LMFDB - Embedded newform 684.2.c.b.647.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [684,2,Mod(647,684)] 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("684.647"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(684, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			647.24
Character	$\chi$	$=$	684.647
Dual form			684.2.c.b.647.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965364 + 1.03348i) q^{2} +(-0.136143 + 1.99536i) q^{4} +0.0590006i q^{5} +1.27229i q^{7} +(-2.19358 + 1.78555i) q^{8} +(-0.0609757 + 0.0569571i) q^{10} +5.27604 q^{11} -1.40536 q^{13} +(-1.31488 + 1.22822i) q^{14} +(-3.96293 - 0.543311i) q^{16} +8.20009i q^{17} -1.00000i q^{19} +(-0.117728 - 0.00803255i) q^{20} +(5.09330 + 5.45266i) q^{22} -7.75602 q^{23} +4.99652 q^{25} +(-1.35668 - 1.45241i) q^{26} +(-2.53867 - 0.173214i) q^{28} +6.17369i q^{29} -7.05893i q^{31} +(-3.26417 - 4.62008i) q^{32} +(-8.47459 + 7.91607i) q^{34} -0.0750657 q^{35} -5.75595 q^{37} +(1.03348 - 0.965364i) q^{38} +(-0.105349 - 0.129423i) q^{40} +7.99536i q^{41} -4.49049i q^{43} +(-0.718299 + 10.5276i) q^{44} +(-7.48738 - 8.01565i) q^{46} +6.31694 q^{47} +5.38129 q^{49} +(4.82346 + 5.16378i) q^{50} +(0.191331 - 2.80420i) q^{52} -10.5521i q^{53} +0.311290i q^{55} +(-2.27173 - 2.79087i) q^{56} +(-6.38036 + 5.95986i) q^{58} +6.05569 q^{59} +6.72327 q^{61} +(7.29524 - 6.81444i) q^{62} +(1.62363 - 7.83351i) q^{64} -0.0829171i q^{65} -2.89516i q^{67} +(-16.3621 - 1.11639i) q^{68} +(-0.0724658 - 0.0775786i) q^{70} +8.96642 q^{71} -3.05558 q^{73} +(-5.55659 - 5.94863i) q^{74} +(1.99536 + 0.136143i) q^{76} +6.71264i q^{77} -2.67861i q^{79} +(0.0320557 - 0.233815i) q^{80} +(-8.26301 + 7.71843i) q^{82} +9.34505 q^{83} -0.483810 q^{85} +(4.64082 - 4.33496i) q^{86} +(-11.5735 + 9.42064i) q^{88} -2.25918i q^{89} -1.78802i q^{91} +(1.05593 - 15.4761i) q^{92} +(6.09815 + 6.52840i) q^{94} +0.0590006 q^{95} -14.2821 q^{97} +(5.19490 + 5.56143i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4} - 8 q^{10} - 24 q^{16} - 64 q^{25} + 48 q^{34} + 32 q^{37} + 8 q^{40} + 32 q^{46} + 16 q^{49} - 32 q^{58} + 56 q^{64} - 72 q^{70} - 48 q^{73} - 112 q^{82} - 16 q^{85} - 40 q^{88} + 88 q^{94}+ \cdots - 128 q^{97}+O(q^{100}) $ 32 * q + 8 * q^4 - 8 * q^10 - 24 * q^16 - 64 * q^25 + 48 * q^34 + 32 * q^37 + 8 * q^40 + 32 * q^46 + 16 * q^49 - 32 * q^58 + 56 * q^64 - 72 * q^70 - 48 * q^73 - 112 * q^82 - 16 * q^85 - 40 * q^88 + 88 * q^94 - 128 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	0.965364	+	1.03348i	0.682616	+	0.730778i
$2$	0.965364	+	1.03348i	0.682616	+	0.730778i
$3$		0			0
$3$		0			0
$4$	−0.136143	+	1.99536i	−0.0680717	+	0.997680i
$5$			0.0590006i			0.0263859i	0.999913	+	0.0131929i	$0.00419956\pi$
$5$			0.0590006i			0.0263859i	−0.999913	+	0.0131929i	$0.995800\pi$
$6$		0			0
$7$			1.27229i			0.480879i	0.970664	+	0.240440i	$0.0772916\pi$
$7$			1.27229i			0.480879i	−0.970664	+	0.240440i	$0.922708\pi$
$8$	−2.19358	+	1.78555i	−0.775549	+	0.631287i
$9$		0			0
$10$	−0.0609757	+	0.0569571i	−0.0192822	+	0.0180114i
$11$	5.27604			1.59079			0.795394	−	0.606093i	$-0.207264\pi$
$11$	5.27604			1.59079			0.795394	+	0.606093i	$0.207264\pi$
$12$		0			0
$13$	−1.40536			−0.389777			−0.194888	−	0.980825i	$-0.562434\pi$
$13$	−1.40536			−0.389777			−0.194888	+	0.980825i	$0.562434\pi$
$14$	−1.31488	+	1.22822i	−0.351416	+	0.328256i
$15$		0			0
$16$	−3.96293	−	0.543311i	−0.990732	−	0.135828i
$17$			8.20009i			1.98881i	0.105618	+	0.994407i	$0.466318\pi$
$17$			8.20009i			1.98881i	−0.105618	+	0.994407i	$0.533682\pi$
$18$		0			0
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−0.117728	−	0.00803255i	−0.0263247	−	0.00179613i
$21$		0			0
$22$	5.09330	+	5.45266i	1.08590	+	1.16251i
$23$	−7.75602			−1.61724			−0.808621	−	0.588330i	$-0.799785\pi$
$23$	−7.75602			−1.61724			−0.808621	+	0.588330i	$0.799785\pi$
$24$		0			0
$25$	4.99652			0.999304
$26$	−1.35668	−	1.45241i	−0.266068	−	0.284840i
$27$		0			0
$28$	−2.53867	−	0.173214i	−0.479764	−	0.0327343i
$29$			6.17369i			1.14643i	0.819407	+	0.573213i	$0.194303\pi$
$29$			6.17369i			1.14643i	−0.819407	+	0.573213i	$0.805697\pi$
$30$		0			0
$31$		−	7.05893i		−	1.26782i	−0.773406	−	0.633911i	$-0.781449\pi$
$31$		−	7.05893i		−	1.26782i	0.773406	−	0.633911i	$-0.218551\pi$
$32$	−3.26417	−	4.62008i	−0.577030	−	0.816723i
$33$		0			0
$34$	−8.47459	+	7.91607i	−1.45338	+	1.35760i
$35$	−0.0750657			−0.0126884
$36$		0			0
$37$	−5.75595			−0.946272			−0.473136	−	0.880989i	$-0.656878\pi$
$37$	−5.75595			−0.946272			−0.473136	+	0.880989i	$0.656878\pi$
$38$	1.03348	−	0.965364i	0.167652	−	0.156603i
$39$		0			0
$40$	−0.105349	−	0.129423i	−0.0166571	−	0.0204636i
$41$			7.99536i			1.24867i	0.781159	+	0.624333i	$0.214629\pi$
$41$			7.99536i			1.24867i	−0.781159	+	0.624333i	$0.785371\pi$
$42$		0			0
$43$		−	4.49049i		−	0.684794i	−0.939555	−	0.342397i	$-0.888761\pi$
$43$		−	4.49049i		−	0.684794i	0.939555	−	0.342397i	$-0.111239\pi$
$44$	−0.718299	+	10.5276i	−0.108288	+	1.58710i
$45$		0			0
$46$	−7.48738	−	8.01565i	−1.10395	−	1.18184i
$47$	6.31694			0.921421			0.460710	−	0.887551i	$-0.347595\pi$
$47$	6.31694			0.921421			0.460710	+	0.887551i	$0.347595\pi$
$48$		0			0
$49$	5.38129			0.768755
$50$	4.82346	+	5.16378i	0.682140	+	0.730269i
$51$		0			0
$52$	0.191331	−	2.80420i	0.0265328	−	0.388873i
$53$		−	10.5521i		−	1.44944i	−0.689043	−	0.724720i	$-0.741969\pi$
$53$		−	10.5521i		−	1.44944i	0.689043	−	0.724720i	$-0.258031\pi$
$54$		0			0
$55$			0.311290i			0.0419743i
$56$	−2.27173	−	2.79087i	−0.303573	−	0.372946i
$57$		0			0
$58$	−6.38036	+	5.95986i	−0.837782	+	0.782568i
$59$	6.05569			0.788384			0.394192	−	0.919028i	$-0.371025\pi$
$59$	6.05569			0.788384			0.394192	+	0.919028i	$0.371025\pi$
$60$		0			0
$61$	6.72327			0.860827			0.430413	−	0.902632i	$-0.358368\pi$
$61$	6.72327			0.860827			0.430413	+	0.902632i	$0.358368\pi$
$62$	7.29524	−	6.81444i	0.926496	−	0.865435i
$63$		0			0
$64$	1.62363	−	7.83351i	0.202953	−	0.979188i
$65$		−	0.0829171i		−	0.0102846i
$66$		0			0
$67$		−	2.89516i		−	0.353701i	−0.984238	−	0.176850i	$-0.943409\pi$
$67$		−	2.89516i		−	0.353701i	0.984238	−	0.176850i	$-0.0565908\pi$
$68$	−16.3621	−	1.11639i	−1.98420	−	0.135382i
$69$		0			0
$70$	−0.0724658	−	0.0775786i	−0.00866132	−	0.00927241i
$71$	8.96642			1.06412			0.532059	−	0.846707i	$-0.321418\pi$
$71$	8.96642			1.06412			0.532059	+	0.846707i	$0.321418\pi$
$72$		0			0
$73$	−3.05558			−0.357629			−0.178815	−	0.983883i	$-0.557226\pi$
$73$	−3.05558			−0.357629			−0.178815	+	0.983883i	$0.557226\pi$
