LMFDB - Embedded newform 81.5.f.a.8.10

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			8.10
Character	$\chi$	$=$	81.8
Dual form			81.5.f.a.71.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(6.19782 + 1.09284i) q^{2} +(22.1836 + 8.07418i) q^{4} +(7.06026 + 8.41408i) q^{5} +(62.3269 - 22.6852i) q^{7} +(41.4621 + 23.9381i) q^{8} +(34.5629 + 59.8648i) q^{10} +(-18.2440 + 21.7424i) q^{11} +(38.7578 + 219.806i) q^{13} +(411.083 - 72.4850i) q^{14} +(-58.5343 - 49.1161i) q^{16} +(-287.497 + 165.987i) q^{17} +(283.914 - 491.754i) q^{19} +(88.6853 + 243.661i) q^{20} +(-136.834 + 114.818i) q^{22} +(50.3714 - 138.394i) q^{23} +(87.5805 - 496.694i) q^{25} +1404.68i q^{26} +1565.80 q^{28} +(-1292.76 - 227.949i) q^{29} +(-1356.31 - 493.655i) q^{31} +(-801.497 - 955.187i) q^{32} +(-1963.25 + 714.566i) q^{34} +(630.919 + 364.261i) q^{35} +(630.312 + 1091.73i) q^{37} +(2297.06 - 2737.53i) q^{38} +(91.3153 + 517.875i) q^{40} +(-264.956 + 46.7189i) q^{41} +(184.572 + 154.874i) q^{43} +(-580.271 + 335.020i) q^{44} +(463.437 - 802.696i) q^{46} +(458.931 + 1260.90i) q^{47} +(1530.76 - 1284.46i) q^{49} +(1085.62 - 2982.71i) q^{50} +(-914.968 + 5189.04i) q^{52} +1318.19i q^{53} -311.750 q^{55} +(3127.25 + 551.418i) q^{56} +(-7763.20 - 2825.58i) q^{58} +(-893.408 - 1064.72i) q^{59} +(2681.63 - 976.034i) q^{61} +(-7866.66 - 4541.82i) q^{62} +(-3312.38 - 5737.21i) q^{64} +(-1575.83 + 1878.00i) q^{65} +(252.937 + 1434.48i) q^{67} +(-7717.94 + 1360.88i) q^{68} +(3512.24 + 2947.12i) q^{70} +(880.106 - 508.129i) q^{71} +(-1701.39 + 2946.89i) q^{73} +(2713.47 + 7455.20i) q^{74} +(10268.8 - 8616.51i) q^{76} +(-643.865 + 1769.01i) q^{77} +(250.938 - 1423.14i) q^{79} -839.284i q^{80} -1693.21 q^{82} +(9629.68 + 1697.97i) q^{83} +(-3426.43 - 1247.12i) q^{85} +(974.689 + 1161.59i) q^{86} +(-1276.91 + 464.756i) q^{88} +(10139.4 + 5854.01i) q^{89} +(7402.00 + 12820.6i) q^{91} +(2234.84 - 2663.38i) q^{92} +(1466.40 + 8316.39i) q^{94} +(6142.16 - 1083.03i) q^{95} +(4082.19 + 3425.36i) q^{97} +(10891.1 - 6287.97i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	6.19782	+	1.09284i	1.54946	+	0.273211i	0.881932	−	0.471377i	$-0.156243\pi$
$2$	6.19782	+	1.09284i	1.54946	+	0.273211i	0.667524	+	0.744588i	$0.267354\pi$
$3$		0			0
$3$		0			0
$4$	22.1836	+	8.07418i	1.38648	+	0.504637i
$5$	7.06026	+	8.41408i	0.282410	+	0.336563i	0.888537	−	0.458804i	$-0.151722\pi$
$5$	7.06026	+	8.41408i	0.282410	+	0.336563i	−0.606127	+	0.795368i	$0.707278\pi$
$6$		0			0
$7$	62.3269	−	22.6852i	1.27198	−	0.462962i	0.384207	−	0.923247i	$-0.374475\pi$
$7$	62.3269	−	22.6852i	1.27198	−	0.462962i	0.887771	+	0.460285i	$0.152253\pi$
$8$	41.4621	+	23.9381i	0.647845	+	0.374033i
$9$		0			0
$10$	34.5629	+	59.8648i	0.345629	+	0.598648i
$11$	−18.2440	+	21.7424i	−0.150777	+	0.179689i	−0.836146	−	0.548507i	$-0.815196\pi$
$11$	−18.2440	+	21.7424i	−0.150777	+	0.179689i	0.685369	+	0.728196i	$0.259641\pi$
$12$		0			0
$13$	38.7578	+	219.806i	0.229336	+	1.30063i	0.854220	+	0.519912i	$0.174035\pi$
$13$	38.7578	+	219.806i	0.229336	+	1.30063i	−0.624884	+	0.780718i	$0.714854\pi$
$14$	411.083	−	72.4850i	2.09736	−	0.369821i
$15$		0			0
$16$	−58.5343	−	49.1161i	−0.228649	−	0.191860i
$17$	−287.497	+	165.987i	−0.994800	+	0.574348i	−0.906706	−	0.421764i	$-0.861411\pi$
$17$	−287.497	+	165.987i	−0.994800	+	0.574348i	−0.0880945	+	0.996112i	$0.528078\pi$
$18$		0			0
$19$	283.914	−	491.754i	0.786466	−	1.36220i	−0.141654	−	0.989916i	$-0.545242\pi$
$19$	283.914	−	491.754i	0.786466	−	1.36220i	0.928120	−	0.372282i	$-0.121425\pi$
$20$	88.6853	+	243.661i	0.221713	+	0.609152i
$21$		0			0
$22$	−136.834	+	114.818i	−0.282716	+	0.237227i
$23$	50.3714	−	138.394i	0.0952201	−	0.261615i	−0.882934	−	0.469498i	$-0.844435\pi$
$23$	50.3714	−	138.394i	0.0952201	−	0.261615i	0.978154	+	0.207883i	$0.0666572\pi$
$24$		0			0
$25$	87.5805	−	496.694i	0.140129	−	0.794710i
$26$			1404.68i			2.07793i
$27$		0			0
$28$	1565.80			1.99720
$29$	−1292.76	−	227.949i	−1.53717	−	0.271045i	−0.660017	−	0.751251i	$-0.729451\pi$
$29$	−1292.76	−	227.949i	−1.53717	−	0.271045i	−0.877156	+	0.480205i	$0.840562\pi$
$30$		0			0
$31$	−1356.31	−	493.655i	−1.41135	−	0.513689i	−0.479823	−	0.877365i	$-0.659299\pi$
$31$	−1356.31	−	493.655i	−1.41135	−	0.513689i	−0.931525	+	0.363677i	$0.881521\pi$
$32$	−801.497	−	955.187i	−0.782712	−	0.932800i
$33$		0			0
$34$	−1963.25	+	714.566i	−1.69832	+	0.618137i
$35$	630.919	+	364.261i	0.515036	+	0.297356i
$36$		0			0
$37$	630.312	+	1091.73i	0.460418	+	0.797467i	0.998982	−	0.0451175i	$-0.0143662\pi$
$37$	630.312	+	1091.73i	0.460418	+	0.797467i	−0.538564	+	0.842585i	$0.681033\pi$
$38$	2297.06	−	2737.53i	1.59076	−	1.89580i
$39$		0			0
$40$	91.3153	+	517.875i	0.0570721	+	0.323672i
$41$	−264.956	+	46.7189i	−0.157618	+	0.0277924i	−0.251900	−	0.967753i	$-0.581056\pi$
$41$	−264.956	+	46.7189i	−0.157618	+	0.0277924i	0.0942821	+	0.995546i	$0.469944\pi$
$42$		0			0
$43$	184.572	+	154.874i	0.0998224	+	0.0837609i	0.691333	−	0.722536i	$-0.257024\pi$
$43$	184.572	+	154.874i	0.0998224	+	0.0837609i	−0.591511	+	0.806297i	$0.701468\pi$
$44$	−580.271	+	335.020i	−0.299727	+	0.173047i
$45$		0			0
$46$	463.437	−	802.696i	0.219015	−	0.379346i
$47$	458.931	+	1260.90i	0.207755	+	0.570802i	0.999181	−	0.0404627i	$-0.0128832\pi$
$47$	458.931	+	1260.90i	0.207755	+	0.570802i	−0.791426	+	0.611265i	$0.790661\pi$
$48$		0			0
$49$	1530.76	−	1284.46i	0.637551	−	0.534968i
$50$	1085.62	−	2982.71i	0.434247	−	1.19308i
$51$		0			0
$52$	−914.968	+	5189.04i	−0.338376	+	1.91902i
$53$			1318.19i			0.469274i	0.972083	+	0.234637i	$0.0753902\pi$
$53$			1318.19i			0.469274i	−0.972083	+	0.234637i	$0.924610\pi$
$54$		0			0
$55$	−311.750			−0.103058
$56$	3127.25	+	551.418i	0.997208	+	0.175835i
$57$		0			0
$58$	−7763.20	−	2825.58i	−2.30773	−	0.839945i
$59$	−893.408	−	1064.72i	−0.256653	−	0.305867i	0.622297	−	0.782781i	$-0.286200\pi$
$59$	−893.408	−	1064.72i	−0.256653	−	0.305867i	−0.878950	+	0.476915i	$0.841755\pi$
$60$		0			0
$61$	2681.63	−	976.034i	0.720675	−	0.262304i	0.0444625	−	0.999011i	$-0.485842\pi$
$61$	2681.63	−	976.034i	0.720675	−	0.262304i	0.676212	+	0.736707i	$0.263620\pi$
$62$	−7866.66	−	4541.82i	−2.04648	−	1.18153i
$63$		0			0
$64$	−3312.38	−	5737.21i	−0.808687	−	1.40069i
$65$	−1575.83	+	1878.00i	−0.372977	+	0.444497i
$66$		0			0
$67$	252.937	+	1434.48i	0.0563460	+	0.319554i	0.999933	−	0.0115704i	$-0.00368306\pi$
$67$	252.937	+	1434.48i	0.0563460	+	0.319554i	−0.943587	+	0.331125i	$0.892572\pi$
$68$	−7717.94	+	1360.88i	−1.66911	+	0.294308i
$69$		0			0
$70$	3512.24	+	2947.12i	0.716785	+	0.601454i
$71$	880.106	−	508.129i	0.174590	−	0.100799i	−0.410159	−	0.912014i	$-0.634527\pi$
$71$	880.106	−	508.129i	0.174590	−	0.100799i	0.584748	+	0.811215i	$0.301193\pi$
$72$		0			0
$73$	−1701.39	+	2946.89i	−0.319270	+	0.552992i	−0.980336	−	0.197336i	$-0.936771\pi$
$73$	−1701.39	+	2946.89i	−0.319270	+	0.552992i	0.661066	+	0.750328i	$0.270104\pi$
$74$	2713.47	+	7455.20i	0.495521	+	1.36143i
$75$		0			0
$76$	10268.8	−	8616.51i	1.77783	−	1.49178i
$77$	−643.865	+	1769.01i	−0.108596	+	0.298365i
$78$		0			0
$79$	250.938	−	1423.14i	0.0402079	−	0.228030i	−0.958082	−	0.286496i	$-0.907510\pi$
$79$	250.938	−	1423.14i	0.0402079	−	0.228030i	0.998289	+	0.0584653i	$0.0186207\pi$
$80$		−	839.284i		−	0.131138i
$81$		0			0
$82$	−1693.21			−0.251816
$83$	9629.68	+	1697.97i	1.39783	+	0.246476i	0.821253	−	0.570564i	$-0.193275\pi$
