LMFDB - Embedded newform 81.6.e.a.73.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [81,6,Mod(10,81)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("81.10"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(81, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	81.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$12.9910894049$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			73.3
Character	$\chi$	$=$	81.73
Dual form			81.6.e.a.10.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40309 + 7.95730i) q^{2} +(-31.2798 - 11.3849i) q^{4} +(-15.2280 + 12.7778i) q^{5} +(-70.6933 + 25.7303i) q^{7} +(5.20070 - 9.00788i) q^{8} +(-80.3108 - 139.102i) q^{10} +(-144.573 - 121.311i) q^{11} +(-145.413 - 824.679i) q^{13} +(-105.555 - 598.630i) q^{14} +(-751.604 - 630.671i) q^{16} +(465.095 + 805.567i) q^{17} +(1078.70 - 1868.37i) q^{19} +(621.804 - 226.318i) q^{20} +(1168.16 - 980.203i) q^{22} +(-2223.04 - 809.122i) q^{23} +(-474.031 + 2688.36i) q^{25} +6766.25 q^{26} +2504.21 q^{28} +(17.6525 - 100.112i) q^{29} +(5477.24 + 1993.55i) q^{31} +(6327.98 - 5309.80i) q^{32} +(-7062.71 + 2570.62i) q^{34} +(747.743 - 1295.13i) q^{35} +(-5390.69 - 9336.95i) q^{37} +(13353.7 + 11205.0i) q^{38} +(35.9047 + 203.626i) q^{40} +(-2497.97 - 14166.7i) q^{41} +(512.502 + 430.040i) q^{43} +(3141.11 + 5440.55i) q^{44} +(9557.55 - 16554.2i) q^{46} +(-26728.7 + 9728.44i) q^{47} +(-8539.41 + 7165.41i) q^{49} +(-20727.0 - 7544.01i) q^{50} +(-4840.41 + 27451.3i) q^{52} -25335.8 q^{53} +3751.66 q^{55} +(-135.880 + 770.613i) q^{56} +(771.857 + 280.933i) q^{58} +(-11752.3 + 9861.37i) q^{59} +(-8422.09 + 3065.39i) q^{61} +(-23548.3 + 40786.9i) q^{62} +(17674.6 + 30613.3i) q^{64} +(12752.0 + 10700.2i) q^{65} +(-10635.1 - 60314.5i) q^{67} +(-5376.75 - 30493.1i) q^{68} +(9256.58 + 7767.19i) q^{70} +(2552.14 + 4420.44i) q^{71} +(-17695.8 + 30650.1i) q^{73} +(81860.5 - 29794.8i) q^{74} +(-55012.9 + 46161.3i) q^{76} +(13341.7 + 4856.00i) q^{77} +(-9551.12 + 54167.1i) q^{79} +19504.0 q^{80} +116233. q^{82} +(16596.8 - 94125.4i) q^{83} +(-17375.9 - 6324.30i) q^{85} +(-4141.04 + 3474.75i) q^{86} +(-1844.64 + 671.394i) q^{88} +(-50371.1 + 87245.3i) q^{89} +(31499.0 + 54557.8i) q^{91} +(60324.6 + 50618.4i) q^{92} +(-39909.5 - 226338. i) q^{94} +(7447.18 + 42235.0i) q^{95} +(71726.7 + 60185.8i) q^{97} +(-45035.8 - 78004.3i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 6 q^{2} - 6 q^{4} + 93 q^{5} - 6 q^{7} - 573 q^{8} - 3 q^{10} - 111 q^{11} - 6 q^{13} + 1641 q^{14} + 90 q^{16} - 3465 q^{17} - 3 q^{19} - 9987 q^{20} - 2850 q^{22} + 7716 q^{23} + 4953 q^{25} + 7806 q^{26}+ \cdots - 463410 q^{98}+O(q^{100}) $ 84 * q + 6 * q^2 - 6 * q^4 + 93 * q^5 - 6 * q^7 - 573 * q^8 - 3 * q^10 - 111 * q^11 - 6 * q^13 + 1641 * q^14 + 90 * q^16 - 3465 * q^17 - 3 * q^19 - 9987 * q^20 - 2850 * q^22 + 7716 * q^23 + 4953 * q^25 + 7806 * q^26 - 12 * q^28 + 20418 * q^29 - 6657 * q^31 - 51192 * q^32 - 11394 * q^34 - 35868 * q^35 - 3 * q^37 + 44076 * q^38 + 12441 * q^40 + 79077 * q^41 - 9465 * q^43 - 110757 * q^44 - 3 * q^46 - 103557 * q^47 + 5484 * q^49 + 105513 * q^50 + 68625 * q^52 + 206406 * q^53 - 12 * q^55 + 147237 * q^56 - 9753 * q^58 - 116484 * q^59 - 70116 * q^61 - 246066 * q^62 - 86019 * q^64 + 19815 * q^65 + 48117 * q^67 + 48105 * q^68 + 270111 * q^70 - 279531 * q^71 - 27012 * q^73 - 233691 * q^74 - 125670 * q^76 + 345135 * q^77 - 216186 * q^79 + 924114 * q^80 - 12 * q^82 + 370401 * q^83 - 43731 * q^85 - 116682 * q^86 + 371418 * q^88 - 154827 * q^89 - 91002 * q^91 - 1279059 * q^92 + 11667 * q^94 - 1087671 * q^95 - 420621 * q^97 - 463410 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−1.40309	+	7.95730i	−0.248033	+	1.40667i	0.565309	+	0.824879i	$0.308757\pi$
$2$	−1.40309	+	7.95730i	−0.248033	+	1.40667i	−0.813342	+	0.581786i	$0.802354\pi$
$3$		0			0
$3$		0			0
$4$	−31.2798	−	11.3849i	−0.977495	−	0.355779i
$5$	−15.2280	+	12.7778i	−0.272407	+	0.228577i	−0.768749	−	0.639550i	$-0.779121\pi$
$5$	−15.2280	+	12.7778i	−0.272407	+	0.228577i	0.496342	+	0.868127i	$0.334676\pi$
$6$		0			0
$7$	−70.6933	+	25.7303i	−0.545297	+	0.198472i	−0.599956	−	0.800033i	$-0.704815\pi$
$7$	−70.6933	+	25.7303i	−0.545297	+	0.198472i	0.0546585	+	0.998505i	$0.482593\pi$
$8$	5.20070	−	9.00788i	0.0287301	−	0.0497620i
$9$		0			0
$10$	−80.3108	−	139.102i	−0.253965	−	0.439880i
$11$	−144.573	−	121.311i	−0.360252	−	0.302287i	0.444639	−	0.895710i	$-0.353332\pi$
$11$	−144.573	−	121.311i	−0.360252	−	0.302287i	−0.804891	+	0.593423i	$0.797776\pi$
$12$		0			0
$13$	−145.413	−	824.679i	−0.238641	−	1.35340i	−0.834808	−	0.550541i	$-0.814422\pi$
$13$	−145.413	−	824.679i	−0.238641	−	1.35340i	0.596167	−	0.802860i	$-0.296690\pi$
$14$	−105.555	−	598.630i	−0.143932	−	0.816279i
$15$		0			0
$16$	−751.604	−	630.671i	−0.733988	−	0.615889i
$17$	465.095	+	805.567i	0.390318	+	0.676051i	0.992491	−	0.122314i	$-0.0390316\pi$
$17$	465.095	+	805.567i	0.390318	+	0.676051i	−0.602173	+	0.798366i	$0.705698\pi$
$18$		0			0
$19$	1078.70	−	1868.37i	0.685517	−	1.18735i	−0.287758	−	0.957703i	$-0.592910\pi$
$19$	1078.70	−	1868.37i	0.685517	−	1.18735i	0.973274	−	0.229646i	$-0.0737569\pi$
$20$	621.804	−	226.318i	0.347599	−	0.126516i
$21$		0			0
$22$	1168.16	−	980.203i	0.514571	−	0.431777i
$23$	−2223.04	−	809.122i	−0.876251	−	0.318929i	−0.135555	−	0.990770i	$-0.543282\pi$
$23$	−2223.04	−	809.122i	−0.876251	−	0.318929i	−0.740696	+	0.671841i	$0.765504\pi$
$24$		0			0
$25$	−474.031	+	2688.36i	−0.151690	+	0.860276i
$26$	6766.25			1.96297
$27$		0			0
$28$	2504.21			0.603637
$29$	17.6525	−	100.112i	0.00389773	−	0.0221051i	−0.982797	−	0.184690i	$-0.940872\pi$
$29$	17.6525	−	100.112i	0.00389773	−	0.0221051i	0.986695	+	0.162585i	$0.0519831\pi$
$30$		0			0
$31$	5477.24	+	1993.55i	1.02366	+	0.372583i	0.798665	−	0.601776i	$-0.205540\pi$
$31$	5477.24	+	1993.55i	1.02366	+	0.372583i	0.224999	+	0.974359i	$0.427762\pi$
$32$	6327.98	−	5309.80i	1.09242	−	0.916650i
$33$		0			0
$34$	−7062.71	+	2570.62i	−1.04779	+	0.381364i
$35$	747.743	−	1295.13i	0.103177	−	0.178707i
$36$		0			0
$37$	−5390.69	−	9336.95i	−0.647351	−	1.12125i	−0.983753	−	0.179527i	$-0.942543\pi$
$37$	−5390.69	−	9336.95i	−0.647351	−	1.12125i	0.336402	−	0.941718i	$-0.390790\pi$
$38$	13353.7	+	11205.0i	1.50017	+	1.25879i
$39$		0			0
$40$	35.9047	+	203.626i	0.00354815	+	0.0201225i
$41$	−2497.97	−	14166.7i	−0.232074	−	1.31616i	−0.848689	−	0.528893i	$-0.822607\pi$
$41$	−2497.97	−	14166.7i	−0.232074	−	1.31616i	0.616615	−	0.787265i	$-0.288504\pi$
$42$		0			0
$43$	512.502	+	430.040i	0.0422692	+	0.0354681i	0.663678	−	0.748019i	$-0.268995\pi$
$43$	512.502	+	430.040i	0.0422692	+	0.0354681i	−0.621408	+	0.783487i	$0.713439\pi$
$44$	3141.11	+	5440.55i	0.244597	+	0.423654i
$45$		0			0
$46$	9557.55	−	16554.2i	0.665966	−	1.15349i
$47$	−26728.7	+	9728.44i	−1.76495	+	0.642390i	−0.999999	−	0.00169735i	$-0.999460\pi$
$47$	−26728.7	+	9728.44i	−1.76495	+	0.642390i	−0.764952	+	0.644087i	$0.777237\pi$
$48$		0			0
$49$	−8539.41	+	7165.41i	−0.508086	+	0.426335i
$50$	−20727.0	−	7544.01i	−1.17250	−	0.426754i
$51$		0			0
$52$	−4840.41	+	27451.3i	−0.248241	+	1.40785i
$53$	−25335.8			−1.23892			−0.619461	−	0.785027i	$-0.712649\pi$
$53$	−25335.8			−1.23892			−0.619461	+	0.785027i	$0.712649\pi$
$54$		0			0
$55$	3751.66			0.167231
$56$	−135.880	+	770.613i	−0.00579008	+	0.0328372i
$57$		0			0
$58$	771.857	+	280.933i	0.0301277	+	0.0109656i
$59$	−11752.3	+	9861.37i	−0.439535	+	0.368814i	−0.835535	−	0.549437i	$-0.814842\pi$
$59$	−11752.3	+	9861.37i	−0.439535	+	0.368814i	0.396000	+	0.918250i	$0.370398\pi$
$60$		0			0
$61$	−8422.09	+	3065.39i	−0.289798	+	0.105478i	−0.482829	−	0.875715i	$-0.660391\pi$
$61$	−8422.09	+	3065.39i	−0.289798	+	0.105478i	0.193031	+	0.981193i	$0.438168\pi$
$62$	−23548.3	+	40786.9i	−0.778002	+	1.34754i
$63$		0			0
$64$	17674.6	+	30613.3i	0.539386	+	0.934244i
$65$	12752.0	+	10700.2i	0.374364	+	0.314128i
$66$		0			0
$67$	−10635.1	−	60314.5i	−0.289437	−	1.64148i	−0.688993	−	0.724768i	$-0.741947\pi$