$74$	−5.55659	−	5.94863i	−0.645940	−	0.691515i
$75$		0			0
$76$	1.99536	+	0.136143i	0.228884	+	0.0156167i
$77$			6.71264i			0.764977i
$78$		0			0
$79$		−	2.67861i		−	0.301367i	−0.988582	−	0.150683i	$-0.951853\pi$
$79$		−	2.67861i		−	0.301367i	0.988582	−	0.150683i	$-0.0481474\pi$
$80$	0.0320557	−	0.233815i	0.00358393	−	0.0261413i
$81$		0			0
$82$	−8.26301	+	7.71843i	−0.912497	+	0.852359i
$83$	9.34505			1.02575			0.512876	−	0.858463i	$-0.328580\pi$
$83$	9.34505			1.02575			0.512876	+	0.858463i	$0.328580\pi$
$84$		0			0
$85$	−0.483810			−0.0524766
$86$	4.64082	−	4.33496i	0.500432	−	0.467451i
$87$		0			0
$88$	−11.5735	+	9.42064i	−1.23373	+	1.00424i
$89$		−	2.25918i		−	0.239472i	−0.992806	−	0.119736i	$-0.961795\pi$
$89$		−	2.25918i		−	0.239472i	0.992806	−	0.119736i	$-0.0382049\pi$
$90$		0			0
$91$		−	1.78802i		−	0.187436i
$92$	1.05593	−	15.4761i	0.110088	−	1.61349i
$93$		0			0
$94$	6.09815	+	6.52840i	0.628976	+	0.673353i
$95$	0.0590006			0.00605334
$96$		0			0
$97$	−14.2821			−1.45013			−0.725065	−	0.688681i	$-0.758190\pi$
$97$	−14.2821			−1.45013			−0.725065	+	0.688681i	$0.758190\pi$
$98$	5.19490	+	5.56143i	0.524764	+	0.561789i
$99$		0			0
$100$	−0.680243	+	9.96986i	−0.0680243	+	0.996986i
$101$		−	8.91661i		−	0.887235i	−0.896216	−	0.443618i	$-0.853695\pi$
$101$		−	8.91661i		−	0.887235i	0.896216	−	0.443618i	$-0.146305\pi$
$102$		0			0
$103$		−	4.17304i		−	0.411182i	−0.978638	−	0.205591i	$-0.934088\pi$
$103$		−	4.17304i		−	0.411182i	0.978638	−	0.205591i	$-0.0659116\pi$
$104$	3.08278	−	2.50934i	0.302291	−	0.246061i
$105$		0			0
$106$	10.9053	−	10.1866i	1.05922	−	0.989411i
$107$	−12.7308			−1.23073			−0.615367	−	0.788241i	$-0.710992\pi$
$107$	−12.7308			−1.23073			−0.615367	+	0.788241i	$0.710992\pi$
$108$		0			0
$109$	15.2273			1.45852			0.729258	−	0.684239i	$-0.239866\pi$
$109$	15.2273			1.45852			0.729258	+	0.684239i	$0.239866\pi$
$110$	−0.321710	+	0.300508i	−0.0306739	+	0.0286523i
$111$		0			0
$112$	0.691247	−	5.04198i	0.0653167	−	0.476423i
$113$			2.72179i			0.256045i	0.991771	+	0.128022i	$0.0408629\pi$
$113$			2.72179i			0.256045i	−0.991771	+	0.128022i	$0.959137\pi$
$114$		0			0
$115$		−	0.457610i		−	0.0426723i
$116$	−12.3187	−	0.840507i	−1.14377	−	0.0780392i
$117$		0			0
$118$	5.84595	+	6.25841i	0.538163	+	0.576133i
$119$	−10.4329			−0.956379
$120$		0			0
$121$	16.8366			1.53060
$122$	6.49041	+	6.94834i	0.587614	+	0.629073i
$123$		0			0
$124$	14.0851	+	0.961028i	1.26488	+	0.0863028i
$125$			0.589801i			0.0527534i
$126$		0			0
$127$		−	17.9702i		−	1.59459i	−0.603587	−	0.797297i	$-0.706262\pi$
$127$		−	17.9702i		−	1.59459i	0.603587	−	0.797297i	$-0.293738\pi$
$128$	9.66313	−	5.88421i	0.854108	−	0.520095i
$129$		0			0
$130$	0.0856928	−	0.0800452i	0.00751576	−	0.00702043i
$131$	17.1149			1.49534			0.747669	−	0.664072i	$-0.231173\pi$
$131$	17.1149			1.49534			0.747669	+	0.664072i	$0.231173\pi$
$132$		0			0
$133$	1.27229			0.110321
$134$	2.99208	−	2.79489i	0.258476	−	0.241442i
$135$		0			0
$136$	−14.6417	−	17.9876i	−1.25551	−	1.54242i
$137$		−	16.6962i		−	1.42645i	−0.700935	−	0.713225i	$-0.747234\pi$
$137$		−	16.6962i		−	1.42645i	0.700935	−	0.713225i	$-0.252766\pi$
$138$		0			0
$139$			9.43783i			0.800506i	0.916405	+	0.400253i	$0.131078\pi$
$139$			9.43783i			0.800506i	−0.916405	+	0.400253i	$0.868922\pi$
$140$	0.0102197	−	0.149783i	0.000863723	−	0.0126590i
$141$		0			0
$142$	8.65586	+	9.26658i	0.726384	+	0.777634i
$143$	−7.41474			−0.620052
$144$		0			0
$145$	−0.364252			−0.0302494
$146$	−2.94975	−	3.15787i	−0.244123	−	0.261347i
$147$		0			0
$148$	0.783635	−	11.4852i	0.0644144	−	0.944077i
$149$			4.82279i			0.395098i	0.980293	+	0.197549i	$0.0632982\pi$
$149$			4.82279i			0.395098i	−0.980293	+	0.197549i	$0.936702\pi$
$150$		0			0
$151$			2.91310i			0.237065i	0.992950	+	0.118532i	$0.0378189\pi$
$151$			2.91310i			0.237065i	−0.992950	+	0.118532i	$0.962181\pi$
$152$	1.78555	+	2.19358i	0.144827	+	0.177923i
$153$		0			0
$154$	−6.93735	+	6.48015i	−0.559028	+	0.522185i
$155$	0.416481			0.0334526
$156$		0			0
$157$	13.5208			1.07908			0.539540	−	0.841960i	$-0.318598\pi$
$157$	13.5208			1.07908			0.539540	+	0.841960i	$0.318598\pi$
$158$	2.76828	−	2.58583i	0.220232	−	0.205718i
$159$		0			0
$160$	0.272588	−	0.192588i	0.0215500	−	0.0152254i
$161$		−	9.86788i		−	0.777698i
$162$		0			0
$163$		−	0.626149i		−	0.0490438i	−0.999699	−	0.0245219i	$-0.992194\pi$
$163$		−	0.626149i		−	0.0490438i	0.999699	−	0.0245219i	$-0.00780634\pi$
$164$	−15.9536	−	1.08852i	−1.24577	−	0.0849988i
$165$		0			0
$166$	9.02138	+	9.65788i	0.700195	+	0.749597i
$167$	−6.55967			−0.507602			−0.253801	−	0.967256i	$-0.581681\pi$
$167$	−6.55967			−0.507602			−0.253801	+	0.967256i	$0.581681\pi$
$168$		0			0
$169$	−11.0250			−0.848074
$170$	−0.467053	−	0.500006i	−0.0358213	−	0.0383487i
$171$		0			0
$172$	8.96016	+	0.611351i	0.683206	+	0.0466151i
$173$			10.2796i			0.781547i	0.920487	+	0.390773i	$0.127792\pi$
$173$			10.2796i			0.781547i	−0.920487	+	0.390773i	$0.872208\pi$
$174$		0			0
$175$			6.35701i			0.480544i
$176$	−20.9086	−	2.86653i	−1.57604	−	0.216073i
$177$		0			0
$178$	2.33480	−	2.18093i	0.175001	−	0.163468i
$179$	−18.6314			−1.39258			−0.696288	−	0.717762i	$-0.745166\pi$
$179$	−18.6314			−1.39258			−0.696288	+	0.717762i	$0.745166\pi$
$180$		0			0
$181$	−3.58568			−0.266522			−0.133261	−	0.991081i	$-0.542545\pi$
$181$	−3.58568			−0.266522			−0.133261	+	0.991081i	$0.542545\pi$
$182$	1.84788	−	1.72609i	0.136974	−	0.127946i
$183$		0			0
$184$	17.0135	−	13.8487i	1.25425	−	1.02094i
$185$		−	0.339605i		−	0.0249682i
$186$		0			0
$187$			43.2640i			3.16378i
$188$	−0.860010	+	12.6046i	−0.0627227	+	0.919283i
$189$		0			0
$190$	0.0569571	+	0.0609757i	0.00413210	+	0.00442364i
$191$	3.91466			0.283255			0.141627	−	0.989920i	$-0.454767\pi$
$191$	3.91466			0.283255			0.141627	+	0.989920i	$0.454767\pi$
$192$		0			0
$193$	7.01999			0.505310			0.252655	−	0.967556i	$-0.418696\pi$
$193$	7.01999			0.505310			0.252655	+	0.967556i	$0.418696\pi$
$194$	−13.7874	−	14.7602i	−0.989881	−	1.05972i
$195$		0			0
$196$	−0.732627	+	10.7376i	−0.0523305	+	0.766972i
$197$		−	5.42454i		−	0.386483i	−0.981151	−	0.193241i	$-0.938100\pi$
$197$		−	5.42454i		−	0.386483i	0.981151	−	0.193241i	$-0.0619000\pi$
$198$		0			0
$199$			1.02347i			0.0725521i	0.999342	+	0.0362761i	$0.0115496\pi$
$199$			1.02347i			0.0725521i	−0.999342	+	0.0362761i	$0.988450\pi$
$200$	−10.9603	+	8.92153i	−0.775009	+	0.630847i
$201$		0			0
$202$	9.21509	−	8.60777i	0.648372	−	0.605641i
$203$	−7.85470			−0.551292
$204$		0			0
$205$	−0.471731			−0.0329471
