LMFDB - Embedded newform 750.2.l.a.107.3

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			107.3
Character	$\chi$	$=$	750.107
Dual form			750.2.l.a.743.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.891007 - 0.453990i) q^{2} +(0.102145 + 1.72904i) q^{3} +(0.587785 + 0.809017i) q^{4} +(0.693954 - 1.58696i) q^{6} +(2.97677 + 2.97677i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-2.97913 + 0.353226i) q^{9} +O(q^{10})$	\(q+(-0.891007 - 0.453990i) q^{2} +(0.102145 + 1.72904i) q^{3} +(0.587785 + 0.809017i) q^{4} +(0.693954 - 1.58696i) q^{6} +(2.97677 + 2.97677i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-2.97913 + 0.353226i) q^{9} +(-4.73921 + 1.53986i) q^{11} +(-1.33878 + 1.09894i) 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} +(2.81479 + 1.03777i) q^{18} +(-1.09331 + 1.50481i) q^{19} +(-4.84289 + 5.45101i) q^{21} +(4.92175 + 0.779529i) q^{22} +(-0.951606 + 1.86763i) q^{23} +(1.69177 - 0.371369i) q^{24} -1.76655i q^{26} +(-0.915046 - 5.11495i) 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} +(-3.14657 - 8.03698i) q^{33} +(-1.35733 - 0.441023i) q^{34} +(-2.03686 - 2.20255i) q^{36} +(2.29429 - 1.16900i) q^{37} +(1.65732 - 0.844446i) q^{38} +(-2.63959 + 1.54746i) q^{39} +(3.58757 + 1.16567i) q^{41} +(6.78975 - 2.65826i) 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} +(-1.67598 - 0.437156i) q^{48} +10.7224i q^{49} +(0.530010 + 2.41446i) q^{51} +(-0.801995 + 1.57400i) q^{52} +(-5.05783 - 0.801081i) q^{53} +(-1.50683 + 4.97287i) q^{54} +(2.47446 - 3.40580i) q^{56} +(-2.71355 - 1.73666i) 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} +(-9.91968 - 7.81673i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-0.845099 + 8.58951i) q^{66} +(1.01259 + 6.39326i) q^{67} +(1.00917 + 1.00917i) q^{68} +(-3.32641 - 1.45459i) q^{69} +(-8.85681 - 12.1904i) q^{71} +(0.814916 + 2.88720i) q^{72} +(8.23800 + 4.19747i) q^{73} -2.57494 q^{74} -1.86005 q^{76} +(-18.6914 - 9.52374i) q^{77} +(3.05442 - 0.180445i) q^{78} +(-2.20434 - 3.03401i) q^{79} +(8.75046 - 2.10462i) q^{81} +(-2.66735 - 2.66735i) q^{82} +(2.63941 + 16.6646i) q^{83} +(-7.25654 - 0.713952i) q^{84} +(8.42648 - 2.73793i) q^{86} +(6.22047 + 7.57807i) 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} +(6.04544 - 9.44605i) q^{93} +(2.75161 - 3.78726i) q^{94} +(1.29484 + 1.15039i) 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
$3$	0.102145	+	1.72904i	0.0589737	+	0.998260i
$3$	0.102145	+	1.72904i	0.0589737	+	0.998260i
$4$	0.587785	+	0.809017i	0.293893	+	0.404508i
$5$		0			0
$5$		0			0
$6$	0.693954	−	1.58696i	0.283305	−	0.647872i
$7$	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
$9$	−2.97913	+	0.353226i	−0.993044	+	0.117742i
$10$		0			0
$11$	−4.73921	+	1.53986i	−1.42893	+	0.464286i	−0.918426	−	0.395592i	$-0.870539\pi$
$11$	−4.73921	+	1.53986i	−1.42893	+	0.464286i	−0.510499	+	0.859878i	$0.670539\pi$
$12$	−1.33878	+	1.09894i	−0.386473	+	0.317236i
$13$	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	0.0168665	−	0.999858i	$-0.494631\pi$
$17$	1.40961	−	0.223260i	0.341881	−	0.0541486i	0.325014	+	0.945709i	$0.394631\pi$
$18$	2.81479	+	1.03777i	0.663452	+	0.244605i
$19$	−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
$21$	−4.84289	+	5.45101i	−1.05680	+	1.18951i
$22$	4.92175	+	0.779529i	1.04932	+	0.166196i
$23$	−0.951606	+	1.86763i	−0.198424	+	0.389428i	−0.968682	−	0.248303i	$-0.920127\pi$
$23$	−0.951606	+	1.86763i	−0.198424	+	0.389428i	0.770259	+	0.637731i	$0.220127\pi$
$24$	1.69177	−	0.371369i	0.345331	−	0.0758053i
$25$		0			0
$26$		−	1.76655i		−	0.346448i
$27$	−0.915046	−	5.11495i	−0.176101	−	0.984372i
$28$	−0.658557	+	4.15797i	−0.124456	+	0.785782i
$29$	4.57938	−	3.32712i	0.850370	−	0.617830i	−0.0748779	−	0.997193i	$-0.523857\pi$
$29$	4.57938	−	3.32712i	0.850370	−	0.617830i	0.925248	+	0.379363i	$0.123857\pi$
$30$		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
$33$	−3.14657	−	8.03698i	−0.547747	−	1.39906i
$34$	−1.35733	−	0.441023i	−0.232780	−	0.0756348i
$35$		0			0
$36$	−2.03686	−	2.20255i	−0.339476	−	0.367091i
$37$	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
$39$	−2.63959	+	1.54746i	−0.422673	+	0.247791i
$40$		0			0
$41$	3.58757	+	1.16567i	0.560285	+	0.182048i	0.575449	−	0.817837i	$-0.304827\pi$
$41$	3.58757	+	1.16567i	0.560285	+	0.182048i	−0.0151644	+	0.999885i	$0.504827\pi$
$42$	6.78975	−	2.65826i	1.04768	−	0.410179i
$43$	−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	$0.160908\pi$
$47$	−0.732319	+	4.62368i	−0.106820	+	0.674433i	−0.981749	+	0.190182i	$0.939092\pi$
$48$	−1.67598	−	0.437156i	−0.241906	−	0.0630980i
$49$			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	$-0.564397\pi$
$53$	−5.05783	−	0.801081i	−0.694746	−	0.110037i	−0.493813	+	0.869568i	$0.664397\pi$
$54$	−1.50683	+	4.97287i	−0.205053	+	0.676722i
$55$		0			0
$56$	2.47446	−	3.40580i	0.330663	−	0.455119i
$57$	−2.71355	−	1.73666i	−0.359419	−	0.230027i
$58$	−5.59074	+	0.885486i	−0.734100	+	0.116270i
$59$	−3.44032	+	10.5882i	−0.447892	+	1.37847i	0.431389	+	0.902166i	$0.358024\pi$
$59$	−3.44032	+	10.5882i	−0.447892	+	1.37847i	−0.879281	+	0.476303i	$0.841976\pi$
$60$		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
$63$	−9.91968	−	7.81673i	−1.24976	−	0.984816i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$		0			0
$66$	−0.845099	+	8.58951i	−0.104025	+	1.05730i
$67$	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
$69$	−3.32641	−	1.45459i	−0.400452	−	0.175112i
$70$		0			0
$71$	−8.85681	−	12.1904i	−1.05111	−	1.44673i	−0.887842	−	0.460147i	$-0.847797\pi$
$71$	−8.85681	−	12.1904i	−1.05111	−	1.44673i	−0.163268	−	0.986582i	$-0.552203\pi$
