LMFDB - Embedded newform 930.2.br.a.11.17

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			11.17
Character	$\chi$	$=$	930.11
Dual form			930.2.br.a.761.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(-0.567467 + 1.63645i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.0340008 + 1.73172i) q^{6} +(0.503857 + 4.79388i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-2.35596 - 1.85727i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(-0.567467 + 1.63645i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.0340008 + 1.73172i) q^{6} +(0.503857 + 4.79388i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-2.35596 - 1.85727i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(-3.34625 - 1.48985i) q^{11} +(0.502793 + 1.65747i) q^{12} +(0.191369 + 0.900318i) q^{13} +(1.96059 + 4.40355i) q^{14} +(-0.326786 - 1.70094i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-3.22729 + 1.43688i) q^{17} +(-2.81458 - 1.03833i) q^{18} +(-2.91014 - 0.618569i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(-8.13089 - 1.89583i) q^{21} +(-3.64286 - 0.382880i) q^{22} +(0.0893379 + 0.0649078i) q^{23} +(0.990371 + 1.42097i) q^{24} +(0.500000 - 0.866025i) q^{25} +(0.460216 + 0.797118i) q^{26} +(4.37626 - 2.80149i) 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} +(4.33695 - 4.63055i) q^{33} +(-2.62532 + 2.36385i) q^{34} +(-2.83329 - 3.89970i) q^{35} +(-2.99769 - 0.117760i) q^{36} +(-0.546407 - 0.315469i) q^{37} +(-2.95885 + 0.310988i) q^{38} +(-1.58192 - 0.197735i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(-7.90791 - 7.12032i) q^{41} +(-8.31878 + 0.709543i) q^{42} +(-2.30910 + 10.8635i) q^{43} +(-3.58288 + 0.761566i) q^{44} +(2.96896 + 0.430458i) q^{45} +(0.105023 + 0.0341240i) q^{46} +(-1.38892 - 0.451286i) q^{47} +(1.38100 + 1.04538i) q^{48} +(-15.8804 + 3.37549i) q^{49} +(0.207912 - 0.978148i) q^{50} +(-0.520012 - 6.09670i) q^{51} +(0.684014 + 0.615889i) q^{52} +(-0.987013 + 9.39081i) q^{53} +(3.29636 - 4.01671i) q^{54} +(3.64286 - 0.382880i) q^{55} +(4.17449 + 2.41014i) q^{56} +(2.66367 - 4.41129i) q^{57} +(1.94665 + 2.67933i) q^{58} +(-0.439186 + 0.395444i) q^{59} +(-1.26417 - 1.18401i) 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} +(2.69377 - 5.74410i) q^{66} +(6.53705 + 11.3225i) q^{67} +(-1.76636 + 3.05942i) q^{68} +(-0.156915 + 0.109364i) q^{69} +(-3.89970 - 2.83329i) q^{70} +(11.4080 + 1.19903i) q^{71} +(-2.88736 + 0.814340i) q^{72} +(-0.190059 + 0.426879i) q^{73} +(-0.617150 - 0.131179i) q^{74} +(1.13348 + 1.30967i) q^{75} +(-2.71794 + 1.21010i) q^{76} +(5.45612 - 16.7922i) q^{77} +(-1.56560 + 0.300785i) q^{78} +(1.63235 + 3.66631i) q^{79} +(0.207912 + 0.978148i) q^{80} +(2.10112 + 8.75130i) q^{81} +(-9.72117 - 4.32814i) q^{82} +(6.02984 - 6.69682i) q^{83} +(-7.69237 + 3.24546i) q^{84} +(2.07648 - 2.85802i) q^{85} +(1.16091 + 11.0453i) q^{86} +(-5.73517 - 0.112605i) q^{87} +(-3.17219 + 1.83146i) q^{88} +(-8.73850 + 6.34889i) q^{89} +(2.95666 - 0.508068i) q^{90} +(-4.21960 + 1.37103i) q^{91} +0.110428 q^{92} +(2.25610 + 9.37603i) q^{93} -1.46039 q^{94} +(2.82954 - 0.919372i) q^{95} +(1.63645 + 0.567467i) q^{96} +(-9.20631 + 6.68877i) q^{97} +(-14.0601 + 8.11759i) q^{98} +(5.11660 + 9.72490i) 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
$3$	−0.567467	+	1.63645i	−0.327627	+	0.944807i
$3$	−0.567467	+	1.63645i	−0.327627	+	0.944807i
$4$	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
$6$	−0.0340008	+	1.73172i	−0.0138808	+	0.706971i
$7$	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
$9$	−2.35596	−	1.85727i	−0.785321	−	0.619089i
$10$	−0.669131	+	0.743145i	−0.211598	+	0.235003i
$11$	−3.34625	−	1.48985i	−1.00893	−	0.449206i	−0.165367	−	0.986232i	$-0.552881\pi$
$11$	−3.34625	−	1.48985i	−1.00893	−	0.449206i	−0.843566	+	0.537026i	$0.819548\pi$
$12$	0.502793	+	1.65747i	0.145144	+	0.478470i
$13$	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
$15$	−0.326786	−	1.70094i	−0.0843759	−	0.439182i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−3.22729	+	1.43688i	−0.782733	+	0.348495i	−0.758889	−	0.651220i	$-0.774257\pi$
$17$	−3.22729	+	1.43688i	−0.782733	+	0.348495i	−0.0238447	+	0.999716i	$0.507591\pi$
$18$	−2.81458	−	1.03833i	−0.663403	−	0.244737i
$19$	−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
$21$	−8.13089	−	1.89583i	−1.77431	−	0.413704i
$22$	−3.64286	−	0.382880i	−0.776661	−	0.0816303i
$23$	0.0893379	+	0.0649078i	0.0186282	+	0.0135342i	0.597060	−	0.802196i	$-0.296335\pi$
$23$	0.0893379	+	0.0649078i	0.0186282	+	0.0135342i	−0.578432	+	0.815730i	$0.696335\pi$
$24$	0.990371	+	1.42097i	0.202159	+	0.290055i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	0.460216	+	0.797118i	0.0902558	+	0.156328i
$27$	4.37626	−	2.80149i	0.842212	−	0.539147i
$28$	3.22540	+	3.58217i	0.609544	+	0.676967i
$29$	1.02341	+	3.14975i	0.190043	+	0.584893i	0.999999	−	0.00159839i	$-0.000508785\pi$
$29$	1.02341	+	3.14975i	0.190043	+	0.584893i	−0.809955	+	0.586491i	$0.800509\pi$
$30$	−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
$33$	4.33695	−	4.63055i	0.754966	−	0.806075i
$34$	−2.62532	+	2.36385i	−0.450238	+	0.405396i
$35$	−2.83329	−	3.89970i	−0.478914	−	0.659169i
$36$	−2.99769	−	0.117760i	−0.499615	−	0.0196266i
$37$	−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
$39$	−1.58192	−	0.197735i	−0.253311	−	0.0316629i
$40$	−0.104528	+	0.994522i	−0.0165274	+	0.157248i
$41$	−7.90791	−	7.12032i	−1.23501	−	1.11201i	−0.989789	−	0.142539i	$-0.954473\pi$
$41$	−7.90791	−	7.12032i	−1.23501	−	1.11201i	−0.245220	−	0.969468i	$-0.578860\pi$
$42$	−8.31878	+	0.709543i	−1.28362	+	0.109485i
$43$	−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
$45$	2.96896	+	0.430458i	0.442586	+	0.0641689i
$46$	0.105023	+	0.0341240i	0.0154848	+	0.00503132i
$47$	−1.38892	−	0.451286i	−0.202594	−	0.0658268i	0.205962	−	0.978560i	$-0.433968\pi$
$47$	−1.38892	−	0.451286i	−0.202594	−	0.0658268i	−0.408556	+	0.912733i	$0.633968\pi$
$48$	1.38100	+	1.04538i	0.199331	+	0.150888i
$49$	−15.8804	+	3.37549i	−2.26863	+	0.482212i
$50$	0.207912	−	0.978148i	0.0294032	−	0.138331i
$51$	−0.520012	−	6.09670i	−0.0728163	−	0.853709i
$52$	0.684014	+	0.615889i	0.0948557	+	0.0854085i
$53$	−0.987013	+	9.39081i	−0.135577	+	1.28993i	0.689243	+	0.724530i	$0.257943\pi$
$53$	−0.987013	+	9.39081i	−0.135577	+	1.28993i	−0.824820	+	0.565396i	$0.808723\pi$
$54$	3.29636	−	4.01671i	0.448578	−	0.546605i
$55$	3.64286	−	0.382880i	0.491203	−	0.0516276i
$56$	4.17449	+	2.41014i	0.557840	+	0.322069i
$57$	2.66367	−	4.41129i	0.352811	−	0.584290i
$58$	1.94665	+	2.67933i	0.255608	+	0.351814i
$59$	−0.439186	+	0.395444i	−0.0571771	+	0.0514825i	−0.697224	−	0.716853i	$-0.745582\pi$
$59$	−0.439186	+	0.395444i	−0.0571771	+	0.0514825i	0.640047	+	0.768336i	$0.278915\pi$
$60$	−1.26417	−	1.18401i	−0.163203	−	0.152855i
$61$			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
$66$	2.69377	−	5.74410i	0.331580	−	0.707050i
$67$	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
$69$	−0.156915	+	0.109364i	−0.0188903	+	0.0131659i
$70$	−3.89970	−	2.83329i	−0.466103	−	0.338644i
$71$	11.4080	+	1.19903i	1.35388	+	0.142298i	0.753515	−	0.657431i	$-0.228357\pi$
$71$	11.4080	+	1.19903i	1.35388	+	0.142298i	0.600361	+	0.799729i	$0.295023\pi$
$72$	−2.88736	+	0.814340i	−0.340279	+	0.0959709i
$73$	−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
