LMFDB - Embedded newform 750.2.l.a.107.8

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			107.8
Character	$\chi$	$=$	750.107
Dual form			750.2.l.a.743.8

$q$-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 $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$-1$

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	0.990960	+	0.134155i	$0.0428318\pi$
$7$	2.97677	+	2.97677i	1.12511	+	1.12511i	0.134155	+	0.990960i	$0.457168\pi$
$8$	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	0.510499	−	0.859878i	$-0.329461\pi$
$11$	4.73921	−	1.53986i	1.42893	−	0.464286i	0.918426	+	0.395592i	$0.129461\pi$
$12$	−1.67598	+	0.437156i	−0.483813	+	0.126196i
$13$	0.801995	+	1.57400i	0.222433	+	0.436550i	0.975074	−	0.221882i	$-0.0712200\pi$
$13$	0.801995	+	1.57400i	0.222433	+	0.436550i	−0.752640	+	0.658432i	$0.771220\pi$
$14$	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	−0.325014	−	0.945709i	$-0.605369\pi$
$17$	−1.40961	+	0.223260i	−0.341881	+	0.0541486i	−0.0168665	+	0.999858i	$0.505369\pi$
$18$	−1.03777	−	2.81479i	−0.244605	−	0.663452i
$19$	−1.09331	+	1.50481i	−0.250823	+	0.345228i	−0.915799	−	0.401636i	$-0.868442\pi$
$19$	−1.09331	+	1.50481i	−0.250823	+	0.345228i	0.664977	+	0.746864i	$0.268442\pi$
$20$		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	−0.770259	−	0.637731i	$-0.779873\pi$
$23$	0.951606	−	1.86763i	0.198424	−	0.389428i	0.968682	+	0.248303i	$0.0798730\pi$
$24$	−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	−0.925248	−	0.379363i	$-0.876143\pi$
$29$	−4.57938	+	3.32712i	−0.850370	+	0.617830i	0.0748779	+	0.997193i	$0.476143\pi$
$30$		0			0
$31$	−5.23835	−	3.80588i	−0.940835	−	0.683557i	0.00778619	−	0.999970i	$-0.497522\pi$
$31$	−5.23835	−	3.80588i	−0.940835	−	0.683557i	−0.948622	+	0.316413i	$0.897522\pi$
$32$	−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	−0.255116	−	0.966911i	$-0.582114\pi$
$37$	2.29429	−	1.16900i	0.377178	−	0.192182i	0.632294	+	0.774729i	$0.282114\pi$
$38$	−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	0.0151644	−	0.999885i	$-0.495173\pi$
$41$	−3.58757	−	1.16567i	−0.560285	−	0.182048i	−0.575449	+	0.817837i	$0.695173\pi$
$42$	−7.27889	−	0.430011i	−1.12316	−	0.0663522i
$43$	−6.26505	+	6.26505i	−0.955411	+	0.955411i	−0.999047	−	0.0436361i	$-0.986106\pi$
$43$	−6.26505	+	6.26505i	−0.955411	+	0.955411i	0.0436361	+	0.999047i	$0.486106\pi$
$44$	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	−0.874929	−	0.484251i	$-0.839092\pi$
$47$	0.732319	−	4.62368i	0.106820	−	0.674433i	0.981749	−	0.190182i	$-0.0609079\pi$
$48$	−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	0.493813	−	0.869568i	$-0.335603\pi$
$53$	5.05783	+	0.801081i	0.694746	+	0.110037i	0.200933	+	0.979605i	$0.435603\pi$
$54$	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	−0.431389	−	0.902166i	$-0.641976\pi$
$59$	3.44032	−	10.5882i	0.447892	−	1.37847i	0.879281	−	0.476303i	$-0.158024\pi$
$60$		0			0
$61$	−2.99979	−	9.23241i	−0.384084	−	1.18209i	−0.937142	−	0.348947i	$-0.886539\pi$
$61$	−2.99979	−	9.23241i	−0.384084	−	1.18209i	0.553058	−	0.833143i	$-0.313461\pi$
$62$	−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	0.969055	+	0.246844i	$0.0793935\pi$
$67$	1.01259	+	6.39326i	0.123708	+	0.781061i	−0.845347	+	0.534217i	$0.820607\pi$
$68$	−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	0.887842	+	0.460147i	$0.152203\pi$
$71$	8.85681	+	12.1904i	1.05111	+	1.44673i	0.163268	+	0.986582i	$0.447797\pi$
$72$	1.66722	−	2.49407i	0.196484	−	0.293928i
$73$	8.23800	+	4.19747i	0.964185	+	0.491277i	0.863890	−	0.503681i	$-0.168021\pi$
$73$	8.23800	+	4.19747i	0.964185	+	0.491277i	0.100295	+	0.994958i	$0.468021\pi$
$74$	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	0.666805	−	0.745232i	$-0.267661\pi$
$79$	−2.20434	−	3.03401i	−0.248007	−	0.341353i	−0.914812	+	0.403880i	$0.867661\pi$
$80$		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	−0.517761	−	0.855525i	$-0.673234\pi$
