LMFDB - Embedded newform 819.2.et.c.514.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(136,819)]

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, 2, 5]))

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

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

chi := DirichletCharacter("819.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.et (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:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			514.2
Character	$\chi$	$=$	819.514
Dual form			819.2.et.c.145.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.55654 - 1.55654i) q^{2} +2.84566i q^{4} +(-3.12520 - 0.837395i) q^{5} +(1.93981 - 1.79920i) q^{7} +(1.31631 - 1.31631i) q^{8} +O(q^{10})$	\(q+(-1.55654 - 1.55654i) q^{2} +2.84566i q^{4} +(-3.12520 - 0.837395i) q^{5} +(1.93981 - 1.79920i) q^{7} +(1.31631 - 1.31631i) q^{8} +(3.56107 + 6.16796i) q^{10} +(3.89463 + 1.04356i) q^{11} +(-2.61925 + 2.47781i) q^{13} +(-5.81994 - 0.218864i) q^{14} +1.59353 q^{16} +7.61003 q^{17} +(-0.714314 - 2.66585i) q^{19} +(2.38294 - 8.89327i) q^{20} +(-4.43782 - 7.68652i) q^{22} +4.49695i q^{23} +(4.73553 + 2.73406i) q^{25} +(7.93380 + 0.220148i) q^{26} +(5.11992 + 5.52005i) q^{28} +(-1.49169 + 2.58368i) q^{29} +(0.691794 + 2.58181i) q^{31} +(-5.11302 - 5.11302i) q^{32} +(-11.8454 - 11.8454i) q^{34} +(-7.56895 + 3.99848i) q^{35} +(1.20113 - 1.20113i) q^{37} +(-3.03766 + 5.26138i) q^{38} +(-5.21601 + 3.01147i) q^{40} +(-2.95120 - 11.0140i) q^{41} +(6.30996 - 3.64306i) q^{43} +(-2.96963 + 11.0828i) q^{44} +(6.99971 - 6.99971i) q^{46} +(0.666302 - 2.48667i) q^{47} +(0.525739 - 6.98023i) q^{49} +(-3.11538 - 11.6267i) q^{50} +(-7.05102 - 7.45349i) q^{52} +(3.91287 - 6.77729i) q^{53} +(-11.2976 - 6.52269i) q^{55} +(0.185085 - 4.92171i) q^{56} +(6.34349 - 1.69973i) q^{58} +(5.78594 + 5.78594i) q^{59} +(-7.97503 - 4.60439i) q^{61} +(2.94189 - 5.09551i) q^{62} +12.7302i q^{64} +(10.2606 - 5.55032i) q^{65} +(2.02258 - 7.54839i) q^{67} +21.6556i q^{68} +(18.0052 + 5.55759i) q^{70} +(0.721147 - 2.69136i) q^{71} +(1.69255 - 0.453517i) q^{73} -3.73923 q^{74} +(7.58612 - 2.03270i) q^{76} +(9.43244 - 4.98292i) q^{77} +(4.31023 + 7.46554i) q^{79} +(-4.98010 - 1.33441i) q^{80} +(-12.5501 + 21.7375i) q^{82} +(-1.63865 + 1.63865i) q^{83} +(-23.7829 - 6.37260i) q^{85} +(-15.4923 - 4.15115i) q^{86} +(6.50021 - 3.75290i) q^{88} +(-12.7524 - 12.7524i) q^{89} +(-0.622758 + 9.51904i) q^{91} -12.7968 q^{92} +(-4.90774 + 2.83349i) q^{94} +8.92950i q^{95} +(12.7508 + 3.41658i) q^{97} +(-11.6834 + 10.0467i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{7}+O(q^{10}) $ 36 * q + 6 * q^7	$ 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) $ 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.55654	−	1.55654i	−1.10064	−	1.10064i	−0.994333	−	0.106310i	$-0.966096\pi$
$2$	−1.55654	−	1.55654i	−1.10064	−	1.10064i	−0.106310	−	0.994333i	$-0.533904\pi$
$3$		0			0
$3$		0			0
$4$			2.84566i			1.42283i
$5$	−3.12520	−	0.837395i	−1.39763	−	0.374495i	−0.520139	−	0.854082i	$-0.674120\pi$
$5$	−3.12520	−	0.837395i	−1.39763	−	0.374495i	−0.877494	+	0.479587i	$0.840786\pi$
$6$		0			0
$7$	1.93981	−	1.79920i	0.733180	−	0.680035i
$7$	1.93981	−	1.79920i	0.733180	−	0.680035i
$8$	1.31631	−	1.31631i	0.465386	−	0.465386i
$9$		0			0
$10$	3.56107	+	6.16796i	1.12611	+	1.95048i
$11$	3.89463	+	1.04356i	1.17428	+	0.314646i	0.792654	−	0.609672i	$-0.208699\pi$
$11$	3.89463	+	1.04356i	1.17428	+	0.314646i	0.381622	+	0.924318i	$0.375366\pi$
$12$		0			0
$13$	−2.61925	+	2.47781i	−0.726448	+	0.687221i
$13$	−2.61925	+	2.47781i	−0.726448	+	0.687221i
$14$	−5.81994	−	0.218864i	−1.55545	−	0.0584939i
$15$		0			0
$16$	1.59353			0.398382
$17$	7.61003			1.84570			0.922852	−	0.385156i	$-0.125852\pi$
$17$	7.61003			1.84570			0.922852	+	0.385156i	$0.125852\pi$
$18$		0			0
$19$	−0.714314	−	2.66585i	−0.163875	−	0.611589i	−0.998181	−	0.0602878i	$-0.980798\pi$
$19$	−0.714314	−	2.66585i	−0.163875	−	0.611589i	0.834306	−	0.551301i	$-0.185869\pi$
$20$	2.38294	−	8.89327i	0.532843	−	1.98860i
$21$		0			0
$22$	−4.43782	−	7.68652i	−0.946146	−	1.63877i
$23$			4.49695i			0.937679i	0.883283	+	0.468840i	$0.155328\pi$
$23$			4.49695i			0.937679i	−0.883283	+	0.468840i	$0.844672\pi$
$24$		0			0
$25$	4.73553	+	2.73406i	0.947106	+	0.546812i
$26$	7.93380	+	0.220148i	1.55595	+	0.0431746i
$27$		0			0
$28$	5.11992	+	5.52005i	0.967575	+	1.04319i
$29$	−1.49169	+	2.58368i	−0.276999	+	0.479777i	−0.970638	−	0.240547i	$-0.922673\pi$
$29$	−1.49169	+	2.58368i	−0.276999	+	0.479777i	0.693638	+	0.720323i	$0.256007\pi$
$30$		0			0
$31$	0.691794	+	2.58181i	0.124250	+	0.463707i	0.999812	−	0.0193991i	$-0.00617531\pi$
$31$	0.691794	+	2.58181i	0.124250	+	0.463707i	−0.875562	+	0.483106i	$0.839509\pi$
$32$	−5.11302	−	5.11302i	−0.903863	−	0.903863i
$33$		0			0
$34$	−11.8454	−	11.8454i	−2.03146	−	2.03146i
$35$	−7.56895	+	3.99848i	−1.27939	+	0.675867i
$36$		0			0
$37$	1.20113	−	1.20113i	0.197465	−	0.197465i	−0.601447	−	0.798912i	$-0.705409\pi$
$37$	1.20113	−	1.20113i	0.197465	−	0.197465i	0.798912	+	0.601447i	$0.205409\pi$
$38$	−3.03766	+	5.26138i	−0.492774	+	0.853509i
$39$		0			0
$40$	−5.21601	+	3.01147i	−0.824724	+	0.476155i
$41$	−2.95120	−	11.0140i	−0.460900	−	1.72010i	−0.670138	−	0.742236i	$-0.733765\pi$
$41$	−2.95120	−	11.0140i	−0.460900	−	1.72010i	0.209239	−	0.977865i	$-0.432901\pi$
$42$		0			0
$43$	6.30996	−	3.64306i	0.962260	−	0.555561i	0.0653923	−	0.997860i	$-0.479170\pi$
$43$	6.30996	−	3.64306i	0.962260	−	0.555561i	0.896868	+	0.442298i	$0.145837\pi$
$44$	−2.96963	+	11.0828i	−0.447689	+	1.67080i
$45$		0			0
$46$	6.99971	−	6.99971i	1.03205	−	1.03205i
$47$	0.666302	−	2.48667i	0.0971901	−	0.362718i	−0.900152	−	0.435575i	$-0.856545\pi$
$47$	0.666302	−	2.48667i	0.0971901	−	0.362718i	0.997342	+	0.0728569i	$0.0232116\pi$
$48$		0			0
$49$	0.525739	−	6.98023i	0.0751056	−	0.997176i
$50$	−3.11538	−	11.6267i	−0.440581	−	1.64427i
$51$		0			0
$52$	−7.05102	−	7.45349i	−0.977800	−	1.03361i
$53$	3.91287	−	6.77729i	0.537474	−	0.930933i	−0.461565	−	0.887106i	$-0.652712\pi$
$53$	3.91287	−	6.77729i	0.537474	−	0.930933i	0.999039	−	0.0438262i	$-0.0139548\pi$
$54$		0			0
$55$	−11.2976	−	6.52269i	−1.52337	−	0.879520i
$56$	0.185085	−	4.92171i	0.0247331	−	0.657691i
$57$		0			0
$58$	6.34349	−	1.69973i	0.832941	−	0.223186i
$59$	5.78594	+	5.78594i	0.753265	+	0.753265i	0.975087	−	0.221822i	$-0.0712003\pi$
$59$	5.78594	+	5.78594i	0.753265	+	0.753265i	−0.221822	+	0.975087i	$0.571200\pi$
$60$		0			0
$61$	−7.97503	−	4.60439i	−1.02110	−	0.589531i	−0.106676	−	0.994294i	$-0.534021\pi$
$61$	−7.97503	−	4.60439i	−1.02110	−	0.589531i	−0.914422	+	0.404763i	$0.867354\pi$
$62$	2.94189	−	5.09551i	0.373621	−	0.647130i
$63$		0			0
$64$			12.7302i			1.59128i
$65$	10.2606	−	5.55032i	1.27267	−	0.688432i
$66$		0			0
$67$	2.02258	−	7.54839i	0.247098	−	0.922182i	−0.725219	−	0.688518i	$-0.758262\pi$
$67$	2.02258	−	7.54839i	0.247098	−	0.922182i	0.972317	−	0.233664i	$-0.0750717\pi$
$68$			21.6556i			2.62612i
$69$		0			0
$70$	18.0052	+	5.55759i	2.15204	+	0.664259i
$71$	0.721147	−	2.69136i	0.0855844	−	0.319405i	−0.909840	−	0.414960i	$-0.863796\pi$
$71$	0.721147	−	2.69136i	0.0855844	−	0.319405i	0.995424	+	0.0955544i	$0.0304624\pi$
$72$		0			0
$73$	1.69255	−	0.453517i	0.198098	−	0.0530802i	−0.158406	−	0.987374i	$-0.550635\pi$
$73$	1.69255	−	0.453517i	0.198098	−	0.0530802i	0.356504	+	0.934294i	$0.383969\pi$
$74$	−3.73923			−0.434677
$75$		0			0
