LMFDB - Embedded newform 1050.2.bc.h.943.2

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			943.2
Root			$0.117630 - 0.893490i$ of defining polynomial
Character	$\chi$	$=$	1050.943
Dual form			1050.2.bc.h.157.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$			1.00000i			0.408248i
$7$	2.55046	−	0.703686i	0.963982	−	0.265968i
$7$	2.55046	−	0.703686i	0.963982	−	0.265968i
$8$	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	$0.736911\pi$
$12$	0.965926	−	0.258819i	0.278839	−	0.0747146i
$13$	−2.19222	+	2.19222i	−0.608011	+	0.608011i	−0.942426	−	0.334415i	$-0.891461\pi$
$13$	−2.19222	+	2.19222i	−0.608011	+	0.608011i	0.334415	+	0.942426i	$0.391461\pi$
$14$	−1.33981	−	2.28142i	−0.358081	−	0.609736i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.19130	+	4.44599i	−0.288932	+	1.07831i	0.656985	+	0.753903i	$0.271831\pi$
$17$	−1.19130	+	4.44599i	−0.288932	+	1.07831i	−0.945918	+	0.324407i	$0.894835\pi$
$18$	0.258819	−	0.965926i	0.0610042	−	0.227671i
$19$	−2.10939	+	3.65357i	−0.483928	+	0.838188i	−0.999830	−	0.0184602i	$-0.994124\pi$
$19$	−2.10939	+	3.65357i	−0.483928	+	0.838188i	0.515902	+	0.856648i	$0.327457\pi$
$20$		0			0
$21$	−2.64568	+	0.0196015i	−0.577334	+	0.00427740i
$22$	1.39919	−	1.39919i	0.298308	−	0.298308i
$23$	−5.68202	+	1.52249i	−1.18478	+	0.317462i	−0.796822	−	0.604214i	$-0.793487\pi$
$23$	−5.68202	+	1.52249i	−1.18478	+	0.317462i	−0.387961	+	0.921676i	$0.626821\pi$
$24$	−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
$28$	−1.85692	+	1.88464i	−0.350924	+	0.356163i
$29$		−	8.94996i		−	1.66197i	−0.556298	−	0.830983i	$-0.687779\pi$
$29$		−	8.94996i		−	1.66197i	0.556298	−	0.830983i	$-0.312221\pi$
$30$		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	$0.383098\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	−0.512139	−	1.91133i	−0.0891519	−	0.332720i
$34$	4.60282			0.789378
$35$		0			0
$36$	−1.00000			−0.166667
$37$	0.717425	+	2.67747i	0.117944	+	0.440173i	0.999490	−	0.0319248i	$-0.0101637\pi$
$37$	0.717425	+	2.67747i	0.117944	+	0.440173i	−0.881546	+	0.472097i	$0.843497\pi$
$38$	4.07503	+	1.09190i	0.661058	+	0.177130i
$39$	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	$0.828902\pi$
$42$	0.703686	+	2.55046i	0.108581	+	0.393544i
$43$	6.33724	+	6.33724i	0.966421	+	0.966421i	0.999454	−	0.0330335i	$-0.0105168\pi$
$43$	6.33724	+	6.33724i	0.966421	+	0.966421i	−0.0330335	+	0.999454i	$0.510517\pi$
$44$	−1.71365	−	0.989376i	−0.258342	−	0.149154i
$45$		0			0
$46$	2.94123	+	5.09436i	0.433661	+	0.751122i
$47$	−5.87298	+	1.57366i	−0.856663	+	0.229542i	−0.660312	−	0.750992i	$-0.729576\pi$
$47$	−5.87298	+	1.57366i	−0.856663	+	0.229542i	−0.196351	+	0.980534i	$0.562909\pi$
$48$	−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
$52$	0.802407	−	2.99462i	0.111274	−	0.415280i
$53$	−2.95926	+	11.0441i	−0.406485	+	1.51702i	0.394814	+	0.918761i	$0.370809\pi$
$53$	−2.95926	+	11.0441i	−0.406485	+	1.51702i	−0.801300	+	0.598263i	$0.795858\pi$
$54$	−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
$58$	−8.64500	+	2.31642i	−1.13514	+	0.304161i
$59$	2.10351	+	3.64339i	0.273854	+	0.474329i	0.969845	−	0.243721i	$-0.0783682\pi$
$59$	2.10351	+	3.64339i	0.273854	+	0.474329i	−0.695991	+	0.718050i	$0.745035\pi$
$60$		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
$63$	2.56060	+	0.665818i	0.322606	+	0.0838852i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−1.71365	+	0.989376i	−0.210936	+	0.121784i
$67$	5.32434	+	1.42665i	0.650472	+	0.174294i	0.568942	−	0.822377i	$-0.307353\pi$
$67$	5.32434	+	1.42665i	0.650472	+	0.174294i	0.0815298	+	0.996671i	$0.474019\pi$
$68$	−1.19130	−	4.44599i	−0.144466	−	0.539155i
$69$	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	$0.573562\pi$
$72$	0.258819	+	0.965926i	0.0305021	+	0.113835i
$73$	14.7013	+	3.93920i	1.72066	+	0.461048i	0.977997	−	0.208621i	$-0.0668974\pi$
$73$	14.7013	+	3.93920i	1.72066	+	0.461048i	0.742660	+	0.669669i	$0.233564\pi$
$74$	2.40055	−	1.38596i	0.279058	−	0.161114i
$75$		0			0
$76$		−	4.21878i		−	0.483928i
$77$	3.72923	+	3.67438i	0.424985	+	0.418734i
$78$	−2.19222	−	2.19222i	−0.248220	−	0.248220i
$79$	−2.21282	−	1.27757i	−0.248962	−	0.143738i	0.370327	−	0.928901i	$-0.379246\pi$
$79$	−2.21282	−	1.27757i	−0.248962	−	0.143738i	−0.619289	+	0.785163i	$0.712579\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	6.33349	−	1.69705i	0.699416	−	0.187408i
$83$	9.52969	−	9.52969i	1.04602	−	1.04602i	0.0471311	−	0.998889i	$-0.484992\pi$
$83$	9.52969	−	9.52969i	1.04602	−	1.04602i	0.998889	−	0.0471311i	$-0.0150078\pi$
$84$	2.28142	−	1.33981i	0.248924	−	0.146186i
$85$		0			0
$86$	4.48111	−	7.76151i	0.483210	−	0.836945i
$87$	−2.31642	+	8.64500i	−0.248346	+	0.926841i
$88$	−0.512139	+	1.91133i	−0.0545942	+	0.203748i
$89$	−3.09593	+	5.36231i	−0.328168	+	0.568404i	−0.982148	−	0.188108i	$-0.939765\pi$
$89$	−3.09593	+	5.36231i	−0.328168	+	0.568404i	0.653980	+	0.756512i	$0.273098\pi$
$90$		0			0
$91$	−4.04852	+	7.13378i	−0.424400	+	0.747824i
$92$	4.15953	−	4.15953i	0.433661	−	0.433661i
$93$	1.67478	−	0.448756i	0.173667	−	0.0465339i
$94$	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	$-0.283894\pi$
$97$	−1.48031	−	1.48031i	−0.150303	−	0.150303i	−0.778253	+	0.627951i	$0.783894\pi$
$98$	−5.02254	−	4.87586i	−0.507354	−	0.492537i
$99$			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	$0.499951\pi$
$102$	−4.44599	−	1.19130i	−0.440218	−	0.117956i
$103$	−1.29095	−	4.81790i	−0.127201	−	0.474722i	0.872707	−	0.488244i	$-0.162362\pi$
$103$	−1.29095	−	4.81790i	−0.127201	−	0.474722i	−0.999909	+	0.0135219i	$0.995696\pi$
$104$	−3.10026			−0.304006
$105$		0			0
$106$	11.4337			1.11054
$107$	−1.56576	−	5.84351i	−0.151368	−	0.564913i	−0.999389	−	0.0349507i	$-0.988873\pi$
$107$	−1.56576	−	5.84351i	−0.151368	−	0.564913i	0.848021	−	0.529963i	$-0.177794\pi$
$108$	0.965926	+	0.258819i	0.0929463	+	0.0249049i
$109$	−8.44287	+	4.87449i	−0.808680	+	0.466892i	−0.846497	−	0.532393i	$-0.821293\pi$
$109$	−8.44287	+	4.87449i	−0.808680	+	0.466892i	0.0378171	+	0.999285i	$0.487960\pi$
