LMFDB - Embedded newform 81.5.f.a.17.1

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			17.1
Character	$\chi$	$=$	81.17
Dual form			81.5.f.a.62.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.52261 + 6.93081i) q^{2} +(-29.4158 - 24.6828i) q^{4} +(-21.3946 - 3.77244i) q^{5} +(-45.7826 + 38.4162i) q^{7} +(143.077 - 82.6054i) q^{8} +(80.1161 - 138.765i) q^{10} +(103.631 - 18.2729i) q^{11} +(214.739 - 78.1587i) q^{13} +(-150.764 - 414.219i) q^{14} +(104.907 + 594.959i) q^{16} +(-64.7695 - 37.3947i) q^{17} +(-82.6450 - 143.145i) q^{19} +(536.224 + 639.047i) q^{20} +(-134.774 + 764.340i) q^{22} +(-63.6548 + 75.8608i) q^{23} +(-143.812 - 52.3434i) q^{25} +1685.48i q^{26} +2294.95 q^{28} +(431.252 - 1184.85i) q^{29} +(-1129.02 - 947.356i) q^{31} +(-1784.97 - 314.738i) q^{32} +(422.563 - 354.573i) q^{34} +(1124.42 - 649.185i) q^{35} +(279.857 - 484.726i) q^{37} +(1200.59 - 211.697i) q^{38} +(-3372.69 + 1227.56i) q^{40} +(63.9089 + 175.588i) q^{41} +(-121.465 - 688.861i) q^{43} +(-3499.41 - 2020.38i) q^{44} +(-365.201 - 632.546i) q^{46} +(-231.919 - 276.390i) q^{47} +(203.316 - 1153.06i) q^{49} +(725.564 - 864.694i) q^{50} +(-8245.91 - 3001.27i) q^{52} +176.131i q^{53} -2286.07 q^{55} +(-3377.05 + 9278.36i) q^{56} +(7124.12 + 5977.85i) q^{58} +(-4044.66 - 713.183i) q^{59} +(3799.73 - 3188.35i) q^{61} +(9414.01 - 5435.18i) q^{62} +(1851.07 - 3206.15i) q^{64} +(-4889.10 + 862.080i) q^{65} +(5460.16 - 1987.33i) q^{67} +(982.242 + 2698.69i) q^{68} +(1662.90 + 9430.78i) q^{70} +(3882.84 + 2241.76i) q^{71} +(1087.02 + 1882.78i) q^{73} +(2653.58 + 3162.41i) q^{74} +(-1102.16 + 6250.65i) q^{76} +(-4042.51 + 4817.68i) q^{77} +(-9033.76 - 3288.02i) q^{79} -13124.6i q^{80} -1378.18 q^{82} +(1749.95 - 4807.94i) q^{83} +(1244.64 + 1044.38i) q^{85} +(5080.77 + 895.877i) q^{86} +(13317.7 - 11174.9i) q^{88} +(-7759.36 + 4479.87i) q^{89} +(-6828.77 + 11827.8i) q^{91} +(3744.92 - 660.330i) q^{92} +(2500.64 - 910.160i) q^{94} +(1228.15 + 3374.30i) q^{95} +(-1725.07 - 9783.37i) q^{97} +(7478.77 + 4317.87i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.52261	+	6.93081i	−0.630652	+	1.73270i	0.0486226	+	0.998817i	$0.484517\pi$
$2$	−2.52261	+	6.93081i	−0.630652	+	1.73270i	−0.679274	+	0.733884i	$0.737705\pi$
$3$		0			0
$3$		0			0
$4$	−29.4158	−	24.6828i	−1.83849	−	1.54268i
$5$	−21.3946	−	3.77244i	−0.855782	−	0.150897i	−0.271490	−	0.962441i	$-0.587516\pi$
$5$	−21.3946	−	3.77244i	−0.855782	−	0.150897i	−0.584292	+	0.811544i	$0.698628\pi$
$6$		0			0
$7$	−45.7826	+	38.4162i	−0.934339	+	0.784004i	−0.976591	−	0.215103i	$-0.930991\pi$
$7$	−45.7826	+	38.4162i	−0.934339	+	0.784004i	0.0422522	+	0.999107i	$0.486547\pi$
$8$	143.077	−	82.6054i	2.23558	−	1.29071i
$9$		0			0
$10$	80.1161	−	138.765i	0.801161	−	1.38765i
$11$	103.631	−	18.2729i	0.856452	−	0.151016i	0.271854	−	0.962339i	$-0.412363\pi$
$11$	103.631	−	18.2729i	0.856452	−	0.151016i	0.584598	+	0.811323i	$0.301252\pi$
$12$		0			0
$13$	214.739	−	78.1587i	1.27065	−	0.462478i	0.383319	−	0.923616i	$-0.374781\pi$
$13$	214.739	−	78.1587i	1.27065	−	0.462478i	0.887328	+	0.461139i	$0.152559\pi$
$14$	−150.764	−	414.219i	−0.769202	−	2.11336i
$15$		0			0
$16$	104.907	+	594.959i	0.409794	+	2.32406i
$17$	−64.7695	−	37.3947i	−0.224116	−	0.129393i	0.383739	−	0.923442i	$-0.374636\pi$
$17$	−64.7695	−	37.3947i	−0.224116	−	0.129393i	−0.607855	+	0.794048i	$0.707970\pi$
$18$		0			0
$19$	−82.6450	−	143.145i	−0.228934	−	0.396524i	0.728559	−	0.684983i	$-0.240191\pi$
$19$	−82.6450	−	143.145i	−0.228934	−	0.396524i	−0.957492	+	0.288459i	$0.906857\pi$
$20$	536.224	+	639.047i	1.34056	+	1.59762i
$21$		0			0
$22$	−134.774	+	764.340i	−0.278458	+	1.57921i
$23$	−63.6548	+	75.8608i	−0.120330	+	0.143404i	−0.822847	−	0.568264i	$-0.807615\pi$
$23$	−63.6548	+	75.8608i	−0.120330	+	0.143404i	0.702516	+	0.711668i	$0.252060\pi$
$24$		0			0
$25$	−143.812	−	52.3434i	−0.230100	−	0.0837495i
$26$			1685.48i			2.49331i
$27$		0			0
$28$	2294.95			2.92723
$29$	431.252	−	1184.85i	0.512785	−	1.40886i	−0.365538	−	0.930796i	$-0.619115\pi$
$29$	431.252	−	1184.85i	0.512785	−	1.40886i	0.878323	−	0.478068i	$-0.158663\pi$
$30$		0			0
$31$	−1129.02	−	947.356i	−1.17483	−	0.985803i	−0.999999	−	0.00120490i	$-0.999616\pi$
$31$	−1129.02	−	947.356i	−1.17483	−	0.985803i	−0.174835	−	0.984598i	$-0.555939\pi$
$32$	−1784.97	−	314.738i	−1.74313	−	0.307362i
$33$		0			0
$34$	422.563	−	354.573i	0.365539	−	0.306724i
$35$	1124.42	−	649.185i	0.917895	−	0.529947i
$36$		0			0
$37$	279.857	−	484.726i	0.204424	−	0.354073i	−0.745525	−	0.666478i	$-0.767801\pi$
$37$	279.857	−	484.726i	0.204424	−	0.354073i	0.949949	+	0.312405i	$0.101134\pi$
$38$	1200.59	−	211.697i	0.831436	−	0.146605i
$39$		0			0
$40$	−3372.69	+	1227.56i	−2.10793	+	0.767224i
$41$	63.9089	+	175.588i	0.0380184	+	0.104455i	0.957249	−	0.289264i	$-0.0934106\pi$
$41$	63.9089	+	175.588i	0.0380184	+	0.104455i	−0.919231	+	0.393719i	$0.871188\pi$
$42$		0			0
$43$	−121.465	−	688.861i	−0.0656921	−	0.372559i	−0.999876	−	0.0157659i	$-0.994981\pi$
$43$	−121.465	−	688.861i	−0.0656921	−	0.372559i	0.934184	−	0.356793i	$-0.116130\pi$
$44$	−3499.41	−	2020.38i	−1.80755	−	1.04359i
$45$		0			0
$46$	−365.201	−	632.546i	−0.172590	−	0.298935i
$47$	−231.919	−	276.390i	−0.104988	−	0.125120i	0.710992	−	0.703200i	$-0.248246\pi$
$47$	−231.919	−	276.390i	−0.104988	−	0.125120i	−0.815980	+	0.578081i	$0.803802\pi$
$48$		0			0
$49$	203.316	−	1153.06i	0.0846797	−	0.480243i
$50$	725.564	−	864.694i	0.290226	−	0.345878i
$51$		0			0
$52$	−8245.91	−	3001.27i	−3.04952	−	1.10994i
$53$			176.131i			0.0627023i	0.999508	+	0.0313512i	$0.00998102\pi$
$53$			176.131i			0.0627023i	−0.999508	+	0.0313512i	$0.990019\pi$
$54$		0			0
$55$	−2286.07			−0.755724
$56$	−3377.05	+	9278.36i	−1.07686	+	2.95866i
$57$		0			0
$58$	7124.12	+	5977.85i	2.11775	+	1.77701i
$59$	−4044.66	−	713.183i	−1.16193	−	0.204879i	−0.440749	−	0.897630i	$-0.645287\pi$
$59$	−4044.66	−	713.183i	−1.16193	−	0.204879i	−0.721177	+	0.692751i	$0.756398\pi$
$60$		0			0
$61$	3799.73	−	3188.35i	1.02116	−	0.856854i	0.0313863	−	0.999507i	$-0.490008\pi$
$61$	3799.73	−	3188.35i	1.02116	−	0.856854i	0.989773	+	0.142653i	$0.0455634\pi$
$62$	9414.01	−	5435.18i	2.44901	−	1.41394i
$63$		0			0
$64$	1851.07	−	3206.15i	0.451921	−	0.782751i
$65$	−4889.10	+	862.080i	−1.15718	+	0.204043i
$66$		0			0
$67$	5460.16	−	1987.33i	1.21634	−	0.442712i	0.347442	−	0.937701i	$-0.387050\pi$
$67$	5460.16	−	1987.33i	1.21634	−	0.442712i	0.868899	+	0.494989i	$0.164828\pi$
$68$	982.242	+	2698.69i	0.212423	+	0.583626i
$69$		0			0
$70$	1662.90	+	9430.78i	0.339368	+	1.92465i
$71$	3882.84	+	2241.76i	0.770251	+	0.444705i	0.832964	−	0.553327i	$-0.186642\pi$
$71$	3882.84	+	2241.76i	0.770251	+	0.444705i	−0.0627128	+	0.998032i	$0.519975\pi$
$72$		0			0
$73$	1087.02	+	1882.78i	0.203982	+	0.353308i	0.949808	−	0.312833i	$-0.101278\pi$
$73$	1087.02	+	1882.78i	0.203982	+	0.353308i	−0.745826	+	0.666141i	$0.767945\pi$
$74$	2653.58	+	3162.41i	0.484583	+	0.577503i
$75$		0			0
$76$	−1102.16	+	6250.65i	−0.190817	+	1.08218i
$77$	−4042.51	+	4817.68i	−0.681820	+	0.812561i
$78$		0			0
$79$	−9033.76	−	3288.02i	−1.44749	−	0.526842i	−0.505598	−	0.862769i	$-0.668728\pi$
$79$	−9033.76	−	3288.02i	−1.44749	−	0.526842i	−0.941888	+	0.335927i	$0.890950\pi$
$80$		−	13124.6i		−	2.05072i
$81$		0			0
$82$	−1378.18			−0.204965
$83$	1749.95	−	4807.94i	0.254020	−	0.697915i	−0.745487	−	0.666520i	$-0.767783\pi$
