LMFDB - Embedded newform 3610.2.a.bj.1.4

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			1.4
Root			$0.576411$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.576411 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.576411 q^{6} -4.86419 q^{7} +1.00000 q^{8} -2.66775 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.576411 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.576411 q^{6} -4.86419 q^{7} +1.00000 q^{8} -2.66775 q^{9} +1.00000 q^{10} -5.36907 q^{11} -0.576411 q^{12} +3.85718 q^{13} -4.86419 q^{14} -0.576411 q^{15} +1.00000 q^{16} +1.40209 q^{17} -2.66775 q^{18} +1.00000 q^{20} +2.80377 q^{21} -5.36907 q^{22} +5.33891 q^{23} -0.576411 q^{24} +1.00000 q^{25} +3.85718 q^{26} +3.26695 q^{27} -4.86419 q^{28} +3.63378 q^{29} -0.576411 q^{30} -8.20377 q^{31} +1.00000 q^{32} +3.09479 q^{33} +1.40209 q^{34} -4.86419 q^{35} -2.66775 q^{36} +10.4594 q^{37} -2.22332 q^{39} +1.00000 q^{40} +1.90830 q^{41} +2.80377 q^{42} +1.47864 q^{43} -5.36907 q^{44} -2.66775 q^{45} +5.33891 q^{46} -3.12031 q^{47} -0.576411 q^{48} +16.6603 q^{49} +1.00000 q^{50} -0.808181 q^{51} +3.85718 q^{52} +1.80001 q^{53} +3.26695 q^{54} -5.36907 q^{55} -4.86419 q^{56} +3.63378 q^{58} +7.32507 q^{59} -0.576411 q^{60} +8.11505 q^{61} -8.20377 q^{62} +12.9764 q^{63} +1.00000 q^{64} +3.85718 q^{65} +3.09479 q^{66} -8.44489 q^{67} +1.40209 q^{68} -3.07740 q^{69} -4.86419 q^{70} -6.02641 q^{71} -2.66775 q^{72} -1.27628 q^{73} +10.4594 q^{74} -0.576411 q^{75} +26.1162 q^{77} -2.22332 q^{78} +16.6320 q^{79} +1.00000 q^{80} +6.12015 q^{81} +1.90830 q^{82} +14.4610 q^{83} +2.80377 q^{84} +1.40209 q^{85} +1.47864 q^{86} -2.09455 q^{87} -5.36907 q^{88} -9.60851 q^{89} -2.66775 q^{90} -18.7621 q^{91} +5.33891 q^{92} +4.72874 q^{93} -3.12031 q^{94} -0.576411 q^{96} +6.07912 q^{97} +16.6603 q^{98} +14.3233 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.576411	−0.332791	−0.166395	−	0.986059i	$-0.553213\pi$
$3$	−0.576411	−0.332791	−0.166395	+	0.986059i	$0.553213\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.576411	−0.235319
$7$	−4.86419	−1.83849	−0.919245	−	0.393686i	$-0.871200\pi$
$7$	−4.86419	−1.83849	−0.919245	+	0.393686i	$0.871200\pi$
$8$	1.00000	0.353553
$9$	−2.66775	−0.889250
$10$	1.00000	0.316228
$11$	−5.36907	−1.61884	−0.809418	−	0.587233i	$-0.800217\pi$
$11$	−5.36907	−1.61884	−0.809418	+	0.587233i	$0.800217\pi$
$12$	−0.576411	−0.166395
$13$	3.85718	1.06979	0.534895	−	0.844919i	$-0.320351\pi$
$13$	3.85718	1.06979	0.534895	+	0.844919i	$0.320351\pi$
$14$	−4.86419	−1.30001
$15$	−0.576411	−0.148829
$16$	1.00000	0.250000
$17$	1.40209	0.340058	0.170029	−	0.985439i	$-0.445614\pi$
$17$	1.40209	0.340058	0.170029	+	0.985439i	$0.445614\pi$
$18$	−2.66775	−0.628795
$19$	0	0
$19$	0	0
$20$	1.00000	0.223607
$21$	2.80377	0.611833
$22$	−5.36907	−1.14469
$23$	5.33891	1.11324	0.556620	−	0.830767i	$-0.312098\pi$
$23$	5.33891	1.11324	0.556620	+	0.830767i	$0.312098\pi$
$24$	−0.576411	−0.117659
$25$	1.00000	0.200000
$26$	3.85718	0.756456
$27$	3.26695	0.628725
$28$	−4.86419	−0.919245
$29$	3.63378	0.674776	0.337388	−	0.941366i	$-0.390457\pi$
$29$	3.63378	0.674776	0.337388	+	0.941366i	$0.390457\pi$
$30$	−0.576411	−0.105238
$31$	−8.20377	−1.47344	−0.736721	−	0.676197i	$-0.763627\pi$
$31$	−8.20377	−1.47344	−0.736721	+	0.676197i	$0.763627\pi$
$32$	1.00000	0.176777
$33$	3.09479	0.538734
$34$	1.40209	0.240457
$35$	−4.86419	−0.822198
$36$	−2.66775	−0.444625
$37$	10.4594	1.71951	0.859755	−	0.510706i	$-0.170616\pi$
$37$	10.4594	1.71951	0.859755	+	0.510706i	$0.170616\pi$
$38$	0	0
$39$	−2.22332	−0.356016
$40$	1.00000	0.158114
$41$	1.90830	0.298027	0.149013	−	0.988835i	$-0.452390\pi$
$41$	1.90830	0.298027	0.149013	+	0.988835i	$0.452390\pi$
$42$	2.80377	0.432631
$43$	1.47864	0.225491	0.112745	−	0.993624i	$-0.464036\pi$
$43$	1.47864	0.225491	0.112745	+	0.993624i	$0.464036\pi$
$44$	−5.36907	−0.809418
$45$	−2.66775	−0.397685
$46$	5.33891	0.787179
$47$	−3.12031	−0.455144	−0.227572	−	0.973761i	$-0.573079\pi$
$47$	−3.12031	−0.455144	−0.227572	+	0.973761i	$0.573079\pi$
$48$	−0.576411	−0.0831977
$49$	16.6603	2.38005
$50$	1.00000	0.141421
$51$	−0.808181	−0.113168
$52$	3.85718	0.534895
$53$	1.80001	0.247250	0.123625	−	0.992329i	$-0.460548\pi$
$53$	1.80001	0.247250	0.123625	+	0.992329i	$0.460548\pi$
$54$	3.26695	0.444576
$55$	−5.36907	−0.723965
$56$	−4.86419	−0.650004
$57$	0	0
$58$	3.63378	0.477139
$59$	7.32507	0.953642	0.476821	−	0.879000i	$-0.341789\pi$
$59$	7.32507	0.953642	0.476821	+	0.879000i	$0.341789\pi$
$60$	−0.576411	−0.0744143
$61$	8.11505	1.03903	0.519513	−	0.854463i	$-0.326113\pi$
$61$	8.11505	1.03903	0.519513	+	0.854463i	$0.326113\pi$
$62$	−8.20377	−1.04188
$63$	12.9764	1.63488
$64$	1.00000	0.125000
$65$	3.85718	0.478425
$66$	3.09479	0.380942
$67$	−8.44489	−1.03171	−0.515854	−	0.856677i	$-0.672525\pi$
$67$	−8.44489	−1.03171	−0.515854	+	0.856677i	$0.672525\pi$
$68$	1.40209	0.170029
$69$	−3.07740	−0.370476
$70$	−4.86419	−0.581382
$71$	−6.02641	−0.715203	−0.357601	−	0.933874i	$-0.616405\pi$
$71$	−6.02641	−0.715203	−0.357601	+	0.933874i	$0.616405\pi$
$72$	−2.66775	−0.314397
$73$	−1.27628	−0.149378	−0.0746888	−	0.997207i	$-0.523796\pi$
$73$	−1.27628	−0.149378	−0.0746888	+	0.997207i	$0.523796\pi$
$74$	10.4594	1.21588
$75$	−0.576411	−0.0665582
$76$	0	0
$77$	26.1162	2.97621
$78$	−2.22332	−0.251742
$79$	16.6320	1.87125	0.935623	−	0.353001i	$-0.114839\pi$
$79$	16.6320	1.87125	0.935623	+	0.353001i	$0.114839\pi$
$80$	1.00000	0.111803
$81$	6.12015	0.680016
$82$	1.90830	0.210737
