LMFDB - Embedded newform 575.2.p.a.49.2

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			49.2
Root			$-0.755750 + 0.654861i$ of defining polynomial
Character	$\chi$	$=$	575.49
Dual form			575.2.p.a.399.2

$q$-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 $\left(\mathbb{Z}/575\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$e\left(\frac{8}{11}\right)$	$-1$

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	−0.111395	−	0.993776i	$-0.535532\pi$
$2$	0.0872586	−	0.0125459i	0.0617012	−	0.00887129i	0.173096	+	0.984905i	$0.444623\pi$
$3$	0.909632	+	0.415415i	0.525176	+	0.239840i	0.660318	−	0.750986i	$-0.270422\pi$
$3$	0.909632	+	0.415415i	0.525176	+	0.239840i	−0.135141	+	0.990826i	$0.543149\pi$
$4$	−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	0.646560	−	0.762863i	$-0.276207\pi$
$7$	−0.835939	−	1.30075i	−0.315955	−	0.491636i	−0.962515	+	0.271227i	$0.912571\pi$
$8$	−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	−0.898468	−	0.439038i	$-0.855319\pi$
$11$	0.289532	−	2.01374i	0.0872971	−	0.607165i	0.985765	−	0.168126i	$-0.0537717\pi$
$12$	−1.97195	−	0.283524i	−0.569253	−	0.0818462i
$13$	1.15727	−	1.80075i	0.320969	−	0.499437i	−0.642851	−	0.765991i	$-0.722249\pi$
$13$	1.15727	−	1.80075i	0.320969	−	0.499437i	0.963820	+	0.266554i	$0.0858850\pi$
$14$	−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	−0.665548	−	0.746355i	$-0.731802\pi$
$17$	1.22809	−	4.18251i	0.297857	−	1.01441i	0.963405	−	0.268052i	$-0.0863798\pi$
$18$	−0.133248	−	0.115460i	−0.0314068	−	0.0272141i
$19$	7.12381	−	2.09174i	1.63431	−	0.479878i	0.669499	−	0.742813i	$-0.266509\pi$
$19$	7.12381	−	2.09174i	1.63431	−	0.479878i	0.964814	+	0.262935i	$0.0846905\pi$
$20$		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	0.655519	−	0.755179i	$-0.272450\pi$
$29$	4.30111	+	1.26292i	0.798695	+	0.234518i	0.143177	+	0.989697i	$0.454268\pi$
$30$		0			0
$31$	−0.376329	−	0.824045i	−0.0675906	−	0.148003i	0.872822	−	0.488039i	$-0.162288\pi$
$31$	−0.376329	−	0.824045i	−0.0675906	−	0.148003i	−0.940412	+	0.340037i	$0.889561\pi$
$32$	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	−0.420641	+	0.907227i	$0.638195\pi$
$37$	−8.38507	+	7.26571i	−1.37850	+	1.19447i	−0.957856	+	0.287248i	$0.907260\pi$
$38$	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	−0.357279	−	0.933998i	$-0.616295\pi$
$41$	3.95750	−	4.56720i	0.618058	−	0.713277i	0.975337	+	0.220720i	$0.0708408\pi$
$42$	−0.0384020	−	0.130785i	−0.00592556	−	0.0201806i
$43$	−4.90745	−	2.24116i	−0.748379	−	0.341773i	0.00444961	−	0.999990i	$-0.498584\pi$
$43$	−4.90745	−	2.24116i	−0.748379	−	0.341773i	−0.752828	+	0.658217i	$0.771311\pi$
$44$	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	$-0.936238\pi$
$47$		−	2.72825i		−	0.397956i	0.980004	−	0.198978i	$-0.0637623\pi$
$48$	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	0.851288	−	0.524698i	$-0.175822\pi$
$53$	0.148283	+	0.230732i	0.0203682	+	0.0316935i	−0.830920	+	0.556392i	$0.812185\pi$
$54$	−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	0.0218707	−	0.999761i	$-0.493038\pi$
$59$	−6.74757	−	4.33640i	−0.878458	−	0.564551i	−0.900329	+	0.435210i	$0.856674\pi$
$60$		0			0
$61$	−1.33718	−	2.92802i	−0.171208	−	0.374894i	0.804505	−	0.593946i	$-0.202431\pi$
$61$	−1.33718	−	2.92802i	−0.171208	−	0.374894i	−0.975713	+	0.219052i	$0.929704\pi$
$62$	−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	−0.260080	−	0.965587i	$-0.583749\pi$
$67$	−1.94473	+	0.279610i	−0.237587	+	0.0341598i	0.0224928	+	0.999747i	$0.492840\pi$
$68$			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	0.836301	+	0.548271i	$0.184714\pi$
$71$	1.58700	+	11.0378i	0.188342	+	1.30995i	−0.647959	+	0.761675i	$0.724377\pi$
$72$	0.640269	+	0.292401i	0.0754564	+	0.0344598i
$73$	−2.92170	−	9.95039i	−0.341959	−	1.16461i	−0.933574	−	0.358385i	$-0.883328\pi$
