LMFDB - Embedded newform 912.2.cc.d.497.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(257,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 9, 17]))

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

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

chi := DirichletCharacter("912.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.cc (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + \cdots + 19683 $ x^18 - x^15 - 18x^14 + 36x^13 + 10x^12 + 18x^11 + 90x^10 - 567x^9 + 270x^8 + 162x^7 + 270x^6 + 2916x^5 - 4374x^4 - 729x^3 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			497.1
Root			$1.40849 + 1.00804i$ of defining polynomial
Character	$\chi$	$=$	912.497
Dual form			912.2.cc.d.545.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.57724 - 0.715766i) q^{3} +(0.262261 + 0.0462437i) q^{5} +(-0.604656 - 1.04730i) q^{7} +(1.97536 + 2.25787i) q^{9} +O(q^{10})$	\(q+(-1.57724 - 0.715766i) q^{3} +(0.262261 + 0.0462437i) q^{5} +(-0.604656 - 1.04730i) q^{7} +(1.97536 + 2.25787i) q^{9} +(2.03630 + 1.17566i) q^{11} +(1.01749 - 2.79553i) q^{13} +(-0.380548 - 0.260655i) q^{15} +(-0.576470 + 0.687011i) q^{17} +(-1.97979 + 3.88335i) q^{19} +(0.204068 + 2.08463i) q^{21} +(5.53770 - 0.976446i) q^{23} +(-4.63182 - 1.68584i) q^{25} +(-1.49950 - 4.97509i) q^{27} +(-1.92487 + 1.61516i) q^{29} +(8.98131 - 5.18536i) q^{31} +(-2.37023 - 3.31181i) q^{33} +(-0.110147 - 0.302626i) q^{35} -3.95916i q^{37} +(-3.60577 + 3.68093i) q^{39} +(10.4227 - 3.79356i) q^{41} +(0.834031 - 4.73003i) q^{43} +(0.413647 + 0.683499i) q^{45} +(1.24341 + 1.48183i) q^{47} +(2.76878 - 4.79567i) q^{49} +(1.40097 - 0.670961i) q^{51} +(-0.998339 - 5.66186i) q^{53} +(0.479676 + 0.402496i) q^{55} +(5.90217 - 4.70791i) q^{57} +(-9.78136 - 8.20754i) q^{59} +(-0.153642 - 0.871345i) q^{61} +(1.17024 - 3.43401i) q^{63} +(0.396123 - 0.686106i) q^{65} +(-3.28864 - 3.91925i) q^{67} +(-9.43317 - 2.42361i) q^{69} +(-1.64669 + 9.33885i) q^{71} +(0.320853 - 0.116781i) q^{73} +(6.09881 + 5.97428i) q^{75} -2.84348i q^{77} +(-2.33914 - 6.42674i) q^{79} +(-1.19593 + 8.92019i) q^{81} +(12.2240 - 7.05752i) q^{83} +(-0.182956 + 0.153518i) q^{85} +(4.19206 - 1.16973i) q^{87} +(11.5580 + 4.20677i) q^{89} +(-3.54297 + 0.624722i) q^{91} +(-17.8772 + 1.75003i) q^{93} +(-0.698802 + 0.926900i) q^{95} +(3.88456 - 4.62944i) q^{97} +(1.36794 + 6.92004i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q+O(q^{10}) $ 18 * q	$ 18 q - 12 q^{13} + 24 q^{15} - 6 q^{17} + 6 q^{19} - 18 q^{25} + 3 q^{27} + 6 q^{29} - 27 q^{33} - 24 q^{35} - 6 q^{39} - 3 q^{41} + 6 q^{43} + 54 q^{45} + 30 q^{47} + 21 q^{49} + 33 q^{51} + 60 q^{53} - 30 q^{55} + 12 q^{57} + 3 q^{59} + 54 q^{61} - 84 q^{63} - 24 q^{65} + 15 q^{67} + 24 q^{69} + 36 q^{71} - 42 q^{73} + 6 q^{79} + 36 q^{83} + 54 q^{87} + 60 q^{89} + 18 q^{91} - 84 q^{93} + 6 q^{95} + 9 q^{97} + 30 q^{99}+O(q^{100}) $ 18 * q - 12 * q^13 + 24 * q^15 - 6 * q^17 + 6 * q^19 - 18 * q^25 + 3 * q^27 + 6 * q^29 - 27 * q^33 - 24 * q^35 - 6 * q^39 - 3 * q^41 + 6 * q^43 + 54 * q^45 + 30 * q^47 + 21 * q^49 + 33 * q^51 + 60 * q^53 - 30 * q^55 + 12 * q^57 + 3 * q^59 + 54 * q^61 - 84 * q^63 - 24 * q^65 + 15 * q^67 + 24 * q^69 + 36 * q^71 - 42 * q^73 + 6 * q^79 + 36 * q^83 + 54 * q^87 + 60 * q^89 + 18 * q^91 - 84 * q^93 + 6 * q^95 + 9 * q^97 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$	$-1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.57724	−	0.715766i	−0.910619	−	0.413248i
$3$	−1.57724	−	0.715766i	−0.910619	−	0.413248i
$4$		0			0
$5$	0.262261	+	0.0462437i	0.117287	+	0.0206808i	0.231983	−	0.972720i	$-0.425478\pi$
$5$	0.262261	+	0.0462437i	0.117287	+	0.0206808i	−0.114697	+	0.993401i	$0.536590\pi$
$6$		0			0
$7$	−0.604656	−	1.04730i	−0.228539	−	0.395840i	0.728837	−	0.684688i	$-0.240061\pi$
$7$	−0.604656	−	1.04730i	−0.228539	−	0.395840i	−0.957375	+	0.288847i	$0.906728\pi$
$8$		0			0
$9$	1.97536	+	2.25787i	0.658452	+	0.752623i
$10$		0			0
$11$	2.03630	+	1.17566i	0.613968	+	0.354474i	0.774517	−	0.632553i	$-0.217993\pi$
$11$	2.03630	+	1.17566i	0.613968	+	0.354474i	−0.160549	+	0.987028i	$0.551326\pi$
$12$		0			0
$13$	1.01749	−	2.79553i	0.282201	−	0.775340i	−0.714899	−	0.699228i	$-0.753527\pi$
$13$	1.01749	−	2.79553i	0.282201	−	0.775340i	0.997099	−	0.0761119i	$-0.0242506\pi$
$14$		0			0
$15$	−0.380548	−	0.260655i	−0.0982572	−	0.0673008i
$16$		0			0
$17$	−0.576470	+	0.687011i	−0.139815	+	0.166625i	−0.831408	−	0.555663i	$-0.812465\pi$
$17$	−0.576470	+	0.687011i	−0.139815	+	0.166625i	0.691593	+	0.722287i	$0.256909\pi$
$18$		0			0
$19$	−1.97979	+	3.88335i	−0.454194	+	0.890903i
$19$	−1.97979	+	3.88335i	−0.454194	+	0.890903i
$20$		0			0
$21$	0.204068	+	2.08463i	0.0445312	+	0.454903i
$22$		0			0
$23$	5.53770	−	0.976446i	1.15469	−	0.203603i	0.436668	−	0.899623i	$-0.356159\pi$
$23$	5.53770	−	0.976446i	1.15469	−	0.203603i	0.718022	+	0.696020i	$0.245048\pi$
$24$		0			0
$25$	−4.63182	−	1.68584i	−0.926364	−	0.337169i
$26$		0			0
$27$	−1.49950	−	4.97509i	−0.288579	−	0.957456i
$28$		0			0
$29$	−1.92487	+	1.61516i	−0.357440	+	0.299928i	−0.803769	−	0.594941i	$-0.797175\pi$
$29$	−1.92487	+	1.61516i	−0.357440	+	0.299928i	0.446329	+	0.894869i	$0.352731\pi$
$30$		0			0
$31$	8.98131	−	5.18536i	1.61309	−	0.931319i	0.624443	−	0.781070i	$-0.285326\pi$
$31$	8.98131	−	5.18536i	1.61309	−	0.931319i	0.988648	−	0.150249i	$-0.0480075\pi$
$32$		0			0
$33$	−2.37023	−	3.31181i	−0.412605	−	0.576512i
$34$		0			0
$35$	−0.110147	−	0.302626i	−0.0186182	−	0.0511532i
$36$		0			0
$37$		−	3.95916i		−	0.650882i	−0.945562	−	0.325441i	$-0.894487\pi$
$37$		−	3.95916i		−	0.650882i	0.945562	−	0.325441i	$-0.105513\pi$
$38$		0			0
$39$	−3.60577	+	3.68093i	−0.577385	+	0.589420i
$40$		0			0
$41$	10.4227	−	3.79356i	1.62776	−	0.592455i	0.642920	−	0.765934i	$-0.277723\pi$
$41$	10.4227	−	3.79356i	1.62776	−	0.592455i	0.984838	+	0.173479i	$0.0555007\pi$
$42$		0			0
$43$	0.834031	−	4.73003i	0.127189	−	0.721322i	−0.852795	−	0.522245i	$-0.825095\pi$
$43$	0.834031	−	4.73003i	0.127189	−	0.721322i	0.979984	−	0.199077i	$-0.0637944\pi$
$44$		0			0
$45$	0.413647	+	0.683499i	0.0616629	+	0.101890i
$46$		0			0
$47$	1.24341	+	1.48183i	0.181369	+	0.216147i	0.849067	−	0.528285i	$-0.177165\pi$
$47$	1.24341	+	1.48183i	0.181369	+	0.216147i	−0.667698	+	0.744432i	$0.732720\pi$
$48$		0			0
$49$	2.76878	−	4.79567i	0.395540	−	0.685096i
$50$		0			0
$51$	1.40097	−	0.670961i	0.196175	−	0.0939533i
$52$		0			0
$53$	−0.998339	−	5.66186i	−0.137132	−	0.777717i	−0.973351	−	0.229320i	$-0.926350\pi$
$53$	−0.998339	−	5.66186i	−0.137132	−	0.777717i	0.836219	−	0.548396i	$-0.184761\pi$
$54$		0			0
$55$	0.479676	+	0.402496i	0.0646794	+	0.0542725i
$56$		0			0
$57$	5.90217	−	4.70791i	0.781762	−	0.623578i
$58$		0			0
$59$	−9.78136	−	8.20754i	−1.27342	−	1.06853i	−0.994115	−	0.108329i	$-0.965450\pi$
$59$	−9.78136	−	8.20754i	−1.27342	−	1.06853i	−0.279310	−	0.960201i	$-0.590106\pi$
$60$		0			0
$61$	−0.153642	−	0.871345i	−0.0196718	−	0.111564i	0.973391	−	0.229152i	$-0.0735951\pi$
$61$	−0.153642	−	0.871345i	−0.0196718	−	0.111564i	−0.993063	+	0.117587i	$0.962484\pi$
