LMFDB - Embedded newform 144.3.j.a.125.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(53,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("144.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.j (of order $4$, 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:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			125.4
Character	$\chi$	$=$	144.125
Dual form			144.3.j.a.53.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.56339 - 1.24732i) q^{2} +(0.888382 + 3.90010i) q^{4} +(-1.84570 - 1.84570i) q^{5} -0.226665i q^{7} +(3.47579 - 7.20548i) q^{8} +O(q^{10})$	\(q+(-1.56339 - 1.24732i) q^{2} +(0.888382 + 3.90010i) q^{4} +(-1.84570 - 1.84570i) q^{5} -0.226665i q^{7} +(3.47579 - 7.20548i) q^{8} +(0.583370 + 5.18772i) q^{10} +(-11.5821 - 11.5821i) q^{11} +(-8.11369 - 8.11369i) q^{13} +(-0.282724 + 0.354366i) q^{14} +(-14.4216 + 6.92956i) q^{16} +6.20082i q^{17} +(-4.43355 - 4.43355i) q^{19} +(5.55872 - 8.83809i) q^{20} +(3.66074 + 32.5538i) q^{22} -28.6638 q^{23} -18.1868i q^{25} +(2.56449 + 22.8052i) q^{26} +(0.884017 - 0.201365i) q^{28} +(-15.7561 + 15.7561i) q^{29} -33.5751 q^{31} +(31.1899 + 7.15469i) q^{32} +(7.73441 - 9.69430i) q^{34} +(-0.418355 + 0.418355i) q^{35} +(43.8384 - 43.8384i) q^{37} +(1.40131 + 12.4614i) q^{38} +(-19.7144 + 6.88388i) q^{40} +62.2969 q^{41} +(18.3048 - 18.3048i) q^{43} +(34.8819 - 55.4605i) q^{44} +(44.8128 + 35.7530i) q^{46} +13.8029i q^{47} +48.9486 q^{49} +(-22.6848 + 28.4331i) q^{50} +(24.4361 - 38.8522i) q^{52} +(37.9167 + 37.9167i) q^{53} +42.7539i q^{55} +(-1.63323 - 0.787840i) q^{56} +(44.2857 - 4.98002i) q^{58} +(-70.4759 - 70.4759i) q^{59} +(-60.3861 - 60.3861i) q^{61} +(52.4910 + 41.8789i) q^{62} +(-39.8378 - 50.0894i) q^{64} +29.9508i q^{65} +(61.9736 + 61.9736i) q^{67} +(-24.1838 + 5.50869i) q^{68} +(1.17588 - 0.132230i) q^{70} +32.5259 q^{71} +130.954i q^{73} +(-123.217 + 13.8560i) q^{74} +(13.3526 - 21.2300i) q^{76} +(-2.62525 + 2.62525i) q^{77} -132.387 q^{79} +(39.4077 + 13.8280i) q^{80} +(-97.3944 - 77.7042i) q^{82} +(19.2783 - 19.2783i) q^{83} +(11.4448 - 11.4448i) q^{85} +(-51.4494 + 5.78559i) q^{86} +(-123.711 + 43.1975i) q^{88} +91.2401 q^{89} +(-1.83909 + 1.83909i) q^{91} +(-25.4644 - 111.792i) q^{92} +(17.2166 - 21.5793i) q^{94} +16.3660i q^{95} -20.0808 q^{97} +(-76.5258 - 61.0546i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 40 q^{10} + 48 q^{16} + 64 q^{19} - 88 q^{22} - 120 q^{28} - 248 q^{34} - 184 q^{40} + 128 q^{43} + 24 q^{46} - 224 q^{49} + 632 q^{52} + 456 q^{58} + 64 q^{61} - 48 q^{64} - 64 q^{67} - 312 q^{70} - 576 q^{76} - 512 q^{79} - 720 q^{82} + 320 q^{85} - 400 q^{88} - 192 q^{91} + 696 q^{94}+O(q^{100}) $ 32 * q + 40 * q^10 + 48 * q^16 + 64 * q^19 - 88 * q^22 - 120 * q^28 - 248 * q^34 - 184 * q^40 + 128 * q^43 + 24 * q^46 - 224 * q^49 + 632 * q^52 + 456 * q^58 + 64 * q^61 - 48 * q^64 - 64 * q^67 - 312 * q^70 - 576 * q^76 - 512 * q^79 - 720 * q^82 + 320 * q^85 - 400 * q^88 - 192 * q^91 + 696 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−1.56339	−	1.24732i	−0.781695	−	0.623660i
$2$	−1.56339	−	1.24732i	−0.781695	−	0.623660i
$3$		0			0
$3$		0			0
$4$	0.888382	+	3.90010i	0.222096	+	0.975025i
$5$	−1.84570	−	1.84570i	−0.369140	−	0.369140i	0.498024	−	0.867163i	$-0.334059\pi$
$5$	−1.84570	−	1.84570i	−0.369140	−	0.369140i	−0.867163	+	0.498024i	$0.834059\pi$
$6$		0			0
$7$		−	0.226665i		−	0.0323807i	−0.999869	−	0.0161904i	$-0.994846\pi$
$7$		−	0.226665i		−	0.0323807i	0.999869	−	0.0161904i	$-0.00515378\pi$
$8$	3.47579	−	7.20548i	0.434473	−	0.900685i
$9$		0			0
$10$	0.583370	+	5.18772i	0.0583370	+	0.518772i
$11$	−11.5821	−	11.5821i	−1.05291	−	1.05291i	−0.998520	−	0.0543946i	$-0.982677\pi$
$11$	−11.5821	−	11.5821i	−1.05291	−	1.05291i	−0.0543946	−	0.998520i	$-0.517323\pi$
$12$		0			0
$13$	−8.11369	−	8.11369i	−0.624130	−	0.624130i	0.322455	−	0.946585i	$-0.395492\pi$
$13$	−8.11369	−	8.11369i	−0.624130	−	0.624130i	−0.946585	+	0.322455i	$0.895492\pi$
$14$	−0.282724	+	0.354366i	−0.0201946	+	0.0253119i
$15$		0			0
$16$	−14.4216	+	6.92956i	−0.901347	+	0.433097i
$17$			6.20082i			0.364754i	0.983229	+	0.182377i	$0.0583791\pi$
$17$			6.20082i			0.364754i	−0.983229	+	0.182377i	$0.941621\pi$
$18$		0			0
$19$	−4.43355	−	4.43355i	−0.233345	−	0.233345i	0.580743	−	0.814087i	$-0.302762\pi$
$19$	−4.43355	−	4.43355i	−0.233345	−	0.233345i	−0.814087	+	0.580743i	$0.802762\pi$
$20$	5.55872	−	8.83809i	0.277936	−	0.441904i
$21$		0			0
$22$	3.66074	+	32.5538i	0.166397	+	1.47972i
$23$	−28.6638			−1.24625			−0.623127	−	0.782121i	$-0.714138\pi$
$23$	−28.6638			−1.24625			−0.623127	+	0.782121i	$0.714138\pi$
$24$		0			0
$25$		−	18.1868i		−	0.727472i
$26$	2.56449	+	22.8052i	0.0986344	+	0.877124i
$27$		0			0
$28$	0.884017	−	0.201365i	0.0315720	−	0.00719162i
$29$	−15.7561	+	15.7561i	−0.543312	+	0.543312i	−0.924498	−	0.381186i	$-0.875516\pi$
$29$	−15.7561	+	15.7561i	−0.543312	+	0.543312i	0.381186	+	0.924498i	$0.375516\pi$
$30$		0			0
$31$	−33.5751			−1.08307			−0.541534	−	0.840679i	$-0.682156\pi$
$31$	−33.5751			−1.08307			−0.541534	+	0.840679i	$0.682156\pi$
$32$	31.1899	+	7.15469i	0.974685	+	0.223584i
$33$		0			0
$34$	7.73441	−	9.69430i	0.227483	−	0.285126i
$35$	−0.418355	+	0.418355i	−0.0119530	+	0.0119530i
$36$		0			0
$37$	43.8384	−	43.8384i	1.18482	−	1.18482i	0.206342	−	0.978480i	$-0.433844\pi$
$37$	43.8384	−	43.8384i	1.18482	−	1.18482i	0.978480	−	0.206342i	$-0.0661558\pi$
$38$	1.40131	+	12.4614i	0.0368767	+	0.327932i
$39$		0			0
$40$	−19.7144	+	6.88388i	−0.492860	+	0.172097i
$41$	62.2969			1.51944			0.759719	−	0.650252i	$-0.225337\pi$
$41$	62.2969			1.51944			0.759719	+	0.650252i	$0.225337\pi$
$42$		0			0
$43$	18.3048	−	18.3048i	0.425692	−	0.425692i	−0.461466	−	0.887158i	$-0.652676\pi$
$43$	18.3048	−	18.3048i	0.425692	−	0.425692i	0.887158	+	0.461466i	$0.152676\pi$
$44$	34.8819	−	55.4605i	0.792770	−	1.26047i
$45$		0			0
$46$	44.8128	+	35.7530i	0.974190	+	0.777239i
$47$			13.8029i			0.293678i	0.989160	+	0.146839i	$0.0469099\pi$
$47$			13.8029i			0.293678i	−0.989160	+	0.146839i	$0.953090\pi$
$48$		0			0
$49$	48.9486			0.998951
$50$	−22.6848	+	28.4331i	−0.453695	+	0.568662i
$51$		0			0
$52$	24.4361	−	38.8522i	0.469926	−	0.747158i
$53$	37.9167	+	37.9167i	0.715409	+	0.715409i	0.967661	−	0.252252i	$-0.0811713\pi$
$53$	37.9167	+	37.9167i	0.715409	+	0.715409i	−0.252252	+	0.967661i	$0.581171\pi$
$54$		0			0
$55$			42.7539i			0.777344i
$56$	−1.63323	−	0.787840i	−0.0291648	−	0.0140686i
$57$		0			0
$58$	44.2857	−	4.98002i	0.763547	−	0.0858624i
$59$	−70.4759	−	70.4759i	−1.19451	−	1.19451i	−0.975788	−	0.218719i	$-0.929812\pi$
$59$	−70.4759	−	70.4759i	−1.19451	−	1.19451i	−0.218719	−	0.975788i	$-0.570188\pi$
$60$		0			0
$61$	−60.3861	−	60.3861i	−0.989936	−	0.989936i	0.0100137	−	0.999950i	$-0.496813\pi$
$61$	−60.3861	−	60.3861i	−0.989936	−	0.989936i	−0.999950	+	0.0100137i	$0.996813\pi$
$62$	52.4910	+	41.8789i	0.846629	+	0.675466i
$63$		0			0
$64$	−39.8378	−	50.0894i	−0.622466	−	0.782647i
$65$			29.9508i			0.460782i
$66$		0			0
$67$	61.9736	+	61.9736i	0.924979	+	0.924979i	0.997376	−	0.0723967i	$-0.0230648\pi$
$67$	61.9736	+	61.9736i	0.924979	+	0.924979i	−0.0723967	+	0.997376i	$0.523065\pi$
$68$	−24.1838	+	5.50869i	−0.355644	+	0.0810102i
$69$		0			0
$70$	1.17588	−	0.132230i	0.0167982	−	0.00188900i
$71$	32.5259			0.458111			0.229055	−	0.973413i	$-0.426436\pi$
