LMFDB - Embedded newform 819.2.et.c.145.6

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			145.6
Character	$\chi$	$=$	819.145
Dual form			819.2.et.c.514.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.745928 - 0.745928i) q^{2} +0.887184i q^{4} +(-3.80456 + 1.01943i) q^{5} +(0.148943 - 2.64156i) q^{7} +(2.15363 + 2.15363i) q^{8} +O(q^{10})$	\(q+(0.745928 - 0.745928i) q^{2} +0.887184i q^{4} +(-3.80456 + 1.01943i) q^{5} +(0.148943 - 2.64156i) q^{7} +(2.15363 + 2.15363i) q^{8} +(-2.07751 + 3.59835i) q^{10} +(0.913987 - 0.244902i) q^{11} +(-0.783899 - 3.51930i) q^{13} +(-1.85931 - 2.08151i) q^{14} +1.43854 q^{16} -7.96173 q^{17} +(0.451695 - 1.68575i) q^{19} +(-0.904422 - 3.37535i) q^{20} +(0.499089 - 0.864448i) q^{22} -6.93477i q^{23} +(9.10535 - 5.25697i) q^{25} +(-3.20988 - 2.04041i) q^{26} +(2.34355 + 0.132140i) q^{28} +(-1.71573 - 2.97173i) q^{29} +(-1.17258 + 4.37613i) q^{31} +(-3.23422 + 3.23422i) q^{32} +(-5.93888 + 5.93888i) q^{34} +(2.12622 + 10.2018i) q^{35} +(-6.88481 - 6.88481i) q^{37} +(-0.920514 - 1.59438i) q^{38} +(-10.3891 - 5.99815i) q^{40} +(0.117207 - 0.437421i) q^{41} +(0.0936549 + 0.0540717i) q^{43} +(0.217273 + 0.810875i) q^{44} +(-5.17284 - 5.17284i) q^{46} +(-1.19435 - 4.45738i) q^{47} +(-6.95563 - 0.786882i) q^{49} +(2.87061 - 10.7132i) q^{50} +(3.12227 - 0.695463i) q^{52} +(-0.747827 - 1.29527i) q^{53} +(-3.22766 + 1.86349i) q^{55} +(6.00970 - 5.36817i) q^{56} +(-3.49650 - 0.936885i) q^{58} +(3.42925 - 3.42925i) q^{59} +(-5.73215 + 3.30946i) q^{61} +(2.38961 + 4.13893i) q^{62} +7.70205i q^{64} +(6.57008 + 12.5903i) q^{65} +(1.17090 + 4.36986i) q^{67} -7.06353i q^{68} +(9.19581 + 6.02380i) q^{70} +(2.68009 + 10.0022i) q^{71} +(3.95501 + 1.05974i) q^{73} -10.2711 q^{74} +(1.49557 + 0.400736i) q^{76} +(-0.510791 - 2.45082i) q^{77} +(0.473848 - 0.820728i) q^{79} +(-5.47300 + 1.46649i) q^{80} +(-0.238857 - 0.413712i) q^{82} +(8.26062 + 8.26062i) q^{83} +(30.2909 - 8.11643i) q^{85} +(0.110193 - 0.0295262i) q^{86} +(2.49582 + 1.44096i) q^{88} +(-3.79135 + 3.79135i) q^{89} +(-9.41319 + 1.54654i) q^{91} +6.15242 q^{92} +(-4.21578 - 2.43398i) q^{94} +6.87400i q^{95} +(-11.5503 + 3.09490i) q^{97} +(-5.77535 + 4.60144i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.745928	−	0.745928i	0.527450	−	0.527450i	−0.392361	−	0.919811i	$-0.628342\pi$
$2$	0.745928	−	0.745928i	0.527450	−	0.527450i	0.919811	+	0.392361i	$0.128342\pi$
$3$		0			0
$3$		0			0
$4$			0.887184i			0.443592i
$5$	−3.80456	+	1.01943i	−1.70145	+	0.455903i	−0.973305	−	0.229517i	$-0.926285\pi$
$5$	−3.80456	+	1.01943i	−1.70145	+	0.455903i	−0.728148	+	0.685420i	$0.759619\pi$
$6$		0			0
$7$	0.148943	−	2.64156i	0.0562951	−	0.998414i
$7$	0.148943	−	2.64156i	0.0562951	−	0.998414i
$8$	2.15363	+	2.15363i	0.761423	+	0.761423i
$9$		0			0
$10$	−2.07751	+	3.59835i	−0.656966	+	1.13790i
$11$	0.913987	−	0.244902i	0.275578	−	0.0738408i	−0.118383	−	0.992968i	$-0.537771\pi$
$11$	0.913987	−	0.244902i	0.275578	−	0.0738408i	0.393961	+	0.919127i	$0.371105\pi$
$12$		0			0
$13$	−0.783899	−	3.51930i	−0.217414	−	0.976079i
$13$	−0.783899	−	3.51930i	−0.217414	−	0.976079i
$14$	−1.85931	−	2.08151i	−0.496921	−	0.556307i
$15$		0			0
$16$	1.43854			0.359634
$17$	−7.96173			−1.93100			−0.965502	−	0.260395i	$-0.916147\pi$
$17$	−7.96173			−1.93100			−0.965502	+	0.260395i	$0.916147\pi$
$18$		0			0
$19$	0.451695	−	1.68575i	0.103626	−	0.386737i	−0.894560	−	0.446948i	$-0.852511\pi$
$19$	0.451695	−	1.68575i	0.103626	−	0.386737i	0.998186	+	0.0602114i	$0.0191775\pi$
$20$	−0.904422	−	3.37535i	−0.202235	−	0.754751i
$21$		0			0
$22$	0.499089	−	0.864448i	0.106406	−	0.184301i
$23$		−	6.93477i		−	1.44600i	−0.690848	−	0.723000i	$-0.742763\pi$
$23$		−	6.93477i		−	1.44600i	0.690848	−	0.723000i	$-0.257237\pi$
$24$		0			0
$25$	9.10535	−	5.25697i	1.82107	−	1.05139i
$26$	−3.20988	−	2.04041i	−0.629509	−	0.400158i
$27$		0			0
$28$	2.34355	+	0.132140i	0.442889	+	0.0249721i
$29$	−1.71573	−	2.97173i	−0.318603	−	0.551836i	0.661594	−	0.749862i	$-0.269880\pi$
$29$	−1.71573	−	2.97173i	−0.318603	−	0.551836i	−0.980197	+	0.198026i	$0.936547\pi$
$30$		0			0
$31$	−1.17258	+	4.37613i	−0.210602	+	0.785976i	0.777067	+	0.629418i	$0.216707\pi$
$31$	−1.17258	+	4.37613i	−0.210602	+	0.785976i	−0.987669	+	0.156558i	$0.949960\pi$
$32$	−3.23422	+	3.23422i	−0.571734	+	0.571734i
$33$		0			0
$34$	−5.93888	+	5.93888i	−1.01851	+	1.01851i
$35$	2.12622	+	10.2018i	0.359396	+	1.72442i
$36$		0			0
$37$	−6.88481	−	6.88481i	−1.13186	−	1.13186i	−0.989868	−	0.141988i	$-0.954651\pi$
$37$	−6.88481	−	6.88481i	−1.13186	−	1.13186i	−0.141988	−	0.989868i	$-0.545349\pi$
$38$	−0.920514	−	1.59438i	−0.149327	−	0.258642i
$39$		0			0
$40$	−10.3891	−	5.99815i	−1.64266	−	0.948391i
$41$	0.117207	−	0.437421i	0.0183046	−	0.0683137i	−0.956169	−	0.292814i	$-0.905408\pi$
$41$	0.117207	−	0.437421i	0.0183046	−	0.0683137i	0.974474	+	0.224500i	$0.0720750\pi$
$42$		0			0
$43$	0.0936549	+	0.0540717i	0.0142822	+	0.00824585i	0.507124	−	0.861873i	$-0.330709\pi$
$43$	0.0936549	+	0.0540717i	0.0142822	+	0.00824585i	−0.492842	+	0.870119i	$0.664042\pi$
$44$	0.217273	+	0.810875i	0.0327552	+	0.122244i
$45$		0			0
$46$	−5.17284	−	5.17284i	−0.762693	−	0.762693i
$47$	−1.19435	−	4.45738i	−0.174214	−	0.650175i	−0.996684	−	0.0813671i	$-0.974071\pi$
$47$	−1.19435	−	4.45738i	−0.174214	−	0.650175i	0.822470	−	0.568808i	$-0.192595\pi$
$48$		0			0
$49$	−6.95563	−	0.786882i	−0.993662	−	0.112412i
$50$	2.87061	−	10.7132i	0.405965	−	1.51508i
$51$		0			0
$52$	3.12227	−	0.695463i	0.432981	−	0.0964433i
$53$	−0.747827	−	1.29527i	−0.102722	−	0.177920i	0.810083	−	0.586315i	$-0.199422\pi$
$53$	−0.747827	−	1.29527i	−0.102722	−	0.177920i	−0.912805	+	0.408395i	$0.866089\pi$
$54$		0			0
$55$	−3.22766	+	1.86349i	−0.435218	+	0.251273i
$56$	6.00970	−	5.36817i	0.803080	−	0.717351i
$57$		0			0
$58$	−3.49650	−	0.936885i	−0.459113	−	0.123019i
$59$	3.42925	−	3.42925i	0.446451	−	0.446451i	−0.447722	−	0.894173i	$-0.647765\pi$
$59$	3.42925	−	3.42925i	0.446451	−	0.446451i	0.894173	+	0.447722i	$0.147765\pi$
$60$		0			0
$61$	−5.73215	+	3.30946i	−0.733926	+	0.423733i	−0.819857	−	0.572568i	$-0.805947\pi$
$61$	−5.73215	+	3.30946i	−0.733926	+	0.423733i	0.0859304	+	0.996301i	$0.472614\pi$
$62$	2.38961	+	4.13893i	0.303481	+	0.525645i
$63$		0			0
$64$			7.70205i			0.962757i
$65$	6.57008	+	12.5903i	0.814918	+	1.56163i
$66$		0			0
$67$	1.17090	+	4.36986i	0.143048	+	0.533863i	0.999835	+	0.0181915i	$0.00579086\pi$
$67$	1.17090	+	4.36986i	0.143048	+	0.533863i	−0.856786	+	0.515672i	$0.827542\pi$
$68$		−	7.06353i		−	0.856578i
$69$		0			0
$70$	9.19581	+	6.02380i	1.09911	+	0.719982i
$71$	2.68009	+	10.0022i	0.318068	+	1.18705i	0.921099	+	0.389329i	$0.127293\pi$
$71$	2.68009	+	10.0022i	0.318068	+	1.18705i	−0.603030	+	0.797718i	$0.706040\pi$
$72$		0			0
$73$	3.95501	+	1.05974i	0.462899	+	0.124033i	0.482729	−	0.875770i	$-0.339646\pi$
$73$	3.95501	+	1.05974i	0.462899	+	0.124033i	−0.0198296	+	0.999803i	$0.506312\pi$
$74$	−10.2711			−1.19400
$75$		0			0
$76$	1.49557	+	0.400736i	0.171553	+	0.0459676i
$77$	−0.510791	−	2.45082i	−0.0582100	−	0.279297i
$78$		0			0
$79$	0.473848	−	0.820728i	0.0533120	−	0.0923391i	−0.838138	−	0.545459i	$-0.816356\pi$
$79$	0.473848	−	0.820728i	0.0533120	−	0.0923391i	0.891450	+	0.453119i	$0.149689\pi$
$80$	−5.47300	+	1.46649i	−0.611900	+	0.163958i
$81$		0			0
$82$	−0.238857	−	0.413712i	−0.0263773	−	0.0456869i
$83$	8.26062	+	8.26062i	0.906721	+	0.906721i	0.996006	−	0.0892850i	$-0.0284582\pi$
