LMFDB - Embedded newform 750.2.l.a.743.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(107,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("750.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.l (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			743.8
Character	$\chi$	$=$	750.743
Dual form			750.2.l.a.107.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.891007 - 0.453990i) q^{2} +(-0.631448 - 1.61285i) q^{3} +(0.587785 - 0.809017i) q^{4} +(-1.29484 - 1.15039i) q^{6} +(2.97677 - 2.97677i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-2.20255 + 2.03686i) q^{9} +O(q^{10})$	\(q+(0.891007 - 0.453990i) q^{2} +(-0.631448 - 1.61285i) q^{3} +(0.587785 - 0.809017i) q^{4} +(-1.29484 - 1.15039i) q^{6} +(2.97677 - 2.97677i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-2.20255 + 2.03686i) q^{9} +(4.73921 + 1.53986i) q^{11} +(-1.67598 - 0.437156i) q^{12} +(0.801995 - 1.57400i) q^{13} +(1.30090 - 4.00375i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(-1.40961 - 0.223260i) q^{17} +(-1.03777 + 2.81479i) q^{18} +(-1.09331 - 1.50481i) q^{19} +(-6.68076 - 2.92140i) q^{21} +(4.92175 - 0.779529i) q^{22} +(0.951606 + 1.86763i) q^{23} +(-1.69177 + 0.371369i) q^{24} -1.76655i q^{26} +(4.67593 + 2.26620i) q^{27} +(-0.658557 - 4.15797i) q^{28} +(-4.57938 - 3.32712i) q^{29} +(-5.23835 + 3.80588i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.509001 - 8.61596i) q^{33} +(-1.35733 + 0.441023i) q^{34} +(0.353226 + 2.97913i) q^{36} +(2.29429 + 1.16900i) q^{37} +(-1.65732 - 0.844446i) q^{38} +(-3.04504 - 0.299594i) q^{39} +(-3.58757 + 1.16567i) q^{41} +(-7.27889 + 0.430011i) q^{42} +(-6.26505 - 6.26505i) q^{43} +(4.03141 - 2.92899i) q^{44} +(1.69577 + 1.23205i) q^{46} +(0.732319 + 4.62368i) q^{47} +(-1.33878 + 1.09894i) q^{48} -10.7224i q^{49} +(0.530010 + 2.41446i) q^{51} +(-0.801995 - 1.57400i) q^{52} +(5.05783 - 0.801081i) q^{53} +(5.19512 - 0.103626i) q^{54} +(-2.47446 - 3.40580i) q^{56} +(-1.73666 + 2.71355i) q^{57} +(-5.59074 - 0.885486i) q^{58} +(3.44032 + 10.5882i) q^{59} +(-2.99979 + 9.23241i) q^{61} +(-2.93957 + 5.76923i) q^{62} +(-0.493226 + 12.6197i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(-4.36509 - 7.44580i) q^{66} +(1.01259 - 6.39326i) q^{67} +(-1.00917 + 1.00917i) q^{68} +(2.41131 - 2.71411i) q^{69} +(8.85681 - 12.1904i) q^{71} +(1.66722 + 2.49407i) q^{72} +(8.23800 - 4.19747i) q^{73} +2.57494 q^{74} -1.86005 q^{76} +(18.6914 - 9.52374i) q^{77} +(-2.84917 + 1.11548i) q^{78} +(-2.20434 + 3.03401i) q^{79} +(0.702433 - 8.97255i) q^{81} +(-2.66735 + 2.66735i) q^{82} +(-2.63941 + 16.6646i) q^{83} +(-6.29032 + 3.68769i) q^{84} +(-8.42648 - 2.73793i) q^{86} +(-2.47449 + 9.48674i) q^{87} +(2.26228 - 4.43998i) q^{88} +(-0.351151 + 1.08073i) q^{89} +(-2.29810 - 7.07281i) q^{91} +(2.07029 + 0.327901i) q^{92} +(9.44605 + 6.04544i) q^{93} +(2.75161 + 3.78726i) q^{94} +(-0.693954 + 1.58696i) q^{96} +(-3.47236 + 0.549968i) q^{97} +(-4.86785 - 9.55370i) q^{98} +(-13.5748 + 6.26147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) $ 80 * q - 4 * q^3 - 4 * q^7	$ 80 q - 4 q^{3} - 4 q^{7} - 16 q^{12} + 20 q^{16} + 8 q^{18} + 40 q^{19} - 4 q^{22} + 56 q^{27} - 4 q^{28} + 96 q^{33} + 40 q^{34} + 64 q^{37} + 40 q^{39} + 4 q^{42} + 24 q^{43} - 16 q^{48} + 64 q^{57} - 20 q^{58} - 4 q^{63} + 104 q^{67} - 140 q^{69} - 8 q^{72} + 60 q^{73} + 60 q^{78} - 80 q^{79} - 40 q^{81} - 96 q^{82} - 60 q^{84} - 80 q^{87} - 24 q^{88} - 12 q^{93} + 12 q^{97}+O(q^{100}) $ 80 * q - 4 * q^3 - 4 * q^7 - 16 * q^12 + 20 * q^16 + 8 * q^18 + 40 * q^19 - 4 * q^22 + 56 * q^27 - 4 * q^28 + 96 * q^33 + 40 * q^34 + 64 * q^37 + 40 * q^39 + 4 * q^42 + 24 * q^43 - 16 * q^48 + 64 * q^57 - 20 * q^58 - 4 * q^63 + 104 * q^67 - 140 * q^69 - 8 * q^72 + 60 * q^73 + 60 * q^78 - 80 * q^79 - 40 * q^81 - 96 * q^82 - 60 * q^84 - 80 * q^87 - 24 * q^88 - 12 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{7}{20}\right)$	$-1$

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 $

$2$	0.891007	−	0.453990i	0.630037	−	0.321020i
$2$	0.891007	−	0.453990i	0.630037	−	0.321020i
$3$	−0.631448	−	1.61285i	−0.364566	−	0.931177i
$3$	−0.631448	−	1.61285i	−0.364566	−	0.931177i
$4$	0.587785	−	0.809017i	0.293893	−	0.404508i
$5$		0			0
$5$		0			0
$6$	−1.29484	−	1.15039i	−0.528617	−	0.469643i
$7$	2.97677	−	2.97677i	1.12511	−	1.12511i	0.134155	−	0.990960i	$-0.457168\pi$
$7$	2.97677	−	2.97677i	1.12511	−	1.12511i	0.990960	−	0.134155i	$-0.0428318\pi$
$8$	0.156434	−	0.987688i	0.0553079	−	0.349201i
$9$	−2.20255	+	2.03686i	−0.734183	+	0.678952i
$10$		0			0
$11$	4.73921	+	1.53986i	1.42893	+	0.464286i	0.918426	−	0.395592i	$-0.129461\pi$
$11$	4.73921	+	1.53986i	1.42893	+	0.464286i	0.510499	+	0.859878i	$0.329461\pi$
$12$	−1.67598	−	0.437156i	−0.483813	−	0.126196i
$13$	0.801995	−	1.57400i	0.222433	−	0.436550i	−0.752640	−	0.658432i	$-0.771220\pi$
$13$	0.801995	−	1.57400i	0.222433	−	0.436550i	0.975074	+	0.221882i	$0.0712200\pi$
$14$	1.30090	−	4.00375i	0.347680	−	1.07005i
$15$		0			0
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	−1.40961	−	0.223260i	−0.341881	−	0.0541486i	−0.0168665	−	0.999858i	$-0.505369\pi$
$17$	−1.40961	−	0.223260i	−0.341881	−	0.0541486i	−0.325014	+	0.945709i	$0.605369\pi$
$18$	−1.03777	+	2.81479i	−0.244605	+	0.663452i
$19$	−1.09331	−	1.50481i	−0.250823	−	0.345228i	0.664977	−	0.746864i	$-0.268442\pi$
$19$	−1.09331	−	1.50481i	−0.250823	−	0.345228i	−0.915799	+	0.401636i	$0.868442\pi$
$20$		0			0
$21$	−6.68076	−	2.92140i	−1.45786	−	0.637502i
$22$	4.92175	−	0.779529i	1.04932	−	0.166196i
$23$	0.951606	+	1.86763i	0.198424	+	0.389428i	0.968682	−	0.248303i	$-0.0798730\pi$
$23$	0.951606	+	1.86763i	0.198424	+	0.389428i	−0.770259	+	0.637731i	$0.779873\pi$
$24$	−1.69177	+	0.371369i	−0.345331	+	0.0758053i
$25$		0			0
$26$		−	1.76655i		−	0.346448i
$27$	4.67593	+	2.26620i	0.899883	+	0.436131i
$28$	−0.658557	−	4.15797i	−0.124456	−	0.785782i
$29$	−4.57938	−	3.32712i	−0.850370	−	0.617830i	0.0748779	−	0.997193i	$-0.476143\pi$
$29$	−4.57938	−	3.32712i	−0.850370	−	0.617830i	−0.925248	+	0.379363i	$0.876143\pi$
$30$		0			0
$31$	−5.23835	+	3.80588i	−0.940835	+	0.683557i	−0.948622	−	0.316413i	$-0.897522\pi$
$31$	−5.23835	+	3.80588i	−0.940835	+	0.683557i	0.00778619	+	0.999970i	$0.497522\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−0.509001	−	8.61596i	−0.0886057	−	1.49985i
$34$	−1.35733	+	0.441023i	−0.232780	+	0.0756348i
$35$		0			0
$36$	0.353226	+	2.97913i	0.0588710	+	0.496522i
$37$	2.29429	+	1.16900i	0.377178	+	0.192182i	0.632294	−	0.774729i	$-0.282114\pi$
$37$	2.29429	+	1.16900i	0.377178	+	0.192182i	−0.255116	+	0.966911i	$0.582114\pi$
$38$	−1.65732	−	0.844446i	−0.268852	−	0.136987i
$39$	−3.04504	−	0.299594i	−0.487597	−	0.0479734i
$40$		0			0
$41$	−3.58757	+	1.16567i	−0.560285	+	0.182048i	−0.575449	−	0.817837i	$-0.695173\pi$
$41$	−3.58757	+	1.16567i	−0.560285	+	0.182048i	0.0151644	+	0.999885i	$0.495173\pi$
$42$	−7.27889	+	0.430011i	−1.12316	+	0.0663522i
$43$	−6.26505	−	6.26505i	−0.955411	−	0.955411i	0.0436361	−	0.999047i	$-0.486106\pi$
$43$	−6.26505	−	6.26505i	−0.955411	−	0.955411i	−0.999047	+	0.0436361i	$0.986106\pi$
$44$	4.03141	−	2.92899i	0.607758	−	0.441562i
$45$		0			0
$46$	1.69577	+	1.23205i	0.250028	+	0.181656i
$47$	0.732319	+	4.62368i	0.106820	+	0.674433i	0.981749	+	0.190182i	$0.0609079\pi$
$47$	0.732319	+	4.62368i	0.106820	+	0.674433i	−0.874929	+	0.484251i	$0.839092\pi$
$48$	−1.33878	+	1.09894i	−0.193236	+	0.158618i
$49$		−	10.7224i		−	1.53177i
$50$		0			0
$51$	0.530010	+	2.41446i	0.0742163	+	0.338092i
$52$	−0.801995	−	1.57400i	−0.111217	−	0.218275i
$53$	5.05783	−	0.801081i	0.694746	−	0.110037i	0.200933	−	0.979605i	$-0.435603\pi$
$53$	5.05783	−	0.801081i	0.694746	−	0.110037i	0.493813	+	0.869568i	$0.335603\pi$
$54$	5.19512	−	0.103626i	0.706966	−	0.0141017i
$55$		0			0
$56$	−2.47446	−	3.40580i	−0.330663	−	0.455119i
$57$	−1.73666	+	2.71355i	−0.230027	+	0.359419i
$58$	−5.59074	−	0.885486i	−0.734100	−	0.116270i
$59$	3.44032	+	10.5882i	0.447892	+	1.37847i	0.879281	+	0.476303i	$0.158024\pi$
$59$	3.44032	+	10.5882i	0.447892	+	1.37847i	−0.431389	+	0.902166i	$0.641976\pi$
$60$		0			0
$61$	−2.99979	+	9.23241i	−0.384084	+	1.18209i	0.553058	+	0.833143i	$0.313461\pi$
$61$	−2.99979	+	9.23241i	−0.384084	+	1.18209i	−0.937142	+	0.348947i	$0.886539\pi$
$62$	−2.93957	+	5.76923i	−0.373326	+	0.732693i
$63$	−0.493226	+	12.6197i	−0.0621407	+	1.58994i
$64$	−0.951057	−	0.309017i	−0.118882	−	0.0386271i
$65$		0			0
$66$	−4.36509	−	7.44580i	−0.537305	−	0.916514i
$67$	1.01259	−	6.39326i	0.123708	−	0.781061i	−0.845347	−	0.534217i	$-0.820607\pi$