$110$		0			0
$111$		−	2.77192i		−	0.263099i
$112$	0.665818	−	2.56060i	0.0629139	−	0.241954i
$113$	−6.02504	−	6.02504i	−0.566788	−	0.566788i	0.364439	−	0.931227i	$-0.381261\pi$
$113$	−6.02504	−	6.02504i	−0.566788	−	0.566788i	−0.931227	+	0.364439i	$0.881261\pi$
$114$	−3.65357	−	2.10939i	−0.342189	−	0.197563i
$115$		0			0
$116$	4.47498	+	7.75089i	0.415491	+	0.719652i
$117$	−2.99462	+	0.802407i	−0.276853	+	0.0741826i
$118$	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
$122$	2.87806	−	10.7411i	0.260567	−	0.972451i
$123$	1.69705	−	6.33349i	0.153018	−	0.571071i
$124$	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	−0.189647	−	0.981852i	$-0.560734\pi$
$127$	8.92770	−	8.92770i	0.792205	−	0.792205i	0.981852	+	0.189647i	$0.0607345\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	−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
$133$	−2.80894	+	10.8026i	−0.243566	+	0.936707i
$134$		−	5.51217i		−	0.476179i
$135$		0			0
$136$	−3.98616	+	2.30141i	−0.341811	+	0.197344i
$137$	−11.1877	−	2.99773i	−0.955829	−	0.256114i	−0.252995	−	0.967468i	$-0.581416\pi$
$137$	−11.1877	−	2.99773i	−0.955829	−	0.256114i	−0.702834	+	0.711354i	$0.748082\pi$
$138$	−1.52249	−	5.68202i	−0.129603	−	0.483686i
$139$	−2.87054			−0.243476			−0.121738	−	0.992562i	$-0.538847\pi$
$139$	−2.87054			−0.243476			−0.121738	+	0.992562i	$0.538847\pi$
$140$		0			0
$141$	6.08016			0.512042
$142$	0.999046	+	3.72849i	0.0838381	+	0.312888i
$143$	−5.92562	−	1.58776i	−0.495525	−	0.132776i
$144$	0.866025	−	0.500000i	0.0721688	−	0.0416667i
$145$		0			0
$146$		−	15.2199i		−	1.25961i
$147$	−6.73389	+	1.91172i	−0.555402	+	0.157676i
$148$	−1.96004	−	1.96004i	−0.161114	−	0.161114i
$149$	13.4924	+	7.78982i	1.10534	+	0.638167i	0.937618	−	0.347668i	$-0.113026\pi$
$149$	13.4924	+	7.78982i	1.10534	+	0.638167i	0.167720	+	0.985835i	$0.446360\pi$
$150$		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	$-0.497601\pi$
$152$	−4.07503	+	1.09190i	−0.330529	+	0.0885649i
$153$	−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
$157$	−3.92974	+	14.6660i	−0.313627	+	1.17047i	0.611633	+	0.791141i	$0.290513\pi$
$157$	−3.92974	+	14.6660i	−0.313627	+	1.17047i	−0.925261	+	0.379332i	$0.876154\pi$
$158$	−0.661320	+	2.46808i	−0.0526118	+	0.196350i
$159$	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
$163$	21.5624	−	5.77762i	1.68890	−	0.452538i	0.718792	−	0.695225i	$-0.244695\pi$
$163$	21.5624	−	5.77762i	1.68890	−	0.452538i	0.970105	+	0.242687i	$0.0780288\pi$
$164$	−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	$-0.373464\pi$
$167$	−6.91224	−	6.91224i	−0.534885	−	0.534885i	−0.922022	+	0.387137i	$0.873464\pi$
$168$	−1.88464	−	1.85692i	−0.145403	−	0.143264i
$169$			3.38837i			0.260644i
$170$		0			0
$171$	−3.65357	+	2.10939i	−0.279396	+	0.161309i
$172$	−8.65684	−	2.31959i	−0.660078	−	0.176867i
$173$	1.17183	+	4.37334i	0.0890928	+	0.332499i	0.996058	−	0.0887072i	$-0.0282735\pi$
$173$	1.17183	+	4.37334i	0.0890928	+	0.332499i	−0.906965	+	0.421206i	$0.861607\pi$
$174$	8.94996			0.678495
$175$		0			0
$176$	1.97875			0.149154
$177$	−1.08886	−	4.06367i	−0.0818436	−	0.305444i
$178$	5.98088	+	1.60257i	0.448286	+	0.120118i
$179$	−1.79084	+	1.03394i	−0.133853	+	0.0772803i	−0.565431	−	0.824795i	$-0.691290\pi$
$179$	−1.79084	+	1.03394i	−0.133853	+	0.0772803i	0.431578	+	0.902076i	$0.357957\pi$
$180$		0			0
$181$			6.13199i			0.455787i	0.973686	+	0.227894i	$0.0731839\pi$
$181$			6.13199i			0.455787i	−0.973686	+	0.227894i	$0.926816\pi$
$182$	7.93854	+	2.06421i	0.588444	+	0.153010i
$183$	−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
$187$	−8.79751	+	2.35728i	−0.643337	+	0.172382i
$188$	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	$-0.0321876\pi$
$192$	0.258819	−	0.965926i	0.0186787	−	0.0697097i
$193$	−5.63991	+	21.0484i	−0.405969	+	1.51510i	0.396292	+	0.918125i	$0.370297\pi$
$193$	−5.63991	+	21.0484i	−0.405969	+	1.51510i	−0.802261	+	0.596973i	$0.796370\pi$
$194$	−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	−0.684377	−	0.729129i	$-0.739926\pi$
$197$	0.628120	−	0.628120i	0.0447517	−	0.0447517i	0.729129	+	0.684377i	$0.239926\pi$
$198$	1.91133	−	0.512139i	0.135832	−	0.0363961i
$199$	4.81248	+	8.33546i	0.341147	+	0.590885i	0.984646	−	0.174563i	$-0.0558511\pi$
$199$	4.81248	+	8.33546i	0.341147	+	0.590885i	−0.643499	+	0.765447i	$0.722518\pi$
$200$		0			0
$201$	−4.77368	−	2.75608i	−0.336709	−	0.194399i
$202$	7.10444	+	7.10444i	0.499866	+	0.499866i
$203$	−6.29796	−	22.8265i	−0.442030	−	1.60210i
$204$			4.60282i			0.322262i
$205$		0			0
$206$	−4.31961	+	2.49393i	−0.300962	+	0.173760i
$207$	−5.68202	−	1.52249i	−0.394928	−	0.105821i
$208$	0.802407	+	2.99462i	0.0556369	+	0.207640i
$209$	−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	$0.373227\pi$
$212$	−2.95926	−	11.0441i	−0.203243	−	0.758512i
$213$	3.72849	+	0.999046i	0.255472	+	0.0684535i
$214$	−5.23915	+	3.02482i	−0.358141	+	0.206773i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	−3.21964	+	3.26770i	−0.218563	+	0.221826i
$218$	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
$222$	−2.67747	+	0.717425i	−0.179700	+	0.0481504i
$223$	−13.1718	+	13.1718i	−0.882048	+	0.882048i	−0.993743	−	0.111694i	$-0.964372\pi$
$223$	−13.1718	+	13.1718i	−0.882048	+	0.882048i	0.111694	+	0.993743i	$0.464372\pi$
$224$	−2.64568	+	0.0196015i	−0.176772	+	0.00130968i
$225$		0			0
$226$	−4.26035	+	7.37914i	−0.283394	+	0.490853i
$227$	−6.96589	+	25.9971i	−0.462343	+	1.72549i	0.203210	+	0.979135i	$0.434863\pi$
$227$	−6.96589	+	25.9971i	−0.462343	+	1.72549i	−0.665552	+	0.746351i	$0.731804\pi$
$228$	−1.09190	+	4.07503i	−0.0723130	+	0.269876i
$229$	−13.4452	+	23.2878i	−0.888486	+	1.53890i	−0.0468199	+	0.998903i	$0.514909\pi$
$229$	−13.4452	+	23.2878i	−0.888486	+	1.53890i	−0.841666	+	0.539999i	$0.818425\pi$
$230$		0			0
$231$	−2.65116	−	4.51437i	−0.174434	−	0.297024i
$232$	6.32858	−	6.32858i	0.415491	−	0.415491i
$233$	−0.889853	+	0.238436i	−0.0582962	+	0.0156204i	−0.287849	−	0.957676i	$-0.592940\pi$
