LMFDB - Embedded newform 936.2.ed.e.739.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(19,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.ed (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			739.3
Character	$\chi$	$=$	936.739
Dual form			936.2.ed.e.19.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.21599 - 0.722056i) q^{2} +(0.957270 + 1.75603i) q^{4} +(0.403590 - 0.403590i) q^{5} +(4.65174 - 1.24643i) q^{7} +(0.103920 - 2.82652i) q^{8} +(-0.782176 + 0.199347i) q^{10} +(5.72510 + 1.53404i) q^{11} +(-0.849788 - 3.50398i) q^{13} +(-6.55647 - 1.84317i) q^{14} +(-2.16727 + 3.36198i) q^{16} +(0.917794 + 0.529889i) q^{17} +(0.617530 - 0.165467i) q^{19} +(1.09506 + 0.322371i) q^{20} +(-5.85401 - 5.99922i) q^{22} +(-1.02761 - 1.77988i) q^{23} +4.67423i q^{25} +(-1.49673 + 4.87440i) q^{26} +(6.64174 + 6.97542i) q^{28} +(-4.86733 + 2.81016i) q^{29} +(-2.54931 + 2.54931i) q^{31} +(5.06292 - 2.52325i) q^{32} +(-0.733420 - 1.30704i) q^{34} +(1.37435 - 2.38044i) q^{35} +(1.83349 - 6.84268i) q^{37} +(-0.870387 - 0.244685i) q^{38} +(-1.09881 - 1.18269i) q^{40} +(-1.37457 + 5.12996i) q^{41} +(-8.58213 - 4.95490i) q^{43} +(2.78665 + 11.5219i) q^{44} +(-0.0356035 + 2.90631i) q^{46} +(5.92269 + 5.92269i) q^{47} +(14.0230 - 8.09616i) q^{49} +(3.37506 - 5.68382i) q^{50} +(5.33961 - 4.84650i) q^{52} +1.19577i q^{53} +(2.92971 - 1.69147i) q^{55} +(-3.03965 - 13.2778i) q^{56} +(7.94772 + 0.0973630i) q^{58} +(-2.11560 - 7.89551i) q^{59} +(5.30143 + 3.06078i) q^{61} +(4.94068 - 1.25919i) q^{62} +(-7.97840 - 0.587462i) q^{64} +(-1.75714 - 1.07120i) q^{65} +(-2.06834 + 7.71916i) q^{67} +(-0.0519231 + 2.11892i) q^{68} +(-3.39001 + 1.90224i) q^{70} +(-0.113135 - 0.422224i) q^{71} +(7.34514 - 7.34514i) q^{73} +(-7.17031 + 6.99675i) q^{74} +(0.881707 + 0.926004i) q^{76} +28.5438 q^{77} +7.20853i q^{79} +(0.482175 + 2.23155i) q^{80} +(5.37559 - 5.24547i) q^{82} +(-7.79731 - 7.79731i) q^{83} +(0.584270 - 0.156555i) q^{85} +(6.85808 + 12.2219i) q^{86} +(4.93093 - 16.0227i) q^{88} +(0.708365 + 0.189806i) q^{89} +(-8.32047 - 15.2404i) q^{91} +(2.14181 - 3.50834i) q^{92} +(-2.92542 - 11.4784i) q^{94} +(0.182448 - 0.316009i) q^{95} +(-4.48735 + 1.20238i) q^{97} +(-22.8977 - 0.280506i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 12 q^{8} + 28 q^{14} + 12 q^{16} - 8 q^{19} + 4 q^{20} + 10 q^{22} - 34 q^{26} - 14 q^{28} + 30 q^{32} + 56 q^{34} - 28 q^{40} - 40 q^{41} + 44 q^{44} - 18 q^{46} + 24 q^{49} + 72 q^{50} + 32 q^{52}+ \cdots - 4 q^{98}+O(q^{100}) $ 56 * q + 12 * q^8 + 28 * q^14 + 12 * q^16 - 8 * q^19 + 4 * q^20 + 10 * q^22 - 34 * q^26 - 14 * q^28 + 30 * q^32 + 56 * q^34 - 28 * q^40 - 40 * q^41 + 44 * q^44 - 18 * q^46 + 24 * q^49 + 72 * q^50 + 32 * q^52 + 54 * q^56 - 16 * q^58 - 32 * q^59 - 48 * q^65 - 24 * q^67 + 26 * q^68 + 64 * q^70 + 44 * q^73 + 6 * q^74 + 6 * q^76 + 4 * q^80 - 30 * q^82 - 40 * q^83 + 28 * q^86 + 126 * q^88 + 68 * q^89 - 72 * q^91 - 52 * q^92 + 34 * q^94 - 4 * q^97 - 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.21599	−	0.722056i	−0.859836	−	0.510571i
$2$	−1.21599	−	0.722056i	−0.859836	−	0.510571i
$3$		0			0
$3$		0			0
$4$	0.957270	+	1.75603i	0.478635	+	0.878014i
$5$	0.403590	−	0.403590i	0.180491	−	0.180491i	−0.611079	−	0.791570i	$-0.709264\pi$
$5$	0.403590	−	0.403590i	0.180491	−	0.180491i	0.791570	+	0.611079i	$0.209264\pi$
$6$		0			0
$7$	4.65174	−	1.24643i	1.75819	−	0.471107i	0.771850	−	0.635805i	$-0.219332\pi$
$7$	4.65174	−	1.24643i	1.75819	−	0.471107i	0.986344	+	0.164698i	$0.0526649\pi$
$8$	0.103920	−	2.82652i	0.0367412	−	0.999325i
$9$		0			0
$10$	−0.782176	+	0.199347i	−0.247346	+	0.0630391i
$11$	5.72510	+	1.53404i	1.72618	+	0.462529i	0.979298	−	0.202424i	$-0.0648819\pi$
$11$	5.72510	+	1.53404i	1.72618	+	0.462529i	0.746885	+	0.664953i	$0.231549\pi$
$12$		0			0
$13$	−0.849788	−	3.50398i	−0.235689	−	0.971829i
$13$	−0.849788	−	3.50398i	−0.235689	−	0.971829i
$14$	−6.55647	−	1.84317i	−1.75229	−	0.492608i
$15$		0			0
$16$	−2.16727	+	3.36198i	−0.541818	+	0.840496i
$17$	0.917794	+	0.529889i	0.222598	+	0.128517i	0.607153	−	0.794585i	$-0.292312\pi$
$17$	0.917794	+	0.529889i	0.222598	+	0.128517i	−0.384555	+	0.923102i	$0.625645\pi$
$18$		0			0
$19$	0.617530	−	0.165467i	0.141671	−	0.0379606i	−0.187287	−	0.982305i	$-0.559969\pi$
$19$	0.617530	−	0.165467i	0.141671	−	0.0379606i	0.328958	+	0.944345i	$0.393303\pi$
$20$	1.09506	+	0.322371i	0.244863	+	0.0720843i
$21$		0			0
$22$	−5.85401	−	5.99922i	−1.24808	−	1.27904i
$23$	−1.02761	−	1.77988i	−0.214272	−	0.371130i	0.738775	−	0.673952i	$-0.235405\pi$
$23$	−1.02761	−	1.77988i	−0.214272	−	0.371130i	−0.953047	+	0.302822i	$0.902071\pi$
$24$		0			0
$25$			4.67423i			0.934846i
$26$	−1.49673	+	4.87440i	−0.293534	+	0.955949i
$27$		0			0
$28$	6.64174	+	6.97542i	1.25517	+	1.31823i
$29$	−4.86733	+	2.81016i	−0.903841	+	0.521833i	−0.878444	−	0.477845i	$-0.841418\pi$
$29$	−4.86733	+	2.81016i	−0.903841	+	0.521833i	−0.0253965	+	0.999677i	$0.508085\pi$
$30$		0			0
$31$	−2.54931	+	2.54931i	−0.457869	+	0.457869i	−0.897956	−	0.440086i	$-0.854948\pi$
$31$	−2.54931	+	2.54931i	−0.457869	+	0.457869i	0.440086	+	0.897956i	$0.354948\pi$
$32$	5.06292	−	2.52325i	0.895007	−	0.446052i
$33$		0			0
$34$	−0.733420	−	1.30704i	−0.125781	−	0.224155i
$35$	1.37435	−	2.38044i	0.232308	−	0.402368i
$36$		0			0
$37$	1.83349	−	6.84268i	0.301424	−	1.12493i	−0.634556	−	0.772877i	$-0.718817\pi$
$37$	1.83349	−	6.84268i	0.301424	−	1.12493i	0.935980	−	0.352053i	$-0.114516\pi$
$38$	−0.870387	−	0.244685i	−0.141195	−	0.0396932i
$39$		0			0
$40$	−1.09881	−	1.18269i	−0.173738	−	0.187000i
$41$	−1.37457	+	5.12996i	−0.214672	+	0.801166i	0.771610	+	0.636096i	$0.219452\pi$
$41$	−1.37457	+	5.12996i	−0.214672	+	0.801166i	−0.986282	+	0.165070i	$0.947215\pi$
$42$		0			0
$43$	−8.58213	−	4.95490i	−1.30876	−	0.755615i	−0.326873	−	0.945068i	$-0.605995\pi$
$43$	−8.58213	−	4.95490i	−1.30876	−	0.755615i	−0.981890	+	0.189454i	$0.939328\pi$
$44$	2.78665	+	11.5219i	0.420104	+	1.73700i
$45$		0			0
$46$	−0.0356035	+	2.90631i	−0.00524945	+	0.428512i
$47$	5.92269	+	5.92269i	0.863912	+	0.863912i	0.991790	−	0.127878i	$-0.0408164\pi$
$47$	5.92269	+	5.92269i	0.863912	+	0.863912i	−0.127878	+	0.991790i	$0.540816\pi$
$48$		0			0
$49$	14.0230	−	8.09616i	2.00328	−	1.15659i
$50$	3.37506	−	5.68382i	0.477305	−	0.803814i
$51$		0			0
$52$	5.33961	−	4.84650i	0.740470	−	0.672089i
$53$			1.19577i			0.164251i	0.996622	+	0.0821255i	$0.0261708\pi$
$53$			1.19577i			0.164251i	−0.996622	+	0.0821255i	$0.973829\pi$
$54$		0			0
$55$	2.92971	−	1.69147i	0.395043	−	0.228078i
$56$	−3.03965	−	13.2778i	−0.406191	−	1.77432i
$57$		0			0
$58$	7.94772	+	0.0973630i	1.04359	+	0.0127844i
$59$	−2.11560	−	7.89551i	−0.275427	−	1.02791i	−0.955555	−	0.294814i	$-0.904742\pi$
$59$	−2.11560	−	7.89551i	−0.275427	−	1.02791i	0.680127	−	0.733094i	$-0.261924\pi$
$60$		0			0
$61$	5.30143	+	3.06078i	0.678778	+	0.391893i	0.799395	−	0.600806i	$-0.205154\pi$
$61$	5.30143	+	3.06078i	0.678778	+	0.391893i	−0.120616	+	0.992699i	$0.538487\pi$
$62$	4.94068	−	1.25919i	0.627467	−	0.159918i
$63$		0			0
$64$	−7.97840	−	0.587462i	−0.997300	−	0.0734327i
$65$	−1.75714	−	1.07120i	−0.217946	−	0.132866i
$66$		0			0
$67$	−2.06834	+	7.71916i	−0.252688	+	0.943045i	0.716674	+	0.697409i	$0.245664\pi$
$67$	−2.06834	+	7.71916i	−0.252688	+	0.943045i	−0.969362	+	0.245637i	$0.921003\pi$
$68$	−0.0519231	+	2.11892i	−0.00629660	+	0.256957i
$69$		0			0
$70$	−3.39001	+	1.90224i	−0.405184	+	0.227361i
$71$	−0.113135	−	0.422224i	−0.0134266	−	0.0501087i	0.958888	−	0.283786i	$-0.0915906\pi$
$71$	−0.113135	−	0.422224i	−0.0134266	−	0.0501087i	−0.972314	+	0.233678i	$0.924924\pi$
$72$		0			0
$73$	7.34514	−	7.34514i	0.859684	−	0.859684i	−0.131617	−	0.991301i	$-0.542017\pi$
