LMFDB - Embedded newform 81.5.f.a.17.5

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			17.5
Character	$\chi$	$=$	81.17
Dual form			81.5.f.a.62.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.498289 + 1.36904i) q^{2} +(10.6307 + 8.92025i) q^{4} +(15.7451 + 2.77629i) q^{5} +(22.4150 - 18.8084i) q^{7} +(-37.6967 + 21.7642i) q^{8} +(-11.6465 + 20.1723i) q^{10} +(135.197 - 23.8388i) q^{11} +(-169.717 + 61.7718i) q^{13} +(14.5803 + 40.0591i) q^{14} +(27.5445 + 156.213i) q^{16} +(265.471 + 153.270i) q^{17} +(223.274 + 386.722i) q^{19} +(142.617 + 169.964i) q^{20} +(-34.7308 + 196.968i) q^{22} +(125.552 - 149.627i) q^{23} +(-347.107 - 126.337i) q^{25} -263.129i q^{26} +406.064 q^{28} +(-320.474 + 880.496i) q^{29} +(115.628 + 97.0232i) q^{31} +(-913.460 - 161.068i) q^{32} +(-342.114 + 287.068i) q^{34} +(405.145 - 233.911i) q^{35} +(944.419 - 1635.78i) q^{37} +(-640.692 + 112.971i) q^{38} +(-653.963 + 238.023i) q^{40} +(-796.872 - 2189.39i) q^{41} +(-432.194 - 2451.10i) q^{43} +(1649.89 + 952.564i) q^{44} +(142.284 + 246.443i) q^{46} +(441.904 + 526.641i) q^{47} +(-268.253 + 1521.34i) q^{49} +(345.919 - 412.250i) q^{50} +(-2355.23 - 857.235i) q^{52} -3259.62i q^{53} +2194.87 q^{55} +(-435.622 + 1196.86i) q^{56} +(-1045.74 - 877.483i) q^{58} +(-5572.36 - 982.557i) q^{59} +(4765.70 - 3998.90i) q^{61} +(-190.444 + 109.953i) q^{62} +(-593.306 + 1027.64i) q^{64} +(-2843.71 + 501.422i) q^{65} +(-1895.82 + 690.021i) q^{67} +(1454.95 + 3997.44i) q^{68} +(118.353 + 671.214i) q^{70} +(1215.38 + 701.697i) q^{71} +(1186.68 + 2055.39i) q^{73} +(1768.85 + 2108.04i) q^{74} +(-1076.09 + 6102.80i) q^{76} +(2582.07 - 3077.19i) q^{77} +(-4163.44 - 1515.37i) q^{79} +2536.06i q^{80} +3394.43 q^{82} +(-353.761 + 971.950i) q^{83} +(3754.36 + 3150.28i) q^{85} +(3571.00 + 629.663i) q^{86} +(-4577.64 + 3841.09i) q^{88} +(11599.9 - 6697.21i) q^{89} +(-2642.37 + 4576.73i) q^{91} +(2669.42 - 470.691i) q^{92} +(-941.187 + 342.564i) q^{94} +(2441.82 + 6708.86i) q^{95} +(1042.57 + 5912.70i) q^{97} +(-1949.10 - 1125.32i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.498289	+	1.36904i	−0.124572	+	0.342259i	−0.986265	−	0.165171i	$-0.947182\pi$
$2$	−0.498289	+	1.36904i	−0.124572	+	0.342259i	0.861693	+	0.507430i	$0.169405\pi$
$3$		0			0
$3$		0			0
$4$	10.6307	+	8.92025i	0.664421	+	0.557516i
$5$	15.7451	+	2.77629i	0.629805	+	0.111052i	0.479434	−	0.877578i	$-0.340842\pi$
$5$	15.7451	+	2.77629i	0.629805	+	0.111052i	0.150371	+	0.988630i	$0.451953\pi$
$6$		0			0
$7$	22.4150	−	18.8084i	0.457450	−	0.383846i	−0.384742	−	0.923024i	$-0.625710\pi$
$7$	22.4150	−	18.8084i	0.457450	−	0.383846i	0.842192	+	0.539178i	$0.181265\pi$
$8$	−37.6967	+	21.7642i	−0.589011	+	0.340066i
$9$		0			0
$10$	−11.6465	+	20.1723i	−0.116465	+	0.201723i
$11$	135.197	−	23.8388i	1.11733	−	0.197015i	0.415661	−	0.909520i	$-0.363550\pi$
$11$	135.197	−	23.8388i	1.11733	−	0.197015i	0.701667	+	0.712505i	$0.252439\pi$
$12$		0			0
$13$	−169.717	+	61.7718i	−1.00424	+	0.365514i	−0.791219	−	0.611534i	$-0.790553\pi$
$13$	−169.717	+	61.7718i	−1.00424	+	0.365514i	−0.213022	+	0.977047i	$0.568331\pi$
$14$	14.5803	+	40.0591i	0.0743893	+	0.204383i
$15$		0			0
$16$	27.5445	+	156.213i	0.107596	+	0.610206i
$17$	265.471	+	153.270i	0.918586	+	0.530346i	0.883184	−	0.469027i	$-0.155395\pi$
$17$	265.471	+	153.270i	0.918586	+	0.530346i	0.0354023	+	0.999373i	$0.488729\pi$
$18$		0			0
$19$	223.274	+	386.722i	0.618488	+	1.07125i	0.989762	+	0.142729i	$0.0455877\pi$
$19$	223.274	+	386.722i	0.618488	+	1.07125i	−0.371274	+	0.928523i	$0.621079\pi$
$20$	142.617	+	169.964i	0.356543	+	0.424911i
$21$		0			0
$22$	−34.7308	+	196.968i	−0.0717578	+	0.406959i
$23$	125.552	−	149.627i	0.237338	−	0.282849i	−0.634207	−	0.773163i	$-0.718673\pi$
$23$	125.552	−	149.627i	0.237338	−	0.282849i	0.871546	+	0.490314i	$0.163118\pi$
$24$		0			0
$25$	−347.107	−	126.337i	−0.555371	−	0.202138i
$26$		−	263.129i		−	0.389244i
$27$		0			0
$28$	406.064			0.517939
$29$	−320.474	+	880.496i	−0.381064	+	1.04696i	0.589846	+	0.807516i	$0.299189\pi$
$29$	−320.474	+	880.496i	−0.381064	+	1.04696i	−0.970909	+	0.239448i	$0.923034\pi$
$30$		0			0
$31$	115.628	+	97.0232i	0.120320	+	0.100961i	0.700962	−	0.713198i	$-0.252754\pi$
$31$	115.628	+	97.0232i	0.120320	+	0.100961i	−0.580642	+	0.814159i	$0.697198\pi$
$32$	−913.460	−	161.068i	−0.892051	−	0.157293i
$33$		0			0
$34$	−342.114	+	287.068i	−0.295946	+	0.248328i
$35$	405.145	−	233.911i	0.330731	−	0.190947i
$36$		0			0
$37$	944.419	−	1635.78i	0.689860	−	1.19487i	−0.282022	−	0.959408i	$-0.591005\pi$
$37$	944.419	−	1635.78i	0.689860	−	1.19487i	0.971883	−	0.235465i	$-0.0756614\pi$
$38$	−640.692	+	112.971i	−0.443692	+	0.0782349i
$39$		0			0
$40$	−653.963	+	238.023i	−0.408727	+	0.148764i
$41$	−796.872	−	2189.39i	−0.474046	−	1.30243i	−0.914474	−	0.404644i	$-0.867396\pi$
$41$	−796.872	−	2189.39i	−0.474046	−	1.30243i	0.440428	−	0.897788i	$-0.354827\pi$
$42$		0			0
$43$	−432.194	−	2451.10i	−0.233745	−	1.32563i	−0.845241	−	0.534385i	$-0.820543\pi$
$43$	−432.194	−	2451.10i	−0.233745	−	1.32563i	0.611496	−	0.791247i	$-0.290568\pi$
$44$	1649.89	+	952.564i	0.852215	+	0.492027i
$45$		0			0
$46$	142.284	+	246.443i	0.0672419	+	0.116466i
$47$	441.904	+	526.641i	0.200047	+	0.238407i	0.856737	−	0.515754i	$-0.172488\pi$
$47$	441.904	+	526.641i	0.200047	+	0.238407i	−0.656689	+	0.754161i	$0.728044\pi$
$48$		0			0
$49$	−268.253	+	1521.34i	−0.111726	+	0.633627i
$50$	345.919	−	412.250i	0.138368	−	0.164900i
$51$		0			0
$52$	−2355.23	−	857.235i	−0.871019	−	0.317025i
$53$		−	3259.62i		−	1.16042i	−0.814467	−	0.580210i	$-0.802971\pi$
$53$		−	3259.62i		−	1.16042i	0.814467	−	0.580210i	$-0.197029\pi$
$54$		0			0
$55$	2194.87			0.725577
$56$	−435.622	+	1196.86i	−0.138910	+	0.381653i
$57$		0			0
$58$	−1045.74	−	877.483i	−0.310863	−	0.260845i
$59$	−5572.36	−	982.557i	−1.60079	−	0.282263i	−0.699225	−	0.714901i	$-0.746472\pi$
$59$	−5572.36	−	982.557i	−1.60079	−	0.282263i	−0.901568	+	0.432638i	$0.857583\pi$
$60$		0			0
$61$	4765.70	−	3998.90i	1.28076	−	1.07468i	0.287619	−	0.957745i	$-0.407136\pi$
$61$	4765.70	−	3998.90i	1.28076	−	1.07468i	0.993139	−	0.116939i	$-0.0373081\pi$
$62$	−190.444	+	109.953i	−0.0495433	+	0.0286038i
$63$		0			0
$64$	−593.306	+	1027.64i	−0.144850	+	0.250888i
$65$	−2843.71	+	501.422i	−0.673067	+	0.118680i
$66$		0			0
$67$	−1895.82	+	690.021i	−0.422325	+	0.153714i	−0.544435	−	0.838803i	$-0.683256\pi$
$67$	−1895.82	+	690.021i	−0.422325	+	0.153714i	0.122110	+	0.992517i	$0.461034\pi$
$68$	1454.95	+	3997.44i	0.314652	+	0.864499i
$69$		0			0
$70$	118.353	+	671.214i	0.0241537	+	0.136982i
$71$	1215.38	+	701.697i	0.241098	+	0.139198i	0.615681	−	0.787995i	$-0.288881\pi$
$71$	1215.38	+	701.697i	0.241098	+	0.139198i	−0.374583	+	0.927193i	$0.622214\pi$
$72$		0			0
$73$	1186.68	+	2055.39i	0.222684	+	0.385699i	0.955622	−	0.294596i	$-0.0951850\pi$
$73$	1186.68	+	2055.39i	0.222684	+	0.385699i	−0.732938	+	0.680295i	$0.761852\pi$
$74$	1768.85	+	2108.04i	0.323019	+	0.384959i
$75$		0			0
$76$	−1076.09	+	6102.80i	−0.186303	+	1.05658i
$77$	2582.07	−	3077.19i	0.435498	−	0.519006i
$78$		0			0
$79$	−4163.44	−	1515.37i	−0.667112	−	0.242809i	−0.0138079	−	0.999905i	$-0.504395\pi$
$79$	−4163.44	−	1515.37i	−0.667112	−	0.242809i	−0.653304	+	0.757096i	$0.726618\pi$
$80$			2536.06i			0.396259i
$81$		0			0
$82$	3394.43			0.504822
$83$	−353.761	+	971.950i	−0.0513515	+	0.141087i	−0.962717	−	0.270511i	$-0.912807\pi$
