LMFDB - Embedded newform 637.2.x.a.215.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(19,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 5]))

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

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

chi := DirichletCharacter("637.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.x (of order $12$, degree $4$, not 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			215.1
Character	$\chi$	$=$	637.215
Dual form			637.2.x.a.80.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.629770 + 2.35033i) q^{2} -1.97095i q^{3} +(-3.39540 - 1.96034i) q^{4} +(-0.0608458 - 0.227080i) q^{5} +(4.63238 + 1.24124i) q^{6} +(3.30464 - 3.30464i) q^{8} -0.884626 q^{9} +O(q^{10})$	\(q+(-0.629770 + 2.35033i) q^{2} -1.97095i q^{3} +(-3.39540 - 1.96034i) q^{4} +(-0.0608458 - 0.227080i) q^{5} +(4.63238 + 1.24124i) q^{6} +(3.30464 - 3.30464i) q^{8} -0.884626 q^{9} +0.572032 q^{10} +(-2.02271 + 2.02271i) q^{11} +(-3.86372 + 6.69215i) q^{12} +(-2.03197 + 2.97844i) q^{13} +(-0.447562 + 0.119924i) q^{15} +(1.76516 + 3.05735i) q^{16} +(2.01588 - 3.49161i) q^{17} +(0.557110 - 2.07916i) q^{18} +(3.88663 - 3.88663i) q^{19} +(-0.238557 + 0.890305i) q^{20} +(-3.48019 - 6.02787i) q^{22} +(5.23962 - 3.02510i) q^{23} +(-6.51326 - 6.51326i) q^{24} +(4.28226 - 2.47237i) q^{25} +(-5.72065 - 6.65153i) q^{26} -4.16929i q^{27} +(3.54072 - 6.13271i) q^{29} -1.12744i q^{30} +(-2.22176 - 0.595317i) q^{31} +(0.730993 - 0.195869i) q^{32} +(3.98664 + 3.98664i) q^{33} +(6.93691 + 6.93691i) q^{34} +(3.00366 + 1.73416i) q^{36} +(-10.0386 - 2.68984i) q^{37} +(6.68720 + 11.5826i) q^{38} +(5.87034 + 4.00490i) q^{39} +(-0.951490 - 0.549343i) q^{40} +(-0.0713473 - 0.266272i) q^{41} +(3.91398 - 2.25974i) q^{43} +(10.8331 - 2.90272i) q^{44} +(0.0538258 + 0.200881i) q^{45} +(3.81023 + 14.2200i) q^{46} +(3.14513 - 0.842735i) q^{47} +(6.02588 - 3.47904i) q^{48} +(3.11404 + 11.6218i) q^{50} +(-6.88178 - 3.97320i) q^{51} +(12.7381 - 6.12966i) q^{52} +(-3.96785 - 6.87251i) q^{53} +(9.79921 + 2.62569i) q^{54} +(0.582389 + 0.336242i) q^{55} +(-7.66035 - 7.66035i) q^{57} +(12.1841 + 12.1841i) q^{58} +(0.702149 - 0.188140i) q^{59} +(1.75474 + 0.470182i) q^{60} -2.28077i q^{61} +(2.79839 - 4.84695i) q^{62} +8.90209i q^{64} +(0.799980 + 0.280193i) q^{65} +(-11.8806 + 6.85927i) q^{66} +(1.88222 + 1.88222i) q^{67} +(-13.6895 + 7.90362i) q^{68} +(-5.96230 - 10.3270i) q^{69} +(-0.362587 + 1.35319i) q^{71} +(-2.92337 + 2.92337i) q^{72} +(-3.50729 + 13.0894i) q^{73} +(12.6440 - 21.9001i) q^{74} +(-4.87290 - 8.44011i) q^{75} +(-20.8158 + 5.57758i) q^{76} +(-13.1098 + 11.2751i) q^{78} +(-1.91392 + 3.31501i) q^{79} +(0.586860 - 0.586860i) q^{80} -10.8713 q^{81} +0.670760 q^{82} +(4.19588 - 4.19588i) q^{83} +(-0.915533 - 0.245316i) q^{85} +(2.84623 + 10.6223i) q^{86} +(-12.0872 - 6.97857i) q^{87} +13.3686i q^{88} +(0.893381 - 3.33414i) q^{89} -0.506034 q^{90} -23.7208 q^{92} +(-1.17334 + 4.37896i) q^{93} +7.92283i q^{94} +(-1.11906 - 0.646091i) q^{95} +(-0.386047 - 1.44075i) q^{96} +(2.61723 + 0.701285i) q^{97} +(1.78934 - 1.78934i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{6} - 4 q^{8} - 12 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^6 - 4 * q^8 - 12 * q^9	$ 28 q - 2 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{6} - 4 q^{8} - 12 q^{9} + 12 q^{10} + 2 q^{11} - 8 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} - 4 q^{18} + 8 q^{19} + 36 q^{20} - 8 q^{22} - 6 q^{23} - 12 q^{24} - 24 q^{26} - 8 q^{29} + 38 q^{31} - 20 q^{32} - 18 q^{33} - 12 q^{34} + 54 q^{36} - 16 q^{37} + 28 q^{39} - 48 q^{40} - 18 q^{41} + 48 q^{43} - 6 q^{44} - 12 q^{45} + 18 q^{46} + 42 q^{47} - 12 q^{48} + 10 q^{50} + 12 q^{51} + 28 q^{52} + 12 q^{53} + 30 q^{54} + 6 q^{55} + 12 q^{57} + 62 q^{58} + 6 q^{59} + 16 q^{60} + 36 q^{62} - 2 q^{65} - 66 q^{66} - 4 q^{67} - 30 q^{68} - 42 q^{69} - 42 q^{71} - 38 q^{72} - 14 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} + 4 q^{79} - 12 q^{80} + 12 q^{81} + 108 q^{82} + 66 q^{83} - 54 q^{85} - 30 q^{86} - 42 q^{87} + 30 q^{89} + 72 q^{90} - 156 q^{92} + 14 q^{93} - 6 q^{95} - 18 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^6 - 4 * q^8 - 12 * q^9 + 12 * q^10 + 2 * q^11 - 8 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 - 4 * q^18 + 8 * q^19 + 36 * q^20 - 8 * q^22 - 6 * q^23 - 12 * q^24 - 24 * q^26 - 8 * q^29 + 38 * q^31 - 20 * q^32 - 18 * q^33 - 12 * q^34 + 54 * q^36 - 16 * q^37 + 28 * q^39 - 48 * q^40 - 18 * q^41 + 48 * q^43 - 6 * q^44 - 12 * q^45 + 18 * q^46 + 42 * q^47 - 12 * q^48 + 10 * q^50 + 12 * q^51 + 28 * q^52 + 12 * q^53 + 30 * q^54 + 6 * q^55 + 12 * q^57 + 62 * q^58 + 6 * q^59 + 16 * q^60 + 36 * q^62 - 2 * q^65 - 66 * q^66 - 4 * q^67 - 30 * q^68 - 42 * q^69 - 42 * q^71 - 38 * q^72 - 14 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 + 4 * q^79 - 12 * q^80 + 12 * q^81 + 108 * q^82 + 66 * q^83 - 54 * q^85 - 30 * q^86 - 42 * q^87 + 30 * q^89 + 72 * q^90 - 156 * q^92 + 14 * q^93 - 6 * q^95 - 18 * q^96 - 62 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.629770	+	2.35033i	−0.445314	+	1.66194i	0.269791	+	0.962919i	$0.413046\pi$
$2$	−0.629770	+	2.35033i	−0.445314	+	1.66194i	−0.715105	+	0.699017i	$0.753621\pi$
$3$		−	1.97095i		−	1.13793i	−0.822363	−	0.568963i	$-0.807345\pi$
$3$		−	1.97095i		−	1.13793i	0.822363	−	0.568963i	$-0.192655\pi$
$4$	−3.39540	−	1.96034i	−1.69770	−	0.980168i
$5$	−0.0608458	−	0.227080i	−0.0272111	−	0.101553i	0.950985	−	0.309238i	$-0.100074\pi$
$5$	−0.0608458	−	0.227080i	−0.0272111	−	0.101553i	−0.978196	+	0.207685i	$0.933407\pi$
$6$	4.63238	+	1.24124i	1.89116	+	0.506735i
$7$		0			0
$7$		0			0
$8$	3.30464	−	3.30464i	1.16837	−	1.16837i
$9$	−0.884626			−0.294875
$10$	0.572032			0.180892
$11$	−2.02271	+	2.02271i	−0.609869	+	0.609869i	−0.942912	−	0.333043i	$-0.891925\pi$
$11$	−2.02271	+	2.02271i	−0.609869	+	0.609869i	0.333043	+	0.942912i	$0.391925\pi$
$12$	−3.86372	+	6.69215i	−1.11536	+	1.93186i
$13$	−2.03197	+	2.97844i	−0.563566	+	0.826071i
$13$	−2.03197	+	2.97844i	−0.563566	+	0.826071i
$14$		0			0
$15$	−0.447562	+	0.119924i	−0.115560	+	0.0309642i
$16$	1.76516	+	3.05735i	0.441291	+	0.764338i
$17$	2.01588	−	3.49161i	0.488924	−	0.846841i	−0.510995	−	0.859584i	$-0.670723\pi$
$17$	2.01588	−	3.49161i	0.488924	−	0.846841i	0.999919	+	0.0127429i	$0.00405631\pi$
$18$	0.557110	−	2.07916i	0.131312	−	0.490064i
$19$	3.88663	−	3.88663i	0.891655	−	0.891655i	−0.103024	−	0.994679i	$-0.532852\pi$
$19$	3.88663	−	3.88663i	0.891655	−	0.891655i	0.994679	+	0.103024i	$0.0328518\pi$
$20$	−0.238557	+	0.890305i	−0.0533429	+	0.199078i
$21$		0			0
$22$	−3.48019	−	6.02787i	−0.741979	−	1.28515i
$23$	5.23962	−	3.02510i	1.09254	−	0.630776i	0.158286	−	0.987393i	$-0.449403\pi$
$23$	5.23962	−	3.02510i	1.09254	−	0.630776i	0.934251	+	0.356617i	$0.116070\pi$
$24$	−6.51326	−	6.51326i	−1.32951	−	1.32951i
$25$	4.28226	−	2.47237i	0.856453	−	0.494473i
$26$	−5.72065	−	6.65153i	−1.12191	−	1.30447i
$27$		−	4.16929i		−	0.802380i
$28$		0			0
$29$	3.54072	−	6.13271i	0.657495	−	1.13882i	−0.323766	−	0.946137i	$-0.604949\pi$
$29$	3.54072	−	6.13271i	0.657495	−	1.13882i	0.981262	−	0.192679i	$-0.0617175\pi$
$30$		−	1.12744i		−	0.205842i
$31$	−2.22176	−	0.595317i	−0.399039	−	0.106922i	0.0537180	−	0.998556i	$-0.482893\pi$
$31$	−2.22176	−	0.595317i	−0.399039	−	0.106922i	−0.452757	+	0.891634i	$0.649559\pi$
$32$	0.730993	−	0.195869i	0.129223	−	0.0346251i
$33$	3.98664	+	3.98664i	0.693985	+	0.693985i
$34$	6.93691	+	6.93691i	1.18967	+	1.18967i
$35$		0			0
$36$	3.00366	+	1.73416i	0.500610	+	0.289027i
$37$	−10.0386	−	2.68984i	−1.65034	−	0.442207i	−0.690631	−	0.723208i	$-0.742667\pi$
$37$	−10.0386	−	2.68984i	−1.65034	−	0.442207i	−0.959707	+	0.281001i	$0.909334\pi$
$38$	6.68720	+	11.5826i	1.08481	+	1.87894i
$39$	5.87034	+	4.00490i	0.940007	+	0.641297i
$40$	−0.951490	−	0.549343i	−0.150444	−	0.0868587i
$41$	−0.0713473	−	0.266272i	−0.0111426	−	0.0415847i	0.960131	−	0.279551i	$-0.0901857\pi$
$41$	−0.0713473	−	0.266272i	−0.0111426	−	0.0415847i	−0.971273	+	0.237967i	$0.923519\pi$
$42$		0			0
$43$	3.91398	−	2.25974i	0.596877	−	0.344607i	−0.170935	−	0.985282i	$-0.554679\pi$
$43$	3.91398	−	2.25974i	0.596877	−	0.344607i	0.767812	+	0.640675i	$0.221345\pi$
$44$	10.8331	−	2.90272i	1.63315	−	0.437601i
$45$	0.0538258	+	0.200881i	0.00802388	+	0.0299455i
$46$	3.81023	+	14.2200i	0.561787	+	2.09662i
$47$	3.14513	−	0.842735i	0.458764	−	0.122926i	−0.0220331	−	0.999757i	$-0.507014\pi$
$47$	3.14513	−	0.842735i	0.458764	−	0.122926i	0.480797	+	0.876832i	$0.340347\pi$
$48$	6.02588	−	3.47904i	0.869760	−	0.502156i
$49$		0			0
$50$	3.11404	+	11.6218i	0.440392	+	1.64357i
$51$	−6.88178	−	3.97320i	−0.963642	−	0.556359i
$52$	12.7381	−	6.12966i	1.76646	−	0.850031i
$53$	−3.96785	−	6.87251i	−0.545026	−	0.944012i	−0.998605	−	0.0527963i	$-0.983187\pi$