$206$	4.31273	−	4.02850i	0.300482	−	0.280679i
$207$		0			0
$208$	5.56934	+	0.763547i	0.386165	+	0.0529425i
$209$		−	5.27604i		−	0.364952i
$210$		0			0
$211$			12.6167i			0.868572i	0.900775	+	0.434286i	$0.142999\pi$
$211$			12.6167i			0.868572i	−0.900775	+	0.434286i	$0.857001\pi$
$212$	21.0552	+	1.43660i	1.44608	+	0.0986659i
$213$		0			0
$214$	−12.2899	−	13.1570i	−0.840118	−	0.899392i
$215$	0.264942			0.0180689
$216$		0			0
$217$	8.98099			0.609669
$218$	14.6999	+	15.7371i	0.995605	+	1.06585i
$219$		0			0
$220$	−0.621136	−	0.0423801i	−0.0418770	−	0.00285726i
$221$		−	11.5241i		−	0.775193i
$222$		0			0
$223$		−	27.0222i		−	1.80954i	−0.425898	−	0.904771i	$-0.640042\pi$
$223$		−	27.0222i		−	1.80954i	0.425898	−	0.904771i	$-0.359958\pi$
$224$	5.87807	−	4.15296i	0.392745	−	0.277482i
$225$		0			0
$226$	−2.81291	+	2.62752i	−0.187112	+	0.174780i
$227$	20.2086			1.34129			0.670645	−	0.741778i	$-0.266017\pi$
$227$	20.2086			1.34129			0.670645	+	0.741778i	$0.266017\pi$
$228$		0			0
$229$	9.92551			0.655896			0.327948	−	0.944696i	$-0.393643\pi$
$229$	9.92551			0.655896			0.327948	+	0.944696i	$0.393643\pi$
$230$	0.472928	−	0.441760i	0.0311840	−	0.0291288i
$231$		0			0
$232$	−11.0234	−	13.5425i	−0.723723	−	0.889109i
$233$		−	1.92511i		−	0.126118i	−0.998010	−	0.0630591i	$-0.979914\pi$
$233$		−	1.92511i		−	0.126118i	0.998010	−	0.0630591i	$-0.0200857\pi$
$234$		0			0
$235$			0.372703i			0.0243125i
$236$	−0.824442	+	12.0833i	−0.0536666	+	0.786555i
$237$		0			0
$238$	−10.0715	−	10.7821i	−0.652839	−	0.698900i
$239$	−20.3148			−1.31406			−0.657029	−	0.753866i	$-0.728187\pi$
$239$	−20.3148			−1.31406			−0.657029	+	0.753866i	$0.728187\pi$
$240$		0			0
$241$	0.879196			0.0566340			0.0283170	−	0.999599i	$-0.490985\pi$
$241$	0.879196			0.0566340			0.0283170	+	0.999599i	$0.490985\pi$
$242$	16.2535	+	17.4003i	1.04481	+	1.11853i
$243$		0			0
$244$	−0.915329	+	13.4154i	−0.0585980	+	0.858830i
$245$			0.317499i			0.0202843i
$246$		0			0
$247$			1.40536i			0.0894209i
$248$	12.6041	+	15.4844i	0.800359	+	0.983258i
$249$		0			0
$250$	−0.609545	+	0.569373i	−0.0385510	+	0.0360103i
$251$	−10.2545			−0.647259			−0.323630	−	0.946184i	$-0.604903\pi$
$251$	−10.2545			−0.647259			−0.323630	+	0.946184i	$0.604903\pi$
$252$		0			0
$253$	−40.9211			−2.57269
$254$	18.5717	−	17.3478i	1.16529	−	1.08850i
$255$		0			0
$256$	15.4096	+	4.30620i	0.963102	+	0.269138i
$257$		−	12.9473i		−	0.807633i	−0.914840	−	0.403816i	$-0.867683\pi$
$257$		−	12.9473i		−	0.807633i	0.914840	−	0.403816i	$-0.132317\pi$
$258$		0			0
$259$		−	7.32322i		−	0.455043i
$260$	0.165450	+	0.0112886i	0.0102607	+	0.000700091i
$261$		0			0
$262$	16.5221	+	17.6878i	1.02074	+	1.09276i
$263$	1.76321			0.108724			0.0543620	−	0.998521i	$-0.482687\pi$
$263$	1.76321			0.108724			0.0543620	+	0.998521i	$0.482687\pi$
$264$		0			0
$265$	0.622580			0.0382448
$266$	1.22822	+	1.31488i	0.0753070	+	0.0806203i
$267$		0			0
$268$	5.77690	+	0.394158i	0.352880	+	0.0240770i
$269$		−	0.479329i		−	0.0292252i	−0.999893	−	0.0146126i	$-0.995349\pi$
$269$		−	0.479329i		−	0.0292252i	0.999893	−	0.0146126i	$-0.00465150\pi$
$270$		0			0
$271$			17.1638i			1.04262i	0.853366	+	0.521312i	$0.174557\pi$
$271$			17.1638i			1.04262i	−0.853366	+	0.521312i	$0.825443\pi$
$272$	4.45520	−	32.4964i	0.270136	−	1.97038i
$273$		0			0
$274$	17.2551	−	16.1179i	1.04242	−	0.973718i
$275$	26.3619			1.58968
$276$		0			0
$277$	−14.0304			−0.843006			−0.421503	−	0.906827i	$-0.638497\pi$
$277$	−14.0304			−0.843006			−0.421503	+	0.906827i	$0.638497\pi$
$278$	−9.75377	+	9.11094i	−0.584992	+	0.546438i
$279$		0			0
$280$	0.164663	−	0.134034i	0.00984050	−	0.00801004i
$281$			14.7356i			0.879053i	0.898230	+	0.439526i	$0.144854\pi$
$281$			14.7356i			0.879053i	−0.898230	+	0.439526i	$0.855146\pi$
$282$		0			0
$283$		−	14.8917i		−	0.885219i	−0.896715	−	0.442609i	$-0.854053\pi$
$283$		−	14.8917i		−	0.885219i	0.896715	−	0.442609i	$-0.145947\pi$
$284$	−1.22072	+	17.8912i	−0.0724364	+	1.06165i
$285$		0			0
$286$	−7.15793	−	7.66296i	−0.423257	−	0.453120i
$287$	−10.1724			−0.600457
$288$		0			0
$289$	−50.2415			−2.95538
$290$	−0.351635	−	0.376445i	−0.0206487	−	0.0221056i
$291$		0			0
$292$	0.415998	−	6.09699i	0.0243444	−	0.356799i
$293$			30.9507i			1.80816i	0.427362	+	0.904081i	$0.359443\pi$
$293$			30.9507i			1.80816i	−0.427362	+	0.904081i	$0.640557\pi$
$294$		0			0
$295$			0.357289i			0.0208022i
$296$	12.6262	−	10.2775i	0.733881	−	0.597369i
$297$		0			0
$298$	−4.98423	+	4.65575i	−0.288729	+	0.269700i
$299$	10.9000			0.630363
$300$		0			0
$301$	5.71320			0.329303
$302$	−3.01062	+	2.81220i	−0.173241	+	0.161824i
$303$		0			0
$304$	−0.543311	+	3.96293i	−0.0311610	+	0.227290i
$305$			0.396677i			0.0227137i
$306$		0			0
$307$			25.0882i			1.43186i	0.698172	+	0.715930i	$0.253997\pi$
$307$			25.0882i			1.43186i	−0.698172	+	0.715930i	$0.746003\pi$
$308$	−13.3941	−	0.913882i	−0.763202	−	0.0520733i
$309$		0			0
$310$	0.402056	+	0.430423i	0.0228353	+	0.0244464i
$311$	−29.1948			−1.65548			−0.827742	−	0.561108i	$-0.810375\pi$
$311$	−29.1948			−1.65548			−0.827742	+	0.561108i	$0.810375\pi$
$312$		0			0
$313$	−13.6549			−0.771819			−0.385909	−	0.922537i	$-0.626112\pi$
$313$	−13.6549			−0.771819			−0.385909	+	0.922537i	$0.626112\pi$
$314$	13.0525	+	13.9735i	0.736597	+	0.788568i
$315$		0			0
$316$	5.34479	+	0.364675i	0.300668	+	0.0205146i
$317$		−	10.3696i		−	0.582414i	−0.956660	−	0.291207i	$-0.905943\pi$
$317$		−	10.3696i		−	0.582414i	0.956660	−	0.291207i	$-0.0940568\pi$
$318$		0			0
$319$			32.5727i			1.82372i
$320$	0.462182	+	0.0957950i	0.0258367	+	0.00535511i
$321$		0			0
$322$	10.1982	−	9.52610i	0.568324	−	0.530869i
$323$	8.20009			0.456265
$324$		0			0
$325$	−7.02191			−0.389505
$326$	0.647110	−	0.604462i	0.0358401	−	0.0334780i
$327$		0			0
$328$	−14.2761	−	17.5385i	−0.788266	−	0.968402i
$329$			8.03696i			0.443092i
$330$		0			0
$331$		−	24.2153i		−	1.33099i	−0.746402	−	0.665496i	$-0.768220\pi$
$331$		−	24.2153i		−	1.33099i	0.746402	−	0.665496i	$-0.231780\pi$
$332$	−1.27227	+	18.6467i	−0.0698247	+	1.02337i
$333$		0			0
$334$	−6.33247	−	6.77926i	−0.346497	−	0.370944i
$335$	0.170816			0.00933270
$336$		0			0
$337$	−11.8973			−0.648085			−0.324043	−	0.946042i	$-0.605042\pi$
$337$	−11.8973			−0.648085			−0.324043	+	0.946042i	$0.605042\pi$
$338$	−10.6431	−	11.3940i	−0.578909	−	0.619753i
$339$		0			0
$340$	0.0658676	−	0.965376i	0.00357217	−	0.0523549i
$341$		−	37.2432i		−	2.01683i
$342$		0			0
$343$			15.7525i			0.850558i
$344$	8.01800	+	9.85028i	0.432302	+	0.531091i
$345$		0			0
