i
$601$			11.7003i			0.477265i	0.971110	+	0.238632i	$0.0766991\pi$
$601$			11.7003i			0.477265i	−0.971110	+	0.238632i	$0.923301\pi$
$602$	8.38387	−	27.1204i	0.341701	−	1.10535i
$603$	−3.05545	−	3.05545i	−0.124428	−	0.124428i
$604$			11.7678i			0.478823i
$605$	29.2253	+	0.971657i	1.18818	+	0.0395035i
$606$	18.1504			0.737309
$607$	23.2749	+	23.2749i	0.944697	+	0.944697i	0.998549	−	0.0538519i	$-0.0171499\pi$
$607$	23.2749	+	23.2749i	0.944697	+	0.944697i	−0.0538519	+	0.998549i	$0.517150\pi$
$608$	0.894921	−	0.894921i	0.0362939	−	0.0362939i
$609$	−11.1541	+	5.88629i	−0.451985	+	0.238525i
$610$	3.50950	+	3.75089i	0.142096	+	0.151869i
$611$	−5.01473			−0.202874
$612$	−2.74632	−	2.74632i	−0.111013	−	0.111013i
$613$	18.1372	+	18.1372i	0.732554	+	0.732554i	0.971125	−	0.238571i	$-0.0766789\pi$
$613$	18.1372	+	18.1372i	0.732554	+	0.732554i	−0.238571	+	0.971125i	$0.576679\pi$
$614$	−29.4172			−1.18718
$615$	8.32106	+	8.89339i	0.335538	+	0.358616i
$616$	11.4816	−	6.05914i	0.462607	−	0.244130i
$617$	1.59063	−	1.59063i	0.0640365	−	0.0640365i	−0.674363	−	0.738400i	$-0.735582\pi$
$617$	1.59063	−	1.59063i	0.0640365	−	0.0640365i	0.738400	+	0.674363i	$0.235582\pi$
$618$	−8.36459	−	8.36459i	−0.336473	−	0.336473i
$619$	39.2232			1.57651			0.788257	−	0.615346i	$-0.210984\pi$
$619$	39.2232			1.57651			0.788257	+	0.615346i	$0.210984\pi$
$620$	−15.7678	−	0.524233i	−0.633248	−	0.0210537i
$621$		−	1.49264i		−	0.0598974i
$622$	8.11091	+	8.11091i	0.325218	+	0.325218i
$623$	−12.0022	+	38.8250i	−0.480856	+	1.55549i
$624$			4.82843i			0.193292i
$625$	24.7794	+	3.31371i	0.991177	+	0.132548i
$626$			0.866125i			0.0346173i
$627$	−4.39124	+	4.39124i	−0.175369	+	0.175369i
$628$	−13.7132	+	13.7132i	−0.547216	+	0.547216i
$629$	−26.0698			−1.03947
$630$	5.32106	−	2.58579i	0.211996	−	0.103020i
$631$	−1.69542			−0.0674935			−0.0337468	−	0.999430i	$-0.510744\pi$
$631$	−1.69542			−0.0674935			−0.0337468	+	0.999430i	$0.510744\pi$
$632$	−10.4697	+	10.4697i	−0.416461	+	0.416461i
$633$	−11.7028	+	11.7028i	−0.465144	+	0.465144i
$634$			9.95583i			0.395397i
$635$	−25.8072	+	24.1464i	−1.02413	+	0.958221i
$636$			1.78984i			0.0709719i
$637$	33.2175	−	6.24264i	1.31612	−	0.247342i
$638$	−16.5395	−	16.5395i	−0.654804	−	0.654804i
$639$			13.0334i			0.515592i
$640$	−1.52773	−	1.63280i	−0.0603887	−	0.0645423i
$641$	23.0043			0.908615			0.454308	−	0.890845i	$-0.349887\pi$
$641$	23.0043			0.908615			0.454308	+	0.890845i	$0.349887\pi$
$642$	−3.77297	−	3.77297i	−0.148907	−	0.148907i
$643$	−13.9948	+	13.9948i	−0.551900	+	0.551900i	−0.926989	−	0.375089i	$-0.877612\pi$
$643$	−13.9948	+	13.9948i	−0.551900	+	0.551900i	0.375089	+	0.926989i	$0.377612\pi$
$644$	1.84316	+	3.49264i	0.0726305	+	0.137629i
$645$	23.9779	+	0.797197i	0.944130	+	0.0313896i
$646$	−4.91548			−0.193397
$647$	5.22955	+	5.22955i	0.205595	+	0.205595i	0.802392	−	0.596797i	$-0.203560\pi$
$647$	5.22955	+	5.22955i	0.205595	+	0.205595i	−0.596797	+	0.802392i	$0.703560\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	6.85656			0.269144
$650$	1.60354	−	24.0888i	0.0628961	−	0.944841i
$651$	16.5091	−	8.71231i	0.647044	−	0.341462i
$652$	−7.21967	+	7.21967i	−0.282744	+	0.282744i
$653$	1.74516	+	1.74516i	0.0682933	+	0.0682933i	0.740428	−	0.672135i	$-0.234623\pi$
$653$	1.74516	+	1.74516i	0.0682933	+	0.0682933i	−0.672135	+	0.740428i	$0.734623\pi$
$654$	−0.0870500			−0.00340392
$655$	0.953787	−	28.6878i	0.0372676	−	1.12093i
$656$			5.44670i			0.212658i
$657$	−5.04441	−	5.04441i	−0.196801	−	0.196801i
$658$	−0.811559	+	2.62526i	−0.0316379	+	0.102343i
