LMFDB - Embedded newform 930.2.br.a.11.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(11,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 0, 23]))

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

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

chi := DirichletCharacter("930.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.br (of order $30$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			11.19
Character	$\chi$	$=$	930.11
Dual form			930.2.br.a.761.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(0.997625 - 1.41589i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.511264 - 1.65487i) q^{6} +(0.00579634 + 0.0551485i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.00949 - 2.82505i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(0.997625 - 1.41589i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.511264 - 1.65487i) q^{6} +(0.00579634 + 0.0551485i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.00949 - 2.82505i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(4.39351 + 1.95612i) q^{11} +(-0.0251432 - 1.73187i) q^{12} +(-1.17337 - 5.52027i) q^{13} +(0.0225545 + 0.0506582i) q^{14} +(-0.156024 + 1.72501i) q^{15} +(0.309017 - 0.951057i) q^{16} +(4.22241 - 1.87994i) q^{17} +(-1.83307 - 2.37484i) q^{18} +(-7.24514 - 1.54000i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(0.0838668 + 0.0468106i) q^{21} +(4.78295 + 0.502709i) q^{22} +(1.07181 + 0.778717i) q^{23} +(-0.559089 - 1.63933i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-2.82180 - 4.88750i) q^{26} +(-5.00706 - 1.38902i) q^{27} +(0.0371048 + 0.0412091i) q^{28} +(0.765615 + 2.35632i) q^{29} +(0.384669 + 1.68880i) q^{30} +(5.26534 + 1.81001i) q^{31} -1.00000i q^{32} +(7.15273 - 4.26926i) q^{33} +(3.43482 - 3.09273i) q^{34} +(-0.0325940 - 0.0448618i) q^{35} +(-2.47722 - 1.69216i) q^{36} +(4.18646 + 2.41705i) q^{37} +(-7.36642 + 0.774242i) q^{38} +(-8.98667 - 3.84580i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(-7.04768 - 6.34576i) q^{41} +(0.0942273 + 0.0186032i) q^{42} +(0.517215 - 2.43330i) q^{43} +(4.70420 - 0.999909i) q^{44} +(2.28677 + 1.94183i) q^{45} +(1.25999 + 0.409396i) q^{46} +(0.349977 + 0.113714i) q^{47} +(-1.03831 - 1.38633i) q^{48} +(6.84403 - 1.45474i) q^{49} +(0.207912 - 0.978148i) q^{50} +(1.55060 - 7.85395i) q^{51} +(-4.19401 - 3.77630i) q^{52} +(-0.476094 + 4.52973i) q^{53} +(-5.19123 + 0.226225i) q^{54} +(-4.78295 + 0.502709i) q^{55} +(0.0480231 + 0.0277261i) q^{56} +(-9.40841 + 8.72197i) q^{57} +(1.45629 + 2.00441i) q^{58} +(-4.67634 + 4.21060i) q^{59} +(0.887709 + 1.48727i) q^{60} +6.01788i q^{61} +(5.56696 + 0.0943451i) q^{62} +(0.149946 - 0.0720467i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(3.77630 + 4.19401i) q^{65} +(5.48337 - 6.27062i) q^{66} +(-1.65285 - 2.86283i) q^{67} +(2.31100 - 4.00278i) q^{68} +(2.17185 - 0.740700i) q^{69} +(-0.0448618 - 0.0325940i) q^{70} +(3.05457 + 0.321048i) q^{71} +(-2.87888 - 0.843833i) q^{72} +(-2.89385 + 6.49970i) q^{73} +(4.72847 + 1.00507i) q^{74} +(-0.727384 - 1.57191i) q^{75} +(-6.76663 + 3.01270i) q^{76} +(-0.0824107 + 0.253634i) q^{77} +(-9.73525 - 0.880536i) q^{78} +(5.28619 + 11.8730i) q^{79} +(0.207912 + 0.978148i) q^{80} +(-6.96187 + 5.70371i) q^{81} +(-8.66369 - 3.85732i) q^{82} +(-1.77637 + 1.97286i) q^{83} +(0.0953642 - 0.0114251i) q^{84} +(-2.71675 + 3.73928i) q^{85} +(-0.260032 - 2.47404i) q^{86} +(4.10009 + 1.26670i) q^{87} +(4.16497 - 2.40465i) q^{88} +(-6.09663 + 4.42946i) q^{89} +(2.77490 + 1.14014i) q^{90} +(0.297633 - 0.0967069i) q^{91} +1.32483 q^{92} +(7.81562 - 5.64943i) q^{93} +0.367987 q^{94} +(7.04448 - 2.28889i) q^{95} +(-1.41589 - 0.997625i) q^{96} +(1.98975 - 1.44564i) q^{97} +(6.05951 - 3.49846i) q^{98} +(1.09095 - 14.3866i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9	$ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 q^{99}+O(q^{100}) $ 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9 - 22 * q^10 - 38 * q^13 - 44 * q^16 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{23}{30}\right)$

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 $

$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$3$	0.997625	−	1.41589i	0.575979	−	0.817464i
$3$	0.997625	−	1.41589i	0.575979	−	0.817464i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	0.511264	−	1.65487i	0.208723	−	0.675600i
$7$	0.00579634	+	0.0551485i	0.00219081	+	0.0208442i	0.995563	−	0.0941006i	$-0.0299975\pi$
$7$	0.00579634	+	0.0551485i	0.00219081	+	0.0208442i	−0.993372	+	0.114945i	$0.963331\pi$
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	−1.00949	−	2.82505i	−0.336496	−	0.941685i
$10$	−0.669131	+	0.743145i	−0.211598	+	0.235003i
$11$	4.39351	+	1.95612i	1.32469	+	0.589792i	0.942474	−	0.334280i	$-0.108493\pi$
$11$	4.39351	+	1.95612i	1.32469	+	0.589792i	0.382220	+	0.924071i	$0.375160\pi$
$12$	−0.0251432	−	1.73187i	−0.00725822	−	0.499947i
$13$	−1.17337	−	5.52027i	−0.325434	−	1.53105i	−0.771607	−	0.636100i	$-0.780547\pi$
$13$	−1.17337	−	5.52027i	−0.325434	−	1.53105i	0.446173	−	0.894947i	$-0.352787\pi$
$14$	0.0225545	+	0.0506582i	0.00602793	+	0.0135390i
$15$	−0.156024	+	1.72501i	−0.0402852	+	0.445395i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	4.22241	−	1.87994i	1.02409	−	0.455952i	0.175202	−	0.984532i	$-0.443942\pi$
$17$	4.22241	−	1.87994i	1.02409	−	0.455952i	0.848883	+	0.528580i	$0.177275\pi$
$18$	−1.83307	−	2.37484i	−0.432059	−	0.559755i
$19$	−7.24514	−	1.54000i	−1.66215	−	0.353301i	−0.721430	−	0.692487i	$-0.756515\pi$
$19$	−7.24514	−	1.54000i	−1.66215	−	0.353301i	−0.940719	+	0.339187i	$0.889848\pi$
$20$	−0.406737	+	0.913545i	−0.0909491	+	0.204275i
$21$	0.0838668	+	0.0468106i	0.0183012	+	0.0102149i
$22$	4.78295	+	0.502709i	1.01973	+	0.107178i
$23$	1.07181	+	0.778717i	0.223488	+	0.162374i	0.693896	−	0.720076i	$-0.255893\pi$
$23$	1.07181	+	0.778717i	0.223488	+	0.162374i	−0.470407	+	0.882449i	$0.655893\pi$
$24$	−0.559089	−	1.63933i	−0.114124	−	0.334628i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−2.82180	−	4.88750i	−0.553400	−	0.958517i
$27$	−5.00706	−	1.38902i	−0.963608	−	0.267318i
$28$	0.0371048	+	0.0412091i	0.00701215	+	0.00778778i
$29$	0.765615	+	2.35632i	0.142171	+	0.437558i	0.996636	−	0.0819507i	$-0.0261150\pi$
$29$	0.765615	+	2.35632i	0.142171	+	0.437558i	−0.854465	+	0.519509i	$0.826115\pi$
$30$	0.384669	+	1.68880i	0.0702307	+	0.308330i
$31$	5.26534	+	1.81001i	0.945684	+	0.325088i
$31$	5.26534	+	1.81001i	0.945684	+	0.325088i
$32$		−	1.00000i		−	0.176777i
$33$	7.15273	−	4.26926i	1.24513	−	0.743182i
$34$	3.43482	−	3.09273i	0.589067	−	0.530398i
$35$	−0.0325940	−	0.0448618i	−0.00550940	−	0.00758303i
$36$	−2.47722	−	1.69216i	−0.412870	−	0.282026i
$37$	4.18646	+	2.41705i	0.688249	+	0.397361i	0.802956	−	0.596039i	$-0.203259\pi$
$37$	4.18646	+	2.41705i	0.688249	+	0.397361i	−0.114707	+	0.993399i	$0.536593\pi$
$38$	−7.36642	+	0.774242i	−1.19499	+	0.125599i
$39$	−8.98667	−	3.84580i	−1.43902	−	0.615820i
$40$	−0.104528	+	0.994522i	−0.0165274	+	0.157248i
$41$	−7.04768	−	6.34576i	−1.10066	−	0.991041i	−0.100670	−	0.994920i	$-0.532099\pi$
$41$	−7.04768	−	6.34576i	−1.10066	−	0.991041i	−0.999992	+	0.00387861i	$0.998765\pi$
$42$	0.0942273	+	0.0186032i	0.0145396	+	0.00287054i
$43$	0.517215	−	2.43330i	0.0788745	−	0.371075i	−0.920953	−	0.389675i	$-0.872587\pi$
$43$	0.517215	−	2.43330i	0.0788745	−	0.371075i	0.999827	+	0.0185995i	$0.00592073\pi$
$44$	4.70420	−	0.999909i	0.709185	−	0.150742i
$45$	2.28677	+	1.94183i	0.340891	+	0.289470i
$46$	1.25999	+	0.409396i	0.185776	+	0.0603621i
$47$	0.349977	+	0.113714i	0.0510494	+	0.0165869i	0.334430	−	0.942420i	$-0.391456\pi$
$47$	0.349977	+	0.113714i	0.0510494	+	0.0165869i	−0.283381	+	0.959007i	$0.591456\pi$
$48$	−1.03831	−	1.38633i	−0.149867	−	0.200100i
$49$	6.84403	−	1.45474i	0.977718	−	0.207820i
$50$	0.207912	−	0.978148i	0.0294032	−	0.138331i
$51$	1.55060	−	7.85395i	0.217127	−	1.09977i
$52$	−4.19401	−	3.77630i	−0.581604	−	0.523679i
$53$	−0.476094	+	4.52973i	−0.0653965	+	0.622206i	0.911912	+	0.410386i	$0.134606\pi$
$53$	−0.476094	+	4.52973i	−0.0653965	+	0.622206i	−0.977309	+	0.211820i	$0.932061\pi$
$54$	−5.19123	+	0.226225i	−0.706436	+	0.0307854i
$55$	−4.78295	+	0.502709i	−0.644933	+	0.0677852i
$56$	0.0480231	+	0.0277261i	0.00641735	+	0.00370506i
$57$	−9.40841	+	8.72197i	−1.24617	+	1.15525i
$58$	1.45629	+	2.00441i	0.191220	+	0.263192i
$59$	−4.67634	+	4.21060i	−0.608808	+	0.548173i	−0.914824	−	0.403853i	$-0.867671\pi$
$59$	−4.67634	+	4.21060i	−0.608808	+	0.548173i	0.306016	+	0.952026i	$0.401004\pi$
$60$	0.887709	+	1.48727i	0.114603	+	0.192006i
$61$			6.01788i			0.770511i	0.922810	+	0.385256i	$0.125887\pi$
$61$			6.01788i			0.770511i	−0.922810	+	0.385256i	$0.874113\pi$
$62$	5.56696	+	0.0943451i	0.707005	+	0.0119818i
$63$	0.149946	−	0.0720467i	0.0188914	−	0.00907703i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	3.77630	+	4.19401i	0.468393	+	0.520203i
$66$	5.48337	−	6.27062i	0.674957	−	0.771860i
$67$	−1.65285	−	2.86283i	−0.201928	−	0.349750i	0.747222	−	0.664575i	$-0.231387\pi$
$67$	−1.65285	−	2.86283i	−0.201928	−	0.349750i	−0.949150	+	0.314825i	$0.898054\pi$
$68$	2.31100	−	4.00278i	0.280250	−	0.485408i
$69$	2.17185	−	0.740700i	0.261459	−	0.0891698i
$70$	−0.0448618	−	0.0325940i	−0.00536201	−	0.00389573i
$71$	3.05457	+	0.321048i	0.362511	+	0.0381014i	0.284033	−	0.958814i	$-0.408327\pi$
$71$	3.05457	+	0.321048i	0.362511	+	0.0381014i	0.0784776	+	0.996916i	$0.474994\pi$
$72$	−2.87888	−	0.843833i	−0.339279	−	0.0994467i
