LMFDB - Embedded newform 936.2.g.f.469.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(469,936)] 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("936.469"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] 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:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			469.1
Character	$\chi$	$=$	936.469
Dual form			936.2.g.f.469.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40752 - 0.137446i) q^{2} +(1.96222 + 0.386915i) q^{4} -4.18566i q^{5} +2.70923 q^{7} +(-2.70868 - 0.814289i) q^{8} +(-0.575302 + 5.89140i) q^{10} -0.956799i q^{11} -1.00000i q^{13} +(-3.81329 - 0.372372i) q^{14} +(3.70059 + 1.51842i) q^{16} +4.96511 q^{17} -5.59682i q^{19} +(1.61950 - 8.21318i) q^{20} +(-0.131508 + 1.34671i) q^{22} +5.16007 q^{23} -12.5198 q^{25} +(-0.137446 + 1.40752i) q^{26} +(5.31610 + 1.04824i) q^{28} +4.46122i q^{29} +6.37531 q^{31} +(-4.99995 - 2.64584i) q^{32} +(-6.98848 - 0.682433i) q^{34} -11.3399i q^{35} +1.66608i q^{37} +(-0.769259 + 7.87763i) q^{38} +(-3.40834 + 11.3376i) q^{40} -8.64689 q^{41} +7.67092i q^{43} +(0.370200 - 1.87745i) q^{44} +(-7.26289 - 0.709230i) q^{46} -8.01021 q^{47} +0.339928 q^{49} +(17.6218 + 1.72079i) q^{50} +(0.386915 - 1.96222i) q^{52} -0.0797782i q^{53} -4.00484 q^{55} +(-7.33843 - 2.20610i) q^{56} +(0.613176 - 6.27925i) q^{58} +4.70716i q^{59} -8.10132i q^{61} +(-8.97336 - 0.876259i) q^{62} +(6.67387 + 4.41129i) q^{64} -4.18566 q^{65} -13.7670i q^{67} +(9.74262 + 1.92108i) q^{68} +(-1.55863 + 15.9612i) q^{70} +1.15489 q^{71} +1.66608 q^{73} +(0.228995 - 2.34503i) q^{74} +(2.16549 - 10.9822i) q^{76} -2.59219i q^{77} +4.30121 q^{79} +(6.35561 - 15.4894i) q^{80} +(12.1707 + 1.18848i) q^{82} -14.0185i q^{83} -20.7823i q^{85} +(1.05434 - 10.7970i) q^{86} +(-0.779111 + 2.59166i) q^{88} +11.6601 q^{89} -2.70923i q^{91} +(10.1252 + 1.99651i) q^{92} +(11.2745 + 1.10097i) q^{94} -23.4264 q^{95} -6.17018 q^{97} +(-0.478454 - 0.0467216i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{4} - 8 q^{7} + 12 q^{10} - 4 q^{16} + 4 q^{22} - 24 q^{25} + 8 q^{28} + 40 q^{31} - 16 q^{34} - 36 q^{40} - 24 q^{46} + 24 q^{49} - 4 q^{52} - 16 q^{55} - 24 q^{58} + 8 q^{64} - 16 q^{70} - 16 q^{76}+ \cdots - 16 q^{97}+O(q^{100}) $ 24 * q + 8 * q^4 - 8 * q^7 + 12 * q^10 - 4 * q^16 + 4 * q^22 - 24 * q^25 + 8 * q^28 + 40 * q^31 - 16 * q^34 - 36 * q^40 - 24 * q^46 + 24 * q^49 - 4 * q^52 - 16 * q^55 - 24 * q^58 + 8 * q^64 - 16 * q^70 - 16 * q^76 + 68 * q^82 + 28 * q^88 + 12 * q^94 - 16 * q^97

Character values

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

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.40752	−	0.137446i	−0.995266	−	0.0971889i
$2$	−1.40752	−	0.137446i	−0.995266	−	0.0971889i
$3$		0			0
$3$		0			0
$4$	1.96222	+	0.386915i	0.981109	+	0.193458i
$5$		−	4.18566i		−	1.87189i	−0.352152	−	0.935943i	$-0.614550\pi$
$5$		−	4.18566i		−	1.87189i	0.352152	−	0.935943i	$-0.385450\pi$
$6$		0			0
$7$	2.70923			1.02399			0.511996	−	0.858988i	$-0.328906\pi$
$7$	2.70923			1.02399			0.511996	+	0.858988i	$0.328906\pi$
$8$	−2.70868	−	0.814289i	−0.957662	−	0.287895i
$9$		0			0
$10$	−0.575302	+	5.89140i	−0.181927	+	1.86302i
$11$		−	0.956799i		−	0.288486i	−0.989542	−	0.144243i	$-0.953925\pi$
$11$		−	0.956799i		−	0.288486i	0.989542	−	0.144243i	$-0.0460747\pi$
$12$		0			0
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−3.81329	−	0.372372i	−1.01915	−	0.0995207i
$15$		0			0
$16$	3.70059	+	1.51842i	0.925148	+	0.379606i
$17$	4.96511			1.20422			0.602108	−	0.798415i	$-0.294328\pi$
$17$	4.96511			1.20422			0.602108	+	0.798415i	$0.294328\pi$
$18$		0			0
$19$		−	5.59682i		−	1.28400i	−0.766705	−	0.641999i	$-0.778105\pi$
$19$		−	5.59682i		−	1.28400i	0.766705	−	0.641999i	$-0.221895\pi$
$20$	1.61950	−	8.21318i	0.362131	−	1.83652i
$21$		0			0
$22$	−0.131508	+	1.34671i	−0.0280376	+	0.287120i
$23$	5.16007			1.07595			0.537974	−	0.842961i	$-0.319190\pi$
$23$	5.16007			1.07595			0.537974	+	0.842961i	$0.319190\pi$
$24$		0			0
$25$	−12.5198			−2.50396
$26$	−0.137446	+	1.40752i	−0.0269553	+	0.276037i
$27$		0			0
$28$	5.31610	+	1.04824i	1.00465	+	0.198099i
$29$			4.46122i			0.828428i	0.910180	+	0.414214i	$0.135943\pi$
$29$			4.46122i			0.828428i	−0.910180	+	0.414214i	$0.864057\pi$
$30$		0			0
$31$	6.37531			1.14504			0.572519	−	0.819891i	$-0.305966\pi$
$31$	6.37531			1.14504			0.572519	+	0.819891i	$0.305966\pi$
$32$	−4.99995	−	2.64584i	−0.883875	−	0.467723i
$33$		0			0
$34$	−6.98848	−	0.682433i	−1.19851	−	0.117036i
$35$		−	11.3399i		−	1.91680i
$36$		0			0
$37$			1.66608i			0.273901i	0.990578	+	0.136951i	$0.0437301\pi$
$37$			1.66608i			0.273901i	−0.990578	+	0.136951i	$0.956270\pi$
$38$	−0.769259	+	7.87763i	−0.124790	+	1.27792i
$39$		0			0
$40$	−3.40834	+	11.3376i	−0.538906	+	1.79263i
$41$	−8.64689			−1.35042			−0.675208	−	0.737627i	$-0.735946\pi$
$41$	−8.64689			−1.35042			−0.675208	+	0.737627i	$0.735946\pi$
$42$		0			0
$43$			7.67092i			1.16980i	0.811104	+	0.584902i	$0.198867\pi$
$43$			7.67092i			1.16980i	−0.811104	+	0.584902i	$0.801133\pi$
$44$	0.370200	−	1.87745i	0.0558098	−	0.283036i
$45$		0			0
$46$	−7.26289	−	0.709230i	−1.07086	−	0.104570i
$47$	−8.01021			−1.16841			−0.584205	−	0.811606i	$-0.698593\pi$
$47$	−8.01021			−1.16841			−0.584205	+	0.811606i	$0.698593\pi$
$48$		0			0
$49$	0.339928			0.0485611
$50$	17.6218	+	1.72079i	2.49210	+	0.243357i
$51$		0			0
$52$	0.386915	−	1.96222i	0.0536555	−	0.272111i
$53$		−	0.0797782i		−	0.0109584i	−0.999985	−	0.00547919i	$-0.998256\pi$
$53$		−	0.0797782i		−	0.0109584i	0.999985	−	0.00547919i	$-0.00174409\pi$
$54$		0			0
$55$	−4.00484			−0.540012
$56$	−7.33843	−	2.20610i	−0.980639	−	0.294802i
$57$		0			0
$58$	0.613176	−	6.27925i	0.0805140	−	0.824506i
$59$			4.70716i			0.612820i	0.951900	+	0.306410i	$0.0991278\pi$
$59$			4.70716i			0.612820i	−0.951900	+	0.306410i	$0.900872\pi$
$60$		0			0
$61$		−	8.10132i		−	1.03727i	−0.854996	−	0.518634i	$-0.826441\pi$
$61$		−	8.10132i		−	1.03727i	0.854996	−	0.518634i	$-0.173559\pi$
$62$	−8.97336	−	0.876259i	−1.13962	−	0.111285i
$63$		0			0
$64$	6.67387	+	4.41129i	0.834233	+	0.551411i
$65$	−4.18566			−0.519168
$66$		0			0
$67$		−	13.7670i		−	1.68191i	−0.541108	−	0.840953i	$-0.681995\pi$
$67$		−	13.7670i		−	1.68191i	0.541108	−	0.840953i	$-0.318005\pi$
$68$	9.74262	+	1.92108i	1.18147	+	0.232965i
$69$		0			0
$70$	−1.55863	+	15.9612i	−0.186291	+	1.90772i
$71$	1.15489			0.137061			0.0685303	−	0.997649i	$-0.478169\pi$
$71$	1.15489			0.137061			0.0685303	+	0.997649i	$0.478169\pi$
$72$		0			0
$73$	1.66608			0.194999			0.0974997	−	0.995236i	$-0.468916\pi$
