LMFDB - Embedded newform 750.2.l.b.143.1

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			143.1
Character	$\chi$	$=$	750.143
Dual form			750.2.l.b.257.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 + 0.891007i) q^{2} +(-1.72904 + 0.102145i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(0.693954 - 1.58696i) q^{6} +(2.97677 - 2.97677i) q^{7} +(0.987688 - 0.156434i) q^{8} +(2.97913 - 0.353226i) q^{9} +O(q^{10})$	\(q+(-0.453990 + 0.891007i) q^{2} +(-1.72904 + 0.102145i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(0.693954 - 1.58696i) q^{6} +(2.97677 - 2.97677i) q^{7} +(0.987688 - 0.156434i) q^{8} +(2.97913 - 0.353226i) q^{9} +(-4.73921 + 1.53986i) q^{11} +(1.09894 + 1.33878i) q^{12} +(-1.57400 + 0.801995i) q^{13} +(1.30090 + 4.00375i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-0.223260 - 1.40961i) q^{17} +(-1.03777 + 2.81479i) q^{18} +(1.09331 - 1.50481i) q^{19} +(-4.84289 + 5.45101i) q^{21} +(0.779529 - 4.92175i) q^{22} +(-1.86763 - 0.951606i) q^{23} +(-1.69177 + 0.371369i) q^{24} -1.76655i q^{26} +(-5.11495 + 0.915046i) q^{27} +(-4.15797 - 0.658557i) q^{28} +(-4.57938 + 3.32712i) q^{29} +(-5.23835 - 3.80588i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(8.03698 - 3.14657i) q^{33} +(1.35733 + 0.441023i) q^{34} +(-2.03686 - 2.20255i) q^{36} +(-1.16900 - 2.29429i) q^{37} +(0.844446 + 1.65732i) q^{38} +(2.63959 - 1.54746i) q^{39} +(3.58757 + 1.16567i) q^{41} +(-2.65826 - 6.78975i) q^{42} +(-6.26505 - 6.26505i) q^{43} +(4.03141 + 2.92899i) q^{44} +(1.69577 - 1.23205i) q^{46} +(4.62368 + 0.732319i) q^{47} +(0.437156 - 1.67598i) q^{48} -10.7224i q^{49} +(0.530010 + 2.41446i) q^{51} +(1.57400 + 0.801995i) q^{52} +(0.801081 - 5.05783i) q^{53} +(1.50683 - 4.97287i) q^{54} +(2.47446 - 3.40580i) q^{56} +(-1.73666 + 2.71355i) q^{57} +(-0.885486 - 5.59074i) q^{58} +(3.44032 - 10.5882i) q^{59} +(-2.99979 - 9.23241i) q^{61} +(5.76923 - 2.93957i) q^{62} +(7.81673 - 9.91968i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-0.845099 + 8.58951i) q^{66} +(6.39326 - 1.01259i) q^{67} +(-1.00917 + 1.00917i) q^{68} +(3.32641 + 1.45459i) q^{69} +(-8.85681 - 12.1904i) q^{71} +(2.88720 - 0.814916i) q^{72} +(-4.19747 + 8.23800i) q^{73} +2.57494 q^{74} -1.86005 q^{76} +(-9.52374 + 18.6914i) q^{77} +(0.180445 + 3.05442i) q^{78} +(2.20434 + 3.03401i) q^{79} +(8.75046 - 2.10462i) q^{81} +(-2.66735 + 2.66735i) q^{82} +(-16.6646 + 2.63941i) q^{83} +(7.25654 + 0.713952i) q^{84} +(8.42648 - 2.73793i) q^{86} +(7.57807 - 6.22047i) q^{87} +(-4.43998 + 2.26228i) q^{88} +(-0.351151 - 1.08073i) q^{89} +(-2.29810 + 7.07281i) q^{91} +(0.327901 + 2.07029i) q^{92} +(9.44605 + 6.04544i) q^{93} +(-2.75161 + 3.78726i) q^{94} +(1.29484 + 1.15039i) q^{96} +(-0.549968 + 3.47236i) q^{97} +(9.55370 + 4.86785i) 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} + 4 q^{12} + 20 q^{16} + 8 q^{18} - 40 q^{19} + 36 q^{22} - 4 q^{27} + 16 q^{28} - 4 q^{33} - 40 q^{34} + 24 q^{37} - 40 q^{39} + 4 q^{42} + 24 q^{43} + 4 q^{48} + 64 q^{57} - 20 q^{58} - 64 q^{63} - 96 q^{67} + 140 q^{69} - 8 q^{72} - 100 q^{73} - 100 q^{78} + 80 q^{79} - 40 q^{81} - 96 q^{82} + 60 q^{84} - 80 q^{87} - 4 q^{88} - 12 q^{93} + 32 q^{97}+O(q^{100}) $ 80 * q - 4 * q^3 - 4 * q^7 + 4 * q^12 + 20 * q^16 + 8 * q^18 - 40 * q^19 + 36 * q^22 - 4 * q^27 + 16 * q^28 - 4 * q^33 - 40 * q^34 + 24 * q^37 - 40 * q^39 + 4 * q^42 + 24 * q^43 + 4 * q^48 + 64 * q^57 - 20 * q^58 - 64 * q^63 - 96 * q^67 + 140 * q^69 - 8 * q^72 - 100 * q^73 - 100 * q^78 + 80 * q^79 - 40 * q^81 - 96 * q^82 + 60 * q^84 - 80 * q^87 - 4 * q^88 - 12 * q^93 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$-1$

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 $

$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$3$	−1.72904	+	0.102145i	−0.998260	+	0.0589737i
$3$	−1.72904	+	0.102145i	−0.998260	+	0.0589737i
$4$	−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	0.134155	−	0.990960i	$-0.457168\pi$
$7$	2.97677	−	2.97677i	1.12511	−	1.12511i	0.990960	−	0.134155i	$-0.0428318\pi$
$8$	0.987688	−	0.156434i	0.349201	−	0.0553079i
$9$	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	$0.670539\pi$
$12$	1.09894	+	1.33878i	0.317236	+	0.386473i
$13$	−1.57400	+	0.801995i	−0.436550	+	0.222433i	−0.658432	−	0.752640i	$-0.728780\pi$
$13$	−1.57400	+	0.801995i	−0.436550	+	0.222433i	0.221882	+	0.975074i	$0.428780\pi$
$14$	1.30090	+	4.00375i	0.347680	+	1.07005i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−0.223260	−	1.40961i	−0.0541486	−	0.341881i	−0.999858	−	0.0168665i	$-0.994631\pi$
$17$	−0.223260	−	1.40961i	−0.0541486	−	0.341881i	0.945709	−	0.325014i	$-0.105369\pi$
$18$	−1.03777	+	2.81479i	−0.244605	+	0.663452i
$19$	1.09331	−	1.50481i	0.250823	−	0.345228i	−0.664977	−	0.746864i	$-0.731558\pi$
$19$	1.09331	−	1.50481i	0.250823	−	0.345228i	0.915799	+	0.401636i	$0.131558\pi$
$20$		0			0
$21$	−4.84289	+	5.45101i	−1.05680	+	1.18951i
$22$	0.779529	−	4.92175i	0.166196	−	1.04932i
$23$	−1.86763	−	0.951606i	−0.389428	−	0.198424i	0.248303	−	0.968682i	$-0.420127\pi$
$23$	−1.86763	−	0.951606i	−0.389428	−	0.198424i	−0.637731	+	0.770259i	$0.720127\pi$
$24$	−1.69177	+	0.371369i	−0.345331	+	0.0758053i
$25$		0			0
$26$		−	1.76655i		−	0.346448i
$27$	−5.11495	+	0.915046i	−0.984372	+	0.176101i
$28$	−4.15797	−	0.658557i	−0.785782	−	0.124456i
$29$	−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
$33$	8.03698	−	3.14657i	1.39906	−	0.547747i
$34$	1.35733	+	0.441023i	0.232780	+	0.0756348i
$35$		0			0
$36$	−2.03686	−	2.20255i	−0.339476	−	0.367091i
$37$	−1.16900	−	2.29429i	−0.192182	−	0.377178i	0.774729	−	0.632294i	$-0.217886\pi$
$37$	−1.16900	−	2.29429i	−0.192182	−	0.377178i	−0.966911	+	0.255116i	$0.917886\pi$
$38$	0.844446	+	1.65732i	0.136987	+	0.268852i
$39$	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	$0.504827\pi$
$42$	−2.65826	−	6.78975i	−0.410179	−	1.04768i
$43$	−6.26505	−	6.26505i	−0.955411	−	0.955411i	0.0436361	−	0.999047i	$-0.486106\pi$
$43$	−6.26505	−	6.26505i	−0.955411	−	0.955411i	−0.999047	+	0.0436361i	$0.986106\pi$
$44$	4.03141	+	2.92899i	0.607758	+	0.441562i
$45$		0			0
$46$	1.69577	−	1.23205i	0.250028	−	0.181656i
$47$	4.62368	+	0.732319i	0.674433	+	0.106820i	0.484251	−	0.874929i	$-0.339092\pi$
$47$	4.62368	+	0.732319i	0.674433	+	0.106820i	0.190182	+	0.981749i	$0.439092\pi$
$48$	0.437156	−	1.67598i	0.0630980	−	0.241906i
$49$		−	10.7224i		−	1.53177i
$50$		0			0
$51$	0.530010	+	2.41446i	0.0742163	+	0.338092i
$52$	1.57400	+	0.801995i	0.218275	+	0.111217i
$53$	0.801081	−	5.05783i	0.110037	−	0.694746i	−0.869568	−	0.493813i	$-0.835603\pi$
$53$	0.801081	−	5.05783i	0.110037	−	0.694746i	0.979605	−	0.200933i	$-0.0643973\pi$
$54$	1.50683	−	4.97287i	0.205053	−	0.676722i
$55$		0			0
$56$	2.47446	−	3.40580i	0.330663	−	0.455119i
$57$	−1.73666	+	2.71355i	−0.230027	+	0.359419i
$58$	−0.885486	−	5.59074i	−0.116270	−	0.734100i
$59$	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	$-0.313461\pi$
$62$	5.76923	−	2.93957i	0.732693	−	0.373326i
