LMFDB - Embedded newform 575.2.k.a.26.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(26,575)]

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([0, 16]))

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

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

chi := DirichletCharacter("575.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.k (of order $11$, degree $10$, 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:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 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:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			26.1
Root			$-0.415415 - 0.909632i$ of defining polynomial
Character	$\chi$	$=$	575.26
Dual form			575.2.k.a.376.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0125459 + 0.0872586i) q^{2} +(0.415415 - 0.909632i) q^{3} +(1.91153 - 0.561276i) q^{4} +(0.0845850 + 0.0248364i) q^{6} +(1.30075 - 0.835939i) q^{7} +(0.146201 + 0.320135i) q^{8} +(1.30972 + 1.51150i) q^{9} +(0.289532 - 2.01374i) q^{11} +(0.283524 - 1.97195i) q^{12} +(-1.80075 - 1.15727i) q^{13} +(0.0892619 + 0.103014i) q^{14} +(3.32584 - 2.13739i) q^{16} +(4.18251 + 1.22809i) q^{17} +(-0.115460 + 0.133248i) q^{18} +(-7.12381 + 2.09174i) q^{19} +(-0.220047 - 1.53046i) q^{21} +0.179348 q^{22} +(2.79310 + 3.89854i) q^{23} +0.351939 q^{24} +(0.0783898 - 0.171650i) q^{26} +(4.79746 - 1.40866i) q^{27} +(2.01722 - 2.32800i) q^{28} +(-4.30111 - 1.26292i) q^{29} +(-0.376329 - 0.824045i) q^{31} +(0.689173 + 0.795348i) q^{32} +(-1.71148 - 1.09990i) q^{33} +(-0.0546886 + 0.380367i) q^{34} +(3.35194 + 2.15416i) q^{36} +(-7.26571 - 8.38507i) q^{37} +(-0.271897 - 0.595371i) q^{38} +(-1.80075 + 1.15727i) q^{39} +(3.95750 - 4.56720i) q^{41} +(0.130785 - 0.0384020i) q^{42} +(-2.24116 + 4.90745i) q^{43} +(-0.576814 - 4.01183i) q^{44} +(-0.305139 + 0.292633i) q^{46} +2.72825 q^{47} +(-0.562632 - 3.91319i) q^{48} +(-1.91476 + 4.19273i) q^{49} +(2.85459 - 3.29437i) q^{51} +(-4.09173 - 1.20144i) q^{52} +(0.230732 - 0.148283i) q^{53} +(0.183106 + 0.400947i) q^{54} +(0.457783 + 0.294199i) q^{56} +(-1.05662 + 7.34898i) q^{57} +(0.0562393 - 0.391153i) q^{58} +(6.74757 + 4.33640i) q^{59} +(-1.33718 - 2.92802i) q^{61} +(0.0671837 - 0.0431763i) q^{62} +(2.96714 + 0.871230i) q^{63} +(5.11714 - 5.90549i) q^{64} +(0.0745040 - 0.163141i) q^{66} +(-0.279610 - 1.94473i) q^{67} +8.68428 q^{68} +(4.70653 - 0.921186i) q^{69} +(1.58700 + 11.0378i) q^{71} +(-0.292401 + 0.640269i) q^{72} +(-9.95039 + 2.92170i) q^{73} +(0.640515 - 0.739194i) q^{74} +(-12.4433 + 7.99684i) q^{76} +(-1.30675 - 2.86139i) q^{77} +(-0.123574 - 0.142612i) q^{78} +(2.70849 + 1.74064i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(0.448178 + 0.288027i) q^{82} +(-2.85563 - 3.29557i) q^{83} +(-1.27964 - 2.80202i) q^{84} +(-0.456334 - 0.133992i) q^{86} +(-2.93553 + 3.38779i) q^{87} +(0.686997 - 0.201720i) q^{88} +(0.266861 - 0.584343i) q^{89} -3.30972 q^{91} +(7.52725 + 5.88446i) q^{92} -0.905910 q^{93} +(0.0342284 + 0.238063i) q^{94} +(1.00977 - 0.296494i) q^{96} +(-3.62848 + 4.18748i) q^{97} +(-0.389875 - 0.114478i) q^{98} +(3.42297 - 2.19981i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - q^{3} - q^{4} + 6 q^{6} - 5 q^{7} + 16 q^{8} + 2 q^{9} + 8 q^{11} - q^{12} - 3 q^{14} + 5 q^{16} + 23 q^{17} + 10 q^{18} - 13 q^{19} + 6 q^{21} - 4 q^{22} + 21 q^{23} - 6 q^{24} + 11 q^{26}+ \cdots + 6 q^{99}+O(q^{100}) $ 10 * q - 5 * q^2 - q^3 - q^4 + 6 * q^6 - 5 * q^7 + 16 * q^8 + 2 * q^9 + 8 * q^11 - q^12 - 3 * q^14 + 5 * q^16 + 23 * q^17 + 10 * q^18 - 13 * q^19 + 6 * q^21 - 4 * q^22 + 21 * q^23 - 6 * q^24 + 11 * q^26 + 5 * q^27 + 6 * q^28 + 2 * q^29 - 20 * q^31 + 15 * q^32 - 3 * q^33 + 16 * q^34 + 24 * q^36 - 13 * q^37 - 21 * q^38 - 5 * q^41 - 3 * q^42 - 15 * q^43 + 19 * q^44 - 16 * q^46 + 52 * q^47 - 6 * q^48 + 4 * q^49 - 10 * q^51 - 22 * q^52 - 6 * q^53 - 30 * q^54 + 3 * q^56 - 2 * q^57 - 45 * q^58 + 5 * q^59 - 3 * q^61 + 54 * q^62 + 10 * q^63 - 34 * q^64 - 4 * q^66 - 20 * q^67 - 32 * q^68 - q^69 - 22 * q^71 - 32 * q^72 - 43 * q^73 + q^74 - 2 * q^76 - 4 * q^77 - 11 * q^78 + 51 * q^79 - q^81 - 58 * q^82 + 17 * q^83 + 6 * q^84 - 9 * q^86 + 2 * q^87 - 7 * q^88 + 57 * q^89 - 22 * q^91 + 43 * q^92 - 20 * q^93 - 81 * q^94 - 7 * q^96 - 52 * q^97 - 24 * q^98 + 6 * 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 $

$2$	0.0125459	+	0.0872586i	0.00887129	+	0.0617012i	0.993776	−	0.111395i	$-0.0355319\pi$
$2$	0.0125459	+	0.0872586i	0.00887129	+	0.0617012i	−0.984905	+	0.173096i	$0.944623\pi$
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i	−0.750986	−	0.660318i	$-0.770422\pi$
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i	0.990826	+	0.135141i	$0.0431489\pi$
$4$	1.91153	−	0.561276i	0.955765	−	0.280638i
$5$		0			0
$5$		0			0
$6$	0.0845850	+	0.0248364i	0.0345317	+	0.0101394i
$7$	1.30075	−	0.835939i	0.491636	−	0.315955i	−0.271227	−	0.962515i	$-0.587429\pi$
$7$	1.30075	−	0.835939i	0.491636	−	0.315955i	0.762863	+	0.646560i	$0.223793\pi$
$8$	0.146201	+	0.320135i	0.0516897	+	0.113185i
$9$	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	$-0.0537717\pi$
$12$	0.283524	−	1.97195i	0.0818462	−	0.569253i
$13$	−1.80075	−	1.15727i	−0.499437	−	0.320969i	0.266554	−	0.963820i	$-0.414115\pi$
$13$	−1.80075	−	1.15727i	−0.499437	−	0.320969i	−0.765991	+	0.642851i	$0.777751\pi$
$14$	0.0892619	+	0.103014i	0.0238563	+	0.0275316i
$15$		0			0
$16$	3.32584	−	2.13739i	0.831460	−	0.534347i
$17$	4.18251	+	1.22809i	1.01441	+	0.297857i	0.746355	−	0.665548i	$-0.231802\pi$
$17$	4.18251	+	1.22809i	1.01441	+	0.297857i	0.268052	+	0.963405i	$0.413620\pi$
$18$	−0.115460	+	0.133248i	−0.0272141	+	0.0314068i
$19$	−7.12381	+	2.09174i	−1.63431	+	0.479878i	−0.964814	−	0.262935i	$-0.915310\pi$
$19$	−7.12381	+	2.09174i	−1.63431	+	0.479878i	−0.669499	+	0.742813i	$0.733491\pi$
$20$		0			0
$21$	−0.220047	−	1.53046i	−0.0480182	−	0.333974i
$22$	0.179348			0.0382372
$23$	2.79310	+	3.89854i	0.582402	+	0.812901i
$23$	2.79310	+	3.89854i	0.582402	+	0.812901i
$24$	0.351939			0.0718392
$25$		0			0
$26$	0.0783898	−	0.171650i	0.0153735	−	0.0336633i
$27$	4.79746	−	1.40866i	0.923273	−	0.271097i
$28$	2.01722	−	2.32800i	0.381219	−	0.439951i
$29$	−4.30111	−	1.26292i	−0.798695	−	0.234518i	−0.143177	−	0.989697i	$-0.545732\pi$
$29$	−4.30111	−	1.26292i	−0.798695	−	0.234518i	−0.655519	+	0.755179i	$0.727550\pi$
$30$		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	$0.889561\pi$
$32$	0.689173	+	0.795348i	0.121830	+	0.140599i
$33$	−1.71148	−	1.09990i	−0.297931	−	0.191469i
$34$	−0.0546886	+	0.380367i	−0.00937901	+	0.0652325i
$35$		0			0
$36$	3.35194	+	2.15416i	0.558656	+	0.359027i
$37$	−7.26571	−	8.38507i	−1.19447	−	1.37850i	−0.907227	−	0.420641i	$-0.861805\pi$
$37$	−7.26571	−	8.38507i	−1.19447	−	1.37850i	−0.287248	−	0.957856i	$-0.592740\pi$
$38$	−0.271897	−	0.595371i	−0.0441075	−	0.0965819i
$39$	−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	$0.0708408\pi$
$42$	0.130785	−	0.0384020i	0.0201806	−	0.00592556i
$43$	−2.24116	+	4.90745i	−0.341773	+	0.748379i	−0.999990	−	0.00444961i	$-0.998584\pi$
$43$	−2.24116	+	4.90745i	−0.341773	+	0.748379i	0.658217	+	0.752828i	$0.271311\pi$
$44$	−0.576814	−	4.01183i	−0.0869579	−	0.604806i
$45$		0			0
$46$	−0.305139	+	0.292633i	−0.0449903	+	0.0431464i
$47$	2.72825			0.397956			0.198978	−	0.980004i	$-0.436238\pi$
$47$	2.72825			0.397956			0.198978	+	0.980004i	$0.436238\pi$
$48$	−0.562632	−	3.91319i	−0.0812089	−	0.564821i
$49$	−1.91476	+	4.19273i	−0.273537	+	0.598962i
$50$		0			0
$51$	2.85459	−	3.29437i	0.399723	−	0.461305i
$52$	−4.09173	−	1.20144i	−0.567420	−	0.166610i
$53$	0.230732	−	0.148283i	0.0316935	−	0.0203682i	−0.524698	−	0.851288i	$-0.675822\pi$
$53$	0.230732	−	0.148283i	0.0316935	−	0.0203682i	0.556392	+	0.830920i	$0.312185\pi$
$54$	0.183106	+	0.400947i	0.0249176	+	0.0545620i
$55$		0			0
$56$	0.457783	+	0.294199i	0.0611738	+	0.0393140i
$57$	−1.05662	+	7.34898i	−0.139953	+	0.973396i
