LMFDB - Embedded newform 630.4.bo.b.89.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,4,Mod(89,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("630.89");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	630.bo (of order $6$, degree $2$, 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:	$37.1712033036$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.9
Character	$\chi$	$=$	630.89
Dual form			630.4.bo.b.269.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-3.68683 + 10.5550i) q^{5} +(-16.1725 - 9.02502i) q^{7} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-3.68683 + 10.5550i) q^{5} +(-16.1725 - 9.02502i) q^{7} -8.00000 q^{8} +(14.5949 + 16.9407i) q^{10} +(45.4573 - 26.2448i) q^{11} +35.2498 q^{13} +(-31.8043 + 18.9865i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(-49.3571 + 28.4963i) q^{17} +(-62.1955 - 35.9086i) q^{19} +(43.9371 - 8.33836i) q^{20} -104.979i q^{22} +(-65.3635 + 113.213i) q^{23} +(-97.8145 - 77.8288i) q^{25} +(35.2498 - 61.0544i) q^{26} +(1.08137 + 74.0731i) q^{28} +60.9387i q^{29} +(-76.9739 + 44.4409i) q^{31} +(16.0000 + 27.7128i) q^{32} +113.985i q^{34} +(154.884 - 137.426i) q^{35} +(280.463 + 161.925i) q^{37} +(-124.391 + 71.8172i) q^{38} +(29.4947 - 84.4397i) q^{40} +426.208 q^{41} +536.476i q^{43} +(-181.829 - 104.979i) q^{44} +(130.727 + 226.426i) q^{46} +(278.107 + 160.565i) q^{47} +(180.098 + 291.914i) q^{49} +(-232.618 + 91.5909i) q^{50} +(-70.4996 - 122.109i) q^{52} +(-215.372 - 373.036i) q^{53} +(109.419 + 576.560i) q^{55} +(129.380 + 72.2002i) q^{56} +(105.549 + 60.9387i) q^{58} +(334.131 + 578.732i) q^{59} +(554.467 + 320.122i) q^{61} +177.764i q^{62} +64.0000 q^{64} +(-129.960 + 372.060i) q^{65} +(-720.975 + 416.255i) q^{67} +(197.428 + 113.985i) q^{68} +(-83.1451 - 405.693i) q^{70} -1107.40i q^{71} +(9.18705 + 15.9124i) q^{73} +(560.926 - 323.851i) q^{74} +287.269i q^{76} +(-972.017 + 14.1902i) q^{77} +(-422.703 + 732.142i) q^{79} +(-116.759 - 135.526i) q^{80} +(426.208 - 738.214i) q^{82} +407.470i q^{83} +(-118.806 - 626.023i) q^{85} +(929.204 + 536.476i) q^{86} +(-363.658 + 209.958i) q^{88} +(629.442 - 1090.22i) q^{89} +(-570.076 - 318.130i) q^{91} +522.908 q^{92} +(556.214 - 321.130i) q^{94} +(608.318 - 524.082i) q^{95} -295.338 q^{97} +(685.708 - 20.0251i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{2} - 96 q^{4} + 18 q^{5} - 384 q^{8}+O(q^{10}) $ 48 * q + 48 * q^2 - 96 * q^4 + 18 * q^5 - 384 * q^8	$ 48 q + 48 q^{2} - 96 q^{4} + 18 q^{5} - 384 q^{8} + 36 q^{10} - 384 q^{16} - 432 q^{19} + 216 q^{23} + 78 q^{25} + 828 q^{31} + 768 q^{32} + 348 q^{35} - 864 q^{38} - 144 q^{40} - 432 q^{46} + 324 q^{47} + 588 q^{49} + 312 q^{50} - 96 q^{53} + 2592 q^{61} + 3072 q^{64} - 252 q^{65} + 564 q^{70} - 3768 q^{77} - 756 q^{79} - 288 q^{80} - 960 q^{85} - 4476 q^{91} - 1728 q^{92} + 648 q^{94} - 1332 q^{95} + 2280 q^{98}+O(q^{100}) $ 48 * q + 48 * q^2 - 96 * q^4 + 18 * q^5 - 384 * q^8 + 36 * q^10 - 384 * q^16 - 432 * q^19 + 216 * q^23 + 78 * q^25 + 828 * q^31 + 768 * q^32 + 348 * q^35 - 864 * q^38 - 144 * q^40 - 432 * q^46 + 324 * q^47 + 588 * q^49 + 312 * q^50 - 96 * q^53 + 2592 * q^61 + 3072 * q^64 - 252 * q^65 + 564 * q^70 - 3768 * q^77 - 756 * q^79 - 288 * q^80 - 960 * q^85 - 4476 * q^91 - 1728 * q^92 + 648 * q^94 - 1332 * q^95 + 2280 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	−3.68683	+	10.5550i	−0.329760	+	0.944065i
$5$	−3.68683	+	10.5550i	−0.329760	+	0.944065i
$6$		0			0
$7$	−16.1725	−	9.02502i	−0.873232	−	0.487305i
$7$	−16.1725	−	9.02502i	−0.873232	−	0.487305i
$8$	−8.00000			−0.353553
$9$		0			0
$10$	14.5949	+	16.9407i	0.461531	+	0.535713i
$11$	45.4573	−	26.2448i	1.24599	−	0.719373i	0.275683	−	0.961249i	$-0.411096\pi$
$11$	45.4573	−	26.2448i	1.24599	−	0.719373i	0.970307	+	0.241876i	$0.0777627\pi$
$12$		0			0
$13$	35.2498			0.752041			0.376020	−	0.926611i	$-0.377292\pi$
$13$	35.2498			0.752041			0.376020	+	0.926611i	$0.377292\pi$
$14$	−31.8043	+	18.9865i	−0.607146	+	0.362455i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−49.3571	+	28.4963i	−0.704167	+	0.406551i	−0.808898	−	0.587949i	$-0.799935\pi$
$17$	−49.3571	+	28.4963i	−0.704167	+	0.406551i	0.104730	+	0.994501i	$0.466602\pi$
$18$		0			0
$19$	−62.1955	−	35.9086i	−0.750980	−	0.433579i	0.0750677	−	0.997178i	$-0.476083\pi$
$19$	−62.1955	−	35.9086i	−0.750980	−	0.433579i	−0.826048	+	0.563600i	$0.809416\pi$
$20$	43.9371	−	8.33836i	0.491232	−	0.0932257i
$21$		0			0
$22$		−	104.979i		−	1.01735i
$23$	−65.3635	+	113.213i	−0.592575	+	1.02637i	0.401309	+	0.915943i	$0.368555\pi$
$23$	−65.3635	+	113.213i	−0.592575	+	1.02637i	−0.993884	+	0.110427i	$0.964778\pi$
$24$		0			0
$25$	−97.8145	−	77.8288i	−0.782516	−	0.622630i
$26$	35.2498	−	61.0544i	0.265887	−	0.460529i
$27$		0			0
$28$	1.08137	+	74.0731i	0.00729857	+	0.499947i
$29$			60.9387i			0.390208i	0.980783	+	0.195104i	$0.0625045\pi$
$29$			60.9387i			0.390208i	−0.980783	+	0.195104i	$0.937496\pi$
$30$		0			0
$31$	−76.9739	+	44.4409i	−0.445965	+	0.257478i	−0.706125	−	0.708088i	$-0.749558\pi$
$31$	−76.9739	+	44.4409i	−0.445965	+	0.257478i	0.260159	+	0.965566i	$0.416225\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$		0			0
$34$			113.985i			0.574950i
$35$	154.884	−	137.426i	0.748005	−	0.663693i
$36$		0			0
$37$	280.463	+	161.925i	1.24616	+	0.719469i	0.970341	−	0.241741i	$-0.0777185\pi$
$37$	280.463	+	161.925i	1.24616	+	0.719469i	0.275816	+	0.961210i	$0.411052\pi$
$38$	−124.391	+	71.8172i	−0.531023	+	0.306586i
$39$		0			0
$40$	29.4947	−	84.4397i	0.116588	−	0.333777i
$41$	426.208			1.62348			0.811738	−	0.584022i	$-0.198522\pi$
$41$	426.208			1.62348			0.811738	+	0.584022i	$0.198522\pi$
$42$		0			0
$43$			536.476i			1.90260i	0.308265	+	0.951300i	$0.400252\pi$
$43$			536.476i			1.90260i	−0.308265	+	0.951300i	$0.599748\pi$
$44$	−181.829	−	104.979i	−0.622995	−	0.359686i
$45$		0			0
$46$	130.727	+	226.426i	0.419014	+	0.725753i
$47$	278.107	+	160.565i	0.863108	+	0.498316i	0.865052	−	0.501683i	$-0.167285\pi$
$47$	278.107	+	160.565i	0.863108	+	0.498316i	−0.00194390	+	0.999998i	$0.500619\pi$
$48$		0			0
$49$	180.098	+	291.914i	0.525067	+	0.851061i
$50$	−232.618	+	91.5909i	−0.657943	+	0.259058i
$51$		0			0
$52$	−70.4996	−	122.109i	−0.188010	−	0.325643i
$53$	−215.372	−	373.036i	−0.558182	−	0.966800i	−0.997648	−	0.0685407i	$-0.978166\pi$
$53$	−215.372	−	373.036i	−0.558182	−	0.966800i	0.439466	−	0.898259i	$-0.355168\pi$
$54$		0			0
$55$	109.419	+	576.560i	0.268256	+	1.41352i
$56$	129.380	+	72.2002i	0.308734	+	0.172288i
$57$		0			0
$58$	105.549	+	60.9387i	0.238953	+	0.137959i
$59$	334.131	+	578.732i	0.737291	+	1.27702i	0.953711	+	0.300725i	$0.0972285\pi$
$59$	334.131	+	578.732i	0.737291	+	1.27702i	−0.216420	+	0.976300i	$0.569438\pi$
$60$		0			0
$61$	554.467	+	320.122i	1.16381	+	0.671924i	0.952213	−	0.305434i	$-0.0988014\pi$
$61$	554.467	+	320.122i	1.16381	+	0.671924i	0.211593	+	0.977358i	$0.432135\pi$
$62$			177.764i			0.364129i
$63$		0			0
$64$	64.0000			0.125000
$65$	−129.960	+	372.060i	−0.247993	+	0.709975i
$66$		0			0
$67$	−720.975	+	416.255i	−1.31464	+	0.759009i	−0.982861	−	0.184347i	$-0.940983\pi$
$67$	−720.975	+	416.255i	−1.31464	+	0.759009i	−0.331781	+	0.943356i	$0.607650\pi$
$68$	197.428	+	113.985i	0.352084	+	0.203276i
$69$		0			0
$70$	−83.1451	−	405.693i	−0.141968	−	0.692709i
$71$		−	1107.40i		−	1.85105i	−0.378688	−	0.925524i	$-0.623625\pi$