$83$	9629.68	+	1697.97i	1.39783	+	0.246476i	0.576581	+	0.817040i	$0.304386\pi$
$84$		0			0
$85$	−3426.43	−	1247.12i	−0.474246	−	0.172612i
$86$	974.689	+	1161.59i	0.131786	+	0.157056i
$87$		0			0
$88$	−1276.91	+	464.756i	−0.164890	+	0.0600150i
$89$	10139.4	+	5854.01i	1.28007	+	0.739050i	0.976861	−	0.213874i	$-0.0686082\pi$
$89$	10139.4	+	5854.01i	1.28007	+	0.739050i	0.303210	+	0.952924i	$0.401941\pi$
$90$		0			0
$91$	7402.00	+	12820.6i	0.893853	+	1.54820i
$92$	2234.84	−	2663.38i	0.264041	−	0.314672i
$93$		0			0
$94$	1466.40	+	8316.39i	0.165958	+	0.941194i
$95$	6142.16	−	1083.03i	0.680572	−	0.120003i
$96$		0			0
$97$	4082.19	+	3425.36i	0.433860	+	0.364052i	0.833406	−	0.552662i	$-0.186388\pi$
$97$	4082.19	+	3425.36i	0.433860	+	0.364052i	−0.399546	+	0.916713i	$0.630832\pi$
$98$	10891.1	−	6287.97i	1.13402	−	0.654724i
$99$		0			0
$100$	5953.25	−	10311.3i	0.595325	−	1.03113i
$101$	−5579.65	−	15330.0i	−0.546971	−	1.50279i	−0.837780	−	0.546009i	$-0.816147\pi$
$101$	−5579.65	−	15330.0i	−0.546971	−	1.50279i	0.290809	−	0.956781i	$-0.406076\pi$
$102$		0			0
$103$	5565.88	−	4670.32i	0.524637	−	0.440223i	−0.341608	−	0.939843i	$-0.610971\pi$
$103$	5565.88	−	4670.32i	0.524637	−	0.440223i	0.866245	+	0.499620i	$0.166527\pi$
$104$	−3654.78	+	10041.4i	−0.337905	+	0.928386i
$105$		0			0
$106$	−1440.58	+	8169.92i	−0.128211	+	0.727120i
$107$			20589.5i			1.79836i	0.437575	+	0.899182i	$0.355837\pi$
$107$			20589.5i			1.79836i	−0.437575	+	0.899182i	$0.644163\pi$
$108$		0			0
$109$	6506.21			0.547614			0.273807	−	0.961785i	$-0.411717\pi$
$109$	6506.21			0.547614			0.273807	+	0.961785i	$0.411717\pi$
$110$	−1932.17	−	340.694i	−0.159684	−	0.0281565i
$111$		0			0
$112$	−4762.47	−	1733.40i	−0.379661	−	0.138185i
$113$	−3348.18	−	3990.21i	−0.262212	−	0.312492i	0.618835	−	0.785521i	$-0.287605\pi$
$113$	−3348.18	−	3990.21i	−0.262212	−	0.312492i	−0.881047	+	0.473029i	$0.843161\pi$
$114$		0			0
$115$	1520.10	−	553.270i	0.114941	−	0.0418352i
$116$	−26837.7	−	15494.7i	−1.99448	−	1.15151i
$117$		0			0
$118$	−4373.61	−	7575.31i	−0.314106	−	0.544047i
$119$	−14153.4	+	16867.4i	−0.999463	+	1.19111i
$120$		0			0
$121$	2402.50	+	13625.2i	0.164094	+	0.930622i
$122$	17686.9	−	3118.68i	1.18832	−	0.209533i
$123$		0			0
$124$	−26101.9	−	21902.1i	−1.69758	−	1.42444i
$125$	10742.7	−	6202.31i	0.687534	−	0.396948i
$126$		0			0
$127$	−8010.15	+	13874.0i	−0.496630	+	0.860189i	−0.999992	−	0.00388641i	$-0.998763\pi$
$127$	−8010.15	+	13874.0i	−0.496630	+	0.860189i	0.503362	+	0.864076i	$0.332096\pi$
$128$	−7436.20	−	20430.8i	−0.453869	−	1.24700i
$129$		0			0
$130$	−11819.1	+	9917.38i	−0.699354	+	0.586827i
$131$	3109.27	−	8542.66i	0.181183	−	0.497795i	−0.815539	−	0.578702i	$-0.803559\pi$
$131$	3109.27	−	8542.66i	0.181183	−	0.497795i	0.996722	+	0.0809069i	$0.0257817\pi$
$132$		0			0
$133$	6539.99	−	37090.1i	0.369721	−	2.09679i
$134$			9167.07i			0.510530i
$135$		0			0
$136$	−15893.6			−0.859302
$137$	−31865.7	−	5618.77i	−1.69778	−	0.299365i	−0.760863	−	0.648913i	$-0.775224\pi$
$137$	−31865.7	−	5618.77i	−1.69778	−	0.299365i	−0.936918	+	0.349548i	$0.886335\pi$
$138$		0			0
$139$	92.1216	+	33.5295i	0.00476795	+	0.00173539i	0.344403	−	0.938822i	$-0.388081\pi$
$139$	92.1216	+	33.5295i	0.00476795	+	0.00173539i	−0.339635	+	0.940557i	$0.610304\pi$
$140$	11055.0	+	13174.8i	0.564029	+	0.672183i
$141$		0			0
$142$	6010.05	−	2187.48i	0.298058	−	0.108484i
$143$	−5486.21	−	3167.47i	−0.268288	−	0.154896i
$144$		0			0
$145$	−7209.25	−	12486.8i	−0.342890	−	0.593902i
$146$	−13765.4	+	16405.0i	−0.645778	+	0.769608i
$147$		0			0
$148$	5167.77	+	29307.9i	0.235928	+	1.33801i
$149$	748.137	−	131.917i	0.0336983	−	0.00594193i	−0.156774	−	0.987635i	$-0.550109\pi$
$149$	748.137	−	131.917i	0.0336983	−	0.00594193i	0.190472	+	0.981693i	$0.438998\pi$
$150$		0			0
$151$	−10700.5	−	8978.81i	−0.469301	−	0.393790i	0.377238	−	0.926116i	$-0.376874\pi$
$151$	−10700.5	−	8978.81i	−0.469301	−	0.393790i	−0.846540	+	0.532326i	$0.821318\pi$
$152$	23543.3	−	13592.8i	1.01902	−	0.588329i
$153$		0			0
$154$	−5923.81	+	10260.3i	−0.249781	+	0.432634i
$155$	−5422.21	−	14897.4i	−0.225690	−	0.620079i
$156$		0			0
$157$	−18051.3	+	15146.9i	−0.732336	+	0.614503i	−0.930767	−	0.365612i	$-0.880860\pi$
$157$	−18051.3	+	15146.9i	−0.732336	+	0.614503i	0.198431	+	0.980115i	$0.436415\pi$
$158$	3110.53	−	8546.12i	0.124601	−	0.342338i
$159$		0			0
$160$	2378.25	−	13487.7i	0.0929004	−	0.526865i
$161$		−	9768.38i		−	0.376852i
$162$		0			0
$163$	−11897.4			−0.447791			−0.223895	−	0.974613i	$-0.571877\pi$
$163$	−11897.4			−0.447791			−0.223895	+	0.974613i	$0.571877\pi$
$164$	−6254.91	−	1102.91i	−0.232559	−	0.0410065i
$165$		0			0
$166$	57827.4	+	21047.5i	2.09854	+	0.763807i
$167$	11583.2	+	13804.3i	0.415332	+	0.494974i	0.932631	−	0.360831i	$-0.117507\pi$
$167$	11583.2	+	13804.3i	0.415332	+	0.494974i	−0.517299	+	0.855805i	$0.673062\pi$
$168$		0			0
$169$	−19974.1	+	7269.98i	−0.699349	+	0.254542i
$170$	−19873.5	−	11474.0i	−0.687664	−	0.397023i
$171$		0			0
$172$	2843.99	+	4925.93i	0.0961327	+	0.166507i
$173$	28468.3	−	33927.2i	0.951196	−	1.13359i	−0.0397341	−	0.999210i	$-0.512651\pi$
$173$	28468.3	−	33927.2i	0.951196	−	1.13359i	0.990930	−	0.134381i	$-0.0429045\pi$
$174$		0			0
$175$	−5808.95	−	32944.2i	−0.189680	−	1.07573i
$176$	2135.80	−	376.599i	0.0689502	−	0.0121578i
$177$		0			0
$178$	56445.0	+	47363.0i	1.78150	+	1.49485i
$179$	23089.5	−	13330.7i	0.720625	−	0.416053i	−0.0943579	−	0.995538i	$-0.530080\pi$
$179$	23089.5	−	13330.7i	0.720625	−	0.416053i	0.814983	+	0.579485i	$0.196746\pi$
$180$		0			0
$181$	−1292.58	+	2238.81i	−0.0394547	+	0.0683375i	−0.885078	−	0.465442i	$-0.845895\pi$
$181$	−1292.58	+	2238.81i	−0.0394547	+	0.0683375i	0.845624	+	0.533779i	$0.179229\pi$
$182$	31865.3	+	87549.3i	0.962001	+	2.64308i
$183$		0			0
$184$	5401.41	−	4532.32i	0.159541	−	0.133871i
$185$	−4735.77	+	13011.4i	−0.138372	+	0.380173i
$186$		0			0
$187$	1636.16	−	9279.14i	0.0467890	−	0.265353i
$188$			31676.9i			0.896245i
$189$		0			0
$190$	39251.6			1.08730
$191$	−10928.8	−	1927.04i	−0.299574	−	0.0528230i	0.0218407	−	0.999761i	$-0.493047\pi$
$191$	−10928.8	−	1927.04i	−0.299574	−	0.0528230i	−0.321415	+	0.946938i	$0.604158\pi$
$192$		0			0
$193$	8390.83	+	3054.01i	0.225263	+	0.0819892i	0.452186	−	0.891924i	$-0.350644\pi$
$193$	8390.83	+	3054.01i	0.225263	+	0.0819892i	−0.226923	+	0.973913i	$0.572867\pi$
$194$	21557.3	+	25691.0i	0.572784	+	0.682617i
$195$		0			0
$196$	44328.8	−	16134.4i	1.15391	−	0.419990i
$197$	9119.33	+	5265.05i	0.234980	+	0.135666i	0.612867	−	0.790186i	$-0.290016\pi$
$197$	9119.33	+	5265.05i	0.234980	+	0.135666i	−0.377888	+	0.925852i	$0.623349\pi$
$198$		0			0
$199$	13293.1	+	23024.3i	0.335675	+	0.581406i	0.983614	−	0.180286i	$-0.0577023\pi$
$199$	13293.1	+	23024.3i	0.335675	+	0.581406i	−0.647939	+	0.761692i	$0.724369\pi$
$200$	15521.2	−	18497.4i	0.388030	−	0.462436i
$201$		0			0
$202$	−17828.4	−	101110.i	−0.436929	−	2.47795i
$203$	−85745.0	+	15119.2i	−2.08073	+	0.366890i
$204$		0			0
$205$	−2263.76	−	1899.52i	−0.0538669	−	0.0451997i
$206$	39600.3	−	22863.2i	0.933176	−	0.538769i
$207$		0			0
$208$	8527.37	−	14769.8i	0.197101	−	0.341388i
$209$	5512.16	+	15144.5i	0.126191	+	0.346708i
$210$		0			0
$211$	27035.8	−	22685.8i	0.607260	−	0.509552i	−0.286510	−	0.958077i	$-0.592495\pi$
$211$	27035.8	−	22685.8i	0.607260	−	0.509552i	0.893770	+	0.448525i	$0.148051\pi$
$212$	−10643.3	+	29242.3i	−0.236813	+	0.650638i
