LMFDB - Embedded newform 819.2.gh.d.262.8

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			262.8
Character	$\chi$	$=$	819.262
Dual form			819.2.gh.d.397.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.449968 + 1.67930i) q^{2} +(-0.885540 + 0.511267i) q^{4} +(0.524353 - 1.95691i) q^{5} +(-0.616155 + 2.57300i) q^{7} +(1.20163 + 1.20163i) q^{8} +O(q^{10})$	\(q+(0.449968 + 1.67930i) q^{2} +(-0.885540 + 0.511267i) q^{4} +(0.524353 - 1.95691i) q^{5} +(-0.616155 + 2.57300i) q^{7} +(1.20163 + 1.20163i) q^{8} +3.52219 q^{10} +(-2.56310 - 2.56310i) q^{11} +(1.78841 + 3.13075i) q^{13} +(-4.59811 + 0.123058i) q^{14} +(-2.49975 + 4.32969i) q^{16} +(0.752896 + 1.30405i) q^{17} +(2.92473 + 2.92473i) q^{19} +(0.536169 + 2.00101i) q^{20} +(3.15091 - 5.45753i) q^{22} +(3.21414 + 1.85568i) q^{23} +(0.775564 + 0.447772i) q^{25} +(-4.45275 + 4.41202i) q^{26} +(-0.769862 - 2.59352i) q^{28} +(1.84505 + 3.19572i) q^{29} +(7.05794 - 1.89117i) q^{31} +(-5.11274 - 1.36995i) q^{32} +(-1.85112 + 1.85112i) q^{34} +(4.71206 + 2.55493i) q^{35} +(-2.52920 + 0.677697i) q^{37} +(-3.59548 + 6.22755i) q^{38} +(2.98158 - 1.72141i) q^{40} +(-1.33248 + 4.97288i) q^{41} +(-4.51217 - 2.60510i) q^{43} +(3.58015 + 0.959299i) q^{44} +(-1.67000 + 6.23251i) q^{46} +(-0.255554 - 0.0684756i) q^{47} +(-6.24071 - 3.17074i) q^{49} +(-0.402966 + 1.50389i) q^{50} +(-3.18436 - 1.85805i) q^{52} +(2.63938 - 4.57154i) q^{53} +(-6.35973 + 3.67179i) q^{55} +(-3.83220 + 2.35142i) q^{56} +(-4.53637 + 4.53637i) q^{58} +(-1.24693 - 0.334114i) q^{59} +10.6182i q^{61} +(6.35170 + 11.0015i) q^{62} +0.796700i q^{64} +(7.06436 - 1.85815i) q^{65} +(9.48626 - 9.48626i) q^{67} +(-1.33344 - 0.769862i) q^{68} +(-2.17022 + 9.06262i) q^{70} +(-3.11400 - 11.6216i) q^{71} +(-0.744113 - 2.77707i) q^{73} +(-2.27612 - 3.94235i) q^{74} +(-4.08528 - 1.09465i) q^{76} +(8.17413 - 5.01560i) q^{77} +(-8.09801 - 14.0262i) q^{79} +(7.16207 + 7.16207i) q^{80} -8.95055 q^{82} +(-10.3721 - 10.3721i) q^{83} +(2.94671 - 0.789567i) q^{85} +(2.34443 - 8.74952i) q^{86} -6.15981i q^{88} +(2.60486 + 9.72147i) q^{89} +(-9.15737 + 2.67257i) q^{91} -3.79500 q^{92} -0.459965i q^{94} +(7.25704 - 4.18985i) q^{95} +(0.645956 - 0.173083i) q^{97} +(2.51652 - 11.9068i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.449968	+	1.67930i	0.318176	+	1.18745i	0.920997	+	0.389571i	$0.127377\pi$
$2$	0.449968	+	1.67930i	0.318176	+	1.18745i	−0.602821	+	0.797876i	$0.705957\pi$
$3$		0			0
$3$		0			0
$4$	−0.885540	+	0.511267i	−0.442770	+	0.255633i
$5$	0.524353	−	1.95691i	0.234498	−	0.875158i	−0.743877	−	0.668317i	$-0.767015\pi$
$5$	0.524353	−	1.95691i	0.234498	−	0.875158i	0.978375	−	0.206841i	$-0.0663183\pi$
$6$		0			0
$7$	−0.616155	+	2.57300i	−0.232885	+	0.972504i
$7$	−0.616155	+	2.57300i	−0.232885	+	0.972504i
$8$	1.20163	+	1.20163i	0.424842	+	0.424842i
$9$		0			0
$10$	3.52219			1.11382
$11$	−2.56310	−	2.56310i	−0.772803	−	0.772803i	0.205793	−	0.978596i	$-0.434023\pi$
$11$	−2.56310	−	2.56310i	−0.772803	−	0.772803i	−0.978596	+	0.205793i	$0.934023\pi$
$12$		0			0
$13$	1.78841	+	3.13075i	0.496016	+	0.868313i
$13$	1.78841	+	3.13075i	0.496016	+	0.868313i
$14$	−4.59811	+	0.123058i	−1.22890	+	0.0328887i
$15$		0			0
$16$	−2.49975	+	4.32969i	−0.624937	+	1.08242i
$17$	0.752896	+	1.30405i	0.182604	+	0.316280i	0.942767	−	0.333453i	$-0.108214\pi$
$17$	0.752896	+	1.30405i	0.182604	+	0.316280i	−0.760162	+	0.649733i	$0.774881\pi$
$18$		0			0
$19$	2.92473	+	2.92473i	0.670979	+	0.670979i	0.957942	−	0.286963i	$-0.0926455\pi$
$19$	2.92473	+	2.92473i	0.670979	+	0.670979i	−0.286963	+	0.957942i	$0.592646\pi$
$20$	0.536169	+	2.00101i	0.119891	+	0.447439i
$21$		0			0
$22$	3.15091	−	5.45753i	0.671776	−	1.16355i
$23$	3.21414	+	1.85568i	0.670194	+	0.386937i	0.796150	−	0.605099i	$-0.206867\pi$
$23$	3.21414	+	1.85568i	0.670194	+	0.386937i	−0.125956	+	0.992036i	$0.540200\pi$
$24$		0			0
$25$	0.775564	+	0.447772i	0.155113	+	0.0895544i
$26$	−4.45275	+	4.41202i	−0.873256	+	0.865269i
$27$		0			0
$28$	−0.769862	−	2.59352i	−0.145490	−	0.490129i
$29$	1.84505	+	3.19572i	0.342617	+	0.593430i	0.984918	−	0.173023i	$-0.0553534\pi$
$29$	1.84505	+	3.19572i	0.342617	+	0.593430i	−0.642301	+	0.766452i	$0.722020\pi$
$30$		0			0
$31$	7.05794	−	1.89117i	1.26764	−	0.339664i	0.438516	−	0.898723i	$-0.355504\pi$
$31$	7.05794	−	1.89117i	1.26764	−	0.339664i	0.829128	+	0.559059i	$0.188838\pi$
$32$	−5.11274	−	1.36995i	−0.903814	−	0.242176i
$33$		0			0
$34$	−1.85112	+	1.85112i	−0.317465	+	0.317465i
$35$	4.71206	+	2.55493i	0.796484	+	0.431861i
$36$		0			0
$37$	−2.52920	+	0.677697i	−0.415798	+	0.111413i	−0.460652	−	0.887581i	$-0.652384\pi$
$37$	−2.52920	+	0.677697i	−0.415798	+	0.111413i	0.0448541	+	0.998994i	$0.485718\pi$
$38$	−3.59548	+	6.22755i	−0.583263	+	1.01024i
$39$		0			0
$40$	2.98158	−	1.72141i	0.471428	−	0.272179i
$41$	−1.33248	+	4.97288i	−0.208098	+	0.776634i	0.780384	+	0.625300i	$0.215023\pi$
$41$	−1.33248	+	4.97288i	−0.208098	+	0.776634i	−0.988483	+	0.151334i	$0.951643\pi$
$42$		0			0
$43$	−4.51217	−	2.60510i	−0.688099	−	0.397274i	0.114800	−	0.993389i	$-0.463377\pi$
$43$	−4.51217	−	2.60510i	−0.688099	−	0.397274i	−0.802900	+	0.596114i	$0.796711\pi$
$44$	3.58015	+	0.959299i	0.539728	+	0.144620i
$45$		0			0
$46$	−1.67000	+	6.23251i	−0.246228	+	0.918934i
$47$	−0.255554	−	0.0684756i	−0.0372764	−	0.00998819i	0.240133	−	0.970740i	$-0.422809\pi$
$47$	−0.255554	−	0.0684756i	−0.0372764	−	0.00998819i	−0.277409	+	0.960752i	$0.589476\pi$
$48$		0			0
$49$	−6.24071	−	3.17074i	−0.891529	−	0.452963i
$50$	−0.402966	+	1.50389i	−0.0569881	+	0.212682i
$51$		0			0
$52$	−3.18436	−	1.85805i	−0.441591	−	0.257665i
$53$	2.63938	−	4.57154i	0.362547	−	0.627949i	−0.625832	−	0.779958i	$-0.715241\pi$
$53$	2.63938	−	4.57154i	0.362547	−	0.627949i	0.988379	+	0.152008i	$0.0485740\pi$
$54$		0			0
$55$	−6.35973	+	3.67179i	−0.857546	+	0.495104i
$56$	−3.83220	+	2.35142i	−0.512100	+	0.314221i
$57$		0			0
$58$	−4.53637	+	4.53637i	−0.595654	+	0.595654i
$59$	−1.24693	−	0.334114i	−0.162337	−	0.0434980i	0.176735	−	0.984258i	$-0.443446\pi$
$59$	−1.24693	−	0.334114i	−0.162337	−	0.0434980i	−0.339072	+	0.940760i	$0.610113\pi$
$60$		0			0
$61$			10.6182i			1.35952i	0.733433	+	0.679762i	$0.237917\pi$
$61$			10.6182i			1.35952i	−0.733433	+	0.679762i	$0.762083\pi$
$62$	6.35170	+	11.0015i	0.806667	+	1.39719i
$63$		0			0
$64$			0.796700i			0.0995875i
$65$	7.06436	−	1.85815i	0.876226	−	0.230475i
$66$		0			0
$67$	9.48626	−	9.48626i	1.15893	−	1.15893i	0.174225	−	0.984706i	$-0.444258\pi$
$67$	9.48626	−	9.48626i	1.15893	−	1.15893i	0.984706	−	0.174225i	$-0.0557421\pi$
$68$	−1.33344	−	0.769862i	−0.161703	−	0.0933595i
$69$		0			0
$70$	−2.17022	+	9.06262i	−0.259391	+	1.08319i
$71$	−3.11400	−	11.6216i	−0.369564	−	1.37923i	−0.861127	−	0.508390i	$-0.830241\pi$
$71$	−3.11400	−	11.6216i	−0.369564	−	1.37923i	0.491562	−	0.870842i	$-0.336426\pi$
$72$		0			0
$73$	−0.744113	−	2.77707i	−0.0870919	−	0.325031i	0.908610	−	0.417645i	$-0.137144\pi$
$73$	−0.744113	−	2.77707i	−0.0870919	−	0.325031i	−0.995702	+	0.0926138i	$0.970478\pi$
$74$	−2.27612	−	3.94235i	−0.264593	−	0.458289i
$75$		0			0
$76$	−4.08528	−	1.09465i	−0.468614	−	0.125565i
$77$	8.17413	−	5.01560i	0.931528	−	0.571580i
$78$		0			0
$79$	−8.09801	−	14.0262i	−0.911098	−	1.57807i	−0.812516	−	0.582939i	$-0.801903\pi$
$79$	−8.09801	−	14.0262i	−0.911098	−	1.57807i	−0.0985815	−	0.995129i	$-0.531431\pi$
$80$	7.16207	+	7.16207i	0.800744	+	0.800744i
