LMFDB - Embedded newform 1050.2.bc.g.607.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(157,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(12))

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("1050.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.bc (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			607.4
Root			$0.117630 - 0.893490i$ of defining polynomial
Character	$\chi$	$=$	1050.607
Dual form			1050.2.bc.g.493.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(0.703686 + 2.55046i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(0.703686 + 2.55046i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(0.989376 + 1.71365i) q^{11} +(0.258819 + 0.965926i) q^{12} +(2.19222 + 2.19222i) q^{13} +(1.33981 + 2.28142i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-4.44599 - 1.19130i) q^{17} +(-0.965926 - 0.258819i) q^{18} +(2.10939 - 3.65357i) q^{19} +(-2.64568 + 0.0196015i) q^{21} +(1.39919 + 1.39919i) q^{22} +(1.52249 + 5.68202i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.68491 + 1.55013i) q^{26} +(0.707107 - 0.707107i) q^{27} +(1.88464 + 1.85692i) q^{28} +8.94996i q^{29} +(-1.50157 + 0.866930i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-1.91133 + 0.512139i) q^{33} -4.60282 q^{34} -1.00000 q^{36} +(-2.67747 + 0.717425i) q^{37} +(1.09190 - 4.07503i) q^{38} +(-2.68491 + 1.55013i) q^{39} +6.55691i q^{41} +(-2.55046 + 0.703686i) q^{42} +(6.33724 - 6.33724i) q^{43} +(1.71365 + 0.989376i) q^{44} +(2.94123 + 5.09436i) q^{46} +(-1.57366 - 5.87298i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-6.00965 + 3.58944i) q^{49} +(2.30141 - 3.98616i) q^{51} +(2.99462 + 0.802407i) q^{52} +(11.0441 + 2.95926i) q^{53} +(0.500000 - 0.866025i) q^{54} +(2.30103 + 1.30586i) q^{56} +(2.98313 + 2.98313i) q^{57} +(2.31642 + 8.64500i) q^{58} +(-2.10351 - 3.64339i) q^{59} +(9.63018 + 5.55999i) q^{61} +(-1.22602 + 1.22602i) q^{62} +(0.665818 - 2.56060i) q^{63} -1.00000i q^{64} +(-1.71365 + 0.989376i) q^{66} +(-1.42665 + 5.32434i) q^{67} +(-4.44599 + 1.19130i) q^{68} -5.88246 q^{69} -3.86002 q^{71} +(-0.965926 + 0.258819i) q^{72} +(3.93920 - 14.7013i) q^{73} +(-2.40055 + 1.38596i) q^{74} -4.21878i q^{76} +(-3.67438 + 3.72923i) q^{77} +(-2.19222 + 2.19222i) q^{78} +(2.21282 + 1.27757i) q^{79} +(0.500000 + 0.866025i) q^{81} +(1.69705 + 6.33349i) q^{82} +(-9.52969 - 9.52969i) q^{83} +(-2.28142 + 1.33981i) q^{84} +(4.48111 - 7.76151i) q^{86} +(-8.64500 - 2.31642i) q^{87} +(1.91133 + 0.512139i) q^{88} +(3.09593 - 5.36231i) q^{89} +(-4.04852 + 7.13378i) q^{91} +(4.15953 + 4.15953i) q^{92} +(-0.448756 - 1.67478i) q^{93} +(-3.04008 - 5.26557i) q^{94} +(0.866025 + 0.500000i) q^{96} +(1.48031 - 1.48031i) q^{97} +(-4.87586 + 5.02254i) q^{98} -1.97875i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{7}+O(q^{10}) $ 16 * q + 4 * q^7	$ 16 q + 4 q^{7} + 4 q^{11} - 16 q^{13} - 16 q^{14} + 8 q^{16} - 12 q^{17} + 8 q^{19} + 8 q^{21} - 4 q^{22} + 40 q^{23} + 8 q^{24} - 12 q^{26} + 4 q^{28} - 24 q^{31} - 4 q^{33} - 16 q^{34} - 16 q^{36} + 8 q^{37} + 20 q^{38} + 12 q^{39} - 8 q^{42} + 24 q^{43} - 4 q^{46} - 52 q^{49} + 8 q^{51} - 8 q^{52} + 28 q^{53} + 8 q^{54} + 8 q^{56} + 8 q^{57} + 12 q^{58} - 8 q^{59} + 24 q^{61} + 8 q^{62} + 4 q^{63} + 84 q^{67} - 12 q^{68} + 8 q^{69} - 32 q^{71} - 16 q^{73} + 24 q^{74} - 44 q^{77} + 16 q^{78} - 12 q^{79} + 8 q^{81} - 36 q^{82} - 16 q^{83} - 4 q^{84} - 8 q^{86} - 48 q^{87} + 4 q^{88} + 16 q^{89} + 8 q^{91} - 8 q^{92} + 32 q^{93} - 8 q^{94} + 44 q^{97} - 24 q^{98}+O(q^{100}) $ 16 * q + 4 * q^7 + 4 * q^11 - 16 * q^13 - 16 * q^14 + 8 * q^16 - 12 * q^17 + 8 * q^19 + 8 * q^21 - 4 * q^22 + 40 * q^23 + 8 * q^24 - 12 * q^26 + 4 * q^28 - 24 * q^31 - 4 * q^33 - 16 * q^34 - 16 * q^36 + 8 * q^37 + 20 * q^38 + 12 * q^39 - 8 * q^42 + 24 * q^43 - 4 * q^46 - 52 * q^49 + 8 * q^51 - 8 * q^52 + 28 * q^53 + 8 * q^54 + 8 * q^56 + 8 * q^57 + 12 * q^58 - 8 * q^59 + 24 * q^61 + 8 * q^62 + 4 * q^63 + 84 * q^67 - 12 * q^68 + 8 * q^69 - 32 * q^71 - 16 * q^73 + 24 * q^74 - 44 * q^77 + 16 * q^78 - 12 * q^79 + 8 * q^81 - 36 * q^82 - 16 * q^83 - 4 * q^84 - 8 * q^86 - 48 * q^87 + 4 * q^88 + 16 * q^89 + 8 * q^91 - 8 * q^92 + 32 * q^93 - 8 * q^94 + 44 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$			1.00000i			0.408248i
$7$	0.703686	+	2.55046i	0.265968	+	0.963982i
$7$	0.703686	+	2.55046i	0.265968	+	0.963982i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$		0			0
$11$	0.989376	+	1.71365i	0.298308	+	0.516685i	0.975749	−	0.218892i	$-0.0702443\pi$
$11$	0.989376	+	1.71365i	0.298308	+	0.516685i	−0.677441	+	0.735577i	$0.736911\pi$
$12$	0.258819	+	0.965926i	0.0747146	+	0.278839i
$13$	2.19222	+	2.19222i	0.608011	+	0.608011i	0.942426	−	0.334415i	$-0.108539\pi$
$13$	2.19222	+	2.19222i	0.608011	+	0.608011i	−0.334415	+	0.942426i	$0.608539\pi$
$14$	1.33981	+	2.28142i	0.358081	+	0.609736i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−4.44599	−	1.19130i	−1.07831	−	0.288932i	−0.324407	−	0.945918i	$-0.605165\pi$
$17$	−4.44599	−	1.19130i	−1.07831	−	0.288932i	−0.753903	+	0.656985i	$0.771831\pi$
$18$	−0.965926	−	0.258819i	−0.227671	−	0.0610042i
$19$	2.10939	−	3.65357i	0.483928	−	0.838188i	−0.515902	−	0.856648i	$-0.672543\pi$
$19$	2.10939	−	3.65357i	0.483928	−	0.838188i	0.999830	+	0.0184602i	$0.00587639\pi$
$20$		0			0
$21$	−2.64568	+	0.0196015i	−0.577334	+	0.00427740i
$22$	1.39919	+	1.39919i	0.298308	+	0.298308i
$23$	1.52249	+	5.68202i	0.317462	+	1.18478i	0.921676	+	0.387961i	$0.126821\pi$
$23$	1.52249	+	5.68202i	0.317462	+	1.18478i	−0.604214	+	0.796822i	$0.706513\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	2.68491	+	1.55013i	0.526553	+	0.304006i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	1.88464	+	1.85692i	0.356163	+	0.350924i
$29$			8.94996i			1.66197i	0.556298	+	0.830983i	$0.312221\pi$
$29$			8.94996i			1.66197i	−0.556298	+	0.830983i	$0.687779\pi$
$30$		0			0
$31$	−1.50157	+	0.866930i	−0.269689	+	0.155705i	−0.628747	−	0.777610i	$-0.716432\pi$
$31$	−1.50157	+	0.866930i	−0.269689	+	0.155705i	0.359057	+	0.933316i	$0.383098\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−1.91133	+	0.512139i	−0.332720	+	0.0891519i
$34$	−4.60282			−0.789378
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−2.67747	+	0.717425i	−0.440173	+	0.117944i	−0.472097	−	0.881546i	$-0.656503\pi$
$37$	−2.67747	+	0.717425i	−0.440173	+	0.117944i	0.0319248	+	0.999490i	$0.489836\pi$
$38$	1.09190	−	4.07503i	0.177130	−	0.661058i
$39$	−2.68491	+	1.55013i	−0.429929	+	0.248220i
$40$		0			0
$41$			6.55691i			1.02402i	0.858980	+	0.512008i	$0.171098\pi$
$41$			6.55691i			1.02402i	−0.858980	+	0.512008i	$0.828902\pi$
$42$	−2.55046	+	0.703686i	−0.393544	+	0.108581i
$43$	6.33724	−	6.33724i	0.966421	−	0.966421i	−0.0330335	−	0.999454i	$-0.510517\pi$
$43$	6.33724	−	6.33724i	0.966421	−	0.966421i	0.999454	+	0.0330335i	$0.0105168\pi$
$44$	1.71365	+	0.989376i	0.258342	+	0.149154i
$45$		0			0
$46$	2.94123	+	5.09436i	0.433661	+	0.751122i
$47$	−1.57366	−	5.87298i	−0.229542	−	0.856663i	−0.980534	−	0.196351i	$-0.937091\pi$
$47$	−1.57366	−	5.87298i	−0.229542	−	0.856663i	0.750992	−	0.660312i	$-0.229576\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$	−6.00965	+	3.58944i	−0.858522	+	0.512777i
$50$		0			0
$51$	2.30141	−	3.98616i	0.322262	−	0.558174i
$52$	2.99462	+	0.802407i	0.415280	+	0.111274i
$53$	11.0441	+	2.95926i	1.51702	+	0.406485i	0.918761	−	0.394814i	$-0.129191\pi$
$53$	11.0441	+	2.95926i	1.51702	+	0.406485i	0.598263	+	0.801300i	$0.295858\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$	2.30103	+	1.30586i	0.307487	+	0.174503i
$57$	2.98313	+	2.98313i	0.395125	+	0.395125i
$58$	2.31642	+	8.64500i	0.304161	+	1.13514i
$59$	−2.10351	−	3.64339i	−0.273854	−	0.474329i	0.695991	−	0.718050i	$-0.254965\pi$
$59$	−2.10351	−	3.64339i	−0.273854	−	0.474329i	−0.969845	+	0.243721i	$0.921632\pi$
$60$		0			0
$61$	9.63018	+	5.55999i	1.23302	+	0.711883i	0.967658	−	0.252266i	$-0.0811759\pi$
$61$	9.63018	+	5.55999i	1.23302	+	0.711883i	0.265360	+	0.964149i	$0.414509\pi$
$62$	−1.22602	+	1.22602i	−0.155705	+	0.155705i
$63$	0.665818	−	2.56060i	0.0838852	−	0.322606i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−1.71365	+	0.989376i	−0.210936	+	0.121784i
$67$	−1.42665	+	5.32434i	−0.174294	+	0.650472i	0.822377	+	0.568942i	$0.192647\pi$
$67$	−1.42665	+	5.32434i	−0.174294	+	0.650472i	−0.996671	+	0.0815298i	$0.974019\pi$
$68$	−4.44599	+	1.19130i	−0.539155	+	0.144466i
