LMFDB - Embedded newform 930.2.br.a.11.1

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			11.1
Character	$\chi$	$=$	930.11
Dual form			930.2.br.a.761.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(-1.68681 + 0.393302i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.48271 - 0.895304i) q^{6} +(0.503857 + 4.79388i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(2.69063 - 1.32685i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(-1.68681 + 0.393302i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.48271 - 0.895304i) q^{6} +(0.503857 + 4.79388i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(2.69063 - 1.32685i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(3.34625 + 1.48985i) q^{11} +(-1.13348 + 1.30967i) q^{12} +(0.191369 + 0.900318i) q^{13} +(-1.96059 - 4.40355i) q^{14} +(-1.26417 + 1.18401i) q^{15} +(0.309017 - 0.951057i) q^{16} +(3.22729 - 1.43688i) q^{17} +(-2.14892 + 2.09336i) q^{18} +(-2.91014 - 0.618569i) q^{19} +(0.406737 - 0.913545i) q^{20} +(-2.73535 - 7.88818i) q^{21} +(-3.64286 - 0.382880i) q^{22} +(-0.0893379 - 0.0649078i) q^{23} +(0.673291 - 1.59583i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-0.460216 - 0.797118i) q^{26} +(-4.01671 + 3.29636i) q^{27} +(3.22540 + 3.58217i) q^{28} +(-1.02341 - 3.14975i) q^{29} +(0.836413 - 1.51671i) q^{30} +(4.68773 - 3.00420i) q^{31} +1.00000i q^{32} +(-6.23044 - 1.19700i) q^{33} +(-2.62532 + 2.36385i) q^{34} +(2.83329 + 3.89970i) q^{35} +(1.39686 - 2.65495i) q^{36} +(-0.546407 - 0.315469i) q^{37} +(2.95885 - 0.310988i) q^{38} +(-0.676899 - 1.44340i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(7.90791 + 7.12032i) q^{41} +(5.03906 + 6.65684i) q^{42} +(-2.30910 + 10.8635i) q^{43} +(3.58288 - 0.761566i) q^{44} +(1.66673 - 2.49440i) q^{45} +(0.105023 + 0.0341240i) q^{46} +(1.38892 + 0.451286i) q^{47} +(-0.147199 + 1.72578i) q^{48} +(-15.8804 + 3.37549i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(-4.87869 + 3.69304i) q^{51} +(0.684014 + 0.615889i) q^{52} +(0.987013 - 9.39081i) q^{53} +(2.80149 - 4.37626i) q^{54} +(3.64286 - 0.382880i) q^{55} +(-4.17449 - 2.41014i) q^{56} +(5.15212 - 0.101158i) q^{57} +(1.94665 + 2.67933i) q^{58} +(0.439186 - 0.395444i) q^{59} +(-0.326786 + 1.70094i) q^{60} +6.64933i q^{61} +(-3.52995 + 4.30575i) q^{62} +(7.71645 + 12.2300i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.615889 + 0.684014i) q^{65} +(6.29539 - 0.786900i) q^{66} +(6.53705 + 11.3225i) q^{67} +(1.76636 - 3.05942i) q^{68} +(0.176224 + 0.0743500i) q^{69} +(-3.89970 - 2.83329i) q^{70} +(-11.4080 - 1.19903i) q^{71} +(-0.508068 + 2.95666i) q^{72} +(-0.190059 + 0.426879i) q^{73} +(0.617150 + 0.131179i) q^{74} +(-0.502793 + 1.65747i) q^{75} +(-2.71794 + 1.21010i) q^{76} +(-5.45612 + 16.7922i) q^{77} +(1.08980 + 1.16358i) q^{78} +(1.63235 + 3.66631i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(5.47895 - 7.14011i) q^{81} +(-9.72117 - 4.32814i) q^{82} +(-6.02984 + 6.69682i) q^{83} +(-6.84950 - 4.77387i) q^{84} +(2.07648 - 2.85802i) q^{85} +(-1.16091 - 11.0453i) q^{86} +(2.96510 + 4.91050i) q^{87} +(-3.17219 + 1.83146i) q^{88} +(8.73850 - 6.34889i) q^{89} +(-0.814340 + 2.88736i) q^{90} +(-4.21960 + 1.37103i) q^{91} -0.110428 q^{92} +(-6.72573 + 6.91119i) q^{93} -1.46039 q^{94} +(-2.82954 + 0.919372i) q^{95} +(-0.393302 - 1.68681i) q^{96} +(-9.20631 + 6.68877i) q^{97} +(14.0601 - 8.11759i) q^{98} +(10.9803 - 0.431345i) 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
$3$	−1.68681	+	0.393302i	−0.973878	+	0.227073i
$3$	−1.68681	+	0.393302i	−0.973878	+	0.227073i
$4$	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
$6$	1.48271	−	0.895304i	0.605314	−	0.365506i
$7$	0.503857	+	4.79388i	0.190440	+	1.81192i	0.505479	+	0.862839i	$0.331316\pi$
$7$	0.503857	+	4.79388i	0.190440	+	1.81192i	−0.315039	+	0.949079i	$0.602018\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	2.69063	−	1.32685i	0.896876	−	0.442283i
$10$	−0.669131	+	0.743145i	−0.211598	+	0.235003i
$11$	3.34625	+	1.48985i	1.00893	+	0.449206i	0.843566	−	0.537026i	$-0.180452\pi$
$11$	3.34625	+	1.48985i	1.00893	+	0.449206i	0.165367	+	0.986232i	$0.447119\pi$
$12$	−1.13348	+	1.30967i	−0.327207	+	0.378068i
$13$	0.191369	+	0.900318i	0.0530761	+	0.249703i	0.996685	−	0.0813594i	$-0.0259261\pi$
$13$	0.191369	+	0.900318i	0.0530761	+	0.249703i	−0.943609	+	0.331063i	$0.892593\pi$
$14$	−1.96059	−	4.40355i	−0.523989	−	1.17690i
$15$	−1.26417	+	1.18401i	−0.326406	+	0.305711i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	3.22729	−	1.43688i	0.782733	−	0.348495i	0.0238447	−	0.999716i	$-0.492409\pi$
$17$	3.22729	−	1.43688i	0.782733	−	0.348495i	0.758889	+	0.651220i	$0.225743\pi$
$18$	−2.14892	+	2.09336i	−0.506505	+	0.493409i
$19$	−2.91014	−	0.618569i	−0.667631	−	0.141909i	−0.138386	−	0.990378i	$-0.544192\pi$
$19$	−2.91014	−	0.618569i	−0.667631	−	0.141909i	−0.529245	+	0.848469i	$0.677525\pi$
$20$	0.406737	−	0.913545i	0.0909491	−	0.204275i
$21$	−2.73535	−	7.88818i	−0.596903	−	1.72134i
$22$	−3.64286	−	0.382880i	−0.776661	−	0.0816303i
$23$	−0.0893379	−	0.0649078i	−0.0186282	−	0.0135342i	0.578432	−	0.815730i	$-0.303665\pi$
$23$	−0.0893379	−	0.0649078i	−0.0186282	−	0.0135342i	−0.597060	+	0.802196i	$0.703665\pi$
$24$	0.673291	−	1.59583i	0.137435	−	0.325748i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−0.460216	−	0.797118i	−0.0902558	−	0.156328i
$27$	−4.01671	+	3.29636i	−0.773017	+	0.634386i
$28$	3.22540	+	3.58217i	0.609544	+	0.676967i
$29$	−1.02341	−	3.14975i	−0.190043	−	0.584893i	0.809955	−	0.586491i	$-0.199491\pi$
$29$	−1.02341	−	3.14975i	−0.190043	−	0.584893i	−0.999999	+	0.00159839i	$0.999491\pi$
$30$	0.836413	−	1.51671i	0.152707	−	0.276912i
$31$	4.68773	−	3.00420i	0.841941	−	0.539570i
$31$	4.68773	−	3.00420i	0.841941	−	0.539570i
$32$			1.00000i			0.176777i
$33$	−6.23044	−	1.19700i	−1.08458	−	0.208370i
$34$	−2.62532	+	2.36385i	−0.450238	+	0.405396i
$35$	2.83329	+	3.89970i	0.478914	+	0.659169i
$36$	1.39686	−	2.65495i	0.232810	−	0.442492i
$37$	−0.546407	−	0.315469i	−0.0898288	−	0.0518627i	0.454413	−	0.890791i	$-0.349849\pi$
$37$	−0.546407	−	0.315469i	−0.0898288	−	0.0518627i	−0.544242	+	0.838929i	$0.683182\pi$
$38$	2.95885	−	0.310988i	0.479989	−	0.0504489i
$39$	−0.676899	−	1.44340i	−0.108391	−	0.231128i
$40$	−0.104528	+	0.994522i	−0.0165274	+	0.157248i
$41$	7.90791	+	7.12032i	1.23501	+	1.11201i	0.989789	+	0.142539i	$0.0455267\pi$
$41$	7.90791	+	7.12032i	1.23501	+	1.11201i	0.245220	+	0.969468i	$0.421140\pi$
$42$	5.03906	+	6.65684i	0.777544	+	1.02717i
$43$	−2.30910	+	10.8635i	−0.352134	+	1.65666i	0.344165	+	0.938909i	$0.388162\pi$
$43$	−2.30910	+	10.8635i	−0.352134	+	1.65666i	−0.696299	+	0.717752i	$0.745171\pi$
$44$	3.58288	−	0.761566i	0.540140	−	0.114810i
$45$	1.66673	−	2.49440i	0.248461	−	0.371843i
$46$	0.105023	+	0.0341240i	0.0154848	+	0.00503132i
$47$	1.38892	+	0.451286i	0.202594	+	0.0658268i	0.408556	−	0.912733i	$-0.366032\pi$
$47$	1.38892	+	0.451286i	0.202594	+	0.0658268i	−0.205962	+	0.978560i	$0.566032\pi$
$48$	−0.147199	+	1.72578i	−0.0212464	+	0.249096i
$49$	−15.8804	+	3.37549i	−2.26863	+	0.482212i
$50$	−0.207912	+	0.978148i	−0.0294032	+	0.138331i
$51$	−4.87869	+	3.69304i	−0.683153	+	0.517130i
$52$	0.684014	+	0.615889i	0.0948557	+	0.0854085i
$53$	0.987013	−	9.39081i	0.135577	−	1.28993i	−0.689243	−	0.724530i	$-0.742057\pi$
$53$	0.987013	−	9.39081i	0.135577	−	1.28993i	0.824820	−	0.565396i	$-0.191277\pi$
$54$	2.80149	−	4.37626i	0.381234	−	0.595534i
$55$	3.64286	−	0.382880i	0.491203	−	0.0516276i
$56$	−4.17449	−	2.41014i	−0.557840	−	0.322069i
$57$	5.15212	−	0.101158i	0.682415	−	0.0133986i
$58$	1.94665	+	2.67933i	0.255608	+	0.351814i
$59$	0.439186	−	0.395444i	0.0571771	−	0.0514825i	−0.640047	−	0.768336i	$-0.721085\pi$
$59$	0.439186	−	0.395444i	0.0571771	−	0.0514825i	0.697224	+	0.716853i	$0.254418\pi$
$60$	−0.326786	+	1.70094i	−0.0421879	+	0.219591i
$61$			6.64933i			0.851360i	0.904874	+	0.425680i	$0.139965\pi$
$61$			6.64933i			0.851360i	−0.904874	+	0.425680i	$0.860035\pi$
$62$	−3.52995	+	4.30575i	−0.448304	+	0.546831i
$63$	7.71645	+	12.2300i	0.972181	+	1.54084i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	0.615889	+	0.684014i	0.0763917	+	0.0848415i
$66$	6.29539	−	0.786900i	0.774909	−	0.0968608i
$67$	6.53705	+	11.3225i	0.798627	+	1.38326i	0.920510	+	0.390719i	$0.127773\pi$
$67$	6.53705	+	11.3225i	0.798627	+	1.38326i	−0.121883	+	0.992544i	$0.538893\pi$
$68$	1.76636	−	3.05942i	0.214202	−	0.371009i
$69$	0.176224	+	0.0743500i	0.0212149	+	0.00895069i
$70$	−3.89970	−	2.83329i	−0.466103	−	0.338644i
$71$	−11.4080	−	1.19903i	−1.35388	−	0.142298i	−0.600361	−	0.799729i	$-0.704977\pi$
$71$	−11.4080	−	1.19903i	−1.35388	−	0.142298i	−0.753515	+	0.657431i	$0.771643\pi$
$72$	−0.508068	+	2.95666i	−0.0598764	+	0.348446i
$73$	−0.190059	+	0.426879i	−0.0222447	+	0.0499623i	−0.924326	−	0.381603i	$-0.875372\pi$
$73$	−0.190059	+	0.426879i	−0.0222447	+	0.0499623i	0.902081	+	0.431566i	$0.142039\pi$
$74$	0.617150	+	0.131179i	0.0717422	+	0.0152493i
$75$	−0.502793	+	1.65747i	−0.0580576	+	0.191388i
$76$	−2.71794	+	1.21010i	−0.311769	+	0.138808i
$77$	−5.45612	+	16.7922i	−0.621782	+	1.91365i
$78$	1.08980	+	1.16358i	0.123396	+	0.131749i
$79$	1.63235	+	3.66631i	0.183654	+	0.412493i	0.981786	−	0.189989i	$-0.0608453\pi$
$79$	1.63235	+	3.66631i	0.183654	+	0.412493i	−0.798133	+	0.602482i	$0.794179\pi$
