LMFDB - Embedded newform 936.2.r.f.601.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(601,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 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("936.601"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.r (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			601.15
Character	$\chi$	$=$	936.601
Dual form			936.2.r.f.841.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.17173 - 1.27555i) q^{3} +(-0.185033 - 0.320487i) q^{5} +(-0.110414 - 0.191243i) q^{7} +(-0.254080 - 2.98922i) q^{9} +4.20860 q^{11} +(3.45336 + 1.03649i) q^{13} +(-0.625609 - 0.139505i) q^{15} +(-1.24758 + 2.16087i) q^{17} +(0.226112 - 0.391637i) q^{19} +(-0.373317 - 0.0832466i) q^{21} +(1.02622 - 1.77746i) q^{23} +(2.43153 - 4.21153i) q^{25} +(-4.11063 - 3.17848i) q^{27} -3.70170 q^{29} +(-0.816082 - 1.41349i) q^{31} +(4.93135 - 5.36829i) q^{33} +(-0.0408606 + 0.0707727i) q^{35} +(-5.00558 - 8.66991i) q^{37} +(5.36851 - 3.19046i) q^{39} +(2.03588 - 3.52625i) q^{41} +(5.75733 + 9.97199i) q^{43} +(-0.910994 + 0.634535i) q^{45} +(0.918184 - 1.59034i) q^{47} +(3.47562 - 6.01995i) q^{49} +(1.29447 + 4.12331i) q^{51} -7.12781 q^{53} +(-0.778731 - 1.34880i) q^{55} +(-0.234611 - 0.747311i) q^{57} -4.81685 q^{59} +(3.91401 + 6.77926i) q^{61} +(-0.543614 + 0.378644i) q^{63} +(-0.306806 - 1.29854i) q^{65} +(5.82974 - 10.0974i) q^{67} +(-1.06479 - 3.39171i) q^{69} +(-6.89204 + 11.9374i) q^{71} +8.58734 q^{73} +(-2.52293 - 8.03633i) q^{75} +(-0.464689 - 0.804865i) q^{77} +(-6.36242 + 11.0200i) q^{79} +(-8.87089 + 1.51900i) q^{81} +(-5.54460 + 9.60353i) q^{83} +0.923373 q^{85} +(-4.33740 + 4.72172i) q^{87} +(-0.114134 - 0.197686i) q^{89} +(-0.183079 - 0.774874i) q^{91} +(-2.75922 - 0.615283i) q^{93} -0.167353 q^{95} +(-5.11306 - 8.85609i) q^{97} +(-1.06932 - 12.5804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + q^{5} + 7 q^{7} + 6 q^{9} + 11 q^{15} - q^{17} + 2 q^{19} - 30 q^{21} - q^{23} - 23 q^{25} - 3 q^{27} - 24 q^{29} + 8 q^{31} + 4 q^{33} - 12 q^{35} + 18 q^{37} + 6 q^{39} - 3 q^{41} + 8 q^{43}+ \cdots + 28 q^{99}+O(q^{100}) $ 40 * q + q^5 + 7 * q^7 + 6 * q^9 + 11 * q^15 - q^17 + 2 * q^19 - 30 * q^21 - q^23 - 23 * q^25 - 3 * q^27 - 24 * q^29 + 8 * q^31 + 4 * q^33 - 12 * q^35 + 18 * q^37 + 6 * q^39 - 3 * q^41 + 8 * q^43 + 24 * q^45 + 4 * q^47 - 23 * q^49 - 37 * q^51 - 40 * q^53 - 14 * q^55 + 7 * q^57 + 8 * q^59 - 3 * q^61 + 10 * q^63 - 32 * q^65 + 27 * q^67 - 38 * q^69 + q^71 - 12 * q^73 + 32 * q^75 - 4 * q^77 + 13 * q^79 + 26 * q^81 - 15 * q^83 - 10 * q^85 + 25 * q^87 + 12 * q^89 - 57 * q^91 - 7 * q^93 - 2 * q^95 + 35 * q^97 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	1.17173	−	1.27555i	0.676501	−	0.736442i
$3$	1.17173	−	1.27555i	0.676501	−	0.736442i
$4$		0			0
$5$	−0.185033	−	0.320487i	−0.0827494	−	0.143326i	0.821681	−	0.569948i	$-0.193037\pi$
$5$	−0.185033	−	0.320487i	−0.0827494	−	0.143326i	−0.904430	+	0.426622i	$0.859703\pi$
$6$		0			0
$7$	−0.110414	−	0.191243i	−0.0417327	−	0.0722831i	0.844405	−	0.535706i	$-0.179954\pi$
$7$	−0.110414	−	0.191243i	−0.0417327	−	0.0722831i	−0.886137	+	0.463423i	$0.846621\pi$
$8$		0			0
$9$	−0.254080	−	2.98922i	−0.0846933	−	0.996407i
$10$		0			0
$11$	4.20860			1.26894			0.634470	−	0.772948i	$-0.281219\pi$
$11$	4.20860			1.26894			0.634470	+	0.772948i	$0.281219\pi$
$12$		0			0
$13$	3.45336	+	1.03649i	0.957790	+	0.287470i
$13$	3.45336	+	1.03649i	0.957790	+	0.287470i
$14$		0			0
$15$	−0.625609	−	0.139505i	−0.161531	−	0.0360202i
$16$		0			0
$17$	−1.24758	+	2.16087i	−0.302582	+	0.524087i	−0.976720	−	0.214518i	$-0.931182\pi$
$17$	−1.24758	+	2.16087i	−0.302582	+	0.524087i	0.674138	+	0.738605i	$0.264515\pi$
$18$		0			0
$19$	0.226112	−	0.391637i	0.0518735	−	0.0898476i	−0.838923	−	0.544251i	$-0.816814\pi$
$19$	0.226112	−	0.391637i	0.0518735	−	0.0898476i	0.890796	+	0.454403i	$0.150147\pi$
$20$		0			0
$21$	−0.373317	−	0.0832466i	−0.0814645	−	0.0181659i
$22$		0			0
$23$	1.02622	−	1.77746i	0.213981	−	0.370626i	−0.738976	−	0.673732i	$-0.764690\pi$
$23$	1.02622	−	1.77746i	0.213981	−	0.370626i	0.952957	+	0.303106i	$0.0980236\pi$
$24$		0			0
$25$	2.43153	−	4.21153i	0.486305	−	0.842305i
$26$		0			0
$27$	−4.11063	−	3.17848i	−0.791091	−	0.611699i
$28$		0			0
$29$	−3.70170			−0.687388			−0.343694	−	0.939082i	$-0.611678\pi$
$29$	−3.70170			−0.687388			−0.343694	+	0.939082i	$0.611678\pi$
$30$		0			0
$31$	−0.816082	−	1.41349i	−0.146573	−	0.253871i	0.783386	−	0.621536i	$-0.213491\pi$
$31$	−0.816082	−	1.41349i	−0.146573	−	0.253871i	−0.929959	+	0.367664i	$0.880158\pi$
$32$		0			0
$33$	4.93135	−	5.36829i	0.858438	−	0.934500i
$34$		0			0
$35$	−0.0408606	+	0.0707727i	−0.00690671	+	0.0119628i
$36$		0			0
$37$	−5.00558	−	8.66991i	−0.822912	−	1.42533i	−0.903505	−	0.428578i	$-0.859015\pi$
$37$	−5.00558	−	8.66991i	−0.822912	−	1.42533i	0.0805930	−	0.996747i	$-0.474319\pi$
$38$		0			0
$39$	5.36851	−	3.19046i	0.859650	−	0.510883i
$40$		0			0
$41$	2.03588	−	3.52625i	0.317951	−	0.550707i	−0.662110	−	0.749407i	$-0.730339\pi$
$41$	2.03588	−	3.52625i	0.317951	−	0.550707i	0.980060	+	0.198700i	$0.0636720\pi$
$42$		0			0
$43$	5.75733	+	9.97199i	0.877985	+	1.52071i	0.853549	+	0.521013i	$0.174446\pi$
$43$	5.75733	+	9.97199i	0.877985	+	1.52071i	0.0244362	+	0.999701i	$0.492221\pi$
$44$		0			0
$45$	−0.910994	+	0.634535i	−0.135803	+	0.0945909i
$46$		0			0
$47$	0.918184	−	1.59034i	0.133931	−	0.231975i	−0.791258	−	0.611483i	$-0.790573\pi$
$47$	0.918184	−	1.59034i	0.133931	−	0.231975i	0.925189	+	0.379508i	$0.123907\pi$
$48$		0			0
$49$	3.47562	−	6.01995i	0.496517	−	0.859992i
$50$		0			0
$51$	1.29447	+	4.12331i	0.181263	+	0.577379i
$52$		0			0
$53$	−7.12781			−0.979080			−0.489540	−	0.871981i	$-0.662835\pi$
$53$	−7.12781			−0.979080			−0.489540	+	0.871981i	$0.662835\pi$
$54$		0			0
$55$	−0.778731	−	1.34880i	−0.105004	−	0.181872i
$56$		0			0
$57$	−0.234611	−	0.747311i	−0.0310750	−	0.0989838i
$58$		0			0
$59$	−4.81685			−0.627101			−0.313550	−	0.949572i	$-0.601518\pi$
$59$	−4.81685			−0.627101			−0.313550	+	0.949572i	$0.601518\pi$
$60$		0			0
$61$	3.91401	+	6.77926i	0.501137	+	0.867995i	0.999999	+	0.00131357i	$0.000418122\pi$
$61$	3.91401	+	6.77926i	0.501137	+	0.867995i	−0.498862	+	0.866681i	$0.666249\pi$
$62$		0			0
$63$	−0.543614	+	0.378644i	−0.0684889	+	0.0477046i
$64$		0			0
$65$	−0.306806	−	1.29854i	−0.0380546	−	0.161064i
$66$		0			0
$67$	5.82974	−	10.0974i	0.712216	−	1.23359i	−0.251807	−	0.967777i	$-0.581025\pi$
$67$	5.82974	−	10.0974i	0.712216	−	1.23359i	0.964023	−	0.265817i	$-0.0856418\pi$
$68$		0			0
$69$	−1.06479	−	3.39171i	−0.128186	−	0.408313i
$70$		0			0
$71$	−6.89204	+	11.9374i	−0.817935	+	1.41670i	0.0892667	+	0.996008i	$0.471548\pi$