$69$	−5.88246			−0.708165
$70$		0			0
$71$	−3.86002			−0.458100			−0.229050	−	0.973415i	$-0.573562\pi$
$71$	−3.86002			−0.458100			−0.229050	+	0.973415i	$0.573562\pi$
$72$	−0.965926	+	0.258819i	−0.113835	+	0.0305021i
$73$	3.93920	−	14.7013i	0.461048	−	1.72066i	−0.208621	−	0.977997i	$-0.566897\pi$
$73$	3.93920	−	14.7013i	0.461048	−	1.72066i	0.669669	−	0.742660i	$-0.266436\pi$
$74$	−2.40055	+	1.38596i	−0.279058	+	0.161114i
$75$		0			0
$76$		−	4.21878i		−	0.483928i
$77$	−3.67438	+	3.72923i	−0.418734	+	0.424985i
$78$	−2.19222	+	2.19222i	−0.248220	+	0.248220i
$79$	2.21282	+	1.27757i	0.248962	+	0.143738i	0.619289	−	0.785163i	$-0.287421\pi$
$79$	2.21282	+	1.27757i	0.248962	+	0.143738i	−0.370327	+	0.928901i	$0.620754\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	1.69705	+	6.33349i	0.187408	+	0.699416i
$83$	−9.52969	−	9.52969i	−1.04602	−	1.04602i	−0.998889	−	0.0471311i	$-0.984992\pi$
$83$	−9.52969	−	9.52969i	−1.04602	−	1.04602i	−0.0471311	−	0.998889i	$-0.515008\pi$
$84$	−2.28142	+	1.33981i	−0.248924	+	0.146186i
$85$		0			0
$86$	4.48111	−	7.76151i	0.483210	−	0.836945i
$87$	−8.64500	−	2.31642i	−0.926841	−	0.248346i
$88$	1.91133	+	0.512139i	0.203748	+	0.0545942i
$89$	3.09593	−	5.36231i	0.328168	−	0.568404i	−0.653980	−	0.756512i	$-0.726902\pi$
$89$	3.09593	−	5.36231i	0.328168	−	0.568404i	0.982148	+	0.188108i	$0.0602354\pi$
$90$		0			0
$91$	−4.04852	+	7.13378i	−0.424400	+	0.747824i
$92$	4.15953	+	4.15953i	0.433661	+	0.433661i
$93$	−0.448756	−	1.67478i	−0.0465339	−	0.173667i
$94$	−3.04008	−	5.26557i	−0.313560	−	0.543102i
$95$		0			0
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	1.48031	−	1.48031i	0.150303	−	0.150303i	−0.627951	−	0.778253i	$-0.716106\pi$
$97$	1.48031	−	1.48031i	0.150303	−	0.150303i	0.778253	+	0.627951i	$0.216106\pi$
$98$	−4.87586	+	5.02254i	−0.492537	+	0.507354i
$99$		−	1.97875i		−	0.198872i
$100$		0			0
$101$	−8.70112	+	5.02360i	−0.865794	+	0.499866i	−0.865948	−	0.500134i	$-0.833284\pi$
$101$	−8.70112	+	5.02360i	−0.865794	+	0.499866i	0.000154194		1.00000i	$0.499951\pi$
$102$	1.19130	−	4.44599i	0.117956	−	0.440218i
$103$	−4.81790	+	1.29095i	−0.474722	+	0.127201i	−0.488244	−	0.872707i	$-0.662362\pi$
$103$	−4.81790	+	1.29095i	−0.474722	+	0.127201i	0.0135219	+	0.999909i	$0.495696\pi$
$104$	3.10026			0.304006
$105$		0			0
$106$	11.4337			1.11054
$107$	5.84351	−	1.56576i	0.564913	−	0.151368i	0.0349507	−	0.999389i	$-0.488873\pi$
$107$	5.84351	−	1.56576i	0.564913	−	0.151368i	0.529963	+	0.848021i	$0.322206\pi$
$108$	0.258819	−	0.965926i	0.0249049	−	0.0929463i
$109$	8.44287	−	4.87449i	0.808680	−	0.466892i	−0.0378171	−	0.999285i	$-0.512040\pi$
$109$	8.44287	−	4.87449i	0.808680	−	0.466892i	0.846497	+	0.532393i	$0.178707\pi$
$110$		0			0
$111$		−	2.77192i		−	0.263099i
$112$	2.56060	+	0.665818i	0.241954	+	0.0629139i
$113$	−6.02504	+	6.02504i	−0.566788	+	0.566788i	−0.931227	−	0.364439i	$-0.881261\pi$
$113$	−6.02504	+	6.02504i	−0.566788	+	0.566788i	0.364439	+	0.931227i	$0.381261\pi$
$114$	3.65357	+	2.10939i	0.342189	+	0.197563i
$115$		0			0
$116$	4.47498	+	7.75089i	0.415491	+	0.719652i
$117$	−0.802407	−	2.99462i	−0.0741826	−	0.276853i
$118$	−2.97481	−	2.97481i	−0.273854	−	0.273854i
$119$	−0.0902224	−	12.1776i	−0.00827067	−	1.11632i
$120$		0			0
$121$	3.54227	−	6.13539i	0.322024	−	0.557763i
$122$	10.7411	+	2.87806i	0.972451	+	0.260567i
$123$	−6.33349	−	1.69705i	−0.571071	−	0.153018i
$124$	−0.866930	+	1.50157i	−0.0778527	+	0.134845i
$125$		0			0
$126$	−0.0196015	−	2.64568i	−0.00174624	−	0.235696i
$127$	8.92770	+	8.92770i	0.792205	+	0.792205i	0.981852	−	0.189647i	$-0.0607345\pi$
$127$	8.92770	+	8.92770i	0.792205	+	0.792205i	−0.189647	+	0.981852i	$0.560734\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	4.48111	+	7.76151i	0.394540	+	0.683363i
$130$		0			0
$131$	−4.43543	−	2.56080i	−0.387526	−	0.223738i	0.293562	−	0.955940i	$-0.405159\pi$
$131$	−4.43543	−	2.56080i	−0.387526	−	0.223738i	−0.681087	+	0.732202i	$0.738493\pi$
$132$	−1.39919	+	1.39919i	−0.121784	+	0.121784i
$133$	10.8026	+	2.80894i	0.936707	+	0.243566i
$134$			5.51217i			0.476179i
$135$		0			0
$136$	−3.98616	+	2.30141i	−0.341811	+	0.197344i
$137$	2.99773	−	11.1877i	0.256114	−	0.955829i	−0.711354	−	0.702834i	$-0.751918\pi$
$137$	2.99773	−	11.1877i	0.256114	−	0.955829i	0.967468	−	0.252995i	$-0.0814157\pi$
$138$	−5.68202	+	1.52249i	−0.483686	+	0.129603i
$139$	2.87054			0.243476			0.121738	−	0.992562i	$-0.461153\pi$
$139$	2.87054			0.243476			0.121738	+	0.992562i	$0.461153\pi$
$140$		0			0
$141$	6.08016			0.512042
$142$	−3.72849	+	0.999046i	−0.312888	+	0.0838381i
$143$	−1.58776	+	5.92562i	−0.132776	+	0.495525i
$144$	−0.866025	+	0.500000i	−0.0721688	+	0.0416667i
$145$		0			0
$146$		−	15.2199i		−	1.25961i
$147$	−1.91172	−	6.73389i	−0.157676	−	0.555402i
$148$	−1.96004	+	1.96004i	−0.161114	+	0.161114i
$149$	−13.4924	−	7.78982i	−1.10534	−	0.638167i	−0.167720	−	0.985835i	$-0.553640\pi$
$149$	−13.4924	−	7.78982i	−1.10534	−	0.638167i	−0.937618	+	0.347668i	$0.886974\pi$
$150$		0			0
$151$	−10.5953	−	18.3516i	−0.862232	−	1.49343i	−0.869769	−	0.493459i	$-0.835732\pi$
$151$	−10.5953	−	18.3516i	−0.862232	−	1.49343i	0.00753703	−	0.999972i	$-0.497601\pi$
$152$	−1.09190	−	4.07503i	−0.0885649	−	0.330529i
$153$	3.25469	+	3.25469i	0.263126	+	0.263126i
$154$	−2.58398	+	4.55316i	−0.208223	+	0.366904i
$155$		0			0
$156$	−1.55013	+	2.68491i	−0.124110	+	0.214965i
$157$	−14.6660	−	3.92974i	−1.17047	−	0.313627i	−0.379332	−	0.925261i	$-0.623846\pi$
$157$	−14.6660	−	3.92974i	−1.17047	−	0.313627i	−0.791141	+	0.611633i	$0.790513\pi$
$158$	2.46808	+	0.661320i	0.196350	+	0.0526118i
$159$	−5.71685	+	9.90187i	−0.453375	+	0.785269i
$160$		0			0
$161$	−13.4204	+	7.88141i	−1.05767	+	0.621142i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	−5.77762	−	21.5624i	−0.452538	−	1.68890i	−0.695225	−	0.718792i	$-0.744695\pi$
$163$	−5.77762	−	21.5624i	−0.452538	−	1.68890i	0.242687	−	0.970105i	$-0.421971\pi$
$164$	3.27845	+	5.67845i	0.256004	+	0.443412i
$165$		0			0
$166$	−11.6714	−	6.73851i	−0.905880	−	0.523010i
$167$	6.91224	−	6.91224i	0.534885	−	0.534885i	−0.387137	−	0.922022i	$-0.626536\pi$
$167$	6.91224	−	6.91224i	0.534885	−	0.534885i	0.922022	+	0.387137i	$0.126536\pi$
$168$	−1.85692	+	1.88464i	−0.143264	+	0.145403i
$169$		−	3.38837i		−	0.260644i
$170$		0			0
$171$	−3.65357	+	2.10939i	−0.279396	+	0.161309i
$172$	2.31959	−	8.65684i	0.176867	−	0.660078i
$173$	4.37334	−	1.17183i	0.332499	−	0.0890928i	−0.0887072	−	0.996058i	$-0.528274\pi$
$173$	4.37334	−	1.17183i	0.332499	−	0.0890928i	0.421206	+	0.906965i	$0.361607\pi$
$174$	−8.94996			−0.678495
$175$		0			0
$176$	1.97875			0.149154
$177$	4.06367	−	1.08886i	0.305444	−	0.0818436i
$178$	1.60257	−	5.98088i	0.120118	−	0.448286i
$179$	1.79084	−	1.03394i	0.133853	−	0.0772803i	−0.431578	−	0.902076i	$-0.642043\pi$
$179$	1.79084	−	1.03394i	0.133853	−	0.0772803i	0.565431	+	0.824795i	$0.308710\pi$
$180$		0			0
$181$			6.13199i			0.455787i	0.973686	+	0.227894i	$0.0731839\pi$
$181$			6.13199i			0.455787i	−0.973686	+	0.227894i	$0.926816\pi$
$182$	−2.06421	+	7.93854i	−0.153010	+	0.588444i
$183$	−7.86301	+	7.86301i	−0.581250	+	0.581250i
$184$	5.09436	+	2.94123i	0.375561	+	0.216830i
$185$		0			0
$186$	−0.866930	−	1.50157i	−0.0635664	−	0.110100i
$187$	−2.35728	−	8.79751i	−0.172382	−	0.643337i
$188$	−4.29932	−	4.29932i	−0.313560	−	0.313560i
$189$	2.30103	+	1.30586i	0.167375	+	0.0949876i
$190$		0			0
$191$	8.08306	−	14.0003i	0.584869	−	1.01302i	−0.410022	−	0.912075i	$-0.634479\pi$
$191$	8.08306	−	14.0003i	0.584869	−	1.01302i	0.994892	−	0.100948i	$-0.0321876\pi$
$192$	0.965926	+	0.258819i	0.0697097	+	0.0186787i
$193$	21.0484	+	5.63991i	1.51510	+	0.405969i	0.918125	−	0.396292i	$-0.129703\pi$
$193$	21.0484	+	5.63991i	1.51510	+	0.405969i	0.596973	+	0.802261i	$0.296370\pi$
$194$	1.04674	−	1.81300i	0.0751514	−	0.130166i
$195$		0			0
$196$	−3.40979	+	6.11337i	−0.243557	+	0.436669i
$197$	0.628120	+	0.628120i	0.0447517	+	0.0447517i	0.729129	−	0.684377i	$-0.239926\pi$
$197$	0.628120	+	0.628120i	0.0447517	+	0.0447517i	−0.684377	+	0.729129i	$0.739926\pi$
$198$	−0.512139	−	1.91133i	−0.0363961	−	0.135832i
$199$	−4.81248	−	8.33546i	−0.341147	−	0.590885i	0.643499	−	0.765447i	$-0.277482\pi$
$199$	−4.81248	−	8.33546i	−0.341147	−	0.590885i	−0.984646	+	0.174563i	$0.944149\pi$
$200$		0			0
$201$	−4.77368	−	2.75608i	−0.336709	−	0.194399i
$202$	−7.10444	+	7.10444i	−0.499866	+	0.499866i
$203$	−22.8265	+	6.29796i	−1.60210	+	0.442030i