$73$	−2.89385	+	6.49970i	−0.338700	+	0.760733i	0.661244	+	0.750171i	$0.270029\pi$
$73$	−2.89385	+	6.49970i	−0.338700	+	0.760733i	−0.999944	+	0.0105619i	$0.996638\pi$
$74$	4.72847	+	1.00507i	0.549673	+	0.116837i
$75$	−0.727384	−	1.57191i	−0.0839910	−	0.181509i
$76$	−6.76663	+	3.01270i	−0.776186	+	0.345580i
$77$	−0.0824107	+	0.253634i	−0.00939157	+	0.0289043i
$78$	−9.73525	−	0.880536i	−1.10230	−	0.0997011i
$79$	5.28619	+	11.8730i	0.594743	+	1.33582i	0.920641	+	0.390410i	$0.127667\pi$
$79$	5.28619	+	11.8730i	0.594743	+	1.33582i	−0.325898	+	0.945405i	$0.605667\pi$
$80$	0.207912	+	0.978148i	0.0232452	+	0.109360i
$81$	−6.96187	+	5.70371i	−0.773541	+	0.633746i
$82$	−8.66369	−	3.85732i	−0.956745	−	0.425970i
$83$	−1.77637	+	1.97286i	−0.194982	+	0.216549i	−0.832706	−	0.553716i	$-0.813209\pi$
$83$	−1.77637	+	1.97286i	−0.194982	+	0.216549i	0.637724	+	0.770265i	$0.279876\pi$
$84$	0.0953642	−	0.0114251i	0.0104051	−	0.00124658i
$85$	−2.71675	+	3.73928i	−0.294673	+	0.405582i
$86$	−0.260032	−	2.47404i	−0.0280400	−	0.266782i
$87$	4.10009	+	1.26670i	0.439576	+	0.135804i
$88$	4.16497	−	2.40465i	0.443988	−	0.256336i
$89$	−6.09663	+	4.42946i	−0.646242	+	0.469522i	−0.861989	−	0.506927i	$-0.830781\pi$
$89$	−6.09663	+	4.42946i	−0.646242	+	0.469522i	0.215747	+	0.976449i	$0.430781\pi$
$90$	2.77490	+	1.14014i	0.292501	+	0.120181i
$91$	0.297633	−	0.0967069i	0.0312004	−	0.0101376i
$92$	1.32483			0.138123
$93$	7.81562	−	5.64943i	0.810442	−	0.585819i
$94$	0.367987			0.0379550
$95$	7.04448	−	2.28889i	0.722748	−	0.234835i
$96$	−1.41589	−	0.997625i	−0.144509	−	0.101820i
$97$	1.98975	−	1.44564i	0.202029	−	0.146782i	−0.482171	−	0.876077i	$-0.660152\pi$
$97$	1.98975	−	1.44564i	0.202029	−	0.146782i	0.684200	+	0.729295i	$0.260152\pi$
$98$	6.05951	−	3.49846i	0.612103	−	0.353398i
$99$	1.09095	−	14.3866i	0.109644	−	1.44591i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	−10.3220	+	14.2070i	−1.02708	+	1.41365i	−0.119960	+	0.992779i	$0.538277\pi$
$101$	−10.3220	+	14.2070i	−1.02708	+	1.41365i	−0.907119	+	0.420874i	$0.861723\pi$
$102$	−0.952295	−	7.94871i	−0.0942913	−	0.787039i
$103$	4.35531	−	4.83706i	0.429141	−	0.476610i	−0.489329	−	0.872099i	$-0.662758\pi$
$103$	4.35531	−	4.83706i	0.429141	−	0.476610i	0.918471	+	0.395489i	$0.129425\pi$
$104$	−5.15568	−	2.29546i	−0.505556	−	0.225088i
$105$	−0.0960360	+	0.00139425i	−0.00937216	+	0.000136065i
$106$	0.946971	+	4.45515i	0.0919779	+	0.432722i
$107$	8.15087	+	18.3072i	0.787974	+	1.76982i	0.620924	+	0.783871i	$0.286758\pi$
$107$	8.15087	+	18.3072i	0.787974	+	1.76982i	0.167050	+	0.985948i	$0.446576\pi$
$108$	−4.86724	+	1.81933i	−0.468351	+	0.175065i
$109$	3.12570	−	9.61992i	0.299388	−	0.921421i	−0.682324	−	0.731050i	$-0.739031\pi$
$109$	3.12570	−	9.61992i	0.299388	−	0.921421i	0.981712	−	0.190372i	$-0.0609693\pi$
$110$	−4.39351	+	1.95612i	−0.418905	+	0.186509i
$111$	7.59879	−	3.51625i	0.721246	−	0.333748i
$112$	0.0542405	+	0.0115292i	0.00512525	+	0.00108940i
$113$	0.478150	−	1.07394i	0.0449805	−	0.101028i	−0.889658	−	0.456628i	$-0.849057\pi$
$113$	0.478150	−	1.07394i	0.0449805	−	0.101028i	0.934638	+	0.355600i	$0.115724\pi$
$114$	−6.25269	+	11.2024i	−0.585618	+	1.04921i
$115$	−1.31758	−	0.138483i	−0.122865	−	0.0129136i
$116$	2.00441	+	1.45629i	0.186105	+	0.135213i
$117$	−14.4106	+	8.88747i	−1.33226	+	0.821647i
$118$	−3.14632	+	5.44959i	−0.289642	+	0.501675i
$119$	0.128150	+	0.221963i	0.0117475	+	0.0203473i
$120$	1.30385	+	1.14016i	0.119025	+	0.104082i
$121$	8.11612	+	9.01387i	0.737829	+	0.819442i
$122$	1.85963	+	5.72335i	0.168363	+	0.518168i
$123$	−16.0158	+	3.64805i	−1.44410	+	0.328933i
$124$	5.32365	−	1.63056i	0.478078	−	0.146429i
$125$			1.00000i			0.0894427i
$126$	0.120344	−	0.114856i	0.0107211	−	0.0102322i
$127$	2.52970	−	2.27775i	0.224475	−	0.202118i	−0.549218	−	0.835679i	$-0.685074\pi$
$127$	2.52970	−	2.27775i	0.224475	−	0.202118i	0.773692	+	0.633561i	$0.218408\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$	−2.92930	−	3.15984i	−0.257911	−	0.278209i
$130$	4.88750	+	2.82180i	0.428662	+	0.247488i
$131$	0.219272	−	0.0230464i	0.0191579	−	0.00201357i	−0.0949447	−	0.995483i	$-0.530267\pi$
$131$	0.219272	−	0.0230464i	0.0191579	−	0.00201357i	0.114103	+	0.993469i	$0.463601\pi$
$132$	3.27727	−	7.65817i	0.285250	−	0.666558i
$133$	0.0429335	−	0.408485i	0.00372281	−	0.0354201i
$134$	−2.45662	−	2.21195i	−0.212219	−	0.191083i
$135$	5.03075	−	1.30060i	0.432978	−	0.111938i
$136$	0.960969	−	4.52100i	0.0824024	−	0.387673i
$137$	7.90566	−	1.68040i	0.675426	−	0.143566i	0.142586	−	0.989782i	$-0.454458\pi$
$137$	7.90566	−	1.68040i	0.675426	−	0.143566i	0.532840	+	0.846216i	$0.321125\pi$
$138$	1.83666	−	1.37558i	0.156347	−	0.117098i
$139$	−2.87855	−	0.935296i	−0.244155	−	0.0793308i	0.184383	−	0.982854i	$-0.440971\pi$
$139$	−2.87855	−	0.935296i	−0.244155	−	0.0793308i	−0.428538	+	0.903524i	$0.640971\pi$
$140$	−0.0527382	−	0.0171357i	−0.00445719	−	0.00144823i
$141$	0.510153	−	0.382084i	0.0429626	−	0.0321773i
$142$	3.00428	−	0.638579i	0.252113	−	0.0535884i
$143$	5.64308	−	26.5486i	0.471898	−	2.22011i
$144$	−2.99874	+	0.0870895i	−0.249895	+	0.00725746i
$145$	−1.84120	−	1.65783i	−0.152904	−	0.137675i
$146$	−0.743700	+	7.07583i	−0.0615491	+	0.585600i
$147$	4.76802	−	11.1417i	0.393260	−	0.918950i
$148$	4.80762	−	0.505301i	0.395184	−	0.0415355i
$149$	−7.38731	−	4.26507i	−0.605192	−	0.349408i	0.165889	−	0.986144i	$-0.446951\pi$
$149$	−7.38731	−	4.26507i	−0.605192	−	0.349408i	−0.771081	+	0.636736i	$0.780284\pi$
$150$	−1.17753	−	1.27020i	−0.0961450	−	0.103712i
$151$	10.5873	+	14.5722i	0.861586	+	1.18587i	0.981189	+	0.193050i	$0.0618378\pi$
$151$	10.5873	+	14.5722i	0.861586	+	1.18587i	−0.119603	+	0.992822i	$0.538162\pi$
$152$	−5.50447	+	4.95625i	−0.446472	+	0.402005i
$153$	−9.57340	−	10.0308i	−0.773964	−	0.810940i
$154$			0.266686i			0.0214902i
$155$	−5.46493	+	1.06515i	−0.438954	+	0.0855552i
$156$	−9.53087	+	2.17092i	−0.763081	+	0.173813i
$157$	−2.87228	−	8.83996i	−0.229233	−	0.705506i	−0.997834	−	0.0657780i	$-0.979047\pi$
$157$	−2.87228	−	8.83996i	−0.229233	−	0.705506i	0.768602	−	0.639728i	$-0.220953\pi$
$158$	8.69642	+	9.65836i	0.691850	+	0.768378i
$159$	5.93863	+	5.19307i	0.470964	+	0.411837i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−0.0367325	+	0.0636226i	−0.00289493	+	0.00501416i
$162$	−4.85859	+	7.57589i	−0.381727	+	0.595218i
$163$	16.4984	+	11.9868i	1.29225	+	0.938876i	0.999848	−	0.0174189i	$-0.00554490\pi$
$163$	16.4984	+	11.9868i	1.29225	+	0.938876i	0.292404	+	0.956295i	$0.405545\pi$
$164$	−9.43164	−	0.991305i	−0.736487	−	0.0774079i
$165$	−4.05981	+	7.27365i	−0.316056	+	0.566253i
$166$	−1.07978	+	2.42523i	−0.0838072	+	0.188234i
$167$	19.9666	+	4.24403i	1.54506	+	0.328413i	0.900059	−	0.435768i	$-0.143523\pi$
$167$	19.9666	+	4.24403i	1.54506	+	0.328413i	0.645002	+	0.764181i	$0.276857\pi$
$168$	0.0871662	−	0.0403351i	0.00672502	−	0.00311192i
$169$	−17.2205	+	7.66705i	−1.32465	+	0.589773i
$170$	−1.42828	+	4.39579i	−0.109544	+	0.337142i
$171$	2.96329	+	22.0225i	0.226608	+	1.68411i
$172$	−1.01182	−	2.27260i	−0.0771509	−	0.173284i
$173$	2.83694	+	13.3467i	0.215688	+	1.01473i	0.944117	+	0.329612i	$0.106918\pi$
$173$	2.83694	+	13.3467i	0.215688	+	1.01473i	−0.728428	+	0.685122i	$0.759749\pi$
$174$	4.29085	−	0.0622944i	0.325288	−	0.00472253i
$175$	0.0506582	+	0.0225545i	0.00382940	+	0.00170496i
$176$	3.21805	−	3.57401i	0.242570	−	0.269401i
$177$	1.29650	+	10.8218i	0.0974512	+	0.813415i
$178$	−4.42946	+	6.09663i	−0.332002	+	0.456962i
$179$	−1.42880	−	13.5941i	−0.106793	−	1.01607i	−0.908367	−	0.418174i	$-0.862670\pi$
$179$	−1.42880	−	13.5941i	−0.106793	−	1.01607i	0.801573	−	0.597896i	$-0.203997\pi$
$180$	2.99141	+	0.226841i	0.222967	+	0.0169077i
$181$	7.46802	−	4.31166i	0.555094	−	0.320483i	−0.196080	−	0.980588i	$-0.562821\pi$
$181$	7.46802	−	4.31166i	0.555094	−	0.320483i	0.751174	+	0.660104i	$0.229488\pi$
$182$	0.253182	−	0.183947i	0.0187671	−	0.0136351i
$183$	8.52066	+	6.00359i	0.629865	+	0.443798i
$184$	1.25999	−	0.409396i	0.0928878	−	0.0301811i
$185$	−4.83410			−0.355410
$186$	5.68733	−	7.78809i	0.417015	−	0.571050i
$187$	22.2286			1.62552
$188$	0.349977	−	0.113714i	0.0255247	−	0.00829347i
$189$	0.0475800	−	0.284183i	0.00346093	−	0.0206713i
$190$	5.99239	−	4.35373i	0.434734	−	0.315852i
$191$	−6.80966	+	3.93156i	−0.492730	+	0.284478i	−0.725706	−	0.688005i	$-0.758487\pi$
$191$	−6.80966	+	3.93156i	−0.492730	+	0.284478i	0.232976	+	0.972482i	$0.425154\pi$
$192$	−1.65487	−	0.511264i	−0.119430	−	0.0368973i
$193$	−0.400990	−	3.81517i	−0.0288639	−	0.274622i	−0.999429	−	0.0337835i	$-0.989244\pi$
$193$	−0.400990	−	3.81517i	−0.0288639	−	0.274622i	0.970565	−	0.240838i	$-0.0774223\pi$
$194$	1.44564	−	1.98975i	0.103791	−	0.142856i
$195$	9.70559	−	1.16278i	0.695031	−	0.0832683i
$196$	4.68186	−	5.19973i	0.334418	−	0.371409i
$197$	12.2730	+	5.46427i	0.874412	+	0.389313i	0.794338	−	0.607476i	$-0.207818\pi$
$197$	12.2730	+	5.46427i	0.874412	+	0.389313i	0.0800734	+	0.996789i	$0.474485\pi$
$198$	−3.40815	−	14.0196i	−0.242207	−	0.996328i
$199$	−4.60196	−	21.6505i	−0.326224	−	1.53476i	−0.769658	−	0.638457i	$-0.779573\pi$
$199$	−4.60196	−	21.6505i	−0.326224	−	1.53476i	0.443434	−	0.896307i	$-0.353760\pi$
$200$	−0.406737	−	0.913545i	−0.0287606	−	0.0645974i
$201$	−5.70237	−	0.515770i	−0.402214	−	0.0363796i
$202$	−5.42660	+	16.7014i	−0.381815	+	1.17510i
$203$	−0.125510	+	0.0558806i	−0.00880906	+	0.00392205i
$204$	−3.36197	−	7.26540i	−0.235385	−	0.508679i
$205$	9.27635	+	1.97175i	0.647888	+	0.137713i
