LMFDB - Embedded newform 840.2.dd.b.73.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(73,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 0, 0, 9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.73"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.dd (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.10
Character	$\chi$	$=$	840.73
Dual form			840.2.dd.b.817.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.258819 + 0.965926i) q^{3} +(-0.0101553 - 2.23604i) q^{5} +(-2.07473 + 1.64180i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(0.922533 - 1.59787i) q^{11} +(-4.81186 + 4.81186i) q^{13} +(2.15723 - 0.588540i) q^{15} +(-2.51042 + 0.672666i) q^{17} +(2.31260 + 4.00554i) q^{19} +(-2.12284 - 1.57910i) q^{21} +(-0.995848 + 3.71655i) q^{23} +(-4.99979 + 0.0454155i) q^{25} +(-0.707107 - 0.707107i) q^{27} +2.58536i q^{29} +(5.63490 + 3.25331i) q^{31} +(1.78220 + 0.477538i) q^{33} +(3.69221 + 4.62251i) q^{35} +(-7.85903 - 2.10582i) q^{37} +(-5.89331 - 3.40250i) q^{39} +7.23170i q^{41} +(-0.333540 - 0.333540i) q^{43} +(1.12682 + 1.93139i) q^{45} +(-1.06734 + 3.98335i) q^{47} +(1.60898 - 6.81258i) q^{49} +(-1.29949 - 2.25079i) q^{51} +(4.34910 - 1.16534i) q^{53} +(-3.58229 - 2.04660i) q^{55} +(-3.27051 + 3.27051i) q^{57} +(4.10291 - 7.10646i) q^{59} +(-5.56336 + 3.21201i) q^{61} +(0.975866 - 2.45920i) q^{63} +(10.8084 + 10.7107i) q^{65} +(-1.65608 - 6.18056i) q^{67} -3.84766 q^{69} -8.70813 q^{71} +(-0.813014 - 3.03421i) q^{73} +(-1.33791 - 4.81768i) q^{75} +(0.709387 + 4.82977i) q^{77} +(-6.74536 + 3.89444i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-0.681980 + 0.681980i) q^{83} +(1.52961 + 5.60659i) q^{85} +(-2.49727 + 0.669141i) q^{87} +(0.659941 + 1.14305i) q^{89} +(2.08318 - 17.8834i) q^{91} +(-1.68404 + 6.28491i) q^{93} +(8.93308 - 5.21175i) q^{95} +(-10.1590 - 10.1590i) q^{97} +1.84507i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{7} - 4 q^{11} - 16 q^{13} - 4 q^{15} + 4 q^{17} - 8 q^{19} + 48 q^{23} - 20 q^{25} + 24 q^{33} - 4 q^{37} + 12 q^{39} + 16 q^{43} + 4 q^{45} - 12 q^{47} + 12 q^{49} - 52 q^{53} + 56 q^{55} + 8 q^{57}+ \cdots - 44 q^{97}+O(q^{100}) $ 48 * q + 4 * q^7 - 4 * q^11 - 16 * q^13 - 4 * q^15 + 4 * q^17 - 8 * q^19 + 48 * q^23 - 20 * q^25 + 24 * q^33 - 4 * q^37 + 12 * q^39 + 16 * q^43 + 4 * q^45 - 12 * q^47 + 12 * q^49 - 52 * q^53 + 56 * q^55 + 8 * q^57 - 8 * q^59 + 12 * q^65 + 68 * q^67 + 8 * q^69 + 16 * q^71 + 52 * q^73 + 24 * q^75 + 16 * q^77 - 108 * q^79 + 24 * q^81 - 64 * q^83 + 32 * q^85 - 8 * q^87 - 64 * q^89 + 48 * q^91 + 48 * q^93 - 84 * q^95 - 44 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$		0			0
$5$	−0.0101553	−	2.23604i	−0.00454159	−	0.999990i
$5$	−0.0101553	−	2.23604i	−0.00454159	−	0.999990i
$6$		0			0
$7$	−2.07473	+	1.64180i	−0.784173	+	0.620542i
$7$	−2.07473	+	1.64180i	−0.784173	+	0.620542i
$8$		0			0
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$		0			0
$11$	0.922533	−	1.59787i	0.278154	−	0.481777i	−0.692772	−	0.721157i	$-0.743611\pi$
$11$	0.922533	−	1.59787i	0.278154	−	0.481777i	0.970926	+	0.239380i	$0.0769440\pi$
$12$		0			0
$13$	−4.81186	+	4.81186i	−1.33457	+	1.33457i	−0.433341	+	0.901230i	$0.642666\pi$
$13$	−4.81186	+	4.81186i	−1.33457	+	1.33457i	−0.901230	+	0.433341i	$0.857334\pi$
$14$		0			0
$15$	2.15723	−	0.588540i	0.556993	−	0.151960i
$16$		0			0
$17$	−2.51042	+	0.672666i	−0.608867	+	0.163146i	−0.550062	−	0.835124i	$-0.685396\pi$
$17$	−2.51042	+	0.672666i	−0.608867	+	0.163146i	−0.0588056	+	0.998269i	$0.518729\pi$
$18$		0			0
$19$	2.31260	+	4.00554i	0.530547	+	0.918934i	0.999365	+	0.0356392i	$0.0113467\pi$
$19$	2.31260	+	4.00554i	0.530547	+	0.918934i	−0.468818	+	0.883295i	$0.655320\pi$
$20$		0			0
$21$	−2.12284	−	1.57910i	−0.463241	−	0.344588i
$22$		0			0
$23$	−0.995848	+	3.71655i	−0.207649	+	0.774955i	0.780977	+	0.624559i	$0.214721\pi$
$23$	−0.995848	+	3.71655i	−0.207649	+	0.774955i	−0.988626	+	0.150396i	$0.951945\pi$
$24$		0			0
$25$	−4.99979	+	0.0454155i	−0.999959	+	0.00908310i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$			2.58536i			0.480090i	0.970762	+	0.240045i	$0.0771622\pi$
$29$			2.58536i			0.480090i	−0.970762	+	0.240045i	$0.922838\pi$
$30$		0			0
$31$	5.63490	+	3.25331i	1.01206	+	0.584312i	0.911793	−	0.410649i	$-0.134698\pi$
$31$	5.63490	+	3.25331i	1.01206	+	0.584312i	0.100264	+	0.994961i	$0.468031\pi$
$32$		0			0
$33$	1.78220	+	0.477538i	0.310241	+	0.0831288i
$34$		0			0
$35$	3.69221	+	4.62251i	0.624097	+	0.781347i
$36$		0			0
$37$	−7.85903	−	2.10582i	−1.29202	−	0.346195i	−0.453591	−	0.891210i	$-0.649857\pi$
$37$	−7.85903	−	2.10582i	−1.29202	−	0.346195i	−0.838426	+	0.545015i	$0.816524\pi$
$38$		0			0
$39$	−5.89331	−	3.40250i	−0.943684	−	0.544836i
$40$		0			0
$41$			7.23170i			1.12940i	0.825296	+	0.564701i	$0.191008\pi$
$41$			7.23170i			1.12940i	−0.825296	+	0.564701i	$0.808992\pi$
$42$		0			0
$43$	−0.333540	−	0.333540i	−0.0508644	−	0.0508644i	0.681217	−	0.732081i	$-0.261451\pi$
$43$	−0.333540	−	0.333540i	−0.0508644	−	0.0508644i	−0.732081	+	0.681217i	$0.761451\pi$
$44$		0			0
$45$	1.12682	+	1.93139i	0.167976	+	0.287915i
$46$		0			0
$47$	−1.06734	+	3.98335i	−0.155687	+	0.581031i	0.843359	+	0.537351i	$0.180575\pi$
$47$	−1.06734	+	3.98335i	−0.155687	+	0.581031i	−0.999046	+	0.0436803i	$0.986092\pi$
$48$		0			0
$49$	1.60898	−	6.81258i	0.229854	−	0.973225i
$50$		0			0
$51$	−1.29949	−	2.25079i	−0.181965	−	0.315173i
$52$		0			0
$53$	4.34910	−	1.16534i	0.597395	−	0.160072i	0.0525643	−	0.998618i	$-0.483261\pi$
$53$	4.34910	−	1.16534i	0.597395	−	0.160072i	0.544831	+	0.838546i	$0.316594\pi$
$54$		0			0
$55$	−3.58229	−	2.04660i	−0.483036	−	0.275963i
$56$		0			0
$57$	−3.27051	+	3.27051i	−0.433190	+	0.433190i
$58$		0			0
$59$	4.10291	−	7.10646i	0.534154	−	0.925182i	−0.465050	−	0.885285i	$-0.653964\pi$
$59$	4.10291	−	7.10646i	0.534154	−	0.925182i	0.999204	−	0.0398973i	$-0.0127031\pi$
$60$		0			0
$61$	−5.56336	+	3.21201i	−0.712315	+	0.411255i	−0.811918	−	0.583772i	$-0.801576\pi$
$61$	−5.56336	+	3.21201i	−0.712315	+	0.411255i	0.0996028	+	0.995027i	$0.468243\pi$
$62$		0			0
$63$	0.975866	−	2.45920i	0.122948	−	0.309831i
$64$		0			0
$65$	10.8084	+	10.7107i	1.34062	+	1.32850i
$66$		0			0
$67$	−1.65608	−	6.18056i	−0.202322	−	0.755076i	−0.990249	−	0.139307i	$-0.955512\pi$
$67$	−1.65608	−	6.18056i	−0.202322	−	0.755076i	0.787927	−	0.615768i	$-0.211154\pi$
$68$		0			0
$69$	−3.84766			−0.463204
$70$		0			0
$71$	−8.70813			−1.03346			−0.516732	−	0.856147i	$-0.672852\pi$
$71$	−8.70813			−1.03346			−0.516732	+	0.856147i	$0.672852\pi$
$72$		0			0
$73$	−0.813014	−	3.03421i	−0.0951561	−	0.355127i	0.901887	−	0.431972i	$-0.142182\pi$
$73$	−0.813014	−	3.03421i	−0.0951561	−	0.355127i	−0.997043	+	0.0768447i	$0.975515\pi$
$74$		0			0
$75$	−1.33791	−	4.81768i	−0.154489	−	0.556297i