$73$	7.34514	−	7.34514i	0.859684	−	0.859684i	0.991301	+	0.131617i	$0.0420169\pi$
$74$	−7.17031	+	6.99675i	−0.833531	+	0.813356i
$75$		0			0
$76$	0.881707	+	0.926004i	0.101139	+	0.106220i
$77$	28.5438			3.25287
$78$		0			0
$79$			7.20853i			0.811023i	0.914090	+	0.405511i	$0.132907\pi$
$79$			7.20853i			0.811023i	−0.914090	+	0.405511i	$0.867093\pi$
$80$	0.482175	+	2.23155i	0.0539088	+	0.249495i
$81$		0			0
$82$	5.37559	−	5.24547i	0.593634	−	0.579266i
$83$	−7.79731	−	7.79731i	−0.855866	−	0.855866i	0.134982	−	0.990848i	$-0.456902\pi$
$83$	−7.79731	−	7.79731i	−0.855866	−	0.855866i	−0.990848	+	0.134982i	$0.956902\pi$
$84$		0			0
$85$	0.584270	−	0.156555i	0.0633730	−	0.0169807i
$86$	6.85808	+	12.2219i	0.739526	+	1.31792i
$87$		0			0
$88$	4.93093	−	16.0227i	0.525639	−	1.70802i
$89$	0.708365	+	0.189806i	0.0750865	+	0.0201194i	0.296167	−	0.955136i	$-0.404292\pi$
$89$	0.708365	+	0.189806i	0.0750865	+	0.0201194i	−0.221080	+	0.975256i	$0.570958\pi$
$90$		0			0
$91$	−8.32047	−	15.2404i	−0.872222	−	1.59763i
$92$	2.14181	−	3.50834i	0.223299	−	0.365770i
$93$		0			0
$94$	−2.92542	−	11.4784i	−0.301734	−	1.18391i
$95$	0.182448	−	0.316009i	0.0187188	−	0.0324219i
$96$		0			0
$97$	−4.48735	+	1.20238i	−0.455621	+	0.122083i	−0.479329	−	0.877636i	$-0.659120\pi$
$97$	−4.48735	+	1.20238i	−0.455621	+	0.122083i	0.0237071	+	0.999719i	$0.492453\pi$
$98$	−22.8977	−	0.280506i	−2.31301	−	0.0283354i
$99$		0			0
$100$	−8.20808	+	4.47450i	−0.820808	+	0.447450i
$101$	−2.03641	−	3.52717i	−0.202631	−	0.350966i	0.746745	−	0.665111i	$-0.231616\pi$
$101$	−2.03641	−	3.52717i	−0.202631	−	0.350966i	−0.949375	+	0.314144i	$0.898282\pi$
$102$		0			0
$103$	−0.447521			−0.0440955			−0.0220478	−	0.999757i	$-0.507019\pi$
$103$	−0.447521			−0.0440955			−0.0220478	+	0.999757i	$0.507019\pi$
$104$	−9.99236	+	2.03781i	−0.979832	+	0.199824i
$105$		0			0
$106$	0.863410	−	1.45404i	0.0838618	−	0.141229i
$107$	−3.67665	−	6.36815i	−0.355436	−	0.615632i	0.631757	−	0.775167i	$-0.282334\pi$
$107$	−3.67665	−	6.36815i	−0.355436	−	0.615632i	−0.987192	+	0.159534i	$0.949001\pi$
$108$		0			0
$109$	−1.83648	+	1.83648i	−0.175903	+	0.175903i	−0.789567	−	0.613664i	$-0.789695\pi$
$109$	−1.83648	+	1.83648i	−0.175903	+	0.175903i	0.613664	+	0.789567i	$0.289695\pi$
$110$	−4.78384	−	0.0586041i	−0.456122	−	0.00558768i
$111$		0			0
$112$	−5.89110	+	18.3404i	−0.556657	+	1.73301i
$113$	9.71582	−	16.8283i	0.913987	−	1.58307i	0.105609	−	0.994408i	$-0.466321\pi$
$113$	9.71582	−	16.8283i	0.913987	−	1.58307i	0.808378	−	0.588664i	$-0.200346\pi$
$114$		0			0
$115$	−1.13307	−	0.303606i	−0.105660	−	0.0283114i
$116$	−9.59406	−	5.85710i	−0.890786	−	0.543818i
$117$		0			0
$118$	−3.12846	+	11.1285i	−0.287998	+	1.02446i
$119$	4.92981	+	1.32094i	0.451915	+	0.121090i
$120$		0			0
$121$	20.8972	+	12.0650i	1.89975	+	1.09682i
$122$	−4.23644	−	7.54981i	−0.383549	−	0.683528i
$123$		0			0
$124$	−6.91703	−	2.03628i	−0.621168	−	0.182864i
$125$	3.90442	+	3.90442i	0.349222	+	0.349222i
$126$		0			0
$127$	−6.86367	−	11.8882i	−0.609053	−	1.05491i	−0.991397	−	0.130890i	$-0.958217\pi$
$127$	−6.86367	−	11.8882i	−0.609053	−	1.05491i	0.382344	−	0.924020i	$-0.375117\pi$
$128$	9.27749	+	6.47520i	0.820022	+	0.572332i
$129$		0			0
$130$	1.36319	+	2.57133i	0.119560	+	0.225520i
$131$	5.90363			0.515802			0.257901	−	0.966171i	$-0.416969\pi$
$131$	5.90363			0.515802			0.257901	+	0.966171i	$0.416969\pi$
$132$		0			0
$133$	2.66635	−	1.53942i	0.231202	−	0.133484i
$134$	8.08875	−	7.89297i	0.698762	−	0.681849i
$135$		0			0
$136$	1.59312	−	2.53909i	0.136609	−	0.217726i
$137$	4.50130	+	16.7991i	0.384572	+	1.43524i	0.838840	+	0.544378i	$0.183234\pi$
$137$	4.50130	+	16.7991i	0.384572	+	1.43524i	−0.454268	+	0.890865i	$0.650099\pi$
$138$		0			0
$139$	−7.04702	+	12.2058i	−0.597721	+	1.03528i	0.395436	+	0.918494i	$0.370594\pi$
$139$	−7.04702	+	12.2058i	−0.597721	+	1.03528i	−0.993157	+	0.116789i	$0.962740\pi$
$140$	5.49575	+	0.134671i	0.464476	+	0.0113818i
$141$		0			0
$142$	−0.167299	+	0.595110i	−0.0140394	+	0.0499405i
$143$	0.510104	−	21.3642i	0.0426570	−	1.78657i
$144$		0			0
$145$	−0.830256	+	3.09856i	−0.0689490	+	0.257321i
$146$	−14.2352	+	3.62802i	−1.17812	+	0.300257i
$147$		0			0
$148$	13.7711	−	3.33063i	1.13198	−	0.273776i
$149$	−2.88789	−	10.7777i	−0.236585	−	0.882947i	−0.977428	−	0.211269i	$-0.932240\pi$
$149$	−2.88789	−	10.7777i	−0.236585	−	0.882947i	0.740843	−	0.671678i	$-0.234426\pi$
$150$		0			0
$151$	−8.18475	−	8.18475i	−0.666066	−	0.666066i	0.290737	−	0.956803i	$-0.406099\pi$
$151$	−8.18475	−	8.18475i	−0.666066	−	0.666066i	−0.956803	+	0.290737i	$0.906099\pi$
$152$	−0.403521	−	1.76265i	−0.0327299	−	0.142970i
$153$		0			0
$154$	−34.7090	−	20.6102i	−2.79693	−	1.66082i
$155$			2.05775i			0.165283i
$156$		0			0
$157$			19.5674i			1.56165i	0.624750	+	0.780825i	$0.285201\pi$
$157$			19.5674i			1.56165i	−0.624750	+	0.780825i	$0.714799\pi$
$158$	5.20496	−	8.76551i	0.414085	−	0.697346i
$159$		0			0
$160$	1.02499	−	3.06170i	0.0810322	−	0.242049i
$161$	−6.99869	−	6.99869i	−0.551574	−	0.551574i
$162$		0			0
$163$	−1.63834	−	6.11436i	−0.128325	−	0.478914i	0.871612	−	0.490197i	$-0.163075\pi$
$163$	−1.63834	−	6.11436i	−0.128325	−	0.478914i	−0.999936	+	0.0112829i	$0.996408\pi$
$164$	−10.3242	+	2.49697i	−0.806184	+	0.194981i
$165$		0			0
$166$	3.85136	+	15.1116i	0.298924	+	1.17288i
$167$	−1.29517	+	4.83364i	−0.100223	+	0.374039i	−0.997760	−	0.0669022i	$-0.978688\pi$
$167$	−1.29517	+	4.83364i	−0.100223	+	0.374039i	0.897536	+	0.440941i	$0.145355\pi$
$168$		0			0
$169$	−11.5557	+	5.95528i	−0.888901	+	0.458098i
$170$	−0.823509	−	0.231507i	−0.0631602	−	0.0177558i
$171$		0			0
$172$	0.485524	−	19.8136i	0.0370208	−	1.51078i
$173$	−6.02967	+	10.4437i	−0.458427	+	0.794019i	−0.998878	−	0.0473563i	$-0.984920\pi$
$173$	−6.02967	+	10.4437i	−0.458427	+	0.794019i	0.540451	+	0.841376i	$0.318254\pi$
$174$		0			0
$175$	5.82611	+	21.7433i	0.440412	+	1.64364i
$176$	−17.5652	+	15.9230i	−1.32403	+	1.20024i
$177$		0			0
$178$	−0.724315	−	0.742281i	−0.0542897	−	0.0556363i
$179$	15.2086	−	8.78071i	1.13675	−	0.656301i	0.191123	−	0.981566i	$-0.438787\pi$
$179$	15.2086	−	8.78071i	1.13675	−	0.656301i	0.945623	+	0.325265i	$0.105454\pi$
$180$		0			0
$181$	7.03736			0.523083			0.261541	−	0.965192i	$-0.415769\pi$
$181$	7.03736			0.523083			0.261541	+	0.965192i	$0.415769\pi$
$182$	−0.886817	+	24.5400i	−0.0657352	+	1.81903i
$183$		0			0
$184$	−5.13764	+	2.71960i	−0.378752	+	0.200492i
$185$	−2.02166	−	3.50161i	−0.148635	−	0.257444i
$186$		0			0
$187$	4.44160	+	4.44160i	0.324802	+	0.324802i
$188$	−4.73080	+	16.0700i	−0.345029	+	1.17203i
$189$		0			0
$190$	−0.450032	+	0.252527i	−0.0326488	+	0.0183202i
$191$	17.8511	+	10.3063i	1.29166	+	0.745740i	0.978948	−	0.204108i	$-0.0654295\pi$
$191$	17.8511	+	10.3063i	1.29166	+	0.745740i	0.312711	+	0.949848i	$0.398763\pi$
$192$		0			0
$193$	−4.18310	−	1.12086i	−0.301106	−	0.0806812i	0.105103	−	0.994461i	$-0.466483\pi$
$193$	−4.18310	−	1.12086i	−0.301106	−	0.0806812i	−0.406209	+	0.913780i	$0.633150\pi$
$194$	6.32477	+	1.77803i	0.454092	+	0.127655i
$195$		0			0
$196$	27.6408	+	16.8745i	1.97435	+	1.20532i
$197$	−10.2512	−	2.74681i	−0.730370	−	0.195702i	−0.125576	−	0.992084i	$-0.540078\pi$
$197$	−10.2512	−	2.74681i	−0.730370	−	0.195702i	−0.604794	+	0.796382i	$0.706745\pi$
$198$		0			0
$199$	−12.0604	+	20.8892i	−0.854937	+	1.48079i	0.0217665	+	0.999763i	$0.493071\pi$
$199$	−12.0604	+	20.8892i	−0.854937	+	1.48079i	−0.876703	+	0.481031i	$0.840262\pi$
$200$	13.2118	+	0.485745i	0.934215	+	0.0343473i
$201$		0			0
$202$	−0.0705552	+	5.75941i	−0.00496425	+	0.405231i
$203$	−19.1389	+	19.1389i	−1.34329	+	1.34329i
$204$		0			0
$205$	1.51564	+	2.62516i	0.105857	+	0.183349i
