LMFDB - Embedded newform 820.2.bk.c.43.78

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(43,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 15, 13])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.43"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bk (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [960,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$960$
Relative dimension:	$120$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			43.78
Character	$\chi$	$=$	820.43
Dual form			820.2.bk.c.267.78

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.584633 + 1.28771i) q^{2} +0.0874408i q^{3} +(-1.31641 + 1.50568i) q^{4} +(2.22071 + 0.261598i) q^{5} +(-0.112599 + 0.0511208i) q^{6} +(-1.03653 + 3.19012i) q^{7} +(-2.70850 - 0.814885i) q^{8} +2.99235 q^{9} +(0.961440 + 3.01258i) q^{10} +(0.441826 + 2.78958i) q^{11} +(-0.131658 - 0.115108i) q^{12} +(-0.681038 - 2.09602i) q^{13} +(-4.71394 + 0.530293i) q^{14} +(-0.0228743 + 0.194181i) q^{15} +(-0.534140 - 3.96418i) q^{16} +(-1.31324 - 0.954122i) q^{17} +(1.74943 + 3.85329i) q^{18} +(-4.39283 + 2.23826i) q^{19} +(-3.31725 + 2.99931i) q^{20} +(-0.278946 - 0.0906351i) q^{21} +(-3.33387 + 2.19983i) q^{22} +(7.22827 + 3.68299i) q^{23} +(0.0712542 - 0.236833i) q^{24} +(4.86313 + 1.16187i) q^{25} +(2.30091 - 2.10238i) q^{26} +0.523976i q^{27} +(-3.43879 - 5.76018i) q^{28} +(-6.02052 - 0.953557i) q^{29} +(-0.263422 + 0.0840690i) q^{30} +(4.48863 - 6.17807i) q^{31} +(4.79244 - 3.00541i) q^{32} +(-0.243923 + 0.0386336i) q^{33} +(0.460874 - 2.24888i) q^{34} +(-3.13637 + 6.81318i) q^{35} +(-3.93916 + 4.50553i) q^{36} +(-1.10771 + 6.99381i) q^{37} +(-5.45042 - 4.34814i) q^{38} +(0.183277 - 0.0595505i) q^{39} +(-5.80163 - 2.51816i) q^{40} +(-6.31926 - 1.03296i) q^{41} +(-0.0463692 - 0.412191i) q^{42} +(0.0681104 - 0.133674i) q^{43} +(-4.78184 - 3.00698i) q^{44} +(6.64516 + 0.782793i) q^{45} +(-0.516743 + 11.4611i) q^{46} +(-7.25028 + 2.35576i) q^{47} +(0.346631 - 0.0467056i) q^{48} +(-3.43932 - 2.49881i) q^{49} +(1.34700 + 6.94158i) q^{50} +(0.0834292 - 0.114830i) q^{51} +(4.05246 + 1.73379i) q^{52} +(-2.11326 + 1.53538i) q^{53} +(-0.674731 + 0.306334i) q^{54} +(0.251421 + 6.31044i) q^{55} +(5.40702 - 7.79577i) q^{56} +(-0.195715 - 0.384112i) q^{57} +(-2.29189 - 8.31019i) q^{58} +(-0.934995 - 2.87762i) q^{59} +(-0.262262 - 0.290063i) q^{60} +(5.95586 + 1.93517i) q^{61} +(10.5798 + 2.16816i) q^{62} +(-3.10167 + 9.54596i) q^{63} +(6.67192 + 4.41423i) q^{64} +(-0.964075 - 4.83281i) q^{65} +(-0.192355 - 0.291516i) q^{66} +(4.74172 + 6.52642i) q^{67} +(3.16536 - 0.721299i) q^{68} +(-0.322043 + 0.632046i) q^{69} +(-10.6070 - 0.0555286i) q^{70} +(-2.11086 - 13.3274i) q^{71} +(-8.10479 - 2.43842i) q^{72} +(7.23913 - 7.23913i) q^{73} +(-9.65362 + 2.66240i) q^{74} +(-0.101595 + 0.425236i) q^{75} +(2.41265 - 9.56065i) q^{76} +(-9.35705 - 1.48201i) q^{77} +(0.183834 + 0.201194i) q^{78} +(-4.92171 + 4.92171i) q^{79} +(-0.149152 - 8.94303i) q^{80} +8.93125 q^{81} +(-2.36429 - 8.74129i) q^{82} +(2.96110 - 2.96110i) q^{83} +(0.503674 - 0.300691i) q^{84} +(-2.66673 - 2.46237i) q^{85} +(0.211954 + 0.00955625i) q^{86} +(0.0833798 - 0.526439i) q^{87} +(1.07650 - 7.91561i) q^{88} +(13.4242 - 6.84000i) q^{89} +(2.87697 + 9.01470i) q^{90} +7.39246 q^{91} +(-15.0608 + 6.03514i) q^{92} +(0.540215 + 0.392489i) q^{93} +(-7.27229 - 7.95902i) q^{94} +(-10.3407 + 3.82137i) q^{95} +(0.262795 + 0.419055i) q^{96} +(-7.15121 + 5.19566i) q^{97} +(1.20701 - 5.88975i) q^{98} +(1.32210 + 8.34741i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q - 10 q^{2} - 20 q^{5} - 16 q^{6} - 22 q^{8} - 960 q^{9} + 20 q^{12} + 12 q^{13} + 8 q^{14} - 28 q^{16} - 52 q^{17} + 12 q^{18} + 14 q^{20} - 40 q^{21} + 18 q^{22} + 48 q^{24} - 4 q^{25} - 20 q^{26}+ \cdots + 42 q^{98}+O(q^{100}) $ 960 * q - 10 * q^2 - 20 * q^5 - 16 * q^6 - 22 * q^8 - 960 * q^9 + 20 * q^12 + 12 * q^13 + 8 * q^14 - 28 * q^16 - 52 * q^17 + 12 * q^18 + 14 * q^20 - 40 * q^21 + 18 * q^22 + 48 * q^24 - 4 * q^25 - 20 * q^26 - 2 * q^28 + 30 * q^30 + 16 * q^33 + 20 * q^34 - 100 * q^36 - 112 * q^37 - 36 * q^38 - 16 * q^40 - 24 * q^41 - 104 * q^42 + 20 * q^45 - 20 * q^46 + 12 * q^48 - 224 * q^49 + 12 * q^50 + 190 * q^52 + 12 * q^53 + 52 * q^54 + 96 * q^56 + 48 * q^57 - 10 * q^58 + 14 * q^60 - 40 * q^61 - 10 * q^62 + 120 * q^64 - 92 * q^65 - 12 * q^66 + 104 * q^69 - 120 * q^70 + 36 * q^72 + 72 * q^73 + 28 * q^74 - 40 * q^76 + 36 * q^77 + 16 * q^78 - 130 * q^80 + 592 * q^81 + 146 * q^82 + 92 * q^84 + 112 * q^85 - 12 * q^86 + 100 * q^88 - 136 * q^89 - 136 * q^90 + 160 * q^92 - 24 * q^93 + 32 * q^94 - 44 * q^96 - 72 * q^97 + 42 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.584633	+	1.28771i	0.413398	+	0.910550i
$2$	0.584633	+	1.28771i	0.413398	+	0.910550i
$3$			0.0874408i			0.0504840i	0.999681	+	0.0252420i	$0.00803562\pi$
$3$			0.0874408i			0.0504840i	−0.999681	+	0.0252420i	$0.991964\pi$
$4$	−1.31641	+	1.50568i	−0.658204	+	0.752840i
$5$	2.22071	+	0.261598i	0.993133	+	0.116990i
$5$	2.22071	+	0.261598i	0.993133	+	0.116990i
$6$	−0.112599	+	0.0511208i	−0.0459682	+	0.0208700i
$7$	−1.03653	+	3.19012i	−0.391772	+	1.20575i	0.539675	+	0.841873i	$0.318547\pi$
$7$	−1.03653	+	3.19012i	−0.391772	+	1.20575i	−0.931447	+	0.363877i	$0.881453\pi$
$8$	−2.70850	−	0.814885i	−0.957599	−	0.288105i
$9$	2.99235			0.997451
$10$	0.961440	+	3.01258i	0.304034	+	0.952661i
$11$	0.441826	+	2.78958i	0.133216	+	0.841090i	0.960291	+	0.278999i	$0.0900028\pi$
$11$	0.441826	+	2.78958i	0.133216	+	0.841090i	−0.827076	+	0.562091i	$0.809997\pi$
$12$	−0.131658	−	0.115108i	−0.0380063	−	0.0332287i
$13$	−0.681038	−	2.09602i	−0.188886	−	0.581331i	0.811108	−	0.584897i	$-0.198865\pi$
$13$	−0.681038	−	2.09602i	−0.188886	−	0.581331i	−0.999994	+	0.00356578i	$0.998865\pi$
$14$	−4.71394	+	0.530293i	−1.25985	+	0.141727i
$15$	−0.0228743	+	0.194181i	−0.00590612	+	0.0501373i
$16$	−0.534140	−	3.96418i	−0.133535	−	0.991044i
$17$	−1.31324	−	0.954122i	−0.318507	−	0.231409i	0.417031	−	0.908892i	$-0.363071\pi$
$17$	−1.31324	−	0.954122i	−0.318507	−	0.231409i	−0.735538	+	0.677483i	$0.763071\pi$
$18$	1.74943	+	3.85329i	0.412345	+	0.908230i
$19$	−4.39283	+	2.23826i	−1.00778	+	0.513491i	−0.878310	−	0.478091i	$-0.841329\pi$
$19$	−4.39283	+	2.23826i	−1.00778	+	0.513491i	−0.129474	+	0.991583i	$0.541329\pi$
$20$	−3.31725	+	2.99931i	−0.741759	+	0.670667i
$21$	−0.278946	−	0.0906351i	−0.0608711	−	0.0197782i
$22$	−3.33387	+	2.19983i	−0.710784	+	0.469005i
$23$	7.22827	+	3.68299i	1.50720	+	0.767956i	0.995815	−	0.0913962i	$-0.0291330\pi$
$23$	7.22827	+	3.68299i	1.50720	+	0.767956i	0.511384	+	0.859352i	$0.329133\pi$
$24$	0.0712542	−	0.236833i	0.0145447	−	0.0483434i
$25$	4.86313	+	1.16187i	0.972627	+	0.232373i
$26$	2.30091	−	2.10238i	0.451246	−	0.412311i
$27$			0.523976i			0.100839i
$28$	−3.43879	−	5.76018i	−0.649871	−	1.08857i
$29$	−6.02052	−	0.953557i	−1.11798	−	0.177071i	−0.430022	−	0.902818i	$-0.641494\pi$
$29$	−6.02052	−	0.953557i	−1.11798	−	0.177071i	−0.687961	+	0.725747i	$0.741494\pi$
$30$	−0.263422	+	0.0840690i	−0.0480941	+	0.0153488i
$31$	4.48863	−	6.17807i	0.806182	−	1.10961i	−0.185719	−	0.982603i	$-0.559461\pi$
$31$	4.48863	−	6.17807i	0.806182	−	1.10961i	0.991901	−	0.127012i	$-0.0405386\pi$
$32$	4.79244	−	3.00541i	0.847192	−	0.531286i
$33$	−0.243923	+	0.0386336i	−0.0424615	+	0.00672525i
$34$	0.460874	−	2.24888i	0.0790392	−	0.385680i
$35$	−3.13637	+	6.81318i	−0.530143	+	1.15164i
$36$	−3.93916	+	4.50553i	−0.656526	+	0.750921i
$37$	−1.10771	+	6.99381i	−0.182107	+	1.14978i	0.712086	+	0.702092i	$0.247751\pi$
$37$	−1.10771	+	6.99381i	−0.182107	+	1.14978i	−0.894192	+	0.447683i	$0.852249\pi$
$38$	−5.45042	−	4.34814i	−0.884176	−	0.705361i
$39$	0.183277	−	0.0595505i	0.0293479	−	0.00953571i
$40$	−5.80163	−	2.51816i	−0.917317	−	0.398157i
$41$	−6.31926	−	1.03296i	−0.986902	−	0.161322i
$41$	−6.31926	−	1.03296i	−0.986902	−	0.161322i
$42$	−0.0463692	−	0.412191i	−0.00715493	−	0.0636024i
$43$	0.0681104	−	0.133674i	0.0103867	−	0.0203851i	−0.885755	−	0.464153i	$-0.846359\pi$
$43$	0.0681104	−	0.133674i	0.0103867	−	0.0203851i	0.896142	+	0.443768i	$0.146359\pi$
$44$	−4.78184	−	3.00698i	−0.720889	−	0.453319i
$45$	6.64516	+	0.782793i	0.990602	+	0.116692i
$46$	−0.516743	+	11.4611i	−0.0761896	+	1.68985i
$47$	−7.25028	+	2.35576i	−1.05756	+	0.343623i	−0.785632	−	0.618694i	$-0.787662\pi$
$47$	−7.25028	+	2.35576i	−1.05756	+	0.343623i	−0.271930	+	0.962317i	$0.587662\pi$
$48$	0.346631	−	0.0467056i	0.0500318	−	0.00674138i
$49$	−3.43932	−	2.49881i	−0.491332	−	0.356973i
$50$	1.34700	+	6.94158i	0.190494	+	0.981688i
$51$	0.0834292	−	0.114830i	0.0116824	−	0.0160795i
$52$	4.05246	+	1.73379i	0.561974	+	0.240434i
$53$	−2.11326	+	1.53538i	−0.290279	+	0.210900i	−0.723388	−	0.690441i	$-0.757416\pi$
$53$	−2.11326	+	1.53538i	−0.290279	+	0.210900i	0.433109	+	0.901341i	$0.357416\pi$
$54$	−0.674731	+	0.306334i	−0.0918192	+	0.0416868i
$55$	0.251421	+	6.31044i	0.0339016	+	0.850899i
$56$	5.40702	−	7.79577i	0.722544	−	1.04175i
$57$	−0.195715	−	0.384112i	−0.0259231	−	0.0508769i
$58$	−2.29189	−	8.31019i	−0.300940	−	1.09118i
$59$	−0.934995	−	2.87762i	−0.121726	−	0.374634i	0.871564	−	0.490281i	$-0.163106\pi$
$59$	−0.934995	−	2.87762i	−0.121726	−	0.374634i	−0.993290	+	0.115647i	$0.963106\pi$
$60$	−0.262262	−	0.290063i	−0.0338579	−	0.0374469i
$61$	5.95586	+	1.93517i	0.762569	+	0.247774i	0.664381	−	0.747394i	$-0.268695\pi$
$61$	5.95586	+	1.93517i	0.762569	+	0.247774i	0.0981882	+	0.995168i	$0.468695\pi$
$62$	10.5798	+	2.16816i	1.34363	+	0.275357i
$63$	−3.10167	+	9.54596i	−0.390774	+	1.20268i
$64$	6.67192	+	4.41423i	0.833991	+	0.551779i
$65$	−0.964075	−	4.83281i	−0.119579	−	0.599437i