$76$	7.58612	−	2.03270i	0.870188	−	0.233166i
$77$	9.43244	−	4.98292i	1.07493	−	0.567856i
$78$		0			0
$79$	4.31023	+	7.46554i	0.484939	+	0.839939i	0.999850	−	0.0173043i	$-0.00550840\pi$
$79$	4.31023	+	7.46554i	0.484939	+	0.839939i	−0.514911	+	0.857244i	$0.672175\pi$
$80$	−4.98010	−	1.33441i	−0.556792	−	0.149192i
$81$		0			0
$82$	−12.5501	+	21.7375i	−1.38593	+	2.40050i
$83$	−1.63865	+	1.63865i	−0.179865	+	0.179865i	−0.791297	−	0.611432i	$-0.790594\pi$
$83$	−1.63865	+	1.63865i	−0.179865	+	0.179865i	0.611432	+	0.791297i	$0.290594\pi$
$84$		0			0
$85$	−23.7829	−	6.37260i	−2.57962	−	0.691206i
$86$	−15.4923	−	4.15115i	−1.67058	−	0.447631i
$87$		0			0
$88$	6.50021	−	3.75290i	0.692924	−	0.400060i
$89$	−12.7524	−	12.7524i	−1.35175	−	1.35175i	−0.883703	−	0.468049i	$-0.844957\pi$
$89$	−12.7524	−	12.7524i	−1.35175	−	1.35175i	−0.468049	−	0.883703i	$-0.655043\pi$
$90$		0			0
$91$	−0.622758	+	9.51904i	−0.0652827	+	0.997867i
$92$	−12.7968			−1.33416
$93$		0			0
$94$	−4.90774	+	2.83349i	−0.506195	+	0.292252i
$95$			8.92950i			0.916147i
$96$		0			0
$97$	12.7508	+	3.41658i	1.29465	+	0.346901i	0.839425	−	0.543475i	$-0.182892\pi$
$97$	12.7508	+	3.41658i	1.29465	+	0.346901i	0.455226	+	0.890376i	$0.349559\pi$
$98$	−11.6834	+	10.0467i	−1.18020	+	1.01487i
$99$		0			0
$100$	−7.78021	+	13.4757i	−0.778021	+	1.34757i
$101$	−1.98582	−	3.43954i	−0.197597	−	0.342247i	0.750152	−	0.661265i	$-0.229980\pi$
$101$	−1.98582	−	3.43954i	−0.197597	−	0.342247i	−0.947749	+	0.319018i	$0.896647\pi$
$102$		0			0
$103$	−1.90417	−	3.29812i	−0.187623	−	0.324973i	0.756834	−	0.653607i	$-0.226745\pi$
$103$	−1.90417	−	3.29812i	−0.187623	−	0.324973i	−0.944457	+	0.328634i	$0.893412\pi$
$104$	−0.186171	+	6.70932i	−0.0182556	+	0.657903i
$105$		0			0
$106$	−16.6397	+	4.45860i	−1.61619	+	0.433057i
$107$	6.86597			0.663758			0.331879	−	0.943322i	$-0.392317\pi$
$107$	6.86597			0.663758			0.331879	+	0.943322i	$0.392317\pi$
$108$		0			0
$109$	−4.71023	+	1.26210i	−0.451158	+	0.120887i	−0.477241	−	0.878772i	$-0.658363\pi$
$109$	−4.71023	+	1.26210i	−0.451158	+	0.120887i	0.0260833	+	0.999660i	$0.491696\pi$
$110$	7.43241	+	27.7381i	0.708653	+	2.64473i
$111$		0			0
$112$	3.09115	−	2.86708i	0.292086	−	0.270914i
$113$	4.45378	+	7.71418i	0.418977	+	0.725689i	0.995837	−	0.0911542i	$-0.0290556\pi$
$113$	4.45378	+	7.71418i	0.418977	+	0.725689i	−0.576860	+	0.816843i	$0.695722\pi$
$114$		0			0
$115$	3.76573	−	14.0539i	0.351156	−	1.31053i
$116$	−7.35227	−	4.24484i	−0.682642	−	0.394123i
$117$		0			0
$118$		−	18.0122i		−	1.65815i
$119$	14.7620	−	13.6920i	1.35323	−	1.25514i
$120$		0			0
$121$	4.55286	+	2.62860i	0.413896	+	0.238963i
$122$	5.24656	+	19.5804i	0.475001	+	1.77273i
$123$		0			0
$124$	−7.34696	+	1.96861i	−0.659776	+	0.176787i
$125$	−1.07096	−	1.07096i	−0.0957897	−	0.0957897i
$126$		0			0
$127$	5.06664	+	2.92523i	0.449592	+	0.259572i	0.707658	−	0.706555i	$-0.249752\pi$
$127$	5.06664	+	2.92523i	0.449592	+	0.259572i	−0.258066	+	0.966127i	$0.583085\pi$
$128$	9.58914	−	9.58914i	0.847568	−	0.847568i
$129$		0			0
$130$	−24.6104	−	7.33173i	−2.15847	−	0.643035i
$131$	−2.26616	+	1.30837i	−0.197995	+	0.114313i	−0.595720	−	0.803192i	$-0.703133\pi$
$131$	−2.26616	+	1.30837i	−0.197995	+	0.114313i	0.397725	+	0.917505i	$0.369800\pi$
$132$		0			0
$133$	−6.18205	−	3.88606i	−0.536051	−	0.336964i
$134$	−14.8976	+	8.60116i	−1.28696	+	0.743027i
$135$		0			0
$136$	10.0172	−	10.0172i	0.858965	−	0.858965i
$137$	7.97460	−	7.97460i	0.681316	−	0.681316i	−0.278981	−	0.960297i	$-0.589997\pi$
$137$	7.97460	−	7.97460i	0.681316	−	0.681316i	0.960297	+	0.278981i	$0.0899966\pi$
$138$		0			0
$139$	−2.50525	+	1.44641i	−0.212493	+	0.122683i	−0.602469	−	0.798142i	$-0.705816\pi$
$139$	−2.50525	+	1.44641i	−0.212493	+	0.122683i	0.389977	+	0.920825i	$0.372483\pi$
$140$	−11.3783	−	21.5387i	−0.961645	−	1.82035i
$141$		0			0
$142$	−5.31171	+	3.06672i	−0.445749	+	0.257353i
$143$	−12.7868	+	6.91682i	−1.06928	+	0.578413i
$144$		0			0
$145$	6.82538	−	6.82538i	0.566817	−	0.566817i
$146$	−3.34045	−	1.92861i	−0.276458	−	0.159613i
$147$		0			0
$148$	3.41802	+	3.41802i	0.280959	+	0.280959i
$149$	−1.38788	+	0.371881i	−0.113699	+	0.0304657i	−0.315220	−	0.949019i	$-0.602078\pi$
$149$	−1.38788	+	0.371881i	−0.113699	+	0.0304657i	0.201521	+	0.979484i	$0.435412\pi$
$150$		0			0
$151$	2.07821	+	7.75599i	0.169122	+	0.631174i	0.997478	+	0.0709714i	$0.0226099\pi$
$151$	2.07821	+	7.75599i	0.169122	+	0.631174i	−0.828356	+	0.560202i	$0.810723\pi$
$152$	−4.44936	−	2.56884i	−0.360890	−	0.208360i
$153$		0			0
$154$	−22.4381	−	6.92588i	−1.80812	−	0.558103i
$155$		−	8.64798i		−	0.694623i
$156$		0			0
$157$	−1.71529	−	0.990321i	−0.136895	−	0.0790362i	0.429989	−	0.902834i	$-0.358518\pi$
$157$	−1.71529	−	0.990321i	−0.136895	−	0.0790362i	−0.566883	+	0.823798i	$0.691851\pi$
$158$	4.91138	−	18.3295i	0.390728	−	1.45822i
$159$		0			0
$160$	11.6976	+	20.2609i	0.924777	+	1.60176i
$161$	8.09093	+	8.72324i	0.637654	+	0.687488i
$162$		0			0
$163$	−0.0288858	−	0.107803i	−0.00226251	−	0.00844379i	0.964785	−	0.263038i	$-0.0847246\pi$
$163$	−0.0288858	−	0.107803i	−0.00226251	−	0.00844379i	−0.967048	+	0.254595i	$0.918058\pi$
$164$	31.3422	−	8.39811i	2.44741	−	0.655782i
$165$		0			0
$166$	5.10125			0.395934
$167$	21.7275	−	5.82186i	1.68132	−	0.450509i	0.713195	−	0.700965i	$-0.247247\pi$
$167$	21.7275	−	5.82186i	1.68132	−	0.450509i	0.968128	+	0.250456i	$0.0805805\pi$
$168$		0			0
$169$	0.720896	−	12.9800i	0.0554536	−	0.998461i
$170$	27.0999	+	46.9384i	2.07847	+	3.60001i
$171$		0			0
$172$	10.3669	+	17.9560i	0.790470	+	1.36913i
$173$	−2.36409	+	4.09472i	−0.179738	+	0.311316i	−0.941791	−	0.336199i	$-0.890858\pi$
$173$	−2.36409	+	4.09472i	−0.179738	+	0.311316i	0.762053	+	0.647515i	$0.224192\pi$
$174$		0			0
$175$	14.1052	−	3.21662i	1.06625	−	0.243153i
$176$	6.20621	+	1.66295i	0.467811	+	0.125350i
$177$		0			0
$178$			39.6994i			2.97559i
$179$	−19.8416	+	11.4556i	−1.48303	+	0.856228i	−0.999814	−	0.0192725i	$-0.993865\pi$
$179$	−19.8416	+	11.4556i	−1.48303	+	0.856228i	−0.483217	+	0.875501i	$0.660532\pi$
$180$		0			0
$181$	4.84056			0.359796			0.179898	−	0.983685i	$-0.442423\pi$
$181$	4.84056			0.359796			0.179898	+	0.983685i	$0.442423\pi$
$182$	15.7862	−	13.8475i	1.17015	−	1.02644i
$183$		0			0
$184$	5.91939	+	5.91939i	0.436383	+	0.436383i
$185$	−4.75961	+	2.74796i	−0.349933	+	0.202034i
$186$		0			0
$187$	29.6383	+	7.94155i	2.16737	+	0.580744i
$188$	7.07623	+	1.89607i	0.516087	+	0.138285i
$189$		0			0
$190$	13.8992	−	13.8992i	1.00835	−	1.00835i
$191$	7.41350	−	12.8406i	0.536422	−	0.929111i	−0.462671	−	0.886530i	$-0.653109\pi$
$191$	7.41350	−	12.8406i	0.536422	−	0.929111i	0.999093	−	0.0425804i	$-0.0135579\pi$
$192$		0			0
$193$	15.1925	+	4.07082i	1.09358	+	0.293024i	0.760148	−	0.649750i	$-0.225126\pi$
$193$	15.1925	+	4.07082i	1.09358	+	0.293024i	0.333433	+	0.942774i	$0.391793\pi$
$194$	−14.5292	−	25.1653i	−1.04313	−	1.80676i
$195$		0			0
$196$	19.8634	+	1.49608i	1.41881	+	0.106863i
$197$	8.62996	−	2.31239i	0.614859	−	0.164751i	0.0620697	−	0.998072i	$-0.480230\pi$
$197$	8.62996	−	2.31239i	0.614859	−	0.164751i	0.552790	+	0.833321i	$0.313563\pi$
$198$		0			0
$199$	6.81178			0.482874			0.241437	−	0.970416i	$-0.422381\pi$
$199$	6.81178			0.482874			0.241437	+	0.970416i	$0.422381\pi$
$200$	9.83230	−	2.63456i	0.695249	−	0.186291i
$201$		0			0
$202$	−2.26278	+	8.44483i	−0.159209	+	0.594176i
$203$	1.75497	+	7.69569i	0.123175	+	0.540132i
$204$		0			0
$205$			36.8924i			2.57667i