$76$		0			0
$77$	0.709387	+	4.82977i	0.0808422	+	0.550403i
$78$		0			0
$79$	−6.74536	+	3.89444i	−0.758912	+	0.438158i	−0.828905	−	0.559389i	$-0.811036\pi$
$79$	−6.74536	+	3.89444i	−0.758912	+	0.438158i	0.0699928	+	0.997547i	$0.477702\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$		0			0
$83$	−0.681980	+	0.681980i	−0.0748570	+	0.0748570i	−0.743544	−	0.668687i	$-0.766857\pi$
$83$	−0.681980	+	0.681980i	−0.0748570	+	0.0748570i	0.668687	+	0.743544i	$0.266857\pi$
$84$		0			0
$85$	1.52961	+	5.60659i	0.165909	+	0.608120i
$86$		0			0
$87$	−2.49727	+	0.669141i	−0.267735	+	0.0717395i
$88$		0			0
$89$	0.659941	+	1.14305i	0.0699536	+	0.121163i	0.898881	−	0.438193i	$-0.144382\pi$
$89$	0.659941	+	1.14305i	0.0699536	+	0.121163i	−0.828927	+	0.559357i	$0.811048\pi$
$90$		0			0
$91$	2.08318	−	17.8834i	0.218377	−	1.87469i
$92$		0			0
$93$	−1.68404	+	6.28491i	−0.174626	+	0.651715i
$94$		0			0
$95$	8.93308	−	5.21175i	0.916515	−	0.534715i
$96$		0			0
$97$	−10.1590	−	10.1590i	−1.03149	−	1.03149i	−0.999488	−	0.0319978i	$-0.989813\pi$
$97$	−10.1590	−	10.1590i	−1.03149	−	1.03149i	−0.0319978	−	0.999488i	$-0.510187\pi$
$98$		0			0
$99$			1.84507i			0.185436i
$100$		0			0
$101$	−1.47692	−	0.852702i	−0.146959	−	0.0848470i	0.424717	−	0.905326i	$-0.360373\pi$
$101$	−1.47692	−	0.852702i	−0.146959	−	0.0848470i	−0.571677	+	0.820479i	$0.693707\pi$
$102$		0			0
$103$	12.5511	+	3.36305i	1.23670	+	0.331372i	0.817183	−	0.576378i	$-0.195534\pi$
$103$	12.5511	+	3.36305i	1.23670	+	0.331372i	0.419512	+	0.907750i	$0.362201\pi$
$104$		0			0
$105$	−3.50939	+	4.76279i	−0.342481	+	0.464801i
$106$		0			0
$107$	11.8778	+	3.18264i	1.14827	+	0.307678i	0.782271	−	0.622938i	$-0.214061\pi$
$107$	11.8778	+	3.18264i	1.14827	+	0.307678i	0.365998	+	0.930616i	$0.380728\pi$
$108$		0			0
$109$	−2.91372	−	1.68224i	−0.279083	−	0.161129i	0.353925	−	0.935274i	$-0.384847\pi$
$109$	−2.91372	−	1.68224i	−0.279083	−	0.161129i	−0.633008	+	0.774145i	$0.718180\pi$
$110$		0			0
$111$		−	8.13627i		−	0.772260i
$112$		0			0
$113$	−12.9390	−	12.9390i	−1.21720	−	1.21720i	−0.968609	−	0.248587i	$-0.920034\pi$
$113$	−12.9390	−	12.9390i	−1.21720	−	1.21720i	−0.248587	−	0.968609i	$-0.579966\pi$
$114$		0			0
$115$	8.32049	+	2.18902i	0.775890	+	0.204127i
$116$		0			0
$117$	1.76126	−	6.57313i	0.162829	−	0.607686i
$118$		0			0
$119$	4.10406	−	5.51722i	0.376219	−	0.505762i
$120$		0			0
$121$	3.79786	+	6.57810i	0.345260	+	0.598009i
$122$		0			0
$123$	−6.98528	+	1.87170i	−0.629842	+	0.168766i
$124$		0			0
$125$	0.152326	+	11.1793i	0.0136244	+	0.999907i
$126$		0			0
$127$	−9.20357	+	9.20357i	−0.816685	+	0.816685i	−0.985626	−	0.168941i	$-0.945965\pi$
$127$	−9.20357	+	9.20357i	−0.816685	+	0.816685i	0.168941	+	0.985626i	$0.445965\pi$
$128$		0			0
$129$	0.235849	−	0.408502i	0.0207653	−	0.0359666i
$130$		0			0
$131$	−4.02477	+	2.32370i	−0.351646	+	0.203023i	−0.665410	−	0.746478i	$-0.731743\pi$
$131$	−4.02477	+	2.32370i	−0.351646	+	0.203023i	0.313764	+	0.949501i	$0.398410\pi$
$132$		0			0
$133$	−11.3743	−	4.51357i	−0.986278	−	0.391376i
$134$		0			0
$135$	−1.57394	+	1.58830i	−0.135463	+	0.136699i
$136$		0			0
$137$	3.44285	+	12.8489i	0.294142	+	1.09775i	0.941896	+	0.335904i	$0.109042\pi$
$137$	3.44285	+	12.8489i	0.294142	+	1.09775i	−0.647754	+	0.761849i	$0.724292\pi$
$138$		0			0
$139$	20.2234			1.71533			0.857664	−	0.514211i	$-0.171915\pi$
$139$	20.2234			1.71533			0.857664	+	0.514211i	$0.171915\pi$
$140$		0			0
$141$	−4.12387			−0.347292
$142$		0			0
$143$	3.24965	+	12.1279i	0.271749	+	1.01418i
$144$		0			0
$145$	5.78099	−	0.0262552i	0.480085	−	0.00218037i
$146$		0			0
$147$	6.99688	−	0.209068i	0.577093	−	0.0172436i
$148$		0			0
$149$	15.6505	−	9.03581i	1.28214	−	0.740243i	0.304899	−	0.952385i	$-0.401377\pi$
$149$	15.6505	−	9.03581i	1.28214	−	0.740243i	0.977239	+	0.212142i	$0.0680440\pi$
$150$		0			0
$151$	0.599963	−	1.03917i	0.0488243	−	0.0845661i	−0.840580	−	0.541687i	$-0.817786\pi$
$151$	0.599963	−	1.03917i	0.0488243	−	0.0845661i	0.889405	+	0.457121i	$0.151119\pi$
$152$		0			0
$153$	1.83776	−	1.83776i	0.148574	−	0.148574i
$154$		0			0
$155$	7.21732	−	12.6329i	0.579709	−	1.01470i
$156$		0			0
$157$	0.683081	−	0.183031i	0.0545158	−	0.0146075i	−0.231458	−	0.972845i	$-0.574350\pi$
$157$	0.683081	−	0.183031i	0.0545158	−	0.0146075i	0.285974	+	0.958237i	$0.407683\pi$
$158$		0			0
$159$	2.25126	+	3.89930i	0.178537	+	0.309234i
$160$		0			0
$161$	−4.03573	−	9.34582i	−0.318060	−	0.736553i
$162$		0			0
$163$	0.884617	−	3.30144i	0.0692886	−	0.258588i	−0.922589	−	0.385784i	$-0.873931\pi$
$163$	0.884617	−	3.30144i	0.0692886	−	0.258588i	0.991878	+	0.127196i	$0.0405976\pi$
$164$		0			0
$165$	1.04970	−	3.98992i	0.0817189	−	0.310615i
$166$		0			0
$167$	4.49985	+	4.49985i	0.348209	+	0.348209i	0.859442	−	0.511233i	$-0.170811\pi$
$167$	4.49985	+	4.49985i	0.348209	+	0.348209i	−0.511233	+	0.859442i	$0.670811\pi$
$168$		0			0
$169$		−	33.3081i		−	2.56216i
$170$		0			0
$171$	−4.00554	−	2.31260i	−0.306311	−	0.176849i
$172$		0			0
$173$	24.3539	+	6.52561i	1.85159	+	0.496133i	0.999623	−	0.0274585i	$-0.00874140\pi$
$173$	24.3539	+	6.52561i	1.85159	+	0.496133i	0.851970	+	0.523591i	$0.175408\pi$
$174$		0			0
$175$	10.2986	−	8.30289i	0.778504	−	0.627639i
$176$		0			0
$177$	7.92622	+	2.12382i	0.595771	+	0.159636i
$178$		0			0
$179$	19.0980	+	11.0262i	1.42745	+	0.824137i	0.996919	−	0.0784393i	$-0.0249937\pi$
$179$	19.0980	+	11.0262i	1.42745	+	0.824137i	0.430529	+	0.902577i	$0.358327\pi$
$180$		0			0
$181$			24.6589i			1.83288i	0.400168	+	0.916442i	$0.368952\pi$
$181$			24.6589i			1.83288i	−0.400168	+	0.916442i	$0.631048\pi$
$182$		0			0
$183$	−4.54246	−	4.54246i	−0.335788	−	0.335788i
$184$		0			0
$185$	−4.62890	+	17.5945i	−0.340323	+	1.29358i
$186$		0			0
$187$	−1.24111	+	4.63190i	−0.0907593	+	0.338718i
$188$		0			0
$189$	2.62798	+	0.306125i	0.191158	+	0.0222673i
$190$		0			0
$191$	−12.3948	−	21.4685i	−0.896860	−	1.55341i	−0.831486	−	0.555546i	$-0.812509\pi$
$191$	−12.3948	−	21.4685i	−0.896860	−	1.55341i	−0.0653737	−	0.997861i	$-0.520824\pi$
$192$		0			0
$193$	13.4705	−	3.60942i	0.969631	−	0.259812i	0.260959	−	0.965350i	$-0.415961\pi$
$193$	13.4705	−	3.60942i	0.969631	−	0.259812i	0.708672	+	0.705538i	$0.249295\pi$
$194$		0			0
$195$	−7.54830	+	13.2123i	−0.540545	+	0.946149i
$196$		0			0
$197$	−1.09593	+	1.09593i	−0.0780819	+	0.0780819i	−0.745069	−	0.666987i	$-0.767584\pi$
$197$	−1.09593	+	1.09593i	−0.0780819	+	0.0780819i	0.666987	+	0.745069i	$0.267584\pi$
$198$		0			0
$199$	6.98766	−	12.1030i	0.495342	−	0.857957i	−0.504644	−	0.863328i	$-0.668376\pi$
$199$	6.98766	−	12.1030i	0.495342	−	0.857957i	0.999986	+	0.00537047i	$0.00170948\pi$
$200$		0			0
$201$	5.54134	−	3.19929i	0.390856	−	0.225661i
$202$		0			0
$203$	−4.24465	−	5.36392i	−0.297916	−	0.376474i
