LMFDB - Embedded newform 575.2.p.a.399.1

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			399.1
Root			$0.755750 + 0.654861i$ of defining polynomial
Character	$\chi$	$=$	575.399
Dual form			575.2.p.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0872586 - 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	0.111395	−	0.993776i	$-0.464468\pi$
$2$	−0.0872586	−	0.0125459i	−0.0617012	−	0.00887129i	−0.173096	+	0.984905i	$0.555377\pi$
$3$	−0.909632	+	0.415415i	−0.525176	+	0.239840i	−0.660318	−	0.750986i	$-0.729578\pi$
$3$	−0.909632	+	0.415415i	−0.525176	+	0.239840i	0.135141	+	0.990826i	$0.456851\pi$
$4$	−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	$-0.723793\pi$
$7$	0.835939	−	1.30075i	0.315955	−	0.491636i	0.962515	+	0.271227i	$0.0874294\pi$
$8$	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	0.642851	−	0.765991i	$-0.277751\pi$
$13$	−1.15727	−	1.80075i	−0.320969	−	0.499437i	−0.963820	+	0.266554i	$0.914115\pi$
$14$	−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	$-0.913620\pi$
$17$	−1.22809	−	4.18251i	−0.297857	−	1.01441i	0.665548	−	0.746355i	$-0.268198\pi$
$18$	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	$0.0927404\pi$
$37$	8.38507	+	7.26571i	1.37850	+	1.19447i	0.420641	+	0.907227i	$0.361805\pi$
$38$	−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	−0.00444961	−	0.999990i	$-0.501416\pi$
$43$	4.90745	−	2.24116i	0.748379	−	0.341773i	0.752828	+	0.658217i	$0.228689\pi$
$44$	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	$-0.824178\pi$
$53$	−0.148283	+	0.230732i	−0.0203682	+	0.0316935i	0.830920	+	0.556392i	$0.187815\pi$
$54$	−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	0.260080	−	0.965587i	$-0.416251\pi$
$67$	1.94473	+	0.279610i	0.237587	+	0.0341598i	−0.0224928	+	0.999747i	$0.507160\pi$
$68$			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	$-0.701509\pi$
$73$	2.92170	−	9.95039i	0.341959	−	1.16461i	0.933574	−	0.358385i	$-0.116672\pi$
$74$	−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	0.454963	−	0.890510i	$-0.349653\pi$
$83$	−3.29557	−	2.85563i	−0.361736	−	0.313446i	−0.816698	+	0.577065i	$0.804198\pi$
$84$	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	−0.841006	−	0.541026i	$-0.818036\pi$
$97$	−4.18748	+	3.62848i	−0.425175	+	0.368416i	0.415831	+	0.909442i	$0.363491\pi$
$98$	−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	−0.599510	−	0.800367i	$-0.704638\pi$
$103$	−9.63380	+	1.38513i	−0.949247	+	0.136481i	−0.349737	+	0.936848i	$0.613729\pi$
$104$	−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	$-0.480019\pi$
$107$	−6.72833	−	3.07272i	−0.650452	−	0.297051i	−0.713182	+	0.700979i	$0.752747\pi$
$108$	−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	0.967417	−	0.253189i	$-0.0814795\pi$
$113$	19.3927	+	2.78825i	1.82431	+	0.262297i	0.856898	+	0.515486i	$0.172389\pi$
$114$	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	$-0.829447\pi$
$127$	−17.3667	+	2.49696i	−1.54105	+	0.221569i	−0.681192	+	0.732105i	$0.738538\pi$
$128$	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	$0.371471\pi$
$137$			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	0.717665	+	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	−0.868756	−	0.495241i	$-0.835080\pi$
$157$	1.62683	−	5.54048i	0.129835	−	0.442179i	0.998591	+	0.0530620i	$0.0168981\pi$
$158$	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	$-0.342500\pi$
$163$	8.71401	+	1.25289i	0.682534	+	0.0981335i	0.207678	+	0.978197i	$0.433409\pi$
$164$	−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	$0.181721\pi$
$167$	5.50159	+	18.7367i	0.425726	+	1.44989i	−0.415692	+	0.909505i	$0.636461\pi$
$168$	−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	$-0.851725\pi$
$173$	−21.3627	+	3.07149i	−1.62417	+	0.233521i	−0.730721	+	0.682676i	$0.760816\pi$
$174$	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	0.776366	−	0.630283i	$-0.217061\pi$