$204$		−	4.60282i		−	0.322262i
$205$		0			0
$206$	−4.31961	+	2.49393i	−0.300962	+	0.173760i
$207$	1.52249	−	5.68202i	0.105821	−	0.394928i
$208$	2.99462	−	0.802407i	0.207640	−	0.0556369i
$209$	8.34793			0.577439
$210$		0			0
$211$	11.2669			0.775648			0.387824	−	0.921733i	$-0.373227\pi$
$211$	11.2669			0.775648			0.387824	+	0.921733i	$0.373227\pi$
$212$	11.0441	−	2.95926i	0.758512	−	0.203243i
$213$	0.999046	−	3.72849i	0.0684535	−	0.255472i
$214$	5.23915	−	3.02482i	0.358141	−	0.206773i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	−3.26770	−	3.21964i	−0.221826	−	0.218563i
$218$	6.89357	−	6.89357i	0.466892	−	0.466892i
$219$	13.1808	+	7.60995i	0.890677	+	0.514233i
$220$		0			0
$221$	−7.13498	−	12.3581i	−0.479951	−	0.831299i
$222$	−0.717425	−	2.67747i	−0.0481504	−	0.179700i
$223$	13.1718	+	13.1718i	0.882048	+	0.882048i	0.993743	−	0.111694i	$-0.0356277\pi$
$223$	13.1718	+	13.1718i	0.882048	+	0.882048i	−0.111694	+	0.993743i	$0.535628\pi$
$224$	2.64568	−	0.0196015i	0.176772	−	0.00130968i
$225$		0			0
$226$	−4.26035	+	7.37914i	−0.283394	+	0.490853i
$227$	−25.9971	−	6.96589i	−1.72549	−	0.462343i	−0.746351	−	0.665552i	$-0.768196\pi$
$227$	−25.9971	−	6.96589i	−1.72549	−	0.462343i	−0.979135	+	0.203210i	$0.934863\pi$
$228$	4.07503	+	1.09190i	0.269876	+	0.0723130i
$229$	13.4452	−	23.2878i	0.888486	−	1.53890i	0.0468199	−	0.998903i	$-0.485091\pi$
$229$	13.4452	−	23.2878i	0.888486	−	1.53890i	0.841666	−	0.539999i	$-0.181575\pi$
$230$		0			0
$231$	−2.65116	−	4.51437i	−0.174434	−	0.297024i
$232$	6.32858	+	6.32858i	0.415491	+	0.415491i
$233$	0.238436	+	0.889853i	0.0156204	+	0.0582962i	0.973296	−	0.229553i	$-0.0737264\pi$
$233$	0.238436	+	0.889853i	0.0156204	+	0.0582962i	−0.957676	+	0.287849i	$0.907060\pi$
$234$	−1.55013	−	2.68491i	−0.101335	−	0.175518i
$235$		0			0
$236$	−3.64339	−	2.10351i	−0.237164	−	0.136927i
$237$	−1.80676	+	1.80676i	−0.117362	+	0.117362i
$238$	−3.23894	−	11.7393i	−0.209949	−	0.760946i
$239$			25.3432i			1.63931i	0.572856	+	0.819656i	$0.305836\pi$
$239$			25.3432i			1.63931i	−0.572856	+	0.819656i	$0.694164\pi$
$240$		0			0
$241$	18.2905	−	10.5600i	1.17819	−	0.680230i	0.222597	−	0.974911i	$-0.428547\pi$
$241$	18.2905	−	10.5600i	1.17819	−	0.680230i	0.955596	+	0.294681i	$0.0952134\pi$
$242$	1.83361	−	6.84314i	0.117869	−	0.439894i
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	11.1200			0.711883
$245$		0			0
$246$	−6.55691			−0.418053
$247$	12.6337	−	3.38518i	0.803861	−	0.215394i
$248$	−0.448756	+	1.67478i	−0.0284960	+	0.106349i
$249$	11.6714	−	6.73851i	0.739648	−	0.427036i
$250$		0			0
$251$			2.70623i			0.170816i	0.996346	+	0.0854078i	$0.0272193\pi$
$251$			2.70623i			0.170816i	−0.996346	+	0.0854078i	$0.972781\pi$
$252$	−0.703686	−	2.55046i	−0.0443280	−	0.160664i
$253$	−8.23068	+	8.23068i	−0.517458	+	0.517458i
$254$	10.9342	+	6.31283i	0.686070	+	0.396102i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.21737	+	23.2035i	0.387829	+	1.44740i	0.833660	+	0.552279i	$0.186242\pi$
$257$	6.21737	+	23.2035i	0.387829	+	1.44740i	−0.445831	+	0.895117i	$0.647092\pi$
$258$	6.33724	+	6.33724i	0.394540	+	0.394540i
$259$	−3.71385	−	6.32392i	−0.230768	−	0.392949i
$260$		0			0
$261$	4.47498	−	7.75089i	0.276994	−	0.479768i
$262$	−4.94708	−	1.32557i	−0.305632	−	0.0818938i
$263$	0.821351	+	0.220080i	0.0506467	+	0.0135707i	0.284053	−	0.958808i	$-0.408321\pi$
$263$	0.821351	+	0.220080i	0.0506467	+	0.0135707i	−0.233407	+	0.972379i	$0.574987\pi$
$264$	−0.989376	+	1.71365i	−0.0608919	+	0.105468i
$265$		0			0
$266$	11.1615	−	0.0826946i	0.684359	−	0.00507033i
$267$	4.37831	+	4.37831i	0.267948	+	0.267948i
$268$	1.42665	+	5.32434i	0.0871468	+	0.325236i
$269$	−5.82171	−	10.0835i	−0.354956	−	0.614802i	0.632154	−	0.774842i	$-0.282171\pi$
$269$	−5.82171	−	10.0835i	−0.354956	−	0.614802i	−0.987110	+	0.160041i	$0.948837\pi$
$270$		0			0
$271$	−20.2171	−	11.6724i	−1.22810	−	0.709046i	−0.261471	−	0.965211i	$-0.584208\pi$
$271$	−20.2171	−	11.6724i	−1.22810	−	0.709046i	−0.966633	+	0.256165i	$0.917541\pi$
$272$	−3.25469	+	3.25469i	−0.197344	+	0.197344i
$273$	−5.84287	−	5.75693i	−0.353627	−	0.348425i
$274$		−	11.5824i		−	0.699715i
$275$		0			0
$276$	−5.09436	+	2.94123i	−0.306644	+	0.177041i
$277$	−2.44577	+	9.12775i	−0.146952	+	0.548433i	0.852708	+	0.522387i	$0.174958\pi$
$277$	−2.44577	+	9.12775i	−0.146952	+	0.548433i	−0.999661	+	0.0260462i	$0.991708\pi$
$278$	2.77273	−	0.742949i	0.166297	−	0.0445591i
$279$	1.73386			0.103804
$280$		0			0
$281$	−11.7320			−0.699871			−0.349935	−	0.936774i	$-0.613796\pi$
$281$	−11.7320			−0.699871			−0.349935	+	0.936774i	$0.613796\pi$
$282$	5.87298	−	1.57366i	0.349731	−	0.0937101i
$283$	−0.944117	+	3.52349i	−0.0561219	+	0.209450i	−0.988293	−	0.152568i	$-0.951246\pi$
$283$	−0.944117	+	3.52349i	−0.0561219	+	0.209450i	0.932171	+	0.362018i	$0.117912\pi$
$284$	−3.34287	+	1.93001i	−0.198363	+	0.114525i
$285$		0			0
$286$			6.13465i			0.362750i
$287$	−16.7231	+	4.61400i	−0.987133	+	0.272356i
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$	3.62517	+	2.09299i	0.213245	+	0.123117i
$290$		0			0
$291$	1.04674	+	1.81300i	0.0613609	+	0.106280i
$292$	−3.93920	−	14.7013i	−0.230524	−	0.860328i
$293$	−8.62354	−	8.62354i	−0.503793	−	0.503793i	0.408822	−	0.912614i	$-0.365940\pi$
$293$	−8.62354	−	8.62354i	−0.503793	−	0.503793i	−0.912614	+	0.408822i	$0.865940\pi$
$294$	−3.58944	−	6.00965i	−0.209340	−	0.350490i
$295$		0			0
$296$	−1.38596	+	2.40055i	−0.0805572	+	0.139529i
$297$	1.91133	+	0.512139i	0.110907	+	0.0297173i
$298$	−15.0488	−	4.03231i	−0.871752	−	0.233585i
$299$	−9.11859	+	15.7939i	−0.527341	+	0.913382i
$300$		0			0
$301$	20.6223	+	11.7034i	1.18865	+	0.674575i
$302$	−14.9840	−	14.9840i	−0.862232	−	0.862232i
$303$	−2.60040	−	9.70484i	−0.149389	−	0.557529i
$304$	−2.10939	−	3.65357i	−0.120982	−	0.209547i
$305$		0			0
$306$	3.98616	+	2.30141i	0.227874	+	0.131563i
$307$	15.9933	−	15.9933i	0.912785	−	0.912785i	−0.0837060	−	0.996490i	$-0.526676\pi$
$307$	15.9933	−	15.9933i	0.912785	−	0.912785i	0.996490	+	0.0837060i	$0.0266757\pi$
$308$	−1.31749	+	5.06680i	−0.0750710	+	0.288708i
$309$		−	4.98786i		−	0.283750i
$310$		0			0
$311$	6.70522	−	3.87126i	0.380218	−	0.219519i	−0.297695	−	0.954661i	$-0.596218\pi$
$311$	6.70522	−	3.87126i	0.380218	−	0.219519i	0.677913	+	0.735142i	$0.262885\pi$
$312$	−0.802407	+	2.99462i	−0.0454273	+	0.169537i
$313$	−19.3623	+	5.18810i	−1.09442	+	0.293249i	−0.760490	−	0.649349i	$-0.775041\pi$
$313$	−19.3623	+	5.18810i	−1.09442	+	0.293249i	−0.333929	+	0.942598i	$0.608375\pi$
$314$	−15.1833			−0.856846
$315$		0			0
$316$	2.55514			0.143738
$317$	−2.87877	+	0.771364i	−0.161688	+	0.0433241i	−0.338755	−	0.940875i	$-0.610006\pi$
$317$	−2.87877	+	0.771364i	−0.161688	+	0.0433241i	0.177067	+	0.984199i	$0.443339\pi$
$318$	−2.95926	+	11.0441i	−0.165947	+	0.619322i
$319$	−15.3371	+	8.85488i	−0.858713	+	0.495778i
$320$		0			0
$321$			6.04965i			0.337658i
$322$	−10.9232	+	11.0863i	−0.608728	+	0.617816i
$323$	−13.7308	+	13.7308i	−0.764004	+	0.764004i
$324$	0.866025	+	0.500000i	0.0481125	+	0.0277778i
$325$		0			0
$326$	−11.1615	−	19.3323i	−0.618179	−	1.07072i
$327$	2.52322	+	9.41680i	0.139535	+	0.520750i
$328$	4.63643	+	4.63643i	0.256004	+	0.256004i
$329$	13.8714	−	8.14629i	0.764756	−	0.449119i
$330$		0			0
$331$	−13.9186	+	24.1077i	−0.765035	+	1.32508i	0.175194	+	0.984534i	$0.443945\pi$
$331$	−13.9186	+	24.1077i	−0.765035	+	1.32508i	−0.940228	+	0.340545i	$0.889388\pi$
$332$	−13.0178	−	3.48811i	−0.714445	−	0.191435i
$333$	2.67747	+	0.717425i	0.146724	+	0.0393146i
$334$	4.88769	−	8.46573i	0.267442	−	0.463224i
$335$		0			0
$336$	−1.30586	+	2.30103i	−0.0712407	+	0.125531i
$337$	17.1567	+	17.1567i	0.934583	+	0.934583i	0.997988	−	0.0634051i	$-0.0201960\pi$
$337$	17.1567	+	17.1567i	0.934583	+	0.934583i	−0.0634051	+	0.997988i	$0.520196\pi$
$338$	−0.876975	−	3.27292i	−0.0477012	−	0.178023i
$339$	−4.26035	−	7.37914i	−0.231390	−	0.400780i
$340$		0			0
$341$	−2.97123	−	1.71544i	−0.160901	−	0.0928963i
$342$	−2.98313	+	2.98313i	−0.161309	+	0.161309i
$343$	−13.3836	−	12.8015i	−0.722647	−	0.691217i
$344$		−	8.96222i		−	0.483210i
$345$		0			0
$346$	3.92103	−	2.26381i	0.210796	−	0.121703i
$347$	6.48156	−	24.1895i	0.347948	−	1.29856i	−0.541181	−	0.840906i	$-0.682023\pi$
$347$	6.48156	−	24.1895i	0.347948	−	1.29856i	0.889130	−	0.457655i	$-0.151311\pi$
$348$	−8.64500	+	2.31642i	−0.463421	+	0.124173i
$349$	18.0130			0.964212			0.482106	−	0.876113i	$-0.339872\pi$