$83$	1749.95	−	4807.94i	0.254020	−	0.697915i	0.999507	−	0.0313946i	$-0.00999486\pi$
$84$		0			0
$85$	1244.64	+	1044.38i	0.172269	+	0.144551i
$86$	5080.77	+	895.877i	0.686962	+	0.121130i
$87$		0			0
$88$	13317.7	−	11174.9i	1.71975	−	1.44304i
$89$	−7759.36	+	4479.87i	−0.979594	+	0.565569i	−0.902147	−	0.431428i	$-0.858010\pi$
$89$	−7759.36	+	4479.87i	−0.979594	+	0.565569i	−0.0774461	+	0.996997i	$0.524677\pi$
$90$		0			0
$91$	−6828.77	+	11827.8i	−0.824631	+	1.42830i
$92$	3744.92	−	660.330i	0.442452	−	0.0780163i
$93$		0			0
$94$	2500.64	−	910.160i	0.283006	−	0.103006i
$95$	1228.15	+	3374.30i	0.136083	+	0.373884i
$96$		0			0
$97$	−1725.07	−	9783.37i	−0.183343	−	1.03979i	−0.928066	−	0.372415i	$-0.878530\pi$
$97$	−1725.07	−	9783.37i	−0.183343	−	1.03979i	0.744723	−	0.667373i	$-0.232581\pi$
$98$	7478.77	+	4317.87i	0.778714	+	0.449591i
$99$		0			0
$100$	2938.38	+	5089.42i	0.293838	+	0.508942i
$101$	−4925.66	−	5870.18i	−0.482861	−	0.575451i	0.468526	−	0.883450i	$-0.344785\pi$
$101$	−4925.66	−	5870.18i	−0.482861	−	0.575451i	−0.951387	+	0.307999i	$0.900341\pi$
$102$		0			0
$103$	−1736.36	+	9847.40i	−0.163669	+	0.928212i	0.786757	+	0.617262i	$0.211758\pi$
$103$	−1736.36	+	9847.40i	−0.163669	+	0.928212i	−0.950426	+	0.310950i	$0.899353\pi$
$104$	24267.9	−	28921.3i	2.24370	−	2.67394i
$105$		0			0
$106$	−1220.73	−	444.309i	−0.108644	−	0.0395433i
$107$		−	10041.9i		−	0.877097i	−0.898707	−	0.438549i	$-0.855493\pi$
$107$		−	10041.9i		−	0.877097i	0.898707	−	0.438549i	$-0.144507\pi$
$108$		0			0
$109$	4648.23			0.391232			0.195616	−	0.980681i	$-0.437329\pi$
$109$	4648.23			0.391232			0.195616	+	0.980681i	$0.437329\pi$
$110$	5766.85	−	15844.3i	0.476599	−	1.30944i
$111$		0			0
$112$	−27659.0	−	23208.6i	−2.20496	−	1.85018i
$113$	−10131.3	−	1786.41i	−0.793426	−	0.139902i	−0.237778	−	0.971320i	$-0.576419\pi$
$113$	−10131.3	−	1786.41i	−0.793426	−	0.139902i	−0.555649	+	0.831417i	$0.687530\pi$
$114$		0			0
$115$	1648.05	−	1382.87i	0.124616	−	0.104565i
$116$	−41931.2	+	24209.0i	−3.11617	+	1.79912i
$117$		0			0
$118$	15146.0	−	26233.7i	1.08776	−	1.88406i
$119$	4401.88	−	776.170i	0.310845	−	0.0548104i
$120$		0			0
$121$	−3352.61	+	1220.25i	−0.228988	+	0.0833447i
$122$	12512.6	+	34378.2i	0.840677	+	2.30974i
$123$		0			0
$124$	9827.50	+	55734.5i	0.639145	+	3.62477i
$125$	14638.1	+	8451.32i	0.936840	+	0.540885i
$126$		0			0
$127$	1339.59	+	2320.23i	0.0830546	+	0.143855i	0.904561	−	0.426345i	$-0.140199\pi$
$127$	1339.59	+	2320.23i	0.0830546	+	0.143855i	−0.821506	+	0.570200i	$0.806866\pi$
$128$	−1089.24	−	1298.10i	−0.0664818	−	0.0792299i
$129$		0			0
$130$	6358.37	−	36060.1i	0.376235	−	2.13373i
$131$	−16301.2	+	19427.0i	−0.949898	+	1.13204i	0.0412321	+	0.999150i	$0.486872\pi$
$131$	−16301.2	+	19427.0i	−0.949898	+	1.13204i	−0.991130	+	0.132895i	$0.957573\pi$
$132$		0			0
$133$	9282.80	+	3378.66i	0.524778	+	0.191004i
$134$			42856.5i			2.38675i
$135$		0			0
$136$	−12356.0			−0.668037
$137$	−991.834	+	2725.04i	−0.0528442	+	0.145188i	−0.963306	−	0.268404i	$-0.913504\pi$
$137$	−991.834	+	2725.04i	−0.0528442	+	0.145188i	0.910462	+	0.413592i	$0.135726\pi$
$138$		0			0
$139$	9156.36	+	7683.10i	0.473907	+	0.397655i	0.848217	−	0.529648i	$-0.177676\pi$
$139$	9156.36	+	7683.10i	0.473907	+	0.397655i	−0.374310	+	0.927303i	$0.622121\pi$
$140$	−49099.5	−	8657.56i	−2.50507	−	0.441712i
$141$		0			0
$142$	−25332.1	+	21256.1i	−1.25630	+	1.05416i
$143$	20825.4	−	12023.6i	1.01841	−	0.587978i
$144$		0			0
$145$	−13696.2	+	23722.6i	−0.651426	+	1.12830i
$146$	−15791.3	+	2784.43i	−0.740819	+	0.130626i
$147$		0			0
$148$	−20196.6	+	7350.97i	−0.922052	+	0.335599i
$149$	−13624.2	−	37432.2i	−0.613676	−	1.68606i	−0.721955	−	0.691940i	$-0.756756\pi$
$149$	−13624.2	−	37432.2i	−0.613676	−	1.68606i	0.108279	−	0.994121i	$-0.465466\pi$
$150$		0			0
$151$	−2099.22	−	11905.3i	−0.0920669	−	0.522137i	−0.995607	−	0.0936332i	$-0.970152\pi$
$151$	−2099.22	−	11905.3i	−0.0920669	−	0.522137i	0.903540	−	0.428504i	$-0.140959\pi$
$152$	−23649.2	−	13653.9i	−1.02360	−	0.590974i
$153$		0			0
$154$	−23192.7	−	40171.0i	−0.977936	−	1.69383i
$155$	20580.9	+	24527.4i	0.856647	+	1.02091i
$156$		0			0
$157$	5503.73	−	31213.2i	0.223284	−	1.26631i	−0.642654	−	0.766156i	$-0.722167\pi$
$157$	5503.73	−	31213.2i	0.223284	−	1.26631i	0.865938	−	0.500151i	$-0.166722\pi$
$158$	45577.3	−	54316.9i	1.82572	−	2.17581i
$159$		0			0
$160$	37001.3	+	13467.4i	1.44536	+	0.526069i
$161$		−	5918.48i		−	0.228328i
$162$		0			0
$163$	6984.52			0.262882			0.131441	−	0.991324i	$-0.458040\pi$
$163$	6984.52			0.262882			0.131441	+	0.991324i	$0.458040\pi$
$164$	2454.08	−	6742.52i	0.0912432	−	0.250689i
$165$		0			0
$166$	28908.5	+	24257.1i	1.04908	+	0.880283i
$167$	9614.67	+	1695.33i	0.344748	+	0.0607883i	0.343341	−	0.939211i	$-0.388441\pi$
$167$	9614.67	+	1695.33i	0.344748	+	0.0607883i	0.00140631	+	0.999999i	$0.499552\pi$
$168$		0			0
$169$	18125.2	−	15208.8i	0.634613	−	0.532504i
$170$	−10378.2	+	5991.83i	−0.359106	+	0.207330i
$171$		0			0
$172$	−13430.0	+	23261.5i	−0.453963	+	0.786286i
$173$	43917.3	−	7743.80i	1.46738	−	0.258739i	0.617859	−	0.786289i	$-0.288000\pi$
$173$	43917.3	−	7743.80i	1.46738	−	0.258739i	0.849524	+	0.527550i	$0.176889\pi$
$174$		0			0
$175$	8594.94	−	3128.30i	0.280651	−	0.102149i
$176$	21743.2	+	59739.1i	0.701938	+	1.92856i
$177$		0			0
$178$	−11475.3	−	65079.6i	−0.362179	−	2.05402i
$179$	−1176.35	−	679.166i	−0.0367139	−	0.0211968i	0.481531	−	0.876429i	$-0.340081\pi$
$179$	−1176.35	−	679.166i	−0.0367139	−	0.0211968i	−0.518245	+	0.855232i	$0.673414\pi$
$180$		0			0
$181$	−7938.82	−	13750.4i	−0.242325	−	0.419720i	0.719051	−	0.694957i	$-0.244577\pi$
$181$	−7938.82	−	13750.4i	−0.242325	−	0.419720i	−0.961376	+	0.275238i	$0.911243\pi$
$182$	−64749.7	−	77165.7i	−1.95477	−	2.32960i
$183$		0			0
$184$	−2841.01	+	16112.2i	−0.0839145	+	0.475903i
$185$	−7816.01	+	9314.76i	−0.228371	+	0.272162i
$186$		0			0
$187$	−7395.42	−	2691.71i	−0.211485	−	0.0769742i
$188$			13854.6i			0.391994i
$189$		0			0
$190$	−26484.8			−0.733650
$191$	−1671.83	+	4593.33i	−0.0458275	+	0.125910i	−0.960495	−	0.278297i	$-0.910230\pi$
$191$	−1671.83	+	4593.33i	−0.0458275	+	0.125910i	0.914668	+	0.404207i	$0.132452\pi$
$192$		0			0
$193$	−47354.8	−	39735.4i	−1.27130	−	1.06675i	−0.994381	−	0.105858i	$-0.966241\pi$
$193$	−47354.8	−	39735.4i	−1.27130	−	1.06675i	−0.276923	−	0.960892i	$-0.589315\pi$
$194$	72158.3	+	12723.5i	1.91727	+	0.338066i
$195$		0			0
$196$	−34441.5	+	28899.9i	−0.896541	+	0.752287i
$197$	53245.4	−	30741.2i	1.37199	−	0.792116i	0.380808	−	0.924654i	$-0.375646\pi$
$197$	53245.4	−	30741.2i	1.37199	−	0.792116i	0.991178	+	0.132538i	$0.0423126\pi$
$198$		0			0
$199$	−18250.2	+	31610.2i	−0.460851	+	0.798217i	−0.999004	−	0.0446304i	$-0.985789\pi$
$199$	−18250.2	+	31610.2i	−0.460851	+	0.798217i	0.538153	+	0.842847i	$0.319122\pi$
$200$	−24900.1	+	4390.55i	−0.622502	+	0.109764i
$201$		0			0
$202$	53110.6	−	19330.7i	1.30160	−	0.473745i
$203$	25773.8	+	70812.8i	0.625440	+	1.71838i
$204$		0			0
$205$	−704.906	−	3997.72i	−0.0167735	−	0.0951273i
$206$	−63870.3	−	36875.5i	−1.50510	−	0.868968i
$207$		0			0
$208$	69028.9	+	119562.i	1.59553	+	2.76354i
$209$	−11180.2	−	13324.1i	−0.255952	−	0.305032i
$210$		0			0
$211$	−13914.8	+	78914.7i	−0.312544	+	1.77253i	0.273126	+	0.961978i	$0.411943\pi$
$211$	−13914.8	+	78914.7i	−0.312544	+	1.77253i	−0.585670	+	0.810549i	$0.699169\pi$