$206$	0.544182	+	0.323135i	0.0379149	+	0.0225139i
$207$		0			0
$208$	13.6220	+	4.73709i	0.944519	+	0.328458i
$209$	3.78925			0.262108
$210$		0			0
$211$	−7.25156	−	12.5601i	−0.499218	−	0.864671i	0.500782	−	0.865574i	$-0.333046\pi$
$211$	−7.25156	−	12.5601i	−0.499218	−	0.864671i	−1.00000		0.000902928i	$0.999713\pi$
$212$	−2.09980	+	1.14467i	−0.144215	+	0.0786162i
$213$		0			0
$214$	−0.127384	+	10.3984i	−0.00870782	+	0.710818i
$215$	−5.46341	+	1.46392i	−0.372601	+	0.0998382i
$216$		0			0
$217$	−8.68120	+	15.0363i	−0.589318	+	1.02073i
$218$	3.55919	−	0.907102i	0.241059	−	0.0614367i
$219$		0			0
$220$	5.77480	+	3.52547i	0.389337	+	0.237687i
$221$	1.07679	−	3.66622i	0.0724325	−	0.246617i
$222$		0			0
$223$	23.4642	+	6.28722i	1.57128	+	0.421024i	0.936213	−	0.351432i	$-0.114305\pi$
$223$	23.4642	+	6.28722i	1.57128	+	0.421024i	0.635068	+	0.772456i	$0.280972\pi$
$224$	20.4064	−	18.0481i	1.36346	−	1.20589i
$225$		0			0
$226$	−23.9653	+	13.4477i	−1.59415	+	0.894527i
$227$	−19.5131	+	5.22852i	−1.29513	+	0.347029i	−0.839607	−	0.543195i	$-0.817215\pi$
$227$	−19.5131	+	5.22852i	−1.29513	+	0.347029i	−0.455524	+	0.890224i	$0.650548\pi$
$228$		0			0
$229$	0.537694	+	0.537694i	0.0355318	+	0.0355318i	0.724649	−	0.689118i	$-0.242002\pi$
$229$	0.537694	+	0.537694i	0.0355318	+	0.0355318i	−0.689118	+	0.724649i	$0.742002\pi$
$230$	1.15859	+	1.18733i	0.0763950	+	0.0782900i
$231$		0			0
$232$	7.43714	+	14.0496i	0.488272	+	0.922403i
$233$			5.06336i			0.331712i	0.986150	+	0.165856i	$0.0530387\pi$
$233$			5.06336i			0.331712i	−0.986150	+	0.165856i	$0.946961\pi$
$234$		0			0
$235$	4.78067			0.311857
$236$	11.8395	−	11.2732i	0.770689	−	0.733822i
$237$		0			0
$238$	−5.04082	−	5.16585i	−0.326748	−	0.334853i
$239$	−20.1780	+	20.1780i	−1.30521	+	1.30521i	−0.380376	+	0.924832i	$0.624205\pi$
$239$	−20.1780	+	20.1780i	−1.30521	+	1.30521i	−0.924832	+	0.380376i	$0.875795\pi$
$240$		0			0
$241$	3.50678	+	13.0875i	0.225891	+	0.843038i	0.982045	+	0.188645i	$0.0604094\pi$
$241$	3.50678	+	13.0875i	0.225891	+	0.843038i	−0.756154	+	0.654394i	$0.772924\pi$
$242$	−16.6992	−	29.7599i	−1.07347	−	1.91304i
$243$		0			0
$244$	−0.299922	+	12.2395i	−0.0192005	+	0.783551i
$245$	2.39200	−	8.92705i	0.152819	−	0.570328i
$246$		0			0
$247$	−1.10456	−	2.02320i	−0.0702815	−	0.128733i
$248$	6.94074	+	7.47059i	0.440738	+	0.474383i
$249$		0			0
$250$	−1.92853	−	7.56695i	−0.121971	−	0.478576i
$251$	−14.5185	−	8.38225i	−0.916398	−	0.529083i	−0.0339142	−	0.999425i	$-0.510797\pi$
$251$	−14.5185	−	8.38225i	−0.916398	−	0.529083i	−0.882484	+	0.470342i	$0.844131\pi$
$252$		0			0
$253$	−3.15279	−	11.7664i	−0.198214	−	0.739745i
$254$	−0.237805	+	19.4119i	−0.0149212	+	1.21801i
$255$		0			0
$256$	−6.60588	−	14.5727i	−0.412868	−	0.910791i
$257$	7.66304	−	4.42426i	0.478007	−	0.275978i	−0.241578	−	0.970381i	$-0.577665\pi$
$257$	7.66304	−	4.42426i	0.478007	−	0.275978i	0.719586	+	0.694404i	$0.244332\pi$
$258$		0			0
$259$		−	34.1157i		−	2.11985i
$260$	0.199012	−	4.11101i	0.0123422	−	0.254954i
$261$		0			0
$262$	−7.17876	−	4.26275i	−0.443505	−	0.263354i
$263$	5.49660	−	3.17346i	0.338935	−	0.195684i	−0.320866	−	0.947125i	$-0.603974\pi$
$263$	5.49660	−	3.17346i	0.338935	−	0.195684i	0.659801	+	0.751440i	$0.270641\pi$
$264$		0			0
$265$	0.482599	+	0.482599i	0.0296458	+	0.0296458i
$266$	−4.35380	−	0.0533359i	−0.266949	−	0.00327024i
$267$		0			0
$268$	−15.5350	+	3.75725i	−0.948952	+	0.229510i
$269$	5.51917	+	3.18649i	0.336509	+	0.194284i	0.658727	−	0.752382i	$-0.271095\pi$
$269$	5.51917	+	3.18649i	0.336509	+	0.194284i	−0.322218	+	0.946666i	$0.604428\pi$
$270$		0			0
$271$	2.27246	−	8.48094i	0.138042	−	0.515181i	−0.861925	−	0.507036i	$-0.830741\pi$
$271$	2.27246	−	8.48094i	0.138042	−	0.515181i	0.999967	−	0.00814415i	$-0.00259239\pi$
$272$	−3.77058	+	1.93720i	−0.228625	+	0.117460i
$273$		0			0
$274$	6.65634	−	23.6777i	0.402124	−	1.43042i
$275$	−7.17044	+	26.7604i	−0.432394	+	1.61372i
$276$		0			0
$277$	3.44140	−	5.96068i	0.206774	−	0.358143i	−0.743923	−	0.668266i	$-0.767037\pi$
$277$	3.44140	−	5.96068i	0.206774	−	0.358143i	0.950696	+	0.310123i	$0.100370\pi$
$278$	17.3824	−	9.75380i	1.04253	−	0.584994i
$279$		0			0
$280$	−6.58554	−	4.13200i	−0.393562	−	0.246934i
$281$	−1.24628	+	1.24628i	−0.0743466	+	0.0743466i	−0.743302	−	0.668956i	$-0.766742\pi$
$281$	−1.24628	+	1.24628i	−0.0743466	+	0.0743466i	0.668956	+	0.743302i	$0.266742\pi$
$282$		0			0
$283$	11.6080	−	6.70190i	0.690025	−	0.398386i	−0.113596	−	0.993527i	$-0.536237\pi$
$283$	11.6080	−	6.70190i	0.690025	−	0.398386i	0.803622	+	0.595141i	$0.202904\pi$
$284$	0.633137	−	0.602849i	0.0375697	−	0.0357725i
$285$		0			0
$286$	−16.0465	+	25.6104i	−0.948847	+	1.51437i
$287$			25.5766i			1.50974i
$288$		0			0
$289$	−7.93844	−	13.7498i	−0.466967	−	0.808810i
$290$	3.24692	−	3.16833i	0.190665	−	0.186051i
$291$		0			0
$292$	19.9296	+	5.86700i	1.16629	+	0.343340i
$293$	−22.6215	+	6.06142i	−1.32156	+	0.354112i	−0.849563	−	0.527486i	$-0.823135\pi$
$293$	−22.6215	+	6.06142i	−1.32156	+	0.354112i	−0.472000	+	0.881598i	$0.656468\pi$
$294$		0			0
$295$	−4.04038	−	2.33272i	−0.235240	−	0.135816i
$296$	−19.1504	−	5.89348i	−1.11310	−	0.342552i
$297$		0			0
$298$	−4.27049	+	15.1909i	−0.247383	+	0.879983i
$299$	−5.36340	+	5.11325i	−0.310173	+	0.295707i
$300$		0			0
$301$	−46.0978	−	12.3519i	−2.65703	−	0.711950i
$302$	4.04274	+	15.8624i	0.232633	+	0.912781i
$303$		0			0
$304$	−0.782058	+	2.43474i	−0.0448541	+	0.139642i
$305$	3.37490	−	0.904303i	0.193246	−	0.0517802i
$306$		0			0
$307$	−21.1986	+	21.1986i	−1.20987	+	1.20987i	−0.238798	+	0.971069i	$0.576753\pi$
$307$	−21.1986	+	21.1986i	−1.20987	+	1.20987i	−0.971069	+	0.238798i	$0.923247\pi$
$308$	27.3241	+	50.1237i	1.55693	+	2.85606i
$309$		0			0
$310$	1.48581	−	2.50221i	0.0843884	−	0.142116i
$311$	−23.6077			−1.33867			−0.669335	−	0.742961i	$-0.733421\pi$
$311$	−23.6077			−1.33867			−0.669335	+	0.742961i	$0.733421\pi$
$312$		0			0
$313$	−1.67315			−0.0945720			−0.0472860	−	0.998881i	$-0.515057\pi$
$313$	−1.67315			−0.0945720			−0.0472860	+	0.998881i	$0.515057\pi$
$314$	14.1288	−	23.7938i	0.797333	−	1.34276i
$315$		0			0
$316$	−12.6584	+	6.90050i	−0.712089	+	0.388184i
$317$	1.99292	−	1.99292i	0.111933	−	0.111933i	−0.648922	−	0.760855i	$-0.724780\pi$
$317$	1.99292	−	1.99292i	0.111933	−	0.111933i	0.760855	+	0.648922i	$0.224780\pi$
$318$		0			0
$319$	−32.1768	+	8.62176i	−1.80156	+	0.482726i
$320$	−3.45710	+	2.98291i	−0.193258	+	0.166750i
$321$		0			0
$322$	3.45690	+	13.5638i	0.192645	+	0.755880i
$323$	0.654444	+	0.175358i	0.0364142	+	0.00975717i
$324$		0			0
$325$	16.3784	−	3.97211i	0.908510	−	0.220333i
$326$	−2.42271	+	8.61799i	−0.134181	+	0.477306i
$327$		0			0
$328$	14.3571	+	4.41835i	0.792737	+	0.243962i
$329$	34.9330	+	20.1686i	1.92592	+	1.11193i
$330$		0			0
$331$	−5.44493	+	1.45897i	−0.299281	+	0.0801920i	−0.405335	−	0.914168i	$-0.632845\pi$
$331$	−5.44493	+	1.45897i	−0.299281	+	0.0801920i	0.106054	+	0.994360i	$0.466178\pi$
$332$	6.22817	−	21.1564i	0.341815	−	1.16111i
$333$		0			0
$334$	5.06508	−	4.94248i	0.277149	−	0.270441i
$335$	2.28061	+	3.95014i	0.124603	+	0.215819i
$336$		0			0
$337$			9.98987i			0.544183i	0.962271	+	0.272091i	$0.0877153\pi$
$337$			9.98987i			0.544183i	−0.962271	+	0.272091i	$0.912285\pi$
$338$	18.3517	+	1.10231i	0.998201	+	0.0599578i
$339$		0			0
$340$	0.834218	+	0.876130i	0.0452418	+	0.0475148i
$341$	−18.5058	+	10.6843i	−1.00214	+	0.578588i
$342$		0			0
$343$	31.3027	−	31.3027i	1.69019	−	1.69019i
$344$	−14.8970	+	23.7426i	−0.803190	+	1.28012i
$345$		0			0
$346$	14.8730	−	8.34568i	0.799575	−	0.448666i
$347$	11.8582	−	20.5391i	0.636584	−	1.10260i	−0.349594	−	0.936901i	$-0.613680\pi$
