LMFDB - Embedded newform 1428.2.cc.c.361.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1428,2,Mod(361,1428)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1428, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 0, 8, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1428.361"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1428 = 2^{2} \cdot 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1428.cc (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$11.4026374086$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			361.18
Character	$\chi$	$=$	1428.361
Dual form			1428.2.cc.c.625.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.258819 + 0.965926i) q^{3} +(4.11475 + 1.10254i) q^{5} +(1.20191 + 2.35699i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(4.92080 - 1.31853i) q^{11} -2.39520 q^{13} +4.25990i q^{15} +(4.03409 + 0.852138i) q^{17} +(-5.27196 + 3.04377i) q^{19} +(-1.96560 + 1.77099i) q^{21} +(0.964781 - 3.60061i) q^{23} +(11.3854 + 6.57339i) q^{25} +(-0.707107 - 0.707107i) q^{27} +(0.754976 - 0.754976i) q^{29} +(-2.20834 - 8.24163i) q^{31} +(2.54720 + 4.41187i) q^{33} +(2.34687 + 11.0236i) q^{35} +(-4.69701 - 1.25856i) q^{37} +(-0.619924 - 2.31359i) q^{39} +(-1.06291 - 1.06291i) q^{41} -5.55521i q^{43} +(-4.11475 + 1.10254i) q^{45} +(-5.27390 - 9.13467i) q^{47} +(-4.11083 + 5.66578i) q^{49} +(0.220997 + 4.11718i) q^{51} +(0.745169 + 0.430223i) q^{53} +21.7016 q^{55} +(-4.30454 - 4.30454i) q^{57} +(-6.11933 - 3.53300i) q^{59} +(-0.783732 + 2.92493i) q^{61} +(-2.21938 - 1.44026i) q^{63} +(-9.85566 - 2.64082i) q^{65} +(-4.16873 + 7.22046i) q^{67} +3.72763 q^{69} +(-7.20048 + 7.20048i) q^{71} +(-2.48048 - 9.25727i) q^{73} +(-3.40263 + 12.6988i) q^{75} +(9.02212 + 10.0136i) q^{77} +(-0.788112 + 2.94128i) q^{79} +(0.500000 - 0.866025i) q^{81} -0.914192i q^{83} +(15.6597 + 7.95409i) q^{85} +(0.924653 + 0.533848i) q^{87} +(6.61396 + 11.4557i) q^{89} +(-2.87882 - 5.64547i) q^{91} +(7.38925 - 4.26618i) q^{93} +(-25.0487 + 6.71177i) q^{95} +(2.56368 - 2.56368i) q^{97} +(-3.60228 + 3.60228i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 12 q^{5} - 20 q^{7} + 8 q^{11} + 24 q^{13} - 16 q^{17} + 20 q^{21} - 28 q^{23} + 48 q^{29} - 28 q^{31} + 24 q^{33} + 68 q^{35} + 20 q^{37} + 32 q^{41} - 12 q^{45} + 44 q^{47} - 4 q^{51} + 48 q^{55}+ \cdots - 16 q^{99}+O(q^{100}) $ 72 * q + 12 * q^5 - 20 * q^7 + 8 * q^11 + 24 * q^13 - 16 * q^17 + 20 * q^21 - 28 * q^23 + 48 * q^29 - 28 * q^31 + 24 * q^33 + 68 * q^35 + 20 * q^37 + 32 * q^41 - 12 * q^45 + 44 * q^47 - 4 * q^51 + 48 * q^55 - 16 * q^61 + 16 * q^63 - 16 * q^65 - 16 * q^67 - 48 * q^69 + 8 * q^71 + 40 * q^73 + 24 * q^75 + 20 * q^79 + 36 * q^81 + 8 * q^85 - 16 * q^89 - 20 * q^91 - 68 * q^95 + 120 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1428\mathbb{Z}\right)^\times$.

$n$	$409$	$715$	$953$	$1261$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$		0			0
$5$	4.11475	+	1.10254i	1.84017	+	0.493073i	0.998871	−	0.0474948i	$-0.0151238\pi$
$5$	4.11475	+	1.10254i	1.84017	+	0.493073i	0.841301	+	0.540567i	$0.181790\pi$
$6$		0			0
$7$	1.20191	+	2.35699i	0.454279	+	0.890859i
$7$	1.20191	+	2.35699i	0.454279	+	0.890859i
$8$		0			0
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$		0			0
$11$	4.92080	−	1.31853i	1.48368	−	0.397550i	0.576081	−	0.817392i	$-0.304581\pi$
$11$	4.92080	−	1.31853i	1.48368	−	0.397550i	0.907597	+	0.419842i	$0.137914\pi$
$12$		0			0
$13$	−2.39520			−0.664310			−0.332155	−	0.943225i	$-0.607776\pi$
$13$	−2.39520			−0.664310			−0.332155	+	0.943225i	$0.607776\pi$
$14$		0			0
$15$			4.25990i			1.09990i
$16$		0			0
$17$	4.03409	+	0.852138i	0.978410	+	0.206674i
$17$	4.03409	+	0.852138i	0.978410	+	0.206674i
$18$		0			0
$19$	−5.27196	+	3.04377i	−1.20947	+	0.698288i	−0.962644	−	0.270771i	$-0.912721\pi$
$19$	−5.27196	+	3.04377i	−1.20947	+	0.698288i	−0.246827	+	0.969060i	$0.579388\pi$
$20$		0			0
$21$	−1.96560	+	1.77099i	−0.428930	+	0.386462i
$22$		0			0
$23$	0.964781	−	3.60061i	0.201171	−	0.750779i	−0.789412	−	0.613864i	$-0.789614\pi$
$23$	0.964781	−	3.60061i	0.201171	−	0.750779i	0.990583	−	0.136916i	$-0.0437189\pi$
$24$		0			0
$25$	11.3854	+	6.57339i	2.27709	+	1.31468i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$	0.754976	−	0.754976i	0.140195	−	0.140195i	−0.633526	−	0.773721i	$-0.718393\pi$
$29$	0.754976	−	0.754976i	0.140195	−	0.140195i	0.773721	+	0.633526i	$0.218393\pi$
$30$		0			0
$31$	−2.20834	−	8.24163i	−0.396629	−	1.48024i	−0.818987	−	0.573812i	$-0.805464\pi$
$31$	−2.20834	−	8.24163i	−0.396629	−	1.48024i	0.422358	−	0.906429i	$-0.361203\pi$
$32$		0			0
$33$	2.54720	+	4.41187i	0.443410	+	0.768009i
$34$		0			0
$35$	2.34687	+	11.0236i	0.396693	+	1.86333i
$36$		0			0
$37$	−4.69701	−	1.25856i	−0.772183	−	0.206906i	−0.148847	−	0.988860i	$-0.547556\pi$
$37$	−4.69701	−	1.25856i	−0.772183	−	0.206906i	−0.623336	+	0.781954i	$0.714223\pi$
$38$		0			0
$39$	−0.619924	−	2.31359i	−0.0992673	−	0.370471i
$40$		0			0
$41$	−1.06291	−	1.06291i	−0.165999	−	0.165999i	0.619219	−	0.785218i	$-0.287449\pi$
$41$	−1.06291	−	1.06291i	−0.165999	−	0.165999i	−0.785218	+	0.619219i	$0.787449\pi$
$42$		0			0
$43$		−	5.55521i		−	0.847162i	−0.905858	−	0.423581i	$-0.860773\pi$
$43$		−	5.55521i		−	0.847162i	0.905858	−	0.423581i	$-0.139227\pi$
$44$		0			0
$45$	−4.11475	+	1.10254i	−0.613391	+	0.164358i
$46$		0			0
$47$	−5.27390	−	9.13467i	−0.769278	−	1.33243i	−0.937955	−	0.346757i	$-0.887283\pi$
$47$	−5.27390	−	9.13467i	−0.769278	−	1.33243i	0.168677	−	0.985671i	$-0.446050\pi$
$48$		0			0
$49$	−4.11083	+	5.66578i	−0.587261	+	0.809397i
$50$		0			0
$51$	0.220997	+	4.11718i	0.0309458	+	0.576520i
$52$		0			0
$53$	0.745169	+	0.430223i	0.102357	+	0.0590957i	0.550305	−	0.834964i	$-0.314512\pi$
$53$	0.745169	+	0.430223i	0.102357	+	0.0590957i	−0.447948	+	0.894060i	$0.647845\pi$
$54$		0			0
$55$	21.7016			2.92625
$56$		0			0
$57$	−4.30454	−	4.30454i	−0.570150	−	0.570150i
$58$		0			0
$59$	−6.11933	−	3.53300i	−0.796669	−	0.459957i	0.0456364	−	0.998958i	$-0.485468\pi$
$59$	−6.11933	−	3.53300i	−0.796669	−	0.459957i	−0.842305	+	0.539001i	$0.818802\pi$
$60$		0			0
$61$	−0.783732	+	2.92493i	−0.100347	+	0.374499i	−0.997776	−	0.0666601i	$-0.978766\pi$
$61$	−0.783732	+	2.92493i	−0.100347	+	0.374499i	0.897429	+	0.441159i	$0.145432\pi$
$62$		0			0
$63$	−2.21938	−	1.44026i	−0.279616	−	0.181456i
$64$		0			0
$65$	−9.85566	−	2.64082i	−1.22244	−	0.327553i
$66$		0			0
$67$	−4.16873	+	7.22046i	−0.509292	+	0.882120i	0.490650	+	0.871357i	$0.336759\pi$
$67$	−4.16873	+	7.22046i	−0.509292	+	0.882120i	−0.999942	+	0.0107629i	$0.996574\pi$
$68$		0			0
$69$	3.72763			0.448754
$70$		0			0
$71$	−7.20048	+	7.20048i	−0.854540	+	0.854540i	−0.990688	−	0.136149i	$-0.956527\pi$
$71$	−7.20048	+	7.20048i	−0.854540	+	0.854540i	0.136149	+	0.990688i	$0.456527\pi$