$62$		0			0
$63$	1.17024	−	3.43401i	0.147437	−	0.432645i
$64$		0			0
$65$	0.396123	−	0.686106i	0.0491331	−	0.0851010i
$66$		0			0
$67$	−3.28864	−	3.91925i	−0.401771	−	0.478812i	0.526788	−	0.849997i	$-0.323396\pi$
$67$	−3.28864	−	3.91925i	−0.401771	−	0.478812i	−0.928559	+	0.371184i	$0.878952\pi$
$68$		0			0
$69$	−9.43317	−	2.42361i	−1.13562	−	0.291769i
$70$		0			0
$71$	−1.64669	+	9.33885i	−0.195426	+	1.10832i	0.716384	+	0.697706i	$0.245796\pi$
$71$	−1.64669	+	9.33885i	−0.195426	+	1.10832i	−0.911810	+	0.410612i	$0.865315\pi$
$72$		0			0
$73$	0.320853	−	0.116781i	0.0375530	−	0.0136682i	−0.323175	−	0.946339i	$-0.604750\pi$
$73$	0.320853	−	0.116781i	0.0375530	−	0.0136682i	0.360728	+	0.932671i	$0.382528\pi$
$74$		0			0
$75$	6.09881	+	5.97428i	0.704230	+	0.689850i
$76$		0			0
$77$		−	2.84348i		−	0.324044i
$78$		0			0
$79$	−2.33914	−	6.42674i	−0.263174	−	0.723064i	−0.998949	−	0.0458383i	$-0.985404\pi$
$79$	−2.33914	−	6.42674i	−0.263174	−	0.723064i	0.735775	−	0.677226i	$-0.236818\pi$
$80$		0			0
$81$	−1.19593	+	8.92019i	−0.132881	+	0.991132i
$82$		0			0
$83$	12.2240	−	7.05752i	1.34176	−	0.774663i	0.354691	−	0.934984i	$-0.384586\pi$
$83$	12.2240	−	7.05752i	1.34176	−	0.774663i	0.987065	+	0.160320i	$0.0512527\pi$
$84$		0			0
$85$	−0.182956	+	0.153518i	−0.0198443	+	0.0166514i
$86$		0			0
$87$	4.19206	−	1.16973i	0.449436	−	0.125408i
$88$		0			0
$89$	11.5580	+	4.20677i	1.22515	+	0.445917i	0.871933	−	0.489626i	$-0.162867\pi$
$89$	11.5580	+	4.20677i	1.22515	+	0.445917i	0.353213	+	0.935543i	$0.385089\pi$
$90$		0			0
$91$	−3.54297	+	0.624722i	−0.371405	+	0.0654887i
$92$		0			0
$93$	−17.8772	+	1.75003i	−1.85378	+	0.181469i
$94$		0			0
$95$	−0.698802	+	0.926900i	−0.0716956	+	0.0950979i
$96$		0			0
$97$	3.88456	−	4.62944i	0.394418	−	0.470049i	−0.531892	−	0.846812i	$-0.678519\pi$
$97$	3.88456	−	4.62944i	0.394418	−	0.470049i	0.926309	+	0.376764i	$0.122963\pi$
$98$		0			0
$99$	1.36794	+	6.92004i	0.137483	+	0.695490i
$100$		0			0
$101$	−3.54557	+	9.74137i	−0.352797	+	0.969302i	0.628670	+	0.777672i	$0.283600\pi$
$101$	−3.54557	+	9.74137i	−0.352797	+	0.969302i	−0.981467	+	0.191630i	$0.938623\pi$
$102$		0			0
$103$	12.7994	+	7.38973i	1.26116	+	0.728131i	0.973299	−	0.229541i	$-0.0737224\pi$
$103$	12.7994	+	7.38973i	1.26116	+	0.728131i	0.287861	+	0.957672i	$0.407056\pi$
$104$		0			0
$105$	−0.0428818	+	0.556153i	−0.00418484	+	0.0542750i
$106$		0			0
$107$	−8.08439	−	14.0026i	−0.781547	−	1.35368i	−0.931040	−	0.364917i	$-0.881097\pi$
$107$	−8.08439	−	14.0026i	−0.781547	−	1.35368i	0.149493	−	0.988763i	$-0.452236\pi$
$108$		0			0
$109$	17.9876	+	3.17170i	1.72290	+	0.303794i	0.945599	−	0.325334i	$-0.105477\pi$
$109$	17.9876	+	3.17170i	1.72290	+	0.303794i	0.777302	+	0.629128i	$0.216588\pi$
$110$		0			0
$111$	−2.83383	+	6.24453i	−0.268975	+	0.592705i
$112$		0			0
$113$	−2.40020			−0.225792			−0.112896	−	0.993607i	$-0.536013\pi$
$113$	−2.40020			−0.225792			−0.112896	+	0.993607i	$0.536013\pi$
$114$		0			0
$115$	1.49748			0.139640
$116$		0			0
$117$	8.32184	−	3.22481i	0.769354	−	0.298134i
$118$		0			0
$119$	1.06807	+	0.188329i	0.0979098	+	0.0172641i
$120$		0			0
$121$	−2.73565	−	4.73829i	−0.248696	−	0.430754i
$122$		0			0
$123$	−19.1544	−	1.47689i	−1.72710	−	0.133167i
$124$		0			0
$125$	−2.28993	−	1.32209i	−0.204818	−	0.118251i
$126$		0			0
$127$	2.02408	−	5.56112i	0.179608	−	0.493470i	−0.816918	−	0.576754i	$-0.804319\pi$
$127$	2.02408	−	5.56112i	0.179608	−	0.493470i	0.996526	+	0.0832849i	$0.0265411\pi$
$128$		0			0
$129$	−4.70106	+	6.86340i	−0.413905	+	0.604289i
$130$		0			0
$131$	−11.1080	+	13.2379i	−0.970506	+	1.15660i	0.0171319	+	0.999853i	$0.494546\pi$
$131$	−11.1080	+	13.2379i	−0.970506	+	1.15660i	−0.987638	+	0.156751i	$0.949898\pi$
$132$		0			0
$133$	5.26411	−	0.274672i	0.456456	−	0.0238171i
$134$		0			0
$135$	−0.163194	−	1.37411i	−0.0140455	−	0.118265i
$136$		0			0
$137$	−18.0150	+	3.17653i	−1.53912	+	0.271389i	−0.877917	−	0.478813i	$-0.841067\pi$
$137$	−18.0150	+	3.17653i	−1.53912	+	0.271389i	−0.661208	+	0.750203i	$0.729956\pi$
$138$		0			0
$139$	2.16057	+	0.786381i	0.183257	+	0.0667000i	0.432019	−	0.901865i	$-0.357801\pi$
$139$	2.16057	+	0.786381i	0.183257	+	0.0667000i	−0.248762	+	0.968565i	$0.580024\pi$
$140$		0			0
$141$	−0.900499	−	3.22719i	−0.0758357	−	0.271778i
$142$		0			0
$143$	5.35850	−	4.49632i	0.448100	−	0.376001i
$144$		0			0
$145$	−0.579510	+	0.334580i	−0.0481257	+	0.0277854i
$146$		0			0
$147$	−7.79961	+	5.58211i	−0.643301	+	0.460405i
$148$		0			0
$149$	2.67853	+	7.35921i	0.219434	+	0.602890i	0.999747	−	0.0224995i	$-0.00716240\pi$
$149$	2.67853	+	7.35921i	0.219434	+	0.602890i	−0.780313	+	0.625389i	$0.784940\pi$
$150$		0			0
$151$		−	11.1343i		−	0.906098i	−0.891486	−	0.453049i	$-0.850336\pi$
$151$		−	11.1343i		−	0.906098i	0.891486	−	0.453049i	$-0.149664\pi$
$152$		0			0
$153$	−2.68991	+	0.0554973i	−0.217467	+	0.00448669i
$154$		0			0
$155$	2.59524	−	0.944590i	0.208455	−	0.0758713i
$156$		0			0
$157$	−3.68519	+	20.8997i	−0.294110	+	1.66798i	0.376688	+	0.926340i	$0.377063\pi$
$157$	−3.68519	+	20.8997i	−0.294110	+	1.66798i	−0.670798	+	0.741640i	$0.734048\pi$
$158$		0			0
$159$	−2.47795	+	9.64468i	−0.196515	+	0.764873i
$160$		0			0
$161$	−4.37103	−	5.20919i	−0.344485	−	0.410542i
$162$		0			0
$163$	−1.74061	+	3.01482i	−0.136335	+	0.236139i	−0.926107	−	0.377262i	$-0.876866\pi$
$163$	−1.74061	+	3.01482i	−0.136335	+	0.236139i	0.789772	+	0.613401i	$0.210199\pi$
$164$		0			0
$165$	−0.468470	−	0.978167i	−0.0364703	−	0.0761502i
$166$		0			0
$167$	3.56671	+	20.2278i	0.276000	+	1.56527i	0.735767	+	0.677235i	$0.236822\pi$
$167$	3.56671	+	20.2278i	0.276000	+	1.56527i	−0.459767	+	0.888040i	$0.652067\pi$
$168$		0			0
$169$	3.17888	+	2.66740i	0.244529	+	0.205185i
$170$		0			0
$171$	−12.6789	+	3.20091i	−0.969579	+	0.244780i
$172$		0			0
$173$	−6.38346	−	5.35636i	−0.485326	−	0.407237i	0.367022	−	0.930212i	$-0.380377\pi$
$173$	−6.38346	−	5.35636i	−0.485326	−	0.407237i	−0.852348	+	0.522976i	$0.824822\pi$
$174$		0			0
$175$	1.03508	+	5.87024i	0.0782448	+	0.443748i
$176$		0			0
$177$	9.55285	+	19.9464i	0.718036	+	1.49926i
$178$		0			0
$179$	−4.51280	+	7.81640i	−0.337302	+	0.584225i	−0.983924	−	0.178586i	$-0.942848\pi$
$179$	−4.51280	+	7.81640i	−0.337302	+	0.584225i	0.646622	+	0.762811i	$0.276181\pi$
$180$		0			0
$181$	5.90976	+	7.04297i	0.439269	+	0.523500i	0.939573	−	0.342350i	$-0.111223\pi$
$181$	5.90976	+	7.04297i	0.439269	+	0.523500i	−0.500304	+	0.865850i	$0.666778\pi$
$182$		0			0
$183$	−0.381350	+	1.48429i	−0.0281902	+	0.109722i
$184$		0			0
$185$	0.183086	−	1.03833i	0.0134608	−	0.0763398i
$186$		0			0
$187$	−1.98156	+	0.721228i	−0.144906	+	0.0527414i
$188$		0			0
$189$	−4.30370	+	4.57864i	−0.313048	+	0.333047i
$190$		0			0
$191$			7.33252i			0.530562i	0.964171	+	0.265281i	$0.0854648\pi$
$191$			7.33252i			0.530562i	−0.964171	+	0.265281i	$0.914535\pi$
$192$		0			0
$193$	0.613121	+	1.68453i	0.0441334	+	0.121255i	0.959801	−	0.280680i	$-0.0905599\pi$
$193$	0.613121	+	1.68453i	0.0441334	+	0.121255i	−0.915668	+	0.401935i	$0.868338\pi$
$194$		0			0