$83$	−353.761	+	971.950i	−0.0513515	+	0.141087i	0.911365	+	0.411599i	$0.135029\pi$
$84$		0			0
$85$	3754.36	+	3150.28i	0.519634	+	0.436025i
$86$	3571.00	+	629.663i	0.482828	+	0.0851357i
$87$		0			0
$88$	−4577.64	+	3841.09i	−0.591121	+	0.496009i
$89$	11599.9	−	6697.21i	1.46445	−	0.845500i	0.465237	−	0.885186i	$-0.345969\pi$
$89$	11599.9	−	6697.21i	1.46445	−	0.845500i	0.999212	+	0.0396855i	$0.0126356\pi$
$90$		0			0
$91$	−2642.37	+	4576.73i	−0.319089	+	0.552678i
$92$	2669.42	−	470.691i	0.315385	−	0.0556109i
$93$		0			0
$94$	−941.187	+	342.564i	−0.106517	+	0.0387691i
$95$	2441.82	+	6708.86i	0.270562	+	0.743364i
$96$		0			0
$97$	1042.57	+	5912.70i	0.110806	+	0.628409i	0.988742	+	0.149632i	$0.0478088\pi$
$97$	1042.57	+	5912.70i	0.110806	+	0.628409i	−0.877936	+	0.478777i	$0.841080\pi$
$98$	−1949.10	−	1125.32i	−0.202947	−	0.117172i
$99$		0			0
$100$	−2563.05	−	4439.33i	−0.256305	−	0.443933i
$101$	−388.856	−	463.421i	−0.0381194	−	0.0454289i	0.746648	−	0.665219i	$-0.231662\pi$
$101$	−388.856	−	463.421i	−0.0381194	−	0.0454289i	−0.784767	+	0.619791i	$0.787218\pi$
$102$		0			0
$103$	2001.75	−	11352.5i	0.188684	−	1.07008i	−0.732446	−	0.680825i	$-0.761621\pi$
$103$	2001.75	−	11352.5i	0.188684	−	1.07008i	0.921130	−	0.389255i	$-0.127268\pi$
$104$	5053.35	−	6022.35i	0.467210	−	0.556800i
$105$		0			0
$106$	4462.54	+	1624.23i	0.397164	+	0.144556i
$107$			11288.2i			0.985958i	0.870041	+	0.492979i	$0.164092\pi$
$107$			11288.2i			0.985958i	−0.870041	+	0.492979i	$0.835908\pi$
$108$		0			0
$109$	−4850.97			−0.408297			−0.204148	−	0.978940i	$-0.565443\pi$
$109$	−4850.97			−0.408297			−0.204148	+	0.978940i	$0.565443\pi$
$110$	−1093.68	+	3004.86i	−0.0903868	+	0.248336i
$111$		0			0
$112$	3555.53	+	2983.44i	0.283445	+	0.237838i
$113$	−21485.0	−	3788.39i	−1.68259	−	0.296687i	−0.751031	−	0.660266i	$-0.770443\pi$
$113$	−21485.0	−	3788.39i	−1.68259	−	0.296687i	−0.931563	+	0.363580i	$0.881554\pi$
$114$		0			0
$115$	2392.24	−	2007.33i	0.180888	−	0.151783i
$116$	−11261.1	+	6501.61i	−0.836885	+	0.483176i
$117$		0			0
$118$	4121.80	−	7139.17i	0.296021	−	0.512724i
$119$	8833.32	−	1557.55i	0.623778	−	0.109989i
$120$		0			0
$121$	3951.81	−	1438.34i	0.269914	−	0.0982406i
$122$	3099.95	+	8517.03i	0.208274	+	0.572227i
$123$		0			0
$124$	363.737	+	2062.86i	0.0236562	+	0.134161i
$125$	−13768.3	−	7949.11i	−0.881169	−	0.508743i
$126$		0			0
$127$	−3768.41	−	6527.07i	−0.233642	−	0.404679i	0.725235	−	0.688501i	$-0.241731\pi$
$127$	−3768.41	−	6527.07i	−0.233642	−	0.404679i	−0.958877	+	0.283822i	$0.908398\pi$
$128$	−10650.7	−	12693.1i	−0.650069	−	0.774723i
$129$		0			0
$130$	730.522	−	4142.99i	0.0432261	−	0.245148i
$131$	12206.3	−	14546.9i	0.711283	−	0.847674i	−0.282470	−	0.959276i	$-0.591154\pi$
$131$	12206.3	−	14546.9i	0.711283	−	0.847674i	0.993753	+	0.111602i	$0.0355983\pi$
$132$		0			0
$133$	12278.3	+	4468.95i	0.694123	+	0.252640i
$134$		−	2939.27i		−	0.163693i
$135$		0			0
$136$	−13343.2			−0.721410
$137$	7245.41	−	19906.6i	0.386031	−	1.06061i	−0.582741	−	0.812658i	$-0.698020\pi$
$137$	7245.41	−	19906.6i	0.386031	−	1.06061i	0.968772	−	0.247953i	$-0.0797580\pi$
$138$		0			0
$139$	−21874.2	−	18354.6i	−1.13215	−	0.949983i	−0.132992	−	0.991117i	$-0.542458\pi$
$139$	−21874.2	−	18354.6i	−1.13215	−	0.949983i	−0.999154	+	0.0411346i	$0.986903\pi$
$140$	6393.53	+	1127.35i	0.326201	+	0.0575180i
$141$		0			0
$142$	−1566.26	+	1314.25i	−0.0776760	+	0.0651779i
$143$	−21472.6	+	12397.2i	−1.05005	+	0.606249i
$144$		0			0
$145$	−7490.42	+	12973.8i	−0.356263	+	0.617065i
$146$	−3405.22	+	600.432i	−0.159749	+	0.0281681i
$147$		0			0
$148$	24631.4	−	8965.11i	1.12452	−	0.409291i
$149$	14137.3	+	38842.0i	0.636788	+	1.74956i	0.661588	+	0.749867i	$0.269883\pi$
$149$	14137.3	+	38842.0i	0.636788	+	1.74956i	−0.0248007	+	0.999692i	$0.507895\pi$
$150$		0			0
$151$	2069.43	+	11736.3i	0.0907605	+	0.514729i	0.995964	+	0.0897507i	$0.0286070\pi$
$151$	2069.43	+	11736.3i	0.0907605	+	0.514729i	−0.905204	+	0.424978i	$0.860282\pi$
$152$	−16833.4	−	9718.77i	−0.728592	−	0.420653i
$153$		0			0
$154$	2926.17	+	5068.27i	0.123384	+	0.213707i
$155$	1551.21	+	1848.66i	0.0645664	+	0.0769473i
$156$		0			0
$157$	3842.31	−	21790.8i	0.155881	−	0.884044i	−0.802095	−	0.597196i	$-0.796281\pi$
$157$	3842.31	−	21790.8i	0.155881	−	0.884044i	0.957976	−	0.286848i	$-0.0926075\pi$
$158$	4149.20	−	4944.82i	0.166207	−	0.198078i
$159$		0			0
$160$	−13935.4	−	5072.06i	−0.544351	−	0.198127i
$161$		−	5715.33i		−	0.220490i
$162$		0			0
$163$	−13266.6			−0.499326			−0.249663	−	0.968333i	$-0.580320\pi$
$163$	−13266.6			−0.499326			−0.249663	+	0.968333i	$0.580320\pi$
$164$	11058.5	−	30383.1i	0.411160	−	1.12965i
$165$		0			0
$166$	−1154.36	−	968.623i	−0.0418914	−	0.0351511i
$167$	−18940.3	−	3339.69i	−0.679133	−	0.119750i	−0.176568	−	0.984289i	$-0.556499\pi$
$167$	−18940.3	−	3339.69i	−0.679133	−	0.119750i	−0.502566	+	0.864539i	$0.667611\pi$
$168$		0			0
$169$	3109.01	−	2608.77i	0.108855	−	0.0913402i
$170$	−6183.61	+	3570.11i	−0.213966	+	0.123533i
$171$		0			0
$172$	17269.8	−	29912.2i	0.583756	−	1.01109i
$173$	−4749.58	+	837.478i	−0.158695	+	0.0279822i	−0.252431	−	0.967615i	$-0.581230\pi$
$173$	−4749.58	+	837.478i	−0.158695	+	0.0279822i	0.0937362	+	0.995597i	$0.470119\pi$
$174$		0			0
$175$	−10156.6	+	3696.70i	−0.331644	+	0.120709i
$176$	7447.86	+	20462.8i	0.240440	+	0.660602i
$177$		0			0
$178$	3388.63	+	19217.9i	0.106951	+	0.606547i
$179$	31168.7	+	17995.3i	0.972777	+	0.561633i	0.900082	−	0.435721i	$-0.143507\pi$
$179$	31168.7	+	17995.3i	0.972777	+	0.561633i	0.0726950	+	0.997354i	$0.476840\pi$
$180$		0			0
$181$	6920.06	+	11985.9i	0.211229	+	0.365859i	0.952099	−	0.305789i	$-0.0989202\pi$
$181$	6920.06	+	11985.9i	0.211229	+	0.365859i	−0.740871	+	0.671648i	$0.765587\pi$
$182$	−4949.04	−	5898.04i	−0.149410	−	0.178059i
$183$		0			0
$184$	−1476.38	+	8372.99i	−0.0436077	+	0.247312i
$185$	19411.4	−	23133.6i	0.567170	−	0.675927i
$186$		0			0
$187$	39544.6	+	14393.1i	1.13085	+	0.411595i
$188$			9540.48i			0.269932i
$189$		0			0
$190$	−10401.4			−0.288128
$191$	−16685.8	+	45843.7i	−0.457382	+	1.25665i	0.470045	+	0.882643i	$0.344238\pi$
$191$	−16685.8	+	45843.7i	−0.457382	+	1.25665i	−0.927427	+	0.374005i	$0.877984\pi$
$192$		0			0
$193$	33312.1	+	27952.2i	0.894308	+	0.750414i	0.969070	−	0.246788i	$-0.0793751\pi$
$193$	33312.1	+	27952.2i	0.894308	+	0.750414i	−0.0747615	+	0.997201i	$0.523820\pi$
$194$	−8614.21	−	1518.92i	−0.228882	−	0.0403581i
$195$		0			0
$196$	−16422.5	+	13780.1i	−0.427490	+	0.358707i
$197$	27651.5	−	15964.6i	0.712503	−	0.411364i	−0.0994844	−	0.995039i	$-0.531719\pi$
$197$	27651.5	−	15964.6i	0.712503	−	0.411364i	0.811987	+	0.583676i	$0.198386\pi$
$198$		0			0
$199$	−31413.4	+	54409.7i	−0.793248	+	1.37395i	0.130697	+	0.991422i	$0.458278\pi$
$199$	−31413.4	+	54409.7i	−0.793248	+	1.37395i	−0.923946	+	0.382524i	$0.875055\pi$
$200$	15834.4	−	2792.03i	0.395860	−	0.0698008i
$201$		0			0
$202$	828.203	−	301.441i	0.0202971	−	0.00738754i
$203$	9377.32	+	25764.0i	0.227555	+	0.625203i
$204$		0			0
$205$	−6468.47	−	36684.5i	−0.153920	−	0.872922i
$206$	14544.5	+	8397.29i	0.342740	+	0.197881i
$207$		0			0
$208$	−14324.3	−	24810.4i	−0.331091	−	0.573466i
$209$	39404.9	+	46960.9i	0.902106	+	1.07509i
$210$		0			0
$211$	−7584.30	+	43012.7i	−0.170353	+	0.966122i	0.773018	+	0.634384i	$0.218746\pi$
$211$	−7584.30	+	43012.7i	−0.170353	+	0.966122i	−0.943372	+	0.331738i	$0.892365\pi$
$212$	29076.6	−	34652.2i	0.646952	−	0.771007i