$204$		0			0
$205$	16.1704	−	0.0734402i	1.12939	−	0.00512928i
$206$		0			0
$207$	−0.995848	−	3.71655i	−0.0692162	−	0.258318i
$208$		0			0
$209$	8.53380			0.590295
$210$		0			0
$211$	−10.1097			−0.695978			−0.347989	−	0.937499i	$-0.613135\pi$
$211$	−10.1097			−0.695978			−0.347989	+	0.937499i	$0.613135\pi$
$212$		0			0
$213$	−2.25383	−	8.41141i	−0.154430	−	0.576340i
$214$		0			0
$215$	−0.742424	+	0.749198i	−0.0506329	+	0.0510949i
$216$		0			0
$217$	−17.0322	+	2.50165i	−1.15622	+	0.169823i
$218$		0			0
$219$	2.72040	−	1.57062i	0.183827	−	0.106133i
$220$		0			0
$221$	8.84305	−	15.3166i	0.594848	−	1.03031i
$222$		0			0
$223$	−20.7866	+	20.7866i	−1.39197	+	1.39197i	−0.571070	+	0.820901i	$0.693472\pi$
$223$	−20.7866	+	20.7866i	−1.39197	+	1.39197i	−0.820901	+	0.571070i	$0.806528\pi$
$224$		0			0
$225$	4.30724	−	2.53923i	0.287149	−	0.169282i
$226$		0			0
$227$	8.55694	−	2.29283i	0.567944	−	0.152180i	0.0365905	−	0.999330i	$-0.488350\pi$
$227$	8.55694	−	2.29283i	0.567944	−	0.152180i	0.531354	+	0.847150i	$0.321684\pi$
$228$		0			0
$229$	−6.08921	−	10.5468i	−0.402386	−	0.696953i	0.591627	−	0.806212i	$-0.298486\pi$
$229$	−6.08921	−	10.5468i	−0.402386	−	0.696953i	−0.994013	+	0.109258i	$0.965152\pi$
$230$		0			0
$231$	−4.48159	+	1.93525i	−0.294867	+	0.127330i
$232$		0			0
$233$	4.10496	−	15.3199i	0.268925	−	1.00364i	−0.690880	−	0.722970i	$-0.742777\pi$
$233$	4.10496	−	15.3199i	0.268925	−	1.00364i	0.959804	−	0.280671i	$-0.0905568\pi$
$234$		0			0
$235$	8.91779	+	2.34616i	0.581732	+	0.153046i
$236$		0			0
$237$	−5.50756	−	5.50756i	−0.357755	−	0.357755i
$238$		0			0
$239$		−	20.9394i		−	1.35446i	−0.735773	−	0.677228i	$-0.763181\pi$
$239$		−	20.9394i		−	1.35446i	0.735773	−	0.677228i	$-0.236819\pi$
$240$		0			0
$241$	−18.2216	−	10.5203i	−1.17376	−	0.677670i	−0.219196	−	0.975681i	$-0.570344\pi$
$241$	−18.2216	−	10.5203i	−1.17376	−	0.677670i	−0.954563	+	0.298011i	$0.903677\pi$
$242$		0			0
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$		0			0
$245$	−15.2496	−	3.52857i	−0.974259	−	0.225432i
$246$		0			0
$247$	−30.4020	−	8.14620i	−1.93444	−	0.518330i
$248$		0			0
$249$	−0.835252	−	0.482233i	−0.0529319	−	0.0305603i
$250$		0			0
$251$			15.0184i			0.947950i	0.880538	+	0.473975i	$0.157181\pi$
$251$			15.0184i			0.947950i	−0.880538	+	0.473975i	$0.842819\pi$
$252$		0			0
$253$	5.01988	+	5.01988i	0.315597	+	0.315597i
$254$		0			0
$255$	−5.01966	+	2.92858i	−0.314343	+	0.183395i
$256$		0			0
$257$	3.48224	−	12.9959i	0.217216	−	0.810663i	−0.768158	−	0.640260i	$-0.778827\pi$
$257$	3.48224	−	12.9959i	0.217216	−	0.810663i	0.985375	−	0.170403i	$-0.0545068\pi$
$258$		0			0
$259$	19.7627	−	8.53396i	1.22799	−	0.530274i
$260$		0			0
$261$	−1.29268	−	2.23899i	−0.0800150	−	0.138590i
$262$		0			0
$263$	−14.0656	+	3.76888i	−0.867324	+	0.232399i	−0.664930	−	0.746905i	$-0.731539\pi$
$263$	−14.0656	+	3.76888i	−0.867324	+	0.232399i	−0.202394	+	0.979304i	$0.564872\pi$
$264$		0			0
$265$	−2.64992	−	9.71295i	−0.162783	−	0.596662i
$266$		0			0
$267$	−0.933298	+	0.933298i	−0.0571169	+	0.0571169i
$268$		0			0
$269$	−12.0245	+	20.8271i	−0.733147	+	1.26985i	0.222384	+	0.974959i	$0.428616\pi$
$269$	−12.0245	+	20.8271i	−0.733147	+	1.26985i	−0.955532	+	0.294889i	$0.904717\pi$
$270$		0			0
$271$	−6.31280	+	3.64470i	−0.383475	+	0.221400i	−0.679329	−	0.733834i	$-0.737729\pi$
$271$	−6.31280	+	3.64470i	−0.383475	+	0.221400i	0.295854	+	0.955233i	$0.404396\pi$
$272$		0			0
$273$	17.8132	−	2.61637i	1.07811	−	0.158350i
$274$		0			0
$275$	−4.53991	+	8.03094i	−0.273767	+	0.484284i
$276$		0			0
$277$	−1.37637	−	5.13667i	−0.0826979	−	0.308633i	0.912170	−	0.409811i	$-0.134405\pi$
$277$	−1.37637	−	5.13667i	−0.0826979	−	0.308633i	−0.994868	+	0.101178i	$0.967739\pi$
$278$		0			0
$279$	−6.50662			−0.389541
$280$		0			0
$281$	−12.7351			−0.759714			−0.379857	−	0.925045i	$-0.624027\pi$
$281$	−12.7351			−0.759714			−0.379857	+	0.925045i	$0.624027\pi$
$282$		0			0
$283$	7.83365	+	29.2356i	0.465662	+	1.73788i	0.654684	+	0.755903i	$0.272802\pi$
$283$	7.83365	+	29.2356i	0.465662	+	1.73788i	−0.189021	+	0.981973i	$0.560532\pi$
$284$		0			0
$285$	7.34622	+	7.27979i	0.435153	+	0.431218i
$286$		0			0
$287$	−11.8730	−	15.0038i	−0.700841	−	0.885646i
$288$		0			0
$289$	−8.87268	+	5.12264i	−0.521922	+	0.301332i
$290$		0			0
$291$	7.18347	−	12.4421i	0.421102	−	0.729371i
$292$		0			0
$293$	16.6287	−	16.6287i	0.971457	−	0.971457i	−0.0281472	−	0.999604i	$-0.508961\pi$
$293$	16.6287	−	16.6287i	0.971457	−	0.971457i	0.999604	+	0.0281472i	$0.00896073\pi$
$294$		0			0
$295$	−15.9320	−	9.10213i	−0.927598	−	0.529947i
$296$		0			0
$297$	−1.78220	+	0.477538i	−0.103414	+	0.0277096i
$298$		0			0
$299$	−13.0917	−	22.6754i	−0.757111	−	1.31135i
$300$		0			0
$301$	1.23961	+	0.144398i	0.0714500	+	0.00832298i
$302$		0			0
$303$	0.441391	−	1.64729i	0.0253572	−	0.0946345i
$304$		0			0
$305$	7.23869	+	12.4073i	0.414486	+	0.710440i
$306$		0			0
$307$	22.7973	+	22.7973i	1.30111	+	1.30111i	0.927644	+	0.373465i	$0.121830\pi$
$307$	22.7973	+	22.7973i	1.30111	+	1.30111i	0.373465	+	0.927644i	$0.378170\pi$
$308$		0			0
$309$			12.9938i			0.739194i
$310$		0			0
$311$	9.06971	+	5.23640i	0.514296	+	0.296929i	0.734598	−	0.678503i	$-0.237371\pi$
$311$	9.06971	+	5.23640i	0.514296	+	0.296929i	−0.220302	+	0.975432i	$0.570704\pi$
$312$		0			0
$313$	17.6280	+	4.72341i	0.996395	+	0.266983i	0.719934	−	0.694042i	$-0.244172\pi$
$313$	17.6280	+	4.72341i	0.996395	+	0.266983i	0.276460	+	0.961025i	$0.410839\pi$
$314$		0			0
$315$	−5.50880	−	2.15711i	−0.310386	−	0.121539i
$316$		0			0
$317$	−4.85327	−	1.30043i	−0.272587	−	0.0730394i	0.119936	−	0.992782i	$-0.461731\pi$
$317$	−4.85327	−	1.30043i	−0.272587	−	0.0730394i	−0.392523	+	0.919742i	$0.628398\pi$
$318$		0			0
$319$	4.13109	+	2.38508i	0.231296	+	0.133539i
$320$		0			0
$321$			12.2968i			0.686340i
$322$		0			0
$323$	−8.50000	−	8.50000i	−0.472953	−	0.472953i
$324$		0			0
$325$	23.8398	−	24.2769i	1.32239	−	1.34664i
$326$		0			0
$327$	0.870789	−	3.24983i	0.0481547	−	0.179716i
$328$		0			0
$329$	−4.32544	−	10.0167i	−0.238469	−	0.552239i
$330$		0			0
$331$	7.83310	+	13.5673i	0.430546	+	0.745728i	0.996920	−	0.0784204i	$-0.0249876\pi$
$331$	7.83310	+	13.5673i	0.430546	+	0.745728i	−0.566374	+	0.824148i	$0.691654\pi$
$332$		0			0
$333$	7.85903	−	2.10582i	0.430672	−	0.115398i
$334$		0			0
$335$	−13.8032	+	3.76583i	−0.754149	+	0.205749i
$336$		0			0
$337$	−7.66529	+	7.66529i	−0.417555	+	0.417555i	−0.884360	−	0.466805i	$-0.845405\pi$
$337$	−7.66529	+	7.66529i	−0.417555	+	0.417555i	0.466805	+	0.884360i	$0.345405\pi$
$338$		0			0
$339$	9.14924	−	15.8470i	0.496919	−	0.860688i
$340$		0			0
$341$	10.3968	−	6.00257i	0.563016	−	0.325057i
$342$		0			0
$343$	7.84669	+	16.7759i	0.423682	+	0.905811i
$344$		0			0
$345$	0.0390742	+	8.60354i	0.00210368	+	0.463199i
