LMFDB - Embedded newform 210.2.m.b.13.1

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			13.1
Root			$-2.16053i$ of defining polynomial
Character	$\chi$	$=$	210.13
Dual form			210.2.m.b.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-2.23483 - 0.0743018i) q^{5} +1.00000i q^{6} +(2.52773 - 0.781409i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(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} +(2.52773 - 0.781409i) 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} +(-0.781409 - 2.52773i) 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} +(-5.70711 + 1.55850i) 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} +(0.781409 + 2.52773i) 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} +(-0.781409 - 2.52773i) 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} +(2.93351 - 5.13756i) 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} +(12.4032 - 3.83425i) 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} +(-1.29289 + 6.87957i) q^{98} -4.90685i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{7}+O(q^{10}) $ 8 * q + 8 * q^7	$ 8 q + 8 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} - 4 q^{28} + 4 q^{30} - 8 q^{33} - 16 q^{34} - 40 q^{35} - 8 q^{36} - 28 q^{37} + 4 q^{38} + 4 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} - 4 q^{63} - 16 q^{65} - 12 q^{68} + 8 q^{69} + 4 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} - 16 q^{98}+O(q^{100}) $ 8 * q + 8 * 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 - 4 * q^28 + 4 * q^30 - 8 * q^33 - 16 * q^34 - 40 * q^35 - 8 * q^36 - 28 * q^37 + 4 * q^38 + 4 * 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 - 4 * q^63 - 16 * q^65 - 12 * q^68 + 8 * q^69 + 4 * 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 - 16 * q^98

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
$7$	2.52773	−	0.781409i	0.955391	−	0.295345i
$7$	2.52773	−	0.781409i	0.955391	−	0.295345i
$8$	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	−0.0517287	−	0.998661i	$-0.516473\pi$
$13$	3.41421	−	3.41421i	0.946932	−	0.946932i	0.998661	+	0.0517287i	$0.0164731\pi$
$14$	−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	0.290726	−	0.956806i	$-0.406103\pi$
$17$	−2.74632	−	2.74632i	−0.666080	−	0.666080i	−0.956806	+	0.290726i	$0.906103\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	−1.26561			−0.290351			−0.145175	−	0.989406i	$-0.546375\pi$
$19$	−1.26561			−0.290351			−0.145175	+	0.989406i	$0.546375\pi$
$20$	−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
$28$	−0.781409	−	2.52773i	−0.147672	−	0.477695i
$29$			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	$0.218423\pi$
$31$			7.05545i			1.26720i	−0.773662	+	0.633598i	$0.781577\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	3.46967	−	3.46967i	0.603991	−	0.603991i
$34$	3.88388			0.666080
$35$	−5.70711	+	1.55850i	−0.964677	+	0.263435i
$36$	−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	$0.139837\pi$
$41$			5.44670i			0.850631i	−0.905045	+	0.425316i	$0.860163\pi$
$42$	0.781409	+	2.52773i	0.120574	+	0.390037i
$43$	−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	0.651514	−	0.758636i	$-0.274134\pi$
$47$	−0.734390	−	0.734390i	−0.107122	−	0.107122i	−0.758636	+	0.651514i	$0.774134\pi$
$48$	−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	$-0.528993\pi$
$59$	−1.39735			−0.181919			−0.0909594	+	0.995855i	$0.528993\pi$
$60$	1.52773	+	1.63280i	0.197229	+	0.210794i