$659$			21.4234i			0.834536i	0.908784	+	0.417268i	$0.137012\pi$
$659$			21.4234i			0.834536i	−0.908784	+	0.417268i	$0.862988\pi$
$660$	7.49632	+	8.01193i	0.291794	+	0.311864i
$661$		−	15.6881i		−	0.610196i	−0.952321	−	0.305098i	$-0.901311\pi$
$661$		−	15.6881i		−	0.610196i	0.952321	−	0.305098i	$-0.0986892\pi$
$662$	−7.19543	+	7.19543i	−0.279658	+	0.279658i
$663$	13.2604	−	13.2604i	0.514991	−	0.514991i
$664$	−13.1495			−0.510299
$665$	2.44786	−	7.07601i	0.0949238	−	0.274396i
$666$	−6.71231			−0.260097
$667$	5.03121	−	5.03121i	0.194809	−	0.194809i
$668$	−6.73439	+	6.73439i	−0.260561	+	0.260561i
$669$		−	11.6824i		−	0.451666i
$670$	−0.321063	+	9.65685i	−0.0124037	+	0.373077i
$671$		−	11.2720i		−	0.435153i
$672$	2.52773	+	0.781409i	0.0975092	+	0.0301435i
$673$	26.0502	+	26.0502i	1.00416	+	1.00416i	0.999991	+	0.00417159i	$0.00132786\pi$
$673$	26.0502	+	26.0502i	1.00416	+	1.00416i	0.00417159	+	0.999991i	$0.498672\pi$
$674$			23.7782i			0.915901i
$675$	3.29289	+	3.76256i	0.126744	+	0.144821i
$676$	−10.3137			−0.396681
$677$	−3.99149	−	3.99149i	−0.153405	−	0.153405i	0.626232	−	0.779637i	$-0.284596\pi$
$677$	−3.99149	−	3.99149i	−0.153405	−	0.153405i	−0.779637	+	0.626232i	$0.784596\pi$
$678$	2.03248	−	2.03248i	0.0780571	−	0.0780571i
$679$	−27.8832	+	14.7147i	−1.07006	+	0.564699i
$680$	−0.288579	+	8.67982i	−0.0110665	+	0.332856i
$681$	−8.36217			−0.320439
$682$	24.4801	+	24.4801i	0.937390	+	0.937390i
$683$	−28.2530	−	28.2530i	−1.08107	−	1.08107i	−0.996410	−	0.0846629i	$-0.973019\pi$
$683$	−28.2530	−	28.2530i	−1.08107	−	1.08107i	−0.0846629	−	0.996410i	$-0.526981\pi$
$684$	−1.26561			−0.0483918
$685$	−8.36916	+	7.83057i	−0.319769	+	0.299191i
$686$	2.10767	−	18.3999i	0.0804713	−	0.702513i
$687$	6.58579	−	6.58579i	0.251263	−	0.251263i
$688$	7.58667	+	7.58667i	0.289239	+	0.289239i
$689$	−8.64213			−0.329239
$690$	−2.43718	+	2.28034i	−0.0927820	+	0.0868110i
$691$		−	2.45366i		−	0.0933418i	−0.998910	−	0.0466709i	$-0.985139\pi$
$691$		−	2.45366i		−	0.0933418i	0.998910	−	0.0466709i	$-0.0148612\pi$
$692$	−14.1605	−	14.1605i	−0.538303	−	0.538303i
$693$	−12.4032	−	3.83425i	−0.471158	−	0.145651i
$694$		−	11.0863i		−	0.420830i
$695$	8.72918	+	0.290220i	0.331116	+	0.0110087i
$696$		−	4.76687i		−	0.180688i
$697$	14.9584	−	14.9584i	0.566588	−	0.566588i
$698$	3.61217	−	3.61217i	0.136723	−	0.136723i
$699$	−22.7071			−0.858861
$700$	−12.3512	−	4.73788i	−0.466832	−	0.179075i
$701$	−6.34833			−0.239773			−0.119887	−	0.992788i	$-0.538253\pi$
$701$	−6.34833			−0.239773			−0.119887	+	0.992788i	$0.538253\pi$
$702$	3.41421	−	3.41421i	0.128861	−	0.128861i
$703$	−6.00699	+	6.00699i	−0.226558	+	0.226558i
$704$			4.90685i			0.184934i
$705$	−2.32106	−	0.0771687i	−0.0874163	−	0.00290634i
$706$			17.0867i			0.643066i
$707$	45.8792	+	14.1829i	1.72546	+	0.533401i
$708$	0.988072	+	0.988072i	0.0371340	+	0.0371340i
$709$		−	20.3645i		−	0.764805i	−0.923996	−	0.382402i	$-0.875097\pi$
$709$		−	20.3645i		−	0.764805i	0.923996	−	0.382402i	$-0.124903\pi$
$710$	21.2810	−	19.9114i	0.798660	−	0.747262i
$711$	14.8063			0.555281
$712$	−10.8609	−	10.8609i	−0.407030	−	0.407030i
$713$	−7.44670	+	7.44670i	−0.278881	+	0.278881i
$714$	−4.79594	−	9.08794i	−0.179484	−	0.340107i
$715$	−38.6850	+	36.1954i	−1.44674	+	1.35363i
$716$	−3.28123			−0.122625
$717$	−1.19213	−	1.19213i	−0.0445209	−	0.0445209i
$718$	2.76193	+	2.76193i	0.103074	+	0.103074i
$719$	25.9031			0.966021			0.483011	−	0.875614i	$-0.339543\pi$
$719$	25.9031			0.966021			0.483011	+	0.875614i	$0.339543\pi$
$720$	−0.0743018	+	2.23483i	−0.00276906	+	0.0832873i