$67$	−10635.1	−	60314.5i	−0.289437	−	1.64148i	0.399556	−	0.916709i	$-0.369164\pi$
$68$	−5376.75	−	30493.1i	−0.141009	−	0.799703i
$69$		0			0
$70$	9256.58	+	7767.19i	0.225790	+	0.189461i
$71$	2552.14	+	4420.44i	0.0600840	+	0.104068i	0.894503	−	0.447062i	$-0.147530\pi$
$71$	2552.14	+	4420.44i	0.0600840	+	0.104068i	−0.834419	+	0.551131i	$0.814196\pi$
$72$		0			0
$73$	−17695.8	+	30650.1i	−0.388655	+	0.673170i	−0.992269	−	0.124107i	$-0.960393\pi$
$73$	−17695.8	+	30650.1i	−0.388655	+	0.673170i	0.603614	+	0.797277i	$0.293727\pi$
$74$	81860.5	−	29794.8i	1.73778	−	0.632501i
$75$		0			0
$76$	−55012.9	+	46161.3i	−1.09252	+	0.916735i
$77$	13341.7	+	4856.00i	0.256440	+	0.0933365i
$78$		0			0
$79$	−9551.12	+	54167.1i	−0.172182	+	0.976490i	0.769165	+	0.639050i	$0.220672\pi$
$79$	−9551.12	+	54167.1i	−0.172182	+	0.976490i	−0.941347	+	0.337440i	$0.890439\pi$
$80$	19504.0			0.340722
$81$		0			0
$82$	116233.			1.90896
$83$	16596.8	−	94125.4i	0.264442	−	1.49972i	−0.506178	−	0.862429i	$-0.668942\pi$
$83$	16596.8	−	94125.4i	0.264442	−	1.49972i	0.770620	−	0.637295i	$-0.219947\pi$
$84$		0			0
$85$	−17375.9	−	6324.30i	−0.260855	−	0.0949435i
$86$	−4141.04	+	3474.75i	−0.0603759	+	0.0506614i
$87$		0			0
$88$	−1844.64	+	671.394i	−0.0253925	+	0.00924211i
$89$	−50371.1	+	87245.3i	−0.674072	+	1.16753i	0.302667	+	0.953096i	$0.402123\pi$
$89$	−50371.1	+	87245.3i	−0.674072	+	1.16753i	−0.976739	+	0.214431i	$0.931210\pi$
$90$		0			0
$91$	31499.0	+	54557.8i	0.398743	+	0.690642i
$92$	60324.6	+	50618.4i	0.743062	+	0.623503i
$93$		0			0
$94$	−39909.5	−	226338.i	−0.465861	−	2.64203i
$95$	7447.18	+	42235.0i	0.0846609	+	0.480136i
$96$		0			0
$97$	71726.7	+	60185.8i	0.774019	+	0.649479i	0.941735	−	0.336357i	$-0.109195\pi$
$97$	71726.7	+	60185.8i	0.774019	+	0.649479i	−0.167716	+	0.985835i	$0.553639\pi$
$98$	−45035.8	−	78004.3i	−0.473689	−	0.820453i
$99$		0			0
$100$	45434.4	−	78694.7i	0.454344	−	0.786947i
$101$	81030.2	−	29492.6i	0.790394	−	0.287680i	0.0848941	−	0.996390i	$-0.472945\pi$
$101$	81030.2	−	29492.6i	0.790394	−	0.287680i	0.705500	+	0.708710i	$0.250723\pi$
$102$		0			0
$103$	−91777.0	+	77010.0i	−0.852395	+	0.715244i	−0.960316	−	0.278916i	$-0.910025\pi$
$103$	−91777.0	+	77010.0i	−0.852395	+	0.715244i	0.107921	+	0.994159i	$0.465581\pi$
$104$	−8184.86	−	2979.05i	−0.0742041	−	0.0270081i
$105$		0			0
$106$	35548.3	−	201604.i	0.307294	−	1.74275i
$107$	−127097.			−1.07319			−0.536593	−	0.843841i	$-0.680289\pi$
$107$	−127097.			−1.07319			−0.536593	+	0.843841i	$0.680289\pi$
$108$		0			0
$109$	−112941.			−0.910511			−0.455256	−	0.890361i	$-0.650452\pi$
$109$	−112941.			−0.910511			−0.455256	+	0.890361i	$0.650452\pi$
$110$	−5263.91	+	29853.1i	−0.0414788	+	0.235238i
$111$		0			0
$112$	69360.7	+	25245.2i	0.522479	+	0.190167i
$113$	72005.2	−	60419.5i	0.530478	−	0.445124i	−0.337788	−	0.941222i	$-0.609679\pi$
$113$	72005.2	−	60419.5i	0.530478	−	0.445124i	0.868267	+	0.496098i	$0.165234\pi$
$114$		0			0
$115$	44191.4	−	16084.3i	0.311597	−	0.113412i
$116$	−1691.94	+	2930.53i	−0.0116745	+	0.0202209i
$117$		0			0
$118$	−61980.3	−	107353.i	−0.409778	−	0.709757i
$119$	−53606.6	−	44981.2i	−0.347017	−	0.291182i
$120$		0			0
$121$	−21781.2	−	123528.i	−0.135244	−	0.767009i
$122$	−12575.3	−	71318.1i	−0.0764926	−	0.433811i
$123$		0			0
$124$	−148631.	−	124716.i	−0.868068	−	0.728396i
$125$	−58193.5	−	100794.i	−0.333119	−	0.576979i
$126$		0			0
$127$	−23373.5	+	40484.0i	−0.128592	+	0.222728i	−0.923131	−	0.384485i	$-0.874379\pi$
$127$	−23373.5	+	40484.0i	−0.128592	+	0.222728i	0.794539	+	0.607213i	$0.207712\pi$
$128$	−20001.2	+	7279.84i	−0.107902	+	0.0392733i
$129$		0			0
$130$	−103037.	+	86457.9i	−0.534728	+	0.448690i
$131$	113984.	+	41486.6i	0.580315	+	0.211218i	0.615465	−	0.788165i	$-0.288968\pi$
$131$	113984.	+	41486.6i	0.580315	+	0.211218i	−0.0351492	+	0.999382i	$0.511191\pi$
$132$		0			0
$133$	−28183.5	+	159837.i	−0.138155	+	0.783514i
$134$	494863.			2.38080
$135$		0			0
$136$	9675.27			0.0448555
$137$	−42054.7	+	238504.i	−0.191431	+	1.08566i	0.725979	+	0.687717i	$0.241387\pi$
$137$	−42054.7	+	238504.i	−0.191431	+	1.08566i	−0.917410	+	0.397943i	$0.869724\pi$
$138$		0			0
$139$	318192.	+	115813.i	1.39686	+	0.508416i	0.927245	−	0.374456i	$-0.122170\pi$
$139$	318192.	+	115813.i	1.39686	+	0.508416i	0.469615	+	0.882871i	$0.344393\pi$
$140$	−38134.2	+	31998.4i	−0.164435	+	0.137977i
$141$		0			0
$142$	−38755.6	+	14105.9i	−0.161292	+	0.0587056i
$143$	−79020.1	+	136867.i	−0.323145	+	0.559703i
$144$		0			0
$145$	1010.41	+	1750.07i	0.00399095	+	0.00691252i
$146$	−219063.	−	183816.i	−0.850526	−	0.713676i
$147$		0			0
$148$	62319.4	+	353431.i	0.233867	+	1.32632i
$149$	13321.8	+	75551.7i	0.0491583	+	0.278791i	0.999472	−	0.0325045i	$-0.0103483\pi$
$149$	13321.8	+	75551.7i	0.0491583	+	0.278791i	−0.950313	+	0.311295i	$0.899237\pi$
$150$		0			0
$151$	261998.	+	219842.i	0.935094	+	0.784637i	0.976725	−	0.214496i	$-0.0688109\pi$
$151$	261998.	+	219842.i	0.935094	+	0.784637i	−0.0416308	+	0.999133i	$0.513255\pi$
$152$	−11220.0	−	19433.7i	−0.0393899	−	0.0682253i
$153$		0			0
$154$	−57360.3	+	99350.9i	−0.194899	+	0.337575i
$155$	−108881.	+	39629.3i	−0.364017	+	0.132491i
$156$		0			0
$157$	−34235.4	+	28726.9i	−0.110847	+	0.0930121i	−0.696527	−	0.717531i	$-0.745272\pi$
$157$	−34235.4	+	28726.9i	−0.110847	+	0.0930121i	0.585679	+	0.810543i	$0.300828\pi$
$158$	−417623.	−	152002.i	−1.33089	−	0.484404i
$159$		0			0
$160$	−28514.8	+	161716.i	−0.0880584	+	0.499404i
$161$	177973.			0.541116
$162$		0			0
$163$	−102723.			−0.302831			−0.151415	−	0.988470i	$-0.548383\pi$
$163$	−102723.			−0.302831			−0.151415	+	0.988470i	$0.548383\pi$
$164$	−83150.5	+	471570.i	−0.241410	+	1.36910i
$165$		0			0
$166$	725697.	+	264132.i	2.04402	+	0.743963i
$167$	39669.8	−	33286.9i	0.110070	−	0.0923596i	−0.586092	−	0.810245i	$-0.699334\pi$
$167$	39669.8	−	33286.9i	0.110070	−	0.0923596i	0.696162	+	0.717885i	$0.254890\pi$
$168$		0			0
$169$	−310049.	+	112849.i	−0.835052	+	0.303934i
$170$	74704.2	−	129391.i	0.198254	−	0.343387i
$171$		0			0
$172$	−11135.0	−	19286.4i	−0.0286991	−	0.0497084i
$173$	−252329.	−	211729.i	−0.640991	−	0.537855i	0.263332	−	0.964705i	$-0.415179\pi$
$173$	−252329.	−	211729.i	−0.640991	−	0.537855i	−0.904322	+	0.426850i	$0.859623\pi$
$174$		0			0
$175$	−35661.5	−	202246.i	−0.0880246	−	0.499212i
$176$	32154.3	+	182356.i	0.0782452	+	0.443751i
$177$		0			0
$178$	−623562.	−	523231.i	−1.47513	−	1.23778i
$179$	−162697.	−	281800.i	−0.379531	−	0.657367i	0.611463	−	0.791273i	$-0.290581\pi$
$179$	−162697.	−	281800.i	−0.379531	−	0.657367i	−0.990994	+	0.133906i	$0.957248\pi$
$180$		0			0
$181$	113357.	−	196341.i	0.257189	−	0.445465i	−0.708299	−	0.705913i	$-0.750537\pi$
$181$	113357.	−	196341.i	0.257189	−	0.445465i	0.965488	+	0.260448i	$0.0838703\pi$
$182$	−478329.	+	174097.i	−1.07040	+	0.389595i
$183$		0			0
$184$	−18849.9	+	15816.9i	−0.0410453	+	0.0344411i
$185$	201395.	+	73301.9i	0.432634	+	0.157466i
$186$		0			0
$187$	30484.2	−	172885.i	0.0637487	−	0.361537i
$188$	946825.			1.95378
$189$		0			0
$190$	−346526.			−0.696389
$191$	71114.8	−	403312.i	0.141051	−	0.799940i	−0.829402	−	0.558652i	$-0.811319\pi$
$191$	71114.8	−	403312.i	0.141051	−	0.799940i	0.970453	−	0.241289i	$-0.0775700\pi$
$192$		0			0
$193$	−444586.	−	161816.i	−0.859137	−	0.312700i	−0.125377	−	0.992109i	$-0.540014\pi$
$193$	−444586.	−	161816.i	−0.859137	−	0.312700i	−0.733760	+	0.679409i	$0.762236\pi$
$194$	−579556.	+	486305.i	−1.10558	+	0.927693i
$195$		0			0
$196$	348689.	−	126912.i	0.648333	−	0.235974i
$197$	−186041.	+	322233.i	−0.341542	+	0.591567i	−0.984719	−	0.174150i	$-0.944282\pi$
$197$	−186041.	+	322233.i	−0.341542	+	0.591567i	0.643178	+	0.765717i	$0.277616\pi$
$198$		0			0
$199$	−306334.	−	530585.i	−0.548355	−	0.949779i	−0.998387	−	0.0567666i	$-0.981921\pi$
$199$	−306334.	−	530585.i	−0.548355	−	0.949779i	0.450032	−	0.893012i	$-0.351412\pi$
$200$	21751.2	+	18251.4i	0.0384510	+	0.0322642i
$201$		0			0
