LMFDB - Embedded newform 81.5.f.a.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,5,Mod(8,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("81.8");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	81.f (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.37296700979$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.3
Character	$\chi$	$=$	81.17
Dual form			81.5.f.a.62.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.62498 + 4.46460i) q^{2} +(-5.03539 - 4.22519i) q^{4} +(1.85566 + 0.327202i) q^{5} +(-15.2767 + 12.8186i) q^{7} +(-38.7874 + 22.3939i) q^{8} +(-4.47623 + 7.75306i) q^{10} +(-163.801 + 28.8826i) q^{11} +(19.7931 - 7.20410i) q^{13} +(-32.4058 - 89.0343i) q^{14} +(-55.2139 - 313.134i) q^{16} +(-273.361 - 157.825i) q^{17} +(138.878 + 240.543i) q^{19} +(-7.96145 - 9.48809i) q^{20} +(137.225 - 778.241i) q^{22} +(476.678 - 568.083i) q^{23} +(-583.971 - 212.548i) q^{25} +100.075i q^{26} +131.085 q^{28} +(-255.430 + 701.787i) q^{29} +(-395.273 - 331.673i) q^{31} +(782.021 + 137.891i) q^{32} +(1148.83 - 963.986i) q^{34} +(-32.5425 + 18.7884i) q^{35} +(-1056.20 + 1829.39i) q^{37} +(-1299.60 + 229.155i) q^{38} +(-79.3033 + 28.8640i) q^{40} +(-78.0433 - 214.422i) q^{41} +(447.021 + 2535.18i) q^{43} +(946.837 + 546.657i) q^{44} +(1761.67 + 3051.30i) q^{46} +(-153.262 - 182.650i) q^{47} +(-347.870 + 1972.87i) q^{49} +(1897.89 - 2261.81i) q^{50} +(-130.105 - 47.3542i) q^{52} +4752.36i q^{53} -313.409 q^{55} +(305.482 - 839.305i) q^{56} +(-2718.13 - 2280.78i) q^{58} +(-653.572 - 115.242i) q^{59} +(5458.87 - 4580.53i) q^{61} +(2123.10 - 1225.77i) q^{62} +(657.314 - 1138.50i) q^{64} +(39.0864 - 6.89198i) q^{65} +(-5444.09 + 1981.49i) q^{67} +(709.638 + 1949.72i) q^{68} +(-31.0018 - 175.820i) q^{70} +(6331.20 + 3655.32i) q^{71} +(-3172.37 - 5494.71i) q^{73} +(-6451.18 - 7688.22i) q^{74} +(317.039 - 1798.02i) q^{76} +(2132.10 - 2540.94i) q^{77} +(1366.51 + 497.371i) q^{79} -599.134i q^{80} +1084.13 q^{82} +(398.389 - 1094.57i) q^{83} +(-455.624 - 382.314i) q^{85} +(-12045.0 - 2123.85i) q^{86} +(5706.62 - 4788.43i) q^{88} +(-6289.55 + 3631.27i) q^{89} +(-210.026 + 363.775i) q^{91} +(-4800.52 + 846.461i) q^{92} +(1064.51 - 387.449i) q^{94} +(179.003 + 491.807i) q^{95} +(2242.60 + 12718.4i) q^{97} +(-8242.80 - 4758.98i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} - 1137 q^{14} - 54 q^{16} + 9 q^{17} - 3 q^{19} + 2487 q^{20} + 1002 q^{22} + 2724 q^{23} + 435 q^{25} - 12 q^{28}+ \cdots + 259938 q^{98}+O(q^{100}) $ 66 * q + 6 * q^2 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 492 * q^11 - 6 * q^13 - 1137 * q^14 - 54 * q^16 + 9 * q^17 - 3 * q^19 + 2487 * q^20 + 1002 * q^22 + 2724 * q^23 + 435 * q^25 - 12 * q^28 - 5016 * q^29 - 1671 * q^31 - 10224 * q^32 - 342 * q^34 + 2682 * q^35 - 3 * q^37 + 6564 * q^38 - 1113 * q^40 - 5754 * q^41 - 1266 * q^43 + 4545 * q^44 - 3 * q^46 + 9159 * q^47 + 5898 * q^49 + 34977 * q^50 + 2871 * q^52 - 12 * q^55 - 39243 * q^56 - 12291 * q^58 - 24762 * q^59 - 8358 * q^61 - 38304 * q^62 + 6141 * q^64 - 23727 * q^65 + 15996 * q^67 + 43533 * q^68 - 7251 * q^70 + 19773 * q^71 + 6108 * q^73 + 74847 * q^74 - 28614 * q^76 + 33909 * q^77 - 5658 * q^79 - 12 * q^82 - 18813 * q^83 + 24219 * q^85 - 96474 * q^86 + 36042 * q^88 - 110232 * q^89 - 6042 * q^91 - 73545 * q^92 + 2631 * q^94 + 65163 * q^95 - 3696 * q^97 + 259938 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−1.62498	+	4.46460i	−0.406246	+	1.11615i	0.552903	+	0.833246i	$0.313520\pi$
$2$	−1.62498	+	4.46460i	−0.406246	+	1.11615i	−0.959148	+	0.282904i	$0.908702\pi$
$3$		0			0
$3$		0			0
$4$	−5.03539	−	4.22519i	−0.314712	−	0.264075i
$5$	1.85566	+	0.327202i	0.0742262	+	0.0130881i	0.210638	−	0.977564i	$-0.432446\pi$
$5$	1.85566	+	0.327202i	0.0742262	+	0.0130881i	−0.136412	+	0.990652i	$0.543557\pi$
$6$		0			0
$7$	−15.2767	+	12.8186i	−0.311769	+	0.261605i	−0.785223	−	0.619214i	$-0.787451\pi$
$7$	−15.2767	+	12.8186i	−0.311769	+	0.261605i	0.473454	+	0.880819i	$0.343007\pi$
$8$	−38.7874	+	22.3939i	−0.606053	+	0.349905i
$9$		0			0
$10$	−4.47623	+	7.75306i	−0.0447623	+	0.0775306i
$11$	−163.801	+	28.8826i	−1.35373	+	0.238699i	−0.802997	−	0.595983i	$-0.796763\pi$
$11$	−163.801	+	28.8826i	−1.35373	+	0.238699i	−0.550732	+	0.834682i	$0.685651\pi$
$12$		0			0
$13$	19.7931	−	7.20410i	0.117119	−	0.0426278i	−0.282796	−	0.959180i	$-0.591262\pi$
$13$	19.7931	−	7.20410i	0.117119	−	0.0426278i	0.399915	+	0.916552i	$0.369040\pi$
$14$	−32.4058	−	89.0343i	−0.165336	−	0.454256i
$15$		0			0
$16$	−55.2139	−	313.134i	−0.215679	−	1.22318i
$17$	−273.361	−	157.825i	−0.945887	−	0.546108i	−0.0540859	−	0.998536i	$-0.517224\pi$
$17$	−273.361	−	157.825i	−0.945887	−	0.546108i	−0.891801	+	0.452428i	$0.850558\pi$
$18$		0			0
$19$	138.878	+	240.543i	0.384703	+	0.666325i	0.991728	−	0.128358i	$-0.0409705\pi$
$19$	138.878	+	240.543i	0.384703	+	0.666325i	−0.607025	+	0.794683i	$0.707637\pi$
$20$	−7.96145	−	9.48809i	−0.0199036	−	0.0237202i
$21$		0			0
$22$	137.225	−	778.241i	0.283522	−	1.60794i
$23$	476.678	−	568.083i	0.901093	−	1.07388i	−0.0958224	−	0.995398i	$-0.530548\pi$
$23$	476.678	−	568.083i	0.901093	−	1.07388i	0.996915	−	0.0784825i	$-0.0250075\pi$
$24$		0			0
$25$	−583.971	−	212.548i	−0.934354	−	0.340077i
$26$			100.075i			0.148040i
$27$		0			0
$28$	131.085			0.167200
$29$	−255.430	+	701.787i	−0.303721	+	0.834467i	0.690124	+	0.723691i	$0.257556\pi$
$29$	−255.430	+	701.787i	−0.303721	+	0.834467i	−0.993845	+	0.110776i	$0.964666\pi$
$30$		0			0
$31$	−395.273	−	331.673i	−0.411314	−	0.345134i	0.413533	−	0.910489i	$-0.364295\pi$
$31$	−395.273	−	331.673i	−0.411314	−	0.345134i	−0.824847	+	0.565355i	$0.808739\pi$
$32$	782.021	+	137.891i	0.763693	+	0.134660i
$33$		0			0
$34$	1148.83	−	963.986i	0.993801	−	0.833898i
$35$	−32.5425	+	18.7884i	−0.0265653	+	0.0153375i
$36$		0			0
$37$	−1056.20	+	1829.39i	−0.771510	+	1.33629i	0.165226	+	0.986256i	$0.447165\pi$
$37$	−1056.20	+	1829.39i	−0.771510	+	1.33629i	−0.936735	+	0.350038i	$0.886169\pi$
$38$	−1299.60	+	229.155i	−0.900003	+	0.158695i
$39$		0			0
$40$	−79.3033	+	28.8640i	−0.0495646	+	0.0180400i
$41$	−78.0433	−	214.422i	−0.0464267	−	0.127556i	0.914312	−	0.405010i	$-0.132732\pi$
$41$	−78.0433	−	214.422i	−0.0464267	−	0.127556i	−0.960739	+	0.277453i	$0.910510\pi$
$42$		0			0
$43$	447.021	+	2535.18i	0.241764	+	1.37111i	0.827890	+	0.560890i	$0.189541\pi$
$43$	447.021	+	2535.18i	0.241764	+	1.37111i	−0.586127	+	0.810219i	$0.699348\pi$
$44$	946.837	+	546.657i	0.489069	+	0.282364i
$45$		0			0
$46$	1761.67	+	3051.30i	0.832548	+	1.44201i
$47$	−153.262	−	182.650i	−0.0693806	−	0.0826846i	0.730238	−	0.683193i	$-0.239409\pi$
$47$	−153.262	−	182.650i	−0.0693806	−	0.0826846i	−0.799618	+	0.600509i	$0.794965\pi$
$48$		0			0
$49$	−347.870	+	1972.87i	−0.144886	+	0.821687i
$50$	1897.89	−	2261.81i	0.759155	−	0.904725i
$51$		0			0
$52$	−130.105	−	47.3542i	−0.0481156	−	0.0175127i
$53$			4752.36i			1.69183i	0.533314	+	0.845917i	$0.320946\pi$
$53$			4752.36i			1.69183i	−0.533314	+	0.845917i	$0.679054\pi$
$54$		0			0
$55$	−313.409			−0.103606
$56$	305.482	−	839.305i	0.0974114	−	0.267636i
$57$		0			0
$58$	−2718.13	−	2280.78i	−0.808006	−	0.677997i
$59$	−653.572	−	115.242i	−0.187754	−	0.0331061i	0.0789804	−	0.996876i	$-0.474834\pi$
$59$	−653.572	−	115.242i	−0.187754	−	0.0331061i	−0.266734	+	0.963770i	$0.585945\pi$
$60$		0			0
$61$	5458.87	−	4580.53i	1.46704	−	1.23100i	0.548215	−	0.836337i	$-0.315308\pi$
$61$	5458.87	−	4580.53i	1.46704	−	1.23100i	0.918828	−	0.394658i	$-0.129137\pi$
$62$	2123.10	−	1225.77i	0.552315	−	0.318879i
$63$		0			0
$64$	657.314	−	1138.50i	0.160477	−	0.277954i
$65$	39.0864	−	6.89198i	0.00925121	−	0.00163124i
$66$		0			0