$63$	7.81673	−	9.91968i	0.984816	−	1.24976i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$		0			0
$66$	−0.845099	+	8.58951i	−0.104025	+	1.05730i
$67$	6.39326	−	1.01259i	0.781061	−	0.123708i	0.246844	−	0.969055i	$-0.420607\pi$
$67$	6.39326	−	1.01259i	0.781061	−	0.123708i	0.534217	+	0.845347i	$0.320607\pi$
$68$	−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	$-0.552203\pi$
$72$	2.88720	−	0.814916i	0.340260	−	0.0960388i
$73$	−4.19747	+	8.23800i	−0.491277	+	0.964185i	0.503681	+	0.863890i	$0.331979\pi$
$73$	−4.19747	+	8.23800i	−0.491277	+	0.964185i	−0.994958	+	0.100295i	$0.968021\pi$
$74$	2.57494			0.299330
$75$		0			0
$76$	−1.86005			−0.213363
$77$	−9.52374	+	18.6914i	−1.08533	+	2.13008i
$78$	0.180445	+	3.05442i	0.0204313	+	0.345845i
$79$	2.20434	+	3.03401i	0.248007	+	0.341353i	0.914812	−	0.403880i	$-0.132339\pi$
$79$	2.20434	+	3.03401i	0.248007	+	0.341353i	−0.666805	+	0.745232i	$0.732339\pi$
$80$		0			0
$81$	8.75046	−	2.10462i	0.972274	−	0.233846i
$82$	−2.66735	+	2.66735i	−0.294559	+	0.294559i
$83$	−16.6646	+	2.63941i	−1.82918	+	0.289713i	−0.973650	−	0.228048i	$-0.926766\pi$
$83$	−16.6646	+	2.63941i	−1.82918	+	0.289713i	−0.855525	+	0.517761i	$0.826766\pi$
$84$	7.25654	+	0.713952i	0.791754	+	0.0778985i
$85$		0			0
$86$	8.42648	−	2.73793i	0.908650	−	0.295238i
$87$	7.57807	−	6.22047i	0.812454	−	0.666904i
$88$	−4.43998	+	2.26228i	−0.473303	+	0.241160i
$89$	−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
$92$	0.327901	+	2.07029i	0.0341860	+	0.215842i
$93$	9.44605	+	6.04544i	0.979510	+	0.626883i
$94$	−2.75161	+	3.78726i	−0.283807	+	0.390626i
$95$		0			0
$96$	1.29484	+	1.15039i	0.132154	+	0.117411i
$97$	−0.549968	+	3.47236i	−0.0558408	+	0.352565i	0.943909	+	0.330205i	$0.107118\pi$
$97$	−0.549968	+	3.47236i	−0.0558408	+	0.352565i	−0.999750	+	0.0223598i	$0.992882\pi$
$98$	9.55370	+	4.86785i	0.965070	+	0.491728i
$99$	−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	$0.688590\pi$
$102$	−2.39192	−	0.623900i	−0.236835	−	0.0617753i
$103$	2.62027	+	0.415010i	0.258183	+	0.0408921i	0.284184	−	0.958770i	$-0.408277\pi$
$103$	2.62027	+	0.415010i	0.258183	+	0.0408921i	−0.0260012	+	0.999662i	$0.508277\pi$
$104$	−1.42917	+	1.03835i	−0.140141	+	0.101819i
$105$		0			0
$106$	4.14287	+	3.00997i	0.402391	+	0.292355i
$107$	−8.35067	−	8.35067i	−0.807290	−	0.807290i	0.176933	−	0.984223i	$-0.443382\pi$
$107$	−8.35067	−	8.35067i	−0.807290	−	0.807290i	−0.984223	+	0.176933i	$0.943382\pi$
$108$	3.74678	+	3.60023i	0.360534	+	0.346432i
$109$	−12.6666	−	4.11563i	−1.21324	−	0.394206i	−0.368625	−	0.929578i	$-0.620172\pi$
$109$	−12.6666	−	4.11563i	−1.21324	−	0.394206i	−0.844617	+	0.535372i	$0.820172\pi$
$110$		0			0
$111$	2.25559	+	3.84749i	0.214091	+	0.365188i
$112$	1.91121	+	3.75095i	0.180592	+	0.354432i
$113$	−0.679445	−	1.33349i	−0.0639168	−	0.125444i	0.856838	−	0.515586i	$-0.172426\pi$
$113$	−0.679445	−	1.33349i	−0.0639168	−	0.125444i	−0.920755	+	0.390142i	$0.872426\pi$
$114$	−1.62936	−	2.77931i	−0.152604	−	0.260306i
$115$		0			0
$116$	5.38339	+	1.74917i	0.499835	+	0.162406i
$117$	−4.40588	+	2.94523i	−0.407324	+	0.272286i
$118$	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
$122$	9.58802	+	1.51859i	0.868058	+	0.137487i
$123$	−6.32211	−	1.64904i	−0.570046	−	0.148689i
$124$			6.47496i			0.581468i
$125$		0			0
$126$	5.28978	+	11.4682i	0.471251	+	1.02167i
$127$	−1.38236	−	0.704349i	−0.122665	−	0.0625009i	0.391581	−	0.920144i	$-0.371928\pi$
$127$	−1.38236	−	0.704349i	−0.122665	−	0.0625009i	−0.514246	+	0.857643i	$0.671928\pi$
$128$	−0.156434	+	0.987688i	−0.0138270	+	0.0873001i
$129$	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	$0.289721\pi$
$132$	−7.26964	−	4.65255i	−0.632741	−	0.404952i
$133$	−1.22495	−	7.73403i	−0.106217	−	0.670625i
$134$	−2.00025	+	6.15614i	−0.172795	+	0.531810i
$135$		0			0
$136$	−0.441023	−	1.35733i	−0.0378174	−	0.116390i
$137$	−3.66124	+	1.86549i	−0.312800	+	0.159380i	−0.603342	−	0.797483i	$-0.706165\pi$
$137$	−3.66124	+	1.86549i	−0.312800	+	0.159380i	0.290542	+	0.956862i	$0.406165\pi$
$138$	−2.80621	+	2.30348i	−0.238880	+	0.196085i
$139$	−10.1584	+	3.30065i	−0.861621	+	0.279958i	−0.706305	−	0.707907i	$-0.749639\pi$
$139$	−10.1584	+	3.30065i	−0.861621	+	0.279958i	−0.155316	+	0.987865i	$0.549639\pi$
$140$		0			0
$141$	−8.06931	−	0.793919i	−0.679559	−	0.0668600i
$142$	14.8826	−	2.35717i	1.24892	−	0.197809i
$143$	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
$147$	1.09524	+	18.5394i	0.0903339	+	1.52910i
$148$	−1.16900	+	2.29429i	−0.0960909	+	0.188589i
$149$	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	$0.194454\pi$
$152$	0.844446	−	1.65732i	0.0684936	−	0.134426i
$153$	−1.16303	−	4.12055i	−0.0940256	−	0.333127i
$154$	−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	−0.362529	−	0.931972i	$-0.618087\pi$
$157$	7.13510	−	7.13510i	0.569443	−	0.569443i	0.931972	+	0.362529i	$0.118087\pi$
$158$	−3.70407	+	0.586667i	−0.294680	+	0.0466727i
$159$	−0.868465	+	8.82699i	−0.0688737	+	0.700026i
$160$		0			0
$161$	−8.39223	+	2.72680i	−0.661401	+	0.214902i
$162$	−2.09740	+	8.75219i	−0.164787	+	0.687637i
$163$	5.00771	−	2.55156i	0.392234	−	0.199853i	−0.246739	−	0.969082i	$-0.579359\pi$
$163$	5.00771	−	2.55156i	0.392234	−	0.199853i	0.638974	+	0.769228i	$0.279359\pi$
$164$	−1.16567	−	3.58757i	−0.0910238	−	0.280143i
$165$		0			0
$166$	5.21383	−	16.0465i	0.404672	−	1.24545i
$167$	−2.62306	−	16.5614i	−0.202979	−	1.28156i	−0.853109	−	0.521734i	$-0.825286\pi$
$167$	−2.62306	−	16.5614i	−0.202979	−	1.28156i	0.650130	−	0.759823i	$-0.274714\pi$
$168$	−3.93054	+	6.14150i	−0.303247	+	0.473827i
$169$	−5.80692	+	7.99254i	−0.446686	+	0.614810i
$170$		0			0
$171$	2.72558	−	4.86922i	0.208430	−	0.372359i
$172$	−1.38603	+	8.75104i	−0.105684	+	0.667260i
$173$	3.98829	+	2.03214i	0.303224	+	0.154500i	0.598982	−	0.800763i	$-0.295572\pi$
$173$	3.98829	+	2.03214i	0.303224	+	0.154500i	−0.295758	+	0.955263i	$0.595572\pi$
$174$	2.10211	+	9.57614i	0.159360	+	0.725966i
$175$		0			0
$176$		−	4.98310i		−	0.375615i
$177$	−4.86690	+	18.6588i	−0.365819	+	1.40248i
$178$	1.12236	+	0.177764i	0.0841243	+	0.0133240i
$179$	−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
$183$	6.12980	+	15.6568i	0.453128	+	1.15738i
$184$	−1.99350	−	0.647728i	−0.146963	−	0.0477511i
$185$		0			0
$186$	−9.67494	+	5.67192i	−0.709401	+	0.415885i
$187$	3.22868	+	6.33665i	0.236105	+	0.463382i
$188$	−2.12527	−	4.17108i	−0.155001	−	0.304207i
$189$	−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	$0.367272\pi$
$192$	−1.61285	+	0.631448i	−0.116397	+	0.0455708i
$193$	3.31568	+	3.31568i	0.238668	+	0.238668i	0.816298	−	0.577630i	$-0.196023\pi$
$193$	3.31568	+	3.31568i	0.238668	+	0.238668i	−0.577630	+	0.816298i	$0.696023\pi$
$194$	−2.84422	−	2.06644i	−0.204203	−	0.148362i
$195$		0			0
$196$	−8.67458	+	6.30245i	−0.619613	+	0.450175i
$197$	12.5246	+	1.98370i	0.892341	+	0.141333i	0.585734	−	0.810503i	$-0.300806\pi$
$197$	12.5246	+	1.98370i	0.892341	+	0.141333i	0.306607	+	0.951836i	$0.400806\pi$
$198$	0.583828	−	14.9379i	0.0414909	−	1.06159i
