LMFDB - Embedded newform 460.2.x.a.17.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(17,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 14]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("460.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.x (of order $44$, degree $20$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			17.9
Character	$\chi$	$=$	460.17
Dual form			460.2.x.a.433.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707493 - 0.386321i) q^{3} +(1.31269 - 1.81021i) q^{5} +(2.84997 + 3.80711i) q^{7} +(-1.27062 + 1.97712i) q^{9} +O(q^{10})$	\(q+(0.707493 - 0.386321i) q^{3} +(1.31269 - 1.81021i) q^{5} +(2.84997 + 3.80711i) q^{7} +(-1.27062 + 1.97712i) q^{9} +(0.570235 - 0.260418i) q^{11} +(1.06388 + 0.796408i) q^{13} +(0.229396 - 1.78783i) q^{15} +(-0.000636289 - 0.00889649i) q^{17} +(1.03459 + 1.19398i) q^{19} +(3.48710 + 1.59250i) q^{21} +(0.0547534 - 4.79552i) q^{23} +(-1.55371 - 4.75247i) q^{25} +(-0.307670 + 4.30179i) q^{27} +(-6.17334 - 5.34923i) q^{29} +(3.66360 - 1.07573i) q^{31} +(0.302833 - 0.404537i) q^{33} +(10.6328 - 0.161495i) q^{35} +(6.22544 - 1.35426i) q^{37} +(1.06035 + 0.152456i) q^{39} +(-1.53162 + 0.984312i) q^{41} +(-0.363086 - 0.664942i) q^{43} +(1.91108 + 4.89543i) q^{45} +(-7.86232 - 7.86232i) q^{47} +(-4.39965 + 14.9838i) q^{49} +(-0.00388707 - 0.00604839i) q^{51} +(-7.13739 + 5.34298i) q^{53} +(0.277129 - 1.37409i) q^{55} +(1.19322 + 0.445049i) q^{57} +(13.2259 - 1.90160i) q^{59} +(3.58247 + 12.2008i) q^{61} +(-11.1483 + 0.797345i) q^{63} +(2.83820 - 0.880405i) q^{65} +(-3.56055 - 9.54621i) q^{67} +(-1.81387 - 3.41395i) q^{69} +(-1.99803 + 4.37507i) q^{71} +(-14.8481 - 1.06195i) q^{73} +(-2.93522 - 2.76211i) q^{75} +(2.61659 + 1.42877i) q^{77} +(-1.03506 - 7.19899i) q^{79} +(-1.48474 - 3.25113i) q^{81} +(-0.0551115 - 0.253344i) q^{83} +(-0.0169397 - 0.0105265i) q^{85} +(-6.43412 - 1.39966i) q^{87} +(-10.5110 - 3.08630i) q^{89} +6.32003i q^{91} +(2.17640 - 2.17640i) q^{93} +(3.51944 - 0.305502i) q^{95} +(2.60690 - 11.9837i) q^{97} +(-0.209674 + 1.45832i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3}+O(q^{10}) $ 240 * q + 4 * q^3	$ 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) $ 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{22}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	0.707493	−	0.386321i	0.408472	−	0.223042i	−0.261857	−	0.965107i	$-0.584335\pi$
$3$	0.707493	−	0.386321i	0.408472	−	0.223042i	0.670329	+	0.742064i	$0.266153\pi$
$4$		0			0
$5$	1.31269	−	1.81021i	0.587051	−	0.809550i
$5$	1.31269	−	1.81021i	0.587051	−	0.809550i
$6$		0			0
$7$	2.84997	+	3.80711i	1.07719	+	1.43895i	0.889621	+	0.456701i	$0.150969\pi$
$7$	2.84997	+	3.80711i	1.07719	+	1.43895i	0.187566	+	0.982252i	$0.439940\pi$
$8$		0			0
$9$	−1.27062	+	1.97712i	−0.423540	+	0.659041i
$10$		0			0
$11$	0.570235	−	0.260418i	0.171932	−	0.0785189i	−0.327590	−	0.944820i	$-0.606236\pi$
$11$	0.570235	−	0.260418i	0.171932	−	0.0785189i	0.499522	+	0.866301i	$0.333509\pi$
$12$		0			0
$13$	1.06388	+	0.796408i	0.295066	+	0.220884i	0.736546	−	0.676387i	$-0.236455\pi$
$13$	1.06388	+	0.796408i	0.295066	+	0.220884i	−0.441480	+	0.897271i	$0.645546\pi$
$14$		0			0
$15$	0.229396	−	1.78783i	0.0592297	−	0.461615i
$16$		0			0
$17$	−0.000636289	−	0.00889649i	−0.000154323	−	0.00215771i	0.997374	−	0.0724180i	$-0.0230716\pi$
$17$	−0.000636289	−	0.00889649i	−0.000154323	−	0.00215771i	−0.997529	+	0.0702603i	$0.977617\pi$
$18$		0			0
$19$	1.03459	+	1.19398i	0.237351	+	0.273917i	0.861911	−	0.507059i	$-0.169267\pi$
$19$	1.03459	+	1.19398i	0.237351	+	0.273917i	−0.624561	+	0.780976i	$0.714722\pi$
$20$		0			0
$21$	3.48710	+	1.59250i	0.760947	+	0.347513i
$22$		0			0
$23$	0.0547534	−	4.79552i	0.0114169	−	0.999935i
$23$	0.0547534	−	4.79552i	0.0114169	−	0.999935i
$24$		0			0
$25$	−1.55371	−	4.75247i	−0.310742	−	0.950494i
$26$		0			0
$27$	−0.307670	+	4.30179i	−0.0592112	+	0.827881i
$28$		0			0
$29$	−6.17334	−	5.34923i	−1.14636	−	0.993328i	−0.999992	−	0.00409759i	$-0.998696\pi$
$29$	−6.17334	−	5.34923i	−1.14636	−	0.993328i	−0.146370	−	0.989230i	$-0.546759\pi$
$30$		0			0
$31$	3.66360	−	1.07573i	0.658002	−	0.193207i	0.0643484	−	0.997927i	$-0.479503\pi$
$31$	3.66360	−	1.07573i	0.658002	−	0.193207i	0.593654	+	0.804721i	$0.297685\pi$
$32$		0			0
$33$	0.302833	−	0.404537i	0.0527164	−	0.0704209i
$34$		0			0
$35$	10.6328	−	0.161495i	1.79727	−	0.0272977i
$36$		0			0
$37$	6.22544	−	1.35426i	1.02346	−	0.222639i	0.330642	−	0.943756i	$-0.392735\pi$
$37$	6.22544	−	1.35426i	1.02346	−	0.222639i	0.692813	+	0.721117i	$0.256371\pi$
$38$		0			0
$39$	1.06035	+	0.152456i	0.169793	+	0.0244125i
$40$		0			0
$41$	−1.53162	+	0.984312i	−0.239199	+	0.153724i	−0.654749	−	0.755847i	$-0.727226\pi$
$41$	−1.53162	+	0.984312i	−0.239199	+	0.153724i	0.415550	+	0.909570i	$0.363589\pi$
$42$		0			0
$43$	−0.363086	−	0.664942i	−0.0553700	−	0.101403i	0.848528	−	0.529150i	$-0.177489\pi$
$43$	−0.363086	−	0.664942i	−0.0553700	−	0.101403i	−0.903898	+	0.427747i	$0.859307\pi$
$44$		0			0
$45$	1.91108	+	4.89543i	0.284887	+	0.729767i
$46$		0			0
$47$	−7.86232	−	7.86232i	−1.14684	−	1.14684i	−0.987171	−	0.159667i	$-0.948958\pi$
$47$	−7.86232	−	7.86232i	−1.14684	−	1.14684i	−0.159667	−	0.987171i	$-0.551042\pi$
$48$		0			0
$49$	−4.39965	+	14.9838i	−0.628521	+	2.14055i
$50$		0			0
$51$	−0.00388707	−	0.00604839i	−0.000544298	−	0.000846945i
$52$		0			0
$53$	−7.13739	+	5.34298i	−0.980396	+	0.733915i	−0.963987	−	0.265950i	$-0.914314\pi$
$53$	−7.13739	+	5.34298i	−0.980396	+	0.733915i	−0.0164092	+	0.999865i	$0.505223\pi$
$54$		0			0
$55$	0.277129	−	1.37409i	0.0373681	−	0.185282i
$56$		0			0
$57$	1.19322	+	0.445049i	0.158046	+	0.0589482i
$58$		0			0
$59$	13.2259	−	1.90160i	1.72187	−	0.247568i	0.790714	−	0.612185i	$-0.209709\pi$
$59$	13.2259	−	1.90160i	1.72187	−	0.247568i	0.931157	+	0.364617i	$0.118800\pi$
$60$		0			0
$61$	3.58247	+	12.2008i	0.458688	+	1.56215i	0.786614	+	0.617445i	$0.211832\pi$
$61$	3.58247	+	12.2008i	0.458688	+	1.56215i	−0.327926	+	0.944704i	$0.606350\pi$
$62$		0			0
$63$	−11.1483	+	0.797345i	−1.40456	+	0.100456i
$64$		0			0
$65$	2.83820	−	0.880405i	0.352035	−	0.109201i
$66$		0			0
$67$	−3.56055	−	9.54621i	−0.434991	−	1.16626i	−0.950869	−	0.309593i	$-0.899807\pi$
$67$	−3.56055	−	9.54621i	−0.434991	−	1.16626i	0.515878	−	0.856662i	$-0.327466\pi$
$68$		0			0
$69$	−1.81387	−	3.41395i	−0.218364	−	0.410991i
$70$		0			0
$71$	−1.99803	+	4.37507i	−0.237122	+	0.519225i	−0.990359	−	0.138524i	$-0.955764\pi$
$71$	−1.99803	+	4.37507i	−0.237122	+	0.519225i	0.753237	+	0.657749i	$0.228491\pi$
$72$		0			0
$73$	−14.8481	−	1.06195i	−1.73783	−	0.124292i	−0.833886	−	0.551937i	$-0.813889\pi$
$73$	−14.8481	−	1.06195i	−1.73783	−	0.124292i	−0.903947	+	0.427644i	$0.859344\pi$
$74$		0			0
$75$	−2.93522	−	2.76211i	−0.338930	−	0.318941i
$76$		0			0
$77$	2.61659	+	1.42877i	0.298188	+	0.162823i
$78$		0			0
