LMFDB - Embedded newform 351.2.bf.a.305.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(206,351)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(351, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("351.206"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.bf (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			305.4
Character	$\chi$	$=$	351.305
Dual form			351.2.bf.a.206.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.308060 + 1.14969i) q^{2} +(0.505155 + 0.291651i) q^{4} +(0.744040 - 2.77680i) q^{5} +(1.04357 + 1.04357i) q^{7} +(-2.17420 + 2.17420i) q^{8} +(2.96326 + 1.71084i) q^{10} +(1.68335 + 0.451052i) q^{11} +(1.90363 - 3.06206i) q^{13} +(-1.52127 + 0.878303i) q^{14} +(-1.24658 - 2.15913i) q^{16} +(0.939625 + 1.62748i) q^{17} +(4.34907 + 1.16533i) q^{19} +(1.18571 - 1.18571i) q^{20} +(-1.03714 + 1.79639i) q^{22} +5.65176 q^{23} +(-2.82688 - 1.63210i) q^{25} +(2.93400 + 3.13189i) q^{26} +(0.222806 + 0.831522i) q^{28} +(-5.80315 + 3.35045i) q^{29} +(-2.52515 - 0.676611i) q^{31} +(-3.07365 + 0.823583i) q^{32} +(-2.16056 + 0.578921i) q^{34} +(3.67424 - 2.12132i) q^{35} +(-11.1775 + 2.99499i) q^{37} +(-2.67955 + 4.64111i) q^{38} +(4.41961 + 7.65499i) q^{40} +(0.459167 + 0.459167i) q^{41} -2.05612i q^{43} +(0.718802 + 0.718802i) q^{44} +(-1.74108 + 6.49779i) q^{46} +(-0.619735 - 2.31288i) q^{47} -4.82193i q^{49} +(2.74726 - 2.74726i) q^{50} +(1.85468 - 0.991618i) q^{52} +11.5633i q^{53} +(2.50496 - 4.33872i) q^{55} -4.53785 q^{56} +(-2.06428 - 7.70398i) q^{58} +(-3.35246 - 12.5115i) q^{59} +10.4856 q^{61} +(1.55579 - 2.69471i) q^{62} -8.77378i q^{64} +(-7.08634 - 7.56428i) q^{65} +(-2.56688 + 2.56688i) q^{67} +1.09617i q^{68} +(1.30699 + 4.87774i) q^{70} +(2.99663 - 11.1836i) q^{71} +(-8.97423 - 8.97423i) q^{73} -13.7733i q^{74} +(1.85709 + 1.85709i) q^{76} +(1.28599 + 2.22739i) q^{77} +(-4.85927 + 8.41651i) q^{79} +(-6.92298 + 1.85501i) q^{80} +(-0.669352 + 0.386451i) q^{82} +(-2.65776 + 0.712145i) q^{83} +(5.21830 - 1.39824i) q^{85} +(2.36391 + 0.633407i) q^{86} +(-4.64061 + 2.67926i) q^{88} +(-1.57286 - 5.86998i) q^{89} +(5.18203 - 1.20890i) q^{91} +(2.85501 + 1.64834i) q^{92} +2.85002 q^{94} +(6.47177 - 11.2094i) q^{95} +(-3.70756 + 3.70756i) q^{97} +(5.54374 + 1.48544i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{2} - 6 q^{4} + 6 q^{5} + 2 q^{7} + 30 q^{8} - 12 q^{10} - 6 q^{11} - 2 q^{13} + 12 q^{14} + 14 q^{16} - 4 q^{19} + 6 q^{20} + 2 q^{22} + 12 q^{23} - 48 q^{26} + 6 q^{29} + 6 q^{31} - 30 q^{32}+ \cdots + 36 q^{98}+O(q^{100}) $ 48 * q + 6 * q^2 - 6 * q^4 + 6 * q^5 + 2 * q^7 + 30 * q^8 - 12 * q^10 - 6 * q^11 - 2 * q^13 + 12 * q^14 + 14 * q^16 - 4 * q^19 + 6 * q^20 + 2 * q^22 + 12 * q^23 - 48 * q^26 + 6 * q^29 + 6 * q^31 - 30 * q^32 - 6 * q^34 + 6 * q^35 - 6 * q^37 + 36 * q^38 - 12 * q^40 - 18 * q^41 + 12 * q^44 - 12 * q^46 - 30 * q^47 + 12 * q^50 - 16 * q^52 - 4 * q^55 + 12 * q^56 - 28 * q^58 - 30 * q^59 - 4 * q^61 + 18 * q^62 - 30 * q^65 - 16 * q^67 - 46 * q^70 - 48 * q^71 - 22 * q^73 - 18 * q^76 + 72 * q^77 + 8 * q^79 - 54 * q^80 - 12 * q^82 - 72 * q^83 + 78 * q^85 - 102 * q^86 - 6 * q^88 - 16 * q^91 - 120 * q^92 - 52 * q^94 + 6 * q^95 + 48 * q^97 + 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.308060	+	1.14969i	−0.217831	+	0.812956i	0.767320	+	0.641265i	$0.221590\pi$
$2$	−0.308060	+	1.14969i	−0.217831	+	0.812956i	−0.985151	+	0.171692i	$0.945077\pi$
$3$		0			0
$3$		0			0
$4$	0.505155	+	0.291651i	0.252578	+	0.145826i
$5$	0.744040	−	2.77680i	0.332745	−	1.24182i	−0.573548	−	0.819172i	$-0.694433\pi$
$5$	0.744040	−	2.77680i	0.332745	−	1.24182i	0.906293	−	0.422650i	$-0.138900\pi$
$6$		0			0
$7$	1.04357	+	1.04357i	0.394432	+	0.394432i	0.876264	−	0.481832i	$-0.160028\pi$
$7$	1.04357	+	1.04357i	0.394432	+	0.394432i	−0.481832	+	0.876264i	$0.660028\pi$
$8$	−2.17420	+	2.17420i	−0.768695	+	0.768695i
$9$		0			0
$10$	2.96326	+	1.71084i	0.937065	+	0.541014i
$11$	1.68335	+	0.451052i	0.507549	+	0.135997i	0.503501	−	0.863994i	$-0.332045\pi$
$11$	1.68335	+	0.451052i	0.507549	+	0.135997i	0.00404763	+	0.999992i	$0.498712\pi$
$12$		0			0
$13$	1.90363	−	3.06206i	0.527971	−	0.849262i
$13$	1.90363	−	3.06206i	0.527971	−	0.849262i
$14$	−1.52127	+	0.878303i	−0.406575	+	0.234736i
$15$		0			0
$16$	−1.24658	−	2.15913i	−0.311644	−	0.539783i
$17$	0.939625	+	1.62748i	0.227893	+	0.394722i	0.957183	−	0.289482i	$-0.0934831\pi$
$17$	0.939625	+	1.62748i	0.227893	+	0.394722i	−0.729291	+	0.684204i	$0.760150\pi$
$18$		0			0
$19$	4.34907	+	1.16533i	0.997745	+	0.267345i	0.720501	−	0.693454i	$-0.243912\pi$
$19$	4.34907	+	1.16533i	0.997745	+	0.267345i	0.277245	+	0.960799i	$0.410579\pi$
$20$	1.18571	−	1.18571i	0.265133	−	0.265133i
$21$		0			0
$22$	−1.03714	+	1.79639i	−0.221120	+	0.382991i
$23$	5.65176			1.17847			0.589237	−	0.807961i	$-0.299429\pi$
$23$	5.65176			1.17847			0.589237	+	0.807961i	$0.299429\pi$
$24$		0			0
$25$	−2.82688	−	1.63210i	−0.565376	−	0.326420i
$26$	2.93400	+	3.13189i	0.575405	+	0.614213i
$27$		0			0
$28$	0.222806	+	0.831522i	0.0421063	+	0.157143i
$29$	−5.80315	+	3.35045i	−1.07762	+	0.622162i	−0.930253	−	0.366920i	$-0.880412\pi$
$29$	−5.80315	+	3.35045i	−1.07762	+	0.622162i	−0.147364	+	0.989082i	$0.547079\pi$
$30$		0			0
$31$	−2.52515	−	0.676611i	−0.453530	−	0.121523i	0.0248208	−	0.999692i	$-0.492098\pi$
$31$	−2.52515	−	0.676611i	−0.453530	−	0.121523i	−0.478350	+	0.878169i	$0.658765\pi$
$32$	−3.07365	+	0.823583i	−0.543350	+	0.145590i
$33$		0			0
$34$	−2.16056	+	0.578921i	−0.370534	+	0.0992842i
$35$	3.67424	−	2.12132i	0.621059	−	0.358569i
$36$		0			0
$37$	−11.1775	+	2.99499i	−1.83756	+	0.492374i	−0.998653	−	0.0518927i	$-0.983475\pi$
$37$	−11.1775	+	2.99499i	−1.83756	+	0.492374i	−0.838912	+	0.544267i	$0.816808\pi$
$38$	−2.67955	+	4.64111i	−0.434680	+	0.752888i
$39$		0			0
$40$	4.41961	+	7.65499i	0.698802	+	1.21036i
$41$	0.459167	+	0.459167i	0.0717098	+	0.0717098i	0.742052	−	0.670342i	$-0.233853\pi$
$41$	0.459167	+	0.459167i	0.0717098	+	0.0717098i	−0.670342	+	0.742052i	$0.733853\pi$
$42$		0			0
$43$		−	2.05612i		−	0.313555i	−0.987634	−	0.156778i	$-0.949889\pi$
$43$		−	2.05612i		−	0.313555i	0.987634	−	0.156778i	$-0.0501106\pi$
$44$	0.718802	+	0.718802i	0.108364	+	0.108364i
$45$		0			0
$46$	−1.74108	+	6.49779i	−0.256708	+	0.958048i
$47$	−0.619735	−	2.31288i	−0.0903977	−	0.337369i	0.905884	−	0.423526i	$-0.139208\pi$
$47$	−0.619735	−	2.31288i	−0.0903977	−	0.337369i	−0.996282	+	0.0861575i	$0.972541\pi$
$48$		0			0
$49$		−	4.82193i		−	0.688847i
$50$	2.74726	−	2.74726i	0.388521	−	0.388521i
$51$		0			0
$52$	1.85468	−	0.991618i	0.257198	−	0.137513i
$53$			11.5633i			1.58834i	0.607698	+	0.794168i	$0.292093\pi$
$53$			11.5633i			1.58834i	−0.607698	+	0.794168i	$0.707907\pi$
$54$		0			0
$55$	2.50496	−	4.33872i	0.337769	−	0.585033i
$56$	−4.53785			−0.606395
$57$		0			0
$58$	−2.06428	−	7.70398i	−0.271053	−	1.01158i
$59$	−3.35246	−	12.5115i	−0.436453	−	1.62886i	−0.737566	−	0.675275i	$-0.764025\pi$
$59$	−3.35246	−	12.5115i	−0.436453	−	1.62886i	0.301113	−	0.953589i	$-0.402642\pi$
$60$		0			0
$61$	10.4856			1.34254			0.671269	−	0.741213i	$-0.265749\pi$
$61$	10.4856			1.34254			0.671269	+	0.741213i	$0.265749\pi$
$62$	1.55579	−	2.69471i	0.197586	−	0.342228i
$63$		0			0
$64$		−	8.77378i		−	1.09672i
$65$	−7.08634	−	7.56428i	−0.878952	−	0.938234i
$66$		0			0
$67$	−2.56688	+	2.56688i	−0.313595	+	0.313595i	−0.846300	−	0.532706i	$-0.821175\pi$
$67$	−2.56688	+	2.56688i	−0.313595	+	0.313595i	0.532706	+	0.846300i	$0.321175\pi$
$68$			1.09617i			0.132930i
$69$		0			0
$70$	1.30699	+	4.87774i	0.156215	+	0.583001i