$199$		−	1.62602i		−	0.115266i	−0.998338	−	0.0576328i	$-0.981645\pi$
$199$		−	1.62602i		−	0.115266i	0.998338	−	0.0576328i	$-0.0183553\pi$
$200$		0			0
$201$	−10.9507	+	2.40385i	−0.772406	+	0.169555i
$202$	−14.8566	−	7.56983i	−1.04531	−	0.532612i
$203$	−3.72772	+	23.5359i	−0.261634	+	1.65189i
$204$	1.64181	−	1.84797i	0.114950	−	0.129384i
$205$		0			0
$206$	−1.55935	+	2.14627i	−0.108645	+	0.149537i
$207$	−5.90005	−	2.17526i	−0.410082	−	0.151191i
$208$	−0.276349	−	1.74480i	−0.0191613	−	0.120980i
$209$	−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	$-0.236489\pi$
$212$	−4.56273	+	2.32483i	−0.313370	+	0.159670i
$213$	16.5589	+	20.1729i	1.13460	+	1.38222i
$214$	11.2316	−	3.64938i	0.767778	−	0.249466i
$215$		0			0
$216$	−4.90883	+	1.70393i	−0.334004	+	0.115938i
$217$	−26.9226	+	4.26413i	−1.82763	+	0.289468i
$218$	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
$222$	−4.45216	+	0.263018i	−0.298809	+	0.0176526i
$223$	−2.82606	+	5.54645i	−0.189247	+	0.371418i	−0.966062	−	0.258311i	$-0.916834\pi$
$223$	−2.82606	+	5.54645i	−0.189247	+	0.371418i	0.776815	+	0.629729i	$0.216834\pi$
$224$	−4.20979			−0.281279
$225$		0			0
$226$	1.49661			0.0995528
$227$	4.15647	−	8.15754i	0.275875	−	0.541435i	−0.710947	−	0.703246i	$-0.751733\pi$
$227$	4.15647	−	8.15754i	0.275875	−	0.541435i	0.986822	+	0.161811i	$0.0517334\pi$
$228$	3.21610	−	0.189996i	0.212991	−	0.0125828i
$229$	10.8714	+	14.9632i	0.718400	+	0.988793i	0.999575	+	0.0291365i	$0.00927575\pi$
$229$	10.8714	+	14.9632i	0.718400	+	0.988793i	−0.281175	+	0.959656i	$0.590724\pi$
$230$		0			0
$231$	14.5576	−	33.2909i	0.957823	−	2.19038i
$232$	−4.00253	+	4.00253i	−0.262779	+	0.262779i
$233$	13.6047	−	2.15478i	0.891276	−	0.141164i	0.306032	−	0.952021i	$-0.400999\pi$
$233$	13.6047	−	2.15478i	0.891276	−	0.141164i	0.585244	+	0.810857i	$0.300999\pi$
$234$	−0.623990	−	5.26277i	−0.0407915	−	0.344038i
$235$		0			0
$236$	−10.5882	+	3.44032i	−0.689234	+	0.223946i
$237$	−4.12129	−	5.02075i	−0.267706	−	0.326133i
$238$	5.35329	−	2.72764i	0.347002	−	0.176806i
$239$	−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	$0.164224\pi$
$242$	2.16369	+	13.6610i	0.139087	+	0.878163i
$243$	−14.9149	+	4.53278i	−0.956791	+	0.290778i
$244$	−5.70595	+	7.85356i	−0.365286	+	0.502773i
$245$		0			0
$246$	4.33948	−	4.88440i	0.276675	−	0.311418i
$247$	−0.514023	+	3.24541i	−0.0327065	+	0.206501i
$248$	−5.76923	−	2.93957i	−0.366346	−	0.186663i
$249$	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	$-0.0379520\pi$
$252$	−12.6197	−	0.493226i	−0.794969	−	0.0310703i
$253$	10.3164	+	1.63396i	0.648589	+	0.102726i
$254$	1.25516	−	0.911927i	0.0787557	−	0.0572194i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−21.7693	−	21.7693i	−1.35793	−	1.35793i	−0.876462	−	0.481471i	$-0.840103\pi$
$257$	−21.7693	−	21.7693i	−1.35793	−	1.35793i	−0.481471	−	0.876462i	$-0.659897\pi$
$258$	−14.2900	+	5.59470i	−0.889657	+	0.348311i
$259$	−10.3094	−	3.34973i	−0.640596	−	0.208142i
$260$		0			0
$261$	−12.4674	+	11.5295i	−0.771711	+	0.713657i
$262$	−2.89062	−	5.67316i	−0.178583	−	0.350489i
$263$	2.51673	+	4.93937i	0.155188	+	0.304574i	0.955490	−	0.295023i	$-0.0953273\pi$
$263$	2.51673	+	4.93937i	0.155188	+	0.304574i	−0.800302	+	0.599598i	$0.795327\pi$
$264$	7.44580	−	4.36509i	0.458257	−	0.268653i
$265$		0			0
$266$	7.44718	+	2.41974i	0.456616	+	0.148364i
$267$	0.717544	+	1.83276i	0.0439130	+	0.112163i
$268$	−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	$0.345704\pi$
$272$	1.40961	+	0.223260i	0.0854701	+	0.0135371i
$273$	3.25104	−	12.4639i	0.196762	−	0.754349i
$274$		−	4.10910i		−	0.248240i
$275$		0			0
$276$	−0.778423	−	3.54611i	−0.0468556	−	0.213450i
$277$	22.1735	+	11.2980i	1.33228	+	0.678829i	0.967644	−	0.252321i	$-0.0811940\pi$
$277$	22.1735	+	11.2980i	1.33228	+	0.678829i	0.364634	+	0.931151i	$0.381194\pi$
$278$	1.67090	−	10.5496i	0.100214	−	0.632725i
$279$	−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	$0.293052\pi$
$282$	4.37078	−	6.82938i	0.260276	−	0.406684i
$283$	0.159612	+	1.00775i	0.00948793	+	0.0599044i	0.991978	−	0.126410i	$-0.0403456\pi$
$283$	0.159612	+	1.00775i	0.00948793	+	0.0599044i	−0.982490	+	0.186315i	$0.940346\pi$
$284$	−4.65630	+	14.3306i	−0.276301	+	0.850366i
$285$		0			0
$286$	2.72024	+	8.37203i	0.160851	+	0.495049i
$287$	14.1493	−	7.20945i	0.835210	−	0.425561i
$288$	−2.35633	−	1.85680i	−0.138848	−	0.109413i
$289$	14.2308	−	4.62387i	0.837106	−	0.271992i
$290$		0			0
$291$	0.596229	−	6.06002i	0.0349516	−	0.355244i
$292$	9.13189	−	1.44635i	0.534403	−	0.0846412i
$293$	−1.45604	+	1.45604i	−0.0850625	+	0.0850625i	−0.748358	−	0.663295i	$-0.769157\pi$
$293$	−1.45604	+	1.45604i	−0.0850625	+	0.0850625i	0.663295	+	0.748358i	$0.269157\pi$
$294$	−17.0159	−	7.44083i	−0.992389	−	0.433958i
$295$		0			0
$296$	−1.51351	−	2.08317i	−0.0879710	−	0.121082i
$297$	22.8318	−	12.2129i	1.32483	−	0.708665i
$298$	−2.33020	+	4.57327i	−0.134985	+	0.264922i
$299$	3.70284			0.214141
$300$		0			0
$301$	−37.2993			−2.14990
$302$	−9.13947	+	17.9372i	−0.525917	+	1.03217i
$303$	−1.70317	−	28.8299i	−0.0978446	−	1.65624i
$304$	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	−0.277080	−	0.960847i	$-0.589367\pi$
$307$	11.9806	−	11.9806i	0.683767	−	0.683767i	0.960847	+	0.277080i	$0.0893667\pi$
$308$	20.7196	−	3.28166i	1.18061	−	0.186990i
$309$	−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	$0.365353\pi$
$312$	2.36502	−	1.94133i	0.133893	−	0.109906i
$313$	−20.3753	+	10.3817i	−1.15168	+	0.586809i	−0.922280	−	0.386523i	$-0.873676\pi$
$313$	−20.3753	+	10.3817i	−1.15168	+	0.586809i	−0.229398	+	0.973333i	$0.573676\pi$
$314$	3.11815	+	9.59669i	0.175968	+	0.541573i
$315$		0			0
$316$	1.15889	−	3.56669i	0.0651926	−	0.200642i
$317$	−1.36994	−	8.64943i	−0.0769432	−	0.485800i	−0.995826	−	0.0912701i	$-0.970907\pi$
$317$	−1.36994	−	8.64943i	−0.0769432	−	0.485800i	0.918883	−	0.394530i	$-0.129093\pi$
$318$	−7.47063	−	4.78118i	−0.418932	−	0.268115i
$319$	16.5794	−	22.8195i	0.928266	−	1.27765i
$320$		0			0
$321$	15.2916	+	13.5856i	0.853494	+	0.758276i
$322$	1.38040	−	8.71548i	0.0769265	−	0.485695i
$323$	−2.36529	−	1.20518i	−0.131608	−	0.0670578i
$324$	−6.84606	−	5.84221i	−0.380337	−	0.324567i
$325$		0			0
$326$			5.62029i			0.311279i
$327$	22.3214	+	5.82224i	1.23438	+	0.321971i
$328$	3.72576	+	0.590102i	0.205721	+	0.0325829i
$329$	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
$333$	−4.29300	−	6.42206i	−0.235255	−	0.351927i
$334$	15.9471	+	5.18154i	0.872588	+	0.283521i
$335$		0			0
$336$	−3.68769	−	6.29032i	−0.201180	−	0.343165i
$337$	−1.10341	−	2.16556i	−0.0601063	−	0.117965i	0.858999	−	0.511977i	$-0.171087\pi$
$337$	−1.10341	−	2.16556i	−0.0601063	−	0.117965i	−0.919105	+	0.394012i	$0.871087\pi$
$338$	−4.48512	−	8.80254i	−0.243958	−	0.478795i
$339$	1.31099	+	2.23624i	0.0712035	+	0.121456i
$340$		0			0
$341$	30.6862	+	9.97055i	1.66175	+	0.539935i
$342$	3.10112	+	4.63909i	0.167690	+	0.250853i
$343$	−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
$347$	22.4456	+	3.55504i	1.20494	+	0.190844i	0.726433	−	0.687237i	$-0.241177\pi$