$71$	32.5259			0.458111			0.229055	+	0.973413i	$0.426436\pi$
$72$		0			0
$73$			130.954i			1.79389i	0.442145	+	0.896944i	$0.354218\pi$
$73$			130.954i			1.79389i	−0.442145	+	0.896944i	$0.645782\pi$
$74$	−123.217	+	13.8560i	−1.66510	+	0.187243i
$75$		0			0
$76$	13.3526	−	21.2300i	0.175692	−	0.279342i
$77$	−2.62525	+	2.62525i	−0.0340941	+	0.0340941i
$78$		0			0
$79$	−132.387			−1.67579			−0.837894	−	0.545833i	$-0.816213\pi$
$79$	−132.387			−1.67579			−0.837894	+	0.545833i	$0.816213\pi$
$80$	39.4077	+	13.8280i	0.492596	+	0.172849i
$81$		0			0
$82$	−97.3944	−	77.7042i	−1.18774	−	0.947613i
$83$	19.2783	−	19.2783i	0.232268	−	0.232268i	−0.581371	−	0.813639i	$-0.697483\pi$
$83$	19.2783	−	19.2783i	0.232268	−	0.232268i	0.813639	+	0.581371i	$0.197483\pi$
$84$		0			0
$85$	11.4448	−	11.4448i	0.134645	−	0.134645i
$86$	−51.4494	+	5.78559i	−0.598249	+	0.0672743i
$87$		0			0
$88$	−123.711	+	43.1975i	−1.40581	+	0.490881i
$89$	91.2401			1.02517			0.512585	−	0.858637i	$-0.328688\pi$
$89$	91.2401			1.02517			0.512585	+	0.858637i	$0.328688\pi$
$90$		0			0
$91$	−1.83909	+	1.83909i	−0.0202098	+	0.0202098i
$92$	−25.4644	−	111.792i	−0.276787	−	1.21513i
$93$		0			0
$94$	17.2166	−	21.5793i	0.183155	−	0.229567i
$95$			16.3660i			0.172274i
$96$		0			0
$97$	−20.0808			−0.207019			−0.103509	−	0.994628i	$-0.533007\pi$
$97$	−20.0808			−0.207019			−0.103509	+	0.994628i	$0.533007\pi$
$98$	−76.5258	−	61.0546i	−0.780876	−	0.623006i
$99$		0			0
$100$	70.9303	−	16.1568i	0.709303	−	0.161568i
$101$	−29.7693	−	29.7693i	−0.294745	−	0.294745i	0.544206	−	0.838951i	$-0.316831\pi$
$101$	−29.7693	−	29.7693i	−0.294745	−	0.294745i	−0.838951	+	0.544206i	$0.816831\pi$
$102$		0			0
$103$			111.006i			1.07773i	0.842392	+	0.538865i	$0.181147\pi$
$103$			111.006i			1.07773i	−0.842392	+	0.538865i	$0.818853\pi$
$104$	−86.6644	+	30.2615i	−0.833312	+	0.290976i
$105$		0			0
$106$	−11.9843	−	106.573i	−0.113060	−	1.00540i
$107$	−13.1409	−	13.1409i	−0.122812	−	0.122812i	0.643029	−	0.765842i	$-0.277677\pi$
$107$	−13.1409	−	13.1409i	−0.122812	−	0.122812i	−0.765842	+	0.643029i	$0.777677\pi$
$108$		0			0
$109$	3.89888	+	3.89888i	0.0357696	+	0.0357696i	0.724765	−	0.688996i	$-0.241948\pi$
$109$	3.89888	+	3.89888i	0.0357696	+	0.0357696i	−0.688996	+	0.724765i	$0.741948\pi$
$110$	53.3279	−	66.8411i	0.484799	−	0.607647i
$111$		0			0
$112$	1.57069	+	3.26886i	0.0140240	+	0.0291863i
$113$		−	117.686i		−	1.04147i	−0.853718	−	0.520735i	$-0.825658\pi$
$113$		−	117.686i		−	1.04147i	0.853718	−	0.520735i	$-0.174342\pi$
$114$		0			0
$115$	52.9048	+	52.9048i	0.460041	+	0.460041i
$116$	−75.4476	−	47.4528i	−0.650410	−	0.409076i
$117$		0			0
$118$	22.2753	+	198.087i	0.188774	+	1.67871i
$119$	1.40551			0.0118110
$120$		0			0
$121$			147.288i			1.21726i
$122$	19.0863	+	169.728i	0.156445	+	1.39121i
$123$		0			0
$124$	−29.8275	−	130.946i	−0.240544	−	1.05602i
$125$	−79.7098	+	79.7098i	−0.637678	+	0.637678i
$126$		0			0
$127$	−43.1157			−0.339494			−0.169747	−	0.985488i	$-0.554295\pi$
$127$	−43.1157			−0.339494			−0.169747	+	0.985488i	$0.554295\pi$
$128$	−0.195463	+	128.000i	−0.00152705	+	0.999999i
$129$		0			0
$130$	37.3583	−	46.8248i	0.287371	−	0.360191i
$131$	97.5874	−	97.5874i	0.744942	−	0.744942i	−0.228583	−	0.973524i	$-0.573409\pi$
$131$	97.5874	−	97.5874i	0.744942	−	0.744942i	0.973524	+	0.228583i	$0.0734092\pi$
$132$		0			0
$133$	−1.00493	+	1.00493i	−0.00755588	+	0.00755588i
$134$	−19.5880	−	174.190i	−0.146179	−	1.29992i
$135$		0			0
$136$	44.6798	+	21.5527i	0.328528	+	0.158476i
$137$	49.2731			0.359658			0.179829	−	0.983698i	$-0.442446\pi$
$137$	49.2731			0.359658			0.179829	+	0.983698i	$0.442446\pi$
$138$		0			0
$139$	172.904	−	172.904i	1.24392	−	1.24392i	0.285552	−	0.958363i	$-0.407823\pi$
$139$	172.904	−	172.904i	1.24392	−	1.24392i	0.958363	−	0.285552i	$-0.0921769\pi$
$140$	−2.00329	−	1.25997i	−0.0143092	−	0.00899977i
$141$		0			0
$142$	−50.8506	−	40.5702i	−0.358103	−	0.285705i
$143$			187.946i			1.31431i
$144$		0			0
$145$	58.1618			0.401116
$146$	163.341	−	204.732i	1.11878	−	1.40227i
$147$		0			0
$148$	209.919	+	132.029i	1.41837	+	0.892087i
$149$	−128.537	−	128.537i	−0.862663	−	0.862663i	0.128984	−	0.991647i	$-0.458828\pi$
$149$	−128.537	−	128.537i	−0.862663	−	0.862663i	−0.991647	+	0.128984i	$0.958828\pi$
$150$		0			0
$151$		−	89.9523i		−	0.595710i	−0.954611	−	0.297855i	$-0.903729\pi$
$151$		−	89.9523i		−	0.595710i	0.954611	−	0.297855i	$-0.0962713\pi$
$152$	−47.3559	+	16.5358i	−0.311552	+	0.108788i
$153$		0			0
$154$	7.37882	−	0.829763i	0.0479144	−	0.00538807i
$155$	61.9695	+	61.9695i	0.399803	+	0.399803i
$156$		0			0
$157$	−95.2413	−	95.2413i	−0.606633	−	0.606633i	0.335432	−	0.942065i	$-0.391118\pi$
$157$	−95.2413	−	95.2413i	−0.606633	−	0.606633i	−0.942065	+	0.335432i	$0.891118\pi$
$158$	206.973	+	165.129i	1.30996	+	1.04512i
$159$		0			0
$160$	−44.3617	−	70.7725i	−0.277261	−	0.442328i
$161$			6.49709i			0.0403546i
$162$		0			0
$163$	−84.2958	−	84.2958i	−0.517152	−	0.517152i	0.399556	−	0.916709i	$-0.369164\pi$
$163$	−84.2958	−	84.2958i	−0.517152	−	0.517152i	−0.916709	+	0.399556i	$0.869164\pi$
$164$	55.3435	+	242.964i	0.337460	+	1.48149i
$165$		0			0
$166$	−54.1856	+	6.09328i	−0.326419	+	0.0367065i
$167$	193.153			1.15661			0.578304	−	0.815821i	$-0.303715\pi$
$167$	193.153			1.15661			0.578304	+	0.815821i	$0.303715\pi$
$168$		0			0
$169$		−	37.3362i		−	0.220924i
$170$	−32.1681	+	3.61737i	−0.189224	+	0.0212786i
$171$		0			0
$172$	87.6520	+	55.1288i	0.509605	+	0.320516i
$173$	−60.1097	+	60.1097i	−0.347455	+	0.347455i	−0.859161	−	0.511706i	$-0.829014\pi$
$173$	−60.1097	+	60.1097i	−0.347455	+	0.347455i	0.511706	+	0.859161i	$0.329014\pi$
$174$		0			0
$175$	−4.12231			−0.0235561
$176$	247.290	+	86.7727i	1.40506	+	0.493027i
$177$		0			0
$178$	−142.644	−	113.806i	−0.801370	−	0.639358i
$179$	−103.680	+	103.680i	−0.579217	+	0.579217i	−0.934687	−	0.355471i	$-0.884321\pi$
$179$	−103.680	+	103.680i	−0.579217	+	0.579217i	0.355471	+	0.934687i	$0.384321\pi$
$180$		0			0
$181$	−3.08029	+	3.08029i	−0.0170182	+	0.0170182i	−0.715565	−	0.698547i	$-0.753831\pi$
$181$	−3.08029	+	3.08029i	−0.0170182	+	0.0170182i	0.698547	+	0.715565i	$0.253831\pi$
$182$	5.16915	−	0.581282i	0.0284019	−	0.00319385i
$183$		0			0
$184$	−99.6293	+	206.537i	−0.541464	+	1.12248i
$185$	−161.825			−0.874729
$186$		0			0
$187$	71.8182	−	71.8182i	0.384054	−	0.384054i
$188$	−53.8326	+	12.2622i	−0.286343	+	0.0652246i
$189$		0			0
$190$	20.4136	−	25.5864i	0.107440	−	0.134665i
$191$			235.549i			1.23324i	0.787261	+	0.616620i	$0.211499\pi$
$191$			235.549i			1.23324i	−0.787261	+	0.616620i	$0.788501\pi$
$192$		0			0
$193$	−9.38546			−0.0486293			−0.0243147	−	0.999704i	$-0.507740\pi$
$193$	−9.38546			−0.0486293			−0.0243147	+	0.999704i	$0.507740\pi$
$194$	31.3941	+	25.0472i	0.161826	+	0.129109i
$195$		0			0
$196$	43.4851	+	190.905i	0.221863	+	0.974003i
$197$	−75.8630	−	75.8630i	−0.385091	−	0.385091i	0.487841	−	0.872932i	$-0.337785\pi$
$197$	−75.8630	−	75.8630i	−0.385091	−	0.385091i	−0.872932	+	0.487841i	$0.837785\pi$
$198$		0			0
$199$		−	315.653i		−	1.58620i	−0.609093	−	0.793099i	$-0.708466\pi$
$199$		−	315.653i		−	1.58620i	0.609093	−	0.793099i	$-0.291534\pi$
$200$	−131.045	−	63.2134i	−0.655223	−	0.316067i
$201$		0			0
$202$	9.40918	+	83.6728i	0.0465801	+	0.414222i
$203$	3.57135	+	3.57135i	0.0175928	+	0.0175928i