$346$		0			0
$347$	6.64247	+	24.7900i	0.356587	+	1.33080i	0.878476	+	0.477786i	$0.158561\pi$
$347$	6.64247	+	24.7900i	0.356587	+	1.33080i	−0.521890	+	0.853013i	$0.674773\pi$
$348$		0			0
$349$	−9.53988			−0.510658			−0.255329	−	0.966854i	$-0.582184\pi$
$349$	−9.53988			−0.510658			−0.255329	+	0.966854i	$0.582184\pi$
$350$		0			0
$351$	6.80500			0.363224
$352$		0			0
$353$	9.68151	+	36.1319i	0.515295	+	1.92311i	0.349453	+	0.936954i	$0.386368\pi$
$353$	9.68151	+	36.1319i	0.515295	+	1.92311i	0.165842	+	0.986152i	$0.446966\pi$
$354$		0			0
$355$	0.0884338	+	19.4718i	0.00469358	+	1.03345i
$356$		0			0
$357$	6.39143	+	2.53626i	0.338270	+	0.134233i
$358$		0			0
$359$	−0.601952	+	0.347537i	−0.0317698	+	0.0183423i	−0.515801	−	0.856709i	$-0.672506\pi$
$359$	−0.601952	+	0.347537i	−0.0317698	+	0.0183423i	0.484031	+	0.875051i	$0.339172\pi$
$360$		0			0
$361$	−1.19624	+	2.07194i	−0.0629598	+	0.109050i
$362$		0			0
$363$	−5.37099	+	5.37099i	−0.281904	+	0.281904i
$364$		0			0
$365$	−6.77637	+	1.84875i	−0.354692	+	0.0967680i
$366$		0			0
$367$	−16.2014	+	4.34114i	−0.845705	+	0.226606i	−0.655553	−	0.755149i	$-0.727565\pi$
$367$	−16.2014	+	4.34114i	−0.845705	+	0.226606i	−0.190151	+	0.981755i	$0.560898\pi$
$368$		0			0
$369$	−3.61585	−	6.26283i	−0.188234	−	0.326030i
$370$		0			0
$371$	−7.10994	+	9.55812i	−0.369130	+	0.496233i
$372$		0			0
$373$	0.671018	−	2.50427i	0.0347440	−	0.129666i	−0.946376	−	0.323069i	$-0.895286\pi$
$373$	0.671018	−	2.50427i	0.0347440	−	0.129666i	0.981120	+	0.193402i	$0.0619522\pi$
$374$		0			0
$375$	−10.7590	+	3.04055i	−0.555590	+	0.157013i
$376$		0			0
$377$	−12.4404	−	12.4404i	−0.640714	−	0.640714i
$378$		0			0
$379$		−	2.58019i		−	0.132535i	−0.997802	−	0.0662676i	$-0.978891\pi$
$379$		−	2.58019i		−	0.132535i	0.997802	−	0.0662676i	$-0.0211091\pi$
$380$		0			0
$381$	−11.2720	−	6.50791i	−0.577484	−	0.333410i
$382$		0			0
$383$	9.40464	+	2.51997i	0.480555	+	0.128764i	0.490961	−	0.871182i	$-0.336646\pi$
$383$	9.40464	+	2.51997i	0.480555	+	0.128764i	−0.0104062	+	0.999946i	$0.503312\pi$
$384$		0			0
$385$	10.7924	−	1.63527i	0.550030	−	0.0833410i
$386$		0			0
$387$	0.455625	+	0.122084i	0.0231607	+	0.00620589i
$388$		0			0
$389$	−2.03441	−	1.17457i	−0.103149	−	0.0595531i	0.447538	−	0.894265i	$-0.352301\pi$
$389$	−2.03441	−	1.17457i	−0.103149	−	0.0595531i	−0.550687	+	0.834712i	$0.685634\pi$
$390$		0			0
$391$		−	10.0000i		−	0.505722i
$392$		0			0
$393$	−3.28621	−	3.28621i	−0.165767	−	0.165767i
$394$		0			0
$395$	8.77663	+	15.0434i	0.441600	+	0.756915i
$396$		0			0
$397$	8.71857	−	32.5381i	0.437572	−	1.63304i	−0.297262	−	0.954796i	$-0.596074\pi$
$397$	8.71857	−	32.5381i	0.437572	−	1.63304i	0.734835	−	0.678246i	$-0.237260\pi$
$398$		0			0
$399$	1.41589	−	12.1549i	0.0708831	−	0.608508i
$400$		0			0
$401$	16.9813	+	29.4124i	0.848004	+	1.46879i	0.882987	+	0.469398i	$0.155529\pi$
$401$	16.9813	+	29.4124i	0.848004	+	1.46879i	−0.0349828	+	0.999388i	$0.511138\pi$
$402$		0			0
$403$	−42.7688	+	11.4599i	−2.13047	+	0.570857i
$404$		0			0
$405$	−1.94155	−	1.10923i	−0.0964764	−	0.0551180i
$406$		0			0
$407$	−10.6151	+	10.6151i	−0.526169	+	0.526169i
$408$		0			0
$409$	−5.63530	+	9.76063i	−0.278648	+	0.482632i	−0.971049	−	0.238881i	$-0.923220\pi$
$409$	−5.63530	+	9.76063i	−0.278648	+	0.482632i	0.692401	+	0.721513i	$0.256553\pi$
$410$		0			0
$411$	−11.5200	+	6.65107i	−0.568239	+	0.328073i
$412$		0			0
$413$	3.15496	+	21.4801i	0.155245	+	1.05697i
$414$		0			0
$415$	1.53186	+	1.51801i	0.0751962	+	0.0745163i
$416$		0			0
$417$	5.23420	+	19.5343i	0.256320	+	0.956600i
$418$		0			0
$419$	−35.0802			−1.71378			−0.856890	−	0.515500i	$-0.827606\pi$
$419$	−35.0802			−1.71378			−0.856890	+	0.515500i	$0.827606\pi$
$420$		0			0
$421$	−16.9301			−0.825123			−0.412561	−	0.910930i	$-0.635366\pi$
$421$	−16.9301			−0.825123			−0.412561	+	0.910930i	$0.635366\pi$
$422$		0			0
$423$	−1.06734	−	3.98335i	−0.0518956	−	0.193677i
$424$		0			0
$425$	12.5211	−	3.47721i	0.607361	−	0.168669i
$426$		0			0
$427$	6.26897	−	15.7980i	0.303377	−	0.764517i
$428$		0			0
$429$	−10.8735	+	6.27784i	−0.524980	+	0.303097i
$430$		0			0
$431$	4.81829	−	8.34553i	0.232089	−	0.401990i	−0.726334	−	0.687342i	$-0.758777\pi$
$431$	4.81829	−	8.34553i	0.232089	−	0.401990i	0.958423	+	0.285352i	$0.0921106\pi$
$432$		0			0
$433$	−19.5507	+	19.5507i	−0.939547	+	0.939547i	−0.998274	−	0.0587275i	$-0.981296\pi$
$433$	−19.5507	+	19.5507i	−0.939547	+	0.939547i	0.0587275	+	0.998274i	$0.481296\pi$
$434$		0			0
$435$	1.52159	+	5.57721i	0.0729547	+	0.267407i
$436$		0			0
$437$	−17.1898	+	4.60599i	−0.822300	+	0.220335i
$438$		0			0
$439$	14.3141	+	24.7928i	0.683177	+	1.18330i	0.974006	+	0.226522i	$0.0727354\pi$
$439$	14.3141	+	24.7928i	0.683177	+	1.18330i	−0.290830	+	0.956775i	$0.593931\pi$
$440$		0			0
$441$	2.01287	+	6.70435i	0.0958509	+	0.319255i
$442$		0			0
$443$	3.98556	−	14.8743i	0.189360	−	0.706701i	−0.804295	−	0.594230i	$-0.797457\pi$
$443$	3.98556	−	14.8743i	0.189360	−	0.706701i	0.993655	−	0.112471i	$-0.0358764\pi$
$444$		0			0
$445$	2.54921	−	1.48727i	0.120844	−	0.0705032i
$446$		0			0
$447$	12.7786	+	12.7786i	0.604406	+	0.604406i
$448$		0			0
$449$		−	1.49829i		−	0.0707086i	−0.999375	−	0.0353543i	$-0.988744\pi$
$449$		−	1.49829i		−	0.0707086i	0.999375	−	0.0353543i	$-0.0112560\pi$
$450$		0			0
$451$	11.5553	+	6.67148i	0.544120	+	0.314148i
$452$		0			0
$453$	1.15904	+	0.310563i	0.0544564	+	0.0145915i
$454$		0			0
$455$	−40.0093	−	4.47647i	−1.87567	−	0.209860i
$456$		0			0
$457$	−23.6542	−	6.33813i	−1.10650	−	0.296485i	−0.341090	−	0.940031i	$-0.610796\pi$
$457$	−23.6542	−	6.33813i	−1.10650	−	0.296485i	−0.765408	+	0.643545i	$0.777463\pi$
$458$		0			0
$459$	2.25079	+	1.29949i	0.105058	+	0.0606551i
$460$		0			0
$461$		−	29.0857i		−	1.35465i	−0.735682	−	0.677327i	$-0.763138\pi$
$461$		−	29.0857i		−	1.35465i	0.735682	−	0.677327i	$-0.236862\pi$
$462$		0			0
$463$	14.6935	+	14.6935i	0.682865	+	0.682865i	0.960645	−	0.277780i	$-0.0895985\pi$
$463$	14.6935	+	14.6935i	0.682865	+	0.682865i	−0.277780	+	0.960645i	$0.589599\pi$
$464$		0			0
$465$	14.0704	+	3.70176i	0.652501	+	0.171665i
$466$		0			0
$467$	−0.445798	+	1.66374i	−0.0206291	+	0.0769887i	−0.975473	−	0.220119i	$-0.929355\pi$
$467$	−0.445798	+	1.66374i	−0.0206291	+	0.0769887i	0.954844	+	0.297108i	$0.0960221\pi$
$468$		0			0
$469$	13.5832	+	10.1040i	0.627212	+	0.466561i
$470$		0			0
$471$	0.353589	+	0.612434i	0.0162925	+	0.0282195i
$472$		0			0
$473$	−0.840658	+	0.225254i	−0.0386535	+	0.0103572i
$474$		0			0
$475$	−11.7444	−	19.9218i	−0.538872	−	0.914077i
$476$		0			0
$477$	−3.18376	+	3.18376i	−0.145774	+	0.145774i
$478$		0			0
$479$	−20.7120	+	35.8742i	−0.946355	+	1.63913i	−0.193338	+	0.981132i	$0.561932\pi$
$479$	−20.7120	+	35.8742i	−0.946355	+	1.63913i	−0.753016	+	0.658002i	$0.771402\pi$