$347$	22.4456	+	3.55504i	1.20494	+	0.190844i	0.478511	+	0.878082i	$0.341177\pi$
$348$	−9.48674	−	2.47449i	−0.508543	−	0.132646i
$349$			12.5328i			0.670865i	0.942064	+	0.335432i	$0.108882\pi$
$349$			12.5328i			0.670865i	−0.942064	+	0.335432i	$0.891118\pi$
$350$		0			0
$351$	7.31708	−	5.54245i	0.390557	−	0.295834i
$352$	4.43998	+	2.26228i	0.236651	+	0.120580i
$353$	−1.11770	+	7.05688i	−0.0594892	+	0.375600i	0.939925	+	0.341381i	$0.110894\pi$
$353$	−1.11770	+	7.05688i	−0.0594892	+	0.375600i	−0.999414	+	0.0342193i	$0.989106\pi$
$354$	−14.4156	−	12.8074i	−0.766181	−	0.680704i
$355$		0			0
$356$	−0.667929	+	0.919325i	−0.0354002	+	0.0487241i
$357$	8.76503	+	5.60959i	0.463894	+	0.296891i
$358$	−0.0272918	−	0.172313i	−0.00144241	−	0.00910704i
$359$	−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
$362$	−10.1373	+	5.16520i	−0.532803	+	0.271477i
$363$	−18.5171	+	15.1998i	−0.971894	+	0.797780i
$364$	7.07281	−	2.29810i	0.370716	−	0.120453i
$365$		0			0
$366$	−16.7331	−	1.64633i	−0.874656	−	0.0860551i
$367$	−4.14629	+	0.656708i	−0.216435	+	0.0342799i	−0.263710	−	0.964602i	$-0.584946\pi$
$367$	−4.14629	+	0.656708i	−0.216435	+	0.0342799i	0.0472753	+	0.998882i	$0.484946\pi$
$368$	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
$372$	−0.661387	−	11.1954i	−0.0342913	−	0.580456i
$373$	2.06631	−	4.05536i	0.106990	−	0.209979i	−0.831305	−	0.555817i	$-0.812405\pi$
$373$	2.06631	−	4.05536i	0.106990	−	0.209979i	0.938294	+	0.345838i	$0.112405\pi$
$374$	−7.11179			−0.367742
$375$		0			0
$376$	4.68132			0.241420
$377$	4.53964	−	8.90954i	0.233803	−	0.458864i
$378$	−10.3176	−	19.2886i	−0.530682	−	0.992099i
$379$	19.3891	+	26.6869i	0.995954	+	1.37081i	0.927775	+	0.373139i	$0.121719\pi$
$379$	19.3891	+	26.6869i	0.995954	+	1.37081i	0.0681783	+	0.997673i	$0.478281\pi$
$380$		0			0
$381$	2.46210	+	1.07664i	0.126137	+	0.0551581i
$382$	−13.0504	+	13.0504i	−0.667715	+	0.667715i
$383$	−16.8791	+	2.67339i	−0.862482	+	0.136604i	−0.571977	−	0.820270i	$-0.693823\pi$
$383$	−16.8791	+	2.67339i	−0.862482	+	0.136604i	−0.290505	+	0.956873i	$0.593823\pi$
$384$	0.169593	−	1.72373i	0.00865451	−	0.0879636i
$385$		0			0
$386$	−4.45958	+	1.44901i	−0.226987	+	0.0737525i
$387$	−20.8774	−	16.4514i	−1.06126	−	0.836274i
$388$	3.13246	−	1.59607i	0.159027	−	0.0810281i
$389$	−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
$392$	−1.67735	−	10.5904i	−0.0847189	−	0.534894i
$393$	5.94477	−	9.28875i	0.299874	−	0.468556i
$394$	−7.45354	+	10.2589i	−0.375504	+	0.516837i
$395$		0			0
$396$	13.0447	+	7.30186i	0.655521	+	0.366932i
$397$	0.577115	−	3.64376i	0.0289646	−	0.182875i	−0.968964	−	0.247200i	$-0.920489\pi$
$397$	0.577115	−	3.64376i	0.0289646	−	0.182875i	0.997929	+	0.0643251i	$0.0204895\pi$
$398$	1.44880	+	0.738199i	0.0726216	+	0.0370026i
$399$	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	$-0.261387\pi$
$402$	2.82969	−	10.8485i	0.141132	−	0.541074i
$403$	11.2975	+	1.78935i	0.562768	+	0.0891336i
$404$	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
$408$	0.901190	+	2.30182i	0.0446155	+	0.113957i
$409$	7.27469	+	2.36369i	0.359710	+	0.116877i	0.483296	−	0.875457i	$-0.339439\pi$
$409$	7.27469	+	2.36369i	0.359710	+	0.116877i	−0.123586	+	0.992334i	$0.539439\pi$
$410$		0			0
$411$	6.13986	−	3.59948i	0.302857	−	0.177549i
$412$	−1.20440	−	2.36378i	−0.0593368	−	0.116455i
$413$	−21.2777	−	41.7598i	−1.04701	−	2.05487i
$414$	4.61674	−	4.26944i	0.226901	−	0.209831i
$415$		0			0
$416$	1.68008	+	0.545893i	0.0823729	+	0.0267646i
$417$	17.2270	−	6.74458i	0.843611	−	0.330283i
$418$	−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	$0.411247\pi$
$422$	11.9302	+	1.88956i	0.580753	+	0.0919823i
$423$	14.0332	+	0.548470i	0.682319	+	0.0266675i
$424$		−	5.12087i		−	0.248692i
$425$		0			0
$426$	−25.4918	+	5.59582i	−1.23508	+	0.271119i
$427$	−36.4125	−	18.5531i	−1.76213	−	0.897848i
$428$	−1.84743	+	11.6642i	−0.0892991	+	0.563812i
$429$	−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	$0.233340\pi$
$432$	0.710346	−	5.14737i	0.0341765	−	0.247653i
$433$	−1.22781	−	7.75206i	−0.0590046	−	0.372540i	−0.999467	−	0.0326428i	$-0.989608\pi$
$433$	−1.22781	−	7.75206i	−0.0590046	−	0.372540i	0.940463	−	0.339897i	$-0.110392\pi$
$434$	8.42326	−	25.9241i	0.404329	−	1.24440i
$435$		0			0
$436$	4.11563	+	12.6666i	0.197103	+	0.606621i
$437$	−3.47389	+	1.77004i	−0.166179	+	0.0846723i
$438$	10.1605	+	12.3780i	0.485487	+	0.591443i
$439$	−19.1294	+	6.21551i	−0.912994	+	0.296650i	−0.727590	−	0.686012i	$-0.759360\pi$
$439$	−19.1294	+	6.21551i	−0.912994	+	0.296650i	−0.185405	+	0.982662i	$0.559360\pi$
$440$		0			0
$441$	−3.78742	−	31.9434i	−0.180353	−	1.52111i
$442$	−2.49014	+	0.394399i	−0.118444	+	0.0187597i
$443$	−11.8995	+	11.8995i	−0.565363	+	0.565363i	−0.930826	−	0.365463i	$-0.880911\pi$
$443$	−11.8995	+	11.8995i	−0.565363	+	0.565363i	0.365463	+	0.930826i	$0.380911\pi$
$444$	1.78689	−	4.08631i	0.0848019	−	0.193928i
$445$		0			0
$446$	−3.65892	−	5.03607i	−0.173255	−	0.238465i
$447$	−8.87463	+	0.524282i	−0.419755	+	0.0247977i
$448$	1.91121	−	3.75095i	0.0902960	−	0.177216i
$449$	−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
$452$	−0.679445	+	1.33349i	−0.0319584	+	0.0627219i
$453$	−34.8079	+	2.05633i	−1.63542	+	0.0966149i
$454$	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	−0.319001	−	0.947754i	$-0.603347\pi$
$457$	13.4412	−	13.4412i	0.628754	−	0.628754i	0.947754	+	0.319001i	$0.103347\pi$
$458$	−18.2678	+	2.89333i	−0.853597	+	0.135196i
$459$	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	$0.132001\pi$
$462$	23.0534	+	28.0847i	1.07254	+	1.30662i
$463$	−2.76320	+	1.40792i	−0.128417	+	0.0654317i	−0.517019	−	0.855974i	$-0.672958\pi$
$463$	−2.76320	+	1.40792i	−0.128417	+	0.0654317i	0.388602	+	0.921406i	$0.372958\pi$
$464$	−1.74917	−	5.38339i	−0.0812031	−	0.249918i
$465$		0			0
$466$	−4.25650	+	13.1002i	−0.197179	+	0.606853i
$467$	6.20197	+	39.1577i	0.286993	+	1.81200i	0.536804	+	0.843707i	$0.319632\pi$
$467$	6.20197	+	39.1577i	0.286993	+	1.81200i	−0.249811	+	0.968295i	$0.580368\pi$
$468$	4.97245	+	1.83327i	0.229852	+	0.0847429i
$469$	16.0170	−	22.0455i	0.739598	−	1.01797i
$470$		0			0
$471$	−11.6080	+	13.0657i	−0.534870	+	0.602034i
$472$	1.74160	−	10.9960i	0.0801638	−	0.506134i
$473$	39.3387	+	20.0441i	1.80880	+	0.921628i
$474$	6.34454	−	1.39272i	0.291415	−	0.0639698i
$475$		0			0
$476$			6.00814i			0.275383i
$477$	0.599970	−	15.3509i	0.0274707	−	0.702869i
$478$	20.4797	+	3.24367i	0.936721	+	0.148362i
$479$	−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
$483$	14.2319	−	5.57197i	0.647576	−	0.253533i
$484$	−13.1543	−	4.27411i	−0.597925	−	0.194278i
$485$		0			0
$486$	2.73249	−	15.3471i	0.123948	−	0.696159i
$487$	−0.947305	−	1.85919i	−0.0429265	−	0.0842480i	0.868547	−	0.495607i	$-0.165054\pi$
$487$	−0.947305	−	1.85919i	−0.0429265	−	0.0842480i	−0.911473	+	0.411359i	$0.865054\pi$
$488$	−4.40713	−	8.64948i	−0.199501	−	0.391543i
$489$	−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	$0.722367\pi$
