LMFDB - Embedded newform 930.2.bk.a.47.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(47,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 5, 4]))

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

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

chi := DirichletCharacter("930.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bk (of order $20$, 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:	$512$
Relative dimension:	$64$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			47.4
Character	$\chi$	$=$	930.47
Dual form			930.2.bk.a.653.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.156434 + 0.987688i) q^{2} +(-1.67858 + 0.427044i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(0.419593 + 2.19635i) q^{5} +(-0.159198 - 1.72472i) q^{6} +(3.17140 - 1.61591i) q^{7} +(0.453990 - 0.891007i) q^{8} +(2.63527 - 1.43366i) q^{9} +O(q^{10})$	\(q+(-0.156434 + 0.987688i) q^{2} +(-1.67858 + 0.427044i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(0.419593 + 2.19635i) q^{5} +(-0.159198 - 1.72472i) q^{6} +(3.17140 - 1.61591i) q^{7} +(0.453990 - 0.891007i) q^{8} +(2.63527 - 1.43366i) q^{9} +(-2.23495 + 0.0708430i) q^{10} +(-4.60595 - 1.49656i) q^{11} +(1.72839 + 0.112567i) q^{12} +(-2.09691 + 0.332117i) q^{13} +(1.09990 + 3.38513i) q^{14} +(-1.64226 - 3.50756i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-6.30300 - 3.21154i) q^{17} +(1.00376 + 2.82710i) q^{18} +(1.58833 + 2.18614i) q^{19} +(0.279652 - 2.21851i) q^{20} +(-4.63338 + 4.06676i) q^{21} +(2.19867 - 4.31513i) q^{22} +(-0.977132 + 1.91773i) q^{23} +(-0.381561 + 1.68950i) q^{24} +(-4.64788 + 1.84315i) q^{25} -2.12304i q^{26} +(-3.81128 + 3.53188i) q^{27} +(-3.51552 + 0.556804i) q^{28} +(-3.28303 + 2.38526i) q^{29} +(3.72128 - 1.07334i) q^{30} +(1.10347 - 5.45732i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(8.37056 + 0.545161i) q^{33} +(4.15801 - 5.72300i) q^{34} +(4.87979 + 6.28746i) q^{35} +(-2.94931 + 0.549145i) q^{36} +(-4.18459 - 4.18459i) q^{37} +(-2.40770 + 1.22678i) q^{38} +(3.37800 - 1.45296i) q^{39} +(2.14745 + 0.623260i) q^{40} +(-6.01151 - 8.27414i) q^{41} +(-3.29187 - 5.21252i) q^{42} +(0.365435 - 2.30727i) q^{43} +(3.91806 + 2.84664i) q^{44} +(4.25454 + 5.18641i) q^{45} +(-1.74126 - 1.26510i) q^{46} +(-2.24420 + 0.355446i) q^{47} +(-1.60901 - 0.641159i) q^{48} +(3.33210 - 4.58624i) q^{49} +(-1.09336 - 4.87899i) q^{50} +(11.9516 + 2.69917i) q^{51} +(2.09691 + 0.332117i) q^{52} +(-1.68827 + 3.31342i) q^{53} +(-2.89218 - 4.31686i) q^{54} +(1.35435 - 10.7442i) q^{55} -3.55934i q^{56} +(-3.59971 - 2.99133i) q^{57} +(-1.84232 - 3.61575i) q^{58} +(2.79980 + 2.03417i) q^{59} +(0.477984 + 3.84338i) q^{60} +5.14839 q^{61} +(5.21751 + 1.94360i) q^{62} +(6.04082 - 8.80503i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-1.60929 - 4.46618i) q^{65} +(-1.84789 + 8.18223i) q^{66} +(-8.91778 - 8.91778i) q^{67} +(5.00209 + 5.00209i) q^{68} +(0.821240 - 3.63634i) q^{69} +(-6.97342 + 3.83614i) q^{70} +(12.5135 - 4.06587i) q^{71} +(-0.0810097 - 2.99891i) q^{72} +(-3.20327 - 6.28677i) q^{73} +(4.78768 - 3.47846i) q^{74} +(7.01474 - 5.07872i) q^{75} +(-0.835032 - 2.56997i) q^{76} +(-17.0256 + 2.69659i) q^{77} +(0.906633 + 3.56370i) q^{78} +(4.60744 - 1.49705i) q^{79} +(-0.951522 + 2.02351i) q^{80} +(4.88927 - 7.55613i) q^{81} +(9.11268 - 4.64314i) q^{82} +(0.0371195 + 0.00587915i) q^{83} +(5.66330 - 2.43592i) q^{84} +(4.40896 - 15.1911i) q^{85} +(2.22169 + 0.721872i) q^{86} +(4.49222 - 5.40585i) q^{87} +(-3.42451 + 3.42451i) q^{88} +(2.39963 - 7.38530i) q^{89} +(-5.78811 + 3.39083i) q^{90} +(-6.11345 + 4.44168i) q^{91} +(1.52192 - 1.52192i) q^{92} +(0.478248 + 9.63178i) q^{93} -2.27217i q^{94} +(-4.13508 + 4.40581i) q^{95} +(0.884970 - 1.48890i) q^{96} +(-9.92914 + 5.05915i) q^{97} +(4.00852 + 4.00852i) q^{98} +(-14.2835 + 2.65950i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q + 8 q^{3} - 12 q^{7}+O(q^{10}) $ 512 * q + 8 * q^3 - 12 * q^7	$ 512 q + 8 q^{3} - 12 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} + 128 q^{16} + 28 q^{22} + 32 q^{25} + 44 q^{27} + 8 q^{28} + 24 q^{30} + 8 q^{31} + 28 q^{33} + 176 q^{37} + 24 q^{42} - 40 q^{45} - 24 q^{46} + 12 q^{48} - 16 q^{51} - 40 q^{55} + 40 q^{57} + 56 q^{58} + 12 q^{60} - 32 q^{61} - 224 q^{63} + 32 q^{66} + 48 q^{67} + 24 q^{70} + 40 q^{73} - 32 q^{75} + 48 q^{76} - 76 q^{78} - 96 q^{81} + 24 q^{85} - 80 q^{87} - 72 q^{88} + 16 q^{90} + 80 q^{91} - 168 q^{93} - 112 q^{97}+O(q^{100}) $ 512 * q + 8 * q^3 - 12 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 + 128 * q^16 + 28 * q^22 + 32 * q^25 + 44 * q^27 + 8 * q^28 + 24 * q^30 + 8 * q^31 + 28 * q^33 + 176 * q^37 + 24 * q^42 - 40 * q^45 - 24 * q^46 + 12 * q^48 - 16 * q^51 - 40 * q^55 + 40 * q^57 + 56 * q^58 + 12 * q^60 - 32 * q^61 - 224 * q^63 + 32 * q^66 + 48 * q^67 + 24 * q^70 + 40 * q^73 - 32 * q^75 + 48 * q^76 - 76 * q^78 - 96 * q^81 + 24 * q^85 - 80 * q^87 - 72 * q^88 + 16 * q^90 + 80 * q^91 - 168 * q^93 - 112 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.156434	+	0.987688i	−0.110616	+	0.698401i
$2$	−0.156434	+	0.987688i	−0.110616	+	0.698401i
$3$	−1.67858	+	0.427044i	−0.969129	+	0.246554i
$3$	−1.67858	+	0.427044i	−0.969129	+	0.246554i
$4$	−0.951057	−	0.309017i	−0.475528	−	0.154508i
$5$	0.419593	+	2.19635i	0.187648	+	0.982236i
$5$	0.419593	+	2.19635i	0.187648	+	0.982236i
$6$	−0.159198	−	1.72472i	−0.0649924	−	0.704114i
$7$	3.17140	−	1.61591i	1.19867	−	0.610755i	0.263403	−	0.964686i	$-0.415155\pi$
$7$	3.17140	−	1.61591i	1.19867	−	0.610755i	0.935272	+	0.353930i	$0.115155\pi$
$8$	0.453990	−	0.891007i	0.160510	−	0.315018i
$9$	2.63527	−	1.43366i	0.878422	−	0.477885i
$10$	−2.23495	+	0.0708430i	−0.706752	+	0.0224025i
$11$	−4.60595	−	1.49656i	−1.38875	−	0.451231i	−0.483212	−	0.875503i	$-0.660530\pi$
$11$	−4.60595	−	1.49656i	−1.38875	−	0.451231i	−0.905535	+	0.424272i	$0.860530\pi$
$12$	1.72839	+	0.112567i	0.498943	+	0.0324954i
$13$	−2.09691	+	0.332117i	−0.581577	+	0.0921128i	−0.440290	−	0.897856i	$-0.645124\pi$
$13$	−2.09691	+	0.332117i	−0.581577	+	0.0921128i	−0.141288	+	0.989969i	$0.545124\pi$
$14$	1.09990	+	3.38513i	0.293960	+	0.904715i
$15$	−1.64226	−	3.50756i	−0.424029	−	0.905649i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−6.30300	−	3.21154i	−1.52870	−	0.778912i	−0.531046	−	0.847343i	$-0.678201\pi$
$17$	−6.30300	−	3.21154i	−1.52870	−	0.778912i	−0.997656	+	0.0684306i	$0.978201\pi$
$18$	1.00376	+	2.82710i	0.236588	+	0.666353i
$19$	1.58833	+	2.18614i	0.364387	+	0.501536i	0.951364	−	0.308068i	$-0.0996823\pi$
$19$	1.58833	+	2.18614i	0.364387	+	0.501536i	−0.586978	+	0.809603i	$0.699682\pi$
$20$	0.279652	−	2.21851i	0.0625320	−	0.496074i
$21$	−4.63338	+	4.06676i	−1.01109	+	0.887439i
$22$	2.19867	−	4.31513i	0.468758	−	0.919989i
$23$	−0.977132	+	1.91773i	−0.203746	+	0.399874i	−0.970157	−	0.242476i	$-0.922040\pi$
$23$	−0.977132	+	1.91773i	−0.203746	+	0.399874i	0.766411	+	0.642350i	$0.222040\pi$
$24$	−0.381561	+	1.68950i	−0.0778858	+	0.344868i
$25$	−4.64788	+	1.84315i	−0.929577	+	0.368629i
$26$		−	2.12304i		−	0.416363i
$27$	−3.81128	+	3.53188i	−0.733480	+	0.679711i
$28$	−3.51552	+	0.556804i	−0.664371	+	0.105226i
$29$	−3.28303	+	2.38526i	−0.609644	+	0.442932i	−0.849289	−	0.527929i	$-0.822969\pi$
$29$	−3.28303	+	2.38526i	−0.609644	+	0.442932i	0.239645	+	0.970861i	$0.422969\pi$
$30$	3.72128	−	1.07334i	0.679410	−	0.195963i
$31$	1.10347	−	5.45732i	0.198189	−	0.980164i
$31$	1.10347	−	5.45732i	0.198189	−	0.980164i
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	8.37056	+	0.545161i	1.45713	+	0.0949004i
$34$	4.15801	−	5.72300i	0.713092	−	0.981487i
$35$	4.87979	+	6.28746i	0.824835	+	1.06278i
$36$	−2.94931	+	0.549145i	−0.491552	+	0.0915241i
$37$	−4.18459	−	4.18459i	−0.687942	−	0.687942i	0.273835	−	0.961777i	$-0.411708\pi$
$37$	−4.18459	−	4.18459i	−0.687942	−	0.687942i	−0.961777	+	0.273835i	$0.911708\pi$
$38$	−2.40770	+	1.22678i	−0.390580	+	0.199010i
$39$	3.37800	−	1.45296i	0.540913	−	0.232659i
$40$	2.14745	+	0.623260i	0.339542	+	0.0985461i
$41$	−6.01151	−	8.27414i	−0.938841	−	1.29220i	−0.956310	−	0.292356i	$-0.905561\pi$
$41$	−6.01151	−	8.27414i	−0.938841	−	1.29220i	0.0174689	−	0.999847i	$-0.494439\pi$
$42$	−3.29187	−	5.21252i	−0.507946	−	0.804309i
$43$	0.365435	−	2.30727i	0.0557283	−	0.351855i	−0.944030	−	0.329860i	$-0.892998\pi$
$43$	0.365435	−	2.30727i	0.0557283	−	0.351855i	0.999758	−	0.0219945i	$-0.00700162\pi$
$44$	3.91806	+	2.84664i	0.590669	+	0.429146i
$45$	4.25454	+	5.18641i	0.634230	+	0.773144i
$46$	−1.74126	−	1.26510i	−0.256735	−	0.186529i
$47$	−2.24420	+	0.355446i	−0.327350	+	0.0518472i	−0.317947	−	0.948109i	$-0.602993\pi$
$47$	−2.24420	+	0.355446i	−0.327350	+	0.0518472i	−0.00940358	+	0.999956i	$0.502993\pi$
$48$	−1.60901	−	0.641159i	−0.232241	−	0.0925434i
$49$	3.33210	−	4.58624i	0.476014	−	0.655177i
$50$	−1.09336	−	4.87899i	−0.154625	−	0.689994i
$51$	11.9516	+	2.69917i	1.67355	+	0.377959i
$52$	2.09691	+	0.332117i	0.290789	+	0.0460564i
$53$	−1.68827	+	3.31342i	−0.231902	+	0.455133i	−0.977407	−	0.211367i	$-0.932208\pi$
$53$	−1.68827	+	3.31342i	−0.231902	+	0.455133i	0.745505	+	0.666500i	$0.232208\pi$
$54$	−2.89218	−	4.31686i	−0.393576	−	0.587450i
$55$	1.35435	−	10.7442i	0.182620	−	1.44875i
$56$		−	3.55934i		−	0.475637i
$57$	−3.59971	−	2.99133i	−0.476793	−	0.396212i
$58$	−1.84232	−	3.61575i	−0.241908	−	0.474771i
$59$	2.79980	+	2.03417i	0.364502	+	0.264826i	0.754928	−	0.655808i	$-0.227672\pi$
$59$	2.79980	+	2.03417i	0.364502	+	0.264826i	−0.390425	+	0.920635i	$0.627672\pi$
$60$	0.477984	+	3.84338i	0.0617074	+	0.496178i
$61$	5.14839			0.659184			0.329592	−	0.944123i	$-0.393089\pi$