$83$	−2.63941	−	16.6646i	−0.289713	−	1.82918i	0.228048	−	0.973650i	$-0.426766\pi$
$84$	−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	0.930719	−	0.365735i	$-0.119182\pi$
$89$	−0.351151	−	1.08073i	−0.0372219	−	0.114557i	−0.967941	+	0.251177i	$0.919182\pi$
$90$		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	−0.0223598	−	0.999750i	$-0.507118\pi$
$97$	−3.47236	−	0.549968i	−0.352565	−	0.0558408i	−0.330205	+	0.943909i	$0.607118\pi$
$98$	−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	$-0.688590\pi$
$101$		−	16.6740i		−	1.65912i	0.558415	−	0.829562i	$-0.311410\pi$
$102$	1.56838	−	1.91068i	0.155293	−	0.189186i
$103$	0.415010	−	2.62027i	0.0408921	−	0.258183i	−0.958770	−	0.284184i	$-0.908277\pi$
$103$	0.415010	−	2.62027i	0.0408921	−	0.258183i	0.999662	+	0.0260012i	$0.00827738\pi$
$104$	−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	−0.984223	−	0.176933i	$-0.943382\pi$
$107$	−8.35067	+	8.35067i	−0.807290	+	0.807290i	0.176933	+	0.984223i	$0.443382\pi$
$108$	4.58184	+	2.45087i	0.440888	+	0.235835i
$109$	12.6666	+	4.11563i	1.21324	+	0.394206i	0.844617	−	0.535372i	$-0.179828\pi$
$109$	12.6666	+	4.11563i	1.21324	+	0.394206i	0.368625	+	0.929578i	$0.379828\pi$
$110$		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	−0.390142	−	0.920755i	$-0.627574\pi$
$113$	1.33349	−	0.679445i	0.125444	−	0.0639168i	0.515586	+	0.856838i	$0.327574\pi$
$114$	−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	−0.857643	−	0.514246i	$-0.828072\pi$
$127$	0.704349	−	1.38236i	0.0625009	−	0.122665i	0.920144	+	0.391581i	$0.128072\pi$
$128$	−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	−0.613599	−	0.789618i	$-0.710279\pi$
$131$	3.74251	−	5.15112i	0.326984	−	0.450055i	0.940584	+	0.339562i	$0.110279\pi$
$132$	−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	0.956862	−	0.290542i	$-0.0938354\pi$
$137$	1.86549	+	3.66124i	0.159380	+	0.312800i	−0.797483	+	0.603342i	$0.793835\pi$
$138$	0.916318	+	3.51300i	0.0780022	+	0.299046i
$139$	10.1584	−	3.30065i	0.861621	−	0.279958i	0.155316	−	0.987865i	$-0.450361\pi$
$139$	10.1584	−	3.30065i	0.861621	−	0.279958i	0.706305	+	0.707907i	$0.250361\pi$
$140$		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	0.931972	−	0.362529i	$-0.118087\pi$
$157$	7.13510	+	7.13510i	0.569443	+	0.569443i	−0.362529	+	0.931972i	$0.618087\pi$
$158$	−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	0.769228	−	0.638974i	$-0.220641\pi$
$163$	−2.55156	−	5.00771i	−0.199853	−	0.392234i	−0.969082	+	0.246739i	$0.920641\pi$
$164$	−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	−0.759823	−	0.650130i	$-0.774714\pi$
$167$	−16.5614	+	2.62306i	−1.28156	+	0.202979i	−0.521734	+	0.853109i	$0.674714\pi$
$168$	−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	−0.955263	−	0.295758i	$-0.904428\pi$
$173$	−2.03214	+	3.98829i	−0.154500	+	0.303224i	0.800763	+	0.598982i	$0.204428\pi$
$174$	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	−0.593047	−	0.805167i	$-0.702075\pi$
$179$	−0.141142	+	0.102546i	−0.0105495	+	0.00766463i	0.582498	+	0.812832i	$0.302075\pi$
$180$		0			0
$181$	9.20445	+	6.68743i	0.684162	+	0.497072i	0.874736	−	0.484600i	$-0.161035\pi$
$181$	9.20445	+	6.68743i	0.684162	+	0.497072i	−0.190574	+	0.981673i	$0.561035\pi$
$182$	−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	−0.404998	−	0.914318i	$-0.632728\pi$
$191$	−17.5527	−	5.70322i	−1.27007	−	0.412671i	−0.865072	+	0.501647i	$0.832728\pi$
$192$	0.102145	−	1.72904i	0.00737171	−	0.124782i
$193$	3.31568	−	3.31568i	0.238668	−	0.238668i	−0.577630	−	0.816298i	$-0.696023\pi$
$193$	3.31568	−	3.31568i	0.238668	−	0.238668i	0.816298	+	0.577630i	$0.196023\pi$
$194$	−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	−0.810503	−	0.585734i	$-0.800806\pi$
$197$	1.98370	−	12.5246i	0.141333	−	0.892341i	0.951836	−	0.306607i	$-0.0991936\pi$
$198$	−9.25260	−	11.7418i	−0.657554	−	0.834457i
