LMFDB - Embedded newform 7381.2.a.v.1.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7381,2,Mod(1,7381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7381, 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("7381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7381 = 11^{2} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7381.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:	$58.9375817319$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	no (minimal twist has level 671)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.32
Character	$\chi$	$=$	7381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0716868 q^{2} +0.156042 q^{3} -1.99486 q^{4} -1.96106 q^{5} +0.0111862 q^{6} -0.846891 q^{7} -0.286379 q^{8} -2.97565 q^{9} +O(q^{10})$	\(q+0.0716868 q^{2} +0.156042 q^{3} -1.99486 q^{4} -1.96106 q^{5} +0.0111862 q^{6} -0.846891 q^{7} -0.286379 q^{8} -2.97565 q^{9} -0.140582 q^{10} -0.311283 q^{12} -4.93802 q^{13} -0.0607109 q^{14} -0.306007 q^{15} +3.96919 q^{16} -1.63877 q^{17} -0.213315 q^{18} +4.70293 q^{19} +3.91203 q^{20} -0.132151 q^{21} -3.54283 q^{23} -0.0446872 q^{24} -1.15426 q^{25} -0.353991 q^{26} -0.932454 q^{27} +1.68943 q^{28} -8.14312 q^{29} -0.0219367 q^{30} +0.555001 q^{31} +0.857296 q^{32} -0.117478 q^{34} +1.66080 q^{35} +5.93601 q^{36} -5.12086 q^{37} +0.337138 q^{38} -0.770540 q^{39} +0.561605 q^{40} -3.33532 q^{41} -0.00947346 q^{42} -7.31942 q^{43} +5.83542 q^{45} -0.253974 q^{46} -6.17008 q^{47} +0.619362 q^{48} -6.28278 q^{49} -0.0827454 q^{50} -0.255717 q^{51} +9.85067 q^{52} -8.15179 q^{53} -0.0668446 q^{54} +0.242532 q^{56} +0.733855 q^{57} -0.583754 q^{58} +3.04444 q^{59} +0.610442 q^{60} +1.00000 q^{61} +0.0397863 q^{62} +2.52005 q^{63} -7.87693 q^{64} +9.68373 q^{65} -12.7415 q^{67} +3.26912 q^{68} -0.552830 q^{69} +0.119057 q^{70} -16.0948 q^{71} +0.852163 q^{72} -2.13972 q^{73} -0.367098 q^{74} -0.180114 q^{75} -9.38169 q^{76} -0.0552375 q^{78} -1.28858 q^{79} -7.78381 q^{80} +8.78145 q^{81} -0.239099 q^{82} +2.17509 q^{83} +0.263622 q^{84} +3.21372 q^{85} -0.524706 q^{86} -1.27067 q^{87} +12.9802 q^{89} +0.418322 q^{90} +4.18197 q^{91} +7.06745 q^{92} +0.0866037 q^{93} -0.442313 q^{94} -9.22270 q^{95} +0.133774 q^{96} -15.2912 q^{97} -0.450392 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9	\( 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9} - 4 q^{10} + 41 q^{12} - q^{13} + 41 q^{14} + 28 q^{15} + 107 q^{16} + 13 q^{17} + 38 q^{18} - q^{19} + 65 q^{20} + q^{21} + 52 q^{23} + 3 q^{24} + 87 q^{25} + 37 q^{26} + 88 q^{27} - q^{28} + 19 q^{29} - 19 q^{30} + 45 q^{31} - 24 q^{32} - 23 q^{34} + 10 q^{35} + 146 q^{36} + 26 q^{37} - 4 q^{38} - 6 q^{39} + 84 q^{40} - 12 q^{41} + 28 q^{42} + 5 q^{43} + 71 q^{45} - 5 q^{46} + 63 q^{47} + 85 q^{48} + 78 q^{49} + 14 q^{50} + 