$72$	0.814916	+	2.88720i	0.0960388	+	0.340260i
$73$	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
$78$	3.05442	−	0.180445i	0.345845	−	0.0204313i
$79$	−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
$81$	8.75046	−	2.10462i	0.972274	−	0.233846i
$82$	−2.66735	−	2.66735i	−0.294559	−	0.294559i
$83$	2.63941	+	16.6646i	0.289713	+	1.82918i	0.517761	+	0.855525i	$0.326766\pi$
$83$	2.63941	+	16.6646i	0.289713	+	1.82918i	−0.228048	+	0.973650i	$0.573234\pi$
$84$	−7.25654	−	0.713952i	−0.791754	−	0.0778985i
$85$		0			0
$86$	8.42648	−	2.73793i	0.908650	−	0.295238i
$87$	6.22047	+	7.57807i	0.666904	+	0.812454i
$88$	2.26228	+	4.43998i	0.241160	+	0.473303i
$89$	0.351151	+	1.08073i	0.0372219	+	0.114557i	0.967941	−	0.251177i	$-0.0808178\pi$
$89$	0.351151	+	1.08073i	0.0372219	+	0.114557i	−0.930719	+	0.365735i	$0.880818\pi$
$90$		0			0
$91$	−2.29810	+	7.07281i	−0.240906	+	0.741432i
$92$	−2.07029	+	0.327901i	−0.215842	+	0.0341860i
$93$	6.04544	−	9.44605i	0.626883	−	0.979510i
$94$	2.75161	−	3.78726i	0.283807	−	0.390626i
$95$		0			0
$96$	1.29484	+	1.15039i	0.132154	+	0.117411i
$97$	−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	$0.311410\pi$
$101$			16.6740i			1.65912i	−0.558415	+	0.829562i	$0.688590\pi$
$102$	0.623900	−	2.39192i	0.0617753	−	0.236835i
$103$	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	−0.176933	−	0.984223i	$-0.556618\pi$
$107$	8.35067	−	8.35067i	0.807290	−	0.807290i	0.984223	+	0.176933i	$0.0566176\pi$
$108$	3.60023	−	3.74678i	0.346432	−	0.360534i
$109$	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
$111$	2.25559	+	3.84749i	0.214091	+	0.365188i
$112$	−3.75095	+	1.91121i	−0.354432	+	0.180592i
$113$	−1.33349	+	0.679445i	−0.125444	+	0.0639168i	−0.515586	−	0.856838i	$-0.672426\pi$
$113$	−1.33349	+	0.679445i	−0.125444	+	0.0639168i	0.390142	+	0.920755i	$0.372426\pi$
$114$	1.62936	+	2.77931i	0.152604	+	0.260306i
$115$		0			0
$116$	5.38339	+	1.74917i	0.499835	+	0.162406i
$117$	−2.94523	−	4.40588i	−0.272286	−	0.407324i
$118$	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
$123$	−1.64904	+	6.32211i	−0.148689	+	0.570046i
$124$		−	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
$129$	−11.4724	−	10.1926i	−1.01009	−	0.897404i
$130$		0			0
$131$	−3.74251	+	5.15112i	−0.326984	+	0.450055i	−0.940584	−	0.339562i	$-0.889721\pi$
$131$	−3.74251	+	5.15112i	−0.326984	+	0.450055i	0.613599	+	0.789618i	$0.289721\pi$
$132$	4.65255	−	7.26964i	0.404952	−	0.632741i
$133$	−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	$-0.206165\pi$
$137$	−1.86549	−	3.66124i	−0.159380	−	0.312800i	−0.956862	+	0.290542i	$0.906165\pi$
$138$	2.30348	+	2.80621i	0.196085	+	0.238880i
$139$	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
$141$	−8.06931	−	0.793919i	−0.679559	−	0.0668600i
$142$	2.35717	+	14.8826i	0.197809	+	1.24892i
$143$	−6.22457	−	6.22457i	−0.520525	−	0.520525i
$144$	0.584665	−	2.94248i	0.0487220	−	0.245206i
$145$		0			0
$146$	−5.43450	−	7.47994i	−0.449762	−	0.619045i
$147$	−18.5394	+	1.09524i	−1.52910	+	0.0903339i
$148$	2.29429	+	1.16900i	0.188589	+	0.0960909i
$149$	−5.13270			−0.420487			−0.210244	−	0.977649i	$-0.567426\pi$
$149$	−5.13270			−0.420487			−0.210244	+	0.977649i	$0.567426\pi$
$150$		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
$153$	−4.12055	+	1.16303i	−0.333127	+	0.0940256i
$154$	12.3305	+	16.9714i	0.993617	+	1.36760i
$155$		0			0
$156$	−2.80343	−	1.22590i	−0.224454	−	0.0981506i
$157$	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
$159$	0.868465	−	8.82699i	0.0688737	−	0.700026i
$160$		0			0
$161$	−8.39223	+	2.72680i	−0.661401	+	0.214902i
$162$	−8.75219	−	2.09740i	−0.687637	−	0.164787i
$163$	−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	0.521734	−	0.853109i	$-0.325286\pi$
$167$	16.5614	−	2.62306i	1.28156	−	0.202979i	0.759823	+	0.650130i	$0.225286\pi$
$168$	6.14150	+	3.93054i	0.473827	+	0.303247i
$169$	5.80692	−	7.99254i	0.446686	−	0.614810i
$170$		0			0
$171$	2.72558	−	4.86922i	0.208430	−	0.372359i
$172$	−8.75104	−	1.38603i	−0.667260	−	0.105684i
$173$	2.03214	−	3.98829i	0.154500	−	0.303224i	−0.800763	−	0.598982i	$-0.795572\pi$
$173$	2.03214	−	3.98829i	0.154500	−	0.303224i	0.955263	+	0.295758i	$0.0955721\pi$
$174$	−2.10211	−	9.57614i	−0.159360	−	0.725966i
$175$		0			0
$176$		−	4.98310i		−	0.375615i
$177$	−18.6588	−	4.86690i	−1.40248	−	0.365819i
$178$	0.177764	−	1.12236i	0.0133240	−	0.0841243i
$179$	0.141142	−	0.102546i	0.0105495	−	0.00766463i	−0.582498	−	0.812832i	$-0.697925\pi$
$179$	0.141142	−	0.102546i	0.0105495	−	0.00766463i	0.593047	+	0.805167i	$0.297925\pi$
$180$		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
$183$	15.6568	−	6.12980i	1.15738	−	0.453128i
$184$	1.99350	+	0.647728i	0.146963	+	0.0477511i
$185$		0			0
$186$	−9.67494	+	5.67192i	−0.709401	+	0.415885i
$187$	−6.33665	+	3.22868i	−0.463382	+	0.236105i
$188$	−4.17108	+	2.12527i	−0.304207	+	0.155001i
$189$	12.5022	−	17.9499i	0.909398	−	1.30567i
$190$		0			0
$191$	17.5527	+	5.70322i	1.27007	+	0.412671i	0.865072	−	0.501647i	$-0.167272\pi$
$191$	17.5527	+	5.70322i	1.27007	+	0.412671i	0.404998	+	0.914318i	$0.367272\pi$
$192$	−0.631448	−	1.61285i	−0.0455708	−	0.116397i
$193$	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	$0.199194\pi$
$197$	−1.98370	+	12.5246i	−0.141333	+	0.892341i	−0.951836	+	0.306607i	$0.900806\pi$
$198$	−14.9379	−	0.583828i	−1.06159	−	0.0414909i
$199$			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
$204$	−1.64181	+	1.84797i	−0.114950	+	0.129384i
$205$		0			0
$206$	−1.55935	+	2.14627i	−0.108645	+	0.149537i
$207$	2.17526	−	5.90005i	0.151191	−	0.410082i
