LMFDB - Embedded newform 81.5.f.a.8.4

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			8.4
Character	$\chi$	$=$	81.8
Dual form			81.5.f.a.71.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.89555 - 0.510564i) q^{2} +(-6.91152 - 2.51559i) q^{4} +(-31.8237 - 37.9260i) q^{5} +(28.2667 - 10.2882i) q^{7} +(59.4692 + 34.3346i) q^{8} +(72.7837 + 126.065i) q^{10} +(-75.7716 + 90.3011i) q^{11} +(3.56465 + 20.2161i) q^{13} +(-87.1005 + 15.3582i) q^{14} +(-64.5172 - 54.1364i) q^{16} +(-203.984 + 117.770i) q^{17} +(47.7809 - 82.7590i) q^{19} +(124.544 + 342.182i) q^{20} +(265.505 - 222.785i) q^{22} +(-85.2078 + 234.107i) q^{23} +(-317.105 + 1798.39i) q^{25} -60.3569i q^{26} -221.247 q^{28} +(1150.78 + 202.914i) q^{29} +(562.326 + 204.670i) q^{31} +(-547.062 - 651.963i) q^{32} +(650.776 - 236.863i) q^{34} +(-1289.74 - 744.633i) q^{35} +(-123.627 - 214.128i) q^{37} +(-180.606 + 215.238i) q^{38} +(-590.358 - 3348.09i) q^{40} +(508.880 - 89.7293i) q^{41} +(-1990.16 - 1669.95i) q^{43} +(750.857 - 433.508i) q^{44} +(366.250 - 634.364i) q^{46} +(176.156 + 483.984i) q^{47} +(-1146.12 + 961.705i) q^{49} +(1836.39 - 5045.44i) q^{50} +(26.2183 - 148.692i) q^{52} +3241.10i q^{53} +5836.10 q^{55} +(2034.24 + 358.691i) q^{56} +(-3228.55 - 1175.09i) q^{58} +(-1210.50 - 1442.62i) q^{59} +(-4396.97 + 1600.37i) q^{61} +(-1523.75 - 879.736i) q^{62} +(1924.95 + 3334.11i) q^{64} +(653.278 - 778.546i) q^{65} +(-473.625 - 2686.06i) q^{67} +(1706.10 - 300.832i) q^{68} +(3354.34 + 2814.62i) q^{70} +(-5060.73 + 2921.81i) q^{71} +(-1626.01 + 2816.33i) q^{73} +(248.643 + 683.140i) q^{74} +(-538.427 + 451.794i) q^{76} +(-1212.77 + 3332.07i) q^{77} +(322.322 - 1827.98i) q^{79} +4169.70i q^{80} -1519.30 q^{82} +(1228.73 + 216.659i) q^{83} +(10958.1 + 3988.42i) q^{85} +(4910.01 + 5851.52i) q^{86} +(-7606.53 + 2768.55i) q^{88} +(-6163.24 - 3558.35i) q^{89} +(308.749 + 534.769i) q^{91} +(1177.83 - 1403.68i) q^{92} +(-262.964 - 1491.34i) q^{94} +(-4659.29 + 821.558i) q^{95} +(7251.91 + 6085.08i) q^{97} +(3809.65 - 2199.50i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.89555	−	0.510564i	−0.723889	−	0.127641i	−0.200449	−	0.979704i	$-0.564240\pi$
$2$	−2.89555	−	0.510564i	−0.723889	−	0.127641i	−0.523439	+	0.852063i	$0.675351\pi$
$3$		0			0
$3$		0			0
$4$	−6.91152	−	2.51559i	−0.431970	−	0.157224i
$5$	−31.8237	−	37.9260i	−1.27295	−	1.51704i	−0.743573	−	0.668655i	$-0.766870\pi$
$5$	−31.8237	−	37.9260i	−1.27295	−	1.51704i	−0.529376	−	0.848387i	$-0.677574\pi$
$6$		0			0
$7$	28.2667	−	10.2882i	0.576871	−	0.209964i	−0.0370743	−	0.999313i	$-0.511804\pi$
$7$	28.2667	−	10.2882i	0.576871	−	0.209964i	0.613945	+	0.789349i	$0.289582\pi$
$8$	59.4692	+	34.3346i	0.929207	+	0.536478i
$9$		0			0
$10$	72.7837	+	126.065i	0.727837	+	1.26065i
$11$	−75.7716	+	90.3011i	−0.626211	+	0.746290i	−0.982125	−	0.188229i	$-0.939725\pi$
$11$	−75.7716	+	90.3011i	−0.626211	+	0.746290i	0.355914	+	0.934519i	$0.384170\pi$
$12$		0			0
$13$	3.56465	+	20.2161i	0.0210926	+	0.119622i	0.993536	−	0.113517i	$-0.0362115\pi$
$13$	3.56465	+	20.2161i	0.0210926	+	0.119622i	−0.972443	+	0.233139i	$0.925100\pi$
$14$	−87.1005	+	15.3582i	−0.444390	+	0.0783580i
$15$		0			0
$16$	−64.5172	−	54.1364i	−0.252020	−	0.211470i
$17$	−203.984	+	117.770i	−0.705827	+	0.407509i	−0.809514	−	0.587101i	$-0.800269\pi$
$17$	−203.984	+	117.770i	−0.705827	+	0.407509i	0.103687	+	0.994610i	$0.466936\pi$
$18$		0			0
$19$	47.7809	−	82.7590i	0.132357	−	0.229249i	−0.792228	−	0.610226i	$-0.791079\pi$
$19$	47.7809	−	82.7590i	0.132357	−	0.229249i	0.924585	+	0.380976i	$0.124412\pi$
$20$	124.544	+	342.182i	0.311360	+	0.855455i
$21$		0			0
$22$	265.505	−	222.785i	0.548565	−	0.460300i
$23$	−85.2078	+	234.107i	−0.161073	+	0.442545i	−0.993806	−	0.111130i	$-0.964553\pi$
$23$	−85.2078	+	234.107i	−0.161073	+	0.442545i	0.832732	+	0.553676i	$0.186775\pi$
$24$		0			0
$25$	−317.105	+	1798.39i	−0.507368	+	2.87743i
$26$		−	60.3569i		−	0.0892854i
$27$		0			0
$28$	−221.247			−0.282202
$29$	1150.78	+	202.914i	1.36835	+	0.241277i	0.809074	−	0.587707i	$-0.199969\pi$
$29$	1150.78	+	202.914i	1.36835	+	0.241277i	0.559274	+	0.828983i	$0.311080\pi$
$30$		0			0
$31$	562.326	+	204.670i	0.585147	+	0.212976i	0.617593	−	0.786497i	$-0.288108\pi$
$31$	562.326	+	204.670i	0.585147	+	0.212976i	−0.0324468	+	0.999473i	$0.510330\pi$
$32$	−547.062	−	651.963i	−0.534240	−	0.636683i
$33$		0			0
$34$	650.776	−	236.863i	0.562955	−	0.204899i
$35$	−1289.74	−	744.633i	−1.05285	−	0.607864i
$36$		0			0
$37$	−123.627	−	214.128i	−0.0903047	−	0.156412i	0.817335	−	0.576163i	$-0.195451\pi$
$37$	−123.627	−	214.128i	−0.0903047	−	0.156412i	−0.907639	+	0.419751i	$0.862117\pi$
$38$	−180.606	+	215.238i	−0.125073	+	0.149057i
$39$		0			0
$40$	−590.358	−	3348.09i	−0.368974	−	2.09256i
$41$	508.880	−	89.7293i	0.302725	−	0.0533785i	−0.0202226	−	0.999796i	$-0.506438\pi$
$41$	508.880	−	89.7293i	0.302725	−	0.0533785i	0.322947	+	0.946417i	$0.395326\pi$
$42$		0			0
$43$	−1990.16	−	1669.95i	−1.07635	−	0.903161i	−0.0807334	−	0.996736i	$-0.525726\pi$
$43$	−1990.16	−	1669.95i	−1.07635	−	0.903161i	−0.995612	+	0.0935745i	$0.970171\pi$
$44$	750.857	−	433.508i	0.387840	−	0.223919i
$45$		0			0
$46$	366.250	−	634.364i	0.173086	−	0.299794i
$47$	176.156	+	483.984i	0.0797446	+	0.219097i	0.973158	−	0.230140i	$-0.0739183\pi$
$47$	176.156	+	483.984i	0.0797446	+	0.219097i	−0.893413	+	0.449236i	$0.851696\pi$
$48$		0			0
$49$	−1146.12	+	961.705i	−0.477349	+	0.400544i
$50$	1836.39	−	5045.44i	0.734556	−	2.01818i
$51$		0			0
$52$	26.2183	−	148.692i	0.00969613	−	0.0549895i
$53$			3241.10i			1.15383i	0.816806	+	0.576913i	$0.195743\pi$
$53$			3241.10i			1.15383i	−0.816806	+	0.576913i	$0.804257\pi$
$54$		0			0
$55$	5836.10			1.92929
$56$	2034.24	+	358.691i	0.648673	+	0.114379i
$57$		0			0
$58$	−3228.55	−	1175.09i	−0.959734	−	0.349315i
$59$	−1210.50	−	1442.62i	−0.347745	−	0.414427i	0.563614	−	0.826038i	$-0.309411\pi$
$59$	−1210.50	−	1442.62i	−0.347745	−	0.414427i	−0.911359	+	0.411611i	$0.864966\pi$
$60$		0			0
$61$	−4396.97	+	1600.37i	−1.18166	+	0.430090i	−0.856789	−	0.515667i	$-0.827544\pi$
$61$	−4396.97	+	1600.37i	−1.18166	+	0.430090i	−0.324874	+	0.945757i	$0.605322\pi$
$62$	−1523.75	−	879.736i	−0.396397	−	0.228860i
$63$		0			0
$64$	1924.95	+	3334.11i	0.469958	+	0.813991i
$65$	653.278	−	778.546i	0.154622	−	0.184271i
$66$		0			0
$67$	−473.625	−	2686.06i	−0.105508	−	0.598365i	−0.991016	−	0.133742i	$-0.957301\pi$
$67$	−473.625	−	2686.06i	−0.105508	−	0.598365i	0.885508	−	0.464624i	$-0.153810\pi$
$68$	1706.10	−	300.832i	0.368967	−	0.0650588i
$69$		0			0
$70$	3354.34	+	2814.62i	0.684559	+	0.574413i
$71$	−5060.73	+	2921.81i	−1.00391	+	0.579610i	−0.909404	−	0.415914i	$-0.863462\pi$
$71$	−5060.73	+	2921.81i	−1.00391	+	0.579610i	−0.0945101	+	0.995524i	$0.530128\pi$
$72$		0			0
$73$	−1626.01	+	2816.33i	−0.305124	+	0.528491i	−0.977289	−	0.211911i	$-0.932031\pi$
$73$	−1626.01	+	2816.33i	−0.305124	+	0.528491i	0.672165	+	0.740402i	$0.265365\pi$
$74$	248.643	+	683.140i	0.0454059	+	0.124752i
$75$		0			0
$76$	−538.427	+	451.794i	−0.0932179	+	0.0782191i
$77$	−1212.77	+	3332.07i	−0.204549	+	0.561995i
$78$		0			0
$79$	322.322	−	1827.98i	0.0516459	−	0.292899i	−0.948035	−	0.318167i	$-0.896933\pi$
$79$	322.322	−	1827.98i	0.0516459	−	0.292899i	0.999681	+	0.0252681i	$0.00804395\pi$
$80$			4169.70i			0.651516i
$81$		0			0
$82$	−1519.30			−0.225952
$83$	1228.73	+	216.659i	0.178362	+	0.0314500i	0.262116	−	0.965037i	$-0.415580\pi$