$71$	−6.89204	+	11.9374i	−0.817935	+	1.41670i	−0.907201	+	0.420697i	$0.861786\pi$
$72$		0			0
$73$	8.58734			1.00507			0.502536	−	0.864556i	$-0.332400\pi$
$73$	8.58734			1.00507			0.502536	+	0.864556i	$0.332400\pi$
$74$		0			0
$75$	−2.52293	−	8.03633i	−0.291323	−	0.927955i
$76$		0			0
$77$	−0.464689	−	0.804865i	−0.0529562	−	0.0917229i
$78$		0			0
$79$	−6.36242	+	11.0200i	−0.715828	+	1.23985i	0.246812	+	0.969063i	$0.420617\pi$
$79$	−6.36242	+	11.0200i	−0.715828	+	1.23985i	−0.962639	+	0.270786i	$0.912716\pi$
$80$		0			0
$81$	−8.87089	+	1.51900i	−0.985654	+	0.168778i
$82$		0			0
$83$	−5.54460	+	9.60353i	−0.608599	+	1.05412i	0.382873	+	0.923801i	$0.374935\pi$
$83$	−5.54460	+	9.60353i	−0.608599	+	1.05412i	−0.991472	+	0.130323i	$0.958399\pi$
$84$		0			0
$85$	0.923373			0.100154
$86$		0			0
$87$	−4.33740	+	4.72172i	−0.465019	+	0.506221i
$88$		0			0
$89$	−0.114134	−	0.197686i	−0.0120982	−	0.0209546i	0.859913	−	0.510441i	$-0.170518\pi$
$89$	−0.114134	−	0.197686i	−0.0120982	−	0.0209546i	−0.872011	+	0.489486i	$0.837184\pi$
$90$		0			0
$91$	−0.183079	−	0.774874i	−0.0191919	−	0.0812289i
$92$		0			0
$93$	−2.75922	−	0.615283i	−0.286118	−	0.0638019i
$94$		0			0
$95$	−0.167353			−0.0171700
$96$		0			0
$97$	−5.11306	−	8.85609i	−0.519153	−	0.899199i	−0.999752	−	0.0222590i	$-0.992914\pi$
$97$	−5.11306	−	8.85609i	−0.519153	−	0.899199i	0.480599	−	0.876940i	$-0.340419\pi$
$98$		0			0
$99$	−1.06932	−	12.5804i	−0.107471	−	1.26438i
$100$		0			0
$101$	7.95139			0.791193			0.395596	−	0.918424i	$-0.370538\pi$
$101$	7.95139			0.791193			0.395596	+	0.918424i	$0.370538\pi$
$102$		0			0
$103$	3.16273	+	5.47801i	0.311633	+	0.539764i	0.978716	−	0.205219i	$-0.0657908\pi$
$103$	3.16273	+	5.47801i	0.311633	+	0.539764i	−0.667083	+	0.744983i	$0.732457\pi$
$104$		0			0
$105$	0.0423967	+	0.135047i	0.00413749	+	0.0131792i
$106$		0			0
$107$	2.59608	+	4.49654i	0.250973	+	0.434697i	0.963794	−	0.266648i	$-0.0859162\pi$
$107$	2.59608	+	4.49654i	0.250973	+	0.434697i	−0.712821	+	0.701346i	$0.752583\pi$
$108$		0			0
$109$	13.6259			1.30513			0.652564	−	0.757733i	$-0.273693\pi$
$109$	13.6259			1.30513			0.652564	+	0.757733i	$0.273693\pi$
$110$		0			0
$111$	−16.9242	−	3.77394i	−1.60637	−	0.358207i
$112$		0			0
$113$	−2.30577			−0.216908			−0.108454	−	0.994101i	$-0.534590\pi$
$113$	−2.30577			−0.216908			−0.108454	+	0.994101i	$0.534590\pi$
$114$		0			0
$115$	−0.759538			−0.0708272
$116$		0			0
$117$	2.22086	−	10.5862i	0.205318	−	0.978695i
$118$		0			0
$119$	0.551001			0.0505102
$120$		0			0
$121$	6.71228			0.610207
$122$		0			0
$123$	−2.11241	−	6.72870i	−0.190470	−	0.606706i
$124$		0			0
$125$	−3.64999			−0.326465
$126$		0			0
$127$	5.26106	+	9.11243i	0.466844	+	0.808597i	0.999283	−	0.0378713i	$-0.0120577\pi$
$127$	5.26106	+	9.11243i	0.466844	+	0.808597i	−0.532439	+	0.846469i	$0.678724\pi$
$128$		0			0
$129$	19.4659	+	4.34073i	1.71388	+	0.382180i
$130$		0			0
$131$	−1.94010	−	3.36036i	−0.169508	−	0.293596i	0.768739	−	0.639562i	$-0.220884\pi$
$131$	−1.94010	−	3.36036i	−0.169508	−	0.293596i	−0.938247	+	0.345967i	$0.887551\pi$
$132$		0			0
$133$	−0.0998637			−0.00865929
$134$		0			0
$135$	−0.258058	+	1.90553i	−0.0222101	+	0.164002i
$136$		0			0
$137$	5.78907	+	10.0270i	0.494594	+	0.856662i	0.999981	−	0.00623124i	$-0.00198348\pi$
$137$	5.78907	+	10.0270i	0.494594	+	0.856662i	−0.505387	+	0.862893i	$0.668650\pi$
$138$		0			0
$139$	5.31863			0.451121			0.225560	−	0.974229i	$-0.427579\pi$
$139$	5.31863			0.451121			0.225560	+	0.974229i	$0.427579\pi$
$140$		0			0
$141$	−0.952701	−	3.03465i	−0.0802319	−	0.255564i
$142$		0			0
$143$	14.5338	+	4.36215i	1.21538	+	0.364782i
$144$		0			0
$145$	0.684938	+	1.18635i	0.0568810	+	0.0985207i
$146$		0			0
$147$	−3.60627	−	11.4871i	−0.297440	−	0.947441i
$148$		0			0
$149$	−17.7627			−1.45518			−0.727589	−	0.686014i	$-0.759359\pi$
$149$	−17.7627			−1.45518			−0.727589	+	0.686014i	$0.759359\pi$
$150$		0			0
$151$	−8.56540	+	14.8357i	−0.697043	+	1.20731i	0.272445	+	0.962171i	$0.412168\pi$
$151$	−8.56540	+	14.8357i	−0.697043	+	1.20731i	−0.969487	+	0.245142i	$0.921166\pi$
$152$		0			0
$153$	6.77629	+	3.18025i	0.547830	+	0.257108i
$154$		0			0
$155$	−0.302005	+	0.523087i	−0.0242576	+	0.0420154i
$156$		0			0
$157$	−3.23205	−	5.59807i	−0.257946	−	0.446775i	0.707746	−	0.706467i	$-0.249712\pi$
$157$	−3.23205	−	5.59807i	−0.257946	−	0.446775i	−0.965691	+	0.259692i	$0.916379\pi$
$158$		0			0
$159$	−8.35190	+	9.09191i	−0.662348	+	0.721036i
$160$		0			0
$161$	−0.453236			−0.0357200
$162$		0			0
$163$	0.657316	−	1.13851i	0.0514850	−	0.0891746i	−0.839134	−	0.543924i	$-0.816938\pi$
$163$	0.657316	−	1.13851i	0.0514850	−	0.0891746i	0.890619	+	0.454750i	$0.150271\pi$
$164$		0			0
$165$	−2.63293	−	0.587122i	−0.204974	−	0.0457074i
$166$		0			0
$167$	−9.29599	+	16.1011i	−0.719346	+	1.24594i	0.241914	+	0.970298i	$0.422225\pi$
$167$	−9.29599	+	16.1011i	−0.719346	+	1.24594i	−0.961259	+	0.275645i	$0.911108\pi$
$168$		0			0
$169$	10.8514	+	7.15872i	0.834722	+	0.550671i
$170$		0			0
$171$	−1.22814	−	0.576390i	−0.0939181	−	0.0440777i
$172$		0			0
$173$	1.03397	+	1.79089i	0.0786116	+	0.136159i	0.902651	−	0.430373i	$-0.141618\pi$
$173$	1.03397	+	1.79089i	0.0786116	+	0.136159i	−0.824040	+	0.566532i	$0.808285\pi$
$174$		0			0
$175$	−1.07390			−0.0811792
$176$		0			0
$177$	−5.64407	+	6.14416i	−0.424234	+	0.461823i
$178$		0			0
$179$	9.02646	+	15.6343i	0.674669	+	1.16856i	0.976565	+	0.215221i	$0.0690471\pi$
$179$	9.02646	+	15.6343i	0.674669	+	1.16856i	−0.301896	+	0.953341i	$0.597620\pi$
$180$		0			0
$181$	12.5383			0.931962			0.465981	−	0.884795i	$-0.345701\pi$
$181$	12.5383			0.931962			0.465981	+	0.884795i	$0.345701\pi$
$182$		0			0
$183$	13.2335	+	2.95096i	0.978248	+	0.218141i
$184$		0			0
$185$	−1.85240	+	3.20845i	−0.136191	+	0.235890i
$186$		0			0
$187$	−5.25054	+	9.09421i	−0.383958	+	0.665034i
$188$		0			0
$189$	−0.153990	+	1.13708i	−0.0112011	+	0.0827103i
$190$		0			0
$191$	3.19606	+	5.53573i	0.231259	+	0.400552i	0.958179	−	0.286170i	$-0.0923823\pi$
$191$	3.19606	+	5.53573i	0.231259	+	0.400552i	−0.726920	+	0.686722i	$0.759049\pi$
$192$		0			0
$193$	−1.82055	+	3.15328i	−0.131046	+	0.226978i	−0.924080	−	0.382199i	$-0.875167\pi$
$193$	−1.82055	+	3.15328i	−0.131046	+	0.226978i	0.793034	+	0.609177i	$0.208500\pi$
$194$		0			0
$195$	−2.01586	−	1.13020i	−0.144359	−	0.0809352i
$196$		0			0
$197$	−5.16259	−	8.94187i	−0.367820	−	0.637082i	0.621405	−	0.783490i	$-0.286562\pi$
$197$	−5.16259	−	8.94187i	−0.367820	−	0.637082i	−0.989224	+	0.146408i	$0.953229\pi$
$198$		0			0
$199$	4.21204	−	7.29547i	0.298584	−	0.517162i	−0.677228	−	0.735773i	$-0.736819\pi$
$199$	4.21204	−	7.29547i	0.298584	−	0.517162i	0.975812	+	0.218611i	$0.0701524\pi$