$61$			2.29721i			0.294127i	0.989127	+	0.147064i	$0.0469822\pi$
$61$			2.29721i			0.294127i	−0.989127	+	0.147064i	$0.953018\pi$
$62$	−4.98896	−	4.98896i	−0.633598	−	0.633598i
$63$	−0.781409	−	2.52773i	−0.0984482	−	0.318464i
$64$			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
$70$	2.93351	−	5.13756i	0.350621	−	0.614056i
$71$	−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	−0.937740	−	0.347337i	$-0.887086\pi$
$73$	−5.04441	+	5.04441i	−0.590404	+	0.590404i	0.347337	+	0.937740i	$0.387086\pi$
$74$		−	6.71231i		−	0.780290i
$75$	3.76256	−	3.29289i	0.434463	−	0.380231i
$76$			1.26561i			0.145175i
$77$	12.4032	−	3.83425i	1.41347	−	0.436954i
$78$	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	$-0.493374\pi$
$83$	9.29809	−	9.29809i	1.02060	−	1.02060i	0.999783	−	0.0208150i	$-0.00662610\pi$
$84$	−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	$-0.197253\pi$
$89$	15.3596			1.62812			0.814060	+	0.580781i	$0.197253\pi$
$90$	−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	0.990810	−	0.135264i	$-0.0431884\pi$
$97$	8.42614	+	8.42614i	0.855545	+	0.855545i	−0.135264	+	0.990810i	$0.543188\pi$
$98$	−1.29289	+	6.87957i	−0.130602	+	0.694941i
$99$		−	4.90685i		−	0.493157i
$100$	0.332104	−	4.98896i	0.0332104	−	0.498896i
$101$		−	18.1504i		−	1.80603i	−0.429609	−	0.903015i	$-0.641349\pi$
$101$		−	18.1504i		−	1.80603i	0.429609	−	0.903015i	$-0.358651\pi$
$102$	2.74632	−	2.74632i	0.271926	−	0.271926i
$103$	−8.36459	+	8.36459i	−0.824187	+	0.824187i	−0.986706	−	0.162518i	$-0.948038\pi$
$103$	−8.36459	+	8.36459i	−0.824187	+	0.824187i	0.162518	+	0.986706i	$0.448038\pi$
$104$	4.82843			0.473466
$105$	−2.93351	+	5.13756i	−0.286281	+	0.501375i
$106$	−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
$112$	−2.52773	+	0.781409i	−0.238848	+	0.0738362i
$113$	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	$0.189496\pi$
$131$			12.8367i			1.12154i	−0.827970	+	0.560772i	$0.810504\pi$
$132$	−3.46967	−	3.46967i	−0.301996	−	0.301996i
$133$	−3.19912	+	0.988958i	−0.277399	+	0.0857536i
$134$			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	$-0.552972\pi$
$139$	−3.90596			−0.331299			−0.165650	+	0.986185i	$0.552972\pi$
$140$	1.55850	+	5.70711i	0.131718	+	0.482339i
$141$	−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
$147$	1.29289	−	6.87957i	0.106636	−	0.567417i
$148$	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	$0.0316868\pi$
$157$	13.7132	+	13.7132i	1.09443	+	1.09443i	0.0993827	+	0.995049i	$0.468313\pi$
$158$	−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	0.917910	−	0.396788i	$-0.129875\pi$
$167$	6.73439	+	6.73439i	0.521123	+	0.521123i	−0.396788	+	0.917910i	$0.629875\pi$
$168$	2.52773	−	0.781409i	0.195018	−	0.0602870i
$169$		−	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	$0.525426\pi$
$173$	−14.1605	+	14.1605i	−1.07661	+	1.07661i	−0.996811	+	0.0797939i	$0.974574\pi$
$174$	−4.76687			−0.361376
$175$	12.8702	−	3.05895i	0.972898	−	0.231235i
$176$	−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	$-0.743798\pi$
$181$		−	19.3934i		−	1.44150i	0.693196	−	0.720749i	$-0.256202\pi$
$182$	3.77297	+	12.2049i	0.279671	+	0.904691i
$183$	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	$-0.636743\pi$
$199$	−11.7509			−0.832999			−0.416499	+	0.909136i	$0.636743\pi$
$200$	3.29289	+	3.76256i	0.232843	+	0.266053i
$201$		−	4.32106i		−	0.304784i
$202$	12.8343	+	12.8343i	0.903015	+	0.903015i