$83$	1228.73	+	216.659i	0.178362	+	0.0314500i	−0.0837539	+	0.996486i	$0.526691\pi$
$84$		0			0
$85$	10958.1	+	3988.42i	1.51669	+	0.552030i
$86$	4910.01	+	5851.52i	0.663874	+	0.791174i
$87$		0			0
$88$	−7606.53	+	2768.55i	−0.982248	+	0.357509i
$89$	−6163.24	−	3558.35i	−0.778089	−	0.449230i	0.0576637	−	0.998336i	$-0.481635\pi$
$89$	−6163.24	−	3558.35i	−0.778089	−	0.449230i	−0.835753	+	0.549106i	$0.814968\pi$
$90$		0			0
$91$	308.749	+	534.769i	0.0372840	+	0.0645779i
$92$	1177.83	−	1403.68i	0.139158	−	0.165842i
$93$		0			0
$94$	−262.964	−	1491.34i	−0.0297605	−	0.168780i
$95$	−4659.29	+	821.558i	−0.516265	+	0.0910314i
$96$		0			0
$97$	7251.91	+	6085.08i	0.770742	+	0.646730i	0.940899	−	0.338687i	$-0.109983\pi$
$97$	7251.91	+	6085.08i	0.770742	+	0.646730i	−0.170157	+	0.985417i	$0.554427\pi$
$98$	3809.65	−	2199.50i	0.396673	−	0.229020i
$99$		0			0
$100$	6715.69	−	11631.9i	0.671569	−	1.16319i
$101$	732.417	+	2012.30i	0.0717986	+	0.197265i	0.970401	−	0.241498i	$-0.0776388\pi$
$101$	732.417	+	2012.30i	0.0717986	+	0.197265i	−0.898603	+	0.438763i	$0.855417\pi$
$102$		0			0
$103$	−8587.90	+	7206.10i	−0.809492	+	0.679244i	−0.950486	−	0.310766i	$-0.899414\pi$
$103$	−8587.90	+	7206.10i	−0.809492	+	0.679244i	0.140995	+	0.990010i	$0.454970\pi$
$104$	−482.126	+	1324.63i	−0.0445752	+	0.122469i
$105$		0			0
$106$	1654.79	−	9384.78i	0.147276	−	0.835242i
$107$			8544.65i			0.746323i	0.927766	+	0.373162i	$0.121726\pi$
$107$			8544.65i			0.746323i	−0.927766	+	0.373162i	$0.878274\pi$
$108$		0			0
$109$	−7006.31			−0.589707			−0.294853	−	0.955542i	$-0.595271\pi$
$109$	−7006.31			−0.589707			−0.294853	+	0.955542i	$0.595271\pi$
$110$	−16898.7	−	2979.70i	−1.39659	−	0.246256i
$111$		0			0
$112$	−2380.65	−	866.487i	−0.189784	−	0.0690759i
$113$	−9643.22	−	11492.3i	−0.755206	−	0.900019i	0.242329	−	0.970194i	$-0.422089\pi$
$113$	−9643.22	−	11492.3i	−0.755206	−	0.900019i	−0.997535	+	0.0701748i	$0.977644\pi$
$114$		0			0
$115$	11590.4	−	4218.55i	0.876398	−	0.318983i
$116$	−7443.20	−	4297.33i	−0.553151	−	0.319362i
$117$		0			0
$118$	2768.52	+	4795.22i	0.198831	+	0.344385i
$119$	−4554.30	+	5427.61i	−0.321609	+	0.383278i
$120$		0			0
$121$	129.435	+	734.062i	0.00884058	+	0.0501374i
$122$	13548.7	−	2389.01i	0.910289	−	0.160509i
$123$		0			0
$124$	−3371.66	−	2829.16i	−0.219281	−	0.183999i
$125$	51499.9	−	29733.5i	3.29599	−	1.90294i
$126$		0			0
$127$	−11799.6	+	20437.4i	−0.731574	+	1.26712i	0.224636	+	0.974443i	$0.427881\pi$
$127$	−11799.6	+	20437.4i	−0.731574	+	1.26712i	−0.956210	+	0.292681i	$0.905453\pi$
$128$	785.853	+	2159.11i	0.0479647	+	0.131782i
$129$		0			0
$130$	−2289.10	+	1920.78i	−0.135450	+	0.113656i
$131$	−3886.76	+	10678.8i	−0.226488	+	0.622270i	−0.999933	−	0.0115932i	$-0.996310\pi$
$131$	−3886.76	+	10678.8i	−0.226488	+	0.622270i	0.773445	+	0.633863i	$0.218532\pi$
$132$		0			0
$133$	499.165	−	2830.90i	0.0282189	−	0.160037i
$134$			8019.46i			0.446617i
$135$		0			0
$136$	−16174.4			−0.874479
$137$	8987.88	+	1584.81i	0.478868	+	0.0844374i	0.407872	−	0.913039i	$-0.366271\pi$
$137$	8987.88	+	1584.81i	0.478868	+	0.0844374i	0.0709965	+	0.997477i	$0.477382\pi$
$138$		0			0
$139$	12824.5	+	4667.73i	0.663758	+	0.241588i	0.651858	−	0.758341i	$-0.273990\pi$
$139$	12824.5	+	4667.73i	0.663758	+	0.241588i	0.0119002	+	0.999929i	$0.496212\pi$
$140$	7040.90	+	8391.01i	0.359229	+	0.428113i
$141$		0			0
$142$	16145.4	−	5876.44i	0.800704	−	0.291432i
$143$	−2095.64	−	1209.92i	−0.102481	−	0.0591676i
$144$		0			0
$145$	−28926.4	−	50102.0i	−1.37581	−	2.38297i
$146$	6146.11	−	7324.65i	0.288333	−	0.343622i
$147$		0			0
$148$	315.793	+	1790.95i	0.0144171	+	0.0817635i
$149$	−34884.9	+	6151.14i	−1.57132	+	0.277066i	−0.890361	−	0.455256i	$-0.849548\pi$
$149$	−34884.9	+	6151.14i	−1.57132	+	0.277066i	−0.680958	+	0.732322i	$0.738437\pi$
$150$		0			0
$151$	−27267.1	−	22879.8i	−1.19587	−	1.00346i	−0.999738	−	0.0228781i	$-0.992717\pi$
$151$	−27267.1	−	22879.8i	−1.19587	−	1.00346i	−0.196133	−	0.980577i	$-0.562839\pi$
$152$	5682.99	−	3281.08i	0.245974	−	0.142013i
$153$		0			0
$154$	5212.88	−	9028.98i	0.219805	−	0.380713i
$155$	−10133.0	−	27840.2i	−0.421769	−	1.15880i
$156$		0			0
$157$	26009.7	−	21824.7i	1.05520	−	0.885419i	0.0615708	−	0.998103i	$-0.480389\pi$
$157$	26009.7	−	21824.7i	1.05520	−	0.885419i	0.993631	+	0.112683i	$0.0359446\pi$
$158$	−1866.60	+	5128.45i	−0.0747718	+	0.205434i
$159$		0			0
$160$	−7316.83	+	41495.8i	−0.285814	+	1.62093i
$161$			7494.05i			0.289111i
$162$		0			0
$163$	−4748.87			−0.178737			−0.0893686	−	0.995999i	$-0.528485\pi$
$163$	−4748.87			−0.178737			−0.0893686	+	0.995999i	$0.528485\pi$
$164$	−3742.86	−	659.967i	−0.139160	−	0.0245377i
$165$		0			0
$166$	−3447.25	−	1254.69i	−0.125100	−	0.0455325i
$167$	23833.0	+	28403.1i	0.854567	+	1.01843i	0.999579	+	0.0290038i	$0.00923349\pi$
$167$	23833.0	+	28403.1i	0.854567	+	1.01843i	−0.145012	+	0.989430i	$0.546322\pi$
$168$		0			0
$169$	26442.6	−	9624.31i	0.925828	−	0.336974i
$170$	−29693.4	−	17143.5i	−1.02745	−	0.593201i
$171$		0			0
$172$	9554.16	+	16548.3i	0.322950	+	0.559366i
$173$	20128.4	−	23988.1i	0.672539	−	0.801501i	−0.316588	−	0.948563i	$-0.602537\pi$
$173$	20128.4	−	23988.1i	0.672539	−	0.801501i	0.989127	+	0.147062i	$0.0469817\pi$
$174$		0			0
$175$	9538.76	+	54097.0i	0.311470	+	1.76643i
$176$	9777.14	−	1723.97i	0.315636	−	0.0556552i
$177$		0			0
$178$	16029.2	+	13450.1i	0.505909	+	0.424508i
$179$	−3361.98	+	1941.04i	−0.104927	+	0.0605798i	−0.551545	−	0.834145i	$-0.685962\pi$
$179$	−3361.98	+	1941.04i	−0.104927	+	0.0605798i	0.446618	+	0.894725i	$0.352628\pi$
$180$		0			0
$181$	−4830.64	+	8366.92i	−0.147451	+	0.255393i	−0.930285	−	0.366838i	$-0.880440\pi$
$181$	−4830.64	+	8366.92i	−0.147451	+	0.255393i	0.782834	+	0.622231i	$0.213774\pi$
$182$	−620.966	−	1706.09i	−0.0187467	−	0.0515062i
$183$		0			0
$184$	−13105.2	+	10996.6i	−0.387086	+	0.324804i
$185$	−4186.77	+	11503.1i	−0.122331	+	0.336101i
$186$		0			0
$187$	4821.42	−	27343.6i	0.137877	−	0.781939i
$188$		−	3788.20i		−	0.107181i
$189$		0			0
$190$	13910.7			0.385338
$191$	−29595.2	−	5218.44i	−0.811251	−	0.143045i	−0.247391	−	0.968916i	$-0.579573\pi$
$191$	−29595.2	−	5218.44i	−0.811251	−	0.143045i	−0.563860	+	0.825870i	$0.690684\pi$
$192$		0			0
$193$	−21435.3	−	7801.80i	−0.575459	−	0.209450i	0.0378629	−	0.999283i	$-0.487945\pi$
$193$	−21435.3	−	7801.80i	−0.575459	−	0.209450i	−0.613322	+	0.789833i	$0.710167\pi$
$194$	−17891.5	−	21322.2i	−0.475382	−	0.566539i
$195$		0			0
$196$	10340.7	−	3763.69i	0.269176	−	0.0979720i
$197$	8182.86	+	4724.37i	0.210849	+	0.121734i	0.601706	−	0.798718i	$-0.294488\pi$
$197$	8182.86	+	4724.37i	0.210849	+	0.121734i	−0.390857	+	0.920452i	$0.627821\pi$
$198$		0			0
$199$	24364.4	+	42200.4i	0.615247	+	1.06564i	0.990341	+	0.138652i	$0.0442770\pi$
$199$	24364.4	+	42200.4i	0.615247	+	1.06564i	−0.375094	+	0.926987i	$0.622390\pi$
$200$	−80605.0	+	96061.3i	−2.01513	+	2.40153i
$201$		0			0
$202$	−1093.35	−	6200.67i	−0.0267951	−	0.151962i
$203$	34616.4	−	6103.80i	0.840019	−	0.148118i
$204$		0			0
$205$	−19597.5	−	16444.3i	−0.466330	−	0.391298i
$206$	28545.9	−	16481.0i	0.672681	−	0.388373i
$207$		0			0
$208$	864.448	−	1497.27i	0.0199808	−	0.0346077i
$209$	3852.79	+	10585.4i	0.0882028	+	0.242335i
$210$		0			0
$211$	−20693.8	+	17364.1i	−0.464809	+	0.390021i	−0.844897	−	0.534929i	$-0.820338\pi$
$211$	−20693.8	+	17364.1i	−0.464809	+	0.390021i	0.380088	+	0.924950i	$0.375894\pi$