$53$	−3.96785	−	6.87251i	−0.545026	−	0.944012i	0.453580	−	0.891216i	$-0.350147\pi$
$54$	9.79921	+	2.62569i	1.33350	+	0.357311i
$55$	0.582389	+	0.336242i	0.0785293	+	0.0453389i
$56$		0			0
$57$	−7.66035	−	7.66035i	−1.01464	−	1.01464i
$58$	12.1841	+	12.1841i	1.59985	+	1.59985i
$59$	0.702149	−	0.188140i	0.0914121	−	0.0244938i	−0.212823	−	0.977091i	$-0.568266\pi$
$59$	0.702149	−	0.188140i	0.0914121	−	0.0244938i	0.304235	+	0.952597i	$0.401599\pi$
$60$	1.75474	+	0.470182i	0.226536	+	0.0607002i
$61$		−	2.28077i		−	0.292022i	−0.989283	−	0.146011i	$-0.953356\pi$
$61$		−	2.28077i		−	0.292022i	0.989283	−	0.146011i	$-0.0466435\pi$
$62$	2.79839	−	4.84695i	0.355396	−	0.615563i
$63$		0			0
$64$			8.90209i			1.11276i
$65$	0.799980	+	0.280193i	0.0992254	+	0.0347537i
$66$	−11.8806	+	6.85927i	−1.46240	+	0.844318i
$67$	1.88222	+	1.88222i	0.229950	+	0.229950i	0.812672	−	0.582722i	$-0.198012\pi$
$67$	1.88222	+	1.88222i	0.229950	+	0.229950i	−0.582722	+	0.812672i	$0.698012\pi$
$68$	−13.6895	+	7.90362i	−1.66009	+	0.958455i
$69$	−5.96230	−	10.3270i	−0.717776	−	1.24323i
$70$		0			0
$71$	−0.362587	+	1.35319i	−0.0430312	+	0.160595i	−0.984098	−	0.177626i	$-0.943158\pi$
$71$	−0.362587	+	1.35319i	−0.0430312	+	0.160595i	0.941067	+	0.338220i	$0.109825\pi$
$72$	−2.92337	+	2.92337i	−0.344522	+	0.344522i
$73$	−3.50729	+	13.0894i	−0.410497	+	1.53200i	0.383190	+	0.923670i	$0.374826\pi$
$73$	−3.50729	+	13.0894i	−0.410497	+	1.53200i	−0.793687	+	0.608326i	$0.791841\pi$
$74$	12.6440	−	21.9001i	1.46984	−	2.54584i
$75$	−4.87290	−	8.44011i	−0.562674	−	0.974580i
$76$	−20.8158	+	5.57758i	−2.38774	+	0.639792i
$77$		0			0
$78$	−13.1098	+	11.2751i	−1.48439	+	1.27665i
$79$	−1.91392	+	3.31501i	−0.215333	+	0.372967i	−0.953375	−	0.301787i	$-0.902417\pi$
$79$	−1.91392	+	3.31501i	−0.215333	+	0.372967i	0.738043	+	0.674754i	$0.235750\pi$
$80$	0.586860	−	0.586860i	0.0656130	−	0.0656130i
$81$	−10.8713			−1.20792
$82$	0.670760			0.0740730
$83$	4.19588	−	4.19588i	0.460558	−	0.460558i	−0.438280	−	0.898838i	$-0.644412\pi$
$83$	4.19588	−	4.19588i	0.460558	−	0.460558i	0.898838	+	0.438280i	$0.144412\pi$
$84$		0			0
$85$	−0.915533	−	0.245316i	−0.0993035	−	0.0266083i
$86$	2.84623	+	10.6223i	0.306917	+	1.14543i
$87$	−12.0872	−	6.97857i	−1.29589	−	0.748181i
$88$			13.3686i			1.42510i
$89$	0.893381	−	3.33414i	0.0946982	−	0.353419i	−0.902275	−	0.431160i	$-0.858104\pi$
$89$	0.893381	−	3.33414i	0.0946982	−	0.353419i	0.996974	+	0.0777418i	$0.0247710\pi$
$90$	−0.506034			−0.0533407
$91$		0			0
$92$	−23.7208			−2.47307
$93$	−1.17334	+	4.37896i	−0.121670	+	0.454077i
$94$			7.92283i			0.817178i
$95$	−1.11906	−	0.646091i	−0.114813	−	0.0662875i
$96$	−0.386047	−	1.44075i	−0.0394008	−	0.147046i
$97$	2.61723	+	0.701285i	0.265739	+	0.0712047i	0.389228	−	0.921141i	$-0.372742\pi$
$97$	2.61723	+	0.701285i	0.265739	+	0.0712047i	−0.123489	+	0.992346i	$0.539408\pi$
$98$		0			0
$99$	1.78934	−	1.78934i	0.179835	−	0.179835i
$100$	−19.3867			−1.93867
$101$	13.7823			1.37139			0.685697	−	0.727888i	$-0.259498\pi$
$101$	13.7823			1.37139			0.685697	+	0.727888i	$0.259498\pi$
$102$	13.6723	−	13.6723i	1.35376	−	1.35376i
$103$	−4.01282	+	6.95040i	−0.395395	+	0.684843i	−0.993151	−	0.116834i	$-0.962725\pi$
$103$	−4.01282	+	6.95040i	−0.395395	+	0.684843i	0.597757	+	0.801677i	$0.296059\pi$
$104$	3.12775	+	16.5576i	0.306701	+	1.62360i
$105$		0			0
$106$	18.6515	−	4.99766i	1.81160	−	0.485415i
$107$	−2.08938	−	3.61892i	−0.201988	−	0.349854i	0.747181	−	0.664621i	$-0.231407\pi$
$107$	−2.08938	−	3.61892i	−0.201988	−	0.349854i	−0.949169	+	0.314767i	$0.898074\pi$
$108$	−8.17321	+	14.1564i	−0.786467	+	1.36220i
$109$	−3.64596	+	13.6069i	−0.349220	+	1.30331i	0.538385	+	0.842699i	$0.319035\pi$
$109$	−3.64596	+	13.6069i	−0.349220	+	1.30331i	−0.887604	+	0.460607i	$0.847632\pi$
$110$	−1.15705	+	1.15705i	−0.110321	+	0.110321i
$111$	−5.30152	+	19.7856i	−0.503198	+	1.87796i
$112$		0			0
$113$	2.30697	+	3.99579i	0.217022	+	0.375892i	0.953896	−	0.300137i	$-0.0970325\pi$
$113$	2.30697	+	3.99579i	0.217022	+	0.375892i	−0.736874	+	0.676030i	$0.763699\pi$
$114$	22.8286	−	13.1801i	2.13810	−	1.23443i
$115$	−1.00575	−	1.00575i	−0.0937864	−	0.0937864i
$116$	−24.0443	+	13.8820i	−2.23246	+	1.28891i
$117$	1.79753	−	2.63480i	0.166182	−	0.243588i
$118$			1.76877i			0.162828i
$119$		0			0
$120$	−1.08272	+	1.87533i	−0.0988388	+	0.171194i
$121$			2.81732i			0.256120i
$122$	5.36056	+	1.43636i	0.485322	+	0.130042i
$123$	−0.524807	+	0.140622i	−0.0473203	+	0.0126794i
$124$	6.37673	+	6.37673i	0.572647	+	0.572647i
$125$	−1.65315	−	1.65315i	−0.147862	−	0.147862i
$126$		0			0
$127$	3.63943	+	2.10123i	0.322947	+	0.186454i	0.652705	−	0.757612i	$-0.273634\pi$
$127$	3.63943	+	2.10123i	0.322947	+	0.186454i	−0.329758	+	0.944065i	$0.606967\pi$
$128$	−19.4609	−	5.21453i	−1.72011	−	0.460903i
$129$	−4.45382	−	7.71425i	−0.392137	−	0.679202i
$130$	−1.16235	+	1.70376i	−0.101945	+	0.149430i
$131$	11.9149	+	6.87908i	1.04101	+	0.601028i	0.920119	−	0.391638i	$-0.128092\pi$
$131$	11.9149	+	6.87908i	1.04101	+	0.601028i	0.120891	+	0.992666i	$0.461425\pi$
$132$	−5.72109	−	21.3514i	−0.497957	−	1.85840i
$133$		0			0
$134$	−5.60922	+	3.23848i	−0.484562	+	0.279762i
$135$	−0.946761	+	0.253684i	−0.0814842	+	0.0218336i
$136$	−4.87675	−	18.2003i	−0.418178	−	1.56066i
$137$	−3.57106	−	13.3274i	−0.305096	−	1.13863i	−0.932863	−	0.360232i	$-0.882697\pi$
$137$	−3.57106	−	13.3274i	−0.305096	−	1.13863i	0.627766	−	0.778402i	$-0.283969\pi$
$138$	28.0268	−	7.50975i	2.38580	−	0.639272i
$139$	12.9252	−	7.46236i	1.09630	−	0.632949i	0.161053	−	0.986946i	$-0.448511\pi$
$139$	12.9252	−	7.46236i	1.09630	−	0.632949i	0.935247	+	0.353997i	$0.115178\pi$
$140$		0			0
$141$	−1.66098	−	6.19888i	−0.139880	−	0.522040i
$142$	−2.95211	−	1.70440i	−0.247735	−	0.143030i
$143$	−1.91444	−	10.1346i	−0.160093	−	0.847496i
$144$	−1.56151	−	2.70461i	−0.130126	−	0.225384i
$145$	−1.60805	−	0.430876i	−0.133541	−	0.0357823i
$146$	−28.5556	−	16.4866i	−2.36328	−	1.36444i
$147$		0			0
$148$	28.8121	+	28.8121i	2.36834	+	2.36834i
$149$	−7.47691	−	7.47691i	−0.612532	−	0.612532i	0.331073	−	0.943605i	$-0.392589\pi$
$149$	−7.47691	−	7.47691i	−0.612532	−	0.612532i	−0.943605	+	0.331073i	$0.892589\pi$
$150$	22.9059	−	6.13761i	1.87026	−	0.501134i
$151$	4.34514	+	1.16428i	0.353603	+	0.0947476i	0.431248	−	0.902233i	$-0.358073\pi$
$151$	4.34514	+	1.16428i	0.353603	+	0.0947476i	−0.0776451	+	0.996981i	$0.524740\pi$
$152$		−	25.6878i		−	2.08356i
$153$	−1.78330	+	3.08877i	−0.144171	+	0.249712i
$154$		0			0
$155$			0.540738i			0.0434331i
$156$	−12.0812	−	25.1061i	−0.967273	−	2.01010i
$157$	−11.2646	+	6.50360i	−0.899010	+	0.519044i	−0.876879	−	0.480711i	$-0.840378\pi$
$157$	−11.2646	+	6.50360i	−0.899010	+	0.519044i	−0.0221312	+	0.999755i	$0.507045\pi$
$158$	−6.58604	−	6.58604i	−0.523957	−	0.523957i
$159$	−13.5453	+	7.82041i	−1.07422	+	0.620199i
$160$	−0.0889558	−	0.154076i	−0.00703257	−	0.0121808i
$161$		0			0
$162$	6.84642	−	25.5512i	0.537906	−	2.00749i
$163$	11.6009	−	11.6009i	0.908650	−	0.908650i	−0.0875130	−	0.996163i	$-0.527892\pi$
$163$	11.6009	−	11.6009i	0.908650	−	0.908650i	0.996163	+	0.0875130i	$0.0278919\pi$
$164$	−0.279729	+	1.04396i	−0.0218432	+	0.0815199i
$165$	0.662715	−	1.14786i	0.0515923	−	0.0893605i
$166$	7.21928	+	12.5042i	0.560325	+	0.970511i
$167$	9.84852	−	2.63890i	0.762101	−	0.204204i	0.143222	−	0.989691i	$-0.454254\pi$
$167$	9.84852	−	2.63890i	0.762101	−	0.204204i	0.618879	+	0.785486i	$0.287587\pi$
$168$		0			0
$169$	−4.74221	−	12.1042i	−0.364786	−	0.931091i
$170$	1.15315	−	1.99731i	0.0884426	−	0.153187i
$171$	−3.43822	+	3.43822i	−0.262927	+	0.262927i
$172$	−17.7194			−1.35109
$173$	−14.9762			−1.13862			−0.569309	−	0.822124i	$-0.692789\pi$
$173$	−14.9762			−1.13862			−0.569309	+	0.822124i	$0.692789\pi$
$174$	24.0141	−	24.0141i	1.82051	−	1.82051i
$175$		0			0
$176$	−9.75453	−	2.61372i	−0.735276	−	0.197017i
$177$	−0.370814	−	1.38390i	−0.0278721	−	0.104020i
$178$	7.27372	+	4.19949i	0.545189	+	0.314765i
$179$			9.18362i			0.686416i	0.939259	+	0.343208i	$0.111514\pi$
$179$			9.18362i			0.686416i	−0.939259	+	0.343208i	$0.888486\pi$
$180$	0.211033	−	0.787587i	0.0157295	−	0.0587033i
$181$	−12.8202			−0.952919			−0.476459	−	0.879197i	$-0.658080\pi$
$181$	−12.8202			−0.952919			−0.476459	+	0.879197i	$0.658080\pi$
$182$		0			0
$183$	−4.49527			−0.332300
$184$	7.31820	−	27.3119i	0.539505	−	2.01346i
$185$			2.44323i			0.179630i
$186$	−9.55307	−	5.51547i	−0.700465	−	0.404414i
$187$	2.98497	+	11.1400i	0.218282	+	0.814641i
$188$	−12.3310	−	3.30409i	−0.899332	−	0.240975i
$189$		0			0
$190$	2.22328	−	2.22328i	0.161294	−	0.161294i
$191$	−5.39162			−0.390124			−0.195062	−	0.980791i	$-0.562491\pi$
$191$	−5.39162			−0.390124			−0.195062	+	0.980791i	$0.562491\pi$
$192$	17.5455			1.26624
$193$	−2.36272	+	2.36272i	−0.170073	+	0.170073i	−0.787011	−	0.616939i	$-0.788373\pi$
$193$	−2.36272	+	2.36272i	−0.170073	+	0.170073i	0.616939	+	0.787011i	$0.288373\pi$