$206$	2.64741	−	5.94618i	0.184454	−	0.414290i
$207$	1.11794	−	3.81403i	0.0777021	−	0.265094i
$208$	−5.61268	−	0.589916i	−0.389169	−	0.0409033i
$209$	−28.8192	−	20.9384i	−1.99347	−	1.44834i
$210$	−0.0909048	+	0.0310028i	−0.00627303	+	0.00213939i
$211$	−2.10081	+	3.63872i	−0.144626	+	0.250500i	−0.929233	−	0.369493i	$-0.879531\pi$
$211$	−2.10081	+	3.63872i	−0.144626	+	0.250500i	0.784607	+	0.619993i	$0.212865\pi$
$212$	2.27734	+	3.94447i	0.156408	+	0.270907i
$213$	3.50189	−	4.00465i	0.239945	−	0.274394i
$214$	13.4092	+	14.8924i	0.916631	+	1.01802i
$215$	0.768731	+	2.36591i	0.0524270	+	0.161354i
$216$	−4.06682	+	3.23435i	−0.276712	+	0.220069i
$217$	−0.0692998	+	0.300867i	−0.00470438	+	0.0204242i
$218$		−	10.1150i		−	0.685073i
$219$	6.31588	+	10.5816i	0.426788	+	0.715041i
$220$	−3.57401	+	3.21805i	−0.240959	+	0.216961i
$221$	−15.3322	−	21.1030i	−1.03136	−	1.41954i
$222$	6.14030	−	5.69231i	0.412110	−	0.382043i
$223$	−17.2637	−	9.96720i	−1.15606	−	0.667453i	−0.205706	−	0.978614i	$-0.565949\pi$
$223$	−17.2637	−	9.96720i	−1.15606	−	0.667453i	−0.950357	+	0.311161i	$0.899282\pi$
$224$	0.0551485	−	0.00579634i	0.00368476	−	0.000387284i
$225$	−2.95131	−	0.538286i	−0.196754	−	0.0358857i
$226$	0.122881	−	1.16914i	0.00817393	−	0.0777697i
$227$	4.17651	+	3.76054i	0.277204	+	0.249596i	0.795992	−	0.605307i	$-0.206950\pi$
$227$	4.17651	+	3.76054i	0.277204	+	0.249596i	−0.518788	+	0.854903i	$0.673616\pi$
$228$	−2.48491	+	12.5863i	−0.164567	+	0.833551i
$229$	−4.76991	+	22.4407i	−0.315205	+	1.48292i	0.480370	+	0.877066i	$0.340502\pi$
$229$	−4.76991	+	22.4407i	−0.315205	+	1.48292i	−0.795575	+	0.605855i	$0.792831\pi$
$230$	−1.29588	+	0.275448i	−0.0854480	+	0.0181625i
$231$	0.276903	+	0.369716i	0.0182189	+	0.0243255i
$232$	2.35632	+	0.765615i	0.154700	+	0.0502651i
$233$	−16.5162	−	5.36645i	−1.08202	−	0.351568i	−0.286859	−	0.957973i	$-0.592611\pi$
$233$	−16.5162	−	5.36645i	−1.08202	−	0.351568i	−0.795156	+	0.606405i	$0.792611\pi$
$234$	−10.9589	+	12.9056i	−0.716404	+	0.843665i
$235$	−0.359946	+	0.0765089i	−0.0234803	+	0.00499089i
$236$	−1.30831	+	6.15513i	−0.0851639	+	0.400665i
$237$	22.0845	+	4.36012i	1.43454	+	0.283220i
$238$	0.190469	+	0.171499i	0.0123462	+	0.0111166i
$239$	0.710742	−	6.76226i	0.0459741	−	0.437414i	−0.947189	−	0.320677i	$-0.896090\pi$
$239$	0.710742	−	6.76226i	0.0459741	−	0.437414i	0.993163	−	0.116737i	$-0.0372436\pi$
$240$	1.59237	+	0.681445i	0.102787	+	0.0439871i
$241$	23.6259	−	2.48318i	1.52188	−	0.159956i	0.693635	−	0.720327i	$-0.256008\pi$
$241$	23.6259	−	2.48318i	1.52188	−	0.159956i	0.828242	+	0.560371i	$0.189342\pi$
$242$	10.5043	+	6.06468i	0.675244	+	0.389852i
$243$	1.13049	+	15.5474i	0.0725211	+	0.997367i
$244$	3.53722	+	4.86857i	0.226448	+	0.311678i
$245$	−5.19973	+	4.68186i	−0.332198	+	0.299113i
$246$	−14.1047	+	8.41867i	−0.899280	+	0.536755i
$247$			41.8021i			2.65980i
$248$	4.55922	−	3.19585i	0.289511	−	0.202937i
$249$	1.02120	+	4.48331i	0.0647157	+	0.284118i
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	−12.5247	−	13.9101i	−0.790554	−	0.877999i	0.204343	−	0.978899i	$-0.434494\pi$
$251$	−12.5247	−	13.9101i	−0.790554	−	0.877999i	−0.994897	+	0.100901i	$0.967828\pi$
$252$	0.0789610	−	0.146423i	0.00497408	−	0.00922379i
$253$	3.18576	+	5.51790i	0.200287	+	0.346907i
$254$	1.70202	−	2.94799i	0.106795	−	0.184974i
$255$	2.58411	+	7.57702i	0.161824	+	0.474491i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−13.9544	−	1.46667i	−0.870454	−	0.0914884i	−0.341240	−	0.939976i	$-0.610847\pi$
$257$	−13.9544	−	1.46667i	−0.870454	−	0.0914884i	−0.529215	+	0.848488i	$0.677513\pi$
$258$	−3.76238	−	2.09999i	−0.234235	−	0.130739i
$259$	−0.109031	+	0.244887i	−0.00677483	+	0.0152165i
$260$	5.52027	+	1.17337i	0.342352	+	0.0727693i
$261$	5.88386	−	4.54158i	0.364202	−	0.281117i
$262$	0.201418	−	0.0896771i	0.0124436	−	0.00554027i
$263$	1.19730	−	3.68491i	0.0738287	−	0.227221i	−0.907332	−	0.420415i	$-0.861885\pi$
$263$	1.19730	−	3.68491i	0.0738287	−	0.227221i	0.981161	+	0.193194i	$0.0618845\pi$
$264$	0.750366	−	8.29608i	0.0461818	−	0.510589i
$265$	−1.85255	−	4.16091i	−0.113802	−	0.255602i
$266$	−0.0853966	−	0.401759i	−0.00523600	−	0.0246335i
$267$	0.189476	+	13.0511i	0.0115957	+	0.798714i
$268$	−3.01991	−	1.34455i	−0.184471	−	0.0821316i
$269$	16.7866	−	18.6434i	1.02349	−	1.13671i	0.0329584	−	0.999457i	$-0.489507\pi$
$269$	16.7866	−	18.6434i	1.02349	−	1.13671i	0.990537	−	0.137249i	$-0.0438262\pi$
$270$	4.38262	−	2.79153i	0.266718	−	0.169887i
$271$	−14.5086	+	19.9693i	−0.881333	+	1.21305i	0.0947168	+	0.995504i	$0.469805\pi$
$271$	−14.5086	+	19.9693i	−0.881333	+	1.21305i	−0.976050	+	0.217547i	$0.930195\pi$
$272$	−0.483131	−	4.59669i	−0.0292941	−	0.278715i
$273$	0.160000	−	0.517893i	0.00968365	−	0.0313443i
$274$	6.99946	−	4.04114i	0.422853	−	0.244134i
$275$	3.89080	−	2.82683i	0.234624	−	0.170465i
$276$	1.32169	−	1.87582i	0.0795562	−	0.112911i
$277$	−18.1270	+	5.88982i	−1.08915	+	0.353885i	−0.797917	−	0.602768i	$-0.794064\pi$
$277$	−18.1270	+	5.88982i	−1.08915	+	0.353885i	−0.291230	+	0.956653i	$0.594064\pi$
$278$	−3.02668			−0.181528
$279$	−0.201908	−	16.7021i	−0.0120879	−	0.999927i
$280$	−0.0554523			−0.00331391
$281$	−31.1820	+	10.1317i	−1.86016	+	0.604404i	−0.865540	+	0.500839i	$0.833025\pi$
$281$	−31.1820	+	10.1317i	−1.86016	+	0.604404i	−0.994623	+	0.103564i	$0.966975\pi$
$282$	0.367113	−	0.521029i	0.0218613	−	0.0310269i
$283$	−15.1384	+	10.9987i	−0.899885	+	0.653805i	−0.938436	−	0.345452i	$-0.887726\pi$
$283$	−15.1384	+	10.9987i	−0.899885	+	0.653805i	0.0385517	+	0.999257i	$0.487726\pi$
$284$	2.65991	−	1.53570i	0.157836	−	0.0911269i
$285$	3.78693	−	12.2577i	0.224319	−	0.726081i
$286$	−2.83708	−	26.9930i	−0.167760	−	1.59613i
$287$	0.309108	−	0.425451i	0.0182461	−	0.0251136i
$288$	−2.82505	+	1.00949i	−0.166468	+	0.0594846i
$289$	2.91938	−	3.24230i	0.171728	−	0.190724i
$290$	−2.26338	−	1.00772i	−0.132911	−	0.0591756i
$291$	−0.0618390	−	4.25947i	−0.00362506	−	0.249695i
$292$	1.47925	+	6.95933i	0.0865667	+	0.407264i
$293$	0.942288	+	2.11641i	0.0550491	+	0.123642i	0.938976	−	0.343983i	$-0.111776\pi$
$293$	0.942288	+	2.11641i	0.0550491	+	0.123642i	−0.883927	+	0.467625i	$0.845110\pi$
$294$	1.09169	−	12.0698i	0.0636686	−	0.703923i
$295$	1.94453	−	5.98466i	0.113215	−	0.348440i
$296$	4.41617	−	1.96621i	0.256685	−	0.114283i
$297$	−19.2815	−	15.8971i	−1.11882	−	0.922442i
$298$	−8.34373	−	1.77351i	−0.483339	−	0.102737i
$299$	3.04110	−	6.83041i	0.175871	−	0.395013i
$300$	−1.51241	−	0.844159i	−0.0873192	−	0.0487376i
$301$	0.137191	+	0.0144194i	0.00790756	+	0.000831118i
$302$	14.5722	+	10.5873i	0.838538	+	0.609233i
$303$	9.81809	+	28.7881i	0.564035	+	1.65383i
$304$	−3.70350	+	6.41465i	−0.212410	+	0.367905i
$305$	−3.00894	−	5.21164i	−0.172292	−	0.298418i
$306$	−12.2045	−	6.58149i	−0.697686	−	0.376239i
$307$	8.41836	+	9.34953i	0.480461	+	0.533606i	0.933830	−	0.357717i	$-0.116445\pi$
$307$	8.41836	+	9.34953i	0.480461	+	0.533606i	−0.453369	+	0.891323i	$0.649778\pi$
$308$	0.0824107	+	0.253634i	0.00469578	+	0.0144521i
$309$	−2.50378	−	10.9922i	−0.142435	−	0.625325i
$310$	−4.86831	+	2.70178i	−0.276501	+	0.153451i
$311$			7.04247i			0.399342i	0.979863	+	0.199671i	$0.0639873\pi$
$311$			7.04247i			0.399342i	−0.979863	+	0.199671i	$0.936013\pi$
$312$	−8.39355	+	5.00987i	−0.475191	+	0.283628i
$313$	11.4480	−	10.3078i	0.647081	−	0.582634i	−0.278847	−	0.960336i	$-0.589952\pi$
$313$	11.4480	−	10.3078i	0.647081	−	0.582634i	0.925927	+	0.377702i	$0.123286\pi$
$314$	−5.46340	−	7.51972i	−0.308317	−	0.424362i
$315$	−0.0938339	+	0.137367i	−0.00528694	+	0.00773977i
$316$	11.2554	+	6.49830i	0.633165	+	0.365558i
$317$	−0.195632	+	0.0205617i	−0.0109878	+	0.00115486i	−0.110021	−	0.993929i	$-0.535092\pi$
$317$	−0.195632	+	0.0205617i	−0.0109878	+	0.00115486i	0.0990330	+	0.995084i	$0.468425\pi$
$318$	7.25272	+	3.10376i	0.406712	+	0.174050i
$319$	−1.24550	+	11.8502i	−0.0697347	+	0.663482i
$320$	0.743145	+	0.669131i	0.0415431	+	0.0374055i
$321$	34.0524	+	6.72295i	1.90062	+	0.375238i
$322$	−0.0152742	+	0.0718596i	−0.000851200	+	0.00400458i
$323$	−33.4871	+	7.11790i	−1.86327	+	0.396051i
$324$	−2.27971	+	8.70649i	−0.126651	+	0.483694i
$325$	−5.36738	−	1.74397i	−0.297728	−	0.0967378i
$326$	19.3950	+	6.30182i	1.07419	+	0.349025i
$327$	−10.5025	−	14.0227i	−0.580788	−	0.775458i
$328$	−9.27635	+	1.97175i	−0.512201	+	0.108872i
$329$	−0.00424259	+	0.0199598i	−0.000233902	+	0.00110042i
$330$	−1.61343	+	8.17220i	−0.0888165	+	0.449865i
$331$	−22.7083	−	20.4467i	−1.24816	−	1.12385i	−0.987366	−	0.158458i	$-0.949348\pi$
$331$	−22.7083	−	20.4467i	−1.24816	−	1.12385i	−0.260798	−	0.965393i	$-0.583986\pi$
$332$	−0.277496	+	2.64020i	−0.0152296	+	0.144900i
$333$	2.60213	−	14.2670i	0.142596	−	0.781824i
$334$	20.3008	−	2.13370i	1.11081	−	0.116751i
$335$	2.86283	+	1.65285i	0.156413	+	0.0903050i
$336$	0.0704357	−	0.0652968i	0.00384258	−	0.00356223i
$337$	−18.0451	−	24.8370i	−0.982980	−	1.35296i	−0.935208	−	0.354098i	$-0.884788\pi$
$337$	−18.0451	−	24.8370i	−0.982980	−	1.35296i	−0.0477716	−	0.998858i	$-0.515212\pi$
$338$	−14.0084	+	12.6132i	−0.761956	+	0.686068i
$339$	−1.04357	−	1.74840i	−0.0566789	−	0.0949600i
$340$			4.62201i			0.250664i
$341$	19.5928	+	18.2520i	1.06101	+	0.988399i
$342$	9.62359	+	20.0290i	0.520384	+	1.08304i
$343$	0.239847	+	0.738173i	0.0129505	+	0.0398576i
$344$	−1.66457	−	1.84870i	−0.0897478	−	0.0996750i
$345$	−1.51052	+	1.72739i	−0.0813238	+	0.0929994i
$346$	6.82245	+	11.8168i	0.366777	+	0.635277i
$347$	−10.9628	+	18.9881i	−0.588514	+	1.01934i	0.405914	+	0.913911i	$0.366953\pi$