$58$	0.0562393	−	0.391153i	0.00738458	−	0.0513609i
$59$	6.74757	+	4.33640i	0.878458	+	0.564551i	0.900329	−	0.435210i	$-0.143326\pi$
$59$	6.74757	+	4.33640i	0.878458	+	0.564551i	−0.0218707	+	0.999761i	$0.506962\pi$
$60$		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	$0.929704\pi$
$62$	0.0671837	−	0.0431763i	0.00853233	−	0.00548340i
$63$	2.96714	+	0.871230i	0.373824	+	0.109765i
$64$	5.11714	−	5.90549i	0.639642	−	0.738187i
$65$		0			0
$66$	0.0745040	−	0.163141i	0.00917081	−	0.0200813i
$67$	−0.279610	−	1.94473i	−0.0341598	−	0.237587i	0.965587	−	0.260080i	$-0.0837488\pi$
$67$	−0.279610	−	1.94473i	−0.0341598	−	0.237587i	−0.999747	+	0.0224928i	$0.992840\pi$
$68$	8.68428			1.05312
$69$	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	$0.724377\pi$
$72$	−0.292401	+	0.640269i	−0.0344598	+	0.0754564i
$73$	−9.95039	+	2.92170i	−1.16461	+	0.341959i	−0.806221	−	0.591615i	$-0.798491\pi$
$73$	−9.95039	+	2.92170i	−1.16461	+	0.341959i	−0.358385	+	0.933574i	$0.616672\pi$
$74$	0.640515	−	0.739194i	0.0744584	−	0.0859295i
$75$		0			0
$76$	−12.4433	+	7.99684i	−1.42735	+	0.917300i
$77$	−1.30675	−	2.86139i	−0.148919	−	0.326086i
$78$	−0.123574	−	0.142612i	−0.0139920	−	0.0161476i
$79$	2.70849	+	1.74064i	0.304729	+	0.195837i	0.684064	−	0.729422i	$-0.260211\pi$
$79$	2.70849	+	1.74064i	0.304729	+	0.195837i	−0.379335	+	0.925259i	$0.623847\pi$
$80$		0			0
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	0.448178	+	0.288027i	0.0494930	+	0.0318072i
$83$	−2.85563	−	3.29557i	−0.313446	−	0.361736i	0.577065	−	0.816698i	$-0.304198\pi$
$83$	−2.85563	−	3.29557i	−0.313446	−	0.361736i	−0.890510	+	0.454963i	$0.849653\pi$
$84$	−1.27964	−	2.80202i	−0.139620	−	0.305725i
$85$		0			0
$86$	−0.456334	−	0.133992i	−0.0492078	−	0.0144487i
$87$	−2.93553	+	3.38779i	−0.314722	+	0.363209i
$88$	0.686997	−	0.201720i	0.0732341	−	0.0215035i
$89$	0.266861	−	0.584343i	0.0282872	−	0.0619403i	−0.894961	−	0.446144i	$-0.852797\pi$
$89$	0.266861	−	0.584343i	0.0282872	−	0.0619403i	0.923248	+	0.384204i	$0.125524\pi$
$90$		0			0
$91$	−3.30972			−0.346953
$92$	7.52725	+	5.88446i	0.784770	+	0.613498i
$93$	−0.905910			−0.0939385
$94$	0.0342284	+	0.238063i	0.00353038	+	0.0245544i
$95$		0			0
$96$	1.00977	−	0.296494i	0.103059	−	0.0302608i
$97$	−3.62848	+	4.18748i	−0.368416	+	0.425175i	−0.909442	−	0.415831i	$-0.863491\pi$
$97$	−3.62848	+	4.18748i	−0.368416	+	0.425175i	0.541026	+	0.841006i	$0.318036\pi$
$98$	−0.389875	−	0.114478i	−0.0393833	−	0.0115640i
$99$	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	$0.844563\pi$
$102$	0.323276	+	0.207757i	0.0320091	+	0.0205710i
$103$	1.38513	−	9.63380i	0.136481	−	0.949247i	−0.800367	−	0.599510i	$-0.795362\pi$
$103$	1.38513	−	9.63380i	0.136481	−	0.949247i	0.936848	−	0.349737i	$-0.113729\pi$
$104$	0.107212	−	0.745675i	0.0105130	−	0.0731194i
$105$		0			0
$106$	0.0158337	+	0.0182730i	0.00153790	+	0.00177483i
$107$	3.07272	+	6.72833i	0.297051	+	0.650452i	0.998031	−	0.0627299i	$-0.0199807\pi$
$107$	3.07272	+	6.72833i	0.297051	+	0.650452i	−0.700979	+	0.713182i	$0.747253\pi$
$108$	8.37985	−	5.38540i	0.806351	−	0.518210i
$109$	−9.99029	−	2.93341i	−0.956897	−	0.280970i	−0.234241	−	0.972179i	$-0.575260\pi$
$109$	−9.99029	−	2.93341i	−0.956897	−	0.280970i	−0.722656	+	0.691208i	$0.757079\pi$
$110$		0			0
$111$	−10.6456	+	3.12583i	−1.01044	+	0.296691i
$112$	2.53935	−	5.56040i	0.239946	−	0.525408i
$113$	2.78825	+	19.3927i	0.262297	+	1.82431i	0.515486	+	0.856898i	$0.327611\pi$
$113$	2.78825	+	19.3927i	0.262297	+	1.82431i	−0.253189	+	0.967417i	$0.581480\pi$
$114$	−0.654518			−0.0613012
$115$		0			0
$116$	−8.93053			−0.829179
$117$	−0.609264	−	4.23753i	−0.0563265	−	0.391760i
$118$	−0.293734	+	0.643187i	−0.0270404	+	0.0592102i
$119$	6.46699	−	1.89888i	0.592828	−	0.174070i
$120$		0			0
$121$	6.58311	+	1.93298i	0.598465	+	0.175725i
$122$	0.238719	−	0.153415i	0.0216126	−	0.0138896i
$123$	−2.51047	−	5.49716i	−0.226361	−	0.495662i
$124$	−1.18188	−	1.36396i	−0.106136	−	0.122487i
$125$		0			0
$126$	−0.0387969	+	0.269839i	−0.00345631	+	0.0240391i
$127$	−2.49696	+	17.3667i	−0.221569	+	1.54105i	0.510536	+	0.859856i	$0.329447\pi$
$127$	−2.49696	+	17.3667i	−0.221569	+	1.54105i	−0.732105	+	0.681192i	$0.761462\pi$
$128$	2.35017	+	1.51036i	0.207727	+	0.133498i
$129$	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	$0.511240\pi$
$132$	−3.88890	−	1.14188i	−0.338486	−	0.0993883i
$133$	−7.51770	+	8.67589i	−0.651867	+	0.752295i
$134$	0.166187	−	0.0487968i	0.0143563	−	0.00421540i
$135$		0			0
$136$	0.218329	+	1.51851i	0.0187216	+	0.130211i
$137$	−21.5268			−1.83916			−0.919580	−	0.392903i	$-0.871471\pi$
$137$	−21.5268			−1.83916			−0.919580	+	0.392903i	$0.871471\pi$
$138$	0.139429	+	0.399128i	0.0118690	+	0.0339760i
$139$	−16.3719			−1.38864			−0.694322	−	0.719665i	$-0.744295\pi$
$139$	−16.3719			−1.38864			−0.694322	+	0.719665i	$0.744295\pi$
$140$		0			0
$141$	1.13336	−	2.48170i	0.0954458	−	0.208997i
$142$	−0.943233	+	0.276958i	−0.0791544	+	0.0232418i
$143$	−2.85181	+	3.29117i	−0.238480	+	0.275221i
$144$	7.58658	+	2.22762i	0.632215	+	0.185635i
$145$		0			0
$146$	−0.379780	−	0.831602i	−0.0314308	−	0.0688239i
$147$	3.01843	+	3.48345i	0.248956	+	0.287310i
$148$	−18.5950	−	11.9502i	−1.52850	−	0.982304i
$149$	−2.74972	+	19.1247i	−0.225266	+	1.56676i	0.492399	+	0.870370i	$0.336120\pi$
$149$	−2.74972	+	19.1247i	−0.225266	+	1.56676i	−0.717665	+	0.696389i	$0.754789\pi$
$150$		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	$0.378913\pi$
$152$	−1.71114	−	1.97476i	−0.138792	−	0.160174i
$153$	3.62165	+	7.93032i	0.292793	+	0.641128i
$154$	0.233287	−	0.149924i	0.0187988	−	0.0120812i
$155$		0			0
$156$	−2.79263	+	3.22287i	−0.223590	+	0.258036i
$157$	5.54048	−	1.62683i	0.442179	−	0.129835i	−0.0530620	−	0.998591i	$-0.516898\pi$
$157$	5.54048	−	1.62683i	0.442179	−	0.129835i	0.495241	+	0.868756i	$0.335080\pi$
$158$	−0.117905	+	0.258177i	−0.00938006	+	0.0205395i
$159$	−0.0390330	−	0.271480i	−0.00309552	−	0.0215298i
$160$		0			0
$161$	6.89206	+	2.73614i	0.543170	+	0.215638i
$162$	−0.0881559			−0.00692618
$163$	1.25289	+	8.71401i	0.0981335	+	0.682534i	0.978197	+	0.207678i	$0.0665906\pi$
$163$	1.25289	+	8.71401i	0.0981335	+	0.682534i	−0.880064	+	0.474856i	$0.842500\pi$
$164$	5.00143	−	10.9516i	0.390546	−	0.855176i
$165$		0			0
$166$	0.251740	−	0.290524i	0.0195388	−	0.0225490i
$167$	−18.7367	−	5.50159i	−1.44989	−	0.425726i	−0.540384	−	0.841418i	$-0.681721\pi$
$167$	−18.7367	−	5.50159i	−1.44989	−	0.425726i	−0.909505	+	0.415692i	$0.863539\pi$
$168$	0.457783	−	0.294199i	0.0353187	−	0.0226980i
$169$	−3.49698	−	7.65732i	−0.268998	−	0.589024i
$170$		0			0
$171$	−12.4919	−	8.02803i	−0.955276	−	0.613919i
$172$	−1.52960	+	10.6386i	−0.116631	+	0.811188i
$173$	3.07149	−	21.3627i	0.233521	−	1.62417i	−0.449155	−	0.893454i	$-0.648275\pi$
$173$	3.07149	−	21.3627i	0.233521	−	1.62417i	0.682676	−	0.730721i	$-0.260816\pi$
$174$	−0.332443	−	0.213648i	−0.0252024	−	0.0161966i
$175$		0			0
$176$	−3.34120	−	7.31621i	−0.251852	−	0.551480i
$177$	6.74757	−	4.33640i	0.507178	−	0.325944i
$178$	0.0543370	+	0.0159548i	0.00407273	+	0.00119586i
$179$	10.0553	−	11.6044i	0.751567	−	0.867354i	−0.243152	−	0.969988i	$-0.578182\pi$
$179$	10.0553	−	11.6044i	0.751567	−	0.867354i	0.994719	+	0.102634i	$0.0327270\pi$
$180$		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	$0.126674\pi$
$182$	−0.0415234	−	0.288802i	−0.00307792	−	0.0214074i
$183$	−3.21890			−0.237948
$184$	−0.839703	+	1.46414i	−0.0619037	+	0.107938i
$185$		0			0
$186$	−0.0113655	−	0.0790485i	−0.000833356	−	0.00579612i
$187$	3.68403	−	8.06690i	0.269403	−	0.589910i
$188$	5.21513	−	1.53130i	0.380353	−	0.111682i
$189$	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	$0.367505\pi$
$192$	−3.24609	−	7.10794i	−0.234266	−	0.512972i
$193$	3.16580	+	3.65352i	0.227879	+	0.262986i	0.858162	−	0.513379i	$-0.171607\pi$
$193$	3.16580	+	3.65352i	0.227879	+	0.262986i	−0.630283	+	0.776366i	$0.717061\pi$
$194$	−0.410917	−	0.264080i	−0.0295021	−	0.0189598i