$194$	−3.29650	+	5.70971i	−0.236675	+	0.409933i
$195$	0.552245	−	1.57672i	0.0395471	−	0.112911i
$196$		0			0
$197$	3.67856	−	0.985668i	0.262087	−	0.0702259i	−0.125383	−	0.992108i	$-0.540016\pi$
$197$	3.67856	−	0.985668i	0.262087	−	0.0702259i	0.387470	+	0.921882i	$0.373349\pi$
$198$	3.07867	+	5.33241i	0.218791	+	0.378958i
$199$	11.1334	−	19.2837i	0.789229	−	1.36698i	−0.137211	−	0.990542i	$-0.543814\pi$
$199$	11.1334	−	19.2837i	0.789229	−	1.36698i	0.926440	−	0.376443i	$-0.122853\pi$
$200$	5.98106	−	22.3216i	0.422925	−	1.57838i
$201$	3.70976	−	3.70976i	0.261666	−	0.261666i
$202$	−8.67969	+	32.3931i	−0.610701	+	2.27917i
$203$		0			0
$204$	15.5776	+	26.9812i	1.09065	+	1.88906i
$205$	−0.0561237	+	0.0324031i	−0.00391985	+	0.00226313i
$206$	−13.8086	−	13.8086i	−0.962091	−	0.962091i
$207$	−4.63510	+	2.67608i	−0.322162	+	0.186000i
$208$	−12.6929	−	0.955008i	−0.880094	−	0.0662179i
$209$			15.7230i			1.08759i
$210$		0			0
$211$	−7.76031	+	13.4412i	−0.534242	+	0.925334i	0.464958	+	0.885333i	$0.346069\pi$
$211$	−7.76031	+	13.4412i	−0.534242	+	0.925334i	−0.999200	+	0.0400009i	$0.987264\pi$
$212$			31.1132i			2.13687i
$213$	2.66707	+	0.714640i	0.182745	+	0.0489663i
$214$	9.82149	−	2.63166i	0.671384	−	0.179897i
$215$	−0.751291	−	0.751291i	−0.0512376	−	0.0512376i
$216$	−13.7780	−	13.7780i	−0.937473	−	0.937473i
$217$		0			0
$218$	−29.6846	−	17.1384i	−2.01050	−	1.16076i
$219$	25.7985	+	6.91267i	1.74330	+	0.467115i
$220$	−1.31830	−	2.28336i	−0.0888795	−	0.153944i
$221$	6.30335	+	13.0990i	0.424009	+	0.881137i
$222$	−43.1639	−	24.9207i	−2.89697	−	1.67257i
$223$	1.32002	+	4.92639i	0.0883952	+	0.329895i	0.995935	−	0.0900697i	$-0.0287090\pi$
$223$	1.32002	+	4.92639i	0.0883952	+	0.329895i	−0.907540	+	0.419965i	$0.862042\pi$
$224$		0			0
$225$	−3.78820	+	2.18712i	−0.252547	+	0.145808i
$226$	−10.8443	+	2.90572i	−0.721352	+	0.193286i
$227$	−2.79628	−	10.4359i	−0.185596	−	0.692653i	−0.994502	−	0.104716i	$-0.966607\pi$
$227$	−2.79628	−	10.4359i	−0.185596	−	0.692653i	0.808906	−	0.587938i	$-0.200060\pi$
$228$	10.9931	+	41.0268i	0.728036	+	2.71707i
$229$	−12.7721	+	3.42227i	−0.844002	+	0.226150i	−0.654813	−	0.755791i	$-0.727253\pi$
$229$	−12.7721	+	3.42227i	−0.844002	+	0.226150i	−0.189189	+	0.981941i	$0.560586\pi$
$230$	2.99723	−	1.73045i	0.197631	−	0.114103i
$231$		0			0
$232$	−8.56558	−	31.9672i	−0.562358	−	2.09875i
$233$	10.5909	+	6.11465i	0.693832	+	0.400584i	0.805046	−	0.593212i	$-0.202141\pi$
$233$	10.5909	+	6.11465i	0.693832	+	0.400584i	−0.111214	+	0.993796i	$0.535474\pi$
$234$	5.06064	+	5.88411i	0.330824	+	0.384657i
$235$	−0.382736	−	0.662918i	−0.0249670	−	0.0432440i
$236$	−2.75290	−	0.737637i	−0.179198	−	0.0480161i
$237$	6.53370	+	3.77223i	0.424409	+	0.245033i
$238$		0			0
$239$	4.36940	+	4.36940i	0.282633	+	0.282633i	0.834158	−	0.551525i	$-0.185954\pi$
$239$	4.36940	+	4.36940i	0.282633	+	0.282633i	−0.551525	+	0.834158i	$0.685954\pi$
$240$	−1.15667	−	1.15667i	−0.0746627	−	0.0746627i
$241$	11.8071	−	3.16371i	0.760565	−	0.203793i	0.142365	−	0.989814i	$-0.454529\pi$
$241$	11.8071	−	3.16371i	0.760565	−	0.203793i	0.618199	+	0.786021i	$0.287863\pi$
$242$	−6.62165	−	1.77427i	−0.425656	−	0.114054i
$243$			8.91890i			0.572148i
$244$	−4.47107	+	7.74412i	−0.286231	+	0.495767i
$245$		0			0
$246$		−	1.32203i		−	0.0842896i
$247$	3.67859	+	19.4736i	0.234063	+	1.23908i
$248$	−9.30940	+	5.37479i	−0.591148	+	0.341299i
$249$	−8.26985	−	8.26985i	−0.524081	−	0.524081i
$250$	4.92656	−	2.84435i	0.311583	−	0.179893i
$251$	13.4971	+	23.3777i	0.851929	+	1.47558i	0.879465	+	0.475964i	$0.157901\pi$
$251$	13.4971	+	23.3777i	0.851929	+	1.47558i	−0.0275356	+	0.999621i	$0.508766\pi$
$252$		0			0
$253$	−4.47933	+	16.7171i	−0.281613	+	1.05099i
$254$	−7.23058	+	7.23058i	−0.453687	+	0.453687i
$255$	−0.483505	+	1.80447i	−0.0302783	+	0.113000i
$256$	15.6097	−	27.0367i	0.975603	−	1.68979i
$257$	−9.64610	−	16.7075i	−0.601707	−	1.04219i	−0.992563	−	0.121735i	$-0.961154\pi$
$257$	−9.64610	−	16.7075i	−0.601707	−	1.04219i	0.390855	−	0.920452i	$-0.372179\pi$
$258$	20.9359	−	5.60977i	1.30341	−	0.349249i
$259$		0			0
$260$	−2.16698	−	2.51960i	−0.134391	−	0.156259i
$261$	−3.13221	+	5.42515i	−0.193879	+	0.335808i
$262$	−23.6718	+	23.6718i	−1.46245	+	1.46245i
$263$	−19.9186			−1.22824			−0.614118	−	0.789214i	$-0.710488\pi$
$263$	−19.9186			−1.22824			−0.614118	+	0.789214i	$0.710488\pi$
$264$	26.3488			1.62166
$265$	−1.31918	+	1.31918i	−0.0810367	+	0.0810367i
$266$		0			0
$267$	−6.57142	−	1.76081i	−0.402164	−	0.107760i
$268$	−2.70111	−	10.0807i	−0.164997	−	0.615776i
$269$	−22.7548	−	13.1375i	−1.38738	−	0.801006i	−0.394363	−	0.918955i	$-0.629035\pi$
$269$	−22.7548	−	13.1375i	−1.38738	−	0.801006i	−0.993020	+	0.117949i	$0.962368\pi$
$270$		−	2.38497i		−	0.145144i
$271$	1.39038	−	5.18896i	0.0844594	−	0.315207i	−0.910752	−	0.412954i	$-0.864497\pi$
$271$	1.39038	−	5.18896i	0.0844594	−	0.315207i	0.995211	+	0.0977473i	$0.0311637\pi$
$272$	14.2335			0.863031
$273$		0			0
$274$	33.5727			2.02820
$275$	−3.66089	+	13.6626i	−0.220760	+	0.823887i
$276$			46.7524i			2.81417i
$277$	5.63883	+	3.25558i	0.338804	+	0.195609i	0.659743	−	0.751491i	$-0.270665\pi$
$277$	5.63883	+	3.25558i	0.338804	+	0.195609i	−0.320939	+	0.947100i	$0.603998\pi$
$278$	9.39913	+	35.0780i	0.563722	+	2.10384i
$279$	1.96542	+	0.526633i	0.117667	+	0.0315287i
$280$		0			0
$281$	−11.1540	+	11.1540i	−0.665390	+	0.665390i	−0.956645	−	0.291255i	$-0.905927\pi$
$281$	−11.1540	+	11.1540i	−0.665390	+	0.665390i	0.291255	+	0.956645i	$0.405927\pi$
$282$	15.6155			0.929887
$283$	−2.37799			−0.141357			−0.0706784	−	0.997499i	$-0.522516\pi$
$283$	−2.37799			−0.141357			−0.0706784	+	0.997499i	$0.522516\pi$
$284$	3.88384	−	3.88384i	0.230464	−	0.230464i
$285$	−1.27341	+	2.20561i	−0.0754303	+	0.130649i
$286$	25.0253	+	1.88289i	1.47978	+	0.111338i
$287$		0			0
$288$	−0.646655	+	0.173271i	−0.0381045	+	0.0102101i
$289$	0.372423	+	0.645056i	0.0219072	+	0.0379445i
$290$	2.02541	−	3.50811i	0.118936	−	0.206003i
$291$	1.38219	−	5.15842i	0.0810256	−	0.302392i
$292$	37.5682	−	37.5682i	2.19852	−	2.19852i
$293$	8.69014	−	32.4321i	0.507684	−	1.89470i	0.0653221	−	0.997864i	$-0.479193\pi$
$293$	8.69014	−	32.4321i	0.507684	−	1.89470i	0.442361	−	0.896837i	$-0.354141\pi$
$294$		0			0
$295$	−0.0854457	−	0.147996i	−0.00497484	−	0.00861668i
$296$	−42.0629	+	24.2850i	−2.44486	+	1.41154i
$297$	8.43324	+	8.43324i	0.489346	+	0.489346i
$298$	22.2820	−	12.8645i	1.29076	−	0.745220i
$299$	−1.63667	+	21.7528i	−0.0946511	+	1.25800i
$300$			38.2101i			2.20606i
$301$		0			0
$302$	−5.47288	+	9.47931i	−0.314929	+	0.545473i
$303$		−	27.1642i		−	1.56054i
$304$	18.7434	+	5.02227i	1.07501	+	0.288047i
$305$	−0.517916	+	0.138775i	−0.0296558	+	0.00794625i
$306$	−6.13657	−	6.13657i	−0.350804	−	0.350804i
$307$	−19.1548	−	19.1548i	−1.09322	−	1.09322i	−0.995183	−	0.0980380i	$-0.968743\pi$
$307$	−19.1548	−	19.1548i	−1.09322	−	1.09322i	−0.0980380	−	0.995183i	$-0.531257\pi$
$308$		0			0
$309$	13.6989	+	7.90904i	0.779301	+	0.449930i
$310$	−1.27091	−	0.340541i	−0.0721831	−	0.0193414i
$311$	16.5705	+	28.7009i	0.939627	+	1.62748i	0.766168	+	0.642640i	$0.222161\pi$
$311$	16.5705	+	28.7009i	0.939627	+	1.62748i	0.173458	+	0.984841i	$0.444506\pi$
$312$	32.6341	−	6.16462i	1.84754	−	0.349003i
$313$	1.14049	+	0.658460i	0.0644641	+	0.0372183i	0.531886	−	0.846816i	$-0.321484\pi$
$313$	1.14049	+	0.658460i	0.0644641	+	0.0372183i	−0.467422	+	0.884035i	$0.654817\pi$
$314$	−8.19154	−	30.5712i	−0.462275	−	1.72523i
$315$		0			0
$316$	12.9971	−	7.50385i	0.731142	−	0.422125i
$317$	−8.37022	+	2.24279i	−0.470118	+	0.125968i	−0.486098	−	0.873904i	$-0.661580\pi$
$317$	−8.37022	+	2.24279i	−0.470118	+	0.125968i	0.0159793	+	0.999872i	$0.494913\pi$
$318$	−9.85011	−	36.7611i	−0.552367	−	2.06146i
$319$	5.24283	+	19.5665i	0.293542	+	1.09551i
$320$	2.02148	−	0.541655i	0.113004	−	0.0302794i
$321$	−7.13269	+	4.11806i	−0.398108	+	0.229848i
$322$		0			0
$323$	−5.73562	−	21.4056i	−0.319139	−	1.19104i
$324$	36.9125	+	21.3114i	2.05069	+	1.18397i
$325$	−1.33763	+	17.7782i	−0.0741982	+	0.986159i
$326$	19.9600	+	34.5718i	1.10548	+	1.91475i
$327$	26.8185	+	7.18599i	1.48307	+	0.397386i
$328$	−1.11571	−	0.644155i	−0.0616047	−	0.0355675i
$329$		0			0
$330$	2.28049	+	2.28049i	0.125537	+	0.125537i
$331$	16.5348	+	16.5348i	0.908837	+	0.908837i	0.996178	−	0.0873418i	$-0.0278372\pi$
$331$	16.5348	+	16.5348i	0.908837	+	0.908837i	−0.0873418	+	0.996178i	$0.527837\pi$
$332$	−22.4720	+	6.02137i	−1.23331	+	0.330465i
$333$	8.88041	+	2.37950i	0.486644	+	0.130396i
$334$			24.8092i			1.35750i
$335$	0.312889	−	0.541940i	0.0170950	−	0.0296094i
$336$		0			0
$337$			5.08165i			0.276815i	0.990375	+	0.138407i	$0.0441984\pi$
$337$			5.08165i			0.276815i	−0.990375	+	0.138407i	$0.955802\pi$
$338$	31.4354	−	3.52293i	1.70986	−	0.191622i
$339$	7.87549	−	4.54691i	0.427738	−	0.246955i
