LMFDB - Embedded newform 945.2.cc.a.703.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(82,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("945.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.cc (of order $12$, degree $4$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			703.16
Character	$\chi$	$=$	945.703
Dual form			945.2.cc.a.82.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.121772 - 0.0326286i) q^{2} +(-1.71829 - 0.992054i) q^{4} +(-0.668137 + 2.13391i) q^{5} +(1.10538 + 2.40378i) q^{7} +(0.355155 + 0.355155i) q^{8} +O(q^{10})$	\(q+(-0.121772 - 0.0326286i) q^{2} +(-1.71829 - 0.992054i) q^{4} +(-0.668137 + 2.13391i) q^{5} +(1.10538 + 2.40378i) q^{7} +(0.355155 + 0.355155i) q^{8} +(0.150987 - 0.238050i) q^{10} +(1.85074 - 3.20557i) q^{11} +(2.74441 - 2.74441i) q^{13} +(-0.0561718 - 0.328778i) q^{14} +(1.95245 + 3.38174i) q^{16} +(-7.27655 + 1.94975i) q^{17} +(0.435731 + 0.754709i) q^{19} +(3.26501 - 3.00385i) q^{20} +(-0.329960 + 0.329960i) q^{22} +(-1.21737 + 4.54328i) q^{23} +(-4.10719 - 2.85150i) q^{25} +(-0.423738 + 0.244645i) q^{26} +(0.485317 - 5.22697i) q^{28} +8.58490i q^{29} +(3.28003 + 1.89373i) q^{31} +(-0.387403 - 1.44581i) q^{32} +0.949694 q^{34} +(-5.86800 + 0.752731i) q^{35} +(-11.1910 - 2.99861i) q^{37} +(-0.0284346 - 0.106119i) q^{38} +(-0.995163 + 0.520578i) q^{40} +7.21562i q^{41} +(-0.545286 - 0.545286i) q^{43} +(-6.36019 + 3.67206i) q^{44} +(0.296481 - 0.513521i) q^{46} +(-1.86365 + 6.95523i) q^{47} +(-4.55628 + 5.31416i) q^{49} +(0.407098 + 0.481243i) q^{50} +(-7.43829 + 1.99308i) q^{52} +(-0.701093 + 0.187857i) q^{53} +(5.60387 + 6.09108i) q^{55} +(-0.461133 + 1.24629i) q^{56} +(0.280113 - 1.04540i) q^{58} +(0.887254 - 1.53677i) q^{59} +(3.95514 - 2.28350i) q^{61} +(-0.337625 - 0.337625i) q^{62} -7.62109i q^{64} +(4.02270 + 7.68999i) q^{65} +(2.01631 + 7.52498i) q^{67} +(14.4375 + 3.86850i) q^{68} +(0.739116 + 0.0998033i) q^{70} -9.65572 q^{71} +(1.40459 + 5.24201i) q^{73} +(1.26490 + 0.730291i) q^{74} -1.72907i q^{76} +(9.75124 + 0.905389i) q^{77} +(3.99531 - 2.30670i) q^{79} +(-8.52084 + 1.90689i) q^{80} +(0.235436 - 0.878657i) q^{82} +(-3.03903 + 3.03903i) q^{83} +(0.701142 - 16.8302i) q^{85} +(0.0486084 + 0.0841923i) q^{86} +(1.79577 - 0.481176i) q^{88} +(4.90134 + 8.48937i) q^{89} +(9.63057 + 3.56334i) q^{91} +(6.59896 - 6.59896i) q^{92} +(0.453879 - 0.786141i) q^{94} +(-1.90161 + 0.425564i) q^{95} +(3.30555 + 3.30555i) q^{97} +(0.728219 - 0.498449i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 8 q^{7}+O(q^{10}) $ 128 * q - 8 * q^7	$ 128 q - 8 q^{7} + 24 q^{10} + 64 q^{16} - 32 q^{22} + 8 q^{25} - 8 q^{28} - 8 q^{37} + 120 q^{40} - 32 q^{43} - 48 q^{58} - 24 q^{61} + 16 q^{67} + 160 q^{70} - 144 q^{73} - 168 q^{82} - 32 q^{85} - 96 q^{88} - 120 q^{91}+O(q^{100}) $ 128 * q - 8 * q^7 + 24 * q^10 + 64 * q^16 - 32 * q^22 + 8 * q^25 - 8 * q^28 - 8 * q^37 + 120 * q^40 - 32 * q^43 - 48 * q^58 - 24 * q^61 + 16 * q^67 + 160 * q^70 - 144 * q^73 - 168 * q^82 - 32 * q^85 - 96 * q^88 - 120 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.121772	−	0.0326286i	−0.0861055	−	0.0230719i	0.215509	−	0.976502i	$-0.430859\pi$
$2$	−0.121772	−	0.0326286i	−0.0861055	−	0.0230719i	−0.301615	+	0.953430i	$0.597526\pi$
$3$		0			0
$3$		0			0
$4$	−1.71829	−	0.992054i	−0.859144	−	0.496027i
$5$	−0.668137	+	2.13391i	−0.298800	+	0.954316i
$5$	−0.668137	+	2.13391i	−0.298800	+	0.954316i
$6$		0			0
$7$	1.10538	+	2.40378i	0.417794	+	0.908542i
$7$	1.10538	+	2.40378i	0.417794	+	0.908542i
$8$	0.355155	+	0.355155i	0.125566	+	0.125566i
$9$		0			0
$10$	0.150987	−	0.238050i	0.0477462	−	0.0752779i
$11$	1.85074	−	3.20557i	0.558018	−	0.966516i	−0.439644	−	0.898172i	$-0.644895\pi$
$11$	1.85074	−	3.20557i	0.558018	−	0.966516i	0.997662	−	0.0683435i	$-0.0217714\pi$
$12$		0			0
$13$	2.74441	−	2.74441i	0.761163	−	0.761163i	−0.215369	−	0.976533i	$-0.569096\pi$
$13$	2.74441	−	2.74441i	0.761163	−	0.761163i	0.976533	+	0.215369i	$0.0690956\pi$
$14$	−0.0561718	−	0.328778i	−0.0150125	−	0.0878697i
$15$		0			0
$16$	1.95245	+	3.38174i	0.488112	+	0.845435i
$17$	−7.27655	+	1.94975i	−1.76482	+	0.472883i	−0.987686	−	0.156449i	$-0.949995\pi$
$17$	−7.27655	+	1.94975i	−1.76482	+	0.472883i	−0.777137	+	0.629332i	$0.783329\pi$
$18$		0			0
$19$	0.435731	+	0.754709i	0.0999636	+	0.173142i	0.911669	−	0.410925i	$-0.134794\pi$
$19$	0.435731	+	0.754709i	0.0999636	+	0.173142i	−0.811706	+	0.584067i	$0.801461\pi$
$20$	3.26501	−	3.00385i	0.730078	−	0.671681i
$21$		0			0
$22$	−0.329960	+	0.329960i	−0.0703478	+	0.0703478i
$23$	−1.21737	+	4.54328i	−0.253839	+	0.947339i	0.714894	+	0.699233i	$0.246475\pi$
$23$	−1.21737	+	4.54328i	−0.253839	+	0.947339i	−0.968733	+	0.248106i	$0.920192\pi$
$24$		0			0
$25$	−4.10719	−	2.85150i	−0.821437	−	0.570299i
$26$	−0.423738	+	0.244645i	−0.0831018	+	0.0479789i
$27$		0			0
$28$	0.485317	−	5.22697i	0.0917163	−	0.987805i
$29$			8.58490i			1.59418i	0.603864	+	0.797088i	$0.293627\pi$
$29$			8.58490i			1.59418i	−0.603864	+	0.797088i	$0.706373\pi$
$30$		0			0
$31$	3.28003	+	1.89373i	0.589112	+	0.340124i	0.764746	−	0.644332i	$-0.222864\pi$
$31$	3.28003	+	1.89373i	0.589112	+	0.340124i	−0.175635	+	0.984455i	$0.556198\pi$
$32$	−0.387403	−	1.44581i	−0.0684838	−	0.255585i
$33$		0			0
$34$	0.949694			0.162871
$35$	−5.86800	+	0.752731i	−0.991873	+	0.127235i
$36$		0			0
$37$	−11.1910	−	2.99861i	−1.83978	−	0.492969i	−0.840945	−	0.541121i	$-0.818000\pi$
$37$	−11.1910	−	2.99861i	−1.83978	−	0.492969i	−0.998840	+	0.0481520i	$0.984667\pi$
$38$	−0.0284346	−	0.106119i	−0.00461270	−	0.0172148i
$39$		0			0
$40$	−0.995163	+	0.520578i	−0.157349	+	0.0823107i
$41$			7.21562i			1.12689i	0.826153	+	0.563445i	$0.190524\pi$
$41$			7.21562i			1.12689i	−0.826153	+	0.563445i	$0.809476\pi$
$42$		0			0
$43$	−0.545286	−	0.545286i	−0.0831554	−	0.0831554i	0.664306	−	0.747461i	$-0.268727\pi$
$43$	−0.545286	−	0.545286i	−0.0831554	−	0.0831554i	−0.747461	+	0.664306i	$0.768727\pi$
$44$	−6.36019	+	3.67206i	−0.958835	+	0.553584i
$45$		0			0
$46$	0.296481	−	0.513521i	0.0437138	−	0.0757145i
$47$	−1.86365	+	6.95523i	−0.271841	+	1.01452i	0.686088	+	0.727519i	$0.259327\pi$
$47$	−1.86365	+	6.95523i	−0.271841	+	1.01452i	−0.957929	+	0.287006i	$0.907340\pi$
$48$		0			0
$49$	−4.55628	+	5.31416i	−0.650897	+	0.759166i
$50$	0.407098	+	0.481243i	0.0575724	+	0.0680580i
$51$		0			0
$52$	−7.43829	+	1.99308i	−1.03151	+	0.276391i
$53$	−0.701093	+	0.187857i	−0.0963026	+	0.0258042i	−0.306649	−	0.951823i	$-0.599208\pi$
$53$	−0.701093	+	0.187857i	−0.0963026	+	0.0258042i	0.210346	+	0.977627i	$0.432541\pi$
$54$		0			0
$55$	5.60387	+	6.09108i	0.755625	+	0.821320i
$56$	−0.461133	+	1.24629i	−0.0616214	+	0.166543i
$57$		0			0
$58$	0.280113	−	1.04540i	0.0367807	−	0.137267i
$59$	0.887254	−	1.53677i	0.115511	−	0.200070i	−0.802473	−	0.596688i	$-0.796483\pi$
$59$	0.887254	−	1.53677i	0.115511	−	0.200070i	0.917984	+	0.396618i	$0.129816\pi$
$60$		0			0
$61$	3.95514	−	2.28350i	0.506404	−	0.292372i	−0.224950	−	0.974370i	$-0.572222\pi$
$61$	3.95514	−	2.28350i	0.506404	−	0.292372i	0.731354	+	0.681998i	$0.238889\pi$
$62$	−0.337625	−	0.337625i	−0.0428784	−	0.0428784i
$63$		0			0
$64$		−	7.62109i		−	0.952636i
$65$	4.02270	+	7.68999i	0.498954	+	0.953826i
$66$		0			0
$67$	2.01631	+	7.52498i	0.246332	+	0.919322i	0.972709	+	0.232027i	$0.0745357\pi$
$67$	2.01631	+	7.52498i	0.246332	+	0.919322i	−0.726378	+	0.687296i	$0.758798\pi$
$68$	14.4375	+	3.86850i	1.75080	+	0.469125i
$69$		0			0
$70$	0.739116	+	0.0998033i	0.0883412	+	0.0119288i
$71$	−9.65572			−1.14592			−0.572961	−	0.819582i	$-0.694206\pi$
$71$	−9.65572			−1.14592			−0.572961	+	0.819582i	$0.694206\pi$
$72$		0			0
$73$	1.40459	+	5.24201i	0.164395	+	0.613531i	0.998117	+	0.0613458i	$0.0195392\pi$