$492$	2.38195	+	6.08398i	0.107386	+	0.274287i
$493$	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
$497$	−62.6527	−	9.92321i	−2.81036	−	0.445117i
$498$	−7.37582	+	28.2776i	−0.330519	+	1.26715i
$499$		−	36.0457i		−	1.61363i	−0.590806	−	0.806813i	$-0.701190\pi$
$499$		−	36.0457i		−	1.61363i	0.590806	−	0.806813i	$-0.298810\pi$
$500$		0			0
$501$	6.22704	+	28.3673i	0.278203	+	1.26736i
$502$	3.35817	+	1.71107i	0.149882	+	0.0763689i
$503$	−4.92776	+	31.1126i	−0.219718	+	1.38724i	0.593289	+	0.804990i	$0.297829\pi$
$503$	−4.92776	+	31.1126i	−0.219718	+	1.38724i	−0.813007	+	0.582255i	$0.802171\pi$
$504$	6.16871	−	11.0204i	0.274776	−	0.490886i
$505$		0			0
$506$	−6.13944	+	8.45021i	−0.272931	+	0.375658i
$507$	9.22397	−	14.4125i	0.409651	−	0.640083i
$508$	0.242702	+	1.53236i	0.0107682	+	0.0679876i
$509$	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
$512$	0.891007	−	0.453990i	0.0393773	−	0.0200637i
$513$	−4.21525	+	8.69747i	−0.186108	+	0.384003i
$514$	29.2797	−	9.51354i	1.29147	−	0.419624i
$515$		0			0
$516$	1.50261	−	15.2724i	0.0661489	−	0.672332i
$517$	−23.0403	+	3.64922i	−1.01331	+	0.160493i
$518$	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	$-0.456740\pi$
$522$	−4.61278	−	16.3428i	−0.201896	−	0.715304i
$523$	18.1177	−	35.5580i	0.792232	−	1.55484i	−0.0392100	−	0.999231i	$-0.512484\pi$
$523$	18.1177	−	35.5580i	0.792232	−	1.55484i	0.831442	−	0.555612i	$-0.187516\pi$
$524$	6.36713			0.278150
$525$		0			0
$526$	−5.54358			−0.241712
$527$	−4.19530	+	8.23373i	−0.182750	+	0.358667i
$528$	0.509001	+	8.61596i	0.0221514	+	0.374962i
$529$	−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
$533$	−6.58172	+	1.04244i	−0.285086	+	0.0451532i
$534$	−1.95876	−	0.192717i	−0.0847636	−	0.00833967i
$535$		0			0
$536$	6.15614	−	2.00025i	0.265905	−	0.0863977i
$537$	0.233565	−	0.191722i	0.0100791	−	0.00827343i
$538$	−3.08583	+	1.57231i	−0.133040	+	0.0677872i
$539$	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	$-0.0831100\pi$
$542$	−0.736991	−	4.65318i	−0.0316565	−	0.199871i
$543$	−16.5979	−	10.6226i	−0.712285	−	0.455860i
$544$	−0.838876	+	1.15461i	−0.0359665	+	0.0495036i
$545$		0			0
$546$	9.62947	+	8.55518i	0.412103	+	0.366128i
$547$	−6.44292	+	40.6790i	−0.275479	+	1.73931i	0.330482	+	0.943812i	$0.392789\pi$
$547$	−6.44292	+	40.6790i	−0.275479	+	1.73931i	−0.605961	+	0.795495i	$0.707211\pi$
$548$	3.66124	+	1.86549i	0.156400	+	0.0796899i
$549$	−12.1979	−	26.4450i	−0.520594	−	1.12864i
$550$		0			0
$551$			10.5287i			0.448537i
$552$	3.51300	+	0.916318i	0.149523	+	0.0390011i
$553$	15.5934	+	2.46975i	0.663098	+	0.105024i
$554$	−20.1331	+	14.6276i	−0.855375	+	0.621466i
$555$		0			0
$556$	8.64122	+	6.27821i	0.366469	+	0.266256i
$557$	17.7694	+	17.7694i	0.752915	+	0.752915i	0.975022	−	0.222107i	$-0.0712934\pi$
$557$	17.7694	+	17.7694i	0.752915	+	0.752915i	−0.222107	+	0.975022i	$0.571293\pi$
$558$	16.1490	−	10.7952i	0.683640	−	0.456998i
$559$	14.8858	+	4.83667i	0.629600	+	0.204570i
$560$		0			0
$561$	−6.22977	−	10.6265i	−0.263021	−	0.448651i
$562$	−4.38632	−	8.60864i	−0.185026	−	0.363133i
$563$	−4.70734	−	9.23868i	−0.198391	−	0.389364i	0.770282	−	0.637703i	$-0.220115\pi$
$563$	−4.70734	−	9.23868i	−0.198391	−	0.389364i	−0.968673	+	0.248339i	$0.920115\pi$
$564$	4.10073	+	6.99487i	0.172672	+	0.294537i
$565$		0			0
$566$	−0.970373	−	0.315293i	−0.0407878	−	0.0132528i
$567$	19.7832	−	32.3131i	0.830816	−	1.35702i
$568$	−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	$0.175777\pi$
$572$	−8.69450	−	1.37707i	−0.363535	−	0.0575783i
$573$	−30.9318	−	8.06815i	−1.29220	−	0.337052i
$574$			15.8802i			0.662826i
$575$		0			0
$576$	2.72417	−	1.25654i	0.113507	−	0.0523559i
$577$	5.29743	+	2.69918i	0.220535	+	0.112368i	0.560768	−	0.827973i	$-0.310506\pi$
$577$	5.29743	+	2.69918i	0.220535	+	0.112368i	−0.340233	+	0.940341i	$0.610506\pi$
$578$	−2.34075	+	14.7789i	−0.0973625	+	0.614723i
$579$	−6.07162	−	5.39425i	−0.252328	−	0.224177i
$580$		0			0
$581$	−41.7498	+	57.4636i	−1.73207	+	2.38399i
$582$	5.12883	+	3.28243i	0.212597	+	0.136061i
$583$	3.99187	+	25.2037i	0.165326	+	1.04383i
$584$	−2.85708	+	8.79320i	−0.118227	+	0.363865i
$585$		0			0
$586$	−0.636311	−	1.95836i	−0.0262858	−	0.0808992i
$587$	23.3146	−	11.8794i	0.962295	−	0.490314i	0.0990406	−	0.995083i	$-0.468423\pi$
$587$	23.3146	−	11.8794i	0.962295	−	0.490314i	0.863254	+	0.504770i	$0.168423\pi$
$588$	14.3549	−	11.7832i	0.591986	−	0.485932i
$589$	−11.4543	+	3.72172i	−0.471966	+	0.153351i
$590$		0			0
$591$	−21.8581	−	2.15056i	−0.899122	−	0.0884623i
$592$	2.54323	−	0.402809i	0.104526	−	0.0165553i
$593$	23.6228	−	23.6228i	0.970072	−	0.970072i	−0.0294930	−	0.999565i	$-0.509389\pi$
$593$	23.6228	−	23.6228i	0.970072	−	0.970072i	0.999565	+	0.0294930i	$0.00938927\pi$
$594$	0.516378	+	25.8878i	0.0211872	+	1.06219i
$595$		0			0
$596$	−3.01693	−	4.15244i	−0.123578	−	0.170091i
$597$	0.166091	+	2.81145i	0.00679764	+	0.115065i
$598$	−1.68106	+	3.29926i	−0.0687435	+	0.134917i
$599$	−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	$0.610912\pi$
$602$	16.9335	−	33.2339i	0.690159	−	1.35451i
$603$	18.6887	−	5.27491i	0.761062	−	0.214811i
$604$	−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	−0.997121	−	0.0758281i	$-0.975840\pi$
$607$	−22.6982	+	22.6982i	−0.921293	+	0.921293i	0.0758281	+	0.997121i	$0.475840\pi$
$608$	−1.83715	+	0.290976i	−0.0745063	+	0.0118006i
$609$	4.04127	−	41.0751i	0.163761	−	1.66445i
$610$		0			0
$611$	−7.86501	+	2.55550i	−0.318184	+	0.103384i
$612$	−2.64998	+	3.36291i	−0.107119	+	0.135938i
$613$	38.6048	−	19.6701i	1.55923	−	0.794470i	0.559818	−	0.828616i	$-0.310871\pi$
$613$	38.6048	−	19.6701i	1.55923	−	0.794470i	0.999417	+	0.0341460i	$0.0108711\pi$
$614$	5.23570	+	16.1138i	0.211296	+	0.650301i
$615$		0			0
$616$	−6.48251	+	19.9511i	−0.261188	+	0.803853i
$617$	−3.81403	−	24.0808i	−0.153547	−	0.969458i	−0.937335	−	0.348429i	$-0.886715\pi$
$617$	−3.81403	−	24.0808i	−0.153547	−	0.969458i	0.783788	−	0.621028i	$-0.213285\pi$
$618$	2.47695	−	3.87025i	0.0996374	−	0.155684i
$619$	−23.7633	+	32.7074i	−0.955130	+	1.31462i	−0.00591868	+	0.999982i	$0.501884\pi$
$619$	−23.7633	+	32.7074i	−0.955130	+	1.31462i	−0.949211	+	0.314641i	$0.898116\pi$
$620$		0			0
$621$	10.4236	+	3.15845i	0.418285	+	0.126744i
$622$	−0.599376	+	3.78431i	−0.0240328	+	0.151737i
$623$	−4.26239	−	2.17180i	−0.170769	−	0.0870112i
$624$	0.656040	+	2.98859i	0.0262626	+	0.119639i
$625$		0			0
$626$		−	22.8677i		−	0.913977i
$627$	4.05192	−	15.5343i	0.161818	−	0.620381i
$628$	−9.96632	−	1.57851i	−0.397700	−	0.0629894i
$629$	−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
$633$	7.62720	+	19.4814i	0.303154	+	0.774318i
$634$	8.32864	+	2.70614i	0.330772	+	0.107474i
$635$		0			0
$636$	7.65166	−	4.48577i	0.303408	−	0.177873i
$637$	8.59929	+	16.8771i	0.340716	+	0.668693i
$638$	12.8055	+	25.1322i	0.506974	+	0.994992i
$639$	−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	$0.658247\pi$
$642$	−19.0471	+	7.45716i	−0.751730	+	0.294311i
$643$	32.6751	+	32.6751i	1.28858	+	1.28858i	0.935649	+	0.352932i	$0.114815\pi$