$721$	−14.6072	−	27.6795i	−0.544002	−	1.03084i
$722$	12.3024	−	12.3024i	0.457848	−	0.457848i
$723$	2.55672	+	2.55672i	0.0950853	+	0.0950853i
$724$	19.3934			0.720749
$725$	−1.58310	+	23.7817i	−0.0587948	+	0.883231i
$726$		−	13.0772i		−	0.485339i
$727$	−36.3373	−	36.3373i	−1.34768	−	1.34768i	−0.888180	−	0.459495i	$-0.848030\pi$
$727$	−36.3373	−	36.3373i	−1.34768	−	1.34768i	−0.459495	−	0.888180i	$-0.651970\pi$
$728$	−3.77297	+	12.2049i	−0.139836	+	0.452345i
$729$			1.00000i			0.0370370i
$730$	−0.530060	+	15.9430i	−0.0196184	+	0.590078i
$731$		−	41.6708i		−	1.54125i
$732$	1.62437	−	1.62437i	0.0600385	−	0.0600385i
$733$	18.3535	−	18.3535i	0.677904	−	0.677904i	−0.281622	−	0.959525i	$-0.590872\pi$
$733$	18.3535	−	18.3535i	0.677904	−	0.677904i	0.959525	+	0.281622i	$0.0908723\pi$
$734$	5.62959			0.207792
$735$	15.4707	−	2.37824i	0.570647	−	0.0877226i
$736$	−1.49264			−0.0550193
$737$	14.9926	−	14.9926i	0.552261	−	0.552261i
$738$	3.85140	−	3.85140i	0.141772	−	0.141772i
$739$		−	21.3934i		−	0.786968i	−0.919331	−	0.393484i	$-0.871270\pi$
$739$		−	21.3934i		−	0.786968i	0.919331	−	0.393484i	$-0.128730\pi$
$740$	10.2546	+	10.9599i	0.376965	+	0.402894i
$741$		−	6.11091i		−	0.224490i
$742$	−1.39860	+	4.52423i	−0.0513442	+	0.166090i
$743$	−29.9264	−	29.9264i	−1.09789	−	1.09789i	−0.994657	−	0.103235i	$-0.967081\pi$
$743$	−29.9264	−	29.9264i	−1.09789	−	1.09789i	−0.103235	−	0.994657i	$-0.532919\pi$
$744$			7.05545i			0.258665i
$745$	−0.419154	+	12.6072i	−0.0153566	+	0.461893i
$746$	12.6664			0.463749
$747$	9.29809	+	9.29809i	0.340199	+	0.340199i
$748$	13.4758	−	13.4758i	0.492723	−	0.492723i
$749$	−6.58881	−	12.4853i	−0.240750	−	0.456202i
$750$	1.11289	−	11.1248i	0.0406369	−	0.406221i
$751$	−19.3081			−0.704563			−0.352281	−	0.935894i	$-0.614594\pi$
$751$	−19.3081			−0.704563			−0.352281	+	0.935894i	$0.614594\pi$
$752$	−0.734390	−	0.734390i	−0.0267804	−	0.0267804i
$753$	−3.38630	−	3.38630i	−0.123404	−	0.123404i
$754$	23.0165			0.838212
$755$	−26.2990	−	0.874366i	−0.957118	−	0.0318214i
$756$	−1.23483	−	2.33991i	−0.0449104	−	0.0851018i
$757$	−30.9872	+	30.9872i	−1.12625	+	1.12625i	−0.135465	+	0.990782i	$0.543253\pi$
$757$	−30.9872	+	30.9872i	−1.12625	+	1.12625i	−0.990782	+	0.135465i	$0.956747\pi$
$758$	9.91295	+	9.91295i	0.360055	+	0.360055i
$759$	7.32414			0.265849
$760$	1.93351	+	2.06649i	0.0701356	+	0.0749596i
$761$			47.3418i			1.71614i	0.513532	+	0.858070i	$0.328337\pi$
$761$			47.3418i			1.71614i	−0.513532	+	0.858070i	$0.671663\pi$
$762$	11.1761	+	11.1761i	0.404869	+	0.404869i
$763$	−0.220039	−	0.0680216i	−0.00796593	−	0.00246255i
$764$			16.8453i			0.609441i
$765$	6.34162	−	5.93351i	0.229282	−	0.214526i
$766$			9.91295i			0.358169i
$767$	−4.77083	+	4.77083i	−0.172265	+	0.172265i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	44.0520			1.58856			0.794278	−	0.607554i	$-0.207849\pi$
$769$	44.0520			1.58856			0.794278	+	0.607554i	$0.207849\pi$
$770$	12.6881	+	26.1097i	0.457246	+	0.940927i
$771$	−29.4316			−1.05995
$772$	−4.81370	+	4.81370i	−0.173249	+	0.173249i
$773$	11.1336	−	11.1336i	0.400448	−	0.400448i	−0.477943	−	0.878391i	$-0.658617\pi$
$773$	11.1336	−	11.1336i	0.400448	−	0.400448i	0.878391	+	0.477943i	$0.158617\pi$
$774$		−	10.7292i		−	0.385652i
$775$	2.34315	−	35.1994i	0.0841683	−	1.26440i
$776$		−	11.9164i		−	0.427773i
$777$	−16.9669	−	5.24505i	−0.608683	−	0.188165i
$778$	−13.1918	−	13.1918i	−0.472948	−	0.472948i
$779$		−	6.89339i		−	0.246981i
$780$	−10.7907	−	0.358761i	−0.386370	−	0.0128457i
$781$	−63.9528			−2.28841
$782$	4.09925	+	4.09925i	0.146589	+	0.146589i