$73$	1.40459	+	5.24201i	0.164395	+	0.613531i	−0.833721	+	0.552185i	$0.813794\pi$
$74$	1.26490	+	0.730291i	0.147042	+	0.0848947i
$75$		0			0
$76$		−	1.72907i		−	0.198338i
$77$	9.75124	+	0.905389i	1.11126	+	0.103179i
$78$		0			0
$79$	3.99531	−	2.30670i	0.449508	−	0.259524i	−0.258114	−	0.966114i	$-0.583101\pi$
$79$	3.99531	−	2.30670i	0.449508	−	0.259524i	0.707622	+	0.706591i	$0.249768\pi$
$80$	−8.52084	+	1.90689i	−0.952659	+	0.213197i
$81$		0			0
$82$	0.235436	−	0.878657i	0.0259995	−	0.0970315i
$83$	−3.03903	+	3.03903i	−0.333577	+	0.333577i	−0.853943	−	0.520366i	$-0.825795\pi$
$83$	−3.03903	+	3.03903i	−0.333577	+	0.333577i	0.520366	+	0.853943i	$0.325795\pi$
$84$		0			0
$85$	0.701142	−	16.8302i	0.0760496	−	1.82550i
$86$	0.0486084	+	0.0841923i	0.00524158	+	0.00907869i
$87$		0			0
$88$	1.79577	−	0.481176i	0.191430	−	0.0512935i
$89$	4.90134	+	8.48937i	0.519541	+	0.899872i	0.999742	+	0.0227132i	$0.00723046\pi$
$89$	4.90134	+	8.48937i	0.519541	+	0.899872i	−0.480201	+	0.877159i	$0.659436\pi$
$90$		0			0
$91$	9.63057	+	3.56334i	1.00956	+	0.373539i
$92$	6.59896	−	6.59896i	0.687989	−	0.687989i
$93$		0			0
$94$	0.453879	−	0.786141i	0.0468140	−	0.0810842i
$95$	−1.90161	+	0.425564i	−0.195101	+	0.0436620i
$96$		0			0
$97$	3.30555	+	3.30555i	0.335628	+	0.335628i	0.854719	−	0.519091i	$-0.173730\pi$
$97$	3.30555	+	3.30555i	0.335628	+	0.335628i	−0.519091	+	0.854719i	$0.673730\pi$
$98$	0.728219	−	0.498449i	0.0735612	−	0.0503510i
$99$		0			0
$100$	4.22849	+	8.97424i	0.422849	+	0.897424i
$101$	−7.57630	−	4.37418i	−0.753870	−	0.435247i	0.0732204	−	0.997316i	$-0.476672\pi$
$101$	−7.57630	−	4.37418i	−0.753870	−	0.435247i	−0.827091	+	0.562069i	$0.810006\pi$
$102$		0			0
$103$	5.00477	+	1.34103i	0.493135	+	0.132135i	0.496812	−	0.867858i	$-0.334504\pi$
$103$	5.00477	+	1.34103i	0.493135	+	0.132135i	−0.00367708	+	0.999993i	$0.501170\pi$
$104$	1.94938			0.191153
$105$		0			0
$106$	0.0915027			0.00888753
$107$	−12.1512	−	3.25590i	−1.17470	−	0.314759i	−0.381877	−	0.924213i	$-0.624722\pi$
$107$	−12.1512	−	3.25590i	−1.17470	−	0.314759i	−0.792821	+	0.609454i	$0.791389\pi$
$108$		0			0
$109$	5.47631	+	3.16175i	0.524535	+	0.302840i	0.738788	−	0.673938i	$-0.235398\pi$
$109$	5.47631	+	3.16175i	0.524535	+	0.302840i	−0.214253	+	0.976778i	$0.568732\pi$
$110$	−0.483648	−	0.924566i	−0.0461141	−	0.0881539i
$111$		0			0
$112$	−5.97075	+	8.43135i	−0.564183	+	0.796687i
$113$	−12.8216	−	12.8216i	−1.20615	−	1.20615i	−0.972263	−	0.233889i	$-0.924855\pi$
$113$	−12.8216	−	12.8216i	−1.20615	−	1.20615i	−0.233889	−	0.972263i	$-0.575145\pi$
$114$		0			0
$115$	−8.88160	−	5.63329i	−0.828213	−	0.525307i
$116$	8.51668	−	14.7513i	0.790754	−	1.36963i
$117$		0			0
$118$	−0.158185	+	0.158185i	−0.0145621	+	0.0145621i
$119$	−12.7301	−	15.3360i	−1.16697	−	1.40585i
$120$		0			0
$121$	−1.35045	−	2.33905i	−0.122768	−	0.212641i
$122$	−0.556131	+	0.149015i	−0.0503497	+	0.0134912i
$123$		0			0
$124$	−3.75736	−	6.50794i	−0.337421	−	0.584430i
$125$	8.82901	−	6.85919i	0.789691	−	0.613505i
$126$		0			0
$127$	−8.04604	+	8.04604i	−0.713971	+	0.713971i	−0.967363	−	0.253393i	$-0.918453\pi$
$127$	−8.04604	+	8.04604i	−0.713971	+	0.713971i	0.253393	+	0.967363i	$0.418453\pi$
$128$	−1.02347	+	3.81965i	−0.0904629	+	0.337612i
$129$		0			0
$130$	−0.238937	−	1.06768i	−0.0209561	−	0.0936414i
$131$	14.3809	−	8.30279i	1.25646	−	0.725418i	0.284076	−	0.958802i	$-0.408313\pi$
$131$	14.3809	−	8.30279i	1.25646	−	0.725418i	0.972385	+	0.233384i	$0.0749798\pi$
$132$		0			0
$133$	−1.33250	+	1.88164i	−0.115543	+	0.163159i
$134$		−	0.982118i		−	0.0848420i
$135$		0			0
$136$	−3.27677	−	1.89184i	−0.280980	−	0.162224i
$137$	0.137341	+	0.512564i	0.0117338	+	0.0437913i	0.971545	−	0.236857i	$-0.0761173\pi$
$137$	0.137341	+	0.512564i	0.0117338	+	0.0437913i	−0.959811	+	0.280648i	$0.909451\pi$
$138$		0			0
$139$	−16.5564			−1.40429			−0.702147	−	0.712032i	$-0.747775\pi$
$139$	−16.5564			−1.40429			−0.702147	+	0.712032i	$0.747775\pi$
$140$	10.8297	+	4.52796i	0.915273	+	0.382682i
$141$		0			0
$142$	1.17579	+	0.315052i	0.0986703	+	0.0264386i
$143$	−3.71822	−	13.8766i	−0.310933	−	1.16042i
$144$		0			0
$145$	−18.3194	−	5.73589i	−1.52135	−	0.476340i
$146$		−	0.684158i		−	0.0566213i
$147$		0			0
$148$	16.2545	+	16.2545i	1.33611	+	1.33611i
$149$	6.72136	−	3.88058i	0.550635	−	0.317909i	−0.198743	−	0.980052i	$-0.563686\pi$
$149$	6.72136	−	3.88058i	0.550635	−	0.317909i	0.749378	+	0.662142i	$0.230353\pi$
$150$		0			0
$151$	7.15689	−	12.3961i	0.582420	−	1.00878i	−0.412772	−	0.910834i	$-0.635439\pi$
$151$	7.15689	−	12.3961i	0.582420	−	1.00878i	0.995192	−	0.0979460i	$-0.0312272\pi$
$152$	−0.113286	+	0.422791i	−0.00918874	+	0.0342929i
$153$		0			0
$154$	−1.15788	−	0.428420i	−0.0933048	−	0.0345230i
$155$	−6.23257	+	5.73404i	−0.500612	+	0.460570i
$156$		0			0
$157$	12.2632	−	3.28591i	0.978708	−	0.262244i	0.266208	−	0.963916i	$-0.414229\pi$
$157$	12.2632	−	3.28591i	0.978708	−	0.262244i	0.712500	+	0.701672i	$0.247563\pi$
$158$	−0.561780	+	0.150528i	−0.0446928	+	0.0119754i
$159$		0			0
$160$	3.34407	+	0.139313i	0.264372	+	0.0110136i
$161$	−12.2667	+	2.09576i	−0.966749	+	0.165169i
$162$		0			0
$163$	−0.921031	+	3.43733i	−0.0721407	+	0.269233i	−0.992570	−	0.121677i	$-0.961173\pi$
$163$	−0.921031	+	3.43733i	−0.0721407	+	0.269233i	0.920429	+	0.390910i	$0.127839\pi$
$164$	7.15828	−	12.3985i	0.558968	−	0.968161i
$165$		0			0
$166$	0.469227	−	0.270908i	0.0364191	−	0.0210266i
$167$	11.5442	+	11.5442i	0.893316	+	0.893316i	0.994834	−	0.101518i	$-0.0323698\pi$
$167$	11.5442	+	11.5442i	0.893316	+	0.893316i	−0.101518	+	0.994834i	$0.532370\pi$
$168$		0			0
$169$		−	2.06360i		−	0.158739i
$170$	−0.634526	+	2.02657i	−0.0486659	+	0.155431i
$171$		0			0
$172$	0.396005	+	1.47791i	0.0301951	+	0.112690i
$173$	1.34338	+	0.359958i	0.102135	+	0.0273671i	0.309525	−	0.950891i	$-0.399830\pi$
$173$	1.34338	+	0.359958i	0.102135	+	0.0273671i	−0.207389	+	0.978258i	$0.566497\pi$
$174$		0			0
$175$	2.31436	−	13.0247i	0.174949	−	0.984577i
$176$	14.4539			1.08950
$177$		0			0
$178$	−0.319848	−	1.19369i	−0.0239736	−	0.0894707i
$179$	−8.14219	−	4.70090i	−0.608576	−	0.351362i	0.163832	−	0.986488i	$-0.447615\pi$
$179$	−8.14219	−	4.70090i	−0.608576	−	0.351362i	−0.772408	+	0.635127i	$0.780948\pi$
$180$		0			0
$181$		−	15.5072i		−	1.15264i	−0.817225	−	0.576319i	$-0.804488\pi$
$181$		−	15.5072i		−	1.15264i	0.817225	−	0.576319i	$-0.195512\pi$
$182$	−1.05646	−	0.748145i	−0.0783102	−	0.0554562i
$183$		0			0
$184$	−2.04592	+	1.18121i	−0.150827	+	0.0870802i
$185$	13.8759	−	21.8771i	1.02018	−	1.60844i
$186$		0			0
$187$	−7.21693	+	26.9340i	−0.527754	+	1.96961i
$188$	10.1022	−	10.1022i	0.736782	−	0.736782i
$189$		0			0
$190$	0.245448	+	0.0102253i	0.0178067	+	0.000741820i
$191$	11.3444	+	19.6491i	0.820853	+	1.42176i	0.905048	+	0.425310i	$0.139835\pi$
$191$	11.3444	+	19.6491i	0.820853	+	1.42176i	−0.0841943	+	0.996449i	$0.526832\pi$
$192$		0			0
$193$	−3.74163	+	1.00257i	−0.269328	+	0.0721663i	−0.390956	−	0.920410i	$-0.627855\pi$
$193$	−3.74163	+	1.00257i	−0.269328	+	0.0721663i	0.121627	+	0.992576i	$0.461189\pi$
$194$	−0.294666	−	0.510377i	−0.0211558	−	0.0366429i
$195$		0			0
$196$	13.1009	−	4.61119i	0.935781	−	0.329371i
$197$	6.60630	−	6.60630i	0.470679	−	0.470679i	−0.431455	−	0.902134i	$-0.642000\pi$
$197$	6.60630	−	6.60630i	0.470679	−	0.470679i	0.902134	+	0.431455i	$0.142000\pi$
$198$		0			0
$199$	3.62824	−	6.28430i	0.257199	−	0.445482i	−0.708291	−	0.705920i	$-0.750534\pi$
$199$	3.62824	−	6.28430i	0.257199	−	0.445482i	0.965491	+	0.260438i	$0.0838670\pi$
$200$	−0.445965	−	2.47141i	−0.0315345	−	0.174755i
$201$		0			0
$202$	0.779855	+	0.779855i	0.0548704	+	0.0548704i
$203$	−20.6362	+	9.48956i	−1.44838	+	0.666036i