$83$	14.4610	1.58730	0.793649	−	0.608376i	$-0.208179\pi$
$83$	14.4610	1.58730	0.793649	+	0.608376i	$0.208179\pi$
$84$	2.80377	0.305916
$85$	1.40209	0.152078
$86$	1.47864	0.159446
$87$	−2.09455	−0.224559
$88$	−5.36907	−0.572345
$89$	−9.60851	−1.01850	−0.509250	−	0.860619i	$-0.670077\pi$
$89$	−9.60851	−1.01850	−0.509250	+	0.860619i	$0.670077\pi$
$90$	−2.66775	−0.281206
$91$	−18.7621	−1.96680
$92$	5.33891	0.556620
$93$	4.72874	0.490348
$94$	−3.12031	−0.321836
$95$	0	0
$96$	−0.576411	−0.0588297
$97$	6.07912	0.617241	0.308620	−	0.951185i	$-0.400133\pi$
$97$	6.07912	0.617241	0.308620	+	0.951185i	$0.400133\pi$
$98$	16.6603	1.68295
$99$	14.3233	1.43955
$100$	1.00000	0.100000
$101$	1.25568	0.124944	0.0624722	−	0.998047i	$-0.480102\pi$
$101$	1.25568	0.124944	0.0624722	+	0.998047i	$0.480102\pi$
$102$	−0.808181	−0.0800219
$103$	−7.36705	−0.725897	−0.362948	−	0.931809i	$-0.618230\pi$
$103$	−7.36705	−0.725897	−0.362948	+	0.931809i	$0.618230\pi$
$104$	3.85718	0.378228
$105$	2.80377	0.273620
$106$	1.80001	0.174832
$107$	8.73078	0.844036	0.422018	−	0.906587i	$-0.361322\pi$
$107$	8.73078	0.844036	0.422018	+	0.906587i	$0.361322\pi$
$108$	3.26695	0.314363
$109$	−8.12981	−0.778695	−0.389347	−	0.921091i	$-0.627299\pi$
$109$	−8.12981	−0.778695	−0.389347	+	0.921091i	$0.627299\pi$
$110$	−5.36907	−0.511921
$111$	−6.02889	−0.572237
$112$	−4.86419	−0.459623
$113$	4.48210	0.421640	0.210820	−	0.977525i	$-0.432387\pi$
$113$	4.48210	0.421640	0.210820	+	0.977525i	$0.432387\pi$
$114$	0	0
$115$	5.33891	0.497856
$116$	3.63378	0.337388
$117$	−10.2900	−0.951311
$118$	7.32507	0.674327
$119$	−6.82004	−0.625192
$120$	−0.576411	−0.0526189
$121$	17.8269	1.62063
$122$	8.11505	0.734702
$123$	−1.09997	−0.0991806
$124$	−8.20377	−0.736721
$125$	1.00000	0.0894427
$126$	12.9764	1.15603
$127$	0.139183	0.0123505	0.00617524	−	0.999981i	$-0.498034\pi$
$127$	0.139183	0.0123505	0.00617524	+	0.999981i	$0.498034\pi$
$128$	1.00000	0.0883883
$129$	−0.852306	−0.0750413
$130$	3.85718	0.338297
$131$	12.4301	1.08602	0.543011	−	0.839726i	$-0.317284\pi$
$131$	12.4301	1.08602	0.543011	+	0.839726i	$0.317284\pi$
$132$	3.09479	0.269367
$133$	0	0
$134$	−8.44489	−0.729528
$135$	3.26695	0.281174
$136$	1.40209	0.120229
$137$	−14.3816	−1.22870	−0.614352	−	0.789032i	$-0.710582\pi$
$137$	−14.3816	−1.22870	−0.614352	+	0.789032i	$0.710582\pi$
$138$	−3.07740	−0.261966
$139$	17.8511	1.51411	0.757056	−	0.653350i	$-0.226637\pi$
$139$	17.8511	1.51411	0.757056	+	0.653350i	$0.226637\pi$
$140$	−4.86419	−0.411099
$141$	1.79858	0.151468
$142$	−6.02641	−0.505725
$143$	−20.7095	−1.73181
$144$	−2.66775	−0.222313
$145$	3.63378	0.301769
$146$	−1.27628	−0.105626
$147$	−9.60319	−0.792058
$148$	10.4594	0.859755
$149$	−2.88659	−0.236478	−0.118239	−	0.992985i	$-0.537725\pi$
$149$	−2.88659	−0.236478	−0.118239	+	0.992985i	$0.537725\pi$
$150$	−0.576411	−0.0470637
$151$	−2.01805	−0.164226	−0.0821132	−	0.996623i	$-0.526167\pi$
$151$	−2.01805	−0.164226	−0.0821132	+	0.996623i	$0.526167\pi$
$152$	0	0
$153$	−3.74044	−0.302396
$154$	26.1162	2.10450
$155$	−8.20377	−0.658943
$156$	−2.22332	−0.178008
$157$	−11.0394	−0.881040	−0.440520	−	0.897743i	$-0.645206\pi$
$157$	−11.0394	−0.881040	−0.440520	+	0.897743i	$0.645206\pi$
$158$	16.6320	1.32317
$159$	−1.03754	−0.0822827
$160$	1.00000	0.0790569
$161$	−25.9695	−2.04668
$162$	6.12015	0.480844
$163$	−5.92869	−0.464371	−0.232185	−	0.972672i	$-0.574588\pi$
$163$	−5.92869	−0.464371	−0.232185	+	0.972672i	$0.574588\pi$
$164$	1.90830	0.149013
$165$	3.09479	0.240929
$166$	14.4610	1.12239
$167$	−7.22764	−0.559292	−0.279646	−	0.960103i	$-0.590217\pi$
$167$	−7.22764	−0.559292	−0.279646	+	0.960103i	$0.590217\pi$
$168$	2.80377	0.216316
$169$	1.87786	0.144451
$170$	1.40209	0.107536
$171$	0	0
$172$	1.47864	0.112745
$173$	5.15855	0.392197	0.196098	−	0.980584i	$-0.437173\pi$
$173$	5.15855	0.392197	0.196098	+	0.980584i	$0.437173\pi$
$174$	−2.09455	−0.158787
$175$	−4.86419	−0.367698
$176$	−5.36907	−0.404709
$177$	−4.22225	−0.317363
$178$	−9.60851	−0.720188
$179$	−8.18371	−0.611679	−0.305840	−	0.952083i	$-0.598937\pi$
$179$	−8.18371	−0.611679	−0.305840	+	0.952083i	$0.598937\pi$
$180$	−2.66775	−0.198842
$181$	3.43236	0.255125	0.127563	−	0.991831i	$-0.459285\pi$
$181$	3.43236	0.255125	0.127563	+	0.991831i	$0.459285\pi$
$182$	−18.7621	−1.39074
$183$	−4.67760	−0.345778
$184$	5.33891	0.393590
$185$	10.4594	0.768988
$186$	4.72874	0.346728
$187$	−7.52794	−0.550497
$188$	−3.12031	−0.227572
$189$	−15.8911	−1.15591
$190$	0	0
$191$	3.77584	0.273210	0.136605	−	0.990626i	$-0.456381\pi$
$191$	3.77584	0.273210	0.136605	+	0.990626i	$0.456381\pi$
$192$	−0.576411	−0.0415989
$193$	−12.1779	−0.876582	−0.438291	−	0.898833i	$-0.644416\pi$
$193$	−12.1779	−0.876582	−0.438291	+	0.898833i	$0.644416\pi$
$194$	6.07912	0.436455
$195$	−2.22332	−0.159215
$196$	16.6603	1.19002
$197$	7.20236	0.513147	0.256574	−	0.966525i	$-0.417406\pi$
$197$	7.20236	0.513147	0.256574	+	0.966525i	$0.417406\pi$
$198$	14.3233	1.01792
$199$	5.83709	0.413780	0.206890	−	0.978364i	$-0.433666\pi$
$199$	5.83709	0.413780	0.206890	+	0.978364i	$0.433666\pi$
$200$	1.00000	0.0707107
$201$	4.86773	0.343343
$202$	1.25568	0.0883490
$203$	−17.6754	−1.24057
$204$	−0.808181	−0.0565840
$205$	1.90830	0.133282
$206$	−7.36705	−0.513287
$207$	−14.2429	−0.989948
$208$	3.85718	0.267448
$209$	0	0
$210$	2.80377	0.193478
$211$	−10.6710	−0.734619	−0.367309	−	0.930099i	$-0.619721\pi$
$211$	−10.6710	−0.734619	−0.367309	+	0.930099i	$0.619721\pi$
$212$	1.80001	0.123625
