LMFDB - Embedded newform 936.2.g.f.469.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [936,2,Mod(469,936)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40752 + 0.137446i) q^{2} +(1.96222 - 0.386915i) q^{4} +4.18566i q^{5} +2.70923 q^{7} +(-2.70868 + 0.814289i) q^{8} +(-0.575302 - 5.89140i) q^{10} +0.956799i q^{11} +1.00000i q^{13} +(-3.81329 + 0.372372i) q^{14} +(3.70059 - 1.51842i) q^{16} +4.96511 q^{17} +5.59682i q^{19} +(1.61950 + 8.21318i) q^{20} +(-0.131508 - 1.34671i) q^{22} +5.16007 q^{23} -12.5198 q^{25} +(-0.137446 - 1.40752i) q^{26} +(5.31610 - 1.04824i) q^{28} -4.46122i q^{29} +6.37531 q^{31} +(-4.99995 + 2.64584i) q^{32} +(-6.98848 + 0.682433i) q^{34} +11.3399i q^{35} -1.66608i q^{37} +(-0.769259 - 7.87763i) q^{38} +(-3.40834 - 11.3376i) q^{40} -8.64689 q^{41} -7.67092i q^{43} +(0.370200 + 1.87745i) q^{44} +(-7.26289 + 0.709230i) q^{46} -8.01021 q^{47} +0.339928 q^{49} +(17.6218 - 1.72079i) q^{50} +(0.386915 + 1.96222i) q^{52} +0.0797782i q^{53} -4.00484 q^{55} +(-7.33843 + 2.20610i) q^{56} +(0.613176 + 6.27925i) q^{58} -4.70716i q^{59} +8.10132i q^{61} +(-8.97336 + 0.876259i) q^{62} +(6.67387 - 4.41129i) q^{64} -4.18566 q^{65} +13.7670i q^{67} +(9.74262 - 1.92108i) q^{68} +(-1.55863 - 15.9612i) q^{70} +1.15489 q^{71} +1.66608 q^{73} +(0.228995 + 2.34503i) q^{74} +(2.16549 + 10.9822i) q^{76} +2.59219i q^{77} +4.30121 q^{79} +(6.35561 + 15.4894i) q^{80} +(12.1707 - 1.18848i) q^{82} +14.0185i q^{83} +20.7823i q^{85} +(1.05434 + 10.7970i) q^{86} +(-0.779111 - 2.59166i) q^{88} +11.6601 q^{89} +2.70923i q^{91} +(10.1252 - 1.99651i) q^{92} +(11.2745 - 1.10097i) q^{94} -23.4264 q^{95} -6.17018 q^{97} +(-0.478454 + 0.0467216i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.385450\pi$
$5$			4.18566i			1.87189i	−0.352152	+	0.935943i	$0.614550\pi$
$6$		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	$0.0460747\pi$
$11$			0.956799i			0.288486i	−0.989542	+	0.144243i	$0.953925\pi$
$12$		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	$0.221895\pi$
$19$			5.59682i			1.28400i	−0.766705	+	0.641999i	$0.778105\pi$
$20$	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	$-0.864057\pi$
$29$		−	4.46122i		−	0.828428i	0.910180	−	0.414214i	$-0.135943\pi$
$30$		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	$-0.956270\pi$
$37$		−	1.66608i		−	0.273901i	0.990578	−	0.136951i	$-0.0437301\pi$
$38$	−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	$-0.801133\pi$
$43$		−	7.67092i		−	1.16980i	0.811104	−	0.584902i	$-0.198867\pi$
$44$	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	$0.00174409\pi$
$53$			0.0797782i			0.0109584i	−0.999985	+	0.00547919i	$0.998256\pi$
$54$		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	$-0.900872\pi$
$59$		−	4.70716i		−	0.612820i	0.951900	−	0.306410i	$-0.0991278\pi$
$60$		0			0
$61$			8.10132i			1.03727i	0.854996	+	0.518634i	$0.173559\pi$
$61$			8.10132i			1.03727i	−0.854996	+	0.518634i	$0.826441\pi$
$62$	−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	$0.318005\pi$
$67$			13.7670i			1.68191i	−0.541108	+	0.840953i	$0.681995\pi$
$68$	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	$0.279427\pi$
$83$			14.0185i			1.53873i	−0.638810	+	0.769365i	$0.720573\pi$
$84$		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	$-0.638694\pi$
$101$		−	18.2218i		−	1.81313i	0.422063	−	0.906567i	$-0.361306\pi$
$102$		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	$0.172389\pi$
$107$			10.6645i			1.03097i	−0.856898	+	0.515487i	$0.827611\pi$
$108$		0			0
$109$		−	15.0942i		−	1.44576i	−0.690972	−	0.722882i	$-0.742817\pi$