$61$	5.14839			0.659184			0.329592	+	0.944123i	$0.393089\pi$
$62$	5.21751	+	1.94360i	0.662625	+	0.246837i
$63$	6.04082	−	8.80503i	0.761072	−	1.10933i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	−1.60929	−	4.46618i	−0.199608	−	0.553961i
$66$	−1.84789	+	8.18223i	−0.227460	+	1.00716i
$67$	−8.91778	−	8.91778i	−1.08948	−	1.08948i	−0.995582	−	0.0938988i	$-0.970067\pi$
$67$	−8.91778	−	8.91778i	−1.08948	−	1.08948i	−0.0938988	−	0.995582i	$-0.529933\pi$
$68$	5.00209	+	5.00209i	0.606592	+	0.606592i
$69$	0.821240	−	3.63634i	0.0988657	−	0.437764i
$70$	−6.97342	+	3.83614i	−0.833483	+	0.458506i
$71$	12.5135	−	4.06587i	1.48508	−	0.482530i	0.549451	−	0.835526i	$-0.314837\pi$
$71$	12.5135	−	4.06587i	1.48508	−	0.482530i	0.935625	+	0.352995i	$0.114837\pi$
$72$	−0.0810097	−	2.99891i	−0.00954709	−	0.353424i
$73$	−3.20327	−	6.28677i	−0.374915	−	0.735811i	0.624046	−	0.781387i	$-0.285488\pi$
$73$	−3.20327	−	6.28677i	−0.374915	−	0.735811i	−0.998961	+	0.0455761i	$0.985488\pi$
$74$	4.78768	−	3.47846i	0.556557	−	0.404362i
$75$	7.01474	−	5.07872i	0.809993	−	0.586440i
$76$	−0.835032	−	2.56997i	−0.0957848	−	0.294795i
$77$	−17.0256	+	2.69659i	−1.94025	+	0.307305i
$78$	0.906633	+	3.56370i	0.102656	+	0.403510i
$79$	4.60744	−	1.49705i	0.518378	−	0.168431i	−0.0381312	−	0.999273i	$-0.512140\pi$
$79$	4.60744	−	1.49705i	0.518378	−	0.168431i	0.556509	+	0.830842i	$0.312140\pi$
$80$	−0.951522	+	2.02351i	−0.106383	+	0.226236i
$81$	4.88927	−	7.55613i	0.543252	−	0.839570i
$82$	9.11268	−	4.64314i	1.00633	−	0.512749i
$83$	0.0371195	+	0.00587915i	0.00407439	+	0.000645320i	0.158471	−	0.987364i	$-0.449343\pi$
$83$	0.0371195	+	0.00587915i	0.00407439	+	0.000645320i	−0.154397	+	0.988009i	$0.549343\pi$
$84$	5.66330	−	2.43592i	0.617917	−	0.265781i
$85$	4.40896	−	15.1911i	0.478219	−	1.64771i
$86$	2.22169	+	0.721872i	0.239571	+	0.0778414i
$87$	4.49222	−	5.40585i	0.481617	−	0.579568i
$88$	−3.42451	+	3.42451i	−0.365054	+	0.365054i
$89$	2.39963	−	7.38530i	0.254360	−	0.782840i	−0.739595	−	0.673052i	$-0.764983\pi$
$89$	2.39963	−	7.38530i	0.254360	−	0.782840i	0.993955	−	0.109788i	$-0.0350172\pi$
$90$	−5.78811	+	3.39083i	−0.610121	+	0.357425i
$91$	−6.11345	+	4.44168i	−0.640864	+	0.465615i
$92$	1.52192	−	1.52192i	0.158671	−	0.158671i
$93$	0.478248	+	9.63178i	0.0495921	+	0.998770i
$94$		−	2.27217i		−	0.234357i
$95$	−4.13508	+	4.40581i	−0.424250	+	0.452026i
$96$	0.884970	−	1.48890i	0.0903219	−	0.151960i
$97$	−9.92914	+	5.05915i	−1.00815	+	0.513679i	−0.878430	−	0.477871i	$-0.841408\pi$
$97$	−9.92914	+	5.05915i	−1.00815	+	0.513679i	−0.129722	+	0.991550i	$0.541408\pi$
$98$	4.00852	+	4.00852i	0.404922	+	0.404922i
$99$	−14.2835	+	2.65950i	−1.43554	+	0.267290i
$100$	4.98996	−	0.316661i	0.498996	−	0.0316661i
$101$	−2.41792	+	0.785629i	−0.240592	+	0.0781730i	−0.426831	−	0.904331i	$-0.640370\pi$
$101$	−2.41792	+	0.785629i	−0.240592	+	0.0781730i	0.186239	+	0.982504i	$0.440370\pi$
$102$	−4.53557	+	11.3822i	−0.449089	+	1.12700i
$103$	−3.15738	+	19.9349i	−0.311106	+	1.96425i	−0.0508553	+	0.998706i	$0.516195\pi$
$103$	−3.15738	+	19.9349i	−0.311106	+	1.96425i	−0.260251	+	0.965541i	$0.583805\pi$
$104$	−0.656057	+	2.01914i	−0.0643317	+	0.197993i
$105$	−10.8761	−	8.47013i	−1.06140	−	0.826600i
$106$	−3.00852	−	2.18582i	−0.292213	−	0.212306i
$107$	13.0105	+	6.62919i	1.25777	+	0.640868i	0.950491	−	0.310751i	$-0.100580\pi$
$107$	13.0105	+	6.62919i	1.25777	+	0.640868i	0.307282	+	0.951618i	$0.400580\pi$
$108$	4.71615	−	2.18127i	0.453812	−	0.209893i
$109$	−2.89923	+	3.99045i	−0.277696	+	0.382216i	−0.924969	−	0.380042i	$-0.875909\pi$
$109$	−2.89923	+	3.99045i	−0.277696	+	0.382216i	0.647273	+	0.762258i	$0.275909\pi$
$110$	10.4001	+	3.01844i	0.991608	+	0.287797i
$111$	8.81117	+	5.23717i	0.836320	+	0.497090i
$112$	3.51552	+	0.556804i	0.332185	+	0.0526130i
$113$	−5.82550	+	2.96824i	−0.548017	+	0.279229i	−0.705998	−	0.708214i	$-0.749501\pi$
$113$	−5.82550	+	2.96824i	−0.548017	+	0.279229i	0.157981	+	0.987442i	$0.449501\pi$
$114$	3.51762	−	3.08745i	0.329456	−	0.289166i
$115$	−4.62200	−	1.34145i	−0.431003	−	0.125091i
$116$	3.85943	−	1.25401i	0.358339	−	0.116432i
$117$	−5.04977	+	3.88146i	−0.466851	+	0.358841i
$118$	−2.44711	+	2.44711i	−0.225275	+	0.225275i
$119$	−25.1789			−2.30814
$120$	−3.87083	−	0.129137i	−0.353357	−	0.0117886i
$121$	10.0759	+	7.32058i	0.915992	+	0.665507i
$122$	−0.805386	+	5.08501i	−0.0729162	+	0.460375i
$123$	13.6242	+	11.3216i	1.22846	+	1.02084i
$124$	−2.73587	+	4.84923i	−0.245688	+	0.435474i
$125$	−5.99841	−	9.43499i	−0.536514	−	0.843891i
$126$	7.75164	+	7.34386i	0.690571	+	0.654243i
$127$	1.00389	+	6.33831i	0.0890809	+	0.562434i	0.991348	+	0.131258i	$0.0419015\pi$
$127$	1.00389	+	6.33831i	0.0890809	+	0.562434i	−0.902267	+	0.431177i	$0.858099\pi$
$128$	0.891007	−	0.453990i	0.0787546	−	0.0401275i
$129$	0.371891	+	4.02899i	0.0327432	+	0.354733i
$130$	4.66294	−	0.890815i	0.408967	−	0.0781297i
$131$	−2.88966	−	0.938908i	−0.252471	−	0.0820328i	0.180047	−	0.983658i	$-0.442375\pi$
$131$	−2.88966	−	0.938908i	−0.252471	−	0.0820328i	−0.432518	+	0.901625i	$0.642375\pi$
$132$	−7.79241	−	3.10513i	−0.678243	−	0.270266i
$133$	8.56981	+	4.36654i	0.743097	+	0.378627i
$134$	10.2030	−	7.41294i	0.881408	−	0.640381i
$135$	−9.35642	−	6.88893i	−0.805273	−	0.592905i
$136$	−5.72300	+	4.15801i	−0.490743	+	0.356546i
$137$	−16.2036	+	2.56640i	−1.38437	+	0.219262i	−0.803775	−	0.594934i	$-0.797178\pi$
$137$	−16.2036	+	2.56640i	−1.38437	+	0.219262i	−0.580591	+	0.814196i	$0.697178\pi$
$138$	3.46310	+	1.37998i	0.294799	+	0.117472i
$139$	−4.21313	+	5.79887i	−0.357353	+	0.491854i	−0.949409	−	0.314043i	$-0.898316\pi$
$139$	−4.21313	+	5.79887i	−0.357353	+	0.491854i	0.592056	+	0.805897i	$0.298316\pi$
$140$	−2.69802	−	7.48767i	−0.228025	−	0.632824i
$141$	3.61528	−	1.55502i	0.304462	−	0.130956i
$142$	2.05828	+	12.9955i	0.172727	+	1.09055i
$143$	10.1553	+	1.60844i	0.849228	+	0.134504i
$144$	2.97466	+	0.389120i	0.247888	+	0.0324267i
$145$	−6.61640	−	6.20984i	−0.549462	−	0.515699i
$146$	6.71048	−	2.18037i	0.555363	−	0.180448i
$147$	−3.63467	+	9.12133i	−0.299783	+	0.752315i
$148$	2.68667	+	5.27289i	0.220843	+	0.433429i
$149$	2.34294			0.191941			0.0959704	−	0.995384i	$-0.469405\pi$
$149$	2.34294			0.191941			0.0959704	+	0.995384i	$0.469405\pi$
$150$	3.91884	+	7.72287i	0.319972	+	0.630569i
$151$	3.29936	−	10.1544i	0.268498	−	0.826351i	−0.722369	−	0.691508i	$-0.756947\pi$
$151$	3.29936	−	10.1544i	0.268498	−	0.826351i	0.990867	−	0.134844i	$-0.0430532\pi$
$152$	2.66895	−	0.422721i	0.216481	−	0.0342872i
$153$	−21.2143	+	0.573065i	−1.71508	+	0.0463295i
$154$		−	17.2378i		−	1.38906i
$155$	12.4492	+	0.133752i	0.999942	+	0.0107432i
$156$	−3.66166	+	0.337985i	−0.293167	+	0.0270605i
$157$	17.4899	+	2.77013i	1.39585	+	0.221081i	0.808615	−	0.588338i	$-0.200218\pi$
$157$	17.4899	+	2.77013i	1.39585	+	0.221081i	0.587232	+	0.809418i	$0.300218\pi$
$158$	0.757855	+	4.78491i	0.0602917	+	0.380667i
$159$	1.41892	−	6.28281i	0.112528	−	0.498259i
$160$	−1.84975	−	1.25635i	−0.146236	−	0.0993236i
$161$			7.66083i			0.603758i
$162$	6.69825	+	6.01111i	0.526264	+	0.472277i
$163$	−21.5728	−	10.9919i	−1.68971	−	0.860952i	−0.989071	−	0.147438i	$-0.952897\pi$
$163$	−21.5728	−	10.9919i	−1.68971	−	0.860952i	−0.700641	−	0.713514i	$-0.747103\pi$
$164$	3.16044	+	9.72683i	0.246789	+	0.759538i
$165$	2.31487	+	18.6134i	0.180212	+	1.44905i
$166$	−0.0116135	+	0.0357428i	−0.000901385	+	0.00277418i
$167$	−1.66065	+	10.4849i	−0.128505	+	0.811348i	0.836279	+	0.548304i	$0.184726\pi$
$167$	−1.66065	+	10.4849i	−0.128505	+	0.811348i	−0.964784	+	0.263044i	$0.915274\pi$
$168$	1.51999	+	5.97464i	0.117270	+	0.460954i
$169$	−8.07702	+	2.62438i	−0.621309	+	0.201876i
$170$	14.3144	+	6.73109i	1.09786	+	0.516251i
$171$	7.31984	+	3.48396i	0.559762	+	0.266425i
$172$	−1.06053	+	2.08141i	−0.0808649	+	0.158706i
$173$	1.71639	+	10.8369i	0.130495	+	0.823912i	0.962923	+	0.269778i	$0.0869503\pi$
$173$	1.71639	+	10.8369i	0.130495	+	0.823912i	−0.832428	+	0.554134i	$0.813050\pi$
$174$	4.63656	+	5.28258i	0.351497	+	0.400471i
$175$	−11.7619	+	13.3559i	−0.889118	+	1.00961i
$176$	−2.84664	−	3.91806i	−0.214573	−	0.295335i
$177$	−5.56836	−	2.21888i	−0.418544	−	0.166782i
$178$	6.91899	+	3.52540i	0.518600	+	0.264240i
$179$	4.06758	−	12.5187i	0.304025	−	0.935693i	−0.676014	−	0.736889i	$-0.736294\pi$
$179$	4.06758	−	12.5187i	0.304025	−	0.935693i	0.980039	−	0.198804i	$-0.0637057\pi$
$180$	−2.44362	−	6.24730i	−0.182137	−	0.465646i
$181$	11.4668			0.852321			0.426160	−	0.904648i	$-0.359866\pi$
$181$	11.4668			0.852321			0.426160	+	0.904648i	$0.359866\pi$
$182$	−3.43064	−	6.73301i	−0.254296	−	0.499084i
$183$	−8.64199	+	2.19859i	−0.638835	+	0.162524i
$184$	1.26510	+	1.74126i	0.0932645	+	0.128368i
$185$	7.43498	−	10.9466i	0.546631	−	0.804813i
$186$	−9.58802	−	1.03438i	−0.703027	−	0.0758446i
$187$	24.2250	+	24.2250i	1.77151	+	1.77151i
$188$	2.24420	+	0.355446i	0.163675	+	0.0259236i
$189$	−6.37987	+	17.3597i	−0.464067	+	1.26273i
$190$	−3.70469	−	4.77339i	−0.268767	−	0.346298i
$191$		−	16.8256i		−	1.21746i	−0.793379	−	0.608728i	$-0.791680\pi$
$191$		−	16.8256i		−	1.21746i	0.793379	−	0.608728i	$-0.208320\pi$
$192$	1.33213	+	1.10699i	0.0961383	+	0.0798901i
$193$	−10.4612	−	20.5313i	−0.753015	−	1.47787i	−0.874367	−	0.485265i	$-0.838723\pi$
$193$	−10.4612	−	20.5313i	−0.753015	−	1.47787i	0.121352	−	0.992609i	$-0.461277\pi$
$194$	−3.44360	−	10.5983i	−0.247236	−	0.760915i
$195$	4.60858	+	6.80961i	0.330027	+	0.487646i
$196$	−4.58624	+	3.33210i	−0.327589	+	0.238007i
$197$	−5.08338	−	9.97670i	−0.362176	−	0.710811i	0.635967	−	0.771716i	$-0.280601\pi$
$197$	−5.08338	−	9.97670i	−0.362176	−	0.710811i	−0.998144	+	0.0609052i	$0.980601\pi$
