LMFDB - Embedded newform 575.2.p.a.399.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(49,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 16]))

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

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

chi := DirichletCharacter("575.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.p (of order $22$, degree $10$, 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:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{22})$
Coefficient field:	$\Q(\zeta_{44})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 115)
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			399.2
Root			$-0.755750 - 0.654861i$ of defining polynomial
Character	$\chi$	$=$	575.399
Dual form			575.2.p.a.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0872586 + 0.0125459i) q^{2} +(0.909632 - 0.415415i) q^{3} +(-1.91153 - 0.561276i) q^{4} +(0.0845850 - 0.0248364i) q^{6} +(-0.835939 + 1.30075i) q^{7} +(-0.320135 - 0.146201i) q^{8} +(-1.30972 + 1.51150i) q^{9} +(0.289532 + 2.01374i) q^{11} +(-1.97195 + 0.283524i) q^{12} +(1.15727 + 1.80075i) q^{13} +(-0.0892619 + 0.103014i) q^{14} +(3.32584 + 2.13739i) q^{16} +(1.22809 + 4.18251i) q^{17} +(-0.133248 + 0.115460i) q^{18} +(7.12381 + 2.09174i) q^{19} +(-0.220047 + 1.53046i) q^{21} +0.179348i q^{22} +(-3.89854 - 2.79310i) q^{23} -0.351939 q^{24} +(0.0783898 + 0.171650i) q^{26} +(-1.40866 + 4.79746i) q^{27} +(2.32800 - 2.01722i) q^{28} +(4.30111 - 1.26292i) q^{29} +(-0.376329 + 0.824045i) q^{31} +(0.795348 + 0.689173i) q^{32} +(1.09990 + 1.71148i) q^{33} +(0.0546886 + 0.380367i) q^{34} +(3.35194 - 2.15416i) q^{36} +(-8.38507 - 7.26571i) q^{37} +(0.595371 + 0.271897i) q^{38} +(1.80075 + 1.15727i) q^{39} +(3.95750 + 4.56720i) q^{41} +(-0.0384020 + 0.130785i) q^{42} +(-4.90745 + 2.24116i) q^{43} +(0.576814 - 4.01183i) q^{44} +(-0.305139 - 0.292633i) q^{46} +2.72825i q^{47} +(3.91319 + 0.562632i) q^{48} +(1.91476 + 4.19273i) q^{49} +(2.85459 + 3.29437i) q^{51} +(-1.20144 - 4.09173i) q^{52} +(0.148283 - 0.230732i) q^{53} +(-0.183106 + 0.400947i) q^{54} +(0.457783 - 0.294199i) q^{56} +(7.34898 - 1.05662i) q^{57} +(0.391153 - 0.0562393i) q^{58} +(-6.74757 + 4.33640i) q^{59} +(-1.33718 + 2.92802i) q^{61} +(-0.0431763 + 0.0671837i) q^{62} +(-0.871230 - 2.96714i) q^{63} +(-5.11714 - 5.90549i) q^{64} +(0.0745040 + 0.163141i) q^{66} +(-1.94473 - 0.279610i) q^{67} -8.68428i q^{68} +(-4.70653 - 0.921186i) q^{69} +(1.58700 - 11.0378i) q^{71} +(0.640269 - 0.292401i) q^{72} +(-2.92170 + 9.95039i) q^{73} +(-0.640515 - 0.739194i) q^{74} +(-12.4433 - 7.99684i) q^{76} +(-2.86139 - 1.30675i) q^{77} +(0.142612 + 0.123574i) q^{78} +(-2.70849 + 1.74064i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(0.288027 + 0.448178i) q^{82} +(3.29557 + 2.85563i) q^{83} +(1.27964 - 2.80202i) q^{84} +(-0.456334 + 0.133992i) q^{86} +(3.38779 - 2.93553i) q^{87} +(0.201720 - 0.686997i) q^{88} +(-0.266861 - 0.584343i) q^{89} -3.30972 q^{91} +(5.88446 + 7.52725i) q^{92} +0.905910i q^{93} +(-0.0342284 + 0.238063i) q^{94} +(1.00977 + 0.296494i) q^{96} +(4.18748 - 3.62848i) q^{97} +(0.114478 + 0.389875i) q^{98} +(-3.42297 - 2.19981i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{4} + 12 q^{6} - 4 q^{9} + 16 q^{11} + 6 q^{14} + 10 q^{16} + 26 q^{19} + 12 q^{21} + 12 q^{24} + 22 q^{26} - 4 q^{29} - 40 q^{31} - 32 q^{34} + 48 q^{36} - 10 q^{41} - 38 q^{44} - 32 q^{46}+ \cdots - 12 q^{99}+O(q^{100}) $ 20 * q + 2 * q^4 + 12 * q^6 - 4 * q^9 + 16 * q^11 + 6 * q^14 + 10 * q^16 + 26 * q^19 + 12 * q^21 + 12 * q^24 + 22 * q^26 - 4 * q^29 - 40 * q^31 - 32 * q^34 + 48 * q^36 - 10 * q^41 - 38 * q^44 - 32 * q^46 - 8 * q^49 - 20 * q^51 + 60 * q^54 + 6 * q^56 - 10 * q^59 - 6 * q^61 + 68 * q^64 - 8 * q^66 + 2 * q^69 - 44 * q^71 - 2 * q^74 - 4 * q^76 - 102 * q^79 - 2 * q^81 - 12 * q^84 - 18 * q^86 - 114 * q^89 - 44 * q^91 + 162 * q^94 - 14 * q^96 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/575\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$-1$

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 $

$2$	0.0872586	+	0.0125459i	0.0617012	+	0.00887129i	0.173096	−	0.984905i	$-0.444623\pi$
$2$	0.0872586	+	0.0125459i	0.0617012	+	0.00887129i	−0.111395	+	0.993776i	$0.535532\pi$
$3$	0.909632	−	0.415415i	0.525176	−	0.239840i	−0.135141	−	0.990826i	$-0.543149\pi$
$3$	0.909632	−	0.415415i	0.525176	−	0.239840i	0.660318	+	0.750986i	$0.270422\pi$
$4$	−1.91153	−	0.561276i	−0.955765	−	0.280638i
$5$		0			0
$5$		0			0
$6$	0.0845850	−	0.0248364i	0.0345317	−	0.0101394i
$7$	−0.835939	+	1.30075i	−0.315955	+	0.491636i	−0.962515	−	0.271227i	$-0.912571\pi$
$7$	−0.835939	+	1.30075i	−0.315955	+	0.491636i	0.646560	+	0.762863i	$0.276207\pi$
$8$	−0.320135	−	0.146201i	−0.113185	−	0.0516897i
$9$	−1.30972	+	1.51150i	−0.436574	+	0.503833i
$10$		0			0
$11$	0.289532	+	2.01374i	0.0872971	+	0.607165i	0.985765	+	0.168126i	$0.0537717\pi$
$11$	0.289532	+	2.01374i	0.0872971	+	0.607165i	−0.898468	+	0.439038i	$0.855319\pi$
$12$	−1.97195	+	0.283524i	−0.569253	+	0.0818462i
$13$	1.15727	+	1.80075i	0.320969	+	0.499437i	0.963820	−	0.266554i	$-0.0858850\pi$
$13$	1.15727	+	1.80075i	0.320969	+	0.499437i	−0.642851	+	0.765991i	$0.722249\pi$
$14$	−0.0892619	+	0.103014i	−0.0238563	+	0.0275316i
$15$		0			0
$16$	3.32584	+	2.13739i	0.831460	+	0.534347i
$17$	1.22809	+	4.18251i	0.297857	+	1.01441i	0.963405	+	0.268052i	$0.0863798\pi$
$17$	1.22809	+	4.18251i	0.297857	+	1.01441i	−0.665548	+	0.746355i	$0.731802\pi$
$18$	−0.133248	+	0.115460i	−0.0314068	+	0.0272141i
$19$	7.12381	+	2.09174i	1.63431	+	0.479878i	0.964814	−	0.262935i	$-0.0846905\pi$
$19$	7.12381	+	2.09174i	1.63431	+	0.479878i	0.669499	+	0.742813i	$0.266509\pi$
$20$		0			0
$21$	−0.220047	+	1.53046i	−0.0480182	+	0.333974i
$22$			0.179348i			0.0382372i
$23$	−3.89854	−	2.79310i	−0.812901	−	0.582402i
$23$	−3.89854	−	2.79310i	−0.812901	−	0.582402i
$24$	−0.351939			−0.0718392
$25$		0			0
$26$	0.0783898	+	0.171650i	0.0153735	+	0.0336633i
$27$	−1.40866	+	4.79746i	−0.271097	+	0.923273i
$28$	2.32800	−	2.01722i	0.439951	−	0.381219i
$29$	4.30111	−	1.26292i	0.798695	−	0.234518i	0.143177	−	0.989697i	$-0.454268\pi$
$29$	4.30111	−	1.26292i	0.798695	−	0.234518i	0.655519	+	0.755179i	$0.272450\pi$
$30$		0			0
$31$	−0.376329	+	0.824045i	−0.0675906	+	0.148003i	−0.940412	−	0.340037i	$-0.889561\pi$
$31$	−0.376329	+	0.824045i	−0.0675906	+	0.148003i	0.872822	+	0.488039i	$0.162288\pi$
$32$	0.795348	+	0.689173i	0.140599	+	0.121830i
$33$	1.09990	+	1.71148i	0.191469	+	0.297931i
$34$	0.0546886	+	0.380367i	0.00937901	+	0.0652325i
$35$		0			0
$36$	3.35194	−	2.15416i	0.558656	−	0.359027i
$37$	−8.38507	−	7.26571i	−1.37850	−	1.19447i	−0.957856	−	0.287248i	$-0.907260\pi$
$37$	−8.38507	−	7.26571i	−1.37850	−	1.19447i	−0.420641	−	0.907227i	$-0.638195\pi$
$38$	0.595371	+	0.271897i	0.0965819	+	0.0441075i
$39$	1.80075	+	1.15727i	0.288350	+	0.185311i
$40$		0			0
$41$	3.95750	+	4.56720i	0.618058	+	0.713277i	0.975337	−	0.220720i	$-0.0708408\pi$
$41$	3.95750	+	4.56720i	0.618058	+	0.713277i	−0.357279	+	0.933998i	$0.616295\pi$
$42$	−0.0384020	+	0.130785i	−0.00592556	+	0.0201806i
$43$	−4.90745	+	2.24116i	−0.748379	+	0.341773i	−0.752828	−	0.658217i	$-0.771311\pi$
$43$	−4.90745	+	2.24116i	−0.748379	+	0.341773i	0.00444961	+	0.999990i	$0.498584\pi$
$44$	0.576814	−	4.01183i	0.0869579	−	0.604806i
$45$		0			0
$46$	−0.305139	−	0.292633i	−0.0449903	−	0.0431464i
$47$			2.72825i			0.397956i	0.980004	+	0.198978i	$0.0637623\pi$
$47$			2.72825i			0.397956i	−0.980004	+	0.198978i	$0.936238\pi$
$48$	3.91319	+	0.562632i	0.564821	+	0.0812089i
$49$	1.91476	+	4.19273i	0.273537	+	0.598962i
$50$		0			0
$51$	2.85459	+	3.29437i	0.399723	+	0.461305i
$52$	−1.20144	−	4.09173i	−0.166610	−	0.567420i
$53$	0.148283	−	0.230732i	0.0203682	−	0.0316935i	−0.830920	−	0.556392i	$-0.812185\pi$
$53$	0.148283	−	0.230732i	0.0203682	−	0.0316935i	0.851288	+	0.524698i	$0.175822\pi$
$54$	−0.183106	+	0.400947i	−0.0249176	+	0.0545620i
$55$		0			0
$56$	0.457783	−	0.294199i	0.0611738	−	0.0393140i
$57$	7.34898	−	1.05662i	0.973396	−	0.139953i
$58$	0.391153	−	0.0562393i	0.0513609	−	0.00738458i
$59$	−6.74757	+	4.33640i	−0.878458	+	0.564551i	−0.900329	−	0.435210i	$-0.856674\pi$
$59$	−6.74757	+	4.33640i	−0.878458	+	0.564551i	0.0218707	+	0.999761i	$0.493038\pi$
$60$		0			0
$61$	−1.33718	+	2.92802i	−0.171208	+	0.374894i	−0.975713	−	0.219052i	$-0.929704\pi$
$61$	−1.33718	+	2.92802i	−0.171208	+	0.374894i	0.804505	+	0.593946i	$0.202431\pi$
$62$	−0.0431763	+	0.0671837i	−0.00548340	+	0.00853233i
$63$	−0.871230	−	2.96714i	−0.109765	−	0.373824i