$200$		0			0
$201$	−6.04889	−	19.2676i	−0.426656	−	1.35903i
$202$		0			0
$203$	0.408720	+	0.707924i	0.0286865	+	0.0496865i
$204$		0			0
$205$	−1.50682			−0.105241
$206$		0			0
$207$	−5.57396	−	2.61597i	−0.387417	−	0.181823i
$208$		0			0
$209$	0.951612	−	1.64824i	0.0658244	−	0.114011i
$210$		0			0
$211$	−6.17693	+	10.6988i	−0.425238	+	0.736533i	−0.996443	−	0.0842744i	$-0.973143\pi$
$211$	−6.17693	+	10.6988i	−0.425238	+	0.736533i	0.571205	+	0.820807i	$0.306476\pi$
$212$		0			0
$213$	7.15112	+	22.7786i	0.489987	+	1.56076i
$214$		0			0
$215$	2.13060	−	3.69030i	0.145306	−	0.251677i
$216$		0			0
$217$	−0.180214	+	0.312140i	−0.0122337	+	0.0211894i
$218$		0			0
$219$	10.0621	−	10.9536i	0.679932	−	0.740177i
$220$		0			0
$221$	−6.54804	+	6.16915i	−0.440469	+	0.414982i
$222$		0			0
$223$	−5.56458			−0.372632			−0.186316	−	0.982490i	$-0.559655\pi$
$223$	−5.56458			−0.372632			−0.186316	+	0.982490i	$0.559655\pi$
$224$		0			0
$225$	−13.2070	−	6.19830i	−0.880466	−	0.413220i
$226$		0			0
$227$	−9.89776	−	17.1434i	−0.656937	−	1.13785i	−0.981404	−	0.191952i	$-0.938518\pi$
$227$	−9.89776	−	17.1434i	−0.656937	−	1.13785i	0.324467	−	0.945897i	$-0.394815\pi$
$228$		0			0
$229$	−9.03568	−	15.6502i	−0.597094	−	1.03420i	−0.993248	−	0.116013i	$-0.962988\pi$
$229$	−9.03568	−	15.6502i	−0.597094	−	1.03420i	0.396153	−	0.918184i	$-0.370345\pi$
$230$		0			0
$231$	−1.57114	−	0.350351i	−0.103374	−	0.0230514i
$232$		0			0
$233$	−18.0216			−1.18063			−0.590317	−	0.807172i	$-0.700997\pi$
$233$	−18.0216			−1.18063			−0.590317	+	0.807172i	$0.700997\pi$
$234$		0			0
$235$	−0.679579			−0.0443308
$236$		0			0
$237$	6.60159	+	21.0281i	0.428819	+	1.36592i
$238$		0			0
$239$	−0.100774	−	0.174546i	−0.00651853	−	0.0112904i	0.862748	−	0.505635i	$-0.168742\pi$
$239$	−0.100774	−	0.174546i	−0.00651853	−	0.0112904i	−0.869266	+	0.494344i	$0.835408\pi$
$240$		0			0
$241$	−0.461164	−	0.798760i	−0.0297062	−	0.0514527i	0.850790	−	0.525506i	$-0.176124\pi$
$241$	−0.461164	−	0.798760i	−0.0297062	−	0.0514527i	−0.880496	+	0.474053i	$0.842791\pi$
$242$		0			0
$243$	−8.45675	+	13.0952i	−0.542501	+	0.840055i
$244$		0			0
$245$	−2.57242			−0.164346
$246$		0			0
$247$	1.18677	−	1.11810i	0.0755124	−	0.0711430i
$248$		0			0
$249$	5.75303	+	18.3252i	0.364584	+	1.16131i
$250$		0			0
$251$	4.59028	−	7.95060i	0.289736	−	0.501838i	−0.684011	−	0.729472i	$-0.739766\pi$
$251$	4.59028	−	7.95060i	0.289736	−	0.501838i	0.973747	+	0.227635i	$0.0730991\pi$
$252$		0			0
$253$	4.31893	−	7.48061i	0.271529	−	0.470302i
$254$		0			0
$255$	1.08195	−	1.17781i	0.0677542	−	0.0737575i
$256$		0			0
$257$	−3.53467	+	6.12223i	−0.220487	+	0.381895i	−0.954956	−	0.296748i	$-0.904098\pi$
$257$	−3.53467	+	6.12223i	−0.220487	+	0.381895i	0.734469	+	0.678642i	$0.237431\pi$
$258$		0			0
$259$	−1.10537	+	1.91456i	−0.0686846	+	0.118965i
$260$		0			0
$261$	0.940527	+	11.0652i	0.0582172	+	0.684918i
$262$		0			0
$263$	−1.87296			−0.115491			−0.0577457	−	0.998331i	$-0.518391\pi$
$263$	−1.87296			−0.115491			−0.0577457	+	0.998331i	$0.518391\pi$
$264$		0			0
$265$	1.31888	+	2.28437i	0.0810183	+	0.140328i
$266$		0			0
$267$	−0.385893	−	0.0860509i	−0.0236163	−	0.00526623i
$268$		0			0
$269$	−13.4883	+	23.3625i	−0.822399	+	1.42444i	0.0814922	+	0.996674i	$0.474031\pi$
$269$	−13.4883	+	23.3625i	−0.822399	+	1.42444i	−0.903891	+	0.427763i	$0.859302\pi$
$270$		0			0
$271$	5.17186	+	8.95793i	0.314168	+	0.544155i	0.979260	−	0.202606i	$-0.0649410\pi$
$271$	5.17186	+	8.95793i	0.314168	+	0.544155i	−0.665092	+	0.746761i	$0.731608\pi$
$272$		0			0
$273$	−1.20291	−	0.674419i	−0.0728037	−	0.0408177i
$274$		0			0
$275$	10.2333	−	17.7246i	0.617092	−	1.06883i
$276$		0			0
$277$	4.60119	+	7.96949i	0.276458	+	0.478840i	0.970502	−	0.241093i	$-0.0775058\pi$
$277$	4.60119	+	7.96949i	0.276458	+	0.478840i	−0.694044	+	0.719933i	$0.744173\pi$
$278$		0			0
$279$	−4.01790	+	2.79859i	−0.240545	+	0.167547i
$280$		0			0
$281$	−4.27672	+	7.40750i	−0.255128	+	0.441894i	−0.964930	−	0.262507i	$-0.915451\pi$
$281$	−4.27672	+	7.40750i	−0.255128	+	0.441894i	0.709802	+	0.704401i	$0.248784\pi$
$282$		0			0
$283$	8.40124	−	14.5514i	0.499402	−	0.864989i	−0.500598	−	0.865680i	$-0.666887\pi$
$283$	8.40124	−	14.5514i	0.499402	−	0.864989i	1.00000		0.000690699i	$0.000219856\pi$
$284$		0			0
$285$	−0.196093	+	0.213468i	−0.0116155	+	0.0126447i
$286$		0			0
$287$	−0.899160			−0.0530758
$288$		0			0
$289$	5.38711	+	9.33074i	0.316889	+	0.548867i
$290$		0			0
$291$	−17.2876	−	3.85498i	−1.01342	−	0.225983i
$292$		0			0
$293$	−17.3467			−1.01340			−0.506701	−	0.862122i	$-0.669135\pi$
$293$	−17.3467			−1.01340			−0.506701	+	0.862122i	$0.669135\pi$
$294$		0			0
$295$	0.891279	+	1.54374i	0.0518922	+	0.0898800i
$296$		0			0
$297$	−17.3000	−	13.3769i	−1.00385	−	0.776208i
$298$		0			0
$299$	5.38621	−	5.07455i	0.311493	−	0.293469i
$300$		0			0
$301$	1.27138	−	2.20210i	0.0732813	−	0.126927i
$302$		0			0
$303$	9.31691	−	10.1424i	0.535243	−	0.582667i
$304$		0			0
$305$	1.44844	−	2.50878i	0.0829376	−	0.143652i
$306$		0			0
$307$	−4.98311			−0.284401			−0.142201	−	0.989838i	$-0.545418\pi$
$307$	−4.98311			−0.284401			−0.142201	+	0.989838i	$0.545418\pi$
$308$		0			0
$309$	10.6934	+	2.38453i	0.608325	+	0.135651i
$310$		0			0
$311$	13.8571	+	24.0011i	0.785762	+	1.36098i	0.928543	+	0.371226i	$0.121062\pi$
$311$	13.8571	+	24.0011i	0.785762	+	1.36098i	−0.142781	+	0.989754i	$0.545604\pi$
$312$		0			0
$313$	−6.97711	+	12.0847i	−0.394369	+	0.683068i	−0.993020	−	0.117942i	$-0.962370\pi$
$313$	−6.97711	+	12.0847i	−0.394369	+	0.683068i	0.598651	+	0.801010i	$0.295704\pi$
$314$		0			0
$315$	0.221937	+	0.104160i	0.0125047	+	0.00586873i
$316$		0			0
$317$	−15.2734	+	26.4544i	−0.857842	+	1.48583i	0.0161410	+	0.999870i	$0.494862\pi$
$317$	−15.2734	+	26.4544i	−0.857842	+	1.48583i	−0.873983	+	0.485956i	$0.838471\pi$
$318$		0			0
$319$	−15.5789			−0.872254
$320$		0			0
$321$	8.77750	+	1.95731i	0.489913	+	0.109246i
$322$		0			0
$323$	0.564183	+	0.977193i	0.0313920	+	0.0543725i
$324$		0			0
$325$	12.7621	−	12.0237i	0.707915	−	0.666953i
$326$		0			0
$327$	15.9660	−	17.3806i	0.882921	−	0.961152i
$328$		0			0
$329$	−0.405523			−0.0223572
$330$		0			0
$331$	1.92916	+	3.34140i	0.106036	+	0.183660i	0.914161	−	0.405351i	$-0.132851\pi$
$331$	1.92916	+	3.34140i	0.106036	+	0.183660i	−0.808125	+	0.589011i	$0.799517\pi$
$332$		0			0
$333$	−24.6445	+	17.1656i	−1.35051	+	0.940671i
$334$		0			0
$335$	−4.31479			−0.235742
$336$		0			0
$337$	−4.54153	−	7.86617i	−0.247393	−	0.428497i	0.715409	−	0.698706i	$-0.246241\pi$
$337$	−4.54153	−	7.86617i	−0.247393	−	0.428497i	−0.962802	+	0.270209i	$0.912907\pi$
$338$		0			0
$339$	−2.70174	+	2.94113i	−0.146739	+	0.159740i
$340$		0			0