$198$	−0.392329	−	14.5237i	−0.0278816	−	1.03215i
$199$	8.57698	−	11.8052i	0.608006	−	0.836849i	−0.388405	−	0.921489i	$-0.626974\pi$
$199$	8.57698	−	11.8052i	0.608006	−	0.836849i	0.996412	+	0.0846399i	$0.0269740\pi$
$200$	−0.467840	+	4.97806i	−0.0330813	+	0.352002i
$201$	18.7775	+	11.1609i	1.32446	+	0.787232i
$202$	−0.397711	−	2.51105i	−0.0279828	−	0.176677i
$203$	−6.55743	+	12.8697i	−0.460241	+	0.903274i
$204$	−10.5325	−	6.26030i	−0.737424	−	0.438309i
$205$	15.6505	−	16.6751i	1.09308	−	1.16464i
$206$	−19.1956	−	6.23702i	−1.33742	−	0.434554i
$207$	0.174359	+	6.45460i	0.0121188	+	0.448626i
$208$	−1.89165	−	0.963842i	−0.131162	−	0.0668304i
$209$	−4.04405	−	12.4463i	−0.279733	−	0.860929i
$210$	10.0673	−	9.41722i	0.694706	−	0.649850i
$211$	−23.4676			−1.61558			−0.807788	−	0.589473i	$-0.799335\pi$
$211$	−23.4676			−1.61558			−0.807788	+	0.589473i	$0.799335\pi$
$212$	2.62954	−	2.62954i	0.180598	−	0.180598i
$213$	−19.2686	+	12.1687i	−1.32026	+	0.833786i
$214$	−8.58286	+	11.8133i	−0.586712	+	0.807540i
$215$	5.22089	−	0.165491i	0.356062	−	0.0112864i
$216$	1.41665	+	4.99931i	0.0963905	+	0.340160i
$217$	−5.31898	−	19.0904i	−0.361076	−	1.29594i
$218$	−3.48778	−	3.48778i	−0.236222	−	0.236222i
$219$	8.06168	+	9.18492i	0.544758	+	0.620659i
$220$	−4.60821	+	9.79984i	−0.310685	+	0.660705i
$221$	14.2834	+	4.64096i	0.960806	+	0.312185i
$222$	−6.55106	+	7.88342i	−0.439678	+	0.529100i
$223$	10.0336	−	10.0336i	0.671898	−	0.671898i	−0.286255	−	0.958153i	$-0.592411\pi$
$223$	10.0336	−	10.0336i	0.671898	−	0.671898i	0.958153	+	0.286255i	$0.0924106\pi$
$224$	−1.09990	+	3.38513i	−0.0734899	+	0.226179i
$225$	−9.60598	+	11.5206i	−0.640399	+	0.768043i
$226$	−2.02039	−	6.21811i	−0.134394	−	0.413623i
$227$	−0.563334	+	3.55675i	−0.0373898	+	0.236070i	−0.999305	−	0.0372785i	$-0.988131\pi$
$227$	−0.563334	+	3.55675i	−0.0373898	+	0.236070i	0.961915	+	0.273348i	$0.0881311\pi$
$228$	2.49916	+	3.95730i	0.165511	+	0.262079i
$229$	15.7503	+	21.6785i	1.04081	+	1.43256i	0.896511	+	0.443021i	$0.146093\pi$
$229$	15.7503	+	21.6785i	1.04081	+	1.43256i	0.144301	+	0.989534i	$0.453907\pi$
$230$	2.04798	−	4.35524i	0.135040	−	0.287176i
$231$	27.4273	−	11.7971i	1.80458	−	0.776194i
$232$	0.634819	+	4.00809i	0.0416779	+	0.263144i
$233$	−0.846026	−	5.34159i	−0.0554250	−	0.349940i	−0.999779	−	0.0210095i	$-0.993312\pi$
$233$	−0.846026	−	5.34159i	−0.0554250	−	0.349940i	0.944354	−	0.328930i	$-0.106688\pi$
$234$	−3.04371	−	5.59479i	−0.198974	−	0.365743i
$235$	−1.72234	−	4.77990i	−0.112353	−	0.311806i
$236$	−2.03417	−	2.79980i	−0.132413	−	0.182251i
$237$	−7.09466	+	4.48050i	−0.460848	+	0.291040i
$238$	3.93884	−	24.8689i	0.255317	−	1.61201i
$239$	5.12748	+	15.7808i	0.331669	+	1.02077i	0.968340	+	0.249637i	$0.0803113\pi$
$239$	5.12748	+	15.7808i	0.331669	+	1.02077i	−0.636670	+	0.771136i	$0.719689\pi$
$240$	0.733079	−	3.80297i	0.0473200	−	0.245481i
$241$	−3.15208	+	9.70112i	−0.203044	+	0.624904i	0.796744	+	0.604316i	$0.206554\pi$
$241$	−3.15208	+	9.70112i	−0.203044	+	0.624904i	−0.999788	+	0.0205876i	$0.993446\pi$
$242$	−8.80667	+	8.80667i	−0.566114	+	0.566114i
$243$	−4.98023	+	14.7715i	−0.319482	+	0.947592i
$244$	−4.89641	−	1.59094i	−0.313461	−	0.101850i
$245$	11.4711	+	5.39409i	0.732862	+	0.344616i
$246$	−13.3135	+	11.6854i	−0.848840	+	0.745034i
$247$	−4.05663	−	4.05663i	−0.258117	−	0.258117i
$248$	−4.36154	−	3.46077i	−0.276958	−	0.219759i
$249$	−0.0648187	+	0.00598302i	−0.00410772	+	0.000379158i
$250$	10.2572	−	4.44860i	0.648722	−	0.281354i
$251$	−13.6055	+	18.7264i	−0.858772	+	1.18200i	0.123089	+	0.992396i	$0.460720\pi$
$251$	−13.6055	+	18.7264i	−0.858772	+	1.18200i	−0.981861	+	0.189603i	$0.939280\pi$
$252$	−8.46607	+	6.50737i	−0.533312	+	0.409926i
$253$	7.37063	−	7.37063i	0.463387	−	0.463387i
$254$	−6.41732			−0.402659
$255$	−0.913520	+	27.3823i	−0.0572068	+	1.71475i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−11.7333	−	5.97843i	−0.731905	−	0.372924i	0.0479789	−	0.998848i	$-0.484722\pi$
$257$	−11.7333	−	5.97843i	−0.731905	−	0.372924i	−0.779884	+	0.625924i	$0.784722\pi$
$258$	−4.03756	−	0.262960i	−0.251368	−	0.0163712i
$259$	−20.0329	−	6.50908i	−1.24478	−	0.404455i
$260$	0.150403	+	4.74489i	0.00932759	+	0.294265i
$261$	−5.23202	+	10.9925i	−0.323854	+	0.680421i
$262$	1.37939	−	2.70721i	0.0852190	−	0.167252i
$263$	3.26607	+	20.6212i	0.201395	+	1.27156i	0.856551	+	0.516062i	$0.172603\pi$
$263$	3.26607	+	20.6212i	0.201395	+	1.27156i	−0.655156	+	0.755493i	$0.727397\pi$
$264$	4.28590	−	7.21073i	0.263779	−	0.443790i
$265$	−7.98581	−	2.31774i	−0.490564	−	0.142378i
$266$	−5.65339	+	7.78123i	−0.346632	+	0.477098i
$267$	−0.874126	+	13.4216i	−0.0534956	+	0.821387i
$268$	5.72557	+	11.2371i	0.349745	+	0.686413i
$269$	0.809753	−	0.588320i	0.0493715	−	0.0358705i	−0.562826	−	0.826576i	$-0.690286\pi$
$269$	0.809753	−	0.588320i	0.0493715	−	0.0358705i	0.612197	+	0.790705i	$0.290286\pi$
$270$	8.26778	−	8.16356i	0.503161	−	0.496819i
$271$	4.01992	+	12.3720i	0.244193	+	0.751548i	0.995768	+	0.0919010i	$0.0292943\pi$
$271$	4.01992	+	12.3720i	0.244193	+	0.751548i	−0.751575	+	0.659647i	$0.770706\pi$
$272$	−3.21154	−	6.30300i	−0.194728	−	0.382175i
$273$	8.36513	−	10.0664i	0.506280	−	0.609248i
$274$		−	16.4056i		−	0.991096i
$275$	24.1663	−	1.53358i	1.45728	−	0.0924785i
$276$	−1.90474	+	3.20459i	−0.114652	+	0.192894i
$277$	−27.2276	−	4.31242i	−1.63595	−	0.259108i	−0.730294	−	0.683132i	$-0.760617\pi$
$277$	−27.2276	−	4.31242i	−1.63595	−	0.259108i	−0.905651	+	0.424024i	$0.860617\pi$
$278$	−5.06840	−	5.06840i	−0.303983	−	0.303983i
$279$	−4.91597	−	15.9635i	−0.294312	−	0.955710i
$280$	7.81755	−	1.49348i	0.467188	−	0.0892522i
$281$	−17.0304	−	23.4403i	−1.01595	−	1.39833i	−0.915006	−	0.403440i	$-0.867814\pi$
$281$	−17.0304	−	23.4403i	−1.01595	−	1.39833i	−0.100942	−	0.994892i	$-0.532186\pi$
$282$	0.970318	+	3.81403i	0.0577816	+	0.227122i
$283$	7.08811	+	13.9112i	0.421344	+	0.826934i	0.999936	+	0.0113172i	$0.00360245\pi$
$283$	7.08811	+	13.9112i	0.421344	+	0.826934i	−0.578592	+	0.815617i	$0.696398\pi$
$284$	−13.1574			−0.780751
$285$	5.05959	−	9.16136i	0.299704	−	0.542672i
$286$	−3.17727	+	9.77864i	−0.187876	+	0.578223i
$287$	−32.4351	−	16.5265i	−1.91458	−	0.975530i
$288$	−0.849668	+	2.87716i	−0.0500672	+	0.169538i
$289$	19.4215	+	26.7314i	1.14244	+	1.57243i
$290$	7.16842	−	5.56351i	0.420944	−	0.326701i
$291$	14.5064	−	12.7324i	0.850380	−	0.746385i
$292$	1.10377	+	6.96894i	0.0645934	+	0.407827i
$293$	−1.11404	+	2.18642i	−0.0650828	+	0.127732i	−0.921256	−	0.388957i	$-0.872836\pi$
$293$	−1.11404	+	2.18642i	−0.0650828	+	0.127732i	0.856173	+	0.516689i	$0.172836\pi$
$294$	−8.44044	−	5.01681i	−0.492257	−	0.292587i
$295$	−3.29297	+	7.00285i	−0.191724	+	0.407722i
$296$	−5.62826	+	1.82873i	−0.327136	+	0.106293i
$297$	22.8402	−	10.5639i	1.32533	−	0.612977i
$298$	−0.366516	+	2.31409i	−0.0212317	+	0.134052i
$299$	1.41204	−	4.34582i	0.0816605	−	0.251325i
$300$	−8.24083	+	2.66247i	−0.475784	+	0.153718i
$301$	−2.56939	−	7.90776i	−0.148097	−	0.455796i
$302$	9.51323	+	4.84723i	0.547425	+	0.278927i
$303$	3.72317	−	2.35130i	0.213891	−	0.135078i
$304$			2.70222i			0.154983i
$305$	2.16023	+	11.3077i	0.123695	+	0.647475i
$306$	2.75264	−	21.0428i	0.157358	−	1.20294i
$307$	−1.21923	−	7.69794i	−0.0695853	−	0.439345i	−0.997742	−	0.0671560i	$-0.978607\pi$
$307$	−1.21923	−	7.69794i	−0.0695853	−	0.439345i	0.928157	−	0.372189i	$-0.121393\pi$
$308$	17.0256	+	2.69659i	0.970124	+	0.153653i
$309$	−3.21317	−	34.8107i	−0.182791	−	1.98031i
$310$	−2.07959	+	12.2750i	−0.118113	+	0.697172i
$311$			24.3298i			1.37961i	0.723993	+	0.689807i	$0.242305\pi$
$311$			24.3298i			1.37961i	−0.723993	+	0.689807i	$0.757695\pi$
$312$	0.238985	−	3.66945i	0.0135299	−	0.207742i
$313$	15.5540	−	2.46351i	0.879162	−	0.139246i	0.299494	−	0.954098i	$-0.403182\pi$
$313$	15.5540	−	2.46351i	0.879162	−	0.139246i	0.579668	+	0.814853i	$0.303182\pi$
$314$	−5.47205	+	16.8412i	−0.308806	+	0.950406i
$315$	21.8736	+	9.57321i	1.23244	+	0.539389i
$316$	−4.84455			−0.272527
$317$	−5.35228	−	10.5044i	−0.300614	−	0.589989i	0.690449	−	0.723381i	$-0.257413\pi$
$317$	−5.35228	−	10.5044i	−0.300614	−	0.589989i	−0.991063	+	0.133392i	$0.957413\pi$
$318$	5.98349	+	2.38430i	0.335537	+	0.133705i
$319$	18.6912	−	6.07313i	1.04651	−	0.340030i
$320$	1.53025	−	1.63044i	0.0855437	−	0.0911443i
$321$	−24.6702	−	5.57157i	−1.37695	−	0.310975i
$322$	−7.56651	−	1.19842i	−0.421665	−	0.0667852i
$323$	−2.99033	−	18.8802i	−0.166387	−	1.05052i
$324$	−6.98494	+	5.67544i	−0.388052	+	0.315302i
$325$	9.13403	−	5.40855i	0.506665	−	0.300012i
$326$	14.2313	−	19.5877i	0.788199	−	1.08486i
$327$	3.16250	−	7.93640i	0.174887	−	0.438884i
$328$	−10.1015	+	1.59992i	−0.557761	+	0.0883407i
$329$	−6.54288	+	4.75368i	−0.360721	+	0.262079i
$330$	−18.7464	−	0.625410i	−1.03195	−	0.0344277i
$331$	1.79794	−	1.30628i	0.0988239	−	0.0717998i	−0.537276	−	0.843407i	$-0.680547\pi$
$331$	1.79794	−	1.30628i	0.0988239	−	0.0717998i	0.636100	+	0.771607i	$0.280547\pi$
$332$	−0.0334860	−	0.0170620i	−0.00183778	−	0.000936396i
$333$	−17.0268	−	5.02825i	−0.933061	−	0.275547i
$334$	−10.0961	−	3.28041i	−0.552432	−	0.179496i
$335$	15.8447	−	23.3284i	0.865689	−	1.27457i
$336$	−6.13886	+	0.566641i	−0.334902	+	0.0309128i
$337$	8.58519	−	4.37437i	0.467665	−	0.238287i	−0.204245	−	0.978920i	$-0.565474\pi$
$337$	8.58519	−	4.37437i	0.467665	−	0.238287i	0.671910	+	0.740633i	$0.265474\pi$
$338$	−1.32855	−	8.38812i	−0.0722635	−	0.456254i
$339$	8.51100	−	7.47017i	0.462254	−	0.405724i
$340$	−8.88748	+	13.0852i	−0.481991	+	0.709643i
$341$	−13.2498	+	23.4847i	−0.717515	+	1.27177i
$342$	−4.58614	+	6.68471i	−0.247990	+	0.361468i