$213$	3.47369	0.238013
$214$	8.73078	0.596824
$215$	1.47864	0.100843
$216$	3.26695	0.222288
$217$	39.9047	2.70891
$218$	−8.12981	−0.550620
$219$	0.735663	0.0497115
$220$	−5.36907	−0.361983
$221$	5.40813	0.363790
$222$	−6.02889	−0.404633
$223$	0.0994685	0.00666090	0.00333045	−	0.999994i	$-0.498940\pi$
$223$	0.0994685	0.00666090	0.00333045	+	0.999994i	$0.498940\pi$
$224$	−4.86419	−0.325002
$225$	−2.66775	−0.177850
$226$	4.48210	0.298145
$227$	13.8262	0.917680	0.458840	−	0.888519i	$-0.348265\pi$
$227$	13.8262	0.917680	0.458840	+	0.888519i	$0.348265\pi$
$228$	0	0
$229$	15.5752	1.02924	0.514619	−	0.857419i	$-0.327934\pi$
$229$	15.5752	1.02924	0.514619	+	0.857419i	$0.327934\pi$
$230$	5.33891	0.352037
$231$	−15.0536	−0.990457
$232$	3.63378	0.238569
$233$	−15.2411	−0.998476	−0.499238	−	0.866465i	$-0.666387\pi$
$233$	−15.2411	−0.998476	−0.499238	+	0.866465i	$0.666387\pi$
$234$	−10.2900	−0.672679
$235$	−3.12031	−0.203547
$236$	7.32507	0.476821
$237$	−9.58686	−0.622734
$238$	−6.82004	−0.442078
$239$	16.8233	1.08821	0.544106	−	0.839017i	$-0.316869\pi$
$239$	16.8233	1.08821	0.544106	+	0.839017i	$0.316869\pi$
$240$	−0.576411	−0.0372071
$241$	9.10698	0.586632	0.293316	−	0.956016i	$-0.405241\pi$
$241$	9.10698	0.586632	0.293316	+	0.956016i	$0.405241\pi$
$242$	17.8269	1.14596
$243$	−13.3286	−0.855028
$244$	8.11505	0.519513
$245$	16.6603	1.06439
$246$	−1.09997	−0.0701313
$247$	0	0
$248$	−8.20377	−0.520940
$249$	−8.33546	−0.528238
$250$	1.00000	0.0632456
$251$	16.8058	1.06077	0.530385	−	0.847757i	$-0.322047\pi$
$251$	16.8058	1.06077	0.530385	+	0.847757i	$0.322047\pi$
$252$	12.9764	0.817439
$253$	−28.6650	−1.80215
$254$	0.139183	0.00873311
$255$	−0.808181	−0.0506103
$256$	1.00000	0.0625000
$257$	9.89728	0.617376	0.308688	−	0.951163i	$-0.400110\pi$
$257$	9.89728	0.617376	0.308688	+	0.951163i	$0.400110\pi$
$258$	−0.852306	−0.0530622
$259$	−50.8764	−3.16130
$260$	3.85718	0.239212
$261$	−9.69402	−0.600045
$262$	12.4301	0.767934
$263$	−22.4125	−1.38202	−0.691008	−	0.722847i	$-0.742833\pi$
$263$	−22.4125	−1.38202	−0.691008	+	0.722847i	$0.742833\pi$
$264$	3.09479	0.190471
$265$	1.80001	0.110574
$266$	0	0
$267$	5.53845	0.338948
$268$	−8.44489	−0.515854
$269$	−7.47284	−0.455627	−0.227814	−	0.973705i	$-0.573158\pi$
$269$	−7.47284	−0.455627	−0.227814	+	0.973705i	$0.573158\pi$
$270$	3.26695	0.198820
$271$	−10.6508	−0.646993	−0.323496	−	0.946229i	$-0.604858\pi$
$271$	−10.6508	−0.646993	−0.323496	+	0.946229i	$0.604858\pi$
$272$	1.40209	0.0850144
$273$	10.8147	0.654533
$274$	−14.3816	−0.868825
$275$	−5.36907	−0.323767
$276$	−3.07740	−0.185238
$277$	−2.32634	−0.139776	−0.0698880	−	0.997555i	$-0.522264\pi$
$277$	−2.32634	−0.139776	−0.0698880	+	0.997555i	$0.522264\pi$
$278$	17.8511	1.07064
$279$	21.8856	1.31026
$280$	−4.86419	−0.290691
$281$	17.0731	1.01850	0.509248	−	0.860620i	$-0.329923\pi$
$281$	17.0731	1.01850	0.509248	+	0.860620i	$0.329923\pi$
$282$	1.79858	0.107104
$283$	8.46792	0.503365	0.251683	−	0.967810i	$-0.419016\pi$
$283$	8.46792	0.503365	0.251683	+	0.967810i	$0.419016\pi$
$284$	−6.02641	−0.357601
$285$	0	0
$286$	−20.7095	−1.22458
$287$	−9.28234	−0.547919
$288$	−2.66775	−0.157199
$289$	−15.0341	−0.884361
$290$	3.63378	0.213383
$291$	−3.50407	−0.205412
$292$	−1.27628	−0.0746888
$293$	2.59244	0.151452	0.0757260	−	0.997129i	$-0.475873\pi$
$293$	2.59244	0.151452	0.0757260	+	0.997129i	$0.475873\pi$
$294$	−9.60319	−0.560069
$295$	7.32507	0.426482
$296$	10.4594	0.607939
$297$	−17.5405	−1.01780
$298$	−2.88659	−0.167215
$299$	20.5931	1.19093
$300$	−0.576411	−0.0332791
$301$	−7.19240	−0.414563
$302$	−2.01805	−0.116126
$303$	−0.723785	−0.0415804
$304$	0	0
$305$	8.11505	0.464666
$306$	−3.74044	−0.213826
$307$	4.12168	0.235237	0.117618	−	0.993059i	$-0.462474\pi$
$307$	4.12168	0.235237	0.117618	+	0.993059i	$0.462474\pi$
$308$	26.1162	1.48811
$309$	4.24645	0.241572
$310$	−8.20377	−0.465943
$311$	2.48306	0.140802	0.0704008	−	0.997519i	$-0.477572\pi$
$311$	2.48306	0.140802	0.0704008	+	0.997519i	$0.477572\pi$
$312$	−2.22332	−0.125871
$313$	5.38145	0.304178	0.152089	−	0.988367i	$-0.451400\pi$
$313$	5.38145	0.304178	0.152089	+	0.988367i	$0.451400\pi$
$314$	−11.0394	−0.622989
$315$	12.9764	0.731140
$316$	16.6320	0.935623
$317$	−19.4653	−1.09328	−0.546641	−	0.837367i	$-0.684094\pi$
$317$	−19.4653	−1.09328	−0.546641	+	0.837367i	$0.684094\pi$
$318$	−1.03754	−0.0581826
$319$	−19.5100	−1.09235
$320$	1.00000	0.0559017
$321$	−5.03251	−0.280888
$322$	−25.9695	−1.44722
$323$	0	0
$324$	6.12015	0.340008
$325$	3.85718	0.213958
$326$	−5.92869	−0.328360
$327$	4.68611	0.259143
$328$	1.90830	0.105368
$329$	15.1778	0.836779
$330$	3.09479	0.170363
$331$	18.7102	1.02841	0.514203	−	0.857668i	$-0.328088\pi$
$331$	18.7102	1.02841	0.514203	+	0.857668i	$0.328088\pi$
$332$	14.4610	0.793649
$333$	−27.9030	−1.52907
$334$	−7.22764	−0.395479
$335$	−8.44489	−0.461394
$336$	2.80377	0.152958
$337$	25.0972	1.36713	0.683565	−	0.729890i	$-0.260429\pi$
$337$	25.0972	1.36713	0.683565	+	0.729890i	$0.260429\pi$
$338$	1.87786	0.102142
$339$	−2.58353	−0.140318
$340$	1.40209	0.0760392
$341$	44.0466	2.38526
$342$	0	0
$343$	−46.9896	−2.53720
$344$	1.47864	0.0797231
$345$	−3.07740	−0.165682
$346$	5.15855	0.277325
$347$	22.7535	1.22147	0.610736	−	0.791834i	$-0.290874\pi$
$347$	22.7535	1.22147	0.610736	+	0.791834i	$0.290874\pi$
$348$	−2.09455	−0.112280
$349$	13.1638	0.704642	0.352321	−	0.935879i	$-0.385392\pi$
$349$	13.1638	0.704642	0.352321	+	0.935879i	$0.385392\pi$
$350$	−4.86419	−0.260002
$351$	12.6012	0.672604