$203$	3.72488	+	12.0494i	0.261435	+	0.845699i
$204$			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
$210$	−1.55850	−	5.70711i	−0.107547	−	0.393828i
$211$	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
$217$	5.51319	+	17.8343i	0.374260	+	1.21067i
$218$	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	−0.374181	−	0.927356i	$-0.622076\pi$
$223$	8.26067	−	8.26067i	0.553175	−	0.553175i	0.927356	+	0.374181i	$0.122076\pi$
$224$	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	0.483106	−	0.875562i	$-0.339509\pi$
$227$	−5.91295	−	5.91295i	−0.392456	−	0.392456i	−0.875562	+	0.483106i	$0.839509\pi$
$228$	0.894921	+	0.894921i	0.0592676	+	0.0592676i
$229$	9.31371			0.615467			0.307734	−	0.951473i	$-0.400429\pi$
$229$	9.31371			0.615467			0.307734	+	0.951473i	$0.400429\pi$
$230$	−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
$238$	9.81739	−	3.03490i	0.636367	−	0.196723i
$239$			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	$0.0371532\pi$
$241$			3.61574i			0.232910i	−0.993196	+	0.116455i	$0.962847\pi$
$242$	−9.24695	+	9.24695i	−0.594417	+	0.594417i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	2.29721			0.147064
$245$	−13.2082	+	8.39905i	−0.843839	+	0.536596i
$246$	−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	$-0.951706\pi$
$251$		−	4.78896i		−	0.302276i	0.988513	−	0.151138i	$-0.0482938\pi$
$252$	−2.52773	+	0.781409i	−0.159232	+	0.0492241i
$253$	−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	$-0.879846\pi$
$257$	−20.8113	−	20.8113i	−1.29817	−	1.29817i	−0.368574	−	0.929599i	$-0.620154\pi$
$258$	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	$-0.630971\pi$
$269$	−13.1192			−0.799890			−0.399945	+	0.916539i	$0.630971\pi$
$270$	−2.23483	−	0.0743018i	−0.136008	−	0.00452186i
$271$		−	18.0836i		−	1.09850i	−0.835658	−	0.549250i	$-0.814913\pi$
$271$		−	18.0836i		−	1.09850i	0.835658	−	0.549250i	$-0.185087\pi$
$272$	2.74632	+	2.74632i	0.166520	+	0.166520i
$273$	−3.77297	−	12.2049i	−0.228351	−	0.738677i
$274$		−	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
$280$	−5.13756	−	2.93351i	−0.307028	−	0.175310i
$281$	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	−0.950682	−	0.310168i	$-0.899615\pi$
$283$	−10.7751	+	10.7751i	−0.640514	+	0.640514i	0.310168	+	0.950682i	$0.399615\pi$
$284$			13.0334i			0.773388i
$285$	2.06649	−	1.93351i	0.122409	−	0.114531i
$286$			23.6924i			1.40096i
$287$	4.25610	+	13.7678i	0.251229	+	0.812685i
$288$	−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	−0.608763	−	0.793352i	$-0.708334\pi$
$293$	3.15965	−	3.15965i	0.184588	−	0.184588i	0.793352	+	0.608763i	$0.208334\pi$
$294$	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	$-0.932868\pi$
$307$	−20.8011	−	20.8011i	−1.18718	−	1.18718i	−0.209340	−	0.977843i	$-0.567132\pi$
$308$	−3.83425	−	12.4032i	−0.218477	−	0.706736i
$309$			11.8293i			0.672946i
$310$	10.7788	+	11.5202i	0.612195	+	0.654302i
$311$			11.4706i			0.650435i	0.945639	+	0.325218i	$0.105438\pi$
$311$			11.4706i			0.650435i	−0.945639	+	0.325218i	$0.894562\pi$
$312$	3.41421	−	3.41421i	0.193292	−	0.193292i
$313$	−0.612443	+	0.612443i	−0.0346173	+	0.0346173i	−0.724204	−	0.689586i	$-0.757792\pi$
$313$	−0.612443	+	0.612443i	−0.0346173	+	0.0346173i	0.689586	+	0.724204i	$0.257792\pi$
$314$	−19.3934			−1.09443
$315$	1.55850	+	5.70711i	0.0878117	+	0.321559i
$316$	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
$322$	3.77297	−	1.16636i	0.210260	−	0.0649986i