$67$	1.01259	−	6.39326i	0.123708	−	0.781061i	0.969055	−	0.246844i	$-0.0793935\pi$
$68$	−1.00917	+	1.00917i	−0.122380	+	0.122380i
$69$	2.41131	−	2.71411i	0.290288	−	0.326740i
$70$		0			0
$71$	8.85681	−	12.1904i	1.05111	−	1.44673i	0.163268	−	0.986582i	$-0.447797\pi$
$71$	8.85681	−	12.1904i	1.05111	−	1.44673i	0.887842	−	0.460147i	$-0.152203\pi$
$72$	1.66722	+	2.49407i	0.196484	+	0.293928i
$73$	8.23800	−	4.19747i	0.964185	−	0.491277i	0.100295	−	0.994958i	$-0.468021\pi$
$73$	8.23800	−	4.19747i	0.964185	−	0.491277i	0.863890	+	0.503681i	$0.168021\pi$
$74$	2.57494			0.299330
$75$		0			0
$76$	−1.86005			−0.213363
$77$	18.6914	−	9.52374i	2.13008	−	1.08533i
$78$	−2.84917	+	1.11548i	−0.322605	+	0.126303i
$79$	−2.20434	+	3.03401i	−0.248007	+	0.341353i	−0.914812	−	0.403880i	$-0.867661\pi$
$79$	−2.20434	+	3.03401i	−0.248007	+	0.341353i	0.666805	+	0.745232i	$0.267661\pi$
$80$		0			0
$81$	0.702433	−	8.97255i	0.0780482	−	0.996950i
$82$	−2.66735	+	2.66735i	−0.294559	+	0.294559i
$83$	−2.63941	+	16.6646i	−0.289713	+	1.82918i	0.228048	+	0.973650i	$0.426766\pi$
$83$	−2.63941	+	16.6646i	−0.289713	+	1.82918i	−0.517761	+	0.855525i	$0.673234\pi$
$84$	−6.29032	+	3.68769i	−0.686330	+	0.402360i
$85$		0			0
$86$	−8.42648	−	2.73793i	−0.908650	−	0.295238i
$87$	−2.47449	+	9.48674i	−0.265293	+	1.01709i
$88$	2.26228	−	4.43998i	0.241160	−	0.473303i
$89$	−0.351151	+	1.08073i	−0.0372219	+	0.114557i	−0.967941	−	0.251177i	$-0.919182\pi$
$89$	−0.351151	+	1.08073i	−0.0372219	+	0.114557i	0.930719	+	0.365735i	$0.119182\pi$
$90$		0			0
$91$	−2.29810	−	7.07281i	−0.240906	−	0.741432i
$92$	2.07029	+	0.327901i	0.215842	+	0.0341860i
$93$	9.44605	+	6.04544i	0.979510	+	0.626883i
$94$	2.75161	+	3.78726i	0.283807	+	0.390626i
$95$		0			0
$96$	−0.693954	+	1.58696i	−0.0708264	+	0.161968i
$97$	−3.47236	+	0.549968i	−0.352565	+	0.0558408i	−0.330205	−	0.943909i	$-0.607118\pi$
$97$	−3.47236	+	0.549968i	−0.352565	+	0.0558408i	−0.0223598	+	0.999750i	$0.507118\pi$
$98$	−4.86785	−	9.55370i	−0.491728	−	0.965070i
$99$	−13.5748	+	6.26147i	−1.36432	+	0.629301i
$100$		0			0
$101$			16.6740i			1.65912i	0.558415	+	0.829562i	$0.311410\pi$
$101$			16.6740i			1.65912i	−0.558415	+	0.829562i	$0.688590\pi$
$102$	1.56838	+	1.91068i	0.155293	+	0.189186i
$103$	0.415010	+	2.62027i	0.0408921	+	0.258183i	0.999662	−	0.0260012i	$-0.00827738\pi$
$103$	0.415010	+	2.62027i	0.0408921	+	0.258183i	−0.958770	+	0.284184i	$0.908277\pi$
$104$	−1.42917	−	1.03835i	−0.140141	−	0.101819i
$105$		0			0
$106$	4.14287	−	3.00997i	0.402391	−	0.292355i
$107$	−8.35067	−	8.35067i	−0.807290	−	0.807290i	0.176933	−	0.984223i	$-0.443382\pi$
$107$	−8.35067	−	8.35067i	−0.807290	−	0.807290i	−0.984223	+	0.176933i	$0.943382\pi$
$108$	4.58184	−	2.45087i	0.440888	−	0.235835i
$109$	12.6666	−	4.11563i	1.21324	−	0.394206i	0.368625	−	0.929578i	$-0.379828\pi$
$109$	12.6666	−	4.11563i	1.21324	−	0.394206i	0.844617	+	0.535372i	$0.179828\pi$
$110$		0			0
$111$	0.436691	−	4.43849i	0.0414489	−	0.421283i
$112$	−3.75095	−	1.91121i	−0.354432	−	0.180592i
$113$	1.33349	+	0.679445i	0.125444	+	0.0639168i	0.515586	−	0.856838i	$-0.327574\pi$
$113$	1.33349	+	0.679445i	0.125444	+	0.0639168i	−0.390142	+	0.920755i	$0.627574\pi$
$114$	−0.315452	+	3.20622i	−0.0295448	+	0.300290i
$115$		0			0
$116$	−5.38339	+	1.74917i	−0.499835	+	0.162406i
$117$	1.43959	+	5.10037i	0.133090	+	0.471529i
$118$	7.87230	+	7.87230i	0.724704	+	0.724704i
$119$	−4.86069	+	3.53149i	−0.445578	+	0.323732i
$120$		0			0
$121$	11.1898	+	8.12983i	1.01725	+	0.739076i
$122$	1.51859	+	9.58802i	0.137487	+	0.868058i
$123$	4.14542	+	5.05015i	0.373780	+	0.455356i
$124$			6.47496i			0.581468i
$125$		0			0
$126$	5.28978	+	11.4682i	0.471251	+	1.02167i
$127$	0.704349	+	1.38236i	0.0625009	+	0.122665i	0.920144	−	0.391581i	$-0.128072\pi$
$127$	0.704349	+	1.38236i	0.0625009	+	0.122665i	−0.857643	+	0.514246i	$0.828072\pi$
$128$	−0.987688	+	0.156434i	−0.0873001	+	0.0138270i
$129$	−6.14851	+	14.0606i	−0.541347	+	1.23797i
$130$		0			0
$131$	3.74251	+	5.15112i	0.326984	+	0.450055i	0.940584	−	0.339562i	$-0.110279\pi$
$131$	3.74251	+	5.15112i	0.326984	+	0.450055i	−0.613599	+	0.789618i	$0.710279\pi$
$132$	−7.26964	−	4.65255i	−0.632741	−	0.404952i
$133$	−7.73403	−	1.22495i	−0.670625	−	0.106217i
$134$	−2.00025	−	6.15614i	−0.172795	−	0.531810i
$135$		0			0
$136$	−0.441023	+	1.35733i	−0.0378174	+	0.116390i
$137$	1.86549	−	3.66124i	0.159380	−	0.312800i	−0.797483	−	0.603342i	$-0.793835\pi$
$137$	1.86549	−	3.66124i	0.159380	−	0.312800i	0.956862	+	0.290542i	$0.0938354\pi$
$138$	0.916318	−	3.51300i	0.0780022	−	0.299046i
$139$	10.1584	+	3.30065i	0.861621	+	0.279958i	0.706305	−	0.707907i	$-0.250361\pi$
$139$	10.1584	+	3.30065i	0.861621	+	0.279958i	0.155316	+	0.987865i	$0.450361\pi$
$140$		0			0
$141$	6.99487	−	4.10073i	0.589074	−	0.345344i
$142$	2.35717	−	14.8826i	0.197809	−	1.24892i
$143$	6.22457	−	6.22457i	0.520525	−	0.520525i
$144$	2.61779	+	1.46532i	0.218149	+	0.122110i
$145$		0			0
$146$	5.43450	−	7.47994i	0.449762	−	0.619045i
$147$	−17.2935	+	6.77062i	−1.42635	+	0.558431i
$148$	2.29429	−	1.16900i	0.188589	−	0.0960909i
$149$	5.13270			0.420487			0.210244	−	0.977649i	$-0.432574\pi$
$149$	5.13270			0.420487			0.210244	+	0.977649i	$0.432574\pi$
$150$		0			0
$151$	20.1314			1.63827			0.819136	−	0.573600i	$-0.194454\pi$
$151$	20.1314			1.63827			0.819136	+	0.573600i	$0.194454\pi$
$152$	−1.65732	+	0.844446i	−0.134426	+	0.0684936i
$153$	3.55948	−	2.37943i	0.287767	−	0.192366i
$154$	12.3305	−	16.9714i	0.993617	−	1.36760i
$155$		0			0
$156$	−2.03221	+	2.28740i	−0.162707	+	0.183138i
$157$	7.13510	−	7.13510i	0.569443	−	0.569443i	−0.362529	−	0.931972i	$-0.618087\pi$
$157$	7.13510	−	7.13510i	0.569443	−	0.569443i	0.931972	+	0.362529i	$0.118087\pi$
$158$	−0.586667	+	3.70407i	−0.0466727	+	0.294680i
$159$	−4.48577	−	7.65166i	−0.355745	−	0.606816i
$160$		0			0
$161$	8.39223	+	2.72680i	0.661401	+	0.214902i
$162$	−3.44758	−	8.31350i	−0.270867	−	0.653170i
$163$	−2.55156	+	5.00771i	−0.199853	+	0.392234i	−0.969082	−	0.246739i	$-0.920641\pi$
$163$	−2.55156	+	5.00771i	−0.199853	+	0.392234i	0.769228	+	0.638974i	$0.220641\pi$
$164$	−1.16567	+	3.58757i	−0.0910238	+	0.280143i
$165$		0			0
$166$	5.21383	+	16.0465i	0.404672	+	1.24545i
$167$	−16.5614	−	2.62306i	−1.28156	−	0.202979i	−0.521734	−	0.853109i	$-0.674714\pi$
$167$	−16.5614	−	2.62306i	−1.28156	−	0.202979i	−0.759823	+	0.650130i	$0.774714\pi$
$168$	−3.93054	+	6.14150i	−0.303247	+	0.473827i
$169$	5.80692	+	7.99254i	0.446686	+	0.614810i
$170$		0			0
$171$	5.47316	+	1.08751i	0.418543	+	0.0831637i
$172$	−8.75104	+	1.38603i	−0.667260	+	0.105684i
$173$	−2.03214	−	3.98829i	−0.154500	−	0.303224i	0.800763	−	0.598982i	$-0.204428\pi$
$173$	−2.03214	−	3.98829i	−0.154500	−	0.303224i	−0.955263	+	0.295758i	$0.904428\pi$
$174$	2.10211	+	9.57614i	0.159360	+	0.725966i
$175$		0			0
$176$		−	4.98310i		−	0.375615i
$177$	14.9048	−	12.2346i	1.12031	−	0.919610i
$178$	0.177764	+	1.12236i	0.0133240	+	0.0841243i
$179$	−0.141142	−	0.102546i	−0.0105495	−	0.00766463i	0.582498	−	0.812832i	$-0.302075\pi$
$179$	−0.141142	−	0.102546i	−0.0105495	−	0.00766463i	−0.593047	+	0.805167i	$0.702075\pi$
$180$		0			0
$181$	9.20445	−	6.68743i	0.684162	−	0.497072i	−0.190574	−	0.981673i	$-0.561035\pi$
$181$	9.20445	−	6.68743i	0.684162	−	0.497072i	0.874736	+	0.484600i	$0.161035\pi$
$182$	−5.25861	−	5.25861i	−0.389794	−	0.389794i
$183$	16.7847	−	0.991580i	1.24076	−	0.0732997i
$184$	1.99350	−	0.647728i	0.146963	−	0.0477511i
$185$		0			0
$186$	11.1611	+	1.09811i	0.818369	+	0.0805172i
$187$	−6.33665	−	3.22868i	−0.463382	−	0.236105i
$188$	4.17108	+	2.12527i	0.304207	+	0.155001i
$189$	20.6652	−	7.17321i	1.50317	−	0.521774i
$190$		0			0
$191$	−17.5527	+	5.70322i	−1.27007	+	0.412671i	−0.865072	−	0.501647i	$-0.832728\pi$
$191$	−17.5527	+	5.70322i	−1.27007	+	0.412671i	−0.404998	+	0.914318i	$0.632728\pi$
$192$	0.102145	+	1.72904i	0.00737171	+	0.124782i
$193$	3.31568	+	3.31568i	0.238668	+	0.238668i	0.816298	−	0.577630i	$-0.196023\pi$
$193$	3.31568	+	3.31568i	0.238668	+	0.238668i	−0.577630	+	0.816298i	$0.696023\pi$
$194$	−2.84422	+	2.06644i	−0.204203	+	0.148362i
$195$		0			0
$196$	−8.67458	−	6.30245i	−0.619613	−	0.450175i
$197$	1.98370	+	12.5246i	0.141333	+	0.892341i	0.951836	+	0.306607i	$0.0991936\pi$
$197$	1.98370	+	12.5246i	0.141333	+	0.892341i	−0.810503	+	0.585734i	$0.800806\pi$
$198$	−9.25260	+	11.7418i	−0.657554	+	0.834457i
$199$		−	1.62602i		−	0.115266i	−0.998338	−	0.0576328i	$-0.981645\pi$
$199$		−	1.62602i		−	0.115266i	0.998338	−	0.0576328i	$-0.0183553\pi$
$200$		0			0
$201$	−10.9507	+	2.40385i	−0.772406	+	0.169555i