22 q^{51} - 24 q^{52} + 86 q^{53} - 114 q^{54} + 119 q^{56} - 29 q^{57} + q^{58} + 119 q^{59} - 22 q^{60} + 64 q^{61} + 13 q^{62} - 28 q^{63} + 135 q^{64} - 30 q^{65} + 2 q^{67} + 59 q^{68} + 63 q^{69} - 2 q^{70} + 126 q^{71} + 48 q^{72} + 8 q^{73} - 27 q^{74} + 107 q^{75} - 82 q^{76} - 13 q^{78} - 5 q^{79} + 119 q^{80} + 96 q^{81} - 27 q^{82} + 14 q^{83} + 182 q^{84} - 52 q^{85} + 60 q^{86} - 8 q^{87} + 59 q^{89} - 45 q^{90} + 83 q^{91} + 111 q^{92} - 7 q^{93} + 21 q^{94} - 26 q^{95} - 86 q^{96} - 39 q^{97} - 57 q^{98}+O(q^{100}) \) 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9 - 4 * q^10 + 41 * q^12 - q^13 + 41 * q^14 + 28 * q^15 + 107 * q^16 + 13 * q^17 + 38 * q^18 - q^19 + 65 * q^20 + q^21 + 52 * q^23 + 3 * q^24 + 87 * q^25 + 37 * q^26 + 88 * q^27 - q^28 + 19 * q^29 - 19 * q^30 + 45 * q^31 - 24 * q^32 - 23 * q^34 + 10 * q^35 + 146 * q^36 + 26 * q^37 - 4 * q^38 - 6 * q^39 + 84 * q^40 - 12 * q^41 + 28 * q^42 + 5 * q^43 + 71 * q^45 - 5 * q^46 + 63 * q^47 + 85 * q^48 + 78 * q^49 + 14 * q^50 + 22 * q^51 - 24 * q^52 + 86 * q^53 - 114 * q^54 + 119 * q^56 - 29 * q^57 + q^58 + 119 * q^59 - 22 * q^60 + 64 * q^61 + 13 * q^62 - 28 * q^63 + 135 * q^64 - 30 * q^65 + 2 * q^67 + 59 * q^68 + 63 * q^69 - 2 * q^70 + 126 * q^71 + 48 * q^72 + 8 * q^73 - 27 * q^74 + 107 * q^75 - 82 * q^76 - 13 * q^78 - 5 * q^79 + 119 * q^80 + 96 * q^81 - 27 * q^82 + 14 * q^83 + 182 * q^84 - 52 * q^85 + 60 * q^86 - 8 * q^87 + 59 * q^89 - 45 * q^90 + 83 * q^91 + 111 * q^92 - 7 * q^93 + 21 * q^94 - 26 * q^95 - 86 * q^96 - 39 * q^97 - 57 * q^98

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 $

$2$	0.0716868	0.0506902	0.0253451	−	0.999679i	$-0.491932\pi$
$2$	0.0716868	0.0506902	0.0253451	+	0.999679i	$0.491932\pi$
$3$	0.156042	0.0900910	0.0450455	−	0.998985i	$-0.485657\pi$
$3$	0.156042	0.0900910	0.0450455	+	0.998985i	$0.485657\pi$
$4$	−1.99486	−0.997431
$5$	−1.96106	−0.877011	−0.438505	−	0.898729i	$-0.644492\pi$
$5$	−1.96106	−0.877011	−0.438505	+	0.898729i	$0.644492\pi$
$6$	0.0111862	0.00456673
$7$	−0.846891	−0.320095	−0.160047	−	0.987109i	$-0.551165\pi$
$7$	−0.846891	−0.320095	−0.160047	+	0.987109i	$0.551165\pi$
$8$	−0.286379	−0.101250
$9$	−2.97565	−0.991884
$10$	−0.140582	−0.0444559
$11$	0	0
$11$	0	0
$12$	−0.311283	−0.0898595
$13$	−4.93802	−1.36956	−0.684781	−	0.728749i	$-0.740102\pi$
$13$	−4.93802	−1.36956	−0.684781	+	0.728749i	$0.740102\pi$
$14$	−0.0607109	−0.0162257
$15$	−0.306007	−0.0790108
$16$	3.96919	0.992298
$17$	−1.63877	−0.397460	−0.198730	−	0.980054i	$-0.563682\pi$
$17$	−1.63877	−0.397460	−0.198730	+	0.980054i	$0.563682\pi$
$18$	−0.213315	−0.0502788
$19$	4.70293	1.07893	0.539463	−	0.842009i	$-0.318627\pi$
$19$	4.70293	1.07893	0.539463	+	0.842009i	$0.318627\pi$
$20$	3.91203	0.874757
$21$	−0.132151	−0.0288376
$22$	0	0
$23$	−3.54283	−0.738730	−0.369365	−	0.929284i	$-0.620425\pi$