$72$		0			0
$73$	−2.48048	−	9.25727i	−0.290318	−	1.08348i	−0.944865	−	0.327460i	$-0.893807\pi$
$73$	−2.48048	−	9.25727i	−0.290318	−	1.08348i	0.654547	−	0.756021i	$-0.272859\pi$
$74$		0			0
$75$	−3.40263	+	12.6988i	−0.392902	+	1.46633i
$76$		0			0
$77$	9.02212	+	10.0136i	1.02817	+	1.14115i
$78$		0			0
$79$	−0.788112	+	2.94128i	−0.0886696	+	0.330919i	−0.995984	−	0.0895339i	$-0.971462\pi$
$79$	−0.788112	+	2.94128i	−0.0886696	+	0.330919i	0.907314	+	0.420453i	$0.138129\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$		0			0
$83$		−	0.914192i		−	0.100346i	−0.998741	−	0.0501728i	$-0.984023\pi$
$83$		−	0.914192i		−	0.100346i	0.998741	−	0.0501728i	$-0.0159772\pi$
$84$		0			0
$85$	15.6597	+	7.95409i	1.69854	+	0.862742i
$86$		0			0
$87$	0.924653	+	0.533848i	0.0991332	+	0.0572346i
$88$		0			0
$89$	6.61396	+	11.4557i	0.701079	+	1.21430i	0.968088	+	0.250610i	$0.0806313\pi$
$89$	6.61396	+	11.4557i	0.701079	+	1.21430i	−0.267009	+	0.963694i	$0.586035\pi$
$90$		0			0
$91$	−2.87882	−	5.64547i	−0.301782	−	0.591806i
$92$		0			0
$93$	7.38925	−	4.26618i	0.766229	−	0.442383i
$94$		0			0
$95$	−25.0487	+	6.71177i	−2.56994	+	0.688614i
$96$		0			0
$97$	2.56368	−	2.56368i	0.260302	−	0.260302i	−0.564875	−	0.825177i	$-0.691075\pi$
$97$	2.56368	−	2.56368i	0.260302	−	0.260302i	0.825177	+	0.564875i	$0.191075\pi$
$98$		0			0
$99$	−3.60228	+	3.60228i	−0.362043	+	0.362043i
$100$		0			0
$101$	8.38869	−	14.5296i	0.834706	−	1.44575i	−0.0595643	−	0.998224i	$-0.518971\pi$
$101$	8.38869	−	14.5296i	0.834706	−	1.44575i	0.894270	−	0.447528i	$-0.147696\pi$
$102$		0			0
$103$	−6.56494	−	11.3708i	−0.646863	−	1.12040i	−0.983868	−	0.178897i	$-0.942747\pi$
$103$	−6.56494	−	11.3708i	−0.646863	−	1.12040i	0.337005	−	0.941503i	$-0.390586\pi$
$104$		0			0
$105$	−10.0406	+	5.12002i	−0.979858	+	0.499662i
$106$		0			0
$107$	−7.48905	−	2.00669i	−0.723994	−	0.193994i	−0.122041	−	0.992525i	$-0.538944\pi$
$107$	−7.48905	−	2.00669i	−0.723994	−	0.193994i	−0.601953	+	0.798531i	$0.705611\pi$
$108$		0			0
$109$	8.44021	−	2.26155i	0.808426	−	0.216617i	0.169146	−	0.985591i	$-0.445899\pi$
$109$	8.44021	−	2.26155i	0.808426	−	0.216617i	0.639280	+	0.768974i	$0.279232\pi$
$110$		0			0
$111$		−	4.86270i		−	0.461547i
$112$		0			0
$113$	3.97383	+	3.97383i	0.373827	+	0.373827i	0.868869	−	0.495042i	$-0.164847\pi$
$113$	3.97383	+	3.97383i	0.373827	+	0.373827i	−0.495042	+	0.868869i	$0.664847\pi$
$114$		0			0
$115$	7.93966	−	13.7519i	0.740377	−	1.28237i
$116$		0			0
$117$	2.07431	−	1.19760i	0.191770	−	0.110718i
$118$		0			0
$119$	2.84012	+	10.5325i	0.260354	+	0.965513i
$120$		0			0
$121$	12.9495	−	7.47642i	1.17723	−	0.679674i
$122$		0			0
$123$	0.751592	−	1.30180i	0.0677688	−	0.117379i
$124$		0			0
$125$	24.5398	+	24.5398i	2.19490	+	2.19490i
$126$		0			0
$127$			20.9257i			1.85686i	0.371510	+	0.928429i	$0.378840\pi$
$127$			20.9257i			1.85686i	−0.371510	+	0.928429i	$0.621160\pi$
$128$		0			0
$129$	5.36592	−	1.43779i	0.472443	−	0.126591i
$130$		0			0
$131$	5.72443	+	1.53386i	0.500146	+	0.134014i	0.500068	−	0.865986i	$-0.333308\pi$
$131$	5.72443	+	1.53386i	0.500146	+	0.134014i	7.80846e−5		1.00000i	$0.499975\pi$
$132$		0			0
$133$	−13.5106	−	8.76764i	−1.17151	−	0.760251i
$134$		0			0
$135$	−2.12995	−	3.68918i	−0.183317	−	0.317514i
$136$		0			0
$137$	−7.24264	+	12.5446i	−0.618780	+	1.07176i	0.370928	+	0.928661i	$0.379040\pi$
$137$	−7.24264	+	12.5446i	−0.618780	+	1.07176i	−0.989709	+	0.143097i	$0.954294\pi$
$138$		0			0
$139$	0.663746	−	0.663746i	0.0562982	−	0.0562982i	−0.678397	−	0.734695i	$-0.737325\pi$
$139$	0.663746	−	0.663746i	0.0562982	−	0.0562982i	0.734695	+	0.678397i	$0.237325\pi$
$140$		0			0
$141$	7.45843	−	7.45843i	0.628113	−	0.628113i
$142$		0			0
$143$	−11.7863	+	3.15814i	−0.985622	+	0.264097i
$144$		0			0
$145$	3.93893	−	2.27414i	0.327110	−	0.188857i
$146$		0			0
$147$	−6.53669	−	2.50434i	−0.539137	−	0.206555i
$148$		0			0
$149$	−2.88555	−	4.99791i	−0.236393	−	0.409445i	0.723283	−	0.690551i	$-0.242632\pi$
$149$	−2.88555	−	4.99791i	−0.236393	−	0.409445i	−0.959677	+	0.281106i	$0.909299\pi$
$150$		0			0
$151$	19.7399	+	11.3968i	1.60641	+	0.927461i	0.990165	+	0.139908i	$0.0446806\pi$
$151$	19.7399	+	11.3968i	1.60641	+	0.927461i	0.616246	+	0.787554i	$0.288653\pi$
$152$		0			0
$153$	−3.91969	+	1.27907i	−0.316888	+	0.103407i
$154$		0			0
$155$		−	36.3471i		−	2.91947i
$156$		0			0
$157$	−8.93548	+	15.4767i	−0.713129	+	1.23517i	0.250548	+	0.968104i	$0.419389\pi$
$157$	−8.93548	+	15.4767i	−0.713129	+	1.23517i	−0.963677	+	0.267071i	$0.913944\pi$
$158$		0			0
$159$	−0.222700	+	0.831127i	−0.0176613	+	0.0659127i
$160$		0			0
$161$	9.64619	−	2.05363i	0.760226	−	0.161848i
$162$		0			0
$163$	−3.32023	+	12.3913i	−0.260061	+	0.970560i	0.705144	+	0.709064i	$0.250882\pi$
$163$	−3.32023	+	12.3913i	−0.260061	+	0.970560i	−0.965205	+	0.261496i	$0.915784\pi$
$164$		0			0
$165$	5.61679	+	20.9622i	0.437267	+	1.63190i
$166$		0			0
$167$	−13.4309	+	13.4309i	−1.03931	+	1.03931i	−0.0401201	+	0.999195i	$0.512774\pi$
$167$	−13.4309	+	13.4309i	−1.03931	+	1.03931i	−0.999195	+	0.0401201i	$0.987226\pi$
$168$		0			0
$169$	−7.26301			−0.558693
$170$		0			0
$171$	3.04377	−	5.27196i	0.232763	−	0.403157i
$172$		0			0
$173$	5.43835	+	1.45720i	0.413470	+	0.110789i	0.459557	−	0.888148i	$-0.348008\pi$
$173$	5.43835	+	1.45720i	0.413470	+	0.110789i	−0.0460865	+	0.998937i	$0.514675\pi$
$174$		0			0
$175$	−1.80916	+	34.7360i	−0.136760	+	2.62580i
$176$		0			0
$177$	1.82881	−	6.82522i	0.137462	−	0.513015i
$178$		0			0
$179$	−14.0690	−	8.12274i	−1.05157	−	0.607122i	−0.128479	−	0.991712i	$-0.541010\pi$
$179$	−14.0690	−	8.12274i	−1.05157	−	0.607122i	−0.923088	+	0.384590i	$0.874343\pi$
$180$		0			0
$181$	−6.88887	−	6.88887i	−0.512046	−	0.512046i	0.403107	−	0.915153i	$-0.367930\pi$
$181$	−6.88887	−	6.88887i	−0.512046	−	0.512046i	−0.915153	+	0.403107i	$0.867930\pi$
$182$		0			0
$183$	−3.02811			−0.223844
$184$		0			0
$185$	−17.9394	−	10.3573i	−1.31893	−	0.761485i
$186$		0			0
$187$	20.9745	−	1.12584i	1.53381	−	0.0823299i
$188$		0			0
$189$	0.816767	−	2.51652i	0.0594111	−	0.183050i
$190$		0			0
$191$	9.27436	+	16.0637i	0.671069	+	1.16233i	0.977601	+	0.210465i	$0.0674979\pi$
$191$	9.27436	+	16.0637i	0.671069	+	1.16233i	−0.306532	+	0.951860i	$0.599169\pi$
$192$		0			0
$193$	23.1910	−	6.21401i	1.66932	−	0.447294i	0.704396	−	0.709807i	$-0.251218\pi$
$193$	23.1910	−	6.21401i	1.66932	−	0.447294i	0.964929	+	0.262513i	$0.0845511\pi$
$194$		0			0
$195$		−	10.2033i		−	0.730676i
$196$		0			0
$197$	10.3235	+	10.3235i	0.735522	+	0.735522i	0.971708	−	0.236186i	$-0.0758973\pi$
$197$	10.3235	+	10.3235i	0.735522	+	0.735522i	−0.236186	+	0.971708i	$0.575897\pi$
$198$		0			0
$199$	−4.44863	−	16.6025i	−0.315355	−	1.17692i	−0.923659	−	0.383216i	$-0.874817\pi$