$64$	−5.11714	−	5.90549i	−0.639642	−	0.738187i
$65$		0			0
$66$	0.0745040	+	0.163141i	0.00917081	+	0.0200813i
$67$	−1.94473	−	0.279610i	−0.237587	−	0.0341598i	0.0224928	−	0.999747i	$-0.492840\pi$
$67$	−1.94473	−	0.279610i	−0.237587	−	0.0341598i	−0.260080	+	0.965587i	$0.583749\pi$
$68$		−	8.68428i		−	1.05312i
$69$	−4.70653	−	0.921186i	−0.566600	−	0.110898i
$70$		0			0
$71$	1.58700	−	11.0378i	0.188342	−	1.30995i	−0.647959	−	0.761675i	$-0.724377\pi$
$71$	1.58700	−	11.0378i	0.188342	−	1.30995i	0.836301	−	0.548271i	$-0.184714\pi$
$72$	0.640269	−	0.292401i	0.0754564	−	0.0344598i
$73$	−2.92170	+	9.95039i	−0.341959	+	1.16461i	0.591615	+	0.806221i	$0.298491\pi$
$73$	−2.92170	+	9.95039i	−0.341959	+	1.16461i	−0.933574	+	0.358385i	$0.883328\pi$
$74$	−0.640515	−	0.739194i	−0.0744584	−	0.0859295i
$75$		0			0
$76$	−12.4433	−	7.99684i	−1.42735	−	0.917300i
$77$	−2.86139	−	1.30675i	−0.326086	−	0.148919i
$78$	0.142612	+	0.123574i	0.0161476	+	0.0139920i
$79$	−2.70849	+	1.74064i	−0.304729	+	0.195837i	−0.684064	−	0.729422i	$-0.739789\pi$
$79$	−2.70849	+	1.74064i	−0.304729	+	0.195837i	0.379335	+	0.925259i	$0.376153\pi$
$80$		0			0
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	0.288027	+	0.448178i	0.0318072	+	0.0494930i
$83$	3.29557	+	2.85563i	0.361736	+	0.313446i	0.816698	−	0.577065i	$-0.195802\pi$
$83$	3.29557	+	2.85563i	0.361736	+	0.313446i	−0.454963	+	0.890510i	$0.650347\pi$
$84$	1.27964	−	2.80202i	0.139620	−	0.305725i
$85$		0			0
$86$	−0.456334	+	0.133992i	−0.0492078	+	0.0144487i
$87$	3.38779	−	2.93553i	0.363209	−	0.314722i
$88$	0.201720	−	0.686997i	0.0215035	−	0.0732341i
$89$	−0.266861	−	0.584343i	−0.0282872	−	0.0619403i	0.894961	−	0.446144i	$-0.147203\pi$
$89$	−0.266861	−	0.584343i	−0.0282872	−	0.0619403i	−0.923248	+	0.384204i	$0.874476\pi$
$90$		0			0
$91$	−3.30972			−0.346953
$92$	5.88446	+	7.52725i	0.613498	+	0.784770i
$93$			0.905910i			0.0939385i
$94$	−0.0342284	+	0.238063i	−0.00353038	+	0.0245544i
$95$		0			0
$96$	1.00977	+	0.296494i	0.103059	+	0.0302608i
$97$	4.18748	−	3.62848i	0.425175	−	0.368416i	−0.415831	−	0.909442i	$-0.636509\pi$
$97$	4.18748	−	3.62848i	0.425175	−	0.368416i	0.841006	+	0.541026i	$0.181964\pi$
$98$	0.114478	+	0.389875i	0.0115640	+	0.0393833i
$99$	−3.42297	−	2.19981i	−0.344021	−	0.221089i
$100$		0			0
$101$	−2.94535	+	3.39912i	−0.293073	+	0.338225i	−0.883122	−	0.469143i	$-0.844563\pi$
$101$	−2.94535	+	3.39912i	−0.293073	+	0.338225i	0.590049	+	0.807367i	$0.299108\pi$
$102$	0.207757	+	0.323276i	0.0205710	+	0.0320091i
$103$	9.63380	−	1.38513i	0.949247	−	0.136481i	0.349737	−	0.936848i	$-0.386271\pi$
$103$	9.63380	−	1.38513i	0.949247	−	0.136481i	0.599510	+	0.800367i	$0.295362\pi$
$104$	−0.107212	−	0.745675i	−0.0105130	−	0.0731194i
$105$		0			0
$106$	0.0158337	−	0.0182730i	0.00153790	−	0.00177483i
$107$	6.72833	+	3.07272i	0.650452	+	0.297051i	0.713182	−	0.700979i	$-0.247253\pi$
$107$	6.72833	+	3.07272i	0.650452	+	0.297051i	−0.0627299	+	0.998031i	$0.519981\pi$
$108$	5.38540	−	8.37985i	0.518210	−	0.806351i
$109$	9.99029	−	2.93341i	0.956897	−	0.280970i	0.234241	−	0.972179i	$-0.424740\pi$
$109$	9.99029	−	2.93341i	0.956897	−	0.280970i	0.722656	+	0.691208i	$0.242921\pi$
$110$		0			0
$111$	−10.6456	−	3.12583i	−1.01044	−	0.296691i
$112$	−5.56040	+	2.53935i	−0.525408	+	0.239946i
$113$	−19.3927	−	2.78825i	−1.82431	−	0.262297i	−0.856898	−	0.515486i	$-0.827611\pi$
$113$	−19.3927	−	2.78825i	−1.82431	−	0.262297i	−0.967417	+	0.253189i	$0.918520\pi$
$114$	0.654518			0.0613012
$115$		0			0
$116$	−8.93053			−0.829179
$117$	−4.23753	−	0.609264i	−0.391760	−	0.0563265i
$118$	−0.643187	+	0.293734i	−0.0592102	+	0.0270404i
$119$	−6.46699	−	1.89888i	−0.592828	−	0.174070i
$120$		0			0
$121$	6.58311	−	1.93298i	0.598465	−	0.175725i
$122$	−0.153415	+	0.238719i	−0.0138896	+	0.0216126i
$123$	5.49716	+	2.51047i	0.495662	+	0.226361i
$124$	1.18188	−	1.36396i	0.106136	−	0.122487i
$125$		0			0
$126$	−0.0387969	−	0.269839i	−0.00345631	−	0.0240391i
$127$	17.3667	−	2.49696i	1.54105	−	0.221569i	0.681192	−	0.732105i	$-0.261462\pi$
$127$	17.3667	−	2.49696i	1.54105	−	0.221569i	0.859856	+	0.510536i	$0.170553\pi$
$128$	−1.51036	−	2.35017i	−0.133498	−	0.207727i
$129$	−3.53296	+	4.07725i	−0.311060	+	0.358982i
$130$		0			0
$131$	−10.9767	−	7.05427i	−0.959035	−	0.616334i	−0.0353039	−	0.999377i	$-0.511240\pi$
$131$	−10.9767	−	7.05427i	−0.959035	−	0.616334i	−0.923731	+	0.383043i	$0.874876\pi$
$132$	−1.14188	−	3.88890i	−0.0993883	−	0.338486i
$133$	−8.67589	+	7.51770i	−0.752295	+	0.651867i
$134$	−0.166187	−	0.0487968i	−0.0143563	−	0.00421540i
$135$		0			0
$136$	0.218329	−	1.51851i	0.0187216	−	0.130211i
$137$		−	21.5268i		−	1.83916i	−0.392903	−	0.919580i	$-0.628529\pi$
$137$		−	21.5268i		−	1.83916i	0.392903	−	0.919580i	$-0.371471\pi$
$138$	−0.399128	−	0.139429i	−0.0339760	−	0.0118690i
$139$	16.3719			1.38864			0.694322	−	0.719665i	$-0.255705\pi$
$139$	16.3719			1.38864			0.694322	+	0.719665i	$0.255705\pi$
$140$		0			0
$141$	1.13336	+	2.48170i	0.0954458	+	0.208997i
$142$	0.276958	−	0.943233i	0.0232418	−	0.0791544i
$143$	−3.29117	+	2.85181i	−0.275221	+	0.238480i
$144$	−7.58658	+	2.22762i	−0.632215	+	0.185635i
$145$		0			0
$146$	−0.379780	+	0.831602i	−0.0314308	+	0.0688239i
$147$	3.48345	+	3.01843i	0.287310	+	0.248956i
$148$	11.9502	+	18.5950i	0.982304	+	1.52850i
$149$	2.74972	+	19.1247i	0.225266	+	1.56676i	0.717665	+	0.696389i	$0.245211\pi$
$149$	2.74972	+	19.1247i	0.225266	+	1.56676i	−0.492399	+	0.870370i	$0.663880\pi$
$150$		0			0
$151$	16.8366	−	10.8202i	1.37015	−	0.880539i	0.371297	−	0.928514i	$-0.378913\pi$
$151$	16.8366	−	10.8202i	1.37015	−	0.880539i	0.998849	+	0.0479750i	$0.0152768\pi$
$152$	−1.97476	−	1.71114i	−0.160174	−	0.138792i
$153$	−7.93032	−	3.62165i	−0.641128	−	0.292793i
$154$	−0.233287	−	0.149924i	−0.0187988	−	0.0120812i
$155$		0			0
$156$	−2.79263	−	3.22287i	−0.223590	−	0.258036i
$157$	−1.62683	+	5.54048i	−0.129835	+	0.442179i	−0.998591	−	0.0530620i	$-0.983102\pi$
$157$	−1.62683	+	5.54048i	−0.129835	+	0.442179i	0.868756	+	0.495241i	$0.164920\pi$
$158$	−0.258177	+	0.117905i	−0.0205395	+	0.00938006i
$159$	0.0390330	−	0.271480i	0.00309552	−	0.0215298i
$160$		0			0
$161$	6.89206	−	2.73614i	0.543170	−	0.215638i
$162$		−	0.0881559i		−	0.00692618i
$163$	−8.71401	−	1.25289i	−0.682534	−	0.0981335i	−0.207678	−	0.978197i	$-0.566591\pi$
$163$	−8.71401	−	1.25289i	−0.682534	−	0.0981335i	−0.474856	+	0.880064i	$0.657500\pi$
$164$	−5.00143	−	10.9516i	−0.390546	−	0.855176i
$165$		0			0
$166$	0.251740	+	0.290524i	0.0195388	+	0.0225490i
$167$	−5.50159	−	18.7367i	−0.425726	−	1.44989i	−0.841418	−	0.540384i	$-0.818279\pi$
$167$	−5.50159	−	18.7367i	−0.425726	−	1.44989i	0.415692	−	0.909505i	$-0.363539\pi$
$168$	0.294199	−	0.457783i	0.0226980	−	0.0353187i
$169$	3.49698	−	7.65732i	0.268998	−	0.589024i
$170$		0			0
$171$	−12.4919	+	8.02803i	−0.955276	+	0.613919i
$172$	10.6386	−	1.52960i	0.811188	−	0.116631i
$173$	21.3627	−	3.07149i	1.62417	−	0.233521i	0.730721	−	0.682676i	$-0.239184\pi$
$173$	21.3627	−	3.07149i	1.62417	−	0.233521i	0.893454	+	0.449155i	$0.148275\pi$
$174$	0.332443	−	0.213648i	0.0252024	−	0.0161966i
$175$		0			0
$176$	−3.34120	+	7.31621i	−0.251852	+	0.551480i
$177$	−4.33640	+	6.74757i	−0.325944	+	0.507178i
$178$	−0.0159548	−	0.0543370i	−0.00119586	−	0.00407273i
$179$	−10.0553	−	11.6044i	−0.751567	−	0.867354i	0.243152	−	0.969988i	$-0.421818\pi$
$179$	−10.0553	−	11.6044i	−0.751567	−	0.867354i	−0.994719	+	0.102634i	$0.967273\pi$
$180$		0			0
$181$	0.340209	+	0.744955i	0.0252876	+	0.0553720i	0.921854	−	0.387537i	$-0.126674\pi$
$181$	0.340209	+	0.744955i	0.0252876	+	0.0553720i	−0.896567	+	0.442909i	$0.853947\pi$
$182$	−0.288802	−	0.0415234i	−0.0214074	−	0.00307792i
$183$			3.21890i			0.237948i
$184$	0.839703	+	1.46414i	0.0619037	+	0.107938i
$185$		0			0
$186$	−0.0113655	+	0.0790485i	−0.000833356	+	0.00579612i
$187$	−8.06690	+	3.68403i	−0.589910	+	0.269403i
$188$	1.53130	−	5.21513i	0.111682	−	0.380353i
$189$	−5.06273	−	5.84270i	−0.368259	−	0.424994i
$190$		0			0
$191$	−3.58868	−	2.30630i	−0.259668	−	0.166878i	0.404329	−	0.914613i	$-0.367505\pi$
$191$	−3.58868	−	2.30630i	−0.259668	−	0.166878i	−0.663997	+	0.747735i	$0.731141\pi$
$192$	−7.10794	−	3.24609i	−0.512972	−	0.234266i
$193$	−3.65352	−	3.16580i	−0.262986	−	0.227879i	0.513379	−	0.858162i	$-0.328393\pi$
$193$	−3.65352	−	3.16580i	−0.262986	−	0.227879i	−0.776366	+	0.630283i	$0.782939\pi$
$194$	0.410917	−	0.264080i	0.0295021	−	0.0189598i
$195$		0			0
$196$	−1.30684	−	9.08924i	−0.0933454	−	0.649232i
$197$	0.141980	+	0.220925i	0.0101157	+	0.0157403i	0.846275	−	0.532747i	$-0.178840\pi$