$75$	1.13348	+	1.30967i	0.130883	+	0.151227i
$76$	−2.71794	+	1.21010i	−0.311769	+	0.138808i
$77$	5.45612	−	16.7922i	0.621782	−	1.91365i
$78$	−1.56560	+	0.300785i	−0.177270	+	0.0340572i
$79$	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
$81$	2.10112	+	8.75130i	0.233458	+	0.972367i
$82$	−9.72117	−	4.32814i	−1.07352	−	0.477964i
$83$	6.02984	−	6.69682i	0.661861	−	0.735071i	−0.314966	−	0.949103i	$-0.601993\pi$
$83$	6.02984	−	6.69682i	0.661861	−	0.735071i	0.976827	+	0.214032i	$0.0686597\pi$
$84$	−7.69237	+	3.24546i	−0.839306	+	0.354109i
$85$	2.07648	−	2.85802i	0.225225	−	0.309996i
$86$	1.16091	+	11.0453i	0.125184	+	1.19105i
$87$	−5.73517	−	0.112605i	−0.614874	−	0.0120725i
$88$	−3.17219	+	1.83146i	−0.338156	+	0.195235i
$89$	−8.73850	+	6.34889i	−0.926279	+	0.672981i	−0.945079	−	0.326842i	$-0.894015\pi$
$89$	−8.73850	+	6.34889i	−0.926279	+	0.672981i	0.0188001	+	0.999823i	$0.494015\pi$
$90$	2.95666	−	0.508068i	0.311660	−	0.0535551i
$91$	−4.21960	+	1.37103i	−0.442334	+	0.143723i
$92$	0.110428			0.0115129
$93$	2.25610	+	9.37603i	0.233947	+	0.972249i
$94$	−1.46039			−0.150628
$95$	2.82954	−	0.919372i	0.290304	−	0.0943256i
$96$	1.63645	+	0.567467i	0.167020	+	0.0579168i
$97$	−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
$99$	5.11660	+	9.72490i	0.514238	+	0.977390i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	7.41830	−	10.2104i	0.738148	−	1.01597i	−0.260575	−	0.965454i	$-0.583912\pi$
$101$	7.41830	−	10.2104i	0.738148	−	1.01597i	0.998723	−	0.0505205i	$-0.0160880\pi$
$102$	−2.37854	−	5.63761i	−0.235511	−	0.558207i
$103$	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
$105$	7.98947	−	2.42361i	0.779693	−	0.236520i
$106$	1.96321	+	9.23619i	0.190684	+	0.897098i
$107$	−0.222657	−	0.500095i	−0.0215250	−	0.0483460i	0.902463	−	0.430767i	$-0.141757\pi$
$107$	−0.222657	−	0.500095i	−0.0215250	−	0.0483460i	−0.923988	+	0.382421i	$0.875090\pi$
$108$	1.89380	−	4.83875i	0.182231	−	0.465609i
$109$	−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
$111$	0.826318	−	0.715153i	0.0784306	−	0.0678793i
$112$	4.71495	+	1.00219i	0.445521	+	0.0946985i
$113$	−1.43471	+	3.22240i	−0.134966	+	0.303138i	−0.968367	−	0.249530i	$-0.919724\pi$
$113$	−1.43471	+	3.22240i	−0.134966	+	0.303138i	0.833401	+	0.552668i	$0.186390\pi$
$114$	1.17013	−	5.01850i	0.109593	−	0.470026i
$115$	−0.109823	−	0.0115428i	−0.0102410	−	0.00107638i
$116$	2.67933	+	1.94665i	0.248770	+	0.180742i
$117$	1.22127	−	2.47654i	0.112907	−	0.228956i
$118$	−0.295491	+	0.511806i	−0.0272022	+	0.0471155i
$119$	−8.51435	−	14.7473i	−0.780509	−	1.35188i
$120$	−1.56817	−	0.735414i	−0.143154	−	0.0671338i
$121$	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
$126$	3.55950	−	14.0159i	0.317105	−	1.24864i
$127$	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
$129$	−16.4672	−	9.94338i	−1.44986	−	0.875466i
$130$	−0.797118	−	0.460216i	−0.0699118	−	0.0403636i
$131$	12.9552	−	1.36164i	1.13190	−	0.118967i	0.479996	−	0.877271i	$-0.340638\pi$
$131$	12.9552	−	1.36164i	1.13190	−	0.118967i	0.651902	+	0.758303i	$0.273971\pi$
$132$	0.786900	−	6.29539i	0.0684909	−	0.547943i
$133$	1.49905	−	14.2625i	0.129984	−	1.23672i
$134$	9.71594	+	8.74827i	0.839330	+	0.755736i
$135$	−2.38921	+	4.61429i	−0.205630	+	0.397135i
$136$	−0.734492	+	3.45551i	−0.0629822	+	0.296308i
$137$	10.7053	−	2.27549i	0.914619	−	0.194408i	0.273520	−	0.961866i	$-0.411812\pi$
$137$	10.7053	−	2.27549i	0.914619	−	0.194408i	0.641099	+	0.767458i	$0.278479\pi$
$138$	−0.115439	+	0.152501i	−0.00982686	+	0.0129818i
$139$	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
$141$	1.52667	−	2.01681i	0.128569	−	0.169846i
$142$	11.2201	−	2.38491i	0.941573	−	0.200138i
$143$	0.700969	−	3.29780i	0.0586180	−	0.275776i
$144$	−2.49440	+	1.66673i	−0.207866	+	0.138894i
$145$	−2.46118	−	2.21605i	−0.204389	−	0.184033i
$146$	−0.0488437	+	0.464717i	−0.00404233	+	0.0384602i
$147$	3.48778	−	27.9030i	0.287667	−	2.30140i
$148$	−0.627481	+	0.0659509i	−0.0515786	+	0.00542113i
$149$	2.56654	+	1.48179i	0.210259	+	0.121393i	0.601432	−	0.798924i	$-0.294597\pi$
$149$	2.56654	+	1.48179i	0.210259	+	0.121393i	−0.391173	+	0.920317i	$0.627931\pi$
$150$	1.48271	+	0.895304i	0.121063	+	0.0731013i
$151$	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
$153$	10.2721	+	2.60870i	0.830447	+	0.210901i
$154$		−	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
$159$	−14.8075	−	6.94417i	−1.17431	−	0.550709i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−0.266147	+	0.460980i	−0.0209753	+	0.0363303i
$162$	4.70259	+	7.67370i	0.369470	+	0.602903i
$163$	−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
$165$	−1.44064	+	6.17865i	−0.112153	+	0.481007i
$166$	3.66529	−	8.23237i	0.284482	−	0.638956i
$167$	−11.4949	−	2.44333i	−0.889506	−	0.189070i	−0.259576	−	0.965723i	$-0.583583\pi$
$167$	−11.4949	−	2.44333i	−0.889506	−	0.189070i	−0.629929	+	0.776652i	$0.716916\pi$
$168$	−6.31298	+	5.46369i	−0.487057	+	0.421533i
$169$	11.1021	−	4.94299i	0.854011	−	0.380230i
$170$	1.09167	−	3.35981i	0.0837271	−	0.257686i
$171$	5.70733	+	6.86223i	0.436450	+	0.524768i
$172$	4.51728	+	10.1460i	0.344439	+	0.773623i
$173$	0.225873	+	1.06265i	0.0171728	+	0.0807918i	0.985900	−	0.167338i	$-0.0535173\pi$
$173$	0.225873	+	1.06265i	0.0171728	+	0.0807918i	−0.968727	+	0.248130i	$0.920184\pi$
$174$	−5.48926	+	1.66517i	−0.416140	+	0.126236i
$175$	4.40355	+	1.96059i	0.332877	+	0.148207i
$176$	−2.45098	+	2.72209i	−0.184749	+	0.205185i
$177$	−0.397903	−	0.943108i	−0.0299083	−	0.0708884i
$178$	−6.34889	+	8.73850i	−0.475869	+	0.654978i
$179$	2.39628	+	22.7991i	0.179107	+	1.70409i	0.602483	+	0.798132i	$0.294178\pi$
$179$	2.39628	+	22.7991i	0.179107	+	1.70409i	−0.423377	+	0.905954i	$0.639155\pi$
$180$	2.65495	−	1.39686i	0.197889	−	0.104116i
$181$	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
$183$	−10.8813	−	3.77328i	−0.804371	−	0.278929i
$184$	0.105023	−	0.0341240i	0.00774240	−	0.00251566i
$185$	0.630937			0.0463874
$186$	5.04304	+	8.21996i	0.369773	+	0.602717i
$187$	12.9401			0.946272
$188$	−1.38892	+	0.451286i	−0.101297	+	0.0329134i
$189$	15.6350	+	19.5677i	1.13728	+	1.42334i
$190$	2.40695	−	1.74875i	0.174618	−	0.126868i
$191$	−9.02705	+	5.21177i	−0.653174	+	0.377110i	−0.789671	−	0.613530i	$-0.789749\pi$
$191$	−9.02705	+	5.21177i	−0.653174	+	0.377110i	0.136497	+	0.990640i	$0.456416\pi$
$192$	1.73172	+	0.0340008i	0.124976	+	0.00245380i
$193$	−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
$195$	1.46885	−	0.619719i	0.105187	−	0.0443790i
$196$	−10.8635	+	12.0651i	−0.775962	+	0.861793i
$197$	3.66543	+	1.63196i	0.261151	+	0.116272i	0.533136	−	0.846030i	$-0.321013\pi$
$197$	3.66543	+	1.63196i	0.261151	+	0.116272i	−0.271985	+	0.962302i	$0.587680\pi$
$198$	7.87134	+	7.66782i	0.559392	+	0.544928i
$199$	−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
$201$	−22.2383	+	4.27244i	−1.56857	+	0.301354i
$202$	3.90003	−	12.0031i	0.274405	−	0.844533i
$203$	−14.5839	+	6.49315i	−1.02359	+	0.455730i
$204$	−4.00425	−	4.62668i	−0.280353	−	0.323932i
$205$	10.4086	+	2.21242i	0.726969	+	0.154522i
$206$	3.08856	−	6.93701i	0.215190	−	0.483324i
$207$	−0.0899258	−	0.318845i	−0.00625027	−	0.0221612i
$208$	0.915390	+	0.0962114i	0.0634709	+	0.00667106i
$209$	8.81648	+	6.40555i	0.609849	+	0.443081i
$210$	6.84950	−	4.77387i	0.472661	−	0.329428i
$211$	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