$341$	−3.43456	−	5.94883i	−0.185992	−	0.322147i
$342$		0			0
$343$	−3.08083			−0.166349
$344$		0			0
$345$	−0.889976	+	0.968832i	−0.0479147	+	0.0521602i
$346$		0			0
$347$	31.0555			1.66715			0.833573	−	0.552409i	$-0.186291\pi$
$347$	31.0555			1.66715			0.833573	+	0.552409i	$0.186291\pi$
$348$		0			0
$349$	−14.3262			−0.766865			−0.383432	−	0.923569i	$-0.625258\pi$
$349$	−14.3262			−0.766865			−0.383432	+	0.923569i	$0.625258\pi$
$350$		0			0
$351$	−10.9010	−	15.2370i	−0.581854	−	0.813293i
$352$		0			0
$353$	25.2920			1.34616			0.673079	−	0.739571i	$-0.264971\pi$
$353$	25.2920			1.34616			0.673079	+	0.739571i	$0.264971\pi$
$354$		0			0
$355$	5.10103			0.270735
$356$		0			0
$357$	0.645626	−	0.702832i	0.0341702	−	0.0371978i
$358$		0			0
$359$	7.28756			0.384623			0.192311	−	0.981334i	$-0.438402\pi$
$359$	7.28756			0.384623			0.192311	+	0.981334i	$0.438402\pi$
$360$		0			0
$361$	9.39775	+	16.2774i	0.494618	+	0.856704i
$362$		0			0
$363$	7.86500	−	8.56188i	0.412806	−	0.449382i
$364$		0			0
$365$	−1.58894	−	2.75213i	−0.0831692	−	0.144053i
$366$		0			0
$367$	−23.8323			−1.24403			−0.622017	−	0.783004i	$-0.713686\pi$
$367$	−23.8323			−1.24403			−0.622017	+	0.783004i	$0.713686\pi$
$368$		0			0
$369$	−11.0580	−	5.18974i	−0.575657	−	0.270167i
$370$		0			0
$371$	0.787012	+	1.36314i	0.0408596	+	0.0707709i
$372$		0			0
$373$	−12.3161			−0.637706			−0.318853	−	0.947804i	$-0.603298\pi$
$373$	−12.3161			−0.637706			−0.318853	+	0.947804i	$0.603298\pi$
$374$		0			0
$375$	−4.27681	+	4.65576i	−0.220854	+	0.240422i
$376$		0			0
$377$	−12.7833	−	3.83676i	−0.658373	−	0.197603i
$378$		0			0
$379$	−7.07147	−	12.2481i	−0.363237	−	0.629145i	0.625255	−	0.780421i	$-0.284995\pi$
$379$	−7.07147	−	12.2481i	−0.363237	−	0.629145i	−0.988492	+	0.151276i	$0.951662\pi$
$380$		0			0
$381$	17.7880	+	3.96657i	0.911305	+	0.203213i
$382$		0			0
$383$	−8.17316			−0.417629			−0.208814	−	0.977955i	$-0.566960\pi$
$383$	−8.17316			−0.417629			−0.208814	+	0.977955i	$0.566960\pi$
$384$		0			0
$385$	−0.171966	+	0.297854i	−0.00876420	+	0.0151800i
$386$		0			0
$387$	28.3457	−	19.7436i	1.44089	−	1.00362i
$388$		0			0
$389$	18.8420	−	32.6353i	0.955326	−	1.65467i	0.221706	−	0.975114i	$-0.428838\pi$
$389$	18.8420	−	32.6353i	0.955326	−	1.65467i	0.733620	−	0.679559i	$-0.237829\pi$
$390$		0			0
$391$	2.56057	+	4.43503i	0.129493	+	0.224289i
$392$		0			0
$393$	−6.55961	−	1.46274i	−0.330888	−	0.0737853i
$394$		0			0
$395$	4.70904			0.236937
$396$		0			0
$397$	8.81974	−	15.2762i	0.442650	−	0.766692i	−0.555235	−	0.831693i	$-0.687372\pi$
$397$	8.81974	−	15.2762i	0.442650	−	0.766692i	0.997885	+	0.0650010i	$0.0207051\pi$
$398$		0			0
$399$	−0.117014	+	0.127382i	−0.00585801	+	0.00637706i
$400$		0			0
$401$	15.7403	−	27.2630i	0.786034	−	1.36145i	−0.142345	−	0.989817i	$-0.545464\pi$
$401$	15.7403	−	27.2630i	0.786034	−	1.36145i	0.928379	−	0.371634i	$-0.121202\pi$
$402$		0			0
$403$	−1.35316	−	5.72716i	−0.0674055	−	0.285290i
$404$		0			0
$405$	2.12823	+	2.56194i	0.105753	+	0.127304i
$406$		0			0
$407$	−21.0665	−	36.4882i	−1.04423	−	1.80865i
$408$		0			0
$409$	−35.9638			−1.77829			−0.889147	−	0.457622i	$-0.848701\pi$
$409$	−35.9638			−1.77829			−0.889147	+	0.457622i	$0.848701\pi$
$410$		0			0
$411$	19.5732	+	4.36466i	0.965475	+	0.215293i
$412$		0			0
$413$	0.531849	+	0.921190i	0.0261706	+	0.0453288i
$414$		0			0
$415$	4.10374			0.201445
$416$		0			0
$417$	6.23202	−	6.78421i	0.305183	−	0.332224i
$418$		0			0
$419$	13.6871	−	23.7068i	0.668661	−	1.15815i	−0.309618	−	0.950861i	$-0.600201\pi$
$419$	13.6871	−	23.7068i	0.668661	−	1.15815i	0.978279	−	0.207294i	$-0.0664655\pi$
$420$		0			0
$421$	8.31205	−	14.3969i	0.405104	−	0.701661i	−0.589229	−	0.807966i	$-0.700568\pi$
$421$	8.31205	−	14.3969i	0.405104	−	0.701661i	0.994334	+	0.106304i	$0.0339018\pi$
$422$		0			0
$423$	−4.98718	−	2.34058i	−0.242485	−	0.113803i
$424$		0			0
$425$	6.06703	+	10.5084i	0.294294	+	0.509732i
$426$		0			0
$427$	0.864324	−	1.49705i	0.0418276	−	0.0724475i
$428$		0			0
$429$	22.5939	−	13.4274i	1.09084	−	0.648280i
$430$		0			0
$431$	6.96462	+	12.0631i	0.335474	+	0.581058i	0.983576	−	0.180496i	$-0.0577703\pi$
$431$	6.96462	+	12.0631i	0.335474	+	0.581058i	−0.648102	+	0.761554i	$0.724437\pi$
$432$		0			0
$433$	−19.6355	+	34.0097i	−0.943621	+	1.63440i	−0.185133	+	0.982714i	$0.559271\pi$
$433$	−19.6355	+	34.0097i	−0.943621	+	1.63440i	−0.758489	+	0.651686i	$0.774062\pi$
$434$		0			0
$435$	2.31581	+	0.516407i	0.111035	+	0.0247598i
$436$		0			0
$437$	−0.464079	−	0.803808i	−0.0221999	−	0.0384514i
$438$		0			0
$439$	35.9687			1.71669			0.858347	−	0.513070i	$-0.171492\pi$
$439$	35.9687			1.71669			0.858347	+	0.513070i	$0.171492\pi$
$440$		0			0
$441$	−18.8780	−	8.85984i	−0.898954	−	0.421897i
$442$		0			0
$443$	−7.79412	+	13.4998i	−0.370310	+	0.641395i	−0.989613	−	0.143757i	$-0.954082\pi$
$443$	−7.79412	+	13.4998i	−0.370310	+	0.641395i	0.619303	+	0.785152i	$0.287415\pi$
$444$		0			0
$445$	−0.0422371	+	0.0731569i	−0.00200223	+	0.00346797i
$446$		0			0
$447$	−20.8132	+	22.6573i	−0.984429	+	1.07165i
$448$		0			0
$449$	18.9254	−	32.7797i	0.893143	−	1.54697i	0.0570564	−	0.998371i	$-0.481829\pi$
$449$	18.9254	−	32.7797i	0.893143	−	1.54697i	0.836086	−	0.548598i	$-0.184838\pi$
$450$		0			0
$451$	8.56819	−	14.8405i	0.403460	−	0.698814i
$452$		0			0
$453$	8.88739	+	28.3091i	0.417566	+	1.33008i
$454$		0			0
$455$	−0.214462	+	0.202052i	−0.0100541	+	0.00947235i
$456$		0			0
$457$	−6.75011			−0.315757			−0.157878	−	0.987459i	$-0.550465\pi$
$457$	−6.75011			−0.315757			−0.157878	+	0.987459i	$0.550465\pi$
$458$		0			0
$459$	11.9966	−	4.91712i	0.559953	−	0.229512i
$460$		0			0
$461$	−11.1795	−	19.3634i	−0.520681	−	0.901845i	−0.999711	−	0.0240468i	$-0.992345\pi$
$461$	−11.1795	−	19.3634i	−0.520681	−	0.901845i	0.479030	−	0.877798i	$-0.340988\pi$
$462$		0			0
$463$	−1.62174	−	2.80893i	−0.0753686	−	0.130542i	0.825878	−	0.563849i	$-0.190680\pi$
$463$	−1.62174	−	2.80893i	−0.0753686	−	0.130542i	−0.901246	+	0.433307i	$0.857347\pi$
$464$		0			0
$465$	0.313358	+	0.998143i	0.0145316	+	0.0462878i
$466$		0			0
$467$	15.5291			0.718603			0.359302	−	0.933221i	$-0.383015\pi$
$467$	15.5291			0.718603			0.359302	+	0.933221i	$0.383015\pi$
$468$		0			0
$469$	−2.57475			−0.118891
$470$		0			0
$471$	−10.9277	−	2.43680i	−0.503524	−	0.112282i
$472$		0			0
$473$	24.2303	+	41.9681i	1.11411	+	1.92969i
$474$		0			0
$475$	−1.09959	−	1.90455i	−0.0504527	−	0.0873867i
$476$		0			0
$477$	1.81103	+	21.3066i	0.0829215	+	0.975562i
$478$		0			0
$479$	3.64033			0.166331			0.0831654	−	0.996536i	$-0.473497\pi$
$479$	3.64033			0.166331			0.0831654	+	0.996536i	$0.473497\pi$
$480$		0			0
$481$	−8.29981	−	35.1285i	−0.378439	−	1.60172i
$482$		0			0