$83$	8.26062	+	8.26062i	0.906721	+	0.906721i	−0.0892850	+	0.996006i	$0.528458\pi$
$84$		0			0
$85$	30.2909	−	8.11643i	3.28551	−	0.880351i
$86$	0.110193	−	0.0295262i	0.0118824	−	0.00318389i
$87$		0			0
$88$	2.49582	+	1.44096i	0.266055	+	0.153607i
$89$	−3.79135	+	3.79135i	−0.401882	+	0.401882i	−0.878896	−	0.477014i	$-0.841719\pi$
$89$	−3.79135	+	3.79135i	−0.401882	+	0.401882i	0.477014	+	0.878896i	$0.341719\pi$
$90$		0			0
$91$	−9.41319	+	1.54654i	−0.986771	+	0.162121i
$92$	6.15242			0.641434
$93$		0			0
$94$	−4.21578	−	2.43398i	−0.434824	−	0.251046i
$95$			6.87400i			0.705258i
$96$		0			0
$97$	−11.5503	+	3.09490i	−1.17276	+	0.314240i	−0.792050	−	0.610456i	$-0.790986\pi$
$97$	−11.5503	+	3.09490i	−1.17276	+	0.314240i	−0.380708	+	0.924695i	$0.624320\pi$
$98$	−5.77535	+	4.60144i	−0.583399	+	0.464816i
$99$		0			0
$100$	4.66390	+	8.07812i	0.466390	+	0.807812i
$101$	9.35838	−	16.2092i	0.931194	−	1.61287i	0.149909	−	0.988700i	$-0.452102\pi$
$101$	9.35838	−	16.2092i	0.931194	−	1.61287i	0.781284	−	0.624175i	$-0.214565\pi$
$102$		0			0
$103$	3.28825	−	5.69542i	0.324001	−	0.561186i	−0.657309	−	0.753621i	$-0.728305\pi$
$103$	3.28825	−	5.69542i	0.324001	−	0.561186i	0.981310	+	0.192435i	$0.0616386\pi$
$104$	5.89105	−	9.26751i	0.577665	−	0.908754i
$105$		0			0
$106$	−1.52400	−	0.408356i	−0.148024	−	0.0396630i
$107$	−5.19352			−0.502077			−0.251038	−	0.967977i	$-0.580772\pi$
$107$	−5.19352			−0.502077			−0.251038	+	0.967977i	$0.580772\pi$
$108$		0			0
$109$	11.0247	+	2.95407i	1.05598	+	0.282949i	0.744720	−	0.667377i	$-0.232583\pi$
$109$	11.0247	+	2.95407i	1.05598	+	0.282949i	0.311259	+	0.950325i	$0.399249\pi$
$110$	−1.01757	+	3.79763i	−0.0970218	+	0.362090i
$111$		0			0
$112$	0.214260	−	3.79997i	0.0202456	−	0.359064i
$113$	1.34429	−	2.32838i	0.126460	−	0.219036i	−0.795842	−	0.605504i	$-0.792972\pi$
$113$	1.34429	−	2.32838i	0.126460	−	0.219036i	0.922303	+	0.386468i	$0.126305\pi$
$114$		0			0
$115$	7.06951	+	26.3838i	0.659236	+	2.46030i
$116$	2.63647	−	1.52217i	0.244790	−	0.141330i
$117$		0			0
$118$		−	5.11595i		−	0.470961i
$119$	−1.18584	+	21.0314i	−0.108706	+	1.92794i
$120$		0			0
$121$	−8.75088	+	5.05232i	−0.795535	+	0.459302i
$122$	−1.80715	+	6.74438i	−0.163612	+	0.610608i
$123$		0			0
$124$	−3.88243	−	1.04029i	−0.348653	−	0.0934212i
$125$	−15.3571	+	15.3571i	−1.37358	+	1.37358i
$126$		0			0
$127$	−7.89995	+	4.56104i	−0.701007	+	0.404727i	−0.807722	−	0.589563i	$-0.799300\pi$
$127$	−7.89995	+	4.56104i	−0.701007	+	0.404727i	0.106715	+	0.994290i	$0.465967\pi$
$128$	−0.723260	−	0.723260i	−0.0639277	−	0.0639277i
$129$		0			0
$130$	14.2922	+	4.49064i	1.25351	+	0.393855i
$131$	6.79059	+	3.92055i	0.593297	+	0.342540i	0.766400	−	0.642364i	$-0.222046\pi$
$131$	6.79059	+	3.92055i	0.593297	+	0.342540i	−0.173103	+	0.984904i	$0.555379\pi$
$132$		0			0
$133$	−4.38572	−	1.44426i	−0.380290	−	0.125233i
$134$	4.13300	+	2.38619i	0.357037	+	0.206135i
$135$		0			0
$136$	−17.1466	−	17.1466i	−1.47031	−	1.47031i
$137$	−5.38162	−	5.38162i	−0.459783	−	0.459783i	0.438801	−	0.898584i	$-0.355403\pi$
$137$	−5.38162	−	5.38162i	−0.459783	−	0.459783i	−0.898584	+	0.438801i	$0.855403\pi$
$138$		0			0
$139$	3.86004	+	2.22859i	0.327404	+	0.189027i	0.654688	−	0.755899i	$-0.272800\pi$
$139$	3.86004	+	2.22859i	0.327404	+	0.189027i	−0.327284	+	0.944926i	$0.606133\pi$
$140$	−9.05088	+	1.88635i	−0.764939	+	0.159425i
$141$		0			0
$142$	9.46010	+	5.46179i	0.793874	+	0.458343i
$143$	−1.57836	−	3.02462i	−0.131989	−	0.252932i
$144$		0			0
$145$	9.55706	+	9.55706i	0.793671	+	0.793671i
$146$	3.74064	−	2.15966i	0.309578	−	0.178735i
$147$		0			0
$148$	6.10810	−	6.10810i	0.502082	−	0.502082i
$149$	0.726851	+	0.194759i	0.0595459	+	0.0159553i	0.288469	−	0.957489i	$-0.406854\pi$
$149$	0.726851	+	0.194759i	0.0595459	+	0.0159553i	−0.228923	+	0.973445i	$0.573520\pi$
$150$		0			0
$151$	−0.0169291	+	0.0631804i	−0.00137767	+	0.00514154i	−0.966611	−	0.256247i	$-0.917514\pi$
$151$	−0.0169291	+	0.0631804i	−0.00137767	+	0.00514154i	0.965234	+	0.261389i	$0.0841805\pi$
$152$	4.60326	−	2.65769i	0.373374	−	0.215567i
$153$		0			0
$154$	−2.20915	−	1.44712i	−0.178018	−	0.116613i
$155$		−	17.8446i		−	1.43331i
$156$		0			0
$157$	6.41355	−	3.70286i	0.511857	−	0.295521i	−0.221740	−	0.975106i	$-0.571174\pi$
$157$	6.41355	−	3.70286i	0.511857	−	0.295521i	0.733597	+	0.679585i	$0.237840\pi$
$158$	−0.258748	−	0.965660i	−0.0205849	−	0.0768238i
$159$		0			0
$160$	9.00773	−	15.6018i	0.712124	−	1.23343i
$161$	−18.3186	−	1.03289i	−1.44371	−	0.0814028i
$162$		0			0
$163$	−1.19910	+	4.47509i	−0.0939206	+	0.350516i	−0.996854	−	0.0792649i	$-0.974743\pi$
$163$	−1.19910	+	4.47509i	−0.0939206	+	0.350516i	0.902933	+	0.429781i	$0.141409\pi$
$164$	0.388073	+	0.103984i	0.0303034	+	0.00811978i
$165$		0			0
$166$	12.3237			0.956501
$167$	−12.2105	−	3.27179i	−0.944874	−	0.253178i	−0.246688	−	0.969095i	$-0.579342\pi$
$167$	−12.2105	−	3.27179i	−0.944874	−	0.253178i	−0.698186	+	0.715916i	$0.746009\pi$
$168$		0			0
$169$	−11.7710	+	5.51756i	−0.905462	+	0.424427i
$170$	16.5406	−	28.6491i	1.26860	−	2.19729i
$171$		0			0
$172$	−0.0479715	+	0.0830891i	−0.00365779	+	0.00633549i
$173$	−9.15937	−	15.8645i	−0.696374	−	1.20616i	−0.969715	−	0.244238i	$-0.921462\pi$
$173$	−9.15937	−	15.8645i	−0.696374	−	1.20616i	0.273341	−	0.961917i	$-0.411871\pi$
$174$		0			0
$175$	−12.5304	−	24.8353i	−0.947210	−	1.87737i
$176$	1.31480	−	0.352301i	0.0991070	−	0.0265557i
$177$		0			0
$178$			5.65615i			0.423946i
$179$	15.5371	+	8.97032i	1.16129	+	0.670473i	0.951614	−	0.307297i	$-0.0994244\pi$
$179$	15.5371	+	8.97032i	1.16129	+	0.670473i	0.209680	+	0.977770i	$0.432758\pi$
$180$		0			0
$181$	−11.3348			−0.842512			−0.421256	−	0.906942i	$-0.638411\pi$
$181$	−11.3348			−0.842512			−0.421256	+	0.906942i	$0.638411\pi$
$182$	−5.86796	+	8.17516i	−0.434962	+	0.605984i
$183$		0			0
$184$	14.9349	−	14.9349i	1.10102	−	1.10102i
$185$	33.2123	+	19.1751i	2.44182	+	1.40978i
$186$		0			0
$187$	−7.27693	+	1.94985i	−0.532141	+	0.142587i
$188$	3.95451	−	1.05961i	0.288413	−	0.0772799i
$189$		0			0
$190$	5.12751	+	5.12751i	0.371989	+	0.371989i
$191$	−7.33438	−	12.7035i	−0.530697	−	0.919194i	−0.999358	−	0.0358162i	$-0.988597\pi$
$191$	−7.33438	−	12.7035i	−0.530697	−	0.919194i	0.468661	−	0.883378i	$-0.344736\pi$
$192$		0			0
$193$	−11.3200	+	3.03319i	−0.814834	+	0.218334i	−0.642087	−	0.766632i	$-0.721931\pi$
$193$	−11.3200	+	3.03319i	−0.814834	+	0.218334i	−0.172747	+	0.984966i	$0.555264\pi$
$194$	−6.30714	+	10.9243i	−0.452826	+	0.784318i
$195$		0			0
$196$	0.698110	−	6.17093i	0.0498650	−	0.440781i
$197$	10.2849	+	2.75584i	0.732772	+	0.196346i	0.605863	−	0.795569i	$-0.292828\pi$
$197$	10.2849	+	2.75584i	0.732772	+	0.196346i	0.126909	+	0.991914i	$0.459495\pi$
$198$		0			0
$199$	21.2553			1.50674			0.753372	−	0.657594i	$-0.228426\pi$
$199$	21.2553			1.50674			0.753372	+	0.657594i	$0.228426\pi$
$200$	30.9311	+	8.28797i	2.18716	+	0.586048i
$201$		0			0
$202$	−5.11021	−	19.0716i	−0.359553	−	1.34187i
$203$	−8.10553	+	4.08957i	−0.568897	+	0.287032i
$204$		0			0
$205$			1.78368i			0.124578i
$206$	−1.79557	−	6.70117i	−0.125103	−	0.466892i
$207$		0			0
$208$	−1.12767	−	5.06264i	−0.0781896	−	0.351031i
$209$		−	1.65137i		−	0.114228i
$210$		0			0
$211$	−11.7558	−	20.3617i	−0.809305	−	1.40176i	−0.913346	−	0.407184i	$-0.866511\pi$
$211$	−11.7558	−	20.3617i	−0.809305	−	1.40176i	0.104041	−	0.994573i	$-0.466823\pi$
$212$	1.14915	−	0.663460i	0.0789237	−	0.0455666i