$79$	−1.03506	−	7.19899i	−0.116453	−	0.809949i	−0.961411	−	0.275116i	$-0.911284\pi$
$79$	−1.03506	−	7.19899i	−0.116453	−	0.809949i	0.844958	−	0.534833i	$-0.179625\pi$
$80$		0			0
$81$	−1.48474	−	3.25113i	−0.164971	−	0.361236i
$82$		0			0
$83$	−0.0551115	−	0.253344i	−0.00604928	−	0.0278081i	0.974023	−	0.226448i	$-0.0727113\pi$
$83$	−0.0551115	−	0.253344i	−0.00604928	−	0.0278081i	−0.980073	+	0.198640i	$0.936348\pi$
$84$		0			0
$85$	−0.0169397	−	0.0105265i	−0.00183737	−	0.00114176i
$86$		0			0
$87$	−6.43412	−	1.39966i	−0.689810	−	0.150059i
$88$		0			0
$89$	−10.5110	−	3.08630i	−1.11416	−	0.327148i	−0.327697	−	0.944783i	$-0.606273\pi$
$89$	−10.5110	−	3.08630i	−1.11416	−	0.327148i	−0.786465	+	0.617635i	$0.788091\pi$
$90$		0			0
$91$			6.32003i			0.662519i
$92$		0			0
$93$	2.17640	−	2.17640i	0.225682	−	0.225682i
$94$		0			0
$95$	3.51944	−	0.305502i	0.361087	−	0.0313438i
$96$		0			0
$97$	2.60690	−	11.9837i	0.264691	−	1.21676i	−0.632304	−	0.774721i	$-0.717890\pi$
$97$	2.60690	−	11.9837i	0.264691	−	1.21676i	0.896994	−	0.442042i	$-0.145746\pi$
$98$		0			0
$99$	−0.209674	+	1.45832i	−0.0210730	+	0.146566i
$100$		0			0
$101$	4.07281	+	2.61744i	0.405260	+	0.260445i	0.727353	−	0.686263i	$-0.240750\pi$
$101$	4.07281	+	2.61744i	0.405260	+	0.260445i	−0.322094	+	0.946708i	$0.604387\pi$
$102$		0			0
$103$	−1.73703	+	4.65716i	−0.171155	+	0.458884i	−0.994000	−	0.109382i	$-0.965113\pi$
$103$	−1.73703	+	4.65716i	−0.171155	+	0.458884i	0.822845	+	0.568266i	$0.192386\pi$
$104$		0			0
$105$	7.46023	−	4.22192i	0.728044	−	0.412017i
$106$		0			0
$107$	2.60431	−	4.76944i	0.251768	−	0.461079i	−0.720976	−	0.692960i	$-0.756306\pi$
$107$	2.60431	−	4.76944i	0.251768	−	0.461079i	0.972744	+	0.231881i	$0.0744880\pi$
$108$		0			0
$109$	−7.31445	+	8.44132i	−0.700597	+	0.808532i	−0.988833	−	0.149027i	$-0.952386\pi$
$109$	−7.31445	+	8.44132i	−0.700597	+	0.808532i	0.288236	+	0.957559i	$0.406931\pi$
$110$		0			0
$111$	3.88128	−	3.36314i	0.368394	−	0.319216i
$112$		0			0
$113$	−1.15932	+	0.432405i	−0.109060	+	0.0406772i	−0.403402	−	0.915023i	$-0.632172\pi$
$113$	−1.15932	+	0.432405i	−0.109060	+	0.0406772i	0.294342	+	0.955700i	$0.404900\pi$
$114$		0			0
$115$	−8.60902	−	6.39413i	−0.802795	−	0.596255i
$116$		0			0
$117$	−2.92638	+	1.09148i	−0.270544	+	0.100908i
$118$		0			0
$119$	0.0320565	−	0.0277771i	0.00293861	−	0.00254632i
$120$		0			0
$121$	−6.94612	+	8.01625i	−0.631465	+	0.728750i
$122$		0			0
$123$	−0.703351	+	1.28809i	−0.0634190	+	0.116143i
$124$		0			0
$125$	−10.6425	−	3.42596i	−0.951894	−	0.306427i
$126$		0			0
$127$	1.23365	−	3.30755i	0.109469	−	0.293497i	−0.870652	−	0.491900i	$-0.836303\pi$
$127$	1.23365	−	3.30755i	0.109469	−	0.293497i	0.980121	+	0.198402i	$0.0635753\pi$
$128$		0			0
$129$	−0.513761	−	0.330174i	−0.0452342	−	0.0290702i
$130$		0			0
$131$	−1.12765	+	7.84298i	−0.0985232	+	0.685244i	0.879370	+	0.476139i	$0.157964\pi$
$131$	−1.12765	+	7.84298i	−0.0985232	+	0.685244i	−0.977893	+	0.209105i	$0.932945\pi$
$132$		0			0
$133$	−1.59706	+	7.34159i	−0.138483	+	0.636596i
$134$		0			0
$135$	7.38327	+	6.20385i	0.635451	+	0.533943i
$136$		0			0
$137$	1.61771	−	1.61771i	0.138210	−	0.138210i	−0.634617	−	0.772827i	$-0.718842\pi$
$137$	1.61771	−	1.61771i	0.138210	−	0.138210i	0.772827	+	0.634617i	$0.218842\pi$
$138$		0			0
$139$		−	1.06918i		−	0.0906863i	−0.998971	−	0.0453431i	$-0.985562\pi$
$139$		−	1.06918i		−	0.0906863i	0.998971	−	0.0453431i	$-0.0144381\pi$
$140$		0			0
$141$	−8.59992	−	2.52517i	−0.724244	−	0.212657i
$142$		0			0
$143$	0.814058	+	0.177088i	0.0680750	+	0.0148088i
$144$		0			0
$145$	−17.7869	+	4.15318i	−1.47712	+	0.344903i
$146$		0			0
$147$	2.67584	+	12.3006i	0.220700	+	1.01454i
$148$		0			0
$149$	2.75058	+	6.02293i	0.225336	+	0.493418i	0.988205	−	0.153135i	$-0.0489371\pi$
$149$	2.75058	+	6.02293i	0.225336	+	0.493418i	−0.762869	+	0.646553i	$0.776210\pi$
$150$		0			0
$151$	2.39587	+	16.6636i	0.194973	+	1.35607i	0.818608	+	0.574352i	$0.194746\pi$
$151$	2.39587	+	16.6636i	0.194973	+	1.35607i	−0.623635	+	0.781716i	$0.714345\pi$
$152$		0			0
$153$	0.0183979	+	0.0100460i	0.00148738	+	0.000812173i
$154$		0			0
$155$	2.86186	−	8.04398i	0.229870	−	0.646108i
$156$		0			0
$157$	−15.9725	−	1.14238i	−1.27475	−	0.0911717i	−0.582499	−	0.812831i	$-0.697925\pi$
$157$	−15.9725	−	1.14238i	−1.27475	−	0.0911717i	−0.692248	+	0.721660i	$0.743380\pi$
$158$		0			0
$159$	−2.98555	+	6.53745i	−0.236770	+	0.518453i
$160$		0			0
$161$	18.4131	−	13.4586i	1.45116	−	1.06069i
$162$		0			0
$163$	−5.29495	−	14.1963i	−0.414732	−	1.11194i	−0.961536	−	0.274679i	$-0.911428\pi$
$163$	−5.29495	−	14.1963i	−0.414732	−	1.11194i	0.546804	−	0.837261i	$-0.315844\pi$
$164$		0			0
$165$	−0.334773	−	1.07922i	−0.0260620	−	0.0840173i
$166$		0			0
$167$	−8.54957	+	0.611477i	−0.661586	+	0.0473175i	−0.398095	−	0.917344i	$-0.630328\pi$
$167$	−8.54957	+	0.611477i	−0.661586	+	0.0473175i	−0.263491	+	0.964662i	$0.584874\pi$
$168$		0			0
$169$	−3.16496	−	10.7788i	−0.243458	−	0.829142i
$170$		0			0
$171$	−3.67521	+	0.528415i	−0.281050	+	0.0404089i
$172$		0			0
$173$	13.3515	+	4.97986i	1.01510	+	0.378612i	0.801298	−	0.598266i	$-0.204143\pi$
$173$	13.3515	+	4.97986i	1.01510	+	0.378612i	0.213800	+	0.976878i	$0.431416\pi$
$174$		0			0
$175$	13.6652	−	19.4595i	1.03299	−	1.47100i
$176$		0			0
$177$	8.62264	−	6.45483i	0.648118	−	0.485175i
$178$		0			0
$179$	7.50178	+	11.6730i	0.560709	+	0.872481i	0.999661	−	0.0260297i	$-0.00828645\pi$
$179$	7.50178	+	11.6730i	0.560709	+	0.872481i	−0.438952	+	0.898511i	$0.644650\pi$
$180$		0			0
$181$	2.84456	−	9.68768i	0.211434	−	0.720080i	−0.783664	−	0.621186i	$-0.786651\pi$
$181$	2.84456	−	9.68768i	0.211434	−	0.720080i	0.995098	−	0.0988940i	$-0.0315305\pi$
$182$		0			0
$183$	7.24798	+	7.24798i	0.535786	+	0.535786i
$184$		0			0
$185$	5.72055	−	13.0471i	0.420583	−	0.959239i
$186$		0			0
$187$	−0.00267964	−	0.00490739i	−0.000195954	−	0.000358864i
$188$		0			0
$189$	−17.2543	+	11.0886i	−1.25506	+	0.806580i
$190$		0			0
$191$	20.5319	+	2.95205i	1.48564	+	0.213603i	0.836878	−	0.547389i	$-0.184378\pi$
$191$	20.5319	+	2.95205i	1.48564	+	0.213603i	0.648761	+	0.760992i	$0.275287\pi$
$192$		0			0
$193$	10.7412	−	2.33661i	0.773169	−	0.168193i	0.191362	−	0.981520i	$-0.438710\pi$
$193$	10.7412	−	2.33661i	0.773169	−	0.168193i	0.581807	+	0.813327i	$0.302346\pi$
$194$		0			0
$195$	1.66789	−	1.71934i	0.119440	−	0.123124i
$196$		0			0
$197$	−5.80947	+	7.76054i	−0.413907	+	0.552915i	−0.958244	−	0.285951i	$-0.907690\pi$
$197$	−5.80947	+	7.76054i	−0.413907	+	0.552915i	0.544337	+	0.838867i	$0.316781\pi$
$198$		0			0
$199$	−3.69373	+	1.08458i	−0.261842	+	0.0768837i	−0.410018	−	0.912077i	$-0.634478\pi$
$199$	−3.69373	+	1.08458i	−0.261842	+	0.0768837i	0.148177	+	0.988961i	$0.452660\pi$
$200$		0			0
$201$	−6.20697	−	5.37837i	−0.437806	−	0.379361i
$202$		0			0
$203$	2.77129	−	38.7477i	0.194507	−	2.71956i
$204$		0			0
$205$	−0.228725	+	4.06464i	−0.0159748	+	0.283887i