$347$	11.8582	−	20.5391i	0.636584	−	1.10260i	0.986177	−	0.165694i	$-0.0529863\pi$
$348$		0			0
$349$	5.11905	−	19.1046i	0.274017	−	1.02264i	−0.682481	−	0.730903i	$-0.739099\pi$
$349$	5.11905	−	19.1046i	0.274017	−	1.02264i	0.956498	−	0.291740i	$-0.0942343\pi$
$350$	8.61541	−	30.6465i	0.460513	−	1.63812i
$351$		0			0
$352$	32.8565	−	6.67917i	1.75126	−	0.356001i
$353$	−2.87468	+	10.7284i	−0.153004	+	0.571017i	0.846264	+	0.532763i	$0.178846\pi$
$353$	−2.87468	+	10.7284i	−0.153004	+	0.571017i	−0.999268	+	0.0382541i	$0.987820\pi$
$354$		0			0
$355$	−0.216065	−	0.124745i	−0.0114675	−	0.00662079i
$356$	0.344792	+	1.42560i	0.0182739	+	0.0755569i
$357$		0			0
$358$	−24.8337	−	0.304224i	−1.31250	−	0.0160787i
$359$	−10.0901	−	10.0901i	−0.532537	−	0.532537i	0.388790	−	0.921327i	$-0.372893\pi$
$359$	−10.0901	−	10.0901i	−0.532537	−	0.532537i	−0.921327	+	0.388790i	$0.872893\pi$
$360$		0			0
$361$	−16.1005	+	9.29564i	−0.847396	+	0.489244i
$362$	−8.55736	−	5.08137i	−0.449765	−	0.267071i
$363$		0			0
$364$	18.7977	−	29.2001i	0.985265	−	1.53050i
$365$		−	5.92885i		−	0.310330i
$366$		0			0
$367$	−5.69564	+	3.28838i	−0.297310	+	0.171652i	−0.641234	−	0.767346i	$-0.721577\pi$
$367$	−5.69564	+	3.28838i	−0.297310	+	0.171652i	0.343924	+	0.938997i	$0.388244\pi$
$368$	8.21103	+	0.402657i	0.428030	+	0.0209899i
$369$		0			0
$370$	−0.0700440	+	5.71768i	−0.00364142	+	0.297248i
$371$	1.49044	+	5.56240i	0.0773798	+	0.288785i
$372$		0			0
$373$	7.36621	+	4.25288i	0.381408	+	0.220206i	0.678431	−	0.734665i	$-0.262660\pi$
$373$	7.36621	+	4.25288i	0.381408	+	0.220206i	−0.297023	+	0.954870i	$0.595994\pi$
$374$	−2.19386	−	8.60802i	−0.113442	−	0.445110i
$375$		0			0
$376$	17.3561	−	16.1251i	0.895070	−	0.831588i
$377$	13.9829	+	14.6670i	0.720157	+	0.755388i
$378$		0			0
$379$	4.52705	−	16.8952i	0.232539	−	0.867847i	−0.746704	−	0.665156i	$-0.768365\pi$
$379$	4.52705	−	16.8952i	0.232539	−	0.867847i	0.979243	−	0.202690i	$-0.0649685\pi$
$380$	0.729574	+	0.0178779i	0.0374263	+	0.000917115i
$381$		0			0
$382$	−14.2650	−	25.4219i	−0.729862	−	1.30070i
$383$	−2.58315	−	9.64043i	−0.131993	−	0.492603i	0.868000	−	0.496565i	$-0.165406\pi$
$383$	−2.58315	−	9.64043i	−0.131993	−	0.492603i	−0.999992	+	0.00396183i	$0.998739\pi$
$384$		0			0
$385$	11.5200	−	11.5200i	0.587113	−	0.587113i
$386$	4.27729	+	4.38339i	0.217709	+	0.223109i
$387$		0			0
$388$	−6.40702	−	6.72891i	−0.325267	−	0.341609i
$389$	−0.803809			−0.0407547			−0.0203774	−	0.999792i	$-0.506487\pi$
$389$	−0.803809			−0.0407547			−0.0203774	+	0.999792i	$0.506487\pi$
$390$		0			0
$391$		−	2.17808i		−	0.110150i
$392$	−21.4267	−	40.4775i	−1.08221	−	2.04442i
$393$		0			0
$394$	10.4821	+	10.7421i	0.528079	+	0.541177i
$395$	2.90929	+	2.90929i	0.146382	+	0.146382i
$396$		0			0
$397$	1.17900	−	0.315913i	0.0591725	−	0.0158552i	−0.229111	−	0.973400i	$-0.573582\pi$
$397$	1.17900	−	0.315913i	0.0591725	−	0.0158552i	0.288284	+	0.957545i	$0.406915\pi$
$398$	29.7485	−	16.6928i	1.49116	−	0.836734i
$399$		0			0
$400$	−15.7147	−	10.1303i	−0.785735	−	0.506516i
$401$	4.73196	+	1.26792i	0.236303	+	0.0633171i	0.375027	−	0.927014i	$-0.377633\pi$
$401$	4.73196	+	1.26792i	0.236303	+	0.0633171i	−0.138724	+	0.990331i	$0.544300\pi$
$402$		0			0
$403$	11.0991	+	6.76635i	0.552885	+	0.337056i
$404$	4.24441	−	6.95245i	0.211167	−	0.345897i
$405$		0			0
$406$	37.0921	−	9.45338i	1.84085	−	0.469164i
$407$	20.9938	−	36.3624i	1.04063	−	1.80242i
$408$		0			0
$409$	13.7141	−	3.67467i	0.678117	−	0.181701i	0.0967086	−	0.995313i	$-0.469169\pi$
$409$	13.7141	−	3.67467i	0.678117	−	0.181701i	0.581408	+	0.813612i	$0.302502\pi$
$410$	0.0525121	−	4.28655i	0.00259339	−	0.211698i
$411$		0			0
$412$	−0.428398	−	0.785859i	−0.0211057	−	0.0387165i
$413$	−19.6824	−	34.0910i	−0.968509	−	1.67751i
$414$		0			0
$415$	−6.29383			−0.308952
$416$	−13.1438	−	15.5961i	−0.644430	−	0.764664i
$417$		0			0
$418$	−4.60770	−	2.73605i	−0.225370	−	0.133825i
$419$	2.36107	+	4.08949i	0.115346	+	0.199785i	0.917918	−	0.396770i	$-0.129869\pi$
$419$	2.36107	+	4.08949i	0.115346	+	0.199785i	−0.802572	+	0.596555i	$0.796536\pi$
$420$		0			0
$421$	4.38018	−	4.38018i	0.213477	−	0.213477i	−0.592266	−	0.805743i	$-0.701766\pi$
$421$	4.38018	−	4.38018i	0.213477	−	0.213477i	0.805743	+	0.592266i	$0.201766\pi$
$422$	−0.251244	+	20.5090i	−0.0122303	+	0.998361i
$423$		0			0
$424$	3.37985	+	0.124264i	0.164140	+	0.00603477i
$425$	−2.47682	+	4.28998i	−0.120143	+	0.208095i
$426$		0			0
$427$	28.4759	+	7.63011i	1.37805	+	0.369247i
$428$	7.66310	−	12.5523i	0.370410	−	0.606740i
$429$		0			0
$430$	7.70049	+	2.16478i	0.371350	+	0.104395i
$431$	−2.21278	−	0.592912i	−0.106586	−	0.0285596i	0.205132	−	0.978734i	$-0.434238\pi$
$431$	−2.21278	−	0.592912i	−0.106586	−	0.0285596i	−0.311718	+	0.950175i	$0.600904\pi$
$432$		0			0
$433$	13.9535	+	8.05603i	0.670560	+	0.387148i	0.796289	−	0.604917i	$-0.206794\pi$
$433$	13.9535	+	8.05603i	0.670560	+	0.387148i	−0.125729	+	0.992065i	$0.540127\pi$
$434$	21.4133	−	12.0157i	1.02787	−	0.576770i
$435$		0			0
$436$	−4.98292	−	1.46690i	−0.238639	−	0.0702520i
$437$	−0.929092	−	0.929092i	−0.0444445	−	0.0444445i
$438$		0			0
$439$	−10.1992	−	17.6656i	−0.486783	−	0.843133i	0.513102	−	0.858328i	$-0.328496\pi$
$439$	−10.1992	−	17.6656i	−0.486783	−	0.843133i	−0.999885	+	0.0151950i	$0.995163\pi$
$440$	−4.47652	−	8.45667i	−0.213410	−	0.403156i
$441$		0			0
$442$	−3.95658	+	3.68059i	−0.188195	+	0.175068i
$443$	−4.48358			−0.213021			−0.106511	−	0.994312i	$-0.533968\pi$
$443$	−4.48358			−0.213021			−0.106511	+	0.994312i	$0.533968\pi$
$444$		0			0
$445$	0.362493	−	0.209285i	0.0171838	−	0.00992107i
$446$	−23.9926	−	24.5877i	−1.13608	−	1.16426i
$447$		0			0
$448$	−37.8457	+	7.21181i	−1.78804	+	0.340726i
$449$	−3.28057	−	12.2433i	−0.154820	−	0.577795i	−0.999121	−	0.0419259i	$-0.986651\pi$
$449$	−3.28057	−	12.2433i	−0.154820	−	0.577795i	0.844301	−	0.535869i	$-0.180016\pi$
$450$		0			0
$451$	−15.7391	+	27.2609i	−0.741125	+	1.28367i
$452$	38.8516	+	0.952040i	1.82743	+	0.0447802i
$453$		0			0
$454$	27.5031	+	7.73172i	1.29078	+	0.362868i
$455$	−9.50893	−	2.79282i	−0.445786	−	0.130929i
$456$		0			0
$457$	6.68865	−	24.9624i	0.312882	−	1.16769i	−0.613064	−	0.790033i	$-0.710063\pi$
$457$	6.68865	−	24.9624i	0.312882	−	1.16769i	0.925946	−	0.377657i	$-0.123270\pi$
$458$	−0.265586	−	1.04208i	−0.0124100	−	0.0486930i
$459$		0			0
$460$	−0.551516	−	2.28034i	−0.0257146	−	0.106322i
$461$	4.57308	+	17.0670i	0.212990	+	0.794888i	0.986865	+	0.161550i	$0.0516491\pi$
$461$	4.57308	+	17.0670i	0.212990	+	0.794888i	−0.773875	+	0.633338i	$0.781684\pi$
$462$		0			0
$463$	−0.916082	−	0.916082i	−0.0425740	−	0.0425740i	0.685499	−	0.728073i	$-0.259584\pi$
$463$	−0.916082	−	0.916082i	−0.0425740	−	0.0425740i	−0.728073	+	0.685499i	$0.759584\pi$
$464$	1.10112	−	22.4543i	0.0511184	−	1.04241i
$465$		0			0
$466$	3.65603	−	6.15700i	0.169362	−	0.285218i
$467$			1.02377i			0.0473745i	0.999719	+	0.0236872i	$0.00754059\pi$
$467$			1.02377i			0.0473745i	−0.999719	+	0.0236872i	$0.992459\pi$
$468$		0			0
$469$			38.4856i			1.77710i
$470$	−5.81326	−	3.45191i	−0.268145	−	0.159225i
$471$		0			0
$472$	−22.5367	+	5.15927i	−1.03733	+	0.237475i
$473$	−41.5326	−	41.5326i	−1.90967	−	1.90967i
$474$		0			0
$475$	0.773429	+	2.88648i	0.0354874	+	0.132441i
$476$	2.39955	+	9.92139i	0.109983	+	0.454746i
$477$		0			0
$478$	39.1060	−	9.96663i	1.78867	−	0.455863i
$479$	0.0511532	−	0.190906i	0.00233725	−	0.00872273i	−0.964747	−	0.263178i	$-0.915229\pi$
$479$	0.0511532	−	0.190906i	0.00233725	−	0.00872273i	0.967085	+	0.254455i	$0.0818961\pi$
$480$		0			0
$481$	−25.5347	−	0.609680i	−1.16428	−	0.0277990i
$482$	5.18568	−	18.4463i	0.236201	−	0.840208i
$483$		0			0
$484$	−1.18224	+	48.2456i	−0.0537380	+	2.19298i