$323$	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
$343$	11.5204	−	14.5011i	0.622042	−	0.782984i
$344$		−	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	$-0.456343\pi$
$349$	5.10838			0.273445			0.136723	+	0.990609i	$0.456343\pi$
$350$	−6.93763	+	11.2636i	−0.370832	+	0.602066i
$351$	−4.82843			−0.257722
$352$	3.46967	−	3.46967i	0.184934	−	0.184934i
$353$	−12.0821	+	12.0821i	−0.643066	+	0.643066i	−0.951308	−	0.308242i	$-0.900259\pi$
$353$	−12.0821	+	12.0821i	−0.643066	+	0.643066i	0.308242	+	0.951308i	$0.400259\pi$
$354$		−	1.39735i		−	0.0742681i
$355$	29.1274	+	0.968403i	1.54592	+	0.0513975i
$356$		−	15.3596i		−	0.814060i
$357$	−9.81739	+	3.03490i	−0.519591	+	0.160624i
$358$	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	0.803328	−	0.595536i	$-0.203060\pi$
$367$	3.98072	+	3.98072i	0.207792	+	0.207792i	−0.595536	+	0.803328i	$0.703060\pi$
$368$	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
$378$	2.52773	−	0.781409i	0.130012	−	0.0401913i
$379$		−	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	−0.863138	−	0.504968i	$-0.831504\pi$
$383$	−7.00951	+	7.00951i	−0.358169	+	0.358169i	0.504968	+	0.863138i	$0.331504\pi$
$384$	−1.00000			−0.0510310
$385$	−28.0039	+	7.64734i	−1.42721	+	0.389745i
$386$	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
$392$	6.87957	+	1.29289i	0.347471	+	0.0653010i
$393$	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	0.0275544	−	0.999620i	$-0.491228\pi$
$397$	−19.3683	−	19.3683i	−0.972066	−	0.972066i	−0.999620	+	0.0275544i	$0.991228\pi$
$398$	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	$-0.350368\pi$
$409$	18.3211			0.905918			0.452959	+	0.891531i	$0.350368\pi$
$410$	8.32106	+	8.89339i	0.410948	+	0.439213i
$411$			5.12563i			0.252829i
$412$	8.36459	+	8.36459i	0.412094	+	0.412094i
$413$	−3.53211	+	1.09190i	−0.173804	+	0.0537288i
$414$		−	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	$-0.457138\pi$
$419$	5.49605			0.268500			0.134250	+	0.990948i	$0.457138\pi$
$420$	5.13756	+	2.93351i	0.250687	+	0.143140i
$421$	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
$427$	1.79506	+	5.80671i	0.0868689	+	0.281006i
$428$	−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	−0.986510	−	0.163700i	$-0.947657\pi$
$433$	−17.1216	+	17.1216i	−0.822811	+	0.822811i	0.163700	+	0.986510i	$0.447657\pi$
$434$	−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	$-0.173500\pi$
$439$	35.8323			1.71018			0.855092	+	0.518476i	$0.173500\pi$
$440$	−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
$448$	0.781409	+	2.52773i	0.0369181	+	0.119424i
$449$		−	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
$455$	−14.1642	+	24.8063i	−0.664029	+	1.16294i
$456$	−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	$0.00636599\pi$
$461$			0.858751i			0.0399960i	−0.999800	+	0.0199980i	$0.993634\pi$
$462$	3.83425	+	12.4032i	0.178386	+	0.577048i
$463$	−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	0.474181	−	0.880428i	$-0.342744\pi$
$467$	−8.77908	−	8.77908i	−0.406247	−	0.406247i	−0.880428	+	0.474181i	$0.842744\pi$
$468$	−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	$-0.491479\pi$
$479$	1.17157			0.0535305			0.0267653	+	0.999642i	$0.491479\pi$
$480$	−0.0743018	+	2.23483i	−0.00339140	+	0.102006i
$481$			32.4099i			1.47776i
$482$	−2.55672	−	2.55672i	−0.116455	−	0.116455i
$483$	−3.77297	+	1.16636i	−0.171676	+	0.0530711i