$480$		0			0
$481$	47.9495	−	27.6837i	2.18631	−	1.26227i
$482$		0			0
$483$	7.98284	−	6.31709i	0.363232	−	0.287438i
$484$		0			0
$485$	−22.6127	+	22.8190i	−1.02679	+	1.03616i
$486$		0			0
$487$	−0.749951	−	2.79886i	−0.0339835	−	0.126828i	0.946850	−	0.321675i	$-0.104246\pi$
$487$	−0.749951	−	2.79886i	−0.0339835	−	0.126828i	−0.980834	+	0.194847i	$0.937579\pi$
$488$		0			0
$489$	3.41790			0.154563
$490$		0			0
$491$	−5.54659			−0.250314			−0.125157	−	0.992137i	$-0.539943\pi$
$491$	−5.54659			−0.250314			−0.125157	+	0.992137i	$0.539943\pi$
$492$		0			0
$493$	−1.73909	−	6.49036i	−0.0783245	−	0.292311i
$494$		0			0
$495$	4.12565	−	0.0187372i	0.185434	−	0.000842176i
$496$		0			0
$497$	18.0670	−	14.2970i	0.810415	−	0.641309i
$498$		0			0
$499$	2.26033	−	1.30500i	0.101186	−	0.0584199i	−0.448553	−	0.893756i	$-0.648060\pi$
$499$	2.26033	−	1.30500i	0.101186	−	0.0584199i	0.549739	+	0.835336i	$0.314727\pi$
$500$		0			0
$501$	−3.18188	+	5.51117i	−0.142156	+	0.246221i
$502$		0			0
$503$	−25.6046	+	25.6046i	−1.14165	+	1.14165i	−0.153507	+	0.988148i	$0.549057\pi$
$503$	−25.6046	+	25.6046i	−1.14165	+	1.14165i	−0.988148	+	0.153507i	$0.950943\pi$
$504$		0			0
$505$	−1.89168	+	3.31112i	−0.0841787	+	0.147343i
$506$		0			0
$507$	32.1731	−	8.62077i	1.42886	−	0.382862i
$508$		0			0
$509$	−7.10908	−	12.3133i	−0.315104	−	0.545777i	0.664355	−	0.747417i	$-0.268706\pi$
$509$	−7.10908	−	12.3133i	−0.315104	−	0.545777i	−0.979460	+	0.201640i	$0.935373\pi$
$510$		0			0
$511$	6.66835	+	4.96035i	0.294990	+	0.219433i
$512$		0			0
$513$	1.19709	−	4.46760i	0.0528528	−	0.197249i
$514$		0			0
$515$	7.39248	−	28.0990i	0.325752	−	1.23819i
$516$		0			0
$517$	5.38024	+	5.38024i	0.236623	+	0.236623i
$518$		0			0
$519$			25.2130i			1.10673i
$520$		0			0
$521$	−31.4173	−	18.1388i	−1.37642	−	0.794676i	−0.384693	−	0.923045i	$-0.625693\pi$
$521$	−31.4173	−	18.1388i	−1.37642	−	0.794676i	−0.991726	+	0.128369i	$0.959026\pi$
$522$		0			0
$523$	−10.4329	−	2.79549i	−0.456200	−	0.122238i	0.0233990	−	0.999726i	$-0.492551\pi$
$523$	−10.4329	−	2.79549i	−0.456200	−	0.122238i	−0.479599	+	0.877488i	$0.659218\pi$
$524$		0			0
$525$	10.6855	+	7.79878i	0.466352	+	0.340367i
$526$		0			0
$527$	−16.3344	−	4.37678i	−0.711537	−	0.190656i
$528$		0			0
$529$	7.09753	+	4.09776i	0.308588	+	0.178163i
$530$		0			0
$531$			8.20583i			0.356103i
$532$		0			0
$533$	−34.7980	−	34.7980i	−1.50727	−	1.50727i
$534$		0			0
$535$	6.99591	−	26.5916i	0.302460	−	1.14965i
$536$		0			0
$537$	−5.70758	+	21.3010i	−0.246300	+	0.919206i
$538$		0			0
$539$	−9.40130	−	8.85578i	−0.404943	−	0.381445i
$540$		0			0
$541$	16.0657	+	27.8266i	0.690719	+	1.19636i	0.971603	+	0.236618i	$0.0760390\pi$
$541$	16.0657	+	27.8266i	0.690719	+	1.19636i	−0.280884	+	0.959742i	$0.590628\pi$
$542$		0			0
$543$	−23.8187	+	6.38220i	−1.02216	+	0.273886i
$544$		0			0
$545$	−3.73196	+	6.53229i	−0.159860	+	0.279812i
$546$		0			0
$547$	5.85090	−	5.85090i	0.250166	−	0.250166i	−0.570872	−	0.821039i	$-0.693395\pi$
$547$	5.85090	−	5.85090i	0.250166	−	0.250166i	0.821039	+	0.570872i	$0.193395\pi$
$548$		0			0
$549$	3.21201	−	5.56336i	0.137085	−	0.237438i
$550$		0			0
$551$	−10.3558	+	5.97891i	−0.441171	+	0.254710i
$552$		0			0
$553$	7.60089	−	19.1544i	0.323223	−	0.814529i
$554$		0			0
$555$	−18.1931	+	0.0826264i	−0.772252	+	0.00350729i
$556$		0			0
$557$	−6.97465	−	26.0298i	−0.295525	−	1.10292i	−0.940799	−	0.338965i	$-0.889923\pi$
$557$	−6.97465	−	26.0298i	−0.295525	−	1.10292i	0.645274	−	0.763951i	$-0.276743\pi$
$558$		0			0
$559$	3.20990			0.135764
$560$		0			0
$561$	−4.79530			−0.202458
$562$		0			0
$563$	−6.45205	−	24.0794i	−0.271921	−	1.01482i	−0.957876	−	0.287181i	$-0.907282\pi$
$563$	−6.45205	−	24.0794i	−0.271921	−	1.01482i	0.685955	−	0.727644i	$-0.259385\pi$
$564$		0			0
$565$	−28.8007	+	29.0635i	−1.21166	+	1.22271i
$566$		0			0
$567$	0.384478	+	2.61767i	0.0161465	+	0.109932i
$568$		0			0
$569$	−14.7838	+	8.53545i	−0.619770	+	0.357825i	−0.776780	−	0.629773i	$-0.783148\pi$
$569$	−14.7838	+	8.53545i	−0.619770	+	0.357825i	0.157009	+	0.987597i	$0.449815\pi$
$570$		0			0
$571$	3.24772	−	5.62522i	0.135913	−	0.235408i	−0.790033	−	0.613064i	$-0.789937\pi$
$571$	3.24772	−	5.62522i	0.135913	−	0.235408i	0.925946	+	0.377656i	$0.123270\pi$
$572$		0			0
$573$	17.5290	−	17.5290i	0.732283	−	0.732283i
$574$		0			0
$575$	4.81024	−	18.6272i	0.200601	−	0.776809i
$576$		0			0
$577$	−13.2903	+	3.56113i	−0.553284	+	0.148252i	−0.524619	−	0.851337i	$-0.675792\pi$
$577$	−13.2903	+	3.56113i	−0.553284	+	0.148252i	−0.0286647	+	0.999589i	$0.509126\pi$
$578$		0			0
$579$	6.97287	+	12.0774i	0.289782	+	0.501918i
$580$		0			0
$581$	0.295247	−	2.53460i	0.0122489	−	0.105153i
$582$		0			0
$583$	2.15013	−	8.02438i	0.0890491	−	0.332336i
$584$		0			0
$585$	−14.7157	−	3.87152i	−0.608419	−	0.160067i
$586$		0			0
$587$	12.8207	+	12.8207i	0.529169	+	0.529169i	0.920325	−	0.391156i	$-0.127925\pi$
$587$	12.8207	+	12.8207i	0.529169	+	0.529169i	−0.391156	+	0.920325i	$0.627925\pi$
$588$		0			0
$589$			30.0944i			1.24002i
$590$		0			0
$591$	−1.34224	−	0.774940i	−0.0552122	−	0.0318768i
$592$		0			0
$593$	3.44851	+	0.924024i	0.141613	+	0.0379451i	0.328929	−	0.944355i	$-0.393312\pi$
$593$	3.44851	+	0.924024i	0.141613	+	0.0379451i	−0.187316	+	0.982300i	$0.559979\pi$
$594$		0			0
$595$	−12.3784	−	9.12084i	−0.507466	−	0.373918i
$596$		0			0
$597$	13.4991	+	3.61708i	0.552482	+	0.148037i
$598$		0			0
$599$	2.21549	+	1.27911i	0.0905225	+	0.0522632i	0.544578	−	0.838710i	$-0.316690\pi$
$599$	2.21549	+	1.27911i	0.0905225	+	0.0522632i	−0.454055	+	0.890973i	$0.650023\pi$
$600$		0			0
$601$			23.0850i			0.941656i	0.882225	+	0.470828i	$0.156045\pi$
$601$			23.0850i			0.941656i	−0.882225	+	0.470828i	$0.843955\pi$
$602$		0			0
$603$	4.52449	+	4.52449i	0.184251	+	0.184251i
$604$		0			0
$605$	14.6703	−	8.55900i	0.596434	−	0.347973i
$606$		0			0
$607$	3.94371	−	14.7181i	0.160070	−	0.597390i	−0.838548	−	0.544828i	$-0.816595\pi$
$607$	3.94371	−	14.7181i	0.160070	−	0.597390i	0.998618	−	0.0525616i	$-0.0167386\pi$
$608$		0			0
$609$	4.08255	−	5.48830i	0.165433	−	0.222397i
$610$		0			0
$611$	−14.0315	−	24.3032i	−0.567653	−	0.983203i
$612$		0			0
$613$	−28.9598	+	7.75975i	−1.16967	+	0.313413i	−0.790823	−	0.612044i	$-0.790347\pi$
$613$	−28.9598	+	7.75975i	−1.16967	+	0.313413i	−0.378851	+	0.925458i	$0.623681\pi$
$614$		0			0
$615$	4.25615	+	15.6004i	0.171624	+	0.629069i
$616$		0			0
$617$	20.8619	−	20.8619i	0.839867	−	0.839867i	−0.148974	−	0.988841i	$-0.547597\pi$
$617$	20.8619	−	20.8619i	0.839867	−	0.839867i	0.988841	+	0.148974i	$0.0475971\pi$
$618$		0			0
$619$	−1.95304	+	3.38276i	−0.0784993	+	0.135965i	−0.902603	−	0.430475i	$-0.858346\pi$
$619$	−1.95304	+	3.38276i	−0.0784993	+	0.135965i	0.824103	+	0.566439i	$0.191680\pi$
