LMFDB - Embedded newform 3610.2.a.bi.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3610,2,Mod(1,3610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3610, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3610 = 2 \cdot 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3610.a (trivial)

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:	yes
Analytic conductor:	$28.8259951297$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 24x^{7} - 6x^{6} + 183x^{5} + 78x^{4} - 455x^{3} - 168x^{2} + 228x - 8 $ x^9 - 24x^7 - 6x^6 + 183x^5 + 78x^4 - 455x^3 - 168x^2 + 228*x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.37131$ of defining polynomial
Character	$\chi$	$=$	3610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.37131 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.37131 q^{6} +3.15542 q^{7} -1.00000 q^{8} +2.62313 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.37131 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.37131 q^{6} +3.15542 q^{7} -1.00000 q^{8} +2.62313 q^{9} -1.00000 q^{10} +1.37777 q^{11} -2.37131 q^{12} -4.32521 q^{13} -3.15542 q^{14} -2.37131 q^{15} +1.00000 q^{16} -1.29660 q^{17} -2.62313 q^{18} +1.00000 q^{20} -7.48249 q^{21} -1.37777 q^{22} -2.12499 q^{23} +2.37131 q^{24} +1.00000 q^{25} +4.32521 q^{26} +0.893684 q^{27} +3.15542 q^{28} -0.130347 q^{29} +2.37131 q^{30} +0.346710 q^{31} -1.00000 q^{32} -3.26713 q^{33} +1.29660 q^{34} +3.15542 q^{35} +2.62313 q^{36} +10.3150 q^{37} +10.2564 q^{39} -1.00000 q^{40} +11.0090 q^{41} +7.48249 q^{42} -11.5252 q^{43} +1.37777 q^{44} +2.62313 q^{45} +2.12499 q^{46} +0.0764422 q^{47} -2.37131 q^{48} +2.95667 q^{49} -1.00000 q^{50} +3.07464 q^{51} -4.32521 q^{52} +6.21960 q^{53} -0.893684 q^{54} +1.37777 q^{55} -3.15542 q^{56} +0.130347 q^{58} -8.18626 q^{59} -2.37131 q^{60} +7.84600 q^{61} -0.346710 q^{62} +8.27707 q^{63} +1.00000 q^{64} -4.32521 q^{65} +3.26713 q^{66} -1.03068 q^{67} -1.29660 q^{68} +5.03902 q^{69} -3.15542 q^{70} +11.6528 q^{71} -2.62313 q^{72} -12.2436 q^{73} -10.3150 q^{74} -2.37131 q^{75} +4.34745 q^{77} -10.2564 q^{78} +14.0099 q^{79} +1.00000 q^{80} -9.98859 q^{81} -11.0090 q^{82} +11.3789 q^{83} -7.48249 q^{84} -1.29660 q^{85} +11.5252 q^{86} +0.309093 q^{87} -1.37777 q^{88} -18.2182 q^{89} -2.62313 q^{90} -13.6478 q^{91} -2.12499 q^{92} -0.822157 q^{93} -0.0764422 q^{94} +2.37131 q^{96} -16.2217 q^{97} -2.95667 q^{98} +3.61407 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} + 9 q^{4} + 9 q^{5} - 9 q^{8} + 21 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 + 9 * q^4 + 9 * q^5 - 9 * q^8 + 21 * q^9	$ 9 q - 9 q^{2} + 9 q^{4} + 9 q^{5} - 9 q^{8} + 21 q^{9} - 9 q^{10} + 12 q^{11} - 9 q^{13} + 9 q^{16} + 6 q^{17} - 21 q^{18} + 9 q^{20} - 6 q^{21} - 12 q^{22} + 18 q^{23} + 9 q^{25} + 9 q^{26} + 18 q^{27} + 6 q^{31} - 9 q^{32} - 6 q^{33} - 6 q^{34} + 21 q^{36} - 6 q^{37} + 24 q^{39} - 9 q^{40} + 6 q^{42} + 18 q^{43} + 12 q^{44} + 21 q^{45} - 18 q^{46} - 3 q^{47} + 39 q^{49} - 9 q^{50} + 48 q^{51} - 9 q^{52} - 18 q^{54} + 12 q^{55} - 21 q^{59} + 18 q^{61} - 6 q^{62} - 12 q^{63} + 9 q^{64} - 9 q^{65} + 6 q^{66} + 6 q^{68} + 30 q^{69} - 18 q^{71} - 21 q^{72} - 36 q^{73} + 6 q^{74} + 15 q^{77} - 24 q^{78} + 6 q^{79} + 9 q^{80} + 69 q^{81} - 6 q^{83} - 6 q^{84} + 6 q^{85} - 18 q^{86} - 24 q^{87} - 12 q^{88} + 18 q^{89} - 21 q^{90} + 60 q^{91} + 18 q^{92} + 3 q^{94} - 18 q^{97} - 39 q^{98} + 54 q^{99}+O(q^{100}) $ 9 * q - 9 * q^2 + 9 * q^4 + 9 * q^5 - 9 * q^8 + 21 * q^9 - 9 * q^10 + 12 * q^11 - 9 * q^13 + 9 * q^16 + 6 * q^17 - 21 * q^18 + 9 * q^20 - 6 * q^21 - 12 * q^22 + 18 * q^23 + 9 * q^25 + 9 * q^26 + 18 * q^27 + 6 * q^31 - 9 * q^32 - 6 * q^33 - 6 * q^34 + 21 * q^36 - 6 * q^37 + 24 * q^39 - 9 * q^40 + 6 * q^42 + 18 * q^43 + 12 * q^44 + 21 * q^45 - 18 * q^46 - 3 * q^47 + 39 * q^49 - 9 * q^50 + 48 * q^51 - 9 * q^52 - 18 * q^54 + 12 * q^55 - 21 * q^59 + 18 * q^61 - 6 * q^62 - 12 * q^63 + 9 * q^64 - 9 * q^65 + 6 * q^66 + 6 * q^68 + 30 * q^69 - 18 * q^71 - 21 * q^72 - 36 * q^73 + 6 * q^74 + 15 * q^77 - 24 * q^78 + 6 * q^79 + 9 * q^80 + 69 * q^81 - 6 * q^83 - 6 * q^84 + 6 * q^85 - 18 * q^86 - 24 * q^87 - 12 * q^88 + 18 * q^89 - 21 * q^90 + 60 * q^91 + 18 * q^92 + 3 * q^94 - 18 * q^97 - 39 * q^98 + 54 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.37131	−1.36908	−0.684539	−	0.728976i	$-0.739997\pi$
$3$	−2.37131	−1.36908	−0.684539	+	0.728976i	$0.739997\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.37131	0.968085
$7$	3.15542	1.19264	0.596318	−	0.802748i	$-0.296630\pi$
$7$	3.15542	1.19264	0.596318	+	0.802748i	$0.296630\pi$
$8$	−1.00000	−0.353553
$9$	2.62313	0.874376
$10$	−1.00000	−0.316228
$11$	1.37777	0.415414	0.207707	−	0.978191i	$-0.433400\pi$
$11$	1.37777	0.415414	0.207707	+	0.978191i	$0.433400\pi$
$12$	−2.37131	−0.684539
$13$	−4.32521	−1.19960	−0.599799	−	0.800151i	$-0.704753\pi$
$13$	−4.32521	−1.19960	−0.599799	+	0.800151i	$0.704753\pi$
$14$	−3.15542	−0.843321
$15$	−2.37131	−0.612270
$16$	1.00000	0.250000
$17$	−1.29660	−0.314472	−0.157236	−	0.987561i	$-0.550258\pi$
$17$	−1.29660	−0.314472	−0.157236	+	0.987561i	$0.550258\pi$
$18$	−2.62313	−0.618277
$19$	0	0
$19$	0	0
$20$	1.00000	0.223607
$21$	−7.48249	−1.63281
$22$	−1.37777	−0.293742
$23$	−2.12499	−0.443091	−0.221546	−	0.975150i	$-0.571110\pi$
$23$	−2.12499	−0.443091	−0.221546	+	0.975150i	$0.571110\pi$
$24$	2.37131	0.484042
$25$	1.00000	0.200000
$26$	4.32521	0.848243
$27$	0.893684	0.171990
$28$	3.15542	0.596318
$29$	−0.130347	−0.0242048	−0.0121024	−	0.999927i	$-0.503852\pi$
$29$	−0.130347	−0.0242048	−0.0121024	+	0.999927i	$0.503852\pi$
$30$	2.37131	0.432941
$31$	0.346710	0.0622709	0.0311355	−	0.999515i	$-0.490088\pi$
$31$	0.346710	0.0622709	0.0311355	+	0.999515i	$0.490088\pi$
$32$	−1.00000	−0.176777
$33$	−3.26713	−0.568734
$34$	1.29660	0.222365
$35$	3.15542	0.533363
$36$	2.62313	0.437188
$37$	10.3150	1.69578	0.847889	−	0.530174i	$-0.177873\pi$
$37$	10.3150	1.69578	0.847889	+	0.530174i	$0.177873\pi$
$38$	0	0
$39$	10.2564	1.64234
$40$	−1.00000	−0.158114