$346$	−10.6238	+	9.92360i	−0.571137	+	0.533496i
$347$	3.57698			0.192022			0.0960112	−	0.995380i	$-0.469392\pi$
$347$	3.57698			0.192022			0.0960112	+	0.995380i	$0.469392\pi$
$348$		0			0
$349$	3.64766			0.195255			0.0976275	−	0.995223i	$-0.468875\pi$
$349$	3.64766			0.195255			0.0976275	+	0.995223i	$0.468875\pi$
$350$	−6.56981	+	6.13683i	−0.351171	+	0.328027i
$351$		0			0
$352$	−17.2219	−	24.3758i	−0.917931	−	1.29923i
$353$		−	1.39070i		−	0.0740197i	−0.999315	−	0.0370098i	$-0.988217\pi$
$353$		−	1.39070i		−	0.0740197i	0.999315	−	0.0370098i	$-0.0117833\pi$
$354$		0			0
$355$			0.529024i			0.0280777i
$356$	4.50787	+	0.307572i	0.238917	+	0.0163013i
$357$		0			0
$358$	−17.9861	−	19.2551i	−0.950595	−	1.01766i
$359$	−31.8137			−1.67906			−0.839531	−	0.543311i	$-0.817170\pi$
$359$	−31.8137			−1.67906			−0.839531	+	0.543311i	$0.817170\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	−3.46149	−	3.70572i	−0.181932	−	0.194768i
$363$		0			0
$364$	3.56775	+	0.243427i	0.187001	+	0.0127591i
$365$		−	0.180281i		−	0.00943636i
$366$		0			0
$367$			13.2863i			0.693537i	0.937951	+	0.346768i	$0.112721\pi$
$367$			13.2863i			0.693537i	−0.937951	+	0.346768i	$0.887279\pi$
$368$	30.7365	+	4.21393i	1.60225	+	0.219666i
$369$		0			0
$370$	0.350973	−	0.327842i	0.0182462	−	0.0170437i
$371$	13.4253			0.697006
$372$		0			0
$373$	−31.1909			−1.61500			−0.807502	−	0.589865i	$-0.799181\pi$
$373$	−31.1909			−1.61500			−0.807502	+	0.589865i	$0.799181\pi$
$374$	−44.7123	+	41.7656i	−2.31202	+	2.15965i
$375$		0			0
$376$	−13.8567	+	11.2792i	−0.714607	+	0.581681i
$377$		−	8.67626i		−	0.446850i
$378$		0			0
$379$		−	9.24887i		−	0.475083i	−0.971377	−	0.237541i	$-0.923658\pi$
$379$		−	9.24887i		−	0.475083i	0.971377	−	0.237541i	$-0.0763415\pi$
$380$	−0.00803255	+	0.117728i	−0.000412061	+	0.00603929i
$381$		0			0
$382$	3.77907	+	4.04570i	0.193354	+	0.206996i
$383$	15.5740			0.795796			0.397898	−	0.917430i	$-0.369740\pi$
$383$	15.5740			0.795796			0.397898	+	0.917430i	$0.369740\pi$
$384$		0			0
$385$	−0.396050			−0.0201846
$386$	6.77685	+	7.25499i	0.344933	+	0.369269i
$387$		0			0
$388$	1.94442	−	28.4980i	0.0987128	−	1.44677i
$389$			19.6827i			0.997951i	0.866616	+	0.498976i	$0.166290\pi$
$389$			19.6827i			0.997951i	−0.866616	+	0.498976i	$0.833710\pi$
$390$		0			0
$391$		−	63.6000i		−	3.21639i
$392$	−11.8043	+	9.60855i	−0.596208	+	0.485305i
$393$		0			0
$394$	5.60613	−	5.23666i	0.282433	−	0.263819i
$395$	0.158039			0.00795183
$396$		0			0
$397$	8.62956			0.433105			0.216553	−	0.976271i	$-0.430519\pi$
$397$	8.62956			0.433105			0.216553	+	0.976271i	$0.430519\pi$
$398$	−1.05773	+	0.988025i	−0.0530195	+	0.0495252i
$399$		0			0
$400$	−19.8009	−	2.71466i	−0.990043	−	0.135733i
$401$		−	20.6012i		−	1.02877i	−0.857558	−	0.514387i	$-0.828019\pi$
$401$		−	20.6012i		−	1.02877i	0.857558	−	0.514387i	$-0.171981\pi$
$402$		0			0
$403$			9.92035i			0.494168i
$404$	17.7918	+	1.21394i	0.885177	+	0.0603956i
$405$		0			0
$406$	−7.58265	−	8.11765i	−0.376321	−	0.402872i
$407$	−30.3686			−1.50532
$408$		0			0
$409$	33.3613			1.64961			0.824805	−	0.565418i	$-0.191285\pi$
$409$	33.3613			1.64961			0.824805	+	0.565418i	$0.191285\pi$
$410$	−0.455392	−	0.487523i	−0.0224902	−	0.0240770i
$411$		0			0
$412$	8.32672	+	0.568132i	0.410228	+	0.0279898i
$413$			7.70457i			0.379117i
$414$		0			0
$415$			0.551364i			0.0270654i
$416$	4.58734	+	6.49288i	0.224913	+	0.318340i
$417$		0			0
$418$	5.45266	−	5.09330i	0.266698	−	0.249122i
$419$	24.8571			1.21435			0.607174	−	0.794569i	$-0.292303\pi$
$419$	24.8571			1.21435			0.607174	+	0.794569i	$0.292303\pi$
$420$		0			0
$421$	18.1678			0.885446			0.442723	−	0.896659i	$-0.354013\pi$
$421$	18.1678			0.885446			0.442723	+	0.896659i	$0.354013\pi$
$422$	−13.0391	+	12.1797i	−0.634733	+	0.592901i
$423$		0			0
$424$	18.8413	+	23.1469i	0.915013	+	1.12411i
$425$			40.9719i			1.98743i
$426$		0			0
$427$			8.55393i			0.413954i
$428$	1.73322	−	25.4025i	0.0837781	−	1.22788i
$429$		0			0
$430$	0.255765	+	0.273811i	0.0123341	+	0.0132043i
$431$	−19.1589			−0.922850			−0.461425	−	0.887179i	$-0.652662\pi$
$431$	−19.1589			−0.922850			−0.461425	+	0.887179i	$0.652662\pi$
$432$		0			0
$433$	−5.63029			−0.270575			−0.135287	−	0.990806i	$-0.543196\pi$
$433$	−5.63029			−0.270575			−0.135287	+	0.990806i	$0.543196\pi$
$434$	8.66993	+	9.28163i	0.416170	+	0.445533i
$435$		0			0
$436$	−2.07310	+	30.3840i	−0.0992836	+	1.45513i
$437$			7.75602i			0.371021i
$438$		0			0
$439$		−	0.947873i		−	0.0452395i	−0.999744	−	0.0226198i	$-0.992799\pi$
$439$		−	0.947873i		−	0.0452395i	0.999744	−	0.0226198i	$-0.00720071\pi$
$440$	−0.555823	−	0.682841i	−0.0264978	−	0.0325532i
$441$		0			0
$442$	11.9099	−	11.1249i	0.566494	−	0.529159i
$443$	14.0866			0.669276			0.334638	−	0.942347i	$-0.391386\pi$
$443$	14.0866			0.669276			0.334638	+	0.942347i	$0.391386\pi$
$444$		0			0
$445$	0.133293			0.00631869
$446$	27.9268	−	26.0863i	1.32237	−	1.23522i
$447$		0			0
$448$	9.96647	+	2.06572i	0.470871	+	0.0975961i
$449$			9.55838i			0.451088i	0.974233	+	0.225544i	$0.0724159\pi$
$449$			9.55838i			0.451088i	−0.974233	+	0.225544i	$0.927584\pi$
$450$		0			0
$451$			42.1839i			1.98636i
$452$	−5.43096	−	0.370554i	−0.255451	−	0.0174294i
$453$		0			0
$454$	19.5086	+	20.8851i	0.915586	+	0.980185i
$455$	0.105494			0.00494565
$456$		0			0
$457$	−13.0167			−0.608895			−0.304448	−	0.952529i	$-0.598472\pi$
$457$	−13.0167			−0.608895			−0.304448	+	0.952529i	$0.598472\pi$
$458$	9.58173	+	10.2578i	0.447725	+	0.479314i
$459$		0			0
$460$	0.913097	+	0.0623006i	0.0425733	+	0.00290478i
$461$			24.7561i			1.15301i	0.817095	+	0.576503i	$0.195583\pi$
$461$			24.7561i			1.15301i	−0.817095	+	0.576503i	$0.804417\pi$
$462$		0			0
$463$			23.0596i			1.07167i	0.844322	+	0.535836i	$0.180003\pi$
$463$			23.0596i			1.07167i	−0.844322	+	0.535836i	$0.819997\pi$
$464$	3.35423	−	24.4659i	0.155716	−	1.13580i
$465$		0			0
$466$	1.98956	−	1.85843i	0.0921644	−	0.0860903i
$467$	−19.2484			−0.890712			−0.445356	−	0.895354i	$-0.646923\pi$
$467$	−19.2484			−0.890712			−0.445356	+	0.895354i	$0.646923\pi$
$468$		0			0
$469$	3.68348			0.170087
$470$	−0.385180	+	0.359795i	−0.0177670	+	0.0165961i
$471$		0			0
$472$	−13.2837	+	10.8127i	−0.611430	+	0.497696i
$473$		−	23.6920i		−	1.08936i
$474$		0			0
$475$		−	4.99652i		−	0.229256i
$476$	1.42037	−	20.8173i	0.0651024	−	0.954161i
$477$		0			0
$478$	−19.6112	−	20.9949i	−0.896996	−	0.960284i
$479$	−24.6787			−1.12760			−0.563799	−	0.825912i	$-0.690661\pi$
$479$	−24.6787			−1.12760			−0.563799	+	0.825912i	$0.690661\pi$