$204$		0			0
$205$	−15.3975	−	4.82102i	−1.07541	−	0.336715i
$206$	−0.565683	−	0.326597i	−0.0394130	−	0.0227551i
$207$		0			0
$208$	14.6392	+	3.92256i	1.01505	+	0.271981i
$209$	3.22570			0.223126
$210$		0			0
$211$	−15.1111			−1.04029			−0.520145	−	0.854078i	$-0.674122\pi$
$211$	−15.1111			−1.04029			−0.520145	+	0.854078i	$0.674122\pi$
$212$	1.39104	+	0.372729i	0.0955373	+	0.0255991i
$213$		0			0
$214$	1.37343	+	0.792951i	0.0938859	+	0.0542050i
$215$	1.52792	−	0.799269i	0.104203	−	0.0545097i
$216$		0			0
$217$	−0.926421	+	9.97776i	−0.0628896	+	0.677334i
$218$	−0.563695	−	0.563695i	−0.0381782	−	0.0381782i
$219$		0			0
$220$	−3.58638	−	16.0256i	−0.241794	−	1.08044i
$221$	−14.6189	+	25.3208i	−0.983377	+	1.70326i
$222$		0			0
$223$	−12.0743	+	12.0743i	−0.808552	+	0.808552i	−0.984415	−	0.175863i	$-0.943729\pi$
$223$	−12.0743	+	12.0743i	−0.808552	+	0.808552i	0.175863	+	0.984415i	$0.443729\pi$
$224$	3.04717	−	2.52939i	0.203598	−	0.169002i
$225$		0			0
$226$	1.14295	+	1.97965i	0.0760281	+	0.131685i
$227$	21.2411	−	5.69153i	1.40982	−	0.377760i	0.527959	−	0.849270i	$-0.322957\pi$
$227$	21.2411	−	5.69153i	1.40982	−	0.377760i	0.881861	+	0.471510i	$0.156291\pi$
$228$		0			0
$229$	0.632861	+	1.09615i	0.0418206	+	0.0724355i	0.886178	−	0.463345i	$-0.153351\pi$
$229$	0.632861	+	1.09615i	0.0418206	+	0.0724355i	−0.844357	+	0.535780i	$0.820018\pi$
$230$	0.897720	+	0.975769i	0.0591939	+	0.0643403i
$231$		0			0
$232$	−3.04897	+	3.04897i	−0.200175	+	0.200175i
$233$	−7.52221	+	28.0733i	−0.492796	+	1.83914i	0.0492411	+	0.998787i	$0.484320\pi$
$233$	−7.52221	+	28.0733i	−0.492796	+	1.83914i	−0.542038	+	0.840354i	$0.682347\pi$
$234$		0			0
$235$	−13.5967	−	8.62391i	−0.886950	−	0.562562i
$236$	−3.04912	+	1.76041i	−0.198481	+	0.114593i
$237$		0			0
$238$	1.04977	+	2.28285i	0.0680466	+	0.147975i
$239$		−	14.2224i		−	0.919969i	−0.887927	−	0.459985i	$-0.847855\pi$
$239$		−	14.2224i		−	0.919969i	0.887927	−	0.459985i	$-0.152145\pi$
$240$		0			0
$241$	23.7218	+	13.6958i	1.52806	+	0.882224i	0.999443	+	0.0333603i	$0.0106209\pi$
$241$	23.7218	+	13.6958i	1.52806	+	0.882224i	0.528613	+	0.848863i	$0.322712\pi$
$242$	0.0881268	+	0.328894i	0.00566500	+	0.0211421i
$243$		0			0
$244$	−9.06142			−0.580098
$245$	−8.29575	−	13.2733i	−0.529996	−	0.848000i
$246$		0			0
$247$	3.26706	+	0.875406i	0.207878	+	0.0557007i
$248$	0.492354	+	1.83749i	0.0312645	+	0.116681i
$249$		0			0
$250$	−1.29893	+	0.547176i	−0.0821514	+	0.0346065i
$251$		−	4.81809i		−	0.304115i	−0.988372	−	0.152058i	$-0.951410\pi$
$251$		−	4.81809i		−	0.304115i	0.988372	−	0.152058i	$-0.0485899\pi$
$252$		0			0
$253$	12.3108	+	12.3108i	0.773971	+	0.773971i
$254$	1.24231	−	0.717248i	0.0779495	−	0.0450041i
$255$		0			0
$256$	−7.37183	+	12.7684i	−0.460740	+	0.798024i
$257$	2.54189	−	9.48647i	0.158559	−	0.591750i	−0.840215	−	0.542253i	$-0.817571\pi$
$257$	2.54189	−	9.48647i	0.158559	−	0.591750i	0.998774	−	0.0494970i	$-0.0157618\pi$
$258$		0			0
$259$	−5.16227	−	30.2152i	−0.320768	−	1.87748i
$260$	0.716727	−	17.2043i	0.0444495	−	1.06697i
$261$		0			0
$262$	−2.02209	+	0.541817i	−0.124925	+	0.0334735i
$263$	27.6390	−	7.40584i	1.70429	−	0.456664i	0.730279	−	0.683150i	$-0.239390\pi$
$263$	27.6390	−	7.40584i	1.70429	−	0.456664i	0.974015	+	0.226486i	$0.0727236\pi$
$264$		0			0
$265$	0.0675548	−	1.62159i	0.00414986	−	0.0996134i
$266$	0.223656	−	0.185652i	0.0137132	−	0.0113831i
$267$		0			0
$268$	4.00058	−	14.9304i	0.244374	−	0.912017i
$269$	8.04725	−	13.9382i	0.490650	−	0.849830i	−0.509293	−	0.860593i	$-0.670093\pi$
$269$	8.04725	−	13.9382i	0.490650	−	0.849830i	0.999942	+	0.0107635i	$0.00342621\pi$
$270$		0			0
$271$	12.7678	−	7.37150i	0.775589	−	0.447787i	−0.0592756	−	0.998242i	$-0.518879\pi$
$271$	12.7678	−	7.37150i	0.775589	−	0.447787i	0.834865	+	0.550455i	$0.185546\pi$
$272$	−20.8006	−	20.8006i	−1.26122	−	1.26122i
$273$		0			0
$274$		−	0.0668969i		−	0.00404139i
$275$	−16.7420	+	7.88850i	−1.00958	+	0.475695i
$276$		0			0
$277$	−2.11668	−	7.89956i	−0.127179	−	0.474639i	0.872729	−	0.488205i	$-0.162348\pi$
$277$	−2.11668	−	7.89956i	−0.127179	−	0.474639i	−0.999908	+	0.0135665i	$0.995682\pi$
$278$	2.01610	+	0.540211i	0.120917	+	0.0323997i
$279$		0			0
$280$	−2.35139	−	1.81671i	−0.140522	−	0.108569i
$281$	6.63025			0.395527			0.197764	−	0.980250i	$-0.436632\pi$
$281$	6.63025			0.395527			0.197764	+	0.980250i	$0.436632\pi$
$282$		0			0
$283$	4.45149	+	16.6132i	0.264613	+	0.987550i	0.962487	+	0.271329i	$0.0874632\pi$
$283$	4.45149	+	16.6132i	0.264613	+	0.987550i	−0.697873	+	0.716221i	$0.745870\pi$
$284$	16.5913	+	9.57899i	0.984512	+	0.568408i
$285$		0			0
$286$			1.81109i			0.107092i
$287$	−17.3447	+	7.97599i	−1.02383	+	0.470808i
$288$		0			0
$289$	34.4242	−	19.8748i	2.02496	−	1.16911i
$290$	2.04363	+	1.29621i	0.120006	+	0.0761158i
$291$		0			0
$292$	2.78686	−	10.4007i	0.163089	−	0.608656i
$293$	15.4579	−	15.4579i	0.903059	−	0.903059i	−0.0926408	−	0.995700i	$-0.529531\pi$
$293$	15.4579	−	15.4579i	0.903059	−	0.903059i	0.995700	+	0.0926408i	$0.0295308\pi$
$294$		0			0
$295$	2.68653	+	2.92010i	0.156416	+	0.170015i
$296$	−2.90956	−	5.03950i	−0.169115	−	0.292915i
$297$		0			0
$298$	−0.945088	+	0.253236i	−0.0547475	+	0.0146695i
$299$	9.12767	+	15.8096i	0.527867	+	0.914292i
$300$		0			0
$301$	0.707999	−	1.91349i	0.0408084	−	0.110292i
$302$	−1.27597	+	1.27597i	−0.0734240	+	0.0734240i
$303$		0			0
$304$	−1.70148	+	2.94706i	−0.0975868	+	0.169025i
$305$	2.23022	+	9.96563i	0.127702	+	0.570630i
$306$		0			0
$307$	0.788081	+	0.788081i	0.0449782	+	0.0449782i	0.729238	−	0.684260i	$-0.239875\pi$
$307$	0.788081	+	0.788081i	0.0449782	+	0.0449782i	−0.684260	+	0.729238i	$0.739875\pi$
$308$	−15.8572	−	11.2295i	−0.903550	−	0.639858i
$309$		0			0
$310$	0.946043	−	0.494884i	0.0537317	−	0.0281075i
$311$	−9.94659	−	5.74267i	−0.564019	−	0.325637i	0.190738	−	0.981641i	$-0.438912\pi$
$311$	−9.94659	−	5.74267i	−0.564019	−	0.325637i	−0.754757	+	0.656004i	$0.772245\pi$
$312$		0			0
$313$	9.65926	+	2.58819i	0.545974	+	0.146293i	0.521255	−	0.853401i	$-0.325464\pi$
$313$	9.65926	+	2.58819i	0.545974	+	0.146293i	0.0247191	+	0.999694i	$0.492131\pi$
$314$	−1.60052			−0.0903226
$315$		0			0
$316$	−9.15346			−0.514922
$317$	8.80889	+	2.36034i	0.494757	+	0.132570i	0.497566	−	0.867426i	$-0.334227\pi$
$317$	8.80889	+	2.36034i	0.494757	+	0.132570i	−0.00280878	+	0.999996i	$0.500894\pi$
$318$		0			0
$319$	27.5195	+	15.8884i	1.54080	+	0.889579i
$320$	16.2628	+	5.09193i	0.909116	+	0.284648i
$321$		0			0
$322$	1.56211	+	0.145040i	0.0870532	+	0.00808277i
$323$	−4.64211	−	4.64211i	−0.258294	−	0.258294i
$324$		0			0
$325$	−19.0975	+	3.44613i	−1.05934	+	0.191157i
$326$	0.224311	−	0.388517i	0.0124234	−	0.0215180i
$327$		0			0
$328$	−2.56266	+	2.56266i	−0.141499	+	0.141499i
$329$	−18.7788	+	3.20837i	−1.03531	+	0.176883i
$330$		0			0
$331$	13.2579	+	22.9634i	0.728722	+	1.26218i	0.957423	+	0.288687i	$0.0932188\pi$
$331$	13.2579	+	22.9634i	0.728722	+	1.26218i	−0.228701	+	0.973497i	$0.573448\pi$
$332$	8.23681	−	2.20705i	0.452054	−	0.121127i
$333$		0			0
$334$	−1.02908	−	1.78242i	−0.0563089	−	0.0975299i
$335$	−17.4048	−	0.725080i	−0.950928	−	0.0396154i
$336$		0			0
$337$	−10.9637	+	10.9637i	−0.597230	+	0.597230i	−0.939574	−	0.342345i	$-0.888779\pi$
$337$	−10.9637	+	10.9637i	−0.597230	+	0.597230i	0.342345	+	0.939574i	$0.388779\pi$
$338$	−0.0673325	+	0.251288i	−0.00366240	+	0.0136683i
$339$		0			0
$340$	−17.9013	+	28.2236i	−0.970832	+	1.53064i
$341$	12.1410	−	7.00959i	0.657470	−	0.379590i
$342$		0			0
$343$	−17.8105	−	5.07811i	−0.961675	−	0.274192i
$344$		−	0.387322i		−	0.0208830i
$345$		0			0
$346$	−0.151841	−	0.0876652i	−0.00816300	−	0.00471291i