$213$		0			0
$214$	−22501.1	+	127610.i	−0.491333	+	2.78649i
$215$			2646.45i			0.0572515i
$216$		0			0
$217$	−95733.0			−2.03302
$218$	40324.3	+	7110.27i	0.848505	+	0.149614i
$219$		0			0
$220$	−6915.75	−	2517.13i	−0.142887	−	0.0520067i
$221$	−47627.7	−	56760.4i	−0.975158	−	1.16215i
$222$		0			0
$223$	−40539.8	+	14755.3i	−0.815214	+	0.296714i	−0.715776	−	0.698330i	$-0.753927\pi$
$223$	−40539.8	+	14755.3i	−0.815214	+	0.296714i	−0.0994383	+	0.995044i	$0.531705\pi$
$224$	−71623.5	−	41351.8i	−1.42744	−	0.824135i
$225$		0			0
$226$	−16390.8	−	28389.7i	−0.320910	−	0.555832i
$227$	34396.1	−	40991.7i	0.667509	−	0.795507i	−0.320933	−	0.947102i	$-0.603997\pi$
$227$	34396.1	−	40991.7i	0.667509	−	0.795507i	0.988443	+	0.151595i	$0.0484410\pi$
$228$		0			0
$229$	−10270.1	−	58244.6i	−0.195841	−	1.11067i	−0.911216	−	0.411929i	$-0.864855\pi$
$229$	−10270.1	−	58244.6i	−0.195841	−	1.11067i	0.715375	−	0.698741i	$-0.246256\pi$
$230$	10025.9	−	1767.84i	0.189526	−	0.0334186i
$231$		0			0
$232$	−48144.0	−	40397.6i	−0.894470	−	0.750550i
$233$	−12167.6	+	7024.97i	−0.224126	+	0.129399i	−0.607859	−	0.794045i	$-0.707972\pi$
$233$	−12167.6	+	7024.97i	−0.224126	+	0.129399i	0.383733	+	0.923444i	$0.374638\pi$
$234$		0			0
$235$	−7369.17	+	12763.8i	−0.133439	+	0.231123i
$236$	−11222.3	−	30832.9i	−0.201492	−	0.553593i
$237$		0			0
$238$	−106154.	+	89073.5i	−1.87405	+	1.57251i
$239$	−20692.1	+	56851.1i	−0.362250	+	0.995274i	0.615982	+	0.787760i	$0.288759\pi$
$239$	−20692.1	+	56851.1i	−0.362250	+	0.995274i	−0.978232	+	0.207514i	$0.933463\pi$
$240$		0			0
$241$	9558.73	−	54210.2i	0.164576	−	0.933356i	−0.784925	−	0.619591i	$-0.787298\pi$
$241$	9558.73	−	54210.2i	0.164576	−	0.933356i	0.949501	−	0.313765i	$-0.101590\pi$
$242$			87072.4i			1.48679i
$243$		0			0
$244$	67369.0			1.13157
$245$	21615.1	+	3811.33i	0.360102	+	0.0634956i
$246$		0			0
$247$	119094.	+	43346.8i	1.95208	+	0.710499i
$248$	−44418.1	−	52935.4i	−0.722198	−	0.860682i
$249$		0			0
$250$	73359.7	−	26700.7i	1.17375	−	0.427212i
$251$	2594.71	+	1498.06i	0.0411852	+	0.0237783i	0.520451	−	0.853891i	$-0.325764\pi$
$251$	2594.71	+	1498.06i	0.0411852	+	0.0237783i	−0.479266	+	0.877670i	$0.659097\pi$
$252$		0			0
$253$	2090.05	+	3620.07i	0.0326524	+	0.0565556i
$254$	−64807.6	+	77234.7i	−1.00452	+	1.19714i
$255$		0			0
$256$	−5354.54	−	30367.1i	−0.0817038	−	0.463365i
$257$	106120.	−	18711.8i	1.60669	−	0.283302i	0.702901	−	0.711288i	$-0.251888\pi$
$257$	106120.	−	18711.8i	1.60669	−	0.283302i	0.903786	+	0.427985i	$0.140777\pi$
$258$		0			0
$259$	64051.5	+	53745.6i	0.954839	+	0.801205i
$260$	−50121.0	+	28937.3i	−0.741434	+	0.428067i
$261$		0			0
$262$	28606.5	−	49548.0i	0.416738	−	0.721811i
$263$	11348.9	+	31180.8i	0.164075	+	0.450791i	0.994298	−	0.106640i	$-0.0340092\pi$
$263$	11348.9	+	31180.8i	0.164075	+	0.450791i	−0.830223	+	0.557431i	$0.811787\pi$
$264$		0			0
$265$	−11091.4	+	9306.77i	−0.157941	+	0.132528i
$266$	81067.4	−	222731.i	1.14573	−	3.14787i
$267$		0			0
$268$	−5971.18	+	33864.2i	−0.0831362	+	0.471489i
$269$		−	68153.7i		−	0.941857i	−0.882171	−	0.470928i	$-0.843919\pi$
$269$		−	68153.7i		−	0.941857i	0.882171	−	0.470928i	$-0.156081\pi$
$270$		0			0
$271$	82407.6			1.12209			0.561046	−	0.827784i	$-0.310399\pi$
$271$	82407.6			1.12209			0.561046	+	0.827784i	$0.310399\pi$
$272$	24981.0	+	4404.83i	0.337655	+	0.0595376i
$273$		0			0
$274$	−191357.	−	69648.4i	−2.54885	−	0.927705i
$275$	9201.49	+	10965.9i	0.121673	+	0.145004i
$276$		0			0
$277$	−132172.	+	48106.5i	−1.72258	+	0.626966i	−0.998058	−	0.0622896i	$-0.980160\pi$
$277$	−132172.	+	48106.5i	−1.72258	+	0.626966i	−0.724518	+	0.689256i	$0.757938\pi$
$278$	534.311	+	308.485i	0.00691361	+	0.00399157i
$279$		0			0
$280$	17439.5	+	30206.1i	0.222442	+	0.385281i
$281$	34857.1	−	41541.1i	0.441448	−	0.526097i	−0.498741	−	0.866751i	$-0.666204\pi$
$281$	34857.1	−	41541.1i	0.441448	−	0.526097i	0.940189	+	0.340654i	$0.110649\pi$
$282$		0			0
$283$	27319.8	+	154938.i	0.341118	+	1.93458i	0.355491	+	0.934680i	$0.384314\pi$
$283$	27319.8	+	154938.i	0.341118	+	1.93458i	−0.0143731	+	0.999897i	$0.504575\pi$
$284$	23626.7	−	4166.02i	0.292932	−	0.0516517i
$285$		0			0
$286$	−30541.0	−	25627.0i	−0.373381	−	0.313304i
$287$	−15454.1	+	8922.42i	−0.187620	+	0.108323i
$288$		0			0
$289$	13342.6	−	23110.1i	0.159752	−	0.276698i
$290$	−31035.6	−	85269.5i	−0.369032	−	1.01391i
$291$		0			0
$292$	−61536.7	+	51635.5i	−0.721720	+	0.605595i
$293$	−30733.6	+	84439.9i	−0.357996	+	0.983586i	0.621728	+	0.783234i	$0.286431\pi$
$293$	−30733.6	+	84439.9i	−0.357996	+	0.983586i	−0.979724	+	0.200353i	$0.935791\pi$
$294$		0			0
$295$	2650.97	−	15034.4i	0.0304622	−	0.172760i
$296$			60354.0i			0.688847i
$297$		0			0
$298$	4780.99			0.0538375
$299$	32372.2	+	5708.10i	0.362102	+	0.0638483i
$300$		0			0
$301$	15017.1	+	5465.79i	0.165750	+	0.0603281i
$302$	−56507.6	−	67343.1i	−0.619574	−	0.738379i
$303$		0			0
$304$	−40771.7	+	14839.7i	−0.441176	+	0.160575i
$305$	27145.4	+	15672.4i	0.291808	+	0.168475i
$306$		0			0
$307$	−15111.7	−	26174.3i	−0.160338	−	0.277714i	0.774652	−	0.632388i	$-0.217925\pi$
$307$	−15111.7	−	26174.3i	−0.160338	−	0.277714i	−0.934990	+	0.354674i	$0.884592\pi$
$308$	−28566.6	+	34044.3i	−0.301132	+	0.358875i
$309$		0			0
$310$	−17325.4	−	98257.1i	−0.180285	−	1.02245i
$311$	−20942.7	+	3692.77i	−0.216527	+	0.0381796i	−0.280859	−	0.959749i	$-0.590619\pi$
$311$	−20942.7	+	3692.77i	−0.216527	+	0.0381796i	0.0643321	+	0.997929i	$0.479508\pi$
$312$		0			0
$313$	−48381.3	−	40596.7i	−0.493843	−	0.414384i	0.361558	−	0.932350i	$-0.382245\pi$
$313$	−48381.3	−	40596.7i	−0.493843	−	0.414384i	−0.855401	+	0.517966i	$0.826689\pi$
$314$	−128432.	+	74150.4i	−1.30261	+	0.752063i
$315$		0			0
$316$	17057.4	−	29544.3i	0.170820	−	0.295869i
$317$	−50318.9	−	138250.i	−0.500741	−	1.37577i	−0.890553	−	0.454879i	$-0.849682\pi$
$317$	−50318.9	−	138250.i	−0.500741	−	1.37577i	0.389813	−	0.920894i	$-0.372540\pi$
$318$		0			0
$319$	28541.4	−	23949.0i	0.280474	−	0.235346i
$320$	24887.1	−	68376.8i	0.243038	−	0.667743i
$321$		0			0
$322$	10675.3	−	60542.7i	0.102960	−	0.583916i
$323$			188504.i			1.80682i
$324$		0			0
$325$	112571.			1.06576
$326$	−73737.7	−	13002.0i	−0.693832	−	0.122341i
$327$		0			0
$328$	−12104.0	−	4405.50i	−0.112507	−	0.0409494i
$329$	57207.5	+	68177.3i	0.528520	+	0.629866i
$330$		0			0
$331$	13320.8	−	4848.39i	0.121584	−	0.0442529i	−0.280512	−	0.959851i	$-0.590504\pi$
$331$	13320.8	−	4848.39i	0.121584	−	0.0442529i	0.402096	+	0.915598i	$0.368282\pi$
$332$	199912.	+	115419.i	1.81368	+	1.04713i
$333$		0			0
$334$	56704.7	+	98215.4i	0.508307	+	0.880413i
$335$	−10284.0	+	12256.0i	−0.0916375	+	0.109209i
$336$		0			0
$337$	−8248.02	−	46776.8i	−0.0726256	−	0.411880i	−0.999347	−	0.0361312i	$-0.988497\pi$
$337$	−8248.02	−	46776.8i	−0.0726256	−	0.411880i	0.926721	−	0.375749i	$-0.122615\pi$
$338$	−131741.	+	23229.5i	−1.15315	+	0.203332i
$339$		0			0
$340$	−65941.2	−	55331.2i	−0.570426	−	0.478644i
$341$	35477.7	−	20483.1i	0.305103	−	0.176151i
$342$		0			0
$343$	−13356.1	+	23133.5i	−0.113525	+	0.196631i
$344$	3945.33	+	10839.7i	0.0333400	+	0.0916010i
$345$		0			0
$346$	213519.	−	179164.i	1.78355	−	1.49657i
$347$	−48527.4	+	133328.i	−0.403021	+	1.10729i	0.557765	+	0.829999i	$0.311659\pi$
$347$	−48527.4	+	133328.i	−0.403021	+	1.10729i	−0.960786	+	0.277292i	$0.910563\pi$
$348$		0			0
$349$	−11095.9	+	62927.9i	−0.0910985	+	0.516645i	0.904775	+	0.425890i	$0.140039\pi$
