LMFDB - Embedded newform 912.2.cc.c.545.3

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			545.3
Root			$1.40849 + 1.00804i$ of defining polynomial
Character	$\chi$	$=$	912.545
Dual form			912.2.cc.c.497.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.748148 + 1.56214i) q^{3} +(-0.262261 + 0.0462437i) q^{5} +(-0.604656 + 1.04730i) q^{7} +(-1.88055 + 2.33742i) q^{9} +O(q^{10})$	\(q+(0.748148 + 1.56214i) q^{3} +(-0.262261 + 0.0462437i) q^{5} +(-0.604656 + 1.04730i) q^{7} +(-1.88055 + 2.33742i) q^{9} +(-2.03630 + 1.17566i) q^{11} +(1.01749 + 2.79553i) q^{13} +(-0.268449 - 0.375091i) q^{15} +(0.576470 + 0.687011i) q^{17} +(-1.97979 - 3.88335i) q^{19} +(-2.08839 - 0.161024i) q^{21} +(-5.53770 - 0.976446i) q^{23} +(-4.63182 + 1.68584i) q^{25} +(-5.05830 - 1.18894i) q^{27} +(1.92487 + 1.61516i) q^{29} +(8.98131 + 5.18536i) q^{31} +(-3.36000 - 2.30141i) q^{33} +(0.110147 - 0.302626i) q^{35} +3.95916i q^{37} +(-3.60577 + 3.68093i) q^{39} +(-10.4227 - 3.79356i) q^{41} +(0.834031 + 4.73003i) q^{43} +(0.385104 - 0.699978i) q^{45} +(-1.24341 + 1.48183i) q^{47} +(2.76878 + 4.79567i) q^{49} +(-0.641920 + 1.41451i) q^{51} +(0.998339 - 5.66186i) q^{53} +(0.479676 - 0.402496i) q^{55} +(4.58516 - 5.99803i) q^{57} +(9.78136 - 8.20754i) q^{59} +(-0.153642 + 0.871345i) q^{61} +(-1.31088 - 3.38283i) q^{63} +(-0.396123 - 0.686106i) q^{65} +(-3.28864 + 3.91925i) q^{67} +(-2.61768 - 9.38117i) q^{69} +(1.64669 + 9.33885i) q^{71} +(0.320853 + 0.116781i) q^{73} +(-6.09881 - 5.97428i) q^{75} -2.84348i q^{77} +(-2.33914 + 6.42674i) q^{79} +(-1.92708 - 8.79127i) q^{81} +(-12.2240 - 7.05752i) q^{83} +(-0.182956 - 0.153518i) q^{85} +(-1.08301 + 4.21529i) q^{87} +(-11.5580 + 4.20677i) q^{89} +(-3.54297 - 0.624722i) q^{91} +(-1.38090 + 17.9095i) q^{93} +(0.698802 + 0.926900i) q^{95} +(3.88456 + 4.62944i) q^{97} +(1.08135 - 6.97057i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{3} - 3 q^{9}+O(q^{10}) $ 18 * q - 3 * q^3 - 3 * q^9	$ 18 q - 3 q^{3} - 3 q^{9} - 12 q^{13} - 18 q^{15} + 6 q^{17} + 6 q^{19} - 18 q^{25} + 6 q^{27} - 6 q^{29} - 24 q^{33} + 24 q^{35} - 6 q^{39} + 3 q^{41} + 6 q^{43} - 54 q^{45} - 30 q^{47} + 21 q^{49} - 42 q^{51} - 60 q^{53} - 30 q^{55} + 12 q^{57} - 3 q^{59} + 54 q^{61} + 18 q^{63} + 24 q^{65} + 15 q^{67} + 30 q^{69} - 36 q^{71} - 42 q^{73} + 6 q^{79} - 3 q^{81} - 36 q^{83} - 60 q^{89} + 18 q^{91} - 66 q^{93} - 6 q^{95} + 9 q^{97} + 102 q^{99}+O(q^{100}) $ 18 * q - 3 * q^3 - 3 * q^9 - 12 * q^13 - 18 * q^15 + 6 * q^17 + 6 * q^19 - 18 * q^25 + 6 * q^27 - 6 * q^29 - 24 * q^33 + 24 * q^35 - 6 * q^39 + 3 * q^41 + 6 * q^43 - 54 * q^45 - 30 * q^47 + 21 * q^49 - 42 * q^51 - 60 * q^53 - 30 * q^55 + 12 * q^57 - 3 * q^59 + 54 * q^61 + 18 * q^63 + 24 * q^65 + 15 * q^67 + 30 * q^69 - 36 * q^71 - 42 * q^73 + 6 * q^79 - 3 * q^81 - 36 * q^83 - 60 * q^89 + 18 * q^91 - 66 * q^93 - 6 * q^95 + 9 * q^97 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$-1$	$1$

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
$3$	0.748148	+	1.56214i	0.431944	+	0.901901i
$3$	0.748148	+	1.56214i	0.431944	+	0.901901i
$4$		0			0
$5$	−0.262261	+	0.0462437i	−0.117287	+	0.0206808i	−0.231983	−	0.972720i	$-0.574522\pi$
$5$	−0.262261	+	0.0462437i	−0.117287	+	0.0206808i	0.114697	+	0.993401i	$0.463410\pi$
$6$		0			0
$7$	−0.604656	+	1.04730i	−0.228539	+	0.395840i	−0.957375	−	0.288847i	$-0.906728\pi$
$7$	−0.604656	+	1.04730i	−0.228539	+	0.395840i	0.728837	+	0.684688i	$0.240061\pi$
$8$		0			0
$9$	−1.88055	+	2.33742i	−0.626849	+	0.779140i
$10$		0			0
$11$	−2.03630	+	1.17566i	−0.613968	+	0.354474i	−0.774517	−	0.632553i	$-0.782007\pi$
$11$	−2.03630	+	1.17566i	−0.613968	+	0.354474i	0.160549	+	0.987028i	$0.448674\pi$
$12$		0			0
$13$	1.01749	+	2.79553i	0.282201	+	0.775340i	0.997099	+	0.0761119i	$0.0242506\pi$
$13$	1.01749	+	2.79553i	0.282201	+	0.775340i	−0.714899	+	0.699228i	$0.753527\pi$
$14$		0			0
$15$	−0.268449	−	0.375091i	−0.0693133	−	0.0968480i
$16$		0			0
$17$	0.576470	+	0.687011i	0.139815	+	0.166625i	0.831408	−	0.555663i	$-0.187535\pi$
$17$	0.576470	+	0.687011i	0.139815	+	0.166625i	−0.691593	+	0.722287i	$0.743091\pi$
$18$		0			0
$19$	−1.97979	−	3.88335i	−0.454194	−	0.890903i
$19$	−1.97979	−	3.88335i	−0.454194	−	0.890903i
$20$		0			0
$21$	−2.08839	−	0.161024i	−0.455724	−	0.0351383i
$22$		0			0
$23$	−5.53770	−	0.976446i	−1.15469	−	0.203603i	−0.436668	−	0.899623i	$-0.643841\pi$
$23$	−5.53770	−	0.976446i	−1.15469	−	0.203603i	−0.718022	+	0.696020i	$0.754952\pi$
$24$		0			0
$25$	−4.63182	+	1.68584i	−0.926364	+	0.337169i
$26$		0			0
$27$	−5.05830	−	1.18894i	−0.973471	−	0.228811i
$28$		0			0
$29$	1.92487	+	1.61516i	0.357440	+	0.299928i	0.803769	−	0.594941i	$-0.202825\pi$
$29$	1.92487	+	1.61516i	0.357440	+	0.299928i	−0.446329	+	0.894869i	$0.647269\pi$
$30$		0			0
$31$	8.98131	+	5.18536i	1.61309	+	0.931319i	0.988648	+	0.150249i	$0.0480075\pi$
$31$	8.98131	+	5.18536i	1.61309	+	0.931319i	0.624443	+	0.781070i	$0.285326\pi$
$32$		0			0
$33$	−3.36000	−	2.30141i	−0.584900	−	0.400625i
$34$		0			0
$35$	0.110147	−	0.302626i	0.0186182	−	0.0511532i
$36$		0			0
$37$			3.95916i			0.650882i	0.945562	+	0.325441i	$0.105513\pi$
$37$			3.95916i			0.650882i	−0.945562	+	0.325441i	$0.894487\pi$
$38$		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	$-0.722277\pi$
$41$	−10.4227	−	3.79356i	−1.62776	−	0.592455i	−0.984838	+	0.173479i	$0.944499\pi$
$42$		0			0
$43$	0.834031	+	4.73003i	0.127189	+	0.721322i	0.979984	+	0.199077i	$0.0637944\pi$
$43$	0.834031	+	4.73003i	0.127189	+	0.721322i	−0.852795	+	0.522245i	$0.825095\pi$
$44$		0			0
$45$	0.385104	−	0.699978i	0.0574079	−	0.104347i
$46$		0			0
$47$	−1.24341	+	1.48183i	−0.181369	+	0.216147i	−0.849067	−	0.528285i	$-0.822835\pi$
$47$	−1.24341	+	1.48183i	−0.181369	+	0.216147i	0.667698	+	0.744432i	$0.267280\pi$
$48$		0			0
$49$	2.76878	+	4.79567i	0.395540	+	0.685096i
$50$		0			0
$51$	−0.641920	+	1.41451i	−0.0898868	+	0.198071i
$52$		0			0
$53$	0.998339	−	5.66186i	0.137132	−	0.777717i	−0.836219	−	0.548396i	$-0.815239\pi$
$53$	0.998339	−	5.66186i	0.137132	−	0.777717i	0.973351	−	0.229320i	$-0.0736504\pi$
$54$		0			0
$55$	0.479676	−	0.402496i	0.0646794	−	0.0542725i
$56$		0			0
$57$	4.58516	−	5.99803i	0.607319	−	0.794458i
$58$		0			0
$59$	9.78136	−	8.20754i	1.27342	−	1.06853i	0.279310	−	0.960201i	$-0.409894\pi$