$71$		−	1107.40i		−	1.85105i	0.378688	−	0.925524i	$-0.376375\pi$
$72$		0			0
$73$	9.18705	+	15.9124i	0.0147296	+	0.0255125i	0.873296	−	0.487190i	$-0.161978\pi$
$73$	9.18705	+	15.9124i	0.0147296	+	0.0255125i	−0.858567	+	0.512702i	$0.828645\pi$
$74$	560.926	−	323.851i	0.881166	−	0.508742i
$75$		0			0
$76$			287.269i			0.433579i
$77$	−972.017	+	14.1902i	−1.43859	+	0.0210016i
$78$		0			0
$79$	−422.703	+	732.142i	−0.601997	+	1.04269i	0.390522	+	0.920594i	$0.372295\pi$
$79$	−422.703	+	732.142i	−0.601997	+	1.04269i	−0.992518	+	0.122095i	$0.961039\pi$
$80$	−116.759	−	135.526i	−0.163176	−	0.189403i
$81$		0			0
$82$	426.208	−	738.214i	0.573985	−	0.994172i
$83$			407.470i			0.538863i	0.963020	+	0.269431i	$0.0868357\pi$
$83$			407.470i			0.538863i	−0.963020	+	0.269431i	$0.913164\pi$
$84$		0			0
$85$	−118.806	−	626.023i	−0.151604	−	0.798844i
$86$	929.204	+	536.476i	1.16510	+	0.672671i
$87$		0			0
$88$	−363.658	+	209.958i	−0.440524	+	0.254337i
$89$	629.442	−	1090.22i	0.749671	−	1.29847i	−0.198310	−	0.980139i	$-0.563545\pi$
$89$	629.442	−	1090.22i	0.749671	−	1.29847i	0.947981	−	0.318328i	$-0.103121\pi$
$90$		0			0
$91$	−570.076	−	318.130i	−0.656706	−	0.366473i
$92$	522.908			0.592575
$93$		0			0
$94$	556.214	−	321.130i	0.610309	−	0.352362i
$95$	608.318	−	524.082i	0.656970	−	0.565997i
$96$		0			0
$97$	−295.338			−0.309145			−0.154572	−	0.987981i	$-0.549400\pi$
$97$	−295.338			−0.309145			−0.154572	+	0.987981i	$0.549400\pi$
$98$	685.708	−	20.0251i	0.706805	−	0.0206413i
$99$		0			0
$100$	−73.9778	+	494.497i	−0.0739778	+	0.494497i
$101$	627.962	+	1087.66i	0.618658	+	1.07155i	0.989731	+	0.142944i	$0.0456569\pi$
$101$	627.962	+	1087.66i	0.618658	+	1.07155i	−0.371072	+	0.928604i	$0.621010\pi$
$102$		0			0
$103$	−400.341	+	693.412i	−0.382979	+	0.663339i	−0.991487	−	0.130209i	$-0.958435\pi$
$103$	−400.341	+	693.412i	−0.382979	+	0.663339i	0.608508	+	0.793548i	$0.291768\pi$
$104$	−281.998			−0.265887
$105$		0			0
$106$	−861.489			−0.789389
$107$	−573.476	+	993.290i	−0.518131	+	0.897430i	0.481647	+	0.876365i	$0.340039\pi$
$107$	−573.476	+	993.290i	−0.518131	+	0.897430i	−0.999778	+	0.0210643i	$0.993295\pi$
$108$		0			0
$109$	749.687	+	1298.50i	0.658780	+	1.14104i	0.980932	+	0.194352i	$0.0622604\pi$
$109$	749.687	+	1298.50i	0.658780	+	1.14104i	−0.322152	+	0.946688i	$0.604406\pi$
$110$	1108.05	+	387.041i	0.960441	+	0.335481i
$111$		0			0
$112$	254.434	−	151.892i	0.214659	−	0.128147i
$113$	279.248			0.232473			0.116236	−	0.993222i	$-0.462917\pi$
$113$	279.248			0.232473			0.116236	+	0.993222i	$0.462917\pi$
$114$		0			0
$115$	−953.973	−	1107.31i	−0.773552	−	0.897885i
$116$	211.098	−	121.877i	0.168965	−	0.0975520i
$117$		0			0
$118$	1336.52			1.04269
$119$	1055.41	−	15.4075i	0.813016	−	0.0118690i
$120$		0			0
$121$	712.077	−	1233.35i	0.534994	−	0.926637i
$122$	1108.93	−	640.243i	0.822936	−	0.475122i
$123$		0			0
$124$	307.896	+	177.764i	0.222983	+	0.128739i
$125$	1182.11	−	745.487i	0.845846	−	0.533427i
$126$		0			0
$127$			341.443i			0.238568i	0.992860	+	0.119284i	$0.0380600\pi$
$127$			341.443i			0.238568i	−0.992860	+	0.119284i	$0.961940\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$		0			0
$130$	514.467	+	597.158i	0.347090	+	0.402878i
$131$	−658.398	+	1140.38i	−0.439118	+	0.760575i	−0.997622	−	0.0689271i	$-0.978042\pi$
$131$	−658.398	+	1140.38i	−0.439118	+	0.760575i	0.558504	+	0.829502i	$0.311376\pi$
$132$		0			0
$133$	681.780	+	1142.05i	0.444495	+	0.744571i
$134$			1665.02i			1.07340i
$135$		0			0
$136$	394.857	−	227.971i	0.248961	−	0.143738i
$137$	−1176.26	−	2037.35i	−0.733541	−	1.27053i	−0.955361	−	0.295442i	$-0.904533\pi$
$137$	−1176.26	−	2037.35i	−0.733541	−	1.27053i	0.221820	−	0.975088i	$-0.428800\pi$
$138$		0			0
$139$			1504.59i			0.918113i	0.888407	+	0.459056i	$0.151812\pi$
$139$			1504.59i			0.918113i	−0.888407	+	0.459056i	$0.848188\pi$
$140$	−785.826	−	261.681i	−0.474389	−	0.157972i
$141$		0			0
$142$	−1918.08	−	1107.40i	−1.13353	−	0.654444i
$143$	1602.36	−	925.123i	0.937035	−	0.540998i
$144$		0			0
$145$	−643.206	−	224.671i	−0.368382	−	0.128675i
$146$	36.7482			0.0208309
$147$		0			0
$148$		−	1295.40i		−	0.719469i
$149$	418.349	+	241.534i	0.230017	+	0.132800i	0.610580	−	0.791955i	$-0.290936\pi$
$149$	418.349	+	241.534i	0.230017	+	0.132800i	−0.380563	+	0.924755i	$0.624270\pi$
$150$		0			0
$151$	−989.430	−	1713.74i	−0.533236	−	0.923592i	−0.999246	−	0.0388129i	$-0.987642\pi$
$151$	−989.430	−	1713.74i	−0.533236	−	0.923592i	0.466010	−	0.884779i	$-0.345691\pi$
$152$	497.564	+	287.269i	0.265512	+	0.153293i
$153$		0			0
$154$	−947.439	+	1697.77i	−0.495758	+	0.888379i
$155$	−185.282	−	976.303i	−0.0960144	−	0.505926i
$156$		0			0
$157$	−119.367	−	206.750i	−0.0606787	−	0.105099i	0.834090	−	0.551628i	$-0.185993\pi$
$157$	−119.367	−	206.750i	−0.0606787	−	0.105099i	−0.894769	+	0.446529i	$0.852660\pi$
$158$	845.405	+	1464.28i	0.425676	+	0.737293i
$159$		0			0
$160$	−351.497	+	66.7069i	−0.173677	+	0.0329603i
$161$	2078.84	−	1241.03i	1.01761	−	0.607494i
$162$		0			0
$163$	−2558.66	−	1477.24i	−1.22951	−	0.709856i	−0.262580	−	0.964910i	$-0.584573\pi$
$163$	−2558.66	−	1477.24i	−1.22951	−	0.709856i	−0.966927	+	0.255054i	$0.917907\pi$
$164$	−852.416	−	1476.43i	−0.405869	−	0.702986i
$165$		0			0
$166$	705.758	+	407.470i	0.329985	+	0.190517i
$167$		−	209.350i		−	0.0970059i	−0.998823	−	0.0485030i	$-0.984555\pi$
$167$		−	209.350i		−	0.0970059i	0.998823	−	0.0485030i	$-0.0154450\pi$
$168$		0			0
$169$	−954.453			−0.434435
$170$	−1203.11	−	420.245i	−0.542790	−	0.189596i
$171$		0			0
$172$	1858.41	−	1072.95i	0.823850	−	0.475650i
$173$	811.040	+	468.254i	0.356429	+	0.205784i	0.667513	−	0.744598i	$-0.267359\pi$
$173$	811.040	+	468.254i	0.356429	+	0.205784i	−0.311084	+	0.950382i	$0.600692\pi$
$174$		0			0
$175$	879.497	+	2141.46i	0.379907	+	0.925025i
$176$			839.833i			0.359686i
$177$		0			0
$178$	−1258.88	−	2180.45i	−0.530097	−	0.918155i
$179$	−2025.65	+	1169.51i	−0.845833	+	0.488342i	−0.859243	−	0.511568i	$-0.829065\pi$
$179$	−2025.65	+	1169.51i	−0.845833	+	0.488342i	0.0134100	+	0.999910i	$0.495731\pi$
$180$		0			0
$181$		−	418.039i		−	0.171672i	−0.996309	−	0.0858358i	$-0.972644\pi$
$181$		−	418.039i		−	0.171672i	0.996309	−	0.0858358i	$-0.0273561\pi$
$182$	−1121.09	+	669.271i	−0.456599	+	0.272581i
$183$		0			0
$184$	522.908	−	905.703i	0.209507	−	0.362877i
$185$	−2743.14	+	2363.28i	−1.09016	+	0.939201i
$186$		0			0
$187$	−1495.76	+	2590.73i	−0.584924	+	1.01312i
$188$		−	1284.52i		−	0.498316i
$189$		0			0
$190$	−299.419	−	1577.72i	−0.114327	−	0.602420i
$191$	−1152.98	−	665.675i	−0.436790	−	0.252181i	0.265445	−	0.964126i	$-0.414481\pi$
$191$	−1152.98	−	665.675i	−0.436790	−	0.252181i	−0.702235	+	0.711945i	$0.747815\pi$
$192$		0			0
$193$	−2301.82	+	1328.96i	−0.858492	+	0.495651i	−0.863507	−	0.504337i	$-0.831737\pi$
$193$	−2301.82	+	1328.96i	−0.858492	+	0.495651i	0.00501499	+	0.999987i	$0.498404\pi$
$194$	−295.338	+	511.540i	−0.109299	+	0.189312i
$195$		0			0
$196$	651.023	−	1207.71i	0.237253	−	0.440126i
$197$	1474.79			0.533372			0.266686	−	0.963783i	$-0.414071\pi$
$197$	1474.79			0.533372			0.266686	+	0.963783i	$0.414071\pi$
$198$		0			0
$199$	2621.59	−	1513.58i	0.933868	−	0.539169i	0.0458353	−	0.998949i	$-0.485405\pi$
$199$	2621.59	−	1513.58i	0.933868	−	0.539169i	0.888033	+	0.459780i	$0.152072\pi$
$200$	782.516	+	622.630i	0.276661	+	0.220133i
$201$		0			0
$202$	2511.85			0.874915