$212$	4347.40	−	5181.03i	0.0967293	−	0.115278i
$213$		0			0
$214$	69598.4	+	25331.7i	1.51975	+	0.553143i
$215$			15196.1i			0.328742i
$216$		0			0
$217$	88083.1			1.87057
$218$	−11725.6	+	32215.9i	−0.246731	+	0.677888i
$219$		0			0
$220$	67246.5	+	56426.5i	1.38939	+	1.16584i
$221$	−16831.3	−	2967.81i	−0.344614	−	0.0607647i
$222$		0			0
$223$	−1913.36	+	1605.50i	−0.0384758	+	0.0322850i	−0.661823	−	0.749660i	$-0.730217\pi$
$223$	−1913.36	+	1605.50i	−0.0384758	+	0.0322850i	0.623347	+	0.781945i	$0.285772\pi$
$224$	93811.6	−	54162.1i	1.86965	−	1.07944i
$225$		0			0
$226$	37938.5	−	65711.4i	0.742785	−	1.28654i
$227$	−59661.7	+	10520.0i	−1.15783	+	0.204156i	−0.719390	−	0.694606i	$-0.755579\pi$
$227$	−59661.7	+	10520.0i	−1.15783	+	0.204156i	−0.438436	+	0.898762i	$0.644468\pi$
$228$		0			0
$229$	−16816.2	+	6120.60i	−0.320669	+	0.116714i	−0.497339	−	0.867556i	$-0.665690\pi$
$229$	−16816.2	+	6120.60i	−0.320669	+	0.116714i	0.176670	+	0.984270i	$0.443467\pi$
$230$	5427.07	+	14910.7i	0.102591	+	0.281867i
$231$		0			0
$232$	−36173.3	−	205149.i	−0.672066	−	3.81148i
$233$	−56263.0	−	32483.4i	−1.03636	−	0.598343i	−0.117560	−	0.993066i	$-0.537507\pi$
$233$	−56263.0	−	32483.4i	−1.03636	−	0.598343i	−0.918800	+	0.394723i	$0.870841\pi$
$234$		0			0
$235$	3919.13	+	6788.14i	0.0709666	+	0.122918i
$236$	101374.	+	120813.i	1.82013	+	2.16914i
$237$		0			0
$238$	−5724.72	+	32466.5i	−0.101065	+	0.573168i
$239$	49542.8	−	59042.8i	0.867330	−	1.03364i	−0.131772	−	0.991280i	$-0.542067\pi$
$239$	49542.8	−	59042.8i	0.867330	−	1.03364i	0.999102	−	0.0423636i	$-0.0134888\pi$
$240$		0			0
$241$	64608.0	+	23515.4i	1.11238	+	0.404872i	0.831865	−	0.554978i	$-0.187273\pi$
$241$	64608.0	+	23515.4i	1.11238	+	0.404872i	0.280512	+	0.959850i	$0.409496\pi$
$242$		−	26314.5i		−	0.449329i
$243$		0			0
$244$	−190470.			−3.19924
$245$	−8699.71	+	23902.3i	−0.144935	+	0.398205i
$246$		0			0
$247$	−28935.2	−	24279.5i	−0.474277	−	0.397966i
$248$	−239793.	−	42281.9i	−3.89882	−	0.687466i
$249$		0			0
$250$	−95500.7	+	80134.6i	−1.52801	+	1.28215i
$251$	−18118.3	+	10460.6i	−0.287588	+	0.166039i	−0.636854	−	0.770985i	$-0.719764\pi$
$251$	−18118.3	+	10460.6i	−0.287588	+	0.166039i	0.349266	+	0.937024i	$0.386431\pi$
$252$		0			0
$253$	−5210.40	+	9024.67i	−0.0814010	+	0.140991i
$254$	−19460.3	+	3431.38i	−0.301636	+	0.0531866i
$255$		0			0
$256$	67406.6	−	24534.0i	1.02854	−	0.374359i
$257$	−16391.4	−	45035.0i	−0.248170	−	0.681842i	−0.999753	−	0.0222038i	$-0.992932\pi$
$257$	−16391.4	−	45035.0i	−0.248170	−	0.681842i	0.751583	−	0.659638i	$-0.229290\pi$
$258$		0			0
$259$	5808.75	+	32943.1i	0.0865931	+	0.491094i
$260$	165095.	+	95317.9i	2.44224	+	1.41003i
$261$		0			0
$262$	−93523.3	−	161987.i	−1.36244	−	2.35982i
$263$	70364.7	+	83857.4i	1.01729	+	1.21236i	0.977016	+	0.213166i	$0.0683776\pi$
$263$	70364.7	+	83857.4i	1.01729	+	1.21236i	0.0402708	+	0.999189i	$0.487178\pi$
$264$		0			0
$265$	664.442	−	3768.24i	0.00946162	−	0.0536595i
$266$	−46833.7	+	55814.3i	−0.661905	+	0.788827i
$267$		0			0
$268$	−209668.	−	76312.9i	−2.91919	−	1.06250i
$269$		−	40040.7i		−	0.553347i	−0.960964	−	0.276673i	$-0.910768\pi$
$269$		−	40040.7i		−	0.553347i	0.960964	−	0.276673i	$-0.0892320\pi$
$270$		0			0
$271$	76589.9			1.04288			0.521438	−	0.853289i	$-0.325396\pi$
$271$	76589.9			1.04288			0.521438	+	0.853289i	$0.325396\pi$
$272$	15453.5	−	42458.1i	0.208876	−	0.573883i
$273$		0			0
$274$	−16384.7	−	13748.4i	−0.218242	−	0.183127i
$275$	−15859.8	−	2796.52i	−0.209717	−	0.0369788i
$276$		0			0
$277$	−62598.7	+	52526.6i	−0.815842	+	0.684573i	−0.951994	−	0.306115i	$-0.900971\pi$
$277$	−62598.7	+	52526.6i	−0.815842	+	0.684573i	0.136153	+	0.990688i	$0.456526\pi$
$278$	−76347.9	+	44079.5i	−0.987888	+	0.570357i
$279$		0			0
$280$	107252.	−	185767.i	1.36802	−	2.36947i
$281$	24750.1	−	4364.12i	0.313448	−	0.0552693i	−0.0147114	−	0.999892i	$-0.504683\pi$
$281$	24750.1	−	4364.12i	0.313448	−	0.0552693i	0.328159	+	0.944623i	$0.393572\pi$
$282$		0			0
$283$	−134029.	+	48782.5i	−1.67350	+	0.609103i	−0.992396	−	0.123087i	$-0.960721\pi$
$283$	−134029.	+	48782.5i	−1.67350	+	0.609103i	−0.681101	+	0.732190i	$0.738498\pi$
$284$	−58884.0	−	161782.i	−0.730063	−	2.00583i
$285$		0			0
$286$	30798.6	+	174668.i	0.376529	+	2.13540i
$287$	−9671.34	−	5583.75i	−0.117415	−	0.0677895i
$288$		0			0
$289$	−38963.8	−	67487.2i	−0.466515	−	0.808027i
$290$	−129866.	−	154769.i	−1.54419	−	1.84029i
$291$		0			0
$292$	14496.6	−	82214.2i	0.170020	−	0.964231i
$293$	−40927.6	+	48775.7i	−0.476740	+	0.568156i	−0.949794	−	0.312877i	$-0.898707\pi$
$293$	−40927.6	+	48775.7i	−0.476740	+	0.568156i	0.473054	+	0.881034i	$0.343152\pi$
$294$		0			0
$295$	83843.3	+	30516.5i	0.963440	+	0.350663i
$296$		−	92470.8i		−	1.05541i
$297$		0			0
$298$	293804.			3.30846
$299$	−7740.00	+	21265.5i	−0.0865763	+	0.237866i
$300$		0			0
$301$	32024.4	+	26871.6i	0.353466	+	0.296593i
$302$	87808.5	+	15483.0i	0.962770	+	0.169762i
$303$		0			0
$304$	76495.5	−	64187.4i	0.827730	−	0.694548i
$305$	−93321.4	+	53879.2i	−1.00319	+	0.579190i
$306$		0			0
$307$	−52523.8	+	90973.9i	−0.557288	+	0.965250i	0.440434	+	0.897785i	$0.354825\pi$
$307$	−52523.8	+	90973.9i	−0.557288	+	0.965250i	−0.997722	+	0.0674654i	$0.978509\pi$
$308$	237828.	−	41935.4i	2.50704	−	0.442058i
$309$		0			0
$310$	−221912.	+	80769.5i	−2.30918	+	0.840473i
$311$	−25478.6	−	70001.8i	−0.263423	−	0.723750i	−0.998931	−	0.0462329i	$-0.985278\pi$
$311$	−25478.6	−	70001.8i	−0.263423	−	0.723750i	0.735507	−	0.677517i	$-0.236944\pi$
$312$		0			0
$313$	1372.40	+	7783.24i	0.0140085	+	0.0794460i	0.991011	−	0.133784i	$-0.0427128\pi$
$313$	1372.40	+	7783.24i	0.0140085	+	0.0794460i	−0.977002	+	0.213230i	$0.931602\pi$
$314$	202449.	+	116884.i	2.05332	+	1.18548i
$315$		0			0
$316$	184578.	+	319698.i	1.84844	+	3.20159i
$317$	102731.	+	122430.i	1.02231	+	1.21834i	0.975628	+	0.219429i	$0.0704196\pi$
$317$	102731.	+	122430.i	1.02231	+	1.21834i	0.0466797	+	0.998910i	$0.485136\pi$
$318$		0			0
$319$	23040.2	−	130668.i	0.226415	−	1.28406i
$320$	−51697.8	+	61611.0i	−0.504861	+	0.601670i
$321$		0			0
$322$	41019.9	+	14930.0i	0.395624	+	0.143995i
$323$			12361.9i			0.118490i
$324$		0			0
$325$	−34973.3			−0.331108
$326$	−17619.2	+	48408.3i	−0.165787	+	0.455496i
$327$		0			0
$328$	23648.4	+	19843.4i	0.219814	+	0.184445i
$329$	21235.7	+	3744.42i	0.196189	+	0.0345934i
$330$		0			0
$331$	121009.	−	101539.i	1.10449	−	0.926777i	0.106771	−	0.994284i	$-0.465949\pi$
$331$	121009.	−	101539.i	1.10449	−	0.926777i	0.997719	+	0.0675065i	$0.0215043\pi$
$332$	−170149.	+	98235.8i	−1.54367	+	0.891238i
$333$		0			0
$334$	−36004.0	+	62360.8i	−0.322744	+	0.559008i
$335$	−124315.	+	21920.0i	−1.10773	+	0.195322i
$336$		0			0
$337$	−38630.3	+	14060.3i	−0.340148	+	0.123804i	−0.506446	−	0.862272i	$-0.669041\pi$
$337$	−38630.3	+	14060.3i	−0.340148	+	0.123804i	0.166298	+	0.986076i	$0.446819\pi$
$338$	59686.8	+	163988.i	0.522450	+	1.43542i
$339$		0			0
$340$	−10834.0	−	61442.6i	−0.0937197	−	0.531511i
$341$	−134312.	−	77544.9i	−1.15506	−	0.666875i
$342$		0			0
$343$	−36759.9	−	63670.1i	−0.312454	−	0.541187i
$344$	−74282.4	−	88526.4i	−0.627725	−	0.748093i
$345$		0			0
$346$	−57115.3	+	323917.i	−0.477090	+	2.70571i
$347$	34115.4	−	40657.1i	0.283329	−	0.337658i	−0.605544	−	0.795812i	$-0.707045\pi$
$347$	34115.4	−	40657.1i	0.283329	−	0.337658i	0.888873	+	0.458153i	$0.151489\pi$
$348$		0			0
$349$	−44594.5	−	16231.1i	−0.366126	−	0.133259i	0.152404	−	0.988318i	$-0.451298\pi$