$208$	−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
$213$	20.1729	−	16.5589i	1.38222	−	1.13460i
$214$	−11.2316	+	3.64938i	−0.767778	+	0.249466i
$215$		0			0
$216$	−4.90883	+	1.70393i	−0.334004	+	0.115938i
$217$	−4.26413	−	26.9226i	−0.289468	−	1.82763i
$218$	−9.41758	−	9.41758i	−0.637839	−	0.637839i
$219$	−6.41610	+	14.6725i	−0.433560	+	0.991479i
$220$		0			0
$221$	1.48191	+	2.03968i	0.0996842	+	0.137204i
$222$	−0.263018	−	4.45216i	−0.0176526	−	0.298809i
$223$	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	0.703246	−	0.710947i	$-0.251733\pi$
$227$	8.15754	+	4.15647i	0.541435	+	0.275875i	−0.161811	+	0.986822i	$0.551733\pi$
$228$	−0.189996	−	3.21610i	−0.0125828	−	0.212991i
$229$	−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
$231$	14.5576	−	33.2909i	0.957823	−	2.19038i
$232$	−4.00253	−	4.00253i	−0.262779	−	0.262779i
$233$	−2.15478	−	13.6047i	−0.141164	−	0.891276i	−0.952021	−	0.306032i	$-0.900999\pi$
$233$	−2.15478	−	13.6047i	−0.141164	−	0.891276i	0.810857	−	0.585244i	$-0.199001\pi$
$234$	0.623990	+	5.26277i	0.0407915	+	0.344038i
$235$		0			0
$236$	−10.5882	+	3.44032i	−0.689234	+	0.223946i
$237$	5.02075	−	4.12129i	0.326133	−	0.267706i
$238$	−2.72764	−	5.35329i	−0.176806	−	0.347002i
$239$	6.40747	+	19.7202i	0.414465	+	1.27559i	0.912729	+	0.408566i	$0.133971\pi$
$239$	6.40747	+	19.7202i	0.414465	+	1.27559i	−0.498264	+	0.867025i	$0.666029\pi$
$240$		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
$243$	4.53278	+	14.9149i	0.290778	+	0.956791i
$244$	5.70595	−	7.85356i	0.365286	−	0.502773i
$245$		0			0
$246$	4.33948	−	4.88440i	0.276675	−	0.311418i
$247$	−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	$-0.0379520\pi$
$252$	0.493226	−	12.6197i	0.0310703	−	0.794969i
$253$	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	$-0.340103\pi$
$257$	21.7693	−	21.7693i	1.35793	−	1.35793i	0.876462	−	0.481471i	$-0.159897\pi$
$258$	5.59470	+	14.2900i	0.348311	+	0.889657i
$259$	10.3094	+	3.34973i	0.640596	+	0.208142i
$260$		0			0
$261$	−12.4674	+	11.5295i	−0.771711	+	0.713657i
$262$	5.67316	−	2.89062i	0.350489	−	0.178583i
$263$	4.93937	−	2.51673i	0.304574	−	0.155188i	−0.295023	−	0.955490i	$-0.595327\pi$
$263$	4.93937	−	2.51673i	0.304574	−	0.155188i	0.599598	+	0.800302i	$0.295327\pi$
$264$	−7.44580	+	4.36509i	−0.458257	+	0.268653i
$265$		0			0
$266$	7.44718	+	2.41974i	0.456616	+	0.148364i
$267$	−1.83276	+	0.717544i	−0.112163	+	0.0439130i
$268$	−4.57707	+	4.57707i	−0.279589	+	0.279589i
$269$	−2.80188	−	2.03568i	−0.170834	−	0.124118i	0.499083	−	0.866554i	$-0.333670\pi$
$269$	−2.80188	−	2.03568i	−0.170834	−	0.124118i	−0.669917	+	0.742436i	$0.733670\pi$
$270$		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
$273$	−12.4639	−	3.25104i	−0.754349	−	0.196762i
$274$			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
$279$	16.9501	+	9.48791i	1.01477	+	0.568026i
$280$		0			0
$281$	−5.67900	+	7.81648i	−0.338781	+	0.466292i	−0.944085	−	0.329702i	$-0.893052\pi$
$281$	−5.67900	+	7.81648i	−0.338781	+	0.466292i	0.605304	+	0.795994i	$0.293052\pi$
$282$	6.82938	+	4.37078i	0.406684	+	0.260276i
$283$	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
$288$	−1.85680	+	2.35633i	−0.109413	+	0.138848i
$289$	−14.2308	+	4.62387i	−0.837106	+	0.271992i
$290$		0			0
$291$	0.596229	−	6.06002i	0.0349516	−	0.355244i
$292$	1.44635	+	9.13189i	0.0846412	+	0.534403i
$293$	1.45604	+	1.45604i	0.0850625	+	0.0850625i	0.748358	−	0.663295i	$-0.230843\pi$
$293$	1.45604	+	1.45604i	0.0850625	+	0.0850625i	−0.663295	+	0.748358i	$0.730843\pi$
$294$	17.0159	+	7.44083i	0.992389	+	0.433958i
$295$		0			0
$296$	−1.51351	−	2.08317i	−0.0879710	−	0.121082i
$297$	12.2129	+	22.8318i	0.708665	+	1.32483i
$298$	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
$303$	−28.8299	+	1.70317i	−1.65624	+	0.0978446i
$304$	−1.09331	−	1.50481i	−0.0627057	−	0.0863069i
$305$		0			0
$306$	4.19945	+	0.834422i	0.240066	+	0.0477007i
$307$	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
$309$	4.57293	+	0.449918i	0.260145	+	0.0255950i
$310$		0			0
$311$	3.64396	−	1.18399i	0.206630	−	0.0671381i	−0.203873	−	0.978997i	$-0.565353\pi$
$311$	3.64396	−	1.18399i	0.206630	−	0.0671381i	0.410503	+	0.911859i	$0.365353\pi$
$312$	1.94133	+	2.36502i	0.109906	+	0.133893i
$313$	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	0.0912701	−	0.995826i	$-0.470907\pi$
$317$	8.64943	−	1.36994i	0.485800	−	0.0769432i	0.394530	+	0.918883i	$0.370907\pi$
$318$	−4.78118	+	7.47063i	−0.268115	+	0.418932i
$319$	−16.5794	+	22.8195i	−0.928266	+	1.27765i
$320$		0			0
$321$	15.2916	+	13.5856i	0.853494	+	0.758276i
$322$	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
$327$	−5.82224	+	22.3214i	−0.321971	+	1.23438i
$328$	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
$333$	−6.42206	+	4.29300i	−0.351927	+	0.235255i
$334$	−15.9471	−	5.18154i	−0.872588	−	0.283521i
$335$		0			0
$336$	−3.68769	−	6.29032i	−0.201180	−	0.343165i
$337$	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
$339$	−1.31099	−	2.23624i	−0.0712035	−	0.121456i
$340$		0			0
$341$	30.6862	+	9.97055i	1.66175	+	0.539935i
$342$	−4.63909	+	3.10112i	−0.250853	+	0.167690i
$343$	−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	$0.258823\pi$
$347$	−3.55504	+	22.4456i	−0.190844	+	1.20494i	−0.878082	+	0.478511i	$0.841177\pi$
$348$	−2.47449	+	9.48674i	−0.132646	+	0.508543i
$349$		−	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	0.341381	−	0.939925i	$-0.389106\pi$
$353$	7.05688	+	1.11770i	0.375600	+	0.0594892i	0.0342193	+	0.999414i	$0.489106\pi$
$354$	14.4156	+	12.8074i	0.766181	+	0.680704i
