LMFDB - Embedded newform 945.2.cc.a.892.16

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			892.16
Character	$\chi$	$=$	945.892
Dual form			945.2.cc.a.838.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0326286 + 0.121772i) q^{2} +(1.71829 + 0.992054i) q^{4} +(2.18209 + 0.488334i) q^{5} +(-2.40378 + 1.10538i) q^{7} +(-0.355155 + 0.355155i) q^{8} +O(q^{10})$	\(q+(-0.0326286 + 0.121772i) q^{2} +(1.71829 + 0.992054i) q^{4} +(2.18209 + 0.488334i) q^{5} +(-2.40378 + 1.10538i) q^{7} +(-0.355155 + 0.355155i) q^{8} +(-0.130664 + 0.249783i) q^{10} +(-1.85074 + 3.20557i) q^{11} +(-2.74441 - 2.74441i) q^{13} +(-0.0561718 - 0.328778i) q^{14} +(1.95245 + 3.38174i) q^{16} +(1.94975 + 7.27655i) q^{17} +(-0.435731 - 0.754709i) q^{19} +(3.26501 + 3.00385i) q^{20} +(-0.329960 - 0.329960i) q^{22} +(-4.54328 - 1.21737i) q^{23} +(4.52306 + 2.13118i) q^{25} +(0.423738 - 0.244645i) q^{26} +(-5.22697 - 0.485317i) q^{28} +8.58490i q^{29} +(3.28003 + 1.89373i) q^{31} +(-1.44581 + 0.387403i) q^{32} -0.949694 q^{34} +(-5.78506 + 1.23819i) q^{35} +(2.99861 - 11.1910i) q^{37} +(0.106119 - 0.0284346i) q^{38} +(-0.948416 + 0.601547i) q^{40} -7.21562i q^{41} +(-0.545286 + 0.545286i) q^{43} +(-6.36019 + 3.67206i) q^{44} +(0.296481 - 0.513521i) q^{46} +(6.95523 + 1.86365i) q^{47} +(4.55628 - 5.31416i) q^{49} +(-0.407098 + 0.481243i) q^{50} +(-1.99308 - 7.43829i) q^{52} +(-0.187857 - 0.701093i) q^{53} +(-5.60387 + 6.09108i) q^{55} +(0.461133 - 1.24629i) q^{56} +(-1.04540 - 0.280113i) q^{58} +(0.887254 - 1.53677i) q^{59} +(3.95514 - 2.28350i) q^{61} +(-0.337625 + 0.337625i) q^{62} +7.62109i q^{64} +(-4.64838 - 7.32875i) q^{65} +(-7.52498 + 2.01631i) q^{67} +(-3.86850 + 14.4375i) q^{68} +(0.0379815 - 0.744856i) q^{70} +9.65572 q^{71} +(5.24201 - 1.40459i) q^{73} +(1.26490 + 0.730291i) q^{74} -1.72907i q^{76} +(0.905389 - 9.75124i) q^{77} +(-3.99531 + 2.30670i) q^{79} +(2.60901 + 8.33271i) q^{80} +(0.878657 + 0.235436i) q^{82} +(-3.03903 - 3.03903i) q^{83} +(0.701142 + 16.8302i) q^{85} +(-0.0486084 - 0.0841923i) q^{86} +(-0.481176 - 1.79577i) q^{88} +(4.90134 + 8.48937i) q^{89} +(9.63057 + 3.56334i) q^{91} +(-6.59896 - 6.59896i) q^{92} +(-0.453879 + 0.786141i) q^{94} +(-0.582256 - 1.85963i) q^{95} +(-3.30555 + 3.30555i) q^{97} +(0.498449 + 0.728219i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.0326286	+	0.121772i	−0.0230719	+	0.0861055i	−0.976502	−	0.215509i	$-0.930859\pi$
$2$	−0.0326286	+	0.121772i	−0.0230719	+	0.0861055i	0.953430	+	0.301615i	$0.0975256\pi$
$3$		0			0
$3$		0			0
$4$	1.71829	+	0.992054i	0.859144	+	0.496027i
$5$	2.18209	+	0.488334i	0.975862	+	0.218389i
$5$	2.18209	+	0.488334i	0.975862	+	0.218389i
$6$		0			0
$7$	−2.40378	+	1.10538i	−0.908542	+	0.417794i
$7$	−2.40378	+	1.10538i	−0.908542	+	0.417794i
$8$	−0.355155	+	0.355155i	−0.125566	+	0.125566i
$9$		0			0
$10$	−0.130664	+	0.249783i	−0.0413195	+	0.0789884i
$11$	−1.85074	+	3.20557i	−0.558018	+	0.966516i	0.439644	+	0.898172i	$0.355105\pi$
$11$	−1.85074	+	3.20557i	−0.558018	+	0.966516i	−0.997662	+	0.0683435i	$0.978229\pi$
$12$		0			0
$13$	−2.74441	−	2.74441i	−0.761163	−	0.761163i	0.215369	−	0.976533i	$-0.430904\pi$
$13$	−2.74441	−	2.74441i	−0.761163	−	0.761163i	−0.976533	+	0.215369i	$0.930904\pi$
$14$	−0.0561718	−	0.328778i	−0.0150125	−	0.0878697i
$15$		0			0
$16$	1.95245	+	3.38174i	0.488112	+	0.845435i
$17$	1.94975	+	7.27655i	0.472883	+	1.76482i	0.629332	+	0.777137i	$0.283329\pi$
$17$	1.94975	+	7.27655i	0.472883	+	1.76482i	−0.156449	+	0.987686i	$0.550005\pi$
$18$		0			0
$19$	−0.435731	−	0.754709i	−0.0999636	−	0.173142i	0.811706	−	0.584067i	$-0.198539\pi$
$19$	−0.435731	−	0.754709i	−0.0999636	−	0.173142i	−0.911669	+	0.410925i	$0.865206\pi$
$20$	3.26501	+	3.00385i	0.730078	+	0.671681i
$21$		0			0
$22$	−0.329960	−	0.329960i	−0.0703478	−	0.0703478i
$23$	−4.54328	−	1.21737i	−0.947339	−	0.253839i	−0.248106	−	0.968733i	$-0.579808\pi$
$23$	−4.54328	−	1.21737i	−0.947339	−	0.253839i	−0.699233	+	0.714894i	$0.746475\pi$
$24$		0			0
$25$	4.52306	+	2.13118i	0.904612	+	0.426236i
$26$	0.423738	−	0.244645i	0.0831018	−	0.0479789i
$27$		0			0
$28$	−5.22697	−	0.485317i	−0.987805	−	0.0917163i
$29$			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	$0.556198\pi$
$32$	−1.44581	+	0.387403i	−0.255585	+	0.0684838i
$33$		0			0
$34$	−0.949694			−0.162871
$35$	−5.78506	+	1.23819i	−0.977853	+	0.209293i
$36$		0			0
$37$	2.99861	−	11.1910i	0.492969	−	1.83978i	−0.0481520	−	0.998840i	$-0.515333\pi$
$37$	2.99861	−	11.1910i	0.492969	−	1.83978i	0.541121	−	0.840945i	$-0.318000\pi$
$38$	0.106119	−	0.0284346i	0.0172148	−	0.00461270i
$39$		0			0
$40$	−0.948416	+	0.601547i	−0.149958	+	0.0951130i
$41$		−	7.21562i		−	1.12689i	−0.826153	−	0.563445i	$-0.809476\pi$
$41$		−	7.21562i		−	1.12689i	0.826153	−	0.563445i	$-0.190524\pi$
$42$		0			0
$43$	−0.545286	+	0.545286i	−0.0831554	+	0.0831554i	−0.747461	−	0.664306i	$-0.768727\pi$
$43$	−0.545286	+	0.545286i	−0.0831554	+	0.0831554i	0.664306	+	0.747461i	$0.268727\pi$
$44$	−6.36019	+	3.67206i	−0.958835	+	0.553584i
$45$		0			0
$46$	0.296481	−	0.513521i	0.0437138	−	0.0757145i
$47$	6.95523	+	1.86365i	1.01452	+	0.271841i	0.727519	−	0.686088i	$-0.240673\pi$
$47$	6.95523	+	1.86365i	1.01452	+	0.271841i	0.287006	+	0.957929i	$0.407340\pi$
$48$		0			0
$49$	4.55628	−	5.31416i	0.650897	−	0.759166i
$50$	−0.407098	+	0.481243i	−0.0575724	+	0.0680580i
$51$		0			0
$52$	−1.99308	−	7.43829i	−0.276391	−	1.03151i
$53$	−0.187857	−	0.701093i	−0.0258042	−	0.0963026i	0.951823	−	0.306649i	$-0.0992076\pi$
$53$	−0.187857	−	0.701093i	−0.0258042	−	0.0963026i	−0.977627	+	0.210346i	$0.932541\pi$
$54$		0			0
$55$	−5.60387	+	6.09108i	−0.755625	+	0.821320i
$56$	0.461133	−	1.24629i	0.0616214	−	0.166543i
$57$		0			0
$58$	−1.04540	−	0.280113i	−0.137267	−	0.0367807i
$59$	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
$65$	−4.64838	−	7.32875i	−0.576560	−	0.909020i
$66$		0			0
$67$	−7.52498	+	2.01631i	−0.919322	+	0.246332i	−0.687296	−	0.726378i	$-0.741202\pi$
$67$	−7.52498	+	2.01631i	−0.919322	+	0.246332i	−0.232027	+	0.972709i	$0.574536\pi$
$68$	−3.86850	+	14.4375i	−0.469125	+	1.75080i
$69$		0			0
$70$	0.0379815	−	0.744856i	0.00453965	−	0.0890273i
$71$	9.65572			1.14592			0.572961	−	0.819582i	$-0.305794\pi$
$71$	9.65572			1.14592			0.572961	+	0.819582i	$0.305794\pi$