$41$	11.0090	1.71932	0.859660	−	0.510867i	$-0.170675\pi$
$41$	11.0090	1.71932	0.859660	+	0.510867i	$0.170675\pi$
$42$	7.48249	1.15457
$43$	−11.5252	−1.75757	−0.878786	−	0.477217i	$-0.841646\pi$
$43$	−11.5252	−1.75757	−0.878786	+	0.477217i	$0.841646\pi$
$44$	1.37777	0.207707
$45$	2.62313	0.391033
$46$	2.12499	0.313313
$47$	0.0764422	0.0111502	0.00557512	−	0.999984i	$-0.498225\pi$
$47$	0.0764422	0.0111502	0.00557512	+	0.999984i	$0.498225\pi$
$48$	−2.37131	−0.342270
$49$	2.95667	0.422382
$50$	−1.00000	−0.141421
$51$	3.07464	0.430536
$52$	−4.32521	−0.599799
$53$	6.21960	0.854327	0.427164	−	0.904174i	$-0.359513\pi$
$53$	6.21960	0.854327	0.427164	+	0.904174i	$0.359513\pi$
$54$	−0.893684	−0.121615
$55$	1.37777	0.185779
$56$	−3.15542	−0.421661
$57$	0	0
$58$	0.130347	0.0171154
$59$	−8.18626	−1.06576	−0.532880	−	0.846191i	$-0.678890\pi$
$59$	−8.18626	−1.06576	−0.532880	+	0.846191i	$0.678890\pi$
$60$	−2.37131	−0.306135
$61$	7.84600	1.00458	0.502289	−	0.864700i	$-0.332491\pi$
$61$	7.84600	1.00458	0.502289	+	0.864700i	$0.332491\pi$
$62$	−0.346710	−0.0440322
$63$	8.27707	1.04281
$64$	1.00000	0.125000
$65$	−4.32521	−0.536476
$66$	3.26713	0.402156
$67$	−1.03068	−0.125918	−0.0629588	−	0.998016i	$-0.520054\pi$
$67$	−1.03068	−0.125918	−0.0629588	+	0.998016i	$0.520054\pi$
$68$	−1.29660	−0.157236
$69$	5.03902	0.606627
$70$	−3.15542	−0.377145
$71$	11.6528	1.38293	0.691467	−	0.722408i	$-0.256965\pi$
$71$	11.6528	1.38293	0.691467	+	0.722408i	$0.256965\pi$
$72$	−2.62313	−0.309138
$73$	−12.2436	−1.43301	−0.716503	−	0.697584i	$-0.754259\pi$
$73$	−12.2436	−1.43301	−0.716503	+	0.697584i	$0.754259\pi$
$74$	−10.3150	−1.19910
$75$	−2.37131	−0.273816
$76$	0	0
$77$	4.34745	0.495438
$78$	−10.2564	−1.16131
$79$	14.0099	1.57624	0.788120	−	0.615522i	$-0.211055\pi$
$79$	14.0099	1.57624	0.788120	+	0.615522i	$0.211055\pi$
$80$	1.00000	0.111803
$81$	−9.98859	−1.10984
$82$	−11.0090	−1.21574
$83$	11.3789	1.24900	0.624499	−	0.781025i	$-0.285303\pi$
$83$	11.3789	1.24900	0.624499	+	0.781025i	$0.285303\pi$
$84$	−7.48249	−0.816406
$85$	−1.29660	−0.140636
$86$	11.5252	1.24279
$87$	0.309093	0.0331383
$88$	−1.37777	−0.146871
$89$	−18.2182	−1.93112	−0.965562	−	0.260171i	$-0.916221\pi$
$89$	−18.2182	−1.93112	−0.965562	+	0.260171i	$0.916221\pi$
$90$	−2.62313	−0.276502
$91$	−13.6478	−1.43068
$92$	−2.12499	−0.221546
$93$	−0.822157	−0.0852537
$94$	−0.0764422	−0.00788441
$95$	0	0
$96$	2.37131	0.242021
$97$	−16.2217	−1.64706	−0.823531	−	0.567271i	$-0.807999\pi$
$97$	−16.2217	−1.64706	−0.823531	+	0.567271i	$0.807999\pi$
$98$	−2.95667	−0.298669
$99$	3.61407	0.363228
$100$	1.00000	0.100000
$101$	6.62325	0.659038	0.329519	−	0.944149i	$-0.393114\pi$
$101$	6.62325	0.659038	0.329519	+	0.944149i	$0.393114\pi$
$102$	−3.07464	−0.304435
$103$	−12.3576	−1.21763	−0.608815	−	0.793312i	$-0.708355\pi$
$103$	−12.3576	−1.21763	−0.608815	+	0.793312i	$0.708355\pi$
$104$	4.32521	0.424122
$105$	−7.48249	−0.730216
$106$	−6.21960	−0.604101
$107$	10.9548	1.05904	0.529521	−	0.848297i	$-0.322372\pi$
$107$	10.9548	1.05904	0.529521	+	0.848297i	$0.322372\pi$
$108$	0.893684	0.0859948
$109$	7.44096	0.712715	0.356357	−	0.934350i	$-0.384019\pi$
$109$	7.44096	0.712715	0.356357	+	0.934350i	$0.384019\pi$
$110$	−1.37777	−0.131365
$111$	−24.4601	−2.32165
$112$	3.15542	0.298159
$113$	−11.6014	−1.09137	−0.545686	−	0.837990i	$-0.683731\pi$
$113$	−11.6014	−1.09137	−0.545686	+	0.837990i	$0.683731\pi$
$114$	0	0
$115$	−2.12499	−0.198156
$116$	−0.130347	−0.0121024
$117$	−11.3456	−1.04890
$118$	8.18626	0.753606
$119$	−4.09132	−0.375050
$120$	2.37131	0.216470
$121$	−9.10174	−0.827431
$122$	−7.84600	−0.710343
$123$	−26.1058	−2.35388
$124$	0.346710	0.0311355
$125$	1.00000	0.0894427
$126$	−8.27707	−0.737380
$127$	16.3985	1.45513	0.727566	−	0.686037i	$-0.240651\pi$
$127$	16.3985	1.45513	0.727566	+	0.686037i	$0.240651\pi$
$128$	−1.00000	−0.0883883
$129$	27.3298	2.40625
$130$	4.32521	0.379346
$131$	11.1367	0.973015	0.486508	−	0.873676i	$-0.338271\pi$
$131$	11.1367	0.973015	0.486508	+	0.873676i	$0.338271\pi$
$132$	−3.26713	−0.284367
$133$	0	0
$134$	1.03068	0.0890371
$135$	0.893684	0.0769161
$136$	1.29660	0.111182
$137$	7.34165	0.627240	0.313620	−	0.949549i	$-0.398458\pi$
$137$	7.34165	0.627240	0.313620	+	0.949549i	$0.398458\pi$
$138$	−5.03902	−0.428950
$139$	11.8115	1.00184	0.500920	−	0.865493i	$-0.332995\pi$
$139$	11.8115	1.00184	0.500920	+	0.865493i	$0.332995\pi$
$140$	3.15542	0.266682
$141$	−0.181268	−0.0152655
$142$	−11.6528	−0.977882
$143$	−5.95915	−0.498329
$144$	2.62313	0.218594
$145$	−0.130347	−0.0108247
$146$	12.2436	1.01329
$147$	−7.01120	−0.578274
$148$	10.3150	0.847889
$149$	3.51451	0.287920	0.143960	−	0.989584i	$-0.454016\pi$
$149$	3.51451	0.287920	0.143960	+	0.989584i	$0.454016\pi$
$150$	2.37131	0.193617
$151$	−0.212620	−0.0173028	−0.00865139	−	0.999963i	$-0.502754\pi$
$151$	−0.212620	−0.0173028	−0.00865139	+	0.999963i	$0.502754\pi$
$152$	0	0
$153$	−3.40114	−0.274966
$154$	−4.34745	−0.350327
$155$	0.346710	0.0278484
$156$	10.2564	0.821171
$157$	7.68751	0.613530	0.306765	−	0.951785i	$-0.400753\pi$
$157$	7.68751	0.613530	0.306765	+	0.951785i	$0.400753\pi$
$158$	−14.0099	−1.11457
$159$	−14.7486	−1.16964
$160$	−1.00000	−0.0790569
$161$	−6.70524	−0.528447
$162$	9.98859	0.784777
$163$	−7.32701	−0.573896	−0.286948	−	0.957946i	$-0.592641\pi$
$163$	−7.32701	−0.573896	−0.286948	+	0.957946i	$0.592641\pi$
$164$	11.0090	0.859660
$165$	−3.26713	−0.254346
$166$	−11.3789	−0.883175
$167$	−15.8439	−1.22604	−0.613018	−	0.790069i	$-0.710045\pi$
$167$	−15.8439	−1.22604	−0.613018	+	0.790069i	$0.710045\pi$
$168$	7.48249	0.577287
$169$	5.70743	0.439033
$170$	1.29660	0.0994446
$171$	0	0
$172$	−11.5252	−0.878786
$173$	16.6402	1.26513	0.632566	−	0.774507i	$-0.282002\pi$
$173$	16.6402	1.26513	0.632566	+	0.774507i	$0.282002\pi$
$174$	−0.309093	−0.0234323
$175$	3.15542	0.238527
$176$	1.37777	0.103853
$177$	19.4122	1.45911
$178$	18.2182	1.36551
$179$	−4.57107	−0.341658	−0.170829	−	0.985301i	$-0.554644\pi$
$179$	−4.57107	−0.341658	−0.170829	+	0.985301i	$0.554644\pi$
$180$	2.62313	0.195516