$352$	−5.36907	−0.286172
$353$	−12.3056	−0.654962	−0.327481	−	0.944858i	$-0.606200\pi$
$353$	−12.3056	−0.654962	−0.327481	+	0.944858i	$0.606200\pi$
$354$	−4.22225	−0.224410
$355$	−6.02641	−0.319848
$356$	−9.60851	−0.509250
$357$	3.93115	0.208058
$358$	−8.18371	−0.432523
$359$	12.5612	0.662955	0.331477	−	0.943463i	$-0.392453\pi$
$359$	12.5612	0.662955	0.331477	+	0.943463i	$0.392453\pi$
$360$	−2.66775	−0.140603
$361$	0	0
$362$	3.43236	0.180401
$363$	−10.2756	−0.539330
$364$	−18.7621	−0.983399
$365$	−1.27628	−0.0668037
$366$	−4.67760	−0.244502
$367$	2.68451	0.140130	0.0700651	−	0.997542i	$-0.477679\pi$
$367$	2.68451	0.140130	0.0700651	+	0.997542i	$0.477679\pi$
$368$	5.33891	0.278310
$369$	−5.09088	−0.265020
$370$	10.4594	0.543757
$371$	−8.75559	−0.454567
$372$	4.72874	0.245174
$373$	18.5424	0.960088	0.480044	−	0.877244i	$-0.340621\pi$
$373$	18.5424	0.960088	0.480044	+	0.877244i	$0.340621\pi$
$374$	−7.52794	−0.389260
$375$	−0.576411	−0.0297657
$376$	−3.12031	−0.160918
$377$	14.0162	0.721868
$378$	−15.8911	−0.817348
$379$	−11.5855	−0.595108	−0.297554	−	0.954705i	$-0.596171\pi$
$379$	−11.5855	−0.595108	−0.297554	+	0.954705i	$0.596171\pi$
$380$	0	0
$381$	−0.0802265	−0.00411013
$382$	3.77584	0.193189
$383$	−29.0791	−1.48587	−0.742937	−	0.669362i	$-0.766568\pi$
$383$	−29.0791	−1.48587	−0.742937	+	0.669362i	$0.766568\pi$
$384$	−0.576411	−0.0294148
$385$	26.1162	1.33100
$386$	−12.1779	−0.619837
$387$	−3.94465	−0.200518
$388$	6.07912	0.308620
$389$	29.7821	1.51001	0.755007	−	0.655717i	$-0.227634\pi$
$389$	29.7821	1.51001	0.755007	+	0.655717i	$0.227634\pi$
$390$	−2.22332	−0.112582
$391$	7.48565	0.378565
$392$	16.6603	0.841473
$393$	−7.16484	−0.361418
$394$	7.20236	0.362850
$395$	16.6320	0.836847
$396$	14.3233	0.719775
$397$	6.26996	0.314680	0.157340	−	0.987544i	$-0.449708\pi$
$397$	6.26996	0.314680	0.157340	+	0.987544i	$0.449708\pi$
$398$	5.83709	0.292587
$399$	0	0
$400$	1.00000	0.0500000
$401$	−9.90132	−0.494448	−0.247224	−	0.968958i	$-0.579518\pi$
$401$	−9.90132	−0.494448	−0.247224	+	0.968958i	$0.579518\pi$
$402$	4.86773	0.242780
$403$	−31.6435	−1.57627
$404$	1.25568	0.0624722
$405$	6.12015	0.304113
$406$	−17.6754	−0.877215
$407$	−56.1571	−2.78360
$408$	−0.808181	−0.0400109
$409$	30.6587	1.51597	0.757987	−	0.652270i	$-0.226183\pi$
$409$	30.6587	1.51597	0.757987	+	0.652270i	$0.226183\pi$
$410$	1.90830	0.0942444
$411$	8.28971	0.408901
$412$	−7.36705	−0.362948
$413$	−35.6305	−1.75326
$414$	−14.2429	−0.699999
$415$	14.4610	0.709861
$416$	3.85718	0.189114
$417$	−10.2896	−0.503882
$418$	0	0
$419$	17.9296	0.875916	0.437958	−	0.898995i	$-0.355702\pi$
$419$	17.9296	0.875916	0.437958	+	0.898995i	$0.355702\pi$
$420$	2.80377	0.136810
$421$	32.2286	1.57073	0.785363	−	0.619035i	$-0.212476\pi$
$421$	32.2286	1.57073	0.785363	+	0.619035i	$0.212476\pi$
$422$	−10.6710	−0.519454
$423$	8.32422	0.404737
$424$	1.80001	0.0874162
$425$	1.40209	0.0680115
$426$	3.47369	0.168301
$427$	−39.4731	−1.91024
$428$	8.73078	0.422018
$429$	11.9372	0.576332
$430$	1.47864	0.0713065
$431$	1.39091	0.0669979	0.0334990	−	0.999439i	$-0.489335\pi$
$431$	1.39091	0.0669979	0.0334990	+	0.999439i	$0.489335\pi$
$432$	3.26695	0.157181
$433$	−33.2535	−1.59806	−0.799030	−	0.601291i	$-0.794653\pi$
$433$	−33.2535	−1.59806	−0.799030	+	0.601291i	$0.794653\pi$
$434$	39.9047	1.91549
$435$	−2.09455	−0.100426
$436$	−8.12981	−0.389347
$437$	0	0
$438$	0.735663	0.0351513
$439$	36.1138	1.72362	0.861809	−	0.507233i	$-0.169332\pi$
$439$	36.1138	1.72362	0.861809	+	0.507233i	$0.169332\pi$
$440$	−5.36907	−0.255960
$441$	−44.4456	−2.11646
$442$	5.40813	0.257239
$443$	31.9877	1.51978	0.759890	−	0.650052i	$-0.225253\pi$
$443$	31.9877	1.51978	0.759890	+	0.650052i	$0.225253\pi$
$444$	−6.02889	−0.286119
$445$	−9.60851	−0.455487
$446$	0.0994685	0.00470997
$447$	1.66386	0.0786978
$448$	−4.86419	−0.229811
$449$	2.18232	0.102990	0.0514951	−	0.998673i	$-0.483601\pi$
$449$	2.18232	0.102990	0.0514951	+	0.998673i	$0.483601\pi$
$450$	−2.66775	−0.125759
$451$	−10.2458	−0.482456
$452$	4.48210	0.210820
$453$	1.16322	0.0546530
$454$	13.8262	0.648898
$455$	−18.7621	−0.879579
$456$	0	0
$457$	−37.2037	−1.74031	−0.870157	−	0.492774i	$-0.835983\pi$
$457$	−37.2037	−1.74031	−0.870157	+	0.492774i	$0.835983\pi$
$458$	15.5752	0.727781
$459$	4.58057	0.213803
$460$	5.33891	0.248928
$461$	−4.88088	−0.227325	−0.113663	−	0.993519i	$-0.536258\pi$
$461$	−4.88088	−0.227325	−0.113663	+	0.993519i	$0.536258\pi$
$462$	−15.0536	−0.700359
$463$	−20.2227	−0.939827	−0.469913	−	0.882713i	$-0.655715\pi$
$463$	−20.2227	−0.939827	−0.469913	+	0.882713i	$0.655715\pi$
$464$	3.63378	0.168694
$465$	4.72874	0.219290
$466$	−15.2411	−0.706029
$467$	39.0126	1.80529	0.902644	−	0.430389i	$-0.141623\pi$
$467$	39.0126	1.80529	0.902644	+	0.430389i	$0.141623\pi$
$468$	−10.2900	−0.475656
$469$	41.0775	1.89678
$470$	−3.12031	−0.143929
$471$	6.36323	0.293202
$472$	7.32507	0.337164
$473$	−7.93894	−0.365033
$474$	−9.58686	−0.440339
$475$	0	0
$476$	−6.82004	−0.312596
$477$	−4.80198	−0.219867
$478$	16.8233	0.769482
$479$	−31.0896	−1.42052	−0.710259	−	0.703940i	$-0.751422\pi$
$479$	−31.0896	−1.42052	−0.710259	+	0.703940i	$0.751422\pi$
$480$	−0.576411	−0.0263094
$481$	40.3437	1.83952
$482$	9.10698	0.414812
$483$	14.9691	0.681116
$484$	17.8269	0.810314
$485$	6.07912	0.276038
$486$	−13.3286	−0.604596
$487$	27.9741	1.26763	0.633813	−	0.773486i	$-0.281489\pi$
$487$	27.9741	1.26763	0.633813	+	0.773486i	$0.281489\pi$
$488$	8.11505	0.367351
$489$	3.41736	0.154538
$490$	16.6603	0.752637