$71$	2.99663	−	11.1836i	0.355635	−	1.32725i	−0.524049	−	0.851688i	$-0.675579\pi$
$71$	2.99663	−	11.1836i	0.355635	−	1.32725i	0.879684	−	0.475559i	$-0.157754\pi$
$72$		0			0
$73$	−8.97423	−	8.97423i	−1.05035	−	1.05035i	−0.998663	−	0.0516906i	$-0.983539\pi$
$73$	−8.97423	−	8.97423i	−1.05035	−	1.05035i	−0.0516906	−	0.998663i	$-0.516461\pi$
$74$		−	13.7733i		−	1.60111i
$75$		0			0
$76$	1.85709	+	1.85709i	0.213022	+	0.213022i
$77$	1.28599	+	2.22739i	0.146552	+	0.253835i
$78$		0			0
$79$	−4.85927	+	8.41651i	−0.546711	+	0.946931i	0.451786	+	0.892126i	$0.350787\pi$
$79$	−4.85927	+	8.41651i	−0.546711	+	0.946931i	−0.998497	+	0.0548048i	$0.982546\pi$
$80$	−6.92298	+	1.85501i	−0.774012	+	0.207396i
$81$		0			0
$82$	−0.669352	+	0.386451i	−0.0739176	+	0.0426763i
$83$	−2.65776	+	0.712145i	−0.291727	+	0.0781681i	−0.401715	−	0.915765i	$-0.631586\pi$
$83$	−2.65776	+	0.712145i	−0.291727	+	0.0781681i	0.109987	+	0.993933i	$0.464919\pi$
$84$		0			0
$85$	5.21830	−	1.39824i	0.566004	−	0.151660i
$86$	2.36391	+	0.633407i	0.254907	+	0.0683020i
$87$		0			0
$88$	−4.64061	+	2.67926i	−0.494690	+	0.285610i
$89$	−1.57286	−	5.86998i	−0.166722	−	0.622217i	−0.997814	−	0.0660814i	$-0.978950\pi$
$89$	−1.57286	−	5.86998i	−0.166722	−	0.622217i	0.831092	−	0.556135i	$-0.187716\pi$
$90$		0			0
$91$	5.18203	−	1.20890i	0.543225	−	0.126727i
$92$	2.85501	+	1.64834i	0.297656	+	0.171852i
$93$		0			0
$94$	2.85002			0.293957
$95$	6.47177	−	11.2094i	0.663990	−	1.15006i
$96$		0			0
$97$	−3.70756	+	3.70756i	−0.376446	+	0.376446i	−0.869818	−	0.493372i	$-0.835764\pi$
$97$	−3.70756	+	3.70756i	−0.376446	+	0.376446i	0.493372	+	0.869818i	$0.335764\pi$
$98$	5.54374	+	1.48544i	0.560003	+	0.150052i
$99$		0			0
$100$	−0.952008	−	1.64893i	−0.0952008	−	0.164893i
$101$	1.51426	+	2.62277i	0.150674	+	0.260975i	0.931475	−	0.363804i	$-0.118522\pi$
$101$	1.51426	+	2.62277i	0.150674	+	0.260975i	−0.780801	+	0.624779i	$0.785189\pi$
$102$		0			0
$103$	−15.9431	+	9.20475i	−1.57092	+	0.906971i	−0.574864	+	0.818249i	$0.694945\pi$
$103$	−15.9431	+	9.20475i	−1.57092	+	0.906971i	−0.996056	+	0.0887220i	$0.971722\pi$
$104$	2.51865	+	10.7964i	0.246974	+	1.05867i
$105$		0			0
$106$	−13.2942	−	3.56217i	−1.29125	−	0.345989i
$107$	3.97340	+	2.29404i	0.384123	+	0.221774i	0.679611	−	0.733573i	$-0.262149\pi$
$107$	3.97340	+	2.29404i	0.384123	+	0.221774i	−0.295487	+	0.955347i	$0.595482\pi$
$108$		0			0
$109$	0.138592	−	0.138592i	0.0132747	−	0.0132747i	−0.700438	−	0.713713i	$-0.747012\pi$
$109$	0.138592	−	0.138592i	0.0132747	−	0.0132747i	0.713713	+	0.700438i	$0.247012\pi$
$110$	4.21652	+	4.21652i	0.402030	+	0.402030i
$111$		0			0
$112$	0.952316	−	3.55409i	0.0899854	−	0.335830i
$113$	−6.46742	−	3.73397i	−0.608404	−	0.351262i	0.163937	−	0.986471i	$-0.447581\pi$
$113$	−6.46742	−	3.73397i	−0.608404	−	0.351262i	−0.772341	+	0.635209i	$0.780914\pi$
$114$		0			0
$115$	4.20514	−	15.6938i	0.392131	−	1.46345i
$116$	−3.90865			−0.362909
$117$		0			0
$118$	15.4172			1.41927
$119$	−0.717822	+	2.67895i	−0.0658027	+	0.245579i
$120$		0			0
$121$	−6.89606	−	3.98144i	−0.626915	−	0.361949i
$122$	−3.23018	+	12.0552i	−0.292447	+	1.09143i
$123$		0			0
$124$	−1.07826	−	1.07826i	−0.0968302	−	0.0968302i
$125$	3.52846	−	3.52846i	0.315595	−	0.315595i
$126$		0			0
$127$	−9.37062	−	5.41013i	−0.831508	−	0.480071i	0.0228608	−	0.999739i	$-0.492723\pi$
$127$	−9.37062	−	5.41013i	−0.831508	−	0.480071i	−0.854369	+	0.519667i	$0.826056\pi$
$128$	3.93985	+	1.05568i	0.348237	+	0.0933099i
$129$		0			0
$130$	10.8796	−	5.81687i	0.954206	−	0.510173i
$131$	−6.84566	+	3.95234i	−0.598108	+	0.345318i	−0.768297	−	0.640094i	$-0.778896\pi$
$131$	−6.84566	+	3.95234i	−0.598108	+	0.345318i	0.170189	+	0.985411i	$0.445562\pi$
$132$		0			0
$133$	3.32245	+	5.75466i	0.288093	+	0.498992i
$134$	−2.16038	−	3.74188i	−0.186628	−	0.323249i
$135$		0			0
$136$	−5.58139	−	1.49553i	−0.478600	−	0.128241i
$137$	−5.98485	+	5.98485i	−0.511320	+	0.511320i	−0.914931	−	0.403611i	$-0.867755\pi$
$137$	−5.98485	+	5.98485i	−0.511320	+	0.511320i	0.403611	+	0.914931i	$0.367755\pi$
$138$		0			0
$139$	−0.234959	+	0.406962i	−0.0199290	+	0.0345180i	−0.875818	−	0.482642i	$-0.839677\pi$
$139$	−0.234959	+	0.406962i	−0.0199290	+	0.0345180i	0.855889	+	0.517160i	$0.173011\pi$
$140$	2.47474			0.209154
$141$		0			0
$142$	11.9346	+	6.89042i	1.00153	+	0.578231i
$143$	4.58562	−	4.29588i	0.383469	−	0.359239i
$144$		0			0
$145$	4.98574	+	18.6070i	0.414043	+	1.54523i
$146$	13.0822	−	7.55302i	1.08269	−	0.625092i
$147$		0			0
$148$	−6.51985	−	1.74699i	−0.535928	−	0.143602i
$149$	5.24080	−	1.40427i	0.429343	−	0.115042i	−0.0376745	−	0.999290i	$-0.511995\pi$
$149$	5.24080	−	1.40427i	0.429343	−	0.115042i	0.467018	+	0.884248i	$0.345328\pi$
$150$		0			0
$151$	19.1087	−	5.12016i	1.55504	−	0.416673i	0.623953	−	0.781462i	$-0.285525\pi$
$151$	19.1087	−	5.12016i	1.55504	−	0.416673i	0.931090	+	0.364789i	$0.118859\pi$
$152$	−11.9894	+	6.92208i	−0.972468	+	0.561455i
$153$		0			0
$154$	−2.95698	+	0.792321i	−0.238280	+	0.0638470i
$155$	−3.75762	+	6.50839i	−0.301819	+	0.522767i
$156$		0			0
$157$	11.5326	+	19.9750i	0.920401	+	1.59418i	0.798796	+	0.601602i	$0.205471\pi$
$157$	11.5326	+	19.9750i	0.920401	+	1.59418i	0.121605	+	0.992579i	$0.461196\pi$
$158$	−8.17946	−	8.17946i	−0.650723	−	0.650723i
$159$		0			0
$160$			9.14769i			0.723188i
$161$	5.89800	+	5.89800i	0.464827	+	0.464827i
$162$		0			0
$163$	1.15428	−	4.30782i	0.0904100	−	0.337415i	−0.905874	−	0.423548i	$-0.860784\pi$
$163$	1.15428	−	4.30782i	0.0904100	−	0.337415i	0.996284	+	0.0861334i	$0.0274511\pi$
$164$	0.0980338	+	0.365867i	0.00765515	+	0.0285694i
$165$		0			0
$166$		−	3.27500i		−	0.254189i
$167$	−0.251999	+	0.251999i	−0.0195002	+	0.0195002i	−0.716790	−	0.697289i	$-0.754389\pi$
$167$	−0.251999	+	0.251999i	−0.0195002	+	0.0195002i	0.697289	+	0.716790i	$0.254389\pi$
$168$		0			0
$169$	−5.75240	−	11.6580i	−0.442492	−	0.896772i
$170$			6.43019i			0.493173i
$171$		0			0
$172$	0.599670	−	1.03866i	0.0457244	−	0.0791970i
$173$	11.8976			0.904559			0.452280	−	0.891876i	$-0.350611\pi$
$173$	11.8976			0.904559			0.452280	+	0.891876i	$0.350611\pi$
$174$		0			0
$175$	−1.24683	−	4.65325i	−0.0942518	−	0.351752i
$176$	−1.12454	−	4.19685i	−0.0847655	−	0.316349i
$177$		0			0
$178$	7.23322			0.542152
$179$	−2.92970	+	5.07439i	−0.218976	+	0.379278i	−0.954495	−	0.298226i	$-0.903605\pi$
$179$	−2.92970	+	5.07439i	−0.218976	+	0.379278i	0.735519	+	0.677504i	$0.236938\pi$
$180$		0			0
$181$			8.29778i			0.616769i	0.951262	+	0.308384i	$0.0997883\pi$
$181$			8.29778i			0.616769i	−0.951262	+	0.308384i	$0.900212\pi$
$182$	−0.206509	+	6.33017i	−0.0153075	+	0.469223i
$183$		0			0
$184$	−12.2880	+	12.2880i	−0.905886	+	0.905886i
$185$			33.2660i			2.44576i
$186$		0			0
$187$	0.847640	+	3.16344i	0.0619856	+	0.231333i
$188$	0.361493	−	1.34911i	0.0263646	−	0.0983940i
$189$		0			0
$190$	10.8937	+	10.8937i	0.790314	+	0.790314i
$191$			7.16012i			0.518088i	0.965865	+	0.259044i	$0.0834075\pi$
$191$			7.16012i			0.518088i	−0.965865	+	0.259044i	$0.916592\pi$
$192$		0			0
$193$	−1.93708	−	1.93708i	−0.139434	−	0.139434i	0.633945	−	0.773378i	$-0.281435\pi$
$193$	−1.93708	−	1.93708i	−0.139434	−	0.139434i	−0.773378	+	0.633945i	$0.781435\pi$
$194$	−3.12041	−	5.40471i	−0.224033	−	0.388036i
$195$		0			0
$196$	1.40632	−	2.43582i	0.100452	−	0.173987i
$197$	−23.1428	+	6.20110i	−1.64886	+	0.441810i	−0.959292	−	0.282414i	$-0.908865\pi$
$197$	−23.1428	+	6.20110i	−1.64886	+	0.441810i	−0.689564	+	0.724224i	$0.742198\pi$
$198$		0			0
$199$	8.08608	−	4.66850i	0.573207	−	0.330941i	−0.185222	−	0.982697i	$-0.559300\pi$
$199$	8.08608	−	4.66850i	0.573207	−	0.330941i	0.758429	+	0.651755i	$0.225967\pi$