$203$	549.973	−	985.530i	0.190150	−	0.340742i
$204$		0			0
$205$	−1571.36	+	4498.61i	−0.535358	+	1.53267i
$206$	800.683	+	1386.82i	0.270807	+	0.469051i
$207$		0			0
$208$	−281.998	+	488.435i	−0.0940051	+	0.162822i
$209$	−3769.65			−1.24762
$210$		0			0
$211$	2456.43			0.801459			0.400729	−	0.916196i	$-0.368757\pi$
$211$	2456.43			0.801459			0.400729	+	0.916196i	$0.368757\pi$
$212$	−861.489	+	1492.14i	−0.279091	+	0.483400i
$213$		0			0
$214$	1146.95	+	1986.58i	0.366374	+	0.634579i
$215$	−5662.49	−	1977.90i	−1.79618	−	0.627402i
$216$		0			0
$217$	1645.94	−	24.0286i	0.514901	−	0.00751689i
$218$	2998.75			0.931655
$219$		0			0
$220$	1778.42	−	1532.16i	0.545006	−	0.469537i
$221$	−1739.83	+	1004.49i	−0.529563	+	0.305743i
$222$		0			0
$223$	4383.32			1.31627			0.658136	−	0.752899i	$-0.271345\pi$
$223$	4383.32			1.31627			0.658136	+	0.752899i	$0.271345\pi$
$224$	−8.65097	−	592.585i	−0.00258043	−	0.176758i
$225$		0			0
$226$	279.248	−	483.671i	0.0821915	−	0.142360i
$227$	−758.674	+	438.020i	−0.221828	+	0.128072i	−0.606796	−	0.794857i	$-0.707546\pi$
$227$	−758.674	+	438.020i	−0.221828	+	0.128072i	0.384968	+	0.922930i	$0.374212\pi$
$228$		0			0
$229$	−3323.63	−	1918.90i	−0.959092	−	0.553732i	−0.0631983	−	0.998001i	$-0.520130\pi$
$229$	−3323.63	−	1918.90i	−0.959092	−	0.553732i	−0.895893	+	0.444269i	$0.853463\pi$
$230$	−2871.88	+	545.024i	−0.823332	+	0.156251i
$231$		0			0
$232$		−	487.510i		−	0.137959i
$233$	773.998	−	1340.60i	0.217624	−	0.376935i	−0.736457	−	0.676484i	$-0.763503\pi$
$233$	773.998	−	1340.60i	0.217624	−	0.376935i	0.954081	+	0.299549i	$0.0968361\pi$
$234$		0			0
$235$	−2720.09	+	2343.43i	−0.755061	+	0.650505i
$236$	1336.52	−	2314.93i	0.368645	−	0.638512i
$237$		0			0
$238$	1028.72	−	1843.42i	0.280176	−	0.502065i
$239$		−	1657.78i		−	0.448674i	−0.974512	−	0.224337i	$-0.927978\pi$
$239$		−	1657.78i		−	0.448674i	0.974512	−	0.224337i	$-0.0720217\pi$
$240$		0			0
$241$	2853.90	−	1647.70i	0.762803	−	0.440405i	−0.0674979	−	0.997719i	$-0.521502\pi$
$241$	2853.90	−	1647.70i	0.762803	−	0.440405i	0.830301	+	0.557315i	$0.188168\pi$
$242$	−1424.15	−	2466.71i	−0.378298	−	0.655231i
$243$		0			0
$244$		−	2560.97i		−	0.671924i
$245$	−3745.13	+	824.691i	−0.976603	+	0.215051i
$246$		0			0
$247$	−2192.38	−	1265.77i	−0.564768	−	0.326069i
$248$	615.791	−	355.527i	0.157673	−	0.0910323i
$249$		0			0
$250$	−109.116	−	2792.95i	−0.0276043	−	0.706568i
$251$	4187.23			1.05297			0.526485	−	0.850184i	$-0.323510\pi$
$251$	4187.23			1.05297			0.526485	+	0.850184i	$0.323510\pi$
$252$		0			0
$253$			6861.80i			1.70513i
$254$	591.397	+	341.443i	0.146093	+	0.0843467i
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	3878.95	+	2239.51i	0.941487	+	0.543568i	0.890426	−	0.455127i	$-0.150406\pi$
$257$	3878.95	+	2239.51i	0.941487	+	0.543568i	0.0510612	+	0.998696i	$0.483740\pi$
$258$		0			0
$259$	−3074.40	−	5149.92i	−0.737583	−	1.23552i
$260$	1548.77	−	293.926i	0.369427	−	0.0701096i
$261$		0			0
$262$	1316.80	+	2280.76i	0.310503	+	0.537808i
$263$	1100.56	+	1906.23i	0.258036	+	0.446931i	0.965716	−	0.259602i	$-0.0835914\pi$
$263$	1100.56	+	1906.23i	0.258036	+	0.446931i	−0.707680	+	0.706533i	$0.750258\pi$
$264$		0			0
$265$	4731.42	−	897.926i	1.09679	−	0.208148i
$266$	2659.86	−	38.8305i	0.613108	−	0.00895057i
$267$		0			0
$268$	2883.90	+	1665.02i	0.657321	+	0.379505i
$269$	−1474.54	−	2553.98i	−0.334217	−	0.578882i	0.649117	−	0.760689i	$-0.275139\pi$
$269$	−1474.54	−	2553.98i	−0.334217	−	0.578882i	−0.983334	+	0.181807i	$0.941805\pi$
$270$		0			0
$271$	−4641.45	−	2679.75i	−1.04040	−	0.600675i	−0.120453	−	0.992719i	$-0.538435\pi$
$271$	−4641.45	−	2679.75i	−1.04040	−	0.600675i	−0.919946	+	0.392044i	$0.871768\pi$
$272$		−	911.882i		−	0.203276i
$273$		0			0
$274$	−4705.06			−1.03738
$275$	−6488.98	−	970.765i	−1.42291	−	0.212870i
$276$		0			0
$277$	4487.02	−	2590.58i	0.973281	−	0.561924i	0.0730461	−	0.997329i	$-0.476728\pi$
$277$	4487.02	−	2590.58i	0.973281	−	0.561924i	0.900235	+	0.435405i	$0.143395\pi$
$278$	2606.03	+	1504.59i	0.562227	+	0.324602i
$279$		0			0
$280$	−1239.07	+	1099.41i	−0.264460	+	0.234651i
$281$		−	2863.38i		−	0.607883i	−0.952691	−	0.303941i	$-0.901697\pi$
$281$		−	2863.38i		−	0.607883i	0.952691	−	0.303941i	$-0.0983027\pi$
$282$		0			0
$283$	3539.53	+	6130.65i	0.743474	+	1.28774i	0.950904	+	0.309485i	$0.100157\pi$
$283$	3539.53	+	6130.65i	0.743474	+	1.28774i	−0.207430	+	0.978250i	$0.566510\pi$
$284$	−3836.15	+	2214.80i	−0.801528	+	0.462762i
$285$		0			0
$286$		−	3700.49i		−	0.765086i
$287$	−6892.84	−	3846.54i	−1.41767	−	0.791128i
$288$		0			0
$289$	−832.420	+	1441.79i	−0.169432	+	0.293465i
$290$	−1032.35	+	889.394i	−0.209040	+	0.180093i
$291$		0			0
$292$	36.7482	−	63.6498i	0.00736482	−	0.0127562i
$293$		−	6984.80i		−	1.39268i	−0.717711	−	0.696342i	$-0.754810\pi$
$293$		−	6984.80i		−	1.39268i	0.717711	−	0.696342i	$-0.245190\pi$
$294$		0			0
$295$	−7340.38	+	1393.05i	−1.44872	+	0.274938i
$296$	−2243.70	−	1295.40i	−0.440583	−	0.254371i
$297$		0			0
$298$	836.698	−	483.068i	0.162646	−	0.0939039i
$299$	−2304.05	+	3990.73i	−0.445641	+	0.771872i
$300$		0			0
$301$	4841.71	−	8676.15i	0.927147	−	1.66141i
$302$	−3957.72			−0.754110
$303$		0			0
$304$	995.128	−	574.537i	0.187745	−	0.108395i
$305$	−5423.10	+	4672.14i	−1.01812	+	0.877135i
$306$		0			0
$307$	−7793.65			−1.44888			−0.724441	−	0.689336i	$-0.757902\pi$
$307$	−7793.65			−1.44888			−0.724441	+	0.689336i	$0.757902\pi$
$308$	1993.19	+	3338.78i	0.368742	+	0.617678i
$309$		0			0
$310$	−1876.29	−	655.385i	−0.343761	−	0.120075i
$311$	3164.63	+	5481.30i	0.577008	+	0.999408i	0.995820	+	0.0913346i	$0.0291133\pi$
$311$	3164.63	+	5481.30i	0.577008	+	0.999408i	−0.418812	+	0.908073i	$0.637553\pi$
$312$		0			0
$313$	150.749	−	261.105i	0.0272232	−	0.0471519i	−0.852093	−	0.523391i	$-0.824667\pi$
$313$	150.749	−	261.105i	0.0272232	−	0.0471519i	0.879316	+	0.476239i	$0.158000\pi$
$314$	−477.469			−0.0858126
$315$		0			0
$316$	3381.62			0.601997
$317$	−4353.20	+	7539.97i	−0.771294	+	1.33592i	0.165560	+	0.986200i	$0.447057\pi$
$317$	−4353.20	+	7539.97i	−0.771294	+	1.33592i	−0.936854	+	0.349720i	$0.886277\pi$
$318$		0			0
$319$	1599.32	+	2770.11i	0.280705	+	0.486195i
$320$	−235.957	+	675.518i	−0.0412200	+	0.118008i
$321$		0			0
$322$	−70.6822	−	4841.68i	−0.0122328	−	0.837938i
$323$	4093.05			0.705088
$324$		0			0
$325$	−3447.94	−	2743.45i	−0.588484	−	0.468243i
$326$	−5117.32	+	2954.48i	−0.869393	+	0.501944i
$327$		0			0
$328$	−3409.66			−0.573985
$329$	−3048.58	−	5106.66i	−0.510861	−	0.855742i
$330$		0			0
$331$	3195.96	−	5535.57i	0.530713	−	0.919222i	−0.468645	−	0.883387i	$-0.655258\pi$
$331$	3195.96	−	5535.57i	0.530713	−	0.919222i	0.999358	−	0.0358349i	$-0.0114090\pi$
$332$	1411.52	−	814.939i	0.233334	−	0.134716i
$333$		0			0
$334$	−362.605	−	209.350i	−0.0594037	−	0.0342968i
$335$	−1735.44	−	9144.52i	−0.283037	−	1.49140i
$336$		0			0
$337$			4996.62i			0.807666i	0.914833	+	0.403833i	$0.132322\pi$
$337$			4996.62i			0.807666i	−0.914833	+	0.403833i	$0.867678\pi$
$338$	−954.453	+	1653.16i	−0.153596	+	0.266036i
$339$		0			0
$340$	−1931.00	+	1663.60i	−0.308009	+	0.265358i
$341$	−2332.68	+	4040.33i	−0.370445	+	0.641630i
$342$		0			0
$343$	−278.104	−	6346.36i	−0.0437790	−	0.999041i
$344$		−	4291.81i		−	0.672671i
$345$		0			0
$346$	1622.08	−	936.508i	0.252033	−	0.145511i
$347$	−260.072	−	450.458i	−0.0402345	−	0.0696883i	0.845207	−	0.534439i	$-0.179477\pi$