$343$	−0.741158	+	4.67949i	−0.0400188	+	0.252669i
$344$	−1.88988	−	1.37308i	−0.101896	−	0.0740316i
$345$	8.33126	+	0.277944i	0.448540	+	0.0149640i
$346$	−10.9719			−0.589856
$347$	12.8385	−	12.8385i	0.689207	−	0.689207i	−0.272850	−	0.962057i	$-0.587966\pi$
$347$	12.8385	−	12.8385i	0.689207	−	0.689207i	0.962057	+	0.272850i	$0.0879661\pi$
$348$	−5.94286	+	3.75310i	−0.318571	+	0.201187i
$349$	−20.1456	+	6.54571i	−1.07837	+	0.350384i	−0.793742	−	0.608254i	$-0.791870\pi$
$349$	−20.1456	+	6.54571i	−1.07837	+	0.350384i	−0.284628	+	0.958638i	$0.591870\pi$
$350$	−11.3515	−	13.7064i	−0.606762	−	0.732640i
$351$	6.81889	−	8.67181i	0.363965	−	0.462867i
$352$	4.31513	−	2.19867i	0.229997	−	0.117189i
$353$	−7.88811	−	1.24935i	−0.419842	−	0.0664964i	−0.0570606	−	0.998371i	$-0.518173\pi$
$353$	−7.88811	−	1.24935i	−0.419842	−	0.0664964i	−0.362781	+	0.931874i	$0.618173\pi$
$354$	3.06265	−	5.15270i	0.162778	−	0.273863i
$355$	14.1806	+	25.7779i	0.752630	+	1.36815i
$356$	−4.56437	+	6.28231i	−0.241911	+	0.332962i
$357$	42.2647	−	10.7525i	2.23689	−	0.569081i
$358$	11.7283	+	5.97586i	0.619859	+	0.315834i
$359$	−12.2373	−	8.89091i	−0.645859	−	0.469244i	0.215999	−	0.976394i	$-0.430699\pi$
$359$	−12.2373	−	8.89091i	−0.645859	−	0.469244i	−0.861858	+	0.507149i	$0.830699\pi$
$360$	6.55265	−	1.43625i	0.345355	−	0.0756968i
$361$	3.61488	−	11.1255i	0.190257	−	0.585551i
$362$	−1.79380	+	11.3256i	−0.0942802	+	0.595262i
$363$	−20.0394	−	7.98532i	−1.05180	−	0.419121i
$364$	7.18679	−	2.33513i	0.376690	−	0.122394i
$365$	12.4639	−	9.67339i	0.652389	−	0.506328i
$366$	−0.819615	−	8.87953i	−0.0428420	−	0.464141i
$367$	2.91576	+	2.91576i	0.152202	+	0.152202i	0.779101	−	0.626899i	$-0.215676\pi$
$367$	2.91576	+	2.91576i	0.152202	+	0.152202i	−0.626899	+	0.779101i	$0.715676\pi$
$368$	−1.91773	+	0.977132i	−0.0999685	+	0.0509365i
$369$	−27.7042	−	13.1861i	−1.44222	−	0.686442i
$370$	9.64878	+	9.05588i	0.501616	+	0.470793i
$371$			13.2363i			0.687192i
$372$	2.52154	−	9.30816i	0.130736	−	0.482606i
$373$	−17.2553	+	17.2553i	−0.893448	+	0.893448i	−0.994846	−	0.101398i	$-0.967668\pi$
$373$	−17.2553	+	17.2553i	−0.893448	+	0.893448i	0.101398	+	0.994846i	$0.467668\pi$
$374$	−27.7164	+	20.1372i	−1.43318	+	1.04127i
$375$	14.0980	+	13.2758i	0.728016	+	0.685560i
$376$	−0.702141	+	2.16097i	−0.0362101	+	0.111443i
$377$	6.09202	−	6.09202i	0.313755	−	0.313755i
$378$	−16.1479	−	9.01698i	−0.830558	−	0.463783i
$379$	−3.89559	−	1.26575i	−0.200103	−	0.0650173i	0.207251	−	0.978288i	$-0.433548\pi$
$379$	−3.89559	−	1.26575i	−0.200103	−	0.0650173i	−0.407354	+	0.913270i	$0.633548\pi$
$380$	5.29416	−	2.91236i	0.271585	−	0.149401i
$381$	−4.39185	−	10.2107i	−0.225001	−	0.523108i
$382$	16.6184	+	2.63210i	0.850272	+	0.134670i
$383$	30.7762	−	15.6813i	1.57259	−	0.801275i	0.572761	−	0.819722i	$-0.305872\pi$
$383$	30.7762	−	15.6813i	1.57259	−	0.801275i	0.999830	+	0.0184471i	$0.00587223\pi$
$384$	−1.30175	+	1.14256i	−0.0664298	+	0.0583059i
$385$	−13.0665	−	36.2627i	−0.665930	−	1.84812i
$386$	21.9150	−	7.12062i	1.11544	−	0.362430i
$387$	−2.34480	−	6.60417i	−0.119193	−	0.335709i
$388$	11.0065	−	1.74326i	0.558772	−	0.0885009i
$389$	2.61102	+	8.03590i	0.132384	+	0.407436i	0.995174	−	0.0981264i	$-0.0312849\pi$
$389$	2.61102	+	8.03590i	0.132384	+	0.407436i	−0.862790	+	0.505563i	$0.831285\pi$
$390$	−7.44671	+	3.48659i	−0.377079	+	0.176550i
$391$	12.3177	−	8.94935i	0.622934	−	0.452588i
$392$	−2.57363	−	5.05103i	−0.129988	−	0.255116i
$393$	5.25148	+	0.342021i	0.264902	+	0.0172527i
$394$	10.6491	−	3.46010i	0.536493	−	0.174317i
$395$	5.22129	+	9.49139i	0.262712	+	0.477564i
$396$	14.4062	+	1.88450i	0.723940	+	0.0946998i
$397$	−16.2890	−	16.2890i	−0.817521	−	0.817521i	0.168227	−	0.985748i	$-0.446196\pi$
$397$	−16.2890	−	16.2890i	−0.817521	−	0.817521i	−0.985748	+	0.168227i	$0.946196\pi$
$398$	10.3181	+	10.3181i	0.517201	+	0.517201i
$399$	−16.2498	−	3.66990i	−0.813509	−	0.183725i
$400$	−4.84359	−	1.24082i	−0.242179	−	0.0620411i
$401$	0.0959110	+	0.132010i	0.00478957	+	0.00659228i	0.811405	−	0.584484i	$-0.198703\pi$
$401$	0.0959110	+	0.132010i	0.00478957	+	0.00659228i	−0.806615	+	0.591077i	$0.798703\pi$
$402$	−13.9610	+	16.8004i	−0.696310	+	0.837926i
$403$	−0.501406	+	11.8100i	−0.0249768	+	0.588297i
$404$	2.54235			0.126487
$405$	18.6474	+	7.56803i	0.926596	+	0.376058i
$406$	−11.6854	−	8.48996i	−0.579938	−	0.421350i
$407$	13.0115	+	25.5365i	0.644957	+	1.26580i
$408$	7.83087	−	9.42352i	0.387686	−	0.466534i
$409$			19.8779i			0.982897i	0.870907	+	0.491449i	$0.163532\pi$
$409$			19.8779i			0.982897i	−0.870907	+	0.491449i	$0.836468\pi$
$410$	14.0216	+	18.0664i	0.692476	+	0.892235i
$411$	26.1031	−	11.2275i	1.28757	−	0.553814i
$412$	9.16308	−	17.9836i	0.451433	−	0.885986i
$413$	12.1663	+	1.92695i	0.598664	+	0.0948191i
$414$	−6.40241	−	0.837510i	−0.314661	−	0.0411614i
$415$	0.00266244	+	0.0839941i	0.000130694	+	0.00412311i
$416$	1.24789	−	1.71758i	0.0611830	−	0.0842112i
$417$	4.59570	−	11.5331i	0.225053	−	0.564777i
$418$	12.9257	−	2.04723i	0.632217	−	0.100133i
$419$	21.6837	+	15.7541i	1.05932	+	0.769638i	0.973962	−	0.226712i	$-0.0727977\pi$
$419$	21.6837	+	15.7541i	1.05932	+	0.769638i	0.0853544	+	0.996351i	$0.472798\pi$
$420$	7.72641	+	11.4165i	0.377010	+	0.557067i
$421$	3.82071	+	2.77591i	0.186210	+	0.135289i	0.676985	−	0.735997i	$-0.263286\pi$
$421$	3.82071	+	2.77591i	0.186210	+	0.135289i	−0.490775	+	0.871286i	$0.663286\pi$
$422$	3.67114	−	23.1787i	0.178708	−	1.12832i
$423$	−5.40448	+	4.15411i	−0.262775	+	0.201980i
$424$	2.18582	+	3.00852i	0.106153	+	0.146107i
$425$	35.2149	+	3.30951i	1.70818	+	0.160535i
$426$	−9.00461	−	20.9349i	−0.436275	−	1.01430i
$427$	16.3276	−	8.31932i	0.790148	−	0.402600i
$428$	−10.3252	−	10.3252i	−0.499087	−	0.499087i
$429$	−17.7333	+	1.63686i	−0.856174	+	0.0790282i
$430$	−0.653273	+	5.18250i	−0.0315036	+	0.249922i
$431$	−5.03931	+	6.93602i	−0.242735	+	0.334096i	−0.912950	−	0.408070i	$-0.866202\pi$
$431$	−5.03931	+	6.93602i	−0.242735	+	0.334096i	0.670215	+	0.742167i	$0.266202\pi$
$432$	−5.15937	+	0.617140i	−0.248230	+	0.0296921i
$433$	−21.9174	+	21.9174i	−1.05328	+	1.05328i	−0.0547857	+	0.998498i	$0.517448\pi$
$433$	−21.9174	+	21.9174i	−1.05328	+	1.05328i	−0.998498	+	0.0547857i	$0.982552\pi$
$434$	19.6875	−	2.26709i	0.945029	−	0.108824i
$435$	13.7580	+	7.59822i	0.659647	+	0.364307i
$436$	3.99045	−	2.89923i	0.191108	−	0.138848i
$437$	−5.74443	+	0.909829i	−0.274794	+	0.0435230i
$438$	−10.3330	+	6.52559i	−0.493728	+	0.311805i
$439$		−	30.4974i		−	1.45556i	−0.685810	−	0.727781i	$-0.740552\pi$
$439$		−	30.4974i		−	1.45556i	0.685810	−	0.727781i	$-0.259448\pi$
$440$	−8.95831	−	6.08451i	−0.427071	−	0.290068i
$441$	2.20588	−	16.8631i	0.105042	−	0.803002i
$442$	−6.81824	+	13.3815i	−0.324311	+	0.636495i
$443$	−3.78285	+	7.42426i	−0.179729	+	0.352737i	−0.963241	−	0.268639i	$-0.913426\pi$
$443$	−3.78285	+	7.42426i	−0.179729	+	0.352737i	0.783512	+	0.621376i	$0.213426\pi$
$444$	−6.76155	−	7.70365i	−0.320889	−	0.365599i
$445$	17.2276	+	2.17160i	0.816664	+	0.102944i
$446$	8.34045	+	11.4796i	0.394932	+	0.543577i
$447$	−3.93281	+	1.00054i	−0.186015	+	0.0473237i
$448$	−3.17140	−	1.61591i	−0.149834	−	0.0763444i
$449$	9.04647	+	6.57265i	0.426929	+	0.310182i	0.780420	−	0.625256i	$-0.215005\pi$
$449$	9.04647	+	6.57265i	0.426929	+	0.310182i	−0.353491	+	0.935438i	$0.615005\pi$
$450$	−9.87610	−	11.2899i	−0.465564	−	0.532213i
$451$	15.3060	+	47.1069i	0.720730	+	2.21818i
$452$	6.45762	−	1.02279i	0.303741	−	0.0481078i
$453$	−1.20187	+	18.4539i	−0.0564690	+	0.867040i
$454$	−3.42483	−	1.11280i	−0.160735	−	0.0522261i
$455$	−12.3206	−	11.5636i	−0.577600	−	0.542108i
$456$	−4.29953	+	1.84933i	−0.201344	+	0.0866028i
$457$	−5.55166	+	10.8957i	−0.259696	+	0.509682i	−0.983633	−	0.180184i	$-0.942331\pi$
$457$	−5.55166	+	10.8957i	−0.259696	+	0.509682i	0.723937	+	0.689866i	$0.242331\pi$
$458$	−23.8755	+	12.1652i	−1.11563	+	0.568441i
$459$	35.3652	−	10.0214i	1.65071	−	0.467758i
$460$	3.98125	+	2.70407i	0.185627	+	0.126078i
$461$	25.9931	+	8.44567i	1.21062	+	0.393354i	0.843658	−	0.536882i	$-0.180398\pi$
$461$	25.9931	+	8.44567i	1.21062	+	0.393354i	0.366962	+	0.930236i	$0.380398\pi$
$462$	7.36131	+	28.9351i	0.342479	+	1.34618i
$463$	−4.03918	+	25.5024i	−0.187717	+	1.18520i	0.696304	+	0.717747i	$0.254827\pi$
$463$	−4.03918	+	25.5024i	−0.187717	+	1.18520i	−0.884020	+	0.467449i	$0.845173\pi$
$464$	−4.05805			−0.188390
$465$	−20.9541	+	5.09183i	−0.971722	+	0.236128i
$466$	5.40818			0.250529
$467$	2.85264	−	18.0108i	0.132004	−	0.833443i	−0.829471	−	0.558550i	$-0.811358\pi$
$467$	2.85264	−	18.0108i	0.132004	−	0.833443i	0.961475	−	0.274892i	$-0.0886422\pi$
$468$	6.00205	−	2.13102i	0.277445	−	0.0985065i
$469$	−42.6921	−	13.8715i	−1.97134	−	0.640527i
$470$	4.99048	−	0.953389i	0.230194	−	0.0439766i
$471$	−30.5412	+	2.81907i	−1.40726	+	0.129896i
$472$	3.08354	−	1.57114i	0.141931	−	0.0723177i
$473$	−5.13615	+	10.0803i	−0.236160	+	0.463491i
$474$	−3.31549	−	7.70822i	−0.152285	−	0.354050i
$475$	−11.4117	−	7.23342i	−0.523606	−	0.331892i
$476$	23.9465	+	7.78069i	1.09759	+	0.356627i
$477$	0.301254	+	11.1521i	0.0137935	+	0.510622i
$478$	−16.3886	+	2.59570i	−0.749597	+	0.118724i
$479$	−5.94075	−	18.2837i	−0.271440	−	0.835406i	−0.990139	−	0.140085i	$-0.955262\pi$
$479$	−5.94075	−	18.2837i	−0.271440	−	0.835406i	0.718700	−	0.695321i	$-0.244738\pi$
$480$	3.64147	+	1.31897i	0.166210	+	0.0602024i
$481$	10.1645	+	7.38492i	0.463460	+	0.336723i
$482$	−9.08859	−	4.63087i	−0.413974	−	0.210930i
$483$	−3.27151	−	12.8593i	−0.148859	−	0.585120i
$484$	−7.32058	−	10.0759i	−0.332753	−	0.457996i
$485$	−15.2779	−	19.6851i	−0.693732	−	0.893853i
$486$	−13.8106	−	7.22969i	−0.626460	−	0.327945i