$349$	−44594.5	−	16231.1i	−0.366126	−	0.133259i	−0.518530	+	0.855059i	$0.673521\pi$
$350$			67461.4i			0.550705i
$351$		0			0
$352$	−190729.			−1.53933
$353$	22124.4	−	60786.2i	0.177550	−	0.487816i	−0.818711	−	0.574206i	$-0.805311\pi$
$353$	22124.4	−	60786.2i	0.177550	−	0.487816i	0.996261	+	0.0863900i	$0.0275331\pi$
$354$		0			0
$355$	−74614.7	−	62609.1i	−0.592063	−	0.496799i
$356$	338824.	+	59743.8i	2.67346	+	0.471403i
$357$		0			0
$358$	7674.63	−	6439.78i	0.0598814	−	0.0502464i
$359$	−29839.9	+	17228.1i	−0.231530	+	0.133674i	−0.611278	−	0.791416i	$-0.709344\pi$
$359$	−29839.9	+	17228.1i	−0.231530	+	0.133674i	0.379747	+	0.925090i	$0.376011\pi$
$360$		0			0
$361$	51500.1	−	89200.8i	0.395179	−	0.684470i
$362$	115328.	−	20335.5i	0.880072	−	0.155180i
$363$		0			0
$364$	492816.	−	179371.i	3.71948	−	1.35378i
$365$	−16153.7	−	44381.9i	−0.121251	−	0.333135i
$366$		0			0
$367$	15268.7	+	86593.3i	0.113363	+	0.642913i	0.987548	+	0.157319i	$0.0502852\pi$
$367$	15268.7	+	86593.3i	0.113363	+	0.642913i	−0.874185	+	0.485593i	$0.838604\pi$
$368$	−51811.9	−	29913.6i	−0.382590	−	0.220889i
$369$		0			0
$370$	−44842.1	−	77668.7i	−0.327553	−	0.567339i
$371$	−6766.27	−	8063.73i	−0.0491589	−	0.0585852i
$372$		0			0
$373$	30169.5	−	171099.i	0.216845	−	1.22979i	−0.660831	−	0.750535i	$-0.729796\pi$
$373$	30169.5	−	171099.i	0.216845	−	1.22979i	0.877676	−	0.479255i	$-0.159093\pi$
$374$	37311.5	−	44466.1i	0.266747	−	0.317896i
$375$		0			0
$376$	−56013.5	−	20387.2i	−0.396202	−	0.144206i
$377$		−	288141.i		−	2.02732i
$378$		0			0
$379$	169412.			1.17941			0.589707	−	0.807617i	$-0.299243\pi$
$379$	169412.			1.17941			0.589707	+	0.807617i	$0.299243\pi$
$380$	47160.3	−	129572.i	0.326595	−	0.897313i
$381$		0			0
$382$	−27618.1	−	23174.3i	−0.189263	−	0.158811i
$383$	−1781.76	−	314.173i	−0.0121465	−	0.00214176i	0.167572	−	0.985860i	$-0.446407\pi$
$383$	−1781.76	−	314.173i	−0.0121465	−	0.00214176i	−0.179718	+	0.983718i	$0.557519\pi$
$384$		0			0
$385$	104662.	−	87821.9i	0.706103	−	0.592491i
$386$	394856.	−	227970.i	2.65011	−	1.53004i
$387$		0			0
$388$	−190737.	+	330365.i	−1.26698	+	2.19448i
$389$	−178130.	+	31409.1i	−1.17717	+	0.207566i	−0.727805	−	0.685784i	$-0.759460\pi$
$389$	−178130.	+	31409.1i	−1.17717	+	0.207566i	−0.449362	+	0.893350i	$0.648348\pi$
$390$		0			0
$391$	6959.68	−	2533.12i	0.0455235	−	0.0165692i
$392$	−66159.4	−	181772.i	−0.430546	−	1.18292i
$393$		0			0
$394$	78744.4	+	446582.i	0.507256	+	2.87679i
$395$	180869.	+	104425.i	1.15923	+	0.669284i
$396$		0			0
$397$	−148101.	−	256519.i	−0.939675	−	1.62756i	−0.766078	−	0.642747i	$-0.777794\pi$
$397$	−148101.	−	256519.i	−0.939675	−	1.62756i	−0.173597	−	0.984817i	$-0.555539\pi$
$398$	−173046.	−	206228.i	−1.09244	−	1.30191i
$399$		0			0
$400$	16055.2	−	91053.7i	0.100345	−	0.569085i
$401$	−44510.5	+	53045.5i	−0.276805	+	0.329883i	−0.886479	−	0.462769i	$-0.846856\pi$
$401$	−44510.5	+	53045.5i	−0.276805	+	0.329883i	0.609674	+	0.792652i	$0.291300\pi$
$402$		0			0
$403$	−316488.	−	115192.i	−1.94871	−	0.709273i
$404$			294255.i			1.80286i
$405$		0			0
$406$	−555807.			−3.37188
$407$	20144.4	−	55346.3i	0.121609	−	0.334118i
$408$		0			0
$409$	119306.	+	100110.i	0.713208	+	0.598452i	0.925497	−	0.378754i	$-0.123648\pi$
$409$	119306.	+	100110.i	0.713208	+	0.598452i	−0.212289	+	0.977207i	$0.568092\pi$
$410$	29485.6	+	5199.11i	0.175405	+	0.0309287i
$411$		0			0
$412$	294138.	−	246811.i	1.73283	−	1.45402i
$413$	212573.	−	122729.i	1.24626	−	0.719528i
$414$		0			0
$415$	−55576.9	+	96262.1i	−0.322700	+	0.558932i
$416$	−407903.	+	71924.2i	−2.35706	+	0.415612i
$417$		0			0
$418$	120550.	−	43876.6i	0.689946	−	0.251120i
$419$	71878.9	+	197486.i	0.409424	+	1.12488i	0.957494	+	0.288452i	$0.0931404\pi$
$419$	71878.9	+	197486.i	0.409424	+	1.12488i	−0.548070	+	0.836432i	$0.684637\pi$
$420$		0			0
$421$	−38834.3	−	220240.i	−0.219104	−	1.24260i	−0.873640	−	0.486572i	$-0.838247\pi$
$421$	−38834.3	−	220240.i	−0.219104	−	1.24260i	0.654536	−	0.756031i	$-0.272864\pi$
$422$	−511841.	−	295512.i	−2.87416	−	1.65939i
$423$		0			0
$424$	14549.4	+	25200.2i	0.0809305	+	0.140176i
$425$	7357.29	+	8768.07i	0.0407324	+	0.0485430i
$426$		0			0
$427$	−51477.3	+	291942.i	−0.282332	+	1.60118i
$428$	−247862.	+	295390.i	−1.35308	+	1.61253i
$429$		0			0
$430$	−105321.	−	38333.8i	−0.569611	−	0.207322i
$431$			317947.i			1.71159i	0.517312	+	0.855797i	$0.326933\pi$
$431$			317947.i			1.71159i	−0.517312	+	0.855797i	$0.673067\pi$
$432$		0			0
$433$	95041.9			0.506920			0.253460	−	0.967346i	$-0.418431\pi$
$433$	95041.9			0.506920			0.253460	+	0.967346i	$0.418431\pi$
$434$	−222199.	+	610487.i	−1.17968	+	3.24113i
$435$		0			0
$436$	−136731.	−	114731.i	−0.719275	−	0.603544i
$437$	16119.9	+	2842.37i	0.0844110	+	0.0148839i
$438$		0			0
$439$	−188629.	+	158279.i	−0.978770	+	0.821285i	−0.983903	−	0.178702i	$-0.942810\pi$
$439$	−188629.	+	158279.i	−0.978770	+	0.821285i	0.00513380	+	0.999987i	$0.498366\pi$
$440$	−327083.	+	188842.i	−1.68948	+	0.975421i
$441$		0			0
$442$	63028.0	−	109168.i	0.322618	−	0.558791i
$443$	275106.	−	48508.6i	1.40182	−	0.247179i	0.578930	−	0.815377i	$-0.303471\pi$
$443$	275106.	−	48508.6i	1.40182	−	0.247179i	0.822891	+	0.568199i	$0.192359\pi$
$444$		0			0
$445$	182908.	−	66573.1i	0.923661	−	0.336185i
$446$	−6300.75	−	17311.2i	−0.0316755	−	0.0870276i
$447$		0			0
$448$	38421.1	+	217897.i	0.191432	+	1.08566i
$449$	−34995.0	−	20204.4i	−0.173586	−	0.100220i	0.410690	−	0.911775i	$-0.365288\pi$
$449$	−34995.0	−	20204.4i	−0.173586	−	0.100220i	−0.584275	+	0.811555i	$0.698621\pi$
$450$		0			0
$451$	9831.43	+	17028.5i	0.0483352	+	0.0837190i
$452$	253926.	+	302617.i	1.24288	+	1.48121i
$453$		0			0
$454$	77591.1	−	440041.i	0.376444	−	2.13492i
$455$	190718.	−	227289.i	0.921232	−	1.09788i
$456$		0			0
$457$	189104.	+	68828.3i	0.905460	+	0.329560i	0.752438	−	0.658663i	$-0.228878\pi$
$457$	189104.	+	68828.3i	0.905460	+	0.329560i	0.153021	+	0.988223i	$0.451100\pi$
$458$		−	131990.i		−	0.629230i
$459$		0			0
$460$	−82611.9			−0.390415
$461$	93148.4	−	255923.i	0.438302	−	1.20423i	−0.502294	−	0.864697i	$-0.667510\pi$
$461$	93148.4	−	255923.i	0.438302	−	1.20423i	0.940596	−	0.339528i	$-0.110267\pi$
$462$		0			0
$463$	86499.1	+	72581.3i	0.403505	+	0.338581i	0.821847	−	0.569709i	$-0.192944\pi$
$463$	86499.1	+	72581.3i	0.403505	+	0.338581i	−0.418341	+	0.908290i	$0.637388\pi$
$464$	750181.	+	132277.i	3.48442	+	0.614397i
$465$		0			0
$466$	367066.	−	308005.i	1.69033	−	1.41836i
$467$	−177670.	+	102578.i	−0.814669	+	0.470349i	−0.848575	−	0.529076i	$-0.822539\pi$
$467$	−177670.	+	102578.i	−0.814669	+	0.470349i	0.0339059	+	0.999425i	$0.489205\pi$
$468$		0			0
$469$	−173634.	+	300744.i	−0.789387	+	1.36726i
$470$	−56933.7	+	10038.9i	−0.257735	+	0.0454456i
$471$		0			0
$472$	−637611.	+	232071.i	−2.86201	+	1.04169i
$473$	−25175.0	−	69167.6i	−0.112524	−	0.309158i
$474$		0			0
$475$	4392.66	+	24912.0i	0.0194688	+	0.110413i
$476$	−148643.	−	85819.0i	−0.656040	−	0.378765i
$477$		0			0
$478$	284237.	+	492313.i	1.24401	+	2.15469i
$479$	−216950.	−	258551.i	−0.945559	−	1.12687i	−0.991782	−	0.127942i	$-0.959163\pi$
$479$	−216950.	−	258551.i	−0.945559	−	1.12687i	0.0462229	−	0.998931i	$-0.485282\pi$
$480$		0			0
$481$	22210.7	−	125963.i	0.0960001	−	0.544444i
$482$	−325961.	+	388465.i	−1.40305	+	1.67208i
$483$		0			0
$484$	128739.	+	46857.2i	0.549565	+	0.200025i