$195$	−1.11587	+	0.798620i	−0.0799093	+	0.0571904i
$196$		0			0
$197$	6.85271	−	3.95642i	0.488236	−	0.281883i	−0.235607	−	0.971849i	$-0.575708\pi$
$197$	6.85271	−	3.95642i	0.488236	−	0.281883i	0.723842	+	0.689966i	$0.242374\pi$
$198$		0			0
$199$	8.01318	−	6.72386i	0.568039	−	0.476642i	−0.312955	−	0.949768i	$-0.601319\pi$
$199$	8.01318	−	6.72386i	0.568039	−	0.476642i	0.880995	+	0.473126i	$0.156875\pi$
$200$		0			0
$201$	2.38170	+	8.53548i	0.167992	+	0.602047i
$202$		0			0
$203$	2.85543	+	1.03929i	0.200412	+	0.0729441i
$204$		0			0
$205$	2.90891	−	0.512919i	0.203167	−	0.0358238i
$206$		0			0
$207$	13.1436	+	10.5746i	0.913544	+	0.734983i
$208$		0			0
$209$	−8.59694	+	5.58012i	−0.594663	+	0.385985i
$210$		0			0
$211$	−8.93046	+	10.6429i	−0.614799	+	0.732688i	−0.980167	−	0.198175i	$-0.936499\pi$
$211$	−8.93046	+	10.6429i	−0.614799	+	0.732688i	0.365368	+	0.930863i	$0.380943\pi$
$212$		0			0
$213$	9.28166	−	13.5509i	0.635969	−	0.928495i
$214$		0			0
$215$	0.437468	−	1.20193i	0.0298351	−	0.0819712i
$216$		0			0
$217$	−10.8612	−	6.27072i	−0.737307	−	0.425684i
$218$		0			0
$219$	−0.589649	−	0.0454645i	−0.0398448	−	0.00307221i
$220$		0			0
$221$	1.33401	+	2.31057i	0.0897349	+	0.155425i
$222$		0			0
$223$	12.2714	+	2.16379i	0.821757	+	0.144898i	0.568691	−	0.822551i	$-0.307450\pi$
$223$	12.2714	+	2.16379i	0.821757	+	0.144898i	0.253066	+	0.967449i	$0.418561\pi$
$224$		0			0
$225$	−5.34308	−	13.7882i	−0.356206	−	0.919212i
$226$		0			0
$227$	1.63948			0.108816			0.0544081	−	0.998519i	$-0.482673\pi$
$227$	1.63948			0.108816			0.0544081	+	0.998519i	$0.482673\pi$
$228$		0			0
$229$	−12.1547			−0.803204			−0.401602	−	0.915814i	$-0.631546\pi$
$229$	−12.1547			−0.803204			−0.401602	+	0.915814i	$0.631546\pi$
$230$		0			0
$231$	−2.03527	+	4.48484i	−0.133911	+	0.295081i
$232$		0			0
$233$	−2.37239	−	0.418316i	−0.155420	−	0.0274048i	0.0953966	−	0.995439i	$-0.469588\pi$
$233$	−2.37239	−	0.418316i	−0.155420	−	0.0274048i	−0.250817	+	0.968035i	$0.580699\pi$
$234$		0			0
$235$	0.257571	+	0.446127i	0.0168021	+	0.0291021i
$236$		0			0
$237$	−0.910662	+	11.8108i	−0.0591538	+	0.767192i
$238$		0			0
$239$	−16.5806	−	9.57284i	−1.07251	−	0.619215i	−0.143646	−	0.989629i	$-0.545883\pi$
$239$	−16.5806	−	9.57284i	−1.07251	−	0.619215i	−0.928867	+	0.370414i	$0.879216\pi$
$240$		0			0
$241$	1.43503	−	3.94271i	0.0924383	−	0.253972i	−0.884854	−	0.465869i	$-0.845742\pi$
$241$	1.43503	−	3.94271i	0.0924383	−	0.253972i	0.977292	+	0.211897i	$0.0679641\pi$
$242$		0			0
$243$	8.27104	−	13.2132i	0.530587	−	0.847630i
$244$		0			0
$245$	0.947913	−	1.12968i	0.0605600	−	0.0721726i
$246$		0			0
$247$	8.84162	+	9.48582i	0.562579	+	0.603568i
$248$		0			0
$249$	−24.3317	+	2.38187i	−1.54196	+	0.150945i
$250$		0			0
$251$	4.15098	−	0.731929i	0.262007	−	0.0461990i	−0.0411012	−	0.999155i	$-0.513087\pi$
$251$	4.15098	−	0.731929i	0.262007	−	0.0461990i	0.303109	+	0.952956i	$0.401976\pi$
$252$		0			0
$253$	12.4244	+	4.52211i	0.781114	+	0.284302i
$254$		0			0
$255$	0.398448	−	0.111181i	0.0249518	−	0.00696242i
$256$		0			0
$257$	−13.6150	+	11.4244i	−0.849282	+	0.712632i	−0.959631	−	0.281260i	$-0.909248\pi$
$257$	−13.6150	+	11.4244i	−0.849282	+	0.712632i	0.110349	+	0.993893i	$0.464803\pi$
$258$		0			0
$259$	−4.14641	+	2.39393i	−0.257645	+	0.148752i
$260$		0			0
$261$	−7.44913	−	1.15559i	−0.461089	−	0.0715293i
$262$		0			0
$263$	0.383160	+	1.05272i	0.0236267	+	0.0649138i	0.950945	−	0.309359i	$-0.100115\pi$
$263$	0.383160	+	1.05272i	0.0236267	+	0.0649138i	−0.927319	+	0.374273i	$0.877892\pi$
$264$		0			0
$265$		−	1.53105i		−	0.0940519i
$266$		0			0
$267$	−15.2187	−	14.9079i	−0.931366	−	0.912349i
$268$		0			0
$269$	−18.2909	+	6.65734i	−1.11522	+	0.405905i	−0.832904	−	0.553418i	$-0.813323\pi$
$269$	−18.2909	+	6.65734i	−1.11522	+	0.405905i	−0.282311	+	0.959323i	$0.591101\pi$
$270$		0			0
$271$	0.0552285	−	0.313217i	0.00335489	−	0.0190266i	−0.983084	−	0.183153i	$-0.941370\pi$
$271$	0.0552285	−	0.313217i	0.00335489	−	0.0190266i	0.986439	+	0.164127i	$0.0524806\pi$
$272$		0			0
$273$	6.03527	+	1.55061i	0.365271	+	0.0938470i
$274$		0			0
$275$	−7.44980	−	8.87833i	−0.449240	−	0.535383i
$276$		0			0
$277$	10.9678	−	18.9968i	0.658993	−	1.14141i	−0.321884	−	0.946779i	$-0.604316\pi$
$277$	10.9678	−	18.9968i	0.658993	−	1.14141i	0.980877	−	0.194630i	$-0.0623506\pi$
$278$		0			0
$279$	29.4492	+	10.0357i	1.76308	+	0.600820i
$280$		0			0
$281$	−2.62001	−	14.8588i	−0.156297	−	0.886403i	−0.957591	−	0.288132i	$-0.906966\pi$
$281$	−2.62001	−	14.8588i	−0.156297	−	0.886403i	0.801294	−	0.598271i	$-0.204145\pi$
$282$		0			0
$283$	5.08697	+	4.26848i	0.302389	+	0.253735i	0.781338	−	0.624108i	$-0.214538\pi$
$283$	5.08697	+	4.26848i	0.302389	+	0.253735i	−0.478949	+	0.877843i	$0.658982\pi$
$284$		0			0
$285$	1.76562	−	0.961763i	0.104586	−	0.0569699i
$286$		0			0
$287$	−10.2751	−	8.62187i	−0.606523	−	0.508933i
$288$		0			0
$289$	2.81235	+	15.9496i	0.165433	+	0.938215i
$290$		0			0
$291$	−9.44048	+	4.52129i	−0.553411	+	0.265043i
$292$		0			0
$293$	14.2028	−	24.5999i	0.829735	−	1.43714i	−0.0685112	−	0.997650i	$-0.521825\pi$
$293$	14.2028	−	24.5999i	0.829735	−	1.43714i	0.898246	−	0.439493i	$-0.144842\pi$
$294$		0			0
$295$	−2.18572	−	2.60484i	−0.127258	−	0.151660i
$296$		0			0
$297$	2.79557	−	11.8937i	0.162215	−	0.690141i
$298$		0			0
$299$	2.90487	−	16.4743i	0.167993	−	0.952734i
$300$		0			0
$301$	−5.45804	+	1.98656i	−0.314596	+	0.114504i
$302$		0			0
$303$	12.5647	−	12.8266i	0.721826	−	0.736872i
$304$		0			0
$305$		−	0.235625i		−	0.0134918i
$306$		0			0
$307$	−1.49097	−	4.09641i	−0.0850942	−	0.233794i	0.889846	−	0.456261i	$-0.150812\pi$
$307$	−1.49097	−	4.09641i	−0.0850942	−	0.233794i	−0.974940	+	0.222466i	$0.928589\pi$
$308$		0			0
$309$	−14.8983	−	20.8167i	−0.847537	−	1.18422i
$310$		0			0
$311$	4.11082	−	2.37338i	0.233103	−	0.134582i	−0.378900	−	0.925438i	$-0.623697\pi$
$311$	4.11082	−	2.37338i	0.233103	−	0.134582i	0.612003	+	0.790856i	$0.290364\pi$
$312$		0			0
$313$	14.5023	−	12.1689i	0.819718	−	0.687825i	−0.133188	−	0.991091i	$-0.542521\pi$
$313$	14.5023	−	12.1689i	0.819718	−	0.687825i	0.952906	+	0.303265i	$0.0980769\pi$
$314$		0			0
$315$	0.465711	−	0.846492i	0.0262398	−	0.0476944i
$316$		0			0
$317$	29.4488	+	10.7185i	1.65401	+	0.602010i	0.989404	−	0.145186i	$-0.0463782\pi$
$317$	29.4488	+	10.7185i	1.65401	+	0.602010i	0.664604	+	0.747196i	$0.268600\pi$
$318$		0			0
$319$	−5.81850	+	1.02596i	−0.325773	+	0.0574426i
$320$		0			0
$321$	2.72843	+	27.8719i	0.152286	+	1.55566i
$322$		0			0
$323$	−1.52662	−	3.59877i	−0.0849432	−	0.200241i
$324$		0			0
$325$	−9.42565	+	11.2331i	−0.522841	+	0.623098i
$326$		0			0
$327$	−26.1005	−	17.8775i	−1.44336	−	0.988626i
$328$		0			0
$329$	0.800083	−	2.19821i	0.0441100	−	0.121191i
$330$		0			0
$331$	3.20610	+	1.85104i	0.176223	+	0.101742i	0.585517	−	0.810660i	$-0.300892\pi$
$331$	3.20610	+	1.85104i	0.176223	+	0.101742i	−0.409294	+	0.912403i	$0.634225\pi$
$332$		0			0
$333$	8.93925	−	7.82075i	0.489868	−	0.428574i
$334$		0			0
$335$	−0.681242	−	1.17995i	−0.0372202	−	0.0644673i
$336$		0			0