$491$	2.97331	0.134184	0.0670918	−	0.997747i	$-0.478628\pi$
$491$	2.97331	0.134184	0.0670918	+	0.997747i	$0.478628\pi$
$492$	−1.09997	−0.0495903
$493$	5.09490	0.229463
$494$	0	0
$495$	14.3233	0.643786
$496$	−8.20377	−0.368360
$497$	29.3136	1.31489
$498$	−8.33546	−0.373521
$499$	18.4370	0.825354	0.412677	−	0.910877i	$-0.364594\pi$
$499$	18.4370	0.825354	0.412677	+	0.910877i	$0.364594\pi$
$500$	1.00000	0.0447214
$501$	4.16609	0.186127
$502$	16.8058	0.750078
$503$	3.26889	0.145753	0.0728764	−	0.997341i	$-0.476782\pi$
$503$	3.26889	0.145753	0.0728764	+	0.997341i	$0.476782\pi$
$504$	12.9764	0.578017
$505$	1.25568	0.0558768
$506$	−28.6650	−1.27431
$507$	−1.08242	−0.0480719
$508$	0.139183	0.00617524
$509$	−37.6204	−1.66750	−0.833748	−	0.552145i	$-0.813809\pi$
$509$	−37.6204	−1.66750	−0.833748	+	0.552145i	$0.813809\pi$
$510$	−0.808181	−0.0357869
$511$	6.20808	0.274629
$512$	1.00000	0.0441942
$513$	0	0
$514$	9.89728	0.436550
$515$	−7.36705	−0.324631
$516$	−0.852306	−0.0375207
$517$	16.7532	0.736804
$518$	−50.8764	−2.23538
$519$	−2.97344	−0.130520
$520$	3.85718	0.169149
$521$	−31.4406	−1.37744	−0.688719	−	0.725028i	$-0.741827\pi$
$521$	−31.4406	−1.37744	−0.688719	+	0.725028i	$0.741827\pi$
$522$	−9.69402	−0.424296
$523$	−4.48641	−0.196177	−0.0980886	−	0.995178i	$-0.531273\pi$
$523$	−4.48641	−0.196177	−0.0980886	+	0.995178i	$0.531273\pi$
$524$	12.4301	0.543011
$525$	2.80377	0.122367
$526$	−22.4125	−0.977233
$527$	−11.5025	−0.501055
$528$	3.09479	0.134683
$529$	5.50394	0.239302
$530$	1.80001	0.0781874
$531$	−19.5415	−0.848027
$532$	0	0
$533$	7.36067	0.318826
$534$	5.53845	0.239672
$535$	8.73078	0.377465
$536$	−8.44489	−0.364764
$537$	4.71718	0.203561
$538$	−7.47284	−0.322177
$539$	−89.4504	−3.85290
$540$	3.26695	0.140587
$541$	22.2271	0.955617	0.477809	−	0.878464i	$-0.341431\pi$
$541$	22.2271	0.955617	0.477809	+	0.878464i	$0.341431\pi$
$542$	−10.6508	−0.457493
$543$	−1.97845	−0.0849034
$544$	1.40209	0.0601143
$545$	−8.12981	−0.348243
$546$	10.8147	0.462824
$547$	28.8453	1.23334	0.616668	−	0.787223i	$-0.288482\pi$
$547$	28.8453	1.23334	0.616668	+	0.787223i	$0.288482\pi$
$548$	−14.3816	−0.614352
$549$	−21.6489	−0.923954
$550$	−5.36907	−0.228938
$551$	0	0
$552$	−3.07740	−0.130983
$553$	−80.9012	−3.44027
$554$	−2.32634	−0.0988366
$555$	−6.02889	−0.255912
$556$	17.8511	0.757056
$557$	−28.0311	−1.18772	−0.593858	−	0.804570i	$-0.702396\pi$
$557$	−28.0311	−1.18772	−0.593858	+	0.804570i	$0.702396\pi$
$558$	21.8856	0.926492
$559$	5.70340	0.241228
$560$	−4.86419	−0.205549
$561$	4.33918	0.183200
$562$	17.0731	0.720186
$563$	6.57229	0.276989	0.138494	−	0.990363i	$-0.455774\pi$
$563$	6.57229	0.276989	0.138494	+	0.990363i	$0.455774\pi$
$564$	1.79858	0.0757340
$565$	4.48210	0.188563
$566$	8.46792	0.355933
$567$	−29.7695	−1.25020
$568$	−6.02641	−0.252862
$569$	−3.90032	−0.163510	−0.0817549	−	0.996652i	$-0.526052\pi$
$569$	−3.90032	−0.163510	−0.0817549	+	0.996652i	$0.526052\pi$
$570$	0	0
$571$	18.1559	0.759802	0.379901	−	0.925027i	$-0.375958\pi$
$571$	18.1559	0.759802	0.379901	+	0.925027i	$0.375958\pi$
$572$	−20.7095	−0.865907
$573$	−2.17644	−0.0909219
$574$	−9.28234	−0.387438
$575$	5.33891	0.222648
$576$	−2.66775	−0.111156
$577$	14.0183	0.583590	0.291795	−	0.956481i	$-0.405748\pi$
$577$	14.0183	0.583590	0.291795	+	0.956481i	$0.405748\pi$
$578$	−15.0341	−0.625338
$579$	7.01945	0.291719
$580$	3.63378	0.150884
$581$	−70.3409	−2.91823
$582$	−3.50407	−0.145248
$583$	−9.66438	−0.400258
$584$	−1.27628	−0.0528130
$585$	−10.2900	−0.425439
$586$	2.59244	0.107093
$587$	−7.61132	−0.314153	−0.157076	−	0.987586i	$-0.550207\pi$
$587$	−7.61132	−0.314153	−0.157076	+	0.987586i	$0.550207\pi$
$588$	−9.60319	−0.396029
$589$	0	0
$590$	7.32507	0.301568
$591$	−4.15152	−0.170771
$592$	10.4594	0.429878
$593$	−9.42248	−0.386935	−0.193467	−	0.981107i	$-0.561973\pi$
$593$	−9.42248	−0.386935	−0.193467	+	0.981107i	$0.561973\pi$
$594$	−17.5405	−0.719695
$595$	−6.82004	−0.279595
$596$	−2.88659	−0.118239
$597$	−3.36456	−0.137702
$598$	20.5931	0.842116
$599$	−14.0334	−0.573391	−0.286696	−	0.958022i	$-0.592557\pi$
$599$	−14.0334	−0.573391	−0.286696	+	0.958022i	$0.592557\pi$
$600$	−0.576411	−0.0235319
$601$	13.5720	0.553613	0.276806	−	0.960926i	$-0.410724\pi$
$601$	13.5720	0.553613	0.276806	+	0.960926i	$0.410724\pi$
$602$	−7.19240	−0.293140
$603$	22.5289	0.917446
$604$	−2.01805	−0.0821132
$605$	17.8269	0.724767
$606$	−0.723785	−0.0294018
$607$	−2.07689	−0.0842984	−0.0421492	−	0.999111i	$-0.513420\pi$
$607$	−2.07689	−0.0842984	−0.0421492	+	0.999111i	$0.513420\pi$
$608$	0	0
$609$	10.1883	0.412850
$610$	8.11505	0.328569
$611$	−12.0356	−0.486909
$612$	−3.74044	−0.151198
$613$	−16.5190	−0.667195	−0.333597	−	0.942716i	$-0.608263\pi$
$613$	−16.5190	−0.667195	−0.333597	+	0.942716i	$0.608263\pi$
$614$	4.12168	0.166337
$615$	−1.09997	−0.0443549
$616$	26.1162	1.05225
$617$	22.8815	0.921175	0.460587	−	0.887614i	$-0.347639\pi$
$617$	22.8815	0.921175	0.460587	+	0.887614i	$0.347639\pi$
$618$	4.24645	0.170817
$619$	−13.3303	−0.535789	−0.267895	−	0.963448i	$-0.586328\pi$
$619$	−13.3303	−0.535789	−0.267895	+	0.963448i	$0.586328\pi$
$620$	−8.20377	−0.329471
$621$	17.4420	0.699922
$622$	2.48306	0.0995617
$623$	46.7376	1.87250
$624$	−2.22332	−0.0890041
$625$	1.00000	0.0400000
$626$	5.38145	0.215086
$627$	0	0
$628$	−11.0394	−0.440520
$629$	14.6650	0.584732
$630$	12.9764	0.516994
$631$	8.72721	0.347425	0.173712	−	0.984796i	$-0.444424\pi$
$631$	8.72721	0.347425	0.173712	+	0.984796i	$0.444424\pi$
$632$	16.6320	0.661585