$485$			215819.i			0.917498i
$486$		0			0
$487$	141608.			0.597078			0.298539	−	0.954398i	$-0.403501\pi$
$487$	141608.			0.597078			0.298539	+	0.954398i	$0.403501\pi$
$488$	280278.	−	770058.i	1.17693	−	3.23358i
$489$		0			0
$490$	−143716.	−	120592.i	−0.598567	−	0.502257i
$491$	−84542.2	−	14907.1i	−0.350680	−	0.0618343i	−0.00446623	−	0.999990i	$-0.501422\pi$
$491$	−84542.2	−	14907.1i	−0.350680	−	0.0618343i	−0.346214	+	0.938156i	$0.612533\pi$
$492$		0			0
$493$	−72239.2	+	60615.9i	−0.297221	+	0.249398i
$494$	241269.	−	139297.i	0.988660	−	0.570803i
$495$		0			0
$496$	445196.	−	771102.i	1.80962	−	3.13436i
$497$	−263886.	+	46530.3i	−1.06833	+	0.188375i
$498$		0			0
$499$	−65507.9	+	23842.9i	−0.263083	+	0.0957543i	−0.470194	−	0.882563i	$-0.655816\pi$
$499$	−65507.9	+	23842.9i	−0.263083	+	0.0957543i	0.207111	+	0.978317i	$0.433594\pi$
$500$	−221990.	−	609912.i	−0.887960	−	2.43965i
$501$		0			0
$502$	−26795.1	−	151963.i	−0.106328	−	0.603017i
$503$	177766.	+	102633.i	0.702609	+	0.405652i	0.808318	−	0.588746i	$-0.200378\pi$
$503$	177766.	+	102633.i	0.702609	+	0.405652i	−0.105709	+	0.994397i	$0.533711\pi$
$504$		0			0
$505$	83237.5	+	144172.i	0.326390	+	0.565323i
$506$	−49404.5	−	58878.0i	−0.192959	−	0.229960i
$507$		0			0
$508$	17864.8	−	101316.i	0.0692263	−	0.392602i
$509$	−240103.	+	286143.i	−0.926748	+	1.10446i	0.0675389	+	0.997717i	$0.478485\pi$
$509$	−240103.	+	286143.i	−0.926748	+	1.10446i	−0.994287	+	0.106739i	$0.965959\pi$
$510$		0			0
$511$	−122096.	−	44439.3i	−0.467583	−	0.170186i
$512$			501959.i			1.91482i
$513$		0			0
$514$	353478.			1.33794
$515$	74297.4	−	204130.i	0.280130	−	0.769650i
$516$		0			0
$517$	−29084.3	−	24404.7i	−0.108812	−	0.0913044i
$518$	−242975.	−	42843.1i	−0.905529	−	0.159669i
$519$		0			0
$520$	−628304.	+	527210.i	−2.32361	+	1.94974i
$521$	−42563.3	+	24573.9i	−0.156805	+	0.0905313i	−0.576349	−	0.817204i	$-0.695523\pi$
$521$	−42563.3	+	24573.9i	−0.156805	+	0.0905313i	0.419544	+	0.907735i	$0.362190\pi$
$522$		0			0
$523$	80649.7	−	139689.i	0.294849	−	0.510693i	−0.680101	−	0.733119i	$-0.738064\pi$
$523$	80649.7	−	139689.i	0.294849	−	0.510693i	0.974950	+	0.222425i	$0.0713974\pi$
$524$	959026.	−	169102.i	3.49275	−	0.615867i
$525$		0			0
$526$	−758702.	+	276145.i	−2.74220	+	0.998080i
$527$	37699.7	+	103579.i	0.135743	+	0.372950i
$528$		0			0
$529$	46890.9	+	265932.i	0.167563	+	0.950296i
$530$	24440.8	+	14110.9i	0.0870090	+	0.0502346i
$531$		0			0
$532$	−189666.	−	328512.i	−0.670142	−	1.16072i
$533$	27447.5	+	32710.7i	0.0966158	+	0.115142i
$534$		0			0
$535$	−37882.4	+	214842.i	−0.132352	+	0.750604i
$536$	617057.	−	735380.i	2.14781	−	2.55966i
$537$		0			0
$538$	277514.	+	101007.i	0.958785	+	0.348969i
$539$		−	123208.i		−	0.424093i
$540$		0			0
$541$	−385473.			−1.31704			−0.658520	−	0.752563i	$-0.728817\pi$
$541$	−385473.			−1.31704			−0.658520	+	0.752563i	$0.728817\pi$
$542$	−193206.	+	530829.i	−0.657692	+	1.80699i
$543$		0			0
$544$	103842.	+	87133.8i	0.350893	+	0.294435i
$545$	−99446.7	−	17535.1i	−0.334809	−	0.0590359i
$546$		0			0
$547$	−14228.4	+	11939.1i	−0.0475535	+	0.0399021i	−0.666255	−	0.745724i	$-0.732104\pi$
$547$	−14228.4	+	11939.1i	−0.0475535	+	0.0399021i	0.618701	+	0.785626i	$0.287659\pi$
$548$	96437.2	−	55678.1i	0.321132	−	0.185406i
$549$		0			0
$550$	59390.3	−	102867.i	0.196332	−	0.340056i
$551$	−205247.	+	36190.6i	−0.676043	+	0.119205i
$552$		0			0
$553$	539902.	−	196508.i	1.76549	−	0.642585i
$554$	−206139.	−	566364.i	−0.671648	−	1.84534i
$555$		0			0
$556$	−79701.4	−	452009.i	−0.257820	−	1.46217i
$557$	413631.	+	238810.i	1.33322	+	0.769737i	0.985792	−	0.167969i	$-0.0537209\pi$
$557$	413631.	+	238810.i	1.33322	+	0.769737i	0.347431	+	0.937706i	$0.387054\pi$
$558$		0			0
$559$	−79923.7	−	138432.i	−0.255771	−	0.443009i
$560$	504198.	+	600880.i	1.60777	+	1.91607i
$561$		0			0
$562$	−32188.0	+	182547.i	−0.101911	+	0.577967i
$563$	−94339.1	+	112429.i	−0.297629	+	0.354700i	−0.894047	−	0.447974i	$-0.852146\pi$
$563$	−94339.1	+	112429.i	−0.297629	+	0.354700i	0.596418	+	0.802674i	$0.296590\pi$
$564$		0			0
$565$	210015.	+	76439.1i	0.657889	+	0.239452i
$566$		−	1.05199e6i		−	3.28380i
$567$		0			0
$568$	740725.			2.29594
$569$	−56131.6	+	154220.i	−0.173373	+	0.476340i	−0.995696	−	0.0926824i	$-0.970456\pi$
$569$	−56131.6	+	154220.i	−0.173373	+	0.476340i	0.822322	+	0.569022i	$0.192678\pi$
$570$		0			0
$571$	294790.	+	247358.i	0.904151	+	0.758673i	0.970997	−	0.239091i	$-0.0768493\pi$
$571$	294790.	+	247358.i	0.904151	+	0.758673i	−0.0668465	+	0.997763i	$0.521294\pi$
$572$	−909371.	−	160347.i	−2.77939	−	0.490081i
$573$		0			0
$574$	63096.9	−	52944.6i	0.191507	−	0.160693i
$575$	13125.2	−	7577.82i	0.0396980	−	0.0229197i
$576$		0			0
$577$	−204899.	+	354895.i	−0.615442	+	1.06598i	0.374865	+	0.927080i	$0.377689\pi$
$577$	−204899.	+	354895.i	−0.615442	+	1.06598i	−0.990307	+	0.138898i	$0.955644\pi$
$578$	566031.	−	99806.6i	1.69428	−	0.298747i
$579$		0			0
$580$	988425.	−	359757.i	2.93824	−	1.06943i
$581$	104585.	+	287346.i	0.309827	+	0.851242i
$582$		0			0
$583$	3218.42	+	18252.6i	0.00946903	+	0.0537016i
$584$	311055.	+	179588.i	0.912036	+	0.526564i
$585$		0			0
$586$	−234810.	−	406703.i	−0.683789	−	1.18436i
$587$	25038.3	+	29839.4i	0.0726654	+	0.0865993i	0.801152	−	0.598460i	$-0.204221\pi$
$587$	25038.3	+	29839.4i	0.0726654	+	0.0865993i	−0.728487	+	0.685060i	$0.759776\pi$
$588$		0			0
$589$	−42302.2	+	239908.i	−0.121936	+	0.691534i
$590$	−423008.	+	504121.i	−1.21519	+	1.44821i
$591$		0			0
$592$	317751.	+	115652.i	0.906659	+	0.329997i
$593$			179775.i			0.511234i	0.966778	+	0.255617i	$0.0822785\pi$
$593$			179775.i			0.511234i	−0.966778	+	0.255617i	$0.917721\pi$
$594$		0			0
$595$	−97104.2			−0.274286
$596$	−523165.	+	1.43738e6i	−1.47281	+	4.04651i
$597$		0			0
$598$	−127862.	−	107289.i	−0.357552	−	0.300022i
$599$	198367.	+	34977.5i	0.552861	+	0.0974843i	0.443098	−	0.896473i	$-0.353880\pi$
$599$	198367.	+	34977.5i	0.552861	+	0.0974843i	0.109764	+	0.993958i	$0.464991\pi$
$600$		0			0
$601$	−333121.	+	279521.i	−0.922258	+	0.773867i	−0.974411	−	0.224773i	$-0.927836\pi$
$601$	−333121.	+	279521.i	−0.922258	+	0.773867i	0.0521530	+	0.998639i	$0.483392\pi$
$602$	−267027.	+	154168.i	−0.736821	+	0.425404i
$603$		0			0
$604$	−232105.	+	402017.i	−0.636224	+	1.10197i
$605$	76330.9	−	13459.2i	0.208540	−	0.0367713i
$606$		0			0
$607$	281891.	−	102600.i	0.765074	−	0.278464i	0.0701392	−	0.997537i	$-0.477656\pi$
$607$	281891.	−	102600.i	0.765074	−	0.278464i	0.694934	+	0.719073i	$0.255433\pi$
$608$	102465.	+	281522.i	0.277185	+	0.761561i
$609$		0			0
$610$	−138013.	−	782709.i	−0.370902	−	2.10349i
$611$	−71404.3	−	41225.3i	−0.191268	−	0.110429i
$612$		0			0
$613$	149401.	+	258771.i	0.397588	+	0.688643i	0.993428	−	0.114461i	$-0.0365140\pi$
$613$	149401.	+	258771.i	0.397588	+	0.688643i	−0.595840	+	0.803103i	$0.703181\pi$
$614$	−498025.	−	593524.i	−1.32104	−	1.57435i
$615$		0			0
$616$	−180423.	+	1.02323e6i	−0.475479	+	2.69657i
$617$	175999.	−	209747.i	0.462317	−	0.550968i	−0.483637	−	0.875269i	$-0.660685\pi$
$617$	175999.	−	209747.i	0.462317	−	0.550968i	0.945954	+	0.324301i	$0.105129\pi$
$618$		0			0
$619$	−349308.	−	127138.i	−0.911648	−	0.331813i	−0.156737	−	0.987640i	$-0.550098\pi$
$619$	−349308.	−	127138.i	−0.911648	−	0.331813i	−0.754911	+	0.655828i	$0.772320\pi$
$620$		−	1.22949e6i		−	3.19846i
$621$		0			0
$622$	549441.			1.42017
$623$	183144.	−	503185.i	0.471865	−	1.29644i