$204$		0			0
$205$	−114.981	−	114.981i	−0.560884	−	0.560884i
$206$	138.460	−	173.546i	0.672137	−	0.842456i
$207$		0			0
$208$	173.236	+	60.7877i	0.832866	+	0.292249i
$209$			102.699i			0.491384i
$210$		0			0
$211$	−20.9669	−	20.9669i	−0.0993692	−	0.0993692i	0.655675	−	0.755044i	$-0.272384\pi$
$211$	−20.9669	−	20.9669i	−0.0993692	−	0.0993692i	−0.755044	+	0.655675i	$0.772384\pi$
$212$	−114.194	+	181.563i	−0.538652	+	0.856431i
$213$		0			0
$214$	4.15345	+	36.9353i	0.0194087	+	0.172595i
$215$	−67.5701			−0.314280
$216$		0			0
$217$			7.61030i			0.0350705i
$218$	−1.23232	−	10.9586i	−0.00565285	−	0.0502690i
$219$		0			0
$220$	−166.745	+	37.9818i	−0.757930	+	0.172645i
$221$	50.3115	−	50.3115i	0.227654	−	0.227654i
$222$		0			0
$223$	317.091			1.42193			0.710966	−	0.703226i	$-0.248258\pi$
$223$	317.091			1.42193			0.710966	+	0.703226i	$0.248258\pi$
$224$	1.62172	−	7.06967i	0.00723982	−	0.0315610i
$225$		0			0
$226$	−146.792	+	183.989i	−0.649524	+	0.814113i
$227$	101.358	−	101.358i	0.446513	−	0.446513i	−0.447681	−	0.894193i	$-0.647750\pi$
$227$	101.358	−	101.358i	0.446513	−	0.446513i	0.894193	+	0.447681i	$0.147750\pi$
$228$		0			0
$229$	−83.7775	+	83.7775i	−0.365841	+	0.365841i	−0.865958	−	0.500117i	$-0.833290\pi$
$229$	−83.7775	+	83.7775i	−0.365841	+	0.365841i	0.500117	+	0.865958i	$0.333290\pi$
$230$	−16.7216	−	148.700i	−0.0727027	−	0.646522i
$231$		0			0
$232$	58.7652	+	168.295i	0.253298	+	0.725408i
$233$	−289.948			−1.24441			−0.622207	−	0.782853i	$-0.713764\pi$
$233$	−289.948			−1.24441			−0.622207	+	0.782853i	$0.713764\pi$
$234$		0			0
$235$	25.4759	−	25.4759i	0.108408	−	0.108408i
$236$	212.254	−	337.473i	0.899379	−	1.42997i
$237$		0			0
$238$	−2.19736	−	1.75312i	−0.00923260	−	0.00736605i
$239$		−	441.865i		−	1.84881i	−0.381413	−	0.924405i	$-0.624562\pi$
$239$		−	441.865i		−	1.84881i	0.381413	−	0.924405i	$-0.375438\pi$
$240$		0			0
$241$	−336.119			−1.39469			−0.697343	−	0.716738i	$-0.745634\pi$
$241$	−336.119			−1.39469			−0.697343	+	0.716738i	$0.745634\pi$
$242$	183.715	−	230.269i	0.759154	−	0.951524i
$243$		0			0
$244$	181.866	−	289.158i	0.745352	−	1.18507i
$245$	−90.3444	−	90.3444i	−0.368752	−	0.368752i
$246$		0			0
$247$			71.9449i			0.291275i
$248$	−116.700	+	241.925i	−0.470564	+	0.975502i
$249$		0			0
$250$	224.041	−	25.1939i	0.896165	−	0.100776i
$251$	73.9741	+	73.9741i	0.294717	+	0.294717i	0.838941	−	0.544223i	$-0.183176\pi$
$251$	73.9741	+	73.9741i	0.294717	+	0.294717i	−0.544223	+	0.838941i	$0.683176\pi$
$252$		0			0
$253$	331.986	+	331.986i	1.31220	+	1.31220i
$254$	67.4067	+	53.7791i	0.265381	+	0.211729i
$255$		0			0
$256$	159.962	−	199.870i	0.624853	−	0.780742i
$257$		−	441.535i		−	1.71803i	−0.511947	−	0.859017i	$-0.671076\pi$
$257$		−	441.535i		−	1.71803i	0.511947	−	0.859017i	$-0.328924\pi$
$258$		0			0
$259$	−9.93664	−	9.93664i	−0.0383654	−	0.0383654i
$260$	−116.811	+	26.6078i	−0.449274	+	0.102338i
$261$		0			0
$262$	−274.290	+	30.8445i	−1.04691	+	0.117727i
$263$	−116.115			−0.441503			−0.220752	−	0.975330i	$-0.570851\pi$
$263$	−116.115			−0.441503			−0.220752	+	0.975330i	$0.570851\pi$
$264$		0			0
$265$		−	139.965i		−	0.528171i
$266$	2.82457	−	0.317629i	0.0106187	−	0.00119409i
$267$		0			0
$268$	−186.647	+	296.760i	−0.696444	+	1.10731i
$269$	−46.5610	+	46.5610i	−0.173089	+	0.173089i	−0.788335	−	0.615246i	$-0.789057\pi$
$269$	−46.5610	+	46.5610i	−0.173089	+	0.173089i	0.615246	+	0.788335i	$0.289057\pi$
$270$		0			0
$271$	−343.577			−1.26781			−0.633907	−	0.773410i	$-0.718550\pi$
$271$	−343.577			−1.26781			−0.633907	+	0.773410i	$0.718550\pi$
$272$	−42.9689	−	89.4254i	−0.157974	−	0.328770i
$273$		0			0
$274$	−77.0331	−	61.4594i	−0.281143	−	0.224304i
$275$	−210.641	+	210.641i	−0.765966	+	0.765966i
$276$		0			0
$277$	10.4668	−	10.4668i	0.0377863	−	0.0377863i	−0.687961	−	0.725747i	$-0.741494\pi$
$277$	10.4668	−	10.4668i	0.0377863	−	0.0377863i	0.725747	+	0.687961i	$0.241494\pi$
$278$	−485.984	+	54.6499i	−1.74814	+	0.196582i
$279$		0			0
$280$	1.56034	+	4.46856i	0.00557263	+	0.0159592i
$281$	56.0486			0.199461			0.0997306	−	0.995014i	$-0.468202\pi$
$281$	56.0486			0.199461			0.0997306	+	0.995014i	$0.468202\pi$
$282$		0			0
$283$	−248.129	+	248.129i	−0.876782	+	0.876782i	−0.993200	−	0.116418i	$-0.962859\pi$
$283$	−248.129	+	248.129i	−0.876782	+	0.876782i	0.116418	+	0.993200i	$0.462859\pi$
$284$	28.8954	+	126.854i	0.101744	+	0.446669i
$285$		0			0
$286$	234.429	−	293.834i	0.819683	−	1.02739i
$287$		−	14.1205i		−	0.0492005i
$288$		0			0
$289$	250.550			0.866955
$290$	−90.9297	−	72.5464i	−0.313551	−	0.250160i
$291$		0			0
$292$	−510.733	+	116.337i	−1.74908	+	0.398414i
$293$	243.305	+	243.305i	0.830392	+	0.830392i	0.987570	−	0.157178i	$-0.0502397\pi$
$293$	243.305	+	243.305i	0.830392	+	0.830392i	−0.157178	+	0.987570i	$0.550240\pi$
$294$		0			0
$295$			260.154i			0.881880i
$296$	−163.504	−	468.250i	−0.552377	−	1.58192i
$297$		0			0
$298$	40.6266	+	361.280i	0.136331	+	1.21235i
$299$	232.569	+	232.569i	0.777824	+	0.777824i
$300$		0			0
$301$	−4.14905	−	4.14905i	−0.0137842	−	0.0137842i
$302$	−112.199	+	140.631i	−0.371521	+	0.465664i
$303$		0			0
$304$	94.6613	+	33.2161i	0.311386	+	0.109264i
$305$			222.909i			0.730849i
$306$		0			0
$307$	−29.1965	−	29.1965i	−0.0951028	−	0.0951028i	0.657955	−	0.753057i	$-0.271422\pi$
$307$	−29.1965	−	29.1965i	−0.0951028	−	0.0951028i	−0.753057	+	0.657955i	$0.771422\pi$
$308$	−12.5710	−	7.90651i	−0.0408148	−	0.0256705i
$309$		0			0
$310$	−19.5867	−	174.178i	−0.0631829	−	0.561866i
$311$	5.31281			0.0170830			0.00854150	−	0.999964i	$-0.497281\pi$
$311$	5.31281			0.0170830			0.00854150	+	0.999964i	$0.497281\pi$
$312$		0			0
$313$		−	71.0570i		−	0.227019i	−0.993537	−	0.113510i	$-0.963791\pi$
$313$		−	71.0570i		−	0.227019i	0.993537	−	0.113510i	$-0.0362093\pi$
$314$	30.1030	+	267.696i	0.0958693	+	0.852535i
$315$		0			0
$316$	−117.610	−	516.323i	−0.372185	−	1.63393i
$317$	340.594	−	340.594i	1.07443	−	1.07443i	0.0774326	−	0.996998i	$-0.475328\pi$
$317$	340.594	−	340.594i	1.07443	−	1.07443i	0.996998	−	0.0774326i	$-0.0246723\pi$
$318$		0			0
$319$	364.975			1.14412
$320$	−18.9213	+	165.978i	−0.0591291	+	0.518683i
$321$		0			0
$322$	8.10395	−	10.1575i	0.0251676	−	0.0315450i
$323$	27.4916	−	27.4916i	0.0851134	−	0.0851134i
$324$		0			0
$325$	−147.562	+	147.562i	−0.454037	+	0.454037i
$326$	26.6434	+	236.931i	0.0817282	+	0.726783i
$327$		0			0
$328$	216.531	−	448.879i	0.660155	−	1.36853i
$329$	3.12863			0.00950951
$330$		0			0
$331$	−283.647	+	283.647i	−0.856939	+	0.856939i	−0.990976	−	0.134038i	$-0.957206\pi$
$331$	−283.647	+	283.647i	−0.856939	+	0.856939i	0.134038	+	0.990976i	$0.457206\pi$
$332$	92.3136	+	58.0607i	0.278053	+	0.174882i
$333$		0			0
$334$	−301.974	−	240.924i	−0.904115	−	0.721330i
$335$		−	228.769i		−	0.682893i
$336$		0			0
$337$	−44.9447			−0.133367			−0.0666835	−	0.997774i	$-0.521242\pi$
$337$	−44.9447			−0.133367			−0.0666835	+	0.997774i	$0.521242\pi$
$338$	−46.5702	+	58.3711i	−0.137782	+	0.172695i
$339$		0			0
$340$	54.8034	+	34.4686i	0.161186	+	0.101378i
$341$	388.869	+	388.869i	1.14038	+	1.14038i
$342$		0			0
$343$		−	22.2015i		−	0.0647275i
$344$	−68.2711	−	195.518i	−0.198463	−	0.568366i
$345$		0			0
$346$	168.951	−	18.9989i	0.488298	−	0.0549101i
$347$	−272.333	−	272.333i	−0.784821	−	0.784821i	0.195819	−	0.980640i	$-0.437263\pi$
