LMFDB - Embedded newform 315.2.bf.b.109.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(109,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("315.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bf (of order $6$, degree $2$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} - 4 x^{13} - 14 x^{12} + 38 x^{11} - 40 x^{10} + 64 x^{9} + 291 x^{8} + \cdots + 1 $ x^16 - 2x^15 + 2x^14 - 4x^13 - 14x^12 + 38x^11 - 40x^10 + 64x^9 + 291x^8 - 630x^7 + 584x^6 - 800x^5 + 734x^4 - 188x^3 + 32x^2 - 8*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			109.3
Root			$-1.96595 - 0.526774i$ of defining polynomial
Character	$\chi$	$=$	315.109
Dual form			315.2.bf.b.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34443 + 0.776205i) q^{2} +(0.204988 - 0.355049i) q^{4} +(-1.88899 + 1.19655i) q^{5} +(-0.478401 - 2.60214i) q^{7} -2.46837i q^{8} +O(q^{10})$	\(q+(-1.34443 + 0.776205i) q^{2} +(0.204988 - 0.355049i) q^{4} +(-1.88899 + 1.19655i) q^{5} +(-0.478401 - 2.60214i) q^{7} -2.46837i q^{8} +(1.61083 - 3.07491i) q^{10} +(2.21538 - 3.83715i) q^{11} +1.73246i q^{13} +(2.66297 + 3.12705i) q^{14} +(2.32594 + 4.02864i) q^{16} +(2.36638 + 1.36623i) q^{17} +(-0.152578 - 0.264273i) q^{19} +(0.0376154 + 0.915960i) q^{20} +6.87834i q^{22} +(6.08316 - 3.51212i) q^{23} +(2.13653 - 4.52053i) q^{25} +(-1.34474 - 2.32916i) q^{26} +(-1.02195 - 0.363551i) q^{28} -7.79430 q^{29} +(2.64243 - 4.57683i) q^{31} +(-1.97875 - 1.14243i) q^{32} -4.24190 q^{34} +(4.01728 + 4.34297i) q^{35} +(3.18183 - 1.83703i) q^{37} +(0.410260 + 0.236864i) q^{38} +(2.95353 + 4.66271i) q^{40} +6.71562 q^{41} -9.71562i q^{43} +(-0.908250 - 1.57313i) q^{44} +(-5.45224 + 9.44356i) q^{46} +(1.57313 - 0.908250i) q^{47} +(-6.54227 + 2.48973i) q^{49} +(0.636449 + 7.73591i) q^{50} +(0.615108 + 0.355133i) q^{52} +(-1.48535 - 0.857566i) q^{53} +(0.406524 + 9.89912i) q^{55} +(-6.42304 + 1.18087i) q^{56} +(10.4789 - 6.04998i) q^{58} +(0.571217 - 0.989377i) q^{59} +(-4.77818 - 8.27604i) q^{61} +8.20428i q^{62} -5.75669 q^{64} +(-2.07298 - 3.27259i) q^{65} +(-7.26104 - 4.19216i) q^{67} +(0.970157 - 0.560120i) q^{68} +(-8.77198 - 2.72057i) q^{70} -10.2888 q^{71} +(11.1028 + 6.41022i) q^{73} +(-2.85183 + 4.93951i) q^{74} -0.125106 q^{76} +(-11.0446 - 3.92903i) q^{77} +(3.35686 + 5.81425i) q^{79} +(-9.21413 - 4.82694i) q^{80} +(-9.02866 + 5.21270i) q^{82} -5.09946i q^{83} +(-6.10482 + 0.250704i) q^{85} +(7.54131 + 13.0619i) q^{86} +(-9.47149 - 5.46837i) q^{88} +(-2.03533 - 3.52529i) q^{89} +(4.50810 - 0.828810i) q^{91} -2.87976i q^{92} +(-1.40998 + 2.44215i) q^{94} +(0.604434 + 0.316641i) q^{95} +2.87834i q^{97} +(6.86305 - 8.42540i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 2 q^{5}+O(q^{10}) $ 16 * q + 8 * q^4 - 2 * q^5	$ 16 q + 8 q^{4} - 2 q^{5} - 4 q^{10} + 24 q^{14} - 24 q^{19} + 8 q^{20} - 4 q^{25} + 12 q^{26} - 24 q^{29} + 16 q^{31} + 16 q^{34} + 10 q^{35} + 32 q^{40} - 16 q^{41} - 20 q^{44} - 32 q^{46} - 40 q^{49} + 40 q^{50} + 8 q^{55} - 84 q^{56} - 4 q^{59} + 16 q^{61} + 16 q^{64} - 30 q^{65} + 16 q^{70} + 56 q^{71} - 40 q^{74} - 64 q^{76} - 16 q^{79} - 52 q^{80} - 64 q^{85} + 48 q^{86} - 16 q^{89} + 8 q^{91} - 32 q^{94} + 22 q^{95}+O(q^{100}) $ 16 * q + 8 * q^4 - 2 * q^5 - 4 * q^10 + 24 * q^14 - 24 * q^19 + 8 * q^20 - 4 * q^25 + 12 * q^26 - 24 * q^29 + 16 * q^31 + 16 * q^34 + 10 * q^35 + 32 * q^40 - 16 * q^41 - 20 * q^44 - 32 * q^46 - 40 * q^49 + 40 * q^50 + 8 * q^55 - 84 * q^56 - 4 * q^59 + 16 * q^61 + 16 * q^64 - 30 * q^65 + 16 * q^70 + 56 * q^71 - 40 * q^74 - 64 * q^76 - 16 * q^79 - 52 * q^80 - 64 * q^85 + 48 * q^86 - 16 * q^89 + 8 * q^91 - 32 * q^94 + 22 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.34443	+	0.776205i	−0.950653	+	0.548860i	−0.893284	−	0.449493i	$-0.851605\pi$
$2$	−1.34443	+	0.776205i	−0.950653	+	0.548860i	−0.0573691	+	0.998353i	$0.518271\pi$
$3$		0			0
$3$		0			0
$4$	0.204988	−	0.355049i	0.102494	−	0.177524i
$5$	−1.88899	+	1.19655i	−0.844780	+	0.535114i
$5$	−1.88899	+	1.19655i	−0.844780	+	0.535114i
$6$		0			0
$7$	−0.478401	−	2.60214i	−0.180818	−	0.983516i
$7$	−0.478401	−	2.60214i	−0.180818	−	0.983516i
$8$		−	2.46837i		−	0.872700i
$9$		0			0
$10$	1.61083	−	3.07491i	0.509390	−	0.972373i
$11$	2.21538	−	3.83715i	0.667961	−	1.15694i	−0.310512	−	0.950569i	$-0.600500\pi$
$11$	2.21538	−	3.83715i	0.667961	−	1.15694i	0.978473	−	0.206373i	$-0.0661662\pi$
$12$		0			0
$13$			1.73246i			0.480498i	0.970711	+	0.240249i	$0.0772291\pi$
$13$			1.73246i			0.480498i	−0.970711	+	0.240249i	$0.922771\pi$
$14$	2.66297	+	3.12705i	0.711708	+	0.835739i
$15$		0			0
$16$	2.32594	+	4.02864i	0.581484	+	1.00716i
$17$	2.36638	+	1.36623i	0.573931	+	0.331359i	0.758718	−	0.651419i	$-0.225826\pi$
$17$	2.36638	+	1.36623i	0.573931	+	0.331359i	−0.184787	+	0.982779i	$0.559159\pi$
$18$		0			0
$19$	−0.152578	−	0.264273i	−0.0350038	−	0.0606284i	0.847993	−	0.530008i	$-0.177811\pi$
$19$	−0.152578	−	0.264273i	−0.0350038	−	0.0606284i	−0.882997	+	0.469379i	$0.844478\pi$
$20$	0.0376154	+	0.915960i	0.00841106	+	0.204815i
$21$		0			0
$22$			6.87834i			1.46647i
$23$	6.08316	−	3.51212i	1.26843	−	0.732327i	0.293737	−	0.955886i	$-0.405101\pi$
$23$	6.08316	−	3.51212i	1.26843	−	0.732327i	0.974690	+	0.223560i	$0.0717678\pi$
$24$		0			0
$25$	2.13653	−	4.52053i	0.427307	−	0.904107i
$26$	−1.34474	−	2.32916i	−0.263726	−	0.456786i
$27$		0			0
$28$	−1.02195	−	0.363551i	−0.193131	−	0.0687046i
$29$	−7.79430			−1.44737			−0.723683	−	0.690132i	$-0.757552\pi$
$29$	−7.79430			−1.44737			−0.723683	+	0.690132i	$0.757552\pi$
$30$		0			0
$31$	2.64243	−	4.57683i	0.474595	−	0.822023i	−0.524982	−	0.851114i	$-0.675928\pi$
$31$	2.64243	−	4.57683i	0.474595	−	0.822023i	0.999577	+	0.0290906i	$0.00926112\pi$
$32$	−1.97875	−	1.14243i	−0.349798	−	0.201956i
$33$		0			0
$34$	−4.24190			−0.727479
$35$	4.01728	+	4.34297i	0.679045	+	0.734097i
$36$		0			0
$37$	3.18183	−	1.83703i	0.523090	−	0.302006i	−0.215108	−	0.976590i	$-0.569010\pi$
$37$	3.18183	−	1.83703i	0.523090	−	0.302006i	0.738198	+	0.674584i	$0.235677\pi$
$38$	0.410260	+	0.236864i	0.0665530	+	0.0384244i
$39$		0			0
$40$	2.95353	+	4.66271i	0.466994	+	0.737240i
$41$	6.71562			1.04880			0.524402	−	0.851471i	$-0.324289\pi$
$41$	6.71562			1.04880			0.524402	+	0.851471i	$0.324289\pi$
$42$		0			0
$43$		−	9.71562i		−	1.48162i	−0.671715	−	0.740809i	$-0.734442\pi$
$43$		−	9.71562i		−	1.48162i	0.671715	−	0.740809i	$-0.265558\pi$
$44$	−0.908250	−	1.57313i	−0.136924	−	0.237159i
$45$		0			0
$46$	−5.45224	+	9.44356i	−0.803889	+	1.39238i
$47$	1.57313	−	0.908250i	0.229465	−	0.132482i	−0.380860	−	0.924633i	$-0.624372\pi$
$47$	1.57313	−	0.908250i	0.229465	−	0.132482i	0.610325	+	0.792151i	$0.291039\pi$
$48$		0			0
$49$	−6.54227	+	2.48973i	−0.934609	+	0.355676i
$50$	0.636449	+	7.73591i	0.0900075	+	1.09402i
$51$		0			0
$52$	0.615108	+	0.355133i	0.0853001	+	0.0492480i
$53$	−1.48535	−	0.857566i	−0.204028	−	0.117796i	0.394505	−	0.918894i	$-0.370916\pi$
$53$	−1.48535	−	0.857566i	−0.204028	−	0.117796i	−0.598533	+	0.801098i	$0.704249\pi$
$54$		0			0
$55$	0.406524	+	9.89912i	0.0548157	+	1.33480i
$56$	−6.42304	+	1.18087i	−0.858315	+	0.157800i
$57$		0			0
$58$	10.4789	−	6.04998i	1.37594	−	0.794401i
$59$	0.571217	−	0.989377i	0.0743661	−	0.128806i	−0.826444	−	0.563018i	$-0.809640\pi$
$59$	0.571217	−	0.989377i	0.0743661	−	0.128806i	0.900810	+	0.434213i	$0.142973\pi$
$60$		0			0
$61$	−4.77818	−	8.27604i	−0.611783	−	1.05964i	−0.990940	−	0.134307i	$-0.957119\pi$
$61$	−4.77818	−	8.27604i	−0.611783	−	1.05964i	0.379157	−	0.925332i	$-0.376214\pi$
$62$			8.20428i			1.04194i
$63$		0			0
$64$	−5.75669			−0.719586
$65$	−2.07298	−	3.27259i	−0.257121	−	0.405915i
$66$		0			0