$484$		−	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
$490$	3.40056	−	15.2786i	0.153622	−	0.690218i
$491$	−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
$497$	−32.9448	+	10.1844i	−1.47778	+	0.456832i
$498$	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	−0.593025	−	0.805184i	$-0.702066\pi$
$503$	4.75825	−	4.75825i	0.212160	−	0.212160i	0.805184	+	0.593025i	$0.202066\pi$
$504$	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	$-0.147714\pi$
$509$	40.3501			1.78849			0.894243	+	0.447581i	$0.147714\pi$
$510$	−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
$518$	−5.24505	−	16.9669i	−0.230454	−	0.745482i
$519$			20.0260i			0.879045i
$520$	−10.7907	−	0.358761i	−0.473205	−	0.0157327i
$521$			8.96879i			0.392930i	0.980511	+	0.196465i	$0.0629462\pi$
$521$			8.96879i			0.392930i	−0.980511	+	0.196465i	$0.937054\pi$
$522$	−3.37069	+	3.37069i	−0.147531	+	0.147531i
$523$	8.40290	−	8.40290i	0.367433	−	0.367433i	−0.499107	−	0.866540i	$-0.666339\pi$
$523$	8.40290	−	8.40290i	0.367433	−	0.367433i	0.866540	+	0.499107i	$0.166339\pi$
$524$	12.8367			0.560772
$525$	6.93763	−	11.2636i	0.302783	−	0.491585i
$526$	−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
$532$	0.988958	+	3.19912i	0.0428768	+	0.138699i
$533$	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
$553$	11.5698	+	37.4264i	0.491998	+	1.59153i
$554$			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
$560$	5.70711	−	1.55850i	0.241169	−	0.0658588i
$561$	−19.0576			−0.804613
$562$	−14.4645	+	14.4645i	−0.610146	+	0.610146i
$563$	7.84316	−	7.84316i	0.330550	−	0.330550i	−0.522246	−	0.852795i	$-0.674906\pi$
$563$	7.84316	−	7.84316i	0.330550	−	0.330550i	0.852795	+	0.522246i	$0.174906\pi$
$564$			1.03858i			0.0437323i
$565$	−4.39124	−	4.69328i	−0.184741	−	0.197448i
$566$		−	15.2383i		−	0.640514i
$567$	−2.52773	+	0.781409i	−0.106155	+	0.0328161i
$568$	−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	0.905323	−	0.424723i	$-0.139629\pi$
$577$	11.5444	+	11.5444i	0.480600	+	0.480600i	−0.424723	+	0.905323i	$0.639629\pi$
$578$	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	0.840632	−	0.541607i	$-0.182184\pi$
$587$	7.24478	+	7.24478i	0.299024	+	0.299024i	−0.541607	+	0.840632i	$0.682184\pi$
$588$	−6.87957	−	1.29289i	−0.283709	−	0.0533180i
$589$		−	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	−0.556605	−	0.830777i	$-0.687896\pi$
$593$	6.67652	−	6.67652i	0.274172	−	0.274172i	0.830777	+	0.556605i	$0.187896\pi$
$594$	4.90685			0.201330
$595$	19.9537	+	11.3934i	0.818021	+	0.467083i
$596$	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	$-0.923301\pi$
$601$		−	11.7003i		−	0.477265i	0.971110	−	0.238632i	$-0.0766991\pi$
$602$	27.1204	−	8.38387i	1.10535	−	0.341701i
$603$	−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	0.0538519	−	0.998549i	$-0.482850\pi$
$607$	−23.2749	−	23.2749i	−0.944697	−	0.944697i	−0.998549	+	0.0538519i	$0.982850\pi$
$608$	−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	$-0.789016\pi$
$619$	−39.2232			−1.57651			−0.788257	+	0.615346i	$0.789016\pi$
$620$	−15.7678	−	0.524233i	−0.633248	−	0.0210537i
$621$			1.49264i			0.0598974i
$622$	−8.11091	−	8.11091i	−0.325218	−	0.325218i
$623$	38.8250	−	12.0022i	1.55549	−	0.480856i
$624$			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
$630$	−5.13756	−	2.93351i	−0.204685	−	0.116874i
$631$	−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
$637$	6.24264	−	33.2175i	0.247342	−	1.31612i