$200$	9.69469	−	2.59768i	0.685518	−	0.183684i
$201$		0			0
$202$	−3.48186	+	0.932962i	−0.244983	+	0.0656429i
$203$	−9.55240	−	2.55956i	−0.670447	−	0.179646i
$204$		0			0
$205$	1.61665	−	0.933374i	0.112912	−	0.0651897i
$206$	−5.67122	−	21.1653i	−0.395133	−	1.47466i
$207$		0			0
$208$	−8.98441	−	0.293098i	−0.622957	−	0.0203227i
$209$	6.79538	+	3.92332i	0.470046	+	0.271381i
$210$		0			0
$211$	5.21114			0.358750			0.179375	−	0.983781i	$-0.442592\pi$
$211$	5.21114			0.358750			0.179375	+	0.983781i	$0.442592\pi$
$212$	−3.37244	+	5.84124i	−0.231620	+	0.401178i
$213$		0			0
$214$	−3.86149	+	3.86149i	−0.263966	+	0.263966i
$215$	−5.70942	−	1.52984i	−0.389379	−	0.104334i
$216$		0			0
$217$	−1.92907	−	3.34125i	−0.130954	−	0.226819i
$218$	0.116643	+	0.202032i	0.00790009	+	0.0136834i
$219$		0			0
$220$	2.53079	−	1.46115i	0.170626	−	0.0985107i
$221$	6.77213	+	0.220927i	0.455543	+	0.0148612i
$222$		0			0
$223$	−6.61056	−	1.77129i	−0.442676	−	0.118615i	0.0305945	−	0.999532i	$-0.490260\pi$
$223$	−6.61056	−	1.77129i	−0.442676	−	0.118615i	−0.473270	+	0.880917i	$0.656927\pi$
$224$	−4.06703	−	2.34810i	−0.271740	−	0.156889i
$225$		0			0
$226$	6.28527	−	6.28527i	0.418090	−	0.418090i
$227$	9.03058	+	9.03058i	0.599381	+	0.599381i	0.940148	−	0.340767i	$-0.110687\pi$
$227$	9.03058	+	9.03058i	0.599381	+	0.599381i	−0.340767	+	0.940148i	$0.610687\pi$
$228$		0			0
$229$	−4.71861	+	17.6101i	−0.311815	+	1.16371i	0.615104	+	0.788446i	$0.289114\pi$
$229$	−4.71861	+	17.6101i	−0.311815	+	1.16371i	−0.926919	+	0.375263i	$0.877553\pi$
$230$	16.7476	+	9.66924i	1.10431	+	0.637571i
$231$		0			0
$232$	5.33265	−	19.9017i	0.350105	−	1.30661i
$233$	4.27048			0.279769			0.139884	−	0.990168i	$-0.455327\pi$
$233$	4.27048			0.279769			0.139884	+	0.990168i	$0.455327\pi$
$234$		0			0
$235$	−6.88351			−0.449031
$236$	1.95550	−	7.29802i	0.127292	−	0.475060i
$237$		0			0
$238$	−2.85884	−	1.65055i	−0.185311	−	0.106989i
$239$	0.291572	−	1.08816i	0.0188603	−	0.0703874i	−0.955854	−	0.293841i	$-0.905066\pi$
$239$	0.291572	−	1.08816i	0.0188603	−	0.0703874i	0.974715	+	0.223453i	$0.0717331\pi$
$240$		0			0
$241$	−6.24227	−	6.24227i	−0.402100	−	0.402100i	0.476872	−	0.878972i	$-0.341770\pi$
$241$	−6.24227	−	6.24227i	−0.402100	−	0.402100i	−0.878972	+	0.476872i	$0.841770\pi$
$242$	6.70184	−	6.70184i	0.430811	−	0.430811i
$243$		0			0
$244$	5.29684	+	3.05813i	0.339095	+	0.195777i
$245$	−13.3895	−	3.58771i	−0.855425	−	0.229210i
$246$		0			0
$247$	11.8473	−	11.0988i	0.753827	−	0.706197i
$248$	6.96125	−	4.01908i	0.442040	−	0.255212i
$249$		0			0
$250$	2.96968	+	5.14363i	0.187819	+	0.325312i
$251$	8.72352	+	15.1096i	0.550624	+	0.953708i	0.998230	+	0.0594773i	$0.0189434\pi$
$251$	8.72352	+	15.1096i	0.550624	+	0.953708i	−0.447606	+	0.894231i	$0.647723\pi$
$252$		0			0
$253$	9.51388	+	2.54924i	0.598133	+	0.160269i
$254$	9.10670	−	9.10670i	0.571405	−	0.571405i
$255$		0			0
$256$	6.34636	−	10.9922i	0.396647	−	0.687013i
$257$	−3.25035			−0.202751			−0.101376	−	0.994848i	$-0.532324\pi$
$257$	−3.25035			−0.202751			−0.101376	+	0.994848i	$0.532324\pi$
$258$		0			0
$259$	−14.7899	−	8.53897i	−0.919002	−	0.530586i
$260$	−1.37356	−	5.88788i	−0.0851849	−	0.365151i
$261$		0			0
$262$	−2.43511	−	9.08797i	−0.150442	−	0.561457i
$263$	15.6551	−	9.03849i	0.965337	−	0.557337i	0.0675253	−	0.997718i	$-0.478490\pi$
$263$	15.6551	−	9.03849i	0.965337	−	0.557337i	0.897811	+	0.440380i	$0.145156\pi$
$264$		0			0
$265$	32.1088	+	8.60353i	1.97243	+	0.528511i
$266$	−7.63961	+	2.04703i	−0.468414	+	0.125511i
$267$		0			0
$268$	−2.04531	+	0.548039i	−0.124937	+	0.0334768i
$269$	−0.992035	+	0.572752i	−0.0604854	+	0.0349213i	−0.529938	−	0.848037i	$-0.677785\pi$
$269$	−0.992035	+	0.572752i	−0.0604854	+	0.0349213i	0.469452	+	0.882958i	$0.344451\pi$
$270$		0			0
$271$	−8.64641	+	2.31680i	−0.525232	+	0.140736i	−0.511686	−	0.859173i	$-0.670979\pi$
$271$	−8.64641	+	2.31680i	−0.525232	+	0.140736i	−0.0135464	+	0.999908i	$0.504312\pi$
$272$	2.34263	−	4.05755i	0.142043	−	0.246025i
$273$		0			0
$274$	−5.03705	−	8.72443i	−0.304299	−	0.527062i
$275$	−4.02246	−	4.02246i	−0.242564	−	0.242564i
$276$		0			0
$277$			25.7028i			1.54433i	0.635422	+	0.772165i	$0.280826\pi$
$277$			25.7028i			1.54433i	−0.635422	+	0.772165i	$0.719174\pi$
$278$	−0.395500	−	0.395500i	−0.0237205	−	0.0237205i
$279$		0			0
$280$	−3.37634	+	12.6007i	−0.201775	+	0.753035i
$281$	−0.232804	−	0.868838i	−0.0138879	−	0.0518305i	0.958634	−	0.284641i	$-0.0918744\pi$
$281$	−0.232804	−	0.868838i	−0.0138879	−	0.0518305i	−0.972522	+	0.232811i	$0.925208\pi$
$282$		0			0
$283$		−	18.1950i		−	1.08158i	−0.841157	−	0.540791i	$-0.818125\pi$
$283$		−	18.1950i		−	1.08158i	0.841157	−	0.540791i	$-0.181875\pi$
$284$	4.77547	−	4.77547i	0.283372	−	0.283372i
$285$		0			0
$286$	3.52630	+	6.59544i	0.208515	+	0.389997i
$287$			0.958344i			0.0565693i
$288$		0			0
$289$	6.73421	−	11.6640i	0.396130	−	0.686117i
$290$	−22.9283			−1.34640
$291$		0			0
$292$	−1.91603	−	7.15072i	−0.112127	−	0.418464i
$293$	−1.18857	−	4.43581i	−0.0694371	−	0.259143i	0.922477	−	0.386051i	$-0.126161\pi$
$293$	−1.18857	−	4.43581i	−0.0694371	−	0.259143i	−0.991914	+	0.126908i	$0.959495\pi$
$294$		0			0
$295$	−37.2364			−2.16799
$296$	17.7903	−	30.8137i	1.03404	−	1.79101i
$297$		0			0
$298$			6.45792i			0.374097i
$299$	10.7588	−	17.3060i	0.622200	−	1.00083i
$300$		0			0
$301$	2.14570	−	2.14570i	0.123676	−	0.123676i
$302$			23.5465i			1.35495i
$303$		0			0
$304$	−2.90535	−	10.8429i	−0.166633	−	0.621883i
$305$	7.80168	−	29.1163i	0.446723	−	1.66719i
$306$		0			0
$307$	3.93098	+	3.93098i	0.224353	+	0.224353i	0.810329	−	0.585976i	$-0.199289\pi$
$307$	3.93098	+	3.93098i	0.224353	+	0.224353i	−0.585976	+	0.810329i	$0.699289\pi$
$308$			1.50024i			0.0854840i
$309$		0			0
$310$	−6.32509	−	6.32509i	−0.359241	−	0.359241i
$311$	−10.9466	−	18.9600i	−0.620724	−	1.07513i	−0.989351	−	0.145548i	$-0.953506\pi$
$311$	−10.9466	−	18.9600i	−0.620724	−	1.07513i	0.368627	−	0.929577i	$-0.379828\pi$
$312$		0			0
$313$	−3.78444	+	6.55485i	−0.213909	+	0.370502i	−0.952935	−	0.303176i	$-0.901953\pi$
$313$	−3.78444	+	6.55485i	−0.213909	+	0.370502i	0.739025	+	0.673678i	$0.235286\pi$
$314$	−26.5179	+	7.10545i	−1.49649	+	0.400984i
$315$		0			0
$316$	−4.90937	+	2.83443i	−0.276174	+	0.159449i
$317$	−28.5136	+	7.64018i	−1.60148	+	0.429116i	−0.945489	−	0.325653i	$-0.894416\pi$
$317$	−28.5136	+	7.64018i	−1.60148	+	0.429116i	−0.655992	+	0.754768i	$0.727749\pi$
$318$		0			0
$319$	−11.2799	+	3.02245i	−0.631556	+	0.169225i
$320$	−24.3630	−	6.52805i	−1.36193	−	0.364929i
$321$		0			0
$322$	−8.59783	+	4.96396i	−0.479138	+	0.276631i
$323$	2.18995	+	8.17300i	0.121852	+	0.454758i
$324$		0			0
$325$	−10.3789	+	5.54916i	−0.575718	+	0.307812i
$326$	4.59709	+	2.65413i	0.254609	+	0.146999i
$327$		0			0
$328$	−1.99664			−0.110246
$329$	1.76692	−	3.06039i	0.0974132	−	0.168725i
$330$		0			0
$331$	13.6196	−	13.6196i	0.748603	−	0.748603i	−0.225614	−	0.974217i	$-0.572439\pi$
$331$	13.6196	−	13.6196i	0.748603	−	0.748603i	0.974217	+	0.225614i	$0.0724387\pi$
$332$	−1.55028	−	0.415396i	−0.0850827	−	0.0227978i
$333$		0			0
$334$	−0.212091	−	0.367352i	−0.0116051	−	0.0201006i
$335$	5.21785	+	9.03757i	0.285081	+	0.493775i
$336$		0			0
$337$	15.6291	−	9.02348i	0.851373	−	0.491541i	−0.00974077	−	0.999953i	$-0.503101\pi$
$337$	15.6291	−	9.02348i	0.851373	−	0.491541i	0.861114	+	0.508412i	$0.169767\pi$
$338$	15.1753	−	3.02213i	0.825425	−	0.164382i
$339$		0			0
$340$	3.04385	+	0.815596i	0.165076	+	0.0442319i
$341$	−3.94552	−	2.27794i	−0.213662	−	0.123358i
$342$		0			0
$343$	12.3370	−	12.3370i	0.666135	−	0.666135i