$66$	−0.192355	−	0.291516i	−0.0236772	−	0.0358832i
$67$	4.74172	+	6.52642i	0.579294	+	0.797329i	0.993618	−	0.112800i	$-0.0359820\pi$
$67$	4.74172	+	6.52642i	0.579294	+	0.797329i	−0.414324	+	0.910129i	$0.635982\pi$
$68$	3.16536	−	0.721299i	0.383856	−	0.0874704i
$69$	−0.322043	+	0.632046i	−0.0387695	+	0.0760893i
$70$	−10.6070	−	0.0555286i	−1.26778	−	0.00663694i
$71$	−2.11086	−	13.3274i	−0.250513	−	1.58167i	−0.716953	−	0.697122i	$-0.754464\pi$
$71$	−2.11086	−	13.3274i	−0.250513	−	1.58167i	0.466440	−	0.884553i	$-0.345536\pi$
$72$	−8.10479	−	2.43842i	−0.955158	−	0.287371i
$73$	7.23913	−	7.23913i	0.847276	−	0.847276i	−0.142516	−	0.989792i	$-0.545519\pi$
$73$	7.23913	−	7.23913i	0.847276	−	0.847276i	0.989792	+	0.142516i	$0.0455193\pi$
$74$	−9.65362	+	2.66240i	−1.12221	+	0.309498i
$75$	−0.101595	+	0.425236i	−0.0117311	+	0.0491020i
$76$	2.41265	−	9.56065i	0.276750	−	1.09668i
$77$	−9.35705	−	1.48201i	−1.06633	−	0.168891i
$78$	0.183834	+	0.201194i	0.0208151	+	0.0227807i
$79$	−4.92171	+	4.92171i	−0.553736	+	0.553736i	−0.927517	−	0.373781i	$-0.878061\pi$
$79$	−4.92171	+	4.92171i	−0.553736	+	0.553736i	0.373781	+	0.927517i	$0.378061\pi$
$80$	−0.149152	−	8.94303i	−0.0166757	−	0.999861i
$81$	8.93125			0.992361
$82$	−2.36429	−	8.74129i	−0.261092	−	0.965314i
$83$	2.96110	−	2.96110i	0.325023	−	0.325023i	−0.525667	−	0.850690i	$-0.676184\pi$
$83$	2.96110	−	2.96110i	0.325023	−	0.325023i	0.850690	+	0.525667i	$0.176184\pi$
$84$	0.503674	−	0.300691i	0.0549554	−	0.0328080i
$85$	−2.66673	−	2.46237i	−0.289247	−	0.267082i
$86$	0.211954	+	0.00955625i	0.0228555	+	0.00103048i
$87$	0.0833798	−	0.526439i	0.00893925	−	0.0564402i
$88$	1.07650	−	7.91561i	0.114755	−	0.843807i
$89$	13.4242	−	6.84000i	1.42297	−	0.725038i	0.438194	−	0.898880i	$-0.355618\pi$
$89$	13.4242	−	6.84000i	1.42297	−	0.725038i	0.984774	+	0.173842i	$0.0556183\pi$
$90$	2.87697	+	9.01470i	0.303259	+	0.950233i
$91$	7.39246			0.774940
$92$	−15.0608	+	6.03514i	−1.57019	+	0.629207i
$93$	0.540215	+	0.392489i	0.0560177	+	0.0406993i
$94$	−7.27229	−	7.95902i	−0.750080	−	0.820910i
$95$	−10.3407	+	3.82137i	−1.06094	+	0.392065i
$96$	0.262795	+	0.419055i	0.0268214	+	0.0427696i
$97$	−7.15121	+	5.19566i	−0.726095	+	0.527539i	−0.888326	−	0.459214i	$-0.848131\pi$
$97$	−7.15121	+	5.19566i	−0.726095	+	0.527539i	0.162231	+	0.986753i	$0.448131\pi$
$98$	1.20701	−	5.88975i	0.121927	−	0.594955i
$99$	1.32210	+	8.34741i	0.132876	+	0.838946i
$100$	−8.15127	+	5.79283i	−0.815127	+	0.579283i
$101$	11.9849	−	6.10663i	1.19255	−	0.607632i	0.258926	−	0.965897i	$-0.416632\pi$
$101$	11.9849	−	6.10663i	1.19255	−	0.607632i	0.933620	+	0.358265i	$0.116632\pi$
$102$	0.196644	+	0.0402991i	0.0194707	+	0.00399021i
$103$	−4.56100	+	2.32395i	−0.449409	+	0.228985i	−0.664021	−	0.747714i	$-0.731151\pi$
$103$	−4.56100	+	2.32395i	−0.449409	+	0.228985i	0.214612	+	0.976699i	$0.431151\pi$
$104$	0.136575	+	6.23203i	0.0133923	+	0.611101i
$105$	−0.595750	−	0.274246i	−0.0581392	−	0.0267637i
$106$	−3.21261	−	1.82364i	−0.312036	−	0.177128i
$107$	5.52265	−	2.81393i	0.533894	−	0.272033i	−0.166189	−	0.986094i	$-0.553146\pi$
$107$	5.52265	−	2.81393i	0.533894	−	0.272033i	0.700083	+	0.714061i	$0.253146\pi$
$108$	−0.788940	−	0.689766i	−0.0759158	−	0.0663728i
$109$	8.17576	−	8.17576i	0.783095	−	0.783095i	−0.197257	−	0.980352i	$-0.563203\pi$
$109$	8.17576	−	8.17576i	0.783095	−	0.783095i	0.980352	+	0.197257i	$0.0632032\pi$
$110$	−7.97904	+	4.01305i	−0.760772	+	0.382629i
$111$	−0.611544	−	0.0968591i	−0.0580452	−	0.00919346i
$112$	13.1998	+	2.40502i	1.24727	+	0.227253i
$113$	1.78647	+	11.2793i	0.168057	+	1.06107i	0.917131	+	0.398585i	$0.130499\pi$
$113$	1.78647	+	11.2793i	0.168057	+	1.06107i	−0.749074	+	0.662486i	$0.769501\pi$
$114$	0.380205	−	0.476589i	0.0356094	−	0.0446367i
$115$	15.0885	+	10.0698i	1.40701	+	0.939010i
$116$	9.36122	−	7.80971i	0.869167	−	0.725113i
$117$	−2.03791	−	6.27203i	−0.188404	−	0.579849i
$118$	3.15892	−	2.88636i	0.290802	−	0.265711i
$119$	4.40497	−	3.20040i	0.403803	−	0.293380i
$120$	0.220190	−	0.507299i	0.0201005	−	0.0463098i
$121$	2.87508	−	0.934169i	0.261370	−	0.0849244i
$122$	0.990042	+	8.80080i	0.0896342	+	0.796787i
$123$	0.0903230	−	0.552561i	0.00814415	−	0.0498227i
$124$	3.39332	+	14.8913i	0.304730	+	1.33728i
$125$	10.4957	+	3.85236i	0.938762	+	0.344565i
$126$	−14.1058	+	1.58682i	−1.25664	+	0.141366i
$127$	−7.73449	−	1.22502i	−0.686325	−	0.108703i	−0.196473	−	0.980509i	$-0.562949\pi$
$127$	−7.73449	−	1.22502i	−0.686325	−	0.108703i	−0.489851	+	0.871806i	$0.662949\pi$
$128$	−1.78363	+	11.1722i	−0.157652	+	0.987495i
$129$	0.0116886	+	0.00595563i	0.00102912	+	0.000524364i
$130$	5.65965	−	4.06688i	0.496384	−	0.356689i
$131$	−8.10031	−	5.88522i	−0.707727	−	0.514194i	0.174712	−	0.984620i	$-0.444100\pi$
$131$	−8.10031	−	5.88522i	−0.707727	−	0.514194i	−0.882440	+	0.470425i	$0.844100\pi$
$132$	0.262932	−	0.418127i	0.0228853	−	0.0363933i
$133$	−2.58700	−	16.3337i	−0.224321	−	1.41631i
$134$	−5.63199	+	9.92154i	−0.486530	+	0.857091i
$135$	−0.137071	+	1.16360i	−0.0117972	+	0.100147i
$136$	2.77940	+	3.65437i	0.238331	+	0.313360i
$137$	8.29161			0.708400			0.354200	−	0.935170i	$-0.384753\pi$
$137$	8.29161			0.708400			0.354200	+	0.935170i	$0.384753\pi$
$138$	−1.00217	−	0.0451844i	−0.0853104	−	0.00384635i
$139$	1.00225	−	3.08462i	0.0850100	−	0.261634i	−0.899512	−	0.436897i	$-0.856078\pi$
$139$	1.00225	−	3.08462i	0.0850100	−	0.261634i	0.984522	+	0.175263i	$0.0560775\pi$
$140$	−6.12972	−	13.6913i	−0.518056	−	1.15712i
$141$	−0.205989	−	0.633970i	−0.0173474	−	0.0533899i
$142$	15.9278	−	10.5098i	1.33663	−	0.881966i
$143$	5.54611	−	2.82588i	0.463789	−	0.236312i
$144$	−1.59834	−	11.8622i	−0.133195	−	0.988518i
$145$	−13.1204	−	3.69253i	−1.08959	−	0.306648i
$146$	13.5542	+	5.08968i	1.12175	+	0.421225i
$147$	0.218498	−	0.300737i	0.0180214	−	0.0248044i
$148$	−9.07224	−	10.8746i	−0.745733	−	0.893884i
$149$	−1.08523	+	6.85190i	−0.0889059	+	0.561330i	0.902519	+	0.430650i	$0.141716\pi$
$149$	−1.08523	+	6.85190i	−0.0889059	+	0.561330i	−0.991425	+	0.130679i	$0.958284\pi$
$150$	−0.606978	+	0.117783i	−0.0495595	+	0.00961690i
$151$	6.43889	−	12.6370i	0.523989	−	1.02839i	−0.465671	−	0.884958i	$-0.654187\pi$
$151$	6.43889	−	12.6370i	0.523989	−	1.02839i	0.989661	−	0.143429i	$-0.0458129\pi$
$152$	13.7219	−	2.48267i	1.11299	−	0.201371i
$153$	−3.92967	−	2.85507i	−0.317695	−	0.230819i
$154$	−3.56204	−	12.9156i	−0.287037	−	1.04077i
$155$	11.5841	−	12.5455i	0.930460	−	1.00768i
$156$	−0.151604	+	0.354350i	−0.0121380	+	0.0283707i
$157$	1.68340	+	0.546971i	0.134350	+	0.0436530i	0.375420	−	0.926855i	$-0.377498\pi$
$157$	1.68340	+	0.546971i	0.134350	+	0.0436530i	−0.241070	+	0.970508i	$0.577498\pi$
$158$	−9.21514	−	3.46035i	−0.733117	−	0.275291i
$159$	−0.134254	−	0.184785i	−0.0106471	−	0.0146544i
$160$	11.4289	−	5.42046i	0.903530	−	0.428525i
$161$	−19.2415	+	19.2415i	−1.51644	+	1.51644i
$162$	5.22150	+	11.5009i	0.410240	+	0.903594i
$163$	0.577449	−	0.577449i	0.0452293	−	0.0452293i	−0.684130	−	0.729360i	$-0.739818\pi$
$163$	0.577449	−	0.577449i	0.0452293	−	0.0452293i	0.729360	+	0.684130i	$0.239818\pi$
$164$	9.87403	−	8.15497i	0.771032	−	0.636796i
$165$	−0.551790	+	0.0219844i	−0.0429568	+	0.00171149i
$166$	5.54420	+	2.08189i	0.430314	+	0.161586i
$167$	4.26749			0.330228			0.165114	−	0.986274i	$-0.447201\pi$
$167$	4.26749			0.330228			0.165114	+	0.986274i	$0.447201\pi$
$168$	0.681668	+	0.472794i	0.0525918	+	0.0364769i
$169$	6.58774	−	4.78627i	0.506749	−	0.368175i
$170$	1.61177	−	4.87356i	0.123617	−	0.373785i
$171$	−13.1449	+	6.69766i	−1.00522	+	0.512183i
$172$	0.111609	+	0.278522i	0.00851014	+	0.0212371i
$173$	1.36508	−	1.36508i	0.103785	−	0.103785i	−0.653307	−	0.757093i	$-0.726619\pi$
$173$	1.36508	−	1.36508i	0.103785	−	0.103785i	0.757093	+	0.653307i	$0.226619\pi$
$174$	0.726649	−	0.200405i	0.0550871	−	0.0151926i
$175$	−8.74728	+	14.3096i	−0.661232	+	1.08171i
$176$	10.8224	−	3.24150i	0.815768	−	0.244338i
$177$	0.251621	−	0.0817567i	0.0189130	−	0.00614521i
$178$	16.6562	+	13.2877i	1.24844	+	0.995954i
$179$	20.7975	+	3.29400i	1.55448	+	0.246205i	0.873767	−	0.486345i	$-0.161670\pi$
$179$	20.7975	+	3.29400i	1.55448	+	0.246205i	0.680713	+	0.732550i	$0.261670\pi$
$180$	−9.92638	+	8.97500i	−0.739868	+	0.668957i
$181$	2.02554	+	12.7887i	0.150557	+	0.950580i	0.941089	+	0.338159i	$0.109804\pi$
$181$	2.02554	+	12.7887i	0.150557	+	0.950580i	−0.790532	+	0.612421i	$0.790196\pi$
$182$	4.32188	+	9.51936i	0.320359	+	0.705622i
$183$	−0.169213	+	0.520785i	−0.0125086	+	0.0384975i
$184$	−16.5765	−	15.8656i	−1.22204	−	1.16963i
$185$	−4.28947	+	15.2415i	−0.315368	+	1.12058i
$186$	−0.189586	+	0.925105i	−0.0139011	+	0.0678320i
$187$	2.08138	−	4.08493i	0.152205	−	0.298720i
$188$	5.99731	−	14.0177i	0.437399	−	1.02235i
$189$	−1.67154	−	0.543118i	−0.121587	−	0.0395060i
$190$	−10.9664	−	11.0818i	−0.795584	−	0.803957i
$191$	4.99906	−	4.99906i	0.361719	−	0.361719i	−0.502726	−	0.864446i	$-0.667670\pi$
$191$	4.99906	−	4.99906i	0.361719	−	0.361719i	0.864446	+	0.502726i	$0.167670\pi$
$192$	−0.385984	+	0.583398i	−0.0278560	+	0.0421031i
$193$	16.5281	−	12.0084i	1.18972	−	0.864381i	0.196484	−	0.980507i	$-0.437048\pi$
$193$	16.5281	−	12.0084i	1.18972	−	0.864381i	0.993234	+	0.116126i	$0.0370477\pi$
$194$	−10.8713	−	6.17115i	−0.780517	−	0.443062i
$195$	0.422585	−	0.0842995i	0.0302619	−	0.00603681i
$196$	8.28996	−	1.88906i	0.592140	−	0.134933i
$197$	3.39437	+	21.4312i	0.241839	+	1.52691i	0.747548	+	0.664207i	$0.231231\pi$
$197$	3.39437	+	21.4312i	0.241839	+	1.52691i	−0.505709	+	0.862704i	$0.668769\pi$
$198$	−9.97612	+	6.58266i	−0.708972	+	0.467809i
$199$	9.41458	−	18.4772i	0.667382	−	1.30981i	−0.270454	−	0.962733i	$-0.587174\pi$