$206$	−2.16974	+	8.09759i	−0.151173	+	0.564186i
$207$		0			0
$208$	−4.17385	+	3.94847i	−0.289404	+	0.273777i
$209$		−	11.1280i		−	0.769737i
$210$		0			0
$211$	−1.65897	+	2.87342i	−0.114208	+	0.197814i	−0.917463	−	0.397821i	$-0.869766\pi$
$211$	−1.65897	+	2.87342i	−0.114208	+	0.197814i	0.803255	+	0.595636i	$0.203100\pi$
$212$	19.2859	+	11.1347i	1.32456	+	0.764735i
$213$		0			0
$214$	−10.6872	−	10.6872i	−0.730561	−	0.730561i
$215$	−22.7706	+	6.10136i	−1.55294	+	0.416109i
$216$		0			0
$217$	5.98715	+	3.76355i	0.406434	+	0.255486i
$218$	9.29619	+	5.36716i	0.629618	+	0.363510i
$219$		0			0
$220$	18.5614	−	32.1493i	1.25141	−	2.16750i
$221$	−19.9325	+	18.8562i	−1.34081	+	1.26841i
$222$		0			0
$223$	−5.97866	−	22.3127i	−0.400361	−	1.49417i	−0.812455	−	0.583024i	$-0.801869\pi$
$223$	−5.97866	−	22.3127i	−0.400361	−	1.49417i	0.412094	−	0.911141i	$-0.364798\pi$
$224$	−19.1177	−	0.718937i	−1.27735	−	0.0480360i
$225$		0			0
$226$	5.07495	−	18.9400i	0.337581	−	1.25987i
$227$	12.2034	−	12.2034i	0.809965	−	0.809965i	−0.174663	−	0.984628i	$-0.555884\pi$
$227$	12.2034	−	12.2034i	0.809965	−	0.809965i	0.984628	+	0.174663i	$0.0558836\pi$
$228$		0			0
$229$	1.95525	−	7.29710i	0.129207	−	0.482206i	−0.870748	−	0.491730i	$-0.836365\pi$
$229$	1.95525	−	7.29710i	0.129207	−	0.482206i	0.999955	+	0.00952370i	$0.00303153\pi$
$230$	−27.7370	+	16.0140i	−1.82892	+	1.05593i
$231$		0			0
$232$	1.43740	+	5.36445i	0.0943699	+	0.352193i
$233$	18.4325	−	10.6420i	1.20755	−	0.697181i	0.245330	−	0.969440i	$-0.421104\pi$
$233$	18.4325	−	10.6420i	1.20755	−	0.697181i	0.962224	+	0.272258i	$0.0877705\pi$
$234$		0			0
$235$	−4.16465	+	7.21339i	−0.271672	+	0.470550i
$236$	−16.4648	+	16.4648i	−1.07177	+	1.07177i
$237$		0			0
$238$	−44.2899	−	1.66556i	−2.87089	−	0.107962i
$239$	14.8128	+	14.8128i	0.958161	+	0.958161i	0.999159	−	0.0409982i	$-0.0130538\pi$
$239$	14.8128	+	14.8128i	0.958161	+	0.958161i	−0.0409982	+	0.999159i	$0.513054\pi$
$240$		0			0
$241$	−3.26162	−	3.26162i	−0.210100	−	0.210100i	0.594210	−	0.804310i	$-0.297465\pi$
$241$	−3.26162	−	3.26162i	−0.210100	−	0.210100i	−0.804310	+	0.594210i	$0.797465\pi$
$242$	−2.99521	−	11.1783i	−0.192539	−	0.718566i
$243$		0			0
$244$	13.1025	−	22.6942i	0.838804	−	1.45285i
$245$	−7.48825	+	21.3744i	−0.478407	+	1.36556i
$246$		0			0
$247$	8.47645	+	5.21259i	0.539344	+	0.331669i
$248$	4.30908	+	2.48785i	0.273627	+	0.157979i
$249$		0			0
$250$			3.33400i			0.210861i
$251$	−7.81358	−	13.5335i	−0.493189	−	0.854228i	0.506780	−	0.862075i	$-0.330835\pi$
$251$	−7.81358	−	13.5335i	−0.493189	−	0.854228i	−0.999969	+	0.00784717i	$0.997502\pi$
$252$		0			0
$253$	−4.69286	+	17.5140i	−0.295037	+	1.10109i
$254$	−3.33321	−	12.4397i	−0.209144	−	0.780536i
$255$		0			0
$256$	−4.39137			−0.274461
$257$	3.90912			0.243844			0.121922	−	0.992540i	$-0.461094\pi$
$257$	3.90912			0.243844			0.121922	+	0.992540i	$0.461094\pi$
$258$		0			0
$259$	0.168890	−	4.49105i	0.0104943	−	0.279060i
$260$	15.7943	+	29.1981i	0.979523	+	1.81079i
$261$		0			0
$262$	5.56391	+	1.49084i	0.343739	+	0.0921047i
$263$	0.922323	+	1.59751i	0.0568729	+	0.0985067i	0.893060	−	0.449937i	$-0.148554\pi$
$263$	0.922323	+	1.59751i	0.0568729	+	0.0985067i	−0.836187	+	0.548444i	$0.815220\pi$
$264$		0			0
$265$	−17.9038	+	17.9038i	−1.09982	+	1.09982i
$266$	3.57380	+	15.6715i	0.219124	+	0.960879i
$267$		0			0
$268$	21.4802	+	5.75559i	1.31211	+	0.351579i
$269$		−	0.812046i		−	0.0495113i	−0.999694	−	0.0247557i	$-0.992119\pi$
$269$		−	0.812046i		−	0.0495113i	0.999694	−	0.0247557i	$-0.00788078\pi$
$270$		0			0
$271$	4.86056	+	4.86056i	0.295258	+	0.295258i	0.839153	−	0.543895i	$-0.183051\pi$
$271$	4.86056	+	4.86056i	0.295258	+	0.295258i	−0.543895	+	0.839153i	$0.683051\pi$
$272$	12.1268			0.735296
$273$		0			0
$274$	−24.8256			−1.49977
$275$	15.5900	+	15.5900i	0.940111	+	0.940111i
$276$		0			0
$277$			19.0090i			1.14214i	0.820902	+	0.571070i	$0.193471\pi$
$277$			19.0090i			1.14214i	−0.820902	+	0.571070i	$0.806529\pi$
$278$	6.15093	+	1.64814i	0.368908	+	0.0988487i
$279$		0			0
$280$	−4.69984	+	15.2263i	−0.280869	+	0.909948i
$281$	−3.58709	+	3.58709i	−0.213988	+	0.213988i	−0.805959	−	0.591971i	$-0.798350\pi$
$281$	−3.58709	+	3.58709i	−0.213988	+	0.213988i	0.591971	+	0.805959i	$0.298350\pi$
$282$		0			0
$283$	−7.04222	−	12.1975i	−0.418616	−	0.725065i	0.577184	−	0.816614i	$-0.304151\pi$
$283$	−7.04222	−	12.1975i	−0.418616	−	0.725065i	−0.995801	+	0.0915492i	$0.970818\pi$
$284$	7.65869	+	2.05214i	0.454460	+	0.121772i
$285$		0			0
$286$	30.6695	+	9.13682i	1.81353	+	0.540271i
$287$	−25.5412	−	16.0553i	−1.50765	−	0.947716i
$288$		0			0
$289$	40.9126			2.40662
$290$	−21.2480			−1.24773
$291$		0			0
$292$	1.29056	+	4.81642i	0.0755241	+	0.281860i
$293$	−7.18612	+	26.8190i	−0.419818	+	1.56678i	0.355168	+	0.934803i	$0.384424\pi$
$293$	−7.18612	+	26.8190i	−0.419818	+	1.56678i	−0.774985	+	0.631979i	$0.782243\pi$
$294$		0			0
$295$	−13.2371	−	22.9274i	−0.770695	−	1.33488i
$296$		−	3.16213i		−	0.183795i
$297$		0			0
$298$	2.73914	+	1.58145i	0.158674	+	0.0916107i
$299$	−11.1426	−	11.7786i	−0.644393	−	0.681175i
$300$		0			0
$301$	5.68554	−	18.4197i	0.327709	−	1.06170i
$302$	8.83772	−	15.3074i	0.508553	−	0.880840i
$303$		0			0
$304$	−1.13828	−	4.24812i	−0.0652848	−	0.243646i
$305$	21.0679	+	21.0679i	1.20634	+	1.20634i
$306$		0			0
$307$	−20.3066	−	20.3066i	−1.15896	−	1.15896i	−0.984700	−	0.174260i	$-0.944247\pi$
$307$	−20.3066	−	20.3066i	−1.15896	−	1.15896i	−0.174260	−	0.984700i	$-0.555753\pi$
$308$	14.1797	+	26.8415i	0.807963	+	1.52944i
$309$		0			0
$310$	−13.4610	+	13.4610i	−0.764532	+	0.764532i
$311$	3.76230	−	6.51650i	0.213341	−	0.369517i	−0.739417	−	0.673247i	$-0.764899\pi$
$311$	3.76230	−	6.51650i	0.213341	−	0.369517i	0.952758	+	0.303731i	$0.0982323\pi$
$312$		0			0
$313$	21.8314	−	12.6043i	1.23398	−	0.712439i	0.266124	−	0.963939i	$-0.414257\pi$
$313$	21.8314	−	12.6043i	1.23398	−	0.712439i	0.967857	+	0.251500i	$0.0809237\pi$
$314$	1.12844	+	4.21140i	0.0636816	+	0.237663i
$315$		0			0
$316$	−21.2444	+	12.2655i	−1.19509	+	0.689987i
$317$	−1.93925	+	7.23738i	−0.108919	+	0.406492i	−0.998760	−	0.0497787i	$-0.984148\pi$
$317$	−1.93925	+	7.23738i	−0.108919	+	0.406492i	0.889841	+	0.456270i	$0.150815\pi$
$318$		0			0
$319$	−8.50581	+	8.50581i	−0.476234	+	0.476234i
$320$	10.6602	−	39.7846i	0.595926	−	2.22402i
$321$		0			0
$322$	0.984222	−	26.1720i	0.0548485	−	1.45851i
$323$	−5.43595	−	20.2872i	−0.302464	−	1.12881i
$324$		0			0
$325$	−19.1780	+	4.57258i	−1.06380	+	0.253641i
$326$	−0.122838	+	0.212762i	−0.00680339	+	0.0117838i
$327$		0			0
$328$	−18.3826	−	10.6132i	−1.01501	−	0.586015i
$329$	−3.18153	−	6.02249i	−0.175403	−	0.332030i
$330$		0			0
$331$	−26.7149	+	7.15824i	−1.46838	+	0.393452i	−0.902377	−	0.430948i	$-0.858179\pi$
$331$	−26.7149	+	7.15824i	−1.46838	+	0.393452i	−0.566008	+	0.824400i	$0.691513\pi$
$332$	−4.66303	−	4.66303i	−0.255917	−	0.255917i
$333$		0			0
$334$	−42.8818	−	24.7578i	−2.34639	−	1.35469i
$335$	−12.6420	+	21.8965i	−0.690704	+	1.19634i
$336$		0			0
$337$			15.1198i			0.823630i	0.911267	+	0.411815i	$0.135105\pi$
$337$			15.1198i			0.823630i	−0.911267	+	0.411815i	$0.864895\pi$
$338$	−21.3261	+	19.0818i	−1.15998	+	1.03792i
$339$		0			0
$340$	18.1343	−	67.6780i	0.983469	−	3.67036i
$341$			10.7771i			0.583614i
$342$		0			0
$343$	−11.5390	−	14.4862i	−0.623048	−	0.782184i
$344$	3.51048	−	13.1013i	0.189272	−	0.706373i
$345$		0			0
$346$	10.0534	−	2.69381i	0.540475	−	0.144820i
$347$	−0.255152			−0.0136973			−0.00684864	−	0.999977i	$-0.502180\pi$