$73$	1.66608			0.194999			0.0974997	+	0.995236i	$0.468916\pi$
$74$	0.228995	−	2.34503i	0.0266201	−	0.272604i
$75$		0			0
$76$	2.16549	−	10.9822i	0.248399	−	1.25974i
$77$		−	2.59219i		−	0.295407i
$78$		0			0
$79$	4.30121			0.483924			0.241962	−	0.970286i	$-0.422209\pi$
$79$	4.30121			0.483924			0.241962	+	0.970286i	$0.422209\pi$
$80$	6.35561	−	15.4894i	0.710579	−	1.73177i
$81$		0			0
$82$	12.1707	+	1.18848i	1.34402	+	0.131245i
$83$		−	14.0185i		−	1.53873i	−0.638810	−	0.769365i	$-0.720573\pi$
$83$		−	14.0185i		−	1.53873i	0.638810	−	0.769365i	$-0.279427\pi$
$84$		0			0
$85$		−	20.7823i		−	2.25415i
$86$	1.05434	−	10.7970i	0.113692	−	1.16427i
$87$		0			0
$88$	−0.779111	+	2.59166i	−0.0830535	+	0.276272i
$89$	11.6601			1.23596			0.617981	−	0.786193i	$-0.287951\pi$
$89$	11.6601			1.23596			0.617981	+	0.786193i	$0.287951\pi$
$90$		0			0
$91$		−	2.70923i		−	0.284004i
$92$	10.1252	+	1.99651i	1.05562	+	0.208150i
$93$		0			0
$94$	11.2745	+	1.10097i	1.16288	+	0.113556i
$95$	−23.4264			−2.40350
$96$		0			0
$97$	−6.17018			−0.626487			−0.313243	−	0.949673i	$-0.601416\pi$
$97$	−6.17018			−0.626487			−0.313243	+	0.949673i	$0.601416\pi$
$98$	−0.478454	−	0.0467216i	−0.0483312	−	0.00471960i
$99$		0			0
$100$	−24.5665	−	4.84409i	−2.45665	−	0.484409i
$101$			18.2218i			1.81313i	0.422063	+	0.906567i	$0.361306\pi$
$101$			18.2218i			1.81313i	−0.422063	+	0.906567i	$0.638694\pi$
$102$		0			0
$103$	−1.61651			−0.159280			−0.0796399	−	0.996824i	$-0.525377\pi$
$103$	−1.61651			−0.159280			−0.0796399	+	0.996824i	$0.525377\pi$
$104$	−0.814289	+	2.70868i	−0.0798476	+	0.265608i
$105$		0			0
$106$	−0.0109652	+	0.112289i	−0.00106503	+	0.0109065i
$107$		−	10.6645i		−	1.03097i	−0.856898	−	0.515487i	$-0.827611\pi$
$107$		−	10.6645i		−	1.03097i	0.856898	−	0.515487i	$-0.172389\pi$
$108$		0			0
$109$			15.0942i			1.44576i	0.690972	+	0.722882i	$0.257183\pi$
$109$			15.0942i			1.44576i	−0.690972	+	0.722882i	$0.742817\pi$
$110$	5.63689	+	0.550449i	0.537456	+	0.0524832i
$111$		0			0
$112$	10.0258	+	4.11376i	0.947345	+	0.388714i
$113$	−14.5746			−1.37106			−0.685530	−	0.728044i	$-0.740430\pi$
$113$	−14.5746			−1.37106			−0.685530	+	0.728044i	$0.740430\pi$
$114$		0			0
$115$		−	21.5983i		−	2.01405i
$116$	−1.72611	+	8.75388i	−0.160266	+	0.812778i
$117$		0			0
$118$	0.646979	−	6.62541i	0.0595593	−	0.609919i
$119$	13.4516			1.23311
$120$		0			0
$121$	10.0845			0.916776
$122$	−1.11349	+	11.4028i	−0.100811	+	1.03236i
$123$		0			0
$124$	12.5097	+	2.46670i	1.12341	+	0.221516i
$125$			31.4753i			2.81524i
$126$		0			0
$127$	−16.1471			−1.43283			−0.716414	−	0.697676i	$-0.754218\pi$
$127$	−16.1471			−1.43283			−0.716414	+	0.697676i	$0.754218\pi$
$128$	−8.78728	−	7.12627i	−0.776693	−	0.629879i
$129$		0			0
$130$	5.89140	+	0.575302i	0.516710	+	0.0504573i
$131$		−	9.42633i		−	0.823582i	−0.911278	−	0.411791i	$-0.864903\pi$
$131$		−	9.42633i		−	0.823582i	0.911278	−	0.411791i	$-0.135097\pi$
$132$		0			0
$133$		−	15.1631i		−	1.31480i
$134$	−1.89222	+	19.3773i	−0.163463	+	1.67394i
$135$		0			0
$136$	−13.4489	−	4.04303i	−1.15323	−	0.346687i
$137$	4.68642			0.400388			0.200194	−	0.979756i	$-0.435843\pi$
$137$	4.68642			0.400388			0.200194	+	0.979756i	$0.435843\pi$
$138$		0			0
$139$		−	9.95019i		−	0.843964i	−0.906604	−	0.421982i	$-0.861334\pi$
$139$		−	9.95019i		−	0.843964i	0.906604	−	0.421982i	$-0.138666\pi$
$140$	4.38759	−	22.2514i	0.370819	−	1.88059i
$141$		0			0
$142$	−1.62553	−	0.158735i	−0.136412	−	0.0133208i
$143$	−0.956799			−0.0800116
$144$		0			0
$145$	18.6732			1.55072
$146$	−2.34503	−	0.228995i	−0.194076	−	0.0189518i
$147$		0			0
$148$	−0.644630	+	3.26920i	−0.0529882	+	0.268727i
$149$			6.19106i			0.507191i	0.967310	+	0.253596i	$0.0816132\pi$
$149$			6.19106i			0.507191i	−0.967310	+	0.253596i	$0.918387\pi$
$150$		0			0
$151$	−8.48441			−0.690451			−0.345226	−	0.938520i	$-0.612198\pi$
$151$	−8.48441			−0.690451			−0.345226	+	0.938520i	$0.612198\pi$
$152$	−4.55743	+	15.1600i	−0.369656	+	1.22964i
$153$		0			0
$154$	−0.356286	+	3.64855i	−0.0287103	+	0.294009i
$155$		−	26.6849i		−	2.14338i
$156$		0			0
$157$		−	16.0239i		−	1.27885i	−0.768855	−	0.639423i	$-0.779173\pi$
$157$		−	16.0239i		−	1.27885i	0.768855	−	0.639423i	$-0.220827\pi$
$158$	−6.05403	−	0.591183i	−0.481633	−	0.0470320i
$159$		0			0
$160$	−11.0746	+	20.9281i	−0.875524	+	1.65451i
$161$	13.9798			1.10176
$162$		0			0
$163$			16.6039i			1.30052i	0.759712	+	0.650260i	$0.225340\pi$
$163$			16.6039i			1.30052i	−0.759712	+	0.650260i	$0.774660\pi$
$164$	−16.9671	−	3.34561i	−1.32491	−	0.261248i
$165$		0			0
$166$	−1.92678	+	19.7313i	−0.149547	+	1.53145i
$167$	6.35953			0.492115			0.246058	−	0.969255i	$-0.420865\pi$
$167$	6.35953			0.492115			0.246058	+	0.969255i	$0.420865\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	−2.85644	+	29.2514i	−0.219079	+	2.24348i
$171$		0			0
$172$	−2.96799	+	15.0520i	−0.226307	+	1.14770i
$173$		−	2.02859i		−	0.154231i	−0.997022	−	0.0771154i	$-0.975429\pi$
$173$		−	2.02859i		−	0.154231i	0.997022	−	0.0771154i	$-0.0245710\pi$
$174$		0			0
$175$	−33.9190			−2.56403
$176$	1.45283	−	3.54072i	0.109511	−	0.266892i
$177$		0			0
$178$	−16.4117	−	1.60263i	−1.23011	−	0.120122i
$179$			17.9220i			1.33955i	0.742563	+	0.669777i	$0.233610\pi$
$179$			17.9220i			1.33955i	−0.742563	+	0.669777i	$0.766390\pi$
$180$		0			0
$181$			3.41179i			0.253596i	0.991929	+	0.126798i	$0.0404701\pi$
$181$			3.41179i			0.253596i	−0.991929	+	0.126798i	$0.959530\pi$
$182$	−0.372372	+	3.81329i	−0.0276021	+	0.282660i
$183$		0			0
$184$	−13.9770	−	4.20179i	−1.03040	−	0.309760i
$185$	6.97363			0.512712
$186$		0			0
$187$		−	4.75061i		−	0.347399i
$188$	−15.7178	−	3.09927i	−1.14634	−	0.226038i
$189$		0			0
$190$	32.9731	+	3.21986i	2.39212	+	0.233593i
$191$	13.0171			0.941886			0.470943	−	0.882164i	$-0.343914\pi$
$191$	13.0171			0.941886			0.470943	+	0.882164i	$0.343914\pi$
$192$		0			0
$193$	2.02198			0.145546			0.0727728	−	0.997349i	$-0.476815\pi$
$193$	2.02198			0.145546			0.0727728	+	0.997349i	$0.476815\pi$
$194$	8.68464	+	0.848065i	0.623521	+	0.0608875i
$195$		0			0
$196$	0.667012	+	0.131523i	0.0476437	+	0.00939451i
$197$			16.5454i			1.17881i	0.807838	+	0.589405i	$0.200638\pi$
$197$			16.5454i			1.17881i	−0.807838	+	0.589405i	$0.799362\pi$
$198$		0			0
$199$	−1.11725			−0.0791999			−0.0395999	−	0.999216i	$-0.512608\pi$
$199$	−1.11725			−0.0791999			−0.0395999	+	0.999216i	$0.512608\pi$
$200$	33.9121	+	10.1947i	2.39794	+	0.720876i
$201$		0			0
$202$	2.50451	−	25.6475i	0.176216	−	1.80455i
$203$			12.0865i			0.848304i
$204$		0			0