$199$	9.41458	−	18.4772i	0.667382	−	1.30981i	0.937836	−	0.347078i	$-0.112826\pi$
$200$	−12.2250	−	7.10981i	−0.864438	−	0.502740i
$201$	−0.570675	+	0.414620i	−0.0402523	+	0.0292450i
$202$	14.8704	+	11.8630i	1.04628	+	0.834679i
$203$	9.28242	−	18.2178i	0.651498	−	1.27864i
$204$	0.0630709	+	0.276781i	0.00441585	+	0.0193786i
$205$	−13.7630	−	3.94702i	−0.961252	−	0.275672i
$206$	−5.65909	−	4.51460i	−0.394287	−	0.314547i
$207$	21.6295	+	11.0208i	1.50336	+	0.765999i
$208$	−7.94522	+	3.81932i	−0.550902	+	0.264822i
$209$	−8.18466	−	11.2652i	−0.566145	−	0.779232i
$210$	0.00485547	−	0.927488i	0.000335059	−	0.0640027i
$211$	−8.74091	−	4.45372i	−0.601749	−	0.306607i	0.126449	−	0.991973i	$-0.459642\pi$
$211$	−8.74091	−	4.45372i	−0.601749	−	0.306607i	−0.728198	+	0.685367i	$0.759642\pi$
$212$	0.470133	−	5.20308i	0.0322889	−	0.357349i
$213$	1.16536	−	0.184575i	0.0798492	−	0.0126469i
$214$	6.85226	+	5.46647i	0.468411	+	0.373680i
$215$	0.186223	−	0.279035i	0.0127003	−	0.0190300i
$216$	0.426980	−	1.41919i	0.0290523	−	0.0965635i
$217$	15.0562	+	20.7230i	1.02208	+	1.40677i
$218$	15.3078	+	5.74821i	1.03678	+	0.389318i
$219$	0.632995	+	0.632995i	0.0427739	+	0.0427739i
$220$	−9.83247	−	7.92855i	−0.662905	−	0.534543i
$221$	−1.10549	+	3.40236i	−0.0743636	+	0.228868i
$222$	−0.232802	−	0.844120i	−0.0156247	−	0.0566536i
$223$	−15.7480	−	8.02402i	−1.05457	−	0.537328i	−0.161323	−	0.986902i	$-0.551576\pi$
$223$	−15.7480	−	8.02402i	−1.05457	−	0.537328i	−0.893243	+	0.449574i	$0.851576\pi$
$224$	4.62008	+	18.4037i	0.308692	+	1.22965i
$225$	14.5522	+	3.47672i	0.970148	+	0.231781i
$226$	−13.4801	+	8.89474i	−0.896684	+	0.591669i
$227$	0.353345	+	0.114809i	0.0234523	+	0.00762012i	0.320720	−	0.947174i	$-0.396075\pi$
$227$	0.353345	+	0.114809i	0.0234523	+	0.00762012i	−0.297267	+	0.954794i	$0.596075\pi$
$228$	0.835990	+	0.210964i	0.0553648	+	0.0139715i
$229$	−18.0658	+	2.86135i	−1.19382	+	0.189083i	−0.721546	−	0.692366i	$-0.756568\pi$
$229$	−18.0658	+	2.86135i	−1.19382	+	0.189083i	−0.472279	+	0.881449i	$0.656568\pi$
$230$	−4.14575	+	25.3167i	−0.273362	+	1.66933i
$231$	0.129588	−	0.818188i	0.00852628	−	0.0538328i
$232$	15.5295	+	7.48874i	1.01956	+	0.491660i
$233$	6.25052	+	19.2371i	0.409485	+	1.26027i	0.917092	+	0.398677i	$0.130530\pi$
$233$	6.25052	+	19.2371i	0.409485	+	1.26027i	−0.507606	+	0.861589i	$0.669470\pi$
$234$	6.88514	−	6.29107i	0.450096	−	0.411260i
$235$	−16.7170	+	3.33481i	−1.09050	+	0.217539i
$236$	5.56361	+	2.38032i	0.362160	+	0.154945i
$237$	−0.430358	−	0.430358i	−0.0279548	−	0.0279548i
$238$	6.69649	+	3.80128i	0.434069	+	0.246400i
$239$	8.51644	+	16.7145i	0.550883	+	1.08117i	0.983722	+	0.179697i	$0.0575118\pi$
$239$	8.51644	+	16.7145i	0.550883	+	1.08117i	−0.432839	+	0.901471i	$0.642488\pi$
$240$	0.781985	−	0.0130420i	0.0504769	−	0.000841858i
$241$	−16.3073	−	22.4451i	−1.05045	−	1.44582i	−0.888420	−	0.459031i	$-0.848197\pi$
$241$	−16.3073	−	22.4451i	−1.05045	−	1.44582i	−0.162028	−	0.986786i	$-0.551803\pi$
$242$	2.88381	+	3.15613i	0.185378	+	0.202883i
$243$			2.35288i			0.150938i
$244$	−10.7541	+	6.42013i	−0.688460	+	0.411007i
$245$	−6.98406	−	6.44887i	−0.446196	−	0.412003i
$246$	0.764345	−	0.206735i	0.0487329	−	0.0131810i
$247$	7.68311	+	7.68311i	0.488865	+	0.488865i
$248$	−17.1919	+	13.0756i	−1.09168	+	0.830300i
$249$	0.258921	+	0.258921i	0.0164084	+	0.0164084i
$250$	1.17539	+	15.7676i	0.0743383	+	0.997233i
$251$	−8.87634	+	6.44904i	−0.560270	+	0.407060i	−0.831558	−	0.555438i	$-0.812550\pi$
$251$	−8.87634	+	6.44904i	−0.560270	+	0.407060i	0.271288	+	0.962498i	$0.412550\pi$
$252$	−10.2901	−	17.2365i	−0.648215	−	1.08580i
$253$	−7.08035	+	21.7911i	−0.445138	+	1.36999i
$254$	−2.94436	−	10.6760i	−0.184746	−	0.669871i
$255$	0.215312	−	0.233181i	0.0134833	−	0.0146023i
$256$	−15.4294	+	4.23485i	−0.964337	+	0.264678i
$257$	7.08552	−	9.75238i	0.441983	−	0.608337i	−0.528669	−	0.848828i	$-0.677309\pi$
$257$	7.08552	−	9.75238i	0.441983	−	0.608337i	0.970651	+	0.240491i	$0.0773086\pi$
$258$	−0.000835606		0.0185334i	−5.20226e−5		0.00115384i
$259$	−21.1629	−	10.7830i	−1.31500	−	0.670025i
$260$	8.54578	+	4.91037i	0.529987	+	0.304528i
$261$	−18.0155	−	2.85338i	−1.11513	−	0.176620i
$262$	2.84276	−	13.8716i	0.175626	−	0.856988i
$263$	−1.83867	−	1.33587i	−0.113377	−	0.0823735i	0.529652	−	0.848215i	$-0.322323\pi$
$263$	−1.83867	−	1.33587i	−0.113377	−	0.0823735i	−0.643029	+	0.765842i	$0.722323\pi$
$264$	0.692147	+	0.0941302i	0.0425987	+	0.00579331i
$265$	−5.09460	+	2.85680i	−0.312959	+	0.175492i
$266$	19.5206	−	12.8805i	1.19689	−	0.789754i
$267$	0.598095	+	1.17383i	0.0366028	+	0.0718370i
$268$	−16.0687	−	1.45192i	−0.981555	−	0.0886901i
$269$	−14.7229	+	4.78375i	−0.897669	+	0.291670i	−0.721275	−	0.692649i	$-0.756443\pi$
$269$	−14.7229	+	4.78375i	−0.897669	+	0.291670i	−0.176394	+	0.984320i	$0.556443\pi$
$270$	−1.57852	+	0.503771i	−0.0960656	+	0.0306586i
$271$	−9.41706	−	3.05979i	−0.572045	−	0.185869i	0.00868853	−	0.999962i	$-0.497234\pi$
$271$	−9.41706	−	3.05979i	−0.572045	−	0.185869i	−0.580734	+	0.814093i	$0.697234\pi$
$272$	−3.08086	+	5.71554i	−0.186804	+	0.346555i
$273$			0.646402i			0.0391221i
$274$	4.84755	+	10.6772i	0.292851	+	0.645034i
$275$	−1.09246	+	14.0794i	−0.0658780	+	0.849022i
$276$	−0.527718	−	1.31692i	−0.0317649	−	0.0792695i
$277$	−27.4851	+	4.35321i	−1.65142	+	0.261559i	−0.911550	−	0.411190i	$-0.865113\pi$
$277$	−27.4851	+	4.35321i	−1.65142	+	0.261559i	−0.739870	+	0.672750i	$0.765113\pi$
$278$	4.55805	−	0.512756i	0.273374	−	0.0307531i
$279$	13.4316	−	18.4870i	0.804128	−	1.10679i
$280$	14.0468	−	15.8977i	0.839457	−	0.950069i
$281$	8.21034	−	16.1137i	0.489788	−	0.961263i	−0.505363	−	0.862907i	$-0.668642\pi$
$281$	8.21034	−	16.1137i	0.489788	−	0.961263i	0.995151	−	0.0983562i	$-0.0313584\pi$
$282$	0.695943	−	0.635895i	0.0414428	−	0.0378670i
$283$	−1.78844	+	11.2918i	−0.106312	+	0.671225i	0.875764	+	0.482739i	$0.160358\pi$
$283$	−1.78844	+	11.2918i	−0.106312	+	0.671225i	−0.982076	+	0.188486i	$0.939642\pi$
$284$	22.8456	+	14.3661i	1.35564	+	0.852469i
$285$	−0.334144	−	0.904202i	−0.0197930	−	0.0535603i
$286$	6.88137	+	5.48969i	0.406904	+	0.324612i
$287$	9.84538	−	19.0885i	0.581154	−	1.12676i
$288$	14.3407	−	8.99325i	0.845033	−	0.529932i
$289$	−4.43905	−	13.6620i	−0.261120	−	0.803646i
$290$	−2.91571	−	19.0541i	−0.171216	−	1.11889i
$291$	−0.454312	−	0.625307i	−0.0266322	−	0.0366561i
$292$	1.37016	+	20.4295i	0.0801826	+	1.19554i
$293$	12.0710	−	3.92211i	0.705197	−	0.229132i	0.0656033	−	0.997846i	$-0.479103\pi$
$293$	12.0710	−	3.92211i	0.705197	−	0.229132i	0.639593	+	0.768714i	$0.279103\pi$
$294$	0.515004	+	0.105542i	0.0300357	+	0.00615534i
$295$	−1.32358	−	6.63496i	−0.0770616	−	0.386302i
$296$	8.69938	−	18.0401i	0.505641	−	1.04856i
$297$	−1.46167	+	0.231506i	−0.0848149	+	0.0134334i
$298$	−9.45775	+	2.60838i	−0.547872	+	0.151099i
$299$	2.79689	−	17.6588i	0.161748	−	1.02124i
$300$	−0.506529	−	0.712753i	−0.0292445	−	0.0411508i
$301$	0.355838	+	0.355838i	0.0205101	+	0.0205101i
$302$	20.0373	+	0.903410i	1.15301	+	0.0519854i
$303$	0.533968	+	1.04797i	0.0306757	+	0.0602044i
$304$	11.2192	+	16.2184i	0.643467	+	0.930189i
$305$	12.7200	+	5.85551i	0.728346	+	0.335285i
$306$	1.37910	−	6.72945i	0.0788377	−	0.384697i
$307$	−3.32785	−	6.53128i	−0.189930	−	0.372760i	0.776330	−	0.630327i	$-0.217079\pi$
$307$	−3.32785	−	6.53128i	−0.189930	−	0.372760i	−0.966260	+	0.257567i	$0.917079\pi$
$308$	14.5491	−	12.1378i	0.829014	−	0.691614i
$309$	−0.203208	−	0.398818i	−0.0115601	−	0.0226879i
$310$	22.9275	+	7.58252i	1.30219	+	0.430658i
$311$	−0.479154	+	0.0758905i	−0.0271703	+	0.00430335i	−0.170005	−	0.985443i	$-0.554378\pi$
$311$	−0.479154	+	0.0758905i	−0.0271703	+	0.00430335i	0.142835	+	0.989747i	$0.454378\pi$
$312$	−0.544934	+	0.0119422i	−0.0308508	+	0.000676097i
$313$	−0.0166392	−	0.0229018i	−0.000940501	−	0.00129449i	0.808546	−	0.588432i	$-0.200255\pi$
$313$	−0.0166392	−	0.0229018i	−0.000940501	−	0.00129449i	−0.809487	+	0.587138i	$0.800255\pi$
$314$	0.279832	+	2.48752i	0.0157918	+	0.140379i
$315$	−9.38512	+	20.3874i	−0.528792	+	1.14870i
$316$	−0.931539	−	13.8895i	−0.0524031	−	0.781345i
$317$	16.4718	−	22.6714i	0.925146	−	1.27335i	−0.0365769	−	0.999331i	$-0.511645\pi$
$317$	16.4718	−	22.6714i	0.925146	−	1.27335i	0.961723	−	0.274024i	$-0.0883546\pi$
$318$	0.159461	−	0.280913i	0.00894212	−	0.0157528i
$319$		−	17.2160i		−	0.963913i
$320$	13.6617	+	11.5481i	0.763711	+	0.645558i
$321$	0.246052	+	0.482905i	0.0137333	+	0.0269531i
$322$	−36.0267	−	13.5283i	−2.00769	−	0.753902i
$323$	7.90439	+	1.25193i	0.439812	+	0.0696594i
$324$	−11.7572	+	13.4476i	−0.653176	+	0.747088i
$325$	−0.876681	−	10.9845i	−0.0486295	−	0.609310i
$326$	1.08118	+	0.405992i	0.0598812	+	0.0224858i
$327$	0.714894	+	0.714894i	0.0395337	+	0.0395337i
$328$	16.2739	+	7.94724i	0.898578	+	0.438813i
$329$		−	25.5710i		−	1.40978i
$330$	−0.350904	−	0.697694i	−0.0193166	−	0.0384068i
$331$	−14.1122	−	14.1122i	−0.775675	−	0.775675i	0.203417	−	0.979092i	$-0.434795\pi$
$331$	−14.1122	−	14.1122i	−0.775675	−	0.775675i	−0.979092	+	0.203417i	$0.934795\pi$
$332$	0.560451	+	8.35648i	0.0307588	+	0.458622i
$333$	−3.31466	+	20.9280i	−0.181642	+	1.14685i
$334$	2.49492	+	5.49530i	0.136516	+	0.300689i
$335$	8.82271	+	15.7337i	0.482036	+	0.859626i
$336$	−0.210297	+	1.15420i	−0.0114727	+	0.0629670i
$337$	15.5590	+	15.5590i	0.847552	+	0.847552i	0.989827	−	0.142275i	$-0.0454418\pi$
$337$	15.5590	+	15.5590i	0.847552	+	0.847552i	−0.142275	+	0.989827i	$0.545442\pi$
$338$	10.0148	+	5.68490i	0.544731	+	0.309218i
$339$	−0.986274	+	0.156210i	−0.0535670	+	0.00848419i
$340$	7.21804	−	0.773748i	0.391453	−	0.0419624i
$341$	19.2174	+	9.79177i	1.04068	+	0.530254i
