LMFDB - Embedded newform 819.2.gh.d.262.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(19,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("819.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.gh (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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			262.10
Character	$\chi$	$=$	819.262
Dual form			819.2.gh.d.397.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.720539 + 2.68909i) q^{2} +(-4.97997 + 2.87519i) q^{4} +(0.470023 - 1.75415i) q^{5} +(1.29491 - 2.30721i) q^{7} +(-7.38279 - 7.38279i) q^{8} +O(q^{10})$	\(q+(0.720539 + 2.68909i) q^{2} +(-4.97997 + 2.87519i) q^{4} +(0.470023 - 1.75415i) q^{5} +(1.29491 - 2.30721i) q^{7} +(-7.38279 - 7.38279i) q^{8} +5.05574 q^{10} +(-3.13543 - 3.13543i) q^{11} +(2.12880 - 2.91002i) q^{13} +(7.13732 + 1.81970i) q^{14} +(8.78302 - 15.2126i) q^{16} +(-0.0321785 - 0.0557347i) q^{17} +(2.15398 + 2.15398i) q^{19} +(2.70281 + 10.0870i) q^{20} +(6.17225 - 10.6907i) q^{22} +(-2.78588 - 1.60843i) q^{23} +(1.47400 + 0.851016i) q^{25} +(9.35918 + 3.62776i) q^{26} +(0.185038 + 15.2129i) q^{28} +(-2.41489 - 4.18271i) q^{29} +(-5.02866 + 1.34743i) q^{31} +(27.0664 + 7.25243i) q^{32} +(0.126690 - 0.126690i) q^{34} +(-3.43855 - 3.35591i) q^{35} +(4.21326 - 1.12894i) q^{37} +(-4.24022 + 7.34428i) q^{38} +(-16.4206 + 9.48045i) q^{40} +(2.12512 - 7.93105i) q^{41} +(-3.22447 - 1.86165i) q^{43} +(24.6293 + 6.59940i) q^{44} +(2.31787 - 8.65041i) q^{46} +(-4.06776 - 1.08995i) q^{47} +(-3.64641 - 5.97525i) q^{49} +(-1.22638 + 4.57691i) q^{50} +(-2.23454 + 20.6125i) q^{52} +(-3.30111 + 5.71769i) q^{53} +(-6.97375 + 4.02629i) q^{55} +(-26.5937 + 7.47358i) q^{56} +(9.50765 - 9.50765i) q^{58} +(4.49313 + 1.20393i) q^{59} -2.19979i q^{61} +(-7.24669 - 12.5516i) q^{62} +42.8777i q^{64} +(-4.10402 - 5.10202i) q^{65} +(4.45013 - 4.45013i) q^{67} +(0.320495 + 0.185038i) q^{68} +(6.54673 - 11.6646i) q^{70} +(1.98467 + 7.40691i) q^{71} +(1.61663 + 6.03336i) q^{73} +(6.07163 + 10.5164i) q^{74} +(-16.9199 - 4.53366i) q^{76} +(-11.2942 + 3.17399i) q^{77} +(0.639030 + 1.10683i) q^{79} +(-22.5570 - 22.5570i) q^{80} +22.8585 q^{82} +(8.90509 + 8.90509i) q^{83} +(-0.112892 + 0.0302493i) q^{85} +(2.68278 - 10.0123i) q^{86} +46.2965i q^{88} +(-0.376284 - 1.40431i) q^{89} +(-3.95740 - 8.67980i) q^{91} +18.4981 q^{92} -11.7239i q^{94} +(4.79083 - 2.76599i) q^{95} +(-8.79969 + 2.35787i) q^{97} +(13.4406 - 14.1109i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7}+O(q^{10}) $ 40 * q - 8 * q^7	$ 40 q - 8 q^{7} - 4 q^{11} + 18 q^{14} + 32 q^{16} - 4 q^{17} + 14 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} + 24 q^{25} + 32 q^{26} + 16 q^{28} - 8 q^{29} + 14 q^{31} + 26 q^{32} - 24 q^{34} - 26 q^{35} + 36 q^{37} + 8 q^{38} - 30 q^{40} + 2 q^{41} - 66 q^{43} + 32 q^{44} - 26 q^{46} + 4 q^{47} - 14 q^{49} + 20 q^{50} + 2 q^{52} + 8 q^{53} - 42 q^{55} - 46 q^{56} + 24 q^{58} - 14 q^{59} - 24 q^{62} - 28 q^{65} - 44 q^{67} + 18 q^{68} - 4 q^{70} + 6 q^{71} + 14 q^{73} + 20 q^{74} - 64 q^{76} - 24 q^{77} - 20 q^{80} + 48 q^{82} + 12 q^{83} + 2 q^{85} + 60 q^{86} + 2 q^{89} - 14 q^{91} - 236 q^{92} - 24 q^{95} - 62 q^{97} + 88 q^{98}+O(q^{100}) $ 40 * q - 8 * q^7 - 4 * q^11 + 18 * q^14 + 32 * q^16 - 4 * q^17 + 14 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 + 24 * q^25 + 32 * q^26 + 16 * q^28 - 8 * q^29 + 14 * q^31 + 26 * q^32 - 24 * q^34 - 26 * q^35 + 36 * q^37 + 8 * q^38 - 30 * q^40 + 2 * q^41 - 66 * q^43 + 32 * q^44 - 26 * q^46 + 4 * q^47 - 14 * q^49 + 20 * q^50 + 2 * q^52 + 8 * q^53 - 42 * q^55 - 46 * q^56 + 24 * q^58 - 14 * q^59 - 24 * q^62 - 28 * q^65 - 44 * q^67 + 18 * q^68 - 4 * q^70 + 6 * q^71 + 14 * q^73 + 20 * q^74 - 64 * q^76 - 24 * q^77 - 20 * q^80 + 48 * q^82 + 12 * q^83 + 2 * q^85 + 60 * q^86 + 2 * q^89 - 14 * q^91 - 236 * q^92 - 24 * q^95 - 62 * q^97 + 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.720539	+	2.68909i	0.509498	+	1.90147i	0.425375	+	0.905017i	$0.360142\pi$
$2$	0.720539	+	2.68909i	0.509498	+	1.90147i	0.0841228	+	0.996455i	$0.473191\pi$
$3$		0			0
$3$		0			0
$4$	−4.97997	+	2.87519i	−2.48998	+	1.43759i
$5$	0.470023	−	1.75415i	0.210201	−	0.784480i	−0.777600	−	0.628759i	$-0.783563\pi$
$5$	0.470023	−	1.75415i	0.210201	−	0.784480i	0.987801	−	0.155721i	$-0.0497702\pi$
$6$		0			0
$7$	1.29491	−	2.30721i	0.489430	−	0.872043i
$7$	1.29491	−	2.30721i	0.489430	−	0.872043i
$8$	−7.38279	−	7.38279i	−2.61021	−	2.61021i
$9$		0			0
$10$	5.05574			1.59876
$11$	−3.13543	−	3.13543i	−0.945368	−	0.945368i	0.0532151	−	0.998583i	$-0.483053\pi$
$11$	−3.13543	−	3.13543i	−0.945368	−	0.945368i	−0.998583	+	0.0532151i	$0.983053\pi$
$12$		0			0
$13$	2.12880	−	2.91002i	0.590424	−	0.807093i
$13$	2.12880	−	2.91002i	0.590424	−	0.807093i
$14$	7.13732	+	1.81970i	1.90753	+	0.486334i
$15$		0			0
$16$	8.78302	−	15.2126i	2.19575	−	3.80316i
$17$	−0.0321785	−	0.0557347i	−0.00780442	−	0.0135177i	0.862097	−	0.506744i	$-0.169151\pi$
$17$	−0.0321785	−	0.0557347i	−0.00780442	−	0.0135177i	−0.869901	+	0.493226i	$0.835818\pi$
$18$		0			0
$19$	2.15398	+	2.15398i	0.494158	+	0.494158i	0.909613	−	0.415456i	$-0.136378\pi$
$19$	2.15398	+	2.15398i	0.494158	+	0.494158i	−0.415456	+	0.909613i	$0.636378\pi$
$20$	2.70281	+	10.0870i	0.604367	+	2.25553i
$21$		0			0
$22$	6.17225	−	10.6907i	1.31593	−	2.27925i
$23$	−2.78588	−	1.60843i	−0.580896	−	0.335380i	0.180593	−	0.983558i	$-0.442198\pi$
$23$	−2.78588	−	1.60843i	−0.580896	−	0.335380i	−0.761489	+	0.648177i	$0.775532\pi$
$24$		0			0
$25$	1.47400	+	0.851016i	0.294800	+	0.170203i
$26$	9.35918	+	3.62776i	1.83549	+	0.711463i
$27$		0			0
$28$	0.185038	+	15.2129i	0.0349689	+	2.87497i
$29$	−2.41489	−	4.18271i	−0.448433	−	0.776709i	0.549851	−	0.835263i	$-0.314684\pi$
$29$	−2.41489	−	4.18271i	−0.448433	−	0.776709i	−0.998284	+	0.0585536i	$0.981351\pi$
$30$		0			0
$31$	−5.02866	+	1.34743i	−0.903174	+	0.242005i	−0.680379	−	0.732860i	$-0.738185\pi$
$31$	−5.02866	+	1.34743i	−0.903174	+	0.242005i	−0.222795	+	0.974865i	$0.571518\pi$
$32$	27.0664	+	7.25243i	4.78472	+	1.28206i
$33$		0			0
$34$	0.126690	−	0.126690i	0.0217271	−	0.0217271i
$35$	−3.43855	−	3.35591i	−0.581222	−	0.567252i
$36$		0			0
$37$	4.21326	−	1.12894i	0.692655	−	0.185596i	0.104717	−	0.994502i	$-0.466606\pi$
$37$	4.21326	−	1.12894i	0.692655	−	0.185596i	0.587938	+	0.808906i	$0.299940\pi$
$38$	−4.24022	+	7.34428i	−0.687855	+	1.19140i
$39$		0			0
$40$	−16.4206	+	9.48045i	−2.59633	+	1.49899i
$41$	2.12512	−	7.93105i	0.331888	−	1.23862i	−0.575317	−	0.817931i	$-0.695121\pi$
$41$	2.12512	−	7.93105i	0.331888	−	1.23862i	0.907204	−	0.420691i	$-0.138212\pi$
$42$		0			0
$43$	−3.22447	−	1.86165i	−0.491727	−	0.283899i	0.233564	−	0.972341i	$-0.424961\pi$
$43$	−3.22447	−	1.86165i	−0.491727	−	0.283899i	−0.725291	+	0.688443i	$0.758295\pi$
$44$	24.6293	+	6.59940i	3.71301	+	0.994897i
$45$		0			0
$46$	2.31787	−	8.65041i	0.341751	−	1.27543i
$47$	−4.06776	−	1.08995i	−0.593343	−	0.158986i	−0.0503625	−	0.998731i	$-0.516038\pi$
$47$	−4.06776	−	1.08995i	−0.593343	−	0.158986i	−0.542981	+	0.839745i	$0.682704\pi$
$48$		0			0
$49$	−3.64641	−	5.97525i	−0.520916	−	0.853608i
$50$	−1.22638	+	4.57691i	−0.173436	+	0.647273i
$51$		0			0
$52$	−2.23454	+	20.6125i	−0.309876	+	2.85844i
$53$	−3.30111	+	5.71769i	−0.453442	+	0.785385i	−0.998597	−	0.0529503i	$-0.983138\pi$
$53$	−3.30111	+	5.71769i	−0.453442	+	0.785385i	0.545155	+	0.838335i	$0.316471\pi$
$54$		0			0
$55$	−6.97375	+	4.02629i	−0.940340	+	0.542905i
$56$	−26.5937	+	7.47358i	−3.55373	+	0.998699i
$57$		0			0
$58$	9.50765	−	9.50765i	1.24842	−	1.24842i
$59$	4.49313	+	1.20393i	0.584956	+	0.156739i	0.539147	−	0.842212i	$-0.318747\pi$
$59$	4.49313	+	1.20393i	0.584956	+	0.156739i	0.0458093	+	0.998950i	$0.485413\pi$
$60$		0			0