$783$	−3.37069	+	3.37069i	−0.120459	+	0.120459i
$784$	5.77880	+	3.95037i	0.206386	+	0.141085i
$785$	−29.6278	−	31.6656i	−1.05746	−	1.13019i
$786$	−12.8367			−0.457869
$787$	11.7098	+	11.7098i	0.417409	+	0.417409i	0.884310	−	0.466901i	$-0.154630\pi$
$787$	11.7098	+	11.7098i	0.417409	+	0.417409i	−0.466901	+	0.884310i	$0.654630\pi$
$788$	−13.0334	−	13.0334i	−0.464295	−	0.464295i
$789$	−9.35965			−0.333212
$790$	−22.6200	−	24.1759i	−0.804785	−	0.860139i
$791$	6.72576	−	3.54936i	0.239141	−	0.126201i
$792$	3.46967	−	3.46967i	0.123289	−	0.123289i
$793$	7.84316	+	7.84316i	0.278519	+	0.278519i
$794$	−27.3909			−0.972066
$795$	−4.00000	−	0.132989i	−0.141865	−	0.00471662i
$796$		−	11.7509i		−	0.416499i
$797$	12.7255	+	12.7255i	0.450760	+	0.450760i	0.895607	−	0.444847i	$-0.146742\pi$
$797$	12.7255	+	12.7255i	0.450760	+	0.450760i	−0.444847	+	0.895607i	$0.646742\pi$
$798$	−3.19912	−	0.988958i	−0.113247	−	0.0350088i
$799$			4.03374i			0.142703i
$800$	3.76256	−	3.29289i	0.133027	−	0.116421i
$801$			15.3596i			0.542706i
$802$	19.7353	−	19.7353i	0.696877	−	0.696877i
$803$	24.7522	−	24.7522i	0.873485	−	0.873485i
$804$	4.32106			0.152392
$805$	−7.94241	+	3.85964i	−0.279933	+	0.136034i
$806$	−34.0667			−1.19995
$807$	−9.27665	+	9.27665i	−0.326554	+	0.326554i
$808$	−12.8343	+	12.8343i	−0.451507	+	0.451507i
$809$			22.8744i			0.804220i	0.915591	+	0.402110i	$0.131723\pi$
$809$			22.8744i			0.804220i	−0.915591	+	0.402110i	$0.868277\pi$
$810$	1.63280	−	1.52773i	0.0573709	−	0.0536788i
$811$			0.722188i			0.0253595i	0.999920	+	0.0126797i	$0.00403619\pi$
$811$			0.722188i			0.0253595i	−0.999920	+	0.0126797i	$0.995964\pi$
$812$	3.72488	−	12.0494i	0.130718	−	0.422849i
$813$	−12.7870	−	12.7870i	−0.448461	−	0.448461i
$814$		−	32.9363i		−	1.15442i
$815$	−15.5983	−	16.6712i	−0.546386	−	0.583967i
$816$	3.88388			0.135963
$817$	−9.60177	−	9.60177i	−0.335923	−	0.335923i
$818$	12.9549	−	12.9549i	0.452959	−	0.452959i
$819$	11.2981	−	5.96230i	0.394787	−	0.208340i
$820$	−12.1725	−	0.404699i	−0.425081	−	0.0141327i
$821$	21.2417			0.741341			0.370671	−	0.928764i	$-0.379128\pi$
$821$	21.2417			0.741341			0.370671	+	0.928764i	$0.379128\pi$
$822$	3.62437	+	3.62437i	0.126414	+	0.126414i
$823$	10.3066	+	10.3066i	0.359266	+	0.359266i	0.863542	−	0.504276i	$-0.168241\pi$
$823$	10.3066	+	10.3066i	0.359266	+	0.359266i	−0.504276	+	0.863542i	$0.668241\pi$
$824$	11.8293			0.412094
$825$	−18.4623	+	16.1577i	−0.642775	+	0.562540i
$826$	1.72549	+	3.26966i	0.0600374	+	0.113766i
$827$	−26.1746	+	26.1746i	−0.910181	+	0.910181i	−0.996286	−	0.0861054i	$-0.972558\pi$
$827$	−26.1746	+	26.1746i	−0.910181	+	0.910181i	0.0861054	+	0.996286i	$0.472558\pi$
$828$	1.05545	+	1.05545i	0.0366795	+	0.0366795i
$829$	−21.0061			−0.729571			−0.364786	−	0.931092i	$-0.618858\pi$
$829$	−21.0061			−0.729571			−0.364786	+	0.931092i	$0.618858\pi$
$830$	0.977031	−	29.3869i	0.0339132	−	1.02003i
$831$			3.72704i			0.129289i
$832$	−3.41421	−	3.41421i	−0.118367	−	0.118367i
$833$	−5.02144	−	26.7194i	−0.173983	−	0.925773i
$834$		−	3.90596i		−	0.135252i
$835$	−14.5499	−	15.5506i	−0.503519	−	0.538151i
$836$		−	6.21016i		−	0.214783i
$837$	4.98896	−	4.98896i	0.172444	−	0.172444i
$838$	3.88629	−	3.88629i	0.134250	−	0.134250i
$839$	50.2886			1.73615			0.868077	−	0.496430i	$-0.165356\pi$
$839$	50.2886			1.73615			0.868077	+	0.496430i	$0.165356\pi$
$840$	−1.93413	+	5.59099i	−0.0667339	+	0.192907i
$841$	6.27692			0.216445
$842$	−17.3851	+	17.3851i	−0.599132	+	0.599132i
$843$	−14.4645	+	14.4645i	−0.498182	+	0.498182i
$844$		−	16.5502i		−	0.569683i