$344$	4.47041	+	4.47041i	0.241028	+	0.241028i
$345$		0			0
$346$	−3.66518	+	13.6786i	−0.197041	+	0.735367i
$347$	21.7625	+	12.5646i	1.16827	+	0.674503i	0.953273	−	0.302111i	$-0.0976914\pi$
$347$	21.7625	+	12.5646i	1.16827	+	0.674503i	0.215000	+	0.976614i	$0.431025\pi$
$348$		0			0
$349$	−6.03993	+	22.5413i	−0.323310	+	1.20661i	0.592689	+	0.805431i	$0.298066\pi$
$349$	−6.03993	+	22.5413i	−0.323310	+	1.20661i	−0.916000	+	0.401179i	$0.868601\pi$
$350$	5.73391			0.306490
$351$		0			0
$352$	−5.54551			−0.295577
$353$	5.17925	−	19.3292i	0.275663	−	1.02879i	−0.679732	−	0.733461i	$-0.737904\pi$
$353$	5.17925	−	19.3292i	0.275663	−	1.02879i	0.955395	−	0.295329i	$-0.0954294\pi$
$354$		0			0
$355$	−28.8249	−	16.6421i	−1.52987	−	0.883269i
$356$	0.917452	−	3.42398i	0.0486248	−	0.181470i
$357$		0			0
$358$	−4.93147	−	4.93147i	−0.260636	−	0.260636i
$359$	−1.97346	+	1.97346i	−0.104155	+	0.104155i	−0.757264	−	0.653109i	$-0.773464\pi$
$359$	−1.97346	+	1.97346i	−0.104155	+	0.104155i	0.653109	+	0.757264i	$0.273464\pi$
$360$		0			0
$361$	1.10195	+	0.636209i	0.0579972	+	0.0334847i
$362$	−9.53991	−	2.55621i	−0.501406	−	0.134351i
$363$		0			0
$364$	2.97031	+	0.900665i	0.155686	+	0.0472077i
$365$	−31.5968	+	18.2424i	−1.65385	+	0.954852i
$366$		0			0
$367$	16.4946	+	28.5695i	0.861011	+	1.49131i	0.870954	+	0.491364i	$0.163502\pi$
$367$	16.4946	+	28.5695i	0.861011	+	1.49131i	−0.00994343	+	0.999951i	$0.503165\pi$
$368$	−7.04535	−	12.2029i	−0.367264	−	0.636120i
$369$		0			0
$370$	−38.2457	−	10.2479i	−1.98830	−	0.532763i
$371$	−12.0671	+	12.0671i	−0.626490	+	0.626490i
$372$		0			0
$373$	2.35231	−	4.07432i	0.121798	−	0.210960i	−0.798679	−	0.601758i	$-0.794467\pi$
$373$	2.35231	−	4.07432i	0.121798	−	0.210960i	0.920477	+	0.390797i	$0.127801\pi$
$374$	−3.89811			−0.201566
$375$		0			0
$376$	6.37609	+	3.68124i	0.328822	+	0.189845i
$377$	−0.787765	+	24.1476i	−0.0405720	+	1.24366i
$378$		0			0
$379$	5.09903	+	19.0299i	0.261920	+	0.977498i	0.964109	+	0.265507i	$0.0855394\pi$
$379$	5.09903	+	19.0299i	0.261920	+	0.977498i	−0.702189	+	0.711991i	$0.747794\pi$
$380$	6.53849	−	3.77500i	0.335418	−	0.193653i
$381$		0			0
$382$	−8.23195	−	2.20574i	−0.421183	−	0.112856i
$383$	−5.52669	+	1.48087i	−0.282401	+	0.0756690i	−0.397239	−	0.917715i	$-0.630032\pi$
$383$	−5.52669	+	1.48087i	−0.282401	+	0.0756690i	0.114838	+	0.993384i	$0.463365\pi$
$384$		0			0
$385$	7.14185	−	1.91365i	0.363982	−	0.0975287i
$386$	2.82378	−	1.63031i	0.143727	−	0.0829806i
$387$		0			0
$388$	−2.95421	+	0.791578i	−0.149977	+	0.0401863i
$389$	8.59884	−	14.8936i	0.435978	−	0.755137i	−0.561397	−	0.827547i	$-0.689736\pi$
$389$	8.59884	−	14.8936i	0.435978	−	0.755137i	0.997375	+	0.0724102i	$0.0230691\pi$
$390$		0			0
$391$	5.31054	+	9.19812i	0.268565	+	0.465169i
$392$	10.4838	+	10.4838i	0.529513	+	0.529513i
$393$		0			0
$394$		−	28.5175i		−	1.43669i
$395$	19.7554	+	19.7554i	0.994004	+	0.994004i
$396$		0			0
$397$	−0.701121	+	2.61662i	−0.0351882	+	0.131324i	−0.981286	−	0.192558i	$-0.938322\pi$
$397$	−0.701121	+	2.61662i	−0.0351882	+	0.131324i	0.946097	+	0.323882i	$0.104988\pi$
$398$	2.87635	+	10.7347i	0.144179	+	0.538082i
$399$		0			0
$400$			8.13814i			0.406907i
$401$	−5.47997	+	5.47997i	−0.273657	+	0.273657i	−0.830570	−	0.556914i	$-0.811985\pi$
$401$	−5.47997	+	5.47997i	−0.273657	+	0.273657i	0.556914	+	0.830570i	$0.311985\pi$
$402$		0			0
$403$	−6.87876	+	6.44413i	−0.342655	+	0.321005i
$404$			1.76654i			0.0878886i
$405$		0			0
$406$	5.88542	−	10.1938i	0.292088	−	0.505912i
$407$	−20.1665			−0.999616
$408$		0			0
$409$	−2.05083	−	7.65382i	−0.101407	−	0.378457i	0.896506	−	0.443032i	$-0.146097\pi$
$409$	−2.05083	−	7.65382i	−0.101407	−	0.378457i	−0.997913	+	0.0645754i	$0.979431\pi$
$410$	0.575070	+	2.14619i	0.0284007	+	0.105993i
$411$		0			0
$412$	−10.7383			−0.529039
$413$	9.55813	−	16.5552i	0.470325	−	0.814627i
$414$		0			0
$415$			7.90993i			0.388283i
$416$	−3.32923	+	10.9795i	−0.163229	+	0.538314i
$417$		0			0
$418$	−6.60400	+	6.60400i	−0.323012	+	0.323012i
$419$		−	30.4873i		−	1.48940i	−0.667399	−	0.744700i	$-0.732592\pi$
$419$		−	30.4873i		−	1.48940i	0.667399	−	0.744700i	$-0.267408\pi$
$420$		0			0
$421$	2.02029	+	7.53981i	0.0984628	+	0.367468i	0.997522	−	0.0703596i	$-0.0224147\pi$
$421$	2.02029	+	7.53981i	0.0984628	+	0.367468i	−0.899059	+	0.437828i	$0.855748\pi$
$422$	−1.60534	+	5.99122i	−0.0781469	+	0.291648i
$423$		0			0
$424$	−25.1408	−	25.1408i	−1.22095	−	1.22095i
$425$		−	6.13425i		−	0.297555i
$426$		0			0
$427$	10.9424	+	10.9424i	0.529540	+	0.529540i
$428$	1.33812	+	2.31770i	0.0646806	+	0.112030i
$429$		0			0
$430$	3.51769	−	6.09281i	0.169638	−	0.293821i
$431$	30.9395	−	8.29022i	1.49030	−	0.399326i	0.580465	−	0.814285i	$-0.302871\pi$
$431$	30.9395	−	8.29022i	1.49030	−	0.399326i	0.909840	+	0.414960i	$0.136204\pi$
$432$		0			0
$433$	19.6303	−	11.3335i	0.943371	−	0.544655i	0.0523555	−	0.998629i	$-0.483327\pi$
$433$	19.6303	−	11.3335i	0.943371	−	0.544655i	0.891015	+	0.453973i	$0.149994\pi$
$434$	4.43569	−	1.18854i	0.212920	−	0.0570517i
$435$		0			0
$436$	0.110431	−	0.0295898i	0.00528867	−	0.00141709i
$437$	24.5799	+	6.58617i	1.17582	+	0.315059i
$438$		0			0
$439$	28.0428	−	16.1905i	1.33841	−	0.772730i	0.351836	−	0.936062i	$-0.385557\pi$
$439$	28.0428	−	16.1905i	1.33841	−	0.772730i	0.986571	+	0.163332i	$0.0522241\pi$
$440$	3.98695	+	14.8795i	0.190070	+	0.709352i
$441$		0			0
$442$	−2.34022	+	7.71782i	−0.111313	+	0.367099i
$443$	−21.0067	−	12.1282i	−0.998059	−	0.576230i	−0.0903854	−	0.995907i	$-0.528810\pi$
$443$	−21.0067	−	12.1282i	−0.998059	−	0.576230i	−0.907673	+	0.419677i	$0.862143\pi$
$444$		0			0
$445$	−17.4700			−0.828158
$446$	4.07289	−	7.05446i	0.192857	−	0.334038i
$447$		0			0
$448$	9.15604	−	9.15604i	0.432582	−	0.432582i
$449$	−10.4048	−	2.78796i	−0.491032	−	0.131572i	0.00480262	−	0.999988i	$-0.498471\pi$
$449$	−10.4048	−	2.78796i	−0.491032	−	0.131572i	−0.495835	+	0.868417i	$0.665138\pi$
$450$		0			0
$451$	0.565830	+	0.980046i	0.0266439	+	0.0461486i
$452$	−2.17803	−	3.77247i	−0.102446	−	0.177442i
$453$		0			0
$454$	−13.1644	+	7.60045i	−0.617834	+	0.356707i
$455$	0.498770	−	15.2889i	0.0233827	−	0.716756i
$456$		0			0
$457$	23.2711	+	6.23548i	1.08858	+	0.291684i	0.758106	−	0.652132i	$-0.226125\pi$
$457$	23.2711	+	6.23548i	1.08858	+	0.291684i	0.330473	+	0.943816i	$0.392792\pi$
$458$	−18.7926	−	10.8499i	−0.878122	−	0.506984i
$459$		0			0
$460$	6.70136	−	6.70136i	0.312453	−	0.312453i
$461$	−2.08882	−	2.08882i	−0.0972863	−	0.0972863i	0.656789	−	0.754075i	$-0.271914\pi$
$461$	−2.08882	−	2.08882i	−0.0972863	−	0.0972863i	−0.754075	+	0.656789i	$0.771914\pi$
$462$		0			0
$463$	−0.480789	+	1.79433i	−0.0223442	+	0.0833896i	−0.976198	−	0.216883i	$-0.930411\pi$
$463$	−0.480789	+	1.79433i	−0.0223442	+	0.0833896i	0.953853	+	0.300273i	$0.0970776\pi$
$464$	14.4681	+	8.35318i	0.671666	+	0.387786i
$465$		0			0
$466$	−1.31556	+	4.90975i	−0.0609423	+	0.227440i
$467$	−16.0374			−0.742122			−0.371061	−	0.928608i	$-0.621006\pi$
$467$	−16.0374			−0.742122			−0.371061	+	0.928608i	$0.621006\pi$
$468$		0			0
$469$	−5.35743			−0.247383
$470$	2.12053	−	7.91394i	0.0978129	−	0.365043i
$471$		0			0
$472$	34.4915	+	19.9137i	1.58760	+	0.916600i
$473$	0.927416	−	3.46117i	0.0426427	−	0.159145i
$474$		0			0
$475$	−10.3924	−	10.3924i	−0.476834	−	0.476834i
$476$	−1.14393	+	1.14393i	−0.0524320	+	0.0524320i
$477$		0			0
$478$	1.16123	+	0.670438i	0.0531136	+	0.0306651i
$479$	35.7803	+	9.58729i	1.63484	+	0.438055i	0.955313	−	0.295595i	$-0.0955178\pi$
$479$	35.7803	+	9.58729i	1.63484	+	0.438055i	0.679528	+	0.733649i	$0.262184\pi$
$480$		0			0
$481$	−12.1069	+	39.9274i	−0.552027	+	1.82053i