$181$	1.68838	0.125497	0.0627483	−	0.998029i	$-0.480013\pi$
$181$	1.68838	0.125497	0.0627483	+	0.998029i	$0.480013\pi$
$182$	13.6478	1.01165
$183$	−18.6053	−1.37535
$184$	2.12499	0.156656
$185$	10.3150	0.758375
$186$	0.822157	0.0602835
$187$	−1.78642	−0.130636
$188$	0.0764422	0.00557512
$189$	2.81995	0.205121
$190$	0	0
$191$	11.2207	0.811901	0.405951	−	0.913895i	$-0.366941\pi$
$191$	11.2207	0.811901	0.405951	+	0.913895i	$0.366941\pi$
$192$	−2.37131	−0.171135
$193$	−21.4878	−1.54673	−0.773364	−	0.633962i	$-0.781428\pi$
$193$	−21.4878	−1.54673	−0.773364	+	0.633962i	$0.781428\pi$
$194$	16.2217	1.16465
$195$	10.2564	0.734478
$196$	2.95667	0.211191
$197$	15.2784	1.08854	0.544271	−	0.838909i	$-0.316806\pi$
$197$	15.2784	1.08854	0.544271	+	0.838909i	$0.316806\pi$
$198$	−3.61407	−0.256841
$199$	0.708758	0.0502425	0.0251213	−	0.999684i	$-0.492003\pi$
$199$	0.708758	0.0502425	0.0251213	+	0.999684i	$0.492003\pi$
$200$	−1.00000	−0.0707107
$201$	2.44406	0.172391
$202$	−6.62325	−0.466010
$203$	−0.411299	−0.0288675
$204$	3.07464	0.215268
$205$	11.0090	0.768903
$206$	12.3576	0.860995
$207$	−5.57412	−0.387428
$208$	−4.32521	−0.299899
$209$	0	0
$210$	7.48249	0.516341
$211$	14.0791	0.969246	0.484623	−	0.874723i	$-0.338957\pi$
$211$	14.0791	0.969246	0.484623	+	0.874723i	$0.338957\pi$
$212$	6.21960	0.427164
$213$	−27.6324	−1.89334
$214$	−10.9548	−0.748855
$215$	−11.5252	−0.786010
$216$	−0.893684	−0.0608075
$217$	1.09401	0.0742665
$218$	−7.44096	−0.503966
$219$	29.0334	1.96190
$220$	1.37777	0.0928894
$221$	5.60806	0.377239
$222$	24.4601	1.64166
$223$	11.7169	0.784619	0.392310	−	0.919833i	$-0.371676\pi$
$223$	11.7169	0.784619	0.392310	+	0.919833i	$0.371676\pi$
$224$	−3.15542	−0.210830
$225$	2.62313	0.174875
$226$	11.6014	0.771717
$227$	−10.2265	−0.678758	−0.339379	−	0.940650i	$-0.610217\pi$
$227$	−10.2265	−0.678758	−0.339379	+	0.940650i	$0.610217\pi$
$228$	0	0
$229$	−5.05689	−0.334169	−0.167084	−	0.985943i	$-0.553435\pi$
$229$	−5.05689	−0.334169	−0.167084	+	0.985943i	$0.553435\pi$
$230$	2.12499	0.140118
$231$	−10.3092	−0.678293
$232$	0.130347	0.00855769
$233$	−7.25845	−0.475517	−0.237759	−	0.971324i	$-0.576413\pi$
$233$	−7.25845	−0.475517	−0.237759	+	0.971324i	$0.576413\pi$
$234$	11.3456	0.741683
$235$	0.0764422	0.00498654
$236$	−8.18626	−0.532880
$237$	−33.2219	−2.15800
$238$	4.09132	0.265201
$239$	15.9731	1.03322	0.516608	−	0.856222i	$-0.327194\pi$
$239$	15.9731	1.03322	0.516608	+	0.856222i	$0.327194\pi$
$240$	−2.37131	−0.153068
$241$	22.1949	1.42970	0.714850	−	0.699278i	$-0.246495\pi$
$241$	22.1949	1.42970	0.714850	+	0.699278i	$0.246495\pi$
$242$	9.10174	0.585082
$243$	21.0050	1.34747
$244$	7.84600	0.502289
$245$	2.95667	0.188895
$246$	26.1058	1.66445
$247$	0	0
$248$	−0.346710	−0.0220161
$249$	−26.9830	−1.70998
$250$	−1.00000	−0.0632456
$251$	22.5526	1.42351	0.711754	−	0.702428i	$-0.247901\pi$
$251$	22.5526	1.42351	0.711754	+	0.702428i	$0.247901\pi$
$252$	8.27707	0.521406
$253$	−2.92775	−0.184066
$254$	−16.3985	−1.02893
$255$	3.07464	0.192542
$256$	1.00000	0.0625000
$257$	10.7146	0.668356	0.334178	−	0.942510i	$-0.391541\pi$
$257$	10.7146	0.668356	0.334178	+	0.942510i	$0.391541\pi$
$258$	−27.3298	−1.70148
$259$	32.5482	2.02245
$260$	−4.32521	−0.268238
$261$	−0.341916	−0.0211641
$262$	−11.1367	−0.688026
$263$	26.6666	1.64433	0.822166	−	0.569247i	$-0.192765\pi$
$263$	26.6666	1.64433	0.822166	+	0.569247i	$0.192765\pi$
$264$	3.26713	0.201078
$265$	6.21960	0.382067
$266$	0	0
$267$	43.2011	2.64386
$268$	−1.03068	−0.0629588
$269$	1.42791	0.0870615	0.0435307	−	0.999052i	$-0.486139\pi$
$269$	1.42791	0.0870615	0.0435307	+	0.999052i	$0.486139\pi$
$270$	−0.893684	−0.0543879
$271$	7.36945	0.447662	0.223831	−	0.974628i	$-0.428144\pi$
$271$	7.36945	0.447662	0.223831	+	0.974628i	$0.428144\pi$
$272$	−1.29660	−0.0786179
$273$	32.3633	1.95872
$274$	−7.34165	−0.443525
$275$	1.37777	0.0830828
$276$	5.03902	0.303313
$277$	−2.52531	−0.151731	−0.0758656	−	0.997118i	$-0.524172\pi$
$277$	−2.52531	−0.151731	−0.0758656	+	0.997118i	$0.524172\pi$
$278$	−11.8115	−0.708408
$279$	0.909464	0.0544482
$280$	−3.15542	−0.188572
$281$	17.2288	1.02778	0.513892	−	0.857855i	$-0.328203\pi$
$281$	17.2288	1.02778	0.513892	+	0.857855i	$0.328203\pi$
$282$	0.181268	0.0107944
$283$	28.2208	1.67755	0.838776	−	0.544477i	$-0.183272\pi$
$283$	28.2208	1.67755	0.838776	+	0.544477i	$0.183272\pi$
$284$	11.6528	0.691467
$285$	0	0
$286$	5.95915	0.352372
$287$	34.7381	2.05052
$288$	−2.62313	−0.154569
$289$	−15.3188	−0.901108
$290$	0.130347	0.00765423
$291$	38.4667	2.25496
$292$	−12.2436	−0.716503
$293$	−12.6181	−0.737156	−0.368578	−	0.929597i	$-0.620155\pi$
$293$	−12.6181	−0.737156	−0.368578	+	0.929597i	$0.620155\pi$
$294$	7.01120	0.408901
$295$	−8.18626	−0.476622
$296$	−10.3150	−0.599548
$297$	1.23129	0.0714469
$298$	−3.51451	−0.203590
$299$	9.19103	0.531531
$300$	−2.37131	−0.136908
$301$	−36.3667	−2.09614
$302$	0.212620	0.0122349
$303$	−15.7058	−0.902274
$304$	0	0
$305$	7.84600	0.449261
$306$	3.40114	0.194431
$307$	9.06469	0.517349	0.258675	−	0.965965i	$-0.416714\pi$
$307$	9.06469	0.517349	0.258675	+	0.965965i	$0.416714\pi$
$308$	4.34745	0.247719
$309$	29.3037	1.66703
$310$	−0.346710	−0.0196918
$311$	−21.7124	−1.23120	−0.615599	−	0.788060i	$-0.711086\pi$
$311$	−21.7124	−1.23120	−0.615599	+	0.788060i	$0.711086\pi$
$312$	−10.2564	−0.580656
$313$	−10.0460	−0.567835	−0.283917	−	0.958849i	$-0.591634\pi$
$313$	−10.0460	−0.567835	−0.283917	+	0.958849i	$0.591634\pi$
$314$	−7.68751	−0.433832
$315$	8.27707	0.466360
$316$	14.0099	0.788120
$317$	−2.10846	−0.118423	−0.0592114	−	0.998245i	$-0.518859\pi$
$317$	−2.10846	−0.118423	−0.0592114	+	0.998245i	$0.518859\pi$
$318$	14.7486	0.827061
$319$	−0.179588	−0.0100550
$320$	1.00000	0.0559017
$321$	−25.9773	−1.44991
$322$	6.70524	0.373668
$323$	0	0
$324$	−9.98859	−0.554921
$325$	−4.32521	−0.239919
$326$	7.32701	0.405805
$327$	−17.6449	−0.975763
$328$	−11.0090	−0.607871
$329$	0.241207	0.0132982
$330$	3.26713	0.179850
$331$	−3.44409	−0.189304	−0.0946521	−	0.995510i	$-0.530174\pi$