$67$	−5444.09	+	1981.49i	−1.21276	+	0.441410i	−0.867661	−	0.497155i	$-0.834378\pi$
$67$	−5444.09	+	1981.49i	−1.21276	+	0.441410i	−0.345102	+	0.938565i	$0.612156\pi$
$68$	709.638	+	1949.72i	0.153468	+	0.421651i
$69$		0			0
$70$	−31.0018	−	175.820i	−0.00632691	−	0.0358817i
$71$	6331.20	+	3655.32i	1.25594	+	0.725118i	0.972283	−	0.233807i	$-0.0751184\pi$
$71$	6331.20	+	3655.32i	1.25594	+	0.725118i	0.283659	+	0.958925i	$0.408452\pi$
$72$		0			0
$73$	−3172.37	−	5494.71i	−0.595303	−	1.03110i	−0.993504	−	0.113797i	$-0.963698\pi$
$73$	−3172.37	−	5494.71i	−0.595303	−	1.03110i	0.398200	−	0.917298i	$-0.369635\pi$
$74$	−6451.18	−	7688.22i	−1.17808	−	1.40398i
$75$		0			0
$76$	317.039	−	1798.02i	0.0548890	−	0.311291i
$77$	2132.10	−	2540.94i	0.359605	−	0.428561i
$78$		0			0
$79$	1366.51	+	497.371i	0.218958	+	0.0796941i	0.449170	−	0.893446i	$-0.351720\pi$
$79$	1366.51	+	497.371i	0.218958	+	0.0796941i	−0.230212	+	0.973140i	$0.573942\pi$
$80$		−	599.134i		−	0.0936148i
$81$		0			0
$82$	1084.13			0.161233
$83$	398.389	−	1094.57i	0.0578298	−	0.158886i	−0.907414	−	0.420239i	$-0.861946\pi$
$83$	398.389	−	1094.57i	0.0578298	−	0.158886i	0.965243	+	0.261353i	$0.0841686\pi$
$84$		0			0
$85$	−455.624	−	382.314i	−0.0630621	−	0.0529154i
$86$	−12045.0	−	2123.85i	−1.62858	−	0.287162i
$87$		0			0
$88$	5706.62	−	4788.43i	0.736909	−	0.618340i
$89$	−6289.55	+	3631.27i	−0.794035	+	0.458436i	−0.841381	−	0.540442i	$-0.818257\pi$
$89$	−6289.55	+	3631.27i	−0.794035	+	0.458436i	0.0473463	+	0.998879i	$0.484924\pi$
$90$		0			0
$91$	−210.026	+	363.775i	−0.0253624	+	0.0439289i
$92$	−4800.52	+	846.461i	−0.567169	+	0.100007i
$93$		0			0
$94$	1064.51	−	387.449i	0.120474	−	0.0438490i
$95$	179.003	+	491.807i	0.0198341	+	0.0544938i
$96$		0			0
$97$	2242.60	+	12718.4i	0.238346	+	1.35173i	0.835451	+	0.549566i	$0.185207\pi$
$97$	2242.60	+	12718.4i	0.238346	+	1.35173i	−0.597104	+	0.802164i	$0.703682\pi$
$98$	−8242.80	−	4758.98i	−0.858268	−	0.495521i
$99$		0			0
$100$	2042.47	+	3537.66i	0.204247	+	0.353766i
$101$	7137.94	+	8506.66i	0.699729	+	0.833905i	0.992496	−	0.122279i	$-0.0390203\pi$
$101$	7137.94	+	8506.66i	0.699729	+	0.833905i	−0.292767	+	0.956184i	$0.594576\pi$
$102$		0			0
$103$	384.623	−	2181.30i	0.0362544	−	0.205609i	−0.961300	−	0.275504i	$-0.911155\pi$
$103$	384.623	−	2181.30i	0.0362544	−	0.205609i	0.997554	+	0.0698950i	$0.0222664\pi$
$104$	−606.394	+	722.673i	−0.0560646	+	0.0668152i
$105$		0			0
$106$	−21217.4	−	7722.50i	−1.88834	−	0.687300i
$107$		−	5073.79i		−	0.443164i	−0.975142	−	0.221582i	$-0.928878\pi$
$107$		−	5073.79i		−	0.443164i	0.975142	−	0.221582i	$-0.0711221\pi$
$108$		0			0
$109$	−5369.02			−0.451900			−0.225950	−	0.974139i	$-0.572549\pi$
$109$	−5369.02			−0.451900			−0.225950	+	0.974139i	$0.572549\pi$
$110$	509.284	−	1399.25i	0.0420896	−	0.115640i
$111$		0			0
$112$	4857.43	+	4075.87i	0.387232	+	0.324926i
$113$	−5225.02	−	921.312i	−0.409196	−	0.0721522i	−0.0347384	−	0.999396i	$-0.511060\pi$
$113$	−5225.02	−	921.312i	−0.409196	−	0.0721522i	−0.374457	+	0.927244i	$0.622171\pi$
$114$		0			0
$115$	1070.43	−	898.196i	0.0809398	−	0.0679165i
$116$	4251.37	−	2454.53i	0.315946	−	0.182412i
$117$		0			0
$118$	1576.55	−	2730.67i	0.113226	−	0.196112i
$119$	6199.15	−	1093.08i	0.437762	−	0.0771893i
$120$		0			0
$121$	12238.6	−	4454.48i	0.835913	−	0.304247i
$122$	11579.7	+	31815.0i	0.777996	+	2.13753i
$123$		0			0
$124$	588.969	+	3340.21i	0.0383044	+	0.217235i
$125$	−2034.00	−	1174.33i	−0.130176	−	0.0751572i
$126$		0			0
$127$	−2667.49	−	4620.24i	−0.165385	−	0.286455i	0.771407	−	0.636342i	$-0.219553\pi$
$127$	−2667.49	−	4620.24i	−0.165385	−	0.286455i	−0.936792	+	0.349887i	$0.886220\pi$
$128$	12181.7	+	14517.6i	0.743511	+	0.886082i
$129$		0			0
$130$	−32.7447	+	185.704i	−0.00193756	+	0.0109884i
$131$	20646.0	−	24605.0i	1.20308	−	1.43377i	0.331544	−	0.943440i	$-0.392430\pi$
$131$	20646.0	−	24605.0i	1.20308	−	1.43377i	0.871535	−	0.490334i	$-0.163125\pi$
$132$		0			0
$133$	−5205.03	−	1894.48i	−0.294252	−	0.107099i
$134$		−	27525.6i		−	1.53295i
$135$		0			0
$136$	14137.3			0.764343
$137$	−3593.24	+	9872.36i	−0.191446	+	0.525993i	−0.997862	−	0.0653555i	$-0.979182\pi$
$137$	−3593.24	+	9872.36i	−0.191446	+	0.525993i	0.806416	+	0.591348i	$0.201404\pi$
$138$		0			0
$139$	15211.8	+	12764.3i	0.787322	+	0.660641i	0.945081	−	0.326836i	$-0.105983\pi$
$139$	15211.8	+	12764.3i	0.787322	+	0.660641i	−0.157759	+	0.987478i	$0.550427\pi$
$140$	243.249	+	42.8913i	0.0124107	+	0.00218833i
$141$		0			0
$142$	−26607.6	+	22326.5i	−1.31956	+	1.10724i
$143$	−3034.06	+	1751.72i	−0.148372	+	0.0856627i
$144$		0			0
$145$	−703.616	+	1218.70i	−0.0334657	+	0.0579642i
$146$	29686.7	−	5234.57i	1.39270	−	0.245570i
$147$		0			0
$148$	13047.9	−	4749.04i	0.595684	−	0.216811i
$149$	840.965	+	2310.53i	0.0378796	+	0.104073i	0.957191	−	0.289459i	$-0.0934753\pi$
$149$	840.965	+	2310.53i	0.0378796	+	0.104073i	−0.919311	+	0.393532i	$0.871253\pi$
$150$		0			0
$151$	−491.537	−	2787.65i	−0.0215577	−	0.122260i	0.972130	−	0.234443i	$-0.0753267\pi$
$151$	−491.537	−	2787.65i	−0.0215577	−	0.122260i	−0.993688	+	0.112183i	$0.964216\pi$
$152$	−10773.4	−	6220.03i	−0.466301	−	0.269219i
$153$		0			0
$154$	7879.65	+	13648.0i	0.332250	+	0.575475i
$155$	−624.966	−	744.806i	−0.0260132	−	0.0310013i
$156$		0			0
$157$	−1222.97	+	6935.82i	−0.0496155	+	0.281383i	−0.999514	−	0.0311753i	$-0.990075\pi$
$157$	−1222.97	+	6935.82i	−0.0496155	+	0.281383i	0.949898	+	0.312559i	$0.101186\pi$
$158$	−4441.12	+	5292.73i	−0.177901	+	0.212014i
$159$		0			0
$160$	1406.04	+	511.758i	0.0549236	+	0.0199905i
$161$			14788.8i			0.570533i
$162$		0			0
$163$	−13689.6			−0.515246			−0.257623	−	0.966246i	$-0.582939\pi$
$163$	−13689.6			−0.515246			−0.257623	+	0.966246i	$0.582939\pi$
$164$	−512.997	+	1409.45i	−0.0190734	+	0.0524036i
$165$		0			0
$166$	4239.42	+	3557.30i	0.153848	+	0.129093i
$167$	−40997.2	−	7228.91i	−1.47001	−	0.259203i	−0.619434	−	0.785049i	$-0.712638\pi$
$167$	−40997.2	−	7228.91i	−1.47001	−	0.259203i	−0.850580	+	0.525846i	$0.823749\pi$
$168$		0			0
$169$	−21539.1	+	18073.5i	−0.754145	+	0.632803i
$170$	2447.26	−	1412.93i	0.0846802	−	0.0488901i
$171$		0			0
$172$	8460.70	−	14654.4i	0.285989	−	0.495348i
$173$	−21652.5	+	3817.93i	−0.723463	+	0.127566i	−0.523241	−	0.852184i	$-0.675277\pi$
$173$	−21652.5	+	3817.93i	−0.723463	+	0.127566i	−0.200222	+	0.979751i	$0.564166\pi$
$174$		0			0
$175$	11645.7	−	4238.69i	0.380268	−	0.138406i
$176$	18088.2	+	49697.0i	0.583943	+	1.60437i
$177$		0			0
$178$	−5991.78	−	33981.1i	−0.189111	−	1.07250i
$179$	−13909.9	−	8030.88i	−0.434128	−	0.250644i	0.266976	−	0.963703i	$-0.413976\pi$
$179$	−13909.9	−	8030.88i	−0.434128	−	0.250644i	−0.701104	+	0.713059i	$0.747309\pi$
$180$		0			0
$181$	−25231.5	−	43702.2i	−0.770168	−	1.33397i	−0.937470	−	0.348065i	$-0.886839\pi$
$181$	−25231.5	−	43702.2i	−0.770168	−	1.33397i	0.167302	−	0.985906i	$-0.446494\pi$
$182$	−1282.82	−	1528.81i	−0.0387279	−	0.0461541i
$183$		0			0
$184$	−5767.50	+	32709.1i	−0.170354	+	0.966125i
$185$	−2558.52	+	3049.12i	−0.0747558	+	0.0890905i
$186$		0			0
$187$	49335.3	+	17956.6i	1.41083	+	0.513500i
$188$			1567.28i			0.0443435i
$189$		0			0
$190$	−2486.60			−0.0688808
$191$	7238.53	−	19887.7i	0.198419	−	0.545152i	−0.800082	−	0.599891i	$-0.795211\pi$
$191$	7238.53	−	19887.7i	0.198419	−	0.545152i	0.998501	+	0.0547393i	$0.0174328\pi$
$192$		0			0
$193$	−24191.9	−	20299.4i	−0.649463	−	0.544964i	0.257445	−	0.966293i	$-0.417119\pi$
$193$	−24191.9	−	20299.4i	−0.649463	−	0.544964i	−0.906908	+	0.421329i	$0.861564\pi$
$194$	−60426.9	−	10654.9i	−1.60556	−	0.283104i
$195$		0			0
$196$	10087.4	−	8464.35i	0.262584	−	0.220334i
$197$	16697.9	−	9640.53i	0.430258	−	0.248410i	−0.269199	−	0.963085i	$-0.586759\pi$