$347$	−272.333	−	272.333i	−0.784821	−	0.784821i	−0.980640	+	0.195819i	$0.937263\pi$
$348$		0			0
$349$	178.956	+	178.956i	0.512768	+	0.512768i	0.915374	−	0.402605i	$-0.131895\pi$
$349$	178.956	+	178.956i	0.512768	+	0.512768i	−0.402605	+	0.915374i	$0.631895\pi$
$350$	6.44479	+	5.14185i	0.0184137	+	0.0146910i
$351$		0			0
$352$	−278.377	−	444.109i	−0.790844	−	1.26167i
$353$			698.328i			1.97827i	0.147025	+	0.989133i	$0.453030\pi$
$353$			698.328i			1.97827i	−0.147025	+	0.989133i	$0.546970\pi$
$354$		0			0
$355$	−60.0329	−	60.0329i	−0.169107	−	0.169107i
$356$	81.0561	+	355.845i	0.227686	+	0.999566i
$357$		0			0
$358$	291.414	−	32.7701i	0.814005	−	0.0915366i
$359$	364.766			1.01606			0.508030	−	0.861339i	$-0.330374\pi$
$359$	364.766			1.01606			0.508030	+	0.861339i	$0.330374\pi$
$360$		0			0
$361$		−	321.687i		−	0.891100i
$362$	8.65779	−	0.973586i	0.0239166	−	0.00268947i
$363$		0			0
$364$	−8.80645	−	5.53882i	−0.0241935	−	0.0152165i
$365$	241.701	−	241.701i	0.662195	−	0.662195i
$366$		0			0
$367$	632.894			1.72451			0.862254	−	0.506476i	$-0.169052\pi$
$367$	632.894			1.72451			0.862254	+	0.506476i	$0.169052\pi$
$368$	413.377	−	198.628i	1.12331	−	0.539749i
$369$		0			0
$370$	252.996	+	201.848i	0.683772	+	0.545534i
$371$	8.59439	−	8.59439i	0.0231655	−	0.0231655i
$372$		0			0
$373$	33.3679	−	33.3679i	0.0894582	−	0.0894582i	−0.660962	−	0.750420i	$-0.729851\pi$
$373$	33.3679	−	33.3679i	0.0894582	−	0.0894582i	0.750420	+	0.660962i	$0.229851\pi$
$374$	−201.860	+	22.6996i	−0.539733	+	0.0606941i
$375$		0			0
$376$	99.4563	+	47.9758i	0.264511	+	0.127595i
$377$	255.679			0.678194
$378$		0			0
$379$	−439.149	+	439.149i	−1.15870	+	1.15870i	−0.173950	+	0.984755i	$0.555653\pi$
$379$	−439.149	+	439.149i	−1.15870	+	1.15870i	−0.984755	+	0.173950i	$0.944347\pi$
$380$	−63.8290	+	14.5393i	−0.167971	+	0.0382612i
$381$		0			0
$382$	293.805	−	368.255i	0.769123	−	0.964018i
$383$		−	168.628i		−	0.440283i	−0.975468	−	0.220142i	$-0.929348\pi$
$383$		−	168.628i		−	0.440283i	0.975468	−	0.220142i	$-0.0706519\pi$
$384$		0			0
$385$	9.69083			0.0251710
$386$	14.6731	+	11.7067i	0.0380133	+	0.0303282i
$387$		0			0
$388$	−17.8394	−	78.3171i	−0.0459779	−	0.201848i
$389$	54.4610	+	54.4610i	0.140003	+	0.140003i	0.773635	−	0.633632i	$-0.218437\pi$
$389$	54.4610	+	54.4610i	0.140003	+	0.140003i	−0.633632	+	0.773635i	$0.718437\pi$
$390$		0			0
$391$		−	177.739i		−	0.454576i
$392$	170.135	−	352.698i	0.434018	−	0.899740i
$393$		0			0
$394$	23.9780	+	213.229i	0.0608579	+	0.541190i
$395$	244.347	+	244.347i	0.618600	+	0.618600i
$396$		0			0
$397$	446.859	+	446.859i	1.12559	+	1.12559i	0.990886	+	0.134704i	$0.0430085\pi$
$397$	446.859	+	446.859i	1.12559	+	1.12559i	0.134704	+	0.990886i	$0.456992\pi$
$398$	−393.721	+	493.489i	−0.989248	+	1.23992i
$399$		0			0
$400$	126.026	+	262.282i	0.315066	+	0.655705i
$401$		−	7.95350i		−	0.0198342i	−0.999951	−	0.00991709i	$-0.996843\pi$
$401$		−	7.95350i		−	0.0198342i	0.999951	−	0.00991709i	$-0.00315676\pi$
$402$		0			0
$403$	272.418	+	272.418i	0.675975	+	0.675975i
$404$	89.6566	−	142.550i	0.221922	−	0.352845i
$405$		0			0
$406$	−1.12880	−	10.0380i	−0.00278029	−	0.0247242i
$407$	−1015.48			−2.49503
$408$		0			0
$409$		−	624.006i		−	1.52569i	−0.646583	−	0.762843i	$-0.723803\pi$
$409$		−	624.006i		−	1.52569i	0.646583	−	0.762843i	$-0.276197\pi$
$410$	36.3422	+	323.179i	0.0886394	+	0.788242i
$411$		0			0
$412$	−432.935	+	98.6158i	−1.05081	+	0.239359i
$413$	−15.9744	+	15.9744i	−0.0386790	+	0.0386790i
$414$		0			0
$415$	−71.1637			−0.171479
$416$	−195.014	−	311.116i	−0.468784	−	0.747875i
$417$		0			0
$418$	128.099	−	160.559i	0.306457	−	0.384113i
$419$	57.4026	−	57.4026i	0.136999	−	0.136999i	−0.635282	−	0.772281i	$-0.719116\pi$
$419$	57.4026	−	57.4026i	0.136999	−	0.136999i	0.772281	+	0.635282i	$0.219116\pi$
$420$		0			0
$421$	−4.45855	+	4.45855i	−0.0105904	+	0.0105904i	−0.712382	−	0.701792i	$-0.752384\pi$
$421$	−4.45855	+	4.45855i	−0.0105904	+	0.0105904i	0.701792	+	0.712382i	$0.252384\pi$
$422$	6.62701	+	58.9319i	0.0157038	+	0.139649i
$423$		0			0
$424$	404.998	−	141.418i	0.955184	−	0.333532i
$425$	112.773			0.265348
$426$		0			0
$427$	−13.6874	+	13.6874i	−0.0320549	+	0.0320549i
$428$	39.5767	−	62.9251i	0.0924690	−	0.147021i
$429$		0			0
$430$	105.639	+	84.2816i	0.245671	+	0.196004i
$431$		−	515.590i		−	1.19626i	−0.801397	−	0.598132i	$-0.795910\pi$
$431$		−	515.590i		−	1.19626i	0.801397	−	0.598132i	$-0.204090\pi$
$432$		0			0
$433$	301.416			0.696111			0.348056	−	0.937474i	$-0.386842\pi$
$433$	301.416			0.696111			0.348056	+	0.937474i	$0.386842\pi$
$434$	9.49249	−	11.8979i	0.0218721	−	0.0274145i
$435$		0			0
$436$	−11.7423	+	18.6697i	−0.0269320	+	0.0428205i
$437$	127.083	+	127.083i	0.290807	+	0.290807i
$438$		0			0
$439$			656.561i			1.49558i	0.663933	+	0.747792i	$0.268886\pi$
$439$			656.561i			1.49558i	−0.663933	+	0.747792i	$0.731114\pi$
$440$	308.063	+	148.604i	0.700142	+	0.337735i
$441$		0			0
$442$	−141.411	+	15.9020i	−0.319934	+	0.0359773i
$443$	−229.799	−	229.799i	−0.518733	−	0.518733i	0.398455	−	0.917188i	$-0.369546\pi$
$443$	−229.799	−	229.799i	−0.518733	−	0.518733i	−0.917188	+	0.398455i	$0.869546\pi$
$444$		0			0
$445$	−168.402	−	168.402i	−0.378431	−	0.378431i
$446$	−495.737	−	395.514i	−1.11152	−	0.886803i
$447$		0			0
$448$	−11.3535	+	9.02985i	−0.0253427	+	0.0201559i
$449$		−	184.489i		−	0.410888i	−0.978669	−	0.205444i	$-0.934136\pi$
$449$		−	184.489i		−	0.410888i	0.978669	−	0.205444i	$-0.0658639\pi$
$450$		0			0
$451$	−721.526	−	721.526i	−1.59984	−	1.59984i
$452$	458.988	−	104.550i	1.01546	−	0.231306i
$453$		0			0
$454$	−284.889	+	32.0364i	−0.627509	+	0.0705647i
$455$	6.78881			0.0149205
$456$		0			0
$457$		−	376.876i		−	0.824673i	−0.911032	−	0.412336i	$-0.864713\pi$
$457$		−	376.876i		−	0.824673i	0.911032	−	0.412336i	$-0.135287\pi$
$458$	235.474	−	26.4796i	0.514136	−	0.0578157i
$459$		0			0
$460$	−159.334	+	253.333i	−0.346379	+	0.550725i
$461$	28.5551	−	28.5551i	0.0619418	−	0.0619418i	−0.675457	−	0.737399i	$-0.736054\pi$
$461$	28.5551	−	28.5551i	0.0619418	−	0.0619418i	0.737399	+	0.675457i	$0.236054\pi$
$462$		0			0
$463$	−144.828			−0.312803			−0.156401	−	0.987694i	$-0.549989\pi$
$463$	−144.828			−0.312803			−0.156401	+	0.987694i	$0.549989\pi$
$464$	118.044	−	336.409i	0.254406	−	0.725020i
$465$		0			0
$466$	453.303	+	361.659i	0.972752	+	0.776091i
$467$	−366.519	+	366.519i	−0.784837	+	0.784837i	−0.980643	−	0.195806i	$-0.937268\pi$
$467$	−366.519	+	366.519i	−0.784837	+	0.784837i	0.195806	+	0.980643i	$0.437268\pi$
$468$		0			0
$469$	14.0473	−	14.0473i	0.0299515	−	0.0299515i
$470$	−71.6055	+	8.05218i	−0.152352	+	0.0171323i
$471$		0			0
$472$	−752.772	+	262.853i	−1.59486	+	0.556893i
$473$	−424.014			−0.896435
$474$		0			0
$475$	−80.6321	+	80.6321i	−0.169752	+	0.169752i
$476$	1.24863	+	5.48162i	0.00262317	+	0.0115160i
$477$		0			0
$478$	−551.148	+	690.808i	−1.15303	+	1.44521i
$479$			119.680i			0.249853i	0.992166	+	0.124927i	$0.0398696\pi$
$479$			119.680i			0.249853i	−0.992166	+	0.124927i	$0.960130\pi$
$480$		0			0
$481$	−711.382			−1.47896
$482$	525.486	+	419.248i	1.09022	+	0.869810i
$483$		0			0
$484$	−574.438	+	130.848i	−1.18686	+	0.270347i
$485$	37.0631	+	37.0631i	0.0764188	+	0.0764188i
$486$		0			0
$487$		−	637.829i		−	1.30971i	−0.755754	−	0.654855i	$-0.772730\pi$
$487$		−	637.829i		−	1.30971i	0.755754	−	0.654855i	$-0.227270\pi$