$213$		0			0
$214$	−3.87399	+	3.87399i	−0.264820	+	0.264820i
$215$	−0.411438	−	0.110245i	−0.0280599	−	0.00751862i
$216$		0			0
$217$	11.3851	+	3.74923i	0.772874	+	0.254514i
$218$	10.4272	−	6.02014i	0.706218	−	0.407735i
$219$		0			0
$220$	−1.65326	−	2.86353i	−0.111463	−	0.193059i
$221$	6.24119	+	28.0198i	0.419828	+	1.88481i
$222$		0			0
$223$	−1.56806	+	5.85209i	−0.105005	+	0.391885i	−0.998346	−	0.0574955i	$-0.981689\pi$
$223$	−1.56806	+	5.85209i	−0.105005	+	0.391885i	0.893341	+	0.449380i	$0.148355\pi$
$224$	8.06165	+	9.02508i	0.538642	+	0.603013i
$225$		0			0
$226$	−0.734061	−	2.73955i	−0.0488290	−	0.182232i
$227$	−14.7585	−	14.7585i	−0.979553	−	0.979553i	0.0202417	−	0.999795i	$-0.493556\pi$
$227$	−14.7585	−	14.7585i	−0.979553	−	0.979553i	−0.999795	+	0.0202417i	$0.993556\pi$
$228$		0			0
$229$	5.67737	+	21.1882i	0.375171	+	1.40016i	0.853094	+	0.521756i	$0.174723\pi$
$229$	5.67737	+	21.1882i	0.375171	+	1.40016i	−0.477923	+	0.878402i	$0.658610\pi$
$230$	24.9537	+	14.4070i	1.64540	+	0.949973i
$231$		0			0
$232$	2.70496	−	10.0950i	0.177589	−	0.662772i
$233$	−9.92317	−	5.72914i	−0.650088	−	0.375329i	0.138402	−	0.990376i	$-0.455803\pi$
$233$	−9.92317	−	5.72914i	−0.650088	−	0.375329i	−0.788490	+	0.615048i	$0.789137\pi$
$234$		0			0
$235$	9.08797	+	15.7408i	0.592833	+	1.02682i
$236$	3.04238	+	3.04238i	0.198042	+	0.198042i
$237$		0			0
$238$	14.8033	+	16.5724i	0.959557	+	1.07423i
$239$	−4.89413	+	4.89413i	−0.316575	+	0.316575i	−0.847450	−	0.530875i	$-0.821863\pi$
$239$	−4.89413	+	4.89413i	−0.316575	+	0.316575i	0.530875	+	0.847450i	$0.321863\pi$
$240$		0			0
$241$	−5.87042	+	5.87042i	−0.378147	+	0.378147i	−0.870433	−	0.492286i	$-0.836161\pi$
$241$	−5.87042	+	5.87042i	−0.378147	+	0.378147i	0.492286	+	0.870433i	$0.336161\pi$
$242$	−2.75886	+	10.2962i	−0.177346	+	0.661864i
$243$		0			0
$244$	−2.93610	−	5.08547i	−0.187964	−	0.325564i
$245$	27.2653	−	4.09704i	1.74192	−	0.261750i
$246$		0			0
$247$	−6.28674	−	0.268196i	−0.400016	−	0.0170649i
$248$	−11.9499	+	6.89926i	−0.758817	+	0.438103i
$249$		0			0
$250$			22.9105i			1.44899i
$251$	7.81291	−	13.5324i	0.493146	−	0.854155i	−0.506822	−	0.862050i	$-0.669180\pi$
$251$	7.81291	−	13.5324i	0.493146	−	0.854155i	0.999969	+	0.00789592i	$0.00251338\pi$
$252$		0			0
$253$	−1.69834	−	6.33829i	−0.106774	−	0.398485i
$254$	−2.49059	+	9.29499i	−0.156273	+	0.583220i
$255$		0			0
$256$	−16.4831			−1.03019
$257$	−0.563873			−0.0351734			−0.0175867	−	0.999845i	$-0.505598\pi$
$257$	−0.563873			−0.0351734			−0.0175867	+	0.999845i	$0.505598\pi$
$258$		0			0
$259$	−19.2121	+	17.1612i	−1.19378	+	1.06634i
$260$	−11.1699	+	5.82887i	−0.692728	+	0.361491i
$261$		0			0
$262$	7.98974	−	2.14084i	0.493608	−	0.132262i
$263$	0.904321	−	1.56633i	0.0557628	−	0.0965840i	−0.836796	−	0.547514i	$-0.815574\pi$
$263$	0.904321	−	1.56633i	0.0557628	−	0.0965840i	0.892559	+	0.450930i	$0.148908\pi$
$264$		0			0
$265$	4.16560	+	4.16560i	0.255891	+	0.255891i
$266$	−4.34874	+	2.19412i	−0.266638	+	0.134530i
$267$		0			0
$268$	−3.87687	+	1.03880i	−0.236817	+	0.0634550i
$269$			4.60590i			0.280827i	0.990093	+	0.140413i	$0.0448431\pi$
$269$			4.60590i			0.280827i	−0.990093	+	0.140413i	$0.955157\pi$
$270$		0			0
$271$	2.86878	−	2.86878i	0.174266	−	0.174266i	−0.614585	−	0.788851i	$-0.710676\pi$
$271$	2.86878	−	2.86878i	0.174266	−	0.174266i	0.788851	+	0.614585i	$0.210676\pi$
$272$	−11.4532			−0.694455
$273$		0			0
$274$	−8.02860			−0.485026
$275$	7.03473	−	7.03473i	0.424210	−	0.424210i
$276$		0			0
$277$		−	12.2090i		−	0.733571i	−0.930306	−	0.366785i	$-0.880458\pi$
$277$		−	12.2090i		−	0.733571i	0.930306	−	0.366785i	$-0.119542\pi$
$278$	4.54168	−	1.21694i	0.272392	−	0.0729871i
$279$		0			0
$280$	−17.3918	+	26.5500i	−1.03936	+	1.58667i
$281$	−0.757979	−	0.757979i	−0.0452172	−	0.0452172i	0.684137	−	0.729354i	$-0.260179\pi$
$281$	−0.757979	−	0.757979i	−0.0452172	−	0.0452172i	−0.729354	+	0.684137i	$0.760179\pi$
$282$		0			0
$283$	10.3386	−	17.9070i	0.614568	−	1.06446i	−0.375893	−	0.926663i	$-0.622664\pi$
$283$	10.3386	−	17.9070i	0.614568	−	1.06446i	0.990460	−	0.137799i	$-0.0440028\pi$
$284$	−8.87383	+	2.37774i	−0.526565	+	0.141093i
$285$		0			0
$286$	−3.43349	−	1.07881i	−0.203026	−	0.0637912i
$287$	−1.13802	−	0.374759i	−0.0671749	−	0.0221213i
$288$		0			0
$289$	46.3892			2.72878
$290$	14.2578			0.837244
$291$		0			0
$292$	−0.940186	+	3.50882i	−0.0550203	+	0.205338i
$293$	0.652210	+	2.43408i	0.0381025	+	0.142201i	0.982357	−	0.187017i	$-0.0598818\pi$
$293$	0.652210	+	2.43408i	0.0381025	+	0.142201i	−0.944254	+	0.329217i	$0.893215\pi$
$294$		0			0
$295$	−9.55094	+	16.5427i	−0.556077	+	0.963154i
$296$		−	29.6547i		−	1.72364i
$297$		0			0
$298$	0.687454	−	0.396902i	0.0398232	−	0.0229919i
$299$	−24.4056	+	5.43616i	−1.41141	+	0.314381i
$300$		0			0
$301$	0.156783	−	0.239341i	0.00903679	−	0.0137954i
$302$	0.0345001	+	0.0597559i	0.00198526	+	0.00343856i
$303$		0			0
$304$	0.649779	−	2.42501i	0.0372674	−	0.139084i
$305$	18.4346	−	18.4346i	1.05556	−	1.05556i
$306$		0			0
$307$	14.0560	−	14.0560i	0.802217	−	0.802217i	−0.181225	−	0.983442i	$-0.558006\pi$
$307$	14.0560	−	14.0560i	0.802217	−	0.802217i	0.983442	+	0.181225i	$0.0580061\pi$
$308$	2.17433	−	0.453165i	0.123894	−	0.0258215i
$309$		0			0
$310$	−13.3108	−	13.3108i	−0.756003	−	0.756003i
$311$	−5.07374	−	8.78798i	−0.287706	−	0.498321i	0.685556	−	0.728020i	$-0.259559\pi$
$311$	−5.07374	−	8.78798i	−0.287706	−	0.498321i	−0.973262	+	0.229699i	$0.926226\pi$
$312$		0			0
$313$	−23.2110	−	13.4009i	−1.31196	−	0.757461i	−0.329540	−	0.944141i	$-0.606894\pi$
$313$	−23.2110	−	13.4009i	−1.31196	−	0.757461i	−0.982421	+	0.186680i	$0.940227\pi$
$314$	2.02197	−	7.54611i	0.114107	−	0.425852i
$315$		0			0
$316$	0.728137	+	0.420390i	0.0409609	+	0.0236488i
$317$	3.31452	+	12.3700i	0.186162	+	0.694767i	0.994379	+	0.105881i	$0.0337664\pi$
$317$	3.31452	+	12.3700i	0.186162	+	0.694767i	−0.808217	+	0.588885i	$0.799567\pi$
$318$		0			0
$319$	−2.29594	−	2.29594i	−0.128548	−	0.128548i
$320$	−7.85171	−	29.3030i	−0.438924	−	1.63809i
$321$		0			0
$322$	−14.4348	+	12.8939i	−0.804420	+	0.718548i
$323$	−3.59627	+	13.4215i	−0.200102	+	0.746791i
$324$		0			0
$325$	−25.6386	−	27.9235i	−1.42217	−	1.54892i
$326$	2.44366	+	4.23254i	0.135342	+	0.234419i
$327$		0			0
$328$	1.19446	−	0.689624i	0.0659532	−	0.0380781i
$329$	−11.9523	+	2.49105i	−0.658951	+	0.137336i
$330$		0			0
$331$	0.730127	+	0.195637i	0.0401314	+	0.0107532i	0.278829	−	0.960341i	$-0.410054\pi$
$331$	0.730127	+	0.195637i	0.0401314	+	0.0107532i	−0.238697	+	0.971094i	$0.576720\pi$
$332$	−7.32869	+	7.32869i	−0.402214	+	0.402214i
$333$		0			0
$334$	−11.5486	+	6.66761i	−0.631913	+	0.364835i
$335$	−8.90953	−	15.4318i	−0.486779	−	0.843127i
$336$		0			0
$337$		−	12.9685i		−	0.706440i	−0.935540	−	0.353220i	$-0.885087\pi$
$337$		−	12.9685i		−	0.706440i	0.935540	−	0.353220i	$-0.114913\pi$
$338$	−4.66462	+	12.8960i	−0.253722	+	0.701451i
$339$		0			0
$340$	7.20077	+	26.8736i	0.390517	+	1.45743i
$341$			4.28689i			0.232148i
$342$		0			0
$343$	−3.11459	+	18.2565i	−0.168172	+	0.985758i
$344$	0.0852476	+	0.318148i	0.00459624	+	0.0171534i
$345$		0			0
$346$	−18.6660	−	5.00154i	−1.00349	−	0.268884i
$347$	14.3863			0.772298			0.386149	−	0.922436i	$-0.373805\pi$
$347$	14.3863			0.772298			0.386149	+	0.922436i	$0.373805\pi$
$348$		0			0
$349$	32.9693	+	8.83410i	1.76481	+	0.472879i	0.987683	−	0.156468i	$-0.0500108\pi$
$349$	32.9693	+	8.83410i	1.76481	+	0.472879i	0.777125	+	0.629347i	$0.216677\pi$