$197$	16697.9	−	9640.53i	0.430258	−	0.248410i	0.699457	+	0.714675i	$0.253425\pi$
$198$		0			0
$199$	7059.56	−	12227.5i	0.178267	−	0.308768i	−0.763020	−	0.646375i	$-0.776284\pi$
$199$	7059.56	−	12227.5i	0.178267	−	0.308768i	0.941287	+	0.337607i	$0.109618\pi$
$200$	27410.5	−	4833.21i	0.685262	−	0.120830i
$201$		0			0
$202$	−49577.9	+	18044.9i	−1.21502	+	0.442233i
$203$	−5093.84	−	13995.2i	−0.123610	−	0.339616i
$204$		0			0
$205$	−74.6621	−	423.430i	−0.00177661	−	0.0100757i
$206$	9113.65	+	5261.77i	0.214762	+	0.123993i
$207$		0			0
$208$	−3348.70	−	5800.12i	−0.0774016	−	0.134063i
$209$	−29695.9	−	35390.2i	−0.679835	−	0.810196i
$210$		0			0
$211$	12177.4	−	69061.2i	0.273519	−	1.55121i	−0.470106	−	0.882610i	$-0.655784\pi$
$211$	12177.4	−	69061.2i	0.273519	−	1.55121i	0.743626	−	0.668596i	$-0.233104\pi$
$212$	20079.6	−	23930.0i	0.446770	−	0.532440i
$213$		0			0
$214$	22652.4	+	8244.82i	0.494638	+	0.180034i
$215$			4850.69i			0.104936i
$216$		0			0
$217$	10290.1			0.218523
$218$	8724.56	−	23970.5i	0.183582	−	0.504388i
$219$		0			0
$220$	1578.14	+	1324.21i	0.0326061	+	0.0273598i
$221$	−6547.66	−	1154.53i	−0.134061	−	0.0236385i
$222$		0			0
$223$	13450.4	−	11286.3i	0.270475	−	0.226955i	−0.497454	−	0.867490i	$-0.665732\pi$
$223$	13450.4	−	11286.3i	0.270475	−	0.226955i	0.767929	+	0.640535i	$0.221287\pi$
$224$	−13714.3	+	7917.93i	−0.273323	+	0.157803i
$225$		0			0
$226$	12603.9	−	21830.5i	0.246767	−	0.427412i
$227$	−61635.7	+	10868.0i	−1.19614	+	0.210911i	−0.736027	−	0.676952i	$-0.763301\pi$
$227$	−61635.7	+	10868.0i	−1.19614	+	0.210911i	−0.460108	+	0.887863i	$0.652189\pi$
$228$		0			0
$229$	−6917.96	+	2517.93i	−0.131919	+	0.0480146i	−0.407136	−	0.913368i	$-0.633473\pi$
$229$	−6917.96	+	2517.93i	−0.131919	+	0.0480146i	0.275217	+	0.961382i	$0.411250\pi$
$230$	2270.66	+	6238.59i	0.0429236	+	0.117932i
$231$		0			0
$232$	−5808.30	−	32940.5i	−0.107913	−	0.612005i
$233$	59079.9	+	34109.8i	1.08825	+	0.628300i	0.933109	−	0.359593i	$-0.117084\pi$
$233$	59079.9	+	34109.8i	1.08825	+	0.628300i	0.155138	+	0.987893i	$0.450418\pi$
$234$		0			0
$235$	−224.638	−	389.084i	−0.00406768	−	0.00704543i
$236$	2804.07	+	3341.76i	0.0503459	+	0.0599999i
$237$		0			0
$238$	−5193.35	+	29453.0i	−0.0916841	+	0.519966i
$239$	34019.0	−	40542.2i	0.595560	−	0.709761i	−0.381104	−	0.924532i	$-0.624456\pi$
$239$	34019.0	−	40542.2i	0.595560	−	0.709761i	0.976664	+	0.214771i	$0.0689006\pi$
$240$		0			0
$241$	42191.0	+	15356.3i	0.726416	+	0.264394i	0.678647	−	0.734465i	$-0.262567\pi$
$241$	42191.0	+	15356.3i	0.726416	+	0.264394i	0.0477690	+	0.998858i	$0.484789\pi$
$242$			61878.9i			1.05660i
$243$		0			0
$244$	−46841.2			−0.786770
$245$	−1291.06	+	3547.15i	−0.0215086	+	0.0590945i
$246$		0			0
$247$	4481.72	+	3760.61i	0.0734600	+	0.0616403i
$248$	22759.1	+	4013.04i	0.370042	+	0.0652484i
$249$		0			0
$250$	8548.14	−	7172.74i	0.136770	−	0.114764i
$251$	40082.7	−	23141.8i	0.636223	−	0.367324i	−0.146935	−	0.989146i	$-0.546941\pi$
$251$	40082.7	−	23141.8i	0.636223	−	0.367324i	0.783158	+	0.621823i	$0.213607\pi$
$252$		0			0
$253$	−61672.8	+	106820.i	−0.963502	+	1.66883i
$254$	24962.1	−	4401.50i	0.386914	−	0.0682234i
$255$		0			0
$256$	−64844.6	+	23601.5i	−0.989450	+	0.360130i
$257$	4989.20	+	13707.7i	0.0755379	+	0.207539i	0.971714	−	0.236159i	$-0.0758886\pi$
$257$	4989.20	+	13707.7i	0.0755379	+	0.207539i	−0.896177	+	0.443698i	$0.853666\pi$
$258$		0			0
$259$	−7315.09	−	41485.9i	−0.109049	−	0.618445i
$260$	−225.935	−	130.444i	−0.00334223	−	0.00192964i
$261$		0			0
$262$	76302.0	+	132159.i	1.11156	+	1.92528i
$263$	−970.286	−	1156.34i	−0.0140278	−	0.0167176i	0.758985	−	0.651108i	$-0.225696\pi$
$263$	−970.286	−	1156.34i	−0.0140278	−	0.0167176i	−0.773013	+	0.634391i	$0.781251\pi$
$264$		0			0
$265$	−1554.98	+	8818.75i	−0.0221429	+	0.125578i
$266$	16916.2	−	20159.9i	0.239077	−	0.284921i
$267$		0			0
$268$	35785.3	+	13024.8i	0.498236	+	0.181343i
$269$			60267.0i			0.832866i	0.909166	+	0.416433i	$0.136720\pi$
$269$			60267.0i			0.832866i	−0.909166	+	0.416433i	$0.863280\pi$
$270$		0			0
$271$	93699.0			1.27584			0.637920	−	0.770103i	$-0.279795\pi$
$271$	93699.0			1.27584			0.637920	+	0.770103i	$0.279795\pi$
$272$	−34327.0	+	94312.8i	−0.463979	+	1.27477i
$273$		0			0
$274$	−38237.2	−	32084.8i	−0.509313	−	0.427364i
$275$	101794.	+	17949.1i	1.34604	+	0.237343i
$276$		0			0
$277$	−92990.1	+	78028.0i	−1.21193	+	1.01693i	−0.212722	+	0.977113i	$0.568233\pi$
$277$	−92990.1	+	78028.0i	−1.21193	+	1.01693i	−0.999207	+	0.0398165i	$0.987323\pi$
$278$	−81706.3	+	47173.1i	−1.05722	+	0.610387i
$279$		0			0
$280$	841.492	−	1457.51i	0.0107333	−	0.0185907i
$281$	−83488.0	+	14721.2i	−1.05733	+	0.186436i	−0.675173	−	0.737660i	$-0.735931\pi$
$281$	−83488.0	+	14721.2i	−1.05733	+	0.186436i	−0.382160	+	0.924096i	$0.624820\pi$
$282$		0			0
$283$	99524.9	−	36224.1i	1.24268	−	0.452298i	0.364758	−	0.931102i	$-0.381152\pi$
$283$	99524.9	−	36224.1i	1.24268	−	0.452298i	0.877922	+	0.478804i	$0.158930\pi$
$284$	−16435.6	−	45156.5i	−0.203774	−	0.559866i
$285$		0			0
$286$	−2890.42	−	16392.4i	−0.0353369	−	0.200406i
$287$	3940.84	+	2275.25i	0.0478438	+	0.0276226i
$288$		0			0
$289$	8057.09	+	13955.3i	0.0964678	+	0.167087i
$290$	−4297.64	−	5121.72i	−0.0511015	−	0.0609004i
$291$		0			0
$292$	−7242.08	+	41071.9i	−0.0849372	+	0.481703i
$293$	51586.3	−	61478.2i	0.600896	−	0.716120i	−0.376765	−	0.926309i	$-0.622964\pi$
$293$	51586.3	−	61478.2i	0.600896	−	0.716120i	0.977661	+	0.210189i	$0.0674080\pi$
$294$		0			0
$295$	−1175.10	−	427.700i	−0.0135030	−	0.00491468i
$296$		−	94609.5i		−	1.07982i
$297$		0			0
$298$	−11682.2			−0.131550
$299$	5342.41	−	14678.2i	0.0597579	−	0.164183i
$300$		0			0
$301$	−39326.6	−	32998.9i	−0.434063	−	0.364222i
$302$	13244.5	+	2335.36i	0.145218	+	0.0256059i
$303$		0			0
$304$	67654.3	−	56768.7i	0.732062	−	0.614273i
$305$	11628.5	−	6713.74i	0.125004	−	0.0721713i
$306$		0			0
$307$	−72803.7	+	126100.i	−0.772461	+	1.33794i	0.163749	+	0.986502i	$0.447641\pi$
$307$	−72803.7	+	126100.i	−0.772461	+	1.33794i	−0.936210	+	0.351440i	$0.885692\pi$
$308$	−21471.9	+	3786.08i	−0.226344	+	0.0399106i
$309$		0			0
$310$	4340.82	−	1579.93i	0.0451698	−	0.0164405i
$311$	3893.50	+	10697.3i	0.0402549	+	0.110599i	0.958192	−	0.286128i	$-0.0923681\pi$
$311$	3893.50	+	10697.3i	0.0402549	+	0.110599i	−0.917937	+	0.396727i	$0.870146\pi$
$312$		0			0
$313$	−1865.86	−	10581.8i	−0.0190454	−	0.108012i	0.973803	−	0.227393i	$-0.0730201\pi$
$313$	−1865.86	−	10581.8i	−0.0190454	−	0.108012i	−0.992849	+	0.119381i	$0.961909\pi$
$314$	−28978.4	−	16730.7i	−0.293910	−	0.169689i
$315$		0			0
$316$	−4779.45	−	8278.24i	−0.0478634	−	0.0829018i
$317$	68121.3	+	81183.8i	0.677898	+	0.807887i	0.989836	−	0.142215i	$-0.0454226\pi$
$317$	68121.3	+	81183.8i	0.677898	+	0.807887i	−0.311938	+	0.950102i	$0.600978\pi$
$318$		0			0
$319$	21570.3	−	122331.i	0.211970	−	1.20214i
$320$	1592.27	−	1897.59i	0.0155495	−	0.0185312i
$321$		0			0
$322$	−66026.0	−	24031.5i	−0.636800	−	0.231776i
$323$		−	87673.7i		−	0.840358i
$324$		0			0
$325$	−13089.8			−0.123927
$326$	22245.3	−	61118.4i	0.209316	−	0.575091i
$327$		0			0
$328$	7828.85	+	6569.18i	0.0727696	+	0.0610610i
$329$	4682.66	+	825.679i	0.0432614	+	0.00762815i
$330$		0			0
$331$	72098.0	−	60497.4i	0.658063	−	0.552180i	−0.251443	−	0.967872i	$-0.580905\pi$
$331$	72098.0	−	60497.4i	0.658063	−	0.552180i	0.909505	+	0.415692i	$0.136461\pi$
$332$	−6630.79	+	3828.29i	−0.0601574	+	0.0347319i
$333$		0			0
$334$	98893.9	−	171289.i	0.886496	−	1.53546i
$335$	−10750.7	+	1895.64i	−0.0957961	+	0.0168914i
$336$		0			0
$337$	30936.9	−	11260.1i	0.272406	−	0.0991477i	−0.202205	−	0.979343i	$-0.564811\pi$
$337$	30936.9	−	11260.1i	0.272406	−	0.0991477i	0.474611	+	0.880195i	$0.342589\pi$