$488$	−645.000	+	225.222i	−1.32172	+	0.461520i
$489$		0			0
$490$	28.5552	+	253.932i	0.0582758	+	0.518228i
$491$	130.249	+	130.249i	0.265273	+	0.265273i	0.827192	−	0.561919i	$-0.189937\pi$
$491$	130.249	+	130.249i	0.265273	+	0.265273i	−0.561919	+	0.827192i	$0.689937\pi$
$492$		0			0
$493$	−97.7004	−	97.7004i	−0.198175	−	0.198175i
$494$	89.7383	−	112.478i	0.181657	−	0.227688i
$495$		0			0
$496$	484.205	−	232.661i	0.976220	−	0.469074i
$497$		−	7.37248i		−	0.0148340i
$498$		0			0
$499$	7.28612	+	7.28612i	0.0146014	+	0.0146014i	0.714370	−	0.699768i	$-0.246713\pi$
$499$	7.28612	+	7.28612i	0.0146014	+	0.0146014i	−0.699768	+	0.714370i	$0.746713\pi$
$500$	−381.689	−	240.063i	−0.763378	−	0.480127i
$501$		0			0
$502$	−23.3810	−	207.920i	−0.0465757	−	0.414183i
$503$	−311.009			−0.618307			−0.309154	−	0.951012i	$-0.600046\pi$
$503$	−311.009			−0.618307			−0.309154	+	0.951012i	$0.600046\pi$
$504$		0			0
$505$			109.890i			0.217604i
$506$	−104.931	−	933.117i	−0.207373	−	1.84410i
$507$		0			0
$508$	−38.3032	−	168.156i	−0.0754001	−	0.331015i
$509$	−431.114	+	431.114i	−0.846983	+	0.846983i	−0.989756	−	0.142773i	$-0.954398\pi$
$509$	−431.114	+	431.114i	−0.846983	+	0.846983i	0.142773	+	0.989756i	$0.454398\pi$
$510$		0			0
$511$	29.6827			0.0580874
$512$	−499.386	+	112.950i	−0.975363	+	0.220606i
$513$		0			0
$514$	−550.735	+	690.291i	−1.07147	+	1.34298i
$515$	204.884	−	204.884i	0.397832	−	0.397832i
$516$		0			0
$517$	159.866	−	159.866i	0.309218	−	0.309218i
$518$	3.14068	+	27.9290i	0.00606308	+	0.0539170i
$519$		0			0
$520$	215.810	+	104.103i	0.415019	+	0.200197i
$521$	−241.849			−0.464201			−0.232101	−	0.972692i	$-0.574560\pi$
$521$	−241.849			−0.464201			−0.232101	+	0.972692i	$0.574560\pi$
$522$		0			0
$523$	183.752	−	183.752i	0.351342	−	0.351342i	−0.509267	−	0.860609i	$-0.670083\pi$
$523$	183.752	−	183.752i	0.351342	−	0.351342i	0.860609	+	0.509267i	$0.170083\pi$
$524$	467.295	+	293.906i	0.891785	+	0.560888i
$525$		0			0
$526$	181.534	+	144.833i	0.345121	+	0.275348i
$527$		−	208.193i		−	0.395053i
$528$		0			0
$529$	292.615			0.553147
$530$	−174.582	+	218.821i	−0.329400	+	0.412869i
$531$		0			0
$532$	−4.81210	−	3.02657i	−0.00904529	−	0.00568904i
$533$	−505.458	−	505.458i	−0.948326	−	0.948326i
$534$		0			0
$535$			48.5083i			0.0906698i
$536$	661.956	−	231.142i	1.23499	−	0.431236i
$537$		0			0
$538$	130.869	−	14.7165i	0.243252	−	0.0273542i
$539$	−566.926	−	566.926i	−1.05181	−	1.05181i
$540$		0			0
$541$	−186.010	−	186.010i	−0.343826	−	0.343826i	0.513978	−	0.857803i	$-0.328171\pi$
$541$	−186.010	−	186.010i	−0.343826	−	0.343826i	−0.857803	+	0.513978i	$0.828171\pi$
$542$	537.146	+	428.551i	0.991044	+	0.790685i
$543$		0			0
$544$	−44.3649	+	193.403i	−0.0815532	+	0.355520i
$545$		−	14.3923i		−	0.0264079i
$546$		0			0
$547$	244.192	+	244.192i	0.446421	+	0.446421i	0.894163	−	0.447742i	$-0.147772\pi$
$547$	244.192	+	244.192i	0.446421	+	0.446421i	−0.447742	+	0.894163i	$0.647772\pi$
$548$	43.7734	+	192.170i	0.0798784	+	0.350675i
$549$		0			0
$550$	592.050	−	66.5772i	1.07645	−	0.121049i
$551$	139.711			0.253558
$552$		0			0
$553$			30.0076i			0.0542632i
$554$	−29.4192	+	3.30824i	−0.0531032	+	0.00597156i
$555$		0			0
$556$	827.949	+	520.739i	1.48912	+	0.936580i
$557$	367.416	−	367.416i	0.659634	−	0.659634i	−0.295659	−	0.955293i	$-0.595539\pi$
$557$	367.416	−	367.416i	0.659634	−	0.659634i	0.955293	+	0.295659i	$0.0955393\pi$
$558$		0			0
$559$	−297.038			−0.531374
$560$	3.13432	−	8.93235i	0.00559699	−	0.0159506i
$561$		0			0
$562$	−87.6259	−	69.9106i	−0.155918	−	0.124396i
$563$	−418.290	+	418.290i	−0.742967	+	0.742967i	−0.973148	−	0.230181i	$-0.926068\pi$
$563$	−418.290	+	418.290i	−0.742967	+	0.742967i	0.230181	+	0.973148i	$0.426068\pi$
$564$		0			0
$565$	−217.213	+	217.213i	−0.384448	+	0.384448i
$566$	697.420	−	78.4263i	1.23219	−	0.138562i
$567$		0			0
$568$	113.053	−	234.364i	0.199037	−	0.412613i
$569$	−439.363			−0.772166			−0.386083	−	0.922464i	$-0.626172\pi$
$569$	−439.363			−0.772166			−0.386083	+	0.922464i	$0.626172\pi$
$570$		0			0
$571$	−81.8476	+	81.8476i	−0.143341	+	0.143341i	−0.775136	−	0.631795i	$-0.782318\pi$
$571$	−81.8476	+	81.8476i	−0.143341	+	0.143341i	0.631795	+	0.775136i	$0.282318\pi$
$572$	−733.009	+	166.968i	−1.28148	+	0.291902i
$573$		0			0
$574$	−17.6128	+	22.0759i	−0.0306844	+	0.0384598i
$575$			521.303i			0.906614i
$576$		0			0
$577$	303.497			0.525992			0.262996	−	0.964797i	$-0.415289\pi$
$577$	303.497			0.525992			0.262996	+	0.964797i	$0.415289\pi$
$578$	−391.707	−	312.516i	−0.677694	−	0.540685i
$579$		0			0
$580$	51.6699	+	226.837i	0.0890861	+	0.391098i
$581$	−4.36971	−	4.36971i	−0.00752101	−	0.00752101i
$582$		0			0
$583$		−	878.306i		−	1.50653i
$584$	943.585	+	455.167i	1.61573	+	0.779396i
$585$		0			0
$586$	−76.9014	−	683.860i	−0.131231	−	1.16700i
$587$	670.665	+	670.665i	1.14253	+	1.14253i	0.987986	+	0.154543i	$0.0493905\pi$
$587$	670.665	+	670.665i	1.14253	+	1.14253i	0.154543	+	0.987986i	$0.450609\pi$
$588$		0			0
$589$	148.857	+	148.857i	0.252728	+	0.252728i
$590$	324.496	−	406.723i	0.549993	−	0.689361i
$591$		0			0
$592$	−328.437	+	935.999i	−0.554792	+	1.58108i
$593$		−	390.656i		−	0.658779i	−0.944194	−	0.329390i	$-0.893157\pi$
$593$		−	390.656i		−	0.658779i	0.944194	−	0.329390i	$-0.106843\pi$
$594$		0			0
$595$	−2.59414	−	2.59414i	−0.00435991	−	0.00435991i
$596$	387.116	−	615.496i	0.649524	−	1.03271i
$597$		0			0
$598$	−73.5082	−	653.685i	−0.122923	−	1.09312i
$599$	788.713			1.31672			0.658358	−	0.752705i	$-0.271251\pi$
$599$	788.713			1.31672			0.658358	+	0.752705i	$0.271251\pi$
$600$		0			0
$601$		−	30.8170i		−	0.0512762i	−0.999671	−	0.0256381i	$-0.991838\pi$
$601$		−	30.8170i		−	0.0512762i	0.999671	−	0.0256381i	$-0.00816176\pi$
$602$	1.31139	+	11.6618i	0.00217839	+	0.0193717i
$603$		0			0
$604$	350.823	−	79.9120i	0.580832	−	0.132305i
$605$	271.849	−	271.849i	0.449337	−	0.449337i
$606$		0			0
$607$	607.774			1.00128			0.500638	−	0.865657i	$-0.333099\pi$
$607$	607.774			1.00128			0.500638	+	0.865657i	$0.333099\pi$
$608$	−106.561	−	170.003i	−0.175265	−	0.279610i
$609$		0			0
$610$	278.039	−	348.494i	0.455802	−	0.571301i
$611$	111.992	−	111.992i	0.183293	−	0.183293i
$612$		0			0
$613$	507.089	−	507.089i	0.827225	−	0.827225i	−0.159907	−	0.987132i	$-0.551119\pi$
$613$	507.089	−	507.089i	0.827225	−	0.827225i	0.987132	+	0.159907i	$0.0511194\pi$
$614$	9.22816	+	82.0631i	0.0150296	+	0.133653i
$615$		0			0
$616$	9.79137	+	28.0410i	0.0158951	+	0.0455211i
$617$	202.840			0.328752			0.164376	−	0.986398i	$-0.447439\pi$
$617$	202.840			0.328752			0.164376	+	0.986398i	$0.447439\pi$
$618$		0			0
$619$	699.181	−	699.181i	1.12953	−	1.12953i	0.139280	−	0.990253i	$-0.455521\pi$
$619$	699.181	−	699.181i	1.12953	−	1.12953i	0.990253	−	0.139280i	$-0.0444787\pi$
$620$	−186.635	+	296.740i	−0.301023	+	0.478612i
$621$		0			0
$622$	−8.30600	−	6.62678i	−0.0133537	−	0.0106540i
$623$		−	20.6809i		−	0.0331957i
$624$		0			0
$625$	−160.430			−0.256687
$626$	−88.6308	+	111.090i	−0.141583	+	0.177460i
$627$		0			0
$628$	286.840	−	456.061i	0.456752	−	0.726212i
$629$	271.834	+	271.834i	0.432168	+	0.432168i
$630$		0			0
$631$			269.488i			0.427081i	0.976934	+	0.213540i	$0.0684995\pi$
$631$			269.488i			0.427081i	−0.976934	+	0.213540i	$0.931501\pi$
$632$	−460.150	+	953.913i	−0.728085	+	1.50936i
$633$		0			0
$634$	−957.313	+	107.652i	−1.50996	+	0.169798i