$197$	0.141980	+	0.220925i	0.0101157	+	0.0157403i	−0.836159	+	0.548487i	$0.815204\pi$
$198$	−0.271085	−	0.234896i	−0.0192652	−	0.0166934i
$199$	1.79719	−	3.93530i	0.127399	−	0.278966i	−0.835175	−	0.549985i	$-0.814633\pi$
$199$	1.79719	−	3.93530i	0.127399	−	0.278966i	0.962574	+	0.271019i	$0.0873607\pi$
$200$		0			0
$201$	−1.88514	+	0.553528i	−0.132968	+	0.0390429i
$202$	−0.299652	+	0.259650i	−0.0210835	+	0.0182689i
$203$	−1.95273	+	6.65037i	−0.137054	+	0.466765i
$204$	−3.60758	−	7.89950i	−0.252581	−	0.553076i
$205$		0			0
$206$	0.858010			0.0597804
$207$	9.32777	−	2.23445i	0.648325	−	0.155305i
$208$			8.46252i			0.586770i
$209$	−2.14964	+	14.9511i	−0.148694	+	1.03419i
$210$		0			0
$211$	6.30147	+	1.85028i	0.433811	+	0.127378i	0.491345	−	0.870965i	$-0.336506\pi$
$211$	6.30147	+	1.85028i	0.433811	+	0.127378i	−0.0575338	+	0.998344i	$0.518324\pi$
$212$	−0.412951	+	0.357824i	−0.0283616	+	0.0245755i
$213$	−3.14169	−	10.6996i	−0.215265	−	0.733125i
$214$	0.548554	+	0.352535i	0.0374984	+	0.0240988i
$215$		0			0
$216$	1.15235	−	1.32989i	0.0784077	−	0.0904874i
$217$	−0.757286	−	1.17836i	−0.0514079	−	0.0799923i
$218$	0.908542	−	0.130629i	0.0615342	−	0.00884728i
$219$	1.47587	+	10.2649i	0.0997301	+	0.693638i
$220$		0			0
$221$	−6.11040	+	7.05178i	−0.411030	+	0.474354i
$222$	−0.889705	−	0.406315i	−0.0597131	−	0.0272701i
$223$	4.97783	−	7.74566i	0.333340	−	0.518688i	−0.633610	−	0.773653i	$-0.718428\pi$
$223$	4.97783	−	7.74566i	0.333340	−	0.518688i	0.966950	+	0.254965i	$0.0820639\pi$
$224$	−1.56130	+	0.458439i	−0.104319	+	0.0306308i
$225$		0			0
$226$	−1.65720	−	0.486598i	−0.110235	−	0.0323680i
$227$	−8.06985	+	3.68538i	−0.535615	+	0.244607i	−0.664810	−	0.747012i	$-0.731488\pi$
$227$	−8.06985	+	3.68538i	−0.535615	+	0.244607i	0.129196	+	0.991619i	$0.458760\pi$
$228$	−14.6408	−	2.10504i	−0.969614	−	0.139409i
$229$	8.38484			0.554086			0.277043	−	0.960858i	$-0.410646\pi$
$229$	8.38484			0.554086			0.277043	+	0.960858i	$0.410646\pi$
$230$		0			0
$231$	−3.14566			−0.206969
$232$	−1.56157	−	0.224520i	−0.102522	−	0.0147405i
$233$	21.8435	−	9.97561i	1.43102	−	0.653524i	0.459002	−	0.888435i	$-0.348207\pi$
$233$	21.8435	−	9.97561i	1.43102	−	0.653524i	0.972017	+	0.234911i	$0.0754799\pi$
$234$	−0.362117	−	0.106327i	−0.0236723	−	0.00695082i
$235$		0			0
$236$	15.3321	−	4.50191i	0.998034	−	0.293049i
$237$	−1.74064	+	2.70849i	−0.113067	+	0.175935i
$238$	−0.540478	−	0.246828i	−0.0350340	−	0.0159995i
$239$	−7.35914	+	8.49290i	−0.476023	+	0.549360i	−0.942077	−	0.335396i	$-0.891130\pi$
$239$	−7.35914	+	8.49290i	−0.476023	+	0.549360i	0.466054	+	0.884756i	$0.345675\pi$
$240$		0			0
$241$	4.00004	+	27.8209i	0.257665	+	1.79210i	0.549355	+	0.835589i	$0.314874\pi$
$241$	4.00004	+	27.8209i	0.257665	+	1.79210i	−0.291689	+	0.956513i	$0.594217\pi$
$242$	0.598684	−	0.0860778i	0.0384849	−	0.00553329i
$243$	−8.65025	−	13.4601i	−0.554914	−	0.863463i
$244$	4.19948	−	4.84646i	0.268844	−	0.310263i
$245$		0			0
$246$	0.448178	+	0.288027i	0.0285748	+	0.0183639i
$247$	4.47747	+	15.2489i	0.284895	+	0.970262i
$248$	0.240952	−	0.208786i	0.0153004	−	0.0132579i
$249$	4.18403	+	1.22854i	0.265152	+	0.0778556i
$250$		0			0
$251$	3.91272	−	27.2135i	0.246969	−	1.71770i	−0.368572	−	0.929599i	$-0.620153\pi$
$251$	3.91272	−	27.2135i	0.246969	−	1.71770i	0.615541	−	0.788105i	$-0.288938\pi$
$252$			6.16077i			0.388092i
$253$	4.49583	−	8.65932i	0.282650	−	0.544407i
$254$	1.54672			0.0970501
$255$		0			0
$256$	6.38987	+	13.9919i	0.399367	+	0.874492i
$257$	−5.00435	+	17.0432i	−0.312163	+	1.06313i	0.642709	+	0.766110i	$0.277810\pi$
$257$	−5.00435	+	17.0432i	−0.312163	+	1.06313i	−0.954872	+	0.297018i	$0.904008\pi$
$258$	−0.359434	+	0.311451i	−0.0223774	+	0.0193901i
$259$	16.4603	−	4.83317i	1.02279	−	0.300318i
$260$		0			0
$261$	−3.72435	+	8.15519i	−0.230531	+	0.504794i
$262$	−0.869305	−	0.753257i	−0.0537059	−	0.0465364i
$263$	−4.72561	−	7.35320i	−0.291394	−	0.453417i	0.664433	−	0.747348i	$-0.268673\pi$
$263$	−4.72561	−	7.35320i	−0.291394	−	0.453417i	−0.955827	+	0.293930i	$0.905037\pi$
$264$	−0.101897	−	0.708712i	−0.00627135	−	0.0436182i
$265$		0			0
$266$	−0.851362	+	0.547137i	−0.0522004	+	0.0335471i
$267$	−0.485490	−	0.420680i	−0.0297115	−	0.0257452i
$268$	3.56047	+	1.62601i	0.217491	+	0.0993246i
$269$	−2.46553	−	1.58450i	−0.150326	−	0.0966086i	0.463316	−	0.886193i	$-0.346660\pi$
$269$	−2.46553	−	1.58450i	−0.150326	−	0.0966086i	−0.613642	+	0.789585i	$0.710296\pi$
$270$		0			0
$271$	4.29616	+	4.95803i	0.260973	+	0.301179i	0.871081	−	0.491139i	$-0.163419\pi$
$271$	4.29616	+	4.95803i	0.260973	+	0.301179i	−0.610108	+	0.792318i	$0.708874\pi$
$272$	−4.85519	+	16.5353i	−0.294389	+	1.00260i
$273$	−3.01063	+	1.37491i	−0.182212	+	0.0832132i
$274$	0.270073	−	1.87840i	0.0163157	−	0.113478i
$275$		0			0
$276$	8.47963	+	4.40253i	0.510414	+	0.265001i
$277$			22.7888i			1.36924i	0.728898	+	0.684622i	$0.240033\pi$
$277$			22.7888i			1.36924i	−0.728898	+	0.684622i	$0.759967\pi$
$278$	1.42859	+	0.205400i	0.0856809	+	0.0123191i
$279$	−0.752658	−	1.64809i	−0.0450604	−	0.0986686i
$280$		0			0
$281$	9.32744	+	10.7644i	0.556429	+	0.642153i	0.962369	−	0.271747i	$-0.0876013\pi$
$281$	9.32744	+	10.7644i	0.556429	+	0.642153i	−0.405940	+	0.913900i	$0.633056\pi$
$282$	0.0677599	+	0.230769i	0.00403504	+	0.0137421i
$283$	−12.8173	+	19.9441i	−0.761910	+	1.18555i	0.215973	+	0.976399i	$0.430708\pi$
$283$	−12.8173	+	19.9441i	−0.761910	+	1.18555i	−0.977882	+	0.209155i	$0.932929\pi$
$284$	−9.22884	+	20.2083i	−0.547631	+	1.19914i
$285$		0			0
$286$	−0.322961	+	0.207554i	−0.0190971	+	0.0122730i
$287$	−9.24901	+	1.32981i	−0.545952	+	0.0784960i
$288$	−2.08337	+	0.299543i	−0.122764	+	0.0176507i
$289$	−1.68384	+	1.08214i	−0.0990493	+	0.0636551i
$290$		0			0
$291$	2.30175	−	5.04012i	0.134931	−	0.295457i
$292$	11.1698	−	17.3806i	0.653664	−	1.01712i
$293$	1.20419	+	4.10110i	0.0703497	+	0.239589i	0.987160	−	0.159734i	$-0.0510635\pi$
$293$	1.20419	+	4.10110i	0.0703497	+	0.239589i	−0.916810	+	0.399323i	$0.869245\pi$
$294$	0.266092	+	0.307087i	0.0155188	+	0.0179097i
$295$		0			0
$296$	1.62210	+	3.55191i	0.0942827	+	0.206450i
$297$	−10.0687	−	1.44766i	−0.584245	−	0.0840017i
$298$			1.70330i			0.0986692i
$299$	0.518014	−	10.2526i	0.0299575	−	0.592926i
$300$		0			0
$301$	1.18715	−	8.25681i	0.0684262	−	0.475915i
$302$	1.60489	−	0.732929i	0.0923511	−	0.0421753i
$303$	−1.26714	+	4.31549i	−0.0727954	+	0.247918i
$304$	19.2218	+	22.1831i	1.10244	+	1.27229i
$305$		0			0
$306$	−0.646552	−	0.415514i	−0.0369609	−	0.0237533i
$307$	8.13661	+	3.71586i	0.464381	+	0.212076i	0.633844	−	0.773461i	$-0.281476\pi$
$307$	8.13661	+	3.71586i	0.464381	+	0.212076i	−0.169463	+	0.985536i	$0.554203\pi$
$308$	4.73619	+	4.10393i	0.269869	+	0.233843i
$309$	8.18781	−	5.26199i	0.465788	−	0.299344i
$310$		0			0
$311$	3.32224	+	23.1067i	0.188387	+	1.31026i	0.836185	+	0.548447i	$0.184781\pi$
$311$	3.32224	+	23.1067i	0.188387	+	1.31026i	−0.647798	+	0.761812i	$0.724310\pi$
$312$	−0.407288	−	0.633752i	−0.0230581	−	0.0358792i
$313$	17.0127	+	14.7416i	0.961615	+	0.833244i	0.986049	−	0.166457i	$-0.0532328\pi$
$313$	17.0127	+	14.7416i	0.961615	+	0.833244i	−0.0244337	+	0.999701i	$0.507778\pi$
$314$	−0.211465	+	0.463045i	−0.0119337	+	0.0261311i
$315$		0			0
$316$	6.15434	−	1.80708i	0.346209	−	0.101656i
$317$	−9.63606	+	8.34970i	−0.541215	+	0.468966i	−0.882049	−	0.471158i	$-0.843836\pi$
$317$	−9.63606	+	8.34970i	−0.541215	+	0.468966i	0.340834	+	0.940124i	$0.389291\pi$
$318$	0.00681193	−	0.0231993i	0.000381994	−	0.00130095i
$319$	3.78849	+	8.29564i	0.212115	+	0.464467i
$320$		0			0
$321$	7.39676			0.412847
$322$	0.635719	−	0.152285i	0.0354272	−	0.00848651i
$323$			32.3642i			1.80079i
$324$	−0.283524	+	1.97195i	−0.0157513	+	0.109553i
$325$		0			0
$326$	−0.744654	−	0.218650i	−0.0412426	−	0.0121099i
$327$	7.86891	−	6.81845i	0.435151	−	0.377061i
$328$	−0.599206	−	2.04071i	−0.0330856	−	0.112679i
$329$	−3.54876	−	2.28065i	−0.195650	−	0.125736i
$330$		0			0
$331$	10.7382	−	12.3926i	0.590227	−	0.681158i	−0.379545	−	0.925173i	$-0.623919\pi$
$331$	10.7382	−	12.3926i	0.590227	−	0.681158i	0.969771	+	0.244015i	$0.0784647\pi$
$332$	−4.69678	−	7.30834i	−0.257769	−	0.401097i
$333$	21.9642	−	3.15798i	1.20363	−	0.173056i
$334$	−0.244993	−	1.70396i	−0.0134054	−	0.0932366i
$335$		0			0
$336$	−4.00303	+	4.61974i	−0.218383	+	0.252028i
$337$	−24.9589	−	11.3983i	−1.35960	−	0.620907i	−0.403776	−	0.914858i	$-0.632303\pi$
$337$	−24.9589	−	11.3983i	−1.35960	−	0.620907i	−0.955821	+	0.293951i	$0.905030\pi$
$338$	0.401210	−	0.624294i	0.0218229	−	0.0339571i
$339$	−18.7985	+	5.51975i	−1.02100	+	0.299792i