$202$	7.56983	+	14.8566i	0.532612	+	1.04531i
$203$	−23.5359	+	3.72772i	−1.65189	+	0.261634i
$204$	2.26487	+	0.990397i	0.158573	+	0.0693417i
$205$		0			0
$206$	1.55935	+	2.14627i	0.108645	+	0.149537i
$207$	−5.90005	−	2.17526i	−0.410082	−	0.151191i
$208$	−1.74480	−	0.276349i	−0.120980	−	0.0191613i
$209$	−2.86422	−	8.81517i	−0.198123	−	0.609758i
$210$		0			0
$211$	−3.73259	+	11.4877i	−0.256962	+	0.790848i	0.736475	+	0.676465i	$0.236489\pi$
$211$	−3.73259	+	11.4877i	−0.256962	+	0.790848i	−0.993437	+	0.114383i	$0.963511\pi$
$212$	2.32483	−	4.56273i	0.159670	−	0.313370i
$213$	−25.2538	−	6.58711i	−1.73036	−	0.451341i
$214$	−11.2316	−	3.64938i	−0.767778	−	0.249466i
$215$		0			0
$216$	2.96978	−	4.26385i	0.202068	−	0.290118i
$217$	−4.26413	+	26.9226i	−0.289468	+	1.82763i
$218$	9.41758	−	9.41758i	0.637839	−	0.637839i
$219$	−11.9717	−	10.6361i	−0.808975	−	0.718724i
$220$		0			0
$221$	−1.48191	+	2.03968i	−0.0996842	+	0.137204i
$222$	−1.62594	−	4.15298i	−0.109126	−	0.278730i
$223$	5.54645	−	2.82606i	0.371418	−	0.189247i	−0.258311	−	0.966062i	$-0.583166\pi$
$223$	5.54645	−	2.82606i	0.371418	−	0.189247i	0.629729	+	0.776815i	$0.283166\pi$
$224$	−4.20979			−0.281279
$225$		0			0
$226$	1.49661			0.0995528
$227$	−8.15754	+	4.15647i	−0.541435	+	0.275875i	−0.703246	−	0.710947i	$-0.748267\pi$
$227$	−8.15754	+	4.15647i	−0.541435	+	0.275875i	0.161811	+	0.986822i	$0.448267\pi$
$228$	1.17452	+	2.99998i	0.0777848	+	0.198678i
$229$	−10.8714	+	14.9632i	−0.718400	+	0.988793i	0.281175	+	0.959656i	$0.409276\pi$
$229$	−10.8714	+	14.9632i	−0.718400	+	0.988793i	−0.999575	+	0.0291365i	$0.990724\pi$
$230$		0			0
$231$	−27.1630	−	24.1326i	−1.78719	−	1.58781i
$232$	−4.00253	+	4.00253i	−0.262779	+	0.262779i
$233$	2.15478	−	13.6047i	0.141164	−	0.891276i	−0.810857	−	0.585244i	$-0.800999\pi$
$233$	2.15478	−	13.6047i	0.141164	−	0.891276i	0.952021	−	0.306032i	$-0.0990014\pi$
$234$	3.59820	+	3.89090i	0.235222	+	0.254356i
$235$		0			0
$236$	10.5882	+	3.44032i	0.689234	+	0.223946i
$237$	6.28531	+	1.63944i	0.408275	+	0.106493i
$238$	−2.72764	+	5.35329i	−0.176806	+	0.347002i
$239$	−6.40747	+	19.7202i	−0.414465	+	1.27559i	0.498264	+	0.867025i	$0.333971\pi$
$239$	−6.40747	+	19.7202i	−0.414465	+	1.27559i	−0.912729	+	0.408566i	$0.866029\pi$
$240$		0			0
$241$	−1.92274	−	5.91757i	−0.123854	−	0.381184i	0.869836	−	0.493340i	$-0.164224\pi$
$241$	−1.92274	−	5.91757i	−0.123854	−	0.381184i	−0.993691	+	0.112156i	$0.964224\pi$
$242$	13.6610	+	2.16369i	0.878163	+	0.139087i
$243$	−14.9149	+	4.53278i	−0.956791	+	0.290778i
$244$	5.70595	+	7.85356i	0.365286	+	0.502773i
$245$		0			0
$246$	5.98631	+	2.61773i	0.381673	+	0.166900i
$247$	−3.24541	+	0.514023i	−0.206501	+	0.0327065i
$248$	2.93957	+	5.76923i	0.186663	+	0.366346i
$249$	28.5441	−	6.26585i	1.80891	−	0.397082i
$250$		0			0
$251$		−	3.76896i		−	0.237895i	−0.992901	−	0.118947i	$-0.962048\pi$
$251$		−	3.76896i		−	0.237895i	0.992901	−	0.118947i	$-0.0379520\pi$
$252$	9.91968	+	7.81673i	0.624881	+	0.492408i
$253$	1.63396	+	10.3164i	0.102726	+	0.648589i
$254$	1.25516	+	0.911927i	0.0787557	+	0.0572194i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−21.7693	−	21.7693i	−1.35793	−	1.35793i	−0.876462	−	0.481471i	$-0.840103\pi$
$257$	−21.7693	−	21.7693i	−1.35793	−	1.35793i	−0.481471	−	0.876462i	$-0.659897\pi$
$258$	0.905021	+	15.3195i	0.0563441	+	0.953749i
$259$	10.3094	−	3.34973i	0.640596	−	0.208142i
$260$		0			0
$261$	16.8632	−	1.99941i	1.04380	−	0.123760i
$262$	5.67316	+	2.89062i	0.350489	+	0.178583i
$263$	−4.93937	−	2.51673i	−0.304574	−	0.155188i	0.295023	−	0.955490i	$-0.404673\pi$
$263$	−4.93937	−	2.51673i	−0.304574	−	0.155188i	−0.599598	+	0.800302i	$0.704673\pi$
$264$	−8.58951	−	0.845099i	−0.528648	−	0.0520123i
$265$		0			0
$266$	−7.44718	+	2.41974i	−0.456616	+	0.148364i
$267$	1.96479	−	0.116073i	0.120243	−	0.00710354i
$268$	−4.57707	−	4.57707i	−0.279589	−	0.279589i
$269$	2.80188	−	2.03568i	0.170834	−	0.124118i	−0.499083	−	0.866554i	$-0.666330\pi$
$269$	2.80188	−	2.03568i	0.170834	−	0.124118i	0.669917	+	0.742436i	$0.266330\pi$
$270$		0			0
$271$	−3.81142	−	2.76916i	−0.231528	−	0.168215i	0.465973	−	0.884799i	$-0.345704\pi$
$271$	−3.81142	−	2.76916i	−0.231528	−	0.168215i	−0.697500	+	0.716584i	$0.745704\pi$
$272$	0.223260	+	1.40961i	0.0135371	+	0.0854701i
$273$	−9.95623	+	8.17259i	−0.602579	+	0.494627i
$274$		−	4.10910i		−	0.248240i
$275$		0			0
$276$	−0.778423	−	3.54611i	−0.0468556	−	0.213450i
$277$	−11.2980	−	22.1735i	−0.678829	−	1.33228i	−0.931151	−	0.364634i	$-0.881194\pi$
$277$	−11.2980	−	22.1735i	−0.678829	−	1.33228i	0.252321	−	0.967644i	$-0.418806\pi$
$278$	10.5496	−	1.67090i	0.632725	−	0.100214i
$279$	3.78568	−	19.0524i	0.226643	−	1.14064i
$280$		0			0
$281$	5.67900	+	7.81648i	0.338781	+	0.466292i	0.944085	−	0.329702i	$-0.106948\pi$
$281$	5.67900	+	7.81648i	0.338781	+	0.466292i	−0.605304	+	0.795994i	$0.706948\pi$
$282$	4.37078	−	6.82938i	0.260276	−	0.406684i
$283$	1.00775	+	0.159612i	0.0599044	+	0.00948793i	0.186315	−	0.982490i	$-0.440346\pi$
$283$	1.00775	+	0.159612i	0.0599044	+	0.00948793i	−0.126410	+	0.991978i	$0.540346\pi$
$284$	−4.65630	−	14.3306i	−0.276301	−	0.850366i
$285$		0			0
$286$	2.72024	−	8.37203i	0.160851	−	0.495049i
$287$	−7.20945	+	14.1493i	−0.425561	+	0.835210i
$288$	2.99771	+	0.117162i	0.176642	+	0.00690381i
$289$	−14.2308	−	4.62387i	−0.837106	−	0.271992i
$290$		0			0
$291$	3.07963	+	5.25311i	0.180531	+	0.307943i
$292$	1.44635	−	9.13189i	0.0846412	−	0.534403i
$293$	−1.45604	+	1.45604i	−0.0850625	+	0.0850625i	−0.748358	−	0.663295i	$-0.769157\pi$
$293$	−1.45604	+	1.45604i	−0.0850625	+	0.0850625i	0.663295	+	0.748358i	$0.269157\pi$
$294$	−12.3349	+	13.8838i	−0.719384	+	0.809718i
$295$		0			0
$296$	1.51351	−	2.08317i	0.0879710	−	0.121082i
$297$	18.6706	+	17.9403i	1.08338	+	1.04100i
$298$	4.57327	−	2.33020i	0.264922	−	0.134985i
$299$	3.70284			0.214141
$300$		0			0
$301$	−37.2993			−2.14990
$302$	17.9372	−	9.13947i	1.03217	−	0.525917i
$303$	26.8926	−	10.5288i	1.54494	−	0.604861i
$304$	−1.09331	+	1.50481i	−0.0627057	+	0.0863069i
$305$		0			0
$306$	2.09128	−	3.73606i	0.119551	−	0.213576i
$307$	11.9806	−	11.9806i	0.683767	−	0.683767i	−0.277080	−	0.960847i	$-0.589367\pi$
$307$	11.9806	−	11.9806i	0.683767	−	0.683767i	0.960847	+	0.277080i	$0.0893667\pi$
$308$	3.28166	−	20.7196i	0.186990	−	1.18061i
$309$	3.96403	−	2.32391i	0.225506	−	0.132203i
$310$		0			0
$311$	−3.64396	−	1.18399i	−0.206630	−	0.0671381i	0.203873	−	0.978997i	$-0.434647\pi$
$311$	−3.64396	−	1.18399i	−0.206630	−	0.0671381i	−0.410503	+	0.911859i	$0.634647\pi$
$312$	−0.772255	+	2.96069i	−0.0437203	+	0.167616i
$313$	10.3817	−	20.3753i	0.586809	−	1.15168i	−0.386523	−	0.922280i	$-0.626324\pi$
$313$	10.3817	−	20.3753i	0.586809	−	1.15168i	0.973333	−	0.229398i	$-0.0736759\pi$
$314$	3.11815	−	9.59669i	0.175968	−	0.541573i
$315$		0			0
$316$	1.15889	+	3.56669i	0.0651926	+	0.200642i
$317$	−8.64943	−	1.36994i	−0.485800	−	0.0769432i	−0.0912701	−	0.995826i	$-0.529093\pi$
$317$	−8.64943	−	1.36994i	−0.485800	−	0.0769432i	−0.394530	+	0.918883i	$0.629093\pi$
$318$	−7.47063	−	4.78118i	−0.418932	−	0.268115i
$319$	−16.5794	−	22.8195i	−0.928266	−	1.27765i
$320$		0			0
$321$	−8.19534	+	18.7414i	−0.457419	+	1.04604i
$322$	8.71548	−	1.38040i	0.485695	−	0.0769265i
$323$	1.20518	+	2.36529i	0.0670578	+	0.131608i
$324$	−6.84606	−	5.84221i	−0.380337	−	0.324567i
$325$		0			0
$326$			5.62029i			0.311279i
$327$	−14.6362	−	17.8305i	−0.809383	−	0.986029i
$328$	0.590102	+	3.72576i	0.0325829	+	0.205721i
$329$	15.9436	+	11.5837i	0.878999	+	0.638630i
$330$		0			0
$331$	4.85309	−	3.52598i	0.266750	−	0.193805i	−0.446367	−	0.894850i	$-0.647283\pi$
$331$	4.85309	−	3.52598i	0.266750	−	0.193805i	0.713118	+	0.701044i	$0.247283\pi$
$332$	11.9305	+	11.9305i	0.654773	+	0.654773i
$333$	−7.43435	+	2.09836i	−0.407400	+	0.114989i
$334$	−15.9471	+	5.18154i	−0.872588	+	0.283521i
$335$		0			0
$336$	−0.713952	+	7.25654i	−0.0389493	+	0.395877i
$337$	2.16556	+	1.10341i	0.117965	+	0.0601063i	0.511977	−	0.858999i	$-0.328913\pi$
$337$	2.16556	+	1.10341i	0.117965	+	0.0601063i	−0.394012	+	0.919105i	$0.628913\pi$
$338$	8.80254	+	4.48512i	0.478795	+	0.243958i
$339$	0.253814	−	2.57974i	0.0137853	−	0.140112i
$340$		0			0
$341$	−30.6862	+	9.97055i	−1.66175	+	0.539935i
$342$	5.37034	−	1.51579i	0.290394	−	0.0819643i
$343$	−11.0807	−	11.0807i	−0.598299	−	0.598299i
$344$	−7.16799	+	5.20785i	−0.386472	+	0.280788i
$345$		0			0
$346$	−3.62129	−	2.63102i	−0.194682	−	0.141445i
$347$	3.55504	+	22.4456i	0.190844	+	1.20494i	0.878082	+	0.478511i	$0.158823\pi$
$347$	3.55504	+	22.4456i	0.190844	+	1.20494i	−0.687237	+	0.726433i	$0.741177\pi$
