LMFDB - Embedded newform 552.2.q.c.73.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [552,2,Mod(25,552)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(552, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("552.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [30,0,3,0,-2,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			73.1
Character	$\chi$	$=$	552.73
Dual form			552.2.q.c.121.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.959493 - 0.281733i) q^{3} +(-2.87348 - 1.84667i) q^{5} +(0.703532 + 4.89317i) q^{7} +(0.841254 - 0.540641i) q^{9} +(-2.09062 + 4.57781i) q^{11} +(-0.491915 + 3.42134i) q^{13} +(-3.27735 - 0.962317i) q^{15} +(-1.38428 - 1.59755i) q^{17} +(3.06735 - 3.53991i) q^{19} +(2.05360 + 4.49676i) q^{21} +(-2.82684 + 3.87414i) q^{23} +(2.76960 + 6.06458i) q^{25} +(0.654861 - 0.755750i) q^{27} +(2.07622 + 2.39609i) q^{29} +(9.36162 + 2.74882i) q^{31} +(-0.716213 + 4.98137i) q^{33} +(7.01450 - 15.3596i) q^{35} +(-2.85280 + 1.83338i) q^{37} +(0.491915 + 3.42134i) q^{39} +(4.76510 + 3.06234i) q^{41} +(-4.85852 + 1.42659i) q^{43} -3.41571 q^{45} -4.92712 q^{47} +(-16.7317 + 4.91288i) q^{49} +(-1.77829 - 1.14284i) q^{51} +(-0.490126 - 3.40890i) q^{53} +(14.4611 - 9.29356i) q^{55} +(1.94579 - 4.26070i) q^{57} +(0.914938 - 6.36353i) q^{59} +(-10.2199 - 3.00085i) q^{61} +(3.23730 + 3.73604i) q^{63} +(7.73161 - 8.92275i) q^{65} +(-4.16641 - 9.12316i) q^{67} +(-1.62087 + 4.51362i) q^{69} +(4.60850 + 10.0912i) q^{71} +(0.668400 - 0.771374i) q^{73} +(4.36600 + 5.03864i) q^{75} +(-23.8708 - 7.00911i) q^{77} +(-0.398732 + 2.77324i) q^{79} +(0.415415 - 0.909632i) q^{81} +(10.5503 - 6.78028i) q^{83} +(1.02756 + 7.14684i) q^{85} +(2.66718 + 1.71409i) q^{87} +(-3.64562 + 1.07045i) q^{89} -17.0873 q^{91} +9.75684 q^{93} +(-15.3510 + 4.50747i) q^{95} +(8.50849 + 5.46808i) q^{97} +(0.716213 + 4.98137i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9} + 13 q^{11} - 13 q^{13} + 2 q^{15} - 11 q^{17} + 11 q^{19} - 9 q^{21} - 12 q^{23} + 17 q^{25} + 3 q^{27} + 9 q^{29} + 33 q^{31} + 9 q^{33} + 62 q^{35} + 11 q^{37}+ \cdots - 9 q^{99}+O(q^{100}) $ 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9 + 13 * q^11 - 13 * q^13 + 2 * q^15 - 11 * q^17 + 11 * q^19 - 9 * q^21 - 12 * q^23 + 17 * q^25 + 3 * q^27 + 9 * q^29 + 33 * q^31 + 9 * q^33 + 62 * q^35 + 11 * q^37 + 13 * q^39 + 2 * q^41 - 40 * q^43 - 2 * q^45 - 38 * q^47 - 13 * q^49 + 11 * q^51 - 25 * q^53 + 62 * q^55 + 22 * q^57 + 73 * q^59 + 4 * q^61 - 2 * q^63 - 12 * q^65 - 29 * q^67 - 21 * q^69 - 19 * q^71 - 38 * q^73 + 27 * q^75 + 4 * q^77 - 12 * q^79 - 3 * q^81 - 65 * q^83 + 8 * q^85 + 2 * q^87 - 61 * q^89 - 150 * q^91 - 22 * q^93 - 9 * q^95 - 9 * q^97 - 9 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$1$	$1$	$1$

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
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$4$		0			0
$5$	−2.87348	−	1.84667i	−1.28506	−	0.825857i	−0.293556	−	0.955942i	$-0.594839\pi$
$5$	−2.87348	−	1.84667i	−1.28506	−	0.825857i	−0.991503	+	0.130085i	$0.958475\pi$
$6$		0			0
$7$	0.703532	+	4.89317i	0.265910	+	1.84945i	0.485991	+	0.873964i	$0.338459\pi$
$7$	0.703532	+	4.89317i	0.265910	+	1.84945i	−0.220080	+	0.975482i	$0.570632\pi$
$8$		0			0
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$		0			0
$11$	−2.09062	+	4.57781i	−0.630344	+	1.38026i	0.277407	+	0.960753i	$0.410525\pi$
$11$	−2.09062	+	4.57781i	−0.630344	+	1.38026i	−0.907751	+	0.419509i	$0.862202\pi$
$12$		0			0
$13$	−0.491915	+	3.42134i	−0.136433	+	0.948910i	0.800483	+	0.599355i	$0.204576\pi$
$13$	−0.491915	+	3.42134i	−0.136433	+	0.948910i	−0.936916	+	0.349555i	$0.886333\pi$
$14$		0			0
$15$	−3.27735	−	0.962317i	−0.846208	−	0.248469i
$16$		0			0
$17$	−1.38428	−	1.59755i	−0.335738	−	0.387462i	0.562628	−	0.826710i	$-0.309790\pi$
$17$	−1.38428	−	1.59755i	−0.335738	−	0.387462i	−0.898366	+	0.439248i	$0.855245\pi$
$18$		0			0
$19$	3.06735	−	3.53991i	0.703699	−	0.812112i	−0.285548	−	0.958364i	$-0.592176\pi$
$19$	3.06735	−	3.53991i	0.703699	−	0.812112i	0.989247	+	0.146252i	$0.0467212\pi$
$20$		0			0
$21$	2.05360	+	4.49676i	0.448132	+	0.981273i
$22$		0			0
$23$	−2.82684	+	3.87414i	−0.589438	+	0.807814i
$23$	−2.82684	+	3.87414i	−0.589438	+	0.807814i
$24$		0			0
$25$	2.76960	+	6.06458i	0.553920	+	1.21292i
$26$		0			0
$27$	0.654861	−	0.755750i	0.126028	−	0.145444i
$28$		0			0
$29$	2.07622	+	2.39609i	0.385545	+	0.444943i	0.915036	−	0.403373i	$-0.132162\pi$
$29$	2.07622	+	2.39609i	0.385545	+	0.444943i	−0.529491	+	0.848316i	$0.677617\pi$
$30$		0			0
$31$	9.36162	+	2.74882i	1.68140	+	0.493703i	0.976484	−	0.215592i	$-0.0691680\pi$
$31$	9.36162	+	2.74882i	1.68140	+	0.493703i	0.704913	+	0.709294i	$0.250986\pi$
$32$		0			0
$33$	−0.716213	+	4.98137i	−0.124677	+	0.867146i
$34$		0			0
$35$	7.01450	−	15.3596i	1.18567	−	2.59625i
$36$		0			0
$37$	−2.85280	+	1.83338i	−0.468997	+	0.301406i	−0.753710	−	0.657207i	$-0.771738\pi$
$37$	−2.85280	+	1.83338i	−0.468997	+	0.301406i	0.284713	+	0.958613i	$0.408102\pi$
$38$		0			0
$39$	0.491915	+	3.42134i	0.0787695	+	0.547854i
$40$		0			0
$41$	4.76510	+	3.06234i	0.744183	+	0.478257i	0.856973	−	0.515362i	$-0.172342\pi$
$41$	4.76510	+	3.06234i	0.744183	+	0.478257i	−0.112790	+	0.993619i	$0.535979\pi$
$42$		0			0
$43$	−4.85852	+	1.42659i	−0.740918	+	0.217553i	−0.630345	−	0.776315i	$-0.717087\pi$
$43$	−4.85852	+	1.42659i	−0.740918	+	0.217553i	−0.110572	+	0.993868i	$0.535268\pi$
$44$		0			0
$45$	−3.41571			−0.509184
$46$		0			0
$47$	−4.92712			−0.718694			−0.359347	−	0.933204i	$-0.617001\pi$
$47$	−4.92712			−0.718694			−0.359347	+	0.933204i	$0.617001\pi$
$48$		0			0
$49$	−16.7317	+	4.91288i	−2.39025	+	0.701840i
$50$		0			0
$51$	−1.77829	−	1.14284i	−0.249011	−	0.160029i
$52$		0			0
$53$	−0.490126	−	3.40890i	−0.0673240	−	0.468249i	−0.995396	−	0.0958480i	$-0.969444\pi$
$53$	−0.490126	−	3.40890i	−0.0673240	−	0.468249i	0.928072	−	0.372401i	$-0.121465\pi$
$54$		0			0
$55$	14.4611	−	9.29356i	1.94993	−	1.25314i
$56$		0			0
$57$	1.94579	−	4.26070i	0.257727	−	0.564343i
$58$		0			0
$59$	0.914938	−	6.36353i	0.119115	−	0.828461i	−0.839419	−	0.543484i	$-0.817105\pi$
$59$	0.914938	−	6.36353i	0.119115	−	0.828461i	0.958534	−	0.284977i	$-0.0919861\pi$
$60$		0			0
$61$	−10.2199	−	3.00085i	−1.30853	−	0.384219i	−0.448189	−	0.893939i	$-0.647931\pi$
$61$	−10.2199	−	3.00085i	−1.30853	−	0.384219i	−0.860340	+	0.509720i	$0.829749\pi$
$62$		0			0
$63$	3.23730	+	3.73604i	0.407861	+	0.470697i
$64$		0			0
$65$	7.73161	−	8.92275i	0.958988	−	1.10673i
$66$		0			0
$67$	−4.16641	−	9.12316i	−0.509008	−	1.11457i	−0.973436	−	0.228961i	$-0.926467\pi$
$67$	−4.16641	−	9.12316i	−0.509008	−	1.11457i	0.464428	−	0.885611i	$-0.346260\pi$
$68$		0			0
$69$	−1.62087	+	4.51362i	−0.195129	+	0.543376i
$70$		0			0
$71$	4.60850	+	10.0912i	0.546928	+	1.19760i	0.958202	+	0.286093i	$0.0923567\pi$