$347$	−4.24408	−	15.8391i	−0.227834	−	0.850289i	−0.981249	−	0.192743i	$-0.938262\pi$
$347$	−4.24408	−	15.8391i	−0.227834	−	0.850289i	0.753415	−	0.657545i	$-0.228405\pi$
$348$		0			0
$349$	16.1944			0.866868			0.433434	−	0.901185i	$-0.357302\pi$
$349$	16.1944			0.866868			0.433434	+	0.901185i	$0.357302\pi$
$350$	−0.706802	+	1.51053i	−0.0377802	+	0.0807411i
$351$		0			0
$352$	−5.35162	−	1.43396i	−0.285242	−	0.0764304i
$353$	−2.94135	−	10.9773i	−0.156552	−	0.584262i	−0.998967	−	0.0454324i	$-0.985533\pi$
$353$	−2.94135	−	10.9773i	−0.156552	−	0.584262i	0.842415	−	0.538829i	$-0.181133\pi$
$354$		0			0
$355$	6.45134	−	20.6045i	0.342402	−	1.09357i
$356$		−	19.4496i		−	1.03083i
$357$		0			0
$358$	0.838104	+	0.838104i	0.0442952	+	0.0442952i
$359$	−28.1308	+	16.2413i	−1.48469	+	0.857186i	−0.999848	−	0.0174170i	$-0.994456\pi$
$359$	−28.1308	+	16.2413i	−1.48469	+	0.857186i	−0.484841	+	0.874603i	$0.661122\pi$
$360$		0			0
$361$	9.12028	−	15.7968i	0.480015	−	0.831410i
$362$	−0.505977	+	1.88833i	−0.0265936	+	0.0992485i
$363$		0			0
$364$	−13.0131	−	15.6769i	−0.682070	−	0.821692i
$365$	−12.1245	−	0.505102i	−0.634624	−	0.0264382i
$366$		0			0
$367$	−16.8299	+	4.50955i	−0.878512	+	0.235397i	−0.669765	−	0.742573i	$-0.733605\pi$
$367$	−16.8299	+	4.50955i	−0.878512	+	0.235397i	−0.208747	+	0.977970i	$0.566939\pi$
$368$	−17.7410	+	4.75369i	−0.924814	+	0.247803i
$369$		0			0
$370$	−2.40351	+	2.21126i	−0.124952	+	0.114958i
$371$	−1.22654	−	1.47762i	−0.0636788	−	0.0767141i
$372$		0			0
$373$	−2.02329	+	7.55101i	−0.104762	+	0.390977i	−0.998318	−	0.0579747i	$-0.981536\pi$
$373$	−2.02329	+	7.55101i	−0.104762	+	0.390977i	0.893556	+	0.448951i	$0.148202\pi$
$374$	1.75763	−	3.04431i	0.0908851	−	0.157418i
$375$		0			0
$376$	−3.13207	+	1.80830i	−0.161524	+	0.0932560i
$377$	23.5605	+	23.5605i	1.21343	+	1.21343i
$378$		0			0
$379$		−	4.54919i		−	0.233676i	−0.993151	−	0.116838i	$-0.962724\pi$
$379$		−	4.54919i		−	0.233676i	0.993151	−	0.116838i	$-0.0372759\pi$
$380$	3.68970	+	1.15526i	0.189278	+	0.0592635i
$381$		0			0
$382$	−0.740305	−	2.76285i	−0.0378773	−	0.141360i
$383$	3.45940	+	0.926942i	0.176767	+	0.0473645i	0.346117	−	0.938191i	$-0.387500\pi$
$383$	3.45940	+	0.926942i	0.176767	+	0.0473645i	−0.169350	+	0.985556i	$0.554167\pi$
$384$		0			0
$385$	−8.44719	+	20.2034i	−0.430509	+	1.02966i
$386$	0.488336			0.0248557
$387$		0			0
$388$	−2.40060	−	8.95916i	−0.121872	−	0.454832i
$389$	12.7185	+	7.34303i	0.644854	+	0.372306i	0.786482	−	0.617613i	$-0.211900\pi$
$389$	12.7185	+	7.34303i	0.644854	+	0.372306i	−0.141628	+	0.989920i	$0.545234\pi$
$390$		0			0
$391$		−	35.4329i		−	1.79192i
$392$	−3.50554	+	0.269167i	−0.177056	+	0.0135950i
$393$		0			0
$394$	−1.02001	+	0.588905i	−0.0513875	+	0.0296686i
$395$	2.25287	+	10.0668i	0.113354	+	0.506518i
$396$		0			0
$397$	−5.64804	+	21.0788i	−0.283467	+	1.05791i	0.666485	+	0.745519i	$0.267798\pi$
$397$	−5.64804	+	21.0788i	−0.283467	+	1.05791i	−0.949952	+	0.312396i	$0.898869\pi$
$398$	−0.646865	+	0.646865i	−0.0324244	+	0.0324244i
$399$		0			0
$400$	1.62395	−	19.4568i	0.0811974	−	0.972841i
$401$	−4.14622	−	7.18147i	−0.207052	−	0.358625i	0.743732	−	0.668478i	$-0.233054\pi$
$401$	−4.14622	−	7.18147i	−0.207052	−	0.358625i	−0.950785	+	0.309852i	$0.899720\pi$
$402$		0			0
$403$	14.1989	−	3.80460i	0.707300	−	0.189520i
$404$	8.67884	+	15.0322i	0.431788	+	0.747880i
$405$		0			0
$406$	2.82253	−	0.482229i	0.140080	−	0.0239326i
$407$	−30.3238	+	30.3238i	−1.50310	+	1.50310i
$408$		0			0
$409$	−12.3875	+	21.4559i	−0.612524	+	1.06092i	0.378289	+	0.925688i	$0.376513\pi$
$409$	−12.3875	+	21.4559i	−0.612524	+	1.06092i	−0.990813	+	0.135236i	$0.956821\pi$
$410$	1.71768	+	1.08946i	0.0848300	+	0.0538047i
$411$		0			0
$412$	−7.26927	−	7.26927i	−0.358131	−	0.358131i
$413$	4.67480	+	0.434049i	0.230032	+	0.0213582i
$414$		0			0
$415$	−4.45455	−	8.51553i	−0.218665	−	0.418011i
$416$	−5.03108	−	2.90470i	−0.246669	−	0.142415i
$417$		0			0
$418$	−0.392798	−	0.105250i	−0.0192124	−	0.00514794i
$419$	−5.14214			−0.251210			−0.125605	−	0.992080i	$-0.540087\pi$
$419$	−5.14214			−0.251210			−0.125605	+	0.992080i	$0.540087\pi$
$420$		0			0
$421$	6.57058			0.320230			0.160115	−	0.987098i	$-0.448813\pi$
$421$	6.57058			0.320230			0.160115	+	0.987098i	$0.448813\pi$
$422$	1.84010	+	0.493053i	0.0895746	+	0.0240014i
$423$		0			0
$424$	−0.315715	−	0.182278i	−0.0153325	−	0.00885222i
$425$	35.4458	+	12.7411i	1.71938	+	0.618033i
$426$		0			0
$427$	9.86095	+	6.98314i	0.477205	+	0.337938i
$428$	17.6492	+	17.6492i	0.853105	+	0.853105i
$429$		0			0
$430$	−0.212136	+	0.0474743i	−0.0102301	+	0.00228941i
$431$	−1.26581	+	2.19244i	−0.0609718	+	0.105606i	−0.894900	−	0.446267i	$-0.852753\pi$
$431$	−1.26581	+	2.19244i	−0.0609718	+	0.105606i	0.833928	+	0.551873i	$0.186087\pi$
$432$		0			0
$433$	−8.64351	+	8.64351i	−0.415381	+	0.415381i	−0.883608	−	0.468227i	$-0.844893\pi$
$433$	−8.64351	+	8.64351i	−0.415381	+	0.415381i	0.468227	+	0.883608i	$0.344893\pi$
$434$	0.438372	−	1.18478i	0.0210425	−	0.0568712i
$435$		0			0
$436$	−6.27325	−	10.8656i	−0.300434	−	0.520367i
$437$	−3.95929	+	1.06089i	−0.189399	+	0.0507492i
$438$		0			0
$439$	−11.7845	−	20.4114i	−0.562444	−	0.974182i	−0.997282	−	0.0736734i	$-0.976528\pi$
$439$	−11.7845	−	20.4114i	−0.562444	−	0.974182i	0.434838	−	0.900509i	$-0.356806\pi$
$440$	−0.173034	+	4.15352i	−0.00824909	+	0.198011i
$441$		0			0
$442$	2.60635	−	2.60635i	0.123972	−	0.123972i
$443$	−3.14174	+	11.7251i	−0.149269	+	0.557078i	0.850260	+	0.526364i	$0.176445\pi$
$443$	−3.14174	+	11.7251i	−0.149269	+	0.557078i	−0.999528	+	0.0307144i	$0.990222\pi$
$444$		0			0
$445$	−21.3904	+	4.78698i	−1.01400	+	0.226925i
$446$	1.86427	−	1.07633i	0.0882756	−	0.0509659i
$447$		0			0
$448$	18.3194	−	8.42419i	0.865510	−	0.398006i
$449$		−	21.4176i		−	1.01076i	−0.862897	−	0.505380i	$-0.831352\pi$
$449$		−	21.4176i		−	1.01076i	0.862897	−	0.505380i	$-0.168648\pi$
$450$		0			0
$451$	23.1302	+	13.3542i	1.08916	+	0.628825i
$452$	9.31146	+	34.7508i	0.437974	+	1.63454i
$453$		0			0
$454$	−2.77227			−0.130109
$455$	−14.0384	+	18.1700i	−0.658131	+	0.851823i
$456$		0			0
$457$	−8.26213	−	2.21383i	−0.386486	−	0.103559i	0.0603436	−	0.998178i	$-0.480780\pi$
$457$	−8.26213	−	2.21383i	−0.386486	−	0.103559i	−0.446830	+	0.894619i	$0.647447\pi$
$458$	−0.0412987	−	0.154129i	−0.00192976	−	0.00720197i
$459$		0			0
$460$	9.67261	+	18.4906i	0.450988	+	0.862130i
$461$		−	10.8496i		−	0.505318i	−0.967555	−	0.252659i	$-0.918695\pi$
$461$		−	10.8496i		−	0.505318i	0.967555	−	0.252659i	$-0.0813051\pi$
$462$		0			0
$463$	11.9276	+	11.9276i	0.554322	+	0.554322i	0.927685	−	0.373363i	$-0.121795\pi$
$463$	11.9276	+	11.9276i	0.554322	+	0.554322i	−0.373363	+	0.927685i	$0.621795\pi$
$464$	−29.0319	+	16.7616i	−1.34777	+	0.778136i
$465$		0			0
$466$	1.83198	−	3.17309i	0.0848650	−	0.146990i
$467$	4.38785	−	16.3757i	0.203045	−	0.757776i	−0.786991	−	0.616964i	$-0.788362\pi$
$467$	4.38785	−	16.3757i	0.203045	−	0.757776i	0.990036	−	0.140811i	$-0.0449711\pi$
$468$		0			0
$469$	−15.8596	+	13.1647i	−0.732327	+	0.607890i
$470$	1.37430	+	1.49379i	0.0633919	+	0.0689033i
$471$		0			0
$472$	0.860905	−	0.230679i	0.0396263	−	0.0106178i
$473$	−2.75714	+	0.738772i	−0.126773	+	0.0339688i
$474$		0			0
$475$	0.362420	−	4.34221i	0.0166289	−	0.199234i
$476$	6.65983	+	38.9806i	0.305253	+	1.78667i
$477$		0			0
$478$	−0.464056	+	1.73188i	−0.0212254	+	0.0792144i
$479$	−4.40083	+	7.62247i	−0.201079	+	0.348279i	−0.948876	−	0.315648i	$-0.897778\pi$
$479$	−4.40083	+	7.62247i	−0.201079	+	0.348279i	0.747797	+	0.663927i	$0.231112\pi$
$480$		0			0
$481$	−38.9421	+	22.4832i	−1.77561	+	1.02515i
$482$	−2.44177	−	2.44177i	−0.111219	−	0.111219i
$483$		0			0
$484$			5.35889i			0.243586i
$485$	−9.26232	+	4.84520i	−0.420580	+	0.220009i