$340$	2.62770	+	2.62770i	0.142507	+	0.142507i
$341$	5.69811	−	3.28980i	0.308570	−	0.178153i
$342$	−5.91567	−	10.2462i	−0.319883	−	0.554053i
$343$		0			0
$344$	5.46668	−	20.4019i	0.294744	−	1.10000i
$345$	−1.98227	+	1.98227i	−0.106722	+	0.106722i
$346$	9.43155	−	35.1990i	0.507043	−	1.89231i
$347$	−0.341991	+	0.592345i	−0.0183590	+	0.0317988i	−0.875059	−	0.484016i	$-0.839178\pi$
$347$	−0.341991	+	0.592345i	−0.0183590	+	0.0317988i	0.856700	+	0.515815i	$0.172511\pi$
$348$	27.3607	+	47.3901i	1.46669	+	2.54038i
$349$	5.07510	−	1.35987i	0.271664	−	0.0727921i	−0.120415	−	0.992724i	$-0.538423\pi$
$349$	5.07510	−	1.35987i	0.271664	−	0.0727921i	0.392079	+	0.919932i	$0.371756\pi$
$350$		0			0
$351$	12.4180	+	8.47186i	0.662822	+	0.452194i
$352$	−1.08240	+	1.87477i	−0.0576920	+	0.0999256i
$353$	−15.3535	+	15.3535i	−0.817186	+	0.817186i	−0.985699	−	0.168514i	$-0.946103\pi$
$353$	−15.3535	+	15.3535i	−0.817186	+	0.817186i	0.168514	+	0.985699i	$0.446103\pi$
$354$	3.48615			0.185287
$355$	0.329345			0.0174798
$356$	−9.56943	+	9.56943i	−0.507179	+	0.507179i
$357$		0			0
$358$	−21.5846	−	5.78356i	−1.14078	−	0.305671i
$359$	−3.67473	−	13.7143i	−0.193945	−	0.723812i	−0.992537	−	0.121940i	$-0.961088\pi$
$359$	−3.67473	−	13.7143i	−0.193945	−	0.723812i	0.798593	−	0.601872i	$-0.205578\pi$
$360$	0.841712	+	0.485963i	0.0443621	+	0.0256125i
$361$		−	11.2119i		−	0.590098i
$362$	8.07378	−	30.1317i	0.424348	−	1.58369i
$363$	5.55279			0.291446
$364$		0			0
$365$	3.18574			0.166749
$366$	2.83098	−	10.5654i	0.147978	−	0.552261i
$367$			3.00518i			0.156869i	0.996919	+	0.0784346i	$0.0249922\pi$
$367$			3.00518i			0.156869i	−0.996919	+	0.0784346i	$0.975008\pi$
$368$	18.4976	+	10.6796i	0.964253	+	0.556712i
$369$	0.0631157	+	0.235551i	0.00328567	+	0.0122623i
$370$	−5.74241	−	1.53867i	−0.298534	−	0.0799918i
$371$		0			0
$372$	12.5682	−	12.5682i	0.651630	−	0.651630i
$373$	−26.1851			−1.35581			−0.677906	−	0.735149i	$-0.737112\pi$
$373$	−26.1851			−1.35581			−0.677906	+	0.735149i	$0.737112\pi$
$374$	−28.0627			−1.45109
$375$	−3.25827	+	3.25827i	−0.168256	+	0.168256i
$376$	7.60858	−	13.1784i	0.392383	−	0.679627i
$377$	11.0713	+	23.0073i	0.570200	+	1.18494i
$378$		0			0
$379$	−5.54850	+	1.48672i	−0.285007	+	0.0763675i	−0.398491	−	0.917172i	$-0.630466\pi$
$379$	−5.54850	+	1.48672i	−0.285007	+	0.0763675i	0.113483	+	0.993540i	$0.463799\pi$
$380$	2.53311	+	4.38747i	0.129946	+	0.225073i
$381$	4.14140	−	7.17312i	0.212170	−	0.367490i
$382$	3.39548	−	12.6721i	0.173728	−	0.648361i
$383$	−11.4850	+	11.4850i	−0.586857	+	0.586857i	−0.936779	−	0.349922i	$-0.886208\pi$
$383$	−11.4850	+	11.4850i	−0.586857	+	0.586857i	0.349922	+	0.936779i	$0.386208\pi$
$384$	−10.2775	+	38.3563i	−0.524474	+	1.95736i
$385$		0			0
$386$	−4.06521	−	7.04116i	−0.206914	−	0.358385i
$387$	−3.46241	+	1.99902i	−0.176004	+	0.101616i
$388$	−7.51179	−	7.51179i	−0.381353	−	0.381353i
$389$	8.04726	−	4.64609i	0.408012	−	0.235566i	−0.281923	−	0.959437i	$-0.590972\pi$
$389$	8.04726	−	4.64609i	0.408012	−	0.235566i	0.689935	+	0.723871i	$0.257639\pi$
$390$	3.35802	+	2.29093i	0.170040	+	0.116006i
$391$		−	24.3930i		−	1.23361i
$392$		0			0
$393$	13.5583	−	23.4836i	0.683925	−	1.18459i
$394$			9.26659i			0.466844i
$395$	0.869225	+	0.232908i	0.0437355	+	0.0117189i
$396$	−9.58322	+	2.56782i	−0.481575	+	0.129038i
$397$	−13.3273	−	13.3273i	−0.668877	−	0.668877i	0.288579	−	0.957456i	$-0.406817\pi$
$397$	−13.3273	−	13.3273i	−0.668877	−	0.668877i	−0.957456	+	0.288579i	$0.906817\pi$
$398$	38.3116	+	38.3116i	1.92039	+	1.92039i
$399$		0			0
$400$	15.1178	+	8.72826i	0.755890	+	0.436413i
$401$	36.1861	+	9.69604i	1.80705	+	0.484197i	0.995042	−	0.0994523i	$-0.0317091\pi$
$401$	36.1861	+	9.69604i	1.80705	+	0.484197i	0.812006	+	0.583649i	$0.198376\pi$
$402$	6.38287	+	11.0555i	0.318349	+	0.551396i
$403$	6.28765	−	5.40770i	0.313210	−	0.269377i
$404$	−46.7965	−	27.0180i	−2.32822	−	1.34420i
$405$	0.661474	+	2.46866i	0.0328689	+	0.122668i
$406$		0			0
$407$	25.7459	−	14.8644i	1.27618	−	0.736801i
$408$	−35.8718	+	9.61181i	−1.77592	+	0.475856i
$409$	5.27659	+	19.6925i	0.260910	+	0.973731i	0.964706	+	0.263328i	$0.0848203\pi$
$409$	5.27659	+	19.6925i	0.260910	+	0.973731i	−0.703796	+	0.710402i	$0.748513\pi$
$410$	−0.0408129	−	0.152316i	−0.00201561	−	0.00752235i
$411$	−26.2675	+	7.03836i	−1.29568	+	0.347177i
$412$	27.2502	−	15.7329i	1.34252	−	0.775106i
$413$		0			0
$414$	−3.37062	−	12.5793i	−0.165657	−	0.618241i
$415$	−1.20810	−	0.697498i	−0.0593034	−	0.0342388i
$416$	−0.901970	+	2.57522i	−0.0442227	+	0.126261i
$417$	−14.7079	−	25.4748i	−0.720249	−	1.24751i
$418$	−36.9544	−	9.90189i	−1.80750	−	0.484317i
$419$	−9.48347	−	5.47529i	−0.463298	−	0.267485i	0.250132	−	0.968212i	$-0.419526\pi$
$419$	−9.48347	−	5.47529i	−0.463298	−	0.267485i	−0.713430	+	0.700727i	$0.752859\pi$
$420$		0			0
$421$	−7.99908	−	7.99908i	−0.389852	−	0.389852i	0.484783	−	0.874634i	$-0.338899\pi$
$421$	−7.99908	−	7.99908i	−0.389852	−	0.389852i	−0.874634	+	0.484783i	$0.838899\pi$
$422$	−26.7042	−	26.7042i	−1.29994	−	1.29994i
$423$	−2.78226	+	0.745505i	−0.135278	+	0.0362477i
$424$	−35.8235	−	9.59886i	−1.73974	−	0.466162i
$425$		−	19.9360i		−	0.967039i
$426$	−3.35928	+	5.81845i	−0.162758	+	0.281905i
$427$		0			0
$428$			16.3836i			0.791930i
$429$	−19.9747	+	3.77325i	−0.964388	+	0.182174i
$430$	2.23892	−	1.29264i	0.107970	−	0.0623368i
$431$	−12.3724	−	12.3724i	−0.595959	−	0.595959i	0.343276	−	0.939235i	$-0.388463\pi$
$431$	−12.3724	−	12.3724i	−0.595959	−	0.595959i	−0.939235	+	0.343276i	$0.888463\pi$
$432$	12.7470	−	7.35948i	0.613290	−	0.354083i
$433$	−3.05668	−	5.29433i	−0.146895	−	0.254429i	0.783183	−	0.621791i	$-0.213595\pi$
$433$	−3.05668	−	5.29433i	−0.146895	−	0.254429i	−0.930078	+	0.367361i	$0.880261\pi$
$434$		0			0
$435$	−0.849234	+	3.16938i	−0.0407176	+	0.151960i
$436$	39.0536	−	39.0536i	1.87033	−	1.87033i
$437$	8.60704	−	32.1219i	0.411731	−	1.53660i
$438$	−32.4942	+	56.2815i	−1.55263	+	2.68924i
$439$	7.86166	+	13.6168i	0.375217	+	0.649895i	0.990359	−	0.138521i	$-0.0442349\pi$
$439$	7.86166	+	13.6168i	0.375217	+	0.649895i	−0.615143	+	0.788416i	$0.710902\pi$
$440$	3.03574	−	0.813425i	0.144723	−	0.0387785i
$441$		0			0
$442$	−34.7568	+	6.56560i	−1.65321	+	0.312294i
$443$	5.63934	−	9.76763i	0.267933	−	0.464074i	−0.700395	−	0.713756i	$-0.746993\pi$
$443$	5.63934	−	9.76763i	0.267933	−	0.464074i	0.968328	+	0.249682i	$0.0803260\pi$
$444$	56.7872	−	56.7872i	2.69500	−	2.69500i
$445$	−0.811475			−0.0384676
$446$	−12.4100			−0.587629
$447$	−14.7366	+	14.7366i	−0.697016	+	0.697016i
$448$		0			0
$449$	4.69271	+	1.25741i	0.221463	+	0.0593407i	0.367844	−	0.929888i	$-0.380096\pi$
$449$	4.69271	+	1.25741i	0.221463	+	0.0593407i	−0.146381	+	0.989228i	$0.546763\pi$
$450$	−2.75476	−	10.2809i	−0.129861	−	0.484647i
$451$	0.682904	+	0.394275i	0.0321567	+	0.0185657i
$452$		−	18.0898i		−	0.850871i
$453$	2.29473	−	8.56404i	0.107816	−	0.402374i
$454$	26.2888			1.23379
$455$		0			0
$456$	−50.6293			−2.37094
$457$	−2.30726	+	8.61081i	−0.107929	+	0.402797i	−0.998661	−	0.0517324i	$-0.983526\pi$
$457$	−2.30726	+	8.61081i	−0.107929	+	0.402797i	0.890732	+	0.454529i	$0.150192\pi$
$458$		−	32.1739i		−	1.50339i
$459$	−14.5575	−	8.40480i	−0.679488	−	0.392302i
$460$	1.44331	+	5.38652i	0.0672948	+	0.251148i
$461$	−11.4373	−	3.06461i	−0.532688	−	0.142733i	−0.0175587	−	0.999846i	$-0.505589\pi$
$461$	−11.4373	−	3.06461i	−0.532688	−	0.142733i	−0.515129	+	0.857113i	$0.672256\pi$
$462$		0			0
$463$	−19.6291	+	19.6291i	−0.912240	+	0.912240i	−0.996448	−	0.0842083i	$-0.973164\pi$
$463$	−19.6291	+	19.6291i	−0.912240	+	0.912240i	0.0842083	+	0.996448i	$0.473164\pi$
$464$	24.9998			1.16059
$465$	1.06577			0.0494237
$466$	−21.0413	+	21.0413i	−0.974719	+	0.974719i
$467$	−12.2870	+	21.2818i	−0.568576	+	0.984803i	0.428131	+	0.903717i	$0.359172\pi$
$467$	−12.2870	+	21.2818i	−0.568576	+	0.984803i	−0.996707	+	0.0810863i	$0.974161\pi$
$468$	−11.2684	+	5.42246i	−0.520884	+	0.250653i
$469$		0			0
$470$	1.79911	−	0.482071i	0.0829870	−	0.0222363i
$471$	12.8182	+	22.2018i	0.590633	+	1.02301i
$472$	1.69861	−	2.94209i	0.0781850	−	0.135420i
$473$	−3.34605	+	12.4876i	−0.153852	+	0.574182i
$474$	−12.9807	+	12.9807i	−0.596224	+	0.596224i
$475$	7.03441	−	26.2528i	0.322761	−	1.20456i
$476$		0			0
$477$	3.51006	+	6.07960i	0.160715	+	0.278366i
$478$	−13.0213	+	7.51783i	−0.595579	+	0.343857i
$479$	14.9483	+	14.9483i	0.683006	+	0.683006i	0.960676	−	0.277670i	$-0.0895622\pi$
$479$	14.9483	+	14.9483i	0.683006	+	0.683006i	−0.277670	+	0.960676i	$0.589562\pi$
$480$	−0.303675	+	0.175327i	−0.0138608	+	0.00800255i
$481$	28.4097	−	24.4337i	1.29537	−	1.11408i
$482$			29.7431i			1.35476i
$483$		0			0
$484$	5.52290	−	9.56595i	0.251041	−	0.434816i
$485$		−	0.636990i		−	0.0289242i
$486$	−20.9624	−	5.61686i	−0.950873	−	0.254786i
$487$	14.9246	−	3.99904i	0.676299	−	0.181214i	0.0957085	−	0.995409i	$-0.469488\pi$