$109$		−	15.0942i		−	1.44576i	0.690972	−	0.722882i	$-0.257183\pi$
$110$	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	$0.135097\pi$
$131$			9.42633i			0.823582i	−0.911278	+	0.411791i	$0.864903\pi$
$132$		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	$0.138666\pi$
$139$			9.95019i			0.843964i	−0.906604	+	0.421982i	$0.861334\pi$
$140$	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	$-0.918387\pi$
$149$		−	6.19106i		−	0.507191i	0.967310	−	0.253596i	$-0.0816132\pi$
$150$		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	$0.220827\pi$
$157$			16.0239i			1.27885i	−0.768855	+	0.639423i	$0.779173\pi$
$158$	−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	$-0.774660\pi$
$163$		−	16.6039i		−	1.30052i	0.759712	−	0.650260i	$-0.225340\pi$
$164$	−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	$0.0245710\pi$
$173$			2.02859i			0.154231i	−0.997022	+	0.0771154i	$0.975429\pi$
$174$		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	$-0.766390\pi$
$179$		−	17.9220i		−	1.33955i	0.742563	−	0.669777i	$-0.233610\pi$
$180$		0			0
$181$		−	3.41179i		−	0.253596i	−0.991929	−	0.126798i	$-0.959530\pi$
$181$		−	3.41179i		−	0.253596i	0.991929	−	0.126798i	$-0.0404701\pi$
$182$	−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	$-0.799362\pi$
$197$		−	16.5454i		−	1.17881i	0.807838	−	0.589405i	$-0.200638\pi$
$198$		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	$-0.720223\pi$
$211$		−	22.3717i		−	1.54013i	0.637964	−	0.770066i	$-0.279777\pi$
$212$	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	$-0.990105\pi$
$227$		−	0.936542i		−	0.0621604i	0.999517	−	0.0310802i	$-0.00989474\pi$
$228$		0			0
$229$			3.40878i			0.225259i	0.993637	+	0.112629i	$0.0359272\pi$
$229$			3.40878i			0.225259i	−0.993637	+	0.112629i	$0.964073\pi$
$230$	−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	$-0.924060\pi$
$251$		−	7.48790i		−	0.472632i	0.971676	−	0.236316i	$-0.0759400\pi$
$252$		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	$-0.906679\pi$
$269$		−	9.47978i		−	0.577992i	0.957330	−	0.288996i	$-0.0933215\pi$
$270$		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	$0.0534835\pi$
$277$			5.56665i			0.334468i	−0.985917	+	0.167234i	$0.946516\pi$
$278$	−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	$0.208049\pi$
$283$			20.4580i			1.21610i	−0.793897	+	0.608052i	$0.791951\pi$
$284$	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	$-0.663399\pi$
$293$		−	29.8221i		−	1.74223i	0.491083	−	0.871113i	$-0.336601\pi$
$294$		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	$0.0903237\pi$
$307$			9.81086i			0.559935i	−0.960009	+	0.279968i	$0.909676\pi$
$308$	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	$0.147936\pi$
$317$			15.9601i			0.896407i	−0.893931	+	0.448204i	$0.852064\pi$
$318$		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	$-0.681751\pi$
$331$		−	30.6147i		−	1.68274i	0.540463	−	0.841368i	$-0.318249\pi$
$332$	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	$0.0307788\pi$
$347$			3.59683i			0.193088i	−0.995329	+	0.0965440i	$0.969221\pi$
$348$		0			0
$349$		−	31.9651i		−	1.71105i	−0.517758	−	0.855527i	$-0.673233\pi$
$349$		−	31.9651i		−	1.71105i	0.517758	−	0.855527i	$-0.326767\pi$
$350$	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	$-0.717635\pi$
$373$		−	29.9442i		−	1.55045i	0.631683	−	0.775227i	$-0.282365\pi$
$374$	−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	$0.0443739\pi$
$379$			5.41028i			0.277907i	−0.990299	+	0.138954i	$0.955626\pi$
$380$	−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	$0.334020\pi$