$213$		0			0
$214$	−15454.0	−	5624.80i	−0.337453	−	0.122823i
$215$		−	39792.7i		−	0.860848i
$216$		0			0
$217$	4416.65			0.0937938
$218$	2417.19	−	6641.17i	0.0508624	−	0.139743i
$219$		0			0
$220$	23333.1	+	19578.8i	0.482089	+	0.404521i
$221$	−54522.7	−	9613.82i	−1.11633	−	0.196839i
$222$		0			0
$223$	−23877.6	+	20035.7i	−0.480154	+	0.402897i	−0.850482	−	0.526004i	$-0.823690\pi$
$223$	−23877.6	+	20035.7i	−0.480154	+	0.402897i	0.370328	+	0.928901i	$0.379245\pi$
$224$	−23504.7	+	13570.4i	−0.468445	+	0.270457i
$225$		0			0
$226$	15892.2	−	27526.1i	0.311148	−	0.538925i
$227$	−32744.2	+	5773.68i	−0.635452	+	0.112047i	−0.482088	−	0.876123i	$-0.660122\pi$
$227$	−32744.2	+	5773.68i	−0.635452	+	0.112047i	−0.153363	+	0.988170i	$0.549010\pi$
$228$		0			0
$229$	−38771.9	+	14111.8i	−0.739343	+	0.269099i	−0.684114	−	0.729375i	$-0.739811\pi$
$229$	−38771.9	+	14111.8i	−0.739343	+	0.269099i	−0.0552288	+	0.998474i	$0.517589\pi$
$230$	1556.08	+	4275.29i	0.0294155	+	0.0808184i
$231$		0			0
$232$	−7082.47	−	40166.7i	−0.131586	−	0.746260i
$233$	43183.6	+	24932.1i	0.795439	+	0.459247i	0.841874	−	0.539674i	$-0.181453\pi$
$233$	43183.6	+	24932.1i	0.795439	+	0.459247i	−0.0464346	+	0.998921i	$0.514786\pi$
$234$		0			0
$235$	5495.73	+	9518.88i	0.0995152	+	0.172365i
$236$	−50473.6	−	60152.2i	−0.906235	−	1.08001i
$237$		0			0
$238$	−2269.20	+	12869.3i	−0.0400607	+	0.227195i
$239$	−21620.3	+	25766.1i	−0.378500	+	0.451079i	−0.921340	−	0.388757i	$-0.872904\pi$
$239$	−21620.3	+	25766.1i	−0.378500	+	0.451079i	0.542840	+	0.839836i	$0.317349\pi$
$240$		0			0
$241$	−106.015	−	38.5864i	−0.00182530	−	0.000664355i	0.341107	−	0.940024i	$-0.389198\pi$
$241$	−106.015	−	38.5864i	−0.00182530	−	0.000664355i	−0.342933	+	0.939360i	$0.611420\pi$
$242$			6126.88i			0.104619i
$243$		0			0
$244$	86334.1			1.45012
$245$	−8447.36	+	23208.9i	−0.140731	+	0.386654i
$246$		0			0
$247$	−61781.9	−	51841.1i	−1.01267	−	0.849729i
$248$	−6470.42	−	1140.91i	−0.105203	−	0.0185502i
$249$		0			0
$250$	17743.2	−	14888.3i	0.283891	−	0.238213i
$251$	24335.7	−	14050.2i	0.386274	−	0.223016i	−0.294270	−	0.955722i	$-0.595077\pi$
$251$	24335.7	−	14050.2i	0.386274	−	0.223016i	0.680545	+	0.732707i	$0.261743\pi$
$252$		0			0
$253$	13407.3	−	23222.1i	0.209459	−	0.362794i
$254$	10813.6	−	1906.72i	0.167610	−	0.0295543i
$255$		0			0
$256$	4843.61	−	1762.93i	0.0739075	−	0.0269001i
$257$	−28525.6	−	78373.3i	−0.431885	−	1.18659i	−0.944654	−	0.328067i	$-0.893603\pi$
$257$	−28525.6	−	78373.3i	−0.431885	−	1.18659i	0.512770	−	0.858526i	$-0.328620\pi$
$258$		0			0
$259$	−9597.33	−	54429.1i	−0.143071	−	0.811394i
$260$	−34703.5	−	20036.1i	−0.513366	−	0.296392i
$261$		0			0
$262$	13833.0	+	23959.5i	0.201518	+	0.349040i
$263$	36920.4	+	44000.0i	0.533771	+	0.636123i	0.963779	−	0.266702i	$-0.0859339\pi$
$263$	36920.4	+	44000.0i	0.533771	+	0.636123i	−0.430008	+	0.902825i	$0.641489\pi$
$264$		0			0
$265$	9049.65	−	51323.1i	0.128866	−	0.730838i
$266$	−12236.3	+	14582.7i	−0.172937	+	0.206098i
$267$		0			0
$268$	−26309.1	−	9575.73i	−0.366300	−	0.133322i
$269$		−	59862.8i		−	0.827280i	−0.910441	−	0.413640i	$-0.864257\pi$
$269$		−	59862.8i		−	0.827280i	0.910441	−	0.413640i	$-0.135743\pi$
$270$		0			0
$271$	64524.3			0.878587			0.439293	−	0.898344i	$-0.355229\pi$
$271$	64524.3			0.878587			0.439293	+	0.898344i	$0.355229\pi$
$272$	−16630.4	+	45691.8i	−0.224784	+	0.617590i
$273$		0			0
$274$	23642.6	+	19838.5i	0.314915	+	0.264245i
$275$	−49939.4	−	8805.66i	−0.660356	−	0.116439i
$276$		0			0
$277$	76081.9	−	63840.3i	0.991566	−	0.832023i	0.00577230	−	0.999983i	$-0.498163\pi$
$277$	76081.9	−	63840.3i	0.991566	−	0.832023i	0.985794	+	0.167961i	$0.0537182\pi$
$278$	36027.8	−	20800.7i	0.466174	−	0.269146i
$279$		0			0
$280$	−10181.8	+	17635.3i	−0.129869	+	0.224940i
$281$	−33494.2	+	5905.93i	−0.424187	+	0.0747956i	−0.381667	−	0.924300i	$-0.624650\pi$
$281$	−33494.2	+	5905.93i	−0.424187	+	0.0747956i	−0.0425202	+	0.999096i	$0.513539\pi$
$282$		0			0
$283$	−51574.7	+	18771.6i	−0.643967	+	0.234385i	−0.643299	−	0.765615i	$-0.722435\pi$
$283$	−51574.7	+	18771.6i	−0.643967	+	0.234385i	−0.000667793		1.00000i	$0.500213\pi$
$284$	6661.02	+	18301.0i	0.0825856	+	0.226902i
$285$		0			0
$286$	−6272.68	−	35574.1i	−0.0766869	−	0.434913i
$287$	−59040.9	−	34087.3i	−0.716785	−	0.413836i
$288$		0			0
$289$	5222.86	+	9046.27i	0.0625335	+	0.108311i
$290$	−14029.2	−	16719.4i	−0.166816	−	0.198803i
$291$		0			0
$292$	−5719.31	+	32435.8i	−0.0670776	+	0.380416i
$293$	40639.7	−	48432.6i	0.473386	−	0.564160i	−0.475525	−	0.879702i	$-0.657742\pi$
$293$	40639.7	−	48432.6i	0.473386	−	0.564160i	0.948912	+	0.315542i	$0.102186\pi$
$294$		0			0
$295$	−85009.6	−	30941.0i	−0.976841	−	0.355541i
$296$			82218.1i			0.938392i
$297$		0			0
$298$	−60220.6			−0.678129
$299$	−12065.5	+	33149.8i	−0.134960	+	0.370799i
$300$		0			0
$301$	−55788.9	−	46812.5i	−0.615765	−	0.516688i
$302$	−17098.6	−	3014.95i	−0.187477	−	0.0330572i
$303$		0			0
$304$	−54260.9	+	45530.3i	−0.587138	+	0.492667i
$305$	86138.6	−	49732.2i	0.925973	−	0.534611i
$306$		0			0
$307$	29615.8	−	51296.1i	0.314229	−	0.544261i	−0.665044	−	0.746804i	$-0.731587\pi$
$307$	29615.8	−	51296.1i	0.314229	−	0.544261i	0.979273	+	0.202543i	$0.0649206\pi$
$308$	54898.6	−	9680.10i	0.578708	−	0.102042i
$309$		0			0
$310$	−3303.83	+	1202.50i	−0.0343791	+	0.0125130i
$311$	−39880.8	−	109571.i	−0.412328	−	1.13286i	−0.955950	−	0.293531i	$-0.905170\pi$
$311$	−39880.8	−	109571.i	−0.412328	−	1.13286i	0.543622	−	0.839330i	$-0.317053\pi$
$312$		0			0
$313$	16845.6	+	95536.1i	0.171948	+	0.975167i	0.941608	+	0.336712i	$0.109315\pi$
$313$	16845.6	+	95536.1i	0.171948	+	0.975167i	−0.769660	+	0.638455i	$0.779574\pi$
$314$	27917.8	+	16118.4i	0.283154	+	0.163479i
$315$		0			0
$316$	−30743.0	−	53248.5i	−0.307873	−	0.533252i
$317$	29494.1	+	35149.7i	0.293506	+	0.349787i	0.892566	−	0.450918i	$-0.148903\pi$
$317$	29494.1	+	35149.7i	0.293506	+	0.349787i	−0.599060	+	0.800704i	$0.704459\pi$
$318$		0			0
$319$	−22337.1	+	126680.i	−0.219505	+	1.24488i
$320$	−12194.7	+	14533.1i	−0.119089	+	0.141924i
$321$		0			0
$322$	7824.50	+	2847.89i	0.0754649	+	0.0274670i
$323$			136885.i			1.31205i
$324$		0			0
$325$	66713.9			0.631610
$326$	6610.59	−	18162.5i	0.0622021	−	0.170899i
$327$		0			0
$328$	77689.8	+	65189.4i	0.722131	+	0.605940i
$329$	19810.6	+	3493.14i	0.183023	+	0.0322719i
$330$		0			0
$331$	−33632.3	+	28220.8i	−0.306973	+	0.257581i	−0.783240	−	0.621720i	$-0.786434\pi$
$331$	−33632.3	+	28220.8i	−0.306973	+	0.257581i	0.476266	+	0.879301i	$0.341990\pi$
$332$	−12430.8	+	7176.91i	−0.112777	+	0.0651120i
$333$		0			0
$334$	14009.9	−	24265.9i	0.125587	−	0.217522i
$335$	−31765.6	+	5601.13i	−0.283053	+	0.0499098i
$336$		0			0
$337$	115383.	−	41995.9i	1.01597	−	0.369783i	0.220247	−	0.975444i	$-0.429314\pi$
$337$	115383.	−	41995.9i	1.01597	−	0.369783i	0.795723	+	0.605661i	$0.207091\pi$
$338$	2022.32	+	5556.27i	0.0177017	+	0.0486351i
$339$		0			0
$340$	11810.3	+	66979.6i	0.102165	+	0.579408i
$341$	17945.4	+	10360.8i	0.154328	+	0.0891013i
$342$		0			0
$343$	57728.7	+	99989.0i	0.490685	+	0.849892i
$344$	69638.5	+	82991.9i	0.588481	+	0.701324i
$345$		0			0
$346$	1220.12	−	6919.65i	0.0101918	−	0.0578006i
$347$	−89906.6	+	107146.i	−0.746676	+	0.889854i	−0.996928	−	0.0783266i	$-0.975042\pi$
$347$	−89906.6	+	107146.i	−0.746676	+	0.889854i	0.250251	+	0.968181i	$0.419487\pi$
$348$		0			0