$482$	9.09969	−	5.25371i	0.414480	−	0.239300i
$483$		0			0
$484$	−2.32239	−	4.02249i	−0.105563	−	0.182841i
$485$	7.53657	+	13.0537i	0.342218	+	0.592739i
$486$		0			0
$487$	19.5635	+	5.24201i	0.886505	+	0.237538i	0.673212	−	0.739450i	$-0.264914\pi$
$487$	19.5635	+	5.24201i	0.886505	+	0.237538i	0.213293	+	0.976988i	$0.431581\pi$
$488$	−22.7977	+	22.7977i	−1.03200	+	1.03200i
$489$		0			0
$490$	8.24954	−	14.2886i	0.372676	−	0.645494i
$491$	−11.3387			−0.511707			−0.255854	−	0.966716i	$-0.582356\pi$
$491$	−11.3387			−0.511707			−0.255854	+	0.966716i	$0.582356\pi$
$492$		0			0
$493$	−10.9056	−	6.29633i	−0.491162	−	0.283572i
$494$	9.11049	+	17.0399i	0.409900	+	0.766660i
$495$		0			0
$496$	1.68689	+	6.29557i	0.0757438	+	0.282680i
$497$	14.7980	−	8.54364i	0.663782	−	0.383235i
$498$		0			0
$499$	4.93618	+	1.32264i	0.220974	+	0.0592097i	0.367607	−	0.929981i	$-0.380177\pi$
$499$	4.93618	+	1.32264i	0.220974	+	0.0592097i	−0.146634	+	0.989191i	$0.546844\pi$
$500$	2.81150	−	0.753340i	0.125734	−	0.0336904i
$501$		0			0
$502$	−20.0588	+	5.37473i	−0.895266	+	0.239886i
$503$	−16.1644	+	9.33251i	−0.720734	+	0.416116i	−0.815023	−	0.579429i	$-0.803276\pi$
$503$	−16.1644	+	9.33251i	−0.720734	+	0.416116i	0.0942889	+	0.995545i	$0.469942\pi$
$504$		0			0
$505$	8.40956	−	2.25333i	0.374220	−	0.100272i
$506$	−5.86169	+	10.1527i	−0.260584	+	0.451344i
$507$		0			0
$508$	−3.15574	−	5.46591i	−0.140013	−	0.242510i
$509$	2.28498	+	2.28498i	0.101280	+	0.101280i	0.755931	−	0.654651i	$-0.227185\pi$
$509$	2.28498	+	2.28498i	0.101280	+	0.101280i	−0.654651	+	0.755931i	$0.727185\pi$
$510$		0			0
$511$		−	18.7304i		−	0.828586i
$512$	16.4510	+	16.4510i	0.727037	+	0.727037i
$513$		0			0
$514$	1.00130	−	3.73691i	0.0441655	−	0.164828i
$515$	13.6974	+	51.1195i	0.603580	+	2.25259i
$516$		0			0
$517$		−	4.17292i		−	0.183525i
$518$	14.3734	−	14.3734i	0.631531	−	0.631531i
$519$		0			0
$520$	31.8533	+	1.03915i	1.39686	+	0.0455698i
$521$			21.9128i			0.960018i	0.877263	+	0.480009i	$0.159367\pi$
$521$			21.9128i			0.960018i	−0.877263	+	0.480009i	$0.840633\pi$
$522$		0			0
$523$	9.66002	−	16.7316i	0.422403	−	0.731624i	−0.573771	−	0.819016i	$-0.694520\pi$
$523$	9.66002	−	16.7316i	0.422403	−	0.731624i	0.996174	+	0.0873922i	$0.0278533\pi$
$524$	−4.61083			−0.201425
$525$		0			0
$526$	5.56879	+	20.7830i	0.242811	+	0.906182i
$527$	−1.27152	−	4.74538i	−0.0553883	−	0.206712i
$528$		0			0
$529$	8.94238			0.388799
$530$	−19.7829	+	34.2649i	−0.859313	+	1.48837i
$531$		0			0
$532$			3.87599i			0.168046i
$533$	2.28008	−	0.531913i	0.0987612	−	0.0230397i
$534$		0			0
$535$	9.32647	−	9.32647i	0.403218	−	0.403218i
$536$		−	11.1618i		−	0.482117i
$537$		0			0
$538$	−0.352883	−	1.31698i	−0.0152139	−	0.0567790i
$539$	2.17494	−	8.11699i	0.0936814	−	0.349624i
$540$		0			0
$541$	−1.88126	−	1.88126i	−0.0808815	−	0.0808815i	0.665509	−	0.746390i	$-0.268215\pi$
$541$	−1.88126	−	1.88126i	−0.0808815	−	0.0808815i	−0.746390	+	0.665509i	$0.768215\pi$
$542$		−	10.6544i		−	0.457647i
$543$		0			0
$544$	−4.22845	−	4.22845i	−0.181293	−	0.181293i
$545$	−0.281723	−	0.487958i	−0.0120677	−	0.0209018i
$546$		0			0
$547$	14.0438	−	24.3246i	0.600469	−	1.04004i	−0.392281	−	0.919846i	$-0.628314\pi$
$547$	14.0438	−	24.3246i	0.600469	−	1.04004i	0.992750	−	0.120198i	$-0.0383529\pi$
$548$	−4.76876	+	1.27779i	−0.203711	+	0.0545843i
$549$		0			0
$550$	5.86376	−	3.38544i	0.250031	−	0.144356i
$551$	−29.1427	+	7.80876i	−1.24152	+	0.332664i
$552$		0			0
$553$	−13.8542	+	3.71222i	−0.589140	+	0.157860i
$554$	−29.5503	−	7.91798i	−1.25547	−	0.336403i
$555$		0			0
$556$	−0.237382	+	0.137052i	−0.0100672	+	0.00581232i
$557$	−3.91190	−	14.5994i	−0.165753	−	0.618597i	−0.997943	−	0.0641073i	$-0.979580\pi$
$557$	−3.91190	−	14.5994i	−0.165753	−	0.618597i	0.832190	−	0.554490i	$-0.187087\pi$
$558$		0			0
$559$	−6.29595	−	3.91408i	−0.266290	−	0.165548i
$560$	−9.16043	−	5.28878i	−0.387099	−	0.223492i
$561$		0			0
$562$	1.07062			0.0451612
$563$	12.7053	−	22.0062i	0.535463	−	0.927450i	−0.463677	−	0.886004i	$-0.653470\pi$
$563$	12.7053	−	22.0062i	0.535463	−	0.927450i	0.999141	−	0.0414457i	$-0.0131964\pi$
$564$		0			0
$565$	−15.1805	+	15.1805i	−0.638648	+	0.638648i
$566$	20.9187	+	5.60516i	0.879280	+	0.235602i
$567$		0			0
$568$	17.8000	+	30.8306i	0.746873	+	1.29362i
$569$	−12.5182	−	21.6821i	−0.524789	−	0.908962i	−0.999583	−	0.0288649i	$-0.990811\pi$
$569$	−12.5182	−	21.6821i	−0.524789	−	0.908962i	0.474794	−	0.880097i	$-0.342523\pi$
$570$		0			0
$571$	23.2909	−	13.4470i	0.974693	−	0.562739i	0.0740294	−	0.997256i	$-0.476414\pi$
$571$	23.2909	−	13.4470i	0.974693	−	0.562739i	0.900664	+	0.434517i	$0.143081\pi$
$572$	3.56935	−	0.832682i	0.149242	−	0.0348162i
$573$		0			0
$574$	−1.10180	−	0.295227i	−0.0459884	−	0.0123225i
$575$	−15.9768	−	9.22423i	−0.666280	−	0.384677i
$576$		0			0
$577$	−12.8490	+	12.8490i	−0.534912	+	0.534912i	−0.922030	−	0.387118i	$-0.873470\pi$
$577$	−12.8490	+	12.8490i	−0.534912	+	0.534912i	0.387118	+	0.922030i	$0.373470\pi$
$578$	11.3355	+	11.3355i	0.471494	+	0.471494i
$579$		0			0
$580$	−2.90819	+	10.8535i	−0.120756	+	0.450668i
$581$	−3.51673	−	2.03038i	−0.145899	−	0.0842345i
$582$		0			0
$583$	−5.21563	+	19.4650i	−0.216009	+	0.806158i
$584$	39.0235			1.61480
$585$		0			0
$586$	5.46598			0.225797
$587$	−3.68465	+	13.7513i	−0.152082	+	0.567576i	0.847256	+	0.531185i	$0.178253\pi$
$587$	−3.68465	+	13.7513i	−0.152082	+	0.567576i	−0.999338	+	0.0363915i	$0.988414\pi$
$588$		0			0
$589$	−10.1936	−	5.88526i	−0.420019	−	0.242498i
$590$	11.4710	−	42.8104i	0.472255	−	1.76248i
$591$		0			0
$592$	20.4002	+	20.4002i	0.838441	+	0.838441i
$593$	−14.8629	+	14.8629i	−0.610345	+	0.610345i	−0.943036	−	0.332691i	$-0.892043\pi$
$593$	−14.8629	+	14.8629i	−0.610345	+	0.610345i	0.332691	+	0.943036i	$0.392043\pi$
$594$		0			0
$595$	6.90481	+	3.98649i	0.283070	+	0.163430i
$596$	3.05698	+	0.819114i	0.125219	+	0.0335522i
$597$		0			0
$598$	16.5823	+	17.7007i	0.678099	+	0.723834i
$599$	29.6012	−	17.0903i	1.20947	−	0.698289i	0.246828	−	0.969059i	$-0.420612\pi$
$599$	29.6012	−	17.0903i	1.20947	−	0.698289i	0.962644	+	0.270770i	$0.0872783\pi$
$600$		0			0
$601$	−4.47135	−	7.74461i	−0.182390	−	0.315909i	0.760304	−	0.649568i	$-0.225050\pi$
$601$	−4.47135	−	7.74461i	−0.182390	−	0.315909i	−0.942694	+	0.333659i	$0.891717\pi$
$602$	1.80590	+	3.12790i	0.0736028	+	0.127484i
$603$		0			0
$604$	11.1462	+	2.98660i	0.453531	+	0.121523i
$605$	−16.1866	+	16.1866i	−0.658079	+	0.658079i
$606$		0			0
$607$	−4.58314	+	7.93823i	−0.186024	+	0.322203i	−0.943921	−	0.330171i	$-0.892894\pi$
$607$	−4.58314	+	7.93823i	−0.186024	+	0.322203i	0.757897	+	0.652374i	$0.226227\pi$
$608$	−14.3273			−0.581048
$609$		0			0
$610$	31.0714	+	17.9391i	1.25805	+	0.726333i
$611$	−8.26193	−	2.50520i	−0.334242	−	0.101350i
$612$		0			0
$613$	−0.197913	−	0.738622i	−0.00799364	−	0.0298327i	0.961814	−	0.273705i	$-0.0882490\pi$
$613$	−0.197913	−	0.738622i	−0.00799364	−	0.0298327i	−0.969807	+	0.243872i	$0.921582\pi$
$614$	−5.73041	+	3.30845i	−0.231260	+	0.133518i
$615$		0			0
$616$	−7.63878	−	2.04680i	−0.307775	−	0.0824681i
$617$	−16.1154	+	4.31810i	−0.648780	+	0.173840i	−0.568177	−	0.822906i	$-0.692351\pi$
$617$	−16.1154	+	4.31810i	−0.648780	+	0.173840i	−0.0806029	+	0.996746i	$0.525685\pi$
$618$		0			0
$619$	3.71367	−	0.995076i	0.149265	−	0.0399955i	−0.183413	−	0.983036i	$-0.558714\pi$
$619$	3.71367	−	0.995076i	0.149265	−	0.0399955i	0.332678	+	0.943041i	$0.392048\pi$
$620$	−3.79636	+	2.19183i	−0.152466	+	0.0880261i
$621$		0			0
$622$	25.1704	−	6.74440i	1.00924	−	0.270426i
$623$	4.48434	−	7.76711i	0.179661	−	0.311183i