$199$			1.62602i			0.115266i	0.998338	+	0.0576328i	$0.0183553\pi$
$199$			1.62602i			0.115266i	−0.998338	+	0.0576328i	$0.981645\pi$
$200$		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	−0.993437	−	0.114383i	$-0.963511\pi$
$211$	−3.73259	−	11.4877i	−0.256962	−	0.790848i	0.736475	−	0.676465i	$-0.236489\pi$
$212$	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	0.629729	−	0.776815i	$-0.283166\pi$
$223$	5.54645	+	2.82606i	0.371418	+	0.189247i	−0.258311	+	0.966062i	$0.583166\pi$
$224$	−4.20979			−0.281279
$225$		0			0
$226$	1.49661			0.0995528
$227$	−8.15754	−	4.15647i	−0.541435	−	0.275875i	0.161811	−	0.986822i	$-0.448267\pi$
$227$	−8.15754	−	4.15647i	−0.541435	−	0.275875i	−0.703246	+	0.710947i	$0.748267\pi$
$228$	1.17452	−	2.99998i	0.0777848	−	0.198678i
$229$	−10.8714	−	14.9632i	−0.718400	−	0.988793i	−0.999575	−	0.0291365i	$-0.990724\pi$
$229$	−10.8714	−	14.9632i	−0.718400	−	0.988793i	0.281175	−	0.959656i	$-0.409276\pi$
$230$		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	0.952021	+	0.306032i	$0.0990014\pi$
$233$	2.15478	+	13.6047i	0.141164	+	0.891276i	−0.810857	+	0.585244i	$0.800999\pi$
$234$	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	−0.912729	−	0.408566i	$-0.866029\pi$
$239$	−6.40747	−	19.7202i	−0.414465	−	1.27559i	0.498264	−	0.867025i	$-0.333971\pi$
$240$		0			0
$241$	−1.92274	+	5.91757i	−0.123854	+	0.381184i	−0.993691	−	0.112156i	$-0.964224\pi$
$241$	−1.92274	+	5.91757i	−0.123854	+	0.381184i	0.869836	+	0.493340i	$0.164224\pi$
$242$	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	$0.0379520\pi$
$251$			3.76896i			0.237895i	−0.992901	+	0.118947i	$0.962048\pi$
$252$	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	−0.481471	+	0.876462i	$0.659897\pi$
$257$	−21.7693	+	21.7693i	−1.35793	+	1.35793i	−0.876462	+	0.481471i	$0.840103\pi$
$258$	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	−0.599598	−	0.800302i	$-0.704673\pi$
$263$	−4.93937	+	2.51673i	−0.304574	+	0.155188i	0.295023	+	0.955490i	$0.404673\pi$
$264$	−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	0.669917	−	0.742436i	$-0.266330\pi$
$269$	2.80188	+	2.03568i	0.170834	+	0.124118i	−0.499083	+	0.866554i	$0.666330\pi$
$270$		0			0
$271$	−3.81142	+	2.76916i	−0.231528	+	0.168215i	−0.697500	−	0.716584i	$-0.745704\pi$
$271$	−3.81142	+	2.76916i	−0.231528	+	0.168215i	0.465973	+	0.884799i	$0.345704\pi$
$272$	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	0.252321	+	0.967644i	$0.418806\pi$
$277$	−11.2980	+	22.1735i	−0.678829	+	1.33228i	−0.931151	+	0.364634i	$0.881194\pi$
$278$	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	−0.605304	−	0.795994i	$-0.706948\pi$
$281$	5.67900	−	7.81648i	0.338781	−	0.466292i	0.944085	+	0.329702i	$0.106948\pi$
$282$	4.37078	+	6.82938i	0.260276	+	0.406684i
$283$	1.00775	−	0.159612i	0.0599044	−	0.00948793i	−0.126410	−	0.991978i	$-0.540346\pi$
$283$	1.00775	−	0.159612i	0.0599044	−	0.00948793i	0.186315	+	0.982490i	$0.440346\pi$
$284$	−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	0.663295	−	0.748358i	$-0.269157\pi$
$293$	−1.45604	−	1.45604i	−0.0850625	−	0.0850625i	−0.748358	+	0.663295i	$0.769157\pi$
$294$	−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	0.960847	−	0.277080i	$-0.0893667\pi$
$307$	11.9806	+	11.9806i	0.683767	+	0.683767i	−0.277080	+	0.960847i	$0.589367\pi$
$308$	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	−0.410503	−	0.911859i	$-0.634647\pi$
$311$	−3.64396	+	1.18399i	−0.206630	+	0.0671381i	0.203873	+	0.978997i	$0.434647\pi$
$312$	−0.772255	−	2.96069i	−0.0437203	−	0.167616i
$313$	10.3817	+	20.3753i	0.586809	+	1.15168i	0.973333	+	0.229398i	$0.0736759\pi$
$313$	10.3817	+	20.3753i	0.586809	+	1.15168i	−0.386523	+	0.922280i	$0.626324\pi$
$314$	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	−0.394530	−	0.918883i	$-0.629093\pi$
$317$	−8.64943	+	1.36994i	−0.485800	+	0.0769432i	−0.0912701	+	0.995826i	$0.529093\pi$