$72$		0			0
$73$	5.24201	−	1.40459i	0.613531	−	0.164395i	0.0613458	−	0.998117i	$-0.480461\pi$
$73$	5.24201	−	1.40459i	0.613531	−	0.164395i	0.552185	+	0.833721i	$0.313794\pi$
$74$	1.26490	+	0.730291i	0.147042	+	0.0848947i
$75$		0			0
$76$		−	1.72907i		−	0.198338i
$77$	0.905389	−	9.75124i	0.103179	−	1.11126i
$78$		0			0
$79$	−3.99531	+	2.30670i	−0.449508	+	0.259524i	−0.707622	−	0.706591i	$-0.750232\pi$
$79$	−3.99531	+	2.30670i	−0.449508	+	0.259524i	0.258114	+	0.966114i	$0.416899\pi$
$80$	2.60901	+	8.33271i	0.291696	+	0.931626i
$81$		0			0
$82$	0.878657	+	0.235436i	0.0970315	+	0.0259995i
$83$	−3.03903	−	3.03903i	−0.333577	−	0.333577i	0.520366	−	0.853943i	$-0.325795\pi$
$83$	−3.03903	−	3.03903i	−0.333577	−	0.333577i	−0.853943	+	0.520366i	$0.825795\pi$
$84$		0			0
$85$	0.701142	+	16.8302i	0.0760496	+	1.82550i
$86$	−0.0486084	−	0.0841923i	−0.00524158	−	0.00907869i
$87$		0			0
$88$	−0.481176	−	1.79577i	−0.0512935	−	0.191430i
$89$	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
$95$	−0.582256	−	1.85963i	−0.0597383	−	0.190794i
$96$		0			0
$97$	−3.30555	+	3.30555i	−0.335628	+	0.335628i	−0.854719	−	0.519091i	$-0.826270\pi$
$97$	−3.30555	+	3.30555i	−0.335628	+	0.335628i	0.519091	+	0.854719i	$0.326270\pi$
$98$	0.498449	+	0.728219i	0.0503510	+	0.0735612i
$99$		0			0
$100$	5.65767	+	8.14910i	0.565767	+	0.814910i
$101$	7.57630	+	4.37418i	0.753870	+	0.435247i	0.827091	−	0.562069i	$-0.189994\pi$
$101$	7.57630	+	4.37418i	0.753870	+	0.435247i	−0.0732204	+	0.997316i	$0.523328\pi$
$102$		0			0
$103$	1.34103	−	5.00477i	0.132135	−	0.493135i	−0.867858	−	0.496812i	$-0.834504\pi$
$103$	1.34103	−	5.00477i	0.132135	−	0.493135i	0.999993	+	0.00367708i	$0.00117045\pi$
$104$	1.94938			0.191153
$105$		0			0
$106$	0.0915027			0.00888753
$107$	−3.25590	+	12.1512i	−0.314759	+	1.17470i	0.609454	+	0.792821i	$0.291389\pi$
$107$	−3.25590	+	12.1512i	−0.314759	+	1.17470i	−0.924213	+	0.381877i	$0.875278\pi$
$108$		0			0
$109$	−5.47631	−	3.16175i	−0.524535	−	0.302840i	0.214253	−	0.976778i	$-0.431268\pi$
$109$	−5.47631	−	3.16175i	−0.524535	−	0.302840i	−0.738788	+	0.673938i	$0.764602\pi$
$110$	−0.558873	−	0.881135i	−0.0532865	−	0.0840129i
$111$		0			0
$112$	−8.43135	−	5.97075i	−0.796687	−	0.564183i
$113$	12.8216	−	12.8216i	1.20615	−	1.20615i	0.233889	−	0.972263i	$-0.424855\pi$
$113$	12.8216	−	12.8216i	1.20615	−	1.20615i	0.972263	−	0.233889i	$-0.0751452\pi$
$114$		0			0
$115$	−9.31937	−	4.87504i	−0.869036	−	0.454600i
$116$	−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
$122$	0.149015	+	0.556131i	0.0134912	+	0.0503497i
$123$		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	0.253393	−	0.967363i	$-0.418453\pi$
$127$	−8.04604	−	8.04604i	−0.713971	−	0.713971i	−0.967363	+	0.253393i	$0.918453\pi$
$128$	−3.81965	−	1.02347i	−0.337612	−	0.0904629i
$129$		0			0
$130$	1.04410	−	0.326913i	0.0915739	−	0.0286722i
$131$	−14.3809	+	8.30279i	−1.25646	+	0.725418i	−0.972385	−	0.233384i	$-0.925020\pi$
$131$	−14.3809	+	8.30279i	−1.25646	+	0.725418i	−0.284076	+	0.958802i	$0.591687\pi$
$132$		0			0
$133$	1.88164	+	1.33250i	0.163159	+	0.115543i
$134$		−	0.982118i		−	0.0848420i
$135$		0			0
$136$	−3.27677	−	1.89184i	−0.280980	−	0.162224i
$137$	0.512564	−	0.137341i	0.0437913	−	0.0117338i	−0.236857	−	0.971545i	$-0.576117\pi$
$137$	0.512564	−	0.137341i	0.0437913	−	0.0117338i	0.280648	+	0.959811i	$0.409451\pi$
$138$		0			0
$139$	16.5564			1.40429			0.702147	−	0.712032i	$-0.252225\pi$
$139$	16.5564			1.40429			0.702147	+	0.712032i	$0.252225\pi$
$140$	−11.1687	−	3.61151i	−0.943931	−	0.305229i
$141$		0			0
$142$	−0.315052	+	1.17579i	−0.0264386	+	0.0986703i
$143$	13.8766	−	3.71822i	1.16042	−	0.310933i
$144$		0			0
$145$	−4.19229	+	18.7330i	−0.348151	+	1.55569i
$146$			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	$-0.0312272\pi$
$152$	0.422791	+	0.113286i	0.0342929	+	0.00918874i
$153$		0			0
$154$	1.15788	+	0.428420i	0.0933048	+	0.0345230i
$155$	6.23257	+	5.73404i	0.500612	+	0.460570i
$156$		0			0
$157$	3.28591	+	12.2632i	0.262244	+	0.978708i	0.963916	+	0.266208i	$0.0857707\pi$
$157$	3.28591	+	12.2632i	0.262244	+	0.978708i	−0.701672	+	0.712500i	$0.747563\pi$
$158$	−0.150528	−	0.561780i	−0.0119754	−	0.0446928i
$159$		0			0
$160$	−3.34407	+	0.139313i	−0.264372	+	0.0110136i
$161$	12.2667	−	2.09576i	0.966749	−	0.165169i
$162$		0			0
$163$	3.43733	+	0.921031i	0.269233	+	0.0721407i	0.390910	−	0.920429i	$-0.372161\pi$
$163$	3.43733	+	0.921031i	0.269233	+	0.0721407i	−0.121677	+	0.992570i	$0.538827\pi$
$164$	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	−0.101518	−	0.994834i	$-0.532370\pi$
$167$	11.5442	−	11.5442i	0.893316	−	0.893316i	0.994834	+	0.101518i	$0.0323698\pi$
$168$		0			0
$169$			2.06360i			0.158739i
$170$	−2.07232	−	0.463768i	−0.158940	−	0.0355694i
$171$		0			0
$172$	−1.47791	+	0.396005i	−0.112690	+	0.0301951i
$173$	−0.359958	+	1.34338i	−0.0273671	+	0.102135i	−0.978258	−	0.207389i	$-0.933503\pi$
$173$	−0.359958	+	1.34338i	−0.0273671	+	0.102135i	0.950891	+	0.309525i	$0.100170\pi$
$174$		0			0
$175$	−13.2282	−	0.123184i	−0.999957	−	0.00931184i
$176$	−14.4539			−1.08950
$177$		0			0
$178$	−1.19369	+	0.319848i	−0.0894707	+	0.0239736i
$179$	−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	$-0.195512\pi$
$182$	−0.748145	+	1.05646i	−0.0554562	+	0.0783102i
$183$		0			0
$184$	2.04592	−	1.18121i	0.150827	−	0.0870802i
$185$	12.0082	−	22.9554i	0.882859	−	1.68772i
$186$		0			0
$187$	−26.9340	−	7.21693i	−1.96961	−	0.527754i
$188$	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	$-0.860165\pi$
$191$	−11.3444	−	19.6491i	−0.820853	−	1.42176i	0.0841943	−	0.996449i	$-0.473168\pi$
$192$		0			0
$193$	1.00257	+	3.74163i	0.0721663	+	0.269328i	0.992576	−	0.121627i	$-0.0388112\pi$
$193$	1.00257	+	3.74163i	0.0721663	+	0.269328i	−0.920410	+	0.390956i	$0.872145\pi$
$194$	−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	$-0.358000\pi$
$197$	−6.60630	−	6.60630i	−0.470679	−	0.470679i	−0.902134	+	0.431455i	$0.858000\pi$
$198$		0			0
$199$	−3.62824	+	6.28430i	−0.257199	+	0.445482i	−0.965491	−	0.260438i	$-0.916133\pi$
$199$	−3.62824	+	6.28430i	−0.257199	+	0.445482i	0.708291	+	0.705920i	$0.249466\pi$
$200$	−2.36329	+	0.849489i	−0.167110	+	0.0600679i
$201$		0			0
$202$	−0.779855	+	0.779855i	−0.0548704	+	0.0548704i