$71$	4.60850	+	10.0912i	0.546928	+	1.19760i	−0.411274	+	0.911512i	$0.634916\pi$
$72$		0			0
$73$	0.668400	−	0.771374i	0.0782302	−	0.0902825i	−0.715285	−	0.698833i	$-0.753703\pi$
$73$	0.668400	−	0.771374i	0.0782302	−	0.0902825i	0.793515	+	0.608550i	$0.208249\pi$
$74$		0			0
$75$	4.36600	+	5.03864i	0.504143	+	0.581812i
$76$		0			0
$77$	−23.8708	−	7.00911i	−2.72033	−	0.798762i
$78$		0			0
$79$	−0.398732	+	2.77324i	−0.0448608	+	0.312014i	0.955020	+	0.296543i	$0.0958338\pi$
$79$	−0.398732	+	2.77324i	−0.0448608	+	0.312014i	−0.999880	+	0.0154708i	$0.995075\pi$
$80$		0			0
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$		0			0
$83$	10.5503	−	6.78028i	1.15805	−	0.744232i	0.186822	−	0.982394i	$-0.440181\pi$
$83$	10.5503	−	6.78028i	1.15805	−	0.744232i	0.971226	+	0.238162i	$0.0765448\pi$
$84$		0			0
$85$	1.02756	+	7.14684i	0.111455	+	0.775183i
$86$		0			0
$87$	2.66718	+	1.71409i	0.285952	+	0.183770i
$88$		0			0
$89$	−3.64562	+	1.07045i	−0.386435	+	0.113467i	−0.469178	−	0.883103i	$-0.655450\pi$
$89$	−3.64562	+	1.07045i	−0.386435	+	0.113467i	0.0827437	+	0.996571i	$0.473632\pi$
$90$		0			0
$91$	−17.0873			−1.79124
$92$		0			0
$93$	9.75684			1.01174
$94$		0			0
$95$	−15.3510	+	4.50747i	−1.57498	+	0.462457i
$96$		0			0
$97$	8.50849	+	5.46808i	0.863907	+	0.555199i	0.895883	−	0.444290i	$-0.146544\pi$
$97$	8.50849	+	5.46808i	0.863907	+	0.555199i	−0.0319767	+	0.999489i	$0.510180\pi$
$98$		0			0
$99$	0.716213	+	4.98137i	0.0719821	+	0.500647i
$100$		0			0
$101$	9.49342	−	6.10105i	0.944630	−	0.607077i	0.0249262	−	0.999689i	$-0.492065\pi$
$101$	9.49342	−	6.10105i	0.944630	−	0.607077i	0.919704	+	0.392612i	$0.128429\pi$
$102$		0			0
$103$	−3.25514	+	7.12775i	−0.320738	+	0.702318i	−0.999486	−	0.0320528i	$-0.989796\pi$
$103$	−3.25514	+	7.12775i	−0.320738	+	0.702318i	0.678748	+	0.734371i	$0.262523\pi$
$104$		0			0
$105$	2.40306	−	16.7137i	0.234515	−	1.63109i
$106$		0			0
$107$	−1.31048	−	0.384792i	−0.126689	−	0.0371993i	0.217773	−	0.975999i	$-0.430121\pi$
$107$	−1.31048	−	0.384792i	−0.126689	−	0.0371993i	−0.344462	+	0.938800i	$0.611939\pi$
$108$		0			0
$109$	4.97531	+	5.74182i	0.476548	+	0.549966i	0.942221	−	0.334991i	$-0.108733\pi$
$109$	4.97531	+	5.74182i	0.476548	+	0.549966i	−0.465673	+	0.884957i	$0.654188\pi$
$110$		0			0
$111$	−2.22072	+	2.56284i	−0.210781	+	0.243254i
$112$		0			0
$113$	−0.631856	−	1.38357i	−0.0594400	−	0.130155i	0.877581	−	0.479428i	$-0.159156\pi$
$113$	−0.631856	−	1.38357i	−0.0594400	−	0.130155i	−0.937021	+	0.349273i	$0.886429\pi$
$114$		0			0
$115$	15.2771	−	5.91200i	1.42460	−	0.551297i
$116$		0			0
$117$	1.43589	+	3.14417i	0.132748	+	0.290678i
$118$		0			0
$119$	6.84319	−	7.89747i	0.627315	−	0.723960i
$120$		0			0
$121$	−9.38221	−	10.8276i	−0.852928	−	0.984331i
$122$		0			0
$123$	5.43484	+	1.59581i	0.490043	+	0.143890i
$124$		0			0
$125$	0.810375	−	5.63628i	0.0724821	−	0.504124i
$126$		0			0
$127$	8.80451	−	19.2792i	0.781274	−	1.71075i	0.0811813	−	0.996699i	$-0.474131\pi$
$127$	8.80451	−	19.2792i	0.781274	−	1.71075i	0.700093	−	0.714052i	$-0.253142\pi$
$128$		0			0
$129$	−4.25980	+	2.73761i	−0.375054	+	0.241033i
$130$		0			0
$131$	1.16636	+	8.11218i	0.101905	+	0.708764i	0.975160	+	0.221501i	$0.0710956\pi$
$131$	1.16636	+	8.11218i	0.101905	+	0.708764i	−0.873255	+	0.487263i	$0.837995\pi$
$132$		0			0
$133$	19.4794	+	12.5186i	1.68908	+	1.08550i
$134$		0			0
$135$	−3.27735	+	0.962317i	−0.282069	+	0.0828230i
$136$		0			0
$137$	4.99660			0.426888			0.213444	−	0.976955i	$-0.431532\pi$
$137$	4.99660			0.426888			0.213444	+	0.976955i	$0.431532\pi$
$138$		0			0
$139$	14.2857			1.21170			0.605850	−	0.795579i	$-0.292833\pi$
$139$	14.2857			1.21170			0.605850	+	0.795579i	$0.292833\pi$
$140$		0			0
$141$	−4.72753	+	1.38813i	−0.398130	+	0.116902i
$142$		0			0
$143$	−14.6339	−	9.40461i	−1.22375	−	0.786453i
$144$		0			0
$145$	−1.54119	−	10.7192i	−0.127989	−	0.890182i
$146$		0			0
$147$	−14.6699	+	9.42775i	−1.20995	+	0.777588i
$148$		0			0
$149$	0.513006	−	1.12333i	0.0420271	−	0.0920266i	−0.887454	−	0.460896i	$-0.847528\pi$
$149$	0.513006	−	1.12333i	0.0420271	−	0.0920266i	0.929481	+	0.368870i	$0.120255\pi$
$150$		0			0
$151$	−0.696590	+	4.84489i	−0.0566877	+	0.394272i	0.941648	+	0.336600i	$0.109277\pi$
$151$	−0.696590	+	4.84489i	−0.0566877	+	0.394272i	−0.998336	+	0.0576721i	$0.981632\pi$
$152$		0			0
$153$	−2.02823	−	0.595543i	−0.163973	−	0.0481468i
$154$		0			0
$155$	−21.8242	−	25.1865i	−1.75296	−	2.02303i
$156$		0			0
$157$	8.95207	−	10.3312i	0.714453	−	0.824522i	−0.276176	−	0.961107i	$-0.589067\pi$
$157$	8.95207	−	10.3312i	0.714453	−	0.824522i	0.990628	+	0.136585i	$0.0436126\pi$
$158$		0			0
$159$	−1.43067	−	3.13273i	−0.113460	−	0.248442i
$160$		0			0
$161$	−20.9456	−	11.1067i	−1.65075	−	0.875327i
$162$		0			0
$163$	−6.49793	−	14.2285i	−0.508957	−	1.11446i	−0.973453	−	0.228885i	$-0.926492\pi$
$163$	−6.49793	−	14.2285i	−0.508957	−	1.11446i	0.464496	−	0.885575i	$-0.346235\pi$
$164$		0			0
$165$	11.2570	−	12.9913i	0.876355	−	1.01137i
$166$		0			0
$167$	−9.46263	−	10.9205i	−0.732241	−	0.845051i	0.260481	−	0.965479i	$-0.416119\pi$
$167$	−9.46263	−	10.9205i	−0.732241	−	0.845051i	−0.992722	+	0.120428i	$0.961573\pi$
$168$		0			0
$169$	1.00979	+	0.296501i	0.0776760	+	0.0228077i
$170$		0			0
$171$	0.666599	−	4.63630i	0.0509761	−	0.354547i
$172$		0			0
$173$	−7.27320	+	15.9261i	−0.552971	+	1.21084i	0.402409	+	0.915460i	$0.368173\pi$
$173$	−7.27320	+	15.9261i	−0.552971	+	1.21084i	−0.955380	+	0.295378i	$0.904554\pi$
$174$		0			0
$175$	−27.7266	+	17.8188i	−2.09593	+	1.34697i
$176$		0			0
$177$	−0.914938	−	6.36353i	−0.0687709	−	0.478312i
$178$		0			0
$179$	19.4108	+	12.4746i	1.45083	+	0.932395i	0.999192	+	0.0401964i	$0.0127984\pi$
$179$	19.4108	+	12.4746i	1.45083	+	0.932395i	0.451643	+	0.892199i	$0.350838\pi$
$180$		0			0
$181$	−7.93691	+	2.33049i	−0.589946	+	0.173224i	−0.563062	−	0.826415i	$-0.690377\pi$
$181$	−7.93691	+	2.33049i	−0.589946	+	0.173224i	−0.0268842	+	0.999639i	$0.508559\pi$
$182$		0			0
$183$	−10.6514			−0.787374
$184$		0			0
$185$	11.5831			0.851607
$186$		0			0
$187$	10.2073	−	2.99713i	0.746430	−	0.219172i
$188$		0			0
$189$	4.15873	+	2.67265i	0.302503	+	0.194407i
$190$		0			0
$191$	1.19467	+	8.30908i	0.0864430	+	0.601224i	0.986290	+	0.165019i	$0.0527686\pi$
$191$	1.19467	+	8.30908i	0.0864430	+	0.601224i	−0.899847	+	0.436205i	$0.856322\pi$
$192$		0			0
$193$	−0.762780	+	0.490209i	−0.0549061	+	0.0352860i	−0.567806	−	0.823162i	$-0.692208\pi$
$193$	−0.762780	+	0.490209i	−0.0549061	+	0.0352860i	0.512900	+	0.858448i	$0.328571\pi$
$194$		0			0
$195$	4.90460	−	10.7396i	0.351225	−	0.769076i
$196$		0			0
$197$	2.37751	−	16.5359i	0.169390	−	1.17814i	−0.710758	−	0.703437i	$-0.751648\pi$
$197$	2.37751	−	16.5359i	0.169390	−	1.17814i	0.880148	−	0.474699i	$-0.157443\pi$
$198$		0			0
$199$	4.96618	+	1.45820i	0.352044	+	0.103369i	0.452973	−	0.891524i	$-0.350363\pi$
