LMFDB - Embedded newform 385.2.a.f.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [385,2,Mod(1,385)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("385.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(385, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,-3,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$3.07424047782$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.311108$ of defining polynomial
Character	$\chi$	$=$	385.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.21432 q^{2} -0.688892 q^{3} -0.525428 q^{4} -1.00000 q^{5} -0.836535 q^{6} -1.00000 q^{7} -3.06668 q^{8} -2.52543 q^{9} -1.21432 q^{10} -1.00000 q^{11} +0.361963 q^{12} -3.73975 q^{13} -1.21432 q^{14} +0.688892 q^{15} -2.67307 q^{16} +0.0666765 q^{17} -3.06668 q^{18} +6.42864 q^{19} +0.525428 q^{20} +0.688892 q^{21} -1.21432 q^{22} -1.09679 q^{23} +2.11261 q^{24} +1.00000 q^{25} -4.54125 q^{26} +3.80642 q^{27} +0.525428 q^{28} -7.80642 q^{29} +0.836535 q^{30} -5.59210 q^{31} +2.88739 q^{32} +0.688892 q^{33} +0.0809666 q^{34} +1.00000 q^{35} +1.32693 q^{36} +1.33185 q^{37} +7.80642 q^{38} +2.57628 q^{39} +3.06668 q^{40} +6.64296 q^{41} +0.836535 q^{42} -11.7605 q^{43} +0.525428 q^{44} +2.52543 q^{45} -1.33185 q^{46} -2.26025 q^{47} +1.84146 q^{48} +1.00000 q^{49} +1.21432 q^{50} -0.0459330 q^{51} +1.96497 q^{52} -1.71900 q^{53} +4.62222 q^{54} +1.00000 q^{55} +3.06668 q^{56} -4.42864 q^{57} -9.47949 q^{58} +2.54125 q^{59} -0.361963 q^{60} +14.4494 q^{61} -6.79060 q^{62} +2.52543 q^{63} +8.85236 q^{64} +3.73975 q^{65} +0.836535 q^{66} +10.3827 q^{67} -0.0350337 q^{68} +0.755569 q^{69} +1.21432 q^{70} -12.5620 q^{71} +7.74467 q^{72} +1.17775 q^{73} +1.61729 q^{74} -0.688892 q^{75} -3.37778 q^{76} +1.00000 q^{77} +3.12843 q^{78} -8.51606 q^{79} +2.67307 q^{80} +4.95407 q^{81} +8.06668 q^{82} -12.1017 q^{83} -0.361963 q^{84} -0.0666765 q^{85} -14.2810 q^{86} +5.37778 q^{87} +3.06668 q^{88} +15.6128 q^{89} +3.06668 q^{90} +3.73975 q^{91} +0.576283 q^{92} +3.85236 q^{93} -2.74467 q^{94} -6.42864 q^{95} -1.98910 q^{96} -13.4193 q^{97} +1.21432 q^{98} +2.52543 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 2 q^{3} + 5 q^{4} - 3 q^{5} + 4 q^{6} - 3 q^{7} - 9 q^{8} - q^{9} + 3 q^{10} - 3 q^{11} - 12 q^{12} + 2 q^{13} + 3 q^{14} + 2 q^{15} + 5 q^{16} - 9 q^{18} + 6 q^{19} - 5 q^{20} + 2 q^{21}+ \cdots + q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - 2 * q^3 + 5 * q^4 - 3 * q^5 + 4 * q^6 - 3 * q^7 - 9 * q^8 - q^9 + 3 * q^10 - 3 * q^11 - 12 * q^12 + 2 * q^13 + 3 * q^14 + 2 * q^15 + 5 * q^16 - 9 * q^18 + 6 * q^19 - 5 * q^20 + 2 * q^21 + 3 * q^22 - 10 * q^23 + 26 * q^24 + 3 * q^25 - 20 * q^26 - 2 * q^27 - 5 * q^28 - 10 * q^29 - 4 * q^30 - 10 * q^31 - 11 * q^32 + 2 * q^33 - 6 * q^34 + 3 * q^35 + 17 * q^36 - 16 * q^37 + 10 * q^38 - 12 * q^39 + 9 * q^40 - 4 * q^42 - 2 * q^43 - 5 * q^44 + q^45 + 16 * q^46 - 20 * q^47 - 34 * q^48 + 3 * q^49 - 3 * q^50 - 20 * q^51 + 32 * q^52 - 12 * q^53 + 14 * q^54 + 3 * q^55 + 9 * q^56 - 2 * q^58 + 14 * q^59 + 12 * q^60 + 10 * q^61 + 6 * q^62 + q^63 + 33 * q^64 - 2 * q^65 - 4 * q^66 - 2 * q^67 + 26 * q^68 + 2 * q^69 - 3 * q^70 - 24 * q^71 - 23 * q^72 + 4 * q^73 + 38 * q^74 - 2 * q^75 - 10 * q^76 + 3 * q^77 + 42 * q^78 + 8 * q^79 - 5 * q^80 - 5 * q^81 + 24 * q^82 - 10 * q^83 + 12 * q^84 - 36 * q^86 + 16 * q^87 + 9 * q^88 + 20 * q^89 + 9 * q^90 - 2 * q^91 - 18 * q^92 + 18 * q^93 + 38 * q^94 - 6 * q^95 + 40 * q^96 - 3 * q^98 + q^99

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 $

$2$	1.21432	0.858654	0.429327	−	0.903149i	$-0.358751\pi$
$2$	1.21432	0.858654	0.429327	+	0.903149i	$0.358751\pi$
$3$	−0.688892	−0.397732	−0.198866	−	0.980027i	$-0.563726\pi$
$3$	−0.688892	−0.397732	−0.198866	+	0.980027i	$0.563726\pi$
$4$	−0.525428	−0.262714
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.836535	−0.341514
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.06668	−1.08423
$9$	−2.52543	−0.841809
$10$	−1.21432	−0.384002
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.361963	0.104490
$13$	−3.73975	−1.03722	−0.518610	−	0.855011i	$-0.673550\pi$
$13$	−3.73975	−1.03722	−0.518610	+	0.855011i	$0.673550\pi$
$14$	−1.21432	−0.324541
$15$	0.688892	0.177871
$16$	−2.67307	−0.668268
$17$	0.0666765	0.0161714	0.00808572	−	0.999967i	$-0.497426\pi$
$17$	0.0666765	0.0161714	0.00808572	+	0.999967i	$0.497426\pi$
$18$	−3.06668	−0.722823
$19$	6.42864	1.47483	0.737416	−	0.675439i	$-0.236046\pi$
$19$	6.42864	1.47483	0.737416	+	0.675439i	$0.236046\pi$
$20$	0.525428	0.117489
$21$	0.688892	0.150329
$22$	−1.21432	−0.258894
$23$	−1.09679	−0.228696	−0.114348	−	0.993441i	$-0.536478\pi$
$23$	−1.09679	−0.228696	−0.114348	+	0.993441i	$0.536478\pi$
$24$	2.11261	0.431235
$25$	1.00000	0.200000
$26$	−4.54125	−0.890612
$27$	3.80642	0.732547
$28$	0.525428	0.0992965
$29$	−7.80642	−1.44962	−0.724808	−	0.688951i	$-0.758072\pi$
$29$	−7.80642	−1.44962	−0.724808	+	0.688951i	$0.758072\pi$
$30$	0.836535	0.152730
$31$	−5.59210	−1.00437	−0.502186	−	0.864760i	$-0.667471\pi$
$31$	−5.59210	−1.00437	−0.502186	+	0.864760i	$0.667471\pi$
$32$	2.88739	0.510423
$33$	0.688892	0.119921
$34$	0.0809666	0.0138857
$35$	1.00000	0.169031
$36$	1.32693	0.221155
$37$	1.33185	0.218955	0.109478	−	0.993989i	$-0.465082\pi$
$37$	1.33185	0.218955	0.109478	+	0.993989i	$0.465082\pi$
$38$	7.80642	1.26637
$39$	2.57628	0.412535
$40$	3.06668	0.484884
$41$	6.64296	1.03746	0.518728	−	0.854939i	$-0.326406\pi$
$41$	6.64296	1.03746	0.518728	+	0.854939i	$0.326406\pi$
$42$	0.836535	0.129080
$43$	−11.7605	−1.79346	−0.896729	−	0.442580i	$-0.854063\pi$
$43$	−11.7605	−1.79346	−0.896729	+	0.442580i	$0.854063\pi$
$44$	0.525428	0.0792112
$45$	2.52543	0.376469
$46$	−1.33185	−0.196371
$47$	−2.26025	−0.329692	−0.164846	−	0.986319i	$-0.552713\pi$
$47$	−2.26025	−0.329692	−0.164846	+	0.986319i	$0.552713\pi$
$48$	1.84146	0.265792
$49$	1.00000	0.142857
$50$	1.21432	0.171731
$51$	−0.0459330	−0.00643190
$52$	1.96497	0.272492