$624$		0			0
$625$	−15.3330	−	26.5575i	−0.613320	−	1.06230i
$626$	−6.37023	−	6.37023i	−0.254606	−	0.254606i
$627$		0			0
$628$			13.4540i			0.536872i
$629$	−15.3769	−	15.3769i	−0.613118	−	0.613118i
$630$		0			0
$631$	3.46710	−	12.9394i	0.138023	−	0.515110i	−0.861944	−	0.507004i	$-0.830753\pi$
$631$	3.46710	−	12.9394i	0.138023	−	0.515110i	0.999967	−	0.00810607i	$-0.00258027\pi$
$632$	−7.73413	−	28.8642i	−0.307647	−	1.14815i
$633$		0			0
$634$		−	35.1355i		−	1.39541i
$635$	−21.9949	+	21.9949i	−0.872843	+	0.872843i
$636$		0			0
$637$	−14.7650	−	9.17916i	−0.585012	−	0.363692i
$638$		−	13.8996i		−	0.550290i
$639$		0			0
$640$	5.86282	−	10.1547i	0.231748	−	0.401400i
$641$	25.4888			1.00675			0.503375	−	0.864068i	$-0.332092\pi$
$641$	25.4888			1.00675			0.503375	+	0.864068i	$0.332092\pi$
$642$		0			0
$643$	−1.44538	−	5.39422i	−0.0570001	−	0.212727i	0.931552	−	0.363609i	$-0.118455\pi$
$643$	−1.44538	−	5.39422i	−0.0570001	−	0.212727i	−0.988552	+	0.150881i	$0.951789\pi$
$644$	1.25924	+	4.69956i	0.0496212	+	0.185189i
$645$		0			0
$646$	−10.0711			−0.396241
$647$	1.23117	−	2.13245i	0.0484024	−	0.0838354i	−0.840809	−	0.541332i	$-0.817920\pi$
$647$	1.23117	−	2.13245i	0.0484024	−	0.0838354i	0.889212	+	0.457496i	$0.151254\pi$
$648$		0			0
$649$		−	22.5734i		−	0.886085i
$650$	−3.18251	−	13.6420i	−0.124828	−	0.535085i
$651$		0			0
$652$	1.83947	−	1.83947i	0.0720393	−	0.0720393i
$653$			32.0947i			1.25596i	0.778229	+	0.627981i	$0.216118\pi$
$653$			32.0947i			1.25596i	−0.778229	+	0.627981i	$0.783882\pi$
$654$		0			0
$655$	5.88141	+	21.9497i	0.229806	+	0.857646i
$656$	0.419016	−	1.56379i	0.0163598	−	0.0610557i
$657$		0			0
$658$	2.97419	+	2.97419i	0.115946	+	0.115946i
$659$		−	5.31859i		−	0.207183i	−0.994620	−	0.103591i	$-0.966967\pi$
$659$		−	5.31859i		−	0.207183i	0.994620	−	0.103591i	$-0.0330335\pi$
$660$		0			0
$661$	−16.1836	−	16.1836i	−0.629470	−	0.629470i	0.318464	−	0.947935i	$-0.396833\pi$
$661$	−16.1836	−	16.1836i	−0.629470	−	0.629470i	−0.947935	+	0.318464i	$0.896833\pi$
$662$	11.4628	+	19.8541i	0.445513	+	0.771651i
$663$		0			0
$664$	4.23015	−	7.32684i	0.164162	−	0.284337i
$665$	18.4516	−	4.94408i	0.715520	−	0.191723i
$666$		0			0
$667$	−32.7980	+	18.9359i	−1.26994	+	0.733202i
$668$	−0.200794	+	0.0538026i	−0.00776896	+	0.00208169i
$669$		0			0
$670$	−11.9979	+	3.21481i	−0.463517	+	0.124199i
$671$	17.6509	+	4.72954i	0.681404	+	0.182582i
$672$		0			0
$673$	−24.6097	+	14.2084i	−0.948633	+	0.547693i	−0.892656	−	0.450739i	$-0.851161\pi$
$673$	−24.6097	+	14.2084i	−0.948633	+	0.547693i	−0.0559769	+	0.998432i	$0.517827\pi$
$674$	5.55954	+	20.7485i	0.214146	+	0.799202i
$675$		0			0
$676$	0.494230	−	7.56681i	0.0190088	−	0.291031i
$677$	−19.5004	−	11.2586i	−0.749461	−	0.432701i	0.0760383	−	0.997105i	$-0.475773\pi$
$677$	−19.5004	−	11.2586i	−0.749461	−	0.432701i	−0.825499	+	0.564404i	$0.809106\pi$
$678$		0			0
$679$	−7.73819			−0.296965
$680$	−8.30556	+	14.3857i	−0.318504	+	0.551665i
$681$		0			0
$682$	3.83439	−	3.83439i	0.146827	−	0.146827i
$683$	38.9958	+	10.4489i	1.49213	+	0.399816i	0.910457	−	0.413604i	$-0.135730\pi$
$683$	38.9958	+	10.4489i	1.49213	+	0.399816i	0.581677	+	0.813420i	$0.302397\pi$
$684$		0			0
$685$	12.1657	+	21.0717i	0.464829	+	0.805107i
$686$	10.3832	+	17.9843i	0.396434	+	0.686644i
$687$		0			0
$688$	−4.43943	+	2.56311i	−0.169252	+	0.0977176i
$689$	35.4074	+	22.0121i	1.34891	+	0.838596i
$690$		0			0
$691$	−32.4618	−	8.69813i	−1.23491	−	0.330892i	−0.418419	−	0.908254i	$-0.637415\pi$
$691$	−32.4618	−	8.69813i	−1.23491	−	0.330892i	−0.816488	+	0.577362i	$0.804082\pi$
$692$	6.01014	+	3.46996i	0.228471	+	0.131908i
$693$		0			0
$694$	−21.1496	+	21.1496i	−0.802828	+	0.802828i
$695$	0.955230	+	0.955230i	0.0362339	+	0.0362339i
$696$		0			0
$697$	−0.315840	+	1.17873i	−0.0119633	+	0.0446476i
$698$	−24.0550	−	13.8882i	−0.910495	−	0.525674i
$699$		0			0
$700$	0.727282	−	2.71425i	0.0274887	−	0.102589i
$701$	−34.8493			−1.31624			−0.658120	−	0.752913i	$-0.728648\pi$
$701$	−34.8493			−1.31624			−0.658120	+	0.752913i	$0.728648\pi$
$702$		0			0
$703$	−52.1018			−1.96506
$704$	3.95743	−	14.7693i	0.149151	−	0.556640i
$705$		0			0
$706$	20.6272	+	11.9091i	0.776313	+	0.448205i
$707$	−1.15681	+	4.31727i	−0.0435062	+	0.162367i
$708$		0			0
$709$	−6.24720	−	6.24720i	−0.234619	−	0.234619i	0.579999	−	0.814617i	$-0.303053\pi$
$709$	−6.24720	−	6.24720i	−0.234619	−	0.234619i	−0.814617	+	0.579999i	$0.803053\pi$
$710$	28.0131	−	28.0131i	1.05131	−	1.05131i
$711$		0			0
$712$	16.1822	+	9.34279i	0.606453	+	0.350136i
$713$	−14.2715	−	3.82404i	−0.534473	−	0.143211i
$714$		0			0
$715$	−8.51689	−	15.9296i	−0.318514	−	0.595735i
$716$	−2.95991	+	1.70890i	−0.110617	+	0.0638647i
$717$		0			0
$718$	−1.66094	−	2.87683i	−0.0619856	−	0.107362i
$719$	12.4677	+	21.5947i	0.464966	+	0.805345i	0.999200	−	0.0399915i	$-0.0127331\pi$
$719$	12.4677	+	21.5947i	0.464966	+	0.805345i	−0.534234	+	0.845337i	$0.679400\pi$
$720$		0			0
$721$	−26.2435	−	7.03193i	−0.977359	−	0.261883i
$722$	−1.07091	+	1.07091i	−0.0398552	+	0.0398552i
$723$		0			0
$724$	−2.42006	+	4.19166i	−0.0899408	+	0.155782i
$725$	21.8730			0.812344
$726$		0			0
$727$	−15.7972	−	9.12055i	−0.585888	−	0.338262i	0.177582	−	0.984106i	$-0.443172\pi$
$727$	−15.7972	−	9.12055i	−0.585888	−	0.338262i	−0.763470	+	0.645844i	$0.776506\pi$
$728$	−8.63837	+	13.8951i	−0.320159	+	0.514989i
$729$		0			0
$730$	−11.2395	−	41.9464i	−0.415993	−	1.55251i
$731$	3.34629	−	1.93198i	0.123767	−	0.0714569i
$732$		0			0
$733$	−22.3310	−	5.98357i	−0.824814	−	0.221008i	−0.178364	−	0.983965i	$-0.557081\pi$
$733$	−22.3310	−	5.98357i	−0.824814	−	0.221008i	−0.646450	+	0.762956i	$0.723747\pi$
$734$	−37.9275	+	10.1626i	−1.39993	+	0.375110i
$735$		0			0
$736$	−17.3715	+	4.65469i	−0.640324	+	0.171574i
$737$	−5.47876	+	3.16316i	−0.201813	+	0.116517i
$738$		0			0
$739$	11.4323	−	3.06326i	0.420542	−	0.112684i	−0.0423409	−	0.999103i	$-0.513482\pi$
$739$	11.4323	−	3.06326i	0.420542	−	0.112684i	0.462883	+	0.886419i	$0.346815\pi$
$740$	−9.70206	+	16.8045i	−0.356655	+	0.617745i
$741$		0			0
$742$	−10.1560	−	17.5908i	−0.372840	−	0.645778i
$743$	31.1023	+	31.1023i	1.14103	+	1.14103i	0.988262	+	0.152771i	$0.0488196\pi$
$743$	31.1023	+	31.1023i	1.14103	+	1.14103i	0.152771	+	0.988262i	$0.451180\pi$
$744$		0			0
$745$		−	15.5975i		−	0.571448i
$746$	3.95957	+	3.95957i	0.144970	+	0.144970i
$747$		0			0
$748$	−0.494431	+	1.84524i	−0.0180782	+	0.0674687i
$749$	1.75252	+	6.54051i	0.0640358	+	0.238985i
$750$		0			0
$751$			37.0028i			1.35025i	0.737702	+	0.675126i	$0.235911\pi$
$751$			37.0028i			1.35025i	−0.737702	+	0.675126i	$0.764089\pi$
$752$	−4.22128	+	4.22128i	−0.153934	+	0.153934i
$753$		0			0
$754$	−27.5196	−	8.34458i	−1.00221	−	0.303892i
$755$		−	56.8706i		−	2.06973i
$756$		0			0
$757$	−23.2842	+	40.3294i	−0.846278	+	1.46580i	0.0382287	+	0.999269i	$0.487828\pi$
$757$	−23.2842	+	40.3294i	−0.846278	+	1.46580i	−0.884507	+	0.466527i	$0.845505\pi$
$758$	−23.4493			−0.851717
$759$		0			0
$760$	10.3006	+	38.4424i	0.373643	+	1.39445i
$761$	−7.83690	−	29.2477i	−0.284088	−	1.06023i	−0.949504	−	0.313756i	$-0.898412\pi$
$761$	−7.83690	−	29.2477i	−0.284088	−	1.06023i	0.665416	−	0.746473i	$-0.268254\pi$
$762$		0			0
$763$	0.289259			0.0104719
$764$	−2.08826	+	3.61697i	−0.0755506	+	0.130857i
$765$		0			0
$766$		−	6.81020i		−	0.246062i
$767$	−44.6929	−	13.5519i	−1.61377	−	0.489331i
$768$		0			0
$769$	37.1880	−	37.1880i	1.34103	−	1.34103i	0.445999	−	0.895033i	$-0.352848\pi$
$769$	37.1880	−	37.1880i	1.34103	−	1.34103i	0.895033	−	0.445999i	$-0.147152\pi$
$770$			8.80046i			0.317146i
$771$		0			0