$480$		0			0
$481$	8.08918			0.368835
$482$	0.848745	+	0.908628i	0.0386593	+	0.0413869i
$483$		0			0
$484$	−2.29220	+	33.5952i	−0.104191	+	1.52705i
$485$		−	0.842654i		−	0.0382629i
$486$		0			0
$487$		−	20.2803i		−	0.918986i	−0.888181	−	0.459493i	$-0.848031\pi$
$487$		−	20.2803i		−	0.918986i	0.888181	−	0.459493i	$-0.151969\pi$
$488$	−14.7481	+	12.0047i	−0.667614	+	0.543429i
$489$		0			0
$490$	−0.328128	+	0.306502i	−0.0148233	+	0.0138464i
$491$	−21.5002			−0.970289			−0.485144	−	0.874434i	$-0.661233\pi$
$491$	−21.5002			−0.970289			−0.485144	+	0.874434i	$0.661233\pi$
$492$		0			0
$493$	−50.6248			−2.28003
$494$	−1.45241	+	1.35668i	−0.0653468	+	0.0610401i
$495$		0			0
$496$	−3.83519	+	27.9741i	−0.172205	+	1.25607i
$497$			11.4079i			0.511712i
$498$		0			0
$499$			13.8397i			0.619551i	0.950810	+	0.309776i	$0.100254\pi$
$499$			13.8397i			0.619551i	−0.950810	+	0.309776i	$0.899746\pi$
$500$	−1.17687	−	0.0802975i	−0.0526310	−	0.00359101i
$501$		0			0
$502$	−9.89934	−	10.5978i	−0.441829	−	0.473002i
$503$	30.3835			1.35473			0.677366	−	0.735646i	$-0.263121\pi$
$503$	30.3835			1.35473			0.677366	+	0.735646i	$0.263121\pi$
$504$		0			0
$505$	0.526085			0.0234105
$506$	−39.5038	−	42.2909i	−1.75616	−	1.88006i
$507$		0			0
$508$	35.8570	+	2.44652i	1.59090	+	0.108547i
$509$			1.67351i			0.0741769i	0.999312	+	0.0370884i	$0.0118083\pi$
$509$			1.67351i			0.0741769i	−0.999312	+	0.0370884i	$0.988192\pi$
$510$		0			0
$511$		−	3.88758i		−	0.171976i
$512$	10.4255	+	20.0825i	0.460748	+	0.887531i
$513$		0			0
$514$	13.3808	−	12.4989i	0.590200	−	0.551303i
$515$	0.246212			0.0108494
$516$		0			0
$517$	33.3285			1.46578
$518$	7.56837	−	7.06958i	0.332535	−	0.310619i
$519$		0			0
$520$	0.148053	+	0.181886i	0.00649254	+	0.00797622i
$521$		−	1.00103i		−	0.0438557i	−0.999760	−	0.0219279i	$-0.993020\pi$
$521$		−	1.00103i		−	0.0438557i	0.999760	−	0.0219279i	$-0.00698042\pi$
$522$		0			0
$523$			10.5428i			0.461003i	0.973072	+	0.230502i	$0.0740367\pi$
$523$			10.5428i			0.461003i	−0.973072	+	0.230502i	$0.925963\pi$
$524$	−2.33008	+	34.1504i	−0.101790	+	1.49187i
$525$		0			0
$526$	1.70214	+	1.82223i	0.0742168	+	0.0794531i
$527$	57.8839			2.52146
$528$		0			0
$529$	37.1558			1.61547
$530$	0.601016	+	0.643421i	0.0261065	+	0.0279484i
$531$		0			0
$532$	−0.173214	+	2.53867i	−0.00750976	+	0.110065i
$533$		−	11.2364i		−	0.486701i
$534$		0			0
$535$		−	0.751125i		−	0.0324740i
$536$	5.16946	+	6.35079i	0.223287	+	0.274312i
$537$		0			0
$538$	0.495375	−	0.462727i	0.0213571	−	0.0199496i
$539$	28.3919			1.22293
$540$		0			0
$541$	12.8721			0.553414			0.276707	−	0.960954i	$-0.410757\pi$
$541$	12.8721			0.553414			0.276707	+	0.960954i	$0.410757\pi$
$542$	−17.7383	+	16.5693i	−0.761926	+	0.711712i
$543$		0			0
$544$	37.8851	−	26.7665i	1.62431	−	1.14760i
$545$			0.898423i			0.0384842i
$546$		0			0
$547$			6.97730i			0.298328i	0.988812	+	0.149164i	$0.0476582\pi$
$547$			6.97730i			0.298328i	−0.988812	+	0.149164i	$0.952342\pi$
$548$	33.3149	+	2.27308i	1.42314	+	0.0971010i
$549$		0			0
$550$	25.4488	+	27.2443i	1.08514	+	1.16170i
$551$	6.17369			0.263008
$552$		0			0
$553$	3.40796			0.144921
$554$	−13.5445	−	14.5001i	−0.575449	−	0.616050i
$555$		0			0
$556$	−18.8319	−	1.28490i	−0.798649	−	0.0544918i
$557$		−	25.0555i		−	1.06164i	−0.847485	−	0.530819i	$-0.821885\pi$
$557$		−	25.0555i		−	1.06164i	0.847485	−	0.530819i	$-0.178115\pi$
$558$		0			0
$559$			6.31076i			0.266917i
$560$	0.297480	+	0.0407840i	0.0125708	+	0.00172344i
$561$		0			0
$562$	−15.2289	+	14.2252i	−0.642392	+	0.600055i
$563$	−3.47474			−0.146443			−0.0732213	−	0.997316i	$-0.523328\pi$
$563$	−3.47474			−0.146443			−0.0732213	+	0.997316i	$0.523328\pi$
$564$		0			0
$565$	−0.160587			−0.00675596
$566$	15.3902	−	14.3759i	0.646898	−	0.604264i
$567$		0			0
$568$	−19.6686	+	16.0100i	−0.825276	+	0.671764i
$569$		−	7.33875i		−	0.307656i	−0.988098	−	0.153828i	$-0.950840\pi$
$569$		−	7.33875i		−	0.307656i	0.988098	−	0.153828i	$-0.0491602\pi$
$570$		0			0
$571$		−	11.2529i		−	0.470918i	−0.971884	−	0.235459i	$-0.924341\pi$
$571$		−	11.2529i		−	0.470918i	0.971884	−	0.235459i	$-0.0756593\pi$
$572$	1.00947	−	14.7951i	0.0422080	−	0.618614i
$573$		0			0
$574$	−9.82006	−	10.5129i	−0.409882	−	0.438801i
$575$	−38.7531			−1.61612
$576$		0			0
$577$	39.2311			1.63321			0.816606	−	0.577196i	$-0.195853\pi$
$577$	39.2311			1.63321			0.816606	+	0.577196i	$0.195853\pi$
$578$	−48.5013	−	51.9233i	−2.01739	−	2.15973i
$579$		0			0
$580$	0.0495905	−	0.726813i	0.00205913	−	0.0301793i
$581$			11.8896i			0.493263i
$582$		0			0
$583$		−	55.6733i		−	2.30575i
$584$	6.70268	−	5.45590i	0.277359	−	0.225767i
$585$		0			0
$586$	−31.9868	+	29.8787i	−1.32136	+	1.23428i
$587$	13.3109			0.549400			0.274700	−	0.961530i	$-0.411421\pi$
$587$	13.3109			0.549400			0.274700	+	0.961530i	$0.411421\pi$
$588$		0			0
$589$	−7.05893			−0.290858
$590$	−0.369250	+	0.344914i	−0.0152018	+	0.0141999i
$591$		0			0
$592$	22.8104	+	3.12727i	0.937503	+	0.128530i
$593$			16.0593i			0.659475i	0.944073	+	0.329737i	$0.106960\pi$
$593$			16.0593i			0.659475i	−0.944073	+	0.329737i	$0.893040\pi$
$594$		0			0
$595$		−	0.615546i		−	0.0252349i
$596$	−9.62320	−	0.656591i	−0.394182	−	0.0268950i
$597$		0			0
$598$	10.5225	+	11.2649i	0.430296	+	0.460655i
$599$	−19.0431			−0.778081			−0.389041	−	0.921221i	$-0.627193\pi$
$599$	−19.0431			−0.778081			−0.389041	+	0.921221i	$0.627193\pi$
$600$		0			0
$601$	19.3126			0.787776			0.393888	−	0.919158i	$-0.371130\pi$
$601$	19.3126			0.787776			0.393888	+	0.919158i	$0.371130\pi$
$602$	5.51532	+	5.90445i	0.224788	+	0.240647i
$603$		0			0
$604$	−5.81268	−	0.396599i	−0.236515	−	0.0161374i
$605$			0.993372i			0.0403863i
$606$		0			0
$607$		−	47.0591i		−	1.91007i	−0.296496	−	0.955034i	$-0.595818\pi$
$607$		−	47.0591i		−	1.91007i	0.296496	−	0.955034i	$-0.404182\pi$
$608$	−4.62008	+	3.26417i	−0.187369	+	0.132380i
$609$		0			0
$610$	−0.409956	+	0.382938i	−0.0165986	+	0.0155047i
$611$	−8.87758			−0.359148
$612$		0			0
$613$	17.2968			0.698611			0.349305	−	0.937009i	$-0.386418\pi$
$613$	17.2968			0.698611			0.349305	+	0.937009i	$0.386418\pi$
$614$	−25.9280	+	24.2193i	−1.04637	+	0.977410i
$615$		0			0
$616$	−11.9858	−	14.7247i	−0.482920	−	0.593277i
$617$		−	41.0256i		−	1.65163i	−0.563943	−	0.825814i	$-0.690716\pi$
$617$		−	41.0256i		−	1.65163i	0.563943	−	0.825814i	$-0.309284\pi$
$618$		0			0
$619$			18.7560i			0.753868i	0.926240	+	0.376934i	$0.123022\pi$
$619$			18.7560i			0.753868i	−0.926240	+	0.376934i	$0.876978\pi$
$620$	−0.0567012	+	0.831031i	−0.00227718	+	0.0333750i