$193$	3.65352	+	3.16580i	0.262986	+	0.227879i	−0.513379	+	0.858162i	$0.671607\pi$
$194$	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	$-0.184796\pi$
$197$	−0.141980	−	0.220925i	−0.0101157	−	0.0157403i	−0.846275	+	0.532747i	$0.821160\pi$
$198$	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	−0.966950	−	0.254965i	$-0.917936\pi$
$223$	−4.97783	+	7.74566i	−0.333340	+	0.518688i	0.633610	+	0.773653i	$0.281572\pi$
$224$	−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	$-0.541240\pi$
$227$	8.06985	−	3.68538i	0.535615	−	0.244607i	0.664810	+	0.747012i	$0.268512\pi$
$228$	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	$-0.924520\pi$
$233$	−21.8435	+	9.97561i	−1.43102	+	0.653524i	−0.459002	+	0.888435i	$0.651793\pi$
$234$	−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	$-0.722190\pi$
$257$	5.00435	−	17.0432i	0.312163	−	1.06313i	0.954872	−	0.297018i	$-0.0959922\pi$
$258$	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	$-0.0949633\pi$
$263$	4.72561	+	7.35320i	0.291394	+	0.453417i	−0.664433	+	0.747348i	$0.731327\pi$
$264$	−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	$-0.759967\pi$
$277$		−	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	0.962369	−	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	$-0.569292\pi$
$283$	12.8173	−	19.9441i	0.761910	−	1.18555i	0.977882	−	0.209155i	$-0.0670713\pi$
$284$	−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	$-0.130755\pi$
$293$	−1.20419	−	4.10110i	−0.0703497	−	0.239589i	−0.987160	+	0.159734i	$0.948936\pi$
$294$	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	$-0.445797\pi$
$307$	−8.13661	−	3.71586i	−0.464381	−	0.212076i	−0.633844	+	0.773461i	$0.718524\pi$
$308$	−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	0.0244337	−	0.999701i	$-0.492222\pi$
$313$	−17.0127	−	14.7416i	−0.961615	−	0.833244i	−0.986049	+	0.166457i	$0.946767\pi$
$314$	−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	$-0.610709\pi$
$317$	9.63606	−	8.34970i	0.541215	−	0.468966i	0.882049	+	0.471158i	$0.156164\pi$
$318$	−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	0.955821	−	0.293951i	$-0.0949701\pi$
$337$	24.9589	+	11.3983i	1.35960	+	0.620907i	0.403776	+	0.914858i	$0.367697\pi$
$338$	−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	$-0.506341\pi$
$347$	−5.97415	−	0.858953i	−0.320709	−	0.0461110i	−0.300789	+	0.953691i	$0.597250\pi$
$348$	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	0.931380	−	0.364049i	$-0.118606\pi$
$353$	23.7892	+	10.8642i	1.26617	+	0.578242i	0.334794	+	0.942291i	$0.391333\pi$
$354$	−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	$-0.895843\pi$
$367$		−	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	$-0.999171\pi$
$373$	−22.0119	+	19.0734i	−1.13973	+	0.987585i	−0.139737	+	0.990189i	$0.544626\pi$
$374$	−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	−0.470044	−	0.882643i	$-0.655762\pi$
$383$	−28.2775	−	12.9139i	−1.44491	−	0.659870i	−0.974870	+	0.222773i	$0.928489\pi$
$384$	−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	$-0.990852\pi$
$397$	−3.47123	−	11.8219i	−0.174216	−	0.593325i	0.825371	−	0.564590i	$-0.190966\pi$
$398$	−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	$-0.605200\pi$
$433$	9.56922	−	32.5898i	0.459867	−	1.56616i	0.784378	−	0.620283i	$-0.212982\pi$
$434$	−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	$0.168241\pi$
$443$	8.62354	+	29.3691i	0.409717	+	1.39537i	−0.453825	+	0.891091i	$0.649941\pi$
$444$	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	−0.356715	−	0.934213i	$-0.616103\pi$
$457$	2.47375	−	1.12972i	0.115717	−	0.0528463i	0.472432	+	0.881367i	$0.343376\pi$
$458$	−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	$0.782661\pi$
$463$	−37.8860	+	17.3020i	−1.76071	+	0.804091i	−0.984899	+	0.173130i	$0.944612\pi$
$464$	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	$-0.952278\pi$