$487$	14.9246	−	3.99904i	0.676299	−	0.181214i	0.580591	+	0.814196i	$0.302822\pi$
$488$	−7.53711	−	7.53711i	−0.341189	−	0.341189i
$489$	−22.8647	−	22.8647i	−1.03398	−	1.03398i
$490$		0			0
$491$	19.0691	+	11.0096i	0.860578	+	0.496855i	0.864206	−	0.503139i	$-0.167822\pi$
$491$	19.0691	+	11.0096i	0.860578	+	0.496855i	−0.00362809	+	0.999993i	$0.501155\pi$
$492$	2.05760	+	0.551331i	0.0927636	+	0.0248559i
$493$	−14.2754	−	24.7257i	−0.642930	−	1.11359i
$494$	−48.0862	−	3.61798i	−2.16350	−	0.162781i
$495$	−0.515196	−	0.297449i	−0.0231563	−	0.0133693i
$496$	−2.10167	−	7.84352i	−0.0943676	−	0.352185i
$497$		0			0
$498$	24.6450	−	14.2288i	1.10437	−	0.637608i
$499$	27.8551	−	7.46375i	1.24697	−	0.334123i	0.425802	−	0.904816i	$-0.359992\pi$
$499$	27.8551	−	7.46375i	1.24697	−	0.334123i	0.821164	+	0.570693i	$0.193325\pi$
$500$	2.37238	+	8.85385i	0.106096	+	0.395956i
$501$	−5.20113	−	19.4109i	−0.232370	−	0.867215i
$502$	−63.4453	+	17.0001i	−2.83170	+	0.758753i
$503$	7.32350	−	4.22823i	0.326539	−	0.188527i	−0.327764	−	0.944759i	$-0.606295\pi$
$503$	7.32350	−	4.22823i	0.326539	−	0.188527i	0.654303	+	0.756232i	$0.272962\pi$
$504$		0			0
$505$	−0.838597	−	3.12969i	−0.0373171	−	0.139269i
$506$	−36.4698	−	21.0558i	−1.62128	−	0.936046i
$507$	−23.8567	+	9.34665i	−1.05951	+	0.415099i
$508$	−8.23822	−	14.2690i	−0.365512	−	0.633085i
$509$	19.6560	+	5.26680i	0.871236	+	0.233447i	0.666622	−	0.745396i	$-0.267739\pi$
$509$	19.6560	+	5.26680i	0.871236	+	0.233447i	0.204614	+	0.978843i	$0.434406\pi$
$510$	−3.93660	−	2.27280i	−0.174315	−	0.100641i
$511$		0			0
$512$	25.2221	+	25.2221i	1.11467	+	1.11467i
$513$	−16.2045	−	16.2045i	−0.715446	−	0.715446i
$514$	45.3431	−	12.1496i	2.00000	−	0.535898i
$515$	1.82246	+	0.488326i	0.0803071	+	0.0215182i
$516$			34.9240i			1.53744i
$517$	−4.65707	+	8.06628i	−0.204818	+	0.354754i
$518$		0			0
$519$			29.5172i			1.29566i
$520$	3.56958	−	1.71771i	0.156537	−	0.0753265i
$521$	15.2229	−	8.78895i	0.666928	−	0.385051i	−0.127984	−	0.991776i	$-0.540851\pi$
$521$	15.2229	−	8.78895i	0.666928	−	0.385051i	0.794911	+	0.606725i	$0.207517\pi$
$522$	−10.7783	−	10.7783i	−0.471755	−	0.471755i
$523$	24.5458	−	14.1715i	1.07331	−	0.619677i	0.144227	−	0.989545i	$-0.453930\pi$
$523$	24.5458	−	14.1715i	1.07331	−	0.619677i	0.929084	+	0.369868i	$0.120597\pi$
$524$	−26.9706	−	46.7145i	−1.17822	−	2.04073i
$525$		0			0
$526$	12.5442	−	46.8154i	0.546951	−	2.04125i
$527$	−6.55742	+	6.55742i	−0.285646	+	0.285646i
$528$	−5.15150	+	19.2257i	−0.224190	+	0.836689i
$529$	6.80241	−	11.7821i	0.295757	−	0.512266i
$530$	−2.26973	−	3.93129i	−0.0985910	−	0.170765i
$531$	−0.621139	+	0.166434i	−0.0269552	+	0.00722261i
$532$		0			0
$533$	0.938050	+	0.328552i	0.0406315	+	0.0142312i
$534$	8.27696	−	14.3361i	0.358179	−	0.620384i
$535$	−0.694653	+	0.694653i	−0.0300325	+	0.0300325i
$536$	12.4401			0.537332
$537$	18.1004			0.781090
$538$	45.2077	−	45.2077i	1.94904	−	1.94904i
$539$		0			0
$540$	3.71194	+	0.994611i	0.159736	+	0.0428012i
$541$	−3.43118	−	12.8053i	−0.147518	−	0.550545i	−0.999630	−	0.0271858i	$-0.991345\pi$
$541$	−3.43118	−	12.8053i	−0.147518	−	0.550545i	0.852112	−	0.523359i	$-0.175321\pi$
$542$	11.3202	+	6.53570i	0.486242	+	0.280732i
$543$			25.2679i			1.08435i
$544$	0.789699	−	2.94720i	0.0338580	−	0.126360i
$545$	3.31170			0.141857
$546$		0			0
$547$	−28.5769			−1.22186			−0.610930	−	0.791685i	$-0.709204\pi$
$547$	−28.5769			−1.22186			−0.610930	+	0.791685i	$0.709204\pi$
$548$	−14.0009	+	52.2523i	−0.598091	+	2.23211i
$549$			2.01763i			0.0861101i
$550$	−29.8062	−	17.2086i	−1.27094	−	0.733778i
$551$	−10.0741	−	37.5971i	−0.429172	−	1.60169i
$552$	−53.8302	−	14.4238i	−2.29117	−	0.613916i
$553$		0			0
$554$	−11.2029	+	11.2029i	−0.475964	+	0.475964i
$555$	4.81548			0.204406
$556$	−58.5149			−2.48158
$557$	31.0198	−	31.0198i	1.31435	−	1.31435i	0.396178	−	0.918174i	$-0.370336\pi$
$557$	31.0198	−	31.0198i	1.31435	−	1.31435i	0.918174	−	0.396178i	$-0.129664\pi$
$558$	−2.47553	+	4.28774i	−0.104797	+	0.181514i
$559$	−1.22259	+	16.2493i	−0.0517100	+	0.687272i
$560$		0			0
$561$	21.9564	−	5.88321i	0.927001	−	0.248389i
$562$	−19.1911	−	33.2400i	−0.809528	−	1.40214i
$563$	3.31175	−	5.73611i	0.139573	−	0.241748i	−0.787762	−	0.615980i	$-0.788760\pi$
$563$	3.31175	−	5.73611i	0.139573	−	0.241748i	0.927335	+	0.374232i	$0.122094\pi$
$564$	−6.51218	+	24.3038i	−0.274212	+	1.02337i
$565$	0.766994	−	0.766994i	0.0322677	−	0.0322677i
$566$	1.49759	−	5.58907i	0.0629482	−	0.234926i
$567$		0			0
$568$	3.27360	+	5.67003i	0.137357	+	0.237909i
$569$	−0.379622	+	0.219175i	−0.0159146	+	0.00918829i	−0.507936	−	0.861395i	$-0.669591\pi$
$569$	−0.379622	+	0.219175i	−0.0159146	+	0.00918829i	0.492022	+	0.870583i	$0.336258\pi$
$570$	−4.38196	−	4.38196i	−0.183540	−	0.183540i
$571$	1.04982	−	0.606116i	0.0439338	−	0.0253652i	−0.477872	−	0.878429i	$-0.658592\pi$
$571$	1.04982	−	0.606116i	0.0439338	−	0.0253652i	0.521806	+	0.853064i	$0.325258\pi$
$572$	−13.3669	+	38.1639i	−0.558898	+	1.59571i
$573$			10.6266i			0.443932i
$574$		0			0
$575$	14.9583	−	25.9085i	0.623804	−	1.08046i
$576$		−	7.87501i		−	0.328126i
$577$	1.50218	+	0.402507i	0.0625365	+	0.0167566i	0.289952	−	0.957041i	$-0.406361\pi$
$577$	1.50218	+	0.402507i	0.0625365	+	0.0167566i	−0.227415	+	0.973798i	$0.573027\pi$
$578$	−1.75064	+	0.469082i	−0.0728169	+	0.0195112i
$579$	4.65680	+	4.65680i	0.193530	+	0.193530i
$580$	4.61532	+	4.61532i	0.191641	+	0.191641i
$581$		0			0
$582$	11.2535	+	6.49723i	0.466474	+	0.269319i
$583$	21.9268	+	5.87528i	0.908117	+	0.243329i
$584$	31.6653	+	54.8460i	1.31032	+	2.26954i
$585$	−0.707683	−	0.247866i	−0.0292591	−	0.0102480i
$586$	70.7533	+	40.8495i	2.92279	+	1.68748i
$587$	4.96434	+	18.5272i	0.204900	+	0.764698i	0.989480	+	0.144670i	$0.0462121\pi$
$587$	4.96434	+	18.5272i	0.204900	+	0.764698i	−0.784580	+	0.620028i	$0.787121\pi$
$588$		0			0
$589$	−10.9489	+	6.32137i	−0.451143	+	0.260467i
$590$	0.401652	−	0.107622i	0.0165357	−	0.00443074i
$591$	−1.94270	−	7.25025i	−0.0799119	−	0.298235i
$592$	−9.49601	−	35.4396i	−0.390284	−	1.45656i
$593$	7.31288	−	1.95948i	0.300304	−	0.0804662i	−0.105521	−	0.994417i	$-0.533651\pi$
$593$	7.31288	−	1.95948i	0.300304	−	0.0804662i	0.405825	+	0.913951i	$0.366984\pi$
$594$	−25.1319	+	14.5099i	−1.03118	+	0.595349i
$595$		0			0
$596$	10.7299	+	40.0444i	0.439512	+	1.64028i
$597$	−38.0071	−	21.9434i	−1.55553	−	0.898084i
$598$	−50.0956	−	17.5460i	−2.04856	−	0.717508i
$599$	18.9239	+	32.7771i	0.773208	+	1.33924i	0.935796	+	0.352542i	$0.114683\pi$
$599$	18.9239	+	32.7771i	0.773208	+	1.33924i	−0.162588	+	0.986694i	$0.551984\pi$
$600$	−43.9947	−	11.7883i	−1.79607	−	0.481257i
$601$	20.0340	+	11.5666i	0.817205	+	0.471813i	0.849452	−	0.527667i	$-0.176933\pi$
$601$	20.0340	+	11.5666i	0.817205	+	0.471813i	−0.0322469	+	0.999480i	$0.510266\pi$
$602$		0			0
$603$	−1.66506	−	1.66506i	−0.0678066	−	0.0678066i
$604$	−12.4711	−	12.4711i	−0.507443	−	0.507443i
$605$	0.639757	−	0.171422i	0.0260098	−	0.00696932i
$606$	63.8449	+	17.1072i	2.59352	+	0.694933i
$607$			9.81244i			0.398275i	0.979972	+	0.199137i	$0.0638140\pi$
$607$			9.81244i			0.398275i	−0.979972	+	0.199137i	$0.936186\pi$
$608$	2.07983	−	3.60238i	0.0843483	−	0.146096i
$609$		0			0
$610$		−	1.30467i		−	0.0528246i
$611$	−3.88077	+	11.0800i	−0.156999	+	0.448249i
$612$	12.1101	−	6.99175i	0.489520	−	0.282625i
$613$	26.3083	+	26.3083i	1.06258	+	1.06258i	0.997906	+	0.0646737i	$0.0206007\pi$
$613$	26.3083	+	26.3083i	1.06258	+	1.06258i	0.0646737	+	0.997906i	$0.479399\pi$
$614$	57.0832	−	32.9570i	2.30369	−	1.33004i
$615$	0.0638647	+	0.110617i	0.00257527	+	0.00446050i
$616$		0			0
$617$	−2.10572	+	7.85866i	−0.0847732	+	0.316378i	−0.995271	−	0.0971357i	$-0.969032\pi$
$617$	−2.10572	+	7.85866i	−0.0847732	+	0.316378i	0.910498	+	0.413514i	$0.135699\pi$
$618$	−27.2160	+	27.2160i	−1.09479	+	1.09479i
$619$	−11.9110	+	44.4523i	−0.478742	+	1.78669i	0.127984	+	0.991776i	$0.459149\pi$
$619$	−11.9110	+	44.4523i	−0.478742	+	1.78669i	−0.606725	+	0.794912i	$0.707517\pi$
$620$	1.06003	−	1.83602i	0.0425718	−	0.0737365i
$621$	−12.6125	−	21.8455i	−0.506122	−	0.876629i
$622$	−77.8924	+	20.8712i	−3.12320	+	0.836859i
$623$		0			0
$624$	−1.88227	+	25.0170i	−0.0753511	+	1.00148i
$625$	12.0870	−	20.9353i	0.483481	−	0.837413i
$626$	−2.26584	+	2.26584i	−0.0905613	+	0.0905613i
$627$	30.9892			1.23759
$628$	50.9970			2.03500
$629$	−29.6286	+	29.6286i	−1.18137	+	1.18137i
$630$		0			0
$631$	5.64724	+	1.51317i	0.224813	+	0.0602384i	0.369467	−	0.929244i	$-0.379540\pi$
$631$	5.64724	+	1.51317i	0.224813	+	0.0602384i	−0.144654	+	0.989482i	$0.546207\pi$
$632$	4.63008	+	17.2797i	0.184175	+	0.687350i
$633$	26.4920	+	15.2951i	1.05296	+	0.607927i
$634$		−	21.0852i		−	0.837402i
$635$	0.255702	−	0.954292i	0.0101472	−	0.0378699i
$636$	61.3225			2.43160
$637$		0			0
$638$	−49.2896			−1.95139
$639$	0.320754	−	1.19707i	0.0126888	−	0.0473554i
$640$			4.73645i			0.187225i