$355$		0			0
$356$	−0.667929	+	0.919325i	−0.0354002	+	0.0487241i
$357$	−5.60959	+	8.76503i	−0.296891	+	0.463894i
$358$	−0.172313	+	0.0272918i	−0.00910704	+	0.00144241i
$359$	3.28973	−	10.1247i	0.173625	−	0.534363i	−0.825943	−	0.563754i	$-0.809357\pi$
$359$	3.28973	−	10.1247i	0.173625	−	0.534363i	0.999568	+	0.0293907i	$0.00935671\pi$
$360$		0			0
$361$	4.80219	+	14.7796i	0.252747	+	0.777875i
$362$	−5.16520	−	10.1373i	−0.271477	−	0.532803i
$363$	15.1998	+	18.5171i	0.797780	+	0.971894i
$364$	−7.07281	+	2.29810i	−0.370716	+	0.120453i
$365$		0			0
$366$	−16.7331	−	1.64633i	−0.874656	−	0.0860551i
$367$	−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
$369$	−11.0996	−	2.20547i	−0.577822	−	0.114812i
$370$		0			0
$371$	−12.6714	−	17.4406i	−0.657865	−	0.905473i
$372$	11.1954	−	0.661387i	0.580456	−	0.0342913i
$373$	−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
$378$	−19.2886	+	10.3176i	−0.992099	+	0.530682i
$379$	−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
$381$	2.46210	+	1.07664i	0.126137	+	0.0551581i
$382$	−13.0504	−	13.0504i	−0.667715	−	0.667715i
$383$	2.67339	+	16.8791i	0.136604	+	0.862482i	0.956873	+	0.290505i	$0.0938233\pi$
$383$	2.67339	+	16.8791i	0.136604	+	0.862482i	−0.820270	+	0.571977i	$0.806177\pi$
$384$	−0.169593	+	1.72373i	−0.00865451	+	0.0879636i
$385$		0			0
$386$	−4.45958	+	1.44901i	−0.226987	+	0.0737525i
$387$	16.4514	−	20.8774i	0.836274	−	1.06126i
$388$	−1.59607	−	3.13246i	−0.0810281	−	0.159027i
$389$	4.34112	+	13.3606i	0.220104	+	0.677409i	0.998752	+	0.0499484i	$0.0159057\pi$
$389$	4.34112	+	13.3606i	0.220104	+	0.677409i	−0.778648	+	0.627461i	$0.784094\pi$
$390$		0			0
$391$	−0.924425	+	2.84509i	−0.0467502	+	0.143882i
$392$	10.5904	−	1.67735i	0.534894	−	0.0847189i
$393$	−9.28875	−	5.94477i	−0.468556	−	0.299874i
$394$	7.45354	−	10.2589i	0.375504	−	0.516837i
$395$		0			0
$396$	13.0447	+	7.30186i	0.655521	+	0.366932i
$397$	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	$-0.738613\pi$
$401$		−	29.3144i		−	1.46389i	0.681364	−	0.731945i	$-0.261387\pi$
$402$	10.8485	+	2.82969i	0.541074	+	0.141132i
$403$	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
$408$	2.30182	−	0.901190i	0.113957	−	0.0446155i
$409$	−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
$411$	6.13986	−	3.59948i	0.302857	−	0.177549i
$412$	2.36378	−	1.20440i	0.116455	−	0.0593368i
$413$	−41.7598	+	21.2777i	−2.05487	+	1.04701i
$414$	−4.61674	+	4.26944i	−0.226901	+	0.209831i
$415$		0			0
$416$	1.68008	+	0.545893i	0.0823729	+	0.0267646i
$417$	6.74458	+	17.2270i	0.330283	+	0.843611i
$418$	−6.55405	+	6.55405i	−0.320569	+	0.320569i
$419$	−8.86483	−	6.44067i	−0.433075	−	0.314648i	0.349802	−	0.936824i	$-0.386249\pi$
$419$	−8.86483	−	6.44067i	−0.433075	−	0.314648i	−0.782877	+	0.622176i	$0.786249\pi$
$420$		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
$423$	0.548470	−	14.0332i	0.0266675	−	0.682319i
$424$			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
$429$	10.1267	−	11.3983i	0.488922	−	0.550316i
$430$		0			0
$431$	−2.55158	+	3.51195i	−0.122905	+	0.169164i	−0.866036	−	0.499982i	$-0.833340\pi$
$431$	−2.55158	+	3.51195i	−0.122905	+	0.169164i	0.743131	+	0.669146i	$0.233340\pi$
$432$	5.14737	+	0.710346i	0.247653	+	0.0341765i
$433$	−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
$438$	12.3780	−	10.1605i	0.591443	−	0.485487i
$439$	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
$441$	−3.78742	−	31.9434i	−0.180353	−	1.52111i
$442$	−0.394399	−	2.49014i	−0.0187597	−	0.118444i
$443$	11.8995	+	11.8995i	0.565363	+	0.565363i	0.930826	−	0.365463i	$-0.119089\pi$
$443$	11.8995	+	11.8995i	0.565363	+	0.565363i	−0.365463	+	0.930826i	$0.619089\pi$
$444$	−1.78689	+	4.08631i	−0.0848019	+	0.193928i
$445$		0			0
$446$	−3.65892	−	5.03607i	−0.173255	−	0.238465i
$447$	−0.524282	−	8.87463i	−0.0247977	−	0.419755i
$448$	−3.75095	−	1.91121i	−0.177216	−	0.0902960i
$449$	3.55771			0.167899			0.0839495	−	0.996470i	$-0.473247\pi$
$449$	3.55771			0.167899			0.0839495	+	0.996470i	$0.473247\pi$
$450$		0			0
$451$	−18.7973			−0.885128
$452$	−1.33349	−	0.679445i	−0.0627219	−	0.0319584i
$453$	2.05633	+	34.8079i	0.0966149	+	1.63542i
$454$	−5.38142	−	7.40689i	−0.252563	−	0.347623i
$455$		0			0
$456$	−1.29079	+	2.95182i	−0.0604468	+	0.138232i
$457$	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
$459$	−2.43182	−	7.00579i	−0.113508	−	0.327002i
$460$		0			0
$461$	30.4642	−	9.89843i	1.41886	−	0.461016i	0.503621	−	0.863925i	$-0.332001\pi$
$461$	30.4642	−	9.89843i	1.41886	−	0.461016i	0.915240	+	0.402908i	$0.132001\pi$
$462$	−28.0847	+	23.0534i	−1.30662	+	1.07254i
$463$	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	−0.968295	−	0.249811i	$-0.919632\pi$
$467$	−39.1577	+	6.20197i	−1.81200	+	0.286993i	−0.843707	+	0.536804i	$0.819632\pi$
$468$	1.83327	−	4.97245i	0.0847429	−	0.229852i
$469$	−16.0170	+	22.0455i	−0.739598	+	1.01797i
$470$		0			0
$471$	−11.6080	+	13.0657i	−0.534870	+	0.602034i
$472$	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
$477$	15.3509	+	0.599970i	0.702869	+	0.0274707i
$478$	3.24367	−	20.4797i	0.148362	−	0.936721i
$479$	10.9031	−	7.92157i	0.498176	−	0.361946i	−0.310144	−	0.950690i	$-0.600377\pi$
$479$	10.9031	−	7.92157i	0.498176	−	0.361946i	0.808320	+	0.588744i	$0.200377\pi$
$480$		0			0
$481$	3.68001	+	2.67368i	0.167794	+	0.121910i
$482$	4.39969	−	4.39969i	0.200400	−	0.200400i
$483$	−5.57197	−	14.2319i	−0.253533	−	0.647576i
$484$	13.1543	+	4.27411i	0.597925	+	0.194278i
$485$		0			0
$486$	2.73249	−	15.3471i	0.123948	−	0.696159i
$487$	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