$206$		0			0
$207$	9.41175	+	6.20153i	0.654162	+	0.431036i
$208$		0			0
$209$	0.900891	+	0.411423i	0.0623159	+	0.0284587i
$210$		0			0
$211$	9.99329	+	11.5329i	0.687967	+	0.793956i	0.987074	−	0.160264i	$-0.0512344\pi$
$211$	9.99329	+	11.5329i	0.687967	+	0.793956i	−0.299108	+	0.954219i	$0.596689\pi$
$212$		0			0
$213$	0.276589	+	3.86721i	0.0189515	+	0.264977i
$214$		0			0
$215$	−1.68030	−	0.215599i	−0.114596	−	0.0147037i
$216$		0			0
$217$	14.5366	+	10.8819i	0.986806	+	0.738714i
$218$		0			0
$219$	−10.9152	+	4.98478i	−0.737578	+	0.336840i
$220$		0			0
$221$	0.00640830	−	0.00997151i	0.000431069	−	0.000670756i
$222$		0			0
$223$	13.4782	+	18.0048i	0.902567	+	1.20569i	0.978014	+	0.208538i	$0.0668705\pi$
$223$	13.4782	+	18.0048i	0.902567	+	1.20569i	−0.0754476	+	0.997150i	$0.524039\pi$
$224$		0			0
$225$	11.3704	+	2.96670i	0.758026	+	0.197780i
$226$		0			0
$227$	23.9697	−	13.0885i	1.59093	−	0.868712i	0.592943	−	0.805244i	$-0.297966\pi$
$227$	23.9697	−	13.0885i	1.59093	−	0.868712i	0.997984	−	0.0634674i	$-0.0202159\pi$
$228$		0			0
$229$	−6.79420			−0.448973			−0.224487	−	0.974477i	$-0.572071\pi$
$229$	−6.79420			−0.448973			−0.224487	+	0.974477i	$0.572071\pi$
$230$		0			0
$231$	2.40318			0.158118
$232$		0			0
$233$	−0.977245	+	0.533616i	−0.0640215	+	0.0349584i	−0.510941	−	0.859616i	$-0.670703\pi$
$233$	−0.977245	+	0.533616i	−0.0640215	+	0.0349584i	0.446919	+	0.894574i	$0.352521\pi$
$234$		0			0
$235$	−24.5532	+	3.91169i	−1.60167	+	0.255170i
$236$		0			0
$237$	−3.51342	−	4.69337i	−0.228221	−	0.304867i
$238$		0			0
$239$	13.5697	−	21.1149i	0.877751	−	1.36581i	−0.0523991	−	0.998626i	$-0.516687\pi$
$239$	13.5697	−	21.1149i	0.877751	−	1.36581i	0.930150	−	0.367180i	$-0.119677\pi$
$240$		0			0
$241$	5.13831	−	2.34659i	0.330987	−	0.151157i	−0.242988	−	0.970029i	$-0.578128\pi$
$241$	5.13831	−	2.34659i	0.330987	−	0.151157i	0.573976	+	0.818872i	$0.305400\pi$
$242$		0			0
$243$	−12.6641	−	9.48023i	−0.812402	−	0.608157i
$244$		0			0
$245$	21.3485	+	27.6333i	1.36391	+	1.76543i
$246$		0			0
$247$	0.149780	+	2.09420i	0.00953028	+	0.133251i
$248$		0			0
$249$	−0.136863	−	0.157948i	−0.00867334	−	0.0100096i
$250$		0			0
$251$	−12.1048	−	5.52807i	−0.764047	−	0.348928i	−0.00501960	−	0.999987i	$-0.501598\pi$
$251$	−12.1048	−	5.52807i	−0.764047	−	0.348928i	−0.759027	+	0.651059i	$0.774325\pi$
$252$		0			0
$253$	−1.21762	−	2.74883i	−0.0765508	−	0.172818i
$254$		0			0
$255$	−0.0160514		0.000903239i	−0.00100517		5.65630e-5i
$256$		0			0
$257$	0.640336	−	8.95307i	0.0399431	−	0.558477i	−0.937596	−	0.347725i	$-0.886954\pi$
$257$	0.640336	−	8.95307i	0.0399431	−	0.558477i	0.977540	−	0.210752i	$-0.0675913\pi$
$258$		0			0
$259$	22.8981	+	19.8413i	1.42282	+	1.23288i
$260$		0			0
$261$	18.4201	−	5.40862i	1.14017	−	0.334785i
$262$		0			0
$263$	−10.7435	+	14.3516i	−0.662470	+	0.884956i	−0.998378	−	0.0569390i	$-0.981866\pi$
$263$	−10.7435	+	14.3516i	−0.662470	+	0.884956i	0.335908	+	0.941895i	$0.390957\pi$
$264$		0			0
$265$	0.302764	+	19.9338i	0.0185986	+	1.22453i
$266$		0			0
$267$	−8.62876	+	1.87707i	−0.528071	+	0.114875i
$268$		0			0
$269$	−6.14402	−	0.883377i	−0.374608	−	0.0538605i	−0.0475603	−	0.998868i	$-0.515145\pi$
$269$	−6.14402	−	0.883377i	−0.374608	−	0.0538605i	−0.327048	+	0.945008i	$0.606054\pi$
$270$		0			0
$271$	−17.1458	+	11.0189i	−1.04153	+	0.669352i	−0.945365	−	0.326013i	$-0.894295\pi$
$271$	−17.1458	+	11.0189i	−1.04153	+	0.669352i	−0.0961667	+	0.995365i	$0.530658\pi$
$272$		0			0
$273$	2.44156	+	4.47138i	0.147770	+	0.270620i
$274$		0			0
$275$	−2.12361	−	2.30541i	−0.128058	−	0.139022i
$276$		0			0
$277$	15.9303	+	15.9303i	0.957158	+	0.957158i	0.999119	−	0.0419616i	$-0.0133607\pi$
$277$	15.9303	+	15.9303i	0.957158	+	0.957158i	−0.0419616	+	0.999119i	$0.513361\pi$
$278$		0			0
$279$	−2.52819	+	8.61023i	−0.151359	+	0.515481i
$280$		0			0
$281$	−3.77266	−	5.87038i	−0.225058	−	0.350197i	0.710300	−	0.703899i	$-0.248559\pi$
$281$	−3.77266	−	5.87038i	−0.225058	−	0.350197i	−0.935358	+	0.353702i	$0.884923\pi$
$282$		0			0
$283$	−0.372623	+	0.278942i	−0.0221501	+	0.0165814i	−0.610295	−	0.792174i	$-0.708949\pi$
$283$	−0.372623	+	0.278942i	−0.0221501	+	0.0165814i	0.588145	+	0.808755i	$0.299858\pi$
$284$		0			0
$285$	2.37196	−	1.57577i	0.140503	−	0.0933407i
$286$		0			0
$287$	−8.11245	−	3.02579i	−0.478863	−	0.178607i
$288$		0			0
$289$	16.8269	−	2.41934i	0.989817	−	0.142314i
$290$		0			0
$291$	−2.78520	−	9.48551i	−0.163271	−	0.556050i
$292$		0			0
$293$	8.77059	−	0.627285i	0.512384	−	0.0366464i	0.187246	−	0.982313i	$-0.440044\pi$
$293$	8.77059	−	0.627285i	0.512384	−	0.0366464i	0.325138	+	0.945667i	$0.394589\pi$
$294$		0			0
$295$	13.9192	−	26.4379i	0.810408	−	1.53928i
$296$		0			0
$297$	0.944818	+	2.53316i	0.0548239	+	0.146989i
$298$		0			0
$299$	3.87744	−	5.05823i	0.224238	−	0.292525i
$300$		0			0
$301$	1.49672	−	3.27737i	0.0862697	−	0.188904i
$302$		0			0
$303$	3.89265	+	0.278408i	0.223627	+	0.0159941i
$304$		0			0
$305$	26.7886	+	9.53076i	1.53391	+	0.545730i
$306$		0			0
$307$	−12.6367	−	6.90017i	−0.721216	−	0.393814i	0.0763213	−	0.997083i	$-0.475683\pi$
$307$	−12.6367	−	6.90017i	−0.721216	−	0.393814i	−0.797537	+	0.603269i	$0.793864\pi$
$308$		0			0
$309$	0.570220	+	3.96596i	0.0324387	+	0.225616i
$310$		0			0
$311$	3.02216	+	6.61762i	0.171371	+	0.375251i	0.975757	−	0.218857i	$-0.0702327\pi$
$311$	3.02216	+	6.61762i	0.171371	+	0.375251i	−0.804386	+	0.594107i	$0.797505\pi$
$312$		0			0
$313$	−4.86015	−	22.3418i	−0.274712	−	1.26283i	−0.883097	−	0.469190i	$-0.844546\pi$
$313$	−4.86015	−	22.3418i	−0.274712	−	1.26283i	0.608385	−	0.793642i	$-0.291818\pi$
$314$		0			0
$315$	−13.1909	+	21.2275i	−0.743224	+	1.19603i
$316$		0			0
$317$	−12.7467	−	2.77288i	−0.715928	−	0.155741i	−0.160176	−	0.987089i	$-0.551206\pi$
$317$	−12.7467	−	2.77288i	−0.715928	−	0.155741i	−0.555752	+	0.831348i	$0.687570\pi$
$318$		0			0
$319$	−4.91329	−	1.44267i	−0.275092	−	0.0807742i
$320$		0			0
$321$		−	4.38045i		−	0.244493i
$322$		0			0
$323$	0.00996391	−	0.00996391i	0.000554407	−	0.000554407i
$324$		0			0
$325$	2.13195	−	6.29343i	0.118259	−	0.349097i
$326$		0			0
$327$	−1.91387	+	8.79790i	−0.105837	+	0.486525i
$328$		0			0
$329$	7.52537	−	52.3401i	0.414887	−	2.88560i
$330$		0			0
$331$	21.3324	+	13.7095i	1.17253	+	0.753541i	0.973999	−	0.226553i	$-0.0727457\pi$
$331$	21.3324	+	13.7095i	1.17253	+	0.753541i	0.198534	+	0.980094i	$0.436382\pi$
$332$		0			0
$333$	−5.23262	+	14.0292i	−0.286746	+	0.768795i
$334$		0			0
$335$	−21.9545	−	6.08583i	−1.19950	−	0.332505i
$336$		0			0
$337$	−1.61202	+	2.95219i	−0.0878122	+	0.160816i	−0.917894	−	0.396825i	$-0.870112\pi$
$337$	−1.61202	+	2.95219i	−0.0878122	+	0.160816i	0.830082	+	0.557642i	$0.188294\pi$
$338$		0			0
$339$	−0.653166	+	0.753794i	−0.0354751	+	0.0409405i
$340$		0			0
$341$	1.80897	−	1.56749i	0.0979615	−	0.0848841i
$342$		0			0
$343$	−38.3932	+	14.3199i	−2.07304	+	0.773203i