$199$	4.96618	+	1.45820i	0.352044	+	0.103369i	−0.100929	+	0.994894i	$0.532182\pi$
$200$		0			0
$201$	−6.56793	−	7.57980i	−0.463266	−	0.534638i
$202$		0			0
$203$	−10.2638	+	11.8450i	−0.720377	+	0.831359i
$204$		0			0
$205$	−8.03726	−	17.5991i	−0.561346	−	1.22918i
$206$		0			0
$207$	−0.283575	+	4.78744i	−0.0197098	+	0.332750i
$208$		0			0
$209$	9.79240	+	21.4424i	0.677354	+	1.48320i
$210$		0			0
$211$	−0.399271	+	0.460783i	−0.0274869	+	0.0317216i	−0.769327	−	0.638856i	$-0.779408\pi$
$211$	−0.399271	+	0.460783i	−0.0274869	+	0.0317216i	0.741840	+	0.670577i	$0.233954\pi$
$212$		0			0
$213$	7.26484	+	8.38407i	0.497779	+	0.574467i
$214$		0			0
$215$	16.5953	+	4.87282i	1.13179	+	0.332324i
$216$		0			0
$217$	−6.86425	+	47.7419i	−0.465976	+	3.24093i
$218$		0			0
$219$	0.424003	−	0.928438i	0.0286515	−	0.0627380i
$220$		0			0
$221$	6.14671	−	3.95025i	0.413473	−	0.265723i
$222$		0			0
$223$	1.51682	+	10.5497i	0.101574	+	0.706463i	0.975435	+	0.220287i	$0.0706994\pi$
$223$	1.51682	+	10.5497i	0.101574	+	0.706463i	−0.873861	+	0.486176i	$0.838392\pi$
$224$		0			0
$225$	5.60870	+	3.60449i	0.373913	+	0.240299i
$226$		0			0
$227$	−5.94430	+	1.74540i	−0.394537	+	0.115846i	−0.472982	−	0.881072i	$-0.656823\pi$
$227$	−5.94430	+	1.74540i	−0.394537	+	0.115846i	0.0784455	+	0.996918i	$0.475004\pi$
$228$		0			0
$229$	11.9929			0.792515			0.396257	−	0.918139i	$-0.370309\pi$
$229$	11.9929			0.792515			0.396257	+	0.918139i	$0.370309\pi$
$230$		0			0
$231$	−24.8786			−1.63689
$232$		0			0
$233$	1.27154	−	0.373357i	0.0833012	−	0.0244594i	−0.239816	−	0.970818i	$-0.577087\pi$
$233$	1.27154	−	0.373357i	0.0833012	−	0.0244594i	0.323118	+	0.946359i	$0.395269\pi$
$234$		0			0
$235$	14.1580	+	9.09877i	0.923564	+	0.593538i
$236$		0			0
$237$	0.398732	+	2.77324i	0.0259004	+	0.180141i
$238$		0			0
$239$	22.0817	−	14.1910i	1.42835	−	0.917942i	0.428449	−	0.903566i	$-0.359060\pi$
$239$	22.0817	−	14.1910i	1.42835	−	0.917942i	0.999897	−	0.0143758i	$-0.00457612\pi$
$240$		0			0
$241$	1.14712	−	2.51184i	0.0738925	−	0.161802i	−0.869081	−	0.494670i	$-0.835289\pi$
$241$	1.14712	−	2.51184i	0.0738925	−	0.161802i	0.942974	+	0.332868i	$0.108016\pi$
$242$		0			0
$243$	0.142315	−	0.989821i	0.00912950	−	0.0634971i
$244$		0			0
$245$	57.1508	+	16.7810i	3.65123	+	1.07210i
$246$		0			0
$247$	10.6024	+	12.2358i	0.674614	+	0.778546i
$248$		0			0
$249$	8.21273	−	9.47800i	0.520461	−	0.600644i
$250$		0			0
$251$	12.0159	+	26.3111i	0.758436	+	1.66074i	0.750585	+	0.660774i	$0.229772\pi$
$251$	12.0159	+	26.3111i	0.758436	+	1.66074i	0.00785143	+	0.999969i	$0.497501\pi$
$252$		0			0
$253$	−11.8252	−	21.0401i	−0.743446	−	1.32278i
$254$		0			0
$255$	2.99943	+	6.56784i	0.187832	+	0.411294i
$256$		0			0
$257$	3.38822	−	3.91022i	0.211351	−	0.243913i	−0.640169	−	0.768234i	$-0.721136\pi$
$257$	3.38822	−	3.91022i	0.211351	−	0.243913i	0.851520	+	0.524322i	$0.175681\pi$
$258$		0			0
$259$	−10.9781	−	12.6694i	−0.682145	−	0.787238i
$260$		0			0
$261$	3.04205	+	0.893228i	0.188298	+	0.0552894i
$262$		0			0
$263$	−2.16806	+	15.0792i	−0.133688	+	0.929824i	0.807000	+	0.590552i	$0.201090\pi$
$263$	−2.16806	+	15.0792i	−0.133688	+	0.929824i	−0.940688	+	0.339272i	$0.889819\pi$
$264$		0			0
$265$	−4.88676	+	10.7005i	−0.300191	+	0.657327i
$266$		0			0
$267$	−3.19636	+	2.05418i	−0.195614	+	0.125714i
$268$		0			0
$269$	0.681017	+	4.73658i	0.0415223	+	0.288794i	0.999994	+	0.00360468i	$0.00114741\pi$
$269$	0.681017	+	4.73658i	0.0415223	+	0.288794i	−0.958471	+	0.285189i	$0.907944\pi$
$270$		0			0
$271$	−8.92505	−	5.73578i	−0.542158	−	0.348424i	0.240724	−	0.970594i	$-0.422615\pi$
$271$	−8.92505	−	5.73578i	−0.542158	−	0.348424i	−0.782882	+	0.622170i	$0.786251\pi$
$272$		0			0
$273$	−16.3952	+	4.81405i	−0.992280	+	0.291360i
$274$		0			0
$275$	−33.5527			−2.02330
$276$		0			0
$277$	−23.5085			−1.41249			−0.706244	−	0.707968i	$-0.749612\pi$
$277$	−23.5085			−1.41249			−0.706244	+	0.707968i	$0.749612\pi$
$278$		0			0
$279$	9.36162	−	2.74882i	0.560465	−	0.164568i
$280$		0			0
$281$	4.14304	+	2.66257i	0.247153	+	0.158835i	0.658352	−	0.752710i	$-0.271254\pi$
$281$	4.14304	+	2.66257i	0.247153	+	0.158835i	−0.411200	+	0.911545i	$0.634890\pi$
$282$		0			0
$283$	4.00486	+	27.8544i	0.238064	+	1.65577i	0.661573	+	0.749881i	$0.269889\pi$
$283$	4.00486	+	27.8544i	0.238064	+	1.65577i	−0.423509	+	0.905892i	$0.639202\pi$
$284$		0			0
$285$	−13.4593	+	8.64977i	−0.797260	+	0.512368i
$286$		0			0
$287$	−11.6322	+	25.4709i	−0.686625	+	1.50350i
$288$		0			0
$289$	1.78343	−	12.4040i	0.104908	−	0.729650i
$290$		0			0
$291$	9.70437	+	2.84946i	0.568881	+	0.167038i
$292$		0			0
$293$	−0.662689	−	0.764784i	−0.0387147	−	0.0446791i	0.736062	−	0.676914i	$-0.236683\pi$
$293$	−0.662689	−	0.764784i	−0.0387147	−	0.0446791i	−0.774777	+	0.632235i	$0.782138\pi$
$294$		0			0
$295$	−14.3804	+	16.5959i	−0.837260	+	0.966250i
$296$		0			0
$297$	2.09062	+	4.57781i	0.121310	+	0.265632i
$298$		0			0
$299$	−11.8642	−	11.5774i	−0.686124	−	0.669536i
$300$		0			0
$301$	−10.3987	−	22.7699i	−0.599370	−	1.31244i
$302$		0			0
$303$	7.39000	−	8.52852i	0.424545	−	0.489951i
$304$		0			0
$305$	23.8252	+	27.4957i	1.36423	+	1.57440i
$306$		0			0
$307$	−5.61007	−	1.64726i	−0.320183	−	0.0940143i	0.117692	−	0.993050i	$-0.462451\pi$
$307$	−5.61007	−	1.64726i	−0.320183	−	0.0940143i	−0.437875	+	0.899036i	$0.644269\pi$
$308$		0			0
$309$	−1.11516	+	7.75611i	−0.0634392	+	0.441229i
$310$		0			0
$311$	−9.67440	+	21.1840i	−0.548585	+	1.20123i	0.408855	+	0.912599i	$0.365928\pi$
$311$	−9.67440	+	21.1840i	−0.548585	+	1.20123i	−0.957440	+	0.288633i	$0.906799\pi$
$312$		0			0
$313$	13.0872	−	8.41063i	0.739732	−	0.475397i	−0.115718	−	0.993282i	$-0.536917\pi$
$313$	13.0872	−	8.41063i	0.739732	−	0.475397i	0.855450	+	0.517885i	$0.173281\pi$
$314$		0			0
$315$	−2.40306	−	16.7137i	−0.135397	−	0.941708i
$316$		0			0
$317$	−14.8692	−	9.55583i	−0.835135	−	0.536709i	0.0517707	−	0.998659i	$-0.483514\pi$
$317$	−14.8692	−	9.55583i	−0.835135	−	0.536709i	−0.886906	+	0.461950i	$0.847150\pi$
$318$		0			0
$319$	−15.3094	+	4.49525i	−0.857164	+	0.251686i
$320$		0			0
$321$	−1.36581			−0.0762319
$322$		0			0
$323$	−9.90127			−0.550921
$324$		0			0
$325$	−22.1114	+	6.49250i	−1.22652	+	0.360139i
$326$		0			0
$327$	6.39143	+	4.10752i	0.353447	+	0.227147i
$328$		0			0
$329$	−3.46639	−	24.1092i	−0.191108	−	1.32919i
$330$		0			0
$331$	19.9332	−	12.8103i	1.09563	−	0.704119i	0.137514	−	0.990500i	$-0.456089\pi$
$331$	19.9332	−	12.8103i	1.09563	−	0.704119i	0.958116	+	0.286381i	$0.0924523\pi$
$332$		0			0
$333$	−1.40872	+	3.08468i	−0.0771977	+	0.169039i
$334$		0			0
$335$	−4.87541	+	33.9092i	−0.266372	+	1.85266i
$336$		0			0
$337$	22.2400	+	6.53024i	1.21149	+	0.355725i	0.824235	−	0.566248i	$-0.191606\pi$
$337$	22.2400	+	6.53024i	1.21149	+	0.355725i	0.387253	+	0.921973i	$0.373424\pi$