$202$	120989.	+	686163.i	0.208625	+	1.18317i
$203$	1328.00	+	7531.48i	0.00226183	+	0.0128275i
$204$		0			0
$205$	219058.	+	183812.i	0.364062	+	0.305484i
$206$	−484021.	−	838349.i	−0.794687	−	1.37644i
$207$		0			0
$208$	−410808.	+	711540.i	−0.658386	+	1.14036i
$209$	−382606.	+	139257.i	−0.605879	+	0.220522i
$210$		0			0
$211$	337586.	−	283268.i	0.522010	−	0.438018i	−0.343322	−	0.939218i	$-0.611552\pi$
$211$	337586.	−	283268.i	0.522010	−	0.438018i	0.865332	+	0.501200i	$0.167108\pi$
$212$	792498.	+	288446.i	1.21104	+	0.440783i
$213$		0			0
$214$	178328.	−	1.01135e6i	0.266186	−	1.50961i
$215$	−13299.4			−0.0196216
$216$		0			0
$217$	−438499.			−0.632148
$218$	158466.	−	898705.i	0.225837	−	1.28078i
$219$		0			0
$220$	−117351.	−	42712.4i	−0.163467	−	0.0594973i
$221$	596704.	−	500694.i	0.821822	−	0.689591i
$222$		0			0
$223$	919313.	−	334602.i	1.23794	−	0.450575i	0.361633	−	0.932320i	$-0.382219\pi$
$223$	919313.	−	334602.i	1.23794	−	0.450575i	0.876311	+	0.481746i	$0.159997\pi$
$224$	−310723.	+	538188.i	−0.413765	+	0.716662i
$225$		0			0
$226$	379747.	+	657741.i	0.494565	+	0.856611i
$227$	843674.	+	707927.i	1.08670	+	0.911851i	0.996460	−	0.0840691i	$-0.0267916\pi$
$227$	843674.	+	707927.i	1.08670	+	0.911851i	0.0902415	+	0.995920i	$0.471236\pi$
$228$		0			0
$229$	−16503.5	−	93596.0i	−0.0207964	−	0.117942i	0.972642	−	0.232308i	$-0.0746276\pi$
$229$	−16503.5	−	93596.0i	−0.0207964	−	0.117942i	−0.993439	+	0.114366i	$0.963516\pi$
$230$	65983.7	+	374212.i	0.0822464	+	0.466442i
$231$		0			0
$232$	−809.995	−	679.667i	−0.000988012	−	0.000829041i
$233$	−538472.	−	932660.i	−0.649790	−	1.12547i	−0.983173	−	0.182678i	$-0.941523\pi$
$233$	−538472.	−	932660.i	−0.649790	−	1.12547i	0.333383	−	0.942792i	$-0.391810\pi$
$234$		0			0
$235$	282716.	−	489679.i	0.333950	−	0.578418i
$236$	479881.	−	174663.i	0.560859	−	0.204136i
$237$		0			0
$238$	433144.	−	363451.i	0.495667	−	0.415914i
$239$	1.18171e6	+	430108.i	1.33819	+	0.487061i	0.909241	−	0.416269i	$-0.136663\pi$
$239$	1.18171e6	+	430108.i	1.33819	+	0.487061i	0.428947	+	0.903330i	$0.358885\pi$
$240$		0			0
$241$	112260.	−	636660.i	0.124504	−	0.706098i	−0.857097	−	0.515155i	$-0.827734\pi$
$241$	112260.	−	636660.i	0.124504	−	0.706098i	0.981601	−	0.190943i	$-0.0611546\pi$
$242$	1.01351e6			1.11247
$243$		0			0
$244$	298341.			0.320803
$245$	38479.9	−	218230.i	0.0409561	−	0.232273i
$246$		0			0
$247$	−1.69766e6	−	617898.i	−1.77055	−	0.644428i
$248$	46443.1	−	38970.4i	0.0479504	−	0.0402352i
$249$		0			0
$250$	883699.	−	321640.i	0.894240	−	0.325477i
$251$	−23452.5	+	40620.9i	−0.0234966	+	0.0406973i	−0.877535	−	0.479513i	$-0.840813\pi$
$251$	−23452.5	+	40620.9i	−0.0234966	+	0.0406973i	0.854038	+	0.520211i	$0.174147\pi$
$252$		0			0
$253$	223237.	+	386658.i	0.219263	+	0.379774i
$254$	−289349.	−	242792.i	−0.281408	−	0.236130i
$255$		0			0
$256$	166562.	+	944620.i	0.158846	+	0.900860i
$257$	105778.	+	599898.i	0.0998995	+	0.566558i	0.993135	+	0.116970i	$0.0373181\pi$
$257$	105778.	+	599898.i	0.0998995	+	0.566558i	−0.893236	+	0.449588i	$0.851571\pi$
$258$		0			0
$259$	621328.	+	521356.i	0.575535	+	0.482931i
$260$	−277058.	−	479879.i	−0.254178	−	0.440249i
$261$		0			0
$262$	−490050.	+	848792.i	−0.441050	+	0.763921i
$263$	767893.	−	279490.i	0.684560	−	0.249159i	0.0237556	−	0.999718i	$-0.492438\pi$
$263$	767893.	−	279490.i	0.684560	−	0.249159i	0.660804	+	0.750558i	$0.270215\pi$
$264$		0			0
$265$	385814.	−	323736.i	0.337491	−	0.283189i
$266$	−1.23232e6	−	448529.i	−1.06788	−	0.388675i
$267$		0			0
$268$	−354013.	+	2.00771e6i	−0.301080	+	1.70751i
$269$	−1.06427e6			−0.896753			−0.448376	−	0.893845i	$-0.647998\pi$
$269$	−1.06427e6			−0.896753			−0.448376	+	0.893845i	$0.647998\pi$
$270$		0			0
$271$	1.32722e6			1.09779			0.548894	−	0.835892i	$-0.315049\pi$
$271$	1.32722e6			1.09779			0.548894	+	0.835892i	$0.315049\pi$
$272$	158481.	−	898789.i	0.129884	−	0.736607i
$273$		0			0
$274$	−1.83884e6	−	669283.i	−1.47968	−	0.538559i
$275$	394661.	−	331160.i	0.314697	−	0.264062i
$276$		0			0
$277$	−1.75176e6	+	637590.i	−1.37175	+	0.499278i	−0.919668	−	0.392697i	$-0.871542\pi$
$277$	−1.75176e6	+	637590.i	−1.37175	+	0.499278i	−0.452086	+	0.891974i	$0.649320\pi$
$278$	−1.36801e6	+	2.36946e6i	−1.06164	+	1.83881i
$279$		0			0
$280$	−7777.57	−	13471.2i	−0.00592856	−	0.0102686i
$281$	347433.	+	291531.i	0.262485	+	0.220251i	0.764526	−	0.644592i	$-0.222973\pi$
$281$	347433.	+	291531.i	0.262485	+	0.220251i	−0.502041	+	0.864844i	$0.667417\pi$
$282$		0			0
$283$	27335.0	+	155025.i	0.0202887	+	0.115063i	0.993270	−	0.115820i	$-0.0369497\pi$
$283$	27335.0	+	155025.i	0.0202887	+	0.115063i	−0.972982	+	0.230883i	$0.925839\pi$
$284$	−29504.2	−	167326.i	−0.0217064	−	0.123103i
$285$		0			0
$286$	−978218.	−	820823.i	−0.707165	−	0.593382i
$287$	541102.	+	937216.i	0.387770	+	0.671637i
$288$		0			0
$289$	277303.	−	480302.i	0.195303	−	0.338275i
$290$	−15343.6	+	5584.60i	−0.0107135	+	0.00389939i
$291$		0			0
$292$	902472.	−	757264.i	0.619408	−	0.519745i
$293$	−2.65866e6	−	967672.i	−1.80923	−	0.658505i	−0.997191	−	0.0748978i	$-0.976137\pi$
$293$	−2.65866e6	−	967672.i	−1.80923	−	0.658505i	−0.812036	−	0.583607i	$-0.801641\pi$
$294$		0			0
$295$	52957.7	−	300338.i	0.0354303	−	0.200935i
$296$	−112141.			−0.0743938
$297$		0			0
$298$	−619879.			−0.404358
$299$	−344006.	+	1.95095e6i	−0.222530	+	1.26203i
$300$		0			0
$301$	−47295.5	−	17214.2i	−0.0300887	−	0.0109514i
$302$	−2.11696e6	+	1.77634e6i	−1.33566	+	1.12075i
$303$		0			0
$304$	−1.98908e6	+	723967.i	−1.23444	+	0.449298i
$305$	89082.8	−	154296.i	0.0548333	−	0.0949740i
$306$		0			0
$307$	62247.4	+	107816.i	0.0376943	+	0.0652884i	0.884257	−	0.467000i	$-0.154665\pi$
$307$	62247.4	+	107816.i	0.0376943	+	0.0652884i	−0.846563	+	0.532289i	$0.821332\pi$
$308$	−362042.	−	303789.i	−0.217462	−	0.182472i
$309$		0			0
$310$	−162574.	−	922000.i	−0.0960828	−	0.544913i
$311$	−350085.	−	1.98543e6i	−0.205245	−	1.16400i	−0.897054	−	0.441921i	$-0.854297\pi$
$311$	−350085.	−	1.98543e6i	−0.205245	−	1.16400i	0.691809	−	0.722081i	$-0.256814\pi$
$312$		0			0
$313$	1.80229e6	+	1.51230e6i	1.03983	+	0.872525i	0.991988	−	0.126330i	$-0.0403198\pi$
$313$	1.80229e6	+	1.51230e6i	1.03983	+	0.872525i	0.0478464	+	0.998855i	$0.484764\pi$
$314$	−180553.	−	312727.i	−0.103343	−	0.178995i
$315$		0			0
$316$	915446.	−	1.58560e6i	0.515721	−	0.893255i
$317$	−527136.	+	191862.i	−0.294628	+	0.107236i	−0.485105	−	0.874456i	$-0.661219\pi$
$317$	−527136.	+	191862.i	−0.294628	+	0.107236i	0.190477	+	0.981692i	$0.438997\pi$
$318$		0			0
$319$	−14696.9	+	12332.1i	−0.00808626	+	0.00678518i
$320$	−660321.	−	240337.i	−0.360479	−	0.131204i
$321$		0			0
$322$	−249712.	+	1.41619e6i	−0.134215	+	0.761169i
$323$	2.00680e6			1.07028
$324$		0			0
$325$	2.28597e6			1.20050
$326$	144130.	−	817400.i	0.0751121	−	0.425982i
$327$		0			0
$328$	−140603.	−	51175.2i	−0.0721621	−	0.0262649i
$329$	1.63922e6	−	1.37547e6i	0.834927	−	0.700587i
$330$		0			0
$331$	−1.76678e6	+	643055.i	−0.886365	+	0.322610i	−0.744775	−	0.667315i	$-0.767443\pi$
$331$	−1.76678e6	+	643055.i	−0.886365	+	0.322610i	−0.141589	+	0.989926i	$0.545221\pi$
$332$	−1.59076e6	+	2.75527e6i	−0.792061	+	1.37189i
$333$		0			0
$334$	209214.	+	362369.i	0.102618	+	0.177740i
$335$	932640.	+	782578.i	0.454048	+	0.380992i
$336$		0			0
$337$	693819.	+	3.93484e6i	0.332791	+	1.88735i	0.448038	+	0.894015i	$0.352123\pi$
$337$	693819.	+	3.93484e6i	0.332791	+	1.88735i	−0.115247	+	0.993337i	$0.536766\pi$
$338$	−462945.	−	2.62549e6i	−0.220413	−	1.25002i
$339$		0			0
$340$	471512.	+	395646.i	0.221205	+	0.185613i
$341$	−550022.	−	952665.i	−0.256150	−	0.443664i
$342$		0			0
$343$	1.05151e6	−	1.82127e6i	0.482589	−	0.835869i
$344$	6539.12	−	2380.04i	0.00297936	−	0.00108440i
$345$		0			0
$346$	2.03883e6	−	1.71078e6i	0.915569	−	0.768254i
$347$	1.26492e6	+	460394.i	0.563949	+	0.205261i	0.608233	−	0.793758i	$-0.291879\pi$
$347$	1.26492e6	+	460394.i	0.563949	+	0.205261i	−0.0442843	+	0.999019i	$0.514101\pi$