$59$	9.78136	−	8.20754i	1.27342	−	1.06853i	0.994115	−	0.108329i	$-0.0345501\pi$
$60$		0			0
$61$	−0.153642	+	0.871345i	−0.0196718	+	0.111564i	−0.993063	−	0.117587i	$-0.962484\pi$
$61$	−0.153642	+	0.871345i	−0.0196718	+	0.111564i	0.973391	+	0.229152i	$0.0735951\pi$
$62$		0			0
$63$	−1.31088	−	3.38283i	−0.165156	−	0.426196i
$64$		0			0
$65$	−0.396123	−	0.686106i	−0.0491331	−	0.0851010i
$66$		0			0
$67$	−3.28864	+	3.91925i	−0.401771	+	0.478812i	−0.928559	−	0.371184i	$-0.878952\pi$
$67$	−3.28864	+	3.91925i	−0.401771	+	0.478812i	0.526788	+	0.849997i	$0.323396\pi$
$68$		0			0
$69$	−2.61768	−	9.38117i	−0.315131	−	1.12936i
$70$		0			0
$71$	1.64669	+	9.33885i	0.195426	+	1.10832i	0.911810	+	0.410612i	$0.134685\pi$
$71$	1.64669	+	9.33885i	0.195426	+	1.10832i	−0.716384	+	0.697706i	$0.754204\pi$
$72$		0			0
$73$	0.320853	+	0.116781i	0.0375530	+	0.0136682i	0.360728	−	0.932671i	$-0.382528\pi$
$73$	0.320853	+	0.116781i	0.0375530	+	0.0136682i	−0.323175	+	0.946339i	$0.604750\pi$
$74$		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	0.735775	+	0.677226i	$0.236818\pi$
$79$	−2.33914	+	6.42674i	−0.263174	+	0.723064i	−0.998949	+	0.0458383i	$0.985404\pi$
$80$		0			0
$81$	−1.92708	−	8.79127i	−0.214120	−	0.976807i
$82$		0			0
$83$	−12.2240	−	7.05752i	−1.34176	−	0.774663i	−0.354691	−	0.934984i	$-0.615414\pi$
$83$	−12.2240	−	7.05752i	−1.34176	−	0.774663i	−0.987065	+	0.160320i	$0.948747\pi$
$84$		0			0
$85$	−0.182956	−	0.153518i	−0.0198443	−	0.0166514i
$86$		0			0
$87$	−1.08301	+	4.21529i	−0.116111	+	0.451927i
$88$		0			0
$89$	−11.5580	+	4.20677i	−1.22515	+	0.445917i	−0.871933	−	0.489626i	$-0.837133\pi$
$89$	−11.5580	+	4.20677i	−1.22515	+	0.445917i	−0.353213	+	0.935543i	$0.614911\pi$
$90$		0			0
$91$	−3.54297	−	0.624722i	−0.371405	−	0.0654887i
$92$		0			0
$93$	−1.38090	+	17.9095i	−0.143192	+	1.85713i
$94$		0			0
$95$	0.698802	+	0.926900i	0.0716956	+	0.0950979i
$96$		0			0
$97$	3.88456	+	4.62944i	0.394418	+	0.470049i	0.926309	−	0.376764i	$-0.122963\pi$
$97$	3.88456	+	4.62944i	0.394418	+	0.470049i	−0.531892	+	0.846812i	$0.678519\pi$
$98$		0			0
$99$	1.08135	−	6.97057i	0.108680	−	0.700569i
$100$		0			0
$101$	3.54557	+	9.74137i	0.352797	+	0.969302i	0.981467	+	0.191630i	$0.0613774\pi$
$101$	3.54557	+	9.74137i	0.352797	+	0.969302i	−0.628670	+	0.777672i	$0.716400\pi$
$102$		0			0
$103$	12.7994	−	7.38973i	1.26116	−	0.728131i	0.287861	−	0.957672i	$-0.407056\pi$
$103$	12.7994	−	7.38973i	1.26116	−	0.728131i	0.973299	+	0.229541i	$0.0737224\pi$
$104$		0			0
$105$	0.555150	−	0.0543446i	0.0541771	−	0.00530349i
$106$		0			0
$107$	8.08439	−	14.0026i	0.781547	−	1.35368i	−0.149493	−	0.988763i	$-0.547764\pi$
$107$	8.08439	−	14.0026i	0.781547	−	1.35368i	0.931040	−	0.364917i	$-0.118903\pi$
$108$		0			0
$109$	17.9876	−	3.17170i	1.72290	−	0.303794i	0.777302	−	0.629128i	$-0.216588\pi$
$109$	17.9876	−	3.17170i	1.72290	−	0.303794i	0.945599	+	0.325334i	$0.105477\pi$
$110$		0			0
$111$	−6.18475	+	2.96204i	−0.587030	+	0.281144i
$112$		0			0
$113$	2.40020			0.225792			0.112896	−	0.993607i	$-0.463987\pi$
$113$	2.40020			0.225792			0.112896	+	0.993607i	$0.463987\pi$
$114$		0			0
$115$	1.49748			0.139640
$116$		0			0
$117$	−8.44777	−	2.87883i	−0.780996	−	0.266148i
$118$		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
$123$	−1.87168	−	19.1199i	−0.168764	−	1.72398i
$124$		0			0
$125$	2.28993	−	1.32209i	0.204818	−	0.118251i
$126$		0			0
$127$	2.02408	+	5.56112i	0.179608	+	0.493470i	0.996526	−	0.0832849i	$-0.0265411\pi$
$127$	2.02408	+	5.56112i	0.179608	+	0.493470i	−0.816918	+	0.576754i	$0.804319\pi$
$128$		0			0
$129$	−6.76497	+	4.84163i	−0.595623	+	0.426282i
$130$		0			0
$131$	11.1080	+	13.2379i	0.970506	+	1.15660i	0.987638	+	0.156751i	$0.0501020\pi$
$131$	11.1080	+	13.2379i	0.970506	+	1.15660i	−0.0171319	+	0.999853i	$0.505454\pi$
$132$		0			0
$133$	5.26411	+	0.274672i	0.456456	+	0.0238171i
$134$		0			0
$135$	1.38158	+	0.0778975i	0.118907	+	0.00670435i
$136$		0			0
$137$	18.0150	+	3.17653i	1.53912	+	0.271389i	0.877917	−	0.478813i	$-0.158933\pi$
$137$	18.0150	+	3.17653i	1.53912	+	0.271389i	0.661208	+	0.750203i	$0.270044\pi$
$138$		0			0
$139$	2.16057	−	0.786381i	0.183257	−	0.0667000i	−0.248762	−	0.968565i	$-0.580024\pi$
$139$	2.16057	−	0.786381i	0.183257	−	0.0667000i	0.432019	+	0.901865i	$0.357801\pi$
$140$		0			0
$141$	−3.24508	−	0.833740i	−0.273285	−	0.0702135i
$142$		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
$147$	−5.42004	+	7.91309i	−0.447037	+	0.652661i
$148$		0			0
$149$	−2.67853	+	7.35921i	−0.219434	+	0.602890i	−0.999747	−	0.0224995i	$-0.992838\pi$
$149$	−2.67853	+	7.35921i	−0.219434	+	0.602890i	0.780313	+	0.625389i	$0.215060\pi$
$150$		0			0
$151$			11.1343i			0.906098i	0.891486	+	0.453049i	$0.149664\pi$
$151$			11.1343i			0.906098i	−0.891486	+	0.453049i	$0.850336\pi$
$152$		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	−0.670798	−	0.741640i	$-0.734048\pi$
$157$	−3.68519	−	20.8997i	−0.294110	−	1.66798i	0.376688	−	0.926340i	$-0.377063\pi$
$158$		0			0
$159$	9.59152	−	2.67637i	0.760657	−	0.212250i
$160$		0			0
$161$	4.37103	−	5.20919i	0.344485	−	0.410542i
$162$		0			0
$163$	−1.74061	−	3.01482i	−0.136335	−	0.236139i	0.789772	−	0.613401i	$-0.210199\pi$
$163$	−1.74061	−	3.01482i	−0.136335	−	0.236139i	−0.926107	+	0.377262i	$0.876866\pi$
$164$		0			0
$165$	0.987622	+	0.448193i	0.0768863	+	0.0348918i
$166$		0			0
$167$	−3.56671	+	20.2278i	−0.276000	+	1.56527i	0.459767	+	0.888040i	$0.347933\pi$
$167$	−3.56671	+	20.2278i	−0.276000	+	1.56527i	−0.735767	+	0.677235i	$0.763178\pi$
$168$		0			0
$169$	3.17888	−	2.66740i	0.244529	−	0.205185i
$170$		0			0
$171$	12.8001	+	2.67524i	0.978850	+	0.204581i
$172$		0			0
$173$	6.38346	−	5.35636i	0.485326	−	0.407237i	−0.367022	−	0.930212i	$-0.619623\pi$
$173$	6.38346	−	5.35636i	0.485326	−	0.407237i	0.852348	+	0.522976i	$0.175178\pi$
$174$		0			0
$175$	1.03508	−	5.87024i	0.0782448	−	0.443748i
$176$		0			0
$177$	20.1392	+	9.13938i	1.51376	+	0.686958i
$178$		0			0
$179$	4.51280	+	7.81640i	0.337302	+	0.584225i	0.983924	−	0.178586i	$-0.0571522\pi$
$179$	4.51280	+	7.81640i	0.337302	+	0.584225i	−0.646622	+	0.762811i	$0.723819\pi$
$180$		0			0
$181$	5.90976	−	7.04297i	0.439269	−	0.523500i	−0.500304	−	0.865850i	$-0.666778\pi$
$181$	5.90976	−	7.04297i	0.439269	−	0.523500i	0.939573	+	0.342350i	$0.111223\pi$