$349$	18.0130			0.964212			0.482106	+	0.876113i	$0.339872\pi$
$350$		0			0
$351$	3.10026			0.165480
$352$	1.91133	−	0.512139i	0.101874	−	0.0272971i
$353$	−1.96651	+	7.33911i	−0.104667	+	0.390621i	−0.998307	−	0.0581623i	$-0.981476\pi$
$353$	−1.96651	+	7.33911i	−0.104667	+	0.390621i	0.893641	+	0.448784i	$0.148143\pi$
$354$	3.64339	−	2.10351i	0.193644	−	0.111800i
$355$		0			0
$356$		−	6.19187i		−	0.328168i
$357$	11.7860	+	3.06464i	0.623781	+	0.162198i
$358$	1.46221	−	1.46221i	0.0772803	−	0.0772803i
$359$	2.84638	+	1.64336i	0.150226	+	0.0867332i	0.573229	−	0.819395i	$-0.305691\pi$
$359$	2.84638	+	1.64336i	0.150226	+	0.0867332i	−0.423003	+	0.906128i	$0.639024\pi$
$360$		0			0
$361$	0.600927	+	1.04084i	0.0316277	+	0.0547808i
$362$	1.58708	+	5.92305i	0.0834149	+	0.311309i
$363$	5.00952	+	5.00952i	0.262932	+	0.262932i
$364$	0.0607699	+	8.20230i	0.00318521	+	0.429917i
$365$		0			0
$366$	−5.55999	+	9.63018i	−0.290625	+	0.503377i
$367$	3.13693	+	0.840538i	0.163746	+	0.0438757i	0.339761	−	0.940512i	$-0.389654\pi$
$367$	3.13693	+	0.840538i	0.163746	+	0.0438757i	−0.176014	+	0.984388i	$0.556321\pi$
$368$	5.68202	+	1.52249i	0.296196	+	0.0793654i
$369$	3.27845	−	5.67845i	0.170669	−	0.295608i
$370$		0			0
$371$	0.224118	+	30.2499i	0.0116356	+	1.57050i
$372$	−1.22602	−	1.22602i	−0.0635664	−	0.0635664i
$373$	4.08060	+	15.2290i	0.211286	+	0.788529i	0.987441	+	0.157987i	$0.0505005\pi$
$373$	4.08060	+	15.2290i	0.211286	+	0.788529i	−0.776156	+	0.630542i	$0.782833\pi$
$374$	−4.55392	−	7.88763i	−0.235478	−	0.407860i
$375$		0			0
$376$	−5.26557	−	3.04008i	−0.271551	−	0.156780i
$377$	−19.6203	+	19.6203i	−1.01049	+	1.01049i
$378$	2.56060	+	0.665818i	0.131703	+	0.0342460i
$379$			21.7428i			1.11685i	0.829555	+	0.558426i	$0.188594\pi$
$379$			21.7428i			1.11685i	−0.829555	+	0.558426i	$0.811406\pi$
$380$		0			0
$381$	−10.9342	+	6.31283i	−0.560174	+	0.323416i
$382$	4.18410	−	15.6153i	0.214077	−	0.798946i
$383$	17.2784	−	4.62973i	0.882883	−	0.236568i	0.211233	−	0.977436i	$-0.432252\pi$
$383$	17.2784	−	4.62973i	0.882883	−	0.236568i	0.671651	+	0.740868i	$0.265586\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	21.7909			1.10913
$387$	−8.65684	+	2.31959i	−0.440052	+	0.117912i
$388$	0.541831	−	2.02214i	0.0275073	−	0.102659i
$389$	−4.36130	+	2.51800i	−0.221127	+	0.127667i	−0.606472	−	0.795105i	$-0.707416\pi$
$389$	−4.36130	+	2.51800i	−0.221127	+	0.127667i	0.385345	+	0.922772i	$0.374082\pi$
$390$		0			0
$391$		−	27.0759i		−	1.36929i
$392$	−1.71135	+	6.78758i	−0.0864362	+	0.342825i
$393$	3.62152	−	3.62152i	0.182681	−	0.182681i
$394$	0.769287	+	0.444148i	0.0387561	+	0.0223759i
$395$		0			0
$396$	−0.989376	−	1.71365i	−0.0497180	−	0.0861142i
$397$	3.81880	+	14.2520i	0.191660	+	0.715285i	0.993106	+	0.117218i	$0.0373977\pi$
$397$	3.81880	+	14.2520i	0.191660	+	0.715285i	−0.801446	+	0.598067i	$0.795936\pi$
$398$	−6.80587	−	6.80587i	−0.341147	−	0.341147i
$399$	−5.50916	+	9.70753i	−0.275803	+	0.485984i
$400$		0			0
$401$	4.34686	−	7.52897i	0.217072	−	0.375979i	−0.736840	−	0.676067i	$-0.763683\pi$
$401$	4.34686	−	7.52897i	0.217072	−	0.375979i	0.953911	+	0.300088i	$0.0970162\pi$
$402$	−5.32434	−	1.42665i	−0.265554	−	0.0711550i
$403$	−5.19226	−	1.39126i	−0.258645	−	0.0693037i
$404$	−5.02360	+	8.70112i	−0.249933	+	0.432897i
$405$		0			0
$406$	−20.4187	+	11.9913i	−1.01336	+	0.595118i
$407$	−3.87844	−	3.87844i	−0.192247	−	0.192247i
$408$	−1.19130	−	4.44599i	−0.0589781	−	0.220109i
$409$	9.49095	+	16.4388i	0.469297	+	0.812847i	0.999384	−	0.0350966i	$-0.0111739\pi$
$409$	9.49095	+	16.4388i	0.469297	+	0.812847i	−0.530087	+	0.847944i	$0.677841\pi$
$410$		0			0
$411$	10.0306	+	5.79118i	0.494774	+	0.285658i
$412$	−3.52695	+	3.52695i	−0.173760	+	0.173760i
$413$	7.81209	−	7.92871i	0.384408	−	0.390147i
$414$		−	5.88246i		−	0.289107i
$415$		0			0
$416$	2.68491	−	1.55013i	0.131638	−	0.0760014i
$417$	−0.742949	+	2.77273i	−0.0363824	+	0.135781i
$418$	8.06348	−	2.16060i	0.394398	−	0.105679i
$419$	−11.9171			−0.582188			−0.291094	−	0.956695i	$-0.594019\pi$
$419$	−11.9171			−0.582188			−0.291094	+	0.956695i	$0.594019\pi$
$420$		0			0
$421$	6.95263			0.338850			0.169425	−	0.985543i	$-0.445809\pi$
$421$	6.95263			0.338850			0.169425	+	0.985543i	$0.445809\pi$
$422$	10.8830	−	2.91610i	0.529778	−	0.141953i
$423$	−1.57366	+	5.87298i	−0.0765140	+	0.285554i
$424$	9.90187	−	5.71685i	0.480877	−	0.277635i
$425$		0			0
$426$		−	3.86002i		−	0.187018i
$427$	−7.40388	+	28.4738i	−0.358299	+	1.37795i
$428$	4.27775	−	4.27775i	0.206773	−	0.206773i
$429$	−5.31277	−	3.06733i	−0.256503	−	0.148092i
$430$		0			0
$431$	−3.12392	−	5.41078i	−0.150474	−	0.260628i	0.780928	−	0.624621i	$-0.214747\pi$
$431$	−3.12392	−	5.41078i	−0.150474	−	0.260628i	−0.931402	+	0.363993i	$0.881413\pi$
$432$	−0.258819	−	0.965926i	−0.0124524	−	0.0464731i
$433$	15.1544	+	15.1544i	0.728274	+	0.728274i	0.970276	−	0.242002i	$-0.0778040\pi$
$433$	15.1544	+	15.1544i	0.728274	+	0.728274i	−0.242002	+	0.970276i	$0.577804\pi$
$434$	−3.98966	−	2.26419i	−0.191510	−	0.108684i
$435$		0			0
$436$	4.87449	−	8.44287i	0.233446	−	0.404340i
$437$	23.9712	+	6.42307i	1.14670	+	0.307257i
$438$	14.7013	+	3.93920i	0.702455	+	0.188222i
$439$	−16.3729	+	28.3588i	−0.781438	+	1.35349i	0.149666	+	0.988737i	$0.452180\pi$
$439$	−16.3729	+	28.3588i	−0.781438	+	1.35349i	−0.931104	+	0.364753i	$0.881153\pi$
$440$		0			0
$441$	6.99923	−	0.103719i	0.333297	−	0.00493899i
$442$	−10.0904	−	10.0904i	−0.479951	−	0.479951i
$443$	−7.95895	−	29.7032i	−0.378141	−	1.41124i	−0.848701	−	0.528874i	$-0.822615\pi$
$443$	−7.95895	−	29.7032i	−0.378141	−	1.41124i	0.470559	−	0.882368i	$-0.344052\pi$
$444$	−1.38596	−	2.40055i	−0.0657747	−	0.113925i
$445$		0			0
$446$	16.1321	+	9.31386i	0.763876	+	0.441024i
$447$	11.0165	−	11.0165i	0.521061	−	0.521061i
$448$	2.55046	−	0.703686i	0.120498	−	0.0332460i
$449$			16.8713i			0.796207i	0.917341	+	0.398103i	$0.130331\pi$
$449$			16.8713i			0.796207i	−0.917341	+	0.398103i	$0.869669\pi$
$450$		0			0
$451$	−11.2362	+	6.48725i	−0.529094	+	0.305473i
$452$	−2.20532	+	8.23036i	−0.103729	+	0.387123i
$453$	20.4685	−	5.48452i	0.961695	−	0.257685i
$454$	−26.9142			−1.26314
$455$		0			0
$456$	4.21878			0.197563
$457$	19.1714	−	5.13696i	0.896800	−	0.240297i	0.219158	−	0.975689i	$-0.429669\pi$
$457$	19.1714	−	5.13696i	0.896800	−	0.240297i	0.677641	+	0.735393i	$0.263002\pi$
$458$	6.95976	−	25.9742i	0.325208	−	1.21369i
$459$	−3.98616	+	2.30141i	−0.186058	+	0.107421i
$460$		0			0
$461$			15.7775i			0.734830i	0.930057	+	0.367415i	$0.119757\pi$
$461$			15.7775i			0.734830i	−0.930057	+	0.367415i	$0.880243\pi$
$462$	−3.72923	−	3.67438i	−0.173500	−	0.170948i
$463$	−4.48617	+	4.48617i	−0.208490	+	0.208490i	−0.803625	−	0.595135i	$-0.797098\pi$
$463$	−4.48617	+	4.48617i	−0.208490	+	0.208490i	0.595135	+	0.803625i	$0.297098\pi$
$464$	7.75089	+	4.47498i	0.359826	+	0.207746i
$465$		0			0
$466$	0.460622	+	0.797821i	0.0213379	+	0.0369583i
$467$	4.51639	+	16.8554i	0.208994	+	0.779975i	0.988195	+	0.153201i	$0.0489583\pi$
$467$	4.51639	+	16.8554i	0.208994	+	0.779975i	−0.779201	+	0.626774i	$0.784375\pi$
$468$	−2.19222	−	2.19222i	−0.101335	−	0.101335i
$469$	−14.5834	+	0.108047i	−0.673400	+	0.00498914i
$470$		0			0
$471$	7.59167	−	13.1492i	0.349806	−	0.605881i
$472$	−4.06367	−	1.08886i	−0.187046	−	0.0501187i
$473$	17.1297	+	4.58990i	0.787626	+	0.211044i
$474$	−1.27757	+	2.21282i	−0.0586808	+	0.101638i
$475$		0			0
$476$	−6.16693	−	10.5010i	−0.282661	−	0.481312i
$477$	−8.08484	−	8.08484i	−0.370180	−	0.370180i
$478$	6.55929	+	24.4796i	0.300015	+	1.11967i
$479$	−15.8748	−	27.4960i	−0.725339	−	1.25632i	−0.958834	−	0.283966i	$-0.908350\pi$
$479$	−15.8748	−	27.4960i	−0.725339	−	1.25632i	0.233495	−	0.972358i	$-0.424984\pi$
$480$		0			0
$481$	−7.44233	−	4.29683i	−0.339341	−	0.195919i
$482$	14.9341	−	14.9341i	0.680230	−	0.680230i
$483$	−4.13940	−	15.0030i	−0.188349	−	0.682658i
$484$		−	7.08454i		−	0.322024i
$485$		0			0
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	7.74077	−	28.8890i	0.350768	−	1.30908i	−0.534960	−	0.844878i	$-0.679673\pi$
$487$	7.74077	−	28.8890i	0.350768	−	1.30908i	0.885727	−	0.464206i	$-0.153660\pi$
$488$	10.7411	−	2.87806i	0.486225	−	0.130284i
$489$	22.3230			1.00948
$490$		0			0
$491$	1.57179			0.0709340			0.0354670	−	0.999371i	$-0.488708\pi$
$491$	1.57179			0.0709340			0.0354670	+	0.999371i	$0.488708\pi$
$492$	−6.33349	+	1.69705i	−0.285536	+	0.0765090i