$348$	6.22047	+	7.57807i	0.333452	+	0.406227i
$349$			12.5328i			0.670865i	0.942064	+	0.335432i	$0.108882\pi$
$349$			12.5328i			0.670865i	−0.942064	+	0.335432i	$0.891118\pi$
$350$		0			0
$351$	7.31708	−	5.54245i	0.390557	−	0.295834i
$352$	−2.26228	−	4.43998i	−0.120580	−	0.236651i
$353$	−7.05688	+	1.11770i	−0.375600	+	0.0594892i	−0.341381	−	0.939925i	$-0.610894\pi$
$353$	−7.05688	+	1.11770i	−0.375600	+	0.0594892i	−0.0342193	+	0.999414i	$0.510894\pi$
$354$	7.72587	−	17.6678i	0.410625	−	0.939031i
$355$		0			0
$356$	0.667929	+	0.919325i	0.0354002	+	0.0487241i
$357$	8.76503	+	5.60959i	0.463894	+	0.296891i
$358$	−0.172313	−	0.0272918i	−0.00910704	−	0.00144241i
$359$	−3.28973	−	10.1247i	−0.173625	−	0.534363i	0.825943	−	0.563754i	$-0.190643\pi$
$359$	−3.28973	−	10.1247i	−0.173625	−	0.534363i	−0.999568	+	0.0293907i	$0.990643\pi$
$360$		0			0
$361$	4.80219	−	14.7796i	0.252747	−	0.777875i
$362$	5.16520	−	10.1373i	0.271477	−	0.532803i
$363$	6.04643	−	23.1809i	0.317355	−	1.21668i
$364$	−7.07281	−	2.29810i	−0.370716	−	0.120453i
$365$		0			0
$366$	14.5051	−	8.50359i	0.758193	−	0.444490i
$367$	−0.656708	+	4.14629i	−0.0342799	+	0.216435i	−0.998882	−	0.0472753i	$-0.984946\pi$
$367$	−0.656708	+	4.14629i	−0.0342799	+	0.216435i	0.964602	+	0.263710i	$0.0849462\pi$
$368$	1.48216	−	1.48216i	0.0772630	−	0.0772630i
$369$	5.52749	−	9.87483i	0.287750	−	0.514063i
$370$		0			0
$371$	12.6714	−	17.4406i	0.657865	−	0.905473i
$372$	10.4431	−	4.08860i	0.541450	−	0.211984i
$373$	−4.05536	+	2.06631i	−0.209979	+	0.106990i	−0.555817	−	0.831305i	$-0.687595\pi$
$373$	−4.05536	+	2.06631i	−0.209979	+	0.106990i	0.345838	+	0.938294i	$0.387595\pi$
$374$	−7.11179			−0.367742
$375$		0			0
$376$	4.68132			0.241420
$377$	−8.90954	+	4.53964i	−0.458864	+	0.233803i
$378$	15.1562	−	15.7732i	0.779552	−	0.811284i
$379$	−19.3891	+	26.6869i	−0.995954	+	1.37081i	−0.0681783	+	0.997673i	$0.521719\pi$
$379$	−19.3891	+	26.6869i	−0.995954	+	1.37081i	−0.927775	+	0.373139i	$0.878281\pi$
$380$		0			0
$381$	1.78478	−	2.00890i	0.0914371	−	0.102919i
$382$	−13.0504	+	13.0504i	−0.667715	+	0.667715i
$383$	−2.67339	+	16.8791i	−0.136604	+	0.862482i	0.820270	+	0.571977i	$0.193823\pi$
$383$	−2.67339	+	16.8791i	−0.136604	+	0.862482i	−0.956873	+	0.290505i	$0.906177\pi$
$384$	0.875978	+	1.49421i	0.0447021	+	0.0762511i
$385$		0			0
$386$	4.45958	+	1.44901i	0.226987	+	0.0737525i
$387$	26.5601	+	1.03807i	1.35012	+	0.0527679i
$388$	−1.59607	+	3.13246i	−0.0810281	+	0.159027i
$389$	−4.34112	+	13.3606i	−0.220104	+	0.677409i	0.778648	+	0.627461i	$0.215906\pi$
$389$	−4.34112	+	13.3606i	−0.220104	+	0.677409i	−0.998752	+	0.0499484i	$0.984094\pi$
$390$		0			0
$391$	−0.924425	−	2.84509i	−0.0467502	−	0.143882i
$392$	−10.5904	−	1.67735i	−0.534894	−	0.0847189i
$393$	5.94477	−	9.28875i	0.299874	−	0.468556i
$394$	7.45354	+	10.2589i	0.375504	+	0.516837i
$395$		0			0
$396$	−2.91344	+	14.6627i	−0.146406	+	0.736826i
$397$	3.64376	−	0.577115i	0.182875	−	0.0289646i	−0.0643251	−	0.997929i	$-0.520489\pi$
$397$	3.64376	−	0.577115i	0.182875	−	0.0289646i	0.247200	+	0.968964i	$0.420489\pi$
$398$	−0.738199	−	1.44880i	−0.0370026	−	0.0726216i
$399$	2.90798	+	13.2473i	0.145581	+	0.663194i
$400$		0			0
$401$		−	29.3144i		−	1.46389i	−0.681364	−	0.731945i	$-0.738613\pi$
$401$		−	29.3144i		−	1.46389i	0.681364	−	0.731945i	$-0.261387\pi$
$402$	−8.66586	+	7.11338i	−0.432214	+	0.354783i
$403$	1.78935	+	11.2975i	0.0891336	+	0.562768i
$404$	13.4895	+	9.80073i	0.671130	+	0.487604i
$405$		0			0
$406$	−19.2783	+	14.0065i	−0.956764	+	0.695130i
$407$	9.07301	+	9.07301i	0.449732	+	0.449732i
$408$	2.46765	−	0.145780i	0.122167	−	0.00721718i
$409$	−7.27469	+	2.36369i	−0.359710	+	0.116877i	−0.483296	−	0.875457i	$-0.660561\pi$
$409$	−7.27469	+	2.36369i	−0.359710	+	0.116877i	0.123586	+	0.992334i	$0.460561\pi$
$410$		0			0
$411$	−7.08297	−	0.696875i	−0.349377	−	0.0343743i
$412$	2.36378	+	1.20440i	0.116455	+	0.0593368i
$413$	41.7598	+	21.2777i	2.05487	+	1.04701i
$414$	−6.24454	+	0.740395i	−0.306902	+	0.0363884i
$415$		0			0
$416$	−1.68008	+	0.545893i	−0.0823729	+	0.0267646i
$417$	−1.09103	−	18.4681i	−0.0534279	−	0.904385i
$418$	−6.55405	−	6.55405i	−0.320569	−	0.320569i
$419$	8.86483	−	6.44067i	0.433075	−	0.314648i	−0.349802	−	0.936824i	$-0.613751\pi$
$419$	8.86483	−	6.44067i	0.433075	−	0.314648i	0.782877	+	0.622176i	$0.213751\pi$
$420$		0			0
$421$	−11.3681	−	8.25943i	−0.554048	−	0.402540i	0.275227	−	0.961379i	$-0.411247\pi$
$421$	−11.3681	−	8.25943i	−0.554048	−	0.402540i	−0.829276	+	0.558839i	$0.811247\pi$
$422$	1.88956	+	11.9302i	0.0919823	+	0.580753i
$423$	−11.0307	−	8.69225i	−0.536333	−	0.422632i
$424$		−	5.12087i		−	0.248692i
$425$		0			0
$426$	−25.4918	+	5.59582i	−1.23508	+	0.271119i
$427$	18.5531	+	36.4125i	0.897848	+	1.76213i
$428$	−11.6642	+	1.84743i	−0.563812	+	0.0892991i
$429$	−13.9698	−	6.10879i	−0.674467	−	0.294935i
$430$		0			0
$431$	2.55158	+	3.51195i	0.122905	+	0.169164i	0.866036	−	0.499982i	$-0.166660\pi$
$431$	2.55158	+	3.51195i	0.122905	+	0.169164i	−0.743131	+	0.669146i	$0.766660\pi$
$432$	0.710346	−	5.14737i	0.0341765	−	0.247653i
$433$	−7.75206	−	1.22781i	−0.372540	−	0.0590046i	−0.0326428	−	0.999467i	$-0.510392\pi$
$433$	−7.75206	−	1.22781i	−0.372540	−	0.0590046i	−0.339897	+	0.940463i	$0.610392\pi$
$434$	8.42326	+	25.9241i	0.404329	+	1.24440i
$435$		0			0
$436$	4.11563	−	12.6666i	0.197103	−	0.606621i
$437$	1.77004	−	3.47389i	0.0846723	−	0.166179i
$438$	−15.4956	−	4.04182i	−0.740409	−	0.193126i
$439$	19.1294	+	6.21551i	0.912994	+	0.296650i	0.727590	−	0.686012i	$-0.240640\pi$
$439$	19.1294	+	6.21551i	0.912994	+	0.296650i	0.185405	+	0.982662i	$0.440640\pi$
$440$		0			0
$441$	21.8399	+	23.6165i	1.04000	+	1.12460i
$442$	−0.394399	+	2.49014i	−0.0187597	+	0.118444i
$443$	−11.8995	+	11.8995i	−0.565363	+	0.565363i	−0.930826	−	0.365463i	$-0.880911\pi$
$443$	−11.8995	+	11.8995i	−0.565363	+	0.565363i	0.365463	+	0.930826i	$0.380911\pi$
$444$	−3.33413	−	2.96217i	−0.158231	−	0.140578i
$445$		0			0
$446$	3.65892	−	5.03607i	0.173255	−	0.238465i
$447$	−3.24103	−	8.27826i	−0.153296	−	0.391548i
$448$	−3.75095	+	1.91121i	−0.177216	+	0.0902960i
$449$	−3.55771			−0.167899			−0.0839495	−	0.996470i	$-0.526753\pi$
$449$	−3.55771			−0.167899			−0.0839495	+	0.996470i	$0.526753\pi$
$450$		0			0
$451$	−18.7973			−0.885128
$452$	1.33349	−	0.679445i	0.0627219	−	0.0319584i
$453$	−12.7119	−	32.4689i	−0.597259	−	1.52552i
$454$	−5.38142	+	7.40689i	−0.252563	+	0.347623i
$455$		0			0
$456$	2.40847	+	2.13978i	0.112787	+	0.100204i
$457$	13.4412	−	13.4412i	0.628754	−	0.628754i	−0.319001	−	0.947754i	$-0.603347\pi$
$457$	13.4412	−	13.4412i	0.628754	−	0.628754i	0.947754	+	0.319001i	$0.103347\pi$
$458$	−2.89333	+	18.2678i	−0.135196	+	0.853597i
$459$	−6.08528	−	4.23841i	−0.284037	−	0.197832i
$460$		0			0
$461$	−30.4642	−	9.89843i	−1.41886	−	0.461016i	−0.503621	−	0.863925i	$-0.667999\pi$
$461$	−30.4642	−	9.89843i	−1.41886	−	0.461016i	−0.915240	+	0.402908i	$0.867999\pi$
$462$	−35.1583	−	9.17058i	−1.63571	−	0.426654i
$463$	1.40792	−	2.76320i	0.0654317	−	0.128417i	−0.855974	−	0.517019i	$-0.827042\pi$
$463$	1.40792	−	2.76320i	0.0654317	−	0.128417i	0.921406	+	0.388602i	$0.127042\pi$
$464$	−1.74917	+	5.38339i	−0.0812031	+	0.249918i
$465$		0			0
$466$	−4.25650	−	13.1002i	−0.197179	−	0.606853i
$467$	39.1577	+	6.20197i	1.81200	+	0.286993i	0.968295	−	0.249811i	$-0.0803684\pi$
$467$	39.1577	+	6.20197i	1.81200	+	0.286993i	0.843707	+	0.536804i	$0.180368\pi$
$468$	4.97245	+	1.83327i	0.229852	+	0.0847429i
$469$	−16.0170	−	22.0455i	−0.739598	−	1.01797i
$470$		0			0
$471$	−16.0133	−	7.00238i	−0.737852	−	0.322653i
$472$	10.9960	−	1.74160i	0.506134	−	0.0801638i
$473$	−20.0441	−	39.3387i	−0.921628	−	1.80880i
$474$	6.34454	−	1.39272i	0.291415	−	0.0639698i
$475$		0			0
$476$			6.00814i			0.275383i
$477$	−9.50842	+	12.0665i	−0.435361	+	0.552486i
$478$	3.24367	+	20.4797i	0.148362	+	0.936721i
$479$	−10.9031	−	7.92157i	−0.498176	−	0.361946i	0.310144	−	0.950690i	$-0.399623\pi$
$479$	−10.9031	−	7.92157i	−0.498176	−	0.361946i	−0.808320	+	0.588744i	$0.799623\pi$
$480$		0			0
$481$	3.68001	−	2.67368i	0.167794	−	0.121910i
$482$	−4.39969	−	4.39969i	−0.200400	−	0.200400i
$483$	−0.901343	−	15.2572i	−0.0410125	−	0.694227i
$484$	13.1543	−	4.27411i	0.597925	−	0.194278i
$485$		0			0
$486$	−11.2314	+	10.8100i	−0.509468	+	0.490349i
$487$	1.85919	+	0.947305i	0.0842480	+	0.0429265i	0.495607	−	0.868547i	$-0.334946\pi$
$487$	1.85919	+	0.947305i	0.0842480	+	0.0429265i	−0.411359	+	0.911473i	$0.634946\pi$
$488$	8.64948	+	4.40713i	0.391543	+	0.199501i