$182$		0			0
$183$	−1.47611	+	0.411886i	−0.109117	+	0.0304475i
$184$		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	−0.915668	−	0.401935i	$-0.868338\pi$
$193$	0.613121	−	1.68453i	0.0441334	−	0.121255i	0.959801	+	0.280680i	$0.0905599\pi$
$194$		0			0
$195$	0.775433	−	1.13211i	0.0555299	−	0.0810720i
$196$		0			0
$197$	−6.85271	−	3.95642i	−0.488236	−	0.281883i	0.235607	−	0.971849i	$-0.424292\pi$
$197$	−6.85271	−	3.95642i	−0.488236	−	0.281883i	−0.723842	+	0.689966i	$0.757626\pi$
$198$		0			0
$199$	8.01318	+	6.72386i	0.568039	+	0.476642i	0.880995	−	0.473126i	$-0.156875\pi$
$199$	8.01318	+	6.72386i	0.568039	+	0.476642i	−0.312955	+	0.949768i	$0.601319\pi$
$200$		0			0
$201$	−8.58280	−	2.20513i	−0.605384	−	0.155538i
$202$		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
$207$	12.6963	−	11.1077i	0.882452	−	0.772037i
$208$		0			0
$209$	8.59694	+	5.58012i	0.594663	+	0.385985i
$210$		0			0
$211$	−8.93046	−	10.6429i	−0.614799	−	0.732688i	0.365368	−	0.930863i	$-0.380943\pi$
$211$	−8.93046	−	10.6429i	−0.614799	−	0.732688i	−0.980167	+	0.198175i	$0.936499\pi$
$212$		0			0
$213$	−13.3566	+	9.55921i	−0.915180	+	0.654986i
$214$		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
$219$	0.0576176	+	0.588585i	0.00389344	+	0.0397729i
$220$		0			0
$221$	−1.33401	+	2.31057i	−0.0897349	+	0.155425i
$222$		0			0
$223$	12.2714	−	2.16379i	0.821757	−	0.144898i	0.253066	−	0.967449i	$-0.418561\pi$
$223$	12.2714	−	2.16379i	0.821757	−	0.144898i	0.568691	+	0.822551i	$0.307450\pi$
$224$		0			0
$225$	4.76983	−	13.9968i	0.317989	−	0.933122i
$226$		0			0
$227$	−1.63948			−0.108816			−0.0544081	−	0.998519i	$-0.517327\pi$
$227$	−1.63948			−0.108816			−0.0544081	+	0.998519i	$0.517327\pi$
$228$		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
$231$	4.44190	−	2.12734i	0.292256	−	0.139969i
$232$		0			0
$233$	2.37239	−	0.418316i	0.155420	−	0.0274048i	−0.0953966	−	0.995439i	$-0.530412\pi$
$233$	2.37239	−	0.418316i	0.155420	−	0.0274048i	0.250817	+	0.968035i	$0.419301\pi$
$234$		0			0
$235$	0.257571	−	0.446127i	0.0168021	−	0.0291021i
$236$		0			0
$237$	−11.7895	+	1.15409i	−0.765809	+	0.0749663i
$238$		0			0
$239$	16.5806	−	9.57284i	1.07251	−	0.619215i	0.143646	−	0.989629i	$-0.454117\pi$
$239$	16.5806	−	9.57284i	1.07251	−	0.619215i	0.928867	+	0.370414i	$0.120784\pi$
$240$		0			0
$241$	1.43503	+	3.94271i	0.0924383	+	0.253972i	0.977292	−	0.211897i	$-0.0679641\pi$
$241$	1.43503	+	3.94271i	0.0924383	+	0.253972i	−0.884854	+	0.465869i	$0.845742\pi$
$242$		0			0
$243$	12.2914	−	9.58753i	0.788496	−	0.615040i
$244$		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
$249$	1.87947	−	24.3756i	0.119106	−	1.54474i
$250$		0			0
$251$	−4.15098	−	0.731929i	−0.262007	−	0.0461990i	0.0411012	−	0.999155i	$-0.486913\pi$
$251$	−4.15098	−	0.731929i	−0.262007	−	0.0461990i	−0.303109	+	0.952956i	$0.598024\pi$
$252$		0			0
$253$	12.4244	−	4.52211i	0.781114	−	0.284302i
$254$		0			0
$255$	0.102938	−	0.400656i	0.00644625	−	0.0250901i
$256$		0			0
$257$	13.6150	+	11.4244i	0.849282	+	0.712632i	0.959631	−	0.281260i	$-0.0907525\pi$
$257$	13.6150	+	11.4244i	0.849282	+	0.712632i	−0.110349	+	0.993893i	$0.535197\pi$
$258$		0			0
$259$	−4.14641	−	2.39393i	−0.257645	−	0.148752i
$260$		0			0
$261$	−7.39512	+	1.46185i	−0.457747	+	0.0904863i
$262$		0			0
$263$	−0.383160	+	1.05272i	−0.0236267	+	0.0649138i	−0.950945	−	0.309359i	$-0.899885\pi$
$263$	−0.383160	+	1.05272i	−0.0236267	+	0.0649138i	0.927319	+	0.374273i	$0.122108\pi$
$264$		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	$-0.186677\pi$
$269$	18.2909	+	6.65734i	1.11522	+	0.405905i	0.282311	+	0.959323i	$0.408899\pi$
$270$		0			0
$271$	0.0552285	+	0.313217i	0.00335489	+	0.0190266i	0.986439	−	0.164127i	$-0.0524806\pi$
$271$	0.0552285	+	0.313217i	0.00335489	+	0.0190266i	−0.983084	+	0.183153i	$0.941370\pi$
$272$		0			0
$273$	−1.67477	−	6.00200i	−0.101362	−	0.363257i
$274$		0			0
$275$	7.44980	−	8.87833i	0.449240	−	0.535383i
$276$		0			0
$277$	10.9678	+	18.9968i	0.658993	+	1.14141i	0.980877	+	0.194630i	$0.0623506\pi$
$277$	10.9678	+	18.9968i	0.658993	+	1.14141i	−0.321884	+	0.946779i	$0.604316\pi$
$278$		0			0
$279$	−29.0102	+	11.2418i	−1.73679	+	0.673028i
$280$		0			0
$281$	2.62001	−	14.8588i	0.156297	−	0.886403i	−0.801294	−	0.598271i	$-0.795855\pi$
$281$	2.62001	−	14.8588i	0.156297	−	0.886403i	0.957591	−	0.288132i	$-0.0930342\pi$
$282$		0			0
$283$	5.08697	−	4.26848i	0.302389	−	0.253735i	−0.478949	−	0.877843i	$-0.658982\pi$
$283$	5.08697	−	4.26848i	0.302389	−	0.253735i	0.781338	+	0.624108i	$0.214538\pi$
$284$		0			0
$285$	−0.925138	+	1.78508i	−0.0548005	+	0.105739i
$286$		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
$291$	−4.32560	+	9.53173i	−0.253571	+	0.558760i
$292$		0			0
$293$	−14.2028	−	24.5999i	−0.829735	−	1.43714i	−0.898246	−	0.439493i	$-0.855158\pi$
$293$	−14.2028	−	24.5999i	−0.829735	−	1.43714i	0.0685112	−	0.997650i	$-0.478175\pi$
$294$		0			0
$295$	−2.18572	+	2.60484i	−0.127258	+	0.151660i
$296$		0			0
$297$	11.6980	−	3.52580i	0.678787	−	0.204588i
$298$		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	−0.974940	−	0.222466i	$-0.928589\pi$
$307$	−1.49097	+	4.09641i	−0.0850942	+	0.233794i	0.889846	+	0.456261i	$0.150812\pi$
$308$		0			0
$309$	21.1196	+	14.4658i	1.20145	+	0.822930i
$310$		0			0
$311$	−4.11082	−	2.37338i	−0.233103	−	0.134582i	0.378900	−	0.925438i	$-0.376303\pi$
$311$	−4.11082	−	2.37338i	−0.233103	−	0.134582i	−0.612003	+	0.790856i	$0.709636\pi$
$312$		0			0
$313$	14.5023	+	12.1689i	0.819718	+	0.687825i	0.952906	−	0.303265i	$-0.0980769\pi$
$313$	14.5023	+	12.1689i	0.819718	+	0.687825i	−0.133188	+	0.991091i	$0.542521\pi$
$314$		0			0
$315$	0.500228	+	0.826563i	0.0281847	+	0.0465716i
$316$		0			0
$317$	−29.4488	+	10.7185i	−1.65401	+	0.602010i	−0.989404	−	0.145186i	$-0.953622\pi$
$317$	−29.4488	+	10.7185i	−1.65401	+	0.602010i	−0.664604	+	0.747196i	$0.731400\pi$
$318$		0			0
$319$	−5.81850	−	1.02596i	−0.325773	−	0.0574426i
$320$		0			0
$321$	27.9223	+	2.15293i	1.55847	+	0.120165i
$322$		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
$327$	18.4120	+	25.7262i	1.01819	+	1.42266i
$328$		0			0
$329$	−0.800083	−	2.19821i	−0.0441100	−	0.121191i
$330$		0			0
$331$	3.20610	−	1.85104i	0.176223	−	0.101742i	−0.409294	−	0.912403i	$-0.634225\pi$