$338$	−45690.2	−	125533.i	−0.399935	−	1.09881i
$339$		0			0
$340$	678.893	+	3850.19i	0.00587278	+	0.0333062i
$341$	74325.8	+	42912.0i	0.639191	+	0.369037i
$342$		0			0
$343$	−43915.9	−	76064.6i	−0.373279	−	0.646538i
$344$	−74111.3	−	88322.4i	−0.626279	−	0.746370i
$345$		0			0
$346$	18139.5	−	102874.i	0.151521	−	0.859317i
$347$	−99295.2	+	118335.i	−0.824649	+	0.982778i	−0.999999	−	0.00172777i	$-0.999450\pi$
$347$	−99295.2	+	118335.i	−0.824649	+	0.982778i	0.175349	+	0.984506i	$0.443894\pi$
$348$		0			0
$349$	−207919.	−	75676.2i	−1.70704	−	0.621310i	−0.710441	−	0.703757i	$-0.751504\pi$
$349$	−207919.	−	75676.2i	−1.70704	−	0.621310i	−0.996595	+	0.0824466i	$0.973727\pi$
$350$			58881.3i			0.480663i
$351$		0			0
$352$	−132079.			−1.06598
$353$	−45001.8	+	123641.i	−0.361144	+	0.992235i	0.617481	+	0.786585i	$0.288153\pi$
$353$	−45001.8	+	123641.i	−0.361144	+	0.992235i	−0.978626	+	0.205650i	$0.934069\pi$
$354$		0			0
$355$	10552.5	+	8854.60i	0.0837334	+	0.0702607i
$356$	47013.1	+	8289.69i	0.370953	+	0.0654091i
$357$		0			0
$358$	58458.0	−	49052.1i	0.456119	−	0.382729i
$359$	−63982.9	+	36940.5i	−0.496449	+	0.286625i	−0.727246	−	0.686377i	$-0.759200\pi$
$359$	−63982.9	+	36940.5i	−0.496449	+	0.286625i	0.230797	+	0.973002i	$0.425867\pi$
$360$		0			0
$361$	26586.4	−	46049.0i	0.204007	−	0.353351i
$362$	236114.	−	41633.2i	1.80179	−	0.317704i
$363$		0			0
$364$	2594.58	−	944.351i	0.0195823	−	0.00712739i
$365$	−4088.95	−	11234.3i	−0.0306921	−	0.0843257i
$366$		0			0
$367$	45822.8	+	259874.i	0.340212	+	1.92944i	0.368007	+	0.929823i	$0.380040\pi$
$367$	45822.8	+	259874.i	0.340212	+	1.92944i	−0.0277952	+	0.999614i	$0.508849\pi$
$368$	−204205.	−	117898.i	−1.50790	−	0.870584i
$369$		0			0
$370$	−9455.57	−	16377.5i	−0.0690692	−	0.119631i
$371$	−60918.8	−	72600.2i	−0.442592	−	0.527461i
$372$		0			0
$373$	−23994.2	+	136078.i	−0.172460	+	0.978072i	0.768574	+	0.639761i	$0.220967\pi$
$373$	−23994.2	+	136078.i	−0.172460	+	0.978072i	−0.941034	+	0.338311i	$0.890144\pi$
$374$	−160338.	+	191083.i	−1.14629	+	1.36609i
$375$		0			0
$376$	10034.9	+	3652.40i	0.0709800	+	0.0258346i
$377$			15730.7i			0.110679i
$378$		0			0
$379$	101556.			0.707014			0.353507	−	0.935432i	$-0.384989\pi$
$379$	101556.			0.707014			0.353507	+	0.935432i	$0.384989\pi$
$380$	1176.63	−	3232.76i	0.00814840	−	0.0223875i
$381$		0			0
$382$	77028.1	+	64634.3i	0.527865	+	0.442931i
$383$	−54179.8	−	9553.36i	−0.369352	−	0.0651267i	−0.0141082	−	0.999900i	$-0.504491\pi$
$383$	−54179.8	−	9553.36i	−0.369352	−	0.0651267i	−0.355243	+	0.934774i	$0.615602\pi$
$384$		0			0
$385$	4787.84	−	4017.48i	0.0323012	−	0.0271039i
$386$	129940.	−	75020.9i	0.872104	−	0.503509i
$387$		0			0
$388$	42445.4	−	73517.6i	0.281947	−	0.488346i
$389$	−109721.	+	19346.8i	−0.725089	+	0.127853i	−0.523997	−	0.851720i	$-0.675560\pi$
$389$	−109721.	+	19346.8i	−0.725089	+	0.127853i	−0.201091	+	0.979573i	$0.564449\pi$
$390$		0			0
$391$	−219963.	+	80060.0i	−1.43879	+	0.523676i
$392$	−30687.3	−	84312.7i	−0.199704	−	0.548682i
$393$		0			0
$394$	15907.3	+	90215.1i	0.102472	+	0.581148i
$395$	2373.04	+	1370.08i	0.0152094	+	0.00878113i
$396$		0			0
$397$	−58336.7	−	101042.i	−0.370136	−	0.641094i	0.619450	−	0.785036i	$-0.287356\pi$
$397$	−58336.7	−	101042.i	−0.370136	−	0.641094i	−0.989586	+	0.143942i	$0.954022\pi$
$398$	43119.3	+	51387.6i	0.272211	+	0.324409i
$399$		0			0
$400$	−34312.7	+	194597.i	−0.214454	+	1.21623i
$401$	−172322.	+	205365.i	−1.07165	+	1.27714i	−0.112676	+	0.993632i	$0.535942\pi$
$401$	−172322.	+	205365.i	−1.07165	+	1.27714i	−0.958970	+	0.283507i	$0.908502\pi$
$402$		0			0
$403$	−10213.1	−	3717.26i	−0.0628850	−	0.0228883i
$404$		−	72993.5i		−	0.447220i
$405$		0			0
$406$	70760.5			0.429278
$407$	120169.	−	330161.i	0.725443	−	1.99314i
$408$		0			0
$409$	134207.	+	112613.i	0.802284	+	0.673196i	0.948753	−	0.316019i	$-0.102346\pi$
$409$	134207.	+	112613.i	0.802284	+	0.673196i	−0.146469	+	0.989215i	$0.546791\pi$
$410$	2011.77	+	354.729i	0.0119677	+	0.00211023i
$411$		0			0
$412$	−11153.2	+	9358.61i	−0.0657057	+	0.0551337i
$413$	11461.6	−	6617.38i	0.0671965	−	0.0387959i
$414$		0			0
$415$	1097.42	−	1900.78i	0.00637200	−	0.0110366i
$416$	16472.0	−	2904.46i	0.0951831	−	0.0167834i
$417$		0			0
$418$	206258.	−	75071.9i	1.18048	−	0.429660i
$419$	14885.3	+	40897.0i	0.0847870	+	0.232950i	0.974840	−	0.222907i	$-0.0715548\pi$
$419$	14885.3	+	40897.0i	0.0847870	+	0.232950i	−0.890053	+	0.455858i	$0.849333\pi$
$420$		0			0
$421$	22869.9	+	129702.i	0.129033	+	0.731783i	0.978830	+	0.204673i	$0.0656132\pi$
$421$	22869.9	+	129702.i	0.129033	+	0.731783i	−0.849797	+	0.527110i	$0.823276\pi$
$422$	288543.	+	166590.i	1.62026	+	0.935459i
$423$		0			0
$424$	−106424.	−	184332.i	−0.591981	−	1.02534i
$425$	126090.	+	150268.i	0.698075	+	0.831933i
$426$		0			0
$427$	−24677.1	+	139951.i	−0.135344	+	0.767571i
$428$	−21437.7	+	25548.5i	−0.117028	+	0.139469i
$429$		0			0
$430$	−21656.4	−	7882.28i	−0.117125	−	0.0426300i
$431$			25320.4i			0.136306i	0.997675	+	0.0681531i	$0.0217106\pi$
$431$			25320.4i			0.136306i	−0.997675	+	0.0681531i	$0.978289\pi$
$432$		0			0
$433$	−85329.9			−0.455119			−0.227560	−	0.973764i	$-0.573075\pi$
$433$	−85329.9			−0.455119			−0.227560	+	0.973764i	$0.573075\pi$
$434$	−16721.1	+	45941.0i	−0.0887742	+	0.243905i
$435$		0			0
$436$	27035.1	+	22685.1i	0.142218	+	0.119335i
$437$	202849.	+	35767.7i	1.06221	+	0.187296i
$438$		0			0
$439$	34199.0	−	28696.4i	0.177454	−	0.148901i	−0.549735	−	0.835339i	$-0.685271\pi$
$439$	34199.0	−	28696.4i	0.177454	−	0.148901i	0.727188	+	0.686438i	$0.240827\pi$
$440$	12156.3	−	7018.45i	0.0627909	−	0.0362523i
$441$		0			0
$442$	15794.3	−	27356.6i	0.0808457	−	0.140029i
$443$	287860.	−	50757.5i	1.46681	−	0.258638i	0.617517	−	0.786558i	$-0.288139\pi$
$443$	287860.	−	50757.5i	1.46681	−	0.258638i	0.849294	+	0.527919i	$0.177028\pi$
$444$		0			0
$445$	−12859.4	+	4680.44i	−0.0649382	+	0.0236356i
$446$	28531.9	+	78390.9i	0.143437	+	0.394090i
$447$		0			0
$448$	4552.48	+	25818.4i	0.0226825	+	0.128639i
$449$	−183382.	−	105876.i	−0.909629	−	0.525175i	−0.0293175	−	0.999570i	$-0.509333\pi$
$449$	−183382.	−	105876.i	−0.909629	−	0.525175i	−0.880312	+	0.474395i	$0.842667\pi$
$450$		0			0
$451$	18976.7	+	32868.5i	0.0932968	+	0.161595i
$452$	22417.3	+	26715.9i	0.109725	+	0.130765i
$453$		0			0
$454$	51635.4	−	292839.i	0.250516	−	1.42075i
$455$	−508.763	+	606.321i	−0.00245750	+	0.00292873i
$456$		0			0
$457$	−64052.8	−	23313.3i	−0.306694	−	0.111628i	0.184088	−	0.982910i	$-0.441067\pi$
$457$	−64052.8	−	23313.3i	−0.306694	−	0.111628i	−0.490782	+	0.871282i	$0.663289\pi$
$458$		−	34977.5i		−	0.166747i
$459$		0			0
$460$	−9185.08			−0.0434077
$461$	28265.9	−	77659.9i	0.133003	−	0.365422i	−0.855257	−	0.518204i	$-0.826601\pi$
$461$	28265.9	−	77659.9i	0.133003	−	0.365422i	0.988260	+	0.152782i	$0.0488231\pi$
$462$		0			0
$463$	−52983.6	−	44458.5i	−0.247161	−	0.207392i	0.510788	−	0.859707i	$-0.329354\pi$
$463$	−52983.6	−	44458.5i	−0.247161	−	0.207392i	−0.757948	+	0.652314i	$0.773798\pi$
$464$	233856.	+	41235.2i	1.08621	+	0.191528i
$465$		0			0
$466$	−248290.	+	208340.i	−1.14337	+	0.959404i
$467$	156825.	−	90543.1i	0.719088	−	0.415166i	−0.0953288	−	0.995446i	$-0.530390\pi$
$467$	156825.	−	90543.1i	0.719088	−	0.415166i	0.814417	+	0.580280i	$0.197057\pi$
$468$		0			0
$469$	57767.6	−	100056.i	0.262627	−	0.454883i
$470$	2102.14	−	370.663i	0.00951623	−	0.00167797i
$471$		0			0
$472$	27931.0	−	10166.1i	0.125373	−	0.0456320i
$473$	−146445.	−	402355.i	−0.654565	−	1.79840i
$474$		0			0
$475$	−29973.6	−	169989.i	−0.132847	−	0.753413i
$476$	−35833.6	−	20688.5i	−0.158153	−	0.0913095i
$477$		0			0
$478$	125725.	+	217762.i	0.550256	+	0.953072i