$338$		0			0
$339$	−0.996059	−	1.14951i	−0.0540985	−	0.0624330i
$340$		0			0
$341$	−32.1551	+	37.1090i	−1.74130	+	2.00956i
$342$		0			0
$343$	−21.4357	−	46.9376i	−1.15742	−	2.53439i
$344$		0			0
$345$	12.9927	−	9.97659i	0.699504	−	0.537121i
$346$		0			0
$347$	10.1681	+	22.2651i	0.545853	+	1.19525i	0.958692	+	0.284448i	$0.0918102\pi$
$347$	10.1681	+	22.2651i	0.545853	+	1.19525i	−0.412838	+	0.910804i	$0.635462\pi$
$348$		0			0
$349$	18.2748	−	21.0903i	0.978230	−	1.12894i	−0.0134107	−	0.999910i	$-0.504269\pi$
$349$	18.2748	−	21.0903i	0.978230	−	1.12894i	0.991641	−	0.129028i	$-0.0411857\pi$
$350$		0			0
$351$	2.26354	+	2.61227i	0.120819	+	0.139433i
$352$		0			0
$353$	−10.3842	−	3.04908i	−0.552696	−	0.162286i	−0.00655351	−	0.999979i	$-0.502086\pi$
$353$	−10.3842	−	3.04908i	−0.552696	−	0.162286i	−0.546142	+	0.837692i	$0.683904\pi$
$354$		0			0
$355$	5.39272	−	37.5072i	0.286216	−	1.99068i
$356$		0			0
$357$	4.34102	−	9.50552i	0.229751	−	0.503085i
$358$		0			0
$359$	2.51927	−	1.61904i	0.132962	−	0.0854496i	−0.472469	−	0.881347i	$-0.656637\pi$
$359$	2.51927	−	1.61904i	0.132962	−	0.0854496i	0.605431	+	0.795898i	$0.293001\pi$
$360$		0			0
$361$	−0.418355	−	2.90972i	−0.0220187	−	0.153143i
$362$		0			0
$363$	−12.0527	−	7.74577i	−0.632601	−	0.406548i
$364$		0			0
$365$	−3.34511	+	0.982212i	−0.175091	+	0.0514113i
$366$		0			0
$367$	34.4089			1.79613			0.898066	−	0.439861i	$-0.144972\pi$
$367$	34.4089			1.79613			0.898066	+	0.439861i	$0.144972\pi$
$368$		0			0
$369$	5.66428			0.294871
$370$		0			0
$371$	16.3355	−	4.79655i	0.848099	−	0.249024i
$372$		0			0
$373$	−25.5434	−	16.4157i	−1.32259	−	0.849975i	−0.327110	−	0.944986i	$-0.606075\pi$
$373$	−25.5434	−	16.4157i	−1.32259	−	0.849975i	−0.995476	+	0.0950116i	$0.969711\pi$
$374$		0			0
$375$	−0.810375	−	5.63628i	−0.0418476	−	0.291056i
$376$		0			0
$377$	−9.21918	+	5.92480i	−0.474812	+	0.305143i
$378$		0			0
$379$	1.36679	−	2.99284i	0.0702071	−	0.153732i	−0.871275	−	0.490795i	$-0.836706\pi$
$379$	1.36679	−	2.99284i	0.0702071	−	0.153732i	0.941482	+	0.337063i	$0.109434\pi$
$380$		0			0
$381$	3.01629	−	20.9788i	0.154529	−	1.07477i
$382$		0			0
$383$	22.1545	+	6.50515i	1.13204	+	0.332398i	0.793510	−	0.608557i	$-0.208251\pi$
$383$	22.1545	+	6.50515i	1.13204	+	0.332398i	0.338533	+	0.940955i	$0.390069\pi$
$384$		0			0
$385$	55.6488	+	64.2221i	2.83613	+	3.27306i
$386$		0			0
$387$	−3.31598	+	3.82684i	−0.168560	+	0.194529i
$388$		0			0
$389$	0.512542	+	1.12231i	0.0259869	+	0.0569034i	0.922180	−	0.386760i	$-0.126406\pi$
$389$	0.512542	+	1.12231i	0.0259869	+	0.0569034i	−0.896193	+	0.443663i	$0.853679\pi$
$390$		0			0
$391$	10.1023	−	0.846887i	0.510894	−	0.0428289i
$392$		0			0
$393$	3.40457	+	7.45498i	0.171738	+	0.376054i
$394$		0			0
$395$	6.26701	−	7.23252i	0.315328	−	0.363907i
$396$		0			0
$397$	4.59445	+	5.30228i	0.230589	+	0.266114i	0.859239	−	0.511575i	$-0.170938\pi$
$397$	4.59445	+	5.30228i	0.230589	+	0.266114i	−0.628650	+	0.777688i	$0.716392\pi$
$398$		0			0
$399$	22.2173	+	6.52357i	1.11225	+	0.326587i
$400$		0			0
$401$	3.95747	−	27.5248i	0.197627	−	1.37452i	−0.613520	−	0.789680i	$-0.710247\pi$
$401$	3.95747	−	27.5248i	0.197627	−	1.37452i	0.811146	−	0.584844i	$-0.198844\pi$
$402$		0			0
$403$	−14.0098	+	30.6771i	−0.697877	+	1.52814i
$404$		0			0
$405$	−2.87348	+	1.84667i	−0.142784	+	0.0917619i
$406$		0			0
$407$	−2.42877	−	16.8925i	−0.120390	−	0.837328i
$408$		0			0
$409$	−27.3570	−	17.5813i	−1.35272	−	0.869340i	−0.354871	−	0.934915i	$-0.615475\pi$
$409$	−27.3570	−	17.5813i	−1.35272	−	0.869340i	−0.997848	+	0.0655754i	$0.979112\pi$
$410$		0			0
$411$	4.79420	−	1.40770i	0.236480	−	0.0694369i
$412$		0			0
$413$	31.7816			1.56387
$414$		0			0
$415$	−42.8371			−2.10279
$416$		0			0
$417$	13.7071	−	4.02476i	0.671238	−	0.197093i
$418$		0			0
$419$	7.98704	+	5.13296i	0.390192	+	0.250761i	0.720998	−	0.692938i	$-0.243684\pi$
$419$	7.98704	+	5.13296i	0.390192	+	0.250761i	−0.330805	+	0.943699i	$0.607320\pi$
$420$		0			0
$421$	4.54775	+	31.6303i	0.221644	+	1.54157i	0.731821	+	0.681497i	$0.238671\pi$
$421$	4.54775	+	31.6303i	0.221644	+	1.54157i	−0.510178	+	0.860069i	$0.670420\pi$
$422$		0			0
$423$	−4.14495	+	2.66380i	−0.201535	+	0.129518i
$424$		0			0
$425$	5.85455	−	12.8197i	0.283987	−	0.621846i
$426$		0			0
$427$	7.49360	−	52.1191i	0.362641	−	2.52222i
$428$		0			0
$429$	−16.6907	−	4.90082i	−0.805833	−	0.236614i
$430$		0			0
$431$	−6.73878	−	7.77697i	−0.324596	−	0.374604i	0.569874	−	0.821732i	$-0.306992\pi$
$431$	−6.73878	−	7.77697i	−0.324596	−	0.374604i	−0.894470	+	0.447129i	$0.852447\pi$
$432$		0			0
$433$	−9.82576	+	11.3395i	−0.472196	+	0.544943i	−0.941021	−	0.338348i	$-0.890132\pi$
$433$	−9.82576	+	11.3395i	−0.472196	+	0.544943i	0.468825	+	0.883291i	$0.344677\pi$
$434$		0			0
$435$	−4.49871	−	9.85081i	−0.215697	−	0.472310i
$436$		0			0
$437$	5.04319	+	21.8901i	0.241248	+	1.04715i
$438$		0			0
$439$	−3.74886	−	8.20886i	−0.178923	−	0.391787i	0.798827	−	0.601561i	$-0.205454\pi$
$439$	−3.74886	−	8.20886i	−0.178923	−	0.391787i	−0.977750	+	0.209774i	$0.932727\pi$
$440$		0			0
$441$	−11.4195	+	13.1788i	−0.543787	+	0.627564i
$442$		0			0
$443$	−10.9300	−	12.6139i	−0.519298	−	0.599302i	0.434157	−	0.900837i	$-0.357046\pi$
$443$	−10.9300	−	12.6139i	−0.519298	−	0.599302i	−0.953455	+	0.301535i	$0.902501\pi$
$444$		0			0
$445$	12.4524	+	3.65635i	0.590299	+	0.173327i
$446$		0			0
$447$	0.175748	−	1.22236i	0.00831260	−	0.0578154i
$448$		0			0
$449$	−5.05854	+	11.0767i	−0.238727	+	0.522740i	−0.990636	−	0.136527i	$-0.956406\pi$
$449$	−5.05854	+	11.0767i	−0.238727	+	0.522740i	0.751909	+	0.659267i	$0.229133\pi$
$450$		0			0
$451$	−23.9808	+	15.4115i	−1.12921	+	0.725700i
$452$		0			0
$453$	0.696590	+	4.84489i	0.0327287	+	0.227633i
$454$		0			0
$455$	49.1000	+	31.5547i	2.30184	+	1.47931i
$456$		0			0
$457$	−14.2626	+	4.18787i	−0.667175	+	0.195900i	−0.597745	−	0.801686i	$-0.703936\pi$
$457$	−14.2626	+	4.18787i	−0.667175	+	0.195900i	−0.0694306	+	0.997587i	$0.522118\pi$
$458$		0			0
$459$	−2.11386			−0.0986665
$460$		0			0
$461$	−39.7608			−1.85185			−0.925924	−	0.377711i	$-0.876711\pi$
$461$	−39.7608			−1.85185			−0.925924	+	0.377711i	$0.876711\pi$
$462$		0			0
$463$	18.2214	−	5.35028i	0.846819	−	0.248649i	0.170592	−	0.985342i	$-0.445432\pi$
$463$	18.2214	−	5.35028i	0.846819	−	0.248649i	0.676227	+	0.736693i	$0.263614\pi$
$464$		0			0
$465$	−28.0361	−	18.0177i	−1.30014	−	0.835550i
$466$		0			0
$467$	2.04411	+	14.2171i	0.0945899	+	0.657887i	0.980859	+	0.194717i	$0.0623790\pi$
$467$	2.04411	+	14.2171i	0.0945899	+	0.657887i	−0.886269	+	0.463170i	$0.846712\pi$
$468$		0			0
$469$	41.7100	−	26.8054i	1.92599	−	1.23776i
$470$		0			0
$471$	5.67880	−	12.4348i	0.261665	−	0.572967i
$472$		0			0
$473$	3.62664	−	25.2238i	0.166753	−	1.15979i
$474$		0			0
$475$	29.9634	+	8.79806i	1.37482	+	0.403683i
$476$		0			0