$349$	139266.	+	50688.6i	1.14339	+	0.416159i	0.843136	−	0.537701i	$-0.180707\pi$
$349$	139266.	+	50688.6i	1.14339	+	0.416159i	0.300252	+	0.953860i	$0.402929\pi$
$350$		−	15746.8i		−	0.128545i
$351$		0			0
$352$	−127336.			−1.02770
$353$	45329.9	−	124543.i	0.363777	−	0.999470i	−0.613905	−	0.789380i	$-0.710402\pi$
$353$	45329.9	−	124543.i	0.363777	−	0.999470i	0.977682	−	0.210090i	$-0.0673756\pi$
$354$		0			0
$355$	17188.1	+	14422.5i	0.136387	+	0.114442i
$356$	183056.	+	32277.8i	1.44439	+	0.254685i
$357$		0			0
$358$	−40167.2	+	33704.3i	−0.313405	+	0.262978i
$359$	−46823.5	+	27033.6i	−0.363308	+	0.209756i	−0.670531	−	0.741882i	$-0.733934\pi$
$359$	−46823.5	+	27033.6i	−0.363308	+	0.209756i	0.307223	+	0.951638i	$0.400600\pi$
$360$		0			0
$361$	−34542.1	+	59828.7i	−0.265054	+	0.459087i
$362$	−19857.3	+	3501.38i	−0.151532	+	0.0267191i
$363$		0			0
$364$	−68915.9	+	25083.3i	−0.520136	+	0.189314i
$365$	12978.1	+	35656.9i	0.0974147	+	0.267645i
$366$		0			0
$367$	−7934.90	−	45001.0i	−0.0589127	−	0.334111i	0.941079	−	0.338187i	$-0.109814\pi$
$367$	−7934.90	−	45001.0i	−0.0589127	−	0.334111i	−0.999992	+	0.00407616i	$0.998703\pi$
$368$	26831.9	+	15491.4i	0.198133	+	0.114392i
$369$		0			0
$370$	21998.3	+	38102.1i	0.160689	+	0.278321i
$371$	−61308.4	−	73064.5i	−0.445422	−	0.530834i
$372$		0			0
$373$	30077.1	−	170576.i	0.216182	−	1.22603i	−0.662663	−	0.748918i	$-0.730574\pi$
$373$	30077.1	−	170576.i	0.216182	−	1.22603i	0.878844	−	0.477109i	$-0.158315\pi$
$374$	−39409.3	+	46966.2i	−0.281744	+	0.335770i
$375$		0			0
$376$	−28120.3	−	10234.9i	−0.198904	−	0.0723952i
$377$		−	169231.i		−	1.19069i
$378$		0			0
$379$	−113547.			−0.790489			−0.395245	−	0.918576i	$-0.629340\pi$
$379$	−113547.			−0.790489			−0.395245	+	0.918576i	$0.629340\pi$
$380$	−33886.3	+	93101.8i	−0.234670	+	0.644749i
$381$		0			0
$382$	−54447.5	−	45686.9i	−0.373122	−	0.313087i
$383$	279819.	+	49339.6i	1.90756	+	0.336355i	0.997026	−	0.0770705i	$-0.0245567\pi$
$383$	279819.	+	49339.6i	1.90756	+	0.336355i	0.910538	+	0.413425i	$0.135668\pi$
$384$		0			0
$385$	49198.1	−	41282.1i	0.331915	−	0.278510i
$386$	−54866.6	+	31677.2i	−0.368242	+	0.212605i
$387$		0			0
$388$	−41659.5	+	72156.4i	−0.276726	+	0.479304i
$389$	2674.74	−	471.628i	0.0176759	−	0.00311674i	−0.164803	−	0.986326i	$-0.552699\pi$
$389$	2674.74	−	471.628i	0.0176759	−	0.00311674i	0.182479	+	0.983210i	$0.441588\pi$
$390$		0			0
$391$	56263.8	−	20478.3i	0.368023	−	0.133950i
$392$	−22998.5	−	63187.8i	−0.149667	−	0.411208i
$393$		0			0
$394$	8077.70	+	45810.9i	0.0520350	+	0.295105i
$395$	−61346.8	−	35418.6i	−0.393186	−	0.227006i
$396$		0			0
$397$	−96669.3	−	167436.i	−0.613349	−	1.06235i	−0.990672	−	0.136270i	$-0.956489\pi$
$397$	−96669.3	−	167436.i	−0.613349	−	1.06235i	0.377323	−	0.926082i	$-0.376845\pi$
$398$	−58835.9	−	70117.9i	−0.371429	−	0.442652i
$399$		0			0
$400$	10174.5	−	57702.4i	0.0635905	−	0.360640i
$401$	−59374.0	+	70759.2i	−0.369239	+	0.440042i	−0.918387	−	0.395683i	$-0.870508\pi$
$401$	−59374.0	+	70759.2i	−0.369239	+	0.440042i	0.549148	+	0.835725i	$0.314952\pi$
$402$		0			0
$403$	−25617.3	−	9323.92i	−0.157733	−	0.0574101i
$404$		−	8395.20i		−	0.0514361i
$405$		0			0
$406$	−39944.5			−0.242329
$407$	88687.2	−	243666.i	0.535392	−	1.47098i
$408$		0			0
$409$	58067.9	+	48724.7i	0.347128	+	0.291275i	0.799636	−	0.600486i	$-0.205026\pi$
$409$	58067.9	+	48724.7i	0.347128	+	0.291275i	−0.452508	+	0.891760i	$0.649471\pi$
$410$	53445.7	+	9423.91i	0.317940	+	0.0560613i
$411$		0			0
$412$	122547.	−	102829.i	0.721952	−	0.605790i
$413$	−143385.	+	82783.4i	−0.840628	+	0.485337i
$414$		0			0
$415$	−8268.42	+	14321.3i	−0.0480094	+	0.0831547i
$416$	164979.	−	29090.2i	0.953327	−	0.168097i
$417$		0			0
$418$	−83926.3	+	30546.7i	−0.480336	+	0.174828i
$419$	24747.6	+	67993.5i	0.140963	+	0.387293i	0.990005	−	0.141033i	$-0.0450423\pi$
$419$	24747.6	+	67993.5i	0.140963	+	0.387293i	−0.849042	+	0.528325i	$0.822820\pi$
$420$		0			0
$421$	38184.0	+	216552.i	0.215436	+	1.22180i	0.880149	+	0.474697i	$0.157442\pi$
$421$	38184.0	+	216552.i	0.215436	+	1.22180i	−0.664714	+	0.747098i	$0.731446\pi$
$422$	−55106.9	−	31816.0i	−0.309443	−	0.178657i
$423$		0			0
$424$	70943.0	+	122877.i	0.394619	+	0.683500i
$425$	−72783.3	−	86739.8i	−0.402953	−	0.480220i
$426$		0			0
$427$	31610.3	−	179271.i	0.173370	−	0.983227i
$428$	−100694.	+	120002.i	−0.549687	+	0.655092i
$429$		0			0
$430$	54477.7	+	19828.3i	0.294633	+	0.107238i
$431$			61615.0i			0.331690i	0.986152	+	0.165845i	$0.0530351\pi$
$431$			61615.0i			0.331690i	−0.986152	+	0.165845i	$0.946965\pi$
$432$		0			0
$433$	−81033.3			−0.432203			−0.216102	−	0.976371i	$-0.569334\pi$
$433$	−81033.3			−0.432203			−0.216102	+	0.976371i	$0.569334\pi$
$434$	−2200.77	+	6046.57i	−0.0116841	+	0.0321018i
$435$		0			0
$436$	−51569.4	−	43271.9i	−0.271281	−	0.227632i
$437$	85896.6	+	15145.9i	0.449793	+	0.0793107i
$438$		0			0
$439$	89923.6	−	75454.9i	0.466600	−	0.391524i	−0.378953	−	0.925416i	$-0.623716\pi$
$439$	89923.6	−	75454.9i	0.466600	−	0.391524i	0.845553	+	0.533892i	$0.179271\pi$
$440$	−82739.5	+	47769.7i	−0.427373	+	0.246744i
$441$		0			0
$442$	40329.7	−	69853.1i	0.206434	−	0.357554i
$443$	−111680.	+	19692.1i	−0.569072	+	0.100343i	−0.450778	−	0.892636i	$-0.648853\pi$
$443$	−111680.	+	19692.1i	−0.569072	+	0.100343i	−0.118293	+	0.992979i	$0.537742\pi$
$444$		0			0
$445$	201235.	−	73243.7i	1.01621	−	0.369871i
$446$	−15531.6	−	42672.8i	−0.0780814	−	0.214527i
$447$		0			0
$448$	6029.26	+	34193.7i	0.0300406	+	0.170369i
$449$	−143134.	−	82638.4i	−0.709986	−	0.409911i	0.101070	−	0.994879i	$-0.467774\pi$
$449$	−143134.	−	82638.4i	−0.709986	−	0.409911i	−0.811056	+	0.584968i	$0.801107\pi$
$450$		0			0
$451$	−159927.	−	277001.i	−0.786264	−	1.36185i
$452$	−194609.	−	231925.i	−0.952544	−	1.13520i
$453$		0			0
$454$	8411.68	−	47705.0i	0.0408104	−	0.231447i
$455$	−54310.8	+	64725.1i	−0.262339	+	0.312644i
$456$		0			0
$457$	−113660.	−	41368.8i	−0.544220	−	0.198080i	0.0552568	−	0.998472i	$-0.482402\pi$
$457$	−113660.	−	41368.8i	−0.544220	−	0.198080i	−0.599476	+	0.800392i	$0.704624\pi$
$458$		−	60111.9i		−	0.286569i
$459$		0			0
$460$	43337.1			0.204807
$461$	2026.76	−	5568.48i	0.00953676	−	0.0262020i	−0.934833	−	0.355088i	$-0.884451\pi$
$461$	2026.76	−	5568.48i	0.00953676	−	0.0262020i	0.944370	+	0.328886i	$0.106673\pi$
$462$		0			0
$463$	−28407.1	−	23836.4i	−0.132515	−	0.111193i	0.574121	−	0.818770i	$-0.305344\pi$
$463$	−28407.1	−	23836.4i	−0.132515	−	0.111193i	−0.706636	+	0.707577i	$0.749788\pi$
$464$	−146372.	−	25809.3i	−0.679864	−	0.119878i
$465$		0			0
$466$	−55650.8	+	46696.6i	−0.256271	+	0.215037i
$467$	−125686.	+	72564.8i	−0.576306	+	0.332730i	−0.759664	−	0.650316i	$-0.774637\pi$
$467$	−125686.	+	72564.8i	−0.576306	+	0.332730i	0.183358	+	0.983046i	$0.441303\pi$
$468$		0			0
$469$	−29516.6	+	51124.2i	−0.134190	+	0.232424i
$470$	−15770.2	+	2780.71i	−0.0713905	+	0.0125881i
$471$		0			0
$472$	231444.	−	84238.8i	1.03887	−	0.378119i
$473$	−116862.	−	321077.i	−0.522339	−	1.43512i
$474$		0			0
$475$	−28642.8	−	162441.i	−0.126949	−	0.719962i
$476$	107798.	+	62237.5i	0.475772	+	0.274687i
$477$		0			0
$478$	−24501.6	−	42437.9i	−0.107235	−	0.185737i
$479$	186476.	+	222233.i	0.812740	+	0.968586i	0.999906	−	0.0137428i	$-0.00437459\pi$
$479$	186476.	+	222233.i	0.812740	+	0.968586i	−0.187166	+	0.982328i	$0.559930\pi$
$480$		0			0
$481$	−59238.4	+	335958.i	−0.256043	+	1.45209i
$482$	105.653	−	125.912i	0.000454764	−	0.000541966i