$486$		0			0
$487$	0.961805	+	3.58951i	0.0435836	+	0.162656i	0.984288	−	0.176572i	$-0.0565008\pi$
$487$	0.961805	+	3.58951i	0.0435836	+	0.162656i	−0.940704	+	0.339228i	$0.889834\pi$
$488$	2.21569	+	0.593691i	0.100299	+	0.0268751i
$489$		0			0
$490$	0.577098	+	1.88699i	0.0260706	+	0.0852455i
$491$	−19.1608			−0.864717			−0.432358	−	0.901702i	$-0.642318\pi$
$491$	−19.1608			−0.864717			−0.432358	+	0.901702i	$0.642318\pi$
$492$		0			0
$493$	−16.7384	−	62.4684i	−0.753858	−	2.81344i
$494$	−0.369272	−	0.213199i	−0.0166143	−	0.00959228i
$495$		0			0
$496$			14.7896i			0.664074i
$497$	−10.6732	−	23.2102i	−0.478759	−	1.04112i
$498$		0			0
$499$	−6.01766	+	3.47430i	−0.269387	+	0.155531i	−0.628609	−	0.777721i	$-0.716375\pi$
$499$	−6.01766	+	3.47430i	−0.269387	+	0.155531i	0.359222	+	0.933252i	$0.383042\pi$
$500$	−21.9755	+	3.02721i	−0.982773	+	0.135381i
$501$		0			0
$502$	−0.157208	+	0.586707i	−0.00701652	+	0.0261860i
$503$	−1.96117	+	1.96117i	−0.0874443	+	0.0874443i	−0.749476	−	0.662032i	$-0.769694\pi$
$503$	−1.96117	+	1.96117i	−0.0874443	+	0.0874443i	0.662032	+	0.749476i	$0.269694\pi$
$504$		0			0
$505$	14.3961	−	13.2446i	0.640620	−	0.589378i
$506$	−1.09742	−	1.90078i	−0.0487862	−	0.0845002i
$507$		0			0
$508$	21.8075	−	5.84330i	0.967552	−	0.259255i
$509$	8.67817	+	15.0310i	0.384653	+	0.666239i	0.991721	−	0.128411i	$-0.0409877\pi$
$509$	8.67817	+	15.0310i	0.384653	+	0.666239i	−0.607068	+	0.794650i	$0.707654\pi$
$510$		0			0
$511$	−11.0480	+	9.17073i	−0.488735	+	0.405689i
$512$	6.90664	−	6.90664i	0.305233	−	0.305233i
$513$		0			0
$514$	−0.619060	+	1.07224i	−0.0273056	+	0.0472947i
$515$	−6.20551	+	9.78377i	−0.273447	+	0.431125i
$516$		0			0
$517$	18.8463	+	18.8463i	0.828861	+	0.828861i
$518$	−0.357262	+	3.84779i	−0.0156972	+	0.169062i
$519$		0			0
$520$	−1.30246	+	4.15982i	−0.0571165	+	0.182420i
$521$	14.5104	+	8.37757i	0.635711	+	0.367028i	0.782961	−	0.622071i	$-0.213709\pi$
$521$	14.5104	+	8.37757i	0.635711	+	0.367028i	−0.147249	+	0.989099i	$0.547042\pi$
$522$		0			0
$523$	−7.02501	−	1.88235i	−0.307182	−	0.0823093i	0.101935	−	0.994791i	$-0.467497\pi$
$523$	−7.02501	−	1.88235i	−0.307182	−	0.0823093i	−0.409117	+	0.912482i	$0.634163\pi$
$524$	−32.9472			−1.43931
$525$		0			0
$526$	−3.60728			−0.157285
$527$	−27.5596	−	7.38458i	−1.20052	−	0.321677i
$528$		0			0
$529$	0.759206	+	0.438328i	0.0330089	+	0.0190577i
$530$	−0.0611364	+	0.195259i	−0.00265559	+	0.00848151i
$531$		0			0
$532$	4.15631	−	1.91128i	0.180199	−	0.0828646i
$533$	19.8026	+	19.8026i	0.857748	+	0.857748i
$534$		0			0
$535$	15.0665	−	23.7542i	0.651380	−	1.02698i
$536$	−1.95643	+	3.38864i	−0.0845049	+	0.146367i
$537$		0			0
$538$	−1.43471	+	1.43471i	−0.0618548	+	0.0618548i
$539$	8.60245	+	24.4406i	0.370534	+	1.05273i
$540$		0			0
$541$	11.1474	+	19.3079i	0.479266	+	0.830113i	0.999717	−	0.0237781i	$-0.00756951\pi$
$541$	11.1474	+	19.3079i	0.479266	+	0.830113i	−0.520451	+	0.853892i	$0.674236\pi$
$542$	−1.79528	+	0.481043i	−0.0771138	+	0.0206626i
$543$		0			0
$544$	5.63791	+	9.76515i	0.241723	+	0.418677i
$545$	−10.4058	+	9.57349i	−0.445737	+	0.410083i
$546$		0			0
$547$	−8.74792	+	8.74792i	−0.374034	+	0.374034i	−0.868944	−	0.494910i	$-0.835201\pi$
$547$	−8.74792	+	8.74792i	−0.374034	+	0.374034i	0.494910	+	0.868944i	$0.335201\pi$
$548$	0.272499	−	1.01698i	0.0116406	−	0.0434433i
$549$		0			0
$550$	2.29609	−	0.414328i	0.0979056	−	0.0176670i
$551$	−6.47910	+	3.74071i	−0.276019	+	0.159360i
$552$		0			0
$553$	9.96111	+	7.05407i	0.423590	+	0.299970i
$554$			1.03101i			0.0438033i
$555$		0			0
$556$	28.4486	+	16.4248i	1.20649	+	0.696567i
$557$	0.284761	+	1.06274i	0.0120657	+	0.0450299i	0.971696	−	0.236234i	$-0.0759131\pi$
$557$	0.284761	+	1.06274i	0.0120657	+	0.0450299i	−0.959631	+	0.281264i	$0.909246\pi$
$558$		0			0
$559$	−2.99298			−0.126590
$560$	−14.0025	−	18.3744i	−0.591713	−	0.776459i
$561$		0			0
$562$	−0.807376	−	0.216336i	−0.0340571	−	0.00912557i
$563$	−0.145941	−	0.544658i	−0.00615066	−	0.0229546i	0.962782	−	0.270278i	$-0.0871156\pi$
$563$	−0.145941	−	0.544658i	−0.00615066	−	0.0229546i	−0.968933	+	0.247323i	$0.920449\pi$
$564$		0			0
$565$	35.9267	−	18.7936i	1.51145	−	0.790652i
$566$		−	2.16826i		−	0.0911387i
$567$		0			0
$568$	−3.42928	−	3.42928i	−0.143889	−	0.143889i
$569$	6.51431	−	3.76104i	0.273094	−	0.157671i	−0.357199	−	0.934028i	$-0.616268\pi$
$569$	6.51431	−	3.76104i	0.273094	−	0.157671i	0.630293	+	0.776357i	$0.282935\pi$
$570$		0			0
$571$	8.37274	−	14.5020i	0.350388	−	0.606890i	−0.635929	−	0.771747i	$-0.719383\pi$
$571$	8.37274	−	14.5020i	0.350388	−	0.606890i	0.986317	+	0.164857i	$0.0527163\pi$
$572$	−7.37735	+	27.5326i	−0.308463	+	1.15120i
$573$		0			0
$574$	2.37234	−	0.405314i	0.0990196	−	0.0169175i
$575$	17.9551	−	15.1888i	0.748779	−	0.633415i
$576$		0			0
$577$	38.1758	−	10.2292i	1.58928	−	0.425846i	0.647495	−	0.762069i	$-0.275817\pi$
$577$	38.1758	−	10.2292i	1.58928	−	0.425846i	0.941782	+	0.336224i	$0.109150\pi$
$578$	−4.84038	+	1.29698i	−0.201333	+	0.0539471i
$579$		0			0
$580$	25.7877	+	28.0298i	1.07078	+	1.16387i
$581$	−10.6644	−	3.94587i	−0.442435	−	0.163702i
$582$		0			0
$583$	−0.695349	+	2.59508i	−0.0287984	+	0.107477i
$584$	−1.36288	+	2.36058i	−0.0563963	+	0.0976813i
$585$		0			0
$586$	−2.38670	+	1.37796i	−0.0985936	+	0.0569230i
$587$	−12.1014	−	12.1014i	−0.499478	−	0.499478i	0.411797	−	0.911276i	$-0.364901\pi$
$587$	−12.1014	−	12.1014i	−0.499478	−	0.499478i	−0.911276	+	0.411797i	$0.864901\pi$
$588$		0			0
$589$			3.30063i			0.136000i
$590$	−0.231864	−	0.443243i	−0.00954569	−	0.0182480i
$591$		0			0
$592$	−11.7093	−	43.6996i	−0.481248	−	1.79604i
$593$	27.1418	+	7.27262i	1.11458	+	0.298651i	0.768688	−	0.639624i	$-0.220910\pi$
$593$	27.1418	+	7.27262i	1.11458	+	0.298651i	0.345891	+	0.938275i	$0.387577\pi$
$594$		0			0
$595$	41.2311	−	16.9184i	1.69031	−	0.693586i
$596$	−15.3990			−0.630766
$597$		0			0
$598$	−0.595646	−	2.22298i	−0.0243578	−	0.0909044i
$599$	−14.3913	−	8.30881i	−0.588012	−	0.339489i	0.176299	−	0.984337i	$-0.443587\pi$
$599$	−14.3913	−	8.30881i	−0.588012	−	0.339489i	−0.764311	+	0.644848i	$0.776921\pi$
$600$		0			0
$601$		−	29.3634i		−	1.19776i	−0.800839	−	0.598880i	$-0.795613\pi$
$601$		−	29.3634i		−	1.19776i	0.800839	−	0.598880i	$-0.204387\pi$
$602$	−0.148649	+	0.209908i	−0.00605847	+	0.00855522i
$603$		0			0
$604$	−24.5952	+	14.2000i	−1.00076	+	0.577791i
$605$	5.89363	−	1.31894i	0.239610	−	0.0536227i
$606$		0			0
$607$	6.17995	−	23.0639i	0.250837	−	0.936135i	−0.719523	−	0.694469i	$-0.755639\pi$
$607$	6.17995	−	23.0639i	0.250837	−	0.936135i	0.970359	−	0.241666i	$-0.0776938\pi$
$608$	0.922359	−	0.922359i	0.0374066	−	0.0374066i
$609$		0			0
$610$	0.0535868	−	1.28630i	0.00216967	−	0.0520807i
$611$	13.9734	+	24.2026i	0.565303	+	0.979134i
$612$		0			0
$613$	−27.8223	+	7.45496i	−1.12373	+	0.301103i	−0.772393	−	0.635145i	$-0.780940\pi$
$613$	−27.8223	+	7.45496i	−1.12373	+	0.301103i	−0.351339	+	0.936248i	$0.614274\pi$
$614$	−0.0702519	−	0.121680i	−0.00283514	−	0.00491060i
$615$		0			0
$616$	3.14165	+	3.78476i	0.126581	+	0.152492i
$617$	−20.2319	+	20.2319i	−0.814506	+	0.814506i	−0.985306	−	0.170800i	$-0.945365\pi$
$617$	−20.2319	+	20.2319i	−0.814506	+	0.814506i	0.170800	+	0.985306i	$0.445365\pi$
$618$		0			0
$619$	−16.6641	+	28.8630i	−0.669785	+	1.16010i	0.308179	+	0.951328i	$0.400280\pi$
$619$	−16.6641	+	28.8630i	−0.669785	+	1.16010i	−0.977964	+	0.208773i	$0.933053\pi$
$620$	16.3978	−	3.66969i	0.658552	−	0.147378i
$621$		0			0
$622$	1.02384	+	1.02384i	0.0410521	+	0.0410521i
$623$	−14.9887	+	21.1657i	−0.600510	+	0.847986i
$624$		0			0
$625$	8.73794	+	23.4232i	0.349518	+	0.936930i
$626$	−1.09177	−	0.630336i	−0.0436361	−	0.0251933i
$627$		0			0