$80$	−0.207912	−	0.978148i	−0.0232452	−	0.109360i
$81$	5.47895	−	7.14011i	0.608772	−	0.793345i
$82$	−9.72117	−	4.32814i	−1.07352	−	0.477964i
$83$	−6.02984	+	6.69682i	−0.661861	+	0.735071i	−0.976827	−	0.214032i	$-0.931340\pi$
$83$	−6.02984	+	6.69682i	−0.661861	+	0.735071i	0.314966	+	0.949103i	$0.398007\pi$
$84$	−6.84950	−	4.77387i	−0.747342	−	0.520872i
$85$	2.07648	−	2.85802i	0.225225	−	0.309996i
$86$	−1.16091	−	11.0453i	−0.125184	−	1.19105i
$87$	2.96510	+	4.91050i	0.317892	+	0.526461i
$88$	−3.17219	+	1.83146i	−0.338156	+	0.195235i
$89$	8.73850	−	6.34889i	0.926279	−	0.672981i	−0.0188001	−	0.999823i	$-0.505985\pi$
$89$	8.73850	−	6.34889i	0.926279	−	0.672981i	0.945079	+	0.326842i	$0.105985\pi$
$90$	−0.814340	+	2.88736i	−0.0858390	+	0.304355i
$91$	−4.21960	+	1.37103i	−0.442334	+	0.143723i
$92$	−0.110428			−0.0115129
$93$	−6.72573	+	6.91119i	−0.697426	+	0.716657i
$94$	−1.46039			−0.150628
$95$	−2.82954	+	0.919372i	−0.290304	+	0.0943256i
$96$	−0.393302	−	1.68681i	−0.0401412	−	0.172159i
$97$	−9.20631	+	6.68877i	−0.934759	+	0.679142i	−0.947153	−	0.320781i	$-0.896055\pi$
$97$	−9.20631	+	6.68877i	−0.934759	+	0.679142i	0.0123944	+	0.999923i	$0.496055\pi$
$98$	14.0601	−	8.11759i	1.42028	−	0.820001i
$99$	10.9803	−	0.431345i	1.10356	−	0.0433518i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	−7.41830	+	10.2104i	−0.738148	+	1.01597i	0.260575	+	0.965454i	$0.416088\pi$
$101$	−7.41830	+	10.2104i	−0.738148	+	1.01597i	−0.998723	+	0.0505205i	$0.983912\pi$
$102$	3.49869	−	5.01989i	0.346422	−	0.497043i
$103$	5.08105	−	5.64307i	0.500650	−	0.556029i	−0.438857	−	0.898557i	$-0.644617\pi$
$103$	5.08105	−	5.64307i	0.500650	−	0.556029i	0.939508	+	0.342528i	$0.111283\pi$
$104$	−0.840857	−	0.374373i	−0.0824528	−	0.0367103i
$105$	−6.31298	−	5.46369i	−0.616083	−	0.533201i
$106$	1.96321	+	9.23619i	0.190684	+	0.897098i
$107$	0.222657	+	0.500095i	0.0215250	+	0.0483460i	0.923988	−	0.382421i	$-0.124910\pi$
$107$	0.222657	+	0.500095i	0.0215250	+	0.0483460i	−0.902463	+	0.430767i	$0.858243\pi$
$108$	−1.31203	+	5.02778i	−0.126251	+	0.483798i
$109$	−4.67185	+	14.3785i	−0.447482	+	1.37721i	0.432256	+	0.901751i	$0.357718\pi$
$109$	−4.67185	+	14.3785i	−0.447482	+	1.37721i	−0.879738	+	0.475458i	$0.842282\pi$
$110$	−3.34625	+	1.48985i	−0.319053	+	0.142051i
$111$	1.04576	+	0.317231i	0.0992589	+	0.0301102i
$112$	4.71495	+	1.00219i	0.445521	+	0.0946985i
$113$	1.43471	−	3.22240i	0.134966	−	0.303138i	−0.833401	−	0.552668i	$-0.813610\pi$
$113$	1.43471	−	3.22240i	0.134966	−	0.303138i	0.968367	+	0.249530i	$0.0802763\pi$
$114$	−4.86870	+	1.68830i	−0.455995	+	0.158124i
$115$	−0.109823	−	0.0115428i	−0.0102410	−	0.00107638i
$116$	−2.67933	−	1.94665i	−0.248770	−	0.180742i
$117$	1.70949	+	2.16850i	0.158042	+	0.200478i
$118$	−0.295491	+	0.511806i	−0.0272022	+	0.0471155i
$119$	8.51435	+	14.7473i	0.780509	+	1.35188i
$120$	−0.214828	−	1.71868i	−0.0196110	−	0.156893i
$121$	1.61732	+	1.79621i	0.147029	+	0.163292i
$122$	−2.05476	−	6.32389i	−0.186029	−	0.572538i
$123$	−16.1395	−	8.90039i	−1.45525	−	0.802521i
$124$	2.02663	−	5.18582i	0.181997	−	0.465701i
$125$		−	1.00000i		−	0.0894427i
$126$	−11.1181	−	9.24692i	−0.990475	−	0.823781i
$127$	9.89521	−	8.90969i	0.878058	−	0.790607i	−0.100852	−	0.994901i	$-0.532157\pi$
$127$	9.89521	−	8.90969i	0.878058	−	0.790607i	0.978909	+	0.204295i	$0.0654901\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$	−0.377618	−	19.2327i	−0.0332474	−	1.69335i
$130$	−0.797118	−	0.460216i	−0.0699118	−	0.0403636i
$131$	−12.9552	+	1.36164i	−1.13190	+	0.118967i	−0.651902	−	0.758303i	$-0.726029\pi$
$131$	−12.9552	+	1.36164i	−1.13190	+	0.118967i	−0.479996	+	0.877271i	$0.659362\pi$
$132$	−5.74410	+	2.69377i	−0.499960	+	0.234462i
$133$	1.49905	−	14.2625i	0.129984	−	1.23672i
$134$	−9.71594	−	8.74827i	−0.839330	−	0.755736i
$135$	−1.83039	+	4.86309i	−0.157535	+	0.418548i
$136$	−0.734492	+	3.45551i	−0.0629822	+	0.296308i
$137$	−10.7053	+	2.27549i	−0.914619	+	0.194408i	−0.641099	−	0.767458i	$-0.721521\pi$
$137$	−10.7053	+	2.27549i	−0.914619	+	0.194408i	−0.273520	+	0.961866i	$0.588188\pi$
$138$	−0.190574	−	0.0162549i	−0.0162228	−	0.00138371i
$139$	0.690568	+	0.224379i	0.0585732	+	0.0190316i	0.338157	−	0.941090i	$-0.390196\pi$
$139$	0.690568	+	0.224379i	0.0585732	+	0.0190316i	−0.279584	+	0.960121i	$0.590196\pi$
$140$	4.58437	+	1.48955i	0.387450	+	0.125890i
$141$	−2.52032	−	0.214968i	−0.212249	−	0.0181036i
$142$	11.2201	−	2.38491i	0.941573	−	0.200138i
$143$	−0.700969	+	3.29780i	−0.0586180	+	0.275776i
$144$	−0.430458	−	2.96896i	−0.0358715	−	0.247413i
$145$	−2.46118	−	2.21605i	−0.204389	−	0.184033i
$146$	0.0488437	−	0.464717i	0.00404233	−	0.0384602i
$147$	25.4596	−	11.9396i	2.09987	−	0.984761i
$148$	−0.627481	+	0.0659509i	−0.0515786	+	0.00542113i
$149$	−2.56654	−	1.48179i	−0.210259	−	0.121393i	0.391173	−	0.920317i	$-0.372069\pi$
$149$	−2.56654	−	1.48179i	−0.210259	−	0.121393i	−0.601432	+	0.798924i	$0.705403\pi$
$150$	−0.0340008	−	1.73172i	−0.00277615	−	0.141394i
$151$	11.8143	+	16.2610i	0.961432	+	1.32330i	0.946258	+	0.323413i	$0.104830\pi$
$151$	11.8143	+	16.2610i	0.961432	+	1.32330i	0.0151738	+	0.999885i	$0.495170\pi$
$152$	2.21097	−	1.99077i	0.179333	−	0.161472i
$153$	6.77691	−	8.14824i	0.547881	−	0.658747i
$154$		−	17.6564i		−	1.42279i
$155$	2.55759	−	4.94558i	0.205431	−	0.397238i
$156$	−1.39603	−	0.769861i	−0.111772	−	0.0616382i
$157$	1.69582	+	5.21921i	0.135341	+	0.416538i	0.995643	−	0.0932473i	$-0.0297247\pi$
$157$	1.69582	+	5.21921i	0.135341	+	0.416538i	−0.860301	+	0.509786i	$0.829725\pi$
$158$	−2.68541	−	2.98245i	−0.213640	−	0.237271i
$159$	2.02852	+	16.2287i	0.160872	+	1.28702i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	0.266147	−	0.460980i	0.0209753	−	0.0363303i
$162$	−3.00437	+	8.48373i	−0.236046	+	0.666545i
$163$	−9.31065	−	6.76459i	−0.729267	−	0.529843i	0.160065	−	0.987107i	$-0.448830\pi$
$163$	−9.31065	−	6.76459i	−0.729267	−	0.529843i	−0.889331	+	0.457263i	$0.848830\pi$
$164$	10.5829	+	1.11230i	0.826382	+	0.0868563i
$165$	−5.99421	+	2.07859i	−0.466649	+	0.161818i
$166$	3.66529	−	8.23237i	0.284482	−	0.638956i
$167$	11.4949	+	2.44333i	0.889506	+	0.189070i	0.629929	−	0.776652i	$-0.283084\pi$
$167$	11.4949	+	2.44333i	0.889506	+	0.189070i	0.259576	+	0.965723i	$0.416417\pi$
$168$	7.98947	+	2.42361i	0.616401	+	0.186986i
$169$	11.1021	−	4.94299i	0.854011	−	0.380230i
$170$	−1.09167	+	3.35981i	−0.0837271	+	0.257686i
$171$	−8.65084	+	2.19697i	−0.661546	+	0.168007i
$172$	4.51728	+	10.1460i	0.344439	+	0.773623i
$173$	−0.225873	−	1.06265i	−0.0171728	−	0.0807918i	0.968727	−	0.248130i	$-0.0798161\pi$
$173$	−0.225873	−	1.06265i	−0.0171728	−	0.0807918i	−0.985900	+	0.167338i	$0.946483\pi$
$174$	−4.33741	−	3.75389i	−0.328818	−	0.284582i
$175$	4.40355	+	1.96059i	0.332877	+	0.148207i
$176$	2.45098	−	2.72209i	0.184749	−	0.205185i
$177$	−0.585292	+	0.839770i	−0.0439932	+	0.0631210i
$178$	−6.34889	+	8.73850i	−0.475869	+	0.654978i
$179$	−2.39628	−	22.7991i	−0.179107	−	1.70409i	−0.602483	−	0.798132i	$-0.705822\pi$
$179$	−2.39628	−	22.7991i	−0.179107	−	1.70409i	0.423377	−	0.905954i	$-0.360845\pi$
$180$	−0.117760	−	2.99769i	−0.00877728	−	0.223434i
$181$	16.5857	−	9.57574i	1.23280	−	0.711759i	0.265189	−	0.964196i	$-0.414566\pi$
$181$	16.5857	−	9.57574i	1.23280	−	0.711759i	0.967613	+	0.252437i	$0.0812322\pi$
$182$	3.58941	−	2.60786i	0.266064	−	0.193307i
$183$	−2.61520	−	11.2161i	−0.193321	−	0.829120i
$184$	0.105023	−	0.0341240i	0.00774240	−	0.00251566i
$185$	−0.630937			−0.0463874
$186$	4.26087	−	8.65130i	0.312422	−	0.634344i
$187$	12.9401			0.946272
$188$	1.38892	−	0.451286i	0.101297	−	0.0329134i
$189$	−17.8262	−	17.5948i	−1.29667	−	1.27983i
$190$	2.40695	−	1.74875i	0.174618	−	0.126868i
$191$	9.02705	−	5.21177i	0.653174	−	0.377110i	−0.136497	−	0.990640i	$-0.543584\pi$
$191$	9.02705	−	5.21177i	0.653174	−	0.377110i	0.789671	+	0.613530i	$0.210251\pi$
$192$	0.895304	+	1.48271i	0.0646130	+	0.107005i
$193$	−2.27402	−	21.6359i	−0.163688	−	1.55739i	−0.700480	−	0.713672i	$-0.747031\pi$
$193$	−2.27402	−	21.6359i	−0.163688	−	1.55739i	0.536793	−	0.843714i	$-0.319636\pi$
$194$	6.68877	−	9.20631i	0.480226	−	0.660974i
$195$	−1.30791	−	0.911569i	−0.0936614	−	0.0652788i
$196$	−10.8635	+	12.0651i	−0.775962	+	0.861793i
$197$	−3.66543	−	1.63196i	−0.261151	−	0.116272i	0.271985	−	0.962302i	$-0.412320\pi$
$197$	−3.66543	−	1.63196i	−0.261151	−	0.116272i	−0.533136	+	0.846030i	$0.678987\pi$
$198$	−10.3096	+	3.80334i	−0.732672	+	0.270291i
$199$	−0.197733	−	0.930262i	−0.0140169	−	0.0659445i	0.970583	−	0.240766i	$-0.0773986\pi$
$199$	−0.197733	−	0.930262i	−0.0140169	−	0.0659445i	−0.984600	+	0.174821i	$0.944065\pi$
$200$	0.406737	+	0.913545i	0.0287606	+	0.0645974i
$201$	−15.4799	−	16.5278i	−1.09187	−	1.16578i
$202$	3.90003	−	12.0031i	0.274405	−	0.844533i
$203$	14.5839	−	6.49315i	1.02359	−	0.455730i
$204$	−1.77622	+	5.85536i	−0.124361	+	0.409957i
$205$	10.4086	+	2.21242i	0.726969	+	0.154522i
$206$	−3.08856	+	6.93701i	−0.215190	+	0.483324i
$207$	−0.326498	−	0.0561048i	−0.0226932	−	0.00389955i
$208$	0.915390	+	0.0962114i	0.0634709	+	0.00667106i
$209$	−8.81648	−	6.40555i	−0.609849	−	0.443081i
$210$	7.69237	+	3.24546i	0.530824	+	0.223958i
$211$	11.9470	−	20.6928i	0.822464	−	1.42455i	−0.0813777	−	0.996683i	$-0.525932\pi$
$211$	11.9470	−	20.6928i	0.822464	−	1.42455i	0.903842	−	0.427866i	$-0.140735\pi$