$203$	−9.48956	−	20.6362i	−0.666036	−	1.44838i
$204$		0			0
$205$	3.52363	−	15.7452i	0.246101	−	1.09969i
$206$	0.565683	+	0.326597i	0.0394130	+	0.0227551i
$207$		0			0
$208$	3.92256	−	14.6392i	0.271981	−	1.01505i
$209$	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	$0.674122\pi$
$212$	0.372729	−	1.39104i	0.0255991	−	0.0955373i
$213$		0			0
$214$	−1.37343	−	0.792951i	−0.0938859	−	0.0542050i
$215$	−1.45615	+	0.923584i	−0.0993084	+	0.0629879i
$216$		0			0
$217$	−9.97776	−	0.926421i	−0.677334	−	0.0628896i
$218$	0.563695	−	0.563695i	0.0381782	−	0.0381782i
$219$		0			0
$220$	−15.6717	+	4.90688i	−1.05659	+	0.330822i
$221$	14.6189	−	25.3208i	0.983377	−	1.70326i
$222$		0			0
$223$	12.0743	+	12.0743i	0.808552	+	0.808552i	0.984415	−	0.175863i	$-0.0562715\pi$
$223$	12.0743	+	12.0743i	0.808552	+	0.808552i	−0.175863	+	0.984415i	$0.556271\pi$
$224$	3.04717	−	2.52939i	0.203598	−	0.169002i
$225$		0			0
$226$	1.14295	+	1.97965i	0.0760281	+	0.131685i
$227$	−5.69153	−	21.2411i	−0.377760	−	1.40982i	−0.849270	−	0.527959i	$-0.822957\pi$
$227$	−5.69153	−	21.2411i	−0.377760	−	1.40982i	0.471510	−	0.881861i	$-0.343709\pi$
$228$		0			0
$229$	−0.632861	−	1.09615i	−0.0418206	−	0.0724355i	0.844357	−	0.535780i	$-0.179982\pi$
$229$	−0.632861	−	1.09615i	−0.0418206	−	0.0724355i	−0.886178	+	0.463345i	$0.846649\pi$
$230$	0.897720	−	0.975769i	0.0591939	−	0.0643403i
$231$		0			0
$232$	−3.04897	−	3.04897i	−0.200175	−	0.200175i
$233$	−28.0733	−	7.52221i	−1.83914	−	0.492796i	−0.840354	−	0.542038i	$-0.817653\pi$
$233$	−28.0733	−	7.52221i	−1.83914	−	0.492796i	−0.998787	+	0.0492411i	$0.984320\pi$
$234$		0			0
$235$	14.2669	+	7.46312i	0.930668	+	0.486841i
$236$	3.04912	−	1.76041i	0.198481	−	0.114593i
$237$		0			0
$238$	2.28285	−	1.04977i	0.147975	−	0.0680466i
$239$		−	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	$0.322712\pi$
$242$	0.328894	−	0.0881268i	0.0211421	−	0.00566500i
$243$		0			0
$244$	9.06142			0.580098
$245$	12.5373	−	9.37102i	0.800979	−	0.598692i
$246$		0			0
$247$	−0.875406	+	3.26706i	−0.0557007	+	0.207878i
$248$	−1.83749	+	0.492354i	−0.116681	+	0.0312645i
$249$		0			0
$250$	−1.12333	+	0.851317i	−0.0710458	+	0.0538420i
$251$			4.81809i			0.304115i	0.988372	+	0.152058i	$0.0485899\pi$
$251$			4.81809i			0.304115i	−0.988372	+	0.152058i	$0.951410\pi$
$252$		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
$257$	−9.48647	−	2.54189i	−0.591750	−	0.158559i	−0.0494970	−	0.998774i	$-0.515762\pi$
$257$	−9.48647	−	2.54189i	−0.591750	−	0.158559i	−0.542253	+	0.840215i	$0.682429\pi$
$258$		0			0
$259$	5.16227	+	30.2152i	0.320768	+	1.87748i
$260$	−0.716727	−	17.2043i	−0.0444495	−	1.06697i
$261$		0			0
$262$	−0.541817	−	2.02209i	−0.0334735	−	0.124925i
$263$	7.40584	+	27.6390i	0.456664	+	1.70429i	0.683150	+	0.730279i	$0.260610\pi$
$263$	7.40584	+	27.6390i	0.456664	+	1.70429i	−0.226486	+	0.974015i	$0.572724\pi$
$264$		0			0
$265$	−0.0675548	−	1.62159i	−0.00414986	−	0.0996134i
$266$	−0.223656	+	0.185652i	−0.0137132	+	0.0113831i
$267$		0			0
$268$	−14.9304	−	4.00058i	−0.912017	−	0.244374i
$269$	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
$275$	−15.2026	+	10.5547i	−0.916754	+	0.636475i
$276$		0			0
$277$	7.89956	−	2.11668i	0.474639	−	0.127179i	−0.0135665	−	0.999908i	$-0.504318\pi$
$277$	7.89956	−	2.11668i	0.474639	−	0.127179i	0.488205	+	0.872729i	$0.337652\pi$
$278$	−0.540211	+	2.01610i	−0.0323997	+	0.120917i
$279$		0			0
$280$	1.61484	−	2.49434i	0.0965052	−	0.149066i
$281$	−6.63025			−0.395527			−0.197764	−	0.980250i	$-0.563368\pi$
$281$	−6.63025			−0.395527			−0.197764	+	0.980250i	$0.563368\pi$
$282$		0			0
$283$	16.6132	−	4.45149i	0.987550	−	0.264613i	0.271329	−	0.962487i	$-0.412537\pi$
$283$	16.6132	−	4.45149i	0.987550	−	0.264613i	0.716221	+	0.697873i	$0.245870\pi$
$284$	16.5913	+	9.57899i	0.984512	+	0.568408i
$285$		0			0
$286$			1.81109i			0.107092i
$287$	7.97599	+	17.3447i	0.470808	+	1.02383i
$288$		0			0
$289$	−34.4242	+	19.8748i	−2.02496	+	1.16911i
$290$	−2.14436	−	1.12174i	−0.125921	−	0.0658706i
$291$		0			0
$292$	10.4007	+	2.78686i	0.608656	+	0.163089i
$293$	15.4579	+	15.4579i	0.903059	+	0.903059i	0.995700	−	0.0926408i	$-0.0295308\pi$
$293$	15.4579	+	15.4579i	0.903059	+	0.903059i	−0.0926408	+	0.995700i	$0.529531\pi$
$294$		0			0
$295$	2.68653	−	2.92010i	0.156416	−	0.170015i
$296$	2.90956	+	5.03950i	0.169115	+	0.292915i
$297$		0			0
$298$	0.253236	+	0.945088i	0.0146695	+	0.0547475i
$299$	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
$305$	9.74560	−	3.05138i	0.558031	−	0.174722i
$306$		0			0
$307$	−0.788081	+	0.788081i	−0.0449782	+	0.0449782i	−0.729238	−	0.684260i	$-0.760125\pi$
$307$	−0.788081	+	0.788081i	−0.0449782	+	0.0449782i	0.684260	+	0.729238i	$0.260125\pi$
$308$	11.2295	−	15.8572i	0.639858	−	0.903550i
$309$		0			0
$310$	−0.901603	+	0.571856i	−0.0512076	+	0.0324792i
$311$	9.94659	+	5.74267i	0.564019	+	0.325637i	0.754757	−	0.656004i	$-0.227755\pi$
$311$	9.94659	+	5.74267i	0.564019	+	0.325637i	−0.190738	+	0.981641i	$0.561088\pi$
$312$		0			0
$313$	2.58819	−	9.65926i	0.146293	−	0.545974i	−0.853401	−	0.521255i	$-0.825464\pi$
$313$	2.58819	−	9.65926i	0.146293	−	0.545974i	0.999694	−	0.0247191i	$-0.00786912\pi$
$314$	−1.60052			−0.0903226
$315$		0			0
$316$	−9.15346			−0.514922
$317$	2.36034	−	8.80889i	0.132570	−	0.494757i	−0.867426	−	0.497566i	$-0.834227\pi$
$317$	2.36034	−	8.80889i	0.132570	−	0.494757i	0.999996	+	0.00280878i	$0.000894065\pi$
$318$		0			0
$319$	−27.5195	−	15.8884i	−1.54080	−	0.889579i
$320$	−3.72164	+	16.6299i	−0.208046	+	0.929641i
$321$		0			0
$322$	−0.145040	+	1.56211i	−0.00808277	+	0.0870532i
$323$	4.64211	−	4.64211i	0.258294	−	0.258294i
$324$		0			0
$325$	−6.56431	−	18.2620i	−0.364122	−	1.01299i
$326$	−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	$0.573448\pi$
$332$	−2.20705	−	8.23681i	−0.121127	−	0.452054i
$333$		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	0.342345	−	0.939574i	$-0.388779\pi$
$337$	−10.9637	−	10.9637i	−0.597230	−	0.597230i	−0.939574	+	0.342345i	$0.888779\pi$
$338$	−0.251288	−	0.0673325i	−0.0136683	−	0.00366240i
$339$		0			0
$340$	−15.4917	+	29.6147i	−0.840157	+	1.60609i
$341$	−12.1410	+	7.00959i	−0.657470	+	0.379590i
$342$		0			0
$343$	−5.07811	+	17.8105i	−0.274192	+	0.961675i
$344$		−	0.387322i		−	0.0208830i