$350$	−27.8721	−	9.17853i	−1.48983	−	0.490613i
$351$		0			0
$352$	−2.16397	+	3.74810i	−0.115340	+	0.199774i
$353$	5.35753	−	1.43555i	0.285152	−	0.0764064i	−0.113408	−	0.993549i	$-0.536177\pi$
$353$	5.35753	−	1.43555i	0.285152	−	0.0764064i	0.398560	+	0.917142i	$0.369510\pi$
$354$		0			0
$355$	−20.3932	−	35.3220i	−1.08236	−	1.87470i
$356$	−3.36363	−	3.36363i	−0.178272	−	0.178272i
$357$		0			0
$358$	18.2807	−	4.89831i	0.966166	−	0.258883i
$359$	6.42126	−	1.72057i	0.338901	−	0.0908083i	−0.0853548	−	0.996351i	$-0.527202\pi$
$359$	6.42126	−	1.72057i	0.338901	−	0.0908083i	0.424256	+	0.905542i	$0.360536\pi$
$360$		0			0
$361$	13.8168	+	7.97711i	0.727198	+	0.419848i
$362$	−8.45497	+	8.45497i	−0.444383	+	0.444383i
$363$		0			0
$364$	−1.37206	−	8.35124i	−0.0719156	−	0.437724i
$365$	−16.1274			−0.844148
$366$		0			0
$367$	−6.19248	−	3.57523i	−0.323245	−	0.186626i	0.329593	−	0.944123i	$-0.393088\pi$
$367$	−6.19248	−	3.57523i	−0.323245	−	0.186626i	−0.652838	+	0.757498i	$0.726422\pi$
$368$		−	9.97592i		−	0.520031i
$369$		0			0
$370$	39.0772	−	10.4707i	2.03153	−	0.544346i
$371$	−3.53292	+	1.78250i	−0.183420	+	0.0925430i
$372$		0			0
$373$	−7.66980	−	13.2845i	−0.397127	−	0.687844i	0.596243	−	0.802804i	$-0.296659\pi$
$373$	−7.66980	−	13.2845i	−0.397127	−	0.687844i	−0.993370	+	0.114960i	$0.963326\pi$
$374$	−3.97361	+	6.88250i	−0.205471	+	0.355886i
$375$		0			0
$376$	7.02735	−	12.1717i	0.362408	−	0.627709i
$377$	−9.11346	+	8.36770i	−0.469367	+	0.430958i
$378$		0			0
$379$	−22.8646	−	6.12656i	−1.17448	−	0.314700i	−0.381743	−	0.924268i	$-0.624676\pi$
$379$	−22.8646	−	6.12656i	−1.17448	−	0.314700i	−0.792734	+	0.609568i	$0.791343\pi$
$380$	−6.09851			−0.312847
$381$		0			0
$382$	−14.9468	−	4.00499i	−0.764746	−	0.204913i
$383$	−0.160303	+	0.598259i	−0.00819110	+	0.0305696i	−0.969900	−	0.243502i	$-0.921704\pi$
$383$	−0.160303	+	0.598259i	−0.00819110	+	0.0305696i	0.961709	+	0.274071i	$0.0883705\pi$
$384$		0			0
$385$	4.44178	+	8.80361i	0.226374	+	0.448673i
$386$	−6.18138	+	10.7065i	−0.314624	+	0.544945i
$387$		0			0
$388$	−2.74575	−	10.2473i	−0.139394	−	0.520226i
$389$	8.18610	−	4.72624i	0.415052	−	0.239630i	−0.277906	−	0.960608i	$-0.589640\pi$
$389$	8.18610	−	4.72624i	0.415052	−	0.239630i	0.692958	+	0.720978i	$0.256307\pi$
$390$		0			0
$391$			55.2128i			2.79223i
$392$	−13.2852	−	16.6745i	−0.671004	−	0.842190i
$393$		0			0
$394$	9.72748	−	5.61616i	0.490063	−	0.282938i
$395$	−0.966109	+	3.60557i	−0.0486102	+	0.181416i
$396$		0			0
$397$	8.63653	+	2.31415i	0.433455	+	0.116144i	0.468948	−	0.883226i	$-0.344633\pi$
$397$	8.63653	+	2.31415i	0.433455	+	0.116144i	−0.0354925	+	0.999370i	$0.511300\pi$
$398$	15.8549	−	15.8549i	0.794733	−	0.794733i
$399$		0			0
$400$	13.0984	−	7.56234i	0.654918	−	0.378117i
$401$	4.68942	+	4.68942i	0.234178	+	0.234178i	0.814434	−	0.580256i	$-0.197047\pi$
$401$	4.68942	+	4.68942i	0.234178	+	0.234178i	−0.580256	+	0.814434i	$0.697047\pi$
$402$		0			0
$403$	16.3201	+	0.696225i	0.812963	+	0.0346814i
$404$	14.3805	+	8.30261i	0.715459	+	0.413070i
$405$		0			0
$406$	−2.99561	+	9.09666i	−0.148670	+	0.451460i
$407$	−7.97874	−	4.60653i	−0.395491	−	0.228337i
$408$		0			0
$409$	11.5748	+	11.5748i	0.572336	+	0.572336i	0.932781	−	0.360444i	$-0.117375\pi$
$409$	11.5748	+	11.5748i	0.572336	+	0.572336i	−0.360444	+	0.932781i	$0.617375\pi$
$410$	1.33050	+	1.33050i	0.0657086	+	0.0657086i
$411$		0			0
$412$	5.05288	+	2.91728i	0.248938	+	0.143724i
$413$	−8.54780	−	9.56933i	−0.420610	−	0.470876i
$414$		0			0
$415$	−39.8492	−	23.0069i	−1.95612	−	1.12937i
$416$	13.9175	+	8.84690i	0.682361	+	0.433755i
$417$		0			0
$418$	−1.23180	−	1.23180i	−0.0602495	−	0.0602495i
$419$	−19.8994	+	11.4889i	−0.972150	+	0.561271i	−0.899891	−	0.436115i	$-0.856354\pi$
$419$	−19.8994	+	11.4889i	−0.972150	+	0.561271i	−0.0722588	+	0.997386i	$0.523021\pi$
$420$		0			0
$421$	−3.33707	+	3.33707i	−0.162639	+	0.162639i	−0.783735	−	0.621096i	$-0.786688\pi$
$421$	−3.33707	+	3.33707i	−0.162639	+	0.162639i	0.621096	+	0.783735i	$0.286688\pi$
$422$	−23.9574	−	6.41935i	−1.16623	−	0.312489i
$423$		0			0
$424$	1.17900	−	4.40008i	0.0572572	−	0.213687i
$425$	−72.4944	+	41.8546i	−3.51649	+	2.03025i
$426$		0			0
$427$	7.88835	+	15.6347i	0.381744	+	0.756617i
$428$		−	4.60761i		−	0.222717i
$429$		0			0
$430$	−0.389138	+	0.224669i	−0.0187659	+	0.0108345i
$431$	−7.29082	−	27.2097i	−0.351186	−	1.31065i	−0.885216	−	0.465180i	$-0.845990\pi$
$431$	−7.29082	−	27.2097i	−0.351186	−	1.31065i	0.534030	−	0.845466i	$-0.320677\pi$
$432$		0			0
$433$	−9.88975	+	17.1295i	−0.475271	+	0.823193i	−0.999599	−	0.0283231i	$-0.990983\pi$
$433$	−9.88975	+	17.1295i	−0.475271	+	0.823193i	0.524328	+	0.851516i	$0.324317\pi$
$434$	11.2891	−	5.69584i	0.541896	−	0.273409i
$435$		0			0
$436$	−2.62081	+	9.78098i	−0.125514	+	0.468424i
$437$	−11.6903	−	3.13240i	−0.559221	−	0.149843i
$438$		0			0
$439$	21.9076			1.04559			0.522797	−	0.852457i	$-0.324889\pi$
$439$	21.9076			1.04559			0.522797	+	0.852457i	$0.324889\pi$
$440$	−10.9645	−	2.93792i	−0.522710	−	0.140060i
$441$		0			0
$442$	25.5562	+	16.2452i	1.21558	+	0.772707i
$443$	−9.87688	+	17.1073i	−0.469265	+	0.812791i	−0.999383	−	0.0351334i	$-0.988814\pi$
$443$	−9.87688	+	17.1073i	−0.469265	+	0.812791i	0.530118	+	0.847924i	$0.322148\pi$
$444$		0			0
$445$	10.5594	−	18.2895i	0.500565	−	0.867003i
$446$	3.19557	+	5.53489i	0.151315	+	0.262085i
$447$		0			0
$448$	20.3454	+	1.14717i	0.961230	+	0.0541985i
$449$	31.7673	−	8.51202i	1.49919	−	0.401707i	0.586362	−	0.810049i	$-0.300560\pi$
$449$	31.7673	−	8.51202i	1.49919	−	0.401707i	0.912829	+	0.408342i	$0.133893\pi$
$450$		0			0
$451$		−	0.428502i		−	0.0201774i
$452$	2.06571	+	1.19264i	0.0971626	+	0.0560969i
$453$		0			0
$454$	−22.0175			−1.03333
$455$	34.2365	−	15.4800i	1.60503	−	0.725713i
$456$		0			0
$457$	11.0934	−	11.0934i	0.518926	−	0.518926i	−0.398320	−	0.917246i	$-0.630407\pi$
$457$	11.0934	−	11.0934i	0.518926	−	0.518926i	0.917246	+	0.398320i	$0.130407\pi$
$458$	20.0398	+	11.5700i	0.936398	+	0.540630i
$459$		0			0
$460$	−23.4073	+	6.27196i	−1.09137	+	0.292432i
$461$	1.60974	−	0.431329i	0.0749731	−	0.0200890i	−0.221138	−	0.975243i	$-0.570977\pi$
$461$	1.60974	−	0.431329i	0.0749731	−	0.0200890i	0.296111	+	0.955154i	$0.404310\pi$
$462$		0			0
$463$	−18.8646	−	18.8646i	−0.876713	−	0.876713i	0.116480	−	0.993193i	$-0.462839\pi$
$463$	−18.8646	−	18.8646i	−0.876713	−	0.876713i	−0.993193	+	0.116480i	$0.962839\pi$
$464$	−2.46814	−	4.27494i	−0.114580	−	0.198459i
$465$		0			0
$466$	−11.6755	+	3.12844i	−0.540857	+	0.144922i
$467$	11.4518	−	19.8351i	0.529926	−	0.917859i	−0.469465	−	0.882951i	$-0.655553\pi$
$467$	11.4518	−	19.8351i	0.529926	−	0.917859i	0.999391	−	0.0349075i	$-0.0111136\pi$
$468$		0			0
$469$	11.7176	−	2.44214i	0.541069	−	0.112767i
$470$	18.5205	+	4.96255i	0.854286	+	0.228905i
$471$		0			0
$472$	14.7707			0.679876
$473$	0.0988416	+	0.0264845i	0.00454474	+	0.00121776i
$474$		0			0
$475$	−4.74909	−	17.7239i	−0.217903	−	0.813226i
$476$	−18.6587	−	1.05206i	−0.855220	−	0.0482212i
$477$		0			0
$478$			7.30134i			0.333956i
$479$	−0.198528	−	0.740918i	−0.00907099	−	0.0338534i	0.961242	−	0.275706i	$-0.0889116\pi$
$479$	−0.198528	−	0.740918i	−0.00907099	−	0.0338534i	−0.970313	+	0.241853i	$0.922245\pi$
$480$		0			0
$481$	−18.8328	+	29.6267i	−0.858700	+	1.35086i
$482$			8.75782i			0.398908i
$483$		0			0
$484$	−4.48234	−	7.76365i	−0.203743	−	0.352893i
$485$	40.7889	−	23.5495i	1.85213	−	1.06933i