$479$	230764.	+	275014.i	1.00577	+	1.19862i	0.980008	+	0.198956i	$0.0637552\pi$
$479$	230764.	+	275014.i	1.00577	+	1.19862i	0.0257572	+	0.999668i	$0.491800\pi$
$480$		0			0
$481$	−7726.33	+	43818.2i	−0.0333951	+	0.189393i
$482$	−137119.	+	163412.i	−0.590206	+	0.703381i
$483$		0			0
$484$	−80447.1	−	29280.4i	−0.343415	−	0.124993i
$485$			24334.8i			0.103453i
$486$		0			0
$487$	−29733.0			−0.125366			−0.0626831	−	0.998033i	$-0.519966\pi$
$487$	−29733.0			−0.125366			−0.0626831	+	0.998033i	$0.519966\pi$
$488$	−109159.	+	299912.i	−0.458374	+	1.25937i
$489$		0			0
$490$	−13738.7	−	11528.1i	−0.0572205	−	0.0480137i
$491$	−61339.6	−	10815.8i	−0.254436	−	0.0448639i	0.0449753	−	0.998988i	$-0.485679\pi$
$491$	−61339.6	−	10815.8i	−0.254436	−	0.0448639i	−0.299411	+	0.954124i	$0.596790\pi$
$492$		0			0
$493$	180584.	−	151528.i	0.742995	−	0.623447i
$494$	−24072.3	+	13898.2i	−0.0986426	+	0.0569513i
$495$		0			0
$496$	−82033.5	+	142086.i	−0.333448	+	0.577549i
$497$	−143576.	+	25316.3i	−0.581258	+	0.102491i
$498$		0			0
$499$	167103.	−	60820.4i	0.671092	−	0.244258i	0.0160740	−	0.999871i	$-0.494883\pi$
$499$	167103.	−	60820.4i	0.671092	−	0.244258i	0.655018	+	0.755613i	$0.272661\pi$
$500$	5280.21	+	14507.3i	0.0211208	+	0.0580290i
$501$		0			0
$502$	38185.1	+	216558.i	0.151526	+	0.859344i
$503$	−343298.	−	198203.i	−1.35686	−	0.783384i	−0.367661	−	0.929960i	$-0.619841\pi$
$503$	−343298.	−	198203.i	−1.35686	−	0.783384i	−0.989199	+	0.146576i	$0.953175\pi$
$504$		0			0
$505$	10462.2	+	18121.0i	0.0410240	+	0.0710557i
$506$	−376693.	−	448926.i	−1.47125	−	1.75337i
$507$		0			0
$508$	−6089.52	+	34535.4i	−0.0235969	+	0.133825i
$509$	−45256.8	+	53934.9i	−0.174682	+	0.208178i	−0.846281	−	0.532737i	$-0.821163\pi$
$509$	−45256.8	+	53934.9i	−0.174682	+	0.208178i	0.671599	+	0.740915i	$0.265608\pi$
$510$		0			0
$511$	118898.	+	43275.3i	0.455337	+	0.165729i
$512$		−	24636.0i		−	0.0939789i
$513$		0			0
$514$	−69306.9			−0.262331
$515$	1427.45	−	3921.90i	0.00538205	−	0.0147871i
$516$		0			0
$517$	30379.9	+	25491.8i	0.113659	+	0.0953715i
$518$	197105.	+	34754.9i	0.734578	+	0.129526i
$519$		0			0
$520$	−1361.72	+	1142.62i	−0.00503594	+	0.00422566i
$521$	−298759.	+	172489.i	−1.10064	+	0.635456i	−0.936389	−	0.350963i	$-0.885854\pi$
$521$	−298759.	+	172489.i	−1.10064	+	0.635456i	−0.164252	+	0.986418i	$0.552521\pi$
$522$		0			0
$523$	−58824.8	+	101888.i	−0.215059	+	0.372493i	−0.953291	−	0.302054i	$-0.902328\pi$
$523$	−58824.8	+	101888.i	−0.215059	+	0.372493i	0.738232	+	0.674547i	$0.235661\pi$
$524$	−207922.	+	36662.2i	−0.757246	+	0.133523i
$525$		0			0
$526$	6739.30	−	2452.90i	0.0243581	−	0.00886562i
$527$	55705.9	+	153051.i	0.200576	+	0.551079i
$528$		0			0
$529$	−46902.3	−	265996.i	−0.167603	−	0.950526i
$530$	−36845.4	−	21272.7i	−0.131169	−	0.0757305i
$531$		0			0
$532$	18204.8	+	31531.7i	0.0643225	+	0.111410i
$533$	−3089.44	−	3681.85i	−0.0108749	−	0.0129602i
$534$		0			0
$535$	1660.15	−	9415.20i	0.00580017	−	0.0328944i
$536$	166789.	−	198771.i	0.580547	−	0.691869i
$537$		0			0
$538$	−269068.	−	97932.8i	−0.929604	−	0.338348i
$539$		−	333206.i		−	1.14693i
$540$		0			0
$541$	439148.			1.50043			0.750217	−	0.661192i	$-0.229949\pi$
$541$	439148.			1.50043			0.750217	+	0.661192i	$0.229949\pi$
$542$	−152259.	+	418328.i	−0.518304	+	1.42403i
$543$		0			0
$544$	−192012.	−	161117.i	−0.648828	−	0.544431i
$545$	−9963.05	−	1756.75i	−0.0335428	−	0.00591450i
$546$		0			0
$547$	66909.6	−	56143.8i	0.223622	−	0.187641i	−0.524093	−	0.851661i	$-0.675596\pi$
$547$	66909.6	−	56143.8i	0.223622	−	0.187641i	0.747715	+	0.664020i	$0.231151\pi$
$548$	59806.0	−	34529.0i	0.199151	−	0.114980i
$549$		0			0
$550$	−245549.	+	425304.i	−0.811733	+	1.40596i
$551$	−204284.	+	36020.7i	−0.672869	+	0.118645i
$552$		0			0
$553$	−27251.4	+	9918.70i	−0.0891125	+	0.0324343i
$554$	−197257.	−	541958.i	−0.642705	−	1.76582i
$555$		0			0
$556$	−22666.1	−	128546.i	−0.0733209	−	0.415823i
$557$	325780.	+	188089.i	1.05006	+	0.606251i	0.922666	−	0.385601i	$-0.126006\pi$
$557$	325780.	+	188089.i	1.05006	+	0.606251i	0.127393	+	0.991852i	$0.459339\pi$
$558$		0			0
$559$	27111.6	+	46958.7i	0.0867625	+	0.150277i
$560$	7680.09	+	9152.77i	0.0244901	+	0.0291861i
$561$		0			0
$562$	69942.3	−	396662.i	0.221446	−	1.25588i
$563$	186793.	−	222611.i	0.589309	−	0.702311i	−0.386164	−	0.922430i	$-0.626200\pi$
$563$	186793.	−	222611.i	0.589309	−	0.702311i	0.975473	+	0.220119i	$0.0706447\pi$
$564$		0			0
$565$	−9394.38	−	3419.27i	−0.0294287	−	0.0107112i
$566$			503203.i			1.57076i
$567$		0			0
$568$	−327428.			−1.01489
$569$	121458.	−	333704.i	0.375148	−	1.03071i	−0.598193	−	0.801352i	$-0.704115\pi$
$569$	121458.	−	333704.i	0.375148	−	1.03071i	0.973342	−	0.229360i	$-0.0736633\pi$
$570$		0			0
$571$	−331981.	−	278565.i	−1.01822	−	0.854387i	−0.0288162	−	0.999585i	$-0.509174\pi$
$571$	−331981.	−	278565.i	−1.01822	−	0.854387i	−0.989403	+	0.145198i	$0.953618\pi$
$572$	22679.0	+	3998.92i	0.0693158	+	0.0122222i
$573$		0			0
$574$	−16561.9	+	13897.1i	−0.0502673	+	0.0421793i
$575$	−399112.	+	230427.i	−1.20714	+	0.696944i
$576$		0			0
$577$	247060.	−	427921.i	0.742082	−	1.28532i	−0.209464	−	0.977816i	$-0.567172\pi$
$577$	247060.	−	427921.i	0.742082	−	1.28532i	0.951546	−	0.307507i	$-0.0994946\pi$
$578$	−75397.4	+	13294.6i	−0.225684	+	0.0397942i
$579$		0			0
$580$	8692.21	−	3163.71i	0.0258389	−	0.00940460i
$581$	7944.78	+	21828.1i	0.0235358	+	0.0646642i
$582$		0			0
$583$	−137260.	−	778443.i	−0.403839	−	2.29029i
$584$	246096.	+	142084.i	0.721570	+	0.416599i
$585$		0			0
$586$	190649.	+	330213.i	0.555186	+	0.961610i
$587$	154023.	+	183557.i	0.447001	+	0.532715i	0.941747	−	0.336323i	$-0.109183\pi$
$587$	154023.	+	183557.i	0.447001	+	0.532715i	−0.494746	+	0.869038i	$0.664739\pi$
$588$		0			0
$589$	24887.2	−	141142.i	0.0717374	−	0.406843i
$590$	3819.02	−	4551.33i	0.0109710	−	0.0130748i
$591$		0			0
$592$	631159.	+	229723.i	1.80093	+	0.655483i
$593$			117438.i			0.333964i	0.985960	+	0.166982i	$0.0534022\pi$
$593$			117438.i			0.333964i	−0.985960	+	0.166982i	$0.946598\pi$
$594$		0			0
$595$	11861.1			0.0335037
$596$	5527.86	−	15187.7i	0.0155620	−	0.0427562i
$597$		0			0
$598$	56850.8	+	47703.5i	0.158977	+	0.133398i
$599$	219751.	+	38748.0i	0.612459	+	0.107993i	0.471269	−	0.881990i	$-0.343796\pi$
$599$	219751.	+	38748.0i	0.612459	+	0.107993i	0.141190	+	0.989983i	$0.454907\pi$
$600$		0			0
$601$	−233356.	+	195809.i	−0.646056	+	0.542106i	−0.905871	−	0.423553i	$-0.860783\pi$
$601$	−233356.	+	195809.i	−0.646056	+	0.542106i	0.259815	+	0.965658i	$0.416338\pi$
$602$	211232.	−	121955.i	0.582863	−	0.336516i
$603$		0			0
$604$	−9303.27	+	16113.7i	−0.0255013	+	0.0441695i
$605$	24168.1	−	4261.49i	0.0660286	−	0.0116426i
$606$		0			0
$607$	−364496.	+	132666.i	−0.989272	+	0.360065i	−0.785438	−	0.618940i	$-0.787562\pi$
$607$	−364496.	+	132666.i	−0.989272	+	0.360065i	−0.203833	+	0.979006i	$0.565340\pi$
$608$	75436.5	+	207260.i	0.204068	+	0.560672i
$609$		0			0
$610$	11078.0	+	62826.5i	0.0297716	+	0.168843i
$611$	−4349.36	−	2511.10i	−0.0116505	−	0.00672639i
$612$		0			0
$613$	−157313.	−	272474.i	−0.418642	−	0.725110i	0.577161	−	0.816630i	$-0.304161\pi$
$613$	−157313.	−	272474.i	−0.418642	−	0.725110i	−0.995803	+	0.0915207i	$0.970827\pi$
$614$	−444680.	−	529949.i	−1.17954	−	1.40572i
$615$		0			0
$616$	−25797.0	+	146302.i	−0.0679843	+	0.385558i
$617$	271816.	−	323938.i	0.714011	−	0.850925i	−0.280024	−	0.959993i	$-0.590342\pi$
$617$	271816.	−	323938.i	0.714011	−	0.850925i	0.994034	+	0.109068i	$0.0347867\pi$
$618$		0			0
$619$	651711.	+	237203.i	1.70088	+	0.619070i	0.995925	−	0.0901821i	$-0.0287449\pi$
$619$	651711.	+	237203.i	1.70088	+	0.619070i	0.704955	+	0.709252i	$0.250967\pi$
$620$			6390.99i			0.0166259i
$621$		0			0
$622$	−54086.0			−0.139799
