LMFDB - Embedded newform 1680.2.di.d.529.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1680,2,Mod(289,1680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1680.289"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1680, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.di (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,2,0,0,0,8,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.27814731656356152999936.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} - 4 x^{13} - 14 x^{12} + 38 x^{11} - 40 x^{10} + 64 x^{9} + 291 x^{8} + \cdots + 1 $ x^16 - 2x^15 + 2x^14 - 4x^13 - 14x^12 + 38x^11 - 40x^10 + 64x^9 + 291x^8 - 630x^7 + 584x^6 - 800x^5 + 734x^4 - 188x^3 + 32x^2 - 8*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.1
Root			$0.526774 - 1.96595i$ of defining polynomial
Character	$\chi$	$=$	1680.529
Dual form			1680.2.di.d.289.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{3} +(-1.98074 + 1.03763i) q^{5} +(-0.478401 - 2.60214i) q^{7} +(0.500000 + 0.866025i) q^{9} +(2.21538 - 3.83715i) q^{11} -1.73246i q^{13} +(2.23418 + 0.0917505i) q^{15} +(2.36638 + 1.36623i) q^{17} +(0.152578 + 0.264273i) q^{19} +(-0.886763 + 2.49272i) q^{21} +(-6.08316 + 3.51212i) q^{23} +(2.84663 - 4.11056i) q^{25} -1.00000i q^{27} +7.79430 q^{29} +(-2.64243 + 4.57683i) q^{31} +(-3.83715 + 2.21538i) q^{33} +(3.64765 + 4.65775i) q^{35} +(-3.18183 + 1.83703i) q^{37} +(-0.866230 + 1.50035i) q^{39} -6.71562 q^{41} -9.71562i q^{43} +(-1.88899 - 1.19655i) q^{45} +(-1.57313 + 0.908250i) q^{47} +(-6.54227 + 2.48973i) q^{49} +(-1.36623 - 2.36638i) q^{51} +(-1.48535 - 0.857566i) q^{53} +(-0.406524 + 9.89912i) q^{55} -0.305156i q^{57} +(0.571217 - 0.989377i) q^{59} +(-4.77818 - 8.27604i) q^{61} +(2.01432 - 1.71538i) q^{63} +(1.79766 + 3.43154i) q^{65} +(-7.26104 - 4.19216i) q^{67} +7.02423 q^{69} -10.2888 q^{71} +(-11.1028 - 6.41022i) q^{73} +(-4.52053 + 2.13653i) q^{75} +(-11.0446 - 3.92903i) q^{77} +(-3.35686 - 5.81425i) q^{79} +(-0.500000 + 0.866025i) q^{81} +5.09946i q^{83} +(-6.10482 - 0.250704i) q^{85} +(-6.75007 - 3.89715i) q^{87} +(2.03533 + 3.52529i) q^{89} +(-4.50810 + 0.828810i) q^{91} +(4.57683 - 2.64243i) q^{93} +(-0.576436 - 0.365135i) q^{95} -2.87834i q^{97} +4.43075 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{5} + 8 q^{9} + 4 q^{15} + 24 q^{19} - 4 q^{21} - 4 q^{25} + 24 q^{29} - 16 q^{31} + 10 q^{35} + 4 q^{39} + 16 q^{41} - 2 q^{45} - 40 q^{49} - 4 q^{51} - 8 q^{55} - 4 q^{59} + 16 q^{61} + 30 q^{65}+ \cdots + 22 q^{95}+O(q^{100}) $ 16 * q + 2 * q^5 + 8 * q^9 + 4 * q^15 + 24 * q^19 - 4 * q^21 - 4 * q^25 + 24 * q^29 - 16 * q^31 + 10 * q^35 + 4 * q^39 + 16 * q^41 - 2 * q^45 - 40 * q^49 - 4 * q^51 - 8 * q^55 - 4 * q^59 + 16 * q^61 + 30 * q^65 + 40 * q^69 + 56 * q^71 - 8 * q^75 + 16 * q^79 - 8 * q^81 - 64 * q^85 + 16 * q^89 - 8 * q^91 + 22 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$1$	$1$

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
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$		0			0
$5$	−1.98074	+	1.03763i	−0.885812	+	0.464044i
$5$	−1.98074	+	1.03763i	−0.885812	+	0.464044i
$6$		0			0
$7$	−0.478401	−	2.60214i	−0.180818	−	0.983516i
$7$	−0.478401	−	2.60214i	−0.180818	−	0.983516i
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	2.21538	−	3.83715i	0.667961	−	1.15694i	−0.310512	−	0.950569i	$-0.600500\pi$
$11$	2.21538	−	3.83715i	0.667961	−	1.15694i	0.978473	−	0.206373i	$-0.0661662\pi$
$12$		0			0
$13$		−	1.73246i		−	0.480498i	−0.970711	−	0.240249i	$-0.922771\pi$
$13$		−	1.73246i		−	0.480498i	0.970711	−	0.240249i	$-0.0772291\pi$
$14$		0			0
$15$	2.23418	+	0.0917505i	0.576864	+	0.0236899i
$16$		0			0
$17$	2.36638	+	1.36623i	0.573931	+	0.331359i	0.758718	−	0.651419i	$-0.225826\pi$
$17$	2.36638	+	1.36623i	0.573931	+	0.331359i	−0.184787	+	0.982779i	$0.559159\pi$
$18$		0			0
$19$	0.152578	+	0.264273i	0.0350038	+	0.0606284i	0.882997	−	0.469379i	$-0.155522\pi$
$19$	0.152578	+	0.264273i	0.0350038	+	0.0606284i	−0.847993	+	0.530008i	$0.822189\pi$
$20$		0			0
$21$	−0.886763	+	2.49272i	−0.193508	+	0.543956i
$22$		0			0
$23$	−6.08316	+	3.51212i	−1.26843	+	0.732327i	−0.974690	−	0.223560i	$-0.928232\pi$
$23$	−6.08316	+	3.51212i	−1.26843	+	0.732327i	−0.293737	+	0.955886i	$0.594899\pi$
$24$		0			0
$25$	2.84663	−	4.11056i	0.569326	−	0.822112i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	7.79430			1.44737			0.723683	−	0.690132i	$-0.242448\pi$
$29$	7.79430			1.44737			0.723683	+	0.690132i	$0.242448\pi$
$30$		0			0
$31$	−2.64243	+	4.57683i	−0.474595	+	0.822023i	−0.999577	−	0.0290906i	$-0.990739\pi$
$31$	−2.64243	+	4.57683i	−0.474595	+	0.822023i	0.524982	+	0.851114i	$0.324072\pi$
$32$		0			0
$33$	−3.83715	+	2.21538i	−0.667961	+	0.385648i
$34$		0			0
$35$	3.64765	+	4.65775i	0.616566	+	0.787303i
$36$		0			0
$37$	−3.18183	+	1.83703i	−0.523090	+	0.302006i	−0.738198	−	0.674584i	$-0.764323\pi$
$37$	−3.18183	+	1.83703i	−0.523090	+	0.302006i	0.215108	+	0.976590i	$0.430990\pi$
$38$		0			0
$39$	−0.866230	+	1.50035i	−0.138708	+	0.240249i
$40$		0			0
$41$	−6.71562			−1.04880			−0.524402	−	0.851471i	$-0.675711\pi$
$41$	−6.71562			−1.04880			−0.524402	+	0.851471i	$0.675711\pi$
$42$		0			0
$43$		−	9.71562i		−	1.48162i	−0.671715	−	0.740809i	$-0.734442\pi$
$43$		−	9.71562i		−	1.48162i	0.671715	−	0.740809i	$-0.265558\pi$
$44$		0			0
$45$	−1.88899	−	1.19655i	−0.281593	−	0.178371i
$46$		0			0
$47$	−1.57313	+	0.908250i	−0.229465	+	0.132482i	−0.610325	−	0.792151i	$-0.708961\pi$
$47$	−1.57313	+	0.908250i	−0.229465	+	0.132482i	0.380860	+	0.924633i	$0.375628\pi$
$48$		0			0
$49$	−6.54227	+	2.48973i	−0.934609	+	0.355676i
$50$		0			0
$51$	−1.36623	−	2.36638i	−0.191310	−	0.331359i
$52$		0			0
$53$	−1.48535	−	0.857566i	−0.204028	−	0.117796i	0.394505	−	0.918894i	$-0.370916\pi$
$53$	−1.48535	−	0.857566i	−0.204028	−	0.117796i	−0.598533	+	0.801098i	$0.704249\pi$
$54$		0			0
$55$	−0.406524	+	9.89912i	−0.0548157	+	1.33480i
$56$		0			0
$57$		−	0.305156i		−	0.0404189i
$58$		0			0
$59$	0.571217	−	0.989377i	0.0743661	−	0.128806i	−0.826444	−	0.563018i	$-0.809640\pi$
$59$	0.571217	−	0.989377i	0.0743661	−	0.128806i	0.900810	+	0.434213i	$0.142973\pi$
$60$		0			0
$61$	−4.77818	−	8.27604i	−0.611783	−	1.05964i	−0.990940	−	0.134307i	$-0.957119\pi$
$61$	−4.77818	−	8.27604i	−0.611783	−	1.05964i	0.379157	−	0.925332i	$-0.376214\pi$
$62$		0			0
$63$	2.01432	−	1.71538i	0.253780	−	0.216117i
$64$		0			0
$65$	1.79766	+	3.43154i	0.222972	+	0.425631i
$66$		0			0
$67$	−7.26104	−	4.19216i	−0.887078	−	0.512154i	−0.0140921	−	0.999901i	$-0.504486\pi$
$67$	−7.26104	−	4.19216i	−0.887078	−	0.512154i	−0.872985	+	0.487746i	$0.837819\pi$
$68$		0			0
$69$	7.02423			0.845618
$70$		0			0
$71$	−10.2888			−1.22106			−0.610529	−	0.791994i	$-0.709043\pi$
$71$	−10.2888			−1.22106			−0.610529	+	0.791994i	$0.709043\pi$
$72$		0			0