$23$	−3.54283	−0.738730	−0.369365	+	0.929284i	$0.620425\pi$
$24$	−0.0446872	−0.00912173
$25$	−1.15426	−0.230852
$26$	−0.353991	−0.0694233
$27$	−0.932454	−0.179451
$28$	1.68943	0.319272
$29$	−8.14312	−1.51214	−0.756070	−	0.654491i	$-0.772883\pi$
$29$	−8.14312	−1.51214	−0.756070	+	0.654491i	$0.772883\pi$
$30$	−0.0219367	−0.00400507
$31$	0.555001	0.0996812	0.0498406	−	0.998757i	$-0.484129\pi$
$31$	0.555001	0.0996812	0.0498406	+	0.998757i	$0.484129\pi$
$32$	0.857296	0.151550
$33$	0	0
$34$	−0.117478	−0.0201474
$35$	1.66080	0.280726
$36$	5.93601	0.989335
$37$	−5.12086	−0.841865	−0.420932	−	0.907092i	$-0.638297\pi$
$37$	−5.12086	−0.841865	−0.420932	+	0.907092i	$0.638297\pi$
$38$	0.337138	0.0546910
$39$	−0.770540	−0.123385
$40$	0.561605	0.0887975
$41$	−3.33532	−0.520890	−0.260445	−	0.965489i	$-0.583869\pi$
$41$	−3.33532	−0.520890	−0.260445	+	0.965489i	$0.583869\pi$
$42$	−0.00947346	−0.00146179
$43$	−7.31942	−1.11620	−0.558101	−	0.829773i	$-0.688470\pi$
$43$	−7.31942	−1.11620	−0.558101	+	0.829773i	$0.688470\pi$
$44$	0	0
$45$	5.83542	0.869892
$46$	−0.253974	−0.0374464
$47$	−6.17008	−0.899999	−0.450000	−	0.893029i	$-0.648576\pi$
$47$	−6.17008	−0.899999	−0.450000	+	0.893029i	$0.648576\pi$
$48$	0.619362	0.0893971
$49$	−6.28278	−0.897539
$50$	−0.0827454	−0.0117020
$51$	−0.255717	−0.0358076
$52$	9.85067	1.36604
$53$	−8.15179	−1.11973	−0.559867	−	0.828582i	$-0.689148\pi$
$53$	−8.15179	−1.11973	−0.559867	+	0.828582i	$0.689148\pi$
$54$	−0.0668446	−0.00909640
$55$	0	0
$56$	0.242532	0.0324096
$57$	0.733855	0.0972015
$58$	−0.583754	−0.0766507
$59$	3.04444	0.396353	0.198176	−	0.980166i	$-0.436498\pi$
$59$	3.04444	0.396353	0.198176	+	0.980166i	$0.436498\pi$
$60$	0.610442	0.0788078
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	0.0397863	0.00505286
$63$	2.52005	0.317497
$64$	−7.87693	−0.984616
$65$	9.68373	1.20112
$66$	0	0
$67$	−12.7415	−1.55662	−0.778312	−	0.627878i	$-0.783924\pi$
$67$	−12.7415	−1.55662	−0.778312	+	0.627878i	$0.783924\pi$
$68$	3.26912	0.396439
$69$	−0.552830	−0.0665530
$70$	0.119057	0.0142301
$71$	−16.0948	−1.91010	−0.955052	−	0.296440i	$-0.904201\pi$
$71$	−16.0948	−1.91010	−0.955052	+	0.296440i	$0.904201\pi$
$72$	0.852163	0.100428
$73$	−2.13972	−0.250435	−0.125217	−	0.992129i	$-0.539963\pi$
$73$	−2.13972	−0.250435	−0.125217	+	0.992129i	$0.539963\pi$
$74$	−0.367098	−0.0426743
$75$	−0.180114	−0.0207977
$76$	−9.38169	−1.07615
$77$	0	0
$78$	−0.0552375	−0.00625442
$79$	−1.28858	−0.144977	−0.0724884	−	0.997369i	$-0.523094\pi$
$79$	−1.28858	−0.144977	−0.0724884	+	0.997369i	$0.523094\pi$
$80$	−7.78381	−0.870256
$81$	8.78145	0.975717
$82$	−0.239099	−0.0264040
$83$	2.17509	0.238748	0.119374	−	0.992849i	$-0.461911\pi$
$83$	2.17509	0.238748	0.119374	+	0.992849i	$0.461911\pi$
$84$	0.263622	0.0287635
$85$	3.21372	0.348577