$347$	−260.072	−	450.458i	−0.0402345	−	0.0696883i	−0.885441	+	0.464751i	$0.846144\pi$
$348$		0			0
$349$			4412.16i			0.676726i	0.941016	+	0.338363i	$0.109873\pi$
$349$			4412.16i			0.676726i	−0.941016	+	0.338363i	$0.890127\pi$
$350$	4588.62	+	618.129i	0.700777	+	0.0944011i
$351$		0			0
$352$	1454.63	+	839.833i	0.220262	+	0.127168i
$353$	−11270.6	+	6507.10i	−1.69936	+	0.981127i	−0.752998	+	0.658022i	$0.771393\pi$
$353$	−11270.6	+	6507.10i	−1.69936	+	0.981127i	−0.946363	+	0.323105i	$0.895273\pi$
$354$		0			0
$355$	11688.6	+	4082.81i	1.74751	+	0.610402i
$356$	−5035.53			−0.749671
$357$		0			0
$358$			4678.03i			0.690619i
$359$	−3753.01	−	2166.80i	−0.551744	−	0.318550i	0.198081	−	0.980186i	$-0.436529\pi$
$359$	−3753.01	−	2166.80i	−0.551744	−	0.318550i	−0.749825	+	0.661636i	$0.769862\pi$
$360$		0			0
$361$	−850.647	−	1473.36i	−0.124019	−	0.214807i
$362$	−724.064	−	418.039i	−0.105127	−	0.0606951i
$363$		0			0
$364$	38.1181	+	2611.06i	0.00548882	+	0.375980i
$365$	−201.826	+	38.3025i	−0.0289427	+	0.00549272i
$366$		0			0
$367$	2709.81	+	4693.53i	0.385425	+	0.667576i	0.991828	−	0.127582i	$-0.0407215\pi$
$367$	2709.81	+	4693.53i	0.385425	+	0.667576i	−0.606403	+	0.795157i	$0.707388\pi$
$368$	−1045.82	−	1811.41i	−0.148144	−	0.256593i
$369$		0			0
$370$	1350.19	+	7114.54i	0.189711	+	0.999641i
$371$	116.449	+	7976.65i	0.0162957	+	1.11625i
$372$		0			0
$373$	617.376	+	356.442i	0.0857011	+	0.0494796i	0.542238	−	0.840225i	$-0.317577\pi$
$373$	617.376	+	356.442i	0.0857011	+	0.0494796i	−0.456537	+	0.889704i	$0.650910\pi$
$374$	2991.52	+	5181.46i	0.413604	+	0.716382i
$375$		0			0
$376$	−2224.86	−	1284.52i	−0.305155	−	0.176181i
$377$			2148.08i			0.293452i
$378$		0			0
$379$	1011.71			0.137118			0.0685592	−	0.997647i	$-0.478160\pi$
$379$	1011.71			0.137118			0.0685592	+	0.997647i	$0.478160\pi$
$380$	−3032.11	−	1059.11i	−0.409326	−	0.142977i
$381$		0			0
$382$	−2305.97	+	1331.35i	−0.308857	+	0.178319i
$383$	−995.977	−	575.028i	−0.132877	−	0.0767168i	0.432088	−	0.901832i	$-0.357777\pi$
$383$	−995.977	−	575.028i	−0.132877	−	0.0767168i	−0.564965	+	0.825115i	$0.691110\pi$
$384$		0			0
$385$	3433.89	−	10311.9i	0.454564	−	1.36505i
$386$			5315.84i			0.700956i
$387$		0			0
$388$	590.676	+	1023.08i	0.0772861	+	0.133864i
$389$	−1624.24	+	937.754i	−0.211702	+	0.122226i	−0.602102	−	0.798419i	$-0.705670\pi$
$389$	−1624.24	+	937.754i	−0.211702	+	0.122226i	0.390400	+	0.920645i	$0.372337\pi$
$390$		0			0
$391$		−	7450.47i		−	0.963648i
$392$	−1440.78	−	2335.31i	−0.185639	−	0.300895i
$393$		0			0
$394$	1474.79	−	2554.41i	0.188575	−	0.326622i
$395$	−6169.30	−	7160.90i	−0.785851	−	0.912162i
$396$		0			0
$397$	1923.72	−	3331.97i	0.243195	−	0.421226i	−0.718427	−	0.695602i	$-0.755138\pi$
$397$	1923.72	−	3331.97i	0.243195	−	0.421226i	0.961623	+	0.274375i	$0.0884711\pi$
$398$		−	6054.31i		−	0.762500i
$399$		0			0
$400$	1860.94	−	732.728i	0.232618	−	0.0915909i
$401$	2352.17	+	1358.02i	0.292922	+	0.169118i	0.639259	−	0.768992i	$-0.279241\pi$
$401$	2352.17	+	1358.02i	0.292922	+	0.169118i	−0.346337	+	0.938110i	$0.612575\pi$
$402$		0			0
$403$	−2713.31	+	1566.53i	−0.335384	+	0.193634i
$404$	2511.85	−	4350.64i	0.309329	−	0.535774i
$405$		0			0
$406$	−1157.01	−	1938.11i	−0.141433	−	0.236913i
$407$	16998.8			2.07027
$408$		0			0
$409$	−5539.60	+	3198.29i	−0.669721	+	0.386663i	−0.795971	−	0.605335i	$-0.793039\pi$
$409$	−5539.60	+	3198.29i	−0.669721	+	0.386663i	0.126250	+	0.991998i	$0.459706\pi$
$410$	6220.46	+	7220.28i	0.749285	+	0.869718i
$411$		0			0
$412$	3202.73			0.382979
$413$	−180.660	−	12375.1i	−0.0215247	−	1.47442i
$414$		0			0
$415$	−4300.83	−	1502.27i	−0.508721	−	0.177696i
$416$	563.997	+	976.871i	0.0664716	+	0.115132i
$417$		0			0
$418$	−3769.65	+	6529.23i	−0.441100	+	0.764007i
$419$	5593.44			0.652166			0.326083	−	0.945341i	$-0.394271\pi$
$419$	5593.44			0.652166			0.326083	+	0.945341i	$0.394271\pi$
$420$		0			0
$421$	−11548.2			−1.33687			−0.668435	−	0.743770i	$-0.733036\pi$
$421$	−11548.2			−1.33687			−0.668435	+	0.743770i	$0.733036\pi$
$422$	2456.43	−	4254.67i	0.283358	−	0.490791i
$423$		0			0
$424$	1722.98	+	2984.29i	0.197347	+	0.341815i
$425$	7045.67	+	1054.05i	0.804154	+	0.120303i
$426$		0			0
$427$	−6078.00	−	10181.2i	−0.688841	−	1.15387i
$428$	4587.81			0.518131
$429$		0			0
$430$	−9088.31	+	7829.82i	−1.01925	+	0.878110i
$431$	9040.92	−	5219.78i	1.01041	−	0.583359i	0.0990965	−	0.995078i	$-0.468405\pi$
$431$	9040.92	−	5219.78i	1.01041	−	0.583359i	0.911311	+	0.411719i	$0.135071\pi$
$432$		0			0
$433$	417.621			0.0463501			0.0231750	−	0.999731i	$-0.492622\pi$
$433$	417.621			0.0463501			0.0231750	+	0.999731i	$0.492622\pi$
$434$	1604.32	−	2874.88i	0.177442	−	0.317969i
$435$		0			0
$436$	2998.75	−	5193.98i	0.329390	−	0.570520i
$437$	8130.63	−	4694.22i	0.890024	−	0.513856i
$438$		0			0
$439$	−9938.51	−	5738.00i	−1.08050	−	0.623827i	−0.149469	−	0.988766i	$-0.547756\pi$
$439$	−9938.51	−	5738.00i	−1.08050	−	0.623827i	−0.931031	+	0.364940i	$0.881090\pi$
$440$	−875.354	−	4612.48i	−0.0948429	−	0.499753i
$441$		0			0
$442$			4017.96i			0.432386i
$443$	−1835.76	+	3179.63i	−0.196884	+	0.341013i	−0.947517	−	0.319707i	$-0.896416\pi$
$443$	−1835.76	+	3179.63i	−0.196884	+	0.341013i	0.750632	+	0.660720i	$0.229749\pi$
$444$		0			0
$445$	9186.64	+	10663.2i	0.978626	+	1.13592i
$446$	4383.32	−	7592.13i	0.465372	−	0.806049i
$447$		0			0
$448$	−1035.04	−	577.601i	−0.109154	−	0.0609132i
$449$			1455.54i			0.152987i	0.997070	+	0.0764936i	$0.0243725\pi$
$449$			1455.54i			0.152987i	−0.997070	+	0.0764936i	$0.975628\pi$
$450$		0			0
$451$	19374.3	−	11185.7i	2.02284	−	1.16788i
$452$	−558.496	−	967.343i	−0.0581182	−	0.100664i
$453$		0			0
$454$			1752.08i			0.181122i
$455$	5459.63	−	4844.24i	0.562530	−	0.499124i
$456$		0			0
$457$	−8916.55	−	5147.97i	−0.912688	−	0.526941i	−0.0313933	−	0.999507i	$-0.509994\pi$
$457$	−8916.55	−	5147.97i	−0.912688	−	0.526941i	−0.881295	+	0.472566i	$0.843328\pi$
$458$	−6647.27	+	3837.80i	−0.678180	+	0.391548i
$459$		0			0
$460$	−1927.87	+	5519.27i	−0.195408	+	0.559429i
$461$	19024.2			1.92200			0.961001	−	0.276543i	$-0.0891889\pi$
$461$	19024.2			1.92200			0.961001	+	0.276543i	$0.0891889\pi$
$462$		0			0
$463$		−	5344.69i		−	0.536477i	−0.963353	−	0.268239i	$-0.913558\pi$
$463$		−	5344.69i		−	0.536477i	0.963353	−	0.268239i	$-0.0864415\pi$
$464$	−844.392	−	487.510i	−0.0844825	−	0.0487760i
$465$		0			0
$466$	−1548.00	−	2681.21i	−0.153883	−	0.266534i
$467$	−1422.48	−	821.269i	−0.140952	−	0.0813786i	0.427866	−	0.903842i	$-0.359266\pi$
$467$	−1422.48	−	821.269i	−0.140952	−	0.0813786i	−0.568818	+	0.822464i	$0.692599\pi$
$468$		0			0
$469$	15416.7	−	225.063i	1.51786	−	0.0221587i
$470$	1338.85	+	7054.77i	0.131397	+	0.692367i
$471$		0			0
$472$	−2673.05	−	4629.85i	−0.260672	−	0.451496i
$473$	14079.7	+	24386.8i	1.36868	+	2.37062i
$474$		0			0
$475$	3288.90	+	8352.98i	0.317695	+	0.806865i
$476$	−2164.18	−	3625.22i	−0.208393	−	0.349079i
$477$		0			0
$478$	−2871.37	−	1657.78i	−0.274756	−	0.158630i
$479$	−648.990	−	1124.08i	−0.0619063	−	0.107225i	0.833411	−	0.552653i	$-0.186385\pi$
$479$	−648.990	−	1124.08i	−0.0619063	−	0.107225i	−0.895317	+	0.445429i	$0.853051\pi$
$480$		0			0
$481$	9886.26	+	5707.83i	0.937161	+	0.541070i
$482$		−	6590.79i		−	0.622826i
$483$		0			0
$484$	−5696.62			−0.534994
$485$	1088.86	−	3117.28i	0.101944	−	0.291852i
$486$		0			0