$73$	−2.92170	−	9.95039i	−0.341959	−	1.16461i	0.591615	−	0.806221i	$-0.298491\pi$
$74$	−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	0.379335	−	0.925259i	$-0.376153\pi$
$79$	−2.70849	−	1.74064i	−0.304729	−	0.195837i	−0.684064	+	0.729422i	$0.739789\pi$
$80$		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	−0.454963	−	0.890510i	$-0.650347\pi$
$83$	3.29557	−	2.85563i	0.361736	−	0.313446i	0.816698	+	0.577065i	$0.195802\pi$
$84$	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	−0.923248	−	0.384204i	$-0.874476\pi$
$89$	−0.266861	+	0.584343i	−0.0282872	+	0.0619403i	0.894961	+	0.446144i	$0.147203\pi$
$90$		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	0.841006	−	0.541026i	$-0.181964\pi$
$97$	4.18748	+	3.62848i	0.425175	+	0.368416i	−0.415831	+	0.909442i	$0.636509\pi$
$98$	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	0.590049	−	0.807367i	$-0.299108\pi$
$101$	−2.94535	−	3.39912i	−0.293073	−	0.338225i	−0.883122	+	0.469143i	$0.844563\pi$
$102$	0.207757	−	0.323276i	0.0205710	−	0.0320091i
$103$	9.63380	+	1.38513i	0.949247	+	0.136481i	0.599510	−	0.800367i	$-0.295362\pi$
$103$	9.63380	+	1.38513i	0.949247	+	0.136481i	0.349737	+	0.936848i	$0.386271\pi$
$104$	−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	−0.0627299	−	0.998031i	$-0.519981\pi$
$107$	6.72833	−	3.07272i	0.650452	−	0.297051i	0.713182	+	0.700979i	$0.247253\pi$
$108$	5.38540	+	8.37985i	0.518210	+	0.806351i
$109$	9.99029	+	2.93341i	0.956897	+	0.280970i	0.722656	−	0.691208i	$-0.242921\pi$
$109$	9.99029	+	2.93341i	0.956897	+	0.280970i	0.234241	+	0.972179i	$0.424740\pi$
$110$		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	−0.967417	−	0.253189i	$-0.918520\pi$
$113$	−19.3927	+	2.78825i	−1.82431	+	0.262297i	−0.856898	+	0.515486i	$0.827611\pi$
$114$	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	0.859856	−	0.510536i	$-0.170553\pi$
$127$	17.3667	+	2.49696i	1.54105	+	0.221569i	0.681192	+	0.732105i	$0.261462\pi$
$128$	−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	−0.923731	−	0.383043i	$-0.874876\pi$
$131$	−10.9767	+	7.05427i	−0.959035	+	0.616334i	−0.0353039	+	0.999377i	$0.511240\pi$
$132$	−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	$0.371471\pi$
$137$			21.5268i			1.83916i	−0.392903	+	0.919580i	$0.628529\pi$
$138$	−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	−0.492399	−	0.870370i	$-0.663880\pi$
$149$	2.74972	−	19.1247i	0.225266	−	1.56676i	0.717665	−	0.696389i	$-0.245211\pi$
$150$		0			0
$151$	16.8366	+	10.8202i	1.37015	+	0.880539i	0.998849	−	0.0479750i	$-0.0152768\pi$
$151$	16.8366	+	10.8202i	1.37015	+	0.880539i	0.371297	+	0.928514i	$0.378913\pi$
$152$	−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	0.868756	−	0.495241i	$-0.164920\pi$
$157$	−1.62683	−	5.54048i	−0.129835	−	0.442179i	−0.998591	+	0.0530620i	$0.983102\pi$
$158$	−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	−0.474856	−	0.880064i	$-0.657500\pi$
$163$	−8.71401	+	1.25289i	−0.682534	+	0.0981335i	−0.207678	+	0.978197i	$0.566591\pi$
$164$	−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	0.415692	+	0.909505i	$0.363539\pi$
$167$	−5.50159	+	18.7367i	−0.425726	+	1.44989i	−0.841418	+	0.540384i	$0.818279\pi$
$168$	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	0.893454	−	0.449155i	$-0.148275\pi$
$173$	21.3627	+	3.07149i	1.62417	+	0.233521i	0.730721	+	0.682676i	$0.239184\pi$
$174$	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	−0.994719	−	0.102634i	$-0.967273\pi$
$179$	−10.0553	+	11.6044i	−0.751567	+	0.867354i	0.243152	+	0.969988i	$0.421818\pi$
$180$		0			0
$181$	0.340209	−	0.744955i	0.0252876	−	0.0553720i	−0.896567	−	0.442909i	$-0.853947\pi$
$181$	0.340209	−	0.744955i	0.0252876	−	0.0553720i	0.921854	+	0.387537i	$0.126674\pi$
$182$	−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	−0.663997	−	0.747735i	$-0.731141\pi$