$348$		0			0
$349$	−457946.	+	2.59714e6i	−0.201257	+	1.14138i	0.701966	+	0.712211i	$0.252306\pi$
$349$	−457946.	+	2.59714e6i	−0.201257	+	1.14138i	−0.903222	+	0.429173i	$0.858805\pi$
$350$	1.65937e6			0.724058
$351$		0			0
$352$	−1.55900e6			−0.670638
$353$	−780431.	+	4.42604e6i	−0.333348	+	1.89051i	0.109624	+	0.993973i	$0.465035\pi$
$353$	−780431.	+	4.42604e6i	−0.333348	+	1.89051i	−0.442972	+	0.896536i	$0.646076\pi$
$354$		0			0
$355$	−95347.6	−	34703.7i	−0.0401549	−	0.0146152i
$356$	2.56888e6	−	2.15555e6i	1.07428	−	0.901431i
$357$		0			0
$358$	2.47064e6	−	899240.i	1.01883	−	0.370824i
$359$	525561.	−	910298.i	0.215222	−	0.372776i	−0.738119	−	0.674670i	$-0.764286\pi$
$359$	525561.	−	910298.i	0.215222	−	0.372776i	0.953341	+	0.301895i	$0.0976191\pi$
$360$		0			0
$361$	−1.08915e6	−	1.88647e6i	−0.439866	−	0.761870i
$362$	1.40329e6	+	1.17750e6i	0.562829	+	0.472269i
$363$		0			0
$364$	−364145.	−	2.06517e6i	−0.144053	−	0.816963i
$365$	−122169.	−	692855.i	−0.0479986	−	0.272214i
$366$		0			0
$367$	−1.31221e6	−	1.10107e6i	−0.508555	−	0.426728i	0.352066	−	0.935975i	$-0.385479\pi$
$367$	−1.31221e6	−	1.10107e6i	−0.508555	−	0.426728i	−0.860620	+	0.509247i	$0.829924\pi$
$368$	1.16056e6	+	2.01015e6i	0.446733	+	0.773764i
$369$		0			0
$370$	−865861.	+	1.49971e6i	−0.328809	+	0.569514i
$371$	1.79107e6	−	651896.i	0.675581	−	0.245892i
$372$		0			0
$373$	−3.67690e6	+	3.08529e6i	−1.36839	+	1.14822i	−0.395100	+	0.918638i	$0.629290\pi$
$373$	−3.67690e6	+	3.08529e6i	−1.36839	+	1.14822i	−0.973290	+	0.229577i	$0.926266\pi$
$374$	1.33292e6	+	485145.i	0.492750	+	0.179346i
$375$		0			0
$376$	−51375.2	+	291363.i	−0.0187406	+	0.106283i
$377$	−85127.5			−0.0308473
$378$		0			0
$379$	1.68242e6			0.601640			0.300820	−	0.953681i	$-0.402740\pi$
$379$	1.68242e6			0.601640			0.300820	+	0.953681i	$0.402740\pi$
$380$	247896.	−	1.40589e6i	0.0880666	−	0.499450i
$381$		0			0
$382$	3.10949e6	+	1.13176e6i	1.09026	+	0.396823i
$383$	−374234.	+	314020.i	−0.130361	+	0.109386i	−0.705637	−	0.708574i	$-0.749339\pi$
$383$	−374234.	+	314020.i	−0.130361	+	0.109386i	0.575276	+	0.817959i	$0.304895\pi$
$384$		0			0
$385$	−265217.	+	96531.2i	−0.0911906	+	0.0331907i
$386$	1.91141e6	−	3.31066e6i	0.652959	−	1.13096i
$387$		0			0
$388$	−1.55839e6	−	2.69921e6i	−0.525528	−	0.910242i
$389$	−1.69918e6	−	1.42578e6i	−0.569333	−	0.477727i	0.312092	−	0.950052i	$-0.398970\pi$
$389$	−1.69918e6	−	1.42578e6i	−0.569333	−	0.477727i	−0.881424	+	0.472325i	$0.843415\pi$
$390$		0			0
$391$	−382123.	−	2.16713e6i	−0.126404	−	0.716874i
$392$	20134.3	+	114187.i	0.00661791	+	0.0375320i
$393$		0			0
$394$	−2.30307e6	−	1.93251e6i	−0.747424	−	0.627163i
$395$	−546693.	−	946900.i	−0.176299	−	0.305360i
$396$		0			0
$397$	572491.	−	991584.i	0.182303	−	0.315757i	−0.760362	−	0.649500i	$-0.774978\pi$
$397$	572491.	−	991584.i	0.182303	−	0.315757i	0.942664	+	0.333743i	$0.108312\pi$
$398$	4.65184e6	−	1.69313e6i	1.47203	−	0.535775i
$399$		0			0
$400$	2.05175e6	−	1.72163e6i	0.641173	−	0.538008i
$401$	−2.21375e6	−	805740.i	−0.687493	−	0.250227i	−0.0254313	−	0.999677i	$-0.508096\pi$
$401$	−2.21375e6	−	805740.i	−0.687493	−	0.250227i	−0.662061	+	0.749450i	$0.730318\pi$
$402$		0			0
$403$	847577.	−	4.80685e6i	0.259966	−	1.47434i
$404$	−2.87038e6			−0.874956
$405$		0			0
$406$	−61793.6			−0.0186049
$407$	−353328.	+	2.00382e6i	−0.105729	+	0.599617i
$408$		0			0
$409$	−3.97038e6	−	1.44510e6i	−1.17361	−	0.427159i	−0.319670	−	0.947529i	$-0.603572\pi$
$409$	−3.97038e6	−	1.44510e6i	−1.17361	−	0.427159i	−0.853941	+	0.520370i	$0.825794\pi$
$410$	−1.77000e6	+	1.48521e6i	−0.520013	+	0.436343i
$411$		0			0
$412$	3.74752e6	−	1.36399e6i	1.08768	−	0.395883i
$413$	577075.	−	999523.i	0.166478	−	0.288349i
$414$		0			0
$415$	949981.	+	1.64541e6i	0.270766	+	0.468981i
$416$	−5.29905e6	−	4.44643e6i	−1.50129	−	1.25973i
$417$		0			0
$418$	−571282.	−	3.23990e6i	−0.159923	−	0.906966i
$419$	343665.	+	1.94902e6i	0.0956314	+	0.542353i	0.994552	+	0.104241i	$0.0332414\pi$
$419$	343665.	+	1.94902e6i	0.0956314	+	0.542353i	−0.898921	+	0.438112i	$0.855647\pi$
$420$		0			0
$421$	1.60683e6	+	1.34829e6i	0.441839	+	0.370747i	0.836397	−	0.548124i	$-0.184658\pi$
$421$	1.60683e6	+	1.34829e6i	0.441839	+	0.370747i	−0.394558	+	0.918871i	$0.629102\pi$
$422$	1.78039e6	+	3.08372e6i	0.486669	+	0.842936i
$423$		0			0
$424$	−131764.	+	228222.i	−0.0355944	+	0.0616513i
$425$	−2.38613e6	+	868479.i	−0.640798	+	0.233231i
$426$		0			0
$427$	516513.	−	433405.i	0.137092	−	0.115034i
$428$	3.97557e6	+	1.44699e6i	1.04903	+	0.381817i
$429$		0			0
$430$	18660.2	−	105827.i	0.00486681	−	0.0276010i
$431$	−4.31651e6			−1.11928			−0.559641	−	0.828735i	$-0.689061\pi$
$431$	−4.31651e6			−1.11928			−0.559641	+	0.828735i	$0.689061\pi$
$432$		0			0
$433$	−4.01768e6			−1.02981			−0.514903	−	0.857249i	$-0.672172\pi$
$433$	−4.01768e6			−1.02981			−0.514903	+	0.857249i	$0.672172\pi$
$434$	615252.	−	3.48927e6i	0.156794	−	0.889221i
$435$		0			0
$436$	3.53277e6	+	1.28582e6i	0.890020	+	0.323941i
$437$	−3.90974e6	+	3.28066e6i	−0.979365	+	0.821785i
$438$		0			0
$439$	−4.80362e6	+	1.74838e6i	−1.18962	+	0.432986i	−0.859589	−	0.510985i	$-0.829281\pi$
$439$	−4.80362e6	+	1.74838e6i	−1.18962	+	0.432986i	−0.330029	+	0.943971i	$0.607058\pi$
$440$	19511.3	−	33794.5i	0.00480456	−	0.00832175i
$441$		0			0
$442$	3.14694e6	+	5.45067e6i	0.766184	+	1.32707i
$443$	1.89927e6	+	1.59367e6i	0.459808	+	0.385825i	0.843060	−	0.537819i	$-0.180752\pi$
$443$	1.89927e6	+	1.59367e6i	0.459808	+	0.385825i	−0.383252	+	0.923644i	$0.625196\pi$
$444$		0			0
$445$	−347753.	−	1.97221e6i	−0.0832475	−	0.472120i
$446$	1.37266e6	+	7.78472e6i	0.326757	+	1.85313i
$447$		0			0
$448$	−2.03717e6	−	1.70939e6i	−0.479547	−	0.402388i
$449$	−1.88192e6	−	3.25958e6i	−0.440540	−	0.763038i	0.557189	−	0.830385i	$-0.311880\pi$
$449$	−1.88192e6	−	3.25958e6i	−0.440540	−	0.763038i	−0.997730	+	0.0673475i	$0.978546\pi$
$450$		0			0
$451$	−1.35744e6	+	2.35115e6i	−0.314253	+	0.544301i
$452$	−2.94018e6	+	1.07014e6i	−0.676906	+	0.246373i
$453$		0			0
$454$	−6.81694e6	+	5.72009e6i	−1.55221	+	1.30246i
$455$	−1.17680e6	−	428319.i	−0.266485	−	0.0969927i
$456$		0			0
$457$	795942.	−	4.51401e6i	0.178275	−	1.01105i	−0.756020	−	0.654549i	$-0.772859\pi$
$457$	795942.	−	4.51401e6i	0.178275	−	1.01105i	0.934295	−	0.356500i	$-0.116030\pi$
$458$	767927.			0.171063
$459$		0			0
$460$	−1.56542e6			−0.344934
$461$	1.21990e6	−	6.91840e6i	0.267345	−	1.51619i	−0.494928	−	0.868934i	$-0.664806\pi$
$461$	1.21990e6	−	6.91840e6i	0.267345	−	1.51619i	0.762273	−	0.647256i	$-0.224083\pi$
$462$		0			0
$463$	6.55566e6	+	2.38607e6i	1.42123	+	0.517285i	0.934404	−	0.356214i	$-0.115933\pi$
$463$	6.55566e6	+	2.38607e6i	1.42123	+	0.517285i	0.486825	+	0.873499i	$0.338155\pi$
$464$	−76405.7	+	64112.0i	−0.0164752	+	0.0138243i
$465$		0			0
$466$	8.17698e6	−	2.97618e6i	1.74433	−	0.634884i
$467$	−311260.	+	539118.i	−0.0660437	+	0.114391i	−0.897156	−	0.441713i	$-0.854371\pi$
$467$	−311260.	+	539118.i	−0.0660437	+	0.114391i	0.831113	+	0.556104i	$0.187704\pi$
$468$		0			0
$469$	2.30374e6	+	3.99019e6i	0.483616	+	0.837648i
$470$	3.49985e6	+	2.93672e6i	0.730810	+	0.613223i
$471$		0			0
$472$	27709.7	+	157150.i	0.00572502	+	0.0324682i
$473$	−21925.3	−	124345.i	−0.00450602	−	0.0255549i
$474$		0			0
$475$	4.51151e6	+	3.78561e6i	0.917462	+	0.769842i
$476$	1.16470e6	+	2.01731e6i	0.235611	+	0.408090i
$477$		0			0
$478$	−5.08055e6	+	8.79976e6i	−1.01705	+	1.76158i
$479$	−2.67506e6	+	973643.i	−0.532715	+	0.193892i	−0.594350	−	0.804206i	$-0.702591\pi$
$479$	−2.67506e6	+	973643.i	−0.532715	+	0.193892i	0.0616352	+	0.998099i	$0.480368\pi$
$480$		0			0
$481$	−6.91611e6	+	5.80330e6i	−1.36301	+	1.14370i
$482$	4.90859e6	+	1.78658e6i	0.962363	+	0.350271i
$483$		0			0
$484$	−725038.	+	4.11190e6i	−0.140685	+	0.797864i
$485$	−1.86130e6			−0.359304
$486$		0			0
$487$	3.37660e6			0.645146			0.322573	−	0.946545i	$-0.395452\pi$
$487$	3.37660e6			0.645146			0.322573	+	0.946545i	$0.395452\pi$