$487$	−5004.30	+	2889.23i	−0.465639	+	0.268837i	−0.714412	−	0.699725i	$-0.753306\pi$
$487$	−5004.30	+	2889.23i	−0.465639	+	0.268837i	0.248773	+	0.968562i	$0.419973\pi$
$488$	−4435.74	−	2560.97i	−0.411468	−	0.237561i
$489$		0			0
$490$	−2316.73	+	7311.45i	−0.213590	+	0.674077i
$491$			836.066i			0.0768455i	0.999262	+	0.0384228i	$0.0122334\pi$
$491$			836.066i			0.0768455i	−0.999262	+	0.0384228i	$0.987767\pi$
$492$		0			0
$493$	−1736.53	−	3007.76i	−0.158640	−	0.274772i
$494$	−4384.76	+	2531.54i	−0.399351	+	0.230566i
$495$		0			0
$496$		−	1422.11i		−	0.128739i
$497$	−9994.32	+	17909.4i	−0.902026	+	1.61639i
$498$		0			0
$499$	−8095.62	+	14022.0i	−0.726272	+	1.25794i	0.232176	+	0.972674i	$0.425415\pi$
$499$	−8095.62	+	14022.0i	−0.726272	+	1.25794i	−0.958448	+	0.285266i	$0.907918\pi$
$500$	−4946.65	−	2603.96i	−0.442442	−	0.232905i
$501$		0			0
$502$	4187.23	−	7252.49i	0.372281	−	0.644810i
$503$		−	19420.3i		−	1.72149i	−0.509038	−	0.860744i	$-0.669999\pi$
$503$		−	19420.3i		−	1.72149i	0.509038	−	0.860744i	$-0.330001\pi$
$504$		0			0
$505$	−13795.4	+	2618.09i	−1.21562	+	0.230700i
$506$	11885.0	+	6861.80i	1.04417	+	0.602854i
$507$		0			0
$508$	1182.79	−	682.887i	0.103303	−	0.0596421i
$509$	4246.46	−	7355.08i	0.369786	−	0.640488i	−0.619746	−	0.784802i	$-0.712764\pi$
$509$	4246.46	−	7355.08i	0.369786	−	0.640488i	0.989532	+	0.144315i	$0.0460978\pi$
$510$		0			0
$511$	−4.96731	−	340.257i	−0.000430021	−	0.0294561i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	7757.90	−	4479.03i	0.665732	−	0.384361i
$515$	−5842.94	−	6782.08i	−0.499943	−	0.580299i
$516$		0			0
$517$	16856.0			1.43390
$518$	−11994.3	+	175.101i	−1.01737	+	0.0148523i
$519$		0			0
$520$	1039.68	−	2976.48i	0.0876789	−	0.251014i
$521$	8975.73	+	15546.4i	0.754767	+	1.30729i	0.945490	+	0.325651i	$0.105583\pi$
$521$	8975.73	+	15546.4i	0.754767	+	1.30729i	−0.190723	+	0.981644i	$0.561083\pi$
$522$		0			0
$523$	1079.63	−	1869.98i	0.0902658	−	0.156345i	−0.817357	−	0.576131i	$-0.804562\pi$
$523$	1079.63	−	1869.98i	0.0902658	−	0.156345i	0.907623	+	0.419786i	$0.137895\pi$
$524$	5267.18			0.439118
$525$		0			0
$526$	4402.24			0.364918
$527$	2532.80	−	4386.95i	0.209356	−	0.362615i
$528$		0			0
$529$	−2461.27	−	4263.04i	−0.202290	−	0.350377i
$530$	3176.17	−	9092.98i	0.260309	−	0.745234i
$531$		0			0
$532$	2592.61	−	4645.85i	0.211285	−	0.378615i
$533$	15023.7			1.22092
$534$		0			0
$535$	−8369.83	−	9715.12i	−0.676373	−	0.785086i
$536$	5767.80	−	3330.04i	0.464796	−	0.268350i
$537$		0			0
$538$	−5898.17			−0.472655
$539$	15848.0	+	8542.98i	1.26646	+	0.682694i
$540$		0			0
$541$	−2814.32	+	4874.55i	−0.223655	+	0.387382i	−0.955915	−	0.293643i	$-0.905132\pi$
$541$	−2814.32	+	4874.55i	−0.223655	+	0.387382i	0.732260	+	0.681025i	$0.238465\pi$
$542$	−9282.91	+	5359.49i	−0.735674	+	0.424741i
$543$		0			0
$544$	−1579.43	−	911.882i	−0.124480	−	0.0718688i
$545$	−16469.5	+	3125.58i	−1.29445	+	0.245661i
$546$		0			0
$547$			6915.22i			0.540537i	0.962785	+	0.270268i	$0.0871124\pi$
$547$			6915.22i			0.540537i	−0.962785	+	0.270268i	$0.912888\pi$
$548$	−4705.06	+	8149.40i	−0.366770	+	0.635265i
$549$		0			0
$550$	−8170.40	+	10268.5i	−0.633431	+	0.796090i
$551$	2188.22	−	3790.11i	0.169186	−	0.293039i
$552$		0			0
$553$	13443.7	−	8025.66i	1.03379	−	0.617153i
$554$		−	10362.3i		−	0.794681i
$555$		0			0
$556$	5212.05	−	3009.18i	0.397554	−	0.229528i
$557$	11356.6	+	19670.2i	0.863905	+	1.49633i	0.868130	+	0.496337i	$0.165322\pi$
$557$	11356.6	+	19670.2i	0.863905	+	1.49633i	−0.00422488	+	0.999991i	$0.501345\pi$
$558$		0			0
$559$			18910.7i			1.43083i
$560$	665.161	+	3245.54i	0.0501932	+	0.244909i
$561$		0			0
$562$	−4959.52	−	2863.38i	−0.372251	−	0.214919i
$563$	3071.44	−	1773.30i	0.229922	−	0.132745i	−0.380614	−	0.924734i	$-0.624287\pi$
$563$	3071.44	−	1773.30i	0.229922	−	0.132745i	0.610536	+	0.791989i	$0.290954\pi$
$564$		0			0
$565$	−1029.54	+	2947.45i	−0.0766603	+	0.219469i
$566$	14158.1			1.05143
$567$		0			0
$568$			8859.22i			0.654444i
$569$	931.747	+	537.944i	0.0686483	+	0.0396341i	0.533931	−	0.845528i	$-0.320714\pi$
$569$	931.747	+	537.944i	0.0686483	+	0.0396341i	−0.465283	+	0.885162i	$0.654047\pi$
$570$		0			0
$571$	4927.96	+	8535.47i	0.361171	+	0.625566i	0.988154	−	0.153467i	$-0.0490438\pi$
$571$	4927.96	+	8535.47i	0.361171	+	0.625566i	−0.626983	+	0.779033i	$0.715710\pi$
$572$	−6409.44	−	3700.49i	−0.468518	−	0.270499i
$573$		0			0
$574$	−13555.2	+	8092.21i	−0.985688	+	0.588436i
$575$	15204.7	−	5986.70i	1.10275	−	0.434196i
$576$		0			0
$577$	1622.74	+	2810.66i	0.117080	+	0.202789i	0.918609	−	0.395167i	$-0.129313\pi$
$577$	1622.74	+	2810.66i	0.117080	+	0.202789i	−0.801529	+	0.597956i	$0.795980\pi$
$578$	1664.84	+	2883.59i	0.119807	+	0.207511i
$579$		0			0
$580$	508.129	+	2677.47i	0.0363774	+	0.191683i
$581$	3677.42	−	6589.79i	0.262591	−	0.470552i
$582$		0			0
$583$	−19580.5	−	11304.8i	−1.39098	−	0.803082i
$584$	−73.4964	−	127.300i	−0.00520771	−	0.00902002i
$585$		0			0
$586$	−12098.0	−	6984.80i	−0.852841	−	0.492388i
$587$		−	6391.30i		−	0.449399i	−0.974428	−	0.224700i	$-0.927860\pi$
$587$		−	6391.30i		−	0.449399i	0.974428	−	0.224700i	$-0.0721401\pi$
$588$		0			0
$589$	6383.24			0.446548
$590$	−4927.54	+	14107.0i	−0.343837	+	0.984363i
$591$		0			0
$592$	−4487.41	+	2590.81i	−0.311539	+	0.179867i
$593$	−12143.6	−	7011.14i	−0.840944	−	0.485519i	0.0166411	−	0.999862i	$-0.494703\pi$
$593$	−12143.6	−	7011.14i	−0.840944	−	0.485519i	−0.857585	+	0.514342i	$0.828036\pi$
$594$		0			0
$595$	−3728.48	+	11196.6i	−0.256895	+	0.771453i
$596$		−	1932.27i		−	0.132800i
$597$		0			0
$598$	4608.10	+	7981.46i	0.315116	+	0.545796i
$599$	−1507.60	+	870.414i	−0.102836	+	0.0593726i	−0.550536	−	0.834811i	$-0.685577\pi$
$599$	−1507.60	+	870.414i	−0.102836	+	0.0593726i	0.447700	+	0.894184i	$0.352243\pi$
$600$		0			0
$601$		−	11826.0i		−	0.802650i	−0.915936	−	0.401325i	$-0.868550\pi$
$601$		−	11826.0i		−	0.802650i	0.915936	−	0.401325i	$-0.131450\pi$
$602$	−10185.8	−	17062.2i	−0.689606	−	1.15516i
$603$		0			0
$604$	−3957.72	+	6854.97i	−0.266618	+	0.461796i
$605$	10392.7	+	12063.1i	0.698385	+	0.810637i
$606$		0			0
$607$	−8627.54	+	14943.3i	−0.576905	+	0.999228i	0.418927	+	0.908020i	$0.362406\pi$
$607$	−8627.54	+	14943.3i	−0.576905	+	0.999228i	−0.995832	+	0.0912084i	$0.970927\pi$
$608$		−	2298.15i		−	0.153293i
$609$		0			0
$610$	2669.29	+	14065.2i	0.177174	+	0.933581i
$611$	9803.21	+	5659.89i	0.649092	+	0.374754i
$612$		0			0
$613$	22443.0	−	12957.5i	1.47874	−	0.853749i	0.479025	−	0.877801i	$-0.340990\pi$
$613$	22443.0	−	12957.5i	1.47874	−	0.853749i	0.999711	+	0.0240525i	$0.00765687\pi$
$614$	−7793.65	+	13499.0i	−0.512257	+	0.887256i
$615$		0			0
$616$	7776.13	−	113.521i	0.508619	−	0.00742517i
$617$	23140.4			1.50988			0.754940	−	0.655794i	$-0.227666\pi$
$617$	23140.4			1.50988			0.754940	+	0.655794i	$0.227666\pi$
$618$		0			0
$619$	−12399.4	+	7158.81i	−0.805129	+	0.464841i	−0.845261	−	0.534353i	$-0.820555\pi$
$619$	−12399.4	+	7158.81i	−0.805129	+	0.464841i	0.0401326	+	0.999194i	$0.487222\pi$
$620$	−3011.45	+	2594.44i	−0.195069	+	0.168057i
$621$		0			0
$622$	12658.5			0.816013
$623$	−20018.9	+	11950.9i	−1.28739	+	0.768545i
$624$		0			0
$625$	3510.36	+	15225.6i	0.224663	+	0.974436i
$626$	−301.498	−	522.211i	−0.0192497	−	0.0333414i
$627$		0			0
$628$	−477.469	+	827.001i	−0.0303393	+	0.0525493i
$629$	−18457.1			−1.17000
$630$		0			0
$631$	12504.7			0.788915			0.394457	−	0.918914i	$-0.370933\pi$