$344$		0			0
$345$	−8.56101	−	1.19796i	−0.460909	−	0.0644961i
$346$		0			0
$347$	8.15057	−	3.04001i	0.437546	−	0.163196i	−0.121031	−	0.992649i	$-0.538620\pi$
$347$	8.15057	−	3.04001i	0.437546	−	0.163196i	0.558577	+	0.829453i	$0.311347\pi$
$348$		0			0
$349$	19.1782	−	16.6180i	1.02659	−	0.889541i	0.0326456	−	0.999467i	$-0.489607\pi$
$349$	19.1782	−	16.6180i	1.02659	−	0.889541i	0.993940	+	0.109926i	$0.0350613\pi$
$350$		0			0
$351$	−3.75331	+	4.33155i	−0.200337	+	0.231201i
$352$		0			0
$353$	14.4606	−	26.4826i	0.769659	−	1.40952i	−0.138267	−	0.990395i	$-0.544153\pi$
$353$	14.4606	−	26.4826i	0.769659	−	1.40952i	0.907926	−	0.419130i	$-0.137665\pi$
$354$		0			0
$355$	5.29701	+	9.35994i	0.281136	+	0.496774i
$356$		0			0
$357$	0.0119489	−	0.0320362i	0.000632402	−	0.00169554i
$358$		0			0
$359$	−6.71098	−	4.31288i	−0.354192	−	0.227625i	0.351430	−	0.936214i	$-0.385696\pi$
$359$	−6.71098	−	4.31288i	−0.354192	−	0.227625i	−0.705621	+	0.708589i	$0.749332\pi$
$360$		0			0
$361$	2.34877	−	16.3361i	0.123619	−	0.859792i
$362$		0			0
$363$	−1.81749	+	8.35487i	−0.0953935	+	0.438517i
$364$		0			0
$365$	−21.4132	+	25.4841i	−1.12082	+	1.33390i
$366$		0			0
$367$	−3.21429	+	3.21429i	−0.167785	+	0.167785i	−0.786005	−	0.618220i	$-0.787854\pi$
$367$	−3.21429	+	3.21429i	−0.167785	+	0.167785i	0.618220	+	0.786005i	$0.287854\pi$
$368$		0			0
$369$		−	4.27888i		−	0.222750i
$370$		0			0
$371$	−40.6827	−	11.9455i	−2.11214	−	0.620180i
$372$		0			0
$373$	−24.5064	−	5.33103i	−1.26889	−	0.276031i	−0.472780	−	0.881180i	$-0.656750\pi$
$373$	−24.5064	−	5.33103i	−1.26889	−	0.276031i	−0.796112	+	0.605150i	$0.793113\pi$
$374$		0			0
$375$	−8.85302	+	1.68757i	−0.457168	+	0.0871459i
$376$		0			0
$377$	−2.30750	−	10.6074i	−0.118842	−	0.546310i
$378$		0			0
$379$	−6.42340	−	14.0653i	−0.329948	−	0.722485i	0.669852	−	0.742495i	$-0.266358\pi$
$379$	−6.42340	−	14.0653i	−0.329948	−	0.722485i	−0.999800	+	0.0200097i	$0.993630\pi$
$380$		0			0
$381$	−0.404974	−	2.81665i	−0.0207474	−	0.144302i
$382$		0			0
$383$	−4.27913	−	2.33658i	−0.218653	−	0.119394i	0.366190	−	0.930540i	$-0.380662\pi$
$383$	−4.27913	−	2.33658i	−0.218653	−	0.119394i	−0.584843	+	0.811146i	$0.698844\pi$
$384$		0			0
$385$	6.02113	−	2.86105i	0.306865	−	0.145813i
$386$		0			0
$387$	1.77601	+	0.127023i	0.0902799	+	0.00645694i
$388$		0			0
$389$	−0.500773	+	1.09654i	−0.0253902	+	0.0555968i	−0.921902	−	0.387423i	$-0.873365\pi$
$389$	−0.500773	+	1.09654i	−0.0253902	+	0.0555968i	0.896512	+	0.443019i	$0.146093\pi$
$390$		0			0
$391$	−0.0426981	+	0.00256422i	−0.00215934	+	0.000129678i
$392$		0			0
$393$	2.23210	+	5.98449i	0.112595	+	0.301878i
$394$		0			0
$395$	−14.3904	−	7.57634i	−0.724059	−	0.381207i
$396$		0			0
$397$	−0.815366	+	0.0583162i	−0.0409221	+	0.00292680i	−0.0917852	−	0.995779i	$-0.529257\pi$
$397$	−0.815366	+	0.0583162i	−0.0409221	+	0.00292680i	0.0508631	+	0.998706i	$0.483803\pi$
$398$		0			0
$399$	1.70629	+	5.81111i	0.0854216	+	0.290919i
$400$		0			0
$401$	−27.7572	+	3.99088i	−1.38613	+	0.199295i	−0.794671	−	0.607041i	$-0.792357\pi$
$401$	−27.7572	+	3.99088i	−1.38613	+	0.199295i	−0.591458	+	0.806336i	$0.701447\pi$
$402$		0			0
$403$	4.75434	+	1.77328i	0.236830	+	0.0883332i
$404$		0			0
$405$	−7.83421	−	1.58002i	−0.389285	−	0.0785118i
$406$		0			0
$407$	3.19729	−	2.39346i	0.158484	−	0.118639i
$408$		0			0
$409$	16.9721	+	26.4091i	0.839216	+	1.30585i	0.950079	+	0.312009i	$0.101002\pi$
$409$	16.9721	+	26.4091i	0.839216	+	1.30585i	−0.110863	+	0.993836i	$0.535362\pi$
$410$		0			0
$411$	0.519564	−	1.76947i	0.0256282	−	0.0872816i
$412$		0			0
$413$	44.9331	+	44.9331i	2.21102	+	2.21102i
$414$		0			0
$415$	−0.530949	−	0.232797i	−0.0260633	−	0.0114276i
$416$		0			0
$417$	−0.413045	−	0.756435i	−0.0202269	−	0.0370428i
$418$		0			0
$419$	−17.2734	+	11.1010i	−0.843863	+	0.542318i	−0.889655	−	0.456633i	$-0.849055\pi$
$419$	−17.2734	+	11.1010i	−0.843863	+	0.542318i	0.0457922	+	0.998951i	$0.485419\pi$
$420$		0			0
$421$	−30.5516	−	4.39265i	−1.48899	−	0.214085i	−0.650712	−	0.759324i	$-0.725530\pi$
$421$	−30.5516	−	4.39265i	−1.48899	−	0.214085i	−0.838280	+	0.545240i	$0.816439\pi$
$422$		0			0
$423$	25.5348	−	5.55475i	1.24154	−	0.270081i
$424$		0			0
$425$	−0.0412917	+	0.0168465i	−0.00200294	+	0.000817176i
$426$		0			0
$427$	−36.2398	+	48.4107i	−1.75377	+	2.34276i
$428$		0			0
$429$	0.644354	−	0.189199i	0.0311097	−	0.00913463i
$430$		0			0
$431$	−26.5347	−	22.9925i	−1.27813	−	1.10751i	−0.988636	−	0.150329i	$-0.951967\pi$
$431$	−26.5347	−	22.9925i	−1.27813	−	1.10751i	−0.289496	−	0.957179i	$-0.593488\pi$
$432$		0			0
$433$	0.504848	−	7.05869i	0.0242614	−	0.339219i	−0.970795	−	0.239910i	$-0.922882\pi$
$433$	0.504848	−	7.05869i	0.0242614	−	0.339219i	0.995057	−	0.0993093i	$-0.0316633\pi$
$434$		0			0
$435$	−10.9796	+	9.80979i	−0.526434	+	0.470343i
$436$		0			0
$437$	5.78239	−	4.89601i	0.276609	−	0.234208i
$438$		0			0
$439$	21.4333	+	9.78825i	1.02295	+	0.467168i	0.855000	−	0.518627i	$-0.173557\pi$
$439$	21.4333	+	9.78825i	1.02295	+	0.467168i	0.167954	+	0.985795i	$0.446284\pi$
$440$		0			0
$441$	−24.0346	−	27.7374i	−1.14450	−	1.32083i
$442$		0			0
$443$	1.55929	+	21.8017i	0.0740839	+	1.03583i	0.889495	+	0.456946i	$0.151057\pi$
$443$	1.55929	+	21.8017i	0.0740839	+	1.03583i	−0.815411	+	0.578883i	$0.803489\pi$
$444$		0			0
$445$	−19.3845	+	14.9757i	−0.918912	+	0.709918i
$446$		0			0
$447$	4.27280	+	3.19858i	0.202097	+	0.151288i
$448$		0			0
$449$	−8.37905	+	3.82658i	−0.395432	+	0.180588i	−0.603199	−	0.797591i	$-0.706108\pi$
$449$	−8.37905	+	3.82658i	−0.395432	+	0.180588i	0.207767	+	0.978178i	$0.433380\pi$
$450$		0			0
$451$	−0.617051	+	0.960150i	−0.0290558	+	0.0452117i
$452$		0			0
$453$	8.13257	+	10.8638i	0.382101	+	0.510428i
$454$		0			0
$455$	11.4406	+	8.29622i	0.536343	+	0.388933i
$456$		0			0
$457$	13.2222	−	7.21984i	0.618506	−	0.337730i	−0.139260	−	0.990256i	$-0.544472\pi$
$457$	13.2222	−	7.21984i	0.618506	−	0.337730i	0.757767	+	0.652526i	$0.226291\pi$
$458$		0			0
$459$	0.0384666			0.00179547
$460$		0			0
$461$	17.4796			0.814107			0.407054	−	0.913404i	$-0.366556\pi$
$461$	17.4796			0.814107			0.407054	+	0.913404i	$0.366556\pi$
$462$		0			0
$463$	15.0900	−	8.23975i	0.701291	−	0.382934i	−0.0886951	−	0.996059i	$-0.528270\pi$
$463$	15.0900	−	8.23975i	0.701291	−	0.382934i	0.789986	+	0.613125i	$0.210088\pi$
$464$		0			0
$465$	−1.08281	−	6.79666i	−0.0502140	−	0.315187i
$466$		0			0
$467$	18.9623	+	25.3306i	0.877469	+	1.17216i	0.984056	+	0.177858i	$0.0569167\pi$
$467$	18.9623	+	25.3306i	0.877469	+	1.17216i	−0.106588	+	0.994303i	$0.533992\pi$
$468$		0			0
$469$	26.1960	−	40.7618i	1.20962	−	1.88221i
$470$		0			0
$471$	−11.7418	+	5.36229i	−0.541033	+	0.247081i
$472$		0			0
$473$	−0.380207	−	0.284619i	−0.0174819	−	0.0130868i
$474$		0			0
$475$	4.06690	−	6.77195i	0.186602	−	0.310718i
$476$		0			0
$477$	−1.49483	−	20.9004i	−0.0684433	−	0.956963i
$478$		0			0