$488$	−16188.1	+	91807.4i	−0.00307714	+	0.0174513i
$489$		0			0
$490$	1.68253e6	+	612392.i	0.316573	+	0.115223i
$491$	5.30712e6	−	4.45321e6i	0.993472	−	0.833622i	0.00740519	−	0.999973i	$-0.497643\pi$
$491$	5.30712e6	−	4.45321e6i	0.993472	−	0.833622i	0.986067	+	0.166351i	$0.0531984\pi$
$492$		0			0
$493$	88857.4	−	32341.4i	0.0164655	−	0.00599297i
$494$	7.29877e6	−	1.26418e7i	1.34565	−	2.33074i
$495$		0			0
$496$	−2.85944e6	−	4.95269e6i	−0.521887	−	0.903935i
$497$	−294158.	−	246828.i	−0.0534183	−	0.0448233i
$498$		0			0
$499$	−445945.	−	2.52908e6i	−0.0801734	−	0.454686i	−0.998294	−	0.0583852i	$-0.981405\pi$
$499$	−445945.	−	2.52908e6i	−0.0801734	−	0.454686i	0.918121	−	0.396301i	$-0.129706\pi$
$500$	672749.	+	3.81535e6i	0.120345	+	0.682510i
$501$		0			0
$502$	−290327.	−	243613.i	−0.0514195	−	0.0431461i
$503$	1.32401e6	+	2.29325e6i	0.233330	+	0.404139i	0.958786	−	0.284129i	$-0.0917045\pi$
$503$	1.32401e6	+	2.29325e6i	0.233330	+	0.404139i	−0.725456	+	0.688268i	$0.758371\pi$
$504$		0			0
$505$	−857079.	+	1.48450e6i	−0.149552	+	0.259032i
$506$	−3.38997e6	+	1.23385e6i	−0.588600	+	0.214233i
$507$		0			0
$508$	1.19203e6	−	1.00023e6i	0.204940	−	0.171965i
$509$	1.24319e6	+	452483.i	0.212687	+	0.0774119i	0.446167	−	0.894950i	$-0.352789\pi$
$509$	1.24319e6	+	452483.i	0.212687	+	0.0774119i	−0.233479	+	0.972362i	$0.575011\pi$
$510$		0			0
$511$	462343.	−	2.62208e6i	0.0783271	−	0.444215i
$512$	−8.43144e6			−1.42143
$513$		0			0
$514$	−4.92198e6			−0.821736
$515$	413561.	−	2.34542e6i	0.0687102	−	0.389675i
$516$		0			0
$517$	5.04442e6	+	1.83602e6i	0.830013	+	0.302100i
$518$	−5.02036e6	+	4.21259e6i	−0.822074	+	0.689802i
$519$		0			0
$520$	162705.	−	59219.8i	0.0263871	−	0.00960414i
$521$	−1.65240e6	+	2.86205e6i	−0.266699	+	0.461937i	−0.968007	−	0.250921i	$-0.919266\pi$
$521$	−1.65240e6	+	2.86205e6i	−0.266699	+	0.461937i	0.701308	+	0.712858i	$0.252600\pi$
$522$		0			0
$523$	−3.50814e6	−	6.07627e6i	−0.560819	−	0.971366i	−0.997425	−	0.0717138i	$-0.977153\pi$
$523$	−3.50814e6	−	6.07627e6i	−0.560819	−	0.971366i	0.436607	−	0.899653i	$-0.356180\pi$
$524$	−3.09306e6	−	2.59539e6i	−0.492108	−	0.412928i
$525$		0			0
$526$	1.14657e6	+	6.50250e6i	0.180690	+	1.02475i
$527$	941493.	+	5.33947e6i	0.147669	+	0.837475i
$528$		0			0
$529$	−643277.	−	539774.i	−0.0999445	−	0.0838634i
$530$	2.03473e6	+	3.52426e6i	0.314643	+	0.544978i
$531$		0			0
$532$	2.70130e6	−	4.67879e6i	0.413803	−	0.716728i
$533$	−1.13197e7	+	4.12004e6i	−1.72591	+	0.628179i
$534$		0			0
$535$	1.93543e6	−	1.62402e6i	0.292344	−	0.245305i
$536$	−598616.	−	217878.i	−0.0899987	−	0.0327568i
$537$		0			0
$538$	1.49327e6	−	8.46875e6i	0.222424	−	1.26143i
$539$	2.10382e6			0.311915
$540$		0			0
$541$	−5.60437e6			−0.823254			−0.411627	−	0.911352i	$-0.635039\pi$
$541$	−5.60437e6			−0.823254			−0.411627	+	0.911352i	$0.635039\pi$
$542$	−1.86220e6	+	1.05611e7i	−0.272288	+	1.54422i
$543$		0			0
$544$	7.22051e6	+	2.62805e6i	1.04609	+	0.380747i
$545$	1.71987e6	−	1.44314e6i	0.248030	−	0.208122i
$546$		0			0
$547$	1.28768e6	−	468679.i	0.184010	−	0.0669741i	−0.248372	−	0.968665i	$-0.579896\pi$
$547$	1.28768e6	−	468679.i	0.184010	−	0.0669741i	0.432382	+	0.901691i	$0.357673\pi$
$548$	4.03081e6	−	6.98157e6i	0.573378	−	0.993120i
$549$		0			0
$550$	2.08140e6	+	3.60508e6i	0.293392	+	0.508169i
$551$	−168005.	−	140973.i	−0.0235745	−	0.0197814i
$552$		0			0
$553$	−718534.	−	4.07501e6i	−0.0999158	−	0.566651i
$554$	−2.61562e6	−	1.48339e7i	−0.362076	−	2.05344i
$555$		0			0
$556$	−8.63449e6	−	7.24520e6i	−1.18454	−	0.993947i
$557$	1.07251e6	+	1.85765e6i	0.146476	+	0.253703i	0.929922	−	0.367756i	$-0.119874\pi$
$557$	1.07251e6	+	1.85765e6i	0.146476	+	0.253703i	−0.783447	+	0.621459i	$0.786540\pi$
$558$		0			0
$559$	280120.	−	485183.i	0.0379154	−	0.0656714i
$560$	−1.37881e6	+	501844.i	−0.185795	+	0.0676237i
$561$		0			0
$562$	−2.80728e6	+	2.35558e6i	−0.374925	+	0.314599i
$563$	−1.21476e7	−	4.42136e6i	−1.61517	−	0.587874i	−0.632718	−	0.774382i	$-0.718061\pi$
$563$	−1.21476e7	−	4.42136e6i	−1.61517	−	0.587874i	−0.982454	+	0.186508i	$0.940283\pi$
$564$		0			0
$565$	−324466.	+	1.84014e6i	−0.0427611	+	0.242510i
$566$	−1.27193e6			−0.166887
$567$		0			0
$568$	53091.7			0.00690487
$569$	−328849.	+	1.86499e6i	−0.0425809	+	0.241489i	−0.998668	−	0.0515938i	$-0.983570\pi$
$569$	−328849.	+	1.86499e6i	−0.0425809	+	0.241489i	0.956087	+	0.293082i	$0.0946810\pi$
$570$		0			0
$571$	5.20969e6	+	1.89617e6i	0.668686	+	0.243382i	0.653982	−	0.756510i	$-0.273097\pi$
$571$	5.20969e6	+	1.89617e6i	0.668686	+	0.243382i	0.0147037	+	0.999892i	$0.495319\pi$
$572$	4.02995e6	−	3.38153e6i	0.515003	−	0.432139i
$573$		0			0
$574$	−8.21692e6	+	2.99071e6i	−1.04095	+	0.378874i
$575$	3.22900e6	−	5.59280e6i	0.407286	−	0.705439i
$576$		0			0
$577$	−3.95063e6	−	6.84269e6i	−0.494000	−	0.855633i	0.505976	−	0.862547i	$-0.331132\pi$
$577$	−3.95063e6	−	6.84269e6i	−0.494000	−	0.855633i	−0.999976	+	0.00691467i	$0.997799\pi$
$578$	3.43283e6	+	2.88049e6i	0.427398	+	0.358630i
$579$		0			0
$580$	−11680.9	−	66245.4i	−0.00144180	−	0.00817685i
$581$	1.24859e6	+	7.08108e6i	0.153454	+	0.870280i
$582$		0			0
$583$	3.66287e6	+	3.07352e6i	0.446324	+	0.374511i
$584$	184062.	+	318804.i	0.0223322	+	0.0386805i
$585$		0			0
$586$	1.14304e7	−	1.97980e7i	1.37504	−	2.38165i
$587$	1.45319e7	−	5.28919e6i	1.74072	−	0.633569i	0.741419	−	0.671042i	$-0.234153\pi$
$587$	1.45319e7	−	5.28919e6i	1.74072	−	0.633569i	0.999298	+	0.0374727i	$0.0119307\pi$
$588$		0			0
$589$	9.63300e6	−	8.08305e6i	1.14412	−	0.960035i
$590$	2.31558e6	+	842801.i	0.273860	+	0.0996771i
$591$		0			0
$592$	−1.83688e6	+	1.04174e7i	−0.215415	+	1.22168i
$593$	6.33686e6			0.740009			0.370005	−	0.929030i	$-0.379356\pi$
$593$	6.33686e6			0.740009			0.370005	+	0.929030i	$0.379356\pi$
$594$		0			0
$595$	1.39108e6			0.161087
$596$	443447.	−	2.51491e6i	0.0511359	−	0.290006i
$597$		0			0
$598$	−1.50417e7	−	5.47472e6i	−1.72006	−	0.626050i
$599$	5.69469e6	−	4.77841e6i	0.648490	−	0.544147i	−0.258123	−	0.966112i	$-0.583104\pi$
$599$	5.69469e6	−	4.77841e6i	0.648490	−	0.544147i	0.906612	+	0.421965i	$0.138659\pi$
$600$		0			0
$601$	−1.05116e7	+	3.82591e6i	−1.18709	+	0.432065i	−0.858700	−	0.512478i	$-0.828727\pi$
$601$	−1.05116e7	+	3.82591e6i	−1.18709	+	0.432065i	−0.328388	+	0.944543i	$0.606505\pi$
$602$	203338.	−	352192.i	0.0228679	−	0.0396085i
$603$		0			0
$604$	−5.69236e6	−	9.85945e6i	−0.634892	−	1.09967i
$605$	1.91010e6	+	1.60276e6i	0.212162	+	0.178025i
$606$		0			0
$607$	−39412.6	−	223520.i	−0.00434174	−	0.0246232i	0.982560	−	0.185946i	$-0.0595350\pi$
$607$	−39412.6	−	223520.i	−0.00434174	−	0.0246232i	−0.986902	+	0.161323i	$0.948424\pi$
$608$	−3.09466e6	−	1.75507e7i	−0.339511	−	1.92546i
$609$		0			0
$610$	1.10279e6	+	925349.i	0.119996	+	0.100689i
$611$	1.19095e7	+	2.06279e7i	1.29060	+	2.23539i
$612$		0			0
$613$	−4.90647e6	+	8.49826e6i	−0.527373	+	0.913438i	0.472118	+	0.881536i	$0.343490\pi$
$613$	−4.90647e6	+	8.49826e6i	−0.527373	+	0.913438i	−0.999491	+	0.0319019i	$0.989844\pi$
$614$	−945260.	+	344047.i	−0.101188	+	0.0368295i
$615$		0			0
$616$	113129.	−	94926.2i	0.0120122	−	0.0100794i
$617$	9.61915e6	+	3.50109e6i	1.01724	+	0.370246i	0.796209	−	0.605021i	$-0.206835\pi$
$617$	9.61915e6	+	3.50109e6i	1.01724	+	0.370246i	0.221032	+	0.975267i	$0.429058\pi$
$618$		0			0
$619$	470254.	−	2.66694e6i	0.0493294	−	0.279761i	−0.950158	−	0.311768i	$-0.899079\pi$
$619$	470254.	−	2.66694e6i	0.0493294	−	0.279761i	0.999488	+	0.0320071i	$0.0101899\pi$
$620$	3.85695e6			0.402962
$621$		0			0
$622$	1.62899e7			1.68827
$623$	1.31606e6	−	7.46372e6i	0.135848	−	0.770434i
$624$		0			0
$625$	−5.84217e6	−	2.12637e6i	−0.598238	−	0.217741i
$626$	−1.45626e7	+	1.22195e7i	−1.48526	+	1.24628i
$627$		0			0
$628$	1.39793e6	−	508805.i	0.141445	−	0.0514816i
$629$	5.01436e6	−	8.68513e6i	0.505346	−	0.875285i
$630$		0			0
$631$	6.63331e6	+	1.14892e7i	0.663219	+	1.14873i	0.979765	+	0.200151i	$0.0641434\pi$
$631$	6.63331e6	+	1.14892e7i	0.663219	+	1.14873i	−0.316546	+	0.948577i	$0.602523\pi$