$213$	−8.43579	+	17.9882i	−0.578011	+	1.23253i
$214$	−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
$219$	−0.590715	−	0.553261i	−0.0399168	−	0.0373859i
$220$	2.72209	−	2.45098i	0.183523	−	0.165245i
$221$	−1.91125	−	2.63062i	−0.128565	−	0.176954i
$222$	0.564880	−	0.935497i	0.0379123	−	0.0627864i
$223$	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
$225$	−2.78642	+	1.11169i	−0.185761	+	0.0741127i
$226$	−0.368709	+	3.50803i	−0.0245262	+	0.233351i
$227$	−11.1073	−	10.0011i	−0.737217	−	0.663793i	0.212408	−	0.977181i	$-0.431869\pi$
$227$	−11.1073	−	10.0011i	−0.737217	−	0.663793i	−0.949625	+	0.313388i	$0.898536\pi$
$228$	−0.437940	−	5.13447i	−0.0290033	−	0.340039i
$229$	−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
$231$	24.3835	+	18.4577i	1.60432	+	1.21443i
$232$	3.14975	+	1.02341i	0.206791	+	0.0671904i
$233$	24.6426	+	8.00688i	1.61439	+	0.524548i	0.970610	−	0.240660i	$-0.0773637\pi$
$233$	24.6426	+	8.00688i	1.61439	+	0.524548i	0.643783	+	0.765208i	$0.277364\pi$
$234$	0.396208	−	2.73272i	0.0259009	−	0.178644i
$235$	1.42848	−	0.303633i	0.0931837	−	0.0198068i
$236$	−0.122872	+	0.578068i	−0.00799830	+	0.0376290i
$237$	−6.92606	+	0.590752i	−0.449896	+	0.0383734i
$238$	−12.6548	−	11.3944i	−0.820288	−	0.738591i
$239$	1.28988	−	12.2724i	0.0834352	−	0.793833i	−0.870166	−	0.492759i	$-0.835988\pi$
$239$	1.28988	−	12.2724i	0.0834352	−	0.793833i	0.953601	−	0.301074i	$-0.0973450\pi$
$240$	−1.71868	−	0.214828i	−0.110940	−	0.0138671i
$241$	−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
$243$	−15.5134	−	1.52768i	−0.995186	−	0.0980006i
$244$	3.90838	+	5.37942i	0.250208	+	0.344382i
$245$	12.0651	−	10.8635i	0.770811	−	0.694041i
$246$	12.5993	−	13.4522i	0.803299	−	0.857679i
$247$		−	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	0.724648	−	0.689119i	$-0.242002\pi$
$251$	−0.577351	−	0.641213i	−0.0364420	−	0.0404730i	−0.761090	+	0.648646i	$0.775336\pi$
$252$	−0.945882	−	14.4299i	−0.0595849	−	0.908998i
$253$	−0.202244	−	0.350298i	−0.0127150	−	0.0220230i
$254$	6.65766	−	11.5314i	0.417739	−	0.723545i
$255$	3.49869	+	5.01989i	0.219097	+	0.314358i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−0.495858	−	0.0521167i	−0.0309308	−	0.00325095i	0.0890504	−	0.996027i	$-0.471617\pi$
$257$	−0.495858	−	0.0521167i	−0.0309308	−	0.00325095i	−0.119981	+	0.992776i	$0.538283\pi$
$258$	−18.7339	−	4.36807i	−1.16632	−	0.271944i
$259$	1.23701	−	2.77836i	0.0768639	−	0.172639i
$260$	−0.900318	−	0.191369i	−0.0558354	−	0.0118682i
$261$	3.43879	−	9.32144i	0.212856	−	0.576982i
$262$	11.9003	−	5.29837i	0.735205	−	0.327334i
$263$	−4.94334	+	15.2140i	−0.304819	+	0.938137i	0.674925	+	0.737886i	$0.264176\pi$
$263$	−4.94334	+	15.2140i	−0.304819	+	0.938137i	−0.979745	+	0.200251i	$0.935824\pi$
$264$	−1.19700	−	6.23044i	−0.0736700	−	0.383457i
$265$	−3.84062	−	8.62618i	−0.235928	−	0.529902i
$266$	−2.98168	−	14.0277i	−0.182819	−	0.860094i
$267$	−5.43086	−	17.9029i	−0.332363	−	1.09564i
$268$	11.9438	+	5.31771i	0.729582	+	0.324831i
$269$	1.22763	−	1.36342i	0.0748500	−	0.0831294i	−0.704557	−	0.709648i	$-0.748854\pi$
$269$	1.22763	−	1.36342i	0.0748500	−	0.0831294i	0.779407	+	0.626519i	$0.215521\pi$
$270$	−0.846379	+	5.12676i	−0.0515090	+	0.312005i
$271$	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
$273$	0.150853	−	7.68319i	0.00913004	−	0.465008i
$274$	9.47822	−	5.47225i	0.572600	−	0.330591i
$275$	−2.96337	+	2.15302i	−0.178698	+	0.129832i
$276$	−0.0626640	+	0.180710i	−0.00377193	+	0.0108775i
$277$	−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
$279$	−16.6237	−	1.62858i	−0.995235	−	0.0975004i
$280$	−4.82029			−0.288067
$281$	−10.1958	+	3.31281i	−0.608230	+	0.197626i	−0.596908	−	0.802310i	$-0.703604\pi$
$281$	−10.1958	+	3.31281i	−0.608230	+	0.197626i	−0.0113224	+	0.999936i	$0.503604\pi$
$282$	0.828724	−	2.38986i	0.0493498	−	0.142314i
$283$	−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
$285$	−0.101158	+	5.15212i	−0.00599206	+	0.305185i
$286$	−0.352415	−	3.35301i	−0.0208388	−	0.198267i
$287$	30.1495	−	41.4972i	1.77967	−	2.44950i
$288$	−1.85727	+	2.35596i	−0.109440	+	0.138826i
$289$	−3.02444	+	3.35898i	−0.177908	+	0.197587i
$290$	−3.02551	−	1.34705i	−0.177664	−	0.0791013i
$291$	−5.72160	−	18.8614i	−0.335406	−	1.10567i
$292$	0.0971523	+	0.457066i	0.00568541	+	0.0267477i
$293$	4.85285	+	10.8997i	0.283506	+	0.636766i	0.998023	−	0.0628528i	$-0.0200199\pi$
$293$	4.85285	+	10.8997i	0.283506	+	0.636766i	−0.714516	+	0.699619i	$0.753353\pi$
$294$	−5.30544	−	27.6151i	−0.309419	−	1.61055i
$295$	0.182624	−	0.562058i	0.0106328	−	0.0327243i
$296$	−0.576390	+	0.256625i	−0.0335020	+	0.0149160i
$297$	−18.8179	+	2.85452i	−1.09192	+	0.165636i
$298$	2.89882	+	0.616163i	0.167924	+	0.0356934i
$299$	−0.0413412	+	0.0928539i	−0.00239082	+	0.00536988i
$300$	1.68681	+	0.393302i	0.0973878	+	0.0227073i
$301$	−53.2416	−	5.59592i	−3.06879	−	0.322543i
$302$	16.2610	+	11.8143i	0.935713	+	0.679835i
$303$	12.4992	+	17.9338i	0.718062	+	1.03027i
$304$	−1.48758	+	2.57656i	−0.0853183	+	0.147776i
$305$	−3.32467	−	5.75849i	−0.190370	−	0.329730i
$306$	10.5754	−	0.693221i	0.604558	−	0.0396288i
$307$	−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	$-0.756385\pi$
$311$		−	24.4347i		−	1.38556i	0.721148	−	0.692782i	$-0.243615\pi$
$312$	−1.08980	+	1.16358i	−0.0616979	+	0.0658747i
$313$	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
$315$	−0.567635	+	14.4497i	−0.0319826	+	0.814150i
$316$	3.47560	+	2.00664i	0.195518	+	0.112882i
$317$	6.00776	−	0.631441i	0.337430	−	0.0354653i	0.0657014	−	0.997839i	$-0.479072\pi$
$317$	6.00776	−	0.631441i	0.337430	−	0.0354653i	0.271728	+	0.962374i	$0.412405\pi$
$318$	−16.2287	−	2.02852i	−0.910058	−	0.113754i
$319$	1.26804	−	12.0646i	0.0709965	−	0.675486i
$320$	0.743145	+	0.669131i	0.0415431	+	0.0374055i
$321$	0.944733	−	0.0805801i	0.0527298	−	0.00449754i
$322$	−0.110670	+	0.520662i	−0.00616740	+	0.0290153i
$323$	10.2807	−	2.18523i	0.572032	−	0.121589i
$324$	6.84373	+	5.84494i	0.380207	+	0.324719i
$325$	0.875383	+	0.284429i	0.0485575	+	0.0157773i
$326$	−10.9453	−	3.55635i	−0.606206	−	0.196968i
$327$	−20.8786	−	15.8046i	−1.15459	−	0.873996i
$328$	−10.4086	+	2.21242i	−0.574720	+	0.122160i
$329$	1.46360	−	6.88568i	0.0806907	−	0.379620i
$330$	0.539180	+	6.32142i	0.0296809	+	0.347983i
$331$	−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
$333$	0.701407	+	1.75806i	0.0384369	+	0.0963409i
$334$	−11.6874	+	1.22839i	−0.639505	+	0.0672146i
$335$	−11.3225	−	6.53705i	−0.618614	−	0.357157i
$336$	−4.31562	+	7.14709i	−0.235437	+	0.389906i
$337$	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
$339$	−4.45916	−	4.17643i	−0.242189	−	0.226833i
$340$		−	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
$345$	0.0812101	−	0.173170i	0.00437220	−	0.00932315i
$346$	0.543195	+	0.940841i	0.0292023	+	0.0505799i
$347$	−9.89519	+	17.1390i	−0.531201	+	0.920068i	0.468135	+	0.883657i	$0.344926\pi$
$347$	−9.89519	+	17.1390i	−0.531201	+	0.920068i	−0.999337	+	0.0364111i	$0.988407\pi$
$348$	−4.70603	+	3.27995i	−0.252270	+	0.175824i
$349$	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
$351$	3.35971	+	3.40391i	0.179328	+	0.181687i
$352$	−1.48985	+	3.34625i	−0.0794091	+	0.178356i
$353$	−17.1263	−	3.64030i	−0.911540	−	0.193754i	−0.271807	−	0.962352i	$-0.587621\pi$
$353$	−17.1263	−	3.64030i	−0.911540	−	0.193754i	−0.639732	+	0.768598i	$0.720955\pi$