$61$		−	2.19979i		−	0.281654i	−0.990034	−	0.140827i	$-0.955024\pi$
$61$		−	2.19979i		−	0.281654i	0.990034	−	0.140827i	$-0.0449761\pi$
$62$	−7.24669	−	12.5516i	−0.920331	−	1.59406i
$63$		0			0
$64$			42.8777i			5.35971i
$65$	−4.10402	−	5.10202i	−0.509041	−	0.632828i
$66$		0			0
$67$	4.45013	−	4.45013i	0.543670	−	0.543670i	−0.380932	−	0.924603i	$-0.624397\pi$
$67$	4.45013	−	4.45013i	0.543670	−	0.543670i	0.924603	+	0.380932i	$0.124397\pi$
$68$	0.320495	+	0.185038i	0.0388658	+	0.0224392i
$69$		0			0
$70$	6.54673	−	11.6646i	0.782484	−	1.39419i
$71$	1.98467	+	7.40691i	0.235538	+	0.879038i	0.977906	+	0.209046i	$0.0670358\pi$
$71$	1.98467	+	7.40691i	0.235538	+	0.879038i	−0.742368	+	0.669992i	$0.766298\pi$
$72$		0			0
$73$	1.61663	+	6.03336i	0.189213	+	0.706151i	0.993689	+	0.112167i	$0.0357791\pi$
$73$	1.61663	+	6.03336i	0.189213	+	0.706151i	−0.804477	+	0.593984i	$0.797554\pi$
$74$	6.07163	+	10.5164i	0.705813	+	1.22250i
$75$		0			0
$76$	−16.9199	−	4.53366i	−1.94084	−	0.520047i
$77$	−11.2942	+	3.17399i	−1.28709	+	0.361709i
$78$		0			0
$79$	0.639030	+	1.10683i	0.0718965	+	0.124528i	0.899732	−	0.436442i	$-0.143762\pi$
$79$	0.639030	+	1.10683i	0.0718965	+	0.124528i	−0.827836	+	0.560970i	$0.810428\pi$
$80$	−22.5570	−	22.5570i	−2.52195	−	2.52195i
$81$		0			0
$82$	22.8585			2.52430
$83$	8.90509	+	8.90509i	0.977461	+	0.977461i	0.999752	−	0.0222904i	$-0.00709586\pi$
$83$	8.90509	+	8.90509i	0.977461	+	0.977461i	−0.0222904	+	0.999752i	$0.507096\pi$
$84$		0			0
$85$	−0.112892	+	0.0302493i	−0.0122448	+	0.00328099i
$86$	2.68278	−	10.0123i	0.289292	−	1.07965i
$87$		0			0
$88$			46.2965i			4.93522i
$89$	−0.376284	−	1.40431i	−0.0398860	−	0.148857i	0.943111	−	0.332478i	$-0.107885\pi$
$89$	−0.376284	−	1.40431i	−0.0398860	−	0.148857i	−0.982997	+	0.183621i	$0.941218\pi$
$90$		0			0
$91$	−3.95740	−	8.67980i	−0.414848	−	0.909891i
$92$	18.4981			1.92856
$93$		0			0
$94$		−	11.7239i		−	1.20923i
$95$	4.79083	−	2.76599i	0.491529	−	0.283785i
$96$		0			0
$97$	−8.79969	+	2.35787i	−0.893473	+	0.239405i	−0.676211	−	0.736708i	$-0.736379\pi$
$97$	−8.79969	+	2.35787i	−0.893473	+	0.239405i	−0.217262	+	0.976113i	$0.569713\pi$
$98$	13.4406	−	14.1109i	1.35771	−	1.42542i
$99$		0			0
$100$	−9.78731			−0.978731
$101$	4.08757			0.406729			0.203364	−	0.979103i	$-0.434812\pi$
$101$	4.08757			0.406729			0.203364	+	0.979103i	$0.434812\pi$
$102$		0			0
$103$	−5.85241	−	10.1367i	−0.576655	−	0.998796i	−0.995860	−	0.0909039i	$-0.971024\pi$
$103$	−5.85241	−	10.1367i	−0.576655	−	0.998796i	0.419205	−	0.907892i	$-0.362309\pi$
$104$	−37.2006	+	5.76751i	−3.64781	+	0.565551i
$105$		0			0
$106$	−17.7539	−	4.75716i	−1.72442	−	0.462056i
$107$	2.36116	−	4.08965i	0.228262	−	0.395362i	−0.729031	−	0.684481i	$-0.760029\pi$
$107$	2.36116	−	4.08965i	0.228262	−	0.395362i	0.957293	+	0.289119i	$0.0933623\pi$
$108$		0			0
$109$	0.511245	+	1.90799i	0.0489684	+	0.182752i	0.986078	−	0.166282i	$-0.0531763\pi$
$109$	0.511245	+	1.90799i	0.0489684	+	0.182752i	−0.937110	+	0.349035i	$0.886510\pi$
$110$	−15.8519	−	15.8519i	−1.51142	−	1.51142i
$111$		0			0
$112$	−23.7255	−	39.9632i	−2.24185	−	3.77617i
$113$	5.68629	−	9.84894i	0.534921	−	0.926510i	−0.464246	−	0.885706i	$-0.653675\pi$
$113$	5.68629	−	9.84894i	0.534921	−	0.926510i	0.999167	−	0.0408040i	$-0.0129919\pi$
$114$		0			0
$115$	−4.13085	+	4.13085i	−0.385204	+	0.385204i
$116$	24.0521	+	13.8865i	2.23318	+	1.28933i
$117$		0			0
$118$			12.9499i			1.19214i
$119$	−0.170260	+	0.00207091i	−0.0156077	+	0.000189840i
$120$		0			0
$121$			8.66185i			0.787441i
$122$	5.91542	−	1.58503i	0.535557	−	0.143502i
$123$		0			0
$124$	21.1685	−	21.1685i	1.90099	−	1.90099i
$125$	8.60627	−	8.60627i	0.769768	−	0.769768i
$126$		0			0
$127$	18.1029	−	10.4517i	1.60637	−	0.927439i	0.616199	−	0.787591i	$-0.288672\pi$
$127$	18.1029	−	10.4517i	1.60637	−	0.927439i	0.990173	−	0.139849i	$-0.0446616\pi$
$128$	−61.1689	+	16.3902i	−5.40662	+	1.44870i
$129$		0			0
$130$	10.7627	−	14.7123i	0.943949	−	1.29035i
$131$	−14.8673	+	8.58365i	−1.29896	+	0.749957i	−0.980225	−	0.197885i	$-0.936593\pi$
$131$	−14.8673	+	8.58365i	−1.29896	+	0.749957i	−0.318739	+	0.947843i	$0.603259\pi$
$132$		0			0
$133$	7.75890	−	2.18047i	0.672782	−	0.189071i
$134$	15.1733	+	8.76031i	1.31077	+	0.756775i
$135$		0			0
$136$	−0.173911	+	0.649045i	−0.0149127	+	0.0556551i
$137$	2.66618	−	9.95031i	0.227787	−	0.850113i	−0.753482	−	0.657469i	$-0.771627\pi$
$137$	2.66618	−	9.95031i	0.227787	−	0.850113i	0.981269	−	0.192644i	$-0.0617062\pi$
$138$		0			0
$139$	−11.4927	−	6.63534i	−0.974802	−	0.562802i	−0.0741052	−	0.997250i	$-0.523610\pi$
$139$	−11.4927	−	6.63534i	−0.974802	−	0.562802i	−0.900697	+	0.434448i	$0.856943\pi$
$140$	26.7727	+	6.82585i	2.26271	+	0.576889i
$141$		0			0
$142$	−18.4878	+	10.6739i	−1.55146	+	0.895736i
$143$	−15.7989	+	2.44943i	−1.32117	+	0.204832i
$144$		0			0
$145$	−8.47215	+	2.27011i	−0.703574	+	0.188522i
$146$	−15.0594	+	8.69454i	−1.24632	+	0.719565i
$147$		0			0
$148$	−17.7360	+	17.7360i	−1.45789	+	1.45789i
$149$	−1.56505	+	1.56505i	−0.128214	+	0.128214i	−0.768302	−	0.640088i	$-0.778898\pi$
$149$	−1.56505	+	1.56505i	−0.128214	+	0.128214i	0.640088	+	0.768302i	$0.278898\pi$
$150$		0			0
$151$	−6.60747	+	1.77047i	−0.537708	+	0.144078i	−0.517445	−	0.855716i	$-0.673117\pi$
$151$	−6.60747	+	1.77047i	−0.537708	+	0.144078i	−0.0202628	+	0.999795i	$0.506450\pi$
$152$		−	31.8048i		−	2.57971i
$153$		0			0
$154$	−16.6730	−	28.0841i	−1.34355	−	2.26308i
$155$			9.45436i			0.759392i
$156$		0			0
$157$	12.8667	+	7.42857i	1.02687	+	0.592865i	0.916087	−	0.400980i	$-0.131330\pi$
$157$	12.8667	+	7.42857i	1.02687	+	0.592865i	0.110785	+	0.993844i	$0.464664\pi$
$158$	−2.51593	+	2.51593i	−0.200156	+	0.200156i
$159$		0			0
$160$	25.4437	−	44.0698i	2.01150	−	3.48403i
$161$	−7.31844	+	4.34483i	−0.576774	+	0.342421i
$162$		0			0
$163$	−2.05667	−	2.05667i	−0.161091	−	0.161091i	0.621959	−	0.783050i	$-0.286337\pi$
$163$	−2.05667	−	2.05667i	−0.161091	−	0.161091i	−0.783050	+	0.621959i	$0.786337\pi$
$164$	12.2202	+	45.6065i	0.954238	+	3.56127i
$165$		0			0
$166$	−17.5301	+	30.3631i	−1.36060	+	2.35663i
$167$	14.0198	+	3.75659i	1.08488	+	0.290693i	0.756595	−	0.653884i	$-0.226862\pi$
$167$	14.0198	+	3.75659i	1.08488	+	0.290693i	0.328288	+	0.944578i	$0.393528\pi$
$168$		0			0
$169$	−3.93638	−	12.3897i	−0.302798	−	0.953055i
$170$	−0.162686	−	0.281780i	−0.0124774	−	0.0216116i
$171$		0			0
$172$	21.4103			1.63252
$173$	15.3963			1.17056			0.585281	−	0.810831i	$-0.300984\pi$
$173$	15.3963			1.17056			0.585281	+	0.810831i	$0.300984\pi$
$174$		0			0
$175$	3.87217	−	2.29884i	0.292709	−	0.173776i
$176$	−75.2367	+	20.1596i	−5.67118	+	1.51959i
$177$		0			0
$178$	3.50519	−	2.02372i	0.262725	−	0.151684i
$179$			16.3786i			1.22419i	0.790784	+	0.612096i	$0.209673\pi$
$179$			16.3786i			1.22419i	−0.790784	+	0.612096i	$0.790327\pi$
$180$		0			0
$181$	5.85927			0.435516			0.217758	−	0.976003i	$-0.430126\pi$
$181$	5.85927			0.435516			0.217758	+	0.976003i	$0.430126\pi$
$182$	20.4893	−	16.8959i	1.51877	−	1.25241i
$183$		0			0
$184$	8.69287	+	32.4422i	0.640847	+	2.39167i
$185$		−	7.92132i		−	0.582387i
$186$		0			0
$187$	−0.0738591	+	0.275646i	−0.00540111	+	0.0201572i
$188$	23.3911	−	6.26763i	1.70597	−	0.457114i
$189$		0			0
$190$	10.8900	+	10.8900i	0.790042	+	0.790042i
$191$	10.8964			0.788434			0.394217	−	0.919017i	$-0.371016\pi$
$191$	10.8964			0.788434			0.394217	+	0.919017i	$0.371016\pi$
$192$		0			0
$193$	16.6731	+	16.6731i	1.20015	+	1.20015i	0.974120	+	0.226034i	$0.0725759\pi$
$193$	16.6731	+	16.6731i	1.20015	+	1.20015i	0.226034	+	0.974120i	$0.427424\pi$
$194$	−12.6810	−	21.9642i	−0.910446	−	1.57694i
$195$		0			0
$196$	35.3390	+	19.2725i	2.52421	+	1.37660i
$197$	18.0741	+	4.84294i	1.28773	+	0.345045i	0.836796	−	0.547515i	$-0.184426\pi$