$205$			36.1930i			2.52783i
$206$	2.27527	+	0.222183i	0.158526	+	0.0154802i
$207$		0			0
$208$	1.51842	−	3.70059i	0.105284	−	0.256590i
$209$	−5.35503			−0.370415
$210$		0			0
$211$			22.3717i			1.54013i	0.637964	+	0.770066i	$0.279777\pi$
$211$			22.3717i			1.54013i	−0.637964	+	0.770066i	$0.720223\pi$
$212$	0.0308674	−	0.156542i	0.00211998	−	0.0107514i
$213$		0			0
$214$	−1.46579	+	15.0104i	−0.100199	+	1.02609i
$215$	32.1079			2.18974
$216$		0			0
$217$	17.2722			1.17251
$218$	2.07464	−	21.2454i	0.140512	−	1.43892i
$219$		0			0
$220$	−7.85837	−	1.54953i	−0.529811	−	0.104470i
$221$		−	4.96511i		−	0.333989i
$222$		0			0
$223$	25.3166			1.69532			0.847661	−	0.530538i	$-0.178010\pi$
$223$	25.3166			1.69532			0.847661	+	0.530538i	$0.178010\pi$
$224$	−13.5460	−	7.16819i	−0.905082	−	0.478945i
$225$		0			0
$226$	20.5140	+	2.00321i	1.36457	+	0.133252i
$227$			0.936542i			0.0621604i	0.999517	+	0.0310802i	$0.00989474\pi$
$227$			0.936542i			0.0621604i	−0.999517	+	0.0310802i	$0.990105\pi$
$228$		0			0
$229$		−	3.40878i		−	0.225259i	−0.993637	−	0.112629i	$-0.964073\pi$
$229$		−	3.40878i		−	0.225259i	0.993637	−	0.112629i	$-0.0359272\pi$
$230$	−2.96860	+	30.4000i	−0.195744	+	2.00452i
$231$		0			0
$232$	3.63272	−	12.0840i	0.238500	−	0.793354i
$233$	13.0000			0.851656			0.425828	−	0.904804i	$-0.359983\pi$
$233$	13.0000			0.851656			0.425828	+	0.904804i	$0.359983\pi$
$234$		0			0
$235$			33.5280i			2.18713i
$236$	−1.82127	+	9.23646i	−0.118555	+	0.601243i
$237$		0			0
$238$	−18.9334	−	1.84887i	−1.22727	−	0.119844i
$239$	−5.91302			−0.382482			−0.191241	−	0.981543i	$-0.561251\pi$
$239$	−5.91302			−0.382482			−0.191241	+	0.981543i	$0.561251\pi$
$240$		0			0
$241$	−12.0209			−0.774333			−0.387166	−	0.922010i	$-0.626546\pi$
$241$	−12.0209			−0.774333			−0.387166	+	0.922010i	$0.626546\pi$
$242$	−14.1942	−	1.38608i	−0.912436	−	0.0891004i
$243$		0			0
$244$	3.13453	−	15.8966i	0.200667	−	1.01767i
$245$		−	1.42282i		−	0.0909008i
$246$		0			0
$247$	−5.59682			−0.356117
$248$	−17.2686	−	5.19134i	−1.09656	−	0.329650i
$249$		0			0
$250$	4.32615	−	44.3021i	0.273610	−	2.80191i
$251$			7.48790i			0.472632i	0.971676	+	0.236316i	$0.0759400\pi$
$251$			7.48790i			0.472632i	−0.971676	+	0.236316i	$0.924060\pi$
$252$		0			0
$253$		−	4.93715i		−	0.310396i
$254$	22.7274	+	2.21936i	1.42604	+	0.139255i
$255$		0			0
$256$	11.3888	+	11.2381i	0.711799	+	0.702383i
$257$	19.5397			1.21885			0.609426	−	0.792843i	$-0.291400\pi$
$257$	19.5397			1.21885			0.609426	+	0.792843i	$0.291400\pi$
$258$		0			0
$259$			4.51378i			0.280473i
$260$	−8.21318	−	1.61950i	−0.509360	−	0.100437i
$261$		0			0
$262$	−1.29561	+	13.2677i	−0.0800430	+	0.819683i
$263$	−14.2733			−0.880130			−0.440065	−	0.897966i	$-0.645045\pi$
$263$	−14.2733			−0.880130			−0.440065	+	0.897966i	$0.645045\pi$
$264$		0			0
$265$	−0.333925			−0.0205128
$266$	−2.08410	+	21.3423i	−0.127784	+	1.30858i
$267$		0			0
$268$	5.32666	−	27.0138i	0.325377	−	1.65013i
$269$			9.47978i			0.577992i	0.957330	+	0.288996i	$0.0933215\pi$
$269$			9.47978i			0.577992i	−0.957330	+	0.288996i	$0.906679\pi$
$270$		0			0
$271$	29.1684			1.77185			0.885926	−	0.463827i	$-0.153524\pi$
$271$	29.1684			1.77185			0.885926	+	0.463827i	$0.153524\pi$
$272$	18.3738	+	7.53913i	1.11408	+	0.457127i
$273$		0			0
$274$	−6.59622	−	0.644129i	−0.398492	−	0.0389132i
$275$			11.9789i			0.722356i
$276$		0			0
$277$		−	5.56665i		−	0.334468i	−0.985917	−	0.167234i	$-0.946516\pi$
$277$		−	5.56665i		−	0.334468i	0.985917	−	0.167234i	$-0.0534835\pi$
$278$	−1.36761	+	14.0051i	−0.0820240	+	0.839969i
$279$		0			0
$280$	−9.23398	+	30.7162i	−0.551836	+	1.83564i
$281$	1.67325			0.0998179			0.0499090	−	0.998754i	$-0.484107\pi$
$281$	1.67325			0.0998179			0.0499090	+	0.998754i	$0.484107\pi$
$282$		0			0
$283$		−	20.4580i		−	1.21610i	−0.793897	−	0.608052i	$-0.791951\pi$
$283$		−	20.4580i		−	1.21610i	0.793897	−	0.608052i	$-0.208049\pi$
$284$	2.26615	+	0.446846i	0.134471	+	0.0265154i
$285$		0			0
$286$	1.34671	+	0.131508i	0.0796328	+	0.00777623i
$287$	−23.4264			−1.38282
$288$		0			0
$289$	7.65230			0.450135
$290$	−26.2828	−	2.56655i	−1.54338	−	0.150713i
$291$		0			0
$292$	3.26920	+	0.644630i	0.191316	+	0.0377241i
$293$			29.8221i			1.74223i	0.491083	+	0.871113i	$0.336601\pi$
$293$			29.8221i			1.74223i	−0.491083	+	0.871113i	$0.663399\pi$
$294$		0			0
$295$	19.7026			1.14713
$296$	1.35667	−	4.51286i	0.0788546	−	0.262305i
$297$		0			0
$298$	0.850935	−	8.71403i	0.0492933	−	0.504790i
$299$		−	5.16007i		−	0.298415i
$300$		0			0
$301$			20.7823i			1.19787i
$302$	11.9420	+	1.16615i	0.687183	+	0.0671042i
$303$		0			0
$304$	8.49834	−	20.7115i	0.487413	−	1.18789i
$305$	−33.9094			−1.94165
$306$		0			0
$307$		−	9.81086i		−	0.559935i	−0.960009	−	0.279968i	$-0.909676\pi$
$307$		−	9.81086i		−	0.559935i	0.960009	−	0.279968i	$-0.0903237\pi$
$308$	1.00296	−	5.08644i	0.0571488	−	0.289827i
$309$		0			0
$310$	−3.66773	+	37.5595i	−0.208313	+	2.13323i
$311$	5.24920			0.297655			0.148827	−	0.988863i	$-0.452450\pi$
$311$	5.24920			0.297655			0.148827	+	0.988863i	$0.452450\pi$
$312$		0			0
$313$	3.78596			0.213995			0.106998	−	0.994259i	$-0.465876\pi$
$313$	3.78596			0.213995			0.106998	+	0.994259i	$0.465876\pi$
$314$	−2.20242	+	22.5539i	−0.124290	+	1.27279i
$315$		0			0
$316$	8.43991	+	1.66420i	0.474782	+	0.0936187i
$317$		−	15.9601i		−	0.896407i	−0.893931	−	0.448204i	$-0.852064\pi$
$317$		−	15.9601i		−	0.896407i	0.893931	−	0.448204i	$-0.147936\pi$
$318$		0			0
$319$	4.26849			0.238990
$320$	18.4642	−	27.9346i	1.03218	−	1.56159i
$321$		0			0
$322$	−19.6768	−	1.92147i	−1.09655	−	0.107079i
$323$		−	27.7888i		−	1.54621i
$324$		0			0
$325$			12.5198i			0.694473i
$326$	2.28214	−	23.3703i	0.126396	−	1.29436i
$327$		0			0
$328$	23.4216	+	7.04106i	1.29324	+	0.388778i
$329$	−21.7015			−1.19644
$330$		0			0
$331$			30.6147i			1.68274i	0.540463	+	0.841368i	$0.318249\pi$
$331$			30.6147i			1.68274i	−0.540463	+	0.841368i	$0.681751\pi$
$332$	5.42397	−	27.5073i	0.297679	−	1.50966i
$333$		0			0
$334$	−8.95115	−	0.874091i	−0.489785	−	0.0478281i
$335$	−57.6240			−3.14834
$336$		0			0
$337$	−19.8679			−1.08227			−0.541137	−	0.840934i	$-0.682006\pi$
$337$	−19.8679			−1.08227			−0.541137	+	0.840934i	$0.682006\pi$
$338$	1.40752	+	0.137446i	0.0765589	+	0.00747607i
$339$		0			0
$340$	8.04098	−	40.7793i	0.436083	−	2.21157i
$341$		−	6.09989i		−	0.330327i
$342$		0			0
$343$	−18.0437			−0.974267
$344$	6.24634	−	20.7780i	0.336780	−	1.12028i
$345$		0			0
$346$	−0.278821	+	2.85528i	−0.0149895	+	0.153501i
$347$		−	3.59683i		−	0.193088i	−0.995329	−	0.0965440i	$-0.969221\pi$