$199$	−4.44863	−	16.6025i	−0.315355	−	1.17692i	0.608304	−	0.793704i	$-0.291850\pi$
$200$		0			0
$201$	−8.05338	−	2.15790i	−0.568041	−	0.152206i
$202$		0			0
$203$	2.68688	+	0.872060i	0.188582	+	0.0612066i
$204$		0			0
$205$	−3.20171	−	5.54552i	−0.223617	−	0.387316i
$206$		0			0
$207$	0.964781	+	3.60061i	0.0670569	+	0.250260i
$208$		0			0
$209$	−21.9290	+	21.9290i	−1.51686	+	1.51686i
$210$		0			0
$211$	−8.61343	−	8.61343i	−0.592973	−	0.592973i	0.345461	−	0.938433i	$-0.387723\pi$
$211$	−8.61343	−	8.61343i	−0.592973	−	0.592973i	−0.938433	+	0.345461i	$0.887723\pi$
$212$		0			0
$213$	−8.81875	−	5.09151i	−0.604251	−	0.348864i
$214$		0			0
$215$	6.12487	−	22.8583i	0.417712	−	1.55892i
$216$		0			0
$217$	16.7712	−	15.1107i	1.13851	−	1.02578i
$218$		0			0
$219$	8.29984	−	4.79192i	0.560852	−	0.323808i
$220$		0			0
$221$	−9.66246	−	2.04104i	−0.649967	−	0.137295i
$222$		0			0
$223$		−	24.1501i		−	1.61721i	−0.588351	−	0.808606i	$-0.700223\pi$
$223$		−	24.1501i		−	1.61721i	0.588351	−	0.808606i	$-0.299777\pi$
$224$		0			0
$225$	−13.1468			−0.876451
$226$		0			0
$227$	−13.5630	+	3.63420i	−0.900209	+	0.241210i	−0.679106	−	0.734040i	$-0.737632\pi$
$227$	−13.5630	+	3.63420i	−0.900209	+	0.241210i	−0.221103	+	0.975251i	$0.570966\pi$
$228$		0			0
$229$	4.42090	−	2.55241i	0.292142	−	0.168668i	−0.346766	−	0.937952i	$-0.612720\pi$
$229$	4.42090	−	2.55241i	0.292142	−	0.168668i	0.638907	+	0.769284i	$0.279387\pi$
$230$		0			0
$231$	−7.33725	+	11.3064i	−0.482756	+	0.743906i
$232$		0			0
$233$	−22.5769	−	6.04946i	−1.47906	−	0.396313i	−0.573034	−	0.819532i	$-0.694234\pi$
$233$	−22.5769	−	6.04946i	−1.47906	−	0.396313i	−0.906028	+	0.423218i	$0.860900\pi$
$234$		0			0
$235$	−11.6294	−	43.4016i	−0.758620	−	2.83121i
$236$		0			0
$237$	−3.04503			−0.197796
$238$		0			0
$239$	15.6211			1.01044			0.505222	−	0.862989i	$-0.331411\pi$
$239$	15.6211			1.01044			0.505222	+	0.862989i	$0.331411\pi$
$240$		0			0
$241$	0.603793	+	2.25338i	0.0388937	+	0.145153i	0.982642	−	0.185511i	$-0.0593940\pi$
$241$	0.603793	+	2.25338i	0.0388937	+	0.145153i	−0.943749	+	0.330664i	$0.892727\pi$
$242$		0			0
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$		0			0
$245$	−23.1618	+	18.7809i	−1.47975	+	1.19987i
$246$		0			0
$247$	12.6274	−	7.29044i	0.803463	−	0.463880i
$248$		0			0
$249$	0.883041	−	0.236610i	0.0559605	−	0.0149946i
$250$		0			0
$251$	−2.32271			−0.146608			−0.0733041	−	0.997310i	$-0.523354\pi$
$251$	−2.32271			−0.146608			−0.0733041	+	0.997310i	$0.523354\pi$
$252$		0			0
$253$		−	18.9900i		−	1.19389i
$254$		0			0
$255$	−3.63002	+	17.1848i	−0.227321	+	1.07616i
$256$		0			0
$257$	8.96197	−	5.17419i	0.559032	−	0.322757i	−0.193725	−	0.981056i	$-0.562057\pi$
$257$	8.96197	−	5.17419i	0.559032	−	0.322757i	0.752757	+	0.658299i	$0.228724\pi$
$258$		0			0
$259$	−2.67896	−	12.5835i	−0.166463	−	0.781900i
$260$		0			0
$261$	−0.276340	+	1.03132i	−0.0171050	+	0.0638369i
$262$		0			0
$263$	−9.98055	−	5.76227i	−0.615427	−	0.355317i	0.159660	−	0.987172i	$-0.448960\pi$
$263$	−9.98055	−	5.76227i	−0.615427	−	0.355317i	−0.775086	+	0.631855i	$0.782294\pi$
$264$		0			0
$265$	2.59184	+	2.59184i	0.159216	+	0.159216i
$266$		0			0
$267$	−9.35356	+	9.35356i	−0.572429	+	0.572429i
$268$		0			0
$269$	0.0494360	+	0.184498i	0.00301417	+	0.0112490i	0.967417	−	0.253190i	$-0.0814798\pi$
$269$	0.0494360	+	0.184498i	0.00301417	+	0.0112490i	−0.964402	+	0.264439i	$0.914813\pi$
$270$		0			0
$271$	−4.59141	−	7.95255i	−0.278908	−	0.483083i	0.692206	−	0.721700i	$-0.256639\pi$
$271$	−4.59141	−	7.95255i	−0.278908	−	0.483083i	−0.971114	+	0.238617i	$0.923306\pi$
$272$		0			0
$273$	4.70802	−	4.24188i	0.284942	−	0.256730i
$274$		0			0
$275$	64.6927	+	17.3344i	3.90112	+	1.04530i
$276$		0			0
$277$	−6.08965	−	22.7269i	−0.365892	−	1.36553i	−0.866208	−	0.499684i	$-0.833450\pi$
$277$	−6.08965	−	22.7269i	−0.365892	−	1.36553i	0.500316	−	0.865843i	$-0.333217\pi$
$278$		0			0
$279$	6.03329	+	6.03329i	0.361204	+	0.361204i
$280$		0			0
$281$		−	12.9619i		−	0.773241i	−0.922239	−	0.386620i	$-0.873642\pi$
$281$		−	12.9619i		−	0.773241i	0.922239	−	0.386620i	$-0.126358\pi$
$282$		0			0
$283$	14.6256	−	3.91891i	0.869399	−	0.232955i	0.203571	−	0.979060i	$-0.434745\pi$
$283$	14.6256	−	3.91891i	0.869399	−	0.232955i	0.665828	+	0.746105i	$0.268078\pi$
$284$		0			0
$285$	−12.9662	−	22.4580i	−0.768049	−	1.33030i
$286$		0			0
$287$	1.22775	−	3.78280i	0.0724719	−	0.223291i
$288$		0			0
$289$	15.5477	+	6.87520i	0.914572	+	0.404423i
$290$		0			0
$291$	3.13985	+	1.81280i	0.184061	+	0.106268i
$292$		0			0
$293$	−5.89205			−0.344217			−0.172109	−	0.985078i	$-0.555058\pi$
$293$	−5.89205			−0.344217			−0.172109	+	0.985078i	$0.555058\pi$
$294$		0			0
$295$	−21.2842	−	21.2842i	−1.23922	−	1.23922i
$296$		0			0
$297$	−4.41187	−	2.54720i	−0.256003	−	0.147803i
$298$		0			0
$299$	−2.31085	+	8.62419i	−0.133640	+	0.498750i
$300$		0			0
$301$	13.0936	−	6.67686i	0.754702	−	0.384848i
$302$		0			0
$303$	16.2057	+	4.34230i	0.930993	+	0.249459i
$304$		0			0
$305$	−6.44972	+	11.1712i	−0.369310	+	0.639664i
$306$		0			0
$307$	2.73082			0.155856			0.0779281	−	0.996959i	$-0.475170\pi$
$307$	2.73082			0.155856			0.0779281	+	0.996959i	$0.475170\pi$
$308$		0			0
$309$	9.28423	−	9.28423i	0.528162	−	0.528162i
$310$		0			0
$311$	−7.89120	−	29.4503i	−0.447469	−	1.66998i	−0.709335	−	0.704872i	$-0.751005\pi$
$311$	−7.89120	−	29.4503i	−0.447469	−	1.66998i	0.261866	−	0.965104i	$-0.415662\pi$
$312$		0			0
$313$	1.97150	−	7.35775i	0.111436	−	0.415885i	−0.887560	−	0.460693i	$-0.847601\pi$
$313$	1.97150	−	7.35775i	0.111436	−	0.415885i	0.998996	+	0.0448080i	$0.0142676\pi$
$314$		0			0
$315$	−7.54424	−	8.37328i	−0.425070	−	0.471781i
$316$		0			0
$317$	3.47921	−	12.9846i	0.195412	−	0.729287i	−0.796748	−	0.604312i	$-0.793448\pi$
$317$	3.47921	−	12.9846i	0.195412	−	0.729287i	0.992160	−	0.124976i	$-0.0398852\pi$
$318$		0			0
$319$	2.71963	−	4.71054i	0.152270	−	0.263740i
$320$		0			0
$321$		−	7.75324i		−	0.432744i
$322$		0			0
$323$	−23.8613	+	7.78639i	−1.32768	+	0.433246i
$324$		0			0
$325$	−27.2704	−	15.7446i	−1.51269	−	0.873353i
$326$		0			0
$327$	4.36898	+	7.56729i	0.241605	+	0.418472i
$328$		0			0
$329$	15.1916	−	23.4096i	0.837540	−	1.29061i
$330$		0			0
$331$	5.45694	−	3.15056i	0.299940	−	0.173171i	−0.342476	−	0.939527i	$-0.611265\pi$
$331$	5.45694	−	3.15056i	0.299940	−	0.173171i	0.642416	+	0.766356i	$0.277932\pi$
$332$		0			0
$333$	4.69701	−	1.25856i	0.257394	−	0.0689686i
$334$		0			0
$335$	−25.1142	+	25.1142i	−1.37213	+	1.37213i
$336$		0			0
$337$	−19.9633	+	19.9633i	−1.08747	+	1.08747i	−0.0916848	+	0.995788i	$0.529225\pi$
$337$	−19.9633	+	19.9633i	−1.08747	+	1.08747i	−0.995788	+	0.0916848i	$0.970775\pi$
$338$		0			0
$339$	−2.80992	+	4.86693i	−0.152614	+	0.264335i
$340$		0			0
$341$	−21.7336	−	37.6437i	−1.17694	−	2.03852i