$621$		0			0
$622$	−28.1836	−	30.1721i	−1.13006	−	1.20979i
$623$	2.87432			0.115157
$624$		0			0
$625$	24.9478			0.997912
$626$	−13.1819	−	14.1120i	−0.526856	−	0.564028i
$627$		0			0
$628$	−1.84077	+	26.9789i	−0.0734549	+	1.07658i
$629$		−	47.1993i		−	1.88196i
$630$		0			0
$631$		−	33.5966i		−	1.33746i	−0.743506	−	0.668729i	$-0.766839\pi$
$631$		−	33.5966i		−	1.33746i	0.743506	−	0.668729i	$-0.233161\pi$
$632$	4.78279	+	5.87575i	0.190249	+	0.233725i
$633$		0			0
$634$	10.7167	−	10.0104i	0.425615	−	0.397565i
$635$	1.06025			0.0420748
$636$		0			0
$637$	−7.56265			−0.299643
$638$	−33.6630	+	31.4445i	−1.33273	+	1.24490i
$639$		0			0
$640$	0.347172	+	0.570131i	0.0137232	+	0.0225364i
$641$			13.0330i			0.514774i	0.966308	+	0.257387i	$0.0828614\pi$
$641$			13.0330i			0.514774i	−0.966308	+	0.257387i	$0.917139\pi$
$642$		0			0
$643$			43.7535i			1.72547i	0.505656	+	0.862735i	$0.331251\pi$
$643$			43.7535i			1.72547i	−0.505656	+	0.862735i	$0.668749\pi$
$644$	19.6900	+	1.34345i	0.775894	+	0.0529392i
$645$		0			0
$646$	7.91607	+	8.47459i	0.311454	+	0.333428i
$647$	−13.7984			−0.542470			−0.271235	−	0.962513i	$-0.587432\pi$
$647$	−13.7984			−0.542470			−0.271235	+	0.962513i	$0.587432\pi$
$648$		0			0
$649$	31.9501			1.25415
$650$	−6.77870	−	7.25697i	−0.265883	−	0.284642i
$651$		0			0
$652$	1.24939	+	0.0852461i	0.0489300	+	0.00333849i
$653$			12.0895i			0.473098i	0.971620	+	0.236549i	$0.0760163\pi$
$653$			12.0895i			0.473098i	−0.971620	+	0.236549i	$0.923984\pi$
$654$		0			0
$655$			1.00979i			0.0394558i
$656$	4.34396	−	31.6850i	0.169603	−	1.23709i
$657$		0			0
$658$	−8.30600	+	7.75860i	−0.323802	+	0.302462i
$659$	11.0743			0.431395			0.215698	−	0.976460i	$-0.430797\pi$
$659$	11.0743			0.431395			0.215698	+	0.976460i	$0.430797\pi$
$660$		0			0
$661$	−22.6286			−0.880151			−0.440075	−	0.897961i	$-0.645048\pi$
$661$	−22.6286			−0.880151			−0.440075	+	0.897961i	$0.645048\pi$
$662$	25.0259	−	23.3766i	0.972659	−	0.908556i
$663$		0			0
$664$	−20.4992	+	16.6860i	−0.795522	+	0.647544i
$665$			0.0750657i			0.00291092i
$666$		0			0
$667$		−	47.8832i		−	1.85405i
$668$	0.893056	−	13.0889i	0.0345534	−	0.506425i
$669$		0			0
$670$	0.164900	+	0.176535i	0.00637065	+	0.00682013i
$671$	35.4723			1.36939
$672$		0			0
$673$	10.8668			0.418885			0.209442	−	0.977821i	$-0.432835\pi$
$673$	10.8668			0.418885			0.209442	+	0.977821i	$0.432835\pi$
$674$	−11.4852	−	12.2955i	−0.442393	−	0.473606i
$675$		0			0
$676$	1.50098	−	21.9988i	0.0577299	−	0.846107i
$677$		−	14.7801i		−	0.568044i	−0.958818	−	0.284022i	$-0.908331\pi$
$677$		−	14.7801i		−	0.568044i	0.958818	−	0.284022i	$-0.0916688\pi$
$678$		0			0
$679$		−	18.1709i		−	0.697337i
$680$	1.06128	−	0.863867i	0.0406982	−	0.0331278i
$681$		0			0
$682$	38.4900	−	35.9533i	1.47386	−	1.37672i
$683$	21.9180			0.838669			0.419334	−	0.907832i	$-0.362263\pi$
$683$	21.9180			0.838669			0.419334	+	0.907832i	$0.362263\pi$
$684$		0			0
$685$	0.985085			0.0376382
$686$	−16.2799	+	15.2069i	−0.621568	+	0.580604i
$687$		0			0
$688$	−2.43973	+	17.7955i	−0.0930140	+	0.678448i
$689$			14.8295i			0.564958i
$690$		0			0
$691$			5.66773i			0.215611i	0.994172	+	0.107805i	$0.0343823\pi$
$691$			5.66773i			0.215611i	−0.994172	+	0.107805i	$0.965618\pi$
$692$	−20.5116	−	1.39951i	−0.779734	−	0.0532012i
$693$		0			0
$694$	3.45309	+	3.69672i	0.131078	+	0.140326i
$695$	−0.556838			−0.0211221
$696$		0			0
$697$	−65.5627			−2.48336
$698$	3.52132	+	3.76977i	0.133284	+	0.142688i
$699$		0			0
$700$	−12.6845	−	0.865465i	−0.479430	−	0.0327115i
$701$		−	23.8905i		−	0.902331i	−0.892440	−	0.451166i	$-0.851008\pi$
$701$		−	23.8905i		−	0.902331i	0.892440	−	0.451166i	$-0.148992\pi$
$702$		0			0
$703$			5.75595i			0.217090i
$704$	8.56633	−	41.3299i	0.322856	−	1.55768i
$705$		0			0
$706$	1.43726	−	1.34254i	0.0540919	−	0.0505270i
$707$	11.3445			0.426653
$708$		0			0
$709$	40.2727			1.51247			0.756237	−	0.654298i	$-0.227036\pi$
$709$	40.2727			1.51247			0.756237	+	0.654298i	$0.227036\pi$
$710$	−0.546734	+	0.510701i	−0.0205186	+	0.0191663i
$711$		0			0
$712$	4.03387	+	4.95570i	0.151176	+	0.185723i
$713$			54.7492i			2.05037i
$714$		0			0
$715$		−	0.437474i		−	0.0163606i
$716$	2.53654	−	37.1764i	0.0947951	−	1.38935i
$717$		0			0
$718$	−30.7118	−	32.8787i	−1.14615	−	1.22702i
$719$	−11.8037			−0.440203			−0.220101	−	0.975477i	$-0.570639\pi$
$719$	−11.8037			−0.440203			−0.220101	+	0.975477i	$0.570639\pi$
$720$		0			0
$721$	5.30930			0.197729
$722$	−0.965364	−	1.03348i	−0.0359271	−	0.0384620i
$723$		0			0
$724$	0.488167	−	7.15473i	0.0181426	−	0.265903i
$725$			30.8470i			1.14563i
$726$		0			0
$727$			16.7659i			0.621813i	0.950441	+	0.310906i	$0.100633\pi$
$727$			16.7659i			0.621813i	−0.950441	+	0.310906i	$0.899367\pi$
$728$	3.19260	+	3.92218i	0.118326	+	0.145366i
$729$		0			0
$730$	0.186316	−	0.174037i	0.00689588	−	0.00644140i
$731$	36.8224			1.36193
$732$		0			0
$733$	20.1955			0.745936			0.372968	−	0.927844i	$-0.378340\pi$
$733$	20.1955			0.745936			0.372968	+	0.927844i	$0.378340\pi$
$734$	−13.7310	+	12.8261i	−0.506821	+	0.473419i
$735$		0			0
$736$	25.3170	+	35.8334i	0.933196	+	1.32084i
$737$		−	15.2750i		−	0.562662i
$738$		0			0
$739$		−	36.9489i		−	1.35919i	−0.733589	−	0.679593i	$-0.762156\pi$
$739$		−	36.9489i		−	1.35919i	0.733589	−	0.679593i	$-0.237844\pi$
$740$	0.677634	+	0.0462349i	0.0249103	+	0.00169963i
$741$		0			0
$742$	12.9603	+	13.8747i	0.475787	+	0.509356i
$743$	−0.783282			−0.0287358			−0.0143679	−	0.999897i	$-0.504574\pi$
$743$	−0.783282			−0.0287358			−0.0143679	+	0.999897i	$0.504574\pi$
$744$		0			0
$745$	−0.284547			−0.0104250
$746$	−30.1106	−	32.2350i	−1.10243	−	1.18021i
$747$		0			0
$748$	−86.3274	−	5.89011i	−3.15644	−	0.215364i
$749$		−	16.1972i		−	0.591834i
$750$		0			0
$751$		−	30.8590i		−	1.12606i	−0.826437	−	0.563030i	$-0.809636\pi$
$751$		−	30.8590i		−	1.12606i	0.826437	−	0.563030i	$-0.190364\pi$
$752$	−25.0336	−	3.43206i	−0.912881	−	0.125154i
$753$		0			0
$754$	8.96670	−	8.37575i	0.326548	−	0.305027i
$755$	−0.171875			−0.00625516
$756$		0			0
$757$	21.0549			0.765255			0.382627	−	0.923903i	$-0.375019\pi$
$757$	21.0549			0.765255			0.382627	+	0.923903i	$0.375019\pi$
$758$	9.55848	−	8.92853i	0.347180	−	0.324299i
$759$		0			0
$760$	−0.129423	+	0.105349i	−0.00469466	+	0.00382139i
$761$		−	2.32164i		−	0.0841592i	−0.999114	−	0.0420796i	$-0.986602\pi$
$761$		−	2.32164i		−	0.0841592i	0.999114	−	0.0420796i	$-0.0133983\pi$
$762$		0			0
$763$			19.3736i			0.701370i
$764$	−0.532955	+	7.81115i	−0.0192816	+	0.282598i
$765$		0			0