$349$	−11095.9	+	62927.9i	−0.0910985	+	0.516645i	−0.995873	+	0.0907548i	$0.971072\pi$
$350$		−	210530.i		−	1.71862i
$351$		0			0
$352$	35390.6			0.285629
$353$	82029.3	+	14464.0i	0.658293	+	0.116075i	0.492809	−	0.870138i	$-0.335970\pi$
$353$	82029.3	+	14464.0i	0.658293	+	0.116075i	0.165484	+	0.986212i	$0.447081\pi$
$354$		0			0
$355$	10489.2	+	3817.76i	0.0832312	+	0.0302937i
$356$	177663.	+	211731.i	1.40184	+	1.67065i
$357$		0			0
$358$	157673.	−	57388.4i	1.23025	−	0.447773i
$359$	−24583.0	−	14193.0i	−0.190742	−	0.110125i	0.401588	−	0.915820i	$-0.368458\pi$
$359$	−24583.0	−	14193.0i	−0.190742	−	0.110125i	−0.592330	+	0.805696i	$0.701792\pi$
$360$		0			0
$361$	−96053.9	−	166370.i	−0.737056	−	1.27662i
$362$	−10457.8	+	12463.1i	−0.0798039	+	0.0951066i
$363$		0			0
$364$	60687.1	+	344173.i	0.458029	+	2.59761i
$365$	−36807.6	+	6490.18i	−0.276282	+	0.0487159i
$366$		0			0
$367$	148368.	+	124495.i	1.10156	+	0.924316i	0.997529	−	0.0702587i	$-0.0223825\pi$
$367$	148368.	+	124495.i	1.10156	+	0.924316i	0.104028	+	0.994574i	$0.466827\pi$
$368$	−9745.84	+	5626.76i	−0.0719654	+	0.0415492i
$369$		0			0
$370$	−43570.9	+	75467.0i	−0.318268	+	0.551256i
$371$	29903.4	+	82158.8i	0.217256	+	0.596907i
$372$		0			0
$373$	89100.8	−	74764.4i	0.640418	−	0.537375i	−0.263728	−	0.964597i	$-0.584952\pi$
$373$	89100.8	−	74764.4i	0.640418	−	0.537375i	0.904147	+	0.427222i	$0.140508\pi$
$374$	20281.3	−	55722.4i	0.144995	−	0.398370i
$375$		0			0
$376$	−11155.4	+	63265.6i	−0.0789061	+	0.447499i
$377$		−	292992.i		−	2.06145i
$378$		0			0
$379$	−162689.			−1.13261			−0.566303	−	0.824197i	$-0.691627\pi$
$379$	−162689.			−1.13261			−0.566303	+	0.824197i	$0.691627\pi$
$380$	145000.	+	25567.4i	1.00416	+	0.177060i
$381$		0			0
$382$	−65628.7	−	23886.9i	−0.449745	−	0.163694i
$383$	−66642.3	−	79421.2i	−0.454310	−	0.541425i	0.489461	−	0.872025i	$-0.337193\pi$
$383$	−66642.3	−	79421.2i	−0.454310	−	0.541425i	−0.943771	+	0.330600i	$0.892749\pi$
$384$		0			0
$385$	−19430.4	+	7072.09i	−0.131087	+	0.0477119i
$386$	48667.4	+	28098.1i	0.326635	+	0.188583i
$387$		0			0
$388$	62900.8	+	108947.i	0.417823	+	0.723691i
$389$	−174142.	+	207534.i	−1.15081	+	1.37148i	−0.233964	+	0.972245i	$0.575170\pi$
$389$	−174142.	+	207534.i	−1.15081	+	1.37148i	−0.916847	+	0.399238i	$0.869275\pi$
$390$		0			0
$391$	8489.97	+	48149.0i	0.0555332	+	0.314944i
$392$	94216.0	−	16612.8i	0.613130	−	0.108111i
$393$		0			0
$394$	50766.1	+	42597.8i	0.327025	+	0.274407i
$395$	13746.1	−	7936.31i	0.0881018	−	0.0508656i
$396$		0			0
$397$	−30297.8	+	52477.3i	−0.192234	+	0.332959i	−0.945990	−	0.324195i	$-0.894907\pi$
$397$	−30297.8	+	52477.3i	−0.192234	+	0.332959i	0.753756	+	0.657154i	$0.228240\pi$
$398$	57226.2	+	157228.i	0.361267	+	0.992573i
$399$		0			0
$400$	−29522.1	+	24772.0i	−0.184513	+	0.154825i
$401$	32918.4	−	90442.5i	0.204715	−	0.562450i	−0.794267	−	0.607569i	$-0.792145\pi$
$401$	32918.4	−	90442.5i	0.204715	−	0.562450i	0.998982	+	0.0451196i	$0.0143669\pi$
$402$		0			0
$403$	55941.1	−	317258.i	0.344446	−	1.95345i
$404$		−	385125.i		−	2.35961i
$405$		0			0
$406$	−547955.			−3.32425
$407$	−35236.3	−	6213.11i	−0.212717	−	0.0375077i
$408$		0			0
$409$	−118507.	−	43133.1i	−0.708432	−	0.257848i	−0.0374253	−	0.999299i	$-0.511916\pi$
$409$	−118507.	−	43133.1i	−0.708432	−	0.257848i	−0.671007	+	0.741451i	$0.734138\pi$
$410$	−11954.5	−	14246.8i	−0.0711153	−	0.0847520i
$411$		0			0
$412$	161180.	−	58664.9i	0.949550	−	0.345608i
$413$	−79836.7	−	46093.8i	−0.468061	−	0.270235i
$414$		0			0
$415$	53701.1	+	93013.1i	0.311808	+	0.540067i
$416$	178892.	−	213195.i	1.03372	−	1.23194i
$417$		0			0
$418$	17612.8	+	99887.1i	0.100804	+	0.571685i
$419$	169373.	−	29865.1i	0.964755	−	0.170112i	0.330987	−	0.943635i	$-0.392618\pi$
$419$	169373.	−	29865.1i	0.964755	−	0.170112i	0.633768	+	0.773523i	$0.281507\pi$
$420$		0			0
$421$	178528.	+	149803.i	1.00726	+	0.845193i	0.987974	−	0.154621i	$-0.0494157\pi$
$421$	178528.	+	149803.i	1.00726	+	0.845193i	0.0192879	+	0.999814i	$0.493860\pi$
$422$	192355.	−	111056.i	1.08014	−	0.623618i
$423$		0			0
$424$	−31555.1	+	54655.0i	−0.175524	+	0.304017i
$425$	57265.3	+	157335.i	0.317040	+	0.871060i
$426$		0			0
$427$	144996.	−	121666.i	0.795246	−	0.667290i
$428$	−166243.	+	456749.i	−0.907520	+	2.49339i
$429$		0			0
$430$	−2892.16	+	16402.2i	−0.0156417	+	0.0887087i
$431$			155134.i			0.835126i	0.908648	+	0.417563i	$0.137116\pi$
$431$			155134.i			0.835126i	−0.908648	+	0.417563i	$0.862884\pi$
$432$		0			0
$433$	−3126.89			−0.0166777			−0.00833887	−	0.999965i	$-0.502654\pi$
$433$	−3126.89			−0.0166777			−0.00833887	+	0.999965i	$0.502654\pi$
$434$	−593336.	−	104621.i	−3.15008	−	0.555444i
$435$		0			0
$436$	144331.	+	52532.3i	0.759255	+	0.276346i
$437$	−53754.8	−	64062.4i	−0.281484	−	0.335460i
$438$		0			0
$439$	−242506.	+	88264.8i	−1.25833	+	0.457993i	−0.883207	−	0.468984i	$-0.844620\pi$
$439$	−242506.	+	88264.8i	−1.25833	+	0.457993i	−0.375118	+	0.926977i	$0.622398\pi$
$440$	−12925.8	−	7462.71i	−0.0667655	−	0.0385471i
$441$		0			0
$442$	−233158.	−	403841.i	−1.19345	−	2.06712i
$443$	150984.	−	179936.i	0.769351	−	0.916877i	−0.229049	−	0.973415i	$-0.573562\pi$
$443$	150984.	−	179936.i	0.769351	−	0.916877i	0.998400	+	0.0565377i	$0.0180061\pi$
$444$		0			0
$445$	22330.9	+	126645.i	0.112768	+	0.639540i
$446$	−267384.	+	47147.0i	−1.34420	+	0.237019i
$447$		0			0
$448$	−336600.	−	282441.i	−1.67710	−	1.40725i
$449$	−188149.	+	108628.i	−0.933274	+	0.538826i	−0.887846	−	0.460142i	$-0.847799\pi$
$449$	−188149.	+	108628.i	−0.933274	+	0.538826i	−0.0454285	+	0.998968i	$0.514465\pi$
$450$		0			0
$451$	3818.09	−	6613.12i	0.0187712	−	0.0325127i
$452$	−42057.2	−	115551.i	−0.205856	−	0.565585i
$453$		0			0
$454$	257978.	−	216470.i	1.25162	−	1.05023i
$455$	−55613.9	+	152798.i	−0.268634	+	0.738065i
$456$		0			0
$457$	13225.3	−	75004.7i	0.0633249	−	0.359133i	−0.936636	−	0.350304i	$-0.886078\pi$
$457$	13225.3	−	75004.7i	0.0633249	−	0.359133i	0.999961	−	0.00882954i	$-0.00281057\pi$
$458$		−	372213.i		−	1.77444i
$459$		0			0
$460$	38188.5			0.180475
$461$	−179478.	−	31646.8i	−0.844519	−	0.148912i	−0.265384	−	0.964143i	$-0.585499\pi$
$461$	−179478.	−	31646.8i	−0.844519	−	0.148912i	−0.579135	+	0.815231i	$0.696610\pi$
$462$		0			0
$463$	−302626.	−	110147.i	−1.41171	−	0.513819i	−0.480076	−	0.877227i	$-0.659391\pi$
$463$	−302626.	−	110147.i	−1.41171	−	0.513819i	−0.931630	+	0.363408i	$0.881613\pi$
$464$	64474.9	+	76838.2i	0.299471	+	0.356896i
$465$		0			0
$466$	−83089.8	+	30242.2i	−0.382627	+	0.139265i
$467$	23093.6	+	13333.1i	0.105891	+	0.0611359i	0.552010	−	0.833837i	$-0.313861\pi$
$467$	23093.6	+	13333.1i	0.105891	+	0.0611359i	−0.446119	+	0.894973i	$0.647194\pi$
$468$		0			0
$469$	48306.2	+	83668.8i	0.219612	+	0.380380i
$470$	−59621.6	+	71054.3i	−0.269903	+	0.321658i
$471$		0			0
$472$	−11555.1	−	65532.1i	−0.0518667	−	0.294151i
$473$	−6734.66	+	1187.50i	−0.0301019	+	0.00530777i
$474$		0			0
$475$	−219386.	−	184086.i	−0.972346	−	0.815895i
$476$	−450164.	+	259902.i	−1.98681	+	1.14709i
$477$		0			0
$478$	−190375.	+	329740.i	−0.833210	+	1.44316i
$479$	−47067.5	−	129317.i	−0.205140	−	0.563617i	0.793871	−	0.608086i	$-0.208063\pi$
$479$	−47067.5	−	129317.i	−0.205140	−	0.563617i	−0.999011	+	0.0444692i	$0.985840\pi$
$480$		0			0
$481$	−215540.	+	180860.i	−0.931619	+	0.781721i
$482$	118487.	−	325539.i	0.510006	−	1.40123i
$483$		0			0