$67$	−7.26104	−	4.19216i	−0.887078	−	0.512154i	−0.0140921	−	0.999901i	$-0.504486\pi$
$67$	−7.26104	−	4.19216i	−0.887078	−	0.512154i	−0.872985	+	0.487746i	$0.837819\pi$
$68$	0.970157	−	0.560120i	0.117649	−	0.0679245i
$69$		0			0
$70$	−8.77198	−	2.72057i	−1.04845	−	0.325171i
$71$	−10.2888			−1.22106			−0.610529	−	0.791994i	$-0.709043\pi$
$71$	−10.2888			−1.22106			−0.610529	+	0.791994i	$0.709043\pi$
$72$		0			0
$73$	11.1028	+	6.41022i	1.29949	+	0.750260i	0.980316	−	0.197437i	$-0.0632618\pi$
$73$	11.1028	+	6.41022i	1.29949	+	0.750260i	0.319172	+	0.947697i	$0.396595\pi$
$74$	−2.85183	+	4.93951i	−0.331518	+	0.574206i
$75$		0			0
$76$	−0.125106			−0.0143507
$77$	−11.0446	−	3.92903i	−1.25865	−	0.447754i
$78$		0			0
$79$	3.35686	+	5.81425i	0.377676	+	0.654154i	0.990724	−	0.135892i	$-0.0433900\pi$
$79$	3.35686	+	5.81425i	0.377676	+	0.654154i	−0.613048	+	0.790046i	$0.710057\pi$
$80$	−9.21413	−	4.82694i	−1.03017	−	0.539668i
$81$		0			0
$82$	−9.02866	+	5.21270i	−0.997049	+	0.575646i
$83$		−	5.09946i		−	0.559739i	−0.960038	−	0.279869i	$-0.909709\pi$
$83$		−	5.09946i		−	0.559739i	0.960038	−	0.279869i	$-0.0902911\pi$
$84$		0			0
$85$	−6.10482	+	0.250704i	−0.662161	+	0.0271927i
$86$	7.54131	+	13.0619i	0.813201	+	1.40850i
$87$		0			0
$88$	−9.47149	−	5.46837i	−1.00966	−	0.582930i
$89$	−2.03533	−	3.52529i	−0.215744	−	0.373680i	0.737758	−	0.675065i	$-0.235884\pi$
$89$	−2.03533	−	3.52529i	−0.215744	−	0.373680i	−0.953503	+	0.301385i	$0.902551\pi$
$90$		0			0
$91$	4.50810	−	0.828810i	0.472577	−	0.0868829i
$92$		−	2.87976i		−	0.300236i
$93$		0			0
$94$	−1.40998	+	2.44215i	−0.145428	+	0.251888i
$95$	0.604434	+	0.316641i	0.0620136	+	0.0324866i
$96$		0			0
$97$			2.87834i			0.292252i	0.989266	+	0.146126i	$0.0466804\pi$
$97$			2.87834i			0.292252i	−0.989266	+	0.146126i	$0.953320\pi$
$98$	6.86305	−	8.42540i	0.693273	−	0.851094i
$99$		0			0
$100$	−1.16705	−	1.68523i	−0.116705	−	0.168523i
$101$	3.60883	−	6.25068i	0.359092	−	0.621966i	−0.628717	−	0.777634i	$-0.716420\pi$
$101$	3.60883	−	6.25068i	0.359092	−	0.621966i	0.987809	+	0.155668i	$0.0497530\pi$
$102$		0			0
$103$	−9.76304	+	5.63670i	−0.961981	+	0.555400i	−0.896782	−	0.442472i	$-0.854102\pi$
$103$	−9.76304	+	5.63670i	−0.961981	+	0.555400i	−0.0651989	+	0.997872i	$0.520768\pi$
$104$	4.27635			0.419331
$105$		0			0
$106$	2.66259			0.258613
$107$	−5.98940	+	3.45798i	−0.579017	+	0.334296i	−0.760743	−	0.649054i	$-0.775165\pi$
$107$	−5.98940	+	3.45798i	−0.579017	+	0.334296i	0.181726	+	0.983349i	$0.441832\pi$
$108$		0			0
$109$	2.21097	−	3.82952i	0.211773	−	0.366801i	−0.740497	−	0.672060i	$-0.765410\pi$
$109$	2.21097	−	3.82952i	0.211773	−	0.366801i	0.952269	+	0.305259i	$0.0987430\pi$
$110$	−8.23029	−	12.9931i	−0.784727	−	1.23884i
$111$		0			0
$112$	9.37035	−	7.97971i	0.885415	−	0.754012i
$113$		−	2.86151i		−	0.269188i	−0.990901	−	0.134594i	$-0.957027\pi$
$113$		−	2.86151i		−	0.269188i	0.990901	−	0.134594i	$-0.0429730\pi$
$114$		0			0
$115$	−7.28858	+	13.9131i	−0.679664	+	1.29741i
$116$	−1.59774	+	2.76736i	−0.148346	+	0.256943i
$117$		0			0
$118$			1.77353i			0.163266i
$119$	2.42304	−	6.81125i	0.222120	−	0.624387i
$120$		0			0
$121$	−4.31579	−	7.47517i	−0.392345	−	0.679561i
$122$	12.8478	+	7.41769i	1.16319	+	0.671566i
$123$		0			0
$124$	−1.08333	−	1.87639i	−0.0972861	−	0.168504i
$125$	1.37317	+	11.0957i	0.122820	+	0.992429i
$126$		0			0
$127$			13.7325i			1.21856i	0.792956	+	0.609279i	$0.208541\pi$
$127$			13.7325i			1.21856i	−0.792956	+	0.609279i	$0.791459\pi$
$128$	11.6970	−	6.75324i	1.03387	−	0.596908i
$129$		0			0
$130$	5.32716	+	2.79070i	0.467223	+	0.244761i
$131$	10.9909	+	19.0368i	0.960277	+	1.66325i	0.721801	+	0.692100i	$0.243314\pi$
$131$	10.9909	+	19.0368i	0.960277	+	1.66325i	0.238476	+	0.971148i	$0.423352\pi$
$132$		0			0
$133$	−0.614682	+	0.523458i	−0.0532997	+	0.0453896i
$134$	13.0159			1.12440
$135$		0			0
$136$	3.37236	−	5.84110i	0.289177	−	0.500870i
$137$	2.59973	+	1.50095i	0.222110	+	0.128235i	0.606927	−	0.794758i	$-0.292402\pi$
$137$	2.59973	+	1.50095i	0.222110	+	0.128235i	−0.384817	+	0.922993i	$0.625735\pi$
$138$		0			0
$139$	21.7364			1.84366			0.921829	−	0.387597i	$-0.126695\pi$
$139$	21.7364			1.84366			0.921829	+	0.387597i	$0.126695\pi$
$140$	2.36546	−	0.536077i	0.199918	−	0.0453067i
$141$		0			0
$142$	13.8325	−	7.98622i	1.16080	−	0.670189i
$143$	6.64770	+	3.83805i	0.555908	+	0.320954i
$144$		0			0
$145$	14.7233	−	9.32628i	1.22271	−	0.774505i
$146$	−19.9026			−1.64715
$147$		0			0
$148$		−	1.50628i		−	0.123815i
$149$	2.60654	+	4.51467i	0.213536	+	0.369856i	0.952819	−	0.303540i	$-0.0981685\pi$
$149$	2.60654	+	4.51467i	0.213536	+	0.369856i	−0.739282	+	0.673396i	$0.764835\pi$
$150$		0			0
$151$	4.85686	−	8.41233i	0.395246	−	0.684585i	−0.597887	−	0.801580i	$-0.703993\pi$
$151$	4.85686	−	8.41233i	0.395246	−	0.684585i	0.993132	+	0.116995i	$0.0373262\pi$
$152$	−0.652324	+	0.376619i	−0.0529104	+	0.0305478i
$153$		0			0
$154$	17.8984	−	3.29060i	1.44230	−	0.265164i
$155$	0.484889	+	11.8074i	0.0389472	+	0.948391i
$156$		0			0
$157$	−8.20284	−	4.73591i	−0.654658	−	0.377967i	0.135581	−	0.990766i	$-0.456710\pi$
$157$	−8.20284	−	4.73591i	−0.654658	−	0.377967i	−0.790238	+	0.612800i	$0.790043\pi$
$158$	−9.02610	−	5.21122i	−0.718078	−	0.414582i
$159$		0			0
$160$	5.10482	−	0.209638i	0.403571	−	0.0165733i
$161$	−12.0492	−	14.1490i	−0.949610	−	1.11510i
$162$		0			0
$163$	4.67358	−	2.69830i	0.366063	−	0.211347i	−0.305674	−	0.952136i	$-0.598882\pi$
$163$	4.67358	−	2.69830i	0.366063	−	0.211347i	0.671737	+	0.740789i	$0.265548\pi$
$164$	1.37662	−	2.38437i	0.107496	−	0.186188i
$165$		0			0
$166$	3.95823	+	6.85585i	0.307218	+	0.532117i
$167$		−	0.312550i		−	0.0241859i	−0.999927	−	0.0120929i	$-0.996151\pi$
$167$		−	0.312550i		−	0.0241859i	0.999927	−	0.0120929i	$-0.00384939\pi$
$168$		0			0
$169$	9.99859			0.769122
$170$	8.01288	−	5.07564i	0.614560	−	0.389284i
$171$		0			0
$172$	−3.44952	−	1.99158i	−0.263024	−	0.151857i
$173$	−8.32661	+	4.80737i	−0.633061	+	0.365498i	−0.781937	−	0.623358i	$-0.785768\pi$
$173$	−8.32661	+	4.80737i	−0.633061	+	0.365498i	0.148876	+	0.988856i	$0.452435\pi$
$174$		0			0
$175$	−12.7852	−	3.39693i	−0.966469	−	0.256784i
$176$	20.6113			1.55363
$177$		0			0
$178$	5.47269	+	3.15966i	0.410196	+	0.236827i
$179$	4.42730	−	7.66831i	0.330912	−	0.573157i	−0.651779	−	0.758409i	$-0.725977\pi$
$179$	4.42730	−	7.66831i	0.330912	−	0.573157i	0.982691	+	0.185252i	$0.0593103\pi$
$180$		0			0
$181$	−16.9234			−1.25790			−0.628952	−	0.777445i	$-0.716516\pi$
$181$	−16.9234			−1.25790			−0.628952	+	0.777445i	$0.716516\pi$
$182$	−5.41748	+	4.61348i	−0.401571	+	0.341974i
$183$		0			0
$184$	−8.66920	−	15.0155i	−0.639102	−	1.10696i
$185$	−3.81233	+	7.27735i	−0.280288	+	0.535042i
$186$		0			0
$187$	10.4848	−	6.05343i	0.766728	−	0.442670i
$188$		−	0.744719i		−	0.0543142i
$189$		0			0
$190$	−1.05839	+	0.0434647i	−0.0767840	+	0.00315326i
$191$	0.159271	+	0.275865i	0.0115244	+	0.0199609i	0.871730	−	0.489986i	$-0.162998\pi$
$191$	0.159271	+	0.275865i	0.0115244	+	0.0199609i	−0.860206	+	0.509947i	$0.829665\pi$
$192$		0			0
$193$	−1.81289	−	1.04667i	−0.130494	−	0.0753410i	0.433332	−	0.901234i	$-0.357338\pi$
$193$	−1.81289	−	1.04667i	−0.130494	−	0.0753410i	−0.563826	+	0.825894i	$0.690671\pi$
$194$	−2.23418	−	3.86972i	−0.160405	−	0.277830i
$195$		0			0
$196$	−0.457107	+	2.83319i	−0.0326505	+	0.202371i
$197$		−	22.5798i		−	1.60874i	−0.594126	−	0.804372i	$-0.702502\pi$
$197$		−	22.5798i		−	1.60874i	0.594126	−	0.804372i	$-0.297498\pi$
$198$		0			0
$199$	−3.75204	+	6.49872i	−0.265975	+	0.460682i	−0.967819	−	0.251649i	$-0.919027\pi$
$199$	−3.75204	+	6.49872i	−0.265975	+	0.460682i	0.701844	+	0.712331i	$0.252361\pi$
$200$	−11.1583	−	5.27375i	−0.789014	−	0.372911i