$212$	8153.27	−	22400.9i	0.181410	−	0.498419i
$213$		0			0
$214$	4362.60	−	24741.5i	0.0952615	−	0.540255i
$215$			128623.i			2.78254i
$216$		0			0
$217$	18000.8			0.382271
$218$	20287.1	+	3577.17i	0.426882	+	0.0752708i
$219$		0			0
$220$	−40336.3	−	14681.2i	−0.833395	−	0.303331i
$221$	−3107.99	−	3703.96i	−0.0636349	−	0.0758371i
$222$		0			0
$223$	−34127.2	+	12421.3i	−0.686263	+	0.249779i	−0.661534	−	0.749915i	$-0.730094\pi$
$223$	−34127.2	+	12421.3i	−0.686263	+	0.249779i	−0.0247285	+	0.999694i	$0.507872\pi$
$224$	−22171.2	−	12800.5i	−0.441868	−	0.255113i
$225$		0			0
$226$	22054.9	+	38200.2i	0.431806	+	0.747909i
$227$	52677.6	−	62778.7i	1.02229	−	1.21832i	0.0466574	−	0.998911i	$-0.485143\pi$
$227$	52677.6	−	62778.7i	1.02229	−	1.21832i	0.975633	−	0.219408i	$-0.0704125\pi$
$228$		0			0
$229$	2581.23	+	14638.9i	0.0492217	+	0.279150i	0.999478	−	0.0323204i	$-0.0102897\pi$
$229$	2581.23	+	14638.9i	0.0492217	+	0.279150i	−0.950256	+	0.311470i	$0.899179\pi$
$230$	−35714.4	+	6297.41i	−0.675130	+	0.119044i
$231$		0			0
$232$	61469.1	+	51578.7i	1.14204	+	0.958284i
$233$	−19670.0	+	11356.5i	−0.362320	+	0.209185i	−0.670098	−	0.742273i	$-0.733748\pi$
$233$	−19670.0	+	11356.5i	−0.362320	+	0.209185i	0.307778	+	0.951458i	$0.400415\pi$
$234$		0			0
$235$	12749.7	−	22083.1i	0.230868	−	0.399875i
$236$	4737.37	+	13015.8i	0.0850577	+	0.233694i
$237$		0			0
$238$	15958.4	−	13390.7i	0.281731	−	0.236400i
$239$	15097.9	−	41481.1i	0.264314	−	0.726196i	−0.734551	−	0.678554i	$-0.762607\pi$
$239$	15097.9	−	41481.1i	0.264314	−	0.726196i	0.998864	−	0.0476424i	$-0.0151708\pi$
$240$		0			0
$241$	4090.96	−	23201.0i	0.0704354	−	0.399459i	−0.929124	−	0.369769i	$-0.879437\pi$
$241$	4090.96	−	23201.0i	0.0704354	−	0.399459i	0.999559	−	0.0296900i	$-0.00945200\pi$
$242$		−	2191.60i		−	0.0374223i
$243$		0			0
$244$	34415.6			0.578064
$245$	72947.3	+	12862.6i	1.21528	+	0.214287i
$246$		0			0
$247$	1843.39	+	670.939i	0.0302151	+	0.0109974i
$248$	26413.8	+	31478.8i	0.429465	+	0.511817i
$249$		0			0
$250$	−164302.	+	59800.9i	−2.62882	+	0.956814i
$251$	−94159.5	−	54363.0i	−1.49457	−	0.862891i	−0.494591	−	0.869126i	$-0.664682\pi$
$251$	−94159.5	−	54363.0i	−1.49457	−	0.862891i	−0.999981	+	0.00623462i	$0.998015\pi$
$252$		0			0
$253$	−14683.7	−	25433.0i	−0.229401	−	0.397334i
$254$	44600.9	−	53153.3i	0.691315	−	0.823878i
$255$		0			0
$256$	−11869.6	−	67315.6i	−0.181115	−	1.02715i
$257$	51865.1	−	9145.22i	0.785252	−	0.138461i	0.233375	−	0.972387i	$-0.425023\pi$
$257$	51865.1	−	9145.22i	0.785252	−	0.138461i	0.551877	+	0.833926i	$0.313912\pi$
$258$		0			0
$259$	−5697.53	−	4780.80i	−0.0849351	−	0.0712690i
$260$	−6473.65	+	3737.56i	−0.0957640	+	0.0552894i
$261$		0			0
$262$	16706.5	−	28936.5i	0.243379	−	0.421545i
$263$	−14888.8	−	40906.7i	−0.215253	−	0.591402i	0.784328	−	0.620346i	$-0.213008\pi$
$263$	−14888.8	−	40906.7i	−0.215253	−	0.591402i	−0.999581	+	0.0289439i	$0.990786\pi$
$264$		0			0
$265$	122922.	−	103144.i	1.75040	−	1.46876i
$266$	−2890.72	+	7942.18i	−0.0408547	+	0.112247i
$267$		0			0
$268$	−3483.56	+	19756.2i	−0.0485013	+	0.275064i
$269$		−	80700.6i		−	1.11525i	−0.830093	−	0.557625i	$-0.811713\pi$
$269$		−	80700.6i		−	1.11525i	0.830093	−	0.557625i	$-0.188287\pi$
$270$		0			0
$271$	−52631.4			−0.716648			−0.358324	−	0.933597i	$-0.616652\pi$
$271$	−52631.4			−0.716648			−0.358324	+	0.933597i	$0.616652\pi$
$272$	19536.1	+	3444.75i	0.264059	+	0.0465607i
$273$		0			0
$274$	−25215.8	−	9177.78i	−0.335870	−	0.122247i
$275$	−138369.	−	164902.i	−1.82967	−	2.18052i
$276$		0			0
$277$	26404.1	−	9610.32i	0.344122	−	0.125250i	−0.164177	−	0.986431i	$-0.552497\pi$
$277$	26404.1	−	9610.32i	0.344122	−	0.125250i	0.508299	+	0.861181i	$0.330275\pi$
$278$	−34750.8	−	20063.4i	−0.449651	−	0.259606i
$279$		0			0
$280$	−51133.4	−	88565.6i	−0.652211	−	1.12966i
$281$	−24684.5	+	29417.8i	−0.312616	+	0.372562i	−0.899358	−	0.437212i	$-0.855966\pi$
$281$	−24684.5	+	29417.8i	−0.312616	+	0.372562i	0.586742	+	0.809774i	$0.300410\pi$
$282$		0			0
$283$	−15332.4	−	86954.2i	−0.191442	−	1.08572i	−0.917396	−	0.397976i	$-0.869713\pi$
$283$	−15332.4	−	86954.2i	−0.191442	−	1.08572i	0.725954	−	0.687743i	$-0.241398\pi$
$284$	42327.4	−	7463.47i	0.524790	−	0.0925346i
$285$		0			0
$286$	5450.30	+	4573.34i	0.0666328	+	0.0559115i
$287$	13461.2	−	7771.82i	0.163425	−	0.0943537i
$288$		0			0
$289$	−14020.9	+	24284.8i	−0.167872	+	0.290763i
$290$	58177.7	+	159842.i	0.691768	+	1.90062i
$291$		0			0
$292$	18322.9	−	15374.7i	0.214896	−	0.180319i
$293$	−5860.54	+	16101.7i	−0.0682656	+	0.187558i	−0.969134	−	0.246534i	$-0.920708\pi$
$293$	−5860.54	+	16101.7i	−0.0682656	+	0.187558i	0.900869	+	0.434092i	$0.142931\pi$
$294$		0			0
$295$	−16190.2	+	91819.1i	−0.186041	+	1.05509i
$296$		−	16978.7i		−	0.193786i
$297$		0			0
$298$	104152.			1.17282
$299$	−5036.47	−	888.065i	−0.0563357	−	0.00993351i
$300$		0			0
$301$	−73436.1	−	26728.5i	−0.810544	−	0.295014i
$302$	67271.7	+	80171.3i	0.737596	+	0.879032i
$303$		0			0
$304$	−7562.97	+	2752.69i	−0.0818361	+	0.0297859i
$305$	200623.	+	115830.i	2.15666	+	1.24515i
$306$		0			0
$307$	70636.7	+	122346.i	0.749469	+	1.29812i	0.948077	+	0.318040i	$0.103025\pi$
$307$	70636.7	+	122346.i	0.749469	+	1.29812i	−0.198608	+	0.980079i	$0.563642\pi$
$308$	16764.2	−	19978.8i	0.176718	−	0.210605i
$309$		0			0
$310$	15126.4	+	85786.2i	0.157403	+	0.892677i
$311$	−108917.	+	19205.1i	−1.12610	+	0.198562i	−0.705517	−	0.708693i	$-0.749285\pi$
$311$	−108917.	+	19205.1i	−1.12610	+	0.198562i	−0.420582	+	0.907254i	$0.638174\pi$
$312$		0			0
$313$	−5442.80	−	4567.05i	−0.0555563	−	0.0466173i	0.614587	−	0.788849i	$-0.289323\pi$
$313$	−5442.80	−	4567.05i	−0.0555563	−	0.0466173i	−0.670143	+	0.742232i	$0.733767\pi$
$314$	−86455.3	+	49915.0i	−0.876864	+	0.506258i
$315$		0			0
$316$	−6826.18	+	11823.3i	−0.0683603	+	0.118403i
$317$	23370.3	+	64209.4i	0.232566	+	0.638969i	0.999998	−	0.00216124i	$-0.000687945\pi$
$317$	23370.3	+	64209.4i	0.232566	+	0.638969i	−0.767432	+	0.641131i	$0.778466\pi$
$318$		0			0
$319$	−105520.	+	88541.6i	−1.03694	+	0.870094i
$320$	65190.5	−	179109.i	0.636626	−	1.74912i
$321$		0			0
$322$	3826.20	−	21699.4i	0.0369025	−	0.209284i
$323$			22508.7i			0.215747i
$324$		0			0
$325$	−37486.9			−0.354906
$326$	13750.6	+	2424.60i	0.129386	+	0.0228142i
$327$		0			0
$328$	33343.5	+	12136.0i	0.309930	+	0.112805i
$329$	9958.68	+	11868.3i	0.0920047	+	0.109647i
$330$		0			0
$331$	159267.	−	57968.4i	1.45368	−	0.529097i	0.510065	−	0.860136i	$-0.329621\pi$
$331$	159267.	−	57968.4i	1.45368	−	0.529097i	0.943617	+	0.331039i	$0.107399\pi$
$332$	−7947.39	−	4588.43i	−0.0721022	−	0.0416282i
$333$		0			0
$334$	−54508.2	−	94411.0i	−0.488618	−	0.846310i
$335$	−86799.2	+	103443.i	−0.773439	+	0.921749i
$336$		0			0
$337$	−743.090	−	4214.27i	−0.00654307	−	0.0371076i	0.981361	−	0.192171i	$-0.0615529\pi$
$337$	−743.090	−	4214.27i	−0.00654307	−	0.0371076i	−0.987904	+	0.155064i	$0.950442\pi$
$338$	−81479.7	+	14367.1i	−0.713208	+	0.125758i
$339$		0			0
$340$	−65703.9	−	55132.1i	−0.568373	−	0.476921i
$341$	−61090.2	+	35270.5i	−0.525367	+	0.303321i
$342$		0			0
$343$	−58614.6	+	101523.i	−0.498216	+	0.862935i
$344$	−61016.6	−	167642.i	−0.515622	−	1.41666i
$345$		0			0
$346$	−70530.4	+	59182.1i	−0.589148	+	0.494354i
$347$	−65820.8	+	180841.i	−0.546643	+	1.50189i	0.291571	+	0.956549i	$0.405822\pi$
$347$	−65820.8	+	180841.i	−0.546643	+	1.50189i	−0.838214	+	0.545341i	$0.816400\pi$