$342$		0			0
$343$	−18.2950	−	2.87944i	−0.987840	−	0.155475i
$344$		0			0
$345$	15.3383	+	4.10987i	0.825784	+	0.221268i
$346$		0			0
$347$	4.63505	−	1.24196i	0.248823	−	0.0666718i	−0.132252	−	0.991216i	$-0.542221\pi$
$347$	4.63505	−	1.24196i	0.248823	−	0.0666718i	0.381075	+	0.924544i	$0.375554\pi$
$348$		0			0
$349$			19.1796i			1.02666i	0.858192	+	0.513329i	$0.171588\pi$
$349$			19.1796i			1.02666i	−0.858192	+	0.513329i	$0.828412\pi$
$350$		0			0
$351$	1.69366	+	1.69366i	0.0904011	+	0.0904011i
$352$		0			0
$353$	−6.29479	+	10.9029i	−0.335038	+	0.580302i	−0.983492	−	0.180951i	$-0.942082\pi$
$353$	−6.29479	+	10.9029i	−0.335038	+	0.580302i	0.648454	+	0.761254i	$0.275416\pi$
$354$		0			0
$355$	−37.5670	+	21.6893i	−1.99385	+	1.15115i
$356$		0			0
$357$	−9.43854	+	5.46936i	−0.499541	+	0.289469i
$358$		0			0
$359$	8.37729	−	4.83663i	0.442136	−	0.255268i	−0.262367	−	0.964968i	$-0.584503\pi$
$359$	8.37729	−	4.83663i	0.442136	−	0.255268i	0.704503	+	0.709701i	$0.251170\pi$
$360$		0			0
$361$	9.02904	−	15.6388i	0.475213	−	0.823092i
$362$		0			0
$363$	10.5732	+	10.5732i	0.554952	+	0.554952i
$364$		0			0
$365$		−	40.8262i		−	2.13694i
$366$		0			0
$367$	2.71990	−	0.728795i	0.141978	−	0.0380428i	−0.187130	−	0.982335i	$-0.559919\pi$
$367$	2.71990	−	0.728795i	0.141978	−	0.0380428i	0.329108	+	0.944292i	$0.393252\pi$
$368$		0			0
$369$	1.45196	+	0.389053i	0.0755862	+	0.0202533i
$370$		0			0
$371$	−0.118408	+	2.27345i	−0.00614744	+	0.118031i
$372$		0			0
$373$	8.60798	+	14.9095i	0.445704	+	0.771982i	0.998101	−	0.0615991i	$-0.0196200\pi$
$373$	8.60798	+	14.9095i	0.445704	+	0.771982i	−0.552397	+	0.833581i	$0.686287\pi$
$374$		0			0
$375$	−17.3522	+	30.0549i	−0.896065	+	1.55203i
$376$		0			0
$377$	−1.80832	+	1.80832i	−0.0931332	+	0.0931332i
$378$		0			0
$379$	11.9223	−	11.9223i	0.612406	−	0.612406i	−0.331167	−	0.943572i	$-0.607442\pi$
$379$	11.9223	−	11.9223i	0.612406	−	0.612406i	0.943572	+	0.331167i	$0.107442\pi$
$380$		0			0
$381$	−20.2127	+	5.41598i	−1.03553	+	0.277469i
$382$		0			0
$383$	−0.285880	+	0.165053i	−0.0146078	+	0.00843382i	−0.507286	−	0.861778i	$-0.669351\pi$
$383$	−0.285880	+	0.165053i	−0.0146078	+	0.00843382i	0.492678	+	0.870212i	$0.336018\pi$
$384$		0			0
$385$	26.0834	+	51.1505i	1.32933	+	2.60687i
$386$		0			0
$387$	2.77761	+	4.81095i	0.141194	+	0.244555i
$388$		0			0
$389$	29.5584	+	17.0655i	1.49867	+	0.865258i	0.999999	−	0.00153346i	$-0.000488115\pi$
$389$	29.5584	+	17.0655i	1.49867	+	0.865258i	0.498671	+	0.866791i	$0.333821\pi$
$390$		0			0
$391$	6.96023	−	13.7031i	0.351994	−	0.692993i
$392$		0			0
$393$			5.92637i			0.298946i
$394$		0			0
$395$	−6.48577	+	11.2337i	−0.326335	+	0.565228i
$396$		0			0
$397$	5.94955	−	22.2040i	0.298599	−	1.11439i	−0.639718	−	0.768610i	$-0.720949\pi$
$397$	5.94955	−	22.2040i	0.298599	−	1.11439i	0.938317	−	0.345777i	$-0.112385\pi$
$398$		0			0
$399$	4.97210	−	15.3194i	0.248916	−	0.766931i
$400$		0			0
$401$	7.08627	−	26.4463i	0.353871	−	1.32067i	−0.528028	−	0.849227i	$-0.677068\pi$
$401$	7.08627	−	26.4463i	0.353871	−	1.32067i	0.881899	−	0.471438i	$-0.156265\pi$
$402$		0			0
$403$	5.28942	+	19.7404i	0.263485	+	0.983338i
$404$		0			0
$405$	3.01221	−	3.01221i	0.149678	−	0.149678i
$406$		0			0
$407$	−24.7725			−1.22793
$408$		0			0
$409$	−12.0278	+	20.8327i	−0.594735	+	1.03011i	0.398849	+	0.917017i	$0.369410\pi$
$409$	−12.0278	+	20.8327i	−0.594735	+	1.03011i	−0.993584	+	0.113095i	$0.963924\pi$
$410$		0			0
$411$	−13.9917	−	3.74906i	−0.690160	−	0.184928i
$412$		0			0
$413$	0.972368	−	18.6695i	0.0478471	−	0.918668i
$414$		0			0
$415$	1.00794	−	3.76167i	0.0494777	−	0.184653i
$416$		0			0
$417$	0.812919	+	0.469339i	0.0398088	+	0.0229836i
$418$		0			0
$419$	−13.8863	−	13.8863i	−0.678391	−	0.678391i	0.281245	−	0.959636i	$-0.409253\pi$
$419$	−13.8863	−	13.8863i	−0.678391	−	0.678391i	−0.959636	+	0.281245i	$0.909253\pi$
$420$		0			0
$421$	6.96968			0.339681			0.169841	−	0.985472i	$-0.445675\pi$
$421$	6.96968			0.339681			0.169841	+	0.985472i	$0.445675\pi$
$422$		0			0
$423$	9.13467	+	5.27390i	0.444143	+	0.256426i
$424$		0			0
$425$	40.3284	+	36.2196i	1.95622	+	1.75691i
$426$		0			0
$427$	−7.83601	+	1.66825i	−0.379211	+	0.0807321i
$428$		0			0
$429$	−6.10105	−	10.5673i	−0.294561	−	0.510195i
$430$		0			0
$431$	24.8820	−	6.66711i	1.19852	−	0.321143i	0.396274	−	0.918132i	$-0.370303\pi$
$431$	24.8820	−	6.66711i	1.19852	−	0.321143i	0.802249	+	0.596989i	$0.203636\pi$
$432$		0			0
$433$			23.2712i			1.11834i	0.829052	+	0.559172i	$0.188881\pi$
$433$			23.2712i			1.11834i	−0.829052	+	0.559172i	$0.811119\pi$
$434$		0			0
$435$	3.21612	+	3.21612i	0.154201	+	0.154201i
$436$		0			0
$437$	5.87314	+	21.9188i	0.280950	+	1.04852i
$438$		0			0
$439$	13.1943	+	3.53540i	0.629729	+	0.168735i	0.559547	−	0.828799i	$-0.310975\pi$
$439$	13.1943	+	3.53540i	0.629729	+	0.168735i	0.0701821	+	0.997534i	$0.477642\pi$
$440$		0			0
$441$	0.727191	−	6.96213i	0.0346281	−	0.331530i
$442$		0			0
$443$	8.93238	+	15.4713i	0.424390	+	0.735065i	0.996363	−	0.0852073i	$-0.0271552\pi$
$443$	8.93238	+	15.4713i	0.424390	+	0.735065i	−0.571973	+	0.820272i	$0.693822\pi$
$444$		0			0
$445$	14.5844	+	54.4296i	0.691366	+	2.58021i
$446$		0			0
$447$	4.08078	−	4.08078i	0.193014	−	0.193014i
$448$		0			0
$449$	−1.01189	−	1.01189i	−0.0477539	−	0.0477539i	0.682827	−	0.730581i	$-0.260750\pi$
$449$	−1.01189	−	1.01189i	−0.0477539	−	0.0477539i	−0.730581	+	0.682827i	$0.760750\pi$
$450$		0			0
$451$	−6.63186	−	3.82890i	−0.312282	−	0.180296i
$452$		0			0
$453$	−5.89944	+	22.0170i	−0.277180	+	1.03445i
$454$		0			0
$455$	−5.62122	−	26.4037i	−0.263527	−	1.23783i
$456$		0			0
$457$	−7.32545	+	4.22935i	−0.342670	+	0.197841i	−0.661452	−	0.749987i	$-0.730060\pi$
$457$	−7.32545	+	4.22935i	−0.342670	+	0.197841i	0.318782	+	0.947828i	$0.396726\pi$
$458$		0			0
$459$	−2.24998	−	3.45508i	−0.105020	−	0.161269i
$460$		0			0
$461$			37.5811i			1.75033i	0.483828	+	0.875163i	$0.339246\pi$
$461$			37.5811i			1.75033i	−0.483828	+	0.875163i	$0.660754\pi$
$462$		0			0
$463$	−0.480130			−0.0223135			−0.0111568	−	0.999938i	$-0.503551\pi$
$463$	−0.480130			−0.0223135			−0.0111568	+	0.999938i	$0.503551\pi$
$464$		0			0
$465$	35.1086	−	9.40731i	1.62812	−	0.436254i
$466$		0			0
$467$	−7.01381	+	4.04942i	−0.324560	+	0.187385i	−0.653423	−	0.756993i	$-0.726668\pi$
$467$	−7.01381	+	4.04942i	−0.324560	+	0.187385i	0.328863	+	0.944378i	$0.393335\pi$
$468$		0			0
$469$	−22.0290	−	1.14734i	−1.01721	−	0.0529792i
$470$		0			0
$471$	−17.2620	−	4.62534i	−0.795392	−	0.213125i
$472$		0			0
$473$	−7.32469	−	27.3361i	−0.336790	−	1.25692i
$474$		0			0
$475$	−80.0314			−3.67209
$476$		0			0
$477$	−0.860446			−0.0393971
$478$		0			0
$479$	−4.86127	−	18.1425i	−0.222117	−	0.828952i	−0.983539	−	0.180695i	$-0.942165\pi$