$331$	3.20610	−	1.85104i	0.176223	−	0.101742i	0.585517	+	0.810660i	$0.300892\pi$
$332$		0			0
$333$	−9.25422	−	7.44539i	−0.507128	−	0.408005i
$334$		0			0
$335$	0.681242	−	1.17995i	0.0372202	−	0.0644673i
$336$		0			0
$337$	−19.7344	+	3.47971i	−1.07500	+	0.189552i	−0.683004	−	0.730415i	$-0.739327\pi$
$337$	−19.7344	+	3.47971i	−1.07500	+	0.189552i	−0.391997	+	0.919967i	$0.628216\pi$
$338$		0			0
$339$	1.79570	+	3.74944i	0.0975292	+	0.203642i
$340$		0			0
$341$	−24.3849			−1.32051
$342$		0			0
$343$	−15.1618			−0.818662
$344$		0			0
$345$	1.12034	+	2.33927i	0.0603168	+	0.125942i
$346$		0			0
$347$	−0.281016	+	0.0495507i	−0.0150857	+	0.00266002i	−0.181186	−	0.983449i	$-0.557994\pi$
$347$	−0.281016	+	0.0495507i	−0.0150857	+	0.00266002i	0.166100	+	0.986109i	$0.446882\pi$
$348$		0			0
$349$	6.98873	−	12.1048i	0.374098	−	0.647957i	−0.616093	−	0.787673i	$-0.711286\pi$
$349$	6.98873	−	12.1048i	0.374098	−	0.647957i	0.990192	+	0.139716i	$0.0446190\pi$
$350$		0			0
$351$	−1.82306	−	15.3504i	−0.0973077	−	0.819342i
$352$		0			0
$353$	−17.7647	+	10.2564i	−0.945519	+	0.545895i	−0.891686	−	0.452654i	$-0.850477\pi$
$353$	−17.7647	+	10.2564i	−0.945519	+	0.545895i	−0.0538327	+	0.998550i	$0.517144\pi$
$354$		0			0
$355$	−0.863726	−	2.37307i	−0.0458418	−	0.125949i
$356$		0			0
$357$	−1.09327	−	1.52757i	−0.0578620	−	0.0808477i
$358$		0			0
$359$	17.9876	+	21.4368i	0.949348	+	1.13139i	0.991214	+	0.132266i	$0.0422254\pi$
$359$	17.9876	+	21.4368i	0.949348	+	1.13139i	−0.0418658	+	0.999123i	$0.513330\pi$
$360$		0			0
$361$	−11.1609	+	15.3764i	−0.587415	+	0.809286i
$362$		0			0
$363$	−9.44854	−	0.728524i	−0.495920	−	0.0382376i
$364$		0			0
$365$	−0.0895476	−	0.0157897i	−0.00468713	−	0.000826468i
$366$		0			0
$367$	−1.43051	+	0.520662i	−0.0746719	+	0.0271783i	−0.379086	−	0.925361i	$-0.623762\pi$
$367$	−1.43051	+	0.520662i	−0.0746719	+	0.0271783i	0.304414	+	0.952540i	$0.401539\pi$
$368$		0			0
$369$	28.4676	−	17.2283i	1.48196	−	0.896871i
$370$		0			0
$371$	5.32599	+	4.46904i	0.276512	+	0.232021i
$372$		0			0
$373$	4.13495	+	2.38731i	0.214100	+	0.123610i	0.603215	−	0.797578i	$-0.293886\pi$
$373$	4.13495	+	2.38731i	0.214100	+	0.123610i	−0.389116	+	0.921189i	$0.627219\pi$
$374$		0			0
$375$	3.77850	+	2.58806i	0.195121	+	0.133647i
$376$		0			0
$377$	−2.55669	+	7.02444i	−0.131676	+	0.361777i
$378$		0			0
$379$		−	13.4129i		−	0.688972i	−0.938791	−	0.344486i	$-0.888053\pi$
$379$		−	13.4129i		−	0.688972i	0.938791	−	0.344486i	$-0.111947\pi$
$380$		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	$-0.701605\pi$
$383$	−30.5956	−	11.1359i	−1.56336	−	0.569017i	−0.971503	+	0.237026i	$0.923827\pi$
$384$		0			0
$385$	0.131493	+	0.745733i	0.00670150	+	0.0380061i
$386$		0			0
$387$	−12.6245	−	6.94556i	−0.641739	−	0.353063i
$388$		0			0
$389$	8.33624	−	9.93474i	0.422664	−	0.503711i	−0.512127	−	0.858910i	$-0.671142\pi$
$389$	8.33624	−	9.93474i	0.422664	−	0.503711i	0.934791	+	0.355199i	$0.115587\pi$
$390$		0			0
$391$	−2.52149	−	4.36735i	−0.127517	−	0.220866i
$392$		0			0
$393$	−12.3691	+	27.2561i	−0.623938	+	1.37489i
$394$		0			0
$395$	0.316270	−	1.79365i	0.0159132	−	0.0902485i
$396$		0			0
$397$	18.9635	−	15.9123i	0.951752	−	0.798615i	−0.0278396	−	0.999612i	$-0.508863\pi$
$397$	18.9635	−	15.9123i	0.951752	−	0.798615i	0.979592	+	0.200997i	$0.0644183\pi$
$398$		0			0
$399$	3.50926	+	8.42876i	0.175683	+	0.421966i
$400$		0			0
$401$	4.89417	−	4.10670i	0.244403	−	0.205079i	−0.512354	−	0.858774i	$-0.671227\pi$
$401$	4.89417	−	4.10670i	0.244403	−	0.205079i	0.756758	+	0.653695i	$0.226782\pi$
$402$		0			0
$403$	−5.35744	+	30.3836i	−0.266873	+	1.51351i
$404$		0			0
$405$	0.911938	+	2.21649i	0.0453146	+	0.110138i
$406$		0			0
$407$	−4.65462	−	8.06204i	−0.230721	−	0.399620i
$408$		0			0
$409$	−18.5835	+	22.1469i	−0.918894	+	1.09510i	0.0762911	+	0.997086i	$0.475692\pi$
$409$	−18.5835	+	22.1469i	−0.918894	+	1.09510i	−0.995185	+	0.0980100i	$0.968752\pi$
$410$		0			0
$411$	8.51571	+	30.5184i	0.420049	+	1.50536i
$412$		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	0.216476	+	0.976288i	$0.430544\pi$
$421$	−11.8370	+	32.5219i	−0.576900	+	1.58502i	−0.793376	+	0.608732i	$0.791678\pi$
$422$		0			0
$423$	−1.12538	−	5.69302i	−0.0547180	−	0.276804i
$424$		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
$429$	3.01491	−	11.7346i	0.145561	−	0.566553i
$430$		0			0
$431$	−30.2120	+	10.9963i	−1.45526	+	0.529671i	−0.944055	−	0.329788i	$-0.893023\pi$
$431$	−30.2120	+	10.9963i	−1.45526	+	0.529671i	−0.511205	+	0.859459i	$0.670801\pi$
$432$		0			0
$433$	−22.7212	−	4.00636i	−1.09191	−	0.192534i	−0.401435	−	0.915888i	$-0.631488\pi$
$433$	−22.7212	−	4.00636i	−1.09191	−	0.192534i	−0.690477	+	0.723354i	$0.742599\pi$
$434$		0			0
$435$	0.0891011	−	1.15559i	0.00427207	−	0.0554063i
$436$		0			0
$437$	7.17158	+	23.4380i	0.343063	+	1.12119i
$438$		0			0
$439$	−7.57338	−	9.02561i	−0.361458	−	0.430769i	0.554413	−	0.832242i	$-0.312943\pi$
$439$	−7.57338	−	9.02561i	−0.361458	−	0.430769i	−0.915871	+	0.401473i	$0.868498\pi$
$440$		0			0
$441$	−16.4163	−	2.54668i	−0.781730	−	0.121271i
$442$		0			0
$443$	7.28357	+	20.0114i	0.346053	+	0.950772i	0.983600	+	0.180361i	$0.0577267\pi$
$443$	7.28357	+	20.0114i	0.346053	+	0.950772i	−0.637548	+	0.770411i	$0.720051\pi$
$444$		0			0
$445$	2.83668	−	1.63776i	0.134471	−	0.0776371i
$446$		0			0
$447$	−13.5000	+	1.32154i	−0.638530	+	0.0625068i
$448$		0			0
$449$	5.96300	−	10.3282i	0.281411	−	0.487419i	−0.690321	−	0.723503i	$-0.742531\pi$
$449$	5.96300	−	10.3282i	0.281411	−	0.487419i	0.971733	+	0.236084i	$0.0758641\pi$
$450$		0			0
$451$	25.6837	−	4.52874i	1.20940	−	0.213250i
$452$		0			0
$453$	−17.3933	+	8.33012i	−0.817211	+	0.391383i
$454$		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
$459$	−2.09915	−	4.16050i	−0.0979799	−	0.194195i
$460$		0			0
$461$	29.6765	−	5.23277i	1.38217	−	0.243715i	0.567376	−	0.823459i	$-0.307959\pi$
$461$	29.6765	−	5.23277i	1.38217	−	0.243715i	0.814798	+	0.579744i	$0.196848\pi$
$462$		0			0
$463$	−12.7896	+	22.1523i	−0.594385	+	1.02950i	0.399248	+	0.916843i	$0.369271\pi$
$463$	−12.7896	+	22.1523i	−0.594385	+	1.02950i	−0.993633	+	0.112662i	$0.964062\pi$
$464$		0			0
$465$	−0.466044	−	4.76082i	−0.0216123	−	0.220778i
$466$		0			0