$489$	9.68785	+	0.953162i	0.438100	+	0.0431035i
$490$		0			0
$491$	15.8067	−	5.13592i	0.713348	−	0.231781i	0.0702111	−	0.997532i	$-0.477633\pi$
$491$	15.8067	−	5.13592i	0.713348	−	0.231781i	0.643137	+	0.765751i	$0.277633\pi$
$492$	6.52227	−	0.385313i	0.294047	−	0.0173712i
$493$	5.71233	+	5.71233i	0.257270	+	0.257270i
$494$	−2.65832	+	1.93138i	−0.119604	+	0.0868970i
$495$		0			0
$496$	5.23835	+	3.80588i	0.235209	+	0.170889i
$497$	−9.92321	−	62.6527i	−0.445117	−	2.81036i
$498$	22.5883	−	18.5416i	1.01221	−	0.830871i
$499$		−	36.0457i		−	1.61363i	−0.590806	−	0.806813i	$-0.701190\pi$
$499$		−	36.0457i		−	1.61363i	0.590806	−	0.806813i	$-0.298810\pi$
$500$		0			0
$501$	6.22704	+	28.3673i	0.278203	+	1.26736i
$502$	−1.71107	−	3.35817i	−0.0763689	−	0.149882i
$503$	−31.1126	+	4.92776i	−1.38724	+	0.219718i	−0.804990	−	0.593289i	$-0.797829\pi$
$503$	−31.1126	+	4.92776i	−1.38724	+	0.219718i	−0.582255	+	0.813007i	$0.697829\pi$
$504$	12.3872	+	2.46132i	0.551771	+	0.109636i
$505$		0			0
$506$	6.13944	+	8.45021i	0.272931	+	0.375658i
$507$	9.22397	−	14.4125i	0.409651	−	0.640083i
$508$	1.53236	+	0.242702i	0.0679876	+	0.0107682i
$509$	0.189892	+	0.584428i	0.00841683	+	0.0259043i	0.955177	−	0.296036i	$-0.0956649\pi$
$509$	0.189892	+	0.584428i	0.00841683	+	0.0259043i	−0.946760	+	0.321941i	$0.895665\pi$
$510$		0			0
$511$	12.0277	−	37.0176i	0.532076	−	1.63756i
$512$	−0.453990	+	0.891007i	−0.0200637	+	0.0393773i
$513$	−1.70203	−	9.51406i	−0.0751465	−	0.420056i
$514$	−29.2797	−	9.51354i	−1.29147	−	0.419624i
$515$		0			0
$516$	7.76127	+	13.2389i	0.341671	+	0.582809i
$517$	−3.64922	+	23.0403i	−0.160493	+	1.01331i
$518$	7.66501	−	7.66501i	0.336781	−	0.336781i
$519$	−5.14932	+	5.79592i	−0.226030	+	0.254413i
$520$		0			0
$521$	19.3712	−	26.6622i	0.848668	−	1.16809i	−0.135487	−	0.990779i	$-0.543260\pi$
$521$	19.3712	−	26.6622i	0.848668	−	1.16809i	0.984155	−	0.177312i	$-0.0567401\pi$
$522$	14.1175	−	9.43721i	0.617905	−	0.413055i
$523$	−35.5580	+	18.1177i	−1.55484	+	0.792232i	−0.999231	−	0.0392100i	$-0.987516\pi$
$523$	−35.5580	+	18.1177i	−1.55484	+	0.792232i	−0.555612	+	0.831442i	$0.687516\pi$
$524$	6.36713			0.278150
$525$		0			0
$526$	−5.54358			−0.241712
$527$	8.23373	−	4.19530i	0.358667	−	0.182750i
$528$	−8.03698	+	3.14657i	−0.349765	+	0.136937i
$529$	10.9366	−	15.0529i	0.475503	−	0.654474i
$530$		0			0
$531$	−29.1442	−	16.3136i	−1.26475	−	0.707951i
$532$	−5.53695	+	5.53695i	−0.240057	+	0.240057i
$533$	−1.04244	+	6.58172i	−0.0451532	+	0.285086i
$534$	1.69794	−	0.995416i	0.0734771	−	0.0430759i
$535$		0			0
$536$	−6.15614	−	2.00025i	−0.265905	−	0.0863977i
$537$	−0.0762667	+	0.292393i	−0.00329115	+	0.0126177i
$538$	1.57231	−	3.08583i	0.0677872	−	0.133040i
$539$	16.5110	−	50.8156i	0.711178	−	2.18878i
$540$		0			0
$541$	7.82078	+	24.0699i	0.336242	+	1.03485i	0.966107	+	0.258141i	$0.0831100\pi$
$541$	7.82078	+	24.0699i	0.336242	+	1.03485i	−0.629865	+	0.776704i	$0.716890\pi$
$542$	−4.65318	−	0.736991i	−0.199871	−	0.0316565i
$543$	−16.5979	−	10.6226i	−0.712285	−	0.455860i
$544$	0.838876	+	1.15461i	0.0359665	+	0.0495036i
$545$		0			0
$546$	−5.16079	+	11.8019i	−0.220861	+	0.505073i
$547$	−40.6790	+	6.44292i	−1.73931	+	0.275479i	−0.943812	−	0.330482i	$-0.892789\pi$
$547$	−40.6790	+	6.44292i	−1.73931	+	0.275479i	−0.795495	+	0.605961i	$0.792789\pi$
$548$	−1.86549	−	3.66124i	−0.0796899	−	0.156400i
$549$	−12.1979	−	26.4450i	−0.520594	−	1.12864i
$550$		0			0
$551$			10.5287i			0.448537i
$552$	−2.30348	−	2.80621i	−0.0980425	−	0.119440i
$553$	2.46975	+	15.5934i	0.105024	+	0.663098i
$554$	−20.1331	−	14.6276i	−0.855375	−	0.621466i
$555$		0			0
$556$	8.64122	−	6.27821i	0.366469	−	0.266256i
$557$	17.7694	+	17.7694i	0.752915	+	0.752915i	0.975022	−	0.222107i	$-0.0712934\pi$
$557$	17.7694	+	17.7694i	0.752915	+	0.752915i	−0.222107	+	0.975022i	$0.571293\pi$
$558$	−5.27655	−	18.6945i	−0.223374	−	0.791400i
$559$	−14.8858	+	4.83667i	−0.629600	+	0.204570i
$560$		0			0
$561$	−1.20611	+	12.2588i	−0.0509220	+	0.517566i
$562$	8.60864	+	4.38632i	0.363133	+	0.185026i
$563$	9.23868	+	4.70734i	0.389364	+	0.198391i	0.637703	−	0.770282i	$-0.279885\pi$
$563$	9.23868	+	4.70734i	0.389364	+	0.198391i	−0.248339	+	0.968673i	$0.579885\pi$
$564$	0.793919	−	8.06931i	0.0334300	−	0.339779i
$565$		0			0
$566$	0.970373	−	0.315293i	0.0407878	−	0.0132528i
$567$	−24.6183	−	28.8002i	−1.03387	−	1.20950i
$568$	−10.6548	−	10.6548i	−0.447064	−	0.447064i
$569$	15.6879	−	11.3979i	0.657671	−	0.477826i	−0.208205	−	0.978085i	$-0.566762\pi$
$569$	15.6879	−	11.3979i	0.657671	−	0.477826i	0.865876	+	0.500259i	$0.166762\pi$
$570$		0			0
$571$	14.7088	+	10.6866i	0.615544	+	0.447219i	0.851362	−	0.524579i	$-0.175777\pi$
$571$	14.7088	+	10.6866i	0.615544	+	0.447219i	−0.235818	+	0.971797i	$0.575777\pi$
$572$	−1.37707	−	8.69450i	−0.0575783	−	0.363535i
$573$	20.2820	+	24.7086i	0.847295	+	1.03221i
$574$			15.8802i			0.662826i
$575$		0			0
$576$	2.72417	−	1.25654i	0.113507	−	0.0523559i
$577$	−2.69918	−	5.29743i	−0.112368	−	0.220535i	0.827973	−	0.560768i	$-0.189494\pi$
$577$	−2.69918	−	5.29743i	−0.112368	−	0.220535i	−0.940341	+	0.340233i	$0.889494\pi$
$578$	−14.7789	+	2.34075i	−0.614723	+	0.0973625i
$579$	3.25401	−	7.44137i	0.135232	−	0.309253i
$580$		0			0
$581$	41.7498	+	57.4636i	1.73207	+	2.38399i
$582$	5.12883	+	3.28243i	0.212597	+	0.136061i
$583$	25.2037	+	3.99187i	1.04383	+	0.165326i
$584$	−2.85708	−	8.79320i	−0.118227	−	0.363865i
$585$		0			0
$586$	−0.636311	+	1.95836i	−0.0262858	+	0.0808992i
$587$	−11.8794	+	23.3146i	−0.490314	+	0.962295i	0.504770	+	0.863254i	$0.331577\pi$
$587$	−11.8794	+	23.3146i	−0.490314	+	0.962295i	−0.995083	+	0.0990406i	$0.968423\pi$
$588$	−4.68734	+	17.9704i	−0.193303	+	0.741088i
$589$	11.4543	+	3.72172i	0.471966	+	0.153351i
$590$		0			0
$591$	18.9476	−	11.1080i	0.779402	−	0.456923i
$592$	0.402809	−	2.54323i	0.0165553	−	0.104526i
$593$	23.6228	−	23.6228i	0.970072	−	0.970072i	−0.0294930	−	0.999565i	$-0.509389\pi$
$593$	23.6228	−	23.6228i	0.970072	−	0.970072i	0.999565	+	0.0294930i	$0.00938927\pi$
$594$	24.7803	+	7.50867i	1.01675	+	0.308084i
$595$		0			0
$596$	3.01693	−	4.15244i	0.123578	−	0.170091i
$597$	−2.62253	+	1.02675i	−0.107333	+	0.0420220i
$598$	3.29926	−	1.68106i	0.134917	−	0.0687435i
$599$	−7.73976			−0.316238			−0.158119	−	0.987420i	$-0.550543\pi$
$599$	−7.73976			−0.316238			−0.158119	+	0.987420i	$0.550543\pi$
$600$		0			0
$601$	−16.7407			−0.682866			−0.341433	−	0.939906i	$-0.610912\pi$
$601$	−16.7407			−0.682866			−0.341433	+	0.939906i	$0.610912\pi$
$602$	−33.2339	+	16.9335i	−1.35451	+	0.690159i
$603$	10.7919	+	16.1440i	0.439479	+	0.657433i
$604$	11.8329	−	16.2867i	0.481476	−	0.662695i
$605$		0			0
$606$	19.1815	−	21.5902i	0.779196	−	0.877041i
$607$	−22.6982	+	22.6982i	−0.921293	+	0.921293i	−0.997121	−	0.0758281i	$-0.975840\pi$
$607$	−22.6982	+	22.6982i	−0.921293	+	0.921293i	0.0758281	+	0.997121i	$0.475840\pi$
$608$	−0.290976	+	1.83715i	−0.0118006	+	0.0745063i
$609$	20.8739	+	35.6059i	0.845853	+	1.44282i
$610$		0			0
$611$	7.86501	+	2.55550i	0.318184	+	0.103384i
$612$	0.167211	−	4.27828i	0.00675909	−	0.172939i
$613$	−19.6701	+	38.6048i	−0.794470	+	1.55923i	0.0341460	+	0.999417i	$0.489129\pi$
$613$	−19.6701	+	38.6048i	−0.794470	+	1.55923i	−0.828616	+	0.559818i	$0.810871\pi$
$614$	5.23570	−	16.1138i	0.211296	−	0.650301i
$615$		0			0
$616$	−6.48251	−	19.9511i	−0.261188	−	0.803853i
$617$	−24.0808	−	3.81403i	−0.969458	−	0.153547i	−0.348429	−	0.937335i	$-0.613285\pi$
$617$	−24.0808	−	3.81403i	−0.969458	−	0.153547i	−0.621028	+	0.783788i	$0.713285\pi$
$618$	2.47695	−	3.87025i	0.0996374	−	0.155684i
$619$	23.7633	+	32.7074i	0.955130	+	1.31462i	0.949211	+	0.314641i	$0.101884\pi$
$619$	23.7633	+	32.7074i	0.955130	+	1.31462i	0.00591868	+	0.999982i	$0.498116\pi$
$620$		0			0
$621$	0.217209	+	10.8894i	0.00871630	+	0.436978i
$622$	−3.78431	+	0.599376i	−0.151737	+	0.0240328i
$623$	2.17180	+	4.26239i	0.0870112	+	0.170769i
$624$	0.656040	+	2.98859i	0.0262626	+	0.119639i
$625$		0			0
$626$		−	22.8677i		−	0.913977i
$627$	−12.4089	+	10.1859i	−0.495564	+	0.406785i
$628$	−1.57851	−	9.96632i	−0.0629894	−	0.397700i
$629$	−2.97306	−	2.16005i	−0.118544	−	0.0861269i
$630$		0			0
$631$	−19.6592	+	14.2832i	−0.782619	+	0.568606i	−0.905764	−	0.423783i	$-0.860702\pi$
$631$	−19.6592	+	14.2832i	−0.782619	+	0.568606i	0.123145	+	0.992389i	$0.460702\pi$
$632$	2.65182	+	2.65182i	0.105484	+	0.105484i
$633$	20.8849	−	1.23381i	0.830100	−	0.0490394i
$634$	−8.32864	+	2.70614i	−0.330772	+	0.107474i
$635$		0			0
$636$	−8.82699	−	0.868465i	−0.350013	−	0.0344369i
$637$	−16.8771	−	8.59929i	−0.668693	−	0.340716i