$479$	−4.86127	−	18.1425i	−0.222117	−	0.828952i	0.761422	−	0.648256i	$-0.224502\pi$
$480$		0			0
$481$	11.2503	+	3.01450i	0.512969	+	0.137450i
$482$		0			0
$483$	4.48027	+	8.78599i	0.203859	+	0.399776i
$484$		0			0
$485$	13.3755	−	7.72233i	0.607349	−	0.350653i
$486$		0			0
$487$	6.14436	−	1.64638i	0.278427	−	0.0746044i	−0.116903	−	0.993143i	$-0.537297\pi$
$487$	6.14436	−	1.64638i	0.278427	−	0.0746044i	0.395331	+	0.918539i	$0.370630\pi$
$488$		0			0
$489$	−12.8284			−0.580120
$490$		0			0
$491$			34.2882i			1.54740i	0.633550	+	0.773702i	$0.281597\pi$
$491$			34.2882i			1.54740i	−0.633550	+	0.773702i	$0.718403\pi$
$492$		0			0
$493$	3.68898	−	2.40229i	0.166143	−	0.108194i
$494$		0			0
$495$	−18.7941	+	10.8508i	−0.844734	+	0.487708i
$496$		0			0
$497$	−25.6258	−	8.31715i	−1.14947	−	0.373075i
$498$		0			0
$499$	3.80914	−	14.2159i	0.170521	−	0.636392i	−0.826751	−	0.562568i	$-0.809813\pi$
$499$	3.80914	−	14.2159i	0.170521	−	0.636392i	0.997271	−	0.0738232i	$-0.0235201\pi$
$500$		0			0
$501$	−16.4494	−	9.49709i	−0.734907	−	0.424299i
$502$		0			0
$503$	18.7473	+	18.7473i	0.835903	+	0.835903i	0.988317	−	0.152414i	$-0.0487046\pi$
$503$	18.7473	+	18.7473i	0.835903	+	0.835903i	−0.152414	+	0.988317i	$0.548705\pi$
$504$		0			0
$505$	50.5369	−	50.5369i	2.24886	−	2.24886i
$506$		0			0
$507$	−1.87980	−	7.01553i	−0.0834850	−	0.311570i
$508$		0			0
$509$	−4.18417	−	7.24720i	−0.185460	−	0.321226i	0.758271	−	0.651939i	$-0.226044\pi$
$509$	−4.18417	−	7.24720i	−0.185460	−	0.321226i	−0.943731	+	0.330713i	$0.892711\pi$
$510$		0			0
$511$	18.8380	−	16.9729i	0.833345	−	0.750836i
$512$		0			0
$513$	5.88011	+	1.57557i	0.259613	+	0.0695631i
$514$		0			0
$515$	−14.4763	−	54.0262i	−0.637901	−	2.38068i
$516$		0			0
$517$	−37.9961	−	37.9961i	−1.67107	−	1.67107i
$518$		0			0
$519$			5.63019i			0.247138i
$520$		0			0
$521$	1.33055	−	0.356521i	0.0582926	−	0.0156195i	−0.229555	−	0.973296i	$-0.573727\pi$
$521$	1.33055	−	0.356521i	0.0582926	−	0.0156195i	0.287847	+	0.957676i	$0.407060\pi$
$522$		0			0
$523$	−2.84968	−	4.93580i	−0.124608	−	0.215827i	0.796972	−	0.604017i	$-0.206434\pi$
$523$	−2.84968	−	4.93580i	−0.124608	−	0.215827i	−0.921580	+	0.388189i	$0.873101\pi$
$524$		0			0
$525$	−34.0206	+	7.24283i	−1.48478	+	0.316103i
$526$		0			0
$527$	−1.88563	−	35.1293i	−0.0821392	−	1.53026i
$528$		0			0
$529$	7.88499	+	4.55240i	0.342826	+	0.197930i
$530$		0			0
$531$	7.06599			0.306638
$532$		0			0
$533$	2.54589	+	2.54589i	0.110275	+	0.110275i
$534$		0			0
$535$	−28.6031	−	16.5140i	−1.23662	−	0.713963i
$536$		0			0
$537$	4.20464	−	15.6919i	0.181444	−	0.677157i
$538$		0			0
$539$	−12.7581	+	33.3004i	−0.549530	+	1.43435i
$540$		0			0
$541$	1.89081	+	0.506641i	0.0812922	+	0.0217822i	0.299236	−	0.954179i	$-0.403268\pi$
$541$	1.89081	+	0.506641i	0.0812922	+	0.0217822i	−0.217944	+	0.975961i	$0.569935\pi$
$542$		0			0
$543$	4.87117	−	8.43711i	0.209042	−	0.362071i
$544$		0			0
$545$	37.2228			1.59445
$546$		0			0
$547$	−8.29629	+	8.29629i	−0.354724	+	0.354724i	−0.861864	−	0.507140i	$-0.830703\pi$
$547$	−8.29629	+	8.29629i	−0.354724	+	0.354724i	0.507140	+	0.861864i	$0.330703\pi$
$548$		0			0
$549$	−0.783732	−	2.92493i	−0.0334489	−	0.124833i
$550$		0			0
$551$	−1.68223	+	6.27817i	−0.0716655	+	0.267459i
$552$		0			0
$553$	−7.87980	+	1.67757i	−0.335083	+	0.0713376i
$554$		0			0
$555$	5.36134	−	20.0088i	0.227576	−	0.849326i
$556$		0			0
$557$	−2.94718	+	5.10466i	−0.124876	+	0.216292i	−0.921684	−	0.387940i	$-0.873187\pi$
$557$	−2.94718	+	5.10466i	−0.124876	+	0.216292i	0.796808	+	0.604232i	$0.206520\pi$
$558$		0			0
$559$			13.3059i			0.562778i
$560$		0			0
$561$	6.51609	+	19.9684i	0.275109	+	0.843068i
$562$		0			0
$563$	−20.4389	−	11.8004i	−0.861399	−	0.497329i	0.00308167	−	0.999995i	$-0.499019\pi$
$563$	−20.4389	−	11.8004i	−0.861399	−	0.497329i	−0.864480	+	0.502666i	$0.832352\pi$
$564$		0			0
$565$	11.9700	+	20.7326i	0.503582	+	0.872229i
$566$		0			0
$567$	2.64217	+	0.137612i	0.110961	+	0.00577918i
$568$		0			0
$569$	5.42959	−	3.13477i	0.227620	−	0.131417i	−0.381854	−	0.924223i	$-0.624714\pi$
$569$	5.42959	−	3.13477i	0.227620	−	0.131417i	0.609474	+	0.792806i	$0.291381\pi$
$570$		0			0
$571$	12.0906	−	3.23968i	0.505978	−	0.135576i	0.00320476	−	0.999995i	$-0.498980\pi$
$571$	12.0906	−	3.23968i	0.505978	−	0.135576i	0.502773	+	0.864419i	$0.332313\pi$
$572$		0			0
$573$	−13.1159	+	13.1159i	−0.547926	+	0.547926i
$574$		0			0
$575$	34.6527	−	34.6527i	1.44512	−	1.44512i
$576$		0			0
$577$	−10.5641	+	18.2975i	−0.439788	+	0.761736i	−0.997673	−	0.0681829i	$-0.978280\pi$
$577$	−10.5641	+	18.2975i	−0.439788	+	0.761736i	0.557885	+	0.829919i	$0.311613\pi$
$578$		0			0
$579$	12.0045	+	20.7925i	0.498892	+	0.864106i
$580$		0			0
$581$	2.15474	−	1.09878i	0.0893938	−	0.0455849i
$582$		0			0
$583$	4.23409	+	1.13452i	0.175358	+	0.0469871i
$584$		0			0
$585$	9.85566	−	2.64082i	0.407481	−	0.109184i
$586$		0			0
$587$		−	2.29594i		−	0.0947635i	−0.998877	−	0.0473817i	$-0.984912\pi$
$587$		−	2.29594i		−	0.0947635i	0.998877	−	0.0473817i	$-0.0150877\pi$
$588$		0			0
$589$	36.7279	+	36.7279i	1.51335	+	1.51335i
$590$		0			0
$591$	−7.29985	+	12.6437i	−0.300276	+	0.520093i
$592$		0			0
$593$	35.1673	−	20.3039i	1.44415	−	0.833779i	0.446025	−	0.895020i	$-0.352839\pi$
$593$	35.1673	−	20.3039i	1.44415	−	0.833779i	0.998123	+	0.0612412i	$0.0195059\pi$
$594$		0			0
$595$	0.0738526	+	46.4700i	0.00302766	+	1.90508i
$596$		0			0
$597$	14.8854	−	8.59408i	0.609218	−	0.351732i
$598$		0			0
$599$	5.50876	−	9.54146i	0.225082	−	0.389853i	−0.731262	−	0.682097i	$-0.761068\pi$
$599$	5.50876	−	9.54146i	0.225082	−	0.389853i	0.956344	+	0.292243i	$0.0944017\pi$
$600$		0			0
$601$	−3.87291	−	3.87291i	−0.157979	−	0.157979i	0.623691	−	0.781671i	$-0.285632\pi$
$601$	−3.87291	−	3.87291i	−0.157979	−	0.157979i	−0.781671	+	0.623691i	$0.785632\pi$
$602$		0			0
$603$		−	8.33747i		−	0.339528i
$604$		0			0
$605$	61.5272	−	16.4862i	2.50143	−	0.670257i
$606$		0			0
$607$	−27.4926	−	7.36662i	−1.11589	−	0.299002i	−0.346671	−	0.937987i	$-0.612688\pi$
$607$	−27.4926	−	7.36662i	−1.11589	−	0.299002i	−0.769219	+	0.638985i	$0.779354\pi$
$608$		0			0
$609$	−0.146928	+	2.82104i	−0.00595383	+	0.114314i
$610$		0			0
$611$	12.6321	+	21.8794i	0.511039	+	0.885145i
$612$		0			0
$613$	−14.7328	+	25.5179i	−0.595052	+	1.03066i	0.398488	+	0.917174i	$0.369535\pi$
$613$	−14.7328	+	25.5179i	−0.595052	+	1.03066i	−0.993540	+	0.113486i	$0.963798\pi$
$614$		0			0
$615$	4.52790	−	4.52790i	0.182583	−	0.182583i
$616$		0			0
$617$	−5.34011	+	5.34011i	−0.214985	+	0.214985i	−0.806381	−	0.591396i	$-0.798577\pi$
$617$	−5.34011	+	5.34011i	−0.214985	+	0.214985i	0.591396	+	0.806381i	$0.298577\pi$
$618$		0			0
$619$	−27.3602	+	7.33114i	−1.09970	+	0.294663i	−0.762642	−	0.646821i	$-0.776098\pi$
$619$	−27.3602	+	7.33114i	−1.09970	+	0.294663i	−0.337056	+	0.941484i	$0.609431\pi$