$53$	−1.71900	−0.236123	−0.118062	−	0.993006i	$-0.537668\pi$
$53$	−1.71900	−0.236123	−0.118062	+	0.993006i	$0.537668\pi$
$54$	4.62222	0.629004
$55$	1.00000	0.134840
$56$	3.06668	0.409802
$57$	−4.42864	−0.586588
$58$	−9.47949	−1.24472
$59$	2.54125	0.330842	0.165421	−	0.986223i	$-0.447102\pi$
$59$	2.54125	0.330842	0.165421	+	0.986223i	$0.447102\pi$
$60$	−0.361963	−0.0467292
$61$	14.4494	1.85005	0.925027	−	0.379901i	$-0.124042\pi$
$61$	14.4494	1.85005	0.925027	+	0.379901i	$0.124042\pi$
$62$	−6.79060	−0.862407
$63$	2.52543	0.318174
$64$	8.85236	1.10654
$65$	3.73975	0.463859
$66$	0.836535	0.102970
$67$	10.3827	1.26845	0.634225	−	0.773149i	$-0.281319\pi$
$67$	10.3827	1.26845	0.634225	+	0.773149i	$0.281319\pi$
$68$	−0.0350337	−0.00424846
$69$	0.755569	0.0909598
$70$	1.21432	0.145139
$71$	−12.5620	−1.49083	−0.745417	−	0.666598i	$-0.767750\pi$
$71$	−12.5620	−1.49083	−0.745417	+	0.666598i	$0.767750\pi$
$72$	7.74467	0.912718
$73$	1.17775	0.137846	0.0689229	−	0.997622i	$-0.478044\pi$
$73$	1.17775	0.137846	0.0689229	+	0.997622i	$0.478044\pi$
$74$	1.61729	0.188007
$75$	−0.688892	−0.0795464
$76$	−3.37778	−0.387458
$77$	1.00000	0.113961
$78$	3.12843	0.354225
$79$	−8.51606	−0.958132	−0.479066	−	0.877779i	$-0.659024\pi$
$79$	−8.51606	−0.958132	−0.479066	+	0.877779i	$0.659024\pi$
$80$	2.67307	0.298858
$81$	4.95407	0.550452
$82$	8.06668	0.890815
$83$	−12.1017	−1.32834	−0.664168	−	0.747584i	$-0.731214\pi$
$83$	−12.1017	−1.32834	−0.664168	+	0.747584i	$0.731214\pi$
$84$	−0.361963	−0.0394934
$85$	−0.0666765	−0.00723209
$86$	−14.2810	−1.53996
$87$	5.37778	0.576559
$88$	3.06668	0.326909
$89$	15.6128	1.65496	0.827479	−	0.561496i	$-0.189774\pi$
$89$	15.6128	1.65496	0.827479	+	0.561496i	$0.189774\pi$
$90$	3.06668	0.323256
$91$	3.73975	0.392032
$92$	0.576283	0.0600816
$93$	3.85236	0.399471
$94$	−2.74467	−0.283091
$95$	−6.42864	−0.659564
$96$	−1.98910	−0.203012
$97$	−13.4193	−1.36252	−0.681260	−	0.732041i	$-0.738568\pi$
$97$	−13.4193	−1.36252	−0.681260	+	0.732041i	$0.738568\pi$
$98$	1.21432	0.122665
$99$	2.52543	0.253815
$100$	−0.525428	−0.0525428
$101$	−8.44938	−0.840745	−0.420373	−	0.907352i	$-0.638101\pi$
$101$	−8.44938	−0.840745	−0.420373	+	0.907352i	$0.638101\pi$
$102$	−0.0557773	−0.00552277
$103$	−9.54617	−0.940612	−0.470306	−	0.882503i	$-0.655856\pi$
$103$	−9.54617	−0.940612	−0.470306	+	0.882503i	$0.655856\pi$
$104$	11.4686	1.12459
$105$	−0.688892	−0.0672290
$106$	−2.08742	−0.202748
$107$	−8.56199	−0.827719	−0.413860	−	0.910341i	$-0.635820\pi$
$107$	−8.56199	−0.827719	−0.413860	+	0.910341i	$0.635820\pi$
$108$	−2.00000	−0.192450
$109$	−6.99063	−0.669581	−0.334791	−	0.942293i	$-0.608666\pi$
$109$	−6.99063	−0.669581	−0.334791	+	0.942293i	$0.608666\pi$
$110$	1.21432	0.115781
$111$	−0.917502	−0.0870854
$112$	2.67307	0.252581
$113$	−1.57136	−0.147821	−0.0739106	−	0.997265i	$-0.523548\pi$
$113$	−1.57136	−0.147821	−0.0739106	+	0.997265i	$0.523548\pi$
$114$	−5.37778	−0.503676
$115$	1.09679	0.102276
$116$	4.10171	0.380834
$117$	9.44446	0.873141
$118$	3.08589	0.284079
$119$	−0.0666765	−0.00611223
$120$	−2.11261	−0.192854
$121$	1.00000	0.0909091
$122$	17.5462	1.58856
$123$	−4.57628	−0.412630
$124$	2.93825	0.263862
$125$	−1.00000	−0.0894427
$126$	3.06668	0.273201
$127$	−13.3778	−1.18709	−0.593543	−	0.804802i	$-0.702271\pi$
$127$	−13.3778	−1.18709	−0.593543	+	0.804802i	$0.702271\pi$
$128$	4.97481	0.439715
$129$	8.10171	0.713316
$130$	4.54125	0.398294
$131$	−2.75557	−0.240755	−0.120378	−	0.992728i	$-0.538411\pi$
$131$	−2.75557	−0.240755	−0.120378	+	0.992728i	$0.538411\pi$
$132$	−0.361963	−0.0315048
$133$	−6.42864	−0.557434
$134$	12.6079	1.08916
$135$	−3.80642	−0.327605
$136$	−0.204475	−0.0175336
$137$	−17.8938	−1.52877	−0.764387	−	0.644758i	$-0.776958\pi$
$137$	−17.8938	−1.52877	−0.764387	+	0.644758i	$0.776958\pi$
$138$	0.917502	0.0781030
$139$	−3.86665	−0.327965	−0.163982	−	0.986463i	$-0.552434\pi$
$139$	−3.86665	−0.327965	−0.163982	+	0.986463i	$0.552434\pi$
$140$	−0.525428	−0.0444067
$141$	1.55707	0.131129
$142$	−15.2543	−1.28011
$143$	3.73975	0.312733
$144$	6.75065	0.562554
$145$	7.80642	0.648288
$146$	1.43017	0.118362
$147$	−0.688892	−0.0568189
$148$	−0.699791	−0.0575225
$149$	4.88892	0.400516	0.200258	−	0.979743i	$-0.435822\pi$
$149$	4.88892	0.400516	0.200258	+	0.979743i	$0.435822\pi$
$150$	−0.836535	−0.0683028
$151$	22.1891	1.80573	0.902863	−	0.429929i	$-0.141461\pi$
$151$	22.1891	1.80573	0.902863	+	0.429929i	$0.141461\pi$
$152$	−19.7146	−1.59906
$153$	−0.168387	−0.0136133
$154$	1.21432	0.0978527
$155$	5.59210	0.449169
$156$	−1.35365	−0.108379
$157$	−4.81579	−0.384342	−0.192171	−	0.981361i	$-0.561553\pi$
$157$	−4.81579	−0.384342	−0.192171	+	0.981361i	$0.561553\pi$
$158$	−10.3412	−0.822703
$159$	1.18421	0.0939138
$160$	−2.88739	−0.228268
$161$	1.09679	0.0864390
$162$	6.01582	0.472648
$163$	6.08742	0.476804	0.238402	−	0.971167i	$-0.423376\pi$
$163$	6.08742	0.476804	0.238402	+	0.971167i	$0.423376\pi$
$164$	−3.49039	−0.272554
$165$	−0.688892	−0.0536302
$166$	−14.6953	−1.14058
$167$	−3.67307	−0.284231	−0.142115	−	0.989850i	$-0.545390\pi$
$167$	−3.67307	−0.284231	−0.142115	+	0.989850i	$0.545390\pi$
$168$	−2.11261	−0.162991
$169$	0.985710	0.0758238
$170$	−0.0809666	−0.00620986
$171$	−16.2351	−1.24153
$172$	6.17929	0.471166
$173$	−0.628669	−0.0477968	−0.0238984	−	0.999714i	$-0.507608\pi$
$173$	−0.628669	−0.0477968	−0.0238984	+	0.999714i	$0.507608\pi$
$174$	6.53035	0.495065
$175$	−1.00000	−0.0755929
$176$	2.67307	0.201490
$177$	−1.75065	−0.131587
$178$	18.9590	1.42104
$179$	−7.70471	−0.575877	−0.287939	−	0.957649i	$-0.592970\pi$
$179$	−7.70471	−0.575877	−0.287939	+	0.957649i	$0.592970\pi$
$180$	−1.32693	−0.0989035
$181$	10.9175	0.811492	0.405746	−	0.913986i	$-0.367012\pi$
$181$	10.9175	0.811492	0.405746	+	0.913986i	$0.367012\pi$
$182$	4.54125	0.336620
$183$	−9.95407	−0.735826
$184$	3.36349	0.247960
$185$	−1.33185	−0.0979197
$186$	4.67799	0.343007
$187$	−0.0666765	−0.00487587
$188$	1.18760	0.0866146
$189$	−3.80642	−0.276877
$190$	−7.80642	−0.566338