$318$	−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	0.713118	−	0.701044i	$-0.247283\pi$
$331$	4.85309	+	3.52598i	0.266750	+	0.193805i	−0.446367	+	0.894850i	$0.647283\pi$
$332$	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	−0.394012	−	0.919105i	$-0.628913\pi$
$337$	2.16556	−	1.10341i	0.117965	−	0.0601063i	0.511977	+	0.858999i	$0.328913\pi$
$338$	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	−0.687237	−	0.726433i	$-0.741177\pi$
$347$	3.55504	−	22.4456i	0.190844	−	1.20494i	0.878082	−	0.478511i	$-0.158823\pi$
$348$	6.22047	−	7.57807i	0.333452	−	0.406227i
$349$		−	12.5328i		−	0.670865i	−0.942064	−	0.335432i	$-0.891118\pi$
$349$		−	12.5328i		−	0.670865i	0.942064	−	0.335432i	$-0.108882\pi$
$350$		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	−0.0342193	−	0.999414i	$-0.510894\pi$
$353$	−7.05688	−	1.11770i	−0.375600	−	0.0594892i	−0.341381	+	0.939925i	$0.610894\pi$
$354$	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	−0.999568	−	0.0293907i	$-0.990643\pi$
$359$	−3.28973	+	10.1247i	−0.173625	+	0.534363i	0.825943	+	0.563754i	$0.190643\pi$
$360$		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	0.964602	−	0.263710i	$-0.0849462\pi$
$367$	−0.656708	−	4.14629i	−0.0342799	−	0.216435i	−0.998882	+	0.0472753i	$0.984946\pi$
$368$	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	0.345838	−	0.938294i	$-0.387595\pi$
$373$	−4.05536	−	2.06631i	−0.209979	−	0.106990i	−0.555817	+	0.831305i	$0.687595\pi$
$374$	−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	−0.927775	−	0.373139i	$-0.878281\pi$
$379$	−19.3891	−	26.6869i	−0.995954	−	1.37081i	−0.0681783	−	0.997673i	$-0.521719\pi$
$380$		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	−0.956873	−	0.290505i	$-0.906177\pi$
$383$	−2.67339	−	16.8791i	−0.136604	−	0.862482i	0.820270	−	0.571977i	$-0.193823\pi$
$384$	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	−0.998752	−	0.0499484i	$-0.984094\pi$
$389$	−4.34112	−	13.3606i	−0.220104	−	0.677409i	0.778648	−	0.627461i	$-0.215906\pi$
$390$		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	0.247200	−	0.968964i	$-0.420489\pi$
$397$	3.64376	+	0.577115i	0.182875	+	0.0289646i	−0.0643251	+	0.997929i	$0.520489\pi$
$398$	−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	$0.261387\pi$
$401$			29.3144i			1.46389i	−0.681364	+	0.731945i	$0.738613\pi$
$402$	−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	0.123586	−	0.992334i	$-0.460561\pi$
$409$	−7.27469	−	2.36369i	−0.359710	−	0.116877i	−0.483296	+	0.875457i	$0.660561\pi$
$410$		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	0.782877	−	0.622176i	$-0.213751\pi$
$419$	8.86483	+	6.44067i	0.433075	+	0.314648i	−0.349802	+	0.936824i	$0.613751\pi$
$420$		0			0
$421$	−11.3681	+	8.25943i	−0.554048	+	0.402540i	−0.829276	−	0.558839i	$-0.811247\pi$
$421$	−11.3681	+	8.25943i	−0.554048	+	0.402540i	0.275227	+	0.961379i	$0.411247\pi$
$422$	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	−0.743131	−	0.669146i	$-0.766660\pi$
$431$	2.55158	−	3.51195i	0.122905	−	0.169164i	0.866036	+	0.499982i	$0.166660\pi$
$432$	0.710346	+	5.14737i	0.0341765	+	0.247653i
$433$	−7.75206	+	1.22781i	−0.372540	+	0.0590046i	−0.339897	−	0.940463i	$-0.610392\pi$
$433$	−7.75206	+	1.22781i	−0.372540	+	0.0590046i	−0.0326428	+	0.999467i	$0.510392\pi$
$434$	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	0.185405	−	0.982662i	$-0.440640\pi$
$439$	19.1294	−	6.21551i	0.912994	−	0.296650i	0.727590	+	0.686012i	$0.240640\pi$
$440$		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	0.365463	−	0.930826i	$-0.380911\pi$
$443$	−11.8995	−	11.8995i	−0.565363	−	0.565363i	−0.930826	+	0.365463i	$0.880911\pi$
$444$	−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	0.947754	−	0.319001i	$-0.103347\pi$
$457$	13.4412	+	13.4412i	0.628754	+	0.628754i	−0.319001	+	0.947754i	$0.603347\pi$