$486$		0			0
$487$	−5.22200	+	5.22200i	−0.236631	+	0.236631i	−0.815454	−	0.578822i	$-0.803512\pi$
$487$	−5.22200	+	5.22200i	−0.236631	+	0.236631i	0.578822	+	0.815454i	$0.303512\pi$
$488$	−19.4723	−	5.21758i	−0.881469	−	0.236189i
$489$		0			0
$490$	17.2819	−	23.3940i	0.780715	−	1.05684i
$491$	−6.17910	+	3.56750i	−0.278859	+	0.160999i	−0.632907	−	0.774228i	$-0.718138\pi$
$491$	−6.17910	+	3.56750i	−0.278859	+	0.160999i	0.354048	+	0.935227i	$0.384805\pi$
$492$		0			0
$493$	13.6602	+	23.6601i	0.615223	+	1.06560i
$494$	−4.88951	+	4.48940i	−0.219989	+	0.201988i
$495$		0			0
$496$	−1.68680	+	6.29522i	−0.0757395	+	0.282664i
$497$	26.8206	−	5.58985i	1.20307	−	0.250739i
$498$		0			0
$499$	−5.54585	−	20.6974i	−0.248266	−	0.926542i	−0.971714	−	0.236163i	$-0.924110\pi$
$499$	−5.54585	−	20.6974i	−0.248266	−	0.926542i	0.723447	−	0.690380i	$-0.242556\pi$
$500$	−13.6246	−	13.6246i	−0.609309	−	0.609309i
$501$		0			0
$502$	−4.26629	−	15.9220i	−0.190414	−	0.710634i
$503$	20.5890	+	11.8871i	0.918020	+	0.530019i	0.883003	−	0.469367i	$-0.155518\pi$
$503$	20.5890	+	11.8871i	0.918020	+	0.530019i	0.0350174	+	0.999387i	$0.488851\pi$
$504$		0			0
$505$	−19.0804	+	71.2091i	−0.849068	+	3.16876i
$506$	−5.99475	−	3.46107i	−0.266499	−	0.153863i
$507$		0			0
$508$	−4.04648	−	7.00871i	−0.179534	−	0.310961i
$509$	−21.9137	−	21.9137i	−0.971309	−	0.971309i	0.0282911	−	0.999600i	$-0.490993\pi$
$509$	−21.9137	−	21.9137i	−0.971309	−	0.971309i	−0.999600	+	0.0282911i	$0.990993\pi$
$510$		0			0
$511$	3.38844	−	10.2895i	0.149896	−	0.455182i
$512$	−10.8487	+	10.8487i	−0.479449	+	0.479449i
$513$		0			0
$514$	−0.420608	+	0.420608i	−0.0185522	+	0.0185522i
$515$	−6.70428	+	25.0207i	−0.295426	+	1.10254i
$516$		0			0
$517$	−2.18324	−	3.78149i	−0.0960189	−	0.166310i
$518$	−1.52981	+	27.1318i	−0.0672162	+	1.19210i
$519$		0			0
$520$	−12.9653	+	41.2643i	−0.568567	+	1.80956i
$521$	−23.5185	+	13.5784i	−1.03036	+	0.594881i	−0.917089	−	0.398683i	$-0.869467\pi$
$521$	−23.5185	+	13.5784i	−1.03036	+	0.594881i	−0.113275	+	0.993564i	$0.536134\pi$
$522$		0			0
$523$		−	42.2101i		−	1.84572i	−0.385137	−	0.922859i	$-0.625846\pi$
$523$		−	42.2101i		−	1.84572i	0.385137	−	0.922859i	$-0.374154\pi$
$524$	−3.47825	+	6.02451i	−0.151948	+	0.263182i
$525$		0			0
$526$	−0.493811	−	1.84293i	−0.0215312	−	0.0803554i
$527$	9.33577	−	34.8416i	0.406673	−	1.51772i
$528$		0			0
$529$	−25.0911			−1.09092
$530$	6.21447			0.269939
$531$		0			0
$532$	1.28132	−	3.89094i	0.0555523	−	0.168694i
$533$	−1.63130	−	0.0695920i	−0.0706593	−	0.00301436i
$534$		0			0
$535$	19.7591	−	5.29443i	0.854260	−	0.228898i
$536$	−6.88937	+	11.9327i	−0.297576	+	0.515416i
$537$		0			0
$538$	3.43567	+	3.43567i	0.148122	+	0.148122i
$539$	−6.55007	+	0.984249i	−0.282131	+	0.0423946i
$540$		0			0
$541$	6.69743	−	1.79457i	0.287945	−	0.0771547i	−0.111955	−	0.993713i	$-0.535711\pi$
$541$	6.69743	−	1.79457i	0.287945	−	0.0771547i	0.399900	+	0.916559i	$0.369045\pi$
$542$		−	4.27980i		−	0.183833i
$543$		0			0
$544$	25.7500	−	25.7500i	1.10402	−	1.10402i
$545$	−44.9558			−1.92570
$546$		0			0
$547$	32.4507			1.38749			0.693747	−	0.720219i	$-0.255959\pi$
$547$	32.4507			1.38749			0.693747	+	0.720219i	$0.255959\pi$
$548$	4.77449	−	4.77449i	0.203956	−	0.203956i
$549$		0			0
$550$		−	10.4948i		−	0.447499i
$551$	−5.78456	+	1.54997i	−0.246431	+	0.0660309i
$552$		0			0
$553$	−2.09742	−	1.37394i	−0.0891915	−	0.0584257i
$554$	−9.10707	−	9.10707i	−0.386922	−	0.386922i
$555$		0			0
$556$	−1.97717	+	3.42456i	−0.0838508	+	0.145234i
$557$	−5.55001	+	1.48712i	−0.235161	+	0.0630113i	−0.374475	−	0.927237i	$-0.622177\pi$
$557$	−5.55001	+	1.48712i	−0.235161	+	0.0630113i	0.139314	+	0.990248i	$0.455510\pi$
$558$		0			0
$559$	0.116879	−	0.371987i	0.00494344	−	0.0157334i
$560$	3.05864	+	14.6757i	0.129251	+	0.620160i
$561$		0			0
$562$	−1.13079			−0.0476997
$563$	43.6474			1.83952			0.919760	−	0.392482i	$-0.128383\pi$
$563$	43.6474			1.83952			0.919760	+	0.392482i	$0.128383\pi$
$564$		0			0
$565$	−2.74083	+	10.2289i	−0.115307	+	0.430333i
$566$	−5.64548	−	21.0692i	−0.237297	−	0.885605i
$567$		0			0
$568$	−15.7692	+	27.3130i	−0.661661	+	1.14603i
$569$		−	3.16172i		−	0.132546i	−0.997802	−	0.0662730i	$-0.978889\pi$
$569$		−	3.16172i		−	0.132546i	0.997802	−	0.0662730i	$-0.0211108\pi$
$570$		0			0
$571$	−31.3887	+	18.1222i	−1.31357	+	0.758393i	−0.982686	−	0.185277i	$-0.940682\pi$
$571$	−31.3887	+	18.1222i	−1.31357	+	0.758393i	−0.330888	+	0.943670i	$0.607348\pi$
$572$	2.68340	−	1.40030i	0.112198	−	0.0585493i
$573$		0			0
$574$	−1.12842	+	0.569334i	−0.0470993	+	0.0237635i
$575$	−36.4559	−	63.1435i	−1.52032	−	2.63327i
$576$		0			0
$577$	1.35035	−	5.03959i	0.0562160	−	0.209801i	−0.932105	−	0.362189i	$-0.882030\pi$
$577$	1.35035	−	5.03959i	0.0562160	−	0.209801i	0.988321	+	0.152388i	$0.0486963\pi$
$578$	34.6030	−	34.6030i	1.43930	−	1.43930i
$579$		0			0
$580$	−8.47888	+	8.47888i	−0.352066	+	0.352066i
$581$	23.0513	−	20.5905i	0.956327	−	0.854239i
$582$		0			0
$583$	−1.00072	−	1.00072i	−0.0414456	−	0.0414456i
$584$	6.23534	+	10.7999i	0.258020	+	0.446904i
$585$		0			0
$586$	2.30215	+	1.32915i	0.0951010	+	0.0549066i
$587$	−9.40982	+	35.1179i	−0.388385	+	1.44947i	0.444377	+	0.895840i	$0.353425\pi$
$587$	−9.40982	+	35.1179i	−0.388385	+	1.44947i	−0.832762	+	0.553632i	$0.813242\pi$
$588$		0			0
$589$	6.84740	+	3.95335i	0.282142	+	0.162895i
$590$	5.21535	+	19.4640i	0.214713	+	0.801319i
$591$		0			0
$592$	−9.90405	−	9.90405i	−0.407054	−	0.407054i
$593$	10.9522	+	40.8740i	0.449751	+	1.67849i	0.703078	+	0.711113i	$0.251809\pi$
$593$	10.9522	+	40.8740i	0.449751	+	1.67849i	−0.253327	+	0.967381i	$0.581525\pi$
$594$		0			0
$595$	−16.9284	−	81.2241i	−0.693996	−	3.32986i
$596$	−0.172787	+	0.644851i	−0.00707764	+	0.0264141i
$597$		0			0
$598$	−14.1498	+	22.2598i	−0.578629	+	0.910270i
$599$	−16.9264	−	29.3174i	−0.691594	−	1.19788i	−0.971315	−	0.237795i	$-0.923575\pi$
$599$	−16.9264	−	29.3174i	−0.691594	−	1.19788i	0.279721	−	0.960081i	$-0.409758\pi$
$600$		0			0
$601$	−21.1918	+	12.2351i	−0.864431	+	0.499080i	−0.865494	−	0.500920i	$-0.832995\pi$
$601$	−21.1918	+	12.2351i	−0.864431	+	0.499080i	0.00106241	+	0.999999i	$0.499662\pi$
$602$	−0.0615826	−	0.295479i	−0.00250992	−	0.0120428i
$603$		0			0
$604$	−0.0560526	−	0.0150193i	−0.00228075	−	0.000611125i
$605$	28.1428	−	28.1428i	1.14417	−	1.14417i
$606$		0			0
$607$	19.8343	−	11.4513i	0.805048	−	0.464795i	−0.0401853	−	0.999192i	$-0.512795\pi$
$607$	19.8343	−	11.4513i	0.805048	−	0.464795i	0.845233	+	0.534398i	$0.179461\pi$
$608$	3.99119	+	6.91295i	0.161864	+	0.280357i
$609$		0			0
$610$		−	27.5017i		−	1.11351i
$611$	−14.7506	+	7.69741i	−0.596746	+	0.311404i
$612$		0			0
$613$	−9.00681	−	33.6139i	−0.363782	−	1.35765i	−0.869065	−	0.494698i	$-0.835279\pi$
$613$	−9.00681	−	33.6139i	−0.363782	−	1.35765i	0.505283	−	0.862954i	$-0.331388\pi$
$614$		−	20.9695i		−	0.846260i
$615$		0			0
$616$	4.17812	−	6.37822i	0.168341	−	0.256986i
$617$	8.38788	+	31.3040i	0.337684	+	1.26025i	0.900930	+	0.433963i	$0.142885\pi$
$617$	8.38788	+	31.3040i	0.337684	+	1.26025i	−0.563247	+	0.826289i	$0.690448\pi$
$618$		0			0
$619$	−38.0001	−	10.1821i	−1.52735	−	0.409253i	−0.605200	−	0.796074i	$-0.706907\pi$
$619$	−38.0001	−	10.1821i	−1.52735	−	0.409253i	−0.922155	+	0.386820i	$0.873573\pi$
$620$	15.8315			0.635807
$621$		0			0
$622$	−10.3398	−	2.77055i	−0.414590	−	0.111089i
$623$	9.45037	+	10.5798i	0.378621	+	0.423869i
$624$		0			0