$633$	6.15085	0.244474
$634$	−19.4653	−0.773067
$635$	0.139183	0.00552330
$636$	−1.03754	−0.0411413
$637$	64.2619	2.54615
$638$	−19.5100	−0.772409
$639$	16.0770	0.635994
$640$	1.00000	0.0395285
$641$	0.873909	0.0345173	0.0172587	−	0.999851i	$-0.494506\pi$
$641$	0.873909	0.0345173	0.0172587	+	0.999851i	$0.494506\pi$
$642$	−5.03251	−0.198617
$643$	−19.0083	−0.749615	−0.374807	−	0.927103i	$-0.622291\pi$
$643$	−19.0083	−0.749615	−0.374807	+	0.927103i	$0.622291\pi$
$644$	−25.9695	−1.02334
$645$	−0.852306	−0.0335595
$646$	0	0
$647$	14.4175	0.566810	0.283405	−	0.959000i	$-0.408536\pi$
$647$	14.4175	0.566810	0.283405	+	0.959000i	$0.408536\pi$
$648$	6.12015	0.240422
$649$	−39.3288	−1.54379
$650$	3.85718	0.151291
$651$	−23.0015	−0.901499
$652$	−5.92869	−0.232185
$653$	10.4677	0.409632	0.204816	−	0.978800i	$-0.434340\pi$
$653$	10.4677	0.409632	0.204816	+	0.978800i	$0.434340\pi$
$654$	4.68611	0.183241
$655$	12.4301	0.485684
$656$	1.90830	0.0745067
$657$	3.40481	0.132834
$658$	15.1778	0.591692
$659$	−5.54427	−0.215974	−0.107987	−	0.994152i	$-0.534441\pi$
$659$	−5.54427	−0.215974	−0.107987	+	0.994152i	$0.534441\pi$
$660$	3.09479	0.120465
$661$	−28.8011	−1.12023	−0.560116	−	0.828414i	$-0.689243\pi$
$661$	−28.8011	−1.12023	−0.560116	+	0.828414i	$0.689243\pi$
$662$	18.7102	0.727193
$663$	−3.11730	−0.121066
$664$	14.4610	0.561195
$665$	0	0
$666$	−27.9030	−1.08122
$667$	19.4004	0.751187
$668$	−7.22764	−0.279646
$669$	−0.0573347	−0.00221669
$670$	−8.44489	−0.326255
$671$	−43.5703	−1.68201
$672$	2.80377	0.108158
$673$	−39.9410	−1.53961	−0.769807	−	0.638277i	$-0.779647\pi$
$673$	−39.9410	−1.53961	−0.769807	+	0.638277i	$0.779647\pi$
$674$	25.0972	0.966707
$675$	3.26695	0.125745
$676$	1.87786	0.0722254
$677$	−14.5804	−0.560372	−0.280186	−	0.959946i	$-0.590396\pi$
$677$	−14.5804	−0.560372	−0.280186	+	0.959946i	$0.590396\pi$
$678$	−2.58353	−0.0992198
$679$	−29.5700	−1.13479
$680$	1.40209	0.0537678
$681$	−7.96959	−0.305395
$682$	44.0466	1.68663
$683$	26.6159	1.01843	0.509214	−	0.860640i	$-0.329936\pi$
$683$	26.6159	1.01843	0.509214	+	0.860640i	$0.329936\pi$
$684$	0	0
$685$	−14.3816	−0.549493
$686$	−46.9896	−1.79407
$687$	−8.97770	−0.342521
$688$	1.47864	0.0563727
$689$	6.94297	0.264506
$690$	−3.07740	−0.117155
$691$	37.2496	1.41704	0.708521	−	0.705690i	$-0.249363\pi$
$691$	37.2496	1.41704	0.708521	+	0.705690i	$0.249363\pi$
$692$	5.15855	0.196098
$693$	−69.6714	−2.64660
$694$	22.7535	0.863712
$695$	17.8511	0.677131
$696$	−2.09455	−0.0793937
$697$	2.67562	0.101346
$698$	13.1638	0.498257
$699$	8.78512	0.332284
$700$	−4.86419	−0.183849
$701$	−39.6094	−1.49602	−0.748012	−	0.663685i	$-0.768992\pi$
$701$	−39.6094	−1.49602	−0.748012	+	0.663685i	$0.768992\pi$
$702$	12.6012	0.475603
$703$	0	0
$704$	−5.36907	−0.202354
$705$	1.79858	0.0677385
$706$	−12.3056	−0.463128
$707$	−6.10784	−0.229709
$708$	−4.22225	−0.158682
$709$	−36.6559	−1.37664	−0.688321	−	0.725406i	$-0.741652\pi$
$709$	−36.6559	−1.37664	−0.688321	+	0.725406i	$0.741652\pi$
$710$	−6.02641	−0.226167
$711$	−44.3700	−1.66401
$712$	−9.60851	−0.360094
$713$	−43.7992	−1.64029
$714$	3.93115	0.147119
$715$	−20.7095	−0.774491
$716$	−8.18371	−0.305840
$717$	−9.69715	−0.362147
$718$	12.5612	0.468780
$719$	10.9965	0.410099	0.205049	−	0.978752i	$-0.434265\pi$
$719$	10.9965	0.410099	0.205049	+	0.978752i	$0.434265\pi$
$720$	−2.66775	−0.0994212
$721$	35.8347	1.33455
$722$	0	0
$723$	−5.24936	−0.195226
$724$	3.43236	0.127563
$725$	3.63378	0.134955
$726$	−10.2756	−0.381364
$727$	45.4135	1.68429	0.842147	−	0.539248i	$-0.181291\pi$
$727$	45.4135	1.68429	0.842147	+	0.539248i	$0.181291\pi$
$728$	−18.7621	−0.695368
$729$	−10.6777	−0.395471
$730$	−1.27628	−0.0472374
$731$	2.07320	0.0766799
$732$	−4.67760	−0.172889
$733$	−27.0336	−0.998510	−0.499255	−	0.866455i	$-0.666393\pi$
$733$	−27.0336	−0.998510	−0.499255	+	0.866455i	$0.666393\pi$
$734$	2.68451	0.0990871
$735$	−9.60319	−0.354219
$736$	5.33891	0.196795
$737$	45.3412	1.67017
$738$	−5.09088	−0.187398
$739$	−1.25863	−0.0462995	−0.0231497	−	0.999732i	$-0.507369\pi$
$739$	−1.25863	−0.0462995	−0.0231497	+	0.999732i	$0.507369\pi$
$740$	10.4594	0.384494
$741$	0	0
$742$	−8.75559	−0.321428
$743$	−52.2222	−1.91585	−0.957923	−	0.287025i	$-0.907334\pi$
$743$	−52.2222	−1.91585	−0.957923	+	0.287025i	$0.907334\pi$
$744$	4.72874	0.173364
$745$	−2.88659	−0.105756
$746$	18.5424	0.678885
$747$	−38.5783	−1.41151
$748$	−7.52794	−0.275249
$749$	−42.4681	−1.55175
$750$	−0.576411	−0.0210475
$751$	−1.05791	−0.0386038	−0.0193019	−	0.999814i	$-0.506144\pi$
$751$	−1.05791	−0.0386038	−0.0193019	+	0.999814i	$0.506144\pi$
$752$	−3.12031	−0.113786
$753$	−9.68702	−0.353015
$754$	14.0162	0.510438
$755$	−2.01805	−0.0734442
$756$	−15.8911	−0.577953
$757$	1.85060	0.0672614	0.0336307	−	0.999434i	$-0.489293\pi$
$757$	1.85060	0.0672614	0.0336307	+	0.999434i	$0.489293\pi$
$758$	−11.5855	−0.420805
$759$	16.5228	0.599739
$760$	0	0
$761$	−31.8442	−1.15435	−0.577176	−	0.816620i	$-0.695845\pi$
$761$	−31.8442	−1.15435	−0.577176	+	0.816620i	$0.695845\pi$
$762$	−0.0802265	−0.00290630
$763$	39.5449	1.43162
$764$	3.77584	0.136605
$765$	−3.74044	−0.135236
$766$	−29.0791	−1.05067
$767$	28.2541	1.02020
$768$	−0.576411	−0.0207994
$769$	0.121302	0.00437427	0.00218713	−	0.999998i	$-0.499304\pi$
$769$	0.121302	0.00437427	0.00218713	+	0.999998i	$0.499304\pi$
$770$	26.1162	0.941161
$771$	−5.70490	−0.205457
$772$	−12.1779	−0.438291
$773$	34.8314	1.25280	0.626400	−	0.779502i	$-0.284528\pi$
$773$	34.8314	1.25280	0.626400	+	0.779502i	$0.284528\pi$