$201$		0			0
$202$			11.2048i			0.788365i
$203$	3.72880	+	20.2819i	0.261710	+	1.42351i
$204$		0			0
$205$	−12.6857	+	8.03558i	−0.886009	+	0.561229i
$206$	8.75046	−	15.1562i	0.609673	−	1.05599i
$207$		0			0
$208$	−6.97945	+	4.02959i	−0.483938	+	0.279402i
$209$	−1.35207			−0.0935248
$210$		0			0
$211$	7.67216			0.528173			0.264087	−	0.964499i	$-0.414930\pi$
$211$	7.67216			0.528173			0.264087	+	0.964499i	$0.414930\pi$
$212$	−0.608955	+	0.351581i	−0.0418232	+	0.0241467i
$213$		0			0
$214$	5.36820	−	9.29800i	0.366963	−	0.635598i
$215$	11.6252	+	18.3527i	0.792834	+	1.25164i
$216$		0			0
$217$	−13.1737	−	4.68643i	−0.894289	−	0.318135i
$218$			6.86467i			0.464934i
$219$		0			0
$220$	3.59801	+	1.88486i	0.242577	+	0.127077i
$221$	−2.36694	+	4.09966i	−0.159217	+	0.275773i
$222$		0			0
$223$			6.90208i			0.462198i	0.972930	+	0.231099i	$0.0742321\pi$
$223$			6.90208i			0.462198i	−0.972930	+	0.231099i	$0.925768\pi$
$224$	−2.02614	+	5.69554i	−0.135377	+	0.380549i
$225$		0			0
$226$	2.22112	+	3.84709i	0.147746	+	0.255904i
$227$	−5.49684	−	3.17360i	−0.364838	−	0.210639i	0.306363	−	0.951915i	$-0.400888\pi$
$227$	−5.49684	−	3.17360i	−0.364838	−	0.210639i	−0.671201	+	0.741275i	$0.734221\pi$
$228$		0			0
$229$	3.37834	+	5.85146i	0.223247	+	0.386676i	0.955792	−	0.294043i	$-0.0950009\pi$
$229$	3.37834	+	5.85146i	0.223247	+	0.386676i	−0.732545	+	0.680719i	$0.761668\pi$
$230$	−1.00049	−	24.3626i	−0.0659705	−	1.60642i
$231$		0			0
$232$			19.2392i			1.26312i
$233$	−6.41899	+	3.70601i	−0.420522	+	0.242789i	−0.695301	−	0.718719i	$-0.744729\pi$
$233$	−6.41899	+	3.70601i	−0.420522	+	0.242789i	0.274779	+	0.961508i	$0.411395\pi$
$234$		0			0
$235$	−1.88486	+	3.59801i	−0.122955	+	0.234708i
$236$	−0.234185	−	0.405620i	−0.0152441	−	0.0264036i
$237$		0			0
$238$	2.02933	+	11.0380i	0.131542	+	0.715488i
$239$	7.36355			0.476309			0.238154	−	0.971227i	$-0.423458\pi$
$239$	7.36355			0.476309			0.238154	+	0.971227i	$0.423458\pi$
$240$		0			0
$241$	−6.84002	+	11.8473i	−0.440605	+	0.763149i	−0.997734	−	0.0672759i	$-0.978569\pi$
$241$	−6.84002	+	11.8473i	−0.440605	+	0.763149i	0.557130	+	0.830425i	$0.311903\pi$
$242$	11.6045	+	6.69988i	0.745967	+	0.430684i
$243$		0			0
$244$	−3.91787			−0.250816
$245$	9.37916	−	12.5312i	0.599212	−	0.800590i
$246$		0			0
$247$	0.457842	−	0.264335i	0.0291318	−	0.0168193i
$248$	−11.2973	−	6.52250i	−0.717380	−	0.414179i
$249$		0			0
$250$	−10.4587	−	13.8515i	−0.661463	−	0.876044i
$251$	−23.4843			−1.48231			−0.741157	−	0.671331i	$-0.765723\pi$
$251$	−23.4843			−1.48231			−0.741157	+	0.671331i	$0.765723\pi$
$252$		0			0
$253$		−	31.1226i		−	1.95666i
$254$	−10.6592	−	18.4623i	−0.668818	−	1.15843i
$255$		0			0
$256$	−4.72710	+	8.18758i	−0.295444	+	0.511724i
$257$	12.6417	−	7.29871i	0.788570	−	0.455281i	−0.0508890	−	0.998704i	$-0.516205\pi$
$257$	12.6417	−	7.29871i	0.788570	−	0.455281i	0.839459	+	0.543423i	$0.182872\pi$
$258$		0			0
$259$	−6.30241	−	7.40074i	−0.391612	−	0.459860i
$260$	−1.58686	+	0.0651672i	−0.0984131	+	0.00404150i
$261$		0			0
$262$	−29.5528	−	17.0623i	−1.82578	−	1.05411i
$263$	−4.40755	−	2.54470i	−0.271781	−	0.156913i	0.357916	−	0.933754i	$-0.383488\pi$
$263$	−4.40755	−	2.54470i	−0.271781	−	0.156913i	−0.629697	+	0.776841i	$0.716821\pi$
$264$		0			0
$265$	3.83192	−	0.157364i	0.235393	−	0.00966680i
$266$	0.420084	−	1.18087i	0.0257570	−	0.0724038i
$267$		0			0
$268$	−2.97685	+	1.71868i	−0.181840	+	0.104985i
$269$	−15.2550	+	26.4224i	−0.930112	+	1.61100i	−0.146984	+	0.989139i	$0.546957\pi$
$269$	−15.2550	+	26.4224i	−0.930112	+	1.61100i	−0.783127	+	0.621862i	$0.786377\pi$
$270$		0			0
$271$	9.74401	+	16.8771i	0.591907	+	1.02521i	0.993975	+	0.109603i	$0.0349579\pi$
$271$	9.74401	+	16.8771i	0.591907	+	1.02521i	−0.402069	+	0.915609i	$0.631709\pi$
$272$			12.7110i			0.770720i
$273$		0			0
$274$	−4.66019			−0.281532
$275$	−12.6127	−	18.2129i	−0.760576	−	1.09828i
$276$		0			0
$277$	22.0665	+	12.7401i	1.32585	+	0.765478i	0.984655	−	0.174515i	$-0.0558357\pi$
$277$	22.0665	+	12.7401i	1.32585	+	0.765478i	0.341193	+	0.939993i	$0.389169\pi$
$278$	−29.2230	+	16.8719i	−1.75268	+	1.01191i
$279$		0			0
$280$	10.7201	−	9.91614i	0.640646	−	0.592603i
$281$	22.1914			1.32383			0.661914	−	0.749580i	$-0.269745\pi$
$281$	22.1914			1.32383			0.661914	+	0.749580i	$0.269745\pi$
$282$		0			0
$283$	15.6960	+	9.06209i	0.933031	+	0.538685i	0.887769	−	0.460290i	$-0.152254\pi$
$283$	15.6960	+	9.06209i	0.933031	+	0.538685i	0.0452618	+	0.998975i	$0.485588\pi$
$284$	−2.10908	+	3.65303i	−0.125151	+	0.216768i
$285$		0			0
$286$	−11.9165			−0.704635
$287$	−3.21276	−	17.4750i	−0.189643	−	1.03152i
$288$		0			0
$289$	−4.76683	−	8.25640i	−0.280402	−	0.485670i
$290$	−12.5553	+	23.9668i	−0.737274	+	1.40738i
$291$		0			0
$292$	4.55188	−	2.62803i	0.266379	−	0.153794i
$293$			13.8958i			0.811801i	0.913917	+	0.405901i	$0.133042\pi$
$293$			13.8958i			0.811801i	−0.913917	+	0.405901i	$0.866958\pi$
$294$		0			0
$295$	0.104819	+	2.55241i	0.00610279	+	0.148607i
$296$	−4.53447	−	7.85394i	−0.263561	−	0.456501i
$297$		0			0
$298$	−7.00861	−	4.04642i	−0.405998	−	0.234403i
$299$	6.08460	+	10.5388i	0.351881	+	0.609476i
$300$		0			0
$301$	−25.2814	+	4.64796i	−1.45720	+	0.267904i
$302$			15.0797i			0.867737i
$303$		0			0
$304$	0.709774	−	1.22936i	0.0407083	−	0.0705089i
$305$	18.9286	+	9.91600i	1.08385	+	0.567788i
$306$		0			0
$307$		−	29.8332i		−	1.70267i	−0.524622	−	0.851335i	$-0.675793\pi$
$307$		−	29.8332i		−	1.70267i	0.524622	−	0.851335i	$-0.324207\pi$
$308$	−3.65901	+	3.11598i	−0.208491	+	0.177549i
$309$		0			0
$310$	−9.81684	−	15.4978i	−0.557559	−	0.880214i
$311$	6.75662	−	11.7028i	0.383133	−	0.663606i	−0.608375	−	0.793650i	$-0.708178\pi$
$311$	6.75662	−	11.7028i	0.383133	−	0.663606i	0.991508	+	0.130044i	$0.0415117\pi$
$312$		0			0
$313$	−25.1023	+	14.4928i	−1.41887	+	0.819184i	−0.996200	−	0.0871001i	$-0.972240\pi$
$313$	−25.1023	+	14.4928i	−1.41887	+	0.819184i	−0.422669	+	0.906284i	$0.638907\pi$
$314$	14.7041			0.829803
$315$		0			0
$316$	2.75246			0.154838
$317$	1.00341	−	0.579319i	0.0563571	−	0.0325378i	−0.471557	−	0.881836i	$-0.656308\pi$
$317$	1.00341	−	0.579319i	0.0563571	−	0.0325378i	0.527914	+	0.849298i	$0.322974\pi$
$318$		0			0
$319$	−17.2673	+	29.9079i	−0.966785	+	1.67452i
$320$	10.8743	−	6.88817i	0.607892	−	0.385060i
$321$		0			0
$322$	27.1818	+	9.66969i	1.51478	+	0.538871i
$323$		−	0.833827i		−	0.0463954i
$324$		0			0
$325$	7.83164	+	3.70146i	0.434421	+	0.205320i
$326$	−4.18886	+	7.25532i	−0.231999	+	0.401835i
$327$		0			0
$328$		−	16.5766i		−	0.915292i
$329$	−3.11598	−	3.65901i	−0.171790	−	0.201728i
$330$		0			0
$331$	14.1746	+	24.5511i	0.779104	+	1.34945i	0.932459	+	0.361277i	$0.117659\pi$
$331$	14.1746	+	24.5511i	0.779104	+	1.34945i	−0.153355	+	0.988171i	$0.549008\pi$
$332$	−1.81056	−	1.04533i	−0.0993673	−	0.0573697i
$333$		0			0
$334$	0.242603	+	0.420201i	0.0132746	+	0.0229924i
$335$	18.7321	−	0.769266i	1.02345	−	0.0420295i
$336$		0			0
$337$		−	15.9729i		−	0.870101i	−0.900406	−	0.435051i	$-0.856730\pi$
$337$		−	15.9729i		−	0.870101i	0.900406	−	0.435051i	$-0.143270\pi$
$338$	−13.4424	+	7.76095i	−0.731168	+	0.422140i
$339$		0			0
$340$	−1.16240	+	2.21890i	−0.0630400	+	0.120337i
$341$	−11.7080	−	20.2788i	−0.634023	−	1.09816i
$342$		0			0
$343$	9.60845	+	15.8328i	0.518808	+	0.854891i
$344$	−23.9817			−1.29301
$345$		0			0
$346$	7.46301	−	12.9263i	0.401214	−	0.694923i
$347$	−11.2687	−	6.50599i	−0.604935	−	0.349260i	0.166045	−	0.986118i	$-0.446900\pi$
$347$	−11.2687	−	6.50599i	−0.604935	−	0.349260i	−0.770981	+	0.636859i	$0.780234\pi$
$348$		0			0
$349$	−32.0724			−1.71680			−0.858398	−	0.512984i	$-0.828540\pi$