$467$	−24.6450	+	14.2288i	−1.14044	+	0.658431i	−0.946539	−	0.322591i	$-0.895446\pi$
$467$	−24.6450	+	14.2288i	−1.14044	+	0.658431i	−0.193898	+	0.981022i	$0.562113\pi$
$468$		0			0
$469$	−2.11611	−	5.81397i	−0.0977131	−	0.268464i
$470$		0			0
$471$	29.8912	−	21.3929i	1.37731	−	0.985732i
$472$		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
$477$	11.3567	+	12.9809i	0.519989	+	0.594357i
$478$		0			0
$479$	12.1691	+	2.14575i	0.556022	+	0.0980417i	0.444596	−	0.895731i	$-0.353347\pi$
$479$	12.1691	+	2.14575i	0.556022	+	0.0980417i	0.111426	+	0.993773i	$0.464458\pi$
$480$		0			0
$481$	−11.0679	+	4.02840i	−0.504655	+	0.183679i
$482$		0			0
$483$	11.4077	+	2.93090i	0.519066	+	0.133361i
$484$		0			0
$485$	−1.23285	−	1.03449i	−0.0559810	−	0.0469736i
$486$		0			0
$487$	−24.3442	−	14.0551i	−1.10314	−	0.636899i	−0.166097	−	0.986109i	$-0.553117\pi$
$487$	−24.3442	−	14.0551i	−1.10314	−	0.636899i	−0.937044	+	0.349210i	$0.886450\pi$
$488$		0			0
$489$	3.40734	−	4.97461i	0.154085	−	0.224959i
$490$		0			0
$491$	−1.17147	+	3.21859i	−0.0528678	+	0.145253i	−0.963316	−	0.268371i	$-0.913515\pi$
$491$	−1.17147	+	3.21859i	−0.0528678	+	0.145253i	0.910448	+	0.413624i	$0.135737\pi$
$492$		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	−0.656862	−	0.754010i	$-0.728117\pi$
$499$	−6.64566	−	37.6894i	−0.297500	−	1.68721i	0.359362	−	0.933198i	$-0.382994\pi$
$500$		0			0
$501$	−34.2670	+	9.56171i	−1.53094	+	0.427186i
$502$		0			0
$503$	−10.1578	+	12.1056i	−0.452916	+	0.539764i	−0.943387	−	0.331693i	$-0.892380\pi$
$503$	−10.1578	+	12.1056i	−0.452916	+	0.539764i	0.490472	+	0.871457i	$0.336825\pi$
$504$		0			0
$505$	−1.38034	−	2.39082i	−0.0614244	−	0.106390i
$506$		0			0
$507$	6.54512	+	2.97024i	0.290679	+	0.131913i
$508$		0			0
$509$	−1.72136	+	9.76234i	−0.0762981	+	0.432708i	0.922599	+	0.385760i	$0.126061\pi$
$509$	−1.72136	+	9.76234i	−0.0762981	+	0.432708i	−0.998897	+	0.0469483i	$0.985050\pi$
$510$		0			0
$511$	−0.316310	+	0.265415i	−0.0139927	+	0.0117413i
$512$		0			0
$513$	5.39730	+	21.9970i	0.238296	+	0.971192i
$514$		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
$519$	13.1431	+	5.96449i	0.576920	+	0.261812i
$520$		0			0
$521$	6.93036	+	12.0037i	0.303625	+	0.525894i	0.976954	−	0.213449i	$-0.0684697\pi$
$521$	6.93036	+	12.0037i	0.303625	+	0.525894i	−0.673329	+	0.739343i	$0.735136\pi$
$522$		0			0
$523$	−24.0581	+	28.6713i	−1.05199	+	1.25371i	−0.0856778	+	0.996323i	$0.527306\pi$
$523$	−24.0581	+	28.6713i	−1.05199	+	1.25371i	−0.966309	+	0.257386i	$0.917139\pi$
$524$		0			0
$525$	9.94452	−	2.77487i	0.434014	−	0.121105i
$526$		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
$537$	−8.83404	+	12.8974i	−0.381217	+	0.556565i
$538$		0			0
$539$	−11.2761	−	6.51028i	−0.485698	−	0.280418i
$540$		0			0
$541$	6.17119	+	5.17824i	0.265320	+	0.222630i	0.765736	−	0.643155i	$-0.222375\pi$
$541$	6.17119	+	5.17824i	0.265320	+	0.222630i	−0.500416	+	0.865785i	$0.666819\pi$
$542$		0			0
$543$	15.4235	+	3.96266i	0.661884	+	0.170054i
$544$		0			0
$545$	−4.57078	+	1.66363i	−0.195791	+	0.0712620i
$546$		0			0
$547$	−25.2004	−	4.44352i	−1.07749	−	0.189991i	−0.393386	−	0.919373i	$-0.628697\pi$
$547$	−25.2004	−	4.44352i	−1.07749	−	0.189991i	−0.684106	+	0.729382i	$0.739808\pi$
$548$		0			0
$549$	−1.74777	−	1.99773i	−0.0745930	−	0.0852611i
$550$		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
$555$	1.48504	−	1.06283i	0.0630366	−	0.0451147i
$556$		0			0
$557$	−4.99606	−	13.7266i	−0.211690	−	0.581613i	0.787718	−	0.616037i	$-0.211263\pi$
$557$	−4.99606	−	13.7266i	−0.211690	−	0.581613i	−0.999407	+	0.0344238i	$0.989040\pi$
$558$		0			0
$559$	−12.3743	+	7.14431i	−0.523377	+	0.302172i
$560$		0			0
$561$	−0.355841	−	3.63505i	−0.0150236	−	0.153472i
$562$		0			0
$563$	−12.5968	+	21.8184i	−0.530893	+	0.919534i	0.468457	+	0.883486i	$0.344810\pi$
$563$	−12.5968	+	21.8184i	−0.530893	+	0.919534i	−0.999350	+	0.0360479i	$0.988523\pi$
$564$		0			0
$565$	−0.629478	+	0.110994i	−0.0264824	+	0.00466955i
$566$		0			0
$567$	10.3723	+	3.29748i	0.435594	+	0.138481i
$568$		0			0
$569$	−42.1013			−1.76498			−0.882490	−	0.470332i	$-0.844134\pi$
$569$	−42.1013			−1.76498			−0.882490	+	0.470332i	$0.844134\pi$
$570$		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
$573$	−11.4544	+	5.48581i	−0.478515	+	0.229173i
$574$		0			0
$575$	27.2958	−	4.81298i	1.13831	−	0.200715i
$576$		0			0
$577$	6.43762	−	11.1503i	0.268002	−	0.464192i	−0.700344	−	0.713805i	$-0.746970\pi$
$577$	6.43762	−	11.1503i	0.268002	−	0.464192i	0.968346	+	0.249613i	$0.0803034\pi$
$578$		0			0
$579$	3.09018	−	0.302503i	0.128424	−	0.0125716i
$580$		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
$585$	2.34865	+	0.364348i	0.0971046	+	0.0150639i
$586$		0			0
$587$	11.6998	+	13.9432i	0.482900	+	0.575498i	0.951397	−	0.307967i	$-0.0996486\pi$
$587$	11.6998	+	13.9432i	0.482900	+	0.575498i	−0.468497	+	0.883465i	$0.655204\pi$
$588$		0			0
$589$	2.35551	−	45.1435i	0.0970573	−	1.86011i
$590$		0			0
$591$	1.05362	−	13.6649i	0.0433402	−	0.562098i
$592$		0			0
$593$	6.08719	+	1.07334i	0.249971	+	0.0440766i	0.297230	−	0.954806i	$-0.403937\pi$
$593$	6.08719	+	1.07334i	0.249971	+	0.0440766i	−0.0472585	+	0.998883i	$0.515048\pi$
$594$		0			0
$595$	0.271404	−	0.0987830i	0.0111265	−	0.00404971i
$596$		0			0
$597$	−4.50854	+	17.5481i	−0.184522	+	0.718197i
$598$		0			0
$599$	−27.9659	−	23.4662i	−1.14266	−	0.958803i	−0.143135	−	0.989703i	$-0.545718\pi$
$599$	−27.9659	−	23.4662i	−1.14266	−	0.958803i	−0.999522	+	0.0308999i	$0.990163\pi$
$600$		0			0
$601$	2.01662	+	1.16430i	0.0822597	+	0.0474927i	0.540566	−	0.841302i	$-0.318210\pi$
$601$	2.01662	+	1.16430i	0.0822597	+	0.0474927i	−0.458306	+	0.888795i	$0.651544\pi$
$602$		0			0
$603$	−2.97649	−	15.0573i	−0.121212	−	0.613180i
$604$		0			0
$605$	0.498339	−	1.36918i	0.0202604	−	0.0556649i
$606$		0			0
$607$		−	24.4621i		−	0.992887i	−0.868069	−	0.496443i	$-0.834639\pi$
$607$		−	24.4621i		−	0.992887i	0.868069	−	0.496443i	$-0.165361\pi$
$608$		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	−0.797428	−	0.603414i	$-0.793807\pi$
$613$	−6.30039	−	35.7313i	−0.254470	−	1.44317i	0.542958	−	0.839760i	$-0.317304\pi$
$614$		0			0
$615$	1.37504	+	4.92785i	0.0554471	+	0.198710i
$616$		0			0
$617$	10.3830	−	12.3740i	0.418006	−	0.498160i	−0.515416	−	0.856940i	$-0.672363\pi$