$624$		0			0
$625$	−208021.	−	174550.i	−0.532533	−	0.446849i
$626$	−57406.2	−	10122.3i	−0.146491	−	0.0258303i
$627$		0			0
$628$	−932326.	+	782314.i	−2.36401	+	1.98364i
$629$	−36252.4	+	20930.3i	−0.0916294	+	0.0529023i
$630$		0			0
$631$	315797.	−	546976.i	0.793139	−	1.37376i	−0.130876	−	0.991399i	$-0.541779\pi$
$631$	315797.	−	546976.i	0.793139	−	1.37376i	0.924014	−	0.382357i	$-0.124888\pi$
$632$	−1.56413e6	+	275798.i	−3.91596	+	0.690490i
$633$		0			0
$634$	−1.10769e6	+	403165.i	−2.75574	+	1.00301i
$635$	−19906.9	−	54693.9i	−0.0493693	−	0.135641i
$636$		0			0
$637$	−46461.9	−	263499.i	−0.114503	−	0.649381i
$638$	847510.	+	489310.i	2.08211	+	1.20211i
$639$		0			0
$640$	18406.7	+	31881.4i	0.0449383	+	0.0778355i
$641$	350320.	+	417495.i	0.852608	+	1.01610i	0.999636	+	0.0269659i	$0.00858456\pi$
$641$	350320.	+	417495.i	0.852608	+	1.01610i	−0.147029	+	0.989132i	$0.546971\pi$
$642$		0			0
$643$	42907.2	−	243339.i	0.103779	−	0.588558i	−0.887922	−	0.459993i	$-0.847852\pi$
$643$	42907.2	−	243339.i	0.103779	−	0.588558i	0.991701	−	0.128565i	$-0.0410370\pi$
$644$	−146085.	+	174097.i	−0.352235	+	0.419778i
$645$		0			0
$646$	−85678.1	−	31184.3i	−0.205308	−	0.0747259i
$647$			116065.i			0.277263i	0.990344	+	0.138632i	$0.0442704\pi$
$647$			116065.i			0.277263i	−0.990344	+	0.138632i	$0.955730\pi$
$648$		0			0
$649$	−432183.			−1.02607
$650$	88223.8	−	242393.i	0.208814	−	0.573711i
$651$		0			0
$652$	−205455.	−	172397.i	−0.483306	−	0.405542i
$653$	216448.	+	38165.6i	0.507606	+	0.0895047i	0.421586	−	0.906789i	$-0.361474\pi$
$653$	216448.	+	38165.6i	0.507606	+	0.0895047i	0.0860208	+	0.996293i	$0.472585\pi$
$654$		0			0
$655$	422044.	−	354137.i	0.983728	−	0.825446i
$656$	−97763.3	+	56443.6i	−0.227179	+	0.131162i
$657$		0			0
$658$	−79521.2	+	137735.i	−0.183667	+	0.318120i
$659$	−547567.	+	96550.9i	−1.26086	+	0.222324i	−0.763834	−	0.645412i	$-0.776686\pi$
$659$	−547567.	+	96550.9i	−1.26086	+	0.222324i	−0.497025	+	0.867736i	$0.665574\pi$
$660$		0			0
$661$	98410.6	−	35818.5i	0.225237	−	0.0819794i	−0.226937	−	0.973910i	$-0.572871\pi$
$661$	98410.6	−	35818.5i	0.225237	−	0.0819794i	0.452173	+	0.891930i	$0.350649\pi$
$662$	398486.	+	1.09483e6i	0.909280	+	2.49823i
$663$		0			0
$664$	−146785.	−	832459.i	−0.332924	−	1.88811i
$665$	−185856.	−	107304.i	−0.420274	−	0.242645i
$666$		0			0
$667$	62432.8	+	108137.i	0.140334	+	0.243065i
$668$	−240978.	−	287186.i	−0.540038	−	0.643592i
$669$		0			0
$670$	161674.	−	916896.i	0.360155	−	2.04254i
$671$	335509.	−	399844.i	0.745176	−	0.888066i
$672$		0			0
$673$	153084.	+	55718.1i	0.337987	+	0.123017i	0.505438	−	0.862863i	$-0.331331\pi$
$673$	153084.	+	55718.1i	0.337987	+	0.123017i	−0.167450	+	0.985881i	$0.553553\pi$
$674$		−	303207.i		−	0.667452i
$675$		0			0
$676$	−908564.			−1.98821
$677$	282532.	−	776249.i	0.616439	−	1.69365i	−0.0990996	−	0.995078i	$-0.531596\pi$
$677$	282532.	−	776249.i	0.616439	−	1.69365i	0.715538	−	0.698574i	$-0.246182\pi$
$678$		0			0
$679$	454818.	+	381638.i	0.986502	+	0.827774i
$680$	264351.	+	46612.3i	0.571694	+	0.100805i
$681$		0			0
$682$	876264.	−	735273.i	1.88394	−	1.58081i
$683$	−378309.	+	218417.i	−0.810970	+	0.468214i	−0.847293	−	0.531126i	$-0.821769\pi$
$683$	−378309.	+	218417.i	−0.810970	+	0.468214i	0.0363224	+	0.999340i	$0.488436\pi$
$684$		0			0
$685$	31499.9	−	54559.4i	0.0671317	−	0.116276i
$686$	534016.	−	94161.4i	1.13476	−	0.200090i
$687$		0			0
$688$	397101.	−	144533.i	0.838927	−	0.305345i
$689$	13766.2	+	37822.2i	0.0289984	+	0.0796725i
$690$		0			0
$691$	−112114.	−	635833.i	−0.234804	−	1.33164i	−0.843026	−	0.537873i	$-0.819228\pi$
$691$	−112114.	−	635833.i	−0.234804	−	1.33164i	0.608222	−	0.793767i	$-0.291883\pi$
$692$	−1.48300e6	−	856211.i	−3.09692	−	1.78801i
$693$		0			0
$694$	195727.	+	339009.i	0.406379	+	0.703869i
$695$	−166912.	−	198918.i	−0.345556	−	0.411817i
$696$		0			0
$697$	2426.72	−	13762.6i	0.00499521	−	0.0283293i
$698$	224989.	−	268131.i	0.461796	−	0.550347i
$699$		0			0
$700$	−330042.	−	120126.i	−0.673556	−	0.245154i
$701$		−	142622.i		−	0.290236i	−0.989414	−	0.145118i	$-0.953644\pi$
$701$		−	142622.i		−	0.290236i	0.989414	−	0.145118i	$-0.0463562\pi$
$702$		0			0
$703$	−92515.1			−0.187198
$704$	133242.	−	366080.i	0.268841	−	0.738636i
$705$		0			0
$706$	365487.	+	306680.i	0.733267	+	0.615284i
$707$	451020.	+	79526.9i	0.902312	+	0.159102i
$708$		0			0
$709$	−314956.	+	264279.i	−0.626552	+	0.525740i	−0.899855	−	0.436188i	$-0.856328\pi$
$709$	−314956.	+	264279.i	−0.626552	+	0.525740i	0.273303	+	0.961928i	$0.411884\pi$
$710$	622155.	−	359202.i	1.23419	−	0.712560i
$711$		0			0
$712$	−740123.	+	1.28193e6i	−1.45997	+	2.52874i
$713$	143735.	−	25344.3i	0.282737	−	0.0498541i
$714$		0			0
$715$	−490908.	+	178676.i	−0.960259	+	0.349506i
$716$	17839.6	+	49013.8i	0.0347983	+	0.0956076i
$717$		0			0
$718$	−44130.0	−	250274.i	−0.0856023	−	0.485475i
$719$	−574218.	−	331525.i	−1.11076	−	0.641296i	−0.171731	−	0.985144i	$-0.554936\pi$
$719$	−574218.	−	331525.i	−1.11076	−	0.641296i	−0.939025	+	0.343848i	$0.888269\pi$
$720$		0			0
$721$	−298804.	−	517544.i	−0.574799	−	0.995582i
$722$	488319.	+	581956.i	0.936762	+	1.11639i
$723$		0			0
$724$	−105872.	+	600433.i	−0.201979	+	1.14548i
$725$	−124039.	+	147824.i	−0.235983	+	0.281234i
$726$		0			0
$727$	−63974.6	−	23284.9i	−0.121043	−	0.0440560i	0.280789	−	0.959770i	$-0.409404\pi$
$727$	−63974.6	−	23284.9i	−0.121043	−	0.0440560i	−0.401831	+	0.915714i	$0.631626\pi$
$728$			2.25637e6i			4.25744i
$729$		0			0
$730$	348352.			0.653691
$731$	−17892.5	+	49159.3i	−0.0334839	+	0.0919964i
$732$		0			0
$733$	−69209.9	−	58074.0i	−0.128813	−	0.108087i	0.576105	−	0.817376i	$-0.304572\pi$
$733$	−69209.9	−	58074.0i	−0.128813	−	0.108087i	−0.704918	+	0.709289i	$0.749016\pi$
$734$	−638678.	−	112616.i	−1.18547	−	0.209030i
$735$		0			0
$736$	137498.	−	115375.i	0.253829	−	0.212988i
$737$	529526.	−	305722.i	0.974882	−	0.562848i
$738$		0			0
$739$	386462.	−	669372.i	0.707650	−	1.22569i	−0.258077	−	0.966124i	$-0.583089\pi$
$739$	386462.	−	669372.i	0.707650	−	1.22569i	0.965727	−	0.259561i	$-0.0835779\pi$
$740$	459829.	−	81080.2i	0.839716	−	0.148065i
$741$		0			0
$742$	72956.8	−	26554.1i	0.132513	−	0.0482307i
$743$	−318668.	−	875534.i	−0.577246	−	1.58597i	−0.792802	−	0.609480i	$-0.791378\pi$
$743$	−318668.	−	875534.i	−0.577246	−	1.58597i	0.215555	−	0.976492i	$-0.430844\pi$
$744$		0			0
$745$	150273.	+	852242.i	0.270751	+	1.53550i
$746$	1.10975e6	+	640715.i	1.99411	+	1.15130i
$747$		0			0
$748$	151103.	+	261718.i	0.270066	+	0.467769i
$749$	385771.	+	459744.i	0.687647	+	0.819506i
$750$		0			0
$751$	88120.6	−	499757.i	0.156242	−	0.886092i	−0.801400	−	0.598129i	$-0.795911\pi$
$751$	88120.6	−	499757.i	0.156242	−	0.886092i	0.957642	−	0.287963i	$-0.0929779\pi$
$752$	140111.	−	166977.i	0.247762	−	0.295272i
$753$		0			0
$754$	1.99705e6	+	726867.i	3.51274	+	1.27853i
$755$			262627.i			0.460728i
$756$		0			0
$757$	−131229.			−0.229001			−0.114501	−	0.993423i	$-0.536527\pi$
$757$	−131229.			−0.229001			−0.114501	+	0.993423i	$0.536527\pi$
$758$	−427360.	+	1.17416e6i	−0.743799	+	2.04357i
$759$		0			0
$760$	454455.	+	381333.i	0.786799	+	0.660203i
$761$	113901.	+	20083.9i	0.196680	+	0.0346799i	0.271120	−	0.962546i	$-0.412606\pi$
$761$	113901.	+	20083.9i	0.196680	+	0.0346799i	−0.0744405	+	0.997225i	$0.523717\pi$
$762$		0			0
$763$	−212808.	+	178567.i	−0.365543	+	0.306727i