$191$	−3.58868	+	2.30630i	−0.259668	+	0.166878i	0.404329	+	0.914613i	$0.367505\pi$
$192$	−7.10794	+	3.24609i	−0.512972	+	0.234266i
$193$	−3.65352	+	3.16580i	−0.262986	+	0.227879i	−0.776366	−	0.630283i	$-0.782939\pi$
$193$	−3.65352	+	3.16580i	−0.262986	+	0.227879i	0.513379	+	0.858162i	$0.328393\pi$
$194$	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	−0.836159	−	0.548487i	$-0.815204\pi$
$197$	0.141980	−	0.220925i	0.0101157	−	0.0157403i	0.846275	+	0.532747i	$0.178840\pi$
$198$	−0.271085	+	0.234896i	−0.0192652	+	0.0166934i
$199$	1.79719	+	3.93530i	0.127399	+	0.278966i	0.962574	−	0.271019i	$-0.0873607\pi$
$199$	1.79719	+	3.93530i	0.127399	+	0.278966i	−0.835175	+	0.549985i	$0.814633\pi$
$200$		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	−0.0575338	−	0.998344i	$-0.518324\pi$
$211$	6.30147	−	1.85028i	0.433811	−	0.127378i	0.491345	+	0.870965i	$0.336506\pi$
$212$	−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	0.966950	−	0.254965i	$-0.0820639\pi$
$223$	4.97783	+	7.74566i	0.333340	+	0.518688i	−0.633610	+	0.773653i	$0.718428\pi$
$224$	−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	0.129196	−	0.991619i	$-0.458760\pi$
$227$	−8.06985	−	3.68538i	−0.535615	−	0.244607i	−0.664810	+	0.747012i	$0.731488\pi$
$228$	−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	0.972017	−	0.234911i	$-0.0754799\pi$
$233$	21.8435	+	9.97561i	1.43102	+	0.653524i	0.459002	+	0.888435i	$0.348207\pi$
$234$	−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	0.466054	−	0.884756i	$-0.345675\pi$
$239$	−7.35914	−	8.49290i	−0.476023	−	0.549360i	−0.942077	+	0.335396i	$0.891130\pi$
$240$		0			0
$241$	4.00004	−	27.8209i	0.257665	−	1.79210i	−0.291689	−	0.956513i	$-0.594217\pi$
$241$	4.00004	−	27.8209i	0.257665	−	1.79210i	0.549355	−	0.835589i	$-0.314874\pi$
$242$	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	0.615541	+	0.788105i	$0.288938\pi$
$251$	3.91272	+	27.2135i	0.246969	+	1.71770i	−0.368572	+	0.929599i	$0.620153\pi$
$252$		−	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	−0.954872	−	0.297018i	$-0.904008\pi$
$257$	−5.00435	−	17.0432i	−0.312163	−	1.06313i	0.642709	−	0.766110i	$-0.277810\pi$
$258$	−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	−0.955827	−	0.293930i	$-0.905037\pi$
$263$	−4.72561	+	7.35320i	−0.291394	+	0.453417i	0.664433	+	0.747348i	$0.268673\pi$
$264$	−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	−0.613642	−	0.789585i	$-0.710296\pi$
$269$	−2.46553	+	1.58450i	−0.150326	+	0.0966086i	0.463316	+	0.886193i	$0.346660\pi$
$270$		0			0
$271$	4.29616	−	4.95803i	0.260973	−	0.301179i	−0.610108	−	0.792318i	$-0.708874\pi$
$271$	4.29616	−	4.95803i	0.260973	−	0.301179i	0.871081	+	0.491139i	$0.163419\pi$
$272$	−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	$-0.759967\pi$
$277$		−	22.7888i		−	1.36924i	0.728898	−	0.684622i	$-0.240033\pi$
$278$	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	−0.405940	−	0.913900i	$-0.633056\pi$
$281$	9.32744	−	10.7644i	0.556429	−	0.642153i	0.962369	+	0.271747i	$0.0876013\pi$
$282$	0.0677599	−	0.230769i	0.00403504	−	0.0137421i
$283$	−12.8173	−	19.9441i	−0.761910	−	1.18555i	−0.977882	−	0.209155i	$-0.932929\pi$
$283$	−12.8173	−	19.9441i	−0.761910	−	1.18555i	0.215973	−	0.976399i	$-0.430708\pi$
$284$	−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	−0.916810	−	0.399323i	$-0.869245\pi$
$293$	1.20419	−	4.10110i	0.0703497	−	0.239589i	0.987160	+	0.159734i	$0.0510635\pi$
$294$	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	−0.169463	−	0.985536i	$-0.554203\pi$
$307$	8.13661	−	3.71586i	0.464381	−	0.212076i	0.633844	+	0.773461i	$0.281476\pi$
$308$	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	−0.647798	−	0.761812i	$-0.724310\pi$
$311$	3.32224	−	23.1067i	0.188387	−	1.31026i	0.836185	−	0.548447i	$-0.184781\pi$