$638$	−25.1322	−	12.8055i	−0.994992	−	0.506974i
$639$	5.32245	+	44.8899i	0.210553	+	1.77582i
$640$		0			0
$641$	8.76326	−	2.84736i	0.346128	−	0.112464i	−0.130794	−	0.991410i	$-0.541753\pi$
$641$	8.76326	−	2.84736i	0.346128	−	0.112464i	0.476922	+	0.878946i	$0.341753\pi$
$642$	1.20630	+	20.4193i	0.0476089	+	0.805885i
$643$	32.6751	+	32.6751i	1.28858	+	1.28858i	0.935649	+	0.352932i	$0.114815\pi$
$643$	32.6751	+	32.6751i	1.28858	+	1.28858i	0.352932	+	0.935649i	$0.385185\pi$
$644$	7.13886	−	5.18669i	0.281311	−	0.204384i
$645$		0			0
$646$	2.14764	+	1.56035i	0.0844978	+	0.0613912i
$647$	−7.60579	−	48.0211i	−0.299015	−	1.88790i	−0.440167	−	0.897916i	$-0.645081\pi$
$647$	−7.60579	−	48.0211i	−0.299015	−	1.88790i	0.141152	−	0.989988i	$-0.454919\pi$
$648$	−8.75219	−	2.09740i	−0.343819	−	0.0823937i
$649$			55.4774i			2.17768i
$650$		0			0
$651$	46.1147	−	10.1229i	1.80738	−	0.396746i
$652$	2.55156	+	5.00771i	0.0999267	+	0.196117i
$653$	19.6349	−	3.10987i	0.768375	−	0.121699i	0.240073	−	0.970755i	$-0.422829\pi$
$653$	19.6349	−	3.10987i	0.768375	−	0.121699i	0.528302	+	0.849056i	$0.322829\pi$
$654$	−21.1358	−	9.24240i	−0.826476	−	0.361407i
$655$		0			0
$656$	2.21724	+	3.05177i	0.0865688	+	0.119152i
$657$	−9.59494	+	26.0247i	−0.374334	+	1.01532i
$658$	19.4647	+	3.08291i	0.758815	+	0.120184i
$659$	9.29483	+	28.6066i	0.362075	+	1.11435i	0.951792	+	0.306743i	$0.0992393\pi$
$659$	9.29483	+	28.6066i	0.362075	+	1.11435i	−0.589717	+	0.807610i	$0.700761\pi$
$660$		0			0
$661$	−4.51392	+	13.8924i	−0.175571	+	0.540352i	−0.999659	−	0.0261096i	$-0.991688\pi$
$661$	−4.51392	+	13.8924i	−0.175571	+	0.540352i	0.824088	+	0.566462i	$0.191688\pi$
$662$	2.72338	−	5.34493i	0.105847	−	0.207736i
$663$	4.22544	+	1.10215i	0.164102	+	0.0428039i
$664$	16.0465	+	5.21383i	0.622726	+	0.202336i
$665$		0			0
$666$	−5.67142	+	5.24478i	−0.219763	+	0.203231i
$667$	1.85606	−	11.7187i	0.0718670	−	0.453750i
$668$	−11.8566	+	11.8566i	−0.458747	+	0.458747i
$669$	−8.06029	−	7.16107i	−0.311629	−	0.276863i
$670$		0			0
$671$	−28.4333	+	39.1351i	−1.09766	+	1.51079i
$672$	2.65826	+	6.78975i	0.102545	+	0.261920i
$673$	30.1630	−	15.3688i	1.16270	−	0.592425i	0.237306	−	0.971435i	$-0.423736\pi$
$673$	30.1630	−	15.3688i	1.16270	−	0.592425i	0.925392	+	0.379010i	$0.123736\pi$
$674$	2.43046			0.0936178
$675$		0			0
$676$	9.87932			0.379974
$677$	6.85459	−	3.49259i	0.263443	−	0.134231i	−0.317280	−	0.948332i	$-0.602770\pi$
$677$	6.85459	−	3.49259i	0.263443	−	0.134231i	0.580724	+	0.814101i	$0.302770\pi$
$678$	−0.945029	−	2.41380i	−0.0362936	−	0.0927013i
$679$	−8.69931	+	11.9736i	−0.333849	+	0.459503i
$680$		0			0
$681$	11.8548	+	10.5323i	0.454278	+	0.403597i
$682$	−22.8151	+	22.8151i	−0.873634	+	0.873634i
$683$	0.454547	−	2.86990i	0.0173928	−	0.109814i	−0.977465	−	0.211099i	$-0.932296\pi$
$683$	0.454547	−	2.86990i	0.0173928	−	0.109814i	0.994857	+	0.101286i	$0.0322957\pi$
$684$	4.09685	−	3.78866i	0.156647	−	0.144863i
$685$		0			0
$686$	−14.9035	−	4.84242i	−0.569016	−	0.184885i
$687$	30.9980	+	8.08540i	1.18265	+	0.308477i
$688$	−4.02241	+	7.89443i	−0.153353	+	0.300972i
$689$	2.79545	−	8.60350i	0.106498	−	0.327767i
$690$		0			0
$691$	−9.12811	−	28.0934i	−0.347249	−	1.06872i	−0.960368	−	0.278733i	$-0.910085\pi$
$691$	−9.12811	−	28.0934i	−0.347249	−	1.06872i	0.613119	−	0.789991i	$-0.289915\pi$
$692$	−4.42106	−	0.700227i	−0.168063	−	0.0266186i
$693$	−21.7702	+	59.0481i	−0.826981	+	2.24305i
$694$	13.3577	+	18.3852i	0.507050	+	0.697894i
$695$		0			0
$696$	8.98285	+	3.92808i	0.340494	+	0.148893i
$697$	5.31733	−	0.842182i	0.201408	−	0.0318999i
$698$	5.68977	+	11.1668i	0.215361	+	0.422670i
$699$	−23.3030	+	5.11535i	−0.881400	+	0.193480i
$700$		0			0
$701$		−	41.1646i		−	1.55476i	−0.629028	−	0.777382i	$-0.716547\pi$
$701$		−	41.1646i		−	1.55476i	0.629028	−	0.777382i	$-0.283453\pi$
$702$	4.00335	−	8.26024i	0.151097	−	0.311763i
$703$	−0.749245	−	4.73055i	−0.0282583	−	0.178416i
$704$	−4.03141	−	2.92899i	−0.151940	−	0.110391i
$705$		0			0
$706$	−5.78030	+	4.19963i	−0.217544	+	0.158055i
$707$	49.6347	+	49.6347i	1.86671	+	1.86671i
$708$	−1.13720	−	19.2496i	−0.0427385	−	0.723443i
$709$	−16.1533	+	5.24852i	−0.606650	+	0.197112i	−0.596204	−	0.802833i	$-0.703325\pi$
$709$	−16.1533	+	5.24852i	−0.606650	+	0.197112i	−0.0104457	+	0.999945i	$0.503325\pi$
$710$		0			0
$711$	−1.32468	−	11.1725i	−0.0496795	−	0.419000i
$712$	1.01249	+	0.515891i	0.0379448	+	0.0193338i
$713$	−12.0928	−	6.16161i	−0.452880	−	0.230754i
$714$	10.3564	+	1.01894i	0.387578	+	0.0381328i
$715$		0			0
$716$	−0.165923	+	0.0539115i	−0.00620082	+	0.00201477i
$717$	35.8516	−	2.11799i	1.33890	−	0.0790976i
$718$	−7.52770	−	7.52770i	−0.280931	−	0.280931i
$719$	−17.4118	+	12.6504i	−0.649349	+	0.471780i	−0.863049	−	0.505120i	$-0.831448\pi$
$719$	−17.4118	+	12.6504i	−0.649349	+	0.471780i	0.213700	+	0.976899i	$0.431448\pi$
$720$		0			0
$721$	9.03534	+	6.56456i	0.336493	+	0.244477i
$722$	−2.43102	−	15.3489i	−0.0904734	−	0.571226i
$723$	−8.33003	+	6.83771i	−0.309797	+	0.254297i
$724$		−	11.3773i		−	0.422835i
$725$		0			0
$726$	−5.13651	−	23.3994i	−0.190634	−	0.868432i
$727$	−15.5168	−	30.4534i	−0.575485	−	1.12945i	−0.976928	−	0.213569i	$-0.931491\pi$
$727$	−15.5168	−	30.4534i	−0.575485	−	1.12945i	0.401443	−	0.915884i	$-0.368509\pi$
$728$	−7.34523	+	1.16337i	−0.272233	+	0.0431174i
$729$	16.7286	+	21.1932i	0.619579	+	0.784934i
$730$		0			0
$731$	7.43254	+	10.2300i	0.274902	+	0.378371i
$732$	9.06358	−	14.1619i	0.335000	−	0.523440i
$733$	−18.4191	−	2.91730i	−0.680326	−	0.107753i	−0.193299	−	0.981140i	$-0.561919\pi$
$733$	−18.4191	−	2.91730i	−0.680326	−	0.107753i	−0.487027	+	0.873387i	$0.661919\pi$
$734$	1.29725	+	3.99251i	0.0478822	+	0.147366i
$735$		0			0
$736$	0.647728	−	1.99350i	0.0238756	−	0.0734815i
$737$	14.6436	−	28.7397i	0.539405	−	1.05864i
$738$	0.441957	−	11.3080i	0.0162687	−	0.416252i
$739$	1.28835	+	0.418609i	0.0473926	+	0.0153988i	0.332617	−	0.943062i	$-0.392068\pi$
$739$	1.28835	+	0.418609i	0.0473926	+	0.0153988i	−0.285225	+	0.958461i	$0.592068\pi$
$740$		0			0
$741$	2.87835	+	4.90977i	0.105739	+	0.180365i
$742$	3.37239	−	21.2924i	0.123804	−	0.781669i
$743$	8.68111	−	8.68111i	0.318479	−	0.318479i	−0.529704	−	0.848183i	$-0.677697\pi$
$743$	8.68111	−	8.68111i	0.318479	−	0.318479i	0.848183	+	0.529704i	$0.177697\pi$
$744$	7.44870	−	8.38404i	0.273082	−	0.307374i
$745$		0			0
$746$	−2.67527	+	3.68219i	−0.0979486	+	0.134815i
$747$	−28.1299	−	42.0806i	−1.02922	−	1.53965i
$748$	−6.33665	+	3.22868i	−0.231691	+	0.118052i
$749$	−49.7161			−1.81659
$750$		0			0
$751$	40.0140			1.46013			0.730066	−	0.683377i	$-0.239489\pi$
$751$	40.0140			1.46013			0.730066	+	0.683377i	$0.239489\pi$
$752$	4.17108	−	2.12527i	0.152104	−	0.0775007i
$753$	−6.07875	+	2.37990i	−0.221522	+	0.0867284i
$754$	−5.87750	+	8.08969i	−0.214046	+	0.294609i
$755$		0			0
$756$	6.34343	−	20.9348i	0.230708	−	0.761391i
$757$	−23.3400	+	23.3400i	−0.848305	+	0.848305i	−0.989922	−	0.141616i	$-0.954770\pi$
$757$	−23.3400	+	23.3400i	−0.848305	+	0.848305i	0.141616	+	0.989922i	$0.454770\pi$
$758$	−5.16027	+	32.5807i	−0.187429	+	1.18338i
$759$	15.6071	−	9.14963i	0.566501	−	0.332110i
$760$		0			0
$761$	−6.88486	−	2.23703i	−0.249576	−	0.0810921i	0.181558	−	0.983380i	$-0.441886\pi$
$761$	−6.88486	−	2.23703i	−0.249576	−	0.0810921i	−0.431133	+	0.902288i	$0.641886\pi$
$762$	0.678231	−	2.60021i	0.0245697	−	0.0941958i
$763$	25.4544	−	49.9570i	0.921509	−	1.80856i
$764$	−5.70322	+	17.5527i	−0.206335	+	0.635035i
$765$		0			0
$766$	5.28095	+	16.2531i	0.190808	+	0.587248i
$767$	19.4250	+	3.07662i	0.701397	+	0.111090i
$768$	1.45886	+	0.933665i	0.0526420	+	0.0336907i
$769$	2.15066	+	2.96013i	0.0775549	+	0.106745i	0.846032	−	0.533132i	$-0.178985\pi$
$769$	2.15066	+	2.96013i	0.0775549	+	0.106745i	−0.768477	+	0.639877i	$0.778985\pi$
$770$		0			0
$771$	−21.3644	+	48.8568i	−0.769420	+	1.75953i
$772$	4.63135	−	0.733534i	0.166686	−	0.0264005i
$773$	15.0283	+	29.4947i	0.540531	+	1.06085i	0.986185	+	0.165646i	$0.0529709\pi$
$773$	15.0283	+	29.4947i	0.540531	+	1.06085i	−0.445655	+	0.895205i	$0.647029\pi$
$774$	24.1365	−	11.1331i	0.867568	−	0.400171i
$775$		0			0
$776$			3.51564i			0.126204i
$777$	−11.9125	−	14.5123i	−0.427357	−	0.520626i
$778$	2.19762	+	13.8752i	0.0787884	+	0.497450i
$779$	5.67645	+	4.12419i	0.203380	+	0.147764i
$780$		0			0
$781$	60.7458	−	44.1344i	2.17366	−	1.57925i
$782$	−2.11531	−	2.11531i	−0.0756434	−	0.0756434i
$783$	−13.8730	−	25.9352i	−0.495779	−	0.926848i
$784$	−10.1976	+	3.31339i	−0.364199	+	0.118336i
$785$		0			0
$786$	1.07982	−	10.9752i	0.0385160	−	0.391473i