$774$	−3.94465	−0.141788
$775$	−8.20377	−0.294688
$776$	6.07912	0.218228
$777$	29.3257	1.05205
$778$	29.7821	1.06774
$779$	0	0
$780$	−2.22332	−0.0796077
$781$	32.3562	1.15780
$782$	7.48565	0.267686
$783$	11.8714	0.424249
$784$	16.6603	0.595011
$785$	−11.0394	−0.394013
$786$	−7.16484	−0.255561
$787$	−19.1725	−0.683427	−0.341713	−	0.939804i	$-0.611007\pi$
$787$	−19.1725	−0.683427	−0.341713	+	0.939804i	$0.611007\pi$
$788$	7.20236	0.256574
$789$	12.9188	0.459922
$790$	16.6320	0.591740
$791$	−21.8018	−0.775181
$792$	14.3233	0.508958
$793$	31.3012	1.11154
$794$	6.26996	0.222513
$795$	−1.03754	−0.0367979
$796$	5.83709	0.206890
$797$	22.4041	0.793593	0.396796	−	0.917907i	$-0.370122\pi$
$797$	22.4041	0.793593	0.396796	+	0.917907i	$0.370122\pi$
$798$	0	0
$799$	−4.37497	−0.154775
$800$	1.00000	0.0353553
$801$	25.6331	0.905702
$802$	−9.90132	−0.349628
$803$	6.85245	0.241818
$804$	4.86773	0.171671
$805$	−25.9695	−0.915303
$806$	−31.6435	−1.11459
$807$	4.30742	0.151629
$808$	1.25568	0.0441745
$809$	45.5946	1.60302	0.801511	−	0.597980i	$-0.204030\pi$
$809$	45.5946	1.60302	0.801511	+	0.597980i	$0.204030\pi$
$810$	6.12015	0.215040
$811$	−37.9093	−1.33117	−0.665587	−	0.746320i	$-0.731819\pi$
$811$	−37.9093	−1.33117	−0.665587	+	0.746320i	$0.731819\pi$
$812$	−17.6754	−0.620284
$813$	6.13926	0.215313
$814$	−56.1571	−1.96831
$815$	−5.92869	−0.207673
$816$	−0.808181	−0.0282920
$817$	0	0
$818$	30.6587	1.07196
$819$	50.0525	1.74898
$820$	1.90830	0.0666408
$821$	55.4809	1.93630	0.968149	−	0.250375i	$-0.0805540\pi$
$821$	55.4809	1.93630	0.968149	+	0.250375i	$0.0805540\pi$
$822$	8.28971	0.289137
$823$	−6.40907	−0.223406	−0.111703	−	0.993742i	$-0.535631\pi$
$823$	−6.40907	−0.223406	−0.111703	+	0.993742i	$0.535631\pi$
$824$	−7.36705	−0.256643
$825$	3.09479	0.107747
$826$	−35.6305	−1.23974
$827$	−4.39245	−0.152740	−0.0763702	−	0.997080i	$-0.524333\pi$
$827$	−4.39245	−0.152740	−0.0763702	+	0.997080i	$0.524333\pi$
$828$	−14.2429	−0.494974
$829$	−50.0939	−1.73983	−0.869916	−	0.493200i	$-0.835827\pi$
$829$	−50.0939	−1.73983	−0.869916	+	0.493200i	$0.835827\pi$
$830$	14.4610	0.501948
$831$	1.34093	0.0465162
$832$	3.85718	0.133724
$833$	23.3593	0.809353
$834$	−10.2896	−0.356299
$835$	−7.22764	−0.250123
$836$	0	0
$837$	−26.8013	−0.926390
$838$	17.9296	0.619366
$839$	−30.2115	−1.04302	−0.521508	−	0.853246i	$-0.674630\pi$
$839$	−30.2115	−1.04302	−0.521508	+	0.853246i	$0.674630\pi$
$840$	2.80377	0.0967392
$841$	−15.7957	−0.544678
$842$	32.2286	1.11067
$843$	−9.84112	−0.338946
$844$	−10.6710	−0.367309
$845$	1.87786	0.0646004
$846$	8.32422	0.286192
$847$	−86.7135	−2.97951
$848$	1.80001	0.0618126
$849$	−4.88100	−0.167515
$850$	1.40209	0.0480914
$851$	55.8416	1.91423
$852$	3.47369	0.119006
$853$	−11.8476	−0.405654	−0.202827	−	0.979215i	$-0.565013\pi$
$853$	−11.8476	−0.405654	−0.202827	+	0.979215i	$0.565013\pi$
$854$	−39.4731	−1.35074
$855$	0	0
$856$	8.73078	0.298412
$857$	−47.6017	−1.62604	−0.813021	−	0.582234i	$-0.802179\pi$
$857$	−47.6017	−1.62604	−0.813021	+	0.582234i	$0.802179\pi$
$858$	11.9372	0.407528
$859$	11.3734	0.388057	0.194028	−	0.980996i	$-0.437845\pi$
$859$	11.3734	0.388057	0.194028	+	0.980996i	$0.437845\pi$
$860$	1.47864	0.0504213
$861$	5.35044	0.182343
$862$	1.39091	0.0473747
$863$	48.8714	1.66360	0.831801	−	0.555073i	$-0.187310\pi$
$863$	48.8714	1.66360	0.831801	+	0.555073i	$0.187310\pi$
$864$	3.26695	0.111144
$865$	5.15855	0.175396
$866$	−33.2535	−1.13000
$867$	8.66584	0.294307
$868$	39.9047	1.35445
$869$	−89.2984	−3.02924
$870$	−2.09455	−0.0710119
$871$	−32.5735	−1.10371
$872$	−8.12981	−0.275310
$873$	−16.2176	−0.548882
$874$	0	0
$875$	−4.86419	−0.164440
$876$	0.735663	0.0248558
$877$	29.4828	0.995564	0.497782	−	0.867302i	$-0.334148\pi$
$877$	29.4828	0.995564	0.497782	+	0.867302i	$0.334148\pi$
$878$	36.1138	1.21878
$879$	−1.49431	−0.0504018
$880$	−5.36907	−0.180991
$881$	−41.7232	−1.40569	−0.702846	−	0.711342i	$-0.748088\pi$
$881$	−41.7232	−1.40569	−0.702846	+	0.711342i	$0.748088\pi$
$882$	−44.4456	−1.49656
$883$	5.92137	0.199270	0.0996350	−	0.995024i	$-0.468232\pi$
$883$	5.92137	0.199270	0.0996350	+	0.995024i	$0.468232\pi$
$884$	5.40813	0.181895
$885$	−4.22225	−0.141929
$886$	31.9877	1.07465
$887$	13.8269	0.464263	0.232132	−	0.972684i	$-0.425430\pi$
$887$	13.8269	0.464263	0.232132	+	0.972684i	$0.425430\pi$
$888$	−6.02889	−0.202316
$889$	−0.677011	−0.0227062
$890$	−9.60851	−0.322078
$891$	−32.8595	−1.10083
$892$	0.0994685	0.00333045
$893$	0	0
$894$	1.66386	0.0556478
$895$	−8.18371	−0.273551
$896$	−4.86419	−0.162501
$897$	−11.8701	−0.396331
$898$	2.18232	0.0728251
$899$	−29.8107	−0.994242
$900$	−2.66775	−0.0889250
$901$	2.52378	0.0840794
$902$	−10.2458	−0.341148
$903$	4.14577	0.137963
$904$	4.48210	0.149072
$905$	3.43236	0.114096
$906$	1.16322	0.0386455
$907$	−8.35598	−0.277456	−0.138728	−	0.990331i	$-0.544301\pi$
$907$	−8.35598	−0.277456	−0.138728	+	0.990331i	$0.544301\pi$
$908$	13.8262	0.458840
$909$	−3.34983	−0.111107
$910$	−18.7621	−0.621956
$911$	−39.5762	−1.31122	−0.655609	−	0.755101i	$-0.727588\pi$
$911$	−39.5762	−1.31122	−0.655609	+	0.755101i	$0.727588\pi$
$912$	0	0
$913$	−77.6420	−2.56958
$914$	−37.2037	−1.23059
$915$	−4.67760	−0.154637
$916$	15.5752	0.514619
$917$	−60.4623	−1.99664
$918$	4.58057	0.151181
$919$	−38.1246	−1.25761	−0.628807	−	0.777561i	$-0.716457\pi$
$919$	−38.1246	−1.25761	−0.628807	+	0.777561i	$0.716457\pi$
$920$	5.33891	0.176019
$921$	−2.37578	−0.0782846
$922$	−4.88088	−0.160743
$923$	−23.2450	−0.765117