$212$	−4.72127	−	8.17747i	−0.324258	−	0.561631i
$213$	19.7146	−	2.46425i	1.35082	−	0.168848i
$214$	−0.366297	−	0.406814i	−0.0250395	−	0.0278092i
$215$	3.43199	+	10.5626i	0.234060	+	0.720362i
$216$	−0.305850	−	5.18714i	−0.0208105	−	0.352940i
$217$	16.7637	+	20.9587i	1.13800	+	1.42277i
$218$		−	15.1184i		−	1.02395i
$219$	0.152700	−	0.794812i	0.0103185	−	0.0537084i
$220$	2.72209	−	2.45098i	0.183523	−	0.165245i
$221$	1.91125	+	2.63062i	0.128565	+	0.176954i
$222$	−1.09260	+	0.0214524i	−0.0733308	+	0.00143979i
$223$	2.08702	+	1.20494i	0.139757	+	0.0806889i	0.568248	−	0.822857i	$-0.307621\pi$
$223$	2.08702	+	1.20494i	0.139757	+	0.0806889i	−0.428491	+	0.903546i	$0.640955\pi$
$224$	−4.79388	+	0.503857i	−0.320305	+	0.0336654i
$225$	0.196229	−	2.99358i	0.0130819	−	0.199572i
$226$	−0.368709	+	3.50803i	−0.0245262	+	0.233351i
$227$	11.1073	+	10.0011i	0.737217	+	0.663793i	0.949625	−	0.313388i	$-0.101464\pi$
$227$	11.1073	+	10.0011i	0.737217	+	0.663793i	−0.212408	+	0.977181i	$0.568131\pi$
$228$	4.10869	−	3.11018i	0.272105	−	0.205977i
$229$	−4.66998	+	21.9705i	−0.308601	+	1.45185i	0.501294	+	0.865277i	$0.332857\pi$
$229$	−4.66998	+	21.9705i	−0.308601	+	1.45185i	−0.809895	+	0.586575i	$0.800476\pi$
$230$	0.108015	−	0.0229592i	0.00712227	−	0.00151389i
$231$	2.59900	−	30.4711i	0.171002	−	2.00485i
$232$	3.14975	+	1.02341i	0.206791	+	0.0671904i
$233$	−24.6426	−	8.00688i	−1.61439	−	0.524548i	−0.643783	−	0.765208i	$-0.722636\pi$
$233$	−24.6426	−	8.00688i	−1.61439	−	0.524548i	−0.970610	+	0.240660i	$0.922636\pi$
$234$	−2.29592	−	1.53411i	−0.150089	−	0.100288i
$235$	1.42848	−	0.303633i	0.0931837	−	0.0198068i
$236$	0.122872	−	0.578068i	0.00799830	−	0.0376290i
$237$	−4.19542	−	5.54235i	−0.272522	−	0.360015i
$238$	−12.6548	−	11.3944i	−0.820288	−	0.738591i
$239$	−1.28988	+	12.2724i	−0.0834352	+	0.793833i	0.870166	+	0.492759i	$0.164012\pi$
$239$	−1.28988	+	12.2724i	−0.0834352	+	0.793833i	−0.953601	+	0.301074i	$0.902655\pi$
$240$	0.735414	+	1.56817i	0.0474708	+	0.101225i
$241$	−14.1499	+	1.48722i	−0.911478	+	0.0958002i	−0.548646	−	0.836055i	$-0.684857\pi$
$241$	−14.1499	+	1.48722i	−0.911478	+	0.0958002i	−0.362832	+	0.931855i	$0.618190\pi$
$242$	−2.09322	−	1.20852i	−0.134557	−	0.0776867i
$243$	−6.43370	+	14.1989i	−0.412722	+	0.910857i
$244$	3.90838	+	5.37942i	0.250208	+	0.344382i
$245$	−12.0651	+	10.8635i	−0.770811	+	0.694041i
$246$	18.1000	+	3.47738i	1.15401	+	0.221710i
$247$		−	2.73843i		−	0.174242i
$248$	−0.324930	+	5.55827i	−0.0206331	+	0.352951i
$249$	7.53730	−	13.6678i	0.477657	−	0.866160i
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	0.577351	+	0.641213i	0.0364420	+	0.0404730i	0.761090	−	0.648646i	$-0.224664\pi$
$251$	0.577351	+	0.641213i	0.0364420	+	0.0404730i	−0.724648	+	0.689119i	$0.757998\pi$
$252$	13.4314	+	5.35867i	0.846096	+	0.337565i
$253$	−0.202244	−	0.350298i	−0.0127150	−	0.0220230i
$254$	−6.65766	+	11.5314i	−0.417739	+	0.723545i
$255$	−2.37854	+	5.63761i	−0.148950	+	0.353041i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	0.495858	+	0.0521167i	0.0309308	+	0.00325095i	0.119981	−	0.992776i	$-0.461717\pi$
$257$	0.495858	+	0.0521167i	0.0309308	+	0.00325095i	−0.0890504	+	0.996027i	$0.528383\pi$
$258$	6.30237	+	18.1747i	0.392368	+	1.13151i
$259$	1.23701	−	2.77836i	0.0768639	−	0.172639i
$260$	0.900318	+	0.191369i	0.0558354	+	0.0118682i
$261$	−6.93286	−	7.11687i	−0.429133	−	0.440523i
$262$	11.9003	−	5.29837i	0.735205	−	0.327334i
$263$	4.94334	−	15.2140i	0.304819	−	0.938137i	−0.674925	−	0.737886i	$-0.735824\pi$
$263$	4.94334	−	15.2140i	0.304819	−	0.938137i	0.979745	−	0.200251i	$-0.0641759\pi$
$264$	4.63055	−	4.33695i	0.284990	−	0.266921i
$265$	−3.84062	−	8.62618i	−0.235928	−	0.529902i
$266$	2.98168	+	14.0277i	0.182819	+	0.860094i
$267$	−12.2431	+	14.1462i	−0.749266	+	0.865734i
$268$	11.9438	+	5.31771i	0.729582	+	0.324831i
$269$	−1.22763	+	1.36342i	−0.0748500	+	0.0831294i	−0.779407	−	0.626519i	$-0.784479\pi$
$269$	−1.22763	+	1.36342i	−0.0748500	+	0.0831294i	0.704557	+	0.709648i	$0.251146\pi$
$270$	0.238030	−	5.19070i	0.0144860	−	0.315896i
$271$	7.90575	−	10.8813i	0.480240	−	0.660994i	−0.498311	−	0.866998i	$-0.666046\pi$
$271$	7.90575	−	10.8813i	0.480240	−	0.660994i	0.978551	+	0.206004i	$0.0660461\pi$
$272$	−0.369269	−	3.51336i	−0.0223902	−	0.213029i
$273$	6.57841	−	3.97224i	0.398144	−	0.240411i
$274$	9.47822	−	5.47225i	0.572600	−	0.330591i
$275$	2.96337	−	2.15302i	0.178698	−	0.129832i
$276$	0.186270	−	0.0434314i	0.0112121	−	0.00261427i
$277$	−21.5830	+	7.01273i	−1.29679	+	0.421354i	−0.874465	−	0.485088i	$-0.838788\pi$
$277$	−21.5830	+	7.01273i	−1.29679	+	0.421354i	−0.422330	+	0.906442i	$0.638788\pi$
$278$	−0.726106			−0.0435489
$279$	8.62681	−	14.3031i	0.516474	−	0.856303i
$280$	−4.82029			−0.288067
$281$	10.1958	−	3.31281i	0.608230	−	0.197626i	0.0113224	−	0.999936i	$-0.496396\pi$
$281$	10.1958	−	3.31281i	0.608230	−	0.197626i	0.596908	+	0.802310i	$0.296396\pi$
$282$	2.46340	−	0.574375i	0.146693	−	0.0342035i
$283$	−18.8167	+	13.6711i	−1.11854	+	0.812665i	−0.983987	−	0.178242i	$-0.942959\pi$
$283$	−18.8167	+	13.6711i	−1.11854	+	0.812665i	−0.134551	+	0.990907i	$0.542959\pi$
$284$	−9.93400	+	5.73540i	−0.589475	+	0.340333i
$285$	4.41129	−	2.66367i	0.261302	−	0.157782i
$286$	−0.352415	−	3.35301i	−0.0208388	−	0.198267i
$287$	−30.1495	+	41.4972i	−1.77967	+	2.44950i
$288$	1.32685	+	2.69063i	0.0781853	+	0.158547i
$289$	−3.02444	+	3.35898i	−0.177908	+	0.197587i
$290$	3.02551	+	1.34705i	0.177664	+	0.0791013i
$291$	12.8985	−	14.9035i	0.756126	−	0.873660i
$292$	0.0971523	+	0.457066i	0.00568541	+	0.0267477i
$293$	−4.85285	−	10.8997i	−0.283506	−	0.636766i	0.714516	−	0.699619i	$-0.246647\pi$
$293$	−4.85285	−	10.8997i	−0.283506	−	0.636766i	−0.998023	+	0.0628528i	$0.979980\pi$
$294$	−20.5240	+	19.2227i	−1.19698	+	1.12109i
$295$	0.182624	−	0.562058i	0.0106328	−	0.0327243i
$296$	0.576390	−	0.256625i	0.0335020	−	0.0149160i
$297$	−18.3520	+	5.04618i	−1.06489	+	0.292809i
$298$	2.89882	+	0.616163i	0.167924	+	0.0356934i
$299$	0.0413412	−	0.0928539i	0.00239082	−	0.00536988i
$300$	0.567467	+	1.63645i	0.0327627	+	0.0944807i
$301$	−53.2416	−	5.59592i	−3.06879	−	0.322543i
$302$	−16.2610	−	11.8143i	−0.935713	−	0.679835i
$303$	8.49745	−	20.1406i	0.488166	−	1.15705i
$304$	−1.48758	+	2.57656i	−0.0853183	+	0.147776i
$305$	3.32467	+	5.75849i	0.190370	+	0.329730i
$306$	−3.92728	+	9.84362i	−0.224508	+	0.562722i
$307$	−4.61303	−	5.12329i	−0.263280	−	0.292402i	0.596982	−	0.802255i	$-0.296366\pi$
$307$	−4.61303	−	5.12329i	−0.263280	−	0.292402i	−0.860261	+	0.509853i	$0.829700\pi$
$308$	5.45612	+	16.7922i	0.310891	+	0.956825i
$309$	−6.35131	+	11.5172i	−0.361313	+	0.655188i
$310$	−0.904148	+	5.49386i	−0.0513521	+	0.312030i
$311$			24.4347i			1.38556i	0.721148	+	0.692782i	$0.243615\pi$
$311$			24.4347i			1.38556i	−0.721148	+	0.692782i	$0.756385\pi$
$312$	1.56560	+	0.300785i	0.0886348	+	0.0170286i
$313$	7.57333	−	6.81905i	0.428070	−	0.385436i	−0.426743	−	0.904373i	$-0.640339\pi$
$313$	7.57333	−	6.81905i	0.428070	−	0.385436i	0.854812	+	0.518938i	$0.173672\pi$
$314$	−3.22565	−	4.43972i	−0.182034	−	0.250548i
$315$	12.7976	+	6.73327i	0.721066	+	0.379377i
$316$	3.47560	+	2.00664i	0.195518	+	0.112882i
$317$	−6.00776	+	0.631441i	−0.337430	+	0.0354653i	−0.271728	−	0.962374i	$-0.587595\pi$
$317$	−6.00776	+	0.631441i	−0.337430	+	0.0354653i	−0.0657014	+	0.997839i	$0.520928\pi$
$318$	−6.94417	−	14.8075i	−0.389410	−	0.830365i
$319$	1.26804	−	12.0646i	0.0709965	−	0.675486i
$320$	−0.743145	−	0.669131i	−0.0415431	−	0.0374055i
$321$	−0.572267	−	0.755992i	−0.0319408	−	0.0421953i
$322$	−0.110670	+	0.520662i	−0.00616740	+	0.0290153i
$323$	−10.2807	+	2.18523i	−0.572032	+	0.121589i
$324$	0.235712	−	8.99691i	0.0130951	−	0.499828i
$325$	0.875383	+	0.284429i	0.0485575	+	0.0157773i
$326$	10.9453	+	3.55635i	0.606206	+	0.196968i
$327$	2.22542	−	26.0912i	0.123066	−	1.44284i
$328$	−10.4086	+	2.21242i	−0.574720	+	0.122160i
$329$	−1.46360	+	6.88568i	−0.0806907	+	0.379620i
$330$	5.05852	−	3.82917i	0.278462	−	0.210789i
$331$	−1.29056	−	1.16203i	−0.0709358	−	0.0638708i	0.632900	−	0.774233i	$-0.281864\pi$
$331$	−1.29056	−	1.16203i	−0.0709358	−	0.0638708i	−0.703836	+	0.710363i	$0.748531\pi$
$332$	−0.941953	+	8.96209i	−0.0516964	+	0.491858i
$333$	−1.88876	−	0.123808i	−0.103503	−	0.00678465i
$334$	−11.6874	+	1.22839i	−0.639505	+	0.0672146i
$335$	11.3225	+	6.53705i	0.618614	+	0.357157i
$336$	−8.34738	+	0.163894i	−0.455387	+	0.00894114i
$337$	10.1682	+	13.9953i	0.553898	+	0.762375i	0.990535	−	0.137263i	$-0.0438304\pi$
$337$	10.1682	+	13.9953i	0.553898	+	0.762375i	−0.436637	+	0.899638i	$0.643830\pi$
$338$	−9.03129	+	8.13181i	−0.491238	+	0.442312i
$339$	−1.15269	+	5.99984i	−0.0626057	+	0.325866i
$340$		−	3.53271i		−	0.191588i
$341$	20.1621	−	3.06881i	1.09184	−	0.166185i
$342$	7.54854	−	4.76270i	0.408178	−	0.257537i
$343$	−13.7563	−	42.3375i	−0.742770	−	2.28601i
$344$	−7.43147	−	8.25348i	−0.400678	−	0.444998i
$345$	0.189790	−	0.0237230i	0.0102179	−	0.00127720i
$346$	0.543195	+	0.940841i	0.0292023	+	0.0505799i
$347$	9.89519	−	17.1390i	0.531201	−	0.920068i	−0.468135	−	0.883657i	$-0.655074\pi$
$347$	9.89519	−	17.1390i	0.531201	−	0.920068i	0.999337	−	0.0364111i	$-0.0115926\pi$
$348$	5.28514	+	2.22983i	0.283313	+	0.119532i
$349$	28.8669	+	20.9730i	1.54521	+	1.12266i	0.946961	+	0.321348i	$0.104136\pi$