$643$	32.6751	+	32.6751i	1.28858	+	1.28858i	0.352932	+	0.935649i	$0.385185\pi$
$644$	7.13886	+	5.18669i	0.281311	+	0.204384i
$645$		0			0
$646$	2.14764	−	1.56035i	0.0844978	−	0.0613912i
$647$	−48.0211	−	7.60579i	−1.88790	−	0.299015i	−0.897916	−	0.440167i	$-0.854919\pi$
$647$	−48.0211	−	7.60579i	−1.88790	−	0.299015i	−0.989988	+	0.141152i	$0.954919\pi$
$648$	8.31350	−	3.44758i	0.326585	−	0.135434i
$649$			55.4774i			2.17768i
$650$		0			0
$651$	46.1147	−	10.1229i	1.80738	−	0.396746i
$652$	−5.00771	−	2.55156i	−0.196117	−	0.0999267i
$653$	3.10987	−	19.6349i	0.121699	−	0.768375i	−0.849056	−	0.528302i	$-0.822829\pi$
$653$	3.10987	−	19.6349i	0.121699	−	0.768375i	0.970755	−	0.240073i	$-0.0771712\pi$
$654$	−15.3214	+	17.2453i	−0.599113	+	0.674345i
$655$		0			0
$656$	−2.21724	+	3.05177i	−0.0865688	+	0.119152i
$657$	−9.59494	+	26.0247i	−0.374334	+	1.01532i
$658$	3.08291	+	19.4647i	0.120184	+	0.758815i
$659$	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	$0.991688\pi$
$662$	−5.34493	+	2.72338i	−0.207736	+	0.105847i
$663$	−2.77062	−	3.37531i	−0.107602	−	0.131086i
$664$	−16.0465	+	5.21383i	−0.622726	+	0.202336i
$665$		0			0
$666$	7.67108	−	0.909535i	0.297248	−	0.0352438i
$667$	11.7187	−	1.85606i	0.453750	−	0.0718670i
$668$	−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
$672$	7.27889	−	0.430011i	0.280789	−	0.0165880i
$673$	−15.3688	+	30.1630i	−0.592425	+	1.16270i	0.379010	+	0.925392i	$0.376264\pi$
$673$	−15.3688	+	30.1630i	−0.592425	+	1.16270i	−0.971435	+	0.237306i	$0.923736\pi$
$674$	2.43046			0.0936178
$675$		0			0
$676$	9.87932			0.379974
$677$	−3.49259	+	6.85459i	−0.134231	+	0.263443i	−0.948332	−	0.317280i	$-0.897230\pi$
$677$	−3.49259	+	6.85459i	−0.134231	+	0.263443i	0.814101	+	0.580724i	$0.197230\pi$
$678$	−2.58769	+	0.152871i	−0.0993795	+	0.00587099i
$679$	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
$683$	2.86990	−	0.454547i	0.109814	−	0.0173928i	−0.101286	−	0.994857i	$-0.532296\pi$
$683$	2.86990	−	0.454547i	0.109814	−	0.0173928i	0.211099	+	0.977465i	$0.432296\pi$
$684$	−5.54134	+	0.657019i	−0.211878	+	0.0251217i
$685$		0			0
$686$	14.9035	−	4.84242i	0.569016	−	0.184885i
$687$	−20.3254	−	24.7614i	−0.775463	−	0.944705i
$688$	7.89443	−	4.02241i	0.300972	−	0.153353i
$689$	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	$0.910085\pi$
$692$	−0.700227	−	4.42106i	−0.0266186	−	0.168063i
$693$	−21.7702	+	59.0481i	−0.826981	+	2.24305i
$694$	−13.3577	+	18.3852i	−0.507050	+	0.697894i
$695$		0			0
$696$	6.51168	−	7.32936i	0.246824	−	0.277819i
$697$	0.842182	−	5.31733i	0.0318999	−	0.201408i
$698$	−11.1668	−	5.68977i	−0.422670	−	0.215361i
$699$	−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	$-0.283453\pi$
$702$	1.61647	+	9.03579i	0.0610097	+	0.341034i
$703$	−4.73055	−	0.749245i	−0.178416	−	0.0282583i
$704$	−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
$708$	17.9560	−	7.02998i	0.674828	−	0.264203i
$709$	16.1533	+	5.24852i	0.606650	+	0.197112i	0.596204	−	0.802833i	$-0.296675\pi$
$709$	16.1533	+	5.24852i	0.606650	+	0.197112i	0.0104457	+	0.999945i	$0.496675\pi$
$710$		0			0
$711$	7.63870	+	8.26008i	0.286474	+	0.309777i
$712$	−0.515891	−	1.01249i	−0.0193338	−	0.0379448i
$713$	6.16161	+	12.0928i	0.230754	+	0.452880i
$714$	−8.97742	+	5.26300i	−0.335971	+	0.196963i
$715$		0			0
$716$	0.165923	+	0.0539115i	0.00620082	+	0.00201477i
$717$	13.0931	+	33.4424i	0.488970	+	1.24893i
$718$	−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
$722$	−15.3489	−	2.43102i	−0.571226	−	0.0904734i
$723$	2.72003	−	10.4281i	0.101159	−	0.387825i
$724$		−	11.3773i		−	0.422835i
$725$		0			0
$726$	−5.13651	−	23.3994i	−0.190634	−	0.868432i
$727$	30.4534	+	15.5168i	1.12945	+	0.575485i	0.915884	−	0.401443i	$-0.131491\pi$
$727$	30.4534	+	15.5168i	1.12945	+	0.575485i	0.213569	+	0.976928i	$0.431491\pi$
$728$	−1.16337	+	7.34523i	−0.0431174	+	0.272233i
$729$	25.3254	−	9.36082i	0.937977	−	0.346697i
$730$		0			0
$731$	−7.43254	+	10.2300i	−0.274902	+	0.378371i
$732$	9.06358	−	14.1619i	0.335000	−	0.523440i
$733$	−2.91730	−	18.4191i	−0.107753	−	0.680326i	−0.981140	−	0.193299i	$-0.938081\pi$
$733$	−2.91730	−	18.4191i	−0.107753	−	0.680326i	0.873387	−	0.487027i	$-0.161919\pi$
$734$	1.29725	−	3.99251i	0.0478822	−	0.147366i
$735$		0			0
$736$	0.647728	+	1.99350i	0.0238756	+	0.0734815i
$737$	−28.7397	+	14.6436i	−1.05864	+	0.539405i
$738$	−7.00421	+	8.88856i	−0.257828	+	0.327192i
$739$	−1.28835	+	0.418609i	−0.0473926	+	0.0153988i	−0.332617	−	0.943062i	$-0.607932\pi$
$739$	−1.28835	+	0.418609i	−0.0473926	+	0.0153988i	0.285225	+	0.958461i	$0.407932\pi$
$740$		0			0
$741$	0.557260	−	5.66394i	0.0204715	−	0.208070i
$742$	21.2924	−	3.37239i	0.781669	−	0.123804i
$743$	8.68111	−	8.68111i	0.318479	−	0.318479i	−0.529704	−	0.848183i	$-0.677697\pi$
$743$	8.68111	−	8.68111i	0.318479	−	0.318479i	0.848183	+	0.529704i	$0.177697\pi$
$744$	10.2755	+	4.49332i	0.376717	+	0.164733i
$745$		0			0
$746$	2.67527	+	3.68219i	0.0979486	+	0.134815i
$747$	−48.7137	+	13.7495i	−1.78234	+	0.503069i
$748$	3.22868	−	6.33665i	0.118052	−	0.231691i
$749$	−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	$0.239489\pi$
$752$	−2.12527	+	4.17108i	−0.0775007	+	0.152104i
$753$	0.384982	+	6.51667i	0.0140295	+	0.237481i
$754$	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	−0.989922	−	0.141616i	$-0.954770\pi$
$757$	−23.3400	+	23.3400i	−0.848305	+	0.848305i	0.141616	+	0.989922i	$0.454770\pi$
$758$	−32.5807	+	5.16027i	−1.18338	+	0.187429i
$759$	−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	$0.358114\pi$
$762$	−2.07707	+	1.70496i	−0.0752442	+	0.0617643i
$763$	−49.9570	+	25.4544i	−1.80856	+	0.921509i
$764$	−5.70322	−	17.5527i	−0.206335	−	0.635035i
$765$		0			0
$766$	5.28095	−	16.2531i	0.190808	−	0.587248i
$767$	3.07662	+	19.4250i	0.111090	+	0.701397i
$768$	1.45886	+	0.933665i	0.0526420	+	0.0336907i
$769$	−2.15066	+	2.96013i	−0.0775549	+	0.106745i	−0.846032	−	0.533132i	$-0.821015\pi$
$769$	−2.15066	+	2.96013i	−0.0775549	+	0.106745i	0.768477	+	0.639877i	$0.221015\pi$
$770$		0			0
$771$	39.8636	+	35.4163i	1.43565	+	1.27549i
$772$	0.733534	−	4.63135i	0.0264005	−	0.166686i
$773$	−29.4947	−	15.0283i	−1.06085	−	0.540531i	−0.165646	−	0.986185i	$-0.552971\pi$
$773$	−29.4947	−	15.0283i	−1.06085	−	0.540531i	−0.895205	+	0.445655i	$0.852971\pi$
$774$	24.1365	−	11.1331i	0.867568	−	0.400171i
$775$		0			0
$776$			3.51564i			0.126204i
$777$	18.1675	+	4.73875i	0.651756	+	0.170002i
$778$	13.8752	+	2.19762i	0.497450	+	0.0787884i
$779$	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
$783$	20.3788	−	21.2084i	0.728280	−	0.757925i
$784$	10.1976	+	3.31339i	0.364199	+	0.118336i
$785$		0			0
$786$	5.57747	+	9.51383i	0.198942	+	0.339347i
$787$	7.51367	+	14.7464i	0.267833	+	0.525653i	0.985277	−	0.170964i	$-0.0546880\pi$
$787$	7.51367	+	14.7464i	0.267833	+	0.525653i	−0.717444	+	0.696616i	$0.754688\pi$
$788$	−5.75693	−	11.2986i	−0.205082	−	0.402496i
$789$	−4.85606	−	8.28327i	−0.172880	−	0.294892i
$790$		0			0