$487$	12.0754	−	23.6994i	0.547190	−	1.07392i	−0.437437	−	0.899249i	$-0.644114\pi$
$487$	12.0754	−	23.6994i	0.547190	−	1.07392i	0.984627	−	0.174671i	$-0.0558862\pi$
$488$	2.33732	−	4.58725i	0.105806	−	0.207655i
$489$	40.9057	+	9.23825i	1.84982	+	0.417768i
$490$	−7.12216	+	10.4861i	−0.321746	+	0.473712i
$491$		−	17.4960i		−	0.789585i	−0.918770	−	0.394792i	$-0.870817\pi$
$491$		−	17.4960i		−	0.789585i	0.918770	−	0.394792i	$-0.129183\pi$
$492$	−9.45884	−	14.9776i	−0.426437	−	0.675244i
$493$	28.3533	−	4.49072i	1.27697	−	0.202252i
$494$	4.64128	−	3.37209i	0.208821	−	0.151717i
$495$	−11.8344	−	30.2556i	−0.531918	−	1.35989i
$496$	4.10046	−	3.76646i	0.184116	−	0.169119i
$497$	33.1151	−	33.1151i	1.48542	−	1.48542i
$498$	0.00423052	−	0.0649566i	0.000189574	−	0.00291078i
$499$	−21.8181	+	30.0300i	−0.976712	+	1.34433i	−0.0381296	+	0.999273i	$0.512140\pi$
$499$	−21.8181	+	30.0300i	−0.976712	+	1.34433i	−0.938582	+	0.345056i	$0.887860\pi$
$500$	2.78925	+	10.8268i	0.124739	+	0.484190i
$501$	−1.68999	−	18.3090i	−0.0755032	−	0.817985i
$502$	−16.3675	−	16.3675i	−0.730515	−	0.730515i
$503$	23.0351	−	11.7370i	1.02709	−	0.523326i	0.142544	−	0.989788i	$-0.454472\pi$
$503$	23.0351	−	11.7370i	1.02709	−	0.523326i	0.884541	+	0.466462i	$0.154472\pi$
$504$	−5.10287	−	9.37981i	−0.227300	−	0.417810i
$505$	−2.74005	−	4.98094i	−0.121931	−	0.221649i
$506$	6.12686	+	8.43290i	0.272372	+	0.374888i
$507$	12.4372	−	7.85448i	0.552356	−	0.348830i
$508$	1.00389	−	6.33831i	0.0445404	−	0.281217i
$509$	7.10224	+	5.16008i	0.314801	+	0.228716i	0.733954	−	0.679199i	$-0.237673\pi$
$509$	7.10224	+	5.16008i	0.314801	+	0.228716i	−0.419153	+	0.907916i	$0.637673\pi$
$510$	−26.9023	−	5.18581i	−1.19125	−	0.229632i
$511$	−20.3177	−	14.7617i	−0.898801	−	0.653017i
$512$	−0.987688	+	0.156434i	−0.0436501	+	0.00691349i
$513$	−13.7747	−	2.72222i	−0.608170	−	0.120189i
$514$	7.74032	−	10.6536i	0.341411	−	0.469912i
$515$	−45.1088	+	1.42986i	−1.98773	+	0.0630069i
$516$	0.891336	−	3.94672i	0.0392389	−	0.173745i
$517$	10.8686	+	1.72142i	0.478002	+	0.0757080i
$518$	9.56278	−	18.7680i	0.420164	−	0.824619i
$519$	−7.50892	−	17.4576i	−0.329605	−	0.766303i
$520$	−4.71000	−	0.593713i	−0.206547	−	0.0260360i
$521$			7.24754i			0.317520i	0.987317	+	0.158760i	$0.0507497\pi$
$521$			7.24754i			0.317520i	−0.987317	+	0.158760i	$0.949250\pi$
$522$	−10.0387	−	6.88722i	−0.439383	−	0.301445i
$523$	0.482111	+	0.946197i	0.0210813	+	0.0413743i	0.901307	−	0.433181i	$-0.142609\pi$
$523$	0.482111	+	0.946197i	0.0210813	+	0.0413743i	−0.880226	+	0.474555i	$0.842609\pi$
$524$	2.45809	+	1.78591i	0.107382	+	0.0780178i
$525$	14.0398	−	27.4418i	0.612747	−	1.19766i
$526$	−20.8782			−0.910333
$527$	−24.4816	+	30.8536i	−1.06643	+	1.34401i
$528$	6.45149	+	5.36114i	0.280765	+	0.233314i
$529$	10.7962	+	14.8596i	0.469398	+	0.646071i
$530$	3.53846	−	7.52491i	0.153701	−	0.326861i
$531$	10.2945	+	1.34664i	0.446744	+	0.0584393i
$532$	−6.80104	−	6.80104i	−0.294863	−	0.294863i
$533$	15.3536	+	15.3536i	0.665037	+	0.665037i
$534$	−13.1196	−	2.96296i	−0.567740	−	0.128220i
$535$	−9.10087	+	31.3572i	−0.393465	+	1.35569i
$536$	−11.9944	+	3.89721i	−0.518079	+	0.168334i
$537$	−1.48172	+	22.7507i	−0.0639408	+	0.981765i
$538$	0.454404	+	0.891818i	0.0195907	+	0.0384490i
$539$	−22.2111	+	16.1373i	−0.956700	+	0.695083i
$540$	6.76969	+	9.44306i	0.291321	+	0.406364i
$541$	2.43100	+	7.48186i	0.104517	+	0.321670i	0.989617	−	0.143731i	$-0.0459100\pi$
$541$	2.43100	+	7.48186i	0.104517	+	0.321670i	−0.885100	+	0.465401i	$0.845910\pi$
$542$	−12.8486	+	2.03502i	−0.551894	+	0.0874114i
$543$	−19.2480	+	4.89683i	−0.826009	+	0.210143i
$544$	6.72779	−	2.18599i	0.288452	−	0.0937237i
$545$	−9.98092	−	4.69336i	−0.427536	−	0.201041i
$546$	8.63390	+	9.83687i	0.369497	+	0.420979i
$547$	26.7408	−	13.6251i	1.14336	−	0.582569i	0.223453	−	0.974715i	$-0.428267\pi$
$547$	26.7408	−	13.6251i	1.14336	−	0.582569i	0.919903	+	0.392146i	$0.128267\pi$
$548$	16.2036	+	2.56640i	0.692183	+	0.109631i
$549$	13.5674	−	7.38102i	0.579042	−	0.315014i
$550$	−2.26574	+	24.1087i	−0.0966116	+	1.02800i
$551$	−10.4290	−	3.38860i	−0.444292	−	0.144359i
$552$	−2.86717	−	2.38259i	−0.122035	−	0.101410i
$553$	12.1929	−	12.1929i	0.518496	−	0.518496i
$554$	8.51866	−	26.2177i	0.361923	−	1.11388i
$555$	−7.80553	+	21.5499i	−0.331326	+	0.914741i
$556$	5.79887	−	4.21313i	0.245927	−	0.178676i
$557$	2.09506	−	2.09506i	0.0887704	−	0.0887704i	−0.661327	−	0.750098i	$-0.730007\pi$
$557$	2.09506	−	2.09506i	0.0887704	−	0.0887704i	0.750098	+	0.661327i	$0.230007\pi$
$558$	16.5360	−	2.35821i	0.700024	−	0.0998309i
$559$			4.95949i			0.209764i
$560$	0.252155	+	7.95493i	0.0106555	+	0.336157i
$561$	−51.0088	−	30.3185i	−2.15359	−	1.28005i
$562$	25.8159	−	13.1538i	1.08898	−	0.554862i
$563$	−30.9964	−	30.9964i	−1.30634	−	1.30634i	−0.924037	−	0.382304i	$-0.875131\pi$
$563$	−30.9964	−	30.9964i	−1.30634	−	1.30634i	−0.382304	−	0.924037i	$-0.624869\pi$
$564$	−3.91886	+	0.361726i	−0.165014	+	0.0152314i
$565$	−8.96363	−	11.5494i	−0.377103	−	0.485886i
$566$	−14.8487	+	4.82465i	−0.624139	+	0.202795i
$567$	3.29580	−	31.8641i	0.138411	−	1.33817i
$568$	2.05828	−	12.9955i	0.0863634	−	0.545277i
$569$	−10.6812	+	32.8733i	−0.447778	+	1.37812i	0.431630	+	0.902051i	$0.357939\pi$
$569$	−10.6812	+	32.8733i	−0.447778	+	1.37812i	−0.879408	+	0.476069i	$0.842061\pi$
$570$	8.25707	+	6.43045i	0.345851	+	0.269342i
$571$	−6.95115	−	5.05031i	−0.290897	−	0.211349i	0.432760	−	0.901509i	$-0.357540\pi$
$571$	−6.95115	−	5.05031i	−0.290897	−	0.211349i	−0.723656	+	0.690161i	$0.757540\pi$
$572$	−9.16122	−	4.66787i	−0.383050	−	0.195174i
$573$	7.18525	+	28.2431i	0.300168	+	1.17987i
$574$	21.3970	−	29.4505i	0.893095	−	1.22924i
$575$	1.00694	−	10.7144i	0.0419923	−	0.446820i
$576$	−2.70882	−	1.28929i	−0.112868	−	0.0537206i
$577$	−30.1994	−	4.78311i	−1.25722	−	0.199124i	−0.507947	−	0.861388i	$-0.669595\pi$
$577$	−30.1994	−	4.78311i	−1.25722	−	0.199124i	−0.749270	+	0.662265i	$0.769595\pi$
$578$	−29.4404	+	15.0007i	−1.22456	+	0.623945i
$579$	26.3278	+	29.9960i	1.09414	+	1.24659i
$580$	4.37363	+	7.95049i	0.181605	+	0.330126i
$581$	0.127221	−	0.0413365i	0.00527800	−	0.00171493i
$582$	10.3063	+	16.3196i	0.427211	+	0.676468i
$583$	12.7348	−	12.7348i	0.527423	−	0.527423i
$584$	−7.05581			−0.291972
$585$	−10.6439	−	9.46241i	−0.440070	−	0.391222i
$586$	−1.98523	−	1.44235i	−0.0820091	−	0.0595831i
$587$	7.49305	−	47.3093i	0.309271	−	1.95266i	0.00528669	−	0.999986i	$-0.498317\pi$
$587$	7.49305	−	47.3093i	0.309271	−	1.95266i	0.303985	−	0.952677i	$-0.401683\pi$
$588$	6.27542	−	7.55172i	0.258794	−	0.311428i
$589$	13.6832	−	6.25566i	0.563805	−	0.257760i
$590$	−6.40150	−	4.34791i	−0.263545	−	0.179001i
$591$	12.7934	+	14.5759i	0.526249	+	0.599571i
$592$	−0.925764	−	5.84504i	−0.0380487	−	0.240230i
$593$	35.5940	−	18.1360i	1.46167	−	0.744758i	0.471141	−	0.882058i	$-0.343842\pi$
$593$	35.5940	−	18.1360i	1.46167	−	0.744758i	0.990530	+	0.137300i	$0.0438425\pi$
$594$	6.86079	+	24.2116i	0.281502	+	0.993414i
$595$	−10.5649	−	55.3015i	−0.433118	−	2.26714i
$596$	−2.22826	−	0.724007i	−0.0912733	−	0.0296565i
$597$	−9.35582	+	23.4787i	−0.382908	+	0.960921i
$598$	4.07142	+	2.07449i	0.166493	+	0.0848324i
$599$	−13.0894	+	9.50997i	−0.534816	+	0.388567i	−0.822156	−	0.569262i	$-0.807229\pi$
$599$	−13.0894	+	9.50997i	−0.534816	+	0.388567i	0.287340	+	0.957829i	$0.407229\pi$
$600$	−1.34054	−	8.55587i	−0.0547275	−	0.349292i
$601$	0.732895	−	0.532479i	0.0298954	−	0.0217203i	−0.572737	−	0.819739i	$-0.694118\pi$
$601$	0.732895	−	0.532479i	0.0298954	−	0.0217203i	0.602633	+	0.798019i	$0.294118\pi$
$602$	8.21234	−	1.30071i	0.334710	−	0.0530129i
$603$	−36.2858	−	10.7157i	−1.47767	−	0.436378i
$604$	−6.27575	+	8.63783i	−0.255357	+	0.351468i
$605$	−11.8507	+	25.2019i	−0.481801	+	1.02460i
$606$	1.73992	+	4.04516i	0.0706793	+	0.164323i
$607$	3.80912	+	24.0499i	0.154608	+	0.976154i	0.935971	+	0.352077i	$0.114525\pi$
$607$	3.80912	+	24.0499i	0.154608	+	0.976154i	−0.781363	+	0.624076i	$0.785475\pi$
$608$	−2.66895	−	0.422721i	−0.108240	−	0.0171436i
$609$	5.51126	−	24.4031i	0.223327	−	0.988864i
$610$	−11.5064	+	0.364728i	−0.465880	+	0.0147674i
$611$	4.58783	−	1.49068i	0.185604	−	0.0603063i
$612$	20.3531	+	6.01057i	0.822726	+	0.242963i
$613$	9.22768	+	18.1103i	0.372702	+	0.731470i	0.998835	−	0.0482466i	$-0.0153633\pi$
$613$	9.22768	+	18.1103i	0.372702	+	0.731470i	−0.626133	+	0.779716i	$0.715363\pi$
$614$	7.79389			0.314536
$615$	−19.1496	+	34.6740i	−0.772186	+	1.39819i
$616$	−5.32678	+	16.3942i	−0.214622	+	0.660539i
$617$	−22.2821	+	3.52914i	−0.897043	+	0.142078i	−0.587896	−	0.808936i	$-0.700044\pi$
$617$	−22.2821	+	3.52914i	−0.897043	+	0.142078i	−0.309147	+	0.951014i	$0.600044\pi$
$618$	34.8848	+	2.27199i	1.40327	+	0.0913929i
$619$		−	7.52175i		−	0.302325i	−0.988509	−	0.151162i	$-0.951698\pi$
$619$		−	7.52175i		−	0.302325i	0.988509	−	0.151162i	$-0.0483016\pi$
$620$	−11.7985	−	3.97421i	−0.473841	−	0.159608i
$621$	−3.04907	−	10.7601i	−0.122355	−	0.431788i
$622$	−24.0302	−	3.80601i	−0.963524	−	0.152607i
$623$	−4.32378	−	27.2993i	−0.173229	−	1.09372i
$624$	3.58688	+	0.810071i	0.143590	+	0.0324288i
$625$	18.2056	−	17.1334i	0.728225	−	0.685338i
$626$			15.7478i			0.629410i
$627$	12.1034	+	19.1651i	0.483362	+	0.765382i
$628$	−15.7779	−	8.03923i	−0.629606	−	0.320800i
$629$	12.9365	+	39.8144i	0.515812	+	1.58751i
$630$	−12.8771	+	20.1067i	−0.513037	+	0.801071i
$631$	4.61327	−	14.1982i	0.183651	−	0.565221i	−0.816271	−	0.577669i	$-0.803963\pi$
$631$	4.61327	−	14.1982i	0.183651	−	0.565221i	0.999923	+	0.0124483i	$0.00396252\pi$
$632$	0.757855	−	4.78491i	0.0301458	−	0.190333i
$633$	39.3923	−	10.0217i	1.56570	−	0.398327i