$458$	−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	−0.915240	−	0.402908i	$-0.867999\pi$
$461$	−30.4642	+	9.89843i	−1.41886	+	0.461016i	−0.503621	+	0.863925i	$0.667999\pi$
$462$	−35.1583	+	9.17058i	−1.63571	+	0.426654i
$463$	1.40792	+	2.76320i	0.0654317	+	0.128417i	0.921406	−	0.388602i	$-0.127042\pi$
$463$	1.40792	+	2.76320i	0.0654317	+	0.128417i	−0.855974	+	0.517019i	$0.827042\pi$
$464$	−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	0.843707	−	0.536804i	$-0.180368\pi$
$467$	39.1577	−	6.20197i	1.81200	−	0.286993i	0.968295	+	0.249811i	$0.0803684\pi$
$468$	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	−0.808320	−	0.588744i	$-0.799623\pi$
$479$	−10.9031	+	7.92157i	−0.498176	+	0.361946i	0.310144	+	0.950690i	$0.399623\pi$
$480$		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	−0.411359	−	0.911473i	$-0.634946\pi$
$487$	1.85919	−	0.947305i	0.0842480	−	0.0429265i	0.495607	+	0.868547i	$0.334946\pi$
$488$	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	0.643137	−	0.765751i	$-0.277633\pi$
$491$	15.8067	+	5.13592i	0.713348	+	0.231781i	0.0702111	+	0.997532i	$0.477633\pi$
$492$	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	$0.298810\pi$
$499$			36.0457i			1.61363i	−0.590806	+	0.806813i	$0.701190\pi$
$500$		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	−0.582255	−	0.813007i	$-0.697829\pi$
$503$	−31.1126	−	4.92776i	−1.38724	−	0.219718i	−0.804990	+	0.593289i	$0.797829\pi$
$504$	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	−0.946760	−	0.321941i	$-0.895665\pi$
$509$	0.189892	−	0.584428i	0.00841683	−	0.0259043i	0.955177	+	0.296036i	$0.0956649\pi$
$510$		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	0.984155	+	0.177312i	$0.0567401\pi$
$521$	19.3712	+	26.6622i	0.848668	+	1.16809i	−0.135487	+	0.990779i	$0.543260\pi$
$522$	14.1175	+	9.43721i	0.617905	+	0.413055i
$523$	−35.5580	−	18.1177i	−1.55484	−	0.792232i	−0.555612	−	0.831442i	$-0.687516\pi$
$523$	−35.5580	−	18.1177i	−1.55484	−	0.792232i	−0.999231	+	0.0392100i	$0.987516\pi$
$524$	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	−0.629865	−	0.776704i	$-0.716890\pi$
$541$	7.82078	−	24.0699i	0.336242	−	1.03485i	0.966107	−	0.258141i	$-0.0831100\pi$
$542$	−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	−0.795495	−	0.605961i	$-0.792789\pi$
$547$	−40.6790	−	6.44292i	−1.73931	−	0.275479i	−0.943812	+	0.330482i	$0.892789\pi$
$548$	−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	−0.222107	−	0.975022i	$-0.571293\pi$
$557$	17.7694	−	17.7694i	0.752915	−	0.752915i	0.975022	+	0.222107i	$0.0712934\pi$
$558$	−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	−0.248339	−	0.968673i	$-0.579885\pi$
$563$	9.23868	−	4.70734i	0.389364	−	0.198391i	0.637703	+	0.770282i	$0.279885\pi$
$564$	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	0.865876	−	0.500259i	$-0.166762\pi$
$569$	15.6879	+	11.3979i	0.657671	+	0.477826i	−0.208205	+	0.978085i	$0.566762\pi$
$570$		0			0
$571$	14.7088	−	10.6866i	0.615544	−	0.447219i	−0.235818	−	0.971797i	$-0.575777\pi$
$571$	14.7088	−	10.6866i	0.615544	−	0.447219i	0.851362	+	0.524579i	$0.175777\pi$
$572$	−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	−0.940341	−	0.340233i	$-0.889494\pi$
$577$	−2.69918	+	5.29743i	−0.112368	+	0.220535i	0.827973	+	0.560768i	$0.189494\pi$
$578$	−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	−0.995083	−	0.0990406i	$-0.968423\pi$
$587$	−11.8794	−	23.3146i	−0.490314	−	0.962295i	0.504770	−	0.863254i	$-0.331577\pi$
$588$	−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	0.999565	−	0.0294930i	$-0.00938927\pi$
$593$	23.6228	+	23.6228i	0.970072	+	0.970072i	−0.0294930	+	0.999565i	$0.509389\pi$
$594$	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	0.0758281	−	0.997121i	$-0.475840\pi$
$607$	−22.6982	−	22.6982i	−0.921293	−	0.921293i	−0.997121	+	0.0758281i	$0.975840\pi$
$608$	−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	−0.828616	−	0.559818i	$-0.810871\pi$