$340$		0			0
$341$	−1.76837	−	0.519240i	−0.0957626	−	0.0281184i
$342$	−1.19074	+	0.543793i	−0.0643879	+	0.0294050i
$343$	−17.7675	−	2.55459i	−0.959357	−	0.137935i
$344$	1.89870			0.102371
$345$		0			0
$346$	1.90261			0.102285
$347$	5.97415	+	0.858953i	0.320709	+	0.0461110i	0.300789	−	0.953691i	$-0.402750\pi$
$347$	5.97415	+	0.858953i	0.320709	+	0.0461110i	0.0199196	+	0.999802i	$0.493659\pi$
$348$	−8.12350	+	3.70988i	−0.435465	+	0.198870i
$349$	8.00915	+	2.35170i	0.428720	+	0.125883i	0.488972	−	0.872300i	$-0.337372\pi$
$349$	8.00915	+	2.35170i	0.428720	+	0.125883i	−0.0602518	+	0.998183i	$0.519190\pi$
$350$		0			0
$351$	−10.2692	+	3.01532i	−0.548130	+	0.160946i
$352$	−1.15753	+	1.80116i	−0.0616968	+	0.0960021i
$353$	−23.7892	−	10.8642i	−1.26617	−	0.578242i	−0.334794	−	0.942291i	$-0.608667\pi$
$353$	−23.7892	−	10.8642i	−1.26617	−	0.578242i	−0.931380	+	0.364049i	$0.881394\pi$
$354$	−0.463042	+	0.534379i	−0.0246104	+	0.0284019i
$355$		0			0
$356$	0.182134	+	1.26677i	0.00965310	+	0.0671388i
$357$	−6.67141	+	0.959204i	−0.353088	+	0.0507664i
$358$	−0.731822	−	1.13874i	−0.0386780	−	0.0601841i
$359$	3.70672	−	4.27779i	0.195633	−	0.225773i	−0.649454	−	0.760401i	$-0.725003\pi$
$359$	3.70672	−	4.27779i	0.195633	−	0.225773i	0.845088	+	0.534628i	$0.179548\pi$
$360$		0			0
$361$	30.3894	+	19.5301i	1.59944	+	1.02790i
$362$	0.0203401	+	0.0692719i	0.00106905	+	0.00364085i
$363$	5.18522	−	4.49302i	0.272154	−	0.235822i
$364$	6.32663	+	1.85767i	0.331605	+	0.0973682i
$365$		0			0
$366$	−0.0403840	+	0.280877i	−0.00211091	+	0.0146817i
$367$			12.3147i			0.642822i	0.946940	+	0.321411i	$0.104157\pi$
$367$			12.3147i			0.642822i	−0.946940	+	0.321411i	$0.895843\pi$
$368$	−6.99596	−	17.6221i	−0.364690	−	0.918615i
$369$	−12.0866			−0.629201
$370$		0			0
$371$	0.176169	+	0.385756i	0.00914624	+	0.0200275i
$372$	0.508465	−	1.73167i	0.0263627	−	0.0897831i
$373$	22.0119	−	19.0734i	1.13973	−	0.987585i	0.139737	−	0.990189i	$-0.455374\pi$
$373$	22.0119	−	19.0734i	1.13973	−	0.987585i	0.999997	+	0.00260397i	$0.000828872\pi$
$374$	−0.750126	+	0.220257i	−0.0387881	+	0.0113892i
$375$		0			0
$376$	0.398872	−	0.873407i	0.0205702	−	0.0450426i
$377$	7.25173	+	6.28366i	0.373483	+	0.323625i
$378$	−0.368465	−	0.573343i	−0.0189518	−	0.0294896i
$379$	−4.74698	−	33.0160i	−0.243836	−	1.69592i	−0.632519	−	0.774545i	$-0.717979\pi$
$379$	−4.74698	−	33.0160i	−0.243836	−	1.69592i	0.388683	−	0.921372i	$-0.372930\pi$
$380$		0			0
$381$	14.7601	−	9.48571i	0.756181	−	0.485968i
$382$	−0.284209	−	0.246268i	−0.0145414	−	0.0126002i
$383$	28.2775	+	12.9139i	1.44491	+	0.659870i	0.974870	−	0.222773i	$-0.0715108\pi$
$383$	28.2775	+	12.9139i	1.44491	+	0.659870i	0.470044	+	0.882643i	$0.344238\pi$
$384$	−2.35017	−	1.51036i	−0.119931	−	0.0770753i
$385$		0			0
$386$	−0.279084	−	0.322080i	−0.0142050	−	0.0163934i
$387$	3.03988	−	10.3529i	0.154526	−	0.526267i
$388$	−10.0411	+	4.58560i	−0.509758	+	0.232799i
$389$	−1.80544	+	12.5571i	−0.0915394	+	0.636670i	0.891465	+	0.453089i	$0.149678\pi$
$389$	−1.80544	+	12.5571i	−0.0915394	+	0.636670i	−0.983005	+	0.183581i	$0.941231\pi$
$390$		0			0
$391$	6.89440	−	19.7358i	0.348665	−	0.998085i
$392$		−	1.62218i		−	0.0819324i
$393$	−12.9152	−	1.85692i	−0.651484	−	0.0936692i
$394$	0.00961727	+	0.0210589i	0.000484511	+	0.00106093i
$395$		0			0
$396$	5.30841	+	6.12623i	0.266757	+	0.307855i
$397$	3.47123	+	11.8219i	0.174216	+	0.593325i	0.999587	+	0.0287344i	$0.00914770\pi$
$397$	3.47123	+	11.8219i	0.174216	+	0.593325i	−0.825371	+	0.564590i	$0.809034\pi$
$398$	0.206192	−	0.320841i	0.0103355	−	0.0160823i
$399$	−4.76890	+	10.4424i	−0.238744	+	0.522776i
$400$		0			0
$401$	−28.3895	+	18.2448i	−1.41770	+	0.911102i	−0.417705	+	0.908583i	$0.637166\pi$
$401$	−28.3895	+	18.2448i	−1.41770	+	0.911102i	−0.999997	+	0.00251937i	$0.999198\pi$
$402$	−0.171440	+	0.0246493i	−0.00855063	+	0.00122940i
$403$	−1.91941	+	0.275970i	−0.0956126	+	0.0137470i
$404$	7.53797	−	4.84436i	0.375028	−	0.241016i
$405$		0			0
$406$	−0.253827	+	0.555804i	−0.0125972	+	0.0275841i
$407$	12.2035	−	18.9890i	0.604904	−	0.941249i
$408$	−0.432214	−	1.47199i	−0.0213978	−	0.0728741i
$409$	10.6316	+	12.2695i	0.525698	+	0.606688i	0.955048	−	0.296450i	$-0.0958028\pi$
$409$	10.6316	+	12.2695i	0.525698	+	0.606688i	−0.429350	+	0.903138i	$0.641257\pi$
$410$		0			0
$411$	−8.94256	−	19.5815i	−0.441104	−	0.965883i
$412$	−19.1927	−	2.75950i	−0.945558	−	0.135951i
$413$		−	12.4018i		−	0.610254i
$414$	0.841961	−	0.0779495i	0.0413801	−	0.00383101i
$415$		0			0
$416$	−0.320594	+	2.22978i	−0.0157184	+	0.109324i
$417$	14.8924	−	6.80112i	0.729282	−	0.333052i
$418$	−0.375150	+	1.27764i	−0.0183492	+	0.0624916i
$419$	−8.76692	−	10.1176i	−0.428292	−	0.494275i	0.500053	−	0.865995i	$-0.333314\pi$
$419$	−8.76692	−	10.1176i	−0.428292	−	0.494275i	−0.928345	+	0.371719i	$0.878768\pi$
$420$		0			0
$421$	−10.9478	−	7.03572i	−0.533563	−	0.342900i	0.245954	−	0.969282i	$-0.420899\pi$
$421$	−10.9478	−	7.03572i	−0.533563	−	0.342900i	−0.779517	+	0.626382i	$0.784535\pi$
$422$	0.526644	+	0.240510i	0.0256366	+	0.0117079i
$423$	−4.12375	−	3.57325i	−0.200504	−	0.173737i
$424$	−0.0812036	+	0.0521864i	−0.00394360	+	0.00253439i
$425$		0			0
$426$	−0.139903	−	0.973048i	−0.00677833	−	0.0471443i
$427$	−2.69081	−	4.18698i	−0.130217	−	0.202622i
$428$	−11.1367	−	9.65005i	−0.538315	−	0.466453i
$429$	−1.80906	+	3.96130i	−0.0873424	+	0.191253i
$430$		0			0
$431$	−8.97982	+	2.63671i	−0.432543	+	0.127006i	−0.490754	−	0.871298i	$-0.663279\pi$
$431$	−8.97982	+	2.63671i	−0.432543	+	0.127006i	0.0582112	+	0.998304i	$0.481460\pi$
$432$	−14.9390	+	12.9447i	−0.718754	+	0.622804i
$433$	−9.56922	+	32.5898i	−0.459867	+	1.56616i	0.324511	+	0.945882i	$0.394800\pi$
$433$	−9.56922	+	32.5898i	−0.459867	+	1.56616i	−0.784378	+	0.620283i	$0.787018\pi$
$434$	−0.0512961	−	0.112323i	−0.00246229	−	0.00539167i
$435$		0			0
$436$	−20.7432			−0.993419
$437$	−21.9300	−	28.0522i	−1.04905	−	1.34192i
$438$			0.914218i			0.0436830i
$439$	4.53831	−	31.5646i	0.216602	−	1.50650i	−0.533854	−	0.845577i	$-0.679257\pi$
$439$	4.53831	−	31.5646i	0.216602	−	1.50650i	0.750456	−	0.660921i	$-0.229834\pi$
$440$		0			0
$441$	−8.84511	−	2.59716i	−0.421196	−	0.123674i
$442$	−0.621656	+	0.538668i	−0.0295691	+	0.0256218i
$443$	−8.62354	−	29.3691i	−0.409717	−	1.39537i	−0.863542	−	0.504277i	$-0.831759\pi$
$443$	−8.62354	−	29.3691i	−0.409717	−	1.39537i	0.453825	−	0.891091i	$-0.350059\pi$
$444$	18.5950	+	11.9502i	0.882477	+	0.567134i
$445$		0			0
$446$	0.531535	−	0.613424i	0.0251689	−	0.0290465i
$447$	10.4459	+	16.2542i	0.494076	+	0.768797i
$448$	11.9592	−	1.71947i	0.565018	−	0.0812373i
$449$	−2.39840	−	16.6812i	−0.113187	−	0.787236i	−0.964785	−	0.263040i	$-0.915275\pi$
$449$	−2.39840	−	16.6812i	−0.113187	−	0.787236i	0.851597	−	0.524196i	$-0.175634\pi$
$450$		0			0
$451$	−8.05133	+	9.29173i	−0.379122	+	0.437530i
$452$	35.5048	+	16.2145i	1.67001	+	0.762666i
$453$	10.8202	−	16.8366i	0.508380	−	0.791054i
$454$	−0.750400	+	0.220337i	−0.0352180	+	0.0103409i
$455$		0			0
$456$	−2.50714	−	0.736163i	−0.117408	−	0.0344740i
$457$	−2.47375	+	1.12972i	−0.115717	+	0.0528463i	−0.472432	−	0.881367i	$-0.656624\pi$
$457$	−2.47375	+	1.12972i	−0.115717	+	0.0528463i	0.356715	+	0.934213i	$0.383897\pi$
$458$	0.731650	+	0.105195i	0.0341877	+	0.00491546i
$459$	−21.7954			−1.01732
$460$		0			0
$461$	−35.7457			−1.66484			−0.832421	−	0.554143i	$-0.813046\pi$
$461$	−35.7457			−1.66484			−0.832421	+	0.554143i	$0.813046\pi$
$462$	−0.274486	−	0.0394651i	−0.0127702	−	0.00183608i
$463$	37.8860	−	17.3020i	1.76071	−	0.804091i	0.775814	−	0.630961i	$-0.217339\pi$
$463$	37.8860	−	17.3020i	1.76071	−	0.804091i	0.984899	−	0.173130i	$-0.0553880\pi$
$464$	17.0041	+	4.99286i	0.789397	+	0.231788i
$465$		0			0
$466$	2.03119	−	0.596411i	0.0940931	−	0.0276282i
$467$	9.55519	−	14.8682i	0.442161	−	0.688017i	−0.546621	−	0.837380i	$-0.684086\pi$
$467$	9.55519	−	14.8682i	0.442161	−	0.688017i	0.988782	+	0.149364i	$0.0477225\pi$
$468$	7.75819	+	3.54305i	0.358623	+	0.163777i
$469$	1.98938	−	2.29587i	0.0918610	−	0.106013i
$470$		0			0
$471$	0.821781	+	5.71561i	0.0378657	+	0.263361i
$472$	2.79411	−	0.401733i	0.128609	−	0.0184913i
$473$	−5.93396	−	9.23343i	−0.272844	−	0.424553i
$474$	−0.185866	+	0.214501i	−0.00853712	+	0.00985237i
$475$		0			0
$476$	11.2961	+	7.25953i	0.517754	+	0.332740i
$477$	0.154543	+	0.526324i	0.00707602	+	0.0240987i
$478$	−0.748699	+	0.648752i	−0.0342447	+	0.0296732i
$479$	−11.4723	−	3.36858i	−0.524184	−	0.153914i	0.00892633	−	0.999960i	$-0.497159\pi$
$479$	−11.4723	−	3.36858i	−0.524184	−	0.153914i	−0.533110	+	0.846046i	$0.678977\pi$