$337$	−19.7344	−	3.47971i	−1.07500	−	0.189552i	−0.391997	−	0.919967i	$-0.628216\pi$
$337$	−19.7344	−	3.47971i	−1.07500	−	0.189552i	−0.683004	+	0.730415i	$0.739327\pi$
$338$		0			0
$339$	3.78568	+	1.71798i	0.205610	+	0.0933079i
$340$		0			0
$341$	24.3849			1.32051
$342$		0			0
$343$	−15.1618			−0.818662
$344$		0			0
$345$	−2.36188	−	1.07184i	−0.127159	−	0.0577062i
$346$		0			0
$347$	0.281016	+	0.0495507i	0.0150857	+	0.00266002i	0.181186	−	0.983449i	$-0.442006\pi$
$347$	0.281016	+	0.0495507i	0.0150857	+	0.00266002i	−0.166100	+	0.986109i	$0.553118\pi$
$348$		0			0
$349$	6.98873	+	12.1048i	0.374098	+	0.647957i	0.990192	−	0.139716i	$-0.0446190\pi$
$349$	6.98873	+	12.1048i	0.374098	+	0.647957i	−0.616093	+	0.787673i	$0.711286\pi$
$350$		0			0
$351$	−15.4337	−	0.870200i	−0.823791	−	0.0464479i
$352$		0			0
$353$	17.7647	+	10.2564i	0.945519	+	0.545895i	0.891686	−	0.452654i	$-0.149523\pi$
$353$	17.7647	+	10.2564i	0.945519	+	0.545895i	0.0538327	+	0.998550i	$0.482856\pi$
$354$		0			0
$355$	−0.863726	+	2.37307i	−0.0458418	+	0.125949i
$356$		0			0
$357$	−1.54980	−	1.06153i	−0.0820241	−	0.0561820i
$358$		0			0
$359$	−17.9876	+	21.4368i	−0.949348	+	1.13139i	0.0418658	+	0.999123i	$0.486670\pi$
$359$	−17.9876	+	21.4368i	−0.949348	+	1.13139i	−0.991214	+	0.132266i	$0.957775\pi$
$360$		0			0
$361$	−11.1609	−	15.3764i	−0.587415	−	0.809286i
$362$		0			0
$363$	0.923266	+	9.43150i	0.0484589	+	0.495025i
$364$		0			0
$365$	0.0895476	−	0.0157897i	0.00468713	−	0.000826468i
$366$		0			0
$367$	−1.43051	−	0.520662i	−0.0746719	−	0.0271783i	0.304414	−	0.952540i	$-0.401539\pi$
$367$	−1.43051	−	0.520662i	−0.0746719	−	0.0271783i	−0.379086	+	0.925361i	$0.623762\pi$
$368$		0			0
$369$	29.1540	+	16.0395i	1.51770	+	0.834983i
$370$		0			0
$371$	−5.32599	+	4.46904i	−0.276512	+	0.232021i
$372$		0			0
$373$	4.13495	−	2.38731i	0.214100	−	0.123610i	−0.389116	−	0.921189i	$-0.627219\pi$
$373$	4.13495	−	2.38731i	0.214100	−	0.123610i	0.603215	+	0.797578i	$0.293886\pi$
$374$		0			0
$375$	2.66545	+	3.72431i	0.137643	+	0.192322i
$376$		0			0
$377$	2.55669	+	7.02444i	0.131676	+	0.361777i
$378$		0			0
$379$			13.4129i			0.688972i	0.938791	+	0.344486i	$0.111947\pi$
$379$			13.4129i			0.688972i	−0.938791	+	0.344486i	$0.888053\pi$
$380$		0			0
$381$	−7.17292	+	7.32244i	−0.367480	+	0.375140i
$382$		0			0
$383$	30.5956	−	11.1359i	1.56336	−	0.569017i	0.591857	−	0.806043i	$-0.298395\pi$
$383$	30.5956	−	11.1359i	1.56336	−	0.569017i	0.971503	+	0.237026i	$0.0761727\pi$
$384$		0			0
$385$	0.131493	−	0.745733i	0.00670150	−	0.0380061i
$386$		0			0
$387$	12.3273	−	7.46036i	0.626631	−	0.379231i
$388$		0			0
$389$	−8.33624	−	9.93474i	−0.422664	−	0.503711i	0.512127	−	0.858910i	$-0.328858\pi$
$389$	−8.33624	−	9.93474i	−0.422664	−	0.503711i	−0.934791	+	0.355199i	$0.884413\pi$
$390$		0			0
$391$	−2.52149	+	4.36735i	−0.127517	+	0.220866i
$392$		0			0
$393$	26.9952	−	12.9287i	1.36173	−	0.652166i
$394$		0			0
$395$	−0.316270	−	1.79365i	−0.0159132	−	0.0902485i
$396$		0			0
$397$	18.9635	+	15.9123i	0.951752	+	0.798615i	0.979592	−	0.200997i	$-0.0644183\pi$
$397$	18.9635	+	15.9123i	0.951752	+	0.798615i	−0.0278396	+	0.999612i	$0.508863\pi$
$398$		0			0
$399$	−8.49935	−	3.33465i	−0.425500	−	0.166941i
$400$		0			0
$401$	−4.89417	−	4.10670i	−0.244403	−	0.205079i	0.512354	−	0.858774i	$-0.328773\pi$
$401$	−4.89417	−	4.10670i	−0.244403	−	0.205079i	−0.756758	+	0.653695i	$0.773218\pi$
$402$		0			0
$403$	−5.35744	−	30.3836i	−0.266873	−	1.51351i
$404$		0			0
$405$	−0.726149	+	2.28411i	−0.0360826	+	0.113499i
$406$		0			0
$407$	4.65462	−	8.06204i	0.230721	−	0.399620i
$408$		0			0
$409$	−18.5835	−	22.1469i	−0.918894	−	1.09510i	−0.995185	−	0.0980100i	$-0.968752\pi$
$409$	−18.5835	−	22.1469i	−0.918894	−	1.09510i	0.0762911	−	0.997086i	$-0.475692\pi$
$410$		0			0
$411$	30.6876	+	7.88439i	1.51371	+	0.388908i
$412$		0			0
$413$	−2.68135	+	15.2067i	−0.131941	+	0.748273i
$414$		0			0
$415$	3.53224	−	1.28563i	0.173391	−	0.0631091i
$416$		0			0
$417$	−2.84486	−	2.78677i	−0.139313	−	0.136469i
$418$		0			0
$419$		−	19.2304i		−	0.939467i	−0.882808	−	0.469733i	$-0.844350\pi$
$419$		−	19.2304i		−	0.939467i	0.882808	−	0.469733i	$-0.155650\pi$
$420$		0			0
$421$	−11.8370	−	32.5219i	−0.576900	−	1.58502i	−0.793376	−	0.608732i	$-0.791678\pi$
$421$	−11.8370	−	32.5219i	−0.576900	−	1.58502i	0.216476	−	0.976288i	$-0.430544\pi$
$422$		0			0
$423$	−0.889613	+	5.73459i	−0.0432545	+	0.278825i
$424$		0			0
$425$	3.82830	−	2.21027i	0.185700	−	0.107214i
$426$		0			0
$427$	−0.819655	+	0.687772i	−0.0396659	+	0.0332836i
$428$		0			0
$429$	−11.6699	+	3.25632i	−0.563430	+	0.157217i
$430$		0			0
$431$	30.2120	+	10.9963i	1.45526	+	0.529671i	0.944055	−	0.329788i	$-0.106977\pi$
$431$	30.2120	+	10.9963i	1.45526	+	0.529671i	0.511205	+	0.859459i	$0.329199\pi$
$432$		0			0
$433$	−22.7212	+	4.00636i	−1.09191	+	0.192534i	−0.690477	−	0.723354i	$-0.742599\pi$
$433$	−22.7212	+	4.00636i	−1.09191	+	0.192534i	−0.401435	+	0.915888i	$0.631488\pi$
$434$		0			0
$435$	1.15351	−	0.112919i	0.0553064	−	0.00541404i
$436$		0			0
$437$	−7.17158	+	23.4380i	−0.343063	+	1.12119i
$438$		0			0
$439$	−7.57338	+	9.02561i	−0.361458	+	0.430769i	−0.915871	−	0.401473i	$-0.868498\pi$
$439$	−7.57338	+	9.02561i	−0.361458	+	0.430769i	0.554413	+	0.832242i	$0.312943\pi$
$440$		0			0
$441$	16.2973	−	3.22162i	0.776063	−	0.153410i
$442$		0			0
$443$	−7.28357	+	20.0114i	−0.346053	+	0.950772i	0.637548	+	0.770411i	$0.279949\pi$
$443$	−7.28357	+	20.0114i	−0.346053	+	0.950772i	−0.983600	+	0.180361i	$0.942273\pi$
$444$		0			0
$445$	2.83668	+	1.63776i	0.134471	+	0.0776371i
$446$		0			0
$447$	1.04279	−	13.5244i	0.0493224	−	0.639683i
$448$		0			0
$449$	−5.96300	−	10.3282i	−0.281411	−	0.487419i	0.690321	−	0.723503i	$-0.257469\pi$
$449$	−5.96300	−	10.3282i	−0.281411	−	0.487419i	−0.971733	+	0.236084i	$0.924136\pi$
$450$		0			0
$451$	25.6837	+	4.52874i	1.20940	+	0.213250i
$452$		0			0
$453$	−7.96957	+	17.5615i	−0.374443	+	0.825110i
$454$		0			0
$455$	−0.958074			−0.0449152
$456$		0			0
$457$	−19.1338			−0.895044			−0.447522	−	0.894273i	$-0.647693\pi$
$457$	−19.1338			−0.895044			−0.447522	+	0.894273i	$0.647693\pi$
$458$		0			0
$459$	4.28236	+	1.83782i	0.199883	+	0.0857820i
$460$		0			0
$461$	−29.6765	−	5.23277i	−1.38217	−	0.243715i	−0.567376	−	0.823459i	$-0.692041\pi$
$461$	−29.6765	−	5.23277i	−1.38217	−	0.243715i	−0.814798	+	0.579744i	$0.803152\pi$
$462$		0			0
$463$	−12.7896	−	22.1523i	−0.594385	−	1.02950i	−0.993633	−	0.112662i	$-0.964062\pi$
$463$	−12.7896	−	22.1523i	−0.594385	−	1.02950i	0.399248	−	0.916843i	$-0.369271\pi$
$464$		0			0
$465$	−4.76942	−	0.367743i	−0.221176	−	0.0170537i
$466$		0			0
$467$	24.6450	+	14.2288i	1.14044	+	0.658431i	0.946539	−	0.322591i	$-0.104554\pi$
$467$	24.6450	+	14.2288i	1.14044	+	0.658431i	0.193898	+	0.981022i	$0.437887\pi$
$468$		0			0
$469$	−2.11611	+	5.81397i	−0.0977131	+	0.268464i
$470$		0			0
$471$	20.7717	−	30.3261i	0.957112	−	1.39735i
$472$		0			0
$473$	7.25924	−	8.65122i	0.333780	−	0.397784i
$474$		0			0
$475$	15.7168	−	14.6494i	0.721134	−	0.672160i
$476$		0			0
$477$	10.8117	−	13.4383i	0.495032	−	0.615298i
$478$		0			0