$312$	−0.407288	+	0.633752i	−0.0230581	+	0.0358792i
$313$	17.0127	−	14.7416i	0.961615	−	0.833244i	−0.0244337	−	0.999701i	$-0.507778\pi$
$313$	17.0127	−	14.7416i	0.961615	−	0.833244i	0.986049	+	0.166457i	$0.0532328\pi$
$314$	−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	0.340834	−	0.940124i	$-0.389291\pi$
$317$	−9.63606	−	8.34970i	−0.541215	−	0.468966i	−0.882049	+	0.471158i	$0.843836\pi$
$318$	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	0.969771	−	0.244015i	$-0.0784647\pi$
$331$	10.7382	+	12.3926i	0.590227	+	0.681158i	−0.379545	+	0.925173i	$0.623919\pi$
$332$	−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	−0.955821	−	0.293951i	$-0.905030\pi$
$337$	−24.9589	+	11.3983i	−1.35960	+	0.620907i	−0.403776	+	0.914858i	$0.632303\pi$
$338$	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	0.0199196	−	0.999802i	$-0.493659\pi$
$347$	5.97415	−	0.858953i	0.320709	−	0.0461110i	0.300789	+	0.953691i	$0.402750\pi$
$348$	−8.12350	−	3.70988i	−0.435465	−	0.198870i
$349$	8.00915	−	2.35170i	0.428720	−	0.125883i	−0.0602518	−	0.998183i	$-0.519190\pi$
$349$	8.00915	−	2.35170i	0.428720	−	0.125883i	0.488972	+	0.872300i	$0.337372\pi$
$350$		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	−0.931380	−	0.364049i	$-0.881394\pi$
$353$	−23.7892	+	10.8642i	−1.26617	+	0.578242i	−0.334794	+	0.942291i	$0.608667\pi$
$354$	−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	0.845088	−	0.534628i	$-0.179548\pi$
$359$	3.70672	+	4.27779i	0.195633	+	0.225773i	−0.649454	+	0.760401i	$0.725003\pi$
$360$		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	$-0.895843\pi$
$367$		−	12.3147i		−	0.642822i	0.946940	−	0.321411i	$-0.104157\pi$
$368$	−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	0.999997	−	0.00260397i	$-0.000828872\pi$
$373$	22.0119	+	19.0734i	1.13973	+	0.987585i	0.139737	+	0.990189i	$0.455374\pi$
$374$	−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	0.388683	+	0.921372i	$0.372930\pi$
$379$	−4.74698	+	33.0160i	−0.243836	+	1.69592i	−0.632519	+	0.774545i	$0.717979\pi$
$380$		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	0.470044	−	0.882643i	$-0.344238\pi$
$383$	28.2775	−	12.9139i	1.44491	−	0.659870i	0.974870	+	0.222773i	$0.0715108\pi$
$384$	−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	−0.983005	−	0.183581i	$-0.941231\pi$
$389$	−1.80544	−	12.5571i	−0.0915394	−	0.636670i	0.891465	−	0.453089i	$-0.149678\pi$
$390$		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	−0.825371	−	0.564590i	$-0.809034\pi$
$397$	3.47123	−	11.8219i	0.174216	−	0.593325i	0.999587	−	0.0287344i	$-0.00914770\pi$
$398$	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	−0.999997	−	0.00251937i	$-0.999198\pi$
$401$	−28.3895	−	18.2448i	−1.41770	−	0.911102i	−0.417705	−	0.908583i	$-0.637166\pi$
$402$	−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	−0.429350	−	0.903138i	$-0.641257\pi$
$409$	10.6316	−	12.2695i	0.525698	−	0.606688i	0.955048	+	0.296450i	$0.0958028\pi$
$410$		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	−0.928345	−	0.371719i	$-0.878768\pi$
$419$	−8.76692	+	10.1176i	−0.428292	+	0.494275i	0.500053	+	0.865995i	$0.333314\pi$
$420$		0			0
$421$	−10.9478	+	7.03572i	−0.533563	+	0.342900i	−0.779517	−	0.626382i	$-0.784535\pi$
$421$	−10.9478	+	7.03572i	−0.533563	+	0.342900i	0.245954	+	0.969282i	$0.420899\pi$
$422$	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	0.0582112	−	0.998304i	$-0.481460\pi$
$431$	−8.97982	−	2.63671i	−0.432543	−	0.127006i	−0.490754	+	0.871298i	$0.663279\pi$
$432$	−14.9390	−	12.9447i	−0.718754	−	0.622804i
$433$	−9.56922	−	32.5898i	−0.459867	−	1.56616i	−0.784378	−	0.620283i	$-0.787018\pi$
$433$	−9.56922	−	32.5898i	−0.459867	−	1.56616i	0.324511	−	0.945882i	$-0.394800\pi$
$434$	−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	0.750456	+	0.660921i	$0.229834\pi$