$489$	8.39789	−	4.92325i	0.379766	−	0.222637i
$490$		0			0
$491$	−15.8067	−	5.13592i	−0.713348	−	0.231781i	−0.0702111	−	0.997532i	$-0.522367\pi$
$491$	−15.8067	−	5.13592i	−0.713348	−	0.231781i	−0.643137	+	0.765751i	$0.722367\pi$
$492$	−6.08398	+	2.38195i	−0.274287	+	0.107386i
$493$	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
$498$	28.2776	+	7.37582i	1.26715	+	0.330519i
$499$			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	0.804990	−	0.593289i	$-0.202171\pi$
$503$	31.1126	+	4.92776i	1.38724	+	0.219718i	0.582255	+	0.813007i	$0.302171\pi$
$504$	−6.16871	+	11.0204i	−0.274776	+	0.490886i
$505$		0			0
$506$	−6.13944	+	8.45021i	−0.272931	+	0.375658i
$507$	14.4125	+	9.22397i	0.640083	+	0.409651i
$508$	1.53236	−	0.242702i	0.0679876	−	0.0107682i
$509$	−0.189892	+	0.584428i	−0.00841683	+	0.0259043i	−0.955177	−	0.296036i	$-0.904335\pi$
$509$	−0.189892	+	0.584428i	−0.00841683	+	0.0259043i	0.946760	+	0.321941i	$0.104335\pi$
$510$		0			0
$511$	12.0277	+	37.0176i	0.532076	+	1.63756i
$512$	0.453990	+	0.891007i	0.0200637	+	0.0393773i
$513$	8.69747	+	4.21525i	0.384003	+	0.186108i
$514$	−29.2797	+	9.51354i	−1.29147	+	0.419624i
$515$		0			0
$516$	1.50261	−	15.2724i	0.0661489	−	0.672332i
$517$	−3.64922	−	23.0403i	−0.160493	−	1.01331i
$518$	−7.66501	−	7.66501i	−0.336781	−	0.336781i
$519$	7.10348	+	3.10625i	0.311808	+	0.136349i
$520$		0			0
$521$	−19.3712	−	26.6622i	−0.848668	−	1.16809i	−0.984155	−	0.177312i	$-0.943260\pi$
$521$	−19.3712	−	26.6622i	−0.848668	−	1.16809i	0.135487	−	0.990779i	$-0.456740\pi$
$522$	16.3428	−	4.61278i	0.715304	−	0.201896i
$523$	−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
$528$	8.61596	−	0.509001i	0.374962	−	0.0221514i
$529$	10.9366	+	15.0529i	0.475503	+	0.654474i
$530$		0			0
$531$	6.50914	−	32.7589i	0.282472	−	1.42162i
$532$	−5.53695	−	5.53695i	−0.240057	−	0.240057i
$533$	1.04244	+	6.58172i	0.0451532	+	0.285086i
$534$	1.95876	+	0.192717i	0.0847636	+	0.00833967i
$535$		0			0
$536$	6.15614	−	2.00025i	0.265905	−	0.0863977i
$537$	0.191722	+	0.233565i	0.00827343	+	0.0100791i
$538$	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
$543$	−10.6226	+	16.5979i	−0.455860	+	0.712285i
$544$	0.838876	−	1.15461i	0.0359665	−	0.0495036i
$545$		0			0
$546$	9.62947	+	8.55518i	0.412103	+	0.366128i
$547$	−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
$552$	−0.916318	+	3.51300i	−0.0390011	+	0.149523i
$553$	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	$-0.928707\pi$
$557$	−17.7694	+	17.7694i	−0.752915	+	0.752915i	0.222107	+	0.975022i	$0.428707\pi$
$558$	−10.7952	−	16.1490i	−0.456998	−	0.683640i
$559$	−14.8858	−	4.83667i	−0.629600	−	0.204570i
$560$		0			0
$561$	−6.22977	−	10.6265i	−0.263021	−	0.448651i
$562$	8.60864	−	4.38632i	0.363133	−	0.185026i
$563$	−9.23868	+	4.70734i	−0.389364	+	0.198391i	−0.637703	−	0.770282i	$-0.720115\pi$
$563$	−9.23868	+	4.70734i	−0.389364	+	0.198391i	0.248339	+	0.968673i	$0.420115\pi$
$564$	−4.10073	−	6.99487i	−0.172672	−	0.294537i
$565$		0			0
$566$	−0.970373	−	0.315293i	−0.0407878	−	0.0132528i
$567$	32.3131	+	19.7832i	1.35702	+	0.830816i
$568$	−10.6548	+	10.6548i	−0.447064	+	0.447064i
$569$	−15.6879	−	11.3979i	−0.657671	−	0.477826i	0.208205	−	0.978085i	$-0.433238\pi$
$569$	−15.6879	−	11.3979i	−0.657671	−	0.477826i	−0.865876	+	0.500259i	$0.833238\pi$
$570$		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
$573$	−8.06815	+	30.9318i	−0.337052	+	1.29220i
$574$		−	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
$579$	6.07162	+	5.39425i	0.252328	+	0.224177i
$580$		0			0
$581$	−41.7498	+	57.4636i	−1.73207	+	2.38399i
$582$	−3.28243	+	5.12883i	−0.136061	+	0.212597i
$583$	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	$0.0315774\pi$
$587$	11.8794	+	23.3146i	0.490314	+	0.962295i	−0.504770	+	0.863254i	$0.668423\pi$
$588$	−11.7832	−	14.3549i	−0.485932	−	0.591986i
$589$	11.4543	−	3.72172i	0.471966	−	0.153351i
$590$		0			0
$591$	−21.8581	−	2.15056i	−0.899122	−	0.0884623i
$592$	0.402809	+	2.54323i	0.0165553	+	0.104526i
$593$	−23.6228	−	23.6228i	−0.970072	−	0.970072i	0.0294930	−	0.999565i	$-0.490611\pi$
$593$	−23.6228	−	23.6228i	−0.970072	−	0.970072i	−0.999565	+	0.0294930i	$0.990611\pi$
$594$	−0.516378	−	25.8878i	−0.0211872	−	1.06219i
$595$		0			0
$596$	−3.01693	−	4.15244i	−0.123578	−	0.170091i
$597$	−2.81145	+	0.166091i	−0.115065	+	0.00679764i
$598$	3.29926	+	1.68106i	0.134917	+	0.0687435i
$599$	7.73976			0.316238			0.158119	−	0.987420i	$-0.449457\pi$
$599$	7.73976			0.316238			0.158119	+	0.987420i	$0.449457\pi$
$600$		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
$603$	−5.27491	−	18.6887i	−0.214811	−	0.761062i
$604$	11.8329	+	16.2867i	0.481476	+	0.662695i
$605$		0			0
$606$	26.4609	+	11.5710i	1.07490	+	0.470039i
$607$	−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
$609$	−4.04127	+	41.0751i	−0.163761	+	1.66445i
$610$		0			0
$611$	−7.86501	+	2.55550i	−0.318184	+	0.103384i
$612$	−3.36291	−	2.64998i	−0.135938	−	0.107119i
$613$	−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	0.348429	−	0.937335i	$-0.386715\pi$
$617$	24.0808	−	3.81403i	0.969458	−	0.153547i	0.621028	+	0.783788i	$0.286715\pi$
$618$	−3.87025	−	2.47695i	−0.155684	−	0.0996374i
$619$	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
$621$	10.4236	+	3.15845i	0.418285	+	0.126744i
$622$	−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
$627$	15.5343	+	4.05192i	0.620381	+	0.161818i
$628$	−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
$633$	19.4814	−	7.62720i	0.774318	−	0.303154i
$634$	−8.32864	−	2.70614i	−0.330772	−	0.107474i
$635$		0			0
$636$	7.65166	−	4.48577i	0.303408	−	0.177873i