$613$	−19.6701	−	38.6048i	−0.794470	−	1.55923i	0.0341460	−	0.999417i	$-0.489129\pi$
$614$	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	−0.621028	−	0.783788i	$-0.713285\pi$
$617$	−24.0808	+	3.81403i	−0.969458	+	0.153547i	−0.348429	+	0.937335i	$0.613285\pi$
$618$	2.47695	+	3.87025i	0.0996374	+	0.155684i
$619$	23.7633	−	32.7074i	0.955130	−	1.31462i	0.00591868	−	0.999982i	$-0.498116\pi$
$619$	23.7633	−	32.7074i	0.955130	−	1.31462i	0.949211	−	0.314641i	$-0.101884\pi$
$620$		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	0.123145	−	0.992389i	$-0.460702\pi$
$631$	−19.6592	−	14.2832i	−0.782619	−	0.568606i	−0.905764	+	0.423783i	$0.860702\pi$
$632$	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	0.476922	−	0.878946i	$-0.341753\pi$
$641$	8.76326	+	2.84736i	0.346128	+	0.112464i	−0.130794	+	0.991410i	$0.541753\pi$
$642$	1.20630	−	20.4193i	0.0476089	−	0.805885i
$643$	32.6751	−	32.6751i	1.28858	−	1.28858i	0.352932	−	0.935649i	$-0.385185\pi$
$643$	32.6751	−	32.6751i	1.28858	−	1.28858i	0.935649	−	0.352932i	$-0.114815\pi$
$644$	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	0.141152	+	0.989988i	$0.454919\pi$
$647$	−7.60579	+	48.0211i	−0.299015	+	1.88790i	−0.440167	+	0.897916i	$0.645081\pi$
$648$	−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	0.528302	−	0.849056i	$-0.322829\pi$
$653$	19.6349	+	3.10987i	0.768375	+	0.121699i	0.240073	+	0.970755i	$0.422829\pi$
$654$	−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	−0.589717	−	0.807610i	$-0.700761\pi$
$659$	9.29483	−	28.6066i	0.362075	−	1.11435i	0.951792	−	0.306743i	$-0.0992393\pi$
$660$		0			0
$661$	−4.51392	−	13.8924i	−0.175571	−	0.540352i	0.824088	−	0.566462i	$-0.191688\pi$
$661$	−4.51392	−	13.8924i	−0.175571	−	0.540352i	−0.999659	+	0.0261096i	$0.991688\pi$
$662$	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	0.925392	−	0.379010i	$-0.123736\pi$
$673$	30.1630	+	15.3688i	1.16270	+	0.592425i	0.237306	+	0.971435i	$0.423736\pi$
$674$	2.43046			0.0936178
$675$		0			0
$676$	9.87932			0.379974
$677$	6.85459	+	3.49259i	0.263443	+	0.134231i	0.580724	−	0.814101i	$-0.302770\pi$
$677$	6.85459	+	3.49259i	0.263443	+	0.134231i	−0.317280	+	0.948332i	$0.602770\pi$
$678$	−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	0.994857	−	0.101286i	$-0.0322957\pi$
$683$	0.454547	+	2.86990i	0.0173928	+	0.109814i	−0.977465	+	0.211099i	$0.932296\pi$
$684$	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	0.613119	+	0.789991i	$0.289915\pi$
$691$	−9.12811	+	28.0934i	−0.347249	+	1.06872i	−0.960368	+	0.278733i	$0.910085\pi$
$692$	−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	$0.283453\pi$
$701$			41.1646i			1.55476i	−0.629028	+	0.777382i	$0.716547\pi$
$702$	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	−0.0104457	−	0.999945i	$-0.503325\pi$
$709$	−16.1533	−	5.24852i	−0.606650	−	0.197112i	−0.596204	+	0.802833i	$0.703325\pi$
$710$		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	0.213700	−	0.976899i	$-0.431448\pi$
$719$	−17.4118	−	12.6504i	−0.649349	−	0.471780i	−0.863049	+	0.505120i	$0.831448\pi$
$720$		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	0.401443	+	0.915884i	$0.368509\pi$
$727$	−15.5168	+	30.4534i	−0.575485	+	1.12945i	−0.976928	+	0.213569i	$0.931491\pi$
$728$	−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	−0.487027	−	0.873387i	$-0.661919\pi$
$733$	−18.4191	+	2.91730i	−0.680326	+	0.107753i	−0.193299	+	0.981140i	$0.561919\pi$
$734$	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	−0.285225	−	0.958461i	$-0.592068\pi$
$739$	1.28835	−	0.418609i	0.0473926	−	0.0153988i	0.332617	+	0.943062i	$0.392068\pi$
$740$		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	0.848183	−	0.529704i	$-0.177697\pi$
$743$	8.68111	+	8.68111i	0.318479	+	0.318479i	−0.529704	+	0.848183i	$0.677697\pi$
$744$	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	0.141616	−	0.989922i	$-0.454770\pi$