$233$	−0.889853	+	0.238436i	−0.0582962	+	0.0156204i	0.229553	+	0.973296i	$0.426274\pi$
$234$	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
$238$	11.7393	−	3.23894i	0.760946	−	0.209949i
$239$		−	25.3432i		−	1.63931i	−0.572856	−	0.819656i	$-0.694164\pi$
$239$		−	25.3432i		−	1.63931i	0.572856	−	0.819656i	$-0.305836\pi$
$240$		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	$0.0952134\pi$
$242$	−6.84314	−	1.83361i	−0.439894	−	0.117869i
$243$	−0.258819	−	0.965926i	−0.0166032	−	0.0619642i
$244$	−11.1200			−0.711883
$245$		0			0
$246$	−6.55691			−0.418053
$247$	−3.38518	−	12.6337i	−0.215394	−	0.803861i
$248$	−1.67478	−	0.448756i	−0.106349	−	0.0284960i
$249$	−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	$0.972781\pi$
$252$	−2.55046	+	0.703686i	−0.160664	+	0.0443280i
$253$	−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
$257$	23.2035	−	6.21737i	1.44740	−	0.387829i	0.552279	−	0.833660i	$-0.313758\pi$
$257$	23.2035	−	6.21737i	1.44740	−	0.387829i	0.895117	+	0.445831i	$0.147092\pi$
$258$	−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
$262$	−1.32557	+	4.94708i	−0.0818938	+	0.305632i
$263$	−0.220080	+	0.821351i	−0.0135707	+	0.0506467i	−0.972379	−	0.233407i	$-0.925013\pi$
$263$	−0.220080	+	0.821351i	−0.0135707	+	0.0506467i	0.958808	+	0.284053i	$0.0916793\pi$
$264$	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
$268$	−5.32434	+	1.42665i	−0.325236	+	0.0871468i
$269$	5.82171	+	10.0835i	0.354956	+	0.614802i	0.987110	−	0.160041i	$-0.0511625\pi$
$269$	5.82171	+	10.0835i	0.354956	+	0.614802i	−0.632154	+	0.774842i	$0.717829\pi$
$270$		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
$273$	5.75693	−	5.84287i	0.348425	−	0.353627i
$274$			11.5824i			0.699715i
$275$		0			0
$276$	−5.09436	+	2.94123i	−0.306644	+	0.177041i
$277$	9.12775	+	2.44577i	0.548433	+	0.146952i	0.522387	−	0.852708i	$-0.325042\pi$
$277$	9.12775	+	2.44577i	0.548433	+	0.146952i	0.0260462	+	0.999661i	$0.491708\pi$
$278$	0.742949	+	2.77273i	0.0445591	+	0.166297i
$279$	−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	$0.613796\pi$
$282$	−1.57366	−	5.87298i	−0.0937101	−	0.349731i
$283$	−3.52349	−	0.944117i	−0.209450	−	0.0561219i	0.152568	−	0.988293i	$-0.451246\pi$
$283$	−3.52349	−	0.944117i	−0.209450	−	0.0561219i	−0.362018	+	0.932171i	$0.617912\pi$
$284$	3.34287	−	1.93001i	0.198363	−	0.114525i
$285$		0			0
$286$			6.13465i			0.362750i
$287$	4.61400	+	16.7231i	0.272356	+	0.987133i
$288$	−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
$292$	−14.7013	+	3.93920i	−0.860328	+	0.230524i
$293$	8.62354	−	8.62354i	0.503793	−	0.503793i	−0.408822	−	0.912614i	$-0.634060\pi$
$293$	8.62354	−	8.62354i	0.503793	−	0.503793i	0.912614	+	0.408822i	$0.134060\pi$
$294$	3.58944	+	6.00965i	0.209340	+	0.350490i
$295$		0			0
$296$	−1.38596	+	2.40055i	−0.0805572	+	0.139529i
$297$	0.512139	−	1.91133i	0.0297173	−	0.110907i
$298$	4.03231	−	15.0488i	0.233585	−	0.871752i
$299$	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
$303$	9.70484	−	2.60040i	0.557529	−	0.149389i
$304$	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	$-0.473324\pi$
$307$	−15.9933	−	15.9933i	−0.912785	−	0.912785i	−0.996490	+	0.0837060i	$0.973324\pi$
$308$	−5.06680	−	1.31749i	−0.288708	−	0.0750710i
$309$			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	$0.262885\pi$
$312$	2.99462	+	0.802407i	0.169537	+	0.0454273i
$313$	−5.18810	−	19.3623i	−0.293249	−	1.09442i	−0.942598	−	0.333929i	$-0.891625\pi$
$313$	−5.18810	−	19.3623i	−0.293249	−	1.09442i	0.649349	−	0.760490i	$-0.275041\pi$
$314$	15.1833			0.856846
$315$		0			0
$316$	2.55514			0.143738
$317$	0.771364	+	2.87877i	0.0433241	+	0.161688i	0.984199	−	0.177067i	$-0.0566609\pi$
$317$	0.771364	+	2.87877i	0.0433241	+	0.161688i	−0.940875	+	0.338755i	$0.889994\pi$
$318$	−11.0441	−	2.95926i	−0.619322	−	0.165947i
$319$	15.3371	−	8.85488i	0.858713	−	0.495778i
$320$		0			0
$321$			6.04965i			0.337658i
$322$	11.0863	+	10.9232i	0.617816	+	0.608728i
$323$	−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
$327$	9.41680	−	2.52322i	0.520750	−	0.139535i
$328$	−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	$0.889388\pi$
$332$	−3.48811	+	13.0178i	−0.191435	+	0.714445i
$333$	−0.717425	+	2.67747i	−0.0393146	+	0.146724i
$334$	−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	−0.0634051	−	0.997988i	$-0.520196\pi$
$337$	17.1567	−	17.1567i	0.934583	−	0.934583i	0.997988	+	0.0634051i	$0.0201960\pi$
$338$	3.27292	−	0.876975i	0.178023	−	0.0477012i
$339$	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
$343$	12.8015	−	13.3836i	0.691217	−	0.722647i
$344$			8.96222i			0.483210i
$345$		0			0
$346$	3.92103	−	2.26381i	0.210796	−	0.121703i
$347$	−24.1895	−	6.48156i	−1.29856	−	0.347948i	−0.457655	−	0.889130i	$-0.651311\pi$
$347$	−24.1895	−	6.48156i	−1.29856	−	0.347948i	−0.840906	+	0.541181i	$0.817977\pi$
$348$	−2.31642	−	8.64500i	−0.124173	−	0.463421i
$349$	−18.0130			−0.964212			−0.482106	−	0.876113i	$-0.660128\pi$
$349$	−18.0130			−0.964212			−0.482106	+	0.876113i	$0.660128\pi$
$350$		0			0
$351$	3.10026			0.165480
$352$	−0.512139	−	1.91133i	−0.0272971	−	0.101874i
$353$	−7.33911	−	1.96651i	−0.390621	−	0.104667i	0.0581623	−	0.998307i	$-0.481476\pi$
$353$	−7.33911	−	1.96651i	−0.390621	−	0.104667i	−0.448784	+	0.893641i	$0.648143\pi$
$354$	−3.64339	+	2.10351i	−0.193644	+	0.111800i
$355$		0			0
$356$		−	6.19187i		−	0.328168i
$357$	3.06464	−	11.7860i	0.162198	−	0.623781i
$358$	1.46221	+	1.46221i	0.0772803	+	0.0772803i
$359$	−2.84638	−	1.64336i	−0.150226	−	0.0867332i	0.423003	−	0.906128i	$-0.360976\pi$
$359$	−2.84638	−	1.64336i	−0.150226	−	0.0867332i	−0.573229	+	0.819395i	$0.694309\pi$
$360$		0			0
$361$	0.600927	+	1.04084i	0.0316277	+	0.0547808i
$362$	5.92305	−	1.58708i	0.311309	−	0.0834149i
$363$	−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
$367$	0.840538	−	3.13693i	0.0438757	−	0.163746i	−0.940512	−	0.339761i	$-0.889654\pi$
$367$	0.840538	−	3.13693i	0.0438757	−	0.163746i	0.984388	+	0.176014i	$0.0563205\pi$