$637$	−16.8771	+	8.59929i	−0.668693	+	0.340716i
$638$	25.1322	−	12.8055i	0.994992	−	0.506974i
$639$	30.6916	+	33.1882i	1.21414	+	1.31291i
$640$		0			0
$641$	−8.76326	−	2.84736i	−0.346128	−	0.112464i	0.130794	−	0.991410i	$-0.458247\pi$
$641$	−8.76326	−	2.84736i	−0.346128	−	0.112464i	−0.476922	+	0.878946i	$0.658247\pi$
$642$	−7.45716	−	19.0471i	−0.294311	−	0.751730i
$643$	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	$-0.545081\pi$
$647$	7.60579	−	48.0211i	0.299015	−	1.88790i	0.440167	−	0.897916i	$-0.354919\pi$
$648$	−3.44758	−	8.31350i	−0.135434	−	0.326585i
$649$		−	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	$-0.577171\pi$
$653$	−19.6349	−	3.10987i	−0.768375	−	0.121699i	−0.528302	+	0.849056i	$0.677171\pi$
$654$	15.3214	−	17.2453i	0.599113	−	0.674345i
$655$		0			0
$656$	−2.21724	+	3.05177i	−0.0865688	+	0.119152i
$657$	−26.0247	−	9.59494i	−1.01532	−	0.374334i
$658$	19.4647	−	3.08291i	0.758815	−	0.120184i
$659$	−9.29483	+	28.6066i	−0.362075	+	1.11435i	0.589717	+	0.807610i	$0.299239\pi$
$659$	−9.29483	+	28.6066i	−0.362075	+	1.11435i	−0.951792	+	0.306743i	$0.900761\pi$
$660$		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
$663$	−3.37531	+	2.77062i	−0.131086	+	0.107602i
$664$	16.0465	−	5.21383i	0.622726	−	0.202336i
$665$		0			0
$666$	7.67108	−	0.909535i	0.297248	−	0.0352438i
$667$	1.85606	+	11.7187i	0.0718670	+	0.453750i
$668$	11.8566	+	11.8566i	0.458747	+	0.458747i
$669$	−4.31981	+	9.87868i	−0.167014	+	0.381932i
$670$		0			0
$671$	28.4333	+	39.1351i	1.09766	+	1.51079i
$672$	0.430011	+	7.27889i	0.0165880	+	0.280789i
$673$	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	0.317280	−	0.948332i	$-0.397230\pi$
$677$	−6.85459	−	3.49259i	−0.263443	−	0.134231i	−0.580724	+	0.814101i	$0.697230\pi$
$678$	0.152871	+	2.58769i	0.00587099	+	0.0993795i
$679$	−8.69931	−	11.9736i	−0.333849	−	0.459503i
$680$		0			0
$681$	−6.35344	+	14.5292i	−0.243464	+	0.556762i
$682$	−22.8151	−	22.8151i	−0.873634	−	0.873634i
$683$	−0.454547	−	2.86990i	−0.0173928	−	0.109814i	0.977465	−	0.211099i	$-0.0677043\pi$
$683$	−0.454547	−	2.86990i	−0.0173928	−	0.109814i	−0.994857	+	0.101286i	$0.967704\pi$
$684$	5.54134	−	0.657019i	0.211878	−	0.0251217i
$685$		0			0
$686$	14.9035	−	4.84242i	0.569016	−	0.184885i
$687$	24.7614	−	20.3254i	0.944705	−	0.775463i
$688$	−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
$693$	59.0481	+	21.7702i	2.24305	+	0.826981i
$694$	13.3577	−	18.3852i	0.507050	−	0.697894i
$695$		0			0
$696$	6.51168	−	7.32936i	0.246824	−	0.277819i
$697$	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	$-0.283453\pi$
$702$	−9.03579	+	1.61647i	−0.341034	+	0.0610097i
$703$	−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
$708$	−7.02998	−	17.9560i	−0.264203	−	0.674828i
$709$	−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
$711$	7.63870	+	8.26008i	0.286474	+	0.309777i
$712$	1.01249	−	0.515891i	0.0379448	−	0.0193338i
$713$	12.0928	−	6.16161i	0.452880	−	0.230754i
$714$	8.97742	−	5.26300i	0.335971	−	0.196963i
$715$		0			0
$716$	0.165923	+	0.0539115i	0.00620082	+	0.00201477i
$717$	−33.4424	+	13.0931i	−1.24893	+	0.488970i
$718$	−7.52770	+	7.52770i	−0.280931	+	0.280931i
$719$	17.4118	+	12.6504i	0.649349	+	0.471780i	0.863049	−	0.505120i	$-0.168552\pi$
$719$	17.4118	+	12.6504i	0.649349	+	0.471780i	−0.213700	+	0.976899i	$0.568552\pi$
$720$		0			0
$721$	9.03534	−	6.56456i	0.336493	−	0.244477i
$722$	2.43102	−	15.3489i	0.0904734	−	0.571226i
$723$	−10.4281	−	2.72003i	−0.387825	−	0.101159i
$724$			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
$729$	−25.3254	+	9.36082i	−0.937977	+	0.346697i
$730$		0			0
$731$	−7.43254	+	10.2300i	−0.274902	+	0.378371i
$732$	14.1619	+	9.06358i	0.523440	+	0.335000i
$733$	−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
$738$	8.88856	+	7.00421i	0.327192	+	0.257828i
$739$	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
$741$	0.557260	−	5.66394i	0.0204715	−	0.208070i
$742$	3.37239	+	21.2924i	0.123804	+	0.781669i
$743$	−8.68111	−	8.68111i	−0.318479	−	0.318479i	0.529704	−	0.848183i	$-0.322303\pi$
$743$	−8.68111	−	8.68111i	−0.318479	−	0.318479i	−0.848183	+	0.529704i	$0.822303\pi$
$744$	−10.2755	−	4.49332i	−0.376717	−	0.164733i
$745$		0			0
$746$	2.67527	+	3.68219i	0.0979486	+	0.134815i
$747$	−13.7495	−	48.7137i	−0.503069	−	1.78234i
$748$	−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
$753$	6.51667	−	0.384982i	0.237481	−	0.0140295i
$754$	−5.87750	−	8.08969i	−0.214046	−	0.294609i
$755$		0			0
$756$	21.8704	−	0.436243i	0.795418	−	0.0158660i
$757$	−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
$759$	18.0044	+	1.77141i	0.653519	+	0.0642980i
$760$		0			0
$761$	6.88486	−	2.23703i	0.249576	−	0.0810921i	−0.181558	−	0.983380i	$-0.558114\pi$
$761$	6.88486	−	2.23703i	0.249576	−	0.0810921i	0.431133	+	0.902288i	$0.358114\pi$
$762$	−1.70496	−	2.07707i	−0.0617643	−	0.0752442i
$763$	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
$768$	0.933665	−	1.45886i	0.0336907	−	0.0526420i
$769$	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
$771$	39.8636	+	35.4163i	1.43565	+	1.27549i
$772$	4.63135	+	0.733534i	0.166686	+	0.0264005i
$773$	−15.0283	+	29.4947i	−0.540531	+	1.06085i	0.445655	+	0.895205i	$0.352971\pi$
$773$	−15.0283	+	29.4947i	−0.540531	+	1.06085i	−0.986185	+	0.165646i	$0.947029\pi$
$774$	−24.1365	+	11.1331i	−0.867568	+	0.400171i
$775$		0			0
$776$			3.51564i			0.126204i
$777$	−4.73875	+	18.1675i	−0.170002	+	0.651756i
$778$	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
$783$	−21.2084	−	20.3788i	−0.757925	−	0.728280i
$784$	−10.1976	−	3.31339i	−0.364199	−	0.118336i