$331$	−3.44409	−0.189304	−0.0946521	+	0.995510i	$0.530174\pi$
$332$	11.3789	0.624499
$333$	27.0576	1.48275
$334$	15.8439	0.866938
$335$	−1.03068	−0.0563120
$336$	−7.48249	−0.408203
$337$	−25.8586	−1.40861	−0.704305	−	0.709898i	$-0.748741\pi$
$337$	−25.8586	−1.40861	−0.704305	+	0.709898i	$0.748741\pi$
$338$	−5.70743	−0.310443
$339$	27.5107	1.49417
$340$	−1.29660	−0.0703180
$341$	0.477687	0.0258682
$342$	0	0
$343$	−12.7584	−0.688889
$344$	11.5252	0.621395
$345$	5.03902	0.271292
$346$	−16.6402	−0.894583
$347$	2.52322	0.135453	0.0677266	−	0.997704i	$-0.478425\pi$
$347$	2.52322	0.135453	0.0677266	+	0.997704i	$0.478425\pi$
$348$	0.309093	0.0165691
$349$	3.67945	0.196956	0.0984782	−	0.995139i	$-0.468603\pi$
$349$	3.67945	0.196956	0.0984782	+	0.995139i	$0.468603\pi$
$350$	−3.15542	−0.168664
$351$	−3.86537	−0.206318
$352$	−1.37777	−0.0734355
$353$	2.79636	0.148835	0.0744175	−	0.997227i	$-0.476290\pi$
$353$	2.79636	0.148835	0.0744175	+	0.997227i	$0.476290\pi$
$354$	−19.4122	−1.03175
$355$	11.6528	0.618467
$356$	−18.2182	−0.965562
$357$	9.70179	0.513473
$358$	4.57107	0.241588
$359$	20.1404	1.06297	0.531484	−	0.847069i	$-0.321635\pi$
$359$	20.1404	1.06297	0.531484	+	0.847069i	$0.321635\pi$
$360$	−2.62313	−0.138251
$361$	0	0
$362$	−1.68838	−0.0887395
$363$	21.5831	1.13282
$364$	−13.6478	−0.715342
$365$	−12.2436	−0.640860
$366$	18.6053	0.972516
$367$	−4.52133	−0.236011	−0.118006	−	0.993013i	$-0.537650\pi$
$367$	−4.52133	−0.236011	−0.118006	+	0.993013i	$0.537650\pi$
$368$	−2.12499	−0.110773
$369$	28.8780	1.50333
$370$	−10.3150	−0.536252
$371$	19.6254	1.01890
$372$	−0.822157	−0.0426269
$373$	23.2704	1.20490	0.602449	−	0.798157i	$-0.294192\pi$
$373$	23.2704	1.20490	0.602449	+	0.798157i	$0.294192\pi$
$374$	1.78642	0.0923735
$375$	−2.37131	−0.122454
$376$	−0.0764422	−0.00394220
$377$	0.563778	0.0290360
$378$	−2.81995	−0.145043
$379$	9.34667	0.480106	0.240053	−	0.970760i	$-0.422835\pi$
$379$	9.34667	0.480106	0.240053	+	0.970760i	$0.422835\pi$
$380$	0	0
$381$	−38.8860	−1.99219
$382$	−11.2207	−0.574101
$383$	32.8362	1.67785	0.838925	−	0.544248i	$-0.183185\pi$
$383$	32.8362	1.67785	0.838925	+	0.544248i	$0.183185\pi$
$384$	2.37131	0.121011
$385$	4.34745	0.221566
$386$	21.4878	1.09370
$387$	−30.2320	−1.53678
$388$	−16.2217	−0.823531
$389$	10.6737	0.541176	0.270588	−	0.962695i	$-0.412782\pi$
$389$	10.6737	0.541176	0.270588	+	0.962695i	$0.412782\pi$
$390$	−10.2564	−0.519354
$391$	2.75526	0.139340
$392$	−2.95667	−0.149335
$393$	−26.4085	−1.33213
$394$	−15.2784	−0.769716
$395$	14.0099	0.704916
$396$	3.61407	0.181614
$397$	10.0563	0.504709	0.252355	−	0.967635i	$-0.418795\pi$
$397$	10.0563	0.504709	0.252355	+	0.967635i	$0.418795\pi$
$398$	−0.708758	−0.0355268
$399$	0	0
$400$	1.00000	0.0500000
$401$	12.0791	0.603201	0.301600	−	0.953434i	$-0.402479\pi$
$401$	12.0791	0.603201	0.301600	+	0.953434i	$0.402479\pi$
$402$	−2.44406	−0.121899
$403$	−1.49959	−0.0747000
$404$	6.62325	0.329519
$405$	−9.98859	−0.496337
$406$	0.411299	0.0204124
$407$	14.2117	0.704449
$408$	−3.07464	−0.152218
$409$	−39.5462	−1.95544	−0.977718	−	0.209922i	$-0.932679\pi$
$409$	−39.5462	−1.95544	−0.977718	+	0.209922i	$0.932679\pi$
$410$	−11.0090	−0.543697
$411$	−17.4094	−0.858740
$412$	−12.3576	−0.608815
$413$	−25.8311	−1.27106
$414$	5.57412	0.273953
$415$	11.3789	0.558569
$416$	4.32521	0.212061
$417$	−28.0088	−1.37160
$418$	0	0
$419$	28.5326	1.39391	0.696954	−	0.717116i	$-0.254538\pi$
$419$	28.5326	1.39391	0.696954	+	0.717116i	$0.254538\pi$
$420$	−7.48249	−0.365108
$421$	2.03904	0.0993767	0.0496884	−	0.998765i	$-0.484177\pi$
$421$	2.03904	0.0993767	0.0496884	+	0.998765i	$0.484177\pi$
$422$	−14.0791	−0.685361
$423$	0.200517	0.00974949
$424$	−6.21960	−0.302050
$425$	−1.29660	−0.0628943
$426$	27.6324	1.33880
$427$	24.7574	1.19810
$428$	10.9548	0.529521
$429$	14.1310	0.682252
$430$	11.5252	0.555793
$431$	13.5707	0.653679	0.326840	−	0.945080i	$-0.394016\pi$
$431$	13.5707	0.653679	0.326840	+	0.945080i	$0.394016\pi$
$432$	0.893684	0.0429974
$433$	28.9638	1.39191	0.695957	−	0.718084i	$-0.254980\pi$
$433$	28.9638	1.39191	0.695957	+	0.718084i	$0.254980\pi$
$434$	−1.09401	−0.0525144
$435$	0.309093	0.0148199
$436$	7.44096	0.356357
$437$	0	0
$438$	−29.0334	−1.38727
$439$	−11.2138	−0.535206	−0.267603	−	0.963529i	$-0.586232\pi$
$439$	−11.2138	−0.535206	−0.267603	+	0.963529i	$0.586232\pi$
$440$	−1.37777	−0.0656827
$441$	7.75573	0.369320
$442$	−5.60806	−0.266748
$443$	7.44997	0.353959	0.176979	−	0.984215i	$-0.443367\pi$
$443$	7.44997	0.353959	0.176979	+	0.984215i	$0.443367\pi$
$444$	−24.4601	−1.16083
$445$	−18.2182	−0.863625
$446$	−11.7169	−0.554810
$447$	−8.33401	−0.394185
$448$	3.15542	0.149080
$449$	5.30384	0.250304	0.125152	−	0.992138i	$-0.460058\pi$
$449$	5.30384	0.250304	0.125152	+	0.992138i	$0.460058\pi$
$450$	−2.62313	−0.123655
$451$	15.1679	0.714229
$452$	−11.6014	−0.545686
$453$	0.504189	0.0236889
$454$	10.2265	0.479955
$455$	−13.6478	−0.639821
$456$	0	0
$457$	14.9890	0.701154	0.350577	−	0.936534i	$-0.385986\pi$
$457$	14.9890	0.701154	0.350577	+	0.936534i	$0.385986\pi$
$458$	5.05689	0.236293
$459$	−1.15875	−0.0540858
$460$	−2.12499	−0.0990782
$461$	−6.86196	−0.319593	−0.159797	−	0.987150i	$-0.551084\pi$
$461$	−6.86196	−0.319593	−0.159797	+	0.987150i	$0.551084\pi$
$462$	10.3092	0.479626
$463$	20.6389	0.959170	0.479585	−	0.877496i	$-0.340787\pi$
$463$	20.6389	0.959170	0.479585	+	0.877496i	$0.340787\pi$
$464$	−0.130347	−0.00605120
$465$	−0.822157	−0.0381266
$466$	7.25845	0.336241
$467$	−12.0350	−0.556913	−0.278457	−	0.960449i	$-0.589823\pi$
$467$	−12.0350	−0.556913	−0.278457	+	0.960449i	$0.589823\pi$
$468$	−11.3456	−0.524449
$469$	−3.25223	−0.150174
$470$	−0.0764422	−0.00352601
$471$	−18.2295	−0.839971
$472$	8.18626	0.376803
$473$	−15.8790	−0.730119
$474$	33.2219	1.52593
$475$	0	0
$476$	−4.09132	−0.187525
$477$	16.3148	0.747003
$478$	−15.9731	−0.730595
$479$	22.7790	1.04080	0.520400	−	0.853923i	$-0.325783\pi$
$479$	22.7790	1.04080	0.520400	+	0.853923i	$0.325783\pi$
$480$	2.37131	0.108235
$481$	−44.6146	−2.03425
$482$	−22.1949	−1.01095
$483$	15.9002	0.723485