$631$	12504.7			0.788915			0.394457	+	0.918914i	$0.370933\pi$
$632$	3381.62	−	5857.14i	0.212838	−	0.368646i
$633$		0			0
$634$	8706.40	+	15079.9i	0.545387	+	0.944638i
$635$	−3603.92	−	1258.84i	−0.225224	−	0.0786704i
$636$		0			0
$637$	6348.42	+	10289.9i	0.394872	+	0.640032i
$638$	6397.29			0.396977
$639$		0			0
$640$	934.074	+	1084.21i	0.0576914	+	0.0669642i
$641$	10217.4	−	5899.05i	0.629587	−	0.363492i	−0.151005	−	0.988533i	$-0.548251\pi$
$641$	10217.4	−	5899.05i	0.629587	−	0.363492i	0.780592	+	0.625041i	$0.214918\pi$
$642$		0			0
$643$	2289.37			0.140410			0.0702051	−	0.997533i	$-0.477635\pi$
$643$	2289.37			0.140410			0.0702051	+	0.997533i	$0.477635\pi$
$644$	−8456.71	−	4719.25i	−0.517455	−	0.288765i
$645$		0			0
$646$	4093.05	−	7089.37i	0.249286	−	0.431776i
$647$	−13928.9	+	8041.83i	−0.846368	+	0.488651i	−0.859424	−	0.511264i	$-0.829177\pi$
$647$	−13928.9	+	8041.83i	−0.846368	+	0.488651i	0.0130558	+	0.999915i	$0.495844\pi$
$648$		0			0
$649$	30377.4	+	17538.4i	1.83731	+	1.06077i
$650$	−8199.73	+	3228.56i	−0.494800	+	0.194822i
$651$		0			0
$652$			11817.9i			0.709856i
$653$	−11525.3	+	19962.5i	−0.690692	+	1.19631i	0.280920	+	0.959731i	$0.409361\pi$
$653$	−11525.3	+	19962.5i	−0.690692	+	1.19631i	−0.971612	+	0.236582i	$0.923973\pi$
$654$		0			0
$655$	−9609.25	−	11153.8i	−0.573228	−	0.665363i
$656$	−3409.66	+	5905.71i	−0.202935	+	0.351493i
$657$		0			0
$658$	−11893.6	+	173.631i	−0.704650	+	0.0102870i
$659$			8159.46i			0.482318i	0.970486	+	0.241159i	$0.0775275\pi$
$659$			8159.46i			0.482318i	−0.970486	+	0.241159i	$0.922472\pi$
$660$		0			0
$661$	−1697.52	+	980.063i	−0.0998878	+	0.0576702i	−0.549112	−	0.835749i	$-0.685034\pi$
$661$	−1697.52	+	980.063i	−0.0998878	+	0.0576702i	0.449224	+	0.893419i	$0.351701\pi$
$662$	−6391.92	−	11071.1i	−0.375271	−	0.649988i
$663$		0			0
$664$		−	3259.76i		−	0.190517i
$665$	−14567.9	+	2985.62i	−0.849500	+	0.174102i
$666$		0			0
$667$	−6899.05	−	3983.17i	−0.400498	−	0.231228i
$668$	−725.210	+	418.700i	−0.0420048	+	0.0242515i
$669$		0			0
$670$	−17574.2	−	6138.65i	−1.01336	−	0.353965i
$671$	33606.1			1.93346
$672$		0			0
$673$		−	11563.1i		−	0.662293i	−0.943579	−	0.331146i	$-0.892565\pi$
$673$		−	11563.1i		−	0.662293i	0.943579	−	0.331146i	$-0.107435\pi$
$674$	8654.40	+	4996.62i	0.494592	+	0.285553i
$675$		0			0
$676$	1908.91	+	3306.32i	0.108609	+	0.188116i
$677$	27447.2	+	15846.6i	1.55817	+	0.899609i	0.997432	+	0.0716153i	$0.0228154\pi$
$677$	27447.2	+	15846.6i	1.55817	+	0.899609i	0.560737	+	0.827994i	$0.310518\pi$
$678$		0			0
$679$	4776.35	+	2665.43i	0.269955	+	0.150648i
$680$	950.450	+	5008.19i	0.0536002	+	0.282434i
$681$		0			0
$682$	4665.37	+	8080.65i	0.261945	+	0.453701i
$683$	−6087.01	−	10543.0i	−0.341014	−	0.590654i	0.643607	−	0.765356i	$-0.277437\pi$
$683$	−6087.01	−	10543.0i	−0.341014	−	0.590654i	−0.984621	+	0.174702i	$0.944104\pi$
$684$		0			0
$685$	25840.8	−	4904.06i	1.44135	−	0.273539i
$686$	−11270.3	−	5864.67i	−0.627264	−	0.326405i
$687$		0			0
$688$	−7433.63	−	4291.81i	−0.411925	−	0.237825i
$689$	−7591.83	−	13149.4i	−0.419776	−	0.727073i
$690$		0			0
$691$	−12283.0	−	7091.59i	−0.676219	−	0.390415i	0.122210	−	0.992504i	$-0.461002\pi$
$691$	−12283.0	−	7091.59i	−0.676219	−	0.390415i	−0.798429	+	0.602089i	$0.794335\pi$
$692$		−	3746.03i		−	0.205784i
$693$		0			0
$694$	−1040.29			−0.0569002
$695$	−15880.9	−	5547.17i	−0.866758	−	0.302757i
$696$		0			0
$697$	−21036.4	+	12145.4i	−1.14320	+	0.660026i
$698$	7642.09	+	4412.16i	0.414409	+	0.239259i
$699$		0			0
$700$	5659.25	−	7329.59i	0.305571	−	0.395761i
$701$			5857.40i			0.315593i	0.987472	+	0.157797i	$0.0504391\pi$
$701$			5857.40i			0.315593i	−0.987472	+	0.157797i	$0.949561\pi$
$702$		0			0
$703$	−11629.0	−	20142.1i	−0.623893	−	1.08061i
$704$	2909.27	−	1679.67i	0.155749	−	0.0899216i
$705$		0			0
$706$			26028.4i			1.38752i
$707$	−339.530	−	23257.5i	−0.0180613	−	1.23719i
$708$		0			0
$709$	−3185.12	+	5516.79i	−0.168716	+	0.292225i	−0.937969	−	0.346720i	$-0.887295\pi$
$709$	−3185.12	+	5516.79i	−0.168716	+	0.292225i	0.769253	+	0.638945i	$0.220629\pi$
$710$	18760.2	−	16162.4i	0.991632	−	0.854317i
$711$		0			0
$712$	−5035.53	+	8721.80i	−0.265049	+	0.459078i
$713$		−	11619.2i		−	0.610300i
$714$		0			0
$715$	3857.01	+	20323.6i	0.201740	+	1.06302i
$716$	8102.59	+	4678.03i	0.422916	+	0.244171i
$717$		0			0
$718$	−7506.02	+	4333.60i	−0.390142	+	0.225249i
$719$	−5777.72	+	10007.3i	−0.299683	+	0.519067i	−0.976063	−	0.217486i	$-0.930214\pi$
$719$	−5777.72	+	10007.3i	−0.299683	+	0.519067i	0.676380	+	0.736553i	$0.263548\pi$
$720$		0			0
$721$	12732.6	−	7601.10i	0.657678	−	0.392621i
$722$	−3402.59			−0.175389
$723$		0			0
$724$	−1448.13	+	836.077i	−0.0743360	+	0.0429179i
$725$	4742.79	−	5960.69i	0.242955	−	0.305344i
$726$		0			0
$727$	22082.0			1.12652			0.563258	−	0.826281i	$-0.309548\pi$
$727$	22082.0			1.12652			0.563258	+	0.826281i	$0.309548\pi$
$728$	4560.61	+	2545.04i	0.232181	+	0.129568i
$729$		0			0
$730$	−135.485	+	387.876i	−0.00686919	+	0.0196657i
$731$	−15287.6	−	26478.9i	−0.773505	−	1.33975i
$732$		0			0
$733$	4523.67	−	7835.23i	0.227948	−	0.394817i	−0.729252	−	0.684245i	$-0.760132\pi$
$733$	4523.67	−	7835.23i	0.227948	−	0.394817i	0.957200	+	0.289428i	$0.0934652\pi$
$734$	10839.2			0.545073
$735$		0			0
$736$	−4183.26			−0.209507
$737$	−21849.0	+	37843.6i	−1.09202	+	1.89144i
$738$		0			0
$739$	−13658.5	−	23657.2i	−0.679885	−	1.17760i	−0.975015	−	0.222138i	$-0.928696\pi$
$739$	−13658.5	−	23657.2i	−0.679885	−	1.17760i	0.295130	−	0.955457i	$-0.404637\pi$
$740$	13672.9	+	4775.93i	0.679225	+	0.237252i
$741$		0			0
$742$	13932.4	+	7774.95i	0.689319	+	0.384673i
$743$	−13388.0			−0.661047			−0.330524	−	0.943798i	$-0.607225\pi$
$743$	−13388.0			−0.661047			−0.330524	+	0.943798i	$0.607225\pi$
$744$		0			0
$745$	−4091.76	+	3525.16i	−0.201222	+	0.173358i
$746$	1234.75	−	712.884i	0.0605998	−	0.0349873i
$747$		0			0
$748$	11966.1			0.584924
$749$	18239.0	−	10888.3i	0.889771	−	0.531176i
$750$		0			0
$751$	14237.9	−	24660.7i	0.691808	−	1.19825i	−0.279437	−	0.960164i	$-0.590148\pi$
$751$	14237.9	−	24660.7i	0.691808	−	1.19825i	0.971245	−	0.238082i	$-0.0765188\pi$
$752$	−4449.71	+	2569.04i	−0.215777	+	0.124579i
$753$		0			0
$754$	3720.58	+	2148.08i	0.179702	+	0.103751i
$755$	21736.4	−	4125.11i	1.04777	−	0.198845i
$756$		0			0
$757$			16852.7i			0.809145i	0.914506	+	0.404573i	$0.132580\pi$
$757$			16852.7i			0.809145i	−0.914506	+	0.404573i	$0.867420\pi$
$758$	1011.71	−	1752.33i	0.0484787	−	0.0839676i
$759$		0			0
$760$	−4866.55	+	4192.66i	−0.232274	+	0.200110i
$761$	−15408.3	+	26687.9i	−0.733967	+	1.27127i	0.221207	+	0.975227i	$0.429000\pi$
$761$	−15408.3	+	26687.9i	−0.733967	+	1.27127i	−0.955175	+	0.296042i	$0.904333\pi$
$762$		0			0
$763$	−405.345	−	27765.8i	−0.0192326	−	1.31742i
$764$			5325.40i			0.252181i
$765$		0			0
$766$	−1991.95	+	1150.06i	−0.0939585	+	0.0542470i
$767$	11778.0	+	20400.2i	0.554473	+	0.960375i
$768$		0			0
$769$		−	3382.34i		−	0.158609i	−0.996850	−	0.0793044i	$-0.974730\pi$
$769$		−	3382.34i		−	0.158609i	0.996850	−	0.0793044i	$-0.0252699\pi$
$770$	−14426.9	−	16259.6i	−0.675206	−	0.760980i
$771$		0			0
$772$	9207.30	+	5315.84i	0.429246	+	0.247825i
$773$	−963.102	+	556.047i	−0.0448129	+	0.0258727i	−0.522239	−	0.852799i	$-0.674903\pi$
$773$	−963.102	+	556.047i	−0.0448129	+	0.0258727i	0.477426	+	0.878672i	$0.341570\pi$
$774$		0			0