$791$	−5.99204	−	1.94693i	−0.213053	−	0.0692250i
$792$	−12.4282	+	8.30795i	−0.441616	+	0.295210i
$793$	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
$797$	39.6609	+	6.28166i	1.40486	+	0.222508i	0.812404	−	0.583095i	$-0.198158\pi$
$797$	39.6609	+	6.28166i	1.40486	+	0.222508i	0.592456	+	0.805603i	$0.298158\pi$
$798$	−13.1236	−	3.42312i	−0.464571	−	0.121177i
$799$		−	6.68108i		−	0.236360i
$800$		0			0
$801$	−1.42787	−	3.09561i	−0.0504512	−	0.109378i
$802$	26.1193	+	13.3084i	0.922304	+	0.469937i
$803$	7.20730	−	45.5051i	0.254340	−	1.60584i
$804$	8.38144	+	7.44639i	0.295591	+	0.262614i
$805$		0			0
$806$	−6.72327	+	9.25378i	−0.236817	+	0.325951i
$807$	−5.05249	−	3.23357i	−0.177856	−	0.113827i
$808$	2.60839	+	16.4687i	0.0917627	+	0.579367i
$809$	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	$-0.356039\pi$
$812$	21.2320	−	10.8183i	0.745098	−	0.379646i
$813$	6.30723	−	5.17730i	0.221204	−	0.181576i
$814$	−12.2032	+	3.96505i	−0.427721	+	0.138975i
$815$		0			0
$816$	−2.46007	−	0.242040i	−0.0861197	−	0.00847309i
$817$	−16.2774	+	2.57808i	−0.569473	+	0.0901957i
$818$	−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	$0.721721\pi$
$822$	0.419726	+	7.10478i	0.0146396	+	0.247808i
$823$	7.77764	−	15.2645i	0.271112	−	0.532086i	−0.714805	−	0.699324i	$-0.753485\pi$
$823$	7.77764	−	15.2645i	0.271112	−	0.532086i	0.985917	+	0.167237i	$0.0534846\pi$
$824$	2.65293			0.0924192
$825$		0			0
$826$	46.8681			1.63075
$827$	17.8399	−	35.0129i	0.620356	−	1.21752i	−0.340442	−	0.940266i	$-0.610577\pi$
$827$	17.8399	−	35.0129i	0.620356	−	1.21752i	0.960798	−	0.277251i	$-0.0894234\pi$
$828$	1.70814	+	6.05183i	0.0593620	+	0.210316i
$829$	−16.9229	−	23.2923i	−0.587756	−	0.808977i	0.406763	−	0.913534i	$-0.366657\pi$
$829$	−16.9229	−	23.2923i	−0.587756	−	0.808977i	−0.994519	+	0.104557i	$0.966657\pi$
$830$		0			0
$831$	−39.4929	−	17.2697i	−1.36999	−	0.599079i
$832$	−1.24914	+	1.24914i	−0.0433060	+	0.0433060i
$833$	−15.1144	+	2.39388i	−0.523681	+	0.0829430i
$834$	−1.81145	+	18.4114i	−0.0627252	+	0.637534i
$835$		0			0
$836$	8.81517	−	2.86422i	0.304879	−	0.0990613i
$837$	30.2764	+	14.6736i	1.04651	+	0.507193i
$838$	−9.76323	+	4.97461i	−0.337265	+	0.171845i
$839$	−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
$842$	−2.19818	−	13.8788i	−0.0757544	−	0.478294i
$843$	9.02079	−	14.0951i	0.310692	−	0.485460i
$844$	−7.09981	+	9.77205i	−0.244385	+	0.336368i
$845$		0			0
$846$	−6.85965	+	12.2547i	−0.235839	+	0.421325i
$847$	9.10870	−	57.5100i	0.312979	−	1.97607i
$848$	4.56273	+	2.32483i	0.156685	+	0.0798349i
$849$	−0.378911	−	1.72613i	−0.0130042	−	0.0592406i
$850$		0			0
$851$			5.39730i			0.185017i
$852$	6.58711	−	25.2538i	0.225671	−	0.865181i
$853$	−48.8210	−	7.73248i	−1.67160	−	0.264755i	−0.752445	−	0.658655i	$-0.771126\pi$
$853$	−48.8210	−	7.73248i	−1.67160	−	0.264755i	−0.919153	+	0.393900i	$0.871126\pi$
$854$	33.0619	−	24.0209i	1.13135	−	0.821977i
$855$		0			0
$856$	−9.55419	−	6.94153i	−0.326556	−	0.237257i
$857$	5.79343	+	5.79343i	0.197900	+	0.197900i	0.799099	−	0.601199i	$-0.205310\pi$
$857$	5.79343	+	5.79343i	0.197900	+	0.197900i	−0.601199	+	0.799099i	$0.705310\pi$
$858$	−5.55855	−	14.1977i	−0.189766	−	0.484701i
$859$	3.26295	+	1.06020i	0.111330	+	0.0361734i	0.364152	−	0.931339i	$-0.381359\pi$
$859$	3.26295	+	1.06020i	0.111330	+	0.0361734i	−0.252822	+	0.967513i	$0.581359\pi$
$860$		0			0
$861$	−23.7283	+	13.9107i	−0.808659	+	0.474075i
$862$	−1.97077	−	3.86786i	−0.0671249	−	0.131740i
$863$	11.6022	+	22.7707i	0.394944	+	0.775122i	0.999775	−	0.0212325i	$-0.00675901\pi$
$863$	11.6022	+	22.7707i	0.394944	+	0.775122i	−0.604830	+	0.796354i	$0.706759\pi$
$864$	4.26385	+	2.96978i	0.145059	+	0.101034i
$865$		0			0
$866$	7.46455	+	2.42538i	0.253656	+	0.0824177i
$867$	−24.1333	+	9.44845i	−0.819609	+	0.320886i
$868$	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
$872$	−13.1545	−	2.08347i	−0.445468	−	0.0705551i
$873$	−0.411899	+	10.5389i	−0.0139407	+	0.356687i
$874$		−	3.89884i		−	0.131880i
$875$		0			0
$876$	−15.6416	+	3.43357i	−0.528482	+	0.116010i
$877$	−26.8672	−	13.6895i	−0.907241	−	0.462262i	−0.0628704	−	0.998022i	$-0.520025\pi$
$877$	−26.8672	−	13.6895i	−0.907241	−	0.462262i	−0.844371	+	0.535759i	$0.820025\pi$
$878$	3.14649	−	19.8662i	0.106189	−	0.670451i
$879$	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	$-0.125453\pi$
$882$	30.1812	+	11.1274i	1.01625	+	0.374678i
$883$	−1.76422	−	11.1388i	−0.0593707	−	0.374852i	−0.999427	−	0.0338339i	$-0.989228\pi$
$883$	−1.76422	−	11.1388i	−0.0593707	−	0.374852i	0.940057	−	0.341018i	$-0.110772\pi$
$884$	0.779087	−	2.39778i	0.0262035	−	0.0806462i
$885$		0			0
$886$	−5.20028	−	16.0048i	−0.174707	−	0.537692i
$887$	−16.7280	+	8.52333i	−0.561671	+	0.286186i	−0.711686	−	0.702498i	$-0.752068\pi$
$887$	−16.7280	+	8.52333i	−0.561671	+	0.286186i	0.150015	+	0.988684i	$0.452068\pi$
$888$	2.82970	+	3.44727i	0.0949585	+	0.115683i
$889$	−6.21167	+	2.01830i	−0.208333	+	0.0676914i
$890$		0			0
$891$	−38.2295	+	23.4487i	−1.28074	+	0.785562i
$892$	6.14829	−	0.973793i	0.205860	−	0.0326050i
$893$	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
$897$	−6.40235	+	0.378228i	−0.213768	+	0.0126287i
$898$	1.61517	−	3.16995i	0.0538989	−	0.105783i
$899$	36.6510			1.22238
$900$		0			0
$901$	−7.30841			−0.243478
$902$	8.53377	−	16.7485i	0.284144	−	0.557663i
$903$	64.4918	−	3.80995i	2.14615	−	0.126787i
$904$	−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	−0.0323248	−	0.999477i	$-0.510291\pi$
$907$	29.1272	−	29.1272i	0.967153	−	0.967153i	0.999477	+	0.0323248i	$0.0102911\pi$
$908$	−9.04270	+	1.43222i	−0.300093	+	0.0475300i
$909$	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	$0.406734\pi$
$912$	−2.04408	−	2.49020i	−0.0676864	−	0.0824587i
$913$	74.9126	−	38.1699i	2.47925	−	1.26324i
$914$	5.87403	+	18.0784i	0.194296	+	0.597980i
$915$		0			0
$916$	5.71542	−	17.5902i	0.188843	−	0.581198i
$917$	4.19312	+	26.4743i	0.138469	+	0.874259i
$918$	−7.34623	−	1.01379i	−0.242462	−	0.0334601i
$919$	14.7998	−	20.3701i	0.488199	−	0.671949i	−0.491855	−	0.870677i	$-0.663681\pi$
$919$	14.7998	−	20.3701i	0.488199	−	0.671949i	0.980055	+	0.198728i	$0.0636811\pi$
$920$		0			0
$921$	−19.4911	+	21.9386i	−0.642252	+	0.722901i
$922$	−5.01091	+	31.6376i	−0.165026	+	1.04193i
$923$	23.7173	+	12.0845i	0.780663	+	0.397768i
$924$	−35.4897	+	7.79051i	−1.16752	+	0.256289i
$925$		0			0
$926$		−	3.10121i		−	0.101912i
$927$	7.95272	+	0.310822i	0.261202	+	0.0102087i
$928$	5.59074	+	0.885486i	0.183525	+	0.0290675i
$929$	−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
$933$	−6.17960	+	2.41938i	−0.202311	+	0.0792070i
$934$	−37.7054	−	12.2512i	−1.23376	−	0.400872i
$935$		0			0
$936$	−3.89090	+	3.59820i	−0.127178	+	0.117611i
$937$	−0.618103	−	1.21310i	−0.0201925	−	0.0396301i	0.880690	−	0.473693i	$-0.157079\pi$
$937$	−0.618103	−	1.21310i	−0.0201925	−	0.0396301i	−0.900882	+	0.434063i	$0.857079\pi$
$938$	12.3711	+	24.2797i	0.403932	+	0.792762i
$939$	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	$0.522663\pi$