$348$		0			0
$349$	−15699.3	+	89035.3i	−0.128893	+	0.730990i	0.850026	+	0.526741i	$0.176586\pi$
$349$	−15699.3	+	89035.3i	−0.128893	+	0.730990i	−0.978919	+	0.204249i	$0.934525\pi$
$350$		−	161511.i		−	1.31846i
$351$		0			0
$352$	100325.			0.809697
$353$	−190086.	−	33517.2i	−1.52546	−	0.268979i	−0.652882	−	0.757460i	$-0.726440\pi$
$353$	−190086.	−	33517.2i	−1.52546	−	0.268979i	−0.872575	+	0.488480i	$0.837551\pi$
$354$		0			0
$355$	271864.	+	98950.5i	2.15722	+	0.785166i
$356$	33646.0	+	40097.8i	0.265481	+	0.316388i
$357$		0			0
$358$	10725.8	−	3903.88i	0.0836882	−	0.0304600i
$359$	32016.9	+	18484.9i	0.248422	+	0.143426i	0.619041	−	0.785358i	$-0.287521\pi$
$359$	32016.9	+	18484.9i	0.248422	+	0.143426i	−0.370620	+	0.928785i	$0.620855\pi$
$360$		0			0
$361$	60594.5	+	104953.i	0.464963	+	0.805340i
$362$	18259.2	−	21760.5i	0.139337	−	0.166055i
$363$		0			0
$364$	−788.668	−	4472.76i	−0.00595239	−	0.0337577i
$365$	158558.	−	27958.0i	1.19015	−	0.209856i
$366$		0			0
$367$	−18276.4	−	15335.7i	−0.135694	−	0.113860i	0.572415	−	0.819964i	$-0.306007\pi$
$367$	−18276.4	−	15335.7i	−0.135694	−	0.113860i	−0.708108	+	0.706104i	$0.750451\pi$
$368$	18171.1	−	10491.1i	0.134179	−	0.0774683i
$369$		0			0
$370$	17996.1	−	31170.1i	0.131454	−	0.227685i
$371$	33345.2	+	91615.1i	0.242262	+	0.665609i
$372$		0			0
$373$	−98510.4	+	82660.0i	−0.708051	+	0.594125i	−0.924051	−	0.382268i	$-0.875143\pi$
$373$	−98510.4	+	82660.0i	−0.708051	+	0.594125i	0.216001	+	0.976393i	$0.430699\pi$
$374$	−27921.3	+	76713.3i	−0.199615	+	0.548438i
$375$		0			0
$376$	−6141.54	+	34830.4i	−0.0434412	+	0.246367i
$377$			23987.7i			0.168774i
$378$		0			0
$379$	−261836.			−1.82285			−0.911424	−	0.411468i	$-0.865016\pi$
$379$	−261836.			−1.82285			−0.911424	+	0.411468i	$0.865016\pi$
$380$	34269.5	+	6042.64i	0.237323	+	0.0418465i
$381$		0			0
$382$	83030.3	+	30220.5i	0.568997	+	0.207098i
$383$	53474.5	+	63728.4i	0.364543	+	0.434446i	0.916872	−	0.399180i	$-0.130705\pi$
$383$	53474.5	+	63728.4i	0.364543	+	0.434446i	−0.552329	+	0.833626i	$0.686261\pi$
$384$		0			0
$385$	164967.	−	60043.1i	1.11295	−	0.405081i
$386$	58083.7	+	33534.6i	0.389834	+	0.225071i
$387$		0			0
$388$	−34814.2	−	60300.0i	−0.231256	−	0.400547i
$389$	91785.3	−	109385.i	0.606560	−	0.722870i	−0.372137	−	0.928178i	$-0.621375\pi$
$389$	91785.3	−	109385.i	0.606560	−	0.722870i	0.978698	+	0.205307i	$0.0658194\pi$
$390$		0			0
$391$	−10189.7	−	57788.9i	−0.0666515	−	0.377999i
$392$	−101178.	+	17840.5i	−0.658439	+	0.116101i
$393$		0			0
$394$	−21281.8	−	17857.6i	−0.137093	−	0.115035i
$395$	−79585.5	+	45948.7i	−0.510082	+	0.294496i
$396$		0			0
$397$	154947.	−	268377.i	0.983112	−	1.70280i	0.333069	−	0.942903i	$-0.391916\pi$
$397$	154947.	−	268377.i	0.983112	−	1.70280i	0.650043	−	0.759897i	$-0.274751\pi$
$398$	−49002.4	−	134633.i	−0.309351	−	0.849935i
$399$		0			0
$400$	117817.	−	98860.3i	0.736357	−	0.617877i
$401$	−31277.9	+	85935.3i	−0.194513	+	0.534420i	−0.998157	−	0.0606907i	$-0.980670\pi$
$401$	−31277.9	+	85935.3i	−0.194513	+	0.534420i	0.803644	+	0.595111i	$0.202892\pi$
$402$		0			0
$403$	−2133.14	+	12097.6i	−0.0131344	+	0.0744887i
$404$		−	15750.5i		−	0.0965011i
$405$		0			0
$406$	−103350.			−0.626986
$407$	28703.4	+	5061.19i	0.173279	+	0.0305537i
$408$		0			0
$409$	−211429.	−	76953.8i	−1.26391	−	0.460027i	−0.378834	−	0.925465i	$-0.623675\pi$
$409$	−211429.	−	76953.8i	−1.26391	−	0.460027i	−0.885081	+	0.465437i	$0.845897\pi$
$410$	48349.9	+	57621.1i	0.287626	+	0.342779i
$411$		0			0
$412$	77483.0	−	28201.5i	0.456470	−	0.166141i
$413$	−49058.9	−	28324.1i	−0.287619	−	0.166057i
$414$		0			0
$415$	−30885.9	−	53495.9i	−0.179334	−	0.310616i
$416$	11230.1	−	13383.5i	0.0648929	−	0.0773363i
$417$		0			0
$418$	−5751.41	−	32617.8i	−0.0329171	−	0.186682i
$419$	1027.79	−	181.228i	0.00585434	−	0.00103228i	−0.170720	−	0.985320i	$-0.554609\pi$
$419$	1027.79	−	181.228i	0.00585434	−	0.00103228i	0.176575	+	0.984287i	$0.443498\pi$
$420$		0			0
$421$	−103499.	−	86846.4i	−0.583948	−	0.489990i	0.302293	−	0.953215i	$-0.402248\pi$
$421$	−103499.	−	86846.4i	−0.583948	−	0.489990i	−0.886241	+	0.463225i	$0.846692\pi$
$422$	68785.4	−	39713.3i	0.386252	−	0.223003i
$423$		0			0
$424$	−111282.	+	192746.i	−0.619002	+	1.07214i
$425$	−147113.	−	404189.i	−0.814465	−	2.23772i
$426$		0			0
$427$	−107823.	+	90474.0i	−0.591364	+	0.496213i
$428$	21494.8	−	59056.6i	0.117340	−	0.322389i
$429$		0			0
$430$	65670.3	−	372435.i	0.355166	−	2.01425i
$431$		−	247960.i		−	1.33483i	−0.744685	−	0.667417i	$-0.767400\pi$
$431$		−	247960.i		−	1.33483i	0.744685	−	0.667417i	$-0.232600\pi$
$432$		0			0
$433$	88166.4			0.470248			0.235124	−	0.971965i	$-0.424450\pi$
$433$	88166.4			0.470248			0.235124	+	0.971965i	$0.424450\pi$
$434$	−52122.2	−	9190.55i	−0.276722	−	0.0487935i
$435$		0			0
$436$	48424.3	+	17625.0i	0.254736	+	0.0927163i
$437$	15303.1	+	18237.5i	0.0801340	+	0.0955000i
$438$		0			0
$439$	−204096.	+	74284.9i	−1.05902	+	0.385453i	−0.812061	−	0.583572i	$-0.801654\pi$
$439$	−204096.	+	74284.9i	−1.05902	+	0.385453i	−0.246962	+	0.969025i	$0.579432\pi$
$440$	347068.	+	200380.i	1.79271	+	1.03502i
$441$		0			0
$442$	7108.25	+	12311.9i	0.0363846	+	0.0630201i
$443$	−54878.4	+	65401.6i	−0.279637	+	0.333258i	−0.887521	−	0.460768i	$-0.847574\pi$
$443$	−54878.4	+	65401.6i	−0.279637	+	0.333258i	0.607884	+	0.794026i	$0.292019\pi$
$444$		0			0
$445$	61183.2	+	346987.i	0.308967	+	1.75224i
$446$	105159.	−	18542.4i	0.528660	−	0.0932170i
$447$		0			0
$448$	88714.0	+	74439.9i	0.442014	+	0.370894i
$449$	−62430.3	+	36044.1i	−0.309672	+	0.178789i	−0.646780	−	0.762677i	$-0.723885\pi$
$449$	−62430.3	+	36044.1i	−0.309672	+	0.178789i	0.337107	+	0.941466i	$0.390551\pi$
$450$		0			0
$451$	−30456.0	+	52751.3i	−0.149734	+	0.259346i
$452$	37739.3	+	103688.i	0.184722	+	0.507518i
$453$		0			0
$454$	−184583.	+	154884.i	−0.895532	+	0.751441i
$455$	10456.1	−	28728.0i	0.0505066	−	0.138766i
$456$		0			0
$457$	51056.8	−	289557.i	0.244467	−	1.38644i	−0.577259	−	0.816561i	$-0.695878\pi$
$457$	51056.8	−	289557.i	0.244467	−	1.38644i	0.821727	−	0.569882i	$-0.193011\pi$
$458$		−	43705.6i		−	0.208356i
$459$		0			0
$460$	−90719.2			−0.428730
$461$	−9786.05	−	1725.54i	−0.0460475	−	0.00811941i	0.150577	−	0.988598i	$-0.451887\pi$
$461$	−9786.05	−	1725.54i	−0.0460475	−	0.00811941i	−0.196624	+	0.980479i	$0.562998\pi$
$462$		0			0
$463$	241845.	+	88024.6i	1.12817	+	0.410622i	0.837629	−	0.546240i	$-0.183941\pi$
$463$	241845.	+	88024.6i	1.12817	+	0.410622i	0.290545	+	0.956861i	$0.406163\pi$
$464$	−63260.1	−	75390.5i	−0.293829	−	0.350171i
$465$		0			0
$466$	62753.7	−	22840.5i	0.288980	−	0.105180i
$467$	295396.	+	170547.i	1.35448	+	0.782008i	0.988873	−	0.148763i	$-0.0475292\pi$
$467$	295396.	+	170547.i	1.35448	+	0.782008i	0.365604	+	0.930771i	$0.380862\pi$
$468$		0			0
$469$	−41022.6	−	71053.3i	−0.186500	−	0.323027i
$470$	−48192.2	+	57433.2i	−0.218163	+	0.259997i
$471$		0			0
$472$	−22455.9	−	127354.i	−0.100797	−	0.571646i
$473$	301596.	−	53179.4i	1.34804	−	0.237696i
$474$		0			0
$475$	133682.	+	112172.i	0.592494	+	0.497162i
$476$	45130.8	−	26056.3i	0.199186	−	0.115000i
$477$		0			0
$478$	−64895.5	+	112402.i	−0.284026	+	0.491948i
$479$	78767.8	+	216413.i	0.343303	+	0.943217i	0.984429	+	0.175782i	$0.0562452\pi$
$479$	78767.8	+	216413.i	0.343303	+	0.943217i	−0.641126	+	0.767435i	$0.721533\pi$
$480$		0			0
$481$	3888.16	−	3262.56i	0.0168056	−	0.0141016i