$81$		0			0
$82$	−8.95055			−0.988423
$83$	−10.3721	−	10.3721i	−1.13849	−	1.13849i	−0.988722	−	0.149764i	$-0.952149\pi$
$83$	−10.3721	−	10.3721i	−1.13849	−	1.13849i	−0.149764	−	0.988722i	$-0.547851\pi$
$84$		0			0
$85$	2.94671	−	0.789567i	0.319615	−	0.0856406i
$86$	2.34443	−	8.74952i	0.252806	−	0.943485i
$87$		0			0
$88$		−	6.15981i		−	0.656638i
$89$	2.60486	+	9.72147i	0.276115	+	1.03047i	0.955091	+	0.296313i	$0.0957572\pi$
$89$	2.60486	+	9.72147i	0.276115	+	1.03047i	−0.678976	+	0.734160i	$0.737576\pi$
$90$		0			0
$91$	−9.15737	+	2.67257i	−0.959953	+	0.280161i
$92$	−3.79500			−0.395656
$93$		0			0
$94$		−	0.459965i		−	0.0474418i
$95$	7.25704	−	4.18985i	0.744556	−	0.429870i
$96$		0			0
$97$	0.645956	−	0.173083i	0.0655869	−	0.0175739i	−0.225876	−	0.974156i	$-0.572525\pi$
$97$	0.645956	−	0.173083i	0.0655869	−	0.0175739i	0.291463	+	0.956582i	$0.405858\pi$
$98$	2.51652	−	11.9068i	0.254207	−	1.20277i
$99$		0			0
$100$	−0.915724			−0.0915724
$101$	−7.25219			−0.721619			−0.360810	−	0.932639i	$-0.617500\pi$
$101$	−7.25219			−0.721619			−0.360810	+	0.932639i	$0.617500\pi$
$102$		0			0
$103$	−7.23449	−	12.5305i	−0.712835	−	1.23467i	−0.963789	−	0.266667i	$-0.914077\pi$
$103$	−7.23449	−	12.5305i	−0.712835	−	1.23467i	0.250954	−	0.967999i	$-0.419256\pi$
$104$	−1.61300	+	5.91103i	−0.158167	+	0.579624i
$105$		0			0
$106$	8.86465	+	2.37527i	0.861010	+	0.230707i
$107$	−2.94039	+	5.09290i	−0.284258	+	0.492350i	−0.972429	−	0.233199i	$-0.925081\pi$
$107$	−2.94039	+	5.09290i	−0.284258	+	0.492350i	0.688171	+	0.725549i	$0.258414\pi$
$108$		0			0
$109$	−0.133153	−	0.496935i	−0.0127538	−	0.0475977i	0.959256	−	0.282539i	$-0.0911768\pi$
$109$	−0.133153	−	0.496935i	−0.0127538	−	0.0475977i	−0.972009	+	0.234942i	$0.924510\pi$
$110$	−9.02773	−	9.02773i	−0.860760	−	0.860760i
$111$		0			0
$112$	−9.60007	−	9.09962i	−0.907122	−	0.859833i
$113$	−3.88416	+	6.72757i	−0.365391	+	0.632876i	−0.988839	−	0.148989i	$-0.952398\pi$
$113$	−3.88416	+	6.72757i	−0.365391	+	0.632876i	0.623448	+	0.781865i	$0.285731\pi$
$114$		0			0
$115$	5.31675	−	5.31675i	0.495790	−	0.495790i
$116$	−3.26773	−	1.88662i	−0.303401	−	0.175169i
$117$		0			0
$118$		−	2.24432i		−	0.206606i
$119$	−3.81924	+	1.13371i	−0.350109	+	0.103927i
$120$		0			0
$121$			2.13894i			0.194449i
$122$	−17.8312	+	4.77786i	−1.61436	+	0.432567i
$123$		0			0
$124$	−5.28320	+	5.28320i	−0.474445	+	0.474445i
$125$	8.44572	−	8.44572i	0.755408	−	0.755408i
$126$		0			0
$127$	16.4913	−	9.52126i	1.46337	−	0.844875i	0.464201	−	0.885730i	$-0.346341\pi$
$127$	16.4913	−	9.52126i	1.46337	−	0.844875i	0.999165	+	0.0408546i	$0.0130081\pi$
$128$	−11.5634	+	3.09840i	−1.02207	+	0.273862i
$129$		0			0
$130$	6.29914	+	11.0271i	0.552471	+	0.967141i
$131$	−15.7198	+	9.07584i	−1.37345	+	0.792960i	−0.991360	−	0.131167i	$-0.958128\pi$
$131$	−15.7198	+	9.07584i	−1.37345	+	0.792960i	−0.382087	+	0.924127i	$0.624794\pi$
$132$		0			0
$133$	−9.32743	+	5.72326i	−0.808791	+	0.496269i
$134$	20.1988	+	11.6618i	1.74491	+	1.00743i
$135$		0			0
$136$	−0.662291	+	2.47170i	−0.0567910	+	0.211947i
$137$	5.21037	−	19.4454i	0.445152	−	1.66133i	−0.270384	−	0.962753i	$-0.587151\pi$
$137$	5.21037	−	19.4454i	0.445152	−	1.66133i	0.715536	−	0.698576i	$-0.246183\pi$
$138$		0			0
$139$	17.7595	+	10.2535i	1.50634	+	0.869687i	0.999973	+	0.00736980i	$0.00234590\pi$
$139$	17.7595	+	10.2535i	1.50634	+	0.869687i	0.506369	+	0.862317i	$0.330987\pi$
$140$	−5.47897	+	0.146633i	−0.463058	+	0.0123927i
$141$		0			0
$142$	18.1150	−	10.4587i	1.52018	−	0.877676i
$143$	3.44054	−	12.6083i	0.287712	−	1.05436i
$144$		0			0
$145$	7.22120	−	1.93491i	0.599688	−	0.160686i
$146$	4.32872	−	2.49919i	0.358247	−	0.206834i
$147$		0			0
$148$	1.89322	−	1.89322i	0.155622	−	0.155622i
$149$	−8.91258	+	8.91258i	−0.730147	+	0.730147i	−0.970649	−	0.240502i	$-0.922688\pi$
$149$	−8.91258	+	8.91258i	−0.730147	+	0.730147i	0.240502	+	0.970649i	$0.422688\pi$
$150$		0			0
$151$	20.3890	−	5.46323i	1.65924	−	0.444591i	0.697059	−	0.717014i	$-0.254491\pi$
$151$	20.3890	−	5.46323i	1.65924	−	0.444591i	0.962178	+	0.272422i	$0.0878248\pi$
$152$			7.02891i			0.570120i
$153$		0			0
$154$	12.1008	+	11.4700i	0.975111	+	0.924278i
$155$		−	14.8034i		−	1.18904i
$156$		0			0
$157$	−3.20707	−	1.85160i	−0.255952	−	0.147774i	0.366535	−	0.930404i	$-0.380544\pi$
$157$	−3.20707	−	1.85160i	−0.255952	−	0.147774i	−0.622487	+	0.782630i	$0.713877\pi$
$158$	19.9104	−	19.9104i	1.58398	−	1.58398i
$159$		0			0
$160$	−5.36177	+	9.28685i	−0.423885	+	0.734190i
$161$	−6.75509	+	7.12660i	−0.532375	+	0.561655i
$162$		0			0
$163$	−6.98158	−	6.98158i	−0.546839	−	0.546839i	0.378686	−	0.925525i	$-0.376376\pi$
$163$	−6.98158	−	6.98158i	−0.546839	−	0.546839i	−0.925525	+	0.378686i	$0.876376\pi$
$164$	−1.36251	−	5.08494i	−0.106394	−	0.397067i
$165$		0			0
$166$	12.7508	−	22.0850i	0.989653	−	1.71413i
$167$	20.4714	+	5.48528i	1.58412	+	0.424464i	0.940199	−	0.340627i	$-0.110639\pi$
$167$	20.4714	+	5.48528i	1.58412	+	0.424464i	0.643922	+	0.765091i	$0.277306\pi$
$168$		0			0
$169$	−6.60316	+	11.1981i	−0.507936	+	0.861395i
$170$	2.65185	+	4.59313i	0.203387	+	0.352277i
$171$		0			0
$172$	5.32761			0.406226
$173$	13.3105			1.01198			0.505990	−	0.862539i	$-0.331127\pi$
$173$	13.3105			1.01198			0.505990	+	0.862539i	$0.331127\pi$
$174$		0			0
$175$	−1.62999	+	1.71963i	−0.123215	+	0.129992i
$176$	17.5045	−	4.69032i	1.31945	−	0.353546i
$177$		0			0
$178$	−15.1532	+	8.74870i	−1.13578	+	0.655743i
$179$			4.66735i			0.348854i	0.984670	+	0.174427i	$0.0558074\pi$
$179$			4.66735i			0.348854i	−0.984670	+	0.174427i	$0.944193\pi$
$180$		0			0
$181$	−1.72036			−0.127874			−0.0639368	−	0.997954i	$-0.520366\pi$
$181$	−1.72036			−0.127874			−0.0639368	+	0.997954i	$0.520366\pi$
$182$	−8.60858	−	14.1754i	−0.638110	−	1.05075i
$183$		0			0
$184$	1.63237	+	6.09207i	0.120340	+	0.449113i
$185$			5.30478i			0.390015i
$186$		0			0
$187$	1.41267	−	5.27217i	0.103305	−	0.385539i
$188$	0.261313	−	0.0700186i	0.0190582	−	0.00510663i
$189$		0			0
$190$	10.3015	+	10.3015i	0.747347	+	0.747347i
$191$	−9.71661			−0.703069			−0.351535	−	0.936175i	$-0.614340\pi$
$191$	−9.71661			−0.703069			−0.351535	+	0.936175i	$0.614340\pi$
$192$		0			0
$193$	−5.21877	−	5.21877i	−0.375655	−	0.375655i	0.493877	−	0.869532i	$-0.335579\pi$
$193$	−5.21877	−	5.21877i	−0.375655	−	0.375655i	−0.869532	+	0.493877i	$0.835579\pi$
$194$	0.581319	+	1.00687i	0.0417363	+	0.0722894i
$195$		0			0
$196$	7.14749	−	0.382848i	0.510535	−	0.0273463i
$197$	−0.502809	−	0.134727i	−0.0358236	−	0.00959892i	0.240863	−	0.970559i	$-0.422570\pi$
$197$	−0.502809	−	0.134727i	−0.0358236	−	0.00959892i	−0.276686	+	0.960960i	$0.589236\pi$
$198$		0			0
$199$	7.84176	+	13.5823i	0.555887	+	0.962825i	0.997834	+	0.0657837i	$0.0209547\pi$
$199$	7.84176	+	13.5823i	0.555887	+	0.962825i	−0.441947	+	0.897041i	$0.645712\pi$
$200$	0.393886	+	1.47000i	0.0278520	+	0.103945i
$201$		0			0
$202$	−3.26325	−	12.1786i	−0.229602	−	0.856885i
$203$	−9.35943	+	2.77826i	−0.656903	+	0.194996i
$204$		0			0
$205$	9.03281	+	5.21509i	0.630879	+	0.364238i
$206$	17.7872	−	17.7872i	1.23929	−	1.23929i
$207$		0			0
$208$	−18.0257	−	0.0828099i	−1.24986	−	0.00574183i
$209$		−	14.9927i		−	1.03707i
$210$		0			0
$211$	−2.58812	−	4.48276i	−0.178174	−	0.308606i	0.763081	−	0.646302i	$-0.223686\pi$
$211$	−2.58812	−	4.48276i	−0.178174	−	0.308606i	−0.941255	+	0.337697i	$0.890352\pi$
$212$			5.39771i			0.370716i
$213$		0			0