$347$		−	3.59683i		−	0.193088i	0.995329	−	0.0965440i	$-0.0307788\pi$
$348$		0			0
$349$			31.9651i			1.71105i	0.517758	+	0.855527i	$0.326767\pi$
$349$			31.9651i			1.71105i	−0.517758	+	0.855527i	$0.673233\pi$
$350$	47.7416	+	4.66202i	2.55190	+	0.249196i
$351$		0			0
$352$	−2.53154	+	4.78395i	−0.134931	+	0.254985i
$353$	16.7537			0.891707			0.445854	−	0.895106i	$-0.352900\pi$
$353$	16.7537			0.891707			0.445854	+	0.895106i	$0.352900\pi$
$354$		0			0
$355$		−	4.83399i		−	0.256562i
$356$	22.8796	+	4.51145i	1.21261	+	0.239106i
$357$		0			0
$358$	2.46330	−	25.2256i	0.130190	−	1.33321i
$359$	31.7820			1.67739			0.838694	−	0.544603i	$-0.183320\pi$
$359$	31.7820			1.67739			0.838694	+	0.544603i	$0.183320\pi$
$360$		0			0
$361$	−12.3244			−0.648651
$362$	0.468936	−	4.80216i	0.0246467	−	0.252396i
$363$		0			0
$364$	1.04824	−	5.31610i	0.0549428	−	0.278639i
$365$		−	6.97363i		−	0.365017i
$366$		0			0
$367$	27.8497			1.45374			0.726872	−	0.686773i	$-0.240973\pi$
$367$	27.8497			1.45374			0.726872	+	0.686773i	$0.240973\pi$
$368$	19.0953	+	7.83517i	0.995412	+	0.408436i
$369$		0			0
$370$	−9.81552	−	0.958497i	−0.510284	−	0.0498299i
$371$		−	0.216137i		−	0.0112213i
$372$		0			0
$373$			29.9442i			1.55045i	0.631683	+	0.775227i	$0.282365\pi$
$373$			29.9442i			1.55045i	−0.631683	+	0.775227i	$0.717635\pi$
$374$	−0.652952	+	6.68657i	−0.0337633	+	0.345754i
$375$		0			0
$376$	21.6971	+	6.52262i	1.11894	+	0.336379i
$377$	4.46122			0.229765
$378$		0			0
$379$		−	5.41028i		−	0.277907i	−0.990299	−	0.138954i	$-0.955626\pi$
$379$		−	5.41028i		−	0.277907i	0.990299	−	0.138954i	$-0.0443739\pi$
$380$	−45.9677	−	9.06403i	−2.35809	−	0.464975i
$381$		0			0
$382$	−18.3219	−	1.78915i	−0.937428	−	0.0915409i
$383$	2.35907			0.120543			0.0602714	−	0.998182i	$-0.480803\pi$
$383$	2.35907			0.120543			0.0602714	+	0.998182i	$0.480803\pi$
$384$		0			0
$385$	−10.8500			−0.552969
$386$	−2.84598	−	0.277913i	−0.144857	−	0.0141454i
$387$		0			0
$388$	−12.1072	−	2.38734i	−0.614651	−	0.121199i
$389$		−	34.2038i		−	1.73420i	−0.498131	−	0.867102i	$-0.665980\pi$
$389$		−	34.2038i		−	1.73420i	0.498131	−	0.867102i	$-0.334020\pi$
$390$		0			0
$391$	25.6203			1.29567
$392$	−0.920754	−	0.276799i	−0.0465051	−	0.0139805i
$393$		0			0
$394$	2.27409	−	23.2879i	0.114567	−	1.17323i
$395$		−	18.0034i		−	0.905850i
$396$		0			0
$397$		−	16.8214i		−	0.844240i	−0.906540	−	0.422120i	$-0.861286\pi$
$397$		−	16.8214i		−	0.844240i	0.906540	−	0.422120i	$-0.138714\pi$
$398$	1.57255	+	0.153562i	0.0788249	+	0.00769735i
$399$		0			0
$400$	−46.3306	−	19.0103i	−2.31653	−	0.950517i
$401$	−3.03043			−0.151333			−0.0756663	−	0.997133i	$-0.524108\pi$
$401$	−3.03043			−0.151333			−0.0756663	+	0.997133i	$0.524108\pi$
$402$		0			0
$403$		−	6.37531i		−	0.317577i
$404$	−7.05028	+	35.7551i	−0.350764	+	1.77888i
$405$		0			0
$406$	1.66124	−	17.0119i	0.0824457	−	0.844288i
$407$	1.59410			0.0790166
$408$		0			0
$409$	−36.7145			−1.81542			−0.907708	−	0.419602i	$-0.862169\pi$
$409$	−36.7145			−1.81542			−0.907708	+	0.419602i	$0.862169\pi$
$410$	4.97457	−	50.9423i	0.245677	−	2.51586i
$411$		0			0
$412$	−3.17195	−	0.625454i	−0.156271	−	0.0308139i
$413$			12.7528i			0.627523i
$414$		0			0
$415$	−58.6767			−2.88033
$416$	−2.64584	+	4.99995i	−0.129723	+	0.245143i
$417$		0			0
$418$	7.53731	+	0.736027i	0.368662	+	0.0360002i
$419$			18.2783i			0.892956i	0.894795	+	0.446478i	$0.147322\pi$
$419$			18.2783i			0.892956i	−0.894795	+	0.446478i	$0.852678\pi$
$420$		0			0
$421$		−	0.991796i		−	0.0483372i	−0.999708	−	0.0241686i	$-0.992306\pi$
$421$		−	0.991796i		−	0.0483372i	0.999708	−	0.0241686i	$-0.00769385\pi$
$422$	3.07490	−	31.4886i	0.149684	−	1.53284i
$423$		0			0
$424$	−0.0649625	+	0.216093i	−0.00315486	+	0.0104944i
$425$	−62.1621			−3.01530
$426$		0			0
$427$		−	21.9484i		−	1.06216i
$428$	4.12624	−	20.9260i	0.199450	−	1.01150i
$429$		0			0
$430$	−45.1924	−	4.41309i	−2.17937	−	0.212818i
$431$	1.05847			0.0509847			0.0254923	−	0.999675i	$-0.491885\pi$
$431$	1.05847			0.0509847			0.0254923	+	0.999675i	$0.491885\pi$
$432$		0			0
$433$	−26.5935			−1.27800			−0.639002	−	0.769205i	$-0.720652\pi$
$433$	−26.5935			−1.27800			−0.639002	+	0.769205i	$0.720652\pi$
$434$	−24.3109	−	2.37399i	−1.16696	−	0.113955i
$435$		0			0
$436$	−5.84018	+	29.6181i	−0.279694	+	1.41845i
$437$		−	28.8800i		−	1.38152i
$438$		0			0
$439$	28.5184			1.36111			0.680554	−	0.732698i	$-0.261739\pi$
$439$	28.5184			1.36111			0.680554	+	0.732698i	$0.261739\pi$
$440$	10.8478	+	3.26110i	0.517149	+	0.155467i
$441$		0			0
$442$	−0.682433	+	6.98848i	−0.0324600	+	0.332408i
$443$		−	8.16454i		−	0.387909i	−0.981011	−	0.193955i	$-0.937869\pi$
$443$		−	8.16454i		−	0.387909i	0.981011	−	0.193955i	$-0.0621315\pi$
$444$		0			0
$445$		−	48.8051i		−	2.31358i
$446$	−35.6335	−	3.47966i	−1.68730	−	0.164766i
$447$		0			0
$448$	18.0810	+	11.9512i	0.854249	+	0.564641i
$449$	−1.19420			−0.0563577			−0.0281788	−	0.999603i	$-0.508971\pi$
$449$	−1.19420			−0.0563577			−0.0281788	+	0.999603i	$0.508971\pi$
$450$		0			0
$451$			8.27333i			0.389576i
$452$	−28.5985	−	5.63912i	−1.34516	−	0.265242i
$453$		0			0
$454$	0.128724	−	1.31820i	0.00604130	−	0.0618662i
$455$	−11.3399			−0.531624
$456$		0			0
$457$	−15.9989			−0.748397			−0.374198	−	0.927349i	$-0.622082\pi$
$457$	−15.9989			−0.748397			−0.374198	+	0.927349i	$0.622082\pi$
$458$	−0.468523	+	4.79792i	−0.0218926	+	0.224192i
$459$		0			0
$460$	8.35672	−	42.3806i	0.389634	−	1.97601i
$461$			6.35688i			0.296069i	0.988982	+	0.148035i	$0.0472947\pi$
$461$			6.35688i			0.296069i	−0.988982	+	0.148035i	$0.952705\pi$
$462$		0			0
$463$	17.3832			0.807866			0.403933	−	0.914789i	$-0.367643\pi$
$463$	17.3832			0.807866			0.403933	+	0.914789i	$0.367643\pi$
$464$	−6.77402	+	16.5092i	−0.314476	+	0.766419i
$465$		0			0
$466$	−18.2977	−	1.78679i	−0.847624	−	0.0827715i
$467$			1.59410i			0.0737661i	0.999320	+	0.0368831i	$0.0117429\pi$
$467$			1.59410i			0.0737661i	−0.999320	+	0.0368831i	$0.988257\pi$
$468$		0			0
$469$		−	37.2980i		−	1.72226i
$470$	4.60829	−	47.1913i	0.212565	−	2.17677i
$471$		0			0
$472$	3.83299	−	12.7502i	0.176427	−	0.586874i
$473$	7.33952			0.337472
$474$		0			0
$475$			70.0710i			3.21508i
$476$	26.3950	+	5.20464i	1.20981	+	0.238554i
$477$		0			0
$478$	8.32269	+	0.812721i	0.380671	+	0.0371730i
$479$	17.9730			0.821206			0.410603	−	0.911814i	$-0.365318\pi$
$479$	17.9730			0.821206			0.410603	+	0.911814i	$0.365318\pi$
$480$		0			0
$481$	1.66608			0.0759665
$482$	16.9196	+	1.65222i	0.770667	+	0.0752565i
$483$		0			0
$484$	19.7880	+	3.90186i	0.899457	+	0.177357i