$845$	0.766327	−	23.0494i	0.0263625	−	0.792924i
$846$			1.03858i			0.0357073i
$847$	10.2186	−	33.0555i	0.351116	−	1.13580i
$848$	−1.26561	−	1.26561i	−0.0434612	−	0.0434612i
$849$			15.2383i			0.522978i
$850$	−19.3765	−	1.28985i	−0.664609	−	0.0442416i
$851$	10.0190			0.343448
$852$	−9.21598	−	9.21598i	−0.315734	−	0.315734i
$853$	−13.1647	+	13.1647i	−0.450751	+	0.450751i	−0.895604	−	0.444853i	$-0.853256\pi$
$853$	−13.1647	+	13.1647i	−0.450751	+	0.450751i	0.444853	+	0.895604i	$0.353256\pi$
$854$	5.37526	−	2.83667i	0.183938	−	0.0970688i
$855$	0.0940371	−	2.82843i	0.00321600	−	0.0967302i
$856$	5.33579			0.182374
$857$	−19.5839	−	19.5839i	−0.668973	−	0.668973i	0.288505	−	0.957478i	$-0.406842\pi$
$857$	−19.5839	−	19.5839i	−0.668973	−	0.668973i	−0.957478	+	0.288505i	$0.906842\pi$
$858$	16.7530	+	16.7530i	0.571939	+	0.571939i
$859$	7.58185			0.258689			0.129345	−	0.991600i	$-0.458713\pi$
$859$	7.58185			0.258689			0.129345	+	0.991600i	$0.458713\pi$
$860$	−17.5187	+	16.3912i	−0.597381	+	0.558937i
$861$	12.7448	−	6.72576i	0.434341	−	0.229213i
$862$	−16.1315	+	16.1315i	−0.549440	+	0.549440i
$863$	−22.1829	−	22.1829i	−0.755113	−	0.755113i	0.220315	−	0.975429i	$-0.429291\pi$
$863$	−22.1829	−	22.1829i	−0.755113	−	0.755113i	−0.975429	+	0.220315i	$0.929291\pi$
$864$	1.00000			0.0340207
$865$	32.6986	−	30.5943i	1.11179	−	1.04024i
$866$			24.2136i			0.822811i
$867$	1.35445	+	1.35445i	0.0459994	+	0.0459994i
$868$	−5.51319	+	17.8343i	−0.187130	+	0.605334i
$869$			72.6525i			2.46457i
$870$	10.6532	+	0.354187i	0.361176	+	0.0120081i
$871$			20.8639i			0.706948i
$872$	0.0615536	−	0.0615536i	0.00208447	−	0.00208447i
$873$	−8.42614	+	8.42614i	−0.285182	+	0.285182i
$874$	1.88909			0.0638996
$875$	11.5061	−	27.2509i	0.388977	−	0.921247i
$876$	7.13387			0.241031
$877$	−5.71511	+	5.71511i	−0.192985	+	0.192985i	−0.796985	−	0.603999i	$-0.793573\pi$
$877$	−5.71511	+	5.71511i	−0.192985	+	0.192985i	0.603999	+	0.796985i	$0.293573\pi$
$878$	25.3373	−	25.3373i	0.855092	−	0.855092i
$879$		−	4.46841i		−	0.150716i
$880$	−10.9660	−	0.364588i	−0.369663	−	0.0122902i
$881$			31.8033i			1.07148i	0.844383	+	0.535740i	$0.179967\pi$
$881$			31.8033i			1.07148i	−0.844383	+	0.535740i	$0.820033\pi$
$882$	−1.29289	−	6.87957i	−0.0435340	−	0.231647i
$883$	−16.9653	−	16.9653i	−0.570929	−	0.570929i	0.361459	−	0.932388i	$-0.382279\pi$
$883$	−16.9653	−	16.9653i	−0.570929	−	0.570929i	−0.932388	+	0.361459i	$0.882279\pi$
$884$			18.7530i			0.630733i
$885$	−2.28159	+	2.13476i	−0.0766949	+	0.0717592i
$886$	−4.14519			−0.139260
$887$	−7.70801	−	7.70801i	−0.258810	−	0.258810i	0.565760	−	0.824570i	$-0.308583\pi$
$887$	−7.70801	−	7.70801i	−0.258810	−	0.258810i	−0.824570	+	0.565760i	$0.808583\pi$
$888$	4.74632	−	4.74632i	0.159276	−	0.159276i
$889$	19.5171	+	36.9834i	0.654583	+	1.24038i
$890$	25.0793	−	23.4653i	0.840660	−	0.786560i
$891$	−4.90685			−0.164386
$892$	8.26067	+	8.26067i	0.276588	+	0.276588i
$893$	0.929451	+	0.929451i	0.0311029	+	0.0311029i
$894$	5.64124			0.188671
$895$	0.243801	−	7.33299i	0.00814937	−	0.245115i
$896$	−2.33991	+	1.23483i	−0.0781710	+	0.0412529i
$897$	−5.09618	+	5.09618i	−0.170156	+	0.170156i
$898$	1.20406	+	1.20406i	0.0401799	+	0.0401799i
$899$	33.6325			1.12171
$900$	−4.98896	−	0.332104i	−0.166299	−	0.0110701i
$901$			6.95153i			0.231589i
$902$	18.8982	+	18.8982i	0.629242	+	0.629242i
$903$	8.38387	−	27.1204i	0.278998	−	0.902511i
$904$			2.87437i			0.0956000i
$905$	−1.44096	+	43.3410i	−0.0478992	+	1.44070i
$906$			11.7678i			0.390958i
$907$	0.997860	−	0.997860i	0.0331334	−	0.0331334i	−0.690346	−	0.723479i	$-0.742542\pi$