$389$			34.2038i			1.73420i	−0.498131	+	0.867102i	$0.665980\pi$
$390$		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	$0.138714\pi$
$397$			16.8214i			0.844240i	−0.906540	+	0.422120i	$0.861286\pi$
$398$	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	$-0.852678\pi$
$419$		−	18.2783i		−	0.892956i	0.894795	−	0.446478i	$-0.147322\pi$
$420$		0			0
$421$			0.991796i			0.0483372i	0.999708	+	0.0241686i	$0.00769385\pi$
$421$			0.991796i			0.0483372i	−0.999708	+	0.0241686i	$0.992306\pi$
$422$	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	$0.0621315\pi$
$443$			8.16454i			0.387909i	−0.981011	+	0.193955i	$0.937869\pi$
$444$		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	$-0.952705\pi$
$461$		−	6.35688i		−	0.296069i	0.988982	−	0.148035i	$-0.0472947\pi$
$462$		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	$-0.988257\pi$
$467$		−	1.59410i		−	0.0737661i	0.999320	−	0.0368831i	$-0.0117429\pi$
$468$		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	$-0.953485\pi$
$491$		−	6.45310i		−	0.291224i	0.989342	−	0.145612i	$-0.0465152\pi$
$492$		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	$0.321743\pi$
$499$			37.8522i			1.69450i	−0.531197	+	0.847249i	$0.678257\pi$
$500$	−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	$0.0986591\pi$
$509$			13.7626i			0.610016i	−0.952350	+	0.305008i	$0.901341\pi$
$510$		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	$-0.656924\pi$
$523$		−	40.2919i		−	1.76184i	0.473264	−	0.880921i	$-0.343076\pi$
$524$	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	$-0.788896\pi$
$541$		−	28.6390i		−	1.23129i	0.788025	−	0.615643i	$-0.211104\pi$
$542$	−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	$0.0444505\pi$
$547$			6.51086i			0.278384i	−0.990265	+	0.139192i	$0.955549\pi$
$548$	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	$0.0435741\pi$
$557$			6.44138i			0.272930i	−0.990645	+	0.136465i	$0.956426\pi$
$558$		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	$0.258033\pi$
$563$			34.3919i			1.44945i	−0.689040	+	0.724724i	$0.741967\pi$
$564$		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	$-0.791056\pi$
$571$		−	29.1661i		−	1.22056i	0.792185	−	0.610281i	$-0.208944\pi$
$572$	−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	$0.305517\pi$
$587$			39.6896i			1.63817i	−0.573675	+	0.819083i	$0.694483\pi$
$588$		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	$-0.862680\pi$
$613$		−	20.7056i		−	0.836293i	0.908380	−	0.418147i	$-0.137320\pi$
$614$	−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	$-0.914772\pi$
$619$		−	13.1646i		−	0.529129i	0.964368	−	0.264565i	$-0.0852282\pi$
$620$	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	$0.0139591\pi$
$643$			2.22333i			0.0876794i	−0.999039	+	0.0438397i	$0.986041\pi$
$644$	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	$-0.969701\pi$
$653$		−	4.85741i		−	0.190085i	0.995473	−	0.0950426i	$-0.0302987\pi$
$654$		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	$-0.815345\pi$
$659$		−	28.1414i		−	1.09623i	0.836402	−	0.548116i	$-0.184655\pi$
$660$		0			0
$661$		−	25.8016i		−	1.00356i	−0.864994	−	0.501782i	$-0.832678\pi$
$661$		−	25.8016i		−	1.00356i	0.864994	−	0.501782i	$-0.167322\pi$
$662$	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	$0.117283\pi$
$677$			18.7430i			0.720351i	−0.932885	+	0.360175i	$0.882717\pi$
$678$		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	$0.194883\pi$
$683$			30.0389i			1.14941i	−0.818362	+	0.574704i	$0.805117\pi$
$684$		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	$0.222510\pi$