$73$	−11.1028	−	6.41022i	−1.29949	−	0.750260i	−0.319172	−	0.947697i	$-0.603405\pi$
$73$	−11.1028	−	6.41022i	−1.29949	−	0.750260i	−0.980316	+	0.197437i	$0.936738\pi$
$74$		0			0
$75$	−4.52053	+	2.13653i	−0.521986	+	0.246706i
$76$		0			0
$77$	−11.0446	−	3.92903i	−1.25865	−	0.447754i
$78$		0			0
$79$	−3.35686	−	5.81425i	−0.377676	−	0.654154i	0.613048	−	0.790046i	$-0.289943\pi$
$79$	−3.35686	−	5.81425i	−0.377676	−	0.654154i	−0.990724	+	0.135892i	$0.956610\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			5.09946i			0.559739i	0.960038	+	0.279869i	$0.0902911\pi$
$83$			5.09946i			0.559739i	−0.960038	+	0.279869i	$0.909709\pi$
$84$		0			0
$85$	−6.10482	−	0.250704i	−0.662161	−	0.0271927i
$86$		0			0
$87$	−6.75007	−	3.89715i	−0.723683	−	0.417819i
$88$		0			0
$89$	2.03533	+	3.52529i	0.215744	+	0.373680i	0.953503	−	0.301385i	$-0.0974489\pi$
$89$	2.03533	+	3.52529i	0.215744	+	0.373680i	−0.737758	+	0.675065i	$0.764116\pi$
$90$		0			0
$91$	−4.50810	+	0.828810i	−0.472577	+	0.0868829i
$92$		0			0
$93$	4.57683	−	2.64243i	0.474595	−	0.274008i
$94$		0			0
$95$	−0.576436	−	0.365135i	−0.0591411	−	0.0374620i
$96$		0			0
$97$		−	2.87834i		−	0.292252i	−0.989266	−	0.146126i	$-0.953320\pi$
$97$		−	2.87834i		−	0.292252i	0.989266	−	0.146126i	$-0.0466804\pi$
$98$		0			0
$99$	4.43075			0.445308
$100$		0			0
$101$	−3.60883	+	6.25068i	−0.359092	+	0.621966i	−0.987809	−	0.155668i	$-0.950247\pi$
$101$	−3.60883	+	6.25068i	−0.359092	+	0.621966i	0.628717	+	0.777634i	$0.283580\pi$
$102$		0			0
$103$	−9.76304	+	5.63670i	−0.961981	+	0.555400i	−0.896782	−	0.442472i	$-0.854102\pi$
$103$	−9.76304	+	5.63670i	−0.961981	+	0.555400i	−0.0651989	+	0.997872i	$0.520768\pi$
$104$		0			0
$105$	−0.830088	−	5.85756i	−0.0810083	−	0.571639i
$106$		0			0
$107$	5.98940	−	3.45798i	0.579017	−	0.334296i	−0.181726	−	0.983349i	$-0.558168\pi$
$107$	5.98940	−	3.45798i	0.579017	−	0.334296i	0.760743	+	0.649054i	$0.224835\pi$
$108$		0			0
$109$	2.21097	−	3.82952i	0.211773	−	0.366801i	−0.740497	−	0.672060i	$-0.765410\pi$
$109$	2.21097	−	3.82952i	0.211773	−	0.366801i	0.952269	+	0.305259i	$0.0987430\pi$
$110$		0			0
$111$	3.67406			0.348727
$112$		0			0
$113$		−	2.86151i		−	0.269188i	−0.990901	−	0.134594i	$-0.957027\pi$
$113$		−	2.86151i		−	0.269188i	0.990901	−	0.134594i	$-0.0429730\pi$
$114$		0			0
$115$	8.40485	−	13.2687i	0.783756	−	1.23731i
$116$		0			0
$117$	1.50035	−	0.866230i	0.138708	−	0.0800830i
$118$		0			0
$119$	2.42304	−	6.81125i	0.222120	−	0.624387i
$120$		0			0
$121$	−4.31579	−	7.47517i	−0.392345	−	0.679561i
$122$		0			0
$123$	5.81590	+	3.35781i	0.524402	+	0.302764i
$124$		0			0
$125$	−1.37317	+	11.0957i	−0.122820	+	0.992429i
$126$		0			0
$127$			13.7325i			1.21856i	0.792956	+	0.609279i	$0.208541\pi$
$127$			13.7325i			1.21856i	−0.792956	+	0.609279i	$0.791459\pi$
$128$		0			0
$129$	−4.85781	+	8.41398i	−0.427706	+	0.740809i
$130$		0			0
$131$	10.9909	+	19.0368i	0.960277	+	1.66325i	0.721801	+	0.692100i	$0.243314\pi$
$131$	10.9909	+	19.0368i	0.960277	+	1.66325i	0.238476	+	0.971148i	$0.423352\pi$
$132$		0			0
$133$	0.614682	−	0.523458i	0.0532997	−	0.0453896i
$134$		0			0
$135$	1.03763	+	1.98074i	0.0893053	+	0.170475i
$136$		0			0
$137$	2.59973	+	1.50095i	0.222110	+	0.128235i	0.606927	−	0.794758i	$-0.292402\pi$
$137$	2.59973	+	1.50095i	0.222110	+	0.128235i	−0.384817	+	0.922993i	$0.625735\pi$
$138$		0			0
$139$	−21.7364			−1.84366			−0.921829	−	0.387597i	$-0.873305\pi$
$139$	−21.7364			−1.84366			−0.921829	+	0.387597i	$0.873305\pi$
$140$		0			0
$141$	1.81650			0.152977
$142$		0			0
$143$	−6.64770	−	3.83805i	−0.555908	−	0.320954i
$144$		0			0
$145$	−15.4385	+	8.08764i	−1.28209	+	0.671642i
$146$		0			0
$147$	6.91063	+	1.11496i	0.569979	+	0.0919606i
$148$		0			0
$149$	−2.60654	−	4.51467i	−0.213536	−	0.369856i	0.739282	−	0.673396i	$-0.235165\pi$
$149$	−2.60654	−	4.51467i	−0.213536	−	0.369856i	−0.952819	+	0.303540i	$0.901832\pi$
$150$		0			0
$151$	−4.85686	+	8.41233i	−0.395246	+	0.684585i	−0.993132	−	0.116995i	$-0.962674\pi$
$151$	−4.85686	+	8.41233i	−0.395246	+	0.684585i	0.597887	+	0.801580i	$0.296007\pi$
$152$		0			0
$153$			2.73246i			0.220906i
$154$		0			0
$155$	0.484889	−	11.8074i	0.0389472	−	0.948391i
$156$		0			0
$157$	8.20284	+	4.73591i	0.654658	+	0.377967i	0.790238	−	0.612800i	$-0.209957\pi$
$157$	8.20284	+	4.73591i	0.654658	+	0.377967i	−0.135581	+	0.990766i	$0.543290\pi$
$158$		0			0
$159$	0.857566	+	1.48535i	0.0680094	+	0.117796i
$160$		0			0
$161$	12.0492	+	14.1490i	0.949610	+	1.11510i
$162$		0			0
$163$	4.67358	−	2.69830i	0.366063	−	0.211347i	−0.305674	−	0.952136i	$-0.598882\pi$
$163$	4.67358	−	2.69830i	0.366063	−	0.211347i	0.671737	+	0.740789i	$0.265548\pi$
$164$		0			0
$165$	5.30162	−	8.36963i	0.412731	−	0.651575i
$166$		0			0
$167$			0.312550i			0.0241859i	0.999927	+	0.0120929i	$0.00384939\pi$
$167$			0.312550i			0.0241859i	−0.999927	+	0.0120929i	$0.996151\pi$
$168$		0			0
$169$	9.99859			0.769122
$170$		0			0
$171$	−0.152578	+	0.264273i	−0.0116679	+	0.0202095i
$172$		0			0
$173$	−8.32661	+	4.80737i	−0.633061	+	0.365498i	−0.781937	−	0.623358i	$-0.785768\pi$
$173$	−8.32661	+	4.80737i	−0.633061	+	0.365498i	0.148876	+	0.988856i	$0.452435\pi$
$174$		0			0
$175$	−12.0581	−	5.44084i	−0.911505	−	0.411289i
$176$		0			0
$177$	−0.989377	+	0.571217i	−0.0743661	+	0.0429353i
$178$		0			0
$179$	4.42730	−	7.66831i	0.330912	−	0.573157i	−0.651779	−	0.758409i	$-0.725977\pi$
$179$	4.42730	−	7.66831i	0.330912	−	0.573157i	0.982691	+	0.185252i	$0.0593103\pi$
$180$		0			0
$181$	−16.9234			−1.25790			−0.628952	−	0.777445i	$-0.716516\pi$
$181$	−16.9234			−1.25790			−0.628952	+	0.777445i	$0.716516\pi$
$182$		0			0
$183$			9.55635i			0.706426i
$184$		0			0
$185$	4.39620	−	6.94026i	0.323215	−	0.510258i
$186$		0			0
$187$	10.4848	−	6.05343i	0.766728	−	0.442670i
$188$		0			0
$189$	−2.60214	+	0.478401i	−0.189278	+	0.0347985i
$190$		0			0
$191$	0.159271	+	0.275865i	0.0115244	+	0.0199609i	0.871730	−	0.489986i	$-0.162998\pi$
$191$	0.159271	+	0.275865i	0.0115244	+	0.0199609i	−0.860206	+	0.509947i	$0.829665\pi$
$192$		0			0
$193$	1.81289	+	1.04667i	0.130494	+	0.0753410i	0.563826	−	0.825894i	$-0.309329\pi$
$193$	1.81289	+	1.04667i	0.130494	+	0.0753410i	−0.433332	+	0.901234i	$0.642662\pi$
$194$		0			0
$195$	0.158954	−	3.87063i	0.0113829	−	0.277182i
$196$		0			0
$197$		−	22.5798i		−	1.60874i	−0.594126	−	0.804372i	$-0.702502\pi$
$197$		−	22.5798i		−	1.60874i	0.594126	−	0.804372i	$-0.297498\pi$
$198$		0			0
$199$	3.75204	−	6.49872i	0.265975	−	0.460682i	−0.701844	−	0.712331i	$-0.747639\pi$
$199$	3.75204	−	6.49872i	0.265975	−	0.460682i	0.967819	+	0.251649i	$0.0809728\pi$
$200$		0			0
$201$	4.19216	+	7.26104i	0.295693	+	0.512154i
$202$		0			0
$203$	−3.72880	−	20.2819i	−0.261710	−	1.42351i
$204$		0			0
$205$	13.3019	−	6.96836i	0.929043	−	0.486691i
$206$		0			0
$207$	−6.08316	−	3.51212i	−0.422809	−	0.244109i
$208$		0			0