$483$		0			0
$484$	54841.0	+	19960.5i	0.234107	+	0.0852081i
$485$			95990.7i			0.408080i
$486$		0			0
$487$	36077.7			0.152118			0.0760591	−	0.997103i	$-0.475766\pi$
$487$	36077.7			0.152118			0.0760591	+	0.997103i	$0.475766\pi$
$488$	−92618.4	+	254467.i	−0.388918	+	1.06854i
$489$		0			0
$490$	−27564.7	−	23129.5i	−0.114805	−	0.0963328i
$491$	354380.	+	62486.7i	1.46996	+	0.259194i	0.850559	−	0.525879i	$-0.176264\pi$
$491$	354380.	+	62486.7i	1.46996	+	0.259194i	0.619403	+	0.785073i	$0.287375\pi$
$492$		0			0
$493$	−220030.	+	184627.i	−0.905292	+	0.759631i
$494$	101758.	−	58749.8i	0.416978	−	0.240742i
$495$		0			0
$496$	−11971.3	+	20735.0i	−0.0486609	+	0.0842831i
$497$	40440.5	−	7130.75i	0.163721	−	0.0288684i
$498$		0			0
$499$	−224040.	+	81543.8i	−0.899754	+	0.327484i	−0.750154	−	0.661263i	$-0.770021\pi$
$499$	−224040.	+	81543.8i	−0.899754	+	0.327484i	−0.149600	+	0.988747i	$0.547799\pi$
$500$	−75458.8	−	207321.i	−0.301835	−	0.829285i
$501$		0			0
$502$	7109.06	+	40317.5i	0.0282101	+	0.159988i
$503$	270952.	+	156434.i	1.07092	+	0.618295i	0.928432	−	0.371502i	$-0.121157\pi$
$503$	270952.	+	156434.i	1.07092	+	0.618295i	0.142486	+	0.989797i	$0.454490\pi$
$504$		0			0
$505$	−4836.00	−	8376.19i	−0.0189628	−	0.0328446i
$506$	25111.2	+	29926.4i	0.0980769	+	0.116883i
$507$		0			0
$508$	18162.2	−	103003.i	0.0703785	−	0.399136i
$509$	−92146.9	+	109816.i	−0.355668	+	0.423869i	−0.913978	−	0.405764i	$-0.867006\pi$
$509$	−92146.9	+	109816.i	−0.355668	+	0.423869i	0.558310	+	0.829633i	$0.311450\pi$
$510$		0			0
$511$	65258.2	+	23752.0i	0.249916	+	0.0909618i
$512$		−	257604.i		−	0.982682i
$513$		0			0
$514$	121510.			0.459924
$515$	63035.6	−	173189.i	0.237668	−	0.652988i
$516$		0			0
$517$	72298.5	+	60665.6i	0.270488	+	0.226966i
$518$	79297.8	+	13982.3i	0.295530	+	0.0521099i
$519$		0			0
$520$	96285.4	−	80793.0i	0.356085	−	0.298791i
$521$	96772.6	−	55871.7i	0.356514	−	0.205834i	−0.311036	−	0.950398i	$-0.600676\pi$
$521$	96772.6	−	55871.7i	0.356514	−	0.205834i	0.667551	+	0.744564i	$0.267343\pi$
$522$		0			0
$523$	−60888.2	+	105461.i	−0.222602	+	0.385559i	−0.955597	−	0.294675i	$-0.904789\pi$
$523$	−60888.2	+	105461.i	−0.222602	+	0.385559i	0.732995	+	0.680234i	$0.238122\pi$
$524$	259525.	−	45761.2i	0.945183	−	0.166661i
$525$		0			0
$526$	−78634.7	+	28620.7i	−0.284212	+	0.103445i
$527$	15825.1	+	43479.1i	0.0569804	+	0.156552i
$528$		0			0
$529$	41968.9	+	238018.i	0.149974	+	0.850546i
$530$	65753.9	+	37963.0i	0.234083	+	0.135148i
$531$		0			0
$532$	90663.6	+	157034.i	0.320339	+	0.554844i
$533$	270485.	+	322351.i	0.952113	+	1.13468i
$534$		0			0
$535$	−31339.4	+	177735.i	−0.109492	+	0.620961i
$536$	56448.3	−	67272.5i	0.196481	−	0.234157i
$537$		0			0
$538$	81954.4	+	29829.0i	0.283144	+	0.103056i
$539$			212075.i			0.729981i
$540$		0			0
$541$	301102.			1.02877			0.514386	−	0.857559i	$-0.328020\pi$
$541$	301102.			1.02877			0.514386	+	0.857559i	$0.328020\pi$
$542$	−32151.7	+	88336.1i	−0.109447	+	0.300704i
$543$		0			0
$544$	−217811.	−	182765.i	−0.736006	−	0.617583i
$545$	−76379.2	−	13467.7i	−0.257147	−	0.0453420i
$546$		0			0
$547$	−208316.	+	174798.i	−0.696223	+	0.584201i	−0.920696	−	0.390280i	$-0.872378\pi$
$547$	−208316.	+	174798.i	−0.696223	+	0.584201i	0.224473	+	0.974480i	$0.427934\pi$
$548$	254596.	−	146991.i	0.847794	−	0.489474i
$549$		0			0
$550$	36939.5	−	63981.1i	0.122114	−	0.211508i
$551$	−412061.	+	72657.4i	−1.35724	+	0.239319i
$552$		0			0
$553$	−121825.	+	44340.8i	−0.398371	+	0.144995i
$554$	49489.0	+	135970.i	0.161246	+	0.443020i
$555$		0			0
$556$	−68810.9	−	390246.i	−0.222591	−	1.26238i
$557$	−79557.6	−	45932.6i	−0.256432	−	0.148051i	0.366274	−	0.930507i	$-0.380633\pi$
$557$	−79557.6	−	45932.6i	−0.256432	−	0.148051i	−0.622706	+	0.782456i	$0.713967\pi$
$558$		0			0
$559$	224759.	+	389294.i	0.719273	+	1.24582i
$560$	47699.4	+	56845.9i	0.152103	+	0.181269i
$561$		0			0
$562$	8604.35	−	48797.7i	0.0272424	−	0.154499i
$563$	−20835.2	+	24830.5i	−0.0657328	+	0.0783373i	−0.797909	−	0.602778i	$-0.794060\pi$
$563$	−20835.2	+	24830.5i	−0.0657328	+	0.0783373i	0.732176	+	0.681115i	$0.238505\pi$
$564$		0			0
$565$	−327767.	−	119297.i	−1.02676	−	0.373710i
$566$		−	79961.3i		−	0.249602i
$567$		0			0
$568$	−61087.6			−0.189346
$569$	22923.8	−	62982.7i	0.0708048	−	0.194535i	−0.899243	−	0.437450i	$-0.855882\pi$
$569$	22923.8	−	62982.7i	0.0708048	−	0.194535i	0.970047	+	0.242916i	$0.0781038\pi$
$570$		0			0
$571$	345064.	+	289543.i	1.05834	+	0.888057i	0.993946	−	0.109868i	$-0.0350427\pi$
$571$	345064.	+	289543.i	1.05834	+	0.888057i	0.0643983	+	0.997924i	$0.479487\pi$
$572$	−338855.	−	59749.3i	−1.03567	−	0.182617i
$573$		0			0
$574$	76086.2	−	63843.9i	0.230931	−	0.193774i
$575$	−62483.3	+	36074.8i	−0.188985	+	0.109111i
$576$		0			0
$577$	124686.	−	215962.i	0.374511	−	0.648672i	−0.615743	−	0.787947i	$-0.711144\pi$
$577$	124686.	−	215962.i	0.374511	−	0.648672i	0.990254	+	0.139275i	$0.0444773\pi$
$578$	−14987.2	+	2642.64i	−0.0448605	+	0.00791012i
$579$		0			0
$580$	−195358.	+	71104.6i	−0.580732	+	0.211369i
$581$	10351.3	+	28440.0i	0.0306650	+	0.0842514i
$582$		0			0
$583$	−77705.5	−	440690.i	−0.228620	−	1.29657i
$584$	−89467.9	−	51654.3i	−0.262326	−	0.151454i
$585$		0			0
$586$	46055.6	+	79770.7i	0.134118	+	0.232300i
$587$	−221146.	−	263552.i	−0.641806	−	0.764875i	0.342848	−	0.939391i	$-0.388608\pi$
$587$	−221146.	−	263552.i	−0.641806	−	0.764875i	−0.984654	+	0.174516i	$0.944164\pi$
$588$		0			0
$589$	−11704.3	+	66378.5i	−0.0337377	+	0.191336i
$590$	84718.7	−	100964.i	0.243375	−	0.290043i
$591$		0			0
$592$	281543.	+	102473.i	0.803345	+	0.292394i
$593$			358704.i			1.02006i	0.860156	+	0.510032i	$0.170366\pi$
$593$			358704.i			1.02006i	−0.860156	+	0.510032i	$0.829634\pi$
$594$		0			0
$595$	143406.			0.405073
$596$	−196190.	+	539027.i	−0.552312	+	1.51746i
$597$		0			0
$598$	−39371.2	−	33036.3i	−0.110097	−	0.0923825i
$599$	125950.	+	22208.3i	0.351029	+	0.0618960i	0.346383	−	0.938093i	$-0.387410\pi$
$599$	125950.	+	22208.3i	0.351029	+	0.0618960i	0.00464659	+	0.999989i	$0.498521\pi$
$600$		0			0
$601$	−6649.24	+	5579.38i	−0.0184087	+	0.0154467i	−0.651946	−	0.758266i	$-0.726047\pi$
$601$	−6649.24	+	5579.38i	−0.0184087	+	0.0154467i	0.633537	+	0.773713i	$0.281603\pi$
$602$	91887.0	−	53051.0i	0.253549	−	0.146386i
$603$		0			0
$604$	−82691.4	+	143226.i	−0.226666	+	0.392597i
$605$	66215.0	−	11675.5i	0.180903	−	0.0318981i
$606$		0			0
$607$	−249490.	+	90806.9i	−0.677135	+	0.246457i	−0.657617	−	0.753352i	$-0.728435\pi$
$607$	−249490.	+	90806.9i	−0.677135	+	0.246457i	−0.0195183	+	0.999810i	$0.506213\pi$
$608$	−141664.	−	389217.i	−0.383222	−	1.05290i
$609$		0			0
$610$	25163.3	+	142708.i	0.0676250	+	0.383521i
$611$	−107530.	−	62082.5i	−0.288037	−	0.166298i
$612$		0			0
$613$	−46414.5	−	80392.3i	−0.123519	−	0.213941i	0.797634	−	0.603142i	$-0.206085\pi$
$613$	−46414.5	−	80392.3i	−0.123519	−	0.213941i	−0.921153	+	0.389201i	$0.872751\pi$
$614$	55469.0	+	66105.4i	0.147134	+	0.175348i
$615$		0			0
$616$	−30362.9	+	172197.i	−0.0800169	+	0.453798i
$617$	−200519.	+	238970.i	−0.526727	+	0.627729i	−0.962158	−	0.272493i	$-0.912152\pi$
$617$	−200519.	+	238970.i	−0.526727	+	0.627729i	0.435430	+	0.900222i	$0.356596\pi$
$618$		0			0
$619$	−184160.	−	67028.8i	−0.480634	−	0.174936i	0.0903294	−	0.995912i	$-0.471208\pi$
$619$	−184160.	−	67028.8i	−0.480634	−	0.174936i	−0.570963	+	0.820975i	$0.693430\pi$
$620$			33489.8i			0.0871222i