$691$			33.8302i			1.28696i	−0.765462	+	0.643481i	$0.777490\pi$
$692$	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	$-0.944382\pi$
$701$		−	9.20542i		−	0.347684i	0.984774	−	0.173842i	$-0.0556182\pi$
$702$		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	$0.294700\pi$
$709$			42.5563i			1.59824i	−0.601174	+	0.799119i	$0.705300\pi$
$710$	−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	$-0.878641\pi$
$733$		−	20.1480i		−	0.744183i	0.928196	−	0.372092i	$-0.121359\pi$
$734$	−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	$0.0766888\pi$
$739$			12.9725i			0.477202i	−0.971118	+	0.238601i	$0.923311\pi$
$740$	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	$-0.944825\pi$
$757$		−	9.49056i		−	0.344940i	0.985015	−	0.172470i	$-0.0551748\pi$
$758$	−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	$-0.878979\pi$
$773$		−	20.6355i		−	0.742207i	0.928591	−	0.371104i	$-0.121021\pi$
$774$		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	$0.0245989\pi$
$787$			4.33162i			0.154406i	−0.997015	+	0.0772028i	$0.975401\pi$
$788$	−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	$0.158446\pi$
$797$			26.9591i			0.954941i	−0.878648	+	0.477471i	$0.841554\pi$
$798$		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	$0.0615786\pi$
$811$			10.9498i			0.384501i	−0.981346	+	0.192251i	$0.938421\pi$
$812$	−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	$0.0593459\pi$
$821$			10.6224i			0.370725i	−0.982670	+	0.185362i	$0.940654\pi$
$822$		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	$0.0161647\pi$
$827$			2.91954i			0.101522i	−0.998711	+	0.0507611i	$0.983835\pi$
$828$		0			0
$829$			33.7216i			1.17120i	0.810600	+	0.585600i	$0.199141\pi$
$829$			33.7216i			1.17120i	−0.810600	+	0.585600i	$0.800859\pi$
$830$	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	$-0.937798\pi$
$853$		−	11.3421i		−	0.388347i	0.980967	−	0.194174i	$-0.0622025\pi$
$854$	−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	$0.131298\pi$
$859$			23.4990i			0.801776i	−0.916127	+	0.400888i	$0.868702\pi$
$860$	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	$0.264973\pi$
$877$			43.8038i			1.47915i	−0.673074	+	0.739575i	$0.735027\pi$
$878$	−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	$0.184126\pi$
$883$			32.4922i			1.09345i	−0.837312	+	0.546725i	$0.815874\pi$
$884$	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	$-0.839970\pi$
$907$		−	29.0224i		−	0.963671i	0.876262	−	0.481836i	$-0.160030\pi$
$908$	−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	$-0.851467\pi$
$941$		−	27.6008i		−	0.899760i	0.893089	−	0.449880i	$-0.148533\pi$
$942$		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	$0.439560\pi$
$947$			60.4406i			1.96405i	−0.188740	+	0.982027i	$0.560440\pi$
$948$		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	$-0.826045\pi$
$971$		−	32.3884i		−	1.03939i	0.854351	−	0.519697i	$-0.173955\pi$
$972$		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	$0.0789398\pi$
$997$			15.5011i			0.490925i	−0.969406	+	0.245463i	$0.921060\pi$
$998$	−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.469.2	yes	24
3.2	odd	2	inner	936.2.g.f.469.23	yes	24
4.3	odd	2		3744.2.g.f.1873.12		24
8.3	odd	2		3744.2.g.f.1873.11		24
8.5	even	2	inner	936.2.g.f.469.1	✓	24
12.11	even	2		3744.2.g.f.1873.23		24
24.5	odd	2	inner	936.2.g.f.469.24	yes	24
24.11	even	2		3744.2.g.f.1873.24		24

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

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

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Database

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