$787$	−14.7464	−	7.51367i	−0.525653	−	0.267833i	0.170964	−	0.985277i	$-0.445312\pi$
$787$	−14.7464	−	7.51367i	−0.525653	−	0.267833i	−0.696616	+	0.717444i	$0.745312\pi$
$788$	11.2986	+	5.75693i	0.402496	+	0.205082i
$789$	−0.940153	+	9.55563i	−0.0334703	+	0.340189i
$790$		0			0
$791$	5.99204	−	1.94693i	0.213053	−	0.0692250i
$792$	4.06081	+	14.3872i	0.144295	+	0.511227i
$793$	12.1260	+	12.1260i	0.430608	+	0.430608i
$794$	2.98461	−	2.16845i	0.105920	−	0.0769552i
$795$		0			0
$796$	−1.31548	−	0.955752i	−0.0466260	−	0.0338757i
$797$	6.28166	+	39.6609i	0.222508	+	1.40486i	0.805603	+	0.592456i	$0.201842\pi$
$797$	6.28166	+	39.6609i	0.222508	+	1.40486i	−0.583095	+	0.812404i	$0.698158\pi$
$798$	8.60517	+	10.4832i	0.304620	+	0.371102i
$799$		−	6.68108i		−	0.236360i
$800$		0			0
$801$	−1.42787	−	3.09561i	−0.0504512	−	0.109378i
$802$	−13.3084	−	26.1193i	−0.469937	−	0.922304i
$803$	45.5051	−	7.20730i	1.60584	−	0.254340i
$804$	−4.49193	+	10.2723i	−0.158418	+	0.362276i
$805$		0			0
$806$	6.72327	+	9.25378i	0.236817	+	0.325951i
$807$	−5.05249	−	3.23357i	−0.177856	−	0.113827i
$808$	16.4687	+	2.60839i	0.579367	+	0.0917627i
$809$	5.01595	+	15.4375i	0.176351	+	0.542753i	0.999693	−	0.0247932i	$-0.00789272\pi$
$809$	5.01595	+	15.4375i	0.176351	+	0.542753i	−0.823341	+	0.567546i	$0.807893\pi$
$810$		0			0
$811$	−12.6792	+	39.0226i	−0.445227	+	1.37027i	0.437007	+	0.899458i	$0.356039\pi$
$811$	−12.6792	+	39.0226i	−0.445227	+	1.37027i	−0.882234	+	0.470811i	$0.843961\pi$
$812$	−10.8183	+	21.2320i	−0.379646	+	0.745098i
$813$	−2.05952	+	7.89582i	−0.0722305	+	0.276919i
$814$	12.2032	+	3.96505i	0.427721	+	0.138975i
$815$		0			0
$816$	2.13251	−	1.25018i	0.0746527	−	0.0437650i
$817$	−2.57808	+	16.2774i	−0.0901957	+	0.569473i
$818$	−5.40870	+	5.40870i	−0.189111	+	0.189111i
$819$	19.4680	+	10.8973i	0.680266	+	0.380783i
$820$		0			0
$821$	−8.20025	+	11.2867i	−0.286191	+	0.393907i	−0.927772	−	0.373147i	$-0.878279\pi$
$821$	−8.20025	+	11.2867i	−0.286191	+	0.393907i	0.641582	+	0.767055i	$0.278279\pi$
$822$	−6.62735	+	2.59468i	−0.231155	+	0.0904999i
$823$	−15.2645	+	7.77764i	−0.532086	+	0.271112i	−0.699324	−	0.714805i	$-0.746515\pi$
$823$	−15.2645	+	7.77764i	−0.532086	+	0.271112i	0.167237	+	0.985917i	$0.446515\pi$
$824$	2.65293			0.0924192
$825$		0			0
$826$	46.8681			1.63075
$827$	−35.0129	+	17.8399i	−1.21752	+	0.620356i	−0.940266	−	0.340442i	$-0.889423\pi$
$827$	−35.0129	+	17.8399i	−1.21752	+	0.620356i	−0.277251	+	0.960798i	$0.589423\pi$
$828$	−5.22779	+	3.49466i	−0.181678	+	0.121448i
$829$	16.9229	−	23.2923i	0.587756	−	0.808977i	−0.406763	−	0.913534i	$-0.633343\pi$
$829$	16.9229	−	23.2923i	0.587756	−	0.808977i	0.994519	+	0.104557i	$0.0333425\pi$
$830$		0			0
$831$	−28.6284	+	32.2233i	−0.993109	+	1.11781i
$832$	−1.24914	+	1.24914i	−0.0433060	+	0.0433060i
$833$	−2.39388	+	15.1144i	−0.0829430	+	0.523681i
$834$	−9.35644	−	15.9599i	−0.323987	−	0.552644i
$835$		0			0
$836$	−8.81517	−	2.86422i	−0.304879	−	0.0990613i
$837$	−33.1191	+	5.92488i	−1.14476	+	0.204794i
$838$	4.97461	−	9.76323i	0.171845	−	0.337265i
$839$	−10.2985	+	31.6954i	−0.355542	+	1.09425i	0.600152	+	0.799886i	$0.295107\pi$
$839$	−10.2985	+	31.6954i	−0.355542	+	1.09425i	−0.955695	+	0.294360i	$0.904893\pi$
$840$		0			0
$841$	0.939554	+	2.89165i	0.0323984	+	0.0997121i
$842$	−13.8788	−	2.19818i	−0.478294	−	0.0757544i
$843$	9.02079	−	14.0951i	0.310692	−	0.485460i
$844$	7.09981	+	9.77205i	0.244385	+	0.336368i
$845$		0			0
$846$	−13.7747	−	2.73700i	−0.473583	−	0.0941000i
$847$	57.5100	−	9.10870i	1.97607	−	0.312979i
$848$	−2.32483	−	4.56273i	−0.0798349	−	0.156685i
$849$	−0.378911	−	1.72613i	−0.0130042	−	0.0592406i
$850$		0			0
$851$			5.39730i			0.185017i
$852$	−20.1729	+	16.5589i	−0.691112	+	0.567300i
$853$	−7.73248	−	48.8210i	−0.264755	−	1.67160i	−0.658655	−	0.752445i	$-0.728874\pi$
$853$	−7.73248	−	48.8210i	−0.264755	−	1.67160i	0.393900	−	0.919153i	$-0.371126\pi$
$854$	33.0619	+	24.0209i	1.13135	+	0.821977i
$855$		0			0
$856$	−9.55419	+	6.94153i	−0.326556	+	0.237257i
$857$	5.79343	+	5.79343i	0.197900	+	0.197900i	0.799099	−	0.601199i	$-0.205310\pi$
$857$	5.79343	+	5.79343i	0.197900	+	0.197900i	−0.601199	+	0.799099i	$0.705310\pi$
$858$	−15.2205	+	0.899173i	−0.519619	+	0.0306973i
$859$	−3.26295	+	1.06020i	−0.111330	+	0.0361734i	−0.364152	−	0.931339i	$-0.618641\pi$
$859$	−3.26295	+	1.06020i	−0.111330	+	0.0361734i	0.252822	+	0.967513i	$0.418641\pi$
$860$		0			0
$861$	27.3731	+	2.69317i	0.932873	+	0.0917829i
$862$	3.86786	+	1.97077i	0.131740	+	0.0671249i
$863$	−22.7707	−	11.6022i	−0.775122	−	0.394944i	0.0212325	−	0.999775i	$-0.493241\pi$
$863$	−22.7707	−	11.6022i	−0.775122	−	0.394944i	−0.796354	+	0.604830i	$0.793241\pi$
$864$	−1.70393	−	4.90883i	−0.0579690	−	0.167002i
$865$		0			0
$866$	−7.46455	+	2.42538i	−0.253656	+	0.0824177i
$867$	1.52842	+	25.8718i	0.0519078	+	0.878654i
$868$	19.2745	+	19.2745i	0.654219	+	0.654219i
$869$	−15.1188	+	10.9844i	−0.512869	+	0.372621i
$870$		0			0
$871$	−9.25092	−	6.72119i	−0.313455	−	0.227739i
$872$	−2.08347	−	13.1545i	−0.0705551	−	0.445468i
$873$	6.52784	−	8.28403i	0.220934	−	0.280372i
$874$		−	3.89884i		−	0.131880i
$875$		0			0
$876$	−15.6416	+	3.43357i	−0.528482	+	0.116010i
$877$	13.6895	+	26.8672i	0.462262	+	0.907241i	0.998022	+	0.0628704i	$0.0200255\pi$
$877$	13.6895	+	26.8672i	0.462262	+	0.907241i	−0.535759	+	0.844371i	$0.679975\pi$
$878$	19.8662	−	3.14649i	0.670451	−	0.106189i
$879$	3.26777	+	1.42895i	0.110219	+	0.0481973i
$880$		0			0
$881$	−29.7770	−	40.9845i	−1.00321	−	1.38080i	−0.923334	−	0.383997i	$-0.874547\pi$
$881$	−29.7770	−	40.9845i	−1.00321	−	1.38080i	−0.0798773	−	0.996805i	$-0.525453\pi$
$882$	30.1812	+	11.1274i	1.01625	+	0.374678i
$883$	−11.1388	−	1.76422i	−0.374852	−	0.0593707i	−0.0338339	−	0.999427i	$-0.510772\pi$
$883$	−11.1388	−	1.76422i	−0.374852	−	0.0593707i	−0.341018	+	0.940057i	$0.610772\pi$
$884$	0.779087	+	2.39778i	0.0262035	+	0.0806462i
$885$		0			0
$886$	−5.20028	+	16.0048i	−0.174707	+	0.537692i
$887$	8.52333	−	16.7280i	0.286186	−	0.561671i	−0.702498	−	0.711686i	$-0.747932\pi$
$887$	8.52333	−	16.7280i	0.286186	−	0.561671i	0.988684	+	0.150015i	$0.0479321\pi$
$888$	−4.31553	−	1.12565i	−0.144820	−	0.0377743i
$889$	6.21167	+	2.01830i	0.208333	+	0.0676914i
$890$		0			0
$891$	17.1455	−	41.4411i	0.574395	−	1.38833i
$892$	0.973793	−	6.14829i	0.0326050	−	0.205860i
$893$	6.15712	−	6.15712i	0.206040	−	0.206040i
$894$	−6.64603	−	5.90458i	−0.222277	−	0.197479i
$895$		0			0
$896$	−2.47446	+	3.40580i	−0.0826657	+	0.113780i
$897$	−2.33815	−	5.97212i	−0.0780686	−	0.199403i
$898$	−3.16995	+	1.61517i	−0.105783	+	0.0538989i
$899$	36.6510			1.22238
$900$		0			0
$901$	−7.30841			−0.243478
$902$	−16.7485	+	8.53377i	−0.557663	+	0.284144i
$903$	23.5525	+	60.1580i	0.783780	+	2.00193i
$904$	0.879683	−	1.21078i	0.0292578	−	0.0402699i
$905$		0			0
$906$	−26.0670	−	23.1589i	−0.866017	−	0.769402i
$907$	29.1272	−	29.1272i	0.967153	−	0.967153i	−0.0323248	−	0.999477i	$-0.510291\pi$
$907$	29.1272	−	29.1272i	0.967153	−	0.967153i	0.999477	+	0.0323248i	$0.0102911\pi$
$908$	−1.43222	+	9.04270i	−0.0475300	+	0.300093i
$909$	−33.9625	−	36.7253i	−1.12647	−	1.21810i
$910$		0			0
$911$	1.21439	+	0.394580i	0.0402346	+	0.0130730i	0.329065	−	0.944307i	$-0.393266\pi$
$911$	1.21439	+	0.394580i	0.0402346	+	0.0130730i	−0.288831	+	0.957380i	$0.593266\pi$
$912$	3.11740	+	0.813132i	0.103227	+	0.0269255i
$913$	−38.1699	+	74.9126i	−1.26324	+	2.47925i
$914$	5.87403	−	18.0784i	0.194296	−	0.597980i
$915$		0			0
$916$	5.71542	+	17.5902i	0.188843	+	0.581198i
$917$	26.4743	+	4.19312i	0.874259	+	0.138469i
$918$	−7.34623	−	1.01379i	−0.242462	−	0.0334601i
$919$	−14.7998	−	20.3701i	−0.488199	−	0.671949i	0.491855	−	0.870677i	$-0.336319\pi$
$919$	−14.7998	−	20.3701i	−0.488199	−	0.671949i	−0.980055	+	0.198728i	$0.936319\pi$
$920$		0			0
$921$	−26.8879	−	11.7577i	−0.885987	−	0.387430i
$922$	−31.6376	+	5.01091i	−1.04193	+	0.165026i
$923$	−12.0845	−	23.7173i	−0.397768	−	0.780663i
$924$	−35.4897	+	7.79051i	−1.16752	+	0.256289i
$925$		0			0
$926$		−	3.10121i		−	0.101912i
$927$	−6.25119	−	4.92595i	−0.205316	−	0.161789i
$928$	0.885486	+	5.59074i	0.0290675	+	0.183525i
$929$	−24.8975	−	18.0891i	−0.816859	−	0.593483i	0.0989519	−	0.995092i	$-0.468451\pi$
$929$	−24.8975	−	18.0891i	−0.816859	−	0.593483i	−0.915811	+	0.401609i	$0.868451\pi$
$930$		0			0
$931$	−16.1352	+	11.7229i	−0.528809	+	0.384202i
$932$	−9.73992	−	9.73992i	−0.319042	−	0.319042i
$933$	0.391369	+	6.62478i	0.0128128	+	0.216885i
$934$	37.7054	−	12.2512i	1.23376	−	0.400872i
$935$		0			0
$936$	5.26277	−	0.623990i	0.172019	−	0.0203958i