$191$	−10.9175	−0.789963	−0.394981	−	0.918689i	$-0.629249\pi$
$191$	−10.9175	−0.789963	−0.394981	+	0.918689i	$0.629249\pi$
$192$	−6.09832	−0.440108
$193$	11.7003	0.842204	0.421102	−	0.907013i	$-0.361643\pi$
$193$	11.7003	0.842204	0.421102	+	0.907013i	$0.361643\pi$
$194$	−16.2953	−1.16993
$195$	−2.57628	−0.184491
$196$	−0.525428	−0.0375305
$197$	10.8430	0.772531	0.386265	−	0.922388i	$-0.373765\pi$
$197$	10.8430	0.772531	0.386265	+	0.922388i	$0.373765\pi$
$198$	3.06668	0.217939
$199$	2.08097	0.147516	0.0737579	−	0.997276i	$-0.476501\pi$
$199$	2.08097	0.147516	0.0737579	+	0.997276i	$0.476501\pi$
$200$	−3.06668	−0.216847
$201$	−7.15257	−0.504503
$202$	−10.2603	−0.721909
$203$	7.80642	0.547904
$204$	0.0241344	0.00168975
$205$	−6.64296	−0.463964
$206$	−11.5921	−0.807660
$207$	2.76986	0.192518
$208$	9.99661	0.693140
$209$	−6.42864	−0.444678
$210$	−0.836535	−0.0577264
$211$	23.0923	1.58974	0.794871	−	0.606778i	$-0.207538\pi$
$211$	23.0923	1.58974	0.794871	+	0.606778i	$0.207538\pi$
$212$	0.903212	0.0620328
$213$	8.65386	0.592953
$214$	−10.3970	−0.710724
$215$	11.7605	0.802059
$216$	−11.6731	−0.794252
$217$	5.59210	0.379617
$218$	−8.48886	−0.574938
$219$	−0.811346	−0.0548257
$220$	−0.525428	−0.0354243
$221$	−0.249353	−0.0167733
$222$	−1.11414	−0.0747762
$223$	−21.5462	−1.44284	−0.721419	−	0.692499i	$-0.756510\pi$
$223$	−21.5462	−1.44284	−0.721419	+	0.692499i	$0.756510\pi$
$224$	−2.88739	−0.192922
$225$	−2.52543	−0.168362
$226$	−1.90813	−0.126927
$227$	−27.2257	−1.80703	−0.903516	−	0.428553i	$-0.859023\pi$
$227$	−27.2257	−1.80703	−0.903516	+	0.428553i	$0.859023\pi$
$228$	2.32693	0.154105
$229$	25.0005	1.65208	0.826039	−	0.563613i	$-0.190589\pi$
$229$	25.0005	1.65208	0.826039	+	0.563613i	$0.190589\pi$
$230$	1.33185	0.0878197
$231$	−0.688892	−0.0453258
$232$	23.9398	1.57172
$233$	−3.65878	−0.239695	−0.119847	−	0.992792i	$-0.538241\pi$
$233$	−3.65878	−0.239695	−0.119847	+	0.992792i	$0.538241\pi$
$234$	11.4686	0.749726
$235$	2.26025	0.147443
$236$	−1.33524	−0.0869169
$237$	5.86665	0.381080
$238$	−0.0809666	−0.00524829
$239$	14.7052	0.951200	0.475600	−	0.879662i	$-0.342231\pi$
$239$	14.7052	0.951200	0.475600	+	0.879662i	$0.342231\pi$
$240$	−1.84146	−0.118866
$241$	13.6938	0.882096	0.441048	−	0.897483i	$-0.354607\pi$
$241$	13.6938	0.882096	0.441048	+	0.897483i	$0.354607\pi$
$242$	1.21432	0.0780594
$243$	−14.8321	−0.951479
$244$	−7.59210	−0.486035
$245$	−1.00000	−0.0638877
$246$	−5.55707	−0.354306
$247$	−24.0415	−1.52972
$248$	17.1492	1.08897
$249$	8.33677	0.528322
$250$	−1.21432	−0.0768003
$251$	−11.0114	−0.695032	−0.347516	−	0.937674i	$-0.612975\pi$
$251$	−11.0114	−0.695032	−0.347516	+	0.937674i	$0.612975\pi$
$252$	−1.32693	−0.0835887
$253$	1.09679	0.0689545
$254$	−16.2449	−1.01930
$255$	0.0459330	0.00287643
$256$	−11.6637	−0.728981
$257$	−15.9496	−0.994910	−0.497455	−	0.867490i	$-0.665732\pi$
$257$	−15.9496	−0.994910	−0.497455	+	0.867490i	$0.665732\pi$
$258$	9.83807	0.612491
$259$	−1.33185	−0.0827572
$260$	−1.96497	−0.121862
$261$	19.7146	1.22030
$262$	−3.34614	−0.206725
$263$	−5.11108	−0.315163	−0.157581	−	0.987506i	$-0.550370\pi$
$263$	−5.11108	−0.315163	−0.157581	+	0.987506i	$0.550370\pi$
$264$	−2.11261	−0.130022
$265$	1.71900	0.105598
$266$	−7.80642	−0.478643
$267$	−10.7556	−0.658230
$268$	−5.45536	−0.333239
$269$	−18.2351	−1.11181	−0.555906	−	0.831245i	$-0.687628\pi$
$269$	−18.2351	−1.11181	−0.555906	+	0.831245i	$0.687628\pi$
$270$	−4.62222	−0.281299
$271$	6.23506	0.378753	0.189377	−	0.981905i	$-0.439353\pi$
$271$	6.23506	0.378753	0.189377	+	0.981905i	$0.439353\pi$
$272$	−0.178231	−0.0108068
$273$	−2.57628	−0.155924
$274$	−21.7288	−1.31269
$275$	−1.00000	−0.0603023
$276$	−0.396997	−0.0238964
$277$	6.32248	0.379881	0.189941	−	0.981796i	$-0.439170\pi$
$277$	6.32248	0.379881	0.189941	+	0.981796i	$0.439170\pi$
$278$	−4.69535	−0.281608
$279$	14.1225	0.845489
$280$	−3.06668	−0.183269
$281$	−25.2257	−1.50484	−0.752419	−	0.658684i	$-0.771113\pi$
$281$	−25.2257	−1.50484	−0.752419	+	0.658684i	$0.771113\pi$
$282$	1.89078	0.112594
$283$	13.4193	0.797693	0.398846	−	0.917018i	$-0.369411\pi$
$283$	13.4193	0.797693	0.398846	+	0.917018i	$0.369411\pi$
$284$	6.60042	0.391663
$285$	4.42864	0.262330
$286$	4.54125	0.268530
$287$	−6.64296	−0.392121
$288$	−7.29190	−0.429679
$289$	−16.9956	−0.999738
$290$	9.47949	0.556655
$291$	9.24443	0.541918
$292$	−0.618825	−0.0362140
$293$	17.6064	1.02858	0.514288	−	0.857617i	$-0.328056\pi$
$293$	17.6064	1.02858	0.514288	+	0.857617i	$0.328056\pi$
$294$	−0.836535	−0.0487877
$295$	−2.54125	−0.147957
$296$	−4.08436	−0.237398
$297$	−3.80642	−0.220871
$298$	5.93671	0.343905
$299$	4.10171	0.237208
$300$	0.361963	0.0208979
$301$	11.7605	0.677863
$302$	26.9447	1.55049
$303$	5.82071	0.334391
$304$	−17.1842	−0.985582
$305$	−14.4494	−0.827369
$306$	−0.204475	−0.0116891
$307$	26.3368	1.50312	0.751560	−	0.659665i	$-0.229302\pi$
$307$	26.3368	1.50312	0.751560	+	0.659665i	$0.229302\pi$
$308$	−0.525428	−0.0299390
$309$	6.57628	0.374112
$310$	6.79060	0.385680
$311$	5.96052	0.337990	0.168995	−	0.985617i	$-0.445948\pi$
$311$	5.96052	0.337990	0.168995	+	0.985617i	$0.445948\pi$
$312$	−7.90063	−0.447285
$313$	−5.52098	−0.312064	−0.156032	−	0.987752i	$-0.549870\pi$
$313$	−5.52098	−0.312064	−0.156032	+	0.987752i	$0.549870\pi$
$314$	−5.84791	−0.330017
$315$	−2.52543	−0.142292
$316$	4.47457	0.251714
$317$	−15.7146	−0.882618	−0.441309	−	0.897355i	$-0.645486\pi$
$317$	−15.7146	−0.882618	−0.441309	+	0.897355i	$0.645486\pi$
$318$	1.43801	0.0806395
$319$	7.80642	0.437076
$320$	−8.85236	−0.494862
$321$	5.89829	0.329210
$322$	1.33185	0.0742212
$323$	0.428639	0.0238501
$324$	−2.60300	−0.144611
$325$	−3.73975	−0.207444
$326$	7.39207	0.409409
$327$	4.81579	0.266314
$328$	−20.3718	−1.12484
$329$	2.26025	0.124612
$330$	−0.836535	−0.0460498
$331$	18.2351	1.00229	0.501145	−	0.865363i	$-0.332912\pi$
$331$	18.2351	1.00229	0.501145	+	0.865363i	$0.332912\pi$
$332$	6.35857	0.348972
$333$	−3.36349	−0.184318
$334$	−4.46028	−0.244056