$485$			25.8263i			1.17271i
$486$		0			0
$487$	27.5020			1.24623			0.623117	−	0.782129i	$-0.285866\pi$
$487$	27.5020			1.24623			0.623117	+	0.782129i	$0.285866\pi$
$488$	−6.59682	+	21.9439i	−0.298624	+	0.993353i
$489$		0			0
$490$	−0.195561	+	2.00265i	−0.00883455	+	0.0904705i
$491$			6.45310i			0.291224i	0.989342	+	0.145612i	$0.0465152\pi$
$491$			6.45310i			0.291224i	−0.989342	+	0.145612i	$0.953485\pi$
$492$		0			0
$493$			22.1504i			0.997606i
$494$	7.87763	+	0.769259i	0.354431	+	0.0346106i
$495$		0			0
$496$	23.5924	+	9.68041i	1.05933	+	0.434663i
$497$	3.12887			0.140349
$498$		0			0
$499$		−	37.8522i		−	1.69450i	−0.531197	−	0.847249i	$-0.678257\pi$
$499$		−	37.8522i		−	1.69450i	0.531197	−	0.847249i	$-0.321743\pi$
$500$	−12.1783	+	61.7614i	−0.544629	+	2.76205i
$501$		0			0
$502$	1.02918	−	10.5394i	0.0459346	−	0.470395i
$503$	4.57973			0.204200			0.102100	−	0.994774i	$-0.467444\pi$
$503$	4.57973			0.204200			0.102100	+	0.994774i	$0.467444\pi$
$504$		0			0
$505$	76.2702			3.39398
$506$	−0.678591	+	6.94913i	−0.0301670	+	0.308927i
$507$		0			0
$508$	−31.6842	−	6.24757i	−1.40576	−	0.277191i
$509$		−	13.7626i		−	0.610016i	−0.952350	−	0.305008i	$-0.901341\pi$
$509$		−	13.7626i		−	0.610016i	0.952350	−	0.305008i	$-0.0986591\pi$
$510$		0			0
$511$	4.51378			0.199678
$512$	−14.4853	−	17.3832i	−0.640165	−	0.768237i
$513$		0			0
$514$	−27.5025	−	2.68565i	−1.21308	−	0.118459i
$515$			6.76618i			0.298154i
$516$		0			0
$517$			7.66416i			0.337069i
$518$	0.620400	−	6.35323i	0.0272588	−	0.279145i
$519$		0			0
$520$	11.3376	+	3.40834i	0.497187	+	0.149466i
$521$	32.5790			1.42731			0.713656	−	0.700496i	$-0.247038\pi$
$521$	32.5790			1.42731			0.713656	+	0.700496i	$0.247038\pi$
$522$		0			0
$523$			40.2919i			1.76184i	0.473264	+	0.880921i	$0.343076\pi$
$523$			40.2919i			1.76184i	−0.473264	+	0.880921i	$0.656924\pi$
$524$	3.64719	−	18.4965i	0.159328	−	0.808024i
$525$		0			0
$526$	20.0900	+	1.96181i	0.875964	+	0.0855389i
$527$	31.6541			1.37887
$528$		0			0
$529$	3.62631			0.157666
$530$	0.470005	+	0.0458966i	0.0204157	+	0.00199362i
$531$		0			0
$532$	5.86682	−	29.7532i	0.254359	−	1.28997i
$533$			8.64689i			0.374538i
$534$		0			0
$535$	−44.6379			−1.92986
$536$	−11.2103	+	37.2904i	−0.484212	+	1.61070i
$537$		0			0
$538$	1.30296	−	13.3430i	0.0561744	−	0.575256i
$539$		−	0.325242i		−	0.0140092i
$540$		0			0
$541$			28.6390i			1.23129i	0.788025	+	0.615643i	$0.211104\pi$
$541$			28.6390i			1.23129i	−0.788025	+	0.615643i	$0.788896\pi$
$542$	−41.0550	−	4.00907i	−1.76346	−	0.172204i
$543$		0			0
$544$	−24.8253	−	13.1369i	−1.06438	−	0.563239i
$545$	63.1793			2.70630
$546$		0			0
$547$		−	6.51086i		−	0.278384i	−0.990265	−	0.139192i	$-0.955549\pi$
$547$		−	6.51086i		−	0.278384i	0.990265	−	0.139192i	$-0.0444505\pi$
$548$	9.19577	+	1.81325i	0.392824	+	0.0774580i
$549$		0			0
$550$	1.64645	−	16.8606i	0.0702050	−	0.718936i
$551$	24.9686			1.06370
$552$		0			0
$553$	11.6530			0.495534
$554$	−0.765113	+	7.83517i	−0.0325066	+	0.332884i
$555$		0			0
$556$	3.84988	−	19.5244i	0.163271	−	0.828021i
$557$		−	6.44138i		−	0.272930i	−0.990645	−	0.136465i	$-0.956426\pi$
$557$		−	6.44138i		−	0.272930i	0.990645	−	0.136465i	$-0.0435741\pi$
$558$		0			0
$559$	7.67092			0.324445
$560$	17.2188	−	41.9645i	0.727627	−	1.77332i
$561$		0			0
$562$	−2.35514	−	0.229982i	−0.0993454	−	0.00970119i
$563$		−	34.3919i		−	1.44945i	−0.689040	−	0.724724i	$-0.741967\pi$
$563$		−	34.3919i		−	1.44945i	0.689040	−	0.724724i	$-0.258033\pi$
$564$		0			0
$565$			61.0043i			2.56647i
$566$	−2.81187	+	28.7951i	−0.118192	+	1.21035i
$567$		0			0
$568$	−3.12823	−	0.940417i	−0.131258	−	0.0394590i
$569$	43.8071			1.83649			0.918244	−	0.396014i	$-0.129607\pi$
$569$	43.8071			1.83649			0.918244	+	0.396014i	$0.129607\pi$
$570$		0			0
$571$			29.1661i			1.22056i	0.792185	+	0.610281i	$0.208944\pi$
$571$			29.1661i			1.22056i	−0.792185	+	0.610281i	$0.791056\pi$
$572$	−1.87745	−	0.370200i	−0.0785000	−	0.0154788i
$573$		0			0
$574$	32.9731	+	3.21986i	1.37627	+	0.134394i
$575$	−64.6030			−2.69413
$576$		0			0
$577$	−10.5041			−0.437291			−0.218646	−	0.975804i	$-0.570164\pi$
$577$	−10.5041			−0.437291			−0.218646	+	0.975804i	$0.570164\pi$
$578$	−10.7707	−	1.05178i	−0.448004	−	0.0437481i
$579$		0			0
$580$	36.6408	+	7.22493i	1.52143	+	0.299999i
$581$		−	37.9793i		−	1.57565i
$582$		0			0
$583$	−0.0763317			−0.00316134
$584$	−4.51286	−	1.35667i	−0.186744	−	0.0561393i
$585$		0			0
$586$	4.09892	−	41.9752i	0.169325	−	1.73398i
$587$		−	39.6896i		−	1.63817i	−0.573675	−	0.819083i	$-0.694483\pi$
$587$		−	39.6896i		−	1.63817i	0.573675	−	0.819083i	$-0.305517\pi$
$588$		0			0
$589$		−	35.6814i		−	1.47023i
$590$	−27.7317	−	2.70804i	−1.14170	−	0.111488i
$591$		0			0
$592$	−2.52981	+	6.16547i	−0.103974	+	0.253399i
$593$	−18.9670			−0.778882			−0.389441	−	0.921051i	$-0.627332\pi$
$593$	−18.9670			−0.778882			−0.389441	+	0.921051i	$0.627332\pi$
$594$		0			0
$595$		−	56.3040i		−	2.30824i
$596$	−2.39541	+	12.1482i	−0.0981199	+	0.497609i
$597$		0			0
$598$	−0.709230	+	7.26289i	−0.0290026	+	0.297002i
$599$	1.68323			0.0687750			0.0343875	−	0.999409i	$-0.489052\pi$
$599$	1.68323			0.0687750			0.0343875	+	0.999409i	$0.489052\pi$
$600$		0			0
$601$	−7.76439			−0.316716			−0.158358	−	0.987382i	$-0.550620\pi$
$601$	−7.76439			−0.316716			−0.158358	+	0.987382i	$0.550620\pi$
$602$	2.85644	−	29.2514i	0.116420	−	1.19220i
$603$		0			0
$604$	−16.6482	−	3.28275i	−0.677408	−	0.133573i
$605$		−	42.2105i		−	1.71610i
$606$		0			0
$607$	−4.45424			−0.180792			−0.0903961	−	0.995906i	$-0.528813\pi$
$607$	−4.45424			−0.180792			−0.0903961	+	0.995906i	$0.528813\pi$
$608$	−14.8083	+	27.9838i	−0.600555	+	1.13489i
$609$		0			0
$610$	47.7281	+	4.66071i	1.93246	+	0.188707i
$611$			8.01021i			0.324058i
$612$		0			0
$613$			20.7056i			0.836293i	0.908380	+	0.418147i	$0.137320\pi$
$613$			20.7056i			0.836293i	−0.908380	+	0.418147i	$0.862680\pi$
$614$	−1.34846	+	13.8090i	−0.0544195	+	0.557284i
$615$		0			0
$616$	−2.11079	+	7.02140i	−0.0850462	+	0.282900i
$617$	−31.2889			−1.25964			−0.629821	−	0.776740i	$-0.716872\pi$
$617$	−31.2889			−1.25964			−0.629821	+	0.776740i	$0.716872\pi$
$618$		0			0
$619$			13.1646i			0.529129i	0.964368	+	0.264565i	$0.0852282\pi$
$619$			13.1646i			0.529129i	−0.964368	+	0.264565i	$0.914772\pi$
$620$	10.3248	−	52.3615i	0.414653	−	2.10289i
$621$		0			0
$622$	−7.38835	−	0.721481i	−0.296246	−	0.0289287i
$623$	31.5898			1.26562
$624$		0			0
$625$	69.1461			2.76584
$626$	−5.32881	−	0.520365i	−0.212982	−	0.0207980i
$627$		0			0
$628$	6.19988	−	31.4423i	0.247402	−	1.25469i