$623$	49535.3	−	136097.i	0.127626	−	0.350649i
$624$		0			0
$625$	294146.	+	246818.i	0.753014	+	0.631854i
$626$	50275.5	+	8864.93i	0.128294	+	0.0226218i
$627$		0			0
$628$	35463.3	−	29757.3i	0.0899208	−	0.0754525i
$629$	577447.	−	333389.i	1.45952	−	0.842655i
$630$		0			0
$631$	−168075.	+	291114.i	−0.422127	+	0.731146i	−0.996147	−	0.0876956i	$-0.972050\pi$
$631$	−168075.	+	291114.i	−0.422127	+	0.731146i	0.574020	+	0.818841i	$0.305383\pi$
$632$	−64141.6	+	11309.9i	−0.160585	+	0.0283155i
$633$		0			0
$634$	−473149.	+	172212.i	−1.17712	+	0.428435i
$635$	−3438.20	−	9446.38i	−0.00852675	−	0.0234271i
$636$		0			0
$637$	7327.33	+	41555.3i	0.0180579	+	0.102411i
$638$	511108.	+	295088.i	1.25566	+	0.724954i
$639$		0			0
$640$	17854.8	+	30925.5i	0.0435909	+	0.0755016i
$641$	−29289.6	−	34906.0i	−0.0712848	−	0.0849540i	0.729223	−	0.684276i	$-0.239881\pi$
$641$	−29289.6	−	34906.0i	−0.0712848	−	0.0849540i	−0.800508	+	0.599322i	$0.795437\pi$
$642$		0			0
$643$	−93762.9	+	531756.i	−0.226782	+	1.28615i	0.632466	+	0.774588i	$0.282043\pi$
$643$	−93762.9	+	531756.i	−0.226782	+	1.28615i	−0.859249	+	0.511558i	$0.829068\pi$
$644$	62485.4	−	74467.2i	0.150663	−	0.179553i
$645$		0			0
$646$	391428.	+	142468.i	0.937966	+	0.341392i
$647$			163593.i			0.390802i	0.980723	+	0.195401i	$0.0626009\pi$
$647$			163593.i			0.390802i	−0.980723	+	0.195401i	$0.937399\pi$
$648$		0			0
$649$	110384.			0.262070
$650$	21270.7	−	58440.9i	0.0503449	−	0.138322i
$651$		0			0
$652$	68932.2	+	57841.0i	0.162154	+	0.136063i
$653$	−685030.	−	120789.i	−1.60651	−	0.283271i	−0.702790	−	0.711397i	$-0.748063\pi$
$653$	−685030.	−	120789.i	−1.60651	−	0.283271i	−0.903719	+	0.428126i	$0.859174\pi$
$654$		0			0
$655$	46362.7	−	38903.0i	0.108065	−	0.0906776i
$656$	−62833.8	+	36277.1i	−0.146011	+	0.0842995i
$657$		0			0
$658$	−11295.6	+	19564.5i	−0.0260889	+	0.0451873i
$659$	121484.	−	21420.8i	0.279735	−	0.0493248i	−0.0320204	−	0.999487i	$-0.510194\pi$
$659$	121484.	−	21420.8i	0.279735	−	0.0493248i	0.311755	+	0.950162i	$0.399083\pi$
$660$		0			0
$661$	−440861.	+	160460.i	−1.00902	+	0.367252i	−0.793055	−	0.609149i	$-0.791511\pi$
$661$	−440861.	+	160460.i	−1.00902	+	0.367252i	−0.215962	+	0.976402i	$0.569289\pi$
$662$	152939.	+	420196.i	0.348981	+	0.958818i
$663$		0			0
$664$	9059.11	+	51376.8i	0.0205471	+	0.116528i
$665$	−9038.86	−	5218.59i	−0.0204395	−	0.0118008i
$666$		0			0
$667$	276916.	+	479632.i	0.622437	+	1.07809i
$668$	175893.	+	209621.i	0.394182	+	0.469767i
$669$		0			0
$670$	9006.43	−	51078.0i	0.0200633	−	0.113785i
$671$	−761872.	+	907963.i	−1.69214	+	2.01662i
$672$		0			0
$673$	279041.	+	101563.i	0.616081	+	0.224235i	0.631162	−	0.775651i	$-0.282578\pi$
$673$	279041.	+	101563.i	0.616081	+	0.224235i	−0.0150807	+	0.999886i	$0.504801\pi$
$674$			156418.i			0.344325i
$675$		0			0
$676$	184822.			0.404445
$677$	3442.16	−	9457.26i	0.00751024	−	0.0206342i	−0.935881	−	0.352317i	$-0.885394\pi$
$677$	3442.16	−	9457.26i	0.00751024	−	0.0206342i	0.943391	+	0.331682i	$0.107616\pi$
$678$		0			0
$679$	−197292.	−	165548.i	−0.427928	−	0.359074i
$680$	26233.9	+	4625.75i	0.0567343	+	0.0100038i
$681$		0			0
$682$	−312363.	+	262104.i	−0.671569	+	0.563514i
$683$	−635684.	+	367012.i	−1.36270	+	0.786754i	−0.989982	−	0.141191i	$-0.954907\pi$
$683$	−635684.	+	367012.i	−1.36270	+	0.786754i	−0.372716	+	0.927945i	$0.621573\pi$
$684$		0			0
$685$	−9898.08	+	17144.0i	−0.0210945	+	0.0365368i
$686$	410961.	−	72463.5i	0.873277	−	0.153982i
$687$		0			0
$688$	769169.	−	279955.i	1.62497	−	0.591440i
$689$	34236.5	+	94064.0i	0.0721192	+	0.198146i
$690$		0			0
$691$	62021.4	+	351741.i	0.129893	+	0.736660i	0.978281	+	0.207284i	$0.0664626\pi$
$691$	62021.4	+	351741.i	0.129893	+	0.736660i	−0.848388	+	0.529375i	$0.822426\pi$
$692$	125160.	+	72261.4i	0.261369	+	0.150902i
$693$		0			0
$694$	−366967.	−	635606.i	−0.761919	−	1.31968i
$695$	24051.5	+	28663.4i	0.0497934	+	0.0593414i
$696$		0			0
$697$	−12507.2	+	70932.0i	−0.0257451	+	0.146008i
$698$	675728.	−	805302.i	1.38695	−	1.65290i
$699$		0			0
$700$	−76550.0	−	27861.9i	−0.156224	−	0.0568611i
$701$		−	173679.i		−	0.353436i	−0.984262	−	0.176718i	$-0.943452\pi$
$701$		−	173679.i		−	0.353436i	0.984262	−	0.176718i	$-0.0565480\pi$
$702$		0			0
$703$	−586729.			−1.18721
$704$	−74786.0	+	205473.i	−0.150895	+	0.414581i
$705$		0			0
$706$	−478883.	−	401830.i	−0.960771	−	0.806182i
$707$	−218088.	−	38454.7i	−0.436307	−	0.0769327i
$708$		0			0
$709$	−221488.	+	185850.i	−0.440613	+	0.369718i	−0.835939	−	0.548823i	$-0.815076\pi$
$709$	−221488.	+	185850.i	−0.440613	+	0.369718i	0.395326	+	0.918541i	$0.370632\pi$
$710$	−56679.9	+	32724.2i	−0.112438	+	0.0649160i
$711$		0			0
$712$	162637.	−	281695.i	0.320818	−	0.555673i
$713$	−376836.	+	66446.3i	−0.741265	+	0.130705i
$714$		0			0
$715$	−6203.34	+	2257.83i	−0.0121343	+	0.00441651i
$716$	36109.7	+	99210.6i	0.0704365	+	0.193523i
$717$		0			0
$718$	−60953.7	−	345686.i	−0.118236	−	0.670552i
$719$	−35089.4	−	20258.8i	−0.0678762	−	0.0391884i	0.465678	−	0.884954i	$-0.345811\pi$
$719$	−35089.4	−	20258.8i	−0.0678762	−	0.0391884i	−0.533554	+	0.845766i	$0.679144\pi$
$720$		0			0
$721$	22085.6	+	38253.4i	0.0424853	+	0.0735867i
$722$	162388.	+	193526.i	0.311515	+	0.371250i
$723$		0			0
$724$	−57599.9	+	326665.i	−0.109887	+	0.623198i
$725$	298327.	−	355532.i	0.567567	−	0.676399i
$726$		0			0
$727$	−714632.	−	260105.i	−1.35211	−	0.492129i	−0.438507	−	0.898728i	$-0.644493\pi$
$727$	−714632.	−	260105.i	−1.35211	−	0.492129i	−0.913607	+	0.406598i	$0.866715\pi$
$728$		−	18813.2i		−	0.0354976i
$729$		0			0
$730$	56801.1			0.106589
$731$	277917.	−	763571.i	0.520093	−	1.42894i
$732$		0			0
$733$	649822.	+	545266.i	1.20945	+	1.01485i	0.999309	+	0.0371747i	$0.0118358\pi$
$733$	649822.	+	545266.i	1.20945	+	1.01485i	0.210138	+	0.977672i	$0.432609\pi$
$734$	−1.23469e6	−	217710.i	−2.29175	−	0.404098i
$735$		0			0
$736$	451106.	−	378523.i	0.832766	−	0.698774i
$737$	834519.	−	481810.i	1.53639	−	0.887035i
$738$		0			0
$739$	105879.	−	183388.i	0.193875	−	0.335801i	−0.752656	−	0.658414i	$-0.771228\pi$
$739$	105879.	−	183388.i	0.193875	−	0.335801i	0.946531	+	0.322613i	$0.104561\pi$
$740$	25766.3	−	4543.29i	0.0470531	−	0.00829672i
$741$		0			0
$742$	423123.	−	154004.i	0.768527	−	0.279721i
$743$	289038.	+	794124.i	0.523572	+	1.43850i	0.866517	+	0.499148i	$0.166354\pi$
$743$	289038.	+	794124.i	0.523572	+	1.43850i	−0.342944	+	0.939356i	$0.611424\pi$
$744$		0			0
$745$	804.530	+	4562.72i	0.00144954	+	0.00822075i
$746$	−568544.	−	328249.i	−1.02161	−	0.589829i
$747$		0			0
$748$	−172552.	−	298870.i	−0.308402	−	0.534169i
$749$	65039.1	+	77510.6i	0.115934	+	0.138165i
$750$		0			0
$751$	55207.1	−	313095.i	0.0978847	−	0.555132i	−0.895940	−	0.444174i	$-0.853497\pi$
$751$	55207.1	−	313095.i	0.0978847	−	0.555132i	0.993825	−	0.110958i	$-0.0353918\pi$
$752$	−48731.8	+	58076.3i	−0.0861741	+	0.102698i
$753$		0			0
$754$	−70231.2	−	25562.1i	−0.123534	−	0.0449628i
$755$		−	5333.75i		−	0.00935704i
$756$		0			0
$757$	41402.7			0.0722498			0.0361249	−	0.999347i	$-0.488499\pi$
$757$	41402.7			0.0722498			0.0361249	+	0.999347i	$0.488499\pi$
$758$	−165027.	+	453408.i	−0.287221	+	0.789134i
$759$		0			0
$760$	−17956.5	−	15067.3i	−0.0310882	−	0.0260861i
$761$	465248.	+	82035.8i	0.803369	+	0.141656i	0.560231	−	0.828336i	$-0.310712\pi$
$761$	465248.	+	82035.8i	0.803369	+	0.141656i	0.243138	+	0.969992i	$0.421823\pi$
$762$		0			0
$763$	82020.7	−	68823.5i	0.140888	−	0.118219i
$764$	−120478.	+	69558.1i	−0.206406	+	0.119168i
$765$		0			0
$766$	130693.	−	226367.i	0.222739	−	0.385795i
$767$	−13766.4	+	2427.39i	−0.0234008	+	0.00412619i
$768$		0			0
$769$	466733.	−	169877.i	0.789253	−	0.287264i	0.0842273	−	0.996447i	$-0.473158\pi$