$335$	−10.3827	−0.567268
$336$	−1.84146	−0.100460
$337$	32.2908	1.75899	0.879497	−	0.475904i	$-0.157879\pi$
$337$	32.2908	1.75899	0.879497	+	0.475904i	$0.157879\pi$
$338$	1.19697	0.0651064
$339$	1.08250	0.0587932
$340$	0.0350337	0.00189997
$341$	5.59210	0.302829
$342$	−19.7146	−1.06604
$343$	−1.00000	−0.0539949
$344$	36.0656	1.94453
$345$	−0.755569	−0.0406785
$346$	−0.763405	−0.0410409
$347$	22.6909	1.21811	0.609056	−	0.793127i	$-0.291549\pi$
$347$	22.6909	1.21811	0.609056	+	0.793127i	$0.291549\pi$
$348$	−2.82564	−0.151470
$349$	16.9097	0.905154	0.452577	−	0.891725i	$-0.350505\pi$
$349$	16.9097	0.905154	0.452577	+	0.891725i	$0.350505\pi$
$350$	−1.21432	−0.0649081
$351$	−14.2351	−0.759811
$352$	−2.88739	−0.153898
$353$	24.3970	1.29852	0.649261	−	0.760566i	$-0.275078\pi$
$353$	24.3970	1.29852	0.649261	+	0.760566i	$0.275078\pi$
$354$	−2.12584	−0.112987
$355$	12.5620	0.666721
$356$	−8.20342	−0.434780
$357$	0.0459330	0.00243103
$358$	−9.35599	−0.494479
$359$	−32.8113	−1.73172	−0.865858	−	0.500289i	$-0.833227\pi$
$359$	−32.8113	−1.73172	−0.865858	+	0.500289i	$0.833227\pi$
$360$	−7.74467	−0.408180
$361$	22.3274	1.17513
$362$	13.2573	0.696790
$363$	−0.688892	−0.0361575
$364$	−1.96497	−0.102992
$365$	−1.17775	−0.0616465
$366$	−12.0874	−0.631820
$367$	−6.94269	−0.362406	−0.181203	−	0.983446i	$-0.557999\pi$
$367$	−6.94269	−0.362406	−0.181203	+	0.983446i	$0.557999\pi$
$368$	2.93179	0.152830
$369$	−16.7763	−0.873340
$370$	−1.61729	−0.0840791
$371$	1.71900	0.0892462
$372$	−2.02413	−0.104946
$373$	36.9733	1.91440	0.957202	−	0.289421i	$-0.0934627\pi$
$373$	36.9733	1.91440	0.957202	+	0.289421i	$0.0934627\pi$
$374$	−0.0809666	−0.00418669
$375$	0.688892	0.0355742
$376$	6.93146	0.357463
$377$	29.1941	1.50357
$378$	−4.62222	−0.237741
$379$	−23.6414	−1.21438	−0.607189	−	0.794557i	$-0.707703\pi$
$379$	−23.6414	−1.21438	−0.607189	+	0.794557i	$0.707703\pi$
$380$	3.37778	0.173277
$381$	9.21585	0.472142
$382$	−13.2573	−0.678304
$383$	13.7210	0.701111	0.350555	−	0.936542i	$-0.385993\pi$
$383$	13.7210	0.701111	0.350555	+	0.936542i	$0.385993\pi$
$384$	−3.42711	−0.174889
$385$	−1.00000	−0.0509647
$386$	14.2079	0.723161
$387$	29.7003	1.50975
$388$	7.05086	0.357953
$389$	−15.5526	−0.788549	−0.394275	−	0.918993i	$-0.629004\pi$
$389$	−15.5526	−0.788549	−0.394275	+	0.918993i	$0.629004\pi$
$390$	−3.12843	−0.158414
$391$	−0.0731300	−0.00369835
$392$	−3.06668	−0.154891
$393$	1.89829	0.0957561
$394$	13.1669	0.663337
$395$	8.51606	0.428489
$396$	−1.32693	−0.0666807
$397$	−0.253799	−0.0127378	−0.00636891	−	0.999980i	$-0.502027\pi$
$397$	−0.253799	−0.0127378	−0.00636891	+	0.999980i	$0.502027\pi$
$398$	2.52696	0.126665
$399$	4.42864	0.221709
$400$	−2.67307	−0.133654
$401$	20.3684	1.01715	0.508575	−	0.861018i	$-0.330172\pi$
$401$	20.3684	1.01715	0.508575	+	0.861018i	$0.330172\pi$
$402$	−8.68550	−0.433193
$403$	20.9131	1.04175
$404$	4.43954	0.220875
$405$	−4.95407	−0.246170
$406$	9.47949	0.470459
$407$	−1.33185	−0.0660174
$408$	0.140862	0.00697368
$409$	12.1225	0.599417	0.299708	−	0.954031i	$-0.403111\pi$
$409$	12.1225	0.599417	0.299708	+	0.954031i	$0.403111\pi$
$410$	−8.06668	−0.398385
$411$	12.3269	0.608043
$412$	5.01582	0.247112
$413$	−2.54125	−0.125047
$414$	3.36349	0.165307
$415$	12.1017	0.594050
$416$	−10.7981	−0.529421
$417$	2.66370	0.130442
$418$	−7.80642	−0.381825
$419$	−21.4400	−1.04741	−0.523707	−	0.851899i	$-0.675451\pi$
$419$	−21.4400	−1.04741	−0.523707	+	0.851899i	$0.675451\pi$
$420$	0.361963	0.0176620
$421$	29.8622	1.45539	0.727697	−	0.685898i	$-0.240591\pi$
$421$	29.8622	1.45539	0.727697	+	0.685898i	$0.240591\pi$
$422$	28.0415	1.36504
$423$	5.70810	0.277538
$424$	5.27163	0.256013
$425$	0.0666765	0.00323429
$426$	10.5086	0.509141
$427$	−14.4494	−0.699255
$428$	4.49871	0.217453
$429$	−2.57628	−0.124384
$430$	14.2810	0.688691
$431$	−19.6588	−0.946930	−0.473465	−	0.880813i	$-0.656997\pi$
$431$	−19.6588	−0.946930	−0.473465	+	0.880813i	$0.656997\pi$
$432$	−10.1748	−0.489537
$433$	−32.9719	−1.58453	−0.792264	−	0.610178i	$-0.791098\pi$
$433$	−32.9719	−1.58453	−0.792264	+	0.610178i	$0.791098\pi$
$434$	6.79060	0.325959
$435$	−5.37778	−0.257845
$436$	3.67307	0.175908
$437$	−7.05086	−0.337288
$438$	−0.985233	−0.0470763
$439$	−0.815792	−0.0389356	−0.0194678	−	0.999810i	$-0.506197\pi$
$439$	−0.815792	−0.0389356	−0.0194678	+	0.999810i	$0.506197\pi$
$440$	−3.06668	−0.146198
$441$	−2.52543	−0.120258
$442$	−0.302795	−0.0144025
$443$	24.9763	1.18666	0.593331	−	0.804959i	$-0.297813\pi$
$443$	24.9763	1.18666	0.593331	+	0.804959i	$0.297813\pi$
$444$	0.482081	0.0228785
$445$	−15.6128	−0.740120
$446$	−26.1639	−1.23890
$447$	−3.36794	−0.159298
$448$	−8.85236	−0.418235
$449$	0.414349	0.0195544	0.00977718	−	0.999952i	$-0.496888\pi$
$449$	0.414349	0.0195544	0.00977718	+	0.999952i	$0.496888\pi$
$450$	−3.06668	−0.144565
$451$	−6.64296	−0.312805
$452$	0.825636	0.0388347
$453$	−15.2859	−0.718195
$454$	−33.0607	−1.55162
$455$	−3.73975	−0.175322
$456$	13.5812	0.635998
$457$	9.33185	0.436526	0.218263	−	0.975890i	$-0.429961\pi$
$457$	9.33185	0.436526	0.218263	+	0.975890i	$0.429961\pi$
$458$	30.3586	1.41856
$459$	0.253799	0.0118463
$460$	−0.576283	−0.0268693
$461$	29.9891	1.39673	0.698366	−	0.715741i	$-0.253911\pi$
$461$	29.9891	1.39673	0.698366	+	0.715741i	$0.253911\pi$
$462$	−0.836535	−0.0389191
$463$	−31.5353	−1.46557	−0.732784	−	0.680461i	$-0.761780\pi$
$463$	−31.5353	−1.46557	−0.732784	+	0.680461i	$0.761780\pi$
$464$	20.8671	0.968732
$465$	−3.85236	−0.178649
$466$	−4.44293	−0.205815
$467$	−5.67952	−0.262817	−0.131409	−	0.991328i	$-0.541950\pi$
$467$	−5.67952	−0.262817	−0.131409	+	0.991328i	$0.541950\pi$
$468$	−4.96238	−0.229386
$469$	−10.3827	−0.479429
$470$	2.74467	0.126602
$471$	3.31756	0.152865
$472$	−7.79319	−0.358711
$473$	11.7605	0.540748
$474$	7.12399	0.327215
$475$	6.42864	0.294966
$476$	0.0350337	0.00160577
$477$	4.34122	0.198771
$478$	17.8568	0.816751
$479$	−39.4608	−1.80301	−0.901504	−	0.432771i	$-0.857536\pi$