$349$	−32.0724			−1.71680			−0.858398	+	0.512984i	$0.828540\pi$
$350$	19.8254	−	5.35699i	1.05971	−	0.286343i
$351$		0			0
$352$	−8.76737	+	5.06185i	−0.467303	+	0.269797i
$353$	11.5778	+	6.68445i	0.616225	+	0.355778i	0.775398	−	0.631473i	$-0.217549\pi$
$353$	11.5778	+	6.68445i	0.616225	+	0.355778i	−0.159173	+	0.987251i	$0.550883\pi$
$354$		0			0
$355$	19.4354	−	12.3111i	1.03152	−	0.653405i
$356$	−1.66887			−0.0884498
$357$		0			0
$358$			13.7460i			0.726497i
$359$	6.55974	+	11.3618i	0.346210	+	0.599653i	0.985573	−	0.169252i	$-0.0541352\pi$
$359$	6.55974	+	11.3618i	0.346210	+	0.599653i	−0.639363	+	0.768905i	$0.720802\pi$
$360$		0			0
$361$	9.45344	−	16.3738i	0.497549	−	0.861781i
$362$	22.7522	−	13.1360i	1.19583	−	0.690412i
$363$		0			0
$364$	0.629837	−	1.77049i	0.0330124	−	0.0927990i
$365$	−28.6432	+	1.17628i	−1.49926	+	0.0615694i
$366$		0			0
$367$	11.3761	+	6.56798i	0.593826	+	0.342846i	0.766609	−	0.642114i	$-0.221943\pi$
$367$	11.3761	+	6.56798i	0.593826	+	0.342846i	−0.172783	+	0.984960i	$0.555276\pi$
$368$	28.2981	+	16.3379i	1.47514	+	0.851672i
$369$		0			0
$370$	−0.523313	−	12.7430i	−0.0272057	−	0.662478i
$371$	−1.52091	+	4.27534i	−0.0789620	+	0.221965i
$372$		0			0
$373$	−25.6514	+	14.8099i	−1.32818	+	0.766826i	−0.985018	−	0.172450i	$-0.944832\pi$
$373$	−25.6514	+	14.8099i	−1.32818	+	0.766826i	−0.343163	+	0.939276i	$0.611498\pi$
$374$	−9.39740	+	16.2768i	−0.485928	+	0.841652i
$375$		0			0
$376$	−2.24190	−	3.88308i	−0.115617	−	0.200254i
$377$		−	13.5033i		−	0.695456i
$378$		0			0
$379$	−7.47689			−0.384062			−0.192031	−	0.981389i	$-0.561507\pi$
$379$	−7.47689			−0.384062			−0.192031	+	0.981389i	$0.561507\pi$
$380$	0.236324	−	0.149696i	0.0121232	−	0.00767925i
$381$		0			0
$382$	−0.428255	−	0.247253i	−0.0219114	−	0.0126506i
$383$	20.5586	−	11.8695i	1.05050	−	0.606505i	0.127709	−	0.991812i	$-0.459238\pi$
$383$	20.5586	−	11.8695i	1.05050	−	0.606505i	0.922789	+	0.385307i	$0.125904\pi$
$384$		0			0
$385$	25.5644	−	5.79358i	1.30288	−	0.295268i
$386$	3.24972			0.165406
$387$		0			0
$388$	1.02195	+	0.590025i	0.0518818	+	0.0299540i
$389$	7.06523	−	12.2373i	0.358221	−	0.620458i	−0.629442	−	0.777047i	$-0.716717\pi$
$389$	7.06523	−	12.2373i	0.358221	−	0.620458i	0.987664	+	0.156589i	$0.0500499\pi$
$390$		0			0
$391$	19.1934			0.970653
$392$	6.14558	+	16.1487i	0.310398	+	0.815634i
$393$		0			0
$394$	17.5265	+	30.3569i	0.882975	+	1.52936i
$395$	−13.2981	−	6.96638i	−0.669100	−	0.350517i
$396$		0			0
$397$	−9.75974	+	5.63479i	−0.489827	+	0.282802i	−0.724503	−	0.689272i	$-0.757931\pi$
$397$	−9.75974	+	5.63479i	−0.489827	+	0.282802i	0.234676	+	0.972074i	$0.424597\pi$
$398$		−	11.6494i		−	0.583932i
$399$		0			0
$400$	23.1810	−	1.90715i	1.15905	−	0.0953576i
$401$	11.6484	+	20.1757i	0.581694	+	1.00752i	0.995279	+	0.0970583i	$0.0309433\pi$
$401$	11.6484	+	20.1757i	0.581694	+	1.00752i	−0.413584	+	0.910466i	$0.635723\pi$
$402$		0			0
$403$	7.92917	+	4.57791i	0.394980	+	0.228042i
$404$	−1.47953	−	2.56262i	−0.0736094	−	0.127495i
$405$		0			0
$406$	−20.7560	−	24.3732i	−1.03010	−	1.20962i
$407$		−	16.2789i		−	0.806914i
$408$		0			0
$409$	10.3239	−	17.8815i	0.510484	−	0.884184i	−0.489443	−	0.872036i	$-0.662800\pi$
$409$	10.3239	−	17.8815i	0.510484	−	0.884184i	0.999926	−	0.0121481i	$-0.00386695\pi$
$410$	10.8177	−	20.6500i	0.534250	−	1.01983i
$411$		0			0
$412$			4.62181i			0.227700i
$413$	−2.84777	−	1.01307i	−0.140130	−	0.0498498i
$414$		0			0
$415$	6.10176	+	9.63281i	0.299524	+	0.472856i
$416$	1.97922	−	3.42811i	0.0970393	−	0.168077i
$417$		0			0
$418$	1.81776	−	1.04948i	0.0889096	−	0.0513320i
$419$	−5.48254			−0.267839			−0.133920	−	0.990992i	$-0.542756\pi$
$419$	−5.48254			−0.267839			−0.133920	+	0.990992i	$0.542756\pi$
$420$		0			0
$421$	−3.78079			−0.184264			−0.0921322	−	0.995747i	$-0.529368\pi$
$421$	−3.78079			−0.184264			−0.0921322	+	0.995747i	$0.529368\pi$
$422$	−10.3146	+	5.95517i	−0.502109	+	0.289893i
$423$		0			0
$424$	−2.11679	+	3.66639i	−0.102800	+	0.178055i
$425$	11.2319	−	7.77830i	0.544829	−	0.377303i
$426$		0			0
$427$	−19.2495	+	16.3927i	−0.931551	+	0.793301i
$428$			2.83537i			0.137053i
$429$		0			0
$430$	−29.8747	−	15.6502i	−1.44069	−	0.754722i
$431$	−13.7564	+	23.8267i	−0.662621	+	1.14769i	0.317303	+	0.948324i	$0.397223\pi$
$431$	−13.7564	+	23.8267i	−0.662621	+	1.14769i	−0.979924	+	0.199369i	$0.936111\pi$
$432$		0			0
$433$			8.75514i			0.420745i	0.977621	+	0.210373i	$0.0674677\pi$
$433$			8.75514i			0.420745i	−0.977621	+	0.210373i	$0.932532\pi$
$434$	21.3487	−	3.92493i	1.02477	−	0.188403i
$435$		0			0
$436$	−0.906444	−	1.57001i	−0.0434108	−	0.0751897i
$437$	−1.85631	−	1.07174i	−0.0887996	−	0.0512685i
$438$		0			0
$439$	−5.30636	−	9.19088i	−0.253259	−	0.438657i	0.711163	−	0.703028i	$-0.248169\pi$
$439$	−5.30636	−	9.19088i	−0.253259	−	0.438657i	−0.964421	+	0.264371i	$0.914836\pi$
$440$	24.4347	−	1.00345i	1.16488	−	0.0478377i
$441$		0			0
$442$		−	7.34891i		−	0.349552i
$443$	−17.3080	+	9.99278i	−0.822328	+	0.474771i	−0.851219	−	0.524811i	$-0.824136\pi$
$443$	−17.3080	+	9.99278i	−0.822328	+	0.474771i	0.0288905	+	0.999583i	$0.490803\pi$
$444$		0			0
$445$	8.06289	+	4.22385i	0.382218	+	0.200230i
$446$	−5.35743	−	9.27934i	−0.253682	−	0.439390i
$447$		0			0
$448$	2.75400	+	14.9797i	0.130114	+	0.707725i
$449$	3.02578			0.142795			0.0713976	−	0.997448i	$-0.477254\pi$
$449$	3.02578			0.142795			0.0713976	+	0.997448i	$0.477254\pi$
$450$		0			0
$451$	14.8776	−	25.7688i	0.700561	−	1.21341i
$452$	−1.01598	−	0.586574i	−0.0477875	−	0.0275901i
$453$		0			0
$454$	9.85346			0.462446
$455$	−7.52403	+	6.95978i	−0.352732	+	0.326280i
$456$		0			0
$457$	1.97570	−	1.14067i	0.0924195	−	0.0533584i	−0.453078	−	0.891471i	$-0.649674\pi$
$457$	1.97570	−	1.14067i	0.0924195	−	0.0533584i	0.545497	+	0.838112i	$0.316341\pi$
$458$	−9.08387	−	5.24457i	−0.424461	−	0.245063i
$459$		0			0
$460$	3.44578	+	5.43982i	0.160660	+	0.253633i
$461$	24.0678			1.12095			0.560475	−	0.828171i	$-0.310619\pi$
$461$	24.0678			1.12095			0.560475	+	0.828171i	$0.310619\pi$
$462$		0			0
$463$		−	11.1290i		−	0.517211i	−0.965983	−	0.258605i	$-0.916737\pi$
$463$		−	11.1290i		−	0.517211i	0.965983	−	0.258605i	$-0.0832629\pi$
$464$	−18.1290	−	31.4004i	−0.841620	−	1.45773i
$465$		0			0
$466$	5.75324	−	9.96490i	0.266514	−	0.461615i
$467$	−24.7481	+	14.2883i	−1.14521	+	0.661185i	−0.947714	−	0.319120i	$-0.896613\pi$
$467$	−24.7481	+	14.2883i	−1.14521	+	0.661185i	−0.197491	+	0.980305i	$0.563279\pi$
$468$		0			0
$469$	−7.43491	+	20.8998i	−0.343312	+	0.965062i
$470$	−0.258732	−	6.30029i	−0.0119344	−	0.290611i
$471$		0			0
$472$	−2.44215	−	1.40998i	−0.112409	−	0.0648994i
$473$	−37.2803	−	21.5238i	−1.71415	−	0.989664i
$474$		0			0
$475$	−1.52064	+	0.125106i	−0.0697719	+	0.00574028i
$476$	−1.92163	−	2.25652i	−0.0880780	−	0.103427i
$477$		0			0
$478$	−9.89975	+	5.71562i	−0.452804	+	0.261427i
$479$	2.79005	−	4.83250i	0.127480	−	0.220803i	−0.795219	−	0.606322i	$-0.792644\pi$
$479$	2.79005	−	4.83250i	0.127480	−	0.220803i	0.922700	+	0.385519i	$0.125978\pi$
$480$		0			0
$481$	3.18258	+	5.51240i	0.145113	+	0.251344i
$482$		−	21.2370i		−	0.967320i
$483$		0			0
$484$	−3.53873			−0.160852
$485$	−3.44409	−	5.43715i	−0.156388	−	0.246888i
$486$		0			0
$487$	−7.22858	−	4.17342i	−0.327558	−	0.189116i	0.327198	−	0.944956i	$-0.393895\pi$
$487$	−7.22858	−	4.17342i	−0.327558	−	0.189116i	−0.654756	+	0.755840i	$0.727229\pi$
$488$	−20.4283	+	11.7943i	−0.924747	+	0.533903i
$489$		0			0
$490$	−2.88279	+	24.1274i	−0.130231	+	1.08997i
$491$	−0.557405			−0.0251554			−0.0125777	−	0.999921i	$-0.504004\pi$
$491$	−0.557405			−0.0251554			−0.0125777	+	0.999921i	$0.504004\pi$
$492$		0			0
$493$	−18.4443	−	10.6488i	−0.830689	−	0.479598i