$345$		0			0
$346$	−0.151841	−	0.0876652i	−0.00816300	−	0.00471291i
$347$	−15.8391	+	4.24408i	−0.850289	+	0.227834i	−0.657545	−	0.753415i	$-0.728405\pi$
$347$	−15.8391	+	4.24408i	−0.850289	+	0.227834i	−0.192743	+	0.981249i	$0.561738\pi$
$348$		0			0
$349$	−16.1944			−0.866868			−0.433434	−	0.901185i	$-0.642698\pi$
$349$	−16.1944			−0.866868			−0.433434	+	0.901185i	$0.642698\pi$
$350$	0.446617	−	1.60680i	0.0238727	−	0.0858869i
$351$		0			0
$352$	1.43396	−	5.35162i	0.0764304	−	0.285242i
$353$	10.9773	−	2.94135i	0.584262	−	0.156552i	0.0454324	−	0.998967i	$-0.485533\pi$
$353$	10.9773	−	2.94135i	0.584262	−	0.156552i	0.538829	+	0.842415i	$0.318867\pi$
$354$		0			0
$355$	21.0697	+	4.71521i	1.11826	+	0.250257i
$356$			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
$362$	1.88833	+	0.505977i	0.0992485	+	0.0265936i
$363$		0			0
$364$	13.0131	+	15.6769i	0.682070	+	0.821692i
$365$	12.1245	−	0.505102i	0.634624	−	0.0264382i
$366$		0			0
$367$	−4.50955	−	16.8299i	−0.235397	−	0.878512i	−0.977970	−	0.208747i	$-0.933061\pi$
$367$	−4.50955	−	16.8299i	−0.235397	−	0.878512i	0.742573	−	0.669765i	$-0.233605\pi$
$368$	−4.75369	−	17.7410i	−0.247803	−	0.924814i
$369$		0			0
$370$	2.40351	+	2.21126i	0.124952	+	0.114958i
$371$	1.22654	+	1.47762i	0.0636788	+	0.0767141i
$372$		0			0
$373$	7.55101	+	2.02329i	0.390977	+	0.104762i	0.448951	−	0.893556i	$-0.351798\pi$
$373$	7.55101	+	2.02329i	0.390977	+	0.104762i	−0.0579747	+	0.998318i	$0.518464\pi$
$374$	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	$0.0372759\pi$
$379$			4.54919i			0.233676i	−0.993151	+	0.116838i	$0.962724\pi$
$380$	0.844365	−	3.77300i	0.0433150	−	0.193551i
$381$		0			0
$382$	2.76285	−	0.740305i	0.141360	−	0.0378773i
$383$	−0.926942	+	3.45940i	−0.0473645	+	0.176767i	−0.985556	−	0.169350i	$-0.945833\pi$
$383$	−0.926942	+	3.45940i	−0.0473645	+	0.176767i	0.938191	+	0.346117i	$0.112500\pi$
$384$		0			0
$385$	6.73750	−	20.8360i	0.343375	−	1.06190i
$386$	−0.488336			−0.0248557
$387$		0			0
$388$	−8.95916	+	2.40060i	−0.454832	+	0.121872i
$389$	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
$392$	0.269167	+	3.50554i	0.0135950	+	0.177056i
$393$		0			0
$394$	1.02001	−	0.588905i	0.0513875	−	0.0296686i
$395$	−9.84458	+	3.08238i	−0.495335	+	0.155091i
$396$		0			0
$397$	−21.0788	−	5.64804i	−1.05791	−	0.283467i	−0.312396	−	0.949952i	$-0.601131\pi$
$397$	−21.0788	−	5.64804i	−1.05791	−	0.283467i	−0.745519	+	0.666485i	$0.767798\pi$
$398$	−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	0.950785	−	0.309852i	$-0.100280\pi$
$401$	4.14622	+	7.18147i	0.207052	+	0.358625i	−0.743732	+	0.668478i	$0.766946\pi$
$402$		0			0
$403$	−3.80460	−	14.1989i	−0.189520	−	0.707300i
$404$	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	$-0.623487\pi$
$409$	12.3875	−	21.4559i	0.612524	−	1.06092i	0.990813	−	0.135236i	$-0.0431792\pi$
$410$	1.80234	+	0.942820i	0.0890113	+	0.0465626i
$411$		0			0
$412$	7.26927	−	7.26927i	0.358131	−	0.358131i
$413$	−0.434049	+	4.67480i	−0.0213582	+	0.230032i
$414$		0			0
$415$	−5.14739	−	8.11551i	−0.252675	−	0.398375i
$416$	5.03108	+	2.90470i	0.246669	+	0.142415i
$417$		0			0
$418$	−0.105250	+	0.392798i	−0.00514794	+	0.0192124i
$419$	−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	$0.448813\pi$
$422$	0.493053	−	1.84010i	0.0240014	−	0.0895746i
$423$		0			0
$424$	0.315715	+	0.182278i	0.0153325	+	0.00885222i
$425$	−6.68881	+	37.0675i	−0.324455	+	1.79804i
$426$		0			0
$427$	−6.98314	+	9.86095i	−0.337938	+	0.477205i
$428$	−17.6492	+	17.6492i	−0.853105	+	0.853105i
$429$		0			0
$430$	−0.0649542	−	0.207453i	−0.00313237	−	0.0100043i
$431$	1.26581	−	2.19244i	0.0609718	−	0.105606i	−0.833928	−	0.551873i	$-0.813913\pi$
$431$	1.26581	−	2.19244i	0.0609718	−	0.105606i	0.894900	+	0.446267i	$0.147247\pi$
$432$		0			0
$433$	8.64351	+	8.64351i	0.415381	+	0.415381i	0.883608	−	0.468227i	$-0.155107\pi$
$433$	8.64351	+	8.64351i	0.415381	+	0.415381i	−0.468227	+	0.883608i	$0.655107\pi$
$434$	0.438372	−	1.18478i	0.0210425	−	0.0568712i
$435$		0			0
$436$	−6.27325	−	10.8656i	−0.300434	−	0.520367i
$437$	1.06089	+	3.95929i	0.0507492	+	0.189399i
$438$		0			0
$439$	11.7845	+	20.4114i	0.562444	+	0.974182i	0.997282	+	0.0736734i	$0.0234722\pi$
$439$	11.7845	+	20.4114i	0.562444	+	0.974182i	−0.434838	+	0.900509i	$0.643194\pi$
$440$	−0.173034	−	4.15352i	−0.00824909	−	0.198011i
$441$		0			0
$442$	2.60635	+	2.60635i	0.123972	+	0.123972i
$443$	−11.7251	−	3.14174i	−0.557078	−	0.149269i	−0.0307144	−	0.999528i	$-0.509778\pi$
$443$	−11.7251	−	3.14174i	−0.557078	−	0.149269i	−0.526364	+	0.850260i	$0.676445\pi$
$444$		0			0
$445$	6.54954	+	20.9181i	0.310478	+	0.991613i
$446$	−1.86427	+	1.07633i	−0.0882756	+	0.0509659i
$447$		0			0
$448$	−8.42419	−	18.3194i	−0.398006	−	0.865510i
$449$		−	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
$452$	34.7508	−	9.31146i	1.63454	−	0.437974i
$453$		0			0
$454$	2.77227			0.130109
$455$	19.2747	+	12.4785i	0.903612	+	0.585000i
$456$		0			0
$457$	2.21383	−	8.26213i	0.103559	−	0.386486i	−0.894619	−	0.446830i	$-0.852553\pi$
$457$	2.21383	−	8.26213i	0.103559	−	0.386486i	0.998178	+	0.0603436i	$0.0192196\pi$
$458$	0.154129	−	0.0412987i	0.00720197	−	0.00192976i
$459$		0			0
$460$	−11.1771	−	17.6220i	−0.521133	−	0.821632i
$461$			10.8496i			0.505318i	0.967555	+	0.252659i	$0.0813051\pi$
$461$			10.8496i			0.505318i	−0.967555	+	0.252659i	$0.918695\pi$
$462$		0			0
$463$	11.9276	−	11.9276i	0.554322	−	0.554322i	−0.373363	−	0.927685i	$-0.621795\pi$
$463$	11.9276	−	11.9276i	0.554322	−	0.554322i	0.927685	+	0.373363i	$0.121795\pi$
$464$	−29.0319	+	16.7616i	−1.34777	+	0.778136i
$465$		0			0
$466$	1.83198	−	3.17309i	0.0848650	−	0.146990i
$467$	−16.3757	−	4.38785i	−0.757776	−	0.203045i	−0.140811	−	0.990036i	$-0.544971\pi$
$467$	−16.3757	−	4.38785i	−0.757776	−	0.203045i	−0.616964	+	0.786991i	$0.711638\pi$
$468$		0			0
$469$	15.8596	−	13.1647i	0.732327	−	0.607890i
$470$	−1.37430	+	1.49379i	−0.0633919	+	0.0689033i
$471$		0			0
$472$	0.230679	+	0.860905i	0.0106178	+	0.0396263i
$473$	−0.738772	−	2.75714i	−0.0339688	−	0.126773i
$474$		0			0
$475$	−0.362420	−	4.34221i	−0.0166289	−	0.199234i
$476$	−6.65983	−	38.9806i	−0.305253	−	1.78667i
$477$		0			0
$478$	1.73188	+	0.464056i	0.0792144	+	0.0212254i