$342$	−16.3096	−	13.0112i	−0.881922	−	0.703564i
$343$	−7.45925	+	5.41946i	−0.402762	+	0.292623i
$344$	−0.293406	+	0.306554i	−0.0158194	+	0.0165283i
$345$	−0.880508	+	1.31935i	−0.0474049	+	0.0710312i
$346$	2.55591	+	0.959762i	0.137407	+	0.0515971i
$347$	−15.3738	−	4.99525i	−0.825309	−	0.268159i	−0.134241	−	0.990949i	$-0.542860\pi$
$347$	−15.3738	−	4.99525i	−0.825309	−	0.268159i	−0.691068	+	0.722790i	$0.742860\pi$
$348$	0.682887	+	0.818552i	0.0366066	+	0.0438790i
$349$	−8.25397	+	25.4031i	−0.441825	+	1.35980i	0.444103	+	0.895976i	$0.353522\pi$
$349$	−8.25397	+	25.4031i	−0.441825	+	1.35980i	−0.885928	+	0.463822i	$0.846478\pi$
$350$	−23.5407	−	2.89809i	−1.25830	−	0.154910i
$351$	1.09826	−	0.356847i	0.0586210	−	0.0190471i
$352$	10.5013	+	12.0410i	0.559719	+	0.641789i
$353$	−13.0960	+	6.67274i	−0.697029	+	0.355154i	−0.766335	−	0.642442i	$-0.777922\pi$
$353$	−13.0960	+	6.67274i	−0.697029	+	0.355154i	0.0693059	+	0.997595i	$0.477922\pi$
$354$	0.252385	+	0.276218i	0.0134141	+	0.0146808i
$355$	−1.20118	−	30.1486i	−0.0637521	−	1.60012i
$356$	−7.37295	+	29.2168i	−0.390765	+	1.54849i
$357$	0.279845	+	0.385174i	0.0148110	+	0.0203856i
$358$	7.91719	+	28.7070i	0.418437	+	1.51721i
$359$	−26.3433	−	19.1395i	−1.39035	−	1.01015i	−0.995827	−	0.0912570i	$-0.970912\pi$
$359$	−26.3433	−	19.1395i	−1.39035	−	1.01015i	−0.394518	−	0.918888i	$-0.629088\pi$
$360$	−17.3605	−	7.53524i	−0.914980	−	0.397142i
$361$	3.11921	−	4.29323i	0.164169	−	0.225959i
$362$	−15.2840	+	10.0850i	−0.803311	+	0.530058i
$363$	0.0816844	+	0.251399i	0.00428732	+	0.0131950i
$364$	−9.73149	+	11.1307i	−0.510069	+	0.583406i
$365$	17.9698	−	14.1823i	0.940581	−	0.742335i
$366$	−0.769549	+	0.0865700i	−0.0402249	+	0.00452509i
$367$	−25.5442	−	13.0154i	−1.33339	−	0.679398i	−0.365513	−	0.930806i	$-0.619106\pi$
$367$	−25.5442	−	13.0154i	−1.33339	−	0.679398i	−0.967881	+	0.251408i	$0.919106\pi$
$368$	10.7391	−	30.6214i	0.559814	−	1.59625i
$369$	−18.9094	−	3.09099i	−0.984387	−	0.160910i
$370$	−22.1344	+	3.38706i	−1.15071	+	0.176085i
$371$	−2.70756	−	8.33302i	−0.140570	−	0.432629i
$372$	−1.30211	+	0.296715i	−0.0675111	+	0.0153840i
$373$	−10.6469	−	1.68630i	−0.551273	−	0.0873131i	−0.125417	−	0.992104i	$-0.540027\pi$
$373$	−10.6469	−	1.68630i	−0.551273	−	0.0873131i	−0.425856	+	0.904791i	$0.640027\pi$
$374$	6.47706	+	0.292028i	0.334921	+	0.0151004i
$375$	−0.336853	+	0.917751i	−0.0173950	+	0.0473924i
$376$	21.5570	−	0.472424i	1.11172	−	0.0243634i
$377$	2.10153	+	13.2685i	0.108234	+	0.683365i
$378$	−0.277861	−	2.46999i	−0.0142916	−	0.127043i
$379$	25.7316	+	18.6951i	1.32174	+	0.960301i	0.999909	+	0.0135045i	$0.00429876\pi$
$379$	25.7316	+	18.6951i	1.32174	+	0.960301i	0.321832	+	0.946797i	$0.395701\pi$
$380$	7.85886	−	20.6003i	0.403151	−	1.05677i
$381$	0.107117	−	0.676310i	0.00548777	−	0.0346484i
$382$	9.35997	+	3.51473i	0.478897	+	0.179829i
$383$	12.0350			0.614959			0.307480	−	0.951555i	$-0.400514\pi$
$383$	12.0350			0.614959			0.307480	+	0.951555i	$0.400514\pi$
$384$	−0.976908	−	0.155962i	−0.0498526	−	0.00795890i
$385$	−20.3916	−	5.73891i	−1.03925	−	0.292482i
$386$	25.1262	+	14.2629i	1.27889	+	0.725965i
$387$	0.203810	−	0.400001i	0.0103603	−	0.0203332i
$388$	1.59091	−	17.6070i	0.0807664	−	0.893861i
$389$	6.55855	−	20.1851i	0.332532	−	1.02343i	−0.635394	−	0.772188i	$-0.719162\pi$
$389$	6.55855	−	20.1851i	0.332532	−	1.02343i	0.967925	−	0.251238i	$-0.0808378\pi$
$390$	0.355611	+	0.494884i	0.0180071	+	0.0250594i
$391$	−5.97841	−	11.7333i	−0.302341	−	0.593378i
$392$	7.27915	+	9.57069i	0.367653	+	0.483393i
$393$	0.514608	−	0.708297i	0.0259585	−	0.0357289i
$394$	−25.6128	+	16.9004i	−1.29035	+	0.851429i
$395$	−12.2172	+	9.64220i	−0.614715	+	0.485152i
$396$	−14.3089	−	8.99794i	−0.719052	−	0.452163i
$397$	−17.4963	+	5.68490i	−0.878115	+	0.285317i	−0.713174	−	0.700987i	$-0.752743\pi$
$397$	−17.4963	+	5.68490i	−0.878115	+	0.285317i	−0.164941	+	0.986304i	$0.552743\pi$
$398$	29.2974	+	1.32092i	1.46854	+	0.0662115i
$399$	1.42823	−	0.226209i	0.0715008	−	0.0113246i
$400$	2.00825	−	19.8989i	0.100413	−	0.994946i
$401$			18.9583i			0.946733i	0.880866	+	0.473366i	$0.156961\pi$
$401$			18.9583i			0.946733i	−0.880866	+	0.473366i	$0.843039\pi$
$402$	−0.867547	−	0.492465i	−0.0432693	−	0.0245619i
$403$	−16.0063	−	5.20076i	−0.797330	−	0.259068i
$404$	−6.58244	+	26.0843i	−0.327489	+	1.29774i
$405$	19.8337	+	2.33639i	0.985546	+	0.116096i
$406$	28.8861	+	1.30237i	1.43359	+	0.0646357i
$407$	−19.9992			−0.991324
$408$	−0.319541	+	0.243033i	−0.0158197	+	0.0120319i
$409$			0.258705i			0.0127922i	0.999980	+	0.00639608i	$0.00203595\pi$
$409$			0.258705i			0.0127922i	−0.999980	+	0.00639608i	$0.997964\pi$
$410$	−2.96370	−	20.0304i	−0.146367	−	0.989230i
$411$			0.725025i			0.0357628i
$412$	2.50502	−	9.92667i	0.123414	−	0.489052i
$413$	10.1491			0.499404
$414$	−1.54628	+	34.2958i	−0.0759954	+	1.68555i
$415$	7.35037	−	5.80114i	0.360816	−	0.284767i
$416$	−9.56323	−	7.99826i	−0.468876	−	0.392147i
$417$	0.269721	+	0.0876377i	0.0132083	+	0.00429164i
$418$	9.72134	−	17.1255i	0.475486	−	0.837636i
$419$			16.3736i			0.799904i	0.916536	+	0.399952i	$0.130973\pi$
$419$			16.3736i			0.799904i	−0.916536	+	0.399952i	$0.869027\pi$
$420$	1.19718	−	0.535988i	0.0584162	−	0.0261535i
$421$	−29.1808	+	4.62178i	−1.42218	+	0.225252i	−0.819661	−	0.572849i	$-0.805838\pi$
$421$	−29.1808	+	4.62178i	−1.42218	+	0.225252i	−0.602523	+	0.798101i	$0.705838\pi$
$422$	0.624880	−	13.8596i	0.0304187	−	0.674674i
$423$	−21.6954	+	7.04926i	−1.05487	+	0.342747i
$424$	6.97492	−	2.43650i	0.338732	−	0.118327i
$425$	−5.27788	−	6.16583i	−0.256015	−	0.299087i
$426$	0.918988	+	1.39274i	0.0445251	+	0.0674785i
$427$	−12.3469	+	16.9940i	−0.597507	+	0.822397i
$428$	−3.03318	+	12.0196i	−0.146614	+	0.580990i
$429$	0.247098	+	0.484956i	0.0119300	+	0.0234139i
$430$	0.468188	+	0.0766683i	0.0225780	+	0.00369727i
$431$	−3.61303	+	11.1197i	−0.174033	+	0.535619i	−0.999588	−	0.0287027i	$-0.990862\pi$
$431$	−3.61303	+	11.1197i	−0.174033	+	0.535619i	0.825555	+	0.564322i	$0.190862\pi$
$432$	2.07713	−	0.279877i	0.0999361	−	0.0134656i
$433$	2.57599	−	5.05567i	0.123794	−	0.242960i	−0.820789	−	0.571231i	$-0.806466\pi$
$433$	2.57599	−	5.05567i	0.123794	−	0.242960i	0.944584	+	0.328271i	$0.106466\pi$
$434$	−17.8830	+	31.5034i	−0.858410	+	1.51221i
$435$	0.322878	−	1.14726i	0.0154808	−	0.0550068i
$436$	1.54744	+	23.0727i	0.0741088	+	1.10498i
$437$	−39.9960			−1.91327
$438$	−0.445046	+	1.18519i	−0.0212651	+	0.0566304i
$439$	−2.16546	+	13.6722i	−0.103352	+	0.652538i	0.880567	+	0.473922i	$0.157162\pi$
$439$	−2.16546	+	13.6722i	−0.103352	+	0.652538i	−0.983919	+	0.178616i	$0.942838\pi$
$440$	4.46131	−	17.2967i	0.212685	−	0.824587i
$441$	−10.2917	−	7.47734i	−0.490080	−	0.356064i
$442$	−5.02757	+	0.565575i	−0.239137	+	0.0269016i
$443$	−4.71834	−	29.7904i	−0.224175	−	1.41539i	−0.801071	−	0.598569i	$-0.795736\pi$
$443$	−4.71834	−	29.7904i	−0.224175	−	1.41539i	0.576896	−	0.816817i	$-0.304264\pi$
$444$	0.950880	−	0.793283i	0.0451268	−	0.0376476i
$445$	31.6007	−	11.6779i	1.49802	−	0.553586i
$446$	1.12581	−	24.9700i	0.0533088	−	1.18237i
$447$	−0.599136	−	0.0948938i	−0.0283381	−	0.00448832i
$448$	−20.9976	+	16.7087i	−0.992042	+	0.789413i
$449$	−10.5273	−	32.3997i	−0.496814	−	1.52904i	−0.814111	−	0.580709i	$-0.802775\pi$
$449$	−10.5273	−	32.3997i	−0.496814	−	1.52904i	0.317297	−	0.948326i	$-0.397225\pi$
$450$	4.03069	+	20.7717i	0.190009	+	0.979186i
$451$	0.0895198	−	18.0845i	0.00421532	−	0.851564i
$452$	−19.3348	−	12.1584i	−0.909432	−	0.571881i
$453$	1.10499	+	0.563021i	0.0519170	+	0.0264531i
$454$	0.0587365	+	0.522128i	0.00275664	+	0.0245047i
$455$	16.4165	+	1.93385i	0.769619	+	0.0906603i
$456$	0.217086	+	1.19985i	0.0101660	+	0.0561882i
$457$	−6.46776	−	19.9057i	−0.302549	−	0.931151i	−0.980580	−	0.196118i	$-0.937167\pi$
$457$	−6.46776	−	19.9057i	−0.302549	−	0.931151i	0.678031	−	0.735033i	$-0.262833\pi$
$458$	−14.2465	−	21.5908i	−0.665695	−	1.00887i
$459$	0.499937	−	0.688105i	0.0233351	−	0.0321180i
$460$	−35.0244	+	9.46246i	−1.63302	+	0.441190i
$461$	−26.6317	−	19.3491i	−1.24036	−	0.901176i	−0.242739	−	0.970092i	$-0.578046\pi$
$461$	−26.6317	−	19.3491i	−1.24036	−	0.901176i	−0.997622	+	0.0689158i	$0.978046\pi$
$462$	1.12935	−	0.311467i	0.0525422	−	0.0144908i
$463$	−3.61048	−	4.96941i	−0.167793	−	0.230948i	0.716837	−	0.697241i	$-0.245589\pi$
$463$	−3.61048	−	4.96941i	−0.167793	−	0.230948i	−0.884630	+	0.466293i	$0.845589\pi$
$464$	−0.564265	+	24.3758i	−0.0261953	+	1.13162i
$465$	1.09699	+	1.01293i	0.0508717	+	0.0469733i
$466$	−21.1176	+	19.2955i	−0.978255	+	0.893848i
$467$	8.19346	−	4.17478i	0.379148	−	0.193186i	−0.254022	−	0.967199i	$-0.581753\pi$
$467$	8.19346	−	4.17478i	0.379148	−	0.193186i	0.633170	+	0.774013i	$0.281753\pi$
$468$	12.1264	+	5.18812i	0.560542	+	0.239821i
$469$	−25.7350	+	8.36180i	−1.18833	+	0.386112i
$470$	−14.0676	−	19.5771i	−0.648891	−	0.903025i
$471$	−0.0478276	+	0.147198i	−0.00220378	+	0.00678253i
$472$	0.187504	+	8.55594i	0.00863056	+	0.393819i
$473$	0.402988	+	0.130939i	0.0185294	+	0.00602057i
$474$	0.302576	−	0.805779i	0.0138978	−	0.0370107i
$475$	−23.9635	+	5.78106i	−1.09952	+	0.265253i
$476$	−0.979965	+	10.8455i	−0.0449166	+	0.497103i
$477$	−6.32363	+	4.59439i	−0.289539	+	0.210363i
$478$	−16.5444	+	20.7386i	−0.756724	+	0.948560i
$479$	23.1893	+	11.8155i	1.05955	+	0.539865i	0.894798	−	0.446471i	$-0.147319\pi$
$479$	23.1893	+	11.8155i	1.05955	+	0.539865i	0.164747	+	0.986336i	$0.447319\pi$
$480$	0.473969	+	0.999348i	0.0216336	+	0.0456138i
$481$	15.4135	−	2.44127i	0.702797	−	0.111312i
$482$	19.3691	−	34.1213i	0.882237	−	1.55418i
$483$	−1.68249	−	1.68249i	−0.0765560	−	0.0765560i
$484$	−2.37821	+	5.55869i	−0.108101	+	0.252668i