$354$	−0.669865	−	0.773990i	−0.0356029	−	0.0411371i
$355$	−10.4791	+	4.66559i	−0.556173	+	0.247624i
$356$	−3.33781	+	10.2727i	−0.176904	+	0.544453i
$357$	28.9649	−	5.56475i	1.53298	−	0.294518i
$358$	9.32431	+	20.9427i	0.492805	+	1.10686i
$359$	5.99431	+	28.2010i	0.316368	+	1.48839i	0.792963	+	0.609270i	$0.208537\pi$
$359$	5.99431	+	28.2010i	0.316368	+	1.48839i	−0.476596	+	0.879123i	$0.658129\pi$
$360$	2.09336	−	2.14892i	0.110330	−	0.113258i
$361$	−9.27109	−	4.12776i	−0.487952	−	0.217250i
$362$	12.8148	−	14.2323i	0.673533	−	0.748034i
$363$	−3.85719	+	1.62737i	−0.202450	+	0.0854150i
$364$	−2.60786	+	3.58941i	−0.136689	+	0.188136i
$365$	−0.0488437	−	0.464717i	−0.00255660	−	0.0243244i
$366$	−11.5148	−	0.226083i	−0.601886	−	0.0118175i
$367$	−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
$369$	5.40643	+	31.4623i	0.281447	+	1.63786i
$370$	0.600057	−	0.194970i	0.0311955	−	0.0101360i
$371$	−45.5157			−2.36306
$372$	7.33632	+	6.25927i	0.380370	+	0.324528i
$373$	−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
$375$	−1.63645	−	0.567467i	−0.0845061	−	0.0293039i
$376$	−1.18148	+	0.858397i	−0.0609303	+	0.0442684i
$377$	−2.63992	+	1.52416i	−0.135963	+	0.0784983i
$378$	20.9166	+	13.7785i	1.07583	+	0.708691i
$379$	−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
$381$	8.96509	+	21.2490i	0.459295	+	1.08862i
$382$	−6.97471	+	7.74620i	−0.356857	+	0.396330i
$383$	−3.74522	−	1.66748i	−0.191372	−	0.0852041i	0.308814	−	0.951123i	$-0.400068\pi$
$383$	−3.74522	−	1.66748i	−0.191372	−	0.0852041i	−0.500185	+	0.865918i	$0.666735\pi$
$384$	1.65747	−	0.502793i	0.0845823	−	0.0256581i
$385$	3.67097	+	17.2705i	0.187090	+	0.880188i
$386$	−8.84859	−	19.8742i	−0.450381	−	1.01157i
$387$	25.6165	−	21.3053i	1.30216	−	1.08301i
$388$	−3.51650	+	10.8227i	−0.178523	+	0.549438i
$389$	−32.5954	+	14.5124i	−1.65265	+	0.735808i	−0.999766	−	0.0216475i	$-0.993109\pi$
$389$	−32.5954	+	14.5124i	−1.65265	+	0.735808i	−0.652887	+	0.757456i	$0.726442\pi$
$390$	1.20546	−	1.04329i	0.0610408	−	0.0528290i
$391$	−0.381584	−	0.0811083i	−0.0192976	−	0.00410182i
$392$	−6.60345	+	14.8316i	−0.333524	+	0.749108i
$393$	−5.12336	+	21.9732i	−0.258439	+	1.10840i
$394$	3.99034	+	0.419401i	0.201030	+	0.0211291i
$395$	−3.24681	−	2.35895i	−0.163365	−	0.118692i
$396$	9.85557	+	4.86015i	0.495261	+	0.244232i
$397$	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
$399$	22.4893	+	10.5466i	1.12587	+	0.527992i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	−10.4732	−	32.2332i	−0.523007	−	1.60965i	−0.768223	−	0.640182i	$-0.778859\pi$
$401$	−10.4732	−	32.2332i	−0.523007	−	1.60965i	0.245216	−	0.969468i	$-0.421141\pi$
$402$	−19.8296	+	10.9353i	−0.989012	+	0.545405i
$403$	3.60182	+	3.64554i	0.179419	+	0.181597i
$404$		−	12.6208i		−	0.627907i
$405$	−6.19528	−	6.52829i	−0.307846	−	0.324393i
$406$	−11.8636	+	10.6820i	−0.588779	+	0.530139i
$407$	1.35842	+	1.86970i	0.0673342	+	0.0926776i
$408$	−5.23799	−	3.16285i	−0.259319	−	0.156584i
$409$	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
$411$	−2.35119	+	18.8101i	−0.115976	+	0.927832i
$412$	0.793737	−	7.55191i	0.0391046	−	0.372056i
$413$	−2.11700	−	1.90616i	−0.104171	−	0.0937958i
$414$	−0.184053	−	0.275451i	−0.00904571	−	0.0135377i
$415$	−1.87359	+	8.81453i	−0.0919707	+	0.432688i
$416$	0.900318	−	0.191369i	0.0441417	−	0.00938262i
$417$	−0.759060	+	1.00275i	−0.0371713	+	0.0491051i
$418$	10.3644	+	3.36760i	0.506939	+	0.164714i
$419$	26.7584	+	8.69434i	1.30723	+	0.424746i	0.878092	−	0.478491i	$-0.158816\pi$
$419$	26.7584	+	8.69434i	1.30723	+	0.424746i	0.429142	+	0.903237i	$0.358816\pi$
$420$	5.03906	−	6.65684i	0.245881	−	0.324820i
$421$	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
$423$	2.43407	+	3.64280i	0.118349	+	0.177119i
$424$	7.01717	+	6.31829i	0.340784	+	0.306843i
$425$	−0.369269	+	3.51336i	−0.0179122	+	0.170423i
$426$	−2.46425	+	19.7146i	−0.119393	+	0.955175i
$427$	−31.8761	+	3.35032i	−1.54259	+	0.162133i
$428$	−0.474081	−	0.273711i	−0.0229156	−	0.0132303i
$429$	4.99892	+	3.01850i	0.241350	+	0.145734i
$430$	−6.52803	−	8.98506i	−0.314810	−	0.433298i
$431$	6.98873	−	6.29268i	0.336635	−	0.303108i	−0.483424	−	0.875386i	$-0.660607\pi$
$431$	6.98873	−	6.29268i	0.336635	−	0.303108i	0.820059	+	0.572279i	$0.193940\pi$
$432$	−1.31203	−	5.02778i	−0.0631253	−	0.241899i
$433$		−	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
$438$	−0.732771	−	0.343642i	−0.0350131	−	0.0164198i
$439$	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
$441$	43.6828	+	21.5416i	2.08014	+	1.02579i
$442$	−2.63062	−	1.91125i	−0.125126	−	0.0909091i
$443$	−4.97646	−	0.523047i	−0.236439	−	0.0248507i	−0.0144320	−	0.999896i	$-0.504594\pi$
$443$	−4.97646	−	0.523047i	−0.236439	−	0.0248507i	−0.222007	+	0.975045i	$0.571261\pi$
$444$	0.248149	−	1.06427i	0.0117766	−	0.0505079i
$445$	4.39332	−	9.86755i	0.208263	−	0.467767i
$446$	2.35722	+	0.501043i	0.111618	+	0.0237251i
$447$	−3.88131	+	3.35915i	−0.183580	+	0.158883i
$448$	4.40355	−	1.96059i	0.208048	−	0.0926291i
$449$	−7.69476	+	23.6820i	−0.363138	+	1.11762i	0.588001	+	0.808860i	$0.299915\pi$
$449$	−7.69476	+	23.6820i	−0.363138	+	1.11762i	−0.951139	+	0.308764i	$0.900085\pi$
$450$	−2.30651	+	1.91833i	−0.108730	+	0.0904311i
$451$	15.8537	+	35.6080i	0.746521	+	1.67671i
$452$	0.733379	+	3.45028i	0.0344952	+	0.162287i
$453$	−33.3145	+	10.1060i	−1.56525	+	0.474820i
$454$	−13.6542	−	6.07922i	−0.640821	−	0.285312i
$455$	2.96876	−	3.29715i	0.139178	−	0.154573i
$456$	−2.00314	−	4.74784i	−0.0938058	−	0.222338i
$457$	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
$459$	−10.0981	+	15.3294i	−0.471337	+	0.715515i
$460$	−0.0956332	+	0.0552139i	−0.00445892	+	0.00257436i
$461$	−22.5883	+	16.4114i	−1.05204	+	0.764355i	−0.972600	−	0.232485i	$-0.925314\pi$
$461$	−22.5883	+	16.4114i	−1.05204	+	0.764355i	−0.0794438	+	0.996839i	$0.525314\pi$
$462$	28.8938	+	10.0194i	1.34426	+	0.466145i
$463$	−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
$465$	−6.64186	−	6.99183i	−0.308009	−	0.324238i
$466$	25.9108			1.20029
$467$	17.3511	−	5.63770i	0.802912	−	0.260882i	0.121319	−	0.992614i	$-0.461288\pi$
$467$	17.3511	−	5.63770i	0.802912	−	0.260882i	0.681593	+	0.731732i	$0.261288\pi$
$468$	−0.467642	−	2.72141i	−0.0216168	−	0.125797i
$469$	−50.9850	+	37.0428i	−2.35427	+	1.71048i
$470$	1.26474	−	0.730196i	0.0583379	−	0.0336814i
$471$	−9.50332	−	0.186590i	−0.437890	−	0.00859760i
$472$	0.0617745	+	0.587745i	0.00284340	+	0.0270532i
$473$	23.9117	−	32.9116i	1.09946	−	1.51328i
$474$	−6.40452	+	2.70211i	−0.294169	+	0.124112i
$475$	−1.99077	+	2.21097i	−0.0913426	+	0.101446i
$476$	−15.5565	−	6.92619i	−0.713030	−	0.317462i
$477$	19.7666	−	20.2912i	0.905050	−	0.929072i
$478$	−2.56562	−	12.0703i	−0.117349	−	0.552083i
$479$	−14.9007	−	33.4675i	−0.680830	−	1.52917i	−0.840390	−	0.541982i	$-0.817674\pi$
$479$	−14.9007	−	33.4675i	−0.680830	−	1.52917i	0.159560	−	0.987188i	$-0.448993\pi$
$480$	−1.70094	+	0.326786i	−0.0776371	+	0.0149157i
$481$	0.179457	−	0.552311i	0.00818253	−	0.0251832i
$482$	−12.9978	+	5.78700i	−0.592035	+	0.263591i
$483$	−0.603343	−	0.697128i	−0.0274530	−	0.0317204i
$484$	2.36422	+	0.502531i	0.107465	+	0.0228423i
$485$	4.62851	−	10.3958i	0.210170	−	0.472049i
$486$	−15.2262	+	3.34100i	−0.690675	+	0.151551i
$487$	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