$493$	10.6621	−	39.7914i	0.480196	−	1.79211i
$494$	11.3270	−	6.53967i	0.509628	−	0.294234i
$495$		0			0
$496$			1.73386i			0.0778527i
$497$	−2.71624	−	9.84480i	−0.121840	−	0.441600i
$498$	9.52969	−	9.52969i	0.427036	−	0.427036i
$499$	−12.3491	−	7.12977i	−0.552823	−	0.319172i	0.197437	−	0.980316i	$-0.436738\pi$
$499$	−12.3491	−	7.12977i	−0.552823	−	0.319172i	−0.750260	+	0.661143i	$0.770072\pi$
$500$		0			0
$501$	4.88769	+	8.46573i	0.218366	+	0.378221i
$502$	0.700423	+	2.61401i	0.0312614	+	0.116669i
$503$	28.7896	+	28.7896i	1.28367	+	1.28367i	0.938566	+	0.345100i	$0.112155\pi$
$503$	28.7896	+	28.7896i	1.28367	+	1.28367i	0.345100	+	0.938566i	$0.387845\pi$
$504$	−1.33981	−	2.28142i	−0.0596801	−	0.101623i
$505$		0			0
$506$	−5.81997	+	10.0805i	−0.258729	+	0.448132i
$507$	3.27292	+	0.876975i	0.145355	+	0.0389478i
$508$	12.1955	+	3.26776i	0.541086	+	0.144984i
$509$	−7.30942	+	12.6603i	−0.323984	+	0.561157i	−0.981306	−	0.192453i	$-0.938356\pi$
$509$	−7.30942	+	12.6603i	−0.323984	+	0.561157i	0.657322	+	0.753610i	$0.271689\pi$
$510$		0			0
$511$	40.2670	−	0.298333i	1.78131	−	0.0131975i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−1.09190	−	4.07503i	−0.0482086	−	0.179917i
$514$	12.0110	+	20.8037i	0.529784	+	0.917612i
$515$		0			0
$516$	7.76151	+	4.48111i	0.341681	+	0.197270i
$517$	8.50729	−	8.50729i	0.374150	−	0.374150i
$518$	−5.22406	−	5.14722i	−0.229532	−	0.226156i
$519$			4.52762i			0.198740i
$520$		0			0
$521$	−13.3153	+	7.68757i	−0.583352	+	0.336798i	−0.762464	−	0.647030i	$-0.776011\pi$
$521$	−13.3153	+	7.68757i	−0.583352	+	0.336798i	0.179112	+	0.983829i	$0.442677\pi$
$522$	2.31642	−	8.64500i	0.101387	−	0.378381i
$523$	−22.6178	+	6.06041i	−0.989006	+	0.265003i	−0.716833	−	0.697245i	$-0.754409\pi$
$523$	−22.6178	+	6.06041i	−0.989006	+	0.265003i	−0.272173	+	0.962248i	$0.587742\pi$
$524$	−5.12160			−0.223738
$525$		0			0
$526$	0.850325			0.0370759
$527$	7.70872	−	2.06555i	0.335797	−	0.0899766i
$528$	−0.512139	+	1.91133i	−0.0222880	+	0.0831799i
$529$	−10.0488	+	5.80167i	−0.436904	+	0.252247i
$530$		0			0
$531$			4.20702i			0.182569i
$532$	10.7598	−	2.96870i	0.466498	−	0.128709i
$533$	−14.3742	+	14.3742i	−0.622614	+	0.622614i
$534$	5.36231	+	3.09593i	0.232050	+	0.133974i
$535$		0			0
$536$	2.75608	+	4.77368i	0.119045	+	0.206191i
$537$	0.535206	+	1.99742i	0.0230959	+	0.0861949i
$538$	−8.23314	−	8.23314i	−0.354956	−	0.354956i
$539$	−12.0969	−	6.74714i	−0.521048	−	0.290620i
$540$		0			0
$541$	−3.98437	+	6.90113i	−0.171301	+	0.296703i	−0.938875	−	0.344258i	$-0.888131\pi$
$541$	−3.98437	+	6.90113i	−0.171301	+	0.296703i	0.767574	+	0.640961i	$0.221464\pi$
$542$	−22.5493	−	6.04206i	−0.968575	−	0.259529i
$543$	−5.92305	−	1.58708i	−0.254182	−	0.0681080i
$544$	−2.30141	+	3.98616i	−0.0986722	+	0.170905i
$545$		0			0
$546$	−7.13378	−	4.04852i	−0.305298	−	0.173261i
$547$	5.88082	+	5.88082i	0.251446	+	0.251446i	0.821563	−	0.570117i	$-0.193102\pi$
$547$	5.88082	+	5.88082i	0.251446	+	0.251446i	−0.570117	+	0.821563i	$0.693102\pi$
$548$	−2.99773	−	11.1877i	−0.128057	−	0.477915i
$549$	−5.55999	−	9.63018i	−0.237294	−	0.411006i
$550$		0			0
$551$	32.6994	+	18.8790i	1.39304	+	0.804272i
$552$	−4.15953	+	4.15953i	−0.177041	+	0.177041i
$553$	−1.70126	+	6.54271i	−0.0723450	+	0.278224i
$554$			9.44974i			0.401481i
$555$		0			0
$556$	2.48596	−	1.43527i	0.105428	−	0.0608689i
$557$	−6.78443	+	25.3198i	−0.287466	+	1.07284i	0.659553	+	0.751658i	$0.270746\pi$
$557$	−6.78443	+	25.3198i	−0.287466	+	1.07284i	−0.947019	+	0.321178i	$0.895921\pi$
$558$	1.67478	−	0.448756i	0.0708991	−	0.0189974i
$559$	27.7852			1.17519
$560$		0			0
$561$	9.10785			0.384534
$562$	−11.3322	+	3.03646i	−0.478020	+	0.128085i
$563$	−0.226316	+	0.844624i	−0.00953810	+	0.0355967i	−0.970531	−	0.240977i	$-0.922532\pi$
$563$	−0.226316	+	0.844624i	−0.00953810	+	0.0355967i	0.960993	+	0.276573i	$0.0891989\pi$
$564$	5.26557	−	3.04008i	0.221721	−	0.128010i
$565$		0			0
$566$			3.64779i			0.153328i
$567$	−1.85692	+	1.88464i	−0.0779832	+	0.0791473i
$568$	−2.72944	+	2.72944i	−0.114525	+	0.114525i
$569$	−28.5877	−	16.5051i	−1.19846	−	0.691929i	−0.238246	−	0.971205i	$-0.576572\pi$
$569$	−28.5877	−	16.5051i	−1.19846	−	0.691929i	−0.960211	+	0.279275i	$0.909906\pi$
$570$		0			0
$571$	−2.39594	−	4.14989i	−0.100267	−	0.173668i	0.811528	−	0.584314i	$-0.198636\pi$
$571$	−2.39594	−	4.14989i	−0.100267	−	0.173668i	−0.911795	+	0.410646i	$0.865303\pi$
$572$	1.58776	+	5.92562i	0.0663878	+	0.247763i
$573$	11.4312	+	11.4312i	0.477544	+	0.477544i
$574$	−14.9591	+	8.78504i	−0.624380	+	0.366680i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−31.5375	−	8.45046i	−1.31293	−	0.351797i	−0.466602	−	0.884467i	$-0.654522\pi$
$577$	−31.5375	−	8.45046i	−1.31293	−	0.351797i	−0.846323	+	0.532670i	$0.821189\pi$
$578$	4.04335	+	1.08341i	0.168181	+	0.0450640i
$579$	−10.8955	+	18.8715i	−0.452800	+	0.784272i
$580$		0			0
$581$	17.5992	−	31.0110i	0.730136	−	1.28655i
$582$	1.48031	+	1.48031i	0.0613609	+	0.0613609i
$583$	5.85564	+	21.8535i	0.242516	+	0.905081i
$584$	−7.60995	−	13.1808i	−0.314902	−	0.545426i
$585$		0			0
$586$	−10.5616	−	6.09777i	−0.436297	−	0.251896i
$587$	6.03856	−	6.03856i	0.249238	−	0.249238i	−0.571420	−	0.820658i	$-0.693607\pi$
$587$	6.03856	−	6.03856i	0.249238	−	0.249238i	0.820658	+	0.571420i	$0.193607\pi$
$588$	−5.02254	−	4.87586i	−0.207126	−	0.201077i
$589$			7.31479i			0.301401i
$590$		0			0
$591$	−0.769287	+	0.444148i	−0.0316442	+	0.0182698i
$592$	−0.717425	+	2.67747i	−0.0294860	+	0.110043i
$593$	−3.93171	+	1.05350i	−0.161456	+	0.0432620i	−0.338642	−	0.940915i	$-0.609967\pi$
$593$	−3.93171	+	1.05350i	−0.161456	+	0.0432620i	0.177186	+	0.984177i	$0.443301\pi$
$594$	1.97875			0.0811892
$595$		0			0
$596$	−15.5796			−0.638167
$597$	9.29699	−	2.49112i	0.380501	−	0.101955i
$598$	−4.72013	+	17.6158i	−0.193020	+	0.720362i
$599$	29.5547	−	17.0634i	1.20757	−	0.697193i	0.245345	−	0.969436i	$-0.421099\pi$
$599$	29.5547	−	17.0634i	1.20757	−	0.697193i	0.962229	+	0.272243i	$0.0877654\pi$
$600$		0			0
$601$			9.99405i			0.407666i	0.979006	+	0.203833i	$0.0653399\pi$
$601$			9.99405i			0.407666i	−0.979006	+	0.203833i	$0.934660\pi$
$602$	22.9487	+	5.96721i	0.935318	+	0.243205i
$603$	3.89769	−	3.89769i	0.158726	−	0.158726i
$604$	−18.3516	−	10.5953i	−0.746715	−	0.431116i
$605$		0			0
$606$	−5.02360	−	8.70112i	−0.204070	−	0.353459i
$607$	−4.73109	−	17.6567i	−0.192029	−	0.716662i	−0.993016	−	0.117980i	$-0.962358\pi$
$607$	−4.73109	−	17.6567i	−0.192029	−	0.716662i	0.800987	−	0.598682i	$-0.204309\pi$
$608$	−2.98313	−	2.98313i	−0.120982	−	0.120982i
$609$	−0.175433	−	23.6787i	−0.00710890	−	0.959510i
$610$		0			0
$611$	9.42504	−	16.3247i	0.381296	−	0.660425i
$612$	4.44599	+	1.19130i	0.179718	+	0.0481554i
$613$	−28.8155	−	7.72109i	−1.16385	−	0.311852i	−0.375346	−	0.926885i	$-0.622476\pi$
$613$	−28.8155	−	7.72109i	−1.16385	−	0.311852i	−0.788501	+	0.615033i	$0.789143\pi$
$614$	11.3090	−	19.5877i	0.456392	−	0.790495i
$615$		0			0
$616$	0.0387866	+	5.23514i	0.00156276	+	0.210930i
$617$	35.0246	+	35.0246i	1.41004	+	1.41004i	0.759317	+	0.650721i	$0.225533\pi$
$617$	35.0246	+	35.0246i	1.41004	+	1.41004i	0.650721	+	0.759317i	$0.274467\pi$
$618$	−1.29095	−	4.81790i	−0.0519298	−	0.193805i
$619$	5.75770	+	9.97263i	0.231422	+	0.400834i	0.958227	−	0.286010i	$-0.0923290\pi$
$619$	5.75770	+	9.97263i	0.231422	+	0.400834i	−0.726805	+	0.686844i	$0.758996\pi$
$620$		0			0
$621$	5.09436	+	2.94123i	0.204430	+	0.118028i
$622$	5.47479	−	5.47479i	0.219519	−	0.219519i
$623$	15.8549	+	4.12266i	0.635214	+	0.165171i
$624$			3.10026i			0.124110i
$625$		0			0
$626$	−17.3597	+	10.0226i	−0.693834	+	0.400585i
$627$	−2.16060	+	8.06348i	−0.0862862	+	0.322024i
$628$	−14.6660	+	3.92974i	−0.585237	+	0.156814i
$629$	12.7586			0.508720
$630$		0			0
$631$	18.4477			0.734390			0.367195	−	0.930144i	$-0.380318\pi$
$631$	18.4477			0.734390			0.367195	+	0.930144i	$0.380318\pi$
$632$	2.46808	−	0.661320i	0.0981749	−	0.0263059i
$633$	−2.91610	+	10.8830i	−0.115905	+	0.432562i
$634$	−2.58104	+	1.49016i	−0.102506	+	0.0591819i
$635$		0			0
$636$			11.4337i			0.453375i
$637$	−21.0433	−	5.30563i	−0.833765	−	0.210217i
$638$	−12.5227	+	12.5227i	−0.495778	+	0.495778i
$639$	3.34287	+	1.93001i	0.132242	+	0.0763499i
$640$		0			0
$641$	9.74229	+	16.8741i	0.384797	+	0.666488i	0.991741	−	0.128256i	$-0.0409380\pi$
$641$	9.74229	+	16.8741i	0.384797	+	0.666488i	−0.606944	+	0.794745i	$0.707605\pi$
$642$	1.56576	+	5.84351i	0.0617958	+	0.230625i