$197$	18.0741	+	4.84294i	1.28773	+	0.345045i	0.450929	+	0.892560i	$0.351093\pi$
$198$		0			0
$199$	−0.361184	−	0.625590i	−0.0256037	−	0.0443469i	0.852940	−	0.522010i	$-0.174817\pi$
$199$	−0.361184	−	0.625590i	−0.0256037	−	0.0443469i	−0.878543	+	0.477663i	$0.841484\pi$
$200$	−4.59938	−	17.1651i	−0.325225	−	1.21376i
$201$		0			0
$202$	2.94525	+	10.9918i	0.207227	+	0.773383i
$203$	−12.7774	+	0.155415i	−0.896800	+	0.0109080i
$204$		0			0
$205$	−12.9134	−	7.45555i	−0.901911	−	0.520719i
$206$	23.0415	−	23.0415i	1.60538	−	1.60538i
$207$		0			0
$208$	−25.5717	−	57.9434i	−1.77308	−	4.01765i
$209$		−	13.5073i		−	0.934321i
$210$		0			0
$211$	−3.17996	−	5.50785i	−0.218917	−	0.379176i	0.735560	−	0.677460i	$-0.236919\pi$
$211$	−3.17996	−	5.50785i	−0.218917	−	0.379176i	−0.954477	+	0.298284i	$0.903586\pi$
$212$		−	37.9652i		−	2.60746i
$213$		0			0
$214$	12.6987	+	3.40262i	0.868069	+	0.232598i
$215$	−4.78119	+	4.78119i	−0.326074	+	0.326074i
$216$		0			0
$217$	−3.40288	+	13.3470i	−0.231002	+	0.906051i
$218$	−4.76238	+	2.74956i	−0.322549	+	0.186224i
$219$		0			0
$220$	23.1527	−	40.1016i	1.56095	−	2.70365i
$221$	−0.230691	−	0.0250085i	−0.0155179	−	0.00168226i
$222$		0			0
$223$	0.323776	−	1.20835i	0.0216816	−	0.0809170i	−0.954237	−	0.299050i	$-0.903330\pi$
$223$	0.323776	−	1.20835i	0.0216816	−	0.0809170i	0.975919	+	0.218133i	$0.0699968\pi$
$224$	51.7815	−	53.0567i	3.45980	−	3.54500i
$225$		0			0
$226$	30.5819	+	8.19438i	2.03427	+	0.545082i
$227$	0.548856	−	2.04836i	0.0364288	−	0.135954i	−0.945316	−	0.326154i	$-0.894247\pi$
$227$	0.548856	−	2.04836i	0.0364288	−	0.135954i	0.981745	+	0.190200i	$0.0609137\pi$
$228$		0			0
$229$	14.4347	+	3.86775i	0.953869	+	0.255588i	0.702003	−	0.712174i	$-0.252289\pi$
$229$	14.4347	+	3.86775i	0.953869	+	0.255588i	0.251866	+	0.967762i	$0.418956\pi$
$230$	−14.0847	−	8.13179i	−0.928716	−	0.536194i
$231$		0			0
$232$	−13.0514	+	48.7087i	−0.856869	+	3.19788i
$233$	−15.8759	+	9.16593i	−1.04006	+	0.600480i	−0.919851	−	0.392268i	$-0.871691\pi$
$233$	−15.8759	+	9.16593i	−1.04006	+	0.600480i	−0.120211	+	0.992748i	$0.538357\pi$
$234$		0			0
$235$	−3.82388	+	6.62316i	−0.249443	+	0.432047i
$236$	−25.8372	+	6.92306i	−1.68186	+	0.450653i
$237$		0			0
$238$	−0.128248	−	0.456352i	−0.00831306	−	0.0295809i
$239$	−5.38085	+	5.38085i	−0.348058	+	0.348058i	−0.859386	−	0.511328i	$-0.829154\pi$
$239$	−5.38085	+	5.38085i	−0.348058	+	0.348058i	0.511328	+	0.859386i	$0.329154\pi$
$240$		0			0
$241$	−24.6342	−	6.60072i	−1.58683	−	0.425190i	−0.645799	−	0.763508i	$-0.723476\pi$
$241$	−24.6342	−	6.60072i	−1.58683	−	0.425190i	−0.941032	+	0.338318i	$0.890142\pi$
$242$	−23.2925	+	6.24120i	−1.49730	+	0.401200i
$243$		0			0
$244$	6.32479	+	10.9549i	0.404903	+	0.701313i
$245$	−12.1954	+	3.58785i	−0.779136	+	0.229219i
$246$		0			0
$247$	10.8535	−	1.68271i	0.690594	−	0.107069i
$248$	47.0733	+	27.1778i	2.98916	+	1.72579i
$249$		0			0
$250$	29.3442	+	16.9419i	1.85589	+	1.07150i
$251$	−12.8632	+	22.2797i	−0.811918	+	1.40628i	0.0996013	+	0.995027i	$0.468243\pi$
$251$	−12.8632	+	22.2797i	−0.811918	+	1.40628i	−0.911520	+	0.411256i	$0.865090\pi$
$252$		0			0
$253$	3.69182	+	13.7780i	0.232102	+	0.866218i
$254$	41.1494	+	41.1494i	2.58194	+	2.58194i
$255$		0			0
$256$	−45.2715	−	78.4126i	−2.82947	−	4.90079i
$257$	−2.81670	+	4.87868i	−0.175701	+	0.304323i	−0.940404	−	0.340060i	$-0.889553\pi$
$257$	−2.81670	+	4.87868i	−0.175701	+	0.304323i	0.764703	+	0.644383i	$0.222886\pi$
$258$		0			0
$259$	2.85109	−	11.1827i	0.177158	−	0.694861i
$260$	35.1071	+	13.6081i	2.17725	+	0.843938i
$261$		0			0
$262$	−33.7947	−	33.7947i	−2.08784	−	2.08784i
$263$	−1.66951			−0.102947			−0.0514733	−	0.998674i	$-0.516392\pi$
$263$	−1.66951			−0.102947			−0.0514733	+	0.998674i	$0.516392\pi$
$264$		0			0
$265$	8.47809	+	8.47809i	0.520805	+	0.520805i
$266$	11.4541	+	19.2933i	0.702294	+	1.18295i
$267$		0			0
$268$	−9.36656	+	34.9565i	−0.572154	+	2.13531i
$269$	−14.2757	+	8.24206i	−0.870403	+	0.502527i	−0.867482	−	0.497469i	$-0.834263\pi$
$269$	−14.2757	+	8.24206i	−0.870403	+	0.502527i	−0.00292053	+	0.999996i	$0.500930\pi$
$270$		0			0
$271$	0.857328	+	3.19959i	0.0520790	+	0.194361i	0.987064	−	0.160325i	$-0.0512543\pi$
$271$	0.857328	+	3.19959i	0.0520790	+	0.194361i	−0.934985	+	0.354686i	$0.884588\pi$
$272$	−1.13050			−0.0685464
$273$		0			0
$274$	28.6784			1.73252
$275$	−1.95333	−	7.28993i	−0.117790	−	0.439599i
$276$		0			0
$277$	−6.45920	+	3.72922i	−0.388096	+	0.224067i	−0.681335	−	0.731972i	$-0.738600\pi$
$277$	−6.45920	+	3.72922i	−0.388096	+	0.224067i	0.293239	+	0.956039i	$0.405267\pi$
$278$	9.56204	−	35.6860i	0.573493	−	2.14031i
$279$		0			0
$280$	0.610132	+	50.1621i	0.0364624	+	2.99776i
$281$	−4.23533	−	4.23533i	−0.252658	−	0.252658i	0.569401	−	0.822060i	$-0.307175\pi$
$281$	−4.23533	−	4.23533i	−0.252658	−	0.252658i	−0.822060	+	0.569401i	$0.807175\pi$
$282$		0			0
$283$	−26.1099			−1.55207			−0.776036	−	0.630689i	$-0.782772\pi$
$283$	−26.1099			−1.55207			−0.776036	+	0.630689i	$0.782772\pi$
$284$	−31.1798	−	31.1798i	−1.85018	−	1.85018i
$285$		0			0
$286$	−17.9704	−	40.7196i	−1.06261	−	2.40780i
$287$	−15.5467	−	15.1731i	−0.917695	−	0.895639i
$288$		0			0
$289$	8.49793	−	14.7188i	0.499878	−	0.865814i
$290$	−12.2090	−	21.1467i	−0.716939	−	1.24178i
$291$		0			0
$292$	−25.3978	−	25.3978i	−1.48629	−	1.48629i
$293$	3.41192	+	12.7335i	0.199326	+	0.743896i	0.991104	+	0.133087i	$0.0424890\pi$
$293$	3.41192	+	12.7335i	0.199326	+	0.743896i	−0.791778	+	0.610809i	$0.790844\pi$
$294$		0			0
$295$	4.22376	−	7.31576i	0.245917	−	0.425940i
$296$	−39.4403	−	22.7709i	−2.29242	−	1.32353i
$297$		0			0
$298$	−5.33625	−	3.08089i	−0.309121	−	0.178471i
$299$	−10.6111	+	4.68292i	−0.613658	+	0.270820i
$300$		0			0
$301$	−8.47060	+	5.02885i	−0.488238	+	0.289858i
$302$	−9.52188	−	16.4924i	−0.547922	−	0.949030i
$303$		0			0
$304$	51.6862	−	13.8493i	2.96441	−	0.794310i
$305$	−3.85876	−	1.03395i	−0.220952	−	0.0592038i
$306$		0			0
$307$	−21.4079	+	21.4079i	−1.22181	+	1.22181i	−0.254824	+	0.966987i	$0.582018\pi$
$307$	−21.4079	+	21.4079i	−1.22181	+	1.22181i	−0.966987	+	0.254824i	$0.917982\pi$
$308$	47.1189	−	48.2793i	2.68485	−	2.75097i
$309$		0			0
$310$	−25.4236	+	6.81223i	−1.44396	+	0.386909i
$311$	9.99754	−	17.3163i	0.566909	−	0.981915i	−0.429961	−	0.902848i	$-0.641473\pi$
$311$	9.99754	−	17.3163i	0.566909	−	0.981915i	0.996869	−	0.0790670i	$-0.0251941\pi$
$312$		0			0
$313$	14.5090	−	8.37678i	0.820098	−	0.473484i	−0.0303525	−	0.999539i	$-0.509663\pi$
$313$	14.5090	−	8.37678i	0.820098	−	0.473484i	0.850450	+	0.526056i	$0.176330\pi$
$314$	−10.7052	+	39.9522i	−0.604127	+	2.25463i
$315$		0			0
$316$	−6.36470	−	3.67466i	−0.358042	−	0.206716i
$317$	−21.1839	−	5.67622i	−1.18981	−	0.318808i	−0.390999	−	0.920391i	$-0.627870\pi$
$317$	−21.1839	−	5.67622i	−1.18981	−	0.318808i	−0.798810	+	0.601583i	$0.794537\pi$
$318$		0			0
$319$	−5.54288	+	20.6863i	−0.310342	+	1.15821i
$320$	75.2139	+	20.1535i	4.20458	+	1.12662i
$321$		0			0
$322$	−16.9569	−	16.5493i	−0.944969	−	0.922257i
$323$	0.0507398	−	0.189364i	0.00282324	−	0.0105365i
$324$		0			0
$325$	5.61433	−	2.47772i	0.311427	−	0.137439i
$326$	4.04866	−	7.01248i	0.224235	−	0.388386i
$327$		0			0
$328$	−74.2426	+	42.8640i	−4.09936	+	2.36677i
$329$	−7.78213	+	7.97377i	−0.429042	+	0.439608i
$330$		0			0
$331$	23.2841	−	23.2841i	1.27981	−	1.27981i	0.339041	−	0.940772i	$-0.389898\pi$
$331$	23.2841	−	23.2841i	1.27981	−	1.27981i	0.940772	−	0.339041i	$-0.110102\pi$
$332$	−69.9509	−	18.7433i	−3.83905	−	1.02867i
$333$		0			0
$334$			40.4072i			2.21098i
$335$	−5.71454	−	9.89787i	−0.312219	−	0.540779i
$336$		0			0
$337$		−	21.6306i		−	1.17829i	−0.808027	−	0.589146i	$-0.799464\pi$
$337$		−	21.6306i		−	1.17829i	0.808027	−	0.589146i	$-0.200536\pi$
$338$	30.4807	−	19.5125i	1.65793	−	1.06134i