$347$	−0.255152			−0.0136973			−0.00684864	+	0.999977i	$0.502180\pi$
$348$		0			0
$349$	23.4871	−	6.29335i	1.25723	−	0.336875i	0.432108	−	0.901822i	$-0.357770\pi$
$349$	23.4871	−	6.29335i	1.25723	−	0.336875i	0.825127	+	0.564947i	$0.191103\pi$
$350$	−26.9621	−	16.9485i	−1.44119	−	0.905936i
$351$		0			0
$352$	−14.5776	−	25.2491i	−0.776988	−	1.34578i
$353$	−9.33450	−	2.50117i	−0.496825	−	0.133124i	0.00170096	−	0.999999i	$-0.499459\pi$
$353$	−9.33450	−	2.50117i	−0.496825	−	0.133124i	−0.498526	+	0.866875i	$0.666125\pi$
$354$		0			0
$355$	−4.50746	+	7.80715i	−0.239231	+	0.414360i
$356$	36.2890	−	36.2890i	1.92331	−	1.92331i
$357$		0			0
$358$	48.7154	+	13.0533i	2.57469	+	0.689886i
$359$	−19.6234	−	5.25807i	−1.03568	−	0.277510i	−0.299360	−	0.954140i	$-0.596773\pi$
$359$	−19.6234	−	5.25807i	−1.03568	−	0.277510i	−0.736323	+	0.676630i	$0.763440\pi$
$360$		0			0
$361$	9.85794	−	5.69149i	0.518839	−	0.299552i
$362$	−7.53454	−	7.53454i	−0.396007	−	0.396007i
$363$		0			0
$364$	−27.0880	−	1.77216i	−1.41980	−	0.0928863i
$365$	−5.66933			−0.296746
$366$		0			0
$367$	−18.8485	+	10.8822i	−0.983886	+	0.568047i	−0.903441	−	0.428712i	$-0.858967\pi$
$367$	−18.8485	+	10.8822i	−0.983886	+	0.568047i	−0.0804448	+	0.996759i	$0.525634\pi$
$368$			7.16603i			0.373555i
$369$		0			0
$370$	11.6859	+	3.13122i	0.607519	+	0.162784i
$371$	−4.60349	−	20.1867i	−0.239001	−	1.04804i
$372$		0			0
$373$	−7.76385	+	13.4474i	−0.401997	+	0.696279i	−0.993967	−	0.109681i	$-0.965017\pi$
$373$	−7.76385	+	13.4474i	−0.401997	+	0.696279i	0.591970	+	0.805960i	$0.298350\pi$
$374$	−33.7719	−	58.4947i	−1.74630	−	3.02469i
$375$		0			0
$376$	−2.39617	−	4.15030i	−0.123573	−	0.214035i
$377$	−2.49477	−	10.4634i	−0.128487	−	0.538893i
$378$		0			0
$379$	22.4101	−	6.00477i	1.15113	−	0.308444i	0.367712	−	0.929940i	$-0.380141\pi$
$379$	22.4101	−	6.00477i	1.15113	−	0.308444i	0.783418	+	0.621495i	$0.213474\pi$
$380$	−25.4103			−1.30352
$381$		0			0
$382$	−31.5264	+	8.44746i	−1.61303	+	0.432210i
$383$	0.417833	+	1.55937i	0.0213503	+	0.0796803i	0.975779	−	0.218759i	$-0.0702007\pi$
$383$	0.417833	+	1.55937i	0.0213503	+	0.0796803i	−0.954429	+	0.298439i	$0.903534\pi$
$384$		0			0
$385$	−33.6509	+	7.67394i	−1.71501	+	0.391100i
$386$	−17.3114	−	29.9842i	−0.881127	−	1.52616i
$387$		0			0
$388$	−9.72242	+	36.2846i	−0.493581	+	1.84207i
$389$	−14.1958	−	8.19595i	−0.719756	−	0.415551i	0.0949069	−	0.995486i	$-0.469745\pi$
$389$	−14.1958	−	8.19595i	−0.719756	−	0.415551i	−0.814663	+	0.579935i	$0.803078\pi$
$390$		0			0
$391$			34.2219i			1.73068i
$392$	−8.49612	−	9.88019i	−0.429119	−	0.499025i
$393$		0			0
$394$	−17.0323	−	9.83358i	−0.858073	−	0.495409i
$395$	−7.21874	−	26.9407i	−0.363214	−	1.35553i
$396$		0			0
$397$	−33.4523	+	8.96351i	−1.67892	+	0.449866i	−0.967494	−	0.252894i	$-0.918618\pi$
$397$	−33.4523	+	8.96351i	−1.67892	+	0.449866i	−0.711428	+	0.702759i	$0.751951\pi$
$398$	−10.6028	−	10.6028i	−0.531472	−	0.531472i
$399$		0			0
$400$	7.54620	+	4.35680i	0.377310	+	0.217840i
$401$	−25.6135	+	25.6135i	−1.27908	+	1.27908i	−0.337895	+	0.941184i	$0.609715\pi$
$401$	−25.6135	+	25.6135i	−1.27908	+	1.27908i	−0.941184	+	0.337895i	$0.890285\pi$
$402$		0			0
$403$	−8.20922	−	5.04826i	−0.408930	−	0.251472i
$404$	9.78778	−	5.65098i	0.486960	−	0.281147i
$405$		0			0
$406$	9.24701	−	14.7104i	0.458921	−	0.730064i
$407$	5.93143	−	3.42451i	0.294010	−	0.169747i
$408$		0			0
$409$	−15.6288	+	15.6288i	−0.772795	+	0.772795i	−0.978594	−	0.205799i	$-0.934021\pi$
$409$	−15.6288	+	15.6288i	−0.772795	+	0.772795i	0.205799	+	0.978594i	$0.434021\pi$
$410$	57.4246	−	57.4246i	2.83600	−	2.83600i
$411$		0			0
$412$	9.38533	−	5.41862i	0.462382	−	0.266956i
$413$	21.6337	+	0.813555i	1.06453	+	0.0400324i
$414$		0			0
$415$	6.49329	−	3.74890i	0.318743	−	0.184026i
$416$	26.0614	+	0.723154i	1.27776	+	0.0354556i
$417$		0			0
$418$	−17.3212	+	17.3212i	−0.847206	+	0.847206i
$419$	−6.99593	−	4.03910i	−0.341774	−	0.197323i	0.319282	−	0.947660i	$-0.396558\pi$
$419$	−6.99593	−	4.03910i	−0.341774	−	0.197323i	−0.661056	+	0.750336i	$0.729891\pi$
$420$		0			0
$421$	5.31808	+	5.31808i	0.259187	+	0.259187i	0.824724	−	0.565536i	$-0.191331\pi$
$421$	5.31808	+	5.31808i	0.259187	+	0.259187i	−0.565536	+	0.824724i	$0.691331\pi$
$422$	7.05487	−	1.89035i	0.343425	−	0.0920206i
$423$		0			0
$424$	−3.77047	−	14.0716i	−0.183110	−	0.683377i
$425$	36.0375	+	20.8063i	1.74808	+	1.00925i
$426$		0			0
$427$	−23.7543	+	5.41706i	−1.14955	+	0.262150i
$428$			19.5382i			0.944416i
$429$		0			0
$430$	44.9405	+	25.9464i	2.16722	+	1.25125i
$431$	2.71448	−	10.1306i	0.130752	−	0.487973i	−0.869227	−	0.494413i	$-0.835383\pi$
$431$	2.71448	−	10.1306i	0.130752	−	0.487973i	0.999979	+	0.00643990i	$0.00204990\pi$
$432$		0			0
$433$	2.59289	+	4.49102i	0.124607	+	0.215825i	0.921579	−	0.388191i	$-0.126900\pi$
$433$	2.59289	+	4.49102i	0.124607	+	0.215825i	−0.796973	+	0.604016i	$0.793566\pi$
$434$	−3.46114	−	15.1774i	−0.166140	−	0.728538i
$435$		0			0
$436$	−3.59151	−	13.4037i	−0.172002	−	0.641921i
$437$	11.9882	−	3.21223i	0.573474	−	0.153662i
$438$		0			0
$439$	8.67818			0.414187			0.207093	−	0.978321i	$-0.433600\pi$
$439$	8.67818			0.414187			0.207093	+	0.978321i	$0.433600\pi$
$440$	−23.4571	+	6.28531i	−1.11827	+	0.299641i
$441$		0			0
$442$	60.3764	+	1.67533i	2.87181	+	0.0796875i
$443$	−5.13279	−	8.89025i	−0.243866	−	0.422388i	0.717946	−	0.696099i	$-0.245082\pi$
$443$	−5.13279	−	8.89025i	−0.243866	−	0.422388i	−0.961812	+	0.273710i	$0.911749\pi$
$444$		0			0
$445$	29.1750	+	50.5326i	1.38303	+	2.39548i
$446$	−25.4246	+	44.0367i	−1.20389	+	2.08520i
$447$		0			0
$448$	22.9043	+	24.6943i	1.08213	+	1.16669i
$449$	−7.73538	−	2.07269i	−0.365055	−	0.0978162i	0.0716285	−	0.997431i	$-0.477180\pi$
$449$	−7.73538	−	2.07269i	−0.365055	−	0.0978162i	−0.436684	+	0.899615i	$0.643847\pi$
$450$		0			0
$451$		−	45.9753i		−	2.16489i
$452$	−21.9519	+	12.6740i	−1.03253	+	0.596133i
$453$		0			0
$454$	−37.9901			−1.78297
$455$	9.91744	−	29.2274i	0.464937	−	1.37020i
$456$		0			0
$457$	−18.3530	−	18.3530i	−0.858515	−	0.858515i	0.132648	−	0.991163i	$-0.457652\pi$
$457$	−18.3530	−	18.3530i	−0.858515	−	0.858515i	−0.991163	+	0.132648i	$0.957652\pi$
$458$	−14.4017	+	8.31482i	−0.672947	+	0.388526i
$459$		0			0
$460$	39.9926	+	10.7160i	1.86466	+	0.499635i
$461$	−14.2955	−	3.83046i	−0.665807	−	0.178402i	−0.0899418	−	0.995947i	$-0.528668\pi$
$461$	−14.2955	−	3.83046i	−0.665807	−	0.178402i	−0.575865	+	0.817545i	$0.695335\pi$
$462$		0			0
$463$	6.69179	−	6.69179i	0.310994	−	0.310994i	−0.534301	−	0.845294i	$-0.679425\pi$
$463$	6.69179	−	6.69179i	0.310994	−	0.310994i	0.845294	+	0.534301i	$0.179425\pi$
$464$	−2.37705	+	4.11717i	−0.110352	+	0.191135i
$465$		0			0
$466$	−45.2558	−	12.1263i	−2.09643	−	0.561738i
$467$	15.6442	+	27.0965i	0.723925	+	1.25388i	0.959415	+	0.281998i	$0.0909973\pi$
$467$	15.6442	+	27.0965i	0.723925	+	1.25388i	−0.235490	+	0.971877i	$0.575669\pi$
$468$		0			0
$469$	−9.65765	−	18.2815i	−0.445949	−	0.844161i
$470$	17.7104	−	4.74550i	0.816922	−	0.218894i
$471$		0			0
$472$	15.2322			0.701119
$473$	28.3767	−	7.60353i	1.30476	−	0.349611i
$474$		0			0
$475$	3.90595	−	14.5772i	0.179217	−	0.668848i
$476$	38.9628	+	42.0077i	1.78586	+	1.92542i
$477$		0			0
$478$		−	46.1136i		−	2.10919i
$479$	−8.45059	+	31.5380i	−0.386117	+	1.44101i	0.450280	+	0.892887i	$0.351324\pi$
$479$	−8.45059	+	31.5380i	−0.386117	+	1.44101i	−0.836398	+	0.548123i	$0.815343\pi$
$480$		0			0