$484$	−56716.5	+	321655.i	−0.242113	+	1.37309i
$485$			58531.8i			0.248833i
$486$		0			0
$487$	327215.			1.37967			0.689834	−	0.723967i	$-0.257683\pi$
$487$	327215.			1.37967			0.689834	+	0.723967i	$0.257683\pi$
$488$	134550.	+	23724.9i	0.564996	+	0.0996241i
$489$		0			0
$490$	129801.	+	47243.9i	0.540614	+	0.196767i
$491$	−238624.	−	284382.i	−0.989810	−	1.17961i	−0.983735	−	0.179629i	$-0.942510\pi$
$491$	−238624.	−	284382.i	−0.989810	−	1.17961i	−0.00607590	−	0.999982i	$-0.501934\pi$
$492$		0			0
$493$	409502.	−	149047.i	1.68485	−	0.613237i
$494$	690755.	+	398808.i	2.83055	+	1.63422i
$495$		0			0
$496$	55143.9	+	95512.1i	0.224148	+	0.388235i
$497$	43327.3	−	51635.5i	0.175408	−	0.209043i
$498$		0			0
$499$	−24139.4	−	136901.i	−0.0969449	−	0.549802i	−0.994134	−	0.108155i	$-0.965506\pi$
$499$	−24139.4	−	136901.i	−0.0969449	−	0.549802i	0.897189	−	0.441646i	$-0.145605\pi$
$500$	288391.	−	50851.2i	1.15357	−	0.203405i
$501$		0			0
$502$	14444.4	+	12120.3i	0.0573182	+	0.0480957i
$503$	105718.	−	61036.5i	0.417844	−	0.241243i	−0.276310	−	0.961068i	$-0.589112\pi$
$503$	105718.	−	61036.5i	0.417844	−	0.241243i	0.694155	+	0.719826i	$0.255778\pi$
$504$		0			0
$505$	89593.8	−	155181.i	0.351314	−	0.608493i
$506$	8997.57	+	24720.6i	0.0351418	+	0.0965514i
$507$		0			0
$508$	−289716.	+	243100.i	−1.12265	+	0.942015i
$509$	67757.9	−	186163.i	0.261532	−	0.718552i	−0.737533	−	0.675311i	$-0.764009\pi$
$509$	67757.9	−	186163.i	0.261532	−	0.718552i	0.999065	−	0.0432413i	$-0.0137684\pi$
$510$		0			0
$511$	−39191.7	+	222267.i	−0.150090	+	0.851203i
$512$			153810.i			0.586739i
$513$		0			0
$514$	678163.			2.56689
$515$	78593.0	+	13858.1i	0.296326	+	0.0522502i
$516$		0			0
$517$	−35787.8	−	13025.7i	−0.133892	−	0.0487326i
$518$	338245.	+	403104.i	1.26058	+	1.50230i
$519$		0			0
$520$	−110293.	+	40143.4i	−0.407888	+	0.148459i
$521$	330879.	+	191033.i	1.21897	+	0.703773i	0.964698	−	0.263359i	$-0.0848305\pi$
$521$	330879.	+	191033.i	1.21897	+	0.703773i	0.254273	+	0.967132i	$0.418164\pi$
$522$		0			0
$523$	187042.	+	323966.i	0.683811	+	1.18440i	0.973809	+	0.227368i	$0.0730120\pi$
$523$	187042.	+	323966.i	0.683811	+	1.18440i	−0.289998	+	0.957027i	$0.593655\pi$
$524$	137950.	−	164402.i	0.502411	−	0.598750i
$525$		0			0
$526$	36262.6	+	205656.i	0.131065	+	0.743308i
$527$	471874.	−	83204.2i	1.69905	−	0.299588i
$528$		0			0
$529$	197755.	+	165936.i	0.706669	+	0.592966i
$530$	−78913.2	+	45560.6i	−0.280930	+	0.162195i
$531$		0			0
$532$	444553.	−	769989.i	1.57073	−	2.72058i
$533$	−20538.2	−	56428.4i	−0.0722951	−	0.198629i
$534$		0			0
$535$	−173241.	+	145367.i	−0.605263	+	0.507876i
$536$	−23851.5	+	65531.3i	−0.0830205	+	0.228097i
$537$		0			0
$538$	74481.3	−	422405.i	0.257326	−	1.45937i
$539$			56716.1i			0.195222i
$540$		0			0
$541$	−179687.			−0.613936			−0.306968	−	0.951720i	$-0.599314\pi$
$541$	−179687.			−0.613936			−0.306968	+	0.951720i	$0.599314\pi$
$542$	510748.	+	90058.6i	1.73863	+	0.306568i
$543$		0			0
$544$	388977.	+	141576.i	1.31439	+	0.478400i
$545$	45935.5	+	54743.8i	0.154652	+	0.184307i
$546$		0			0
$547$	−188810.	+	68721.1i	−0.631030	+	0.229676i	−0.637679	−	0.770302i	$-0.720106\pi$
$547$	−188810.	+	68721.1i	−0.631030	+	0.229676i	0.00664982	+	0.999978i	$0.497883\pi$
$548$	−661529.	−	381934.i	−2.20286	−	1.27182i
$549$		0			0
$550$	45045.2	+	78020.5i	0.148910	+	0.257919i
$551$	−479128.	+	571003.i	−1.57815	+	1.88077i
$552$		0			0
$553$	−16643.9	−	94392.4i	−0.0544259	−	0.308665i
$554$	−871749.	+	153713.i	−2.84035	+	0.500830i
$555$		0			0
$556$	1772.87	+	1487.61i	0.00573492	+	0.00481217i
$557$	−51655.6	+	29823.4i	−0.166497	+	0.0961272i	−0.580933	−	0.813951i	$-0.697312\pi$
$557$	−51655.6	+	29823.4i	−0.166497	+	0.0961272i	0.414436	+	0.910079i	$0.363979\pi$
$558$		0			0
$559$	−26888.7	+	46572.6i	−0.0860490	+	0.149041i
$560$	−19039.3	−	52310.0i	−0.0607120	−	0.166805i
$561$		0			0
$562$	261436.	−	219371.i	0.827739	−	0.694556i
$563$	207044.	−	568850.i	0.653201	−	1.79465i	0.0476268	−	0.998865i	$-0.484834\pi$
$563$	207044.	−	568850.i	0.653201	−	1.79465i	0.605574	−	0.795789i	$-0.292944\pi$
$564$		0			0
$565$	9934.94	−	56343.8i	0.0311220	−	0.176502i
$566$			990137.i			3.09074i
$567$		0			0
$568$	48654.7			0.150809
$569$	−174871.	−	30834.4i	−0.540122	−	0.0952381i	−0.103070	−	0.994674i	$-0.532867\pi$
$569$	−174871.	−	30834.4i	−0.540122	−	0.0952381i	−0.437053	+	0.899436i	$0.643978\pi$
$570$		0			0
$571$	10666.5	+	3882.28i	0.0327151	+	0.0119073i	0.358326	−	0.933597i	$-0.383348\pi$
$571$	10666.5	+	3882.28i	0.0327151	+	0.0119073i	−0.325611	+	0.945504i	$0.605570\pi$
$572$	−96129.5	−	114563.i	−0.293809	−	0.350147i
$573$		0			0
$574$	−105533.	+	38410.7i	−0.320304	+	0.116581i
$575$	−64328.1	−	37139.8i	−0.194565	−	0.112332i
$576$		0			0
$577$	−111023.	−	192298.i	−0.333474	−	0.577593i	0.649717	−	0.760176i	$-0.274888\pi$
$577$	−111023.	−	192298.i	−0.333474	−	0.577593i	−0.983190	+	0.182583i	$0.941554\pi$
$578$	107951.	−	128651.i	0.323125	−	0.385085i
$579$		0			0
$580$	−59106.8	−	335211.i	−0.175704	−	0.996467i
$581$	638707.	−	112621.i	1.89212	−	0.333633i
$582$		0			0
$583$	−28660.6	−	24049.1i	−0.0843235	−	0.0707558i
$584$	−141086.	+	81456.2i	−0.413675	+	0.238835i
$585$		0			0
$586$	−282761.	+	489757.i	−0.823426	+	1.42622i
$587$	6758.00	+	18567.4i	0.0196129	+	0.0538860i	0.949113	−	0.314937i	$-0.101983\pi$
$587$	6758.00	+	18567.4i	0.0196129	+	0.0538860i	−0.929500	+	0.368823i	$0.879761\pi$
$588$		0			0
$589$	−627831.	+	526813.i	−1.80972	+	1.51854i
$590$	32860.5	−	90283.6i	0.0943997	−	0.259361i
$591$		0			0
$592$	16726.8	−	94862.2i	0.0477275	−	0.270676i
$593$		−	550403.i		−	1.56521i	−0.622521	−	0.782603i	$-0.713892\pi$
$593$		−	550403.i		−	1.56521i	0.622521	−	0.782603i	$-0.286108\pi$
$594$		0			0
$595$	−241850.			−0.683144
$596$	17661.5	+	3114.20i	0.0497205	+	0.00876707i
$597$		0			0
$598$	194399.	+	70755.6i	0.543617	+	0.197860i
$599$	−128103.	−	152667.i	−0.357031	−	0.425493i	0.557394	−	0.830248i	$-0.311801\pi$
$599$	−128103.	−	152667.i	−0.357031	−	0.425493i	−0.914425	+	0.404755i	$0.867357\pi$
$600$		0			0
$601$	133684.	−	48657.0i	0.370110	−	0.134709i	−0.150268	−	0.988645i	$-0.548014\pi$
$601$	133684.	−	48657.0i	0.370110	−	0.134709i	0.520377	+	0.853936i	$0.325791\pi$
$602$	87100.2	+	50287.3i	0.240340	+	0.138760i
$603$		0			0
$604$	−164880.	−	285581.i	−0.451954	−	0.782808i
$605$	−97681.6	+	116412.i	−0.266871	+	0.318045i
$606$		0			0
$607$	−90199.7	−	511548.i	−0.244809	−	1.38838i	−0.820936	−	0.571021i	$-0.806548\pi$
$607$	−90199.7	−	511548.i	−0.244809	−	1.38838i	0.576127	−	0.817361i	$-0.304564\pi$
$608$	−697273.	+	122948.i	−1.88624	+	0.332594i
$609$		0			0
$610$	151115.	+	126801.i	0.406114	+	0.340770i
$611$	−259367.	+	149746.i	−0.694757	+	0.401118i
$612$		0			0
$613$	164250.	−	284490.i	0.437104	−	0.757087i	−0.560360	−	0.828249i	$-0.689337\pi$
$613$	164250.	−	284490.i	0.437104	−	0.757087i	0.997465	+	0.0711618i	$0.0226707\pi$
$614$	−65055.4	−	178738.i	−0.172563	−	0.474112i
$615$		0			0
$616$	−69042.7	+	57933.7i	−0.181952	+	0.152676i
$617$	−200393.	+	550576.i	−0.526396	+	1.44626i	0.336889	+	0.941544i	$0.390625\pi$
$617$	−200393.	+	550576.i	−0.526396	+	1.44626i	−0.863285	+	0.504717i	$0.831597\pi$
$618$		0			0
$619$	−5535.97	+	31396.1i	−0.0144482	+	0.0819396i	−0.991179	−	0.132528i	$-0.957691\pi$
$619$	−5535.97	+	31396.1i	−0.0144482	+	0.0819396i	0.976731	+	0.214468i	$0.0688017\pi$
$620$		−	374258.i		−	0.973617i
$621$		0			0