$632$	438258.	+	367742.i	0.0436453	+	0.0366228i
$633$		0			0
$634$	−787084.	−	4.46378e6i	−0.0777675	−	0.441041i
$635$	−161366.	−	915154.i	−0.0158810	−	0.0900658i
$636$		0			0
$637$	7.15091e6	+	6.00032e6i	0.698253	+	0.585904i
$638$	−77509.5	−	134250.i	−0.00753882	−	0.0130576i
$639$		0			0
$640$	211558.	−	366430.i	0.0204164	−	0.0353623i
$641$	1.54658e7	−	5.62908e6i	1.48671	−	0.541118i	0.534129	−	0.845403i	$-0.320640\pi$
$641$	1.54658e7	−	5.62908e6i	1.48671	−	0.541118i	0.952581	+	0.304284i	$0.0984173\pi$
$642$		0			0
$643$	6.81488e6	−	5.71836e6i	0.650026	−	0.545437i	−0.257053	−	0.966397i	$-0.582751\pi$
$643$	6.81488e6	−	5.71836e6i	0.650026	−	0.545437i	0.907079	+	0.420961i	$0.138307\pi$
$644$	−5.56698e6	−	2.02621e6i	−0.528938	−	0.192518i
$645$		0			0
$646$	−2.81571e6	+	1.59687e7i	−0.265464	+	1.50552i
$647$	−8.09399e6			−0.760154			−0.380077	−	0.924955i	$-0.624103\pi$
$647$	−8.09399e6			−0.760154			−0.380077	+	0.924955i	$0.624103\pi$
$648$		0			0
$649$	2.89537e6			0.269831
$650$	−3.20741e6	+	1.81901e7i	−0.297763	+	1.68870i
$651$		0			0
$652$	3.21317e6	+	1.16950e6i	0.296015	+	0.107741i
$653$	6.97748e6	−	5.85480e6i	0.640348	−	0.537315i	−0.263777	−	0.964584i	$-0.584968\pi$
$653$	6.97748e6	−	5.85480e6i	0.640348	−	0.537315i	0.904125	+	0.427268i	$0.140524\pi$
$654$		0			0
$655$	−2.26585e6	+	824703.i	−0.206361	+	0.0751094i
$656$	−7.05702e6	+	1.22231e7i	−0.640268	+	1.10898i
$657$		0			0
$658$	8.64507e6	+	1.49737e7i	0.778402	+	1.34823i
$659$	−6.90678e6	−	5.79548e6i	−0.619530	−	0.519847i	0.278126	−	0.960545i	$-0.410287\pi$
$659$	−6.90678e6	−	5.79548e6i	−0.619530	−	0.519847i	−0.897656	+	0.440697i	$0.854731\pi$
$660$		0			0
$661$	1.78471e6	+	1.01216e7i	0.158878	+	0.901044i	0.955154	+	0.296110i	$0.0956895\pi$
$661$	1.78471e6	+	1.01216e7i	0.158878	+	0.901044i	−0.796275	+	0.604934i	$0.793199\pi$
$662$	−2.63804e6	−	1.49611e7i	−0.233957	−	1.32684i
$663$		0			0
$664$	−761555.	−	639020.i	−0.0670318	−	0.0562464i
$665$	−1.61318e6	−	2.79412e6i	−0.141459	−	0.245014i
$666$		0			0
$667$	−120245.	+	208271.i	−0.0104654	+	0.0181265i
$668$	−1.61983e6	+	589571.i	−0.140452	+	0.0511205i
$669$		0			0
$670$	−7.53578e6	+	6.32327e6i	−0.648547	+	0.544195i
$671$	1.58948e6	+	578522.i	0.136285	+	0.0496037i
$672$		0			0
$673$	584432.	−	3.31448e6i	0.0497389	−	0.282083i	−0.949786	−	0.312900i	$-0.898700\pi$
$673$	584432.	−	3.31448e6i	0.0497389	−	0.282083i	0.999525	+	0.0308164i	$0.00981072\pi$
$674$	−3.22842e7			−2.73742
$675$		0			0
$676$	1.09831e7			0.924392
$677$	1.36986e6	−	7.76886e6i	0.114869	−	0.651457i	−0.871945	−	0.489603i	$-0.837142\pi$
$677$	1.36986e6	−	7.76886e6i	0.114869	−	0.651457i	0.986815	−	0.161854i	$-0.0517473\pi$
$678$		0			0
$679$	−6.61920e6	−	2.40919e6i	−0.550974	−	0.200538i
$680$	−147335.	+	123629.i	−0.0122190	+	0.0102529i
$681$		0			0
$682$	8.35237e6	−	3.04002e6i	0.687621	−	0.250273i
$683$	−5.56506e6	+	9.63896e6i	−0.456476	+	0.790640i	−0.998772	−	0.0495481i	$-0.984222\pi$
$683$	−5.56506e6	+	9.63896e6i	−0.456476	+	0.790640i	0.542296	+	0.840188i	$0.317555\pi$
$684$		0			0
$685$	−2.40715e6	−	4.16931e6i	−0.196009	−	0.339498i
$686$	1.30170e7	+	1.09226e7i	1.05609	+	0.886165i
$687$		0			0
$688$	−113985.	−	646440.i	−0.00918070	−	0.0520663i
$689$	3.68415e6	+	2.08939e7i	0.295658	+	1.67676i
$690$		0			0
$691$	−5.40132e6	−	4.53224e6i	−0.430333	−	0.361092i	0.401744	−	0.915752i	$-0.368404\pi$
$691$	−5.40132e6	−	4.53224e6i	−0.430333	−	0.361092i	−0.832077	+	0.554660i	$0.812848\pi$
$692$	5.48228e6	+	9.49559e6i	0.435207	+	0.753801i
$693$		0			0
$694$	−5.43829e6	+	9.41939e6i	−0.428611	+	0.742376i
$695$	−6.32528e6	+	2.30221e6i	−0.496727	+	0.180794i
$696$		0			0
$697$	1.02504e7	−	8.60112e6i	0.799207	−	0.670614i
$698$	−2.00237e7	−	7.28802e6i	−1.55563	−	0.566202i
$699$		0			0
$700$	−1.18707e6	+	6.73223e6i	−0.0915657	+	0.519295i
$701$	−7.27260e6			−0.558978			−0.279489	−	0.960149i	$-0.590165\pi$
$701$	−7.27260e6			−0.558978			−0.279489	+	0.960149i	$0.590165\pi$
$702$		0			0
$703$	−2.32598e7			−1.77508
$704$	1.15847e6	−	6.57000e6i	0.0880952	−	0.499613i
$705$		0			0
$706$	−3.41243e7	−	1.24202e7i	−2.57663	−	0.937817i
$707$	−4.96944e6	+	4.16986e6i	−0.373903	+	0.313742i
$708$		0			0
$709$	1.85022e7	−	6.73425e6i	1.38232	−	0.503122i	0.459437	−	0.888210i	$-0.348051\pi$
$709$	1.85022e7	−	6.73425e6i	1.38232	−	0.503122i	0.922880	+	0.385088i	$0.125829\pi$
$710$	409929.	−	710017.i	0.0305184	−	0.0528595i
$711$		0			0
$712$	523930.	+	907474.i	0.0387323	+	0.0670863i
$713$	−1.05631e7	−	8.86351e6i	−0.778159	−	0.652953i
$714$		0			0
$715$	−545541.	−	3.09392e6i	−0.0399082	−	0.226331i
$716$	1.88087e6	+	1.06669e7i	0.137112	+	0.777602i
$717$		0			0
$718$	6.50611e6	+	5.45927e6i	0.470988	+	0.395206i
$719$	−3.97787e6	−	6.88987e6i	−0.286965	−	0.497037i	0.686119	−	0.727489i	$-0.259313\pi$
$719$	−3.97787e6	−	6.88987e6i	−0.286965	−	0.497037i	−0.973084	+	0.230452i	$0.925980\pi$
$720$		0			0
$721$	4.50653e6	−	7.80554e6i	0.322853	−	0.559197i
$722$	1.65393e7	−	6.01983e6i	1.18080	−	0.429775i
$723$		0			0
$724$	−5.78112e6	+	4.85093e6i	−0.409888	+	0.343937i
$725$	260771.	+	94912.7i	0.0184253	+	0.00670624i
$726$		0			0
$727$	1.10525e6	−	6.26818e6i	0.0775575	−	0.439850i	−0.921158	−	0.389188i	$-0.872756\pi$
$727$	1.10525e6	−	6.26818e6i	0.0775575	−	0.439850i	0.998716	−	0.0506624i	$-0.0161333\pi$
$728$	655267.			0.0458236
$729$		0			0
$730$	5.68467e6			0.394819
$731$	−108064.	+	612864.i	−0.00747979	+	0.0424200i
$732$		0			0
$733$	−2.40900e7	−	8.76803e6i	−1.65606	−	0.602757i	−0.666324	−	0.745662i	$-0.732133\pi$
$733$	−2.40900e7	−	8.76803e6i	−1.65606	−	0.602757i	−0.989736	+	0.142906i	$0.954355\pi$
$734$	1.06027e7	−	8.89674e6i	0.726402	−	0.609524i
$735$		0			0
$736$	−1.83637e7	+	6.68382e6i	−1.24958	+	0.454810i
$737$	−5.77929e6	+	1.00100e7i	−0.391927	+	0.678838i
$738$		0			0
$739$	3.31109e6	+	5.73498e6i	0.223028	+	0.386296i	0.955726	−	0.294258i	$-0.0950724\pi$
$739$	3.31109e6	+	5.73498e6i	0.223028	+	0.386296i	−0.732698	+	0.680554i	$0.761739\pi$
$740$	−5.46508e6	−	4.58574e6i	−0.366874	−	0.307844i
$741$		0			0
$742$	2.67431e6	+	1.51667e7i	0.178321	+	1.01131i
$743$	62505.3	+	354485.i	0.00415379	+	0.0235573i	0.986814	−	0.161857i	$-0.0517484\pi$
$743$	62505.3	+	354485.i	0.00415379	+	0.0235573i	−0.982660	+	0.185414i	$0.940637\pi$
$744$		0			0
$745$	−1.16825e6	−	980279.i	−0.0771162	−	0.0647081i
$746$	−1.93915e7	−	3.35871e7i	−1.27575	−	2.20966i
$747$		0			0
$748$	−2.92182e6	+	5.06074e6i	−0.190941	+	0.330720i
$749$	8.98490e6	−	3.27024e6i	0.585206	−	0.212997i
$750$		0			0
$751$	3.97959e6	−	3.33927e6i	0.257477	−	0.216049i	−0.504907	−	0.863174i	$-0.668473\pi$
$751$	3.97959e6	−	3.33927e6i	0.257477	−	0.216049i	0.762384	+	0.647125i	$0.224029\pi$
$752$	2.62248e7	+	9.54505e6i	1.69109	+	0.615508i
$753$		0			0
$754$	119441.	−	677385.i	0.00765114	−	0.0433918i
$755$	−6.79881e6			−0.434076
$756$		0			0
$757$	6.85707e6			0.434909			0.217455	−	0.976070i	$-0.430225\pi$
$757$	6.85707e6			0.434909			0.217455	+	0.976070i	$0.430225\pi$
$758$	−2.36058e6	+	1.33875e7i	−0.149227	+	0.846307i
$759$		0			0
$760$	419179.	+	152569.i	0.0263248	+	0.00958145i
$761$	−8.70747e6	+	7.30643e6i	−0.545042	+	0.457345i	−0.873258	−	0.487258i	$-0.837997\pi$
$761$	−8.70747e6	+	7.30643e6i	−0.545042	+	0.457345i	0.328216	+	0.944603i	$0.393553\pi$
$762$		0			0
$763$	7.98417e6	−	2.90600e6i	0.496499	−	0.180711i
$764$	−6.81613e6	+	1.18059e7i	−0.422479	+	0.731754i
$765$		0			0
$766$	−1.97367e6	−	3.41849e6i	−0.121535	−	0.210505i
$767$	9.84140e6	+	8.25792e6i	0.604044	+	0.506853i
$768$		0			0
$769$	718369.	+	4.07407e6i	0.0438058	+	0.248435i	0.998845	−	0.0480437i	$-0.0152987\pi$
$769$	718369.	+	4.07407e6i	0.0438058	+	0.248435i	−0.955039	+	0.296479i	$0.904188\pi$
$770$	−396005.	−	2.24586e6i	−0.0240699	−	0.136507i
$771$		0			0
$772$	1.20643e7	+	1.01232e7i	0.728550	+	0.611326i
$773$	−774280.	−	1.34109e6i	−0.0466068	−	0.0807254i	0.841781	−	0.539819i	$-0.181507\pi$
$773$	−774280.	−	1.34109e6i	−0.0466068	−	0.0807254i	−0.888388	+	0.459094i	$0.848174\pi$