$485$	−1.32578	+	2.29632i	−0.0602006	+	0.104270i
$486$		0			0
$487$	2.09884	+	7.83299i	0.0951077	+	0.354947i	0.997036	−	0.0769395i	$-0.0245148\pi$
$487$	2.09884	+	7.83299i	0.0951077	+	0.354947i	−0.901928	+	0.431886i	$0.857848\pi$
$488$	9.20228	−	14.6665i	0.416567	−	0.663922i
$489$		0			0
$490$	−9.35448	+	9.12806i	−0.422592	+	0.412364i
$491$	−13.2895	+	7.67272i	−0.599748	+	0.346265i	−0.768943	−	0.639318i	$-0.779217\pi$
$491$	−13.2895	+	7.67272i	−0.599748	+	0.346265i	0.169194	+	0.985583i	$0.445884\pi$
$492$		0			0
$493$	−5.95628			−0.268257
$494$	−0.117727	+	3.25775i	−0.00529679	+	0.146573i
$495$		0			0
$496$	−3.04570	−	14.0958i	−0.136756	−	0.632919i
$497$	−1.05255	−	1.82306i	−0.0472131	−	0.0817755i
$498$		0			0
$499$	10.5996	+	10.5996i	0.474502	+	0.474502i	0.903368	−	0.428866i	$-0.141087\pi$
$499$	10.5996	+	10.5996i	0.474502	+	0.474502i	−0.428866	+	0.903368i	$0.641087\pi$
$500$	−3.11869	+	10.5939i	−0.139472	+	0.473772i
$501$		0			0
$502$	11.6019	+	20.6759i	0.517818	+	0.922811i
$503$	−32.2230	−	18.6039i	−1.43675	−	0.829508i	−0.439128	−	0.898424i	$-0.644713\pi$
$503$	−32.2230	−	18.6039i	−1.43675	−	0.829508i	−0.997622	+	0.0689162i	$0.978046\pi$
$504$		0			0
$505$	−2.24541	−	0.601655i	−0.0999192	−	0.0267733i
$506$	−4.66222	+	16.5843i	−0.207261	+	0.737262i
$507$		0			0
$508$	14.3057	−	23.4330i	0.634712	−	1.03967i
$509$	39.9366	+	10.7010i	1.77016	+	0.474312i	0.988733	−	0.149687i	$-0.0478267\pi$
$509$	39.9366	+	10.7010i	1.77016	+	0.474312i	0.781425	+	0.624000i	$0.214493\pi$
$510$		0			0
$511$	25.0125	−	43.3229i	1.10649	−	1.91649i
$512$	−2.48958	+	22.4900i	−0.110025	+	0.993929i
$513$		0			0
$514$	−12.5127	−	0.153286i	−0.551914	−	0.00676118i
$515$	−0.180615	+	0.180615i	−0.00795884	+	0.00795884i
$516$		0			0
$517$	24.8224	+	42.9936i	1.09169	+	1.89086i
$518$	−24.6335	+	41.4844i	−1.08233	+	1.82272i
$519$		0			0
$520$	−3.21038	+	4.85526i	−0.140784	+	0.212917i
$521$	−35.6854			−1.56341			−0.781703	−	0.623650i	$-0.785649\pi$
$521$	−35.6854			−1.56341			−0.781703	+	0.623650i	$0.785649\pi$
$522$		0			0
$523$	2.52621	+	4.37553i	0.110464	+	0.191328i	0.915957	−	0.401276i	$-0.131433\pi$
$523$	2.52621	+	4.37553i	0.110464	+	0.191328i	−0.805494	+	0.592604i	$0.798100\pi$
$524$	5.65136	+	10.3669i	0.246881	+	0.452882i
$525$		0			0
$526$	−8.97524	−	0.109950i	−0.391339	−	0.00479407i
$527$	−3.69059	+	0.988891i	−0.160765	+	0.0430768i
$528$		0			0
$529$	9.38802	−	16.2605i	0.408175	−	0.706980i
$530$	−0.238372	−	0.935299i	−0.0103542	−	0.0406268i
$531$		0			0
$532$	5.25567	+	3.20855i	0.227862	+	0.139108i
$533$	19.1434	+	0.457077i	0.829191	+	0.0197982i
$534$		0			0
$535$	−4.05398	−	1.08626i	−0.175269	−	0.0469632i
$536$	21.6034	+	6.64838i	0.933125	+	0.287166i
$537$		0			0
$538$	−4.41043	−	7.85989i	−0.190147	−	0.338864i
$539$	92.7027	−	24.8396i	3.99299	−	1.06992i
$540$		0			0
$541$	−16.2450	−	16.2450i	−0.698429	−	0.698429i	0.265643	−	0.964072i	$-0.414416\pi$
$541$	−16.2450	−	16.2450i	−0.698429	−	0.698429i	−0.964072	+	0.265643i	$0.914416\pi$
$542$	−8.88701	+	8.67191i	−0.381730	+	0.372490i
$543$		0			0
$544$	5.98376	+	0.366959i	0.256552	+	0.0157332i
$545$			1.48237i			0.0634978i
$546$		0			0
$547$	−6.47392			−0.276805			−0.138402	−	0.990376i	$-0.544197\pi$
$547$	−6.47392			−0.276805			−0.138402	+	0.990376i	$0.544197\pi$
$548$	−25.1907	+	23.9857i	−1.07609	+	1.02462i
$549$		0			0
$550$	28.0417	−	27.3630i	1.19570	−	1.16676i
$551$	−2.54074	+	2.54074i	−0.108239	+	0.108239i
$552$		0			0
$553$	8.98493	+	33.5322i	0.382078	+	1.42594i
$554$	−8.48866	+	4.76325i	−0.360649	+	0.202371i
$555$		0			0
$556$	−28.1796	−	0.690529i	−1.19508	−	0.0292849i
$557$	−4.79101	+	17.8803i	−0.203002	+	0.757612i	0.787048	+	0.616892i	$0.211608\pi$
$557$	−4.79101	+	17.8803i	−0.203002	+	0.757612i	−0.990049	+	0.140720i	$0.955058\pi$
$558$		0			0
$559$	−10.0688	+	34.2822i	−0.425867	+	1.44998i
$560$	5.02443	+	9.77961i	0.212321	+	0.413264i
$561$		0			0
$562$	2.41534	−	0.615579i	0.101885	−	0.0259666i
$563$	−11.7692	−	6.79494i	−0.496012	−	0.286373i	0.231053	−	0.972941i	$-0.425783\pi$
$563$	−11.7692	−	6.79494i	−0.496012	−	0.286373i	−0.727065	+	0.686568i	$0.759116\pi$
$564$		0			0
$565$	−2.87052	−	10.7129i	−0.120764	−	0.450696i
$566$	−18.9544	−	0.232199i	−0.796713	−	0.00976007i
$567$		0			0
$568$	−1.20518	+	0.275899i	−0.0505682	+	0.0115765i
$569$	−5.17128	+	2.98564i	−0.216791	+	0.125164i	−0.604464	−	0.796633i	$-0.706613\pi$
$569$	−5.17128	+	2.98564i	−0.216791	+	0.125164i	0.387672	+	0.921797i	$0.373279\pi$
$570$		0			0
$571$			7.35140i			0.307647i	0.988098	+	0.153823i	$0.0491587\pi$
$571$			7.35140i			0.307647i	−0.988098	+	0.153823i	$0.950841\pi$
$572$	38.0045	−	19.5556i	1.58905	−	0.817660i
$573$		0			0
$574$	18.4677	−	31.1009i	0.770828	−	1.29813i
$575$	8.31956	−	4.80330i	0.346949	−	0.200311i
$576$		0			0
$577$	8.59954	+	8.59954i	0.358004	+	0.358004i	0.863077	−	0.505073i	$-0.168534\pi$
$577$	8.59954	+	8.59954i	0.358004	+	0.358004i	−0.505073	+	0.863077i	$0.668534\pi$
$578$	−0.275042	+	22.4516i	−0.0114402	+	0.933864i
$579$		0			0
$580$	−6.23593	+	1.50820i	−0.258933	+	0.0626247i
$581$	−45.9899	−	26.5523i	−1.90798	−	1.10157i
$582$		0			0
$583$	−1.83435	+	6.84588i	−0.0759709	+	0.283527i
$584$	−19.9979	−	21.5245i	−0.827518	−	0.890689i
$585$		0			0
$586$	31.8843	+	8.96338i	1.31713	+	0.370274i
$587$	−5.77087	+	21.5372i	−0.238189	+	0.888934i	0.738496	+	0.674258i	$0.235536\pi$
$587$	−5.77087	+	21.5372i	−0.238189	+	0.888934i	−0.976685	+	0.214676i	$0.931130\pi$
$588$		0			0
$589$	−1.15245	+	1.99610i	−0.0474858	+	0.0822479i
$590$	3.22872	+	5.75395i	0.132924	+	0.236886i
$591$		0			0
$592$	19.0313	+	20.9941i	0.782182	+	0.862852i
$593$	−24.9155	+	24.9155i	−1.02316	+	1.02316i	−0.0234302	+	0.999725i	$0.507459\pi$
$593$	−24.9155	+	24.9155i	−1.02316	+	1.02316i	−0.999725	+	0.0234302i	$0.992541\pi$
$594$		0			0
$595$	2.52274	−	1.45650i	0.103422	−	0.0597109i
$596$	16.1615	−	15.3884i	0.662002	−	0.630334i
$597$		0			0
$598$	10.2139	−	2.34499i	0.417677	−	0.0958939i
$599$		−	32.0155i		−	1.30812i	−0.756444	−	0.654059i	$-0.773065\pi$
$599$		−	32.0155i		−	1.30812i	0.756444	−	0.654059i	$-0.226935\pi$
$600$		0			0
$601$	−6.17445	−	10.6945i	−0.251861	−	0.436236i	0.712177	−	0.702000i	$-0.247709\pi$
$601$	−6.17445	−	10.6945i	−0.251861	−	0.436236i	−0.964038	+	0.265764i	$0.914376\pi$
$602$	47.1358	+	48.3050i	1.92111	+	1.96876i
$603$		0			0
$604$	6.53764	−	22.2077i	0.266013	−	0.903617i
$605$	13.3032	−	3.56459i	0.540853	−	0.144921i
$606$		0			0
$607$	−23.6311	−	13.6435i	−0.959159	−	0.553771i	−0.0632447	−	0.997998i	$-0.520145\pi$
$607$	−23.6311	−	13.6435i	−0.959159	−	0.553771i	−0.895914	+	0.444227i	$0.853478\pi$
$608$	2.70899	−	2.39593i	0.109864	−	0.0971678i
$609$		0			0
$610$	−4.75681	−	1.33725i	−0.192598	−	0.0541435i
$611$	15.7199	−	25.7860i	0.635960	−	1.04319i
$612$		0			0
$613$	1.68752	+	0.452170i	0.0681583	+	0.0182630i	0.292737	−	0.956193i	$-0.405434\pi$
$613$	1.68752	+	0.452170i	0.0681583	+	0.0182630i	−0.224579	+	0.974456i	$0.572101\pi$
$614$	41.0839	−	10.4707i	1.65801	−	0.422564i
$615$		0			0
$616$	2.96626	−	80.6795i	0.119514	−	3.25067i
$617$	21.8225	−	5.84731i	0.878539	−	0.235404i	0.208762	−	0.977966i	$-0.433057\pi$
$617$	21.8225	−	5.84731i	0.878539	−	0.235404i	0.669777	+	0.742563i	$0.266390\pi$
$618$		0			0
$619$	−16.8078	+	16.8078i	−0.675564	+	0.675564i	−0.958993	−	0.283429i	$-0.908528\pi$
$619$	−16.8078	+	16.8078i	−0.675564	+	0.675564i	0.283429	+	0.958993i	$0.408528\pi$
$620$	−3.61347	+	1.96982i	−0.145120	+	0.0791100i
$621$		0			0
$622$	28.7068	+	17.0461i	1.15104	+	0.683486i
$623$	3.53171			0.141495
$624$		0			0
$625$	−20.2196			−0.808783
$626$	2.03454	+	1.20811i	0.0813164	+	0.0482857i
$627$		0			0
$628$	−34.3609	+	18.7313i	−1.37115	+	0.747460i