$620$		0			0
$621$	3.33217	−	1.92383i	0.133715	−	0.0772006i
$622$		0			0
$623$	−3.24586	−	1.28803i	−0.130043	−	0.0516038i
$624$		0			0
$625$	24.9959	−	0.454136i	0.999835	−	0.0181654i
$626$		0			0
$627$	2.20871	+	8.24302i	0.0882074	+	0.329194i
$628$		0			0
$629$	21.1460			0.843147
$630$		0			0
$631$	3.08630			0.122864			0.0614318	−	0.998111i	$-0.480433\pi$
$631$	3.08630			0.122864			0.0614318	+	0.998111i	$0.480433\pi$
$632$		0			0
$633$	−2.61657	−	9.76519i	−0.103999	−	0.388131i
$634$		0			0
$635$	20.6731	+	20.4861i	0.820386	+	0.812968i
$636$		0			0
$637$	25.0390	+	40.5234i	0.992081	+	1.60560i
$638$		0			0
$639$	7.54146	−	4.35406i	0.298336	−	0.172244i
$640$		0			0
$641$	11.7935	−	20.4270i	0.465816	−	0.806817i	−0.533422	−	0.845849i	$-0.679094\pi$
$641$	11.7935	−	20.4270i	0.465816	−	0.806817i	0.999238	+	0.0390324i	$0.0124276\pi$
$642$		0			0
$643$	16.3072	−	16.3072i	0.643092	−	0.643092i	−0.308222	−	0.951314i	$-0.599734\pi$
$643$	16.3072	−	16.3072i	0.643092	−	0.643092i	0.951314	+	0.308222i	$0.0997340\pi$
$644$		0			0
$645$	−0.915823	−	0.523220i	−0.0360605	−	0.0206018i
$646$		0			0
$647$	20.5609	−	5.50928i	0.808333	−	0.216592i	0.169093	−	0.985600i	$-0.445916\pi$
$647$	20.5609	−	5.50928i	0.808333	−	0.216592i	0.639239	+	0.769008i	$0.279249\pi$
$648$		0			0
$649$	−7.57015	−	13.1119i	−0.297154	−	0.514686i
$650$		0			0
$651$	−6.82465	−	15.8043i	−0.267479	−	0.619420i
$652$		0			0
$653$	4.79324	−	17.8886i	0.187574	−	0.700036i	−0.806491	−	0.591247i	$-0.798636\pi$
$653$	4.79324	−	17.8886i	0.187574	−	0.700036i	0.994065	−	0.108789i	$-0.0346973\pi$
$654$		0			0
$655$	5.23678	+	8.97597i	0.204618	+	0.350720i
$656$		0			0
$657$	2.22120	+	2.22120i	0.0866571	+	0.0866571i
$658$		0			0
$659$			29.9043i			1.16491i	0.812865	+	0.582453i	$0.197907\pi$
$659$			29.9043i			1.16491i	−0.812865	+	0.582453i	$0.802093\pi$
$660$		0			0
$661$	15.7238	+	9.07814i	0.611585	+	0.353099i	0.773586	−	0.633692i	$-0.218461\pi$
$661$	15.7238	+	9.07814i	0.611585	+	0.353099i	−0.162000	+	0.986791i	$0.551795\pi$
$662$		0			0
$663$	17.0835	+	4.57750i	0.663466	+	0.177775i
$664$		0			0
$665$	−9.97704	+	25.4793i	−0.386893	+	0.988045i
$666$		0			0
$667$	−9.60864	−	2.57463i	−0.372048	−	0.0996900i
$668$		0			0
$669$	−25.4582	−	14.6983i	−0.984272	−	0.568270i
$670$		0			0
$671$			11.8527i			0.457569i
$672$		0			0
$673$	9.53778	+	9.53778i	0.367654	+	0.367654i	0.866621	−	0.498967i	$-0.166287\pi$
$673$	9.53778	+	9.53778i	0.367654	+	0.367654i	−0.498967	+	0.866621i	$0.666287\pi$
$674$		0			0
$675$	3.56750	+	3.50327i	0.137313	+	0.134841i
$676$		0			0
$677$	6.47060	−	24.1486i	0.248685	−	0.928106i	−0.722810	−	0.691047i	$-0.757150\pi$
$677$	6.47060	−	24.1486i	0.248685	−	0.928106i	0.971495	−	0.237059i	$-0.0761835\pi$
$678$		0			0
$679$	37.7560	+	4.39808i	1.44894	+	0.168783i
$680$		0			0
$681$	4.42940	+	7.67194i	0.169735	+	0.293989i
$682$		0			0
$683$	40.6157	−	10.8829i	1.55412	−	0.416424i	0.623322	−	0.781966i	$-0.285783\pi$
$683$	40.6157	−	10.8829i	1.55412	−	0.416424i	0.930795	+	0.365541i	$0.119116\pi$
$684$		0			0
$685$	28.6957	−	7.82884i	1.09641	−	0.299125i
$686$		0			0
$687$	8.61144	−	8.61144i	0.328547	−	0.328547i
$688$		0			0
$689$	−15.3198	+	26.5347i	−0.583639	+	1.01089i
$690$		0			0
$691$	−21.3081	+	12.3022i	−0.810598	+	0.467999i	−0.847164	−	0.531332i	$-0.821692\pi$
$691$	−21.3081	+	12.3022i	−0.810598	+	0.467999i	0.0365653	+	0.999331i	$0.488358\pi$
$692$		0			0
$693$	−3.02923	−	3.82801i	−0.115071	−	0.145414i
$694$		0			0
$695$	−0.205375	−	45.2205i	−0.00779032	−	1.71531i
$696$		0			0
$697$	−4.86452	−	18.1546i	−0.184257	−	0.687656i
$698$		0			0
$699$	15.8603			0.599893
$700$		0			0
$701$	5.48135			0.207028			0.103514	−	0.994628i	$-0.466991\pi$
$701$	5.48135			0.207028			0.103514	+	0.994628i	$0.466991\pi$
$702$		0			0
$703$	−9.73984	−	36.3496i	−0.367345	−	1.37095i
$704$		0			0
$705$	0.0418792	+	9.22115i	0.00157726	+	0.347289i
$706$		0			0
$707$	4.46418	−	0.655690i	0.167893	−	0.0246597i
$708$		0			0
$709$	4.20161	−	2.42580i	0.157795	−	0.0911028i	−0.419023	−	0.907975i	$-0.637627\pi$
$709$	4.20161	−	2.42580i	0.157795	−	0.0911028i	0.576818	+	0.816873i	$0.304294\pi$
$710$		0			0
$711$	3.89444	−	6.74536i	0.146053	−	0.252971i
$712$		0			0
$713$	−17.7026	+	17.7026i	−0.662967	+	0.662967i
$714$		0			0
$715$	27.0854	−	7.38953i	1.01294	−	0.276353i
$716$		0			0
$717$	20.2259	−	5.41951i	0.755350	−	0.202395i
$718$		0			0
$719$	−22.6273	−	39.1916i	−0.843856	−	1.46160i	−0.886611	−	0.462515i	$-0.846947\pi$
$719$	−22.6273	−	39.1916i	−0.843856	−	1.46160i	0.0427557	−	0.999086i	$-0.486386\pi$
$720$		0			0
$721$	−31.5615	+	13.6290i	−1.17541	+	0.507569i
$722$		0			0
$723$	5.44569	−	20.3236i	0.202527	−	0.755843i
$724$		0			0
$725$	−0.117416	−	12.9263i	−0.00436070	−	0.480070i
$726$		0			0
$727$	−18.6646	−	18.6646i	−0.692232	−	0.692232i	0.270491	−	0.962723i	$-0.412814\pi$
$727$	−18.6646	−	18.6646i	−0.692232	−	0.692232i	−0.962723	+	0.270491i	$0.912814\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	1.06169	+	0.612967i	0.0392680	+	0.0226714i
$732$		0			0
$733$	44.1182	+	11.8214i	1.62954	+	0.436635i	0.953785	−	0.300489i	$-0.0971498\pi$
$733$	44.1182	+	11.8214i	1.62954	+	0.436635i	0.675758	+	0.737124i	$0.263817\pi$
$734$		0			0
$735$	−0.538541	−	15.6432i	−0.0198644	−	0.577008i
$736$		0			0
$737$	−11.4035	−	3.05557i	−0.420055	−	0.112553i
$738$		0			0
$739$	−12.5100	−	7.22266i	−0.460188	−	0.265690i	0.251935	−	0.967744i	$-0.418933\pi$
$739$	−12.5100	−	7.22266i	−0.460188	−	0.265690i	−0.712123	+	0.702054i	$0.752266\pi$
$740$		0			0
$741$		−	31.4745i		−	1.15624i
$742$		0			0
$743$	9.54339	+	9.54339i	0.350113	+	0.350113i	0.860152	−	0.510038i	$-0.170369\pi$
$743$	9.54339	+	9.54339i	0.350113	+	0.350113i	−0.510038	+	0.860152i	$0.670369\pi$
$744$		0			0
$745$	−20.3634	−	34.9034i	−0.746058	−	1.27876i
$746$		0			0
$747$	0.249622	−	0.931602i	0.00913319	−	0.0340855i
$748$		0			0
$749$	−29.8684	+	12.8978i	−1.09137	+	0.471277i
$750$		0			0
$751$	20.2684	+	35.1060i	0.739606	+	1.28104i	0.952673	+	0.303998i	$0.0983215\pi$
$751$	20.2684	+	35.1060i	0.739606	+	1.28104i	−0.213067	+	0.977038i	$0.568345\pi$
$752$		0			0
$753$	−14.5066	+	3.88704i	−0.528650	+	0.141651i
$754$		0			0
$755$	−2.32971	−	1.33099i	−0.0847870	−	0.0484397i
$756$		0			0
$757$	−32.0068	+	32.0068i	−1.16331	+	1.16331i	−0.179560	+	0.983747i	$0.557467\pi$
$757$	−32.0068	+	32.0068i	−1.16331	+	1.16331i	−0.983747	+	0.179560i	$0.942533\pi$
$758$		0			0
$759$	−3.54959	+	6.14808i	−0.128842	+	0.223161i
$760$		0			0
$761$	−24.6857	+	14.2523i	−0.894857	+	0.516646i	−0.875528	−	0.483167i	$-0.839486\pi$
$761$	−24.6857	+	14.2523i	−0.894857	+	0.516646i	−0.0193292	+	0.999813i	$0.506153\pi$
$762$		0			0
$763$	8.80706	−	1.29356i	0.318837	−	0.0468302i
$764$		0			0
$765$	−4.12797	−	4.09065i	−0.149247	−	0.147898i