$484$	−9.10174	−0.413716
$485$	−16.2217	−0.736589
$486$	−21.0050	−0.952807
$487$	6.44912	0.292237	0.146119	−	0.989267i	$-0.453322\pi$
$487$	6.44912	0.292237	0.146119	+	0.989267i	$0.453322\pi$
$488$	−7.84600	−0.355172
$489$	17.3746	0.785708
$490$	−2.95667	−0.133569
$491$	−24.3637	−1.09952	−0.549760	−	0.835323i	$-0.685281\pi$
$491$	−24.3637	−1.09952	−0.549760	+	0.835323i	$0.685281\pi$
$492$	−26.1058	−1.17694
$493$	0.169008	0.00761173
$494$	0	0
$495$	3.61407	0.162440
$496$	0.346710	0.0155677
$497$	36.7695	1.64934
$498$	26.9830	1.20914
$499$	1.62471	0.0727319	0.0363659	−	0.999339i	$-0.488422\pi$
$499$	1.62471	0.0727319	0.0363659	+	0.999339i	$0.488422\pi$
$500$	1.00000	0.0447214
$501$	37.5708	1.67854
$502$	−22.5526	−1.00657
$503$	35.1957	1.56930	0.784650	−	0.619938i	$-0.212842\pi$
$503$	35.1957	1.56930	0.784650	+	0.619938i	$0.212842\pi$
$504$	−8.27707	−0.368690
$505$	6.62325	0.294731
$506$	2.92775	0.130154
$507$	−13.5341	−0.601071
$508$	16.3985	0.727566
$509$	−24.2278	−1.07388	−0.536938	−	0.843622i	$-0.680419\pi$
$509$	−24.2278	−1.07388	−0.536938	+	0.843622i	$0.680419\pi$
$510$	−3.07464	−0.136148
$511$	−38.6337	−1.70906
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−10.7146	−0.472599
$515$	−12.3576	−0.544541
$516$	27.3298	1.20313
$517$	0.105320	0.00463196
$518$	−32.5482	−1.43009
$519$	−39.4591	−1.73206
$520$	4.32521	0.189673
$521$	−7.91718	−0.346858	−0.173429	−	0.984846i	$-0.555485\pi$
$521$	−7.91718	−0.346858	−0.173429	+	0.984846i	$0.555485\pi$
$522$	0.341916	0.0149653
$523$	−2.45716	−0.107444	−0.0537220	−	0.998556i	$-0.517108\pi$
$523$	−2.45716	−0.107444	−0.0537220	+	0.998556i	$0.517108\pi$
$524$	11.1367	0.486508
$525$	−7.48249	−0.326563
$526$	−26.6666	−1.16272
$527$	−0.449544	−0.0195824
$528$	−3.26713	−0.142184
$529$	−18.4844	−0.803670
$530$	−6.21960	−0.270162
$531$	−21.4736	−0.931874
$532$	0	0
$533$	−47.6163	−2.06249
$534$	−43.2011	−1.86949
$535$	10.9548	0.473618
$536$	1.03068	0.0445186
$537$	10.8394	0.467756
$538$	−1.42791	−0.0615618
$539$	4.07362	0.175463
$540$	0.893684	0.0384580
$541$	22.4703	0.966072	0.483036	−	0.875601i	$-0.339534\pi$
$541$	22.4703	0.966072	0.483036	+	0.875601i	$0.339534\pi$
$542$	−7.36945	−0.316545
$543$	−4.00369	−0.171815
$544$	1.29660	0.0555912
$545$	7.44096	0.318736
$546$	−32.3633	−1.38502
$547$	−26.7980	−1.14580	−0.572899	−	0.819626i	$-0.694181\pi$
$547$	−26.7980	−1.14580	−0.572899	+	0.819626i	$0.694181\pi$
$548$	7.34165	0.313620
$549$	20.5811	0.878378
$550$	−1.37777	−0.0587484
$551$	0	0
$552$	−5.03902	−0.214475
$553$	44.2072	1.87988
$554$	2.52531	0.107290
$555$	−24.4601	−1.03827
$556$	11.8115	0.500920
$557$	−39.1057	−1.65696	−0.828481	−	0.560017i	$-0.810795\pi$
$557$	−39.1057	−1.65696	−0.828481	+	0.560017i	$0.810795\pi$
$558$	−0.909464	−0.0385007
$559$	49.8487	2.10838
$560$	3.15542	0.133341
$561$	4.23616	0.178851
$562$	−17.2288	−0.726753
$563$	8.62151	0.363353	0.181677	−	0.983358i	$-0.441848\pi$
$563$	8.62151	0.363353	0.181677	+	0.983358i	$0.441848\pi$
$564$	−0.181268	−0.00763277
$565$	−11.6014	−0.488077
$566$	−28.2208	−1.18621
$567$	−31.5182	−1.32364
$568$	−11.6528	−0.488941
$569$	23.0260	0.965300	0.482650	−	0.875813i	$-0.339674\pi$
$569$	23.0260	0.965300	0.482650	+	0.875813i	$0.339674\pi$
$570$	0	0
$571$	−29.9673	−1.25409	−0.627047	−	0.778981i	$-0.715737\pi$
$571$	−29.9673	−1.25409	−0.627047	+	0.778981i	$0.715737\pi$
$572$	−5.95915	−0.249165
$573$	−26.6078	−1.11156
$574$	−34.7381	−1.44994
$575$	−2.12499	−0.0886182
$576$	2.62313	0.109297
$577$	4.54516	0.189217	0.0946087	−	0.995515i	$-0.469840\pi$
$577$	4.54516	0.189217	0.0946087	+	0.995515i	$0.469840\pi$
$578$	15.3188	0.637179
$579$	50.9544	2.11759
$580$	−0.130347	−0.00541236
$581$	35.9053	1.48960
$582$	−38.4667	−1.59450
$583$	8.56919	0.354899
$584$	12.2436	0.506644
$585$	−11.3456	−0.469082
$586$	12.6181	0.521248
$587$	18.4678	0.762247	0.381123	−	0.924524i	$-0.375537\pi$
$587$	18.4678	0.762247	0.381123	+	0.924524i	$0.375537\pi$
$588$	−7.01120	−0.289137
$589$	0	0
$590$	8.18626	0.337023
$591$	−36.2299	−1.49030
$592$	10.3150	0.423944
$593$	−15.9918	−0.656703	−0.328352	−	0.944556i	$-0.606493\pi$
$593$	−15.9918	−0.656703	−0.328352	+	0.944556i	$0.606493\pi$
$594$	−1.23129	−0.0505206
$595$	−4.09132	−0.167728
$596$	3.51451	0.143960
$597$	−1.68069	−0.0687859
$598$	−9.19103	−0.375849
$599$	3.95495	0.161595	0.0807975	−	0.996731i	$-0.474253\pi$
$599$	3.95495	0.161595	0.0807975	+	0.996731i	$0.474253\pi$
$600$	2.37131	0.0968085
$601$	−2.21709	−0.0904372	−0.0452186	−	0.998977i	$-0.514398\pi$
$601$	−2.21709	−0.0904372	−0.0452186	+	0.998977i	$0.514398\pi$
$602$	36.3667	1.48220
$603$	−2.70360	−0.110099
$604$	−0.212620	−0.00865139
$605$	−9.10174	−0.370039
$606$	15.7058	0.638004
$607$	17.4964	0.710155	0.355078	−	0.934837i	$-0.384454\pi$
$607$	17.4964	0.710155	0.355078	+	0.934837i	$0.384454\pi$
$608$	0	0
$609$	0.975319	0.0395219
$610$	−7.84600	−0.317675
$611$	−0.330628	−0.0133758
$612$	−3.40114	−0.137483
$613$	9.12790	0.368672	0.184336	−	0.982863i	$-0.440986\pi$
$613$	9.12790	0.368672	0.184336	+	0.982863i	$0.440986\pi$
$614$	−9.06469	−0.365821
$615$	−26.1058	−1.05269
$616$	−4.34745	−0.175164
$617$	1.55613	0.0626473	0.0313236	−	0.999509i	$-0.490028\pi$
$617$	1.55613	0.0626473	0.0313236	+	0.999509i	$0.490028\pi$
$618$	−29.3037	−1.17877
$619$	32.4280	1.30339	0.651695	−	0.758481i	$-0.274058\pi$
$619$	32.4280	1.30339	0.651695	+	0.758481i	$0.274058\pi$
$620$	0.346710	0.0139242
$621$	−1.89907	−0.0762071
$622$	21.7124	0.870589
$623$	−57.4861	−2.30313
$624$	10.2564	0.410586
$625$	1.00000	0.0400000
$626$	10.0460	0.401520
$627$	0	0
$628$	7.68751	0.306765
$629$	−13.3744	−0.533274
$630$	−8.27707	−0.329766
$631$	−9.65999	−0.384558	−0.192279	−	0.981340i	$-0.561588\pi$
$631$	−9.65999	−0.384558	−0.192279	+	0.981340i	$0.561588\pi$
$632$	−14.0099	−0.557285
$633$	−33.3860	−1.32697
$634$	2.10846	0.0837376
$635$	16.3985	0.650755
$636$	−14.7486	−0.584821
$637$	−12.7882	−0.506688
$638$	0.179588	0.00710997
$639$	30.5668	1.20920
$640$	−1.00000	−0.0395285
$641$	40.6433	1.60531	0.802656	−	0.596442i	$-0.203420\pi$