$764$	162555.	−	93850.9i	0.278492	−	0.160787i
$765$		0			0
$766$	6672.16	−	11556.5i	0.0113713	−	0.0196956i
$767$	−924290.	+	162977.i	−1.57115	+	0.277036i
$768$		0			0
$769$	−764397.	+	278218.i	−1.29261	+	0.470470i	−0.894582	−	0.446905i	$-0.852526\pi$
$769$	−764397.	+	278218.i	−1.29261	+	0.470470i	−0.398024	+	0.917375i	$0.630304\pi$
$770$	344655.	+	946933.i	0.581304	+	1.59712i
$771$		0			0
$772$	412199.	+	2.33770e6i	0.691628	+	3.92242i
$773$	−407984.	−	235550.i	−0.682786	−	0.394207i	0.118118	−	0.993000i	$-0.462314\pi$
$773$	−407984.	−	235550.i	−0.682786	−	0.394207i	−0.800904	+	0.598793i	$0.795647\pi$
$774$		0			0
$775$	112779.	+	195338.i	0.187769	+	0.325225i
$776$	−1.05498e6	−	1.25727e6i	−1.75194	−	2.08788i
$777$		0			0
$778$	231662.	−	1.31382e6i	0.382732	−	2.17058i
$779$	19852.9	−	23659.7i	0.0327151	−	0.0389884i
$780$		0			0
$781$	443345.	+	161364.i	0.726841	+	0.264549i
$782$			54626.3i			0.0893281i
$783$		0			0
$784$	707354.			1.15081
$785$	−235500.	+	647030.i	−0.382165	+	1.04999i
$786$		0			0
$787$	−758382.	−	636358.i	−1.22444	−	1.02743i	−0.998580	−	0.0532707i	$-0.983035\pi$
$787$	−758382.	−	636358.i	−1.22444	−	1.02743i	−0.225863	−	0.974159i	$-0.572520\pi$
$788$	−2.32504e6	−	409967.i	−3.74436	−	0.660231i
$789$		0			0
$790$	−1.18001e6	+	990148.i	−1.89074	+	1.58652i
$791$	532463.	−	307418.i	0.851013	−	0.491333i
$792$		0			0
$793$	566754.	−	981647.i	0.901257	−	1.56102i
$794$	2.15148e6	−	379365.i	3.41269	−	0.601749i
$795$		0			0
$796$	1.31707e6	−	479375.i	2.07866	−	0.756570i
$797$	−20232.1	−	55587.3i	−0.0318511	−	0.0875102i	0.922748	−	0.385404i	$-0.125938\pi$
$797$	−20232.1	−	55587.3i	−0.0318511	−	0.0875102i	−0.954599	+	0.297894i	$0.903716\pi$
$798$		0			0
$799$	4685.74	+	26574.1i	0.00733981	+	0.0416261i
$800$	240226.	+	138695.i	0.375353	+	0.216710i
$801$		0			0
$802$	−255366.	−	442307.i	−0.397022	−	0.687661i
$803$	147053.	+	175251.i	0.228056	+	0.271787i
$804$		0			0
$805$	−22327.1	+	126623.i	−0.0344541	+	0.195399i
$806$	1.59675e6	−	1.90293e6i	2.45792	−	2.92923i
$807$		0			0
$808$	−1.18966e6	−	433000.i	−1.82221	−	0.663231i
$809$			332453.i			0.507964i	0.967209	+	0.253982i	$0.0817404\pi$
$809$			332453.i			0.507964i	−0.967209	+	0.253982i	$0.918260\pi$
$810$		0			0
$811$	481760.			0.732469			0.366235	−	0.930523i	$-0.380647\pi$
$811$	481760.			0.732469			0.366235	+	0.930523i	$0.380647\pi$
$812$	989702.	−	2.71918e6i	1.50104	−	4.12408i
$813$		0			0
$814$	332778.	+	279234.i	0.502234	+	0.421424i
$815$	−149431.	−	26348.7i	−0.224970	−	0.0396683i
$816$		0			0
$817$	−88568.8	+	74318.0i	−0.132689	+	0.111340i
$818$	−994804.	+	574350.i	−1.48673	+	0.858361i
$819$		0			0
$820$	−77939.6	+	134995.i	−0.115913	+	0.200766i
$821$	17048.1	−	3006.03i	0.0252923	−	0.00445972i	−0.160988	−	0.986956i	$-0.551468\pi$
$821$	17048.1	−	3006.03i	0.0252923	−	0.00445972i	0.186280	+	0.982497i	$0.440357\pi$
$822$		0			0
$823$	−6205.19	+	2258.50i	−0.00916126	+	0.00333443i	−0.346597	−	0.938014i	$-0.612663\pi$
$823$	−6205.19	+	2258.50i	−0.00916126	+	0.00333443i	0.337435	+	0.941349i	$0.390441\pi$
$824$	565016.	+	1.55237e6i	0.832159	+	2.28634i
$825$		0			0
$826$	314373.	+	1.78290e6i	0.460772	+	2.61317i
$827$	280787.	+	162112.i	0.410549	+	0.237031i	0.691026	−	0.722830i	$-0.257159\pi$
$827$	280787.	+	162112.i	0.410549	+	0.237031i	−0.280476	+	0.959861i	$0.590492\pi$
$828$		0			0
$829$	398558.	+	690323.i	0.579939	+	1.00448i	0.995486	+	0.0949122i	$0.0302570\pi$
$829$	398558.	+	690323.i	0.579939	+	1.00448i	−0.415546	+	0.909572i	$0.636410\pi$
$830$	−526975.	−	628024.i	−0.764951	−	0.911634i
$831$		0			0
$832$	146909.	−	833163.i	0.212228	−	1.20360i
$833$	−56287.1	+	67080.3i	−0.0811183	+	0.0966730i
$834$		0			0
$835$	−199306.	−	72541.4i	−0.285856	−	0.104043i
$836$			667899.i			0.955648i
$837$		0			0
$838$	−1.55006e6			−2.20729
$839$	−33686.8	+	92553.8i	−0.0478560	+	0.131483i	−0.961318	−	0.275441i	$-0.911176\pi$
$839$	−33686.8	+	92553.8i	−0.0478560	+	0.131483i	0.913462	+	0.406924i	$0.133399\pi$
$840$		0			0
$841$	−676094.	−	567310.i	−0.955906	−	0.802100i
$842$	1.62441e6	+	286427.i	2.29124	+	0.404007i
$843$		0			0
$844$	2.35715e6	−	1.97788e6i	3.30904	−	2.77662i
$845$	−445155.	+	257010.i	−0.623444	+	0.359946i
$846$		0			0
$847$	106614.	−	184661.i	0.148610	−	0.257400i
$848$	−104791.	+	18477.4i	−0.145724	+	0.0256950i
$849$		0			0
$850$	−79329.4	+	28873.5i	−0.109798	+	0.0399634i
$851$	18957.5	+	52085.3i	0.0261771	+	0.0719211i
$852$		0			0
$853$	133616.	+	757773.i	0.183637	+	1.04146i	0.927694	+	0.373341i	$0.121788\pi$
$853$	133616.	+	757773.i	0.183637	+	1.04146i	−0.744057	+	0.668116i	$0.767101\pi$
$854$	−1.89354e6	−	1.09324e6i	−2.59632	−	1.49899i
$855$		0			0
$856$	−829514.	−	1.43676e6i	−1.13208	−	1.96082i
$857$	578341.	+	689240.i	0.787449	+	0.938446i	0.999244	−	0.0388684i	$-0.0123753\pi$
$857$	578341.	+	689240.i	0.787449	+	0.938446i	−0.211795	+	0.977314i	$0.567931\pi$
$858$		0			0
$859$	−167429.	+	949536.i	−0.226905	+	1.28684i	0.632105	+	0.774883i	$0.282191\pi$
$859$	−167429.	+	949536.i	−0.226905	+	1.28684i	−0.859010	+	0.511959i	$0.828920\pi$
$860$	375082.	−	447005.i	0.507142	−	0.604388i
$861$		0			0
$862$	−2.20363e6	−	802056.i	−2.96568	−	1.07942i
$863$			76954.8i			0.103327i	0.998665	+	0.0516635i	$0.0164523\pi$
$863$			76954.8i			0.103327i	−0.998665	+	0.0516635i	$0.983548\pi$
$864$		0			0
$865$	−968804.			−1.29480
$866$	−239753.	+	658717.i	−0.319690	+	0.878341i
$867$		0			0
$868$	−2.59104e6	−	2.17414e6i	−3.43901	−	2.88568i
$869$	−996257.	−	175667.i	−1.31926	−	0.232622i
$870$		0			0
$871$	1.01718e6	−	853517.i	1.34080	−	1.12506i
$872$	665053.	−	383969.i	0.874628	−	0.504967i
$873$		0			0
$874$	−60364.0	+	104554.i	−0.0790233	+	0.136872i
$875$	−994839.	+	175417.i	−1.29938	+	0.229116i
$876$		0			0
$877$	665011.	−	242044.i	0.864629	−	0.314699i	0.128639	−	0.991692i	$-0.458939\pi$
$877$	665011.	−	242044.i	0.864629	−	0.314699i	0.735990	+	0.676992i	$0.236717\pi$
$878$	−621162.	−	1.70663e6i	−0.805779	−	2.21386i
$879$		0			0
$880$	−239825.	−	1.36012e6i	−0.309691	−	1.75635i
$881$	−732035.	−	422641.i	−0.943149	−	0.544527i	−0.0522027	−	0.998637i	$-0.516624\pi$
$881$	−732035.	−	422641.i	−0.943149	−	0.544527i	−0.890946	+	0.454109i	$0.849958\pi$
$882$		0			0
$883$	412901.	+	715165.i	0.529571	+	0.917244i	0.999405	+	0.0344895i	$0.0109805\pi$
$883$	412901.	+	715165.i	0.529571	+	0.917244i	−0.469834	+	0.882755i	$0.655686\pi$
$884$	421852.	+	502743.i	0.539828	+	0.643342i
$885$		0			0
$886$	−357781.	+	2.02907e6i	−0.455774	+	2.58482i
$887$	−293621.	+	349924.i	−0.373199	+	0.444761i	−0.919655	−	0.392726i	$-0.871532\pi$
$887$	−293621.	+	349924.i	−0.373199	+	0.444761i	0.546456	+	0.837488i	$0.315976\pi$
$888$		0			0
$889$	−150464.	−	54764.5i	−0.190384	−	0.0692941i
$890$			1.43564e6i			1.81245i
$891$		0			0
$892$	95911.3			0.120542
$893$	−20397.0	+	56040.3i	−0.0255778	+	0.0702745i
$894$		0			0
$895$	22605.4	+	18968.2i	0.0282205	+	0.0236798i
$896$	99736.3	+	17586.2i	0.124233	+	0.0219056i
$897$		0			0
$898$	228311.	−	191576.i	0.283123	−	0.237568i
$899$	−1.60937e6	+	929170.i	−1.99130	+	1.14968i
$900$		0			0
$901$	6586.36	−	11407.9i	0.00811326	−	0.0140526i
$902$	−142822.	+	25183.4i	−0.175543	+	0.0309529i
$903$		0			0
$904$	−1.59712e6	+	581303.i	−1.95434	+	0.711321i
$905$	117975.	+	324133.i	0.144043	+	0.395755i
$906$		0			0
$907$	−29650.7	−	168158.i	−0.0360430	−	0.204410i	0.961468	−	0.274915i	$-0.0886499\pi$
$907$	−29650.7	−	168158.i	−0.0360430	−	0.204410i	−0.997511	+	0.0705055i	$0.977539\pi$