$439$	4.53831	+	31.5646i	0.216602	+	1.50650i	−0.533854	+	0.845577i	$0.679257\pi$
$440$		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	0.453825	+	0.891091i	$0.350059\pi$
$443$	−8.62354	+	29.3691i	−0.409717	+	1.39537i	−0.863542	+	0.504277i	$0.831759\pi$
$444$	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	0.851597	+	0.524196i	$0.175634\pi$
$449$	−2.39840	+	16.6812i	−0.113187	+	0.787236i	−0.964785	+	0.263040i	$0.915275\pi$
$450$		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	0.356715	−	0.934213i	$-0.383897\pi$
$457$	−2.47375	−	1.12972i	−0.115717	−	0.0528463i	−0.472432	+	0.881367i	$0.656624\pi$
$458$	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	0.984899	+	0.173130i	$0.0553880\pi$
$463$	37.8860	+	17.3020i	1.76071	+	0.804091i	0.775814	+	0.630961i	$0.217339\pi$
$464$	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	0.988782	−	0.149364i	$-0.0477225\pi$
$467$	9.55519	+	14.8682i	0.442161	+	0.688017i	−0.546621	+	0.837380i	$0.684086\pi$
$468$	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	−0.533110	−	0.846046i	$-0.678977\pi$
$479$	−11.4723	+	3.36858i	−0.524184	+	0.153914i	0.00892633	+	0.999960i	$0.497159\pi$
$480$		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	0.987843	+	0.155455i	$0.0496843\pi$
$487$	5.31536	+	18.1024i	0.240862	+	0.820300i	−0.746981	+	0.664845i	$0.768497\pi$
$488$	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	0.996055	+	0.0887373i	$0.0282832\pi$
$491$	9.10363	+	19.9342i	0.410841	+	0.899616i	−0.585214	+	0.810879i	$0.698990\pi$
$492$	−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	−0.716655	−	0.697428i	$-0.754328\pi$
$499$	−8.48768	+	5.45470i	−0.379961	+	0.244186i	0.336694	+	0.941614i	$0.390691\pi$
$500$		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	0.124576	−	0.992210i	$-0.460243\pi$
$503$	−12.1941	−	5.56885i	−0.543707	−	0.248303i	−0.668283	+	0.743907i	$0.732970\pi$
$504$	−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	0.643766	+	0.765222i	$0.277371\pi$
$509$	−8.03460	+	17.5933i	−0.356127	+	0.779810i	−0.999894	+	0.0145879i	$0.995356\pi$
$510$		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	0.779281	−	0.626674i	$-0.215584\pi$
$521$	−4.67119	−	10.2285i	−0.204648	−	0.448117i	−0.983930	+	0.178557i	$0.942857\pi$
$522$	−0.427296	−	0.664885i	−0.0187022	−	0.0291012i
$523$	5.09404	−	17.3487i	0.222747	−	0.758605i	−0.769964	−	0.638087i	$-0.779726\pi$
$523$	5.09404	−	17.3487i	0.222747	−	0.758605i	0.992711	−	0.120519i	$-0.0384558\pi$
$524$	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	−0.902324	−	0.431059i	$-0.858140\pi$
$541$	1.97456	−	13.7333i	0.0848928	−	0.590442i	0.987217	−	0.159384i	$-0.0509507\pi$
$542$	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	0.987764	−	0.155953i	$-0.0498448\pi$
$547$	22.7793	+	19.7384i	0.973973	+	0.843952i	−0.0137919	+	0.999905i	$0.504390\pi$
$548$	−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	0.235824	−	0.971796i	$-0.424221\pi$
$557$	−16.3440	−	14.1622i	−0.692519	−	0.600071i	−0.928343	+	0.371724i	$0.878767\pi$
$558$	−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	0.148283	−	0.988945i	$-0.452625\pi$
$563$	0.283349	+	0.0407395i	0.0119418	+	0.00171696i	−0.136341	+	0.990662i	$0.543534\pi$
$564$	−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	0.246721	−	0.969087i	$-0.420647\pi$
$569$	−1.66147	−	0.487852i	−0.0696525	−	0.0204518i	−0.316373	+	0.948635i	$0.602465\pi$
$570$		0			0
$571$	−19.8922	+	5.84086i	−0.832461	+	0.244433i	−0.670074	−	0.742295i	$-0.733738\pi$
$571$	−19.8922	+	5.84086i	−0.832461	+	0.244433i	−0.162387	+	0.986727i	$0.551919\pi$
$572$	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	0.373917	−	0.927462i	$-0.378014\pi$
$577$	23.8763	−	3.43290i	0.993985	−	0.142913i	0.620067	+	0.784549i	$0.287105\pi$
$578$	−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	0.788617	−	0.614885i	$-0.210798\pi$