$195$		0			0
$196$	−1.30684	+	9.08924i	−0.0933454	+	0.649232i
$197$	0.220925	+	0.141980i	0.0157403	+	0.0101157i	0.548487	−	0.836159i	$-0.315204\pi$
$197$	0.220925	+	0.141980i	0.0157403	+	0.0101157i	−0.532747	+	0.846275i	$0.678840\pi$
$198$	0.234896	+	0.271085i	0.0166934	+	0.0192652i
$199$	−1.79719	−	3.93530i	−0.127399	−	0.278966i	0.835175	−	0.549985i	$-0.185367\pi$
$199$	−1.79719	−	3.93530i	−0.127399	−	0.278966i	−0.962574	+	0.271019i	$0.912639\pi$
$200$		0			0
$201$	−1.88514	−	0.553528i	−0.132968	−	0.0390429i
$202$	0.259650	−	0.299652i	0.0182689	−	0.0210835i
$203$	−6.65037	+	1.95273i	−0.466765	+	0.137054i
$204$	3.60758	−	7.89950i	0.252581	−	0.553076i
$205$		0			0
$206$	0.858010			0.0597804
$207$	−2.23445	+	9.32777i	−0.155305	+	0.648325i
$208$	−8.46252			−0.586770
$209$	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	$0.336506\pi$
$212$	0.357824	−	0.412951i	0.0245755	−	0.0283616i
$213$	10.6996	+	3.14169i	0.733125	+	0.215265i
$214$	−0.548554	+	0.352535i	−0.0374984	+	0.0240988i
$215$		0			0
$216$	1.15235	+	1.32989i	0.0784077	+	0.0904874i
$217$	−1.17836	−	0.757286i	−0.0799923	−	0.0514079i
$218$	0.130629	−	0.908542i	0.00884728	−	0.0615342i
$219$	−1.47587	+	10.2649i	−0.0997301	+	0.693638i
$220$		0			0
$221$	−6.11040	−	7.05178i	−0.411030	−	0.474354i
$222$	−0.406315	−	0.889705i	−0.0272701	−	0.0597131i
$223$	7.74566	−	4.97783i	0.518688	−	0.333340i	−0.254965	−	0.966950i	$-0.582064\pi$
$223$	7.74566	−	4.97783i	0.518688	−	0.333340i	0.773653	+	0.633610i	$0.218428\pi$
$224$	1.56130	+	0.458439i	0.104319	+	0.0306308i
$225$		0			0
$226$	−1.65720	+	0.486598i	−0.110235	+	0.0323680i
$227$	3.68538	−	8.06985i	0.244607	−	0.535615i	−0.747012	−	0.664810i	$-0.768512\pi$
$227$	3.68538	−	8.06985i	0.244607	−	0.535615i	0.991619	+	0.129196i	$0.0412396\pi$
$228$	2.10504	+	14.6408i	0.139409	+	0.969614i
$229$	−8.38484			−0.554086			−0.277043	−	0.960858i	$-0.589354\pi$
$229$	−8.38484			−0.554086			−0.277043	+	0.960858i	$0.589354\pi$
$230$		0			0
$231$	−3.14566			−0.206969
$232$	−0.224520	−	1.56157i	−0.0147405	−	0.102522i
$233$	9.97561	−	21.8435i	0.653524	−	1.43102i	−0.234911	−	0.972017i	$-0.575480\pi$
$233$	9.97561	−	21.8435i	0.653524	−	1.43102i	0.888435	−	0.459002i	$-0.151793\pi$
$234$	0.362117	−	0.106327i	0.0236723	−	0.00695082i
$235$		0			0
$236$	15.3321	+	4.50191i	0.998034	+	0.293049i
$237$	2.70849	−	1.74064i	0.175935	−	0.113067i
$238$	0.246828	+	0.540478i	0.0159995	+	0.0350340i
$239$	7.35914	+	8.49290i	0.476023	+	0.549360i	0.942077	−	0.335396i	$-0.108870\pi$
$239$	7.35914	+	8.49290i	0.476023	+	0.549360i	−0.466054	+	0.884756i	$0.654325\pi$
$240$		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	$-0.314874\pi$
$242$	−0.0860778	+	0.598684i	−0.00553329	+	0.0384849i
$243$	13.4601	+	8.65025i	0.863463	+	0.554914i
$244$	−4.19948	−	4.84646i	−0.268844	−	0.310263i
$245$		0			0
$246$	0.448178	−	0.288027i	0.0285748	−	0.0183639i
$247$	15.2489	+	4.47747i	0.970262	+	0.284895i
$248$	0.208786	−	0.240952i	0.0132579	−	0.0153004i
$249$	−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	$0.620153\pi$
$252$	6.16077			0.388092
$253$	8.65932	−	4.49583i	0.544407	−	0.282650i
$254$	−1.54672			−0.0970501
$255$		0			0
$256$	6.38987	−	13.9919i	0.399367	−	0.874492i
$257$	17.0432	−	5.00435i	1.06313	−	0.312163i	0.297018	−	0.954872i	$-0.404008\pi$
$257$	17.0432	−	5.00435i	1.06313	−	0.312163i	0.766110	+	0.642709i	$0.222190\pi$
$258$	−0.311451	+	0.359434i	−0.0193901	+	0.0223774i
$259$	−16.4603	−	4.83317i	−1.02279	−	0.300318i
$260$		0			0
$261$	−3.72435	−	8.15519i	−0.230531	−	0.504794i
$262$	−0.753257	−	0.869305i	−0.0465364	−	0.0537059i
$263$	7.35320	+	4.72561i	0.453417	+	0.291394i	0.747348	−	0.664433i	$-0.231327\pi$
$263$	7.35320	+	4.72561i	0.453417	+	0.291394i	−0.293930	+	0.955827i	$0.594963\pi$
$264$	0.101897	−	0.708712i	0.00627135	−	0.0436182i
$265$		0			0
$266$	−0.851362	−	0.547137i	−0.0522004	−	0.0335471i
$267$	−0.420680	−	0.485490i	−0.0257452	−	0.0297115i
$268$	−1.62601	−	3.56047i	−0.0993246	−	0.217491i
$269$	2.46553	−	1.58450i	0.150326	−	0.0966086i	−0.463316	−	0.886193i	$-0.653340\pi$
$269$	2.46553	−	1.58450i	0.150326	−	0.0966086i	0.613642	+	0.789585i	$0.289704\pi$
$270$		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	$0.163419\pi$
$272$	16.5353	−	4.85519i	1.00260	−	0.294389i
$273$	−1.37491	+	3.01063i	−0.0832132	+	0.182212i
$274$	−0.270073	−	1.87840i	−0.0163157	−	0.113478i
$275$		0			0
$276$	8.47963	−	4.40253i	0.510414	−	0.265001i
$277$	22.7888			1.36924			0.684622	−	0.728898i	$-0.259967\pi$
$277$	22.7888			1.36924			0.684622	+	0.728898i	$0.259967\pi$
$278$	−0.205400	−	1.42859i	−0.0123191	−	0.0856809i
$279$	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	$0.0876013\pi$
$282$	0.230769	+	0.0677599i	0.0137421	+	0.00403504i
$283$	−19.9441	+	12.8173i	−1.18555	+	0.761910i	−0.976399	−	0.215973i	$-0.930708\pi$
$283$	−19.9441	+	12.8173i	−1.18555	+	0.761910i	−0.209155	+	0.977882i	$0.567071\pi$
$284$	9.22884	+	20.2083i	0.547631	+	1.19914i
$285$		0			0
$286$	−0.322961	−	0.207554i	−0.0190971	−	0.0122730i
$287$	1.32981	−	9.24901i	0.0784960	−	0.545952i
$288$	−0.299543	+	2.08337i	−0.0176507	+	0.122764i
$289$	1.68384	+	1.08214i	0.0990493	+	0.0636551i
$290$		0			0
$291$	2.30175	+	5.04012i	0.134931	+	0.295457i
$292$	−17.3806	+	11.1698i	−1.01712	+	0.653664i
$293$	−4.10110	−	1.20419i	−0.239589	−	0.0703497i	0.159734	−	0.987160i	$-0.448936\pi$
$293$	−4.10110	−	1.20419i	−0.239589	−	0.0703497i	−0.399323	+	0.916810i	$0.630755\pi$
$294$	−0.266092	+	0.307087i	−0.0155188	+	0.0179097i
$295$		0			0
$296$	1.62210	−	3.55191i	0.0942827	−	0.206450i
$297$	−1.44766	−	10.0687i	−0.0840017	−	0.584245i
$298$	−1.70330			−0.0986692
$299$	−0.518014	−	10.2526i	−0.0299575	−	0.592926i
$300$		0			0
$301$	1.18715	+	8.25681i	0.0684262	+	0.475915i
$302$	−0.732929	+	1.60489i	−0.0421753	+	0.0923511i
$303$	−4.31549	+	1.26714i	−0.247918	+	0.0727954i
$304$	−19.2218	+	22.1831i	−1.10244	+	1.27229i
$305$		0			0
$306$	−0.646552	+	0.415514i	−0.0369609	+	0.0237533i
$307$	3.71586	+	8.13661i	0.212076	+	0.464381i	0.985536	−	0.169463i	$-0.0542034\pi$
$307$	3.71586	+	8.13661i	0.212076	+	0.464381i	−0.773461	+	0.633844i	$0.781476\pi$
$308$	−4.10393	−	4.73619i	−0.233843	−	0.269869i
$309$	−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	$-0.184781\pi$
$312$	−0.633752	−	0.407288i	−0.0358792	−	0.0230581i
$313$	−14.7416	−	17.0127i	−0.833244	−	0.961615i	0.166457	−	0.986049i	$-0.446767\pi$
$313$	−14.7416	−	17.0127i	−0.833244	−	0.961615i	−0.999701	+	0.0244337i	$0.992222\pi$
$314$	0.211465	+	0.463045i	0.0119337	+	0.0261311i
$315$		0			0
$316$	6.15434	+	1.80708i	0.346209	+	0.101656i
$317$	8.34970	−	9.63606i	0.468966	−	0.541215i	−0.471158	−	0.882049i	$-0.656164\pi$
$317$	8.34970	−	9.63606i	0.468966	−	0.541215i	0.940124	+	0.340834i	$0.110709\pi$
$318$	0.0231993	−	0.00681193i	0.00130095	−	0.000381994i
$319$	−3.78849	+	8.29564i	−0.212115	+	0.464467i
$320$		0			0
$321$	7.39676			0.412847
$322$	−0.152285	+	0.635719i	−0.00848651	+	0.0354272i
$323$	−32.3642			−1.80079
$324$	0.283524	+	1.97195i	0.0157513	+	0.109553i
$325$		0			0
$326$	−0.744654	+	0.218650i	−0.0412426	+	0.0121099i
$327$	−6.81845	+	7.86891i	−0.377061	+	0.435151i
$328$	2.04071	+	0.599206i	0.112679	+	0.0330856i
$329$	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	$0.623919\pi$
$332$	−7.30834	−	4.69678i	−0.401097	−	0.257769i
$333$	3.15798	−	21.9642i	0.173056	−	1.20363i
$334$	0.244993	−	1.70396i	0.0134054	−	0.0932366i
$335$		0			0
$336$	−4.00303	−	4.61974i	−0.218383	−	0.252028i
$337$	−11.3983	−	24.9589i	−0.620907	−	1.35960i	−0.914858	−	0.403776i	$-0.867697\pi$
$337$	−11.3983	−	24.9589i	−0.620907	−	1.35960i	0.293951	−	0.955821i	$-0.405030\pi$
$338$	0.624294	−	0.401210i	0.0339571	−	0.0218229i
$339$	18.7985	+	5.51975i	1.02100	+	0.299792i
$340$		0			0
$341$	−1.76837	+	0.519240i	−0.0957626	+	0.0281184i
$342$	0.543793	−	1.19074i	0.0294050	−	0.0643879i
$343$	2.55459	+	17.7675i	0.137935	+	0.959357i
$344$	−1.89870			−0.102371