$942$	−6.37166	−	16.2745i	−0.207600	−	0.530252i
$943$	−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
$947$	−6.67988	−	1.05799i	−0.217067	−	0.0343800i	0.0469536	−	0.998897i	$-0.485049\pi$
$947$	−6.67988	−	1.05799i	−0.217067	−	0.0343800i	−0.264021	+	0.964517i	$0.585049\pi$
$948$	−1.63944	+	6.28531i	−0.0532465	+	0.204137i
$949$		−	16.3330i		−	0.530191i
$950$		0			0
$951$	3.25217	+	14.8152i	0.105459	+	0.480417i
$952$	−5.35329	−	2.72764i	−0.173501	−	0.0884032i
$953$	2.66239	−	16.8097i	0.0862434	−	0.544519i	−0.906301	−	0.422633i	$-0.861106\pi$
$953$	2.66239	−	16.8097i	0.0862434	−	0.544519i	0.992544	−	0.121886i	$-0.0388942\pi$
$954$	13.4054	+	7.50374i	0.434015	+	0.242943i
$955$		0			0
$956$	−12.1877	+	16.7750i	−0.394180	+	0.542542i
$957$	−26.3354	+	41.1493i	−0.851303	+	1.33017i
$958$	−2.10827	−	13.3111i	−0.0681150	−	0.430061i
$959$	−5.34552	+	16.4518i	−0.172616	+	0.531257i
$960$		0			0
$961$	3.37603	+	10.3904i	0.108904	+	0.335173i
$962$	−4.05296	+	2.06509i	−0.130673	+	0.0665811i
$963$	−27.8274	−	21.9281i	−0.896727	−	0.706623i
$964$	5.91757	−	1.92274i	0.190592	−	0.0619271i
$965$		0			0
$966$	−1.49651	+	15.2104i	−0.0481494	+	0.489386i
$967$	−38.7579	+	6.13865i	−1.24637	+	0.197406i	−0.744550	−	0.667566i	$-0.767336\pi$
$967$	−38.7579	+	6.13865i	−1.24637	+	0.197406i	−0.501820	+	0.864972i	$0.667336\pi$
$968$	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	$0.961483\pi$
$972$	12.4338	+	9.40210i	0.398816	+	0.301573i
$973$	−20.4139	+	40.0644i	−0.654438	+	1.28441i
$974$	2.08662			0.0668596
$975$		0			0
$976$	9.70753			0.310731
$977$	19.1478	−	37.5797i	0.612593	−	1.20228i	−0.351368	−	0.936238i	$-0.614283\pi$
$977$	19.1478	−	37.5797i	0.612593	−	1.20228i	0.963961	−	0.266044i	$-0.0857167\pi$
$978$	−0.574087	−	9.71768i	−0.0183573	−	0.310737i
$979$	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
$983$	−14.2241	+	2.25288i	−0.453679	+	0.0718557i	−0.379092	−	0.925359i	$-0.623764\pi$
$983$	−14.2241	+	2.25288i	−0.453679	+	0.0718557i	−0.0745867	+	0.997215i	$0.523764\pi$
$984$	−6.50225	−	0.639739i	−0.207284	−	0.0203941i
$985$		0			0
$986$	−7.68307	+	2.49638i	−0.244679	+	0.0795009i
$987$	−26.3838	+	21.6572i	−0.839807	+	0.689357i
$988$	2.92773	−	1.49175i	0.0931434	−	0.0474589i
$989$	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	$0.0921882\pi$
$992$	1.01291	+	6.39524i	0.0321598	+	0.203049i
$993$	−8.75133	−	5.60082i	−0.277715	−	0.177737i
$994$	37.2854	−	51.3189i	1.18262	−	1.62774i
$995$		0			0
$996$	−21.8470	−	19.4097i	−0.692247	−	0.615019i
$997$	7.78106	−	49.1277i	0.246429	−	1.55589i	−0.485333	−	0.874329i	$-0.661302\pi$
$997$	7.78106	−	49.1277i	0.246429	−	1.55589i	0.731762	−	0.681560i	$-0.238698\pi$
$998$	32.1169	+	16.3644i	1.01664	+	0.518006i
$999$	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.b.143.1		80
3.2	odd	2	inner	750.2.l.b.143.6		80
5.2	odd	4		750.2.l.a.107.3		80
5.3	odd	4		750.2.l.c.107.8		80
5.4	even	2		150.2.l.a.83.10	yes	80
15.2	even	4		750.2.l.a.107.8		80
15.8	even	4		750.2.l.c.107.3		80
15.14	odd	2		150.2.l.a.83.5	yes	80
25.3	odd	20		150.2.l.a.47.5	✓	80
25.4	even	10		750.2.l.c.743.3		80
25.21	even	5		750.2.l.a.743.8		80
25.22	odd	20	inner	750.2.l.b.257.6		80
75.29	odd	10		750.2.l.c.743.8		80
75.47	even	20	inner	750.2.l.b.257.1		80
75.53	even	20		150.2.l.a.47.10	yes	80
75.71	odd	10		750.2.l.a.743.3		80

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

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)

\(f(q)\)	\(=\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-1.72904 + 0.102145i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(0.693954 - 1.58696i) q^{6} +(2.97677 - 2.97677i) q^{7} +(0.987688 - 0.156434i) q^{8} +(2.97913 - 0.353226i) q^{9} +O(q^{10})\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-1.72904 + 0.102145i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(0.693954 - 1.58696i) q^{6} +(2.97677 - 2.97677i) q^{7} +(0.987688 - 0.156434i) q^{8} +(2.97913 - 0.353226i) q^{9} +(-4.73921 + 1.53986i) q^{11} +(1.09894 + 1.33878i) q^{12} +(-1.57400 + 0.801995i) q^{13} +(1.30090 + 4.00375i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-0.223260 - 1.40961i) q^{17} +(-1.03777 + 2.81479i) q^{18} +(1.09331 - 1.50481i) q^{19} +(-4.84289 + 5.45101i) q^{21} +(0.779529 - 4.92175i) q^{22} +(-1.86763 - 0.951606i) q^{23} +(-1.69177 + 0.371369i) q^{24} -1.76655i q^{26} +(-5.11495 + 0.915046i) q^{27} +(-4.15797 - 0.658557i) q^{28} +(-4.57938 + 3.32712i) q^{29} +(-5.23835 - 3.80588i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(8.03698 - 3.14657i) q^{33} +(1.35733 + 0.441023i) q^{34} +(-2.03686 - 2.20255i) q^{36} +(-1.16900 - 2.29429i) q^{37} +(0.844446 + 1.65732i) q^{38} +(2.63959 - 1.54746i) q^{39} +(3.58757 + 1.16567i) q^{41} +(-2.65826 - 6.78975i) q^{42} +(-6.26505 - 6.26505i) q^{43} +(4.03141 + 2.92899i) q^{44} +(1.69577 - 1.23205i) q^{46} +(4.62368 + 0.732319i) q^{47} +(0.437156 - 1.67598i) q^{48} -10.7224i q^{49} +(0.530010 + 2.41446i) q^{51} +(1.57400 + 0.801995i) q^{52} +(0.801081 - 5.05783i) q^{53} +(1.50683 - 4.97287i) q^{54} +(2.47446 - 3.40580i) q^{56} +(-1.73666 + 2.71355i) q^{57} +(-0.885486 - 5.59074i) q^{58} +(3.44032 - 10.5882i) q^{59} +(-2.99979 - 9.23241i) q^{61} +(5.76923 - 2.93957i) q^{62} +(7.81673 - 9.91968i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-0.845099 + 8.58951i) q^{66} +(6.39326 - 1.01259i) q^{67} +(-1.00917 + 1.00917i) q^{68} +(3.32641 + 1.45459i) q^{69} +(-8.85681 - 12.1904i) q^{71} +(2.88720 - 0.814916i) q^{72} +(-4.19747 + 8.23800i) q^{73} +2.57494 q^{74} -1.86005 q^{76} +(-9.52374 + 18.6914i) q^{77} +(0.180445 + 3.05442i) q^{78} +(2.20434 + 3.03401i) q^{79} +(8.75046 - 2.10462i) q^{81} +(-2.66735 + 2.66735i) q^{82} +(-16.6646 + 2.63941i) q^{83} +(7.25654 + 0.713952i) q^{84} +(8.42648 - 2.73793i) q^{86} +(7.57807 - 6.22047i) q^{87} +(-4.43998 + 2.26228i) q^{88} +(-0.351151 - 1.08073i) q^{89} +(-2.29810 + 7.07281i) q^{91} +(0.327901 + 2.07029i) q^{92} +(9.44605 + 6.04544i) q^{93} +(-2.75161 + 3.78726i) q^{94} +(1.29484 + 1.15039i) q^{96} +(-0.549968 + 3.47236i) q^{97} +(9.55370 + 4.86785i) 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	\( 80 q - 4 q^{3} - 4 q^{7} + 4 q^{12} + 20 q^{16} + 8 q^{18} - 40 q^{19} + 36 q^{22} - 4 q^{27} + 16 q^{28} - 4 q^{33} - 40 q^{34} + 24 q^{37} - 40 q^{39} + 4 q^{42} + 24 q^{43} + 4 q^{48} + 64 q^{57} - 20 q^{58} - 64 q^{63} - 96 q^{67} + 140 q^{69} - 8 q^{72} - 100 q^{73} - 100 q^{78} + 80 q^{79} - 40 q^{81} - 96 q^{82} + 60 q^{84} - 80 q^{87} - 4 q^{88} - 12 q^{93} + 32 q^{97}+O(q^{100}) \) 80 * q - 4 * q^3 - 4 * q^7 + 4 * q^12 + 20 * q^16 + 8 * q^18 - 40 * q^19 + 36 * q^22 - 4 * q^27 + 16 * q^28 - 4 * q^33 - 40 * q^34 + 24 * q^37 - 40 * q^39 + 4 * q^42 + 24 * q^43 + 4 * q^48 + 64 * q^57 - 20 * q^58 - 64 * q^63 - 96 * q^67 + 140 * q^69 - 8 * q^72 - 100 * q^73 - 100 * q^78 + 80 * q^79 - 40 * q^81 - 96 * q^82 + 60 * q^84 - 80 * q^87 - 4 * q^88 - 12 * q^93 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

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