$625$	16.4867	−	28.5558i	0.659467	−	1.14223i
$626$	−27.3098	+	7.31763i	−1.09152	+	0.292471i
$627$		0			0
$628$	3.28512	+	5.69000i	0.131091	+	0.227056i
$629$	54.8150	+	54.8150i	2.18562	+	2.18562i
$630$		0			0
$631$	15.0028	−	4.01998i	0.597251	−	0.160033i	0.0524858	−	0.998622i	$-0.483286\pi$
$631$	15.0028	−	4.01998i	0.597251	−	0.160033i	0.544765	+	0.838589i	$0.316619\pi$
$632$	2.78804	−	0.747052i	0.110902	−	0.0297161i
$633$		0			0
$634$	11.6995	+	6.75471i	0.464646	+	0.268264i
$635$	25.4062	−	25.4062i	1.00821	−	1.00821i
$636$		0			0
$637$	2.68323	+	25.0958i	0.106314	+	0.994333i
$638$	−3.42520			−0.135605
$639$		0			0
$640$	3.48900	+	2.01438i	0.137915	+	0.0796252i
$641$		−	13.5078i		−	0.533526i	−0.963762	−	0.266763i	$-0.914046\pi$
$641$		−	13.5078i		−	0.533526i	0.963762	−	0.266763i	$-0.0859541\pi$
$642$		0			0
$643$	25.1020	−	6.72606i	0.989926	−	0.265250i	0.272706	−	0.962097i	$-0.412081\pi$
$643$	25.1020	−	6.72606i	0.989926	−	0.265250i	0.717219	+	0.696848i	$0.245415\pi$
$644$	0.916360	−	16.2520i	0.0361096	−	0.640417i
$645$		0			0
$646$	7.32889	+	12.6940i	0.288351	+	0.499439i
$647$	−11.5556	+	20.0149i	−0.454298	+	0.786868i	−0.998648	−	0.0519911i	$-0.983443\pi$
$647$	−11.5556	+	20.0149i	−0.454298	+	0.786868i	0.544349	+	0.838859i	$0.316777\pi$
$648$		0			0
$649$	2.29446	−	3.97413i	0.0900656	−	0.155998i
$650$	−39.9535	−	1.70444i	−1.56710	−	0.0668535i
$651$		0			0
$652$	−3.97023	−	1.06382i	−0.155486	−	0.0416624i
$653$	33.5022			1.31104			0.655522	−	0.755176i	$-0.272449\pi$
$653$	33.5022			1.31104			0.655522	+	0.755176i	$0.272449\pi$
$654$		0			0
$655$	−29.8320	−	7.99345i	−1.16563	−	0.312330i
$656$	0.168606	−	0.629246i	0.00658296	−	0.0245679i
$657$		0			0
$658$	−7.05741	+	10.7737i	−0.275126	+	0.420002i
$659$	−0.940246	+	1.62855i	−0.0366268	+	0.0634395i	−0.883758	−	0.467945i	$-0.844995\pi$
$659$	−0.940246	+	1.62855i	−0.0366268	+	0.0634395i	0.847131	+	0.531384i	$0.178328\pi$
$660$		0			0
$661$	−12.6624	−	47.2568i	−0.492511	−	1.83807i	−0.543548	−	0.839378i	$-0.682920\pi$
$661$	−12.6624	−	47.2568i	−0.492511	−	1.83807i	0.0510377	−	0.998697i	$-0.483747\pi$
$662$	0.690553	−	0.398691i	0.0268391	−	0.0154956i
$663$		0			0
$664$			35.5807i			1.38080i
$665$	18.1581	+	1.02383i	0.704139	+	0.0397026i
$666$		0			0
$667$	−20.6082	+	11.8982i	−0.797955	+	0.460699i
$668$	2.90268	−	10.8329i	0.112308	−	0.419139i
$669$		0			0
$670$	−18.1568	−	4.86511i	−0.701460	−	0.187956i
$671$	−4.42862	+	4.42862i	−0.170965	+	0.170965i
$672$		0			0
$673$	−16.4185	+	9.47923i	−0.632887	+	0.365397i	−0.781869	−	0.623442i	$-0.785734\pi$
$673$	−16.4185	+	9.47923i	−0.632887	+	0.365397i	0.148982	+	0.988840i	$0.452400\pi$
$674$	−9.67357	−	9.67357i	−0.372612	−	0.372612i
$675$		0			0
$676$	−4.89509	−	10.4431i	−0.188273	−	0.401656i
$677$	7.78358	+	4.49385i	0.299147	+	0.172713i	0.642060	−	0.766655i	$-0.278080\pi$
$677$	7.78358	+	4.49385i	0.299147	+	0.172713i	−0.342913	+	0.939367i	$0.611413\pi$
$678$		0			0
$679$	6.45501	+	30.9718i	0.247721	+	1.18859i
$680$	82.7153	+	47.7557i	3.17199	+	1.83135i
$681$		0			0
$682$	3.19771	+	3.19771i	0.122447	+	0.122447i
$683$	20.5680	+	20.5680i	0.787011	+	0.787011i	0.981003	−	0.193992i	$-0.0621437\pi$
$683$	20.5680	+	20.5680i	0.787011	+	0.787011i	−0.193992	+	0.981003i	$0.562144\pi$
$684$		0			0
$685$	25.9609	+	14.9885i	0.991916	+	0.572683i
$686$	11.2948	+	15.9413i	0.431236	+	0.608641i
$687$		0			0
$688$	0.134726	+	0.0777840i	0.00513638	+	0.00296549i
$689$	−3.97224	+	3.64719i	−0.151330	+	0.138947i
$690$		0			0
$691$	−14.2144	−	14.2144i	−0.540741	−	0.540741i	0.383005	−	0.923746i	$-0.374889\pi$
$691$	−14.2144	−	14.2144i	−0.540741	−	0.540741i	−0.923746	+	0.383005i	$0.874889\pi$
$692$	14.0747	−	8.12605i	0.535041	−	0.308906i
$693$		0			0
$694$	10.7311	−	10.7311i	0.407349	−	0.407349i
$695$	−16.9577	−	4.54379i	−0.643240	−	0.172356i
$696$		0			0
$697$	−0.933168	+	3.48263i	−0.0353463	+	0.131914i
$698$	31.1823	−	18.0031i	1.18027	−	0.681428i
$699$		0			0
$700$	22.0335	−	11.1168i	0.832786	−	0.420175i
$701$			26.4403i			0.998636i	0.866419	+	0.499318i	$0.166416\pi$
$701$			26.4403i			0.998636i	−0.866419	+	0.499318i	$0.833584\pi$
$702$		0			0
$703$	−14.7159	+	8.49622i	−0.555020	+	0.320441i
$704$	1.88625	+	7.03958i	0.0710907	+	0.265314i
$705$		0			0
$706$	2.92551	−	5.06714i	0.110103	−	0.190704i
$707$	−41.4236	−	27.1349i	−1.55790	−	1.02051i
$708$		0			0
$709$	0.263276	−	0.982560i	0.00988755	−	0.0369008i	−0.960806	−	0.277222i	$-0.910586\pi$
$709$	0.263276	−	0.982560i	0.00988755	−	0.0369008i	0.970693	+	0.240321i	$0.0772528\pi$
$710$	−41.5595	−	11.1358i	−1.55970	−	0.417920i
$711$		0			0
$712$	−16.3303			−0.612005
$713$	30.3475	+	8.13158i	1.13652	+	0.304530i
$714$		0			0
$715$	9.08836	+	9.89834i	0.339885	+	0.370177i
$716$	−7.95833	+	13.7842i	−0.297417	+	0.515141i
$717$		0			0
$718$	3.50637	−	6.07322i	0.130857	−	0.226650i
$719$	−16.1333	−	27.9438i	−0.601672	−	1.04213i	−0.992568	−	0.121691i	$-0.961168\pi$
$719$	−16.1333	−	27.9438i	−0.601672	−	1.04213i	0.390896	−	0.920435i	$-0.372165\pi$
$720$		0			0
$721$	−14.5550	−	9.53439i	−0.542057	−	0.355079i
$722$	16.2567	−	4.35596i	0.605010	−	0.162112i
$723$		0			0
$724$		−	10.0561i		−	0.373732i
$725$	−31.2446	−	18.0391i	−1.16039	−	0.669954i
$726$		0			0
$727$	−14.6393			−0.542941			−0.271471	−	0.962447i	$-0.587510\pi$
$727$	−14.6393			−0.542941			−0.271471	+	0.962447i	$0.587510\pi$
$728$	−23.6032	−	16.9419i	−0.874793	−	0.627908i
$729$		0			0
$730$	−12.0299	+	12.0299i	−0.445246	+	0.445246i
$731$	−0.745655	−	0.430504i	−0.0275791	−	0.0159228i
$732$		0			0
$733$	48.6040	−	13.0234i	1.79523	−	0.481031i	0.802014	−	0.597305i	$-0.203762\pi$
$733$	48.6040	−	13.0234i	1.79523	−	0.481031i	0.993217	+	0.116275i	$0.0370952\pi$
$734$	−7.28601	+	1.95228i	−0.268931	+	0.0720599i
$735$		0			0
$736$	22.4286	+	22.4286i	0.826728	+	0.826728i
$737$	2.14038	+	3.70724i	0.0788417	+	0.136558i
$738$		0			0
$739$	20.1849	−	5.40853i	0.742514	−	0.198956i	0.132319	−	0.991207i	$-0.457758\pi$
$739$	20.1849	−	5.40853i	0.742514	−	0.198956i	0.610195	+	0.792251i	$0.291091\pi$
$740$	−17.0119	+	29.4654i	−0.625369	+	1.08317i
$741$		0			0
$742$	−1.30568	+	3.96492i	−0.0479332	+	0.145557i
$743$	−25.4705	−	6.82479i	−0.934421	−	0.250377i	−0.240682	−	0.970604i	$-0.577371\pi$
$743$	−25.4705	−	6.82479i	−0.934421	−	0.250377i	−0.693739	+	0.720227i	$0.744038\pi$
$744$		0			0
$745$	−2.96389			−0.108589
$746$	−15.6304	−	4.18815i	−0.572269	−	0.153339i
$747$		0			0
$748$	−1.72987	−	6.45597i	−0.0632504	−	0.236054i
$749$	−0.773538	+	13.7190i	−0.0282645	+	0.501280i
$750$		0			0
$751$		−	15.3030i		−	0.558416i	−0.960231	−	0.279208i	$-0.909928\pi$
$751$		−	15.3030i		−	0.558416i	0.960231	−	0.279208i	$-0.0900719\pi$
$752$	−1.71812	−	6.41209i	−0.0626532	−	0.233825i
$753$		0			0
$754$	−0.556280	+	13.0397i	−0.0202585	+	0.474877i
$755$		−	0.257632i		−	0.00937618i
$756$		0			0
$757$	9.00227	+	15.5924i	0.327193	+	0.566715i	0.981954	−	0.189121i	$-0.0605640\pi$
$757$	9.00227	+	15.5924i	0.327193	+	0.566715i	−0.654761	+	0.755836i	$0.727231\pi$
$758$	−21.6253	+	12.4854i	−0.785467	+	0.453490i
$759$		0			0
$760$	−14.8041	+	14.8041i	−0.537000	+	0.537000i
$761$	40.8513	+	10.9461i	1.48086	+	0.396795i	0.906639	−	0.421907i	$-0.138639\pi$
$761$	40.8513	+	10.9461i	1.48086	+	0.396795i	0.574219	+	0.818701i	$0.305306\pi$
$762$		0			0
$763$	9.44540	−	28.6825i	0.341947	−	1.03838i
$764$	11.2704	−	6.50694i	0.407747	−	0.235413i
$765$		0			0
$766$	0.326683	+	0.565832i	0.0118035	+	0.0204443i