$347$	−10.9628	+	18.9881i	−0.588514	+	1.01934i	−0.994427	+	0.105424i	$0.966380\pi$
$348$	4.06159	−	1.38519i	0.217724	−	0.0742540i
$349$	9.43959	+	6.85826i	0.505289	+	0.367114i	0.811034	−	0.584999i	$-0.198905\pi$
$349$	9.43959	+	6.85826i	0.505289	+	0.367114i	−0.305744	+	0.952114i	$0.598905\pi$
$350$	0.0551485	+	0.00579634i	0.00294781	+	0.000309827i
$351$	−1.79266	+	29.2701i	−0.0956850	+	1.56232i
$352$	1.95612	−	4.39351i	0.104261	−	0.234175i
$353$	−33.0664	−	7.02849i	−1.75995	−	0.374089i	−0.789191	−	0.614148i	$-0.789500\pi$
$353$	−33.0664	−	7.02849i	−1.75995	−	0.374089i	−0.970758	+	0.240059i	$0.922833\pi$
$354$	4.57716	+	9.89149i	0.243274	+	0.525727i
$355$	−2.80586	+	1.24925i	−0.148920	+	0.0663033i
$356$	−2.32871	+	7.16702i	−0.123421	+	0.379851i
$357$	0.442121	+	0.0399891i	0.0233995	+	0.00211645i
$358$	−5.55968	−	12.4872i	−0.293838	−	0.659971i
$359$	−5.26772	−	24.7827i	−0.278020	−	1.30798i	−0.866382	−	0.499383i	$-0.833560\pi$
$359$	−5.26772	−	24.7827i	−0.278020	−	1.30798i	0.588362	−	0.808598i	$-0.299773\pi$
$360$	2.91510	−	0.708659i	0.153639	−	0.0373496i
$361$	32.7631	+	14.5871i	1.72437	+	0.767740i
$362$	5.77013	−	6.40838i	0.303271	−	0.336817i
$363$	20.8595	−	2.49907i	1.09484	−	0.131167i
$364$	0.183947	−	0.253182i	0.00964146	−	0.0132703i
$365$	−0.743700	−	7.07583i	−0.0389270	−	0.370366i
$366$	9.95884	+	3.07673i	0.520557	+	0.160823i
$367$	−5.69923	+	3.29045i	−0.297497	+	0.171760i	−0.641318	−	0.767275i	$-0.721612\pi$
$367$	−5.69923	+	3.29045i	−0.297497	+	0.171760i	0.343821	+	0.939035i	$0.388279\pi$
$368$	1.07181	−	0.778717i	0.0558721	−	0.0405934i
$369$	−10.8126	+	26.3160i	−0.562880	+	1.36996i
$370$	−4.59751	+	1.49382i	−0.239013	+	0.0776600i
$371$	−0.252567			−0.0131126
$372$	3.00232	−	9.16439i	0.155663	−	0.475152i
$373$	4.24372			0.219732			0.109866	−	0.993946i	$-0.464958\pi$
$373$	4.24372			0.219732			0.109866	+	0.993946i	$0.464958\pi$
$374$	21.1407	−	6.86902i	1.09316	−	0.355188i
$375$	1.41589	+	0.997625i	0.0731162	+	0.0515172i
$376$	0.297708	−	0.216298i	0.0153531	−	0.0111547i
$377$	12.1092	−	6.99124i	0.623654	−	0.360067i
$378$	−0.0425661	−	0.284977i	−0.00218936	−	0.0146576i
$379$	−3.46762	−	32.9922i	−0.178120	−	1.69469i	−0.609710	−	0.792625i	$-0.708714\pi$
$379$	−3.46762	−	32.9922i	−0.178120	−	1.69469i	0.431590	−	0.902070i	$-0.357953\pi$
$380$	4.35373	−	5.99239i	0.223341	−	0.307403i
$381$	−0.701353	−	5.85412i	−0.0359314	−	0.299916i
$382$	−5.26145	+	5.84344i	−0.269199	+	0.298976i
$383$	24.9969	+	11.1293i	1.27728	+	0.568682i	0.929475	−	0.368885i	$-0.120260\pi$
$383$	24.9969	+	11.1293i	1.27728	+	0.568682i	0.347805	+	0.937567i	$0.386927\pi$
$384$	−1.73187	+	0.0251432i	−0.0883790	+	0.00128308i
$385$	−0.0554472	−	0.260859i	−0.00282585	−	0.0132946i
$386$	−1.56032	−	3.50453i	−0.0794180	−	0.178376i
$387$	−7.39634	+	0.995229i	−0.375977	+	0.0505904i
$388$	0.760017	−	2.33909i	0.0385840	−	0.118749i
$389$	30.3902	−	13.5306i	1.54084	−	0.686027i	0.551843	−	0.833948i	$-0.313925\pi$
$389$	30.3902	−	13.5306i	1.54084	−	0.686027i	0.988999	+	0.147921i	$0.0472582\pi$
$390$	8.87124	−	4.10506i	0.449213	−	0.207868i
$391$	5.98958	+	1.27312i	0.302906	+	0.0643846i
$392$	2.84591	−	6.39201i	0.143740	−	0.322845i
$393$	0.186120	−	0.333456i	0.00938851	−	0.0168206i
$394$	13.3608	+	1.40428i	0.673108	+	0.0707466i
$395$	−10.5145	−	7.63921i	−0.529040	−	0.384370i
$396$	−7.57363	−	12.2802i	−0.380589	−	0.617105i
$397$	−2.60107	+	4.50518i	−0.130544	+	0.226109i	−0.923886	−	0.382667i	$-0.875006\pi$
$397$	−2.60107	+	4.50518i	−0.130544	+	0.226109i	0.793342	+	0.608776i	$0.208339\pi$
$398$	−11.0671	−	19.1688i	−0.554743	−	0.960844i
$399$	−0.535538	−	0.468304i	−0.0268104	−	0.0234445i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	−10.2012	−	31.3960i	−0.509423	−	1.56784i	−0.793206	−	0.608954i	$-0.791589\pi$
$401$	−10.2012	−	31.3960i	−0.509423	−	1.56784i	0.283783	−	0.958889i	$-0.408411\pi$
$402$	−5.58266	+	1.27160i	−0.278438	+	0.0634218i
$403$	3.81357	−	31.1899i	0.189968	−	1.55368i
$404$			17.5609i			0.873685i
$405$	3.17730	−	8.42050i	0.157881	−	0.418418i
$406$	−0.102099	+	0.0919302i	−0.00506708	+	0.00456242i
$407$	13.6652	+	18.8085i	0.677359	+	0.932305i
$408$	−5.44256	−	5.87090i	−0.269447	−	0.290653i
$409$	−16.0188	−	9.24846i	−0.792079	−	0.457307i	0.0486150	−	0.998818i	$-0.484519\pi$
$409$	−16.0188	−	9.24846i	−0.792079	−	0.457307i	−0.840694	+	0.541511i	$0.817853\pi$
$410$	9.43164	−	0.991305i	0.465795	−	0.0489571i
$411$	5.50763	−	12.8700i	0.271671	−	0.634828i
$412$	0.680366	−	6.47325i	0.0335192	−	0.318914i
$413$	−0.259314	−	0.233487i	−0.0127600	−	0.0114892i
$414$	−0.115379	−	3.97282i	−0.00567057	−	0.195254i
$415$	0.551951	−	2.59673i	0.0270942	−	0.127468i
$416$	−5.52027	+	1.17337i	−0.270653	+	0.0575292i
$417$	−4.19599	+	3.14263i	−0.205478	+	0.153895i
$418$	−33.8790	−	11.0080i	−1.65708	−	0.538417i
$419$	1.99398	+	0.647883i	0.0974123	+	0.0316512i	0.357318	−	0.933983i	$-0.383691\pi$
$419$	1.99398	+	0.647883i	0.0974123	+	0.0316512i	−0.259905	+	0.965634i	$0.583691\pi$
$420$	−0.0768752	+	0.0575765i	−0.00375113	+	0.00280945i
$421$	−9.89485	+	2.10321i	−0.482245	+	0.102504i	−0.442618	−	0.896710i	$-0.645950\pi$
$421$	−9.89485	+	2.10321i	−0.482245	+	0.102504i	−0.0396271	+	0.999215i	$0.512617\pi$
$422$	−0.873567	+	4.10981i	−0.0425246	+	0.200063i
$423$	−0.0320478	−	1.10350i	−0.00155822	−	0.0536538i
$424$	3.38479	+	3.04767i	0.164380	+	0.148008i
$425$	0.483131	−	4.59669i	0.0234353	−	0.222972i
$426$	2.09299	−	4.89079i	0.101406	−	0.236960i
$427$	−0.331877	+	0.0348817i	−0.0160607	+	0.00168804i
$428$	17.3549	+	10.0198i	0.838879	+	0.484327i
$429$	−31.9602	−	34.4756i	−1.54305	−	1.66450i
$430$	1.46221	+	2.01256i	0.0705142	+	0.0970544i
$431$	−3.40460	+	3.06551i	−0.163994	+	0.147661i	−0.747042	−	0.664777i	$-0.768527\pi$
$431$	−3.40460	+	3.06551i	−0.163994	+	0.147661i	0.583048	+	0.812438i	$0.301860\pi$
$432$	−2.86831	+	4.33276i	−0.138001	+	0.208460i
$433$		−	0.0498821i		−	0.00239718i	−0.999999	−	0.00119859i	$-0.999618\pi$
$433$		−	0.0498821i		−	0.00239718i	0.999999	−	0.00119859i	$-0.000381523\pi$
$434$	0.0270650	+	0.307557i	0.00129916	+	0.0147632i
$435$	−4.18413	+	0.953051i	−0.200614	+	0.0456953i
$436$	−3.12570	−	9.61992i	−0.149694	−	0.460711i
$437$	−6.56621	−	7.29251i	−0.314104	−	0.348848i
$438$	9.27667	+	8.11203i	0.443256	+	0.387608i
$439$	−14.9447	−	25.8850i	−0.713273	−	1.23543i	−0.963622	−	0.267269i	$-0.913879\pi$
$439$	−14.9447	−	25.8850i	−0.713273	−	1.23543i	0.250349	−	0.968156i	$-0.419455\pi$
$440$	−2.40465	+	4.16497i	−0.114637	+	0.198557i
$441$	−11.0187	−	17.8662i	−0.524699	−	0.850772i
$442$	−21.1030	−	15.3322i	−1.00377	−	0.729279i
$443$	32.6130	+	3.42777i	1.54949	+	0.162858i	0.840286	−	0.542144i	$-0.182387\pi$
$443$	32.6130	+	3.42777i	1.54949	+	0.162858i	0.709205	+	0.705002i	$0.249054\pi$
$444$	4.08075	−	7.31116i	0.193664	−	0.346972i
$445$	3.06511	−	6.88434i	0.145300	−	0.326349i
$446$	−19.4988	−	4.14460i	−0.923294	−	0.196252i
$447$	−13.4086	+	6.20468i	−0.634207	+	0.293471i
$448$	0.0506582	−	0.0225545i	0.00239337	−	0.00106560i
$449$	−7.83440	+	24.1118i	−0.369728	+	1.13791i	0.577239	+	0.816575i	$0.304130\pi$
$449$	−7.83440	+	24.1118i	−0.369728	+	1.13791i	−0.946967	+	0.321331i	$0.895870\pi$
$450$	−2.97320	+	0.400066i	−0.140158	+	0.0188593i
$451$	−18.5510	−	41.6663i	−0.873533	−	1.96199i
$452$	−0.244416	−	1.14989i	−0.0114964	−	0.0540861i
$453$	31.1949	−	0.452887i	1.46566	−	0.0212785i
$454$	5.13416	+	2.28588i	0.240958	+	0.107282i
$455$	−0.209404	+	0.232567i	−0.00981703	+	0.0109029i
$456$	1.52610	+	12.7382i	0.0714663	+	0.596521i
$457$	3.62253	−	4.98599i	0.169455	−	0.233235i	−0.715840	−	0.698264i	$-0.753956\pi$
$457$	3.62253	−	4.98599i	0.169455	−	0.233235i	0.885295	+	0.465029i	$0.153956\pi$
$458$	2.39809	+	22.8163i	0.112056	+	1.06614i
$459$	−23.7531	+	3.54793i	−1.10870	+	0.165603i
$460$	−1.14734	+	0.662417i	−0.0534950	+	0.0308853i
$461$	−20.8915	+	15.1785i	−0.973013	+	0.706935i	−0.956136	−	0.292922i	$-0.905372\pi$
$461$	−20.8915	+	15.1785i	−0.973013	+	0.706935i	−0.0168765	+	0.999858i	$0.505372\pi$
$462$	0.377599	+	0.266053i	0.0175675	+	0.0123779i
$463$	−11.9045	+	3.86802i	−0.553251	+	0.179762i	−0.572282	−	0.820057i	$-0.693942\pi$
$463$	−11.9045	+	3.86802i	−0.553251	+	0.179762i	0.0190314	+	0.999819i	$0.493942\pi$
$464$	2.47758			0.115019
$465$	−3.94381	+	8.80036i	−0.182890	+	0.408107i
$466$	−17.3662			−0.804474
$467$	−3.68440	+	1.19713i	−0.170494	+	0.0553968i	−0.393020	−	0.919530i	$-0.628570\pi$
$467$	−3.68440	+	1.19713i	−0.170494	+	0.0553968i	0.222526	+	0.974927i	$0.428570\pi$
$468$	−6.43446	+	15.6604i	−0.297433	+	0.723904i
$469$	0.148300	−	0.107746i	0.00684786	−	0.00497526i
$470$	−0.318686	+	0.183994i	−0.0146999	+	0.00848699i
$471$	−15.3819	−	4.75214i	−0.708759	−	0.218967i
$472$	0.657760	+	6.25817i	0.0302759	+	0.288056i
$473$	7.03222	−	9.67902i	0.323342	−	0.445042i
$474$	22.3509	−	2.67775i	1.02661	−	0.122993i
$475$	−4.95625	+	5.50447i	−0.227408	+	0.252563i
$476$	0.234142	+	0.104247i	0.0107319	+	0.00477815i
$477$	13.2773	−	3.22771i	0.607928	−	0.147787i
$478$	−1.41370	−	6.65092i	−0.0646610	−	0.304206i
$479$	3.37512	+	7.58063i	0.154213	+	0.346368i	0.974086	−	0.226177i	$-0.0726228\pi$
$479$	3.37512	+	7.58063i	0.154213	+	0.346368i	−0.819873	+	0.572545i	$0.805956\pi$
$480$	1.72501	+	0.156024i	0.0787355	+	0.00712149i
$481$	8.43051	−	25.9464i	0.384398	−	1.18306i
$482$	21.7022	−	9.66244i	0.988508	−	0.440112i
$483$	0.0534372	+	0.115481i	0.00243148	+	0.00525455i
$484$	11.8643	+	2.52183i	0.539286	+	0.114629i