$214$	−9.87562	−	2.64616i	−0.675083	−	0.180888i
$215$	−7.46393	+	7.46393i	−0.509036	+	0.509036i
$216$		0			0
$217$	0.517201	+	19.3254i	0.0351099	+	1.31189i
$218$	0.774590	−	0.447210i	0.0524618	−	0.0302889i
$219$		0			0
$220$	3.75453	−	6.50304i	0.253130	−	0.438435i
$221$	−2.73618	+	4.68932i	−0.184055	+	0.315437i
$222$		0			0
$223$	−3.25346	+	12.1421i	−0.217868	+	0.813093i	0.767270	+	0.641325i	$0.221615\pi$
$223$	−3.25346	+	12.1421i	−0.217868	+	0.813093i	−0.985137	+	0.171769i	$0.945052\pi$
$224$	6.67514	−	12.3110i	0.446002	−	0.822563i
$225$		0			0
$226$	−13.0454	−	3.49550i	−0.867766	−	0.232517i
$227$	1.70352	−	6.35762i	0.113067	−	0.421970i	−0.886068	−	0.463554i	$-0.846574\pi$
$227$	1.70352	−	6.35762i	0.113067	−	0.421970i	0.999135	+	0.0415843i	$0.0132405\pi$
$228$		0			0
$229$	−8.83413	−	2.36710i	−0.583776	−	0.156422i	−0.0451689	−	0.998979i	$-0.514383\pi$
$229$	−8.83413	−	2.36710i	−0.583776	−	0.156422i	−0.538607	+	0.842557i	$0.681049\pi$
$230$	11.3208	+	6.53608i	0.746472	+	0.430976i
$231$		0			0
$232$	−1.62301	+	6.05716i	−0.106556	+	0.397672i
$233$	6.66005	−	3.84518i	0.436315	−	0.251906i	−0.265719	−	0.964051i	$-0.585609\pi$
$233$	6.66005	−	3.84518i	0.436315	−	0.251906i	0.702033	+	0.712144i	$0.252276\pi$
$234$		0			0
$235$	−0.268002	+	0.464192i	−0.0174825	+	0.0302806i
$236$	1.27503	−	0.341643i	0.0829974	−	0.0222391i
$237$		0			0
$238$	−3.62237	−	5.90353i	−0.234804	−	0.382669i
$239$	14.4981	−	14.4981i	0.937806	−	0.937806i	−0.0603699	−	0.998176i	$-0.519228\pi$
$239$	14.4981	−	14.4981i	0.937806	−	0.937806i	0.998176	+	0.0603699i	$0.0192280\pi$
$240$		0			0
$241$	9.63068	+	2.58053i	0.620366	+	0.166227i	0.555294	−	0.831654i	$-0.312606\pi$
$241$	9.63068	+	2.58053i	0.620366	+	0.166227i	0.0650721	+	0.997881i	$0.479272\pi$
$242$	−3.59194	+	0.962456i	−0.230898	+	0.0618690i
$243$		0			0
$244$	−5.42875	−	9.40286i	−0.347540	−	0.601957i
$245$	−9.47720	+	10.5499i	−0.605476	+	0.674010i
$246$		0			0
$247$	−3.92597	+	14.3872i	−0.249804	+	0.915437i
$248$	10.7536	+	6.20857i	0.682852	+	0.394245i
$249$		0			0
$250$	17.9832	+	10.3826i	1.13736	+	0.656655i
$251$	−3.38103	+	5.85611i	−0.213409	+	0.369635i	−0.952779	−	0.303664i	$-0.901790\pi$
$251$	−3.38103	+	5.85611i	−0.213409	+	0.369635i	0.739371	+	0.673299i	$0.235123\pi$
$252$		0			0
$253$	−3.48185	−	12.9944i	−0.218902	−	0.816954i
$254$	23.4096	+	23.4096i	1.46885	+	1.46885i
$255$		0			0
$256$	−9.60961	−	16.6443i	−0.600601	−	1.04027i
$257$	9.65309	−	16.7196i	0.602143	−	1.04294i	−0.390353	−	0.920665i	$-0.627647\pi$
$257$	9.65309	−	16.7196i	0.602143	−	1.04294i	0.992496	−	0.122277i	$-0.0390198\pi$
$258$		0			0
$259$	−0.185338	−	6.92521i	−0.0115163	−	0.430311i
$260$	−5.30577	+	5.25724i	−0.329050	+	0.326040i
$261$		0			0
$262$	−22.3145	−	22.3145i	−1.37860	−	1.37860i
$263$	−28.1759			−1.73740			−0.868701	−	0.495336i	$-0.835045\pi$
$263$	−28.1759			−1.73740			−0.868701	+	0.495336i	$0.835045\pi$
$264$		0			0
$265$	−7.56214	−	7.56214i	−0.464539	−	0.464539i
$266$	−13.8081	−	13.0883i	−0.846631	−	0.802496i
$267$		0			0
$268$	−3.55045	+	13.2505i	−0.216879	+	0.809402i
$269$	−15.1416	+	8.74198i	−0.923197	+	0.533008i	−0.884654	−	0.466249i	$-0.845605\pi$
$269$	−15.1416	+	8.74198i	−0.923197	+	0.533008i	−0.0385436	+	0.999257i	$0.512272\pi$
$270$		0			0
$271$	−2.13748	−	7.97719i	−0.129843	−	0.484580i	0.870123	−	0.492834i	$-0.164039\pi$
$271$	−2.13748	−	7.97719i	−0.129843	−	0.484580i	−0.999966	+	0.00825451i	$0.997372\pi$
$272$	−7.52820			−0.456464
$273$		0			0
$274$	34.9992			2.11438
$275$	−0.840163	−	3.13553i	−0.0506637	−	0.189080i
$276$		0			0
$277$	−17.8724	+	10.3186i	−1.07385	+	0.619987i	−0.929231	−	0.369501i	$-0.879529\pi$
$277$	−17.8724	+	10.3186i	−1.07385	+	0.619987i	−0.144618	+	0.989488i	$0.546195\pi$
$278$	−9.22746	+	34.4373i	−0.553426	+	2.06541i
$279$		0			0
$280$	2.59209	+	8.73226i	0.154907	+	0.521853i
$281$	−3.70317	−	3.70317i	−0.220913	−	0.220913i	0.587970	−	0.808883i	$-0.299927\pi$
$281$	−3.70317	−	3.70317i	−0.220913	−	0.220913i	−0.808883	+	0.587970i	$0.799927\pi$
$282$		0			0
$283$	0.843947			0.0501674			0.0250837	−	0.999685i	$-0.492015\pi$
$283$	0.843947			0.0501674			0.0250837	+	0.999685i	$0.492015\pi$
$284$	8.69933	+	8.69933i	0.516210	+	0.516210i
$285$		0			0
$286$	22.7213	+	0.104381i	1.34354	+	0.00617219i
$287$	−11.9742	−	6.49254i	−0.706817	−	0.383243i
$288$		0			0
$289$	7.36629	−	12.7588i	0.433311	−	0.750517i
$290$	6.49862	+	11.2559i	0.381612	+	0.660971i
$291$		0			0
$292$	2.07877	+	2.07877i	0.121651	+	0.121651i
$293$	−4.34707	−	16.2235i	−0.253959	−	0.947787i	−0.968667	−	0.248364i	$-0.920107\pi$
$293$	−4.34707	−	16.2235i	−0.253959	−	0.947787i	0.714708	−	0.699423i	$-0.246560\pi$
$294$		0			0
$295$	−1.30767	+	2.26494i	−0.0761352	+	0.131870i
$296$	−3.85352	−	2.22483i	−0.223981	−	0.129316i
$297$		0			0
$298$	−18.9773	−	10.9566i	−1.09933	−	0.634696i
$299$	−0.0614738	+	13.3814i	−0.00355512	+	0.773865i
$300$		0			0
$301$	9.48314	−	10.0047i	0.546599	−	0.576660i
$302$	18.3488	+	31.7811i	1.05586	+	1.82880i
$303$		0			0
$304$	−19.9743	+	5.35208i	−1.14560	+	0.306963i
$305$	20.7789	+	5.56770i	1.18980	+	0.318806i
$306$		0			0
$307$	19.8317	−	19.8317i	1.13185	−	1.13185i	0.141986	−	0.989869i	$-0.454651\pi$
$307$	19.8317	−	19.8317i	1.13185	−	1.13185i	0.989869	−	0.141986i	$-0.0453488\pi$
$308$	−4.67421	+	8.62067i	−0.266338	+	0.491208i
$309$		0			0
$310$	24.8594	−	6.66107i	1.41192	−	0.378323i
$311$	11.9512	−	20.7001i	0.677690	−	1.17379i	−0.297985	−	0.954571i	$-0.596314\pi$
$311$	11.9512	−	20.7001i	0.677690	−	1.17379i	0.975675	−	0.219223i	$-0.0703522\pi$
$312$		0			0
$313$	−21.1920	+	12.2352i	−1.19784	+	0.691576i	−0.960074	−	0.279746i	$-0.909750\pi$
$313$	−21.1920	+	12.2352i	−1.19784	+	0.691576i	−0.237770	+	0.971321i	$0.576417\pi$
$314$	1.66632	−	6.21881i	0.0940361	−	0.350948i
$315$		0			0
$316$	14.3422	+	8.28049i	0.806814	+	0.465814i
$317$	24.0424	+	6.44215i	1.35036	+	0.361827i	0.860267	−	0.509844i	$-0.170297\pi$
$317$	24.0424	+	6.44215i	1.35036	+	0.361827i	0.490091	+	0.871671i	$0.336963\pi$
$318$		0			0
$319$	3.46190	−	12.9200i	0.193829	−	0.723380i
$320$	1.55907	+	0.417752i	0.0871548	+	0.0233531i
$321$		0			0
$322$	−15.0073	−	8.13710i	−0.836324	−	0.453463i
$323$	−1.61199	+	6.01603i	−0.0896935	+	0.334741i
$324$		0			0
$325$	−0.0148335	+	3.22890i	−0.000822814	+	0.179107i
$326$	8.58270	−	14.8657i	0.475352	−	0.823334i
$327$		0			0
$328$	−7.57674	+	4.37443i	−0.418355	+	0.241538i
$329$	0.333649	−	0.615351i	0.0183947	−	0.0339254i
$330$		0			0
$331$	3.49185	−	3.49185i	0.191930	−	0.191930i	−0.604600	−	0.796529i	$-0.706667\pi$
$331$	3.49185	−	3.49185i	0.191930	−	0.191930i	0.796529	+	0.604600i	$0.206667\pi$
$332$	14.4878	+	3.88200i	0.795122	+	0.213052i
$333$		0			0
$334$			36.8458i			2.01611i
$335$	−13.5896	−	23.5379i	−0.742481	−	1.28602i
$336$		0			0
$337$			4.37276i			0.238200i	0.992882	+	0.119100i	$0.0380009\pi$
$337$			4.37276i			0.238200i	−0.992882	+	0.119100i	$0.961999\pi$
$338$	−21.7763	−	6.04992i	−1.18447	−	0.329072i
$339$		0			0
$340$	−2.20575	+	2.20575i	−0.119623	+	0.119623i
$341$	−22.9375	−	13.2429i	−1.24213	−	0.717146i
$342$		0			0
$343$	12.0036	−	14.1037i	0.648132	−	0.761528i
$344$	−2.29160	−	8.55236i	−0.123555	−	0.461112i
$345$		0			0
$346$	5.98931	+	22.3524i	0.321987	+	1.20167i
$347$	13.6420	+	23.6286i	0.732338	+	1.26845i	0.955881	+	0.293753i	$0.0949044\pi$
$347$	13.6420	+	23.6286i	0.732338	+	1.26845i	−0.223543	+	0.974694i	$0.571762\pi$
$348$		0			0