$634$	11.2124	−	3.64313i	0.445301	−	0.144687i
$635$	−13.4999	+	4.86441i	−0.535728	+	0.193038i
$636$	−3.29097	+	5.53683i	−0.130496	+	0.219550i
$637$	−5.46393	+	10.7236i	−0.216489	+	0.424883i
$638$	3.07442	+	19.4111i	0.121717	+	0.768493i
$639$	27.1473	−	28.6547i	1.07393	−	1.13356i
$640$	1.37098	+	1.76647i	0.0541928	+	0.0698258i
$641$	−14.9714	−	20.6064i	−0.591336	−	0.813904i	0.403545	−	0.914960i	$-0.367778\pi$
$641$	−14.9714	−	20.6064i	−0.591336	−	0.813904i	−0.994881	+	0.101056i	$0.967778\pi$
$642$	9.36223	−	23.4948i	0.369498	−	0.927267i
$643$	0.469021	+	0.238978i	0.0184964	+	0.00942438i	0.463214	−	0.886246i	$-0.346696\pi$
$643$	0.469021	+	0.238978i	0.0184964	+	0.00942438i	−0.444718	+	0.895671i	$0.646696\pi$
$644$	2.36733	−	7.28588i	0.0932858	−	0.287104i
$645$	−8.69301	+	2.50734i	−0.342287	+	0.0987264i
$646$	19.1156			0.752092
$647$	8.30607	+	16.3016i	0.326545	+	0.640881i	0.994663	−	0.103174i	$-0.0328999\pi$
$647$	8.30607	+	16.3016i	0.326545	+	0.640881i	−0.668118	+	0.744055i	$0.732900\pi$
$648$	−4.51288	−	7.78678i	−0.177283	−	0.305894i
$649$	−9.85146	−	13.5594i	−0.386704	−	0.532252i
$650$	3.91308	+	9.86766i	0.153484	+	0.387042i
$651$	17.0808	+	29.7734i	0.669449	+	1.16691i
$652$	17.1203	+	17.1203i	0.670482	+	0.670482i
$653$	5.16324	+	0.817777i	0.202053	+	0.0320021i	0.256641	−	0.966507i	$-0.417384\pi$
$653$	5.16324	+	0.817777i	0.202053	+	0.0320021i	−0.0545874	+	0.998509i	$0.517384\pi$
$654$	7.34396	+	4.36509i	0.287172	+	0.170689i
$655$	0.849685	−	6.74066i	0.0331999	−	0.263379i
$656$		−	10.2274i		−	0.399313i
$657$	−17.4545	−	11.9749i	−0.680967	−	0.467187i
$658$	−3.67162	−	7.20596i	−0.143135	−	0.280918i
$659$	11.3433	+	34.9110i	0.441871	+	1.35994i	0.885879	+	0.463917i	$0.153556\pi$
$659$	11.3433	+	34.9110i	0.441871	+	1.35994i	−0.444007	+	0.896023i	$0.646444\pi$
$660$	3.55029	−	18.4177i	0.138195	−	0.716909i
$661$	18.5797	−	13.4990i	0.722667	−	0.525049i	−0.164568	−	0.986366i	$-0.552623\pi$
$661$	18.5797	−	13.4990i	0.722667	−	0.525049i	0.887235	+	0.461317i	$0.152623\pi$
$662$	1.00894	+	1.98015i	0.0392135	+	0.0769609i
$663$	−25.9577	−	1.69059i	−1.00812	−	0.0656569i
$664$	0.0220903	−	0.0304046i	0.000857268	−	0.00117993i
$665$	−5.99460	+	20.6545i	−0.232460	+	0.800945i
$666$	7.62992	−	16.0305i	0.295653	−	0.621171i
$667$	−1.36633	−	8.62668i	−0.0529046	−	0.334026i
$668$	4.81939	−	9.45859i	0.186468	−	0.365964i
$669$	−12.5574	+	21.1269i	−0.485497	+	0.816815i
$670$	20.5625	+	19.2990i	0.794399	+	0.745585i
$671$	−23.7133	−	7.70490i	−0.915440	−	0.297445i
$672$	0.400665	−	6.15193i	0.0154560	−	0.237316i
$673$	17.9878	+	9.16524i	0.693379	+	0.353294i	0.764904	−	0.644145i	$-0.222787\pi$
$673$	17.9878	+	9.16524i	0.693379	+	0.353294i	−0.0715249	+	0.997439i	$0.522787\pi$
$674$	2.97750	+	9.16379i	0.114689	+	0.352976i
$675$	11.2046	−	23.4405i	0.431265	−	0.902225i
$676$	8.49268			0.326642
$677$	13.4102	−	13.4102i	0.515395	−	0.515395i	−0.400780	−	0.916174i	$-0.631261\pi$
$677$	13.4102	−	13.4102i	0.515395	−	0.515395i	0.916174	+	0.400780i	$0.131261\pi$
$678$	6.04679	+	9.57481i	0.232226	+	0.367718i
$679$	−23.3141	+	32.0891i	−0.894714	+	1.23147i
$680$	−11.5338	−	10.8250i	−0.442299	−	0.415121i
$681$	−0.573286	−	6.21086i	−0.0219684	−	0.238001i
$682$	−21.1229	−	16.7605i	−0.808837	−	0.641792i
$683$	−27.4052	−	27.4052i	−1.04863	−	1.04863i	−0.998756	−	0.0498743i	$-0.984118\pi$
$683$	−27.4052	−	27.4052i	−1.04863	−	1.04863i	−0.0498743	−	0.998756i	$-0.515882\pi$
$684$	−5.88498	−	5.57540i	−0.225018	−	0.213181i
$685$	−12.4356	−	34.5119i	−0.475140	−	1.31863i
$686$	−4.50593	−	1.46407i	−0.172037	−	0.0558983i
$687$	−35.6959	−	29.6630i	−1.36188	−	1.13171i
$688$	1.65182	−	1.65182i	0.0629750	−	0.0629750i
$689$	2.43970	−	7.50863i	0.0929453	−	0.286056i
$690$	−1.57782	+	8.18520i	−0.0600665	+	0.311605i
$691$	−10.2837	−	31.6501i	−0.391212	−	1.20403i	−0.931873	−	0.362786i	$-0.881826\pi$
$691$	−10.2837	−	31.6501i	−0.391212	−	1.20403i	0.540661	−	0.841241i	$-0.318174\pi$
$692$	1.71639	−	10.8369i	0.0652474	−	0.411956i
$693$	−41.0010	+	31.5151i	−1.55750	+	1.19716i
$694$	10.6721	+	14.6888i	0.405106	+	0.557580i
$695$	−14.5041	−	6.82033i	−0.550174	−	0.258710i
$696$	−2.77722	−	6.45680i	−0.105270	−	0.244745i
$697$	11.3178	+	71.4581i	0.428694	+	2.70667i
$698$	−3.31365	−	20.9216i	−0.125424	−	0.791893i
$699$	3.70122	+	8.60501i	0.139993	+	0.325471i
$700$	15.3135	−	9.06757i	0.578794	−	0.342722i
$701$	0.513235	+	0.706407i	0.0193846	+	0.0266806i	0.818599	−	0.574365i	$-0.194751\pi$
$701$	0.513235	+	0.706407i	0.0193846	+	0.0266806i	−0.799215	+	0.601046i	$0.794751\pi$
$702$	7.49834	+	8.09151i	0.283007	+	0.305394i
$703$	2.50162	−	15.7946i	0.0943503	−	0.595705i
$704$	1.49656	+	4.60595i	0.0564039	+	0.173593i
$705$	4.93231	+	7.28794i	0.185761	+	0.274480i
$706$	2.46795	−	7.59556i	0.0928824	−	0.285863i
$707$	−6.39867	+	6.39867i	−0.240647	+	0.240647i
$708$	4.61016	+	3.83100i	0.173260	+	0.143978i
$709$	−39.9969	−	12.9958i	−1.50212	−	0.488067i	−0.561482	−	0.827489i	$-0.689769\pi$
$709$	−39.9969	−	12.9958i	−1.50212	−	0.488067i	−0.940634	+	0.339422i	$0.889769\pi$
$710$	−27.6789	+	9.97350i	−1.03877	+	0.374299i
$711$	9.99559	−	10.5506i	0.374864	−	0.395679i
$712$	−5.49094	−	5.49094i	−0.205782	−	0.205782i
$713$	9.38743	+	7.44868i	0.351562	+	0.278955i
$714$	4.00843	+	43.4264i	0.150012	+	1.62519i
$715$	0.728399	+	22.9794i	0.0272406	+	0.859382i
$716$	−7.73699	+	10.6491i	−0.289145	+	0.397974i
$717$	−15.3460	−	24.2996i	−0.573106	−	0.907487i
$718$	10.6958	−	10.6958i	0.399163	−	0.399163i
$719$	−17.0217			−0.634803			−0.317402	−	0.948291i	$-0.602810\pi$
$719$	−17.0217			−0.634803			−0.317402	+	0.948291i	$0.602810\pi$
$720$	0.393504	+	6.69665i	0.0146650	+	0.249570i
$721$	22.1997	+	68.3236i	0.826759	+	2.54450i
$722$	10.4230	+	5.31078i	0.387904	+	0.197647i
$723$	1.14823	−	17.6302i	0.0427030	−	0.655674i
$724$	−10.9056	−	3.54344i	−0.405303	−	0.131691i
$725$	10.8628	−	17.1375i	0.403433	−	0.636471i
$726$	11.0219	−	18.5435i	0.409060	−	0.688215i
$727$	3.92555	−	7.70432i	0.145590	−	0.285737i	−0.806683	−	0.590985i	$-0.798739\pi$
$727$	3.92555	−	7.70432i	0.145590	−	0.285737i	0.952273	+	0.305248i	$0.0987393\pi$
$728$	1.18212	+	7.46360i	0.0438122	+	0.276620i
$729$	2.05164	−	26.9219i	0.0759867	−	0.997109i
$730$	7.60451	+	13.8237i	0.281456	+	0.511637i
$731$	−9.71321	+	13.3691i	−0.359256	+	0.494473i
$732$	8.89843	+	0.579540i	0.328895	+	0.0214204i
$733$	21.1709	+	41.5502i	0.781964	+	1.53469i	0.843833	+	0.536606i	$0.180294\pi$
$733$	21.1709	+	41.5502i	0.781964	+	1.53469i	−0.0618688	+	0.998084i	$0.519706\pi$
$734$	−3.33599	+	2.42374i	−0.123134	+	0.0894618i
$735$	−21.5587	−	4.15575i	−0.795204	−	0.153287i
$736$	−0.665103	−	2.04698i	−0.0245160	−	0.0754525i
$737$	27.7288	+	54.4209i	1.02141	+	2.00462i
$738$	17.3577	−	25.3004i	0.638945	−	0.931319i
$739$		−	44.7691i		−	1.64686i	−0.567421	−	0.823428i	$-0.692059\pi$
$739$		−	44.7691i		−	1.64686i	0.567421	−	0.823428i	$-0.307941\pi$
$740$	−10.4538	+	8.11333i	−0.384289	+	0.298252i
$741$	8.54173	+	5.07702i	0.313788	+	0.186509i
$742$	−13.0733	−	2.07061i	−0.479936	−	0.0760143i
$743$	27.8874	+	27.8874i	1.02309	+	1.02309i	0.999727	+	0.0233622i	$0.00743711\pi$
$743$	27.8874	+	27.8874i	1.02309	+	1.02309i	0.0233622	+	0.999727i	$0.492563\pi$
$744$	8.79910	+	3.94662i	0.322591	+	0.144690i
$745$	0.983080	+	5.14590i	0.0360173	+	0.188531i
$746$	−14.3436	−	19.7422i	−0.525155	−	0.722814i
$747$	0.106248	−	0.0377234i	0.00388743	−	0.00138023i
$748$	−15.5534	−	30.5253i	−0.568690	−	1.11612i
$749$	51.9736			1.89908
$750$	−15.3178	+	11.8476i	−0.559326	+	0.432613i
$751$	5.16336	−	15.8912i	0.188414	−	0.579877i	−0.811577	−	0.584246i	$-0.801390\pi$
$751$	5.16336	−	15.8912i	0.188414	−	0.579877i	0.999990	+	0.00436829i	$0.00139048\pi$
$752$	−2.02452	−	1.03155i	−0.0738267	−	0.0376166i
$753$	14.8410	−	37.2439i	0.540835	−	1.35724i
$754$	5.06402	+	6.97002i	0.184421	+	0.253833i
$755$	23.6869	+	2.98582i	0.862055	+	0.108665i
$756$	11.4320	−	14.5385i	0.415780	−	0.528761i
$757$	6.15038	+	38.8320i	0.223539	+	1.41137i	0.802809	+	0.596236i	$0.203338\pi$
$757$	6.15038	+	38.8320i	0.223539	+	1.41137i	−0.579270	+	0.815136i	$0.696662\pi$
$758$	1.85957	−	3.64962i	0.0675427	−	0.132560i
$759$	−9.22461	+	15.5198i	−0.334832	+	0.563332i
$760$	2.04832	+	5.68458i	0.0743002	+	0.206201i
$761$	−11.7832	+	3.82859i	−0.427140	+	0.138786i	−0.514695	−	0.857374i	$-0.672095\pi$
$761$	−11.7832	+	3.82859i	−0.427140	+	0.138786i	0.0875547	+	0.996160i	$0.472095\pi$
$762$	10.7720	−	2.74048i	0.390228	−	0.0992770i
$763$	−2.74642	+	17.3402i	−0.0994270	+	0.627757i
$764$	−5.19939	+	16.0021i	−0.188107	+	0.578934i
$765$	−10.1600	−	46.3536i	−0.367337	−	1.67592i
$766$	10.6737	+	32.8504i	0.385658	+	1.18693i
$767$	−6.54649	−	3.33560i	−0.236380	−	0.120442i
$768$	−0.924853	−	1.46446i	−0.0333728	−	0.0528442i
$769$			8.28756i			0.298857i	0.988773	+	0.149429i	$0.0477434\pi$
$769$			8.28756i			0.298857i	−0.988773	+	0.149429i	$0.952257\pi$
$770$	37.8603	−	7.23288i	1.36439	−	0.260655i
$771$	22.2484	+	5.02463i	0.801256	+	0.180958i
$772$	3.60469	+	22.7591i	0.129736	+	0.819118i
$773$	−30.4195	−	4.81798i	−1.09411	−	0.173291i	−0.416810	−	0.908994i	$-0.636852\pi$
$773$	−30.4195	−	4.81798i	−1.09411	−	0.173291i	−0.677304	+	0.735703i	$0.736852\pi$
$774$	6.88967	−	1.28282i	0.247644	−	0.0461099i
$775$	4.92983	+	27.3988i	0.177085	+	0.984196i
$776$			11.1437i			0.400037i
$777$	36.4065	+	2.37110i	1.30608	+	0.0850626i
$778$	−8.34542	+	1.32178i	−0.299198	+	0.0473883i
$779$	8.54021	−	26.2841i	0.305985	−	0.941724i
$780$	−2.27874	−	7.90045i	−0.0815919	−	0.282882i
$781$	−63.7213			−2.28013
$782$	6.91225	+	13.5661i	0.247182	+	0.485121i
$783$	4.08808	−	20.6862i	0.146096	−	0.739263i