$477$	−2.25531	−	2.60277i	−0.103264	−	0.119173i
$478$		0			0
$479$	15.9907	−	18.4542i	0.730632	−	0.843194i	−0.261911	−	0.965092i	$-0.584353\pi$
$479$	15.9907	−	18.4542i	0.730632	−	0.843194i	0.992543	+	0.121898i	$0.0388981\pi$
$480$		0			0
$481$	−4.86930	−	10.6623i	−0.222021	−	0.486158i
$482$		0			0
$483$	−23.2263	−	4.75570i	−1.05683	−	0.216392i
$484$		0			0
$485$	−14.3512	−	31.4248i	−0.651655	−	1.42693i
$486$		0			0
$487$	−25.3548	+	29.2610i	−1.14894	+	1.32594i	−0.211666	+	0.977342i	$0.567889\pi$
$487$	−25.3548	+	29.2610i	−1.14894	+	1.32594i	−0.937271	+	0.348602i	$0.886657\pi$
$488$		0			0
$489$	−10.2433	−	11.8214i	−0.463220	−	0.534584i
$490$		0			0
$491$	2.83917	+	0.833654i	0.128130	+	0.0376223i	0.345169	−	0.938541i	$-0.387822\pi$
$491$	2.83917	+	0.833654i	0.128130	+	0.0376223i	−0.217039	+	0.976163i	$0.569640\pi$
$492$		0			0
$493$	0.953787	−	6.63374i	0.0429564	−	0.298768i
$494$		0			0
$495$	7.14094	−	15.6365i	0.320961	−	0.702807i
$496$		0			0
$497$	−46.1358	+	29.6497i	−2.06947	+	1.32997i
$498$		0			0
$499$	1.62160	+	11.2785i	0.0725929	+	0.504895i	0.993384	+	0.114839i	$0.0366352\pi$
$499$	1.62160	+	11.2785i	0.0725929	+	0.504895i	−0.920791	+	0.390056i	$0.872456\pi$
$500$		0			0
$501$	−12.1560	−	7.81217i	−0.543089	−	0.349022i
$502$		0			0
$503$	−5.84300	+	1.71566i	−0.260526	+	0.0764975i	−0.409387	−	0.912361i	$-0.634258\pi$
$503$	−5.84300	+	1.71566i	−0.260526	+	0.0764975i	0.148861	+	0.988858i	$0.452439\pi$
$504$		0			0
$505$	−38.5458			−1.71526
$506$		0			0
$507$	1.05242			0.0467395
$508$		0			0
$509$	15.7927	−	4.63716i	0.699999	−	0.205538i	0.0876798	−	0.996149i	$-0.472055\pi$
$509$	15.7927	−	4.63716i	0.699999	−	0.205538i	0.612320	+	0.790610i	$0.290237\pi$
$510$		0			0
$511$	4.24471	+	2.72791i	0.187775	+	0.120676i
$512$		0			0
$513$	−0.666599	−	4.63630i	−0.0294311	−	0.204698i
$514$		0			0
$515$	22.5162	−	14.4703i	0.992182	−	0.637636i
$516$		0			0
$517$	10.3007	−	22.5554i	0.453025	−	0.991986i
$518$		0			0
$519$	−2.49169	+	17.3301i	−0.109373	+	0.760706i
$520$		0			0
$521$	−4.15206	−	1.21915i	−0.181905	−	0.0534121i	0.189511	−	0.981879i	$-0.439310\pi$
$521$	−4.15206	−	1.21915i	−0.181905	−	0.0534121i	−0.371416	+	0.928466i	$0.621128\pi$
$522$		0			0
$523$	−6.04191	−	6.97273i	−0.264194	−	0.304896i	0.608117	−	0.793847i	$-0.291925\pi$
$523$	−6.04191	−	6.97273i	−0.264194	−	0.304896i	−0.872311	+	0.488951i	$0.837380\pi$
$524$		0			0
$525$	−21.5833	+	24.9085i	−0.941973	+	1.08709i
$526$		0			0
$527$	−8.56776	−	18.7608i	−0.373218	−	0.817233i
$528$		0			0
$529$	−7.01790	−	21.9032i	−0.305126	−	0.952312i
$530$		0			0
$531$	−2.67069	−	5.84800i	−0.115898	−	0.253781i
$532$		0			0
$533$	−12.8213	+	14.7966i	−0.555354	+	0.640913i
$534$		0			0
$535$	3.05506	+	3.52572i	0.132082	+	0.152430i
$536$		0			0
$537$	22.1391	+	6.50062i	0.955372	+	0.280522i
$538$		0			0
$539$	12.4894	−	86.8657i	0.537957	−	3.74157i
$540$		0			0
$541$	3.26356	−	7.14619i	0.140311	−	0.307239i	−0.826411	−	0.563068i	$-0.809621\pi$
$541$	3.26356	−	7.14619i	0.140311	−	0.307239i	0.966722	+	0.255829i	$0.0823483\pi$
$542$		0			0
$543$	−6.95884	+	4.47217i	−0.298632	+	0.191919i
$544$		0			0
$545$	−3.69320	−	25.6867i	−0.158199	−	1.10030i
$546$		0			0
$547$	0.583208	+	0.374805i	0.0249362	+	0.0160255i	0.553050	−	0.833148i	$-0.313464\pi$
$547$	0.583208	+	0.374805i	0.0249362	+	0.0160255i	−0.528113	+	0.849174i	$0.677100\pi$
$548$		0			0
$549$	−10.2199	+	3.00085i	−0.436177	+	0.128073i
$550$		0			0
$551$	14.8505			0.632651
$552$		0			0
$553$	−13.8505			−0.588982
$554$		0			0
$555$	11.1139	−	3.26334i	0.471759	−	0.138521i
$556$		0			0
$557$	24.0186	+	15.4358i	1.01770	+	0.654037i	0.939375	−	0.342891i	$-0.111406\pi$
$557$	24.0186	+	15.4358i	1.01770	+	0.654037i	0.0783260	+	0.996928i	$0.475043\pi$
$558$		0			0
$559$	−2.49088	−	17.3244i	−0.105353	−	0.732746i
$560$		0			0
$561$	8.94943	−	5.75145i	0.377845	−	0.242826i
$562$		0			0
$563$	5.74643	−	12.5829i	0.242183	−	0.530307i	−0.749037	−	0.662528i	$-0.769484\pi$
$563$	5.74643	−	12.5829i	0.242183	−	0.530307i	0.991220	+	0.132221i	$0.0422109\pi$
$564$		0			0
$565$	−0.739379	+	5.14249i	−0.0311059	+	0.216346i
$566$		0			0
$567$	4.74325	+	1.39274i	0.199198	+	0.0584897i
$568$		0			0
$569$	−21.3939	−	24.6899i	−0.896880	−	1.03506i	−0.999188	−	0.0403022i	$-0.987168\pi$
$569$	−21.3939	−	24.6899i	−0.896880	−	1.03506i	0.102307	−	0.994753i	$-0.467378\pi$
$570$		0			0
$571$	13.3700	−	15.4298i	0.559517	−	0.645716i	−0.403557	−	0.914954i	$-0.632226\pi$
$571$	13.3700	−	15.4298i	0.559517	−	0.645716i	0.963074	+	0.269238i	$0.0867718\pi$
$572$		0			0
$573$	3.48721	+	7.63593i	0.145680	+	0.318996i
$574$		0			0
$575$	−31.3243	−	6.41381i	−1.30631	−	0.267474i
$576$		0			0
$577$	18.2715	+	40.0090i	0.760652	+	1.66560i	0.746219	+	0.665701i	$0.231867\pi$
$577$	18.2715	+	40.0090i	0.760652	+	1.66560i	0.0144333	+	0.999896i	$0.495406\pi$
$578$		0			0
$579$	−0.593774	+	0.685252i	−0.0246764	+	0.0284781i
$580$		0			0
$581$	40.5996	+	46.8544i	1.68435	+	1.94385i
$582$		0			0
$583$	16.6300	+	4.88300i	0.688743	+	0.202233i
$584$		0			0
$585$	1.68024	−	11.6863i	0.0694693	−	0.483170i
$586$		0			0
$587$	−4.91947	+	10.7721i	−0.203048	+	0.444614i	−0.983573	−	0.180511i	$-0.942225\pi$
$587$	−4.91947	+	10.7721i	−0.203048	+	0.444614i	0.780525	+	0.625125i	$0.214952\pi$
$588$		0			0
$589$	38.4460	−	24.7077i	1.58414	−	1.01806i
$590$		0			0
$591$	−2.37751	−	16.5359i	−0.0977976	−	0.680197i
$592$		0			0
$593$	21.7045	+	13.9486i	0.891296	+	0.572801i	0.904197	−	0.427116i	$-0.140470\pi$
$593$	21.7045	+	13.9486i	0.891296	+	0.572801i	−0.0129013	+	0.999917i	$0.504107\pi$
$594$		0			0
$595$	−34.2478	+	10.0561i	−1.40402	+	0.412258i
$596$		0			0
$597$	5.17584			0.211833
$598$		0			0
$599$	14.7880			0.604222			0.302111	−	0.953273i	$-0.402309\pi$
$599$	14.7880			0.604222			0.302111	+	0.953273i	$0.402309\pi$
$600$		0			0
$601$	−5.55362	+	1.63069i	−0.226537	+	0.0665172i	−0.393031	−	0.919525i	$-0.628573\pi$
$601$	−5.55362	+	1.63069i	−0.226537	+	0.0665172i	0.166494	+	0.986042i	$0.446755\pi$
$602$		0			0
$603$	−8.43736	−	5.42236i	−0.343596	−	0.220816i
$604$		0			0
$605$	6.96446	+	48.4389i	0.283145	+	1.96932i
$606$		0			0
$607$	4.97908	−	3.19986i	0.202095	−	0.129878i	−0.435679	−	0.900102i	$-0.643492\pi$
$607$	4.97908	−	3.19986i	0.202095	−	0.129878i	0.637774	+	0.770224i	$0.279855\pi$
$608$		0			0
$609$	−6.51090	+	14.2569i	−0.263835	+	0.577718i
$610$		0			0
$611$	2.42372	−	16.8574i	0.0980533	−	0.681976i
$612$		0			0
$613$	−32.1008	−	9.42563i	−1.29654	−	0.380698i	−0.440566	−	0.897720i	$-0.645222\pi$
$613$	−32.1008	−	9.42563i	−1.29654	−	0.380698i	−0.855972	+	0.517023i	$0.827040\pi$
$614$		0			0
$615$	−12.6699	−	14.6219i	−0.510901	−	0.589612i
$616$		0			0
$617$	−17.9120	+	20.6715i	−0.721108	+	0.832203i	−0.991440	−	0.130564i	$-0.958321\pi$
$617$	−17.9120	+	20.6715i	−0.721108	+	0.832203i	0.270332	+	0.962767i	$0.412867\pi$
$618$		0			0