$481$	−0.169881	+	6.12224i	−0.00774590	+	0.279150i
$482$			10.1537i			0.462489i
$483$		0			0
$484$	−7.48010	+	12.9559i	−0.340004	+	0.588905i
$485$	−36.9879	−	21.3550i	−1.67953	−	0.969679i
$486$		0			0
$487$	0.388513	+	0.388513i	0.0176052	+	0.0176052i	0.715855	−	0.698249i	$-0.246037\pi$
$487$	0.388513	+	0.388513i	0.0176052	+	0.0176052i	−0.698249	+	0.715855i	$0.746037\pi$
$488$	−16.5584	+	4.43682i	−0.749565	+	0.200845i
$489$		0			0
$490$	44.9260	−	21.6144i	2.02955	−	0.976438i
$491$	11.1482	+	6.43644i	0.503113	+	0.290472i	0.729998	−	0.683449i	$-0.239521\pi$
$491$	11.1482	+	6.43644i	0.503113	+	0.290472i	−0.226885	+	0.973921i	$0.572854\pi$
$492$		0			0
$493$	−11.3518	+	19.6619i	−0.511259	+	0.885526i
$494$	−5.08034	−	21.3076i	−0.228575	−	0.958675i
$495$		0			0
$496$	1.10239	+	4.11419i	0.0494989	+	0.184733i
$497$	−3.44341	−	6.51821i	−0.154458	−	0.292382i
$498$		0			0
$499$	0.964321	−	3.59890i	0.0431689	−	0.161109i	−0.940977	−	0.338472i	$-0.890090\pi$
$499$	0.964321	−	3.59890i	0.0431689	−	0.161109i	0.984145	+	0.177363i	$0.0567567\pi$
$500$	3.04760	−	3.04760i	0.136293	−	0.136293i
$501$		0			0
$502$	−8.90334	+	33.2277i	−0.397375	+	1.48303i
$503$	−12.0422	+	6.95256i	−0.536935	+	0.309999i	−0.743836	−	0.668362i	$-0.766996\pi$
$503$	−12.0422	+	6.95256i	−0.536935	+	0.309999i	0.206901	+	0.978362i	$0.433662\pi$
$504$		0			0
$505$	3.32584	+	12.4122i	0.147998	+	0.552335i
$506$	34.5659	−	19.9566i	1.53664	−	0.887181i
$507$		0			0
$508$	−8.32421	+	14.4179i	−0.369327	+	0.639693i
$509$	−13.0210	+	13.0210i	−0.577144	+	0.577144i	−0.934115	−	0.356971i	$-0.883809\pi$
$509$	−13.0210	+	13.0210i	−0.577144	+	0.577144i	0.356971	+	0.934115i	$0.383809\pi$
$510$		0			0
$511$	2.46726	−	3.92498i	0.109145	−	0.173631i
$512$	−12.3429	−	12.3429i	−0.545485	−	0.545485i
$513$		0			0
$514$	−6.08472	−	6.08472i	−0.268386	−	0.268386i
$515$	3.18908	+	11.9018i	0.140528	+	0.524457i
$516$		0			0
$517$	5.19000	−	8.98935i	0.228256	−	0.395351i
$518$	−7.25341	+	6.72764i	−0.318697	+	0.295596i
$519$		0			0
$520$	6.20017	−	20.8121i	0.271896	−	0.912670i
$521$	−2.00007	−	1.15474i	−0.0876246	−	0.0505901i	0.455547	−	0.890211i	$-0.349444\pi$
$521$	−2.00007	−	1.15474i	−0.0876246	−	0.0505901i	−0.543172	+	0.839621i	$0.682777\pi$
$522$		0			0
$523$		−	0.544569i		−	0.0238124i	−0.999929	−	0.0119062i	$-0.996210\pi$
$523$		−	0.544569i		−	0.0238124i	0.999929	−	0.0119062i	$-0.00378994\pi$
$524$	−3.72317	−	6.44872i	−0.162647	−	0.281714i
$525$		0			0
$526$	1.05096	−	3.92223i	0.0458240	−	0.171017i
$527$	5.26457	+	19.6476i	0.229328	+	0.855865i
$528$		0			0
$529$	2.77742			0.120757
$530$	55.7361			2.42102
$531$		0			0
$532$	11.0584	−	17.5920i	0.479443	−	0.762711i
$533$	35.0206	+	21.5359i	1.51691	+	0.932824i
$534$		0			0
$535$	−21.4575	−	5.74953i	−0.927690	−	0.248574i
$536$	−7.27368	−	12.5984i	−0.314175	−	0.544167i
$537$		0			0
$538$	−1.26399	+	1.26399i	−0.0544943	+	0.0544943i
$539$	9.33187	−	26.6368i	0.401952	−	1.14733i
$540$		0			0
$541$	35.8145	+	9.59647i	1.53979	+	0.412584i	0.926196	−	0.377041i	$-0.123059\pi$
$541$	35.8145	+	9.59647i	1.53979	+	0.412584i	0.613589	+	0.789626i	$0.289725\pi$
$542$		−	15.1314i		−	0.649948i
$543$		0			0
$544$	−38.9103	−	38.9103i	−1.66826	−	1.66826i
$545$	15.7773			0.675825
$546$		0			0
$547$	−11.4043			−0.487613			−0.243806	−	0.969824i	$-0.578396\pi$
$547$	−11.4043			−0.487613			−0.243806	+	0.969824i	$0.578396\pi$
$548$	22.6930	+	22.6930i	0.969397	+	0.969397i
$549$		0			0
$550$		−	48.5330i		−	2.06945i
$551$	7.95324	+	2.13106i	0.338819	+	0.0907864i
$552$		0			0
$553$	21.7931	+	6.72676i	0.926736	+	0.286051i
$554$	29.5883	−	29.5883i	1.25709	−	1.25709i
$555$		0			0
$556$	−4.11599	−	7.12910i	−0.174557	−	0.302341i
$557$	2.44687	+	0.655638i	0.103677	+	0.0277803i	0.310285	−	0.950644i	$-0.399576\pi$
$557$	2.44687	+	0.655638i	0.103677	+	0.0277803i	−0.206607	+	0.978424i	$0.566242\pi$
$558$		0			0
$559$	−7.50053	+	25.1770i	−0.317239	+	1.06487i
$560$	−12.0613	+	6.37170i	−0.509685	+	0.269253i
$561$		0			0
$562$	11.1669			0.471048
$563$	14.6059			0.615564			0.307782	−	0.951457i	$-0.400413\pi$
$563$	14.6059			0.615564			0.307782	+	0.951457i	$0.400413\pi$
$564$		0			0
$565$	−7.45915	−	27.8379i	−0.313809	−	1.17115i
$566$	−8.02439	+	29.9474i	−0.337290	+	1.25879i
$567$		0			0
$568$	−2.59341	−	4.49192i	−0.108817	−	0.188477i
$569$		−	17.4403i		−	0.731137i	−0.930784	−	0.365568i	$-0.880875\pi$
$569$		−	17.4403i		−	0.731137i	0.930784	−	0.365568i	$-0.119125\pi$
$570$		0			0
$571$	−30.0741	−	17.3633i	−1.25856	−	0.726630i	−0.285766	−	0.958299i	$-0.592248\pi$
$571$	−30.0741	−	17.3633i	−1.25856	−	0.726630i	−0.972795	+	0.231669i	$0.925581\pi$
$572$	−19.6829	−	36.3868i	−0.822985	−	1.52141i
$573$		0			0
$574$	14.7652	+	64.7469i	0.616289	+	2.70248i
$575$	−12.2949	+	21.2954i	−0.512734	+	0.888081i
$576$		0			0
$577$	4.83633	+	18.0494i	0.201339	+	0.751407i	0.990534	+	0.137265i	$0.0438311\pi$
$577$	4.83633	+	18.0494i	0.201339	+	0.751407i	−0.789196	+	0.614142i	$0.789502\pi$
$578$	−63.6822	−	63.6822i	−2.64883	−	2.64883i
$579$		0			0
$580$	19.4227	+	19.4227i	0.806485	+	0.806485i
$581$	−0.230408	+	6.12692i	−0.00955895	+	0.254187i
$582$		0			0
$583$	22.3117	−	22.3117i	0.924058	−	0.924058i
$584$	1.63095	−	2.82489i	0.0674893	−	0.116895i
$585$		0			0
$586$	52.9305	−	30.5594i	2.18654	−	1.26240i
$587$	8.61022	+	32.1338i	0.355382	+	1.32630i	0.880004	+	0.474967i	$0.157540\pi$
$587$	8.61022	+	32.1338i	0.355382	+	1.32630i	−0.524622	+	0.851335i	$0.675793\pi$
$588$		0			0
$589$	6.38857	−	3.68844i	0.263237	−	0.151980i
$590$	−15.0833	+	56.2916i	−0.620969	+	2.31749i
$591$		0			0
$592$	1.91404	−	1.91404i	0.0786666	−	0.0786666i
$593$	−1.18632	+	4.42742i	−0.0487164	+	0.181812i	−0.985997	−	0.166764i	$-0.946668\pi$
$593$	−1.18632	+	4.42742i	−0.0487164	+	0.181812i	0.937280	+	0.348576i	$0.113335\pi$
$594$		0			0
$595$	−57.5999	+	30.4286i	−2.36137	+	1.24745i
$596$	−1.05825	−	3.94943i	−0.0433475	−	0.161775i
$597$		0			0
$598$	−0.989995	+	35.6779i	−0.0404839	+	1.45898i
$599$	9.84386	−	17.0501i	0.402209	−	0.696646i	−0.591783	−	0.806097i	$-0.701576\pi$
$599$	9.84386	−	17.0501i	0.402209	−	0.696646i	0.993992	+	0.109451i	$0.0349092\pi$
$600$		0			0
$601$	−10.6224	−	6.13284i	−0.433296	−	0.250164i	0.267454	−	0.963571i	$-0.413818\pi$
$601$	−10.6224	−	6.13284i	−0.433296	−	0.250164i	−0.700750	+	0.713407i	$0.747151\pi$
$602$	−37.5210	+	19.8214i	−1.52924	+	0.807859i
$603$		0			0
$604$	−22.0709	+	5.91389i	−0.898054	+	0.240633i
$605$	−12.0274	−	12.0274i	−0.488985	−	0.488985i
$606$		0			0
$607$	20.8458	+	12.0353i	0.846105	+	0.488499i	0.859335	−	0.511413i	$-0.170878\pi$
$607$	20.8458	+	12.0353i	0.846105	+	0.488499i	−0.0132296	+	0.999912i	$0.504211\pi$
$608$	−9.97828	+	17.2829i	−0.404672	+	0.700913i
$609$		0			0
$610$		−	65.5862i		−	2.65551i
$611$	4.41630	+	8.16418i	0.178664	+	0.330287i
$612$		0			0
$613$	−12.5294	+	46.7603i	−0.506057	+	1.88863i	−0.0498516	+	0.998757i	$0.515875\pi$
$613$	−12.5294	+	46.7603i	−0.506057	+	1.88863i	−0.456206	+	0.889874i	$0.650792\pi$
$614$			63.2163i			2.55120i
$615$		0			0
$616$	5.85696	−	18.9751i	0.235983	−	0.764529i
$617$	−4.83334	+	18.0383i	−0.194583	+	0.726194i	0.797791	+	0.602934i	$0.206002\pi$
$617$	−4.83334	+	18.0383i	−0.194583	+	0.726194i	−0.992374	+	0.123260i	$0.960665\pi$
$618$		0			0
$619$	9.70855	−	2.60140i	0.390219	−	0.104559i	−0.0583743	−	0.998295i	$-0.518592\pi$
$619$	9.70855	−	2.60140i	0.390219	−	0.104559i	0.448594	+	0.893736i	$0.351925\pi$
$620$	24.6092			0.988331
$621$		0			0