$339$		0			0
$340$	0.475225	−	0.475225i	0.0257727	−	0.0257727i
$341$	19.9918	+	11.5423i	1.08262	+	0.625048i
$342$		0			0
$343$	−18.5079	+	0.675614i	−0.999334	+	0.0364798i
$344$	10.0614	+	37.5497i	0.542475	+	2.02455i
$345$		0			0
$346$	11.0937	+	41.4021i	0.596399	+	2.22579i
$347$	−0.0648962	−	0.112404i	−0.00348381	−	0.00603414i	0.864278	−	0.503014i	$-0.167776\pi$
$347$	−0.0648962	−	0.112404i	−0.00348381	−	0.00603414i	−0.867762	+	0.496980i	$0.834442\pi$
$348$		0			0
$349$	21.4920	+	5.75876i	1.15044	+	0.308260i	0.783142	−	0.621843i	$-0.213616\pi$
$349$	21.4920	+	5.75876i	1.15044	+	0.308260i	0.367299	+	0.930103i	$0.380283\pi$
$350$	8.97183	+	8.75620i	0.479565	+	0.468039i
$351$		0			0
$352$	−62.1255	−	107.604i	−3.31130	−	5.73534i
$353$	−6.59244	−	6.59244i	−0.350880	−	0.350880i	0.509557	−	0.860437i	$-0.329809\pi$
$353$	−6.59244	−	6.59244i	−0.350880	−	0.350880i	−0.860437	+	0.509557i	$0.829809\pi$
$354$		0			0
$355$	13.9257			0.739098
$356$	5.91154	+	5.91154i	0.313311	+	0.313311i
$357$		0			0
$358$	−44.0434	+	11.8014i	−2.32777	+	0.623723i
$359$	−1.41626	+	5.28557i	−0.0747476	+	0.278962i	−0.993176	−	0.116625i	$-0.962792\pi$
$359$	−1.41626	+	5.28557i	−0.0747476	+	0.278962i	0.918428	+	0.395587i	$0.129459\pi$
$360$		0			0
$361$		−	9.72072i		−	0.511617i
$362$	4.22183	+	15.7561i	0.221895	+	0.828122i
$363$		0			0
$364$	44.6638	+	31.8469i	2.34102	+	1.66923i
$365$	11.3433			0.593734
$366$		0			0
$367$			16.9836i			0.886538i	0.896389	+	0.443269i	$0.146181\pi$
$367$			16.9836i			0.886538i	−0.896389	+	0.443269i	$0.853819\pi$
$368$	−48.9368	+	28.2537i	−2.55101	+	1.47283i
$369$		0			0
$370$	21.3011	−	5.70762i	1.10739	−	0.296725i
$371$	8.91726	+	15.0202i	0.462961	+	0.779812i
$372$		0			0
$373$	3.15843			0.163537			0.0817685	−	0.996651i	$-0.473943\pi$
$373$	3.15843			0.163537			0.0817685	+	0.996651i	$0.473943\pi$
$374$	−0.794454			−0.0410802
$375$		0			0
$376$	21.9845	+	38.0783i	1.13376	+	1.96374i
$377$	−17.3126	−	1.87681i	−0.891642	−	0.0966606i
$378$		0			0
$379$	−17.2294	−	4.61662i	−0.885017	−	0.237140i	−0.212447	−	0.977173i	$-0.568143\pi$
$379$	−17.2294	−	4.61662i	−0.885017	−	0.237140i	−0.672571	+	0.740033i	$0.734810\pi$
$380$	−15.9055	+	27.5491i	−0.815933	+	1.41324i
$381$		0			0
$382$	7.85126	+	29.3013i	0.401706	+	1.49919i
$383$	1.51030	+	1.51030i	0.0771727	+	0.0771727i	0.744640	−	0.667467i	$-0.232621\pi$
$383$	1.51030	+	1.51030i	0.0771727	+	0.0771727i	−0.667467	+	0.744640i	$0.732621\pi$
$384$		0			0
$385$	0.259120	+	21.3036i	0.0132060	+	1.08573i
$386$	−32.8217	+	56.8489i	−1.67058	+	2.89353i
$387$		0			0
$388$	37.0429	−	37.0429i	1.88057	−	1.88057i
$389$	−0.209807	−	0.121132i	−0.0106376	−	0.00614163i	0.494672	−	0.869080i	$-0.335288\pi$
$389$	−0.209807	−	0.121132i	−0.0106376	−	0.00614163i	−0.505309	+	0.862938i	$0.668622\pi$
$390$		0			0
$391$			0.207027i			0.0104698i
$392$	−17.1933	+	71.0348i	−0.868395	+	3.58780i
$393$		0			0
$394$			52.0923i			2.62437i
$395$	2.24191	−	0.600718i	0.112803	−	0.0302254i
$396$		0			0
$397$	−4.84558	+	4.84558i	−0.243193	+	0.243193i	−0.818170	−	0.574977i	$-0.805011\pi$
$397$	−4.84558	+	4.84558i	−0.243193	+	0.243193i	0.574977	+	0.818170i	$0.305011\pi$
$398$	1.42202	−	1.42202i	0.0712793	−	0.0712793i
$399$		0			0
$400$	25.8924	−	14.9490i	1.29462	−	0.747448i
$401$	26.1997	−	7.02018i	1.30835	−	0.350571i	0.463748	−	0.885967i	$-0.346504\pi$
$401$	26.1997	−	7.02018i	1.30835	−	0.350571i	0.844601	+	0.535396i	$0.179838\pi$
$402$		0			0
$403$	−6.78401	+	17.5019i	−0.337936	+	0.871831i
$404$	−20.3560	+	11.7525i	−1.01275	+	0.584710i
$405$		0			0
$406$	−9.62456	−	34.2477i	−0.477659	−	1.69968i
$407$	−16.7501	−	9.67067i	−0.830271	−	0.479357i
$408$		0			0
$409$	−9.40033	+	35.0825i	−0.464816	+	1.73472i	0.192681	+	0.981261i	$0.438282\pi$
$409$	−9.40033	+	35.0825i	−0.464816	+	1.73472i	−0.657497	+	0.753457i	$0.728385\pi$
$410$	10.7440	−	40.0973i	0.530610	−	1.98026i
$411$		0			0
$412$	58.2896	+	33.6535i	2.87172	+	1.65799i
$413$	8.59593	−	8.80761i	0.422978	−	0.433394i
$414$		0			0
$415$	19.8065	−	11.4353i	0.972262	−	0.561336i
$416$	78.7239	−	63.3248i	3.85976	−	3.10475i
$417$		0			0
$418$	36.3224	−	9.73256i	1.77659	−	0.476035i
$419$	30.5830	−	17.6571i	1.49408	−	0.862607i	0.494102	−	0.869404i	$-0.335497\pi$
$419$	30.5830	−	17.6571i	1.49408	−	0.862607i	0.999977	+	0.00679720i	$0.00216363\pi$
$420$		0			0
$421$	1.17730	−	1.17730i	0.0573782	−	0.0573782i	−0.677835	−	0.735214i	$-0.737082\pi$
$421$	1.17730	−	1.17730i	0.0573782	−	0.0573782i	0.735214	+	0.677835i	$0.237082\pi$
$422$	12.5198	−	12.5198i	0.609455	−	0.609455i
$423$		0			0
$424$	66.5839	−	17.8411i	3.23360	−	0.866441i
$425$		−	0.109538i		−	0.00531335i
$426$		0			0
$427$	−5.07536	−	2.84853i	−0.245614	−	0.137850i
$428$			27.1551i			1.31259i
$429$		0			0
$430$	−16.3021	−	9.41200i	−0.786155	−	0.453887i
$431$	6.04806	−	6.04806i	0.291325	−	0.291325i	−0.546279	−	0.837604i	$-0.683956\pi$
$431$	6.04806	−	6.04806i	0.291325	−	0.291325i	0.837604	+	0.546279i	$0.183956\pi$
$432$		0			0
$433$	12.8971	−	22.3384i	0.619793	−	1.07351i	−0.369730	−	0.929139i	$-0.620550\pi$
$433$	12.8971	−	22.3384i	0.619793	−	1.07351i	0.989523	−	0.144374i	$-0.0461169\pi$
$434$	−38.3431	+	0.466375i	−1.84053	+	0.0223867i
$435$		0			0
$436$	−8.03181	−	8.03181i	−0.384654	−	0.384654i
$437$	−2.53621	−	9.46526i	−0.121323	−	0.452785i
$438$		0			0
$439$	−16.5241	+	28.6206i	−0.788652	+	1.36598i	0.138141	+	0.990413i	$0.455887\pi$
$439$	−16.5241	+	28.6206i	−0.788652	+	1.36598i	−0.926793	+	0.375572i	$0.877446\pi$
$440$	81.2110	+	21.7604i	3.87158	+	1.03739i
$441$		0			0
$442$	−0.0989714	−	0.638367i	−0.00470759	−	0.0303640i
$443$	9.97640	+	17.2796i	0.473993	+	0.820980i	0.999557	−	0.0297740i	$-0.00947876\pi$
$443$	9.97640	+	17.2796i	0.473993	+	0.820980i	−0.525563	+	0.850754i	$0.676145\pi$
$444$		0			0
$445$	−2.64024			−0.125159
$446$	3.48265			0.164908
$447$		0			0
$448$	98.9277	+	55.5227i	4.67389	+	2.62320i
$449$	36.3738	−	9.74632i	1.71658	−	0.459957i	0.739560	−	0.673090i	$-0.235033\pi$
$449$	36.3738	−	9.74632i	1.71658	−	0.459957i	0.977023	+	0.213133i	$0.0683668\pi$
$450$		0			0
$451$	−31.5304	+	18.2041i	−1.48471	+	0.857197i
$452$			65.3965i			3.07599i
$453$		0			0
$454$	5.90369			0.277074
$455$	−17.0858	+	2.86216i	−0.800993	+	0.134180i
$456$		0			0
$457$	6.38471	+	23.8280i	0.298664	+	1.11463i	0.938264	+	0.345921i	$0.112433\pi$
$457$	6.38471	+	23.8280i	0.298664	+	1.11463i	−0.639600	+	0.768708i	$0.720900\pi$
$458$			41.6029i			1.94398i
$459$		0			0
$460$	8.69455	−	32.4485i	0.405385	−	1.51292i
$461$	−3.39930	+	0.910841i	−0.158321	+	0.0424221i	−0.337109	−	0.941466i	$-0.609449\pi$
$461$	−3.39930	+	0.910841i	−0.158321	+	0.0424221i	0.178788	+	0.983888i	$0.442782\pi$
$462$		0			0
$463$	8.73615	+	8.73615i	0.406003	+	0.406003i	0.880342	−	0.474339i	$-0.157313\pi$
$463$	8.73615	+	8.73615i	0.406003	+	0.406003i	−0.474339	+	0.880342i	$0.657313\pi$
$464$	−84.8400			−3.93860
$465$		0			0
$466$	−36.0872	−	36.0872i	−1.67171	−	1.67171i
$467$	7.58013	+	13.1292i	0.350767	+	0.607546i	0.986384	−	0.164459i	$-0.0525877\pi$
$467$	7.58013	+	13.1292i	0.350767	+	0.607546i	−0.635617	+	0.772004i	$0.719254\pi$
$468$		0			0
$469$	−4.50486	−	16.0299i	−0.208015	−	0.740192i
$470$	−20.5655	−	5.51051i	−0.948616	−	0.254181i
$471$		0			0
$472$	−24.2835	−	42.0603i	−1.11774	−	1.93598i
$473$	4.27303	+	15.9472i	0.196474	+	0.733251i
$474$		0			0
$475$	1.34190	+	5.00805i	0.0615707	+	0.229785i
$476$	0.841934	−	0.499842i	0.0385900	−	0.0229102i
$477$		0			0
$478$	−18.3467	−	10.5925i	−0.839159	−	0.484488i
$479$	−13.5550	+	13.5550i	−0.619345	+	0.619345i	−0.945363	−	0.326019i	$-0.894293\pi$
$479$	−13.5550	+	13.5550i	−0.619345	+	0.619345i	0.326019	+	0.945363i	$0.394293\pi$
$480$		0			0
$481$	5.68397	−	14.6639i	0.259167	−	0.668618i
$482$		−	70.9997i		−	3.23395i