$619$	11.0893	+	24.2823i	0.445718	+	0.975987i	0.990513	+	0.137418i	$0.0438803\pi$
$619$	11.0893	+	24.2823i	0.445718	+	0.975987i	−0.544795	+	0.838569i	$0.683392\pi$
$620$		0			0
$621$	1.07669	+	4.67341i	0.0432061	+	0.187537i
$622$		0			0
$623$	−7.80271	−	17.0855i	−0.312609	−	0.684518i
$624$		0			0
$625$	9.09307	−	10.4940i	0.363723	−	0.419758i
$626$		0			0
$627$	15.4367	+	17.8150i	0.616484	+	0.711461i
$628$		0			0
$629$	6.87800	+	2.01956i	0.274244	+	0.0805252i
$630$		0			0
$631$	1.28615	−	8.94537i	0.0512008	−	0.356109i	−0.948075	−	0.318048i	$-0.896973\pi$
$631$	1.28615	−	8.94537i	0.0512008	−	0.356109i	0.999275	−	0.0380614i	$-0.0121182\pi$
$632$		0			0
$633$	−0.253280	+	0.554606i	−0.0100670	+	0.0220436i
$634$		0			0
$635$	−60.9019	+	39.1393i	−2.41682	+	1.55319i
$636$		0			0
$637$	−8.57807	−	59.6618i	−0.339875	−	2.36389i
$638$		0			0
$639$	9.33263	+	5.99772i	0.369193	+	0.237266i
$640$		0			0
$641$	−3.97575	+	1.16739i	−0.157033	+	0.0461090i	−0.359304	−	0.933221i	$-0.616986\pi$
$641$	−3.97575	+	1.16739i	−0.157033	+	0.0461090i	0.202271	+	0.979330i	$0.435168\pi$
$642$		0			0
$643$	2.10692			0.0830890			0.0415445	−	0.999137i	$-0.486772\pi$
$643$	2.10692			0.0830890			0.0415445	+	0.999137i	$0.486772\pi$
$644$		0			0
$645$	17.2959			0.681026
$646$		0			0
$647$	−17.2173	+	5.05547i	−0.676884	+	0.198751i	−0.602066	−	0.798446i	$-0.705656\pi$
$647$	−17.2173	+	5.05547i	−0.676884	+	0.198751i	−0.0748177	+	0.997197i	$0.523837\pi$
$648$		0			0
$649$	27.2183	+	17.4921i	1.06841	+	0.686626i
$650$		0			0
$651$	6.86425	+	47.7419i	0.269031	+	1.87115i
$652$		0			0
$653$	−9.13678	+	5.87185i	−0.357550	+	0.229783i	−0.707067	−	0.707147i	$-0.749982\pi$
$653$	−9.13678	+	5.87185i	−0.357550	+	0.229783i	0.349517	+	0.936930i	$0.386346\pi$
$654$		0			0
$655$	11.6290	−	25.4640i	0.454384	−	0.994962i
$656$		0			0
$657$	0.145257	−	1.01029i	0.00566702	−	0.0394150i
$658$		0			0
$659$	4.20751	+	1.23544i	0.163901	+	0.0481257i	0.362654	−	0.931924i	$-0.381871\pi$
$659$	4.20751	+	1.23544i	0.163901	+	0.0481257i	−0.198752	+	0.980050i	$0.563689\pi$
$660$		0			0
$661$	2.63120	+	3.03657i	0.102342	+	0.118109i	0.804610	−	0.593804i	$-0.202375\pi$
$661$	2.63120	+	3.03657i	0.102342	+	0.118109i	−0.702268	+	0.711913i	$0.747829\pi$
$662$		0			0
$663$	4.78481	−	5.52197i	0.185827	−	0.214456i
$664$		0			0
$665$	−32.8558	−	71.9441i	−1.27409	−	2.78987i
$666$		0			0
$667$	−15.1519	+	1.27021i	−0.586686	+	0.0491826i
$668$		0			0
$669$	4.42758	+	9.69506i	0.171180	+	0.374833i
$670$		0			0
$671$	35.1033	−	40.5113i	1.35515	−	1.56392i
$672$		0			0
$673$	18.9582	+	21.8789i	0.730784	+	0.843369i	0.992560	−	0.121759i	$-0.0388536\pi$
$673$	18.9582	+	21.8789i	0.730784	+	0.843369i	−0.261776	+	0.965129i	$0.584308\pi$
$674$		0			0
$675$	6.39701	+	1.87833i	0.246221	+	0.0722970i
$676$		0			0
$677$	3.08907	−	21.4850i	0.118723	−	0.825734i	−0.840243	−	0.542210i	$-0.817588\pi$
$677$	3.08907	−	21.4850i	0.118723	−	0.825734i	0.958965	−	0.283523i	$-0.0915034\pi$
$678$		0			0
$679$	−20.7702	+	45.4805i	−0.797089	+	1.74538i
$680$		0			0
$681$	−5.21177	+	3.34940i	−0.199716	+	0.128349i
$682$		0			0
$683$	1.69873	+	11.8149i	0.0650002	+	0.452086i	0.996165	+	0.0874890i	$0.0278843\pi$
$683$	1.69873	+	11.8149i	0.0650002	+	0.452086i	−0.931165	+	0.364597i	$0.881207\pi$
$684$		0			0
$685$	−14.3576	−	9.22707i	−0.548576	−	0.352548i
$686$		0			0
$687$	11.5071	−	3.37880i	0.439024	−	0.128909i
$688$		0			0
$689$	11.9041			0.453511
$690$		0			0
$691$	21.4766			0.817009			0.408505	−	0.912756i	$-0.366050\pi$
$691$	21.4766			0.817009			0.408505	+	0.912756i	$0.366050\pi$
$692$		0			0
$693$	−23.8708	+	7.00911i	−0.906778	+	0.266254i
$694$		0			0
$695$	−41.0498	−	26.3811i	−1.55711	−	1.00069i
$696$		0			0
$697$	−1.70401	−	11.8516i	−0.0645438	−	0.448912i
$698$		0			0
$699$	1.11484	−	0.716467i	0.0421673	−	0.0270993i
$700$		0			0
$701$	−19.7155	+	43.1709i	−0.744644	+	1.63054i	0.0311179	+	0.999516i	$0.490093\pi$
$701$	−19.7155	+	43.1709i	−0.744644	+	1.63054i	−0.775761	+	0.631026i	$0.782634\pi$
$702$		0			0
$703$	−2.26052	+	15.7223i	−0.0852573	+	0.592977i
$704$		0			0
$705$	16.1479	+	4.74145i	0.608164	+	0.178573i
$706$		0			0
$707$	36.5324	+	42.1607i	1.37394	+	1.58561i
$708$		0			0
$709$	−8.52521	+	9.83861i	−0.320171	+	0.369497i	−0.892906	−	0.450244i	$-0.851337\pi$
$709$	−8.52521	+	9.83861i	−0.320171	+	0.369497i	0.572735	+	0.819741i	$0.305883\pi$
$710$		0			0
$711$	1.16389	+	2.54857i	0.0436494	+	0.0955788i
$712$		0			0
$713$	−37.1131	+	28.4977i	−1.38990	+	1.06725i
$714$		0			0
$715$	24.6828	+	54.0479i	0.923086	+	2.02128i
$716$		0			0
$717$	17.1891	−	19.8373i	0.641940	−	0.740839i
$718$		0			0
$719$	−28.1192	−	32.4513i	−1.04867	−	1.21023i	−0.977097	−	0.212793i	$-0.931744\pi$
$719$	−28.1192	−	32.4513i	−1.04867	−	1.21023i	−0.0715713	−	0.997435i	$-0.522801\pi$
$720$		0			0
$721$	−37.1674	−	10.9133i	−1.38419	−	0.406434i
$722$		0			0
$723$	0.392986	−	2.73328i	0.0146153	−	0.101652i
$724$		0			0
$725$	−8.78097	+	19.2276i	−0.326117	+	0.714097i
$726$		0			0
$727$	7.41518	−	4.76544i	0.275014	−	0.176741i	−0.395863	−	0.918310i	$-0.629554\pi$
$727$	7.41518	−	4.76544i	0.275014	−	0.176741i	0.670876	+	0.741569i	$0.265918\pi$
$728$		0			0
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$		0			0
$731$	9.00462	+	5.78692i	0.333048	+	0.214037i
$732$		0			0
$733$	14.5715	−	4.27859i	0.538212	−	0.158033i	−0.00131905	−	0.999999i	$-0.500420\pi$
$733$	14.5715	−	4.27859i	0.538212	−	0.158033i	0.539531	+	0.841966i	$0.318602\pi$
$734$		0			0
$735$	59.5635			2.19703
$736$		0			0
$737$	50.4745			1.85925
$738$		0			0
$739$	−14.0846	+	4.13560i	−0.518109	+	0.152131i	−0.530324	−	0.847795i	$-0.677930\pi$
$739$	−14.0846	+	4.13560i	−0.518109	+	0.152131i	0.0122151	+	0.999925i	$0.496112\pi$
$740$		0			0
$741$	13.6201	+	8.75313i	0.500348	+	0.321554i
$742$		0			0
$743$	−4.45729	−	31.0012i	−0.163522	−	1.13732i	−0.891928	−	0.452177i	$-0.850648\pi$
$743$	−4.45729	−	31.0012i	−0.163522	−	1.13732i	0.728406	−	0.685145i	$-0.240261\pi$
$744$		0			0
$745$	−3.54853	+	2.28050i	−0.130008	+	0.0835511i
$746$		0			0
$747$	5.20980	−	11.4079i	0.190617	−	0.417392i
$748$		0			0
$749$	0.960889	−	6.68313i	0.0351101	−	0.244196i
$750$		0			0
$751$	7.55474	+	2.21827i	0.275676	+	0.0809459i	0.416648	−	0.909068i	$-0.363205\pi$
$751$	7.55474	+	2.21827i	0.275676	+	0.0809459i	−0.140972	+	0.990014i	$0.545023\pi$
$752$		0			0
$753$	18.9419	+	21.8601i	0.690280	+	0.796625i
$754$		0			0
$755$	10.9486	−	12.6353i	0.398459	−	0.459846i
$756$		0			0
$757$	−21.6496	−	47.4061i	−0.786869	−	1.72300i	−0.685403	−	0.728164i	$-0.740374\pi$
$757$	−21.6496	−	47.4061i	−0.786869	−	1.72300i	−0.101466	−	0.994839i	$-0.532353\pi$
$758$		0			0
$759$	−17.2739	−	16.8563i	−0.627003	−	0.611844i
$760$		0			0
$761$	−12.0339	−	26.3505i	−0.436227	−	0.955203i	−0.992276	−	0.124054i	$-0.960410\pi$
$761$	−12.0339	−	26.3505i	−0.436227	−	0.955203i	0.556049	−	0.831150i	$-0.312317\pi$