$209$	1.35207			0.0935248
$210$		0			0
$211$	−7.67216			−0.528173			−0.264087	−	0.964499i	$-0.585070\pi$
$211$	−7.67216			−0.528173			−0.264087	+	0.964499i	$0.585070\pi$
$212$		0			0
$213$	8.91037	+	5.14441i	0.610529	+	0.352489i
$214$		0			0
$215$	10.0813	+	19.2441i	0.687536	+	1.31244i
$216$		0			0
$217$	13.1737	+	4.68643i	0.894289	+	0.318135i
$218$		0			0
$219$	6.41022	+	11.1028i	0.433163	+	0.750260i
$220$		0			0
$221$	2.36694	−	4.09966i	0.159217	−	0.275773i
$222$		0			0
$223$			6.90208i			0.462198i	0.972930	+	0.231099i	$0.0742321\pi$
$223$			6.90208i			0.462198i	−0.972930	+	0.231099i	$0.925768\pi$
$224$		0			0
$225$	4.98316	+	0.409975i	0.332211	+	0.0273317i
$226$		0			0
$227$	5.49684	+	3.17360i	0.364838	+	0.210639i	0.671201	−	0.741275i	$-0.265779\pi$
$227$	5.49684	+	3.17360i	0.364838	+	0.210639i	−0.306363	+	0.951915i	$0.599112\pi$
$228$		0			0
$229$	3.37834	+	5.85146i	0.223247	+	0.386676i	0.955792	−	0.294043i	$-0.0950009\pi$
$229$	3.37834	+	5.85146i	0.223247	+	0.386676i	−0.732545	+	0.680719i	$0.761668\pi$
$230$		0			0
$231$	7.60041	+	8.92495i	0.500071	+	0.587219i
$232$		0			0
$233$	−6.41899	+	3.70601i	−0.420522	+	0.242789i	−0.695301	−	0.718719i	$-0.744729\pi$
$233$	−6.41899	+	3.70601i	−0.420522	+	0.242789i	0.274779	+	0.961508i	$0.411395\pi$
$234$		0			0
$235$	2.17353	−	3.43134i	0.141786	−	0.223836i
$236$		0			0
$237$			6.71372i			0.436103i
$238$		0			0
$239$	7.36355			0.476309			0.238154	−	0.971227i	$-0.423458\pi$
$239$	7.36355			0.476309			0.238154	+	0.971227i	$0.423458\pi$
$240$		0			0
$241$	−6.84002	+	11.8473i	−0.440605	+	0.763149i	−0.997734	−	0.0672759i	$-0.978569\pi$
$241$	−6.84002	+	11.8473i	−0.440605	+	0.763149i	0.557130	+	0.830425i	$0.311903\pi$
$242$		0			0
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$		0			0
$245$	10.3751	−	11.7200i	0.662839	−	0.748762i
$246$		0			0
$247$	0.457842	−	0.264335i	0.0291318	−	0.0168193i
$248$		0			0
$249$	2.54973	−	4.41626i	0.161583	−	0.279869i
$250$		0			0
$251$	−23.4843			−1.48231			−0.741157	−	0.671331i	$-0.765723\pi$
$251$	−23.4843			−1.48231			−0.741157	+	0.671331i	$0.765723\pi$
$252$		0			0
$253$			31.1226i			1.95666i
$254$		0			0
$255$	5.16158	+	3.26953i	0.323230	+	0.204746i
$256$		0			0
$257$	12.6417	−	7.29871i	0.788570	−	0.455281i	−0.0508890	−	0.998704i	$-0.516205\pi$
$257$	12.6417	−	7.29871i	0.788570	−	0.455281i	0.839459	+	0.543423i	$0.182872\pi$
$258$		0			0
$259$	6.30241	+	7.40074i	0.391612	+	0.459860i
$260$		0			0
$261$	3.89715	+	6.75007i	0.241228	+	0.417819i
$262$		0			0
$263$	4.40755	+	2.54470i	0.271781	+	0.156913i	0.629697	−	0.776841i	$-0.283179\pi$
$263$	4.40755	+	2.54470i	0.271781	+	0.156913i	−0.357916	+	0.933754i	$0.616512\pi$
$264$		0			0
$265$	3.83192	+	0.157364i	0.235393	+	0.00966680i
$266$		0			0
$267$		−	4.07065i		−	0.249120i
$268$		0			0
$269$	15.2550	−	26.4224i	0.930112	−	1.61100i	0.146984	−	0.989139i	$-0.453043\pi$
$269$	15.2550	−	26.4224i	0.930112	−	1.61100i	0.783127	−	0.621862i	$-0.213623\pi$
$270$		0			0
$271$	−9.74401	−	16.8771i	−0.591907	−	1.02521i	−0.993975	−	0.109603i	$-0.965042\pi$
$271$	−9.74401	−	16.8771i	−0.591907	−	1.02521i	0.402069	−	0.915609i	$-0.368291\pi$
$272$		0			0
$273$	4.31854	+	1.53628i	0.261370	+	0.0929799i
$274$		0			0
$275$	−9.46645	−	20.0294i	−0.570849	−	1.20782i
$276$		0			0
$277$	−22.0665	−	12.7401i	−1.32585	−	0.765478i	−0.341193	−	0.939993i	$-0.610831\pi$
$277$	−22.0665	−	12.7401i	−1.32585	−	0.765478i	−0.984655	+	0.174515i	$0.944164\pi$
$278$		0			0
$279$	−5.28487			−0.316397
$280$		0			0
$281$	−22.1914			−1.32383			−0.661914	−	0.749580i	$-0.730255\pi$
$281$	−22.1914			−1.32383			−0.661914	+	0.749580i	$0.730255\pi$
$282$		0			0
$283$	15.6960	+	9.06209i	0.933031	+	0.538685i	0.887769	−	0.460290i	$-0.152254\pi$
$283$	15.6960	+	9.06209i	0.933031	+	0.538685i	0.0452618	+	0.998975i	$0.485588\pi$
$284$		0			0
$285$	0.316641	+	0.604434i	0.0187562	+	0.0358036i
$286$		0			0
$287$	3.21276	+	17.4750i	0.189643	+	1.03152i
$288$		0			0
$289$	−4.76683	−	8.25640i	−0.280402	−	0.485670i
$290$		0			0
$291$	−1.43917	+	2.49272i	−0.0843658	+	0.146126i
$292$		0			0
$293$			13.8958i			0.811801i	0.913917	+	0.405901i	$0.133042\pi$
$293$			13.8958i			0.811801i	−0.913917	+	0.405901i	$0.866958\pi$
$294$		0			0
$295$	−0.104819	+	2.55241i	−0.00610279	+	0.148607i
$296$		0			0
$297$	−3.83715	−	2.21538i	−0.222654	−	0.128549i
$298$		0			0
$299$	6.08460	+	10.5388i	0.351881	+	0.609476i
$300$		0			0
$301$	−25.2814	+	4.64796i	−1.45720	+	0.267904i
$302$		0			0
$303$	6.25068	−	3.60883i	0.359092	−	0.207322i
$304$		0			0
$305$	18.0518	+	11.4347i	1.03364	+	0.654747i
$306$		0			0
$307$		−	29.8332i		−	1.70267i	−0.524622	−	0.851335i	$-0.675793\pi$
$307$		−	29.8332i		−	1.70267i	0.524622	−	0.851335i	$-0.324207\pi$
$308$		0			0
$309$	11.2734			0.641321
$310$		0			0
$311$	6.75662	−	11.7028i	0.383133	−	0.663606i	−0.608375	−	0.793650i	$-0.708178\pi$
$311$	6.75662	−	11.7028i	0.383133	−	0.663606i	0.991508	+	0.130044i	$0.0415117\pi$
$312$		0			0
$313$	25.1023	−	14.4928i	1.41887	−	0.819184i	0.422669	−	0.906284i	$-0.361093\pi$
$313$	25.1023	−	14.4928i	1.41887	−	0.819184i	0.996200	+	0.0871001i	$0.0277600\pi$
$314$		0			0
$315$	−2.20990	+	5.48784i	−0.124514	+	0.309205i
$316$		0			0
$317$	1.00341	−	0.579319i	0.0563571	−	0.0325378i	−0.471557	−	0.881836i	$-0.656308\pi$
$317$	1.00341	−	0.579319i	0.0563571	−	0.0325378i	0.527914	+	0.849298i	$0.322974\pi$
$318$		0			0
$319$	17.2673	−	29.9079i	0.966785	−	1.67452i
$320$		0			0
$321$	−6.91596			−0.386011
$322$		0			0
$323$			0.833827i			0.0463954i
$324$		0			0
$325$	−7.12138	−	4.93167i	−0.395023	−	0.273560i
$326$		0			0
$327$	−3.82952	+	2.21097i	−0.211773	+	0.122267i
$328$		0			0
$329$	3.11598	+	3.65901i	0.171790	+	0.201728i
$330$		0			0
$331$	−14.1746	−	24.5511i	−0.779104	−	1.34945i	−0.932459	−	0.361277i	$-0.882341\pi$
$331$	−14.1746	−	24.5511i	−0.779104	−	1.34945i	0.153355	−	0.988171i	$-0.450992\pi$
$332$		0			0
$333$	−3.18183	−	1.83703i	−0.174363	−	0.100669i
$334$		0			0
$335$	18.7321	+	0.769266i	1.02345	+	0.0420295i
$336$		0			0
$337$			15.9729i			0.870101i	0.900406	+	0.435051i	$0.143270\pi$
$337$			15.9729i			0.870101i	−0.900406	+	0.435051i	$0.856730\pi$
$338$		0			0
$339$	−1.43075	+	2.47814i	−0.0777079	+	0.134594i
$340$		0			0
$341$	11.7080	+	20.2788i	0.634023	+	1.09816i
$342$		0			0
$343$	9.60845	+	15.8328i	0.518808	+	0.854891i
$344$		0			0
$345$	−13.9131	+	7.28858i	−0.749059	+	0.392404i
$346$		0			0
$347$	11.2687	+	6.50599i	0.604935	+	0.349260i	0.770981	−	0.636859i	$-0.219766\pi$
$347$	11.2687	+	6.50599i	0.604935	+	0.349260i	−0.166045	+	0.986118i	$0.553100\pi$
$348$		0			0
$349$	−32.0724			−1.71680			−0.858398	−	0.512984i	$-0.828540\pi$
$349$	−32.0724			−1.71680			−0.858398	+	0.512984i	$0.828540\pi$
$350$		0			0
$351$	−1.73246			−0.0924718
$352$		0			0
$353$	11.5778	+	6.68445i	0.616225	+	0.355778i	0.775398	−	0.631473i	$-0.217549\pi$