$641$	38.5365	+	22.2490i	1.52210	+	0.878785i	0.999659	+	0.0261086i	$0.00831158\pi$
$641$	38.5365	+	22.2490i	1.52210	+	0.878785i	0.522440	+	0.852676i	$0.325022\pi$
$642$	−5.18686	−	19.3576i	−0.204709	−	0.763985i
$643$	−27.5723	−	7.38796i	−1.08734	−	0.291353i	−0.329743	−	0.944071i	$-0.606962\pi$
$643$	−27.5723	−	7.38796i	−1.08734	−	0.291353i	−0.757601	+	0.652718i	$0.773629\pi$
$644$		0			0
$645$	−1.48075	+	1.48075i	−0.0583046	+	0.0583046i
$646$	53.9225			2.12155
$647$	35.2243			1.38481			0.692404	−	0.721510i	$-0.256552\pi$
$647$	35.2243			1.38481			0.692404	+	0.721510i	$0.256552\pi$
$648$	−35.9258	+	35.9258i	−1.41130	+	1.41130i
$649$	−1.03969	+	1.80079i	−0.0408114	+	0.0706874i
$650$	−40.9424	−	14.3401i	−1.60589	−	0.562463i
$651$		0			0
$652$	−62.1312	+	16.6480i	−2.43325	+	0.651987i
$653$	7.69807	+	13.3335i	0.301249	+	0.521778i	0.976419	−	0.215884i	$-0.0692632\pi$
$653$	7.69807	+	13.3335i	0.301249	+	0.521778i	−0.675170	+	0.737662i	$0.735930\pi$
$654$	−33.7789	+	58.5068i	−1.32086	+	2.28780i
$655$	0.837126	−	3.12420i	0.0327092	−	0.122073i
$656$	0.688147	−	0.688147i	0.0268676	−	0.0268676i
$657$	3.10264	−	11.5792i	0.121045	−	0.451748i
$658$		0			0
$659$	5.17792	+	8.96841i	0.201703	+	0.349360i	0.949077	−	0.315043i	$-0.102019\pi$
$659$	5.17792	+	8.96841i	0.201703	+	0.349360i	−0.747374	+	0.664403i	$0.768686\pi$
$660$	−4.50037	+	2.59829i	−0.175177	+	0.101138i
$661$	14.4049	+	14.4049i	0.560286	+	0.560286i	0.929389	−	0.369103i	$-0.120335\pi$
$661$	14.4049	+	14.4049i	0.560286	+	0.560286i	−0.369103	+	0.929389i	$0.620335\pi$
$662$	−49.2755	+	28.4492i	−1.91515	+	1.10571i
$663$	25.8175	−	12.4236i	1.00267	−	0.482491i
$664$		−	27.7317i		−	1.07620i
$665$		0			0
$666$	−11.1852	+	19.3734i	−0.433419	+	0.750704i
$667$		−	42.8441i		−	1.65893i
$668$	−38.6128	−	10.3463i	−1.49397	−	0.400309i
$669$	9.70964	−	2.60169i	0.375396	−	0.100587i
$670$	1.07669	+	1.07669i	0.0415962	+	0.0415962i
$671$	4.61332	+	4.61332i	0.178095	+	0.178095i
$672$		0			0
$673$	−28.0255	−	16.1805i	−1.08030	−	0.623714i	−0.149326	−	0.988788i	$-0.547710\pi$
$673$	−28.0255	−	16.1805i	−1.08030	−	0.623714i	−0.930979	+	0.365074i	$0.881044\pi$
$674$	−11.9436	−	3.20027i	−0.460049	−	0.123270i
$675$	−10.3080	−	17.8540i	−0.396755	−	0.687200i
$676$	−7.62656	+	50.3949i	−0.293329	+	1.93827i
$677$	−11.3616	−	6.55960i	−0.436660	−	0.252106i	0.265520	−	0.964105i	$-0.414456\pi$
$677$	−11.3616	−	6.55960i	−0.436660	−	0.252106i	−0.702180	+	0.712000i	$0.747790\pi$
$678$	5.72702	+	21.3735i	0.219945	+	0.820845i
$679$		0			0
$680$	−3.83619	+	2.21482i	−0.147111	+	0.0849346i
$681$	−20.5685	+	5.51132i	−0.788188	+	0.211194i
$682$	4.14364	+	15.4643i	0.158668	+	0.592157i
$683$	−9.94737	−	37.1241i	−0.380625	−	1.42051i	−0.844949	−	0.534848i	$-0.820369\pi$
$683$	−9.94737	−	37.1241i	−0.380625	−	1.42051i	0.464323	−	0.885666i	$-0.346298\pi$
$684$	18.4142	−	4.93407i	0.704084	−	0.188659i
$685$	−2.80909	+	1.62183i	−0.107330	+	0.0619669i
$686$		0			0
$687$	6.74510	+	25.1731i	0.257342	+	0.960412i
$688$	13.8177	+	7.97762i	0.526793	+	0.304144i
$689$	28.5319	+	2.14673i	1.08698	+	0.0817838i
$690$	−3.41062	−	5.90737i	−0.129840	−	0.224890i
$691$	16.1675	+	4.33206i	0.615040	+	0.164799i	0.552872	−	0.833266i	$-0.313532\pi$
$691$	16.1675	+	4.33206i	0.615040	+	0.164799i	0.0621679	+	0.998066i	$0.480199\pi$
$692$	50.8502	+	29.3584i	1.93303	+	1.11604i
$693$		0			0
$694$	−1.17683	−	1.17683i	−0.0446720	−	0.0446720i
$695$	−2.48099	−	2.48099i	−0.0941094	−	0.0941094i
$696$	−63.0056	+	16.8823i	−2.38822	+	0.639922i
$697$	−1.07355	−	0.287656i	−0.0406635	−	0.0108957i
$698$			12.7846i			0.483903i
$699$	12.0516	−	20.8741i	0.455835	−	0.789529i
$700$		0			0
$701$		−	22.9034i		−	0.865051i	−0.901622	−	0.432525i	$-0.857623\pi$
$701$		−	22.9034i		−	0.865051i	0.901622	−	0.432525i	$-0.142377\pi$
$702$	−27.7321	+	23.8510i	−1.04668	+	0.900200i
$703$	−49.4708	+	28.5620i	−1.86583	+	1.07724i
$704$	−18.0063	−	18.0063i	−0.678638	−	0.678638i
$705$	−1.30658	+	0.754352i	−0.0492085	+	0.0284105i
$706$	−26.4167	−	45.7551i	−0.994206	−	1.72201i
$707$		0			0
$708$	−1.45384	+	5.42581i	−0.0546387	+	0.203914i
$709$	−4.72408	+	4.72408i	−0.177417	+	0.177417i	−0.790229	−	0.612812i	$-0.790038\pi$
$709$	−4.72408	+	4.72408i	−0.177417	+	0.177417i	0.612812	+	0.790229i	$0.290038\pi$
$710$	−0.207411	+	0.774070i	−0.00778401	+	0.0290503i
$711$	1.69310	−	2.93254i	0.0634963	−	0.109979i
$712$	−8.06584	−	13.9704i	−0.302280	−	0.523564i
$713$	−13.4420	+	3.60178i	−0.503408	+	0.134888i
$714$		0			0
$715$	−2.18487	+	1.05138i	−0.0817096	+	0.0393193i
$716$	18.0030	−	31.1821i	0.672803	−	1.16533i
$717$	8.61185	−	8.61185i	0.321615	−	0.321615i
$718$	34.5473			1.28930
$719$	11.1449			0.415635			0.207818	−	0.978168i	$-0.433364\pi$
$719$	11.1449			0.415635			0.207818	+	0.978168i	$0.433364\pi$
$720$	−0.519152	+	0.519152i	−0.0193476	+	0.0193476i
$721$		0			0
$722$	26.3516	+	7.06089i	0.980705	+	0.262779i
$723$	−6.23551	−	23.2712i	−0.231901	−	0.865466i
$724$	43.5298	+	25.1319i	1.61777	+	0.934020i
$725$		−	35.0158i		−	1.30046i
$726$	−3.49698	+	13.0509i	−0.129785	+	0.484365i
$727$	−2.66009			−0.0986574			−0.0493287	−	0.998783i	$-0.515708\pi$
$727$	−2.66009			−0.0986574			−0.0493287	+	0.998783i	$0.515708\pi$
$728$		0			0
$729$	−15.0353			−0.556862
$730$	−2.00628	+	7.48754i	−0.0742558	+	0.277126i
$731$		−	18.2215i		−	0.673946i
$732$	15.2632	+	8.81224i	0.564146	+	0.325710i
$733$	4.88442	+	18.2289i	0.180410	+	0.673299i	0.995567	+	0.0940588i	$0.0299842\pi$
$733$	4.88442	+	18.2289i	0.180410	+	0.673299i	−0.815157	+	0.579241i	$0.803349\pi$
$734$	−7.06318	−	1.89257i	−0.260707	−	0.0698561i
$735$		0			0
$736$	3.23760	−	3.23760i	0.119340	−	0.119340i
$737$	−7.61436			−0.280479
$738$	−0.593371			−0.0218423
$739$	−29.8756	+	29.8756i	−1.09899	+	1.09899i	−0.104465	+	0.994529i	$0.533313\pi$
$739$	−29.8756	+	29.8756i	−1.09899	+	1.09899i	−0.994529	+	0.104465i	$0.966687\pi$
$740$	4.78956	−	8.29575i	0.176068	−	0.304958i
$741$	38.3815	−	7.25031i	1.40998	−	0.266347i
$742$		0			0
$743$	23.2394	−	6.22698i	0.852571	−	0.228446i	0.194035	−	0.980995i	$-0.437842\pi$
$743$	23.2394	−	6.22698i	0.852571	−	0.228446i	0.658536	+	0.752549i	$0.271176\pi$
$744$	10.5934	+	18.3483i	0.388373	+	0.672682i
$745$	−1.24292	+	2.15279i	−0.0455369	+	0.0788723i
$746$	16.4906	−	61.5436i	0.603762	−	2.25327i
$747$	−3.71178	+	3.71178i	−0.135807	+	0.135807i
$748$	11.7031	−	43.6765i	0.427907	−	1.59697i
$749$		0			0
$750$	−5.60606	−	9.70998i	−0.204704	−	0.354558i
$751$	−14.5002	+	8.37167i	−0.529118	+	0.305486i	−0.740657	−	0.671883i	$-0.765486\pi$
$751$	−14.5002	+	8.37167i	−0.529118	+	0.305486i	0.211539	+	0.977370i	$0.432152\pi$
$752$	8.12821	+	8.12821i	0.296405	+	0.296405i
$753$	46.0761	−	26.6020i	1.67911	−	0.969432i
$754$	−61.0471	+	11.5319i	−2.22321	+	0.419967i
$755$		−	1.05754i		−	0.0384877i
$756$		0			0
$757$	−13.8538	+	23.9955i	−0.503524	+	0.872130i	0.496467	+	0.868055i	$0.334630\pi$
$757$	−13.8538	+	23.9955i	−0.503524	+	0.872130i	−0.999992	+	0.00407434i	$0.998703\pi$
$758$		−	13.9771i		−	0.507671i
$759$	32.9485	+	8.82851i	1.19595	+	0.320455i
$760$	−5.83319	+	1.56300i	−0.211592	+	0.0566959i
$761$	−16.0131	−	16.0131i	−0.580474	−	0.580474i	0.354559	−	0.935034i	$-0.384631\pi$
$761$	−16.0131	−	16.0131i	−0.580474	−	0.580474i	−0.935034	+	0.354559i	$0.884631\pi$
$762$	14.2511	+	14.2511i	0.516262	+	0.516262i
$763$		0			0
$764$	18.3067	+	10.5694i	0.662314	+	0.382387i
$765$	0.809904	+	0.217013i	0.0292821	+	0.00784613i
$766$	−19.7607	−	34.2265i	−0.713983	−	1.23665i
$767$	−0.866380	+	2.47361i	−0.0312832	+	0.0893167i
$768$	−53.2879	−	30.7658i	−1.92286	−	1.11016i
$769$	5.25290	+	19.6041i	0.189424	+	0.706941i	0.993640	+	0.112604i	$0.0359191\pi$
$769$	5.25290	+	19.6041i	0.189424	+	0.706941i	−0.804216	+	0.594338i	$0.797414\pi$
$770$		0			0
$771$	−32.9296	+	19.0119i	−1.18593	+	0.684698i
$772$	12.6541	−	3.39066i	0.455432	−	0.122033i
$773$	5.28554	+	19.7259i	0.190108	+	0.709492i	0.993479	+	0.114014i	$0.0363708\pi$
$773$	5.28554	+	19.7259i	0.190108	+	0.709492i	−0.803371	+	0.595478i	$0.796963\pi$
$774$	−2.51785	−	9.39674i	−0.0905022	−	0.337759i
$775$	−10.9860	+	2.94369i	−0.394628	+	0.105740i
$776$	10.9665	−	6.33150i	0.393674	−	0.227288i
$777$		0			0
$778$	5.85193	+	21.8397i	0.209802	+	0.782991i
$779$	−1.31220	−	0.757600i	−0.0470145	−	0.0271438i
$780$	−4.96599	+	4.27100i	−0.177811	+	0.152926i
$781$	−2.00371	−	3.47052i	−0.0716982	−	0.124185i
$782$	57.3316	+	15.3620i	2.05017	+	0.549342i
$783$	−25.5690	−	14.7623i	−0.913763	−	0.527561i
$784$		0			0
$785$	2.16224	+	2.16224i	0.0771736	+	0.0771736i
$786$	46.6557	+	46.6557i	1.66416	+	1.66416i
$787$	−34.0496	+	9.12356i	−1.21374	+	0.325220i	−0.808227	−	0.588871i	$-0.799573\pi$
$787$	−34.0496	+	9.12356i	−1.21374	+	0.325220i	−0.405510	+	0.914091i	$0.632906\pi$
$788$	−14.4224	−	3.86448i	−0.513778	−	0.137666i
$789$			39.2586i			1.39764i
$790$	−1.09482	+	1.89629i	−0.0389521	+	0.0674670i