$628$	−24.3315	−	6.51959i	−0.970931	−	0.260160i
$629$	87.2782			3.48001
$630$		0			0
$631$	−40.8064			−1.62448			−0.812238	−	0.583327i	$-0.801751\pi$
$631$	−40.8064			−1.62448			−0.812238	+	0.583327i	$0.801751\pi$
$632$	2.23819	+	0.599721i	0.0890305	+	0.0238556i
$633$		0			0
$634$	−0.995658	−	0.574844i	−0.0395426	−	0.0228300i
$635$	−11.7937	−	22.5454i	−0.468019	−	0.894688i
$636$		0			0
$637$	2.07995	+	27.0886i	0.0824107	+	1.07329i
$638$	−2.83268	−	2.83268i	−0.112147	−	0.112147i
$639$		0			0
$640$	−7.46698	−	4.73605i	−0.295158	−	0.187209i
$641$	10.5565	−	18.2844i	0.416957	−	0.722191i	−0.578674	−	0.815559i	$-0.696430\pi$
$641$	10.5565	−	18.2844i	0.416957	−	0.722191i	0.995632	+	0.0933673i	$0.0297631\pi$
$642$		0			0
$643$	−24.4664	+	24.4664i	−0.964860	+	0.964860i	−0.999403	−	0.0345429i	$-0.989002\pi$
$643$	−24.4664	+	24.4664i	−0.964860	+	0.964860i	0.0345429	+	0.999403i	$0.489002\pi$
$644$	23.1568	+	8.56807i	0.912505	+	0.337629i
$645$		0			0
$646$	0.413811	+	0.716742i	0.0162812	+	0.0281999i
$647$	−3.04988	+	0.817214i	−0.119903	+	0.0321280i	−0.318272	−	0.948000i	$-0.603102\pi$
$647$	−3.04988	+	0.817214i	−0.119903	+	0.0321280i	0.198368	+	0.980128i	$0.436436\pi$
$648$		0			0
$649$	−3.28415	−	5.68831i	−0.128914	−	0.223286i
$650$	2.43797	+	0.203484i	0.0956252	+	0.00798128i
$651$		0			0
$652$	4.99261	−	4.99261i	0.195526	−	0.195526i
$653$	2.24234	−	8.36853i	0.0877496	−	0.327486i	−0.908071	−	0.418816i	$-0.862445\pi$
$653$	2.24234	−	8.36853i	0.0877496	−	0.327486i	0.995821	+	0.0913301i	$0.0291118\pi$
$654$		0			0
$655$	8.10906	+	36.2349i	0.316847	+	1.41582i
$656$	−24.4013	+	14.0881i	−0.952712	+	0.550049i
$657$		0			0
$658$	2.39141	+	0.222039i	0.0932270	+	0.00865600i
$659$			41.9974i			1.63599i	0.575228	+	0.817993i	$0.304913\pi$
$659$			41.9974i			1.63599i	−0.575228	+	0.817993i	$0.695087\pi$
$660$		0			0
$661$	−38.1356	−	22.0176i	−1.48330	−	0.856385i	−0.483482	−	0.875354i	$-0.660628\pi$
$661$	−38.1356	−	22.0176i	−1.48330	−	0.856385i	−0.999820	+	0.0189695i	$0.993961\pi$
$662$	−0.865176	−	3.22888i	−0.0336260	−	0.125494i
$663$		0			0
$664$	−2.15866			−0.0837721
$665$	−3.12496	−	4.10064i	−0.121181	−	0.159016i
$666$		0			0
$667$	−39.0036	−	10.4510i	−1.51022	−	0.404663i
$668$	−8.38378	−	31.2887i	−0.324378	−	1.21060i
$669$		0			0
$670$	2.09576	+	0.656189i	0.0809661	+	0.0253508i
$671$		−	16.9046i		−	0.652596i
$672$		0			0
$673$	−17.4071	−	17.4071i	−0.670993	−	0.670993i	0.286952	−	0.957945i	$-0.407358\pi$
$673$	−17.4071	−	17.4071i	−0.670993	−	0.670993i	−0.957945	+	0.286952i	$0.907358\pi$
$674$	1.69279	−	0.977335i	0.0652040	−	0.0376455i
$675$		0			0
$676$	−2.04721	+	3.54586i	−0.0787387	+	0.136379i
$677$	6.21465	−	23.1934i	0.238848	−	0.891394i	−0.737528	−	0.675317i	$-0.764007\pi$
$677$	6.21465	−	23.1934i	0.238848	−	0.891394i	0.976376	−	0.216078i	$-0.0693264\pi$
$678$		0			0
$679$	−4.29192	+	11.5997i	−0.164709	+	0.445155i
$680$	6.22636	−	5.72833i	0.238770	−	0.219671i
$681$		0			0
$682$	−1.70714	+	0.457426i	−0.0653696	+	0.0175157i
$683$	16.8662	−	4.51928i	0.645366	−	0.172925i	0.0787333	−	0.996896i	$-0.474912\pi$
$683$	16.8662	−	4.51928i	0.645366	−	0.172925i	0.566633	+	0.823970i	$0.308246\pi$
$684$		0			0
$685$	−1.18553	−	0.0493888i	−0.0452968	−	0.00188705i
$686$	2.00312	+	1.19950i	0.0764794	+	0.0457971i
$687$		0			0
$688$	0.779373	−	2.90866i	0.0297133	−	0.110892i
$689$	−1.40853	+	2.43965i	−0.0536608	+	0.0929432i
$690$		0			0
$691$	18.6772	−	10.7833i	0.710515	−	0.410216i	−0.100736	−	0.994913i	$-0.532120\pi$
$691$	18.6772	−	10.7833i	0.710515	−	0.410216i	0.811252	+	0.584697i	$0.198787\pi$
$692$	−1.95122	−	1.95122i	−0.0741741	−	0.0741741i
$693$		0			0
$694$			2.06723i			0.0784711i
$695$	11.0619	−	35.3299i	0.419603	−	1.34014i
$696$		0			0
$697$	−14.0686	−	52.5048i	−0.532887	−	1.98876i
$698$	−1.97202	−	0.528402i	−0.0746421	−	0.0200003i
$699$		0			0
$700$	−16.8980	+	20.0843i	−0.638683	+	0.759114i
$701$	22.3591			0.844490			0.422245	−	0.906482i	$-0.361242\pi$
$701$	22.3591			0.844490			0.422245	+	0.906482i	$0.361242\pi$
$702$		0			0
$703$	−2.61318	−	9.75251i	−0.0985579	−	0.367823i
$704$	−24.4299	−	14.1046i	−0.920738	−	0.531588i
$705$		0			0
$706$			1.43269i			0.0539201i
$707$	2.13987	−	23.0469i	0.0804781	−	0.866766i
$708$		0			0
$709$	18.6895	−	10.7904i	0.701901	−	0.405243i	−0.106154	−	0.994350i	$-0.533854\pi$
$709$	18.6895	−	10.7904i	0.701901	−	0.405243i	0.808055	+	0.589107i	$0.200520\pi$
$710$	−1.45789	+	2.29854i	−0.0547135	+	0.0862627i
$711$		0			0
$712$	−1.27431	+	4.75578i	−0.0477567	+	0.178230i
$713$	−12.5967	+	12.5967i	−0.471752	+	0.471752i
$714$		0			0
$715$	32.0958	+	1.33710i	1.20031	+	0.0500047i
$716$	9.32708	+	16.1550i	0.348570	+	0.603740i
$717$		0			0
$718$	3.95547	−	1.05986i	0.147617	−	0.0395538i
$719$	−22.2333	−	38.5092i	−0.829162	−	1.43615i	−0.898696	−	0.438571i	$-0.855485\pi$
$719$	−22.2333	−	38.5092i	−0.829162	−	1.43615i	0.0695345	−	0.997580i	$-0.477849\pi$
$720$		0			0
$721$	2.30864	+	13.5127i	0.0859784	+	0.503239i
$722$	−1.62602	+	1.62602i	−0.0605141	+	0.0605141i
$723$		0			0
$724$	−15.3839	+	26.6458i	−0.571740	+	0.990282i
$725$	24.4798	−	35.2598i	0.909157	−	1.30951i
$726$		0			0
$727$	6.94393	+	6.94393i	0.257536	+	0.257536i	0.824051	−	0.566515i	$-0.191709\pi$
$727$	6.94393	+	6.94393i	0.257536	+	0.257536i	−0.566515	+	0.824051i	$0.691709\pi$
$728$	2.15481	+	4.68588i	0.0798625	+	0.173670i
$729$		0			0
$730$	1.45993	+	0.457111i	0.0540346	+	0.0169184i
$731$	5.03097	+	2.90463i	0.186077	+	0.107432i
$732$		0			0
$733$	14.2431	+	3.81642i	0.526080	+	0.140963i	0.512077	−	0.858939i	$-0.328876\pi$
$733$	14.2431	+	3.81642i	0.526080	+	0.140963i	0.0140023	+	0.999902i	$0.495543\pi$
$734$	2.19654			0.0810758
$735$		0			0
$736$	7.04031			0.259509
$737$	27.8535	+	7.46332i	1.02600	+	0.274915i
$738$		0			0
$739$	26.2034	+	15.1285i	0.963908	+	0.556512i	0.897374	−	0.441272i	$-0.145473\pi$
$739$	26.2034	+	15.1285i	0.963908	+	0.556512i	0.0665342	+	0.997784i	$0.478806\pi$
$740$	−45.5460	+	23.8255i	−1.67430	+	0.875843i
$741$		0			0
$742$	0.101145	+	0.219952i	0.00371316	+	0.00807470i
$743$	−17.1499	−	17.1499i	−0.629167	−	0.629167i	0.318691	−	0.947859i	$-0.396757\pi$
$743$	−17.1499	−	17.1499i	−0.629167	−	0.629167i	−0.947859	+	0.318691i	$0.896757\pi$
$744$		0			0
$745$	3.79003	+	16.9356i	0.138856	+	0.620471i
$746$	0.492758	−	0.853482i	0.0180411	−	0.0312482i
$747$		0			0
$748$	39.1207	−	39.1207i	1.43039	−	1.43039i
$749$	−5.60519	−	32.8077i	−0.204809	−	1.19877i
$750$		0			0
$751$	−22.6658	−	39.2583i	−0.827087	−	1.43256i	−0.900314	−	0.435242i	$-0.856663\pi$
$751$	−22.6658	−	39.2583i	−0.827087	−	1.43256i	0.0732264	−	0.997315i	$-0.476670\pi$
$752$	−27.1594	+	7.27735i	−0.990403	+	0.265378i
$753$		0			0
$754$	−2.10025	−	3.63775i	−0.0764867	−	0.132479i
$755$	21.6704	+	23.5545i	0.788668	+	0.857236i
$756$		0			0
$757$	20.6760	−	20.6760i	0.751482	−	0.751482i	−0.223273	−	0.974756i	$-0.571674\pi$
$757$	20.6760	−	20.6760i	0.751482	−	0.751482i	0.974756	+	0.223273i	$0.0716743\pi$
$758$	−0.148434	+	0.553962i	−0.00539135	+	0.0201208i
$759$		0			0
$760$	−0.826509	−	0.524226i	−0.0299806	−	0.0190157i
$761$	−8.05627	+	4.65129i	−0.292039	+	0.168609i	−0.638861	−	0.769322i	$-0.720594\pi$
$761$	−8.05627	+	4.65129i	−0.292039	+	0.168609i	0.346822	+	0.937931i	$0.387261\pi$
$762$		0			0
$763$	−1.54674	+	16.6587i	−0.0559958	+	0.603087i
$764$		−	45.0171i		−	1.62866i
$765$		0			0
$766$	−0.391011	−	0.225750i	−0.0141278	−	0.00815669i
$767$	−1.78254	−	6.65252i	−0.0643637	−	0.240209i
$768$		0			0
$769$	42.1028			1.51827			0.759133	−	0.650936i	$-0.225623\pi$
$769$	42.1028			1.51827			0.759133	+	0.650936i	$0.225623\pi$
$770$	1.68784	−	2.18458i	0.0608254	−	0.0787267i
$771$		0			0
$772$	7.42379	+	1.98920i	0.267188	+	0.0715929i