$345$		0			0
$346$	1.90261			0.102285
$347$	0.858953	+	5.97415i	0.0461110	+	0.320709i	0.999802	+	0.0199196i	$0.00634104\pi$
$347$	0.858953	+	5.97415i	0.0461110	+	0.320709i	−0.953691	+	0.300789i	$0.902750\pi$
$348$	−3.70988	+	8.12350i	−0.198870	+	0.435465i
$349$	−8.00915	+	2.35170i	−0.428720	+	0.125883i	−0.488972	−	0.872300i	$-0.662628\pi$
$349$	−8.00915	+	2.35170i	−0.428720	+	0.125883i	0.0602518	+	0.998183i	$0.480810\pi$
$350$		0			0
$351$	−10.2692	−	3.01532i	−0.548130	−	0.160946i
$352$	1.80116	−	1.15753i	0.0960021	−	0.0616968i
$353$	10.8642	+	23.7892i	0.578242	+	1.26617i	0.942291	+	0.334794i	$0.108667\pi$
$353$	10.8642	+	23.7892i	0.578242	+	1.26617i	−0.364049	+	0.931380i	$0.618606\pi$
$354$	0.463042	+	0.534379i	0.0246104	+	0.0284019i
$355$		0			0
$356$	0.182134	−	1.26677i	0.00965310	−	0.0671388i
$357$	0.959204	−	6.67141i	0.0507664	−	0.353088i
$358$	1.13874	+	0.731822i	0.0601841	+	0.0386780i
$359$	−3.70672	−	4.27779i	−0.195633	−	0.225773i	0.649454	−	0.760401i	$-0.274997\pi$
$359$	−3.70672	−	4.27779i	−0.195633	−	0.225773i	−0.845088	+	0.534628i	$0.820452\pi$
$360$		0			0
$361$	30.3894	−	19.5301i	1.59944	−	1.02790i
$362$	0.0692719	+	0.0203401i	0.00364085	+	0.00106905i
$363$	4.49302	−	5.18522i	0.235822	−	0.272154i
$364$	−6.32663	+	1.85767i	−0.331605	+	0.0973682i
$365$		0			0
$366$	−0.0403840	−	0.280877i	−0.00211091	−	0.0146817i
$367$	12.3147			0.642822			0.321411	−	0.946940i	$-0.395843\pi$
$367$	12.3147			0.642822			0.321411	+	0.946940i	$0.395843\pi$
$368$	17.6221	+	6.99596i	0.918615	+	0.364690i
$369$	12.0866			0.629201
$370$		0			0
$371$	0.176169	−	0.385756i	0.00914624	−	0.0200275i
$372$	−1.73167	+	0.508465i	−0.0897831	+	0.0263627i
$373$	19.0734	−	22.0119i	0.987585	−	1.13973i	−0.00260397	−	0.999997i	$-0.500829\pi$
$373$	19.0734	−	22.0119i	0.987585	−	1.13973i	0.990189	−	0.139737i	$-0.0446257\pi$
$374$	0.750126	+	0.220257i	0.0387881	+	0.0113892i
$375$		0			0
$376$	0.398872	+	0.873407i	0.0205702	+	0.0450426i
$377$	6.28366	+	7.25173i	0.323625	+	0.373483i
$378$	0.573343	+	0.368465i	0.0294896	+	0.0189518i
$379$	4.74698	−	33.0160i	0.243836	−	1.69592i	−0.388683	−	0.921372i	$-0.627070\pi$
$379$	4.74698	−	33.0160i	0.243836	−	1.69592i	0.632519	−	0.774545i	$-0.282021\pi$
$380$		0			0
$381$	14.7601	+	9.48571i	0.756181	+	0.485968i
$382$	−0.246268	−	0.284209i	−0.0126002	−	0.0145414i
$383$	−12.9139	−	28.2775i	−0.659870	−	1.44491i	−0.882643	−	0.470044i	$-0.844238\pi$
$383$	−12.9139	−	28.2775i	−0.659870	−	1.44491i	0.222773	−	0.974870i	$-0.428489\pi$
$384$	2.35017	−	1.51036i	0.119931	−	0.0770753i
$385$		0			0
$386$	−0.279084	+	0.322080i	−0.0142050	+	0.0163934i
$387$	−10.3529	+	3.03988i	−0.526267	+	0.154526i
$388$	−4.58560	+	10.0411i	−0.232799	+	0.509758i
$389$	1.80544	+	12.5571i	0.0915394	+	0.636670i	0.983005	+	0.183581i	$0.0587690\pi$
$389$	1.80544	+	12.5571i	0.0915394	+	0.636670i	−0.891465	+	0.453089i	$0.850322\pi$
$390$		0			0
$391$	6.89440	+	19.7358i	0.348665	+	0.998085i
$392$	−1.62218			−0.0819324
$393$	1.85692	+	12.9152i	0.0936692	+	0.651484i
$394$	−0.00961727	+	0.0210589i	−0.000484511	+	0.00106093i
$395$		0			0
$396$	5.30841	−	6.12623i	0.266757	−	0.307855i
$397$	11.8219	+	3.47123i	0.593325	+	0.174216i	0.564590	−	0.825371i	$-0.309034\pi$
$397$	11.8219	+	3.47123i	0.593325	+	0.174216i	0.0287344	+	0.999587i	$0.490852\pi$
$398$	0.320841	−	0.206192i	0.0160823	−	0.0103355i
$399$	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	$-0.637166\pi$
$402$	0.0246493	−	0.171440i	0.00122940	−	0.00855063i
$403$	−0.275970	+	1.91941i	−0.0137470	+	0.0956126i
$404$	−7.53797	−	4.84436i	−0.375028	−	0.241016i
$405$		0			0
$406$	−0.253827	−	0.555804i	−0.0125972	−	0.0275841i
$407$	−18.9890	+	12.2035i	−0.941249	+	0.604904i
$408$	1.47199	+	0.432214i	0.0728741	+	0.0213978i
$409$	−10.6316	+	12.2695i	−0.525698	+	0.606688i	−0.955048	−	0.296450i	$-0.904197\pi$
$409$	−10.6316	+	12.2695i	−0.525698	+	0.606688i	0.429350	+	0.903138i	$0.358743\pi$
$410$		0			0
$411$	−8.94256	+	19.5815i	−0.441104	+	0.965883i
$412$	−2.75950	−	19.1927i	−0.135951	−	0.945558i
$413$	12.4018			0.610254
$414$	−0.841961	−	0.0779495i	−0.0413801	−	0.00383101i
$415$		0			0
$416$	−0.320594	−	2.22978i	−0.0157184	−	0.109324i
$417$	−6.80112	+	14.8924i	−0.333052	+	0.729282i
$418$	−1.27764	+	0.375150i	−0.0624916	+	0.0183492i
$419$	8.76692	−	10.1176i	0.428292	−	0.494275i	−0.500053	−	0.865995i	$-0.666686\pi$
$419$	8.76692	−	10.1176i	0.428292	−	0.494275i	0.928345	+	0.371719i	$0.121232\pi$
$420$		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	$0.420899\pi$
$422$	0.240510	+	0.526644i	0.0117079	+	0.0256366i
$423$	3.57325	+	4.12375i	0.173737	+	0.200504i
$424$	0.0812036	+	0.0521864i	0.00394360	+	0.00253439i
$425$		0			0
$426$	−0.139903	+	0.973048i	−0.00677833	+	0.0471443i
$427$	−4.18698	−	2.69081i	−0.202622	−	0.130217i
$428$	9.65005	+	11.1367i	0.466453	+	0.538315i
$429$	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	$0.663279\pi$
$432$	12.9447	−	14.9390i	0.622804	−	0.718754i
$433$	−32.5898	+	9.56922i	−1.56616	+	0.459867i	−0.945882	−	0.324511i	$-0.894800\pi$
$433$	−32.5898	+	9.56922i	−1.56616	+	0.459867i	−0.620283	+	0.784378i	$0.712982\pi$
$434$	0.0512961	−	0.112323i	0.00246229	−	0.00539167i
$435$		0			0
$436$	−20.7432			−0.993419
$437$	−28.0522	−	21.9300i	−1.34192	−	1.04905i
$438$	−0.914218			−0.0436830
$439$	−4.53831	−	31.5646i	−0.216602	−	1.50650i	−0.750456	−	0.660921i	$-0.770166\pi$
$439$	−4.53831	−	31.5646i	−0.216602	−	1.50650i	0.533854	−	0.845577i	$-0.320743\pi$
$440$		0			0
$441$	−8.84511	+	2.59716i	−0.421196	+	0.123674i
$442$	0.538668	−	0.621656i	0.0256218	−	0.0295691i
$443$	29.3691	+	8.62354i	1.39537	+	0.409717i	0.891091	−	0.453825i	$-0.149941\pi$
$443$	29.3691	+	8.62354i	1.39537	+	0.409717i	0.504277	+	0.863542i	$0.331759\pi$
$444$	−18.5950	+	11.9502i	−0.882477	+	0.567134i
$445$		0			0
$446$	0.531535	+	0.613424i	0.0251689	+	0.0290465i
$447$	16.2542	+	10.4459i	0.768797	+	0.494076i
$448$	1.71947	−	11.9592i	0.0812373	−	0.565018i
$449$	2.39840	−	16.6812i	0.113187	−	0.787236i	−0.851597	−	0.524196i	$-0.824366\pi$
$449$	2.39840	−	16.6812i	0.113187	−	0.787236i	0.964785	−	0.263040i	$-0.0847251\pi$
$450$		0			0
$451$	−8.05133	−	9.29173i	−0.379122	−	0.437530i
$452$	16.2145	+	35.5048i	0.762666	+	1.67001i
$453$	16.8366	−	10.8202i	0.791054	−	0.508380i
$454$	0.750400	+	0.220337i	0.0352180	+	0.0103409i
$455$		0			0
$456$	−2.50714	+	0.736163i	−0.117408	+	0.0344740i
$457$	1.12972	−	2.47375i	0.0528463	−	0.115717i	−0.881367	−	0.472432i	$-0.843376\pi$
$457$	1.12972	−	2.47375i	0.0528463	−	0.115717i	0.934213	+	0.356715i	$0.116103\pi$
$458$	−0.105195	−	0.731650i	−0.00491546	−	0.0341877i
$459$	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	$0.813046\pi$
$462$	−0.0394651	−	0.274486i	−0.00183608	−	0.0127702i
$463$	17.3020	−	37.8860i	0.804091	−	1.76071i	0.173130	−	0.984899i	$-0.444612\pi$
$463$	17.3020	−	37.8860i	0.804091	−	1.76071i	0.630961	−	0.775814i	$-0.282661\pi$
$464$	−17.0041	+	4.99286i	−0.789397	+	0.231788i
$465$		0			0
$466$	2.03119	+	0.596411i	0.0940931	+	0.0276282i
$467$	−14.8682	+	9.55519i	−0.688017	+	0.442161i	−0.837380	−	0.546621i	$-0.815914\pi$
$467$	−14.8682	+	9.55519i	−0.688017	+	0.442161i	0.149364	+	0.988782i	$0.452278\pi$
$468$	−3.54305	−	7.75819i	−0.163777	−	0.358623i
$469$	−1.98938	−	2.29587i	−0.0918610	−	0.106013i
$470$		0			0
$471$	0.821781	−	5.71561i	0.0378657	−	0.263361i
$472$	−0.401733	+	2.79411i	−0.0184913	+	0.128609i
$473$	9.23343	+	5.93396i	0.424553	+	0.272844i
$474$	0.185866	+	0.214501i	0.00853712	+	0.00985237i
$475$		0			0
$476$	11.2961	−	7.25953i	0.517754	−	0.332740i
$477$	0.526324	+	0.154543i	0.0240987	+	0.00707602i
$478$	−0.648752	+	0.748699i	−0.0296732	+	0.0342447i
$479$	11.4723	−	3.36858i	0.524184	−	0.153914i	−0.00892633	−	0.999960i	$-0.502841\pi$
$479$	11.4723	−	3.36858i	0.524184	−	0.153914i	0.533110	+	0.846046i	$0.321023\pi$
$480$		0			0
$481$	3.37991	+	23.5078i	0.154111	+	1.07186i
$482$	2.47780			0.112861
$483$	5.35195	−	5.13260i	0.243522	−	0.233541i