$772$	−0.413573	−	1.54347i	−0.0148848	−	0.0555508i
$773$	5.09988	−	19.0330i	0.183430	−	0.684570i	−0.811531	−	0.584309i	$-0.801366\pi$
$773$	5.09988	−	19.0330i	0.183430	−	0.684570i	0.994961	−	0.100261i	$-0.0319677\pi$
$774$		0			0
$775$	6.03398	+	6.03398i	0.216747	+	0.216747i
$776$		−	16.1219i		−	0.578744i
$777$		0			0
$778$	14.4742	+	14.4742i	0.518924	+	0.518924i
$779$	1.46187	+	2.53203i	0.0523769	+	0.0907194i
$780$		0			0
$781$	10.0888	−	17.4742i	0.361004	−	0.625277i
$782$	−12.2110	+	3.27192i	−0.436664	+	0.117004i
$783$		0			0
$784$	−10.4112	+	6.01090i	−0.371828	+	0.214675i
$785$	64.0473	−	17.1614i	2.28595	−	0.612517i
$786$		0			0
$787$	9.80128	−	2.62624i	0.349378	−	0.0936155i	−0.0798623	−	0.996806i	$-0.525448\pi$
$787$	9.80128	−	2.62624i	0.349378	−	0.0936155i	0.429240	+	0.903190i	$0.358781\pi$
$788$	−13.4993	−	3.61712i	−0.480891	−	0.128854i
$789$		0			0
$790$	−28.7986	+	16.6269i	−1.02461	+	0.591557i
$791$	−2.85255	−	10.6459i	−0.101425	−	0.378523i
$792$		0			0
$793$	19.9606	−	32.1074i	0.708822	−	1.14017i
$794$	−2.79232	−	1.61215i	−0.0990958	−	0.0572130i
$795$		0			0
$796$	5.44630			0.193039
$797$	20.6189	−	35.7129i	0.730358	−	1.26502i	−0.226373	−	0.974041i	$-0.572687\pi$
$797$	20.6189	−	35.7129i	0.730358	−	1.26502i	0.956730	−	0.290976i	$-0.0939799\pi$
$798$		0			0
$799$	3.18185	−	3.18185i	0.112566	−	0.112566i
$800$	10.0330	+	2.68834i	0.354720	+	0.0950471i
$801$		0			0
$802$	−4.61213	−	7.98844i	−0.162860	−	0.282082i
$803$	−11.0589	−	19.1546i	−0.390261	−	0.675951i
$804$		0			0
$805$	20.7659	−	11.9892i	0.731902	−	0.422564i
$806$	−5.28971	−	9.89365i	−0.186322	−	0.348489i
$807$		0			0
$808$	−8.99470	−	2.41012i	−0.316432	−	0.0847878i
$809$	−22.9401	−	13.2445i	−0.806532	−	0.465651i	0.0392184	−	0.999231i	$-0.487513\pi$
$809$	−22.9401	−	13.2445i	−0.806532	−	0.465651i	−0.845750	+	0.533579i	$0.820847\pi$
$810$		0			0
$811$	−27.7759	+	27.7759i	−0.975343	+	0.975343i	−0.999703	−	0.0243602i	$-0.992245\pi$
$811$	−27.7759	+	27.7759i	−0.975343	+	0.975343i	0.0243602	+	0.999703i	$0.492245\pi$
$812$	−4.07894	−	4.07894i	−0.143143	−	0.143143i
$813$		0			0
$814$	6.21248	−	23.1853i	0.217747	−	0.812644i
$815$	−11.1031	−	6.41039i	−0.388925	−	0.224546i
$816$		0			0
$817$	2.39606	−	8.94221i	0.0838274	−	0.312848i
$818$	9.43133			0.329759
$819$		0			0
$820$	1.08888			0.0380253
$821$	−7.32634	+	27.3423i	−0.255691	+	0.954251i	0.712014	+	0.702165i	$0.247783\pi$
$821$	−7.32634	+	27.3423i	−0.255691	+	0.954251i	−0.967705	+	0.252086i	$0.918883\pi$
$822$		0			0
$823$	2.76090	+	1.59401i	0.0962390	+	0.0555636i	0.547347	−	0.836906i	$-0.315638\pi$
$823$	2.76090	+	1.59401i	0.0962390	+	0.0555636i	−0.451108	+	0.892469i	$0.648971\pi$
$824$	14.6505	−	54.6764i	0.510374	−	1.90474i
$825$		0			0
$826$	16.0889	+	16.0889i	0.559805	+	0.559805i
$827$	40.4226	−	40.4226i	1.40563	−	1.40563i	0.625027	−	0.780603i	$-0.285088\pi$
$827$	40.4226	−	40.4226i	1.40563	−	1.40563i	0.780603	−	0.625027i	$-0.214912\pi$
$828$		0			0
$829$	0.372721	+	0.215190i	0.0129451	+	0.00747387i	0.506459	−	0.862264i	$-0.330954\pi$
$829$	0.372721	+	0.215190i	0.0129451	+	0.00747387i	−0.493513	+	0.869738i	$0.664288\pi$
$830$	−9.09400	−	2.43673i	−0.315657	−	0.0845801i
$831$		0			0
$832$	−26.8658	−	16.7020i	−0.931405	−	0.579038i
$833$	7.84759	−	4.53081i	0.271903	−	0.156983i
$834$		0			0
$835$	0.512252	+	0.887247i	0.0177272	+	0.0307044i
$836$	2.28848	+	3.96376i	0.0791488	+	0.137090i
$837$		0			0
$838$	35.0510	+	9.39190i	1.21082	+	0.324438i
$839$	3.41628	−	3.41628i	0.117943	−	0.117943i	−0.645672	−	0.763615i	$-0.723423\pi$
$839$	3.41628	−	3.41628i	0.117943	−	0.117943i	0.763615	+	0.645672i	$0.223423\pi$
$840$		0			0
$841$	7.95100	−	13.7715i	0.274172	−	0.474880i
$842$	−9.29085			−0.320184
$843$		0			0
$844$	2.63244	+	1.51984i	0.0906122	+	0.0523150i
$845$	−36.6520	+	7.29919i	−1.26087	+	0.251100i
$846$		0			0
$847$	−3.04160	−	11.3514i	−0.104511	−	0.390040i
$848$	24.9666	−	14.4145i	0.857357	−	0.494995i
$849$		0			0
$850$	7.05251	+	1.88971i	0.241899	+	0.0648166i
$851$	−63.1724	+	16.9270i	−2.16552	+	0.580250i
$852$		0			0
$853$	43.1437	−	11.5603i	1.47721	−	0.395818i	0.571815	−	0.820383i	$-0.306240\pi$
$853$	43.1437	−	11.5603i	1.47721	−	0.395818i	0.905397	+	0.424565i	$0.139573\pi$
$854$	−15.9513	+	9.20951i	−0.545843	+	0.315143i
$855$		0			0
$856$	−13.6267	+	3.65125i	−0.465750	+	0.124797i
$857$	25.1388	−	43.5417i	0.858725	−	1.48736i	−0.0144207	−	0.999896i	$-0.504590\pi$
$857$	25.1388	−	43.5417i	0.858725	−	1.48736i	0.873146	−	0.487459i	$-0.162076\pi$
$858$		0			0
$859$	25.1679	+	43.5920i	0.858717	+	1.48734i	0.873153	+	0.487445i	$0.162071\pi$
$859$	25.1679	+	43.5920i	0.858717	+	1.48734i	−0.0144366	+	0.999896i	$0.504595\pi$
$860$	−2.43796	−	2.43796i	−0.0831339	−	0.0831339i
$861$		0			0
$862$			38.1249i			1.29854i
$863$	−29.3689	−	29.3689i	−0.999728	−	0.999728i	0.000272025	−	1.00000i	$-0.499913\pi$
$863$	−29.3689	−	29.3689i	−0.999728	−	0.999728i	−1.00000		0.000272025i	$0.999913\pi$
$864$		0			0
$865$	8.85231	−	33.0373i	0.300988	−	1.12330i
$866$	6.98281	+	26.0602i	0.237286	+	0.885562i
$867$		0			0
$868$		−	2.25047i		−	0.0763858i
$869$	−11.9761	+	11.9761i	−0.406263	+	0.406263i
$870$		0			0
$871$	2.97355	+	12.7463i	0.100755	+	0.431893i
$872$			0.602650i			0.0204083i
$873$		0			0
$874$	−15.1442	+	26.2304i	−0.512259	+	0.887258i
$875$	7.36439			0.248962
$876$		0			0
$877$	−4.54744	−	16.9713i	−0.153556	−	0.573080i	−0.999225	−	0.0393710i	$-0.987465\pi$
$877$	−4.54744	−	16.9713i	−0.153556	−	0.573080i	0.845668	−	0.533709i	$-0.179202\pi$
$878$	9.97527	+	37.2282i	0.336649	+	1.25639i
$879$		0			0
$880$	−12.4905			−0.421054
$881$	−11.7668	+	20.3807i	−0.396434	+	0.686644i	−0.993283	−	0.115710i	$-0.963086\pi$
$881$	−11.7668	+	20.3807i	−0.396434	+	0.686644i	0.596849	+	0.802354i	$0.296419\pi$
$882$		0			0
$883$		−	5.09275i		−	0.171385i	−0.996322	−	0.0856923i	$-0.972690\pi$
$883$		−	5.09275i		−	0.171385i	0.996322	−	0.0856923i	$-0.0273102\pi$
$884$	3.35654	+	2.08670i	0.112893	+	0.0701835i
$885$		0			0
$886$	20.4151	−	20.4151i	0.685858	−	0.685858i
$887$			13.2225i			0.443969i	0.975050	+	0.221985i	$0.0712535\pi$
$887$			13.2225i			0.443969i	−0.975050	+	0.221985i	$0.928747\pi$
$888$		0			0
$889$	−4.13304	−	15.4247i	−0.138618	−	0.517329i
$890$	5.38181	−	20.0852i	0.180399	−	0.673256i
$891$		0			0
$892$	−2.82276	−	2.82276i	−0.0945129	−	0.0945129i
$893$		−	10.7811i		−	0.360775i
$894$		0			0
$895$	11.9107	+	11.9107i	0.398132	+	0.398132i
$896$	3.00983	+	5.21318i	0.100551	+	0.174160i
$897$		0			0
$898$	6.41059	−	11.1035i	0.213924	−	0.370528i
$899$	16.9207	−	4.53390i	0.564338	−	0.151214i
$900$		0			0
$901$	−18.8190	+	10.8651i	−0.626951	+	0.361970i
$902$	−1.30106	+	0.348619i	−0.0433207	+	0.0116077i
$903$		0			0
$904$	22.1798	−	5.94307i	0.737690	−	0.197664i
$905$	23.0412	+	6.17388i	0.765917	+	0.205227i
$906$		0			0
$907$	8.56612	−	4.94565i	0.284433	−	0.164218i	−0.350995	−	0.936377i	$-0.614157\pi$
$907$	8.56612	−	4.94565i	0.284433	−	0.164218i	0.635429	+	0.772160i	$0.280823\pi$
$908$	1.92806	+	7.19562i	0.0639850	+	0.238795i
$909$		0			0
$910$	17.4239	+	5.28333i	0.577598	+	0.175141i
$911$	10.2559	+	5.92123i	0.339792	+	0.196179i	0.660180	−	0.751107i	$-0.270480\pi$
$911$	10.2559	+	5.92123i	0.339792	+	0.196179i	−0.320388	+	0.947286i	$0.603813\pi$
$912$		0			0
$913$	−4.79516			−0.158697
$914$	−14.3378	+	24.8338i	−0.474252	+	0.821429i
$915$		0			0
$916$	−7.51964	+	7.51964i	−0.248456	+	0.248456i
$917$	−11.2685	−	3.01937i	−0.372117	−	0.0997085i
$918$		0			0
$919$	−1.00599	−	1.74243i	−0.0331846	−	0.0574775i	0.848956	−	0.528463i	$-0.177232\pi$
$919$	−1.00599	−	1.74243i	−0.0331846	−	0.0574775i	−0.882141	+	0.470986i	$0.843898\pi$