$629$	5.30862	−	5.30862i	0.211669	−	0.211669i
$630$		0			0
$631$	−28.5528	+	7.65071i	−1.13667	+	0.304570i	−0.777612	−	0.628745i	$-0.783569\pi$
$631$	−28.5528	+	7.65071i	−1.13667	+	0.304570i	−0.359059	+	0.933315i	$0.616902\pi$
$632$	20.3750	+	0.749108i	0.810475	+	0.0297979i
$633$		0			0
$634$	−3.86237	+	0.984372i	−0.153394	+	0.0390944i
$635$	−7.56808	−	2.02786i	−0.300330	−	0.0804732i
$636$		0			0
$637$	−40.2853	−	42.2561i	−1.59616	−	1.67425i
$638$	45.3522	+	12.7495i	1.79551	+	0.504758i
$639$		0			0
$640$	6.35763	−	1.13097i	0.251307	−	0.0447056i
$641$	−16.7228	−	9.65492i	−0.660511	−	0.381346i	0.131961	−	0.991255i	$-0.457873\pi$
$641$	−16.7228	−	9.65492i	−0.660511	−	0.381346i	−0.792472	+	0.609909i	$0.791206\pi$
$642$		0			0
$643$	20.6865	−	5.54294i	0.815797	−	0.218592i	0.173289	−	0.984871i	$-0.444561\pi$
$643$	20.6865	−	5.54294i	0.815797	−	0.218592i	0.642508	+	0.766279i	$0.277894\pi$
$644$	5.59026	−	18.9895i	0.220287	−	0.748292i
$645$		0			0
$646$	−0.669180	−	0.685779i	−0.0263285	−	0.0269816i
$647$	13.1707	+	22.8124i	0.517794	+	0.896846i	0.999786	+	0.0206706i	$0.00658014\pi$
$647$	13.1707	+	22.8124i	0.517794	+	0.896846i	−0.481992	+	0.876176i	$0.660087\pi$
$648$		0			0
$649$		−	48.4480i		−	1.90175i
$650$	−22.7841	−	6.99608i	−0.893665	−	0.274409i
$651$		0			0
$652$	9.16866	−	8.73006i	0.359073	−	0.341896i
$653$	−4.85800	+	2.80477i	−0.190108	+	0.109759i	−0.592033	−	0.805914i	$-0.701675\pi$
$653$	−4.85800	+	2.80477i	−0.190108	+	0.109759i	0.401925	+	0.915673i	$0.368341\pi$
$654$		0			0
$655$	2.38264	−	2.38264i	0.0930976	−	0.0930976i
$656$	−14.2678	−	15.7393i	−0.557064	−	0.614516i
$657$		0			0
$658$	−27.9154	−	49.7485i	−1.08826	−	1.93940i
$659$	−18.1430	+	31.4246i	−0.706751	+	1.22413i	0.259305	+	0.965795i	$0.416507\pi$
$659$	−18.1430	+	31.4246i	−0.706751	+	1.22413i	−0.966056	+	0.258333i	$0.916827\pi$
$660$		0			0
$661$	3.16335	−	11.8058i	0.123040	−	0.459192i	−0.876722	−	0.480997i	$-0.840275\pi$
$661$	3.16335	−	11.8058i	0.123040	−	0.459192i	0.999762	+	0.0218054i	$0.00694141\pi$
$662$	7.67444	+	2.15746i	0.298276	+	0.0838520i
$663$		0			0
$664$	−22.8495	+	21.2289i	−0.886734	+	0.823842i
$665$	0.454818	−	1.69740i	0.0176371	−	0.0658225i
$666$		0			0
$667$	10.0035	+	5.77550i	0.387336	+	0.223628i
$668$	−9.72784	+	2.35274i	−0.376382	+	0.0910304i
$669$		0			0
$670$	0.0790160	−	6.45006i	0.00305265	−	0.249188i
$671$	25.6559	+	25.6559i	0.990434	+	0.990434i
$672$		0			0
$673$	21.4840	−	12.4038i	0.828146	−	0.478130i	−0.0250717	−	0.999686i	$-0.507981\pi$
$673$	21.4840	−	12.4038i	0.828146	−	0.478130i	0.853217	+	0.521556i	$0.174648\pi$
$674$	7.21325	−	12.1476i	0.277844	−	0.467908i
$675$		0			0
$676$	−21.5196	−	14.5914i	−0.827676	−	0.561206i
$677$			41.5137i			1.59550i	0.602988	+	0.797750i	$0.293977\pi$
$677$			41.5137i			1.59550i	−0.602988	+	0.797750i	$0.706023\pi$
$678$		0			0
$679$	−19.3753	+	11.1863i	−0.743557	+	0.429293i
$680$	−0.381787	−	1.66772i	−0.0146409	−	0.0639541i
$681$		0			0
$682$	30.2176	+	0.370178i	1.15709	+	0.0141748i
$683$	9.94935	+	37.1315i	0.380701	+	1.42080i	0.844833	+	0.535030i	$0.179700\pi$
$683$	9.94935	+	37.1315i	0.380701	+	1.42080i	−0.464132	+	0.885766i	$0.653634\pi$
$684$		0			0
$685$	8.59662	+	4.96326i	0.328460	+	0.189636i
$686$	−60.6662	+	15.4615i	−2.31625	+	0.590323i
$687$		0			0
$688$	35.2581	−	18.1144i	1.34420	−	0.690605i
$689$	4.18994	−	1.01615i	0.159624	−	0.0387121i
$690$		0			0
$691$	−0.476425	+	1.77804i	−0.0181241	+	0.0676399i	−0.974396	−	0.224840i	$-0.927814\pi$
$691$	−0.476425	+	1.77804i	−0.0181241	+	0.0676399i	0.956272	+	0.292480i	$0.0944806\pi$
$692$	−24.1114	−	0.590839i	−0.916579	−	0.0224603i
$693$		0			0
$694$	−29.2499	+	16.4130i	−1.11031	+	0.623030i
$695$	2.08203	+	7.77025i	0.0789760	+	0.294742i
$696$		0			0
$697$	−3.97988	+	3.97988i	−0.150749	+	0.150749i
$698$	−20.0193	+	19.5347i	−0.757741	+	0.739401i
$699$		0			0
$700$	−32.6047	+	31.0450i	−1.23234	+	1.17339i
$701$	30.7524			1.16150			0.580752	−	0.814081i	$-0.302759\pi$
$701$	30.7524			1.16150			0.580752	+	0.814081i	$0.302759\pi$
$702$		0			0
$703$		−	4.52894i		−	0.170812i
$704$	−44.7760	−	15.6024i	−1.68756	−	0.588039i
$705$		0			0
$706$	11.2421	−	10.9700i	0.423103	−	0.412862i
$707$	−13.8692	−	13.8692i	−0.521607	−	0.521607i
$708$		0			0
$709$	6.75910	−	1.81110i	0.253844	−	0.0680172i	−0.129653	−	0.991559i	$-0.541386\pi$
$709$	6.75910	−	1.81110i	0.253844	−	0.0680172i	0.383497	+	0.923542i	$0.374720\pi$
$710$	0.172660	+	0.307700i	0.00647982	+	0.0115478i
$711$		0			0
$712$	0.610102	−	1.98248i	0.0228646	−	0.0742966i
$713$	7.15716	+	1.91775i	0.268038	+	0.0718205i
$714$		0			0
$715$	−8.41652	−	8.82826i	−0.314760	−	0.330158i
$716$	29.9779	+	18.3013i	1.12033	+	0.683951i
$717$		0			0
$718$	4.98387	+	19.5552i	0.185996	+	0.729792i
$719$	−10.9833	+	19.0236i	−0.409608	+	0.709461i	−0.994846	−	0.101400i	$-0.967668\pi$
$719$	−10.9833	+	19.0236i	−0.409608	+	0.709461i	0.585238	+	0.810862i	$0.301001\pi$
$720$		0			0
$721$	−2.08175	+	0.557804i	−0.0775285	+	0.0207737i
$722$	26.2901	+	0.322064i	0.978415	+	0.0119860i
$723$		0			0
$724$	6.73665	+	12.3578i	0.250365	+	0.459274i
$725$	−13.1353	−	22.7510i	−0.487833	−	0.844952i
$726$		0			0
$727$	32.3235			1.19881			0.599407	−	0.800445i	$-0.295403\pi$
$727$	32.3235			1.19881			0.599407	+	0.800445i	$0.295403\pi$
$728$	−43.9419	+	21.9342i	−1.62860	+	0.812934i
$729$		0			0
$730$	−4.28096	+	7.20943i	−0.158446	+	0.266833i
$731$	−5.25109	−	9.09515i	−0.194218	−	0.336396i
$732$		0			0
$733$	−27.9317	+	27.9317i	−1.03168	+	1.03168i	−0.0321977	+	0.999482i	$0.510251\pi$
$733$	−27.9317	+	27.9317i	−1.03168	+	1.03168i	−0.999482	+	0.0321977i	$0.989749\pi$
$734$	9.30024	+	0.113932i	0.343278	+	0.00420530i
$735$		0			0
$736$	−9.69380	−	6.41846i	−0.357318	−	0.236587i
$737$	−23.6829	+	41.0200i	−0.872372	+	1.51099i
$738$		0			0
$739$	33.0386	+	8.85267i	1.21534	+	0.325651i	0.808857	−	0.588005i	$-0.200087\pi$
$739$	33.0386	+	8.85267i	1.21534	+	0.325651i	0.406488	+	0.913656i	$0.366753\pi$
$740$	4.21366	−	6.90208i	0.154897	−	0.253725i
$741$		0			0
$742$	2.20400	−	7.84001i	0.0809114	−	0.287816i
$743$	48.6992	+	13.0489i	1.78660	+	0.478718i	0.991761	−	0.128102i	$-0.0408884\pi$
$743$	48.6992	+	13.0489i	1.78660	+	0.478718i	0.794839	+	0.606820i	$0.207555\pi$
$744$		0			0
$745$	−5.51531	−	3.18427i	−0.202065	−	0.116662i
$746$	−5.88642	−	10.4903i	−0.215517	−	0.384077i
$747$		0			0
$748$	−3.54776	+	12.0514i	−0.129719	+	0.440642i
$749$	−25.0403	−	25.0403i	−0.914953	−	0.914953i
$750$		0			0
$751$	24.4568	+	42.3605i	0.892443	+	1.54576i	0.836938	+	0.547298i	$0.184343\pi$
$751$	24.4568	+	42.3605i	0.892443	+	1.54576i	0.0555049	+	0.998458i	$0.482323\pi$
$752$	−32.7480	+	7.07592i	−1.19420	+	0.258032i
$753$		0			0
$754$	−6.41273	−	27.9314i	−0.233538	−	1.01720i
$755$	−6.60657			−0.240438
$756$		0			0
$757$	1.35085	−	0.779913i	0.0490974	−	0.0283464i	−0.475250	−	0.879851i	$-0.657643\pi$
$757$	1.35085	−	0.779913i	0.0490974	−	0.0283464i	0.524348	+	0.851504i	$0.324309\pi$
$758$	−17.7041	+	17.2756i	−0.643042	+	0.627478i
$759$		0			0
$760$	−0.874246	−	0.548532i	−0.0317122	−	0.0198974i
$761$	2.75025	+	10.2641i	0.0996966	+	0.372073i	0.997690	−	0.0679370i	$-0.0216417\pi$
$761$	2.75025	+	10.2641i	0.0996966	+	0.372073i	−0.897993	+	0.440010i	$0.854975\pi$
$762$		0			0
$763$	−6.25379	+	10.8319i	−0.226402	+	0.392141i
$764$	−1.00990	+	41.2130i	−0.0365370	+	1.49103i
$765$		0			0
$766$	−3.81985	+	13.5879i	−0.138017	+	0.490949i
$767$	−25.8679	+	14.1225i	−0.934036	+	0.509935i
$768$		0			0
$769$	−11.1442	+	41.5908i	−0.401871	+	1.49980i	0.407885	+	0.913033i	$0.366267\pi$
$769$	−11.1442	+	41.5908i	−0.401871	+	1.49980i	−0.809755	+	0.586768i	$0.800400\pi$
$770$	−22.3263	+	5.69012i	−0.804583	+	0.205058i
$771$		0			0