$643$	−28.2707	−	28.2707i	−1.11489	−	1.11489i	−0.992480	−	0.122408i	$-0.960938\pi$
$643$	−28.2707	−	28.2707i	−1.11489	−	1.11489i	−0.122408	−	0.992480i	$-0.539062\pi$
$644$	−7.68169	+	13.5357i	−0.302701	+	0.533381i
$645$		0			0
$646$	−9.70916	+	16.8168i	−0.382002	+	0.661647i
$647$	24.0797	+	6.45214i	0.946672	+	0.253660i	0.698949	−	0.715171i	$-0.253651\pi$
$647$	24.0797	+	6.45214i	0.946672	+	0.253660i	0.247722	+	0.968831i	$0.420318\pi$
$648$	0.965926	+	0.258819i	0.0379452	+	0.0101674i
$649$	4.16233	−	7.20937i	0.163386	−	0.282992i
$650$		0			0
$651$	3.95567	−	2.32305i	0.155035	−	0.0910476i
$652$	−15.7848	−	15.7848i	−0.618179	−	0.618179i
$653$	12.8743	+	48.0477i	0.503812	+	1.88025i	0.473666	+	0.880705i	$0.342930\pi$
$653$	12.8743	+	48.0477i	0.503812	+	1.88025i	0.0301458	+	0.999546i	$0.490403\pi$
$654$	4.87449	+	8.44287i	0.190608	+	0.330142i
$655$		0			0
$656$	5.67845	+	3.27845i	0.221706	+	0.128002i
$657$	−10.7621	+	10.7621i	−0.419869	+	0.419869i
$658$	11.2903	−	11.4589i	0.440144	−	0.446714i
$659$		−	39.5644i		−	1.54121i	−0.637312	−	0.770606i	$-0.719954\pi$
$659$		−	39.5644i		−	1.54121i	0.637312	−	0.770606i	$-0.280046\pi$
$660$		0			0
$661$	−1.74995	+	1.01033i	−0.0680651	+	0.0392974i	−0.533646	−	0.845708i	$-0.679179\pi$
$661$	−1.74995	+	1.01033i	−0.0680651	+	0.0392974i	0.465581	+	0.885005i	$0.345845\pi$
$662$	−7.20479	+	26.8886i	−0.280022	+	1.04506i
$663$	13.7837	−	3.69334i	0.535315	−	0.143437i
$664$	−13.4770			−0.523010
$665$		0			0
$666$	2.77192			0.107410
$667$	−50.8539	+	13.6263i	−1.96907	+	0.527611i
$668$	2.53005	−	9.44229i	0.0978907	−	0.365333i
$669$	−16.1321	+	9.31386i	−0.623702	+	0.360095i
$670$		0			0
$671$			22.0037i			0.849442i
$672$	−0.665818	+	2.56060i	−0.0256845	+	0.0987774i
$673$	19.7775	−	19.7775i	0.762366	−	0.762366i	−0.214383	−	0.976750i	$-0.568774\pi$
$673$	19.7775	−	19.7775i	0.762366	−	0.762366i	0.976750	+	0.214383i	$0.0687742\pi$
$674$	21.0125	+	12.1316i	0.809372	+	0.467291i
$675$		0			0
$676$	−1.69419	−	2.93442i	−0.0651610	−	0.112862i
$677$	4.44120	+	16.5748i	0.170689	+	0.637021i	0.997246	+	0.0741672i	$0.0236298\pi$
$677$	4.44120	+	16.5748i	0.170689	+	0.637021i	−0.826557	+	0.562854i	$0.809703\pi$
$678$	−6.02504	−	6.02504i	−0.231390	−	0.231390i
$679$	4.81714	+	2.73379i	0.184865	+	0.104913i
$680$		0			0
$681$	13.4571	−	23.3083i	0.515676	−	0.893177i
$682$	−3.31398	−	0.887978i	−0.126899	−	0.0340024i
$683$	0.487181	+	0.130540i	0.0186414	+	0.00499496i	0.268128	−	0.963383i	$-0.413595\pi$
$683$	0.487181	+	0.130540i	0.0186414	+	0.00499496i	−0.249486	+	0.968378i	$0.580262\pi$
$684$	−2.10939	+	3.65357i	−0.0806546	+	0.139698i
$685$		0			0
$686$	−16.2409	−	8.90138i	−0.620079	−	0.339856i
$687$	19.0144	+	19.0144i	0.725445	+	0.725445i
$688$	−2.31959	−	8.65684i	−0.0884336	−	0.330039i
$689$	17.7237	+	30.6984i	0.675220	+	1.16952i
$690$		0			0
$691$	13.5396	+	7.81710i	0.515071	+	0.297376i	0.734916	−	0.678158i	$-0.237222\pi$
$691$	13.5396	+	7.81710i	0.515071	+	0.297376i	−0.219845	+	0.975535i	$0.570555\pi$
$692$	3.20151	−	3.20151i	0.121703	−	0.121703i
$693$	5.04672	−	1.39242i	0.191709	−	0.0528937i
$694$		−	25.0428i		−	0.950613i
$695$		0			0
$696$	−7.75089	+	4.47498i	−0.293797	+	0.169624i
$697$	7.81123	−	29.1519i	0.295871	−	1.10421i
$698$	17.3992	−	4.66210i	0.658569	−	0.176463i
$699$	−0.921244			−0.0348447
$700$		0			0
$701$	8.02724			0.303185			0.151592	−	0.988443i	$-0.451560\pi$
$701$	8.02724			0.303185			0.151592	+	0.988443i	$0.451560\pi$
$702$	2.99462	−	0.802407i	0.113025	−	0.0302849i
$703$	−3.02666	+	11.2956i	−0.114153	+	0.426023i
$704$	1.71365	−	0.989376i	0.0645856	−	0.0372885i
$705$		0			0
$706$			7.59800i			0.285955i
$707$	−18.9353	−	18.6568i	−0.712136	−	0.701661i
$708$	2.97481	−	2.97481i	0.111800	−	0.111800i
$709$	−11.8457	−	6.83914i	−0.444876	−	0.256849i	0.260788	−	0.965396i	$-0.416018\pi$
$709$	−11.8457	−	6.83914i	−0.444876	−	0.256849i	−0.705664	+	0.708547i	$0.749351\pi$
$710$		0			0
$711$	−1.27757	−	2.21282i	−0.0479127	−	0.0829872i
$712$	−1.60257	−	5.98088i	−0.0600590	−	0.224143i
$713$	−7.21204	−	7.21204i	−0.270093	−	0.270093i
$714$	12.1776	−	0.0902224i	0.455735	−	0.00337649i
$715$		0			0
$716$	1.03394	−	1.79084i	0.0386401	−	0.0669267i
$717$	−24.4796	−	6.55929i	−0.914208	−	0.244961i
$718$	3.17473	+	0.850665i	0.118480	+	0.0317465i
$719$	10.5235	−	18.2273i	0.392462	−	0.679764i	−0.600312	−	0.799766i	$-0.704957\pi$
$719$	10.5235	−	18.2273i	0.392462	−	0.679764i	0.992774	+	0.120002i	$0.0382901\pi$
$720$		0			0
$721$	−6.68281	−	11.3794i	−0.248881	−	0.423792i
$722$	0.849839	+	0.849839i	0.0316277	+	0.0316277i
$723$	5.46626	+	20.4004i	0.203292	+	0.758698i
$724$	3.06600	+	5.31046i	0.113947	+	0.197362i
$725$		0			0
$726$	6.13539	+	3.54227i	0.227706	+	0.131466i
$727$	−11.2251	+	11.2251i	−0.416317	+	0.416317i	−0.883932	−	0.467615i	$-0.845113\pi$
$727$	−11.2251	+	11.2251i	−0.416317	+	0.416317i	0.467615	+	0.883932i	$0.345113\pi$
$728$	2.18161	+	7.90708i	0.0808559	+	0.293056i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−35.7248	+	20.6258i	−1.32133	+	0.762871i
$732$	−2.87806	+	10.7411i	−0.106376	+	0.397001i
$733$	−27.7719	+	7.44145i	−1.02578	+	0.274856i	−0.732208	−	0.681081i	$-0.761510\pi$
$733$	−27.7719	+	7.44145i	−1.02578	+	0.274856i	−0.293570	+	0.955938i	$0.594843\pi$
$734$	3.24759			0.119871
$735$		0			0
$736$	5.88246			0.216830
$737$	−10.5356	+	2.82300i	−0.388082	+	0.103986i
$738$	1.69705	−	6.33349i	0.0624694	−	0.233139i
$739$	−36.3593	+	20.9921i	−1.33750	+	0.772205i	−0.986436	−	0.164147i	$-0.947513\pi$
$739$	−36.3593	+	20.9921i	−1.33750	+	0.772205i	−0.351063	+	0.936352i	$0.614180\pi$
$740$		0			0
$741$			13.0793i			0.480482i
$742$	8.04573	+	29.1611i	0.295368	+	1.07054i
$743$	−8.63799	+	8.63799i	−0.316897	+	0.316897i	−0.847574	−	0.530677i	$-0.821938\pi$
$743$	−8.63799	+	8.63799i	−0.316897	+	0.316897i	0.530677	+	0.847574i	$0.321938\pi$
$744$	−1.50157	−	0.866930i	−0.0550501	−	0.0317832i
$745$		0			0
$746$	7.88312	+	13.6540i	0.288622	+	0.499907i
$747$	3.48811	+	13.0178i	0.127623	+	0.476297i
$748$	−6.44022	−	6.44022i	−0.235478	−	0.235478i
$749$	8.10541	+	13.8018i	0.296165	+	0.504307i
$750$		0			0
$751$	−15.8723	+	27.4916i	−0.579188	+	1.00318i	0.416384	+	0.909189i	$0.363297\pi$
$751$	−15.8723	+	27.4916i	−0.579188	+	1.00318i	−0.995573	+	0.0939948i	$0.970036\pi$
$752$	−5.87298	−	1.57366i	−0.214166	−	0.0573855i
$753$	−2.61401	−	0.700423i	−0.0952600	−	0.0255248i
$754$	−13.8736	+	24.0298i	−0.505247	+	0.875114i
$755$		0			0
$756$	2.64568	−	0.0196015i	0.0962224	−	0.000712901i
$757$	9.81959	+	9.81959i	0.356899	+	0.356899i	0.862669	−	0.505770i	$-0.168791\pi$
$757$	9.81959	+	9.81959i	0.356899	+	0.356899i	−0.505770	+	0.862669i	$0.668791\pi$
$758$	5.62744	+	21.0019i	0.204398	+	0.762824i
$759$	−5.81997	−	10.0805i	−0.211251	−	0.365898i
$760$		0			0
$761$	27.6636	+	15.9716i	1.00280	+	0.578970i	0.909077	−	0.416628i	$-0.136788\pi$
$761$	27.6636	+	15.9716i	1.00280	+	0.578970i	0.0937278	+	0.995598i	$0.470122\pi$
$762$	−8.92770	+	8.92770i	−0.323416	+	0.323416i
$763$	18.3733	+	18.1031i	0.665158	+	0.655375i
$764$		−	16.1661i		−	0.584869i
$765$		0			0
$766$	15.4914	−	8.94394i	0.559726	−	0.323158i
$767$	3.37574	−	12.5985i	0.121891	−	0.454904i
$768$	0.965926	−	0.258819i	0.0348548	−	0.00933933i
$769$	26.3715			0.950981			0.475490	−	0.879721i	$-0.342271\pi$
$769$	26.3715			0.950981			0.475490	+	0.879721i	$0.342271\pi$
$770$		0			0
$771$	−24.0221			−0.865133
$772$	21.0484	−	5.63991i	0.757549	−	0.202985i
$773$	11.9120	−	44.4561i	0.428444	−	1.59898i	−0.327841	−	0.944733i	$-0.606321\pi$
$773$	11.9120	−	44.4561i	0.428444	−	1.59898i	0.756285	−	0.654242i	$-0.227012\pi$
$774$	−7.76151	+	4.48111i	−0.278982	+	0.161070i
$775$		0			0
$776$		−	2.09348i		−	0.0751514i
$777$	7.06965	−	1.95056i	0.253622	−	0.0699759i
$778$	−3.56098	+	3.56098i	−0.127667	+	0.127667i
$779$	23.9561	+	13.8311i	0.858318	+	0.495550i
$780$		0			0
$781$	−3.81901	−	6.61472i	−0.136655	−	0.236693i
$782$	−7.00777	−	26.1533i	−0.250597	−	0.935241i
$783$	6.32858	+	6.32858i	0.226165	+	0.226165i
$784$	0.103719	+	6.99923i	0.00370424	+	0.249973i
$785$		0			0
$786$	2.56080	−	4.43543i	0.0913407	−	0.158207i
$787$	10.9433	+	2.93226i	0.390088	+	0.104524i	0.448532	−	0.893767i	$-0.351947\pi$
$787$	10.9433	+	2.93226i	0.390088	+	0.104524i	−0.0584437	+	0.998291i	$0.518614\pi$
$788$	0.858028	+	0.229908i	0.0305660	+	0.00819013i
$789$	−0.425163	+	0.736403i	−0.0151362	+	0.0262167i
$790$		0			0
$791$	−19.6063	−	11.1269i	−0.697121	−	0.395626i