$629$			8.27224i			0.329836i
$630$		0			0
$631$	−6.38498			−0.254182			−0.127091	−	0.991891i	$-0.540564\pi$
$631$	−6.38498			−0.254182			−0.127091	+	0.991891i	$0.540564\pi$
$632$	−11.6506	−	3.50243i	−0.463435	−	0.139319i
$633$		0			0
$634$	−2.19365	+	22.4641i	−0.0871208	+	0.892164i
$635$			67.5865i			2.68209i
$636$		0			0
$637$		−	0.339928i		−	0.0134684i
$638$	−6.00798	−	0.586687i	−0.237858	−	0.0232271i
$639$		0			0
$640$	−29.8282	+	36.7806i	−1.17906	+	1.45388i
$641$	−0.671299			−0.0265147			−0.0132574	−	0.999912i	$-0.504220\pi$
$641$	−0.671299			−0.0265147			−0.0132574	+	0.999912i	$0.504220\pi$
$642$		0			0
$643$		−	2.22333i		−	0.0876794i	−0.999039	−	0.0438397i	$-0.986041\pi$
$643$		−	2.22333i		−	0.0876794i	0.999039	−	0.0438397i	$-0.0139591\pi$
$644$	27.4314	+	5.40900i	1.08095	+	0.213145i
$645$		0			0
$646$	−3.81946	+	39.1133i	−0.150274	+	1.53889i
$647$	21.6075			0.849480			0.424740	−	0.905315i	$-0.360366\pi$
$647$	21.6075			0.849480			0.424740	+	0.905315i	$0.360366\pi$
$648$		0			0
$649$	4.50380			0.176790
$650$	1.72079	−	17.6218i	0.0674950	−	0.691185i
$651$		0			0
$652$	−6.42431	+	32.5805i	−0.251595	+	1.27595i
$653$			4.85741i			0.190085i	0.995473	+	0.0950426i	$0.0302987\pi$
$653$			4.85741i			0.190085i	−0.995473	+	0.0950426i	$0.969701\pi$
$654$		0			0
$655$	−39.4554			−1.54165
$656$	−31.9986	−	13.1296i	−1.24934	−	0.512626i
$657$		0			0
$658$	30.5453	+	2.98278i	1.19078	+	0.116281i
$659$			28.1414i			1.09623i	0.836402	+	0.548116i	$0.184655\pi$
$659$			28.1414i			1.09623i	−0.836402	+	0.548116i	$0.815345\pi$
$660$		0			0
$661$			25.8016i			1.00356i	0.864994	+	0.501782i	$0.167322\pi$
$661$			25.8016i			1.00356i	−0.864994	+	0.501782i	$0.832678\pi$
$662$	4.20786	−	43.0908i	0.163543	−	1.67477i
$663$		0			0
$664$	−11.4151	+	37.9716i	−0.442992	+	1.47358i
$665$	−63.4675			−2.46116
$666$		0			0
$667$			23.0202i			0.891346i
$668$	12.4788	+	2.46060i	0.482818	+	0.0952034i
$669$		0			0
$670$	81.1069	+	7.92018i	3.13343	+	0.305983i
$671$	−7.75134			−0.299237
$672$		0			0
$673$	13.6803			0.527336			0.263668	−	0.964613i	$-0.415068\pi$
$673$	13.6803			0.527336			0.263668	+	0.964613i	$0.415068\pi$
$674$	27.9645	+	2.73076i	1.07715	+	0.105185i
$675$		0			0
$676$	−1.96222	−	0.386915i	−0.0754699	−	0.0148814i
$677$		−	18.7430i		−	0.720351i	−0.932885	−	0.360175i	$-0.882717\pi$
$677$		−	18.7430i		−	0.720351i	0.932885	−	0.360175i	$-0.117283\pi$
$678$		0			0
$679$	−16.7164			−0.641518
$680$	−16.9228	+	56.2925i	−0.648959	+	2.15872i
$681$		0			0
$682$	−0.838404	+	8.58570i	−0.0321041	+	0.328764i
$683$		−	30.0389i		−	1.14941i	−0.818362	−	0.574704i	$-0.805117\pi$
$683$		−	30.0389i		−	1.14941i	0.818362	−	0.574704i	$-0.194883\pi$
$684$		0			0
$685$		−	19.6158i		−	0.749480i
$686$	25.3968	+	2.48003i	0.969654	+	0.0946879i
$687$		0			0
$688$	−11.6477	+	28.3869i	−0.444064	+	1.08224i
$689$	−0.0797782			−0.00303931
$690$		0			0
$691$		−	33.8302i		−	1.28696i	−0.765462	−	0.643481i	$-0.777490\pi$
$691$		−	33.8302i		−	1.28696i	0.765462	−	0.643481i	$-0.222510\pi$
$692$	0.784892	−	3.98053i	0.0298371	−	0.151317i
$693$		0			0
$694$	−0.494369	+	5.06261i	−0.0187660	+	0.192174i
$695$	−41.6482			−1.57981
$696$		0			0
$697$	−42.9327			−1.62619
$698$	4.39347	−	44.9915i	0.166295	−	1.70295i
$699$		0			0
$700$	−66.5564	−	13.1238i	−2.51560	−	0.496032i
$701$			9.20542i			0.347684i	0.984774	+	0.173842i	$0.0556182\pi$
$701$			9.20542i			0.347684i	−0.984774	+	0.173842i	$0.944382\pi$
$702$		0			0
$703$	9.32472			0.351689
$704$	4.22072	−	6.38555i	0.159074	−	0.240664i
$705$		0			0
$706$	−23.5811	−	2.30272i	−0.887486	−	0.0866640i
$707$			49.3670i			1.85664i
$708$		0			0
$709$		−	42.5563i		−	1.59824i	−0.601174	−	0.799119i	$-0.705300\pi$
$709$		−	42.5563i		−	1.59824i	0.601174	−	0.799119i	$-0.294700\pi$
$710$	−0.664412	+	6.80394i	−0.0249350	+	0.255347i
$711$		0			0
$712$	−31.5833	−	9.49465i	−1.18363	−	0.355827i
$713$	32.8970			1.23200
$714$		0			0
$715$			4.00484i			0.149773i
$716$	−6.93429	+	35.1669i	−0.259147	+	1.31425i
$717$		0			0
$718$	−44.7337	−	4.36830i	−1.66945	−	0.163023i
$719$	−25.0205			−0.933107			−0.466554	−	0.884493i	$-0.654505\pi$
$719$	−25.0205			−0.933107			−0.466554	+	0.884493i	$0.654505\pi$
$720$		0			0
$721$	−4.37951			−0.163101
$722$	17.3468	+	1.69393i	0.645581	+	0.0630417i
$723$		0			0
$724$	−1.32007	+	6.69467i	−0.0490601	+	0.248806i
$725$		−	55.8535i		−	2.07435i
$726$		0			0
$727$	17.7041			0.656609			0.328305	−	0.944572i	$-0.393523\pi$
$727$	17.7041			0.656609			0.328305	+	0.944572i	$0.393523\pi$
$728$	−2.20610	+	7.33843i	−0.0817634	+	0.271980i
$729$		0			0
$730$	−0.958497	+	9.81552i	−0.0354756	+	0.363289i
$731$			38.0869i			1.40870i
$732$		0			0
$733$			20.1480i			0.744183i	0.928196	+	0.372092i	$0.121359\pi$
$733$			20.1480i			0.744183i	−0.928196	+	0.372092i	$0.878641\pi$
$734$	−39.1990	−	3.82783i	−1.44686	−	0.141288i
$735$		0			0
$736$	−25.8001	−	13.6527i	−0.951004	−	0.503246i
$737$	−13.1722			−0.485206
$738$		0			0
$739$		−	12.9725i		−	0.477202i	−0.971118	−	0.238601i	$-0.923311\pi$
$739$		−	12.9725i		−	0.477202i	0.971118	−	0.238601i	$-0.0766888\pi$
$740$	13.6838	+	2.69820i	0.503026	+	0.0991879i
$741$		0			0
$742$	−0.0297072	+	0.304217i	−0.00109059	+	0.0111682i
$743$	31.3522			1.15020			0.575100	−	0.818083i	$-0.304963\pi$
$743$	31.3522			1.15020			0.575100	+	0.818083i	$0.304963\pi$
$744$		0			0
$745$	25.9137			0.949404
$746$	4.11571	−	42.1471i	0.150687	−	1.54311i
$747$		0			0
$748$	1.83808	−	9.32173i	0.0672070	−	0.340836i
$749$		−	28.8925i		−	1.05571i
$750$		0			0
$751$	−13.4231			−0.489814			−0.244907	−	0.969547i	$-0.578757\pi$
$751$	−13.4231			−0.489814			−0.244907	+	0.969547i	$0.578757\pi$
$752$	−29.6425	−	12.1629i	−1.08095	−	0.443535i
$753$		0			0
$754$	−6.27925	−	0.613176i	−0.228677	−	0.0223306i
$755$			35.5129i			1.29245i
$756$		0			0
$757$			9.49056i			0.344940i	0.985015	+	0.172470i	$0.0551748\pi$
$757$			9.49056i			0.344940i	−0.985015	+	0.172470i	$0.944825\pi$
$758$	−0.743620	+	7.61507i	−0.0270095	+	0.276592i
$759$		0			0
$760$	63.4546	+	19.0759i	2.30174	+	0.691954i
$761$	13.4197			0.486466			0.243233	−	0.969968i	$-0.421792\pi$
$761$	13.4197			0.486466			0.243233	+	0.969968i	$0.421792\pi$
$762$		0			0
$763$			40.8937i			1.48045i
$764$	25.5424	+	5.03653i	0.924093	+	0.182215i
$765$		0			0
$766$	−3.32043	−	0.324244i	−0.119972	−	0.0117154i
$767$	4.70716			0.169966
$768$		0			0
$769$	6.84250			0.246747			0.123373	−	0.992360i	$-0.460629\pi$
$769$	6.84250			0.246747			0.123373	+	0.992360i	$0.460629\pi$
$770$	15.2716	+	1.49129i	0.550351	+	0.0537424i
$771$		0			0