$489$	16.3534	−	11.3978i	0.739527	−	0.515425i
$490$	8.11759	−	14.0601i	0.366716	−	0.635170i
$491$	16.1760	+	28.0176i	0.730012	+	1.26442i	0.956878	+	0.290491i	$0.0938188\pi$
$491$	16.1760	+	28.0176i	0.730012	+	1.26442i	−0.226866	+	0.973926i	$0.572848\pi$
$492$	7.82565	−	16.6872i	0.352808	−	0.752315i
$493$	−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
$498$	11.3920	+	10.6697i	0.510486	+	0.478119i
$499$	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
$501$	10.5214	−	17.4244i	0.470061	−	0.778467i
$502$	−0.747239	−	0.431418i	−0.0333509	−	0.0192551i
$503$	24.7277	−	2.59898i	1.10255	−	0.115883i	0.464276	−	0.885691i	$-0.346315\pi$
$503$	24.7277	−	2.59898i	1.10255	−	0.115883i	0.638276	+	0.769808i	$0.279648\pi$
$504$	−5.35867	−	13.4314i	−0.238694	−	0.598280i
$505$	−1.31923	+	12.5516i	−0.0587049	+	0.558540i
$506$	−0.300594	−	0.270656i	−0.0133630	−	0.0120321i
$507$	1.78888	+	20.9731i	0.0794471	+	0.931449i
$508$	2.76841	−	13.0243i	0.122828	−	0.577862i
$509$	−38.4523	+	8.17328i	−1.70437	+	0.362274i	−0.954245	−	0.299026i	$-0.903338\pi$
$509$	−38.4523	+	8.17328i	−1.70437	+	0.362274i	−0.750121	+	0.661300i	$0.770005\pi$
$510$	4.87869	+	3.69304i	0.216032	+	0.163531i
$511$	−2.14217	−	0.696033i	−0.0947639	−	0.0307907i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	−14.4684	+	5.44570i	−0.638797	+	0.240433i
$514$	−0.487694	+	0.103662i	−0.0215112	+	0.00457236i
$515$	−1.57878	+	7.42757i	−0.0695693	+	0.327298i
$516$	−19.1668	+	1.63482i	−0.843772	+	0.0719688i
$517$	3.97531	+	3.57939i	0.174834	+	0.157421i
$518$	0.317902	−	3.02464i	0.0139678	−	0.132895i
$519$	−1.86715	−	0.233387i	−0.0819589	−	0.0102446i
$520$	−0.915390	+	0.0962114i	−0.0401425	+	0.00421915i
$521$	−15.7215	−	9.07681i	−0.688771	−	0.397662i	0.114380	−	0.993437i	$-0.463512\pi$
$521$	−15.7215	−	9.07681i	−0.688771	−	0.397662i	−0.803151	+	0.595775i	$0.796845\pi$
$522$	0.390001	−	9.92786i	0.0170699	−	0.434530i
$523$	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
$525$	−5.70728	+	6.09364i	−0.249086	+	0.265948i
$526$			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
$531$	1.76915	−	0.115968i	0.0767746	−	0.00503258i
$532$	−7.17055	−	12.4198i	−0.310883	−	0.538464i
$533$	4.89723	−	8.48225i	0.212122	−	0.367407i
$534$	−10.6974	−	15.3485i	−0.462920	−	0.664193i
$535$	0.442874	+	0.321767i	0.0191471	+	0.0139112i
$536$	13.0025	+	1.36661i	0.561621	+	0.0590288i
$537$	−38.6695	−	9.01633i	−1.66871	−	0.389083i
$538$	0.746226	−	1.67605i	0.0321721	−	0.0722597i
$539$	58.1688	+	12.3642i	2.50551	+	0.532562i
$540$	0.779301	+	5.13738i	0.0335358	+	0.221078i
$541$	−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
$543$	6.25844	+	32.5756i	0.268575	+	1.39795i
$544$	1.43688	+	3.22729i	0.0616059	+	0.138369i
$545$	−3.14330	−	14.7881i	−0.134644	−	0.633451i
$546$	−2.23077	−	7.35377i	−0.0954680	−	0.314712i
$547$	−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
$549$	12.3496	−	15.6656i	0.527067	−	0.668591i
$550$	−2.15302	+	2.96337i	−0.0918049	+	0.126359i
$551$	−1.02994	−	9.79924i	−0.0438770	−	0.417462i
$552$	−0.00375463	+	0.191230i	−0.000159808	+	0.00813927i
$553$	−16.7534	+	9.67259i	−0.712428	+	0.411320i
$554$	−18.3596	+	13.3390i	−0.780023	+	0.566720i
$555$	−0.358036	+	1.03250i	−0.0151978	+	0.0438272i
$556$	0.690568	−	0.224379i	0.0292866	−	0.00951579i
$557$	−9.91670			−0.420184			−0.210092	−	0.977682i	$-0.567376\pi$
$557$	−9.91670			−0.420184			−0.210092	+	0.977682i	$0.567376\pi$
$558$	−16.3133	+	3.58814i	−0.690599	+	0.151898i
$559$	−10.2225			−0.432364
$560$	−4.58437	+	1.48955i	−0.193725	+	0.0629450i
$561$	−7.34306	+	21.1758i	−0.310024	+	0.894044i
$562$	−8.67306	+	6.30135i	−0.365851	+	0.265806i
$563$	29.8772	−	17.2496i	1.25917	−	0.726984i	0.286259	−	0.958152i	$-0.407588\pi$
$563$	29.8772	−	17.2496i	1.25917	−	0.726984i	0.972914	+	0.231168i	$0.0742548\pi$
$564$	0.0496545	−	2.52899i	0.00209083	−	0.106489i
$565$	−0.368709	−	3.50803i	−0.0155117	−	0.147584i
$566$	−13.6711	+	18.8167i	−0.574641	+	0.790926i
$567$	−40.8941	+	14.4820i	−1.71739	+	0.608185i
$568$	7.67546	−	8.52447i	0.322055	−	0.357679i
$569$	−22.2487	−	9.90574i	−0.932712	−	0.415270i	−0.116610	−	0.993178i	$-0.537203\pi$
$569$	−22.2487	−	9.90574i	−0.932712	−	0.415270i	−0.816102	+	0.577908i	$0.803869\pi$
$570$	1.49589	+	4.93122i	0.0626558	+	0.206546i
$571$	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
$573$	−3.40627	−	17.7299i	−0.142299	−	0.740675i
$574$	15.8505	−	48.7829i	0.661589	−	2.03616i
$575$	0.100881	−	0.0449150i	0.00420702	−	0.00187308i
$576$	−1.03833	+	2.81458i	−0.0432639	+	0.117274i
$577$	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
$579$	36.6966	+	8.55631i	1.52506	+	0.355588i
$580$	−3.29370	−	0.346181i	−0.136763	−	0.0143744i
$581$	35.1419	+	25.5321i	1.45793	+	1.05925i
$582$	−11.2700	−	16.1701i	−0.467158	−	0.670274i
$583$	17.2937	−	29.9535i	0.716230	−	1.24055i
$584$	0.233638	+	0.404673i	0.00966802	+	0.0167455i
$585$	0.180616	+	2.75538i	0.00746754	+	0.113921i
$586$	7.98352	+	8.86660i	0.329796	+	0.366276i
$587$	13.6649	+	42.0562i	0.564010	+	1.73584i	0.670874	+	0.741571i	$0.265919\pi$
$587$	13.6649	+	42.0562i	0.564010	+	1.73584i	−0.106864	+	0.994274i	$0.534081\pi$
$588$	−13.5793	−	24.6241i	−0.560002	−	1.01548i
$589$	−15.5002	+	5.84295i	−0.638676	+	0.240755i
$590$		−	0.590982i		−	0.0243304i
$591$	−4.75063	+	5.07223i	−0.195415	+	0.208644i
$592$	−0.468878	+	0.422179i	−0.0192707	+	0.0173515i
$593$	9.91987	+	13.6535i	0.407360	+	0.560683i	0.962572	−	0.271026i	$-0.0873628\pi$
$593$	9.91987	+	13.6535i	0.407360	+	0.560683i	−0.555212	+	0.831709i	$0.687363\pi$
$594$	−17.0148	+	8.52985i	−0.698124	+	0.349984i
$595$	14.7473	+	8.51435i	0.604580	+	0.349054i
$596$	2.94735	−	0.309779i	0.120728	−	0.0126890i
$597$	1.63454	+	0.204311i	0.0668972	+	0.00836190i
$598$	−0.0106244	+	0.101084i	−0.000434464	+	0.00413365i
$599$	−28.8717	−	25.9962i	−1.17967	−	1.06218i	−0.996873	−	0.0790249i	$-0.974819\pi$
$599$	−28.8717	−	25.9962i	−1.17967	−	1.06218i	−0.182794	−	0.983151i	$-0.558514\pi$
$600$	1.72578	−	0.147199i	0.0704549	−	0.00600938i
$601$	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
$603$	5.62785	−	38.8164i	0.229184	−	1.58073i
$604$	19.1159	+	6.21113i	0.777815	+	0.252727i
$605$	−2.29874	−	0.746907i	−0.0934572	−	0.0303661i
$606$	17.4293	+	13.1936i	0.708018	+	0.535952i
$607$	−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
$609$	−2.34989	−	27.5505i	−0.0952224	−	1.11640i
$610$	−4.94142	−	4.44927i	−0.200072	−	0.180146i
$611$	0.140506	−	1.33683i	0.00568427	−	0.0540823i
$612$	9.84362	−	3.92728i	0.397905	−	0.158751i
$613$	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
$615$	−9.52706	+	15.7777i	−0.384168	+	0.636220i
$616$	−10.3782	−	14.2843i	−0.418148	−	0.575531i
$617$	−6.50200	+	5.85443i	−0.261761	+	0.235690i	−0.789552	−	0.613684i	$-0.789687\pi$
$617$	−6.50200	+	5.85443i	−0.261761	+	0.235690i	0.527791	+	0.849374i	$0.323020\pi$
$618$	9.59945	+	8.99080i	0.386146	+	0.361663i
$619$		−	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
$624$	−0.676899	+	1.44340i	−0.0270976	+	0.0577821i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	5.09546	−	8.82559i	0.203655	−	0.352742i
$627$	−15.4854	+	10.7928i	−0.618429	+	0.431024i
$628$	4.43972	+	3.22565i	0.177164	+	0.128717i
$629$	2.21671	+	0.232985i	0.0883859	+	0.00928974i
$630$	3.92536	+	13.9179i	0.156390	+	0.554503i
$631$	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