$479$	−12.1691	+	2.14575i	−0.556022	+	0.0980417i	−0.444596	−	0.895731i	$-0.646653\pi$
$479$	−12.1691	+	2.14575i	−0.556022	+	0.0980417i	−0.111426	+	0.993773i	$0.535542\pi$
$480$		0			0
$481$	−11.0679	−	4.02840i	−0.504655	−	0.183679i
$482$		0			0
$483$	3.16559	+	11.3448i	0.144039	+	0.516205i
$484$		0			0
$485$	1.23285	−	1.03449i	0.0559810	−	0.0469736i
$486$		0			0
$487$	−24.3442	+	14.0551i	−1.10314	+	0.636899i	−0.937044	−	0.349210i	$-0.886450\pi$
$487$	−24.3442	+	14.0551i	−1.10314	+	0.636899i	−0.166097	+	0.986109i	$0.553117\pi$
$488$		0			0
$489$	4.90326	−	3.50922i	0.221733	−	0.158693i
$490$		0			0
$491$	1.17147	+	3.21859i	0.0528678	+	0.145253i	0.963316	−	0.268371i	$-0.0864852\pi$
$491$	1.17147	+	3.21859i	0.0528678	+	0.145253i	−0.910448	+	0.413624i	$0.864263\pi$
$492$		0			0
$493$		−	2.25350i		−	0.101493i
$494$		0			0
$495$	0.0387486	+	1.87812i	0.00174162	+	0.0844151i
$496$		0			0
$497$	10.7762	−	3.92222i	0.483379	−	0.175936i
$498$		0			0
$499$	−6.64566	+	37.6894i	−0.297500	+	1.68721i	0.359362	+	0.933198i	$0.382994\pi$
$499$	−6.64566	+	37.6894i	−0.297500	+	1.68721i	−0.656862	+	0.754010i	$0.728117\pi$
$500$		0			0
$501$	8.85284	−	34.4570i	0.395516	−	1.53942i
$502$		0			0
$503$	10.1578	+	12.1056i	0.452916	+	0.539764i	0.943387	−	0.331693i	$-0.107620\pi$
$503$	10.1578	+	12.1056i	0.452916	+	0.539764i	−0.490472	+	0.871457i	$0.663175\pi$
$504$		0			0
$505$	−1.38034	+	2.39082i	−0.0614244	+	0.106390i
$506$		0			0
$507$	−3.10462	−	6.48246i	−0.137881	−	0.287896i
$508$		0			0
$509$	1.72136	+	9.76234i	0.0762981	+	0.432708i	0.998897	+	0.0469483i	$0.0149496\pi$
$509$	1.72136	+	9.76234i	0.0762981	+	0.432708i	−0.922599	+	0.385760i	$0.873939\pi$
$510$		0			0
$511$	−0.316310	−	0.265415i	−0.0139927	−	0.0117413i
$512$		0			0
$513$	22.2887	+	4.02652i	0.984071	+	0.177775i
$514$		0			0
$515$	3.01505	+	2.52993i	0.132859	+	0.111482i
$516$		0			0
$517$	0.789817	+	4.47928i	0.0347361	+	0.196998i
$518$		0			0
$519$	6.23433	+	13.0173i	0.273657	+	0.571397i
$520$		0			0
$521$	−6.93036	+	12.0037i	−0.303625	+	0.525894i	−0.976954	−	0.213449i	$-0.931530\pi$
$521$	−6.93036	+	12.0037i	−0.303625	+	0.525894i	0.673329	+	0.739343i	$0.264864\pi$
$522$		0			0
$523$	−24.0581	−	28.6713i	−1.05199	−	1.25371i	−0.966309	−	0.257386i	$-0.917139\pi$
$523$	−24.0581	−	28.6713i	−1.05199	−	1.25371i	−0.0856778	−	0.996323i	$-0.527306\pi$
$524$		0			0
$525$	2.56915	−	9.99964i	0.112127	−	0.436420i
$526$		0			0
$527$	−1.61506	+	9.15947i	−0.0703532	+	0.398993i
$528$		0			0
$529$	8.09973	−	2.94806i	0.352162	−	0.128177i
$530$		0			0
$531$	−0.790147	−	38.2978i	−0.0342895	−	1.66198i
$532$		0			0
$533$		−	32.9970i		−	1.42926i
$534$		0			0
$535$	−1.47269	−	4.04618i	−0.0636699	−	0.174932i
$536$		0			0
$537$	12.7125	−	9.09820i	0.548584	−	0.392616i
$538$		0			0
$539$	11.2761	−	6.51028i	0.485698	−	0.280418i
$540$		0			0
$541$	6.17119	−	5.17824i	0.265320	−	0.222630i	−0.500416	−	0.865785i	$-0.666819\pi$
$541$	6.17119	−	5.17824i	0.265320	−	0.222630i	0.765736	+	0.643155i	$0.222375\pi$
$542$		0			0
$543$	−4.27996	−	15.3384i	−0.183671	−	0.658236i
$544$		0			0
$545$	4.57078	+	1.66363i	0.195791	+	0.0712620i
$546$		0			0
$547$	−25.2004	+	4.44352i	−1.07749	+	0.189991i	−0.684106	−	0.729382i	$-0.739808\pi$
$547$	−25.2004	+	4.44352i	−1.07749	+	0.189991i	−0.393386	+	0.919373i	$0.628697\pi$
$548$		0			0
$549$	1.66388	−	2.06812i	0.0710128	−	0.0882652i
$550$		0			0
$551$	−2.46140	−	10.6726i	−0.104859	−	0.454670i
$552$		0			0
$553$	−5.31631	+	6.33574i	−0.226073	+	0.269423i
$554$		0			0
$555$	−1.03197	+	1.50665i	−0.0438049	+	0.0639538i
$556$		0			0
$557$	4.99606	−	13.7266i	0.211690	−	0.581613i	−0.787718	−	0.616037i	$-0.788737\pi$
$557$	4.99606	−	13.7266i	0.211690	−	0.581613i	0.999407	+	0.0344238i	$0.0109596\pi$
$558$		0			0
$559$	−12.3743	−	7.14431i	−0.523377	−	0.302172i
$560$		0			0
$561$	3.64162	+	0.280785i	0.153749	+	0.0118547i
$562$		0			0
$563$	12.5968	+	21.8184i	0.530893	+	0.919534i	0.999350	+	0.0360479i	$0.0114769\pi$
$563$	12.5968	+	21.8184i	0.530893	+	0.919534i	−0.468457	+	0.883486i	$0.655190\pi$
$564$		0			0
$565$	−0.629478	−	0.110994i	−0.0264824	−	0.00466955i
$566$		0			0
$567$	10.0652	−	4.14115i	0.422699	−	0.173912i
$568$		0			0
$569$	42.1013			1.76498			0.882490	−	0.470332i	$-0.155866\pi$
$569$	42.1013			1.76498			0.882490	+	0.470332i	$0.155866\pi$
$570$		0			0
$571$	12.9487			0.541887			0.270944	−	0.962595i	$-0.412664\pi$
$571$	12.9487			0.541887			0.270944	+	0.962595i	$0.412664\pi$
$572$		0			0
$573$	5.24837	−	11.5651i	0.219254	−	0.483140i
$574$		0			0
$575$	−27.2958	−	4.81298i	−1.13831	−	0.200715i
$576$		0			0
$577$	6.43762	+	11.1503i	0.268002	+	0.464192i	0.968346	−	0.249613i	$-0.0803034\pi$
$577$	6.43762	+	11.1503i	0.268002	+	0.464192i	−0.700344	+	0.713805i	$0.746970\pi$
$578$		0			0
$579$	0.238697	−	3.09576i	0.00991990	−	0.128656i
$580$		0			0
$581$	−14.7826	−	8.53474i	−0.613286	−	0.354081i
$582$		0			0
$583$	4.62350	−	12.7030i	0.191486	−	0.526103i
$584$		0			0
$585$	2.33162	−	0.460910i	0.0964007	−	0.0190563i
$586$		0			0
$587$	−11.6998	+	13.9432i	−0.482900	+	0.575498i	−0.951397	−	0.307967i	$-0.900351\pi$
$587$	−11.6998	+	13.9432i	−0.482900	+	0.575498i	0.468497	+	0.883465i	$0.344796\pi$
$588$		0			0
$589$	2.35551	+	45.1435i	0.0970573	+	1.86011i
$590$		0			0
$591$	−13.6402	+	1.33527i	−0.561084	+	0.0549255i
$592$		0			0
$593$	−6.08719	+	1.07334i	−0.249971	+	0.0440766i	−0.297230	−	0.954806i	$-0.596063\pi$
$593$	−6.08719	+	1.07334i	−0.249971	+	0.0440766i	0.0472585	+	0.998883i	$0.484952\pi$
$594$		0			0
$595$	0.271404	+	0.0987830i	0.0111265	+	0.00404971i
$596$		0			0
$597$	−17.4514	+	4.86955i	−0.714238	+	0.199298i
$598$		0			0
$599$	27.9659	−	23.4662i	1.14266	−	0.958803i	0.143135	−	0.989703i	$-0.454282\pi$
$599$	27.9659	−	23.4662i	1.14266	−	0.958803i	0.999522	+	0.0308999i	$0.00983730\pi$
$600$		0			0
$601$	2.01662	−	1.16430i	0.0822597	−	0.0474927i	−0.458306	−	0.888795i	$-0.651544\pi$
$601$	2.01662	−	1.16430i	0.0822597	−	0.0474927i	0.540566	+	0.841302i	$0.318210\pi$
$602$		0			0
$603$	2.35291	−	15.1672i	0.0958178	−	0.617657i
$604$		0			0
$605$	−0.498339	−	1.36918i	−0.0202604	−	0.0556649i
$606$		0			0
$607$			24.4621i			0.992887i	0.868069	+	0.496443i	$0.165361\pi$
$607$			24.4621i			0.992887i	−0.868069	+	0.496443i	$0.834639\pi$
$608$		0			0
$609$	−3.75981	−	3.68304i	−0.152355	−	0.149244i
$610$		0			0
$611$	5.40766	−	1.96823i	0.218770	−	0.0796259i
$612$		0			0
$613$	−6.30039	+	35.7313i	−0.254470	+	1.44317i	0.542958	+	0.839760i	$0.317304\pi$
$613$	−6.30039	+	35.7313i	−0.254470	+	1.44317i	−0.797428	+	0.603414i	$0.793807\pi$
$614$		0			0
$615$	−4.95517	−	1.27310i	−0.199812	−	0.0513365i
$616$		0			0
$617$	−10.3830	−	12.3740i	−0.418006	−	0.498160i	0.515416	−	0.856940i	$-0.327637\pi$
$617$	−10.3830	−	12.3740i	−0.418006	−	0.498160i	−0.933422	+	0.358780i	$0.883193\pi$
$618$		0			0
$619$	15.2492	−	26.4123i	0.612916	−	1.06160i	−0.377831	−	0.925875i	$-0.623330\pi$
$619$	15.2492	−	26.4123i	0.612916	−	1.06160i	0.990746	−	0.135726i	$-0.0433368\pi$
$620$		0			0
$621$	−13.1617	−	26.0864i	−0.528160	−	1.04681i
$622$		0			0