$485$	−17.2399	+	9.66732i	−0.782826	+	0.438970i
$486$	−3.02984	+	1.37557i	−0.137436	+	0.0623973i
$487$	−6.13561	+	38.7387i	−0.278031	+	1.75542i	0.313924	+	0.949448i	$0.398356\pi$
$487$	−6.13561	+	38.7387i	−0.278031	+	1.75542i	−0.591955	+	0.805971i	$0.701644\pi$
$488$	−14.5545	−	10.0948i	−0.658850	−	0.456968i
$489$	0.0504926	+	0.0504926i	0.00228335	+	0.00228335i
$490$	4.22117	−	12.7637i	0.190693	−	0.576605i
$491$			9.05402i			0.408602i	0.978908	+	0.204301i	$0.0654921\pi$
$491$			9.05402i			0.408602i	−0.978908	+	0.204301i	$0.934508\pi$
$492$	0.713077	+	0.863393i	0.0321480	+	0.0389247i
$493$	6.99656	+	6.99656i	0.315109	+	0.315109i
$494$	−5.40184	+	14.3854i	−0.243040	+	0.647231i
$495$	0.752340	+	18.8831i	0.0338152	+	0.848731i
$496$	−26.8885	−	14.4938i	−1.20733	−	0.650790i
$497$	44.7040	+	7.08042i	2.00525	+	0.317600i
$498$	−0.182042	+	0.484789i	−0.00815749	+	0.0217239i
$499$	3.93488	+	7.72264i	0.176149	+	0.345713i	0.962153	−	0.272509i	$-0.0878534\pi$
$499$	3.93488	+	7.72264i	0.176149	+	0.345713i	−0.786004	+	0.618222i	$0.787853\pi$
$500$	−19.6170	+	10.7319i	−0.877300	+	0.479943i
$501$			0.373153i			0.0166712i
$502$	−13.4939	−	7.65986i	−0.602263	−	0.341876i
$503$	5.21733	−	7.18103i	0.232629	−	0.320186i	−0.676704	−	0.736255i	$-0.736592\pi$
$503$	5.21733	−	7.18103i	0.232629	−	0.320186i	0.909333	+	0.416069i	$0.136592\pi$
$504$	16.1797	−	23.3277i	0.720702	−	1.03910i
$505$	28.2126	−	10.4258i	1.25544	−	0.463944i
$506$	−32.2001	+	3.62233i	−1.43147	+	0.161032i
$507$	0.418515	+	0.576037i	0.0185869	+	0.0255827i
$508$	12.0262	−	10.0330i	0.533578	−	0.445144i
$509$	−9.61667	+	1.52313i	−0.426251	+	0.0675116i	−0.365875	−	0.930664i	$-0.619230\pi$
$509$	−9.61667	+	1.52313i	−0.426251	+	0.0675116i	−0.0603765	+	0.998176i	$0.519230\pi$
$510$	0.426148	+	0.140934i	0.0188701	+	0.00624068i
$511$	15.5901	+	30.5973i	0.689665	+	1.35354i
$512$	−14.4738	−	17.3928i	−0.639658	−	0.768660i
$513$	−1.17279	−	2.30174i	−0.0517801	−	0.101624i
$514$	16.7007	+	3.42255i	0.736636	+	0.150962i
$515$	−10.7366	+	3.96767i	−0.473112	+	0.174836i
$516$	−0.0243542	+	0.00975921i	−0.00107213	+	0.000429625i
$517$	−9.77494	−	19.1844i	−0.429901	−	0.843729i
$518$	1.51292	−	33.5558i	0.0664737	−	1.47436i
$519$	0.119364	+	0.119364i	0.00523950	+	0.00523950i
$520$	−1.32699	+	13.8753i	−0.0581924	+	0.608471i
$521$	−5.96773	+	37.6787i	−0.261451	+	1.65074i	0.411766	+	0.911290i	$0.364912\pi$
$521$	−5.96773	+	37.6787i	−0.261451	+	1.65074i	−0.673216	+	0.739446i	$0.735088\pi$
$522$	−6.85815	−	24.8670i	−0.300173	−	1.08840i
$523$	40.4499	−	6.40663i	1.76875	−	0.280143i	0.814721	−	0.579854i	$-0.196890\pi$
$523$	40.4499	−	6.40663i	1.76875	−	0.280143i	0.954030	+	0.299711i	$0.0968903\pi$
$524$	19.5246	−	4.44912i	0.852935	−	0.194361i
$525$	−1.25125	−	0.764869i	−0.0546089	−	0.0333816i
$526$	0.645272	−	3.14868i	0.0281352	−	0.137289i
$527$	−11.7893	+	3.83057i	−0.513549	+	0.166862i
$528$	0.283440	+	0.946318i	0.0123351	+	0.0411832i
$529$	25.1644	+	34.6359i	1.09411	+	1.50591i
$530$	−6.65722	−	4.89020i	−0.289171	−	0.212417i
$531$	−2.79784	−	8.61085i	−0.121416	−	0.373679i
$532$	27.9988	+	17.6066i	1.21390	+	0.763341i
$533$	2.13854	+	13.9488i	0.0926306	+	0.604188i
$534$	−1.16189	+	1.45643i	−0.0502797	+	0.0630260i
$535$	13.0003	−	4.80422i	0.562053	−	0.207704i
$536$	−7.52467	−	21.5408i	−0.325016	−	0.930419i
$537$	−0.288030	+	1.81855i	−0.0124294	+	0.0784763i
$538$	−14.7676	−	16.1621i	−0.636675	−	0.696797i
$539$	5.45106	−	10.6983i	0.234794	−	0.460809i
$540$	−1.57157	−	1.73816i	−0.0676295	−	0.0747984i
$541$	−21.7339	+	29.9142i	−0.934415	+	1.28611i	0.0236972	+	0.999719i	$0.492456\pi$
$541$	−21.7339	+	29.9142i	−0.934415	+	1.28611i	−0.958112	+	0.286393i	$0.907544\pi$
$542$	−1.56540	−	13.9153i	−0.0672396	−	0.597714i
$543$	−1.11826	+	0.177115i	−0.0479891	+	0.00760072i
$544$	−9.16114	−	0.625765i	−0.392781	−	0.0268295i
$545$	20.2948	−	16.0172i	0.869332	−	0.686103i
$546$	−0.832381	+	0.377908i	−0.0356226	+	0.0161730i
$547$		−	23.2717i		−	0.995025i	−0.867457	−	0.497512i	$-0.834247\pi$
$547$		−	23.2717i		−	0.995025i	0.867457	−	0.497512i	$-0.165753\pi$
$548$	−10.9151	+	12.4845i	−0.466272	+	0.533312i
$549$	17.8220	+	5.79073i	0.760626	+	0.247142i
$550$	−18.7690	+	6.82453i	−0.800311	+	0.290999i
$551$	28.5814	−	9.28667i	1.21761	−	0.395625i
$552$	1.38730	−	1.44947i	0.0590473	−	0.0616934i
$553$	−10.5993	−	20.8023i	−0.450729	−	0.884605i
$554$	−21.6744	−	32.8479i	−0.920857	−	1.39557i
$555$	−1.33273	−	0.375075i	−0.0565711	−	0.0159210i
$556$	3.32507	+	5.56968i	0.141014	+	0.236207i
$557$	−4.82048	−	3.50229i	−0.204250	−	0.148397i	0.480958	−	0.876744i	$-0.340289\pi$
$557$	−4.82048	−	3.50229i	−0.204250	−	0.148397i	−0.685209	+	0.728347i	$0.740289\pi$
$558$	31.6585	+	6.48791i	1.34021	+	0.274655i
$559$	−0.326569	−	0.0517235i	−0.0138124	−	0.00218767i
$560$	28.6839	+	8.79392i	1.21212	+	0.371611i
$561$	0.357190	+	0.181997i	0.0150806	+	0.00768393i
$562$	25.5499	+	1.15195i	1.07776	+	0.0485923i
$563$	−19.4444	+	26.7630i	−0.819486	+	1.12793i	0.170304	+	0.985392i	$0.445525\pi$
$563$	−19.4444	+	26.7630i	−0.819486	+	1.12793i	−0.989790	+	0.142534i	$0.954475\pi$
$564$	1.22572	+	0.524409i	0.0516122	+	0.0220816i
$565$	1.01659	+	25.5155i	0.0427683	+	1.07345i
$566$	−15.5861	+	4.29854i	−0.655133	+	0.180681i
$567$	−9.25752	+	28.4917i	−0.388779	+	1.19654i
$568$	−5.14307	+	37.8174i	−0.215798	+	1.58678i
$569$	−1.59465	+	1.15858i	−0.0668511	+	0.0485702i	−0.620709	−	0.784041i	$-0.713155\pi$
$569$	−1.59465	+	1.15858i	−0.0668511	+	0.0485702i	0.553858	+	0.832611i	$0.313155\pi$
$570$	0.969000	−	0.958907i	0.0405870	−	0.0401642i
$571$	−1.76942	−	1.76942i	−0.0740479	−	0.0740479i	0.669113	−	0.743161i	$-0.266674\pi$
$571$	−1.76942	−	1.76942i	−0.0740479	−	0.0740479i	−0.743161	+	0.669113i	$0.766674\pi$
$572$	−3.04607	+	12.0707i	−0.127363	+	0.504701i
$573$	0.437121	+	0.437121i	0.0182610	+	0.0182610i
$574$	30.3364	+	1.51827i	1.26622	+	0.0633713i
$575$	30.8729	+	26.3092i	1.28749	+	1.09717i
$576$	19.9648	+	13.2089i	0.831865	+	0.550372i
$577$		−	17.3765i		−	0.723393i	−0.932296	−	0.361696i	$-0.882198\pi$
$577$		−	17.3765i		−	0.723393i	0.932296	−	0.361696i	$-0.117802\pi$
$578$	14.9975	−	13.7035i	0.623814	−	0.569989i
$579$	1.05002	+	1.44523i	0.0436374	+	0.0600617i
$580$	22.8316	−	14.8942i	0.948030	−	0.618450i
$581$	6.37698	+	12.5155i	0.264562	+	0.519232i
$582$	0.539610	−	0.950599i	0.0223675	−	0.0394036i
$583$	−5.21675	−	5.21675i	−0.216056	−	0.216056i
$584$	−25.5062	+	13.7081i	−1.05546	+	0.567246i
$585$	−2.88486	−	14.4615i	−0.119274	−	0.597909i
$586$	12.1077	+	13.2510i	0.500163	+	0.547394i
$587$	−11.9591	−	36.8064i	−0.493606	−	1.51916i	−0.819118	−	0.573625i	$-0.805537\pi$
$587$	−11.9591	−	36.8064i	−0.493606	−	1.51916i	0.325512	−	0.945538i	$-0.394463\pi$
$588$	0.165181	+	0.724881i	0.00681194	+	0.0298936i
$589$	−5.88967	+	37.1859i	−0.242680	+	1.53222i
$590$	7.77011	−	5.58340i	0.319890	−	0.229865i
$591$	−1.87396	+	0.296807i	−0.0770845	+	0.0122090i
$592$	28.3164	+	0.655485i	1.16380	+	0.0269403i
$593$	5.53303	+	1.79779i	0.227214	+	0.0738265i	0.420412	−	0.907334i	$-0.361886\pi$
$593$	5.53303	+	1.79779i	0.227214	+	0.0738265i	−0.193197	+	0.981160i	$0.561886\pi$
$594$	−1.15266	−	1.74687i	−0.0472941	−	0.0716749i
$595$	10.6194	−	5.95484i	0.435353	−	0.244125i
$596$	−8.88816	−	10.6539i	−0.364073	−	0.436401i
$597$	1.61566	+	0.823218i	0.0661244	+	0.0336921i
$598$	24.3747	−	6.72236i	0.996754	−	0.274898i
$599$	−9.54360	+	29.3722i	−0.389941	+	1.20012i	0.542891	+	0.839803i	$0.317330\pi$
$599$	−9.54360	+	29.3722i	−0.389941	+	1.20012i	−0.932832	+	0.360312i	$0.882670\pi$
$600$	0.621687	−	1.06896i	0.0253803	−	0.0436402i
$601$	−14.9944	−	14.9944i	−0.611635	−	0.611635i	0.331737	−	0.943372i	$-0.392365\pi$
$601$	−14.9944	−	14.9944i	−0.611635	−	0.611635i	−0.943372	+	0.331737i	$0.892365\pi$
$602$	−0.250182	+	0.666251i	−0.0101967	+	0.0271544i
$603$	14.1889	+	19.5294i	0.577817	+	0.795297i
$604$	10.5511	+	26.3304i	0.429319	+	1.07137i
$605$	6.62909	−	1.32241i	0.269511	−	0.0537635i
$606$	−1.03731	+	1.30028i	−0.0421379	+	0.0528202i
$607$	−3.47000	+	0.549594i	−0.140843	+	0.0223073i	−0.226458	−	0.974021i	$-0.572715\pi$
$607$	−3.47000	+	0.549594i	−0.140843	+	0.0223073i	0.0856148	+	0.996328i	$0.472715\pi$
$608$	−14.3255	+	23.9290i	−0.580976	+	0.970447i
$609$	1.59298	+	0.811662i	0.0645507	+	0.0328902i
$610$	−0.103670	+	19.8030i	−0.00419749	+	0.801802i
$611$	9.87542	+	13.5924i	0.399517	+	0.549888i
$612$	9.47187	−	2.15838i	0.382878	−	0.0872474i
$613$	−5.94641	−	3.02985i	−0.240173	−	0.122374i	0.329762	−	0.944064i	$-0.393032\pi$
$613$	−5.94641	−	3.02985i	−0.240173	−	0.122374i	−0.569935	+	0.821690i	$0.693032\pi$
$614$	6.46483	−	8.10372i	0.260899	−	0.327039i
$615$	0.345130	−	1.20345i	0.0139170	−	0.0485278i
$616$	24.1359	+	11.6389i	0.972462	+	0.468946i
$617$	−6.64461	+	13.0408i	−0.267502	+	0.525002i	−0.985212	−	0.171340i	$-0.945190\pi$
$617$	−6.64461	+	13.0408i	−0.267502	+	0.525002i	0.717710	+	0.696342i	$0.245190\pi$
$618$	0.394760	−	0.494835i	0.0158796	−	0.0199052i
$619$	29.2174	−	21.2277i	1.17434	−	0.853212i	0.182822	−	0.983146i	$-0.441477\pi$
$619$	29.2174	−	21.2277i	1.17434	−	0.853212i	0.991523	+	0.129934i	$0.0414767\pi$
$620$	3.64007	+	33.9570i	0.146189	+	1.36375i
$621$	−1.92980	+	3.78744i	−0.0774401	+	0.151985i
$622$	−0.377854	−	0.572644i	−0.0151506	−	0.0229609i
$623$	7.90572	+	49.9148i	0.316736	+	1.99979i
$624$	−0.333964	−	0.694736i	−0.0133693	−	0.0278117i
$625$	22.3001	+	11.3006i	0.892005	+	0.452025i
$626$	0.0197632	−	0.0348156i	0.000789896	−	0.00139151i
$627$	0.985040	−	0.715673i	0.0393387	−	0.0285812i
$628$	−3.03961	+	1.81463i	−0.121294	+	0.0724116i
$629$	8.12764	−	8.12764i	0.324070	−	0.324070i
$630$	−31.7400	−	0.166161i	−1.26455	−	0.00662002i