$479$	−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
$485$	−8.82722	+	5.59880i	−0.400824	+	0.254229i
$486$		0			0
$487$	−3.58951	+	0.961805i	−0.162656	+	0.0435836i	−0.339228	−	0.940704i	$-0.610166\pi$
$487$	−3.58951	+	0.961805i	−0.162656	+	0.0435836i	0.176572	+	0.984288i	$0.443499\pi$
$488$	−0.593691	+	2.21569i	−0.0268751	+	0.100299i
$489$		0			0
$490$	0.732048	+	1.83245i	0.0330706	+	0.0827817i
$491$	19.1608			0.864717			0.432358	−	0.901702i	$-0.357682\pi$
$491$	19.1608			0.864717			0.432358	+	0.901702i	$0.357682\pi$
$492$		0			0
$493$	−62.4684	+	16.7384i	−2.81344	+	0.753858i
$494$	−0.369272	−	0.213199i	−0.0166143	−	0.00959228i
$495$		0			0
$496$			14.7896i			0.664074i
$497$	−23.2102	+	10.6732i	−1.04112	+	0.478759i
$498$		0			0
$499$	6.01766	−	3.47430i	0.269387	−	0.155531i	−0.359222	−	0.933252i	$-0.616958\pi$
$499$	6.01766	−	3.47430i	0.269387	−	0.155531i	0.628609	+	0.777721i	$0.283625\pi$
$500$	8.36609	+	20.5449i	0.374143	+	0.918797i
$501$		0			0
$502$	−0.586707	−	0.157208i	−0.0261860	−	0.00701652i
$503$	−1.96117	−	1.96117i	−0.0874443	−	0.0874443i	0.662032	−	0.749476i	$-0.269694\pi$
$503$	−1.96117	−	1.96117i	−0.0874443	−	0.0874443i	−0.749476	+	0.662032i	$0.769694\pi$
$504$		0			0
$505$	14.3961	+	13.2446i	0.640620	+	0.589378i
$506$	1.09742	+	1.90078i	0.0487862	+	0.0845002i
$507$		0			0
$508$	−5.84330	−	21.8075i	−0.259255	−	0.967552i
$509$	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
$515$	5.37024	−	10.2660i	0.236641	−	0.452375i
$516$		0			0
$517$	−18.8463	+	18.8463i	−0.828861	+	0.828861i
$518$	−3.84779	−	0.357262i	−0.169062	−	0.0156972i
$519$		0			0
$520$	4.25374	+	0.951950i	0.186539	+	0.0417458i
$521$	−14.5104	−	8.37757i	−0.635711	−	0.367028i	0.147249	−	0.989099i	$-0.452958\pi$
$521$	−14.5104	−	8.37757i	−0.635711	−	0.367028i	−0.782961	+	0.622071i	$0.786291\pi$
$522$		0			0
$523$	−1.88235	+	7.02501i	−0.0823093	+	0.307182i	−0.994791	−	0.101935i	$-0.967497\pi$
$523$	−1.88235	+	7.02501i	−0.0823093	+	0.307182i	0.912482	+	0.409117i	$0.134163\pi$
$524$	−32.9472			−1.43931
$525$		0			0
$526$	−3.60728			−0.157285
$527$	−7.38458	+	27.5596i	−0.321677	+	1.20052i
$528$		0			0
$529$	−0.759206	−	0.438328i	−0.0330089	−	0.0190577i
$530$	0.199668	+	0.0446839i	0.00867300	+	0.00194094i
$531$		0			0
$532$	1.91128	+	4.15631i	0.0828646	+	0.180199i
$533$	−19.8026	+	19.8026i	−0.857748	+	0.857748i
$534$		0			0
$535$	−13.0385	+	24.9250i	−0.563703	+	1.07760i
$536$	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	$0.674236\pi$
$542$	0.481043	+	1.79528i	0.0206626	+	0.0771138i
$543$		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	0.494910	−	0.868944i	$-0.335201\pi$
$547$	−8.74792	−	8.74792i	−0.374034	−	0.374034i	−0.868944	+	0.494910i	$0.835201\pi$
$548$	1.01698	+	0.272499i	0.0434433	+	0.0116406i
$549$		0			0
$550$	−0.789226	−	2.19564i	−0.0336527	−	0.0936222i
$551$	6.47910	−	3.74071i	0.276019	−	0.159360i
$552$		0			0
$553$	7.05407	−	9.96111i	0.299970	−	0.423590i
$554$			1.03101i			0.0438033i
$555$		0			0
$556$	28.4486	+	16.4248i	1.20649	+	0.696567i
$557$	1.06274	−	0.284761i	0.0450299	−	0.0120657i	−0.236234	−	0.971696i	$-0.575913\pi$
$557$	1.06274	−	0.284761i	0.0450299	−	0.0120657i	0.281264	+	0.959631i	$0.409246\pi$
$558$		0			0
$559$	2.99298			0.126590
$560$	−15.4823	−	17.1460i	−0.654245	−	0.724552i
$561$		0			0
$562$	0.216336	−	0.807376i	0.00912557	−	0.0340571i
$563$	0.544658	−	0.145941i	0.0229546	−	0.00615066i	−0.247323	−	0.968933i	$-0.579551\pi$
$563$	0.544658	−	0.145941i	0.0229546	−	0.00615066i	0.270278	+	0.962782i	$0.412884\pi$
$564$		0			0
$565$	34.2391	−	21.7167i	1.44045	−	0.913627i
$566$			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	$0.0527163\pi$
$572$	27.5326	+	7.37735i	1.15120	+	0.308463i
$573$		0			0
$574$	−2.37234	+	0.405314i	−0.0990196	+	0.0169175i
$575$	−17.9551	−	15.1888i	−0.748779	−	0.633415i
$576$		0			0
$577$	10.2292	+	38.1758i	0.425846	+	1.58928i	0.762069	+	0.647495i	$0.224183\pi$
$577$	10.2292	+	38.1758i	0.425846	+	1.58928i	−0.336224	+	0.941782i	$0.609150\pi$
$578$	−1.29698	−	4.84038i	−0.0539471	−	0.201333i
$579$		0			0
$580$	−25.7877	+	28.0298i	−1.07078	+	1.16387i
$581$	10.6644	+	3.94587i	0.442435	+	0.163702i
$582$		0			0
$583$	2.59508	+	0.695349i	0.107477	+	0.0287984i
$584$	−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	−0.911276	−	0.411797i	$-0.864901\pi$
$587$	−12.1014	+	12.1014i	−0.499478	+	0.499478i	0.411797	+	0.911276i	$0.364901\pi$
$588$		0			0
$589$		−	3.30063i		−	0.136000i
$590$	0.267927	+	0.422421i	0.0110304	+	0.0173908i
$591$		0			0
$592$	43.6996	−	11.7093i	1.79604	−	0.481248i
$593$	−7.27262	+	27.1418i	−0.298651	+	1.11458i	0.639624	+	0.768688i	$0.279090\pi$
$593$	−7.27262	+	27.1418i	−0.298651	+	1.11458i	−0.938275	+	0.345891i	$0.887577\pi$
$594$		0			0
$595$	−20.2892	−	39.6811i	−0.831775	−	1.62677i
$596$	15.3990			0.630766
$597$		0			0
$598$	−2.22298	+	0.595646i	−0.0909044	+	0.0243578i
$599$	−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	$-0.204387\pi$
$602$	0.209908	+	0.148649i	0.00855522	+	0.00605847i
$603$		0			0
$604$	24.5952	−	14.2000i	1.00076	−	0.577791i
$605$	−1.80458	−	5.76350i	−0.0733664	−	0.234320i
$606$		0			0
$607$	23.0639	+	6.17995i	0.936135	+	0.250837i	0.694469	−	0.719523i	$-0.255639\pi$
$607$	23.0639	+	6.17995i	0.936135	+	0.250837i	0.241666	+	0.970359i	$0.422306\pi$
$608$	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
$613$	7.45496	+	27.8223i	0.301103	+	1.12373i	0.936248	+	0.351339i	$0.114274\pi$
$613$	7.45496	+	27.8223i	0.301103	+	1.12373i	−0.635145	+	0.772393i	$0.719060\pi$
$614$	−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	$-0.0546351\pi$
$617$	20.2319	+	20.2319i	0.814506	+	0.814506i	−0.170800	+	0.985306i	$0.554635\pi$
$618$		0			0
$619$	16.6641	−	28.8630i	0.669785	−	1.16010i	−0.308179	−	0.951328i	$-0.599720\pi$
$619$	16.6641	−	28.8630i	0.669785	−	1.16010i	0.977964	−	0.208773i	$-0.0669470\pi$
$620$	5.02087	+	16.0358i	0.201643	+	0.644012i
$621$		0			0
$622$	−1.02384	+	1.02384i	−0.0410521	+	0.0410521i
$623$	−21.1657	−	14.9887i	−0.847986	−	0.600510i
$624$		0			0
$625$	15.9162	+	19.2789i	0.636646	+	0.771156i
$626$	1.09177	+	0.630336i	0.0436361	+	0.0251933i
$627$		0			0
$628$	−6.51959	+	24.3315i	−0.260160	+	0.970931i
$629$	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	$0.801751\pi$