$621$		0			0
$622$	169880.			0.439097
$623$	134048.	−	368294.i	0.345370	−	0.948897i
$624$		0			0
$625$	−17861.4	−	14987.5i	−0.0457252	−	0.0383680i
$626$	−139186.	−	24542.3i	−0.355180	−	0.0626278i
$627$		0			0
$628$	235226.	−	197378.i	0.596439	−	0.500472i
$629$	501432.	−	289502.i	1.26739	−	0.731729i
$630$		0			0
$631$	234657.	−	406439.i	0.589353	−	1.02079i	−0.404964	−	0.914333i	$-0.632716\pi$
$631$	234657.	−	406439.i	0.589353	−	1.02079i	0.994317	−	0.106457i	$-0.0339507\pi$
$632$	189929.	−	33489.6i	0.475507	−	0.0838448i
$633$		0			0
$634$	−62817.9	+	22863.8i	−0.156280	+	0.0568814i
$635$	−41213.0	−	113232.i	−0.102208	−	0.280815i
$636$		0			0
$637$	−48448.9	−	274767.i	−0.119400	−	0.677152i
$638$	−162299.	−	93703.5i	−0.398726	−	0.230205i
$639$		0			0
$640$	−132458.	−	229423.i	−0.323383	−	0.560115i
$641$	235723.	+	280924.i	0.573703	+	0.683712i	0.972386	−	0.233376i	$-0.0749774\pi$
$641$	235723.	+	280924.i	0.573703	+	0.683712i	−0.398684	+	0.917088i	$0.630533\pi$
$642$		0			0
$643$	−44811.0	+	254136.i	−0.108383	+	0.614672i	0.881432	+	0.472312i	$0.156580\pi$
$643$	−44811.0	+	254136.i	−0.108383	+	0.614672i	−0.989815	+	0.142360i	$0.954531\pi$
$644$	50982.2	−	60758.2i	0.122927	−	0.146499i
$645$		0			0
$646$	−187400.	−	68208.2i	−0.449061	−	0.163445i
$647$		−	376550.i		−	0.899527i	−0.893148	−	0.449763i	$-0.851508\pi$
$647$		−	376550.i		−	0.899527i	0.893148	−	0.449763i	$-0.148492\pi$
$648$		0			0
$649$	−776787.			−1.84422
$650$	−33242.8	+	91333.8i	−0.0786811	+	0.216175i
$651$		0			0
$652$	−141034.	−	118341.i	−0.331763	−	0.278382i
$653$	−655412.	−	115567.i	−1.53705	−	0.271023i	−0.659941	−	0.751317i	$-0.729419\pi$
$653$	−655412.	−	115567.i	−1.53705	−	0.271023i	−0.877108	+	0.480294i	$0.840530\pi$
$654$		0			0
$655$	232577.	−	195155.i	0.542105	−	0.454880i
$656$	320061.	−	184787.i	0.743746	−	0.429402i
$657$		0			0
$658$	−14653.6	+	25380.9i	−0.0338450	+	0.0586212i
$659$	−540148.	+	95242.6i	−1.24377	+	0.219311i	−0.756533	−	0.653956i	$-0.773108\pi$
$659$	−540148.	+	95242.6i	−1.24377	+	0.219311i	−0.487242	+	0.873267i	$0.661997\pi$
$660$		0			0
$661$	380003.	−	138310.i	0.869729	−	0.316555i	0.131672	−	0.991293i	$-0.457966\pi$
$661$	380003.	−	138310.i	0.869729	−	0.316555i	0.738057	+	0.674738i	$0.235743\pi$
$662$	−21876.8	−	60106.0i	−0.0499192	−	0.137152i
$663$		0			0
$664$	−7818.10	−	44338.6i	−0.0177323	−	0.100565i
$665$	180917.	+	104452.i	0.409106	+	0.236197i
$666$		0			0
$667$	91509.8	+	158500.i	0.205691	+	0.356268i
$668$	−171559.	−	204456.i	−0.384468	−	0.458192i
$669$		0			0
$670$	8160.28	−	46279.2i	0.0181784	−	0.103095i
$671$	548978.	−	654246.i	1.21930	−	1.45310i
$672$		0			0
$673$	−46201.6	−	16816.0i	−0.102006	−	0.0371273i	0.290513	−	0.956871i	$-0.406174\pi$
$673$	−46201.6	−	16816.0i	−0.102006	−	0.0371273i	−0.392519	+	0.919744i	$0.628396\pi$
$674$			178889.i			0.393790i
$675$		0			0
$676$	56321.9			0.123249
$677$	−168209.	+	462149.i	−0.367004	+	1.00833i	0.609491	+	0.792793i	$0.291374\pi$
$677$	−168209.	+	462149.i	−0.367004	+	1.00833i	−0.976495	+	0.215542i	$0.930848\pi$
$678$		0			0
$679$	134578.	+	112924.i	0.291900	+	0.244933i
$680$	−210090.	−	37044.6i	−0.454348	−	0.0801137i
$681$		0			0
$682$	−23126.3	+	19405.3i	−0.0497207	+	0.0417206i
$683$	−499325.	+	288285.i	−1.07039	+	0.617990i	−0.928288	−	0.371862i	$-0.878719\pi$
$683$	−499325.	+	288285.i	−1.07039	+	0.617990i	−0.142102	+	0.989852i	$0.545386\pi$
$684$		0			0
$685$	169346.	−	293317.i	0.360907	−	0.625109i
$686$	−165654.	+	29209.3i	−0.352009	+	0.0620687i
$687$		0			0
$688$	370988.	−	135028.i	0.783759	−	0.285265i
$689$	201353.	+	553212.i	0.424149	+	1.16534i
$690$		0			0
$691$	−30249.8	−	171555.i	−0.0633530	−	0.359293i	−0.999960	−	0.00891178i	$-0.997163\pi$
$691$	−30249.8	−	171555.i	−0.0633530	−	0.359293i	0.936607	−	0.350381i	$-0.113948\pi$
$692$	−57962.0	−	33464.4i	−0.121041	−	0.0698829i
$693$		0			0
$694$	−101888.	−	176475.i	−0.211546	−	0.366408i
$695$	−293454.	−	349725.i	−0.607534	−	0.724030i
$696$		0			0
$697$	124021.	−	703356.i	0.255287	−	1.44780i
$698$	−138789.	+	165402.i	−0.284869	+	0.339493i
$699$		0			0
$700$	−140948.	−	51300.8i	−0.287648	−	0.104695i
$701$		−	238377.i		−	0.485096i	−0.970139	−	0.242548i	$-0.922017\pi$
$701$		−	238377.i		−	0.485096i	0.970139	−	0.242548i	$-0.0779832\pi$
$702$		0			0
$703$	843457.			1.70668
$704$	−55715.3	+	153077.i	−0.112416	+	0.308861i
$705$		0			0
$706$	147917.	+	124117.i	0.296761	+	0.249012i
$707$	−17432.4	−	3073.81i	−0.0348754	−	0.00614948i
$708$		0			0
$709$	−613316.	+	514633.i	−1.22009	+	1.02378i	−0.221269	+	0.975213i	$0.571020\pi$
$709$	−613316.	+	514633.i	−1.22009	+	1.02378i	−0.998820	+	0.0485633i	$0.984536\pi$
$710$	−28309.7	+	16344.6i	−0.0561588	+	0.0324233i
$711$		0			0
$712$	−291519.	+	504926.i	−0.575052	+	0.996019i
$713$	29034.6	−	5119.58i	0.0571132	−	0.0100706i
$714$		0			0
$715$	−372506.	+	135581.i	−0.728655	+	0.265209i
$716$	170824.	+	469336.i	0.333214	+	0.915499i
$717$		0			0
$718$	−13678.3	−	77573.6i	−0.0265329	−	0.150475i
$719$	280426.	+	161904.i	0.542451	+	0.313184i	0.746072	−	0.665866i	$-0.231938\pi$
$719$	280426.	+	161904.i	0.542451	+	0.313184i	−0.203621	+	0.979050i	$0.565271\pi$
$720$		0			0
$721$	−168653.	−	292116.i	−0.324432	−	0.561934i
$722$	−64695.7	−	77101.4i	−0.124108	−	0.147907i
$723$		0			0
$724$	−33351.8	+	189148.i	−0.0636271	+	0.360847i
$725$	222478.	−	265139.i	0.423263	−	0.504425i
$726$		0			0
$727$	724109.	+	263554.i	1.37005	+	0.498656i	0.919146	−	0.393918i	$-0.128881\pi$
$727$	724109.	+	263554.i	1.37005	+	0.498656i	0.450901	+	0.892574i	$0.351103\pi$
$728$		−	230037.i		−	0.434045i
$729$		0			0
$730$	−55282.5			−0.103739
$731$	260944.	−	716938.i	0.488329	−	1.34167i
$732$		0			0
$733$	−44106.6	−	37009.9i	−0.0820911	−	0.0688826i	0.600819	−	0.799385i	$-0.294841\pi$
$733$	−44106.6	−	37009.9i	−0.0820911	−	0.0688826i	−0.682910	+	0.730503i	$0.739286\pi$
$734$	65562.0	+	11560.3i	0.121691	+	0.0214575i
$735$		0			0
$736$	−138787.	+	116456.i	−0.256208	+	0.214984i
$737$	−239859.	+	138483.i	−0.441592	+	0.254953i
$738$		0			0
$739$	56693.7	−	98196.4i	0.103812	−	0.179807i	−0.809440	−	0.587202i	$-0.800229\pi$
$739$	56693.7	−	98196.4i	0.103812	−	0.179807i	0.913252	+	0.407395i	$0.133563\pi$
$740$	412715.	−	72772.8i	0.753680	−	0.132894i
$741$		0			0
$742$	130577.	−	47526.2i	0.237170	−	0.0863228i
$743$	322270.	+	885430.i	0.583771	+	1.60390i	0.781682	+	0.623677i	$0.214362\pi$
$743$	322270.	+	885430.i	0.583771	+	1.60390i	−0.197911	+	0.980220i	$0.563416\pi$
$744$		0			0
$745$	114757.	+	650821.i	0.206761	+	1.17260i
$746$	218538.	+	126173.i	0.392689	+	0.226719i
$747$		0			0
$748$	291999.	+	505757.i	0.521889	+	0.903938i
$749$	212314.	+	253026.i	0.378456	+	0.451026i
$750$		0			0
$751$	−42803.6	+	242751.i	−0.0758928	+	0.430410i	0.923060	+	0.384656i	$0.125680\pi$
$751$	−42803.6	+	242751.i	−0.0758928	+	0.430410i	−0.998953	+	0.0457535i	$0.985431\pi$
$752$	−70096.0	+	83537.2i	−0.123953	+	0.147722i
$753$		0			0
$754$	231684.	+	84326.0i	0.407524	+	0.148327i
$755$			190535.i			0.334258i
$756$		0			0
$757$	−1.07013e6			−1.86742			−0.933712	−	0.358025i	$-0.883450\pi$
$757$	−1.07013e6			−1.86742			−0.933712	+	0.358025i	$0.883450\pi$
$758$	56579.0	−	155450.i	0.0984730	−	0.270552i
$759$		0			0
$760$	−238062.	−	199758.i	−0.412157	−	0.345841i
$761$	−15959.4	−	2814.08i	−0.0275580	−	0.00485923i	0.159852	−	0.987141i	$-0.448898\pi$
$761$	−15959.4	−	2814.08i	−0.0275580	−	0.00485923i	−0.187410	+	0.982282i	$0.560009\pi$