$485$	−1.00036	+	2.24684i	−0.0454238	+	0.102024i
$486$	5.87958	+	14.4371i	0.266703	+	0.654881i
$487$	38.4362	+	4.03981i	1.74171	+	0.183061i	0.921337	−	0.388766i	$-0.127099\pi$
$487$	38.4362	+	4.03981i	1.74171	+	0.183061i	0.820374	+	0.571827i	$0.193765\pi$
$488$	4.86857	+	3.53722i	0.220390	+	0.160123i
$489$	33.4311	−	11.4016i	1.51181	−	0.515597i
$490$	−3.49846	+	6.05951i	−0.158044	+	0.273741i
$491$	−1.15064	−	1.99297i	−0.0519277	−	0.0899415i	0.838893	−	0.544296i	$-0.183203\pi$
$491$	−1.15064	−	1.99297i	−0.0519277	−	0.0899415i	−0.890821	+	0.454355i	$0.849870\pi$
$492$	−10.8128	+	12.3652i	−0.487480	+	0.557467i
$493$	7.66249	+	8.51005i	0.345101	+	0.383274i
$494$	12.9176	+	39.7562i	0.581189	+	1.78871i
$495$	6.24851	+	13.0046i	0.280850	+	0.584514i
$496$	3.34851	−	4.44831i	0.150352	−	0.199735i
$497$			0.170316i			0.00763971i
$498$	2.35664	+	3.94832i	0.105603	+	0.176928i
$499$	10.8749	−	9.79176i	0.486825	−	0.438339i	−0.388806	−	0.921320i	$-0.627112\pi$
$499$	10.8749	−	9.79176i	0.486825	−	0.438339i	0.875631	+	0.482980i	$0.160446\pi$
$500$	0.587785	+	0.809017i	0.0262866	+	0.0361803i
$501$	25.9283	−	24.0365i	1.15839	−	1.07387i
$502$	−16.2102	−	9.35895i	−0.723496	−	0.417711i
$503$	22.0793	−	2.32063i	0.984466	−	0.103472i	0.401406	−	0.915900i	$-0.368522\pi$
$503$	22.0793	−	2.32063i	0.984466	−	0.103472i	0.583060	+	0.812429i	$0.301855\pi$
$504$	0.0298492	−	0.163657i	0.00132959	−	0.00728986i
$505$	1.83561	−	17.4647i	0.0816836	−	0.777167i
$506$	4.73496	+	4.26338i	0.210495	+	0.189530i
$507$	−6.32388	+	32.0311i	−0.280853	+	1.42255i
$508$	0.707742	−	3.32966i	0.0314010	−	0.147730i
$509$	−42.6201	+	9.05919i	−1.88910	+	0.401542i	−0.998574	−	0.0533821i	$-0.983000\pi$
$509$	−42.6201	+	9.05919i	−1.88910	+	0.401542i	−0.890530	+	0.454924i	$0.849667\pi$
$510$	4.79907	+	6.40764i	0.212506	+	0.283735i
$511$	−0.375223	−	0.121917i	−0.0165989	−	0.00539330i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	34.1377	+	17.7745i	1.50722	+	0.784766i
$514$	−13.7247	+	2.91727i	−0.605370	+	0.128675i
$515$	−1.35328	+	6.36667i	−0.0596326	+	0.280549i
$516$	−4.22717	−	0.834567i	−0.186091	−	0.0367397i
$517$	1.31519	+	1.18420i	0.0578419	+	0.0520811i
$518$	−0.0280201	+	0.266593i	−0.00123113	+	0.0117134i
$519$	21.7277	+	9.29825i	0.953740	+	0.408148i
$520$	5.61268	−	0.589916i	0.246132	−	0.0258695i
$521$	−6.88015	−	3.97226i	−0.301425	−	0.174028i	0.341658	−	0.939824i	$-0.389012\pi$
$521$	−6.88015	−	3.97226i	−0.301425	−	0.174028i	−0.643083	+	0.765797i	$0.722345\pi$
$522$	4.19246	−	6.13751i	0.183499	−	0.268632i
$523$	16.0130	+	22.0400i	0.700198	+	0.963741i	0.999953	+	0.00972406i	$0.00309531\pi$
$523$	16.0130	+	22.0400i	0.700198	+	0.963741i	−0.299754	+	0.954016i	$0.596905\pi$
$524$	0.163848	−	0.147530i	0.00715774	−	0.00644486i
$525$	0.0824725	−	0.0492255i	0.00359940	−	0.00214838i
$526$		−	3.87455i		−	0.168938i
$527$	25.6352	−	2.25590i	1.11669	−	0.0982685i
$528$	−1.84999	−	8.12192i	−0.0805105	−	0.353461i
$529$	−6.56501	−	20.2050i	−0.285435	−	0.878479i
$530$	−3.04767	−	3.38479i	−0.132383	−	0.147026i
$531$	16.6159	+	8.96038i	0.721068	+	0.388847i
$532$	−0.205367	−	0.355707i	−0.00890381	−	0.0154219i
$533$	−26.7608	+	46.3510i	−1.15914	+	2.00768i
$534$	4.21321	+	12.3538i	0.182324	+	0.534600i
$535$	−16.2124	−	11.7790i	−0.700925	−	0.509252i
$536$	−3.28760	−	0.345540i	−0.142003	−	0.0149251i
$537$	−20.6732	−	11.5388i	−0.892112	−	0.497936i
$538$	10.2039	−	22.9182i	0.439919	−	0.988075i
$539$	32.9150	+	6.99629i	1.41775	+	0.301352i
$540$	3.30549	−	4.00921i	0.142246	−	0.172529i
$541$	−30.9134	+	13.7635i	−1.32907	+	0.591740i	−0.943633	−	0.330995i	$-0.892616\pi$
$541$	−30.9134	+	13.7635i	−1.32907	+	0.591740i	−0.385436	+	0.922734i	$0.625949\pi$
$542$	−7.62761	+	23.4754i	−0.327634	+	1.00835i
$543$	1.34545	−	14.8753i	0.0577386	−	0.638361i
$544$	−1.87994	−	4.22241i	−0.0806017	−	0.181034i
$545$	2.10302	+	9.89395i	0.0900836	+	0.423810i
$546$	−0.00786857	−	0.541988i	−0.000336744	−	0.0231950i
$547$	13.8563	+	6.16924i	0.592454	+	0.263778i	0.680987	−	0.732296i	$-0.261551\pi$
$547$	13.8563	+	6.16924i	0.592454	+	0.263778i	−0.0885327	+	0.996073i	$0.528218\pi$
$548$	5.40810	−	6.00630i	0.231023	−	0.256577i
$549$	17.0009	−	6.07498i	0.725579	−	0.259274i
$550$	2.82683	−	3.89080i	0.120537	−	0.165904i
$551$	−1.91825	−	18.2509i	−0.0817202	−	0.777516i
$552$	0.677340	−	2.19243i	0.0288295	−	0.0933161i
$553$	−0.624137	+	0.360345i	−0.0265410	+	0.0153234i
$554$	−15.4198	+	11.2031i	−0.655123	+	0.475974i
$555$	−4.82262	+	6.84456i	−0.204709	+	0.290535i
$556$	−2.87855	+	0.935296i	−0.122078	+	0.0396654i
$557$	2.66733			0.113018			0.0565092	−	0.998402i	$-0.482003\pi$
$557$	2.66733			0.113018			0.0565092	+	0.998402i	$0.482003\pi$
$558$	−5.35325	−	15.8222i	−0.226621	−	0.669808i
$559$	−14.0394			−0.593802
$560$	−0.0527382	+	0.0171357i	−0.00222860	+	0.000724115i
$561$	22.1758	−	31.4733i	0.936264	−	1.32880i
$562$	−26.5250	+	19.2715i	−1.11889	+	0.812921i
$563$	34.4344	−	19.8807i	1.45124	−	0.837873i	0.452687	−	0.891670i	$-0.350466\pi$
$563$	34.4344	−	19.8807i	1.45124	−	0.837873i	0.998552	+	0.0537967i	$0.0171323\pi$
$564$	0.188139	−	0.608973i	0.00792207	−	0.0256424i
$565$	0.122881	+	1.16914i	0.00516965	+	0.0491859i
$566$	−10.9987	+	15.1384i	−0.462310	+	0.636315i
$567$	−0.354905	−	0.350876i	−0.0149046	−	0.0147354i
$568$	2.05516	−	2.28249i	0.0862328	−	0.0957712i
$569$	−36.6236	−	16.3059i	−1.53534	−	0.683578i	−0.547182	−	0.837013i	$-0.684300\pi$
$569$	−36.6236	−	16.3059i	−1.53534	−	0.683578i	−0.988159	+	0.153436i	$0.950966\pi$
$570$	−0.186236	−	12.8280i	−0.00780056	−	0.537304i
$571$	−4.26990	−	20.0883i	−0.178690	−	0.840670i	−0.972573	−	0.232599i	$-0.925277\pi$
$571$	−4.26990	−	20.0883i	−0.178690	−	0.840670i	0.793883	−	0.608071i	$-0.208056\pi$
$572$	−11.0395	−	24.7952i	−0.461586	−	1.03674i
$573$	−1.22684	+	13.5640i	−0.0512518	+	0.566642i
$574$	0.162508	−	0.500148i	0.00678295	−	0.0208758i
$575$	1.21030	−	0.538858i	0.0504728	−	0.0224719i
$576$	−2.37484	+	1.83307i	−0.0989516	+	0.0763779i
$577$	33.4289	+	7.10553i	1.39166	+	0.295807i	0.841954	−	0.539550i	$-0.181405\pi$
$577$	33.4289	+	7.10553i	1.39166	+	0.295807i	0.549708	+	0.835357i	$0.314739\pi$
$578$	1.77457	−	3.98575i	0.0738124	−	0.165785i
$579$	−5.80190	−	3.23835i	−0.241119	−	0.134581i
$580$	−2.46401	−	0.258978i	−0.102312	−	0.0107535i
$581$	−0.119096	−	0.0865286i	−0.00494095	−	0.00358981i
$582$	−1.37506	−	4.03189i	−0.0569982	−	0.167127i
$583$	−10.9524	+	18.9701i	−0.453602	+	0.785662i
$584$	3.55740	+	6.16161i	0.147206	+	0.254969i
$585$	8.03617	−	14.9021i	0.332255	−	0.616124i
$586$	1.55018	+	1.72165i	0.0640372	+	0.0711206i
$587$	−13.4062	−	41.2600i	−0.553332	−	1.70298i	−0.700308	−	0.713841i	$-0.746954\pi$
$587$	−13.4062	−	41.2600i	−0.553332	−	1.70298i	0.146975	−	0.989140i	$-0.453046\pi$
$588$	−2.69150	−	11.8164i	−0.110996	−	0.487299i
$589$	−35.3607	−	21.2224i	−1.45701	−	0.874456i
$590$		−	6.29264i		−	0.259064i
$591$	19.9806	−	11.9259i	0.821892	−	0.490564i
$592$	3.59244	−	3.23465i	0.147648	−	0.132943i
$593$	−24.0691	−	33.1283i	−0.988401	−	1.36042i	−0.932178	−	0.361999i	$-0.882094\pi$
$593$	−24.0691	−	33.1283i	−0.988401	−	1.36042i	−0.0562229	−	0.998418i	$-0.517906\pi$
$594$	−23.2502	−	9.16072i	−0.953969	−	0.375869i
$595$	−0.221963	−	0.128150i	−0.00909959	−	0.00525365i
$596$	−8.48341	+	0.891642i	−0.347494	+	0.0365231i
$597$	−35.2458	−	15.0832i	−1.44251	−	0.617316i
$598$	0.781540	−	7.43586i	0.0319596	−	0.304075i
$599$	25.6952	+	23.1361i	1.04988	+	0.945316i	0.998575	−	0.0533675i	$-0.0169955\pi$
$599$	25.6952	+	23.1361i	1.04988	+	0.945316i	0.0513043	+	0.998683i	$0.483662\pi$
$600$	−1.69925	−	0.335482i	−0.0693716	−	0.0136960i
$601$	1.15150	−	5.41737i	0.0469706	−	0.220979i	−0.948402	−	0.317071i	$-0.897301\pi$
$601$	1.15150	−	5.41737i	0.0469706	−	0.220979i	0.995373	+	0.0960914i	$0.0306341\pi$
$602$	0.134932	−	0.0286807i	0.00549943	−	0.00116894i
$603$	−6.41910	+	7.55939i	−0.261406	+	0.307842i
$604$	17.1307	+	5.56610i	0.697038	+	0.226481i
$605$	−11.5357	−	3.74818i	−0.468993	−	0.152385i
$606$	18.2336	+	24.3452i	0.740689	+	0.988955i
$607$	41.6095	−	8.84438i	1.68888	−	0.358982i	0.739510	−	0.673145i	$-0.235057\pi$
$607$	41.6095	−	8.84438i	1.68888	−	0.358982i	0.949369	+	0.314163i	$0.101724\pi$
$608$	−1.54000	+	7.24514i	−0.0624553	+	0.293829i
$609$	−0.0460911	+	0.233456i	−0.00186770	+	0.00946011i
$610$	−4.47216	−	4.02675i	−0.181072	−	0.163038i
$611$	0.217082	−	2.06539i	0.00878218	−	0.0835569i
$612$	−13.6410	−	2.48796i	−0.551404	−	0.100570i
$613$	−38.4636	+	4.04269i	−1.55353	+	0.163283i	−0.842041	−	0.539414i	$-0.818646\pi$
$613$	−38.4636	+	4.04269i	−1.55353	+	0.163283i	−0.711489	+	0.702697i	$0.751979\pi$
$614$	10.8955	+	6.29052i	0.439707	+	0.253865i
$615$	12.0461	−	11.1672i	0.485746	−	0.450306i
$616$	0.156754	+	0.215754i	0.00631581	+	0.00869297i
$617$	−5.69407	+	5.12696i	−0.229235	+	0.206404i	−0.775741	−	0.631051i	$-0.782624\pi$
$617$	−5.69407	+	5.12696i	−0.229235	+	0.206404i	0.546507	+	0.837455i	$0.315957\pi$
$618$	−5.77802	−	9.68051i	−0.232426	−	0.389407i
$619$			18.7668i			0.754300i	0.926152	+	0.377150i	$0.123096\pi$
$619$			18.7668i			0.754300i	−0.926152	+	0.377150i	$0.876904\pi$
$620$	−3.79514	+	4.07393i	−0.152416	+	0.163613i
$621$	−4.28497	−	5.38785i	−0.171950	−	0.216207i
$622$	2.17624	+	6.69779i	0.0872594	+	0.268557i
$623$	−0.279616	−	0.310545i	−0.0112026	−	0.0124417i
$624$	−6.43461	+	7.35842i	−0.257590	+	0.294572i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	7.70242	−	13.3410i	0.307851	−	0.533213i
$627$	−58.3972	+	19.9161i	−2.33216	+	0.795374i