$368$	−1.52249	+	5.68202i	−0.0793654	+	0.296196i
$369$	−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
$373$	−15.2290	+	4.08060i	−0.788529	+	0.211286i	−0.630542	−	0.776156i	$-0.717167\pi$
$373$	−15.2290	+	4.08060i	−0.788529	+	0.211286i	−0.157987	+	0.987441i	$0.550500\pi$
$374$	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
$378$	−0.665818	+	2.56060i	−0.0342460	+	0.131703i
$379$		−	21.7428i		−	1.11685i	−0.829555	−	0.558426i	$-0.811406\pi$
$379$		−	21.7428i		−	1.11685i	0.829555	−	0.558426i	$-0.188594\pi$
$380$		0			0
$381$	−10.9342	+	6.31283i	−0.560174	+	0.323416i
$382$	−15.6153	−	4.18410i	−0.798946	−	0.214077i
$383$	4.62973	+	17.2784i	0.236568	+	0.882883i	0.977436	+	0.211233i	$0.0677478\pi$
$383$	4.62973	+	17.2784i	0.236568	+	0.882883i	−0.740868	+	0.671651i	$0.765586\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	21.7909			1.10913
$387$	2.31959	+	8.65684i	0.117912	+	0.440052i
$388$	2.02214	+	0.541831i	0.102659	+	0.0275073i
$389$	4.36130	−	2.51800i	0.221127	−	0.127667i	−0.385345	−	0.922772i	$-0.625918\pi$
$389$	4.36130	−	2.51800i	0.221127	−	0.127667i	0.606472	+	0.795105i	$0.292584\pi$
$390$		0			0
$391$		−	27.0759i		−	1.36929i
$392$	6.78758	+	1.71135i	0.342825	+	0.0864362i
$393$	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
$397$	14.2520	−	3.81880i	0.715285	−	0.191660i	0.117218	−	0.993106i	$-0.462602\pi$
$397$	14.2520	−	3.81880i	0.715285	−	0.191660i	0.598067	+	0.801446i	$0.295936\pi$
$398$	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	$0.0970162\pi$
$402$	−1.42665	+	5.32434i	−0.0711550	+	0.265554i
$403$	1.39126	−	5.19226i	0.0693037	−	0.258645i
$404$	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
$408$	4.44599	−	1.19130i	0.220109	−	0.0589781i
$409$	−9.49095	−	16.4388i	−0.469297	−	0.812847i	0.530087	−	0.847944i	$-0.322159\pi$
$409$	−9.49095	−	16.4388i	−0.469297	−	0.812847i	−0.999384	+	0.0350966i	$0.988826\pi$
$410$		0			0
$411$	10.0306	+	5.79118i	0.494774	+	0.285658i
$412$	3.52695	+	3.52695i	0.173760	+	0.173760i
$413$	7.92871	+	7.81209i	0.390147	+	0.384408i
$414$			5.88246i			0.289107i
$415$		0			0
$416$	2.68491	−	1.55013i	0.131638	−	0.0760014i
$417$	2.77273	+	0.742949i	0.135781	+	0.0363824i
$418$	2.16060	+	8.06348i	0.105679	+	0.394398i
$419$	11.9171			0.582188			0.291094	−	0.956695i	$-0.405981\pi$
$419$	11.9171			0.582188			0.291094	+	0.956695i	$0.405981\pi$
$420$		0			0
$421$	6.95263			0.338850			0.169425	−	0.985543i	$-0.445809\pi$
$421$	6.95263			0.338850			0.169425	+	0.985543i	$0.445809\pi$
$422$	−2.91610	−	10.8830i	−0.141953	−	0.529778i
$423$	−5.87298	−	1.57366i	−0.285554	−	0.0765140i
$424$	−9.90187	+	5.71685i	−0.480877	+	0.277635i
$425$		0			0
$426$		−	3.86002i		−	0.187018i
$427$	28.4738	+	7.40388i	1.37795	+	0.358299i
$428$	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	$0.881413\pi$
$432$	−0.965926	+	0.258819i	−0.0464731	+	0.0124524i
$433$	−15.1544	+	15.1544i	−0.728274	+	0.728274i	−0.970276	−	0.242002i	$-0.922196\pi$
$433$	−15.1544	+	15.1544i	−0.728274	+	0.728274i	0.242002	+	0.970276i	$0.422196\pi$
$434$	3.98966	+	2.26419i	0.191510	+	0.108684i
$435$		0			0
$436$	4.87449	−	8.44287i	0.233446	−	0.404340i
$437$	6.42307	−	23.9712i	0.307257	−	1.14670i
$438$	−3.93920	+	14.7013i	−0.188222	+	0.702455i
$439$	16.3729	−	28.3588i	0.781438	−	1.35349i	−0.149666	−	0.988737i	$-0.547820\pi$
$439$	16.3729	−	28.3588i	0.781438	−	1.35349i	0.931104	−	0.364753i	$-0.118847\pi$
$440$		0			0
$441$	6.99923	−	0.103719i	0.333297	−	0.00493899i
$442$	−10.0904	+	10.0904i	−0.479951	+	0.479951i
$443$	29.7032	−	7.95895i	1.41124	−	0.378141i	0.528874	−	0.848701i	$-0.322615\pi$
$443$	29.7032	−	7.95895i	1.41124	−	0.378141i	0.882368	+	0.470559i	$0.155948\pi$
$444$	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
$448$	0.703686	+	2.55046i	0.0332460	+	0.120498i
$449$		−	16.8713i		−	0.796207i	−0.917341	−	0.398103i	$-0.869669\pi$
$449$		−	16.8713i		−	0.796207i	0.917341	−	0.398103i	$-0.130331\pi$
$450$		0			0
$451$	−11.2362	+	6.48725i	−0.529094	+	0.305473i
$452$	8.23036	+	2.20532i	0.387123	+	0.103729i
$453$	5.48452	+	20.4685i	0.257685	+	0.961695i
$454$	26.9142			1.26314
$455$		0			0
$456$	4.21878			0.197563
$457$	−5.13696	−	19.1714i	−0.240297	−	0.896800i	−0.975689	−	0.219158i	$-0.929669\pi$
$457$	−5.13696	−	19.1714i	−0.240297	−	0.896800i	0.735393	−	0.677641i	$-0.236998\pi$
$458$	25.9742	+	6.95976i	1.21369	+	0.325208i
$459$	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	$0.880243\pi$
$462$	−3.67438	+	3.72923i	−0.170948	+	0.173500i
$463$	−4.48617	−	4.48617i	−0.208490	−	0.208490i	0.595135	−	0.803625i	$-0.297098\pi$
$463$	−4.48617	−	4.48617i	−0.208490	−	0.208490i	−0.803625	+	0.595135i	$0.797098\pi$
$464$	−7.75089	−	4.47498i	−0.359826	−	0.207746i
$465$		0			0
$466$	0.460622	+	0.797821i	0.0213379	+	0.0369583i
$467$	16.8554	−	4.51639i	0.779975	−	0.208994i	0.153201	−	0.988195i	$-0.451042\pi$
$467$	16.8554	−	4.51639i	0.779975	−	0.208994i	0.626774	+	0.779201i	$0.284375\pi$
$468$	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
$472$	−1.08886	+	4.06367i	−0.0501187	+	0.187046i
$473$	−4.58990	+	17.1297i	−0.211044	+	0.787626i
$474$	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
$478$	−24.4796	+	6.55929i	−1.11967	+	0.300015i
$479$	15.8748	+	27.4960i	0.725339	+	1.25632i	0.958834	+	0.283966i	$0.0916503\pi$
$479$	15.8748	+	27.4960i	0.725339	+	1.25632i	−0.233495	+	0.972358i	$0.575016\pi$
$480$		0			0
$481$	−7.44233	−	4.29683i	−0.339341	−	0.195919i
$482$	−14.9341	−	14.9341i	−0.680230	−	0.680230i
$483$	15.0030	−	4.13940i	0.682658	−	0.188349i
$484$			7.08454i			0.322024i
$485$		0			0
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	−28.8890	−	7.74077i	−1.30908	−	0.350768i	−0.464206	−	0.885727i	$-0.653660\pi$
$487$	−28.8890	−	7.74077i	−1.30908	−	0.350768i	−0.844878	+	0.534960i	$0.820327\pi$
$488$	2.87806	+	10.7411i	0.130284	+	0.486225i
$489$	−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	$0.488708\pi$
$492$	1.69705	+	6.33349i	0.0765090	+	0.285536i
$493$	39.7914	+	10.6621i	1.79211	+	0.480196i