$587$	33.2423	+	4.77952i	1.37206	+	0.197272i	0.583439	+	0.812157i	$0.301707\pi$
$588$	−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	0.980639	−	0.195827i	$-0.0627389\pi$
$593$	22.5585	+	19.5470i	0.926365	+	0.802700i	−0.0542739	+	0.998526i	$0.517284\pi$
$594$	−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	−0.636792	−	0.771036i	$-0.719739\pi$
$601$	8.89729	−	19.4823i	0.362928	−	0.794701i	0.999720	−	0.0236658i	$-0.00753375\pi$
$602$	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	−0.184891	+	0.982759i	$0.559193\pi$
$607$	−29.1696	+	25.2756i	−1.18396	+	1.02591i	−0.999069	+	0.0431477i	$0.986261\pi$
$608$	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	−0.0386125	−	0.999254i	$-0.512294\pi$
$613$	17.1155	−	7.81638i	0.691288	−	0.315700i	0.729900	+	0.683554i	$0.239567\pi$
$614$	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	−0.999233	−	0.0391580i	$-0.987532\pi$
$617$	−4.46602	−	15.2099i	−0.179795	−	0.612326i	0.819438	−	0.573168i	$-0.194286\pi$
$618$	0.780473	+	0.356430i	0.0313952	+	0.0143377i
$619$	−4.22984	−	29.4192i	−0.170012	−	1.18246i	−0.878854	−	0.477091i	$-0.841691\pi$
$619$	−4.22984	−	29.4192i	−0.170012	−	1.18246i	0.708842	−	0.705367i	$-0.249218\pi$
$620$		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	0.230677	−	0.973030i	$-0.425906\pi$
$631$	−14.0318	−	9.01768i	−0.558597	−	0.358988i	−0.789273	+	0.614042i	$0.789542\pi$
$632$	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	0.481934	+	0.876208i	$0.339935\pi$
$641$	−12.5542	+	27.4898i	−0.495859	+	1.08578i	−0.977793	+	0.209573i	$0.932793\pi$
$642$	0.645431	−	0.0927990i	0.0254731	−	0.00366248i
$643$			7.45857i			0.294137i	0.989126	+	0.147069i	$0.0469838\pi$
$643$			7.45857i			0.294137i	−0.989126	+	0.147069i	$0.953016\pi$
$644$	−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	0.547202	−	0.837001i	$-0.315693\pi$
$647$	6.94356	+	3.17102i	0.272980	+	0.124666i	−0.274222	+	0.961666i	$0.588420\pi$
$648$	−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	−0.149686	+	0.988734i	$0.547826\pi$
$653$	−29.3782	+	25.4564i	−1.14966	+	0.996185i	−0.999972	+	0.00745135i	$0.997628\pi$
$654$	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	0.985030	−	0.172381i	$-0.0551460\pi$
$659$	5.38310	+	11.7873i	0.209696	+	0.459170i	−0.775335	+	0.631551i	$0.782419\pi$
$660$		0			0
$661$	28.9778	+	8.50866i	1.12711	+	0.330949i	0.791570	−	0.611078i	$-0.209264\pi$
$661$	28.9778	+	8.50866i	1.12711	+	0.330949i	0.335537	+	0.942027i	$0.391082\pi$
$662$	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	−0.945634	−	0.325232i	$-0.894558\pi$
$673$	0.667173	−	2.27218i	0.0257176	−	0.0875862i	0.971352	+	0.237646i	$0.0763758\pi$
$674$	−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	−0.266425	−	0.963856i	$-0.585842\pi$
$677$	18.7600	−	29.1912i	0.721006	−	1.12191i	0.987431	−	0.158052i	$-0.0505213\pi$
$678$	−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	0.993965	−	0.109702i	$-0.0349895\pi$
$683$	12.5776	+	19.5711i	0.481269	+	0.748869i	−0.512696	+	0.858570i	$0.671353\pi$
$684$	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	0.823600	+	0.567171i	$0.191962\pi$
$701$	−3.34738	+	23.2815i	−0.126429	+	0.879332i	−0.950029	+	0.312161i	$0.898947\pi$
$702$	−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	−0.833062	−	0.553180i	$-0.813414\pi$
$709$	−32.8793	+	9.65422i	−1.23481	+	0.362572i	−0.401745	+	0.915752i	$0.631596\pi$
$710$		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	0.671050	−	0.741412i	$-0.265844\pi$
$719$	22.3827	+	6.57217i	0.834735	+	0.245100i	0.163685	+	0.986513i	$0.447662\pi$
$720$		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	0.129343	−	0.991600i	$-0.458713\pi$
$727$	30.4481	−	26.3834i	1.12926	−	0.978507i	0.999914	+	0.0130932i	$0.00416783\pi$