$628$	−7.51972	−	5.46340i	−0.300070	−	0.218013i
$629$	22.2209	+	2.33551i	0.886004	+	0.0931227i
$630$	−0.0467925	+	0.159640i	−0.00186426	+	0.00636022i
$631$	4.65845	−	10.4631i	0.185450	−	0.416528i	−0.796764	−	0.604290i	$-0.793457\pi$
$631$	4.65845	−	10.4631i	0.185450	−	0.416528i	0.982214	+	0.187762i	$0.0601235\pi$
$632$	12.7126	+	2.70215i	0.505680	+	0.107486i
$633$	3.05620	+	6.60460i	0.121473	+	0.262509i
$634$	−0.179703	+	0.0800088i	−0.00713691	+	0.00317756i
$635$	−1.05191	+	3.23744i	−0.0417437	+	0.128474i
$636$	7.85686	+	0.710639i	0.311545	+	0.0281787i
$637$	−16.0611	−	36.0739i	−0.636365	−	1.42930i
$638$	2.47736	+	11.6551i	0.0980796	+	0.461428i
$639$	−2.17657	−	8.95342i	−0.0861038	−	0.354192i
$640$	0.913545	+	0.406737i	0.0361111	+	0.0160777i
$641$	14.4259	−	16.0216i	0.569790	−	0.632816i	−0.387526	−	0.921859i	$-0.626670\pi$
$641$	14.4259	−	16.0216i	0.569790	−	0.632816i	0.957316	+	0.289043i	$0.0933371\pi$
$642$	34.4633	−	4.12887i	1.36016	−	0.162954i
$643$	−23.9445	+	32.9568i	−0.944280	+	1.29969i	0.00974134	+	0.999953i	$0.496899\pi$
$643$	−23.9445	+	32.9568i	−0.944280	+	1.29969i	−0.954022	+	0.299738i	$0.903101\pi$
$644$	0.00767918	+	0.0730625i	0.000302602	+	0.00287907i
$645$	4.11677	+	1.27185i	0.162098	+	0.0500792i
$646$	−29.6486	+	17.1176i	−1.16651	+	0.673483i
$647$	18.8482	−	13.6940i	0.740998	−	0.538367i	−0.152025	−	0.988377i	$-0.548580\pi$
$647$	18.8482	−	13.6940i	0.740998	−	0.538367i	0.893024	+	0.450010i	$0.148580\pi$
$648$	0.522317	+	8.98483i	0.0205185	+	0.352957i
$649$	−28.7820	+	9.35184i	−1.12979	+	0.367092i
$650$	−5.64359			−0.221360
$651$	0.356860	+	0.398274i	0.0139864	+	0.0156096i
$652$	20.3931			0.798656
$653$	−23.6532	+	7.68539i	−0.925622	+	0.300753i	−0.732771	−	0.680475i	$-0.761773\pi$
$653$	−23.6532	+	7.68539i	−0.925622	+	0.300753i	−0.192851	+	0.981228i	$0.561773\pi$
$654$	−14.3217	−	10.0910i	−0.560023	−	0.394588i
$655$	−0.178372	+	0.129595i	−0.00696956	+	0.00506368i
$656$	−8.21303	+	4.74179i	−0.320665	+	0.185136i
$657$	21.2833	+	1.61393i	0.830342	+	0.0629654i
$658$	0.00213298	+	0.0202939i	8.31522e−5	+	0.000791140i
$659$	−6.52985	+	8.98756i	−0.254367	+	0.350106i	−0.917035	−	0.398808i	$-0.869424\pi$
$659$	−6.52985	+	8.98756i	−0.254367	+	0.350106i	0.662668	+	0.748913i	$0.269424\pi$
$660$	0.990884	+	8.27080i	0.0385701	+	0.321941i
$661$	−11.8590	+	13.1707i	−0.461260	+	0.512281i	−0.928238	−	0.371988i	$-0.878676\pi$
$661$	−11.8590	+	13.1707i	−0.461260	+	0.512281i	0.466978	+	0.884269i	$0.345343\pi$
$662$	−27.9153	−	12.4287i	−1.08496	−	0.483055i
$663$	−45.1753	+	0.655854i	−1.75446	+	0.0254713i
$664$	0.551951	+	2.59673i	0.0214199	+	0.100773i
$665$	0.167061	+	0.375225i	0.00647835	+	0.0145506i
$666$	−1.93396	−	14.3728i	−0.0749394	−	0.556934i
$667$	−1.01431	+	3.12173i	−0.0392743	+	0.120874i
$668$	18.6479	−	8.30257i	0.721508	−	0.321236i
$669$	−31.3352	+	14.5000i	−1.21149	+	0.560601i
$670$	3.23347	+	0.687295i	0.124920	+	0.0265525i
$671$	−11.7717	+	26.4397i	−0.454441	+	1.02069i
$672$	0.0468106	−	0.0838668i	0.00180576	−	0.00323523i
$673$	20.7893	+	2.18504i	0.801367	+	0.0842271i	0.496353	−	0.868121i	$-0.334672\pi$
$673$	20.7893	+	2.18504i	0.801367	+	0.0842271i	0.305014	+	0.952348i	$0.401339\pi$
$674$	−24.8370	−	18.0451i	−0.956684	−	0.695072i
$675$	−3.70646	+	3.64173i	−0.142662	+	0.140170i
$676$	−9.42507	+	16.3247i	−0.362503	+	0.627873i
$677$	−16.8300	−	29.1503i	−0.646828	−	1.12034i	−0.983876	−	0.178851i	$-0.942762\pi$
$677$	−16.8300	−	29.1503i	−0.646828	−	1.12034i	0.337048	−	0.941487i	$-0.390571\pi$
$678$	−1.53278	−	1.34035i	−0.0588660	−	0.0514757i
$679$	0.0912581	+	0.101352i	0.00350216	+	0.00388955i
$680$	1.42828	+	4.39579i	0.0547720	+	0.168571i
$681$	9.49110	−	2.16186i	0.363700	−	0.0828426i
$682$	24.2740	+	11.3041i	0.929499	+	0.432858i
$683$		−	3.06638i		−	0.117332i	−0.998278	−	0.0586659i	$-0.981315\pi$
$683$		−	3.06638i		−	0.117332i	0.998278	−	0.0586659i	$-0.0186847\pi$
$684$	15.3419	+	16.0748i	0.586611	+	0.614636i
$685$	−6.00630	+	5.40810i	−0.229489	+	0.206633i
$686$	0.456216	+	0.627928i	0.0174184	+	0.0239744i
$687$	27.0149	+	29.1411i	1.03068	+	1.11180i
$688$	−2.15438	−	1.24383i	−0.0821350	−	0.0474207i
$689$	25.5639	−	2.68688i	0.973909	−	0.102362i
$690$	−0.902801	+	2.10962i	−0.0343690	+	0.0803119i
$691$	3.20024	−	30.4483i	0.121743	−	1.15831i	−0.747618	−	0.664129i	$-0.768803\pi$
$691$	3.20024	−	30.4483i	0.121743	−	1.15831i	0.869361	−	0.494178i	$-0.164531\pi$
$692$	10.1401	+	9.13023i	0.385470	+	0.347079i
$693$	0.799722	−	0.0232256i	0.0303789	−	0.000882267i
$694$	−4.55859	+	21.4465i	−0.173042	+	0.814097i
$695$	2.96054	−	0.629283i	0.112300	−	0.0238700i
$696$	3.43475	−	2.57249i	0.130194	−	0.0975102i
$697$	−41.6879	−	13.5452i	−1.57904	−	0.513061i
$698$	11.0969	+	3.60560i	0.420024	+	0.136474i
$699$	−24.0753	+	18.0315i	−0.910613	+	0.682013i
$700$	0.0542405	−	0.0115292i	0.00205010	−	0.000435762i
$701$	2.85404	−	13.4272i	0.107796	−	0.507138i	−0.890811	−	0.454373i	$-0.849863\pi$
$701$	2.85404	−	13.4272i	0.107796	−	0.507138i	0.998607	−	0.0527651i	$-0.0168035\pi$
$702$	7.34005	+	28.3915i	0.277032	+	1.07157i
$703$	−26.6092	−	23.9590i	−1.00358	−	0.903632i
$704$	0.502709	−	4.78295i	0.0189465	−	0.180264i
$705$	−0.250763	+	0.585971i	−0.00944428	+	0.0220689i
$706$	−33.6200	+	3.53360i	−1.26530	+	0.132989i
$707$	−0.843326	−	0.486895i	−0.0317166	−	0.0183116i
$708$	7.40978	+	7.99294i	0.278477	+	0.300393i
$709$	17.2317	+	23.7174i	0.647151	+	0.890727i	0.998972	−	0.0453406i	$-0.0144373\pi$
$709$	17.2317	+	23.7174i	0.647151	+	0.890727i	−0.351821	+	0.936067i	$0.614437\pi$
$710$	−2.28249	+	2.05516i	−0.0856604	+	0.0771290i
$711$	28.2055	−	26.9194i	1.05779	−	1.00956i
$712$			7.53585i			0.282418i
$713$	4.23397	+	6.04021i	0.158563	+	0.226208i
$714$	0.432839	−	0.0985911i	0.0161986	−	0.00368968i
$715$	8.38725	+	25.8133i	0.313666	+	0.965363i
$716$	−9.14633	−	10.1580i	−0.341815	−	0.379623i
$717$	−8.86556	−	7.75253i	−0.331090	−	0.289524i
$718$	−12.6682	−	21.9419i	−0.472772	−	0.818865i
$719$	10.8375	−	18.7710i	0.404169	−	0.700041i	−0.590055	−	0.807363i	$-0.700894\pi$
$719$	10.8375	−	18.7710i	0.404169	−	0.700041i	0.994224	+	0.107321i	$0.0342274\pi$
$720$	2.55344	−	1.57479i	0.0951610	−	0.0586889i
$721$	0.292002	+	0.212152i	0.0108747	+	0.00790094i
$722$	35.6672	+	3.74877i	1.32740	+	0.139515i
$723$	20.0539	−	35.9289i	0.745811	−	1.33621i
$724$	3.50742	−	7.87780i	0.130352	−	0.292776i
$725$	2.42344	+	0.515119i	0.0900044	+	0.0191310i
$726$	19.0663	−	8.82269i	0.707617	−	0.327441i
$727$	27.8518	−	12.4004i	1.03297	−	0.459906i	0.180988	−	0.983485i	$-0.442070\pi$
$727$	27.8518	−	12.4004i	1.03297	−	0.459906i	0.851977	+	0.523579i	$0.175404\pi$
$728$	0.0967069	−	0.297633i	0.00358420	−	0.0110310i
$729$	23.1412	+	13.9098i	0.857082	+	0.515179i
$730$	−2.89385	−	6.49970i	−0.107106	−	0.240565i
$731$	−2.39057	−	11.2467i	−0.0884184	−	0.415976i
$732$	10.4222	−	0.151309i	0.385215	−	0.00559254i
$733$	9.20971	+	4.10043i	0.340168	+	0.151453i	0.569709	−	0.821846i	$-0.307056\pi$
$733$	9.20971	+	4.10043i	0.340168	+	0.151453i	−0.229541	+	0.973299i	$0.573722\pi$
$734$	−4.40348	+	4.89056i	−0.162535	+	0.180514i
$735$	1.44161	+	12.0330i	0.0531746	+	0.443843i
$736$	0.778717	−	1.07181i	0.0287039	−	0.0395075i
$737$	−1.66181	−	15.8110i	−0.0612134	−	0.582407i
$738$	−2.15127	+	28.3693i	−0.0791892	+	1.04429i
$739$	−15.8869	+	9.17233i	−0.584410	+	0.337409i	−0.762884	−	0.646535i	$-0.776217\pi$
$739$	−15.8869	+	9.17233i	−0.584410	+	0.337409i	0.178474	+	0.983945i	$0.442884\pi$
$740$	−3.91087	+	2.84141i	−0.143766	+	0.104452i
$741$	59.1872	+	41.7028i	2.17429	+	1.53199i
$742$	−0.240206	+	0.0780476i	−0.00881823	+	0.00286522i
$743$	9.74870			0.357645			0.178823	−	0.983881i	$-0.442771\pi$
$743$	9.74870			0.357645			0.178823	+	0.983881i	$0.442771\pi$
$744$	0.0234219	−	9.64362i	0.000858688	−	0.353552i
$745$	8.53013			0.312520
$746$	4.03602	−	1.31138i	0.147769	−	0.0480131i
$747$	7.36665	+	3.02676i	0.269532	+	0.110743i
$748$	17.9833	−	13.0656i	0.657535	−	0.477727i
$749$	−0.962367	+	0.555623i	−0.0351641	+	0.0203020i
$750$	1.65487	+	0.511264i	0.0604275	+	0.0186687i
$751$	3.83030	+	36.4428i	0.139770	+	1.32982i	0.809459	+	0.587177i	$0.199761\pi$
$751$	3.83030	+	36.4428i	0.139770	+	1.32982i	−0.669689	+	0.742641i	$0.733573\pi$
$752$	0.216298	−	0.297708i	0.00788756	−	0.0108563i
$753$	−32.1902	+	3.85654i	−1.17308	+	0.140540i
$754$	9.35610	−	10.3910i	0.340729	−	0.378418i
$755$	−16.4550	−	7.32625i	−0.598860	−	0.266630i
$756$	−0.128545	−	0.257876i	−0.00467515	−	0.00937884i
$757$	−5.82549	−	27.4068i	−0.211731	−	0.996116i	−0.947715	−	0.319117i	$-0.896614\pi$
$757$	−5.82549	−	27.4068i	−0.211731	−	0.996116i	0.735984	−	0.676998i	$-0.236720\pi$
$758$	−13.4930	−	30.3059i	−0.490089	−	1.10076i
$759$	10.9909	+	0.994110i	0.398945	+	0.0360839i
$760$	2.28889	−	7.04448i	0.0830267	−	0.255530i
$761$	7.18615	−	3.19948i	0.260498	−	0.115981i	−0.272332	−	0.962203i	$-0.587795\pi$
$761$	7.18615	−	3.19948i	0.260498	−	0.115981i	0.532830	+	0.846222i	$0.321128\pi$
$762$	−2.47605	−	5.35087i	−0.0896978	−	0.193842i
$763$	0.548642	+	0.116617i	0.0198622	+	0.00422183i
$764$	−3.19822	+	7.18332i	−0.115708	+	0.259883i
$765$	13.3062	+	3.90020i	0.481087	+	0.141012i
$766$	27.2126	+	2.86016i	0.983231	+	0.103342i
$767$	28.7307	+	20.8741i	1.03741	+	0.753719i
$768$	−1.63933	+	0.559089i	−0.0591544	+	0.0201744i
$769$	−20.1776	+	34.9486i	−0.727623	+	1.26028i	0.230262	+	0.973129i	$0.426042\pi$
$769$	−20.1776	+	34.9486i	−0.727623	+	1.26028i	−0.957885	+	0.287151i	$0.907292\pi$
$770$	−0.133343	−	0.230957i	−0.00480536	−	0.00832312i