$638$	−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	−0.375089	−	0.926989i	$-0.622388\pi$
$643$	13.9948	−	13.9948i	0.551900	−	0.551900i	0.926989	+	0.375089i	$0.122388\pi$
$644$	−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	0.596797	−	0.802392i	$-0.296440\pi$
$647$	−5.22955	−	5.22955i	−0.205595	−	0.205595i	−0.802392	+	0.596797i	$0.796440\pi$
$648$	−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
$658$	2.62526	−	0.811559i	0.102343	−	0.0316379i
$659$			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	$0.0986892\pi$
$661$			15.6881i			0.610196i	−0.952321	+	0.305098i	$0.901311\pi$
$662$	−7.19543	+	7.19543i	−0.279658	+	0.279658i
$663$	−13.2604	+	13.2604i	−0.514991	+	0.514991i
$664$	13.1495			0.510299
$665$	7.22297	−	1.97246i	0.280095	−	0.0764886i
$666$	−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
$672$	−0.781409	−	2.52773i	−0.0301435	−	0.0975092i
$673$	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	0.779637	−	0.626232i	$-0.215404\pi$
$677$	3.99149	+	3.99149i	0.153405	+	0.153405i	−0.626232	+	0.779637i	$0.715404\pi$
$678$	−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	$0.0148612\pi$
$691$			2.45366i			0.0933418i	−0.998910	+	0.0466709i	$0.985139\pi$
$692$	14.1605	+	14.1605i	0.538303	+	0.538303i
$693$	−3.83425	−	12.4032i	−0.145651	−	0.471158i
$694$		−	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
$700$	−3.05895	−	12.8702i	−0.115617	−	0.486449i
$701$	−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
$707$	−14.1829	−	45.8792i	−0.533401	−	1.72546i
$708$	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	$-0.660457\pi$
$719$	−25.9031			−0.966021			−0.483011	+	0.875614i	$0.660457\pi$
$720$	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	$0.151970\pi$
$727$	36.3373	+	36.3373i	1.34768	+	1.34768i	0.459495	+	0.888180i	$0.348030\pi$
$728$	12.2049	−	3.77297i	0.452345	−	0.139836i
$729$			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	−0.959525	−	0.281622i	$-0.909128\pi$
$733$	−18.3535	+	18.3535i	−0.677904	+	0.677904i	0.281622	+	0.959525i	$0.409128\pi$
$734$	−5.62959			−0.207792
$735$	−3.40056	+	15.2786i	−0.125432	+	0.563560i
$736$	−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
$742$	−4.52423	+	1.39860i	−0.166090	+	0.0513442i
$743$	−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	$-0.671663\pi$
$761$		−	47.3418i		−	1.71614i	0.513532	−	0.858070i	$-0.328337\pi$
$762$	−11.1761	−	11.1761i	−0.404869	−	0.404869i
$763$	−0.0680216	−	0.220039i	−0.00246255	−	0.00796593i
$764$			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	$-0.792151\pi$
$769$	−44.0520			−1.58856			−0.794278	+	0.607554i	$0.792151\pi$
$770$	14.3943	−	25.2092i	0.518733	−	0.908478i
$771$	−29.4316			−1.05995
$772$	−4.81370	+	4.81370i	−0.173249	+	0.173249i
$773$	−11.1336	+	11.1336i	−0.400448	+	0.400448i	−0.878391	−	0.477943i	$-0.841383\pi$
$773$	−11.1336	+	11.1336i	−0.400448	+	0.400448i	0.477943	+	0.878391i	$0.341383\pi$
$774$		−	10.7292i		−	0.385652i
$775$	−2.34315	+	35.1994i	−0.0841683	+	1.26440i
$776$			11.9164i			0.427773i
$777$	5.24505	+	16.9669i	0.188165	+	0.608683i
$778$	−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	0.466901	−	0.884310i	$-0.345370\pi$
$787$	−11.7098	−	11.7098i	−0.417409	−	0.417409i	−0.884310	+	0.466901i	$0.845370\pi$
$788$	−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	0.444847	−	0.895607i	$-0.353258\pi$
$797$	−12.7255	−	12.7255i	−0.450760	−	0.450760i	−0.895607	+	0.444847i	$0.853258\pi$