$479$	−14.1736	−	16.3572i	−0.647609	−	0.747381i	0.333092	−	0.942894i	$-0.391908\pi$
$479$	−14.1736	−	16.3572i	−0.647609	−	0.747381i	−0.980701	+	0.195513i	$0.937363\pi$
$480$		0			0
$481$	7.70164	+	3.51722i	0.351164	+	0.160371i
$482$		0			0
$483$	7.82782	−	16.6353i	0.356178	−	0.756930i
$484$		0			0
$485$	−18.2710	−	20.4499i	−0.829644	−	0.928582i
$486$		0			0
$487$	−2.37273	+	33.1751i	−0.107519	+	1.50331i	0.601929	+	0.798550i	$0.294399\pi$
$487$	−2.37273	+	33.1751i	−0.107519	+	1.50331i	−0.709448	+	0.704758i	$0.751056\pi$
$488$		0			0
$489$	−9.23046	−	7.99824i	−0.417416	−	0.361693i
$490$		0			0
$491$	25.1948	−	7.39785i	1.13702	−	0.333860i	0.341559	−	0.939860i	$-0.389045\pi$
$491$	25.1948	−	7.39785i	1.13702	−	0.333860i	0.795465	+	0.606000i	$0.207227\pi$
$492$		0			0
$493$	−0.0436613	+	0.0583247i	−0.00196641	+	0.00262681i
$494$		0			0
$495$	2.36462	+	2.29386i	0.106282	+	0.103102i
$496$		0			0
$497$	−22.3507	+	4.86210i	−1.00257	+	0.218095i
$498$		0			0
$499$	38.0046	+	5.46423i	1.70132	+	0.244613i	0.923424	−	0.383782i	$-0.125379\pi$
$499$	38.0046	+	5.46423i	1.70132	+	0.244613i	0.777895	+	0.628395i	$0.216288\pi$
$500$		0			0
$501$	−5.81254	+	3.73549i	−0.259685	+	0.166889i
$502$		0			0
$503$	−0.106154	−	0.194406i	−0.00473315	−	0.00866812i	0.875302	−	0.483577i	$-0.160663\pi$
$503$	−0.106154	−	0.194406i	−0.00473315	−	0.00866812i	−0.880035	+	0.474909i	$0.842481\pi$
$504$		0			0
$505$	10.0844	−	3.93676i	0.448751	−	0.175184i
$506$		0			0
$507$	−6.40328	−	6.40328i	−0.284380	−	0.284380i
$508$		0			0
$509$	−9.73463	+	33.1531i	−0.431480	+	1.46948i	0.401334	+	0.915932i	$0.368547\pi$
$509$	−9.73463	+	33.1531i	−0.431480	+	1.46948i	−0.832814	+	0.553553i	$0.813272\pi$
$510$		0			0
$511$	−38.2735	−	59.5547i	−1.69312	−	2.63455i
$512$		0			0
$513$	−5.45456	+	4.08323i	−0.240825	+	0.180279i
$514$		0			0
$515$	6.15026	+	9.25779i	0.271013	+	0.407947i
$516$		0			0
$517$	−6.53086	−	2.43589i	−0.287227	−	0.107130i
$518$		0			0
$519$	11.3699	−	1.63475i	0.499085	−	0.0717576i
$520$		0			0
$521$	3.61946	+	12.3267i	0.158571	+	0.540044i	1.00000		0.000324153i	$-0.000103181\pi$
$521$	3.61946	+	12.3267i	0.158571	+	0.540044i	−0.841429	+	0.540368i	$0.818285\pi$
$522$		0			0
$523$	9.40670	−	0.672781i	0.411326	−	0.0294187i	0.135857	−	0.990728i	$-0.456621\pi$
$523$	9.40670	−	0.672781i	0.411326	−	0.0294187i	0.275470	+	0.961310i	$0.411167\pi$
$524$		0			0
$525$	2.15039	−	19.0466i	0.0938506	−	0.831263i
$526$		0			0
$527$	−0.0119013	−	0.0319087i	−0.000518430	−	0.00138996i
$528$		0			0
$529$	−22.9940	−	0.525142i	−0.999739	−	0.0228323i
$530$		0			0
$531$	−13.0454	+	28.5655i	−0.566124	+	1.23964i
$532$		0			0
$533$	−2.41337	−	0.172607i	−0.104535	−	0.00747646i
$534$		0			0
$535$	−5.21504	−	10.9751i	−0.225466	−	0.474496i
$536$		0			0
$537$	9.81698	+	5.36048i	0.423634	+	0.231322i
$538$		0			0
$539$	1.39322	+	9.69005i	0.0600102	+	0.417380i
$540$		0			0
$541$	−2.48291	−	5.43681i	−0.106749	−	0.233747i	0.848718	−	0.528845i	$-0.177375\pi$
$541$	−2.48291	−	5.43681i	−0.106749	−	0.233747i	−0.955467	+	0.295099i	$0.904648\pi$
$542$		0			0
$543$	−1.73004	−	7.95288i	−0.0742433	−	0.341291i
$544$		0			0
$545$	5.67898	+	24.3215i	0.243261	+	1.04182i
$546$		0			0
$547$	−36.9766	−	8.04376i	−1.58100	−	0.343927i	−0.665552	−	0.746352i	$-0.731804\pi$
$547$	−36.9766	−	8.04376i	−1.58100	−	0.343927i	−0.915453	+	0.402425i	$0.868167\pi$
$548$		0			0
$549$	−28.6744	−	8.41955i	−1.22379	−	0.359338i
$550$		0			0
$551$		−	12.9051i		−	0.549775i
$552$		0			0
$553$	24.4575	−	24.4575i	1.04004	−	1.04004i
$554$		0			0
$555$	−0.993098	−	11.4407i	−0.0421547	−	0.485630i
$556$		0			0
$557$	−2.54623	+	11.7048i	−0.107887	+	0.495950i	0.891215	+	0.453582i	$0.149854\pi$
$557$	−2.54623	+	11.7048i	−0.107887	+	0.495950i	−0.999102	+	0.0423685i	$0.986510\pi$
$558$		0			0
$559$	0.143287	−	0.996580i	0.00606038	−	0.0421508i
$560$		0			0
$561$	−0.00379165	−	0.00243675i	−0.000160084	−	0.000102879i
$562$		0			0
$563$	−1.03904	+	2.78578i	−0.0437904	+	0.117407i	−0.957004	−	0.290074i	$-0.906320\pi$
$563$	−1.03904	+	2.78578i	−0.0437904	+	0.117407i	0.913214	+	0.407481i	$0.133593\pi$
$564$		0			0
$565$	−0.739083	+	2.66623i	−0.0310935	+	0.112169i
$566$		0			0
$567$	8.14594	−	14.9182i	0.342097	−	0.626504i
$568$		0			0
$569$	−14.9545	+	17.2584i	−0.626925	+	0.723510i	−0.977007	−	0.213209i	$-0.931608\pi$
$569$	−14.9545	+	17.2584i	−0.626925	+	0.723510i	0.350081	+	0.936719i	$0.386154\pi$
$570$		0			0
$571$	5.99000	−	5.19036i	0.250674	−	0.217210i	−0.520455	−	0.853889i	$-0.674238\pi$
$571$	5.99000	−	5.19036i	0.250674	−	0.217210i	0.771129	+	0.636679i	$0.219692\pi$
$572$		0			0
$573$	15.6667	−	5.84336i	0.654484	−	0.244110i
$574$		0			0
$575$	−22.8756	+	7.19064i	−0.953980	+	0.299870i
$576$		0			0
$577$	23.7175	−	8.84617i	0.987373	−	0.368271i	0.196669	−	0.980470i	$-0.436988\pi$
$577$	23.7175	−	8.84617i	0.987373	−	0.368271i	0.790704	+	0.612199i	$0.209715\pi$
$578$		0			0
$579$	6.69666	−	5.80268i	0.278303	−	0.241151i
$580$		0			0
$581$	0.807441	−	0.931837i	0.0334983	−	0.0386591i
$582$		0			0
$583$	−2.67858	+	4.90546i	−0.110936	+	0.203163i
$584$		0			0
$585$	−1.86560	+	6.73013i	−0.0771332	+	0.278257i
$586$		0			0
$587$	4.61737	−	12.3796i	0.190579	−	0.510962i	−0.806156	−	0.591703i	$-0.798456\pi$
$587$	4.61737	−	12.3796i	0.190579	−	0.510962i	0.996735	+	0.0807407i	$0.0257286\pi$
$588$		0			0
$589$	5.07472	+	3.26132i	0.209100	+	0.134380i
$590$		0			0
$591$	−1.11210	+	7.73485i	−0.0457458	+	0.318169i
$592$		0			0
$593$	−9.35666	+	43.0119i	−0.384232	+	1.76629i	0.226063	+	0.974113i	$0.427414\pi$
$593$	−9.35666	+	43.0119i	−0.384232	+	1.76629i	−0.610295	+	0.792174i	$0.708949\pi$
$594$		0			0
$595$	−0.00820226	−	0.0944916i	−0.000336260	−	0.00387378i
$596$		0			0
$597$	−2.19430	+	2.19430i	−0.0898066	+	0.0898066i
$598$		0			0
$599$			41.5618i			1.69817i	0.528255	+	0.849086i	$0.322846\pi$
$599$			41.5618i			1.69817i	−0.528255	+	0.849086i	$0.677154\pi$
$600$		0			0
$601$	−33.7322	−	9.90466i	−1.37596	−	0.404019i	−0.491602	−	0.870820i	$-0.663588\pi$
$601$	−33.7322	−	9.90466i	−1.37596	−	0.404019i	−0.884362	+	0.466801i	$0.845407\pi$
$602$		0			0
$603$	23.3981	+	5.08995i	0.952846	+	0.207279i
$604$		0			0
$605$	5.39301	+	23.0967i	0.219257	+	0.939016i
$606$		0			0
$607$	3.47673	+	15.9823i	0.141116	+	0.648700i	0.992303	+	0.123837i	$0.0395199\pi$
$607$	3.47673	+	15.9823i	0.141116	+	0.648700i	−0.851187	+	0.524863i	$0.824117\pi$
$608$		0			0
$609$	−13.0084	−	28.4844i	−0.527126	−	1.15425i
$610$		0			0
$611$	−2.10292	−	14.6262i	−0.0850752	−	0.591711i
$612$		0			0
$613$	6.32670	+	3.45464i	0.255533	+	0.139532i	0.601910	−	0.798564i	$-0.294406\pi$
$613$	6.32670	+	3.45464i	0.255533	+	0.139532i	−0.346377	+	0.938095i	$0.612588\pi$
$614$		0			0
$615$	1.40843	+	2.96407i	0.0567936	+	0.119523i
$616$		0			0
$617$	43.8491	+	3.13615i	1.76530	+	0.126257i	0.915877	−	0.401459i	$-0.131497\pi$
$617$	43.8491	+	3.13615i	1.76530	+	0.126257i	0.849421	+	0.527716i	$0.176951\pi$