$632$	0.599721	−	2.23819i	0.0238556	−	0.0890305i
$633$		0			0
$634$	0.995658	+	0.574844i	0.0395426	+	0.0228300i
$635$	−13.6281	−	21.4864i	−0.540813	−	0.852660i
$636$		0			0
$637$	−27.0886	+	2.07995i	−1.07329	+	0.0824107i
$638$	2.83268	−	2.83268i	0.112147	−	0.112147i
$639$		0			0
$640$	−7.83503	−	4.09857i	−0.309707	−	0.162010i
$641$	−10.5565	+	18.2844i	−0.416957	+	0.722191i	−0.995632	−	0.0933673i	$-0.970237\pi$
$641$	−10.5565	+	18.2844i	−0.416957	+	0.722191i	0.578674	+	0.815559i	$0.303570\pi$
$642$		0			0
$643$	24.4664	+	24.4664i	0.964860	+	0.964860i	0.999403	−	0.0345429i	$-0.0109975\pi$
$643$	24.4664	+	24.4664i	0.964860	+	0.964860i	−0.0345429	+	0.999403i	$0.510998\pi$
$644$	23.1568	+	8.56807i	0.912505	+	0.337629i
$645$		0			0
$646$	0.413811	+	0.716742i	0.0162812	+	0.0281999i
$647$	0.817214	+	3.04988i	0.0321280	+	0.119903i	0.980128	−	0.198368i	$-0.0635642\pi$
$647$	0.817214	+	3.04988i	0.0321280	+	0.119903i	−0.948000	+	0.318272i	$0.896898\pi$
$648$		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
$653$	8.36853	+	2.24234i	0.327486	+	0.0877496i	0.418816	−	0.908071i	$-0.362445\pi$
$653$	8.36853	+	2.24234i	0.327486	+	0.0877496i	−0.0913301	+	0.995821i	$0.529112\pi$
$654$		0			0
$655$	−35.4349	+	11.0948i	−1.38456	+	0.433510i
$656$	24.4013	−	14.0881i	0.952712	−	0.550049i
$657$		0			0
$658$	0.222039	−	2.39141i	0.00865600	−	0.0932270i
$659$			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	$0.993961\pi$
$662$	−3.22888	+	0.865176i	−0.125494	+	0.0336260i
$663$		0			0
$664$	2.15866			0.0837721
$665$	3.45520	+	3.82651i	0.133987	+	0.148386i
$666$		0			0
$667$	10.4510	−	39.0036i	0.404663	−	1.51022i
$668$	31.2887	−	8.38378i	1.21060	−	0.324378i
$669$		0			0
$670$	0.479601	−	2.14307i	0.0185286	−	0.0827941i
$671$			16.9046i			0.652596i
$672$		0			0
$673$	−17.4071	+	17.4071i	−0.670993	+	0.670993i	−0.957945	−	0.286952i	$-0.907358\pi$
$673$	−17.4071	+	17.4071i	−0.670993	+	0.670993i	0.286952	+	0.957945i	$0.407358\pi$
$674$	1.69279	−	0.977335i	0.0652040	−	0.0376455i
$675$		0			0
$676$	−2.04721	+	3.54586i	−0.0787387	+	0.136379i
$677$	−23.1934	−	6.21465i	−0.891394	−	0.238848i	−0.216078	−	0.976376i	$-0.569326\pi$
$677$	−23.1934	−	6.21465i	−0.891394	−	0.238848i	−0.675317	+	0.737528i	$0.735993\pi$
$678$		0			0
$679$	4.29192	−	11.5997i	0.164709	−	0.445155i
$680$	−6.22636	−	5.72833i	−0.238770	−	0.219671i
$681$		0			0
$682$	−0.457426	−	1.70714i	−0.0175157	−	0.0653696i
$683$	4.51928	+	16.8662i	0.172925	+	0.645366i	0.996896	+	0.0787333i	$0.0250876\pi$
$683$	4.51928	+	16.8662i	0.172925	+	0.645366i	−0.823970	+	0.566633i	$0.808246\pi$
$684$		0			0
$685$	1.18553	−	0.0493888i	0.0452968	−	0.00188705i
$686$	−2.00312	−	1.19950i	−0.0764794	−	0.0457971i
$687$		0			0
$688$	−2.90866	−	0.779373i	−0.110892	−	0.0297133i
$689$	−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
$695$	36.1275	+	8.08503i	1.37040	+	0.306683i
$696$		0			0
$697$	52.5048	−	14.0686i	1.98876	−	0.532887i
$698$	0.528402	−	1.97202i	0.0200003	−	0.0746421i
$699$		0			0
$700$	−22.6076	−	13.3347i	−0.854487	−	0.504005i
$701$	−22.3591			−0.844490			−0.422245	−	0.906482i	$-0.638758\pi$
$701$	−22.3591			−0.844490			−0.422245	+	0.906482i	$0.638758\pi$
$702$		0			0
$703$	−9.75251	+	2.61318i	−0.367823	+	0.0985579i
$704$	−24.4299	−	14.1046i	−0.920738	−	0.531588i
$705$		0			0
$706$			1.43269i			0.0539201i
$707$	−23.0469	−	2.13987i	−0.866766	−	0.0804781i
$708$		0			0
$709$	−18.6895	+	10.7904i	−0.701901	+	0.405243i	−0.808055	−	0.589107i	$-0.799480\pi$
$709$	−18.6895	+	10.7904i	−0.701901	+	0.405243i	0.106154	+	0.994350i	$0.466146\pi$
$710$	−1.26165	+	2.41184i	−0.0473490	+	0.0905146i
$711$		0			0
$712$	−4.75578	−	1.27431i	−0.178230	−	0.0477567i
$713$	−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
$718$	−1.05986	−	3.95547i	−0.0395538	−	0.147617i
$719$	−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
$725$	−18.2960	+	38.8300i	−0.679495	+	1.44211i
$726$		0			0
$727$	−6.94393	+	6.94393i	−0.257536	+	0.257536i	−0.824051	−	0.566515i	$-0.808291\pi$
$727$	−6.94393	+	6.94393i	−0.257536	+	0.257536i	0.566515	+	0.824051i	$0.308291\pi$
$728$	−4.68588	+	2.15481i	−0.173670	+	0.0798625i
$729$		0			0
$730$	−0.334097	+	1.49290i	−0.0123655	+	0.0552546i
$731$	−5.03097	−	2.90463i	−0.186077	−	0.107432i
$732$		0			0
$733$	3.81642	−	14.2431i	0.140963	−	0.526080i	−0.858939	−	0.512077i	$-0.828876\pi$
$733$	3.81642	−	14.2431i	0.140963	−	0.526080i	0.999902	−	0.0140023i	$-0.00445722\pi$
$734$	2.19654			0.0810758
$735$		0			0
$736$	7.04031			0.259509
$737$	7.46332	−	27.8535i	0.274915	−	1.02600i
$738$		0			0
$739$	−26.2034	−	15.1285i	−0.963908	−	0.556512i	−0.0665342	−	0.997784i	$-0.521194\pi$
$739$	−26.2034	−	15.1285i	−0.963908	−	0.556512i	−0.897374	+	0.441272i	$0.854527\pi$
$740$	43.4065	−	27.5313i	1.59566	−	1.01207i
$741$		0			0
$742$	−0.219952	+	0.101145i	−0.00807470	+	0.00371316i
$743$	17.1499	−	17.1499i	0.629167	−	0.629167i	−0.318691	−	0.947859i	$-0.603243\pi$
$743$	17.1499	−	17.1499i	0.629167	−	0.629167i	0.947859	+	0.318691i	$0.103243\pi$
$744$		0			0
$745$	16.5616	−	5.18552i	0.606772	−	0.189983i
$746$	−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	$-0.476670\pi$
$752$	7.27735	+	27.1594i	0.265378	+	0.990403i
$753$		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	0.974756	−	0.223273i	$-0.0716743\pi$
$757$	20.6760	+	20.6760i	0.751482	+	0.751482i	−0.223273	+	0.974756i	$0.571674\pi$
$758$	−0.553962	−	0.148434i	−0.0201208	−	0.00539135i
$759$		0			0
$760$	0.867247	+	0.453665i	0.0314584	+	0.0164561i
$761$	8.05627	−	4.65129i	0.292039	−	0.168609i	−0.346822	−	0.937931i	$-0.612739\pi$
$761$	8.05627	−	4.65129i	0.292039	−	0.168609i	0.638861	+	0.769322i	$0.279406\pi$
$762$		0			0
$763$	16.6587	+	1.54674i	0.603087	+	0.0559958i
$764$		−	45.0171i		−	1.62866i
$765$		0			0
$766$	−0.391011	−	0.225750i	−0.0141278	−	0.00815669i
$767$	−6.65252	+	1.78254i	−0.240209	+	0.0643637i
$768$		0			0
$769$	−42.1028			−1.51827			−0.759133	−	0.650936i	$-0.774377\pi$
$769$	−42.1028			−1.51827			−0.759133	+	0.650936i	$0.774377\pi$
$770$	2.31739	+	1.50028i	0.0835131	+	0.0540665i
$771$		0			0
$772$	−1.98920	+	7.42379i	−0.0715929	+	0.267188i
$773$	0.941195	−	0.252193i	0.0338524	−	0.00907074i	−0.241853	−	0.970313i	$-0.577755\pi$
$773$	0.941195	−	0.252193i	0.0338524	−	0.00907074i	0.275706	+	0.961242i	$0.411089\pi$