$762$		0			0
$763$	−108735.	+	91239.3i	−0.186775	+	0.156723i
$764$	−586320.	+	338512.i	−1.00449	+	0.579945i
$765$		0			0
$766$	−206978.	+	358497.i	−0.352750	+	0.610981i
$767$	1.00642e6	−	177458.i	1.71075	−	0.301652i
$768$		0			0
$769$	522315.	−	190107.i	0.883242	−	0.321474i	0.139725	−	0.990190i	$-0.455378\pi$
$769$	522315.	−	190107.i	0.883242	−	0.321474i	0.743517	+	0.668716i	$0.233156\pi$
$770$	32001.9	+	87924.5i	0.0539752	+	0.148296i
$771$		0			0
$772$	104792.	+	594304.i	0.175830	+	0.997181i
$773$	−287445.	−	165957.i	−0.481056	−	0.277738i	0.239800	−	0.970822i	$-0.422918\pi$
$773$	−287445.	−	165957.i	−0.481056	−	0.277738i	−0.720857	+	0.693084i	$0.756251\pi$
$774$		0			0
$775$	−27877.6	−	48285.4i	−0.0464143	−	0.0803919i
$776$	−167987.	−	200199.i	−0.278966	−	0.332459i
$777$		0			0
$778$	−687.115	+	3896.82i	−0.00113519	+	0.00643801i
$779$	668764.	−	797001.i	1.10204	−	1.31336i
$780$		0			0
$781$	181042.	+	65894.0i	0.296810	+	0.108030i
$782$			87231.4i			0.142646i
$783$		0			0
$784$	−245042.			−0.398665
$785$	120995.	−	332432.i	0.196349	−	0.539465i
$786$		0			0
$787$	−347977.	−	291987.i	−0.561825	−	0.471427i	0.317097	−	0.948393i	$-0.397292\pi$
$787$	−347977.	−	291987.i	−0.561825	−	0.471427i	−0.878922	+	0.476966i	$0.841736\pi$
$788$	436364.	+	76942.8i	0.702743	+	0.123913i
$789$		0			0
$790$	79057.8	−	66337.4i	0.126675	−	0.106293i
$791$	−552842.	+	319183.i	−0.883584	+	0.510138i
$792$		0			0
$793$	−561800.	+	973066.i	−0.893378	+	1.54738i
$794$	277396.	−	48912.3i	0.440006	−	0.0775849i
$795$		0			0
$796$	−819296.	+	298199.i	−1.29305	+	0.470631i
$797$	166032.	+	456169.i	0.261382	+	0.718140i	0.999075	+	0.0430040i	$0.0136928\pi$
$797$	166032.	+	456169.i	0.261382	+	0.718140i	−0.737693	+	0.675136i	$0.764085\pi$
$798$		0			0
$799$	36594.7	+	207539.i	0.0573224	+	0.325092i
$800$	296720.	+	171311.i	0.463624	+	0.267674i
$801$		0			0
$802$	−67286.6	−	116544.i	−0.104612	−	0.181193i
$803$	209433.	+	249593.i	0.324799	+	0.387080i
$804$		0			0
$805$	15867.4	−	89988.6i	0.0244858	−	0.138866i
$806$	25529.6	−	30425.0i	0.0392983	−	0.0468339i
$807$		0			0
$808$	24744.6	+	9006.29i	0.0379016	+	0.0137951i
$809$		−	157871.i		−	0.241216i	−0.992700	−	0.120608i	$-0.961516\pi$
$809$		−	157871.i		−	0.241216i	0.992700	−	0.120608i	$-0.0384843\pi$
$810$		0			0
$811$	711539.			1.08183			0.540913	−	0.841079i	$-0.318079\pi$
$811$	711539.			1.08183			0.540913	+	0.841079i	$0.318079\pi$
$812$	−130133.	+	357538.i	−0.197368	+	0.542263i
$813$		0			0
$814$	289396.	+	242832.i	0.436761	+	0.366486i
$815$	−208884.	−	36831.9i	−0.314478	−	0.0554509i
$816$		0			0
$817$	851395.	−	714405.i	1.27552	−	1.07029i
$818$	−95640.6	+	55218.1i	−0.142934	+	0.0825230i
$819$		0			0
$820$	258470.	−	447684.i	0.384400	−	0.665800i
$821$	−1.26250e6	+	222613.i	−1.87303	+	0.330266i	−0.990226	−	0.139473i	$-0.955459\pi$
$821$	−1.26250e6	+	222613.i	−1.87303	+	0.330266i	−0.882805	+	0.469739i	$0.844348\pi$
$822$		0			0
$823$	956538.	−	348151.i	1.41222	−	0.514006i	0.480440	−	0.877028i	$-0.340477\pi$
$823$	956538.	−	348151.i	1.41222	−	0.514006i	0.931781	+	0.363021i	$0.118255\pi$
$824$	171618.	+	471518.i	0.252761	+	0.694454i
$825$		0			0
$826$	−41886.4	−	237549.i	−0.0613921	−	0.348172i
$827$	−897693.	−	518283.i	−1.31255	−	0.757803i	−0.330035	−	0.943969i	$-0.607060\pi$
$827$	−897693.	−	518283.i	−1.31255	−	0.757803i	−0.982518	+	0.186166i	$0.940394\pi$
$828$		0			0
$829$	−298497.	−	517012.i	−0.434341	−	0.752300i	0.562901	−	0.826524i	$-0.309685\pi$
$829$	−298497.	−	517012.i	−0.434341	−	0.752300i	−0.997242	+	0.0742242i	$0.976352\pi$
$830$	−15486.4	−	18455.9i	−0.0224798	−	0.0267904i
$831$		0			0
$832$	37215.0	−	211057.i	0.0537615	−	0.304896i
$833$	−304389.	+	362757.i	−0.438671	+	0.522788i
$834$		0			0
$835$	−288946.	−	105168.i	−0.414423	−	0.150838i
$836$			850731.i			1.21725i
$837$		0			0
$838$	−105417.			−0.150115
$839$	429660.	−	1.18048e6i	0.610380	−	1.67701i	−0.118997	−	0.992895i	$-0.537968\pi$
$839$	429660.	−	1.18048e6i	0.610380	−	1.67701i	0.729377	−	0.684112i	$-0.239810\pi$
$840$		0			0
$841$	−130761.	−	109722.i	−0.184879	−	0.155132i
$842$	−315495.	−	55630.3i	−0.445008	−	0.0784670i
$843$		0			0
$844$	−464311.	+	389603.i	−0.651815	+	0.546937i
$845$	56194.4	−	32443.9i	0.0787009	−	0.0454380i
$846$		0			0
$847$	61527.0	−	106568.i	0.0857628	−	0.148545i
$848$	509194.	−	89784.6i	0.708095	−	0.124856i
$849$		0			0
$850$	155017.	−	56421.6i	0.214557	−	0.0780922i
$851$	−126183.	−	346686.i	−0.174238	−	0.478715i
$852$		0			0
$853$	174171.	+	987772.i	0.239374	+	1.35756i	0.833203	+	0.552967i	$0.186505\pi$
$853$	174171.	+	987772.i	0.239374	+	1.35756i	−0.593829	+	0.804591i	$0.702384\pi$
$854$	229677.	+	132604.i	0.314922	+	0.181820i
$855$		0			0
$856$	−245680.	−	425529.i	−0.335291	−	0.580740i
$857$	307505.	+	366471.i	0.418689	+	0.498974i	0.933624	−	0.358256i	$-0.116628\pi$
$857$	307505.	+	366471.i	0.418689	+	0.498974i	−0.514935	+	0.857229i	$0.672184\pi$
$858$		0			0
$859$	229557.	−	1.30188e6i	0.311102	−	1.76435i	−0.282186	−	0.959360i	$-0.591060\pi$
$859$	229557.	−	1.30188e6i	0.311102	−	1.76435i	0.593288	−	0.804990i	$-0.297829\pi$
$860$	354961.	−	423026.i	0.479936	−	0.571966i
$861$		0			0
$862$	−84353.2	−	30702.1i	−0.113524	−	0.0413193i
$863$		−	549709.i		−	0.738094i	−0.929411	−	0.369047i	$-0.879684\pi$
$863$		−	549709.i		−	0.738094i	0.929411	−	0.369047i	$-0.120316\pi$
$864$		0			0
$865$	−77107.8			−0.103054
$866$	40378.0	−	110938.i	0.0538405	−	0.147926i
$867$		0			0
$868$	46952.3	+	39397.7i	0.0623186	+	0.0522915i
$869$	−599008.	−	105621.i	−0.793219	−	0.139866i
$870$		0			0
$871$	279128.	−	234216.i	0.367932	−	0.308731i
$872$	182866.	−	105578.i	0.240491	−	0.138848i
$873$		0			0
$874$	−63536.6	+	110049.i	−0.0831766	+	0.144066i
$875$	−458126.	+	80780.0i	−0.598369	+	0.105509i
$876$		0			0
$877$	−736533.	+	268076.i	−0.957620	+	0.348545i	−0.773100	−	0.634284i	$-0.781295\pi$
$877$	−736533.	+	268076.i	−0.957620	+	0.348545i	−0.184520	+	0.982829i	$0.559073\pi$
$878$	58492.6	+	160707.i	0.0758773	+	0.208471i
$879$		0			0
$880$	60456.7	+	342867.i	0.0780691	+	0.442752i
$881$	112271.	+	64819.8i	0.144649	+	0.0835133i	0.570578	−	0.821243i	$-0.306719\pi$
$881$	112271.	+	64819.8i	0.144649	+	0.0835133i	−0.425929	+	0.904757i	$0.640053\pi$
$882$		0			0
$883$	161874.	+	280373.i	0.207613	+	0.359596i	0.950962	−	0.309307i	$-0.100097\pi$
$883$	161874.	+	280373.i	0.207613	+	0.359596i	−0.743349	+	0.668904i	$0.766764\pi$
$884$	−493859.	−	588558.i	−0.631973	−	0.753156i
$885$		0			0
$886$	28689.5	−	162706.i	0.0365473	−	0.207270i
$887$	358344.	−	427058.i	0.455463	−	0.542800i	−0.488624	−	0.872494i	$-0.662501\pi$
$887$	358344.	−	427058.i	0.455463	−	0.542800i	0.944088	+	0.329694i	$0.106946\pi$
$888$		0			0
$889$	−207233.	−	75426.6i	−0.262214	−	0.0954380i
$890$			311995.i			0.393884i
$891$		0			0
$892$	−432559.			−0.543646
$893$	−104998.	+	288479.i	−0.131667	+	0.361753i
$894$		0			0
$895$	440795.	+	369871.i	0.550289	+	0.461748i
$896$	−477473.	−	84191.4i	−0.594748	−	0.104870i
$897$		0			0
$898$	184457.	−	154778.i	0.228740	−	0.191936i
$899$	−122484.	+	70716.3i	−0.151552	+	0.0874984i
$900$		0			0
$901$	499602.	−	865335.i	0.615424	−	1.06595i
$902$	458915.	−	80919.1i	0.564052	−	0.0994576i
$903$		0			0
$904$	892367.	−	324795.i	1.09196	−	0.397441i
$905$	75680.8	+	207931.i	0.0924036	+	0.253877i
$906$		0			0
$907$	−89372.8	−	506859.i	−0.108640	−	0.616130i	−0.989704	−	0.143132i	$-0.954283\pi$