$618$		0			0
$619$	11.2716	−	24.6814i	0.453044	−	0.992029i	−0.535974	−	0.844235i	$-0.680055\pi$
$619$	11.2716	−	24.6814i	0.453044	−	0.992029i	0.989018	−	0.147794i	$-0.0472173\pi$
$620$		0			0
$621$	20.6125	+	1.71098i	0.827151	+	0.0686591i
$622$		0			0
$623$	−18.2061	−	48.8123i	−0.729411	−	1.95563i
$624$		0			0
$625$	−20.1720	+	14.7679i	−0.806878	+	0.590717i
$626$		0			0
$627$	0.796316	−	0.0569536i	0.0318018	−	0.00227451i
$628$		0			0
$629$	−0.0160093	−	0.0545228i	−0.000638334	−	0.00217397i
$630$		0			0
$631$	27.3097	−	3.92654i	1.08718	−	0.156313i	0.424658	−	0.905354i	$-0.360394\pi$
$631$	27.3097	−	3.92654i	1.08718	−	0.156313i	0.662524	+	0.749041i	$0.269485\pi$
$632$		0			0
$633$	11.5256	+	4.29882i	0.458101	+	0.170863i
$634$		0			0
$635$	−4.36796	−	6.57494i	−0.173337	−	0.260919i
$636$		0			0
$637$	−16.6139	+	12.4370i	−0.658268	+	0.492773i
$638$		0			0
$639$	−6.11132	−	9.50939i	−0.241760	−	0.376186i
$640$		0			0
$641$	−6.30561	+	21.4749i	−0.249057	+	0.848209i	0.736147	+	0.676822i	$0.236643\pi$
$641$	−6.30561	+	21.4749i	−0.249057	+	0.848209i	−0.985204	+	0.171388i	$0.945175\pi$
$642$		0			0
$643$	14.5855	+	14.5855i	0.575196	+	0.575196i	0.933576	−	0.358380i	$-0.116671\pi$
$643$	14.5855	+	14.5855i	0.575196	+	0.575196i	−0.358380	+	0.933576i	$0.616671\pi$
$644$		0			0
$645$	−1.27209	+	0.496600i	−0.0500886	+	0.0195536i
$646$		0			0
$647$	−10.9237	−	20.0053i	−0.429456	−	0.786490i	0.569924	−	0.821698i	$-0.306973\pi$
$647$	−10.9237	−	20.0053i	−0.429456	−	0.786490i	−0.999380	+	0.0352072i	$0.988791\pi$
$648$		0			0
$649$	7.04669	−	4.52863i	0.276607	−	0.177764i
$650$		0			0
$651$	14.4884	+	2.08312i	0.567847	+	0.0816441i
$652$		0			0
$653$	−1.76368	+	0.383665i	−0.0690181	+	0.0150140i	−0.246942	−	0.969030i	$-0.579426\pi$
$653$	−1.76368	+	0.383665i	−0.0690181	+	0.0150140i	0.177924	+	0.984044i	$0.443062\pi$
$654$		0			0
$655$	12.7172	+	12.3366i	0.496901	+	0.482033i
$656$		0			0
$657$	20.9658	−	28.0071i	0.817955	−	1.09266i
$658$		0			0
$659$	28.4687	−	8.35916i	1.10898	−	0.325627i	0.324568	−	0.945862i	$-0.394781\pi$
$659$	28.4687	−	8.35916i	1.10898	−	0.325627i	0.784416	+	0.620236i	$0.212963\pi$
$660$		0			0
$661$	19.1389	+	16.5839i	0.744416	+	0.645040i	0.942141	−	0.335218i	$-0.108810\pi$
$661$	19.1389	+	16.5839i	0.744416	+	0.645040i	−0.197725	+	0.980258i	$0.563355\pi$
$662$		0			0
$663$	0.000681630	−	0.00953043i	2.64723e−5	−	0.000370131i
$664$		0			0
$665$	11.1934	+	12.5282i	0.434060	+	0.485824i
$666$		0			0
$667$	−25.9904	+	29.3115i	−1.00635	+	1.13495i
$668$		0			0
$669$	16.4913	+	7.53134i	0.637592	+	0.291179i
$670$		0			0
$671$	5.22015	+	6.02437i	0.201522	+	0.232568i
$672$		0			0
$673$	−2.10308	−	29.4048i	−0.0810676	−	1.13347i	−0.861338	−	0.508032i	$-0.830373\pi$
$673$	−2.10308	−	29.4048i	−0.0810676	−	1.13347i	0.780271	−	0.625442i	$-0.215081\pi$
$674$		0			0
$675$	20.9222	−	5.22155i	0.805295	−	0.200978i
$676$		0			0
$677$	12.9568	+	9.69932i	0.497969	+	0.372775i	0.818540	−	0.574449i	$-0.194784\pi$
$677$	12.9568	+	9.69932i	0.497969	+	0.372775i	−0.320571	+	0.947225i	$0.603875\pi$
$678$		0			0
$679$	53.0530	−	24.2285i	2.03599	−	0.929803i
$680$		0			0
$681$	11.9021	−	18.5200i	0.456089	−	0.709688i
$682$		0			0
$683$	−2.38962	−	3.19215i	−0.0914361	−	0.122144i	0.752490	−	0.658603i	$-0.228852\pi$
$683$	−2.38962	−	3.19215i	−0.0914361	−	0.122144i	−0.843926	+	0.536459i	$0.819762\pi$
$684$		0			0
$685$	−0.804847	−	5.05193i	−0.0307516	−	0.193024i
$686$		0			0
$687$	−4.80685	+	2.62474i	−0.183393	+	0.100140i
$688$		0			0
$689$	−11.8485			−0.451392
$690$		0			0
$691$	12.1312			0.461491			0.230745	−	0.973014i	$-0.425884\pi$
$691$	12.1312			0.461491			0.230745	+	0.973014i	$0.425884\pi$
$692$		0			0
$693$	−6.14953	+	3.35790i	−0.233601	+	0.127556i
$694$		0			0
$695$	−1.93543	−	1.40349i	−0.0734151	−	0.0532375i
$696$		0			0
$697$	0.00973147	+	0.0129997i	0.000368606	+	0.000492400i
$698$		0			0
$699$	−0.485248	+	0.755060i	−0.0183538	+	0.0285590i
$700$		0			0
$701$	43.2280	−	19.7416i	1.63270	−	0.745628i	0.633103	−	0.774068i	$-0.281781\pi$
$701$	43.2280	−	19.7416i	1.63270	−	0.745628i	0.999596	+	0.0284393i	$0.00905374\pi$
$702$		0			0
$703$	8.05772	+	6.03193i	0.303903	+	0.227499i
$704$		0			0
$705$	−15.8601	+	12.2529i	−0.597325	+	0.461471i
$706$		0			0
$707$	1.64251	+	22.9652i	0.0617728	+	0.863697i
$708$		0			0
$709$	8.94131	+	10.3188i	0.335798	+	0.387531i	0.898387	−	0.439206i	$-0.144740\pi$
$709$	8.94131	+	10.3188i	0.335798	+	0.387531i	−0.562589	+	0.826737i	$0.690195\pi$
$710$		0			0
$711$	15.5484	+	7.10074i	0.583112	+	0.266298i
$712$		0			0
$713$	−4.95809	−	17.6278i	−0.185682	−	0.660165i
$714$		0			0
$715$	1.38917	−	1.24116i	0.0519520	−	0.0464166i
$716$		0			0
$717$	1.44336	−	20.1809i	0.0539035	−	0.753669i
$718$		0			0
$719$	−18.1026	−	15.6860i	−0.675113	−	0.584989i	0.248352	−	0.968670i	$-0.420111\pi$
$719$	−18.1026	−	15.6860i	−0.675113	−	0.584989i	−0.923466	+	0.383681i	$0.874656\pi$
$720$		0			0
$721$	−22.6808	+	6.65969i	−0.844678	+	0.248020i
$722$		0			0
$723$	2.72878	−	3.64523i	0.101485	−	0.135568i
$724$		0			0
$725$	−15.8305	+	37.6498i	−0.587929	+	1.39828i
$726$		0			0
$727$	14.3872	−	3.12975i	0.533592	−	0.116076i	0.0623076	−	0.998057i	$-0.480154\pi$
$727$	14.3872	−	3.12975i	0.533592	−	0.116076i	0.471285	+	0.881981i	$0.343790\pi$
$728$		0			0
$729$	−2.00898	−	0.288848i	−0.0744066	−	0.0106981i
$730$		0			0
$731$	−0.00568462	+	0.00365328i	−0.000210253	+	0.000135121i
$732$		0			0
$733$	−14.6650	−	26.8570i	−0.541665	−	0.991986i	−0.994926	−	0.100608i	$-0.967921\pi$
$733$	−14.6650	−	26.8570i	−0.541665	−	0.991986i	0.453261	−	0.891378i	$-0.350261\pi$
$734$		0			0
$735$	25.7793	+	11.3030i	0.950882	+	0.416919i
$736$		0			0
$737$	−4.51635	−	4.51635i	−0.166362	−	0.166362i
$738$		0			0
$739$	−8.99966	+	30.6500i	−0.331058	+	1.12748i	0.610888	+	0.791717i	$0.290812\pi$
$739$	−8.99966	+	30.6500i	−0.331058	+	1.12748i	−0.941946	+	0.335763i	$0.891006\pi$
$740$		0			0
$741$	0.915001	+	1.42377i	0.0336134	+	0.0523035i
$742$		0			0
$743$	0.357862	−	0.267892i	0.0131287	−	0.00982801i	−0.592693	−	0.805428i	$-0.701935\pi$
$743$	0.357862	−	0.267892i	0.0131287	−	0.00982801i	0.605822	+	0.795600i	$0.292844\pi$
$744$		0			0
$745$	14.5134	+	2.92709i	0.531730	+	0.107240i
$746$		0			0
$747$	0.570917	+	0.212941i	0.0208888	+	0.00779110i
$748$		0			0
$749$	25.5800	−	3.67785i	0.934673	−	0.134386i
$750$		0			0
$751$	11.6274	+	39.5994i	0.424291	+	1.44500i	0.843508	+	0.537117i	$0.180487\pi$
$751$	11.6274	+	39.5994i	0.424291	+	1.44500i	−0.419216	+	0.907886i	$0.637695\pi$
$752$		0			0
$753$	−10.6997	+	0.765255i	−0.389917	+	0.0278874i
$754$		0			0
$755$	33.3097	+	17.5371i	1.21226	+	0.638240i
$756$		0			0
$757$	−9.14804	−	24.5268i	−0.332491	−	0.891443i	−0.990386	−	0.138333i	$-0.955826\pi$
$757$	−9.14804	−	24.5268i	−0.332491	−	0.891443i	0.657895	−	0.753110i	$-0.271447\pi$
$758$		0			0
$759$	−1.92339	−	1.47439i	−0.0698145	−	0.0535170i