$785$		0			0
$786$	5.57747	+	9.51383i	0.198942	+	0.339347i
$787$	−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
$789$	4.85606	+	8.28327i	0.172880	+	0.294892i
$790$		0			0
$791$	−5.99204	−	1.94693i	−0.213053	−	0.0692250i
$792$	−8.30795	−	12.4282i	−0.295210	−	0.441616i
$793$	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	$0.301842\pi$
$797$	−6.28166	+	39.6609i	−0.222508	+	1.40486i	−0.805603	+	0.592456i	$0.798158\pi$
$798$	−3.42312	+	13.1236i	−0.121177	+	0.464571i
$799$			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
$804$	−8.38144	−	7.44639i	−0.295591	−	0.262614i
$805$		0			0
$806$	−6.72327	+	9.25378i	−0.236817	+	0.325951i
$807$	3.23357	−	5.05249i	0.113827	−	0.177856i
$808$	16.4687	−	2.60839i	0.579367	−	0.0917627i
$809$	−5.01595	+	15.4375i	−0.176351	+	0.542753i	−0.999693	−	0.0247932i	$-0.992107\pi$
$809$	−5.01595	+	15.4375i	−0.176351	+	0.542753i	0.823341	+	0.567546i	$0.192107\pi$
$810$		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
$813$	−5.17730	−	6.30723i	−0.181576	−	0.221204i
$814$	12.2032	−	3.96505i	0.427721	−	0.138975i
$815$		0			0
$816$	−2.46007	−	0.242040i	−0.0861197	−	0.00847309i
$817$	−2.57808	−	16.2774i	−0.0901957	−	0.569473i
$818$	5.40870	+	5.40870i	0.189111	+	0.189111i
$819$	4.34803	−	21.8826i	0.151932	−	0.764640i
$820$		0			0
$821$	8.20025	+	11.2867i	0.286191	+	0.393907i	0.927772	−	0.373147i	$-0.121721\pi$
$821$	8.20025	+	11.2867i	0.286191	+	0.393907i	−0.641582	+	0.767055i	$0.721721\pi$
$822$	−7.10478	+	0.419726i	−0.247808	+	0.0146396i
$823$	−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	0.940266	−	0.340442i	$-0.110577\pi$
$827$	35.0129	+	17.8399i	1.21752	+	0.620356i	0.277251	+	0.960798i	$0.410577\pi$
$828$	6.05183	−	1.70814i	0.210316	−	0.0593620i
$829$	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
$831$	−39.4929	−	17.2697i	−1.36999	−	0.599079i
$832$	−1.24914	−	1.24914i	−0.0433060	−	0.0433060i
$833$	2.39388	+	15.1144i	0.0829430	+	0.523681i
$834$	1.81145	−	18.4114i	0.0627252	−	0.637534i
$835$		0			0
$836$	8.81517	−	2.86422i	0.304879	−	0.0990613i
$837$	−14.6736	+	30.2764i	−0.507193	+	1.04651i
$838$	4.97461	+	9.76323i	0.171845	+	0.337265i
$839$	10.2985	+	31.6954i	0.355542	+	1.09425i	0.955695	+	0.294360i	$0.0951066\pi$
$839$	10.2985	+	31.6954i	0.355542	+	1.09425i	−0.600152	+	0.799886i	$0.704893\pi$
$840$		0			0
$841$	0.939554	−	2.89165i	0.0323984	−	0.0997121i
$842$	13.8788	−	2.19818i	0.478294	−	0.0757544i
$843$	−14.0951	−	9.02079i	−0.485460	−	0.310692i
$844$	7.09981	−	9.77205i	0.244385	−	0.336368i
$845$		0			0
$846$	−6.85965	+	12.2547i	−0.235839	+	0.421325i
$847$	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
$852$	25.2538	+	6.58711i	0.865181	+	0.225671i
$853$	−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	−0.799099	−	0.601199i	$-0.794690\pi$
$857$	−5.79343	+	5.79343i	−0.197900	+	0.197900i	0.601199	+	0.799099i	$0.294690\pi$
$858$	−14.1977	+	5.55855i	−0.484701	+	0.189766i
$859$	−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
$861$	−23.7283	+	13.9107i	−0.808659	+	0.474075i
$862$	3.86786	−	1.97077i	0.131740	−	0.0671249i
$863$	22.7707	−	11.6022i	0.775122	−	0.394944i	−0.0212325	−	0.999775i	$-0.506759\pi$
$863$	22.7707	−	11.6022i	0.775122	−	0.394944i	0.796354	+	0.604830i	$0.206759\pi$
$864$	−4.26385	−	2.96978i	−0.145059	−	0.101034i
$865$		0			0
$866$	7.46455	+	2.42538i	0.253656	+	0.0824177i
$867$	−9.44845	−	24.1333i	−0.320886	−	0.819609i
$868$	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
$873$	10.5389	+	0.411899i	0.356687	+	0.0139407i
$874$			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
$879$	−2.36881	+	2.66627i	−0.0798980	+	0.0899309i
$880$		0			0
$881$	29.7770	−	40.9845i	1.00321	−	1.38080i	0.0798773	−	0.996805i	$-0.474547\pi$
$881$	29.7770	−	40.9845i	1.00321	−	1.38080i	0.923334	−	0.383997i	$-0.125453\pi$
$882$	−11.1274	+	30.1812i	−0.374678	+	1.01625i
$883$	−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	0.702498	−	0.711686i	$-0.252068\pi$
$887$	−8.52333	−	16.7280i	−0.286186	−	0.561671i	−0.988684	+	0.150015i	$0.952068\pi$
$888$	3.44727	−	2.82970i	0.115683	−	0.0949585i
$889$	6.21167	−	2.01830i	0.208333	−	0.0676914i
$890$		0			0
$891$	−38.2295	+	23.4487i	−1.28074	+	0.785562i
$892$	0.973793	+	6.14829i	0.0326050	+	0.205860i
$893$	−6.15712	−	6.15712i	−0.206040	−	0.206040i
$894$	−3.56186	+	8.14537i	−0.119126	+	0.272422i
$895$		0			0
$896$	2.47446	+	3.40580i	0.0826657	+	0.113780i
$897$	−0.378228	−	6.40235i	−0.0126287	−	0.213768i
$898$	−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
$903$	−3.80995	−	64.4918i	−0.126787	−	2.14615i
$904$	0.879683	+	1.21078i	0.0292578	+	0.0402699i
$905$		0			0
$906$	13.9703	−	31.9477i	0.464131	−	1.06139i
$907$	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
$909$	−5.88969	−	49.6740i	−0.195349	−	1.64758i
$910$		0			0
$911$	−1.21439	+	0.394580i	−0.0402346	+	0.0130730i	−0.329065	−	0.944307i	$-0.606734\pi$
$911$	−1.21439	+	0.394580i	−0.0402346	+	0.0130730i	0.288831	+	0.957380i	$0.406734\pi$
$912$	2.49020	−	2.04408i	0.0824587	−	0.0676864i
$913$	−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
$918$	−1.01379	+	7.34623i	−0.0334601	+	0.242462i
$919$	−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
$921$	−19.4911	+	21.9386i	−0.642252	+	0.722901i
$922$	−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
$927$	−0.310822	+	7.95272i	−0.0102087	+	0.261202i
$928$	0.885486	−	5.59074i	0.0290675	−	0.183525i
$929$	24.8975	−	18.0891i	0.816859	−	0.593483i	−0.0989519	−	0.995092i	$-0.531549\pi$
$929$	24.8975	−	18.0891i	0.816859	−	0.593483i	0.915811	+	0.401609i	$0.131549\pi$
$930$		0			0