$349$	4.48654	+	1.20217i	0.240159	+	0.0643505i	0.376891	−	0.926258i	$-0.376993\pi$
$349$	4.48654	+	1.20217i	0.240159	+	0.0643505i	−0.136732	+	0.990608i	$0.543660\pi$
$350$	−3.62123	−	1.96346i	−0.193563	−	0.104952i
$351$		0			0
$352$	9.59313	+	16.6158i	0.511315	+	0.885624i
$353$	2.96642	+	2.96642i	0.157886	+	0.157886i	0.781629	−	0.623743i	$-0.214389\pi$
$353$	2.96642	+	2.96642i	0.157886	+	0.157886i	−0.623743	+	0.781629i	$0.714389\pi$
$354$		0			0
$355$	−24.3753			−1.29371
$356$	−7.27697	−	7.27697i	−0.385679	−	0.385679i
$357$		0			0
$358$	−7.83790	+	2.10016i	−0.414246	+	0.110997i
$359$	1.84503	−	6.88575i	0.0973770	−	0.363416i	−0.899992	−	0.435906i	$-0.856428\pi$
$359$	1.84503	−	6.88575i	0.0973770	−	0.363416i	0.997369	+	0.0724902i	$0.0230946\pi$
$360$		0			0
$361$		−	1.89190i		−	0.0995738i
$362$	−0.774109	−	2.88901i	−0.0406862	−	0.151843i
$363$		0			0
$364$	6.74282	−	7.04852i	0.353420	−	0.369443i
$365$	−5.82466			−0.304877
$366$		0			0
$367$			3.11291i			0.162492i	0.996694	+	0.0812462i	$0.0258900\pi$
$367$			3.11291i			0.162492i	−0.996694	+	0.0812462i	$0.974110\pi$
$368$	−16.0691	+	9.27747i	−0.837657	+	0.483622i
$369$		0			0
$370$	−8.90833	+	2.38698i	−0.463122	+	0.124093i
$371$	10.1363	+	9.60792i	0.526252	+	0.498818i
$372$		0			0
$373$	12.2136			0.632395			0.316197	−	0.948693i	$-0.397594\pi$
$373$	12.2136			0.632395			0.316197	+	0.948693i	$0.397594\pi$
$374$	9.48923			0.490676
$375$		0			0
$376$	−0.224800	−	0.389366i	−0.0115932	−	0.0200800i
$377$	−6.70528	+	11.4916i	−0.345339	+	0.591849i
$378$		0			0
$379$	−24.7492	−	6.63154i	−1.27128	−	0.340639i	−0.440760	−	0.897625i	$-0.645291\pi$
$379$	−24.7492	−	6.63154i	−1.27128	−	0.340639i	−0.830522	+	0.556986i	$0.811958\pi$
$380$	−4.28426	+	7.42056i	−0.219778	+	0.380667i
$381$		0			0
$382$	−4.37217	−	16.3171i	−0.223699	−	0.834858i
$383$	−25.5467	−	25.5467i	−1.30538	−	1.30538i	−0.924714	−	0.380664i	$-0.875696\pi$
$383$	−25.5467	−	25.5467i	−1.30538	−	1.30538i	−0.380664	−	0.924714i	$-0.624304\pi$
$384$		0			0
$385$	−5.52896	−	18.6260i	−0.281782	−	0.949269i
$386$	6.41562	−	11.1122i	0.326547	−	0.565595i
$387$		0			0
$388$	−0.483528	+	0.483528i	−0.0245474	+	0.0245474i
$389$	10.5275	+	6.07805i	0.533765	+	0.308170i	0.742548	−	0.669792i	$-0.233617\pi$
$389$	10.5275	+	6.07805i	0.533765	+	0.308170i	−0.208783	+	0.977962i	$0.566950\pi$
$390$		0			0
$391$			5.58855i			0.282625i
$392$	−3.68898	−	11.3091i	−0.186321	−	0.571197i
$393$		0			0
$394$		−	0.904992i		−	0.0455928i
$395$	−31.6942	+	8.49244i	−1.59471	+	0.427301i
$396$		0			0
$397$	−10.5534	+	10.5534i	−0.529660	+	0.529660i	−0.920471	−	0.390811i	$-0.872195\pi$
$397$	−10.5534	+	10.5534i	−0.529660	+	0.529660i	0.390811	+	0.920471i	$0.372195\pi$
$398$	−19.2803	+	19.2803i	−0.966434	+	0.966434i
$399$		0			0
$400$	−3.87743	+	2.23863i	−0.193871	+	0.111932i
$401$	4.31771	−	1.15693i	0.215616	−	0.0577741i	−0.149394	−	0.988778i	$-0.547732\pi$
$401$	4.31771	−	1.15693i	0.215616	−	0.0577741i	0.365010	+	0.931004i	$0.381066\pi$
$402$		0			0
$403$	18.5433	+	18.7144i	0.923707	+	0.932233i
$404$	6.42210	−	3.70780i	0.319512	−	0.184470i
$405$		0			0
$406$	−8.87699	−	14.4672i	−0.440558	−	0.717995i
$407$	8.21959	+	4.74558i	0.407430	+	0.235230i
$408$		0			0
$409$	−0.143340	+	0.534951i	−0.00708769	+	0.0264516i	−0.969379	−	0.245569i	$-0.921025\pi$
$409$	−0.143340	+	0.534951i	−0.00708769	+	0.0264516i	0.962291	+	0.272021i	$0.0876919\pi$
$410$	−4.69325	+	17.5155i	−0.231783	+	0.865027i
$411$		0			0
$412$	12.8129	+	7.39751i	0.631244	+	0.364449i
$413$	1.62798	−	3.00249i	0.0801077	−	0.147743i
$414$		0			0
$415$	−25.7359	+	14.8587i	−1.26333	+	0.729383i
$416$	−4.85471	−	18.4567i	−0.238022	−	0.904917i
$417$		0			0
$418$	25.1774	−	6.74626i	1.23147	−	0.329970i
$419$	−20.1383	+	11.6268i	−0.983819	+	0.568008i	−0.903421	−	0.428754i	$-0.858953\pi$
$419$	−20.1383	+	11.6268i	−0.983819	+	0.568008i	−0.0803983	+	0.996763i	$0.525619\pi$
$420$		0			0
$421$	−19.0536	+	19.0536i	−0.928614	+	0.928614i	−0.997617	−	0.0690021i	$-0.978018\pi$
$421$	−19.0536	+	19.0536i	−0.928614	+	0.928614i	0.0690021	+	0.997617i	$0.478018\pi$
$422$	6.36334	−	6.36334i	0.309763	−	0.309763i
$423$		0			0
$424$	8.66489	−	2.32175i	0.420804	−	0.112754i
$425$			1.34850i			0.0654121i
$426$		0			0
$427$	−27.3207	−	6.54247i	−1.32214	−	0.316612i
$428$		−	6.01330i		−	0.290664i
$429$		0			0
$430$	−15.8927	−	9.17568i	−0.766416	−	0.442490i
$431$	14.4777	−	14.4777i	0.697365	−	0.697365i	−0.266476	−	0.963842i	$-0.585859\pi$
$431$	14.4777	−	14.4777i	0.697365	−	0.697365i	0.963842	+	0.266476i	$0.0858593\pi$
$432$		0			0
$433$	13.7982	−	23.8993i	0.663101	−	1.14852i	−0.316695	−	0.948527i	$-0.602573\pi$
$433$	13.7982	−	23.8993i	0.663101	−	1.14852i	0.979796	−	0.199997i	$-0.0640934\pi$
$434$	−32.2205	+	9.56434i	−1.54663	+	0.459103i
$435$		0			0
$436$	0.371979	+	0.371979i	0.0178146	+	0.0178146i
$437$	3.97311	+	14.8279i	0.190060	+	0.709313i
$438$		0			0
$439$	−9.02753	+	15.6361i	−0.430860	+	0.746272i	−0.996948	−	0.0780733i	$-0.975123\pi$
$439$	−9.02753	+	15.6361i	−0.430860	+	0.746272i	0.566087	+	0.824345i	$0.308456\pi$
$440$	−12.0542	−	3.22992i	−0.574662	−	0.153980i
$441$		0			0
$442$	−9.10598	−	2.48483i	−0.433127	−	0.118191i
$443$	19.5401	+	33.8445i	0.928380	+	1.60800i	0.786033	+	0.618185i	$0.212132\pi$
$443$	19.5401	+	33.8445i	0.928380	+	1.60800i	0.142348	+	0.989817i	$0.454535\pi$
$444$		0			0
$445$	20.3899			0.966576
$446$	−21.8542			−1.03483
$447$		0			0
$448$	−2.04991	−	0.490891i	−0.0968493	−	0.0231924i
$449$	−21.8252	+	5.84805i	−1.03000	+	0.275987i	−0.733962	−	0.679191i	$-0.762331\pi$
$449$	−21.8252	+	5.84805i	−1.03000	+	0.275987i	−0.296034	+	0.955177i	$0.595664\pi$
$450$		0			0
$451$	16.1613	−	9.33071i	0.761004	−	0.439366i
$452$		−	7.94338i		−	0.373625i
$453$		0			0
$454$	11.4429			0.537042
$455$	0.428283	+	19.3215i	0.0200782	+	0.905808i
$456$		0			0
$457$	5.08518	+	18.9781i	0.237875	+	0.887760i	0.976832	+	0.214008i	$0.0686519\pi$
$457$	5.08518	+	18.9781i	0.237875	+	0.887760i	−0.738957	+	0.673752i	$0.764681\pi$
$458$		−	15.9003i		−	0.742973i
$459$		0			0
$460$	−1.98992	+	7.42648i	−0.0927804	+	0.346261i
$461$	14.3331	−	3.84054i	0.667559	−	0.178872i	0.0909042	−	0.995860i	$-0.471024\pi$
$461$	14.3331	−	3.84054i	0.667559	−	0.178872i	0.576655	+	0.816988i	$0.304358\pi$
$462$		0			0
$463$	−21.6764	−	21.6764i	−1.00739	−	1.00739i	−0.999972	−	0.00741751i	$-0.997639\pi$
$463$	−21.6764	−	21.6764i	−1.00739	−	1.00739i	−0.00741751	−	0.999972i	$-0.502361\pi$
$464$	−18.4486			−0.856455
$465$		0			0
$466$	9.45404	+	9.45404i	0.437950	+	0.437950i
$467$	−10.6105	−	18.3780i	−0.490996	−	0.850431i	0.508950	−	0.860796i	$-0.330034\pi$
$467$	−10.6105	−	18.3780i	−0.490996	−	0.850431i	−0.999946	+	0.0103654i	$0.996701\pi$
$468$		0			0
$469$	18.5632	+	30.2532i	0.857168	+	1.39696i
$470$	−0.900112	−	0.241184i	−0.0415191	−	0.0111250i
$471$		0			0
$472$	−1.09687	−	1.89984i	−0.0504877	−	0.0874472i
$473$	4.88800	+	18.2423i	0.224750	+	0.838780i
$474$		0			0
$475$	0.958703	+	3.57793i	0.0439883	+	0.164167i
$476$	2.80246	−	2.95659i	0.128451	−	0.135515i
$477$		0			0
$478$	30.8705	+	17.8231i	1.41198	+	0.815208i
$479$	−7.56345	+	7.56345i	−0.345583	+	0.345583i	−0.858461	−	0.512878i	$-0.828579\pi$
$479$	−7.56345	+	7.56345i	−0.345583	+	0.345583i	0.512878	+	0.858461i	$0.328579\pi$
$480$		0			0
$481$	−6.64495	−	6.70628i	−0.302984	−	0.305780i
$482$			17.3340i			0.789542i
$483$		0			0
$484$	−1.09357	−	1.89412i	−0.0497078	−	0.0860964i
$485$		−	1.35484i		−	0.0615199i