$767$	−14.7568	−	9.38040i	−0.532836	−	0.338707i
$768$		0			0
$769$	2.44052	−	9.10816i	0.0880075	−	0.328449i	−0.907859	−	0.419275i	$-0.862284\pi$
$769$	2.44052	−	9.10816i	0.0880075	−	0.328449i	0.995867	+	0.0908266i	$0.0289509\pi$
$770$	9.88010	+	3.25361i	0.356054	+	0.117252i
$771$		0			0
$772$	−2.69100	−	10.0430i	−0.0968513	−	0.361454i
$773$	17.2254	+	17.2254i	0.619556	+	0.619556i	0.945418	−	0.325861i	$-0.105654\pi$
$773$	17.2254	+	17.2254i	0.619556	+	0.619556i	−0.325861	+	0.945418i	$0.605654\pi$
$774$		0			0
$775$	12.3284	+	46.0104i	0.442851	+	1.65274i
$776$	−31.5404	−	18.2099i	−1.13223	−	0.653696i
$777$		0			0
$778$	2.58080	−	9.63167i	0.0925261	−	0.345312i
$779$	−0.684440	−	0.395162i	−0.0245226	−	0.0141581i
$780$		0			0
$781$	4.89914	+	8.48556i	0.175305	+	0.303637i
$782$	41.1848	+	41.1848i	1.47276	+	1.47276i
$783$		0			0
$784$	−10.0059	−	1.13196i	−0.357354	−	0.0404271i
$785$	−20.6259	+	20.6259i	−0.736171	+	0.736171i
$786$		0			0
$787$	−11.7876	+	11.7876i	−0.420182	+	0.420182i	−0.885266	−	0.465085i	$-0.846024\pi$
$787$	−11.7876	+	11.7876i	−0.420182	+	0.420182i	0.465085	+	0.885266i	$0.346024\pi$
$788$	−2.44494	+	9.12464i	−0.0870974	+	0.325052i
$789$		0			0
$790$	1.96884	+	3.41014i	0.0700484	+	0.121327i
$791$	−5.95033	−	3.89782i	−0.211570	−	0.138591i
$792$		0			0
$793$	16.1404	+	17.5789i	0.573163	+	0.624245i
$794$	8.16842	−	4.71604i	0.289886	−	0.167366i
$795$		0			0
$796$			18.8573i			0.668380i
$797$	7.91214	−	13.7042i	0.280263	−	0.485429i	−0.691187	−	0.722676i	$-0.742912\pi$
$797$	7.91214	−	13.7042i	0.280263	−	0.485429i	0.971449	+	0.237247i	$0.0762451\pi$
$798$		0			0
$799$	9.50910	+	35.4884i	0.336408	+	1.25549i
$800$	−12.4465	+	46.4509i	−0.440049	+	1.64229i
$801$		0			0
$802$	6.99594			0.247035
$803$	3.87436			0.136723
$804$		0			0
$805$	70.7472	−	14.7448i	2.49351	−	0.519687i
$806$	12.6930	−	11.6543i	0.447090	−	0.410505i
$807$		0			0
$808$	55.0631	−	14.7541i	1.93711	−	0.519048i
$809$	−18.2488	+	31.6079i	−0.641594	+	1.11127i	0.343483	+	0.939159i	$0.388393\pi$
$809$	−18.2488	+	31.6079i	−0.641594	+	1.11127i	−0.985077	+	0.172115i	$0.944940\pi$
$810$		0			0
$811$	33.0051	+	33.0051i	1.15897	+	1.15897i	0.984698	+	0.174269i	$0.0557563\pi$
$811$	33.0051	+	33.0051i	1.15897	+	1.15897i	0.174269	+	0.984698i	$0.444244\pi$
$812$	−3.62820	−	7.19110i	−0.127325	−	0.252358i
$813$		0			0
$814$	−9.38769	+	2.51542i	−0.329038	+	0.0881656i
$815$		−	18.2482i		−	0.639206i
$816$		0			0
$817$	0.133455	−	0.133455i	0.00466898	−	0.00466898i
$818$	17.2679			0.603758
$819$		0			0
$820$	−1.58245			−0.0552617
$821$	24.7866	−	24.7866i	0.865059	−	0.865059i	−0.126861	−	0.991920i	$-0.540490\pi$
$821$	24.7866	−	24.7866i	0.865059	−	0.865059i	0.991920	+	0.126861i	$0.0404903\pi$
$822$		0			0
$823$			12.9225i			0.450449i	0.974307	+	0.225225i	$0.0723116\pi$
$823$			12.9225i			0.450449i	−0.974307	+	0.225225i	$0.927688\pi$
$824$	19.3475	−	5.18415i	0.674002	−	0.180598i
$825$		0			0
$826$	−13.5141	−	0.761985i	−0.470215	−	0.0265128i
$827$	−16.1945	−	16.1945i	−0.563138	−	0.563138i	0.367059	−	0.930198i	$-0.380365\pi$
$827$	−16.1945	−	16.1945i	−0.563138	−	0.563138i	−0.930198	+	0.367059i	$0.880365\pi$
$828$		0			0
$829$	9.01082	−	15.6072i	0.312959	−	0.542060i	−0.666043	−	0.745914i	$-0.732013\pi$
$829$	9.01082	−	15.6072i	0.312959	−	0.542060i	0.979001	+	0.203853i	$0.0653465\pi$
$830$	−46.8861	+	12.5631i	−1.62744	+	0.436072i
$831$		0			0
$832$	27.1059	−	6.03763i	0.939727	−	0.209317i
$833$	55.3789	+	6.26495i	1.91877	+	0.217068i
$834$		0			0
$835$	49.7909			1.72308
$836$	1.46507			0.0506706
$837$		0			0
$838$	−6.27361	+	23.4134i	−0.216718	+	0.808803i
$839$	−9.35633	−	34.9183i	−0.323016	−	1.20551i	−0.916291	−	0.400513i	$-0.868832\pi$
$839$	−9.35633	−	34.9183i	−0.323016	−	1.20551i	0.593275	−	0.805000i	$-0.297835\pi$
$840$		0			0
$841$	8.61256	−	14.9174i	0.296985	−	0.514393i
$842$			4.97843i			0.171568i
$843$		0			0
$844$	18.0646	−	10.4296i	0.621808	−	0.359001i
$845$	39.1588	−	32.9916i	1.34710	−	1.13495i
$846$		0			0
$847$	12.0426	+	23.8685i	0.413789	+	0.820130i
$848$	−1.07578	−	1.86330i	−0.0369423	−	0.0639859i
$849$		0			0
$850$	−22.8550	+	85.2961i	−0.783920	+	2.92563i
$851$	−47.7446	+	47.7446i	−1.63666	+	1.63666i
$852$		0			0
$853$	9.67121	−	9.67121i	0.331136	−	0.331136i	−0.521882	−	0.853018i	$-0.674770\pi$
$853$	9.67121	−	9.67121i	0.331136	−	0.331136i	0.853018	+	0.521882i	$0.174770\pi$
$854$	17.5465	+	5.77822i	0.600429	+	0.197727i
$855$		0			0
$856$	−11.1849	−	11.1849i	−0.382293	−	0.382293i
$857$	−15.8586	−	27.4680i	−0.541720	−	0.938287i	−0.998805	−	0.0488643i	$-0.984440\pi$
$857$	−15.8586	−	27.4680i	−0.541720	−	0.938287i	0.457085	−	0.889423i	$-0.348894\pi$
$858$		0			0
$859$	3.30317	+	1.90709i	0.112703	+	0.0650690i	0.555292	−	0.831656i	$-0.312607\pi$
$859$	3.30317	+	1.90709i	0.112703	+	0.0650690i	−0.442589	+	0.896725i	$0.645940\pi$
$860$	0.0978072	−	0.365022i	0.00333520	−	0.0124471i
$861$		0			0
$862$	−25.7349	−	14.8581i	−0.876534	−	0.506067i
$863$	6.89611	+	25.7366i	0.234746	+	0.876086i	0.978263	+	0.207368i	$0.0664898\pi$
$863$	6.89611	+	25.7366i	0.234746	+	0.876086i	−0.743517	+	0.668718i	$0.766844\pi$
$864$		0			0
$865$	51.0202	+	51.0202i	1.73474	+	1.73474i
$866$	5.40036	+	20.1544i	0.183512	+	0.684875i
$867$		0			0
$868$	−3.32626	+	10.1007i	−0.112901	+	0.342841i
$869$	0.232093	−	0.866181i	0.00787320	−	0.0293832i
$870$		0			0
$871$	14.4610	−	7.54628i	0.489992	−	0.255696i
$872$	17.3812	+	30.1052i	0.588603	+	1.01949i
$873$		0			0
$874$	−11.0566	+	6.38355i	−0.373996	+	0.215927i
$875$	38.2793	+	42.8539i	1.29408	+	1.44873i
$876$		0			0
$877$	0.296491	+	0.0794445i	0.0100118	+	0.00268265i	0.263821	−	0.964572i	$-0.415017\pi$
$877$	0.296491	+	0.0794445i	0.0100118	+	0.00268265i	−0.253810	+	0.967254i	$0.581684\pi$
$878$	16.3415	−	16.3415i	0.551499	−	0.551499i
$879$		0			0
$880$	−4.64311	+	2.68070i	−0.156519	+	0.0903664i
$881$	4.00050	+	6.92907i	0.134780	+	0.233446i	0.925513	−	0.378715i	$-0.123634\pi$
$881$	4.00050	+	6.92907i	0.134780	+	0.233446i	−0.790733	+	0.612161i	$0.790300\pi$
$882$		0			0
$883$		−	49.8829i		−	1.67869i	−0.543597	−	0.839346i	$-0.682938\pi$
$883$		−	49.8829i		−	1.67869i	0.543597	−	0.839346i	$-0.317062\pi$
$884$	−24.8587	+	5.53709i	−0.836088	+	0.186232i
$885$		0			0
$886$	5.39334	+	20.1282i	0.181193	+	0.676221i
$887$		−	9.86893i		−	0.331366i	−0.986179	−	0.165683i	$-0.947017\pi$
$887$		−	9.86893i		−	0.331366i	0.986179	−	0.165683i	$-0.0529829\pi$
$888$		0			0
$889$	10.8716	+	21.5475i	0.364621	+	0.722680i
$890$	−5.76604	−	21.5192i	−0.193278	−	0.721324i
$891$		0			0
$892$	−5.19188	−	1.39116i	−0.173837	−	0.0465795i
$893$	−8.05349			−0.269500
$894$		0			0
$895$	−68.2563	−	18.2892i	−2.28156	−	0.611341i
$896$	−2.01825	+	1.80281i	−0.0674252	+	0.0602275i
$897$		0			0
$898$	17.3467	−	30.0454i	0.578868	−	1.00263i
$899$	15.0165	−	4.02366i	0.500828	−	0.134196i
$900$		0			0
$901$	5.95400	+	10.3126i	0.198356	+	0.343563i
$902$	−0.319631	−	0.319631i	−0.0106426	−	0.0106426i
$903$		0			0
$904$	7.90959	−	2.11937i	0.263069	−	0.0704891i
$905$	43.1241	−	11.5551i	1.43349	−	0.384104i
$906$		0			0
$907$	17.9912	+	10.3872i	0.597389	+	0.344903i	0.768014	−	0.640433i	$-0.221245\pi$
$907$	17.9912	+	10.3872i	0.597389	+	0.344903i	−0.170625	+	0.985336i	$0.554579\pi$
$908$	13.0935	−	13.0935i	0.434522	−	0.434522i
$909$		0			0
$910$	13.9910	−	37.0849i	0.463798	−	1.22935i
$911$	−15.1029			−0.500380			−0.250190	−	0.968197i	$-0.580493\pi$
$911$	−15.1029			−0.500380			−0.250190	+	0.968197i	$0.580493\pi$