$792$	−1.39919	−	1.39919i	−0.0497180	−	0.0497180i
$793$	8.92274	+	33.3001i	0.316856	+	1.18252i
$794$	7.37735	+	12.7780i	0.261813	+	0.453473i
$795$		0			0
$796$	−8.33546	−	4.81248i	−0.295442	−	0.170574i
$797$	24.7239	−	24.7239i	0.875767	−	0.875767i	−0.117327	−	0.993093i	$-0.537432\pi$
$797$	24.7239	−	24.7239i	0.875767	−	0.875767i	0.993093	+	0.117327i	$0.0374325\pi$
$798$	−2.80894	+	10.8026i	−0.0994356	+	0.382409i
$799$			27.9859i			0.990070i
$800$		0			0
$801$	−5.36231	+	3.09593i	−0.189468	+	0.109389i
$802$	2.25010	−	8.39748i	0.0794537	−	0.296525i
$803$	29.0902	−	7.79470i	1.02657	−	0.275069i
$804$	−5.51217			−0.194399
$805$		0			0
$806$	−5.37542			−0.189341
$807$	11.2467	−	3.01354i	0.395902	−	0.106082i
$808$	−2.60040	+	9.70484i	−0.0914819	+	0.341415i
$809$	−5.02215	+	2.89954i	−0.176569	+	0.101942i	−0.585680	−	0.810542i	$-0.699172\pi$
$809$	−5.02215	+	2.89954i	−0.176569	+	0.101942i	0.409110	+	0.912485i	$0.365839\pi$
$810$		0			0
$811$		−	28.8064i		−	1.01153i	−0.862671	−	0.505765i	$-0.831210\pi$
$811$		−	28.8064i		−	1.01153i	0.862671	−	0.505765i	$-0.168790\pi$
$812$	−16.6193	+	16.8674i	−0.583224	+	0.591931i
$813$	16.5072	−	16.5072i	0.578934	−	0.578934i
$814$	−4.75009	−	2.74247i	−0.166491	−	0.0961235i
$815$		0			0
$816$	−2.30141	−	3.98616i	−0.0805655	−	0.139544i
$817$	−9.78586	−	36.5213i	−0.342364	−	1.27772i
$818$	13.4222	+	13.4222i	0.469297	+	0.469297i
$819$	7.07301	−	4.15378i	0.247151	−	0.145145i
$820$		0			0
$821$	−2.25899	+	3.91269i	−0.0788395	+	0.136554i	−0.902749	−	0.430167i	$-0.858455\pi$
$821$	−2.25899	+	3.91269i	−0.0788395	+	0.136554i	0.823910	+	0.566721i	$0.191788\pi$
$822$	11.1877	+	2.99773i	0.390216	+	0.104558i
$823$	−21.6187	−	5.79271i	−0.753580	−	0.201921i	−0.138474	−	0.990366i	$-0.544220\pi$
$823$	−21.6187	−	5.79271i	−0.753580	−	0.201921i	−0.615105	+	0.788445i	$0.710887\pi$
$824$	−2.49393	+	4.31961i	−0.0868802	+	0.150481i
$825$		0			0
$826$	5.49380	−	9.68047i	0.191154	−	0.336827i
$827$	−22.5410	−	22.5410i	−0.783826	−	0.783826i	0.196648	−	0.980474i	$-0.436994\pi$
$827$	−22.5410	−	22.5410i	−0.783826	−	0.783826i	−0.980474	+	0.196648i	$0.936994\pi$
$828$	−1.52249	−	5.68202i	−0.0529103	−	0.197464i
$829$	−3.61347	−	6.25871i	−0.125501	−	0.217374i	0.796428	−	0.604734i	$-0.206720\pi$
$829$	−3.61347	−	6.25871i	−0.125501	−	0.217374i	−0.921929	+	0.387360i	$0.873387\pi$
$830$		0			0
$831$	−8.18372	−	4.72487i	−0.283890	−	0.163904i
$832$	2.19222	−	2.19222i	0.0760014	−	0.0760014i
$833$	30.9949	−	8.79930i	1.07391	−	0.304878i
$834$			2.87054i			0.0993985i
$835$		0			0
$836$	7.22952	−	4.17397i	0.250038	−	0.144360i
$837$	−0.448756	+	1.67478i	−0.0155113	+	0.0578889i
$838$	−11.5110	+	3.08437i	−0.397642	+	0.106548i
$839$	−5.52622			−0.190786			−0.0953932	−	0.995440i	$-0.530411\pi$
$839$	−5.52622			−0.190786			−0.0953932	+	0.995440i	$0.530411\pi$
$840$		0			0
$841$	−51.1018			−1.76213
$842$	6.71572	−	1.79947i	0.231439	−	0.0620139i
$843$	3.03646	−	11.3322i	0.104581	−	0.390302i
$844$	9.75746	−	5.63347i	0.335866	−	0.193912i
$845$		0			0
$846$			6.08016i			0.209040i
$847$	18.1407	+	4.71702i	0.623321	+	0.162079i
$848$	8.08484	−	8.08484i	0.277635	−	0.277635i
$849$	−3.15908	−	1.82389i	−0.108419	−	0.0625959i
$850$		0			0
$851$	−8.15284	−	14.1211i	−0.279476	−	0.484066i
$852$	−0.999046	−	3.72849i	−0.0342267	−	0.127736i
$853$	−10.4649	−	10.4649i	−0.358313	−	0.358313i	0.504878	−	0.863191i	$-0.331538\pi$
$853$	−10.4649	−	10.4649i	−0.358313	−	0.358313i	−0.863191	+	0.504878i	$0.831538\pi$
$854$	0.217968	+	29.4199i	0.00745873	+	1.00673i
$855$		0			0
$856$	3.02482	−	5.23915i	0.103386	−	0.179070i
$857$	−2.07640	−	0.556370i	−0.0709286	−	0.0190053i	0.223180	−	0.974777i	$-0.428356\pi$
$857$	−2.07640	−	0.556370i	−0.0709286	−	0.0190053i	−0.294109	+	0.955772i	$0.595023\pi$
$858$	−5.92562	−	1.58776i	−0.202297	−	0.0542054i
$859$	3.59455	−	6.22594i	0.122644	−	0.212426i	−0.798165	−	0.602439i	$-0.794196\pi$
$859$	3.59455	−	6.22594i	0.122644	−	0.212426i	0.920810	+	0.390012i	$0.127529\pi$
$860$		0			0
$861$	−0.128525	−	17.3475i	−0.00438013	−	0.591200i
$862$	−4.41788	−	4.41788i	−0.150474	−	0.150474i
$863$	−10.4926	−	39.1589i	−0.357172	−	1.33298i	−0.877729	−	0.479157i	$-0.840943\pi$
$863$	−10.4926	−	39.1589i	−0.357172	−	1.33298i	0.520557	−	0.853827i	$-0.325724\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$		0			0
$866$	18.5603	+	10.7158i	0.630704	+	0.364137i
$867$	−2.95994	+	2.95994i	−0.100525	+	0.100525i
$868$	−4.43973	−	1.15444i	−0.150694	−	0.0391841i
$869$			5.05600i			0.171513i
$870$		0			0
$871$	−14.7997	+	8.54458i	−0.501467	+	0.289522i
$872$	2.52322	−	9.41680i	0.0854471	−	0.318893i
$873$	−2.02214	+	0.541831i	−0.0684391	+	0.0183382i
$874$	24.8168			0.839442
$875$		0			0
$876$	15.2199			0.514233
$877$	−49.3516	+	13.2237i	−1.66648	+	0.446533i	−0.964159	−	0.265324i	$-0.914521\pi$
$877$	−49.3516	+	13.2237i	−1.66648	+	0.446533i	−0.702325	+	0.711857i	$0.747855\pi$
$878$	−8.47526	+	31.6301i	−0.286026	+	1.06746i
$879$	10.5616	−	6.09777i	0.356235	−	0.205673i
$880$		0			0
$881$		−	27.9972i		−	0.943251i	−0.881799	−	0.471625i	$-0.843667\pi$
$881$		−	27.9972i		−	0.943251i	0.881799	−	0.471625i	$-0.156333\pi$
$882$	6.73389	−	1.91172i	0.226742	−	0.0643709i
$883$	−4.66131	+	4.66131i	−0.156865	+	0.156865i	−0.781176	−	0.624311i	$-0.785380\pi$
$883$	−4.66131	+	4.66131i	−0.156865	+	0.156865i	0.624311	+	0.781176i	$0.285380\pi$
$884$	−12.3581	−	7.13498i	−0.415650	−	0.239975i
$885$		0			0
$886$	−15.3755	−	26.6312i	−0.516550	−	0.894692i
$887$	3.60517	+	13.4547i	0.121050	+	0.451763i	0.999668	−	0.0257610i	$-0.00820090\pi$
$887$	3.60517	+	13.4547i	0.121050	+	0.451763i	−0.878619	+	0.477524i	$0.841534\pi$
$888$	−1.96004	−	1.96004i	−0.0657747	−	0.0657747i
$889$	−16.4874	+	29.0520i	−0.552970	+	0.974372i
$890$		0			0
$891$	−0.989376	+	1.71365i	−0.0331454	+	0.0574094i
$892$	17.9930	+	4.82121i	0.602450	+	0.161426i
$893$	−24.7768	−	6.63894i	−0.829126	−	0.222164i
$894$	7.78982	−	13.4924i	0.260531	−	0.451252i
$895$		0			0
$896$	2.28142	−	1.33981i	0.0762170	−	0.0447601i
$897$	−12.8956	−	12.8956i	−0.430573	−	0.430573i
$898$	4.36662	+	16.2964i	0.145716	+	0.543819i
$899$	−7.75899	−	13.4390i	−0.258777	−	0.448215i
$900$		0			0
$901$	−45.5766	−	26.3136i	−1.51838	−	0.876634i
$902$	−9.17435	+	9.17435i	−0.305473	+	0.305473i
$903$	−16.6421	+	16.8905i	−0.553814	+	0.562082i
$904$			8.52069i			0.283394i
$905$		0			0
$906$	18.3516	−	10.5953i	0.609690	−	0.352005i
$907$	−6.98519	+	26.0691i	−0.231939	+	0.865610i	0.747565	+	0.664188i	$0.231223\pi$
$907$	−6.98519	+	26.0691i	−0.231939	+	0.865610i	−0.979505	+	0.201421i	$0.935444\pi$
$908$	−25.9971	+	6.96589i	−0.862743	+	0.231171i
$909$	10.0472			0.333244
$910$		0			0
$911$	−15.5364			−0.514744			−0.257372	−	0.966312i	$-0.582857\pi$
$911$	−15.5364			−0.514744			−0.257372	+	0.966312i	$0.582857\pi$
$912$	4.07503	−	1.09190i	0.134938	−	0.0361565i
$913$	6.90211	−	25.7590i	0.228426	−	0.852499i
$914$	17.1886	−	9.92384i	0.568548	−	0.328251i
$915$		0			0
$916$		−	26.8905i		−	0.888486i
$917$	3.41005	−	13.1144i	0.112610	−	0.433075i
$918$	−3.25469	+	3.25469i	−0.107421	+	0.107421i
$919$	−32.7915	−	18.9322i	−1.08169	−	0.624515i	−0.150339	−	0.988634i	$-0.548037\pi$
$919$	−32.7915	−	18.9322i	−1.08169	−	0.624515i	−0.931352	+	0.364120i	$0.881370\pi$
$920$		0			0
$921$	11.3090	+	19.5877i	0.372643	+	0.645436i
$922$	4.08351	+	15.2399i	0.134483	+	0.501898i
$923$	−8.46199	−	8.46199i	−0.278530	−	0.278530i
$924$	−4.55316	−	2.58398i	−0.149788	−	0.0850068i
$925$		0			0
$926$	−3.17220	+	5.49441i	−0.104245	+	0.180558i
$927$	4.81790	+	1.29095i	0.158241	+	0.0424005i
$928$	8.64500	+	2.31642i	0.283786	+	0.0760402i
$929$	−8.75685	+	15.1673i	−0.287303	+	0.497624i	−0.973165	−	0.230108i	$-0.926092\pi$
$929$	−8.75685	+	15.1673i	−0.287303	+	0.497624i	0.685862	+	0.727732i	$0.259425\pi$
$930$		0			0
$931$	0.437567	+	29.5283i	0.0143407	+	0.967749i
$932$	0.651418	+	0.651418i	0.0213379	+	0.0213379i
$933$	2.00391	+	7.47870i	0.0656051	+	0.244842i
$934$	8.72500	+	15.1121i	0.285491	+	0.494484i
$935$		0			0
$936$	−2.68491	−	1.55013i	−0.0877589	−	0.0506676i
$937$	2.68964	−	2.68964i	0.0878666	−	0.0878666i	−0.661807	−	0.749674i	$-0.730210\pi$
$937$	2.68964	−	2.68964i	0.0878666	−	0.0878666i	0.749674	+	0.661807i	$0.230210\pi$
$938$	−14.0585	+	3.87883i	−0.459028	+	0.126648i
$939$		−	20.0453i		−	0.654153i
$940$		0			0
$941$	28.0634	−	16.2024i	0.914839	−	0.528183i	0.0328543	−	0.999460i	$-0.489540\pi$