$766$		0			0
$767$	14.4526	+	53.9380i	0.521855	+	1.94759i
$768$		0			0
$769$	−21.9243			−0.790611			−0.395305	−	0.918550i	$-0.629361\pi$
$769$	−21.9243			−0.790611			−0.395305	+	0.918550i	$0.629361\pi$
$770$		0			0
$771$	13.4544			0.484547
$772$		0			0
$773$	−5.76008	−	21.4969i	−0.207176	−	0.773190i	−0.988775	−	0.149410i	$-0.952263\pi$
$773$	−5.76008	−	21.4969i	−0.207176	−	0.773190i	0.781600	−	0.623780i	$-0.214404\pi$
$774$		0			0
$775$	−28.3211	−	16.0100i	−1.01732	−	0.575095i
$776$		0			0
$777$	13.3581	+	16.8805i	0.479220	+	0.605586i
$778$		0			0
$779$	−28.9669	+	16.7240i	−1.03785	+	0.599200i
$780$		0			0
$781$	−8.03354	+	13.9145i	−0.287463	+	0.497900i
$782$		0			0
$783$	1.82813	−	1.82813i	0.0653320	−	0.0653320i
$784$		0			0
$785$	−0.416202	−	1.52554i	−0.0148549	−	0.0544489i
$786$		0			0
$787$	13.3749	−	3.58379i	0.476763	−	0.127748i	−0.0124319	−	0.999923i	$-0.503957\pi$
$787$	13.3749	−	3.58379i	0.476763	−	0.127748i	0.489195	+	0.872174i	$0.337291\pi$
$788$		0			0
$789$	−7.28091	−	12.6109i	−0.259207	−	0.448960i
$790$		0			0
$791$	48.0881	+	5.60162i	1.70982	+	0.199171i
$792$		0			0
$793$	11.3144	−	42.2259i	0.401786	−	1.49948i
$794$		0			0
$795$	8.69614	−	5.07352i	0.308420	−	0.179939i
$796$		0			0
$797$	1.68212	+	1.68212i	0.0595839	+	0.0595839i	0.736271	−	0.676687i	$-0.236585\pi$
$797$	1.68212	+	1.68212i	0.0595839	+	0.0595839i	−0.676687	+	0.736271i	$0.736585\pi$
$798$		0			0
$799$		−	10.7179i		−	0.379171i
$800$		0			0
$801$	−1.14305	−	0.659941i	−0.0403878	−	0.0233179i
$802$		0			0
$803$	−5.59832	−	1.50006i	−0.197560	−	0.0529361i
$804$		0			0
$805$	−20.8567	+	9.11898i	−0.735101	+	0.321402i
$806$		0			0
$807$	−23.2296	−	6.22434i	−0.817719	−	0.219107i
$808$		0			0
$809$	41.2669	+	23.8255i	1.45087	+	0.837659i	0.998531	−	0.0541888i	$-0.0172573\pi$
$809$	41.2669	+	23.8255i	1.45087	+	0.837659i	0.452336	+	0.891847i	$0.350591\pi$
$810$		0			0
$811$			2.87597i			0.100989i	0.998724	+	0.0504946i	$0.0160798\pi$
$811$			2.87597i			0.100989i	−0.998724	+	0.0504946i	$0.983920\pi$
$812$		0			0
$813$	−5.15438	−	5.15438i	−0.180772	−	0.180772i
$814$		0			0
$815$	−7.39114	−	1.94452i	−0.258900	−	0.0681135i
$816$		0			0
$817$	0.564664	−	2.10735i	0.0197551	−	0.0737270i
$818$		0			0
$819$	7.13763	+	16.5291i	0.249409	+	0.577573i
$820$		0			0
$821$	15.8331	+	27.4238i	0.552580	+	0.957096i	0.998087	+	0.0618181i	$0.0196899\pi$
$821$	15.8331	+	27.4238i	0.552580	+	0.957096i	−0.445508	+	0.895278i	$0.646977\pi$
$822$		0			0
$823$	−39.2507	+	10.5172i	−1.36819	+	0.366606i	−0.866819	−	0.498623i	$-0.833839\pi$
$823$	−39.2507	+	10.5172i	−1.36819	+	0.366606i	−0.501375	+	0.865230i	$0.667172\pi$
$824$		0			0
$825$	−8.93231	−	2.30665i	−0.310983	−	0.0803074i
$826$		0			0
$827$	37.8981	−	37.8981i	1.31785	−	1.31785i	0.402369	−	0.915477i	$-0.368187\pi$
$827$	37.8981	−	37.8981i	1.31785	−	1.31785i	0.915477	−	0.402369i	$-0.131813\pi$
$828$		0			0
$829$	6.35527	−	11.0076i	0.220728	−	0.382311i	−0.734302	−	0.678823i	$-0.762490\pi$
$829$	6.35527	−	11.0076i	0.220728	−	0.382311i	0.955029	+	0.296512i	$0.0958235\pi$
$830$		0			0
$831$	4.60541	−	2.65894i	0.159760	−	0.0922375i
$832$		0			0
$833$	0.543364	+	18.1848i	0.0188264	+	0.630065i
$834$		0			0
$835$	10.0162	−	10.1076i	0.346624	−	0.349787i
$836$		0			0
$837$	−1.68404	−	6.28491i	−0.0582088	−	0.217238i
$838$		0			0
$839$	54.5807			1.88434			0.942168	−	0.335141i	$-0.108784\pi$
$839$	54.5807			1.88434			0.942168	+	0.335141i	$0.108784\pi$
$840$		0			0
$841$	22.3159			0.769514
$842$		0			0
$843$	−3.29609	−	12.3012i	−0.113523	−	0.423675i
$844$		0			0
$845$	−74.4784	+	0.338254i	−2.56213	+	0.0116363i
$846$		0			0
$847$	−18.6795	−	7.41241i	−0.641834	−	0.254693i
$848$		0			0
$849$	−26.2119	+	15.1335i	−0.899591	+	0.519379i
$850$		0			0
$851$	15.6528	−	27.1114i	0.536571	−	0.929368i
$852$		0			0
$853$	8.87853	−	8.87853i	0.303995	−	0.303995i	−0.538579	−	0.842575i	$-0.681039\pi$
$853$	8.87853	−	8.87853i	0.303995	−	0.303995i	0.842575	+	0.538579i	$0.181039\pi$
$854$		0			0
$855$	−5.13040	+	8.98005i	−0.175456	+	0.307111i
$856$		0			0
$857$	1.82789	−	0.489782i	0.0624396	−	0.0167306i	−0.227464	−	0.973786i	$-0.573043\pi$
$857$	1.82789	−	0.489782i	0.0624396	−	0.0167306i	0.289904	+	0.957056i	$0.406377\pi$
$858$		0			0
$859$	4.20573	+	7.28453i	0.143498	+	0.248545i	0.928811	−	0.370553i	$-0.120832\pi$
$859$	4.20573	+	7.28453i	0.143498	+	0.248545i	−0.785314	+	0.619098i	$0.787498\pi$
$860$		0			0
$861$	11.4196	−	15.3517i	0.389179	−	0.523185i
$862$		0			0
$863$	9.35914	−	34.9288i	0.318589	−	1.18899i	−0.602013	−	0.798487i	$-0.705634\pi$
$863$	9.35914	−	34.9288i	0.318589	−	1.18899i	0.920602	−	0.390503i	$-0.127699\pi$
$864$		0			0
$865$	14.3442	−	54.5227i	0.487718	−	1.85383i
$866$		0			0
$867$	−7.24451	−	7.24451i	−0.246037	−	0.246037i
$868$		0			0
$869$			14.3710i			0.487502i
$870$		0			0
$871$	37.7088	+	21.7712i	1.27772	+	0.737689i
$872$		0			0
$873$	13.8774	+	3.71844i	0.469679	+	0.125850i
$874$		0			0
$875$	−18.6702	−	22.9439i	−0.631169	−	0.775646i
$876$		0			0
$877$	36.6078	+	9.80903i	1.23616	+	0.331227i	0.816974	−	0.576674i	$-0.195650\pi$
$877$	36.6078	+	9.80903i	1.23616	+	0.331227i	0.419183	+	0.907902i	$0.362316\pi$
$878$		0			0
$879$	20.3659	+	11.7582i	0.686924	+	0.396595i
$880$		0			0
$881$		−	31.4413i		−	1.05928i	−0.848221	−	0.529642i	$-0.822326\pi$
$881$		−	31.4413i		−	1.05928i	0.848221	−	0.529642i	$-0.177674\pi$
$882$		0			0
$883$	−3.66702	−	3.66702i	−0.123405	−	0.123405i	0.642707	−	0.766112i	$-0.277811\pi$
$883$	−3.66702	−	3.66702i	−0.123405	−	0.123405i	−0.766112	+	0.642707i	$0.777811\pi$
$884$		0			0
$885$	4.66847	−	17.7450i	0.156929	−	0.596490i
$886$		0			0
$887$	−6.58295	+	24.5679i	−0.221034	+	0.824909i	0.762921	+	0.646492i	$0.223765\pi$
$887$	−6.58295	+	24.5679i	−0.221034	+	0.824909i	−0.983955	+	0.178418i	$0.942902\pi$
$888$		0			0
$889$	3.98447	−	34.2053i	0.133635	−	1.14721i
$890$		0			0
$891$	−0.922533	−	1.59787i	−0.0309060	−	0.0535308i
$892$		0			0
$893$	−18.4238	+	4.93664i	−0.616529	+	0.165198i
$894$		0			0
$895$	24.4611	−	42.8159i	0.817646	−	1.43118i
$896$		0			0
$897$	18.5144	−	18.5144i	0.618178	−	0.618178i
$898$		0			0
$899$	−8.41099	+	14.5683i	−0.280522	+	0.485878i
$900$		0			0
$901$	−10.1342	+	5.85099i	−0.337619	+	0.194925i
$902$		0			0
$903$	0.181357	+	1.23475i	0.00603519	+	0.0410898i
$904$		0			0
$905$	55.1385	−	0.250419i	1.83286	−	0.00832422i
$906$		0			0
$907$	11.6247	+	43.3841i	0.385993	+	1.44055i	0.836596	+	0.547821i	$0.184542\pi$
$907$	11.6247	+	43.3841i	0.385993	+	1.44055i	−0.450603	+	0.892724i	$0.648791\pi$
$908$		0			0
$909$	1.70540			0.0565647
$910$		0			0
$911$	32.3653			1.07231			0.536155	−	0.844119i	$-0.319876\pi$
$911$	32.3653			1.07231			0.536155	+	0.844119i	$0.319876\pi$
$912$		0			0
$913$	0.460569	+	1.71887i	0.0152426	+	0.0568862i
$914$		0			0