$349$	28.8669	+	20.9730i	1.54521	+	1.12266i	0.598247	+	0.801312i	$0.295864\pi$
$350$	−4.79388	−	0.503857i	−0.256244	−	0.0269323i
$351$	−3.73645	−	2.98550i	−0.199437	−	0.159354i
$352$	−1.48985	+	3.34625i	−0.0794091	+	0.178356i
$353$	17.1263	+	3.64030i	0.911540	+	0.193754i	0.639732	−	0.768598i	$-0.279045\pi$
$353$	17.1263	+	3.64030i	0.911540	+	0.193754i	0.271807	+	0.962352i	$0.412379\pi$
$354$	0.297142	−	0.979534i	0.0157929	−	0.0520617i
$355$	−10.4791	+	4.66559i	−0.556173	+	0.247624i
$356$	3.33781	−	10.2727i	0.176904	−	0.544453i
$357$	−20.1622	−	21.5271i	−1.06710	−	1.13933i
$358$	9.32431	+	20.9427i	0.492805	+	1.10686i
$359$	−5.99431	−	28.2010i	−0.316368	−	1.48839i	−0.792963	−	0.609270i	$-0.791463\pi$
$359$	−5.99431	−	28.2010i	−0.316368	−	1.48839i	0.476596	−	0.879123i	$-0.341871\pi$
$360$	1.03833	+	2.81458i	0.0547249	+	0.148341i
$361$	−9.27109	−	4.12776i	−0.487952	−	0.217250i
$362$	−12.8148	+	14.2323i	−0.673533	+	0.748034i
$363$	−3.43455	−	2.39377i	−0.180267	−	0.125640i
$364$	−2.60786	+	3.58941i	−0.136689	+	0.188136i
$365$	0.0488437	+	0.464717i	0.00255660	+	0.0243244i
$366$	5.95318	+	9.85904i	0.311177	+	0.515340i
$367$	−21.2211	+	12.2520i	−1.10773	+	0.639548i	−0.938240	−	0.345984i	$-0.887545\pi$
$367$	−21.2211	+	12.2520i	−1.10773	+	0.639548i	−0.169489	+	0.985532i	$0.554212\pi$
$368$	−0.0893379	+	0.0649078i	−0.00465706	+	0.00338355i
$369$	30.7248	+	8.66552i	1.59947	+	0.451109i
$370$	0.600057	−	0.194970i	0.0311955	−	0.0101360i
$371$	45.5157			2.36306
$372$	−1.37893	+	9.54456i	−0.0714943	+	0.494862i
$373$	−12.1021			−0.626622			−0.313311	−	0.949651i	$-0.601438\pi$
$373$	−12.1021			−0.626622			−0.313311	+	0.949651i	$0.601438\pi$
$374$	−12.3067	+	3.99870i	−0.636366	+	0.206768i
$375$	0.393302	+	1.68681i	0.0203100	+	0.0871063i
$376$	−1.18148	+	0.858397i	−0.0609303	+	0.0442684i
$377$	2.63992	−	1.52416i	0.135963	−	0.0784983i
$378$	22.3908	+	11.2250i	1.15166	+	0.577352i
$379$	−2.32962	−	22.1649i	−0.119665	−	1.13853i	−0.875314	−	0.483556i	$-0.839345\pi$
$379$	−2.32962	−	22.1649i	−0.119665	−	1.13853i	0.755649	−	0.654977i	$-0.227322\pi$
$380$	−1.74875	+	2.40695i	−0.0897090	+	0.123474i
$381$	−13.1871	+	18.9207i	−0.675596	+	0.969338i
$382$	−6.97471	+	7.74620i	−0.356857	+	0.396330i
$383$	3.74522	+	1.66748i	0.191372	+	0.0852041i	0.500185	−	0.865918i	$-0.333265\pi$
$383$	3.74522	+	1.66748i	0.191372	+	0.0852041i	−0.308814	+	0.951123i	$0.599932\pi$
$384$	−1.30967	−	1.13348i	−0.0668337	−	0.0578425i
$385$	3.67097	+	17.2705i	0.187090	+	0.880188i
$386$	8.84859	+	19.8742i	0.450381	+	1.01157i
$387$	8.20123	+	32.2933i	0.416892	+	1.64156i
$388$	−3.51650	+	10.8227i	−0.178523	+	0.549438i
$389$	32.5954	−	14.5124i	1.65265	−	0.735808i	0.652887	−	0.757456i	$-0.273558\pi$
$389$	32.5954	−	14.5124i	1.65265	−	0.735808i	0.999766	+	0.0216475i	$0.00689115\pi$
$390$	1.52559	+	0.462787i	0.0772511	+	0.0234341i
$391$	−0.381584	−	0.0811083i	−0.0192976	−	0.00410182i
$392$	6.60345	−	14.8316i	0.333524	−	0.749108i
$393$	21.3173	−	7.39212i	1.07532	−	0.372883i
$394$	3.99034	+	0.419401i	0.201030	+	0.0211291i
$395$	3.24681	+	2.35895i	0.163365	+	0.118692i
$396$	8.62972	−	6.80303i	0.433660	−	0.341865i
$397$	19.3015	−	33.4311i	0.968713	−	1.67786i	0.269423	−	0.963022i	$-0.413167\pi$
$397$	19.3015	−	33.4311i	0.968713	−	1.67786i	0.699290	−	0.714838i	$-0.253500\pi$
$398$	0.475522	+	0.823628i	0.0238358	+	0.0412848i
$399$	3.08087	+	24.6477i	0.154237	+	1.23393i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	10.4732	+	32.2332i	0.523007	+	1.60965i	0.768223	+	0.640182i	$0.221141\pi$
$401$	10.4732	+	32.2332i	0.523007	+	1.60965i	−0.245216	+	0.969468i	$0.578859\pi$
$402$	19.8296	+	10.9353i	0.989012	+	0.545405i
$403$	3.60182	+	3.64554i	0.179419	+	0.181597i
$404$			12.6208i			0.627907i
$405$	1.17485	−	8.92299i	0.0583790	−	0.443387i
$406$	−11.8636	+	10.6820i	−0.588779	+	0.530139i
$407$	−1.35842	−	1.86970i	−0.0673342	−	0.0926776i
$408$	−0.120115	−	6.11766i	−0.00594658	−	0.302869i
$409$	15.4533	+	8.92199i	0.764119	+	0.441164i	0.830773	−	0.556612i	$-0.187899\pi$
$409$	15.4533	+	8.92199i	0.764119	+	0.441164i	−0.0666538	+	0.997776i	$0.521232\pi$
$410$	−10.5829	+	1.11230i	−0.522650	+	0.0549327i
$411$	17.1629	−	8.04874i	0.846582	−	0.397015i
$412$	0.793737	−	7.55191i	0.0391046	−	0.372056i
$413$	2.11700	+	1.90616i	0.104171	+	0.0937958i
$414$	0.327855	−	0.0475345i	0.0161132	−	0.00233619i
$415$	−1.87359	+	8.81453i	−0.0919707	+	0.432688i
$416$	−0.900318	+	0.191369i	−0.0441417	+	0.00938262i
$417$	−1.25310	−	0.106882i	−0.0613647	−	0.00523404i
$418$	10.3644	+	3.36760i	0.506939	+	0.164714i
$419$	−26.7584	−	8.69434i	−1.30723	−	0.424746i	−0.429142	−	0.903237i	$-0.641184\pi$
$419$	−26.7584	−	8.69434i	−1.30723	−	0.424746i	−0.878092	+	0.478491i	$0.841184\pi$
$420$	−8.31878	−	0.709543i	−0.405915	−	0.0346221i
$421$	2.95660	−	0.628445i	0.144096	−	0.0306286i	−0.135299	−	0.990805i	$-0.543199\pi$
$421$	2.95660	−	0.628445i	0.144096	−	0.0306286i	0.279395	+	0.960176i	$0.409866\pi$
$422$	−4.96783	+	23.3718i	−0.241830	+	1.13772i
$423$	4.33584	−	0.628638i	0.210816	−	0.0305654i
$424$	7.01717	+	6.31829i	0.340784	+	0.306843i
$425$	0.369269	−	3.51336i	0.0179122	−	0.170423i
$426$	−17.9882	+	8.43579i	−0.871531	+	0.408715i
$427$	−31.8761	+	3.35032i	−1.54259	+	0.162133i
$428$	0.474081	+	0.273711i	0.0229156	+	0.0132303i
$429$	−0.114633	−	5.83844i	−0.00553453	−	0.281883i
$430$	−6.52803	−	8.98506i	−0.314810	−	0.433298i
$431$	−6.98873	+	6.29268i	−0.336635	+	0.303108i	−0.820059	−	0.572279i	$-0.806060\pi$
$431$	−6.98873	+	6.29268i	−0.336635	+	0.303108i	0.483424	+	0.875386i	$0.339393\pi$
$432$	1.89380	+	4.83875i	0.0911153	+	0.232805i
$433$		−	27.3145i		−	1.31265i	−0.754477	−	0.656326i	$-0.772110\pi$
$433$		−	27.3145i		−	1.31265i	0.754477	−	0.656326i	$-0.227890\pi$
$434$	−22.4199	−	14.7527i	−1.07619	−	0.708151i
$435$	5.02310	+	2.77006i	0.240839	+	0.132814i
$436$	4.67185	+	14.3785i	0.223741	+	0.688605i
$437$	0.219836	+	0.244152i	0.0105162	+	0.0116794i
$438$	0.100384	+	0.803097i	0.00479654	+	0.0383735i
$439$	0.224629	+	0.389069i	0.0107210	+	0.0185693i	0.871336	−	0.490687i	$-0.163254\pi$
$439$	0.224629	+	0.389069i	0.0107210	+	0.0185693i	−0.860615	+	0.509256i	$0.829921\pi$
$440$	−1.83146	+	3.17219i	−0.0873116	+	0.151228i
$441$	−38.2495	+	30.1531i	−1.82141	+	1.43586i
$442$	−2.63062	−	1.91125i	−0.125126	−	0.0909091i
$443$	4.97646	+	0.523047i	0.236439	+	0.0248507i	0.222007	−	0.975045i	$-0.428739\pi$
$443$	4.97646	+	0.523047i	0.236439	+	0.0248507i	0.0144320	+	0.999896i	$0.495406\pi$
$444$	1.03250	−	0.358036i	0.0490003	−	0.0169916i
$445$	4.39332	−	9.86755i	0.208263	−	0.467767i
$446$	−2.35722	−	0.501043i	−0.111618	−	0.0237251i
$447$	4.91204	+	1.49007i	0.232332	+	0.0704779i
$448$	4.40355	−	1.96059i	0.208048	−	0.0926291i
$449$	7.69476	−	23.6820i	0.363138	−	1.11762i	−0.588001	−	0.808860i	$-0.700085\pi$
$449$	7.69476	−	23.6820i	0.363138	−	1.11762i	0.951139	−	0.308764i	$-0.0999152\pi$
$450$	0.738441	+	2.90770i	0.0348104	+	0.137070i
$451$	15.8537	+	35.6080i	0.746521	+	1.67671i
$452$	−0.733379	−	3.45028i	−0.0344952	−	0.162287i
$453$	−26.3238	−	22.7825i	−1.23680	−	1.07041i
$454$	−13.6542	−	6.07922i	−0.640821	−	0.285312i
$455$	−2.96876	+	3.29715i	−0.139178	+	0.154573i
$456$	−2.94650	+	4.22761i	−0.137983	+	0.197976i
$457$	8.81194	−	12.1286i	0.412205	−	0.567352i	−0.551549	−	0.834142i	$-0.685963\pi$
$457$	8.81194	−	12.1286i	0.412205	−	0.567352i	0.963755	+	0.266790i	$0.0859631\pi$
$458$	−2.34785	−	22.3383i	−0.109708	−	1.04380i
$459$	−8.22662	+	16.4099i	−0.383986	+	0.765948i
$460$	−0.0956332	+	0.0552139i	−0.00445892	+	0.00257436i
$461$	22.5883	−	16.4114i	1.05204	−	0.764355i	0.0794438	−	0.996839i	$-0.474686\pi$
$461$	22.5883	−	16.4114i	1.05204	−	0.764355i	0.972600	+	0.232485i	$0.0746856\pi$
$462$	6.94429	+	29.7829i	0.323077	+	1.38562i
$463$	−17.7819	+	5.77769i	−0.826394	+	0.268512i	−0.691526	−	0.722352i	$-0.743061\pi$
$463$	−17.7819	+	5.77769i	−0.826394	+	0.268512i	−0.134868	+	0.990864i	$0.543061\pi$
$464$	−3.31184			−0.153748
$465$	−2.36906	+	9.34813i	−0.109862	+	0.433509i
$466$	25.9108			1.20029
$467$	−17.3511	+	5.63770i	−0.802912	+	0.260882i	−0.681593	−	0.731732i	$-0.738712\pi$
$467$	−17.3511	+	5.63770i	−0.802912	+	0.260882i	−0.121319	+	0.992614i	$0.538712\pi$
$468$	2.65762	+	0.749545i	0.122848	+	0.0346477i
$469$	−50.9850	+	37.0428i	−2.35427	+	1.71048i
$470$	−1.26474	+	0.730196i	−0.0583379	+	0.0336814i
$471$	−4.91325	−	8.13682i	−0.226391	−	0.374925i
$472$	0.0617745	+	0.587745i	0.00284340	+	0.0270532i
$473$	−23.9117	+	32.9116i	−1.09946	+	1.51328i
$474$	5.70277	+	3.97463i	0.261937	+	0.182561i
$475$	−1.99077	+	2.21097i	−0.0913426	+	0.101446i
$476$	15.5565	+	6.92619i	0.713030	+	0.317462i
$477$	−9.80449	−	26.5768i	−0.448917	−	1.21687i
$478$	−2.56562	−	12.0703i	−0.117349	−	0.552083i
$479$	14.9007	+	33.4675i	0.680830	+	1.52917i	0.840390	+	0.541982i	$0.182326\pi$
$479$	14.9007	+	33.4675i	0.680830	+	1.52917i	−0.159560	+	0.987188i	$0.551007\pi$
$480$	−1.18401	−	1.26417i	−0.0540425	−	0.0577010i
$481$	0.179457	−	0.552311i	0.00818253	−	0.0251832i
$482$	12.9978	−	5.78700i	0.592035	−	0.263591i
$483$	−0.267634	+	0.882259i	−0.0121778	+	0.0401442i
$484$	2.36422	+	0.502531i	0.107465	+	0.0228423i
$485$	−4.62851	+	10.3958i	−0.210170	+	0.472049i
$486$	1.73113	−	15.4920i	0.0785255	−	0.702733i
$487$	34.6520	+	3.64207i	1.57023	+	0.165038i	0.849278	−	0.527945i	$-0.177037\pi$