$484$	13.6687			0.621306
$485$		0			0
$486$	−0.585941	+	1.28303i	−0.0265788	+	0.0581995i
$487$	−18.1024	+	5.31536i	−0.820300	+	0.240862i	−0.664845	−	0.746981i	$-0.731503\pi$
$487$	−18.1024	+	5.31536i	−0.820300	+	0.240862i	−0.155455	+	0.987843i	$0.549684\pi$
$488$	0.741863	−	0.856156i	0.0335826	−	0.0387563i
$489$	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	$0.698990\pi$
$492$	−7.88425	−	9.09891i	−0.355450	−	0.410211i
$493$	−16.4384	−	10.5643i	−0.740349	−	0.475794i
$494$	−0.199387	+	1.38677i	−0.00897086	+	0.0623937i
$495$		0			0
$496$	−3.01291	−	1.93628i	−0.135284	−	0.0869416i
$497$	11.2912	+	13.0308i	0.506480	+	0.584509i
$498$	−0.159693	−	0.349679i	−0.00715602	−	0.0156695i
$499$	8.48768	−	5.45470i	0.379961	−	0.244186i	−0.336694	−	0.941614i	$-0.609309\pi$
$499$	8.48768	−	5.45470i	0.379961	−	0.244186i	0.716655	+	0.697428i	$0.245672\pi$
$500$		0			0
$501$	−12.7879	+	14.7581i	−0.571323	+	0.659341i
$502$	−2.32553	+	0.682837i	−0.103793	+	0.0304765i
$503$	−5.56885	+	12.1941i	−0.248303	+	0.543707i	−0.992210	−	0.124576i	$-0.960243\pi$
$503$	−5.56885	+	12.1941i	−0.248303	+	0.543707i	0.743907	+	0.668283i	$0.232970\pi$
$504$	0.154886	+	1.07726i	0.00689918	+	0.0479849i
$505$		0			0
$506$	0.500939	+	0.699196i	0.0222694	+	0.0310831i
$507$	−8.41804			−0.373858
$508$	4.97451	+	34.5985i	0.220708	+	1.53506i
$509$	8.03460	−	17.5933i	0.356127	−	0.779810i	−0.643766	−	0.765222i	$-0.722629\pi$
$509$	8.03460	−	17.5933i	0.356127	−	0.779810i	0.999894	−	0.0145879i	$-0.00464363\pi$
$510$		0			0
$511$	−10.5006	+	12.1183i	−0.464518	+	0.536082i
$512$	6.66205	+	1.95615i	0.294424	+	0.0864506i
$513$	−31.2297	+	20.0701i	−1.37882	+	0.886116i
$514$	0.650495	+	1.42439i	0.0286921	+	0.0628270i
$515$		0			0
$516$	9.04182	+	5.81083i	0.398044	+	0.255807i
$517$	0.789915	−	5.49398i	0.0347404	−	0.241625i
$518$	0.215227	−	1.49694i	0.00945652	−	0.0657716i
$519$	−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	$0.942857\pi$
$522$	0.664885	−	0.427296i	0.0291012	−	0.0187022i
$523$	−17.3487	−	5.09404i	−0.758605	−	0.222747i	−0.120519	−	0.992711i	$-0.538456\pi$
$523$	−17.3487	−	5.09404i	−0.758605	−	0.222747i	−0.638087	+	0.769964i	$0.720274\pi$
$524$	−17.0228	+	19.6454i	−0.743645	+	0.858212i
$525$		0			0
$526$	−0.320098	+	0.700917i	−0.0139569	+	0.0305614i
$527$	−0.561992	−	3.90874i	−0.0244808	−	0.170267i
$528$	−8.04304			−0.350028
$529$	−7.39715	+	21.7780i	−0.321615	+	0.946870i
$530$		0			0
$531$	2.28297	+	15.8784i	0.0990725	+	0.689064i
$532$	−9.50074	+	20.8037i	−0.411909	+	0.901955i
$533$	−12.4119	+	3.64448i	−0.537621	+	0.157860i
$534$	0.0370854	−	0.0427988i	0.00160484	−	0.00185209i
$535$		0			0
$536$	0.581697	−	0.373834i	0.0251255	−	0.0161472i
$537$	−6.37863	−	13.9672i	−0.275258	−	0.602731i
$538$	0.169194	+	0.195260i	0.00729445	+	0.00841825i
$539$	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	$-0.0509507\pi$
$542$	0.486530	+	0.312674i	0.0208983	+	0.0134305i
$543$	−0.536306	−	0.618931i	−0.0230151	−	0.0265609i
$544$	1.90571	+	4.17292i	0.0817065	+	0.178912i
$545$		0			0
$546$	−0.279953	−	0.0822015i	−0.0119809	−	0.00351790i
$547$	−19.7384	+	22.7793i	−0.843952	+	0.973973i	−0.999905	−	0.0137919i	$-0.995610\pi$
$547$	−19.7384	+	22.7793i	−0.843952	+	0.973973i	0.155953	+	0.987764i	$0.450155\pi$
$548$	−41.1491	+	12.0825i	−1.75780	+	0.516138i
$549$	2.67436	−	5.85603i	0.114139	−	0.249929i
$550$		0			0
$551$	33.2819			1.41786
$552$	0.983001	+	1.37204i	0.0418393	+	0.0583981i
$553$	4.97813			0.211692
$554$	0.285906	+	1.98852i	0.0121470	+	0.0844840i
$555$		0			0
$556$	−31.2953	+	9.18913i	−1.32722	+	0.389706i
$557$	14.1622	−	16.3440i	0.600071	−	0.692519i	−0.371724	−	0.928343i	$-0.621233\pi$
$557$	14.1622	−	16.3440i	0.600071	−	0.692519i	0.971796	+	0.235824i	$0.0757788\pi$
$558$	0.153253	+	0.0449991i	0.00648771	+	0.00190496i
$559$	9.71499	−	6.24345i	0.410900	−	0.264070i
$560$		0			0
$561$	−5.80751	−	6.70222i	−0.245193	−	0.282968i
$562$	1.05631	+	0.678850i	0.0445578	+	0.0286356i
$563$	0.0407395	−	0.283349i	0.00171696	−	0.0119418i	−0.988945	−	0.148283i	$-0.952625\pi$
$563$	0.0407395	−	0.283349i	0.00171696	−	0.0119418i	0.990662	+	0.136341i	$0.0435344\pi$
$564$	0.773524	−	5.37998i	0.0325712	−	0.226538i
$565$		0			0
$566$	−1.36864	−	1.57949i	−0.0575281	−	0.0663910i
$567$	0.642315	+	1.40647i	0.0269747	+	0.0590663i
$568$	−3.30156	+	2.12179i	−0.138531	+	0.0890282i
$569$	1.66147	+	0.487852i	0.0696525	+	0.0204518i	0.316373	−	0.948635i	$-0.397535\pi$
$569$	1.66147	+	0.487852i	0.0696525	+	0.0204518i	−0.246721	+	0.969087i	$0.579353\pi$
$570$		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	$0.551919\pi$
$572$	−3.60407	+	7.89181i	−0.150694	+	0.329973i
$573$	0.607097	+	4.22245i	0.0253618	+	0.176395i
$574$	0.823739			0.0343822
$575$		0			0
$576$	15.6282			0.651174
$577$	3.43290	+	23.8763i	0.142913	+	0.993985i	0.927462	+	0.373917i	$0.121986\pi$
$577$	3.43290	+	23.8763i	0.142913	+	0.993985i	−0.784549	+	0.620067i	$0.787105\pi$
$578$	−0.0733005	+	0.160506i	−0.00304890	+	0.00667616i
$579$	4.63848	−	1.36198i	0.192769	−	0.0566020i
$580$		0			0
$581$	−6.46934	−	1.89957i	−0.268394	−	0.0788074i
$582$	−0.410917	+	0.264080i	−0.0170330	+	0.0109465i
$583$	−0.231798	−	0.507567i	−0.00960009	−	0.0210213i
$584$	−2.39009	−	2.75831i	−0.0989026	−	0.114140i
$585$		0			0
$586$	0.0536241	−	0.372964i	0.00221519	−	0.0154070i
$587$	−4.77952	+	33.2423i	−0.197272	+	1.37206i	0.614885	+	0.788617i	$0.289202\pi$
$587$	−4.77952	+	33.2423i	−0.197272	+	1.37206i	−0.812157	+	0.583439i	$0.801707\pi$
$588$	7.72499	+	4.96455i	0.318573	+	0.204734i
$589$	4.40458	+	5.08316i	0.181488	+	0.209448i
$590$		0			0
$591$	0.220925	−	0.141980i	0.00908764	−	0.00584027i
$592$	−42.0867	−	12.3578i	−1.72975	−	0.507901i
$593$	19.5470	−	22.5585i	0.802700	−	0.926365i	−0.195827	−	0.980639i	$-0.562739\pi$
$593$	19.5470	−	22.5585i	0.802700	−	0.926365i	0.998526	+	0.0542739i	$0.0172844\pi$
$594$	0.860418	−	0.252641i	0.0353034	−	0.0103660i
$595$		0			0
$596$	5.47807	+	38.1008i	0.224391	+	1.56067i
$597$	−4.32625			−0.177062
$598$	0.888133	−	0.173830i	0.0363185	−	0.00710843i
$599$	4.70186			0.192113			0.0960564	−	0.995376i	$-0.469377\pi$
$599$	4.70186			0.192113			0.0960564	+	0.995376i	$0.469377\pi$
$600$		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	$-0.00753375\pi$
$602$	−0.705584	+	0.207178i	−0.0287575	+	0.00844395i
$603$	2.57325	−	2.96969i	0.104791	−	0.120935i
$604$	38.2569	+	11.2332i	1.55665	+	0.457073i
$605$		0			0
$606$	−0.164711	−	0.360666i	−0.00669091	−	0.0146511i
$607$	−25.2756	−	29.1696i	−1.02591	−	1.18396i	−0.982759	−	0.184891i	$-0.940807\pi$
$607$	−25.2756	−	29.1696i	−1.02591	−	1.18396i	−0.0431477	−	0.999069i	$-0.513739\pi$
$608$	−6.57319	−	4.22433i	−0.266578	−	0.171319i
$609$	−0.986403	+	6.86058i	−0.0399711	+	0.278005i
$610$		0			0
$611$	−4.91289	−	3.15732i	−0.198754	−	0.127732i
$612$	11.3740	+	13.1263i	0.459766	+	0.530599i
$613$	−7.81638	−	17.1155i	−0.315700	−	0.691288i	0.683554	−	0.729900i	$-0.260433\pi$
$613$	−7.81638	−	17.1155i	−0.315700	−	0.691288i	−0.999254	+	0.0386125i	$0.987706\pi$
$614$	−0.663370	+	0.426322i	−0.0267714	+	0.0172050i
$615$		0			0
$616$	0.724983	−	0.836675i	0.0292104	−	0.0337106i
$617$	15.2099	−	4.46602i	0.612326	−	0.179795i	0.0391580	−	0.999233i	$-0.487532\pi$
$617$	15.2099	−	4.46602i	0.612326	−	0.179795i	0.573168	+	0.819438i	$0.305714\pi$
$618$	0.356430	−	0.780473i	0.0143377	−	0.0313952i
$619$	4.22984	+	29.4192i	0.170012	+	1.18246i	0.878854	+	0.477091i	$0.158309\pi$
$619$	4.22984	+	29.4192i	0.170012	+	1.18246i	−0.708842	+	0.705367i	$0.750782\pi$
$620$		0			0
$621$	18.8915	+	14.7685i	0.758091	+	0.592641i
$622$	2.05794			0.0825158
$623$	−0.141357	−	0.983162i	−0.00566336	−	0.0393896i
$624$	−3.51546	+	7.69778i	−0.140731	+	0.308158i
$625$		0			0
$626$	1.29956	−	1.49977i	0.0519408	−	0.0599429i
$627$	14.4930	+	4.25553i	0.578794	+	0.169949i
$628$	9.67769	−	6.21947i	0.386182	−	0.248184i
$629$	−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	$0.789542\pi$