$635$	79.5786	+	79.5786i	0.125321	+	0.125321i
$636$		0			0
$637$	−397.154	−	397.154i	−0.623475	−	0.623475i
$638$	−570.598	−	455.241i	−0.894355	−	0.713544i
$639$		0			0
$640$	236.610	−	235.888i	0.369703	−	0.368575i
$641$			638.869i			0.996676i	0.866983	+	0.498338i	$0.166056\pi$
$641$			638.869i			0.996676i	−0.866983	+	0.498338i	$0.833944\pi$
$642$		0			0
$643$	161.282	+	161.282i	0.250827	+	0.250827i	0.821310	−	0.570483i	$-0.193244\pi$
$643$	161.282	+	161.282i	0.250827	+	0.250827i	−0.570483	+	0.821310i	$0.693244\pi$
$644$	−25.3393	+	5.77190i	−0.0393467	+	0.00896258i
$645$		0			0
$646$	−77.2710	+	8.68929i	−0.119615	+	0.0134509i
$647$	921.712			1.42459			0.712297	−	0.701878i	$-0.247655\pi$
$647$	921.712			1.42459			0.712297	+	0.701878i	$0.247655\pi$
$648$		0			0
$649$			1632.51i			2.51543i
$650$	414.754	−	46.6399i	0.638083	−	0.0717538i
$651$		0			0
$652$	253.875	−	403.649i	0.389379	−	0.619093i
$653$	−661.262	+	661.262i	−1.01265	+	1.01265i	−0.0127331	+	0.999919i	$0.504053\pi$
$653$	−661.262	+	661.262i	−1.01265	+	1.01265i	−0.999919	+	0.0127331i	$0.995947\pi$
$654$		0			0
$655$	−360.234			−0.549975
$656$	−898.418	+	431.690i	−1.36954	+	0.658064i
$657$		0			0
$658$	−4.89127	−	3.90240i	−0.00743354	−	0.00593070i
$659$	702.485	−	702.485i	1.06599	−	1.06599i	0.0683229	−	0.997663i	$-0.478235\pi$
$659$	702.485	−	702.485i	1.06599	−	1.06599i	0.997663	−	0.0683229i	$-0.0217648\pi$
$660$		0			0
$661$	−451.292	+	451.292i	−0.682741	+	0.682741i	−0.960617	−	0.277876i	$-0.910370\pi$
$661$	−451.292	+	451.292i	−0.682741	+	0.682741i	0.277876	+	0.960617i	$0.410370\pi$
$662$	797.249	−	89.6523i	1.20430	−	0.135426i
$663$		0			0
$664$	−71.9020	−	205.916i	−0.108286	−	0.310115i
$665$	3.70960			0.00557835
$666$		0			0
$667$	451.629	−	451.629i	0.677104	−	0.677104i
$668$	171.594	+	753.318i	0.256877	+	1.12772i
$669$		0			0
$670$	−285.348	+	357.656i	−0.425893	+	0.533814i
$671$			1398.79i			2.08464i
$672$		0			0
$673$	−626.462			−0.930849			−0.465425	−	0.885088i	$-0.654098\pi$
$673$	−626.462			−0.930849			−0.465425	+	0.885088i	$0.654098\pi$
$674$	70.2661	+	56.0604i	0.104252	+	0.0831757i
$675$		0			0
$676$	145.615	−	33.1688i	0.215407	−	0.0490663i
$677$	−652.167	−	652.167i	−0.963318	−	0.963318i	0.0360323	−	0.999351i	$-0.488528\pi$
$677$	−652.167	−	652.167i	−0.963318	−	0.963318i	−0.999351	+	0.0360323i	$0.988528\pi$
$678$		0			0
$679$			4.55162i			0.00670342i
$680$	−42.6857	−	122.245i	−0.0627731	−	0.179772i
$681$		0			0
$682$	−122.910	−	1093.00i	−0.180220	−	1.60264i
$683$	331.471	+	331.471i	0.485316	+	0.485316i	0.906824	−	0.421509i	$-0.138499\pi$
$683$	331.471	+	331.471i	0.485316	+	0.485316i	−0.421509	+	0.906824i	$0.638499\pi$
$684$		0			0
$685$	−90.9433	−	90.9433i	−0.132764	−	0.132764i
$686$	−27.6924	+	34.7097i	−0.0403680	+	0.0505972i
$687$		0			0
$688$	−137.139	+	390.827i	−0.199330	+	0.568063i
$689$		−	615.288i		−	0.893016i
$690$		0			0
$691$	648.386	+	648.386i	0.938331	+	0.938331i	0.998206	−	0.0598752i	$-0.0190703\pi$
$691$	648.386	+	648.386i	0.938331	+	0.938331i	−0.0598752	+	0.998206i	$0.519070\pi$
$692$	−287.834	−	181.034i	−0.415946	−	0.261609i
$693$		0			0
$694$	86.0763	+	765.449i	0.124029	+	1.10295i
$695$	−638.258			−0.918357
$696$		0			0
$697$			386.292i			0.554221i
$698$	−56.5627	−	502.994i	−0.0810354	−	0.720622i
$699$		0			0
$700$	−3.66219	−	16.0774i	−0.00523170	−	0.0229678i
$701$	−557.872	+	557.872i	−0.795823	+	0.795823i	−0.982434	−	0.186611i	$-0.940250\pi$
$701$	−557.872	+	557.872i	−0.795823	+	0.795823i	0.186611	+	0.982434i	$0.440250\pi$
$702$		0			0
$703$	−388.720			−0.552944
$704$	−118.734	+	1041.54i	−0.168657	+	1.47946i
$705$		0			0
$706$	871.039	−	1091.76i	1.23377	−	1.54640i
$707$	−6.74765	+	6.74765i	−0.00954407	+	0.00954407i
$708$		0			0
$709$	−409.754	+	409.754i	−0.577932	+	0.577932i	−0.934333	−	0.356401i	$-0.884004\pi$
$709$	−409.754	+	409.754i	−0.577932	+	0.577932i	0.356401	+	0.934333i	$0.384004\pi$
$710$	18.9746	+	168.735i	0.0267248	+	0.237655i
$711$		0			0
$712$	317.131	−	657.428i	0.445409	−	0.923354i
$713$	962.391			1.34978
$714$		0			0
$715$	346.892	−	346.892i	0.485164	−	0.485164i
$716$	−496.469	−	312.254i	−0.693392	−	0.436109i
$717$		0			0
$718$	−570.271	−	454.980i	−0.794250	−	0.633677i
$719$		−	700.847i		−	0.974752i	−0.873192	−	0.487376i	$-0.837954\pi$
$719$		−	700.847i		−	0.974752i	0.873192	−	0.487376i	$-0.162046\pi$
$720$		0			0
$721$	25.1612			0.0348977
$722$	−401.247	+	502.923i	−0.555744	+	0.696569i
$723$		0			0
$724$	−14.7499	−	9.27695i	−0.0203728	−	0.0128135i
$725$	286.552	+	286.552i	0.395244	+	0.395244i
$726$		0			0
$727$			1106.88i			1.52253i	0.648439	+	0.761267i	$0.275422\pi$
$727$			1106.88i			1.52253i	−0.648439	+	0.761267i	$0.724578\pi$
$728$	6.85924	+	19.6438i	0.00942203	+	0.0269832i
$729$		0			0
$730$	−679.352	+	76.3945i	−0.930619	+	0.104650i
$731$	113.504	+	113.504i	0.155273	+	0.155273i
$732$		0			0
$733$	185.291	+	185.291i	0.252784	+	0.252784i	0.822111	−	0.569327i	$-0.192796\pi$
$733$	185.291	+	185.291i	0.252784	+	0.252784i	−0.569327	+	0.822111i	$0.692796\pi$
$734$	−989.461	−	789.422i	−1.34804	−	1.07551i
$735$		0			0
$736$	−894.022	−	205.081i	−1.21470	−	0.278643i
$737$		−	1435.56i		−	1.94785i
$738$		0			0
$739$	−764.710	−	764.710i	−1.03479	−	1.03479i	−0.999373	−	0.0354181i	$-0.988724\pi$
$739$	−764.710	−	764.710i	−1.03479	−	1.03479i	−0.0354181	−	0.999373i	$-0.511276\pi$
$740$	−143.762	−	631.133i	−0.194273	−	0.852883i
$741$		0			0
$742$	−24.1564	+	2.71643i	−0.0325557	+	0.00366096i
$743$	860.679			1.15838			0.579192	−	0.815191i	$-0.303368\pi$
$743$	860.679			1.15838			0.579192	+	0.815191i	$0.303368\pi$
$744$		0			0
$745$			474.480i			0.636886i
$746$	−93.7875	+	10.5466i	−0.125721	+	0.0141375i
$747$		0			0
$748$	343.900	+	216.296i	0.459759	+	0.289166i
$749$	−2.97859	+	2.97859i	−0.00397675	+	0.00397675i
$750$		0			0
$751$	−1060.33			−1.41189			−0.705943	−	0.708268i	$-0.749477\pi$
$751$	−1060.33			−1.41189			−0.705943	+	0.708268i	$0.749477\pi$
$752$	−95.6478	−	199.059i	−0.127191	−	0.264706i
$753$		0			0
$754$	−399.727	−	318.914i	−0.530142	−	0.422963i
$755$	−166.025	+	166.025i	−0.219900	+	0.219900i
$756$		0			0
$757$	85.8730	−	85.8730i	0.113439	−	0.113439i	−0.648109	−	0.761548i	$-0.724440\pi$
$757$	85.8730	−	85.8730i	0.113439	−	0.113439i	0.761548	+	0.648109i	$0.224440\pi$
$758$	1234.32	−	138.802i	1.62839	−	0.183116i
$759$		0			0
$760$	117.925	+	56.8847i	0.155164	+	0.0748483i
$761$	587.026			0.771388			0.385694	−	0.922627i	$-0.373962\pi$
$761$	587.026			0.771388			0.385694	+	0.922627i	$0.373962\pi$
$762$		0			0
$763$	0.883741	−	0.883741i	0.00115825	−	0.00115825i
$764$	−918.664	+	209.257i	−1.20244	+	0.273897i
$765$		0			0
$766$	−210.334	+	263.632i	−0.274587	+	0.344167i
$767$			1143.64i			1.49105i
$768$		0			0
$769$	1048.36			1.36328			0.681642	−	0.731686i	$-0.261266\pi$
$769$	1048.36			1.36328			0.681642	+	0.731686i	$0.261266\pi$
$770$	−15.1506	−	12.0876i	−0.0196760	−	0.0156981i
$771$		0			0
$772$	−8.33788	−	36.6042i	−0.0108004	−	0.0474148i
$773$	−1027.31	−	1027.31i	−1.32899	−	1.32899i	−0.906249	−	0.422744i	$-0.861067\pi$
$773$	−1027.31	−	1027.31i	−1.32899	−	1.32899i	−0.422744	−	0.906249i	$-0.638933\pi$
$774$		0			0
$775$			610.623i			0.787901i
$776$	−69.7966	+	144.692i	−0.0899441	+	0.186458i
$777$		0			0
$778$	−17.2135	−	153.074i	−0.0221253	−	0.196753i
$779$	−276.197	−	276.197i	−0.354553	−	0.354553i