$622$	−133835.			−0.345930
$623$	764760.	+	134848.i	1.97038	+	0.347430i
$624$		0			0
$625$	−168179.	−	61212.2i	−0.430538	−	0.156703i
$626$	−255493.	−	304485.i	−0.651974	−	0.776993i
$627$		0			0
$628$	−522743.	+	190263.i	−1.32547	+	0.482431i
$629$	−362426.	−	209247.i	−0.916048	−	0.528880i
$630$		0			0
$631$	−25960.6	−	44965.1i	−0.0652013	−	0.112932i	0.831582	−	0.555402i	$-0.187436\pi$
$631$	−25960.6	−	44965.1i	−0.0652013	−	0.112932i	−0.896783	+	0.442470i	$0.854102\pi$
$632$	44471.7	−	52999.3i	0.111340	−	0.132689i
$633$		0			0
$634$	−160782.	−	911840.i	−0.399999	−	2.26851i
$635$	−173291.	+	30555.8i	−0.429762	+	0.0757786i
$636$		0			0
$637$	341661.	+	286688.i	0.842009	+	0.706530i
$638$	203067.	−	117241.i	0.498882	−	0.288030i
$639$		0			0
$640$	119405.	−	206815.i	0.291516	−	0.504920i
$641$	16727.5	+	45958.4i	0.0407113	+	0.111853i	0.958383	−	0.285487i	$-0.0921554\pi$
$641$	16727.5	+	45958.4i	0.0407113	+	0.111853i	−0.917671	+	0.397341i	$0.869933\pi$
$642$		0			0
$643$	99454.3	−	83452.1i	0.240548	−	0.201844i	−0.514542	−	0.857465i	$-0.672038\pi$
$643$	99454.3	−	83452.1i	0.240548	−	0.201844i	0.755089	+	0.655622i	$0.227593\pi$
$644$	78871.7	−	216698.i	0.190173	−	0.522497i
$645$		0			0
$646$	−206005.	+	1.16831e6i	−0.493643	+	2.79959i
$647$			219579.i			0.524544i	0.964994	+	0.262272i	$0.0844717\pi$
$647$			219579.i			0.524544i	−0.964994	+	0.262272i	$0.915528\pi$
$648$		0			0
$649$	39448.9			0.0936582
$650$	697694.	+	123022.i	1.65135	+	0.291177i
$651$		0			0
$652$	−263927.	−	96061.5i	−0.620852	−	0.225972i
$653$	12945.7	+	15428.1i	0.0303598	+	0.0361814i	0.781011	−	0.624518i	$-0.214704\pi$
$653$	12945.7	+	15428.1i	0.0303598	+	0.0361814i	−0.750651	+	0.660699i	$0.770260\pi$
$654$		0			0
$655$	93830.9	−	34151.7i	0.218707	−	0.0796030i
$656$	17803.7	+	10279.0i	0.0413716	+	0.0238859i
$657$		0			0
$658$	280055.	+	485070.i	0.646832	+	1.12035i
$659$	482438.	−	574947.i	1.11089	−	1.32391i	0.169904	−	0.985461i	$-0.445654\pi$
$659$	482438.	−	574947.i	1.11089	−	1.32391i	0.940986	−	0.338446i	$-0.109901\pi$
$660$		0			0
$661$	−28440.2	−	161292.i	−0.0650923	−	0.369157i	−0.999902	−	0.0140075i	$-0.995541\pi$
$661$	−28440.2	−	161292.i	−0.0650923	−	0.369157i	0.934810	−	0.355149i	$-0.115570\pi$
$662$	87858.8	−	15491.9i	0.200479	−	0.0353499i
$663$		0			0
$664$	358620.	+	300918.i	0.813390	+	0.682515i
$665$	358254.	−	206838.i	0.810116	−	0.467721i
$666$		0			0
$667$	−96665.2	+	167429.i	−0.217279	+	0.376339i
$668$	145499.	+	399755.i	0.326067	+	0.895862i
$669$		0			0
$670$	−77132.5	+	64721.8i	−0.171826	+	0.144179i
$671$	−27702.4	+	76111.9i	−0.0615280	+	0.169047i
$672$		0			0
$673$	−84265.1	+	477891.i	−0.186045	+	1.05511i	0.738561	+	0.674187i	$0.235506\pi$
$673$	−84265.1	+	477891.i	−0.186045	+	1.05511i	−0.924606	+	0.380926i	$0.875605\pi$
$674$		−	298928.i		−	0.658032i
$675$		0			0
$676$	−501798.			−1.09808
$677$	−744551.	−	131284.i	−1.62449	−	0.286441i	−0.714053	−	0.700091i	$-0.753143\pi$
$677$	−744551.	−	131284.i	−1.62449	−	0.286441i	−0.910436	+	0.413650i	$0.864254\pi$
$678$		0			0
$679$	332135.	+	120887.i	0.720402	+	0.262205i
$680$	−112213.	−	133730.i	−0.242676	−	0.289210i
$681$		0			0
$682$	242269.	−	88178.9i	0.520871	−	0.189581i
$683$	−331391.	−	191329.i	−0.710393	−	0.410146i	0.100813	−	0.994905i	$-0.467856\pi$
$683$	−331391.	−	191329.i	−0.710393	−	0.410146i	−0.811207	+	0.584760i	$0.801189\pi$
$684$		0			0
$685$	−177703.	−	307790.i	−0.378716	−	0.655955i
$686$	−108060.	+	128781.i	−0.229624	+	0.273655i
$687$		0			0
$688$	−3196.96	−	18130.9i	−0.00675399	−	0.0383038i
$689$	−289747.	+	51090.2i	−0.610352	+	0.107621i
$690$		0			0
$691$	−569224.	−	477636.i	−1.19214	−	1.00032i	−0.999820	−	0.0189914i	$-0.993954\pi$
$691$	−569224.	−	477636.i	−1.19214	−	1.00032i	−0.192320	−	0.981332i	$-0.561601\pi$
$692$	905466.	−	522771.i	1.89086	−	1.09169i
$693$		0			0
$694$	−446471.	+	773310.i	−0.926988	+	1.60559i
$695$	368.282	+	1011.85i	0.000762449	+	0.00209481i
$696$		0			0
$697$	68419.5	−	57410.8i	0.140836	−	0.118176i
$698$	−137541.	+	377890.i	−0.282306	+	0.775630i
$699$		0			0
$700$	137134.	−	777724.i	0.279865	−	1.58719i
$701$			357201.i			0.726902i	0.931613	+	0.363451i	$0.118402\pi$
$701$			357201.i			0.726902i	−0.931613	+	0.363451i	$0.881598\pi$
$702$		0			0
$703$	715818.			1.44841
$704$	185172.	+	32650.8i	0.373620	+	0.0658792i
$705$		0			0
$706$	492596.	+	179290.i	0.988284	+	0.359706i
$707$	−695525.	−	828894.i	−1.39147	−	1.65829i
$708$		0			0
$709$	121993.	−	44401.9i	0.242685	−	0.0883301i	−0.217814	−	0.975990i	$-0.569893\pi$
$709$	121993.	−	44401.9i	0.242685	−	0.0883301i	0.460499	+	0.887660i	$0.347670\pi$
$710$	60838.1	+	35124.9i	0.120687	+	0.0696784i
$711$		0			0
$712$	280268.	+	485439.i	0.552859	+	0.957579i
$713$	−136638.	+	162839.i	−0.268777	+	0.320316i
$714$		0			0
$715$	−12082.7	−	68524.6i	−0.0236349	−	0.134040i
$716$	619845.	−	109295.i	1.20909	−	0.213194i
$717$		0			0
$718$	−136850.	−	114831.i	−0.265459	−	0.222746i
$719$	−667081.	+	385139.i	−1.29039	+	0.745007i	−0.978723	−	0.205185i	$-0.934220\pi$
$719$	−667081.	+	385139.i	−1.29039	+	0.745007i	−0.311666	+	0.950192i	$0.600887\pi$
$720$		0			0
$721$	240957.	−	417350.i	0.463521	−	0.802841i
$722$	−413509.	−	1.13611e6i	−0.793250	−	2.17944i
$723$		0			0
$724$	−46750.6	+	39228.4i	−0.0891887	+	0.0748382i
$725$	−226442.	+	622143.i	−0.430804	+	1.18363i
$726$		0			0
$727$	−72177.6	+	409339.i	−0.136563	+	0.774488i	0.837195	+	0.546904i	$0.184194\pi$
$727$	−72177.6	+	409339.i	−0.136563	+	0.774488i	−0.973758	+	0.227584i	$0.926917\pi$
$728$			708760.i			1.33732i
$729$		0			0
$730$	−235220.			−0.441396
$731$	−78770.8	−	13889.4i	−0.147411	−	0.0259926i
$732$		0			0
$733$	79575.9	+	28963.2i	0.148106	+	0.0539063i	0.415010	−	0.909817i	$-0.363778\pi$
$733$	79575.9	+	28963.2i	0.148106	+	0.0539063i	−0.266903	+	0.963723i	$0.586000\pi$
$734$	783502.	+	933742.i	1.45428	+	1.73314i
$735$		0			0
$736$	−172565.	+	62808.6i	−0.318565	+	0.115948i
$737$	−35803.6	−	20671.2i	−0.0659161	−	0.0380567i
$738$		0			0
$739$	−343960.	−	595756.i	−0.629824	−	1.09089i	−0.987587	−	0.157074i	$-0.949794\pi$
$739$	−343960.	−	595756.i	−0.629824	−	1.09089i	0.357763	−	0.933812i	$-0.383540\pi$
$740$	−210113.	+	250403.i	−0.383698	+	0.457274i
$741$		0			0
$742$	95549.1	+	541886.i	0.173548	+	0.984237i
$743$	23488.6	−	4141.68i	0.0425481	−	0.00750238i	−0.152334	−	0.988329i	$-0.548679\pi$
$743$	23488.6	−	4141.68i	0.0425481	−	0.00750238i	0.194882	+	0.980827i	$0.437568\pi$
$744$		0			0
$745$	6392.00	+	5363.52i	0.0115166	+	0.00966357i
$746$	633937.	−	366004.i	1.13912	−	0.657669i
$747$		0			0
$748$	111218.	−	192634.i	0.198779	−	0.344295i
$749$	467075.	+	1.28328e6i	0.832574	+	2.28748i
$750$		0			0
$751$	806672.	−	676878.i	1.43027	−	1.20014i	0.484712	−	0.874674i	$-0.338924\pi$
$751$	806672.	−	676878.i	1.43027	−	1.20014i	0.945555	−	0.325462i	$-0.105520\pi$
$752$	35067.4	−	96346.9i	0.0620109	−	0.170373i
$753$		0			0
$754$	320195.	−	1.81591e6i	0.563211	−	3.19413i
$755$		−	153428.i		−	0.269160i
$756$		0			0
$757$	7573.14			0.0132155			0.00660776	−	0.999978i	$-0.497897\pi$
$757$	7573.14			0.0132155			0.00660776	+	0.999978i	$0.497897\pi$
$758$	−1.00832e6	−	177793.i	−1.75492	−	0.309441i
$759$		0			0
$760$	280593.	+	102127.i	0.485790	+	0.176813i
$761$	559188.	+	666414.i	0.965580	+	1.15073i	0.988534	+	0.150997i	$0.0482484\pi$
$761$	559188.	+	666414.i	0.965580	+	1.15073i	−0.0229542	+	0.999737i	$0.507307\pi$
$762$		0			0
$763$	405512.	−	147594.i	0.696554	−	0.253525i