$480$		0			0
$481$	3.37991	−	23.5078i	0.154111	−	1.07186i
$482$			2.47780i			0.112861i
$483$	5.13260	−	5.35195i	0.233541	−	0.243522i
$484$	−13.6687			−0.621306
$485$		0			0
$486$	−0.585941	−	1.28303i	−0.0265788	−	0.0581995i
$487$	5.31536	−	18.1024i	0.240862	−	0.820300i	−0.746981	−	0.664845i	$-0.768497\pi$
$487$	5.31536	−	18.1024i	0.240862	−	0.820300i	0.987843	−	0.155455i	$-0.0496843\pi$
$488$	0.856156	−	0.741863i	0.0387563	−	0.0335826i
$489$	−8.44701	+	2.48026i	−0.381987	+	0.112161i
$490$		0			0
$491$	9.10363	−	19.9342i	0.410841	−	0.899616i	−0.585214	−	0.810879i	$-0.698990\pi$
$491$	9.10363	−	19.9342i	0.410841	−	0.899616i	0.996055	−	0.0887373i	$-0.0282832\pi$
$492$	−9.09891	−	7.88425i	−0.410211	−	0.355450i
$493$	10.5643	+	16.4384i	0.475794	+	0.740349i
$494$	0.199387	+	1.38677i	0.00897086	+	0.0623937i
$495$		0			0
$496$	−3.01291	+	1.93628i	−0.135284	+	0.0869416i
$497$	13.0308	+	11.2912i	0.584509	+	0.506480i
$498$	0.349679	+	0.159693i	0.0156695	+	0.00715602i
$499$	−8.48768	−	5.45470i	−0.379961	−	0.244186i	0.336694	−	0.941614i	$-0.390691\pi$
$499$	−8.48768	−	5.45470i	−0.379961	−	0.244186i	−0.716655	+	0.697428i	$0.754328\pi$
$500$		0			0
$501$	−12.7879	−	14.7581i	−0.571323	−	0.659341i
$502$	0.682837	−	2.32553i	0.0304765	−	0.103793i
$503$	−12.1941	+	5.56885i	−0.543707	+	0.248303i	−0.668283	−	0.743907i	$-0.732970\pi$
$503$	−12.1941	+	5.56885i	−0.543707	+	0.248303i	0.124576	+	0.992210i	$0.460243\pi$
$504$	−0.154886	+	1.07726i	−0.00689918	+	0.0479849i
$505$		0			0
$506$	0.500939	−	0.699196i	0.0222694	−	0.0310831i
$507$		−	8.41804i		−	0.373858i
$508$	−34.5985	−	4.97451i	−1.53506	−	0.220708i
$509$	−8.03460	−	17.5933i	−0.356127	−	0.779810i	−0.999894	−	0.0145879i	$-0.995356\pi$
$509$	−8.03460	−	17.5933i	−0.356127	−	0.779810i	0.643766	−	0.765222i	$-0.277371\pi$
$510$		0			0
$511$	−10.5006	−	12.1183i	−0.464518	−	0.536082i
$512$	1.95615	+	6.66205i	0.0864506	+	0.294424i
$513$	−20.0701	+	31.2297i	−0.886116	+	1.37882i
$514$	−0.650495	+	1.42439i	−0.0286921	+	0.0628270i
$515$		0			0
$516$	9.04182	−	5.81083i	0.398044	−	0.255807i
$517$	−5.49398	+	0.789915i	−0.241625	+	0.0347404i
$518$	1.49694	−	0.215227i	0.0657716	−	0.00945652i
$519$	18.1562	−	11.6683i	0.796970	−	0.512182i
$520$		0			0
$521$	−4.67119	+	10.2285i	−0.204648	+	0.448117i	−0.983930	−	0.178557i	$-0.942857\pi$
$521$	−4.67119	+	10.2285i	−0.204648	+	0.448117i	0.779281	+	0.626674i	$0.215584\pi$
$522$	−0.427296	+	0.664885i	−0.0187022	+	0.0291012i
$523$	5.09404	+	17.3487i	0.222747	+	0.758605i	0.992711	+	0.120519i	$0.0384558\pi$
$523$	5.09404	+	17.3487i	0.222747	+	0.758605i	−0.769964	+	0.638087i	$0.779726\pi$
$524$	17.0228	+	19.6454i	0.743645	+	0.858212i
$525$		0			0
$526$	−0.320098	−	0.700917i	−0.0139569	−	0.0305614i
$527$	−3.90874	−	0.561992i	−0.170267	−	0.0244808i
$528$			8.04304i			0.350028i
$529$	7.39715	+	21.7780i	0.321615	+	0.946870i
$530$		0			0
$531$	2.28297	−	15.8784i	0.0990725	−	0.689064i
$532$	20.8037	−	9.50074i	0.901955	−	0.411909i
$533$	−3.64448	+	12.4119i	−0.157860	+	0.537621i
$534$	−0.0370854	−	0.0427988i	−0.00160484	−	0.00185209i
$535$		0			0
$536$	0.581697	+	0.373834i	0.0251255	+	0.0161472i
$537$	−13.9672	−	6.37863i	−0.602731	−	0.275258i
$538$	−0.195260	−	0.169194i	−0.00841825	−	0.00729445i
$539$	−7.88869	+	5.06975i	−0.339790	+	0.218370i
$540$		0			0
$541$	1.97456	+	13.7333i	0.0848928	+	0.590442i	0.987217	+	0.159384i	$0.0509507\pi$
$541$	1.97456	+	13.7333i	0.0848928	+	0.590442i	−0.902324	+	0.431059i	$0.858140\pi$
$542$	0.312674	+	0.486530i	0.0134305	+	0.0208983i
$543$	0.618931	+	0.536306i	0.0265609	+	0.0230151i
$544$	−1.90571	+	4.17292i	−0.0817065	+	0.178912i
$545$		0			0
$546$	−0.279953	+	0.0822015i	−0.0119809	+	0.00351790i
$547$	22.7793	−	19.7384i	0.973973	−	0.843952i	−0.0137919	−	0.999905i	$-0.504390\pi$
$547$	22.7793	−	19.7384i	0.973973	−	0.843952i	0.987764	+	0.155953i	$0.0498448\pi$
$548$	−12.0825	+	41.1491i	−0.516138	+	1.75780i
$549$	−2.67436	−	5.85603i	−0.114139	−	0.249929i
$550$		0			0
$551$	33.2819			1.41786
$552$	1.37204	+	0.983001i	0.0583981	+	0.0418393i
$553$		−	4.97813i		−	0.211692i
$554$	−0.285906	+	1.98852i	−0.0121470	+	0.0844840i
$555$		0			0
$556$	−31.2953	−	9.18913i	−1.32722	−	0.389706i
$557$	−16.3440	+	14.1622i	−0.692519	+	0.600071i	−0.928343	−	0.371724i	$-0.878767\pi$
$557$	−16.3440	+	14.1622i	−0.692519	+	0.600071i	0.235824	+	0.971796i	$0.424221\pi$
$558$	−0.0449991	−	0.153253i	−0.00190496	−	0.00648771i
$559$	−9.71499	−	6.24345i	−0.410900	−	0.264070i
$560$		0			0
$561$	−5.80751	+	6.70222i	−0.245193	+	0.282968i
$562$	0.678850	+	1.05631i	0.0286356	+	0.0445578i
$563$	0.283349	−	0.0407395i	0.0119418	−	0.00171696i	−0.136341	−	0.990662i	$-0.543534\pi$
$563$	0.283349	−	0.0407395i	0.0119418	−	0.00171696i	0.148283	+	0.988945i	$0.452625\pi$
$564$	−0.773524	−	5.37998i	−0.0325712	−	0.226538i
$565$		0			0
$566$	−1.36864	+	1.57949i	−0.0575281	+	0.0663910i
$567$	1.40647	+	0.642315i	0.0590663	+	0.0269747i
$568$	−2.12179	+	3.30156i	−0.0890282	+	0.138531i
$569$	−1.66147	+	0.487852i	−0.0696525	+	0.0204518i	−0.316373	−	0.948635i	$-0.602465\pi$
$569$	−1.66147	+	0.487852i	−0.0696525	+	0.0204518i	0.246721	+	0.969087i	$0.420647\pi$
$570$		0			0
$571$	−19.8922	−	5.84086i	−0.832461	−	0.244433i	−0.162387	−	0.986727i	$-0.551919\pi$
$571$	−19.8922	−	5.84086i	−0.832461	−	0.244433i	−0.670074	+	0.742295i	$0.733738\pi$
$572$	7.89181	−	3.60407i	0.329973	−	0.150694i
$573$	−4.22245	−	0.607097i	−0.176395	−	0.0253618i
$574$	−0.823739			−0.0343822
$575$		0			0
$576$	15.6282			0.651174
$577$	23.8763	+	3.43290i	0.993985	+	0.142913i	0.620067	−	0.784549i	$-0.287105\pi$
$577$	23.8763	+	3.43290i	0.993985	+	0.142913i	0.373917	+	0.927462i	$0.378014\pi$
$578$	−0.160506	+	0.0733005i	−0.00667616	+	0.00304890i
$579$	−4.63848	−	1.36198i	−0.192769	−	0.0566020i
$580$		0			0
$581$	−6.46934	+	1.89957i	−0.268394	+	0.0788074i
$582$	0.264080	−	0.410917i	0.0109465	−	0.0170330i
$583$	0.507567	+	0.231798i	0.0210213	+	0.00960009i
$584$	2.39009	−	2.75831i	0.0989026	−	0.114140i
$585$		0			0
$586$	0.0536241	+	0.372964i	0.00221519	+	0.0154070i
$587$	33.2423	−	4.77952i	1.37206	−	0.197272i	0.583439	−	0.812157i	$-0.301707\pi$
$587$	33.2423	−	4.77952i	1.37206	−	0.197272i	0.788617	+	0.614885i	$0.210798\pi$
$588$	−4.96455	−	7.72499i	−0.204734	−	0.318573i
$589$	−4.40458	+	5.08316i	−0.181488	+	0.209448i
$590$		0			0
$591$	0.220925	+	0.141980i	0.00908764	+	0.00584027i
$592$	−12.3578	−	42.0867i	−0.507901	−	1.72975i
$593$	22.5585	−	19.5470i	0.926365	−	0.802700i	−0.0542739	−	0.998526i	$-0.517284\pi$
$593$	22.5585	−	19.5470i	0.926365	−	0.802700i	0.980639	+	0.195827i	$0.0627389\pi$
$594$	−0.860418	−	0.252641i	−0.0353034	−	0.0103660i
$595$		0			0
$596$	5.47807	−	38.1008i	0.224391	−	1.56067i
$597$		−	4.32625i		−	0.177062i
$598$	0.173830	−	0.888133i	0.00710843	−	0.0363185i
$599$	−4.70186			−0.192113			−0.0960564	−	0.995376i	$-0.530623\pi$
$599$	−4.70186			−0.192113			−0.0960564	+	0.995376i	$0.530623\pi$
$600$		0			0
$601$	8.89729	+	19.4823i	0.362928	+	0.794701i	0.999720	+	0.0236658i	$0.00753375\pi$
$601$	8.89729	+	19.4823i	0.362928	+	0.794701i	−0.636792	+	0.771036i	$0.719739\pi$
$602$	0.207178	−	0.705584i	0.00844395	−	0.0287575i
$603$	2.96969	−	2.57325i	0.120935	−	0.104791i
$604$	−38.2569	+	11.2332i	−1.55665	+	0.457073i
$605$		0			0
$606$	−0.164711	+	0.360666i	−0.00669091	+	0.0146511i
$607$	−29.1696	−	25.2756i	−1.18396	−	1.02591i	−0.999069	−	0.0431477i	$-0.986261\pi$
$607$	−29.1696	−	25.2756i	−1.18396	−	1.02591i	−0.184891	−	0.982759i	$-0.559193\pi$
$608$	4.22433	+	6.57319i	0.171319	+	0.266578i
$609$	0.986403	+	6.86058i	0.0399711	+	0.278005i
$610$		0			0
$611$	−4.91289	+	3.15732i	−0.198754	+	0.127732i
$612$	13.1263	+	11.3740i	0.530599	+	0.459766i
$613$	17.1155	+	7.81638i	0.691288	+	0.315700i	0.729900	−	0.683554i	$-0.239567\pi$
$613$	17.1155	+	7.81638i	0.691288	+	0.315700i	−0.0386125	+	0.999254i	$0.512294\pi$
$614$	0.663370	+	0.426322i	0.0267714	+	0.0172050i
$615$		0			0
$616$	0.724983	+	0.836675i	0.0292104	+	0.0337106i
$617$	−4.46602	+	15.2099i	−0.179795	+	0.612326i	0.819438	+	0.573168i	$0.194286\pi$
$617$	−4.46602	+	15.2099i	−0.179795	+	0.612326i	−0.999233	+	0.0391580i	$0.987532\pi$
$618$	0.780473	−	0.356430i	0.0313952	−	0.0143377i
$619$	−4.22984	+	29.4192i	−0.170012	+	1.18246i	0.708842	+	0.705367i	$0.249218\pi$
$619$	−4.22984	+	29.4192i	−0.170012	+	1.18246i	−0.878854	+	0.477091i	$0.841691\pi$
$620$		0			0
$621$	18.8915	−	14.7685i	0.758091	−	0.592641i
$622$			2.05794i			0.0825158i
$623$	0.983162	+	0.141357i	0.0393896	+	0.00566336i
$624$	3.51546	+	7.69778i	0.140731	+	0.308158i
$625$		0			0