$483$	−0.531072	+	0.578127i	−0.0241646	+	0.0263057i
$484$		0			0
$485$	−1.89217	+	3.27734i	−0.0859192	+	0.148816i
$486$		0			0
$487$	10.2651	−	17.7797i	0.465157	−	0.805676i	−0.534051	−	0.845452i	$-0.679331\pi$
$487$	10.2651	−	17.7797i	0.465157	−	0.805676i	0.999209	+	0.0397759i	$0.0126644\pi$
$488$		0			0
$489$	−0.682026	−	2.17247i	−0.0308423	−	0.0982424i
$490$		0			0
$491$	21.6613	−	37.5185i	0.977561	−	1.69319i	0.306351	−	0.951918i	$-0.400892\pi$
$491$	21.6613	−	37.5185i	0.977561	−	1.69319i	0.671210	−	0.741267i	$-0.265775\pi$
$492$		0			0
$493$	4.61815	−	7.99887i	0.207991	−	0.360251i
$494$		0			0
$495$	−3.83400	+	2.67050i	−0.172326	+	0.120030i
$496$		0			0
$497$	3.04392			0.136538
$498$		0			0
$499$	−7.22040	−	12.5061i	−0.323229	−	0.559850i	0.657923	−	0.753085i	$-0.271435\pi$
$499$	−7.22040	−	12.5061i	−0.323229	−	0.559850i	−0.981152	+	0.193235i	$0.938102\pi$
$500$		0			0
$501$	9.64545	+	30.7238i	0.430927	+	1.37264i
$502$		0			0
$503$	10.9732	−	19.0061i	0.489269	−	0.847439i	−0.510655	−	0.859786i	$-0.670597\pi$
$503$	10.9732	−	19.0061i	0.489269	−	0.847439i	0.999924	+	0.0123470i	$0.00393026\pi$
$504$		0			0
$505$	−1.47127	−	2.54832i	−0.0654708	−	0.113399i
$506$		0			0
$507$	21.8463	−	5.45342i	0.970228	−	0.242195i
$508$		0			0
$509$	2.76993	−	4.79766i	0.122775	−	0.212652i	−0.798086	−	0.602544i	$-0.794154\pi$
$509$	2.76993	−	4.79766i	0.122775	−	0.212652i	0.920861	+	0.389891i	$0.127487\pi$
$510$		0			0
$511$	−0.948165	−	1.64227i	−0.0419443	−	0.0726497i
$512$		0			0
$513$	−2.17427	+	0.891182i	−0.0959963	+	0.0393467i
$514$		0			0
$515$	1.17042	−	2.02723i	0.0515749	−	0.0893303i
$516$		0			0
$517$	3.86427	−	6.69311i	0.169950	−	0.294362i
$518$		0			0
$519$	3.49593	+	0.779562i	0.153454	+	0.0342190i
$520$		0			0
$521$	−22.2041			−0.972779			−0.486390	−	0.873742i	$-0.661686\pi$
$521$	−22.2041			−0.972779			−0.486390	+	0.873742i	$0.661686\pi$
$522$		0			0
$523$	−10.1092	−	17.5096i	−0.442043	−	0.765641i	0.555798	−	0.831317i	$-0.312413\pi$
$523$	−10.1092	−	17.5096i	−0.442043	−	0.765641i	−0.997841	+	0.0656764i	$0.979080\pi$
$524$		0			0
$525$	−1.25833	+	1.36982i	−0.0549178	+	0.0597838i
$526$		0			0
$527$	4.07250			0.177401
$528$		0			0
$529$	9.39376	+	16.2705i	0.408424	+	0.707411i
$530$		0			0
$531$	1.22387	+	14.3986i	0.0531112	+	0.624848i
$532$		0			0
$533$	10.6855	−	10.0672i	0.462842	−	0.436060i
$534$		0			0
$535$	0.960723	−	1.66402i	0.0415357	−	0.0719419i
$536$		0			0
$537$	30.5190	+	6.80548i	1.31699	+	0.293678i
$538$		0			0
$539$	14.6275	−	25.3355i	0.630050	−	1.09128i
$540$		0			0
$541$	27.3228			1.17470			0.587349	−	0.809334i	$-0.300172\pi$
$541$	27.3228			1.17470			0.587349	+	0.809334i	$0.300172\pi$
$542$		0			0
$543$	14.6915	−	15.9933i	0.630473	−	0.686336i
$544$		0			0
$545$	−2.52125	−	4.36694i	−0.107999	−	0.187059i
$546$		0			0
$547$	−17.0211	+	29.4815i	−0.727771	+	1.26054i	0.230052	+	0.973178i	$0.426110\pi$
$547$	−17.0211	+	29.4815i	−0.727771	+	1.26054i	−0.957823	+	0.287358i	$0.907223\pi$
$548$		0			0
$549$	19.2702	−	13.4223i	0.822433	−	0.572850i
$550$		0			0
$551$	−0.836996	+	1.44972i	−0.0356572	+	0.0617602i
$552$		0			0
$553$	2.81001			0.119494
$554$		0			0
$555$	1.92203	+	6.12228i	0.0815857	+	0.259876i
$556$		0			0
$557$	−15.8408	−	27.4371i	−0.671196	−	1.16255i	−0.977565	−	0.210633i	$-0.932447\pi$
$557$	−15.8408	−	27.4371i	−0.671196	−	1.16255i	0.306369	−	0.951913i	$-0.400886\pi$
$558$		0			0
$559$	9.54630	+	40.4043i	0.403766	+	1.70892i
$560$		0			0
$561$	5.44792	+	17.3533i	0.230011	+	0.732659i
$562$		0			0
$563$	−37.8657			−1.59585			−0.797925	−	0.602757i	$-0.794069\pi$
$563$	−37.8657			−1.59585			−0.797925	+	0.602757i	$0.794069\pi$
$564$		0			0
$565$	0.426644	+	0.738968i	0.0179490	+	0.0310886i
$566$		0			0
$567$	1.26997	+	1.52878i	0.0533338	+	0.0642026i
$568$		0			0
$569$	−12.2613			−0.514020			−0.257010	−	0.966409i	$-0.582737\pi$
$569$	−12.2613			−0.514020			−0.257010	+	0.966409i	$0.582737\pi$
$570$		0			0
$571$	−9.51424	−	16.4791i	−0.398158	−	0.689631i	0.595340	−	0.803474i	$-0.297017\pi$
$571$	−9.51424	−	16.4791i	−0.398158	−	0.689631i	−0.993499	+	0.113843i	$0.963684\pi$
$572$		0			0
$573$	10.8061	+	2.40966i	0.451430	+	0.100665i
$574$		0			0
$575$	−4.99055	−	8.64388i	−0.208120	−	0.360475i
$576$		0			0
$577$	−14.0939			−0.586735			−0.293368	−	0.956000i	$-0.594776\pi$
$577$	−14.0939			−0.586735			−0.293368	+	0.956000i	$0.594776\pi$
$578$		0			0
$579$	1.88898	+	6.01701i	0.0785035	+	0.250058i
$580$		0			0
$581$	2.44881			0.101594
$582$		0			0
$583$	−29.9981			−1.24239
$584$		0			0
$585$	−3.80368	+	1.24704i	−0.157263	+	0.0515590i
$586$		0			0
$587$	−23.8250			−0.983361			−0.491681	−	0.870776i	$-0.663617\pi$
$587$	−23.8250			−0.983361			−0.491681	+	0.870776i	$0.663617\pi$
$588$		0			0
$589$	−0.738102			−0.0304130
$590$		0			0
$591$	−17.4550	−	3.89233i	−0.718004	−	0.160109i
$592$		0			0
$593$	0.951141			0.0390587			0.0195293	−	0.999809i	$-0.493783\pi$
$593$	0.951141			0.0390587			0.0195293	+	0.999809i	$0.493783\pi$
$594$		0			0
$595$	−0.101954	−	0.176589i	−0.00417969	−	0.00723943i
$596$		0			0
$597$	−4.37038	−	13.9210i	−0.178868	−	0.569750i
$598$		0			0
$599$	3.59422	+	6.22538i	0.146856	+	0.254362i	0.930064	−	0.367398i	$-0.119751\pi$
$599$	3.59422	+	6.22538i	0.146856	+	0.254362i	−0.783208	+	0.621760i	$0.786418\pi$
$600$		0			0
$601$	−29.1543			−1.18923			−0.594613	−	0.804012i	$-0.702695\pi$
$601$	−29.1543			−1.18923			−0.594613	+	0.804012i	$0.702695\pi$
$602$		0			0
$603$	−31.6646	−	14.8608i	−1.28948	−	0.605180i
$604$		0			0
$605$	−1.24200	−	2.15120i	−0.0504943	−	0.0874587i
$606$		0			0
$607$	−25.7206			−1.04397			−0.521984	−	0.852956i	$-0.674808\pi$
$607$	−25.7206			−1.04397			−0.521984	+	0.852956i	$0.674808\pi$
$608$		0			0
$609$	1.38191	+	0.308154i	0.0559977	+	0.0124870i
$610$		0			0
$611$	4.81919	−	4.54034i	0.194964	−	0.183682i
$612$		0			0
$613$	10.8372	+	18.7706i	0.437711	+	0.758138i	0.997513	−	0.0704890i	$-0.0224560\pi$
$613$	10.8372	+	18.7706i	0.437711	+	0.758138i	−0.559802	+	0.828627i	$0.689123\pi$
$614$		0			0
$615$	−1.76559	+	1.92203i	−0.0711956	+	0.0775039i
$616$		0			0
$617$	23.8698			0.960961			0.480480	−	0.877005i	$-0.340462\pi$
$617$	23.8698			0.960961			0.480480	+	0.877005i	$0.340462\pi$
$618$		0			0
$619$	14.1119	−	24.4426i	0.567206	−	0.982430i	−0.429634	−	0.903003i	$-0.641358\pi$
$619$	14.1119	−	24.4426i	0.567206	−	0.982430i	0.996841	−	0.0794271i	$-0.0253091\pi$
$620$		0			0
$621$	−9.86802	+	4.04467i	−0.395990	+	0.162307i
$622$		0			0
$623$	−0.0252040	+	0.0436546i	−0.00100978	+	0.00174899i
$624$		0			0
$625$	−11.4823	−	19.8879i	−0.459290	−	0.795514i
$626$		0			0
$627$	−0.987385	−	3.14513i	−0.0394323	−	0.125604i
$628$		0			0
$629$	24.9794			0.995992
$630$		0			0