$762$		0			0
$763$	−24.5954	+	28.3846i	−0.890414	+	1.02759i
$764$		0			0
$765$	4.72831	+	5.45676i	0.170952	+	0.197290i
$766$		0			0
$767$	21.3218	+	6.26064i	0.769884	+	0.226058i
$768$		0			0
$769$	−0.0824698	+	0.573590i	−0.00297394	+	0.0206842i	−0.991254	−	0.131965i	$-0.957871\pi$
$769$	−0.0824698	+	0.573590i	−0.00297394	+	0.0206842i	0.988280	+	0.152649i	$0.0487804\pi$
$770$		0			0
$771$	2.14934	−	4.70640i	0.0774066	−	0.169497i
$772$		0			0
$773$	23.5018	−	15.1037i	0.845301	−	0.543242i	−0.0448051	−	0.998996i	$-0.514267\pi$
$773$	23.5018	−	15.1037i	0.845301	−	0.543242i	0.890106	+	0.455754i	$0.150630\pi$
$774$		0			0
$775$	9.25752	+	64.3875i	0.332540	+	2.31287i
$776$		0			0
$777$	−14.1028	−	9.06331i	−0.505934	−	0.325144i
$778$		0			0
$779$	25.4567	−	7.47475i	0.912079	−	0.267811i
$780$		0			0
$781$	−55.8302			−1.99776
$782$		0			0
$783$	3.17048			0.113304
$784$		0			0
$785$	−44.8020	+	13.1550i	−1.59905	+	0.469524i
$786$		0			0
$787$	−31.2614	−	20.0905i	−1.11435	−	0.716148i	−0.152112	−	0.988363i	$-0.548607\pi$
$787$	−31.2614	−	20.0905i	−1.11435	−	0.716148i	−0.962236	+	0.272215i	$0.912244\pi$
$788$		0			0
$789$	2.16806	+	15.0792i	0.0771851	+	0.536834i
$790$		0			0
$791$	6.32553	−	4.06517i	0.224910	−	0.144541i
$792$		0			0
$793$	15.2943	−	33.4898i	0.543116	−	1.18926i
$794$		0			0
$795$	−1.67413	+	11.6438i	−0.0593752	+	0.412964i
$796$		0			0
$797$	−29.8641	−	8.76890i	−1.05784	−	0.310610i	−0.293860	−	0.955848i	$-0.594940\pi$
$797$	−29.8641	−	8.76890i	−1.05784	−	0.310610i	−0.763982	+	0.645238i	$0.776758\pi$
$798$		0			0
$799$	6.82053	+	7.87131i	0.241293	+	0.278467i
$800$		0			0
$801$	−2.48816	+	2.87149i	−0.0879148	+	0.101459i
$802$		0			0
$803$	2.13384	+	4.67245i	0.0753015	+	0.164887i
$804$		0			0
$805$	39.6764	+	70.5944i	1.39841	+	2.48813i
$806$		0			0
$807$	1.98788	+	4.35285i	0.0699766	+	0.153227i
$808$		0			0
$809$	4.22705	−	4.87828i	0.148615	−	0.171511i	−0.676561	−	0.736387i	$-0.736530\pi$
$809$	4.22705	−	4.87828i	0.148615	−	0.171511i	0.825176	+	0.564876i	$0.191076\pi$
$810$		0			0
$811$	11.3684	+	13.1199i	0.399200	+	0.460701i	0.919389	−	0.393350i	$-0.128684\pi$
$811$	11.3684	+	13.1199i	0.399200	+	0.460701i	−0.520189	+	0.854051i	$0.674138\pi$
$812$		0			0
$813$	−10.1795	−	2.98896i	−0.357010	−	0.104828i
$814$		0			0
$815$	−7.60368	+	52.8848i	−0.266345	+	1.85247i
$816$		0			0
$817$	−9.85279	+	21.5746i	−0.344706	+	0.754800i
$818$		0			0
$819$	−14.3748	+	9.23810i	−0.502295	+	0.322805i
$820$		0			0
$821$	−2.26018	−	15.7199i	−0.0788807	−	0.548628i	−0.990492	−	0.137573i	$-0.956070\pi$
$821$	−2.26018	−	15.7199i	−0.0788807	−	0.548628i	0.911611	−	0.411054i	$-0.134839\pi$
$822$		0			0
$823$	−43.7424	−	28.1115i	−1.52476	−	0.979906i	−0.990939	−	0.134310i	$-0.957118\pi$
$823$	−43.7424	−	28.1115i	−1.52476	−	0.979906i	−0.533824	−	0.845596i	$-0.679245\pi$
$824$		0			0
$825$	−32.1936	+	9.45288i	−1.12084	+	0.329107i
$826$		0			0
$827$	−2.12984			−0.0740616			−0.0370308	−	0.999314i	$-0.511790\pi$
$827$	−2.12984			−0.0740616			−0.0370308	+	0.999314i	$0.511790\pi$
$828$		0			0
$829$	10.9168			0.379155			0.189577	−	0.981866i	$-0.439288\pi$
$829$	10.9168			0.379155			0.189577	+	0.981866i	$0.439288\pi$
$830$		0			0
$831$	−22.5562	+	6.62311i	−0.782467	+	0.229753i
$832$		0			0
$833$	31.0100	+	19.9289i	1.07443	+	0.690497i
$834$		0			0
$835$	7.02416	+	48.8541i	0.243081	+	1.69067i
$836$		0			0
$837$	8.20798	−	5.27495i	0.283709	−	0.182329i
$838$		0			0
$839$	16.9393	−	37.0919i	0.584810	−	1.28056i	−0.353717	−	0.935352i	$-0.615083\pi$
$839$	16.9393	−	37.0919i	0.584810	−	1.28056i	0.938528	−	0.345204i	$-0.112190\pi$
$840$		0			0
$841$	2.69659	−	18.7552i	0.0929858	−	0.646731i
$842$		0			0
$843$	4.72535	+	1.38749i	0.162750	+	0.0477876i
$844$		0			0
$845$	−2.35406	−	2.71674i	−0.0809823	−	0.0934585i
$846$		0			0
$847$	46.3809	−	53.5264i	1.59367	−	1.83919i
$848$		0			0
$849$	11.6901	+	25.5978i	0.401204	+	0.878515i
$850$		0			0
$851$	0.961639	−	16.2348i	0.0329645	−	0.556522i
$852$		0			0
$853$	11.7017	+	25.6231i	0.400658	+	0.877320i	0.997203	+	0.0747397i	$0.0238126\pi$
$853$	11.7017	+	25.6231i	0.400658	+	0.877320i	−0.596545	+	0.802580i	$0.703460\pi$
$854$		0			0
$855$	−10.4772	+	12.0913i	−0.358312	+	0.413514i
$856$		0			0
$857$	−2.95650	−	3.41199i	−0.100992	−	0.116551i	0.703003	−	0.711187i	$-0.251842\pi$
$857$	−2.95650	−	3.41199i	−0.100992	−	0.116551i	−0.803996	+	0.594635i	$0.797296\pi$
$858$		0			0
$859$	−38.1809	−	11.2109i	−1.30272	−	0.382512i	−0.444490	−	0.895784i	$-0.646615\pi$
$859$	−38.1809	−	11.2109i	−1.30272	−	0.382512i	−0.858226	+	0.513271i	$0.828433\pi$
$860$		0			0
$861$	−3.98500	+	27.7163i	−0.135809	+	0.944569i
$862$		0			0
$863$	−4.92546	+	10.7852i	−0.167664	+	0.367134i	−0.974749	−	0.223301i	$-0.928317\pi$
$863$	−4.92546	+	10.7852i	−0.167664	+	0.367134i	0.807085	+	0.590435i	$0.201044\pi$
$864$		0			0
$865$	50.3097	−	32.3321i	1.71058	−	1.09932i
$866$		0			0
$867$	−1.78343	−	12.4040i	−0.0605685	−	0.421263i
$868$		0			0
$869$	−11.8618	−	7.62310i	−0.402383	−	0.258596i
$870$		0			0
$871$	33.2630	−	9.76690i	1.12707	−	0.330939i
$872$		0			0
$873$	10.1141			0.342309
$874$		0			0
$875$	28.1494			0.951624
$876$		0			0
$877$	−34.4233	+	10.1076i	−1.16239	+	0.341309i	−0.805362	−	0.592783i	$-0.798029\pi$
$877$	−34.4233	+	10.1076i	−1.16239	+	0.341309i	−0.357031	+	0.934093i	$0.616211\pi$
$878$		0			0
$879$	−0.851310	−	0.547104i	−0.0287140	−	0.0184533i
$880$		0			0
$881$	−1.36864	−	9.51909i	−0.0461106	−	0.320706i	−0.999802	−	0.0199182i	$-0.993659\pi$
$881$	−1.36864	−	9.51909i	−0.0461106	−	0.320706i	0.953691	−	0.300788i	$-0.0972497\pi$
$882$		0			0
$883$	−21.1778	+	13.6101i	−0.712689	+	0.458017i	−0.846087	−	0.533045i	$-0.821048\pi$
$883$	−21.1778	+	13.6101i	−0.712689	+	0.458017i	0.133398	+	0.991063i	$0.457411\pi$
$884$		0			0
$885$	−9.12230	+	19.9751i	−0.306643	+	0.671454i
$886$		0			0
$887$	0.988822	−	6.87740i	0.0332014	−	0.230921i	−0.966464	−	0.256804i	$-0.917331\pi$
$887$	0.988822	−	6.87740i	0.0332014	−	0.230921i	0.999665	+	0.0258830i	$0.00823973\pi$
$888$		0			0
$889$	100.531	+	29.5185i	3.37169	+	0.990018i
$890$		0			0
$891$	3.29565	+	3.80338i	0.110408	+	0.127418i
$892$		0			0
$893$	−15.1132	+	17.4416i	−0.505744	+	0.583660i
$894$		0			0
$895$	−32.7402	−	71.6909i	−1.09438	−	2.39636i
$896$		0			0
$897$	−14.6453	−	7.76586i	−0.488993	−	0.259295i
$898$		0			0
$899$	12.8504	+	28.1384i	0.428585	+	0.938470i
$900$		0			0
$901$	−4.76741	+	5.50189i	−0.158826	+	0.183295i
$902$		0			0
$903$	−16.3925	−	18.9179i	−0.545508	−	0.629550i
$904$		0			0
$905$	27.1102	+	7.96027i	0.901173	+	0.264608i
$906$		0			0
$907$	−5.47630	+	38.0885i	−0.181838	+	1.26471i	0.670576	+	0.741841i	$0.266047\pi$
$907$	−5.47630	+	38.0885i	−0.181838	+	1.26471i	−0.852414	+	0.522868i	$0.824862\pi$
$908$		0			0
$909$	4.68789	−	10.2651i	0.155488	−	0.340470i