$791$		0			0
$792$		−	11.8262i		−	0.420226i
$793$	6.79313	+	4.63445i	0.241231	+	0.164574i
$794$	39.7167	−	22.9304i	1.40949	−	0.813770i
$795$	2.60003	+	2.60003i	0.0922137	+	0.0922137i
$796$	−75.6050	+	43.6506i	−2.67975	+	1.54715i
$797$	10.0235	+	17.3612i	0.355050	+	0.614964i	0.987126	−	0.159942i	$-0.0511306\pi$
$797$	10.0235	+	17.3612i	0.355050	+	0.614964i	−0.632077	+	0.774906i	$0.717797\pi$
$798$		0			0
$799$	3.39771	−	12.6804i	0.120202	−	0.448602i
$800$	2.64605	−	2.64605i	0.0935519	−	0.0935519i
$801$	−0.790308	+	2.94947i	−0.0279242	+	0.104214i
$802$	−45.5778	+	78.9431i	−1.60941	+	2.78758i
$803$	−19.3817	−	33.5702i	−0.683967	−	1.18467i
$804$	−19.8685	+	5.32375i	−0.700708	+	0.187754i
$805$		0			0
$806$	8.75012	+	18.1837i	0.308210	+	0.640493i
$807$	−25.8932	+	44.8484i	−0.911485	+	1.57874i
$808$	45.5456	−	45.5456i	1.60229	−	1.60229i
$809$	34.4945			1.21276			0.606381	−	0.795174i	$-0.292620\pi$
$809$	34.4945			1.21276			0.606381	+	0.795174i	$0.292620\pi$
$810$	−6.21874			−0.218504
$811$	15.8161	−	15.8161i	0.555379	−	0.555379i	−0.372609	−	0.927988i	$-0.621537\pi$
$811$	15.8161	−	15.8161i	0.555379	−	0.555379i	0.927988	+	0.372609i	$0.121537\pi$
$812$		0			0
$813$	−10.2272	−	2.74036i	−0.358682	−	0.0961085i
$814$	18.7223	+	69.8726i	0.656217	+	2.44903i
$815$	−3.34019	−	1.92846i	−0.117002	−	0.0675510i
$816$		−	28.0534i		−	0.982065i
$817$	6.42944	−	23.9950i	0.224938	−	0.839479i
$818$	−49.6069			−1.73447
$819$		0			0
$820$	0.254084			0.00887298
$821$	−9.98764	+	37.2744i	−0.348571	+	1.30088i	0.539814	+	0.841784i	$0.318495\pi$
$821$	−9.98764	+	37.2744i	−0.348571	+	1.30088i	−0.888385	+	0.459100i	$0.848172\pi$
$822$		−	66.1700i		−	2.30794i
$823$	8.19006	+	4.72853i	0.285487	+	0.164826i	0.635905	−	0.771767i	$-0.280627\pi$
$823$	8.19006	+	4.72853i	0.285487	+	0.164826i	−0.350418	+	0.936594i	$0.613960\pi$
$824$	9.70766	+	36.2295i	0.338182	+	1.26211i
$825$	26.9283	+	7.21541i	0.937523	+	0.251208i
$826$		0			0
$827$	12.1614	−	12.1614i	0.422895	−	0.422895i	−0.463304	−	0.886199i	$-0.653336\pi$
$827$	12.1614	−	12.1614i	0.422895	−	0.422895i	0.886199	+	0.463304i	$0.153336\pi$
$828$	20.9840			0.729246
$829$	−5.88244			−0.204305			−0.102153	−	0.994769i	$-0.532573\pi$
$829$	−5.88244			−0.204305			−0.102153	+	0.994769i	$0.532573\pi$
$830$	2.40018	−	2.40018i	0.0833114	−	0.0833114i
$831$	6.41657	−	11.1138i	0.222588	−	0.385534i
$832$	−26.5143	−	18.0888i	−0.919219	−	0.627115i
$833$		0			0
$834$	69.1369	−	18.5252i	2.39401	−	0.641474i
$835$	−1.19848	−	2.07583i	−0.0414752	−	0.0718372i
$836$	30.8224	−	53.3860i	1.06602	−	1.84639i
$837$	−2.48205	+	9.26314i	−0.0857922	+	0.320181i
$838$	18.8411	−	18.8411i	0.650857	−	0.650857i
$839$	−3.66834	+	13.6904i	−0.126645	+	0.472646i	−0.999893	−	0.0146305i	$-0.995343\pi$
$839$	−3.66834	+	13.6904i	−0.126645	+	0.472646i	0.873248	+	0.487276i	$0.162009\pi$
$840$		0			0
$841$	−10.5734	−	18.3137i	−0.364601	−	0.631507i
$842$	23.8381	−	13.7629i	0.821515	−	0.474302i
$843$	21.9839	+	21.9839i	0.757165	+	0.757165i
$844$	52.6987	−	30.4256i	1.81397	−	1.04729i
$845$	−2.46007	+	1.81335i	−0.0846291	+	0.0623812i
$846$		−	7.00874i		−	0.240965i
$847$		0			0
$848$	14.0078	−	24.2622i	0.481030	−	0.833168i
$849$			4.68689i			0.160854i
$850$	46.8563	+	12.5551i	1.60716	+	0.430636i
$851$	−60.7355	+	16.2740i	−2.08199	+	0.557867i
$852$	−7.65484	−	7.65484i	−0.262251	−	0.262251i
$853$	−0.313002	−	0.313002i	−0.0107170	−	0.0107170i	0.701728	−	0.712445i	$-0.252412\pi$
$853$	−0.313002	−	0.313002i	−0.0107170	−	0.0107170i	−0.712445	+	0.701728i	$0.752412\pi$
$854$		0			0
$855$	0.989951	+	0.571548i	0.0338556	+	0.0195465i
$856$	−18.8639	−	5.05456i	−0.644754	−	0.172761i
$857$	−17.0917	−	29.6037i	−0.583842	−	1.01124i	−0.995019	−	0.0996889i	$-0.968215\pi$
$857$	−17.0917	−	29.6037i	−0.583842	−	1.01124i	0.411176	−	0.911556i	$-0.365118\pi$
$858$	3.71108	−	49.3235i	0.126694	−	1.68388i
$859$	3.41700	+	1.97280i	0.116586	+	0.0673112i	0.557159	−	0.830406i	$-0.311891\pi$
$859$	3.41700	+	1.97280i	0.116586	+	0.0673112i	−0.440573	+	0.897717i	$0.645225\pi$
$860$	1.07815	+	4.02372i	0.0367647	+	0.137208i
$861$		0			0
$862$	36.8711	−	21.2875i	1.25583	−	0.725056i
$863$	34.9889	−	9.37524i	1.19104	−	0.319137i	0.391740	−	0.920076i	$-0.371873\pi$
$863$	34.9889	−	9.37524i	1.19104	−	0.319137i	0.799295	+	0.600939i	$0.205206\pi$
$864$	−0.816634	−	3.04772i	−0.0277825	−	0.103686i
$865$	0.911239	+	3.40079i	0.0309830	+	0.115630i
$866$	14.3684	−	3.85001i	0.488260	−	0.130829i
$867$	1.27137	−	0.734026i	0.0431780	−	0.0249288i
$868$		0			0
$869$	−2.83399	−	10.5766i	−0.0961364	−	0.358786i
$870$	−6.91428	−	3.99196i	−0.234416	−	0.135340i
$871$	−9.43070	+	1.78147i	−0.319547	+	0.0603629i
$872$	32.9173	+	57.0145i	1.11472	+	1.93075i
$873$	−2.31527	−	0.620374i	−0.0783600	−	0.0209965i
$874$	70.0768	+	40.4588i	2.37038	+	1.36854i
$875$		0			0
$876$	−74.0450	−	74.0450i	−2.50175	−	2.50175i
$877$	−27.9442	−	27.9442i	−0.943609	−	0.943609i	0.0548838	−	0.998493i	$-0.482521\pi$
$877$	−27.9442	−	27.9442i	−0.943609	−	0.943609i	−0.998493	+	0.0548838i	$0.982521\pi$
$878$	−36.9551	+	9.90208i	−1.24717	+	0.334179i
$879$	−63.9218	−	17.1278i	−2.15603	−	0.577706i
$880$			2.37409i			0.0800306i
$881$	3.07636	−	5.32841i	0.103645	−	0.179519i	−0.809539	−	0.587067i	$-0.800283\pi$
$881$	3.07636	−	5.32841i	0.103645	−	0.179519i	0.913184	+	0.407548i	$0.133616\pi$
$882$		0			0
$883$		−	2.86401i		−	0.0963817i	−0.998838	−	0.0481909i	$-0.984654\pi$
$883$		−	2.86401i		−	0.0963817i	0.998838	−	0.0481909i	$-0.0153456\pi$
$884$	4.27610	−	56.8332i	0.143821	−	1.91151i
$885$	−0.291693	+	0.168409i	−0.00980515	+	0.00566100i
$886$	19.4057	+	19.4057i	0.651947	+	0.651947i
$887$	−46.7839	+	27.0107i	−1.57085	+	0.906930i	−0.574784	+	0.818305i	$0.694914\pi$
$887$	−46.7839	+	27.0107i	−1.57085	+	0.906930i	−0.996065	+	0.0886250i	$0.971753\pi$
$888$	47.8645	+	82.9037i	1.60623	+	2.78207i
$889$		0			0
$890$	0.511042	−	1.90724i	0.0171302	−	0.0639307i
$891$	21.9895	−	21.9895i	0.736675	−	0.736675i
$892$	5.17537	−	19.3148i	0.173284	−	0.646706i
$893$	8.94857	−	15.4994i	0.299452	−	0.518667i
$894$	−25.3552	−	43.9165i	−0.848005	−	1.46879i
$895$	2.08541	−	0.558785i	0.0697077	−	0.0186781i
$896$		0			0
$897$	42.8736	+	3.22579i	1.43151	+	0.107706i
$898$	−5.91065	+	10.2375i	−0.197241	+	0.341631i
$899$	−11.5175	+	11.5175i	−0.384131	+	0.384131i
$900$	17.1500			0.571665
$901$	−31.9949			−1.06590
$902$	−1.35675	+	1.35675i	−0.0451748	+	0.0451748i
$903$		0			0
$904$	20.8283	+	5.58094i	0.692741	+	0.185619i
$905$	0.780056	+	2.91121i	0.0259299	+	0.0967719i
$906$	18.6832	+	10.7867i	0.620708	+	0.358366i
$907$		−	3.41414i		−	0.113365i	−0.998392	−	0.0566823i	$-0.981948\pi$
$907$		−	3.41414i		−	0.113365i	0.998392	−	0.0566823i	$-0.0180522\pi$
$908$	−10.9633	+	40.9156i	−0.363830	+	1.35783i
$909$	−12.1922			−0.404390
$910$		0			0
$911$	40.6913			1.34816			0.674082	−	0.738656i	$-0.264539\pi$
$911$	40.6913			1.34816			0.674082	+	0.738656i	$0.264539\pi$
$912$	9.89862	−	36.9422i	0.327776	−	1.22328i
$913$			16.9741i			0.561760i
$914$	−18.7852	−	10.8457i	−0.621360	−	0.358742i
$915$	0.273518	+	1.02078i	0.00904224	+	0.0337461i
$916$	50.0751	+	13.4176i	1.65453	+	0.443330i
$917$		0			0
$918$	28.9220	−	28.9220i	0.954567	−	0.954567i
$919$	−22.2730			−0.734718			−0.367359	−	0.930079i	$-0.619738\pi$
$919$	−22.2730			−0.734718			−0.367359	+	0.930079i	$0.619738\pi$
$920$	−6.64726			−0.219154
$921$	−37.7530	+	37.7530i	−1.24400	+	1.24400i
$922$	14.4057	−	24.9514i	0.474427	−	0.821732i
$923$	−3.29364	−	3.82959i	−0.108412	−	0.126053i
$924$		0			0
$925$	−49.6383	+	13.3005i	−1.63210	+	0.437319i
$926$	−33.7730	−	58.4966i	−1.10985	−	1.92232i
$927$	3.54984	−	6.14850i	0.116592	−	0.201943i
$928$	1.38704	−	5.17649i	0.0455317	−	0.169927i
$929$	37.7292	−	37.7292i	1.23785	−	1.23785i	0.276978	−	0.960876i	$-0.410667\pi$
$929$	37.7292	−	37.7292i	1.23785	−	1.23785i	0.960876	−	0.276978i	$-0.0893330\pi$
$930$	−0.671187	+	2.50490i	−0.0220091	+	0.0821390i
$931$		0			0
$932$	−23.9735	−	41.5234i	−0.785280	−	1.36014i
$933$	56.5680	−	32.6595i	1.85195	−	1.06923i
$934$	−42.2812	−	42.2812i	−1.38348	−	1.38348i
$935$	2.34806	−	1.35565i	0.0767897	−	0.0443345i
$936$	−2.76689	−	14.6473i	−0.0904385	−	0.478761i
$937$		−	41.0483i		−	1.34099i	−0.741914	−	0.670495i	$-0.766082\pi$
$937$		−	41.0483i		−	1.34099i	0.741914	−	0.670495i	$-0.233918\pi$
$938$		0			0
$939$	1.29779	−	2.24784i	0.0423517	−	0.0733553i
$940$			3.00117i			0.0978873i
$941$	3.36117	+	0.900623i	0.109571	+	0.0293595i	0.313188	−	0.949691i	$-0.398603\pi$
$941$	3.36117	+	0.900623i	0.109571	+	0.0293595i	−0.203617	+	0.979051i	$0.565270\pi$
$942$	−60.2542	+	16.1451i	−1.96319	+	0.526035i
$943$	−1.17933	−	1.17933i	−0.0384043	−	0.0384043i
$944$	1.81462	+	1.81462i	0.0590609	+	0.0590609i
$945$		0			0
$946$	−27.2428	−	15.7287i	−0.885741	−	0.511383i
$947$	−13.1491	−	3.52329i	−0.427288	−	0.114491i	0.0387649	−	0.999248i	$-0.487658\pi$