$632$	−0.161257	+	1.12156i	−0.00641444	+	0.0446134i
$633$	0.934652	−	6.50065i	0.0371491	−	0.258378i
$634$	0.945584	+	0.607690i	0.0375539	+	0.0241345i
$635$		0			0
$636$	−0.226988	−	0.497034i	−0.00900066	−	0.0197087i
$637$	8.30012	−	5.33416i	0.328863	−	0.211347i
$638$	−0.771397	−	0.226502i	−0.0305399	−	0.00896732i
$639$	−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	$0.932793\pi$
$642$	0.0927990	+	0.645431i	0.00366248	+	0.0254731i
$643$	7.45857			0.294137			0.147069	−	0.989126i	$-0.453016\pi$
$643$	7.45857			0.294137			0.147069	+	0.989126i	$0.453016\pi$
$644$	14.7101	+	1.36187i	0.579659	+	0.0536653i
$645$		0			0
$646$	−0.406038	−	2.82406i	−0.0159754	−	0.111111i
$647$	−3.17102	+	6.94356i	−0.124666	+	0.272980i	−0.961666	−	0.274222i	$-0.911580\pi$
$647$	−3.17102	+	6.94356i	−0.124666	+	0.272980i	0.837001	+	0.547202i	$0.184307\pi$
$648$	−0.337683	+	0.0991526i	−0.0132654	+	0.00389508i
$649$	10.6860	−	12.3323i	0.419462	−	0.484085i
$650$		0			0
$651$	−1.17836	+	0.757286i	−0.0461836	+	0.0296804i
$652$	7.28589	+	15.9539i	0.285337	+	0.624802i
$653$	25.4564	+	29.3782i	0.996185	+	1.14966i	0.988734	+	0.149686i	$0.0478264\pi$
$653$	25.4564	+	29.3782i	0.996185	+	1.14966i	0.00745135	+	0.999972i	$0.497628\pi$
$654$	−0.772173	−	0.496246i	−0.0301944	−	0.0194047i
$655$		0			0
$656$	3.40014	−	23.6485i	0.132753	−	0.923319i
$657$	−17.4484	−	11.2134i	−0.680726	−	0.437476i
$658$	0.243529	+	0.281047i	0.00949374	+	0.0109564i
$659$	−5.38310	−	11.7873i	−0.209696	−	0.459170i	0.775335	−	0.631551i	$-0.217581\pi$
$659$	−5.38310	−	11.7873i	−0.209696	−	0.459170i	−0.985030	+	0.172381i	$0.944854\pi$
$660$		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	$0.391082\pi$
$662$	−0.946639	+	1.09248i	−0.0367922	+	0.0424604i
$663$	−8.95287	+	2.62880i	−0.347701	+	0.102094i
$664$	0.637531	−	1.39600i	0.0247410	−	0.0541753i
$665$		0			0
$666$	1.95619			0.0758007
$667$	−7.08990	−	20.2955i	−0.274522	−	0.785844i
$668$	−38.9037			−1.50523
$669$	−1.31033	−	9.11356i	−0.0506604	−	0.352351i
$670$		0			0
$671$	−6.28342	+	1.84498i	−0.242569	+	0.0712246i
$672$	1.06560	−	1.22977i	0.0411064	−	0.0474393i
$673$	−2.27218	−	0.667173i	−0.0875862	−	0.0257176i	0.237646	−	0.971352i	$-0.423624\pi$
$673$	−2.27218	−	0.667173i	−0.0875862	−	0.0257176i	−0.325232	+	0.945634i	$0.605442\pi$
$674$	2.03488	−	1.30773i	0.0783805	−	0.0503721i
$675$		0			0
$676$	−10.9824	−	12.6744i	−0.422402	−	0.487478i
$677$	29.1912	+	18.7600i	1.12191	+	0.721006i	0.963856	−	0.266425i	$-0.0858423\pi$
$677$	29.1912	+	18.7600i	1.12191	+	0.721006i	0.158052	+	0.987431i	$0.449479\pi$
$678$	−0.245801	+	1.70958i	−0.00943993	+	0.0656562i
$679$	−1.21925	+	8.48004i	−0.0467904	+	0.325434i
$680$		0			0
$681$	−5.80963	−	6.70467i	−0.222626	−	0.256924i
$682$	−0.0674940	−	0.147791i	−0.00258448	−	0.00565922i
$683$	19.5711	−	12.5776i	0.748869	−	0.481269i	−0.109702	−	0.993965i	$-0.534990\pi$
$683$	19.5711	−	12.5776i	0.748869	−	0.481269i	0.858570	+	0.512696i	$0.171353\pi$
$684$	−28.3845	−	8.33444i	−1.08531	−	0.318675i
$685$		0			0
$686$	−1.51832	+	0.445819i	−0.0579698	+	0.0170215i
$687$	−3.48319	+	7.62712i	−0.132892	+	0.290993i
$688$	3.03539	+	21.1116i	0.115723	+	0.804872i
$689$	−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	$0.827133\pi$
$692$	−6.11911	−	42.5593i	−0.232614	−	1.61786i
$693$	2.61351	−	5.72279i	0.0992790	−	0.217391i
$694$	−0.510520	+	0.149902i	−0.0193791	+	0.00569020i
$695$		0			0
$696$	−1.51372	−	0.444470i	−0.0573776	−	0.0168476i
$697$	22.1612	−	14.2422i	0.839417	−	0.539461i
$698$	−0.305688	−	0.669363i	−0.0115705	−	0.0253358i
$699$	−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	$0.898947\pi$
$702$	0.134276	−	0.933908i	0.00506791	−	0.0352481i
$703$	69.2989	+	44.5357i	2.61366	+	1.67969i
$704$	−10.4105	−	12.0144i	−0.392362	−	0.452810i
$705$		0			0
$706$	−1.93952	+	1.24645i	−0.0729946	+	0.0469108i
$707$	−6.67261	−	1.95925i	−0.250949	−	0.0736854i
$708$	10.4643	−	12.0764i	0.393271	−	0.453859i
$709$	32.8793	−	9.65422i	1.23481	−	0.362572i	0.401745	−	0.915752i	$-0.368404\pi$
$709$	32.8793	−	9.65422i	1.23481	−	0.362572i	0.833062	+	0.553180i	$0.186586\pi$
$710$		0			0
$711$	0.916390	+	6.37363i	0.0343673	+	0.239030i
$712$	0.226084			0.00847285
$713$	2.16144	−	3.76877i	0.0809467	−	0.141142i
$714$	0.594172			0.0222363
$715$		0			0
$716$	12.7077	−	27.8260i	0.474909	−	1.03990i
$717$	10.7825	−	3.16603i	0.402680	−	0.118238i
$718$	0.326770	−	0.377112i	0.0121949	−	0.0140737i
$719$	−22.3827	−	6.57217i	−0.834735	−	0.245100i	−0.163685	−	0.986513i	$-0.552338\pi$
$719$	−22.3827	−	6.57217i	−0.834735	−	0.245100i	−0.671050	+	0.741412i	$0.734156\pi$
$720$		0			0
$721$	−6.25157	−	13.6890i	−0.232821	−	0.509806i
$722$	2.08543	+	2.40672i	0.0776117	+	0.0895687i
$723$	−23.6451	−	15.1958i	−0.879371	−	0.565138i
$724$	0.232195	−	1.61495i	0.00862947	−	0.0600193i
$725$		0			0
$726$	0.508824	+	0.327001i	0.0188842	+	0.0121362i
$727$	26.3834	+	30.4481i	0.978507	+	1.12926i	0.991600	+	0.129343i	$0.0412867\pi$
$727$	26.3834	+	30.4481i	0.978507	+	1.12926i	−0.0130932	+	0.999914i	$0.504168\pi$
$728$	−0.483883	−	1.05956i	−0.0179339	−	0.0392698i
$729$	10.9363	−	7.02833i	0.405048	−	0.260309i
$730$		0			0
$731$	−15.4005	+	17.7731i	−0.569607	+	0.657361i
$732$	−6.15303	+	1.80669i	−0.227422	+	0.0667773i
$733$	9.43781	−	20.6659i	0.348594	−	0.763313i	−0.651396	−	0.758738i	$-0.725816\pi$
$733$	9.43781	−	20.6659i	0.348594	−	0.763313i	0.999990	−	0.00457542i	$-0.00145641\pi$
$734$	0.154499	+	1.07456i	0.00570266	+	0.0396629i
$735$		0			0
$736$	−1.17576	+	4.90825i	−0.0433391	+	0.180921i
$737$	−3.99714			−0.147236
$738$	0.151637	+	1.05466i	0.00558182	+	0.0388224i
$739$	−7.47356	+	16.3648i	−0.274919	+	0.601989i	−0.995849	−	0.0910188i	$-0.970988\pi$
$739$	−7.47356	+	16.3648i	−0.274919	+	0.601989i	0.720930	+	0.693008i	$0.243715\pi$
$740$		0			0
$741$	10.4075	−	12.0109i	0.382328	−	0.441230i
$742$	0.0358708	+	0.0105326i	0.00131686	+	0.000386664i
$743$	4.89833	−	3.14797i	0.179702	−	0.115488i	−0.447697	−	0.894185i	$-0.647756\pi$
$743$	4.89833	−	3.14797i	0.179702	−	0.115488i	0.627399	+	0.778698i	$0.284119\pi$
$744$	−0.132445	−	0.290013i	−0.00485566	−	0.0106324i
$745$		0			0
$746$	2.16002	+	1.38816i	0.0790840	+	0.0508242i
$747$	1.24117	−	8.63256i	0.0454122	−	0.315849i
$748$	2.51438	−	17.4879i	0.0919347	−	0.639420i
$749$	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	$0.809589\pi$
$752$	9.07372	−	5.83133i	0.330885	−	0.212647i
$753$	26.3797	+	7.74578i	0.961330	+	0.282272i
$754$	−0.553942	+	0.639283i	−0.0201734	+	0.0232813i
$755$		0			0
$756$	6.39819	−	14.0101i	0.232700	−	0.509542i
$757$	−1.15607	−	8.04064i	−0.0420180	−	0.292242i	−0.999986	−	0.00536536i	$-0.998292\pi$
$757$	−1.15607	−	8.04064i	−0.0420180	−	0.292242i	0.957968	−	0.286877i	$-0.0926169\pi$
$758$	2.94048			0.106803
$759$	−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	$-0.223184\pi$
$762$	−0.642532	+	1.40695i	−0.0232765	+	0.0509684i
$763$	−15.4470	+	4.53565i	−0.559219	+	0.164201i
$764$	−5.56539	+	6.42281i	−0.201349	+	0.232369i
$765$		0			0
$766$	2.30544	−	1.48162i	0.0832990	−	0.0535330i
$767$	−7.13228	−	15.6175i	−0.257532	−	0.563915i
$768$	−10.0730	−	11.6249i	−0.363478	−	0.419476i
$769$	12.2803	+	7.89208i	0.442840	+	0.284596i	0.742998	−	0.669294i	$-0.233403\pi$
$769$	12.2803	+	7.89208i	0.442840	+	0.284596i	−0.300158	+	0.953889i	$0.597040\pi$
$770$		0			0
$771$	2.52790	−	17.5820i	0.0910403	−	0.633199i
$772$	8.10215	+	5.20693i	0.291603	+	0.187402i
$773$	−11.3054	−	13.0471i	−0.406625	−	0.469271i	0.515091	−	0.857136i	$-0.327758\pi$
$773$	−11.3054	−	13.0471i	−0.406625	−	0.469271i	−0.921716	+	0.387865i	$0.873213\pi$
$774$	−0.395142	−	0.865241i	−0.0142031	−	0.0311004i
$775$		0			0
$776$	−1.87104	−	0.549388i	−0.0671666	−	0.0197219i
$777$	−11.2342	+	12.9650i	−0.403026	+	0.465117i
$778$	−1.07306	+	0.315080i	−0.0384712	+	0.0112962i
$779$	−18.6391	+	40.8139i	−0.667815	+	1.46231i
$780$		0			0
$781$	22.6867			0.811795
$782$	−1.63563	+	0.849200i	−0.0584899	+	0.0303673i