$780$		0			0
$781$	−376.716	−	376.716i	−0.482351	−	0.482351i
$782$	−221.698	+	277.876i	−0.283501	+	0.355340i
$783$		0			0
$784$	−705.915	+	339.192i	−0.900402	+	0.432643i
$785$			351.573i			0.447864i
$786$		0			0
$787$	998.571	+	998.571i	1.26883	+	1.26883i	0.946692	+	0.322141i	$0.104402\pi$
$787$	998.571	+	998.571i	1.26883	+	1.26883i	0.322141	+	0.946692i	$0.395598\pi$
$788$	228.478	−	363.268i	0.289946	−	0.461001i
$789$		0			0
$790$	−77.2308	−	686.788i	−0.0977605	−	0.869353i
$791$	−26.6754			−0.0337236
$792$		0			0
$793$			979.908i			1.23570i
$794$	−141.239	−	1255.99i	−0.177883	−	1.58185i
$795$		0			0
$796$	1231.08	−	280.421i	1.54658	−	0.352287i
$797$	261.834	−	261.834i	0.328524	−	0.328524i	−0.523501	−	0.852025i	$-0.675374\pi$
$797$	261.834	−	261.834i	0.328524	−	0.328524i	0.852025	+	0.523501i	$0.175374\pi$
$798$		0			0
$799$	−85.5890			−0.107120
$800$	130.121	−	567.245i	0.162651	−	0.709056i
$801$		0			0
$802$	−9.92057	+	12.4344i	−0.0123698	+	0.0155043i
$803$	1516.71	−	1516.71i	1.88881	−	1.88881i
$804$		0			0
$805$	11.9917	−	11.9917i	0.0148965	−	0.0148965i
$806$	−86.1031	−	765.688i	−0.106828	−	0.949985i
$807$		0			0
$808$	−317.973	+	111.030i	−0.393531	+	0.137414i
$809$	−652.165			−0.806137			−0.403069	−	0.915170i	$-0.632056\pi$
$809$	−652.165			−0.806137			−0.403069	+	0.915170i	$0.632056\pi$
$810$		0			0
$811$	−150.173	+	150.173i	−0.185171	+	0.185171i	−0.793605	−	0.608434i	$-0.791798\pi$
$811$	−150.173	+	150.173i	−0.185171	+	0.185171i	0.608434	+	0.793605i	$0.291798\pi$
$812$	−10.7559	+	17.1013i	−0.0132462	+	0.0210608i
$813$		0			0
$814$	1587.59	+	1266.63i	1.95035	+	1.55605i
$815$			311.169i			0.381803i
$816$		0			0
$817$	−162.310			−0.198666
$818$	−778.335	+	975.565i	−0.951510	+	1.19262i
$819$		0			0
$820$	346.291	−	550.586i	0.422306	−	0.671446i
$821$	−979.062	−	979.062i	−1.19252	−	1.19252i	−0.976356	−	0.216167i	$-0.930644\pi$
$821$	−979.062	−	979.062i	−1.19252	−	1.19252i	−0.216167	−	0.976356i	$-0.569356\pi$
$822$		0			0
$823$		−	453.787i		−	0.551381i	−0.961246	−	0.275691i	$-0.911093\pi$
$823$		−	453.787i		−	0.551381i	0.961246	−	0.275691i	$-0.0889065\pi$
$824$	799.852	+	385.833i	0.970694	+	0.468244i
$825$		0			0
$826$	44.8995	−	5.04904i	0.0543578	−	0.00611264i
$827$	−1162.48	−	1162.48i	−1.40566	−	1.40566i	−0.780488	−	0.625171i	$-0.785029\pi$
$827$	−1162.48	−	1162.48i	−1.40566	−	1.40566i	−0.625171	−	0.780488i	$-0.714971\pi$
$828$		0			0
$829$	126.113	+	126.113i	0.152127	+	0.152127i	0.779067	−	0.626940i	$-0.215693\pi$
$829$	126.113	+	126.113i	0.152127	+	0.152127i	−0.626940	+	0.779067i	$0.715693\pi$
$830$	111.257	+	88.7639i	0.134044	+	0.106944i
$831$		0			0
$832$	−83.1781	+	729.641i	−0.0999737	+	0.876973i
$833$			303.521i			0.364371i
$834$		0			0
$835$	−356.503	−	356.503i	−0.426950	−	0.426950i
$836$	−400.537	+	91.2362i	−0.479112	+	0.109134i
$837$		0			0
$838$	−161.342	+	18.1432i	−0.192532	+	0.0216506i
$839$	82.9161			0.0988273			0.0494137	−	0.998778i	$-0.484265\pi$
$839$	82.9161			0.0988273			0.0494137	+	0.998778i	$0.484265\pi$
$840$		0			0
$841$			344.494i			0.409624i
$842$	12.5317	−	1.40921i	0.0148833	−	0.00167365i
$843$		0			0
$844$	63.1464	−	100.400i	0.0748180	−	0.118957i
$845$	−68.9113	+	68.9113i	−0.0815519	+	0.0815519i
$846$		0			0
$847$	33.3851			0.0394157
$848$	−809.563	−	284.072i	−0.954674	−	0.334990i
$849$		0			0
$850$	−176.308	−	140.664i	−0.207421	−	0.165487i
$851$	−1256.58	+	1256.58i	−1.47659	+	1.47659i
$852$		0			0
$853$	558.406	−	558.406i	0.654638	−	0.654638i	−0.299468	−	0.954106i	$-0.596809\pi$
$853$	558.406	−	558.406i	0.654638	−	0.654638i	0.954106	+	0.299468i	$0.0968092\pi$
$854$	38.4714	−	4.32619i	0.0450485	−	0.00506579i
$855$		0			0
$856$	−140.362	+	49.0116i	−0.163974	+	0.0572565i
$857$	429.366			0.501011			0.250505	−	0.968115i	$-0.419403\pi$
$857$	429.366			0.501011			0.250505	+	0.968115i	$0.419403\pi$
$858$		0			0
$859$	−63.4781	+	63.4781i	−0.0738977	+	0.0738977i	−0.743090	−	0.669192i	$-0.766640\pi$
$859$	−63.4781	+	63.4781i	−0.0738977	+	0.0738977i	0.669192	+	0.743090i	$0.266640\pi$
$860$	−60.0281	−	263.530i	−0.0698001	−	0.306431i
$861$		0			0
$862$	−643.106	+	806.069i	−0.746063	+	0.935114i
$863$			176.985i			0.205081i	0.994729	+	0.102540i	$0.0326971\pi$
$863$			176.985i			0.205081i	−0.994729	+	0.102540i	$0.967303\pi$
$864$		0			0
$865$	221.889			0.256519
$866$	−471.231	−	375.963i	−0.544147	−	0.434137i
$867$		0			0
$868$	−29.6809	+	6.76086i	−0.0341946	+	0.00778901i
$869$	1533.32	+	1533.32i	1.76446	+	1.76446i
$870$		0			0
$871$		−	1005.67i		−	1.15461i
$872$	41.6450	−	14.5416i	0.0477580	−	0.0166762i
$873$		0			0
$874$	−40.1670	−	357.192i	−0.0459577	−	0.408687i
$875$	18.0674	+	18.0674i	0.0206485	+	0.0206485i
$876$		0			0
$877$	−852.573	−	852.573i	−0.972147	−	0.972147i	0.0274758	−	0.999622i	$-0.491253\pi$
$877$	−852.573	−	852.573i	−0.972147	−	0.972147i	−0.999622	+	0.0274758i	$0.991253\pi$
$878$	818.942	−	1026.46i	0.932736	−	1.16909i
$879$		0			0
$880$	−296.266	−	616.578i	−0.336666	−	0.700657i
$881$			756.244i			0.858393i	0.903211	+	0.429196i	$0.141203\pi$
$881$			756.244i			0.858393i	−0.903211	+	0.429196i	$0.858797\pi$
$882$		0			0
$883$	617.889	+	617.889i	0.699761	+	0.699761i	0.964359	−	0.264598i	$-0.0852393\pi$
$883$	617.889	+	617.889i	0.699761	+	0.699761i	−0.264598	+	0.964359i	$0.585239\pi$
$884$	240.916	+	151.524i	0.272529	+	0.171407i
$885$		0			0
$886$	72.6325	+	645.897i	0.0819780	+	0.729004i
$887$	−311.194			−0.350838			−0.175419	−	0.984494i	$-0.556128\pi$
$887$	−311.194			−0.350838			−0.175419	+	0.984494i	$0.556128\pi$
$888$		0			0
$889$			9.77283i			0.0109931i
$890$	53.2267	+	473.328i	0.0598053	+	0.531830i
$891$		0			0
$892$	281.698	+	1236.69i	0.315805	+	1.38642i
$893$	61.1957	−	61.1957i	0.0685282	−	0.0685282i
$894$		0			0
$895$	382.723			0.427624
$896$	29.0131	+	0.0443045i	0.0323807	+	4.94470e-5i
$897$		0			0
$898$	−230.117	+	288.428i	−0.256255	+	0.321189i
$899$	529.011	−	529.011i	0.588444	−	0.588444i
$900$		0			0
$901$	−235.114	+	235.114i	−0.260948	+	0.260948i
$902$	228.053	+	2028.00i	0.252830	+	2.24834i
$903$		0			0
$904$	−847.985	−	409.052i	−0.938037	−	0.452491i
$905$	11.3706			0.0125641
$906$		0			0
$907$	593.896	−	593.896i	0.654792	−	0.654792i	−0.299351	−	0.954143i	$-0.596770\pi$
$907$	593.896	−	593.896i	0.654792	−	0.654792i	0.954143	+	0.299351i	$0.0967702\pi$
$908$	485.353	+	305.263i	0.534530	+	0.336193i
$909$		0			0
$910$	−10.6136	−	8.46782i	−0.0116633	−	0.00930530i
$911$		−	499.219i		−	0.547991i	−0.961731	−	0.273995i	$-0.911655\pi$
$911$		−	499.219i		−	0.547991i	0.961731	−	0.273995i	$-0.0883453\pi$
$912$		0			0
$913$	−446.564			−0.489117
$914$	−470.085	+	589.204i	−0.514316	+	0.644643i
$915$		0			0
$916$	−401.167	−	252.314i	−0.437955	−	0.275452i
$917$	−22.1197	−	22.1197i	−0.0241218	−	0.0241218i
$918$		0			0
$919$			405.667i			0.441422i	0.975339	+	0.220711i	$0.0708378\pi$
$919$			405.667i			0.441422i	−0.975339	+	0.220711i	$0.929162\pi$
$920$	565.090	−	197.318i	0.614228	−	0.214477i
$921$		0			0
$922$	−80.2603	+	9.02543i	−0.0870502	+	0.00978897i
$923$	−263.905	−	263.905i	−0.285921	−	0.285921i
$924$		0			0
$925$	−797.280	−	797.280i	−0.861925	−	0.861925i
$926$	226.422	+	180.647i	0.244517	+	0.195083i
$927$		0			0
$928$	−604.160	+	378.700i	−0.651034	+	0.408082i
$929$			640.107i			0.689028i	0.938781	+	0.344514i	$0.111956\pi$
$929$			640.107i			0.689028i	−0.938781	+	0.344514i	$0.888044\pi$