$771$	−15.9980	+	18.2948i	−0.576152	+	0.658870i
$772$	−2.56691	−	2.85084i	−0.0923850	−	0.102604i
$773$	7.06065	+	21.7304i	0.253954	+	0.781589i	0.994034	+	0.109071i	$0.0347875\pi$
$773$	7.06065	+	21.7304i	0.253954	+	0.781589i	−0.740080	+	0.672519i	$0.765212\pi$
$774$	−6.72679	+	3.23211i	−0.241790	+	0.116176i
$775$	4.20019	−	3.65491i	0.150875	−	0.131288i
$776$		−	2.45947i		−	0.0882898i
$777$	0.237961	+	0.398681i	0.00853680	+	0.0143026i
$778$	24.7216	−	22.2594i	0.886312	−	0.798038i
$779$	41.2890	+	56.8294i	1.47933	+	2.03612i
$780$	7.16852	−	6.64551i	0.256674	−	0.237947i
$781$	12.7923	+	7.38563i	0.457744	+	0.264279i
$782$	6.08984	−	0.640068i	0.217772	−	0.0228888i
$783$	−0.560492	−	12.8617i	−0.0200304	−	0.459639i
$784$	0.731378	−	6.95860i	0.0261206	−	0.248521i
$785$	6.90745	+	6.21949i	0.246537	+	0.221983i
$786$	0.0739669	−	0.374650i	0.00263831	−	0.0133633i
$787$	−0.105509	+	0.496378i	−0.00376097	+	0.0176940i	−0.979988	−	0.199056i	$-0.936212\pi$
$787$	−0.105509	+	0.496378i	−0.00376097	+	0.0176940i	0.976227	+	0.216750i	$0.0695457\pi$
$788$	13.1408	−	2.79317i	0.468123	−	0.0995026i
$789$	−4.02297	−	5.37141i	−0.143222	−	0.191227i
$790$	−12.3605	−	4.01617i	−0.439767	−	0.142889i
$791$	0.0619978	+	0.0201443i	0.00220439	+	0.000716249i
$792$	−10.9978	−	9.33882i	−0.390788	−	0.331840i
$793$	33.2203	−	7.06120i	1.17969	−	0.250751i
$794$	−1.08159	+	5.08846i	−0.0383840	+	0.180583i
$795$	−7.73954	−	1.52801i	−0.274493	−	0.0541930i
$796$	−16.4489	−	14.8107i	−0.583016	−	0.524950i
$797$	1.29483	−	12.3195i	0.0458653	−	0.436380i	−0.947360	−	0.320172i	$-0.896259\pi$
$797$	1.29483	−	12.3195i	0.0458653	−	0.436380i	0.993225	−	0.116208i	$-0.0370739\pi$
$798$	−0.654041	−	0.279893i	−0.0231528	−	0.00990811i
$799$	1.69152	−	0.177786i	0.0598418	−	0.00628962i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$	18.6679	+	12.7518i	0.659599	+	0.450564i
$802$	−19.4038	−	26.7071i	−0.685172	−	0.943059i
$803$	−25.4284	+	22.8958i	−0.897348	+	0.807975i
$804$	−4.91648	+	2.93450i	−0.173391	+	0.103492i
$805$		−	0.0734650i		−	0.00258930i
$806$	−6.01129	−	30.8418i	−0.211739	−	1.08636i
$807$	−9.65025	−	42.3670i	−0.339705	−	1.49139i
$808$	5.42660	+	16.7014i	0.190907	+	0.587552i
$809$	20.0230	+	22.2378i	0.703972	+	0.781840i	0.984003	−	0.178151i	$-0.0570115\pi$
$809$	20.0230	+	22.2378i	0.703972	+	0.781840i	−0.280031	+	0.959991i	$0.590345\pi$
$810$	0.419715	−	8.99021i	0.0147473	−	0.315884i
$811$	−5.49777	−	9.52242i	−0.193053	−	0.334377i	0.753208	−	0.657783i	$-0.228506\pi$
$811$	−5.49777	−	9.52242i	−0.193053	−	0.334377i	−0.946260	+	0.323406i	$0.895172\pi$
$812$	−0.0686938	+	0.118981i	−0.00241068	+	0.00417542i
$813$	13.8003	+	40.4645i	0.483996	+	1.41915i
$814$	18.8085	+	13.6652i	0.659239	+	0.478965i
$815$	−20.2814	−	2.13166i	−0.710426	−	0.0746688i
$816$	−6.99039	−	3.90171i	−0.244712	−	0.136587i
$817$	−7.49459	+	16.8331i	−0.262202	+	0.588916i
$818$	−18.0927	−	3.84573i	−0.632597	−	0.134463i
$819$	−0.573659	−	0.743206i	−0.0200453	−	0.0259697i
$820$	8.66369	−	3.85732i	0.302549	−	0.134704i
$821$	−7.30538	+	22.4836i	−0.254959	+	0.784684i	0.738878	+	0.673839i	$0.235356\pi$
$821$	−7.30538	+	22.4836i	−0.254959	+	0.784684i	−0.993838	+	0.110845i	$0.964644\pi$
$822$	1.26103	−	13.9420i	0.0439835	−	0.486283i
$823$	12.5934	+	28.2853i	0.438979	+	0.985964i	0.988602	+	0.150551i	$0.0481048\pi$
$823$	12.5934	+	28.2853i	0.438979	+	0.985964i	−0.549623	+	0.835413i	$0.685229\pi$
$824$	−1.35328	−	6.36667i	−0.0471437	−	0.221794i
$825$	−0.120921	−	8.32907i	−0.00420994	−	0.289981i
$826$	−0.318774	−	0.141927i	−0.0110916	−	0.00493828i
$827$	14.8064	−	16.4442i	0.514870	−	0.571821i	−0.428509	−	0.903537i	$-0.640961\pi$
$827$	14.8064	−	16.4442i	0.514870	−	0.571821i	0.943379	+	0.331716i	$0.107628\pi$
$828$	−1.33740	−	3.74273i	−0.0464779	−	0.130069i
$829$	4.39246	−	6.04570i	0.152556	−	0.209976i	−0.725898	−	0.687803i	$-0.758575\pi$
$829$	4.39246	−	6.04570i	0.152556	−	0.209976i	0.878454	+	0.477827i	$0.158575\pi$
$830$	−0.277496	−	2.64020i	−0.00963202	−	0.0916426i
$831$	−9.74463	+	31.5417i	−0.338037	+	1.09417i
$832$	−4.88750	+	2.82180i	−0.169443	+	0.0978282i
$833$	26.1635	−	19.0089i	0.906511	−	0.658619i
$834$	−3.01949	+	4.28545i	−0.104557	+	0.148393i
$835$	−19.4136	+	6.30786i	−0.671835	+	0.218292i
$836$	−35.6225			−1.23203
$837$	−23.8497	−	16.3765i	−0.824367	−	0.566056i
$838$	2.09659			0.0724256
$839$	35.8569	−	11.6506i	1.23792	−	0.402224i	0.384342	−	0.923191i	$-0.374428\pi$
$839$	35.8569	−	11.6506i	1.23792	−	0.402224i	0.853577	+	0.520967i	$0.174428\pi$
$840$	−0.0553206	+	0.0785143i	−0.00190874	+	0.00270900i
$841$	18.4954	−	13.4377i	0.637773	−	0.463369i
$842$	−8.76063	+	5.05795i	−0.301911	+	0.174309i
$843$	−16.7627	+	54.2579i	−0.577337	+	1.86874i
$844$	0.439190	+	4.17861i	0.0151175	+	0.143834i
$845$	11.0798	−	15.2501i	0.381158	−	0.524619i
$846$	−0.371479	−	1.03958i	−0.0127717	−	0.0357416i
$847$	−0.450057	+	0.499839i	−0.0154641	+	0.0171747i
$848$	4.16091	+	1.85255i	0.142886	+	0.0636170i
$849$	0.470482	+	32.4069i	0.0161469	+	1.11220i
$850$	−0.960969	−	4.52100i	−0.0329610	−	0.155069i
$851$	2.60490	+	5.85069i	0.0892947	+	0.200559i
$852$	0.479212	−	5.29819i	0.0164175	−	0.181513i
$853$	−0.811071	+	2.49622i	−0.0277705	+	0.0854689i	−0.963981	−	0.265970i	$-0.914308\pi$
$853$	−0.811071	+	2.49622i	−0.0277705	+	0.0854689i	0.936211	+	0.351439i	$0.114308\pi$
$854$	−0.304855	+	0.135730i	−0.0104319	+	0.00464459i
$855$	−13.5775	−	17.5904i	−0.464342	−	0.601580i
$856$	19.6018	+	4.16648i	0.669974	+	0.142407i
$857$	−18.8426	+	42.3211i	−0.643650	+	1.44566i	0.236816	+	0.971554i	$0.423896\pi$
$857$	−18.8426	+	42.3211i	−0.643650	+	1.44566i	−0.880467	+	0.474108i	$0.842771\pi$
$858$	−41.0495	−	22.9119i	−1.40141	−	0.782201i
$859$	−18.5082	−	1.94530i	−0.631493	−	0.0663726i	−0.216626	−	0.976255i	$-0.569505\pi$
$859$	−18.5082	−	1.94530i	−0.631493	−	0.0663726i	−0.414867	+	0.909882i	$0.636172\pi$
$860$	2.01256	+	1.46221i	0.0686278	+	0.0498611i
$861$	−0.294018	−	0.862104i	−0.0100201	−	0.0293804i
$862$	−2.29067	+	3.96755i	−0.0780205	+	0.135135i
$863$	−6.44495	−	11.1630i	−0.219389	−	0.379993i	0.735232	−	0.677815i	$-0.237073\pi$
$863$	−6.44495	−	11.1630i	−0.219389	−	0.379993i	−0.954621	+	0.297822i	$0.903740\pi$
$864$	−1.38902	+	5.00706i	−0.0472555	+	0.170344i
$865$	−9.13023	−	10.1401i	−0.310437	−	0.344775i
$866$	−0.0154144	−	0.0474407i	−0.000523803	−	0.00161210i
$867$	−1.67829	−	7.36812i	−0.0569978	−	0.250235i
$868$	0.120781	+	0.284140i	0.00409956	+	0.00964434i
$869$			62.5045i			2.12032i
$870$	−3.68484	+	2.19937i	−0.124928	+	0.0745657i
$871$	−13.8642	+	12.4833i	−0.469769	+	0.422982i
$872$	−5.94544	−	8.18319i	−0.201338	−	0.277118i
$873$	−6.09264	−	4.16180i	−0.206205	−	0.140856i
$874$	−8.49834	−	4.90652i	−0.287461	−	0.165966i
$875$	−0.0551485	+	0.00579634i	−0.00186436	+	0.000195952i
$876$	11.3294	+	4.84835i	0.382785	+	0.163811i
$877$	−4.56922	+	43.4732i	−0.154292	+	1.46799i	0.593919	+	0.804525i	$0.297580\pi$
$877$	−4.56922	+	43.4732i	−0.154292	+	1.46799i	−0.748211	+	0.663461i	$0.769087\pi$
$878$	−22.2122	−	20.0000i	−0.749625	−	0.674966i
$879$	3.93666	+	0.777212i	0.132780	+	0.0262147i
$880$	−0.999909	+	4.70420i	−0.0337069	+	0.158579i
$881$	−1.69509	+	0.360302i	−0.0571089	+	0.0121389i	−0.236378	−	0.971661i	$-0.575960\pi$
$881$	−1.69509	+	0.360302i	−0.0571089	+	0.0121389i	0.179269	+	0.983800i	$0.442627\pi$
$882$	−16.0004	−	13.5868i	−0.538760	−	0.457492i
$883$	48.4255	+	15.7344i	1.62965	+	0.529505i	0.974191	−	0.225726i	$-0.0724756\pi$
$883$	48.4255	+	15.7344i	1.62965	+	0.529505i	0.655458	+	0.755231i	$0.272476\pi$
$884$	−24.8080	−	8.06062i	−0.834385	−	0.271108i
$885$	−6.53370	−	8.72369i	−0.219628	−	0.293244i
$886$	32.0761	−	6.81798i	1.07762	−	0.229054i
$887$	−2.64089	+	12.4244i	−0.0886724	+	0.417171i	0.911313	+	0.411715i	$0.135070\pi$
$887$	−2.64089	+	12.4244i	−0.0886724	+	0.417171i	−0.999985	+	0.00545591i	$0.998263\pi$
$888$	1.62175	−	8.21435i	0.0544225	−	0.275656i
$889$	0.140278	+	0.126307i	0.00470476	+	0.00423619i
$890$	0.787711	−	7.49457i	0.0264041	−	0.251218i
$891$	−41.7442	+	11.4411i	−1.39848	+	0.383291i
$892$	−19.8252	+	2.08371i	−0.663797	+	0.0697679i
$893$	−2.36051	−	1.36284i	−0.0789915	−	0.0456057i
$894$	−10.8350	+	10.0445i	−0.362377	+	0.335938i
$895$	8.03443	+	11.0584i	0.268561	+	0.369643i
$896$	0.0412091	−	0.0371048i	0.00137670	−	0.00123958i
$897$	−6.63724	−	11.1201i	−0.221611	−	0.371288i
$898$			25.3526i			0.846029i
$899$	−0.233748	+	13.7926i	−0.00779593	+	0.460010i
$900$	−2.70406	+	1.29926i	−0.0901353	+	0.0433085i
$901$	6.50535	+	20.0214i	0.216725	+	0.667010i
$902$	−30.5187	−	33.8944i	−1.01616	−	1.12856i
$903$	0.157281	−	0.179862i	0.00523400	−	0.00598544i
$904$	−0.587788	−	1.01808i	−0.0195495	−	0.0338608i
$905$	−4.31166	+	7.46802i	−0.143325	+	0.248245i
$906$	29.5281	−	10.0705i	0.981007	−	0.334569i
$907$	−8.01607	−	5.82401i	−0.266169	−	0.193383i	0.446693	−	0.894687i	$-0.352602\pi$
$907$	−8.01607	−	5.82401i	−0.266169	−	0.193383i	−0.712862	+	0.701304i	$0.752602\pi$
$908$	5.58926	+	0.587454i	0.185486	+	0.0194954i
$909$	50.5556	+	14.8184i	1.67682	+	0.491497i
$910$	−0.127288	+	0.285894i	−0.00421956	+	0.00947730i
$911$	4.29245	+	0.912388i	0.142215	+	0.0302288i	0.278469	−	0.960445i	$-0.410173\pi$
$911$	4.29245	+	0.912388i	0.142215	+	0.0302288i	−0.136254	+	0.990674i	$0.543506\pi$
$912$	5.38773	+	11.6432i	0.178406	+	0.385544i
$913$	−11.6636	+	5.19298i	−0.386010	+	0.171863i
$914$	1.90448	−	5.86138i	0.0629945	−	0.193877i
$915$	−10.3809	−	0.938935i	−0.343182	−	0.0310402i
$916$	9.33136	+	20.9586i	0.308317	+	0.692491i