$760$		0			0
$761$	10.5128	−	23.0198i	0.381088	−	0.834466i	−0.617755	−	0.786371i	$-0.711958\pi$
$761$	10.5128	−	23.0198i	0.381088	−	0.834466i	0.998843	−	0.0480954i	$-0.0153152\pi$
$762$		0			0
$763$	−52.9830	−	3.78942i	−1.91811	−	0.137186i
$764$		0			0
$765$	0.0423361	−	0.0201168i	0.00153066	−	0.000727324i
$766$		0			0
$767$	15.5852	+	8.51018i	0.562750	+	0.307285i
$768$		0			0
$769$	−5.27256	−	36.6715i	−0.190134	−	1.32241i	−0.831651	−	0.555299i	$-0.812604\pi$
$769$	−5.27256	−	36.6715i	−0.190134	−	1.32241i	0.641517	−	0.767109i	$-0.278305\pi$
$770$		0			0
$771$	−3.00572	−	6.58161i	−0.108248	−	0.237031i
$772$		0			0
$773$	10.5853	+	48.6597i	0.380726	+	1.75017i	0.625153	+	0.780502i	$0.285036\pi$
$773$	10.5853	+	48.6597i	0.380726	+	1.75017i	−0.244427	+	0.969668i	$0.578600\pi$
$774$		0			0
$775$	−10.8046	−	15.7398i	−0.388111	−	0.565390i
$776$		0			0
$777$	23.8654	+	5.19159i	0.856166	+	0.186247i
$778$		0			0
$779$	−2.75984	−	0.810363i	−0.0988816	−	0.0290343i
$780$		0			0
$781$			3.01514i			0.107890i
$782$		0			0
$783$	24.9106	−	24.9106i	0.890234	−	0.890234i
$784$		0			0
$785$	−23.0349	+	27.4140i	−0.822149	+	0.978449i
$786$		0			0
$787$	−0.353076	+	1.62306i	−0.0125858	+	0.0578560i	−0.983011	−	0.183544i	$-0.941243\pi$
$787$	−0.353076	+	1.62306i	−0.0125858	+	0.0578560i	0.970426	+	0.241400i	$0.0776066\pi$
$788$		0			0
$789$	−2.05661	+	14.3041i	−0.0732174	+	0.509238i
$790$		0			0
$791$	−4.95024	−	3.18133i	−0.176010	−	0.113115i
$792$		0			0
$793$	−5.90549	+	15.8332i	−0.209710	+	0.562254i
$794$		0			0
$795$	7.91505	+	13.9861i	0.280718	+	0.496035i
$796$		0			0
$797$	14.0159	−	25.6682i	0.496469	−	0.909216i	−0.502533	−	0.864558i	$-0.667598\pi$
$797$	14.0159	−	25.6682i	0.496469	−	0.909216i	0.999002	−	0.0446577i	$-0.0142197\pi$
$798$		0			0
$799$	−0.0649443	+	0.0749498i	−0.00229757	+	0.00265153i
$800$		0			0
$801$	19.4575	−	16.8600i	0.687495	−	0.595718i
$802$		0			0
$803$	−8.74343	+	3.26113i	−0.308549	+	0.115083i
$804$		0			0
$805$	−0.192272	−	50.9985i	−0.00677671	−	1.79746i
$806$		0			0
$807$	−4.68812	+	1.74858i	−0.165030	+	0.0615529i
$808$		0			0
$809$	−32.1592	+	27.8661i	−1.13066	+	0.979721i	−0.999932	−	0.0116973i	$-0.996277\pi$
$809$	−32.1592	+	27.8661i	−1.13066	+	0.979721i	−0.130727	+	0.991418i	$0.541731\pi$
$810$		0			0
$811$	3.51682	−	4.05863i	0.123492	−	0.142518i	−0.690636	−	0.723202i	$-0.742670\pi$
$811$	3.51682	−	4.05863i	0.123492	−	0.142518i	0.814129	+	0.580684i	$0.197215\pi$
$812$		0			0
$813$	−7.87369	+	14.4196i	−0.276142	+	0.505717i
$814$		0			0
$815$	−32.6489	−	9.05033i	−1.14364	−	0.317019i
$816$		0			0
$817$	0.418282	−	1.12146i	0.0146338	−	0.0392348i
$818$		0			0
$819$	−12.4955	−	8.03035i	−0.436627	−	0.280603i
$820$		0			0
$821$	−4.39020	+	30.5345i	−0.153219	+	1.06566i	0.757560	+	0.652766i	$0.226391\pi$
$821$	−4.39020	+	30.5345i	−0.153219	+	1.06566i	−0.910779	+	0.412895i	$0.864518\pi$
$822$		0			0
$823$	−7.62546	+	35.0537i	−0.265807	+	1.22189i	0.629697	+	0.776841i	$0.283179\pi$
$823$	−7.62546	+	35.0537i	−0.265807	+	1.22189i	−0.895504	+	0.445054i	$0.853185\pi$
$824$		0			0
$825$	−2.39307	−	0.810670i	−0.0833159	−	0.0282239i
$826$		0			0
$827$	−2.45032	+	2.45032i	−0.0852061	+	0.0852061i	−0.748425	−	0.663219i	$-0.769190\pi$
$827$	−2.45032	+	2.45032i	−0.0852061	+	0.0852061i	0.663219	+	0.748425i	$0.269190\pi$
$828$		0			0
$829$			9.29242i			0.322739i	0.986894	+	0.161370i	$0.0515911\pi$
$829$			9.29242i			0.322739i	−0.986894	+	0.161370i	$0.948409\pi$
$830$		0			0
$831$	17.4248	+	5.11637i	0.604458	+	0.177485i
$832$		0			0
$833$	0.136103	+	0.0296074i	0.00471569	+	0.00102583i
$834$		0			0
$835$	−10.1160	+	16.2792i	−0.350079	+	0.563364i
$836$		0			0
$837$	3.50039	+	16.0910i	0.120991	+	0.556187i
$838$		0			0
$839$	1.35194	+	2.96033i	0.0466741	+	0.102202i	0.931533	−	0.363658i	$-0.118472\pi$
$839$	1.35194	+	2.96033i	0.0466741	+	0.102202i	−0.884858	+	0.465860i	$0.845745\pi$
$840$		0			0
$841$	5.36875	+	37.3405i	0.185129	+	1.28760i
$842$		0			0
$843$	−4.93698	−	2.69580i	−0.170039	−	0.0928481i
$844$		0			0
$845$	−23.6666	−	8.42001i	−0.814154	−	0.289657i
$846$		0			0
$847$	−50.3149	−	3.59860i	−1.72884	−	0.123649i
$848$		0			0
$849$	−0.155867	+	0.341302i	−0.00534935	+	0.0117134i
$850$		0			0
$851$	−6.15352	−	29.9283i	−0.210940	−	1.02593i
$852$		0			0
$853$	−19.0789	−	51.1526i	−0.653250	−	1.75143i	−0.659787	−	0.751453i	$-0.729353\pi$
$853$	−19.0789	−	51.1526i	−0.653250	−	1.75143i	0.00653654	−	0.999979i	$-0.497919\pi$
$854$		0			0
$855$	−3.86785	+	7.34654i	−0.132278	+	0.251246i
$856$		0			0
$857$	−8.34173	+	0.596612i	−0.284948	+	0.0203799i	−0.213082	−	0.977034i	$-0.568350\pi$
$857$	−8.34173	+	0.596612i	−0.284948	+	0.0203799i	−0.0718664	+	0.997414i	$0.522896\pi$
$858$		0			0
$859$	−1.43164	−	4.87573i	−0.0488471	−	0.166358i	0.931457	−	0.363851i	$-0.118538\pi$
$859$	−1.43164	−	4.87573i	−0.0488471	−	0.166358i	−0.980304	+	0.197493i	$0.936720\pi$
$860$		0			0
$861$	−6.90843	+	0.993282i	−0.235439	+	0.0338510i
$862$		0			0
$863$	10.6949	+	3.98899i	0.364058	+	0.135787i	0.524835	−	0.851204i	$-0.324127\pi$
$863$	10.6949	+	3.98899i	0.364058	+	0.135787i	−0.160776	+	0.986991i	$0.551400\pi$
$864$		0			0
$865$	26.5409	−	17.6320i	0.902419	−	0.599508i
$866$		0			0
$867$	10.9703	−	8.21224i	0.372570	−	0.278902i
$868$		0			0
$869$	−2.46497	−	3.83557i	−0.0836184	−	0.130113i
$870$		0			0
$871$	3.81469	−	12.9916i	0.129256	−	0.440205i
$872$		0			0
$873$	20.3809	+	20.3809i	0.689789	+	0.689789i
$874$		0			0
$875$	−17.2878	−	50.2810i	−0.584433	−	1.69981i
$876$		0			0
$877$	17.8560	+	32.7007i	0.602953	+	1.10423i	0.983746	+	0.179565i	$0.0574691\pi$
$877$	17.8560	+	32.7007i	0.602953	+	1.10423i	−0.380793	+	0.924660i	$0.624349\pi$
$878$		0			0
$879$	5.96280	−	3.83206i	0.201120	−	0.129252i
$880$		0			0
$881$	−15.3048	−	2.20050i	−0.515631	−	0.0741366i	−0.120413	−	0.992724i	$-0.538422\pi$
$881$	−15.3048	−	2.20050i	−0.515631	−	0.0741366i	−0.395218	+	0.918587i	$0.629331\pi$
$882$		0			0
$883$	28.9462	−	6.29687i	0.974119	−	0.211907i	0.302783	−	0.953060i	$-0.402084\pi$
$883$	28.9462	−	6.29687i	0.974119	−	0.211907i	0.671336	+	0.741153i	$0.265721\pi$
$884$		0			0
$885$	−0.365767	−	24.0820i	−0.0122951	−	0.809506i
$886$		0			0
$887$	30.6935	−	41.0018i	1.03059	−	1.37670i	0.106592	−	0.994303i	$-0.466006\pi$
$887$	30.6935	−	41.0018i	1.03059	−	1.37670i	0.923996	−	0.382402i	$-0.124903\pi$
$888$		0			0
$889$	16.1081	−	4.72976i	0.540247	−	0.158631i
$890$		0			0
$891$	−1.69330	−	1.46725i	−0.0567277	−	0.0491549i
$892$		0			0
$893$	1.25318	−	17.5217i	0.0419360	−	0.586342i
$894$		0			0
$895$	30.9780	+	1.74319i	1.03548	+	0.0582685i
$896$		0			0
$897$	0.789164	−	5.07660i	0.0263494	−	0.169503i
$898$		0			0
$899$	−28.3710	−	12.9566i	−0.946226	−	0.432127i
$900$		0			0
$901$	0.0520752	+	0.0600980i	0.00173488	+	0.00200215i
$902$		0			0
$903$	−0.207193	−	2.89693i	−0.00689494	−	0.0964039i
$904$		0			0
$905$	−13.8027	−	17.8661i	−0.458818	−	0.593890i