$910$		0			0
$911$	17.3325	−	11.1389i	0.574251	−	0.369049i	−0.221051	−	0.975262i	$-0.570949\pi$
$911$	17.3325	−	11.1389i	0.574251	−	0.369049i	0.795302	+	0.606214i	$0.207312\pi$
$912$		0			0
$913$	8.98216	+	62.4723i	0.297266	+	2.06753i
$914$		0			0
$915$	30.6066	+	19.6696i	1.01182	+	0.650258i
$916$		0			0
$917$	−38.8737	+	11.4144i	−1.28372	+	0.376935i
$918$		0			0
$919$	10.7289			0.353912			0.176956	−	0.984219i	$-0.443375\pi$
$919$	10.7289			0.353912			0.176956	+	0.984219i	$0.443375\pi$
$920$		0			0
$921$	−5.84691			−0.192662
$922$		0			0
$923$	−36.7925	+	10.8032i	−1.21104	+	0.355593i
$924$		0			0
$925$	−19.0198	−	12.2233i	−0.625367	−	0.401899i
$926$		0			0
$927$	1.11516	+	7.75611i	0.0366267	+	0.254744i
$928$		0			0
$929$	26.8515	−	17.2564i	0.880971	−	0.566165i	−0.0201193	−	0.999798i	$-0.506405\pi$
$929$	26.8515	−	17.2564i	0.880971	−	0.566165i	0.901090	+	0.433632i	$0.142768\pi$
$930$		0			0
$931$	−33.9310	+	74.2985i	−1.11204	+	2.43503i
$932$		0			0
$933$	−3.31430	+	23.0515i	−0.108505	+	0.754671i
$934$		0			0
$935$	−34.8651	−	10.2373i	−1.14021	−	0.334796i
$936$		0			0
$937$	−12.7153	−	14.6743i	−0.415391	−	0.479387i	0.509036	−	0.860745i	$-0.330002\pi$
$937$	−12.7153	−	14.6743i	−0.415391	−	0.479387i	−0.924427	+	0.381358i	$0.875457\pi$
$938$		0			0
$939$	10.1875	−	11.7570i	0.332457	−	0.383676i
$940$		0			0
$941$	−17.6723	−	38.6969i	−0.576100	−	1.26148i	−0.943485	−	0.331415i	$-0.892474\pi$
$941$	−17.6723	−	38.6969i	−0.576100	−	1.26148i	0.367385	−	0.930069i	$-0.380253\pi$
$942$		0			0
$943$	−25.3341	+	9.80388i	−0.824992	+	0.319258i
$944$		0			0
$945$	−7.01450	−	15.3596i	−0.228182	−	0.499648i
$946$		0			0
$947$	−20.7791	+	23.9804i	−0.675231	+	0.779259i	−0.985185	−	0.171493i	$-0.945141\pi$
$947$	−20.7791	+	23.9804i	−0.675231	+	0.779259i	0.309954	+	0.950752i	$0.399686\pi$
$948$		0			0
$949$	2.31034	+	2.66628i	0.0749969	+	0.0865510i
$950$		0			0
$951$	−16.9590	−	4.97962i	−0.549935	−	0.161475i
$952$		0			0
$953$	−2.78316	+	19.3573i	−0.0901553	+	0.627044i	0.893778	+	0.448509i	$0.148045\pi$
$953$	−2.78316	+	19.3573i	−0.0901553	+	0.627044i	−0.983934	+	0.178535i	$0.942864\pi$
$954$		0			0
$955$	11.9113	−	26.0821i	0.385441	−	0.843998i
$956$		0			0
$957$	−13.4228	+	8.62633i	−0.433899	+	0.278850i
$958$		0			0
$959$	3.51527	+	24.4492i	0.113514	+	0.789506i
$960$		0			0
$961$	54.0050	+	34.7069i	1.74210	+	1.11958i
$962$		0			0
$963$	−1.31048	+	0.384792i	−0.0422297	+	0.0123998i
$964$		0			0
$965$	3.09709			0.0996987
$966$		0			0
$967$	32.1644			1.03434			0.517168	−	0.855884i	$-0.326986\pi$
$967$	32.1644			1.03434			0.517168	+	0.855884i	$0.326986\pi$
$968$		0			0
$969$	−9.50020	+	2.78951i	−0.305190	+	0.0896120i
$970$		0			0
$971$	−5.81066	−	3.73428i	−0.186473	−	0.119839i	0.444074	−	0.895990i	$-0.353533\pi$
$971$	−5.81066	−	3.73428i	−0.186473	−	0.119839i	−0.630547	+	0.776151i	$0.717169\pi$
$972$		0			0
$973$	10.0505	+	69.9026i	0.322204	+	2.24097i
$974$		0			0
$975$	−19.3866	+	12.4590i	−0.620869	+	0.399008i
$976$		0			0
$977$	23.4685	−	51.3888i	0.750824	−	1.64407i	−0.0140556	−	0.999901i	$-0.504474\pi$
$977$	23.4685	−	51.3888i	0.750824	−	1.64407i	0.764879	−	0.644174i	$-0.222799\pi$
$978$		0			0
$979$	2.72127	−	18.9268i	0.0869722	−	0.604905i
$980$		0			0
$981$	7.28976	+	2.14047i	0.232744	+	0.0683398i
$982$		0			0
$983$	−32.9111	−	37.9814i	−1.04970	−	1.21142i	−0.976816	−	0.214079i	$-0.931325\pi$
$983$	−32.9111	−	37.9814i	−1.04970	−	1.21142i	−0.0728848	−	0.997340i	$-0.523221\pi$
$984$		0			0
$985$	−37.3682	+	43.1252i	−1.19065	+	1.37408i
$986$		0			0
$987$	−10.1183	−	22.1561i	−0.322070	−	0.705235i
$988$		0			0
$989$	8.20747	−	22.8553i	0.260982	−	0.726757i
$990$		0			0
$991$	7.40268	+	16.2096i	0.235154	+	0.514915i	0.990014	−	0.140971i	$-0.0450224\pi$
$991$	7.40268	+	16.2096i	0.235154	+	0.514915i	−0.754860	+	0.655886i	$0.772295\pi$
$992$		0			0
$993$	15.5167	−	17.9073i	0.492408	−	0.568270i
$994$		0			0
$995$	−11.5774	−	13.3610i	−0.367028	−	0.423573i
$996$		0			0
$997$	12.6886	+	3.72571i	0.401852	+	0.117994i	0.476412	−	0.879222i	$-0.341937\pi$
$997$	12.6886	+	3.72571i	0.401852	+	0.117994i	−0.0745601	+	0.997217i	$0.523755\pi$
$998$		0			0
$999$	−0.482608	+	3.35661i	−0.0152690	+	0.106198i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.c.73.1	✓	30
23.6	even	11	inner	552.2.q.c.121.1	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.c.73.1	✓	30	1.1	even	1	trivial
552.2.q.c.121.1	yes	30	23.6	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.959493 - 0.281733i) q^{3} +(-2.87348 - 1.84667i) q^{5} +(0.703532 + 4.89317i) q^{7} +(0.841254 - 0.540641i) q^{9} +(-2.09062 + 4.57781i) q^{11} +(-0.491915 + 3.42134i) q^{13} +(-3.27735 - 0.962317i) q^{15} +(-1.38428 - 1.59755i) q^{17} +(3.06735 - 3.53991i) q^{19} +(2.05360 + 4.49676i) q^{21} +(-2.82684 + 3.87414i) q^{23} +(2.76960 + 6.06458i) q^{25} +(0.654861 - 0.755750i) q^{27} +(2.07622 + 2.39609i) q^{29} +(9.36162 + 2.74882i) q^{31} +(-0.716213 + 4.98137i) q^{33} +(7.01450 - 15.3596i) q^{35} +(-2.85280 + 1.83338i) q^{37} +(0.491915 + 3.42134i) q^{39} +(4.76510 + 3.06234i) q^{41} +(-4.85852 + 1.42659i) q^{43} -3.41571 q^{45} -4.92712 q^{47} +(-16.7317 + 4.91288i) q^{49} +(-1.77829 - 1.14284i) q^{51} +(-0.490126 - 3.40890i) q^{53} +(14.4611 - 9.29356i) q^{55} +(1.94579 - 4.26070i) q^{57} +(0.914938 - 6.36353i) q^{59} +(-10.2199 - 3.00085i) q^{61} +(3.23730 + 3.73604i) q^{63} +(7.73161 - 8.92275i) q^{65} +(-4.16641 - 9.12316i) q^{67} +(-1.62087 + 4.51362i) q^{69} +(4.60850 + 10.0912i) q^{71} +(0.668400 - 0.771374i) q^{73} +(4.36600 + 5.03864i) q^{75} +(-23.8708 - 7.00911i) q^{77} +(-0.398732 + 2.77324i) q^{79} +(0.415415 - 0.909632i) q^{81} +(10.5503 - 6.78028i) q^{83} +(1.02756 + 7.14684i) q^{85} +(2.66718 + 1.71409i) q^{87} +(-3.64562 + 1.07045i) q^{89} -17.0873 q^{91} +9.75684 q^{93} +(-15.3510 + 4.50747i) q^{95} +(8.50849 + 5.46808i) q^{97} +(0.716213 + 4.98137i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9} + 13 q^{11} - 13 q^{13} + 2 q^{15} - 11 q^{17} + 11 q^{19} - 9 q^{21} - 12 q^{23} + 17 q^{25} + 3 q^{27} + 9 q^{29} + 33 q^{31} + 9 q^{33} + 62 q^{35} + 11 q^{37}+ \cdots - 9 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9 + 13 * q^11 - 13 * q^13 + 2 * q^15 - 11 * q^17 + 11 * q^19 - 9 * q^21 - 12 * q^23 + 17 * q^25 + 3 * q^27 + 9 * q^29 + 33 * q^31 + 9 * q^33 + 62 * q^35 + 11 * q^37 + 13 * q^39 + 2 * q^41 - 40 * q^43 - 2 * q^45 - 38 * q^47 - 13 * q^49 + 11 * q^51 - 25 * q^53 + 62 * q^55 + 22 * q^57 + 73 * q^59 + 4 * q^61 - 2 * q^63 - 12 * q^65 - 29 * q^67 - 21 * q^69 - 19 * q^71 - 38 * q^73 + 27 * q^75 + 4 * q^77 - 12 * q^79 - 3 * q^81 - 65 * q^83 + 8 * q^85 + 2 * q^87 - 61 * q^89 - 150 * q^91 - 22 * q^93 - 9 * q^95 - 9 * q^97 - 9 * q^99

Introduction

L-functions

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Database

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