$622$	−15.9994	+	4.28703i	−0.641518	+	0.171894i
$623$	−47.6814	−	1.79310i	−1.91032	−	0.0718391i
$624$		0			0
$625$	−11.2201	−	19.4339i	−0.448806	−	0.777354i
$626$	−53.6007	−	14.3623i	−2.14231	−	0.574031i
$627$		0			0
$628$	2.81812	−	4.88112i	0.112455	−	0.194778i
$629$	9.14066	−	9.14066i	0.364462	−	0.364462i
$630$		0			0
$631$	8.95627	+	2.39983i	0.356543	+	0.0955355i	0.432645	−	0.901565i	$-0.357581\pi$
$631$	8.95627	+	2.39983i	0.356543	+	0.0955355i	−0.0761011	+	0.997100i	$0.524247\pi$
$632$	15.5006	+	4.15337i	0.616580	+	0.165212i
$633$		0			0
$634$	14.2838	−	8.24678i	0.567284	−	0.327521i
$635$	−13.3847	−	13.3847i	−0.531156	−	0.531156i
$636$		0			0
$637$	15.9187	+	19.5856i	0.630720	+	0.776010i
$638$	26.4793			1.04833
$639$		0			0
$640$	−37.9979	+	21.9381i	−1.50200	+	0.867179i
$641$			32.1058i			1.26810i	0.773291	+	0.634052i	$0.218609\pi$
$641$			32.1058i			1.26810i	−0.773291	+	0.634052i	$0.781391\pi$
$642$		0			0
$643$	7.89631	+	2.11581i	0.311400	+	0.0834393i	0.411134	−	0.911575i	$-0.365133\pi$
$643$	7.89631	+	2.11581i	0.311400	+	0.0834393i	−0.0997345	+	0.995014i	$0.531799\pi$
$644$	−24.8234	+	23.0241i	−0.978179	+	0.907275i
$645$		0			0
$646$	−23.1167	+	40.0393i	−0.909514	+	1.57532i
$647$	−4.00052	−	6.92910i	−0.157276	−	0.272411i	0.776609	−	0.629983i	$-0.216938\pi$
$647$	−4.00052	−	6.92910i	−0.157276	−	0.272411i	−0.933886	+	0.357572i	$0.883605\pi$
$648$		0			0
$649$	16.4961	+	28.5721i	0.647529	+	1.12155i
$650$	36.9688	+	22.7340i	1.45004	+	0.891700i
$651$		0			0
$652$	0.306771	−	0.0821991i	0.0120141	−	0.00321917i
$653$	45.0155			1.76159			0.880797	−	0.473495i	$-0.157008\pi$
$653$	45.0155			1.76159			0.880797	+	0.473495i	$0.157008\pi$
$654$		0			0
$655$	8.17782	−	2.19124i	0.319534	−	0.0856189i
$656$	−4.70282	−	17.5512i	−0.183614	−	0.685258i
$657$		0			0
$658$	−4.42208	+	14.3265i	−0.172391	+	0.558504i
$659$	−15.9656	−	27.6532i	−0.621930	−	1.07721i	−0.989126	−	0.147071i	$-0.953015\pi$
$659$	−15.9656	−	27.6532i	−0.621930	−	1.07721i	0.367196	−	0.930144i	$-0.380318\pi$
$660$		0			0
$661$	4.10014	−	15.3019i	0.159477	−	0.595175i	−0.839204	−	0.543817i	$-0.816978\pi$
$661$	4.10014	−	15.3019i	0.159477	−	0.595175i	0.998680	−	0.0513580i	$-0.0163549\pi$
$662$	52.7251	+	30.4408i	2.04922	+	1.18312i
$663$		0			0
$664$			4.31394i			0.167413i
$665$	16.0660	+	17.3215i	0.623012	+	0.671701i
$666$		0			0
$667$	−11.6187	−	6.70804i	−0.449877	−	0.259737i
$668$	16.5671	+	61.8291i	0.640999	+	2.39224i
$669$		0			0
$670$	53.7607	−	14.4051i	2.07696	−	0.556519i
$671$	−26.2548	−	26.2548i	−1.01356	−	1.01356i
$672$		0			0
$673$	−2.46102	−	1.42087i	−0.0948654	−	0.0547706i	0.451817	−	0.892111i	$-0.350776\pi$
$673$	−2.46102	−	1.42087i	−0.0948654	−	0.0547706i	−0.546682	+	0.837340i	$0.684109\pi$
$674$	23.5347	−	23.5347i	0.906523	−	0.906523i
$675$		0			0
$676$	36.9367	+	2.05143i	1.42064	+	0.0789011i
$677$	−5.65487	+	3.26484i	−0.217334	+	0.125478i	−0.604715	−	0.796442i	$-0.706713\pi$
$677$	−5.65487	+	3.26484i	−0.217334	+	0.125478i	0.387381	+	0.921920i	$0.373380\pi$
$678$		0			0
$679$	30.8813	−	16.3138i	1.18512	−	0.626067i
$680$	−39.6940	+	22.9173i	−1.52220	+	0.878840i
$681$		0			0
$682$	16.7751	−	16.7751i	0.642351	−	0.642351i
$683$	23.0449	−	23.0449i	0.881789	−	0.881789i	−0.111928	−	0.993716i	$-0.535703\pi$
$683$	23.0449	−	23.0449i	0.881789	−	0.881789i	0.993716	+	0.111928i	$0.0357025\pi$
$684$		0			0
$685$	−31.6001	+	18.2443i	−1.20738	+	0.697080i
$686$	−4.58749	+	40.5095i	−0.175151	+	1.54666i
$687$		0			0
$688$	10.0551	−	5.80532i	0.383347	−	0.221326i
$689$	6.54408	+	27.4468i	0.249310	+	1.04564i
$690$		0			0
$691$	−18.4648	+	18.4648i	−0.702433	+	0.702433i	−0.964932	−	0.262500i	$-0.915453\pi$
$691$	−18.4648	+	18.4648i	−0.702433	+	0.702433i	0.262500	+	0.964932i	$0.415453\pi$
$692$	−11.6522	−	6.72739i	−0.442950	−	0.255737i
$693$		0			0
$694$	0.397155	+	0.397155i	0.0150758	+	0.0150758i
$695$	9.04063	−	2.42243i	0.342931	−	0.0918880i
$696$		0			0
$697$	−22.4587	−	83.8170i	−0.850684	−	3.17480i
$698$	−46.3546	−	26.7628i	−1.75455	−	1.01299i
$699$		0			0
$700$	9.15341	+	40.1385i	0.345966	+	1.51709i
$701$		−	41.5208i		−	1.56822i	−0.620623	−	0.784109i	$-0.713120\pi$
$701$		−	41.5208i		−	1.56822i	0.620623	−	0.784109i	$-0.286880\pi$
$702$		0			0
$703$	−4.06003	−	2.34406i	−0.153127	−	0.0884079i
$704$	−13.2848	+	49.5796i	−0.500690	+	1.86860i
$705$		0			0
$706$	10.6364	+	18.4227i	0.400305	+	0.693349i
$707$	−10.0406	−	3.09917i	−0.377614	−	0.116556i
$708$		0			0
$709$	−11.8453	−	44.2073i	−0.444860	−	1.66024i	−0.716305	−	0.697787i	$-0.754168\pi$
$709$	−11.8453	−	44.2073i	−0.444860	−	1.66024i	0.271445	−	0.962454i	$-0.412499\pi$
$710$	19.1682	−	5.13611i	0.719371	−	0.192755i
$711$		0			0
$712$	−33.5723			−1.25817
$713$	−11.6103	+	3.11096i	−0.434808	+	0.116507i
$714$		0			0
$715$	45.7533	−	10.9089i	1.71108	−	0.407969i
$716$	−32.5986	−	56.4625i	−1.21827	−	2.11010i
$717$		0			0
$718$	22.3603	+	38.7291i	0.834478	+	1.44536i
$719$	21.2541	−	36.8132i	0.792645	−	1.37290i	−0.131679	−	0.991292i	$-0.542037\pi$
$719$	21.2541	−	36.8132i	0.792645	−	1.37290i	0.924324	−	0.381608i	$-0.124630\pi$
$720$		0			0
$721$	−9.62771	−	2.97174i	−0.358555	−	0.110673i
$722$	−24.2034	−	6.48528i	−0.900757	−	0.241357i
$723$		0			0
$724$			13.7746i			0.511929i
$725$	−14.1279	+	8.15672i	−0.524695	+	0.302933i
$726$		0			0
$727$	44.5147			1.65096			0.825479	−	0.564433i	$-0.190905\pi$
$727$	44.5147			1.65096			0.825479	+	0.564433i	$0.190905\pi$
$728$	11.7103	+	13.3498i	0.434012	+	0.494775i
$729$		0			0
$730$	8.82457	+	8.82457i	0.326612	+	0.326612i
$731$	48.0190	−	27.7238i	1.77605	−	1.02540i
$732$		0			0
$733$	0.0758491	+	0.0203237i	0.00280155	+	0.000750673i	0.260220	−	0.965549i	$-0.416205\pi$
$733$	0.0758491	+	0.0203237i	0.00280155	+	0.000750673i	−0.257418	+	0.966300i	$0.582872\pi$
$734$	46.2772	+	12.3999i	1.70812	+	0.457691i
$735$		0			0
$736$	22.9930	−	22.9930i	0.847534	−	0.847534i
$737$	15.7544	−	27.2875i	0.580322	−	1.00515i
$738$		0			0
$739$	39.9436	+	10.7028i	1.46935	+	0.393711i	0.902708	−	0.430255i	$-0.141576\pi$
$739$	39.9436	+	10.7028i	1.46935	+	0.393711i	0.566640	+	0.823965i	$0.308243\pi$
$740$	−7.81977	−	13.5442i	−0.287460	−	0.497896i
$741$		0			0
$742$	−24.2560	+	38.5871i	−0.890466	+	1.41658i
$743$	−28.0978	+	7.52879i	−1.03081	+	0.276205i	−0.734300	−	0.678825i	$-0.762489\pi$
$743$	−28.0978	+	7.52879i	−1.03081	+	0.276205i	−0.296510	+	0.955030i	$0.595823\pi$
$744$		0			0
$745$	4.64881			0.170319
$746$	33.0162	−	8.84667i	1.20881	−	0.323900i
$747$		0			0
$748$	−22.5990	+	84.3405i	−0.826300	+	3.08380i
$749$	13.3187	−	12.3533i	0.486654	−	0.451379i
$750$		0			0
$751$			1.29328i			0.0471923i	0.999722	+	0.0235961i	$0.00751158\pi$
$751$			1.29328i			0.0471923i	−0.999722	+	0.0235961i	$0.992488\pi$
$752$	1.06177	−	3.96258i	0.0387188	−	0.144501i
$753$		0			0
$754$	−12.4035	+	20.1700i	−0.451710	+	0.734547i
$755$		−	25.9793i		−	0.945484i
$756$		0			0
$757$	23.6428	−	40.9506i	0.859313	−	1.48837i	−0.0132729	−	0.999912i	$-0.504225\pi$
$757$	23.6428	−	40.9506i	0.859313	−	1.48837i	0.872586	−	0.488461i	$-0.162442\pi$
$758$	−44.2290	−	25.5356i	−1.60647	−	0.927496i
$759$		0			0
$760$	11.7540	+	11.7540i	0.426362	+	0.426362i
$761$	−20.6122	+	5.52303i	−0.747193	+	0.200210i	−0.612273	−	0.790647i	$-0.709744\pi$
$761$	−20.6122	+	5.52303i	−0.747193	+	0.200210i	−0.134920	+	0.990856i	$0.543078\pi$
$762$		0			0
$763$	−6.86617	+	10.9229i	−0.248572	+	0.395435i
$764$	36.5399	+	21.0963i	1.32197	+	0.763238i
$765$		0			0
$766$	1.77686	−	3.07761i	0.0642005	−	0.111199i