$479$	−39.4608	−1.80301	−0.901504	+	0.432771i	$0.857536\pi$
$480$	1.98910	0.0907896
$481$	−4.98079	−0.227104
$482$	16.6287	0.757415
$483$	−0.755569	−0.0343796
$484$	−0.525428	−0.0238831
$485$	13.4193	0.609338
$486$	−18.0109	−0.816991
$487$	−3.19850	−0.144938	−0.0724689	−	0.997371i	$-0.523088\pi$
$487$	−3.19850	−0.144938	−0.0724689	+	0.997371i	$0.523088\pi$
$488$	−44.3116	−2.00589
$489$	−4.19358	−0.189640
$490$	−1.21432	−0.0548574
$491$	26.3511	1.18921	0.594603	−	0.804019i	$-0.297309\pi$
$491$	26.3511	1.18921	0.594603	+	0.804019i	$0.297309\pi$
$492$	2.40451	0.108403
$493$	−0.520505	−0.0234424
$494$	−29.1941	−1.31350
$495$	−2.52543	−0.113510
$496$	14.9481	0.671189
$497$	12.5620	0.563482
$498$	10.1235	0.453645
$499$	3.52987	0.158019	0.0790094	−	0.996874i	$-0.474824\pi$
$499$	3.52987	0.158019	0.0790094	+	0.996874i	$0.474824\pi$
$500$	0.525428	0.0234978
$501$	2.53035	0.113048
$502$	−13.3713	−0.596792
$503$	22.7368	1.01379	0.506893	−	0.862009i	$-0.330794\pi$
$503$	22.7368	1.01379	0.506893	+	0.862009i	$0.330794\pi$
$504$	−7.74467	−0.344975
$505$	8.44938	0.375993
$506$	1.33185	0.0592080
$507$	−0.679048	−0.0301576
$508$	7.02906	0.311864
$509$	−36.2351	−1.60609	−0.803045	−	0.595918i	$-0.796788\pi$
$509$	−36.2351	−1.60609	−0.803045	+	0.595918i	$0.796788\pi$
$510$	0.0557773	0.00246986
$511$	−1.17775	−0.0521008
$512$	−24.1131	−1.06566
$513$	24.4701	1.08038
$514$	−19.3679	−0.854283
$515$	9.54617	0.420655
$516$	−4.25686	−0.187398
$517$	2.26025	0.0994058
$518$	−1.61729	−0.0710598
$519$	0.433085	0.0190103
$520$	−11.4686	−0.502931
$521$	−6.79706	−0.297784	−0.148892	−	0.988853i	$-0.547571\pi$
$521$	−6.79706	−0.297784	−0.148892	+	0.988853i	$0.547571\pi$
$522$	23.9398	1.04782
$523$	34.0701	1.48978	0.744890	−	0.667187i	$-0.232502\pi$
$523$	34.0701	1.48978	0.744890	+	0.667187i	$0.232502\pi$
$524$	1.44785	0.0632497
$525$	0.688892	0.0300657
$526$	−6.20648	−0.270616
$527$	−0.372862	−0.0162421
$528$	−1.84146	−0.0801392
$529$	−21.7971	−0.947698
$530$	2.08742	0.0906717
$531$	−6.41774	−0.278506
$532$	3.37778	0.146446
$533$	−24.8430	−1.07607
$534$	−13.0607	−0.565192
$535$	8.56199	0.370167
$536$	−31.8404	−1.37530
$537$	5.30772	0.229045
$538$	−22.1432	−0.954661
$539$	−1.00000	−0.0430730
$540$	2.00000	0.0860663
$541$	−27.1941	−1.16916	−0.584582	−	0.811335i	$-0.698741\pi$
$541$	−27.1941	−1.16916	−0.584582	+	0.811335i	$0.698741\pi$
$542$	7.57136	0.325218
$543$	−7.52098	−0.322756
$544$	0.192521	0.00825428
$545$	6.99063	0.299446
$546$	−3.12843	−0.133884
$547$	−40.2449	−1.72075	−0.860374	−	0.509663i	$-0.829770\pi$
$547$	−40.2449	−1.72075	−0.860374	+	0.509663i	$0.829770\pi$
$548$	9.40192	0.401630
$549$	−36.4909	−1.55739
$550$	−1.21432	−0.0517788
$551$	−50.1847	−2.13794
$552$	−2.31708	−0.0986217
$553$	8.51606	0.362140
$554$	7.67752	0.326186
$555$	0.917502	0.0389458
$556$	2.03164	0.0861608
$557$	−7.09679	−0.300701	−0.150350	−	0.988633i	$-0.548040\pi$
$557$	−7.09679	−0.300701	−0.150350	+	0.988633i	$0.548040\pi$
$558$	17.1492	0.725982
$559$	43.9813	1.86021
$560$	−2.67307	−0.112958
$561$	0.0459330	0.00193929
$562$	−30.6321	−1.29214
$563$	−18.7971	−0.792201	−0.396101	−	0.918207i	$-0.629637\pi$
$563$	−18.7971	−0.792201	−0.396101	+	0.918207i	$0.629637\pi$
$564$	−0.818128	−0.0344494
$565$	1.57136	0.0661076
$566$	16.2953	0.684942
$567$	−4.95407	−0.208051
$568$	38.5236	1.61641
$569$	−0.0316429	−0.00132654	−0.000663269	−	1.00000i	$-0.500211\pi$
$569$	−0.0316429	−0.00132654	−0.000663269		1.00000i	$0.500211\pi$
$570$	5.37778	0.225251
$571$	0.0503787	0.00210828	0.00105414	−	0.999999i	$-0.499664\pi$
$571$	0.0503787	0.00210828	0.00105414	+	0.999999i	$0.499664\pi$
$572$	−1.96497	−0.0821594
$573$	7.52098	0.314194
$574$	−8.06668	−0.336697
$575$	−1.09679	−0.0457392
$576$	−22.3560	−0.931499
$577$	−13.6316	−0.567490	−0.283745	−	0.958900i	$-0.591577\pi$
$577$	−13.6316	−0.567490	−0.283745	+	0.958900i	$0.591577\pi$
$578$	−20.6380	−0.858429
$579$	−8.06022	−0.334971
$580$	−4.10171	−0.170314
$581$	12.1017	0.502064
$582$	11.2257	0.465320
$583$	1.71900	0.0711939
$584$	−3.61179	−0.149457
$585$	−9.44446	−0.390480
$586$	21.3798	0.883191
$587$	1.63804	0.0676090	0.0338045	−	0.999428i	$-0.489238\pi$
$587$	1.63804	0.0676090	0.0338045	+	0.999428i	$0.489238\pi$
$588$	0.361963	0.0149271
$589$	−35.9496	−1.48128
$590$	−3.08589	−0.127044
$591$	−7.46965	−0.307260
$592$	−3.56013	−0.146321
$593$	8.46367	0.347561	0.173781	−	0.984784i	$-0.444402\pi$
$593$	8.46367	0.347561	0.173781	+	0.984784i	$0.444402\pi$
$594$	−4.62222	−0.189652
$595$	0.0666765	0.00273347
$596$	−2.56877	−0.105221
$597$	−1.43356	−0.0586718
$598$	4.98079	0.203680
$599$	−26.9590	−1.10151	−0.550757	−	0.834665i	$-0.685661\pi$
$599$	−26.9590	−1.10151	−0.550757	+	0.834665i	$0.685661\pi$
$600$	2.11261	0.0862469
$601$	−16.4909	−0.672677	−0.336338	−	0.941741i	$-0.609189\pi$
$601$	−16.4909	−0.672677	−0.336338	+	0.941741i	$0.609189\pi$
$602$	14.2810	0.582050
$603$	−26.2208	−1.06779
$604$	−11.6588	−0.474389
$605$	−1.00000	−0.0406558
$606$	7.06821	0.287126
$607$	19.5526	0.793617	0.396808	−	0.917902i	$-0.370118\pi$
$607$	19.5526	0.793617	0.396808	+	0.917902i	$0.370118\pi$
$608$	18.5620	0.752788
$609$	−5.37778	−0.217919
$610$	−17.5462	−0.710424
$611$	8.45277	0.341963
$612$	0.0884751	0.00357639
$613$	−39.5955	−1.59925	−0.799623	−	0.600502i	$-0.794968\pi$
$613$	−39.5955	−1.59925	−0.799623	+	0.600502i	$0.794968\pi$
$614$	31.9813	1.29066
$615$	4.57628	0.184534
$616$	−3.06668	−0.123560
$617$	23.1669	0.932662	0.466331	−	0.884610i	$-0.345575\pi$
$617$	23.1669	0.932662	0.466331	+	0.884610i	$0.345575\pi$
$618$	7.98571	0.321232
$619$	3.43017	0.137870	0.0689351	−	0.997621i	$-0.478040\pi$
$619$	3.43017	0.137870	0.0689351	+	0.997621i	$0.478040\pi$
$620$	−2.93825	−0.118003
$621$	−4.17484	−0.167531
$622$	7.23798	0.290216
$623$	−15.6128	−0.625516
$624$	−6.88659	−0.275684
$625$	1.00000	0.0400000
$626$	−6.70424	−0.267955
$627$	4.42864	0.176863
$628$	2.53035	0.100972
$629$	0.0888033	0.00354082
$630$	−3.06668	−0.122179
$631$	10.9590	0.436270	0.218135	−	0.975919i	$-0.430003\pi$