$482$	−23691.2	+	65091.0i	−0.101975	+	0.280173i
$483$		0			0
$484$	952.005	−	5399.09i	0.00406395	−	0.0230478i
$485$		−	468686.i		−	1.99250i
$486$		0			0
$487$	219527.			0.925615			0.462808	−	0.886459i	$-0.346842\pi$
$487$	219527.			0.925615			0.462808	+	0.886459i	$0.346842\pi$
$488$	−316432.	−	55795.5i	−1.32874	−	0.234293i
$489$		0			0
$490$	−204656.	−	74488.6i	−0.852377	−	0.310240i
$491$	−134136.	−	159857.i	−0.556392	−	0.663083i	0.412387	−	0.911009i	$-0.364695\pi$
$491$	−134136.	−	159857.i	−0.556392	−	0.663083i	−0.968779	+	0.247926i	$0.920251\pi$
$492$		0			0
$493$	−258638.	+	94136.5i	−1.06414	+	0.387315i
$494$	−4995.08	−	2883.91i	−0.0204686	−	0.0118176i
$495$		0			0
$496$	−25199.6	−	43647.0i	−0.102431	−	0.177415i
$497$	−112990.	+	134656.i	−0.457432	+	0.545146i
$498$		0			0
$499$	−57335.2	−	325164.i	−0.230261	−	1.30587i	−0.852368	−	0.522942i	$-0.824834\pi$
$499$	−57335.2	−	325164.i	−0.230261	−	1.30587i	0.622107	−	0.782932i	$-0.286277\pi$
$500$	−430740.	+	75951.0i	−1.72296	+	0.303804i
$501$		0			0
$502$	244888.	+	205486.i	0.971763	+	0.815406i
$503$	−246836.	+	142511.i	−0.975602	+	0.563264i	−0.900939	−	0.433945i	$-0.857121\pi$
$503$	−246836.	+	142511.i	−0.975602	+	0.563264i	−0.0746622	+	0.997209i	$0.523788\pi$
$504$		0			0
$505$	53010.3	−	91816.6i	0.207863	−	0.360030i
$506$	29532.4	+	81139.6i	0.115345	+	0.316907i
$507$		0			0
$508$	132965.	−	111571.i	0.515241	−	0.432338i
$509$	−42394.2	+	116477.i	−0.163633	+	0.449578i	−0.994227	−	0.107301i	$-0.965779\pi$
$509$	−42394.2	+	116477.i	−0.163633	+	0.449578i	0.830594	+	0.556879i	$0.188001\pi$
$510$		0			0
$511$	−16986.8	+	96336.9i	−0.0650534	+	0.368936i
$512$			164213.i			0.626424i
$513$		0			0
$514$	−154848.			−0.586109
$515$	546598.	+	96380.0i	2.06088	+	0.363389i
$516$		0			0
$517$	−57051.9	−	20765.2i	−0.213446	−	0.0776882i
$518$	14056.6	+	16752.0i	0.0523867	+	0.0624320i
$519$		0			0
$520$	65581.0	−	23869.5i	0.242533	−	0.0882749i
$521$	−171993.	−	99300.3i	−0.633630	−	0.365826i	0.148527	−	0.988908i	$-0.452547\pi$
$521$	−171993.	−	99300.3i	−0.633630	−	0.365826i	−0.782157	+	0.623082i	$0.785880\pi$
$522$		0			0
$523$	−216878.	−	375645.i	−0.792890	−	1.37333i	−0.924170	−	0.381981i	$-0.875242\pi$
$523$	−216878.	−	375645.i	−0.792890	−	1.37333i	0.131280	−	0.991345i	$-0.458091\pi$
$524$	53726.8	−	64029.1i	0.195672	−	0.233193i
$525$		0			0
$526$	22225.9	+	126049.i	0.0803318	+	0.455584i
$527$	−138810.	+	24475.9i	−0.499802	+	0.0881286i
$528$		0			0
$529$	166825.	+	139983.i	0.596143	+	0.500223i
$530$	−408589.	+	235899.i	−1.45457	+	0.839797i
$531$		0			0
$532$	−10571.4	+	18310.2i	−0.0373515	+	0.0646947i
$533$	3627.96	+	9967.74i	0.0127705	+	0.0350867i
$534$		0			0
$535$	324065.	−	271923.i	1.13220	−	0.950032i
$536$	64058.7	−	176000.i	0.222971	−	0.612608i
$537$		0			0
$538$	−41202.9	+	233673.i	−0.142352	+	0.807317i
$539$		−	176365.i		−	0.607066i
$540$		0			0
$541$	290726.			0.993320			0.496660	−	0.867945i	$-0.334560\pi$
$541$	290726.			0.993320			0.496660	+	0.867945i	$0.334560\pi$
$542$	152397.	+	26871.7i	0.518774	+	0.0914738i
$543$		0			0
$544$	188374.	+	68562.4i	0.636535	+	0.231680i
$545$	222967.	+	265722.i	0.750667	+	0.894610i
$546$		0			0
$547$	−392794.	+	142965.i	−1.31277	+	0.477811i	−0.901136	−	0.433537i	$-0.857265\pi$
$547$	−392794.	+	142965.i	−1.31277	+	0.477811i	−0.411638	+	0.911347i	$0.635043\pi$
$548$	−58133.2	−	33563.2i	−0.193581	−	0.111764i
$549$		0			0
$550$	316462.	+	548129.i	1.04616	+	1.81200i
$551$	71778.3	−	85542.0i	0.236423	−	0.281758i
$552$		0			0
$553$	−9695.70	−	54987.0i	−0.0317051	−	0.179808i
$554$	−81361.3	+	14346.2i	−0.265093	+	0.0467430i
$555$		0			0
$556$	−76894.6	−	64522.2i	−0.248740	−	0.208718i
$557$	294946.	−	170287.i	0.950675	−	0.548873i	0.0573846	−	0.998352i	$-0.481724\pi$
$557$	294946.	−	170287.i	0.950675	−	0.548873i	0.893291	+	0.449480i	$0.148391\pi$
$558$		0			0
$559$	26665.6	−	46186.2i	0.0853352	−	0.147805i
$560$	42898.9	+	117864.i	0.136795	+	0.375841i
$561$		0			0
$562$	86495.0	−	72577.9i	0.273854	−	0.229790i
$563$	−3983.63	+	10944.9i	−0.0125679	+	0.0345300i	−0.945818	−	0.324697i	$-0.894738\pi$
$563$	−3983.63	+	10944.9i	−0.0125679	+	0.0345300i	0.933250	+	0.359227i	$0.116960\pi$
$564$		0			0
$565$	−128976.	+	731459.i	−0.404028	+	2.29136i
$566$			259609.i			0.810376i
$567$		0			0
$568$	−401277.			−1.24379
$569$	−219065.	−	38627.1i	−0.676627	−	0.119308i	−0.175233	−	0.984527i	$-0.556068\pi$
$569$	−219065.	−	38627.1i	−0.676627	−	0.119308i	−0.501393	+	0.865219i	$0.667179\pi$
$570$		0			0
$571$	110761.	+	40313.8i	0.339716	+	0.123646i	0.506244	−	0.862390i	$-0.331034\pi$
$571$	110761.	+	40313.8i	0.339716	+	0.123646i	−0.166528	+	0.986037i	$0.553256\pi$
$572$	11440.4	+	13634.1i	0.0349663	+	0.0416712i
$573$		0			0
$574$	−42945.6	+	15630.9i	−0.130345	+	0.0474418i
$575$	−393996.	−	227473.i	−1.19167	−	0.688010i
$576$		0			0
$577$	79405.7	+	137535.i	0.238506	+	0.413105i	0.960286	−	0.279018i	$-0.0900089\pi$
$577$	79405.7	+	137535.i	0.238506	+	0.413105i	−0.721780	+	0.692123i	$0.756676\pi$
$578$	52997.1	−	63159.5i	0.158634	−	0.189053i
$579$		0			0
$580$	73889.5	+	419048.i	0.219648	+	1.24568i
$581$	36961.2	−	6517.26i	0.109495	−	0.0193069i
$582$		0			0
$583$	−292675.	−	245583.i	−0.861089	−	0.722539i
$584$	−193395.	+	111657.i	−0.567047	+	0.327385i
$585$		0			0
$586$	25190.4	−	43631.1i	0.0733568	−	0.127058i
$587$	160654.	+	441393.i	0.466246	+	1.28100i	0.920714	+	0.390238i	$0.127607\pi$
$587$	160654.	+	441393.i	0.466246	+	1.28100i	−0.454467	+	0.890763i	$0.650170\pi$
$588$		0			0
$589$	43806.7	−	36758.2i	0.126273	−	0.105956i
$590$	93759.1	−	257601.i	0.269345	−	0.740020i
$591$		0			0
$592$	−3616.06	+	20507.7i	−0.0103179	+	0.0585158i
$593$			515426.i			1.46574i	0.680368	+	0.732870i	$0.261820\pi$
$593$			515426.i			1.46574i	−0.680368	+	0.732870i	$0.738180\pi$
$594$		0			0
$595$	350783.			0.990841
$596$	256581.	+	45242.2i	0.722324	+	0.127365i
$597$		0			0
$598$	14130.0	+	5142.88i	0.0395129	+	0.0143815i
$599$	−450250.	−	536588.i	−1.25488	−	1.49550i	−0.793848	−	0.608116i	$-0.791926\pi$
$599$	−450250.	−	536588.i	−1.25488	−	1.49550i	−0.461027	−	0.887386i	$-0.652519\pi$
$600$		0			0
$601$	563518.	−	205104.i	1.56012	−	0.567838i	0.589358	−	0.807872i	$-0.299381\pi$
$601$	563518.	−	205104.i	1.56012	−	0.567838i	0.970764	+	0.240034i	$0.0771587\pi$
$602$	198991.	+	114888.i	0.549087	+	0.317016i
$603$		0			0
$604$	130901.	+	226727.i	0.358813	+	0.621483i
$605$	23721.0	−	28269.5i	0.0648069	−	0.0772339i
$606$		0			0
$607$	−87130.8	−	494143.i	−0.236480	−	1.34114i	−0.839475	−	0.543399i	$-0.817137\pi$
$607$	−87130.8	−	494143.i	−0.236480	−	1.34114i	0.602995	−	0.797745i	$-0.293974\pi$
$608$	−80095.0	+	14122.9i	−0.216670	+	0.0382047i
$609$		0			0
$610$	−521777.	−	437823.i	−1.40225	−	1.17663i
$611$	−9156.36	+	5286.43i	−0.0245268	+	0.0141605i
$612$		0			0
$613$	88778.8	−	153769.i	0.236259	−	0.409213i	−0.723379	−	0.690451i	$-0.757412\pi$
$613$	88778.8	−	153769.i	0.236259	−	0.409213i	0.959638	+	0.281239i	$0.0907453\pi$
$614$	−142067.	−	390325.i	−0.376839	−	1.03536i
$615$		0			0
$616$	−186528.	+	156515.i	−0.491566	+	0.412473i
$617$	76122.3	−	209144.i	0.199959	−	0.549383i	−0.798668	−	0.601772i	$-0.794461\pi$
$617$	76122.3	−	209144.i	0.199959	−	0.549383i	0.998627	+	0.0523891i	$0.0166836\pi$
$618$		0			0
$619$	44170.8	−	250505.i	0.115280	−	0.653785i	−0.871331	−	0.490695i	$-0.836743\pi$
$619$	44170.8	−	250505.i	0.115280	−	0.653785i	0.986611	−	0.163090i	$-0.0521461\pi$