$620$		0			0
$621$	−3.22822	+	1.86381i	−0.129544	+	0.0747923i
$622$		0			0
$623$	−19.0517	+	29.3578i	−0.763289	+	1.17620i
$624$		0			0
$625$	41.0519	+	71.1039i	1.64207	+	2.84416i
$626$		0			0
$627$	−26.8574	−	15.5061i	−1.07258	−	0.619256i
$628$		0			0
$629$	−17.8757	−	9.07963i	−0.712750	−	0.362029i
$630$		0			0
$631$		−	7.43975i		−	0.296172i	−0.988975	−	0.148086i	$-0.952689\pi$
$631$		−	7.43975i		−	0.296172i	0.988975	−	0.148086i	$-0.0473112\pi$
$632$		0			0
$633$	6.09061	−	10.5492i	0.242080	−	0.419295i
$634$		0			0
$635$	−23.0715	+	86.1041i	−0.915566	+	3.41694i
$636$		0			0
$637$	9.84627	−	13.5707i	0.390123	−	0.537691i
$638$		0			0
$639$	2.63556	−	9.83604i	0.104261	−	0.389108i
$640$		0			0
$641$	−8.86823	−	33.0967i	−0.350274	−	1.30724i	−0.886328	−	0.463057i	$-0.846752\pi$
$641$	−8.86823	−	33.0967i	−0.350274	−	1.30724i	0.536054	−	0.844184i	$-0.319914\pi$
$642$		0			0
$643$	−13.7087	+	13.7087i	−0.540619	+	0.540619i	−0.923710	−	0.383091i	$-0.874859\pi$
$643$	−13.7087	+	13.7087i	−0.540619	+	0.540619i	0.383091	+	0.923710i	$0.374859\pi$
$644$		0			0
$645$	23.6647			0.931795
$646$		0			0
$647$	−4.49360	+	7.78314i	−0.176662	+	0.305987i	−0.940735	−	0.339142i	$-0.889863\pi$
$647$	−4.49360	+	7.78314i	−0.176662	+	0.305987i	0.764073	+	0.645129i	$0.223196\pi$
$648$		0			0
$649$	−34.7704	−	9.31669i	−1.36486	−	0.365712i
$650$		0			0
$651$	18.9366	+	12.2888i	0.742183	+	0.481637i
$652$		0			0
$653$	−1.41708	+	5.28861i	−0.0554545	+	0.206959i	−0.988094	−	0.153850i	$-0.950833\pi$
$653$	−1.41708	+	5.28861i	−0.0554545	+	0.206959i	0.932640	+	0.360809i	$0.117499\pi$
$654$		0			0
$655$	21.8635	+	12.6229i	0.854276	+	0.493216i
$656$		0			0
$657$	6.77679	+	6.77679i	0.264388	+	0.264388i
$658$		0			0
$659$	7.47863			0.291326			0.145663	−	0.989334i	$-0.453468\pi$
$659$	7.47863			0.291326			0.145663	+	0.989334i	$0.453468\pi$
$660$		0			0
$661$	−23.9665	−	13.8371i	−0.932188	−	0.538199i	−0.0446851	−	0.999001i	$-0.514228\pi$
$661$	−23.9665	−	13.8371i	−0.932188	−	0.538199i	−0.887503	+	0.460802i	$0.847562\pi$
$662$		0			0
$663$	−0.529332	−	9.86148i	−0.0205576	−	0.382988i
$664$		0			0
$665$	−45.9258	−	50.9726i	−1.78093	−	1.97663i
$666$		0			0
$667$	−1.98999	−	3.44676i	−0.0770526	−	0.133459i
$668$		0			0
$669$	23.3272	−	6.25051i	0.901883	−	0.241659i
$670$		0			0
$671$			15.4264i			0.595528i
$672$		0			0
$673$	8.83882	+	8.83882i	0.340711	+	0.340711i	0.856635	−	0.515923i	$-0.172551\pi$
$673$	8.83882	+	8.83882i	0.340711	+	0.340711i	−0.515923	+	0.856635i	$0.672551\pi$
$674$		0			0
$675$	−3.40263	−	12.6988i	−0.130967	−	0.488777i
$676$		0			0
$677$	3.12635	+	0.837704i	0.120156	+	0.0321956i	0.318396	−	0.947958i	$-0.396856\pi$
$677$	3.12635	+	0.837704i	0.120156	+	0.0321956i	−0.198240	+	0.980153i	$0.563523\pi$
$678$		0			0
$679$	9.12389	+	2.96126i	0.350143	+	0.113643i
$680$		0			0
$681$	−7.02073	−	12.1603i	−0.269035	−	0.465982i
$682$		0			0
$683$	4.70832	+	17.5717i	0.180159	+	0.672362i	0.995615	+	0.0935432i	$0.0298193\pi$
$683$	4.70832	+	17.5717i	0.180159	+	0.672362i	−0.815456	+	0.578818i	$0.803514\pi$
$684$		0			0
$685$	−43.6326	+	43.6326i	−1.66712	+	1.66712i
$686$		0			0
$687$	3.60965	+	3.60965i	0.137717	+	0.137717i
$688$		0			0
$689$	−1.78483	−	1.03047i	−0.0679966	−	0.0392578i
$690$		0			0
$691$	−11.6980	+	43.6574i	−0.445012	+	1.66081i	0.270894	+	0.962609i	$0.412681\pi$
$691$	−11.6980	+	43.6574i	−0.445012	+	1.66081i	−0.715905	+	0.698197i	$0.753986\pi$
$692$		0			0
$693$	−12.8202	−	4.16093i	−0.486998	−	0.158061i
$694$		0			0
$695$	3.46296	−	1.99934i	0.131357	−	0.0758392i
$696$		0			0
$697$	−3.38213	−	5.19362i	−0.128107	−	0.196723i
$698$		0			0
$699$		−	23.3733i		−	0.884060i
$700$		0			0
$701$	21.9211			0.827949			0.413975	−	0.910288i	$-0.364140\pi$
$701$	21.9211			0.827949			0.413975	+	0.910288i	$0.364140\pi$
$702$		0			0
$703$	28.5932	−	7.66152i	1.07841	−	0.288960i
$704$		0			0
$705$	38.9128	−	22.4663i	1.46554	−	0.846130i
$706$		0			0
$707$	44.3287	+	2.30877i	1.66715	+	0.0868304i
$708$		0			0
$709$	−4.06415	−	1.08899i	−0.152632	−	0.0408977i	0.181694	−	0.983355i	$-0.441842\pi$
$709$	−4.06415	−	1.08899i	−0.152632	−	0.0408977i	−0.334326	+	0.942457i	$0.608509\pi$
$710$		0			0
$711$	−0.788112	−	2.94128i	−0.0295565	−	0.110306i
$712$		0			0
$713$	−31.8055			−1.19112
$714$		0			0
$715$	−51.9798			−1.94393
$716$		0			0
$717$	4.04304	+	15.0888i	0.150990	+	0.563502i
$718$		0			0
$719$	38.9731	+	10.4428i	1.45345	+	0.389451i	0.897223	−	0.441578i	$-0.145581\pi$
$719$	38.9731	+	10.4428i	1.45345	+	0.389451i	0.556229	+	0.831029i	$0.312248\pi$
$720$		0			0
$721$	18.9105	−	29.1402i	0.704263	−	1.08524i
$722$		0			0
$723$	−2.02033	+	1.16644i	−0.0751368	+	0.0433803i
$724$		0			0
$725$	13.5585	−	3.63298i	0.503549	−	0.134926i
$726$		0			0
$727$	40.5821			1.50511			0.752553	−	0.658532i	$-0.228822\pi$
$727$	40.5821			1.50511			0.752553	+	0.658532i	$0.228822\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	4.73381	−	22.4102i	0.175086	−	0.828872i
$732$		0			0
$733$	6.63734	−	3.83207i	0.245156	−	0.141541i	−0.372388	−	0.928077i	$-0.621461\pi$
$733$	6.63734	−	3.83207i	0.245156	−	0.141541i	0.617544	+	0.786536i	$0.288128\pi$
$734$		0			0
$735$	−24.1357	−	17.5117i	−0.890258	−	0.645930i
$736$		0			0
$737$	−10.9932	+	41.0271i	−0.404939	+	1.51125i
$738$		0			0
$739$	21.1801	+	12.2283i	0.779122	+	0.449826i	0.836119	−	0.548548i	$-0.184819\pi$
$739$	21.1801	+	12.2283i	0.779122	+	0.449826i	−0.0569971	+	0.998374i	$0.518153\pi$
$740$		0			0
$741$	10.3102	+	10.3102i	0.378756	+	0.378756i
$742$		0			0
$743$	6.22577	−	6.22577i	0.228402	−	0.228402i	−0.583623	−	0.812025i	$-0.698365\pi$
$743$	6.22577	−	6.22577i	0.228402	−	0.228402i	0.812025	+	0.583623i	$0.198365\pi$
$744$		0			0
$745$	−6.36288	−	23.7466i	−0.233118	−	0.870008i
$746$		0			0
$747$	0.457096	+	0.791713i	0.0167243	+	0.0289673i
$748$		0			0
$749$	−4.27142	−	20.0635i	−0.156074	−	0.733104i
$750$		0			0
$751$	−6.14101	−	1.64548i	−0.224088	−	0.0600443i	0.145028	−	0.989428i	$-0.453673\pi$
$751$	−6.14101	−	1.64548i	−0.224088	−	0.0600443i	−0.369116	+	0.929383i	$0.620340\pi$
$752$		0			0
$753$	−0.601162	−	2.24357i	−0.0219076	−	0.0817601i
$754$		0			0
$755$	68.6592	+	68.6592i	2.49877	+	2.49877i
$756$		0			0
$757$		−	15.0097i		−	0.545536i	−0.962080	−	0.272768i	$-0.912061\pi$
$757$		−	15.0097i		−	0.545536i	0.962080	−	0.272768i	$-0.0879391\pi$
$758$		0			0
$759$	18.3429	−	4.91497i	0.665806	−	0.178402i
$760$		0			0
$761$	−2.68756	−	4.65500i	−0.0974242	−	0.168744i	0.813194	−	0.581993i	$-0.197727\pi$
$761$	−2.68756	−	4.65500i	−0.0974242	−	0.168744i	−0.910618	+	0.413250i	$0.864394\pi$
$762$		0			0
$763$	15.4748	+	17.1753i	0.560226	+	0.621789i
$764$		0			0
$765$	−17.5388	+	0.941425i	−0.634116	+	0.0340373i
$766$		0			0
$767$	14.6570	+	8.46224i	0.529235	+	0.305554i
$768$		0			0