$631$	−9.61993	−	3.12571i	−0.382964	−	0.124432i	0.111207	−	0.993797i	$-0.464528\pi$
$631$	−9.61993	−	3.12571i	−0.382964	−	0.124432i	−0.494171	+	0.869365i	$0.664528\pi$
$632$	17.3411	−	9.31981i	0.689791	−	0.370722i
$633$	0.389437	−	0.764312i	0.0154787	−	0.0303787i
$634$	38.8242	+	7.95642i	1.54191	+	0.315990i
$635$	−16.8556	−	4.74375i	−0.668895	−	0.188250i
$636$	0.454961	+	0.0411088i	0.0180404	+	0.00163007i
$637$	−2.89525	+	8.91067i	−0.114714	+	0.353054i
$638$	22.1693	−	10.0651i	0.877692	−	0.398480i
$639$	−6.31643	−	39.8804i	−0.249874	−	1.57764i
$640$	−6.88356	+	24.3437i	−0.272097	+	0.962270i
$641$	30.2858	+	4.79679i	1.19622	+	0.189462i	0.722598	−	0.691268i	$-0.242948\pi$
$641$	30.2858	+	4.79679i	1.19622	+	0.189462i	0.473618	+	0.880730i	$0.342948\pi$
$642$	−0.477992	+	0.599167i	−0.0188648	+	0.0236472i
$643$	−31.5408	+	10.2482i	−1.24385	+	0.404151i	−0.855713	−	0.517451i	$-0.826881\pi$
$643$	−31.5408	+	10.2482i	−1.24385	+	0.404151i	−0.388136	+	0.921602i	$0.626881\pi$
$644$	−3.64186	−	54.3012i	−0.143509	−	2.13977i
$645$	0.0243990	+	0.0162834i	0.000960710	+	0.000641160i
$646$	3.00904	+	10.9105i	0.118389	+	0.429268i
$647$	35.5349	−	35.5349i	1.39702	−	1.39702i	0.588581	−	0.808438i	$-0.299687\pi$
$647$	35.5349	−	35.5349i	1.39702	−	1.39702i	0.808438	−	0.588581i	$-0.200313\pi$
$648$	−24.1903	−	7.27794i	−0.950283	−	0.285904i
$649$	7.61424	−	3.87965i	0.298885	−	0.152290i
$650$	13.6323	−	7.55081i	0.534704	−	0.296167i
$651$	−1.81204	+	1.31652i	−0.0710193	+	0.0515986i
$652$	0.109294	+	1.62961i	0.00428030	+	0.0638205i
$653$	6.37159			0.249339			0.124670	−	0.992198i	$-0.460213\pi$
$653$	6.37159			0.249339			0.124670	+	0.992198i	$0.460213\pi$
$654$	−0.502628	+	1.33853i	−0.0196543	+	0.0523406i
$655$	−16.4489	−	15.1884i	−0.642712	−	0.593460i
$656$	−0.719477	+	25.6024i	−0.0280908	+	0.999605i
$657$	21.6620	−	21.6620i	0.845117	−	0.845117i
$658$	32.9282	−	14.9497i	1.28367	−	0.582799i
$659$	22.2224	−	22.2224i	0.865664	−	0.865664i	−0.126325	−	0.991989i	$-0.540318\pi$
$659$	22.2224	−	22.2224i	0.865664	−	0.865664i	0.991989	+	0.126325i	$0.0403183\pi$
$660$	0.693279	−	0.859759i	0.0269858	−	0.0334661i
$661$	−14.4899	−	19.9436i	−0.563591	−	0.775716i	0.428187	−	0.903690i	$-0.359153\pi$
$661$	−14.4899	−	19.9436i	−0.563591	−	0.775716i	−0.991777	+	0.127974i	$0.959153\pi$
$662$	9.92198	−	26.4229i	0.385629	−	1.02695i
$663$	−0.297505	−	0.0966653i	−0.0115541	−	0.00375417i
$664$	−10.4331	+	5.60718i	−0.404882	+	0.217601i
$665$	−1.47213	−	36.9491i	−0.0570867	−	1.43282i
$666$	−28.8871	+	7.96685i	−1.11935	+	0.308709i
$667$	−40.0060	−	29.0661i	−1.54904	−	1.12544i
$668$	−5.61776	+	6.42547i	−0.217358	+	0.248609i
$669$	0.701627	−	1.37702i	0.0271265	−	0.0532387i
$670$	−15.1025	+	20.5596i	−0.583460	+	0.794286i
$671$	−2.76687	+	17.4693i	−0.106814	+	0.674397i
$672$	−1.60923	+	0.403984i	−0.0620774	+	0.0155840i
$673$	1.68613	−	2.32076i	0.0649957	−	0.0894589i	−0.775282	−	0.631616i	$-0.782392\pi$
$673$	1.68613	−	2.32076i	0.0649957	−	0.0894589i	0.840277	+	0.542157i	$0.182392\pi$
$674$	−10.9392	+	29.1318i	−0.421362	+	1.12212i
$675$	−0.608791	+	2.54817i	−0.0234324	+	0.0980789i
$676$	−1.46556	+	16.2197i	−0.0563677	+	0.623835i
$677$	−16.4911	+	8.40263i	−0.633804	+	0.322939i	−0.741207	−	0.671276i	$-0.765746\pi$
$677$	−16.4911	+	8.40263i	−0.633804	+	0.322939i	0.107403	+	0.994216i	$0.465746\pi$
$678$	−0.777763	−	1.17871i	−0.0298698	−	0.0452681i
$679$	−9.16229	−	28.1986i	−0.351616	−	1.08216i
$680$	5.21627	+	8.84240i	0.200035	+	0.339091i
$681$	−0.0100390	+	0.0308968i	−0.000384694	+	0.00118397i
$682$	−1.37384	+	30.4711i	−0.0526069	+	1.16680i
$683$	7.24141			0.277085			0.138543	−	0.990356i	$-0.455758\pi$
$683$	7.24141			0.277085			0.138543	+	0.990356i	$0.455758\pi$
$684$	7.21952	−	28.6088i	0.276045	−	1.09389i
$685$	18.4133	+	2.16907i	0.703536	+	0.0828758i
$686$	−11.3396	−	6.43697i	−0.432949	−	0.245765i
$687$	−0.250199	−	1.57969i	−0.00954567	−	0.0602690i
$688$	−0.566289	−	0.198601i	−0.0215896	−	0.00757159i
$689$	4.65739	+	3.38379i	0.177432	+	0.128912i
$690$	−2.21371	−	0.362507i	−0.0842746	−	0.0138004i
$691$	30.7830	+	15.6847i	1.17104	+	0.596675i	0.927722	−	0.373272i	$-0.121764\pi$
$691$	30.7830	+	15.6847i	1.17104	+	0.596675i	0.243318	+	0.969946i	$0.421764\pi$
$692$	0.258371	+	3.85239i	0.00982180	+	0.146446i
$693$	−27.9996	−	4.43470i	−1.06362	−	0.168460i
$694$	−2.55559	−	22.7174i	−0.0970088	−	0.862342i
$695$	3.03264	−	6.58786i	0.115035	−	0.249892i
$696$	−0.654822	+	1.35792i	−0.0248209	+	0.0514716i
$697$	7.31310	+	7.38587i	0.277004	+	0.279760i
$698$	−37.5375	+	4.22276i	−1.42081	+	0.159834i
$699$	−1.68211	+	0.546550i	−0.0636232	+	0.0206724i
$700$	−10.0307	−	32.0079i	−0.379127	−	1.20979i
$701$	−30.4791	+	22.1444i	−1.15118	+	0.836382i	−0.988637	−	0.150320i	$-0.951970\pi$
$701$	−30.4791	+	22.1444i	−1.15118	+	0.836382i	−0.162543	+	0.986701i	$0.551970\pi$
$702$	1.10160	+	1.20562i	0.0415772	+	0.0455033i
$703$	−10.7880	−	33.2019i	−0.406876	−	1.25223i
$704$	−9.36602	+	20.5622i	−0.352995	+	0.774967i
$705$	−0.291598	−	1.46175i	−0.0109822	−	0.0550527i
$706$	−16.2489	−	12.9628i	−0.611536	−	0.487860i
$707$	7.05809	+	44.5630i	0.265447	+	1.67597i
$708$	−0.208137	+	0.486486i	−0.00782226	+	0.0182833i
$709$	−10.8206	−	1.71381i	−0.406375	−	0.0643635i	−0.0500991	−	0.998744i	$-0.515954\pi$
$709$	−10.8206	−	1.71381i	−0.406375	−	0.0643635i	−0.356276	+	0.934381i	$0.615954\pi$
$710$	38.1205	−	19.1726i	1.43064	−	0.719537i
$711$	−14.7275	+	14.7275i	−0.552324	+	0.552324i
$712$	−41.9334	+	7.58690i	−1.57152	+	0.284331i
$713$	55.1988	−	28.1252i	2.06721	−	1.05330i
$714$	−0.332387	+	0.585546i	−0.0124393	+	0.0219135i
$715$	13.0556	−	4.82463i	0.488251	−	0.180431i
$716$	−32.3377	+	26.9781i	−1.20852	+	1.00822i
$717$	−1.46153	+	0.744684i	−0.0545817	+	0.0278107i
$718$	9.24504	−	45.1122i	0.345022	−	1.68357i
$719$	3.86089	−	1.96722i	0.143987	−	0.0733651i	−0.380513	−	0.924776i	$-0.624252\pi$
$719$	3.86089	−	1.96722i	0.143987	−	0.0733651i	0.524500	+	0.851411i	$0.324252\pi$
$720$	−0.446317	−	26.7607i	−0.0166332	−	0.997313i
$721$	−2.68604	−	16.9590i	−0.100033	−	0.631585i
$722$	7.35204	+	1.50669i	0.273615	+	0.0560730i
$723$	1.96262	−	1.42593i	0.0729906	−	0.0530308i
$724$	−21.9222	−	13.7854i	−0.814732	−	0.512330i
$725$	−28.1707	−	11.6323i	−1.04623	−	0.432014i
$726$	−0.275974	+	0.252162i	−0.0102424	+	0.00935862i
$727$	−39.4950	−	28.6948i	−1.46479	−	1.06423i	−0.982083	−	0.188451i	$-0.939653\pi$
$727$	−39.4950	−	28.6948i	−1.46479	−	1.06423i	−0.482708	−	0.875782i	$-0.660347\pi$
$728$	−20.0225	−	6.02400i	−0.742082	−	0.223264i
$729$	26.5880			0.984741
$730$	28.7684	+	14.8485i	1.06477	+	0.549566i
$731$	−0.216987	+	0.110560i	−0.00802554	+	0.00408922i
$732$	−0.561381	−	0.940346i	−0.0207492	−	0.0347562i
$733$	−5.30591	+	33.5002i	−0.195978	+	1.23736i	0.671923	+	0.740621i	$0.265469\pi$
$733$	−5.30591	+	33.5002i	−0.195978	+	1.23736i	−0.867901	+	0.496737i	$0.834531\pi$
$734$	1.82613	−	40.5028i	0.0674037	−	1.49498i
$735$	0.563894	−	0.610692i	0.0207995	−	0.0225257i
$736$	45.7100	−	4.07339i	1.68489	−	0.150147i
$737$	−16.1110	+	16.1110i	−0.593455	+	0.593455i
$738$	−7.07479	−	26.1570i	−0.260426	−	0.962854i
$739$	−24.6730			−0.907612			−0.453806	−	0.891101i	$-0.649934\pi$
$739$	−24.6730			−0.907612			−0.453806	+	0.891101i	$0.649934\pi$
$740$	−17.3021	−	26.5226i	−0.636037	−	0.974989i
$741$	−0.671817	+	0.671817i	−0.0246798	+	0.0246798i
$742$	9.14760	−	8.35832i	0.335819	−	0.306844i
$743$	41.7434	+	6.61151i	1.53142	+	0.242553i	0.864521	−	0.502597i	$-0.167622\pi$
$743$	41.7434	+	6.61151i	1.53142	+	0.242553i	0.666897	+	0.745150i	$0.267622\pi$
$744$	−1.14334	−	1.50327i	−0.0419168	−	0.0551126i
$745$	−4.20244	+	14.9322i	−0.153965	+	0.547074i
$746$	−4.05304	−	14.6960i	−0.148392	−	0.538057i
$747$	8.86066	−	8.86066i	0.324195	−	0.324195i
$748$	3.41066	+	8.51133i	0.124706	+	0.311205i
$749$	3.25236	+	20.5346i	0.118839	+	0.750318i
$750$	−1.37873	+	0.102777i	−0.0503443	+	0.00375289i
$751$	17.1039	−	33.5683i	0.624129	−	1.22492i	−0.335070	−	0.942193i	$-0.608760\pi$
$751$	17.1039	−	33.5683i	0.624129	−	1.22492i	0.959200	−	0.282730i	$-0.0912400\pi$
$752$	13.2113	+	27.4831i	0.481767	+	1.00220i
$753$	−0.563909	−	0.776154i	−0.0205500	−	0.0282846i
$754$	−15.8574	+	10.4634i	−0.577494	+	0.381054i
$755$	17.6047	−	26.3788i	0.640702	−	0.960024i
$756$	3.01820	−	1.80185i	0.109771	−	0.0655325i
$757$	−6.46020	+	19.8824i	−0.234800	+	0.722640i	0.762348	+	0.647167i	$0.224047\pi$
$757$	−6.46020	+	19.8824i	−0.234800	+	0.722640i	−0.997148	+	0.0754725i	$0.975953\pi$
$758$	−9.03036	+	44.0646i	−0.327997	+	1.60050i
$759$	−1.90543	−	0.619111i	−0.0691627	−	0.0224723i
$760$	31.1218	−	1.92367i	1.12891	−	0.0697790i
$761$	−3.11611	−	9.59039i	−0.112959	−	0.347651i	0.878557	−	0.477637i	$-0.158507\pi$
$761$	−3.11611	−	9.59039i	−0.112959	−	0.347651i	−0.991516	+	0.129986i	$0.958507\pi$
$762$	0.933517	−	0.257457i	0.0338177	−	0.00932669i
$763$	17.6072	+	34.5560i	0.637423	+	1.25101i
$764$	0.946178	+	14.1078i	0.0342315	+	0.510401i
$765$	−7.97979	−	7.36829i	−0.288510	−	0.266401i
$766$	7.03606	+	15.4976i	0.254223	+	0.559952i
$767$	−5.39478	+	3.91953i	−0.194794	+	0.141526i
$768$	−0.370299	−	1.34916i	−0.0133620	−	0.0486835i
$769$	22.7398	−	31.2986i	0.820017	−	1.12866i	−0.169683	−	0.985499i	$-0.554274\pi$
$769$	22.7398	−	31.2986i	0.820017	−	1.12866i	0.989700	−	0.143157i	$-0.0457255\pi$
$770$	−4.53156	−	29.6137i	−0.163306	−	1.06720i
$771$	0.852756	+	0.619564i	0.0307113	+	0.0223130i
$772$	−3.67697	+	40.6939i	−0.132337	+	1.46461i
$773$	−9.30455	+	3.02323i	−0.334662	+	0.108738i	−0.471527	−	0.881851i	$-0.656297\pi$
$773$	−9.30455	+	3.02323i	−0.334662	+	0.108738i	0.136866	+	0.990590i	$0.456297\pi$