$798$	−0.988958	−	3.19912i	−0.0350088	−	0.113247i
$799$			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
$805$	7.66851	+	4.37866i	0.270279	+	0.154327i
$806$	−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	$-0.995964\pi$
$811$		−	0.722188i		−	0.0253595i	0.999920	−	0.0126797i	$-0.00403619\pi$
$812$	12.0494	−	3.72488i	0.422849	−	0.130718i
$813$	−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	$-0.381142\pi$
$829$	21.0061			0.729571			0.364786	+	0.931092i	$0.381142\pi$
$830$	0.977031	−	29.3869i	0.0339132	−	1.02003i
$831$		−	3.72704i		−	0.129289i
$832$	3.41421	+	3.41421i	0.118367	+	0.118367i
$833$	−26.7194	−	5.02144i	−0.925773	−	0.173983i
$834$		−	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	$-0.834644\pi$
$839$	−50.2886			−1.73615			−0.868077	+	0.496430i	$0.834644\pi$
$840$	−5.70711	+	1.55850i	−0.196914	+	0.0537735i
$841$	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
$847$	33.0555	−	10.2186i	1.13580	−	0.351116i
$848$	−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	−0.444853	−	0.895604i	$-0.646744\pi$
$853$	13.1647	−	13.1647i	0.450751	−	0.450751i	0.895604	+	0.444853i	$0.146744\pi$
$854$	−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	0.957478	−	0.288505i	$-0.0931583\pi$
$857$	19.5839	+	19.5839i	0.668973	+	0.668973i	−0.288505	+	0.957478i	$0.593158\pi$
$858$	16.7530	+	16.7530i	0.571939	+	0.571939i
$859$	−7.58185			−0.258689			−0.129345	−	0.991600i	$-0.541287\pi$
$859$	−7.58185			−0.258689			−0.129345	+	0.991600i	$0.541287\pi$
$860$	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
$868$	17.8343	−	5.51319i	0.605334	−	0.187130i
$869$			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
$875$	−28.9901	+	5.87995i	−0.980044	+	0.198779i
$876$	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	$-0.820033\pi$
$881$		−	31.8033i		−	1.07148i	0.844383	−	0.535740i	$-0.179967\pi$
$882$	6.87957	+	1.29289i	0.231647	+	0.0435340i
$883$	−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	0.824570	−	0.565760i	$-0.191417\pi$
$887$	7.70801	+	7.70801i	0.258810	+	0.258810i	−0.565760	+	0.824570i	$0.691417\pi$
$888$	−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
$903$	−27.1204	+	8.38387i	−0.902511	+	0.278998i
$904$			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
$910$	−7.52512	−	27.5563i	−0.249455	−	0.913484i
$911$	−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
$917$	10.0307	+	32.4476i	0.331242	+	1.07151i
$918$	−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	$-0.443273\pi$
$929$	10.8063			0.354545			0.177272	+	0.984162i	$0.443273\pi$
$930$	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	0.762233	−	0.647303i	$-0.224103\pi$
$937$	3.51804	+	3.51804i	0.114929	+	0.114929i	−0.647303	+	0.762233i	$0.724103\pi$
$938$	3.37652	+	10.9225i	0.110247	+	0.356631i
$939$			0.866125i			0.0282649i
$940$	1.69581	−	1.58667i	0.0553111	−	0.0517516i
$941$			54.9021i			1.78976i	0.446309	+	0.894879i	$0.352738\pi$
$941$			54.9021i			1.78976i	−0.446309	+	0.894879i	$0.647262\pi$
$942$	−13.7132	+	13.7132i	−0.446800	+	0.446800i
$943$	5.74873	−	5.74873i	0.187204	−	0.187204i
$944$	1.39735			0.0454797
$945$	5.13756	+	2.93351i	0.167125	+	0.0954269i
$946$	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
$952$	−3.03490	−	9.81739i	−0.0983616	−	0.318183i
$953$	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	$-0.731721\pi$