$353$	11.5778	+	6.68445i	0.616225	+	0.355778i	−0.159173	+	0.987251i	$0.550883\pi$
$354$		0			0
$355$	20.3794	−	10.6760i	1.08163	−	0.566624i
$356$		0			0
$357$	−5.50404	+	4.68720i	−0.291305	+	0.248073i
$358$		0			0
$359$	6.55974	+	11.3618i	0.346210	+	0.599653i	0.985573	−	0.169252i	$-0.0541352\pi$
$359$	6.55974	+	11.3618i	0.346210	+	0.599653i	−0.639363	+	0.768905i	$0.720802\pi$
$360$		0			0
$361$	9.45344	−	16.3738i	0.497549	−	0.861781i
$362$		0			0
$363$			8.63158i			0.453041i
$364$		0			0
$365$	28.6432	+	1.17628i	1.49926	+	0.0615694i
$366$		0			0
$367$	11.3761	+	6.56798i	0.593826	+	0.342846i	0.766609	−	0.642114i	$-0.221943\pi$
$367$	11.3761	+	6.56798i	0.593826	+	0.342846i	−0.172783	+	0.984960i	$0.555276\pi$
$368$		0			0
$369$	−3.35781	−	5.81590i	−0.174801	−	0.302764i
$370$		0			0
$371$	−1.52091	+	4.27534i	−0.0789620	+	0.221965i
$372$		0			0
$373$	25.6514	−	14.8099i	1.32818	−	0.766826i	0.343163	−	0.939276i	$-0.388502\pi$
$373$	25.6514	−	14.8099i	1.32818	−	0.766826i	0.985018	+	0.172450i	$0.0551682\pi$
$374$		0			0
$375$	6.73704	−	8.92257i	0.347900	−	0.460759i
$376$		0			0
$377$		−	13.5033i		−	0.695456i
$378$		0			0
$379$	7.47689			0.384062			0.192031	−	0.981389i	$-0.438493\pi$
$379$	7.47689			0.384062			0.192031	+	0.981389i	$0.438493\pi$
$380$		0			0
$381$	6.86623	−	11.8927i	0.351768	−	0.609279i
$382$		0			0
$383$	−20.5586	+	11.8695i	−1.05050	+	0.606505i	−0.922789	−	0.385307i	$-0.874096\pi$
$383$	−20.5586	+	11.8695i	−1.05050	+	0.606505i	−0.127709	+	0.991812i	$0.540762\pi$
$384$		0			0
$385$	25.9534	−	3.67791i	1.32271	−	0.187444i
$386$		0			0
$387$	8.41398	−	4.85781i	0.427706	−	0.246936i
$388$		0			0
$389$	−7.06523	+	12.2373i	−0.358221	+	0.620458i	−0.987664	−	0.156589i	$-0.949950\pi$
$389$	−7.06523	+	12.2373i	−0.358221	+	0.620458i	0.629442	+	0.777047i	$0.283283\pi$
$390$		0			0
$391$	−19.1934			−0.970653
$392$		0			0
$393$		−	21.9817i		−	1.10883i
$394$		0			0
$395$	12.6821	+	8.03330i	0.638106	+	0.404199i
$396$		0			0
$397$	9.75974	−	5.63479i	0.489827	−	0.282802i	−0.234676	−	0.972074i	$-0.575403\pi$
$397$	9.75974	−	5.63479i	0.489827	−	0.282802i	0.724503	+	0.689272i	$0.242069\pi$
$398$		0			0
$399$	−0.794059	+	0.145987i	−0.0397527	+	0.00730849i
$400$		0			0
$401$	−11.6484	−	20.1757i	−0.581694	−	1.00752i	−0.995279	−	0.0970583i	$-0.969057\pi$
$401$	−11.6484	−	20.1757i	−0.581694	−	1.00752i	0.413584	−	0.910466i	$-0.364277\pi$
$402$		0			0
$403$	7.92917	+	4.57791i	0.394980	+	0.228042i
$404$		0			0
$405$	0.0917505	−	2.23418i	0.00455912	−	0.111018i
$406$		0			0
$407$			16.2789i			0.806914i
$408$		0			0
$409$	10.3239	−	17.8815i	0.510484	−	0.884184i	−0.489443	−	0.872036i	$-0.662800\pi$
$409$	10.3239	−	17.8815i	0.510484	−	0.884184i	0.999926	−	0.0121481i	$-0.00386695\pi$
$410$		0			0
$411$	−1.50095	−	2.59973i	−0.0740366	−	0.128235i
$412$		0			0
$413$	−2.84777	−	1.01307i	−0.140130	−	0.0498498i
$414$		0			0
$415$	−5.29138	−	10.1007i	−0.259743	−	0.495823i
$416$		0			0
$417$	18.8243	+	10.8682i	0.921829	+	0.532218i
$418$		0			0
$419$	−5.48254			−0.267839			−0.133920	−	0.990992i	$-0.542756\pi$
$419$	−5.48254			−0.267839			−0.133920	+	0.990992i	$0.542756\pi$
$420$		0			0
$421$	−3.78079			−0.184264			−0.0921322	−	0.995747i	$-0.529368\pi$
$421$	−3.78079			−0.184264			−0.0921322	+	0.995747i	$0.529368\pi$
$422$		0			0
$423$	−1.57313	−	0.908250i	−0.0764884	−	0.0441606i
$424$		0			0
$425$	12.3522	−	5.83799i	0.599168	−	0.283184i
$426$		0			0
$427$	−19.2495	+	16.3927i	−0.931551	+	0.793301i
$428$		0			0
$429$	3.83805	+	6.64770i	0.185303	+	0.320954i
$430$		0			0
$431$	−13.7564	+	23.8267i	−0.662621	+	1.14769i	0.317303	+	0.948324i	$0.397223\pi$
$431$	−13.7564	+	23.8267i	−0.662621	+	1.14769i	−0.979924	+	0.199369i	$0.936111\pi$
$432$		0			0
$433$		−	8.75514i		−	0.420745i	−0.977621	−	0.210373i	$-0.932532\pi$
$433$		−	8.75514i		−	0.420745i	0.977621	−	0.210373i	$-0.0674677\pi$
$434$		0			0
$435$	17.4139	+	0.715131i	0.834933	+	0.0342879i
$436$		0			0
$437$	−1.85631	−	1.07174i	−0.0887996	−	0.0512685i
$438$		0			0
$439$	5.30636	+	9.19088i	0.253259	+	0.438657i	0.964421	−	0.264371i	$-0.0851643\pi$
$439$	5.30636	+	9.19088i	0.253259	+	0.438657i	−0.711163	+	0.703028i	$0.751831\pi$
$440$		0			0
$441$	−5.42730	−	4.42090i	−0.258443	−	0.210519i
$442$		0			0
$443$	17.3080	−	9.99278i	0.822328	−	0.474771i	−0.0288905	−	0.999583i	$-0.509197\pi$
$443$	17.3080	−	9.99278i	0.822328	−	0.474771i	0.851219	+	0.524811i	$0.175864\pi$
$444$		0			0
$445$	−7.68941	−	4.87074i	−0.364513	−	0.230895i
$446$		0			0
$447$			5.21309i			0.246571i
$448$		0			0
$449$	−3.02578			−0.142795			−0.0713976	−	0.997448i	$-0.522746\pi$
$449$	−3.02578			−0.142795			−0.0713976	+	0.997448i	$0.522746\pi$
$450$		0			0
$451$	−14.8776	+	25.7688i	−0.700561	+	1.21341i
$452$		0			0
$453$	8.41233	−	4.85686i	0.395246	−	0.228195i
$454$		0			0
$455$	8.06936	−	6.31941i	0.378297	−	0.296259i
$456$		0			0
$457$	−1.97570	+	1.14067i	−0.0924195	+	0.0533584i	−0.545497	−	0.838112i	$-0.683659\pi$
$457$	−1.97570	+	1.14067i	−0.0924195	+	0.0533584i	0.453078	+	0.891471i	$0.350326\pi$
$458$		0			0
$459$	1.36623	−	2.36638i	0.0637701	−	0.110453i
$460$		0			0
$461$	−24.0678			−1.12095			−0.560475	−	0.828171i	$-0.689381\pi$
$461$	−24.0678			−1.12095			−0.560475	+	0.828171i	$0.689381\pi$
$462$		0			0
$463$		−	11.1290i		−	0.517211i	−0.965983	−	0.258605i	$-0.916737\pi$
$463$		−	11.1290i		−	0.517211i	0.965983	−	0.258605i	$-0.0832629\pi$
$464$		0			0
$465$	−6.32361	+	9.98304i	−0.293251	+	0.462952i
$466$		0			0
$467$	24.7481	−	14.2883i	1.14521	−	0.661185i	0.197491	−	0.980305i	$-0.436721\pi$
$467$	24.7481	−	14.2883i	1.14521	−	0.661185i	0.947714	+	0.319120i	$0.103387\pi$
$468$		0			0
$469$	−7.43491	+	20.8998i	−0.343312	+	0.965062i
$470$		0			0
$471$	−4.73591	−	8.20284i	−0.218219	−	0.377967i
$472$		0			0
$473$	−37.2803	−	21.5238i	−1.71415	−	0.989664i
$474$		0			0
$475$	1.52064	+	0.125106i	0.0697719	+	0.00574028i
$476$		0			0
$477$		−	1.71513i		−	0.0785305i
$478$		0			0
$479$	2.79005	−	4.83250i	0.127480	−	0.220803i	−0.795219	−	0.606322i	$-0.792644\pi$
$479$	2.79005	−	4.83250i	0.127480	−	0.220803i	0.922700	+	0.385519i	$0.125978\pi$
$480$		0			0
$481$	3.18258	+	5.51240i	0.145113	+	0.251344i
$482$		0			0
$483$	−3.36040	−	18.2780i	−0.152903	−	0.831679i
$484$		0			0
$485$	2.98667	+	5.70124i	0.135618	+	0.258880i
$486$		0			0
$487$	−7.22858	−	4.17342i	−0.327558	−	0.189116i	0.327198	−	0.944956i	$-0.393895\pi$
$487$	−7.22858	−	4.17342i	−0.327558	−	0.189116i	−0.654756	+	0.755840i	$0.727229\pi$
$488$		0			0
$489$	−5.39659			−0.244042
$490$		0			0
$491$	−0.557405			−0.0251554			−0.0125777	−	0.999921i	$-0.504004\pi$
$491$	−0.557405			−0.0251554			−0.0125777	+	0.999921i	$0.504004\pi$
$492$		0			0
$493$	18.4443	+	10.6488i	0.830689	+	0.479598i
$494$		0			0
$495$	−8.77615	+	4.59750i	−0.394459	+	0.206642i
$496$		0			0
$497$	4.92217	+	26.7729i	0.220790	+	1.20093i