$772$	3.96757	+	0.782336i	0.142796	+	0.0281569i
$773$			20.6355i			0.742207i	0.928591	+	0.371104i	$0.121021\pi$
$773$			20.6355i			0.742207i	−0.928591	+	0.371104i	$0.878979\pi$
$774$		0			0
$775$	−79.8174			−2.86713
$776$	16.7130	+	5.02431i	0.599962	+	0.180362i
$777$		0			0
$778$	−4.70118	+	48.1425i	−0.168545	+	1.72599i
$779$			48.3950i			1.73393i
$780$		0			0
$781$		−	1.10500i		−	0.0395400i
$782$	−36.0610	−	3.52140i	−1.28954	−	0.125925i
$783$		0			0
$784$	1.25793	+	0.516154i	0.0449262	+	0.0184341i
$785$	−67.0706			−2.39385
$786$		0			0
$787$		−	4.33162i		−	0.154406i	−0.997015	−	0.0772028i	$-0.975401\pi$
$787$		−	4.33162i		−	0.154406i	0.997015	−	0.0772028i	$-0.0245989\pi$
$788$	−6.40166	+	32.4656i	−0.228050	+	1.15654i
$789$		0			0
$790$	−2.47449	+	25.3401i	−0.0880386	+	0.901562i
$791$	−39.4859			−1.40396
$792$		0			0
$793$	−8.10132			−0.287686
$794$	−2.31203	+	23.6764i	−0.0820508	+	0.840244i
$795$		0			0
$796$	−2.19229	−	0.432282i	−0.0777037	−	0.0153218i
$797$		−	26.9591i		−	0.954941i	−0.878648	−	0.477471i	$-0.841554\pi$
$797$		−	26.9591i		−	0.954941i	0.878648	−	0.477471i	$-0.158446\pi$
$798$		0			0
$799$	−39.7716			−1.40702
$800$	62.5983	+	33.1253i	2.21319	+	1.17116i
$801$		0			0
$802$	4.26539	+	0.416521i	0.150616	+	0.0147079i
$803$		−	1.59410i		−	0.0562545i
$804$		0			0
$805$		−	58.5148i		−	2.06238i
$806$	−0.876259	+	8.97336i	−0.0308649	+	0.316073i
$807$		0			0
$808$	14.8378	−	49.3569i	0.521991	−	1.73637i
$809$	−0.217636			−0.00765166			−0.00382583	−	0.999993i	$-0.501218\pi$
$809$	−0.217636			−0.00765166			−0.00382583	+	0.999993i	$0.501218\pi$
$810$		0			0
$811$		−	10.9498i		−	0.384501i	−0.981346	−	0.192251i	$-0.938421\pi$
$811$		−	10.9498i		−	0.384501i	0.981346	−	0.192251i	$-0.0615786\pi$
$812$	−4.67644	+	23.7163i	−0.164111	+	0.832279i
$813$		0			0
$814$	−2.24372	−	0.219102i	−0.0786425	−	0.00767953i
$815$	69.4984			2.43442
$816$		0			0
$817$	42.9327			1.50203
$818$	51.6764	+	5.04626i	1.80682	+	0.176438i
$819$		0			0
$820$	−14.0036	+	71.0184i	−0.489027	+	2.48007i
$821$		−	10.6224i		−	0.370725i	−0.982670	−	0.185362i	$-0.940654\pi$
$821$		−	10.6224i		−	0.370725i	0.982670	−	0.185362i	$-0.0593459\pi$
$822$		0			0
$823$	28.0573			0.978017			0.489008	−	0.872279i	$-0.337359\pi$
$823$	28.0573			0.978017			0.489008	+	0.872279i	$0.337359\pi$
$824$	4.37861	+	1.31631i	0.152536	+	0.0458558i
$825$		0			0
$826$	1.75282	−	17.9498i	0.0609882	−	0.624552i
$827$		−	2.91954i		−	0.101522i	−0.998711	−	0.0507611i	$-0.983835\pi$
$827$		−	2.91954i		−	0.101522i	0.998711	−	0.0507611i	$-0.0161647\pi$
$828$		0			0
$829$		−	33.7216i		−	1.17120i	−0.810600	−	0.585600i	$-0.800859\pi$
$829$		−	33.7216i		−	1.17120i	0.810600	−	0.585600i	$-0.199141\pi$
$830$	82.5886	+	8.06487i	2.86669	+	0.279936i
$831$		0			0
$832$	4.41129	−	6.67387i	0.152934	−	0.231375i
$833$	1.68778			0.0584780
$834$		0			0
$835$		−	26.6189i		−	0.921183i
$836$	−10.5077	−	2.07194i	−0.363418	−	0.0716596i
$837$		0			0
$838$	2.51228	−	25.7271i	0.0867854	−	0.888728i
$839$	−19.6980			−0.680050			−0.340025	−	0.940416i	$-0.610436\pi$
$839$	−19.6980			−0.680050			−0.340025	+	0.940416i	$0.610436\pi$
$840$		0			0
$841$	9.09751			0.313707
$842$	−0.136318	+	1.39597i	−0.00469784	+	0.0481084i
$843$		0			0
$844$	−8.65596	+	43.8982i	−0.297950	+	1.51104i
$845$			4.18566i			0.143991i
$846$		0			0
$847$	27.3213			0.938772
$848$	0.121137	−	0.295227i	0.00415986	−	0.0101381i
$849$		0			0
$850$	87.4943	+	8.54392i	3.00103	+	0.293054i
$851$			8.59706i			0.294704i
$852$		0			0
$853$			11.3421i			0.388347i	0.980967	+	0.194174i	$0.0622025\pi$
$853$			11.3421i			0.388347i	−0.980967	+	0.194174i	$0.937798\pi$
$854$	−3.01671	+	30.8927i	−0.103230	+	1.05713i
$855$		0			0
$856$	−8.68396	+	28.8866i	−0.296812	+	0.987324i
$857$	15.8724			0.542192			0.271096	−	0.962552i	$-0.412614\pi$
$857$	15.8724			0.542192			0.271096	+	0.962552i	$0.412614\pi$
$858$		0			0
$859$		−	23.4990i		−	0.801776i	−0.916127	−	0.400888i	$-0.868702\pi$
$859$		−	23.4990i		−	0.801776i	0.916127	−	0.400888i	$-0.131298\pi$
$860$	63.0026	+	12.4230i	2.14837	+	0.423622i
$861$		0			0
$862$	−1.48982	−	0.145482i	−0.0507433	−	0.00495514i
$863$	6.45060			0.219581			0.109790	−	0.993955i	$-0.464982\pi$
$863$	6.45060			0.219581			0.109790	+	0.993955i	$0.464982\pi$
$864$		0			0
$865$	−8.49099			−0.288702
$866$	37.4309	+	3.65517i	1.27195	+	0.124208i
$867$		0			0
$868$	33.8917	+	6.68286i	1.15036	+	0.226831i
$869$		−	4.11539i		−	0.139605i
$870$		0			0
$871$	−13.7670			−0.466477
$872$	12.2911	−	40.8854i	0.416228	−	1.38455i
$873$		0			0
$874$	−3.96943	+	40.6491i	−0.134268	+	1.37498i
$875$			85.2738i			2.88278i
$876$		0			0
$877$		−	43.8038i		−	1.47915i	−0.673074	−	0.739575i	$-0.735027\pi$
$877$		−	43.8038i		−	1.47915i	0.673074	−	0.739575i	$-0.264973\pi$
$878$	−40.1401	−	3.91973i	−1.35466	−	0.132285i
$879$		0			0
$880$	−14.8203	−	6.08104i	−0.499592	−	0.204992i
$881$	−54.1923			−1.82579			−0.912893	−	0.408199i	$-0.866157\pi$
$881$	−54.1923			−1.82579			−0.912893	+	0.408199i	$0.866157\pi$
$882$		0			0
$883$		−	32.4922i		−	1.09345i	−0.837312	−	0.546725i	$-0.815874\pi$
$883$		−	32.4922i		−	1.09345i	0.837312	−	0.546725i	$-0.184126\pi$
$884$	1.92108	−	9.74262i	0.0646128	−	0.327680i
$885$		0			0
$886$	−1.12218	+	11.4917i	−0.0377005	+	0.386073i
$887$	−30.3801			−1.02006			−0.510032	−	0.860156i	$-0.670366\pi$
$887$	−30.3801			−1.02006			−0.510032	+	0.860156i	$0.670366\pi$
$888$		0			0
$889$	−43.7463			−1.46720
$890$	−6.70805	+	68.6940i	−0.224854	+	2.30263i
$891$		0			0
$892$	49.6766	+	9.79536i	1.66330	+	0.327973i
$893$			44.8317i			1.50024i
$894$		0			0
$895$	75.0155			2.50749
$896$	−23.8068	−	19.3067i	−0.795328	−	0.644992i
$897$		0			0
$898$	1.68086	+	0.164138i	0.0560909	+	0.00547734i
$899$			28.4416i			0.948582i
$900$		0			0
$901$		−	0.396107i		−	0.0131962i
$902$	1.13714	−	11.6449i	0.0378625	−	0.387732i
$903$		0			0
$904$	39.4778	+	11.8679i	1.31301	+	0.394721i
$905$	14.2806			0.474703
$906$		0			0
$907$			29.0224i			0.963671i	0.876262	+	0.481836i	$0.160030\pi$
$907$			29.0224i			0.963671i	−0.876262	+	0.481836i	$0.839970\pi$
$908$	−0.362362	+	1.83770i	−0.0120254	+	0.0609862i
$909$		0			0
$910$	15.9612	+	1.55863i	0.529107	+	0.0516679i
$911$	48.1729			1.59604			0.798019	−	0.602632i	$-0.205881\pi$
$911$	48.1729			1.59604			0.798019	+	0.602632i	$0.205881\pi$
$912$		0			0
$913$	−13.4129			−0.443902
$914$	22.5187	+	2.19898i	0.744854	+	0.0727358i
$915$		0			0
$916$	1.31891	−	6.68877i	0.0435780	−	0.221003i
$917$		−	25.5381i		−	0.843342i
$918$		0			0
$919$	25.1063			0.828180			0.414090	−	0.910236i	$-0.364100\pi$