$775$	10987.9	+	1643.82i	0.509289	+	0.0761906i
$776$	2362.70			0.109299
$777$		0			0
$778$			3751.02i			0.172854i
$779$	−26508.2	−	15304.5i	−1.21920	−	0.703905i
$780$		0			0
$781$	−29063.5	−	50339.5i	−1.33159	−	2.30639i
$782$	−12904.6	−	7450.47i	−0.590112	−	0.340701i
$783$		0			0
$784$	−5485.66	+	160.201i	−0.249893	+	0.00729779i
$785$	2622.33	−	497.664i	0.119229	−	0.0226273i
$786$		0			0
$787$	−17775.2	−	30787.5i	−0.805105	−	1.39448i	−0.916220	−	0.400674i	$-0.868776\pi$
$787$	−17775.2	−	30787.5i	−0.805105	−	1.39448i	0.111116	−	0.993807i	$-0.464557\pi$
$788$	−2949.58	−	5108.81i	−0.133343	−	0.230957i
$789$		0			0
$790$	−18572.3	+	3524.65i	−0.836423	+	0.158736i
$791$	−4516.13	−	2520.22i	−0.203003	−	0.113285i
$792$		0			0
$793$	19544.8	+	11284.2i	0.875230	+	0.505314i
$794$	−3847.43	−	6663.94i	−0.171965	−	0.297852i
$795$		0			0
$796$	−10486.4	−	6054.31i	−0.466934	−	0.269585i
$797$		−	33716.2i		−	1.49848i	−0.662297	−	0.749241i	$-0.730418\pi$
$797$		−	33716.2i		−	1.49848i	0.662297	−	0.749241i	$-0.269582\pi$
$798$		0			0
$799$	−18302.1			−0.810363
$800$	591.822	−	3955.98i	0.0261551	−	0.174831i
$801$		0			0
$802$	4704.33	−	2716.05i	0.207127	−	0.119585i
$803$	835.237	+	482.224i	0.0367060	+	0.0211922i
$804$		0			0
$805$	5434.66	+	26517.5i	0.237946	+	1.16102i
$806$			6266.13i			0.273840i
$807$		0			0
$808$	−5023.69	−	8701.29i	−0.218729	−	0.378849i
$809$	21487.5	−	12405.8i	0.933822	−	0.539142i	0.0458035	−	0.998950i	$-0.485415\pi$
$809$	21487.5	−	12405.8i	0.933822	−	0.539142i	0.888018	+	0.459808i	$0.152082\pi$
$810$		0			0
$811$		−	3596.41i		−	0.155718i	−0.996964	−	0.0778588i	$-0.975192\pi$
$811$		−	3596.41i		−	0.155718i	0.996964	−	0.0778588i	$-0.0248083\pi$
$812$	−4513.92	+	65.8974i	−0.195083	+	0.00284796i
$813$		0			0
$814$	16998.8	−	29442.8i	0.731950	−	1.26777i
$815$	25025.6	−	21560.2i	1.07559	−	0.926652i
$816$		0			0
$817$	19264.1	−	33366.4i	0.824927	−	1.42882i
$818$			12793.2i			0.546825i
$819$		0			0
$820$	18726.4	−	3553.88i	0.797504	−	0.151350i
$821$	−18754.0	−	10827.6i	−0.797223	−	0.460277i	0.0452760	−	0.998975i	$-0.485583\pi$
$821$	−18754.0	−	10827.6i	−0.797223	−	0.460277i	−0.842499	+	0.538697i	$0.818917\pi$
$822$		0			0
$823$	−21855.0	+	12618.0i	−0.925660	+	0.534430i	−0.885436	−	0.464760i	$-0.846140\pi$
$823$	−21855.0	+	12618.0i	−0.925660	+	0.534430i	−0.0402238	+	0.999191i	$0.512807\pi$
$824$	3202.73	−	5547.29i	0.135403	−	0.234526i
$825$		0			0
$826$	−21614.9	−	12062.2i	−0.910507	−	0.508107i
$827$	30961.7			1.30187			0.650933	−	0.759135i	$-0.274378\pi$
$827$	30961.7			1.30187			0.650933	+	0.759135i	$0.274378\pi$
$828$		0			0
$829$	−716.458	+	413.647i	−0.0300164	+	0.0173300i	−0.514933	−	0.857230i	$-0.672183\pi$
$829$	−716.458	+	413.647i	−0.0300164	+	0.0173300i	0.484917	+	0.874560i	$0.338850\pi$
$830$	−6902.84	+	5946.98i	−0.288676	+	0.248702i
$831$		0			0
$832$	2255.99			0.0940051
$833$	−17207.6	−	9275.88i	−0.715735	−	0.385823i
$834$		0			0
$835$	2209.68	+	771.838i	0.0915798	+	0.0319887i
$836$	7539.30	+	13058.5i	0.311905	+	0.540235i
$837$		0			0
$838$	5593.44	−	9688.13i	0.230575	−	0.399368i
$839$	−31299.1			−1.28792			−0.643960	−	0.765059i	$-0.722710\pi$
$839$	−31299.1			−1.28792			−0.643960	+	0.765059i	$0.722710\pi$
$840$		0			0
$841$	20675.5			0.847738
$842$	−11548.2	+	20002.0i	−0.472655	+	0.818663i
$843$		0			0
$844$	−4912.86	−	8509.33i	−0.200365	−	0.347042i
$845$	3518.91	−	10074.2i	0.143259	−	0.410134i
$846$		0			0
$847$	−22647.1	+	13519.9i	−0.918729	+	0.548463i
$848$	6891.91			0.279091
$849$		0			0
$850$	8871.33	−	11149.4i	0.357981	−	0.449908i
$851$	−36664.1	+	21168.0i	−1.47688	+	0.852679i
$852$		0			0
$853$	27266.1			1.09446			0.547229	−	0.836983i	$-0.315683\pi$
$853$	27266.1			1.09446			0.547229	+	0.836983i	$0.315683\pi$
$854$	−23712.4	+	346.170i	−0.950143	+	0.0138708i
$855$		0			0
$856$	4587.81	−	7946.32i	0.183187	−	0.317289i
$857$	−20501.4	+	11836.5i	−0.817169	+	0.471792i	−0.849439	−	0.527687i	$-0.823060\pi$
$857$	−20501.4	+	11836.5i	−0.817169	+	0.471792i	0.0322705	+	0.999479i	$0.489726\pi$
$858$		0			0
$859$	26894.3	+	15527.4i	1.06824	+	0.616750i	0.927701	−	0.373325i	$-0.121782\pi$
$859$	26894.3	+	15527.4i	1.06824	+	0.616750i	0.140542	+	0.990075i	$0.455116\pi$
$860$	4473.33	+	23571.2i	0.177371	+	0.934619i
$861$		0			0
$862$		−	20879.1i		−	0.824994i
$863$	−8906.72	+	15426.9i	−0.351319	+	0.608503i	−0.986481	−	0.163877i	$-0.947600\pi$
$863$	−8906.72	+	15426.9i	−0.351319	+	0.608503i	0.635162	+	0.772379i	$0.280933\pi$
$864$		0			0
$865$	−7932.57	+	6834.12i	−0.311810	+	0.268632i
$866$	417.621	−	723.340i	0.0163872	−	0.0283835i
$867$		0			0
$868$	−3375.11	−	5653.64i	−0.131980	−	0.221080i
$869$			44374.9i			1.73224i
$870$		0			0
$871$	−25414.2	+	14672.9i	−0.988665	+	0.570806i
$872$	−5997.50	−	10388.0i	−0.232914	−	0.403419i
$873$		0			0
$874$		−	18776.9i		−	0.726702i
$875$	−25845.6	+	1387.85i	−0.998561	+	0.0536203i
$876$		0			0
$877$	−31684.3	−	18292.9i	−1.21996	−	0.704343i	−0.255049	−	0.966928i	$-0.582092\pi$
$877$	−31684.3	−	18292.9i	−1.21996	−	0.704343i	−0.964909	+	0.262585i	$0.915425\pi$
$878$	−19877.0	+	11476.0i	−0.764029	+	0.441112i
$879$		0			0
$880$	−8864.41	−	3096.32i	−0.339567	−	0.118610i
$881$	−49033.9			−1.87513			−0.937567	−	0.347806i	$-0.886927\pi$
$881$	−49033.9			−1.87513			−0.937567	+	0.347806i	$0.886927\pi$
$882$		0			0
$883$			38011.3i			1.44868i	0.689445	+	0.724338i	$0.257854\pi$
$883$			38011.3i			1.44868i	−0.689445	+	0.724338i	$0.742146\pi$
$884$	6959.30	+	4017.96i	0.264781	+	0.152872i
$885$		0			0
$886$	3671.52	+	6359.26i	0.139218	+	0.241133i
$887$	35306.0	+	20383.9i	1.33648	+	0.771617i	0.986284	−	0.165059i	$-0.0527815\pi$
$887$	35306.0	+	20383.9i	1.33648	+	0.771617i	0.350197	+	0.936676i	$0.386115\pi$
$888$		0			0
$889$	3081.53	−	5521.98i	0.116256	−	0.208326i
$890$	27655.9	−	5248.51i	1.04160	−	0.197675i
$891$		0			0
$892$	−8766.64	−	15184.3i	−0.329068	−	0.569962i
$893$	−11531.3	−	19972.9i	−0.432118	−	0.748450i
$894$		0			0
$895$	−4875.89	−	25692.4i	−0.182104	−	0.959556i
$896$	−2035.47	+	1215.14i	−0.0758933	+	0.0453068i
$897$		0			0
$898$	2521.07	+	1455.54i	0.0936851	+	0.0540891i
$899$	−2708.17	−	4690.69i	−0.100470	−	0.174019i
$900$		0			0
$901$	21260.3	+	12274.6i	0.786107	+	0.453859i
$902$		−	44743.0i		−	1.65164i
$903$		0			0
$904$	−2233.98			−0.0821915
$905$	4412.38	+	1541.24i	0.162069	+	0.0566105i
$906$		0			0
$907$	−40933.8	+	23633.1i	−1.49855	+	0.865187i	−0.999999	−	0.00167384i	$-0.999467\pi$
$907$	−40933.8	+	23633.1i	−1.49855	+	0.865187i	−0.498550	+	0.866861i	$0.666134\pi$
$908$	3034.69	+	1752.08i	0.110914	+	0.0640362i
$909$		0			0
$910$	−2930.85	−	14300.6i	−0.106766	−	0.520945i
$911$		−	21289.6i		−	0.774264i	−0.922024	−	0.387132i	$-0.873466\pi$
$911$		−	21289.6i		−	0.774264i	0.922024	−	0.387132i	$-0.126534\pi$
$912$		0			0
$913$	10694.0	+	18522.5i	0.387643	+	0.671417i
$914$	−17833.1	+	10295.9i	−0.645368	+	0.372604i
$915$		0			0
$916$			15351.2i			0.553732i
$917$	20939.9	−	12500.7i	0.754084	−	0.450174i
$918$		0			0
$919$	−6778.30	+	11740.4i	−0.243303	+	0.421413i	−0.961653	−	0.274269i	$-0.911564\pi$
$919$	−6778.30	+	11740.4i	−0.243303	+	0.421413i	0.718350	+	0.695682i	$0.244898\pi$
$920$	7631.79	+	8858.45i	0.273492	+	0.317450i
$921$		0			0
$922$	19024.2	−	32950.8i	0.679531	−	1.17698i
$923$		−	39035.7i		−	1.39206i
$924$		0			0
$925$	−14830.9	−	37666.7i	−0.527175	−	1.33889i
$926$	−9257.28	−	5344.69i	−0.328524	−	0.189673i