$487$	34.6520	+	3.64207i	1.57023	+	0.165038i	0.720953	+	0.692983i	$0.243704\pi$
$488$	−5.37942	−	3.90838i	−0.243515	−	0.176924i
$489$	18.3658	+	7.74864i	0.830530	+	0.350406i
$490$	8.11759	−	14.0601i	0.366716	−	0.635170i
$491$	−16.1760	−	28.0176i	−0.730012	−	1.26442i	−0.956878	−	0.290491i	$-0.906181\pi$
$491$	−16.1760	−	28.0176i	−0.730012	−	1.26442i	0.226866	−	0.973926i	$-0.427152\pi$
$492$	−18.2887	+	2.28602i	−0.824518	+	0.103062i
$493$	−7.82867	−	8.69462i	−0.352586	−	0.391586i
$494$	0.846220	+	2.60440i	0.0380732	+	0.117177i
$495$	9.29356	−	5.86371i	0.417714	−	0.263554i
$496$	−1.40857	−	5.38664i	−0.0632469	−	0.241867i
$497$		−	55.2926i		−	2.48021i
$498$	−2.94482	+	15.3280i	−0.131961	+	0.686863i
$499$	5.51928	−	4.96958i	0.247077	−	0.222469i	−0.536282	−	0.844039i	$-0.680172\pi$
$499$	5.51928	−	4.96958i	0.247077	−	0.222469i	0.783359	+	0.621570i	$0.213505\pi$
$500$	−0.587785	−	0.809017i	−0.0262866	−	0.0361803i
$501$	−20.3507	+	0.399569i	−0.909203	+	0.0178514i
$502$	−0.747239	−	0.431418i	−0.0333509	−	0.0192551i
$503$	−24.7277	+	2.59898i	−1.10255	+	0.115883i	−0.638276	−	0.769808i	$-0.720352\pi$
$503$	−24.7277	+	2.59898i	−1.10255	+	0.115883i	−0.464276	+	0.885691i	$0.653685\pi$
$504$	−14.4299	−	0.945882i	−0.642759	−	0.0421329i
$505$	−1.31923	+	12.5516i	−0.0587049	+	0.558540i
$506$	0.300594	+	0.270656i	0.0133630	+	0.0120321i
$507$	−16.7831	+	12.7044i	−0.745362	+	0.564220i
$508$	2.76841	−	13.0243i	0.122828	−	0.577862i
$509$	38.4523	−	8.17328i	1.70437	−	0.362274i	0.750121	−	0.661300i	$-0.229995\pi$
$509$	38.4523	−	8.17328i	1.70437	−	0.362274i	0.954245	+	0.299026i	$0.0966617\pi$
$510$	0.520012	−	6.09670i	0.0230265	−	0.269966i
$511$	−2.14217	−	0.696033i	−0.0947639	−	0.0307907i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	13.7282	−	7.10826i	0.606116	−	0.313837i
$514$	−0.487694	+	0.103662i	−0.0215112	+	0.00457236i
$515$	1.57878	−	7.42757i	0.0695693	−	0.327298i
$516$	−11.6102	−	15.3376i	−0.511111	−	0.675202i
$517$	3.97531	+	3.57939i	0.174834	+	0.157421i
$518$	−0.317902	+	3.02464i	−0.0139678	+	0.132895i
$519$	0.798947	+	1.70365i	0.0350699	+	0.0747818i
$520$	−0.915390	+	0.0962114i	−0.0401425	+	0.00421915i
$521$	15.7215	+	9.07681i	0.688771	+	0.397662i	0.803151	−	0.595775i	$-0.203155\pi$
$521$	15.7215	+	9.07681i	0.688771	+	0.397662i	−0.114380	+	0.993437i	$0.536488\pi$
$522$	8.79278	+	4.62618i	0.384849	+	0.202482i
$523$	8.57818	+	11.8069i	0.375098	+	0.516278i	0.954278	−	0.298922i	$-0.0966271\pi$
$523$	8.57818	+	11.8069i	0.375098	+	0.516278i	−0.579180	+	0.815200i	$0.696627\pi$
$524$	−9.68060	+	8.71645i	−0.422899	+	0.380780i
$525$	−8.19904	−	1.57521i	−0.357836	−	0.0687476i
$526$			15.9970i			0.697502i
$527$	10.8120	−	16.4311i	0.470978	−	0.715752i
$528$	−3.06372	+	5.55560i	−0.133331	+	0.241777i
$529$	−7.10362	−	21.8627i	−0.308853	−	0.950552i
$530$	6.31829	+	7.01717i	0.274449	+	0.304806i
$531$	0.656990	−	1.64673i	0.0285109	−	0.0714618i
$532$	−7.17055	−	12.4198i	−0.310883	−	0.538464i
$533$	−4.89723	+	8.48225i	−0.212122	+	0.367407i
$534$	7.27247	−	17.2372i	0.314711	−	0.745926i
$535$	0.442874	+	0.321767i	0.0191471	+	0.0139112i
$536$	−13.0025	−	1.36661i	−0.561621	−	0.0590288i
$537$	13.0090	+	37.5152i	0.561380	+	1.61890i
$538$	0.746226	−	1.67605i	0.0321721	−	0.0722597i
$539$	−58.1688	−	12.3642i	−2.50551	−	0.532562i
$540$	1.37763	+	5.01020i	0.0592839	+	0.215605i
$541$	−9.95531	+	4.43239i	−0.428012	+	0.190563i	−0.609425	−	0.792844i	$-0.708600\pi$
$541$	−9.95531	+	4.43239i	−0.428012	+	0.190563i	0.181413	+	0.983407i	$0.441933\pi$
$542$	−4.15630	+	12.7918i	−0.178528	+	0.549454i
$543$	−24.2106	+	22.6756i	−1.03898	+	0.973102i
$544$	1.43688	+	3.22729i	0.0616059	+	0.138369i
$545$	3.14330	+	14.7881i	0.134644	+	0.633451i
$546$	−5.02895	+	5.81067i	−0.215219	+	0.248674i
$547$	−21.8746	−	9.73920i	−0.935291	−	0.416418i	−0.118241	−	0.992985i	$-0.537725\pi$
$547$	−21.8746	−	9.73920i	−0.935291	−	0.416418i	−0.817050	+	0.576567i	$0.804392\pi$
$548$	−7.32330	+	8.13335i	−0.312836	+	0.347440i
$549$	8.82266	+	17.8909i	0.376542	+	0.763564i
$550$	−2.15302	+	2.96337i	−0.0918049	+	0.126359i
$551$	1.02994	+	9.79924i	0.0438770	+	0.417462i
$552$	−0.163732	+	0.0988664i	−0.00696891	+	0.00420803i
$553$	−16.7534	+	9.67259i	−0.712428	+	0.411320i
$554$	18.3596	−	13.3390i	0.780023	−	0.566720i
$555$	1.06427	−	0.248149i	0.0451757	−	0.0105333i
$556$	0.690568	−	0.224379i	0.0292866	−	0.00951579i
$557$	9.91670			0.420184			0.210092	−	0.977682i	$-0.432624\pi$
$557$	9.91670			0.420184			0.210092	+	0.977682i	$0.432624\pi$
$558$	−3.78469	+	16.2689i	−0.160219	+	0.688716i
$559$	−10.2225			−0.432364
$560$	4.58437	−	1.48955i	0.193725	−	0.0629450i
$561$	−21.8274	+	5.08936i	−0.921553	+	0.214873i
$562$	−8.67306	+	6.30135i	−0.365851	+	0.265806i
$563$	−29.8772	+	17.2496i	−1.25917	+	0.726984i	−0.972914	−	0.231168i	$-0.925745\pi$
$563$	−29.8772	+	17.2496i	−1.25917	+	0.726984i	−0.286259	+	0.958152i	$0.592412\pi$
$564$	−2.16534	+	1.30749i	−0.0911772	+	0.0550555i
$565$	−0.368709	−	3.50803i	−0.0155117	−	0.147584i
$566$	13.6711	−	18.8167i	0.574641	−	0.790926i
$567$	36.9895	+	22.6678i	1.55341	+	0.951960i
$568$	7.67546	−	8.52447i	0.322055	−	0.357679i
$569$	22.2487	+	9.90574i	0.932712	+	0.415270i	0.816102	−	0.577908i	$-0.196131\pi$
$569$	22.2487	+	9.90574i	0.932712	+	0.415270i	0.116610	+	0.993178i	$0.462797\pi$
$570$	−3.37227	+	3.89646i	−0.141249	+	0.163205i
$571$	6.70056	+	31.5236i	0.280410	+	1.31922i	0.862483	+	0.506087i	$0.168908\pi$
$571$	6.70056	+	31.5236i	0.280410	+	1.31922i	−0.582073	+	0.813137i	$0.697758\pi$
$572$	1.37130	+	3.08000i	0.0573371	+	0.128781i
$573$	−13.1771	+	12.3416i	−0.550480	+	0.515578i
$574$	15.8505	−	48.7829i	0.661589	−	2.03616i
$575$	−0.100881	+	0.0449150i	−0.00420702	+	0.00187308i
$576$	−2.09336	−	2.14892i	−0.0872232	−	0.0895383i
$577$	22.8745	+	4.86212i	0.952277	+	0.202413i	0.657755	−	0.753232i	$-0.271506\pi$
$577$	22.8745	+	4.86212i	0.952277	+	0.202413i	0.294522	+	0.955645i	$0.404840\pi$
$578$	1.83843	−	4.12918i	0.0764685	−	0.171751i
$579$	12.3453	+	35.6012i	0.513052	+	1.47953i
$580$	−3.29370	−	0.346181i	−0.136763	−	0.0143744i
$581$	−35.1419	−	25.5321i	−1.45793	−	1.05925i
$582$	−7.66180	+	18.1600i	−0.317592	+	0.752755i
$583$	17.2937	−	29.9535i	0.716230	−	1.24055i
$584$	−0.233638	−	0.404673i	−0.00966802	−	0.0167455i
$585$	2.56471	+	1.02324i	0.106038	+	0.0423056i
$586$	7.98352	+	8.86660i	0.329796	+	0.366276i
$587$	−13.6649	−	42.0562i	−0.564010	−	1.73584i	−0.670874	−	0.741571i	$-0.734081\pi$
$587$	−13.6649	−	42.0562i	−0.564010	−	1.73584i	0.106864	−	0.994274i	$-0.465919\pi$
$588$	13.5793	−	24.6241i	0.560002	−	1.01548i
$589$	−15.5002	+	5.84295i	−0.638676	+	0.240755i
$590$			0.590982i			0.0243304i
$591$	6.82472	+	1.31117i	0.280732	+	0.0539343i
$592$	−0.468878	+	0.422179i	−0.0192707	+	0.0173515i
$593$	−9.91987	−	13.6535i	−0.407360	−	0.560683i	0.555212	−	0.831709i	$-0.312637\pi$
$593$	−9.91987	−	13.6535i	−0.407360	−	0.560683i	−0.962572	+	0.271026i	$0.912637\pi$
$594$	15.8944	−	10.4703i	0.652157	−	0.429601i
$595$	14.7473	+	8.51435i	0.604580	+	0.349054i
$596$	−2.94735	+	0.309779i	−0.120728	+	0.0126890i
$597$	0.699411	+	1.49140i	0.0286250	+	0.0610390i
$598$	−0.0106244	+	0.101084i	−0.000434464	+	0.00413365i
$599$	28.8717	+	25.9962i	1.17967	+	1.06218i	0.996873	+	0.0790249i	$0.0251807\pi$
$599$	28.8717	+	25.9962i	1.17967	+	1.06218i	0.182794	+	0.983151i	$0.441486\pi$
$600$	−1.04538	−	1.38100i	−0.0426777	−	0.0563792i
$601$	8.64817	−	40.6865i	0.352766	−	1.65964i	−0.341473	−	0.939891i	$-0.610926\pi$
$601$	8.64817	−	40.6865i	0.352766	−	1.65964i	0.694240	−	0.719744i	$-0.255741\pi$
$602$	52.3650	−	11.1305i	2.13424	−	0.453646i
$603$	32.6120	+	21.7909i	1.32806	+	0.887396i
$604$	19.1159	+	6.21113i	0.777815	+	0.252727i
$605$	2.29874	+	0.746907i	0.0934572	+	0.0303661i
$606$	−1.85777	+	21.7807i	−0.0754666	+	0.884781i
$607$	−4.79493	+	1.01919i	−0.194620	+	0.0413678i	−0.304190	−	0.952611i	$-0.598386\pi$
$607$	−4.79493	+	1.01919i	−0.194620	+	0.0413678i	0.109570	+	0.993979i	$0.465053\pi$
$608$	0.618569	−	2.91014i	0.0250863	−	0.118022i
$609$	−22.0464	+	16.6885i	−0.893364	+	0.676254i
$610$	−4.94142	−	4.44927i	−0.200072	−	0.180146i
$611$	−0.140506	+	1.33683i	−0.00568427	+	0.0540823i
$612$	0.693221	−	10.5754i	0.0280218	−	0.427487i
$613$	39.1122	−	4.11085i	1.57973	−	0.166036i	0.726347	−	0.687328i	$-0.241217\pi$
$613$	39.1122	−	4.11085i	1.57973	−	0.166036i	0.853378	+	0.521292i	$0.174550\pi$
$614$	5.97044	+	3.44703i	0.240947	+	0.139111i
$615$	−18.4275	+	0.361808i	−0.743067	+	0.0145895i
$616$	−10.3782	−	14.2843i	−0.418148	−	0.575531i
$617$	6.50200	−	5.85443i	0.261761	−	0.235690i	−0.527791	−	0.849374i	$-0.676980\pi$
$617$	6.50200	−	5.85443i	0.261761	−	0.235690i	0.789552	+	0.613684i	$0.210313\pi$
$618$	2.48145	−	12.9161i	0.0998187	−	0.519563i
$619$		−	1.31823i		−	0.0529841i	−0.999649	−	0.0264920i	$-0.991566\pi$
$619$		−	1.31823i		−	0.0529841i	0.999649	−	0.0264920i	$-0.00843366\pi$
$620$	−0.837801	−	5.50437i	−0.0336469	−	0.221061i
$621$	0.572804	−	0.0337743i	0.0229858	−	0.00135532i
$622$	−7.55073	−	23.2388i	−0.302757	−	0.931789i
$623$	34.8388	+	38.6924i	1.39579	+	1.55018i
$624$	−1.58192	+	0.197735i	−0.0633277	+	0.00791573i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−5.09546	+	8.82559i	−0.203655	+	0.352742i
$627$	17.3910	+	7.33737i	0.694530	+	0.293026i
$628$	4.43972	+	3.22565i	0.177164	+	0.128717i