$764$	−226881.	−	130990.i	−0.388697	−	0.224414i
$765$		0			0
$766$	−326242.	−	565068.i	−0.556010	−	0.963037i
$767$	199406.	−	237643.i	0.338959	−	0.403956i
$768$		0			0
$769$	139267.	+	789822.i	0.235502	+	1.33560i	0.841553	+	0.540175i	$0.181642\pi$
$769$	139267.	+	789822.i	0.235502	+	1.33560i	−0.606051	+	0.795426i	$0.707247\pi$
$770$	−128155.	+	22597.2i	−0.216149	+	0.0381130i
$771$		0			0
$772$	161481.	+	135498.i	0.270948	+	0.227352i
$773$	728698.	−	420714.i	1.21952	−	0.704090i	0.254705	−	0.967019i	$-0.418022\pi$
$773$	728698.	−	420714.i	1.21952	−	0.704090i	0.964815	+	0.262929i	$0.0846884\pi$
$774$		0			0
$775$	−363981.	+	630434.i	−0.606004	+	1.04963i
$776$	87259.2	+	239743.i	0.144906	+	0.398127i
$777$		0			0
$778$	−1.30610e6	+	1.09595e6i	−2.15784	+	1.81064i
$779$	−52250.6	+	143557.i	−0.0861026	+	0.236565i
$780$		0			0
$781$	−5008.73	+	28405.9i	−0.00821156	+	0.0465701i
$782$			307697.i			0.503165i
$783$		0			0
$784$	−152689.			−0.248414
$785$	−254894.	−	44944.7i	−0.413638	−	0.0729356i
$786$		0			0
$787$	−372205.	−	135472.i	−0.600943	−	0.218725i	0.0235926	−	0.999722i	$-0.492490\pi$
$787$	−372205.	−	135472.i	−0.600943	−	0.218725i	−0.624536	+	0.780996i	$0.714712\pi$
$788$	159789.	+	190429.i	0.257332	+	0.306677i
$789$		0			0
$790$	93869.0	−	34165.5i	0.150407	−	0.0547436i
$791$	−299201.	−	172744.i	−0.478200	−	0.276089i
$792$		0			0
$793$	318473.	+	551611.i	0.506437	+	0.877175i
$794$	−245130.	+	292134.i	−0.388826	+	0.463384i
$795$		0			0
$796$	108986.	+	618093.i	0.172007	+	0.975500i
$797$	1.05154e6	−	185415.i	1.65542	−	0.291896i	0.733623	−	0.679557i	$-0.237828\pi$
$797$	1.05154e6	−	185415.i	1.65542	−	0.291896i	0.921802	+	0.387661i	$0.126717\pi$
$798$		0			0
$799$	−341234.	−	286330.i	−0.534514	−	0.448511i
$800$	−544631.	+	314443.i	−0.850986	+	0.491317i
$801$		0			0
$802$	302862.	−	524572.i	0.470864	−	0.815561i
$803$	−33032.3	−	90755.4i	−0.0512280	−	0.140748i
$804$		0			0
$805$	82192.0	−	68967.3i	0.126835	−	0.106427i
$806$	693426.	−	1.90517e6i	1.06741	−	2.93268i
$807$		0			0
$808$	135627.	−	769178.i	0.207741	−	1.17816i
$809$			689350.i			1.05328i	0.850089	+	0.526639i	$0.176548\pi$
$809$			689350.i			1.05328i	−0.850089	+	0.526639i	$0.823452\pi$
$810$		0			0
$811$	−693300.			−1.05409			−0.527047	−	0.849836i	$-0.676701\pi$
$811$	−693300.			−1.05409			−0.527047	+	0.849836i	$0.676701\pi$
$812$	−2.02421e6	−	356923.i	−3.07004	−	0.541331i
$813$		0			0
$814$	−211599.	−	77015.6i	−0.319348	−	0.116233i
$815$	−83998.4	−	100105.i	−0.126461	−	0.150710i
$816$		0			0
$817$	128562.	−	46792.8i	0.192606	−	0.0701028i
$818$	−687349.	−	396841.i	−1.02724	−	0.593076i
$819$		0			0
$820$	−34881.3	−	60416.2i	−0.0518758	−	0.0898516i
$821$	180372.	−	214959.i	0.267599	−	0.318911i	−0.615466	−	0.788164i	$-0.711032\pi$
$821$	180372.	−	214959.i	0.267599	−	0.318911i	0.883064	+	0.469252i	$0.155476\pi$
$822$		0			0
$823$	132869.	+	753539.i	0.196167	+	1.11252i	0.910748	+	0.412963i	$0.135506\pi$
$823$	132869.	+	753539.i	0.196167	+	1.11252i	−0.714581	+	0.699553i	$0.753383\pi$
$824$	342572.	−	60404.6i	0.504542	−	0.0889643i
$825$		0			0
$826$	−444441.	−	372930.i	−0.651409	−	0.546597i
$827$	320685.	−	185148.i	0.468886	−	0.270712i	−0.246887	−	0.969044i	$-0.579408\pi$
$827$	320685.	−	185148.i	0.468886	−	0.270712i	0.715773	+	0.698333i	$0.246074\pi$
$828$		0			0
$829$	138822.	−	240446.i	0.201999	−	0.349872i	−0.747174	−	0.664629i	$-0.768590\pi$
$829$	138822.	−	240446.i	0.201999	−	0.349872i	0.949172	+	0.314757i	$0.101923\pi$
$830$	231181.	+	635166.i	0.335580	+	0.922000i
$831$		0			0
$832$	1.13270e6	−	950444.i	1.63631	−	1.37303i
$833$	−226886.	+	623364.i	−0.326977	+	0.898363i
$834$		0			0
$835$	−34370.4	+	194924.i	−0.0492959	+	0.279571i
$836$			380467.i			0.544383i
$837$		0			0
$838$	1.08238e6			1.54132
$839$	290551.	+	51232.0i	0.412761	+	0.0727808i	0.376173	−	0.926550i	$-0.377240\pi$
$839$	290551.	+	51232.0i	0.412761	+	0.0727808i	0.0365880	+	0.999330i	$0.488351\pi$
$840$		0			0
$841$	954648.	+	347463.i	1.34974	+	0.491266i
$842$	942775.	+	1.12356e6i	1.32979	+	1.58478i
$843$		0			0
$844$	782922.	−	284960.i	1.09909	−	0.400037i
$845$	−202193.	−	116736.i	−0.283173	−	0.163490i
$846$		0			0
$847$	458831.	+	794718.i	0.639566	+	1.10776i
$848$	64744.4	−	77159.3i	0.0900348	−	0.107299i
$849$		0			0
$850$	182978.	+	1.03772e6i	0.253256	+	1.43629i
$851$	182839.	−	32239.5i	0.252470	−	0.0445174i
$852$		0			0
$853$	−302369.	−	253718.i	−0.415565	−	0.348701i	0.410908	−	0.911677i	$-0.365212\pi$
$853$	−302369.	−	253718.i	−0.415565	−	0.348701i	−0.826473	+	0.562976i	$0.809656\pi$
$854$	1.03162e6	−	595609.i	1.41451	−	0.816667i
$855$		0			0
$856$	−492874.	+	853682.i	−0.672648	+	1.16506i
$857$	−159679.	−	438714.i	−0.217413	−	0.597338i	0.782259	−	0.622954i	$-0.214067\pi$
$857$	−159679.	−	438714.i	−0.217413	−	0.597338i	−0.999672	+	0.0256160i	$0.991845\pi$
$858$		0			0
$859$	−35253.9	+	29581.5i	−0.0477772	+	0.0400898i	−0.666364	−	0.745627i	$-0.732150\pi$
$859$	−35253.9	+	29581.5i	−0.0477772	+	0.0400898i	0.618586	+	0.785717i	$0.287706\pi$
$860$	−21367.9	+	58707.9i	−0.0288912	+	0.0793779i
$861$		0			0
$862$	−169537.	+	961492.i	−0.228166	+	1.29399i
$863$		−	489117.i		−	0.656737i	−0.944550	−	0.328369i	$-0.893501\pi$
$863$		−	489117.i		−	0.656737i	0.944550	−	0.328369i	$-0.106499\pi$
$864$		0			0
$865$	486460.			0.650153
$866$	−19379.9	−	3417.21i	−0.0258414	−	0.00455654i
$867$		0			0
$868$	−2.12371e6	−	772966.i	−2.81874	−	1.02594i
$869$	26364.3	+	31419.8i	0.0349122	+	0.0416067i
$870$		0			0
$871$	−305504.	+	111194.i	−0.402699	+	0.146571i
$872$	269761.	+	155747.i	0.354769	+	0.204826i
$873$		0			0
$874$	−263152.	−	455793.i	−0.344496	−	0.596685i
$875$	528861.	−	630272.i	0.690757	−	0.823212i
$876$		0			0
$877$	110165.	+	624775.i	0.143233	+	0.812315i	0.968769	+	0.247966i	$0.0797620\pi$
$877$	110165.	+	624775.i	0.143233	+	0.812315i	−0.825536	+	0.564350i	$0.809127\pi$
$878$	−1.59947e6	+	282029.i	−2.07485	+	0.365852i
$879$		0			0
$880$	18248.0	+	15311.9i	0.0235641	+	0.0197726i
$881$	−329154.	+	190037.i	−0.424079	+	0.244842i	−0.696821	−	0.717245i	$-0.745403\pi$
$881$	−329154.	+	190037.i	−0.424079	+	0.244842i	0.272742	+	0.962087i	$0.412070\pi$
$882$		0			0
$883$	669958.	−	1.16040e6i	0.859263	−	1.48829i	−0.0133692	−	0.999911i	$-0.504256\pi$
$883$	669958.	−	1.16040e6i	0.859263	−	1.48829i	0.872633	−	0.488377i	$-0.162411\pi$
$884$	−598261.	−	1.64371e6i	−0.765572	−	2.10339i
$885$		0			0
$886$	1.13242e6	−	950211.i	1.44258	−	1.21047i
$887$	−225118.	+	618507.i	−0.286130	+	0.786135i	0.710469	+	0.703729i	$0.248483\pi$
$887$	−225118.	+	618507.i	−0.286130	+	0.786135i	−0.996599	+	0.0824068i	$0.973739\pi$
$888$		0			0
$889$	−184515.	+	1.04644e6i	−0.233468	+	1.32406i
$890$			809328.i			1.02175i
$891$		0			0
$892$	−1.01846e6			−1.28001
$893$	750350.	+	132307.i	0.940938	+	0.165913i
$894$		0			0
$895$	275184.	+	100159.i	0.343540	+	0.125038i
$896$	−926951.	−	1.10470e6i	−1.15462	−	1.37603i
$897$		0			0
$898$	−1.28483e6	+	467639.i	−1.59328	+	0.579907i
$899$	1.64085e6	+	947347.i	2.03025	+	1.17217i
$900$		0			0
$901$	−218802.	−	378976.i	−0.269527	−	0.466834i
$902$	30891.0	−	36814.4i	0.0379681	−	0.0452486i
$903$		0			0
$904$	−43304.5	−	245592.i	−0.0529902	−	0.300523i
$905$	−27963.4	+	4930.70i	−0.0341423	+	0.00602021i
$906$		0			0
$907$	−458046.	−	384346.i	−0.556794	−	0.467205i	0.320440	−	0.947269i	$-0.396169\pi$
$907$	−458046.	−	384346.i	−0.556794	−	0.467205i	−0.877234	+	0.480063i	$0.840614\pi$