$915$	−10.1110	+	10.2033i	−0.334260	+	0.337310i
$916$		0			0
$917$	4.53524	−	11.4289i	0.149767	−	0.377416i
$918$		0			0
$919$	0.145073	−	0.0837577i	0.00478550	−	0.00276291i	−0.497605	−	0.867404i	$-0.665787\pi$
$919$	0.145073	−	0.0837577i	0.00478550	−	0.00276291i	0.502391	+	0.864641i	$0.332454\pi$
$920$		0			0
$921$	−16.1201	+	27.9208i	−0.531176	+	0.920023i
$922$		0			0
$923$	41.9023	−	41.9023i	1.37923	−	1.37923i
$924$		0			0
$925$	39.3892	+	10.1717i	1.29511	+	0.334445i
$926$		0			0
$927$	−12.5511	+	3.36305i	−0.412232	+	0.110457i
$928$		0			0
$929$	17.2974	+	29.9599i	0.567509	+	0.982954i	0.996811	+	0.0797932i	$0.0254260\pi$
$929$	17.2974	+	29.9599i	0.567509	+	0.982954i	−0.429303	+	0.903161i	$0.641241\pi$
$930$		0			0
$931$	31.0090	−	9.30992i	1.01628	−	0.305120i
$932$		0			0
$933$	−2.71056	+	10.1160i	−0.0887398	+	0.331181i
$934$		0			0
$935$	10.3697	+	2.72815i	0.339127	+	0.0892200i
$936$		0			0
$937$	−5.99941	−	5.99941i	−0.195992	−	0.195992i	0.602287	−	0.798279i	$-0.294256\pi$
$937$	−5.99941	−	5.99941i	−0.195992	−	0.195992i	−0.798279	+	0.602287i	$0.794256\pi$
$938$		0			0
$939$			18.2499i			0.595562i
$940$		0			0
$941$	34.0383	+	19.6520i	1.10962	+	0.640637i	0.938730	−	0.344654i	$-0.112004\pi$
$941$	34.0383	+	19.6520i	1.10962	+	0.640637i	0.170886	+	0.985291i	$0.445337\pi$
$942$		0			0
$943$	−26.8770	−	7.20167i	−0.875235	−	0.234519i
$944$		0			0
$945$	0.657821	−	5.87939i	0.0213989	−	0.191257i
$946$		0			0
$947$	23.4522	+	6.28399i	0.762094	+	0.204202i	0.618876	−	0.785489i	$-0.287588\pi$
$947$	23.4522	+	6.28399i	0.762094	+	0.204202i	0.143218	+	0.989691i	$0.454255\pi$
$948$		0			0
$949$	18.5123	+	10.6881i	0.600935	+	0.346950i
$950$		0			0
$951$		−	5.02448i		−	0.162930i
$952$		0			0
$953$	−41.7677	−	41.7677i	−1.35299	−	1.35299i	−0.882298	−	0.470690i	$-0.844005\pi$
$953$	−41.7677	−	41.7677i	−1.35299	−	1.35299i	−0.470690	−	0.882298i	$-0.655995\pi$
$954$		0			0
$955$	−47.8787	+	27.9335i	−1.54932	+	0.903905i
$956$		0			0
$957$	−1.23461	+	4.60763i	−0.0399093	+	0.148943i
$958$		0			0
$959$	−28.2383	−	21.0054i	−0.911861	−	0.678301i
$960$		0			0
$961$	5.66804	+	9.81734i	0.182840	+	0.316688i
$962$		0			0
$963$	−11.8778	+	3.18264i	−0.382756	+	0.102559i
$964$		0			0
$965$	−8.20762	−	30.0841i	−0.264213	−	0.968441i
$966$		0			0
$967$	−18.6667	+	18.6667i	−0.600281	+	0.600281i	−0.940387	−	0.340106i	$-0.889537\pi$
$967$	−18.6667	+	18.6667i	−0.600281	+	0.600281i	0.340106	+	0.940387i	$0.389537\pi$
$968$		0			0
$969$	6.01041	−	10.4103i	0.193082	−	0.334428i
$970$		0			0
$971$	−25.7352	+	14.8582i	−0.825881	+	0.476822i	−0.852440	−	0.522825i	$-0.824878\pi$
$971$	−25.7352	+	14.8582i	−0.825881	+	0.476822i	0.0265596	+	0.999647i	$0.491545\pi$
$972$		0			0
$973$	−41.9581	+	33.2028i	−1.34511	+	1.06443i
$974$		0			0
$975$	29.6198	+	16.7442i	0.948594	+	0.536242i
$976$		0			0
$977$	6.07326	+	22.6657i	0.194301	+	0.725140i	0.992447	+	0.122676i	$0.0391477\pi$
$977$	6.07326	+	22.6657i	0.194301	+	0.725140i	−0.798146	+	0.602464i	$0.794186\pi$
$978$		0			0
$979$	2.43527			0.0778316
$980$		0			0
$981$	3.36447			0.107419
$982$		0			0
$983$	8.83444	+	32.9706i	0.281775	+	1.05160i	0.951164	+	0.308686i	$0.0998894\pi$
$983$	8.83444	+	32.9706i	0.281775	+	1.05160i	−0.669389	+	0.742912i	$0.733444\pi$
$984$		0			0
$985$	2.46168	+	2.43942i	0.0784357	+	0.0777264i
$986$		0			0
$987$	8.55590	−	6.77057i	0.272337	−	0.215510i
$988$		0			0
$989$	1.57178	−	0.907465i	0.0499796	−	0.0288557i
$990$		0			0
$991$	17.7855	−	30.8053i	0.564974	−	0.978564i	−0.432078	−	0.901836i	$-0.642219\pi$
$991$	17.7855	−	30.8053i	0.564974	−	0.978564i	0.997052	−	0.0767277i	$-0.0244472\pi$
$992$		0			0
$993$	−11.0777	+	11.0777i	−0.351539	+	0.351539i
$994$		0			0
$995$	−27.1338	−	15.5018i	−0.860198	−	0.491440i
$996$		0			0
$997$	−12.8447	+	3.44172i	−0.406795	+	0.109000i	−0.456413	−	0.889768i	$-0.650866\pi$
$997$	−12.8447	+	3.44172i	−0.406795	+	0.109000i	0.0496183	+	0.998768i	$0.484200\pi$
$998$		0			0
$999$	4.06813	+	7.04621i	0.128710	+	0.222932i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.dd.b.73.10	yes	48
5.2	odd	4		840.2.dd.a.577.12	yes	48
7.5	odd	6		840.2.dd.a.313.12	✓	48
35.12	even	12	inner	840.2.dd.b.817.10	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.dd.a.313.12	✓	48	7.5	odd	6
840.2.dd.a.577.12	yes	48	5.2	odd	4
840.2.dd.b.73.10	yes	48	1.1	even	1	trivial
840.2.dd.b.817.10	yes	48	35.12	even	12	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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.dd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{3} +(-0.0101553 - 2.23604i) q^{5} +(-2.07473 + 1.64180i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(0.922533 - 1.59787i) q^{11} +(-4.81186 + 4.81186i) q^{13} +(2.15723 - 0.588540i) q^{15} +(-2.51042 + 0.672666i) q^{17} +(2.31260 + 4.00554i) q^{19} +(-2.12284 - 1.57910i) q^{21} +(-0.995848 + 3.71655i) q^{23} +(-4.99979 + 0.0454155i) q^{25} +(-0.707107 - 0.707107i) q^{27} +2.58536i q^{29} +(5.63490 + 3.25331i) q^{31} +(1.78220 + 0.477538i) q^{33} +(3.69221 + 4.62251i) q^{35} +(-7.85903 - 2.10582i) q^{37} +(-5.89331 - 3.40250i) q^{39} +7.23170i q^{41} +(-0.333540 - 0.333540i) q^{43} +(1.12682 + 1.93139i) q^{45} +(-1.06734 + 3.98335i) q^{47} +(1.60898 - 6.81258i) q^{49} +(-1.29949 - 2.25079i) q^{51} +(4.34910 - 1.16534i) q^{53} +(-3.58229 - 2.04660i) q^{55} +(-3.27051 + 3.27051i) q^{57} +(4.10291 - 7.10646i) q^{59} +(-5.56336 + 3.21201i) q^{61} +(0.975866 - 2.45920i) q^{63} +(10.8084 + 10.7107i) q^{65} +(-1.65608 - 6.18056i) q^{67} -3.84766 q^{69} -8.70813 q^{71} +(-0.813014 - 3.03421i) q^{73} +(-1.33791 - 4.81768i) q^{75} +(0.709387 + 4.82977i) q^{77} +(-6.74536 + 3.89444i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-0.681980 + 0.681980i) q^{83} +(1.52961 + 5.60659i) q^{85} +(-2.49727 + 0.669141i) q^{87} +(0.659941 + 1.14305i) q^{89} +(2.08318 - 17.8834i) q^{91} +(-1.68404 + 6.28491i) q^{93} +(8.93308 - 5.21175i) q^{95} +(-10.1590 - 10.1590i) q^{97} +1.84507i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7} - 4 q^{11} - 16 q^{13} - 4 q^{15} + 4 q^{17} - 8 q^{19} + 48 q^{23} - 20 q^{25} + 24 q^{33} - 4 q^{37} + 12 q^{39} + 16 q^{43} + 4 q^{45} - 12 q^{47} + 12 q^{49} - 52 q^{53} + 56 q^{55} + 8 q^{57}+ \cdots - 44 q^{97}+O(q^{100}) \) 48 * q + 4 * q^7 - 4 * q^11 - 16 * q^13 - 4 * q^15 + 4 * q^17 - 8 * q^19 + 48 * q^23 - 20 * q^25 + 24 * q^33 - 4 * q^37 + 12 * q^39 + 16 * q^43 + 4 * q^45 - 12 * q^47 + 12 * q^49 - 52 * q^53 + 56 * q^55 + 8 * q^57 - 8 * q^59 + 12 * q^65 + 68 * q^67 + 8 * q^69 + 16 * q^71 + 52 * q^73 + 24 * q^75 + 16 * q^77 - 108 * q^79 + 24 * q^81 - 64 * q^83 + 32 * q^85 - 8 * q^87 - 64 * q^89 + 48 * q^91 + 48 * q^93 - 84 * q^95 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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