$757$	−23.3400	−	23.3400i	−0.848305	−	0.848305i	−0.989922	+	0.141616i	$0.954770\pi$
$758$	−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	−0.431133	−	0.902288i	$-0.641886\pi$
$761$	−6.88486	+	2.23703i	−0.249576	+	0.0810921i	0.181558	+	0.983380i	$0.441886\pi$
$762$	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	−0.768477	−	0.639877i	$-0.778985\pi$
$769$	2.15066	−	2.96013i	0.0775549	−	0.106745i	0.846032	+	0.533132i	$0.178985\pi$
$770$		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	−0.445655	−	0.895205i	$-0.647029\pi$
$773$	15.0283	−	29.4947i	0.540531	−	1.06085i	0.986185	−	0.165646i	$-0.0529709\pi$
$774$	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	−0.696616	−	0.717444i	$-0.745312\pi$
$787$	−14.7464	+	7.51367i	−0.525653	+	0.267833i	0.170964	+	0.985277i	$0.445312\pi$
$788$	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	−0.583095	−	0.812404i	$-0.698158\pi$
$797$	6.28166	−	39.6609i	0.222508	−	1.40486i	0.805603	−	0.592456i	$-0.201842\pi$
$798$	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	−0.823341	−	0.567546i	$-0.807893\pi$
$809$	5.01595	−	15.4375i	0.176351	−	0.542753i	0.999693	+	0.0247932i	$0.00789272\pi$
$810$		0			0
$811$	−12.6792	−	39.0226i	−0.445227	−	1.37027i	−0.882234	−	0.470811i	$-0.843961\pi$
$811$	−12.6792	−	39.0226i	−0.445227	−	1.37027i	0.437007	−	0.899458i	$-0.356039\pi$
$812$	−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	0.641582	−	0.767055i	$-0.278279\pi$
$821$	−8.20025	−	11.2867i	−0.286191	−	0.393907i	−0.927772	+	0.373147i	$0.878279\pi$
$822$	−6.62735	−	2.59468i	−0.231155	−	0.0904999i
$823$	−15.2645	−	7.77764i	−0.532086	−	0.271112i	0.167237	−	0.985917i	$-0.446515\pi$
$823$	−15.2645	−	7.77764i	−0.532086	−	0.271112i	−0.699324	+	0.714805i	$0.746515\pi$
$824$	2.65293			0.0924192
$825$		0			0
$826$	46.8681			1.63075
$827$	−35.0129	−	17.8399i	−1.21752	−	0.620356i	−0.277251	−	0.960798i	$-0.589423\pi$
$827$	−35.0129	−	17.8399i	−1.21752	−	0.620356i	−0.940266	+	0.340442i	$0.889423\pi$
$828$	−5.22779	−	3.49466i	−0.181678	−	0.121448i
$829$	16.9229	+	23.2923i	0.587756	+	0.808977i	0.994519	−	0.104557i	$-0.0333425\pi$
$829$	16.9229	+	23.2923i	0.587756	+	0.808977i	−0.406763	+	0.913534i	$0.633343\pi$
$830$		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	−0.955695	−	0.294360i	$-0.904893\pi$
$839$	−10.2985	−	31.6954i	−0.355542	−	1.09425i	0.600152	−	0.799886i	$-0.295107\pi$
$840$		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	0.393900	+	0.919153i	$0.371126\pi$
$853$	−7.73248	+	48.8210i	−0.264755	+	1.67160i	−0.658655	+	0.752445i	$0.728874\pi$
$854$	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	−0.601199	−	0.799099i	$-0.705310\pi$
$857$	5.79343	−	5.79343i	0.197900	−	0.197900i	0.799099	+	0.601199i	$0.205310\pi$
$858$	−15.2205	−	0.899173i	−0.519619	−	0.0306973i
$859$	−3.26295	−	1.06020i	−0.111330	−	0.0361734i	0.252822	−	0.967513i	$-0.418641\pi$
$859$	−3.26295	−	1.06020i	−0.111330	−	0.0361734i	−0.364152	+	0.931339i	$0.618641\pi$
$860$		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	−0.796354	−	0.604830i	$-0.793241\pi$
$863$	−22.7707	+	11.6022i	−0.775122	+	0.394944i	0.0212325	+	0.999775i	$0.493241\pi$
$864$	−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	−0.535759	−	0.844371i	$-0.679975\pi$
$877$	13.6895	−	26.8672i	0.462262	−	0.907241i	0.998022	−	0.0628704i	$-0.0200255\pi$
$878$	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	−0.0798773	+	0.996805i	$0.525453\pi$
$881$	−29.7770	+	40.9845i	−1.00321	+	1.38080i	−0.923334	+	0.383997i	$0.874547\pi$
$882$	30.1812	−	11.1274i	1.01625	−	0.374678i
$883$	−11.1388	+	1.76422i	−0.374852	+	0.0593707i	−0.341018	−	0.940057i	$-0.610772\pi$
$883$	−11.1388	+	1.76422i	−0.374852	+	0.0593707i	−0.0338339	+	0.999427i	$0.510772\pi$
$884$	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	0.988684	−	0.150015i	$-0.0479321\pi$
$887$	8.52333	+	16.7280i	0.286186	+	0.561671i	−0.702498	+	0.711686i	$0.747932\pi$