$908$	1.09400e6	−	631624.i	1.32693	−	0.766102i
$909$		0			0
$910$	−511670.	+	886238.i	−0.617884	+	1.07021i
$911$	−223451.	−	613928.i	−0.269244	−	0.739742i	−0.998461	−	0.0554595i	$-0.982338\pi$
$911$	−223451.	−	613928.i	−0.269244	−	0.739742i	0.729217	−	0.684283i	$-0.239885\pi$
$912$		0			0
$913$	−212602.	+	178394.i	−0.255050	+	0.214013i
$914$	163937.	−	450412.i	0.196238	−	0.539160i
$915$		0			0
$916$	242450.	−	1.37500e6i	0.288955	−	1.63875i
$917$		−	602972.i		−	0.717065i
$918$		0			0
$919$	−1.18656e6			−1.40495			−0.702473	−	0.711710i	$-0.747921\pi$
$919$	−1.18656e6			−1.40495			−0.702473	+	0.711710i	$0.747921\pi$
$920$	76270.7	+	13448.6i	0.0901118	+	0.0158891i
$921$		0			0
$922$	−1.07779e6	−	392283.i	−1.26786	−	0.461464i
$923$	145801.	+	173759.i	0.171142	+	0.203959i
$924$		0			0
$925$	597460.	−	217458.i	0.698273	−	0.254151i
$926$	−1.75525e6	−	1.01339e6i	−2.04700	−	1.18183i
$927$		0			0
$928$	818412.	+	1.41753e6i	0.950333	+	1.64603i
$929$	−480817.	+	573015.i	−0.557119	+	0.663949i	−0.968934	−	0.247319i	$-0.920451\pi$
$929$	−480817.	+	573015.i	−0.557119	+	0.663949i	0.411815	+	0.911267i	$0.364895\pi$
$930$		0			0
$931$	−197033.	−	1.11743e6i	−0.227322	−	1.28920i
$932$	−326643.	+	57595.9i	−0.376046	+	0.0663070i
$933$		0			0
$934$	128559.	+	107874.i	0.147370	+	0.123658i
$935$	89627.2	−	51746.3i	0.102522	−	0.0591911i
$936$		0			0
$937$	−340190.	+	589226.i	−0.387474	+	0.671124i	−0.992109	−	0.125378i	$-0.959986\pi$
$937$	−340190.	+	589226.i	−0.387474	+	0.671124i	0.604635	+	0.796502i	$0.293319\pi$
$938$	207956.	+	571355.i	0.236356	+	0.649383i
$939$		0			0
$940$	−266532.	+	223647.i	−0.301643	+	0.253109i
$941$	−90092.8	+	247528.i	−0.101745	+	0.279541i	−0.980112	−	0.198445i	$-0.936411\pi$
$941$	−90092.8	+	247528.i	−0.101745	+	0.279541i	0.878367	+	0.477986i	$0.158633\pi$
$942$		0			0
$943$	−6880.59	+	39021.8i	−0.00773753	+	0.0438817i
$944$			106203.i			0.119177i
$945$		0			0
$946$	−43038.0			−0.0480917
$947$	1.01479e6	+	178935.i	1.13156	+	0.199525i	0.707911	−	0.706302i	$-0.249638\pi$
$947$	1.01479e6	+	178935.i	1.13156	+	0.199525i	0.423649	+	0.905826i	$0.360749\pi$
$948$		0			0
$949$	−713688.	−	259761.i	−0.792457	−	0.288431i
$950$	−1.15854e6	−	1.38069e6i	−1.28370	−	1.52985i
$951$		0			0
$952$	−990602.	+	360550.i	−1.09301	+	0.397824i
$953$	−1.32645e6	−	765824.i	−1.46051	−	0.843225i	−0.461474	−	0.887154i	$-0.652679\pi$
$953$	−1.32645e6	−	765824.i	−1.46051	−	0.843225i	−0.999035	+	0.0439291i	$0.986012\pi$
$954$		0			0
$955$	−60945.7	−	105561.i	−0.0668246	−	0.115744i
$956$	−918052.	+	1.09409e6i	−1.00450	+	1.19712i
$957$		0			0
$958$	−150393.	−	852921.i	−0.163869	−	0.929347i
$959$	−2.11355e6	+	372676.i	−2.29814	+	0.405223i
$960$		0			0
$961$	888412.	+	745466.i	0.961983	+	0.807200i
$962$	−1.53353e6	+	885385.i	−1.65708	+	0.956714i
$963$		0			0
$964$	649751.	−	1.12540e6i	0.699186	−	1.21103i
$965$	33544.7	+	92163.3i	0.0360221	+	0.0989700i
$966$		0			0
$967$	670376.	−	562512.i	0.716912	−	0.601560i	−0.209617	−	0.977783i	$-0.567222\pi$
$967$	670376.	−	562512.i	0.716912	−	0.601560i	0.926529	+	0.376223i	$0.122777\pi$
$968$	−226550.	+	622442.i	−0.241776	+	0.664275i
$969$		0			0
$970$	−63966.1	+	362770.i	−0.0679839	+	0.385556i
$971$		−	836356.i		−	0.887059i	−0.896260	−	0.443530i	$-0.853726\pi$
$971$		−	836356.i		−	0.887059i	0.896260	−	0.443530i	$-0.146274\pi$
$972$		0			0
$973$	6502.28			0.00686816
$974$	2.02802e6	+	357594.i	2.13774	+	0.376940i
$975$		0			0
$976$	−204906.	−	74579.8i	−0.215107	−	0.0782927i
$977$	−160169.	−	190882.i	−0.167799	−	0.199975i	0.675591	−	0.737276i	$-0.263888\pi$
$977$	−160169.	−	190882.i	−0.167799	−	0.199975i	−0.843391	+	0.537301i	$0.819444\pi$
$978$		0			0
$979$	−312265.	+	113655.i	−0.325805	+	0.118583i
$980$	448728.	+	259073.i	0.467231	+	0.269756i
$981$		0			0
$982$	−1.16817e6	−	2.02333e6i	−1.21139	−	2.09818i
$983$	−449001.	+	535098.i	−0.464665	+	0.553766i	−0.946587	−	0.322448i	$-0.895494\pi$
$983$	−449001.	+	535098.i	−0.464665	+	0.553766i	0.481922	+	0.876214i	$0.339939\pi$
$984$		0			0
$985$	20084.2	+	113903.i	0.0207006	+	0.117399i
$986$	2.70091e6	−	476243.i	2.77815	−	0.489863i
$987$		0			0
$988$	2.29196e6	+	1.92318e6i	2.34797	+	1.97018i
$989$	30730.8	−	17742.4i	0.0314182	−	0.0181393i
$990$		0			0
$991$	−684350.	+	1.18533e6i	−0.696836	+	1.20696i	0.272722	+	0.962093i	$0.412076\pi$
$991$	−684350.	+	1.18533e6i	−0.696836	+	1.20696i	−0.969558	+	0.244863i	$0.921257\pi$
$992$	615543.	+	1.69119e6i	0.625511	+	1.71858i
$993$		0			0
$994$	324965.	−	272678.i	0.328900	−	0.275980i
$995$	−99875.7	+	274406.i	−0.100882	+	0.277171i
$996$		0			0
$997$	−4282.13	+	24285.2i	−0.00430794	+	0.0244315i	−0.986886	−	0.161419i	$-0.948393\pi$
$997$	−4282.13	+	24285.2i	−0.00430794	+	0.0244315i	0.982578	+	0.185851i	$0.0595040\pi$
$998$		−	874870.i		−	0.878380i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.5.f.a.8.10		66
3.2	odd	2		27.5.f.a.2.2	✓	66
27.13	even	9		27.5.f.a.14.2	yes	66
27.14	odd	18	inner	81.5.f.a.71.10		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.f.a.2.2	✓	66	3.2	odd	2
27.5.f.a.14.2	yes	66	27.13	even	9
81.5.f.a.8.10		66	1.1	even	1	trivial
81.5.f.a.71.10		66	27.14	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)

\(f(q)\)	\(=\)	\(q+(6.19782 + 1.09284i) q^{2} +(22.1836 + 8.07418i) q^{4} +(7.06026 + 8.41408i) q^{5} +(62.3269 - 22.6852i) q^{7} +(41.4621 + 23.9381i) q^{8} +(34.5629 + 59.8648i) q^{10} +(-18.2440 + 21.7424i) q^{11} +(38.7578 + 219.806i) q^{13} +(411.083 - 72.4850i) q^{14} +(-58.5343 - 49.1161i) q^{16} +(-287.497 + 165.987i) q^{17} +(283.914 - 491.754i) q^{19} +(88.6853 + 243.661i) q^{20} +(-136.834 + 114.818i) q^{22} +(50.3714 - 138.394i) q^{23} +(87.5805 - 496.694i) q^{25} +1404.68i q^{26} +1565.80 q^{28} +(-1292.76 - 227.949i) q^{29} +(-1356.31 - 493.655i) q^{31} +(-801.497 - 955.187i) q^{32} +(-1963.25 + 714.566i) q^{34} +(630.919 + 364.261i) q^{35} +(630.312 + 1091.73i) q^{37} +(2297.06 - 2737.53i) q^{38} +(91.3153 + 517.875i) q^{40} +(-264.956 + 46.7189i) q^{41} +(184.572 + 154.874i) q^{43} +(-580.271 + 335.020i) q^{44} +(463.437 - 802.696i) q^{46} +(458.931 + 1260.90i) q^{47} +(1530.76 - 1284.46i) q^{49} +(1085.62 - 2982.71i) q^{50} +(-914.968 + 5189.04i) q^{52} +1318.19i q^{53} -311.750 q^{55} +(3127.25 + 551.418i) q^{56} +(-7763.20 - 2825.58i) q^{58} +(-893.408 - 1064.72i) q^{59} +(2681.63 - 976.034i) q^{61} +(-7866.66 - 4541.82i) q^{62} +(-3312.38 - 5737.21i) q^{64} +(-1575.83 + 1878.00i) q^{65} +(252.937 + 1434.48i) q^{67} +(-7717.94 + 1360.88i) q^{68} +(3512.24 + 2947.12i) q^{70} +(880.106 - 508.129i) q^{71} +(-1701.39 + 2946.89i) q^{73} +(2713.47 + 7455.20i) q^{74} +(10268.8 - 8616.51i) q^{76} +(-643.865 + 1769.01i) q^{77} +(250.938 - 1423.14i) q^{79} -839.284i q^{80} -1693.21 q^{82} +(9629.68 + 1697.97i) q^{83} +(-3426.43 - 1247.12i) q^{85} +(974.689 + 1161.59i) q^{86} +(-1276.91 + 464.756i) q^{88} +(10139.4 + 5854.01i) q^{89} +(7402.00 + 12820.6i) q^{91} +(2234.84 - 2663.38i) q^{92} +(1466.40 + 8316.39i) q^{94} +(6142.16 - 1083.03i) q^{95} +(4082.19 + 3425.36i) q^{97} +(10891.1 - 6287.97i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} - 1137 q^{14} - 54 q^{16} + 9 q^{17} - 3 q^{19} + 2487 q^{20} + 1002 q^{22} + 2724 q^{23} + 435 q^{25} - 12 q^{28}+ \cdots + 259938 q^{98}+O(q^{100}) \) 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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