$941$	28.0634	−	16.2024i	0.914839	−	0.528183i	0.881985	+	0.471277i	$0.156207\pi$
$942$	3.92974	−	14.6660i	0.128038	−	0.477844i
$943$	−37.2565	+	9.98284i	−1.21324	+	0.325086i
$944$	−4.20702			−0.136927
$945$		0			0
$946$	17.7340			0.576582
$947$	−37.0654	+	9.93164i	−1.20446	+	0.322735i	−0.804587	−	0.593834i	$-0.797614\pi$
$947$	−37.0654	+	9.93164i	−1.20446	+	0.322735i	−0.399876	+	0.916569i	$0.630947\pi$
$948$	−0.661320	+	2.46808i	−0.0214787	+	0.0801595i
$949$	40.8640	−	23.5928i	1.32650	−	0.765856i
$950$		0			0
$951$		−	2.98032i		−	0.0966436i
$952$	−8.67465	−	8.54706i	−0.281147	−	0.277012i
$953$	−12.2232	+	12.2232i	−0.395949	+	0.395949i	−0.876801	−	0.480853i	$-0.840327\pi$
$953$	−12.2232	+	12.2232i	−0.395949	+	0.395949i	0.480853	+	0.876801i	$0.340327\pi$
$954$	−9.90187	−	5.71685i	−0.320585	−	0.185090i
$955$		0			0
$956$	12.6716	+	21.9478i	0.409828	+	0.709843i
$957$	−4.58362	−	17.1063i	−0.148167	−	0.552969i
$958$	−22.4504	−	22.4504i	−0.725339	−	0.725339i
$959$	30.6432	−	0.227032i	0.989520	−	0.00733124i
$960$		0			0
$961$	−13.9969	+	24.2433i	−0.451512	+	0.782041i
$962$	−8.30084	−	2.22420i	−0.267630	−	0.0717112i
$963$	−5.84351	−	1.56576i	−0.188304	−	0.0504560i
$964$	10.5600	−	18.2905i	0.340115	−	0.589096i
$965$		0			0
$966$	−7.88141	−	13.4204i	−0.253580	−	0.431794i
$967$	−24.7551	−	24.7551i	−0.796071	−	0.796071i	0.186402	−	0.982474i	$-0.440317\pi$
$967$	−24.7551	−	24.7551i	−0.796071	−	0.796071i	−0.982474	+	0.186402i	$0.940317\pi$
$968$	−1.83361	−	6.84314i	−0.0589346	−	0.219947i
$969$	−9.70916	−	16.8168i	−0.311903	−	0.540232i
$970$		0			0
$971$	8.84412	+	5.10615i	0.283821	+	0.163864i	0.635152	−	0.772387i	$-0.280937\pi$
$971$	8.84412	+	5.10615i	0.283821	+	0.163864i	−0.351331	+	0.936251i	$0.614271\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	2.01996	+	7.32118i	0.0647568	+	0.234706i
$974$		−	29.9080i		−	0.958316i
$975$		0			0
$976$	9.63018	−	5.55999i	0.308254	−	0.177971i
$977$	4.14558	−	15.4715i	0.132629	−	0.494977i	−0.867368	−	0.497668i	$-0.834190\pi$
$977$	4.14558	−	15.4715i	0.132629	−	0.494977i	0.999996	+	0.00269080i	$0.000856509\pi$
$978$	21.5624	−	5.77762i	0.689489	−	0.184748i
$979$	12.2522			0.391581
$980$		0			0
$981$	−9.74899			−0.311261
$982$	1.51824	−	0.406810i	0.0484488	−	0.0129818i
$983$	−1.97394	+	7.36683i	−0.0629588	+	0.234965i	−0.990234	−	0.139415i	$-0.955478\pi$
$983$	−1.97394	+	7.36683i	−0.0629588	+	0.234965i	0.927275	+	0.374380i	$0.122145\pi$
$984$	−5.67845	+	3.27845i	−0.181022	+	0.104513i
$985$		0			0
$986$		−	41.1951i		−	1.31192i
$987$	4.27852	+	15.5072i	0.136187	+	0.493599i
$988$	9.24849	−	9.24849i	0.294234	−	0.294234i
$989$	45.6568	+	26.3599i	1.45180	+	0.838198i
$990$		0			0
$991$	−25.4379	−	44.0597i	−0.808060	−	1.39960i	−0.914206	−	0.405251i	$-0.867184\pi$
$991$	−25.4379	−	44.0597i	−0.808060	−	1.39960i	0.106145	−	0.994351i	$-0.466149\pi$
$992$	0.448756	+	1.67478i	0.0142480	+	0.0531743i
$993$	−19.6839	−	19.6839i	−0.624648	−	0.624648i
$994$	−5.17171	−	8.80633i	−0.164037	−	0.279320i
$995$		0			0
$996$	6.73851	−	11.6714i	0.213518	−	0.369824i
$997$	39.3361	+	10.5401i	1.24579	+	0.333808i	0.820708	−	0.571348i	$-0.193579\pi$
$997$	39.3361	+	10.5401i	1.24579	+	0.333808i	0.425080	+	0.905156i	$0.360246\pi$
$998$	−13.7737	−	3.69064i	−0.435997	−	0.116825i
$999$	−1.38596	+	2.40055i	−0.0438498	+	0.0759500i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.bc.g.607.4		16
5.2	odd	4		210.2.u.a.103.3	✓	16
5.3	odd	4		1050.2.bc.h.943.2		16
5.4	even	2		210.2.u.b.187.2	yes	16
7.3	odd	6		1050.2.bc.h.157.2		16
15.2	even	4		630.2.bv.a.523.2		16
15.14	odd	2		630.2.bv.b.397.3		16
35.2	odd	12		1470.2.m.d.1273.7		16
35.3	even	12	inner	1050.2.bc.g.493.4		16
35.9	even	6		1470.2.m.e.97.6		16
35.12	even	12		1470.2.m.e.1273.6		16
35.17	even	12		210.2.u.b.73.2	yes	16
35.19	odd	6		1470.2.m.d.97.7		16
35.24	odd	6		210.2.u.a.157.3	yes	16
105.17	odd	12		630.2.bv.b.73.3		16
105.59	even	6		630.2.bv.a.577.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.103.3	✓	16	5.2	odd	4
210.2.u.a.157.3	yes	16	35.24	odd	6
210.2.u.b.73.2	yes	16	35.17	even	12
210.2.u.b.187.2	yes	16	5.4	even	2
630.2.bv.a.523.2		16	15.2	even	4
630.2.bv.a.577.2		16	105.59	even	6
630.2.bv.b.73.3		16	105.17	odd	12
630.2.bv.b.397.3		16	15.14	odd	2
1050.2.bc.g.493.4		16	35.3	even	12	inner
1050.2.bc.g.607.4		16	1.1	even	1	trivial
1050.2.bc.h.157.2		16	7.3	odd	6
1050.2.bc.h.943.2		16	5.3	odd	4
1470.2.m.d.97.7		16	35.19	odd	6
1470.2.m.d.1273.7		16	35.2	odd	12
1470.2.m.e.97.6		16	35.9	even	6
1470.2.m.e.1273.6		16	35.12	even	12

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(0.703686 + 2.55046i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(0.703686 + 2.55046i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(0.989376 + 1.71365i) q^{11} +(0.258819 + 0.965926i) q^{12} +(2.19222 + 2.19222i) q^{13} +(1.33981 + 2.28142i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-4.44599 - 1.19130i) q^{17} +(-0.965926 - 0.258819i) q^{18} +(2.10939 - 3.65357i) q^{19} +(-2.64568 + 0.0196015i) q^{21} +(1.39919 + 1.39919i) q^{22} +(1.52249 + 5.68202i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.68491 + 1.55013i) q^{26} +(0.707107 - 0.707107i) q^{27} +(1.88464 + 1.85692i) q^{28} +8.94996i q^{29} +(-1.50157 + 0.866930i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-1.91133 + 0.512139i) q^{33} -4.60282 q^{34} -1.00000 q^{36} +(-2.67747 + 0.717425i) q^{37} +(1.09190 - 4.07503i) q^{38} +(-2.68491 + 1.55013i) q^{39} +6.55691i q^{41} +(-2.55046 + 0.703686i) q^{42} +(6.33724 - 6.33724i) q^{43} +(1.71365 + 0.989376i) q^{44} +(2.94123 + 5.09436i) q^{46} +(-1.57366 - 5.87298i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-6.00965 + 3.58944i) q^{49} +(2.30141 - 3.98616i) q^{51} +(2.99462 + 0.802407i) q^{52} +(11.0441 + 2.95926i) q^{53} +(0.500000 - 0.866025i) q^{54} +(2.30103 + 1.30586i) q^{56} +(2.98313 + 2.98313i) q^{57} +(2.31642 + 8.64500i) q^{58} +(-2.10351 - 3.64339i) q^{59} +(9.63018 + 5.55999i) q^{61} +(-1.22602 + 1.22602i) q^{62} +(0.665818 - 2.56060i) q^{63} -1.00000i q^{64} +(-1.71365 + 0.989376i) q^{66} +(-1.42665 + 5.32434i) q^{67} +(-4.44599 + 1.19130i) q^{68} -5.88246 q^{69} -3.86002 q^{71} +(-0.965926 + 0.258819i) q^{72} +(3.93920 - 14.7013i) q^{73} +(-2.40055 + 1.38596i) q^{74} -4.21878i q^{76} +(-3.67438 + 3.72923i) q^{77} +(-2.19222 + 2.19222i) q^{78} +(2.21282 + 1.27757i) q^{79} +(0.500000 + 0.866025i) q^{81} +(1.69705 + 6.33349i) q^{82} +(-9.52969 - 9.52969i) q^{83} +(-2.28142 + 1.33981i) q^{84} +(4.48111 - 7.76151i) q^{86} +(-8.64500 - 2.31642i) q^{87} +(1.91133 + 0.512139i) q^{88} +(3.09593 - 5.36231i) q^{89} +(-4.04852 + 7.13378i) q^{91} +(4.15953 + 4.15953i) q^{92} +(-0.448756 - 1.67478i) q^{93} +(-3.04008 - 5.26557i) q^{94} +(0.866025 + 0.500000i) q^{96} +(1.48031 - 1.48031i) q^{97} +(-4.87586 + 5.02254i) q^{98} -1.97875i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{7}+O(q^{10}) \) 16 * q + 4 * q^7	\( 16 q + 4 q^{7} + 4 q^{11} - 16 q^{13} - 16 q^{14} + 8 q^{16} - 12 q^{17} + 8 q^{19} + 8 q^{21} - 4 q^{22} + 40 q^{23} + 8 q^{24} - 12 q^{26} + 4 q^{28} - 24 q^{31} - 4 q^{33} - 16 q^{34} - 16 q^{36} + 8 q^{37} + 20 q^{38} + 12 q^{39} - 8 q^{42} + 24 q^{43} - 4 q^{46} - 52 q^{49} + 8 q^{51} - 8 q^{52} + 28 q^{53} + 8 q^{54} + 8 q^{56} + 8 q^{57} + 12 q^{58} - 8 q^{59} + 24 q^{61} + 8 q^{62} + 4 q^{63} + 84 q^{67} - 12 q^{68} + 8 q^{69} - 32 q^{71} - 16 q^{73} + 24 q^{74} - 44 q^{77} + 16 q^{78} - 12 q^{79} + 8 q^{81} - 36 q^{82} - 16 q^{83} - 4 q^{84} - 8 q^{86} - 48 q^{87} + 4 q^{88} + 16 q^{89} + 8 q^{91} - 8 q^{92} + 32 q^{93} - 8 q^{94} + 44 q^{97} - 24 q^{98}+O(q^{100}) \) 16 * q + 4 * q^7 + 4 * q^11 - 16 * q^13 - 16 * q^14 + 8 * q^16 - 12 * q^17 + 8 * q^19 + 8 * q^21 - 4 * q^22 + 40 * q^23 + 8 * q^24 - 12 * q^26 + 4 * q^28 - 24 * q^31 - 4 * q^33 - 16 * q^34 - 16 * q^36 + 8 * q^37 + 20 * q^38 + 12 * q^39 - 8 * q^42 + 24 * q^43 - 4 * q^46 - 52 * q^49 + 8 * q^51 - 8 * q^52 + 28 * q^53 + 8 * q^54 + 8 * q^56 + 8 * q^57 + 12 * q^58 - 8 * q^59 + 24 * q^61 + 8 * q^62 + 4 * q^63 + 84 * q^67 - 12 * q^68 + 8 * q^69 - 32 * q^71 - 16 * q^73 + 24 * q^74 - 44 * q^77 + 16 * q^78 - 12 * q^79 + 8 * q^81 - 36 * q^82 - 16 * q^83 - 4 * q^84 - 8 * q^86 - 48 * q^87 + 4 * q^88 + 16 * q^89 + 8 * q^91 - 8 * q^92 + 32 * q^93 - 8 * q^94 + 44 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

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Database

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