$629$	−2.21671	−	0.232985i	−0.0883859	−	0.00928974i
$630$	−14.2520	−	2.44904i	−0.567812	−	0.0975719i
$631$	2.61741	−	5.87879i	0.104197	−	0.234031i	−0.853922	−	0.520402i	$-0.825782\pi$
$631$	2.61741	−	5.87879i	0.104197	−	0.234031i	0.958119	+	0.286371i	$0.0924489\pi$
$632$	−3.92558	−	0.834408i	−0.156151	−	0.0331910i
$633$	−12.0137	+	39.6035i	−0.477503	+	1.57410i
$634$	5.51860	−	2.45704i	0.219171	−	0.0975814i
$635$	4.11466	−	12.6636i	0.163285	−	0.502540i
$636$	11.1801	+	11.9369i	0.443319	+	0.473330i
$637$	−6.07802	−	13.6515i	−0.240820	−	0.540891i
$638$	2.52218	+	11.8659i	0.0998541	+	0.469777i
$639$	−32.2855	+	11.9105i	−1.27719	+	0.471172i
$640$	0.913545	+	0.406737i	0.0361111	+	0.0160777i
$641$	11.8937	−	13.2093i	0.469773	−	0.521735i	−0.460967	−	0.887417i	$-0.652497\pi$
$641$	11.8937	−	13.2093i	0.469773	−	0.521735i	0.930740	+	0.365682i	$0.119164\pi$
$642$	0.777872	+	0.542151i	0.0307002	+	0.0213970i
$643$	−5.58624	+	7.68880i	−0.220300	+	0.303217i	−0.904834	−	0.425764i	$-0.860005\pi$
$643$	−5.58624	+	7.68880i	−0.220300	+	0.303217i	0.684535	+	0.728980i	$0.260005\pi$
$644$	−0.0556398	−	0.529378i	−0.00219252	−	0.0208604i
$645$	−9.94338	−	16.4672i	−0.391520	−	0.648396i
$646$	9.10223	−	5.25518i	0.358123	−	0.206762i
$647$	9.92997	−	7.21455i	0.390388	−	0.283633i	−0.375227	−	0.926933i	$-0.622435\pi$
$647$	9.92997	−	7.21455i	0.390388	−	0.283633i	0.765614	+	0.643300i	$0.222435\pi$
$648$	2.55602	+	8.62941i	0.100410	+	0.338995i
$649$	2.05878	−	0.668937i	0.0808141	−	0.0262581i
$650$	−0.920432			−0.0361023
$651$	−36.5203	−	28.7601i	−1.43134	−	1.12720i
$652$	−11.5086			−0.450712
$653$	47.8747	−	15.5554i	1.87348	−	0.608732i	0.883329	−	0.468753i	$-0.155297\pi$
$653$	47.8747	−	15.5554i	1.87348	−	0.608732i	0.990155	−	0.139978i	$-0.0447033\pi$
$654$	5.94611	+	25.5019i	0.232511	+	0.997202i
$655$	−10.5387	+	7.65680i	−0.411780	+	0.299176i
$656$	9.21550	−	5.32057i	0.359805	−	0.207734i
$657$	0.0550263	+	1.40075i	0.00214678	+	0.0546485i
$658$	−0.735829	−	7.00095i	−0.0286856	−	0.272925i
$659$	−8.98012	+	12.3601i	−0.349816	+	0.481480i	−0.947276	−	0.320418i	$-0.896177\pi$
$659$	−8.98012	+	12.3601i	−0.349816	+	0.481480i	0.597460	+	0.801898i	$0.296177\pi$
$660$	−3.62766	+	5.20492i	−0.141206	+	0.202601i
$661$	−16.2768	+	18.0772i	−0.633092	+	0.703120i	−0.971275	−	0.237960i	$-0.923521\pi$
$661$	−16.2768	+	18.0772i	−0.633092	+	0.703120i	0.338183	+	0.941080i	$0.390188\pi$
$662$	1.58648	+	0.706349i	0.0616605	+	0.0274530i
$663$	−4.25854	−	3.68564i	−0.165388	−	0.143138i
$664$	−1.87359	−	8.81453i	−0.0727093	−	0.342070i
$665$	−5.83305	−	13.1012i	−0.226196	−	0.508044i
$666$	1.83457	−	0.465910i	0.0710883	−	0.0180536i
$667$	−0.113013	+	0.347819i	−0.00437589	+	0.0134676i
$668$	10.7358	−	4.77987i	0.415379	−	0.184939i
$669$	−3.99430	−	1.21167i	−0.154429	−	0.0468460i
$670$	−12.7884	−	2.71826i	−0.494059	−	0.105015i
$671$	−9.90649	+	22.2503i	−0.382436	+	0.858965i
$672$	7.88818	−	2.73535i	0.304293	−	0.105519i
$673$	27.6426	+	2.90536i	1.06554	+	0.111993i	0.621036	−	0.783782i	$-0.286712\pi$
$673$	27.6426	+	2.90536i	1.06554	+	0.111993i	0.444508	+	0.895775i	$0.353379\pi$
$674$	−13.9953	−	10.1682i	−0.539081	−	0.391665i
$675$	0.846379	+	5.12676i	0.0325771	+	0.197329i
$676$	6.07640	−	10.5246i	0.233708	−	0.404794i
$677$	−18.1212	−	31.3869i	−0.696456	−	1.20630i	−0.969687	−	0.244349i	$-0.921426\pi$
$677$	−18.1212	−	31.3869i	−0.696456	−	1.20630i	0.273231	−	0.961948i	$-0.411908\pi$
$678$	−0.757776	−	6.06239i	−0.0291022	−	0.232825i
$679$	−36.7039	−	40.7638i	−1.40857	−	1.56437i
$680$	1.09167	+	3.35981i	0.0418636	+	0.128843i
$681$	−22.6693	−	12.5013i	−0.868689	−	0.479051i
$682$	−18.2270	+	9.14904i	−0.697948	+	0.350335i
$683$		−	28.3768i		−	1.08581i	−0.839795	−	0.542903i	$-0.817325\pi$
$683$		−	28.3768i		−	1.08581i	0.839795	−	0.542903i	$-0.182675\pi$
$684$	−5.70733	+	6.86223i	−0.218225	+	0.262384i
$685$	−8.13335	+	7.32330i	−0.310759	+	0.279809i
$686$	26.1660	+	36.0144i	0.999023	+	1.37504i
$687$	−0.763704	−	38.8967i	−0.0291371	−	1.48400i
$688$	9.61821	+	5.55308i	0.366691	+	0.211709i
$689$	8.64360	−	0.908479i	0.329295	−	0.0346103i
$690$	−0.173170	+	0.0812101i	−0.00659246	+	0.00309162i
$691$	−2.32829	+	22.1522i	−0.0885724	+	0.842710i	0.856565	+	0.516038i	$0.172594\pi$
$691$	−2.32829	+	22.1522i	−0.0885724	+	0.842710i	−0.945138	+	0.326672i	$0.894073\pi$
$692$	−0.807345	−	0.726937i	−0.0306907	−	0.0276340i
$693$	7.60033	+	52.4210i	0.288713	+	1.99131i
$694$	−4.11465	+	19.3579i	−0.156190	+	0.734816i
$695$	0.710239	−	0.150966i	0.0269409	−	0.00572646i
$696$	−5.71552	−	0.487500i	−0.216646	−	0.0184786i
$697$	35.7522	+	11.6166i	1.35421	+	0.440010i
$698$	−33.9350	−	11.0262i	−1.28446	−	0.417347i
$699$	44.7165	+	3.81405i	1.69133	+	0.144261i
$700$	4.71495	−	1.00219i	0.178209	−	0.0378794i
$701$	−8.02690	+	37.7636i	−0.303172	+	1.42631i	0.517878	+	0.855454i	$0.326722\pi$
$701$	−8.02690	+	37.7636i	−0.303172	+	1.42631i	−0.821050	+	0.570857i	$0.806611\pi$
$702$	4.47615	+	1.68475i	0.168941	+	0.0635869i
$703$	1.39498	+	1.25605i	0.0526127	+	0.0473727i
$704$	0.382880	−	3.64286i	0.0144303	−	0.137296i
$705$	−2.29015	+	1.07399i	−0.0862519	+	0.0404489i
$706$	−17.4130	+	1.83018i	−0.655346	+	0.0688796i
$707$	−52.6853	−	30.4179i	−1.98143	−	1.14398i
$708$	0.0200939	+	1.02341i	0.000755174	+	0.0384623i
$709$	−15.3810	−	21.1701i	−0.577644	−	0.795059i	0.415790	−	0.909460i	$-0.363505\pi$
$709$	−15.3810	−	21.1701i	−0.577644	−	0.795059i	−0.993435	+	0.114401i	$0.963505\pi$
$710$	8.52447	−	7.67546i	0.319918	−	0.288055i
$711$	9.25668	+	7.69881i	0.347153	+	0.288728i
$712$			10.8014i			0.404799i
$713$	−0.613788	−	0.0358812i	−0.0229865	−	0.00134376i
$714$	25.8276	+	14.2430i	0.966574	+	0.533032i
$715$	1.04184	+	3.20646i	0.0389627	+	0.119915i
$716$	−15.3396	−	17.0364i	−0.573268	−	0.636679i
$717$	−2.65097	−	21.2084i	−0.0990023	−	0.792042i
$718$	14.4155	+	24.9684i	0.537982	+	0.931813i
$719$	5.11500	−	8.85944i	0.190757	−	0.330401i	−0.754744	−	0.656019i	$-0.772239\pi$
$719$	5.11500	−	8.85944i	0.190757	−	0.330401i	0.945501	+	0.325618i	$0.105572\pi$
$720$	−1.85727	−	2.35596i	−0.0692162	−	0.0878016i
$721$	29.6124	+	21.5146i	1.10282	+	0.801247i
$722$	10.0929	+	1.06080i	0.375618	+	0.0394790i
$723$	23.2833	−	8.07385i	0.865915	−	0.300270i
$724$	7.78961	−	17.4957i	0.289498	−	0.650224i
$725$	−3.23947	−	0.688570i	−0.120311	−	0.0255728i
$726$	4.00617	+	1.21527i	0.148683	+	0.0451030i
$727$	43.2634	−	19.2621i	1.60455	−	0.714392i	0.607735	−	0.794140i	$-0.292078\pi$
$727$	43.2634	−	19.2621i	1.60455	−	0.714392i	0.996815	+	0.0797477i	$0.0254115\pi$
$728$	1.37103	−	4.21960i	0.0508138	−	0.156389i
$729$	5.26797	−	26.4811i	0.195110	−	0.980781i
$730$	−0.190059	−	0.426879i	−0.00703438	−	0.0157995i
$731$	8.15738	+	38.3775i	0.301712	+	1.41944i
$732$	−8.70842	−	7.53687i	−0.321872	−	0.278571i
$733$	8.42718	+	3.75202i	0.311265	+	0.138584i	0.556423	−	0.830899i	$-0.312173\pi$
$733$	8.42718	+	3.75202i	0.311265	+	0.138584i	−0.245158	+	0.969483i	$0.578840\pi$
$734$	16.3964	−	18.2100i	0.605200	−	0.672143i
$735$	16.0789	−	23.0698i	0.593077	−	0.850942i
$736$	0.0649078	−	0.0893379i	0.00239253	−	0.00329304i
$737$	5.00581	+	47.6271i	0.184391	+	1.75437i
$738$	−31.8988	+	1.25310i	−1.17421	+	0.0461271i
$739$	32.6490	−	18.8499i	1.20101	−	0.693405i	0.240233	−	0.970715i	$-0.422776\pi$
$739$	32.6490	−	18.8499i	1.20101	−	0.693405i	0.960781	+	0.277310i	$0.0894429\pi$
$740$	−0.510439	+	0.370855i	−0.0187641	+	0.0136329i
$741$	1.07703	+	4.61919i	0.0395656	+	0.169690i
$742$	−43.2880	+	14.0651i	−1.58915	+	0.516347i
$743$	0.769278			0.0282221			0.0141110	−	0.999900i	$-0.495508\pi$
$743$	0.769278			0.0282221			0.0141110	+	0.999900i	$0.495508\pi$
$744$	−1.63799	−	9.50353i	−0.0600515	−	0.348416i
$745$	−2.96358			−0.108577
$746$	11.5098	−	3.73975i	0.421403	−	0.136922i
$747$	−7.33839	+	26.0193i	−0.268498	+	0.951997i
$748$	10.4687	−	7.60598i	0.382775	−	0.278102i
$749$	−2.28521	+	1.31937i	−0.0834997	+	0.0482086i
$750$	−0.895304	−	1.48271i	−0.0326919	−	0.0541409i
$751$	−4.53063	−	43.1061i	−0.165325	−	1.57296i	−0.691367	−	0.722504i	$-0.742991\pi$
$751$	−4.53063	−	43.1061i	−0.165325	−	1.57296i	0.526042	−	0.850459i	$-0.323675\pi$
$752$	0.858397	−	1.18148i	0.0313025	−	0.0430842i
$753$	−1.22607	−	0.854528i	−0.0446804	−	0.0311407i
$754$	−2.03973	+	2.26534i	−0.0742824	+	0.0824990i
$755$	18.3619	+	8.17526i	0.668259	+	0.297528i
$756$	−24.7637	−	3.75646i	−0.900646	−	0.136621i
$757$	−4.86744	−	22.8995i	−0.176910	−	0.832297i	−0.973663	−	0.227992i	$-0.926784\pi$
$757$	−4.86744	−	22.8995i	−0.176910	−	0.832297i	0.796753	−	0.604305i	$-0.206549\pi$
$758$	9.06492	+	20.3601i	0.329253	+	0.739514i
$759$	0.478920	+	0.511341i	0.0173837	+	0.0185605i
$760$	0.919372	−	2.82954i	0.0333491	−	0.102638i
$761$	−23.0346	+	10.2556i	−0.835002	+	0.371767i	−0.779277	−	0.626679i	$-0.784414\pi$
$761$	−23.0346	+	10.2556i	−0.835002	+	0.371767i	−0.0557247	+	0.998446i	$0.517747\pi$
$762$	6.69485	−	22.0697i	0.242529	−	0.799501i
$763$	−71.2827	−	15.1516i	−2.58061	−	0.548525i
$764$	4.23963	−	9.52237i	0.153385	−	0.344507i
$765$	1.79486	−	10.4450i	0.0648932	−	0.377641i
$766$	−4.07719	−	0.428530i	−0.147315	−	0.0154834i
$767$	0.440072	+	0.319731i	0.0158901	+	0.0115448i
$768$	1.59583	+	0.673291i	0.0575846	+	0.0242953i
$769$	9.78852	−	16.9542i	0.352983	−	0.611384i	−0.633788	−	0.773507i	$-0.718501\pi$
$769$	9.78852	−	16.9542i	0.352983	−	0.611384i	0.986771	+	0.162123i	$0.0518340\pi$