$631$	1.90270	−	3.29557i	0.0757453	−	0.131195i	−0.825665	−	0.564161i	$-0.809200\pi$
$631$	1.90270	−	3.29557i	0.0757453	−	0.131195i	0.901410	+	0.432966i	$0.142533\pi$
$632$		0			0
$633$	6.40913	+	20.4151i	0.254740	+	0.811428i
$634$		0			0
$635$	1.94694	−	3.37221i	0.0772621	−	0.133822i
$636$		0			0
$637$	18.2422	−	17.1866i	0.722780	−	0.680958i
$638$		0			0
$639$	37.4345	+	17.5688i	1.48089	+	0.695011i
$640$		0			0
$641$	18.1734	+	31.4773i	0.717806	+	1.24328i	0.961867	+	0.273517i	$0.0881869\pi$
$641$	18.1734	+	31.4773i	0.717806	+	1.24328i	−0.244061	+	0.969760i	$0.578480\pi$
$642$		0			0
$643$	−9.88970			−0.390012			−0.195006	−	0.980802i	$-0.562473\pi$
$643$	−9.88970			−0.390012			−0.195006	+	0.980802i	$0.562473\pi$
$644$		0			0
$645$	−2.21069	−	7.04174i	−0.0870458	−	0.277268i
$646$		0			0
$647$	−5.31723	−	9.20972i	−0.209042	−	0.362071i	0.742371	−	0.669989i	$-0.233701\pi$
$647$	−5.31723	−	9.20972i	−0.209042	−	0.362071i	−0.951413	+	0.307918i	$0.900368\pi$
$648$		0			0
$649$	−20.2722			−0.795753
$650$		0			0
$651$	0.186989	+	0.595618i	0.00732867	+	0.0233441i
$652$		0			0
$653$	0.379579	−	0.657450i	0.0148541	−	0.0257280i	−0.858503	−	0.512809i	$-0.828605\pi$
$653$	0.379579	−	0.657450i	0.0148541	−	0.0257280i	0.873357	+	0.487081i	$0.161938\pi$
$654$		0			0
$655$	−0.717968	+	1.24356i	−0.0280533	+	0.0485898i
$656$		0			0
$657$	−2.18187	−	25.6695i	−0.0851229	−	1.00146i
$658$		0			0
$659$	13.3701	+	23.1576i	0.520824	+	0.902094i	0.999707	+	0.0242150i	$0.00770862\pi$
$659$	13.3701	+	23.1576i	0.520824	+	0.902094i	−0.478883	+	0.877879i	$0.658958\pi$
$660$		0			0
$661$	4.46739	−	7.73775i	0.173761	−	0.300964i	−0.765970	−	0.642876i	$-0.777741\pi$
$661$	4.46739	−	7.73775i	0.173761	−	0.300964i	0.939732	+	0.341912i	$0.111074\pi$
$662$		0			0
$663$	0.196531	+	15.5810i	0.00763263	+	0.605115i
$664$		0			0
$665$	0.0184781	+	0.0320051i	0.000716551	+	0.00124110i
$666$		0			0
$667$	−3.79875	+	6.57962i	−0.147088	+	0.254764i
$668$		0			0
$669$	−6.52020	+	7.09792i	−0.252086	+	0.274422i
$670$		0			0
$671$	16.4725	+	28.5312i	0.635913	+	1.10143i
$672$		0			0
$673$	6.05569			0.233430			0.116715	−	0.993165i	$-0.462764\pi$
$673$	6.05569			0.233430			0.116715	+	0.993165i	$0.462764\pi$
$674$		0			0
$675$	−23.3813	+	9.58347i	−0.899948	+	0.368868i
$676$		0			0
$677$	5.52459	−	9.56887i	0.212327	−	0.367761i	−0.740115	−	0.672480i	$-0.765229\pi$
$677$	5.52459	−	9.56887i	0.212327	−	0.367761i	0.952442	+	0.304719i	$0.0985624\pi$
$678$		0			0
$679$	−1.12911	+	1.95568i	−0.0433313	+	0.0750520i
$680$		0			0
$681$	−33.4649	−	7.46239i	−1.28238	−	0.285960i
$682$		0			0
$683$	6.80171	−	11.7809i	0.260260	−	0.450784i	−0.706051	−	0.708161i	$-0.749525\pi$
$683$	6.80171	−	11.7809i	0.260260	−	0.450784i	0.966311	+	0.257377i	$0.0828584\pi$
$684$		0			0
$685$	2.14234	−	3.71065i	0.0818547	−	0.141777i
$686$		0			0
$687$	−30.5502	−	6.81243i	−1.16556	−	0.259910i
$688$		0			0
$689$	−24.6149	−	7.38788i	−0.937753	−	0.281456i
$690$		0			0
$691$	−45.5120			−1.73136			−0.865679	−	0.500599i	$-0.833113\pi$
$691$	−45.5120			−1.73136			−0.865679	+	0.500599i	$0.833113\pi$
$692$		0			0
$693$	−2.28785	+	1.59356i	−0.0869083	+	0.0605343i
$694$		0			0
$695$	−0.984125	−	1.70455i	−0.0373300	−	0.0646574i
$696$		0			0
$697$	5.07983	+	8.79852i	0.192412	+	0.333268i
$698$		0			0
$699$	−21.1165	+	22.9875i	−0.798700	+	0.869468i
$700$		0			0
$701$	−2.09001			−0.0789388			−0.0394694	−	0.999221i	$-0.512567\pi$
$701$	−2.09001			−0.0789388			−0.0394694	+	0.999221i	$0.512567\pi$
$702$		0			0
$703$	−4.52727			−0.170749
$704$		0			0
$705$	−0.796286	+	0.866840i	−0.0299898	+	0.0326471i
$706$		0			0
$707$	−0.877947	−	1.52065i	−0.0330186	−	0.0571899i
$708$		0			0
$709$	−15.4751	−	26.8036i	−0.581178	−	1.00663i	−0.995340	−	0.0964272i	$-0.969259\pi$
$709$	−15.4751	−	26.8036i	−0.581178	−	1.00663i	0.414162	−	0.910203i	$-0.364075\pi$
$710$		0			0
$711$	34.5579	+	16.2187i	1.29602	+	0.608249i
$712$		0			0
$713$	−3.34991			−0.125455
$714$		0			0
$715$	−1.29122	−	5.46504i	−0.0482890	−	0.204381i
$716$		0			0
$717$	−0.340723	−	0.0759784i	−0.0127245	−	0.00283746i
$718$		0			0
$719$	−24.5017	+	42.4382i	−0.913759	+	1.58268i	−0.105051	+	0.994467i	$0.533501\pi$
$719$	−24.5017	+	42.4382i	−0.913759	+	1.58268i	−0.808708	+	0.588210i	$0.799833\pi$
$720$		0			0
$721$	0.698421	−	1.20970i	0.0260105	−	0.0450516i
$722$		0			0
$723$	−1.55922	−	0.347694i	−0.0579882	−	0.0129309i
$724$		0			0
$725$	−9.00077	+	15.5898i	−0.334280	+	0.578990i
$726$		0			0
$727$	−4.70130	+	8.14289i	−0.174361	+	0.302003i	−0.939940	−	0.341339i	$-0.889119\pi$
$727$	−4.70130	+	8.14289i	−0.174361	+	0.302003i	0.765579	+	0.643342i	$0.222453\pi$
$728$		0			0
$729$	6.79455	+	26.1311i	0.251650	+	0.967818i
$730$		0			0
$731$	−28.7308			−1.06265
$732$		0			0
$733$	11.3717	+	19.6963i	0.420022	+	0.727499i	0.995941	−	0.0900077i	$-0.0286892\pi$
$733$	11.3717	+	19.6963i	0.420022	+	0.727499i	−0.575919	+	0.817506i	$0.695356\pi$
$734$		0			0
$735$	−3.01419	+	3.28126i	−0.111180	+	0.121031i
$736$		0			0
$737$	24.5350	−	42.4959i	0.903759	−	1.56536i
$738$		0			0
$739$	24.6444	+	42.6853i	0.906558	+	1.57021i	0.818811	+	0.574063i	$0.194633\pi$
$739$	24.6444	+	42.6853i	0.906558	+	1.57021i	0.0877471	+	0.996143i	$0.472033\pi$
$740$		0			0
$741$	−0.0356194	−	2.82391i	−0.00130851	−	0.103739i
$742$		0			0
$743$	16.3144	−	28.2574i	0.598519	−	1.03667i	−0.394521	−	0.918887i	$-0.629089\pi$
$743$	16.3144	−	28.2574i	0.598519	−	1.03667i	0.993040	−	0.117778i	$-0.0375772\pi$
$744$		0			0
$745$	3.28669	+	5.69272i	0.120415	+	0.208565i
$746$		0			0
$747$	30.1158	+	14.1340i	1.10188	+	0.517135i
$748$		0			0
$749$	0.573289	−	0.992965i	0.0209475	−	0.0362822i
$750$		0			0
$751$	−3.36536	+	5.82897i	−0.122804	+	0.212702i	−0.920872	−	0.389864i	$-0.872522\pi$
$751$	−3.36536	+	5.82897i	−0.122804	+	0.212702i	0.798069	+	0.602567i	$0.205855\pi$
$752$		0			0
$753$	−4.76284	−	15.1711i	−0.173568	−	0.552867i
$754$		0			0
$755$	6.33954			0.230720
$756$		0			0
$757$	−17.1722	−	29.7432i	−0.624135	−	1.08103i	−0.988707	−	0.149859i	$-0.952118\pi$
$757$	−17.1722	−	29.7432i	−0.624135	−	1.08103i	0.364572	−	0.931175i	$-0.381215\pi$
$758$		0			0
$759$	−4.48129	−	14.2743i	−0.162661	−	0.518125i
$760$		0			0
$761$	27.2738			0.988674			0.494337	−	0.869270i	$-0.335411\pi$
$761$	27.2738			0.988674			0.494337	+	0.869270i	$0.335411\pi$
$762$		0			0
$763$	−1.50450	−	2.60587i	−0.0544665	−	0.0943388i
$764$		0			0
$765$	−0.234610	−	2.76017i	−0.00848236	−	0.0997940i
$766$		0			0
$767$	−16.6343	−	4.99260i	−0.600631	−	0.180273i
$768$		0			0
$769$	−19.9223	+	34.5065i	−0.718417	+	1.24434i	0.243209	+	0.969974i	$0.421800\pi$
$769$	−19.9223	+	34.5065i	−0.718417	+	1.24434i	−0.961627	+	0.274361i	$0.911534\pi$
$770$		0			0