$912$		0			0
$913$	9.57315	+	5.52706i	0.316825	+	0.182919i
$914$		−	16.5497i		−	0.547415i
$915$		0			0
$916$	−18.7979	+	5.03687i	−0.621099	+	0.166423i
$917$	11.3678	−	17.3538i	0.375397	−	0.573073i
$918$		0			0
$919$	4.36219	+	7.55554i	0.143896	+	0.249234i	0.928960	−	0.370179i	$-0.120704\pi$
$919$	4.36219	+	7.55554i	0.143896	+	0.249234i	−0.785065	+	0.619414i	$0.787370\pi$
$920$	−41.5958	+	72.0460i	−1.37137	+	2.37529i
$921$		0			0
$922$	0.879010	−	1.52249i	0.0289486	−	0.0501405i
$923$	33.1000	−	17.2728i	1.08950	−	0.568541i
$924$		0			0
$925$	−98.8819	−	26.4953i	−3.25122	−	0.871161i
$926$	−28.1433			−0.924845
$927$		0			0
$928$	15.1602	+	4.06218i	0.497659	+	0.133347i
$929$	4.85394	−	18.1152i	0.159253	−	0.594339i	−0.839451	−	0.543436i	$-0.817123\pi$
$929$	4.85394	−	18.1152i	0.159253	−	0.594339i	0.998704	−	0.0509037i	$-0.0162102\pi$
$930$		0			0
$931$	−4.46831	+	11.3700i	−0.146443	+	0.372637i
$932$	5.08280	−	8.80368i	0.166493	−	0.288374i
$933$		0			0
$934$	−6.25333	−	23.3378i	−0.204615	−	0.763635i
$935$	25.6978	−	14.8366i	0.840408	−	0.485210i
$936$		0			0
$937$		−	21.0904i		−	0.688992i	−0.938788	−	0.344496i	$-0.888050\pi$
$937$		−	21.0904i		−	0.688992i	0.938788	−	0.344496i	$-0.111950\pi$
$938$	6.91884	−	10.5622i	0.225908	−	0.344866i
$939$		0			0
$940$	−13.9650	+	8.06270i	−0.455488	+	0.262976i
$941$	1.19811	−	4.47139i	0.0390572	−	0.145763i	−0.943644	−	0.330963i	$-0.892626\pi$
$941$	1.19811	−	4.47139i	0.0390572	−	0.145763i	0.982701	+	0.185200i	$0.0592932\pi$
$942$		0			0
$943$	−3.03342	−	0.812801i	−0.0987816	−	0.0264685i
$944$	4.93311	−	4.93311i	0.160559	−	0.160559i
$945$		0			0
$946$	0.0934842	−	0.0539732i	0.00303943	−	0.00175482i
$947$	−23.2547	−	23.2547i	−0.755675	−	0.755675i	0.219857	−	0.975532i	$-0.429441\pi$
$947$	−23.2547	−	23.2547i	−0.755675	−	0.755675i	−0.975532	+	0.219857i	$0.929441\pi$
$948$		0			0
$949$	0.629227	−	14.7496i	0.0204256	−	0.478793i
$950$	−16.7632	−	9.67823i	−0.543870	−	0.314003i
$951$		0			0
$952$	−47.8477	+	42.7399i	−1.55075	+	1.38521i
$953$	2.61428	+	1.50935i	0.0846848	+	0.0488928i	0.541744	−	0.840543i	$-0.317764\pi$
$953$	2.61428	+	1.50935i	0.0846848	+	0.0488928i	−0.457060	+	0.889436i	$0.651097\pi$
$954$		0			0
$955$	40.8545	+	40.8545i	1.32202	+	1.32202i
$956$	−4.34200	−	4.34200i	−0.140430	−	0.140430i
$957$		0			0
$958$	−0.700759	−	0.404583i	−0.0226405	−	0.0130715i
$959$	−15.0174	+	13.4143i	−0.484938	+	0.433170i
$960$		0			0
$961$	9.07123	+	5.23728i	0.292620	+	0.168944i
$962$	8.05153	+	36.1473i	0.259592	+	1.16543i
$963$		0			0
$964$	−5.20815	−	5.20815i	−0.167743	−	0.167743i
$965$	39.9757	−	23.0800i	1.28686	−	0.742970i
$966$		0			0
$967$	−13.5833	+	13.5833i	−0.436809	+	0.436809i	−0.890936	−	0.454128i	$-0.849951\pi$
$967$	−13.5833	+	13.5833i	−0.436809	+	0.436809i	0.454128	+	0.890936i	$0.349951\pi$
$968$	−29.7270	−	7.96533i	−0.955462	−	0.256015i
$969$		0			0
$970$	12.8594	−	47.9918i	0.412889	−	1.54092i
$971$	−26.0930	+	15.0648i	−0.837364	+	0.483452i	−0.856367	−	0.516367i	$-0.827284\pi$
$971$	−26.0930	+	15.0648i	−0.837364	+	0.483452i	0.0190035	+	0.999819i	$0.493951\pi$
$972$		0			0
$973$	6.46188	−	9.86457i	0.207158	−	0.316243i
$974$			7.79047i			0.249623i
$975$		0			0
$976$	−8.24590	+	4.76077i	−0.263945	+	0.152389i
$977$	−5.41586	−	20.2122i	−0.173269	−	0.646647i	−0.996840	−	0.0794347i	$-0.974688\pi$
$977$	−5.41586	−	20.2122i	−0.173269	−	0.646647i	0.823571	−	0.567212i	$-0.191978\pi$
$978$		0			0
$979$	−2.53674	+	4.39376i	−0.0810745	+	0.140425i
$980$	3.63483	+	24.1894i	0.116110	+	0.772701i
$981$		0			0
$982$	−1.94806	+	7.27026i	−0.0621651	+	0.232003i
$983$	−5.48673	−	1.47016i	−0.174999	−	0.0468910i	0.170255	−	0.985400i	$-0.445541\pi$
$983$	−5.48673	−	1.47016i	−0.174999	−	0.0468910i	−0.345255	+	0.938509i	$0.612207\pi$
$984$		0			0
$985$	−41.9391			−1.33629
$986$	27.8382	+	7.45923i	0.886549	+	0.237550i
$987$		0			0
$988$	0.237939	−	5.57750i	0.00756985	−	0.177444i
$989$	0.374975	−	0.649475i	0.0119235	−	0.0206521i
$990$		0			0
$991$	26.3329	−	45.6099i	0.836492	−	1.44885i	−0.0563182	−	0.998413i	$-0.517936\pi$
$991$	26.3329	−	45.6099i	0.836492	−	1.44885i	0.892810	−	0.450433i	$-0.148731\pi$
$992$	−10.3610	−	17.9457i	−0.328961	−	0.569777i
$993$		0			0
$994$	15.8366	−	24.1759i	0.502308	−	0.766812i
$995$	−80.8670	+	21.6682i	−2.56366	+	0.686929i
$996$		0			0
$997$		−	26.4946i		−	0.839092i	−0.907734	−	0.419546i	$-0.862189\pi$
$997$		−	26.4946i		−	0.839092i	0.907734	−	0.419546i	$-0.137811\pi$
$998$	−19.5755	−	11.3019i	−0.619653	−	0.357757i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.c.145.6		36
3.2	odd	2		273.2.bt.a.145.4	✓	36
7.3	odd	6		819.2.gh.c.262.6		36
13.7	odd	12		819.2.gh.c.397.6		36
21.17	even	6		273.2.cg.a.262.4	yes	36
39.20	even	12		273.2.cg.a.124.4	yes	36
91.59	even	12	inner	819.2.et.c.514.6		36
273.59	odd	12		273.2.bt.a.241.4	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.145.4	✓	36	3.2	odd	2
273.2.bt.a.241.4	yes	36	273.59	odd	12
273.2.cg.a.124.4	yes	36	39.20	even	12
273.2.cg.a.262.4	yes	36	21.17	even	6
819.2.et.c.145.6		36	1.1	even	1	trivial
819.2.et.c.514.6		36	91.59	even	12	inner
819.2.gh.c.262.6		36	7.3	odd	6
819.2.gh.c.397.6		36	13.7	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.et (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.745928 - 0.745928i) q^{2} +0.887184i q^{4} +(-3.80456 + 1.01943i) q^{5} +(0.148943 - 2.64156i) q^{7} +(2.15363 + 2.15363i) q^{8} +O(q^{10})\)	\(q+(0.745928 - 0.745928i) q^{2} +0.887184i q^{4} +(-3.80456 + 1.01943i) q^{5} +(0.148943 - 2.64156i) q^{7} +(2.15363 + 2.15363i) q^{8} +(-2.07751 + 3.59835i) q^{10} +(0.913987 - 0.244902i) q^{11} +(-0.783899 - 3.51930i) q^{13} +(-1.85931 - 2.08151i) q^{14} +1.43854 q^{16} -7.96173 q^{17} +(0.451695 - 1.68575i) q^{19} +(-0.904422 - 3.37535i) q^{20} +(0.499089 - 0.864448i) q^{22} -6.93477i q^{23} +(9.10535 - 5.25697i) q^{25} +(-3.20988 - 2.04041i) q^{26} +(2.34355 + 0.132140i) q^{28} +(-1.71573 - 2.97173i) q^{29} +(-1.17258 + 4.37613i) q^{31} +(-3.23422 + 3.23422i) q^{32} +(-5.93888 + 5.93888i) q^{34} +(2.12622 + 10.2018i) q^{35} +(-6.88481 - 6.88481i) q^{37} +(-0.920514 - 1.59438i) q^{38} +(-10.3891 - 5.99815i) q^{40} +(0.117207 - 0.437421i) q^{41} +(0.0936549 + 0.0540717i) q^{43} +(0.217273 + 0.810875i) q^{44} +(-5.17284 - 5.17284i) q^{46} +(-1.19435 - 4.45738i) q^{47} +(-6.95563 - 0.786882i) q^{49} +(2.87061 - 10.7132i) q^{50} +(3.12227 - 0.695463i) q^{52} +(-0.747827 - 1.29527i) q^{53} +(-3.22766 + 1.86349i) q^{55} +(6.00970 - 5.36817i) q^{56} +(-3.49650 - 0.936885i) q^{58} +(3.42925 - 3.42925i) q^{59} +(-5.73215 + 3.30946i) q^{61} +(2.38961 + 4.13893i) q^{62} +7.70205i q^{64} +(6.57008 + 12.5903i) q^{65} +(1.17090 + 4.36986i) q^{67} -7.06353i q^{68} +(9.19581 + 6.02380i) q^{70} +(2.68009 + 10.0022i) q^{71} +(3.95501 + 1.05974i) q^{73} -10.2711 q^{74} +(1.49557 + 0.400736i) q^{76} +(-0.510791 - 2.45082i) q^{77} +(0.473848 - 0.820728i) q^{79} +(-5.47300 + 1.46649i) q^{80} +(-0.238857 - 0.413712i) q^{82} +(8.26062 + 8.26062i) q^{83} +(30.2909 - 8.11643i) q^{85} +(0.110193 - 0.0295262i) q^{86} +(2.49582 + 1.44096i) q^{88} +(-3.79135 + 3.79135i) q^{89} +(-9.41319 + 1.54654i) q^{91} +6.15242 q^{92} +(-4.21578 - 2.43398i) q^{94} +6.87400i q^{95} +(-11.5503 + 3.09490i) q^{97} +(-5.77535 + 4.60144i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{7}+O(q^{10}) \) 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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