$631$	10.9590	0.436270	0.218135	+	0.975919i	$0.430003\pi$
$632$	26.1160	1.03884
$633$	−15.9081	−0.632292
$634$	−19.0825	−0.757863
$635$	13.3778	0.530881
$636$	−0.622216	−0.0246725
$637$	−3.73975	−0.148174
$638$	9.47949	0.375297
$639$	31.7244	1.25500
$640$	−4.97481	−0.196647
$641$	−14.9862	−0.591919	−0.295959	−	0.955201i	$-0.595639\pi$
$641$	−14.9862	−0.591919	−0.295959	+	0.955201i	$0.595639\pi$
$642$	7.16241	0.282678
$643$	−14.4222	−0.568755	−0.284378	−	0.958712i	$-0.591787\pi$
$643$	−14.4222	−0.568755	−0.284378	+	0.958712i	$0.591787\pi$
$644$	−0.576283	−0.0227087
$645$	−8.10171	−0.319005
$646$	0.520505	0.0204790
$647$	−33.7309	−1.32610	−0.663048	−	0.748577i	$-0.730738\pi$
$647$	−33.7309	−1.32610	−0.663048	+	0.748577i	$0.730738\pi$
$648$	−15.1925	−0.596819
$649$	−2.54125	−0.0997527
$650$	−4.54125	−0.178122
$651$	−3.85236	−0.150986
$652$	−3.19850	−0.125263
$653$	36.7971	1.43998	0.719990	−	0.693984i	$-0.244146\pi$
$653$	36.7971	1.43998	0.719990	+	0.693984i	$0.244146\pi$
$654$	5.84791	0.228671
$655$	2.75557	0.107669
$656$	−17.7571	−0.693298
$657$	−2.97433	−0.116040
$658$	2.74467	0.106998
$659$	3.79213	0.147721	0.0738603	−	0.997269i	$-0.476468\pi$
$659$	3.79213	0.147721	0.0738603	+	0.997269i	$0.476468\pi$
$660$	0.361963	0.0140894
$661$	−35.2543	−1.37123	−0.685616	−	0.727963i	$-0.740467\pi$
$661$	−35.2543	−1.37123	−0.685616	+	0.727963i	$0.740467\pi$
$662$	22.1432	0.860620
$663$	0.171778	0.00667129
$664$	37.1120	1.44023
$665$	6.42864	0.249292
$666$	−4.08436	−0.158266
$667$	8.56199	0.331522
$668$	1.92993	0.0746713
$669$	14.8430	0.573863
$670$	−12.6079	−0.487087
$671$	−14.4494	−0.557812
$672$	1.98910	0.0767312
$673$	−35.1383	−1.35448	−0.677240	−	0.735762i	$-0.736824\pi$
$673$	−35.1383	−1.35448	−0.677240	+	0.735762i	$0.736824\pi$
$674$	39.2114	1.51037
$675$	3.80642	0.146509
$676$	−0.517919	−0.0199200
$677$	23.1907	0.891290	0.445645	−	0.895210i	$-0.352974\pi$
$677$	23.1907	0.891290	0.445645	+	0.895210i	$0.352974\pi$
$678$	1.31450	0.0504830
$679$	13.4193	0.514984
$680$	0.204475	0.00784127
$681$	18.7556	0.718715
$682$	6.79060	0.260026
$683$	−7.74758	−0.296453	−0.148227	−	0.988953i	$-0.547356\pi$
$683$	−7.74758	−0.296453	−0.148227	+	0.988953i	$0.547356\pi$
$684$	8.53035	0.326166
$685$	17.8938	0.683689
$686$	−1.21432	−0.0463629
$687$	−17.2226	−0.657084
$688$	31.4366	1.19851
$689$	6.42864	0.244912
$690$	−0.917502	−0.0349287
$691$	−14.7763	−0.562117	−0.281059	−	0.959691i	$-0.590686\pi$
$691$	−14.7763	−0.562117	−0.281059	+	0.959691i	$0.590686\pi$
$692$	0.330320	0.0125569
$693$	−2.52543	−0.0959331
$694$	27.5540	1.04594
$695$	3.86665	0.146670
$696$	−16.4919	−0.625125
$697$	0.442930	0.0167772
$698$	20.5337	0.777214
$699$	2.52051	0.0953343
$700$	0.525428	0.0198593
$701$	−19.8765	−0.750725	−0.375362	−	0.926878i	$-0.622482\pi$
$701$	−19.8765	−0.750725	−0.375362	+	0.926878i	$0.622482\pi$
$702$	−17.2859	−0.652415
$703$	8.56199	0.322922
$704$	−8.85236	−0.333636
$705$	−1.55707	−0.0586427
$706$	29.6258	1.11498
$707$	8.44938	0.317772
$708$	0.919838	0.0345696
$709$	0.368416	0.0138362	0.00691808	−	0.999976i	$-0.497798\pi$
$709$	0.368416	0.0138362	0.00691808	+	0.999976i	$0.497798\pi$
$710$	15.2543	0.572483
$711$	21.5067	0.806564
$712$	−47.8796	−1.79436
$713$	6.13335	0.229696
$714$	0.0557773	0.00208741
$715$	−3.73975	−0.139859
$716$	4.04827	0.151291
$717$	−10.1303	−0.378323
$718$	−39.8435	−1.48694
$719$	−5.86865	−0.218864	−0.109432	−	0.993994i	$-0.534903\pi$
$719$	−5.86865	−0.218864	−0.109432	+	0.993994i	$0.534903\pi$
$720$	−6.75065	−0.251582
$721$	9.54617	0.355518
$722$	27.1126	1.00903
$723$	−9.43356	−0.350838
$724$	−5.73636	−0.213190
$725$	−7.80642	−0.289923
$726$	−0.836535	−0.0310467
$727$	1.19066	0.0441592	0.0220796	−	0.999756i	$-0.492971\pi$
$727$	1.19066	0.0441592	0.0220796	+	0.999756i	$0.492971\pi$
$728$	−11.4686	−0.425054
$729$	−4.64449	−0.172018
$730$	−1.43017	−0.0529330
$731$	−0.784149	−0.0290028
$732$	5.23014	0.193312
$733$	19.6795	0.726880	0.363440	−	0.931618i	$-0.381602\pi$
$733$	19.6795	0.726880	0.363440	+	0.931618i	$0.381602\pi$
$734$	−8.43065	−0.311181
$735$	0.688892	0.0254102
$736$	−3.16686	−0.116732
$737$	−10.3827	−0.382452
$738$	−20.3718	−0.749897
$739$	27.1427	0.998461	0.499231	−	0.866469i	$-0.333616\pi$
$739$	27.1427	0.998461	0.499231	+	0.866469i	$0.333616\pi$
$740$	0.699791	0.0257248
$741$	16.5620	0.608420
$742$	2.08742	0.0766316
$743$	−31.0509	−1.13915	−0.569573	−	0.821941i	$-0.692891\pi$
$743$	−31.0509	−1.13915	−0.569573	+	0.821941i	$0.692891\pi$
$744$	−11.8139	−0.433120
$745$	−4.88892	−0.179116
$746$	44.8974	1.64381
$747$	30.5620	1.11820
$748$	0.0350337	0.00128096
$749$	8.56199	0.312848
$750$	0.836535	0.0305460
$751$	−35.8292	−1.30743	−0.653713	−	0.756743i	$-0.726789\pi$
$751$	−35.8292	−1.30743	−0.653713	+	0.756743i	$0.726789\pi$
$752$	6.04182	0.220322
$753$	7.58565	0.276436
$754$	35.4509	1.29105
$755$	−22.1891	−0.807545
$756$	2.00000	0.0727393
$757$	−1.15563	−0.0420020	−0.0210010	−	0.999779i	$-0.506685\pi$
$757$	−1.15563	−0.0420020	−0.0210010	+	0.999779i	$0.506685\pi$
$758$	−28.7083	−1.04273
$759$	−0.755569	−0.0274254
$760$	19.7146	0.715122
$761$	36.5640	1.32544	0.662722	−	0.748866i	$-0.269401\pi$
$761$	36.5640	1.32544	0.662722	+	0.748866i	$0.269401\pi$
$762$	11.1910	0.405407
$763$	6.99063	0.253078
$764$	5.73636	0.207534
$765$	0.168387	0.00608804
$766$	16.6617	0.602012
$767$	−9.50363	−0.343156
$768$	8.03503	0.289939
$769$	−38.7545	−1.39752	−0.698762	−	0.715354i	$-0.746265\pi$
$769$	−38.7545	−1.39752	−0.698762	+	0.715354i	$0.746265\pi$
$770$	−1.21432	−0.0437610
$771$	10.9876	0.395708
$772$	−6.14764	−0.221259
$773$	55.3372	1.99034	0.995171	−	0.0981537i	$-0.0312937\pi$
$773$	55.3372	1.99034	0.995171	+	0.0981537i	$0.0312937\pi$
$774$	36.0656	1.29635
$775$	−5.59210	−0.200874
$776$	41.1526	1.47729
$777$	0.917502	0.0329152
$778$	−18.8859	−0.677091
$779$	42.7052	1.53007
$780$	1.35365	0.0484684
$781$	12.5620	0.449503
$782$	−0.0888033	−0.00317560
$783$	−29.7146	−1.06191
$784$	−2.67307	−0.0954668