$494$	−11.3270	+	6.53967i	−0.509628	+	0.294234i
$495$		0			0
$496$			1.73386i			0.0778527i
$497$	−9.84480	+	2.71624i	−0.441600	+	0.121840i
$498$	9.52969	+	9.52969i	0.427036	+	0.427036i
$499$	12.3491	+	7.12977i	0.552823	+	0.319172i	0.750260	−	0.661143i	$-0.229928\pi$
$499$	12.3491	+	7.12977i	0.552823	+	0.319172i	−0.197437	+	0.980316i	$0.563262\pi$
$500$		0			0
$501$	4.88769	+	8.46573i	0.218366	+	0.378221i
$502$	2.61401	−	0.700423i	0.116669	−	0.0312614i
$503$	−28.7896	+	28.7896i	−1.28367	+	1.28367i	−0.345100	+	0.938566i	$0.612155\pi$
$503$	−28.7896	+	28.7896i	−1.28367	+	1.28367i	−0.938566	+	0.345100i	$0.887845\pi$
$504$	1.33981	+	2.28142i	0.0596801	+	0.101623i
$505$		0			0
$506$	−5.81997	+	10.0805i	−0.258729	+	0.448132i
$507$	0.876975	−	3.27292i	0.0389478	−	0.145355i
$508$	−3.26776	+	12.1955i	−0.144984	+	0.541086i
$509$	7.30942	−	12.6603i	0.323984	−	0.561157i	−0.657322	−	0.753610i	$-0.728311\pi$
$509$	7.30942	−	12.6603i	0.323984	−	0.561157i	0.981306	+	0.192453i	$0.0616442\pi$
$510$		0			0
$511$	40.2670	−	0.298333i	1.78131	−	0.0131975i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	4.07503	−	1.09190i	0.179917	−	0.0482086i
$514$	−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
$518$	5.14722	−	5.22406i	0.226156	−	0.229532i
$519$		−	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	$0.442677\pi$
$522$	−8.64500	−	2.31642i	−0.378381	−	0.101387i
$523$	−6.06041	−	22.6178i	−0.265003	−	0.989006i	−0.962248	−	0.272173i	$-0.912258\pi$
$523$	−6.06041	−	22.6178i	−0.265003	−	0.989006i	0.697245	−	0.716833i	$-0.254409\pi$
$524$	5.12160			0.223738
$525$		0			0
$526$	0.850325			0.0370759
$527$	−2.06555	−	7.70872i	−0.0899766	−	0.335797i
$528$	−1.91133	−	0.512139i	−0.0831799	−	0.0222880i
$529$	10.0488	−	5.80167i	0.436904	−	0.252247i
$530$		0			0
$531$			4.20702i			0.182569i
$532$	−2.96870	−	10.7598i	−0.128709	−	0.466498i
$533$	−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
$537$	1.99742	−	0.535206i	0.0861949	−	0.0230959i
$538$	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	$0.221464\pi$
$542$	−6.04206	+	22.5493i	−0.259529	+	0.968575i
$543$	1.58708	−	5.92305i	0.0681080	−	0.254182i
$544$	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	−0.570117	−	0.821563i	$-0.693102\pi$
$547$	5.88082	−	5.88082i	0.251446	−	0.251446i	0.821563	+	0.570117i	$0.193102\pi$
$548$	11.1877	−	2.99773i	0.477915	−	0.128057i
$549$	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
$553$	−6.54271	−	1.70126i	−0.278224	−	0.0723450i
$554$		−	9.44974i		−	0.401481i
$555$		0			0
$556$	2.48596	−	1.43527i	0.105428	−	0.0608689i
$557$	25.3198	+	6.78443i	1.07284	+	0.287466i	0.751658	−	0.659553i	$-0.229254\pi$
$557$	25.3198	+	6.78443i	1.07284	+	0.287466i	0.321178	+	0.947019i	$0.395921\pi$
$558$	0.448756	+	1.67478i	0.0189974	+	0.0708991i
$559$	−27.7852			−1.17519
$560$		0			0
$561$	9.10785			0.384534
$562$	3.03646	+	11.3322i	0.128085	+	0.478020i
$563$	−0.844624	−	0.226316i	−0.0355967	−	0.00953810i	0.240977	−	0.970531i	$-0.422532\pi$
$563$	−0.844624	−	0.226316i	−0.0355967	−	0.00953810i	−0.276573	+	0.960993i	$0.589199\pi$
$564$	−5.26557	+	3.04008i	−0.221721	+	0.128010i
$565$		0			0
$566$			3.64779i			0.153328i
$567$	1.88464	+	1.85692i	0.0791473	+	0.0779832i
$568$	−2.72944	−	2.72944i	−0.114525	−	0.114525i
$569$	28.5877	+	16.5051i	1.19846	+	0.691929i	0.960211	−	0.279275i	$-0.0900943\pi$
$569$	28.5877	+	16.5051i	1.19846	+	0.691929i	0.238246	+	0.971205i	$0.423428\pi$
$570$		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	$0.865303\pi$
$572$	5.92562	−	1.58776i	0.247763	−	0.0663878i
$573$	−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
$577$	−8.45046	+	31.5375i	−0.351797	+	1.31293i	0.532670	+	0.846323i	$0.321189\pi$
$577$	−8.45046	+	31.5375i	−0.351797	+	1.31293i	−0.884467	+	0.466602i	$0.845478\pi$
$578$	−1.08341	+	4.04335i	−0.0450640	+	0.168181i
$579$	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
$583$	−21.8535	+	5.85564i	−0.905081	+	0.242516i
$584$	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	$-0.306393\pi$
$587$	−6.03856	−	6.03856i	−0.249238	−	0.249238i	−0.820658	+	0.571420i	$0.806393\pi$
$588$	4.87586	−	5.02254i	0.201077	−	0.207126i
$589$		−	7.31479i		−	0.301401i
$590$		0			0
$591$	−0.769287	+	0.444148i	−0.0316442	+	0.0182698i
$592$	2.67747	+	0.717425i	0.110043	+	0.0294860i
$593$	−1.05350	−	3.93171i	−0.0432620	−	0.161456i	0.940915	−	0.338642i	$-0.109967\pi$
$593$	−1.05350	−	3.93171i	−0.0432620	−	0.161456i	−0.984177	+	0.177186i	$0.943301\pi$
$594$	−1.97875			−0.0811892
$595$		0			0
$596$	−15.5796			−0.638167
$597$	−2.49112	−	9.29699i	−0.101955	−	0.380501i
$598$	−17.6158	−	4.72013i	−0.720362	−	0.193020i
$599$	−29.5547	+	17.0634i	−1.20757	+	0.697193i	−0.962229	−	0.272243i	$-0.912235\pi$
$599$	−29.5547	+	17.0634i	−1.20757	+	0.697193i	−0.245345	+	0.969436i	$0.578901\pi$
$600$		0			0
$601$			9.99405i			0.407666i	0.979006	+	0.203833i	$0.0653399\pi$
$601$			9.99405i			0.407666i	−0.979006	+	0.203833i	$0.934660\pi$
$602$	5.96721	−	22.9487i	0.243205	−	0.935318i
$603$	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
$607$	−17.6567	+	4.73109i	−0.716662	+	0.192029i	−0.598682	−	0.800987i	$-0.704309\pi$
$607$	−17.6567	+	4.73109i	−0.716662	+	0.192029i	−0.117980	+	0.993016i	$0.537642\pi$
$608$	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
$612$	1.19130	−	4.44599i	0.0481554	−	0.179718i
$613$	7.72109	−	28.8155i	0.311852	−	1.16385i	−0.615033	−	0.788501i	$-0.710857\pi$
$613$	7.72109	−	28.8155i	0.311852	−	1.16385i	0.926885	−	0.375346i	$-0.122476\pi$
$614$	−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	0.650721	−	0.759317i	$-0.274467\pi$
$617$	35.0246	−	35.0246i	1.41004	−	1.41004i	0.759317	−	0.650721i	$-0.225533\pi$
$618$	4.81790	−	1.29095i	0.193805	−	0.0519298i
$619$	−5.75770	−	9.97263i	−0.231422	−	0.400834i	0.726805	−	0.686844i	$-0.241004\pi$
$619$	−5.75770	−	9.97263i	−0.231422	−	0.400834i	−0.958227	+	0.286010i	$0.907671\pi$
$620$		0			0
$621$	5.09436	+	2.94123i	0.204430	+	0.118028i