$498$		0			0
$499$	13.0168	+	22.5458i	0.582713	+	1.00929i	0.995156	+	0.0983057i	$0.0313423\pi$
$499$	13.0168	+	22.5458i	0.582713	+	1.00929i	−0.412443	+	0.910983i	$0.635324\pi$
$500$		0			0
$501$	0.156275	−	0.270676i	0.00698186	−	0.0120929i
$502$		0			0
$503$		−	5.52409i		−	0.246307i	−0.992388	−	0.123154i	$-0.960699\pi$
$503$		−	5.52409i		−	0.246307i	0.992388	−	0.123154i	$-0.0393008\pi$
$504$		0			0
$505$	0.662224	−	16.1256i	0.0294686	−	0.717580i
$506$		0			0
$507$	−8.65903	−	4.99929i	−0.384561	−	0.222026i
$508$		0			0
$509$	11.4446	+	19.8227i	0.507274	+	0.878625i	0.999965	+	0.00842016i	$0.00268025\pi$
$509$	11.4446	+	19.8227i	0.507274	+	0.878625i	−0.492690	+	0.870205i	$0.663986\pi$
$510$		0			0
$511$	−11.3687	+	31.9578i	−0.502921	+	1.41373i
$512$		0			0
$513$	0.264273	−	0.152578i	0.0116679	−	0.00673649i
$514$		0			0
$515$	13.4892	−	21.2953i	0.594404	−	0.938382i
$516$		0			0
$517$			8.04846i			0.353971i
$518$		0			0
$519$	9.61475			0.422041
$520$		0			0
$521$	−13.0995	+	22.6889i	−0.573898	+	0.994020i	0.422263	+	0.906474i	$0.361236\pi$
$521$	−13.0995	+	22.6889i	−0.573898	+	0.994020i	−0.996160	+	0.0875466i	$0.972097\pi$
$522$		0			0
$523$	23.2753	−	13.4380i	1.01776	−	0.587603i	0.104304	−	0.994545i	$-0.466738\pi$
$523$	23.2753	−	13.4380i	1.01776	−	0.587603i	0.913454	+	0.406943i	$0.133405\pi$
$524$		0			0
$525$	7.72218	+	10.7409i	0.337024	+	0.468773i
$526$		0			0
$527$	−12.5060	+	7.22034i	−0.544770	+	0.314523i
$528$		0			0
$529$	13.1699	−	22.8109i	0.572605	−	0.991780i
$530$		0			0
$531$	1.14243			0.0495774
$532$		0			0
$533$			11.6345i			0.503948i
$534$		0			0
$535$	−8.27530	+	13.0641i	−0.357772	+	0.564812i
$536$		0			0
$537$	−7.66831	+	4.42730i	−0.330912	+	0.191052i
$538$		0			0
$539$	−4.94013	+	30.6193i	−0.212786	+	1.31887i
$540$		0			0
$541$	9.39222	+	16.2678i	0.403803	+	0.699408i	0.994181	−	0.107719i	$-0.0343547\pi$
$541$	9.39222	+	16.2678i	0.403803	+	0.699408i	−0.590378	+	0.807127i	$0.701021\pi$
$542$		0			0
$543$	14.6561	+	8.46168i	0.628952	+	0.363125i
$544$		0			0
$545$	−0.405716	+	9.87944i	−0.0173789	+	0.423189i
$546$		0			0
$547$		−	13.4126i		−	0.573483i	−0.958008	−	0.286742i	$-0.907428\pi$
$547$		−	13.4126i		−	0.573483i	0.958008	−	0.286742i	$-0.0925721\pi$
$548$		0			0
$549$	4.77818	−	8.27604i	0.203928	−	0.353213i
$550$		0			0
$551$	1.18924	+	2.05982i	0.0506633	+	0.0877515i
$552$		0			0
$553$	−13.5236	+	11.5166i	−0.575081	+	0.489734i
$554$		0			0
$555$	−7.27735	+	3.81233i	−0.308906	+	0.161825i
$556$		0			0
$557$	34.8008	+	20.0922i	1.47456	+	0.851336i	0.999589	−	0.0286677i	$-0.00912646\pi$
$557$	34.8008	+	20.0922i	1.47456	+	0.851336i	0.474968	+	0.880003i	$0.342460\pi$
$558$		0			0
$559$	−16.8319			−0.711914
$560$		0			0
$561$	−12.1069			−0.511152
$562$		0			0
$563$	−21.8134	−	12.5940i	−0.919325	−	0.530772i	−0.0359052	−	0.999355i	$-0.511431\pi$
$563$	−21.8134	−	12.5940i	−0.919325	−	0.530772i	−0.883420	+	0.468583i	$0.844765\pi$
$564$		0			0
$565$	2.96920	+	5.66789i	0.124915	+	0.238450i
$566$		0			0
$567$	2.49272	+	0.886763i	0.104684	+	0.0372405i
$568$		0			0
$569$	−5.51757	−	9.55672i	−0.231309	−	0.400638i	0.726885	−	0.686759i	$-0.240967\pi$
$569$	−5.51757	−	9.55672i	−0.231309	−	0.400638i	−0.958194	+	0.286121i	$0.907634\pi$
$570$		0			0
$571$	14.3573	−	24.8677i	0.600836	−	1.04068i	−0.391858	−	0.920026i	$-0.628168\pi$
$571$	14.3573	−	24.8677i	0.600836	−	1.04068i	0.992695	−	0.120654i	$-0.0384990\pi$
$572$		0			0
$573$		−	0.318541i		−	0.0133073i
$574$		0			0
$575$	−2.87976	+	35.0029i	−0.120094	+	1.45972i
$576$		0			0
$577$	−5.94444	−	3.43202i	−0.247470	−	0.142877i	0.371135	−	0.928579i	$-0.378969\pi$
$577$	−5.94444	−	3.43202i	−0.247470	−	0.142877i	−0.618605	+	0.785702i	$0.712302\pi$
$578$		0			0
$579$	−1.04667	−	1.81289i	−0.0434981	−	0.0753410i
$580$		0			0
$581$	13.2695	−	2.43959i	0.550512	−	0.101211i
$582$		0			0
$583$	−6.58121	+	3.79966i	−0.272566	+	0.157366i
$584$		0			0
$585$	−2.07298	+	3.27259i	−0.0857070	+	0.135305i
$586$		0			0
$587$			9.03965i			0.373106i	0.982445	+	0.186553i	$0.0597317\pi$
$587$			9.03965i			0.373106i	−0.982445	+	0.186553i	$0.940268\pi$
$588$		0			0
$589$	−1.61271			−0.0664506
$590$		0			0
$591$	−11.2899	+	19.5547i	−0.464404	+	0.804372i
$592$		0			0
$593$	−4.42364	+	2.55399i	−0.181657	+	0.104880i	−0.588071	−	0.808809i	$-0.700112\pi$
$593$	−4.42364	+	2.55399i	−0.181657	+	0.104880i	0.406414	+	0.913689i	$0.366779\pi$
$594$		0			0
$595$	2.26818	+	16.0055i	0.0929864	+	0.656163i
$596$		0			0
$597$	−6.49872	+	3.75204i	−0.265975	+	0.153561i
$598$		0			0
$599$	14.9721	−	25.9325i	0.611745	−	1.05957i	−0.379202	−	0.925314i	$-0.623801\pi$
$599$	14.9721	−	25.9325i	0.611745	−	1.05957i	0.990946	−	0.134259i	$-0.0428654\pi$
$600$		0			0
$601$	−12.5387			−0.511466			−0.255733	−	0.966747i	$-0.582317\pi$
$601$	−12.5387			−0.511466			−0.255733	+	0.966747i	$0.582317\pi$
$602$		0			0
$603$		−	8.38433i		−	0.341436i
$604$		0			0
$605$	16.3049	+	10.3281i	0.662890	+	0.419898i
$606$		0			0
$607$	8.31216	−	4.79903i	0.337380	−	0.194786i	−0.321733	−	0.946831i	$-0.604265\pi$
$607$	8.31216	−	4.79903i	0.337380	−	0.194786i	0.659113	+	0.752044i	$0.270932\pi$
$608$		0			0
$609$	−6.91170	+	19.4290i	−0.280076	+	0.787304i
$610$		0			0
$611$	1.57351	+	2.72539i	0.0636572	+	0.110258i
$612$		0			0
$613$	−23.9583	−	13.8323i	−0.967665	−	0.558682i	−0.0691416	−	0.997607i	$-0.522026\pi$
$613$	−23.9583	−	13.8323i	−0.967665	−	0.558682i	−0.898524	+	0.438925i	$0.855359\pi$
$614$		0			0
$615$	−15.0039	−	0.616162i	−0.605017	−	0.0248460i
$616$		0			0
$617$			20.4155i			0.821896i	0.911659	+	0.410948i	$0.134802\pi$
$617$			20.4155i			0.821896i	−0.911659	+	0.410948i	$0.865198\pi$
$618$		0			0
$619$	7.72112	−	13.3734i	0.310338	−	0.537521i	−0.668098	−	0.744074i	$-0.732891\pi$
$619$	7.72112	−	13.3734i	0.310338	−	0.537521i	0.978435	+	0.206553i	$0.0662245\pi$
$620$		0			0
$621$	3.51212	+	6.08316i	0.140936	+	0.244109i
$622$		0			0
$623$	8.19960	−	6.98271i	0.328510	−	0.279756i
$624$		0			0
$625$	−8.79339	−	23.4025i	−0.351735	−	0.936099i
$626$		0			0
$627$	−1.17093	−	0.676036i	−0.0467624	−	0.0269983i
$628$		0			0
$629$	−10.0392			−0.400290
$630$		0			0
$631$	38.1722			1.51961			0.759805	−	0.650151i	$-0.225295\pi$
$631$	38.1722			1.51961			0.759805	+	0.650151i	$0.225295\pi$
$632$		0			0
$633$	6.64428	+	3.83608i	0.264087	+	0.152470i
$634$		0			0
$635$	−14.2493	−	27.2004i	−0.565465	−	1.07941i
$636$		0			0
$637$	4.31336	+	11.3342i	0.170901	+	0.449078i
$638$		0			0
$639$	−5.14441	−	8.91037i	−0.203510	−	0.352489i
$640$		0			0
$641$	8.39007	−	14.5320i	0.331388	−	0.573981i	−0.651396	−	0.758738i	$-0.725816\pi$
$641$	8.39007	−	14.5320i	0.331388	−	0.573981i	0.982784	+	0.184757i	$0.0591498\pi$
$642$		0			0
$643$			14.2002i			0.560001i	0.960000	+	0.280001i	$0.0903346\pi$
$643$			14.2002i			0.560001i	−0.960000	+	0.280001i	$0.909665\pi$
$644$		0			0