$483$		0			0
$484$	−24.9044	−	43.1357i	−1.13202	−	1.96072i
$485$			16.5442i			0.751235i
$486$		0			0
$487$	−17.3586	−	4.65122i	−0.786593	−	0.210767i	−0.156904	−	0.987614i	$-0.550151\pi$
$487$	−17.3586	−	4.65122i	−0.786593	−	0.210767i	−0.629690	+	0.776847i	$0.716818\pi$
$488$	−16.2406	+	16.2406i	−0.735175	+	0.735175i
$489$		0			0
$490$	−18.4353	−	30.2093i	−0.832823	−	1.36472i
$491$	10.2354	−	5.90939i	0.461915	−	0.266687i	−0.250934	−	0.968004i	$-0.580738\pi$
$491$	10.2354	−	5.90939i	0.461915	−	0.266687i	0.712849	+	0.701317i	$0.247404\pi$
$492$		0			0
$493$	−0.155415	+	0.269186i	−0.00699953	+	0.0121235i
$494$	12.3454	+	27.9736i	0.555444	+	1.25859i
$495$		0			0
$496$	−23.6689	+	88.3336i	−1.06277	+	3.96630i
$497$	19.6592	+	5.01222i	0.881838	+	0.224829i
$498$		0			0
$499$	−31.9343	−	8.55677i	−1.42958	−	0.383054i	−0.540705	−	0.841212i	$-0.681842\pi$
$499$	−31.9343	−	8.55677i	−1.42958	−	0.383054i	−0.888870	+	0.458159i	$0.848509\pi$
$500$	−18.1143	+	67.6035i	−0.810097	+	3.02332i
$501$		0			0
$502$	−69.1806	−	18.5369i	−3.08768	−	0.827342i
$503$	11.0429	+	6.37561i	0.492378	+	0.284274i	0.725560	−	0.688159i	$-0.241581\pi$
$503$	11.0429	+	6.37561i	0.492378	+	0.284274i	−0.233183	+	0.972433i	$0.574914\pi$
$504$		0			0
$505$	1.92125	−	7.17022i	0.0854947	−	0.319071i
$506$	−34.3903	+	19.8552i	−1.52883	+	0.882673i
$507$		0			0
$508$	−60.1012	+	104.098i	−2.66656	+	4.61862i
$509$	23.0349	−	6.17218i	1.02100	−	0.273577i	0.290783	−	0.956789i	$-0.406084\pi$
$509$	23.0349	−	6.17218i	1.02100	−	0.273577i	0.730220	+	0.683212i	$0.239418\pi$
$510$		0			0
$511$	16.0136	+	4.08275i	0.708400	+	0.180610i
$512$	88.6809	−	88.6809i	3.91918	−	3.91918i
$513$		0			0
$514$	−15.1487	−	4.05909i	−0.668182	−	0.179039i
$515$	−20.5320	+	5.50154i	−0.904749	+	0.242427i
$516$		0			0
$517$	9.33670	+	16.1716i	0.410628	+	0.711228i
$518$	32.1257	−	0.390752i	1.41152	−	0.0171686i
$519$		0			0
$520$	−7.36804	+	67.9663i	−0.323110	+	2.98052i
$521$	9.61490	+	5.55117i	0.421237	+	0.243201i	0.695606	−	0.718423i	$-0.255136\pi$
$521$	9.61490	+	5.55117i	0.421237	+	0.243201i	−0.274370	+	0.961624i	$0.588469\pi$
$522$		0			0
$523$	−9.26532	−	5.34934i	−0.405144	−	0.233910i	0.283557	−	0.958955i	$-0.408486\pi$
$523$	−9.26532	−	5.34934i	−0.405144	−	0.233910i	−0.688701	+	0.725045i	$0.741819\pi$
$524$	49.3592	−	85.4926i	2.15627	−	3.73476i
$525$		0			0
$526$	−1.20295	−	4.48947i	−0.0524511	−	0.195750i
$527$	0.236913	+	0.236913i	0.0103201	+	0.0103201i
$528$		0			0
$529$	−6.32592	−	10.9568i	−0.275040	−	0.476383i
$530$	−16.6895	+	28.9071i	−0.724947	+	1.25565i
$531$		0			0
$532$	−32.3698	+	33.1670i	−1.40341	+	1.43797i
$533$	−18.5555	−	23.0678i	−0.803728	−	0.999176i
$534$		0			0
$535$	−6.06407	−	6.06407i	−0.262173	−	0.262173i
$536$	−65.7088			−2.83819
$537$		0			0
$538$	−32.4498	−	32.4498i	−1.39901	−	1.39901i
$539$	−7.30192	+	30.1681i	−0.314516	+	1.29943i
$540$		0			0
$541$	−6.76474	+	25.2463i	−0.290839	+	1.08543i	0.653627	+	0.756816i	$0.273246\pi$
$541$	−6.76474	+	25.2463i	−0.290839	+	1.08543i	−0.944466	+	0.328609i	$0.893420\pi$
$542$	−7.98624	+	4.61086i	−0.343039	+	0.198053i
$543$		0			0
$544$	−0.466744	−	1.74191i	−0.0200115	−	0.0746839i
$545$	3.58720			0.153659
$546$		0			0
$547$	19.4637			0.832209			0.416105	−	0.909317i	$-0.363395\pi$
$547$	19.4637			0.832209			0.416105	+	0.909317i	$0.363395\pi$
$548$	15.3315	+	57.2180i	0.654930	+	2.44423i
$549$		0			0
$550$	18.1958	−	10.5054i	0.775872	−	0.447950i
$551$	3.80785	−	14.2111i	0.162220	−	0.605413i
$552$		0			0
$553$	3.38118	−	0.0411260i	0.143782	−	0.00174886i
$554$	−14.6823	−	14.6823i	−0.623792	−	0.623792i
$555$		0			0
$556$	76.3113			3.23632
$557$	−1.97123	−	1.97123i	−0.0835238	−	0.0835238i	0.664111	−	0.747634i	$-0.268810\pi$
$557$	−1.97123	−	1.97123i	−0.0835238	−	0.0835238i	−0.747634	+	0.664111i	$0.768810\pi$
$558$		0			0
$559$	−12.2817	+	5.42017i	−0.519460	+	0.229249i
$560$	−81.2531	+	22.8344i	−3.43357	+	0.964930i
$561$		0			0
$562$	8.33745	−	14.4409i	0.351694	−	0.609152i
$563$	−16.8506	−	29.1861i	−0.710168	−	1.23005i	−0.964794	−	0.263007i	$-0.915286\pi$
$563$	−16.8506	−	29.1861i	−0.710168	−	1.23005i	0.254626	−	0.967040i	$-0.418048\pi$
$564$		0			0
$565$	−14.6038	−	14.6038i	−0.614388	−	0.614388i
$566$	−18.8132	−	70.2118i	−0.790777	−	2.95122i
$567$		0			0
$568$	40.0312	−	69.3361i	1.67967	−	2.90928i
$569$	12.1196	+	6.99725i	0.508080	+	0.293340i	0.732044	−	0.681257i	$-0.238567\pi$
$569$	12.1196	+	6.99725i	0.508080	+	0.293340i	−0.223964	+	0.974597i	$0.571900\pi$
$570$		0			0
$571$	35.5855	+	20.5453i	1.48921	+	0.859795i	0.999924	−	0.0123295i	$-0.00392469\pi$
$571$	35.5855	+	20.5453i	1.48921	+	0.859795i	0.489284	+	0.872124i	$0.337258\pi$
$572$	71.6353	−	57.6228i	2.99522	−	2.40933i
$573$		0			0
$574$	29.5997	−	52.7393i	1.23547	−	2.20130i
$575$	−2.73759	−	4.74165i	−0.114166	−	0.197741i
$576$		0			0
$577$	−16.6678	+	4.46613i	−0.693890	+	0.185927i	−0.588492	−	0.808503i	$-0.700278\pi$
$577$	−16.6678	+	4.46613i	−0.693890	+	0.185927i	−0.105398	+	0.994430i	$0.533612\pi$
$578$	45.7034	+	12.2462i	1.90101	+	0.509374i
$579$		0			0
$580$	35.6641	−	35.6641i	1.48087	−	1.48087i
$581$	32.0772	−	9.01460i	1.33079	−	0.373989i
$582$		0			0
$583$	28.2778	−	7.57702i	1.17115	−	0.313808i
$584$	32.6077	−	56.4783i	1.34932	−	2.33709i
$585$		0			0
$586$	−31.7830	+	18.3499i	−1.31294	+	0.758027i
$587$	−7.39660	+	27.6045i	−0.305291	+	1.13936i	0.627404	+	0.778694i	$0.284117\pi$
$587$	−7.39660	+	27.6045i	−0.305291	+	1.13936i	−0.932695	+	0.360666i	$0.882549\pi$
$588$		0			0
$589$	−13.7340	−	7.92932i	−0.565899	−	0.326722i
$590$	22.7161	+	6.08676i	0.935208	+	0.250588i
$591$		0			0
$592$	19.8310	−	74.0102i	0.815048	−	3.04180i
$593$	22.6418	+	6.06684i	0.929786	+	0.249135i	0.691763	−	0.722124i	$-0.256834\pi$
$593$	22.6418	+	6.06684i	0.929786	+	0.249135i	0.238022	+	0.971260i	$0.423501\pi$
$594$		0			0
$595$	−0.0763934	+	0.299635i	−0.00313183	+	0.0122838i
$596$	3.29410	−	12.2937i	0.134932	−	0.503571i
$597$		0			0
$598$	−20.2385	−	25.1601i	−0.827615	−	1.02887i
$599$	−6.93880	+	12.0184i	−0.283512	+	0.491057i	−0.972247	−	0.233956i	$-0.924833\pi$
$599$	−6.93880	+	12.0184i	−0.283512	+	0.491057i	0.688735	+	0.725013i	$0.258166\pi$
$600$		0			0
$601$	30.9970	−	17.8961i	1.26439	−	0.729998i	0.290472	−	0.956883i	$-0.406188\pi$
$601$	30.9970	−	17.8961i	1.26439	−	0.729998i	0.973921	+	0.226886i	$0.0728543\pi$
$602$	−19.6264	−	19.1547i	−0.799913	−	0.780688i
$603$		0			0
$604$	27.8146	−	27.8146i	1.13176	−	1.13176i
$605$	15.1942	+	4.07127i	0.617732	+	0.165521i
$606$		0			0
$607$		−	24.1417i		−	0.979880i	−0.871756	−	0.489940i	$-0.837019\pi$
$607$		−	24.1417i		−	0.979880i	0.871756	−	0.489940i	$-0.162981\pi$
$608$	42.6790	+	73.9223i	1.73086	+	2.99794i
$609$		0			0
$610$		−	11.1215i		−	0.450298i
$611$	−11.8312	+	9.51694i	−0.478641	+	0.385014i
$612$		0			0
$613$	4.24663	−	4.24663i	0.171520	−	0.171520i	−0.616127	−	0.787647i	$-0.711299\pi$
$613$	4.24663	−	4.24663i	0.171520	−	0.171520i	0.787647	+	0.616127i	$0.211299\pi$
$614$	−72.9929	−	42.1424i	−2.94575	−	1.70073i
$615$		0			0
$616$	106.816	+	59.9498i	4.30372	+	2.41545i
$617$	−11.3696	−	42.4321i	−0.457724	−	1.70825i	−0.679953	−	0.733256i	$-0.738000\pi$
$617$	−11.3696	−	42.4321i	−0.457724	−	1.70825i	0.222228	−	0.974995i	$-0.428667\pi$
$618$		0			0
$619$	3.81017	+	14.2198i	0.153144	+	0.571541i	0.999257	+	0.0385375i	$0.0122699\pi$
$619$	3.81017	+	14.2198i	0.153144	+	0.571541i	−0.846113	+	0.533003i	$0.821063\pi$
$620$	−27.1830	−	47.0824i	−1.09170	−	1.89087i
$621$		0			0
$622$	53.7685	+	14.4072i	2.15592	+	0.577678i
$623$	−3.72729	−	0.950292i	−0.149331	−	0.0380726i
$624$		0			0
$625$	−6.79647	−	11.7718i	−0.271859	−	0.470873i
$626$	32.9802	+	32.9802i	1.31815	+	1.31815i
$627$		0			0
$628$	−85.4341			−3.40919
$629$	−0.198497	−	0.198497i	−0.00791460	−	0.00791460i