$888$	−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	0.999477	−	0.0323248i	$-0.0102911\pi$
$907$	29.1272	+	29.1272i	0.967153	+	0.967153i	−0.0323248	+	0.999477i	$0.510291\pi$
$908$	−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	−0.288831	−	0.957380i	$-0.593266\pi$
$911$	1.21439	−	0.394580i	0.0402346	−	0.0130730i	0.329065	+	0.944307i	$0.393266\pi$
$912$	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	−0.980055	−	0.198728i	$-0.936319\pi$
$919$	−14.7998	+	20.3701i	−0.488199	+	0.671949i	0.491855	+	0.870677i	$0.336319\pi$
$920$		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	−0.915811	−	0.401609i	$-0.868451\pi$
$929$	−24.8975	+	18.0891i	−0.816859	+	0.593483i	0.0989519	+	0.995092i	$0.468451\pi$
$930$		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	−0.434063	−	0.900882i	$-0.642921\pi$
$937$	1.21310	−	0.618103i	0.0396301	−	0.0201925i	0.473693	+	0.880690i	$0.342921\pi$
$938$	−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	0.0711384	−	0.997466i	$-0.477337\pi$
$941$	−14.0374	−	4.56102i	−0.457606	−	0.148685i	−0.528744	+	0.848781i	$0.677337\pi$
$942$	−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	−0.998897	−	0.0469536i	$-0.985049\pi$
$947$	−1.05799	+	6.67988i	−0.0343800	+	0.217067i	0.964517	+	0.264021i	$0.0850487\pi$
$948$	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	0.422633	−	0.906301i	$-0.361106\pi$
$953$	16.8097	+	2.66239i	0.544519	+	0.0862434i	0.121886	+	0.992544i	$0.461106\pi$
$954$	−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	−0.864972	−	0.501820i	$-0.832664\pi$
$967$	−6.13865	−	38.7579i	−0.197406	−	1.24637i	0.667566	−	0.744550i	$-0.267336\pi$
$968$	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	0.992688	−	0.120710i	$-0.0385171\pi$
$971$	17.7969	+	24.4953i	0.571129	+	0.786091i	−0.421559	+	0.906801i	$0.638517\pi$
$972$	−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	−0.266044	−	0.963961i	$-0.585717\pi$
$977$	−37.5797	−	19.1478i	−1.20228	−	0.612593i	−0.936238	+	0.351368i	$0.885717\pi$
$978$	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	−0.997215	−	0.0745867i	$-0.976236\pi$
$983$	−2.25288	−	14.2241i	−0.0718557	−	0.453679i	0.925359	−	0.379092i	$-0.123764\pi$
$984$	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	−0.943187	−	0.332262i	$-0.892188\pi$
$991$	0.477429	−	1.46938i	0.0151660	−	0.0466762i	0.958353	+	0.285586i	$0.0921882\pi$
$992$	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	0.874329	−	0.485333i	$-0.161302\pi$
$997$	49.1277	+	7.78106i	1.55589	+	0.246429i	0.681560	+	0.731762i	$0.261302\pi$
$998$	−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.107.8		80
3.2	odd	2	inner	750.2.l.a.107.3		80
5.2	odd	4		150.2.l.a.83.5	yes	80
5.3	odd	4		750.2.l.b.143.6		80
5.4	even	2		750.2.l.c.107.3		80
15.2	even	4		150.2.l.a.83.10	yes	80
15.8	even	4		750.2.l.b.143.1		80
15.14	odd	2		750.2.l.c.107.8		80
25.3	odd	20	inner	750.2.l.a.743.3		80
25.4	even	10		150.2.l.a.47.10	yes	80
25.21	even	5		750.2.l.b.257.1		80
25.22	odd	20		750.2.l.c.743.8		80
75.29	odd	10		150.2.l.a.47.5	✓	80
75.47	even	20		750.2.l.c.743.3		80
75.53	even	20	inner	750.2.l.a.743.8		80
75.71	odd	10		750.2.l.b.257.6		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.47.5	✓	80	75.29	odd	10
150.2.l.a.47.10	yes	80	25.4	even	10
150.2.l.a.83.5	yes	80	5.2	odd	4
150.2.l.a.83.10	yes	80	15.2	even	4
750.2.l.a.107.3		80	3.2	odd	2	inner
750.2.l.a.107.8		80	1.1	even	1	trivial
750.2.l.a.743.3		80	25.3	odd	20	inner
750.2.l.a.743.8		80	75.53	even	20	inner
750.2.l.b.143.1		80	15.8	even	4
750.2.l.b.143.6		80	5.3	odd	4
750.2.l.b.257.1		80	25.21	even	5
750.2.l.b.257.6		80	75.71	odd	10
750.2.l.c.107.3		80	5.4	even	2
750.2.l.c.107.8		80	15.14	odd	2
750.2.l.c.743.3		80	75.47	even	20
750.2.l.c.743.8		80	25.22	odd	20

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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