$728$	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	0.758738	−	0.651396i	$-0.225816\pi$
$733$	20.6659	+	9.43781i	0.763313	+	0.348594i	0.00457542	+	0.999990i	$0.498544\pi$
$734$	−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	−0.720930	−	0.693008i	$-0.756285\pi$
$739$	7.47356	−	16.3648i	0.274919	−	0.601989i	0.995849	+	0.0910188i	$0.0290123\pi$
$740$		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	0.894185	−	0.447697i	$-0.147756\pi$
$743$	3.14797	+	4.89833i	0.115488	+	0.179702i	−0.778698	+	0.627399i	$0.784119\pi$
$744$	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	0.966748	−	0.255732i	$-0.0823164\pi$
$751$	3.84740	+	8.42462i	0.140393	+	0.307419i	−0.826354	+	0.563151i	$0.809589\pi$
$752$	−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	−0.286877	−	0.957968i	$-0.592617\pi$
$757$	−8.04064	+	1.15607i	−0.292242	+	0.0420180i	−0.00536536	+	0.999986i	$0.501708\pi$
$758$			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	−0.914893	−	0.403697i	$-0.867725\pi$
$761$	−4.15984	−	28.9323i	−0.150794	−	1.04880i	0.764099	−	0.645099i	$-0.223184\pi$
$762$	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	0.300158	−	0.953889i	$-0.402960\pi$
$769$	−12.2803	−	7.89208i	−0.442840	−	0.284596i	−0.742998	+	0.669294i	$0.766597\pi$
$770$		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	−0.387865	−	0.921716i	$-0.626787\pi$
$773$	13.0471	−	11.3054i	0.469271	−	0.406625i	0.857136	+	0.515091i	$0.172242\pi$
$774$	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	0.423243	−	0.906016i	$-0.360892\pi$
$787$	−11.5950	−	10.0471i	−0.413318	−	0.358142i	−0.836561	+	0.547875i	$0.815437\pi$
$788$	−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	−0.776755	−	0.629803i	$-0.783136\pi$
$797$	−22.8517	+	10.4360i	−0.809448	+	0.369663i	−0.0326932	+	0.999465i	$0.510408\pi$
$798$	−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	0.126761	−	0.991933i	$-0.459542\pi$
$809$	21.8919	−	6.42804i	0.769678	−	0.225998i	0.642917	+	0.765935i	$0.277724\pi$
$810$		0			0
$811$	41.7803	+	12.2678i	1.46711	+	0.430781i	0.915157	−	0.403097i	$-0.132066\pi$
$811$	41.7803	+	12.2678i	1.46711	+	0.430781i	0.551949	+	0.833878i	$0.313884\pi$
$812$	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	0.427942	−	0.903806i	$-0.359239\pi$
$821$	40.9122	−	26.2927i	1.42785	−	0.917621i	0.999905	−	0.0138148i	$-0.00439753\pi$
$822$	−0.534648	+	1.82085i	−0.0186480	+	0.0635093i
$823$	0.868528	+	0.752583i	0.0302750	+	0.0262334i	0.669867	−	0.742481i	$-0.266351\pi$
$823$	0.868528	+	0.752583i	0.0302750	+	0.0262334i	−0.639592	+	0.768715i	$0.720897\pi$
$824$	−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	$-0.913791\pi$
$827$		−	15.3873i		−	0.535069i	0.963548	−	0.267534i	$-0.0862089\pi$
$828$	−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	0.943116	+	0.332462i	$0.107879\pi$
$839$	−1.60650	+	11.1735i	−0.0554627	+	0.385751i	−0.998579	+	0.0532888i	$0.983030\pi$
$840$		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	−0.419727	−	0.907651i	$-0.637874\pi$
$853$	−16.5522	+	2.37985i	−0.566737	+	0.0814845i	−0.147010	+	0.989135i	$0.546965\pi$
$854$	−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	−0.924351	−	0.381543i	$-0.875393\pi$
$857$	1.74302	−	5.93618i	0.0595405	−	0.202776i	0.983891	+	0.178767i	$0.0572109\pi$
$858$	−0.207554	−	0.322961i	−0.00708579	−	0.0110257i
$859$	3.60612	+	7.89631i	0.123039	+	0.269419i	0.961122	−	0.276125i	$-0.0890504\pi$
$859$	3.60612	+	7.89631i	0.123039	+	0.269419i	−0.838082	+	0.545544i	$0.816323\pi$
$860$		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	0.330248	−	0.943894i	$-0.392868\pi$
$863$	11.1982	+	1.61006i	0.381192	+	0.0548072i	0.0509446	+	0.998701i	$0.483777\pi$
$864$	−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	0.757805	−	0.652481i	$-0.226272\pi$
$877$	22.5349	+	10.2913i	0.760950	+	0.347514i	0.00314460	+	0.999995i	$0.498999\pi$