$772$	−2.03610	−	8.41861i	−0.0732808	−	0.302993i
$773$	−4.01263	−	14.9753i	−0.144324	−	0.538626i	−0.999785	−	0.0207572i	$-0.993392\pi$
$773$	−4.01263	−	14.9753i	−0.144324	−	0.538626i	0.855460	−	0.517869i	$-0.173274\pi$
$774$		0			0
$775$	−11.9161	−	11.9161i	−0.428037	−	0.428037i
$776$	2.93223	+	12.8085i	0.105261	+	0.459799i
$777$		0			0
$778$	0.977425	+	0.580395i	0.0350424	+	0.0208082i
$779$			3.39535i			0.121651i
$780$		0			0
$781$		−	2.59083i		−	0.0927070i
$782$	−1.57270	+	2.64853i	−0.0562395	+	0.0947111i
$783$		0			0
$784$	−3.17238	+	64.6915i	−0.113299	+	2.31041i
$785$	7.89721	+	7.89721i	0.281863	+	0.281863i
$786$		0			0
$787$	9.97812	+	37.2389i	0.355682	+	1.32742i	0.879624	+	0.475669i	$0.157794\pi$
$787$	9.97812	+	37.2389i	0.355682	+	1.32742i	−0.523943	+	0.851753i	$0.675539\pi$
$788$	−4.98972	−	20.6309i	−0.177751	−	0.734945i
$789$		0			0
$790$	−1.43700	−	5.63834i	−0.0511262	−	0.200603i
$791$	24.2202	−	90.3910i	0.861171	−	3.21393i
$792$		0			0
$793$	6.21982	−	21.1771i	0.220872	−	0.752021i
$794$	−1.66176	−	0.467159i	−0.0589738	−	0.0165789i
$795$		0			0
$796$	−48.2270	−	1.18178i	−1.70936	−	0.0418871i
$797$	−2.47797	+	4.29197i	−0.0877742	+	0.152029i	−0.906570	−	0.422055i	$-0.861309\pi$
$797$	−2.47797	+	4.29197i	−0.0877742	+	0.152029i	0.818796	+	0.574085i	$0.194642\pi$
$798$		0			0
$799$	2.29744	+	8.57417i	0.0812776	+	0.303332i
$800$	11.7943	+	23.6653i	0.416990	+	0.836694i
$801$		0			0
$802$	−4.83851	−	4.95852i	−0.170854	−	0.175092i
$803$	53.3194	−	30.7840i	1.88160	−	1.08634i
$804$		0			0
$805$	−5.64920			−0.199108
$806$	−8.61072	−	16.2420i	−0.303300	−	0.572100i
$807$		0			0
$808$	−10.1812	+	5.38941i	−0.358174	+	0.189599i
$809$	−24.9370	−	43.1921i	−0.876738	−	1.51855i	−0.854900	−	0.518793i	$-0.826382\pi$
$809$	−24.9370	−	43.1921i	−0.876738	−	1.51855i	−0.0218374	−	0.999762i	$-0.506952\pi$
$810$		0			0
$811$	−25.0953	−	25.0953i	−0.881216	−	0.881216i	0.112442	−	0.993658i	$-0.464133\pi$
$811$	−25.0953	−	25.0953i	−0.881216	−	0.881216i	−0.993658	+	0.112442i	$0.964133\pi$
$812$	−51.9296	−	15.2874i	−1.82237	−	0.536482i
$813$		0			0
$814$	−51.7840	+	29.0576i	−1.81503	+	1.01847i
$815$	−3.12891	−	1.80648i	−0.109601	−	0.0632782i
$816$		0			0
$817$	−6.11959	−	1.63974i	−0.214097	−	0.0573672i
$818$	−19.3295	−	5.43396i	−0.675840	−	0.189994i
$819$		0			0
$820$	−3.15899	+	5.17449i	−0.110317	+	0.180701i
$821$	41.6756	+	11.1669i	1.45449	+	0.389729i	0.897582	−	0.440847i	$-0.145322\pi$
$821$	41.6756	+	11.1669i	1.45449	+	0.389729i	0.556906	+	0.830576i	$0.311988\pi$
$822$		0			0
$823$	6.03038	−	10.4449i	0.210206	−	0.364087i	−0.741573	−	0.670872i	$-0.765920\pi$
$823$	6.03038	−	10.4449i	0.210206	−	0.364087i	0.951779	+	0.306785i	$0.0992532\pi$
$824$	−0.0465062	+	1.26493i	−0.00162012	+	0.0440658i
$825$		0			0
$826$	−0.681934	+	55.6661i	−0.0237275	+	1.93687i
$827$	13.3380	−	13.3380i	0.463809	−	0.463809i	−0.436093	−	0.899902i	$-0.643638\pi$
$827$	13.3380	−	13.3380i	0.463809	−	0.463809i	0.899902	+	0.436093i	$0.143638\pi$
$828$		0			0
$829$	−19.5075	−	33.7880i	−0.677524	−	1.17351i	−0.975724	−	0.219002i	$-0.929720\pi$
$829$	−19.5075	−	33.7880i	−0.677524	−	1.17351i	0.298201	−	0.954503i	$-0.403613\pi$
$830$	7.65324	+	4.54450i	0.265648	+	0.157742i
$831$		0			0
$832$	4.72150	+	28.4554i	0.163689	+	0.986512i
$833$	17.1603			0.594567
$834$		0			0
$835$	1.42809	+	2.47353i	0.0494212	+	0.0856000i
$836$	3.62734	+	6.65403i	0.125454	+	0.230135i
$837$		0			0
$838$	0.0818036	−	6.67762i	0.00282586	−	0.230674i
$839$	−35.6287	+	9.54667i	−1.23004	+	0.329588i	−0.814594	−	0.580031i	$-0.803040\pi$
$839$	−35.6287	+	9.54667i	−1.23004	+	0.329588i	−0.415444	+	0.909619i	$0.636374\pi$
$840$		0			0
$841$	1.29395	−	2.24118i	0.0446189	−	0.0772822i
$842$	−8.48899	+	2.16352i	−0.292550	+	0.0745599i
$843$		0			0
$844$	15.1141	−	24.7573i	0.520250	−	0.852182i
$845$	−2.26028	+	7.06726i	−0.0777560	+	0.243121i
$846$		0			0
$847$	112.247	+	30.0764i	3.85685	+	1.03344i
$848$	−4.02014	−	2.59155i	−0.138052	−	0.0889941i
$849$		0			0
$850$	6.10940	−	3.42817i	0.209551	−	0.117585i
$851$	−14.0632	+	3.76824i	−0.482082	+	0.129173i
$852$		0			0
$853$	30.9178	+	30.9178i	1.05861	+	1.05861i	0.998172	+	0.0604339i	$0.0192484\pi$
$853$	30.9178	+	30.9178i	1.05861	+	1.05861i	0.0604339	+	0.998172i	$0.480752\pi$
$854$	−29.1171	−	29.8394i	−0.996368	−	1.02108i
$855$		0			0
$856$	−18.3818	+	9.73035i	−0.628276	+	0.332576i
$857$			3.63834i			0.124283i	0.998067	+	0.0621417i	$0.0197931\pi$
$857$			3.63834i			0.124283i	−0.998067	+	0.0621417i	$0.980207\pi$
$858$		0			0
$859$	−10.4247			−0.355686			−0.177843	−	0.984059i	$-0.556912\pi$
$859$	−10.4247			−0.355686			−0.177843	+	0.984059i	$0.556912\pi$
$860$	−7.80063	−	8.19254i	−0.265999	−	0.279363i
$861$		0			0
$862$	2.26260	+	2.31873i	0.0770646	+	0.0789762i
$863$	−23.3831	+	23.3831i	−0.795970	+	0.795970i	−0.982457	−	0.186488i	$-0.940290\pi$
$863$	−23.3831	+	23.3831i	−0.795970	+	0.795970i	0.186488	+	0.982457i	$0.440290\pi$
$864$		0			0
$865$	1.78146	+	6.64848i	0.0605713	+	0.226055i
$866$	−11.1504	−	19.8712i	−0.378905	−	0.675252i
$867$		0			0
$868$	−34.7144	−	0.850659i	−1.17828	−	0.0288732i
$869$	−11.0581	+	41.2695i	−0.375122	+	1.39997i
$870$		0			0
$871$	28.8054	+	0.687774i	0.976034	+	0.0233043i
$872$	5.00000	+	5.38169i	0.169321	+	0.182247i
$873$		0			0
$874$	0.458911	+	1.80062i	0.0155229	+	0.0609070i
$875$	23.0290	+	13.2958i	0.778521	+	0.449479i
$876$		0			0
$877$	1.72948	+	6.45450i	0.0584004	+	0.217953i	0.988959	−	0.148190i	$-0.0473447\pi$
$877$	1.72948	+	6.45450i	0.0584004	+	0.217953i	−0.930559	+	0.366143i	$0.880678\pi$
$878$	−0.353371	+	28.8456i	−0.0119257	+	0.973493i
$879$		0			0
$880$	−0.662781	+	13.5155i	−0.0223424	+	0.455608i
$881$	5.79984	−	3.34854i	0.195401	−	0.112815i	−0.399107	−	0.916904i	$-0.630680\pi$
$881$	5.79984	−	3.34854i	0.195401	−	0.112815i	0.594509	+	0.804089i	$0.297347\pi$
$882$		0			0
$883$		−	6.47692i		−	0.217966i	−0.994044	−	0.108983i	$-0.965241\pi$
$883$		−	6.47692i		−	0.217966i	0.994044	−	0.108983i	$-0.0347594\pi$
$884$	7.46877	−	1.61870i	0.251202	−	0.0544426i
$885$		0			0
$886$	5.45199	+	3.23740i	0.183163	+	0.108762i
$887$	24.2718	−	14.0133i	0.814967	−	0.470521i	−0.0337108	−	0.999432i	$-0.510733\pi$
$887$	24.2718	−	14.0133i	0.814967	−	0.470521i	0.848678	+	0.528910i	$0.177399\pi$
$888$		0			0
$889$	−46.7459	−	46.7459i	−1.56781	−	1.56781i
$890$	−0.591904	−	0.00725107i	−0.0198407	−	0.000243056i
$891$		0			0
$892$	11.4211	+	47.2224i	0.382405	+	1.58112i
$893$	4.63744	+	2.67743i	0.155186	+	0.0895967i
$894$		0			0
$895$	2.59424	−	9.68185i	0.0867160	−	0.323629i
$896$	51.2274	+	18.5572i	1.71139	+	0.619954i
$897$		0			0
$898$	−4.85118	+	17.2565i	−0.161886	+	0.575855i
$899$	5.24438	−	19.5723i	0.174910	−	0.652772i
$900$		0			0
$901$	−0.633623	+	1.09747i	−0.0211090	+	0.0365619i
$902$	38.8225	−	21.7845i	1.29265	−	0.725345i
$903$		0			0
$904$	−46.5558	−	29.2107i	−1.54842	−	0.971534i
$905$	2.84021	−	2.84021i	0.0944116	−	0.0944116i
$906$		0			0
$907$	12.9360	−	7.46860i	0.429533	−	0.247991i	−0.269615	−	0.962968i	$-0.586896\pi$
$907$	12.9360	−	7.46860i	0.429533	−	0.247991i	0.699148	+	0.714977i	$0.253563\pi$
$908$	−27.8607	−	29.2605i	−0.924591	−	0.971043i
$909$		0			0
$910$	9.54620	+	10.2620i	0.316454	+	0.340183i
$911$			47.5530i			1.57550i	0.615995	+	0.787750i	$0.288754\pi$
$911$			47.5530i			1.57550i	−0.615995	+	0.787750i	$0.711246\pi$
$912$		0			0
$913$	−32.6790	−	56.6017i	−1.08152	−	1.87324i
$914$	−26.1576	+	25.5244i	−0.865215	+	0.844273i
$915$		0			0
$916$	−0.429487	+	1.45892i	−0.0141907	+	0.0482042i
$917$	27.4622	−	7.35846i	0.906880	−	0.242998i
$918$		0			0
$919$	−23.4113	−	13.5165i	−0.772268	−	0.445869i	0.0614148	−	0.998112i	$-0.480439\pi$
$919$	−23.4113	−	13.5165i	−0.772268	−	0.445869i	−0.833683	+	0.552243i	$0.813772\pi$