$623$	−2.58289	−	14.6483i	−0.103481	−	0.586871i
$624$		0			0
$625$	18.3401	+	15.3891i	0.733602	+	0.615565i
$626$		0			0
$627$	17.5535	−	2.64778i	0.701019	−	0.105742i
$628$		0			0
$629$	2.71998	+	2.28234i	0.108453	+	0.0910028i
$630$		0			0
$631$	5.03370	+	28.5475i	0.200388	+	1.13646i	0.904533	+	0.426403i	$0.140219\pi$
$631$	5.03370	+	28.5475i	0.200388	+	1.13646i	−0.704145	+	0.710056i	$0.748670\pi$
$632$		0			0
$633$	21.7033	−	10.3943i	0.862629	−	0.413135i
$634$		0			0
$635$	0.788005	−	1.36486i	0.0312710	−	0.0541630i
$636$		0			0
$637$	−10.5892	−	12.6198i	−0.419561	−	0.500013i
$638$		0			0
$639$	−24.3387	+	14.7296i	−0.962824	+	0.582692i
$640$		0			0
$641$	−4.38869	+	24.8895i	−0.173343	+	0.983076i	0.766696	+	0.642010i	$0.221899\pi$
$641$	−4.38869	+	24.8895i	−0.173343	+	0.983076i	−0.940039	+	0.341066i	$0.889212\pi$
$642$		0			0
$643$	−11.3227	+	4.12111i	−0.446522	+	0.162521i	−0.555488	−	0.831525i	$-0.687468\pi$
$643$	−11.3227	+	4.12111i	−0.446522	+	0.162521i	0.108966	+	0.994046i	$0.465246\pi$
$644$		0			0
$645$	−1.55029	+	1.58261i	−0.0610428	+	0.0623152i
$646$		0			0
$647$		−	27.8093i		−	1.09330i	−0.837362	−	0.546649i	$-0.815903\pi$
$647$		−	27.8093i		−	1.09330i	0.837362	−	0.546649i	$-0.184097\pi$
$648$		0			0
$649$	−10.2685	−	28.2126i	−0.403075	−	1.10744i
$650$		0			0
$651$	12.6423	+	17.6645i	0.495492	+	0.692327i
$652$		0			0
$653$	−2.53710	+	1.46480i	−0.0992846	+	0.0573220i	−0.548820	−	0.835940i	$-0.684923\pi$
$653$	−2.53710	+	1.46480i	−0.0992846	+	0.0573220i	0.449536	+	0.893262i	$0.351589\pi$
$654$		0			0
$655$	−3.52536	+	2.95812i	−0.137747	+	0.115583i
$656$		0			0
$657$	0.897474	+	0.493759i	0.0350138	+	0.0192634i
$658$		0			0
$659$	−25.4128	−	9.24952i	−0.989944	−	0.360310i	−0.204245	−	0.978920i	$-0.565474\pi$
$659$	−25.4128	−	9.24952i	−0.989944	−	0.360310i	−0.785699	+	0.618610i	$0.787696\pi$
$660$		0			0
$661$	13.9832	−	2.46561i	0.543883	−	0.0959013i	0.105045	−	0.994467i	$-0.466501\pi$
$661$	13.9832	−	2.46561i	0.543883	−	0.0959013i	0.438838	+	0.898566i	$0.355390\pi$
$662$		0			0
$663$	−0.450218	−	4.59915i	−0.0174850	−	0.178616i
$664$		0			0
$665$	1.39327	+	0.171396i	0.0540288	+	0.00664645i
$666$		0			0
$667$	−9.08225	+	10.8238i	−0.351666	+	0.419099i
$668$		0			0
$669$	−17.8062	−	12.1963i	−0.688428	−	0.471536i
$670$		0			0
$671$	0.711543	−	1.95495i	0.0274688	−	0.0754700i
$672$		0			0
$673$	−4.68491	−	2.70483i	−0.180590	−	0.104264i	0.406980	−	0.913437i	$-0.366582\pi$
$673$	−4.68491	−	2.70483i	−0.180590	−	0.104264i	−0.587570	+	0.809173i	$0.699915\pi$
$674$		0			0
$675$	−1.44181	+	25.5716i	−0.0554952	+	0.984253i
$676$		0			0
$677$	11.2154	+	19.4256i	0.431043	+	0.746588i	0.996963	−	0.0778720i	$-0.0248125\pi$
$677$	11.2154	+	19.4256i	0.431043	+	0.746588i	−0.565921	+	0.824460i	$0.691479\pi$
$678$		0			0
$679$	−7.19722	−	1.26906i	−0.276204	−	0.0487022i
$680$		0			0
$681$	−2.58585	−	1.17349i	−0.0990901	−	0.0449681i
$682$		0			0
$683$	5.63051			0.215446			0.107723	−	0.994181i	$-0.465644\pi$
$683$	5.63051			0.215446			0.107723	+	0.994181i	$0.465644\pi$
$684$		0			0
$685$	−4.87153			−0.186131
$686$		0			0
$687$	19.1708	+	8.69991i	0.731412	+	0.331922i
$688$		0			0
$689$	−16.8437	−	2.97000i	−0.641694	−	0.113148i
$690$		0			0
$691$	−8.10408	−	14.0367i	−0.308294	−	0.533980i	0.669696	−	0.742636i	$-0.266425\pi$
$691$	−8.10408	−	14.0367i	−0.308294	−	0.533980i	−0.977989	+	0.208655i	$0.933091\pi$
$692$		0			0
$693$	6.42019	−	5.61688i	0.243883	−	0.213368i
$694$		0			0
$695$	0.530267	+	0.306150i	0.0201142	+	0.0116129i
$696$		0			0
$697$	−3.40218	+	9.34740i	−0.128867	+	0.354058i
$698$		0			0
$699$	3.44240	+	2.35786i	0.130204	+	0.0891824i
$700$		0			0
$701$	−25.1621	+	29.9870i	−0.950360	+	1.13260i	0.0406990	+	0.999171i	$0.487042\pi$
$701$	−25.1621	+	29.9870i	−0.950360	+	1.13260i	−0.991059	+	0.133424i	$0.957403\pi$
$702$		0			0
$703$	15.3748	+	7.83829i	0.579872	+	0.295627i
$704$		0			0
$705$	−0.0869287	−	0.888009i	−0.00327392	−	0.0334443i
$706$		0			0
$707$	12.3459	−	2.17692i	0.464317	−	0.0818715i
$708$		0			0
$709$	−0.294067	−	0.107032i	−0.0110439	−	0.00401966i	0.336492	−	0.941686i	$-0.390759\pi$
$709$	−0.294067	−	0.107032i	−0.0110439	−	0.00401966i	−0.347536	+	0.937667i	$0.612982\pi$
$710$		0			0
$711$	9.89008	−	17.9766i	0.370907	−	0.674174i
$712$		0			0
$713$	44.6726	−	37.4847i	1.67300	−	1.40381i
$714$		0			0
$715$	1.61325	−	0.931412i	0.0603322	−	0.0348328i
$716$		0			0
$717$	19.2997	+	26.9665i	0.720760	+	1.00708i
$718$		0			0
$719$	−9.97683	−	27.4111i	−0.372073	−	1.02226i	−0.974559	−	0.224132i	$-0.928045\pi$
$719$	−9.97683	−	27.4111i	−0.372073	−	1.02226i	0.602486	−	0.798130i	$-0.294177\pi$
$720$		0			0
$721$		−	17.8730i		−	0.665624i
$722$		0			0
$723$	−5.08544	+	5.19144i	−0.189129	+	0.193072i
$724$		0			0
$725$	11.6386	−	4.23609i	0.432246	−	0.157325i
$726$		0			0
$727$	−1.39364	+	7.90374i	−0.0516873	+	0.293133i	−0.999684	−	0.0251476i	$-0.991994\pi$
$727$	−1.39364	+	7.90374i	−0.0516873	+	0.293133i	0.947996	+	0.318281i	$0.103106\pi$
$728$		0			0
$729$	−22.5030	+	14.9203i	−0.833444	+	0.552604i
$730$		0			0
$731$	2.76878	+	3.29971i	0.102407	+	0.122044i
$732$		0			0
$733$	−8.60205	+	14.8992i	−0.317724	+	0.550314i	−0.980013	−	0.198935i	$-0.936252\pi$
$733$	−8.60205	+	14.8992i	−0.317724	+	0.550314i	0.662289	+	0.749249i	$0.269585\pi$
$734$		0			0
$735$	−2.30367	+	1.10329i	−0.0849722	+	0.0406954i
$736$		0			0
$737$	−2.08896	−	11.8471i	−0.0769479	−	0.436393i
$738$		0			0
$739$	19.8776	+	16.6793i	0.731210	+	0.613558i	0.930461	−	0.366390i	$-0.119407\pi$
$739$	19.8776	+	16.6793i	0.731210	+	0.613558i	−0.199251	+	0.979948i	$0.563851\pi$
$740$		0			0
$741$	−7.15569	−	21.2899i	−0.262871	−	0.782105i
$742$		0			0
$743$	−35.8677	−	30.0966i	−1.31586	−	1.10414i	−0.987166	−	0.159700i	$-0.948947\pi$
$743$	−35.8677	−	30.0966i	−1.31586	−	1.10414i	−0.328693	−	0.944437i	$-0.606608\pi$
$744$		0			0
$745$	0.362158	+	2.05390i	0.0132684	+	0.0752491i
$746$		0			0
$747$	40.0817	+	13.6590i	1.46651	+	0.499757i
$748$		0			0
$749$	−9.77655	+	16.9335i	−0.357227	+	0.618736i
$750$		0			0
$751$	1.93570	+	2.30687i	0.0706346	+	0.0841791i	0.800205	−	0.599727i	$-0.204724\pi$
$751$	1.93570	+	2.30687i	0.0706346	+	0.0841791i	−0.729570	+	0.683906i	$0.760280\pi$
$752$		0			0
$753$	−7.07097	−	1.81670i	−0.257680	−	0.0662044i
$754$		0			0
$755$	0.514892	−	2.92010i	0.0187389	−	0.106273i
$756$		0			0
$757$	6.18347	−	2.25060i	0.224742	−	0.0817994i	−0.227195	−	0.973849i	$-0.572955\pi$
$757$	6.18347	−	2.25060i	0.224742	−	0.0817994i	0.451937	+	0.892050i	$0.350733\pi$
$758$		0			0
$759$	−16.3594	−	16.0254i	−0.593810	−	0.581685i
$760$		0			0
$761$			12.0756i			0.437741i	0.975754	+	0.218870i	$0.0702372\pi$
$761$			12.0756i			0.437741i	−0.975754	+	0.218870i	$0.929763\pi$
$762$		0			0
$763$	−7.55461	−	20.7561i	−0.273495	−	0.751422i
$764$		0			0
$765$	−0.708026	−	0.109837i	−0.0255987	−	0.00397116i
$766$		0			0
$767$	−32.8968	+	18.9930i	−1.18784	+	0.685797i
$768$		0			0
$769$	−28.1846	+	23.6497i	−1.01636	+	0.852830i	−0.989166	−	0.146800i	$-0.953103\pi$
$769$	−28.1846	+	23.6497i	−1.01636	+	0.852830i	−0.0271972	+	0.999630i	$0.508658\pi$