$486$		0			0
$487$	−30.8488	−	8.26590i	−1.39789	−	0.374564i	−0.520304	−	0.853981i	$-0.674181\pi$
$487$	−30.8488	−	8.26590i	−1.39789	−	0.374564i	−0.877587	+	0.479417i	$0.840848\pi$
$488$	−12.7592	+	12.7592i	−0.577583	+	0.577583i
$489$		0			0
$490$	−21.9810	−	11.1680i	−0.992999	−	0.504517i
$491$	−7.33827	+	4.23675i	−0.331171	+	0.191202i	−0.656361	−	0.754447i	$-0.727905\pi$
$491$	−7.33827	+	4.23675i	−0.331171	+	0.191202i	0.325190	+	0.945649i	$0.394572\pi$
$492$		0			0
$493$	−2.77826	+	4.81209i	−0.125127	+	0.216725i
$494$	−25.9271	−	0.119109i	−1.16651	−	0.00535895i
$495$		0			0
$496$	−9.45489	+	35.2861i	−0.424537	+	1.58439i
$497$	31.8212	−	0.851625i	1.42738	−	0.0382006i
$498$		0			0
$499$	−24.4581	−	6.55352i	−1.09489	−	0.293376i	−0.334210	−	0.942499i	$-0.608469\pi$
$499$	−24.4581	−	6.55352i	−1.09489	−	0.293376i	−0.760684	+	0.649123i	$0.775136\pi$
$500$	−3.16101	+	11.7970i	−0.141365	+	0.527580i
$501$		0			0
$502$	−11.3555	−	3.04271i	−0.506823	−	0.135803i
$503$	−5.83735	−	3.37020i	−0.260275	−	0.150270i	0.364185	−	0.931327i	$-0.381348\pi$
$503$	−5.83735	−	3.37020i	−0.260275	−	0.150270i	−0.624460	+	0.781057i	$0.714681\pi$
$504$		0			0
$505$	−3.80271	+	14.1919i	−0.169218	+	0.631531i
$506$	20.2549	−	11.6942i	0.900440	−	0.519869i
$507$		0			0
$508$	−9.73581	+	16.8629i	−0.431957	+	0.748171i
$509$	2.97301	−	0.796615i	0.131776	−	0.0353094i	−0.192328	−	0.981331i	$-0.561604\pi$
$509$	2.97301	−	0.796615i	0.131776	−	0.0353094i	0.324104	+	0.946021i	$0.394937\pi$
$510$		0			0
$511$	7.60390	−	0.203502i	0.336377	−	0.00900239i
$512$	6.69691	−	6.69691i	0.295964	−	0.295964i
$513$		0			0
$514$	32.4210	+	8.68717i	1.43003	+	0.383175i
$515$	−28.3145	+	7.58685i	−1.24769	+	0.334317i
$516$		0			0
$517$	0.479501	+	0.830521i	0.0210884	+	0.0365263i
$518$	11.5461	−	3.42736i	0.507308	−	0.150590i
$519$		0			0
$520$	10.7216	+	6.25596i	0.470173	+	0.274342i
$521$	22.0369	+	12.7230i	0.965453	+	0.557405i	0.897847	−	0.440308i	$-0.145131\pi$
$521$	22.0369	+	12.7230i	0.965453	+	0.557405i	0.0676060	+	0.997712i	$0.478464\pi$
$522$		0			0
$523$	12.9246	+	7.46200i	0.565151	+	0.326290i	0.755211	−	0.655482i	$-0.227535\pi$
$523$	12.9246	+	7.46200i	0.565151	+	0.326290i	−0.190059	+	0.981773i	$0.560868\pi$
$524$	9.28035	−	16.0740i	0.405414	−	0.702198i
$525$		0			0
$526$	−12.6783	−	47.3160i	−0.552799	−	2.06307i
$527$	7.78009	+	7.78009i	0.338906	+	0.338906i
$528$		0			0
$529$	−4.61288	−	7.98975i	−0.200560	−	0.347380i
$530$	9.29641	−	16.1019i	0.403810	−	0.699420i
$531$		0			0
$532$	5.33370	−	9.83698i	0.231245	−	0.426487i
$533$	−17.9519	+	4.72190i	−0.777581	+	0.204528i
$534$		0			0
$535$	8.42457	+	8.42457i	0.364226	+	0.364226i
$536$	22.7980			0.984725
$537$		0			0
$538$	−21.4937	−	21.4937i	−0.926658	−	0.926658i
$539$	7.86862	+	24.1225i	0.338926	+	1.03903i
$540$		0			0
$541$	2.99446	−	11.1755i	0.128742	−	0.480471i	−0.871204	−	0.490922i	$-0.836660\pi$
$541$	2.99446	−	11.1755i	0.128742	−	0.480471i	0.999945	+	0.0104509i	$0.00332668\pi$
$542$	12.4343	−	7.17896i	0.534100	−	0.308363i
$543$		0			0
$544$	−2.06287	−	7.69873i	−0.0884447	−	0.330080i
$545$	−1.04228			−0.0446463
$546$		0			0
$547$	−1.37820			−0.0589275			−0.0294637	−	0.999566i	$-0.509380\pi$
$547$	−1.37820			−0.0589275			−0.0294637	+	0.999566i	$0.509380\pi$
$548$	5.32778	+	19.8835i	0.227591	+	0.849382i
$549$		0			0
$550$	4.88746	−	2.82178i	0.208402	−	0.120321i
$551$	−3.95034	+	14.7429i	−0.168290	+	0.628068i
$552$		0			0
$553$	41.0790	−	12.1939i	1.74686	−	0.518539i
$554$	−25.3701	−	25.3701i	−1.07787	−	1.07787i
$555$		0			0
$556$	−20.9690			−0.889284
$557$	−20.8703	−	20.8703i	−0.884303	−	0.884303i	0.109666	−	0.993969i	$-0.465022\pi$
$557$	−20.8703	−	20.8703i	−0.884303	−	0.884303i	−0.993969	+	0.109666i	$0.965022\pi$
$558$		0			0
$559$	0.0863000	−	18.7855i	0.00365010	−	0.794540i
$560$	−22.8410	+	14.0151i	−0.965208	+	0.592246i
$561$		0			0
$562$	4.55244	−	7.88506i	0.192033	−	0.332611i
$563$	17.4133	+	30.1607i	0.733882	+	1.27112i	0.955212	+	0.295922i	$0.0956270\pi$
$563$	17.4133	+	30.1607i	0.733882	+	1.27112i	−0.221330	+	0.975199i	$0.571040\pi$
$564$		0			0
$565$	11.1286	+	11.1286i	0.468183	+	0.468183i
$566$	0.379749	+	1.41724i	0.0159620	+	0.0595712i
$567$		0			0
$568$	10.2230	−	17.7068i	0.428949	−	0.742962i
$569$	33.8192	+	19.5255i	1.41777	+	0.818553i	0.996103	−	0.0881961i	$-0.0281102\pi$
$569$	33.8192	+	19.5255i	1.41777	+	0.818553i	0.421672	+	0.906749i	$0.361444\pi$
$570$		0			0
$571$	−10.3165	−	5.95625i	−0.431733	−	0.249261i	0.268351	−	0.963321i	$-0.413521\pi$
$571$	−10.3165	−	5.95625i	−0.431733	−	0.249261i	−0.700085	+	0.714060i	$0.746854\pi$
$572$	3.39947	+	12.9242i	0.142139	+	0.540387i
$573$		0			0
$574$	5.51493	−	23.0298i	0.230189	−	0.961246i
$575$	1.66185	+	2.87840i	0.0693038	+	0.120038i
$576$		0			0
$577$	24.4431	−	6.54951i	1.01758	−	0.272660i	0.288787	−	0.957393i	$-0.406748\pi$
$577$	24.4431	−	6.54951i	1.01758	−	0.272660i	0.728793	+	0.684734i	$0.240082\pi$
$578$	24.7405	+	6.62920i	1.02907	+	0.275738i
$579$		0			0
$580$	−5.40540	+	5.40540i	−0.224447	+	0.224447i
$581$	33.0783	−	20.2966i	1.37232	−	0.842046i
$582$		0			0
$583$	−18.4823	+	4.95232i	−0.765459	+	0.205104i
$584$	2.44287	−	4.23117i	0.101087	−	0.175087i
$585$		0			0
$586$	25.2881	−	14.6001i	1.04464	−	0.603125i
$587$	−0.718902	+	2.68298i	−0.0296723	+	0.110738i	−0.979174	−	0.203024i	$-0.934923\pi$
$587$	−0.718902	+	2.68298i	−0.0296723	+	0.110738i	0.949501	+	0.313763i	$0.101590\pi$
$588$		0			0
$589$	26.1737	+	15.1114i	1.07847	+	0.622655i
$590$	−4.39194	−	1.17682i	−0.180813	−	0.0484487i
$591$		0			0
$592$	3.38814	−	12.6447i	0.139252	−	0.519694i
$593$	25.9060	+	6.94149i	1.06383	+	0.285053i	0.747956	−	0.663748i	$-0.231035\pi$
$593$	25.9060	+	6.94149i	1.06383	+	0.285053i	0.315875	+	0.948801i	$0.397702\pi$
$594$		0			0
$595$	0.215933	+	8.06838i	0.00885238	+	0.330771i
$596$	3.33574	−	12.4492i	0.136637	−	0.509937i
$597$		0			0
$598$	−22.4991	+	5.91796i	−0.920055	+	0.242003i
$599$	12.6948	−	21.9880i	0.518695	−	0.898407i	−0.481069	−	0.876683i	$-0.659751\pi$
$599$	12.6948	−	21.9880i	0.518695	−	0.898407i	0.999764	−	0.0217238i	$-0.00691543\pi$
$600$		0			0
$601$	−27.2508	+	15.7333i	−1.11158	+	0.641774i	−0.939239	−	0.343263i	$-0.888468\pi$
$601$	−27.2508	+	15.7333i	−1.11158	+	0.641774i	−0.172345	+	0.985037i	$0.555134\pi$
$602$	21.0680	+	11.4233i	0.858668	+	0.465578i
$603$		0			0
$604$	−15.2622	+	15.2622i	−0.621008	+	0.621008i
$605$	4.18573	+	1.12156i	0.170174	+	0.0455980i
$606$		0			0
$607$			33.5338i			1.36110i	0.732704	+	0.680548i	$0.238258\pi$
$607$			33.5338i			1.36110i	−0.732704	+	0.680548i	$0.761742\pi$
$608$	−10.9466	−	18.9601i	−0.443945	−	0.768935i
$609$		0			0
$610$			37.3995i			1.51426i
$611$	−0.242657	−	0.922539i	−0.00981684	−	0.0373219i
$612$		0			0
$613$	22.6604	−	22.6604i	0.915245	−	0.915245i	−0.0814340	−	0.996679i	$-0.525950\pi$
$613$	22.6604	−	22.6604i	0.915245	−	0.915245i	0.996679	+	0.0814340i	$0.0259500\pi$
$614$	42.2271	+	24.3798i	1.70415	+	0.983889i
$615$		0			0
$616$	15.8492	+	3.79540i	0.638584	+	0.152921i
$617$	−1.63790	−	6.11271i	−0.0659392	−	0.246088i	0.925087	−	0.379755i	$-0.123992\pi$
$617$	−1.63790	−	6.11271i	−0.0659392	−	0.246088i	−0.991026	+	0.133666i	$0.957325\pi$
$618$		0			0
$619$	5.22223	+	19.4896i	0.209899	+	0.783355i	0.987900	+	0.155092i	$0.0495673\pi$
$619$	5.22223	+	19.4896i	0.209899	+	0.783355i	−0.778001	+	0.628263i	$0.783766\pi$
$620$	7.56850	+	13.1090i	0.303958	+	0.526471i
$621$		0			0