$645$	0.891413	−	21.7065i	0.0350994	−	0.854692i
$646$		0			0
$647$	−12.5474	−	7.24426i	−0.493290	−	0.284801i	0.232648	−	0.972561i	$-0.425261\pi$
$647$	−12.5474	−	7.24426i	−0.493290	−	0.284801i	−0.725938	+	0.687760i	$0.758594\pi$
$648$		0			0
$649$	−2.53092	−	4.38369i	−0.0993474	−	0.172075i
$650$		0			0
$651$	−9.06554	−	10.6454i	−0.355307	−	0.417227i
$652$		0			0
$653$	8.90562	−	5.14166i	0.348504	−	0.201209i	−0.315522	−	0.948918i	$-0.602180\pi$
$653$	8.90562	−	5.14166i	0.348504	−	0.201209i	0.664026	+	0.747709i	$0.268846\pi$
$654$		0			0
$655$	−41.5232	−	26.3023i	−1.62245	−	1.02771i
$656$		0			0
$657$		−	12.8204i		−	0.500173i
$658$		0			0
$659$	14.9773			0.583433			0.291717	−	0.956505i	$-0.405774\pi$
$659$	14.9773			0.583433			0.291717	+	0.956505i	$0.405774\pi$
$660$		0			0
$661$	−1.22323	+	2.11870i	−0.0475782	+	0.0824079i	−0.888834	−	0.458230i	$-0.848484\pi$
$661$	−1.22323	+	2.11870i	−0.0475782	+	0.0824079i	0.841256	+	0.540638i	$0.181817\pi$
$662$		0			0
$663$	−4.09966	+	2.36694i	−0.159217	+	0.0919242i
$664$		0			0
$665$	−0.674365	+	1.67465i	−0.0261507	+	0.0649400i
$666$		0			0
$667$	−47.4140	+	27.3745i	−1.83588	+	1.05994i
$668$		0			0
$669$	3.45104	−	5.97738i	0.133425	−	0.231099i
$670$		0			0
$671$	−42.3418			−1.63459
$672$		0			0
$673$			17.2596i			0.665310i	0.943049	+	0.332655i	$0.107945\pi$
$673$			17.2596i			0.665310i	−0.943049	+	0.332655i	$0.892055\pi$
$674$		0			0
$675$	−4.11056	−	2.84663i	−0.158215	−	0.109567i
$676$		0			0
$677$	−10.0791	+	5.81918i	−0.387372	+	0.223649i	−0.681021	−	0.732264i	$-0.738464\pi$
$677$	−10.0791	+	5.81918i	−0.387372	+	0.223649i	0.293649	+	0.955913i	$0.405130\pi$
$678$		0			0
$679$	−7.48986	+	1.37700i	−0.287434	+	0.0528445i
$680$		0			0
$681$	−3.17360	−	5.49684i	−0.121613	−	0.210639i
$682$		0			0
$683$	−26.9299	−	15.5480i	−1.03044	−	0.594928i	−0.113333	−	0.993557i	$-0.536153\pi$
$683$	−26.9299	−	15.5480i	−1.03044	−	0.594928i	−0.917112	+	0.398629i	$0.869486\pi$
$684$		0			0
$685$	−6.70681	−	0.275426i	−0.256254	−	0.0105235i
$686$		0			0
$687$		−	6.75669i		−	0.257784i
$688$		0			0
$689$	−1.48570	+	2.57330i	−0.0566006	+	0.0980351i
$690$		0			0
$691$	−8.96695	−	15.5312i	−0.341119	−	0.590835i	0.643522	−	0.765428i	$-0.277473\pi$
$691$	−8.96695	−	15.5312i	−0.341119	−	0.590835i	−0.984641	+	0.174592i	$0.944139\pi$
$692$		0			0
$693$	−2.11968	−	11.5294i	−0.0805198	−	0.437967i
$694$		0			0
$695$	43.0541	−	22.5544i	1.63313	−	0.855538i
$696$		0			0
$697$	−15.8917	−	9.17508i	−0.601941	−	0.347531i
$698$		0			0
$699$	7.41201			0.280348
$700$		0			0
$701$	7.04488			0.266081			0.133041	−	0.991111i	$-0.457526\pi$
$701$	7.04488			0.266081			0.133041	+	0.991111i	$0.457526\pi$
$702$		0			0
$703$	−0.970956	−	0.560582i	−0.0366203	−	0.0211427i
$704$		0			0
$705$	−3.59801	+	1.88486i	−0.135509	+	0.0709880i
$706$		0			0
$707$	17.9916	+	6.40036i	0.676644	+	0.240710i
$708$		0			0
$709$	−12.9622	−	22.4511i	−0.486804	−	0.843170i	0.513080	−	0.858341i	$-0.328504\pi$
$709$	−12.9622	−	22.4511i	−0.486804	−	0.843170i	−0.999885	+	0.0151705i	$0.995171\pi$
$710$		0			0
$711$	3.35686	−	5.81425i	0.125892	−	0.218051i
$712$		0			0
$713$		−	37.1221i		−	1.39023i
$714$		0			0
$715$	17.1498	+	0.704286i	0.641367	+	0.0263388i
$716$		0			0
$717$	−6.37702	−	3.68178i	−0.238154	−	0.137498i
$718$		0			0
$719$	−15.6427	−	27.0940i	−0.583376	−	1.01044i	−0.995076	−	0.0991173i	$-0.968398\pi$
$719$	−15.6427	−	27.0940i	−0.583376	−	1.01044i	0.411700	−	0.911320i	$-0.364935\pi$
$720$		0			0
$721$	19.3381	+	22.7082i	0.720189	+	0.845698i
$722$		0			0
$723$	11.8473	−	6.84002i	0.440605	−	0.254383i
$724$		0			0
$725$	22.1875	−	32.0389i	0.824023	−	1.18990i
$726$		0			0
$727$		−	22.8312i		−	0.846761i	−0.905952	−	0.423380i	$-0.860843\pi$
$727$		−	22.8312i		−	0.846761i	0.905952	−	0.423380i	$-0.139157\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	13.2738	−	22.9908i	0.490948	−	0.850347i
$732$		0			0
$733$	5.15661	−	2.97717i	0.190464	−	0.109964i	−0.401736	−	0.915756i	$-0.631593\pi$
$733$	5.15661	−	2.97717i	0.190464	−	0.109964i	0.592200	+	0.805791i	$0.298260\pi$
$734$		0			0
$735$	−14.8451	+	4.96226i	−0.547568	+	0.183036i
$736$		0			0
$737$	−32.1719	+	18.5745i	−1.18507	+	0.684199i
$738$		0			0
$739$	−20.7539	+	35.9469i	−0.763446	+	1.32233i	0.177618	+	0.984099i	$0.443161\pi$
$739$	−20.7539	+	35.9469i	−0.763446	+	1.32233i	−0.941064	+	0.338228i	$0.890173\pi$
$740$		0			0
$741$	−0.528671			−0.0194212
$742$		0			0
$743$		−	6.80015i		−	0.249473i	−0.992190	−	0.124737i	$-0.960191\pi$
$743$		−	6.80015i		−	0.249473i	0.992190	−	0.124737i	$-0.0398086\pi$
$744$		0			0
$745$	9.84745	+	6.23773i	0.360783	+	0.228533i
$746$		0			0
$747$	−4.41626	+	2.54973i	−0.161583	+	0.0932898i
$748$		0			0
$749$	−11.8635	−	13.9310i	−0.433482	−	0.509026i
$750$		0			0
$751$	11.8056	+	20.4480i	0.430794	+	0.746157i	0.996942	−	0.0781464i	$-0.0249001\pi$
$751$	11.8056	+	20.4480i	0.430794	+	0.746157i	−0.566148	+	0.824304i	$0.691567\pi$
$752$		0			0
$753$	20.3380	+	11.7421i	0.741157	+	0.427907i
$754$		0			0
$755$	0.891238	−	21.7022i	0.0324355	−	0.789825i
$756$		0			0
$757$			16.2267i			0.589769i	0.955533	+	0.294884i	$0.0952811\pi$
$757$			16.2267i			0.589769i	−0.955533	+	0.294884i	$0.904719\pi$
$758$		0			0
$759$	15.5613	−	26.9530i	0.564840	−	0.978332i
$760$		0			0
$761$	1.27754	+	2.21276i	0.0463108	+	0.0802126i	0.888252	−	0.459357i	$-0.151920\pi$
$761$	1.27754	+	2.21276i	0.0463108	+	0.0802126i	−0.841941	+	0.539570i	$0.818587\pi$
$762$		0			0
$763$	−11.0227	−	3.92122i	−0.399047	−	0.141958i
$764$		0			0
$765$	−2.83529	−	5.41228i	−0.102510	−	0.195681i
$766$		0			0
$767$	−1.71406	−	0.989610i	−0.0618910	−	0.0357328i
$768$		0			0
$769$	45.4525			1.63906			0.819530	−	0.573037i	$-0.194235\pi$
$769$	45.4525			1.63906			0.819530	+	0.573037i	$0.194235\pi$
$770$		0			0
$771$	−14.5974			−0.525713
$772$		0			0
$773$	−44.5909	−	25.7446i	−1.60382	−	0.925968i	−0.990713	−	0.135970i	$-0.956585\pi$
$773$	−44.5909	−	25.7446i	−1.60382	−	0.925968i	−0.613110	−	0.789997i	$-0.710082\pi$
$774$		0			0
$775$	11.2913	+	23.8904i	0.405595	+	0.858170i
$776$		0			0
$777$	−1.75767	−	9.56043i	−0.0630562	−	0.342979i
$778$		0			0
$779$	−1.02466	−	1.77476i	−0.0367121	−	0.0635873i
$780$		0			0
$781$	−22.7936	+	39.4797i	−0.815619	+	1.41269i
$782$		0			0
$783$		−	7.79430i		−	0.278546i
$784$		0			0
$785$	−21.1618	−	0.869044i	−0.755297	−	0.0310175i
$786$		0			0
$787$	17.4517	+	10.0757i	0.622085	+	0.359161i	0.777680	−	0.628660i	$-0.216396\pi$
$787$	17.4517	+	10.0757i	0.622085	+	0.359161i	−0.155596	+	0.987821i	$0.549730\pi$
$788$		0			0
$789$	−2.54470	−	4.40755i	−0.0905937	−	0.156913i
$790$		0			0
$791$	−7.44605	+	1.36895i	−0.264751	+	0.0486742i
$792$		0			0
$793$	−14.3379	+	8.27800i	−0.509154	+	0.293960i
$794$		0			0
$795$	−3.23986	−	2.05224i	−0.114906	−	0.0727855i
$796$		0			0
$797$		−	13.0702i		−	0.462971i	−0.972838	−	0.231486i	$-0.925641\pi$