$947$	−13.1491	−	3.52329i	−0.427288	−	0.114491i	−0.466053	+	0.884757i	$0.654324\pi$
$948$	−14.7897	−	25.6165i	−0.480347	−	0.831985i
$949$	−31.8592	−	37.0434i	−1.03419	−	1.20248i
$950$	57.2727	+	33.0664i	1.85817	+	1.07282i
$951$	4.42042	+	16.4972i	0.143342	+	0.534960i
$952$		0			0
$953$	−50.4563	+	29.1309i	−1.63444	+	0.943643i	−0.651737	+	0.758445i	$0.725960\pi$
$953$	−50.4563	+	29.1309i	−1.63444	+	0.943643i	−0.982701	+	0.185199i	$0.940707\pi$
$954$	−16.4996	+	4.42106i	−0.534195	+	0.143137i
$955$	0.328058	+	1.22433i	0.0106157	+	0.0396183i
$956$	−6.27038	−	23.4014i	−0.202799	−	0.756854i
$957$	38.5645	−	10.3333i	1.24661	−	0.334029i
$958$	−44.5475	+	25.7195i	−1.43927	+	0.830960i
$959$		0			0
$960$	−1.06757	−	3.98423i	−0.0344557	−	0.128591i
$961$	−22.2650	−	12.8547i	−0.718226	−	0.414668i
$962$	39.5359	+	82.1598i	1.27469	+	2.64894i
$963$	1.84832	+	3.20139i	0.0595614	+	0.103163i
$964$	−46.2919	−	12.4039i	−1.49096	−	0.399502i
$965$	0.680289	+	0.392765i	0.0218993	+	0.0126435i
$966$		0			0
$967$	29.7856	+	29.7856i	0.957840	+	0.957840i	0.999147	−	0.0413063i	$-0.0131520\pi$
$967$	29.7856	+	29.7856i	0.957840	+	0.957840i	−0.0413063	+	0.999147i	$0.513152\pi$
$968$	9.31024	+	9.31024i	0.299242	+	0.299242i
$969$	−42.1893	+	11.3046i	−1.35532	+	0.363156i
$970$	1.49714	+	0.401157i	0.0480702	+	0.0128804i
$971$			16.4097i			0.526613i	0.964712	+	0.263306i	$0.0848130\pi$
$971$			16.4097i			0.526613i	−0.964712	+	0.263306i	$0.915187\pi$
$972$	17.4841	−	30.2833i	0.560801	−	0.971336i
$973$		0			0
$974$			37.5963i			1.20466i
$975$	35.0399	+	2.63639i	1.12218	+	0.0844320i
$976$	6.97311	−	4.02593i	0.223204	−	0.128867i
$977$	15.9039	+	15.9039i	0.508810	+	0.508810i	0.914161	−	0.405351i	$-0.132851\pi$
$977$	15.9039	+	15.9039i	0.508810	+	0.508810i	−0.405351	+	0.914161i	$0.632851\pi$
$978$	68.1391	−	39.3401i	2.17885	−	1.25796i
$979$	4.93694	+	8.55104i	0.157785	+	0.273292i
$980$		0			0
$981$	3.22531	−	12.0370i	0.102976	−	0.384313i
$982$	−37.8853	+	37.8853i	−1.20897	+	1.20897i
$983$	14.8319	−	55.3533i	0.473063	−	1.76550i	−0.155603	−	0.987820i	$-0.549732\pi$
$983$	14.8319	−	55.3533i	0.473063	−	1.76550i	0.628666	−	0.777675i	$-0.283601\pi$
$984$	−1.26959	+	2.19900i	−0.0404732	+	0.0701016i
$985$	−0.447651	−	0.775354i	−0.0142633	−	0.0247048i
$986$	67.1037	−	17.9804i	2.13702	−	0.572612i
$987$		0			0
$988$	25.6846	−	73.3321i	0.817134	−	2.33300i
$989$	13.6719	−	23.6804i	0.434740	−	0.752991i
$990$	1.02356	−	1.02356i	0.0325308	−	0.0325308i
$991$	17.5621			0.557879			0.278940	−	0.960309i	$-0.410017\pi$
$991$	17.5621			0.557879			0.278940	+	0.960309i	$0.410017\pi$
$992$	−1.74069			−0.0552670
$993$	32.5893	−	32.5893i	1.03419	−	1.03419i
$994$		0			0
$995$	−5.05636	−	1.35485i	−0.160297	−	0.0429516i
$996$	11.8678	+	44.2912i	0.376045	+	1.40342i
$997$	−46.9206	−	27.0896i	−1.48599	−	0.857936i	−0.486117	−	0.873894i	$-0.661587\pi$
$997$	−46.9206	−	27.0896i	−1.48599	−	0.857936i	−0.999873	+	0.0159574i	$0.994920\pi$
$998$			70.1692i			2.22117i
$999$	−11.2147	+	41.8539i	−0.354818	+	1.32420i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.x.a.215.1		28
7.2	even	3		637.2.bd.b.293.7		28
7.3	odd	6		637.2.bb.a.423.1		28
7.4	even	3		91.2.ba.a.59.1	yes	28
7.5	odd	6		637.2.bd.a.293.7		28
7.6	odd	2		91.2.w.a.33.1	✓	28
13.2	odd	12		637.2.bb.a.509.1		28
21.11	odd	6		819.2.et.b.514.7		28
21.20	even	2		819.2.gh.b.397.7		28
91.2	odd	12		637.2.bd.a.587.7		28
91.41	even	12		91.2.ba.a.54.1	yes	28
91.54	even	12		637.2.bd.b.587.7		28
91.67	odd	12		91.2.w.a.80.1	yes	28
91.80	even	12	inner	637.2.x.a.80.1		28
273.41	odd	12		819.2.et.b.145.7		28
273.158	even	12		819.2.gh.b.262.7		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.33.1	✓	28	7.6	odd	2
91.2.w.a.80.1	yes	28	91.67	odd	12
91.2.ba.a.54.1	yes	28	91.41	even	12
91.2.ba.a.59.1	yes	28	7.4	even	3
637.2.x.a.80.1		28	91.80	even	12	inner
637.2.x.a.215.1		28	1.1	even	1	trivial
637.2.bb.a.423.1		28	7.3	odd	6
637.2.bb.a.509.1		28	13.2	odd	12
637.2.bd.a.293.7		28	7.5	odd	6
637.2.bd.a.587.7		28	91.2	odd	12
637.2.bd.b.293.7		28	7.2	even	3
637.2.bd.b.587.7		28	91.54	even	12
819.2.et.b.145.7		28	273.41	odd	12
819.2.et.b.514.7		28	21.11	odd	6
819.2.gh.b.262.7		28	273.158	even	12
819.2.gh.b.397.7		28	21.20	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.629770 + 2.35033i) q^{2} -1.97095i q^{3} +(-3.39540 - 1.96034i) q^{4} +(-0.0608458 - 0.227080i) q^{5} +(4.63238 + 1.24124i) q^{6} +(3.30464 - 3.30464i) q^{8} -0.884626 q^{9} +O(q^{10})\)	\(q+(-0.629770 + 2.35033i) q^{2} -1.97095i q^{3} +(-3.39540 - 1.96034i) q^{4} +(-0.0608458 - 0.227080i) q^{5} +(4.63238 + 1.24124i) q^{6} +(3.30464 - 3.30464i) q^{8} -0.884626 q^{9} +0.572032 q^{10} +(-2.02271 + 2.02271i) q^{11} +(-3.86372 + 6.69215i) q^{12} +(-2.03197 + 2.97844i) q^{13} +(-0.447562 + 0.119924i) q^{15} +(1.76516 + 3.05735i) q^{16} +(2.01588 - 3.49161i) q^{17} +(0.557110 - 2.07916i) q^{18} +(3.88663 - 3.88663i) q^{19} +(-0.238557 + 0.890305i) q^{20} +(-3.48019 - 6.02787i) q^{22} +(5.23962 - 3.02510i) q^{23} +(-6.51326 - 6.51326i) q^{24} +(4.28226 - 2.47237i) q^{25} +(-5.72065 - 6.65153i) q^{26} -4.16929i q^{27} +(3.54072 - 6.13271i) q^{29} -1.12744i q^{30} +(-2.22176 - 0.595317i) q^{31} +(0.730993 - 0.195869i) q^{32} +(3.98664 + 3.98664i) q^{33} +(6.93691 + 6.93691i) q^{34} +(3.00366 + 1.73416i) q^{36} +(-10.0386 - 2.68984i) q^{37} +(6.68720 + 11.5826i) q^{38} +(5.87034 + 4.00490i) q^{39} +(-0.951490 - 0.549343i) q^{40} +(-0.0713473 - 0.266272i) q^{41} +(3.91398 - 2.25974i) q^{43} +(10.8331 - 2.90272i) q^{44} +(0.0538258 + 0.200881i) q^{45} +(3.81023 + 14.2200i) q^{46} +(3.14513 - 0.842735i) q^{47} +(6.02588 - 3.47904i) q^{48} +(3.11404 + 11.6218i) q^{50} +(-6.88178 - 3.97320i) q^{51} +(12.7381 - 6.12966i) q^{52} +(-3.96785 - 6.87251i) q^{53} +(9.79921 + 2.62569i) q^{54} +(0.582389 + 0.336242i) q^{55} +(-7.66035 - 7.66035i) q^{57} +(12.1841 + 12.1841i) q^{58} +(0.702149 - 0.188140i) q^{59} +(1.75474 + 0.470182i) q^{60} -2.28077i q^{61} +(2.79839 - 4.84695i) q^{62} +8.90209i q^{64} +(0.799980 + 0.280193i) q^{65} +(-11.8806 + 6.85927i) q^{66} +(1.88222 + 1.88222i) q^{67} +(-13.6895 + 7.90362i) q^{68} +(-5.96230 - 10.3270i) q^{69} +(-0.362587 + 1.35319i) q^{71} +(-2.92337 + 2.92337i) q^{72} +(-3.50729 + 13.0894i) q^{73} +(12.6440 - 21.9001i) q^{74} +(-4.87290 - 8.44011i) q^{75} +(-20.8158 + 5.57758i) q^{76} +(-13.1098 + 11.2751i) q^{78} +(-1.91392 + 3.31501i) q^{79} +(0.586860 - 0.586860i) q^{80} -10.8713 q^{81} +0.670760 q^{82} +(4.19588 - 4.19588i) q^{83} +(-0.915533 - 0.245316i) q^{85} +(2.84623 + 10.6223i) q^{86} +(-12.0872 - 6.97857i) q^{87} +13.3686i q^{88} +(0.893381 - 3.33414i) q^{89} -0.506034 q^{90} -23.7208 q^{92} +(-1.17334 + 4.37896i) q^{93} +7.92283i q^{94} +(-1.11906 - 0.646091i) q^{95} +(-0.386047 - 1.44075i) q^{96} +(2.61723 + 0.701285i) q^{97} +(1.78934 - 1.78934i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{6} - 4 q^{8} - 12 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^6 - 4 * q^8 - 12 * q^9	\( 28 q - 2 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{6} - 4 q^{8} - 12 q^{9} + 12 q^{10} + 2 q^{11} - 8 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} - 4 q^{18} + 8 q^{19} + 36 q^{20} - 8 q^{22} - 6 q^{23} - 12 q^{24} - 24 q^{26} - 8 q^{29} + 38 q^{31} - 20 q^{32} - 18 q^{33} - 12 q^{34} + 54 q^{36} - 16 q^{37} + 28 q^{39} - 48 q^{40} - 18 q^{41} + 48 q^{43} - 6 q^{44} - 12 q^{45} + 18 q^{46} + 42 q^{47} - 12 q^{48} + 10 q^{50} + 12 q^{51} + 28 q^{52} + 12 q^{53} + 30 q^{54} + 6 q^{55} + 12 q^{57} + 62 q^{58} + 6 q^{59} + 16 q^{60} + 36 q^{62} - 2 q^{65} - 66 q^{66} - 4 q^{67} - 30 q^{68} - 42 q^{69} - 42 q^{71} - 38 q^{72} - 14 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} + 4 q^{79} - 12 q^{80} + 12 q^{81} + 108 q^{82} + 66 q^{83} - 54 q^{85} - 30 q^{86} - 42 q^{87} + 30 q^{89} + 72 q^{90} - 156 q^{92} + 14 q^{93} - 6 q^{95} - 18 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^6 - 4 * q^8 - 12 * q^9 + 12 * q^10 + 2 * q^11 - 8 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 - 4 * q^18 + 8 * q^19 + 36 * q^20 - 8 * q^22 - 6 * q^23 - 12 * q^24 - 24 * q^26 - 8 * q^29 + 38 * q^31 - 20 * q^32 - 18 * q^33 - 12 * q^34 + 54 * q^36 - 16 * q^37 + 28 * q^39 - 48 * q^40 - 18 * q^41 + 48 * q^43 - 6 * q^44 - 12 * q^45 + 18 * q^46 + 42 * q^47 - 12 * q^48 + 10 * q^50 + 12 * q^51 + 28 * q^52 + 12 * q^53 + 30 * q^54 + 6 * q^55 + 12 * q^57 + 62 * q^58 + 6 * q^59 + 16 * q^60 + 36 * q^62 - 2 * q^65 - 66 * q^66 - 4 * q^67 - 30 * q^68 - 42 * q^69 - 42 * q^71 - 38 * q^72 - 14 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 + 4 * q^79 - 12 * q^80 + 12 * q^81 + 108 * q^82 + 66 * q^83 - 54 * q^85 - 30 * q^86 - 42 * q^87 + 30 * q^89 + 72 * q^90 - 156 * q^92 + 14 * q^93 - 6 * q^95 - 18 * q^96 - 62 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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