$908$	2.01466e6	+	1.16316e6i	2.44360	+	1.41081i
$909$		0			0
$910$	1.09419e6	+	1.89519e6i	1.32132	+	2.28860i
$911$	−637177.	−	759358.i	−0.767757	−	0.914977i	0.230555	−	0.973059i	$-0.425946\pi$
$911$	−637177.	−	759358.i	−0.767757	−	0.914977i	−0.998312	+	0.0580825i	$0.981501\pi$
$912$		0			0
$913$	93493.3	−	530227.i	0.112160	−	0.636092i
$914$	−954072.	+	1.13702e6i	−1.14206	+	1.36105i
$915$		0			0
$916$	645737.	+	235029.i	0.769599	+	0.280111i
$917$		−	1.51565e6i		−	1.80244i
$918$		0			0
$919$	1.04171e6			1.23343			0.616717	−	0.787185i	$-0.288462\pi$
$919$	1.04171e6			1.23343			0.616717	+	0.787185i	$0.288462\pi$
$920$	121564.	−	333995.i	0.143625	−	0.394606i
$921$		0			0
$922$	1.53878e6	+	1.29119e6i	1.81015	+	1.51889i
$923$	1.00901e6	+	177916.i	1.18438	+	0.208839i
$924$		0			0
$925$	−65619.1	+	55061.0i	−0.0766914	+	0.0643518i
$926$	−721250.	+	416414.i	−0.841132	+	0.485628i
$927$		0			0
$928$	−1.14269e6	+	1.97920e6i	−1.32688	+	2.29823i
$929$	1.68711e6	−	297482.i	1.95484	−	0.344691i	0.956187	−	0.292756i	$-0.0945723\pi$
$929$	1.68711e6	−	297482.i	1.95484	−	0.344691i	0.998650	−	0.0519347i	$-0.0165388\pi$
$930$		0			0
$931$	−181859.	+	66191.1i	−0.209814	+	0.0763660i
$932$	853239.	+	2.34426e6i	0.982288	+	2.69881i
$933$		0			0
$934$	−262756.	−	1.49016e6i	−0.301202	−	1.70820i
$935$	148067.	+	85486.7i	0.169370	+	0.0977857i
$936$		0			0
$937$	−119828.	−	207549.i	−0.136484	−	0.236397i	0.789680	−	0.613519i	$-0.210247\pi$
$937$	−119828.	−	207549.i	−0.136484	−	0.236397i	−0.926163	+	0.377123i	$0.876913\pi$
$938$	−1.64638e6	−	1.96208e6i	−1.87122	−	2.23004i
$939$		0			0
$940$	52265.7	−	296414.i	0.0591509	−	0.335461i
$941$	−212705.	+	253491.i	−0.240214	+	0.286275i	−0.872660	−	0.488329i	$-0.837607\pi$
$941$	−212705.	+	253491.i	−0.240214	+	0.286275i	0.632446	+	0.774604i	$0.282051\pi$
$942$		0			0
$943$	−17388.4	−	6328.85i	−0.0195540	−	0.00711708i
$944$		−	2.48123e6i		−	2.78434i
$945$		0			0
$946$	542894.			0.606642
$947$	−19893.5	+	54657.1i	−0.0221826	+	0.0609462i	−0.950290	−	0.311367i	$-0.899213\pi$
$947$	−19893.5	+	54657.1i	−0.0221826	+	0.0609462i	0.928107	+	0.372313i	$0.121435\pi$
$948$		0			0
$949$	380582.	+	319346.i	0.422587	+	0.354592i
$950$	−183741.	−	32398.5i	−0.203591	−	0.0358986i
$951$		0			0
$952$	565691.	−	474671.i	0.624173	−	0.523743i
$953$	864845.	−	499318.i	0.952253	−	0.549784i	0.0584729	−	0.998289i	$-0.481377\pi$
$953$	864845.	−	499318.i	0.952253	−	0.549784i	0.893780	+	0.448505i	$0.148044\pi$
$954$		0			0
$955$	53096.2	−	91965.3i	0.0582179	−	0.100836i
$956$	−2.91468e6	+	513937.i	−3.18915	+	0.562334i
$957$		0			0
$958$	2.33925e6	−	851416.i	2.54885	−	0.927707i
$959$	−59276.9	−	162862.i	−0.0644538	−	0.177085i
$960$		0			0
$961$	216824.	+	1.22967e6i	0.234780	+	1.33150i
$962$	816997.	+	471693.i	0.882816	+	0.509694i
$963$		0			0
$964$	−1.32007e6	−	2.28643e6i	−1.42051	−	2.46039i
$965$	863235.	+	1.02876e6i	0.926989	+	1.10474i
$966$		0			0
$967$	−79204.2	+	449189.i	−0.0847023	+	0.480371i	0.912718	+	0.408590i	$0.133979\pi$
$967$	−79204.2	+	449189.i	−0.0847023	+	0.480371i	−0.997420	+	0.0717808i	$0.977132\pi$
$968$	−378882.	+	451533.i	−0.404346	+	0.481880i
$969$		0			0
$970$	−1.49580e6	−	544425.i	−1.58975	−	0.578622i
$971$		−	795103.i		−	0.843305i	−0.906757	−	0.421653i	$-0.861450\pi$
$971$		−	795103.i		−	0.843305i	0.906757	−	0.421653i	$-0.138550\pi$
$972$		0			0
$973$	−714357.			−0.754553
$974$	−357222.	+	981460.i	−0.376548	+	1.03456i
$975$		0			0
$976$	2.29556e6	+	1.92620e6i	2.40984	+	2.02210i
$977$	−1.09358e6	−	192828.i	−1.14568	−	0.202014i	−0.431591	−	0.902070i	$-0.642047\pi$
$977$	−1.09358e6	−	192828.i	−1.14568	−	0.202014i	−0.714088	+	0.700056i	$0.753159\pi$
$978$		0			0
$979$	−722248.	+	606038.i	−0.753565	+	0.632316i
$980$	845884.	−	488371.i	0.880762	−	0.508508i
$981$		0			0
$982$	316585.	−	548341.i	0.328297	−	0.568628i
$983$	342960.	−	60473.2i	0.354925	−	0.0625829i	0.00665711	−	0.999978i	$-0.497881\pi$
$983$	342960.	−	60473.2i	0.354925	−	0.0625829i	0.348268	+	0.937395i	$0.386770\pi$
$984$		0			0
$985$	−1.25513e6	+	456830.i	−1.29365	+	0.470850i
$986$	−237886.	−	653586.i	−0.244689	−	0.672278i
$987$		0			0
$988$	251866.	+	1.42840e6i	0.258021	+	1.46331i
$989$	59989.4	+	34634.9i	0.0613312	+	0.0354096i
$990$		0			0
$991$	202871.	+	351383.i	0.206572	+	0.357794i	0.950633	−	0.310319i	$-0.100436\pi$
$991$	202871.	+	351383.i	0.206572	+	0.357794i	−0.744060	+	0.668113i	$0.767102\pi$
$992$	1.71709e6	+	2.04635e6i	1.74490	+	2.07948i
$993$		0			0
$994$	343189.	−	1.94632e6i	0.347345	−	1.96989i
$995$	509701.	−	607438.i	0.514837	−	0.613558i
$996$		0			0
$997$	830173.	+	302158.i	0.835177	+	0.303980i	0.723982	−	0.689819i	$-0.242310\pi$
$997$	830173.	+	302158.i	0.835177	+	0.303980i	0.111195	+	0.993799i	$0.464532\pi$
$998$		−	514169.i		−	0.516232i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.5.f.a.17.1		66
3.2	odd	2		27.5.f.a.23.11	yes	66
27.7	even	9		27.5.f.a.20.11	✓	66
27.20	odd	18	inner	81.5.f.a.62.1		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.f.a.20.11	✓	66	27.7	even	9
27.5.f.a.23.11	yes	66	3.2	odd	2
81.5.f.a.17.1		66	1.1	even	1	trivial
81.5.f.a.62.1		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)

\(f(q)\)	\(=\)	\(q+(-2.52261 + 6.93081i) q^{2} +(-29.4158 - 24.6828i) q^{4} +(-21.3946 - 3.77244i) q^{5} +(-45.7826 + 38.4162i) q^{7} +(143.077 - 82.6054i) q^{8} +(80.1161 - 138.765i) q^{10} +(103.631 - 18.2729i) q^{11} +(214.739 - 78.1587i) q^{13} +(-150.764 - 414.219i) q^{14} +(104.907 + 594.959i) q^{16} +(-64.7695 - 37.3947i) q^{17} +(-82.6450 - 143.145i) q^{19} +(536.224 + 639.047i) q^{20} +(-134.774 + 764.340i) q^{22} +(-63.6548 + 75.8608i) q^{23} +(-143.812 - 52.3434i) q^{25} +1685.48i q^{26} +2294.95 q^{28} +(431.252 - 1184.85i) q^{29} +(-1129.02 - 947.356i) q^{31} +(-1784.97 - 314.738i) q^{32} +(422.563 - 354.573i) q^{34} +(1124.42 - 649.185i) q^{35} +(279.857 - 484.726i) q^{37} +(1200.59 - 211.697i) q^{38} +(-3372.69 + 1227.56i) q^{40} +(63.9089 + 175.588i) q^{41} +(-121.465 - 688.861i) q^{43} +(-3499.41 - 2020.38i) q^{44} +(-365.201 - 632.546i) q^{46} +(-231.919 - 276.390i) q^{47} +(203.316 - 1153.06i) q^{49} +(725.564 - 864.694i) q^{50} +(-8245.91 - 3001.27i) q^{52} +176.131i q^{53} -2286.07 q^{55} +(-3377.05 + 9278.36i) q^{56} +(7124.12 + 5977.85i) q^{58} +(-4044.66 - 713.183i) q^{59} +(3799.73 - 3188.35i) q^{61} +(9414.01 - 5435.18i) q^{62} +(1851.07 - 3206.15i) q^{64} +(-4889.10 + 862.080i) q^{65} +(5460.16 - 1987.33i) q^{67} +(982.242 + 2698.69i) q^{68} +(1662.90 + 9430.78i) q^{70} +(3882.84 + 2241.76i) q^{71} +(1087.02 + 1882.78i) q^{73} +(2653.58 + 3162.41i) q^{74} +(-1102.16 + 6250.65i) q^{76} +(-4042.51 + 4817.68i) q^{77} +(-9033.76 - 3288.02i) q^{79} -13124.6i q^{80} -1378.18 q^{82} +(1749.95 - 4807.94i) q^{83} +(1244.64 + 1044.38i) q^{85} +(5080.77 + 895.877i) q^{86} +(13317.7 - 11174.9i) q^{88} +(-7759.36 + 4479.87i) q^{89} +(-6828.77 + 11827.8i) q^{91} +(3744.92 - 660.330i) q^{92} +(2500.64 - 910.160i) q^{94} +(1228.15 + 3374.30i) q^{95} +(-1725.07 - 9783.37i) q^{97} +(7478.77 + 4317.87i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} - 1137 q^{14} - 54 q^{16} + 9 q^{17} - 3 q^{19} + 2487 q^{20} + 1002 q^{22} + 2724 q^{23} + 435 q^{25} - 12 q^{28}+ \cdots + 259938 q^{98}+O(q^{100}) \) 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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