$878$	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	0.0251917	−	0.999683i	$-0.491980\pi$
$881$	28.0492	−	18.0261i	0.945000	−	0.607315i	0.919808	+	0.392368i	$0.128344\pi$
$882$	−0.739229	+	0.337594i	−0.0248911	+	0.0113674i
$883$	9.88198	−	8.56278i	0.332555	−	0.288161i	−0.472537	−	0.881311i	$-0.656662\pi$
$883$	9.88198	−	8.56278i	0.332555	−	0.288161i	0.805092	+	0.593150i	$0.202116\pi$
$884$	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	−0.982103	−	0.188343i	$-0.939688\pi$
$887$	−11.9964	+	18.6668i	−0.402800	+	0.626770i	0.579303	+	0.815112i	$0.303325\pi$
$888$	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	−0.593924	−	0.804521i	$-0.702422\pi$
$907$	11.5834	−	18.0240i	0.384619	−	0.598479i	0.978543	+	0.206042i	$0.0660585\pi$
$908$	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	0.999920	−	0.0126696i	$-0.00403297\pi$
$911$	25.5067	+	29.4363i	0.845076	+	0.975269i	−0.154844	+	0.987939i	$0.549488\pi$
$912$	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	0.606266	−	0.795262i	$-0.292667\pi$
$929$	−8.14358	−	9.39819i	−0.267182	−	0.308345i	−0.873448	+	0.486917i	$0.838121\pi$
$930$		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	−0.903861	−	0.427826i	$-0.859280\pi$
$937$	2.68807	−	9.15473i	0.0878155	−	0.299072i	0.991677	+	0.128754i	$0.0410978\pi$
$938$	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	0.996191	−	0.0871966i	$-0.0277908\pi$
$941$	0.484266	+	3.36814i	0.0157866	+	0.109798i	−0.980405	+	0.196995i	$0.936882\pi$
$942$		−	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	0.882759	−	0.469826i	$-0.155683\pi$
$947$	−3.50424	−	11.9343i	−0.113872	−	0.387814i	−0.996631	+	0.0820124i	$0.973865\pi$
$948$	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	−0.704057	−	0.710143i	$-0.748630\pi$
$953$	7.23572	−	11.2590i	0.234388	−	0.364715i	0.938445	+	0.345429i	$0.112266\pi$
$954$	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	$-0.869645\pi$
$967$		−	24.7635i		−	0.796341i	0.917311	−	0.398170i	$-0.130355\pi$
$968$	−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	−0.911374	−	0.411580i	$-0.864977\pi$
$971$	−11.6629	+	13.4597i	−0.374281	+	0.431944i	0.537092	+	0.843523i	$0.319523\pi$
$972$	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	0.0261716	−	0.999657i	$-0.491668\pi$
$977$	−7.20015	−	1.03522i	−0.230353	−	0.0331198i	−0.256525	+	0.966538i	$0.582577\pi$
$978$	−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	−0.678442	−	0.734654i	$-0.737345\pi$
$983$	9.07613	−	30.9104i	0.289483	−	0.985890i	0.967926	−	0.251236i	$-0.0808372\pi$
$984$	−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	−0.999533	−	0.0305723i	$-0.990267\pi$
$991$	−1.54572	−	10.7507i	−0.0491013	−	0.341507i	0.950431	−	0.310935i	$-0.100642\pi$
$992$	−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	−0.0877636	−	0.996141i	$-0.527972\pi$
$997$	19.1851	−	8.76152i	0.607597	−	0.277480i	0.695360	+	0.718661i	$0.255245\pi$
$998$	−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.49.2		20
5.2	odd	4		575.2.k.a.26.1		10
5.3	odd	4		115.2.g.a.26.1	✓	10
5.4	even	2	inner	575.2.p.a.49.1		20
23.8	even	11	inner	575.2.p.a.399.1		20
115.8	odd	44		115.2.g.a.31.1	yes	10
115.13	odd	44		2645.2.a.n.1.4		5
115.33	even	44		2645.2.a.o.1.4		5
115.54	even	22	inner	575.2.p.a.399.2		20
115.77	odd	44		575.2.k.a.376.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.a.26.1	✓	10	5.3	odd	4
115.2.g.a.31.1	yes	10	115.8	odd	44
575.2.k.a.26.1		10	5.2	odd	4
575.2.k.a.376.1		10	115.77	odd	44
575.2.p.a.49.1		20	5.4	even	2	inner
575.2.p.a.49.2		20	1.1	even	1	trivial
575.2.p.a.399.1		20	23.8	even	11	inner
575.2.p.a.399.2		20	115.54	even	22	inner
2645.2.a.n.1.4		5	115.13	odd	44
2645.2.a.o.1.4		5	115.33	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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