$770$	−8.82819	−	15.2909i	−0.318146	−	0.551045i
$771$	−0.856913	+	0.107111i	−0.0308610	+	0.00385751i
$772$	−14.5570	−	16.1672i	−0.523917	−	0.581869i
$773$	10.6110	+	32.6572i	0.381650	+	1.17460i	0.938882	+	0.344240i	$0.111863\pi$
$773$	10.6110	+	32.6572i	0.381650	+	1.17460i	−0.557232	+	0.830357i	$0.688137\pi$
$774$	−17.7790	−	28.1785i	−0.639054	−	1.01285i
$775$	−0.257848	−	5.56179i	−0.00926218	−	0.199785i
$776$		−	11.3796i		−	0.408505i
$777$	−0.993855	+	5.17308i	−0.0356544	+	0.185583i
$778$	−26.5155	+	23.8746i	−0.950626	+	0.855948i
$779$	−18.6087	−	25.6127i	−0.666726	−	0.917670i
$780$	−1.59393	+	0.0312954i	−0.0570718	+	0.00112056i
$781$	−36.3875	−	21.0084i	−1.30205	−	0.751738i
$782$	0.387972	−	0.0407775i	0.0138739	−	0.00145820i
$783$	14.4935	+	9.27808i	0.517954	+	0.331571i
$784$	−1.69704	+	16.1463i	−0.0606086	+	0.576652i
$785$	4.07823	+	3.67206i	0.145558	+	0.131061i
$786$	−17.9897	+	13.6177i	−0.641671	+	0.485729i
$787$	7.70654	−	36.2564i	0.274708	−	1.29240i	−0.596947	−	0.802281i	$-0.703620\pi$
$787$	7.70654	−	36.2564i	0.274708	−	1.29240i	0.871655	−	0.490120i	$-0.163047\pi$
$788$	−3.92464	+	0.834207i	−0.139809	+	0.0297174i
$789$	−2.35474	+	27.6073i	−0.0838310	+	0.982847i
$790$	−3.81686	−	1.24017i	−0.135798	−	0.0441233i
$791$	16.1707	+	5.25418i	0.574964	+	0.186817i
$792$	−6.10510	+	9.13680i	−0.216935	+	0.324662i
$793$	−5.98652	+	1.27247i	−0.212587	+	0.0451869i
$794$	−8.02600	+	37.7594i	−0.284832	+	1.34003i
$795$	9.87108	+	13.0402i	0.350091	+	0.462487i
$796$	−0.706764	−	0.636373i	−0.0250506	−	0.0225556i
$797$	2.23860	−	21.2988i	0.0792952	−	0.754444i	−0.880558	−	0.473939i	$-0.842832\pi$
$797$	2.23860	−	21.2988i	0.0792952	−	0.754444i	0.959853	−	0.280504i	$-0.0905017\pi$
$798$	−10.5466	−	22.4893i	−0.373347	−	0.796113i
$799$	5.13088	−	0.539277i	0.181518	−	0.0190783i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$	15.0880	−	28.6772i	0.533109	−	1.01326i
$802$	−19.9212	−	27.4192i	−0.703443	−	0.968206i
$803$	−1.27197	+	1.14528i	−0.0448868	+	0.0404162i
$804$	−22.2383	−	4.27244i	−0.784284	−	0.150677i
$805$		−	0.532294i		−	0.0187609i
$806$	−4.55207	−	2.35409i	−0.160340	−	0.0829193i
$807$	1.53454	−	2.78266i	0.0540183	−	0.0979542i
$808$	−3.90003	−	12.0031i	−0.137203	−	0.422266i
$809$	1.30197	+	1.44598i	0.0457748	+	0.0508381i	0.765597	−	0.643320i	$-0.222444\pi$
$809$	1.30197	+	1.44598i	0.0457748	+	0.0508381i	−0.719823	+	0.694158i	$0.755777\pi$
$810$	1.64000	+	8.84932i	0.0576238	+	0.310933i
$811$	11.7096	+	20.2817i	0.411181	+	0.712187i	0.995019	−	0.0996834i	$-0.0317830\pi$
$811$	11.7096	+	20.2817i	0.411181	+	0.712187i	−0.583838	+	0.811870i	$0.698450\pi$
$812$	7.98201	−	13.8252i	0.280114	−	0.485171i
$813$	−9.05582	+	21.4640i	−0.317601	+	0.752777i
$814$	1.86970	+	1.35842i	0.0655330	+	0.0476125i
$815$	−11.4456	−	1.20298i	−0.400920	−	0.0421384i
$816$	2.00470	+	5.78112i	0.0701784	+	0.202380i
$817$	13.4396	−	30.1858i	0.470192	−	1.05607i
$818$	−17.4541	−	3.70997i	−0.610267	−	0.129716i
$819$	−9.53422	+	9.28770i	−0.333153	+	0.324539i
$820$	9.72117	−	4.32814i	0.339478	−	0.151145i
$821$	0.139134	−	0.428211i	0.00485582	−	0.0149447i	−0.948599	−	0.316480i	$-0.897499\pi$
$821$	0.139134	−	0.428211i	0.00485582	−	0.0149447i	0.953455	+	0.301535i	$0.0974991\pi$
$822$	−13.8357	+	12.9584i	−0.482574	+	0.451977i
$823$	5.29369	+	11.8898i	0.184526	+	0.414453i	0.981995	−	0.188907i	$-0.0604946\pi$
$823$	5.29369	+	11.8898i	0.184526	+	0.414453i	−0.797468	+	0.603361i	$0.793828\pi$
$824$	1.57878	+	7.42757i	0.0549993	+	0.258752i
$825$	−4.15185	+	4.79722i	−0.144549	+	0.167018i
$826$	−2.60242	−	1.15867i	−0.0905499	−	0.0403154i
$827$	−1.35674	+	1.50681i	−0.0471784	+	0.0523970i	−0.766272	−	0.642516i	$-0.777891\pi$
$827$	−1.35674	+	1.50681i	−0.0471784	+	0.0523970i	0.719094	+	0.694913i	$0.244557\pi$
$828$	−0.297120	+	0.146521i	−0.0103256	+	0.00509195i
$829$	−3.27028	+	4.50115i	−0.113581	+	0.156332i	−0.862023	−	0.506870i	$-0.830803\pi$
$829$	−3.27028	+	4.50115i	−0.113581	+	0.156332i	0.748441	+	0.663201i	$0.230803\pi$
$830$	−0.941953	−	8.96209i	−0.0326957	−	0.311079i
$831$	33.6482	−	20.3177i	1.16724	−	0.704815i
$832$	0.797118	−	0.460216i	0.0276351	−	0.0159551i
$833$	−46.4006	+	33.7120i	−1.60768	+	1.16805i
$834$	1.22480	−	0.285579i	0.0424113	−	0.00988879i
$835$	11.1766	−	3.63149i	0.386781	−	0.125673i
$836$	−10.8978			−0.376907
$837$	−8.92632	+	27.5195i	−0.308539	+	0.951212i
$838$	28.1355			0.971923
$839$	4.62854	−	1.50390i	0.159795	−	0.0519206i	−0.228027	−	0.973655i	$-0.573227\pi$
$839$	4.62854	−	1.50390i	0.159795	−	0.0519206i	0.387822	+	0.921734i	$0.373227\pi$
$840$	8.13089	−	1.89583i	0.280542	−	0.0654123i
$841$	14.5880	−	10.5988i	0.503034	−	0.365475i
$842$	−2.61770	+	1.51133i	−0.0902118	+	0.0520838i
$843$	−15.8954	+	9.59810i	−0.547466	+	0.330576i
$844$	−2.49760	−	23.7631i	−0.0859709	−	0.817959i
$845$	7.14324	−	9.83183i	0.245735	−	0.338225i
$846$	−3.92937	+	1.93772i	−0.135095	+	0.0666201i
$847$	−7.79593	+	8.65826i	−0.267871	+	0.297501i
$848$	−8.62618	−	3.84062i	−0.296224	−	0.131888i
$849$	26.3633	−	30.4612i	0.904785	−	1.04543i
$850$	0.734492	+	3.45551i	0.0251929	+	0.118523i
$851$	0.0283385	+	0.0636494i	0.000971432	+	0.00218187i
$852$	14.5010	−	13.5816i	0.496796	−	0.465297i
$853$	5.88286	−	18.1056i	0.201425	−	0.619923i	−0.798416	−	0.602106i	$-0.794328\pi$
$853$	5.88286	−	18.1056i	0.201425	−	0.619923i	0.999841	−	0.0178168i	$-0.00567157\pi$
$854$	29.2807	−	13.0366i	1.00196	−	0.446103i
$855$	−6.39336	+	6.22806i	−0.218648	+	0.212995i
$856$	−0.535460	−	0.113815i	−0.0183016	−	0.00389013i
$857$	8.22188	−	18.4666i	0.280854	−	0.630809i	−0.716944	−	0.697131i	$-0.754460\pi$
$857$	8.22188	−	18.4666i	0.280854	−	0.630809i	0.997798	+	0.0663220i	$0.0211264\pi$
$858$	1.91320	+	5.51727i	0.0653156	+	0.188356i
$859$	−52.4542	−	5.51316i	−1.78972	−	0.188107i	−0.849249	−	0.527993i	$-0.822945\pi$
$859$	−52.4542	−	5.51316i	−1.78972	−	0.188107i	−0.940467	+	0.339886i	$0.889611\pi$
$860$	8.98506	+	6.52803i	0.306388	+	0.222604i
$861$	34.5354	−	81.8556i	1.17696	−	2.78963i
$862$	4.70213	−	8.14433i	0.160155	−	0.277397i
$863$	−4.33677	−	7.51151i	−0.147625	−	0.255695i	0.782724	−	0.622369i	$-0.213830\pi$
$863$	−4.33677	−	7.51151i	−0.147625	−	0.255695i	−0.930349	+	0.366674i	$0.880496\pi$
$864$	−3.29636	−	4.01671i	−0.112145	−	0.136651i
$865$	−0.726937	−	0.807345i	−0.0247166	−	0.0274506i
$866$	8.44065	+	25.9777i	0.286825	+	0.882757i
$867$	3.78054	−	6.85546i	0.128394	−	0.232824i
$868$	25.8814	+	7.10250i	0.878471	+	0.241075i
$869$			14.7004i			0.498675i
$870$	−5.63325	−	1.08226i	−0.190985	−	0.0366922i
$871$	−8.94287	+	8.05219i	−0.303017	+	0.272838i
$872$	−8.88639	−	12.2311i	−0.300931	−	0.414196i
$873$	−15.8958	+	30.2124i	−0.537990	+	1.02253i
$874$	−0.284523	−	0.164270i	−0.00962414	−	0.00555650i
$875$	4.79388	−	0.503857i	0.162063	−	0.0170335i
$876$	−0.343642	−	0.732771i	−0.0116106	−	0.0247580i
$877$	2.36053	−	22.4590i	0.0797095	−	0.758385i	−0.879540	−	0.475825i	$-0.842150\pi$
$877$	2.36053	−	22.4590i	0.0797095	−	0.758385i	0.959250	−	0.282560i	$-0.0911837\pi$
$878$	−0.333864	−	0.300613i	−0.0112674	−	0.0101452i
$879$	12.4727	+	16.4770i	0.420693	+	0.555755i
$880$	0.761566	−	3.58288i	0.0256724	−	0.120779i
$881$	−7.10625	+	1.51048i	−0.239416	+	0.0508893i	−0.326057	−	0.945350i	$-0.605720\pi$
$881$	−7.10625	+	1.51048i	−0.239416	+	0.0508893i	0.0866411	+	0.996240i	$0.472387\pi$
$882$	27.0596	−	40.4970i	0.911145	−	1.36361i
$883$	34.7616	+	11.2947i	1.16982	+	0.380097i	0.828575	−	0.559877i	$-0.189152\pi$
$883$	34.7616	+	11.2947i	1.16982	+	0.380097i	0.341244	+	0.939975i	$0.389152\pi$
$884$	3.09248	+	1.00481i	0.104011	+	0.0337953i
$885$	−0.0869921	+	1.01991i	−0.00292421	+	0.0342838i
$886$	−4.89452	+	1.04036i	−0.164435	+	0.0349517i
$887$	4.32605	−	20.3525i	0.145255	−	0.683369i	−0.843901	−	0.536499i	$-0.819747\pi$
$887$	4.32605	−	20.3525i	0.145255	−	0.683369i	0.989156	−	0.146871i	$-0.0469201\pi$
$888$	−0.871326	+	0.659572i	−0.0292398	+	0.0221338i
$889$	47.6978	+	42.9473i	1.59973	+	1.44041i
$890$	−1.12905	+	10.7422i	−0.0378459	+	0.360080i
$891$	28.9716	−	15.7298i	0.970585	−	0.526968i
$892$	2.39668	−	0.251901i	0.0802469	−	0.00843429i
$893$	−3.76278	−	2.17244i	−0.125917	−	0.0726981i
$894$	−5.13209	+	0.100764i	−0.171643	+	0.00337006i
$895$	−13.4748	−	18.5465i	−0.450413	−	0.619940i
$896$	−3.58217	+	3.22540i	−0.119672	+	0.107753i
$897$	−0.0332150	+	0.172886i	−0.00110902	+	0.00577250i
$898$			24.9008i			0.830949i
$899$	−14.2599	−	11.6906i	−0.475596	−	0.389904i
$900$	−1.60083	−	2.53719i	−0.0533609	−	0.0845731i
$901$	−10.3081	−	31.7251i	−0.343413	−	1.05692i
$902$	−26.0812	−	28.9661i	−0.868409	−	0.964466i
$903$	92.0091	−	11.5008i	3.06187	−	0.382723i
$904$	1.76368	+	3.05478i	0.0586591	+	0.101601i
$905$	9.57574	−	16.5857i	0.318308	−	0.551326i
$906$	32.0756	+	13.5329i	1.06564	+	0.449601i
$907$	−23.2702	−	16.9068i	−0.772674	−	0.561380i	0.130097	−	0.991501i	$-0.458471\pi$
$907$	−23.2702	−	16.9068i	−0.772674	−	0.561380i	−0.902771	+	0.430121i	$0.858471\pi$
$908$	14.8645	+	1.56232i	0.493294	+	0.0518473i
$909$	−6.41221	+	37.3154i	−0.212680	+	1.23767i
$910$	1.80459	−	4.05317i	0.0598215	−	0.134361i
$911$	−35.5416	−	7.55460i	−1.17755	−	0.250295i	−0.422745	−	0.906249i	$-0.638933\pi$
$911$	−35.5416	−	7.55460i	−1.17755	−	0.250295i	−0.754801	+	0.655954i	$0.772267\pi$
$912$	1.49589	−	4.93122i	0.0495338	−	0.163289i