$494$	−0.410357	+	0.710759i	−0.0184628	+	0.0319785i
$495$		0			0
$496$	24.5845			1.10388
$497$	4.92217	+	26.7729i	0.220790	+	1.20093i
$498$		0			0
$499$	−13.0168	−	22.5458i	−0.582713	−	1.00929i	−0.995156	−	0.0983057i	$-0.968658\pi$
$499$	−13.0168	−	22.5458i	−0.582713	−	1.00929i	0.412443	−	0.910983i	$-0.364676\pi$
$500$	4.22100	+	1.78694i	0.188769	+	0.0799143i
$501$		0			0
$502$	31.5729	−	18.2286i	1.40917	−	0.813583i
$503$			5.52409i			0.246307i	0.992388	+	0.123154i	$0.0393008\pi$
$503$			5.52409i			0.246307i	−0.992388	+	0.123154i	$0.960699\pi$
$504$		0			0
$505$	0.662224	+	16.1256i	0.0294686	+	0.717580i
$506$	24.1575	+	41.8421i	1.07393	+	1.86011i
$507$		0			0
$508$	4.87569	+	2.81498i	0.216324	+	0.124895i
$509$	−11.4446	−	19.8227i	−0.507274	−	0.878625i	−0.999965	−	0.00842016i	$-0.997320\pi$
$509$	−11.4446	−	19.8227i	−0.507274	−	0.878625i	0.492690	−	0.870205i	$-0.336014\pi$
$510$		0			0
$511$	11.3687	−	31.9578i	0.502921	−	1.41373i
$512$			12.3362i			0.545186i
$513$		0			0
$514$	−11.3306	+	19.6251i	−0.499771	+	0.865628i
$515$	11.6977	−	22.3296i	0.515460	−	0.983960i
$516$		0			0
$517$		−	8.04846i		−	0.353971i
$518$	14.2176	+	5.05779i	0.624686	+	0.222226i
$519$		0			0
$520$	−8.07796	+	5.11687i	−0.354242	+	0.224390i
$521$	13.0995	−	22.6889i	0.573898	−	0.994020i	−0.422263	−	0.906474i	$-0.638764\pi$
$521$	13.0995	−	22.6889i	0.573898	−	0.994020i	0.996160	−	0.0875466i	$-0.0279027\pi$
$522$		0			0
$523$	23.2753	−	13.4380i	1.01776	−	0.587603i	0.104304	−	0.994545i	$-0.466738\pi$
$523$	23.2753	−	13.4380i	1.01776	−	0.587603i	0.913454	+	0.406943i	$0.133405\pi$
$524$	9.01197			0.393690
$525$		0			0
$526$	7.90083			0.344493
$527$	12.5060	−	7.22034i	0.544770	−	0.314523i
$528$		0			0
$529$	13.1699	−	22.8109i	0.572605	−	0.991780i
$530$	−5.02959	+	3.18592i	−0.218471	+	0.138387i
$531$		0			0
$532$	0.0598510	+	0.325545i	0.00259487	+	0.0141141i
$533$			11.6345i			0.503948i
$534$		0			0
$535$	7.17624	−	13.6987i	0.310256	−	0.592246i
$536$	−10.3478	+	17.9229i	−0.446957	+	0.774153i
$537$		0			0
$538$		−	47.3639i		−	2.04200i
$539$	−4.94013	+	30.6193i	−0.212786	+	1.31887i
$540$		0			0
$541$	9.39222	+	16.2678i	0.403803	+	0.699408i	0.994181	−	0.107719i	$-0.0343547\pi$
$541$	9.39222	+	16.2678i	0.403803	+	0.699408i	−0.590378	+	0.807127i	$0.701021\pi$
$542$	−26.2002	−	15.1267i	−1.12540	−	0.649747i
$543$		0			0
$544$	−3.12166	−	5.40687i	−0.133840	−	0.231817i
$545$	0.405716	+	9.87944i	0.0173789	+	0.423189i
$546$		0			0
$547$		−	13.4126i		−	0.573483i	−0.958008	−	0.286742i	$-0.907428\pi$
$547$		−	13.4126i		−	0.573483i	0.958008	−	0.286742i	$-0.0925721\pi$
$548$	1.06582	−	0.615353i	0.0455297	−	0.0262866i
$549$		0			0
$550$	31.0938	+	14.6958i	1.32584	+	0.626631i
$551$	1.18924	+	2.05982i	0.0506633	+	0.0877515i
$552$		0			0
$553$	13.5236	−	11.5166i	0.575081	−	0.489734i
$554$	−39.5557			−1.68056
$555$		0			0
$556$	4.45569	−	7.71749i	0.188963	−	0.327294i
$557$	34.8008	+	20.0922i	1.47456	+	0.851336i	0.999589	−	0.0286677i	$-0.00912646\pi$
$557$	34.8008	+	20.0922i	1.47456	+	0.851336i	0.474968	+	0.880003i	$0.342460\pi$
$558$		0			0
$559$	16.8319			0.711914
$560$	−8.15233	+	26.2857i	−0.344499	+	1.11077i
$561$		0			0
$562$	−29.8347	+	17.2251i	−1.25850	+	0.726595i
$563$	21.8134	+	12.5940i	0.919325	+	0.530772i	0.883420	−	0.468583i	$-0.155235\pi$
$563$	21.8134	+	12.5940i	0.919325	+	0.530772i	0.0359052	+	0.999355i	$0.488569\pi$
$564$		0			0
$565$	3.42394	+	5.40535i	0.144046	+	0.227405i
$566$	−28.1362			−1.18265
$567$		0			0
$568$			25.3966i			1.06562i
$569$	5.51757	+	9.55672i	0.231309	+	0.400638i	0.958194	−	0.286121i	$-0.0923659\pi$
$569$	5.51757	+	9.55672i	0.231309	+	0.400638i	−0.726885	+	0.686759i	$0.759033\pi$
$570$		0			0
$571$	−14.3573	+	24.8677i	−0.600836	+	1.04068i	0.391858	+	0.920026i	$0.371832\pi$
$571$	−14.3573	+	24.8677i	−0.600836	+	1.04068i	−0.992695	+	0.120654i	$0.961501\pi$
$572$	2.72539	−	1.57351i	0.113954	−	0.0657916i
$573$		0			0
$574$	17.8835	+	21.0001i	0.746442	+	0.876526i
$575$	−2.87976	−	35.0029i	−0.120094	−	1.45972i
$576$		0			0
$577$	5.94444	+	3.43202i	0.247470	+	0.142877i	0.618605	−	0.785702i	$-0.287698\pi$
$577$	5.94444	+	3.43202i	0.247470	+	0.142877i	−0.371135	+	0.928579i	$0.621031\pi$
$578$	12.8173	+	7.40008i	0.533130	+	0.307803i
$579$		0			0
$580$	−0.293186	−	7.13927i	−0.0121739	−	0.296442i
$581$	−13.2695	+	2.43959i	−0.550512	+	0.101211i
$582$		0			0
$583$	−6.58121	+	3.79966i	−0.272566	+	0.157366i
$584$	15.8228	−	27.4059i	0.654752	−	1.13406i
$585$		0			0
$586$	−10.7860	−	18.6819i	−0.445565	−	0.771741i
$587$		−	9.03965i		−	0.373106i	−0.982445	−	0.186553i	$-0.940268\pi$
$587$		−	9.03965i		−	0.373106i	0.982445	−	0.186553i	$-0.0597317\pi$
$588$		0			0
$589$	−1.61271			−0.0664506
$590$	−2.12211	−	3.35016i	−0.0873660	−	0.137924i
$591$		0			0
$592$	14.8015	+	8.54564i	0.608337	+	0.351224i
$593$	−4.42364	+	2.55399i	−0.181657	+	0.104880i	−0.588071	−	0.808809i	$-0.700112\pi$
$593$	−4.42364	+	2.55399i	−0.181657	+	0.104880i	0.406414	+	0.913689i	$0.366779\pi$
$594$		0			0
$595$	3.57292	+	15.7657i	0.146475	+	0.646329i
$596$	2.13724			0.0875446
$597$		0			0
$598$	−16.3606	−	9.44578i	−0.669034	−	0.386267i
$599$	14.9721	−	25.9325i	0.611745	−	1.05957i	−0.379202	−	0.925314i	$-0.623801\pi$
$599$	14.9721	−	25.9325i	0.611745	−	1.05957i	0.990946	−	0.134259i	$-0.0428654\pi$
$600$		0			0
$601$	−12.5387			−0.511466			−0.255733	−	0.966747i	$-0.582317\pi$
$601$	−12.5387			−0.511466			−0.255733	+	0.966747i	$0.582317\pi$
$602$	30.3812	−	25.8724i	1.23825	−	1.05448i
$603$		0			0
$604$	−1.99119	−	3.44884i	−0.0810204	−	0.140331i
$605$	17.0969	+	8.95643i	0.695087	+	0.364130i
$606$		0			0
$607$	8.31216	−	4.79903i	0.337380	−	0.194786i	−0.321733	−	0.946831i	$-0.604265\pi$
$607$	8.31216	−	4.79903i	0.337380	−	0.194786i	0.659113	+	0.752044i	$0.270932\pi$
$608$			0.697242i			0.0282769i
$609$		0			0
$610$	−33.1450	+	1.36115i	−1.34200	+	0.0551115i
$611$	1.57351	+	2.72539i	0.0636572	+	0.110258i
$612$		0			0
$613$	23.9583	+	13.8323i	0.967665	+	0.558682i	0.898524	−	0.438925i	$-0.144641\pi$
$613$	23.9583	+	13.8323i	0.967665	+	0.558682i	0.0691416	+	0.997607i	$0.477974\pi$
$614$	23.1567	+	40.1085i	0.934527	+	1.61865i
$615$		0			0
$616$	−9.69830	+	27.2622i	−0.390755	+	1.09843i
$617$			20.4155i			0.821896i	0.911659	+	0.410948i	$0.134802\pi$
$617$			20.4155i			0.821896i	−0.911659	+	0.410948i	$0.865198\pi$
$618$		0			0
$619$	−7.72112	+	13.3734i	−0.310338	+	0.537521i	−0.978435	−	0.206553i	$-0.933776\pi$
$619$	−7.72112	+	13.3734i	−0.310338	+	0.537521i	0.668098	+	0.744074i	$0.267109\pi$
$620$	4.29159	+	2.24821i	0.172354	+	0.0902901i
$621$		0			0
$622$			20.9781i			0.841145i
$623$	−8.19960	+	6.98271i	−0.328510	+	0.279756i
$624$		0			0
$625$	−15.8705	−	19.3165i	−0.634818	−	0.772662i
$626$	22.4988	−	38.9691i	0.899234	−	1.55752i
$627$		0			0
$628$	−3.36296	+	1.94161i	−0.134197	+	0.0774785i
$629$	10.0392			0.400290
$630$		0			0
$631$	−38.1722			−1.51961			−0.759805	−	0.650151i	$-0.774705\pi$
$631$	−38.1722			−1.51961			−0.759805	+	0.650151i	$0.774705\pi$
$632$	14.3517	−	8.28597i	0.570881	−	0.329598i
$633$		0			0
$634$	−0.899340	+	1.55770i	−0.0357173	+	0.0618643i
$635$	−16.4316	−	25.9404i	−0.652067	−	1.02941i
$636$		0			0
$637$	−4.31336	−	11.3342i	−0.170901	−	0.449078i
$638$		−	53.6119i		−	2.12252i
$639$		0			0
$640$	−14.0148	+	26.7528i	−0.553983	+	1.05750i
$641$	−8.39007	+	14.5320i	−0.331388	+	0.573981i	−0.982784	−	0.184757i	$-0.940850\pi$
$641$	−8.39007	+	14.5320i	−0.331388	+	0.573981i	0.651396	+	0.758738i	$0.274184\pi$
$642$		0			0
$643$			14.2002i			0.560001i	0.960000	+	0.280001i	$0.0903346\pi$
$643$			14.2002i			0.560001i	−0.960000	+	0.280001i	$0.909665\pi$
$644$	−7.49354	+	1.37768i	−0.295287	+	0.0542882i
$645$		0			0