$769$	466733.	−	169877.i	0.789253	−	0.287264i	0.705025	+	0.709182i	$0.250936\pi$
$770$	10156.3	+	27904.1i	0.0171298	+	0.0470638i
$771$		0			0
$772$	36046.6	+	204430.i	0.0604825	+	0.343013i
$773$	−879082.	−	507538.i	−1.47119	−	0.849395i	−0.471718	−	0.881749i	$-0.656366\pi$
$773$	−879082.	−	507538.i	−1.47119	−	0.849395i	−0.999476	+	0.0323544i	$0.989699\pi$
$774$		0			0
$775$	160332.	+	277702.i	0.266941	+	0.462356i
$776$	−371800.	−	443094.i	−0.617427	−	0.735821i
$777$		0			0
$778$	91919.1	−	521299.i	0.151861	−	0.861248i
$779$	40739.4	−	48551.3i	0.0671336	−	0.0800067i
$780$		0			0
$781$	−1.14263e6	−	415885.i	−1.87329	−	0.681822i
$782$		−	1.11214e6i		−	1.81864i
$783$		0			0
$784$	636980.			1.03632
$785$	−4538.83	+	12470.3i	−0.00736554	+	0.0202367i
$786$		0			0
$787$	−562345.	−	471864.i	−0.907933	−	0.761846i	0.0637919	−	0.997963i	$-0.479681\pi$
$787$	−562345.	−	471864.i	−0.907933	−	0.761846i	−0.971725	+	0.236117i	$0.924125\pi$
$788$	−124813.	−	22008.0i	−0.201006	−	0.0354428i
$789$		0			0
$790$	−9972.99	+	8368.33i	−0.0159798	+	0.0134086i
$791$	91630.8	−	52903.1i	0.146450	−	0.0845528i
$792$		0			0
$793$	75049.3	−	129989.i	0.119344	−	0.206710i
$794$	545909.	−	96258.5i	0.865924	−	0.152686i
$795$		0			0
$796$	−87211.2	+	31742.3i	−0.137641	+	0.0500971i
$797$	−46013.8	−	126422.i	−0.0724389	−	0.199024i	0.898189	−	0.439609i	$-0.144883\pi$
$797$	−46013.8	−	126422.i	−0.0724389	−	0.199024i	−0.970628	+	0.240585i	$0.922661\pi$
$798$		0			0
$799$	13069.0	+	74118.1i	0.0204715	+	0.116100i
$800$	−427369.	−	246742.i	−0.667765	−	0.385534i
$801$		0			0
$802$	−636854.	−	1.10306e6i	−0.990127	−	1.71495i
$803$	678340.	+	808414.i	1.05200	+	1.25373i
$804$		0			0
$805$	−4838.92	+	27442.9i	−0.00746718	+	0.0423485i
$806$	33192.2	−	39556.9i	0.0510935	−	0.0608908i
$807$		0			0
$808$	−467359.	−	170105.i	−0.715860	−	0.260552i
$809$			120165.i			0.183603i	0.995777	+	0.0918016i	$0.0292626\pi$
$809$			120165.i			0.183603i	−0.995777	+	0.0918016i	$0.970737\pi$
$810$		0			0
$811$	22600.0			0.0343610			0.0171805	−	0.999852i	$-0.494531\pi$
$811$	22600.0			0.0343610			0.0171805	+	0.999852i	$0.494531\pi$
$812$	−33483.0	+	91993.8i	−0.0507823	+	0.139523i
$813$		0			0
$814$	1.27877e6	+	1.07301e6i	1.92993	+	1.61941i
$815$	−25403.1	−	4479.25i	−0.0382447	−	0.00674358i
$816$		0			0
$817$	−547740.	+	459608.i	−0.820598	+	0.688563i
$818$	−720855.	+	416186.i	−1.07731	+	0.621986i
$819$		0			0
$820$	−1413.12	+	2447.60i	−0.00210161	+	0.00364009i
$821$	−804936.	+	141932.i	−1.19420	+	0.210569i	−0.735188	−	0.677864i	$-0.762906\pi$
$821$	−804936.	+	141932.i	−1.19420	+	0.210569i	−0.459007	+	0.888432i	$0.651795\pi$
$822$		0			0
$823$	387747.	−	141128.i	0.572464	−	0.208360i	−0.0395352	−	0.999218i	$-0.512588\pi$
$823$	387747.	−	141128.i	0.572464	−	0.208360i	0.611999	+	0.790858i	$0.290366\pi$
$824$	33929.4	+	93220.2i	0.0499714	+	0.137295i
$825$		0			0
$826$	10919.0	+	61924.8i	0.0160038	+	0.0907621i
$827$	33841.9	+	19538.6i	0.0494816	+	0.0285682i	0.524537	−	0.851388i	$-0.324239\pi$
$827$	33841.9	+	19538.6i	0.0494816	+	0.0285682i	−0.475055	+	0.879956i	$0.657572\pi$
$828$		0			0
$829$	412006.	+	713616.i	0.599508	+	1.03838i	0.992894	+	0.119004i	$0.0379702\pi$
$829$	412006.	+	713616.i	0.599508	+	1.03838i	−0.393386	+	0.919373i	$0.628696\pi$
$830$	6702.95	+	7988.27i	0.00972994	+	0.0115957i
$831$		0			0
$832$	4808.41	−	27269.8i	0.00694632	−	0.0393945i
$833$	406463.	−	484404.i	0.585775	−	0.698100i
$834$		0			0
$835$	−73711.4	−	26828.7i	−0.105721	−	0.0384793i
$836$			303674.i			0.434505i
$837$		0			0
$838$	−206777.			−0.294452
$839$	−383564.	+	1.05383e6i	−0.544897	+	1.49709i	0.295620	+	0.955306i	$0.404474\pi$
$839$	−383564.	+	1.05383e6i	−0.544897	+	1.49709i	−0.840517	+	0.541786i	$0.817748\pi$
$840$		0			0
$841$	114548.	+	96117.2i	0.161955	+	0.135897i
$842$	−616231.	−	108658.i	−0.869199	−	0.153263i
$843$		0			0
$844$	−353115.	+	296298.i	−0.495714	+	0.415953i
$845$	−45882.9	+	26490.5i	−0.0642595	+	0.0371002i
$846$		0			0
$847$	−129864.	+	224932.i	−0.181019	+	0.313534i
$848$	1.48813e6	−	262397.i	2.06942	−	0.364894i
$849$		0			0
$850$	−875780.	+	318758.i	−1.21215	+	0.441187i
$851$	535777.	+	1.47204e6i	0.739819	+	2.03264i
$852$		0			0
$853$	59860.1	+	339483.i	0.0822696	+	0.466574i	0.997912	+	0.0645813i	$0.0205712\pi$
$853$	59860.1	+	339483.i	0.0822696	+	0.466574i	−0.915643	+	0.401993i	$0.868318\pi$
$854$	−584724.	−	337590.i	−0.801742	−	0.462886i
$855$		0			0
$856$	113622.	+	196799.i	0.155065	+	0.268581i
$857$	239359.	+	285257.i	0.325902	+	0.388395i	0.903972	−	0.427592i	$-0.140638\pi$
$857$	239359.	+	285257.i	0.325902	+	0.388395i	−0.578069	+	0.815988i	$0.696194\pi$
$858$		0			0
$859$	130686.	−	741155.i	0.177109	−	1.00444i	−0.758572	−	0.651590i	$-0.774102\pi$
$859$	130686.	−	741155.i	0.177109	−	1.00444i	0.935681	−	0.352847i	$-0.114786\pi$
$860$	20495.1	−	24425.1i	0.0277110	−	0.0330247i
$861$		0			0
$862$	−113045.	−	41145.2i	−0.152138	−	0.0553738i
$863$		−	691959.i		−	0.929092i	−0.885549	−	0.464546i	$-0.846218\pi$
$863$		−	691959.i		−	0.929092i	0.885549	−	0.464546i	$-0.153782\pi$
$864$		0			0
$865$	−41428.9			−0.0553696
$866$	138660.	−	380964.i	0.184890	−	0.507982i
$867$		0			0
$868$	−51814.4	−	43477.4i	−0.0687719	−	0.0577065i
$869$	−238202.	−	42001.5i	−0.315432	−	0.0556192i
$870$		0			0
$871$	−93480.7	+	78439.6i	−0.123221	+	0.103395i
$872$	208250.	−	120233.i	0.273875	−	0.158122i
$873$		0			0
$874$	−489314.	+	847517.i	−0.640567	+	1.10950i
$875$	46126.1	−	8133.27i	0.0602463	−	0.0106230i
$876$		0			0
$877$	985831.	−	358813.i	1.28175	−	0.466519i	0.390739	−	0.920501i	$-0.372219\pi$
$877$	985831.	−	358813.i	1.28175	−	0.466519i	0.891011	+	0.453983i	$0.149997\pi$
$878$	72545.2	+	199316.i	0.0941065	+	0.258555i
$879$		0			0
$880$	17304.5	+	98139.0i	0.0223457	+	0.126729i
$881$	1.11226e6	+	642162.i	1.43302	+	0.827357i	0.997350	−	0.0727481i	$-0.0231769\pi$
$881$	1.11226e6	+	642162.i	1.43302	+	0.827357i	0.435673	+	0.900105i	$0.356510\pi$
$882$		0			0
$883$	314345.	+	544462.i	0.403167	+	0.698306i	0.994106	−	0.108410i	$-0.0345760\pi$
$883$	314345.	+	544462.i	0.403167	+	0.698306i	−0.590939	+	0.806716i	$0.701243\pi$
$884$	28091.9	+	33478.6i	0.0359481	+	0.0428413i
$885$		0			0
$886$	−241156.	+	1.36766e6i	−0.307206	+	1.74225i
$887$	−368852.	+	439581.i	−0.468819	+	0.558717i	−0.947700	−	0.319163i	$-0.896598\pi$
$887$	−368852.	+	439581.i	−0.468819	+	0.558717i	0.478881	+	0.877880i	$0.341043\pi$
$888$		0			0
$889$	99975.6	+	36388.1i	0.126500	+	0.0460422i
$890$		−	65017.7i		−	0.0820827i
$891$		0			0
$892$	−115415.			−0.145055
$893$	22650.7	−	62232.2i	0.0284039	−	0.0780391i
$894$		0			0
$895$	−23184.3	−	19453.9i	−0.0289432	−	0.0242863i
$896$	−372191.	−	65627.3i	−0.463607	−	0.0817464i
$897$		0			0
$898$	770686.	−	646682.i	0.955707	−	0.801933i
$899$	333728.	−	192678.i	0.412927	−	0.238404i
$900$		0			0
$901$	750043.	−	1.29911e6i	0.923924	−	1.60028i
$902$	−177582.	+	31312.4i	−0.218265	+	0.0384861i
$903$		0			0
$904$	223296.	−	81273.3i	0.273240	−	0.0994514i
$905$	−32521.5	−	89352.0i	−0.0397076	−	0.109096i
$906$		0			0
$907$	278989.	+	1.58222e6i	0.339135	+	1.92333i	0.381815	+	0.924239i	$0.375299\pi$
$907$	278989.	+	1.58222e6i	0.339135	+	1.92333i	−0.0426804	+	0.999089i	$0.513590\pi$
$908$	356279.	+	205698.i	0.432134	+	0.249493i
$909$		0			0
$910$	−1880.25	−	3256.69i	−0.00227056	−	0.00393272i
$911$	−586619.	−	699105.i	−0.706837	−	0.842376i	0.286445	−	0.958097i	$-0.407527\pi$
$911$	−586619.	−	699105.i	−0.706837	−	0.842376i	−0.993282	+	0.115721i	$0.963082\pi$
$912$		0			0
$913$	−33642.8	+	190798.i	−0.0403599	+	0.228892i
$914$	208169.	−	248087.i	0.249186	−	0.296969i
$915$		0			0
$916$	45473.4	+	16551.0i	0.0541959	+	0.0197257i
$917$			640536.i			0.761737i
$918$		0			0