$641$	40.6433	1.60531	0.802656	+	0.596442i	$0.203420\pi$
$642$	25.9773	1.02524
$643$	−42.0682	−1.65901	−0.829504	−	0.558501i	$-0.811377\pi$
$643$	−42.0682	−1.65901	−0.829504	+	0.558501i	$0.811377\pi$
$644$	−6.70524	−0.264223
$645$	27.3298	1.07611
$646$	0	0
$647$	18.0072	0.707936	0.353968	−	0.935258i	$-0.384832\pi$
$647$	18.0072	0.707936	0.353968	+	0.935258i	$0.384832\pi$
$648$	9.98859	0.392389
$649$	−11.2788	−0.442731
$650$	4.32521	0.169649
$651$	−2.59425	−0.101677
$652$	−7.32701	−0.286948
$653$	39.4871	1.54525	0.772624	−	0.634864i	$-0.218944\pi$
$653$	39.4871	1.54525	0.772624	+	0.634864i	$0.218944\pi$
$654$	17.6449	0.689968
$655$	11.1367	0.435146
$656$	11.0090	0.429830
$657$	−32.1166	−1.25299
$658$	−0.241207	−0.00940323
$659$	35.7984	1.39451	0.697253	−	0.716825i	$-0.254405\pi$
$659$	35.7984	1.39451	0.697253	+	0.716825i	$0.254405\pi$
$660$	−3.26713	−0.127173
$661$	13.6046	0.529157	0.264578	−	0.964364i	$-0.414767\pi$
$661$	13.6046	0.529157	0.264578	+	0.964364i	$0.414767\pi$
$662$	3.44409	0.133858
$663$	−13.2985	−0.516470
$664$	−11.3789	−0.441588
$665$	0	0
$666$	−27.0576	−1.04846
$667$	0.276986	0.0107249
$668$	−15.8439	−0.613018
$669$	−27.7844	−1.07421
$670$	1.03068	0.0398186
$671$	10.8100	0.417315
$672$	7.48249	0.288643
$673$	−42.2215	−1.62752	−0.813760	−	0.581201i	$-0.802583\pi$
$673$	−42.2215	−1.62752	−0.813760	+	0.581201i	$0.802583\pi$
$674$	25.8586	0.996038
$675$	0.893684	0.0343979
$676$	5.70743	0.219517
$677$	−43.6710	−1.67841	−0.839207	−	0.543812i	$-0.816980\pi$
$677$	−43.6710	−1.67841	−0.839207	+	0.543812i	$0.816980\pi$
$678$	−27.5107	−1.05654
$679$	−51.1862	−1.96435
$680$	1.29660	0.0497223
$681$	24.2503	0.929273
$682$	−0.477687	−0.0182916
$683$	9.22100	0.352832	0.176416	−	0.984316i	$-0.443550\pi$
$683$	9.22100	0.352832	0.176416	+	0.984316i	$0.443550\pi$
$684$	0	0
$685$	7.34165	0.280510
$686$	12.7584	0.487118
$687$	11.9915	0.457504
$688$	−11.5252	−0.439393
$689$	−26.9011	−1.02485
$690$	−5.03902	−0.191832
$691$	−40.0088	−1.52201	−0.761004	−	0.648748i	$-0.775293\pi$
$691$	−40.0088	−1.52201	−0.761004	+	0.648748i	$0.775293\pi$
$692$	16.6402	0.632566
$693$	11.4039	0.433199
$694$	−2.52322	−0.0957799
$695$	11.8115	0.448037
$696$	−0.309093	−0.0117162
$697$	−14.2743	−0.540677
$698$	−3.67945	−0.139269
$699$	17.2121	0.651020
$700$	3.15542	0.119264
$701$	−1.79696	−0.0678704	−0.0339352	−	0.999424i	$-0.510804\pi$
$701$	−1.79696	−0.0678704	−0.0339352	+	0.999424i	$0.510804\pi$
$702$	3.86537	0.145889
$703$	0	0
$704$	1.37777	0.0519267
$705$	−0.181268	−0.00682696
$706$	−2.79636	−0.105242
$707$	20.8991	0.785992
$708$	19.4122	0.729554
$709$	33.9371	1.27453	0.637266	−	0.770644i	$-0.280065\pi$
$709$	33.9371	1.27453	0.637266	+	0.770644i	$0.280065\pi$
$710$	−11.6528	−0.437322
$711$	36.7498	1.37823
$712$	18.2182	0.682756
$713$	−0.736755	−0.0275917
$714$	−9.70179	−0.363080
$715$	−5.95915	−0.222860
$716$	−4.57107	−0.170829
$717$	−37.8773	−1.41455
$718$	−20.1404	−0.751631
$719$	−5.08453	−0.189621	−0.0948105	−	0.995495i	$-0.530225\pi$
$719$	−5.08453	−0.189621	−0.0948105	+	0.995495i	$0.530225\pi$
$720$	2.62313	0.0977582
$721$	−38.9934	−1.45219
$722$	0	0
$723$	−52.6311	−1.95737
$724$	1.68838	0.0627483
$725$	−0.130347	−0.00484096
$726$	−21.5831	−0.801024
$727$	−21.5808	−0.800388	−0.400194	−	0.916431i	$-0.631057\pi$
$727$	−21.5808	−0.800388	−0.400194	+	0.916431i	$0.631057\pi$
$728$	13.6478	0.505823
$729$	−19.8437	−0.734952
$730$	12.2436	0.453156
$731$	14.9435	0.552706
$732$	−18.6053	−0.687673
$733$	9.47549	0.349985	0.174993	−	0.984570i	$-0.444010\pi$
$733$	9.47549	0.349985	0.174993	+	0.984570i	$0.444010\pi$
$734$	4.52133	0.166885
$735$	−7.01120	−0.258612
$736$	2.12499	0.0783282
$737$	−1.42004	−0.0523079
$738$	−28.8780	−1.06302
$739$	−7.87100	−0.289540	−0.144770	−	0.989465i	$-0.546244\pi$
$739$	−7.87100	−0.289540	−0.144770	+	0.989465i	$0.546244\pi$
$740$	10.3150	0.379187
$741$	0	0
$742$	−19.6254	−0.720473
$743$	48.3850	1.77507	0.887537	−	0.460737i	$-0.152415\pi$
$743$	48.3850	1.77507	0.887537	+	0.460737i	$0.152415\pi$
$744$	0.822157	0.0301418
$745$	3.51451	0.128762
$746$	−23.2704	−0.851991
$747$	29.8483	1.09209
$748$	−1.78642	−0.0653179
$749$	34.5670	1.26305
$750$	2.37131	0.0865881
$751$	−12.1435	−0.443121	−0.221561	−	0.975147i	$-0.571115\pi$
$751$	−12.1435	−0.443121	−0.221561	+	0.975147i	$0.571115\pi$
$752$	0.0764422	0.00278756
$753$	−53.4793	−1.94889
$754$	−0.563778	−0.0205316
$755$	−0.212620	−0.00773804
$756$	2.81995	0.102561
$757$	34.9674	1.27091	0.635456	−	0.772137i	$-0.280812\pi$
$757$	34.9674	1.27091	0.635456	+	0.772137i	$0.280812\pi$
$758$	−9.34667	−0.339486
$759$	6.94262	0.252001
$760$	0	0
$761$	46.9073	1.70039	0.850194	−	0.526470i	$-0.176485\pi$
$761$	46.9073	1.70039	0.850194	+	0.526470i	$0.176485\pi$
$762$	38.8860	1.40869
$763$	23.4794	0.850010
$764$	11.2207	0.405951
$765$	−3.40114	−0.122969
$766$	−32.8362	−1.18642
$767$	35.4073	1.27848
$768$	−2.37131	−0.0855674
$769$	1.38610	0.0499841	0.0249921	−	0.999688i	$-0.492044\pi$
$769$	1.38610	0.0499841	0.0249921	+	0.999688i	$0.492044\pi$
$770$	−4.34745	−0.156671
$771$	−25.4076	−0.915031
$772$	−21.4878	−0.773364
$773$	6.43946	0.231611	0.115806	−	0.993272i	$-0.463055\pi$
$773$	6.43946	0.231611	0.115806	+	0.993272i	$0.463055\pi$
$774$	30.2320	1.08667
$775$	0.346710	0.0124542
$776$	16.2217	0.582325
$777$	−77.1820	−2.76889
$778$	−10.6737	−0.382670
$779$	0	0
$780$	10.2564	0.367239
$781$	16.0549	0.574490
$782$	−2.75526	−0.0985280
$783$	−0.116489	−0.00416298
$784$	2.95667	0.105595
$785$	7.68751	0.274379
$786$	26.4085	0.941961
$787$	8.43683	0.300741	0.150370	−	0.988630i	$-0.451953\pi$
$787$	8.43683	0.300741	0.150370	+	0.988630i	$0.451953\pi$
$788$	15.2784	0.544271
$789$	−63.2348	−2.25122
$790$	−14.0099	−0.498451
$791$	−36.6074	−1.30161
$792$	−3.61407	−0.128420
$793$	−33.9356	−1.20509
$794$	−10.0563	−0.356883
$795$	−14.7486	−0.523079
$796$	0.708758	0.0251213
$797$	−32.4342	−1.14888	−0.574438	−	0.818548i	$-0.694779\pi$
$797$	−32.4342	−1.14888	−0.574438	+	0.818548i	$0.694779\pi$
$798$	0	0
$799$	−0.0991149	−0.00350643