$971$		−	46.5248i		−	1.49305i	0.665357	−	0.746525i	$-0.268279\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	−9.87321	+	3.05215i	−0.316520	+	0.0978475i
$974$			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
$980$	8.39905	+	13.2082i	0.268298	+	0.421920i
$981$	−0.0870500			−0.00277929
$982$	11.9770	−	11.9770i	0.382202	−	0.382202i
$983$	−1.34529	+	1.34529i	−0.0429079	+	0.0429079i	−0.728235	−	0.685327i	$-0.759659\pi$
$983$	−1.34529	+	1.34529i	−0.0429079	+	0.0429079i	0.685327	+	0.728235i	$0.259659\pi$
$984$			5.44670i			0.173634i
$985$	−30.0958	+	28.1590i	−0.958932	+	0.897220i
$986$			18.5140i			0.589605i
$987$	−2.62526	+	0.811559i	−0.0835629	+	0.0258322i
$988$	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	0.00121964	−	0.999999i	$-0.499612\pi$
$997$	−31.5368	−	31.5368i	−0.998780	−	0.998780i	−0.999999	+	0.00121964i	$0.999612\pi$
$998$	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.b.13.1	yes	8
3.2	odd	2		630.2.p.c.433.4		8
4.3	odd	2		1680.2.cz.a.433.1		8
5.2	odd	4		210.2.m.a.97.2	yes	8
5.3	odd	4		1050.2.m.b.307.4		8
5.4	even	2		1050.2.m.a.643.3		8
7.6	odd	2		210.2.m.a.13.2	✓	8
15.2	even	4		630.2.p.b.307.3		8
20.7	even	4		1680.2.cz.b.97.4		8
21.20	even	2		630.2.p.b.433.3		8
28.27	even	2		1680.2.cz.b.433.4		8
35.13	even	4		1050.2.m.a.307.3		8
35.27	even	4	inner	210.2.m.b.97.1	yes	8
35.34	odd	2		1050.2.m.b.643.4		8
105.62	odd	4		630.2.p.c.307.4		8
140.27	odd	4		1680.2.cz.a.97.1		8

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-2.23483 - 0.0743018i) q^{5} +1.00000i q^{6} +(2.52773 - 0.781409i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(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} +(2.52773 - 0.781409i) 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} +(-0.781409 - 2.52773i) 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} +(-5.70711 + 1.55850i) 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} +(0.781409 + 2.52773i) 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} +(-0.781409 - 2.52773i) 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} +(2.93351 - 5.13756i) 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} +(12.4032 - 3.83425i) 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} +(-1.29289 + 6.87957i) q^{98} -4.90685i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{7}+O(q^{10}) \) 8 * q + 8 * q^7	\( 8 q + 8 q^{7} + 4 q^{10} + 8 q^{11} + 16 q^{13} + 8 q^{14} - 4 q^{15} - 8 q^{16} - 12 q^{17} + 8 q^{19} - 4 q^{20} - 8 q^{21} + 8 q^{22} + 16 q^{23} + 8 q^{24} - 4 q^{25} - 4 q^{28} + 4 q^{30} - 8 q^{33} - 16 q^{34} - 40 q^{35} - 8 q^{36} - 28 q^{37} + 4 q^{38} + 4 q^{42} - 4 q^{45} - 8 q^{46} - 24 q^{47} - 4 q^{49} + 16 q^{51} - 16 q^{52} - 8 q^{53} + 8 q^{54} - 28 q^{55} + 4 q^{56} - 4 q^{57} - 12 q^{58} - 8 q^{59} + 4 q^{62} - 4 q^{63} - 16 q^{65} - 12 q^{68} + 8 q^{69} + 4 q^{70} + 8 q^{71} + 28 q^{73} + 44 q^{77} + 16 q^{78} - 8 q^{81} - 24 q^{82} + 16 q^{83} - 4 q^{84} + 28 q^{85} + 8 q^{86} + 12 q^{87} - 8 q^{88} + 64 q^{89} - 8 q^{91} + 16 q^{92} - 4 q^{93} - 8 q^{94} + 28 q^{97} - 16 q^{98}+O(q^{100}) \) 8 * q + 8 * 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 - 4 * q^28 + 4 * q^30 - 8 * q^33 - 16 * q^34 - 40 * q^35 - 8 * q^36 - 28 * q^37 + 4 * q^38 + 4 * 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 - 4 * q^63 - 16 * q^65 - 12 * q^68 + 8 * q^69 + 4 * 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 - 16 * q^98

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