$633$	27.0833	+	31.2932i	1.07646	+	1.24379i
$634$	5.51860	−	2.45704i	0.219171	−	0.0975814i
$635$	−4.11466	+	12.6636i	−0.163285	+	0.502540i
$636$	−16.0612	+	3.08569i	−0.636869	+	0.122356i
$637$	−6.07802	−	13.6515i	−0.240820	−	0.540891i
$638$	−2.52218	−	11.8659i	−0.0998541	−	0.469777i
$639$	−24.6498	−	24.0125i	−0.975132	−	0.949919i
$640$	0.913545	+	0.406737i	0.0361111	+	0.0160777i
$641$	−11.8937	+	13.2093i	−0.469773	+	0.521735i	−0.930740	−	0.365682i	$-0.880836\pi$
$641$	−11.8937	+	13.2093i	−0.469773	+	0.521735i	0.460967	+	0.887417i	$0.347503\pi$
$642$	0.873593	−	0.368575i	0.0344780	−	0.0145465i
$643$	−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
$645$	19.2327	+	0.377618i	0.757287	+	0.0148687i
$646$	9.10223	−	5.25518i	0.358123	−	0.206762i
$647$	−9.92997	+	7.21455i	−0.390388	+	0.283633i	−0.765614	−	0.643300i	$-0.777565\pi$
$647$	−9.92997	+	7.21455i	−0.390388	+	0.283633i	0.375227	+	0.926933i	$0.377565\pi$
$648$	8.31496	+	3.44404i	0.326643	+	0.135295i
$649$	2.05878	−	0.668937i	0.0808141	−	0.0262581i
$650$	0.920432			0.0361023
$651$	−43.8109	+	15.5397i	−1.71708	+	0.609048i
$652$	−11.5086			−0.450712
$653$	−47.8747	+	15.5554i	−1.87348	+	0.608732i	−0.883329	+	0.468753i	$0.844703\pi$
$653$	−47.8747	+	15.5554i	−1.87348	+	0.608732i	−0.990155	+	0.139978i	$0.955297\pi$
$654$	−24.7406	−	8.57921i	−0.967435	−	0.335474i
$655$	−10.5387	+	7.65680i	−0.411780	+	0.299176i
$656$	−9.21550	+	5.32057i	−0.359805	+	0.207734i
$657$	1.24060	−	0.652721i	0.0484003	−	0.0254651i
$658$	−0.735829	−	7.00095i	−0.0286856	−	0.272925i
$659$	8.98012	−	12.3601i	0.349816	−	0.481480i	−0.597460	−	0.801898i	$-0.703823\pi$
$659$	8.98012	−	12.3601i	0.349816	−	0.481480i	0.947276	+	0.320418i	$0.103823\pi$
$660$	2.46622	+	5.84542i	0.0959974	+	0.227533i
$661$	−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
$663$	5.38946	−	1.63489i	0.209309	−	0.0634940i
$664$	−1.87359	−	8.81453i	−0.0727093	−	0.342070i
$665$	5.83305	+	13.1012i	0.226196	+	0.508044i
$666$	1.21035	+	1.45526i	0.0469000	+	0.0563903i
$667$	−0.113013	+	0.347819i	−0.00437589	+	0.0134676i
$668$	−10.7358	+	4.77987i	−0.415379	+	0.184939i
$669$	−3.15615	+	2.73155i	−0.122024	+	0.105608i
$670$	−12.7884	−	2.71826i	−0.494059	−	0.105015i
$671$	9.90649	−	22.2503i	0.382436	−	0.858965i
$672$	−1.89583	+	8.13089i	−0.0731332	+	0.313656i
$673$	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
$675$	−0.238030	−	5.19070i	−0.00916176	−	0.199790i
$676$	6.07640	−	10.5246i	0.233708	−	0.404794i
$677$	18.1212	+	31.3869i	0.696456	+	1.20630i	0.969687	+	0.244349i	$0.0785743\pi$
$677$	18.1212	+	31.3869i	0.696456	+	1.20630i	−0.273231	+	0.961948i	$0.588092\pi$
$678$	−5.53151	−	2.59407i	−0.212436	−	0.0996246i
$679$	−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	$0.182675\pi$
$683$			28.3768i			1.08581i	−0.839795	+	0.542903i	$0.817325\pi$
$684$	8.65084	+	2.19697i	0.330773	+	0.0840034i
$685$	−8.13335	+	7.32330i	−0.310759	+	0.279809i
$686$	−26.1660	−	36.0144i	−0.999023	−	1.37504i
$687$	−33.3037	−	20.1097i	−1.27061	−	0.767234i
$688$	9.61821	+	5.55308i	0.366691	+	0.211709i
$689$	−8.64360	+	0.908479i	−0.329295	+	0.0346103i
$690$	0.0237230	−	0.189790i	0.000903119	−	0.00722516i
$691$	−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
$693$	−44.0420	+	29.4284i	−1.67302	+	1.11789i
$694$	−4.11465	+	19.3579i	−0.156190	+	0.734816i
$695$	−0.710239	+	0.150966i	−0.0269409	+	0.00572646i
$696$	−3.46215	+	4.57366i	−0.131232	+	0.173364i
$697$	35.7522	+	11.6166i	1.35421	+	0.440010i
$698$	33.9350	+	11.0262i	1.28446	+	0.417347i
$699$	−27.0868	+	35.7829i	−1.02452	+	1.35343i
$700$	4.71495	−	1.00219i	0.178209	−	0.0378794i
$701$	8.02690	−	37.7636i	0.303172	−	1.42631i	−0.517878	−	0.855454i	$-0.673278\pi$
$701$	8.02690	−	37.7636i	0.303172	−	1.42631i	0.821050	−	0.570857i	$-0.193389\pi$
$702$	4.24714	+	2.19910i	0.160298	+	0.0829999i
$703$	1.39498	+	1.25605i	0.0526127	+	0.0473727i
$704$	−0.382880	+	3.64286i	−0.0144303	+	0.137296i
$705$	−0.313733	+	2.50994i	−0.0118159	+	0.0945298i
$706$	−17.4130	+	1.83018i	−0.655346	+	0.0688796i
$707$	52.6853	+	30.4179i	1.98143	+	1.14398i
$708$	−0.876256	−	0.529109i	−0.0329317	−	0.0198851i
$709$	−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
$711$	2.96357	−	11.6694i	0.111143	−	0.437637i
$712$			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
$717$	19.3512	+	9.07498i	0.722683	+	0.338911i
$718$	14.4155	+	24.9684i	0.537982	+	0.931813i
$719$	−5.11500	+	8.85944i	−0.190757	+	0.330401i	−0.945501	−	0.325618i	$-0.894428\pi$
$719$	−5.11500	+	8.85944i	−0.190757	+	0.330401i	0.754744	+	0.656019i	$0.227761\pi$
$720$	1.32685	−	2.69063i	0.0494487	−	0.100274i
$721$	29.6124	+	21.5146i	1.10282	+	0.801247i
$722$	−10.0929	−	1.06080i	−0.375618	−	0.0394790i
$723$	5.59586	−	23.9997i	0.208112	−	0.892558i
$724$	7.78961	−	17.4957i	0.289498	−	0.650224i
$725$	3.23947	+	0.688570i	0.120311	+	0.0255728i
$726$	−3.16552	+	2.73966i	−0.117483	+	0.101678i
$727$	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
$729$	11.3033	−	24.5201i	0.418642	−	0.908152i
$730$	−0.190059	−	0.426879i	−0.00703438	−	0.0157995i
$731$	−8.15738	−	38.3775i	−0.301712	−	1.41944i
$732$	−11.0211	+	3.34324i	−0.407350	+	0.123570i
$733$	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
$735$	10.9310	+	25.9086i	0.403197	+	0.955654i
$736$	0.0649078	−	0.0893379i	0.00239253	−	0.00329304i
$737$	−5.00581	−	47.6271i	−0.184391	−	1.75437i
$738$	14.8642	+	28.2518i	0.547159	+	1.03996i
$739$	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
$741$	4.48131	+	1.55397i	0.164625	+	0.0570863i
$742$	−43.2880	+	14.0651i	−1.58915	+	0.516347i
$743$	−0.769278			−0.0282221			−0.0141110	−	0.999900i	$-0.504492\pi$
$743$	−0.769278			−0.0282221			−0.0141110	+	0.999900i	$0.504492\pi$
$744$	8.91147	+	3.68587i	0.326710	+	0.135130i
$745$	−2.96358			−0.108577
$746$	−11.5098	+	3.73975i	−0.421403	+	0.136922i
$747$	−26.6438	+	4.57843i	−0.974847	+	0.167516i
$748$	10.4687	−	7.60598i	0.382775	−	0.278102i
$749$	2.28521	−	1.31937i	0.0834997	−	0.0482086i
$750$	−1.73172	−	0.0340008i	−0.0632334	−	0.00124153i
$751$	−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
$753$	1.37694	−	0.580941i	0.0501786	−	0.0211707i
$754$	−2.03973	+	2.26534i	−0.0742824	+	0.0824990i
$755$	−18.3619	−	8.17526i	−0.668259	−	0.297528i
$756$	24.1506	+	6.64060i	0.878350	+	0.241516i
$757$	−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
$759$	0.688013	−	0.132181i	0.0249733	−	0.00479788i
$760$	0.919372	−	2.82954i	0.0333491	−	0.102638i
$761$	23.0346	−	10.2556i	0.835002	−	0.371767i	0.0557247	−	0.998446i	$-0.482253\pi$
$761$	23.0346	−	10.2556i	0.835002	−	0.371767i	0.779277	+	0.626679i	$0.215586\pi$
$762$	15.0926	+	17.4386i	0.546748	+	0.631735i
$763$	−71.2827	−	15.1516i	−2.58061	−	0.548525i
$764$	−4.23963	+	9.52237i	−0.153385	+	0.344507i
$765$	−10.2002	+	2.87683i	−0.368789	+	0.104012i
$766$	−4.07719	−	0.428530i	−0.147315	−	0.0154834i
$767$	−0.440072	−	0.319731i	−0.0158901	−	0.0115448i
$768$	1.42097	−	0.990371i	0.0512750	−	0.0357369i
$769$	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
$771$	0.366669	−	0.781874i	0.0132053	−	0.0281585i
$772$	−14.5570	−	16.1672i	−0.523917	−	0.581869i
$773$	−10.6110	−	32.6572i	−0.381650	−	1.17460i	−0.938882	−	0.344240i	$-0.888137\pi$
$773$	−10.6110	−	32.6572i	−0.381650	−	1.17460i	0.557232	−	0.830357i	$-0.311863\pi$
$774$	17.7790	−	28.1785i	0.639054	−	1.01285i