$626$	1.29956	+	1.49977i	0.0519408	+	0.0599429i
$627$	4.25553	+	14.4930i	0.169949	+	0.578794i
$628$	6.21947	−	9.67769i	0.248184	−	0.386182i
$629$	20.0912	−	43.9936i	0.801089	−	1.75414i
$630$		0			0
$631$	−14.0318	+	9.01768i	−0.558597	+	0.358988i	−0.789273	−	0.614042i	$-0.789542\pi$
$631$	−14.0318	+	9.01768i	−0.558597	+	0.358988i	0.230677	+	0.973030i	$0.425906\pi$
$632$	1.12156	−	0.161257i	0.0446134	−	0.00641444i
$633$	6.50065	−	0.934652i	0.258378	−	0.0371491i
$634$	−0.945584	+	0.607690i	−0.0375539	+	0.0241345i
$635$		0			0
$636$	−0.226988	+	0.497034i	−0.00900066	+	0.0197087i
$637$	−5.33416	+	8.30012i	−0.211347	+	0.328863i
$638$	0.226502	+	0.771397i	0.00896732	+	0.0305399i
$639$	14.6051	+	16.8552i	0.577769	+	0.666781i
$640$		0			0
$641$	−12.5542	−	27.4898i	−0.495859	−	1.08578i	−0.977793	−	0.209573i	$-0.932793\pi$
$641$	−12.5542	−	27.4898i	−0.495859	−	1.08578i	0.481934	−	0.876208i	$-0.339935\pi$
$642$	0.645431	+	0.0927990i	0.0254731	+	0.00366248i
$643$		−	7.45857i		−	0.294137i	−0.989126	−	0.147069i	$-0.953016\pi$
$643$		−	7.45857i		−	0.294137i	0.989126	−	0.147069i	$-0.0469838\pi$
$644$	−14.7101	+	1.36187i	−0.579659	+	0.0536653i
$645$		0			0
$646$	−0.406038	+	2.82406i	−0.0159754	+	0.111111i
$647$	6.94356	−	3.17102i	0.272980	−	0.124666i	−0.274222	−	0.961666i	$-0.588420\pi$
$647$	6.94356	−	3.17102i	0.272980	−	0.124666i	0.547202	+	0.837001i	$0.315693\pi$
$648$	−0.0991526	+	0.337683i	−0.00389508	+	0.0132654i
$649$	−10.6860	−	12.3323i	−0.419462	−	0.484085i
$650$		0			0
$651$	−1.17836	−	0.757286i	−0.0461836	−	0.0296804i
$652$	15.9539	+	7.28589i	0.624802	+	0.285337i
$653$	−29.3782	−	25.4564i	−1.14966	−	0.996185i	−0.999972	−	0.00745135i	$-0.997628\pi$
$653$	−29.3782	−	25.4564i	−1.14966	−	0.996185i	−0.149686	−	0.988734i	$-0.547826\pi$
$654$	0.772173	−	0.496246i	0.0301944	−	0.0194047i
$655$		0			0
$656$	3.40014	+	23.6485i	0.132753	+	0.923319i
$657$	−11.2134	−	17.4484i	−0.437476	−	0.680726i
$658$	−0.281047	−	0.243529i	−0.0109564	−	0.00949374i
$659$	5.38310	−	11.7873i	0.209696	−	0.459170i	−0.775335	−	0.631551i	$-0.782419\pi$
$659$	5.38310	−	11.7873i	0.209696	−	0.459170i	0.985030	+	0.172381i	$0.0551460\pi$
$660$		0			0
$661$	28.9778	−	8.50866i	1.12711	−	0.330949i	0.335537	−	0.942027i	$-0.391082\pi$
$661$	28.9778	−	8.50866i	1.12711	−	0.330949i	0.791570	+	0.611078i	$0.209264\pi$
$662$	1.09248	−	0.946639i	0.0424604	−	0.0367922i
$663$	−2.62880	+	8.95287i	−0.102094	+	0.347701i
$664$	−0.637531	−	1.39600i	−0.0247410	−	0.0541753i
$665$		0			0
$666$	1.95619			0.0758007
$667$	−20.2955	−	7.08990i	−0.785844	−	0.274522i
$668$			38.9037i			1.50523i
$669$	1.31033	−	9.11356i	0.0506604	−	0.352351i
$670$		0			0
$671$	−6.28342	−	1.84498i	−0.242569	−	0.0712246i
$672$	−1.22977	+	1.06560i	−0.0474393	+	0.0411064i
$673$	0.667173	+	2.27218i	0.0257176	+	0.0875862i	0.971352	−	0.237646i	$-0.0763758\pi$
$673$	0.667173	+	2.27218i	0.0257176	+	0.0875862i	−0.945634	+	0.325232i	$0.894558\pi$
$674$	−2.03488	−	1.30773i	−0.0783805	−	0.0503721i
$675$		0			0
$676$	−10.9824	+	12.6744i	−0.422402	+	0.487478i
$677$	18.7600	+	29.1912i	0.721006	+	1.12191i	0.987431	+	0.158052i	$0.0505213\pi$
$677$	18.7600	+	29.1912i	0.721006	+	1.12191i	−0.266425	+	0.963856i	$0.585842\pi$
$678$	−1.70958	+	0.245801i	−0.0656562	+	0.00943993i
$679$	1.21925	+	8.48004i	0.0467904	+	0.325434i
$680$		0			0
$681$	−5.80963	+	6.70467i	−0.222626	+	0.256924i
$682$	−0.147791	−	0.0674940i	−0.00565922	−	0.00258448i
$683$	12.5776	−	19.5711i	0.481269	−	0.748869i	−0.512696	−	0.858570i	$-0.671353\pi$
$683$	12.5776	−	19.5711i	0.481269	−	0.748869i	0.993965	+	0.109702i	$0.0349895\pi$
$684$	28.3845	−	8.33444i	1.08531	−	0.318675i
$685$		0			0
$686$	−1.51832	−	0.445819i	−0.0579698	−	0.0170215i
$687$	7.62712	−	3.48319i	0.290993	−	0.132892i
$688$	−21.1116	−	3.03539i	−0.804872	−	0.115723i
$689$	0.587093			0.0223665
$690$		0			0
$691$	−45.0096			−1.71225			−0.856123	−	0.516772i	$-0.827133\pi$
$691$	−45.0096			−1.71225			−0.856123	+	0.516772i	$0.827133\pi$
$692$	−42.5593	−	6.11911i	−1.61786	−	0.232614i
$693$	5.72279	−	2.61351i	0.217391	−	0.0992790i
$694$	0.510520	+	0.149902i	0.0193791	+	0.00569020i
$695$		0			0
$696$	−1.51372	+	0.444470i	−0.0573776	+	0.0168476i
$697$	−14.2422	+	22.1612i	−0.539461	+	0.839417i
$698$	0.669363	+	0.305688i	0.0253358	+	0.0115705i
$699$	15.7256	−	18.1483i	0.594796	−	0.686431i
$700$		0			0
$701$	−3.34738	−	23.2815i	−0.126429	−	0.879332i	−0.950029	−	0.312161i	$-0.898947\pi$
$701$	−3.34738	−	23.2815i	−0.126429	−	0.879332i	0.823600	−	0.567171i	$-0.191962\pi$
$702$	−0.933908	+	0.134276i	−0.0352481	+	0.00506791i
$703$	−44.5357	−	69.2989i	−1.67969	−	2.61366i
$704$	10.4105	−	12.0144i	0.392362	−	0.452810i
$705$		0			0
$706$	−1.93952	−	1.24645i	−0.0729946	−	0.0469108i
$707$	−1.95925	−	6.67261i	−0.0736854	−	0.250949i
$708$	12.0764	−	10.4643i	0.453859	−	0.393271i
$709$	−32.8793	−	9.65422i	−1.23481	−	0.362572i	−0.401745	−	0.915752i	$-0.631596\pi$
$709$	−32.8793	−	9.65422i	−1.23481	−	0.362572i	−0.833062	+	0.553180i	$0.813414\pi$
$710$		0			0
$711$	0.916390	−	6.37363i	0.0343673	−	0.239030i
$712$			0.226084i			0.00847285i
$713$	3.76877	−	2.16144i	0.141142	−	0.0809467i
$714$	−0.594172			−0.0222363
$715$		0			0
$716$	12.7077	+	27.8260i	0.474909	+	1.03990i
$717$	−3.16603	+	10.7825i	−0.118238	+	0.402680i
$718$	0.377112	−	0.326770i	0.0140737	−	0.0121949i
$719$	22.3827	−	6.57217i	0.834735	−	0.245100i	0.163685	−	0.986513i	$-0.447662\pi$
$719$	22.3827	−	6.57217i	0.834735	−	0.245100i	0.671050	+	0.741412i	$0.265844\pi$
$720$		0			0
$721$	−6.25157	+	13.6890i	−0.232821	+	0.509806i
$722$	2.40672	+	2.08543i	0.0895687	+	0.0776117i
$723$	15.1958	+	23.6451i	0.565138	+	0.879371i
$724$	−0.232195	−	1.61495i	−0.00862947	−	0.0600193i
$725$		0			0
$726$	0.508824	−	0.327001i	0.0188842	−	0.0121362i
$727$	30.4481	+	26.3834i	1.12926	+	0.978507i	0.999914	−	0.0130932i	$-0.00416783\pi$
$727$	30.4481	+	26.3834i	1.12926	+	0.978507i	0.129343	+	0.991600i	$0.458713\pi$
$728$	1.05956	+	0.483883i	0.0392698	+	0.0179339i
$729$	−10.9363	−	7.02833i	−0.405048	−	0.260309i
$730$		0			0
$731$	−15.4005	−	17.7731i	−0.569607	−	0.657361i
$732$	1.80669	−	6.15303i	0.0667773	−	0.227422i
$733$	20.6659	−	9.43781i	0.763313	−	0.348594i	0.00457542	−	0.999990i	$-0.498544\pi$
$733$	20.6659	−	9.43781i	0.763313	−	0.348594i	0.758738	+	0.651396i	$0.225816\pi$
$734$	−0.154499	+	1.07456i	−0.00570266	+	0.0396629i
$735$		0			0
$736$	−1.17576	−	4.90825i	−0.0433391	−	0.180921i
$737$		−	3.99714i		−	0.147236i
$738$	−1.05466	−	0.151637i	−0.0388224	−	0.00558182i
$739$	7.47356	+	16.3648i	0.274919	+	0.601989i	0.995849	−	0.0910188i	$-0.0290123\pi$
$739$	7.47356	+	16.3648i	0.274919	+	0.601989i	−0.720930	+	0.693008i	$0.756285\pi$
$740$		0			0
$741$	10.4075	+	12.0109i	0.382328	+	0.441230i
$742$	0.0105326	+	0.0358708i	0.000386664	+	0.00131686i
$743$	3.14797	−	4.89833i	0.115488	−	0.179702i	−0.778698	−	0.627399i	$-0.784119\pi$
$743$	3.14797	−	4.89833i	0.115488	−	0.179702i	0.894185	+	0.447697i	$0.147756\pi$
$744$	0.132445	−	0.290013i	0.00485566	−	0.0106324i
$745$		0			0
$746$	2.16002	−	1.38816i	0.0790840	−	0.0508242i
$747$	−8.63256	+	1.24117i	−0.315849	+	0.0454122i
$748$	17.4879	−	2.51438i	0.639420	−	0.0919347i
$749$	−9.62131	+	6.18324i	−0.351555	+	0.225931i
$750$		0			0
$751$	3.84740	−	8.42462i	0.140393	−	0.307419i	−0.826354	−	0.563151i	$-0.809589\pi$
$751$	3.84740	−	8.42462i	0.140393	−	0.307419i	0.966748	+	0.255732i	$0.0823164\pi$
$752$	−5.83133	+	9.07372i	−0.212647	+	0.330885i
$753$	−7.74578	−	26.3797i	−0.282272	−	0.961330i
$754$	0.553942	+	0.639283i	0.0201734	+	0.0232813i
$755$		0			0
$756$	6.39819	+	14.0101i	0.232700	+	0.509542i
$757$	−8.04064	−	1.15607i	−0.292242	−	0.0420180i	−0.00536536	−	0.999986i	$-0.501708\pi$
$757$	−8.04064	−	1.15607i	−0.292242	−	0.0420180i	−0.286877	+	0.957968i	$0.592617\pi$
$758$		−	2.94048i		−	0.106803i
$759$	0.492336	−	9.74443i	0.0178707	−	0.353700i
$760$		0			0
$761$	−4.15984	+	28.9323i	−0.150794	+	1.04880i	0.764099	+	0.645099i	$0.223184\pi$
$761$	−4.15984	+	28.9323i	−0.150794	+	1.04880i	−0.914893	+	0.403697i	$0.867725\pi$
$762$	1.40695	−	0.642532i	0.0509684	−	0.0232765i
$763$	−4.53565	+	15.4470i	−0.164201	+	0.559219i
$764$	5.56539	+	6.42281i	0.201349	+	0.232369i
$765$		0			0
$766$	2.30544	+	1.48162i	0.0832990	+	0.0535330i
$767$	−15.6175	−	7.13228i	−0.563915	−	0.257532i
$768$	11.6249	+	10.0730i	0.419476	+	0.363478i
$769$	−12.2803	+	7.89208i	−0.442840	+	0.284596i	−0.742998	−	0.669294i	$-0.766597\pi$
$769$	−12.2803	+	7.89208i	−0.442840	+	0.284596i	0.300158	+	0.953889i	$0.402960\pi$
$770$		0			0
$771$	2.52790	+	17.5820i	0.0910403	+	0.633199i