$774$		0			0
$775$	10.7999	+	15.5558i	0.387945	+	0.558781i
$776$		−	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
$782$	4.31472	+	1.15613i	0.154294	+	0.0413430i
$783$		0			0
$784$	26.8670	+	5.03251i	0.959536	+	0.179733i
$785$	1.18164	+	28.3640i	0.0421744	+	1.01236i
$786$		0			0
$787$	−0.846679	−	3.15985i	−0.0301809	−	0.112636i	0.949192	−	0.314697i	$-0.101903\pi$
$787$	−0.846679	−	3.15985i	−0.0301809	−	0.112636i	−0.979373	+	0.202061i	$0.935236\pi$
$788$	−4.79772	−	17.9053i	−0.170912	−	0.637851i
$789$		0			0
$790$	−0.0541311	−	1.29936i	−0.00192590	−	0.0462293i
$791$	−16.6475	+	44.9929i	−0.591917	+	1.59976i
$792$		0			0
$793$	−17.1214	−	4.58767i	−0.607999	−	0.162913i
$794$	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	−0.620502	−	0.784205i	$-0.713071\pi$
$797$	4.62151	−	4.62151i	0.163702	−	0.163702i	0.784205	+	0.620502i	$0.213071\pi$
$798$		0			0
$799$			54.2437i			1.91900i
$800$	−7.36510	−	1.32903i	−0.260396	−	0.0469882i
$801$		0			0
$802$	−1.00978	+	0.270571i	−0.0356567	+	0.00955419i
$803$	−5.19906	+	19.4032i	−0.183471	+	0.684723i
$804$		0			0
$805$	27.7904	+	1.41708i	0.979485	+	0.0499456i
$806$	1.85317			0.0652750
$807$		0			0
$808$	−4.24427	+	1.13725i	−0.149313	+	0.0400083i
$809$	−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	$0.943986\pi$
$812$	4.16640	−	44.8730i	0.146212	−	1.57473i
$813$		0			0
$814$	−4.68200	+	2.70315i	−0.164104	+	0.0947455i
$815$	7.05081	+	3.68834i	0.246979	+	0.129197i
$816$		0			0
$817$	0.649131	+	0.173934i	0.0227102	+	0.00608518i
$818$	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	0.905582	−	0.424172i	$-0.139435\pi$
$821$	2.44834	+	4.24064i	0.0854475	+	0.147999i	−0.820134	+	0.572171i	$0.806101\pi$
$822$		0			0
$823$	13.6917	+	51.0981i	0.477262	+	1.78117i	0.612628	+	0.790371i	$0.290112\pi$
$823$	13.6917	+	51.0981i	0.477262	+	1.78117i	−0.135366	+	0.990796i	$0.543221\pi$
$824$	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	$-0.485182\pi$
$827$	−27.3882	−	27.3882i	−0.952381	−	0.952381i	−0.998917	+	0.0465353i	$0.985182\pi$
$828$		0			0
$829$	22.4350	−	38.8585i	0.779199	−	1.34961i	−0.153205	−	0.988194i	$-0.548960\pi$
$829$	22.4350	−	38.8585i	0.779199	−	1.34961i	0.932404	−	0.361417i	$-0.117707\pi$
$830$	1.15619	−	0.362008i	0.0401320	−	0.0125655i
$831$		0			0
$832$	20.9154	−	20.9154i	0.725112	−	0.725112i
$833$	47.5524	+	22.7927i	1.64759	+	0.789721i
$834$		0			0
$835$	30.8279	−	19.5531i	1.06684	−	0.676662i
$836$	5.54267	+	3.20006i	0.191697	+	0.110676i
$837$		0			0
$838$	0.167781	−	0.626167i	0.00579590	−	0.0216306i
$839$	−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
$842$	−0.214389	+	0.800109i	−0.00738832	+	0.0275736i
$843$		0			0
$844$	−25.9652	−	14.9910i	−0.893758	−	0.516011i
$845$	−1.00773	+	4.50297i	−0.0346669	+	0.154907i
$846$		0			0
$847$	5.83173	+	4.12980i	0.200380	+	0.141902i
$848$	2.00413	−	2.00413i	0.0688222	−	0.0688222i
$849$		0			0
$850$	−4.29552	−	2.02397i	−0.147335	−	0.0694215i
$851$	−27.2471	+	47.1933i	−0.934017	+	1.61776i
$852$		0			0
$853$	16.7608	+	16.7608i	0.573879	+	0.573879i	0.933210	−	0.359331i	$-0.116995\pi$
$853$	16.7608	+	16.7608i	0.573879	+	0.573879i	−0.359331	+	0.933210i	$0.616995\pi$
$854$	−0.972934	−	1.17210i	−0.0332931	−	0.0401083i
$855$		0			0
$856$	−3.15920	−	5.47190i	−0.107979	−	0.187026i
$857$	−2.68121	−	10.0064i	−0.0915885	−	0.341813i	0.904892	−	0.425642i	$-0.139952\pi$
$857$	−2.68121	−	10.0064i	−0.0915885	−	0.341813i	−0.996480	+	0.0838291i	$0.973285\pi$
$858$		0			0
$859$	−15.8885	−	27.5197i	−0.542109	−	0.938960i	−0.998783	−	0.0493256i	$-0.984293\pi$
$859$	−15.8885	−	27.5197i	−0.542109	−	0.938960i	0.456674	−	0.889634i	$-0.349041\pi$
$860$	−3.41832	+	0.142406i	−0.116564	+	0.00485601i
$861$		0			0
$862$	0.225676	+	0.225676i	0.00768654	+	0.00768654i
$863$	10.3119	+	2.76308i	0.351022	+	0.0940562i	0.430022	−	0.902818i	$-0.358506\pi$
$863$	10.3119	+	2.76308i	0.351022	+	0.0940562i	−0.0789994	+	0.996875i	$0.525173\pi$
$864$		0			0
$865$	−1.44148	+	2.75560i	−0.0490118	+	0.0936933i
$866$	−1.33456	+	0.770508i	−0.0453502	+	0.0261829i
$867$		0			0
$868$	−16.2256	−	11.4903i	−0.550732	−	0.390007i
$869$		−	17.0763i		−	0.579275i
$870$		0			0
$871$	26.1852	+	15.1181i	0.887253	+	0.512256i
$872$	3.06785	−	0.822028i	0.103890	−	0.0278374i
$873$		0			0
$874$	−0.516745			−0.0174792
$875$	−28.8050	−	6.72857i	−0.973786	−	0.227467i
$876$		0			0
$877$	−9.93421	+	37.0750i	−0.335454	+	1.25193i	0.567921	+	0.823083i	$0.307748\pi$
$877$	−9.93421	+	37.0750i	−0.335454	+	1.25193i	−0.903376	+	0.428850i	$0.858919\pi$
$878$	−2.87004	+	0.769024i	−0.0968591	+	0.0259533i
$879$		0			0
$880$	−31.5397	−	7.05831i	−1.06320	−	0.237936i
$881$		−	49.3063i		−	1.66117i	−0.556892	−	0.830585i	$-0.688006\pi$
$881$		−	49.3063i		−	1.66117i	0.556892	−	0.830585i	$-0.311994\pi$
$882$		0			0
$883$	2.45973	−	2.45973i	0.0827765	−	0.0827765i	−0.664506	−	0.747283i	$-0.731358\pi$
$883$	2.45973	−	2.45973i	0.0827765	−	0.0827765i	0.747283	+	0.664506i	$0.231358\pi$
$884$	50.2391	−	29.0056i	1.68972	−	0.975563i
$885$		0			0
$886$	0.765149	−	1.32528i	0.0257057	−	0.0445236i
$887$	10.9169	+	2.92519i	0.366555	+	0.0982182i	0.437395	−	0.899270i	$-0.355901\pi$
$887$	10.9169	+	2.92519i	0.366555	+	0.0982182i	−0.0708396	+	0.997488i	$0.522568\pi$
$888$		0			0
$889$	28.2348	+	10.4470i	0.946965	+	0.350380i
$890$	−2.76093	+	0.115020i	−0.0925466	+	0.00385546i
$891$		0			0
$892$	8.76873	+	32.7253i	0.293599	+	1.09573i
$893$	−1.62410	−	6.06122i	−0.0543484	−	0.202831i
$894$		0			0
$895$	−15.4714	−	14.2339i	−0.517152	−	0.475787i
$896$	10.3129	−	1.76196i	0.344530	−	0.0588629i
$897$		0			0
$898$	2.60806	+	0.698827i	0.0870321	+	0.0233202i
$899$	−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
$905$	7.57267	−	33.8381i	0.251724	−	1.12482i
$906$		0			0
$907$	2.28481	−	0.612212i	0.0758657	−	0.0203282i	−0.220687	−	0.975345i	$-0.570830\pi$
$907$	2.28481	−	0.612212i	0.0758657	−	0.0203282i	0.296552	+	0.955017i	$0.404163\pi$
$908$	11.2926	−	42.1446i	0.374758	−	1.39862i
$909$		0			0
$910$	−2.14843	+	1.93996i	−0.0712197	+	0.0643089i
$911$	29.0548			0.962629			0.481315	−	0.876548i	$-0.340159\pi$
$911$	29.0548			0.962629			0.481315	+	0.876548i	$0.340159\pi$
$912$		0			0
$913$	15.3663	−	4.11738i	0.508550	−	0.136265i