$766$	15.0346	+	16.0954i	0.543223	+	0.581550i
$767$	−8.51042			−0.307294
$768$		0			0
$769$	−37.4345			−1.34992			−0.674961	−	0.737853i	$-0.735840\pi$
$769$	−37.4345			−1.34992			−0.674961	+	0.737853i	$0.735840\pi$
$770$	−0.382333	−	0.409308i	−0.0137783	−	0.0147504i
$771$		0			0
$772$	−0.955726	+	14.0074i	−0.0343973	+	0.504138i
$773$			7.48535i			0.269229i	0.990898	+	0.134615i	$0.0429797\pi$
$773$			7.48535i			0.269229i	−0.990898	+	0.134615i	$0.957020\pi$
$774$		0			0
$775$		−	35.2701i		−	1.26694i
$776$	31.3290	−	25.5014i	1.12465	−	0.915448i
$777$		0			0
$778$	−20.3416	+	19.0010i	−0.729280	+	0.681217i
$779$	7.99536			0.286463
$780$		0			0
$781$	47.3072			1.69279
$782$	65.7291	−	61.3972i	2.35047	−	2.19556i
$783$		0			0
$784$	−21.3257	−	2.92371i	−0.761631	−	0.104418i
$785$			0.797738i			0.0284725i
$786$		0			0
$787$		−	2.29084i		−	0.0816598i	−0.999166	−	0.0408299i	$-0.987000\pi$
$787$		−	2.29084i		−	0.0816598i	0.999166	−	0.0408299i	$-0.0130002\pi$
$788$	10.8239	+	0.738516i	0.385586	+	0.0263085i
$789$		0			0
$790$	0.152566	+	0.163330i	0.00542804	+	0.00581102i
$791$	−3.46290			−0.123127
$792$		0			0
$793$	−9.44862			−0.335530
$794$	8.33067	+	8.91844i	0.295644	+	0.316504i
$795$		0			0
$796$	−2.04220	−	0.139339i	−0.0723838	−	0.00493875i
$797$		−	9.49545i		−	0.336346i	−0.985757	−	0.168173i	$-0.946213\pi$
$797$		−	9.49545i		−	0.336346i	0.985757	−	0.168173i	$-0.0537868\pi$
$798$		0			0
$799$			51.7995i			1.83253i
$800$	−16.3095	−	23.0843i	−0.576628	−	0.816155i
$801$		0			0
$802$	21.2908	−	19.8877i	0.751805	−	0.702258i
$803$	−16.1214			−0.568912
$804$		0			0
$805$	0.582211			0.0205202
$806$	−10.2524	+	9.57675i	−0.361127	+	0.337327i
$807$		0			0
$808$	15.9210	+	19.5593i	0.560100	+	0.688095i
$809$		−	52.8555i		−	1.85830i	−0.369704	−	0.929150i	$-0.620541\pi$
$809$		−	52.8555i		−	1.85830i	0.369704	−	0.929150i	$-0.379459\pi$
$810$		0			0
$811$		−	53.7682i		−	1.88806i	−0.329863	−	0.944029i	$-0.607002\pi$
$811$		−	53.7682i		−	1.88806i	0.329863	−	0.944029i	$-0.392998\pi$
$812$	1.06937	−	15.6730i	0.0375274	−	0.550013i
$813$		0			0
$814$	−29.3168	−	31.3853i	−1.02755	−	1.10005i
$815$	0.0369432			0.00129406
$816$		0			0
$817$	−4.49049			−0.157103
$818$	32.2058	+	34.4781i	1.12605	+	1.20550i
$819$		0			0
$820$	0.0642231	−	0.941274i	0.00224277	−	0.0328707i
$821$			27.3310i			0.953860i	0.878941	+	0.476930i	$0.158250\pi$
$821$			27.3310i			0.953860i	−0.878941	+	0.476930i	$0.841750\pi$
$822$		0			0
$823$			5.84119i			0.203611i	0.994804	+	0.101805i	$0.0324619\pi$
$823$			5.84119i			0.203611i	−0.994804	+	0.101805i	$0.967538\pi$
$824$	7.45116	+	9.15391i	0.259574	+	0.318892i
$825$		0			0
$826$	−7.96249	+	7.43772i	−0.277050	+	0.258791i
$827$	−42.5549			−1.47978			−0.739889	−	0.672729i	$-0.765122\pi$
$827$	−42.5549			−1.47978			−0.739889	+	0.672729i	$0.765122\pi$
$828$		0			0
$829$	−52.5676			−1.82575			−0.912874	−	0.408240i	$-0.866143\pi$
$829$	−52.5676			−1.82575			−0.912874	+	0.408240i	$0.866143\pi$
$830$	−0.569821	+	0.532267i	−0.0197788	+	0.0184753i
$831$		0			0
$832$	−2.28178	+	11.0089i	−0.0791066	+	0.381665i
$833$			44.1270i			1.52891i
$834$		0			0
$835$		−	0.387024i		−	0.0133935i
$836$	10.5276	+	0.718299i	0.364105	+	0.0248429i
$837$		0			0
$838$	23.9961	+	25.6892i	0.828933	+	0.887418i
$839$	5.79622			0.200108			0.100054	−	0.994982i	$-0.468099\pi$
$839$	5.79622			0.200108			0.100054	+	0.994982i	$0.468099\pi$
$840$		0			0
$841$	−9.11445			−0.314291
$842$	17.5386	+	18.7760i	0.604419	+	0.647064i
$843$		0			0
$844$	−25.1749	−	1.71769i	−0.866557	−	0.0591252i
$845$		−	0.650480i		−	0.0223772i
$846$		0			0
$847$			21.4210i			0.736036i
$848$	−5.73306	+	41.8172i	−0.196874	+	1.43601i
$849$		0			0
$850$	−42.3435	+	39.5528i	−1.45237	+	1.35665i
$851$	44.6432			1.53035
$852$		0			0
$853$	−27.1964			−0.931186			−0.465593	−	0.884999i	$-0.654159\pi$
$853$	−27.1964			−0.931186			−0.465593	+	0.884999i	$0.654159\pi$
$854$	−8.84028	+	8.25766i	−0.302508	+	0.282571i
$855$		0			0
$856$	27.9261	−	22.7315i	0.954494	−	0.776946i
$857$			18.1477i			0.619912i	0.950751	+	0.309956i	$0.100314\pi$
$857$			18.1477i			0.619912i	−0.950751	+	0.309956i	$0.899686\pi$
$858$		0			0
$859$		−	22.4786i		−	0.766959i	−0.923549	−	0.383479i	$-0.874726\pi$
$859$		−	22.4786i		−	0.766959i	0.923549	−	0.383479i	$-0.125274\pi$
$860$	−0.0360701	+	0.528655i	−0.00122998	+	0.0180270i
$861$		0			0
$862$	−18.4953	−	19.8002i	−0.629952	−	0.674398i
$863$	−7.67220			−0.261165			−0.130582	−	0.991437i	$-0.541685\pi$
$863$	−7.67220			−0.261165			−0.130582	+	0.991437i	$0.541685\pi$
$864$		0			0
$865$	−0.606505			−0.0206218
$866$	−5.43528	−	5.81877i	−0.184698	−	0.197730i
$867$		0			0
$868$	−1.22270	+	17.9203i	−0.0415012	+	0.608255i
$869$		−	14.1325i		−	0.479411i
$870$		0			0
$871$			4.06875i			0.137864i
$872$	−33.4025	+	27.1892i	−1.13115	+	0.920742i
$873$		0			0
$874$	−8.01565	+	7.48738i	−0.271134	+	0.253264i
$875$	−0.750396			−0.0253680
$876$		0			0
$877$	23.0069			0.776888			0.388444	−	0.921472i	$-0.373013\pi$
$877$	23.0069			0.776888			0.388444	+	0.921472i	$0.373013\pi$
$878$	0.979604	−	0.915043i	0.0330600	−	0.0308812i
$879$		0			0
$880$	0.169127	−	1.23362i	0.00570127	−	0.0415853i
$881$			10.0755i			0.339452i	0.985491	+	0.169726i	$0.0542883\pi$
$881$			10.0755i			0.339452i	−0.985491	+	0.169726i	$0.945712\pi$
$882$		0			0
$883$			1.12094i			0.0377225i	0.999822	+	0.0188613i	$0.00600408\pi$
$883$			1.12094i			0.0377225i	−0.999822	+	0.0188613i	$0.993996\pi$
$884$	22.9947	+	1.56893i	0.773395	+	0.0527688i
$885$		0			0
$886$	13.5987	+	14.5582i	0.456858	+	0.489092i
$887$	−28.4631			−0.955698			−0.477849	−	0.878442i	$-0.658583\pi$
$887$	−28.4631			−0.955698			−0.477849	+	0.878442i	$0.658583\pi$
$888$		0			0
$889$	22.8632			0.766808
$890$	0.128676	+	0.137755i	0.00431324	+	0.00461756i
$891$		0			0
$892$	53.9191	+	3.67890i	1.80535	+	0.123179i
$893$		−	6.31694i		−	0.211388i
$894$		0			0
$895$		−	1.09926i		−	0.0367444i
$896$	7.48640	+	12.2943i	0.250103	+	0.410723i
$897$		0			0
$898$	−9.87836	+	9.22732i	−0.329645	+	0.307920i
$899$	43.5797			1.45346
$900$		0			0
$901$	86.5281			2.88267
$902$	−43.5960	+	40.7228i	−1.45159	+	1.35592i
$903$		0			0
$904$	−4.85989	−	5.97048i	−0.161638	−	0.198575i
$905$		−	0.211557i		−	0.00703241i
$906$		0			0
$907$			16.6933i			0.554292i	0.960828	+	0.277146i	$0.0893886\pi$
$907$			16.6933i			0.554292i	−0.960828	+	0.277146i	$0.910611\pi$
$908$	−2.75127	+	40.3234i	−0.0913040	+	1.33818i
$909$		0			0
$910$	0.101841	+	0.109026i	0.00337598	+	0.00361417i
$911$	40.2610			1.33391			0.666954	−	0.745099i	$-0.267598\pi$