$774$	0.634240	+	0.0285957i	0.0227973	+	0.00102785i
$775$	29.0069	−	24.8296i	1.04196	−	0.891905i
$776$	23.6029	−	8.24501i	0.847294	−	0.295979i
$777$	0.942877	−	1.85050i	0.0338255	−	0.0663863i
$778$	29.8270	−	3.35538i	1.06935	−	0.120296i
$779$	30.0714	−	9.60649i	1.07742	−	0.344188i
$780$	−0.429366	+	0.747250i	−0.0153738	+	0.0267558i
$781$	36.2453	−	11.7768i	1.29696	−	0.421407i
$782$	11.6139	−	14.5581i	0.415313	−	0.520598i
$783$	0.499641	−	3.15461i	0.0178557	−	0.112737i
$784$	−8.06866	+	14.9688i	−0.288166	+	0.534600i
$785$	3.59527	+	1.65504i	0.128321	+	0.0590709i
$786$	1.21294	+	0.248573i	0.0432642	+	0.00886632i
$787$	−18.0639	+	2.86104i	−0.643909	+	0.101985i	−0.469845	−	0.882749i	$-0.655690\pi$
$787$	−18.0639	+	2.86104i	−0.643909	+	0.101985i	−0.174064	+	0.984734i	$0.555690\pi$
$788$	−36.7369	−	23.1014i	−1.30870	−	0.822953i
$789$	0.116810	−	0.160775i	0.00415854	−	0.00572374i
$790$	−19.5590	−	10.0951i	−0.695877	−	0.359168i
$791$	−37.8341	−	5.99234i	−1.34523	−	0.213063i
$792$	3.22127	−	23.6863i	0.114463	−	0.841656i
$793$		−	13.8015i		−	0.490106i
$794$	−17.5494	−	19.2066i	−0.622806	−	0.681618i
$795$	−0.249801	−	0.445476i	−0.00885953	−	0.0157994i
$796$	15.4272	+	38.4988i	0.546804	+	1.36455i
$797$	24.0206	+	12.2391i	0.850855	+	0.433532i	0.824326	−	0.566116i	$-0.191554\pi$
$797$	24.0206	+	12.2391i	0.850855	+	0.433532i	0.0265293	+	0.999648i	$0.491554\pi$
$798$	1.12628	+	1.70690i	0.0398699	+	0.0604235i
$799$	11.7690	+	3.82398i	0.416358	+	0.135283i
$800$	26.7982	−	9.04752i	0.947459	−	0.319878i
$801$	40.1701	−	20.4677i	1.41934	−	0.723190i
$802$	−24.4128	+	11.0837i	−0.862048	+	0.391377i
$803$	23.3926	+	16.9957i	0.825506	+	0.599765i
$804$	0.126957	−	1.40506i	0.00447743	−	0.0495528i
$805$	−47.7634	+	37.6963i	−1.68344	+	1.32862i
$806$	−2.66072	−	23.6520i	−0.0937200	−	0.833107i
$807$	−0.418295	−	1.28738i	−0.0147247	−	0.0453179i
$808$	−37.4374	+	6.77345i	−1.31704	+	0.238289i
$809$	−1.77460	−	11.2044i	−0.0623917	−	0.393926i	−0.999046	−	0.0436706i	$-0.986095\pi$
$809$	−1.77460	−	11.2044i	−0.0623917	−	0.393926i	0.936654	−	0.350255i	$-0.113905\pi$
$810$	8.58686	+	26.9061i	0.301711	+	0.945383i
$811$	17.1126			0.600906			0.300453	−	0.953797i	$-0.402862\pi$
$811$	17.1126			0.600906			0.300453	+	0.953797i	$0.402862\pi$
$812$	15.2107	+	37.9584i	0.533790	+	1.33208i
$813$	0.267550	−	0.823435i	0.00938339	−	0.0288791i
$814$	−11.6922	−	25.7532i	−0.409811	−	0.902650i
$815$	1.43341	−	1.13129i	0.0502101	−	0.0396273i
$816$	−0.499771	−	0.269392i	−0.0174955	−	0.00943062i
$817$			0.739656i			0.0258773i
$818$	−0.333138	+	0.151248i	−0.0116479	+	0.00528825i
$819$	22.1209			0.772965
$820$	24.0607	−	15.5268i	0.840236	−	0.542220i
$821$	−22.3091			−0.778592			−0.389296	−	0.921113i	$-0.627282\pi$
$821$	−22.3091			−0.778592			−0.389296	+	0.921113i	$0.627282\pi$
$822$	−0.933624	+	0.423874i	−0.0325639	+	0.0147843i
$823$			5.72441i			0.199540i	0.995011	+	0.0997702i	$0.0318108\pi$
$823$			5.72441i			0.199540i	−0.995011	+	0.0997702i	$0.968189\pi$
$824$	14.2472	−	2.57771i	0.496325	−	0.0897989i
$825$	−1.23112	−	0.0955258i	−0.0428620	−	0.00332578i
$826$	5.93349	+	13.0691i	0.206453	+	0.454732i
$827$	9.31432	−	28.6665i	0.323891	−	0.996833i	−0.648048	−	0.761599i	$-0.724414\pi$
$827$	9.31432	−	28.6665i	0.323891	−	0.996833i	0.971939	−	0.235234i	$-0.0755856\pi$
$828$	−45.0671	+	18.0593i	−1.56619	+	0.627604i
$829$	29.3125			1.01807			0.509033	−	0.860747i	$-0.330003\pi$
$829$	29.3125			1.01807			0.509033	+	0.860747i	$0.330003\pi$
$830$	11.7675	+	6.07363i	0.408455	+	0.210819i
$831$	−0.380648	−	2.40332i	−0.0132045	−	0.0833702i
$832$	4.70847	−	16.9907i	0.163237	−	0.589048i
$833$	2.13247	+	6.56307i	0.0738857	+	0.227397i
$834$	0.0448358	+	0.398559i	0.00155254	+	0.0138010i
$835$	9.47687	+	1.11637i	0.327961	+	0.0386334i
$836$	27.7362	+	2.50615i	0.959275	+	0.0866770i
$837$	3.23716	+	2.35194i	0.111893	+	0.0812948i
$838$	−21.0845	+	9.57257i	−0.728353	+	0.330679i
$839$	−22.6367	+	11.5340i	−0.781507	+	0.398198i	−0.798757	−	0.601654i	$-0.794509\pi$
$839$	−22.6367	+	11.5340i	−0.781507	+	0.398198i	0.0172503	+	0.999851i	$0.494509\pi$
$840$	1.39011	+	1.22826i	0.0479633	+	0.0423791i
$841$	7.75681	+	2.52034i	0.267476	+	0.0869082i
$842$	−23.0116	−	34.8744i	−0.793031	−	1.20185i
$843$	1.40899	+	0.717919i	0.0485283	+	0.0247264i
$844$	18.2125	−	7.29810i	0.626899	−	0.251211i
$845$	15.8816	−	8.90560i	0.546342	−	0.306362i
$846$	−21.7613	−	23.8162i	−0.748168	−	0.818818i
$847$			10.1401i			0.348419i
$848$	7.21528	+	7.55724i	0.247774	+	0.259517i
$849$	−0.987360	−	0.156382i	−0.0338861	−	0.00536703i
$850$	4.85419	−	10.4011i	0.166497	−	0.356756i
$851$	−33.7650	+	46.4735i	−1.15745	+	1.59309i
$852$	−1.25618	+	1.99764i	−0.0430360	+	0.0684379i
$853$	−30.9801	+	4.90676i	−1.06074	+	0.168004i	−0.662336	−	0.749207i	$-0.730435\pi$
$853$	−30.9801	+	4.90676i	−1.06074	+	0.168004i	−0.398401	+	0.917211i	$0.630435\pi$
$854$	−29.1018	−	5.96396i	−0.995842	−	0.204082i
$855$	−30.9431	+	11.4349i	−1.05823	+	0.391065i
$856$	−17.2511	+	3.12120i	−0.589631	+	0.106680i
$857$	7.17339	−	45.2910i	0.245038	−	1.54711i	−0.491598	−	0.870822i	$-0.663587\pi$
$857$	7.17339	−	45.2910i	0.245038	−	1.54711i	0.736636	−	0.676289i	$-0.236413\pi$
$858$	−0.480023	+	0.601712i	−0.0163877	+	0.0205421i
$859$	26.7360	−	8.68706i	0.912222	−	0.296399i	0.184950	−	0.982748i	$-0.440788\pi$
$859$	26.7360	−	8.68706i	0.912222	−	0.296399i	0.727272	+	0.686349i	$0.240788\pi$
$860$	0.174992	+	0.647715i	0.00596717	+	0.0220869i
$861$	1.66911	+	0.860887i	0.0568831	+	0.0293390i
$862$	−16.4313	+	1.84844i	−0.559653	+	0.0629580i
$863$	−0.160742	+	0.315474i	−0.00547172	+	0.0107389i	−0.893726	−	0.448613i	$-0.851918\pi$
$863$	−0.160742	+	0.315474i	−0.00547172	+	0.0107389i	0.888254	+	0.459352i	$0.151918\pi$
$864$	1.57476	+	2.51113i	0.0535745	+	0.0854302i
$865$	3.38856	−	2.67436i	0.115215	−	0.0909309i
$866$	8.01626	+	0.361425i	0.272404	+	0.0122817i
$867$	1.19461	−	0.388154i	0.0405712	−	0.0131824i
$868$	−51.0223	−	4.61021i	−1.73181	−	0.156481i
$869$	−15.9040	−	11.5550i	−0.539508	−	0.391975i
$870$	1.66610	−	0.254952i	0.0564862	−	0.00864367i
$871$	10.4502	−	14.3835i	0.354092	−	0.487366i
$872$	−28.8063	+	15.4817i	−0.975505	+	0.524277i
$873$	−21.3989	+	15.5472i	−0.724244	+	0.526194i
$874$	−23.3830	−	51.5034i	−0.790942	−	1.74213i
$875$	−23.1686	+	29.4893i	−0.783241	+	0.996922i
$876$	−1.78637	+	0.119808i	−0.0603558	+	0.00404793i
$877$	−20.1176	−	39.4830i	−0.679322	−	1.33324i	−0.930852	−	0.365395i	$-0.880934\pi$
$877$	−20.1176	−	39.4830i	−0.679322	−	1.33324i	0.251530	−	0.967849i	$-0.419066\pi$
$878$	−18.8719	+	5.20473i	−0.636895	+	0.175651i
$879$	0.342953	+	1.05550i	0.0115675	+	0.0356011i
$880$	24.8814	−	4.36734i	0.838752	−	0.147223i
$881$	22.7112	+	7.37932i	0.765161	+	0.248616i	0.665492	−	0.746405i	$-0.268222\pi$
$881$	22.7112	+	7.37932i	0.765161	+	0.248616i	0.0996686	+	0.995021i	$0.468222\pi$
$882$	3.61181	−	17.6242i	0.121616	−	0.593438i
$883$	−5.94648	+	18.3014i	−0.200115	+	0.615890i	0.799764	+	0.600315i	$0.204958\pi$
$883$	−5.94648	+	18.3014i	−0.200115	+	0.615890i	−0.999879	+	0.0155755i	$0.995042\pi$
$884$	−3.66758	−	6.14342i	−0.123354	−	0.206625i
$885$	0.580166	−	0.115735i	0.0195021	−	0.00389038i
$886$	35.6030	−	23.4923i	1.19611	−	0.789241i
$887$	27.3627	+	37.6615i	0.918748	+	1.26455i	0.964090	+	0.265577i	$0.0855623\pi$
$887$	27.3627	+	37.6615i	0.918748	+	1.26455i	−0.0453418	+	0.998972i	$0.514438\pi$
$888$	1.57744	+	0.760681i	0.0529353	+	0.0255268i
$889$	11.9250	−	23.4041i	0.399952	−	0.784950i
$890$	33.5126	+	33.8654i	1.12335	+	1.13517i
$891$	3.94606	+	24.9144i	0.132198	+	0.834665i
$892$	32.8124	−	13.1486i	1.09864	−	0.440248i
$893$	26.5764	−	26.5764i	0.889346	−	0.889346i
$894$	−0.228079	−	0.826993i	−0.00762809	−	0.0276588i
$895$	45.3236	+	12.7556i	1.51500	+	0.426374i
$896$	−33.7919	−	17.2704i	−1.12891	−	0.576962i
$897$	1.54410	+	0.244562i	0.0515561	+	0.00816568i
$898$	35.5669	−	32.4981i	1.18688	−	1.08447i
$899$	−32.9151	+	32.9151i	−1.09778	+	1.09778i
$900$	−24.3915	+	17.3342i	−0.813049	+	0.577806i
$901$	4.24015			0.141260
$902$	23.3399	−	10.4575i	0.777134	−	0.348197i
$903$	−0.0311147	+	0.0311147i	−0.00103543	+	0.00103543i
$904$	4.35271	−	32.0058i	0.144769	−	1.06450i
$905$	1.15263	+	28.9300i	0.0383148	+	0.961666i
$906$	−0.0789949	+	1.75207i	−0.00262443	+	0.0582087i
$907$	−4.21037	+	26.5832i	−0.139803	+	0.882682i	0.813697	+	0.581289i	$0.197452\pi$
$907$	−4.21037	+	26.5832i	−0.139803	+	0.882682i	−0.953500	+	0.301393i	$0.902548\pi$
$908$	−0.638011	+	0.380889i	−0.0211731	+	0.0126402i
$909$	35.8632	−	18.2732i	1.18951	−	0.606084i
$910$	7.10740	+	22.2704i	0.235608	+	0.738256i
$911$	−15.4649			−0.512374			−0.256187	−	0.966627i	$-0.582466\pi$
$911$	−15.4649			−0.512374			−0.256187	+	0.966627i	$0.582466\pi$
$912$	−1.41815	+	0.981018i	−0.0469596	+	0.0324848i
$913$	9.56852	+	6.95193i	0.316672	+	0.230075i
$914$	21.8516	−	19.9662i	0.722787	−	0.660422i
$915$	−0.512010	+	1.11225i	−0.0169265	+	0.0367698i
$916$	19.4738	−	30.9681i	0.643431	−	1.02321i
$917$	27.1708	−	19.7407i	0.897258	−	0.651896i
$918$	1.17836	+	0.241487i	0.0388917	+	0.00797025i
$919$	6.07542	+	38.3587i	0.200409	+	1.26534i	0.858664	+	0.512540i	$0.171295\pi$
$919$	6.07542	+	38.3587i	0.200409	+	1.26534i	−0.658254	+	0.752796i	$0.728705\pi$
$920$	−32.6614	−	39.5693i	−1.07681	−	1.30456i
$921$	0.571100	−	0.290990i	0.0188184	−	0.00958844i
$922$	9.34626	−	45.6061i	0.307803	−	1.50196i
$923$	−26.4970	+	13.5009i	−0.872158	+	0.444387i
$924$	1.06134	+	1.27219i	0.0349154	+	0.0418519i
$925$	−13.5128	+	32.7248i	−0.444299	+	1.07599i
$926$	4.28836	−	7.55455i	0.140924	−	0.248258i
$927$	−13.6481	+	6.95407i	−0.448264	+	0.228402i
$928$	−31.7189	+	13.5243i	−1.04122	+	0.443956i