$919$	−1.52311e6			−1.80343			−0.901715	−	0.432331i	$-0.857691\pi$
$919$	−1.52311e6			−1.80343			−0.901715	+	0.432331i	$0.857691\pi$
$920$	−21405.0	+	58809.7i	−0.0252895	+	0.0694822i
$921$		0			0
$922$	300789.	+	252392.i	0.353834	+	0.296902i
$923$	151647.	+	26739.5i	0.178005	+	0.0313870i
$924$		0			0
$925$	1.00562e6	−	843817.i	1.17531	−	0.986199i
$926$	284587.	−	164306.i	0.331889	−	0.191616i
$927$		0			0
$928$	−296522.	+	513591.i	−0.344319	+	0.596377i
$929$	298014.	−	52547.9i	0.345307	−	0.0608869i	0.00169476	−	0.999999i	$-0.499461\pi$
$929$	298014.	−	52547.9i	0.345307	−	0.0608869i	0.343612	+	0.939112i	$0.388349\pi$
$930$		0			0
$931$	−522873.	+	190310.i	−0.603249	+	0.219565i
$932$	−153370.	−	421380.i	−0.176566	−	0.485112i
$933$		0			0
$934$	149401.	+	847293.i	0.171261	+	0.971270i
$935$	85673.9	+	49463.8i	0.0979998	+	0.0565802i
$936$		0			0
$937$	−503151.	−	871484.i	−0.573085	−	0.992613i	−0.996247	−	0.0865587i	$-0.972413\pi$
$937$	−503151.	−	871484.i	−0.573085	−	0.992613i	0.423161	−	0.906054i	$-0.360920\pi$
$938$	352841.	+	420499.i	0.401026	+	0.477925i
$939$		0			0
$940$	−512.816	+	2908.32i	−0.000580371	+	0.00329145i
$941$	695867.	−	829302.i	0.785863	−	0.936556i	−0.213319	−	0.976983i	$-0.568427\pi$
$941$	695867.	−	829302.i	0.785863	−	0.936556i	0.999182	+	0.0404270i	$0.0128718\pi$
$942$		0			0
$943$	−159011.	−	57875.4i	−0.178815	−	0.0650834i
$944$			211018.i			0.236797i
$945$		0			0
$946$	2.03432e6			2.27320
$947$	519218.	−	1.42654e6i	0.578962	−	1.59069i	−0.210971	−	0.977492i	$-0.567663\pi$
$947$	519218.	−	1.42654e6i	0.578962	−	1.59069i	0.789933	−	0.613193i	$-0.210115\pi$
$948$		0			0
$949$	−102376.	−	85903.3i	−0.113675	−	0.0953844i
$950$	807639.	+	142408.i	0.894890	+	0.157793i
$951$		0			0
$952$	−215970.	+	181221.i	−0.238298	+	0.199956i
$953$	350869.	−	202574.i	0.386331	−	0.223048i	−0.294238	−	0.955732i	$-0.595066\pi$
$953$	350869.	−	202574.i	0.386331	−	0.223048i	0.680569	+	0.732684i	$0.261733\pi$
$954$		0			0
$955$	19939.5	−	34536.2i	0.0218629	−	0.0378676i
$956$	−342598.	+	60409.2i	−0.374859	+	0.0660978i
$957$		0			0
$958$	−1.60281e6	+	583376.i	−1.74643	+	0.635650i
$959$	−71657.4	−	196877.i	−0.0779155	−	0.214071i
$960$		0			0
$961$	−114134.	−	647288.i	−0.123586	−	0.700891i
$962$	−183076.	−	105699.i	−0.197825	−	0.114214i
$963$		0			0
$964$	−147565.	−	255590.i	−0.158792	−	0.275036i
$965$	−38249.7	−	45584.3i	−0.0410747	−	0.0489509i
$966$		0			0
$967$	20486.5	−	116185.i	0.0219086	−	0.124250i	−0.971892	−	0.235427i	$-0.924351\pi$
$967$	20486.5	−	116185.i	0.0219086	−	0.124250i	0.993801	+	0.111177i	$0.0354622\pi$
$968$	−374950.	+	446848.i	−0.400149	+	0.476880i
$969$		0			0
$970$	−108645.	−	39543.6i	−0.115469	−	0.0420274i
$971$			124920.i			0.132493i	0.997803	+	0.0662466i	$0.0211024\pi$
$971$			124920.i			0.132493i	−0.997803	+	0.0662466i	$0.978898\pi$
$972$		0			0
$973$	−396007.			−0.418289
$974$	48315.6	−	132746.i	0.0509295	−	0.139928i
$975$		0			0
$976$	−1.73573e6	−	1.45645e6i	−1.82214	−	1.52896i
$977$	−928550.	−	163728.i	−0.972783	−	0.171528i	−0.335401	−	0.942076i	$-0.608872\pi$
$977$	−928550.	−	163728.i	−0.972783	−	0.171528i	−0.637382	+	0.770548i	$0.719983\pi$
$978$		0			0
$979$	925355.	−	776465.i	0.965480	−	0.810134i
$980$	21488.3	−	12406.3i	0.0223744	−	0.0129178i
$981$		0			0
$982$	147964.	−	256281.i	0.153438	−	0.265763i
$983$	−793468.	+	139910.i	−0.821150	+	0.144791i	−0.568412	−	0.822744i	$-0.692442\pi$
$983$	−793468.	+	139910.i	−0.821150	+	0.144791i	−0.252738	+	0.967535i	$0.581331\pi$
$984$		0			0
$985$	34139.9	−	12425.9i	0.0351876	−	0.0128072i
$986$	383067.	+	1.05247e6i	0.394022	+	1.08257i
$987$		0			0
$988$	−6677.90	−	37872.3i	−0.00684111	−	0.0387978i
$989$	1.65328e6	+	954521.i	1.69026	+	0.975872i
$990$		0			0
$991$	242535.	+	420082.i	0.246960	+	0.427747i	0.962681	−	0.270639i	$-0.0872350\pi$
$991$	242535.	+	420082.i	0.246960	+	0.427747i	−0.715721	+	0.698386i	$0.753902\pi$
$992$	−263377.	−	313880.i	−0.267642	−	0.318963i
$993$		0			0
$994$	120281.	−	682148.i	0.121738	−	0.690408i
$995$	17101.0	−	20380.2i	0.0172733	−	0.0205855i
$996$		0			0
$997$	593091.	+	215867.i	0.596665	+	0.217168i	0.622658	−	0.782494i	$-0.286053\pi$
$997$	593091.	+	215867.i	0.596665	+	0.217168i	−0.0259933	+	0.999662i	$0.508275\pi$
$998$			844878.i			0.848268i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.5.f.a.17.3		66
3.2	odd	2		27.5.f.a.23.9	yes	66
27.7	even	9		27.5.f.a.20.9	✓	66
27.20	odd	18	inner	81.5.f.a.62.3		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.f.a.20.9	✓	66	27.7	even	9
27.5.f.a.23.9	yes	66	3.2	odd	2
81.5.f.a.17.3		66	1.1	even	1	trivial
81.5.f.a.62.3		66	27.20	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	81.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.62498 + 4.46460i) q^{2} +(-5.03539 - 4.22519i) q^{4} +(1.85566 + 0.327202i) q^{5} +(-15.2767 + 12.8186i) q^{7} +(-38.7874 + 22.3939i) q^{8} +(-4.47623 + 7.75306i) q^{10} +(-163.801 + 28.8826i) q^{11} +(19.7931 - 7.20410i) q^{13} +(-32.4058 - 89.0343i) q^{14} +(-55.2139 - 313.134i) q^{16} +(-273.361 - 157.825i) q^{17} +(138.878 + 240.543i) q^{19} +(-7.96145 - 9.48809i) q^{20} +(137.225 - 778.241i) q^{22} +(476.678 - 568.083i) q^{23} +(-583.971 - 212.548i) q^{25} +100.075i q^{26} +131.085 q^{28} +(-255.430 + 701.787i) q^{29} +(-395.273 - 331.673i) q^{31} +(782.021 + 137.891i) q^{32} +(1148.83 - 963.986i) q^{34} +(-32.5425 + 18.7884i) q^{35} +(-1056.20 + 1829.39i) q^{37} +(-1299.60 + 229.155i) q^{38} +(-79.3033 + 28.8640i) q^{40} +(-78.0433 - 214.422i) q^{41} +(447.021 + 2535.18i) q^{43} +(946.837 + 546.657i) q^{44} +(1761.67 + 3051.30i) q^{46} +(-153.262 - 182.650i) q^{47} +(-347.870 + 1972.87i) q^{49} +(1897.89 - 2261.81i) q^{50} +(-130.105 - 47.3542i) q^{52} +4752.36i q^{53} -313.409 q^{55} +(305.482 - 839.305i) q^{56} +(-2718.13 - 2280.78i) q^{58} +(-653.572 - 115.242i) q^{59} +(5458.87 - 4580.53i) q^{61} +(2123.10 - 1225.77i) q^{62} +(657.314 - 1138.50i) q^{64} +(39.0864 - 6.89198i) q^{65} +(-5444.09 + 1981.49i) q^{67} +(709.638 + 1949.72i) q^{68} +(-31.0018 - 175.820i) q^{70} +(6331.20 + 3655.32i) q^{71} +(-3172.37 - 5494.71i) q^{73} +(-6451.18 - 7688.22i) q^{74} +(317.039 - 1798.02i) q^{76} +(2132.10 - 2540.94i) q^{77} +(1366.51 + 497.371i) q^{79} -599.134i q^{80} +1084.13 q^{82} +(398.389 - 1094.57i) q^{83} +(-455.624 - 382.314i) q^{85} +(-12045.0 - 2123.85i) q^{86} +(5706.62 - 4788.43i) q^{88} +(-6289.55 + 3631.27i) q^{89} +(-210.026 + 363.775i) q^{91} +(-4800.52 + 846.461i) q^{92} +(1064.51 - 387.449i) q^{94} +(179.003 + 491.807i) q^{95} +(2242.60 + 12718.4i) q^{97} +(-8242.80 - 4758.98i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} - 1137 q^{14} - 54 q^{16} + 9 q^{17} - 3 q^{19} + 2487 q^{20} + 1002 q^{22} + 2724 q^{23} + 435 q^{25} - 12 q^{28}+ \cdots + 259938 q^{98}+O(q^{100}) \) 66 * q + 6 * q^2 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 492 * q^11 - 6 * q^13 - 1137 * q^14 - 54 * q^16 + 9 * q^17 - 3 * q^19 + 2487 * q^20 + 1002 * q^22 + 2724 * q^23 + 435 * q^25 - 12 * q^28 - 5016 * q^29 - 1671 * q^31 - 10224 * q^32 - 342 * q^34 + 2682 * q^35 - 3 * q^37 + 6564 * q^38 - 1113 * q^40 - 5754 * q^41 - 1266 * q^43 + 4545 * q^44 - 3 * q^46 + 9159 * q^47 + 5898 * q^49 + 34977 * q^50 + 2871 * q^52 - 12 * q^55 - 39243 * q^56 - 12291 * q^58 - 24762 * q^59 - 8358 * q^61 - 38304 * q^62 + 6141 * q^64 - 23727 * q^65 + 15996 * q^67 + 43533 * q^68 - 7251 * q^70 + 19773 * q^71 + 6108 * q^73 + 74847 * q^74 - 28614 * q^76 + 33909 * q^77 - 5658 * q^79 - 12 * q^82 - 18813 * q^83 + 24219 * q^85 - 96474 * q^86 + 36042 * q^88 - 110232 * q^89 - 6042 * q^91 - 73545 * q^92 + 2631 * q^94 + 65163 * q^95 - 3696 * q^97 + 259938 * q^98

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