$800$	−1.00000	−0.0353553
$801$	−47.7886	−1.68853
$802$	−12.0791	−0.426527
$803$	−16.8689	−0.595291
$804$	2.44406	0.0861955
$805$	−6.70524	−0.236329
$806$	1.49959	0.0528209
$807$	−3.38603	−0.119194
$808$	−6.62325	−0.233005
$809$	−18.0203	−0.633559	−0.316779	−	0.948499i	$-0.602602\pi$
$809$	−18.0203	−0.633559	−0.316779	+	0.948499i	$0.602602\pi$
$810$	9.98859	0.350963
$811$	−26.1607	−0.918626	−0.459313	−	0.888275i	$-0.651904\pi$
$811$	−26.1607	−0.918626	−0.459313	+	0.888275i	$0.651904\pi$
$812$	−0.411299	−0.0144338
$813$	−17.4753	−0.612884
$814$	−14.2117	−0.498121
$815$	−7.32701	−0.256654
$816$	3.07464	0.107634
$817$	0	0
$818$	39.5462	1.38270
$819$	−35.8000	−1.25095
$820$	11.0090	0.384452
$821$	−28.2899	−0.987324	−0.493662	−	0.869654i	$-0.664342\pi$
$821$	−28.2899	−0.987324	−0.493662	+	0.869654i	$0.664342\pi$
$822$	17.4094	0.607221
$823$	49.9553	1.74133	0.870667	−	0.491873i	$-0.163688\pi$
$823$	49.9553	1.74133	0.870667	+	0.491873i	$0.163688\pi$
$824$	12.3576	0.430497
$825$	−3.26713	−0.113747
$826$	25.8311	0.898778
$827$	−5.31234	−0.184728	−0.0923641	−	0.995725i	$-0.529442\pi$
$827$	−5.31234	−0.184728	−0.0923641	+	0.995725i	$0.529442\pi$
$828$	−5.57412	−0.193714
$829$	36.8616	1.28026	0.640129	−	0.768268i	$-0.278881\pi$
$829$	36.8616	1.28026	0.640129	+	0.768268i	$0.278881\pi$
$830$	−11.3789	−0.394968
$831$	5.98830	0.207732
$832$	−4.32521	−0.149950
$833$	−3.83362	−0.132827
$834$	28.0088	0.969867
$835$	−15.8439	−0.548300
$836$	0	0
$837$	0.309849	0.0107099
$838$	−28.5326	−0.985641
$839$	−44.7119	−1.54362	−0.771812	−	0.635850i	$-0.780650\pi$
$839$	−44.7119	−1.54362	−0.771812	+	0.635850i	$0.780650\pi$
$840$	7.48249	0.258170
$841$	−28.9830	−0.999414
$842$	−2.03904	−0.0702699
$843$	−40.8549	−1.40712
$844$	14.0791	0.484623
$845$	5.70743	0.196342
$846$	−0.200517	−0.00689393
$847$	−28.7198	−0.986825
$848$	6.21960	0.213582
$849$	−66.9203	−2.29670
$850$	1.29660	0.0444730
$851$	−21.9193	−0.751384
$852$	−27.6324	−0.946672
$853$	−29.4637	−1.00882	−0.504410	−	0.863464i	$-0.668290\pi$
$853$	−29.4637	−1.00882	−0.504410	+	0.863464i	$0.668290\pi$
$854$	−24.7574	−0.847181
$855$	0	0
$856$	−10.9548	−0.374428
$857$	−47.4733	−1.62166	−0.810828	−	0.585284i	$-0.800983\pi$
$857$	−47.4733	−1.62166	−0.810828	+	0.585284i	$0.800983\pi$
$858$	−14.1310	−0.482425
$859$	0.954643	0.0325720	0.0162860	−	0.999867i	$-0.494816\pi$
$859$	0.954643	0.0325720	0.0162860	+	0.999867i	$0.494816\pi$
$860$	−11.5252	−0.393005
$861$	−82.3748	−2.80733
$862$	−13.5707	−0.462221
$863$	47.0260	1.60078	0.800392	−	0.599478i	$-0.204625\pi$
$863$	47.0260	1.60078	0.800392	+	0.599478i	$0.204625\pi$
$864$	−0.893684	−0.0304038
$865$	16.6402	0.565784
$866$	−28.9638	−0.984232
$867$	36.3257	1.23369
$868$	1.09401	0.0371333
$869$	19.3025	0.654792
$870$	−0.309093	−0.0104792
$871$	4.45790	0.151050
$872$	−7.44096	−0.251983
$873$	−42.5515	−1.44015
$874$	0	0
$875$	3.15542	0.106673
$876$	29.0334	0.980949
$877$	−42.7921	−1.44499	−0.722493	−	0.691378i	$-0.757004\pi$
$877$	−42.7921	−1.44499	−0.722493	+	0.691378i	$0.757004\pi$
$878$	11.2138	0.378448
$879$	29.9214	1.00922
$880$	1.37777	0.0464447
$881$	9.07329	0.305687	0.152843	−	0.988250i	$-0.451157\pi$
$881$	9.07329	0.305687	0.152843	+	0.988250i	$0.451157\pi$
$882$	−7.75573	−0.261149
$883$	−31.3218	−1.05406	−0.527032	−	0.849845i	$-0.676695\pi$
$883$	−31.3218	−1.05406	−0.527032	+	0.849845i	$0.676695\pi$
$884$	5.60806	0.188620
$885$	19.4122	0.652533
$886$	−7.44997	−0.250287
$887$	−3.39444	−0.113974	−0.0569870	−	0.998375i	$-0.518149\pi$
$887$	−3.39444	−0.113974	−0.0569870	+	0.998375i	$0.518149\pi$
$888$	24.4601	0.820828
$889$	51.7442	1.73544
$890$	18.2182	0.610675
$891$	−13.7620	−0.461044
$892$	11.7169	0.392310
$893$	0	0
$894$	8.33401	0.278731
$895$	−4.57107	−0.152794
$896$	−3.15542	−0.105415
$897$	−21.7948	−0.727708
$898$	−5.30384	−0.176991
$899$	−0.0451925	−0.00150726
$900$	2.62313	0.0874376
$901$	−8.06433	−0.268662
$902$	−15.1679	−0.505036
$903$	86.2369	2.86978
$904$	11.6014	0.385858
$905$	1.68838	0.0561238
$906$	−0.504189	−0.0167506
$907$	39.6070	1.31513	0.657565	−	0.753398i	$-0.271586\pi$
$907$	39.6070	1.31513	0.657565	+	0.753398i	$0.271586\pi$
$908$	−10.2265	−0.339379
$909$	17.3736	0.576246
$910$	13.6478	0.452422
$911$	−24.0316	−0.796204	−0.398102	−	0.917341i	$-0.630331\pi$
$911$	−24.0316	−0.796204	−0.398102	+	0.917341i	$0.630331\pi$
$912$	0	0
$913$	15.6776	0.518851
$914$	−14.9890	−0.495790
$915$	−18.6053	−0.615073
$916$	−5.05689	−0.167084
$917$	35.1409	1.16045
$918$	1.15875	0.0382445
$919$	3.85721	0.127237	0.0636187	−	0.997974i	$-0.479736\pi$
$919$	3.85721	0.127237	0.0636187	+	0.997974i	$0.479736\pi$
$920$	2.12499	0.0700589
$921$	−21.4952	−0.708292
$922$	6.86196	0.225987
$923$	−50.4008	−1.65896
$924$	−10.3092	−0.339147
$925$	10.3150	0.339155
$926$	−20.6389	−0.678235
$927$	−32.4156	−1.06467
$928$	0.130347	0.00427885
$929$	20.2822	0.665438	0.332719	−	0.943026i	$-0.392034\pi$
$929$	20.2822	0.665438	0.332719	+	0.943026i	$0.392034\pi$
$930$	0.822157	0.0269596
$931$	0	0
$932$	−7.25845	−0.237759
$933$	51.4869	1.68561
$934$	12.0350	0.393797
$935$	−1.78642	−0.0584221
$936$	11.3456	0.370842
$937$	−27.5926	−0.901412	−0.450706	−	0.892673i	$-0.648828\pi$
$937$	−27.5926	−0.901412	−0.450706	+	0.892673i	$0.648828\pi$
$938$	3.25223	0.106189
$939$	23.8223	0.777410
$940$	0.0764422	0.00249327
$941$	−22.9366	−0.747711	−0.373855	−	0.927487i	$-0.621964\pi$
$941$	−22.9366	−0.747711	−0.373855	+	0.927487i	$0.621964\pi$
$942$	18.2295	0.593949
$943$	−23.3941	−0.761815
$944$	−8.18626	−0.266440
$945$	2.81995	0.0917329
$946$	15.8790	0.516272
$947$	28.0753	0.912326	0.456163	−	0.889896i	$-0.349223\pi$
$947$	28.0753	0.912326	0.456163	+	0.889896i	$0.349223\pi$
$948$	−33.2219	−1.07900
$949$	52.9562	1.71903
$950$	0	0
$951$	4.99982	0.162130
$952$	4.09132	0.132600
$953$	34.3033	1.11119	0.555596	−	0.831452i	$-0.312490\pi$
$953$	34.3033	1.11119	0.555596	+	0.831452i	$0.312490\pi$
$954$	−16.3148	−0.528211
$955$	11.2207	0.363093
$956$	15.9731	0.516608
$957$	0.425860	0.0137661
$958$	−22.7790	−0.735956
$959$	23.1660	0.748069
$960$	−2.37131	−0.0765338