$617$	10.3830	−	12.3740i	0.418006	−	0.498160i	0.933422	+	0.358780i	$0.116807\pi$
$618$		0			0
$619$	15.2492	+	26.4123i	0.612916	+	1.06160i	0.990746	+	0.135726i	$0.0433368\pi$
$619$	15.2492	+	26.4123i	0.612916	+	1.06160i	−0.377831	+	0.925875i	$0.623330\pi$
$620$		0			0
$621$	26.8504	+	11.5231i	1.07747	+	0.462408i
$622$		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
$627$	−2.28513	+	17.6044i	−0.0912594	+	0.703051i
$628$		0			0
$629$	−2.71998	+	2.28234i	−0.108453	+	0.0910028i
$630$		0			0
$631$	5.03370	−	28.5475i	0.200388	−	1.13646i	−0.704145	−	0.710056i	$-0.748670\pi$
$631$	5.03370	−	28.5475i	0.200388	−	1.13646i	0.904533	−	0.426403i	$-0.140219\pi$
$632$		0			0
$633$	9.94438	−	21.9131i	0.395254	−	0.870967i
$634$		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
$639$	−24.9255	−	13.7132i	−0.986038	−	0.542484i
$640$		0			0
$641$	4.38869	+	24.8895i	0.173343	+	0.983076i	0.940039	+	0.341066i	$0.110788\pi$
$641$	4.38869	+	24.8895i	0.173343	+	0.983076i	−0.766696	+	0.642010i	$0.778101\pi$
$642$		0			0
$643$	−11.3227	−	4.12111i	−0.446522	−	0.162521i	0.108966	−	0.994046i	$-0.465246\pi$
$643$	−11.3227	−	4.12111i	−0.446522	−	0.162521i	−0.555488	+	0.831525i	$0.687468\pi$
$644$		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
$651$	−17.9215	−	12.2753i	−0.702400	−	0.481106i
$652$		0			0
$653$	2.53710	+	1.46480i	0.0992846	+	0.0573220i	0.548820	−	0.835940i	$-0.315077\pi$
$653$	2.53710	+	1.46480i	0.0992846	+	0.0573220i	−0.449536	+	0.893262i	$0.648411\pi$
$654$		0			0
$655$	−3.52536	−	2.95812i	−0.137747	−	0.115583i
$656$		0			0
$657$	−0.876345	+	0.530356i	−0.0341895	+	0.0206912i
$658$		0			0
$659$	25.4128	−	9.24952i	0.989944	−	0.360310i	0.204245	−	0.978920i	$-0.434526\pi$
$659$	25.4128	−	9.24952i	0.989944	−	0.360310i	0.785699	+	0.618610i	$0.212304\pi$
$660$		0			0
$661$	13.9832	+	2.46561i	0.543883	+	0.0959013i	0.438838	−	0.898566i	$-0.355390\pi$
$661$	13.9832	+	2.46561i	0.543883	+	0.0959013i	0.105045	+	0.994467i	$0.466501\pi$
$662$		0			0
$663$	−4.60746	−	0.355255i	−0.178939	−	0.0137970i
$664$		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
$669$	12.5610	+	17.5509i	0.485636	+	0.678555i
$670$		0			0
$671$	−0.711543	−	1.95495i	−0.0274688	−	0.0754700i
$672$		0			0
$673$	−4.68491	+	2.70483i	−0.180590	+	0.104264i	−0.587570	−	0.809173i	$-0.699915\pi$
$673$	−4.68491	+	2.70483i	−0.180590	+	0.104264i	0.406980	+	0.913437i	$0.366582\pi$
$674$		0			0
$675$	25.4335	−	3.02057i	0.978936	−	0.116262i
$676$		0			0
$677$	−11.2154	+	19.4256i	−0.431043	+	0.746588i	−0.996963	−	0.0778720i	$-0.975187\pi$
$677$	−11.2154	+	19.4256i	−0.431043	+	0.746588i	0.565921	+	0.824460i	$0.308521\pi$
$678$		0			0
$679$	−7.19722	+	1.26906i	−0.276204	+	0.0487022i
$680$		0			0
$681$	−1.22658	−	2.56110i	−0.0470025	−	0.0981414i
$682$		0			0
$683$	−5.63051			−0.215446			−0.107723	−	0.994181i	$-0.534356\pi$
$683$	−5.63051			−0.215446			−0.107723	+	0.994181i	$0.534356\pi$
$684$		0			0
$685$	−4.87153			−0.186131
$686$		0			0
$687$	−9.09350	−	18.9873i	−0.346939	−	0.724410i
$688$		0			0
$689$	16.8437	−	2.97000i	0.641694	−	0.113148i
$690$		0			0
$691$	−8.10408	+	14.0367i	−0.308294	+	0.533980i	−0.977989	−	0.208655i	$-0.933091\pi$
$691$	−8.10408	+	14.0367i	−0.308294	+	0.533980i	0.669696	+	0.742636i	$0.266425\pi$
$692$		0			0
$693$	6.64640	+	5.34730i	0.252476	+	0.203127i
$694$		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
$699$	2.42836	+	3.39303i	0.0918491	+	0.128336i
$700$		0			0
$701$	25.1621	+	29.9870i	0.950360	+	1.13260i	0.991059	+	0.133424i	$0.0425971\pi$
$701$	25.1621	+	29.9870i	0.950360	+	1.13260i	−0.0406990	+	0.999171i	$0.512958\pi$
$702$		0			0
$703$	15.3748	−	7.83829i	0.579872	−	0.295627i
$704$		0			0
$705$	0.889613	+	0.0685930i	0.0335048	+	0.00258336i
$706$		0			0
$707$	−12.3459	−	2.17692i	−0.464317	−	0.0818715i
$708$		0			0
$709$	−0.294067	+	0.107032i	−0.0110439	+	0.00401966i	−0.347536	−	0.937667i	$-0.612982\pi$
$709$	−0.294067	+	0.107032i	−0.0110439	+	0.00401966i	0.336492	+	0.941686i	$0.390759\pi$
$710$		0			0
$711$	−10.6231	−	17.5533i	−0.398398	−	0.658302i
$712$		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
$717$	27.3589	+	18.7393i	1.02174	+	0.699833i
$718$		0			0
$719$	9.97683	−	27.4111i	0.372073	−	1.02226i	−0.602486	−	0.798130i	$-0.705823\pi$
$719$	9.97683	−	27.4111i	0.372073	−	1.02226i	0.974559	−	0.224132i	$-0.0719548\pi$
$720$		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	0.947996	−	0.318281i	$-0.103106\pi$
$727$	−1.39364	−	7.90374i	−0.0516873	−	0.293133i	−0.999684	+	0.0251476i	$0.991994\pi$
$728$		0			0
$729$	24.1729	+	12.0280i	0.895291	+	0.445482i
$730$		0			0
$731$	−2.76878	+	3.29971i	−0.102407	+	0.122044i
$732$		0			0
$733$	−8.60205	−	14.8992i	−0.317724	−	0.550314i	0.662289	−	0.749249i	$-0.269585\pi$
$733$	−8.60205	−	14.8992i	−0.317724	−	0.550314i	−0.980013	+	0.198935i	$0.936252\pi$
$734$		0			0
$735$	1.05553	−	2.32594i	0.0389340	−	0.0857936i
$736$		0			0
$737$	2.08896	−	11.8471i	0.0769479	−	0.436393i
$738$		0			0
$739$	19.8776	−	16.6793i	0.731210	−	0.613558i	−0.199251	−	0.979948i	$-0.563851\pi$
$739$	19.8776	−	16.6793i	0.731210	−	0.613558i	0.930461	+	0.366390i	$0.119407\pi$
$740$		0			0
$741$	21.4330	+	6.71502i	0.787361	+	0.246682i
$742$		0			0
$743$	35.8677	−	30.0966i	1.31586	−	1.10414i	0.328693	−	0.944437i	$-0.393392\pi$
$743$	35.8677	−	30.0966i	1.31586	−	1.10414i	0.987166	−	0.159700i	$-0.0510527\pi$
$744$		0			0
$745$	0.362158	−	2.05390i	0.0132684	−	0.0752491i
$746$		0			0
$747$	39.4842	−	15.3006i	1.44465	−	0.559819i
$748$		0			0
$749$	9.77655	+	16.9335i	0.357227	+	0.618736i
$750$		0			0
$751$	1.93570	−	2.30687i	0.0706346	−	0.0841791i	−0.729570	−	0.683906i	$-0.760280\pi$
$751$	1.93570	−	2.30687i	0.0706346	−	0.0841791i	0.800205	+	0.599727i	$0.204724\pi$
$752$		0			0
$753$	−1.96217	−	7.03199i	−0.0715055	−	0.256260i
$754$		0			0
$755$	−0.514892	−	2.92010i	−0.0187389	−	0.106273i
$756$		0			0
$757$	6.18347	+	2.25060i	0.224742	+	0.0817994i	0.451937	−	0.892050i	$-0.350733\pi$
$757$	6.18347	+	2.25060i	0.224742	+	0.0817994i	−0.227195	+	0.973849i	$0.572955\pi$
$758$		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
$765$	0.702893	−	0.138946i	0.0254132	−	0.00502362i
$766$		0			0
$767$	32.8968	+	18.9930i	1.18784	+	0.685797i
$768$		0			0
$769$	−28.1846	−	23.6497i	−1.01636	−	0.852830i	−0.0271972	−	0.999630i	$-0.508658\pi$