$907$	0.997860	−	0.997860i	0.0331334	−	0.0331334i	0.723479	+	0.690346i	$0.242542\pi$
$908$	5.91295	−	5.91295i	0.196228	−	0.196228i
$909$	18.1504			0.602010
$910$	−26.9957	−	9.33882i	−0.894898	−	0.309579i
$911$	−21.9623			−0.727643			−0.363821	−	0.931469i	$-0.618528\pi$
$911$	−21.9623			−0.727643			−0.363821	+	0.931469i	$0.618528\pi$
$912$	0.894921	−	0.894921i	0.0296338	−	0.0296338i
$913$	−45.6243	+	45.6243i	−1.50995	+	1.50995i
$914$		−	7.55635i		−	0.249942i
$915$	3.50950	+	3.75089i	0.116021	+	0.124001i
$916$			9.31371i			0.307734i
$917$	−32.4476	−	10.0307i	−1.07151	−	0.331242i
$918$	−2.74632	−	2.74632i	−0.0906420	−	0.0906420i
$919$		−	32.6954i		−	1.07852i	−0.842138	−	0.539262i	$-0.818703\pi$
$919$		−	32.6954i		−	1.07852i	0.842138	−	0.539262i	$-0.181297\pi$
$920$	0.110906	−	3.33579i	0.00365645	−	0.109978i
$921$	−29.4172			−0.969331
$922$	0.607228	+	0.607228i	0.0199980	+	0.0199980i
$923$	44.4987	−	44.4987i	1.46469	−	1.46469i
$924$	11.4816	−	6.05914i	0.377717	−	0.199331i
$925$	−25.2555	+	22.1029i	−0.830394	+	0.726739i
$926$	28.7925			0.946180
$927$	−8.36459	−	8.36459i	−0.274729	−	0.274729i
$928$	3.37069	+	3.37069i	0.110648	+	0.110648i
$929$	−10.8063			−0.354545			−0.177272	−	0.984162i	$-0.556727\pi$
$929$	−10.8063			−0.354545			−0.177272	+	0.984162i	$0.556727\pi$
$930$	−15.7678	−	0.524233i	−0.517045	−	0.0171903i
$931$	−7.31371	−	4.99963i	−0.239697	−	0.163856i
$932$	16.0563	−	16.0563i	0.525943	−	0.525943i
$933$	8.11091	+	8.11091i	0.265539	+	0.265539i
$934$	−12.4155			−0.406247
$935$	29.1148	+	31.1174i	0.952156	+	1.01765i
$936$			4.82843i			0.157822i
$937$	−3.51804	−	3.51804i	−0.114929	−	0.114929i	0.647303	−	0.762233i	$-0.275897\pi$
$937$	−3.51804	−	3.51804i	−0.114929	−	0.114929i	−0.762233	+	0.647303i	$0.775897\pi$
$938$	10.9225	+	3.37652i	0.356631	+	0.110247i
$939$			0.866125i			0.0282649i
$940$	1.69581	−	1.58667i	0.0553111	−	0.0517516i
$941$		−	54.9021i		−	1.78976i	−0.446309	−	0.894879i	$-0.647262\pi$
$941$		−	54.9021i		−	1.78976i	0.446309	−	0.894879i	$-0.352738\pi$
$942$	−13.7132	+	13.7132i	−0.446800	+	0.446800i
$943$	−5.74873	+	5.74873i	−0.187204	+	0.187204i
$944$	−1.39735			−0.0454797
$945$	5.32106	−	2.58579i	0.173094	−	0.0841156i
$946$	52.6464			1.71168
$947$	−30.4494	+	30.4494i	−0.989471	+	0.989471i	−0.999945	−	0.0104740i	$-0.996666\pi$
$947$	−30.4494	+	30.4494i	−0.989471	+	0.989471i	0.0104740	+	0.999945i	$0.496666\pi$
$948$	−10.4697	+	10.4697i	−0.340039	+	0.340039i
$949$			34.4454i			1.11814i
$950$	−4.76193	+	4.16752i	−0.154498	+	0.135212i
$951$			9.95583i			0.322840i
$952$	9.81739	+	3.03490i	0.318183	+	0.0983616i
$953$	40.3553	+	40.3553i	1.30724	+	1.30724i	0.923401	+	0.383836i	$0.125397\pi$
$953$	40.3553	+	40.3553i	1.30724	+	1.30724i	0.383836	+	0.923401i	$0.374603\pi$
$954$			1.78984i			0.0579483i
$955$	−37.6464	−	1.25164i	−1.21821	−	0.0405020i
$956$	1.68592			0.0545267
$957$	−16.5395	−	16.5395i	−0.534645	−	0.534645i
$958$	0.828427	−	0.828427i	0.0267653	−	0.0267653i
$959$	6.32930	+	11.9935i	0.204384	+	0.387291i
$960$	−1.52773	−	1.63280i	−0.0493072	−	0.0526986i
$961$	−18.7794			−0.605788
$962$	22.9172	+	22.9172i	0.738882	+	0.738882i
$963$	−3.77297	−	3.77297i	−0.121582	−	0.121582i
$964$	−3.61574			−0.116455
$965$	−10.4001	−	11.1155i	−0.334793	−	0.357820i
$966$	1.84316	+	3.49264i	0.0593026	+	0.112374i
$967$	30.6566	−	30.6566i	0.985849	−	0.985849i	−0.0140521	−	0.999901i	$-0.504473\pi$
$967$	30.6566	−	30.6566i	0.985849	−	0.985849i	0.999901	+	0.0140521i	$0.00447307\pi$
$968$	9.24695	+	9.24695i	0.297208	+	0.297208i
$969$	−4.91548			−0.157908