$769$	25.4733			0.918592			0.459296	−	0.888283i	$-0.348102\pi$
$769$	25.4733			0.918592			0.459296	+	0.888283i	$0.348102\pi$
$770$		0			0
$771$	7.31741	+	7.31741i	0.263530	+	0.263530i
$772$		0			0
$773$	−13.0397	−	7.52848i	−0.469006	−	0.270781i	0.246818	−	0.969062i	$-0.420615\pi$
$773$	−13.0397	−	7.52848i	−0.469006	−	0.270781i	−0.715824	+	0.698281i	$0.753949\pi$
$774$		0			0
$775$	29.0325	−	108.351i	1.04288	−	3.89208i
$776$		0			0
$777$	11.4613	−	5.84452i	0.411174	−	0.209671i
$778$		0			0
$779$	8.83888	+	2.36837i	0.316686	+	0.0848557i
$780$		0			0
$781$	−25.9381	+	44.9262i	−0.928139	+	1.60758i
$782$		0			0
$783$	−1.06770			−0.0381564
$784$		0			0
$785$	−53.8310	+	53.8310i	−1.92131	+	1.92131i
$786$		0			0
$787$	8.96967	+	33.4753i	0.319734	+	1.19326i	0.919500	+	0.393089i	$0.128594\pi$
$787$	8.96967	+	33.4753i	0.319734	+	1.19326i	−0.599766	+	0.800175i	$0.704740\pi$
$788$		0			0
$789$	2.98277	−	11.1319i	0.106189	−	0.396304i
$790$		0			0
$791$	−4.59011	+	14.1425i	−0.163205	+	0.502849i
$792$		0			0
$793$	1.87720	−	7.00579i	0.0666612	−	0.248783i
$794$		0			0
$795$	−1.83271	+	3.17435i	−0.0649995	+	0.112582i
$796$		0			0
$797$		−	42.4670i		−	1.50426i	−0.659015	−	0.752130i	$-0.729027\pi$
$797$		−	42.4670i		−	1.50426i	0.659015	−	0.752130i	$-0.270973\pi$
$798$		0			0
$799$	−13.4914	−	41.3441i	−0.477291	−	1.46265i
$800$		0			0
$801$	−11.4557	−	6.61396i	−0.404768	−	0.233693i
$802$		0			0
$803$	−24.4119	−	42.2827i	−0.861477	−	1.49212i
$804$		0			0
$805$	41.9559	+	2.18519i	1.47875	+	0.0770179i
$806$		0			0
$807$	−0.165416	+	0.0955031i	−0.00582293	+	0.00336187i
$808$		0			0
$809$	−38.7913	+	10.3941i	−1.36383	+	0.365437i	−0.865221	−	0.501391i	$-0.832822\pi$
$809$	−38.7913	+	10.3941i	−1.36383	+	0.365437i	−0.498608	+	0.866828i	$0.666155\pi$
$810$		0			0
$811$	30.5053	−	30.5053i	1.07119	−	1.07119i	0.0739213	−	0.997264i	$-0.476449\pi$
$811$	30.5053	−	30.5053i	1.07119	−	1.07119i	0.997264	−	0.0739213i	$-0.0235514\pi$
$812$		0			0
$813$	6.49323	−	6.49323i	0.227727	−	0.227727i
$814$		0			0
$815$	−27.3239	+	47.3263i	−0.957113	+	1.65777i
$816$		0			0
$817$	16.9088	+	29.2869i	0.591563	+	1.02462i
$818$		0			0
$819$	5.31586	+	3.44972i	0.185751	+	0.120543i
$820$		0			0
$821$	−33.7910	−	9.05426i	−1.17931	−	0.315996i	−0.384659	−	0.923059i	$-0.625681\pi$
$821$	−33.7910	−	9.05426i	−1.17931	−	0.315996i	−0.794654	+	0.607063i	$0.792348\pi$
$822$		0			0
$823$	−32.0872	+	8.59773i	−1.11849	+	0.299698i	−0.770272	−	0.637716i	$-0.779879\pi$
$823$	−32.0872	+	8.59773i	−1.11849	+	0.299698i	−0.348217	+	0.937414i	$0.613213\pi$
$824$		0			0
$825$			66.9748i			2.33176i
$826$		0			0
$827$	−9.61920	−	9.61920i	−0.334492	−	0.334492i	0.519797	−	0.854290i	$-0.326007\pi$
$827$	−9.61920	−	9.61920i	−0.334492	−	0.334492i	−0.854290	+	0.519797i	$0.826007\pi$
$828$		0			0
$829$	−8.97501	+	15.5452i	−0.311715	+	0.539906i	−0.978734	−	0.205135i	$-0.934237\pi$
$829$	−8.97501	+	15.5452i	−0.311715	+	0.539906i	0.667019	+	0.745041i	$0.267570\pi$
$830$		0			0
$831$	20.3764	−	11.7643i	0.706849	−	0.408099i
$832$		0			0
$833$	−21.4115	+	19.3533i	−0.741863	+	0.670551i
$834$		0			0
$835$	−70.0730	+	40.4567i	−2.42498	+	1.40006i
$836$		0			0
$837$	−4.26618	+	7.38925i	−0.147461	+	0.255410i
$838$		0			0
$839$	29.4007	+	29.4007i	1.01502	+	1.01502i	0.999885	+	0.0151382i	$0.00481882\pi$
$839$	29.4007	+	29.4007i	1.01502	+	1.01502i	0.0151382	+	0.999885i	$0.495181\pi$
$840$		0			0
$841$			27.8600i			0.960690i
$842$		0			0
$843$	12.5202	−	3.35478i	0.431219	−	0.115545i
$844$		0			0
$845$	−29.8855	−	8.00778i	−1.02809	−	0.275476i
$846$		0			0
$847$	33.1860	+	21.5360i	1.14029	+	0.739985i
$848$		0			0
$849$	7.57075	+	13.1129i	0.259827	+	0.450034i
$850$		0			0
$851$	−9.06316	+	15.6979i	−0.310681	+	0.538116i
$852$		0			0
$853$	25.0473	−	25.0473i	0.857604	−	0.857604i	−0.133452	−	0.991055i	$-0.542606\pi$
$853$	25.0473	−	25.0473i	0.857604	−	0.857604i	0.991055	+	0.133452i	$0.0426061\pi$
$854$		0			0
$855$	18.3369	−	18.3369i	0.627109	−	0.627109i
$856$		0			0
$857$	2.14184	−	0.573904i	0.0731638	−	0.0196042i	−0.222051	−	0.975035i	$-0.571275\pi$
$857$	2.14184	−	0.573904i	0.0731638	−	0.0196042i	0.295215	+	0.955431i	$0.404609\pi$
$858$		0			0
$859$	21.3891	−	12.3490i	0.729787	−	0.421342i	−0.0885575	−	0.996071i	$-0.528226\pi$
$859$	21.3891	−	12.3490i	0.729787	−	0.421342i	0.818344	+	0.574729i	$0.194892\pi$
$860$		0			0
$861$	3.97167	+	0.206857i	0.135354	+	0.00704966i
$862$		0			0
$863$	3.62068	+	6.27121i	0.123249	+	0.213474i	0.921047	−	0.389451i	$-0.127335\pi$
$863$	3.62068	+	6.27121i	0.123249	+	0.213474i	−0.797798	+	0.602925i	$0.794002\pi$
$864$		0			0
$865$	20.7708	+	11.9920i	0.706229	+	0.407742i
$866$		0			0
$867$	−2.61688	+	16.7974i	−0.0888740	+	0.570469i
$868$		0			0
$869$			15.5126i			0.526228i
$870$		0			0
$871$	9.98496	−	17.2945i	0.338328	−	0.586001i
$872$		0			0
$873$	−0.938372	+	3.50205i	−0.0317591	+	0.118526i
$874$		0			0
$875$	−28.3455	+	87.3346i	−0.958251	+	2.95245i
$876$		0			0
$877$	6.41192	−	23.9296i	0.216515	−	0.808045i	−0.769113	−	0.639113i	$-0.779301\pi$
$877$	6.41192	−	23.9296i	0.216515	−	0.808045i	0.985628	−	0.168932i	$-0.0540319\pi$
$878$		0			0
$879$	−1.52498	−	5.69128i	−0.0514361	−	0.191962i
$880$		0			0
$881$	−13.8175	+	13.8175i	−0.465523	+	0.465523i	−0.900461	−	0.434937i	$-0.856771\pi$
$881$	−13.8175	+	13.8175i	−0.465523	+	0.465523i	0.434937	+	0.900461i	$0.356771\pi$
$882$		0			0
$883$	13.2185			0.444839			0.222419	−	0.974951i	$-0.428605\pi$
$883$	13.2185			0.444839			0.222419	+	0.974951i	$0.428605\pi$
$884$		0			0
$885$	15.0502	−	26.0677i	0.505907	−	0.876257i
$886$		0			0
$887$	48.4536	+	12.9831i	1.62691	+	0.435930i	0.953022	−	0.302902i	$-0.0979553\pi$
$887$	48.4536	+	12.9831i	1.62691	+	0.435930i	0.673890	+	0.738831i	$0.264622\pi$
$888$		0			0
$889$	−49.3218	+	25.1508i	−1.65420	+	0.843531i
$890$		0			0
$891$	1.31853	−	4.92080i	0.0441723	−	0.164853i
$892$		0			0
$893$	55.6076	+	32.1051i	1.86084	+	1.07436i
$894$		0			0
$895$	−48.9347	−	48.9347i	−1.63571	−	1.63571i
$896$		0			0
$897$	−8.92842			−0.298111
$898$		0			0
$899$	−7.88948	−	4.55499i	−0.263129	−	0.151917i
$900$		0			0
$901$	2.63947	+	2.37054i	0.0879333	+	0.0789743i
$902$		0			0
$903$	9.83822	+	10.9193i	0.327396	+	0.363373i
$904$		0			0
$905$	−20.7507	−	35.9413i	−0.689777	−	1.19473i
$906$		0			0
$907$	−45.2538	+	12.1257i	−1.50263	+	0.402628i	−0.913979	−	0.405761i	$-0.867006\pi$
$907$	−45.2538	+	12.1257i	−1.50263	+	0.402628i	−0.588649	+	0.808389i	$0.700340\pi$
$908$		0			0
$909$			16.7774i			0.556470i
$910$		0			0
$911$	14.7827	+	14.7827i	0.489772	+	0.489772i	0.908234	−	0.418462i	$-0.137431\pi$
$911$	14.7827	+	14.7827i	0.489772	+	0.489772i	−0.418462	+	0.908234i	$0.637431\pi$
$912$		0			0
$913$	−1.20539	−	4.49856i	−0.0398924	−	0.148881i
$914$		0			0
$915$	−12.4599	−	3.33862i	−0.411912	−	0.110371i