$646$	0.647220	+	1.12102i	0.0254645	+	0.0441059i
$647$	12.5474	+	7.24426i	0.493290	+	0.284801i	0.725938	−	0.687760i	$-0.241406\pi$
$647$	12.5474	+	7.24426i	0.493290	+	0.284801i	−0.232648	+	0.972561i	$0.574739\pi$
$648$		0			0
$649$	−2.53092	−	4.38369i	−0.0993474	−	0.172075i
$650$	−13.4021	+	1.10262i	−0.525676	+	0.0432484i
$651$		0			0
$652$		−	2.21247i		−	0.0866469i
$653$	8.90562	−	5.14166i	0.348504	−	0.201209i	−0.315522	−	0.948918i	$-0.602180\pi$
$653$	8.90562	−	5.14166i	0.348504	−	0.201209i	0.664026	+	0.747709i	$0.268846\pi$
$654$		0			0
$655$	−43.5400	−	22.8090i	−1.70125	−	0.891222i
$656$	15.6201	+	27.0548i	0.609863	+	1.05631i
$657$		0			0
$658$	7.02935	+	2.50063i	0.274032	+	0.0974846i
$659$	14.9773			0.583433			0.291717	−	0.956505i	$-0.405774\pi$
$659$	14.9773			0.583433			0.291717	+	0.956505i	$0.405774\pi$
$660$		0			0
$661$	−1.22323	+	2.11870i	−0.0475782	+	0.0824079i	−0.888834	−	0.458230i	$-0.848484\pi$
$661$	−1.22323	+	2.11870i	−0.0475782	+	0.0824079i	0.841256	+	0.540638i	$0.181817\pi$
$662$	−38.1133	−	22.0047i	−1.48131	−	0.855238i
$663$		0			0
$664$	−12.5874			−0.488484
$665$	0.534781	−	1.72430i	0.0207379	−	0.0668656i
$666$		0			0
$667$	−47.4140	+	27.3745i	−1.83588	+	1.05994i
$668$	−0.110971	−	0.0640689i	−0.00429358	−	0.00247890i
$669$		0			0
$670$	−24.5869	+	15.5742i	−0.949874	+	0.601684i
$671$	−42.3418			−1.63459
$672$		0			0
$673$		−	17.2596i		−	0.665310i	−0.943049	−	0.332655i	$-0.892055\pi$
$673$		−	17.2596i		−	0.665310i	0.943049	−	0.332655i	$-0.107945\pi$
$674$	12.3983	+	21.4744i	0.477564	+	0.827164i
$675$		0			0
$676$	2.04959	−	3.54999i	0.0788302	−	0.136538i
$677$	−10.0791	+	5.81918i	−0.387372	+	0.223649i	−0.681021	−	0.732264i	$-0.738464\pi$
$677$	−10.0791	+	5.81918i	−0.387372	+	0.223649i	0.293649	+	0.955913i	$0.405130\pi$
$678$		0			0
$679$	7.48986	−	1.37700i	0.287434	−	0.0528445i
$680$	0.618831	+	15.0689i	0.0237311	+	0.577868i
$681$		0			0
$682$	31.4810	+	18.1756i	1.20547	+	0.695979i
$683$	26.9299	+	15.5480i	1.03044	+	0.594928i	0.917112	−	0.398629i	$-0.130514\pi$
$683$	26.9299	+	15.5480i	1.03044	+	0.594928i	0.113333	+	0.993557i	$0.463847\pi$
$684$		0			0
$685$	−6.70681	+	0.275426i	−0.256254	+	0.0105235i
$686$	−25.2073	−	13.8279i	−0.962421	−	0.527952i
$687$		0			0
$688$	39.1407	−	22.5979i	1.49223	−	0.861537i
$689$	1.48570	−	2.57330i	0.0566006	−	0.0980351i
$690$		0			0
$691$	8.96695	+	15.5312i	0.341119	+	0.590835i	0.984641	−	0.174592i	$-0.0558607\pi$
$691$	8.96695	+	15.5312i	0.341119	+	0.590835i	−0.643522	+	0.765428i	$0.722527\pi$
$692$			3.94181i			0.149845i
$693$		0			0
$694$	20.1999			0.766778
$695$	−41.0597	+	26.0087i	−1.55749	+	0.986566i
$696$		0			0
$697$	15.8917	+	9.17508i	0.601941	+	0.347531i
$698$	43.1190	−	24.8947i	1.63208	−	0.942280i
$699$		0			0
$700$	−3.82688	+	3.84304i	−0.144642	+	0.145253i
$701$	−7.04488			−0.266081			−0.133041	−	0.991111i	$-0.542474\pi$
$701$	−7.04488			−0.266081			−0.133041	+	0.991111i	$0.542474\pi$
$702$		0			0
$703$	−0.970956	−	0.560582i	−0.0366203	−	0.0211427i
$704$	−12.7532	+	22.0893i	−0.480656	+	0.832520i
$705$		0			0
$706$	−20.7540			−0.781088
$707$	−17.9916	−	6.40036i	−0.676644	−	0.240710i
$708$		0			0
$709$	−12.9622	−	22.4511i	−0.486804	−	0.843170i	0.513080	−	0.858341i	$-0.328504\pi$
$709$	−12.9622	−	22.4511i	−0.486804	−	0.843170i	−0.999885	+	0.0151705i	$0.995171\pi$
$710$	−16.5736	+	31.6372i	−0.621995	+	1.18732i
$711$		0			0
$712$	−8.70172	+	5.02394i	−0.326111	+	0.188280i
$713$		−	37.1221i		−	1.39023i
$714$		0			0
$715$	−17.1498	+	0.704286i	−0.641367	+	0.0263388i
$716$	−1.81508	−	3.14382i	−0.0678329	−	0.117490i
$717$		0			0
$718$	−17.6382	−	10.1834i	−0.658251	−	0.380041i
$719$	−15.6427	−	27.0940i	−0.583376	−	1.01044i	−0.995076	−	0.0991173i	$-0.968398\pi$
$719$	−15.6427	−	27.0940i	−0.583376	−	1.01044i	0.411700	−	0.911320i	$-0.364935\pi$
$720$		0			0
$721$	19.3381	+	22.7082i	0.720189	+	0.845698i
$722$			29.3512i			1.09234i
$723$		0			0
$724$	−3.46908	+	6.00862i	−0.128927	+	0.223309i
$725$	−16.6528	+	35.2344i	−0.618469	+	1.30857i
$726$		0			0
$727$		−	22.8312i		−	0.846761i	−0.905952	−	0.423380i	$-0.860843\pi$
$727$		−	22.8312i		−	0.846761i	0.905952	−	0.423380i	$-0.139157\pi$
$728$	−2.04581	−	11.1277i	−0.0758227	−	0.412419i
$729$		0			0
$730$	37.5957	−	23.8144i	1.39148	−	0.881412i
$731$	13.2738	−	22.9908i	0.490948	−	0.850347i
$732$		0			0
$733$	−5.15661	+	2.97717i	−0.190464	+	0.109964i	−0.592200	−	0.805791i	$-0.701740\pi$
$733$	−5.15661	+	2.97717i	−0.190464	+	0.109964i	0.401736	+	0.915756i	$0.368407\pi$
$734$	−20.3924			−0.752696
$735$		0			0
$736$	−16.0494			−0.591590
$737$	−32.1719	+	18.5745i	−1.18507	+	0.684199i
$738$		0			0
$739$	20.7539	−	35.9469i	0.763446	−	1.32233i	−0.177618	−	0.984099i	$-0.556839\pi$
$739$	20.7539	−	35.9469i	0.763446	−	1.32233i	0.941064	−	0.338228i	$-0.109827\pi$
$740$	1.80233	+	2.84533i	0.0662551	+	0.104596i
$741$		0			0
$742$	−1.27378	−	6.92842i	−0.0467620	−	0.254350i
$743$			6.80015i			0.249473i	0.992190	+	0.124737i	$0.0398086\pi$
$743$			6.80015i			0.249473i	−0.992190	+	0.124737i	$0.960191\pi$
$744$		0			0
$745$	−10.3258	−	5.40928i	−0.378306	−	0.198181i
$746$	22.9910	−	39.8216i	0.841760	−	1.45797i
$747$		0			0
$748$		−	4.96351i		−	0.181484i
$749$	11.8635	+	13.9310i	0.433482	+	0.509026i
$750$		0			0
$751$	−11.8056	−	20.4480i	−0.430794	−	0.746157i	0.566148	−	0.824304i	$-0.308433\pi$
$751$	−11.8056	−	20.4480i	−0.430794	−	0.746157i	−0.996942	+	0.0781464i	$0.975100\pi$
$752$	7.31802	+	4.22506i	0.266861	+	0.154072i
$753$		0			0
$754$	10.4813	+	18.1542i	0.381708	+	0.661137i
$755$	0.891238	+	21.7022i	0.0324355	+	0.789825i
$756$		0			0
$757$		−	16.2267i		−	0.589769i	−0.955533	−	0.294884i	$-0.904719\pi$
$757$		−	16.2267i		−	0.589769i	0.955533	−	0.294884i	$-0.0952811\pi$
$758$	10.0521	−	5.80360i	0.365110	−	0.210796i
$759$		0			0
$760$	0.781586	−	1.49197i	0.0283511	−	0.0541193i
$761$	−1.27754	−	2.21276i	−0.0463108	−	0.0802126i	0.841941	−	0.539570i	$-0.181413\pi$
$761$	−1.27754	−	2.21276i	−0.0463108	−	0.0802126i	−0.888252	+	0.459357i	$0.848080\pi$
$762$		0			0
$763$	−11.0227	−	3.92122i	−0.399047	−	0.141958i
$764$	0.130594			0.00472473
$765$		0			0
$766$	−18.4264	+	31.9154i	−0.665772	+	1.15315i
$767$	1.71406	+	0.989610i	0.0618910	+	0.0357328i
$768$		0			0
$769$	45.4525			1.63906			0.819530	−	0.573037i	$-0.194235\pi$
$769$	45.4525			1.63906			0.819530	+	0.573037i	$0.194235\pi$
$770$	−29.8725	+	27.6323i	−1.07653	+	0.995798i
$771$		0			0
$772$	−0.743238	+	0.429109i	−0.0267497	+	0.0154440i
$773$	−44.5909	−	25.7446i	−1.60382	−	0.925968i	−0.990713	−	0.135970i	$-0.956585\pi$
$773$	−44.5909	−	25.7446i	−1.60382	−	0.925968i	−0.613110	−	0.789997i	$-0.710082\pi$
$774$		0			0
$775$	−15.0441	−	21.7238i	−0.540399	−	0.780341i
$776$	7.10482			0.255048
$777$		0			0
$778$			21.9363i			0.786453i
$779$	−1.02466	−	1.77476i	−0.0367121	−	0.0635873i
$780$		0			0
$781$	−22.7936	+	39.4797i	−0.815619	+	1.41269i
$782$	−25.8041	+	14.8980i	−0.922754	+	0.532752i
$783$		0			0
$784$	−25.2471	−	20.5655i	−0.901683	−	0.734481i
$785$	21.1618	−	0.869044i	0.755297	−	0.0310175i
$786$		0			0
$787$	17.4517	+	10.0757i	0.622085	+	0.359161i	0.777680	−	0.628660i	$-0.216396\pi$
$787$	17.4517	+	10.0757i	0.622085	+	0.359161i	−0.155596	+	0.987821i	$0.549730\pi$
$788$	−8.01693	−	4.62858i	−0.285591	−	0.164886i
$789$		0			0
$790$	23.2857	−	0.956264i	0.828466	−	0.0340223i
$791$	−7.44605	+	1.36895i	−0.264751	+	0.0486742i
$792$		0			0
$793$	14.3379	−	8.27800i	0.509154	−	0.293960i
$794$	8.74750	−	15.1511i	0.310437	−	0.537693i
$795$		0			0
$796$	1.53824	+	2.66431i	0.0545216	+	0.0944341i
$797$		−	13.0702i		−	0.462971i	−0.972838	−	0.231486i	$-0.925641\pi$
$797$		−	13.0702i		−	0.462971i	0.972838	−	0.231486i	$-0.0743587\pi$