$771$	3.66755	+	11.6823i	0.132084	+	0.420728i
$772$		0			0
$773$	7.98669	−	13.8334i	0.287261	−	0.497551i	−0.685894	−	0.727702i	$-0.740589\pi$
$773$	7.98669	−	13.8334i	0.287261	−	0.497551i	0.973155	+	0.230151i	$0.0739219\pi$
$774$		0			0
$775$	−7.93729			−0.285116
$776$		0			0
$777$	1.14693	+	3.65333i	0.0411458	+	0.131062i
$778$		0			0
$779$	−0.920671	−	1.59465i	−0.0329865	−	0.0571342i
$780$		0			0
$781$	−29.0058	+	50.2395i	−1.03791	+	1.79771i
$782$		0			0
$783$	15.2163	+	11.7658i	0.543786	+	0.420474i
$784$		0			0
$785$	−1.19607	+	2.07166i	−0.0426897	+	0.0739407i
$786$		0			0
$787$	−54.3863			−1.93866			−0.969331	−	0.245759i	$-0.920963\pi$
$787$	−54.3863			−1.93866			−0.969331	+	0.245759i	$0.920963\pi$
$788$		0			0
$789$	−2.19461	+	2.38906i	−0.0781301	+	0.0850527i
$790$		0			0
$791$	0.254589	+	0.440962i	0.00905216	+	0.0156788i
$792$		0			0
$793$	6.48986	+	27.4680i	0.230462	+	0.975418i
$794$		0			0
$795$	4.45922	+	0.994369i	0.158152	+	0.0352666i
$796$		0			0
$797$	−45.9437			−1.62741			−0.813704	−	0.581279i	$-0.802553\pi$
$797$	−45.9437			−1.62741			−0.813704	+	0.581279i	$0.802553\pi$
$798$		0			0
$799$	2.29101	+	3.96815i	0.0810501	+	0.140383i
$800$		0			0
$801$	−0.561927	+	0.391399i	−0.0198547	+	0.0138294i
$802$		0			0
$803$	36.1406			1.27538
$804$		0			0
$805$	0.0838638	+	0.145256i	0.00295581	+	0.00511961i
$806$		0			0
$807$	13.9954	+	44.5798i	0.492661	+	1.56928i
$808$		0			0
$809$	0.753915	+	1.30582i	0.0265062	+	0.0459101i	0.878974	−	0.476869i	$-0.158228\pi$
$809$	0.753915	+	1.30582i	0.0265062	+	0.0459101i	−0.852468	+	0.522779i	$0.824895\pi$
$810$		0			0
$811$	34.4445			1.20951			0.604755	−	0.796411i	$-0.293271\pi$
$811$	34.4445			1.20951			0.604755	+	0.796411i	$0.293271\pi$
$812$		0			0
$813$	17.4864	+	3.89931i	0.613274	+	0.136755i
$814$		0			0
$815$	−0.486502			−0.0170414
$816$		0			0
$817$	5.20720			0.182177
$818$		0			0
$819$	−2.26975	+	0.744144i	−0.0793116	+	0.0260025i
$820$		0			0
$821$	18.7315			0.653734			0.326867	−	0.945070i	$-0.394007\pi$
$821$	18.7315			0.653734			0.326867	+	0.945070i	$0.394007\pi$
$822$		0			0
$823$	−16.3448			−0.569742			−0.284871	−	0.958566i	$-0.591951\pi$
$823$	−16.3448			−0.569742			−0.284871	+	0.958566i	$0.591951\pi$
$824$		0			0
$825$	−10.6180	−	33.8217i	−0.369671	−	1.17752i
$826$		0			0
$827$	3.88733			0.135176			0.0675878	−	0.997713i	$-0.478470\pi$
$827$	3.88733			0.135176			0.0675878	+	0.997713i	$0.478470\pi$
$828$		0			0
$829$	−4.20485	−	7.28302i	−0.146041	−	0.252950i	0.783720	−	0.621114i	$-0.213320\pi$
$829$	−4.20485	−	7.28302i	−0.146041	−	0.252950i	−0.929761	+	0.368164i	$0.879986\pi$
$830$		0			0
$831$	15.5569	+	3.46905i	0.539662	+	0.120340i
$832$		0			0
$833$	8.67220	+	15.0207i	0.300474	+	0.520436i
$834$		0			0
$835$	6.88028			0.238102
$836$		0			0
$837$	−1.13815	+	8.40425i	−0.0393404	+	0.290493i
$838$		0			0
$839$	−1.68435	−	2.91739i	−0.0581504	−	0.100719i	0.835485	−	0.549514i	$-0.185187\pi$
$839$	−1.68435	−	2.91739i	−0.0581504	−	0.100719i	−0.893635	+	0.448794i	$0.851854\pi$
$840$		0			0
$841$	−15.2974			−0.527498
$842$		0			0
$843$	4.43749	+	14.1348i	0.152835	+	0.486828i
$844$		0			0
$845$	0.286410	−	4.80233i	0.00985280	−	0.165205i
$846$		0			0
$847$	−0.741131	−	1.28368i	−0.0254656	−	0.0441077i
$848$		0			0
$849$	−8.71706	−	27.7666i	−0.299169	−	0.952946i
$850$		0			0
$851$	−20.5472			−0.704350
$852$		0			0
$853$	6.68642	−	11.5812i	0.228939	−	0.396533i	−0.728555	−	0.684987i	$-0.759808\pi$
$853$	6.68642	−	11.5812i	0.228939	−	0.396533i	0.957494	+	0.288454i	$0.0931411\pi$
$854$		0			0
$855$	0.0425210	+	0.500254i	0.00145419	+	0.0171083i
$856$		0			0
$857$	8.35202	−	14.4661i	0.285300	−	0.494153i	−0.687382	−	0.726296i	$-0.741240\pi$
$857$	8.35202	−	14.4661i	0.285300	−	0.494153i	0.972682	+	0.232143i	$0.0745736\pi$
$858$		0			0
$859$	10.2946	+	17.8308i	0.351247	+	0.608378i	0.986468	−	0.163952i	$-0.0524244\pi$
$859$	10.2946	+	17.8308i	0.351247	+	0.608378i	−0.635221	+	0.772330i	$0.719091\pi$
$860$		0			0
$861$	−1.05358	+	1.14693i	−0.0359058	+	0.0390872i
$862$		0			0
$863$	6.86690			0.233752			0.116876	−	0.993147i	$-0.462712\pi$
$863$	6.86690			0.233752			0.116876	+	0.993147i	$0.462712\pi$
$864$		0			0
$865$	0.382639	−	0.662751i	0.0130101	−	0.0225342i
$866$		0			0
$867$	18.2141	+	4.06160i	0.618584	+	0.137939i
$868$		0			0
$869$	−26.7768	+	46.3788i	−0.908342	+	1.57329i
$870$		0			0
$871$	30.5980	−	28.8275i	1.03677	−	0.976784i
$872$		0			0
$873$	−25.1737	+	17.5342i	−0.852000	+	0.593444i
$874$		0			0
$875$	0.403011	+	0.698035i	0.0136242	+	0.0235979i
$876$		0			0
$877$	−3.03387			−0.102447			−0.0512233	−	0.998687i	$-0.516312\pi$
$877$	−3.03387			−0.102447			−0.0512233	+	0.998687i	$0.516312\pi$
$878$		0			0
$879$	−20.3257	+	22.1266i	−0.685568	+	0.746312i
$880$		0			0
$881$	22.4166	+	38.8267i	0.755234	+	1.30810i	0.945258	+	0.326325i	$0.105810\pi$
$881$	22.4166	+	38.8267i	0.755234	+	1.30810i	−0.190024	+	0.981780i	$0.560856\pi$
$882$		0			0
$883$	−4.01343			−0.135063			−0.0675314	−	0.997717i	$-0.521512\pi$
$883$	−4.01343			−0.135063			−0.0675314	+	0.997717i	$0.521512\pi$
$884$		0			0
$885$	3.01347	+	0.671977i	0.101297	+	0.0225883i
$886$		0			0
$887$	19.9660	−	34.5822i	0.670394	−	1.16116i	−0.307399	−	0.951581i	$-0.599459\pi$
$887$	19.9660	−	34.5822i	0.670394	−	1.16116i	0.977793	−	0.209575i	$-0.0672081\pi$
$888$		0			0
$889$	1.16179	−	2.01228i	0.0389653	−	0.0674898i
$890$		0			0
$891$	−37.3340	+	6.39286i	−1.25074	+	0.214169i
$892$		0			0
$893$	−0.415224	−	0.719189i	−0.0138949	−	0.0240667i
$894$		0			0
$895$	3.34039	−	5.78573i	0.111657	−	0.193396i
$896$		0			0
$897$	−0.161660	−	12.8164i	−0.00539768	−	0.427928i
$898$		0			0
$899$	3.02089	+	5.23233i	0.100752	+	0.174508i
$900$		0			0
$901$	8.89249	−	15.4022i	0.296252	−	0.513123i
$902$		0			0
$903$	−1.31918	−	4.20199i	−0.0438995	−	0.139834i
$904$		0			0
$905$	−2.32000	−	4.01836i	−0.0771194	−	0.133575i
$906$		0			0
$907$	57.9364			1.92375			0.961874	−	0.273494i	$-0.0881793\pi$
$907$	57.9364			1.92375			0.961874	+	0.273494i	$0.0881793\pi$
$908$		0			0
$909$	−2.02029	−	23.7685i	−0.0670087	−	0.788350i
$910$		0			0
$911$	16.7679	−	29.0429i	0.555546	−	0.962234i	−0.442315	−	0.896860i	$-0.645843\pi$
$911$	16.7679	−	29.0429i	0.555546	−	0.962234i	0.997861	−	0.0653740i	$-0.0208240\pi$
$912$		0			0
$913$	−23.3350	+	40.4174i	−0.772275	+	1.33762i
$914$		0			0
$915$	−1.50289	−	4.78719i	−0.0496841	−	0.158260i
$916$		0			0
$917$	−0.428430	+	0.742063i	−0.0141480	+	0.0245051i
$918$		0			0
$919$	6.42095	−	11.1214i	0.211807	−	0.366861i	−0.740473	−	0.672086i	$-0.765398\pi$
$919$	6.42095	−	11.1214i	0.211807	−	0.366861i	0.952280	+	0.305225i	$0.0987317\pi$
$920$		0			0
$921$	−5.83888	+	6.35623i	−0.192398	+	0.209445i