$770$		0			0
$771$	29.6513	−	8.27376i	1.06787	−	0.297972i
$772$		0			0
$773$	−15.8791	−	5.77952i	−0.571132	−	0.207875i	0.0402788	−	0.999188i	$-0.487175\pi$
$773$	−15.8791	−	5.77952i	−0.571132	−	0.207875i	−0.611411	+	0.791314i	$0.709398\pi$
$774$		0			0
$775$	−50.3416	+	8.87657i	−1.80832	+	0.318856i
$776$		0			0
$777$	8.25336	−	0.807936i	0.296088	−	0.0289845i
$778$		0			0
$779$	−5.90304	+	47.9856i	−0.211498	+	1.71926i
$780$		0			0
$781$	−14.3325	+	17.0808i	−0.512856	+	0.611198i
$782$		0			0
$783$	10.9219	+	7.15448i	0.390317	+	0.255680i
$784$		0			0
$785$	−1.93296	+	5.31077i	−0.0689904	+	0.189550i
$786$		0			0
$787$	19.2256	+	11.0999i	0.685319	+	0.395669i	0.801856	−	0.597517i	$-0.203846\pi$
$787$	19.2256	+	11.0999i	0.685319	+	0.395669i	−0.116537	+	0.993186i	$0.537179\pi$
$788$		0			0
$789$	0.149170	−	1.93465i	0.00531059	−	0.0688754i
$790$		0			0
$791$	1.45129	+	2.51372i	0.0516021	+	0.0893774i
$792$		0			0
$793$	−2.59220	−	0.457074i	−0.0920516	−	0.0162312i
$794$		0			0
$795$	−1.09588	+	2.41484i	−0.0388667	+	0.0856454i
$796$		0			0
$797$	−34.5294			−1.22309			−0.611547	−	0.791208i	$-0.709453\pi$
$797$	−34.5294			−1.22309			−0.611547	+	0.791208i	$0.709453\pi$
$798$		0			0
$799$	−1.73482			−0.0613736
$800$		0			0
$801$	13.3329	+	34.4063i	0.471093	+	1.21569i
$802$		0			0
$803$	0.790647	+	0.139412i	0.0279013	+	0.00491976i
$804$		0			0
$805$	−0.905459	−	1.56830i	−0.0319132	−	0.0552753i
$806$		0			0
$807$	33.6142	+	2.59180i	1.18328	+	0.0912357i
$808$		0			0
$809$	19.0821	+	11.0171i	0.670892	+	0.387340i	0.796415	−	0.604751i	$-0.206727\pi$
$809$	19.0821	+	11.0171i	0.670892	+	0.387340i	−0.125523	+	0.992091i	$0.540061\pi$
$810$		0			0
$811$	3.43077	−	9.42596i	0.120471	−	0.330990i	−0.864769	−	0.502169i	$-0.832535\pi$
$811$	3.43077	−	9.42596i	0.120471	−	0.330990i	0.985240	+	0.171179i	$0.0547577\pi$
$812$		0			0
$813$	−0.311298	+	0.454486i	−0.0109177	+	0.0159395i
$814$		0			0
$815$	−0.595911	+	0.710179i	−0.0208738	+	0.0248765i
$816$		0			0
$817$	16.7172	+	12.6033i	0.584860	+	0.440933i
$818$		0			0
$819$	−8.40918	−	6.76552i	−0.293840	−	0.236406i
$820$		0			0
$821$	38.9746	−	6.87227i	1.36022	−	0.239844i	0.554523	−	0.832169i	$-0.312901\pi$
$821$	38.9746	−	6.87227i	1.36022	−	0.239844i	0.805699	+	0.592325i	$0.201790\pi$
$822$		0			0
$823$	−35.1506	−	12.7938i	−1.22527	−	0.445963i	−0.353297	−	0.935511i	$-0.614939\pi$
$823$	−35.1506	−	12.7938i	−1.22527	−	0.445963i	−0.871976	+	0.489548i	$0.837162\pi$
$824$		0			0
$825$	5.39530	+	19.3355i	0.187840	+	0.673177i
$826$		0			0
$827$	−12.2053	+	10.2415i	−0.424421	+	0.356132i	−0.829842	−	0.557998i	$-0.811570\pi$
$827$	−12.2053	+	10.2415i	−0.424421	+	0.356132i	0.405421	+	0.914130i	$0.367125\pi$
$828$		0			0
$829$	34.9707	−	20.1903i	1.21458	−	0.701239i	0.250828	−	0.968032i	$-0.419297\pi$
$829$	34.9707	−	20.1903i	1.21458	−	0.701239i	0.963754	+	0.266793i	$0.0859639\pi$
$830$		0			0
$831$	−30.8962	+	22.1121i	−1.07178	+	0.767061i
$832$		0			0
$833$	1.69856	+	4.66675i	0.0588515	+	0.161693i
$834$		0			0
$835$			5.46991i			0.189294i
$836$		0			0
$837$	−39.2651	−	36.9074i	−1.35720	−	1.27571i
$838$		0			0
$839$	−34.2630	+	12.4707i	−1.18289	+	0.430537i	−0.857222	−	0.514947i	$-0.827812\pi$
$839$	−34.2630	+	12.4707i	−1.18289	+	0.430537i	−0.325669	+	0.945484i	$0.605589\pi$
$840$		0			0
$841$	−3.93940	+	22.3415i	−0.135842	+	0.770396i
$842$		0			0
$843$	−6.50306	+	25.3112i	−0.223977	+	0.871764i
$844$		0			0
$845$	0.710347	+	0.846558i	0.0244367	+	0.0291225i
$846$		0			0
$847$	−3.30826	+	5.73007i	−0.113673	+	0.196888i
$848$		0			0
$849$	−4.96813	−	10.3735i	−0.170506	−	0.356017i
$850$		0			0
$851$	−3.86590	−	21.9246i	−0.132521	−	0.751566i
$852$		0			0
$853$	−1.13152	−	0.949455i	−0.0387424	−	0.0325087i	0.623211	−	0.782054i	$-0.285828\pi$
$853$	−1.13152	−	0.949455i	−0.0387424	−	0.0325087i	−0.661953	+	0.749545i	$0.730272\pi$
$854$		0			0
$855$	−3.47320	+	0.253156i	−0.118781	+	0.00865776i
$856$		0			0
$857$	−33.3088	−	27.9494i	−1.13781	−	0.954734i	−0.138443	−	0.990370i	$-0.544210\pi$
$857$	−33.3088	−	27.9494i	−1.13781	−	0.954734i	−0.999365	+	0.0356363i	$0.988654\pi$
$858$		0			0
$859$	3.97170	+	22.5246i	0.135513	+	0.768530i	0.974501	+	0.224381i	$0.0720361\pi$
$859$	3.97170	+	22.5246i	0.135513	+	0.768530i	−0.838989	+	0.544149i	$0.816853\pi$
$860$		0			0
$861$	10.0351	+	20.9534i	0.341995	+	0.714088i
$862$		0			0
$863$	−2.34962	+	4.06966i	−0.0799820	+	0.138533i	−0.903242	−	0.429132i	$-0.858820\pi$
$863$	−2.34962	+	4.06966i	−0.0799820	+	0.138533i	0.823260	+	0.567665i	$0.192153\pi$
$864$		0			0
$865$	−1.42644	−	1.69996i	−0.0485003	−	0.0578004i
$866$		0			0
$867$	6.98047	−	27.1694i	0.237069	−	0.922720i
$868$		0			0
$869$	2.79245	−	15.8368i	0.0947275	−	0.537227i
$870$		0			0
$871$	−14.3025	+	5.20569i	−0.484623	+	0.176388i
$872$		0			0
$873$	18.1261	−	0.373970i	0.613475	−	0.0126570i
$874$		0			0
$875$			3.19764i			0.108100i
$876$		0			0
$877$	5.78823	+	15.9030i	0.195455	+	0.537007i	0.998243	−	0.0592572i	$-0.0188732\pi$
$877$	5.78823	+	15.9030i	0.195455	+	0.537007i	−0.802788	+	0.596264i	$0.796651\pi$
$878$		0			0
$879$	−40.0090	+	28.6341i	−1.34947	+	0.965803i
$880$		0			0
$881$	−8.11257	+	4.68379i	−0.273319	+	0.157801i	−0.630395	−	0.776274i	$-0.717107\pi$
$881$	−8.11257	+	4.68379i	−0.273319	+	0.157801i	0.357076	+	0.934075i	$0.383774\pi$
$882$		0			0
$883$	9.97646	−	8.37124i	0.335735	−	0.281715i	−0.459297	−	0.888283i	$-0.651899\pi$
$883$	9.97646	−	8.37124i	0.335735	−	0.281715i	0.795032	+	0.606568i	$0.207454\pi$
$884$		0			0
$885$	1.58295	+	5.67293i	0.0532101	+	0.190693i
$886$		0			0
$887$	19.4826	+	7.09109i	0.654162	+	0.238095i	0.647714	−	0.761884i	$-0.275725\pi$
$887$	19.4826	+	7.09109i	0.654162	+	0.238095i	0.00644793	+	0.999979i	$0.497948\pi$
$888$		0			0
$889$	−7.04801	+	1.24275i	−0.236383	+	0.0416806i
$890$		0			0
$891$	−12.9224	+	16.7582i	−0.432916	+	0.561420i
$892$		0			0
$893$	−8.21616	+	1.89487i	−0.274943	+	0.0634094i
$894$		0			0
$895$	−1.54499	+	1.84125i	−0.0516433	+	0.0615461i
$896$		0			0
$897$	−16.3734	+	23.9047i	−0.546693	+	0.798155i
$898$		0			0
$899$	−8.91269	+	24.4874i	−0.297255	+	0.816701i
$900$		0			0
$901$	4.46527	+	2.57803i	0.148760	+	0.0858865i
$902$		0			0
$903$	10.0305	+	0.773398i	0.333795	+	0.0257371i
$904$		0			0
$905$	1.22421	+	2.12039i	0.0406940	+	0.0704840i
$906$		0			0
$907$	13.6673	+	2.40991i	0.453815	+	0.0800198i	0.395883	−	0.918301i	$-0.370438\pi$
$907$	13.6673	+	2.40991i	0.453815	+	0.0800198i	0.0579313	+	0.998321i	$0.481550\pi$
$908$		0			0
$909$	−28.9985	+	11.2373i	−0.961819	+	0.372716i
$910$		0			0
$911$	16.4560			0.545212			0.272606	−	0.962126i	$-0.412115\pi$
$911$	16.4560			0.545212			0.272606	+	0.962126i	$0.412115\pi$
$912$		0			0
$913$	33.1889			1.09839
$914$		0			0
$915$	−0.168652	+	0.371636i	−0.00557547	+	0.0122859i
$916$		0			0
$917$	20.5805	+	3.62890i	0.679629	+	0.119837i
$918$		0			0
$919$	26.4636	+	45.8364i	0.872955	+	1.51200i	0.858926	+	0.512100i	$0.171132\pi$
$919$	26.4636	+	45.8364i	0.872955	+	1.51200i	0.0140292	+	0.999902i	$0.495534\pi$
$920$		0			0
$921$	−0.580457	+	7.52819i	−0.0191267	+	0.248062i