$798$		0			0
$799$	4.96351			0.175596
$800$	−9.39209	+	6.50418i	−0.332060	+	0.229957i
$801$		0			0
$802$	−31.3209	−	18.0831i	−1.10598	−	0.638537i
$803$	49.1939	−	28.4021i	1.73602	−	1.00229i
$804$		0			0
$805$	39.6908	+	12.3099i	1.39892	+	0.433865i
$806$	−14.2136			−0.500652
$807$		0			0
$808$	−15.4290	−	8.90793i	−0.542790	−	0.313380i
$809$	0.868598	−	1.50446i	0.0305383	−	0.0528938i	−0.850352	−	0.526214i	$-0.823611\pi$
$809$	0.868598	−	1.50446i	0.0305383	−	0.0528938i	0.880891	+	0.473320i	$0.156945\pi$
$810$		0			0
$811$	−27.9004			−0.979715			−0.489858	−	0.871802i	$-0.662951\pi$
$811$	−27.9004			−0.979715			−0.489858	+	0.871802i	$0.662951\pi$
$812$	7.96541	+	2.83363i	0.279531	+	0.0994408i
$813$		0			0
$814$	12.6357	+	21.8857i	0.442883	+	0.767095i
$815$	−5.59969	+	10.6892i	−0.196148	+	0.374427i
$816$		0			0
$817$	−2.56758	+	1.48239i	−0.0898282	+	0.0518623i
$818$			32.0538i			1.12074i
$819$		0			0
$820$	0.252611	+	6.15124i	0.00882156	+	0.214811i
$821$	8.46799	+	14.6670i	0.295535	+	0.511881i	0.975109	−	0.221725i	$-0.0711688\pi$
$821$	8.46799	+	14.6670i	0.295535	+	0.511881i	−0.679574	+	0.733607i	$0.737835\pi$
$822$		0			0
$823$	−8.56526	−	4.94516i	−0.298566	−	0.172377i	0.343232	−	0.939251i	$-0.388478\pi$
$823$	−8.56526	−	4.94516i	−0.298566	−	0.172377i	−0.641799	+	0.766873i	$0.721812\pi$
$824$	13.9134	+	24.0988i	0.484698	+	0.839521i
$825$		0			0
$826$	4.61496	−	0.848456i	0.160575	−	0.0295216i
$827$			35.3201i			1.22820i	0.789228	+	0.614101i	$0.210481\pi$
$827$			35.3201i			1.22820i	−0.789228	+	0.614101i	$0.789519\pi$
$828$		0			0
$829$	4.64975	−	8.05361i	0.161493	−	0.279713i	−0.773912	−	0.633294i	$-0.781703\pi$
$829$	4.64975	−	8.05361i	0.161493	−	0.279713i	0.935404	+	0.353580i	$0.115036\pi$
$830$	−15.6804	−	8.21438i	−0.544275	−	0.285125i
$831$		0			0
$832$		−	9.97323i		−	0.345760i
$833$	−18.8830	−	3.04659i	−0.654258	−	0.105558i
$834$		0			0
$835$	0.373982	+	0.590403i	0.0129422	+	0.0204317i
$836$	−0.277158	+	0.480052i	−0.00958571	+	0.0166029i
$837$		0			0
$838$	7.37086	−	4.25557i	0.254622	−	0.147006i
$839$	−7.93405			−0.273914			−0.136957	−	0.990577i	$-0.543732\pi$
$839$	−7.93405			−0.273914			−0.136957	+	0.990577i	$0.543732\pi$
$840$		0			0
$841$	31.7512			1.09487
$842$	5.08299	−	2.93467i	0.175171	−	0.101135i
$843$		0			0
$844$	1.57270	−	2.72399i	0.0541345	−	0.0937636i
$845$	−18.8872	+	11.9638i	−0.649739	+	0.411568i
$846$		0			0
$847$	−17.3868	+	14.8064i	−0.597416	+	0.508755i
$848$		−	7.97857i		−	0.273985i
$849$		0			0
$850$	−9.06295	+	19.1756i	−0.310857	+	0.657719i
$851$	12.9037	−	22.3499i	0.442334	−	0.766146i
$852$		0			0
$853$			30.0757i			1.02977i	0.857258	+	0.514887i	$0.172166\pi$
$853$			30.0757i			1.02977i	−0.857258	+	0.514887i	$0.827834\pi$
$854$	13.1555	−	36.9804i	0.450170	−	1.26544i
$855$		0			0
$856$	8.53557	+	14.7840i	0.291740	+	0.505308i
$857$	−40.8221	−	23.5686i	−1.39446	−	0.805090i	−0.400652	−	0.916230i	$-0.631216\pi$
$857$	−40.8221	−	23.5686i	−1.39446	−	0.805090i	−0.993805	+	0.111141i	$0.964550\pi$
$858$		0			0
$859$	−16.3183	−	28.2642i	−0.556774	−	0.964361i	−0.997763	−	0.0668485i	$-0.978706\pi$
$859$	−16.3183	−	28.2642i	−0.556774	−	0.964361i	0.440989	−	0.897512i	$-0.354628\pi$
$860$	8.89912	−	0.365457i	0.303458	−	0.0124620i
$861$		0			0
$862$		−	42.7110i		−	1.45474i
$863$	32.3982	−	18.7051i	1.10285	−	0.636728i	0.165879	−	0.986146i	$-0.446954\pi$
$863$	32.3982	−	18.7051i	1.10285	−	0.636728i	0.936967	+	0.349418i	$0.113621\pi$
$864$		0			0
$865$	9.97659	−	19.0443i	0.339214	−	0.647525i
$866$	−6.79578	−	11.7706i	−0.230930	−	0.399983i
$867$		0			0
$868$	−4.36435	+	3.71665i	−0.148136	+	0.126151i
$869$	29.7468			1.00909
$870$		0			0
$871$	7.26275	−	12.5795i	0.246089	−	0.426239i
$872$	−9.45266	−	5.45750i	−0.320108	−	0.184814i
$873$		0			0
$874$	3.32757			0.112557
$875$	28.2156	−	8.88136i	0.953862	−	0.300245i
$876$		0			0
$877$	29.0687	−	16.7828i	0.981581	−	0.566716i	0.0788336	−	0.996888i	$-0.474880\pi$
$877$	29.0687	−	16.7828i	0.981581	−	0.566716i	0.902747	+	0.430172i	$0.141547\pi$
$878$	14.2680	+	8.23764i	0.481522	+	0.278007i
$879$		0			0
$880$	−38.9344	+	24.6625i	−1.31248	+	0.831371i
$881$	12.1952			0.410867			0.205433	−	0.978671i	$-0.434140\pi$
$881$	12.1952			0.410867			0.205433	+	0.978671i	$0.434140\pi$
$882$		0			0
$883$			11.0408i			0.371552i	0.982592	+	0.185776i	$0.0594799\pi$
$883$			11.0408i			0.371552i	−0.982592	+	0.185776i	$0.940520\pi$
$884$	0.970385	+	1.68076i	0.0326376	+	0.0565300i
$885$		0			0
$886$	15.5129	−	26.8691i	0.521166	−	0.902685i
$887$	−1.35180	+	0.780464i	−0.0453891	+	0.0262054i	−0.522523	−	0.852625i	$-0.675009\pi$
$887$	−1.35180	+	0.780464i	−0.0453891	+	0.0262054i	0.477134	+	0.878831i	$0.341676\pi$
$888$		0			0
$889$	35.7338	−	6.56962i	1.19847	−	0.220338i
$890$	−14.1185	+	0.579801i	−0.473254	+	0.0194350i
$891$		0			0
$892$	2.45058	+	1.41484i	0.0820514	+	0.0473724i
$893$	−0.480052	−	0.277158i	−0.0160643	−	0.00927474i
$894$		0			0
$895$	0.812414	+	19.7828i	0.0271560	+	0.661267i
$896$	−23.1687	−	27.2064i	−0.774012	−	0.908900i
$897$		0			0
$898$	−4.06793	+	2.34862i	−0.135749	+	0.0783745i
$899$	−20.5959	+	35.6732i	−0.686913	+	1.18977i
$900$		0			0
$901$	−2.34326	−	4.05865i	−0.0780654	−	0.135213i
$902$			46.1924i			1.53804i
$903$		0			0
$904$	−7.06326			−0.234921
$905$	31.9680	−	20.2497i	1.06265	−	0.673121i
$906$		0			0
$907$	15.0756	+	8.70390i	0.500577	+	0.289008i	0.728952	−	0.684565i	$-0.240008\pi$
$907$	15.0756	+	8.70390i	0.500577	+	0.289008i	−0.228375	+	0.973573i	$0.573341\pi$
$908$	−2.25357	+	1.30110i	−0.0747873	+	0.0431785i
$909$		0			0
$910$	4.71328	−	15.1971i	0.156244	−	0.503779i
$911$	18.3203			0.606978			0.303489	−	0.952835i	$-0.401848\pi$
$911$	18.3203			0.606978			0.303489	+	0.952835i	$0.401848\pi$
$912$		0			0
$913$	−19.5674	−	11.2972i	−0.647586	−	0.373884i
$914$	−1.77079	+	3.06710i	−0.0585726	+	0.101451i
$915$		0			0
$916$	2.77007			0.0915258
$917$	44.2783	−	37.7070i	1.46220	−	1.24519i
$918$		0			0
$919$	11.2963	+	19.5658i	0.372632	+	0.645417i	0.989970	−	0.141281i	$-0.0451221\pi$
$919$	11.2963	+	19.5658i	0.372632	+	0.645417i	−0.617338	+	0.786698i	$0.711789\pi$
$920$	34.3428	+	17.9909i	1.13225	+	0.593143i
$921$		0			0
$922$	−32.3574	+	18.6816i	−1.06563	+	0.615244i
$923$		−	17.8249i		−	0.586715i
$924$		0			0
$925$	−1.50628	−	18.3085i	−0.0495260	−	0.601979i
$926$	8.63842	+	14.9622i	0.283876	+	0.491688i
$927$		0			0
$928$	15.4230	+	8.90448i	0.506285	+	0.292304i
$929$	−19.3356	−	33.4903i	−0.634381	−	1.09878i	−0.986646	−	0.162880i	$-0.947922\pi$
$929$	−19.3356	−	33.4903i	−0.634381	−	1.09878i	0.352265	−	0.935900i	$-0.385412\pi$
$930$		0			0
$931$	1.65618	+	1.34907i	0.0542790	+	0.0442139i
$932$			3.03874i			0.0995372i
$933$		0			0
$934$	22.1813	−	38.4192i	0.725795	−	1.25711i
$935$	−12.5625	+	23.9805i	−0.410837	+	0.784246i
$936$		0			0
$937$			46.7921i			1.52863i	0.644842	+	0.764316i	$0.276923\pi$
$937$			46.7921i			1.52863i	−0.644842	+	0.764316i	$0.723077\pi$
$938$	−6.22682	−	33.8692i	−0.203313	−	1.10587i
$939$		0			0
$940$	0.891095	+	1.40676i	0.0290643	+	0.0458836i
$941$	−20.9461	+	36.2797i	−0.682824	+	1.18268i	0.291292	+	0.956634i	$0.405915\pi$
$941$	−20.9461	+	36.2797i	−0.682824	+	1.18268i	−0.974116	+	0.226051i	$0.927418\pi$
$942$		0			0
$943$	40.8522	−	23.5860i	1.33033	−	0.768067i
$944$	5.31446			0.172971
$945$		0			0
$946$	66.8274			2.17275
$947$	48.5967	−	28.0573i	1.57918	−	0.911740i	0.584206	−	0.811605i	$-0.301406\pi$
$947$	48.5967	−	28.0573i	1.57918	−	0.911740i	0.994974	−	0.100134i	$-0.0319273\pi$
$948$		0			0
$949$	−11.1054	+	19.2352i	−0.360498	+	0.624401i
$950$	1.94728	−	1.34853i	0.0631782	−	0.0437520i
$951$		0			0
$952$	−16.8127	−	5.98097i	−0.544903	−	0.193844i