$930$		0			0
$931$	−217.016	−	217.016i	−0.233100	−	0.233100i
$932$	−257.585	−	1130.83i	−0.276379	−	1.21333i
$933$		0			0
$934$	1030.18	−	115.846i	1.10297	−	0.124032i
$935$	−265.109			−0.283539
$936$		0			0
$937$		−	1648.87i		−	1.75973i	−0.475224	−	0.879865i	$-0.657633\pi$
$937$		−	1648.87i		−	1.75973i	0.475224	−	0.879865i	$-0.342367\pi$
$938$	−39.4828	+	4.43992i	−0.0420925	+	0.00473339i
$939$		0			0
$940$	121.991	+	76.7263i	0.129778	+	0.0816237i
$941$	−783.146	+	783.146i	−0.832248	+	0.832248i	−0.987824	−	0.155576i	$-0.950277\pi$
$941$	−783.146	+	783.146i	−0.832248	+	0.832248i	0.155576	+	0.987824i	$0.450277\pi$
$942$		0			0
$943$	−1785.67			−1.89360
$944$	1504.74	+	528.005i	1.59400	+	0.559328i
$945$		0			0
$946$	662.899	+	528.881i	0.700739	+	0.559071i
$947$	−510.366	+	510.366i	−0.538929	+	0.538929i	−0.923214	−	0.384286i	$-0.874448\pi$
$947$	−510.366	+	510.366i	−0.538929	+	0.538929i	0.384286	+	0.923214i	$0.374448\pi$
$948$		0			0
$949$	1062.52	−	1062.52i	1.11962	−	1.11962i
$950$	226.634	−	25.4854i	0.238562	−	0.0268267i
$951$		0			0
$952$	4.88525	−	10.1274i	0.00513156	−	0.0106380i
$953$	1381.65			1.44979			0.724897	−	0.688857i	$-0.241887\pi$
$953$	1381.65			1.44979			0.724897	+	0.688857i	$0.241887\pi$
$954$		0			0
$955$	434.752	−	434.752i	0.455238	−	0.455238i
$956$	1723.32	−	392.545i	1.80264	−	0.410612i
$957$		0			0
$958$	149.279	−	187.106i	0.155824	−	0.195309i
$959$		−	11.1685i		−	0.0116460i
$960$		0			0
$961$	166.287			0.173035
$962$	1112.17	+	887.322i	1.15610	+	0.922372i
$963$		0			0
$964$	−298.602	−	1310.90i	−0.309753	−	1.35985i
$965$	17.3227	+	17.3227i	0.0179510	+	0.0179510i
$966$		0			0
$967$			783.542i			0.810281i	0.914254	+	0.405141i	$0.132777\pi$
$967$			783.542i			0.810281i	−0.914254	+	0.405141i	$0.867223\pi$
$968$	1061.28	+	511.942i	1.09636	+	0.528865i
$969$		0			0
$970$	−11.7145	−	104.174i	−0.0120768	−	0.107396i
$971$	73.9020	+	73.9020i	0.0761091	+	0.0761091i	0.744137	−	0.668027i	$-0.232861\pi$
$971$	73.9020	+	73.9020i	0.0761091	+	0.0761091i	−0.668027	+	0.744137i	$0.732861\pi$
$972$		0			0
$973$	−39.1914	−	39.1914i	−0.0402789	−	0.0402789i
$974$	−795.578	+	997.176i	−0.816815	+	1.02380i
$975$		0			0
$976$	1289.31	+	452.412i	1.32101	+	0.463537i
$977$		−	584.085i		−	0.597835i	−0.954279	−	0.298918i	$-0.903374\pi$
$977$		−	584.085i		−	0.597835i	0.954279	−	0.298918i	$-0.0966256\pi$
$978$		0			0
$979$	−1056.75	−	1056.75i	−1.07942	−	1.07942i
$980$	272.092	−	432.612i	0.277645	−	0.441441i
$981$		0			0
$982$	−41.1678	−	366.093i	−0.0419224	−	0.372803i
$983$	−1608.50			−1.63632			−0.818158	−	0.574993i	$-0.805005\pi$
$983$	−1608.50			−1.63632			−0.818158	+	0.574993i	$0.805005\pi$
$984$		0			0
$985$			280.040i			0.284305i
$986$	30.8802	+	274.608i	0.0313186	+	0.278507i
$987$		0			0
$988$	−280.592	+	63.9146i	−0.284000	+	0.0646908i
$989$	−524.685	+	524.685i	−0.530520	+	0.530520i
$990$		0			0
$991$	−477.041			−0.481374			−0.240687	−	0.970603i	$-0.577373\pi$
$991$	−477.041			−0.481374			−0.240687	+	0.970603i	$0.577373\pi$
$992$	−1047.20	−	240.220i	−1.05565	−	0.242157i
$993$		0			0
$994$	−9.19585	+	11.5261i	−0.00925135	+	0.0115956i
$995$	−582.600	+	582.600i	−0.585528	+	0.585528i
$996$		0			0
$997$	783.852	−	783.852i	0.786210	−	0.786210i	−0.194660	−	0.980871i	$-0.562360\pi$
$997$	783.852	−	783.852i	0.786210	−	0.786210i	0.980871	+	0.194660i	$0.0623604\pi$
$998$	−2.30292	−	20.4792i	−0.00230754	−	0.0205202i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.j.a.125.4	yes	32
3.2	odd	2	inner	144.3.j.a.125.13	yes	32
4.3	odd	2		576.3.j.a.17.6		32
8.3	odd	2		1152.3.j.b.161.11		32
8.5	even	2		1152.3.j.a.161.11		32
12.11	even	2		576.3.j.a.17.11		32
16.3	odd	4		1152.3.j.b.737.6		32
16.5	even	4	inner	144.3.j.a.53.13	yes	32
16.11	odd	4		576.3.j.a.305.11		32
16.13	even	4		1152.3.j.a.737.6		32
24.5	odd	2		1152.3.j.a.161.6		32
24.11	even	2		1152.3.j.b.161.6		32
48.5	odd	4	inner	144.3.j.a.53.4	✓	32
48.11	even	4		576.3.j.a.305.6		32
48.29	odd	4		1152.3.j.a.737.11		32
48.35	even	4		1152.3.j.b.737.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.j.a.53.4	✓	32	48.5	odd	4	inner
144.3.j.a.53.13	yes	32	16.5	even	4	inner
144.3.j.a.125.4	yes	32	1.1	even	1	trivial
144.3.j.a.125.13	yes	32	3.2	odd	2	inner
576.3.j.a.17.6		32	4.3	odd	2
576.3.j.a.17.11		32	12.11	even	2
576.3.j.a.305.6		32	48.11	even	4
576.3.j.a.305.11		32	16.11	odd	4
1152.3.j.a.161.6		32	24.5	odd	2
1152.3.j.a.161.11		32	8.5	even	2
1152.3.j.a.737.6		32	16.13	even	4
1152.3.j.a.737.11		32	48.29	odd	4
1152.3.j.b.161.6		32	24.11	even	2
1152.3.j.b.161.11		32	8.3	odd	2
1152.3.j.b.737.6		32	16.3	odd	4
1152.3.j.b.737.11		32	48.35	even	4

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.56339 - 1.24732i) q^{2} +(0.888382 + 3.90010i) q^{4} +(-1.84570 - 1.84570i) q^{5} -0.226665i q^{7} +(3.47579 - 7.20548i) q^{8} +O(q^{10})\)	\(q+(-1.56339 - 1.24732i) q^{2} +(0.888382 + 3.90010i) q^{4} +(-1.84570 - 1.84570i) q^{5} -0.226665i q^{7} +(3.47579 - 7.20548i) q^{8} +(0.583370 + 5.18772i) q^{10} +(-11.5821 - 11.5821i) q^{11} +(-8.11369 - 8.11369i) q^{13} +(-0.282724 + 0.354366i) q^{14} +(-14.4216 + 6.92956i) q^{16} +6.20082i q^{17} +(-4.43355 - 4.43355i) q^{19} +(5.55872 - 8.83809i) q^{20} +(3.66074 + 32.5538i) q^{22} -28.6638 q^{23} -18.1868i q^{25} +(2.56449 + 22.8052i) q^{26} +(0.884017 - 0.201365i) q^{28} +(-15.7561 + 15.7561i) q^{29} -33.5751 q^{31} +(31.1899 + 7.15469i) q^{32} +(7.73441 - 9.69430i) q^{34} +(-0.418355 + 0.418355i) q^{35} +(43.8384 - 43.8384i) q^{37} +(1.40131 + 12.4614i) q^{38} +(-19.7144 + 6.88388i) q^{40} +62.2969 q^{41} +(18.3048 - 18.3048i) q^{43} +(34.8819 - 55.4605i) q^{44} +(44.8128 + 35.7530i) q^{46} +13.8029i q^{47} +48.9486 q^{49} +(-22.6848 + 28.4331i) q^{50} +(24.4361 - 38.8522i) q^{52} +(37.9167 + 37.9167i) q^{53} +42.7539i q^{55} +(-1.63323 - 0.787840i) q^{56} +(44.2857 - 4.98002i) q^{58} +(-70.4759 - 70.4759i) q^{59} +(-60.3861 - 60.3861i) q^{61} +(52.4910 + 41.8789i) q^{62} +(-39.8378 - 50.0894i) q^{64} +29.9508i q^{65} +(61.9736 + 61.9736i) q^{67} +(-24.1838 + 5.50869i) q^{68} +(1.17588 - 0.132230i) q^{70} +32.5259 q^{71} +130.954i q^{73} +(-123.217 + 13.8560i) q^{74} +(13.3526 - 21.2300i) q^{76} +(-2.62525 + 2.62525i) q^{77} -132.387 q^{79} +(39.4077 + 13.8280i) q^{80} +(-97.3944 - 77.7042i) q^{82} +(19.2783 - 19.2783i) q^{83} +(11.4448 - 11.4448i) q^{85} +(-51.4494 + 5.78559i) q^{86} +(-123.711 + 43.1975i) q^{88} +91.2401 q^{89} +(-1.83909 + 1.83909i) q^{91} +(-25.4644 - 111.792i) q^{92} +(17.2166 - 21.5793i) q^{94} +16.3660i q^{95} -20.0808 q^{97} +(-76.5258 - 61.0546i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 40 q^{10} + 48 q^{16} + 64 q^{19} - 88 q^{22} - 120 q^{28} - 248 q^{34} - 184 q^{40} + 128 q^{43} + 24 q^{46} - 224 q^{49} + 632 q^{52} + 456 q^{58} + 64 q^{61} - 48 q^{64} - 64 q^{67} - 312 q^{70} - 576 q^{76} - 512 q^{79} - 720 q^{82} + 320 q^{85} - 400 q^{88} - 192 q^{91} + 696 q^{94}+O(q^{100}) \) 32 * q + 40 * q^10 + 48 * q^16 + 64 * q^19 - 88 * q^22 - 120 * q^28 - 248 * q^34 - 184 * q^40 + 128 * q^43 + 24 * q^46 - 224 * q^49 + 632 * q^52 + 456 * q^58 + 64 * q^61 - 48 * q^64 - 64 * q^67 - 312 * q^70 - 576 * q^76 - 512 * q^79 - 720 * q^82 + 320 * q^85 - 400 * q^88 - 192 * q^91 + 696 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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