$622$	−5.47479	−	5.47479i	−0.219519	−	0.219519i
$623$	−4.12266	+	15.8549i	−0.165171	+	0.635214i
$624$		−	3.10026i		−	0.124110i
$625$		0			0
$626$	−17.3597	+	10.0226i	−0.693834	+	0.400585i
$627$	8.06348	+	2.16060i	0.322024	+	0.0862862i
$628$	−3.92974	−	14.6660i	−0.156814	−	0.585237i
$629$	−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	$0.380318\pi$
$632$	−0.661320	−	2.46808i	−0.0263059	−	0.0981749i
$633$	−10.8830	−	2.91610i	−0.432562	−	0.115905i
$634$	2.58104	−	1.49016i	0.102506	−	0.0591819i
$635$		0			0
$636$			11.4337i			0.453375i
$637$	−5.30563	+	21.0433i	−0.210217	+	0.833765i
$638$	−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	$0.707605\pi$
$642$	5.84351	−	1.56576i	0.230625	−	0.0617958i
$643$	28.2707	−	28.2707i	1.11489	−	1.11489i	0.122408	−	0.992480i	$-0.460938\pi$
$643$	28.2707	−	28.2707i	1.11489	−	1.11489i	0.992480	−	0.122408i	$-0.0390615\pi$
$644$	7.68169	−	13.5357i	0.302701	−	0.533381i
$645$		0			0
$646$	−9.70916	+	16.8168i	−0.382002	+	0.661647i
$647$	6.45214	−	24.0797i	0.253660	−	0.946672i	−0.715171	−	0.698949i	$-0.753651\pi$
$647$	6.45214	−	24.0797i	0.253660	−	0.946672i	0.968831	−	0.247722i	$-0.0796821\pi$
$648$	−0.258819	+	0.965926i	−0.0101674	+	0.0379452i
$649$	−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
$653$	−48.0477	+	12.8743i	−1.88025	+	0.503812i	−0.880705	+	0.473666i	$0.842930\pi$
$653$	−48.0477	+	12.8743i	−1.88025	+	0.503812i	−0.999546	+	0.0301458i	$0.990403\pi$
$654$	−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
$658$	11.4589	+	11.2903i	0.446714	+	0.440144i
$659$			39.5644i			1.54121i	0.637312	+	0.770606i	$0.280046\pi$
$659$			39.5644i			1.54121i	−0.637312	+	0.770606i	$0.719954\pi$
$660$		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	$0.345845\pi$
$662$	26.8886	+	7.20479i	1.04506	+	0.280022i
$663$	3.69334	+	13.7837i	0.143437	+	0.535315i
$664$	13.4770			0.523010
$665$		0			0
$666$	2.77192			0.107410
$667$	13.6263	+	50.8539i	0.527611	+	1.96907i
$668$	9.44229	+	2.53005i	0.365333	+	0.0978907i
$669$	16.1321	−	9.31386i	0.623702	−	0.360095i
$670$		0			0
$671$			22.0037i			0.849442i
$672$	2.56060	+	0.665818i	0.0987774	+	0.0256845i
$673$	19.7775	+	19.7775i	0.762366	+	0.762366i	0.976750	−	0.214383i	$-0.0687742\pi$
$673$	19.7775	+	19.7775i	0.762366	+	0.762366i	−0.214383	+	0.976750i	$0.568774\pi$
$674$	−21.0125	−	12.1316i	−0.809372	−	0.467291i
$675$		0			0
$676$	−1.69419	−	2.93442i	−0.0651610	−	0.112862i
$677$	16.5748	−	4.44120i	0.637021	−	0.170689i	0.0741672	−	0.997246i	$-0.476370\pi$
$677$	16.5748	−	4.44120i	0.637021	−	0.170689i	0.562854	+	0.826557i	$0.309703\pi$
$678$	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
$682$	−0.887978	+	3.31398i	−0.0340024	+	0.126899i
$683$	−0.130540	+	0.487181i	−0.00499496	+	0.0186414i	−0.968378	−	0.249486i	$-0.919738\pi$
$683$	−0.130540	+	0.487181i	−0.00499496	+	0.0186414i	0.963383	+	0.268128i	$0.0864049\pi$
$684$	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
$688$	8.65684	−	2.31959i	0.330039	−	0.0884336i
$689$	−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
$693$	1.39242	+	5.04672i	0.0528937	+	0.191709i
$694$			25.0428i			0.950613i
$695$		0			0
$696$	−7.75089	+	4.47498i	−0.293797	+	0.169624i
$697$	−29.1519	−	7.81123i	−1.10421	−	0.295871i
$698$	4.66210	+	17.3992i	0.176463	+	0.658569i
$699$	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	$0.451560\pi$
$702$	−0.802407	−	2.99462i	−0.0302849	−	0.113025i
$703$	−11.2956	−	3.02666i	−0.426023	−	0.114153i
$704$	−1.71365	+	0.989376i	−0.0645856	+	0.0372885i
$705$		0			0
$706$			7.59800i			0.285955i
$707$	−18.6568	+	18.9353i	−0.701661	+	0.712136i
$708$	2.97481	+	2.97481i	0.111800	+	0.111800i
$709$	11.8457	+	6.83914i	0.444876	+	0.256849i	0.705664	−	0.708547i	$-0.250649\pi$
$709$	11.8457	+	6.83914i	0.444876	+	0.256849i	−0.260788	+	0.965396i	$0.583982\pi$
$710$		0			0
$711$	−1.27757	−	2.21282i	−0.0479127	−	0.0829872i
$712$	−5.98088	+	1.60257i	−0.224143	+	0.0600590i
$713$	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
$717$	−6.55929	+	24.4796i	−0.244961	+	0.914208i
$718$	−0.850665	+	3.17473i	−0.0317465	+	0.118480i
$719$	−10.5235	+	18.2273i	−0.392462	+	0.679764i	−0.992774	−	0.120002i	$-0.961710\pi$
$719$	−10.5235	+	18.2273i	−0.392462	+	0.679764i	0.600312	+	0.799766i	$0.295043\pi$
$720$		0			0
$721$	−6.68281	−	11.3794i	−0.248881	−	0.423792i
$722$	0.849839	−	0.849839i	0.0316277	−	0.0316277i
$723$	−20.4004	+	5.46626i	−0.758698	+	0.203292i
$724$	−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	$-0.154887\pi$
$727$	11.2251	+	11.2251i	0.416317	+	0.416317i	−0.467615	+	0.883932i	$0.654887\pi$
$728$	−7.90708	+	2.18161i	−0.293056	+	0.0808559i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−35.7248	+	20.6258i	−1.32133	+	0.762871i
$732$	10.7411	+	2.87806i	0.397001	+	0.106376i
$733$	−7.44145	−	27.7719i	−0.274856	−	1.02578i	−0.955938	−	0.293570i	$-0.905157\pi$
$733$	−7.44145	−	27.7719i	−0.274856	−	1.02578i	0.681081	−	0.732208i	$-0.261510\pi$
$734$	−3.24759			−0.119871
$735$		0			0
$736$	5.88246			0.216830
$737$	2.82300	+	10.5356i	0.103986	+	0.388082i
$738$	6.33349	+	1.69705i	0.233139	+	0.0624694i
$739$	36.3593	−	20.9921i	1.33750	−	0.772205i	0.351063	−	0.936352i	$-0.385820\pi$
$739$	36.3593	−	20.9921i	1.33750	−	0.772205i	0.986436	+	0.164147i	$0.0524871\pi$
$740$		0			0
$741$			13.0793i			0.480482i
$742$	29.1611	−	8.04573i	1.07054	−	0.295368i
$743$	−8.63799	−	8.63799i	−0.316897	−	0.316897i	0.530677	−	0.847574i	$-0.321938\pi$
$743$	−8.63799	−	8.63799i	−0.316897	−	0.316897i	−0.847574	+	0.530677i	$0.821938\pi$
$744$	1.50157	+	0.866930i	0.0550501	+	0.0317832i
$745$		0			0
$746$	7.88312	+	13.6540i	0.288622	+	0.499907i
$747$	13.0178	−	3.48811i	0.476297	−	0.127623i
$748$	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	$0.970036\pi$
$752$	−1.57366	+	5.87298i	−0.0573855	+	0.214166i
$753$	0.700423	−	2.61401i	0.0255248	−	0.0952600i
$754$	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	−0.505770	−	0.862669i	$-0.668791\pi$