$630$		0			0
$631$	47.4763	−	12.7212i	1.89000	−	0.506424i	0.891419	−	0.453180i	$-0.149711\pi$
$631$	47.4763	−	12.7212i	1.89000	−	0.506424i	0.998582	−	0.0532441i	$-0.0169562\pi$
$632$	3.45369	−	12.8893i	0.137380	−	0.512711i
$633$		0			0
$634$		−	61.0554i		−	2.42482i
$635$	−9.82510	−	36.6678i	−0.389897	−	1.45512i
$636$		0			0
$637$	−25.1506	−	2.10903i	−0.996503	−	0.0835628i
$638$	−59.6211			−2.36042
$639$		0			0
$640$			115.003i			4.54590i
$641$	29.1632	−	16.8374i	1.15188	−	0.665037i	0.202534	−	0.979275i	$-0.435082\pi$
$641$	29.1632	−	16.8374i	1.15188	−	0.665037i	0.949344	+	0.314238i	$0.101749\pi$
$642$		0			0
$643$	−26.4390	+	7.08430i	−1.04265	+	0.279377i	−0.739212	−	0.673473i	$-0.764802\pi$
$643$	−26.4390	+	7.08430i	−1.04265	+	0.279377i	−0.303439	+	0.952851i	$0.598135\pi$
$644$	23.9534	−	42.6790i	0.943896	−	1.68179i
$645$		0			0
$646$	0.545775			0.0214732
$647$	−43.4631			−1.70871			−0.854355	−	0.519690i	$-0.826047\pi$
$647$	−43.4631			−1.70871			−0.854355	+	0.519690i	$0.826047\pi$
$648$		0			0
$649$	−10.3131	−	17.8628i	−0.404823	−	0.701175i
$650$	10.7082	+	13.3121i	0.420009	+	0.522145i
$651$		0			0
$652$	16.1555	+	4.32885i	0.632697	+	0.169531i
$653$	2.05571	−	3.56060i	0.0804462	−	0.139337i	−0.822995	−	0.568048i	$-0.807699\pi$
$653$	2.05571	−	3.56060i	0.0804462	−	0.139337i	0.903442	+	0.428711i	$0.141032\pi$
$654$		0			0
$655$	8.06903	+	30.1140i	0.315283	+	1.17665i
$656$	−101.987	−	101.987i	−3.98193	−	3.98193i
$657$		0			0
$658$	−27.0495	−	15.1814i	−1.05450	−	0.591833i
$659$	16.4983	−	28.5759i	0.642683	−	1.11316i	−0.342148	−	0.939646i	$-0.611154\pi$
$659$	16.4983	−	28.5759i	0.642683	−	1.11316i	0.984831	−	0.173514i	$-0.0555123\pi$
$660$		0			0
$661$	31.3318	−	31.3318i	1.21867	−	1.21867i	0.250566	−	0.968100i	$-0.419383\pi$
$661$	31.3318	−	31.3318i	1.21867	−	1.21867i	0.968100	−	0.250566i	$-0.0806167\pi$
$662$	79.3903	+	45.8360i	3.08559	+	1.78147i
$663$		0			0
$664$		−	131.489i		−	5.10276i
$665$	−0.178011	−	14.6352i	−0.00690295	−	0.567527i
$666$		0			0
$667$			15.5367i			0.601583i
$668$	−80.6189	+	21.6018i	−3.11924	+	0.835798i
$669$		0			0
$670$	22.4987	−	22.4987i	0.869201	−	0.869201i
$671$	−6.89727	+	6.89727i	−0.266266	+	0.266266i
$672$		0			0
$673$	0.169378	−	0.0977906i	0.00652906	−	0.00376955i	−0.496732	−	0.867904i	$-0.665467\pi$
$673$	0.169378	−	0.0977906i	0.00652906	−	0.00376955i	0.503261	+	0.864134i	$0.332133\pi$
$674$	58.1665	−	15.5857i	2.24049	−	0.600337i
$675$		0			0
$676$	55.2258	+	50.3825i	2.12407	+	1.93779i
$677$	0.424711	−	0.245207i	0.0163230	−	0.00942406i	−0.491816	−	0.870699i	$-0.663667\pi$
$677$	0.424711	−	0.245207i	0.0163230	−	0.00942406i	0.508139	+	0.861275i	$0.330334\pi$
$678$		0			0
$679$	−5.95472	+	23.3559i	−0.228521	+	0.896319i
$680$	1.05678	+	0.610132i	0.0405257	+	0.0233975i
$681$		0			0
$682$	−16.6333	+	62.0763i	−0.636922	+	2.37702i
$683$	−5.19490	+	19.3876i	−0.198777	+	0.741847i	0.792479	+	0.609899i	$0.208790\pi$
$683$	−5.19490	+	19.3876i	−0.198777	+	0.741847i	−0.991257	+	0.131948i	$0.957877\pi$
$684$		0			0
$685$	−16.2012	−	9.35376i	−0.619016	−	0.357389i
$686$	−15.1525	−	49.2827i	−0.578524	−	1.88162i
$687$		0			0
$688$	−56.6411	+	32.7018i	−2.15942	+	1.24674i
$689$	9.61115	+	21.7781i	0.366156	+	0.829681i
$690$		0			0
$691$	14.1521	−	3.79204i	0.538370	−	0.144256i	0.0206194	−	0.999787i	$-0.493436\pi$
$691$	14.1521	−	3.79204i	0.538370	−	0.144256i	0.517751	+	0.855532i	$0.326770\pi$
$692$	−76.6732	+	44.2673i	−2.91468	+	1.68279i
$693$		0			0
$694$	0.255503	−	0.255503i	0.00969875	−	0.00969875i
$695$	−17.0413	+	17.0413i	−0.646411	+	0.646411i
$696$		0			0
$697$	−0.510418	+	0.136766i	−0.0193335	+	0.00518038i
$698$			61.9433i			2.34459i
$699$		0			0
$700$	−12.6737	+	22.5814i	−0.479021	+	0.853495i
$701$		−	13.9124i		−	0.525463i	−0.964869	−	0.262731i	$-0.915377\pi$
$701$		−	13.9124i		−	0.525463i	0.964869	−	0.262731i	$-0.0846233\pi$
$702$		0			0
$703$	11.5070	+	6.64357i	0.433995	+	0.250567i
$704$	134.440	−	134.440i	5.06690	−	5.06690i
$705$		0			0
$706$	12.9775	−	22.4778i	0.488416	−	0.845962i
$707$	5.29304	−	9.43088i	0.199065	−	0.354685i
$708$		0			0
$709$	36.1207	+	36.1207i	1.35654	+	1.35654i	0.878142	+	0.478399i	$0.158783\pi$
$709$	36.1207	+	36.1207i	1.35654	+	1.35654i	0.478399	+	0.878142i	$0.341217\pi$
$710$	10.0340	+	37.4474i	0.376569	+	1.40537i
$711$		0			0
$712$	−7.58971	+	13.1458i	−0.284436	+	0.492658i
$713$	16.1765	+	4.33447i	0.605814	+	0.162327i
$714$		0			0
$715$	−3.12917	+	28.8649i	−0.117024	+	1.07949i
$716$	−47.0914	−	81.5647i	−1.75989	−	3.04822i
$717$		0			0
$718$	−15.2338			−0.568522
$719$	25.5016			0.951049			0.475525	−	0.879702i	$-0.342258\pi$
$719$	25.5016			0.951049			0.475525	+	0.879702i	$0.342258\pi$
$720$		0			0
$721$	−30.9657	+	0.376643i	−1.15322	+	0.0140269i
$722$	26.1399	−	7.00416i	0.972825	−	0.260668i
$723$		0			0
$724$	−29.1790	+	16.8465i	−1.08443	+	0.626095i
$725$		−	8.22043i		−	0.305299i
$726$		0			0
$727$	48.7660			1.80863			0.904315	−	0.426866i	$-0.140383\pi$
$727$	48.7660			1.80863			0.904315	+	0.426866i	$0.140383\pi$
$728$	−34.8645	+	93.2978i	−1.29217	+	3.45785i
$729$		0			0
$730$	8.17327	+	30.5031i	0.302506	+	1.12897i
$731$			0.239620i			0.00886266i
$732$		0			0
$733$	9.91590	−	37.0066i	0.366252	−	1.36687i	−0.499463	−	0.866335i	$-0.666469\pi$
$733$	9.91590	−	37.0066i	0.366252	−	1.36687i	0.865716	−	0.500536i	$-0.166864\pi$
$734$	−45.6705	+	12.2374i	−1.68573	+	0.451689i
$735$		0			0
$736$	−63.7388	−	63.7388i	−2.34944	−	2.34944i
$737$	−27.9062			−1.02794
$738$		0			0
$739$	−5.59376	−	5.59376i	−0.205770	−	0.205770i	0.596697	−	0.802467i	$-0.296480\pi$
$739$	−5.59376	−	5.59376i	−0.205770	−	0.205770i	−0.802467	+	0.596697i	$0.796480\pi$
$740$	22.7753	+	39.4479i	0.837235	+	1.45013i
$741$		0			0
$742$	−33.9655	+	34.8020i	−1.24691	+	1.27762i
$743$	−0.896137	−	0.240119i	−0.0328761	−	0.00880912i	0.242344	−	0.970191i	$-0.422084\pi$
$743$	−0.896137	−	0.240119i	−0.0328761	−	0.00880912i	−0.275220	+	0.961381i	$0.588751\pi$
$744$		0			0
$745$	2.00973	+	3.48095i	0.0736308	+	0.127532i
$746$	2.27577	+	8.49328i	0.0833218	+	0.310961i
$747$		0			0
$748$	−0.424717	−	1.58507i	−0.0155292	−	0.0579557i
$749$	−6.37819	−	10.7434i	−0.233054	−	0.392556i
$750$		0			0
$751$	−30.0265	−	17.3358i	−1.09568	−	0.632592i	−0.160598	−	0.987020i	$-0.551342\pi$
$751$	−30.0265	−	17.3358i	−1.09568	−	0.632592i	−0.935083	+	0.354428i	$0.884676\pi$
$752$	−52.3082	+	52.3082i	−1.90748	+	1.90748i
$753$		0			0
$754$	−7.42747	−	47.9073i	−0.270493	−	1.74468i
$755$			12.4227i			0.452107i
$756$		0			0
$757$	18.9075	+	32.7488i	0.687207	+	1.19028i	0.972738	+	0.231907i	$0.0744966\pi$
$757$	18.9075	+	32.7488i	0.687207	+	1.19028i	−0.285531	+	0.958369i	$0.592170\pi$
$758$		−	49.6580i		−	1.80366i
$759$		0			0
$760$	−55.7904	−	14.9490i	−2.02373	−	0.542257i
$761$	8.26100	−	8.26100i	0.299461	−	0.299461i	−0.541342	−	0.840803i	$-0.682083\pi$
$761$	8.26100	−	8.26100i	0.299461	−	0.299461i	0.840803	+	0.541342i	$0.182083\pi$
$762$		0			0
$763$	5.06415	+	1.29113i	0.183334	+	0.0467420i
$764$	−54.2636	+	31.3291i	−1.96319	+	1.13345i
$765$		0			0
$766$	−2.97310	+	5.14956i	−0.107422	+	0.186061i
$767$	13.0685	−	10.5122i	0.471875	−	0.379572i
$768$		0			0
$769$	1.66486	−	6.21334i	0.0600364	−	0.224059i	−0.929389	−	0.369102i	$-0.879665\pi$
$769$	1.66486	−	6.21334i	0.0600364	−	0.224059i	0.989425	+	0.145043i	$0.0463320\pi$
$770$	−57.1005	+	16.0468i	−2.05776	+	0.578288i
$771$		0			0
$772$	−130.969	−	35.0932i	−4.71369	−	1.26303i
$773$	−6.32811	+	23.6168i	−0.227606	+	0.849439i	0.753737	+	0.657176i	$0.228249\pi$
$773$	−6.32811	+	23.6168i	−0.227606	+	0.849439i	−0.981343	+	0.192263i	$0.938417\pi$
$774$		0			0
$775$	−8.55894	−	2.29336i	−0.307446	−	0.0823800i
$776$	82.3739	+	47.5586i	2.95705	+	1.70725i
$777$		0			0