$914$	0.933858	+	0.539163i	0.0308893	+	0.0178339i
$915$		0			0
$916$		−	2.51133i		−	0.0829766i
$917$	25.3906	−	35.8543i	0.838472	−	1.18401i
$918$		0			0
$919$	−10.5899	+	6.11407i	−0.349328	+	0.201685i	−0.664389	−	0.747387i	$-0.731308\pi$
$919$	−10.5899	+	6.11407i	−0.349328	+	0.201685i	0.315061	+	0.949071i	$0.397975\pi$
$920$	5.04122	−	1.57843i	0.166204	−	0.0520392i
$921$		0			0
$922$	−1.32118	−	0.354008i	−0.0435106	−	0.0116586i
$923$	−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
$928$	−3.32581	−	12.4121i	−0.109175	−	0.407447i
$929$	−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
$935$	−55.2481	−	28.9008i	−1.80681	−	0.945156i
$936$		0			0
$937$	−5.41861	+	5.41861i	−0.177018	+	0.177018i	−0.790055	−	0.613036i	$-0.789948\pi$
$937$	−5.41861	+	5.41861i	−0.177018	+	0.177018i	0.613036	+	0.790055i	$0.289948\pi$
$938$	1.08561	+	2.36079i	0.0354465	+	0.0770825i
$939$		0			0
$940$	17.1108	+	26.9773i	0.558092	+	0.879902i
$941$	−21.8564	−	12.6188i	−0.712499	−	0.411361i	0.0994867	−	0.995039i	$-0.468280\pi$
$941$	−21.8564	−	12.6188i	−0.712499	−	0.411361i	−0.811986	+	0.583677i	$0.801613\pi$
$942$		0			0
$943$	−8.78406	+	32.7826i	−0.286048	+	1.06755i
$944$	6.92927			0.225529
$945$		0			0
$946$	0.359846			0.0116996
$947$	9.57571	−	35.7370i	0.311169	−	1.16130i	−0.616335	−	0.787484i	$-0.711383\pi$
$947$	9.57571	−	35.7370i	0.311169	−	1.16130i	0.927504	−	0.373813i	$-0.121950\pi$
$948$		0			0
$949$	−18.2410	−	10.5315i	−0.592129	−	0.341866i
$950$	0.540583	+	0.0975479i	0.0175388	+	0.00316487i
$951$		0			0
$952$	9.96781	+	0.925498i	0.323059	+	0.0299956i
$953$	21.4026	−	21.4026i	0.693300	−	0.693300i	−0.269657	−	0.962956i	$-0.586910\pi$
$953$	21.4026	−	21.4026i	0.693300	−	0.693300i	0.962956	+	0.269657i	$0.0869103\pi$
$954$		0			0
$955$	−15.1593	−	48.4160i	−0.490542	−	1.56671i
$956$	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
$962$	−1.46719	−	5.47563i	−0.0473042	−	0.176542i
$963$		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	0.911538	−	0.411215i	$-0.134895\pi$
$967$	15.5584	+	15.5584i	0.500324	+	0.500324i	−0.411215	+	0.911538i	$0.634895\pi$
$968$	1.31035	+	0.351106i	0.0421161	+	0.0112850i
$969$		0			0
$970$	−0.393755	−	1.25759i	−0.0126427	−	0.0403786i
$971$	−26.4963	+	15.2976i	−0.850307	+	0.490925i	−0.860754	−	0.509021i	$-0.830008\pi$
$971$	−26.4963	+	15.2976i	−0.850307	+	0.490925i	0.0104475	+	0.999945i	$0.496674\pi$
$972$		0			0
$973$	−39.7978	+	18.3011i	−1.27586	+	0.586705i
$974$		−	0.468482i		−	0.0150111i
$975$		0			0
$976$	15.4444	+	8.91683i	0.494364	+	0.285421i
$977$	−1.47706	+	0.395776i	−0.0472552	+	0.0126620i	−0.282369	−	0.959306i	$-0.591120\pi$
$977$	−1.47706	+	0.395776i	−0.0472552	+	0.0126620i	0.235114	+	0.971968i	$0.424454\pi$
$978$		0			0
$979$	−36.2844			−1.15965
$980$	30.8392	−	3.66442i	0.985123	−	0.117055i
$981$		0			0
$982$	−0.625191	+	2.33325i	−0.0199507	+	0.0744569i
$983$	−8.83120	+	2.36631i	−0.281672	+	0.0754737i	−0.396889	−	0.917867i	$-0.629910\pi$
$983$	−8.83120	+	2.36631i	−0.281672	+	0.0754737i	0.115217	+	0.993340i	$0.463244\pi$
$984$		0			0
$985$	−11.1895	−	17.6416i	−0.356527	−	0.562109i
$986$		−	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	$0.0441523\pi$
$992$	−5.47593	−	1.46727i	−0.173861	−	0.0465859i
$993$		0			0
$994$	−0.542379	−	3.17459i	−0.0172032	−	0.100692i
$995$	−10.9860	+	11.9411i	−0.348280	+	0.378559i
$996$		0			0
$997$	15.8887	+	59.2973i	0.503199	+	1.87796i	0.478150	+	0.878278i	$0.341307\pi$
$997$	15.8887	+	59.2973i	0.503199	+	1.87796i	0.0250488	+	0.999686i	$0.492026\pi$
$998$	0.226723	+	0.846141i	0.00717678	+	0.0267841i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.cc.a.82.16	✓	128	21.5	even	6	inner
945.2.cc.a.82.17	yes	128	7.5	odd	6	inner
945.2.cc.a.703.16	yes	128	15.8	even	4	inner
945.2.cc.a.703.17	yes	128	5.3	odd	4	inner
945.2.cc.a.838.16	yes	128	35.33	even	12	inner
945.2.cc.a.838.17	yes	128	105.68	odd	12	inner
945.2.cc.a.892.16	yes	128	1.1	even	1	trivial
945.2.cc.a.892.17	yes	128	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-0.0326286 + 0.121772i) q^{2} +(1.71829 + 0.992054i) q^{4} +(2.18209 + 0.488334i) q^{5} +(-2.40378 + 1.10538i) q^{7} +(-0.355155 + 0.355155i) q^{8} +O(q^{10})\)	\(q+(-0.0326286 + 0.121772i) q^{2} +(1.71829 + 0.992054i) q^{4} +(2.18209 + 0.488334i) q^{5} +(-2.40378 + 1.10538i) q^{7} +(-0.355155 + 0.355155i) q^{8} +(-0.130664 + 0.249783i) q^{10} +(-1.85074 + 3.20557i) q^{11} +(-2.74441 - 2.74441i) q^{13} +(-0.0561718 - 0.328778i) q^{14} +(1.95245 + 3.38174i) q^{16} +(1.94975 + 7.27655i) q^{17} +(-0.435731 - 0.754709i) q^{19} +(3.26501 + 3.00385i) q^{20} +(-0.329960 - 0.329960i) q^{22} +(-4.54328 - 1.21737i) q^{23} +(4.52306 + 2.13118i) q^{25} +(0.423738 - 0.244645i) q^{26} +(-5.22697 - 0.485317i) q^{28} +8.58490i q^{29} +(3.28003 + 1.89373i) q^{31} +(-1.44581 + 0.387403i) q^{32} -0.949694 q^{34} +(-5.78506 + 1.23819i) q^{35} +(2.99861 - 11.1910i) q^{37} +(0.106119 - 0.0284346i) q^{38} +(-0.948416 + 0.601547i) q^{40} -7.21562i q^{41} +(-0.545286 + 0.545286i) q^{43} +(-6.36019 + 3.67206i) q^{44} +(0.296481 - 0.513521i) q^{46} +(6.95523 + 1.86365i) q^{47} +(4.55628 - 5.31416i) q^{49} +(-0.407098 + 0.481243i) q^{50} +(-1.99308 - 7.43829i) q^{52} +(-0.187857 - 0.701093i) q^{53} +(-5.60387 + 6.09108i) q^{55} +(0.461133 - 1.24629i) q^{56} +(-1.04540 - 0.280113i) q^{58} +(0.887254 - 1.53677i) q^{59} +(3.95514 - 2.28350i) q^{61} +(-0.337625 + 0.337625i) q^{62} +7.62109i q^{64} +(-4.64838 - 7.32875i) q^{65} +(-7.52498 + 2.01631i) q^{67} +(-3.86850 + 14.4375i) q^{68} +(0.0379815 - 0.744856i) q^{70} +9.65572 q^{71} +(5.24201 - 1.40459i) q^{73} +(1.26490 + 0.730291i) q^{74} -1.72907i q^{76} +(0.905389 - 9.75124i) q^{77} +(-3.99531 + 2.30670i) q^{79} +(2.60901 + 8.33271i) q^{80} +(0.878657 + 0.235436i) q^{82} +(-3.03903 - 3.03903i) q^{83} +(0.701142 + 16.8302i) q^{85} +(-0.0486084 - 0.0841923i) q^{86} +(-0.481176 - 1.79577i) q^{88} +(4.90134 + 8.48937i) q^{89} +(9.63057 + 3.56334i) q^{91} +(-6.59896 - 6.59896i) q^{92} +(-0.453879 + 0.786141i) q^{94} +(-0.582256 - 1.85963i) q^{95} +(-3.30555 + 3.30555i) q^{97} +(0.498449 + 0.728219i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 8 q^{7}+O(q^{10}) \) 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

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