$767$	−29.4913	−	0.818328i	−1.06487	−	0.0295481i
$768$		0			0
$769$	−6.12447	−	22.8568i	−0.220854	−	0.824238i	−0.984023	−	0.178040i	$-0.943024\pi$
$769$	−6.12447	−	22.8568i	−0.220854	−	0.824238i	0.763169	−	0.646198i	$-0.223642\pi$
$770$	64.3240	+	40.4344i	2.31808	+	1.45715i
$771$		0			0
$772$	−11.5842	+	43.2327i	−0.416924	+	1.55598i
$773$	−35.7559	+	35.7559i	−1.28605	+	1.28605i	−0.348887	+	0.937165i	$0.613440\pi$
$773$	−35.7559	+	35.7559i	−1.28605	+	1.28605i	−0.937165	+	0.348887i	$0.886560\pi$
$774$		0			0
$775$	−3.78281	+	14.1176i	−0.135883	+	0.507121i
$776$	21.2813	−	12.2868i	0.763956	−	0.441070i
$777$		0			0
$778$	9.33904	+	34.8538i	0.334821	+	1.24957i
$779$	−27.2537	+	15.7349i	−0.976465	+	0.563762i
$780$		0			0
$781$	5.61720	−	9.72928i	0.200999	−	0.348141i
$782$	53.2680	−	53.2680i	1.90486	−	1.90486i
$783$		0			0
$784$	0.837781	−	11.1232i	0.0299207	−	0.397257i
$785$	4.53132	+	4.53132i	0.161730	+	0.161730i
$786$		0			0
$787$	−30.7868	−	30.7868i	−1.09743	−	1.09743i	−0.994710	−	0.102719i	$-0.967246\pi$
$787$	−30.7868	−	30.7868i	−1.09743	−	1.09743i	−0.102719	−	0.994710i	$-0.532754\pi$
$788$	6.58029	+	24.5580i	0.234413	+	0.874841i
$789$		0			0
$790$	−30.6981	+	53.1707i	−1.09219	+	1.89173i
$791$	22.5189	+	6.95079i	0.800679	+	0.247142i
$792$		0			0
$793$	32.2974	−	7.70061i	1.14691	−	0.273457i
$794$	66.0221	+	38.1179i	2.34304	+	1.35275i
$795$		0			0
$796$			19.3840i			0.687049i
$797$	4.66397	+	8.07823i	0.165206	+	0.286146i	0.936728	−	0.350057i	$-0.113838\pi$
$797$	4.66397	+	8.07823i	0.165206	+	0.286146i	−0.771522	+	0.636202i	$0.780504\pi$
$798$		0			0
$799$	5.07058	−	18.9236i	0.179384	−	0.669471i
$800$	−10.2336	−	38.1922i	−0.361811	−	1.35030i
$801$		0			0
$802$	79.7372			2.81562
$803$	7.06513			0.249323
$804$		0			0
$805$	−17.9810	−	34.0372i	−0.633746	−	1.19965i
$806$	4.92017	+	20.6359i	0.173306	+	0.726867i
$807$		0			0
$808$	−7.14147	−	1.91355i	−0.251236	−	0.0673185i
$809$	23.5718	+	40.8275i	0.828740	+	1.43542i	0.899027	+	0.437893i	$0.144275\pi$
$809$	23.5718	+	40.8275i	0.828740	+	1.43542i	−0.0702876	+	0.997527i	$0.522392\pi$
$810$		0			0
$811$	−1.45328	+	1.45328i	−0.0510314	+	0.0510314i	−0.732162	−	0.681131i	$-0.761489\pi$
$811$	−1.45328	+	1.45328i	−0.0510314	+	0.0510314i	0.681131	+	0.732162i	$0.261489\pi$
$812$	−21.8994	+	4.99405i	−0.768517	+	0.175257i
$813$		0			0
$814$	−14.5629	−	3.90213i	−0.510431	−	0.136770i
$815$			0.361095i			0.0126486i
$816$		0			0
$817$	−14.2192	−	14.2192i	−0.497465	−	0.497465i
$818$	48.6539			1.70114
$819$		0			0
$820$	−104.983			−3.66617
$821$	8.85777	+	8.85777i	0.309138	+	0.309138i	0.844575	−	0.535437i	$-0.179853\pi$
$821$	8.85777	+	8.85777i	0.309138	+	0.309138i	−0.535437	+	0.844575i	$0.679853\pi$
$822$		0			0
$823$			12.3547i			0.430659i	0.976541	+	0.215330i	$0.0690826\pi$
$823$			12.3547i			0.430659i	−0.976541	+	0.215330i	$0.930917\pi$
$824$	−6.84783	−	1.83487i	−0.238555	−	0.0639207i
$825$		0			0
$826$	−32.4075	−	34.9402i	−1.12760	−	1.21572i
$827$	−39.0342	+	39.0342i	−1.35735	+	1.35735i	−0.480185	+	0.877167i	$0.659430\pi$
$827$	−39.0342	+	39.0342i	−1.35735	+	1.35735i	−0.877167	+	0.480185i	$0.840570\pi$
$828$		0			0
$829$	21.8964	+	37.9258i	0.760495	+	1.31722i	0.942596	+	0.333936i	$0.108377\pi$
$829$	21.8964	+	37.9258i	0.760495	+	1.31722i	−0.182101	+	0.983280i	$0.558290\pi$
$830$	−15.9424	−	4.27176i	−0.553370	−	0.148275i
$831$		0			0
$832$	−31.5431	−	33.3436i	−1.09356	−	1.15598i
$833$	4.00089	−	53.1198i	0.138623	−	1.84049i
$834$		0			0
$835$	−72.7780			−2.51859
$836$	31.6664			1.09521
$837$		0			0
$838$	4.60244	+	17.1765i	0.158989	+	0.593353i
$839$	−13.1086	+	48.9218i	−0.452558	+	1.68897i	0.242612	+	0.970123i	$0.421996\pi$
$839$	−13.1086	+	48.9218i	−0.452558	+	1.68897i	−0.695170	+	0.718846i	$0.744671\pi$
$840$		0			0
$841$	10.0497	+	17.4067i	0.346543	+	0.600230i
$842$		−	16.5557i		−	0.570546i
$843$		0			0
$844$	−8.17678	−	4.72087i	−0.281456	−	0.162499i
$845$	−13.1223	+	39.9614i	−0.451422	+	1.37472i
$846$		0			0
$847$	13.5611	−	3.09254i	0.465964	−	0.106261i
$848$	6.23528	−	10.7998i	0.214120	−	0.370867i
$849$		0			0
$850$	−23.7081	−	88.4799i	−0.813182	−	3.03483i
$851$	5.40144	+	5.40144i	0.185159	+	0.185159i
$852$		0			0
$853$	−12.0121	−	12.0121i	−0.411288	−	0.411288i	0.470899	−	0.882187i	$-0.343930\pi$
$853$	−12.0121	−	12.0121i	−0.411288	−	0.411288i	−0.882187	+	0.470899i	$0.843930\pi$
$854$	45.4065	+	28.5427i	1.55378	+	0.976712i
$855$		0			0
$856$	9.03776	−	9.03776i	0.308904	−	0.308904i
$857$	−25.7042	+	44.5209i	−0.878038	+	1.52081i	−0.0245462	+	0.999699i	$0.507814\pi$
$857$	−25.7042	+	44.5209i	−0.878038	+	1.52081i	−0.853491	+	0.521107i	$0.825519\pi$
$858$		0			0
$859$	−31.2553	+	18.0452i	−1.06642	+	0.615695i	−0.927200	−	0.374567i	$-0.877791\pi$
$859$	−31.2553	+	18.0452i	−1.06642	+	0.615695i	−0.139216	+	0.990262i	$0.544458\pi$
$860$	−17.3624	−	64.7974i	−0.592053	−	2.20957i
$861$		0			0
$862$	−19.9939	+	11.5435i	−0.680995	+	0.393173i
$863$	3.18919	−	11.9022i	0.108561	−	0.405156i	−0.890164	−	0.455641i	$-0.849410\pi$
$863$	3.18919	−	11.9022i	0.108561	−	0.405156i	0.998725	+	0.0504853i	$0.0160768\pi$
$864$		0			0
$865$	10.8171	−	10.8171i	0.367794	−	0.367794i
$866$	2.95452	−	11.0264i	0.100399	−	0.374694i
$867$		0			0
$868$	−10.7098	+	17.0374i	−0.363514	+	0.578287i
$869$	8.99601	+	33.5736i	0.305169	+	1.13890i
$870$		0			0
$871$	13.4058	+	24.7827i	0.454239	+	0.839728i
$872$	−4.53881	+	7.86144i	−0.153703	+	0.266222i
$873$		0			0
$874$	−23.6602	−	13.6602i	−0.800318	−	0.462064i
$875$	−4.00434	−	0.150587i	−0.135371	−	0.00509076i
$876$		0			0
$877$	−30.5772	+	8.19314i	−1.03252	+	0.276663i	−0.735010	−	0.678056i	$-0.762823\pi$
$877$	−30.5772	+	8.19314i	−1.03252	+	0.276663i	−0.297509	+	0.954719i	$0.596156\pi$
$878$	−13.5080	−	13.5080i	−0.455872	−	0.455872i
$879$		0			0
$880$	−18.0031	−	10.3941i	−0.606885	−	0.350385i
$881$	14.4314	−	24.9959i	0.486206	−	0.842133i	−0.513668	−	0.857989i	$-0.671714\pi$
$881$	14.4314	−	24.9959i	0.486206	−	0.842133i	0.999874	+	0.0158554i	$0.00504713\pi$
$882$		0			0
$883$			35.8803i			1.20747i	0.797185	+	0.603735i	$0.206321\pi$
$883$			35.8803i			1.20747i	−0.797185	+	0.603735i	$0.793679\pi$
$884$	−53.6584	−	56.7213i	−1.80473	−	1.90774i
$885$		0			0
$886$	−5.84866	+	21.8275i	−0.196489	+	0.733308i
$887$		−	47.1975i		−	1.58474i	−0.610043	−	0.792368i	$-0.708848\pi$
$887$		−	47.1975i		−	1.58474i	0.610043	−	0.792368i	$-0.291152\pi$
$888$		0			0
$889$	15.0914	−	3.44152i	0.506149	−	0.115425i
$890$	33.2441	−	124.068i	1.11434	−	4.15879i
$891$		0			0
$892$	63.4943	−	17.0132i	2.12595	−	0.569645i
$893$	−7.10505			−0.237762
$894$		0			0
$895$	71.6018	−	19.1857i	2.39339	−	0.641306i
$896$	1.34832	−	35.8539i	0.0450442	−	1.19780i
$897$		0			0
$898$	8.81423	+	15.2667i	0.294135	+	0.509456i
$899$	−7.70250	−	2.06388i	−0.256893	−	0.0688342i
$900$		0			0
$901$	29.7771	−	51.5754i	0.992018	−	1.71823i
$902$	−71.5627	+	71.5627i	−2.38278	+	2.38278i
$903$		0			0
$904$	16.0168	+	4.29170i	0.532712	+	0.142740i
$905$	−15.1277	−	4.05346i	−0.502862	−	0.134742i
$906$		0			0
$907$	−40.1325	+	23.1705i	−1.33258	+	0.769364i	−0.985694	−	0.168544i	$-0.946094\pi$
$907$	−40.1325	+	23.1705i	−1.33258	+	0.769364i	−0.346884	+	0.937908i	$0.612760\pi$
$908$	34.7266	+	34.7266i	1.15244	+	1.15244i
$909$		0			0
$910$	−60.9308	+	30.0569i	−2.01983	+	0.996375i
$911$	−8.52972			−0.282602			−0.141301	−	0.989967i	$-0.545129\pi$
$911$	−8.52972			−0.282602			−0.141301	+	0.989967i	$0.545129\pi$
$912$		0			0