$783$	−22.4134			−0.800991
$784$	2.59332	+	18.0369i	0.0926186	+	0.644176i
$785$		0			0
$786$	−1.10366	+	0.324065i	−0.0393663	+	0.0115590i
$787$	10.0471	−	11.5950i	0.358142	−	0.413318i	−0.547875	−	0.836561i	$-0.684563\pi$
$787$	10.0471	−	11.5950i	0.358142	−	0.413318i	0.906016	+	0.423243i	$0.139108\pi$
$788$	0.501995	+	0.147399i	0.0178828	+	0.00525087i
$789$	7.35320	−	4.72561i	0.261781	−	0.168236i
$790$		0			0
$791$	19.8380	+	22.8942i	0.705356	+	0.814025i
$792$	1.20467	+	0.774198i	0.0428063	+	0.0275099i
$793$	−0.980582	+	6.82010i	−0.0348215	+	0.242189i
$794$	−0.154578	+	1.07511i	−0.00548577	+	0.0381544i
$795$		0			0
$796$	−5.64417	−	6.51371i	−0.200052	−	0.230872i
$797$	−10.4360	−	22.8517i	−0.369663	−	0.809448i	−0.999465	−	0.0326932i	$-0.989592\pi$
$797$	−10.4360	−	22.8517i	−0.369663	−	0.809448i	0.629803	−	0.776755i	$-0.283136\pi$
$798$	−0.851362	+	0.547137i	−0.0301379	+	0.0193685i
$799$	11.4109	+	3.35055i	0.403690	+	0.118534i
$800$		0			0
$801$	1.23275	−	0.361967i	0.0435570	−	0.0127895i
$802$	1.23584	−	2.70612i	0.0436392	−	0.0955565i
$803$	3.00258	+	20.8834i	0.105959	+	0.736959i
$804$	−3.91419			−0.138043
$805$		0			0
$806$	−0.170947			−0.00602136
$807$	−0.417094	−	2.90095i	−0.0146824	−	0.102118i
$808$	0.657563	−	1.43986i	0.0231330	−	0.0506542i
$809$	−21.8919	+	6.42804i	−0.769678	+	0.225998i	−0.642917	−	0.765935i	$-0.722276\pi$
$809$	−21.8919	+	6.42804i	−0.769678	+	0.225998i	−0.126761	+	0.991933i	$0.540458\pi$
$810$		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	$0.313884\pi$
$812$	−11.6164	+	7.46538i	−0.407654	+	0.261984i
$813$	−2.72530	−	5.96757i	−0.0955803	−	0.209292i
$814$	−1.30309	−	1.50385i	−0.0456734	−	0.0527099i
$815$		0			0
$816$	2.45256	−	17.0579i	0.0858567	−	0.597147i
$817$	5.70046	−	39.6476i	0.199434	−	1.38709i
$818$	−1.20400	−	0.773766i	−0.0420970	−	0.0270541i
$819$	−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	$-0.00439753\pi$
$822$	−1.82085	−	0.534648i	−0.0635093	−	0.0186480i
$823$	0.752583	−	0.868528i	0.0262334	−	0.0302750i	−0.742481	−	0.669867i	$-0.766351\pi$
$823$	0.752583	−	0.868528i	0.0262334	−	0.0302750i	0.768715	+	0.639592i	$0.220897\pi$
$824$	3.28662	−	0.965039i	0.114495	−	0.0336187i
$825$		0			0
$826$	0.155592	+	1.08217i	0.00541374	+	0.0376534i
$827$	15.3873			0.535069			0.267534	−	0.963548i	$-0.413791\pi$
$827$	15.3873			0.535069			0.267534	+	0.963548i	$0.413791\pi$
$828$	0.964240	+	19.0844i	0.0335096	+	0.663230i
$829$	−43.7168			−1.51835			−0.759174	−	0.650888i	$-0.774397\pi$
$829$	−43.7168			−1.51835			−0.759174	+	0.650888i	$0.774397\pi$
$830$		0			0
$831$	9.46680	−	20.7294i	0.328400	−	0.719095i
$832$	−16.0489	+	4.71239i	−0.556396	+	0.163373i
$833$	−13.1576	+	15.1846i	−0.455883	+	0.526117i
$834$	−1.38481	−	0.406618i	−0.0479522	−	0.0140800i
$835$		0			0
$836$	12.5008	+	27.3729i	0.432349	+	0.946712i
$837$	−2.96623	−	3.42321i	−0.102528	−	0.118323i
$838$	0.992833	+	0.638055i	0.0342969	+	0.0220413i
$839$	1.60650	−	11.1735i	0.0554627	−	0.385751i	−0.943116	−	0.332462i	$-0.892121\pi$
$839$	1.60650	−	11.1735i	0.0554627	−	0.385751i	0.998579	−	0.0532888i	$-0.0169704\pi$
$840$		0			0
$841$	−7.49181	−	4.81469i	−0.258338	−	0.166024i
$842$	−0.751277	−	0.867020i	−0.0258907	−	0.0298795i
$843$	−5.91692	−	12.9563i	−0.203790	−	0.446237i
$844$	11.0069	−	7.07372i	0.378874	−	0.243488i
$845$		0			0
$846$	−0.315003	+	0.363533i	−0.0108300	+	0.0124985i
$847$	10.1788	−	2.98877i	0.349748	−	0.102695i
$848$	0.450441	−	0.986328i	0.0154682	−	0.0338707i
$849$	3.37394	+	23.4663i	0.115793	+	0.805361i
$850$		0			0
$851$	12.3956	−	51.7460i	0.424917	−	1.77383i
$852$	22.2160			0.761106
$853$	2.37985	+	16.5522i	0.0814845	+	0.566737i	0.989135	+	0.147010i	$0.0469650\pi$
$853$	2.37985	+	16.5522i	0.0814845	+	0.566737i	−0.907651	+	0.419727i	$0.862126\pi$
$854$	0.182267	−	0.399108i	0.00623704	−	0.0136572i
$855$		0			0
$856$	−1.70474	+	1.96737i	−0.0582667	+	0.0672433i
$857$	5.93618	+	1.74302i	0.202776	+	0.0595405i	0.381543	−	0.924351i	$-0.375393\pi$
$857$	5.93618	+	1.74302i	0.202776	+	0.0595405i	−0.178767	+	0.983891i	$0.557211\pi$
$858$	−0.322961	+	0.207554i	−0.0110257	+	0.00708579i
$859$	−3.60612	−	7.89631i	−0.123039	−	0.269419i	0.838082	−	0.545544i	$-0.183677\pi$
$859$	−3.60612	−	7.89631i	−0.123039	−	0.269419i	−0.961122	+	0.276125i	$0.910950\pi$
$860$		0			0
$861$	−7.86077	−	5.05181i	−0.267894	−	0.172165i
$862$	0.117416	−	0.816646i	0.00399921	−	0.0278151i
$863$	1.61006	−	11.1982i	0.0548072	−	0.381192i	−0.943894	−	0.330248i	$-0.892868\pi$
$863$	1.61006	−	11.1982i	0.0548072	−	0.381192i	0.998701	−	0.0509446i	$-0.0162232\pi$
$864$	4.42666	+	2.84484i	0.150598	+	0.0967834i
$865$		0			0
$866$	−1.24386	−	2.72368i	−0.0422682	−	0.0925546i
$867$	1.68384	−	1.08214i	0.0571861	−	0.0367513i
$868$	−2.67752	−	0.786189i	−0.0908808	−	0.0266850i
$869$	4.28939	−	4.95022i	0.145508	−	0.167925i
$870$		0			0
$871$	−1.74707	+	3.82555i	−0.0591973	+	0.129624i
$872$	−0.521499	−	3.62711i	−0.0176602	−	0.122829i
$873$	−11.0817			−0.375058
$874$	1.56164	−	2.72293i	0.0528232	−	0.0921045i
$875$		0			0
$876$	2.94027	+	20.4500i	0.0993426	+	0.690943i
$877$	−10.2913	+	22.5349i	−0.347514	+	0.760950i	0.652481	+	0.757805i	$0.273728\pi$
$877$	−10.2913	+	22.5349i	−0.347514	+	0.760950i	−0.999995	+	0.00314460i	$0.998999\pi$
$878$	2.69735	−	0.792013i	0.0910311	−	0.0267291i
$879$	−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	$0.128344\pi$
$882$	−0.337594	−	0.739229i	−0.0113674	−	0.0248911i
$883$	−8.56278	−	9.88198i	−0.288161	−	0.332555i	0.593150	−	0.805092i	$-0.297884\pi$
$883$	−8.56278	−	9.88198i	−0.288161	−	0.332555i	−0.881311	+	0.472537i	$0.843338\pi$
$884$	−15.6382	−	10.0501i	−0.525969	−	0.338020i
$885$		0			0
$886$	−0.384017	+	2.67090i	−0.0129013	+	0.0897305i
$887$	−18.6668	−	11.9964i	−0.626770	−	0.402800i	0.188343	−	0.982103i	$-0.439688\pi$
$887$	−18.6668	−	11.9964i	−0.626770	−	0.402800i	−0.815112	+	0.579303i	$0.803325\pi$
$888$	−2.55708	−	2.95103i	−0.0858101	−	0.0990301i
$889$	11.2696	+	24.6770i	0.377971	+	0.827641i
$890$		0			0
$891$	1.95204	+	0.573170i	0.0653957	+	0.0192019i
$892$	12.0121	−	13.8627i	0.402195	−	0.464158i
$893$	−19.4355	+	5.70679i	−0.650385	+	0.190970i
$894$	−0.707574	+	1.54937i	−0.0236648	+	0.0518187i
$895$		0			0
$896$	4.31954			0.144306
$897$	−9.54133	−	3.78790i	−0.318576	−	0.126474i
$898$	1.48567			0.0495775
$899$	0.577928	+	4.01958i	0.0192750	+	0.134060i
$900$		0			0
$901$	1.14714	−	0.336832i	0.0382169	−	0.0112215i
$902$	0.709772	−	0.819121i	0.0236328	−	0.0272737i
$903$	8.00382	+	2.35013i	0.266351	+	0.0782076i
$904$	−5.80064	+	3.72784i	−0.192926	+	0.123986i
$905$		0			0
$906$	1.15539	+	1.33339i	0.0383853	+	0.0442990i
$907$	18.0240	+	11.5834i	0.598479	+	0.384619i	0.804521	−	0.593924i	$-0.202422\pi$
$907$	18.0240	+	11.5834i	0.598479	+	0.384619i	−0.206042	+	0.978543i	$0.566058\pi$
$908$	2.51530	−	17.4943i	0.0834730	−	0.580568i
$909$	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	$0.549488\pi$
$912$	12.1935	+	26.6999i	0.403766	+	0.884123i
$913$	−7.46321	+	4.79631i	−0.246996	+	0.158735i
$914$	0.230030	+	0.0675428i	0.00760870	+	0.00223412i
$915$		0			0
$916$	−16.0279	+	4.70621i	−0.529576	+	0.155497i
$917$	−8.38091	+	18.3516i	−0.276762	+	0.606024i
$918$	0.273443	+	1.90184i	0.00902496	+	0.0627700i
$919$	29.9408			0.987657			0.493829	−	0.869559i	$-0.335597\pi$
$919$	29.9408			0.987657			0.493829	+	0.869559i	$0.335597\pi$
$920$		0			0
$921$	8.94494			0.294746
$922$	−0.448462	−	3.11912i	−0.0147693	−	0.102723i
$923$	9.91594	−	21.7129i	0.326387	−	0.714688i
$924$	−6.01302	+	1.76558i	−0.197814	+	0.0580834i
$925$		0			0
$926$	3.52295	+	1.03443i	0.115771	+	0.0339935i
$927$	16.3756	−	10.5240i	0.537846	−	0.345653i
$928$	−1.95974	−	4.29124i	−0.0643318	−	0.140867i
$929$	8.14358	+	9.39819i	0.267182	+	0.308345i	0.873448	−	0.486917i	$-0.161879\pi$
$929$	8.14358	+	9.39819i	0.267182	+	0.308345i	−0.606266	+	0.795262i	$0.707333\pi$
$930$		0			0
$931$	4.87026	−	33.8734i	0.159616	−	1.11016i