$467$	−9.55519	+	14.8682i	−0.442161	+	0.688017i	0.546621	+	0.837380i	$0.315914\pi$
$468$	−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	$0.231503\pi$
$487$	−5.31536	+	18.1024i	−0.240862	+	0.820300i	−0.987843	+	0.155455i	$0.950316\pi$
$488$	−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	−0.124576	−	0.992210i	$-0.539757\pi$
$503$	12.1941	−	5.56885i	0.543707	−	0.248303i	0.668283	+	0.743907i	$0.267030\pi$
$504$	−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	$-0.961544\pi$
$523$	−5.09404	−	17.3487i	−0.222747	−	0.758605i	0.769964	−	0.638087i	$-0.220274\pi$
$524$	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	−0.987764	−	0.155953i	$-0.950155\pi$
$547$	−22.7793	+	19.7384i	−0.973973	+	0.843952i	0.0137919	+	0.999905i	$0.495610\pi$
$548$	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	$-0.575779\pi$
$557$	16.3440	−	14.1622i	0.692519	−	0.600071i	0.928343	+	0.371724i	$0.121233\pi$
$558$	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	$-0.547375\pi$
$563$	−0.283349	+	0.0407395i	−0.0119418	+	0.00171696i	0.136341	+	0.990662i	$0.456466\pi$
$564$	−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	−0.373917	−	0.927462i	$-0.621986\pi$
$577$	−23.8763	−	3.43290i	−0.993985	−	0.142913i	−0.620067	+	0.784549i	$0.712895\pi$
$578$	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	$-0.789202\pi$
$587$	−33.2423	+	4.77952i	−1.37206	+	0.197272i	−0.583439	+	0.812157i	$0.698293\pi$
$588$	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	$-0.937261\pi$
$593$	−22.5585	+	19.5470i	−0.926365	+	0.802700i	0.0542739	+	0.998526i	$0.482716\pi$
$594$	−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	$0.0137386\pi$
$607$	29.1696	+	25.2756i	1.18396	+	1.02591i	0.184891	+	0.982759i	$0.440807\pi$
$608$	−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	$-0.487706\pi$
$613$	−17.1155	−	7.81638i	−0.691288	−	0.315700i	−0.729900	+	0.683554i	$0.760433\pi$
$614$	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	$-0.805714\pi$
$617$	4.46602	−	15.2099i	0.179795	−	0.612326i	0.999233	−	0.0391580i	$-0.0124676\pi$
$618$	−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	$0.0469838\pi$
$643$			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	$-0.684307\pi$
$647$	−6.94356	+	3.17102i	−0.272980	+	0.124666i	0.274222	+	0.961666i	$0.411580\pi$
$648$	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	$0.00237186\pi$
$653$	29.3782	+	25.4564i	1.14966	+	0.996185i	0.149686	+	0.988734i	$0.452174\pi$
$654$	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	0.945634	−	0.325232i	$-0.105442\pi$
$673$	−0.667173	−	2.27218i	−0.0257176	−	0.0875862i	−0.971352	+	0.237646i	$0.923624\pi$
$674$	−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	$-0.949479\pi$
$677$	−18.7600	−	29.1912i	−0.721006	−	1.12191i	0.266425	−	0.963856i	$-0.414158\pi$
$678$	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	$-0.965010\pi$
$683$	−12.5776	+	19.5711i	−0.481269	+	0.748869i	0.512696	+	0.858570i	$0.328647\pi$
$684$	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	−0.129343	−	0.991600i	$-0.541287\pi$
$727$	−30.4481	−	26.3834i	−1.12926	−	0.978507i	−0.999914	+	0.0130932i	$0.995832\pi$
$728$	−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	$-0.774184\pi$
$733$	−20.6659	+	9.43781i	−0.763313	+	0.348594i	−0.00457542	+	0.999990i	$0.501456\pi$
$734$	−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	−0.894185	−	0.447697i	$-0.852244\pi$
$743$	−3.14797	+	4.89833i	−0.115488	+	0.179702i	0.778698	+	0.627399i	$0.215881\pi$
$744$	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	0.286877	−	0.957968i	$-0.407383\pi$
$757$	8.04064	+	1.15607i	0.292242	+	0.0420180i	0.00536536	+	0.999986i	$0.498292\pi$
$758$			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	0.387865	−	0.921716i	$-0.373213\pi$
$773$	−13.0471	−	11.3054i	−0.469271	−	0.406625i	−0.857136	+	0.515091i	$0.827758\pi$