$970$	26.6311	+	0.885407i	0.855073	+	0.0284287i
$971$			46.5248i			1.49305i	0.665357	+	0.746525i	$0.268279\pi$
$971$			46.5248i			1.49305i	−0.665357	+	0.746525i	$0.731721\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	3.05215	−	9.87321i	0.0978475	−	0.316520i
$974$			13.7283i			0.439883i
$975$	1.60354	−	24.0888i	0.0513544	−	0.771460i
$976$			2.29721i			0.0735318i
$977$	42.6690	−	42.6690i	1.36510	−	1.36510i	0.497825	−	0.867278i	$-0.334132\pi$
$977$	42.6690	−	42.6690i	1.36510	−	1.36510i	0.867278	−	0.497825i	$-0.165868\pi$
$978$	−7.21967	+	7.21967i	−0.230860	+	0.230860i
$979$	−75.3675			−2.40875
$980$	−9.25780	+	12.6211i	−0.295730	+	0.403167i
$981$	−0.0870500			−0.00277929
$982$	11.9770	−	11.9770i	0.382202	−	0.382202i
$983$	1.34529	−	1.34529i	0.0429079	−	0.0429079i	−0.685327	−	0.728235i	$-0.740341\pi$
$983$	1.34529	−	1.34529i	0.0429079	−	0.0429079i	0.728235	+	0.685327i	$0.240341\pi$
$984$			5.44670i			0.173634i
$985$	30.0958	−	28.1590i	0.958932	−	0.897220i
$986$		−	18.5140i		−	0.589605i
$987$	−0.811559	+	2.62526i	−0.0258322	+	0.0835629i
$988$	4.32106	+	4.32106i	0.137471	+	0.137471i
$989$			16.0147i			0.509239i
$990$	7.49632	+	8.01193i	0.238249	+	0.254636i
$991$	3.44975			0.109585			0.0547925	−	0.998498i	$-0.482550\pi$
$991$	3.44975			0.109585			0.0547925	+	0.998498i	$0.482550\pi$
$992$	−4.98896	−	4.98896i	−0.158400	−	0.158400i
$993$	−7.19543	+	7.19543i	−0.228340	+	0.228340i
$994$	−16.0940	−	30.4969i	−0.510472	−	0.967304i
$995$	26.2613	+	0.873112i	0.832539	+	0.0276795i
$996$	−13.1495			−0.416658
$997$	31.5368	+	31.5368i	0.998780	+	0.998780i	0.999999	−	0.00121964i	$-0.000388223\pi$
$997$	31.5368	+	31.5368i	0.998780	+	0.998780i	−0.00121964	+	0.999999i	$0.500388\pi$
$998$	21.5043	+	21.5043i	0.680706	+	0.680706i
$999$	−6.71231			−0.212368

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.m.a.13.2	✓	8
3.2	odd	2		630.2.p.b.433.3		8
4.3	odd	2		1680.2.cz.b.433.4		8
5.2	odd	4		210.2.m.b.97.1	yes	8
5.3	odd	4		1050.2.m.a.307.3		8
5.4	even	2		1050.2.m.b.643.4		8
7.6	odd	2		210.2.m.b.13.1	yes	8
15.2	even	4		630.2.p.c.307.4		8
20.7	even	4		1680.2.cz.a.97.1		8
21.20	even	2		630.2.p.c.433.4		8
28.27	even	2		1680.2.cz.a.433.1		8
35.13	even	4		1050.2.m.b.307.4		8
35.27	even	4	inner	210.2.m.a.97.2	yes	8
35.34	odd	2		1050.2.m.a.643.3		8
105.62	odd	4		630.2.p.b.307.3		8
140.27	odd	4		1680.2.cz.b.97.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.m.a.13.2	✓	8	1.1	even	1	trivial
210.2.m.a.97.2	yes	8	35.27	even	4	inner
210.2.m.b.13.1	yes	8	7.6	odd	2
210.2.m.b.97.1	yes	8	5.2	odd	4
630.2.p.b.307.3		8	105.62	odd	4
630.2.p.b.433.3		8	3.2	odd	2
630.2.p.c.307.4		8	15.2	even	4
630.2.p.c.433.4		8	21.20	even	2
1050.2.m.a.307.3		8	5.3	odd	4
1050.2.m.a.643.3		8	35.34	odd	2
1050.2.m.b.307.4		8	35.13	even	4
1050.2.m.b.643.4		8	5.4	even	2
1680.2.cz.a.97.1		8	20.7	even	4
1680.2.cz.a.433.1		8	28.27	even	2
1680.2.cz.b.97.4		8	140.27	odd	4
1680.2.cz.b.433.4		8	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(2.23483 + 0.0743018i) q^{5} -1.00000i q^{6} +(0.781409 - 2.52773i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(2.23483 + 0.0743018i) q^{5} -1.00000i q^{6} +(0.781409 - 2.52773i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(-1.63280 + 1.52773i) q^{10} +4.90685 q^{11} +(0.707107 + 0.707107i) q^{12} +(-3.41421 + 3.41421i) q^{13} +(1.23483 + 2.33991i) q^{14} +(-1.63280 + 1.52773i) q^{15} -1.00000 q^{16} +(2.74632 + 2.74632i) q^{17} +(0.707107 + 0.707107i) q^{18} +1.26561 q^{19} +(0.0743018 - 2.23483i) q^{20} +(1.23483 + 2.33991i) q^{21} +(-3.46967 + 