$757$	9.81959	−	9.81959i	0.356899	−	0.356899i	0.862669	+	0.505770i	$0.168791\pi$
$758$	−21.0019	+	5.62744i	−0.762824	+	0.204398i
$759$	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
$763$	−18.1031	+	18.3733i	−0.655375	+	0.665158i
$764$			16.1661i			0.584869i
$765$		0			0
$766$	15.4914	−	8.94394i	0.559726	−	0.323158i
$767$	−12.5985	−	3.37574i	−0.454904	−	0.121891i
$768$	0.258819	+	0.965926i	0.00933933	+	0.0348548i
$769$	−26.3715			−0.950981			−0.475490	−	0.879721i	$-0.657729\pi$
$769$	−26.3715			−0.950981			−0.475490	+	0.879721i	$0.657729\pi$
$770$		0			0
$771$	−24.0221			−0.865133
$772$	−5.63991	−	21.0484i	−0.202985	−	0.757549i
$773$	44.4561	+	11.9120i	1.59898	+	0.428444i	0.944733	−	0.327841i	$-0.106321\pi$
$773$	44.4561	+	11.9120i	1.59898	+	0.428444i	0.654242	+	0.756285i	$0.272988\pi$
$774$	7.76151	−	4.48111i	0.278982	−	0.161070i
$775$		0			0
$776$		−	2.09348i		−	0.0751514i
$777$	−1.95056	−	7.06965i	−0.0699759	−	0.253622i
$778$	−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
$782$	−26.1533	+	7.00777i	−0.935241	+	0.250597i
$783$	−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
$787$	2.93226	−	10.9433i	0.104524	−	0.390088i	−0.893767	−	0.448532i	$-0.851947\pi$
$787$	2.93226	−	10.9433i	0.104524	−	0.390088i	0.998291	+	0.0584437i	$0.0186138\pi$
$788$	−0.229908	+	0.858028i	−0.00819013	+	0.0305660i
$789$	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
$793$	−33.3001	+	8.92274i	−1.18252	+	0.316856i
$794$	−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	$-0.462568\pi$
$797$	−24.7239	−	24.7239i	−0.875767	−	0.875767i	−0.993093	+	0.117327i	$0.962568\pi$
$798$	−10.8026	−	2.80894i	−0.382409	−	0.0994356i
$799$		−	27.9859i		−	0.990070i
$800$		0			0
$801$	−5.36231	+	3.09593i	−0.189468	+	0.109389i
$802$	−8.39748	−	2.25010i	−0.296525	−	0.0794537i
$803$	7.79470	+	29.0902i	0.275069	+	1.02657i
$804$	5.51217			0.194399
$805$		0			0
$806$	−5.37542			−0.189341
$807$	−3.01354	−	11.2467i	−0.106082	−	0.395902i
$808$	−9.70484	−	2.60040i	−0.341415	−	0.0914819i
$809$	5.02215	−	2.89954i	0.176569	−	0.101942i	−0.409110	−	0.912485i	$-0.634161\pi$
$809$	5.02215	−	2.89954i	0.176569	−	0.101942i	0.585680	+	0.810542i	$0.300828\pi$
$810$		0			0
$811$		−	28.8064i		−	1.01153i	−0.862671	−	0.505765i	$-0.831210\pi$
$811$		−	28.8064i		−	1.01153i	0.862671	−	0.505765i	$-0.168790\pi$
$812$	16.8674	+	16.6193i	0.591931	+	0.583224i
$813$	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
$817$	−36.5213	+	9.78586i	−1.27772	+	0.342364i
$818$	−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	$0.191788\pi$
$822$	2.99773	−	11.1877i	0.104558	−	0.390216i
$823$	5.79271	−	21.6187i	0.201921	−	0.753580i	−0.788445	−	0.615105i	$-0.789113\pi$
$823$	5.79271	−	21.6187i	0.201921	−	0.753580i	0.990366	−	0.138474i	$-0.0442199\pi$
$824$	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	−0.980474	−	0.196648i	$-0.936994\pi$
$827$	−22.5410	+	22.5410i	−0.783826	+	0.783826i	0.196648	+	0.980474i	$0.436994\pi$
$828$	5.68202	−	1.52249i	0.197464	−	0.0529103i
$829$	3.61347	+	6.25871i	0.125501	+	0.217374i	0.921929	−	0.387360i	$-0.126613\pi$
$829$	3.61347	+	6.25871i	0.125501	+	0.217374i	−0.796428	+	0.604734i	$0.793280\pi$
$830$		0			0
$831$	−8.18372	−	4.72487i	−0.283890	−	0.163904i
$832$	−2.19222	−	2.19222i	−0.0760014	−	0.0760014i
$833$	8.79930	+	30.9949i	0.304878	+	1.07391i
$834$		−	2.87054i		−	0.0993985i
$835$		0			0
$836$	7.22952	−	4.17397i	0.250038	−	0.144360i
$837$	1.67478	+	0.448756i	0.0578889	+	0.0155113i
$838$	−3.08437	−	11.5110i	−0.106548	−	0.397642i
$839$	5.52622			0.190786			0.0953932	−	0.995440i	$-0.469589\pi$
$839$	5.52622			0.190786			0.0953932	+	0.995440i	$0.469589\pi$
$840$		0			0
$841$	−51.1018			−1.76213
$842$	−1.79947	−	6.71572i	−0.0620139	−	0.231439i
$843$	11.3322	+	3.03646i	0.390302	+	0.104581i
$844$	−9.75746	+	5.63347i	−0.335866	+	0.193912i
$845$		0			0
$846$			6.08016i			0.209040i
$847$	4.71702	−	18.1407i	0.162079	−	0.623321i
$848$	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
$852$	−3.72849	+	0.999046i	−0.127736	+	0.0342267i
$853$	10.4649	−	10.4649i	0.358313	−	0.358313i	−0.504878	−	0.863191i	$-0.668462\pi$
$853$	10.4649	−	10.4649i	0.358313	−	0.358313i	0.863191	+	0.504878i	$0.168462\pi$
$854$	−0.217968	−	29.4199i	−0.00745873	−	1.00673i
$855$		0			0
$856$	3.02482	−	5.23915i	0.103386	−	0.179070i
$857$	−0.556370	+	2.07640i	−0.0190053	+	0.0709286i	−0.974777	−	0.223180i	$-0.928356\pi$
$857$	−0.556370	+	2.07640i	−0.0190053	+	0.0709286i	0.955772	+	0.294109i	$0.0950228\pi$
$858$	1.58776	−	5.92562i	0.0542054	−	0.202297i
$859$	−3.59455	+	6.22594i	−0.122644	+	0.212426i	−0.920810	−	0.390012i	$-0.872471\pi$
$859$	−3.59455	+	6.22594i	−0.122644	+	0.212426i	0.798165	+	0.602439i	$0.205804\pi$
$860$		0			0
$861$	−0.128525	−	17.3475i	−0.00438013	−	0.591200i
$862$	−4.41788	+	4.41788i	−0.150474	+	0.150474i
$863$	39.1589	−	10.4926i	1.33298	−	0.357172i	0.479157	−	0.877729i	$-0.340943\pi$
$863$	39.1589	−	10.4926i	1.33298	−	0.357172i	0.853827	+	0.520557i	$0.174276\pi$
$864$	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
$868$	1.15444	−	4.43973i	0.0391841	−	0.150694i
$869$		−	5.05600i		−	0.171513i
$870$		0			0
$871$	−14.7997	+	8.54458i	−0.501467	+	0.289522i
$872$	−9.41680	−	2.52322i	−0.318893	−	0.0854471i
$873$	−0.541831	−	2.02214i	−0.0183382	−	0.0684391i
$874$	−24.8168			−0.839442
$875$		0			0
$876$	15.2199			0.514233
$877$	13.2237	+	49.3516i	0.446533	+	1.66648i	0.711857	+	0.702325i	$0.247855\pi$
$877$	13.2237	+	49.3516i	0.446533	+	1.66648i	−0.265324	+	0.964159i	$0.585479\pi$
$878$	−31.6301	−	8.47526i	−1.06746	−	0.286026i
$879$	−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	$-0.156333\pi$
$882$	−1.91172	−	6.73389i	−0.0643709	−	0.226742i
$883$	−4.66131	−	4.66131i	−0.156865	−	0.156865i	0.624311	−	0.781176i	$-0.285380\pi$
$883$	−4.66131	−	4.66131i	−0.156865	−	0.156865i	−0.781176	+	0.624311i	$0.785380\pi$
$884$	12.3581	+	7.13498i	0.415650	+	0.239975i
$885$		0			0
$886$	−15.3755	−	26.6312i	−0.516550	−	0.894692i
$887$	13.4547	−	3.60517i	0.451763	−	0.121050i	−0.0257610	−	0.999668i	$-0.508201\pi$