$620$			217908.i			0.566879i
$621$		0			0
$622$	325182.			0.840515
$623$	−210823.	−	37173.9i	−0.543179	−	0.0957771i
$624$		0			0
$625$	−1.69409e6	−	616597.i	−4.33686	−	1.57849i
$626$	13428.1	+	16003.0i	0.0342663	+	0.0408370i
$627$		0			0
$628$	−234668.	+	85412.3i	−0.595025	+	0.216571i
$629$	50435.9	+	29119.2i	0.127479	+	0.0736000i
$630$		0			0
$631$	92940.0	+	160977.i	0.233423	+	0.404301i	0.958813	−	0.284037i	$-0.0916739\pi$
$631$	92940.0	+	160977.i	0.233423	+	0.404301i	−0.725390	+	0.688338i	$0.758341\pi$
$632$	81931.2	−	97641.8i	0.205123	−	0.244456i
$633$		0			0
$634$	−34887.0	−	197854.i	−0.0867930	−	0.492228i
$635$	1.15062e6	−	202885.i	2.85354	−	0.503156i
$636$		0			0
$637$	−23527.5	−	19741.9i	−0.0579824	−	0.0486530i
$638$	350744.	−	202502.i	0.861687	−	0.497495i
$639$		0			0
$640$	56877.9	−	98515.4i	0.138862	−	0.240516i
$641$	203464.	+	559012.i	0.495189	+	1.36052i	0.895876	+	0.444304i	$0.146549\pi$
$641$	203464.	+	559012.i	0.495189	+	1.36052i	−0.400687	+	0.916215i	$0.631229\pi$
$642$		0			0
$643$	125554.	−	105353.i	0.303676	−	0.254814i	−0.478197	−	0.878253i	$-0.658709\pi$
$643$	125554.	−	105353.i	0.303676	−	0.254814i	0.781872	+	0.623439i	$0.214265\pi$
$644$	18851.9	−	51795.3i	0.0454553	−	0.124887i
$645$		0			0
$646$	11492.1	−	65175.1i	0.0275382	−	0.156177i
$647$		−	159455.i		−	0.380916i	−0.981695	−	0.190458i	$-0.939003\pi$
$647$		−	159455.i		−	0.380916i	0.981695	−	0.190458i	$-0.0609972\pi$
$648$		0			0
$649$	221992.			0.527045
$650$	108545.	+	19139.5i	0.256912	+	0.0453006i
$651$		0			0
$652$	32821.9	+	11946.2i	0.0772091	+	0.0281018i
$653$	−198728.	−	236834.i	−0.466050	−	0.555416i	0.480910	−	0.876770i	$-0.340307\pi$
$653$	−198728.	−	236834.i	−0.466050	−	0.555416i	−0.946959	+	0.321354i	$0.895862\pi$
$654$		0			0
$655$	528695.	−	192429.i	1.23232	−	0.448527i
$656$	−37689.1	−	21759.8i	−0.0875807	−	0.0505648i
$657$		0			0
$658$	−22776.4	−	39449.8i	−0.0526057	−	0.0911157i
$659$	−99185.3	+	118204.i	−0.228390	+	0.272184i	−0.868054	−	0.496471i	$-0.834629\pi$
$659$	−99185.3	+	118204.i	−0.228390	+	0.272184i	0.639664	+	0.768655i	$0.279074\pi$
$660$		0			0
$661$	79881.2	+	453029.i	0.182828	+	1.03687i	0.928715	+	0.370795i	$0.120915\pi$
$661$	79881.2	+	453029.i	0.182828	+	1.03687i	−0.745887	+	0.666072i	$0.767974\pi$
$662$	−490763.	+	86534.7i	−1.11984	+	0.197458i
$663$		0			0
$664$	65632.9	+	55072.6i	0.148863	+	0.124911i
$665$	−123250.	+	71158.6i	−0.278705	+	0.160910i
$666$		0			0
$667$	−145559.	+	252115.i	−0.327180	+	0.566693i
$668$	−93272.0	−	256263.i	−0.209025	−	0.574292i
$669$		0			0
$670$	304146.	−	255209.i	0.677537	−	0.568521i
$671$	188650.	−	518313.i	0.418999	−	1.15119i
$672$		0			0
$673$	−63486.9	+	360052.i	−0.140170	+	0.794942i	0.830950	+	0.556348i	$0.187798\pi$
$673$	−63486.9	+	360052.i	−0.140170	+	0.794942i	−0.971119	+	0.238594i	$0.923313\pi$
$674$			12582.0i			0.0276969i
$675$		0			0
$676$	−206969.			−0.452911
$677$	−86367.5	−	15228.9i	−0.188440	−	0.0332271i	0.0786316	−	0.996904i	$-0.474945\pi$
$677$	−86367.5	−	15228.9i	−0.188440	−	0.0332271i	−0.267072	+	0.963677i	$0.586056\pi$
$678$		0			0
$679$	267592.	+	97395.6i	0.580409	+	0.211251i
$680$	514729.	+	613430.i	1.11317	+	1.32662i
$681$		0			0
$682$	194898.	−	70937.1i	0.419024	−	0.152512i
$683$	−295267.	−	170473.i	−0.632957	−	0.365438i	0.148939	−	0.988846i	$-0.452414\pi$
$683$	−295267.	−	170473.i	−0.632957	−	0.365438i	−0.781896	+	0.623409i	$0.785747\pi$
$684$		0			0
$685$	−225923.	−	391309.i	−0.481480	−	0.833948i
$686$	221556.	−	264040.i	0.470799	−	0.561076i
$687$		0			0
$688$	37995.0	+	215480.i	0.0802694	+	0.455230i
$689$	−65522.5	+	11553.4i	−0.138023	+	0.0243372i
$690$		0			0
$691$	−330573.	−	277384.i	−0.692327	−	0.580932i	0.227252	−	0.973836i	$-0.427026\pi$
$691$	−330573.	−	277384.i	−0.692327	−	0.580932i	−0.919579	+	0.392904i	$0.871470\pi$
$692$	−199462.	+	115160.i	−0.416532	+	0.240485i
$693$		0			0
$694$	282919.	−	490029.i	0.587412	−	1.01743i
$695$	−231094.	−	634926.i	−0.478431	−	1.31448i
$696$		0			0
$697$	−93235.9	+	78234.2i	−0.191919	+	0.161039i
$698$	90916.5	−	249791.i	0.186609	−	0.512703i
$699$		0			0
$700$	70158.4	−	397888.i	0.143180	−	0.812017i
$701$		−	449638.i		−	0.915012i	−0.889206	−	0.457506i	$-0.848743\pi$
$701$		−	449638.i		−	0.915012i	0.889206	−	0.457506i	$-0.151257\pi$
$702$		0			0
$703$	−23628.1			−0.0478099
$704$	−446930.	−	78805.8i	−0.901767	−	0.159006i
$705$		0			0
$706$	533291.	+	194102.i	1.06993	+	0.389422i
$707$	41406.0	+	49345.8i	0.0828370	+	0.0987213i
$708$		0			0
$709$	−842698.	+	306717.i	−1.67641	+	0.610163i	−0.992811	−	0.119697i	$-0.961808\pi$
$709$	−842698.	+	306717.i	−1.67641	+	0.610163i	−0.683597	+	0.729859i	$0.739586\pi$
$710$	−736677.	−	425321.i	−1.46137	−	0.843723i
$711$		0			0
$712$	−244349.	−	423225.i	−0.482004	−	0.834855i
$713$	−95829.1	+	114205.i	−0.188503	+	0.224649i
$714$		0			0
$715$	20803.7	+	117983.i	0.0406937	+	0.230786i
$716$	28119.2	−	4958.18i	0.0548501	−	0.00967156i
$717$		0			0
$718$	−83268.8	−	69870.8i	−0.161523	−	0.135534i
$719$	254619.	−	147004.i	0.492531	−	0.284363i	−0.233093	−	0.972454i	$-0.574885\pi$
$719$	254619.	−	147004.i	0.492531	−	0.284363i	0.725624	+	0.688092i	$0.241551\pi$
$720$		0			0
$721$	−168613.	+	292047.i	−0.324356	+	0.561800i
$722$	−121869.	−	334834.i	−0.233787	−	0.642325i
$723$		0			0
$724$	54434.8	−	45676.2i	0.103848	−	0.0871391i
$725$	−729837.	+	2.00521e6i	−1.38851	+	3.81490i
$726$		0			0
$727$	−9651.65	+	54737.2i	−0.0182613	+	0.103565i	−0.992576	−	0.121625i	$-0.961189\pi$
$727$	−9651.65	+	54737.2i	−0.0182613	+	0.103565i	0.974315	+	0.225191i	$0.0723005\pi$
$728$			42403.1i			0.0800083i
$729$		0			0
$730$	−473387.			−0.888322
$731$	602631.	+	106260.i	1.12776	+	0.198855i
$732$		0			0
$733$	727234.	+	264692.i	1.35353	+	0.492643i	0.914046	−	0.405610i	$-0.132941\pi$
$733$	727234.	+	264692.i	1.35353	+	0.492643i	0.439479	+	0.898253i	$0.355163\pi$
$734$	45090.5	+	53736.8i	0.0836938	+	0.0997423i
$735$		0			0
$736$	199243.	−	72518.4i	0.367813	−	0.133873i
$737$	278442.	+	160758.i	0.512624	+	0.295964i
$738$		0			0
$739$	172753.	+	299218.i	0.316328	+	0.547896i	0.979719	−	0.200377i	$-0.0642166\pi$
$739$	172753.	+	299218.i	0.316328	+	0.547896i	−0.663391	+	0.748273i	$0.730883\pi$
$740$	57873.9	−	68971.4i	0.105686	−	0.125952i
$741$		0			0
$742$	−49777.3	−	282301.i	−0.0904115	−	0.512749i
$743$	284486.	−	50162.6i	0.515328	−	0.0908662i	0.0900647	−	0.995936i	$-0.471293\pi$
$743$	284486.	−	50162.6i	0.515328	−	0.0908662i	0.425263	+	0.905070i	$0.360181\pi$
$744$		0			0
$745$	1.34345e6	+	1.12729e6i	2.42053	+	2.03107i
$746$	327445.	−	189051.i	0.588384	−	0.339704i
$747$		0			0
$748$	−102109.	+	176857.i	−0.182498	+	0.316097i
$749$	87909.3	+	241529.i	0.156701	+	0.430532i
$750$		0			0
$751$	−431649.	+	362197.i	−0.765334	+	0.642192i	−0.939509	−	0.342523i	$-0.888719\pi$
$751$	−431649.	+	362197.i	−0.765334	+	0.642192i	0.174175	+	0.984715i	$0.444274\pi$
$752$	14836.1	−	40761.8i	0.0262351	−	0.0720804i
$753$		0			0
$754$	12247.2	−	69457.6i	0.0215425	−	0.122173i
$755$			1.76225e6i			3.09154i
$756$		0			0
$757$	63666.1			0.111101			0.0555503	−	0.998456i	$-0.482309\pi$
$757$	63666.1			0.111101			0.0555503	+	0.998456i	$0.482309\pi$
$758$	758160.	+	133684.i	1.31954	+	0.232670i
$759$		0			0
$760$	−305292.	−	111117.i	−0.528553	−	0.192378i
$761$	−189279.	−	225574.i	−0.326839	−	0.389512i	0.577454	−	0.816423i	$-0.304046\pi$
$761$	−189279.	−	225574.i	−0.326839	−	0.389512i	−0.904294	+	0.426911i	$0.859602\pi$