$772$	5.20693	+	8.10215i	0.187402	+	0.291603i
$773$	13.0471	+	11.3054i	0.469271	+	0.406625i	0.857136	−	0.515091i	$-0.172242\pi$
$773$	13.0471	+	11.3054i	0.469271	+	0.406625i	−0.387865	+	0.921716i	$0.626787\pi$
$774$	0.395142	−	0.865241i	0.0142031	−	0.0311004i
$775$		0			0
$776$	−1.87104	+	0.549388i	−0.0671666	+	0.0197219i
$777$	12.9650	−	11.2342i	0.465117	−	0.403026i
$778$	−0.315080	+	1.07306i	−0.0112962	+	0.0384712i
$779$	18.6391	+	40.8139i	0.667815	+	1.46231i
$780$		0			0
$781$	22.6867			0.811795
$782$	0.849200	−	1.63563i	0.0303673	−	0.0584899i
$783$			22.4134i			0.800991i
$784$	−2.59332	+	18.0369i	−0.0926186	+	0.644176i
$785$		0			0
$786$	−1.10366	−	0.324065i	−0.0393663	−	0.0115590i
$787$	−11.5950	+	10.0471i	−0.413318	+	0.358142i	−0.836561	−	0.547875i	$-0.815437\pi$
$787$	−11.5950	+	10.0471i	−0.413318	+	0.358142i	0.423243	+	0.906016i	$0.360892\pi$
$788$	−0.147399	−	0.501995i	−0.00525087	−	0.0178828i
$789$	−7.35320	−	4.72561i	−0.261781	−	0.168236i
$790$		0			0
$791$	19.8380	−	22.8942i	0.705356	−	0.814025i
$792$	0.774198	+	1.20467i	0.0275099	+	0.0428063i
$793$	−6.82010	+	0.980582i	−0.242189	+	0.0348215i
$794$	0.154578	+	1.07511i	0.00548577	+	0.0381544i
$795$		0			0
$796$	−5.64417	+	6.51371i	−0.200052	+	0.230872i
$797$	−22.8517	−	10.4360i	−0.809448	−	0.369663i	−0.0326932	−	0.999465i	$-0.510408\pi$
$797$	−22.8517	−	10.4360i	−0.809448	−	0.369663i	−0.776755	+	0.629803i	$0.783136\pi$
$798$	−0.547137	+	0.851362i	−0.0193685	+	0.0301379i
$799$	−11.4109	+	3.35055i	−0.403690	+	0.118534i
$800$		0			0
$801$	1.23275	+	0.361967i	0.0435570	+	0.0127895i
$802$	−2.70612	+	1.23584i	−0.0955565	+	0.0436392i
$803$	−20.8834	−	3.00258i	−0.736959	−	0.105959i
$804$	3.91419			0.138043
$805$		0			0
$806$	−0.170947			−0.00602136
$807$	−2.90095	−	0.417094i	−0.102118	−	0.0146824i
$808$	1.43986	−	0.657563i	0.0506542	−	0.0231330i
$809$	21.8919	+	6.42804i	0.769678	+	0.225998i	0.642917	−	0.765935i	$-0.277724\pi$
$809$	21.8919	+	6.42804i	0.769678	+	0.225998i	0.126761	+	0.991933i	$0.459542\pi$
$810$		0			0
$811$	41.7803	−	12.2678i	1.46711	−	0.430781i	0.551949	−	0.833878i	$-0.313884\pi$
$811$	41.7803	−	12.2678i	1.46711	−	0.430781i	0.915157	+	0.403097i	$0.132066\pi$
$812$	7.46538	−	11.6164i	0.261984	−	0.407654i
$813$	5.96757	+	2.72530i	0.209292	+	0.0955803i
$814$	1.30309	−	1.50385i	0.0456734	−	0.0527099i
$815$		0			0
$816$	2.45256	+	17.0579i	0.0858567	+	0.597147i
$817$	−39.6476	+	5.70046i	−1.38709	+	0.199434i
$818$	0.773766	+	1.20400i	0.0270541	+	0.0420970i
$819$	4.33481	−	5.00264i	0.151471	−	0.174806i
$820$		0			0
$821$	40.9122	+	26.2927i	1.42785	+	0.917621i	0.999905	+	0.0138148i	$0.00439753\pi$
$821$	40.9122	+	26.2927i	1.42785	+	0.917621i	0.427942	+	0.903806i	$0.359239\pi$
$822$	−0.534648	−	1.82085i	−0.0186480	−	0.0635093i
$823$	0.868528	−	0.752583i	0.0302750	−	0.0262334i	−0.639592	−	0.768715i	$-0.720897\pi$
$823$	0.868528	−	0.752583i	0.0302750	−	0.0262334i	0.669867	+	0.742481i	$0.266351\pi$
$824$	−3.28662	−	0.965039i	−0.114495	−	0.0336187i
$825$		0			0
$826$	0.155592	−	1.08217i	0.00541374	−	0.0376534i
$827$			15.3873i			0.535069i	0.963548	+	0.267534i	$0.0862089\pi$
$827$			15.3873i			0.535069i	−0.963548	+	0.267534i	$0.913791\pi$
$828$	−19.0844	−	0.964240i	−0.663230	−	0.0335096i
$829$	43.7168			1.51835			0.759174	−	0.650888i	$-0.225603\pi$
$829$	43.7168			1.51835			0.759174	+	0.650888i	$0.225603\pi$
$830$		0			0
$831$	9.46680	+	20.7294i	0.328400	+	0.719095i
$832$	4.71239	−	16.0489i	0.163373	−	0.556396i
$833$	−15.1846	+	13.1576i	−0.526117	+	0.455883i
$834$	1.38481	−	0.406618i	0.0479522	−	0.0140800i
$835$		0			0
$836$	12.5008	−	27.3729i	0.432349	−	0.946712i
$837$	−3.42321	−	2.96623i	−0.118323	−	0.102528i
$838$	−0.638055	−	0.992833i	−0.0220413	−	0.0342969i
$839$	−1.60650	−	11.1735i	−0.0554627	−	0.385751i	−0.998579	−	0.0532888i	$-0.983030\pi$
$839$	−1.60650	−	11.1735i	−0.0554627	−	0.385751i	0.943116	−	0.332462i	$-0.107879\pi$
$840$		0			0
$841$	−7.49181	+	4.81469i	−0.258338	+	0.166024i
$842$	−0.867020	−	0.751277i	−0.0298795	−	0.0258907i
$843$	12.9563	+	5.91692i	0.446237	+	0.203790i
$844$	−11.0069	−	7.07372i	−0.378874	−	0.243488i
$845$		0			0
$846$	−0.315003	−	0.363533i	−0.0108300	−	0.0124985i
$847$	−2.98877	+	10.1788i	−0.102695	+	0.349748i
$848$	0.986328	−	0.450441i	0.0338707	−	0.0154682i
$849$	−3.37394	+	23.4663i	−0.115793	+	0.805361i
$850$		0			0
$851$	12.3956	+	51.7460i	0.424917	+	1.77383i
$852$			22.2160i			0.761106i
$853$	−16.5522	−	2.37985i	−0.566737	−	0.0814845i	−0.147010	−	0.989135i	$-0.546965\pi$
$853$	−16.5522	−	2.37985i	−0.566737	−	0.0814845i	−0.419727	+	0.907651i	$0.637874\pi$
$854$	−0.182267	−	0.399108i	−0.00623704	−	0.0136572i
$855$		0			0
$856$	−1.70474	−	1.96737i	−0.0582667	−	0.0672433i
$857$	1.74302	+	5.93618i	0.0595405	+	0.202776i	0.983891	−	0.178767i	$-0.0572109\pi$
$857$	1.74302	+	5.93618i	0.0595405	+	0.202776i	−0.924351	+	0.381543i	$0.875393\pi$
$858$	−0.207554	+	0.322961i	−0.00708579	+	0.0110257i
$859$	3.60612	−	7.89631i	0.123039	−	0.269419i	−0.838082	−	0.545544i	$-0.816323\pi$
$859$	3.60612	−	7.89631i	0.123039	−	0.269419i	0.961122	+	0.276125i	$0.0890504\pi$
$860$		0			0
$861$	−7.86077	+	5.05181i	−0.267894	+	0.172165i
$862$	−0.816646	+	0.117416i	−0.0278151	+	0.00399921i
$863$	11.1982	−	1.61006i	0.381192	−	0.0548072i	0.0509446	−	0.998701i	$-0.483777\pi$
$863$	11.1982	−	1.61006i	0.381192	−	0.0548072i	0.330248	+	0.943894i	$0.392868\pi$
$864$	−4.42666	+	2.84484i	−0.150598	+	0.0967834i
$865$		0			0
$866$	−1.24386	+	2.72368i	−0.0422682	+	0.0925546i
$867$	−1.08214	+	1.68384i	−0.0367513	+	0.0571861i
$868$	0.786189	+	2.67752i	0.0266850	+	0.0908808i
$869$	−4.28939	−	4.95022i	−0.145508	−	0.167925i
$870$		0			0
$871$	−1.74707	−	3.82555i	−0.0591973	−	0.129624i
$872$	−3.62711	−	0.521499i	−0.122829	−	0.0176602i
$873$			11.0817i			0.375058i
$874$	−1.56164	−	2.72293i	−0.0528232	−	0.0921045i
$875$		0			0
$876$	2.94027	−	20.4500i	0.0993426	−	0.690943i
$877$	22.5349	−	10.2913i	0.760950	−	0.347514i	0.00314460	−	0.999995i	$-0.498999\pi$
$877$	22.5349	−	10.2913i	0.760950	−	0.347514i	0.757805	+	0.652481i	$0.226272\pi$
$878$	0.792013	−	2.69735i	0.0267291	−	0.0910311i
$879$	2.79903	+	3.23025i	0.0944090	+	0.108954i
$880$		0			0
$881$	28.0492	+	18.0261i	0.945000	+	0.607315i	0.919808	−	0.392368i	$-0.128344\pi$
$881$	28.0492	+	18.0261i	0.945000	+	0.607315i	0.0251917	+	0.999683i	$0.491980\pi$
$882$	−0.739229	−	0.337594i	−0.0248911	−	0.0113674i
$883$	9.88198	+	8.56278i	0.332555	+	0.288161i	0.805092	−	0.593150i	$-0.202116\pi$
$883$	9.88198	+	8.56278i	0.332555	+	0.288161i	−0.472537	+	0.881311i	$0.656662\pi$
$884$	15.6382	−	10.0501i	0.525969	−	0.338020i
$885$		0			0
$886$	−0.384017	−	2.67090i	−0.0129013	−	0.0897305i
$887$	−11.9964	−	18.6668i	−0.402800	−	0.626770i	0.579303	−	0.815112i	$-0.303325\pi$
$887$	−11.9964	−	18.6668i	−0.402800	−	0.626770i	−0.982103	+	0.188343i	$0.939688\pi$
$888$	2.95103	+	2.55708i	0.0990301	+	0.0858101i
$889$	−11.2696	+	24.6770i	−0.377971	+	0.827641i
$890$		0			0
$891$	1.95204	−	0.573170i	0.0653957	−	0.0192019i
$892$	−13.8627	+	12.0121i	−0.464158	+	0.402195i
$893$	−5.70679	+	19.4355i	−0.190970	+	0.650385i
$894$	0.707574	+	1.54937i	0.0236648	+	0.0518187i
$895$		0			0
$896$	4.31954			0.144306
$897$	−3.78790	−	9.54133i	−0.126474	−	0.318576i
$898$		−	1.48567i		−	0.0495775i
$899$	−0.577928	+	4.01958i	−0.0192750	+	0.134060i
$900$		0			0
$901$	1.14714	+	0.336832i	0.0382169	+	0.0112215i
$902$	−0.819121	+	0.709772i	−0.0272737	+	0.0236328i
$903$	−2.35013	−	8.00382i	−0.0782076	−	0.266351i
$904$	5.80064	+	3.72784i	0.192926	+	0.123986i
$905$		0			0
$906$	1.15539	−	1.33339i	0.0383853	−	0.0442990i
$907$	11.5834	+	18.0240i	0.384619	+	0.598479i	0.978543	−	0.206042i	$-0.0660585\pi$
$907$	11.5834	+	18.0240i	0.384619	+	0.598479i	−0.593924	+	0.804521i	$0.702422\pi$
$908$	17.4943	−	2.51530i	0.580568	−	0.0834730i
$909$	−1.28017	−	8.90379i	−0.0424606	−	0.295320i
$910$		0			0
$911$	25.5067	−	29.4363i	0.845076	−	0.975269i	−0.154844	−	0.987939i	$-0.549488\pi$
$911$	25.5067	−	29.4363i	0.845076	−	0.975269i	0.999920	+	0.0126696i	$0.00403297\pi$
$912$	26.6999	+	12.1935i	0.884123	+	0.403766i
$913$	−4.79631	+	7.46321i	−0.158735	+	0.246996i
$914$	−0.230030	+	0.0675428i	−0.00760870	+	0.00223412i
$915$		0			0
$916$	−16.0279	−	4.70621i	−0.529576	−	0.155497i
$917$	18.3516	−	8.38091i	0.606024	−	0.276762i
$918$	−1.90184	−	0.273443i	−0.0627700	−	0.00902496i
$919$	−29.9408			−0.987657			−0.493829	−	0.869559i	$-0.664403\pi$
$919$	−29.9408			−0.987657			−0.493829	+	0.869559i	$0.664403\pi$
$920$		0			0
$921$	8.94494			0.294746
$922$	−3.11912	−	0.448462i	−0.102723	−	0.0147693i