$919$	25.1063			0.828180			0.414090	+	0.910236i	$0.364100\pi$
$920$	−17.5873	+	58.5029i	−0.579835	+	1.92878i
$921$		0			0
$922$	0.873726	−	8.94742i	0.0287746	−	0.294668i
$923$		−	1.15489i		−	0.0380138i
$924$		0			0
$925$		−	20.8589i		−	0.685837i
$926$	−24.4672	−	2.38925i	−0.804042	−	0.0785156i
$927$		0			0
$928$	11.8037	−	22.3059i	0.387475	−	0.732227i
$929$	45.7495			1.50099			0.750497	−	0.660874i	$-0.229814\pi$
$929$	45.7495			1.50099			0.750497	+	0.660874i	$0.229814\pi$
$930$		0			0
$931$		−	1.90251i		−	0.0623523i
$932$	25.5087	+	5.02988i	0.835567	+	0.164759i
$933$		0			0
$934$	0.219102	−	2.24372i	0.00716925	−	0.0734169i
$935$	−19.8845			−0.650291
$936$		0			0
$937$	−41.4498			−1.35411			−0.677053	−	0.735934i	$-0.736743\pi$
$937$	−41.4498			−1.35411			−0.677053	+	0.735934i	$0.736743\pi$
$938$	−5.12645	+	52.4976i	−0.167384	+	1.71411i
$939$		0			0
$940$	−12.9725	+	65.7893i	−0.423117	+	2.14581i
$941$			27.6008i			0.899760i	0.893089	+	0.449880i	$0.148533\pi$
$941$			27.6008i			0.899760i	−0.893089	+	0.449880i	$0.851467\pi$
$942$		0			0
$943$	−44.6185			−1.45298
$944$	−7.14746	+	17.4193i	−0.232630	+	0.566949i
$945$		0			0
$946$	−10.3305	−	1.00879i	−0.335874	−	0.0327985i
$947$		−	60.4406i		−	1.96405i	−0.188740	−	0.982027i	$-0.560440\pi$
$947$		−	60.4406i		−	1.96405i	0.188740	−	0.982027i	$-0.439560\pi$
$948$		0			0
$949$		−	1.66608i		−	0.0540831i
$950$	9.63096	−	98.6262i	0.312470	−	3.19986i
$951$		0			0
$952$	−36.4361	−	10.9535i	−1.18090	−	0.355005i
$953$	23.3201			0.755412			0.377706	−	0.925926i	$-0.376713\pi$
$953$	23.3201			0.755412			0.377706	+	0.925926i	$0.376713\pi$
$954$		0			0
$955$		−	54.4853i		−	1.76310i
$956$	−11.6026	−	2.28784i	−0.375256	−	0.0739940i
$957$		0			0
$958$	−25.2973	−	2.47031i	−0.817319	−	0.0798121i
$959$	12.6966			0.409994
$960$		0			0
$961$	9.64452			0.311114
$962$	−2.34503	−	0.228995i	−0.0756069	−	0.00738310i
$963$		0			0
$964$	−23.5876	−	4.65106i	−0.759705	−	0.149801i
$965$		−	8.46334i		−	0.272445i
$966$		0			0
$967$	−28.4046			−0.913432			−0.456716	−	0.889613i	$-0.650974\pi$
$967$	−28.4046			−0.913432			−0.456716	+	0.889613i	$0.650974\pi$
$968$	−27.3158	−	8.21173i	−0.877962	−	0.263935i
$969$		0			0
$970$	3.54972	−	36.3510i	0.113975	−	1.16716i
$971$			32.3884i			1.03939i	0.854351	+	0.519697i	$0.173955\pi$
$971$			32.3884i			1.03939i	−0.854351	+	0.519697i	$0.826045\pi$
$972$		0			0
$973$		−	26.9574i		−	0.864213i
$974$	−38.7096	−	3.78003i	−1.24033	−	0.121120i
$975$		0			0
$976$	12.3012	−	29.9797i	0.393753	−	0.959627i
$977$	−40.7641			−1.30416			−0.652079	−	0.758151i	$-0.726103\pi$
$977$	−40.7641			−1.30416			−0.652079	+	0.758151i	$0.726103\pi$
$978$		0			0
$979$		−	11.1563i		−	0.356558i
$980$	0.550512	−	2.79189i	0.0175854	−	0.0891835i
$981$		0			0
$982$	0.886952	−	9.08286i	0.0283038	−	0.289846i
$983$	−44.1753			−1.40897			−0.704486	−	0.709718i	$-0.748822\pi$
$983$	−44.1753			−1.40897			−0.704486	+	0.709718i	$0.748822\pi$
$984$		0			0
$985$	69.2534			2.20660
$986$	3.04449	−	31.1772i	0.0969562	−	0.992883i
$987$		0			0
$988$	−10.9822	−	2.16549i	−0.349389	−	0.0688935i
$989$			39.5825i			1.25865i
$990$		0			0
$991$	27.7306			0.880893			0.440446	−	0.897779i	$-0.354820\pi$
$991$	27.7306			0.880893			0.440446	+	0.897779i	$0.354820\pi$
$992$	−31.8762	−	16.8680i	−1.01207	−	0.535561i
$993$		0			0
$994$	−4.40394	−	0.430050i	−0.139685	−	0.0136404i
$995$			4.67644i			0.148253i
$996$		0			0
$997$		−	15.5011i		−	0.490925i	−0.969406	−	0.245463i	$-0.921060\pi$
$997$		−	15.5011i		−	0.490925i	0.969406	−	0.245463i	$-0.0789398\pi$
$998$	−5.20263	+	53.2777i	−0.164686	+	1.68648i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.g.f.469.1	✓	24
3.2	odd	2	inner	936.2.g.f.469.24	yes	24
4.3	odd	2		3744.2.g.f.1873.11		24
8.3	odd	2		3744.2.g.f.1873.12		24
8.5	even	2	inner	936.2.g.f.469.2	yes	24
12.11	even	2		3744.2.g.f.1873.24		24
24.5	odd	2	inner	936.2.g.f.469.23	yes	24
24.11	even	2		3744.2.g.f.1873.23		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.g.f.469.1	✓	24	1.1	even	1	trivial
936.2.g.f.469.2	yes	24	8.5	even	2	inner
936.2.g.f.469.23	yes	24	24.5	odd	2	inner
936.2.g.f.469.24	yes	24	3.2	odd	2	inner
3744.2.g.f.1873.11		24	4.3	odd	2
3744.2.g.f.1873.12		24	8.3	odd	2
3744.2.g.f.1873.23		24	24.11	even	2
3744.2.g.f.1873.24		24	12.11	even	2

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.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40752 - 0.137446i) q^{2} +(1.96222 + 0.386915i) q^{4} -4.18566i q^{5} +2.70923 q^{7} +(-2.70868 - 0.814289i) q^{8} +(-0.575302 + 5.89140i) q^{10} -0.956799i q^{11} -1.00000i q^{13} +(-3.81329 - 0.372372i) q^{14} +(3.70059 + 1.51842i) q^{16} +4.96511 q^{17} -5.59682i q^{19} +(1.61950 - 8.21318i) q^{20} +(-0.131508 + 1.34671i) q^{22} +5.16007 q^{23} -12.5198 q^{25} +(-0.137446 + 1.40752i) q^{26} +(5.31610 + 1.04824i) q^{28} +4.46122i q^{29} +6.37531 q^{31} +(-4.99995 - 2.64584i) q^{32} +(-6.98848 - 0.682433i) q^{34} -11.3399i q^{35} +1.66608i q^{37} +(-0.769259 + 7.87763i) q^{38} +(-3.40834 + 11.3376i) q^{40} -8.64689 q^{41} +7.67092i q^{43} +(0.370200 - 1.87745i) q^{44} +(-7.26289 - 0.709230i) q^{46} -8.01021 q^{47} +0.339928 q^{49} +(17.6218 + 1.72079i) q^{50} +(0.386915 - 1.96222i) q^{52} -0.0797782i q^{53} -4.00484 q^{55} +(-7.33843 - 2.20610i) q^{56} +(0.613176 - 6.27925i) q^{58} +4.70716i q^{59} -8.10132i q^{61} +(-8.97336 - 0.876259i) q^{62} +(6.67387 + 4.41129i) q^{64} -4.18566 q^{65} -13.7670i q^{67} +(9.74262 + 1.92108i) q^{68} +(-1.55863 + 15.9612i) q^{70} +1.15489 q^{71} +1.66608 q^{73} +(0.228995 - 2.34503i) q^{74} +(2.16549 - 10.9822i) q^{76} -2.59219i q^{77} +4.30121 q^{79} +(6.35561 - 15.4894i) q^{80} +(12.1707 + 1.18848i) q^{82} -14.0185i q^{83} -20.7823i q^{85} +(1.05434 - 10.7970i) q^{86} +(-0.779111 + 2.59166i) q^{88} +11.6601 q^{89} -2.70923i q^{91} +(10.1252 + 1.99651i) q^{92} +(11.2745 + 1.10097i) q^{94} -23.4264 q^{95} -6.17018 q^{97} +(-0.478454 - 0.0467216i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{4} - 8 q^{7} + 12 q^{10} - 4 q^{16} + 4 q^{22} - 24 q^{25} + 8 q^{28} + 40 q^{31} - 16 q^{34} - 36 q^{40} - 24 q^{46} + 24 q^{49} - 4 q^{52} - 16 q^{55} - 24 q^{58} + 8 q^{64} - 16 q^{70} - 16 q^{76}+ \cdots - 16 q^{97}+O(q^{100}) \) 24 * q + 8 * q^4 - 8 * q^7 + 12 * q^10 - 4 * q^16 + 4 * q^22 - 24 * q^25 + 8 * q^28 + 40 * q^31 - 16 * q^34 - 36 * q^40 - 24 * q^46 + 24 * q^49 - 4 * q^52 - 16 * q^55 - 24 * q^58 + 8 * q^64 - 16 * q^70 - 16 * q^76 + 68 * q^82 + 28 * q^88 + 12 * q^94 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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