$778$	0.174560	−	0.651469i	0.00625830	−	0.0233563i
$779$	21.6608	−	12.5059i	0.776079	−	0.448069i
$780$		0			0
$781$	17.0010	−	29.4466i	0.608345	−	1.05368i
$782$	−0.556714	+	0.149171i	−0.0199080	+	0.00533434i
$783$		0			0
$784$	−122.926	+	2.99079i	−4.39021	+	0.106814i
$785$	19.0785	−	19.0785i	0.680940	−	0.680940i
$786$		0			0
$787$	−0.624076	−	0.167221i	−0.0222459	−	0.00596077i	0.247679	−	0.968842i	$-0.420332\pi$
$787$	−0.624076	−	0.167221i	−0.0222459	−	0.00596077i	−0.269925	+	0.962881i	$0.586999\pi$
$788$	−103.933	+	27.8487i	−3.70245	+	0.992068i
$789$		0			0
$790$	3.23077	+	5.59586i	0.114946	+	0.199092i
$791$	−15.3603	−	25.8729i	−0.546150	−	0.919936i
$792$		0			0
$793$	−6.40141	−	4.68291i	−0.227321	−	0.166295i
$794$	−16.5216	−	9.53876i	−0.586330	−	0.338518i
$795$		0			0
$796$	3.59737	+	2.07694i	0.127505	+	0.0736153i
$797$	−26.0622	+	45.1410i	−0.923170	+	1.59898i	−0.128692	+	0.991685i	$0.541078\pi$
$797$	−26.0622	+	45.1410i	−0.923170	+	1.59898i	−0.794478	+	0.607293i	$0.792255\pi$
$798$		0			0
$799$	0.0701460	+	0.261788i	0.00248159	+	0.00926140i
$800$	33.7241	+	33.7241i	1.19233	+	1.19233i
$801$		0			0
$802$	37.7558	+	65.3949i	1.33320	+	2.30918i
$803$	13.8483	−	23.9860i	0.488697	−	0.846448i
$804$		0			0
$805$	4.18165	+	14.8798i	0.147384	+	0.524445i
$806$	−51.9523	−	5.63201i	−1.82994	−	0.198379i
$807$		0			0
$808$	−30.1777	−	30.1777i	−1.06165	−	1.06165i
$809$	53.1509			1.86869			0.934343	−	0.356375i	$-0.115987\pi$
$809$	53.1509			1.86869			0.934343	+	0.356375i	$0.115987\pi$
$810$		0			0
$811$	1.14454	+	1.14454i	0.0401904	+	0.0401904i	0.726916	−	0.686726i	$-0.240953\pi$
$811$	1.14454	+	1.14454i	0.0401904	+	0.0401904i	−0.686726	+	0.726916i	$0.740953\pi$
$812$	63.1844	−	37.5115i	2.21734	−	1.31639i
$813$		0			0
$814$	13.9362	−	52.0106i	0.488463	−	1.82297i
$815$	−4.57440	+	2.64103i	−0.160234	+	0.0925112i
$816$		0			0
$817$	−2.93549	−	10.9554i	−0.102700	−	0.383281i
$818$	−101.113			−3.53534
$819$		0			0
$820$	85.7444			2.99433
$821$	−6.04695	−	22.5675i	−0.211040	−	0.787612i	−0.987523	−	0.157474i	$-0.949665\pi$
$821$	−6.04695	−	22.5675i	−0.211040	−	0.787612i	0.776483	−	0.630138i	$-0.217002\pi$
$822$		0			0
$823$	9.47321	−	5.46936i	0.330215	−	0.190650i	−0.325721	−	0.945466i	$-0.605607\pi$
$823$	9.47321	−	5.46936i	0.330215	−	0.190650i	0.655937	+	0.754816i	$0.272274\pi$
$824$	−31.6298	+	118.044i	−1.10188	+	4.11226i
$825$		0			0
$826$	29.8781	+	16.7690i	1.03959	+	0.583467i
$827$	20.4780	+	20.4780i	0.712091	+	0.712091i	0.966972	−	0.254881i	$-0.0820364\pi$
$827$	20.4780	+	20.4780i	0.712091	+	0.712091i	−0.254881	+	0.966972i	$0.582036\pi$
$828$		0			0
$829$	−36.4369			−1.26551			−0.632754	−	0.774353i	$-0.718075\pi$
$829$	−36.4369			−1.26551			−0.632754	+	0.774353i	$0.718075\pi$
$830$	45.0218	+	45.0218i	1.56273	+	1.56273i
$831$		0			0
$832$	124.775	+	91.2782i	4.32578	+	3.16450i
$833$	−0.215693	+	0.395506i	−0.00747333	+	0.0137035i
$834$		0			0
$835$	13.1792	−	22.8271i	0.456086	−	0.789965i
$836$	38.8361	+	67.2661i	1.34317	+	2.32645i
$837$		0			0
$838$	69.5178	+	69.5178i	2.40145	+	2.40145i
$839$	11.8451	+	44.2066i	0.408939	+	1.52618i	0.796673	+	0.604410i	$0.206591\pi$
$839$	11.8451	+	44.2066i	0.408939	+	1.52618i	−0.387734	+	0.921771i	$0.626742\pi$
$840$		0			0
$841$	2.83664	−	4.91321i	0.0978152	−	0.169421i
$842$	4.01416	+	2.31758i	0.138337	+	0.0798690i
$843$		0			0
$844$	31.6722	+	18.2859i	1.09020	+	0.629428i
$845$	−23.5836	+	1.08155i	−0.811301	+	0.0372065i
$846$		0			0
$847$	19.9847	+	11.2163i	0.686682	+	0.385397i
$848$	57.9874	+	100.437i	1.99130	+	3.44902i
$849$		0			0
$850$	0.294556	−	0.0789260i	0.0101032	−	0.00270714i
$851$	−13.5534	−	3.63163i	−0.464606	−	0.124491i
$852$		0			0
$853$	12.9593	−	12.9593i	0.443719	−	0.443719i	−0.449541	−	0.893260i	$-0.648412\pi$
$853$	12.9593	−	12.9593i	0.443719	−	0.443719i	0.893260	+	0.449541i	$0.148412\pi$
$854$	4.00294	−	15.7006i	0.136978	−	0.537262i
$855$		0			0
$856$	−47.6250	+	12.7611i	−1.62779	+	0.436165i
$857$	9.79114	−	16.9588i	0.334459	−	0.579300i	−0.648922	−	0.760855i	$-0.724780\pi$
$857$	9.79114	−	16.9588i	0.334459	−	0.579300i	0.983381	+	0.181555i	$0.0581131\pi$
$858$		0			0
$859$	−25.7753	+	14.8814i	−0.879442	+	0.507746i	−0.870474	−	0.492214i	$-0.836188\pi$
$859$	−25.7753	+	14.8814i	−0.879442	+	0.507746i	−0.00896783	+	0.999960i	$0.502855\pi$
$860$	10.0634	−	37.5570i	0.343158	−	1.28068i
$861$		0			0
$862$	20.6216	+	11.9059i	0.702376	+	0.405517i
$863$	−0.928597	−	0.248817i	−0.0316098	−	0.00846982i	0.242979	−	0.970031i	$-0.421875\pi$
$863$	−0.928597	−	0.248817i	−0.0316098	−	0.00846982i	−0.274589	+	0.961562i	$0.588542\pi$
$864$		0			0
$865$	7.23664	−	27.0075i	0.246053	−	0.918282i
$866$	69.3627	+	18.5857i	2.35704	+	0.631567i
$867$		0			0
$868$	−21.4288	−	76.2513i	−0.727340	−	2.58814i
$869$	1.46676	−	5.47403i	0.0497565	−	0.185694i
$870$		0			0
$871$	−3.47649	−	22.4234i	−0.117796	−	0.759789i
$872$	10.3119	−	17.8607i	0.349205	−	0.604840i
$873$		0			0
$874$	23.6255	−	13.6402i	0.799144	−	0.461386i
$875$	−8.71210	−	31.0008i	−0.294523	−	1.04802i
$876$		0			0
$877$	−9.66471	+	9.66471i	−0.326354	+	0.326354i	−0.851198	−	0.524844i	$-0.824124\pi$
$877$	−9.66471	+	9.66471i	−0.326354	+	0.326354i	0.524844	+	0.851198i	$0.324124\pi$
$878$	−88.8695	−	23.8125i	−2.99920	−	0.803633i
$879$		0			0
$880$			141.452i			4.76835i
$881$	−13.0267	−	22.5630i	−0.438882	−	0.760166i	0.558721	−	0.829355i	$-0.311292\pi$
$881$	−13.0267	−	22.5630i	−0.438882	−	0.760166i	−0.997604	+	0.0691892i	$0.977959\pi$
$882$		0			0
$883$		−	31.8374i		−	1.07141i	−0.844404	−	0.535707i	$-0.820045\pi$
$883$		−	31.8374i		−	1.07141i	0.844404	−	0.535707i	$-0.179955\pi$
$884$	1.22074	−	0.538737i	0.0410578	−	0.0181197i
$885$		0			0
$886$	−39.2781	+	39.2781i	−1.31957	+	1.31957i
$887$	−21.4692	−	12.3952i	−0.720864	−	0.416191i	0.0942065	−	0.995553i	$-0.469969\pi$
$887$	−21.4692	−	12.3952i	−0.720864	−	0.416191i	−0.815071	+	0.579362i	$0.803302\pi$
$888$		0			0
$889$	−0.672640	−	55.3012i	−0.0225596	−	1.85474i
$890$	−1.90239	−	7.09983i	−0.0637684	−	0.237987i
$891$		0			0
$892$	1.86183	+	6.94845i	0.0623387	+	0.232651i
$893$	−6.41414	−	11.1096i	−0.214641	−	0.371769i
$894$		0			0
$895$	28.7305	+	7.69831i	0.960354	+	0.257326i
$896$	−41.3928	+	162.353i	−1.38284	+	5.42384i
$897$		0			0
$898$	52.4174	+	90.7896i	1.74919	+	3.02969i
$899$	17.7795	+	17.7795i	0.592981	+	0.592981i
$900$		0			0
$901$	0.424899			0.0141554
$902$	−71.6713	−	71.6713i	−2.38639	−	2.38639i
$903$		0			0
$904$	−114.693	+	30.7320i	−3.81464	+	1.02213i
$905$	2.75399	−	10.2780i	0.0915458	−	0.341654i
$906$		0			0
$907$		−	6.94768i		−	0.230694i	−0.993325	−	0.115347i	$-0.963202\pi$
$907$		−	6.94768i		−	0.230694i	0.993325	−	0.115347i	$-0.0367980\pi$
$908$	3.15613	+	11.7788i	0.104740	+	0.390894i
$909$		0			0
$910$	−20.0076	−	43.8828i	−0.663244	−	1.45470i
$911$	23.5193			0.779228			0.389614	−	0.920978i	$-0.372608\pi$
$911$	23.5193			0.779228			0.389614	+	0.920978i	$0.372608\pi$
$912$		0			0
$913$		−	55.8426i		−	1.84812i
$914$	−59.4753	+	34.3381i	−1.96727	+	1.13580i
$915$		0			0
$916$	−83.0046	+	22.2410i	−2.74255	+	0.734864i
$917$	0.552417	+	45.4171i	0.0182424	+	1.49980i
$918$		0			0
$919$	22.9518			0.757109			0.378554	−	0.925579i	$-0.376421\pi$
$919$	22.9518			0.757109			0.378554	+	0.925579i	$0.376421\pi$
$920$	60.9945			2.01093
$921$		0			0
$922$	−4.89866	−	8.48473i	−0.161329	−	0.279430i
$923$	25.7792	+	9.99242i	0.848533	+	0.328905i
$924$		0			0
$925$	7.17110	+	1.92149i	0.235784	+	0.0631782i
$926$	−17.1975	+	29.7870i	−0.565146	+	0.978862i
$927$		0			0
$928$	−35.0276	−	130.725i	−1.14984	−	4.29125i
$929$	4.16808	+	4.16808i	0.136750	+	0.136750i	0.772168	−	0.635418i	$-0.219172\pi$
$929$	4.16808	+	4.16808i	0.136750	+	0.136750i	−0.635418	+	0.772168i	$0.719172\pi$
$930$		0			0
$931$	5.01628	−	20.7249i	0.164402	−	0.679231i