$762$		0			0
$763$	−198045.	+	72082.5i	−0.340185	+	0.123817i
$764$	191421.	+	110517.i	0.327946	+	0.189340i
$765$		0			0
$766$	−122301.	−	211831.i	−0.208436	−	0.361021i
$767$	24849.2	−	29614.1i	0.0422398	−	0.0503394i
$768$		0			0
$769$	99576.5	+	564726.i	0.168385	+	0.954960i	0.945505	+	0.325608i	$0.105569\pi$
$769$	99576.5	+	564726.i	0.168385	+	0.954960i	−0.777120	+	0.629353i	$0.783320\pi$
$770$	−508327.	+	89631.8i	−0.857357	+	0.151175i
$771$		0			0
$772$	128524.	+	107845.i	0.215651	+	0.180952i
$773$	558017.	−	322171.i	0.933874	−	0.539172i	0.0458390	−	0.998949i	$-0.485404\pi$
$773$	558017.	−	322171.i	0.933874	−	0.539172i	0.888035	+	0.459777i	$0.152071\pi$
$774$		0			0
$775$	−546393.	+	946381.i	−0.909708	+	1.57566i
$776$	222337.	+	610866.i	0.369223	+	1.01443i
$777$		0			0
$778$	−321618.	+	269869.i	−0.531350	+	0.445856i
$779$	16888.9	−	46401.7i	0.0278308	−	0.0764644i
$780$		0			0
$781$	119617.	−	678380.i	0.196105	−	1.11217i
$782$			172534.i			0.282137i
$783$		0			0
$784$	126007.			0.205005
$785$	−1.65545e6	−	291900.i	−2.68644	−	0.473691i
$786$		0			0
$787$	296328.	+	107855.i	0.478436	+	0.174136i	0.569970	−	0.821666i	$-0.306955\pi$
$787$	296328.	+	107855.i	0.478436	+	0.174136i	−0.0915343	+	0.995802i	$0.529177\pi$
$788$	−44671.4	−	53237.3i	−0.0719411	−	0.0857361i
$789$		0			0
$790$	253904.	−	92413.5i	0.406832	−	0.148075i
$791$	−390818.	−	225639.i	−0.624628	−	0.360629i
$792$		0			0
$793$	−48026.9	−	83185.0i	−0.0763727	−	0.132281i
$794$	−585682.	+	697988.i	−0.929011	+	1.10715i
$795$		0			0
$796$	−62236.3	−	352960.i	−0.0982240	−	0.557056i
$797$	−484473.	+	85425.6i	−0.762698	+	0.134484i	−0.541450	−	0.840733i	$-0.682124\pi$
$797$	−484473.	+	85425.6i	−0.762698	+	0.134484i	−0.221249	+	0.975217i	$0.571013\pi$
$798$		0			0
$799$	−92931.9	−	77979.1i	−0.145570	−	0.122148i
$800$	1.34596e6	−	777091.i	2.10306	−	1.21420i
$801$		0			0
$802$	134442.	−	232861.i	0.209020	−	0.362033i
$803$	−131112.	−	360228.i	−0.203335	−	0.558658i
$804$		0			0
$805$	284220.	−	238489.i	0.438594	−	0.368024i
$806$	12353.2	−	33940.3i	0.0190156	−	0.0522451i
$807$		0			0
$808$	−25535.2	+	144817.i	−0.0391126	+	0.221818i
$809$		−	466812.i		−	0.713255i	−0.934247	−	0.356628i	$-0.883927\pi$
$809$		−	466812.i		−	0.713255i	0.934247	−	0.356628i	$-0.116073\pi$
$810$		0			0
$811$	−335882.			−0.510676			−0.255338	−	0.966852i	$-0.582187\pi$
$811$	−335882.			−0.510676			−0.255338	+	0.966852i	$0.582187\pi$
$812$	−254606.	−	44894.0i	−0.386151	−	0.0680888i
$813$		0			0
$814$	−80528.3	−	29309.9i	−0.121535	−	0.0442350i
$815$	151127.	+	180106.i	0.227523	+	0.271152i
$816$		0			0
$817$	−233295.	+	84912.4i	−0.349511	+	0.127212i
$818$	572914.	+	330772.i	0.856215	+	0.494336i
$819$		0			0
$820$	94081.8	+	162954.i	0.139919	+	0.242347i
$821$	−766388.	+	913346.i	−1.13701	+	1.35503i	−0.211015	+	0.977483i	$0.567677\pi$
$821$	−766388.	+	913346.i	−1.13701	+	1.35503i	−0.925990	+	0.377547i	$0.876768\pi$
$822$		0			0
$823$	−3006.67	−	17051.7i	−0.00443901	−	0.0251749i	0.982508	−	0.186221i	$-0.0596242\pi$
$823$	−3006.67	−	17051.7i	−0.00443901	−	0.0251749i	−0.986947	+	0.161047i	$0.948513\pi$
$824$	−758134.	+	133680.i	−1.11658	+	0.196884i
$825$		0			0
$826$	127591.	+	107062.i	0.187008	+	0.156919i
$827$	403669.	−	233058.i	0.590221	−	0.340764i	−0.174964	−	0.984575i	$-0.555981\pi$
$827$	403669.	−	233058.i	0.590221	−	0.340764i	0.765185	+	0.643811i	$0.222648\pi$
$828$		0			0
$829$	351603.	−	608995.i	0.511616	−	0.886144i	−0.488294	−	0.872679i	$-0.662380\pi$
$829$	351603.	−	608995.i	0.511616	−	0.886144i	0.999909	−	0.0134650i	$-0.00428618\pi$
$830$	62118.6	+	170669.i	0.0901707	+	0.247742i
$831$		0			0
$832$	−60541.1	+	50800.0i	−0.0874588	+	0.0733866i
$833$	120529.	−	331151.i	0.173701	−	0.477239i
$834$		0			0
$835$	318761.	−	1.80779e6i	0.457186	−	2.59283i
$836$		−	82853.6i		−	0.118549i
$837$		0			0
$838$	−3068.56			−0.00436965
$839$	538609.	+	94971.3i	0.765156	+	0.134918i	0.542587	−	0.839999i	$-0.317445\pi$
$839$	538609.	+	94971.3i	0.765156	+	0.134918i	0.222568	+	0.974917i	$0.428556\pi$
$840$		0			0
$841$	618495.	+	225114.i	0.874468	+	0.318280i
$842$	255348.	+	304312.i	0.360170	+	0.429234i
$843$		0			0
$844$	186706.	−	67955.5i	0.262104	−	0.0953982i
$845$	−1.20651e6	−	696581.i	−1.68974	−	0.975569i
$846$		0			0
$847$	11210.9	+	19417.8i	0.0156269	+	0.0270666i
$848$	175461.	−	209107.i	0.244000	−	0.290788i
$849$		0			0
$850$	219608.	+	1.24546e6i	0.303956	+	1.72382i
$851$	60662.9	−	10696.5i	0.0837652	−	0.0147701i
$852$		0			0
$853$	281194.	+	235950.i	0.386463	+	0.324281i	0.815233	−	0.579133i	$-0.196609\pi$
$853$	281194.	+	235950.i	0.386463	+	0.324281i	−0.428770	+	0.903413i	$0.641053\pi$
$854$	358399.	−	206922.i	0.491418	−	0.283721i
$855$		0			0
$856$	−293377.	+	508144.i	−0.400386	+	0.693489i
$857$	−457859.	−	1.25796e6i	−0.623404	−	1.71279i	−0.698497	−	0.715613i	$-0.746148\pi$
$857$	−457859.	−	1.25796e6i	−0.623404	−	1.71279i	0.0750931	−	0.997177i	$-0.476075\pi$
$858$		0			0
$859$	−336636.	+	282471.i	−0.456219	+	0.382814i	−0.841738	−	0.539887i	$-0.818467\pi$
$859$	−336636.	+	282471.i	−0.456219	+	0.382814i	0.385518	+	0.922700i	$0.374023\pi$
$860$	323562.	−	888980.i	0.437483	−	1.20197i
$861$		0			0
$862$	−126600.	+	717982.i	−0.170380	+	0.966271i
$863$			826296.i			1.10947i	0.832028	+	0.554733i	$0.187180\pi$
$863$			826296.i			1.10947i	−0.832028	+	0.554733i	$0.812820\pi$
$864$		0			0
$865$	−1.55034e6			−2.07202
$866$	−255291.	−	45014.6i	−0.340407	−	0.0600230i
$867$		0			0
$868$	−124413.	−	45282.5i	−0.165130	−	0.0601023i
$869$	140646.	+	167615.i	0.186246	+	0.221959i
$870$		0			0
$871$	52613.5	−	19149.8i	0.0693523	−	0.0252422i
$872$	−416660.	−	240559.i	−0.547960	−	0.316365i
$873$		0			0
$874$	−34999.6	−	60621.0i	−0.0458184	−	0.0793598i
$875$	1.14983e6	−	1.37031e6i	1.50181	−	1.78979i
$876$		0			0
$877$	−171539.	−	972846.i	−0.223030	−	1.26487i	−0.866415	−	0.499325i	$-0.833582\pi$
$877$	−171539.	−	972846.i	−0.223030	−	1.26487i	0.643385	−	0.765543i	$-0.277530\pi$
$878$	628898.	−	110892.i	0.815814	−	0.143850i
$879$		0			0
$880$	−376529.	−	315945.i	−0.486220	−	0.407987i
$881$	386704.	−	223264.i	0.498226	−	0.287651i	−0.229754	−	0.973249i	$-0.573792\pi$
$881$	386704.	−	223264.i	0.498226	−	0.287651i	0.727981	+	0.685598i	$0.240459\pi$
$882$		0			0
$883$	734110.	−	1.27152e6i	0.941542	−	1.63080i	0.179010	−	0.983847i	$-0.442711\pi$
$883$	734110.	−	1.27152e6i	0.941542	−	1.63080i	0.762532	−	0.646950i	$-0.223956\pi$
$884$	12163.3	+	33418.4i	0.0155649	+	0.0427643i
$885$		0			0
$886$	192295.	−	161355.i	0.244963	−	0.205549i
$887$	−326437.	+	896880.i	−0.414909	+	1.13995i	0.539639	+	0.841896i	$0.318561\pi$
$887$	−326437.	+	896880.i	−0.414909	+	1.13995i	−0.954548	+	0.298057i	$0.903662\pi$
$888$		0			0
$889$	−123269.	+	699095.i	−0.155974	+	0.884571i
$890$		−	1.03596e6i		−	1.30786i
$891$		0			0
$892$	267117.			0.335716
$893$	48470.9	+	8546.74i	0.0607825	+	0.0107176i
$894$		0			0
$895$	180607.	+	65735.4i	0.225469	+	0.0820641i
$896$	44426.9	+	52945.9i	0.0553389	+	0.0659503i
$897$		0			0
$898$	199173.	−	72493.1i	0.246989	−	0.0898967i
$899$	605583.	+	349634.i	0.749298	+	0.432607i
$900$		0			0
$901$	−381705.	−	661132.i	−0.470195	−	0.814402i
$902$	115120.	−	137195.i	0.141494	−	0.168626i
$903$		0			0
$904$	−178890.	−	1.01454e6i	−0.218902	−	1.24146i
$905$	471053.	−	83059.4i	0.575139	−	0.101412i
$906$		0			0
$907$	−165038.	−	138483.i	−0.200618	−	0.168338i	0.536944	−	0.843618i	$-0.319579\pi$