$961$	−30.8798	−0.996122
$962$	44.6146	1.43843
$963$	28.7358	0.926000
$964$	22.1949	0.714850
$965$	−21.4878	−0.691718
$966$	−15.9002	−0.511581
$967$	14.5333	0.467359	0.233679	−	0.972314i	$-0.424923\pi$
$967$	14.5333	0.467359	0.233679	+	0.972314i	$0.424923\pi$
$968$	9.10174	0.292541
$969$	0	0
$970$	16.2217	0.520847
$971$	49.4242	1.58610	0.793049	−	0.609157i	$-0.208492\pi$
$971$	49.4242	1.58610	0.793049	+	0.609157i	$0.208492\pi$
$972$	21.0050	0.673736
$973$	37.2703	1.19483
$974$	−6.44912	−0.206643
$975$	10.2564	0.328468
$976$	7.84600	0.251144
$977$	−2.91155	−0.0931486	−0.0465743	−	0.998915i	$-0.514830\pi$
$977$	−2.91155	−0.0931486	−0.0465743	+	0.998915i	$0.514830\pi$
$978$	−17.3746	−0.555579
$979$	−25.1005	−0.802216
$980$	2.95667	0.0944474
$981$	19.5186	0.623181
$982$	24.3637	0.777478
$983$	41.2508	1.31570	0.657849	−	0.753150i	$-0.271467\pi$
$983$	41.2508	1.31570	0.657849	+	0.753150i	$0.271467\pi$
$984$	26.1058	0.832223
$985$	15.2784	0.486811
$986$	−0.169008	−0.00538230
$987$	−0.571978	−0.0182062
$988$	0	0
$989$	24.4909	0.778764
$990$	−3.61407	−0.114863
$991$	−28.9551	−0.919790	−0.459895	−	0.887973i	$-0.652113\pi$
$991$	−28.9551	−0.919790	−0.459895	+	0.887973i	$0.652113\pi$
$992$	−0.346710	−0.0110080
$993$	8.16701	0.259172
$994$	−36.7695	−1.16626
$995$	0.708758	0.0224691
$996$	−26.9830	−0.854988
$997$	0.657477	0.0208225	0.0104113	−	0.999946i	$-0.496686\pi$
$997$	0.657477	0.0208225	0.0104113	+	0.999946i	$0.496686\pi$
$998$	−1.62471	−0.0514292
$999$	9.21836	0.291656

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3610.2.a.bi.1.2		9
19.4	even	9		190.2.k.d.111.3	yes	18
19.5	even	9		190.2.k.d.101.3	✓	18
19.18	odd	2		3610.2.a.bj.1.8		9
95.4	even	18		950.2.l.i.301.1		18
95.23	odd	36		950.2.u.g.149.3		36
95.24	even	18		950.2.l.i.101.1		18
95.42	odd	36		950.2.u.g.149.4		36
95.43	odd	36		950.2.u.g.899.4		36
95.62	odd	36		950.2.u.g.899.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.d.101.3	✓	18	19.5	even	9
190.2.k.d.111.3	yes	18	19.4	even	9
950.2.l.i.101.1		18	95.24	even	18
950.2.l.i.301.1		18	95.4	even	18
950.2.u.g.149.3		36	95.23	odd	36
950.2.u.g.149.4		36	95.42	odd	36
950.2.u.g.899.3		36	95.62	odd	36
950.2.u.g.899.4		36	95.43	odd	36
3610.2.a.bi.1.2		9	1.1	even	1	trivial
3610.2.a.bj.1.8		9	19.18	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 3610 = 2 \cdot 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3610.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.37131 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.37131 q^{6} +3.15542 q^{7} -1.00000 q^{8} +2.62313 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.37131 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.37131 q^{6} +3.15542 q^{7} -1.00000 q^{8} +2.62313 q^{9} -1.00000 q^{10} +1.37777 q^{11} -2.37131 q^{12} -4.32521 q^{13} -3.15542 q^{14} -2.37131 q^{15} +1.00000 q^{16} -1.29660 q^{17} -2.62313 q^{18} +1.00000 q^{20} -7.48249 q^{21} -1.37777 q^{22} -2.12499 q^{23} +2.37131 q^{24} +1.00000 q^{25} +4.32521 q^{26} +0.893684 q^{27} +3.15542 q^{28} -0.130347 q^{29} +2.37131 q^{30} +0.346710 q^{31} -1.00000 q^{32} -3.26713 q^{33} +1.29660 q^{34} +3.15542 q^{35} +2.62313 q^{36} +10.3150 q^{37} +10.2564 q^{39} -1.00000 q^{40} +11.0090 q^{41} +7.48249 q^{42} -11.5252 q^{43} +1.37777 q^{44} +2.62313 q^{45} +2.12499 q^{46} +0.0764422 q^{47} -2.37131 q^{48} +2.95667 q^{49} -1.00000 q^{50} +3.07464 q^{51} -4.32521 q^{52} +6.21960 q^{53} -0.893684 q^{54} +1.37777 q^{55} -3.15542 q^{56} +0.130347 q^{58} -8.18626 q^{59} -2.37131 q^{60} +7.84600 q^{61} -0.346710 q^{62} +8.27707 q^{63} +1.00000 q^{64} -4.32521 q^{65} +3.26713 q^{66} -1.03068 q^{67} -1.29660 q^{68} +5.03902 q^{69} -3.15542 q^{70} +11.6528 q^{71} -2.62313 q^{72} -12.2436 q^{73} -10.3150 q^{74} -2.37131 q^{75} +4.34745 q^{77} -10.2564 q^{78} +14.0099 q^{79} +1.00000 q^{80} -9.98859 q^{81} -11.0090 q^{82} +11.3789 q^{83} -7.48249 q^{84} -1.29660 q^{85} +11.5252 q^{86} +0.309093 q^{87} -1.37777 q^{88} -18.2182 q^{89} -2.62313 q^{90} -13.6478 q^{91} -2.12499 q^{92} -0.822157 q^{93} -0.0764422 q^{94} +2.37131 q^{96} -16.2217 q^{97} -2.95667 q^{98} +3.61407 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} + 9 q^{4} + 9 q^{5} - 9 q^{8} + 21 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 + 9 * q^4 + 9 * q^5 - 9 * q^8 + 21 * q^9	\( 9 q - 9 q^{2} + 9 q^{4} + 9 q^{5} - 9 q^{8} + 21 q^{9} - 9 q^{10} + 12 q^{11} - 9 q^{13} + 9 q^{16} + 6 q^{17} - 21 q^{18} + 9 q^{20} - 6 q^{21} - 12 q^{22} + 18 q^{23} + 9 q^{25} + 9 q^{26} + 18 q^{27} + 6 q^{31} - 9 q^{32} - 6 q^{33} - 6 q^{34} + 21 q^{36} - 6 q^{37} + 24 q^{39} - 9 q^{40} + 6 q^{42} + 18 q^{43} + 12 q^{44} + 21 q^{45} - 18 q^{46} - 3 q^{47} + 39 q^{49} - 9 q^{50} + 48 q^{51} - 9 q^{52} - 18 q^{54} + 12 q^{55} - 21 q^{59} + 18 q^{61} - 6 q^{62} - 12 q^{63} + 9 q^{64} - 9 q^{65} + 6 q^{66} + 6 q^{68} + 30 q^{69} - 18 q^{71} - 21 q^{72} - 36 q^{73} + 6 q^{74} + 15 q^{77} - 24 q^{78} + 6 q^{79} + 9 q^{80} + 69 q^{81} - 6 q^{83} - 6 q^{84} + 6 q^{85} - 18 q^{86} - 24 q^{87} - 12 q^{88} + 18 q^{89} - 21 q^{90} + 60 q^{91} + 18 q^{92} + 3 q^{94} - 18 q^{97} - 39 q^{98} + 54 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 + 9 * q^4 + 9 * q^5 - 9 * q^8 + 21 * q^9 - 9 * q^10 + 12 * q^11 - 9 * q^13 + 9 * q^16 + 6 * q^17 - 21 * q^18 + 9 * q^20 - 6 * q^21 - 12 * q^22 + 18 * q^23 + 9 * q^25 + 9 * q^26 + 18 * q^27 + 6 * q^31 - 9 * q^32 - 6 * q^33 - 6 * q^34 + 21 * q^36 - 6 * q^37 + 24 * q^39 - 9 * q^40 + 6 * q^42 + 18 * q^43 + 12 * q^44 + 21 * q^45 - 18 * q^46 - 3 * q^47 + 39 * q^49 - 9 * q^50 + 48 * q^51 - 9 * q^52 - 18 * q^54 + 12 * q^55 - 21 * q^59 + 18 * q^61 - 6 * q^62 - 12 * q^63 + 9 * q^64 - 9 * q^65 + 6 * q^66 + 6 * q^68 + 30 * q^69 - 18 * q^71 - 21 * q^72 - 36 * q^73 + 6 * q^74 + 15 * q^77 - 24 * q^78 + 6 * q^79 + 9 * q^80 + 69 * q^81 - 6 * q^83 - 6 * q^84 + 6 * q^85 - 18 * q^86 - 24 * q^87 - 12 * q^88 + 18 * q^89 - 21 * q^90 + 60 * q^91 + 18 * q^92 + 3 * q^94 - 18 * q^97 - 39 * q^98 + 54 * q^99

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