$932$	52.7075	−	91.2921i	1.72649	−	2.99037i
$933$		0			0
$934$	−29.8437	+	29.8437i	−0.976516	+	0.976516i
$935$	0.448809	+	0.259120i	0.0146776	+	0.00847413i
$936$		0			0
$937$			26.0948i			0.852481i	0.904610	+	0.426240i	$0.140162\pi$
$937$			26.0948i			0.852481i	−0.904610	+	0.426240i	$0.859838\pi$
$938$	39.8599	−	23.6641i	1.30147	−	0.772661i
$939$		0			0
$940$		−	43.9775i		−	1.43439i
$941$	−16.0551	+	4.30196i	−0.523382	+	0.140240i	−0.510831	−	0.859681i	$-0.670662\pi$
$941$	−16.0551	+	4.30196i	−0.523382	+	0.140240i	−0.0125516	+	0.999921i	$0.503995\pi$
$942$		0			0
$943$	−18.6768	+	18.6768i	−0.608201	+	0.608201i
$944$	57.7782	−	57.7782i	1.88052	−	1.88052i
$945$		0			0
$946$	−39.8044	+	22.9811i	−1.29415	+	0.747180i
$947$	−29.7042	+	7.95922i	−0.965257	+	0.258640i	−0.706824	−	0.707389i	$-0.749873\pi$
$947$	−29.7042	+	7.95922i	−0.965257	+	0.258640i	−0.258433	+	0.966029i	$0.583206\pi$
$948$		0			0
$949$	20.9987	+	8.13941i	0.681645	+	0.264216i
$950$	−12.5002	+	7.21699i	−0.405560	+	0.234150i
$951$		0			0
$952$	1.27228	+	1.24170i	0.0412349	+	0.0402438i
$953$	7.27321	+	4.19919i	0.235602	+	0.136025i	0.613154	−	0.789963i	$-0.289901\pi$
$953$	7.27321	+	4.19919i	0.235602	+	0.136025i	−0.377551	+	0.925989i	$0.623234\pi$
$954$		0			0
$955$	5.12155	−	19.1139i	0.165730	−	0.618511i
$956$	11.3255	−	42.2674i	0.366294	−	1.36703i
$957$		0			0
$958$	−46.2176	−	26.6837i	−1.49322	−	0.862112i
$959$	−19.5050	−	19.0362i	−0.629849	−	0.614711i
$960$		0			0
$961$	−3.37490	+	1.94850i	−0.108868	+	0.0628549i
$962$	43.5281	+	4.71877i	1.40340	+	0.152139i
$963$		0			0
$964$	141.656	−	37.9566i	4.56243	−	1.22250i
$965$	37.0838	−	21.4103i	1.19377	−	0.689223i
$966$		0			0
$967$	8.67793	−	8.67793i	0.279063	−	0.279063i	−0.553672	−	0.832735i	$-0.686774\pi$
$967$	8.67793	−	8.67793i	0.279063	−	0.279063i	0.832735	+	0.553672i	$0.186774\pi$
$968$	63.9486	−	63.9486i	2.05539	−	2.05539i
$969$		0			0
$970$	−44.4889	+	11.9208i	−1.42845	+	0.382753i
$971$		−	24.3725i		−	0.782150i	−0.920359	−	0.391075i	$-0.872103\pi$
$971$		−	24.3725i		−	0.782150i	0.920359	−	0.391075i	$-0.127897\pi$
$972$		0			0
$973$	−30.1912	+	17.9240i	−0.967885	+	0.574616i
$974$		−	50.0302i		−	1.60307i
$975$		0			0
$976$	−33.4645	−	19.3207i	−1.07117	−	0.618442i
$977$	−1.36813	+	1.36813i	−0.0437705	+	0.0437705i	−0.728653	−	0.684883i	$-0.759853\pi$
$977$	−1.36813	+	1.36813i	−0.0437705	+	0.0437705i	0.684883	+	0.728653i	$0.259853\pi$
$978$		0			0
$979$	−3.22331	+	5.58293i	−0.103017	+	0.178431i
$980$	50.4170	−	52.9314i	1.61051	−	1.69083i
$981$		0			0
$982$	23.2658	+	23.2658i	0.742443	+	0.742443i
$983$	8.95798	+	33.4316i	0.285715	+	1.06630i	0.948315	+	0.317330i	$0.102786\pi$
$983$	8.95798	+	33.4316i	0.285715	+	1.06630i	−0.662600	+	0.748973i	$0.730547\pi$
$984$		0			0
$985$	16.9905	−	29.4284i	0.541362	−	0.937666i
$986$	−0.835848	−	0.223965i	−0.0266188	−	0.00713249i
$987$		0			0
$988$	−49.2121	+	39.5858i	−1.56565	+	1.25939i
$989$	5.98865	+	10.3726i	0.190428	+	0.329831i
$990$		0			0
$991$	16.8655			0.535750			0.267875	−	0.963454i	$-0.413679\pi$
$991$	16.8655			0.535750			0.267875	+	0.963454i	$0.413679\pi$
$992$	−145.880			−4.63170
$993$		0			0
$994$	0.686941	+	56.4769i	0.0217885	+	1.79134i
$995$	−1.26714	+	0.339530i	−0.0401712	+	0.0107638i
$996$		0			0
$997$	20.5237	−	11.8493i	0.649991	−	0.375272i	−0.138462	−	0.990368i	$-0.544216\pi$
$997$	20.5237	−	11.8493i	0.649991	−	0.375272i	0.788453	+	0.615095i	$0.210882\pi$
$998$		−	92.0396i		−	2.91346i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.gh.d.262.10		40
3.2	odd	2		273.2.cg.b.262.1	yes	40
7.5	odd	6		819.2.et.d.145.10		40
13.7	odd	12		819.2.et.d.514.10		40
21.5	even	6		273.2.bt.b.145.1	✓	40
39.20	even	12		273.2.bt.b.241.1	yes	40
91.33	even	12	inner	819.2.gh.d.397.10		40
273.215	odd	12		273.2.cg.b.124.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.145.1	✓	40	21.5	even	6
273.2.bt.b.241.1	yes	40	39.20	even	12
273.2.cg.b.124.1	yes	40	273.215	odd	12
273.2.cg.b.262.1	yes	40	3.2	odd	2
819.2.et.d.145.10		40	7.5	odd	6
819.2.et.d.514.10		40	13.7	odd	12
819.2.gh.d.262.10		40	1.1	even	1	trivial
819.2.gh.d.397.10		40	91.33	even	12	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.gh (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.720539 + 2.68909i) q^{2} +(-4.97997 + 2.87519i) q^{4} +(0.470023 - 1.75415i) q^{5} +(1.29491 - 2.30721i) q^{7} +(-7.38279 - 7.38279i) q^{8} +O(q^{10})\)	\(q+(0.720539 + 2.68909i) q^{2} +(-4.97997 + 2.87519i) q^{4} +(0.470023 - 1.75415i) q^{5} +(1.29491 - 2.30721i) q^{7} +(-7.38279 - 7.38279i) q^{8} +5.05574 q^{10} +(-3.13543 - 3.13543i) q^{11} +(2.12880 - 2.91002i) q^{13} +(7.13732 + 1.81970i) q^{14} +(8.78302 - 15.2126i) q^{16} +(-0.0321785 - 0.0557347i) q^{17} +(2.15398 + 2.15398i) q^{19} +(2.70281 + 10.0870i) q^{20} +(6.17225 - 10.6907i) q^{22} +(-2.78588 - 1.60843i) q^{23} +(1.47400 + 0.851016i) q^{25} +(9.35918 + 3.62776i) q^{26} +(0.185038 + 15.2129i) q^{28} +(-2.41489 - 4.18271i) q^{29} +(-5.02866 + 1.34743i) q^{31} +(27.0664 + 7.25243i) q^{32} +(0.126690 - 0.126690i) q^{34} +(-3.43855 - 3.35591i) q^{35} +(4.21326 - 1.12894i) q^{37} +(-4.24022 + 7.34428i) q^{38} +(-16.4206 + 9.48045i) q^{40} +(2.12512 - 7.93105i) q^{41} +(-3.22447 - 1.86165i) q^{43} +(24.6293 + 6.59940i) q^{44} +(2.31787 - 8.65041i) q^{46} +(-4.06776 - 1.08995i) q^{47} +(-3.64641 - 5.97525i) q^{49} +(-1.22638 + 4.57691i) q^{50} +(-2.23454 + 20.6125i) q^{52} +(-3.30111 + 5.71769i) q^{53} +(-6.97375 + 4.02629i) q^{55} +(-26.5937 + 7.47358i) q^{56} +(9.50765 - 9.50765i) q^{58} +(4.49313 + 1.20393i) q^{59} -2.19979i q^{61} +(-7.24669 - 12.5516i) q^{62} +42.8777i q^{64} +(-4.10402 - 5.10202i) q^{65} +(4.45013 - 4.45013i) q^{67} +(0.320495 + 0.185038i) q^{68} +(6.54673 - 11.6646i) q^{70} +(1.98467 + 7.40691i) q^{71} +(1.61663 + 6.03336i) q^{73} +(6.07163 + 10.5164i) q^{74} +(-16.9199 - 4.53366i) q^{76} +(-11.2942 + 3.17399i) q^{77} +(0.639030 + 1.10683i) q^{79} +(-22.5570 - 22.5570i) q^{80} +22.8585 q^{82} +(8.90509 + 8.90509i) q^{83} +(-0.112892 + 0.0302493i) q^{85} +(2.68278 - 10.0123i) q^{86} +46.2965i q^{88} +(-0.376284 - 1.40431i) q^{89} +(-3.95740 - 8.67980i) q^{91} +18.4981 q^{92} -11.7239i q^{94} +(4.79083 - 2.76599i) q^{95} +(-8.79969 + 2.35787i) q^{97} +(13.4406 - 14.1109i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7}+O(q^{10}) \) 40 * q - 8 * q^7	\( 40 q - 8 q^{7} - 4 q^{11} + 18 q^{14} + 32 q^{16} - 4 q^{17} + 14 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} + 24 q^{25} + 32 q^{26} + 16 q^{28} - 8 q^{29} + 14 q^{31} + 26 q^{32} - 24 q^{34} - 26 q^{35} + 36 q^{37} + 8 q^{38} - 30 q^{40} + 2 q^{41} - 66 q^{43} + 32 q^{44} - 26 q^{46} + 4 q^{47} - 14 q^{49} + 20 q^{50} + 2 q^{52} + 8 q^{53} - 42 q^{55} - 46 q^{56} + 24 q^{58} - 14 q^{59} - 24 q^{62} - 28 q^{65} - 44 q^{67} + 18 q^{68} - 4 q^{70} + 6 q^{71} + 14 q^{73} + 20 q^{74} - 64 q^{76} - 24 q^{77} - 20 q^{80} + 48 q^{82} + 12 q^{83} + 2 q^{85} + 60 q^{86} + 2 q^{89} - 14 q^{91} - 236 q^{92} - 24 q^{95} - 62 q^{97} + 88 q^{98}+O(q^{100}) \) 40 * q - 8 * q^7 - 4 * q^11 + 18 * q^14 + 32 * q^16 - 4 * q^17 + 14 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 + 24 * q^25 + 32 * q^26 + 16 * q^28 - 8 * q^29 + 14 * q^31 + 26 * q^32 - 24 * q^34 - 26 * q^35 + 36 * q^37 + 8 * q^38 - 30 * q^40 + 2 * q^41 - 66 * q^43 + 32 * q^44 - 26 * q^46 + 4 * q^47 - 14 * q^49 + 20 * q^50 + 2 * q^52 + 8 * q^53 - 42 * q^55 - 46 * q^56 + 24 * q^58 - 14 * q^59 - 24 * q^62 - 28 * q^65 - 44 * q^67 + 18 * q^68 - 4 * q^70 + 6 * q^71 + 14 * q^73 + 20 * q^74 - 64 * q^76 - 24 * q^77 - 20 * q^80 + 48 * q^82 + 12 * q^83 + 2 * q^85 + 60 * q^86 + 2 * q^89 - 14 * q^91 - 236 * q^92 - 24 * q^95 - 62 * q^97 + 88 * q^98

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