$916$		0			0
$917$	3.26496	+	15.3360i	0.107818	+	0.506439i
$918$		0			0
$919$	26.2526	+	45.4708i	0.865992	+	1.49994i	0.866059	+	0.499942i	$0.166645\pi$
$919$	26.2526	+	45.4708i	0.865992	+	1.49994i	−6.67316e−5		1.00000i	$0.500021\pi$
$920$		0			0
$921$	0.706788	+	2.63777i	0.0232895	+	0.0869175i
$922$		0			0
$923$	17.2466	−	17.2466i	0.567679	−	0.567679i
$924$		0			0
$925$	−45.2045	−	45.2045i	−1.48631	−	1.48631i
$926$		0			0
$927$	11.3708	+	6.56494i	0.373467	+	0.215621i
$928$		0			0
$929$	−4.29232	+	16.0192i	−0.140827	+	0.525572i	0.859079	+	0.511843i	$0.171037\pi$
$929$	−4.29232	+	16.0192i	−0.140827	+	0.525572i	−0.999906	+	0.0137292i	$0.995630\pi$
$930$		0			0
$931$	4.42680	−	42.3822i	0.145082	−	1.38902i
$932$		0			0
$933$	26.4045	−	15.2446i	0.864443	−	0.499086i
$934$		0			0
$935$	87.5462	+	18.4928i	2.86307	+	0.604778i
$936$		0			0
$937$		−	33.5344i		−	1.09552i	−0.836635	−	0.547760i	$-0.815481\pi$
$937$		−	33.5344i		−	1.09552i	0.836635	−	0.547760i	$-0.184519\pi$
$938$		0			0
$939$	7.61731			0.248581
$940$		0			0
$941$	−3.70505	+	0.992766i	−0.120781	+	0.0323633i	−0.318703	−	0.947855i	$-0.603247\pi$
$941$	−3.70505	+	0.992766i	−0.120781	+	0.0323633i	0.197922	+	0.980218i	$0.436581\pi$
$942$		0			0
$943$	−4.85261	+	2.80165i	−0.158023	+	0.0912344i
$944$		0			0
$945$	6.13537	−	9.45434i	0.199584	−	0.307550i
$946$		0			0
$947$	−12.8642	−	3.44694i	−0.418029	−	0.112011i	0.0436723	−	0.999046i	$-0.486094\pi$
$947$	−12.8642	−	3.44694i	−0.418029	−	0.112011i	−0.461702	+	0.887035i	$0.652761\pi$
$948$		0			0
$949$	5.94125	+	22.1730i	0.192861	+	0.719767i
$950$		0			0
$951$	13.4426			0.435907
$952$		0			0
$953$	36.4900			1.18203			0.591014	−	0.806661i	$-0.298728\pi$
$953$	36.4900			1.18203			0.591014	+	0.806661i	$0.298728\pi$
$954$		0			0
$955$	20.4508	+	76.3233i	0.661772	+	2.46977i
$956$		0			0
$957$	5.25393	+	1.40779i	0.169835	+	0.0455073i
$958$		0			0
$959$	−38.2726	−	1.99335i	−1.23589	−	0.0643687i
$960$		0			0
$961$	−36.2010	+	20.9006i	−1.16777	+	0.674214i
$962$		0			0
$963$	7.48905	−	2.00669i	0.241331	−	0.0646645i
$964$		0			0
$965$	102.276			3.29239
$966$		0			0
$967$			8.30768i			0.267157i	0.991038	+	0.133579i	$0.0426468\pi$
$967$			8.30768i			0.267157i	−0.991038	+	0.133579i	$0.957353\pi$
$968$		0			0
$969$	−13.6968	−	21.0329i	−0.440005	−	0.675675i
$970$		0			0
$971$	−49.3188	+	28.4742i	−1.58272	+	0.913781i	−0.588254	+	0.808676i	$0.700184\pi$
$971$	−49.3188	+	28.4742i	−1.58272	+	0.913781i	−0.994461	+	0.105105i	$0.966482\pi$
$972$		0			0
$973$	2.36221	+	0.766682i	0.0757288	+	0.0245787i
$974$		0			0
$975$	8.15000	−	30.4162i	0.261009	−	0.974098i
$976$		0			0
$977$	−50.7231	−	29.2850i	−1.62278	−	0.936910i	−0.986173	−	0.165719i	$-0.947006\pi$
$977$	−50.7231	−	29.2850i	−1.62278	−	0.936910i	−0.636603	−	0.771192i	$-0.719661\pi$
$978$		0			0
$979$	47.6507	+	47.6507i	1.52292	+	1.52292i
$980$		0			0
$981$	−6.17866	+	6.17866i	−0.197270	+	0.197270i
$982$		0			0
$983$	11.7196	+	43.7381i	0.373797	+	1.39503i	0.855095	+	0.518471i	$0.173499\pi$
$983$	11.7196	+	43.7381i	0.373797	+	1.39503i	−0.481299	+	0.876557i	$0.659835\pi$
$984$		0			0
$985$	31.0967	+	53.8610i	0.990822	+	1.71615i
$986$		0			0
$987$	26.5438	+	8.61510i	0.844899	+	0.274222i
$988$		0			0
$989$	−20.0022	−	5.35956i	−0.636032	−	0.170424i
$990$		0			0
$991$	−13.2522	−	49.4579i	−0.420970	−	1.57108i	−0.772569	−	0.634931i	$-0.781029\pi$
$991$	−13.2522	−	49.4579i	−0.420970	−	1.57108i	0.351599	−	0.936151i	$-0.385638\pi$
$992$		0			0
$993$	4.45557	+	4.45557i	0.141393	+	0.141393i
$994$		0			0
$995$		−	73.2199i		−	2.32123i
$996$		0			0
$997$	6.93843	−	1.85915i	0.219742	−	0.0588798i	−0.147268	−	0.989097i	$-0.547048\pi$
$997$	6.93843	−	1.85915i	0.219742	−	0.0588798i	0.367010	+	0.930217i	$0.380381\pi$
$998$		0			0
$999$	2.43135	+	4.21122i	0.0769245	+	0.133237i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1428.2.cc.c.361.18	✓	72
7.2	even	3	inner	1428.2.cc.c.1381.8	yes	72
17.13	even	4	inner	1428.2.cc.c.1033.8	yes	72
119.30	even	12	inner	1428.2.cc.c.625.18	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1428.2.cc.c.361.18	✓	72	1.1	even	1	trivial
1428.2.cc.c.625.18	yes	72	119.30	even	12	inner
1428.2.cc.c.1033.8	yes	72	17.13	even	4	inner
1428.2.cc.c.1381.8	yes	72	7.2	even	3	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:	\( N \)	\(=\)	\( 1428 = 2^{2} \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1428.cc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{3} +(4.11475 + 1.10254i) q^{5} +(1.20191 + 2.35699i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(4.92080 - 1.31853i) q^{11} -2.39520 q^{13} +4.25990i q^{15} +(4.03409 + 0.852138i) q^{17} +(-5.27196 + 3.04377i) q^{19} +(-1.96560 + 1.77099i) q^{21} +(0.964781 - 3.60061i) q^{23} +(11.3854 + 6.57339i) q^{25} +(-0.707107 - 0.707107i) q^{27} +(0.754976 - 0.754976i) q^{29} +(-2.20834 - 8.24163i) q^{31} +(2.54720 + 4.41187i) q^{33} +(2.34687 + 11.0236i) q^{35} +(-4.69701 - 1.25856i) q^{37} +(-0.619924 - 2.31359i) q^{39} +(-1.06291 - 1.06291i) q^{41} -5.55521i q^{43} +(-4.11475 + 1.10254i) q^{45} +(-5.27390 - 9.13467i) q^{47} +(-4.11083 + 5.66578i) q^{49} +(0.220997 + 4.11718i) q^{51} +(0.745169 + 0.430223i) q^{53} +21.7016 q^{55} +(-4.30454 - 4.30454i) q^{57} +(-6.11933 - 3.53300i) q^{59} +(-0.783732 + 2.92493i) q^{61} +(-2.21938 - 1.44026i) q^{63} +(-9.85566 - 2.64082i) q^{65} +(-4.16873 + 7.22046i) q^{67} +3.72763 q^{69} +(-7.20048 + 7.20048i) q^{71} +(-2.48048 - 9.25727i) q^{73} +(-3.40263 + 12.6988i) q^{75} +(9.02212 + 10.0136i) q^{77} +(-0.788112 + 2.94128i) q^{79} +(0.500000 - 0.866025i) q^{81} -0.914192i q^{83} +(15.6597 + 7.95409i) q^{85} +(0.924653 + 0.533848i) q^{87} +(6.61396 + 11.4557i) q^{89} +(-2.87882 - 5.64547i) q^{91} +(7.38925 - 4.26618i) q^{93} +(-25.0487 + 6.71177i) q^{95} +(2.56368 - 2.56368i) q^{97} +(-3.60228 + 3.60228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 12 q^{5} - 20 q^{7} + 8 q^{11} + 24 q^{13} - 16 q^{17} + 20 q^{21} - 28 q^{23} + 48 q^{29} - 28 q^{31} + 24 q^{33} + 68 q^{35} + 20 q^{37} + 32 q^{41} - 12 q^{45} + 44 q^{47} - 4 q^{51} + 48 q^{55}+ \cdots - 16 q^{99}+O(q^{100}) \) 72 * q + 12 * q^5 - 20 * q^7 + 8 * q^11 + 24 * q^13 - 16 * q^17 + 20 * q^21 - 28 * q^23 + 48 * q^29 - 28 * q^31 + 24 * q^33 + 68 * q^35 + 20 * q^37 + 32 * q^41 - 12 * q^45 + 44 * q^47 - 4 * q^51 + 48 * q^55 - 16 * q^61 + 16 * q^63 - 16 * q^65 - 16 * q^67 - 48 * q^69 + 8 * q^71 + 40 * q^73 + 24 * q^75 + 20 * q^79 + 36 * q^81 + 8 * q^85 - 16 * q^89 - 20 * q^91 - 68 * q^95 + 120 * q^97 - 16 * q^99

Introduction

L-functions

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Varieties

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Representations

Groups

Database

Properties

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