$784$	5.39145	−	1.75179i	0.192552	−	0.0625639i
$785$	1.25448	+	39.5763i	0.0447744	+	1.41254i
$786$	−1.15932	+	5.13333i	−0.0413517	+	0.183100i
$787$	−7.75158	−	1.22773i	−0.276314	−	0.0437638i	0.0167395	−	0.999860i	$-0.494671\pi$
$787$	−7.75158	−	1.22773i	−0.276314	−	0.0437638i	−0.293053	+	0.956096i	$0.594671\pi$
$788$	1.75161	+	11.0593i	0.0623987	+	0.393970i
$789$	−14.2885	−	33.2195i	−0.508684	−	1.18265i
$790$	−10.1913	+	3.67223i	−0.362591	+	0.130652i
$791$	−13.6786	+	18.8269i	−0.486354	+	0.669409i
$792$	−4.11493	+	13.9341i	−0.146218	+	0.495125i
$793$	−10.7957	+	1.70987i	−0.383367	+	0.0607193i
$794$	18.6366	−	13.5403i	0.661388	−	0.480527i
$795$	14.3946	+	0.480228i	0.510524	+	0.0170319i
$796$	−11.8052	+	8.57698i	−0.418424	+	0.304003i
$797$	−47.7802	−	24.3452i	−1.69246	−	0.862352i	−0.988338	−	0.152274i	$-0.951340\pi$
$797$	−47.7802	−	24.3452i	−1.69246	−	0.862352i	−0.704123	−	0.710078i	$-0.748660\pi$
$798$	6.16675	−	15.4757i	0.218301	−	0.547833i
$799$	15.2867	+	4.96696i	0.540805	+	0.175718i
$800$	1.98325	−	4.58985i	0.0701184	−	0.162276i
$801$	−4.26431	−	22.9025i	−0.150672	−	0.809219i
$802$	−0.145389	+	0.0740793i	−0.00513386	+	0.00261583i
$803$	5.34555	+	33.7505i	0.188640	+	1.19103i
$804$	−14.4095	−	16.4172i	−0.508186	−	0.578992i
$805$	−16.8258	+	3.21443i	−0.593033	+	0.113294i
$806$	−11.5861	−	2.34272i	−0.408104	−	0.0825188i
$807$	−1.10800	+	1.33334i	−0.0390034	+	0.0469359i
$808$	−0.397711	+	2.51105i	−0.0139914	+	0.0883383i
$809$	13.8829	+	10.0865i	0.488098	+	0.354624i	0.804452	−	0.594017i	$-0.202459\pi$
$809$	13.8829	+	10.0865i	0.488098	+	0.354624i	−0.316354	+	0.948641i	$0.602459\pi$
$810$	−10.3919	+	17.2339i	−0.365136	+	0.605538i
$811$	25.6283			0.899933			0.449966	−	0.893045i	$-0.351436\pi$
$811$	25.6283			0.899933			0.449966	+	0.893045i	$0.351436\pi$
$812$	10.2134	−	10.2134i	0.358421	−	0.358421i
$813$	−12.0312	−	19.0508i	−0.421952	−	0.668141i
$814$	−27.2576	+	8.85652i	−0.955378	+	0.310421i
$815$	15.0902	−	51.9935i	0.528587	−	1.82125i
$816$	8.08248	+	9.20863i	0.282944	+	0.322366i
$817$	5.62444	−	2.86580i	0.196774	−	0.100262i
$818$	−19.6331	−	3.10958i	−0.686457	−	0.108724i
$819$	−9.74273	+	20.4696i	−0.340439	+	0.715265i
$820$	−20.0374	+	11.0227i	−0.699736	+	0.384931i
$821$	0.619834	−	0.853128i	0.0216324	−	0.0297744i	−0.798064	−	0.602573i	$-0.794142\pi$
$821$	0.619834	−	0.853128i	0.0216324	−	0.0297744i	0.819696	+	0.572799i	$0.194142\pi$
$822$	7.00589	+	27.5381i	0.244359	+	0.960500i
$823$	46.7702	+	23.8306i	1.63031	+	0.830683i	0.998453	+	0.0555954i	$0.0177057\pi$
$823$	46.7702	+	23.8306i	1.63031	+	0.830683i	0.631854	+	0.775088i	$0.282294\pi$
$824$	16.3287	+	11.8635i	0.568838	+	0.413285i
$825$	−39.9102	+	12.8943i	−1.38950	+	0.448923i
$826$	−3.80645	+	11.7151i	−0.132443	+	0.407619i
$827$	−0.452546	+	2.85726i	−0.0157366	+	0.0993567i	−0.994306	−	0.106558i	$-0.966017\pi$
$827$	−0.452546	+	2.85726i	−0.0157366	+	0.0993567i	0.978570	+	0.205915i	$0.0660170\pi$
$828$	1.82876	−	6.19257i	0.0635537	−	0.215207i
$829$	7.40778	−	2.40693i	0.257283	−	0.0835963i	−0.177536	−	0.984114i	$-0.556813\pi$
$829$	7.40778	−	2.40693i	0.257283	−	0.0835963i	0.434819	+	0.900518i	$0.356813\pi$
$830$	−0.0833765	−	0.0105099i	−0.00289404	−	0.000364805i
$831$	47.5452	−	4.38861i	1.64933	−	0.152239i
$832$	1.50122	+	1.50122i	0.0520454	+	0.0520454i
$833$	−35.7311	+	18.2059i	−1.23801	+	0.630797i
$834$	10.6722	+	6.34329i	0.369546	+	0.219650i
$835$	−23.7254	+	0.752043i	−0.821050	+	0.0260255i
$836$			13.0868i			0.452617i
$837$	15.0690	+	24.6967i	0.520860	+	0.853642i
$838$	−18.9522	+	18.9522i	−0.654693	+	0.654693i
$839$	36.1168	−	26.2404i	1.24689	−	0.905918i	0.248852	−	0.968542i	$-0.419947\pi$
$839$	36.1168	−	26.2404i	1.24689	−	0.905918i	0.998037	+	0.0626239i	$0.0199469\pi$
$840$	−12.4846	+	5.84536i	−0.430760	+	0.201684i
$841$	−3.87267	+	11.9189i	−0.133540	+	0.410995i
$842$	−3.33942	+	3.33942i	−0.115084	+	0.115084i
$843$	38.5969	+	32.0738i	1.32935	+	1.10468i
$844$	22.3190	+	7.25189i	0.768252	+	0.249620i
$845$	−9.15312	−	16.6388i	−0.314877	−	0.572391i
$846$	−3.25751	−	5.98779i	−0.111996	−	0.205864i
$847$	43.7841	+	6.93471i	1.50444	+	0.238280i
$848$	−3.31342	+	1.68827i	−0.113783	+	0.0579755i
$849$	−17.8386	−	20.3241i	−0.612221	−	0.697522i
$850$	−8.77759	+	34.2637i	−0.301069	+	1.17523i
$851$	12.1138	−	3.93601i	0.415256	−	0.134925i
$852$	22.0858	−	5.61881i	0.756648	−	0.192497i
$853$	−20.3023	+	3.21557i	−0.695138	+	0.110099i	−0.493998	−	0.869463i	$-0.664465\pi$
$853$	−20.3023	+	3.21557i	−0.695138	+	0.110099i	−0.201141	+	0.979562i	$0.564465\pi$
$854$	5.66270	+	17.4280i	0.193774	+	0.596374i
$855$	−4.58063	+	17.5388i	−0.156654	+	0.599813i
$856$	11.8133	−	8.58286i	0.403770	−	0.293356i
$857$	20.5095	+	40.2522i	0.700591	+	1.37499i	0.917080	+	0.398703i	$0.130539\pi$
$857$	20.5095	+	40.2522i	0.700591	+	1.37499i	−0.216489	+	0.976285i	$0.569461\pi$
$858$	1.15740	−	17.7711i	0.0395131	−	0.606695i
$859$	−8.74217	+	2.84050i	−0.298279	+	0.0969168i	−0.454333	−	0.890832i	$-0.650123\pi$
$859$	−8.74217	+	2.84050i	−0.298279	+	0.0969168i	0.156054	+	0.987748i	$0.450123\pi$
$860$	−5.01650	−	1.45595i	−0.171061	−	0.0496476i
$861$	61.5025	+	13.8899i	2.09600	+	0.473366i
$862$	−6.06230	−	6.06230i	−0.206483	−	0.206483i
$863$	−39.5232	−	39.5232i	−1.34538	−	1.34538i	−0.890604	−	0.454780i	$-0.849718\pi$
$863$	−39.5232	−	39.5232i	−1.34538	−	1.34538i	−0.454780	−	0.890604i	$-0.650282\pi$
$864$	0.197562	−	5.19240i	0.00672120	−	0.176649i
$865$	−23.0813	+	8.31687i	−0.784789	+	0.282782i
$866$	−18.2189	−	25.0762i	−0.619105	−	0.852124i
$867$	−44.0160	−	36.5769i	−1.49486	−	1.24222i
$868$	−0.840621	+	19.7997i	−0.0285325	+	0.672047i
$869$	−23.4621			−0.795897
$870$	−9.65690	+	12.4000i	−0.327400	+	0.420400i
$871$	21.6615	+	15.7380i	0.733972	+	0.533262i
$872$	2.23929	+	4.39486i	0.0758321	+	0.148829i
$873$	−18.9129	+	27.5672i	−0.640104	+	0.933008i
$874$		−	5.81604i		−	0.196730i
$875$	−34.2694	−	20.2292i	−1.15852	−	0.683873i
$876$	−4.82881	−	11.2266i	−0.163151	−	0.379311i
$877$	−0.377942	+	0.741752i	−0.0127622	+	0.0250472i	−0.897300	−	0.441422i	$-0.854474\pi$
$877$	−0.377942	+	0.741752i	−0.0127622	+	0.0250472i	0.884537	+	0.466469i	$0.154474\pi$
$878$	30.1219	+	4.77085i	1.01657	+	0.161008i
$879$	0.936304	−	4.14583i	0.0315808	−	0.139835i
$880$	7.41099	−	7.89619i	0.249824	−	0.266181i
$881$	23.6309	−	32.5251i	0.796144	−	1.09580i	−0.197172	−	0.980369i	$-0.563176\pi$
$881$	23.6309	−	32.5251i	0.796144	−	1.09580i	0.993316	−	0.115429i	$-0.0368242\pi$
$882$	16.3104	+	4.81669i	0.549199	+	0.162186i
$883$	−12.4199	+	1.96711i	−0.417961	+	0.0661986i	−0.361873	−	0.932227i	$-0.617863\pi$
$883$	−12.4199	+	1.96711i	−0.417961	+	0.0661986i	−0.0560880	+	0.998426i	$0.517863\pi$
$884$	−12.1502	−	8.82763i	−0.408655	−	0.296905i
$885$	2.53699	−	13.1611i	0.0852801	−	0.442405i
$886$	−6.74109	−	4.89769i	−0.226471	−	0.164541i
$887$	−0.628531	+	3.96839i	−0.0211040	+	0.133246i	−0.995991	−	0.0894554i	$-0.971487\pi$
$887$	−0.628531	+	3.96839i	−0.0211040	+	0.133246i	0.974887	+	0.222701i	$0.0714873\pi$
$888$	8.66654	−	5.47319i	0.290830	−	0.183668i
$889$	13.4259	+	18.4791i	0.450289	+	0.619769i
$890$	−4.83984	+	16.6757i	−0.162232	+	0.558972i
$891$	−33.8280	+	27.4861i	−1.13328	+	0.920818i
$892$	−12.6430	+	6.44195i	−0.423320	+	0.215692i
$893$	−4.34158	−	4.34158i	−0.145285	−	0.145285i
$894$	−0.372991	−	4.04091i	−0.0124747	−	0.135148i
$895$	29.2022	+	3.68104i	0.976121	+	0.123044i
$896$	2.09213	−	2.87957i	0.0698931	−	0.0961996i
$897$	−0.514372	+	7.89781i	−0.0171744	+	0.263700i
$898$	−7.90691	+	7.90691i	−0.263857	+	0.263857i
$899$	9.39441	+	20.5486i	0.313321	+	0.685335i
$900$	12.6959	−	7.98837i	0.423197	−	0.266279i
$901$	21.2823	−	15.4625i	0.709018	−	0.515132i
$902$	−48.9213	+	7.74838i	−1.62890	+	0.257993i
$903$	7.68988	+	12.1766i	0.255903	+	0.405211i
$904$			6.53811i			0.217454i
$905$	4.81139	+	25.1851i	0.159936	+	0.837181i
$906$	−18.0387	−	4.07390i	−0.599296	−	0.135346i
$907$	−4.82107	+	9.46189i	−0.160081	+	0.314177i	−0.957090	−	0.289791i	$-0.906414\pi$
$907$	−4.82107	+	9.46189i	−0.160081	+	0.314177i	0.797009	+	0.603967i	$0.206414\pi$
$908$	1.63486	−	3.20859i	0.0542547	−	0.106481i
$909$	−5.24553	+	5.53680i	−0.173983	+	0.183644i
$910$	13.3486	−	10.3600i	0.442501	−	0.343431i
$911$	−0.820037	−	1.12868i	−0.0271690	−	0.0373950i	0.795216	−	0.606326i	$-0.207357\pi$
$911$	−0.820037	−	1.12868i	−0.0271690	−	0.0373950i	−0.822385	+	0.568931i	$0.807357\pi$
$912$	−1.15397	−	4.53590i	−0.0382117	−	0.150199i
$913$	−0.162172	−	0.0826308i	−0.00536711	−	0.00273468i
$914$	−9.89313	−	7.18778i	−0.327236	−	0.237751i
$915$	−8.45499	−	18.0583i	−0.279513	−	0.596989i
$916$	−8.28045	−	25.4846i	−0.273594	−	0.842035i
$917$	−10.6814	+	1.69177i	−0.352732	+	0.0558673i
$918$	4.36566	+	36.4975i	0.144088	+	1.20460i
$919$	−44.9320	−	14.5993i	−1.48217	−	0.481586i	−0.547408	−	0.836866i	$-0.684386\pi$
$919$	−44.9320	−	14.5993i	−1.48217	−	0.481586i	−0.934760	+	0.355280i	$0.884386\pi$
$920$	−3.29359	+	3.50922i	−0.108586	+	0.115696i
$921$	5.33394	+	12.4009i	0.175759	+	0.408625i
$922$	−12.4079	+	24.3519i	−0.408633	+	0.801987i
$923$	−24.8892	+	12.6817i	−0.819239	+	0.417423i
$924$	−29.7304	+	2.74423i	−0.978059	+	0.0902787i
$925$	27.1623	+	11.7367i	0.893090	+	0.385899i
$926$	−24.5565	−	7.97890i	−0.806978	−	0.262203i
$927$	20.2593	+	57.0605i	0.665402	+	1.87411i
$928$	0.634819	−	4.00809i	0.0208389	−	0.131572i
$929$	−24.0714			−0.789758			−0.394879	−	0.918733i	$-0.629213\pi$
$929$	−24.0714			−0.789758			−0.394879	+	0.918733i	$0.629213\pi$
$930$	−1.75120	−	21.4926i	−0.0574242	−	0.704771i
$931$	15.3186			0.502048
$932$	−0.846026	+	5.34159i	−0.0277125	+	0.174970i
$933$	−10.3899	−	40.8395i	−0.340149	−	1.33702i