$769$	−28.1846	−	23.6497i	−1.01636	−	0.852830i	−0.989166	+	0.146800i	$0.953103\pi$
$770$		0			0
$771$	−7.66037	+	29.8157i	−0.275882	+	1.07379i
$772$		0			0
$773$	15.8791	−	5.77952i	0.571132	−	0.207875i	−0.0402788	−	0.999188i	$-0.512825\pi$
$773$	15.8791	−	5.77952i	0.571132	−	0.207875i	0.611411	+	0.791314i	$0.290602\pi$
$774$		0			0
$775$	−50.3416	−	8.87657i	−1.80832	−	0.318856i
$776$		0			0
$777$	0.637520	−	8.26827i	0.0228709	−	0.296623i
$778$		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
$783$	−7.81626	−	10.4585i	−0.279330	−	0.373757i
$784$		0			0
$785$	1.93296	+	5.31077i	0.0689904	+	0.189550i
$786$		0			0
$787$	19.2256	−	11.0999i	0.685319	−	0.395669i	−0.116537	−	0.993186i	$-0.537179\pi$
$787$	19.2256	−	11.0999i	0.685319	−	0.395669i	0.801856	+	0.597517i	$0.203846\pi$
$788$		0			0
$789$	−1.93116	+	0.189045i	−0.0687512	+	0.00673017i
$790$		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
$795$	−2.39172	+	1.14546i	−0.0848255	+	0.0406251i
$796$		0			0
$797$	34.5294			1.22309			0.611547	−	0.791208i	$-0.290547\pi$
$797$	34.5294			1.22309			0.611547	+	0.791208i	$0.290547\pi$
$798$		0			0
$799$	−1.73482			−0.0613736
$800$		0			0
$801$	11.9024	−	34.9270i	0.420550	−	1.23408i
$802$		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
$807$	3.28462	+	33.5536i	0.115624	+	1.18114i
$808$		0			0
$809$	−19.0821	+	11.0171i	−0.670892	+	0.387340i	−0.796415	−	0.604751i	$-0.793273\pi$
$809$	−19.0821	+	11.0171i	−0.670892	+	0.387340i	0.125523	+	0.992091i	$0.459939\pi$
$810$		0			0
$811$	3.43077	+	9.42596i	0.120471	+	0.330990i	0.985240	−	0.171179i	$-0.0547577\pi$
$811$	3.43077	+	9.42596i	0.120471	+	0.330990i	−0.864769	+	0.502169i	$0.832535\pi$
$812$		0			0
$813$	−0.447968	+	0.320607i	−0.0157109	+	0.0112442i
$814$		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
$819$	8.12297	−	7.10660i	0.283840	−	0.248325i
$820$		0			0
$821$	−38.9746	−	6.87227i	−1.36022	−	0.239844i	−0.554523	−	0.832169i	$-0.687099\pi$
$821$	−38.9746	−	6.87227i	−1.36022	−	0.239844i	−0.805699	+	0.592325i	$0.798210\pi$
$822$		0			0
$823$	−35.1506	+	12.7938i	−1.22527	+	0.445963i	−0.871976	−	0.489548i	$-0.837162\pi$
$823$	−35.1506	+	12.7938i	−1.22527	+	0.445963i	−0.353297	+	0.935511i	$0.614939\pi$
$824$		0			0
$825$	19.4427	+	4.99531i	0.676909	+	0.173914i
$826$		0			0
$827$	12.2053	+	10.2415i	0.424421	+	0.356132i	0.829842	−	0.557998i	$-0.188430\pi$
$827$	12.2053	+	10.2415i	0.424421	+	0.356132i	−0.405421	+	0.914130i	$0.632875\pi$
$828$		0			0
$829$	34.9707	+	20.1903i	1.21458	+	0.701239i	0.963754	−	0.266793i	$-0.0859639\pi$
$829$	34.9707	+	20.1903i	1.21458	+	0.701239i	0.250828	+	0.968032i	$0.419297\pi$
$830$		0			0
$831$	−21.4701	+	31.3457i	−0.744790	+	1.08737i
$832$		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	$-0.172188\pi$
$839$	34.2630	+	12.4707i	1.18289	+	0.430537i	0.325669	+	0.945484i	$0.394411\pi$
$840$		0			0
$841$	−3.93940	−	22.3415i	−0.135842	−	0.770396i
$842$		0			0
$843$	25.1717	−	7.02378i	0.866959	−	0.241912i
$844$		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
$849$	10.4738	+	4.75310i	0.359459	+	0.163126i
$850$		0			0
$851$	3.86590	−	21.9246i	0.132521	−	0.751566i
$852$		0			0
$853$	−1.13152	+	0.949455i	−0.0387424	+	0.0325087i	−0.661953	−	0.749545i	$-0.730272\pi$
$853$	−1.13152	+	0.949455i	−0.0387424	+	0.0325087i	0.623211	+	0.782054i	$0.285828\pi$
$854$		0			0
$855$	−3.48069	−	0.109686i	−0.119037	−	0.00375118i
$856$		0			0
$857$	33.3088	−	27.9494i	1.13781	−	0.954734i	0.138443	−	0.990370i	$-0.455790\pi$
$857$	33.3088	−	27.9494i	1.13781	−	0.954734i	0.999365	+	0.0356363i	$0.0113458\pi$
$858$		0			0
$859$	3.97170	−	22.5246i	0.135513	−	0.768530i	−0.838989	−	0.544149i	$-0.816853\pi$
$859$	3.97170	−	22.5246i	0.135513	−	0.768530i	0.974501	−	0.224381i	$-0.0720361\pi$
$860$		0			0
$861$	21.1559	+	9.60076i	0.720991	+	0.327193i
$862$		0			0
$863$	2.34962	+	4.06966i	0.0799820	+	0.138533i	0.903242	−	0.429132i	$-0.141180\pi$
$863$	2.34962	+	4.06966i	0.0799820	+	0.138533i	−0.823260	+	0.567665i	$0.807847\pi$
$864$		0			0
$865$	−1.42644	+	1.69996i	−0.0485003	+	0.0578004i
$866$		0			0
$867$	27.0196	−	7.53942i	0.917634	−	0.256052i
$868$		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	−0.802788	−	0.596264i	$-0.796651\pi$
$877$	5.78823	−	15.9030i	0.195455	−	0.537007i	0.998243	+	0.0592572i	$0.0188732\pi$
$878$		0			0
$879$	27.8027	−	40.5911i	0.937762	−	1.36910i
$880$		0			0
$881$	8.11257	+	4.68379i	0.273319	+	0.157801i	0.630395	−	0.776274i	$-0.282893\pi$
$881$	8.11257	+	4.68379i	0.273319	+	0.157801i	−0.357076	+	0.934075i	$0.616226\pi$
$882$		0			0
$883$	9.97646	+	8.37124i	0.335735	+	0.281715i	0.795032	−	0.606568i	$-0.207454\pi$
$883$	9.97646	+	8.37124i	0.335735	+	0.281715i	−0.459297	+	0.888283i	$0.651899\pi$
$884$		0			0
$885$	−5.70437	−	1.46559i	−0.191750	−	0.0492653i
$886$		0			0
$887$	−19.4826	+	7.09109i	−0.654162	+	0.238095i	−0.647714	−	0.761884i	$-0.724275\pi$
$887$	−19.4826	+	7.09109i	−0.654162	+	0.238095i	−0.00644793	+	0.999979i	$0.502052\pi$
$888$		0			0
$889$	−7.04801	−	1.24275i	−0.236383	−	0.0416806i
$890$		0			0
$891$	14.2596	+	15.6361i	0.477716	+	0.523828i
$892$		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
$897$	23.5619	−	16.8630i	0.786708	−	0.563040i
$898$		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
$903$	−0.980136	−	10.0124i	−0.0326169	−	0.333193i
$904$		0			0
$905$	−1.22421	+	2.12039i	−0.0406940	+	0.0704840i
$906$		0			0
$907$	13.6673	−	2.40991i	0.453815	−	0.0800198i	0.0579313	−	0.998321i	$-0.481550\pi$
$907$	13.6673	−	2.40991i	0.453815	−	0.0800198i	0.395883	+	0.918301i	$0.370438\pi$
$908$		0			0
$909$	−29.4373	−	10.0316i	−0.976373	−	0.332728i
$910$		0			0
$911$	−16.4560			−0.545212			−0.272606	−	0.962126i	$-0.587885\pi$
$911$	−16.4560			−0.545212			−0.272606	+	0.962126i	$0.587885\pi$
$912$		0			0
$913$	33.1889			1.09839
$914$		0			0
$915$	0.368078	−	0.176282i	0.0121683	−	0.00582771i
$916$		0			0
$917$	−20.5805	+	3.62890i	−0.679629	+	0.119837i
$918$		0			0
$919$	26.4636	−	45.8364i	0.872955	−	1.51200i	0.0140292	−	0.999902i	$-0.495534\pi$
$919$	26.4636	−	45.8364i	0.872955	−	1.51200i	0.858926	−	0.512100i	$-0.171132\pi$
$920$		0			0
$921$	−7.51462	+	0.735619i	−0.247615	+	0.0242395i
$922$		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