$920$	−0.975897	+	3.17110i	−0.0321744	+	0.104548i
$921$		0			0
$922$	6.76248	−	24.0553i	0.222711	−	0.792219i
$923$	−1.38332	+	0.755222i	−0.0455326	+	0.0248584i
$924$		0			0
$925$	31.9843	+	8.57016i	1.05164	+	0.281785i
$926$	0.452485	+	1.77541i	0.0148696	+	0.0583436i
$927$		0			0
$928$	−17.5522	+	26.5091i	−0.576179	+	0.870204i
$929$	8.36041	−	2.24016i	0.274296	−	0.0734974i	−0.119049	−	0.992888i	$-0.537984\pi$
$929$	8.36041	−	2.24016i	0.274296	−	0.0734974i	0.393345	+	0.919391i	$0.371318\pi$
$930$		0			0
$931$	7.31995	−	7.31995i	0.239902	−	0.239902i
$932$	−8.89140	+	4.84700i	−0.291248	+	0.158769i
$933$		0			0
$934$	0.739220	−	1.24490i	0.0241880	−	0.0407343i
$935$	3.58517			0.117247
$936$		0			0
$937$	−24.9116			−0.813826			−0.406913	−	0.913467i	$-0.633395\pi$
$937$	−24.9116			−0.813826			−0.406913	+	0.913467i	$0.633395\pi$
$938$	27.7888	−	46.7982i	0.907335	−	1.52801i
$939$		0			0
$940$	4.57639	+	8.39499i	0.149265	+	0.273815i
$941$	−1.97405	+	1.97405i	−0.0643522	+	0.0643522i	−0.738550	−	0.674198i	$-0.764489\pi$
$941$	−1.97405	+	1.97405i	−0.0643522	+	0.0643522i	0.674198	+	0.738550i	$0.264489\pi$
$942$		0			0
$943$	10.5432	−	2.82505i	0.343335	−	0.0919963i
$944$	31.1297	+	9.99911i	1.01318	+	0.325443i
$945$		0			0
$946$	20.5144	+	80.4921i	0.666981	+	2.61702i
$947$	31.0163	+	8.31080i	1.00790	+	0.270065i	0.724750	−	0.689012i	$-0.241955\pi$
$947$	31.0163	+	8.31080i	1.00790	+	0.270065i	0.283146	+	0.959077i	$0.408622\pi$
$948$		0			0
$949$	−31.9790	−	19.4954i	−1.03808	−	0.632847i
$950$	1.14372	−	4.06839i	0.0371070	−	0.131996i
$951$		0			0
$952$	4.24596	−	13.7969i	0.137612	−	0.447161i
$953$	−12.1425	−	7.01048i	−0.393334	−	0.227092i	0.290269	−	0.956945i	$-0.406255\pi$
$953$	−12.1425	−	7.01048i	−0.393334	−	0.227092i	−0.683604	+	0.729853i	$0.739588\pi$
$954$		0			0
$955$	11.3640	−	3.04499i	0.367732	−	0.0985335i
$956$	−54.7490	−	16.1174i	−1.77071	−	0.521273i
$957$		0			0
$958$	−0.200047	+	0.195205i	−0.00646322	+	0.00630678i
$959$	41.8778	+	72.5345i	1.35230	+	2.34226i
$960$		0			0
$961$			18.0020i			0.580711i
$962$	30.6097	+	19.1788i	0.986897	+	0.618350i
$963$		0			0
$964$	−19.6250	+	18.6862i	−0.632080	+	0.601843i
$965$	−2.14063	+	1.23589i	−0.0689092	+	0.0397847i
$966$		0			0
$967$	5.06111	−	5.06111i	0.162754	−	0.162754i	−0.621031	−	0.783786i	$-0.713286\pi$
$967$	5.06111	−	5.06111i	0.162754	−	0.162754i	0.783786	+	0.621031i	$0.213286\pi$
$968$	36.2736	−	57.8126i	1.16588	−	1.85817i
$969$		0			0
$970$	3.27021	−	1.83502i	0.105000	−	0.0589188i
$971$	−1.08352	+	1.87671i	−0.0347718	+	0.0602264i	−0.882888	−	0.469584i	$-0.844404\pi$
$971$	−1.08352	+	1.87671i	−0.0347718	+	0.0602264i	0.848116	+	0.529811i	$0.177737\pi$
$972$		0			0
$973$	−17.5673	+	65.5619i	−0.563181	+	2.10182i
$974$	3.10368	−	11.0403i	0.0994485	−	0.353755i
$975$		0			0
$976$	−21.7799	+	11.1898i	−0.697159	+	0.358176i
$977$	−4.67577	+	17.4502i	−0.149591	+	0.558282i	0.849917	+	0.526917i	$0.176652\pi$
$977$	−4.67577	+	17.4502i	−0.149591	+	0.558282i	−0.999508	+	0.0313649i	$0.990015\pi$
$978$		0			0
$979$	3.76429	+	2.17331i	0.120307	+	0.0694594i
$980$	17.9659	−	4.34518i	0.573901	−	0.138802i
$981$		0			0
$982$	21.7001	+	0.265835i	0.692478	+	0.00848315i
$983$	−4.75595	−	4.75595i	−0.151691	−	0.151691i	0.627182	−	0.778873i	$-0.284208\pi$
$983$	−4.75595	−	4.75595i	−0.151691	−	0.151691i	−0.778873	+	0.627182i	$0.784208\pi$
$984$		0			0
$985$	−5.24588	+	3.02871i	−0.167148	+	0.0965027i
$986$	7.24278	+	4.30077i	0.230657	+	0.136964i
$987$		0			0
$988$	2.49543	−	3.87639i	0.0793903	−	0.123324i
$989$			20.3669i			0.647628i
$990$		0			0
$991$	−13.6470	+	7.87912i	−0.433512	+	0.250288i	−0.700842	−	0.713317i	$-0.747192\pi$
$991$	−13.6470	+	7.87912i	−0.433512	+	0.250288i	0.267330	+	0.963605i	$0.413859\pi$
$992$	−6.47440	+	19.3395i	−0.205563	+	0.614030i
$993$		0			0
$994$	−0.0364674	+	2.97683i	−0.00115667	+	0.0944192i
$995$	3.56322	+	13.2981i	0.112962	+	0.421578i
$996$		0			0
$997$	43.1151	+	24.8925i	1.36547	+	0.788354i	0.990345	−	0.138621i	$-0.0442671\pi$
$997$	43.1151	+	24.8925i	1.36547	+	0.788354i	0.375123	+	0.926975i	$0.377600\pi$
$998$	−5.23550	−	20.5425i	−0.165727	−	0.650261i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.ed.e.739.3		56
3.2	odd	2		312.2.bt.d.115.12	yes	56
8.3	odd	2	inner	936.2.ed.e.739.14		56
13.6	odd	12	inner	936.2.ed.e.19.14		56
24.11	even	2		312.2.bt.d.115.1	yes	56
39.32	even	12		312.2.bt.d.19.1	✓	56
104.19	even	12	inner	936.2.ed.e.19.3		56
312.227	odd	12		312.2.bt.d.19.12	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bt.d.19.1	✓	56	39.32	even	12
312.2.bt.d.19.12	yes	56	312.227	odd	12
312.2.bt.d.115.1	yes	56	24.11	even	2
312.2.bt.d.115.12	yes	56	3.2	odd	2
936.2.ed.e.19.3		56	104.19	even	12	inner
936.2.ed.e.19.14		56	13.6	odd	12	inner
936.2.ed.e.739.3		56	1.1	even	1	trivial
936.2.ed.e.739.14		56	8.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.ed (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21599 - 0.722056i) q^{2} +(0.957270 + 1.75603i) q^{4} +(0.403590 - 0.403590i) q^{5} +(4.65174 - 1.24643i) q^{7} +(0.103920 - 2.82652i) q^{8} +(-0.782176 + 0.199347i) q^{10} +(5.72510 + 1.53404i) q^{11} +(-0.849788 - 3.50398i) q^{13} +(-6.55647 - 1.84317i) q^{14} +(-2.16727 + 3.36198i) q^{16} +(0.917794 + 0.529889i) q^{17} +(0.617530 - 0.165467i) q^{19} +(1.09506 + 0.322371i) q^{20} +(-5.85401 - 5.99922i) q^{22} +(-1.02761 - 1.77988i) q^{23} +4.67423i q^{25} +(-1.49673 + 4.87440i) q^{26} +(6.64174 + 6.97542i) q^{28} +(-4.86733 + 2.81016i) q^{29} +(-2.54931 + 2.54931i) q^{31} +(5.06292 - 2.52325i) q^{32} +(-0.733420 - 1.30704i) q^{34} +(1.37435 - 2.38044i) q^{35} +(1.83349 - 6.84268i) q^{37} +(-0.870387 - 0.244685i) q^{38} +(-1.09881 - 1.18269i) q^{40} +(-1.37457 + 5.12996i) q^{41} +(-8.58213 - 4.95490i) q^{43} +(2.78665 + 11.5219i) q^{44} +(-0.0356035 + 2.90631i) q^{46} +(5.92269 + 5.92269i) q^{47} +(14.0230 - 8.09616i) q^{49} +(3.37506 - 5.68382i) q^{50} +(5.33961 - 4.84650i) q^{52} +1.19577i q^{53} +(2.92971 - 1.69147i) q^{55} +(-3.03965 - 13.2778i) q^{56} +(7.94772 + 0.0973630i) q^{58} +(-2.11560 - 7.89551i) q^{59} +(5.30143 + 3.06078i) q^{61} +(4.94068 - 1.25919i) q^{62} +(-7.97840 - 0.587462i) q^{64} +(-1.75714 - 1.07120i) q^{65} +(-2.06834 + 7.71916i) q^{67} +(-0.0519231 + 2.11892i) q^{68} +(-3.39001 + 1.90224i) q^{70} +(-0.113135 - 0.422224i) q^{71} +(7.34514 - 7.34514i) q^{73} +(-7.17031 + 6.99675i) q^{74} +(0.881707 + 0.926004i) q^{76} +28.5438 q^{77} +7.20853i q^{79} +(0.482175 + 2.23155i) q^{80} +(5.37559 - 5.24547i) q^{82} +(-7.79731 - 7.79731i) q^{83} +(0.584270 - 0.156555i) q^{85} +(6.85808 + 12.2219i) q^{86} +(4.93093 - 16.0227i) q^{88} +(0.708365 + 0.189806i) q^{89} +(-8.32047 - 15.2404i) q^{91} +(2.14181 - 3.50834i) q^{92} +(-2.92542 - 11.4784i) q^{94} +(0.182448 - 0.316009i) q^{95} +(-4.48735 + 1.20238i) q^{97} +(-22.8977 - 0.280506i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 12 q^{8} + 28 q^{14} + 12 q^{16} - 8 q^{19} + 4 q^{20} + 10 q^{22} - 34 q^{26} - 14 q^{28} + 30 q^{32} + 56 q^{34} - 28 q^{40} - 40 q^{41} + 44 q^{44} - 18 q^{46} + 24 q^{49} + 72 q^{50} + 32 q^{52}+ \cdots - 4 q^{98}+O(q^{100}) \) 56 * q + 12 * q^8 + 28 * q^14 + 12 * q^16 - 8 * q^19 + 4 * q^20 + 10 * q^22 - 34 * q^26 - 14 * q^28 + 30 * q^32 + 56 * q^34 - 28 * q^40 - 40 * q^41 + 44 * q^44 - 18 * q^46 + 24 * q^49 + 72 * q^50 + 32 * q^52 + 54 * q^56 - 16 * q^58 - 32 * q^59 - 48 * q^65 - 24 * q^67 + 26 * q^68 + 64 * q^70 + 44 * q^73 + 6 * q^74 + 6 * q^76 + 4 * q^80 - 30 * q^82 - 40 * q^83 + 28 * q^86 + 126 * q^88 + 68 * q^89 - 72 * q^91 - 52 * q^92 + 34 * q^94 - 4 * q^97 - 4 * q^98

Introduction

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