$774$	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	$-0.639108\pi$
$787$	11.5950	−	10.0471i	0.413318	−	0.358142i	0.836561	+	0.547875i	$0.184563\pi$
$788$	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	$-0.216864\pi$
$797$	22.8517	+	10.4360i	0.809448	+	0.369663i	0.0326932	+	0.999465i	$0.489592\pi$
$798$	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	−0.669867	−	0.742481i	$-0.733649\pi$
$823$	−0.868528	+	0.752583i	−0.0302750	+	0.0262334i	0.639592	+	0.768715i	$0.279103\pi$
$824$	−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	−0.998579	−	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	0.419727	−	0.907651i	$-0.362126\pi$
$853$	16.5522	+	2.37985i	0.566737	+	0.0814845i	0.147010	+	0.989135i	$0.453035\pi$
$854$	−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	$-0.124607\pi$
$857$	−1.74302	−	5.93618i	−0.0595405	−	0.202776i	−0.983891	+	0.178767i	$0.942789\pi$
$858$	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	−0.330248	−	0.943894i	$-0.607132\pi$
$863$	−11.1982	+	1.61006i	−0.381192	+	0.0548072i	−0.0509446	+	0.998701i	$0.516223\pi$
$864$	−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	$-0.773728\pi$
$877$	−22.5349	+	10.2913i	−0.760950	+	0.347514i	−0.00314460	+	0.999995i	$0.501001\pi$
$878$	−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	0.472537	−	0.881311i	$-0.343338\pi$
$883$	−9.88198	−	8.56278i	−0.332555	−	0.288161i	−0.805092	+	0.593150i	$0.797884\pi$
$884$	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	$-0.0603115\pi$
$887$	11.9964	+	18.6668i	0.402800	+	0.626770i	−0.579303	+	0.815112i	$0.696675\pi$
$888$	−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	$-0.297578\pi$
$907$	−11.5834	−	18.0240i	−0.384619	−	0.598479i	−0.978543	+	0.206042i	$0.933942\pi$
$908$	−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	0.903861	−	0.427826i	$-0.140720\pi$
$937$	−2.68807	−	9.15473i	−0.0878155	−	0.299072i	−0.991677	+	0.128754i	$0.958902\pi$
$938$	−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	−0.882759	−	0.469826i	$-0.844317\pi$
$947$	3.50424	−	11.9343i	0.113872	−	0.387814i	0.996631	+	0.0820124i	$0.0261347\pi$
$948$	−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	$-0.251370\pi$
$953$	−7.23572	−	11.2590i	−0.234388	−	0.364715i	−0.938445	+	0.345429i	$0.887734\pi$
$954$	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	0.537092	−	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	−0.0261716	−	0.999657i	$-0.508332\pi$
$977$	7.20015	−	1.03522i	0.230353	−	0.0331198i	0.256525	+	0.966538i	$0.417423\pi$
$978$	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	$-0.919163\pi$
$983$	−9.07613	−	30.9104i	−0.289483	−	0.985890i	0.678442	−	0.734654i	$-0.262655\pi$
$984$	−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	0.0877636	−	0.996141i	$-0.472028\pi$
$997$	−19.1851	−	8.76152i	−0.607597	−	0.277480i	−0.695360	+	0.718661i	$0.744755\pi$
$998$	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.399.1		20
5.2	odd	4		575.2.k.a.376.1		10
5.3	odd	4		115.2.g.a.31.1	yes	10
5.4	even	2	inner	575.2.p.a.399.2		20
23.3	even	11	inner	575.2.p.a.49.2		20
115.3	odd	44		115.2.g.a.26.1	✓	10
115.49	even	22	inner	575.2.p.a.49.1		20
115.53	even	44		2645.2.a.o.1.4		5
115.72	odd	44		575.2.k.a.26.1		10
115.108	odd	44		2645.2.a.n.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.a.26.1	✓	10	115.3	odd	44
115.2.g.a.31.1	yes	10	5.3	odd	4
575.2.k.a.26.1		10	115.72	odd	44
575.2.k.a.376.1		10	5.2	odd	4
575.2.p.a.49.1		20	115.49	even	22	inner
575.2.p.a.49.2		20	23.3	even	11	inner
575.2.p.a.399.1		20	1.1	even	1	trivial
575.2.p.a.399.2		20	5.4	even	2	inner
2645.2.a.n.1.4		5	115.108	odd	44
2645.2.a.o.1.4		5	115.53	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 $\F_{q}$

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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