$775$	−0.257848	−	5.56179i	−0.00926218	−	0.199785i
$776$			11.3796i			0.408505i
$777$	3.84471	+	3.60094i	0.137928	+	0.129183i
$778$	−26.5155	+	23.8746i	−0.950626	+	0.855948i
$779$	18.6087	+	25.6127i	0.666726	+	0.917670i
$780$	0.824067	−	1.36473i	0.0295063	−	0.0488653i
$781$	−36.3875	−	21.0084i	−1.30205	−	0.751738i
$782$	−0.387972	+	0.0407775i	−0.0138739	+	0.00145820i
$783$	13.3027	+	10.9170i	0.475400	+	0.390143i
$784$	−1.69704	+	16.1463i	−0.0606086	+	0.576652i
$785$	−4.07823	−	3.67206i	−0.145558	−	0.131061i
$786$	1.91749	+	22.4810i	0.0683947	+	0.801870i
$787$	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
$789$	−22.0919	−	16.7230i	−0.786492	−	0.595355i
$790$	−3.81686	−	1.24017i	−0.135798	−	0.0441233i
$791$	−16.1707	−	5.25418i	−0.574964	−	0.186817i
$792$	10.8751	+	1.57674i	0.386429	+	0.0560269i
$793$	−5.98652	+	1.27247i	−0.212587	+	0.0451869i
$794$	8.02600	−	37.7594i	0.284832	−	1.34003i
$795$	16.2958	−	1.38993i	0.577952	−	0.0492958i
$796$	−0.706764	−	0.636373i	−0.0250506	−	0.0225556i
$797$	−2.23860	+	21.2988i	−0.0792952	+	0.754444i	0.880558	+	0.473939i	$0.157168\pi$
$797$	−2.23860	+	21.2988i	−0.0792952	+	0.754444i	−0.959853	+	0.280504i	$0.909498\pi$
$798$	24.6477	+	3.08087i	0.872519	+	0.109062i
$799$	5.13088	−	0.539277i	0.181518	−	0.0190783i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$	32.3792	+	1.27197i	1.14406	+	0.0449427i
$802$	−19.9212	−	27.4192i	−0.703443	−	0.968206i
$803$	1.27197	−	1.14528i	0.0448868	−	0.0404162i
$804$	−15.4799	+	16.5278i	−0.545934	+	0.582891i
$805$		−	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	0.719823	−	0.694158i	$-0.244223\pi$
$809$	−1.30197	−	1.44598i	−0.0457748	−	0.0508381i	−0.765597	+	0.643320i	$0.777556\pi$
$810$	−7.90941	−	4.29432i	−0.277908	−	0.150887i
$811$	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
$813$	13.3206	+	19.1122i	0.467172	+	0.670294i
$814$	1.86970	+	1.35842i	0.0655330	+	0.0476125i
$815$	11.4456	+	1.20298i	0.400920	+	0.0421384i
$816$	−5.95900	−	1.38942i	−0.208607	−	0.0486395i
$817$	13.4396	−	30.1858i	0.470192	−	1.05607i
$818$	17.4541	+	3.70997i	0.610267	+	0.129716i
$819$	12.4876	+	4.60682i	0.436352	+	0.160975i
$820$	9.72117	−	4.32814i	0.339478	−	0.151145i
$821$	−0.139134	+	0.428211i	−0.00485582	+	0.0149447i	−0.953455	−	0.301535i	$-0.902501\pi$
$821$	−0.139134	+	0.428211i	−0.00485582	+	0.0149447i	0.948599	+	0.316480i	$0.102501\pi$
$822$	3.57651	+	18.6160i	0.124745	+	0.649307i
$823$	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
$825$	−1.84170	−	6.07118i	−0.0641196	−	0.211372i
$826$	−2.60242	−	1.15867i	−0.0905499	−	0.0403154i
$827$	1.35674	−	1.50681i	0.0471784	−	0.0523970i	−0.719094	−	0.694913i	$-0.755443\pi$
$827$	1.35674	−	1.50681i	0.0471784	−	0.0523970i	0.766272	+	0.642516i	$0.222109\pi$
$828$	−0.260164	−	0.205094i	−0.00904131	−	0.00712750i
$829$	−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
$831$	0.771603	−	39.2990i	0.0267666	−	1.36327i
$832$	0.797118	−	0.460216i	0.0276351	−	0.0159551i
$833$	46.4006	−	33.7120i	1.60768	−	1.16805i
$834$	−0.412041	+	1.18824i	−0.0142678	+	0.0411453i
$835$	11.1766	−	3.63149i	0.386781	−	0.125673i
$836$	10.8978			0.376907
$837$	12.0985	−	26.2798i	0.418185	−	0.908362i
$838$	28.1355			0.971923
$839$	−4.62854	+	1.50390i	−0.159795	+	0.0519206i	−0.387822	−	0.921734i	$-0.626773\pi$
$839$	−4.62854	+	1.50390i	−0.159795	+	0.0519206i	0.228027	+	0.973655i	$0.426773\pi$
$840$	2.73535	−	7.88818i	0.0943787	−	0.272168i
$841$	14.5880	−	10.5988i	0.503034	−	0.365475i
$842$	2.61770	−	1.51133i	0.0902118	−	0.0520838i
$843$	0.364505	−	18.5649i	0.0125542	−	0.639408i
$844$	−2.49760	−	23.7631i	−0.0859709	−	0.817959i
$845$	−7.14324	+	9.83183i	−0.245735	+	0.338225i
$846$	3.44063	+	2.71234i	0.118291	+	0.0932520i
$847$	−7.79593	+	8.65826i	−0.267871	+	0.297501i
$848$	8.62618	+	3.84062i	0.296224	+	0.131888i
$849$	−11.6943	−	38.5506i	−0.401349	−	1.32305i
$850$	0.734492	+	3.45551i	0.0251929	+	0.118523i
$851$	−0.0283385	−	0.0636494i	−0.000971432	−	0.00218187i
$852$	3.74850	+	19.5112i	0.128422	+	0.668442i
$853$	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
$855$	−8.37381	−	3.08920i	−0.286378	−	0.105648i
$856$	−0.535460	−	0.113815i	−0.0183016	−	0.00389013i
$857$	−8.22188	+	18.4666i	−0.280854	+	0.630809i	−0.997798	−	0.0663220i	$-0.978874\pi$
$857$	−8.22188	+	18.4666i	−0.280854	+	0.630809i	0.716944	+	0.697131i	$0.245540\pi$
$858$	5.68703	+	1.32601i	0.194152	+	0.0452692i
$859$	−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
$861$	50.7995	+	72.8866i	1.73124	+	2.48397i
$862$	4.70213	−	8.14433i	0.160155	−	0.277397i
$863$	4.33677	+	7.51151i	0.147625	+	0.255695i	0.930349	−	0.366674i	$-0.119504\pi$
$863$	4.33677	+	7.51151i	0.147625	+	0.255695i	−0.782724	+	0.622369i	$0.786170\pi$
$864$	−2.80149	−	4.37626i	−0.0953086	−	0.148883i
$865$	−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
$870$	3.92126	−	4.18671i	0.132943	−	0.141943i
$871$	−8.94287	+	8.05219i	−0.303017	+	0.272838i
$872$	8.88639	+	12.2311i	0.300931	+	0.414196i
$873$	34.1126	+	1.34006i	1.15454	+	0.0453541i
$874$	−0.284523	−	0.164270i	−0.00962414	−	0.00555650i
$875$	−4.79388	+	0.503857i	−0.162063	+	0.0170335i
$876$	−0.803097	−	0.100384i	−0.0271341	−	0.00339167i
$877$	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
$879$	−20.5906	+	1.75626i	−0.694505	+	0.0592372i
$880$	0.761566	−	3.58288i	0.0256724	−	0.120779i
$881$	7.10625	−	1.51048i	0.239416	−	0.0508893i	−0.0866411	−	0.996240i	$-0.527613\pi$
$881$	7.10625	−	1.51048i	0.239416	−	0.0508893i	0.326057	+	0.945350i	$0.394280\pi$
$882$	48.2016	+	6.98857i	1.62303	+	0.235317i
$883$	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
$885$	0.816149	+	0.617804i	0.0274345	+	0.0207673i
$886$	−4.89452	+	1.04036i	−0.164435	+	0.0349517i
$887$	−4.32605	+	20.3525i	−0.145255	+	0.683369i	0.843901	+	0.536499i	$0.180253\pi$
$887$	−4.32605	+	20.3525i	−0.145255	+	0.683369i	−0.989156	+	0.146871i	$0.953080\pi$
$888$	−0.0928734	−	1.08886i	−0.00311663	−	0.0365398i
$889$	47.6978	+	42.9473i	1.59973	+	1.44041i
$890$	1.12905	−	10.7422i	0.0378459	−	0.360080i
$891$	6.00721	−	32.4144i	0.201249	−	1.08592i
$892$	2.39668	−	0.251901i	0.0802469	−	0.00843429i
$893$	3.76278	+	2.17244i	0.125917	+	0.0726981i
$894$	−2.65331	+	4.39413i	−0.0887399	+	0.146962i
$895$	−13.4748	−	18.5465i	−0.450413	−	0.619940i
$896$	3.58217	−	3.22540i	0.119672	−	0.107753i
$897$	−0.128491	−	0.120344i	−0.00429020	−	0.00401818i
$898$			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
$903$	39.3703	−	83.9519i	1.31016	−	2.79374i
$904$	1.76368	+	3.05478i	0.0586591	+	0.101601i
$905$	−9.57574	+	16.5857i	−0.318308	+	0.551326i
$906$	−28.5611	+	19.9061i	−0.948878	+	0.661336i
$907$	−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
$909$	−36.4407	+	10.2776i	−1.20866	+	0.340887i
$910$	1.80459	−	4.05317i	0.0598215	−	0.134361i
$911$	35.5416	+	7.55460i	1.17755	+	0.250295i	0.754801	−	0.655954i	$-0.227733\pi$
$911$	35.5416	+	7.55460i	1.17755	+	0.250295i	0.422745	+	0.906249i	$0.361067\pi$
$912$	−3.37227	−	3.89646i	−0.111667	−	0.129025i
$913$	−30.1546	+	13.4257i	−0.997971	+	0.444325i
$914$	4.63271	−	14.2580i	0.153237	−	0.471614i
$915$	11.3101	−	2.17291i	0.373902	−	0.0718343i
$916$	9.13585	+	20.5195i	0.301857	+	0.677982i
$917$	13.0551	+	61.4195i	0.431118	+	2.02825i
$918$	−4.86678	+	17.6996i	−0.160628	+	0.584174i
$919$	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