$924$	−15.0536	−0.495228
$925$	10.4594	0.343902
$926$	−20.2227	−0.664558
$927$	19.6534	0.645504
$928$	3.63378	0.119285
$929$	38.2798	1.25592	0.627959	−	0.778246i	$-0.283890\pi$
$929$	38.2798	1.25592	0.627959	+	0.778246i	$0.283890\pi$
$930$	4.72874	0.155062
$931$	0	0
$932$	−15.2411	−0.499238
$933$	−1.43126	−0.0468575
$934$	39.0126	1.27653
$935$	−7.52794	−0.246190
$936$	−10.2900	−0.336339
$937$	1.88540	0.0615932	0.0307966	−	0.999526i	$-0.490196\pi$
$937$	1.88540	0.0615932	0.0307966	+	0.999526i	$0.490196\pi$
$938$	41.0775	1.34123
$939$	−3.10193	−0.101228
$940$	−3.12031	−0.101773
$941$	14.7879	0.482072	0.241036	−	0.970516i	$-0.422513\pi$
$941$	14.7879	0.482072	0.241036	+	0.970516i	$0.422513\pi$
$942$	6.36323	0.207325
$943$	10.1883	0.331775
$944$	7.32507	0.238411
$945$	−15.8911	−0.516936
$946$	−7.93894	−0.258117
$947$	−5.68023	−0.184583	−0.0922913	−	0.995732i	$-0.529419\pi$
$947$	−5.68023	−0.184583	−0.0922913	+	0.995732i	$0.529419\pi$
$948$	−9.58686	−0.311367
$949$	−4.92286	−0.159803
$950$	0	0
$951$	11.2200	0.363834
$952$	−6.82004	−0.221039
$953$	12.8763	0.417105	0.208552	−	0.978011i	$-0.433125\pi$
$953$	12.8763	0.417105	0.208552	+	0.978011i	$0.433125\pi$
$954$	−4.80198	−0.155470
$955$	3.77584	0.122183
$956$	16.8233	0.544106
$957$	11.2458	0.363524
$958$	−31.0896	−1.00446
$959$	69.9548	2.25896
$960$	−0.576411	−0.0186036
$961$	36.3019	1.17103
$962$	40.3437	1.30073
$963$	−23.2915	−0.750559
$964$	9.10698	0.293316
$965$	−12.1779	−0.392020
$966$	14.9691	0.481622
$967$	−48.7668	−1.56824	−0.784118	−	0.620612i	$-0.786884\pi$
$967$	−48.7668	−1.56824	−0.784118	+	0.620612i	$0.786884\pi$
$968$	17.8269	0.572979
$969$	0	0
$970$	6.07912	0.195189
$971$	−29.9919	−0.962487	−0.481244	−	0.876587i	$-0.659815\pi$
$971$	−29.9919	−0.962487	−0.481244	+	0.876587i	$0.659815\pi$
$972$	−13.3286	−0.427514
$973$	−86.8311	−2.78368
$974$	27.9741	0.896347
$975$	−2.22332	−0.0712033
$976$	8.11505	0.259756
$977$	53.7029	1.71811	0.859054	−	0.511886i	$-0.171053\pi$
$977$	53.7029	1.71811	0.859054	+	0.511886i	$0.171053\pi$
$978$	3.41736	0.109275
$979$	51.5888	1.64878
$980$	16.6603	0.532194
$981$	21.6883	0.692455
$982$	2.97331	0.0948821
$983$	57.9269	1.84758	0.923791	−	0.382897i	$-0.125074\pi$
$983$	57.9269	1.84758	0.923791	+	0.382897i	$0.125074\pi$
$984$	−1.09997	−0.0350656
$985$	7.20236	0.229486
$986$	5.09490	0.162255
$987$	−8.74864	−0.278472
$988$	0	0
$989$	7.89434	0.251025
$990$	14.3233	0.455226
$991$	6.99064	0.222065	0.111033	−	0.993817i	$-0.464584\pi$
$991$	6.99064	0.222065	0.111033	+	0.993817i	$0.464584\pi$
$992$	−8.20377	−0.260470
$993$	−10.7848	−0.342244
$994$	29.3136	0.929770
$995$	5.83709	0.185048
$996$	−8.33546	−0.264119
$997$	37.9661	1.20240	0.601200	−	0.799099i	$-0.294690\pi$
$997$	37.9661	1.20240	0.601200	+	0.799099i	$0.294690\pi$
$998$	18.4370	0.583613
$999$	34.1703	1.08110

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3610.2.a.bj.1.4		9
19.14	odd	18		190.2.k.d.101.2	✓	18
19.15	odd	18		190.2.k.d.111.2	yes	18
19.18	odd	2		3610.2.a.bi.1.6		9
95.14	odd	18		950.2.l.i.101.2		18
95.33	even	36		950.2.u.g.899.5		36
95.34	odd	18		950.2.l.i.301.2		18
95.52	even	36		950.2.u.g.899.2		36
95.53	even	36		950.2.u.g.149.2		36
95.72	even	36		950.2.u.g.149.5		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.d.101.2	✓	18	19.14	odd	18
190.2.k.d.111.2	yes	18	19.15	odd	18
950.2.l.i.101.2		18	95.14	odd	18
950.2.l.i.301.2		18	95.34	odd	18
950.2.u.g.149.2		36	95.53	even	36
950.2.u.g.149.5		36	95.72	even	36
950.2.u.g.899.2		36	95.52	even	36
950.2.u.g.899.5		36	95.33	even	36
3610.2.a.bi.1.6		9	19.18	odd	2
3610.2.a.bj.1.4		9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.576411 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.576411 q^{6} -4.86419 q^{7} +1.00000 q^{8} -2.66775 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.576411 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.576411 q^{6} -4.86419 q^{7} +1.00000 q^{8} -2.66775 q^{9} +1.00000 q^{10} -5.36907 q^{11} -0.576411 q^{12} +3.85718 q^{13} -4.86419 q^{14} -0.576411 q^{15} +1.00000 q^{16} +1.40209 q^{17} -2.66775 q^{18} +1.00000 q^{20} +2.80377 q^{21} -5.36907 q^{22} +5.33891 q^{23} -0.576411 q^{24} +1.00000 q^{25} +3.85718 q^{26} +3.26695 q^{27} -4.86419 q^{28} +3.63378 q^{29} -0.576411 q^{30} -8.20377 q^{31} +1.00000 q^{32} +3.09479 q^{33} +1.40209 q^{34} -4.86419 q^{35} -2.66775 q^{36} +10.4594 q^{37} -2.22332 q^{39} +1.00000 q^{40} +1.90830 q^{41} +2.80377 q^{42} +1.47864 q^{43} -5.36907 q^{44} -2.66775 q^{45} +5.33891 q^{46} -3.12031 q^{47} -0.576411 q^{48} +16.6603 q^{49} +1.00000 q^{50} -0.808181 q^{51} +3.85718 q^{52} +1.80001 q^{53} +3.26695 q^{54} -5.36907 q^{55} -4.86419 q^{56} +3.63378 q^{58} +7.32507 q^{59} -0.576411 q^{60} +8.11505 q^{61} -8.20377 q^{62} +12.9764 q^{63} +1.00000 q^{64} +3.85718 q^{65} +3.09479 q^{66} -8.44489 q^{67} +1.40209 q^{68} -3.07740 q^{69} -4.86419 q^{70} -6.02641 q^{71} -2.66775 q^{72} -1.27628 q^{73} +10.4594 q^{74} -0.576411 q^{75} +26.1162 q^{77} -2.22332 q^{78} +16.6320 q^{79} +1.00000 q^{80} +6.12015 q^{81} +1.90830 q^{82} +14.4610 q^{83} +2.80377 q^{84} +1.40209 q^{85} +1.47864 q^{86} -2.09455 q^{87} -5.36907 q^{88} -9.60851 q^{89} -2.66775 q^{90} -18.7621 q^{91} +5.33891 q^{92} +4.72874 q^{93} -3.12031 q^{94} -0.576411 q^{96} +6.07912 q^{97} +16.6603 q^{98} +14.3233 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{8} + 21 q^{9}+O(q^{10}) \) 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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