3.46967i) q^{22} +(-1.05545 - 1.05545i) q^{23} -1.00000 q^{24} +(4.98896 + 0.332104i) q^{25} -4.82843i q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.52773 - 0.781409i) q^{28} +4.76687i q^{29} +(0.0743018 - 2.23483i) q^{30} -7.05545i q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.46967 + 3.46967i) q^{33} -3.88388 q^{34} +(1.93413 - 5.59099i) q^{35} -1.00000 q^{36} +(-4.74632 + 4.74632i) q^{37} +(-0.894921 + 0.894921i) q^{38} -4.82843i q^{39} +(1.52773 + 1.63280i) q^{40} -5.44670i q^{41} +(-2.52773 - 0.781409i) q^{42} +(-7.58667 - 7.58667i) q^{43} -4.90685i q^{44} +(0.0743018 - 2.23483i) q^{45} +1.49264 q^{46} +(0.734390 + 0.734390i) q^{47} +(0.707107 - 0.707107i) q^{48} +(-5.77880 - 3.95037i) q^{49} +(-3.76256 + 3.29289i) q^{50} -3.88388 q^{51} +(3.41421 + 3.41421i) q^{52} +(1.26561 + 1.26561i) q^{53} -1.00000 q^{54} +(10.9660 + 0.364588i) q^{55} +(2.33991 - 1.23483i) q^{56} +(-0.894921 + 0.894921i) q^{57} +(-3.37069 - 3.37069i) q^{58} +1.39735 q^{59} +(1.52773 + 1.63280i) q^{60} -2.29721i q^{61} +(4.98896 + 4.98896i) q^{62} +(-2.52773 - 0.781409i) q^{63} +1.00000i q^{64} +(-7.88388 + 7.37652i) q^{65} -4.90685i q^{66} +(3.05545 - 3.05545i) q^{67} +(2.74632 - 2.74632i) q^{68} +1.49264 q^{69} +(2.58579 + 5.32106i) q^{70} -13.0334 q^{71} +(0.707107 - 0.707107i) q^{72} +(5.04441 - 5.04441i) q^{73} -6.71231i q^{74} +(-3.76256 + 3.29289i) q^{75} -1.26561i q^{76} +(3.83425 - 12.4032i) q^{77} +(3.41421 + 3.41421i) q^{78} +14.8063i q^{79} +(-2.23483 - 0.0743018i) q^{80} -1.00000 q^{81} +(3.85140 + 3.85140i) q^{82} +(-9.29809 + 9.29809i) q^{83} +(2.33991 - 1.23483i) q^{84} +(5.93351 + 6.34162i) q^{85} +10.7292 q^{86} +(-3.37069 - 3.37069i) q^{87} +(3.46967 + 3.46967i) q^{88} -15.3596 q^{89} +(1.52773 + 1.63280i) q^{90} +(5.96230 + 11.2981i) q^{91} +(-1.05545 + 1.05545i) q^{92} +(4.98896 + 4.98896i) q^{93} -1.03858 q^{94} +(2.82843 + 0.0940371i) q^{95} +1.00000i q^{96} +(-8.42614 - 8.42614i) q^{97} +(6.87957 - 1.29289i) q^{98} -4.90685i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{7}+O(q^{10}) \) 8 * q + 4 * q^7	\( 8 q + 4 q^{7} - 4 q^{10} + 8 q^{11} - 16 q^{13} - 8 q^{14} - 4 q^{15} - 8 q^{16} + 12 q^{17} - 8 q^{19} + 4 q^{20} - 8 q^{21} + 8 q^{22} + 16 q^{23} - 8 q^{24} - 4 q^{25} - 8 q^{28} + 4 q^{30} + 8 q^{33} + 16 q^{34} + 8 q^{35} - 8 q^{36} - 28 q^{37} - 4 q^{38} - 8 q^{42} + 4 q^{45} - 8 q^{46} + 24 q^{47} + 4 q^{49} + 16 q^{51} + 16 q^{52} - 8 q^{53} - 8 q^{54} + 28 q^{55} + 4 q^{56} - 4 q^{57} - 12 q^{58} + 8 q^{59} - 4 q^{62} - 8 q^{63} - 16 q^{65} + 12 q^{68} - 8 q^{69} + 32 q^{70} + 8 q^{71} - 28 q^{73} - 44 q^{77} + 16 q^{78} - 8 q^{81} + 24 q^{82} - 16 q^{83} + 4 q^{84} + 28 q^{85} + 8 q^{86} - 12 q^{87} - 8 q^{88} - 64 q^{89} - 8 q^{91} + 16 q^{92} - 4 q^{93} + 8 q^{94} - 28 q^{97}+O(q^{100}) \) 8 * q + 4 * q^7 - 4 * q^10 + 8 * q^11 - 16 * q^13 - 8 * q^14 - 4 * q^15 - 8 * q^16 + 12 * q^17 - 8 * q^19 + 4 * q^20 - 8 * q^21 + 8 * q^22 + 16 * q^23 - 8 * q^24 - 4 * q^25 - 8 * q^28 + 4 * q^30 + 8 * q^33 + 16 * q^34 + 8 * q^35 - 8 * q^36 - 28 * q^37 - 4 * q^38 - 8 * q^42 + 4 * q^45 - 8 * q^46 + 24 * q^47 + 4 * q^49 + 16 * q^51 + 16 * q^52 - 8 * q^53 - 8 * q^54 + 28 * q^55 + 4 * q^56 - 4 * q^57 - 12 * q^58 + 8 * q^59 - 4 * q^62 - 8 * q^63 - 16 * q^65 + 12 * q^68 - 8 * q^69 + 32 * q^70 + 8 * q^71 - 28 * q^73 - 44 * q^77 + 16 * q^78 - 8 * q^81 + 24 * q^82 - 16 * q^83 + 4 * q^84 + 28 * q^85 + 8 * q^86 - 12 * q^87 - 8 * q^88 - 64 * q^89 - 8 * q^91 + 16 * q^92 - 4 * q^93 + 8 * q^94 - 28 * q^97

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