$907$	−165038.	−	138483.i	−0.200618	−	0.168338i	−0.737562	+	0.675279i	$0.764023\pi$
$908$	−522008.	+	301381.i	−0.633148	+	0.365548i
$909$		0			0
$910$	−44943.8	+	77844.9i	−0.0542734	+	0.0940043i
$911$	86155.1	+	236709.i	0.103811	+	0.285219i	0.980714	−	0.195449i	$-0.0626164\pi$
$911$	86155.1	+	236709.i	0.103811	+	0.285219i	−0.876903	+	0.480668i	$0.840394\pi$
$912$		0			0
$913$	−112668.	+	94539.3i	−0.135163	+	0.113415i
$914$	−295675.	+	812361.i	−0.353934	+	0.972426i
$915$		0			0
$916$	18985.2	−	107670.i	0.0226269	−	0.128323i
$917$			341841.i			0.406524i
$918$		0			0
$919$	427276.			0.505915			0.252958	−	0.967477i	$-0.418597\pi$
$919$	427276.			0.505915			0.252958	+	0.967477i	$0.418597\pi$
$920$	834112.	+	147077.i	0.985483	+	0.173767i
$921$		0			0
$922$	27455.0	+	9992.82i	0.0322969	+	0.0117551i
$923$	−77107.6	−	91893.2i	−0.0905094	−	0.107865i
$924$		0			0
$925$	424290.	−	154429.i	0.495883	−	0.180487i
$926$	−655335.	−	378358.i	−0.764260	−	0.441246i
$927$		0			0
$928$	−497256.	−	861273.i	−0.577410	−	1.00010i
$929$	324820.	−	387105.i	0.376367	−	0.448536i	−0.544297	−	0.838892i	$-0.683204\pi$
$929$	324820.	−	387105.i	0.376367	−	0.448536i	0.920664	+	0.390356i	$0.127648\pi$
$930$		0			0
$931$	24827.3	+	140803.i	0.0286438	+	0.162447i
$932$	164518.	−	29008.9i	0.189400	−	0.0333964i
$933$		0			0
$934$	−768261.	−	644648.i	−0.880674	−	0.738973i
$935$	−1.19047e6	+	687318.i	−1.36174	+	0.786203i
$936$		0			0
$937$	31013.4	−	53716.7i	0.0353240	−	0.0611829i	−0.847823	−	0.530279i	$-0.822087\pi$
$937$	31013.4	−	53716.7i	0.0353240	−	0.0611829i	0.883147	+	0.469096i	$0.155420\pi$
$938$	82506.0	+	226683.i	0.0937734	+	0.257640i
$939$		0			0
$940$	−143672.	+	120555.i	−0.162598	+	0.136436i
$941$	67742.3	−	186120.i	0.0765033	−	0.210191i	−0.895545	−	0.444970i	$-0.853214\pi$
$941$	67742.3	−	186120.i	0.0765033	−	0.210191i	0.972049	+	0.234779i	$0.0754366\pi$
$942$		0			0
$943$	−22354.3	+	126778.i	−0.0251384	+	0.142567i
$944$			158606.i			0.177982i
$945$		0			0
$946$	−900438.			−1.00617
$947$	−95314.0	−	16806.4i	−0.106281	−	0.0187403i	0.120255	−	0.992743i	$-0.461629\pi$
$947$	−95314.0	−	16806.4i	−0.106281	−	0.0187403i	−0.226536	+	0.974003i	$0.572740\pi$
$948$		0			0
$949$	−62731.4	−	22832.4i	−0.0696551	−	0.0253524i
$950$	−329811.	−	393054.i	−0.365442	−	0.435516i
$951$		0			0
$952$	−457196.	+	166406.i	−0.504462	+	0.183609i
$953$	887146.	+	512194.i	0.976808	+	0.563960i	0.901305	−	0.433185i	$-0.142610\pi$
$953$	887146.	+	512194.i	0.976808	+	0.563960i	0.0755032	+	0.997146i	$0.475944\pi$
$954$		0			0
$955$	743916.	+	1.28850e6i	0.815675	+	1.41279i
$956$	−208699.	+	248717.i	−0.228351	+	0.272139i
$957$		0			0
$958$	−117584.	−	666851.i	−0.128120	−	0.726604i
$959$	270362.	−	47672.2i	0.293974	−	0.0518356i
$960$		0			0
$961$	−433137.	−	363445.i	−0.469007	−	0.393543i
$962$	−12924.1	+	7461.75i	−0.0139653	+	0.00806289i
$963$		0			0
$964$	−86638.8	+	150063.i	−0.0932306	+	0.161480i
$965$	386259.	+	1.06124e6i	0.414786	+	1.13961i
$966$		0			0
$967$	−688509.	+	577728.i	−0.736304	+	0.617832i	−0.931842	−	0.362864i	$-0.881799\pi$
$967$	−688509.	+	577728.i	−0.736304	+	0.617832i	0.195539	+	0.980696i	$0.437355\pi$
$968$	−17506.3	+	48098.2i	−0.0186829	+	0.0513308i
$969$		0			0
$970$	−239295.	+	1.35711e6i	−0.254325	+	1.44235i
$971$		−	612535.i		−	0.649669i	−0.945771	−	0.324835i	$-0.894691\pi$
$971$		−	612535.i		−	0.649669i	0.945771	−	0.324835i	$-0.105309\pi$
$972$		0			0
$973$	410528.			0.433628
$974$	−635653.	−	112083.i	−0.670042	−	0.118147i
$975$		0			0
$976$	370318.	+	134785.i	0.388754	+	0.141495i
$977$	11415.2	+	13604.1i	0.0119590	+	0.0142522i	0.771991	−	0.635634i	$-0.219261\pi$
$977$	11415.2	+	13604.1i	0.0119590	+	0.0142522i	−0.760032	+	0.649886i	$0.774817\pi$
$978$		0			0
$979$	788321.	−	286925.i	0.822504	−	0.299367i
$980$	−471820.	−	272406.i	−0.491275	−	0.283638i
$981$		0			0
$982$	306780.	+	531358.i	0.318129	+	0.551016i
$983$	−498988.	+	594670.i	−0.516396	+	0.615417i	−0.959725	−	0.280942i	$-0.909353\pi$
$983$	−498988.	+	594670.i	−0.516396	+	0.615417i	0.443329	+	0.896359i	$0.353797\pi$
$984$		0			0
$985$	−81232.2	−	460691.i	−0.0837251	−	0.474829i
$986$	796963.	−	140526.i	0.819756	−	0.144545i
$987$		0			0
$988$	−11052.8	−	9274.42i	−0.0113229	−	0.00950108i
$989$	560523.	−	323618.i	0.573061	−	0.330857i
$990$		0			0
$991$	−900597.	+	1.55988e6i	−0.917029	+	1.58834i	−0.113126	+	0.993581i	$0.536086\pi$
$991$	−900597.	+	1.55988e6i	−0.917029	+	1.58834i	−0.803903	+	0.594760i	$0.797247\pi$
$992$	−174190.	−	478583.i	−0.177011	−	0.486333i
$993$		0			0
$994$	395918.	−	332215.i	0.400713	−	0.336238i
$995$	825127.	−	2.26702e6i	0.833441	−	2.28986i
$996$		0			0
$997$	−199375.	+	1.13071e6i	−0.200576	+	1.13752i	0.703675	+	0.710522i	$0.251541\pi$
$997$	−199375.	+	1.13071e6i	−0.200576	+	1.13752i	−0.904251	+	0.427002i	$0.859570\pi$
$998$			970804.i			0.974699i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.5.f.a.8.4		66
3.2	odd	2		27.5.f.a.2.8	✓	66
27.13	even	9		27.5.f.a.14.8	yes	66
27.14	odd	18	inner	81.5.f.a.71.4		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.f.a.2.8	✓	66	3.2	odd	2
27.5.f.a.14.8	yes	66	27.13	even	9
81.5.f.a.8.4		66	1.1	even	1	trivial
81.5.f.a.71.4		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)

\(f(q)\)	\(=\)	\(q+(-2.89555 - 0.510564i) q^{2} +(-6.91152 - 2.51559i) q^{4} +(-31.8237 - 37.9260i) q^{5} +(28.2667 - 10.2882i) q^{7} +(59.4692 + 34.3346i) q^{8} +(72.7837 + 126.065i) q^{10} +(-75.7716 + 90.3011i) q^{11} +(3.56465 + 20.2161i) q^{13} +(-87.1005 + 15.3582i) q^{14} +(-64.5172 - 54.1364i) q^{16} +(-203.984 + 117.770i) q^{17} +(47.7809 - 82.7590i) q^{19} +(124.544 + 342.182i) q^{20} +(265.505 - 222.785i) q^{22} +(-85.2078 + 234.107i) q^{23} +(-317.105 + 1798.39i) q^{25} -60.3569i q^{26} -221.247 q^{28} +(1150.78 + 202.914i) q^{29} +(562.326 + 204.670i) q^{31} +(-547.062 - 651.963i) q^{32} +(650.776 - 236.863i) q^{34} +(-1289.74 - 744.633i) q^{35} +(-123.627 - 214.128i) q^{37} +(-180.606 + 215.238i) q^{38} +(-590.358 - 3348.09i) q^{40} +(508.880 - 89.7293i) q^{41} +(-1990.16 - 1669.95i) q^{43} +(750.857 - 433.508i) q^{44} +(366.250 - 634.364i) q^{46} +(176.156 + 483.984i) q^{47} +(-1146.12 + 961.705i) q^{49} +(1836.39 - 5045.44i) q^{50} +(26.2183 - 148.692i) q^{52} +3241.10i q^{53} +5836.10 q^{55} +(2034.24 + 358.691i) q^{56} +(-3228.55 - 1175.09i) q^{58} +(-1210.50 - 1442.62i) q^{59} +(-4396.97 + 1600.37i) q^{61} +(-1523.75 - 879.736i) q^{62} +(1924.95 + 3334.11i) q^{64} +(653.278 - 778.546i) q^{65} +(-473.625 - 2686.06i) q^{67} +(1706.10 - 300.832i) q^{68} +(3354.34 + 2814.62i) q^{70} +(-5060.73 + 2921.81i) q^{71} +(-1626.01 + 2816.33i) q^{73} +(248.643 + 683.140i) q^{74} +(-538.427 + 451.794i) q^{76} +(-1212.77 + 3332.07i) q^{77} +(322.322 - 1827.98i) q^{79} +4169.70i q^{80} -1519.30 q^{82} +(1228.73 + 216.659i) q^{83} +(10958.1 + 3988.42i) q^{85} +(4910.01 + 5851.52i) q^{86} +(-7606.53 + 2768.55i) q^{88} +(-6163.24 - 3558.35i) q^{89} +(308.749 + 534.769i) q^{91} +(1177.83 - 1403.68i) q^{92} +(-262.964 - 1491.34i) q^{94} +(-4659.29 + 821.558i) q^{95} +(7251.91 + 6085.08i) q^{97} +(3809.65 - 2199.50i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} - 1137 q^{14} - 54 q^{16} + 9 q^{17} - 3 q^{19} + 2487 q^{20} + 1002 q^{22} + 2724 q^{23} + 435 q^{25} - 12 q^{28}+ \cdots + 259938 q^{98}+O(q^{100}) \) 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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