$934$	17.3429	+	5.63503i	0.567475	+	0.184384i
$935$	−43.0419	+	63.3713i	−1.40762	+	2.07246i
$936$	1.16586	+	6.26152i	0.0381073	+	0.204664i
$937$	−18.2547	+	9.30122i	−0.596354	+	0.303858i	−0.725991	−	0.687704i	$-0.758619\pi$
$937$	−18.2547	+	9.30122i	−0.596354	+	0.303858i	0.129637	+	0.991562i	$0.458619\pi$
$938$	20.3793	−	39.9965i	0.665406	−	1.30593i
$939$	−25.0566	+	10.7774i	−0.817690	+	0.351708i
$940$	0.160968	+	5.07819i	0.00525019	+	0.165632i
$941$	−23.3110	−	7.57422i	−0.759918	−	0.246912i	−0.0966747	−	0.995316i	$-0.530821\pi$
$941$	−23.3110	−	7.57422i	−0.759918	−	0.246912i	−0.663244	+	0.748404i	$0.730821\pi$
$942$	1.99333	−	30.6062i	0.0649463	−	0.997204i
$943$	21.7416	−	3.44353i	0.708004	−	0.112137i
$944$	1.06943	+	3.29136i	0.0348069	+	0.107125i
$945$	−40.8048	−	6.72842i	−1.32738	−	0.218876i
$946$	−9.15268	−	6.64981i	−0.297579	−	0.216204i
$947$	−28.1327	−	14.3343i	−0.914191	−	0.465804i	−0.0673981	−	0.997726i	$-0.521470\pi$
$947$	−28.1327	−	14.3343i	−0.914191	−	0.465804i	−0.846793	+	0.531922i	$0.821470\pi$
$948$	8.13197	−	2.06884i	0.264114	−	0.0671927i
$949$	8.80491	+	12.1189i	0.285819	+	0.393397i
$950$	8.92955	−	10.1397i	0.289713	−	0.328975i
$951$	13.4701	+	15.3469i	0.436798	+	0.497657i
$952$	−11.4310	+	22.4345i	−0.370480	+	0.727107i
$953$	22.7116	−	44.5741i	0.735701	−	1.44390i	−0.154341	−	0.988018i	$-0.549325\pi$
$953$	22.7116	−	44.5741i	0.735701	−	1.44390i	0.890042	−	0.455878i	$-0.150675\pi$
$954$	−11.0620	−	1.44703i	−0.358144	−	0.0468495i
$955$	36.9548	−	7.05990i	1.19583	−	0.228453i
$956$		−	16.5929i		−	0.536652i
$957$	−28.7812	+	18.1762i	−0.930363	+	0.587553i
$958$	18.9880	−	3.00740i	0.613474	−	0.0971647i
$959$	−47.2409	+	34.3225i	−1.52549	+	1.10833i
$960$	−1.87238	+	3.39031i	−0.0604309	+	0.109422i
$961$	−28.5647	−	12.0440i	−0.921442	−	0.388516i
$962$	−8.88407	+	8.88407i	−0.286434	+	0.286434i
$963$	43.7901	−	1.18291i	1.41112	−	0.0381187i
$964$	5.99562	−	8.25226i	0.193106	−	0.265788i
$965$	40.7044	−	31.5913i	1.31032	−	1.01696i
$966$	13.2128	−	1.21959i	0.425114	−	0.0392397i
$967$	16.9885	+	16.9885i	0.546315	+	0.546315i	0.925373	−	0.379058i	$-0.123752\pi$
$967$	16.9885	+	16.9885i	0.546315	+	0.546315i	−0.379058	+	0.925373i	$0.623752\pi$
$968$	11.0970	−	5.65423i	0.356673	−	0.181734i
$969$	13.0822	+	30.4150i	0.420261	+	0.977070i
$970$	21.8327	−	12.0103i	0.701005	−	0.385629i
$971$	−16.1704	−	22.2566i	−0.518932	−	0.714248i	0.466462	−	0.884541i	$-0.345529\pi$
$971$	−16.1704	−	22.2566i	−0.518932	−	0.714248i	−0.985393	+	0.170293i	$0.945529\pi$
$972$	9.30113	−	12.5096i	0.298334	−	0.401244i
$973$	−3.99106	+	25.1986i	−0.127947	+	0.807828i
$974$	21.5186	+	15.6341i	0.689499	+	0.500950i
$975$	−13.0225	+	12.9793i	−0.417055	+	0.415671i
$976$	4.16514	+	3.02615i	0.133323	+	0.0968647i
$977$	18.6480	−	2.95355i	0.596602	−	0.0944925i	0.149172	−	0.988811i	$-0.452339\pi$
$977$	18.6480	−	2.95355i	0.596602	−	0.0944925i	0.447430	+	0.894319i	$0.352339\pi$
$978$	−15.5236	+	38.9569i	−0.496389	+	1.24570i
$979$	−22.1052	+	30.4251i	−0.706484	+	0.972392i
$980$	−9.24280	−	8.67485i	−0.295251	−	0.277108i
$981$	−1.91932	+	14.6724i	−0.0612792	+	0.468454i
$982$	17.2806	+	2.73698i	0.551447	+	0.0873406i
$983$	7.96483	−	15.6319i	0.254039	−	0.498579i	−0.728403	−	0.685149i	$-0.759737\pi$
$983$	7.96483	−	15.6319i	0.254039	−	0.498579i	0.982442	+	0.186570i	$0.0597371\pi$
$984$	16.2729	−	6.99937i	0.518762	−	0.223132i
$985$	19.7794	−	15.3510i	0.630223	−	0.489125i
$986$			28.7067i			0.914208i
$987$	8.95272	−	10.7735i	0.284968	−	0.342925i
$988$	2.60451	+	5.11165i	0.0828606	+	0.162623i
$989$	4.06763	+	2.95531i	0.129343	+	0.0939733i
$990$	31.7344	−	6.95572i	1.00858	−	0.221067i
$991$	−19.5989			−0.622579			−0.311289	−	0.950315i	$-0.600761\pi$
$991$	−19.5989			−0.622579			−0.311289	+	0.950315i	$0.600761\pi$
$992$	3.07864	+	4.63918i	0.0977468	+	0.147294i
$993$	−2.46015	+	2.96050i	−0.0780706	+	0.0939486i
$994$	27.5271	+	37.8877i	0.873105	+	1.20173i
$995$	29.5272	+	13.8846i	0.936074	+	0.440173i
$996$	0.0634951	+	0.0143399i	0.00201192	+	0.000454377i
$997$	4.46970	+	4.46970i	0.141557	+	0.141557i	0.774334	−	0.632777i	$-0.218085\pi$
$997$	4.46970	+	4.46970i	0.141557	+	0.141557i	−0.632777	+	0.774334i	$0.718085\pi$
$998$	−26.2472	−	26.2472i	−0.830841	−	0.830841i
$999$	30.7281	+	1.16915i	0.972194	+	0.0369904i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bk.a.47.4	✓	512
3.2	odd	2	inner	930.2.bk.a.47.33	yes	512
5.3	odd	4	inner	930.2.bk.a.233.45	yes	512
15.8	even	4	inner	930.2.bk.a.233.16	yes	512
31.2	even	5	inner	930.2.bk.a.467.16	yes	512
93.2	odd	10	inner	930.2.bk.a.467.45	yes	512
155.33	odd	20	inner	930.2.bk.a.653.33	yes	512
465.188	even	20	inner	930.2.bk.a.653.4	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bk.a.47.4	✓	512	1.1	even	1	trivial
930.2.bk.a.47.33	yes	512	3.2	odd	2	inner
930.2.bk.a.233.16	yes	512	15.8	even	4	inner
930.2.bk.a.233.45	yes	512	5.3	odd	4	inner
930.2.bk.a.467.16	yes	512	31.2	even	5	inner
930.2.bk.a.467.45	yes	512	93.2	odd	10	inner
930.2.bk.a.653.4	yes	512	465.188	even	20	inner
930.2.bk.a.653.33	yes	512	155.33	odd	20	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.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.156434 + 0.987688i) q^{2} +(-1.67858 + 0.427044i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(0.419593 + 2.19635i) q^{5} +(-0.159198 - 1.72472i) q^{6} +(3.17140 - 1.61591i) q^{7} +(0.453990 - 0.891007i) q^{8} +(2.63527 - 1.43366i) q^{9} +O(q^{10})\)	\(q+(-0.156434 + 0.987688i) q^{2} +(-1.67858 + 0.427044i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(0.419593 + 2.19635i) q^{5} +(-0.159198 - 1.72472i) q^{6} +(3.17140 - 1.61591i) q^{7} +(0.453990 - 0.891007i) q^{8} +(2.63527 - 1.43366i) q^{9} +(-2.23495 + 0.0708430i) q^{10} +(-4.60595 - 1.49656i) q^{11} +(1.72839 + 0.112567i) q^{12} +(-2.09691 + 0.332117i) q^{13} +(1.09990 + 3.38513i) q^{14} +(-1.64226 - 3.50756i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-6.30300 - 3.21154i) q^{17} +(1.00376 + 2.82710i) q^{18} +(1.58833 + 2.18614i) q^{19} +(0.279652 - 2.21851i) q^{20} +(-4.63338 + 4.06676i) q^{21} +(2.19867 - 4.31513i) q^{22} +(-0.977132 + 1.91773i) q^{23} +(-0.381561 + 1.68950i) q^{24} +(-4.64788 + 1.84315i) q^{25} -2.12304i q^{26} +(-3.81128 + 3.53188i) q^{27} +(-3.51552 + 0.556804i) q^{28} +(-3.28303 + 2.38526i) q^{29} +(3.72128 - 1.07334i) q^{30} +(1.10347 - 5.45732i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(8.37056 + 0.545161i) q^{33} +(4.15801 - 5.72300i) q^{34} +(4.87979 + 6.28746i) q^{35} +(-2.94931 + 0.549145i) q^{36} +(-4.18459 - 4.18459i) q^{37} +(-2.40770 + 1.22678i) q^{38} +(3.37800 - 1.45296i) q^{39} +(2.14745 + 0.623260i) q^{40} +(-6.01151 - 8.27414i) q^{41} +(-3.29187 - 5.21252i) q^{42} +(0.365435 - 2.30727i) q^{43} +(3.91806 + 2.84664i) q^{44} +(4.25454 + 5.18641i) q^{45} +(-1.74126 - 1.26510i) q^{46} +(-2.24420 + 0.355446i) q^{47} +(-1.60901 - 0.641159i) q^{48} +(3.33210 - 4.58624i) q^{49} +(-1.09336 - 4.87899i) q^{50} +(11.9516 + 2.69917i) q^{51} +(2.09691 + 0.332117i) q^{52} +(-1.68827 + 3.31342i) q^{53} +(-2.89218 - 4.31686i) q^{54} +(1.35435 - 10.7442i) q^{55} -3.55934i q^{56} +(-3.59971 - 2.99133i) q^{57} +(-1.84232 - 3.61575i) q^{58} +(2.79980 + 2.03417i) q^{59} +(0.477984 + 3.84338i) q^{60} +5.14839 q^{61} +(5.21751 + 1.94360i) q^{62} +(6.04082 - 8.80503i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-1.60929 - 4.46618i) q^{65} +(-1.84789 + 8.18223i) q^{66} +(-8.91778 - 8.91778i) q^{67} +(5.00209 + 5.00209i) q^{68} +(0.821240 - 3.63634i) q^{69} +(-6.97342 + 3.83614i) q^{70} +(12.5135 - 4.06587i) q^{71} +(-0.0810097 - 2.99891i) q^{72} +(-3.20327 - 6.28677i) q^{73} +(4.78768 - 3.47846i) q^{74} +(7.01474 - 5.07872i) q^{75} +(-0.835032 - 2.56997i) q^{76} +(-17.0256 + 2.69659i) q^{77} +(0.906633 + 3.56370i) q^{78} +(4.60744 - 1.49705i) q^{79} +(-0.951522 + 2.02351i) q^{80} +(4.88927 - 7.55613i) q^{81} +(9.11268 - 4.64314i) q^{82} +(0.0371195 + 0.00587915i) q^{83} +(5.66330 - 2.43592i) q^{84} +(4.40896 - 15.1911i) q^{85} +(2.22169 + 0.721872i) q^{86} +(4.49222 - 5.40585i) q^{87} +(-3.42451 + 3.42451i) q^{88} +(2.39963 - 7.38530i) q^{89} +(-5.78811 + 3.39083i) q^{90} +(-6.11345 + 4.44168i) q^{91} +(1.52192 - 1.52192i) q^{92} +(0.478248 + 9.63178i) q^{93} -2.27217i q^{94} +(-4.13508 + 4.40581i) q^{95} +(0.884970 - 1.48890i) q^{96} +(-9.92914 + 5.05915i) q^{97} +(4.00852 + 4.00852i) q^{98} +(-14.2835 + 2.65950i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q + 8 q^{3} - 12 q^{7}+O(q^{10}) \) 512 * q + 8 * q^3 - 12 * q^7	\( 512 q + 8 q^{3} - 12 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} + 128 q^{16} + 28 q^{22} + 32 q^{25} + 44 q^{27} + 8 q^{28} + 24 q^{30} + 8 q^{31} + 28 q^{33} + 176 q^{37} + 24 q^{42} - 40 q^{45} - 24 q^{46} + 12 q^{48} - 16 q^{51} - 40 q^{55} + 40 q^{57} + 56 q^{58} + 12 q^{60} - 32 q^{61} - 224 q^{63} + 32 q^{66} + 48 q^{67} + 24 q^{70} + 40 q^{73} - 32 q^{75} + 48 q^{76} - 76 q^{78} - 96 q^{81} + 24 q^{85} - 80 q^{87} - 72 q^{88} + 16 q^{90} + 80 q^{91} - 168 q^{93} - 112 q^{97}+O(q^{100}) \) 512 * q + 8 * q^3 - 12 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 + 128 * q^16 + 28 * q^22 + 32 * q^25 + 44 * q^27 + 8 * q^28 + 24 * q^30 + 8 * q^31 + 28 * q^33 + 176 * q^37 + 24 * q^42 - 40 * q^45 - 24 * q^46 + 12 * q^48 - 16 * q^51 - 40 * q^55 + 40 * q^57 + 56 * q^58 + 12 * q^60 - 32 * q^61 - 224 * q^63 + 32 * q^66 + 48 * q^67 + 24 * q^70 + 40 * q^73 - 32 * q^75 + 48 * q^76 - 76 * q^78 - 96 * q^81 + 24 * q^85 - 80 * q^87 - 72 * q^88 + 16 * q^90 + 80 * q^91 - 168 * q^93 - 112 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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