$906$		0			0
$907$	−29.7720	−	22.2871i	−0.988564	−	0.740030i	−0.0228772	−	0.999738i	$-0.507283\pi$
$907$	−29.7720	−	22.2871i	−0.988564	−	0.740030i	−0.965687	+	0.259708i	$0.916374\pi$
$908$		0			0
$909$	−10.3500	+	4.72668i	−0.343287	+	0.156774i
$910$		0			0
$911$	−27.8313	+	43.3063i	−0.922091	+	1.43480i	−0.0216775	+	0.999765i	$0.506901\pi$
$911$	−27.8313	+	43.3063i	−0.922091	+	1.43480i	−0.900413	+	0.435036i	$0.856736\pi$
$912$		0			0
$913$	−0.0974017	−	0.130113i	−0.00322352	−	0.00430612i
$914$		0			0
$915$	22.6347	−	3.60604i	0.748280	−	0.119212i
$916$		0			0
$917$	−33.0728	+	18.0591i	−1.09216	+	0.596365i
$918$		0			0
$919$	15.5736			0.513725			0.256863	−	0.966448i	$-0.417311\pi$
$919$	15.5736			0.513725			0.256863	+	0.966448i	$0.417311\pi$
$920$		0			0
$921$	−11.6061			−0.382433
$922$		0			0
$923$	−5.61000	+	3.06329i	−0.184655	+	0.100829i
$924$		0			0
$925$	−16.1086	−	27.4821i	−0.529648	−	0.903605i
$926$		0			0
$927$	−7.00067	−	9.35181i	−0.229932	−	0.307154i
$928$		0			0
$929$	−32.3419	+	50.3250i	−1.06110	+	1.65111i	−0.368791	+	0.929513i	$0.620228\pi$
$929$	−32.3419	+	50.3250i	−1.06110	+	1.65111i	−0.692313	+	0.721597i	$0.743408\pi$
$930$		0			0
$931$	−22.4422	+	10.2490i	−0.735513	+	0.335898i
$932$		0			0
$933$	4.69468	+	3.51440i	0.153697	+	0.115056i
$934$		0			0
$935$	−0.0124009	−	0.00159116i	−0.000405553	−	5.20364e-5i
$936$		0			0
$937$	2.02895	+	28.3685i	0.0662830	+	0.926758i	0.916426	+	0.400205i	$0.131061\pi$
$937$	2.02895	+	28.3685i	0.0662830	+	0.926758i	−0.850143	+	0.526553i	$0.823484\pi$
$938$		0			0
$939$	−12.0696	−	13.9291i	−0.393877	−	0.454558i
$940$		0			0
$941$	−15.4458	−	7.05384i	−0.503517	−	0.229949i	0.147429	−	0.989073i	$-0.452900\pi$
$941$	−15.4458	−	7.05384i	−0.503517	−	0.229949i	−0.650946	+	0.759124i	$0.725628\pi$
$942$		0			0
$943$	4.63643	+	7.39880i	0.150983	+	0.240938i
$944$		0			0
$945$	−2.57667	+	45.7897i	−0.0838191	+	1.48954i
$946$		0			0
$947$	1.14964	−	16.0741i	0.0373584	−	0.522339i	−0.943974	−	0.330020i	$-0.892945\pi$
$947$	1.14964	−	16.0741i	0.0373584	−	0.522339i	0.981332	−	0.192319i	$-0.0616009\pi$
$948$		0			0
$949$	−14.9507	−	12.9549i	−0.485322	−	0.420534i
$950$		0			0
$951$	−10.0895	+	2.96253i	−0.327173	+	0.0960666i
$952$		0			0
$953$	6.01975	−	8.04144i	0.194999	−	0.260488i	−0.692376	−	0.721537i	$-0.743436\pi$
$953$	6.01975	−	8.04144i	0.194999	−	0.260488i	0.887375	+	0.461049i	$0.152527\pi$
$954$		0			0
$955$	32.2958	−	33.2920i	1.04507	−	1.07730i
$956$		0			0
$957$	−4.03346	+	0.877425i	−0.130383	+	0.0283631i
$958$		0			0
$959$	10.7692	+	1.54838i	0.347756	+	0.0499997i
$960$		0			0
$961$	−13.8141	+	8.87777i	−0.445616	+	0.286380i
$962$		0			0
$963$	6.12068	+	11.2092i	0.197236	+	0.361211i
$964$		0			0
$965$	9.87009	−	22.5111i	0.317729	−	0.724657i
$966$		0			0
$967$	24.7607	+	24.7607i	0.796251	+	0.796251i	0.982502	−	0.186251i	$-0.0596338\pi$
$967$	24.7607	+	24.7607i	0.796251	+	0.796251i	−0.186251	+	0.982502i	$0.559634\pi$
$968$		0			0
$969$	0.00320014	−	0.0108987i	0.000102803	−	0.000350116i
$970$		0			0
$971$	−10.0330	−	15.6116i	−0.321974	−	0.501001i	0.642105	−	0.766616i	$-0.278061\pi$
$971$	−10.0330	−	15.6116i	−0.321974	−	0.501001i	−0.964079	+	0.265616i	$0.914425\pi$
$972$		0			0
$973$	4.07047	−	3.04712i	0.130493	−	0.0976860i
$974$		0			0
$975$	−0.922942	−	5.27618i	−0.0295578	−	0.168973i
$976$		0			0
$977$	−11.7706	−	4.39021i	−0.376575	−	0.140455i	0.154048	−	0.988063i	$-0.450769\pi$
$977$	−11.7706	−	4.39021i	−0.376575	−	0.140455i	−0.530622	+	0.847608i	$0.678042\pi$
$978$		0			0
$979$	−6.79746	+	0.977327i	−0.217248	+	0.0312355i
$980$		0			0
$981$	−7.39565	−	25.1873i	−0.236125	−	0.804167i
$982$		0			0
$983$	13.1130	−	0.937863i	0.418241	−	0.0299132i	0.139367	−	0.990241i	$-0.455493\pi$
$983$	13.1130	−	0.937863i	0.418241	−	0.0299132i	0.278874	+	0.960328i	$0.410039\pi$
$984$		0			0
$985$	6.42219	+	20.7035i	0.204628	+	0.659668i
$986$		0			0
$987$	−14.8959	−	39.9375i	−0.474142	−	1.27122i
$988$		0			0
$989$	−3.20862	+	1.70478i	−0.102028	+	0.0542087i
$990$		0			0
$991$	−17.0800	+	37.4000i	−0.542564	+	1.18805i	0.417605	+	0.908629i	$0.362870\pi$
$991$	−17.0800	+	37.4000i	−0.542564	+	1.18805i	−0.960169	+	0.279421i	$0.909858\pi$
$992$		0			0
$993$	20.3888	+	1.45823i	0.647018	+	0.0462756i
$994$		0			0
$995$	−2.88540	+	8.11014i	−0.0914733	+	0.257109i
$996$		0			0
$997$	−14.6575	−	8.00362i	−0.464209	−	0.253477i	0.230083	−	0.973171i	$-0.426100\pi$
$997$	−14.6575	−	8.00362i	−0.464209	−	0.253477i	−0.694292	+	0.719694i	$0.744282\pi$
$998$		0			0
$999$	3.91037	+	27.1972i	0.123719	+	0.860481i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.x.a.17.9	✓	240
5.3	odd	4	inner	460.2.x.a.293.9	yes	240
23.19	odd	22	inner	460.2.x.a.157.9	yes	240
115.88	even	44	inner	460.2.x.a.433.9	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.17.9	✓	240	1.1	even	1	trivial
460.2.x.a.157.9	yes	240	23.19	odd	22	inner
460.2.x.a.293.9	yes	240	5.3	odd	4	inner
460.2.x.a.433.9	yes	240	115.88	even	44	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707493 - 0.386321i) q^{3} +(1.31269 - 1.81021i) q^{5} +(2.84997 + 3.80711i) q^{7} +(-1.27062 + 1.97712i) q^{9} +O(q^{10})\)	\(q+(0.707493 - 0.386321i) q^{3} +(1.31269 - 1.81021i) q^{5} +(2.84997 + 3.80711i) q^{7} +(-1.27062 + 1.97712i) q^{9} +(0.570235 - 0.260418i) q^{11} +(1.06388 + 0.796408i) q^{13} +(0.229396 - 1.78783i) q^{15} +(-0.000636289 - 0.00889649i) q^{17} +(1.03459 + 1.19398i) q^{19} +(3.48710 + 1.59250i) q^{21} +(0.0547534 - 4.79552i) q^{23} +(-1.55371 - 4.75247i) q^{25} +(-0.307670 + 4.30179i) q^{27} +(-6.17334 - 5.34923i) q^{29} +(3.66360 - 1.07573i) q^{31} +(0.302833 - 0.404537i) q^{33} +(10.6328 - 0.161495i) q^{35} +(6.22544 - 1.35426i) q^{37} +(1.06035 + 0.152456i) q^{39} +(-1.53162 + 0.984312i) q^{41} +(-0.363086 - 0.664942i) q^{43} +(1.91108 + 4.89543i) q^{45} +(-7.86232 - 7.86232i) q^{47} +(-4.39965 + 14.9838i) q^{49} +(-0.00388707 - 0.00604839i) q^{51} +(-7.13739 + 5.34298i) q^{53} +(0.277129 - 1.37409i) q^{55} +(1.19322 + 0.445049i) q^{57} +(13.2259 - 1.90160i) q^{59} +(3.58247 + 12.2008i) q^{61} +(-11.1483 + 0.797345i) q^{63} +(2.83820 - 0.880405i) q^{65} +(-3.56055 - 9.54621i) q^{67} +(-1.81387 - 3.41395i) q^{69} +(-1.99803 + 4.37507i) q^{71} +(-14.8481 - 1.06195i) q^{73} +(-2.93522 - 2.76211i) q^{75} +(2.61659 + 1.42877i) q^{77} +(-1.03506 - 7.19899i) q^{79} +(-1.48474 - 3.25113i) q^{81} +(-0.0551115 - 0.253344i) q^{83} +(-0.0169397 - 0.0105265i) q^{85} +(-6.43412 - 1.39966i) q^{87} +(-10.5110 - 3.08630i) q^{89} +6.32003i q^{91} +(2.17640 - 2.17640i) q^{93} +(3.51944 - 0.305502i) q^{95} +(2.60690 - 11.9837i) q^{97} +(-0.209674 + 1.45832i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3}+O(q^{10}) \) 240 * q + 4 * q^3	\( 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) \) 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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