$932$	6.80843	−	47.3537i	0.223017	−	1.55112i
$933$	−19.6385	−	12.6209i	−0.642934	−	0.413189i
$934$	−1.02031	−	1.17750i	−0.0333855	−	0.0385289i
$935$		0			0
$936$	1.26750	−	0.814576i	0.0414297	−	0.0266252i
$937$	9.15473	+	2.68807i	0.299072	+	0.0878155i	0.427826	−	0.903861i	$-0.359280\pi$
$937$	9.15473	+	2.68807i	0.299072	+	0.0878155i	−0.128754	+	0.991677i	$0.541098\pi$
$938$	0.175376	−	0.202394i	0.00572621	−	0.00660840i
$939$	−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	$0.936882\pi$
$942$	0.509046			0.0165856
$943$	28.8591	+	2.67180i	0.939782	+	0.0870058i
$944$	31.7099			1.03207
$945$		0			0
$946$	−0.401948	+	0.880143i	−0.0130684	+	0.0286159i
$947$	11.9343	−	3.50424i	0.387814	−	0.113872i	−0.0820124	−	0.996631i	$-0.526135\pi$
$947$	11.9343	−	3.50424i	0.387814	−	0.113872i	0.469826	+	0.882759i	$0.344317\pi$
$948$	4.20038	−	4.84750i	0.136422	−	0.157439i
$949$	21.2993	+	6.25405i	0.691405	+	0.203015i
$950$		0			0
$951$	−5.29668	−	11.5981i	−0.171757	−	0.376095i
$952$	1.55338	+	1.79269i	0.0503452	+	0.0581015i
$953$	−11.2590	−	7.23572i	−0.364715	−	0.234388i	0.345429	−	0.938445i	$-0.387734\pi$
$953$	−11.2590	−	7.23572i	−0.364715	−	0.234388i	−0.710143	+	0.704057i	$0.751370\pi$
$954$	−0.00688198	+	0.0478652i	−0.000222812	+	0.00154969i
$955$		0			0
$956$	18.8341	+	12.1039i	0.609137	+	0.391469i
$957$	5.97219	+	6.89227i	0.193053	+	0.222795i
$958$	0.437868	+	0.958797i	0.0141469	+	0.0309773i
$959$	−28.0009	+	17.9951i	−0.904197	+	0.581092i
$960$		0			0
$961$	19.7633	−	22.8080i	0.637524	−	0.735742i
$962$	−2.00885	+	0.589852i	−0.0647680	+	0.0190176i
$963$	−6.14545	+	13.4567i	−0.198034	+	0.433635i
$964$	−7.96900	−	55.4256i	−0.256664	−	1.78514i
$965$		0			0
$966$	0.515009	+	0.402610i	0.0165701	+	0.0129538i
$967$	24.7635			0.796341			0.398170	−	0.917311i	$-0.369645\pi$
$967$	24.7635			0.796341			0.398170	+	0.917311i	$0.369645\pi$
$968$	0.343642	+	2.39008i	0.0110451	+	0.0768202i
$969$	−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	$0.319523\pi$
$972$	30.5845	+	8.98041i	0.980997	+	0.288047i
$973$	−21.2956	+	13.6859i	−0.682707	+	0.438749i
$974$	−0.690922	−	1.51291i	−0.0221386	−	0.0484767i
$975$		0			0
$976$	−10.7056	−	6.88004i	−0.342676	−	0.220225i
$977$	1.03522	−	7.20015i	0.0331198	−	0.230353i	−0.966538	−	0.256525i	$-0.917423\pi$
$977$	1.03522	−	7.20015i	0.0331198	−	0.230353i	0.999657	+	0.0261716i	$0.00833162\pi$
$978$	−0.110449	+	0.768191i	−0.00353178	+	0.0245640i
$979$	−1.09945	−	0.706574i	−0.0351386	−	0.0225822i
$980$		0			0
$981$	−8.65065	−	18.9423i	−0.276194	−	0.604780i
$982$	−1.62521	+	1.04446i	−0.0518627	+	0.0333301i
$983$	−30.9104	−	9.07613i	−0.985890	−	0.289483i	−0.251236	−	0.967926i	$-0.580837\pi$
$983$	−30.9104	−	9.07613i	−0.985890	−	0.289483i	−0.734654	+	0.678442i	$0.762655\pi$
$984$	1.39280	−	1.60738i	0.0444008	−	0.0512412i
$985$		0			0
$986$	0.715594	−	1.56693i	0.0227892	−	0.0499013i
$987$	−0.600344	−	4.17548i	−0.0191092	−	0.132907i
$988$	31.6618			1.00729
$989$	−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	$-0.100642\pi$
$992$	0.396047	−	0.867221i	0.0125745	−	0.0275343i
$993$	15.7335	−	4.61978i	0.499288	−	0.146604i
$994$	−0.995387	+	1.14874i	−0.0315718	+	0.0364358i
$995$		0			0
$996$	−7.30834	+	4.69678i	−0.231574	+	0.148823i
$997$	8.76152	+	19.1851i	0.277480	+	0.607597i	0.996141	−	0.0877636i	$-0.0279720\pi$
$997$	8.76152	+	19.1851i	0.277480	+	0.607597i	−0.718661	+	0.695360i	$0.755245\pi$
$998$	0.582455	+	0.672189i	0.0184373	+	0.0212778i
$999$	−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.k.a.26.1		10
5.2	odd	4		575.2.p.a.49.1		20
5.3	odd	4		575.2.p.a.49.2		20
5.4	even	2		115.2.g.a.26.1	✓	10
23.8	even	11	inner	575.2.k.a.376.1		10
115.8	odd	44		575.2.p.a.399.1		20
115.54	even	22		115.2.g.a.31.1	yes	10
115.59	even	22		2645.2.a.n.1.4		5
115.77	odd	44		575.2.p.a.399.2		20
115.79	odd	22		2645.2.a.o.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.a.26.1	✓	10	5.4	even	2
115.2.g.a.31.1	yes	10	115.54	even	22
575.2.k.a.26.1		10	1.1	even	1	trivial
575.2.k.a.376.1		10	23.8	even	11	inner
575.2.p.a.49.1		20	5.2	odd	4
575.2.p.a.49.2		20	5.3	odd	4
575.2.p.a.399.1		20	115.8	odd	44
575.2.p.a.399.2		20	115.77	odd	44
2645.2.a.n.1.4		5	115.59	even	22
2645.2.a.o.1.4		5	115.79	odd	22

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.k (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0125459 + 0.0872586i) q^{2} +(0.415415 - 0.909632i) q^{3} +(1.91153 - 0.561276i) q^{4} +(0.0845850 + 0.0248364i) q^{6} +(1.30075 - 0.835939i) q^{7} +(0.146201 + 0.320135i) q^{8} +(1.30972 + 1.51150i) q^{9} +(0.289532 - 2.01374i) q^{11} +(0.283524 - 1.97195i) q^{12} +(-1.80075 - 1.15727i) q^{13} +(0.0892619 + 0.103014i) q^{14} +(3.32584 - 2.13739i) q^{16} +(4.18251 + 1.22809i) q^{17} +(-0.115460 + 0.133248i) q^{18} +(-7.12381 + 2.09174i) q^{19} +(-0.220047 - 1.53046i) q^{21} +0.179348 q^{22} +(2.79310 + 3.89854i) q^{23} +0.351939 q^{24} +(0.0783898 - 0.171650i) q^{26} +(4.79746 - 1.40866i) q^{27} +(2.01722 - 2.32800i) q^{28} +(-4.30111 - 1.26292i) q^{29} +(-0.376329 - 0.824045i) q^{31} +(0.689173 + 0.795348i) q^{32} +(-1.71148 - 1.09990i) q^{33} +(-0.0546886 + 0.380367i) q^{34} +(3.35194 + 2.15416i) q^{36} +(-7.26571 - 8.38507i) q^{37} +(-0.271897 - 0.595371i) q^{38} +(-1.80075 + 1.15727i) q^{39} +(3.95750 - 4.56720i) q^{41} +(0.130785 - 0.0384020i) q^{42} +(-2.24116 + 4.90745i) q^{43} +(-0.576814 - 4.01183i) q^{44} +(-0.305139 + 0.292633i) q^{46} +2.72825 q^{47} +(-0.562632 - 3.91319i) q^{48} +(-1.91476 + 4.19273i) q^{49} +(2.85459 - 3.29437i) q^{51} +(-4.09173 - 1.20144i) q^{52} +(0.230732 - 0.148283i) q^{53} +(0.183106 + 0.400947i) q^{54} +(0.457783 + 0.294199i) q^{56} +(-1.05662 + 7.34898i) q^{57} +(0.0562393 - 0.391153i) q^{58} +(6.74757 + 4.33640i) q^{59} +(-1.33718 - 2.92802i) q^{61} +(0.0671837 - 0.0431763i) q^{62} +(2.96714 + 0.871230i) q^{63} +(5.11714 - 5.90549i) q^{64} +(0.0745040 - 0.163141i) q^{66} +(-0.279610 - 1.94473i) q^{67} +8.68428 q^{68} +(4.70653 - 0.921186i) q^{69} +(1.58700 + 11.0378i) q^{71} +(-0.292401 + 0.640269i) q^{72} +(-9.95039 + 2.92170i) q^{73} +(0.640515 - 0.739194i) q^{74} +(-12.4433 + 7.99684i) q^{76} +(-1.30675 - 2.86139i) q^{77} +(-0.123574 - 0.142612i) q^{78} +(2.70849 + 1.74064i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(0.448178 + 0.288027i) q^{82} +(-2.85563 - 3.29557i) q^{83} +(-1.27964 - 2.80202i) q^{84} +(-0.456334 - 0.133992i) q^{86} +(-2.93553 + 3.38779i) q^{87} +(0.686997 - 0.201720i) q^{88} +(0.266861 - 0.584343i) q^{89} -3.30972 q^{91} +(7.52725 + 5.88446i) q^{92} -0.905910 q^{93} +(0.0342284 + 0.238063i) q^{94} +(1.00977 - 0.296494i) q^{96} +(-3.62848 + 4.18748i) q^{97} +(-0.389875 - 0.114478i) q^{98} +(3.42297 - 2.19981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - q^{3} - q^{4} + 6 q^{6} - 5 q^{7} + 16 q^{8} + 2 q^{9} + 8 q^{11} - q^{12} - 3 q^{14} + 5 q^{16} + 23 q^{17} + 10 q^{18} - 13 q^{19} + 6 q^{21} - 4 q^{22} + 21 q^{23} - 6 q^{24} + 11 q^{26}+ \cdots + 6 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - q^3 - q^4 + 6 * q^6 - 5 * q^7 + 16 * q^8 + 2 * q^9 + 8 * q^11 - q^12 - 3 * q^14 + 5 * q^16 + 23 * q^17 + 10 * q^18 - 13 * q^19 + 6 * q^21 - 4 * q^22 + 21 * q^23 - 6 * q^24 + 11 * q^26 + 5 * q^27 + 6 * q^28 + 2 * q^29 - 20 * q^31 + 15 * q^32 - 3 * q^33 + 16 * q^34 + 24 * q^36 - 13 * q^37 - 21 * q^38 - 5 * q^41 - 3 * q^42 - 15 * q^43 + 19 * q^44 - 16 * q^46 + 52 * q^47 - 6 * q^48 + 4 * q^49 - 10 * q^51 - 22 * q^52 - 6 * q^53 - 30 * q^54 + 3 * q^56 - 2 * q^57 - 45 * q^58 + 5 * q^59 - 3 * q^61 + 54 * q^62 + 10 * q^63 - 34 * q^64 - 4 * q^66 - 20 * q^67 - 32 * q^68 - q^69 - 22 * q^71 - 32 * q^72 - 43 * q^73 + q^74 - 2 * q^76 - 4 * q^77 - 11 * q^78 + 51 * q^79 - q^81 - 58 * q^82 + 17 * q^83 + 6 * q^84 - 9 * q^86 + 2 * q^87 - 7 * q^88 + 57 * q^89 - 22 * q^91 + 43 * q^92 - 20 * q^93 - 81 * q^94 - 7 * q^96 - 52 * q^97 - 24 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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