$937$	1.21310	+	0.618103i	0.0396301	+	0.0201925i	0.473693	−	0.880690i	$-0.342921\pi$
$937$	1.21310	+	0.618103i	0.0396301	+	0.0201925i	−0.434063	+	0.900882i	$0.642921\pi$
$938$	−24.2797	−	12.3711i	−0.792762	−	0.403932i
$939$	−39.4177	−	3.87820i	−1.28635	−	0.126560i
$940$		0			0
$941$	−14.0374	+	4.56102i	−0.457606	+	0.148685i	−0.528744	−	0.848781i	$-0.677337\pi$
$941$	−14.0374	+	4.56102i	−0.457606	+	0.148685i	0.0711384	+	0.997466i	$0.477337\pi$
$942$	−17.4469	+	1.03070i	−0.568452	+	0.0335821i
$943$	−5.59101	−	5.59101i	−0.182068	−	0.182068i
$944$	9.00688	−	6.54388i	0.293149	−	0.212985i
$945$		0			0
$946$	−35.7188	−	25.9512i	−1.16132	−	0.843747i
$947$	−1.05799	−	6.67988i	−0.0343800	−	0.217067i	0.964517	−	0.264021i	$-0.0850487\pi$
$947$	−1.05799	−	6.67988i	−0.0343800	−	0.217067i	−0.998897	+	0.0469536i	$0.985049\pi$
$948$	5.02075	−	4.12129i	0.163066	−	0.133853i
$949$		−	16.3330i		−	0.530191i
$950$		0			0
$951$	3.25217	+	14.8152i	0.105459	+	0.480417i
$952$	2.72764	+	5.35329i	0.0884032	+	0.173501i
$953$	16.8097	−	2.66239i	0.544519	−	0.0862434i	0.121886	−	0.992544i	$-0.461106\pi$
$953$	16.8097	−	2.66239i	0.544519	−	0.0862434i	0.422633	+	0.906301i	$0.361106\pi$
$954$	−2.99399	+	15.0681i	−0.0969341	+	0.487846i
$955$		0			0
$956$	12.1877	+	16.7750i	0.394180	+	0.542542i
$957$	−26.3354	+	41.1493i	−0.851303	+	1.33017i
$958$	−13.3111	−	2.10827i	−0.430061	−	0.0681150i
$959$	−5.34552	−	16.4518i	−0.172616	−	0.531257i
$960$		0			0
$961$	3.37603	−	10.3904i	0.108904	−	0.335173i
$962$	2.06509	−	4.05296i	0.0665811	−	0.130673i
$963$	35.4019	+	1.38364i	1.14081	+	0.0445870i
$964$	−5.91757	−	1.92274i	−0.190592	−	0.0619271i
$965$		0			0
$966$	−7.72973	−	13.1851i	−0.248700	−	0.424223i
$967$	−6.13865	+	38.7579i	−0.197406	+	1.24637i	0.667566	+	0.744550i	$0.267336\pi$
$967$	−6.13865	+	38.7579i	−0.197406	+	1.24637i	−0.864972	+	0.501820i	$0.832664\pi$
$968$	9.78020	−	9.78020i	0.314348	−	0.314348i
$969$	3.05385	−	3.43732i	0.0981037	−	0.110423i
$970$		0			0
$971$	17.7969	−	24.4953i	0.571129	−	0.786091i	−0.421559	−	0.906801i	$-0.638517\pi$
$971$	17.7969	−	24.4953i	0.571129	−	0.786091i	0.992688	+	0.120710i	$0.0385171\pi$
$972$	−5.09966	+	14.7307i	−0.163572	+	0.472487i
$973$	40.0644	−	20.4139i	1.28441	−	0.654438i
$974$	2.08662			0.0668596
$975$		0			0
$976$	9.70753			0.310731
$977$	−37.5797	+	19.1478i	−1.20228	+	0.612593i	−0.936238	−	0.351368i	$-0.885717\pi$
$977$	−37.5797	+	19.1478i	−1.20228	+	0.612593i	−0.266044	+	0.963961i	$0.585717\pi$
$978$	9.06466	−	3.54892i	0.289856	−	0.113482i
$979$	−3.32836	+	4.58109i	−0.106375	+	0.146412i
$980$		0			0
$981$	−19.5159	+	34.8650i	−0.623094	+	1.11315i
$982$	11.7522	−	11.7522i	0.375029	−	0.375029i
$983$	−2.25288	+	14.2241i	−0.0718557	+	0.453679i	0.925359	+	0.379092i	$0.123764\pi$
$983$	−2.25288	+	14.2241i	−0.0718557	+	0.453679i	−0.997215	+	0.0745867i	$0.976236\pi$
$984$	5.63646	−	3.30436i	0.179684	−	0.105339i
$985$		0			0
$986$	7.68307	+	2.49638i	0.244679	+	0.0795009i
$987$	8.61519	−	33.0291i	0.274224	−	1.05133i
$988$	−1.49175	+	2.92773i	−0.0474589	+	0.0931434i
$989$	5.73895	−	17.6627i	0.182488	−	0.561640i
$990$		0			0
$991$	0.477429	+	1.46938i	0.0151660	+	0.0466762i	0.958353	−	0.285586i	$-0.0921882\pi$
$991$	0.477429	+	1.46938i	0.0151660	+	0.0466762i	−0.943187	+	0.332262i	$0.892188\pi$
$992$	6.39524	+	1.01291i	0.203049	+	0.0321598i
$993$	−8.75133	−	5.60082i	−0.277715	−	0.177737i
$994$	−37.2854	−	51.3189i	−1.18262	−	1.62774i
$995$		0			0
$996$	11.7086	−	26.7756i	0.371001	−	0.848417i
$997$	49.1277	−	7.78106i	1.55589	−	0.246429i	0.681560	−	0.731762i	$-0.261302\pi$
$997$	49.1277	−	7.78106i	1.55589	−	0.246429i	0.874329	+	0.485333i	$0.161302\pi$
$998$	−16.3644	−	32.1169i	−0.518006	−	1.01664i
$999$	8.07873	+	10.6655i	0.255600	+	0.337440i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.l.a.743.8		80
3.2	odd	2	inner	750.2.l.a.743.3		80
5.2	odd	4		750.2.l.b.257.6		80
5.3	odd	4		150.2.l.a.47.5	✓	80
5.4	even	2		750.2.l.c.743.3		80
15.2	even	4		750.2.l.b.257.1		80
15.8	even	4		150.2.l.a.47.10	yes	80
15.14	odd	2		750.2.l.c.743.8		80
25.6	even	5		750.2.l.b.143.1		80
25.8	odd	20		750.2.l.c.107.8		80
25.17	odd	20	inner	750.2.l.a.107.3		80
25.19	even	10		150.2.l.a.83.10	yes	80
75.8	even	20		750.2.l.c.107.3		80
75.17	even	20	inner	750.2.l.a.107.8		80
75.44	odd	10		150.2.l.a.83.5	yes	80
75.56	odd	10		750.2.l.b.143.6		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.47.5	✓	80	5.3	odd	4
150.2.l.a.47.10	yes	80	15.8	even	4
150.2.l.a.83.5	yes	80	75.44	odd	10
150.2.l.a.83.10	yes	80	25.19	even	10
750.2.l.a.107.3		80	25.17	odd	20	inner
750.2.l.a.107.8		80	75.17	even	20	inner
750.2.l.a.743.3		80	3.2	odd	2	inner
750.2.l.a.743.8		80	1.1	even	1	trivial
750.2.l.b.143.1		80	25.6	even	5
750.2.l.b.143.6		80	75.56	odd	10
750.2.l.b.257.1		80	15.2	even	4
750.2.l.b.257.6		80	5.2	odd	4
750.2.l.c.107.3		80	75.8	even	20
750.2.l.c.107.8		80	25.8	odd	20
750.2.l.c.743.3		80	5.4	even	2
750.2.l.c.743.8		80	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.891007 - 0.453990i) q^{2} +(-0.631448 - 1.61285i) q^{3} +(0.587785 - 0.809017i) q^{4} +(-1.29484 - 1.15039i) q^{6} +(2.97677 - 2.97677i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-2.20255 + 2.03686i) q^{9} +O(q^{10})\)	\(q+(0.891007 - 0.453990i) q^{2} +(-0.631448 - 1.61285i) q^{3} +(0.587785 - 0.809017i) q^{4} +(-1.29484 - 1.15039i) q^{6} +(2.97677 - 2.97677i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-2.20255 + 2.03686i) q^{9} +(4.73921 + 1.53986i) q^{11} +(-1.67598 - 0.437156i) q^{12} +(0.801995 - 1.57400i) q^{13} +(1.30090 - 4.00375i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(-1.40961 - 0.223260i) q^{17} +(-1.03777 + 2.81479i) q^{18} +(-1.09331 - 1.50481i) q^{19} +(-6.68076 - 2.92140i) q^{21} +(4.92175 - 0.779529i) q^{22} +(0.951606 + 1.86763i) q^{23} +(-1.69177 + 0.371369i) q^{24} -1.76655i q^{26} +(4.67593 + 2.26620i) q^{27} +(-0.658557 - 4.15797i) q^{28} +(-4.57938 - 3.32712i) q^{29} +(-5.23835 + 3.80588i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.509001 - 8.61596i) q^{33} +(-1.35733 + 0.441023i) q^{34} +(0.353226 + 2.97913i) q^{36} +(2.29429 + 1.16900i) q^{37} +(-1.65732 - 0.844446i) q^{38} +(-3.04504 - 0.299594i) q^{39} +(-3.58757 + 1.16567i) q^{41} +(-7.27889 + 0.430011i) q^{42} +(-6.26505 - 6.26505i) q^{43} +(4.03141 - 2.92899i) q^{44} +(1.69577 + 1.23205i) q^{46} +(0.732319 + 4.62368i) q^{47} +(-1.33878 + 1.09894i) q^{48} -10.7224i q^{49} +(0.530010 + 2.41446i) q^{51} +(-0.801995 - 1.57400i) q^{52} +(5.05783 - 0.801081i) q^{53} +(5.19512 - 0.103626i) q^{54} +(-2.47446 - 3.40580i) q^{56} +(-1.73666 + 2.71355i) q^{57} +(-5.59074 - 0.885486i) q^{58} +(3.44032 + 10.5882i) q^{59} +(-2.99979 + 9.23241i) q^{61} +(-2.93957 + 5.76923i) q^{62} +(-0.493226 + 12.6197i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(-4.36509 - 7.44580i) q^{66} +(1.01259 - 6.39326i) q^{67} +(-1.00917 + 1.00917i) q^{68} +(2.41131 - 2.71411i) q^{69} +(8.85681 - 12.1904i) q^{71} +(1.66722 + 2.49407i) q^{72} +(8.23800 - 4.19747i) q^{73} +2.57494 q^{74} -1.86005 q^{76} +(18.6914 - 9.52374i) q^{77} +(-2.84917 + 1.11548i) q^{78} +(-2.20434 + 3.03401i) q^{79} +(0.702433 - 8.97255i) q^{81} +(-2.66735 + 2.66735i) q^{82} +(-2.63941 + 16.6646i) q^{83} +(-6.29032 + 3.68769i) q^{84} +(-8.42648 - 2.73793i) q^{86} +(-2.47449 + 9.48674i) q^{87} +(2.26228 - 4.43998i) q^{88} +(-0.351151 + 1.08073i) q^{89} +(-2.29810 - 7.07281i) q^{91} +(2.07029 + 0.327901i) q^{92} +(9.44605 + 6.04544i) q^{93} +(2.75161 + 3.78726i) q^{94} +(-0.693954 + 1.58696i) q^{96} +(-3.47236 + 0.549968i) q^{97} +(-4.86785 - 9.55370i) q^{98} +(-13.5748 + 6.26147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) \) 80 * q - 4 * q^3 - 4 * q^7	\( 80 q - 4 q^{3} - 4 q^{7} - 16 q^{12} + 20 q^{16} + 8 q^{18} + 40 q^{19} - 4 q^{22} + 56 q^{27} - 4 q^{28} + 96 q^{33} + 40 q^{34} + 64 q^{37} + 40 q^{39} + 4 q^{42} + 24 q^{43} - 16 q^{48} + 64 q^{57} - 20 q^{58} - 4 q^{63} + 104 q^{67} - 140 q^{69} - 8 q^{72} + 60 q^{73} + 60 q^{78} - 80 q^{79} - 40 q^{81} - 96 q^{82} - 60 q^{84} - 80 q^{87} - 24 q^{88} - 12 q^{93} + 12 q^{97}+O(q^{100}) \) 80 * q - 4 * q^3 - 4 * q^7 - 16 * q^12 + 20 * q^16 + 8 * q^18 + 40 * q^19 - 4 * q^22 + 56 * q^27 - 4 * q^28 + 96 * q^33 + 40 * q^34 + 64 * q^37 + 40 * q^39 + 4 * q^42 + 24 * q^43 - 16 * q^48 + 64 * q^57 - 20 * q^58 - 4 * q^63 + 104 * q^67 - 140 * q^69 - 8 * q^72 + 60 * q^73 + 60 * q^78 - 80 * q^79 - 40 * q^81 - 96 * q^82 - 60 * q^84 - 80 * q^87 - 24 * q^88 - 12 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

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