$922$		0			0
$923$	−36.1736	+	34.0805i	−1.19067	+	1.12177i
$924$		0			0
$925$	−48.6848			−1.60074
$926$		0			0
$927$	15.5714	−	10.8459i	0.511431	−	0.356228i
$928$		0			0
$929$	−19.1323	−	33.1381i	−0.627711	−	1.08723i	−0.988010	−	0.154390i	$-0.950659\pi$
$929$	−19.1323	−	33.1381i	−0.627711	−	1.08723i	0.360299	−	0.932837i	$-0.382675\pi$
$930$		0			0
$931$	−1.57175	−	2.72236i	−0.0515122	−	0.0892217i
$932$		0			0
$933$	46.8516	+	10.4475i	1.53385	+	0.342036i
$934$		0			0
$935$	3.88610			0.127089
$936$		0			0
$937$	−24.2557			−0.792398			−0.396199	−	0.918165i	$-0.629671\pi$
$937$	−24.2557			−0.792398			−0.396199	+	0.918165i	$0.629671\pi$
$938$		0			0
$939$	7.23939	+	23.0597i	0.236249	+	0.752526i
$940$		0			0
$941$	29.6711	+	51.3919i	0.967250	+	1.67533i	0.703444	+	0.710751i	$0.251645\pi$
$941$	29.6711	+	51.3919i	0.967250	+	1.67533i	0.263807	+	0.964576i	$0.415022\pi$
$942$		0			0
$943$	−4.17851	−	7.23739i	−0.136071	−	0.235682i
$944$		0			0
$945$	0.392913	−	0.161046i	0.0127814	−	0.00523882i
$946$		0			0
$947$	−27.1641			−0.882715			−0.441357	−	0.897331i	$-0.645503\pi$
$947$	−27.1641			−0.882715			−0.441357	+	0.897331i	$0.645503\pi$
$948$		0			0
$949$	29.6552	+	8.90066i	0.962648	+	0.288928i
$950$		0			0
$951$	15.8476	+	50.4796i	0.513894	+	1.63691i
$952$		0			0
$953$	22.4206	−	38.8335i	0.726273	−	1.25794i	−0.232175	−	0.972674i	$-0.574584\pi$
$953$	22.4206	−	38.8335i	0.726273	−	1.25794i	0.958448	−	0.285267i	$-0.0920824\pi$
$954$		0			0
$955$	1.18275	−	2.04859i	0.0382730	−	0.0662908i
$956$		0			0
$957$	−18.2544	+	19.8718i	−0.590080	+	0.642364i
$958$		0			0
$959$	1.27839	−	2.21424i	0.0412814	−	0.0715016i
$960$		0			0
$961$	14.1680	−	24.5397i	0.457033	−	0.791604i
$962$		0			0
$963$	12.7816	−	8.90274i	0.411880	−	0.286887i
$964$		0			0
$965$	1.34745			0.0433758
$966$		0			0
$967$	−11.8394	−	20.5064i	−0.380729	−	0.659443i	0.610437	−	0.792065i	$-0.290994\pi$
$967$	−11.8394	−	20.5064i	−0.380729	−	0.659443i	−0.991167	+	0.132622i	$0.957660\pi$
$968$		0			0
$969$	1.90754	+	0.425364i	0.0612789	+	0.0136647i
$970$		0			0
$971$	−24.3425	+	42.1624i	−0.781187	+	1.35306i	0.150063	+	0.988676i	$0.452052\pi$
$971$	−24.3425	+	42.1624i	−0.781187	+	1.35306i	−0.931251	+	0.364379i	$0.881281\pi$
$972$		0			0
$973$	−0.587253	−	1.01715i	−0.0188265	−	0.0326084i
$974$		0			0
$975$	−0.383039	−	30.3673i	−0.0122671	−	0.972533i
$976$		0			0
$977$	3.89009	−	6.73784i	0.124455	−	0.215563i	−0.797065	−	0.603894i	$-0.793615\pi$
$977$	3.89009	−	6.73784i	0.124455	−	0.215563i	0.921520	+	0.388331i	$0.126948\pi$
$978$		0			0
$979$	−0.480343	−	0.831979i	−0.0153518	−	0.0265902i
$980$		0			0
$981$	−3.46208	−	40.7310i	−0.110536	−	1.30044i
$982$		0			0
$983$	−27.3156	+	47.3121i	−0.871234	+	1.50902i	−0.0105121	+	0.999945i	$0.503346\pi$
$983$	−27.3156	+	47.3121i	−0.871234	+	1.50902i	−0.860722	+	0.509076i	$0.829987\pi$
$984$		0			0
$985$	−1.91050	+	3.30909i	−0.0608737	+	0.105436i
$986$		0			0
$987$	−0.475165	+	0.517266i	−0.0151247	+	0.0164648i
$988$		0			0
$989$	23.6331			0.751489
$990$		0			0
$991$	−11.7645	−	20.3767i	−0.373712	−	0.647288i	0.616421	−	0.787416i	$-0.288582\pi$
$991$	−11.7645	−	20.3767i	−0.373712	−	0.647288i	−0.990133	+	0.140128i	$0.955248\pi$
$992$		0			0
$993$	6.52260	+	1.45449i	0.206989	+	0.0461567i
$994$		0			0
$995$	−3.11747			−0.0988306
$996$		0			0
$997$	−13.6604	−	23.6605i	−0.432629	−	0.749335i	0.564470	−	0.825454i	$-0.309081\pi$
$997$	−13.6604	−	23.6605i	−0.432629	−	0.749335i	−0.997099	+	0.0761187i	$0.975747\pi$
$998$		0			0
$999$	−6.98106	+	51.5489i	−0.220871	+	1.63094i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.r.f.601.15	✓	40
3.2	odd	2		2808.2.r.f.289.12		40
9.4	even	3		936.2.s.f.913.3	yes	40
9.5	odd	6		2808.2.s.f.1225.12		40
13.9	even	3		936.2.s.f.529.3	yes	40
39.35	odd	6		2808.2.s.f.1153.12		40
117.22	even	3	inner	936.2.r.f.841.15	yes	40
117.113	odd	6		2808.2.r.f.2089.12		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.r.f.601.15	✓	40	1.1	even	1	trivial
936.2.r.f.841.15	yes	40	117.22	even	3	inner
936.2.s.f.529.3	yes	40	13.9	even	3
936.2.s.f.913.3	yes	40	9.4	even	3
2808.2.r.f.289.12		40	3.2	odd	2
2808.2.r.f.2089.12		40	117.113	odd	6
2808.2.s.f.1153.12		40	39.35	odd	6
2808.2.s.f.1225.12		40	9.5	odd	6

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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.r (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17173 - 1.27555i) q^{3} +(-0.185033 - 0.320487i) q^{5} +(-0.110414 - 0.191243i) q^{7} +(-0.254080 - 2.98922i) q^{9} +4.20860 q^{11} +(3.45336 + 1.03649i) q^{13} +(-0.625609 - 0.139505i) q^{15} +(-1.24758 + 2.16087i) q^{17} +(0.226112 - 0.391637i) q^{19} +(-0.373317 - 0.0832466i) q^{21} +(1.02622 - 1.77746i) q^{23} +(2.43153 - 4.21153i) q^{25} +(-4.11063 - 3.17848i) q^{27} -3.70170 q^{29} +(-0.816082 - 1.41349i) q^{31} +(4.93135 - 5.36829i) q^{33} +(-0.0408606 + 0.0707727i) q^{35} +(-5.00558 - 8.66991i) q^{37} +(5.36851 - 3.19046i) q^{39} +(2.03588 - 3.52625i) q^{41} +(5.75733 + 9.97199i) q^{43} +(-0.910994 + 0.634535i) q^{45} +(0.918184 - 1.59034i) q^{47} +(3.47562 - 6.01995i) q^{49} +(1.29447 + 4.12331i) q^{51} -7.12781 q^{53} +(-0.778731 - 1.34880i) q^{55} +(-0.234611 - 0.747311i) q^{57} -4.81685 q^{59} +(3.91401 + 6.77926i) q^{61} +(-0.543614 + 0.378644i) q^{63} +(-0.306806 - 1.29854i) q^{65} +(5.82974 - 10.0974i) q^{67} +(-1.06479 - 3.39171i) q^{69} +(-6.89204 + 11.9374i) q^{71} +8.58734 q^{73} +(-2.52293 - 8.03633i) q^{75} +(-0.464689 - 0.804865i) q^{77} +(-6.36242 + 11.0200i) q^{79} +(-8.87089 + 1.51900i) q^{81} +(-5.54460 + 9.60353i) q^{83} +0.923373 q^{85} +(-4.33740 + 4.72172i) q^{87} +(-0.114134 - 0.197686i) q^{89} +(-0.183079 - 0.774874i) q^{91} +(-2.75922 - 0.615283i) q^{93} -0.167353 q^{95} +(-5.11306 - 8.85609i) q^{97} +(-1.06932 - 12.5804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + q^{5} + 7 q^{7} + 6 q^{9} + 11 q^{15} - q^{17} + 2 q^{19} - 30 q^{21} - q^{23} - 23 q^{25} - 3 q^{27} - 24 q^{29} + 8 q^{31} + 4 q^{33} - 12 q^{35} + 18 q^{37} + 6 q^{39} - 3 q^{41} + 8 q^{43}+ \cdots + 28 q^{99}+O(q^{100}) \) 40 * q + q^5 + 7 * q^7 + 6 * q^9 + 11 * q^15 - q^17 + 2 * q^19 - 30 * q^21 - q^23 - 23 * q^25 - 3 * q^27 - 24 * q^29 + 8 * q^31 + 4 * q^33 - 12 * q^35 + 18 * q^37 + 6 * q^39 - 3 * q^41 + 8 * q^43 + 24 * q^45 + 4 * q^47 - 23 * q^49 - 37 * q^51 - 40 * q^53 - 14 * q^55 + 7 * q^57 + 8 * q^59 - 3 * q^61 + 10 * q^63 - 32 * q^65 + 27 * q^67 - 38 * q^69 + q^71 - 12 * q^73 + 32 * q^75 - 4 * q^77 + 13 * q^79 + 26 * q^81 - 15 * q^83 - 10 * q^85 + 25 * q^87 + 12 * q^89 - 57 * q^91 - 7 * q^93 - 2 * q^95 + 35 * q^97 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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