$773$	−0.252193	−	0.941195i	−0.00907074	−	0.0338524i	0.961242	−	0.275706i	$-0.0889115\pi$
$773$	−0.252193	−	0.941195i	−0.00907074	−	0.0338524i	−0.970313	+	0.241853i	$0.922245\pi$
$774$		0			0
$775$	−8.07175	−	17.1309i	−0.289946	−	0.615360i
$776$			2.34796i			0.0842870i
$777$		0			0
$778$	−1.30916	−	1.30916i	−0.0469356	−	0.0469356i
$779$	−5.44569	+	3.14407i	−0.195112	+	0.112648i
$780$		0			0
$781$	−17.8702	+	30.9521i	−0.639446	+	1.10755i
$782$	−1.15613	+	4.31472i	−0.0413430	+	0.154294i
$783$		0			0
$784$	−26.8670	−	5.03251i	−0.959536	−	0.179733i
$785$	−1.18164	+	28.3640i	−0.0421744	+	1.01236i
$786$		0			0
$787$	−3.15985	+	0.846679i	−0.112636	+	0.0301809i	−0.314697	−	0.949192i	$-0.601903\pi$
$787$	−3.15985	+	0.846679i	−0.112636	+	0.0301809i	0.202061	+	0.979373i	$0.435236\pi$
$788$	−17.9053	+	4.79772i	−0.637851	+	0.170912i
$789$		0			0
$790$	0.0541311	−	1.29936i	0.00192590	−	0.0462293i
$791$	16.6475	−	44.9929i	0.591917	−	1.59976i
$792$		0			0
$793$	4.58767	−	17.1214i	0.162913	−	0.607999i
$794$	1.37554	−	2.38251i	0.0488162	−	0.0845521i
$795$		0			0
$796$	−12.4687	+	7.19882i	−0.441942	+	0.255155i
$797$	4.62151	+	4.62151i	0.163702	+	0.163702i	0.784205	−	0.620502i	$-0.213071\pi$
$797$	4.62151	+	4.62151i	0.163702	+	0.163702i	−0.620502	+	0.784205i	$0.713071\pi$
$798$		0			0
$799$		−	54.2437i		−	1.91900i
$800$	−2.53158	+	7.04287i	−0.0895048	+	0.249003i
$801$		0			0
$802$	0.270571	+	1.00978i	0.00955419	+	0.0356567i
$803$	19.4032	+	5.19906i	0.684723	+	0.183471i
$804$		0			0
$805$	3.72364	−	27.5763i	0.131241	−	0.971936i
$806$	−1.85317			−0.0652750
$807$		0			0
$808$	−1.13725	−	4.24427i	−0.0400083	−	0.149313i
$809$	−15.4219	−	8.90381i	−0.542204	−	0.313041i	0.203768	−	0.979019i	$-0.434681\pi$
$809$	−15.4219	−	8.90381i	−0.542204	−	0.313041i	−0.745972	+	0.665978i	$0.768015\pi$
$810$		0			0
$811$			9.97110i			0.350133i	0.984557	+	0.175066i	$0.0560140\pi$
$811$			9.97110i			0.350133i	−0.984557	+	0.175066i	$0.943986\pi$
$812$	44.8730	+	4.16640i	1.57473	+	0.146212i
$813$		0			0
$814$	4.68200	−	2.70315i	0.164104	−	0.0947455i
$815$	−6.71960	−	4.26201i	−0.235377	−	0.149292i
$816$		0			0
$817$	0.173934	−	0.649131i	0.00608518	−	0.0227102i
$818$	2.20852	−	2.20852i	0.0772192	−	0.0772192i
$819$		0			0
$820$	21.6746	+	23.5591i	0.756912	+	0.822718i
$821$	−2.44834	−	4.24064i	−0.0854475	−	0.147999i	0.820134	−	0.572171i	$-0.193899\pi$
$821$	−2.44834	−	4.24064i	−0.0854475	−	0.147999i	−0.905582	+	0.424172i	$0.860565\pi$
$822$		0			0
$823$	−51.0981	+	13.6917i	−1.78117	+	0.477262i	−0.990796	−	0.135366i	$-0.956779\pi$
$823$	−51.0981	+	13.6917i	−1.78117	+	0.477262i	−0.790371	+	0.612628i	$0.790112\pi$
$824$	1.30120	+	2.25374i	0.0453294	+	0.0785129i
$825$		0			0
$826$	−0.555095	−	0.205387i	−0.0193142	−	0.00714633i
$827$	27.3882	−	27.3882i	0.952381	−	0.952381i	−0.0465353	−	0.998917i	$-0.514818\pi$
$827$	27.3882	−	27.3882i	0.952381	−	0.952381i	0.998917	+	0.0465353i	$0.0148180\pi$
$828$		0			0
$829$	−22.4350	+	38.8585i	−0.779199	+	1.34961i	0.153205	+	0.988194i	$0.451040\pi$
$829$	−22.4350	+	38.8585i	−0.779199	+	1.34961i	−0.932404	+	0.361417i	$0.882293\pi$
$830$	0.264587	+	1.18229i	0.00918396	+	0.0410380i
$831$		0			0
$832$	−20.9154	−	20.9154i	−0.725112	−	0.725112i
$833$	22.7927	−	47.5524i	0.789721	−	1.64759i
$834$		0			0
$835$	−32.3474	+	16.9212i	−1.11943	+	0.585583i
$836$	−5.54267	−	3.20006i	−0.191697	−	0.110676i
$837$		0			0
$838$	0.626167	+	0.167781i	0.0216306	+	0.00579590i
$839$	−29.7013			−1.02540			−0.512702	−	0.858567i	$-0.671355\pi$
$839$	−29.7013			−1.02540			−0.512702	+	0.858567i	$0.671355\pi$
$840$		0			0
$841$	−44.7005			−1.54140
$842$	−0.800109	−	0.214389i	−0.0275736	−	0.00738832i
$843$		0			0
$844$	25.9652	+	14.9910i	0.893758	+	0.516011i
$845$	4.40355	+	1.37877i	0.151487	+	0.0474311i
$846$		0			0
$847$	4.12980	−	5.83173i	0.141902	−	0.200380i
$848$	−2.00413	−	2.00413i	−0.0688222	−	0.0688222i
$849$		0			0
$850$	−3.90057	−	2.70805i	−0.133788	−	0.0928853i
$851$	27.2471	−	47.1933i	0.934017	−	1.61776i
$852$		0			0
$853$	−16.7608	+	16.7608i	−0.573879	+	0.573879i	−0.933210	−	0.359331i	$-0.883005\pi$
$853$	−16.7608	+	16.7608i	−0.573879	+	0.573879i	0.359331	+	0.933210i	$0.383005\pi$
$854$	−0.972934	−	1.17210i	−0.0332931	−	0.0401083i
$855$		0			0
$856$	−3.15920	−	5.47190i	−0.107979	−	0.187026i
$857$	10.0064	−	2.68121i	0.341813	−	0.0915885i	−0.0838291	−	0.996480i	$-0.526715\pi$
$857$	10.0064	−	2.68121i	0.341813	−	0.0915885i	0.425642	+	0.904892i	$0.360048\pi$
$858$		0			0
$859$	15.8885	+	27.5197i	0.542109	+	0.938960i	0.998783	+	0.0493256i	$0.0157072\pi$
$859$	15.8885	+	27.5197i	0.542109	+	0.938960i	−0.456674	+	0.889634i	$0.650959\pi$
$860$	−3.41832	−	0.142406i	−0.116564	−	0.00485601i
$861$		0			0
$862$	0.225676	−	0.225676i	0.00768654	−	0.00768654i
$863$	2.76308	−	10.3119i	0.0940562	−	0.351022i	−0.902818	−	0.430022i	$-0.858506\pi$
$863$	2.76308	−	10.3119i	0.0940562	−	0.351022i	0.996875	+	0.0789994i	$0.0251725\pi$
$864$		0			0
$865$	−1.66568	+	2.62616i	−0.0566349	+	0.0892921i
$866$	1.33456	−	0.770508i	0.0453502	−	0.0261829i
$867$		0			0
$868$	11.4903	−	16.2256i	0.390007	−	0.550732i
$869$		−	17.0763i		−	0.579275i
$870$		0			0
$871$	26.1852	+	15.1181i	0.887253	+	0.512256i
$872$	0.822028	+	3.06785i	0.0278374	+	0.103890i
$873$		0			0
$874$	0.516745			0.0174792
$875$	26.2474	+	13.6410i	0.887323	+	0.461149i
$876$		0			0
$877$	37.0750	+	9.93421i	1.25193	+	0.335454i	0.823083	−	0.567921i	$-0.192252\pi$
$877$	37.0750	+	9.93421i	1.25193	+	0.335454i	0.428850	+	0.903376i	$0.358919\pi$
$878$	0.769024	+	2.87004i	0.0259533	+	0.0968591i
$879$		0			0
$880$	−9.65717	+	30.8433i	−0.325543	+	1.03973i
$881$			49.3063i			1.66117i	0.556892	+	0.830585i	$0.311994\pi$
$881$			49.3063i			1.66117i	−0.556892	+	0.830585i	$0.688006\pi$
$882$		0			0
$883$	2.45973	+	2.45973i	0.0827765	+	0.0827765i	0.747283	−	0.664506i	$-0.231358\pi$
$883$	2.45973	+	2.45973i	0.0827765	+	0.0827765i	−0.664506	+	0.747283i	$0.731358\pi$
$884$	50.2391	−	29.0056i	1.68972	−	0.975563i
$885$		0			0
$886$	0.765149	−	1.32528i	0.0257057	−	0.0445236i
$887$	−2.92519	+	10.9169i	−0.0982182	+	0.366555i	−0.997488	−	0.0708396i	$-0.977432\pi$
$887$	−2.92519	+	10.9169i	−0.0982182	+	0.366555i	0.899270	+	0.437395i	$0.144099\pi$
$888$		0			0
$889$	−28.2348	−	10.4470i	−0.946965	−	0.350380i
$890$	2.76093	+	0.115020i	0.0925466	+	0.00385546i
$891$		0			0
$892$	32.7253	−	8.76873i	1.09573	−	0.293599i
$893$	−6.06122	+	1.62410i	−0.202831	+	0.0543484i
$894$		0			0
$895$	15.4714	−	14.2339i	0.517152	−	0.475787i
$896$	−10.3129	+	1.76196i	−0.344530	+	0.0588629i
$897$		0			0
$898$	−0.698827	+	2.60806i	−0.0233202	+	0.0870321i
$899$	−16.2575	+	28.1588i	−0.542217	+	0.939147i
$900$		0			0
$901$	4.73527	−	2.73391i	0.157755	−	0.0910797i
$902$	−2.38087	−	2.38087i	−0.0792743	−	0.0792743i
$903$		0			0
$904$		−	9.10730i		−	0.302904i
$905$	33.0910	+	10.3609i	1.09998	+	0.344409i
$906$		0			0
$907$	−0.612212	−	2.28481i	−0.0203282	−	0.0758657i	0.955017	−	0.296552i	$-0.0958369\pi$
$907$	−0.612212	−	2.28481i	−0.0203282	−	0.0758657i	−0.975345	+	0.220687i	$0.929170\pi$
$908$	−42.1446	−	11.2926i	−1.39862	−	0.374758i
$909$		0			0
$910$	2.30234	−	1.75454i	0.0763218	−	0.0581623i
$911$	−29.0548			−0.962629			−0.481315	−	0.876548i	$-0.659841\pi$
$911$	−29.0548			−0.962629			−0.481315	+	0.876548i	$0.659841\pi$
$912$		0			0
$913$	4.11738	+	15.3663i	0.136265	+	0.508550i
$914$	0.933858	+	0.539163i	0.0308893	+	0.0178339i
$915$		0			0
$916$		−	2.51133i		−	0.0829766i
$917$	35.8543	+	25.3906i	1.18401	+	0.838472i
$918$		0			0
$919$	10.5899	−	6.11407i	0.349328	−	0.201685i	−0.315061	−	0.949071i	$-0.602025\pi$
$919$	10.5899	−	6.11407i	0.349328	−	0.201685i	0.664389	+	0.747387i	$0.268692\pi$
$920$	−1.15365	−	5.15504i	−0.0380348	−	0.169957i