$929$	−25.0345	+	25.0345i	−0.821357	+	0.821357i	−0.986303	−	0.164946i	$-0.947255\pi$
$929$	−25.0345	+	25.0345i	−0.821357	+	0.821357i	0.164946	+	0.986303i	$0.447255\pi$
$930$	−0.663021	+	2.00480i	−0.0217413	+	0.0657399i
$931$	20.7013	+	3.27877i	0.678459	+	0.107457i
$932$	−37.1932	−	15.9126i	−1.21830	−	0.521235i
$933$	−0.00663592	−	0.0418976i	−0.000217250	−	0.00137166i
$934$	10.1661	+	8.11011i	0.332644	+	0.265371i
$935$	5.69075	−	8.52698i	0.186108	−	0.278862i
$936$	0.408682	+	18.6484i	0.0133582	+	0.609543i
$937$	13.1339	+	40.4221i	0.429067	+	1.32053i	0.899046	+	0.437854i	$0.144261\pi$
$937$	13.1339	+	40.4221i	0.429067	+	1.32053i	−0.469979	+	0.882677i	$0.655739\pi$
$938$	−25.8131	−	28.2507i	−0.842829	−	0.922417i
$939$	0.00200255	−	0.00145494i	6.53509e−5	−	4.74802e-5i
$940$	16.9853	−	29.5605i	0.554000	−	0.964156i
$941$	41.0952	−	13.3526i	1.33966	−	0.435283i	0.450462	−	0.892796i	$-0.351259\pi$
$941$	41.0952	−	13.3526i	1.33966	−	0.435283i	0.889203	+	0.457512i	$0.151259\pi$
$942$	−0.217510	+	0.0244687i	−0.00708687	+	0.000797235i
$943$	−41.8729	−	30.7403i	−1.36357	−	1.00104i
$944$	−10.9080	+	5.24354i	−0.355024	+	0.170663i
$945$	−3.56994	−	1.64338i	−0.116130	−	0.0534592i
$946$	0.0669887	+	0.595484i	0.00217799	+	0.0193608i
$947$	−1.17492	−	0.186088i	−0.0381796	−	0.00604706i	0.137315	−	0.990527i	$-0.456153\pi$
$947$	−1.17492	−	0.186088i	−0.0381796	−	0.00604706i	−0.175495	+	0.984480i	$0.556153\pi$
$948$	1.21451	−	0.0814545i	0.0394454	−	0.00264552i
$949$	−20.1035	−	10.2432i	−0.652586	−	0.332509i
$950$	−21.4542	−	27.4783i	−0.696065	−	0.891512i
$951$	1.98241	+	1.44030i	0.0642840	+	0.0467050i
$952$	−14.5388	+	5.07873i	−0.471206	+	0.164603i
$953$	−4.19919	−	26.5127i	−0.136025	−	0.858829i	−0.957468	−	0.288539i	$-0.906831\pi$
$953$	−4.19919	−	26.5127i	−0.136025	−	0.858829i	0.821443	−	0.570291i	$-0.193169\pi$
$954$	−9.61326	−	5.45699i	−0.311241	−	0.176677i
$955$	12.4092	−	9.79373i	0.401553	−	0.316918i
$956$	−36.3777	−	9.18001i	−1.17654	−	0.296903i
$957$	1.50538			0.0486622
$958$	−1.65778	+	36.7689i	−0.0535605	+	1.18795i
$959$	−8.59452	+	26.4512i	−0.277531	+	0.854154i
$960$	−1.00977	+	1.19459i	−0.0325903	+	0.0385552i
$961$	−8.44123	−	25.9794i	−0.272298	−	0.838046i
$962$	12.1549	+	18.4210i	0.391890	+	0.593916i
$963$	16.5257	−	8.42027i	0.532534	−	0.271339i
$964$	55.2623	+	4.99332i	1.77988	+	0.160824i
$965$	39.8455	−	22.3434i	1.28267	−	0.719260i
$966$	1.18292	−	3.15020i	0.0380600	−	0.101356i
$967$	13.6358	−	18.7680i	0.438496	−	0.603538i	−0.531381	−	0.847133i	$-0.678327\pi$
$967$	13.6358	−	18.7680i	0.438496	−	0.603538i	0.969877	+	0.243595i	$0.0783267\pi$
$968$	−8.54838	+	0.187338i	−0.274755	+	0.00602128i
$969$	−0.109470	+	0.691166i	−0.00351668	+	0.0222035i
$970$	−22.5278	−	16.5483i	−0.723323	−	0.531333i
$971$	5.54027	−	10.8734i	0.177796	−	0.348944i	−0.784860	−	0.619674i	$-0.787265\pi$
$971$	5.54027	−	10.8734i	0.177796	−	0.348944i	0.962655	+	0.270730i	$0.0872650\pi$
$972$	−3.54269	−	3.09735i	−0.113632	−	0.0993477i
$973$	8.80142	+	6.39460i	0.282160	+	0.205002i
$974$	−53.4714	+	14.7470i	−1.71334	+	0.472526i
$975$	0.960493	−	0.0766577i	0.0307604	−	0.00245501i
$976$	4.49011	−	24.6437i	0.143725	−	0.788826i
$977$	−6.53693	−	2.12398i	−0.209135	−	0.0679521i	0.202576	−	0.979267i	$-0.435069\pi$
$977$	−6.53693	−	2.12398i	−0.209135	−	0.0679521i	−0.411711	+	0.911314i	$0.635069\pi$
$978$	−0.0355003	+	0.0945395i	−0.00113517	+	0.00302304i
$979$	25.0119	+	34.4259i	0.799384	+	1.10026i
$980$	18.9038	−	2.02642i	0.603860	−	0.0647316i
$981$	24.4648	−	24.4648i	0.781099	−	0.781099i
$982$	−11.6590	+	5.29328i	−0.372053	+	0.168915i
$983$	−31.3301	+	31.3301i	−0.999274	+	0.999274i	−1.00000		0.000726002i	$-0.999769\pi$
$983$	−31.3301	+	31.3301i	−0.999274	+	0.999274i	0.000726002		1.00000i	$0.499769\pi$
$984$	−0.694913	+	1.42301i	−0.0221530	+	0.0453638i
$985$	1.93157	+	48.4806i	0.0615448	+	1.54472i
$986$	−4.91914	+	13.1000i	−0.156657	+	0.417189i
$987$	2.23595			0.0711711
$988$	−21.6824	+	1.45419i	−0.689809	+	0.0462640i
$989$	0.984641	−	0.715384i	0.0313098	−	0.0227479i
$990$	−23.8761	+	12.0085i	−0.758833	+	0.381654i
$991$	21.6206	−	11.0162i	0.686800	−	0.349942i	−0.0755181	−	0.997144i	$-0.524061\pi$
$991$	21.6206	−	11.0162i	0.686800	−	0.349942i	0.762318	+	0.647202i	$0.224061\pi$
$992$	2.94389	−	43.0982i	0.0934685	−	1.36837i
$993$	1.23398	−	1.23398i	0.0391592	−	0.0391592i
$994$	17.0179	+	61.7054i	0.539775	+	1.95718i
$995$	25.7407	−	38.5696i	0.816034	−	1.22274i
$996$	−0.730697	+	0.0490063i	−0.0231530	+	0.00155282i
$997$	−25.5784	+	8.31094i	−0.810077	+	0.263210i	−0.684631	−	0.728890i	$-0.740036\pi$
$997$	−25.5784	+	8.31094i	−0.810077	+	0.263210i	−0.125447	+	0.992100i	$0.540036\pi$
$998$	−7.64407	+	9.58190i	−0.241969	+	0.303310i
$999$	−3.66459	−	0.580414i	−0.115942	−	0.0183635i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bk.c.43.78	yes	960
4.3	odd	2	inner	820.2.bk.c.43.8	✓	960
5.2	odd	4		820.2.bv.c.207.17	yes	960
20.7	even	4		820.2.bv.c.207.54	yes	960
41.21	even	20		820.2.bv.c.103.54	yes	960
164.103	odd	20		820.2.bv.c.103.17	yes	960
205.62	odd	20	inner	820.2.bk.c.267.8	yes	960
820.267	even	20	inner	820.2.bk.c.267.78	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bk.c.43.8	✓	960	4.3	odd	2	inner
820.2.bk.c.43.78	yes	960	1.1	even	1	trivial
820.2.bk.c.267.8	yes	960	205.62	odd	20	inner
820.2.bk.c.267.78	yes	960	820.267	even	20	inner
820.2.bv.c.103.17	yes	960	164.103	odd	20
820.2.bv.c.103.54	yes	960	41.21	even	20
820.2.bv.c.207.17	yes	960	5.2	odd	4
820.2.bv.c.207.54	yes	960	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.584633 + 1.28771i) q^{2} +0.0874408i q^{3} +(-1.31641 + 1.50568i) q^{4} +(2.22071 + 0.261598i) q^{5} +(-0.112599 + 0.0511208i) q^{6} +(-1.03653 + 3.19012i) q^{7} +(-2.70850 - 0.814885i) q^{8} +2.99235 q^{9} +(0.961440 + 3.01258i) q^{10} +(0.441826 + 2.78958i) q^{11} +(-0.131658 - 0.115108i) q^{12} +(-0.681038 - 2.09602i) q^{13} +(-4.71394 + 0.530293i) q^{14} +(-0.0228743 + 0.194181i) q^{15} +(-0.534140 - 3.96418i) q^{16} +(-1.31324 - 0.954122i) q^{17} +(1.74943 + 3.85329i) q^{18} +(-4.39283 + 2.23826i) q^{19} +(-3.31725 + 2.99931i) q^{20} +(-0.278946 - 0.0906351i) q^{21} +(-3.33387 + 2.19983i) q^{22} +(7.22827 + 3.68299i) q^{23} +(0.0712542 - 0.236833i) q^{24} +(4.86313 + 1.16187i) q^{25} +(2.30091 - 2.10238i) q^{26} +0.523976i q^{27} +(-3.43879 - 5.76018i) q^{28} +(-6.02052 - 0.953557i) q^{29} +(-0.263422 + 0.0840690i) q^{30} +(4.48863 - 6.17807i) q^{31} +(4.79244 - 3.00541i) q^{32} +(-0.243923 + 0.0386336i) q^{33} +(0.460874 - 2.24888i) q^{34} +(-3.13637 + 6.81318i) q^{35} +(-3.93916 + 4.50553i) q^{36} +(-1.10771 + 6.99381i) q^{37} +(-5.45042 - 4.34814i) q^{38} +(0.183277 - 0.0595505i) q^{39} +(-5.80163 - 2.51816i) q^{40} +(-6.31926 - 1.03296i) q^{41} +(-0.0463692 - 0.412191i) q^{42} +(0.0681104 - 0.133674i) q^{43} +(-4.78184 - 3.00698i) q^{44} +(6.64516 + 0.782793i) q^{45} +(-0.516743 + 11.4611i) q^{46} +(-7.25028 + 2.35576i) q^{47} +(0.346631 - 0.0467056i) q^{48} +(-3.43932 - 2.49881i) q^{49} +(1.34700 + 6.94158i) q^{50} +(0.0834292 - 0.114830i) q^{51} +(4.05246 + 1.73379i) q^{52} +(-2.11326 + 1.53538i) q^{53} +(-0.674731 + 0.306334i) q^{54} +(0.251421 + 6.31044i) q^{55} +(5.40702 - 7.79577i) q^{56} +(-0.195715 - 0.384112i) q^{57} +(-2.29189 - 8.31019i) q^{58} +(-0.934995 - 2.87762i) q^{59} +(-0.262262 - 0.290063i) q^{60} +(5.95586 + 1.93517i) q^{61} +(10.5798 + 2.16816i) q^{62} +(-3.10167 + 9.54596i) q^{63} +(6.67192 + 4.41423i) q^{64} +(-0.964075 - 4.83281i) q^{65} +(-0.192355 - 0.291516i) q^{66} +(4.74172 + 6.52642i) q^{67} +(3.16536 - 0.721299i) q^{68} +(-0.322043 + 0.632046i) q^{69} +(-10.6070 - 0.0555286i) q^{70} +(-2.11086 - 13.3274i) q^{71} +(-8.10479 - 2.43842i) q^{72} +(7.23913 - 7.23913i) q^{73} +(-9.65362 + 2.66240i) q^{74} +(-0.101595 + 0.425236i) q^{75} +(2.41265 - 9.56065i) q^{76} +(-9.35705 - 1.48201i) q^{77} +(0.183834 + 0.201194i) q^{78} +(-4.92171 + 4.92171i) q^{79} +(-0.149152 - 8.94303i) q^{80} +8.93125 q^{81} +(-2.36429 - 8.74129i) q^{82} +(2.96110 - 2.96110i) q^{83} +(0.503674 - 0.300691i) q^{84} +(-2.66673 - 2.46237i) q^{85} +(0.211954 + 0.00955625i) q^{86} +(0.0833798 - 0.526439i) q^{87} +(1.07650 - 7.91561i) q^{88} +(13.4242 - 6.84000i) q^{89} +(2.87697 + 9.01470i) q^{90} +7.39246 q^{91} +(-15.0608 + 6.03514i) q^{92} +(0.540215 + 0.392489i) q^{93} +(-7.27229 - 7.95902i) q^{94} +(-10.3407 + 3.82137i) q^{95} +(0.262795 + 0.419055i) q^{96} +(-7.15121 + 5.19566i) q^{97} +(1.20701 - 5.88975i) q^{98} +(1.32210 + 8.34741i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q - 10 q^{2} - 20 q^{5} - 16 q^{6} - 22 q^{8} - 960 q^{9} + 20 q^{12} + 12 q^{13} + 8 q^{14} - 28 q^{16} - 52 q^{17} + 12 q^{18} + 14 q^{20} - 40 q^{21} + 18 q^{22} + 48 q^{24} - 4 q^{25} - 20 q^{26}+ \cdots + 42 q^{98}+O(q^{100}) \) 960 * q - 10 * q^2 - 20 * q^5 - 16 * q^6 - 22 * q^8 - 960 * q^9 + 20 * q^12 + 12 * q^13 + 8 * q^14 - 28 * q^16 - 52 * q^17 + 12 * q^18 + 14 * q^20 - 40 * q^21 + 18 * q^22 + 48 * q^24 - 4 * q^25 - 20 * q^26 - 2 * q^28 + 30 * q^30 + 16 * q^33 + 20 * q^34 - 100 * q^36 - 112 * q^37 - 36 * q^38 - 16 * q^40 - 24 * q^41 - 104 * q^42 + 20 * q^45 - 20 * q^46 + 12 * q^48 - 224 * q^49 + 12 * q^50 + 190 * q^52 + 12 * q^53 + 52 * q^54 + 96 * q^56 + 48 * q^57 - 10 * q^58 + 14 * q^60 - 40 * q^61 - 10 * q^62 + 120 * q^64 - 92 * q^65 - 12 * q^66 + 104 * q^69 - 120 * q^70 + 36 * q^72 + 72 * q^73 + 28 * q^74 - 40 * q^76 + 36 * q^77 + 16 * q^78 - 130 * q^80 + 592 * q^81 + 146 * q^82 + 92 * q^84 + 112 * q^85 - 12 * q^86 + 100 * q^88 - 136 * q^89 - 136 * q^90 + 160 * q^92 - 24 * q^93 + 32 * q^94 - 44 * q^96 - 72 * q^97 + 42 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more