$927$		0			0
$928$	−1688.78	+	975.019i	−0.0597382	+	0.0344899i
$929$	−6998.18	+	12121.2i	−0.247151	+	0.428077i	−0.962734	−	0.270450i	$-0.912828\pi$
$929$	−6998.18	+	12121.2i	−0.247151	+	0.428077i	0.715583	+	0.698527i	$0.246161\pi$
$930$		0			0
$931$	−719.075	−	24622.8i	−0.0253133	−	0.866788i
$932$	−6191.99			−0.217624
$933$		0			0
$934$	−2844.96	+	1642.54i	−0.0996680	+	0.0575433i
$935$	−21830.5	−	25339.3i	−0.763564	−	0.886292i
$936$		0			0
$937$	44750.7			1.56024			0.780119	−	0.625631i	$-0.215159\pi$
$937$	44750.7			1.56024			0.780119	+	0.625631i	$0.215159\pi$
$938$	15026.8	−	26927.5i	0.523074	−	0.937328i
$939$		0			0
$940$	13558.1	+	4735.81i	0.470442	+	0.164325i
$941$	9661.03	+	16733.4i	0.334687	+	0.579695i	0.983425	−	0.181317i	$-0.0580361\pi$
$941$	9661.03	+	16733.4i	0.334687	+	0.579695i	−0.648738	+	0.761012i	$0.724703\pi$
$942$		0			0
$943$	−27858.4	+	48252.2i	−0.962031	+	1.66629i
$944$	−10692.2			−0.368645
$945$		0			0
$946$	56318.8			1.93560
$947$	19470.2	−	33723.4i	0.668106	−	1.15719i	−0.310327	−	0.950630i	$-0.600438\pi$
$947$	19470.2	−	33723.4i	0.668106	−	1.15719i	0.978433	−	0.206564i	$-0.0662283\pi$
$948$		0			0
$949$	323.842	+	560.910i	0.0110773	+	0.0191864i
$950$	17756.7	+	2656.44i	0.606424	+	0.0907223i
$951$		0			0
$952$	−8443.25	+	123.260i	−0.287445	+	0.00419631i
$953$	10712.2			0.364114			0.182057	−	0.983288i	$-0.441724\pi$
$953$	10712.2			0.364114			0.182057	+	0.983288i	$0.441724\pi$
$954$		0			0
$955$	11277.0	−	9715.47i	0.382111	−	0.329199i
$956$	−5742.73	+	3315.57i	−0.194282	+	0.112169i
$957$		0			0
$958$	−2595.96			−0.0875487
$959$	635.989	+	43564.8i	0.0214152	+	1.46692i
$960$		0			0
$961$	−10945.5	+	18958.2i	−0.367410	+	0.636373i
$962$	19772.5	−	11415.7i	0.662673	−	0.382594i
$963$		0			0
$964$	−11415.6	−	6590.79i	−0.381402	−	0.220202i
$965$	−5540.67	−	29195.3i	−0.184830	−	0.973918i
$966$		0			0
$967$			15500.7i			0.515479i	0.966214	+	0.257739i	$0.0829776\pi$
$967$			15500.7i			0.515479i	−0.966214	+	0.257739i	$0.917022\pi$
$968$	−5696.62	+	9866.83i	−0.189149	+	0.327616i
$969$		0			0
$970$	−4310.43	−	5003.24i	−0.142680	−	0.165613i
$971$	−8032.85	+	13913.3i	−0.265485	+	0.459834i	−0.967691	−	0.252140i	$-0.918866\pi$
$971$	−8032.85	+	13913.3i	−0.265485	+	0.459834i	0.702205	+	0.711975i	$0.252199\pi$
$972$		0			0
$973$	13579.0	−	24332.9i	0.447401	−	0.801725i
$974$			11556.9i			0.380193i
$975$		0			0
$976$	−8871.47	+	5121.95i	−0.290952	+	0.167981i
$977$	18543.9	+	32119.0i	0.607238	+	1.05177i	0.991693	+	0.128624i	$0.0410560\pi$
$977$	18543.9	+	32119.0i	0.607238	+	1.05177i	−0.384455	+	0.923144i	$0.625611\pi$
$978$		0			0
$979$		−	66078.2i		−	2.15717i
$980$	10347.1	+	11324.1i	0.337271	+	0.369119i
$981$		0			0
$982$	1448.11	+	836.066i	0.0470581	+	0.0271690i
$983$	49.2123	−	28.4127i	0.00159677	−	0.000921897i	−0.499201	−	0.866486i	$-0.666373\pi$
$983$	49.2123	−	28.4127i	0.00159677	−	0.000921897i	0.500798	+	0.865564i	$0.333040\pi$
$984$		0			0
$985$	−5437.30	+	15566.3i	−0.175885	+	0.503538i
$986$	−6946.11			−0.224350
$987$		0			0
$988$			10126.2i			0.326069i
$989$	−60736.0	−	35065.9i	−1.95277	−	1.12743i
$990$		0			0
$991$	−9193.03	−	15922.8i	−0.294678	−	0.510398i	0.680232	−	0.732997i	$-0.261879\pi$
$991$	−9193.03	−	15922.8i	−0.294678	−	0.510398i	−0.974910	+	0.222599i	$0.928546\pi$
$992$	−2463.16	−	1422.11i	−0.0788363	−	0.0455161i
$993$		0			0
$994$	21025.7	+	35220.1i	0.670921	+	1.12386i
$995$	6310.38	+	33251.1i	0.201058	+	1.05943i
$996$		0			0
$997$	−4691.38	−	8125.70i	−0.149024	−	0.258118i	0.781843	−	0.623476i	$-0.214280\pi$
$997$	−4691.38	−	8125.70i	−0.149024	−	0.258118i	−0.930867	+	0.365358i	$0.880947\pi$
$998$	16191.2	+	28044.1i	0.513552	+	0.889498i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.4.bo.b.89.9	yes	48
3.2	odd	2		630.4.bo.a.89.16	yes	48
5.4	even	2		630.4.bo.a.89.7	✓	48
7.3	odd	6	inner	630.4.bo.b.269.18	yes	48
15.14	odd	2	inner	630.4.bo.b.89.18	yes	48
21.17	even	6		630.4.bo.a.269.7	yes	48
35.24	odd	6		630.4.bo.a.269.16	yes	48
105.59	even	6	inner	630.4.bo.b.269.9	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.4.bo.a.89.7	✓	48	5.4	even	2
630.4.bo.a.89.16	yes	48	3.2	odd	2
630.4.bo.a.269.7	yes	48	21.17	even	6
630.4.bo.a.269.16	yes	48	35.24	odd	6
630.4.bo.b.89.9	yes	48	1.1	even	1	trivial
630.4.bo.b.89.18	yes	48	15.14	odd	2	inner
630.4.bo.b.269.9	yes	48	105.59	even	6	inner
630.4.bo.b.269.18	yes	48	7.3	odd	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	630.bo (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-3.68683 + 10.5550i) q^{5} +(-16.1725 - 9.02502i) q^{7} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-3.68683 + 10.5550i) q^{5} +(-16.1725 - 9.02502i) q^{7} -8.00000 q^{8} +(14.5949 + 16.9407i) q^{10} +(45.4573 - 26.2448i) q^{11} +35.2498 q^{13} +(-31.8043 + 18.9865i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(-49.3571 + 28.4963i) q^{17} +(-62.1955 - 35.9086i) q^{19} +(43.9371 - 8.33836i) q^{20} -104.979i q^{22} +(-65.3635 + 113.213i) q^{23} +(-97.8145 - 77.8288i) q^{25} +(35.2498 - 61.0544i) q^{26} +(1.08137 + 74.0731i) q^{28} +60.9387i q^{29} +(-76.9739 + 44.4409i) q^{31} +(16.0000 + 27.7128i) q^{32} +113.985i q^{34} +(154.884 - 137.426i) q^{35} +(280.463 + 161.925i) q^{37} +(-124.391 + 71.8172i) q^{38} +(29.4947 - 84.4397i) q^{40} +426.208 q^{41} +536.476i q^{43} +(-181.829 - 104.979i) q^{44} +(130.727 + 226.426i) q^{46} +(278.107 + 160.565i) q^{47} +(180.098 + 291.914i) q^{49} +(-232.618 + 91.5909i) q^{50} +(-70.4996 - 122.109i) q^{52} +(-215.372 - 373.036i) q^{53} +(109.419 + 576.560i) q^{55} +(129.380 + 72.2002i) q^{56} +(105.549 + 60.9387i) q^{58} +(334.131 + 578.732i) q^{59} +(554.467 + 320.122i) q^{61} +177.764i q^{62} +64.0000 q^{64} +(-129.960 + 372.060i) q^{65} +(-720.975 + 416.255i) q^{67} +(197.428 + 113.985i) q^{68} +(-83.1451 - 405.693i) q^{70} -1107.40i q^{71} +(9.18705 + 15.9124i) q^{73} +(560.926 - 323.851i) q^{74} +287.269i q^{76} +(-972.017 + 14.1902i) q^{77} +(-422.703 + 732.142i) q^{79} +(-116.759 - 135.526i) q^{80} +(426.208 - 738.214i) q^{82} +407.470i q^{83} +(-118.806 - 626.023i) q^{85} +(929.204 + 536.476i) q^{86} +(-363.658 + 209.958i) q^{88} +(629.442 - 1090.22i) q^{89} +(-570.076 - 318.130i) q^{91} +522.908 q^{92} +(556.214 - 321.130i) q^{94} +(608.318 - 524.082i) q^{95} -295.338 q^{97} +(685.708 - 20.0251i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{2} - 96 q^{4} + 18 q^{5} - 384 q^{8}+O(q^{10}) \) 48 * q + 48 * q^2 - 96 * q^4 + 18 * q^5 - 384 * q^8	\( 48 q + 48 q^{2} - 96 q^{4} + 18 q^{5} - 384 q^{8} + 36 q^{10} - 384 q^{16} - 432 q^{19} + 216 q^{23} + 78 q^{25} + 828 q^{31} + 768 q^{32} + 348 q^{35} - 864 q^{38} - 144 q^{40} - 432 q^{46} + 324 q^{47} + 588 q^{49} + 312 q^{50} - 96 q^{53} + 2592 q^{61} + 3072 q^{64} - 252 q^{65} + 564 q^{70} - 3768 q^{77} - 756 q^{79} - 288 q^{80} - 960 q^{85} - 4476 q^{91} - 1728 q^{92} + 648 q^{94} - 1332 q^{95} + 2280 q^{98}+O(q^{100}) \) 48 * q + 48 * q^2 - 96 * q^4 + 18 * q^5 - 384 * q^8 + 36 * q^10 - 384 * q^16 - 432 * q^19 + 216 * q^23 + 78 * q^25 + 828 * q^31 + 768 * q^32 + 348 * q^35 - 864 * q^38 - 144 * q^40 - 432 * q^46 + 324 * q^47 + 588 * q^49 + 312 * q^50 - 96 * q^53 + 2592 * q^61 + 3072 * q^64 - 252 * q^65 + 564 * q^70 - 3768 * q^77 - 756 * q^79 - 288 * q^80 - 960 * q^85 - 4476 * q^91 - 1728 * q^92 + 648 * q^94 - 1332 * q^95 + 2280 * q^98

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