$923$	21.7129	−	9.91594i	0.714688	−	0.326387i
$924$	6.01302	+	1.76558i	0.197814	+	0.0580834i
$925$		0			0
$926$	3.52295	−	1.03443i	0.115771	−	0.0339935i
$927$	−10.5240	+	16.3756i	−0.345653	+	0.537846i
$928$	4.29124	+	1.95974i	0.140867	+	0.0643318i
$929$	−8.14358	+	9.39819i	−0.267182	+	0.308345i	−0.873448	−	0.486917i	$-0.838121\pi$
$929$	−8.14358	+	9.39819i	−0.267182	+	0.308345i	0.606266	+	0.795262i	$0.292667\pi$
$930$		0			0
$931$	4.87026	+	33.8734i	0.159616	+	1.11016i
$932$	−47.3537	+	6.80843i	−1.55112	+	0.223017i
$933$	12.6209	+	19.6385i	0.413189	+	0.642934i
$934$	1.02031	−	1.17750i	0.0333855	−	0.0385289i
$935$		0			0
$936$	1.26750	+	0.814576i	0.0414297	+	0.0266252i
$937$	2.68807	+	9.15473i	0.0878155	+	0.299072i	0.991677	−	0.128754i	$-0.0410978\pi$
$937$	2.68807	+	9.15473i	0.0878155	+	0.299072i	−0.903861	+	0.427826i	$0.859280\pi$
$938$	0.202394	−	0.175376i	0.00660840	−	0.00572621i
$939$	21.5992	+	6.34209i	0.704863	+	0.206966i
$940$		0			0
$941$	0.484266	−	3.36814i	0.0157866	−	0.109798i	−0.980405	−	0.196995i	$-0.936882\pi$
$941$	0.484266	−	3.36814i	0.0157866	−	0.109798i	0.996191	+	0.0871966i	$0.0277908\pi$
$942$			0.509046i			0.0165856i
$943$	−2.67180	−	28.8591i	−0.0870058	−	0.939782i
$944$	−31.7099			−1.03207
$945$		0			0
$946$	−0.401948	−	0.880143i	−0.0130684	−	0.0286159i
$947$	−3.50424	+	11.9343i	−0.113872	+	0.387814i	−0.996631	−	0.0820124i	$-0.973865\pi$
$947$	−3.50424	+	11.9343i	−0.113872	+	0.387814i	0.882759	+	0.469826i	$0.155683\pi$
$948$	4.84750	−	4.20038i	0.157439	−	0.136422i
$949$	−21.2993	+	6.25405i	−0.691405	+	0.203015i
$950$		0			0
$951$	−5.29668	+	11.5981i	−0.171757	+	0.376095i
$952$	1.79269	+	1.55338i	0.0581015	+	0.0503452i
$953$	7.23572	+	11.2590i	0.234388	+	0.364715i	0.938445	−	0.345429i	$-0.112266\pi$
$953$	7.23572	+	11.2590i	0.234388	+	0.364715i	−0.704057	+	0.710143i	$0.748630\pi$
$954$	0.00688198	+	0.0478652i	0.000222812	+	0.00154969i
$955$		0			0
$956$	18.8341	−	12.1039i	0.609137	−	0.391469i
$957$	6.89227	+	5.97219i	0.222795	+	0.193053i
$958$	−0.958797	−	0.437868i	−0.0309773	−	0.0141469i
$959$	28.0009	+	17.9951i	0.904197	+	0.581092i
$960$		0			0
$961$	19.7633	+	22.8080i	0.637524	+	0.735742i
$962$	0.589852	−	2.00885i	0.0190176	−	0.0647680i
$963$	−13.4567	+	6.14545i	−0.433635	+	0.198034i
$964$	7.96900	−	55.4256i	0.256664	−	1.78514i
$965$		0			0
$966$	0.515009	−	0.402610i	0.0165701	−	0.0129538i
$967$			24.7635i			0.796341i	0.917311	+	0.398170i	$0.130355\pi$
$967$			24.7635i			0.796341i	−0.917311	+	0.398170i	$0.869645\pi$
$968$	−2.39008	−	0.343642i	−0.0768202	−	0.0110451i
$969$	13.4446	+	29.4395i	0.431902	+	0.945734i
$970$		0			0
$971$	−11.6629	−	13.4597i	−0.374281	−	0.431944i	0.537092	−	0.843523i	$-0.319523\pi$
$971$	−11.6629	−	13.4597i	−0.374281	−	0.431944i	−0.911374	+	0.411580i	$0.864977\pi$
$972$	8.98041	+	30.5845i	0.288047	+	0.980997i
$973$	−13.6859	+	21.2956i	−0.438749	+	0.682707i
$974$	0.690922	−	1.51291i	0.0221386	−	0.0484767i
$975$		0			0
$976$	−10.7056	+	6.88004i	−0.342676	+	0.220225i
$977$	−7.20015	+	1.03522i	−0.230353	+	0.0331198i	−0.256525	−	0.966538i	$-0.582577\pi$
$977$	−7.20015	+	1.03522i	−0.230353	+	0.0331198i	0.0261716	+	0.999657i	$0.491668\pi$
$978$	−0.768191	+	0.110449i	−0.0245640	+	0.00353178i
$979$	1.09945	−	0.706574i	0.0351386	−	0.0225822i
$980$		0			0
$981$	−8.65065	+	18.9423i	−0.276194	+	0.604780i
$982$	1.04446	−	1.62521i	0.0333301	−	0.0518627i
$983$	9.07613	+	30.9104i	0.289483	+	0.985890i	0.967926	+	0.251236i	$0.0808372\pi$
$983$	9.07613	+	30.9104i	0.289483	+	0.985890i	−0.678442	+	0.734654i	$0.737345\pi$
$984$	−1.39280	−	1.60738i	−0.0444008	−	0.0512412i
$985$		0			0
$986$	0.715594	+	1.56693i	0.0227892	+	0.0499013i
$987$	−4.17548	−	0.600344i	−0.132907	−	0.0191092i
$988$		−	31.6618i		−	1.00729i
$989$	25.3916	+	4.96978i	0.807407	+	0.158030i
$990$		0			0
$991$	−1.54572	+	10.7507i	−0.0491013	+	0.341507i	0.950431	+	0.310935i	$0.100642\pi$
$991$	−1.54572	+	10.7507i	−0.0491013	+	0.341507i	−0.999533	+	0.0305723i	$0.990267\pi$
$992$	−0.867221	+	0.396047i	−0.0275343	+	0.0125745i
$993$	4.61978	−	15.7335i	0.146604	−	0.499288i
$994$	0.995387	+	1.14874i	0.0315718	+	0.0364358i
$995$		0			0
$996$	−7.30834	−	4.69678i	−0.231574	−	0.148823i
$997$	19.1851	+	8.76152i	0.607597	+	0.277480i	0.695360	−	0.718661i	$-0.255245\pi$
$997$	19.1851	+	8.76152i	0.607597	+	0.277480i	−0.0877636	+	0.996141i	$0.527972\pi$
$998$	−0.672189	−	0.582455i	−0.0212778	−	0.0184373i
$999$	46.6687	−	29.9922i	1.47653	−	0.948910i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.p.a.399.2		20
5.2	odd	4		115.2.g.a.31.1	yes	10
5.3	odd	4		575.2.k.a.376.1		10
5.4	even	2	inner	575.2.p.a.399.1		20
23.3	even	11	inner	575.2.p.a.49.1		20
115.3	odd	44		575.2.k.a.26.1		10
115.7	even	44		2645.2.a.o.1.4		5
115.49	even	22	inner	575.2.p.a.49.2		20
115.62	odd	44		2645.2.a.n.1.4		5
115.72	odd	44		115.2.g.a.26.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.a.26.1	✓	10	115.72	odd	44
115.2.g.a.31.1	yes	10	5.2	odd	4
575.2.k.a.26.1		10	115.3	odd	44
575.2.k.a.376.1		10	5.3	odd	4
575.2.p.a.49.1		20	23.3	even	11	inner
575.2.p.a.49.2		20	115.49	even	22	inner
575.2.p.a.399.1		20	5.4	even	2	inner
575.2.p.a.399.2		20	1.1	even	1	trivial
2645.2.a.n.1.4		5	115.62	odd	44
2645.2.a.o.1.4		5	115.7	even	44

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.p (of order \(22\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0872586 + 0.0125459i) q^{2} +(0.909632 - 0.415415i) q^{3} +(-1.91153 - 0.561276i) q^{4} +(0.0845850 - 0.0248364i) q^{6} +(-0.835939 + 1.30075i) q^{7} +(-0.320135 - 0.146201i) q^{8} +(-1.30972 + 1.51150i) q^{9} +(0.289532 + 2.01374i) q^{11} +(-1.97195 + 0.283524i) q^{12} +(1.15727 + 1.80075i) q^{13} +(-0.0892619 + 0.103014i) q^{14} +(3.32584 + 2.13739i) q^{16} +(1.22809 + 4.18251i) q^{17} +(-0.133248 + 0.115460i) q^{18} +(7.12381 + 2.09174i) q^{19} +(-0.220047 + 1.53046i) q^{21} +0.179348i q^{22} +(-3.89854 - 2.79310i) q^{23} -0.351939 q^{24} +(0.0783898 + 0.171650i) q^{26} +(-1.40866 + 4.79746i) q^{27} +(2.32800 - 2.01722i) q^{28} +(4.30111 - 1.26292i) q^{29} +(-0.376329 + 0.824045i) q^{31} +(0.795348 + 0.689173i) q^{32} +(1.09990 + 1.71148i) q^{33} +(0.0546886 + 0.380367i) q^{34} +(3.35194 - 2.15416i) q^{36} +(-8.38507 - 7.26571i) q^{37} +(0.595371 + 0.271897i) q^{38} +(1.80075 + 1.15727i) q^{39} +(3.95750 + 4.56720i) q^{41} +(-0.0384020 + 0.130785i) q^{42} +(-4.90745 + 2.24116i) q^{43} +(0.576814 - 4.01183i) q^{44} +(-0.305139 - 0.292633i) q^{46} +2.72825i q^{47} +(3.91319 + 0.562632i) q^{48} +(1.91476 + 4.19273i) q^{49} +(2.85459 + 3.29437i) q^{51} +(-1.20144 - 4.09173i) q^{52} +(0.148283 - 0.230732i) q^{53} +(-0.183106 + 0.400947i) q^{54} +(0.457783 - 0.294199i) q^{56} +(7.34898 - 1.05662i) q^{57} +(0.391153 - 0.0562393i) q^{58} +(-6.74757 + 4.33640i) q^{59} +(-1.33718 + 2.92802i) q^{61} +(-0.0431763 + 0.0671837i) q^{62} +(-0.871230 - 2.96714i) q^{63} +(-5.11714 - 5.90549i) q^{64} +(0.0745040 + 0.163141i) q^{66} +(-1.94473 - 0.279610i) q^{67} -8.68428i q^{68} +(-4.70653 - 0.921186i) q^{69} +(1.58700 - 11.0378i) q^{71} +(0.640269 - 0.292401i) q^{72} +(-2.92170 + 9.95039i) q^{73} +(-0.640515 - 0.739194i) q^{74} +(-12.4433 - 7.99684i) q^{76} +(-2.86139 - 1.30675i) q^{77} +(0.142612 + 0.123574i) q^{78} +(-2.70849 + 1.74064i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(0.288027 + 0.448178i) q^{82} +(3.29557 + 2.85563i) q^{83} +(1.27964 - 2.80202i) q^{84} +(-0.456334 + 0.133992i) q^{86} +(3.38779 - 2.93553i) q^{87} +(0.201720 - 0.686997i) q^{88} +(-0.266861 - 0.584343i) q^{89} -3.30972 q^{91} +(5.88446 + 7.52725i) q^{92} +0.905910i q^{93} +(-0.0342284 + 0.238063i) q^{94} +(1.00977 + 0.296494i) q^{96} +(4.18748 - 3.62848i) q^{97} +(0.114478 + 0.389875i) q^{98} +(-3.42297 - 2.19981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{4} + 12 q^{6} - 4 q^{9} + 16 q^{11} + 6 q^{14} + 10 q^{16} + 26 q^{19} + 12 q^{21} + 12 q^{24} + 22 q^{26} - 4 q^{29} - 40 q^{31} - 32 q^{34} + 48 q^{36} - 10 q^{41} - 38 q^{44} - 32 q^{46}+ \cdots - 12 q^{99}+O(q^{100}) \) 20 * q + 2 * q^4 + 12 * q^6 - 4 * q^9 + 16 * q^11 + 6 * q^14 + 10 * q^16 + 26 * q^19 + 12 * q^21 + 12 * q^24 + 22 * q^26 - 4 * q^29 - 40 * q^31 - 32 * q^34 + 48 * q^36 - 10 * q^41 - 38 * q^44 - 32 * q^46 - 8 * q^49 - 20 * q^51 + 60 * q^54 + 6 * q^56 - 10 * q^59 - 6 * q^61 + 68 * q^64 - 8 * q^66 + 2 * q^69 - 44 * q^71 - 2 * q^74 - 4 * q^76 - 102 * q^79 - 2 * q^81 - 12 * q^84 - 18 * q^86 - 114 * q^89 - 44 * q^91 + 162 * q^94 - 14 * q^96 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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