$920$	24.9786	+	43.2642i	0.823520	+	1.42638i
$921$		0			0
$922$	3.04499	−	1.75803i	0.100281	−	0.0578975i
$923$	−28.5403	−	30.4652i	−0.939415	−	1.00278i
$924$		0			0
$925$	36.4855	+	9.77625i	1.19963	+	0.321441i
$926$	−1.91482	−	1.10552i	−0.0629248	−	0.0363297i
$927$		0			0
$928$	15.0775	−	15.0775i	0.494943	−	0.494943i
$929$	29.4569	+	29.4569i	0.966450	+	0.966450i	0.999455	−	0.0330054i	$-0.0105078\pi$
$929$	29.4569	+	29.4569i	0.966450	+	0.966450i	−0.0330054	+	0.999455i	$0.510508\pi$
$930$		0			0
$931$	5.61914	−	20.9709i	0.184160	−	0.687294i
$932$	2.15726	+	1.24549i	0.0706633	+	0.0407974i
$933$		0			0
$934$	4.94048	−	18.4381i	0.161657	−	0.603313i
$935$	9.41490			0.307900
$936$		0			0
$937$	47.9819			1.56750			0.783750	−	0.621077i	$-0.213304\pi$
$937$	47.9819			1.56750			0.783750	+	0.621077i	$0.213304\pi$
$938$	1.65041	−	6.15941i	0.0538878	−	0.201112i
$939$		0			0
$940$	−3.47724	−	2.00759i	−0.113415	−	0.0654802i
$941$	−6.36477	+	23.7536i	−0.207485	+	0.774346i	0.781192	+	0.624291i	$0.214612\pi$
$941$	−6.36477	+	23.7536i	−0.207485	+	0.774346i	−0.988678	+	0.150056i	$0.952055\pi$
$942$		0			0
$943$	2.59510	+	2.59510i	0.0845081	+	0.0845081i
$944$	−22.8350	+	22.8350i	−0.743216	+	0.743216i
$945$		0			0
$946$	3.69358	+	2.13249i	0.120089	+	0.0693332i
$947$	40.3879	+	10.8219i	1.31243	+	0.351665i	0.846138	−	0.532965i	$-0.178922\pi$
$947$	40.3879	+	10.8219i	1.31243	+	0.351665i	0.466294	+	0.884630i	$0.345589\pi$
$948$		0			0
$949$	−44.5632	+	10.3960i	−1.44658	+	0.337469i
$950$	15.1495	−	8.74657i	0.491515	−	0.283776i
$951$		0			0
$952$	−4.26388	−	7.38525i	−0.138193	−	0.239357i
$953$	−3.67150	−	6.35923i	−0.118932	−	0.205996i	0.800413	−	0.599449i	$-0.204614\pi$
$953$	−3.67150	−	6.35923i	−0.118932	−	0.205996i	−0.919345	+	0.393453i	$0.871280\pi$
$954$		0			0
$955$	19.8822	+	5.32742i	0.643373	+	0.172391i
$956$	0.464654	−	0.464654i	0.0150280	−	0.0150280i
$957$		0			0
$958$	−22.0449	+	38.1829i	−0.712239	+	1.23363i
$959$	−12.4912			−0.403362
$960$		0			0
$961$	−20.9282	−	12.0829i	−0.675104	−	0.389772i
$962$	−42.1747	−	26.2193i	−1.35977	−	0.845343i
$963$		0			0
$964$	−1.33275	−	4.97388i	−0.0429249	−	0.160198i
$965$	−6.82013	+	3.93760i	−0.219548	+	0.126756i
$966$		0			0
$967$	−25.3368	−	6.78898i	−0.814778	−	0.218319i	−0.172716	−	0.984972i	$-0.555254\pi$
$967$	−25.3368	−	6.78898i	−0.814778	−	0.218319i	−0.642062	+	0.766653i	$0.721921\pi$
$968$	23.6498	−	6.33696i	0.760135	−	0.203677i
$969$		0			0
$970$	−17.3295	+	4.64343i	−0.556417	+	0.149091i
$971$	−11.1860	+	6.45823i	−0.358975	+	0.207255i	−0.668631	−	0.743594i	$-0.733120\pi$
$971$	−11.1860	+	6.45823i	−0.358975	+	0.207255i	0.309656	+	0.950849i	$0.399786\pi$
$972$		0			0
$973$	−0.669888	+	0.179496i	−0.0214756	+	0.00575438i
$974$	−12.0534	+	20.8771i	−0.386217	+	0.668947i
$975$		0			0
$976$	−13.0711	−	22.6397i	−0.418394	−	0.724680i
$977$	24.5234	+	24.5234i	0.784573	+	0.784573i	0.980599	−	0.196026i	$-0.0628037\pi$
$977$	24.5234	+	24.5234i	0.784573	+	0.784573i	−0.196026	+	0.980599i	$0.562804\pi$
$978$		0			0
$979$		−	10.5907i		−	0.338479i
$980$	−5.71742	−	5.71742i	−0.182636	−	0.182636i
$981$		0			0
$982$	3.49299	−	13.0360i	0.111466	−	0.415996i
$983$	−7.33678	−	27.3813i	−0.234007	−	0.873326i	−0.978594	−	0.205801i	$-0.934020\pi$
$983$	−7.33678	−	27.3813i	−0.234007	−	0.873326i	0.744587	−	0.667526i	$-0.232647\pi$
$984$		0			0
$985$			68.8768i			2.19460i
$986$	10.5984	−	10.5984i	0.337522	−	0.337522i
$987$		0			0
$988$	9.22170	−	2.15130i	0.293381	−	0.0684421i
$989$		−	11.6207i		−	0.369516i
$990$		0			0
$991$	0.249119	−	0.431486i	0.00791352	−	0.0137066i	−0.862042	−	0.506838i	$-0.830814\pi$
$991$	0.249119	−	0.431486i	0.00791352	−	0.0137066i	0.869955	+	0.493131i	$0.164148\pi$
$992$	8.31867			0.264118
$993$		0			0
$994$	5.26390	+	19.6451i	0.166961	+	0.623106i
$995$	−6.94711	−	25.9270i	−0.220238	−	0.821940i
$996$		0			0
$997$	39.9905			1.26651			0.633255	−	0.773943i	$-0.281718\pi$
$997$	39.9905			1.26651			0.633255	+	0.773943i	$0.281718\pi$
$998$	−3.04127	+	5.26764i	−0.0962698	+	0.166744i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.bf.a.305.4		48
3.2	odd	2		117.2.bc.a.110.9	yes	48
9.4	even	3		117.2.x.a.32.4	yes	48
9.5	odd	6		351.2.ba.a.71.9		48
13.11	odd	12		351.2.ba.a.89.9		48
39.11	even	12		117.2.x.a.11.4	✓	48
117.50	even	12	inner	351.2.bf.a.206.4		48
117.76	odd	12		117.2.bc.a.50.9	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.11.4	✓	48	39.11	even	12
117.2.x.a.32.4	yes	48	9.4	even	3
117.2.bc.a.50.9	yes	48	117.76	odd	12
117.2.bc.a.110.9	yes	48	3.2	odd	2
351.2.ba.a.71.9		48	9.5	odd	6
351.2.ba.a.89.9		48	13.11	odd	12
351.2.bf.a.206.4		48	117.50	even	12	inner
351.2.bf.a.305.4		48	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.bf (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.308060 + 1.14969i) q^{2} +(0.505155 + 0.291651i) q^{4} +(0.744040 - 2.77680i) q^{5} +(1.04357 + 1.04357i) q^{7} +(-2.17420 + 2.17420i) q^{8} +(2.96326 + 1.71084i) q^{10} +(1.68335 + 0.451052i) q^{11} +(1.90363 - 3.06206i) q^{13} +(-1.52127 + 0.878303i) q^{14} +(-1.24658 - 2.15913i) q^{16} +(0.939625 + 1.62748i) q^{17} +(4.34907 + 1.16533i) q^{19} +(1.18571 - 1.18571i) q^{20} +(-1.03714 + 1.79639i) q^{22} +5.65176 q^{23} +(-2.82688 - 1.63210i) q^{25} +(2.93400 + 3.13189i) q^{26} +(0.222806 + 0.831522i) q^{28} +(-5.80315 + 3.35045i) q^{29} +(-2.52515 - 0.676611i) q^{31} +(-3.07365 + 0.823583i) q^{32} +(-2.16056 + 0.578921i) q^{34} +(3.67424 - 2.12132i) q^{35} +(-11.1775 + 2.99499i) q^{37} +(-2.67955 + 4.64111i) q^{38} +(4.41961 + 7.65499i) q^{40} +(0.459167 + 0.459167i) q^{41} -2.05612i q^{43} +(0.718802 + 0.718802i) q^{44} +(-1.74108 + 6.49779i) q^{46} +(-0.619735 - 2.31288i) q^{47} -4.82193i q^{49} +(2.74726 - 2.74726i) q^{50} +(1.85468 - 0.991618i) q^{52} +11.5633i q^{53} +(2.50496 - 4.33872i) q^{55} -4.53785 q^{56} +(-2.06428 - 7.70398i) q^{58} +(-3.35246 - 12.5115i) q^{59} +10.4856 q^{61} +(1.55579 - 2.69471i) q^{62} -8.77378i q^{64} +(-7.08634 - 7.56428i) q^{65} +(-2.56688 + 2.56688i) q^{67} +1.09617i q^{68} +(1.30699 + 4.87774i) q^{70} +(2.99663 - 11.1836i) q^{71} +(-8.97423 - 8.97423i) q^{73} -13.7733i q^{74} +(1.85709 + 1.85709i) q^{76} +(1.28599 + 2.22739i) q^{77} +(-4.85927 + 8.41651i) q^{79} +(-6.92298 + 1.85501i) q^{80} +(-0.669352 + 0.386451i) q^{82} +(-2.65776 + 0.712145i) q^{83} +(5.21830 - 1.39824i) q^{85} +(2.36391 + 0.633407i) q^{86} +(-4.64061 + 2.67926i) q^{88} +(-1.57286 - 5.86998i) q^{89} +(5.18203 - 1.20890i) q^{91} +(2.85501 + 1.64834i) q^{92} +2.85002 q^{94} +(6.47177 - 11.2094i) q^{95} +(-3.70756 + 3.70756i) q^{97} +(5.54374 + 1.48544i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{2} - 6 q^{4} + 6 q^{5} + 2 q^{7} + 30 q^{8} - 12 q^{10} - 6 q^{11} - 2 q^{13} + 12 q^{14} + 14 q^{16} - 4 q^{19} + 6 q^{20} + 2 q^{22} + 12 q^{23} - 48 q^{26} + 6 q^{29} + 6 q^{31} - 30 q^{32}+ \cdots + 36 q^{98}+O(q^{100}) \) 48 * q + 6 * q^2 - 6 * q^4 + 6 * q^5 + 2 * q^7 + 30 * q^8 - 12 * q^10 - 6 * q^11 - 2 * q^13 + 12 * q^14 + 14 * q^16 - 4 * q^19 + 6 * q^20 + 2 * q^22 + 12 * q^23 - 48 * q^26 + 6 * q^29 + 6 * q^31 - 30 * q^32 - 6 * q^34 + 6 * q^35 - 6 * q^37 + 36 * q^38 - 12 * q^40 - 18 * q^41 + 12 * q^44 - 12 * q^46 - 30 * q^47 + 12 * q^50 - 16 * q^52 - 4 * q^55 + 12 * q^56 - 28 * q^58 - 30 * q^59 - 4 * q^61 + 18 * q^62 - 30 * q^65 - 16 * q^67 - 46 * q^70 - 48 * q^71 - 22 * q^73 - 18 * q^76 + 72 * q^77 + 8 * q^79 - 54 * q^80 - 12 * q^82 - 72 * q^83 + 78 * q^85 - 102 * q^86 - 6 * q^88 - 16 * q^91 - 120 * q^92 - 52 * q^94 + 6 * q^95 + 48 * q^97 + 36 * q^98

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