$913$	−30.1546	+	13.4257i	−0.997971	+	0.444325i
$914$	−4.63271	+	14.2580i	−0.153237	+	0.471614i
$915$	−7.87289	−	8.40586i	−0.260270	−	0.277889i
$916$	9.13585	+	20.5195i	0.301857	+	0.677982i
$917$	−13.0551	−	61.4195i	−0.431118	−	2.02825i
$918$	2.75305	−	18.1489i	0.0908641	−	0.599003i
$919$	27.6385	+	12.3054i	0.911710	+	0.405919i	0.808335	−	0.588723i	$-0.200369\pi$
$919$	27.6385	+	12.3054i	0.911710	+	0.405919i	0.103375	+	0.994642i	$0.467036\pi$
$920$	0.0738906	−	0.0820638i	0.00243610	−	0.00270556i
$921$	9.79628	+	6.82768i	0.322799	+	0.224980i
$922$	−16.4114	+	22.5883i	−0.540480	+	0.743907i
$923$	−1.10362	−	10.5003i	−0.0363261	−	0.345620i
$924$	−15.8078	−	26.1793i	−0.520039	−	0.861235i
$925$	−0.546407	+	0.315469i	−0.0179658	+	0.0103725i
$926$	15.1262	−	10.9898i	0.497077	−	0.361148i
$927$	6.18370	−	21.9252i	0.203099	−	0.720117i
$928$	3.14975	−	1.02341i	0.103395	−	0.0335952i
$929$	−36.1626			−1.18646			−0.593228	−	0.805034i	$-0.702147\pi$
$929$	−36.1626			−1.18646			−0.593228	+	0.805034i	$0.702147\pi$
$930$	−0.635626	−	9.62268i	−0.0208430	−	0.315540i
$931$	48.3022			1.58304
$932$	−24.6426	+	8.00688i	−0.807197	+	0.262274i
$933$	−9.61021	−	41.2165i	−0.314624	−	1.34937i
$934$	14.7597	−	10.7236i	0.482952	−	0.350885i
$935$	11.2064	−	6.47003i	0.366489	−	0.211593i
$936$	−2.75917	+	0.108390i	−0.0901862	+	0.00354283i
$937$	3.58958	+	34.1526i	0.117267	+	1.11572i	0.881961	+	0.471323i	$0.156223\pi$
$937$	3.58958	+	34.1526i	0.117267	+	1.11572i	−0.764694	+	0.644393i	$0.777110\pi$
$938$	37.0428	−	50.9850i	1.20949	−	1.66472i
$939$	−10.0928	+	14.4810i	−0.329365	+	0.472570i
$940$	0.977193	−	1.08528i	0.0318725	−	0.0353980i
$941$	43.7903	+	19.4967i	1.42752	+	0.635575i	0.967624	−	0.252396i	$-0.0812185\pi$
$941$	43.7903	+	19.4967i	1.42752	+	0.635575i	0.459900	+	0.887971i	$0.347885\pi$
$942$	7.18720	+	6.22030i	0.234171	+	0.202668i
$943$	−0.244312	−	1.14940i	−0.00795591	−	0.0374296i
$944$	−0.240374	−	0.539889i	−0.00782351	−	0.0175719i
$945$	−24.2354	−	6.32439i	−0.788376	−	0.205732i
$946$	12.5711	−	38.6900i	0.408723	−	1.25792i
$947$	−18.3445	+	8.16749i	−0.596116	+	0.265408i	−0.682537	−	0.730851i	$-0.739123\pi$
$947$	−18.3445	+	8.16749i	−0.596116	+	0.265408i	0.0864215	+	0.996259i	$0.472457\pi$
$948$	−6.65188	−	2.01785i	−0.216043	−	0.0655367i
$949$	−0.420698	−	0.0894221i	−0.0136564	−	0.00290276i
$950$	1.21010	−	2.71794i	0.0392609	−	0.0881815i
$951$	9.88558	−	3.42798i	0.320562	−	0.111160i
$952$	−16.9354	−	1.77998i	−0.548880	−	0.0576896i
$953$	10.3679	+	7.53269i	0.335848	+	0.244008i	0.742908	−	0.669394i	$-0.233446\pi$
$953$	10.3679	+	7.53269i	0.335848	+	0.244008i	−0.407060	+	0.913401i	$0.633446\pi$
$954$	17.5373	+	22.2463i	0.567791	+	0.720249i
$955$	5.21177	−	9.02705i	0.168649	−	0.292108i
$956$	6.16998	+	10.6867i	0.199551	+	0.345633i
$957$	2.60609	+	20.8493i	0.0842428	+	0.673962i
$958$	−24.5134	−	27.2249i	−0.791993	−	0.879598i
$959$	−16.3024	−	50.1736i	−0.526432	−	1.62019i
$960$	1.51671	+	0.836413i	0.0489516	+	0.0269951i
$961$	12.9496	−	28.1657i	0.417728	−	0.908572i
$962$			0.580735i			0.0187236i
$963$	1.26264	+	1.05014i	0.0406879	+	0.0338402i
$964$	−10.5734	+	9.52031i	−0.340546	+	0.306629i
$965$	−12.7873	−	17.6002i	−0.411638	−	0.566571i
$966$	−0.0180984	−	0.921782i	−0.000582307	−	0.0296578i
$967$	18.2252	+	10.5223i	0.586083	+	0.338375i	0.763547	−	0.645752i	$-0.223456\pi$
$967$	18.2252	+	10.5223i	0.586083	+	0.338375i	−0.177464	+	0.984127i	$0.556789\pi$
$968$	−2.40380	+	0.252650i	−0.0772611	+	0.00812047i
$969$	16.4821	−	7.72946i	0.529480	−	0.248306i
$970$	1.18949	−	11.3173i	0.0381924	−	0.363376i
$971$	−21.5373	−	19.3922i	−0.691163	−	0.622326i	0.246798	−	0.969067i	$-0.420622\pi$
$971$	−21.5373	−	19.3922i	−0.691163	−	0.622326i	−0.937961	+	0.346741i	$0.887288\pi$
$972$	3.14090	+	15.2687i	0.100745	+	0.489745i
$973$	−0.727699	+	3.42356i	−0.0233290	+	0.109754i
$974$	−34.0815	+	7.24424i	−1.09204	+	0.232120i
$975$	−1.58847	−	0.135487i	−0.0508717	−	0.00433905i
$976$	6.32389	+	2.05476i	0.202423	+	0.0657712i
$977$	−40.1426	−	13.0431i	−1.28428	−	0.417287i	−0.414192	−	0.910189i	$-0.635936\pi$
$977$	−40.1426	−	13.0431i	−1.28428	−	0.417287i	−0.870085	+	0.492902i	$0.835936\pi$
$978$	−19.8614	−	1.69406i	−0.635097	−	0.0541700i
$979$	38.7001	−	8.22596i	1.23686	−	0.262903i
$980$	−3.37549	+	15.8804i	−0.107826	+	0.507281i
$981$	6.50785	+	44.8860i	0.207780	+	1.43310i
$982$	24.0422	+	21.6477i	0.767217	+	0.690805i
$983$	−2.35600	+	22.4159i	−0.0751448	+	0.714955i	0.890481	+	0.455020i	$0.150368\pi$
$983$	−2.35600	+	22.4159i	−0.0751448	+	0.714955i	−0.965626	+	0.259935i	$0.916299\pi$
$984$	16.6872	−	7.82565i	0.531967	−	0.249473i
$985$	−3.99034	+	0.419401i	−0.127143	+	0.0133632i
$986$	10.1323	+	5.84988i	0.322678	+	0.186298i
$987$	−0.239349	−	12.1904i	−0.00761857	−	0.388026i
$988$	−1.60961	−	2.21543i	−0.0512084	−	0.0704823i
$989$	0.911413	−	0.820640i	0.0289812	−	0.0260948i
$990$	−7.02671	+	8.44859i	−0.223324	+	0.268514i
$991$			38.0189i			1.20771i	0.797094	+	0.603855i	$0.206369\pi$
$991$			38.0189i			1.20771i	−0.797094	+	0.603855i	$0.793631\pi$
$992$	3.00420	+	4.68773i	0.0953834	+	0.148836i
$993$	2.63396	+	1.45253i	0.0835861	+	0.0460948i
$994$	17.0863	+	52.5864i	0.541946	+	1.66794i
$995$	−0.636373	−	0.706764i	−0.0201744	−	0.0224059i
$996$	−1.93592	−	15.4878i	−0.0613418	−	0.490749i
$997$	12.2488	+	21.2156i	0.387925	+	0.671905i	0.992170	−	0.124893i	$-0.0398587\pi$
$997$	12.2488	+	21.2156i	0.387925	+	0.671905i	−0.604245	+	0.796798i	$0.706525\pi$
$998$	−3.71346	+	6.43190i	−0.117548	+	0.203598i
$999$	3.23466	−	0.534012i	0.102340	−	0.0168954i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.a.11.1	✓	176
3.2	odd	2	inner	930.2.br.a.11.17	yes	176
31.17	odd	30	inner	930.2.br.a.761.17	yes	176
93.17	even	30	inner	930.2.br.a.761.1	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.a.11.1	✓	176	1.1	even	1	trivial
930.2.br.a.11.17	yes	176	3.2	odd	2	inner
930.2.br.a.761.1	yes	176	93.17	even	30	inner
930.2.br.a.761.17	yes	176	31.17	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(-1.68681 + 0.393302i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.48271 - 0.895304i) q^{6} +(0.503857 + 4.79388i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(2.69063 - 1.32685i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(-1.68681 + 0.393302i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.48271 - 0.895304i) q^{6} +(0.503857 + 4.79388i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(2.69063 - 1.32685i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(3.34625 + 1.48985i) q^{11} +(-1.13348 + 1.30967i) q^{12} +(0.191369 + 0.900318i) q^{13} +(-1.96059 - 4.40355i) q^{14} +(-1.26417 + 1.18401i) q^{15} +(0.309017 - 0.951057i) q^{16} +(3.22729 - 1.43688i) q^{17} +(-2.14892 + 2.09336i) q^{18} +(-2.91014 - 0.618569i) q^{19} +(0.406737 - 0.913545i) q^{20} +(-2.73535 - 7.88818i) q^{21} +(-3.64286 - 0.382880i) q^{22} +(-0.0893379 - 0.0649078i) q^{23} +(0.673291 - 1.59583i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-0.460216 - 0.797118i) q^{26} +(-4.01671 + 3.29636i) q^{27} +(3.22540 + 3.58217i) q^{28} +(-1.02341 - 3.14975i) q^{29} +(0.836413 - 1.51671i) q^{30} +(4.68773 - 3.00420i) q^{31} +1.00000i q^{32} +(-6.23044 - 1.19700i) q^{33} +(-2.62532 + 2.36385i) q^{34} +(2.83329 + 3.89970i) q^{35} +(1.39686 - 2.65495i) q^{36} +(-0.546407 - 0.315469i) q^{37} +(2.95885 - 0.310988i) q^{38} +(-0.676899 - 1.44340i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(7.90791 + 7.12032i) q^{41} +(5.03906 + 6.65684i) q^{42} +(-2.30910 + 10.8635i) q^{43} +(3.58288 - 0.761566i) q^{44} +(1.66673 - 2.49440i) q^{45} +(0.105023 + 0.0341240i) q^{46} +(1.38892 + 0.451286i) q^{47} +(-0.147199 + 1.72578i) q^{48} +(-15.8804 + 3.37549i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(-4.87869 + 3.69304i) q^{51} +(0.684014 + 0.615889i) q^{52} +(0.987013 - 9.39081i) q^{53} +(2.80149 - 4.37626i) q^{54} +(3.64286 - 0.382880i) q^{55} +(-4.17449 - 2.41014i) q^{56} +(5.15212 - 0.101158i) q^{57} +(1.94665 + 2.67933i) q^{58} +(0.439186 - 0.395444i) q^{59} +(-0.326786 + 1.70094i) q^{60} +6.64933i q^{61} +(-3.52995 + 4.30575i) q^{62} +(7.71645 + 12.2300i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.615889 + 0.684014i) q^{65} +(6.29539 - 0.786900i) q^{66} +(6.53705 + 11.3225i) q^{67} +(1.76636 - 3.05942i) q^{68} +(0.176224 + 0.0743500i) q^{69} +(-3.89970 - 2.83329i) q^{70} +(-11.4080 - 1.19903i) q^{71} +(-0.508068 + 2.95666i) q^{72} +(-0.190059 + 0.426879i) q^{73} +(0.617150 + 0.131179i) q^{74} +(-0.502793 + 1.65747i) q^{75} +(-2.71794 + 1.21010i) q^{76} +(-5.45612 + 16.7922i) q^{77} +(1.08980 + 1.16358i) q^{78} +(1.63235 + 3.66631i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(5.47895 - 7.14011i) q^{81} +(-9.72117 - 4.32814i) q^{82} +(-6.02984 + 6.69682i) q^{83} +(-6.84950 - 4.77387i) q^{84} +(2.07648 - 2.85802i) q^{85} +(-1.16091 - 11.0453i) q^{86} +(2.96510 + 4.91050i) q^{87} +(-3.17219 + 1.83146i) q^{88} +(8.73850 - 6.34889i) q^{89} +(-0.814340 + 2.88736i) q^{90} +(-4.21960 + 1.37103i) q^{91} -0.110428 q^{92} +(-6.72573 + 6.91119i) q^{93} -1.46039 q^{94} +(-2.82954 + 0.919372i) q^{95} +(-0.393302 - 1.68681i) q^{96} +(-9.20631 + 6.68877i) q^{97} +(14.0601 - 8.11759i) q^{98} +(10.9803 - 0.431345i) 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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