$927$	−6.79695	+	43.8143i	−0.223241	+	1.43905i
$928$		0			0
$929$	35.2607	+	42.0221i	1.15687	+	1.37870i	0.912530	+	0.409010i	$0.134126\pi$
$929$	35.2607	+	42.0221i	1.15687	+	1.37870i	0.244337	+	0.969690i	$0.421430\pi$
$930$		0			0
$931$	13.1417	−	20.2466i	0.430702	−	0.663555i
$932$		0			0
$933$	0.632049	−	8.19731i	0.0206923	−	0.268368i
$934$		0			0
$935$	0.553038	+	0.0975154i	0.0180863	+	0.00318910i
$936$		0			0
$937$	−50.8597	+	18.5114i	−1.66151	+	0.604741i	−0.990599	−	0.136794i	$-0.956320\pi$
$937$	−50.8597	+	18.5114i	−1.66151	+	0.604741i	−0.670914	+	0.741536i	$0.734098\pi$
$938$		0			0
$939$	−8.15959	+	31.7587i	−0.266278	+	1.03641i
$940$		0			0
$941$	−3.61129	−	3.03024i	−0.117725	−	0.0987829i	0.582025	−	0.813171i	$-0.302261\pi$
$941$	−3.61129	−	3.03024i	−0.117725	−	0.0987829i	−0.699750	+	0.714388i	$0.746705\pi$
$942$		0			0
$943$	54.0137	+	31.1848i	1.75893	+	1.01552i
$944$		0			0
$945$	−0.916961	+	1.39982i	−0.0298287	+	0.0455361i
$946$		0			0
$947$	−3.75659	+	10.3211i	−0.122073	+	0.335392i	−0.985645	−	0.168834i	$-0.946000\pi$
$947$	−3.75659	+	10.3211i	−0.122073	+	0.335392i	0.863572	+	0.504226i	$0.168222\pi$
$948$		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	$-0.406225\pi$
$953$	−3.15832	−	1.14953i	−0.102308	−	0.0372371i	−0.392667	+	0.919681i	$0.628448\pi$
$954$		0			0
$955$	−0.339083	−	1.92303i	−0.0109725	−	0.0622279i
$956$		0			0
$957$	−2.75041	−	9.85686i	−0.0889081	−	0.318627i
$958$		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
$963$	17.5268	+	45.2291i	0.564794	+	1.45749i
$964$		0			0
$965$	−0.0828985	+	0.470141i	−0.00266860	+	0.0151344i
$966$		0			0
$967$	14.0085	−	11.7545i	0.450482	−	0.377999i	−0.389133	−	0.921182i	$-0.627225\pi$
$967$	14.0085	−	11.7545i	0.450482	−	0.377999i	0.839615	+	0.543183i	$0.182781\pi$
$968$		0			0
$969$	6.76392	−	0.307630i	0.217288	−	0.00988251i
$970$		0			0
$971$	−24.2199	+	20.3229i	−0.777254	+	0.652193i	−0.942555	−	0.334050i	$-0.891585\pi$
$971$	−24.2199	+	20.3229i	−0.777254	+	0.652193i	0.165302	+	0.986243i	$0.447140\pi$
$972$		0			0
$973$	−0.482826	+	2.73824i	−0.0154787	+	0.0877839i
$974$		0			0
$975$	10.4958	−	23.1282i	0.336134	−	0.740694i
$976$		0			0
$977$	24.2192	+	41.9488i	0.774839	+	1.34206i	0.934885	+	0.354952i	$0.115503\pi$
$977$	24.2192	+	41.9488i	0.774839	+	1.34206i	−0.160045	+	0.987110i	$0.551164\pi$
$978$		0			0
$979$	18.5898	−	22.1545i	0.594134	−	0.708061i
$980$		0			0
$981$	−26.4130	+	48.0092i	−0.843301	+	1.53281i
$982$		0			0
$983$	4.70703	+	26.6949i	0.150131	+	0.851435i	0.963103	+	0.269133i	$0.0867370\pi$
$983$	4.70703	+	26.6949i	0.150131	+	0.851435i	−0.812972	+	0.582303i	$0.802152\pi$
$984$		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	0.333109	+	0.942888i	$0.391902\pi$
$991$	−16.6261	+	45.6797i	−0.528144	+	1.45106i	−0.861253	+	0.508176i	$0.830320\pi$
$992$		0			0
$993$	5.29022	+	3.62351i	0.167880	+	0.114989i
$994$		0			0
$995$	−2.41248	−	1.39285i	−0.0764808	−	0.0441562i
$996$		0			0
$997$	−7.46423	−	6.26323i	−0.236394	−	0.198358i	0.516893	−	0.856050i	$-0.327089\pi$
$997$	−7.46423	−	6.26323i	−0.236394	−	0.198358i	−0.753287	+	0.657692i	$0.771533\pi$
$998$		0			0
$999$	4.70719	−	20.0266i	0.148929	−	0.633614i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.41.3	✓	18	76.3	even	18
114.2.l.a.89.3	yes	18	12.11	even	2
114.2.l.b.41.1	yes	18	228.155	odd	18
114.2.l.b.89.1	yes	18	4.3	odd	2
912.2.cc.c.497.3		18	57.41	even	18	inner
912.2.cc.c.545.3		18	1.1	even	1	trivial
912.2.cc.d.497.1		18	19.3	odd	18
912.2.cc.d.545.1		18	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(0.748148 + 1.56214i) q^{3} +(-0.262261 + 0.0462437i) q^{5} +(-0.604656 + 1.04730i) q^{7} +(-1.88055 + 2.33742i) q^{9} +O(q^{10})\)	\(q+(0.748148 + 1.56214i) q^{3} +(-0.262261 + 0.0462437i) q^{5} +(-0.604656 + 1.04730i) q^{7} +(-1.88055 + 2.33742i) q^{9} +(-2.03630 + 1.17566i) q^{11} +(1.01749 + 2.79553i) q^{13} +(-0.268449 - 0.375091i) q^{15} +(0.576470 + 0.687011i) q^{17} +(-1.97979 - 3.88335i) q^{19} +(-2.08839 - 0.161024i) q^{21} +(-5.53770 - 0.976446i) q^{23} +(-4.63182 + 1.68584i) q^{25} +(-5.05830 - 1.18894i) q^{27} +(1.92487 + 1.61516i) q^{29} +(8.98131 + 5.18536i) q^{31} +(-3.36000 - 2.30141i) q^{33} +(0.110147 - 0.302626i) q^{35} +3.95916i q^{37} +(-3.60577 + 3.68093i) q^{39} +(-10.4227 - 3.79356i) q^{41} +(0.834031 + 4.73003i) q^{43} +(0.385104 - 0.699978i) q^{45} +(-1.24341 + 1.48183i) q^{47} +(2.76878 + 4.79567i) q^{49} +(-0.641920 + 1.41451i) q^{51} +(0.998339 - 5.66186i) q^{53} +(0.479676 - 0.402496i) q^{55} +(4.58516 - 5.99803i) q^{57} +(9.78136 - 8.20754i) q^{59} +(-0.153642 + 0.871345i) q^{61} +(-1.31088 - 3.38283i) q^{63} +(-0.396123 - 0.686106i) q^{65} +(-3.28864 + 3.91925i) q^{67} +(-2.61768 - 9.38117i) q^{69} +(1.64669 + 9.33885i) q^{71} +(0.320853 + 0.116781i) q^{73} +(-6.09881 - 5.97428i) q^{75} -2.84348i q^{77} +(-2.33914 + 6.42674i) q^{79} +(-1.92708 - 8.79127i) q^{81} +(-12.2240 - 7.05752i) q^{83} +(-0.182956 - 0.153518i) q^{85} +(-1.08301 + 4.21529i) q^{87} +(-11.5580 + 4.20677i) q^{89} +(-3.54297 - 0.624722i) q^{91} +(-1.38090 + 17.9095i) q^{93} +(0.698802 + 0.926900i) q^{95} +(3.88456 + 4.62944i) q^{97} +(1.08135 - 6.97057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{3} - 3 q^{9}+O(q^{10}) \) 18 * q - 3 * q^3 - 3 * q^9	\( 18 q - 3 q^{3} - 3 q^{9} - 12 q^{13} - 18 q^{15} + 6 q^{17} + 6 q^{19} - 18 q^{25} + 6 q^{27} - 6 q^{29} - 24 q^{33} + 24 q^{35} - 6 q^{39} + 3 q^{41} + 6 q^{43} - 54 q^{45} - 30 q^{47} + 21 q^{49} - 42 q^{51} - 60 q^{53} - 30 q^{55} + 12 q^{57} - 3 q^{59} + 54 q^{61} + 18 q^{63} + 24 q^{65} + 15 q^{67} + 30 q^{69} - 36 q^{71} - 42 q^{73} + 6 q^{79} - 3 q^{81} - 36 q^{83} - 60 q^{89} + 18 q^{91} - 66 q^{93} - 6 q^{95} + 9 q^{97} + 102 q^{99}+O(q^{100}) \) 18 * q - 3 * q^3 - 3 * q^9 - 12 * q^13 - 18 * q^15 + 6 * q^17 + 6 * q^19 - 18 * q^25 + 6 * q^27 - 6 * q^29 - 24 * q^33 + 24 * q^35 - 6 * q^39 + 3 * q^41 + 6 * q^43 - 54 * q^45 - 30 * q^47 + 21 * q^49 - 42 * q^51 - 60 * q^53 - 30 * q^55 + 12 * q^57 - 3 * q^59 + 54 * q^61 + 18 * q^63 + 24 * q^65 + 15 * q^67 + 30 * q^69 - 36 * q^71 - 42 * q^73 + 6 * q^79 - 3 * q^81 - 36 * q^83 - 60 * q^89 + 18 * q^91 - 66 * q^93 - 6 * q^95 + 9 * q^97 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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