$774$		0			0
$775$	−7.95577e6	+	1.37798e7i	−0.475804	+	0.824116i
$776$	915176.	−	333097.i	0.0545570	−	0.0198571i
$777$		0			0
$778$	1.37295e7	−	1.15204e7i	0.813215	−	0.682369i
$779$	−2.91631e7	−	1.06145e7i	−1.72183	−	0.626695i
$780$		0			0
$781$	167278.	−	948680.i	0.00981321	−	0.0556535i
$782$	1.77807e7			1.03975
$783$		0			0
$784$	1.09373e7			0.635505
$785$	154270.	−	874907.i	0.00893525	−	0.0506743i
$786$		0			0
$787$	2.21710e7	+	8.06958e6i	1.27599	+	0.464423i	0.889105	−	0.457704i	$-0.151328\pi$
$787$	2.21710e7	+	8.06958e6i	1.27599	+	0.464423i	0.386888	+	0.922127i	$0.373550\pi$
$788$	9.48793e6	−	7.96132e6i	0.544322	−	0.456740i
$789$		0			0
$790$	8.30183e6	−	3.02162e6i	0.473267	−	0.172255i
$791$	−3.53568e6	+	6.12397e6i	−0.200924	+	0.348010i
$792$		0			0
$793$	3.75265e6	+	6.49977e6i	0.211912	+	0.367042i
$794$	7.08708e6	+	5.94677e6i	0.398948	+	0.334757i
$795$		0			0
$796$	3.54139e6	+	2.00842e7i	0.198103	+	1.12350i
$797$	−1.77651e6	−	1.00751e7i	−0.0990652	−	0.561827i	−0.993426	−	0.114480i	$-0.963480\pi$
$797$	−1.77651e6	−	1.00751e7i	−0.0990652	−	0.561827i	0.894360	−	0.447347i	$-0.147631\pi$
$798$		0			0
$799$	−2.02683e7	−	1.70071e7i	−1.12318	−	0.942461i
$800$	1.12750e7	+	1.95289e7i	0.622863	+	1.07883i
$801$		0			0
$802$	9.51760e6	−	1.64850e7i	0.522506	−	0.905007i
$803$	6.27655e6	−	2.28448e6i	0.343504	−	0.125025i
$804$		0			0
$805$	−2.71018e6	+	2.27411e6i	−0.147404	+	0.123686i
$806$	3.70603e7	+	1.34889e7i	2.00942	+	0.731371i
$807$		0			0
$808$	155748.	−	883293.i	0.00839257	−	0.0475966i
$809$	2.67937e7			1.43933			0.719667	−	0.694319i	$-0.244294\pi$
$809$	2.67937e7			1.43933			0.719667	+	0.694319i	$0.244294\pi$
$810$		0			0
$811$	−3.77636e6			−0.201614			−0.100807	−	0.994906i	$-0.532142\pi$
$811$	−3.77636e6			−0.201614			−0.100807	+	0.994906i	$0.532142\pi$
$812$	44205.7	−	250703.i	0.00235281	−	0.0133435i
$813$		0			0
$814$	−1.54493e7	−	5.62308e6i	−0.817236	−	0.297450i
$815$	1.56427e6	−	1.31258e6i	0.0824933	−	0.0692201i
$816$		0			0
$817$	1.35631e6	−	493657.i	0.0710893	−	0.0258744i
$818$	1.70699e7	−	2.95659e7i	0.891965	−	1.54493i
$819$		0			0
$820$	−4.75942e6	−	8.24356e6i	−0.247184	−	0.428134i
$821$	−1.97495e7	−	1.65718e7i	−1.02258	−	0.858050i	−0.0326337	−	0.999467i	$-0.510389\pi$
$821$	−1.97495e7	−	1.65718e7i	−1.02258	−	0.858050i	−0.989950	+	0.141418i	$0.954834\pi$
$822$		0			0
$823$	−2.15299e6	−	1.22102e7i	−0.110801	−	0.628383i	−0.988744	−	0.149618i	$-0.952196\pi$
$823$	−2.15299e6	−	1.22102e7i	−0.110801	−	0.628383i	0.877943	−	0.478765i	$-0.158915\pi$
$824$	216392.	+	1.22722e6i	0.0111026	+	0.0629659i
$825$		0			0
$826$	7.14382e6	+	5.99438e6i	0.364318	+	0.305699i
$827$	−638693.	−	1.10625e6i	−0.0324734	−	0.0562456i	0.849332	−	0.527859i	$-0.177005\pi$
$827$	−638693.	−	1.10625e6i	−0.0324734	−	0.0562456i	−0.881805	+	0.471613i	$0.843672\pi$
$828$		0			0
$829$	7.89038e6	−	1.36665e7i	0.398760	−	0.690673i	−0.594813	−	0.803864i	$-0.702774\pi$
$829$	7.89038e6	−	1.36665e7i	0.398760	−	0.690673i	0.993573	+	0.113191i	$0.0361073\pi$
$830$	−1.44260e7	+	5.25062e6i	−0.726858	+	0.264555i
$831$		0			0
$832$	2.26760e7	−	1.90275e7i	1.13569	−	0.952955i
$833$	−9.74385e6	−	3.54647e6i	−0.486540	−	0.177086i
$834$		0			0
$835$	−178758.	+	1.01379e6i	−0.00887257	+	0.0503189i
$836$	1.35533e7			0.670701
$837$		0			0
$838$	−1.59912e7			−0.786629
$839$	6.36209e6	−	3.60812e7i	0.312029	−	1.76960i	−0.276388	−	0.961046i	$-0.589137\pi$
$839$	6.36209e6	−	3.60812e7i	0.312029	−	1.76960i	0.588417	−	0.808558i	$-0.299751\pi$
$840$		0			0
$841$	1.92645e7	+	7.01169e6i	0.939219	+	0.341848i
$842$	−1.29833e7	+	1.08942e7i	−0.631108	+	0.529562i
$843$		0			0
$844$	−1.37846e7	+	5.01719e6i	−0.666099	+	0.242440i
$845$	3.27947e6	−	5.68022e6i	0.158002	−	0.273667i
$846$		0			0
$847$	4.71818e6	+	8.17214e6i	0.225978	+	0.391406i
$848$	1.90425e7	+	1.59785e7i	0.909355	+	0.763039i
$849$		0			0
$850$	−3.56281e6	−	2.02057e7i	−0.169139	−	0.959237i
$851$	4.42901e6	+	2.51182e7i	0.209644	+	1.18895i
$852$		0			0
$853$	4.67099e6	+	3.91942e6i	0.219804	+	0.184438i	0.746040	−	0.665901i	$-0.231953\pi$
$853$	4.67099e6	+	3.91942e6i	0.219804	+	0.184438i	−0.526236	+	0.850339i	$0.676397\pi$
$854$	2.72403e6	+	4.71815e6i	0.127811	+	0.221374i
$855$		0			0
$856$	−660993.	+	1.14487e6i	−0.0308327	+	0.0534039i
$857$	−3.17840e7	+	1.15684e7i	−1.47828	+	0.538050i	−0.950335	−	0.311228i	$-0.899260\pi$
$857$	−3.17840e7	+	1.15684e7i	−1.47828	+	0.538050i	−0.527945	+	0.849278i	$0.677037\pi$
$858$		0			0
$859$	3.51837e6	−	2.95227e6i	0.162689	−	0.136513i	−0.557809	−	0.829970i	$-0.688358\pi$
$859$	3.51837e6	−	2.95227e6i	0.162689	−	0.136513i	0.720498	+	0.693457i	$0.243913\pi$
$860$	416002.	+	151412.i	0.0191800	+	0.00698096i
$861$		0			0
$862$	6.05644e6	−	3.43478e7i	0.277619	−	1.57446i
$863$	4.00578e7			1.83088			0.915441	−	0.402451i	$-0.131842\pi$
$863$	4.00578e7			1.83088			0.915441	+	0.402451i	$0.131842\pi$
$864$		0			0
$865$	6.54791e6			0.297552
$866$	5.63715e6	−	3.19699e7i	0.255426	−	1.44859i
$867$		0			0
$868$	1.37162e7	+	4.99228e6i	0.617922	+	0.224905i
$869$	7.95192e6	−	6.67246e6i	0.357209	−	0.299734i
$870$		0			0
$871$	−4.81936e7	+	1.75410e7i	−2.15251	+	0.783448i
$872$	−587372.	+	1.01736e6i	−0.0261591	+	0.0453088i
$873$		0			0
$874$	−2.06195e7	−	3.57141e7i	−0.913061	−	1.58147i
$875$	6.70735e6	+	5.62813e6i	0.296163	+	0.248510i
$876$		0			0
$877$	4.86976e6	+	2.76178e7i	0.213800	+	1.21252i	0.882976	+	0.469418i	$0.155536\pi$
$877$	4.86976e6	+	2.76178e7i	0.213800	+	1.21252i	−0.669176	+	0.743104i	$0.733353\pi$
$878$	−7.17245e6	−	4.06770e7i	−0.314001	−	1.78079i
$879$		0			0
$880$	−2.81976e6	−	2.36606e6i	−0.122746	−	0.102996i
$881$	−4.53807e6	−	7.86017e6i	−0.196984	−	0.341187i	0.750565	−	0.660797i	$-0.229781\pi$
$881$	−4.53807e6	−	7.86017e6i	−0.196984	−	0.341187i	−0.947549	+	0.319610i	$0.896448\pi$
$882$		0			0
$883$	−1.36576e7	+	2.36557e7i	−0.589486	+	1.02102i	0.404814	+	0.914399i	$0.367336\pi$
$883$	−1.36576e7	+	2.36557e7i	−0.589486	+	1.02102i	−0.994300	+	0.106620i	$0.965997\pi$
$884$	−2.43651e7	+	8.86819e6i	−1.04867	+	0.381684i
$885$		0			0
$886$	−1.53462e7	+	1.28770e7i	−0.656774	+	0.551099i
$887$	−3.46203e7	−	1.26008e7i	−1.47748	−	0.537759i	−0.527360	−	0.849642i	$-0.676818\pi$
$887$	−3.46203e7	−	1.26008e7i	−1.47748	−	0.537759i	−0.950120	+	0.311883i	$0.899040\pi$
$888$		0			0
$889$	610683.	−	3.46336e6i	0.0259156	−	0.146975i
$890$	1.61814e7			0.684763
$891$		0			0
$892$	−3.25654e7			−1.37039
$893$	−1.06560e7	+	6.04331e7i	−0.447162	+	2.53598i
$894$		0			0
$895$	6.07834e6	+	2.21234e6i	0.253646	+	0.0923195i
$896$	1.22664e6	−	1.02927e6i	0.0510443	−	0.0428312i
$897$		0			0
$898$	2.85780e7	−	1.04015e7i	1.18261	−	0.430434i
$899$	296266.	−	513148.i	0.0122260	−	0.0211760i
$900$		0			0
$901$	−1.17835e7	−	2.04097e7i	−0.483574	−	0.837575i
$902$	−1.68042e7	−	1.41004e7i	−0.687705	−	0.577053i
$903$		0			0
$904$	−169774.	−	962838.i	−0.00690957	−	0.0391861i
$905$	782599.	+	4.43834e6i	0.0317627	+	0.180135i
$906$		0			0
$907$	−2.97699e7	−	2.49799e7i	−1.20160	−	1.00826i	−0.999583	−	0.0288777i	$-0.990807\pi$
$907$	−2.97699e7	−	2.49799e7i	−1.20160	−	1.00826i	−0.202015	−	0.979382i	$-0.564749\pi$
$908$	−1.83303e7	−	3.17490e7i	−0.737827	−	1.27795i
$909$		0			0
$910$	5.05941e6	−	8.76316e6i	0.202533	−	0.350798i
$911$	−2.87284e7	+	1.04563e7i	−1.14688	+	0.417428i	−0.844392	−	0.535726i	$-0.820038\pi$
$911$	−2.87284e7	+	1.04563e7i	−1.14688	+	0.417428i	−0.302483	+	0.953155i	$0.597816\pi$
$912$		0			0
$913$	−1.38179e7	+	1.15946e7i	−0.548613	+	0.460341i
$914$	3.48026e7	+	1.26671e7i	1.37799	+	0.501547i
$915$		0			0
$916$	−549357.	+	3.11556e6i	−0.0216329	+	0.122687i
$917$	−9.12534e6			−0.358365
$918$		0			0
$919$	−4.08434e6			−0.159527			−0.0797633	−	0.996814i	$-0.525416\pi$
$919$	−4.08434e6			−0.159527			−0.0797633	+	0.996814i	$0.525416\pi$
$920$	84940.3	−	481721.i	0.00330860	−	0.0187640i
$921$		0			0
$922$	5.33402e7	+	1.94142e7i	2.06646	+	0.752130i
$923$	3.27433e6	−	2.74749e6i	0.126508	−	0.106153i
$924$		0			0