$921$		0			0
$922$	−0.354008	+	1.32118i	−0.0116586	+	0.0435106i
$923$	−26.4993	+	26.4993i	−0.872234	+	0.872234i
$924$		0			0
$925$	37.4129	+	44.2269i	1.23013	+	1.45417i
$926$	−1.06326	−	1.84162i	−0.0349409	−	0.0605195i
$927$		0			0
$928$	12.4121	−	3.32581i	0.407447	−	0.109175i
$929$	−8.75296	−	15.1606i	−0.287175	−	0.497402i	0.685959	−	0.727640i	$-0.259383\pi$
$929$	−8.75296	−	15.1606i	−0.287175	−	0.497402i	−0.973134	+	0.230238i	$0.926050\pi$
$930$		0			0
$931$	−5.99596	−	1.12312i	−0.196510	−	0.0368086i
$932$	40.7755	−	40.7755i	1.33565	−	1.33565i
$933$		0			0
$934$	−1.06863	+	1.85092i	−0.0349666	+	0.0605640i
$935$	−52.6529	−	33.3959i	−1.72193	−	1.09216i
$936$		0			0
$937$	5.41861	+	5.41861i	0.177018	+	0.177018i	0.790055	−	0.613036i	$-0.210052\pi$
$937$	5.41861	+	5.41861i	0.177018	+	0.177018i	−0.613036	+	0.790055i	$0.710052\pi$
$938$	2.36079	−	1.08561i	0.0770825	−	0.0354465i
$939$		0			0
$940$	14.8076	+	28.3070i	0.482972	+	0.923273i
$941$	21.8564	+	12.6188i	0.712499	+	0.411361i	0.811986	−	0.583677i	$-0.198387\pi$
$941$	21.8564	+	12.6188i	0.712499	+	0.411361i	−0.0994867	+	0.995039i	$0.531720\pi$
$942$		0			0
$943$	−32.7826	−	8.78406i	−1.06755	−	0.286048i
$944$	6.92927			0.225529
$945$		0			0
$946$	0.359846			0.0116996
$947$	35.7370	+	9.57571i	1.16130	+	0.311169i	0.787484	−	0.616335i	$-0.211383\pi$
$947$	35.7370	+	9.57571i	1.16130	+	0.311169i	0.373813	+	0.927504i	$0.378050\pi$
$948$		0			0
$949$	18.2410	+	10.5315i	0.592129	+	0.341866i
$950$	−0.185813	+	0.516933i	−0.00602856	+	0.0167715i
$951$		0			0
$952$	0.925498	−	9.96781i	0.0299956	−	0.323059i
$953$	−21.4026	−	21.4026i	−0.693300	−	0.693300i	0.269657	−	0.962956i	$-0.413090\pi$
$953$	−21.4026	−	21.4026i	−0.693300	−	0.693300i	−0.962956	+	0.269657i	$0.913090\pi$
$954$		0			0
$955$	−49.5092	+	11.0797i	−1.60208	+	0.358531i
$956$	−14.1094	+	24.4381i	−0.456329	+	0.790386i
$957$		0			0
$958$	0.784607	−	0.784607i	0.0253495	−	0.0253495i
$959$	−1.08027	+	0.896714i	−0.0348839	+	0.0289564i
$960$		0			0
$961$	−8.32758	−	14.4238i	−0.268632	−	0.465284i
$962$	5.47563	−	1.46719i	0.176542	−	0.0473042i
$963$		0			0
$964$	−27.1739	−	47.0666i	−0.875213	−	1.51591i
$965$	0.360530	−	8.65417i	0.0116059	−	0.278588i
$966$		0			0
$967$	15.5584	−	15.5584i	0.500324	−	0.500324i	−0.411215	−	0.911538i	$-0.634895\pi$
$967$	15.5584	−	15.5584i	0.500324	−	0.500324i	0.911538	+	0.411215i	$0.134895\pi$
$968$	0.351106	−	1.31035i	0.0112850	−	0.0421161i
$969$		0			0
$970$	1.28598	−	0.287791i	0.0412903	−	0.00924041i
$971$	26.4963	−	15.2976i	0.850307	−	0.490925i	−0.0104475	−	0.999945i	$-0.503326\pi$
$971$	26.4963	−	15.2976i	0.850307	−	0.490925i	0.860754	+	0.509021i	$0.169992\pi$
$972$		0			0
$973$	−18.3011	−	39.7978i	−0.586705	−	1.27586i
$974$		−	0.468482i		−	0.0150111i
$975$		0			0
$976$	15.4444	+	8.91683i	0.494364	+	0.285421i
$977$	−0.395776	−	1.47706i	−0.0126620	−	0.0472552i	0.959306	−	0.282369i	$-0.0911203\pi$
$977$	−0.395776	−	1.47706i	−0.0126620	−	0.0472552i	−0.971968	+	0.235114i	$0.924454\pi$
$978$		0			0
$979$	36.2844			1.15965
$980$	1.08666	+	31.0372i	0.0347122	+	0.991446i
$981$		0			0
$982$	2.33325	+	0.625191i	0.0744569	+	0.0199507i
$983$	2.36631	+	8.83120i	0.0754737	+	0.281672i	0.993340	−	0.115217i	$-0.0367565\pi$
$983$	2.36631	+	8.83120i	0.0754737	+	0.281672i	−0.917867	+	0.396889i	$0.870090\pi$
$984$		0			0
$985$	9.68337	+	18.5112i	0.308538	+	0.589816i
$986$			8.15303i			0.259645i
$987$		0			0
$988$	−4.74529	−	4.74529i	−0.150968	−	0.150968i
$989$	3.14120	−	1.81357i	0.0998844	−	0.0576683i
$990$		0			0
$991$	11.8195	−	20.4719i	0.375457	−	0.650311i	−0.614938	−	0.788575i	$-0.710819\pi$
$991$	11.8195	−	20.4719i	0.375457	−	0.650311i	0.990395	+	0.138264i	$0.0441523\pi$
$992$	1.46727	−	5.47593i	0.0465859	−	0.173861i
$993$		0			0
$994$	0.542379	+	3.17459i	0.0172032	+	0.100692i
$995$	10.9860	+	11.9411i	0.348280	+	0.378559i
$996$		0			0
$997$	59.2973	−	15.8887i	1.87796	−	0.503199i	0.878278	−	0.478150i	$-0.158693\pi$
$997$	59.2973	−	15.8887i	1.87796	−	0.503199i	0.999686	−	0.0250488i	$-0.00797413\pi$
$998$	0.846141	−	0.226723i	0.0267841	−	0.00717678i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.cc.a.703.16	yes	128
3.2	odd	2	inner	945.2.cc.a.703.17	yes	128
5.2	odd	4	inner	945.2.cc.a.892.17	yes	128
7.5	odd	6	inner	945.2.cc.a.838.17	yes	128
15.2	even	4	inner	945.2.cc.a.892.16	yes	128
21.5	even	6	inner	945.2.cc.a.838.16	yes	128
35.12	even	12	inner	945.2.cc.a.82.16	✓	128
105.47	odd	12	inner	945.2.cc.a.82.17	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.cc.a.82.16	✓	128	35.12	even	12	inner
945.2.cc.a.82.17	yes	128	105.47	odd	12	inner
945.2.cc.a.703.16	yes	128	1.1	even	1	trivial
945.2.cc.a.703.17	yes	128	3.2	odd	2	inner
945.2.cc.a.838.16	yes	128	21.5	even	6	inner
945.2.cc.a.838.17	yes	128	7.5	odd	6	inner
945.2.cc.a.892.16	yes	128	15.2	even	4	inner
945.2.cc.a.892.17	yes	128	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.cc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.121772 - 0.0326286i) q^{2} +(-1.71829 - 0.992054i) q^{4} +(-0.668137 + 2.13391i) q^{5} +(1.10538 + 2.40378i) q^{7} +(0.355155 + 0.355155i) q^{8} +O(q^{10})\)	\(q+(-0.121772 - 0.0326286i) q^{2} +(-1.71829 - 0.992054i) q^{4} +(-0.668137 + 2.13391i) q^{5} +(1.10538 + 2.40378i) q^{7} +(0.355155 + 0.355155i) q^{8} +(0.150987 - 0.238050i) q^{10} +(1.85074 - 3.20557i) q^{11} +(2.74441 - 2.74441i) q^{13} +(-0.0561718 - 0.328778i) q^{14} +(1.95245 + 3.38174i) q^{16} +(-7.27655 + 1.94975i) q^{17} +(0.435731 + 0.754709i) q^{19} +(3.26501 - 3.00385i) q^{20} +(-0.329960 + 0.329960i) q^{22} +(-1.21737 + 4.54328i) q^{23} +(-4.10719 - 2.85150i) q^{25} +(-0.423738 + 0.244645i) q^{26} +(0.485317 - 5.22697i) q^{28} +8.58490i q^{29} +(3.28003 + 1.89373i) q^{31} +(-0.387403 - 1.44581i) q^{32} +0.949694 q^{34} +(-5.86800 + 0.752731i) q^{35} +(-11.1910 - 2.99861i) q^{37} +(-0.0284346 - 0.106119i) q^{38} +(-0.995163 + 0.520578i) q^{40} +7.21562i q^{41} +(-0.545286 - 0.545286i) q^{43} +(-6.36019 + 3.67206i) q^{44} +(0.296481 - 0.513521i) q^{46} +(-1.86365 + 6.95523i) q^{47} +(-4.55628 + 5.31416i) q^{49} +(0.407098 + 0.481243i) q^{50} +(-7.43829 + 1.99308i) q^{52} +(-0.701093 + 0.187857i) q^{53} +(5.60387 + 6.09108i) q^{55} +(-0.461133 + 1.24629i) q^{56} +(0.280113 - 1.04540i) q^{58} +(0.887254 - 1.53677i) q^{59} +(3.95514 - 2.28350i) q^{61} +(-0.337625 - 0.337625i) q^{62} -7.62109i q^{64} +(4.02270 + 7.68999i) q^{65} +(2.01631 + 7.52498i) q^{67} +(14.4375 + 3.86850i) q^{68} +(0.739116 + 0.0998033i) q^{70} -9.65572 q^{71} +(1.40459 + 5.24201i) q^{73} +(1.26490 + 0.730291i) q^{74} -1.72907i q^{76} +(9.75124 + 0.905389i) q^{77} +(3.99531 - 2.30670i) q^{79} +(-8.52084 + 1.90689i) q^{80} +(0.235436 - 0.878657i) q^{82} +(-3.03903 + 3.03903i) q^{83} +(0.701142 - 16.8302i) q^{85} +(0.0486084 + 0.0841923i) q^{86} +(1.79577 - 0.481176i) q^{88} +(4.90134 + 8.48937i) q^{89} +(9.63057 + 3.56334i) q^{91} +(6.59896 - 6.59896i) q^{92} +(0.453879 - 0.786141i) q^{94} +(-1.90161 + 0.425564i) q^{95} +(3.30555 + 3.30555i) q^{97} +(0.728219 - 0.498449i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 8 q^{7}+O(q^{10}) \) 128 * q - 8 * q^7	\( 128 q - 8 q^{7} + 24 q^{10} + 64 q^{16} - 32 q^{22} + 8 q^{25} - 8 q^{28} - 8 q^{37} + 120 q^{40} - 32 q^{43} - 48 q^{58} - 24 q^{61} + 16 q^{67} + 160 q^{70} - 144 q^{73} - 168 q^{82} - 32 q^{85} - 96 q^{88} - 120 q^{91}+O(q^{100}) \) 128 * q - 8 * q^7 + 24 * q^10 + 64 * q^16 - 32 * q^22 + 8 * q^25 - 8 * q^28 - 8 * q^37 + 120 * q^40 - 32 * q^43 - 48 * q^58 - 24 * q^61 + 16 * q^67 + 160 * q^70 - 144 * q^73 - 168 * q^82 - 32 * q^85 - 96 * q^88 - 120 * q^91

Introduction

L-functions

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