$622$	40.1394	+	10.7553i	1.60944	+	0.431249i
$623$	−26.6184	+	0.712383i	−1.06644	+	0.0285410i
$624$		0			0
$625$	−9.86014	−	17.0783i	−0.394406	−	0.683130i
$626$	−30.0824	−	30.0824i	−1.20233	−	1.20233i
$627$		0			0
$628$	3.78665			0.151104
$629$	−2.78798	−	2.78798i	−0.111164	−	0.111164i
$630$		0			0
$631$	−38.8147	+	10.4004i	−1.54519	+	0.414032i	−0.927938	−	0.372735i	$-0.878420\pi$
$631$	−38.8147	+	10.4004i	−1.54519	+	0.414032i	−0.617250	+	0.786767i	$0.711753\pi$
$632$	7.12348	−	26.5852i	0.283357	−	1.05750i
$633$		0			0
$634$			43.2733i			1.71860i
$635$	−9.98501	−	37.2646i	−0.396243	−	1.47880i
$636$		0			0
$637$	−1.23417	−	25.2087i	−0.0488994	−	0.998804i
$638$	23.2543			0.920647
$639$		0			0
$640$			24.2532i			0.958692i
$641$	4.88340	−	2.81943i	0.192883	−	0.111361i	−0.400449	−	0.916319i	$-0.631146\pi$
$641$	4.88340	−	2.81943i	0.192883	−	0.111361i	0.593331	+	0.804958i	$0.297812\pi$
$642$		0			0
$643$	−6.33945	+	1.69865i	−0.250003	+	0.0669882i	−0.381644	−	0.924309i	$-0.624642\pi$
$643$	−6.33945	+	1.69865i	−0.250003	+	0.0669882i	0.131641	+	0.991297i	$0.457975\pi$
$644$	2.33831	−	9.76454i	0.0921422	−	0.384777i
$645$		0			0
$646$	−10.8281			−0.426025
$647$	35.2920			1.38747			0.693736	−	0.720229i	$-0.255963\pi$
$647$	35.2920			1.38747			0.693736	+	0.720229i	$0.255963\pi$
$648$		0			0
$649$	2.33964	+	4.05238i	0.0918389	+	0.159070i
$650$	−5.42897	+	1.42799i	−0.212942	+	0.0560104i
$651$		0			0
$652$	9.75192	+	2.61302i	0.381914	+	0.102334i
$653$	−25.2072	+	43.6601i	−0.986433	+	1.70855i	−0.351044	+	0.936359i	$0.614173\pi$
$653$	−25.2072	+	43.6601i	−0.986433	+	1.70855i	−0.635389	+	0.772192i	$0.719160\pi$
$654$		0			0
$655$	9.51789	+	35.5213i	0.371895	+	1.38793i
$656$	−18.2002	−	18.2002i	−0.710597	−	0.710597i
$657$		0			0
$658$	1.18349	+	0.283410i	0.0461374	+	0.0110485i
$659$	−3.05790	+	5.29643i	−0.119119	+	0.206320i	−0.919419	−	0.393280i	$-0.871340\pi$
$659$	−3.05790	+	5.29643i	−0.119119	+	0.206320i	0.800300	+	0.599600i	$0.204674\pi$
$660$		0			0
$661$	−3.88313	+	3.88313i	−0.151036	+	0.151036i	−0.778581	−	0.627544i	$-0.784060\pi$
$661$	−3.88313	+	3.88313i	−0.151036	+	0.151036i	0.627544	+	0.778581i	$0.284060\pi$
$662$	7.43510	+	4.29266i	0.288974	+	0.166839i
$663$		0			0
$664$		−	24.9269i		−	0.967353i
$665$	6.30905	+	21.2540i	0.244654	+	0.824194i
$666$		0			0
$667$			13.6953i			0.530284i
$668$	−20.9326	+	5.60889i	−0.809908	+	0.217014i
$669$		0			0
$670$	33.4125	−	33.4125i	1.29084	−	1.29084i
$671$	27.2155	−	27.2155i	1.05064	−	1.05064i
$672$		0			0
$673$	19.0175	−	10.9798i	0.733073	−	0.423240i	−0.0864726	−	0.996254i	$-0.527560\pi$
$673$	19.0175	−	10.9798i	0.733073	−	0.423240i	0.819545	+	0.573015i	$0.194226\pi$
$674$	−7.34320	+	1.96760i	−0.282850	+	0.0757893i
$675$		0			0
$676$	0.122132	−	13.2924i	0.00469740	−	0.511245i
$677$	−6.64801	+	3.83823i	−0.255504	+	0.147515i	−0.622282	−	0.782793i	$-0.713794\pi$
$677$	−6.64801	+	3.83823i	−0.255504	+	0.147515i	0.366778	+	0.930308i	$0.380461\pi$
$678$		0			0
$679$	0.0473352	+	1.76869i	0.00181656	+	0.0678762i
$680$	4.48963	+	2.59209i	0.172170	+	0.0994022i
$681$		0			0
$682$	11.9178	−	44.4779i	0.456356	−	1.70315i
$683$	4.84748	−	18.0911i	0.185484	−	0.692235i	−0.809043	−	0.587750i	$-0.800014\pi$
$683$	4.84748	−	18.0911i	0.185484	−	0.692235i	0.994526	−	0.104485i	$-0.0333195\pi$
$684$		0			0
$685$	−35.3208	−	20.3925i	−1.34954	−	0.779156i
$686$	29.0856	+	13.8114i	1.11049	+	0.527323i
$687$		0			0
$688$	22.5586	−	13.0242i	0.860037	−	0.496542i
$689$	19.0326	+	0.0874356i	0.725086	+	0.00333103i
$690$		0			0
$691$	21.9854	−	5.89097i	0.836364	−	0.224103i	0.184876	−	0.982762i	$-0.440812\pi$
$691$	21.9854	−	5.89097i	0.836364	−	0.224103i	0.651488	+	0.758659i	$0.274145\pi$
$692$	−11.7870	+	6.80523i	−0.448074	+	0.258696i
$693$		0			0
$694$	−33.5411	+	33.5411i	−1.27320	+	1.27320i
$695$	29.3774	−	29.3774i	1.11435	−	1.11435i
$696$		0			0
$697$	−7.48813	+	2.00644i	−0.283633	+	0.0759993i
$698$			8.07521i			0.305651i
$699$		0			0
$700$	0.564228	−	2.35616i	0.0213258	−	0.0890546i
$701$			27.1008i			1.02358i	0.859110	+	0.511791i	$0.171018\pi$
$701$			27.1008i			1.02358i	−0.859110	+	0.511791i	$0.828982\pi$
$702$		0			0
$703$	−9.37931	−	5.41515i	−0.353747	−	0.204236i
$704$	2.04202	−	2.04202i	0.0769616	−	0.0769616i
$705$		0			0
$706$	−3.64672	+	6.31631i	−0.137246	+	0.237717i
$707$	4.46847	−	18.6599i	0.168054	−	0.701778i
$708$		0			0
$709$	16.7885	+	16.7885i	0.630504	+	0.630504i	0.948194	−	0.317691i	$-0.102907\pi$
$709$	16.7885	+	16.7885i	0.630504	+	0.630504i	−0.317691	+	0.948194i	$0.602907\pi$
$710$	−10.9681	−	40.9336i	−0.411627	−	1.53621i
$711$		0			0
$712$	−8.55156	+	14.8117i	−0.320483	+	0.555093i
$713$	26.1946	+	7.01882i	0.980996	+	0.262857i
$714$		0			0
$715$	−22.8693	−	13.3440i	−0.855262	−	0.499039i
$716$	−2.38626	−	4.13313i	−0.0891788	−	0.154462i
$717$		0			0
$718$	12.3935			0.462520
$719$	14.2056			0.529779			0.264890	−	0.964279i	$-0.414664\pi$
$719$	14.2056			0.529779			0.264890	+	0.964279i	$0.414664\pi$
$720$		0			0
$721$	36.6986	−	10.8936i	1.36673	−	0.405700i
$722$	3.17708	−	0.851296i	0.118239	−	0.0316819i
$723$		0			0
$724$	1.52345	−	0.879564i	0.0566186	−	0.0326888i
$725$			3.30464i			0.122731i
$726$		0			0
$727$	−30.9551			−1.14806			−0.574030	−	0.818834i	$-0.694621\pi$
$727$	−30.9551			−1.14806			−0.574030	+	0.818834i	$0.694621\pi$
$728$	−14.2153	−	7.79236i	−0.526852	−	0.288804i
$729$		0			0
$730$	−2.62091	−	9.78138i	−0.0970043	−	0.362025i
$731$		−	7.84549i		−	0.290176i
$732$		0			0
$733$	−2.80061	+	10.4520i	−0.103443	+	0.386054i	−0.998164	−	0.0605714i	$-0.980708\pi$
$733$	−2.80061	+	10.4520i	−0.103443	+	0.386054i	0.894721	+	0.446626i	$0.147374\pi$
$734$	−5.22752	+	1.40071i	−0.192951	+	0.0517011i
$735$		0			0
$736$	−13.8908	−	13.8908i	−0.512023	−	0.512023i
$737$	−48.6284			−1.79125
$738$		0			0
$739$	−20.5838	−	20.5838i	−0.757186	−	0.757186i	0.218624	−	0.975809i	$-0.429843\pi$
$739$	−20.5838	−	20.5838i	−0.757186	−	0.757186i	−0.975809	+	0.218624i	$0.929843\pi$
$740$	−2.71216	−	4.69759i	−0.0997008	−	0.172687i
$741$		0			0
$742$	−11.5736	+	21.3452i	−0.424880	+	0.783608i
$743$	−50.7369	−	13.5949i	−1.86135	−	0.498749i	−0.861397	−	0.507932i	$-0.830410\pi$
$743$	−50.7369	−	13.5949i	−1.86135	−	0.498749i	−0.999958	+	0.00918346i	$0.997077\pi$
$744$		0			0
$745$	12.7678	+	22.1145i	0.467776	+	0.810212i
$746$	5.49572	+	20.5103i	0.201213	+	0.750935i
$747$		0			0
$748$	1.44451	+	5.39097i	0.0528164	+	0.197113i
$749$	−11.2923	−	10.7037i	−0.412613	−	0.391103i
$750$		0			0
$751$	37.0993	+	21.4193i	1.35377	+	0.781600i	0.988776	−	0.149409i	$-0.0477370\pi$
$751$	37.0993	+	21.4193i	1.35377	+	0.781600i	0.364996	+	0.931009i	$0.381070\pi$
$752$	0.935299	−	0.935299i	0.0341068	−	0.0341068i
$753$		0			0
$754$	−22.3151	−	6.08933i	−0.812669	−	0.221760i
$755$		−	42.7643i		−	1.55635i
$756$		0			0
$757$	−3.86571	−	6.69561i	−0.140502	−	0.243356i	0.787184	−	0.616718i	$-0.211538\pi$
$757$	−3.86571	−	6.69561i	−0.140502	−	0.243356i	−0.927686	+	0.373362i	$0.878205\pi$
$758$		−	44.5455i		−	1.61796i
$759$		0			0
$760$	13.7550	+	3.68563i	0.498945	+	0.133692i
$761$	14.9547	−	14.9547i	0.542106	−	0.542106i	−0.382040	−	0.924146i	$-0.624778\pi$
$761$	14.9547	−	14.9547i	0.542106	−	0.542106i	0.924146	+	0.382040i	$0.124778\pi$
$762$		0			0
$763$	1.36066	−	0.0364151i	0.0492591	−	0.00131831i
$764$	8.60445	−	4.96778i	0.311298	−	0.179728i
$765$		0			0
$766$	31.4055	−	54.3960i	1.13473	−	1.96541i
$767$	−1.18400	−	4.50136i	−0.0427518	−	0.162535i