$797$		−	13.0702i		−	0.462971i	0.972838	−	0.231486i	$-0.0743587\pi$
$798$		0			0
$799$	−4.96351			−0.175596
$800$		0			0
$801$	−2.03533	+	3.52529i	−0.0719148	+	0.124560i
$802$		0			0
$803$	−49.1939	+	28.4021i	−1.73602	+	1.00229i
$804$		0			0
$805$	−38.5478	−	15.5229i	−1.35863	−	0.547109i
$806$		0			0
$807$	−26.4224	+	15.2550i	−0.930112	+	0.537000i
$808$		0			0
$809$	−0.868598	+	1.50446i	−0.0305383	+	0.0528938i	−0.880891	−	0.473320i	$-0.843055\pi$
$809$	−0.868598	+	1.50446i	−0.0305383	+	0.0528938i	0.850352	+	0.526214i	$0.176389\pi$
$810$		0			0
$811$	27.9004			0.979715			0.489858	−	0.871802i	$-0.337049\pi$
$811$	27.9004			0.979715			0.489858	+	0.871802i	$0.337049\pi$
$812$		0			0
$813$			19.4880i			0.683475i
$814$		0			0
$815$	−6.45729	+	10.1941i	−0.226189	+	0.357083i
$816$		0			0
$817$	2.56758	−	1.48239i	0.0898282	−	0.0518623i
$818$		0			0
$819$	−2.97182	−	3.48973i	−0.103844	−	0.121941i
$820$		0			0
$821$	−8.46799	−	14.6670i	−0.295535	−	0.511881i	0.679574	−	0.733607i	$-0.262165\pi$
$821$	−8.46799	−	14.6670i	−0.295535	−	0.511881i	−0.975109	+	0.221725i	$0.928831\pi$
$822$		0			0
$823$	−8.56526	−	4.94516i	−0.298566	−	0.172377i	0.343232	−	0.939251i	$-0.388478\pi$
$823$	−8.56526	−	4.94516i	−0.298566	−	0.172377i	−0.641799	+	0.766873i	$0.721812\pi$
$824$		0			0
$825$	−1.81650	+	22.0792i	−0.0632424	+	0.768698i
$826$		0			0
$827$		−	35.3201i		−	1.22820i	−0.789228	−	0.614101i	$-0.789519\pi$
$827$		−	35.3201i		−	1.22820i	0.789228	−	0.614101i	$-0.210481\pi$
$828$		0			0
$829$	4.64975	−	8.05361i	0.161493	−	0.279713i	−0.773912	−	0.633294i	$-0.781703\pi$
$829$	4.64975	−	8.05361i	0.161493	−	0.279713i	0.935404	+	0.353580i	$0.115036\pi$
$830$		0			0
$831$	12.7401	+	22.0665i	0.441949	+	0.765478i
$832$		0			0
$833$	−18.8830	−	3.04659i	−0.654258	−	0.105558i
$834$		0			0
$835$	−0.324313	−	0.619080i	−0.0112233	−	0.0214241i
$836$		0			0
$837$	4.57683	+	2.64243i	0.158198	+	0.0913359i
$838$		0			0
$839$	−7.93405			−0.273914			−0.136957	−	0.990577i	$-0.543732\pi$
$839$	−7.93405			−0.273914			−0.136957	+	0.990577i	$0.543732\pi$
$840$		0			0
$841$	31.7512			1.09487
$842$		0			0
$843$	19.2183	+	11.0957i	0.661914	+	0.382156i
$844$		0			0
$845$	−19.8046	+	10.3749i	−0.681298	+	0.356906i
$846$		0			0
$847$	−17.3868	+	14.8064i	−0.597416	+	0.508755i
$848$		0			0
$849$	−9.06209	−	15.6960i	−0.311010	−	0.538685i
$850$		0			0
$851$	12.9037	−	22.3499i	0.442334	−	0.766146i
$852$		0			0
$853$		−	30.0757i		−	1.02977i	−0.857258	−	0.514887i	$-0.827834\pi$
$853$		−	30.0757i		−	1.02977i	0.857258	−	0.514887i	$-0.172166\pi$
$854$		0			0
$855$	0.0279982	−	0.681775i	0.000957519	−	0.0233162i
$856$		0			0
$857$	−40.8221	−	23.5686i	−1.39446	−	0.805090i	−0.400652	−	0.916230i	$-0.631216\pi$
$857$	−40.8221	−	23.5686i	−1.39446	−	0.805090i	−0.993805	+	0.111141i	$0.964550\pi$
$858$		0			0
$859$	16.3183	+	28.2642i	0.556774	+	0.964361i	0.997763	+	0.0668485i	$0.0212944\pi$
$859$	16.3183	+	28.2642i	0.556774	+	0.964361i	−0.440989	+	0.897512i	$0.645372\pi$
$860$		0			0
$861$	5.95517	−	16.7402i	0.202951	−	0.570503i
$862$		0			0
$863$	−32.3982	+	18.7051i	−1.10285	+	0.636728i	−0.936967	−	0.349418i	$-0.886379\pi$
$863$	−32.3982	+	18.7051i	−1.10285	+	0.636728i	−0.165879	+	0.986146i	$0.553046\pi$
$864$		0			0
$865$	11.5045	−	18.1621i	0.391166	−	0.617531i
$866$		0			0
$867$			9.53367i			0.323780i
$868$		0			0
$869$	−29.7468			−1.00909
$870$		0			0
$871$	−7.26275	+	12.5795i	−0.246089	+	0.426239i
$872$		0			0
$873$	2.49272	−	1.43917i	0.0843658	−	0.0487086i
$874$		0			0
$875$	29.5295	−	1.73501i	0.998278	−	0.0586541i
$876$		0			0
$877$	−29.0687	+	16.7828i	−0.981581	+	0.566716i	−0.902747	−	0.430172i	$-0.858453\pi$
$877$	−29.0687	+	16.7828i	−0.981581	+	0.566716i	−0.0788336	+	0.996888i	$0.525120\pi$
$878$		0			0
$879$	6.94790	−	12.0341i	0.234347	−	0.405901i
$880$		0			0
$881$	−12.1952			−0.410867			−0.205433	−	0.978671i	$-0.565860\pi$
$881$	−12.1952			−0.410867			−0.205433	+	0.978671i	$0.565860\pi$
$882$		0			0
$883$			11.0408i			0.371552i	0.982592	+	0.185776i	$0.0594799\pi$
$883$			11.0408i			0.371552i	−0.982592	+	0.185776i	$0.940520\pi$
$884$		0			0
$885$	1.36698	−	2.15804i	0.0459505	−	0.0725418i
$886$		0			0
$887$	1.35180	−	0.780464i	0.0453891	−	0.0262054i	−0.477134	−	0.878831i	$-0.658324\pi$
$887$	1.35180	−	0.780464i	0.0453891	−	0.0262054i	0.522523	+	0.852625i	$0.324991\pi$
$888$		0			0
$889$	35.7338	−	6.56962i	1.19847	−	0.220338i
$890$		0			0
$891$	2.21538	+	3.83715i	0.0742179	+	0.128549i
$892$		0			0
$893$	−0.480052	−	0.277158i	−0.0160643	−	0.00927474i
$894$		0			0
$895$	−0.812414	+	19.7828i	−0.0271560	+	0.661267i
$896$		0			0
$897$		−	12.1692i		−	0.406318i
$898$		0			0
$899$	−20.5959	+	35.6732i	−0.686913	+	1.18977i
$900$		0			0
$901$	−2.34326	−	4.05865i	−0.0780654	−	0.135213i
$902$		0			0
$903$	24.2183	+	8.61545i	0.805935	+	0.286704i
$904$		0			0
$905$	33.5207	−	17.5603i	1.11427	−	0.583722i
$906$		0			0
$907$	15.0756	+	8.70390i	0.500577	+	0.289008i	0.728952	−	0.684565i	$-0.240008\pi$
$907$	15.0756	+	8.70390i	0.500577	+	0.289008i	−0.228375	+	0.973573i	$0.573341\pi$
$908$		0			0
$909$	−7.21767			−0.239395
$910$		0			0
$911$	18.3203			0.606978			0.303489	−	0.952835i	$-0.401848\pi$
$911$	18.3203			0.606978			0.303489	+	0.952835i	$0.401848\pi$
$912$		0			0
$913$	19.5674	+	11.2972i	0.647586	+	0.373884i
$914$		0			0
$915$	−9.91600	−	18.9286i	−0.327813	−	0.625761i
$916$		0			0
$917$	44.2783	−	37.7070i	1.46220	−	1.24519i
$918$		0			0
$919$	−11.2963	−	19.5658i	−0.372632	−	0.645417i	0.617338	−	0.786698i	$-0.288211\pi$
$919$	−11.2963	−	19.5658i	−0.372632	−	0.645417i	−0.989970	+	0.141281i	$0.954878\pi$
$920$		0			0
$921$	−14.9166	+	25.8363i	−0.491519	+	0.851335i
$922$		0			0
$923$			17.8249i			0.586715i
$924$		0			0
$925$	−1.50628	+	18.3085i	−0.0495260	+	0.601979i
$926$		0			0
$927$	−9.76304	−	5.63670i	−0.320660	−	0.185133i
$928$		0			0
$929$	19.3356	+	33.4903i	0.634381	+	1.09878i	0.986646	+	0.162880i	$0.0520783\pi$
$929$	19.3356	+	33.4903i	0.634381	+	1.09878i	−0.352265	+	0.935900i	$0.614588\pi$
$930$		0			0
$931$	−1.65618	−	1.34907i	−0.0542790	−	0.0442139i
$932$		0			0
$933$	−11.7028	+	6.75662i	−0.383133	+	0.221202i
$934$		0			0
$935$	−14.4865	+	22.8697i	−0.473758	+	0.747918i
$936$		0			0
$937$		−	46.7921i		−	1.52863i	−0.644842	−	0.764316i	$-0.723077\pi$
$937$		−	46.7921i		−	1.52863i	0.644842	−	0.764316i	$-0.276923\pi$
$938$		0			0
$939$	−28.9857			−0.945912
$940$		0			0
$941$	20.9461	−	36.2797i	0.682824	−	1.18268i	−0.291292	−	0.956634i	$-0.594085\pi$
$941$	20.9461	−	36.2797i	0.682824	−	1.18268i	0.974116	−	0.226051i	$-0.0725815\pi$
$942$		0			0
$943$	40.8522	−	23.5860i	1.33033	−	0.768067i
$944$		0			0
$945$	4.65775	−	3.64765i	0.151517	−	0.118658i
$946$		0			0
$947$	−48.5967	+	28.0573i	−1.57918	+	0.911740i	−0.584206	+	0.811605i	$0.698594\pi$