$931$	−16.1352	−	11.7229i	−0.528809	−	0.384202i
$932$	9.73992	−	9.73992i	0.319042	−	0.319042i
$933$	2.41938	+	6.17960i	0.0792070	+	0.202311i
$934$	37.7054	+	12.2512i	1.23376	+	0.400872i
$935$		0			0
$936$	−3.89090	+	3.59820i	−0.127178	+	0.117611i
$937$	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
$939$	−34.1691	+	20.0316i	−1.11507	+	0.653707i
$940$		0			0
$941$	14.0374	+	4.56102i	0.457606	+	0.148685i	0.528744	−	0.848781i	$-0.322663\pi$
$941$	14.0374	+	4.56102i	0.457606	+	0.148685i	−0.0711384	+	0.997466i	$0.522663\pi$
$942$	16.2745	−	6.37166i	0.530252	−	0.207600i
$943$	−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	$-0.914951\pi$
$947$	1.05799	−	6.67988i	0.0343800	−	0.217067i	0.998897	+	0.0469536i	$0.0149513\pi$
$948$	6.28531	+	1.63944i	0.204137	+	0.0532465i
$949$			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	$-0.538894\pi$
$953$	−16.8097	−	2.66239i	−0.544519	−	0.0862434i	−0.422633	+	0.906301i	$0.638894\pi$
$954$	−13.4054	−	7.50374i	−0.434015	−	0.242943i
$955$		0			0
$956$	−12.1877	+	16.7750i	−0.394180	+	0.542542i
$957$	−41.1493	−	26.3354i	−1.33017	−	0.851303i
$958$	−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
$963$	−21.9281	+	27.8274i	−0.706623	+	0.896727i
$964$	−5.91757	+	1.92274i	−0.190592	+	0.0619271i
$965$		0			0
$966$	−1.49651	+	15.2104i	−0.0481494	+	0.489386i
$967$	−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
$969$	−4.21278	−	1.84219i	−0.135334	−	0.0591797i
$970$		0			0
$971$	−17.7969	−	24.4953i	−0.571129	−	0.786091i	0.421559	−	0.906801i	$-0.361483\pi$
$971$	−17.7969	−	24.4953i	−0.571129	−	0.786091i	−0.992688	+	0.120710i	$0.961483\pi$
$972$	−9.40210	+	12.4338i	−0.301573	+	0.398816i
$973$	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	$-0.114283\pi$
$977$	37.5797	+	19.1478i	1.20228	+	0.612593i	0.266044	+	0.963961i	$0.414283\pi$
$978$	−9.71768	+	0.574087i	−0.310737	+	0.0183573i
$979$	−3.32836	−	4.58109i	−0.106375	−	0.146412i
$980$		0			0
$981$	−39.1893	−	7.78684i	−1.25122	−	0.248615i
$982$	11.7522	+	11.7522i	0.375029	+	0.375029i
$983$	2.25288	+	14.2241i	0.0718557	+	0.453679i	0.997215	+	0.0745867i	$0.0237638\pi$
$983$	2.25288	+	14.2241i	0.0718557	+	0.453679i	−0.925359	+	0.379092i	$0.876236\pi$
$984$	6.50225	+	0.639739i	0.207284	+	0.0203941i
$985$		0			0
$986$	−7.68307	+	2.49638i	−0.244679	+	0.0795009i
$987$	−21.6572	−	26.3838i	−0.689357	−	0.839807i
$988$	−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
$993$	−5.60082	+	8.75133i	−0.177737	+	0.277715i
$994$	−37.2854	+	51.3189i	−1.18262	+	1.62774i
$995$		0			0
$996$	−21.8470	−	19.4097i	−0.692247	−	0.615019i
$997$	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.107.3		80
3.2	odd	2	inner	750.2.l.a.107.8		80
5.2	odd	4		150.2.l.a.83.10	yes	80
5.3	odd	4		750.2.l.b.143.1		80
5.4	even	2		750.2.l.c.107.8		80
15.2	even	4		150.2.l.a.83.5	yes	80
15.8	even	4		750.2.l.b.143.6		80
15.14	odd	2		750.2.l.c.107.3		80
25.3	odd	20	inner	750.2.l.a.743.8		80
25.4	even	10		150.2.l.a.47.5	✓	80
25.21	even	5		750.2.l.b.257.6		80
25.22	odd	20		750.2.l.c.743.3		80
75.29	odd	10		150.2.l.a.47.10	yes	80
75.47	even	20		750.2.l.c.743.8		80
75.53	even	20	inner	750.2.l.a.743.3		80
75.71	odd	10		750.2.l.b.257.1		80

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

\(f(q)\)	\(=\)	\(q+(-0.891007 - 0.453990i) q^{2} +(0.102145 + 1.72904i) q^{3} +(0.587785 + 0.809017i) q^{4} +(0.693954 - 1.58696i) q^{6} +(2.97677 + 2.97677i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-2.97913 + 0.353226i) q^{9} +O(q^{10})\)	\(q+(-0.891007 - 0.453990i) q^{2} +(0.102145 + 1.72904i) q^{3} +(0.587785 + 0.809017i) q^{4} +(0.693954 - 1.58696i) q^{6} +(2.97677 + 2.97677i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-2.97913 + 0.353226i) q^{9} +(-4.73921 + 1.53986i) q^{11} +(-1.33878 + 1.09894i) 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} +(2.81479 + 1.03777i) q^{18} +(-1.09331 + 1.50481i) q^{19} +(-4.84289 + 5.45101i) q^{21} +(4.92175 + 0.779529i) q^{22} +(-0.951606 + 1.86763i) q^{23} +(1.69177 - 0.371369i) q^{24} -1.76655i q^{26} +(-0.915046 - 5.11495i) 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} +(-3.14657 - 8.03698i) q^{33} +(-1.35733 - 0.441023i) q^{34} +(-2.03686 - 2.20255i) q^{36} +(2.29429 - 1.16900i) q^{37} +(1.65732 - 0.844446i) q^{38} +(-2.63959 + 1.54746i) q^{39} +(3.58757 + 1.16567i) q^{41} +(6.78975 - 2.65826i) 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} +(-1.67598 - 0.437156i) q^{48} +10.7224i q^{49} +(0.530010 + 2.41446i) q^{51} +(-0.801995 + 1.57400i) q^{52} +(-5.05783 - 0.801081i) q^{53} +(-1.50683 + 4.97287i) q^{54} +(2.47446 - 3.40580i) q^{56} +(-2.71355 - 1.73666i) 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} +(-9.91968 - 7.81673i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-0.845099 + 8.58951i) q^{66} +(1.01259 + 6.39326i) q^{67} +(1.00917 + 1.00917i) q^{68} +(-3.32641 - 1.45459i) q^{69} +(-8.85681 - 12.1904i) q^{71} +(0.814916 + 2.88720i) q^{72} +(8.23800 + 4.19747i) q^{73} -2.57494 q^{74} -1.86005 q^{76} +(-18.6914 - 9.52374i) q^{77} +(3.05442 - 0.180445i) q^{78} +(-2.20434 - 3.03401i) q^{79} +(8.75046 - 2.10462i) q^{81} +(-2.66735 - 2.66735i) q^{82} +(2.63941 + 16.6646i) q^{83} +(-7.25654 - 0.713952i) q^{84} +(8.42648 - 2.73793i) q^{86} +(6.22047 + 7.57807i) 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} +(6.04544 - 9.44605i) q^{93} +(2.75161 - 3.78726i) q^{94} +(1.29484 + 1.15039i) 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

Varieties

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Database

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