$913$	−8.09195	+	4.67189i	−0.267805	+	0.154617i
$914$			57.1344i			1.88984i
$915$		0			0
$916$	20.7651	+	5.56399i	0.686098	+	0.183839i
$917$	−2.04190	+	6.61526i	−0.0674296	+	0.218455i
$918$		0			0
$919$	−11.7540	+	20.3585i	−0.387729	+	0.671566i	−0.992144	−	0.125104i	$-0.960074\pi$
$919$	−11.7540	+	20.3585i	−0.387729	+	0.671566i	0.604415	+	0.796670i	$0.293407\pi$
$920$	−13.5424	−	23.4562i	−0.446480	−	0.773327i
$921$		0			0
$922$	16.2893	+	28.2138i	0.536459	+	0.929174i
$923$	4.77981	+	8.83619i	0.157329	+	0.290847i
$924$		0			0
$925$	8.97197	−	2.40403i	0.294996	−	0.0790441i
$926$	−20.8321			−0.684586
$927$		0			0
$928$	20.8374	−	5.58337i	0.684022	−	0.183283i
$929$	−1.84295	−	6.87797i	−0.0604651	−	0.225659i	0.929081	−	0.369877i	$-0.120600\pi$
$929$	−1.84295	−	6.87797i	−0.0604651	−	0.225659i	−0.989546	+	0.144218i	$0.953933\pi$
$930$		0			0
$931$	−18.9838	+	3.58453i	−0.622170	+	0.117478i
$932$	30.2836	+	52.4527i	0.991972	+	1.71815i
$933$		0			0
$934$	17.8260	−	66.5277i	0.583286	−	2.17685i
$935$	−85.9754	−	49.6379i	−2.81170	−	1.62333i
$936$		0			0
$937$			16.2205i			0.529900i	0.964262	+	0.264950i	$0.0853554\pi$
$937$			16.2205i			0.529900i	−0.964262	+	0.264950i	$0.914645\pi$
$938$	−13.4234	+	43.4885i	−0.438289	+	1.41995i
$939$		0			0
$940$	−20.5269	−	11.8512i	−0.669513	−	0.386544i
$941$	14.8901	+	55.5707i	0.485405	+	1.81155i	0.578232	+	0.815872i	$0.303743\pi$
$941$	14.8901	+	55.5707i	0.485405	+	1.81155i	−0.0928277	+	0.995682i	$0.529591\pi$
$942$		0			0
$943$	49.5295	−	13.2714i	1.61290	−	0.432176i
$944$	9.22007	+	9.22007i	0.300088	+	0.300088i
$945$		0			0
$946$	−56.0049	−	32.3344i	−1.82088	−	1.05128i
$947$	28.4415	−	28.4415i	0.924224	−	0.924224i	−0.0731003	−	0.997325i	$-0.523289\pi$
$947$	28.4415	−	28.4415i	0.924224	−	0.924224i	0.997325	+	0.0731003i	$0.0232893\pi$
$948$		0			0
$949$	−3.30947	+	5.38169i	−0.107430	+	0.174697i
$950$	−28.7699	+	16.6103i	−0.933418	+	0.538909i
$951$		0			0
$952$	1.40850	−	37.4543i	0.0456499	−	1.21390i
$953$	−21.9464	+	12.6708i	−0.710915	+	0.410447i	−0.811400	−	0.584492i	$-0.801294\pi$
$953$	−21.9464	+	12.6708i	−0.710915	+	0.410447i	0.100485	+	0.994939i	$0.467961\pi$
$954$		0			0
$955$	−33.9213	+	33.9213i	−1.09767	+	1.09767i
$956$	−42.1523	+	42.1523i	−1.36330	+	1.36330i
$957$		0			0
$958$	62.2441	−	35.9366i	2.01102	−	1.16106i
$959$	1.12130	−	29.8171i	0.0362087	−	0.962845i
$960$		0			0
$961$	20.6596	−	11.9278i	0.666440	−	0.384769i
$962$	9.79397	−	9.26512i	0.315770	−	0.298719i
$963$		0			0
$964$	9.28147	−	9.28147i	0.298936	−	0.298936i
$965$	−44.0708	−	25.4443i	−1.41869	−	0.819080i
$966$		0			0
$967$	1.97447	+	1.97447i	0.0634945	+	0.0634945i	0.738141	−	0.674646i	$-0.235704\pi$
$967$	1.97447	+	1.97447i	0.0634945	+	0.0634945i	−0.674646	+	0.738141i	$0.735704\pi$
$968$	9.45303	−	2.53293i	0.303832	−	0.0814116i
$969$		0			0
$970$	24.3333	+	90.8133i	0.781297	+	2.91584i
$971$	32.1958	+	18.5882i	1.03321	+	0.596525i	0.917903	−	0.396805i	$-0.129881\pi$
$971$	32.1958	+	18.5882i	1.03321	+	0.596525i	0.115308	+	0.993330i	$0.463214\pi$
$972$		0			0
$973$	−2.25734	+	7.31321i	−0.0723668	+	0.234451i
$974$		−	1.20948i		−	0.0387541i
$975$		0			0
$976$	−12.7084	−	7.33723i	−0.406788	−	0.234859i
$977$	3.07084	−	11.4605i	0.0982450	−	0.366655i	−0.899246	−	0.437442i	$-0.855884\pi$
$977$	3.07084	−	11.4605i	0.0982450	−	0.366655i	0.997491	+	0.0707871i	$0.0225511\pi$
$978$		0			0
$979$	−36.3580	−	62.9739i	−1.16201	−	2.01265i
$980$	−60.8243	−	21.3090i	−1.94296	−	0.680692i
$981$		0			0
$982$	−7.33413	−	27.3713i	−0.234041	−	0.873454i
$983$	0.320026	−	0.0857508i	0.0102073	−	0.00273503i	−0.253712	−	0.967280i	$-0.581651\pi$
$983$	0.320026	−	0.0857508i	0.0102073	−	0.00273503i	0.263919	+	0.964545i	$0.414985\pi$
$984$		0			0
$985$	−28.9068			−0.921046
$986$	48.2741	−	12.9350i	1.53736	−	0.411935i
$987$		0			0
$988$	−14.8333	+	24.1211i	−0.471910	+	0.767395i
$989$	16.3827	+	28.3756i	0.520938	+	0.902291i
$990$		0			0
$991$	−21.1135	−	36.5696i	−0.670691	−	1.16167i	−0.977708	−	0.209967i	$-0.932664\pi$
$991$	−21.1135	−	36.5696i	−0.670691	−	1.16167i	0.307017	−	0.951704i	$-0.400669\pi$
$992$	9.66369	−	16.7380i	0.306823	−	0.531432i
$993$		0			0
$994$	−4.78607	+	15.5057i	−0.151805	+	0.491811i
$995$	−21.2882	−	5.70415i	−0.674881	−	0.180834i
$996$		0			0
$997$		−	1.17146i		−	0.0371004i	−0.999828	−	0.0185502i	$-0.994095\pi$
$997$		−	1.17146i		−	0.0371004i	0.999828	−	0.0185502i	$-0.00590505\pi$
$998$	−7.10285	+	4.10083i	−0.224837	+	0.129810i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.c.514.2		36
3.2	odd	2		273.2.bt.a.241.8	yes	36
7.5	odd	6		819.2.gh.c.397.2		36
13.2	odd	12		819.2.gh.c.262.2		36
21.5	even	6		273.2.cg.a.124.8	yes	36
39.2	even	12		273.2.cg.a.262.8	yes	36
91.54	even	12	inner	819.2.et.c.145.2		36
273.236	odd	12		273.2.bt.a.145.8	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.145.8	✓	36	273.236	odd	12
273.2.bt.a.241.8	yes	36	3.2	odd	2
273.2.cg.a.124.8	yes	36	21.5	even	6
273.2.cg.a.262.8	yes	36	39.2	even	12
819.2.et.c.145.2		36	91.54	even	12	inner
819.2.et.c.514.2		36	1.1	even	1	trivial
819.2.gh.c.262.2		36	13.2	odd	12
819.2.gh.c.397.2		36	7.5	odd	6

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.et (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.55654 - 1.55654i) q^{2} +2.84566i q^{4} +(-3.12520 - 0.837395i) q^{5} +(1.93981 - 1.79920i) q^{7} +(1.31631 - 1.31631i) q^{8} +O(q^{10})\)	\(q+(-1.55654 - 1.55654i) q^{2} +2.84566i q^{4} +(-3.12520 - 0.837395i) q^{5} +(1.93981 - 1.79920i) q^{7} +(1.31631 - 1.31631i) q^{8} +(3.56107 + 6.16796i) q^{10} +(3.89463 + 1.04356i) q^{11} +(-2.61925 + 2.47781i) q^{13} +(-5.81994 - 0.218864i) q^{14} +1.59353 q^{16} +7.61003 q^{17} +(-0.714314 - 2.66585i) q^{19} +(2.38294 - 8.89327i) q^{20} +(-4.43782 - 7.68652i) q^{22} +4.49695i q^{23} +(4.73553 + 2.73406i) q^{25} +(7.93380 + 0.220148i) q^{26} +(5.11992 + 5.52005i) q^{28} +(-1.49169 + 2.58368i) q^{29} +(0.691794 + 2.58181i) q^{31} +(-5.11302 - 5.11302i) q^{32} +(-11.8454 - 11.8454i) q^{34} +(-7.56895 + 3.99848i) q^{35} +(1.20113 - 1.20113i) q^{37} +(-3.03766 + 5.26138i) q^{38} +(-5.21601 + 3.01147i) q^{40} +(-2.95120 - 11.0140i) q^{41} +(6.30996 - 3.64306i) q^{43} +(-2.96963 + 11.0828i) q^{44} +(6.99971 - 6.99971i) q^{46} +(0.666302 - 2.48667i) q^{47} +(0.525739 - 6.98023i) q^{49} +(-3.11538 - 11.6267i) q^{50} +(-7.05102 - 7.45349i) q^{52} +(3.91287 - 6.77729i) q^{53} +(-11.2976 - 6.52269i) q^{55} +(0.185085 - 4.92171i) q^{56} +(6.34349 - 1.69973i) q^{58} +(5.78594 + 5.78594i) q^{59} +(-7.97503 - 4.60439i) q^{61} +(2.94189 - 5.09551i) q^{62} +12.7302i q^{64} +(10.2606 - 5.55032i) q^{65} +(2.02258 - 7.54839i) q^{67} +21.6556i q^{68} +(18.0052 + 5.55759i) q^{70} +(0.721147 - 2.69136i) q^{71} +(1.69255 - 0.453517i) q^{73} -3.73923 q^{74} +(7.58612 - 2.03270i) q^{76} +(9.43244 - 4.98292i) q^{77} +(4.31023 + 7.46554i) q^{79} +(-4.98010 - 1.33441i) q^{80} +(-12.5501 + 21.7375i) q^{82} +(-1.63865 + 1.63865i) q^{83} +(-23.7829 - 6.37260i) q^{85} +(-15.4923 - 4.15115i) q^{86} +(6.50021 - 3.75290i) q^{88} +(-12.7524 - 12.7524i) q^{89} +(-0.622758 + 9.51904i) q^{91} -12.7968 q^{92} +(-4.90774 + 2.83349i) q^{94} +8.92950i q^{95} +(12.7508 + 3.41658i) q^{97} +(-11.6834 + 10.0467i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{7}+O(q^{10}) \) 36 * q + 6 * q^7	\( 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) \) 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

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