$947$	−48.5967	+	28.0573i	−1.57918	+	0.911740i	−0.994974	+	0.100134i	$0.968073\pi$
$948$		0			0
$949$	−11.1054	+	19.2352i	−0.360498	+	0.624401i
$950$		0			0
$951$	−1.15864			−0.0375714
$952$		0			0
$953$		−	17.7705i		−	0.575643i	−0.957684	−	0.287821i	$-0.907069\pi$
$953$		−	17.7705i		−	0.575643i	0.957684	−	0.287821i	$-0.0929309\pi$
$954$		0			0
$955$	−0.601720	−	0.381151i	−0.0194712	−	0.0123337i
$956$		0			0
$957$	−29.9079	+	17.2673i	−0.966785	+	0.558173i
$958$		0			0
$959$	2.66198	−	7.48291i	0.0859598	−	0.241636i
$960$		0			0
$961$	1.53508	+	2.65884i	0.0495188	+	0.0857690i
$962$		0			0
$963$	5.98940	+	3.45798i	0.193006	+	0.111432i
$964$		0			0
$965$	−4.67691	−	0.192065i	−0.150555	−	0.00618279i
$966$		0			0
$967$			22.5942i			0.726579i	0.931676	+	0.363290i	$0.118346\pi$
$967$			22.5942i			0.726579i	−0.931676	+	0.363290i	$0.881654\pi$
$968$		0			0
$969$	0.416913	−	0.722115i	0.0133932	−	0.0231977i
$970$		0			0
$971$	20.5244	+	35.5493i	0.658660	+	1.14083i	0.980963	+	0.194196i	$0.0622096\pi$
$971$	20.5244	+	35.5493i	0.658660	+	1.14083i	−0.322303	+	0.946637i	$0.604457\pi$
$972$		0			0
$973$	10.3987	+	56.5612i	0.333367	+	1.81327i
$974$		0			0
$975$	3.70146	+	7.83164i	0.118541	+	0.250813i
$976$		0			0
$977$	16.8644	+	9.73668i	0.539541	+	0.311504i	0.744893	−	0.667184i	$-0.232501\pi$
$977$	16.8644	+	9.73668i	0.539541	+	0.311504i	−0.205352	+	0.978688i	$0.565834\pi$
$978$		0			0
$979$	18.0361			0.576435
$980$		0			0
$981$	4.42195			0.141182
$982$		0			0
$983$	−44.7970	−	25.8636i	−1.42880	−	0.824920i	−0.431777	−	0.901980i	$-0.642113\pi$
$983$	−44.7970	−	25.8636i	−1.42880	−	0.824920i	−0.997026	+	0.0770602i	$0.975447\pi$
$984$		0			0
$985$	23.4296	+	44.7246i	0.746528	+	1.42505i
$986$		0			0
$987$	−0.869014	−	4.72678i	−0.0276610	−	0.150455i
$988$		0			0
$989$	34.1224	+	59.1017i	1.08503	+	1.87932i
$990$		0			0
$991$	17.9749	−	31.1335i	0.570992	−	0.988988i	−0.425472	−	0.904972i	$-0.639892\pi$
$991$	17.9749	−	31.1335i	0.570992	−	0.988988i	0.996464	−	0.0840162i	$-0.0267747\pi$
$992$		0			0
$993$			28.3491i			0.899632i
$994$		0			0
$995$	−0.688503	+	16.7655i	−0.0218270	+	0.531502i
$996$		0			0
$997$	−48.5493	−	28.0300i	−1.53757	−	0.887718i	−0.998980	−	0.0451513i	$-0.985623\pi$
$997$	−48.5493	−	28.0300i	−1.53757	−	0.887718i	−0.538592	−	0.842567i	$-0.681044\pi$
$998$		0			0
$999$	1.83703	+	3.18183i	0.0581211	+	0.100669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.di.d.529.1		16
4.3	odd	2		105.2.q.a.4.3	✓	16
5.4	even	2	inner	1680.2.di.d.529.8		16
7.2	even	3	inner	1680.2.di.d.289.8		16
12.11	even	2		315.2.bf.b.109.6		16
20.3	even	4		525.2.i.k.151.3		8
20.7	even	4		525.2.i.h.151.2		8
20.19	odd	2		105.2.q.a.4.6	yes	16
28.3	even	6		735.2.d.e.589.3		8
28.11	odd	6		735.2.d.d.589.3		8
28.19	even	6		735.2.q.g.79.6		16
28.23	odd	6		105.2.q.a.79.6	yes	16
28.27	even	2		735.2.q.g.214.3		16
35.9	even	6	inner	1680.2.di.d.289.1		16
60.59	even	2		315.2.bf.b.109.3		16
84.11	even	6		2205.2.d.s.1324.6		8
84.23	even	6		315.2.bf.b.289.3		16
84.59	odd	6		2205.2.d.o.1324.6		8
140.3	odd	12		3675.2.a.bn.1.2		4
140.19	even	6		735.2.q.g.79.3		16
140.23	even	12		525.2.i.k.226.3		8
140.39	odd	6		735.2.d.d.589.6		8
140.59	even	6		735.2.d.e.589.6		8
140.67	even	12		3675.2.a.bz.1.3		4
140.79	odd	6		105.2.q.a.79.3	yes	16
140.87	odd	12		3675.2.a.cb.1.3		4
140.107	even	12		525.2.i.h.226.2		8
140.123	even	12		3675.2.a.bp.1.2		4
140.139	even	2		735.2.q.g.214.6		16
420.59	odd	6		2205.2.d.o.1324.3		8
420.179	even	6		2205.2.d.s.1324.3		8
420.359	even	6		315.2.bf.b.289.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.3	✓	16	4.3	odd	2
105.2.q.a.4.6	yes	16	20.19	odd	2
105.2.q.a.79.3	yes	16	140.79	odd	6
105.2.q.a.79.6	yes	16	28.23	odd	6
315.2.bf.b.109.3		16	60.59	even	2
315.2.bf.b.109.6		16	12.11	even	2
315.2.bf.b.289.3		16	84.23	even	6
315.2.bf.b.289.6		16	420.359	even	6
525.2.i.h.151.2		8	20.7	even	4
525.2.i.h.226.2		8	140.107	even	12
525.2.i.k.151.3		8	20.3	even	4
525.2.i.k.226.3		8	140.23	even	12
735.2.d.d.589.3		8	28.11	odd	6
735.2.d.d.589.6		8	140.39	odd	6
735.2.d.e.589.3		8	28.3	even	6
735.2.d.e.589.6		8	140.59	even	6
735.2.q.g.79.3		16	140.19	even	6
735.2.q.g.79.6		16	28.19	even	6
735.2.q.g.214.3		16	28.27	even	2
735.2.q.g.214.6		16	140.139	even	2
1680.2.di.d.289.1		16	35.9	even	6	inner
1680.2.di.d.289.8		16	7.2	even	3	inner
1680.2.di.d.529.1		16	1.1	even	1	trivial
1680.2.di.d.529.8		16	5.4	even	2	inner
2205.2.d.o.1324.3		8	420.59	odd	6
2205.2.d.o.1324.6		8	84.59	odd	6
2205.2.d.s.1324.3		8	420.179	even	6
2205.2.d.s.1324.6		8	84.11	even	6
3675.2.a.bn.1.2		4	140.3	odd	12
3675.2.a.bp.1.2		4	140.123	even	12
3675.2.a.bz.1.3		4	140.67	even	12
3675.2.a.cb.1.3		4	140.87	odd	12

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:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.di (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{3} +(-1.98074 + 1.03763i) q^{5} +(-0.478401 - 2.60214i) q^{7} +(0.500000 + 0.866025i) q^{9} +(2.21538 - 3.83715i) q^{11} -1.73246i q^{13} +(2.23418 + 0.0917505i) q^{15} +(2.36638 + 1.36623i) q^{17} +(0.152578 + 0.264273i) q^{19} +(-0.886763 + 2.49272i) q^{21} +(-6.08316 + 3.51212i) q^{23} +(2.84663 - 4.11056i) q^{25} -1.00000i q^{27} +7.79430 q^{29} +(-2.64243 + 4.57683i) q^{31} +(-3.83715 + 2.21538i) q^{33} +(3.64765 + 4.65775i) q^{35} +(-3.18183 + 1.83703i) q^{37} +(-0.866230 + 1.50035i) q^{39} -6.71562 q^{41} -9.71562i q^{43} +(-1.88899 - 1.19655i) q^{45} +(-1.57313 + 0.908250i) q^{47} +(-6.54227 + 2.48973i) q^{49} +(-1.36623 - 2.36638i) q^{51} +(-1.48535 - 0.857566i) q^{53} +(-0.406524 + 9.89912i) q^{55} -0.305156i q^{57} +(0.571217 - 0.989377i) q^{59} +(-4.77818 - 8.27604i) q^{61} +(2.01432 - 1.71538i) q^{63} +(1.79766 + 3.43154i) q^{65} +(-7.26104 - 4.19216i) q^{67} +7.02423 q^{69} -10.2888 q^{71} +(-11.1028 - 6.41022i) q^{73} +(-4.52053 + 2.13653i) q^{75} +(-11.0446 - 3.92903i) q^{77} +(-3.35686 - 5.81425i) q^{79} +(-0.500000 + 0.866025i) q^{81} +5.09946i q^{83} +(-6.10482 - 0.250704i) q^{85} +(-6.75007 - 3.89715i) q^{87} +(2.03533 + 3.52529i) q^{89} +(-4.50810 + 0.828810i) q^{91} +(4.57683 - 2.64243i) q^{93} +(-0.576436 - 0.365135i) q^{95} -2.87834i q^{97} +4.43075 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{5} + 8 q^{9} + 4 q^{15} + 24 q^{19} - 4 q^{21} - 4 q^{25} + 24 q^{29} - 16 q^{31} + 10 q^{35} + 4 q^{39} + 16 q^{41} - 2 q^{45} - 40 q^{49} - 4 q^{51} - 8 q^{55} - 4 q^{59} + 16 q^{61} + 30 q^{65}+ \cdots + 22 q^{95}+O(q^{100}) \) 16 * q + 2 * q^5 + 8 * q^9 + 4 * q^15 + 24 * q^19 - 4 * q^21 - 4 * q^25 + 24 * q^29 - 16 * q^31 + 10 * q^35 + 4 * q^39 + 16 * q^41 - 2 * q^45 - 40 * q^49 - 4 * q^51 - 8 * q^55 - 4 * q^59 + 16 * q^61 + 30 * q^65 + 40 * q^69 + 56 * q^71 - 8 * q^75 + 16 * q^79 - 8 * q^81 - 64 * q^85 + 16 * q^89 - 8 * q^91 + 22 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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