$768$		0			0
$769$	8.37135	−	31.2423i	0.301879	−	1.12663i	−0.633720	−	0.773562i	$-0.718473\pi$
$769$	8.37135	−	31.2423i	0.301879	−	1.12663i	0.935599	−	0.353064i	$-0.114860\pi$
$770$	28.7909	−	17.6659i	1.03755	−	0.636635i
$771$		0			0
$772$	7.28962	+	1.95325i	0.262359	+	0.0702989i
$773$	−11.5730	+	43.1908i	−0.416250	+	1.55347i	0.366068	+	0.930588i	$0.380704\pi$
$773$	−11.5730	+	43.1908i	−0.416250	+	1.55347i	−0.782319	+	0.622879i	$0.785963\pi$
$774$		0			0
$775$	6.32070	+	1.69363i	0.227046	+	0.0608369i
$776$	0.984186	+	0.568220i	0.0353302	+	0.0203979i
$777$		0			0
$778$	−5.46986	+	20.4138i	−0.196104	+	0.731870i
$779$	−18.4415	+	10.6472i	−0.660735	+	0.381475i
$780$		0			0
$781$	−21.8059	+	37.7688i	−0.780275	+	1.35148i
$782$	−9.38487	+	2.51467i	−0.335602	+	0.0899243i
$783$		0			0
$784$	29.3285	−	19.0943i	1.04745	−	0.681938i
$785$	−5.30506	+	5.30506i	−0.189346	+	0.189346i
$786$		0			0
$787$	−7.26984	−	1.94795i	−0.259142	−	0.0694369i	0.126909	−	0.991914i	$-0.459494\pi$
$787$	−7.26984	−	1.94795i	−0.259142	−	0.0694369i	−0.386051	+	0.922478i	$0.626161\pi$
$788$	0.514139	−	0.137763i	0.0183154	−	0.00490761i
$789$		0			0
$790$	−28.5228	−	49.4029i	−1.01480	−	1.75768i
$791$	−14.9168	−	14.1392i	−0.530381	−	0.502732i
$792$		0			0
$793$	−33.2430	+	18.9898i	−1.18049	+	0.674346i
$794$	−22.4711	−	12.9737i	−0.797468	−	0.460418i
$795$		0			0
$796$	−13.8884	−	8.01846i	−0.492261	−	0.284207i
$797$	−5.44428	+	9.42978i	−0.192846	+	0.334020i	−0.946192	−	0.323605i	$-0.895105\pi$
$797$	−5.44428	+	9.42978i	−0.192846	+	0.334020i	0.753346	+	0.657624i	$0.228439\pi$
$798$		0			0
$799$	−0.103110	−	0.384812i	−0.00364777	−	0.0136137i
$800$	−3.35183	−	3.35183i	−0.118505	−	0.118505i
$801$		0			0
$802$	3.88566	+	6.73016i	0.137207	+	0.237650i
$803$	−5.21066	+	9.02513i	−0.183880	+	0.318490i
$804$		0			0
$805$	10.4041	+	16.9560i	0.366696	+	0.597620i
$806$	−23.0834	+	39.5607i	−0.813077	+	1.39347i
$807$		0			0
$808$	−8.71448	−	8.71448i	−0.306574	−	0.306574i
$809$	−8.38702			−0.294872			−0.147436	−	0.989072i	$-0.547102\pi$
$809$	−8.38702			−0.294872			−0.147436	+	0.989072i	$0.547102\pi$
$810$		0			0
$811$	24.6534	+	24.6534i	0.865699	+	0.865699i	0.991993	−	0.126294i	$-0.0403083\pi$
$811$	24.6534	+	24.6534i	0.865699	+	0.865699i	−0.126294	+	0.991993i	$0.540308\pi$
$812$	6.86772	−	7.24543i	0.241010	−	0.254265i
$813$		0			0
$814$	−4.27072	+	15.9386i	−0.149689	+	0.558646i
$815$	−17.3232	+	10.0015i	−0.606804	+	0.350338i
$816$		0			0
$817$	−5.57766	−	20.8161i	−0.195138	−	0.728263i
$818$	−0.962843			−0.0336650
$819$		0			0
$820$	−10.6652			−0.372446
$821$	1.62451	+	6.06276i	0.0566959	+	0.211592i	0.988462	−	0.151466i	$-0.0483994\pi$
$821$	1.62451	+	6.06276i	0.0566959	+	0.211592i	−0.931767	+	0.363058i	$0.881733\pi$
$822$		0			0
$823$	21.8835	−	12.6344i	0.762810	−	0.440409i	−0.0674934	−	0.997720i	$-0.521500\pi$
$823$	21.8835	−	12.6344i	0.762810	−	0.440409i	0.830304	+	0.557311i	$0.188167\pi$
$824$	6.36387	−	23.7503i	0.221696	−	0.827380i
$825$		0			0
$826$	5.77464	+	1.38285i	0.200925	+	0.0481154i
$827$	−34.6333	−	34.6333i	−1.20432	−	1.20432i	−0.972840	−	0.231479i	$-0.925644\pi$
$827$	−34.6333	−	34.6333i	−1.20432	−	1.20432i	−0.231479	−	0.972840i	$-0.574356\pi$
$828$		0			0
$829$	−23.5553			−0.818111			−0.409056	−	0.912509i	$-0.634142\pi$
$829$	−23.5553			−0.818111			−0.409056	+	0.912509i	$0.634142\pi$
$830$	−36.5325	−	36.5325i	−1.26806	−	1.26806i
$831$		0			0
$832$	−2.49427	+	1.42483i	−0.0864732	+	0.0493970i
$833$	−0.563786	−	10.5255i	−0.0195340	−	0.364686i
$834$		0			0
$835$	21.4684	−	37.1844i	0.742946	−	1.28682i
$836$	7.66529	+	13.2767i	0.265110	+	0.459183i
$837$		0			0
$838$	−28.5866	−	28.5866i	−0.987507	−	0.987507i
$839$	1.73270	+	6.46654i	0.0598196	+	0.223250i	0.989364	−	0.145460i	$-0.0464663\pi$
$839$	1.73270	+	6.46654i	0.0598196	+	0.223250i	−0.929545	+	0.368710i	$0.879800\pi$
$840$		0			0
$841$	7.69160	−	13.3222i	0.265227	−	0.459387i
$842$	−40.5702	−	23.4232i	−1.39814	−	0.807218i
$843$		0			0
$844$	4.58377	+	2.64644i	0.157780	+	0.0910943i
$845$	18.4514	+	18.7936i	0.634747	+	0.646519i
$846$		0			0
$847$	−5.50351	−	1.31792i	−0.189103	−	0.0452843i
$848$	13.1956	+	22.8554i	0.453137	+	0.784857i
$849$		0			0
$850$	−2.26455	+	0.606784i	−0.0776734	+	0.0208125i
$851$	−9.38678	−	2.51518i	−0.321775	−	0.0862193i
$852$		0			0
$853$	12.3363	−	12.3363i	0.422386	−	0.422386i	−0.463638	−	0.886025i	$-0.653456\pi$
$853$	12.3363	−	12.3363i	0.422386	−	0.422386i	0.886025	+	0.463638i	$0.153456\pi$
$854$	−1.30666	−	48.8237i	−0.0447130	−	1.67071i
$855$		0			0
$856$	−9.65308	+	2.58654i	−0.329936	+	0.0884060i
$857$	11.7995	−	20.4373i	0.403062	−	0.698123i	−0.591032	−	0.806648i	$-0.701279\pi$
$857$	11.7995	−	20.4373i	0.403062	−	0.698123i	0.994094	+	0.108525i	$0.0346127\pi$
$858$		0			0
$859$	8.42384	−	4.86350i	0.287418	−	0.165941i	−0.349359	−	0.936989i	$-0.613601\pi$
$859$	8.42384	−	4.86350i	0.287418	−	0.165941i	0.636777	+	0.771048i	$0.280267\pi$
$860$	2.79355	−	10.4257i	0.0952592	−	0.355512i
$861$		0			0
$862$	30.8269	+	17.7979i	1.04997	+	0.606200i
$863$	−42.3300	−	11.3423i	−1.44093	−	0.386096i	−0.548072	−	0.836431i	$-0.684638\pi$
$863$	−42.3300	−	11.3423i	−1.44093	−	0.386096i	−0.892860	+	0.450335i	$0.851305\pi$
$864$		0			0
$865$	6.97941	−	26.0475i	0.237307	−	0.885642i
$866$	46.3429	+	12.4175i	1.57480	+	0.421965i
$867$		0			0
$868$	−10.3384	−	16.8490i	−0.350909	−	0.571891i
$869$	−15.1944	+	56.7065i	−0.515436	+	1.92363i
$870$		0			0
$871$	46.6644	+	12.7337i	1.58116	+	0.431467i
$872$	0.437132	−	0.757135i	0.0148032	−	0.0256398i
$873$		0			0
$874$	−23.1127	+	13.3441i	−0.781799	+	0.451372i
$875$	16.5270	+	26.9348i	0.558715	+	0.910561i
$876$		0			0
$877$	32.5031	−	32.5031i	1.09755	−	1.09755i	0.102856	−	0.994696i	$-0.467202\pi$
$877$	32.5031	−	32.5031i	1.09755	−	1.09755i	0.994696	−	0.102856i	$-0.0327982\pi$
$878$	−30.3199	−	8.12420i	−1.02325	−	0.274178i
$879$		0			0
$880$		−	36.7142i		−	1.23763i
$881$	0.277040	+	0.479848i	0.00933373	+	0.0161665i	0.870655	−	0.491895i	$-0.163696\pi$
$881$	0.277040	+	0.479848i	0.00933373	+	0.0161665i	−0.861321	+	0.508061i	$0.830362\pi$
$882$		0			0
$883$			21.2142i			0.713914i	0.934121	+	0.356957i	$0.116186\pi$
$883$			21.2142i			0.713914i	−0.934121	+	0.356957i	$0.883814\pi$
$884$	0.0255035	−	5.55149i	0.000857774	−	0.186717i
$885$		0			0
$886$	−48.0428	+	48.0428i	−1.61403	+	1.61403i
$887$	26.5374	+	15.3214i	0.891040	+	0.514442i	0.874282	−	0.485418i	$-0.161332\pi$
$887$	26.5374	+	15.3214i	0.891040	+	0.514442i	0.0167572	+	0.999860i	$0.494666\pi$
$888$		0			0
$889$	14.3370	+	48.2988i	0.480849	+	1.61989i
$890$	9.17482	+	34.2409i	0.307541	+	1.14776i
$891$		0			0
$892$	−3.32677	−	12.4157i	−0.111389	−	0.415708i
$893$	−0.547155	−	0.947701i	−0.0183098	−	0.0317136i
$894$		0			0
$895$	9.13360	+	2.44734i	0.305303	+	0.0818056i
$896$	−0.847357	−	31.6617i	−0.0283082	−	1.05774i
$897$		0			0
$898$	−19.6413	−	34.0198i	−0.655439	−	1.13525i
$899$	19.0659	+	19.0659i	0.635883	+	0.635883i
$900$		0			0
$901$	7.94872			0.264810
$902$	22.9411	+	22.9411i	0.763857	+	0.763857i
$903$		0			0
$904$	−12.7514	+	3.41673i	−0.424106	+	0.113639i
$905$	−0.902078	+	3.36660i	−0.0299861	+	0.111910i
$906$		0			0
$907$			9.33990i			0.310126i	0.987905	+	0.155063i	$0.0495581\pi$
$907$			9.33990i			0.310126i	−0.987905	+	0.155063i	$0.950442\pi$
$908$	1.74191	+	6.50088i	0.0578072	+	0.215739i
$909$		0			0
$910$	−32.2540	+	9.41330i	−1.06921	+	0.312048i