$917$	0.00254195	+	0.0119589i	8.39425e−5	+	0.000394918i
$918$	−21.4942	+	10.7144i	−0.709415	+	0.353628i
$919$	17.3152	+	7.70922i	0.571176	+	0.254304i	0.671939	−	0.740607i	$-0.265462\pi$
$919$	17.3152	+	7.70922i	0.571176	+	0.254304i	−0.100763	+	0.994910i	$0.532128\pi$
$920$	−0.886486	+	0.984543i	−0.0292266	+	0.0324594i
$921$	21.6363	−	2.59213i	0.712940	−	0.0854137i
$922$	−15.1785	+	20.8915i	−0.499879	+	0.688024i
$923$	−1.81187	−	17.2388i	−0.0596383	−	0.567420i
$924$	0.441333	+	0.136347i	0.0145188	+	0.00448549i
$925$	4.18646	−	2.41705i	0.137650	−	0.0794722i
$926$	−10.1266	+	7.35741i	−0.332781	+	0.241779i
$927$	−18.0616	−	7.42104i	−0.593221	−	0.243739i
$928$	2.35632	−	0.765615i	0.0773501	−	0.0251326i
$929$	31.2383			1.02490			0.512448	−	0.858718i	$-0.328739\pi$
$929$	31.2383			1.02490			0.512448	+	0.858718i	$0.328739\pi$
$930$	−1.03133	+	9.58835i	−0.0338185	+	0.314414i
$931$	−51.8262			−1.69854
$932$	−16.5162	+	5.36645i	−0.541008	+	0.175784i
$933$	9.97136	+	7.02574i	0.326448	+	0.230013i
$934$	−3.13414	+	2.27708i	−0.102552	+	0.0745085i
$935$	−19.2505	+	11.1143i	−0.629560	+	0.363477i
$936$	−1.28020	+	16.8823i	−0.0418446	+	0.551816i
$937$	−3.73734	−	35.5584i	−0.122094	−	1.16164i	−0.868339	−	0.495971i	$-0.834812\pi$
$937$	−3.73734	−	35.5584i	−0.122094	−	1.16164i	0.746245	−	0.665671i	$-0.231855\pi$
$938$	0.107746	−	0.148300i	0.00351804	−	0.00484217i
$939$	−3.17394	−	26.4925i	−0.103577	−	0.864550i
$940$	−0.246232	+	0.273468i	−0.00803119	+	0.00891954i
$941$	6.66892	+	2.96920i	0.217401	+	0.0967930i	0.512547	−	0.858659i	$-0.328702\pi$
$941$	6.66892	+	2.96920i	0.217401	+	0.0967930i	−0.295147	+	0.955452i	$0.595369\pi$
$942$	−16.0975	+	0.233703i	−0.524486	+	0.00761447i
$943$	−2.61224	−	12.2896i	−0.0850662	−	0.400205i
$944$	2.55945	+	5.74861i	0.0833029	+	0.187101i
$945$	0.100886	+	0.269900i	0.00328182	+	0.00877983i
$946$	3.69706	−	11.3784i	0.120202	−	0.369943i
$947$	−45.3997	+	20.2132i	−1.47529	+	0.656842i	−0.977592	−	0.210508i	$-0.932488\pi$
$947$	−45.3997	+	20.2132i	−1.47529	+	0.656842i	−0.497699	+	0.867350i	$0.665822\pi$
$948$	20.4295	−	9.45352i	0.663520	−	0.307036i
$949$	39.2757	+	8.34830i	1.27494	+	0.270997i
$950$	−3.01270	+	6.76663i	−0.0977449	+	0.219539i
$951$	−0.166054	+	0.297506i	−0.00538467	+	0.00964728i
$952$	0.254897	+	0.0267907i	0.00826125	+	0.000868292i
$953$	27.2531	+	19.8005i	0.882814	+	0.641402i	0.933995	−	0.357287i	$-0.116298\pi$
$953$	27.2531	+	19.8005i	0.882814	+	0.641402i	−0.0511801	+	0.998689i	$0.516298\pi$
$954$	11.6301	−	7.17266i	0.376538	−	0.232223i
$955$	3.93156	−	6.80966i	0.127222	−	0.220355i
$956$	−3.39975	−	5.88854i	−0.109956	−	0.190449i
$957$	15.5360	+	13.5855i	0.502207	+	0.439157i
$958$	5.55247	+	6.16664i	0.179392	+	0.199235i
$959$	0.138495	+	0.426245i	0.00447225	+	0.0137642i
$960$	1.68880	−	0.384669i	0.0545056	−	0.0124152i
$961$	24.4477	+	19.0607i	0.788635	+	0.614861i
$962$		−	27.2817i		−	0.879598i
$963$	43.4905	−	41.5075i	1.40146	−	1.33756i
$964$	17.6542	−	15.8959i	0.568602	−	0.511972i
$965$	2.25485	+	3.10354i	0.0725863	+	0.0999064i
$966$	0.0865073	+	0.0933156i	0.00278333	+	0.00300238i
$967$	−20.6970	−	11.9494i	−0.665569	−	0.384267i	0.128826	−	0.991667i	$-0.458879\pi$
$967$	−20.6970	−	11.9494i	−0.665569	−	0.384267i	−0.794396	+	0.607400i	$0.792212\pi$
$968$	12.0629	−	1.26786i	0.387716	−	0.0407506i
$969$	−23.3294	+	54.5150i	−0.749448	+	1.75127i
$970$	−0.257084	+	2.44599i	−0.00825448	+	0.0785362i
$971$	1.21162	+	1.09095i	0.0388828	+	0.0350103i	0.688343	−	0.725385i	$-0.258338\pi$
$971$	1.21162	+	1.09095i	0.0388828	+	0.0350103i	−0.649460	+	0.760396i	$0.725005\pi$
$972$	10.0531	+	11.9136i	0.322454	+	0.382130i
$973$	0.0348951	−	0.164169i	0.00111869	−	0.00526301i
$974$	37.8034	−	8.03536i	1.21130	−	0.257469i
$975$	−7.82389	+	5.85979i	−0.250565	+	0.187663i
$976$	5.72335	+	1.85963i	0.183200	+	0.0595253i
$977$	−22.8662	−	7.42969i	−0.731555	−	0.237697i	−0.0805293	−	0.996752i	$-0.525661\pi$
$977$	−22.8662	−	7.42969i	−0.731555	−	0.237697i	−0.651026	+	0.759056i	$0.725661\pi$
$978$	28.2716	−	21.1743i	0.904027	−	0.677080i
$979$	−35.4502	+	7.53517i	−1.13299	+	0.240825i
$980$	−1.45474	+	6.84403i	−0.0464700	+	0.218624i
$981$	−30.3322	+	0.880909i	−0.968431	+	0.0281253i
$982$	−1.71019	−	1.53986i	−0.0545743	−	0.0491389i
$983$	−4.23128	+	40.2579i	−0.134957	+	1.28403i	0.692055	+	0.721845i	$0.256705\pi$
$983$	−4.23128	+	40.2579i	−0.134957	+	1.28403i	−0.827012	+	0.562184i	$0.809961\pi$
$984$	−6.46254	+	15.1014i	−0.206018	+	0.481414i
$985$	−13.3608	+	1.40428i	−0.425711	+	0.0447440i
$986$	9.91721	+	5.72570i	0.315828	+	0.182344i
$987$	0.0240284	+	0.0259195i	0.000764832	+	0.000825025i
$988$	24.5707	+	33.8186i	0.781697	+	1.07591i
$989$	2.44921	−	2.20528i	0.0778804	−	0.0701239i
$990$	9.96134	+	10.4372i	0.316592	+	0.331717i
$991$		−	13.0496i		−	0.414535i	−0.978284	−	0.207268i	$-0.933543\pi$
$991$		−	13.0496i		−	0.414535i	0.978284	−	0.207268i	$-0.0664571\pi$
$992$	1.81001	−	5.26534i	0.0574680	−	0.167175i
$993$	−51.6047	+	11.7544i	−1.63762	+	0.373014i
$994$	0.0526305	+	0.161980i	0.00166934	+	0.00513769i
$995$	14.8107	+	16.4489i	0.469530	+	0.521466i
$996$	3.46139	+	3.02683i	0.109678	+	0.0959088i
$997$	−5.10071	−	8.83469i	−0.161541	−	0.279797i	0.773880	−	0.633332i	$-0.218313\pi$
$997$	−5.10071	−	8.83469i	−0.161541	−	0.279797i	−0.935422	+	0.353534i	$0.884980\pi$
$998$	7.31678	−	12.6730i	0.231609	−	0.401158i
$999$	−17.6045	−	17.9174i	−0.556981	−	0.566881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.a.11.19	yes	176
3.2	odd	2	inner	930.2.br.a.11.11	✓	176
31.17	odd	30	inner	930.2.br.a.761.11	yes	176
93.17	even	30	inner	930.2.br.a.761.19	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.a.11.11	✓	176	3.2	odd	2	inner
930.2.br.a.11.19	yes	176	1.1	even	1	trivial
930.2.br.a.761.11	yes	176	31.17	odd	30	inner
930.2.br.a.761.19	yes	176	93.17	even	30	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.br (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(0.997625 - 1.41589i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.511264 - 1.65487i) q^{6} +(0.00579634 + 0.0551485i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.00949 - 2.82505i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(0.997625 - 1.41589i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.511264 - 1.65487i) q^{6} +(0.00579634 + 0.0551485i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.00949 - 2.82505i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(4.39351 + 1.95612i) q^{11} +(-0.0251432 - 1.73187i) q^{12} +(-1.17337 - 5.52027i) q^{13} +(0.0225545 + 0.0506582i) q^{14} +(-0.156024 + 1.72501i) q^{15} +(0.309017 - 0.951057i) q^{16} +(4.22241 - 1.87994i) q^{17} +(-1.83307 - 2.37484i) q^{18} +(-7.24514 - 1.54000i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(0.0838668 + 0.0468106i) q^{21} +(4.78295 + 0.502709i) q^{22} +(1.07181 + 0.778717i) q^{23} +(-0.559089 - 1.63933i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-2.82180 - 4.88750i) q^{26} +(-5.00706 - 1.38902i) q^{27} +(0.0371048 + 0.0412091i) q^{28} +(0.765615 + 2.35632i) q^{29} +(0.384669 + 1.68880i) q^{30} +(5.26534 + 1.81001i) q^{31} -1.00000i q^{32} +(7.15273 - 4.26926i) q^{33} +(3.43482 - 3.09273i) q^{34} +(-0.0325940 - 0.0448618i) q^{35} +(-2.47722 - 1.69216i) q^{36} +(4.18646 + 2.41705i) q^{37} +(-7.36642 + 0.774242i) q^{38} +(-8.98667 - 3.84580i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(-7.04768 - 6.34576i) q^{41} +(0.0942273 + 0.0186032i) q^{42} +(0.517215 - 2.43330i) q^{43} +(4.70420 - 0.999909i) q^{44} +(2.28677 + 1.94183i) q^{45} +(1.25999 + 0.409396i) q^{46} +(0.349977 + 0.113714i) q^{47} +(-1.03831 - 1.38633i) q^{48} +(6.84403 - 1.45474i) q^{49} +(0.207912 - 0.978148i) q^{50} +(1.55060 - 7.85395i) q^{51} +(-4.19401 - 3.77630i) q^{52} +(-0.476094 + 4.52973i) q^{53} +(-5.19123 + 0.226225i) q^{54} +(-4.78295 + 0.502709i) q^{55} +(0.0480231 + 0.0277261i) q^{56} +(-9.40841 + 8.72197i) q^{57} +(1.45629 + 2.00441i) q^{58} +(-4.67634 + 4.21060i) q^{59} +(0.887709 + 1.48727i) q^{60} +6.01788i q^{61} +(5.56696 + 0.0943451i) q^{62} +(0.149946 - 0.0720467i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(3.77630 + 4.19401i) q^{65} +(5.48337 - 6.27062i) q^{66} +(-1.65285 - 2.86283i) q^{67} +(2.31100 - 4.00278i) q^{68} +(2.17185 - 0.740700i) q^{69} +(-0.0448618 - 0.0325940i) q^{70} +(3.05457 + 0.321048i) q^{71} +(-2.87888 - 0.843833i) q^{72} +(-2.89385 + 6.49970i) q^{73} +(4.72847 + 1.00507i) q^{74} +(-0.727384 - 1.57191i) q^{75} +(-6.76663 + 3.01270i) q^{76} +(-0.0824107 + 0.253634i) q^{77} +(-9.73525 - 0.880536i) q^{78} +(5.28619 + 11.8730i) q^{79} +(0.207912 + 0.978148i) q^{80} +(-6.96187 + 5.70371i) q^{81} +(-8.66369 - 3.85732i) q^{82} +(-1.77637 + 1.97286i) q^{83} +(0.0953642 - 0.0114251i) q^{84} +(-2.71675 + 3.73928i) q^{85} +(-0.260032 - 2.47404i) q^{86} +(4.10009 + 1.26670i) q^{87} +(4.16497 - 2.40465i) q^{88} +(-6.09663 + 4.42946i) q^{89} +(2.77490 + 1.14014i) q^{90} +(0.297633 - 0.0967069i) q^{91} +1.32483 q^{92} +(7.81562 - 5.64943i) q^{93} +0.367987 q^{94} +(7.04448 - 2.28889i) q^{95} +(-1.41589 - 0.997625i) q^{96} +(1.98975 - 1.44564i) q^{97} +(6.05951 - 3.49846i) q^{98} +(1.09095 - 14.3866i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9	\( 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 q^{99}+O(q^{100}) \) 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9 - 22 * q^10 - 38 * q^13 - 44 * q^16 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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