$887$	13.4547	−	3.60517i	0.451763	−	0.121050i	0.477524	+	0.878619i	$0.341534\pi$
$888$	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
$892$	4.82121	−	17.9930i	0.161426	−	0.602450i
$893$	6.63894	−	24.7768i	0.222164	−	0.829126i
$894$	−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
$898$	−16.2964	+	4.36662i	−0.543819	+	0.145716i
$899$	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
$903$	−16.8905	−	16.6421i	−0.562082	−	0.553814i
$904$		−	8.52069i		−	0.283394i
$905$		0			0
$906$	18.3516	−	10.5953i	0.609690	−	0.352005i
$907$	26.0691	+	6.98519i	0.865610	+	0.231939i	0.664188	−	0.747565i	$-0.268777\pi$
$907$	26.0691	+	6.98519i	0.865610	+	0.231939i	0.201421	+	0.979505i	$0.435444\pi$
$908$	−6.96589	−	25.9971i	−0.231171	−	0.862743i
$909$	−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	$0.582857\pi$
$912$	−1.09190	−	4.07503i	−0.0361565	−	0.134938i
$913$	25.7590	+	6.90211i	0.852499	+	0.228426i
$914$	−17.1886	+	9.92384i	−0.568548	+	0.328251i
$915$		0			0
$916$		−	26.8905i		−	0.888486i
$917$	−13.1144	−	3.41005i	−0.433075	−	0.112610i
$918$	−3.25469	−	3.25469i	−0.107421	−	0.107421i
$919$	32.7915	+	18.9322i	1.08169	+	0.624515i	0.931352	−	0.364120i	$-0.118630\pi$
$919$	32.7915	+	18.9322i	1.08169	+	0.624515i	0.150339	+	0.988634i	$0.451963\pi$
$920$		0			0
$921$	11.3090	+	19.5877i	0.372643	+	0.645436i
$922$	15.2399	−	4.08351i	0.501898	−	0.134483i
$923$	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
$927$	1.29095	−	4.81790i	0.0424005	−	0.158241i
$928$	−2.31642	+	8.64500i	−0.0760402	+	0.283786i
$929$	8.75685	−	15.1673i	0.287303	−	0.497624i	−0.685862	−	0.727732i	$-0.740575\pi$
$929$	8.75685	−	15.1673i	0.287303	−	0.497624i	0.973165	+	0.230108i	$0.0739080\pi$
$930$		0			0
$931$	0.437567	+	29.5283i	0.0143407	+	0.967749i
$932$	0.651418	−	0.651418i	0.0213379	−	0.0213379i
$933$	−7.47870	+	2.00391i	−0.244842	+	0.0656051i
$934$	−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	$-0.269790\pi$
$937$	−2.68964	−	2.68964i	−0.0878666	−	0.0878666i	−0.749674	+	0.661807i	$0.769790\pi$
$938$	−3.87883	−	14.0585i	−0.126648	−	0.459028i
$939$			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	$0.156207\pi$
$942$	−14.6660	−	3.92974i	−0.477844	−	0.128038i
$943$	−9.98284	−	37.2565i	−0.325086	−	1.21324i
$944$	4.20702			0.136927
$945$		0			0
$946$	17.7340			0.576582
$947$	9.93164	+	37.0654i	0.322735	+	1.20446i	0.916569	+	0.399876i	$0.130947\pi$
$947$	9.93164	+	37.0654i	0.322735	+	1.20446i	−0.593834	+	0.804587i	$0.702386\pi$
$948$	−2.46808	−	0.661320i	−0.0801595	−	0.0214787i
$949$	−40.8640	+	23.5928i	−1.32650	+	0.765856i
$950$		0			0
$951$		−	2.98032i		−	0.0966436i
$952$	−8.54706	+	8.67465i	−0.277012	+	0.281147i
$953$	−12.2232	−	12.2232i	−0.395949	−	0.395949i	0.480853	−	0.876801i	$-0.340327\pi$
$953$	−12.2232	−	12.2232i	−0.395949	−	0.395949i	−0.876801	+	0.480853i	$0.840327\pi$
$954$	9.90187	+	5.71685i	0.320585	+	0.185090i
$955$		0			0
$956$	12.6716	+	21.9478i	0.409828	+	0.709843i
$957$	−17.1063	+	4.58362i	−0.552969	+	0.148167i
$958$	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
$962$	−2.22420	+	8.30084i	−0.0717112	+	0.267630i
$963$	1.56576	−	5.84351i	0.0504560	−	0.188304i
$964$	−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	−0.982474	−	0.186402i	$-0.940317\pi$
$967$	−24.7551	+	24.7551i	−0.796071	+	0.796071i	0.186402	+	0.982474i	$0.440317\pi$
$968$	6.84314	−	1.83361i	0.219947	−	0.0589346i
$969$	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
$973$	−7.32118	+	2.01996i	−0.234706	+	0.0647568i
$974$			29.9080i			0.958316i
$975$		0			0
$976$	9.63018	−	5.55999i	0.308254	−	0.177971i
$977$	−15.4715	−	4.14558i	−0.494977	−	0.132629i	0.00269080	−	0.999996i	$-0.499143\pi$
$977$	−15.4715	−	4.14558i	−0.494977	−	0.132629i	−0.497668	+	0.867368i	$0.665810\pi$
$978$	5.77762	+	21.5624i	0.184748	+	0.689489i
$979$	−12.2522			−0.391581
$980$		0			0
$981$	−9.74899			−0.311261
$982$	−0.406810	−	1.51824i	−0.0129818	−	0.0484488i
$983$	−7.36683	−	1.97394i	−0.234965	−	0.0629588i	0.139415	−	0.990234i	$-0.455478\pi$
$983$	−7.36683	−	1.97394i	−0.234965	−	0.0629588i	−0.374380	+	0.927275i	$0.622145\pi$
$984$	5.67845	−	3.27845i	0.181022	−	0.104513i
$985$		0			0
$986$		−	41.1951i		−	1.31192i
$987$	15.5072	−	4.27852i	0.493599	−	0.136187i
$988$	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	$-0.466149\pi$
$992$	1.67478	−	0.448756i	0.0531743	−	0.0142480i
$993$	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
$997$	10.5401	−	39.3361i	0.333808	−	1.24579i	−0.571348	−	0.820708i	$-0.693579\pi$
$997$	10.5401	−	39.3361i	0.333808	−	1.24579i	0.905156	−	0.425080i	$-0.139754\pi$
$998$	3.69064	−	13.7737i	0.116825	−	0.435997i
$999$	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.h.943.2		16
5.2	odd	4		1050.2.bc.g.607.4		16
5.3	odd	4		210.2.u.b.187.2	yes	16
5.4	even	2		210.2.u.a.103.3	✓	16
7.3	odd	6		1050.2.bc.g.493.4		16
15.8	even	4		630.2.bv.b.397.3		16
15.14	odd	2		630.2.bv.a.523.2		16
35.3	even	12		210.2.u.a.157.3	yes	16
35.9	even	6		1470.2.m.d.1273.7		16
35.17	even	12	inner	1050.2.bc.h.157.2		16
35.19	odd	6		1470.2.m.e.1273.6		16
35.23	odd	12		1470.2.m.e.97.6		16
35.24	odd	6		210.2.u.b.73.2	yes	16
35.33	even	12		1470.2.m.d.97.7		16
105.38	odd	12		630.2.bv.a.577.2		16
105.59	even	6		630.2.bv.b.73.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.103.3	✓	16	5.4	even	2
210.2.u.a.157.3	yes	16	35.3	even	12
210.2.u.b.73.2	yes	16	35.24	odd	6
210.2.u.b.187.2	yes	16	5.3	odd	4
630.2.bv.a.523.2		16	15.14	odd	2
630.2.bv.a.577.2		16	105.38	odd	12
630.2.bv.b.73.3		16	105.59	even	6
630.2.bv.b.397.3		16	15.8	even	4
1050.2.bc.g.493.4		16	7.3	odd	6
1050.2.bc.g.607.4		16	5.2	odd	4
1050.2.bc.h.157.2		16	35.17	even	12	inner
1050.2.bc.h.943.2		16	1.1	even	1	trivial
1470.2.m.d.97.7		16	35.33	even	12
1470.2.m.d.1273.7		16	35.9	even	6
1470.2.m.e.97.6		16	35.23	odd	12
1470.2.m.e.1273.6		16	35.19	odd	6

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)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more