$922$		0			0
$923$	24.4315	+	14.1056i	0.804174	+	0.464290i
$924$		0			0
$925$	−6.67453	+	18.3381i	−0.219457	+	0.602953i
$926$		0			0
$927$	8.59832	+	43.4966i	0.282406	+	1.42862i
$928$		0			0
$929$	−35.2607	+	42.0221i	−1.15687	+	1.37870i	−0.244337	+	0.969690i	$0.578570\pi$
$929$	−35.2607	+	42.0221i	−1.15687	+	1.37870i	−0.912530	+	0.409010i	$0.865874\pi$
$930$		0			0
$931$	13.1417	+	20.2466i	0.430702	+	0.663555i
$932$		0			0
$933$	−8.18253	+	0.801002i	−0.267884	+	0.0262236i
$934$		0			0
$935$	−0.553038	+	0.0975154i	−0.0180863	+	0.00318910i
$936$		0			0
$937$	−50.8597	−	18.5114i	−1.66151	−	0.604741i	−0.670914	−	0.741536i	$-0.734098\pi$
$937$	−50.8597	−	18.5114i	−1.66151	−	0.604741i	−0.990599	+	0.136794i	$0.956320\pi$
$938$		0			0
$939$	−31.5836	+	8.81294i	−1.03069	+	0.287600i
$940$		0			0
$941$	3.61129	−	3.03024i	0.117725	−	0.0987829i	−0.582025	−	0.813171i	$-0.697739\pi$
$941$	3.61129	−	3.03024i	0.117725	−	0.0987829i	0.699750	+	0.714388i	$0.253295\pi$
$942$		0			0
$943$	54.0137	−	31.1848i	1.75893	−	1.01552i
$944$		0			0
$945$	−1.34043	+	1.00178i	−0.0436041	+	0.0325879i
$946$		0			0
$947$	3.75659	+	10.3211i	0.122073	+	0.335392i	0.985645	−	0.168834i	$-0.0540002\pi$
$947$	3.75659	+	10.3211i	0.122073	+	0.335392i	−0.863572	+	0.504226i	$0.831778\pi$
$948$		0			0
$949$		−	1.01578i		−	0.0329735i
$950$		0			0
$951$	−38.7758	−	37.9840i	−1.25739	−	1.23172i
$952$		0			0
$953$	3.15832	−	1.14953i	0.102308	−	0.0372371i	−0.290359	−	0.956918i	$-0.593775\pi$
$953$	3.15832	−	1.14953i	0.102308	−	0.0372371i	0.392667	+	0.919681i	$0.371552\pi$
$954$		0			0
$955$	−0.339083	+	1.92303i	−0.0109725	+	0.0622279i
$956$		0			0
$957$	9.91150	+	2.54650i	0.320393	+	0.0823168i
$958$		0			0
$959$	14.2196	+	16.9463i	0.459176	+	0.547225i
$960$		0			0
$961$	38.2760	−	66.2960i	1.23471	−	2.13858i
$962$		0			0
$963$	15.6464	−	45.9135i	0.504198	−	1.47954i
$964$		0			0
$965$	0.0828985	+	0.470141i	0.00266860	+	0.0151344i
$966$		0			0
$967$	14.0085	+	11.7545i	0.450482	+	0.377999i	0.839615	−	0.543183i	$-0.182781\pi$
$967$	14.0085	+	11.7545i	0.450482	+	0.377999i	−0.389133	+	0.921182i	$0.627225\pi$
$968$		0			0
$969$	−0.168044	+	6.76882i	−0.00539835	+	0.217446i
$970$		0			0
$971$	24.2199	+	20.3229i	0.777254	+	0.652193i	0.942555	−	0.334050i	$-0.108415\pi$
$971$	24.2199	+	20.3229i	0.777254	+	0.652193i	−0.165302	+	0.986243i	$0.552860\pi$
$972$		0			0
$973$	−0.482826	−	2.73824i	−0.0154787	−	0.0877839i
$974$		0			0
$975$	22.9067	−	10.9706i	0.733603	−	0.351341i
$976$		0			0
$977$	−24.2192	+	41.9488i	−0.774839	+	1.34206i	0.160045	+	0.987110i	$0.448836\pi$
$977$	−24.2192	+	41.9488i	−0.774839	+	1.34206i	−0.934885	+	0.354952i	$0.884497\pi$
$978$		0			0
$979$	18.5898	+	22.1545i	0.594134	+	0.708061i
$980$		0			0
$981$	28.3707	+	46.8789i	0.905806	+	1.49673i
$982$		0			0
$983$	−4.70703	+	26.6949i	−0.150131	+	0.851435i	0.812972	+	0.582303i	$0.197848\pi$
$983$	−4.70703	+	26.6949i	−0.150131	+	0.851435i	−0.963103	+	0.269133i	$0.913263\pi$
$984$		0			0
$985$	1.98016	−	0.720719i	0.0630931	−	0.0229640i
$986$		0			0
$987$	−2.83533	+	2.89443i	−0.0902495	+	0.0921307i
$988$		0			0
$989$		−	27.0079i		−	0.858800i
$990$		0			0
$991$	−16.6261	−	45.6797i	−0.528144	−	1.45106i	−0.861253	−	0.508176i	$-0.830320\pi$
$991$	−16.6261	−	45.6797i	−0.528144	−	1.45106i	0.333109	−	0.942888i	$-0.391902\pi$
$992$		0			0
$993$	−3.73186	−	5.21435i	−0.118427	−	0.165472i
$994$		0			0
$995$	2.41248	−	1.39285i	0.0764808	−	0.0441562i
$996$		0			0
$997$	−7.46423	+	6.26323i	−0.236394	+	0.198358i	−0.753287	−	0.657692i	$-0.771533\pi$
$997$	−7.46423	+	6.26323i	−0.236394	+	0.198358i	0.516893	+	0.856050i	$0.327089\pi$
$998$		0			0
$999$	−19.6972	+	5.93676i	−0.623191	+	0.187831i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.cc.d.497.1		18
3.2	odd	2		912.2.cc.c.497.3		18
4.3	odd	2		114.2.l.a.41.3	✓	18
12.11	even	2		114.2.l.b.41.1	yes	18
19.13	odd	18		912.2.cc.c.545.3		18
57.32	even	18	inner	912.2.cc.d.545.1		18
76.51	even	18		114.2.l.b.89.1	yes	18
228.203	odd	18		114.2.l.a.89.3	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.41.3	✓	18	4.3	odd	2
114.2.l.a.89.3	yes	18	228.203	odd	18
114.2.l.b.41.1	yes	18	12.11	even	2
114.2.l.b.89.1	yes	18	76.51	even	18
912.2.cc.c.497.3		18	3.2	odd	2
912.2.cc.c.545.3		18	19.13	odd	18
912.2.cc.d.497.1		18	1.1	even	1	trivial
912.2.cc.d.545.1		18	57.32	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.cc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.57724 - 0.715766i) q^{3} +(0.262261 + 0.0462437i) q^{5} +(-0.604656 - 1.04730i) q^{7} +(1.97536 + 2.25787i) q^{9} +O(q^{10})\)	\(q+(-1.57724 - 0.715766i) q^{3} +(0.262261 + 0.0462437i) q^{5} +(-0.604656 - 1.04730i) q^{7} +(1.97536 + 2.25787i) q^{9} +(2.03630 + 1.17566i) q^{11} +(1.01749 - 2.79553i) q^{13} +(-0.380548 - 0.260655i) q^{15} +(-0.576470 + 0.687011i) q^{17} +(-1.97979 + 3.88335i) q^{19} +(0.204068 + 2.08463i) q^{21} +(5.53770 - 0.976446i) q^{23} +(-4.63182 - 1.68584i) q^{25} +(-1.49950 - 4.97509i) q^{27} +(-1.92487 + 1.61516i) q^{29} +(8.98131 - 5.18536i) q^{31} +(-2.37023 - 3.31181i) q^{33} +(-0.110147 - 0.302626i) q^{35} -3.95916i q^{37} +(-3.60577 + 3.68093i) q^{39} +(10.4227 - 3.79356i) q^{41} +(0.834031 - 4.73003i) q^{43} +(0.413647 + 0.683499i) q^{45} +(1.24341 + 1.48183i) q^{47} +(2.76878 - 4.79567i) q^{49} +(1.40097 - 0.670961i) q^{51} +(-0.998339 - 5.66186i) q^{53} +(0.479676 + 0.402496i) q^{55} +(5.90217 - 4.70791i) q^{57} +(-9.78136 - 8.20754i) q^{59} +(-0.153642 - 0.871345i) q^{61} +(1.17024 - 3.43401i) q^{63} +(0.396123 - 0.686106i) q^{65} +(-3.28864 - 3.91925i) q^{67} +(-9.43317 - 2.42361i) q^{69} +(-1.64669 + 9.33885i) q^{71} +(0.320853 - 0.116781i) q^{73} +(6.09881 + 5.97428i) q^{75} -2.84348i q^{77} +(-2.33914 - 6.42674i) q^{79} +(-1.19593 + 8.92019i) q^{81} +(12.2240 - 7.05752i) q^{83} +(-0.182956 + 0.153518i) q^{85} +(4.19206 - 1.16973i) q^{87} +(11.5580 + 4.20677i) q^{89} +(-3.54297 + 0.624722i) q^{91} +(-17.8772 + 1.75003i) q^{93} +(-0.698802 + 0.926900i) q^{95} +(3.88456 - 4.62944i) q^{97} +(1.36794 + 6.92004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q+O(q^{10}) \) 18 * q	\( 18 q - 12 q^{13} + 24 q^{15} - 6 q^{17} + 6 q^{19} - 18 q^{25} + 3 q^{27} + 6 q^{29} - 27 q^{33} - 24 q^{35} - 6 q^{39} - 3 q^{41} + 6 q^{43} + 54 q^{45} + 30 q^{47} + 21 q^{49} + 33 q^{51} + 60 q^{53} - 30 q^{55} + 12 q^{57} + 3 q^{59} + 54 q^{61} - 84 q^{63} - 24 q^{65} + 15 q^{67} + 24 q^{69} + 36 q^{71} - 42 q^{73} + 6 q^{79} + 36 q^{83} + 54 q^{87} + 60 q^{89} + 18 q^{91} - 84 q^{93} + 6 q^{95} + 9 q^{97} + 30 q^{99}+O(q^{100}) \) 18 * q - 12 * q^13 + 24 * q^15 - 6 * q^17 + 6 * q^19 - 18 * q^25 + 3 * q^27 + 6 * q^29 - 27 * q^33 - 24 * q^35 - 6 * q^39 - 3 * q^41 + 6 * q^43 + 54 * q^45 + 30 * q^47 + 21 * q^49 + 33 * q^51 + 60 * q^53 - 30 * q^55 + 12 * q^57 + 3 * q^59 + 54 * q^61 - 84 * q^63 - 24 * q^65 + 15 * q^67 + 24 * q^69 + 36 * q^71 - 42 * q^73 + 6 * q^79 + 36 * q^83 + 54 * q^87 + 60 * q^89 + 18 * q^91 - 84 * q^93 + 6 * q^95 + 9 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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