$911$	40.2610			1.33391			0.666954	+	0.745099i	$0.267598\pi$
$912$		0			0
$913$	49.3049			1.63175
$914$	−12.5659	−	13.4524i	−0.415642	−	0.444967i
$915$		0			0
$916$	−1.35129	+	19.8050i	−0.0446480	+	0.654375i
$917$			21.7751i			0.719077i
$918$		0			0
$919$			52.2655i			1.72408i	0.506841	+	0.862040i	$0.330813\pi$
$919$			52.2655i			1.72408i	−0.506841	+	0.862040i	$0.669187\pi$
$920$	0.817085	+	1.00381i	0.0269385	+	0.0330945i
$921$		0			0
$922$	−25.5848	+	23.8986i	−0.842591	+	0.787060i
$923$	−12.6011			−0.414769
$924$		0			0
$925$	−28.7597			−0.945614
$926$	−23.8315	+	22.2609i	−0.783153	+	0.731539i
$927$		0			0
$928$	28.5230	−	20.1520i	0.936312	−	0.661522i
$929$			3.61665i			0.118658i	0.998238	+	0.0593291i	$0.0188961\pi$
$929$			3.61665i			0.118658i	−0.998238	+	0.0593291i	$0.981104\pi$
$930$		0			0
$931$		−	5.38129i		−	0.176365i
$932$	3.84129	+	0.262091i	0.125826	+	0.00858509i
$933$		0			0
$934$	−18.5818	−	19.8928i	−0.608014	−	0.650912i
$935$	−2.55260			−0.0834791
$936$		0			0
$937$	−42.8905			−1.40117			−0.700587	−	0.713567i	$-0.747078\pi$
$937$	−42.8905			−1.40117			−0.700587	+	0.713567i	$0.747078\pi$
$938$	3.55590	+	3.80679i	0.116104	+	0.124296i
$939$		0			0
$940$	−0.743678	−	0.0507411i	−0.0242561	−	0.00165499i
$941$			4.99580i			0.162858i	0.996679	+	0.0814292i	$0.0259484\pi$
$941$			4.99580i			0.162858i	−0.996679	+	0.0814292i	$0.974052\pi$
$942$		0			0
$943$		−	62.0121i		−	2.01939i
$944$	−23.9983	−	3.29012i	−0.781077	−	0.107084i
$945$		0			0
$946$	24.4852	−	22.8715i	0.796081	−	0.743615i
$947$	37.6577			1.22371			0.611856	−	0.790969i	$-0.290423\pi$
$947$	37.6577			1.22371			0.611856	+	0.790969i	$0.290423\pi$
$948$		0			0
$949$	4.29420			0.139396
$950$	5.16378	−	4.82346i	0.167535	−	0.156494i
$951$		0			0
$952$	22.8854	−	18.6284i	0.741719	−	0.603750i
$953$		−	15.6600i		−	0.507278i	−0.967299	−	0.253639i	$-0.918373\pi$
$953$		−	15.6600i		−	0.507278i	0.967299	−	0.253639i	$-0.0816274\pi$
$954$		0			0
$955$			0.230967i			0.00747392i
$956$	2.76573	−	40.5354i	0.0894501	−	1.31101i
$957$		0			0
$958$	−23.8239	−	25.5048i	−0.769716	−	0.824024i
$959$	21.2423			0.685951
$960$		0			0
$961$	−18.8285			−0.607372
$962$	7.80901	+	8.35997i	0.251773	+	0.269536i
$963$		0			0
$964$	−0.119697	+	1.75431i	−0.00385517	+	0.0565026i
$965$			0.414184i			0.0133331i
$966$		0			0
$967$			39.2763i			1.26304i	0.775360	+	0.631520i	$0.217569\pi$
$967$			39.2763i			1.26304i	−0.775360	+	0.631520i	$0.782431\pi$
$968$	−36.9326	+	30.0627i	−1.18706	+	0.966250i
$969$		0			0
$970$	0.870862	−	0.813468i	0.0279617	−	0.0261189i
$971$	30.1803			0.968532			0.484266	−	0.874921i	$-0.339087\pi$
$971$	30.1803			0.968532			0.484266	+	0.874921i	$0.339087\pi$
$972$		0			0
$973$	−12.0076			−0.384947
$974$	20.9591	−	19.5778i	0.671574	−	0.627314i
$975$		0			0
$976$	−26.6439	−	3.65283i	−0.852849	−	0.116924i
$977$		−	4.23963i		−	0.135638i	−0.997698	−	0.0678189i	$-0.978396\pi$
$977$		−	4.23963i		−	0.135638i	0.997698	−	0.0678189i	$-0.0216040\pi$
$978$		0			0
$979$		−	11.9195i		−	0.380950i
$980$	−0.633525	−	0.0432254i	−0.0202372	−	0.00138079i
$981$		0			0
$982$	−20.7555	−	22.2199i	−0.662334	−	0.709065i
$983$	−33.6677			−1.07383			−0.536916	−	0.843635i	$-0.680411\pi$
$983$	−33.6677			−1.07383			−0.536916	+	0.843635i	$0.680411\pi$
$984$		0			0
$985$	0.320051			0.0101977
$986$	−48.8714	−	52.3195i	−1.55638	−	1.66619i
$987$		0			0
$988$	−2.80420	−	0.191331i	−0.0892135	−	0.00608704i
$989$			34.8283i			1.10748i
$990$		0			0
$991$			7.37922i			0.234409i	0.993108	+	0.117204i	$0.0373932\pi$
$991$			7.37922i			0.234409i	−0.993108	+	0.117204i	$0.962607\pi$
$992$	−32.6129	+	23.0416i	−1.03546	+	0.731571i
$993$		0			0
$994$	−11.7897	+	11.0127i	−0.373948	+	0.349303i
$995$	−0.0603856			−0.00191435
$996$		0			0
$997$	−25.7846			−0.816607			−0.408303	−	0.912846i	$-0.633879\pi$
$997$	−25.7846			−0.816607			−0.408303	+	0.912846i	$0.633879\pi$
$998$	−14.3030	+	13.3604i	−0.452754	+	0.422915i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.c.b.647.24	yes	32
3.2	odd	2	inner	684.2.c.b.647.9	✓	32
4.3	odd	2	inner	684.2.c.b.647.10	yes	32
12.11	even	2	inner	684.2.c.b.647.23	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.c.b.647.9	✓	32	3.2	odd	2	inner
684.2.c.b.647.10	yes	32	4.3	odd	2	inner
684.2.c.b.647.23	yes	32	12.11	even	2	inner
684.2.c.b.647.24	yes	32	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965364 + 1.03348i) q^{2} +(-0.136143 + 1.99536i) q^{4} +0.0590006i q^{5} +1.27229i q^{7} +(-2.19358 + 1.78555i) q^{8} +(-0.0609757 + 0.0569571i) q^{10} +5.27604 q^{11} -1.40536 q^{13} +(-1.31488 + 1.22822i) q^{14} +(-3.96293 - 0.543311i) q^{16} +8.20009i q^{17} -1.00000i q^{19} +(-0.117728 - 0.00803255i) q^{20} +(5.09330 + 5.45266i) q^{22} -7.75602 q^{23} +4.99652 q^{25} +(-1.35668 - 1.45241i) q^{26} +(-2.53867 - 0.173214i) q^{28} +6.17369i q^{29} -7.05893i q^{31} +(-3.26417 - 4.62008i) q^{32} +(-8.47459 + 7.91607i) q^{34} -0.0750657 q^{35} -5.75595 q^{37} +(1.03348 - 0.965364i) q^{38} +(-0.105349 - 0.129423i) q^{40} +7.99536i q^{41} -4.49049i q^{43} +(-0.718299 + 10.5276i) q^{44} +(-7.48738 - 8.01565i) q^{46} +6.31694 q^{47} +5.38129 q^{49} +(4.82346 + 5.16378i) q^{50} +(0.191331 - 2.80420i) q^{52} -10.5521i q^{53} +0.311290i q^{55} +(-2.27173 - 2.79087i) q^{56} +(-6.38036 + 5.95986i) q^{58} +6.05569 q^{59} +6.72327 q^{61} +(7.29524 - 6.81444i) q^{62} +(1.62363 - 7.83351i) q^{64} -0.0829171i q^{65} -2.89516i q^{67} +(-16.3621 - 1.11639i) q^{68} +(-0.0724658 - 0.0775786i) q^{70} +8.96642 q^{71} -3.05558 q^{73} +(-5.55659 - 5.94863i) q^{74} +(1.99536 + 0.136143i) q^{76} +6.71264i q^{77} -2.67861i q^{79} +(0.0320557 - 0.233815i) q^{80} +(-8.26301 + 7.71843i) q^{82} +9.34505 q^{83} -0.483810 q^{85} +(4.64082 - 4.33496i) q^{86} +(-11.5735 + 9.42064i) q^{88} -2.25918i q^{89} -1.78802i q^{91} +(1.05593 - 15.4761i) q^{92} +(6.09815 + 6.52840i) q^{94} +0.0590006 q^{95} -14.2821 q^{97} +(5.19490 + 5.56143i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4} - 8 q^{10} - 24 q^{16} - 64 q^{25} + 48 q^{34} + 32 q^{37} + 8 q^{40} + 32 q^{46} + 16 q^{49} - 32 q^{58} + 56 q^{64} - 72 q^{70} - 48 q^{73} - 112 q^{82} - 16 q^{85} - 40 q^{88} + 88 q^{94}+ \cdots - 128 q^{97}+O(q^{100}) \) 32 * q + 8 * q^4 - 8 * q^10 - 24 * q^16 - 64 * q^25 + 48 * q^34 + 32 * q^37 + 8 * q^40 + 32 * q^46 + 16 * q^49 - 32 * q^58 + 56 * q^64 - 72 * q^70 - 48 * q^73 - 112 * q^82 - 16 * q^85 - 40 * q^88 + 88 * q^94 - 128 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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