$925$	2.76564e7	−	1.00661e7i	1.06278	−	0.386819i
$926$	−2.81848e7	+	4.88175e7i	−1.08016	+	1.87089i
$927$		0			0
$928$	−419872.	−	727240.i	−0.0160047	−	0.0277209i
$929$	1.82066e7	+	1.52772e7i	0.692134	+	0.580769i	0.919524	−	0.393035i	$-0.128575\pi$
$929$	1.82066e7	+	1.52772e7i	0.692134	+	0.580769i	−0.227390	+	0.973804i	$0.573019\pi$
$930$		0			0
$931$	4.17615e6	+	2.36841e7i	0.157907	+	0.895536i
$932$	6.22503e6	+	3.53039e7i	0.234748	+	1.33132i
$933$		0			0
$934$	−3.85320e6	−	3.23322e6i	−0.144529	−	0.121274i
$935$	1.74488e6	+	3.02222e6i	0.0652733	+	0.113057i
$936$		0			0
$937$	6.24788e6	−	1.08216e7i	0.232479	−	0.402665i	−0.726058	−	0.687633i	$-0.758650\pi$
$937$	6.24788e6	−	1.08216e7i	0.232479	−	0.402665i	0.958537	+	0.284968i	$0.0919830\pi$
$938$	−3.49835e7	+	1.27330e7i	−1.29824	+	0.472522i
$939$		0			0
$940$	−1.44183e7	+	1.20984e7i	−0.532223	+	0.446588i
$941$	6.24655e6	+	2.27356e6i	0.229967	+	0.0837012i	0.454434	−	0.890781i	$-0.349842\pi$
$941$	6.24655e6	+	2.27356e6i	0.229967	+	0.0837012i	−0.224466	+	0.974482i	$0.572064\pi$
$942$		0			0
$943$	−5.90947e6	+	3.35143e7i	−0.216406	+	1.22730i
$944$	1.50524e7			0.549762
$945$		0			0
$946$	1.02021e6			0.0370648
$947$	−751796.	+	4.26365e6i	−0.0272411	+	0.154492i	−0.995394	−	0.0958671i	$-0.969438\pi$
$947$	−751796.	+	4.26365e6i	−0.0272411	+	0.154492i	0.968153	+	0.250359i	$0.0805487\pi$
$948$		0			0
$949$	2.78497e7	+	1.01365e7i	1.00382	+	0.365360i
$950$	−3.64533e7	+	3.05879e7i	−1.31047	+	1.09962i
$951$		0			0
$952$	−683977.	+	248947.i	−0.0244596	+	0.00890257i
$953$	2.03268e7	−	3.52070e7i	0.724997	−	1.25573i	−0.233978	−	0.972242i	$-0.575174\pi$
$953$	2.03268e7	−	3.52070e7i	0.724997	−	1.25573i	0.958975	−	0.283490i	$-0.0914923\pi$
$954$		0			0
$955$	4.07051e6	+	7.05033e6i	0.144424	+	0.250150i
$956$	−3.20670e7	−	2.69074e7i	−1.13479	−	0.952198i
$957$		0			0
$958$	−3.99422e6	−	2.26524e7i	−0.140611	−	0.797443i
$959$	−3.16378e6	−	1.79427e7i	−0.111086	−	0.630001i
$960$		0			0
$961$	4.09468e6	+	3.43584e6i	0.143025	+	0.120012i
$962$	−3.64747e7	−	6.31761e7i	−1.27073	−	2.20097i
$963$		0			0
$964$	−1.07598e7	+	1.86365e7i	−0.372917	+	0.645911i
$965$	8.83782e6	−	3.21671e6i	0.305511	−	0.111197i
$966$		0			0
$967$	−2.24271e7	+	1.88186e7i	−0.771271	+	0.647173i	−0.941034	−	0.338312i	$-0.890144\pi$
$967$	−2.24271e7	+	1.88186e7i	−0.771271	+	0.647173i	0.169763	+	0.985485i	$0.445700\pi$
$968$	−1.22600e6	−	446227.i	−0.0420535	−	0.0153062i
$969$		0			0
$970$	2.61157e6	−	1.48109e7i	0.0891193	−	0.505420i
$971$	−2.51690e6			−0.0856677			−0.0428338	−	0.999082i	$-0.513639\pi$
$971$	−2.51690e6			−0.0856677			−0.0428338	+	0.999082i	$0.513639\pi$
$972$		0			0
$973$	−2.54740e7			−0.862610
$974$	−4.73767e6	+	2.68687e7i	−0.160017	+	0.907504i
$975$		0			0
$976$	8.26333e6	+	3.00761e6i	0.277671	+	0.101064i
$977$	2.23206e7	−	1.87292e7i	0.748118	−	0.627746i	−0.186886	−	0.982382i	$-0.559840\pi$
$977$	2.23206e7	−	1.87292e7i	0.748118	−	0.627746i	0.935005	+	0.354636i	$0.115395\pi$
$978$		0			0
$979$	1.78662e7	−	6.50275e6i	0.595764	−	0.216840i
$980$	−3.68818e6	+	6.38811e6i	−0.122672	+	0.212475i
$981$		0			0
$982$	2.79891e7	+	4.84786e7i	0.926213	+	1.60425i
$983$	3.82122e6	+	3.20638e6i	0.126130	+	0.105836i	0.703671	−	0.710526i	$-0.251543\pi$
$983$	3.82122e6	+	3.20638e6i	0.126130	+	0.105836i	−0.577541	+	0.816362i	$0.695988\pi$
$984$		0			0
$985$	−1.28440e6	−	7.28417e6i	−0.0421802	−	0.239216i
$986$	132676.	+	752443.i	0.00434610	+	0.0246480i
$987$		0			0
$988$	4.60678e7	+	3.86555e7i	1.50143	+	1.25985i
$989$	−791359.	−	1.37067e6i	−0.0257266	−	0.0445598i
$990$		0			0
$991$	−5.96337e6	+	1.03289e7i	−0.192889	+	0.334094i	−0.946207	−	0.323563i	$-0.895119\pi$
$991$	−5.96337e6	+	1.03289e7i	−0.192889	+	0.334094i	0.753317	+	0.657657i	$0.228452\pi$
$992$	4.52452e7	−	1.64679e7i	1.45980	−	0.531324i
$993$		0			0
$994$	2.37682e6	−	1.99438e6i	0.0763009	−	0.0640240i
$995$	1.14446e7	+	4.16549e6i	0.366473	+	0.133385i
$996$		0			0
$997$	−350452.	+	1.98751e6i	−0.0111658	+	0.0633245i	−0.989882	−	0.141896i	$-0.954680\pi$
$997$	−350452.	+	1.98751e6i	−0.0111658	+	0.0633245i	0.978716	+	0.205221i	$0.0657912\pi$
$998$	2.07504e7			0.659477
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.6.e.a.73.3		84
3.2	odd	2		27.6.e.a.25.12	yes	84
27.11	odd	18		729.6.a.c.1.35		42
27.13	even	9	inner	81.6.e.a.10.3		84
27.14	odd	18		27.6.e.a.13.12	✓	84
27.16	even	9		729.6.a.e.1.8		42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.6.e.a.13.12	✓	84	27.14	odd	18
27.6.e.a.25.12	yes	84	3.2	odd	2
81.6.e.a.10.3		84	27.13	even	9	inner
81.6.e.a.73.3		84	1.1	even	1	trivial
729.6.a.c.1.35		42	27.11	odd	18
729.6.a.e.1.8		42	27.16	even	9

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	81.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.40309 + 7.95730i) q^{2} +(-31.2798 - 11.3849i) q^{4} +(-15.2280 + 12.7778i) q^{5} +(-70.6933 + 25.7303i) q^{7} +(5.20070 - 9.00788i) q^{8} +(-80.3108 - 139.102i) q^{10} +(-144.573 - 121.311i) q^{11} +(-145.413 - 824.679i) q^{13} +(-105.555 - 598.630i) q^{14} +(-751.604 - 630.671i) q^{16} +(465.095 + 805.567i) q^{17} +(1078.70 - 1868.37i) q^{19} +(621.804 - 226.318i) q^{20} +(1168.16 - 980.203i) q^{22} +(-2223.04 - 809.122i) q^{23} +(-474.031 + 2688.36i) q^{25} +6766.25 q^{26} +2504.21 q^{28} +(17.6525 - 100.112i) q^{29} +(5477.24 + 1993.55i) q^{31} +(6327.98 - 5309.80i) q^{32} +(-7062.71 + 2570.62i) q^{34} +(747.743 - 1295.13i) q^{35} +(-5390.69 - 9336.95i) q^{37} +(13353.7 + 11205.0i) q^{38} +(35.9047 + 203.626i) q^{40} +(-2497.97 - 14166.7i) q^{41} +(512.502 + 430.040i) q^{43} +(3141.11 + 5440.55i) q^{44} +(9557.55 - 16554.2i) q^{46} +(-26728.7 + 9728.44i) q^{47} +(-8539.41 + 7165.41i) q^{49} +(-20727.0 - 7544.01i) q^{50} +(-4840.41 + 27451.3i) q^{52} -25335.8 q^{53} +3751.66 q^{55} +(-135.880 + 770.613i) q^{56} +(771.857 + 280.933i) q^{58} +(-11752.3 + 9861.37i) q^{59} +(-8422.09 + 3065.39i) q^{61} +(-23548.3 + 40786.9i) q^{62} +(17674.6 + 30613.3i) q^{64} +(12752.0 + 10700.2i) q^{65} +(-10635.1 - 60314.5i) q^{67} +(-5376.75 - 30493.1i) q^{68} +(9256.58 + 7767.19i) q^{70} +(2552.14 + 4420.44i) q^{71} +(-17695.8 + 30650.1i) q^{73} +(81860.5 - 29794.8i) q^{74} +(-55012.9 + 46161.3i) q^{76} +(13341.7 + 4856.00i) q^{77} +(-9551.12 + 54167.1i) q^{79} +19504.0 q^{80} +116233. q^{82} +(16596.8 - 94125.4i) q^{83} +(-17375.9 - 6324.30i) q^{85} +(-4141.04 + 3474.75i) q^{86} +(-1844.64 + 671.394i) q^{88} +(-50371.1 + 87245.3i) q^{89} +(31499.0 + 54557.8i) q^{91} +(60324.6 + 50618.4i) q^{92} +(-39909.5 - 226338. i) q^{94} +(7447.18 + 42235.0i) q^{95} +(71726.7 + 60185.8i) q^{97} +(-45035.8 - 78004.3i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 6 q^{2} - 6 q^{4} + 93 q^{5} - 6 q^{7} - 573 q^{8} - 3 q^{10} - 111 q^{11} - 6 q^{13} + 1641 q^{14} + 90 q^{16} - 3465 q^{17} - 3 q^{19} - 9987 q^{20} - 2850 q^{22} + 7716 q^{23} + 4953 q^{25} + 7806 q^{26}+ \cdots - 463410 q^{98}+O(q^{100}) \) 84 * q + 6 * q^2 - 6 * q^4 + 93 * q^5 - 6 * q^7 - 573 * q^8 - 3 * q^10 - 111 * q^11 - 6 * q^13 + 1641 * q^14 + 90 * q^16 - 3465 * q^17 - 3 * q^19 - 9987 * q^20 - 2850 * q^22 + 7716 * q^23 + 4953 * q^25 + 7806 * q^26 - 12 * q^28 + 20418 * q^29 - 6657 * q^31 - 51192 * q^32 - 11394 * q^34 - 35868 * q^35 - 3 * q^37 + 44076 * q^38 + 12441 * q^40 + 79077 * q^41 - 9465 * q^43 - 110757 * q^44 - 3 * q^46 - 103557 * q^47 + 5484 * q^49 + 105513 * q^50 + 68625 * q^52 + 206406 * q^53 - 12 * q^55 + 147237 * q^56 - 9753 * q^58 - 116484 * q^59 - 70116 * q^61 - 246066 * q^62 - 86019 * q^64 + 19815 * q^65 + 48117 * q^67 + 48105 * q^68 + 270111 * q^70 - 279531 * q^71 - 27012 * q^73 - 233691 * q^74 - 125670 * q^76 + 345135 * q^77 - 216186 * q^79 + 924114 * q^80 - 12 * q^82 + 370401 * q^83 - 43731 * q^85 - 116682 * q^86 + 371418 * q^88 - 154827 * q^89 - 91002 * q^91 - 1279059 * q^92 + 11667 * q^94 - 1087671 * q^95 - 420621 * q^97 - 463410 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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