$921$	11.0018	−	4.64172i	0.362521	−	0.152950i
$922$	−16.4114	+	22.5883i	−0.540480	+	0.743907i
$923$	1.10362	+	10.5003i	0.0363261	+	0.345620i
$924$	30.5758	+	0.600331i	1.00587	+	0.0197494i
$925$	−0.546407	+	0.315469i	−0.0179658	+	0.0103725i
$926$	−15.1262	+	10.9898i	−0.497077	+	0.361148i
$927$	−22.4514	+	3.85802i	−0.737402	+	0.126714i
$928$	3.14975	−	1.02341i	0.103395	−	0.0335952i
$929$	36.1626			1.18646			0.593228	−	0.805034i	$-0.297853\pi$
$929$	36.1626			1.18646			0.593228	+	0.805034i	$0.297853\pi$
$930$	−8.47738	−	4.59718i	−0.277984	−	0.150747i
$931$	48.3022			1.58304
$932$	24.6426	−	8.00688i	0.807197	−	0.262274i
$933$	39.9862	+	13.8659i	1.30909	+	0.453948i
$934$	14.7597	−	10.7236i	0.482952	−	0.350885i
$935$	−11.2064	+	6.47003i	−0.366489	+	0.211593i
$936$	−1.28572	−	2.44370i	−0.0420249	−	0.0798750i
$937$	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
$939$	6.86146	+	16.2630i	0.223915	+	0.530722i
$940$	0.977193	−	1.08528i	0.0318725	−	0.0353980i
$941$	−43.7903	−	19.4967i	−1.42752	−	0.635575i	−0.459900	−	0.887971i	$-0.652115\pi$
$941$	−43.7903	−	19.4967i	−1.42752	−	0.635575i	−0.967624	+	0.252396i	$0.918781\pi$
$942$	−9.09585	+	2.75923i	−0.296359	+	0.0899006i
$943$	−0.244312	−	1.14940i	−0.00795591	−	0.0374296i
$944$	0.240374	+	0.539889i	0.00782351	+	0.0175719i
$945$	−23.3242	−	9.12865i	−0.758736	−	0.296955i
$946$	12.5711	−	38.6900i	0.408723	−	1.25792i
$947$	18.3445	−	8.16749i	0.596116	−	0.265408i	−0.0864215	−	0.996259i	$-0.527543\pi$
$947$	18.3445	−	8.16749i	0.596116	−	0.265408i	0.682537	+	0.730851i	$0.260877\pi$
$948$	−5.25606	+	4.54896i	−0.170709	+	0.147743i
$949$	−0.420698	−	0.0894221i	−0.0136564	−	0.00290276i
$950$	−1.21010	+	2.71794i	−0.0392609	+	0.0881815i
$951$	−2.37588	+	10.1898i	−0.0770432	+	0.330425i
$952$	−16.9354	−	1.77998i	−0.548880	−	0.0576896i
$953$	−10.3679	−	7.53269i	−0.335848	−	0.244008i	0.407060	−	0.913401i	$-0.366554\pi$
$953$	−10.3679	−	7.53269i	−0.335848	−	0.244008i	−0.742908	+	0.669394i	$0.766554\pi$
$954$	12.5288	−	25.4063i	0.405635	−	0.822560i
$955$	5.21177	−	9.02705i	0.168649	−	0.292108i
$956$	−6.16998	−	10.6867i	−0.199551	−	0.345633i
$957$	19.0235	+	8.92133i	0.614944	+	0.288386i
$958$	−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
$963$	−0.404239	+	1.59174i	−0.0130264	+	0.0512930i
$964$	−10.5734	+	9.52031i	−0.340546	+	0.306629i
$965$	12.7873	+	17.6002i	0.411638	+	0.566571i
$966$	−0.789237	−	0.476565i	−0.0253933	−	0.0153332i
$967$	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
$969$	−2.25792	+	18.0639i	−0.0725349	+	0.580296i
$970$	1.18949	−	11.3173i	0.0381924	−	0.363376i
$971$	21.5373	+	19.3922i	0.691163	+	0.622326i	0.937961	−	0.346741i	$-0.112712\pi$
$971$	21.5373	+	19.3922i	0.691163	+	0.622326i	−0.246798	+	0.969067i	$0.579378\pi$
$972$	−13.4486	+	7.88264i	−0.431363	+	0.252836i
$973$	−0.727699	+	3.42356i	−0.0233290	+	0.109754i
$974$	34.0815	−	7.24424i	1.09204	−	0.232120i
$975$	−0.962206	+	1.27112i	−0.0308153	+	0.0407084i
$976$	6.32389	+	2.05476i	0.202423	+	0.0657712i
$977$	40.1426	+	13.0431i	1.28428	+	0.417287i	0.870085	−	0.492902i	$-0.164064\pi$
$977$	40.1426	+	13.0431i	1.28428	+	0.417287i	0.414192	+	0.910189i	$0.364064\pi$
$978$	12.0309	−	15.8934i	0.384706	−	0.508215i
$979$	38.7001	−	8.22596i	1.23686	−	0.262903i
$980$	3.37549	−	15.8804i	0.107826	−	0.507281i
$981$	37.7114	−	25.1983i	1.20403	−	0.804520i
$982$	24.0422	+	21.6477i	0.767217	+	0.690805i
$983$	2.35600	−	22.4159i	0.0751448	−	0.714955i	−0.890481	−	0.455020i	$-0.849632\pi$
$983$	2.35600	−	22.4159i	0.0751448	−	0.714955i	0.965626	−	0.259935i	$-0.0837013\pi$
$984$	2.28602	−	18.2887i	0.0728756	−	0.583022i
$985$	−3.99034	+	0.419401i	−0.127143	+	0.0133632i
$986$	−10.1323	−	5.84988i	−0.322678	−	0.186298i
$987$	10.4376	+	6.30250i	0.332231	+	0.200611i
$988$	−1.60961	−	2.21543i	−0.0512084	−	0.0704823i
$989$	−0.911413	+	0.820640i	−0.0289812	+	0.0260948i
$990$	−10.6507	−	2.70485i	−0.338501	−	0.0859659i
$991$			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
$996$	14.1315	+	6.62715i	0.447774	+	0.209989i
$997$	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
$999$	−3.27500	+	0.150182i	−0.103617	+	0.00475154i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(-0.567467 + 1.63645i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.0340008 + 1.73172i) q^{6} +(0.503857 + 4.79388i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-2.35596 - 1.85727i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(-0.567467 + 1.63645i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.0340008 + 1.73172i) q^{6} +(0.503857 + 4.79388i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-2.35596 - 1.85727i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(-3.34625 - 1.48985i) q^{11} +(0.502793 + 1.65747i) q^{12} +(0.191369 + 0.900318i) q^{13} +(1.96059 + 4.40355i) q^{14} +(-0.326786 - 1.70094i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-3.22729 + 1.43688i) q^{17} +(-2.81458 - 1.03833i) q^{18} +(-2.91014 - 0.618569i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(-8.13089 - 1.89583i) q^{21} +(-3.64286 - 0.382880i) q^{22} +(0.0893379 + 0.0649078i) q^{23} +(0.990371 + 1.42097i) q^{24} +(0.500000 - 0.866025i) q^{25} +(0.460216 + 0.797118i) q^{26} +(4.37626 - 2.80149i) 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} +(4.33695 - 4.63055i) q^{33} +(-2.62532 + 2.36385i) q^{34} +(-2.83329 - 3.89970i) q^{35} +(-2.99769 - 0.117760i) q^{36} +(-0.546407 - 0.315469i) q^{37} +(-2.95885 + 0.310988i) q^{38} +(-1.58192 - 0.197735i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(-7.90791 - 7.12032i) q^{41} +(-8.31878 + 0.709543i) q^{42} +(-2.30910 + 10.8635i) q^{43} +(-3.58288 + 0.761566i) q^{44} +(2.96896 + 0.430458i) q^{45} +(0.105023 + 0.0341240i) q^{46} +(-1.38892 - 0.451286i) q^{47} +(1.38100 + 1.04538i) q^{48} +(-15.8804 + 3.37549i) q^{49} +(0.207912 - 0.978148i) q^{50} +(-0.520012 - 6.09670i) q^{51} +(0.684014 + 0.615889i) q^{52} +(-0.987013 + 9.39081i) q^{53} +(3.29636 - 4.01671i) q^{54} +(3.64286 - 0.382880i) q^{55} +(4.17449 + 2.41014i) q^{56} +(2.66367 - 4.41129i) q^{57} +(1.94665 + 2.67933i) q^{58} +(-0.439186 + 0.395444i) q^{59} +(-1.26417 - 1.18401i) 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} +(2.69377 - 5.74410i) q^{66} +(6.53705 + 11.3225i) q^{67} +(-1.76636 + 3.05942i) q^{68} +(-0.156915 + 0.109364i) q^{69} +(-3.89970 - 2.83329i) q^{70} +(11.4080 + 1.19903i) q^{71} +(-2.88736 + 0.814340i) q^{72} +(-0.190059 + 0.426879i) q^{73} +(-0.617150 - 0.131179i) q^{74} +(1.13348 + 1.30967i) q^{75} +(-2.71794 + 1.21010i) q^{76} +(5.45612 - 16.7922i) q^{77} +(-1.56560 + 0.300785i) q^{78} +(1.63235 + 3.66631i) q^{79} +(0.207912 + 0.978148i) q^{80} +(2.10112 + 8.75130i) q^{81} +(-9.72117 - 4.32814i) q^{82} +(6.02984 - 6.69682i) q^{83} +(-7.69237 + 3.24546i) q^{84} +(2.07648 - 2.85802i) q^{85} +(1.16091 + 11.0453i) q^{86} +(-5.73517 - 0.112605i) q^{87} +(-3.17219 + 1.83146i) q^{88} +(-8.73850 + 6.34889i) q^{89} +(2.95666 - 0.508068i) q^{90} +(-4.21960 + 1.37103i) q^{91} +0.110428 q^{92} +(2.25610 + 9.37603i) q^{93} -1.46039 q^{94} +(2.82954 - 0.919372i) q^{95} +(1.63645 + 0.567467i) q^{96} +(-9.20631 + 6.68877i) q^{97} +(-14.0601 + 8.11759i) q^{98} +(5.11660 + 9.72490i) 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

Related objects

Downloads

Learn more