$785$	4.81579	0.171883
$786$	2.30513	0.0822213
$787$	−13.6731	−0.487392	−0.243696	−	0.969852i	$-0.578360\pi$
$787$	−13.6731	−0.487392	−0.243696	+	0.969852i	$0.578360\pi$
$788$	−5.69721	−0.202955
$789$	3.52098	0.125350
$790$	10.3412	0.367924
$791$	1.57136	0.0558711
$792$	−7.74467	−0.275195
$793$	−54.0370	−1.91891
$794$	−0.308193	−0.0109374
$795$	−1.18421	−0.0419995
$796$	−1.09340	−0.0387544
$797$	17.8765	0.633218	0.316609	−	0.948556i	$-0.397456\pi$
$797$	17.8765	0.633218	0.316609	+	0.948556i	$0.397456\pi$
$798$	5.37778	0.190372
$799$	−0.150706	−0.00533159
$800$	2.88739	0.102085
$801$	−39.4291	−1.39316
$802$	24.7338	0.873380
$803$	−1.17775	−0.0415621
$804$	3.75815	0.132540
$805$	−1.09679	−0.0386567
$806$	25.3951	0.894506
$807$	12.5620	0.442203
$808$	25.9115	0.911564
$809$	14.6450	0.514890	0.257445	−	0.966293i	$-0.417119\pi$
$809$	14.6450	0.514890	0.257445	+	0.966293i	$0.417119\pi$
$810$	−6.01582	−0.211374
$811$	30.2667	1.06281	0.531404	−	0.847119i	$-0.321665\pi$
$811$	30.2667	1.06281	0.531404	+	0.847119i	$0.321665\pi$
$812$	−4.10171	−0.143942
$813$	−4.29529	−0.150642
$814$	−1.61729	−0.0566861
$815$	−6.08742	−0.213233
$816$	0.122782	0.00429823
$817$	−75.6040	−2.64505
$818$	14.7205	0.514691
$819$	−9.44446	−0.330016
$820$	3.49039	0.121890
$821$	10.4286	0.363962	0.181981	−	0.983302i	$-0.441749\pi$
$821$	10.4286	0.363962	0.181981	+	0.983302i	$0.441749\pi$
$822$	14.9688	0.522098
$823$	4.28100	0.149226	0.0746131	−	0.997213i	$-0.476228\pi$
$823$	4.28100	0.149226	0.0746131	+	0.997213i	$0.476228\pi$
$824$	29.2750	1.01984
$825$	0.688892	0.0239841
$826$	−3.08589	−0.107372
$827$	−13.8336	−0.481042	−0.240521	−	0.970644i	$-0.577318\pi$
$827$	−13.8336	−0.481042	−0.240521	+	0.970644i	$0.577318\pi$
$828$	−1.45536	−0.0505773
$829$	10.8573	0.377089	0.188544	−	0.982065i	$-0.439623\pi$
$829$	10.8573	0.377089	0.188544	+	0.982065i	$0.439623\pi$
$830$	14.6953	0.510083
$831$	−4.35551	−0.151091
$832$	−33.1056	−1.14773
$833$	0.0666765	0.00231021
$834$	3.23459	0.112005
$835$	3.67307	0.127112
$836$	3.37778	0.116823
$837$	−21.2859	−0.735749
$838$	−26.0350	−0.899365
$839$	52.4820	1.81188	0.905940	−	0.423407i	$-0.139166\pi$
$839$	52.4820	1.81188	0.905940	+	0.423407i	$0.139166\pi$
$840$	2.11261	0.0728920
$841$	31.9403	1.10139
$842$	36.2623	1.24968
$843$	17.3778	0.598523
$844$	−12.1334	−0.417647
$845$	−0.985710	−0.0339095
$846$	6.93146	0.238309
$847$	−1.00000	−0.0343604
$848$	4.59502	0.157794
$849$	−9.24443	−0.317268
$850$	0.0809666	0.00277713
$851$	−1.46076	−0.0500742
$852$	−4.54698	−0.155777
$853$	9.89184	0.338690	0.169345	−	0.985557i	$-0.445835\pi$
$853$	9.89184	0.338690	0.169345	+	0.985557i	$0.445835\pi$
$854$	−17.5462	−0.600418
$855$	16.2351	0.555227
$856$	26.2569	0.897441
$857$	−3.58766	−0.122552	−0.0612760	−	0.998121i	$-0.519517\pi$
$857$	−3.58766	−0.122552	−0.0612760	+	0.998121i	$0.519517\pi$
$858$	−3.12843	−0.106803
$859$	−17.2050	−0.587025	−0.293513	−	0.955955i	$-0.594824\pi$
$859$	−17.2050	−0.587025	−0.293513	+	0.955955i	$0.594824\pi$
$860$	−6.17929	−0.210712
$861$	4.57628	0.155959
$862$	−23.8720	−0.813085
$863$	15.0781	0.513263	0.256631	−	0.966509i	$-0.417387\pi$
$863$	15.0781	0.513263	0.256631	+	0.966509i	$0.417387\pi$
$864$	10.9906	0.373909
$865$	0.628669	0.0213754
$866$	−40.0384	−1.36056
$867$	11.7081	0.397628
$868$	−2.93825	−0.0997306
$869$	8.51606	0.288888
$870$	−6.53035	−0.221400
$871$	−38.8287	−1.31566
$872$	21.4380	0.725983
$873$	33.8894	1.14698
$874$	−8.56199	−0.289614
$875$	1.00000	0.0338062
$876$	0.426304	0.0144035
$877$	−31.4750	−1.06284	−0.531418	−	0.847109i	$-0.678341\pi$
$877$	−31.4750	−1.06284	−0.531418	+	0.847109i	$0.678341\pi$
$878$	−0.990632	−0.0334322
$879$	−12.1289	−0.409098
$880$	−2.67307	−0.0901092
$881$	−47.1209	−1.58754	−0.793772	−	0.608215i	$-0.791886\pi$
$881$	−47.1209	−1.58754	−0.793772	+	0.608215i	$0.791886\pi$
$882$	−3.06668	−0.103260
$883$	33.8118	1.13786	0.568929	−	0.822386i	$-0.307358\pi$
$883$	33.8118	1.13786	0.568929	+	0.822386i	$0.307358\pi$
$884$	0.131017	0.00440658
$885$	1.75065	0.0588473
$886$	30.3293	1.01893
$887$	−31.6258	−1.06189	−0.530944	−	0.847407i	$-0.678163\pi$
$887$	−31.6258	−1.06189	−0.530944	+	0.847407i	$0.678163\pi$
$888$	2.81368	0.0944210
$889$	13.3778	0.448676
$890$	−18.9590	−0.635507
$891$	−4.95407	−0.165967
$892$	11.3210	0.379054
$893$	−14.5303	−0.486240
$894$	−4.08976	−0.136782
$895$	7.70471	0.257540
$896$	−4.97481	−0.166197
$897$	−2.82564	−0.0943452
$898$	0.503153	0.0167904
$899$	43.6543	1.45595
$900$	1.32693	0.0442310
$901$	−0.114617	−0.00381845
$902$	−8.06668	−0.268591
$903$	−8.10171	−0.269608
$904$	4.81885	0.160273
$905$	−10.9175	−0.362910
$906$	−18.5620	−0.616681
$907$	−46.8943	−1.55710	−0.778550	−	0.627582i	$-0.784045\pi$
$907$	−46.8943	−1.55710	−0.778550	+	0.627582i	$0.784045\pi$
$908$	14.3051	0.474732
$909$	21.3383	0.707747
$910$	−4.54125	−0.150541
$911$	−28.5620	−0.946301	−0.473151	−	0.880982i	$-0.656883\pi$
$911$	−28.5620	−0.946301	−0.473151	+	0.880982i	$0.656883\pi$
$912$	11.8381	0.391998
$913$	12.1017	0.400508
$914$	11.3319	0.374824
$915$	9.95407	0.329071
$916$	−13.1359	−0.434024
$917$	2.75557	0.0909969
$918$	0.308193	0.0101719
$919$	30.3555	1.00134	0.500668	−	0.865639i	$-0.333088\pi$
$919$	30.3555	1.00134	0.500668	+	0.865639i	$0.333088\pi$
$920$	−3.36349	−0.110891
$921$	−18.1432	−0.597839
$922$	36.4164	1.19931
$923$	46.9787	1.54632
$924$	0.361963	0.0119077
$925$	1.33185	0.0437910
$926$	−38.2939	−1.25842
$927$	24.1082	0.791816
$928$	−22.5402	−0.739918
$929$	2.71408	0.0890461	0.0445231	−	0.999008i	$-0.485823\pi$
$929$	2.71408	0.0890461	0.0445231	+	0.999008i	$0.485823\pi$
$930$	−4.67799	−0.153397
$931$	6.42864	0.210690
$932$	1.92242	0.0629711
$933$	−4.10616	−0.134430
$934$	−6.89676	−0.225669
$935$	0.0666765	0.00218056
$936$	−28.9631	−0.946689
$937$	13.7081	0.447824	0.223912	−	0.974609i	$-0.428117\pi$
$937$	13.7081	0.447824	0.223912	+	0.974609i	$0.428117\pi$
$938$	−12.6079	−0.411663
$939$	3.80336	0.124118
$940$	−1.18760	−0.0387352