$907$	−89372.8	−	506859.i	−0.108640	−	0.616130i	0.881063	−	0.472998i	$-0.156828\pi$
$908$	−399598.	−	230708.i	−0.484676	−	0.279828i
$909$		0			0
$910$	−61548.6	−	106605.i	−0.0743251	−	0.128735i
$911$	−449438.	−	535620.i	−0.541543	−	0.645386i	0.423990	−	0.905667i	$-0.360629\pi$
$911$	−449438.	−	535620.i	−0.541543	−	0.645386i	−0.965533	+	0.260281i	$0.916185\pi$
$912$		0			0
$913$	−24657.1	+	139838.i	−0.0295802	+	0.167758i
$914$	113271.	−	134991.i	0.135589	−	0.161589i
$915$		0			0
$916$	−538055.	−	195836.i	−0.641262	−	0.233400i
$917$		−	555652.i		−	0.660791i
$918$		0			0
$919$	−140843.			−0.166764			−0.0833821	−	0.996518i	$-0.526572\pi$
$919$	−140843.			−0.166764			−0.0833821	+	0.996518i	$0.526572\pi$
$920$	−46491.7	+	127735.i	−0.0549288	+	0.150916i
$921$		0			0
$922$	6613.55	+	5549.43i	0.00777988	+	0.00652809i
$923$	−249615.	−	44013.8i	−0.292999	−	0.0516637i
$924$		0			0
$925$	−534473.	+	448476.i	−0.624658	+	0.524150i
$926$	46787.9	−	27013.0i	0.0545647	−	0.0315029i
$927$		0			0
$928$	434560.	−	752680.i	0.504608	−	0.874006i
$929$	−789115.	+	139142.i	−0.914342	+	0.161223i	−0.610974	−	0.791650i	$-0.709222\pi$
$929$	−789115.	+	139142.i	−0.914342	+	0.161223i	−0.303368	+	0.952874i	$0.598111\pi$
$930$		0			0
$931$	−648229.	+	235936.i	−0.747876	+	0.272204i
$932$	236673.	+	650255.i	0.272469	+	0.748603i
$933$		0			0
$934$	−36716.0	−	208227.i	−0.0420884	−	0.238695i
$935$	582676.	+	336408.i	0.666505	+	0.384807i
$936$		0			0
$937$	21249.5	+	36805.3i	0.0242031	+	0.0419209i	0.877873	−	0.478893i	$-0.158962\pi$
$937$	21249.5	+	36805.3i	0.0242031	+	0.0419209i	−0.853670	+	0.520814i	$0.825629\pi$
$938$	−55283.2	−	65883.9i	−0.0628329	−	0.0748814i
$939$		0			0
$940$	−26487.1	+	150216.i	−0.0299764	+	0.170005i
$941$	129466.	−	154292.i	0.146210	−	0.174246i	−0.687969	−	0.725740i	$-0.741497\pi$
$941$	129466.	−	154292.i	0.146210	−	0.174246i	0.834179	+	0.551494i	$0.185942\pi$
$942$		0			0
$943$	−427640.	−	155648.i	−0.480901	−	0.175034i
$944$		−	897538.i		−	1.00718i
$945$		0			0
$946$	497798.			0.556251
$947$	−465505.	+	1.27896e6i	−0.519068	+	1.42613i	0.352481	+	0.935819i	$0.385338\pi$
$947$	−465505.	+	1.27896e6i	−0.519068	+	1.42613i	−0.871549	+	0.490308i	$0.836884\pi$
$948$		0			0
$949$	−328365.	−	275531.i	−0.364606	−	0.305941i
$950$	236661.	+	41729.7i	0.262228	+	0.0462379i
$951$		0			0
$952$	−299088.	+	250965.i	−0.330009	+	0.276910i
$953$	936391.	−	540626.i	1.03103	−	0.595266i	0.113751	−	0.993509i	$-0.463713\pi$
$953$	936391.	−	540626.i	1.03103	−	0.595266i	0.917280	+	0.398244i	$0.130380\pi$
$954$		0			0
$955$	−389995.	+	675491.i	−0.427614	+	0.740650i
$956$	−459679.	+	81053.9i	−0.502967	+	0.0886866i
$957$		0			0
$958$	−397164.	+	144556.i	−0.432752	+	0.157509i
$959$	−212006.	−	582482.i	−0.230521	−	0.633353i
$960$		0			0
$961$	−156411.	−	887053.i	−0.169364	−	0.960513i
$962$	−430421.	−	248504.i	−0.465097	−	0.268524i
$963$		0			0
$964$	−782.821	−	1355.89i	−0.000842380	−	0.00145905i
$965$	446900.	+	532594.i	0.479905	+	0.571929i
$966$		0			0
$967$	−239395.	+	1.35768e6i	−0.256013	+	1.45192i	0.537445	+	0.843299i	$0.319390\pi$
$967$	−239395.	+	1.35768e6i	−0.256013	+	1.45192i	−0.793458	+	0.608625i	$0.791722\pi$
$968$	−117666.	+	140229.i	−0.125574	+	0.149653i
$969$		0			0
$970$	−131415.	−	47831.1i	−0.139669	−	0.0508355i
$971$			1.18814e6i			1.26017i	0.776526	+	0.630086i	$0.216980\pi$
$971$			1.18814e6i			1.26017i	−0.776526	+	0.630086i	$0.783020\pi$
$972$		0			0
$973$	−835532.			−0.882546
$974$	−17977.1	+	49391.7i	−0.0189497	+	0.0520639i
$975$		0			0
$976$	755948.	+	634315.i	0.793583	+	0.665895i
$977$	−447986.	−	78992.0i	−0.469327	−	0.0827549i	−0.0660169	−	0.997819i	$-0.521029\pi$
$977$	−447986.	−	78992.0i	−0.469327	−	0.0827549i	−0.403310	+	0.915064i	$0.632140\pi$
$978$		0			0
$979$	1.40862e6	−	1.18197e6i	1.46969	−	1.23322i
$980$	−296831.	+	171376.i	−0.309070	+	0.178442i
$981$		0			0
$982$	−262130.	+	454023.i	−0.271828	+	0.470820i
$983$	490692.	−	86522.3i	0.507811	−	0.0895408i	0.0861280	−	0.996284i	$-0.472551\pi$
$983$	490692.	−	86522.3i	0.507811	−	0.0895408i	0.421683	+	0.906743i	$0.361439\pi$
$984$		0			0
$985$	479699.	−	174596.i	0.494420	−	0.179954i
$986$	−143123.	−	393228.i	−0.147216	−	0.404474i
$987$		0			0
$988$	−194351.	−	1.10222e6i	−0.199101	−	1.12916i
$989$	−421013.	−	243072.i	−0.430430	−	0.248509i
$990$		0			0
$991$	880650.	+	1.52533e6i	0.896718	+	1.55316i	0.831664	+	0.555279i	$0.187389\pi$
$991$	880650.	+	1.52533e6i	0.896718	+	1.55316i	0.0650542	+	0.997882i	$0.479278\pi$
$992$	−89994.0	−	107251.i	−0.0914514	−	0.108988i
$993$		0			0
$994$	−10388.8	+	58917.8i	−0.0105146	+	0.0596312i
$995$	−645665.	+	769474.i	−0.652171	+	0.777227i
$996$		0			0
$997$	1.66792e6	+	607075.i	1.67798	+	0.610734i	0.993030	−	0.117860i	$-0.0376034\pi$
$997$	1.66792e6	+	607075.i	1.67798	+	0.610734i	0.684946	+	0.728594i	$0.259826\pi$
$998$		−	347351.i		−	0.348745i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.5.f.a.17.5		66
3.2	odd	2		27.5.f.a.23.7	yes	66
27.7	even	9		27.5.f.a.20.7	✓	66
27.20	odd	18	inner	81.5.f.a.62.5		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.f.a.20.7	✓	66	27.7	even	9
27.5.f.a.23.7	yes	66	3.2	odd	2
81.5.f.a.17.5		66	1.1	even	1	trivial
81.5.f.a.62.5		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)

\(f(q)\)	\(=\)	\(q+(-0.498289 + 1.36904i) q^{2} +(10.6307 + 8.92025i) q^{4} +(15.7451 + 2.77629i) q^{5} +(22.4150 - 18.8084i) q^{7} +(-37.6967 + 21.7642i) q^{8} +(-11.6465 + 20.1723i) q^{10} +(135.197 - 23.8388i) q^{11} +(-169.717 + 61.7718i) q^{13} +(14.5803 + 40.0591i) q^{14} +(27.5445 + 156.213i) q^{16} +(265.471 + 153.270i) q^{17} +(223.274 + 386.722i) q^{19} +(142.617 + 169.964i) q^{20} +(-34.7308 + 196.968i) q^{22} +(125.552 - 149.627i) q^{23} +(-347.107 - 126.337i) q^{25} -263.129i q^{26} +406.064 q^{28} +(-320.474 + 880.496i) q^{29} +(115.628 + 97.0232i) q^{31} +(-913.460 - 161.068i) q^{32} +(-342.114 + 287.068i) q^{34} +(405.145 - 233.911i) q^{35} +(944.419 - 1635.78i) q^{37} +(-640.692 + 112.971i) q^{38} +(-653.963 + 238.023i) q^{40} +(-796.872 - 2189.39i) q^{41} +(-432.194 - 2451.10i) q^{43} +(1649.89 + 952.564i) q^{44} +(142.284 + 246.443i) q^{46} +(441.904 + 526.641i) q^{47} +(-268.253 + 1521.34i) q^{49} +(345.919 - 412.250i) q^{50} +(-2355.23 - 857.235i) q^{52} -3259.62i q^{53} +2194.87 q^{55} +(-435.622 + 1196.86i) q^{56} +(-1045.74 - 877.483i) q^{58} +(-5572.36 - 982.557i) q^{59} +(4765.70 - 3998.90i) q^{61} +(-190.444 + 109.953i) q^{62} +(-593.306 + 1027.64i) q^{64} +(-2843.71 + 501.422i) q^{65} +(-1895.82 + 690.021i) q^{67} +(1454.95 + 3997.44i) q^{68} +(118.353 + 671.214i) q^{70} +(1215.38 + 701.697i) q^{71} +(1186.68 + 2055.39i) q^{73} +(1768.85 + 2108.04i) q^{74} +(-1076.09 + 6102.80i) q^{76} +(2582.07 - 3077.19i) q^{77} +(-4163.44 - 1515.37i) q^{79} +2536.06i q^{80} +3394.43 q^{82} +(-353.761 + 971.950i) q^{83} +(3754.36 + 3150.28i) q^{85} +(3571.00 + 629.663i) q^{86} +(-4577.64 + 3841.09i) q^{88} +(11599.9 - 6697.21i) q^{89} +(-2642.37 + 4576.73i) q^{91} +(2669.42 - 470.691i) q^{92} +(-941.187 + 342.564i) q^{94} +(2441.82 + 6708.86i) q^{95} +(1042.57 + 5912.70i) q^{97} +(-1949.10 - 1125.32i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} - 1137 q^{14} - 54 q^{16} + 9 q^{17} - 3 q^{19} + 2487 q^{20} + 1002 q^{22} + 2724 q^{23} + 435 q^{25} - 12 q^{28}+ \cdots + 259938 q^{98}+O(q^{100}) \) 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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