$911$	23.5831			0.781342			0.390671	−	0.920530i	$-0.372243\pi$
$911$	23.5831			0.781342			0.390671	+	0.920530i	$0.372243\pi$
$912$		0			0
$913$			53.1694i			1.75965i
$914$	−29.5819	+	17.0791i	−0.978483	+	0.564927i
$915$		0			0
$916$	9.03320	−	2.42044i	0.298465	−	0.0799735i
$917$	−13.6663	−	46.0393i	−0.451302	−	1.52035i
$918$		0			0
$919$	1.97069			0.0650071			0.0325036	−	0.999472i	$-0.489652\pi$
$919$	1.97069			0.0650071			0.0325036	+	0.999472i	$0.489652\pi$
$920$	12.7776			0.421265
$921$		0			0
$922$	12.8989	+	22.3415i	0.424802	+	0.735779i
$923$	30.8152	−	30.5334i	1.01430	−	1.00502i
$924$		0			0
$925$	−2.26501	−	0.606908i	−0.0744731	−	0.0199550i
$926$	26.6476	−	46.1551i	0.875696	−	1.51675i
$927$		0			0
$928$	−5.05527	−	18.8665i	−0.165947	−	0.619323i
$929$	41.7592	+	41.7592i	1.37007	+	1.37007i	0.860321	+	0.509753i	$0.170263\pi$
$929$	41.7592	+	41.7592i	1.37007	+	1.37007i	0.509753	+	0.860321i	$0.329737\pi$
$930$		0			0
$931$	−8.97882	−	27.5259i	−0.294269	−	0.902126i
$932$	−3.93183	+	6.81013i	−0.128791	+	0.223073i
$933$		0			0
$934$	26.0878	−	26.0878i	0.853619	−	0.853619i
$935$	−9.57643	−	5.52896i	−0.313183	−	0.180816i
$936$		0			0
$937$		−	49.8381i		−	1.62814i	−0.580767	−	0.814070i	$-0.697247\pi$
$937$		−	49.8381i		−	1.62814i	0.580767	−	0.814070i	$-0.302753\pi$
$938$	−42.4515	+	44.7862i	−1.38609	+	1.46232i
$939$		0			0
$940$		−	0.548081i		−	0.0178764i
$941$	12.2019	−	3.26950i	0.397771	−	0.106583i	−0.0543875	−	0.998520i	$-0.517321\pi$
$941$	12.2019	−	3.26950i	0.397771	−	0.106583i	0.452159	+	0.891937i	$0.350654\pi$
$942$		0			0
$943$	−13.5109	+	13.5109i	−0.439974	+	0.439974i
$944$	4.56362	−	4.56362i	0.148533	−	0.148533i
$945$		0			0
$946$	−28.4349	+	16.4169i	−0.924497	+	0.533759i
$947$	30.7696	−	8.24470i	0.999879	−	0.267917i	0.278484	−	0.960441i	$-0.410168\pi$
$947$	30.7696	−	8.24470i	0.999879	−	0.267917i	0.721395	+	0.692524i	$0.243501\pi$
$948$		0			0
$949$	7.36352	−	7.29617i	0.239030	−	0.236844i
$950$	−5.57705	+	3.21991i	−0.180943	+	0.104468i
$951$		0			0
$952$	−5.95163	−	3.22703i	−0.192893	−	0.104589i
$953$	−30.8939	−	17.8366i	−1.00075	−	0.577784i	−0.0922803	−	0.995733i	$-0.529416\pi$
$953$	−30.8939	−	17.8366i	−1.00075	−	0.577784i	−0.908470	+	0.417949i	$0.862749\pi$
$954$		0			0
$955$	−5.09494	+	19.0146i	−0.164868	+	0.615297i
$956$	−5.42626	+	20.2511i	−0.175498	+	0.654967i
$957$		0			0
$958$	−16.1046	−	9.29802i	−0.520318	−	0.300405i
$959$	46.8226	+	25.3877i	1.51198	+	0.819810i
$960$		0			0
$961$	19.3912	−	11.1955i	0.625524	−	0.361146i
$962$	8.27188	−	14.1765i	0.266696	−	0.457069i
$963$		0			0
$964$	−9.84769	+	2.63868i	−0.317173	+	0.0849862i
$965$	−12.9492	+	7.47620i	−0.416848	+	0.240667i
$966$		0			0
$967$	23.3410	−	23.3410i	0.750597	−	0.750597i	−0.223994	−	0.974591i	$-0.571910\pi$
$967$	23.3410	−	23.3410i	0.750597	−	0.750597i	0.974591	+	0.223994i	$0.0719096\pi$
$968$	−2.57023	+	2.57023i	−0.0826102	+	0.0826102i
$969$		0			0
$970$	2.27518	−	0.609633i	0.0730517	−	0.0195741i
$971$			9.95673i			0.319527i	0.987155	+	0.159763i	$0.0510731\pi$
$971$			9.95673i			0.319527i	−0.987155	+	0.159763i	$0.948927\pi$
$972$		0			0
$973$	−37.3248	+	39.3776i	−1.19658	+	1.26239i
$974$		−	55.5239i		−	1.77910i
$975$		0			0
$976$	−45.9736	−	26.5429i	−1.47158	−	0.849616i
$977$	−11.1637	+	11.1637i	−0.357158	+	0.357158i	−0.862764	−	0.505606i	$-0.831269\pi$
$977$	−11.1637	+	11.1637i	−0.357158	+	0.357158i	0.505606	+	0.862764i	$0.331269\pi$
$978$		0			0
$979$	18.2406	−	31.5936i	0.582971	−	1.00974i
$980$	2.99861	−	14.1878i	0.0957871	−	0.453212i
$981$		0			0
$982$	−10.4168	−	10.4168i	−0.332413	−	0.332413i
$983$	0.434633	+	1.62207i	0.0138626	+	0.0517361i	0.972511	−	0.232858i	$-0.0748078\pi$
$983$	0.434633	+	1.62207i	0.0138626	+	0.0517361i	−0.958648	+	0.284594i	$0.908141\pi$
$984$		0			0
$985$	−0.527299	+	0.913309i	−0.0168011	+	0.0291004i
$986$	−9.33109	−	2.50026i	−0.297162	−	0.0796244i
$987$		0			0
$988$	−3.87910	−	14.7477i	−0.123411	−	0.469186i
$989$	−9.66848	−	16.7463i	−0.307440	−	0.532502i
$990$		0			0
$991$	−16.3645			−0.519837			−0.259918	−	0.965631i	$-0.583696\pi$
$991$	−16.3645			−0.519837			−0.259918	+	0.965631i	$0.583696\pi$
$992$	−38.6763			−1.22797
$993$		0			0
$994$	15.7487	+	53.0543i	0.499517	+	1.68278i
$995$	30.6913	−	8.22370i	0.972979	−	0.260709i
$996$		0			0
$997$	−16.4282	+	9.48480i	−0.520285	+	0.300387i	−0.737051	−	0.675837i	$-0.763782\pi$
$997$	−16.4282	+	9.48480i	−0.520285	+	0.300387i	0.216766	+	0.976224i	$0.430449\pi$
$998$		−	44.0214i		−	1.39347i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.gh.d.262.8		40
3.2	odd	2		273.2.cg.b.262.3	yes	40
7.5	odd	6		819.2.et.d.145.8		40
13.7	odd	12		819.2.et.d.514.8		40
21.5	even	6		273.2.bt.b.145.3	✓	40
39.20	even	12		273.2.bt.b.241.3	yes	40
91.33	even	12	inner	819.2.gh.d.397.8		40
273.215	odd	12		273.2.cg.b.124.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.145.3	✓	40	21.5	even	6
273.2.bt.b.241.3	yes	40	39.20	even	12
273.2.cg.b.124.3	yes	40	273.215	odd	12
273.2.cg.b.262.3	yes	40	3.2	odd	2
819.2.et.d.145.8		40	7.5	odd	6
819.2.et.d.514.8		40	13.7	odd	12
819.2.gh.d.262.8		40	1.1	even	1	trivial
819.2.gh.d.397.8		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)

\(f(q)\)	\(=\)	\(q+(0.449968 + 1.67930i) q^{2} +(-0.885540 + 0.511267i) q^{4} +(0.524353 - 1.95691i) q^{5} +(-0.616155 + 2.57300i) q^{7} +(1.20163 + 1.20163i) q^{8} +O(q^{10})\)	\(q+(0.449968 + 1.67930i) q^{2} +(-0.885540 + 0.511267i) q^{4} +(0.524353 - 1.95691i) q^{5} +(-0.616155 + 2.57300i) q^{7} +(1.20163 + 1.20163i) q^{8} +3.52219 q^{10} +(-2.56310 - 2.56310i) q^{11} +(1.78841 + 3.13075i) q^{13} +(-4.59811 + 0.123058i) q^{14} +(-2.49975 + 4.32969i) q^{16} +(0.752896 + 1.30405i) q^{17} +(2.92473 + 2.92473i) q^{19} +(0.536169 + 2.00101i) q^{20} +(3.15091 - 5.45753i) q^{22} +(3.21414 + 1.85568i) q^{23} +(0.775564 + 0.447772i) q^{25} +(-4.45275 + 4.41202i) q^{26} +(-0.769862 - 2.59352i) q^{28} +(1.84505 + 3.19572i) q^{29} +(7.05794 - 1.89117i) q^{31} +(-5.11274 - 1.36995i) q^{32} +(-1.85112 + 1.85112i) q^{34} +(4.71206 + 2.55493i) q^{35} +(-2.52920 + 0.677697i) q^{37} +(-3.59548 + 6.22755i) q^{38} +(2.98158 - 1.72141i) q^{40} +(-1.33248 + 4.97288i) q^{41} +(-4.51217 - 2.60510i) q^{43} +(3.58015 + 0.959299i) q^{44} +(-1.67000 + 6.23251i) q^{46} +(-0.255554 - 0.0684756i) q^{47} +(-6.24071 - 3.17074i) q^{49} +(-0.402966 + 1.50389i) q^{50} +(-3.18436 - 1.85805i) q^{52} +(2.63938 - 4.57154i) q^{53} +(-6.35973 + 3.67179i) q^{55} +(-3.83220 + 2.35142i) q^{56} +(-4.53637 + 4.53637i) q^{58} +(-1.24693 - 0.334114i) q^{59} +10.6182i q^{61} +(6.35170 + 11.0015i) q^{62} +0.796700i q^{64} +(7.06436 - 1.85815i) q^{65} +(9.48626 - 9.48626i) q^{67} +(-1.33344 - 0.769862i) q^{68} +(-2.17022 + 9.06262i) q^{70} +(-3.11400 - 11.6216i) q^{71} +(-0.744113 - 2.77707i) q^{73} +(-2.27612 - 3.94235i) q^{74} +(-4.08528 - 1.09465i) q^{76} +(8.17413 - 5.01560i) q^{77} +(-8.09801 - 14.0262i) q^{79} +(7.16207 + 7.16207i) q^{80} -8.95055 q^{82} +(-10.3721 - 10.3721i) q^{83} +(2.94671 - 0.789567i) q^{85} +(2.34443 - 8.74952i) q^{86} -6.15981i q^{88} +(2.60486 + 9.72147i) q^{89} +(-9.15737 + 2.67257i) q^{91} -3.79500 q^{92} -0.459965i q^{94} +(7.25704 - 4.18985i) q^{95} +(0.645956 - 0.173083i) q^{97} +(2.51652 - 11.9068i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7}+O(q^{10}) \) 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

Introduction

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