$941$	−21.1635	−0.689909	−0.344955	−	0.938619i	$-0.612106\pi$
$941$	−21.1635	−0.689909	−0.344955	+	0.938619i	$0.612106\pi$
$942$	4.02858	0.131258
$943$	−7.28592	−0.237262
$944$	−6.79294	−0.221091
$945$	3.80642	0.123823
$946$	14.2810	0.464315
$947$	−14.8746	−0.483361	−0.241680	−	0.970356i	$-0.577699\pi$
$947$	−14.8746	−0.483361	−0.241680	+	0.970356i	$0.577699\pi$
$948$	−3.08250	−0.100115
$949$	−4.40451	−0.142976
$950$	7.80642	0.253274
$951$	10.8256	0.351045
$952$	0.204475	0.00662709
$953$	35.0968	1.13690	0.568448	−	0.822719i	$-0.307544\pi$
$953$	35.0968	1.13690	0.568448	+	0.822719i	$0.307544\pi$
$954$	5.27163	0.170675
$955$	10.9175	0.353282
$956$	−7.72651	−0.249893
$957$	−5.37778	−0.173839
$958$	−47.9180	−1.54816
$959$	17.8938	0.577822
$960$	6.09832	0.196822
$961$	0.271628	0.00876221
$962$	−6.04827	−0.195004
$963$	21.6227	0.696782
$964$	−7.19511	−0.231739
$965$	−11.7003	−0.376645
$966$	−0.917502	−0.0295201
$967$	−53.0879	−1.70719	−0.853596	−	0.520936i	$-0.825583\pi$
$967$	−53.0879	−1.70719	−0.853596	+	0.520936i	$0.825583\pi$
$968$	−3.06668	−0.0985667
$969$	−0.295286	−0.00948597
$970$	16.2953	0.523210
$971$	21.4400	0.688043	0.344021	−	0.938962i	$-0.388211\pi$
$971$	21.4400	0.688043	0.344021	+	0.938962i	$0.388211\pi$
$972$	7.79319	0.249967
$973$	3.86665	0.123959
$974$	−3.88400	−0.124451
$975$	2.57628	0.0825071
$976$	−38.6242	−1.23633
$977$	−54.0415	−1.72894	−0.864470	−	0.502684i	$-0.832346\pi$
$977$	−54.0415	−1.72894	−0.864470	+	0.502684i	$0.832346\pi$
$978$	−5.09234	−0.162835
$979$	−15.6128	−0.498989
$980$	0.525428	0.0167842
$981$	17.6543	0.563660
$982$	31.9986	1.02112
$983$	−38.3432	−1.22296	−0.611480	−	0.791260i	$-0.709425\pi$
$983$	−38.3432	−1.22296	−0.611480	+	0.791260i	$0.709425\pi$
$984$	14.0340	0.447387
$985$	−10.8430	−0.345486
$986$	−0.632060	−0.0201289
$987$	−1.55707	−0.0495621
$988$	12.6321	0.401879
$989$	12.8988	0.410157
$990$	−3.06668	−0.0974654
$991$	51.6543	1.64085	0.820427	−	0.571751i	$-0.193736\pi$
$991$	51.6543	1.64085	0.820427	+	0.571751i	$0.193736\pi$
$992$	−16.1466	−0.512655
$993$	−12.5620	−0.398643
$994$	15.2543	0.483836
$995$	−2.08097	−0.0659711
$996$	−4.38037	−0.138797
$997$	41.4445	1.31256	0.656280	−	0.754518i	$-0.272129\pi$
$997$	41.4445	1.31256	0.656280	+	0.754518i	$0.272129\pi$
$998$	4.28639	0.135683
$999$	5.06959	0.160395

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.a.f.1.3	✓	3
3.2	odd	2		3465.2.a.bh.1.1		3
4.3	odd	2		6160.2.a.bn.1.2		3
5.2	odd	4		1925.2.b.n.1849.4		6
5.3	odd	4		1925.2.b.n.1849.3		6
5.4	even	2		1925.2.a.v.1.1		3
7.6	odd	2		2695.2.a.g.1.3		3
11.10	odd	2		4235.2.a.q.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.a.f.1.3	✓	3	1.1	even	1	trivial
1925.2.a.v.1.1		3	5.4	even	2
1925.2.b.n.1849.3		6	5.3	odd	4
1925.2.b.n.1849.4		6	5.2	odd	4
2695.2.a.g.1.3		3	7.6	odd	2
3465.2.a.bh.1.1		3	3.2	odd	2
4235.2.a.q.1.1		3	11.10	odd	2
6160.2.a.bn.1.2		3	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.a (trivial)

\(f(q)\)	\(=\)	\(q+1.21432 q^{2} -0.688892 q^{3} -0.525428 q^{4} -1.00000 q^{5} -0.836535 q^{6} -1.00000 q^{7} -3.06668 q^{8} -2.52543 q^{9} -1.21432 q^{10} -1.00000 q^{11} +0.361963 q^{12} -3.73975 q^{13} -1.21432 q^{14} +0.688892 q^{15} -2.67307 q^{16} +0.0666765 q^{17} -3.06668 q^{18} +6.42864 q^{19} +0.525428 q^{20} +0.688892 q^{21} -1.21432 q^{22} -1.09679 q^{23} +2.11261 q^{24} +1.00000 q^{25} -4.54125 q^{26} +3.80642 q^{27} +0.525428 q^{28} -7.80642 q^{29} +0.836535 q^{30} -5.59210 q^{31} +2.88739 q^{32} +0.688892 q^{33} +0.0809666 q^{34} +1.00000 q^{35} +1.32693 q^{36} +1.33185 q^{37} +7.80642 q^{38} +2.57628 q^{39} +3.06668 q^{40} +6.64296 q^{41} +0.836535 q^{42} -11.7605 q^{43} +0.525428 q^{44} +2.52543 q^{45} -1.33185 q^{46} -2.26025 q^{47} +1.84146 q^{48} +1.00000 q^{49} +1.21432 q^{50} -0.0459330 q^{51} +1.96497 q^{52} -1.71900 q^{53} +4.62222 q^{54} +1.00000 q^{55} +3.06668 q^{56} -4.42864 q^{57} -9.47949 q^{58} +2.54125 q^{59} -0.361963 q^{60} +14.4494 q^{61} -6.79060 q^{62} +2.52543 q^{63} +8.85236 q^{64} +3.73975 q^{65} +0.836535 q^{66} +10.3827 q^{67} -0.0350337 q^{68} +0.755569 q^{69} +1.21432 q^{70} -12.5620 q^{71} +7.74467 q^{72} +1.17775 q^{73} +1.61729 q^{74} -0.688892 q^{75} -3.37778 q^{76} +1.00000 q^{77} +3.12843 q^{78} -8.51606 q^{79} +2.67307 q^{80} +4.95407 q^{81} +8.06668 q^{82} -12.1017 q^{83} -0.361963 q^{84} -0.0666765 q^{85} -14.2810 q^{86} +5.37778 q^{87} +3.06668 q^{88} +15.6128 q^{89} +3.06668 q^{90} +3.73975 q^{91} +0.576283 q^{92} +3.85236 q^{93} -2.74467 q^{94} -6.42864 q^{95} -1.98910 q^{96} -13.4193 q^{97} +1.21432 q^{98} +2.52543 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 2 q^{3} + 5 q^{4} - 3 q^{5} + 4 q^{6} - 3 q^{7} - 9 q^{8} - q^{9} + 3 q^{10} - 3 q^{11} - 12 q^{12} + 2 q^{13} + 3 q^{14} + 2 q^{15} + 5 q^{16} - 9 q^{18} + 6 q^{19} - 5 q^{20} + 2 q^{21}+ \cdots + q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 2 * q^3 + 5 * q^4 - 3 * q^5 + 4 * q^6 - 3 * q^7 - 9 * q^8 - q^9 + 3 * q^10 - 3 * q^11 - 12 * q^12 + 2 * q^13 + 3 * q^14 + 2 * q^15 + 5 * q^16 - 9 * q^18 + 6 * q^19 - 5 * q^20 + 2 * q^21 + 3 * q^22 - 10 * q^23 + 26 * q^24 + 3 * q^25 - 20 * q^26 - 2 * q^27 - 5 * q^28 - 10 * q^29 - 4 * q^30 - 10 * q^31 - 11 * q^32 + 2 * q^33 - 6 * q^34 + 3 * q^35 + 17 * q^36 - 16 * q^37 + 10 * q^38 - 12 * q^39 + 9 * q^40 - 4 * q^42 - 2 * q^43 - 5 * q^44 + q^45 + 16 * q^46 - 20 * q^47 - 34 * q^48 + 3 * q^49 - 3 * q^50 - 20 * q^51 + 32 * q^52 - 12 * q^53 + 14 * q^54 + 3 * q^55 + 9 * q^56 - 2 * q^58 + 14 * q^59 + 12 * q^60 + 10 * q^61 + 6 * q^62 + q^63 + 33 * q^64 - 2 * q^65 - 4 * q^66 - 2 * q^67 + 26 * q^68 + 2 * q^69 - 3 * q^70 - 24 * q^71 - 23 * q^72 + 4 * q^73 + 38 * q^74 - 2 * q^75 - 10 * q^76 + 3 * q^77 + 42 * q^78 + 8 * q^79 - 5 * q^80 - 5 * q^81 + 24 * q^82 - 10 * q^83 + 12 * q^84 - 36 * q^86 + 16 * q^87 + 9 * q^88 + 20 * q^89 + 9 * q^90 - 2 * q^91 - 18 * q^92 + 18 * q^93 + 38 * q^94 - 6 * q^95 + 40 * q^96 - 3 * q^98 + q^99

Introduction

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