$953$		−	17.7705i		−	0.575643i	−0.957684	−	0.287821i	$-0.907069\pi$
$953$		−	17.7705i		−	0.575643i	0.957684	−	0.287821i	$-0.0929309\pi$
$954$		0			0
$955$	−0.630946	−	0.330529i	−0.0204169	−	0.0106957i
$956$	1.50944	−	2.61442i	0.0488187	−	0.0845564i
$957$		0			0
$958$			8.66259i			0.279875i
$959$	2.66198	−	7.48291i	0.0859598	−	0.241636i
$960$		0			0
$961$	1.53508	+	2.65884i	0.0495188	+	0.0857690i
$962$	−8.55750	−	4.94067i	−0.275905	−	0.159294i
$963$		0			0
$964$	2.80424	+	4.85708i	0.0903185	+	0.156436i
$965$	4.67691	−	0.192065i	0.150555	−	0.00618279i
$966$		0			0
$967$			22.5942i			0.726579i	0.931676	+	0.363290i	$0.118346\pi$
$967$			22.5942i			0.726579i	−0.931676	+	0.363290i	$0.881654\pi$
$968$	−18.4515	+	10.6530i	−0.593053	+	0.342399i
$969$		0			0
$970$	8.85066	+	4.63653i	0.284178	+	0.148870i
$971$	20.5244	+	35.5493i	0.658660	+	1.14083i	0.980963	+	0.194196i	$0.0622096\pi$
$971$	20.5244	+	35.5493i	0.658660	+	1.14083i	−0.322303	+	0.946637i	$0.604457\pi$
$972$		0			0
$973$	−10.3987	−	56.5612i	−0.333367	−	1.81327i
$974$	12.9577			0.415192
$975$		0			0
$976$	22.2275	−	38.4991i	0.711484	−	1.23233i
$977$	16.8644	+	9.73668i	0.539541	+	0.311504i	0.744893	−	0.667184i	$-0.232501\pi$
$977$	16.8644	+	9.73668i	0.539541	+	0.311504i	−0.205352	+	0.978688i	$0.565834\pi$
$978$		0			0
$979$	−18.0361			−0.576435
$980$	−2.52658	−	5.89880i	−0.0807088	−	0.188430i
$981$		0			0
$982$	0.749390	−	0.432661i	0.0239140	−	0.0138068i
$983$	44.7970	+	25.8636i	1.42880	+	0.824920i	0.997026	−	0.0770602i	$-0.0245534\pi$
$983$	44.7970	+	25.8636i	1.42880	+	0.824920i	0.431777	+	0.901980i	$0.357887\pi$
$984$		0			0
$985$	27.0179	+	42.6529i	0.860861	+	1.35903i
$986$	33.0626			1.05293
$987$		0			0
$988$		−	0.216742i		−	0.00689548i
$989$	−34.1224	−	59.1017i	−1.08503	−	1.87932i
$990$		0			0
$991$	−17.9749	+	31.1335i	−0.570992	+	0.988988i	0.425472	+	0.904972i	$0.360108\pi$
$991$	−17.9749	+	31.1335i	−0.570992	+	0.988988i	−0.996464	+	0.0840162i	$0.973225\pi$
$992$	−10.4575	+	6.03762i	−0.332025	+	0.191694i
$993$		0			0
$994$	−27.3988	−	32.1736i	−0.869036	−	1.02048i
$995$	−0.688503	−	16.7655i	−0.0218270	−	0.531502i
$996$		0			0
$997$	48.5493	+	28.0300i	1.53757	+	0.887718i	0.998980	+	0.0451513i	$0.0143770\pi$
$997$	48.5493	+	28.0300i	1.53757	+	0.887718i	0.538592	+	0.842567i	$0.318956\pi$
$998$	35.0003	+	20.2075i	1.10792	+	0.639656i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bf.b.109.3		16
3.2	odd	2		105.2.q.a.4.6	yes	16
5.4	even	2	inner	315.2.bf.b.109.6		16
7.2	even	3	inner	315.2.bf.b.289.6		16
7.3	odd	6		2205.2.d.o.1324.3		8
7.4	even	3		2205.2.d.s.1324.3		8
12.11	even	2		1680.2.di.d.529.8		16
15.2	even	4		525.2.i.k.151.3		8
15.8	even	4		525.2.i.h.151.2		8
15.14	odd	2		105.2.q.a.4.3	✓	16
21.2	odd	6		105.2.q.a.79.3	yes	16
21.5	even	6		735.2.q.g.79.3		16
21.11	odd	6		735.2.d.d.589.6		8
21.17	even	6		735.2.d.e.589.6		8
21.20	even	2		735.2.q.g.214.6		16
35.4	even	6		2205.2.d.s.1324.6		8
35.9	even	6	inner	315.2.bf.b.289.3		16
35.24	odd	6		2205.2.d.o.1324.6		8
60.59	even	2		1680.2.di.d.529.1		16
84.23	even	6		1680.2.di.d.289.1		16
105.2	even	12		525.2.i.k.226.3		8
105.17	odd	12		3675.2.a.bn.1.2		4
105.23	even	12		525.2.i.h.226.2		8
105.32	even	12		3675.2.a.bp.1.2		4
105.38	odd	12		3675.2.a.cb.1.3		4
105.44	odd	6		105.2.q.a.79.6	yes	16
105.53	even	12		3675.2.a.bz.1.3		4
105.59	even	6		735.2.d.e.589.3		8
105.74	odd	6		735.2.d.d.589.3		8
105.89	even	6		735.2.q.g.79.6		16
105.104	even	2		735.2.q.g.214.3		16
420.359	even	6		1680.2.di.d.289.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.3	✓	16	15.14	odd	2
105.2.q.a.4.6	yes	16	3.2	odd	2
105.2.q.a.79.3	yes	16	21.2	odd	6
105.2.q.a.79.6	yes	16	105.44	odd	6
315.2.bf.b.109.3		16	1.1	even	1	trivial
315.2.bf.b.109.6		16	5.4	even	2	inner
315.2.bf.b.289.3		16	35.9	even	6	inner
315.2.bf.b.289.6		16	7.2	even	3	inner
525.2.i.h.151.2		8	15.8	even	4
525.2.i.h.226.2		8	105.23	even	12
525.2.i.k.151.3		8	15.2	even	4
525.2.i.k.226.3		8	105.2	even	12
735.2.d.d.589.3		8	105.74	odd	6
735.2.d.d.589.6		8	21.11	odd	6
735.2.d.e.589.3		8	105.59	even	6
735.2.d.e.589.6		8	21.17	even	6
735.2.q.g.79.3		16	21.5	even	6
735.2.q.g.79.6		16	105.89	even	6
735.2.q.g.214.3		16	105.104	even	2
735.2.q.g.214.6		16	21.20	even	2
1680.2.di.d.289.1		16	84.23	even	6
1680.2.di.d.289.8		16	420.359	even	6
1680.2.di.d.529.1		16	60.59	even	2
1680.2.di.d.529.8		16	12.11	even	2
2205.2.d.o.1324.3		8	7.3	odd	6
2205.2.d.o.1324.6		8	35.24	odd	6
2205.2.d.s.1324.3		8	7.4	even	3
2205.2.d.s.1324.6		8	35.4	even	6
3675.2.a.bn.1.2		4	105.17	odd	12
3675.2.a.bp.1.2		4	105.32	even	12
3675.2.a.bz.1.3		4	105.53	even	12
3675.2.a.cb.1.3		4	105.38	odd	12

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34443 + 0.776205i) q^{2} +(0.204988 - 0.355049i) q^{4} +(-1.88899 + 1.19655i) q^{5} +(-0.478401 - 2.60214i) q^{7} -2.46837i q^{8} +O(q^{10})\)	\(q+(-1.34443 + 0.776205i) q^{2} +(0.204988 - 0.355049i) q^{4} +(-1.88899 + 1.19655i) q^{5} +(-0.478401 - 2.60214i) q^{7} -2.46837i q^{8} +(1.61083 - 3.07491i) q^{10} +(2.21538 - 3.83715i) q^{11} +1.73246i q^{13} +(2.66297 + 3.12705i) q^{14} +(2.32594 + 4.02864i) q^{16} +(2.36638 + 1.36623i) q^{17} +(-0.152578 - 0.264273i) q^{19} +(0.0376154 + 0.915960i) q^{20} +6.87834i q^{22} +(6.08316 - 3.51212i) q^{23} +(2.13653 - 4.52053i) q^{25} +(-1.34474 - 2.32916i) q^{26} +(-1.02195 - 0.363551i) q^{28} -7.79430 q^{29} +(2.64243 - 4.57683i) q^{31} +(-1.97875 - 1.14243i) q^{32} -4.24190 q^{34} +(4.01728 + 4.34297i) q^{35} +(3.18183 - 1.83703i) q^{37} +(0.410260 + 0.236864i) q^{38} +(2.95353 + 4.66271i) q^{40} +6.71562 q^{41} -9.71562i q^{43} +(-0.908250 - 1.57313i) q^{44} +(-5.45224 + 9.44356i) q^{46} +(1.57313 - 0.908250i) q^{47} +(-6.54227 + 2.48973i) q^{49} +(0.636449 + 7.73591i) q^{50} +(0.615108 + 0.355133i) q^{52} +(-1.48535 - 0.857566i) q^{53} +(0.406524 + 9.89912i) q^{55} +(-6.42304 + 1.18087i) q^{56} +(10.4789 - 6.04998i) q^{58} +(0.571217 - 0.989377i) q^{59} +(-4.77818 - 8.27604i) q^{61} +8.20428i q^{62} -5.75669 q^{64} +(-2.07298 - 3.27259i) q^{65} +(-7.26104 - 4.19216i) q^{67} +(0.970157 - 0.560120i) q^{68} +(-8.77198 - 2.72057i) q^{70} -10.2888 q^{71} +(11.1028 + 6.41022i) q^{73} +(-2.85183 + 4.93951i) q^{74} -0.125106 q^{76} +(-11.0446 - 3.92903i) q^{77} +(3.35686 + 5.81425i) q^{79} +(-9.21413 - 4.82694i) q^{80} +(-9.02866 + 5.21270i) q^{82} -5.09946i q^{83} +(-6.10482 + 0.250704i) q^{85} +(7.54131 + 13.0619i) q^{86} +(-9.47149 - 5.46837i) q^{88} +(-2.03533 - 3.52529i) q^{89} +(4.50810 - 0.828810i) q^{91} -2.87976i q^{92} +(-1.40998 + 2.44215i) q^{94} +(0.604434 + 0.316641i) q^{95} +2.87834i q^{97} +(6.86305 - 8.42540i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 2 q^{5}+O(q^{10}) \) 16 * q + 8 * q^4 - 2 * q^5	\( 16 q + 8 q^{4} - 2 q^{5} - 4 q^{10} + 24 q^{14} - 24 q^{19} + 8 q^{20} - 4 q^{25} + 12 q^{26} - 24 q^{29} + 16 q^{31} + 16 q^{34} + 10 q^{35} + 32 q^{40} - 16 q^{41} - 20 q^{44} - 32 q^{46} - 40 q^{49} + 40 q^{50} + 8 q^{55} - 84 q^{56} - 4 q^{59} + 16 q^{61} + 16 q^{64} - 30 q^{65} + 16 q^{70} + 56 q^{71} - 40 q^{74} - 64 q^{76} - 16 q^{79} - 52 q^{80} - 64 q^{85} + 48 q^{86} - 16 q^{89} + 8 q^{91} - 32 q^{94} + 22 q^{95}+O(q^{100}) \) 16 * q + 8 * q^4 - 2 * q^5 - 4 * q^10 + 24 * q^14 - 24 * q^19 + 8 * q^20 - 4 * q^25 + 12 * q^26 - 24 * q^29 + 16 * q^31 + 16 * q^34 + 10 * q^35 + 32 * q^40 - 16 * q^41 - 20 * q^44 - 32 * q^46 - 40 * q^49 + 40 * q^50 + 8 * q^55 - 84 * q^56 - 4 * q^59 + 16 * q^61 + 16 * q^64 - 30 * q^65 + 16 * q^70 + 56 * q^71 - 40 * q^74 - 64 * q^76 - 16 * q^79 - 52 * q^80 - 64 * q^85 + 48 * q^86 - 16 * q^89 + 8 * q^91 - 32 * q^94 + 22 * q^95

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