$86$	−0.524706	−0.0565805
$87$	−1.27067	−0.136230
$88$	0	0
$89$	12.9802	1.37590	0.687949	−	0.725759i	$-0.258511\pi$
$89$	12.9802	1.37590	0.687949	+	0.725759i	$0.258511\pi$
$90$	0.418322	0.0440950
$91$	4.18197	0.438389
$92$	7.06745	0.736832
$93$	0.0866037	0.00898038
$94$	−0.442313	−0.0456211
$95$	−9.22270	−0.946229
$96$	0.133774	0.0136533
$97$	−15.2912	−1.55258	−0.776292	−	0.630373i	$-0.782902\pi$
$97$	−15.2912	−1.55258	−0.776292	+	0.630373i	$0.782902\pi$
$98$	−0.450392	−0.0454965
$99$	0	0
$100$	2.30259	0.230259
$101$	−1.51168	−0.150418	−0.0752089	−	0.997168i	$-0.523962\pi$
$101$	−1.51168	−0.150418	−0.0752089	+	0.997168i	$0.523962\pi$
$102$	−0.0183316	−0.00181510
$103$	19.1492	1.88682	0.943412	−	0.331622i	$-0.107596\pi$
$103$	19.1492	1.88682	0.943412	+	0.331622i	$0.107596\pi$
$104$	1.41414	0.138668
$105$	0.259155	0.0252909
$106$	−0.584376	−0.0567596
$107$	4.98639	0.482053	0.241026	−	0.970519i	$-0.422516\pi$
$107$	4.98639	0.482053	0.241026	+	0.970519i	$0.422516\pi$
$108$	1.86012	0.178990
$109$	−14.9006	−1.42722	−0.713609	−	0.700544i	$-0.752941\pi$
$109$	−14.9006	−1.42722	−0.713609	+	0.700544i	$0.752941\pi$
$110$	0	0
$111$	−0.799071	−0.0758445
$112$	−3.36147	−0.317629
$113$	−0.321175	−0.0302136	−0.0151068	−	0.999886i	$-0.504809\pi$
$113$	−0.321175	−0.0302136	−0.0151068	+	0.999886i	$0.504809\pi$
$114$	0.0526077	0.00492717
$115$	6.94768	0.647874
$116$	16.2444	1.50825
$117$	14.6938	1.35845
$118$	0.218246	0.0200912
$119$	1.38786	0.127225
$120$	0.0876340	0.00799986
$121$	0	0
$122$	0.0716868	0.00649022
$123$	−0.520451	−0.0469275
$124$	−1.10715	−0.0994251
$125$	12.0688	1.07947
$126$	0.180654	0.0160940
$127$	−11.9926	−1.06417	−0.532085	−	0.846691i	$-0.678591\pi$
$127$	−11.9926	−1.06417	−0.532085	+	0.846691i	$0.678591\pi$
$128$	−2.27926	−0.201460
$129$	−1.14214	−0.100560
$130$	0.694196	0.0608850
$131$	−15.4719	−1.35178	−0.675892	−	0.737001i	$-0.736241\pi$
$131$	−15.4719	−1.35178	−0.675892	+	0.737001i	$0.736241\pi$
$132$	0	0
$133$	−3.98287	−0.345358
$134$	−0.913398	−0.0789056
$135$	1.82859	0.157380
$136$	0.469309	0.0402429
$137$	−0.369088	−0.0315333	−0.0157667	−	0.999876i	$-0.505019\pi$
$137$	−0.369088	−0.0315333	−0.0157667	+	0.999876i	$0.505019\pi$
$138$	−0.0396306	−0.00337358
$139$	14.6253	1.24050	0.620251	−	0.784404i	$-0.287031\pi$
$139$	14.6253	1.24050	0.620251	+	0.784404i	$0.287031\pi$
$140$	−3.31306	−0.280005
$141$	−0.962793	−0.0810818
$142$	−1.15379	−0.0968235
$143$	0	0
$144$	−11.8109	−0.984244
$145$	15.9691	1.32616
$146$	−0.153389	−0.0126946
$147$	−0.980378	−0.0808602
$148$	10.2154	0.839702
$149$	13.5811	1.11260	0.556302	−	0.830980i	$-0.312220\pi$
$149$	13.5811	1.11260	0.556302	+	0.830980i	$0.312220\pi$
$150$	−0.0129118	−0.00105424
$151$	−6.59193	−0.536444	−0.268222	−	0.963357i	$-0.586436\pi$
$151$	−6.59193	−0.536444	−0.268222	+	0.963357i	$0.586436\pi$
$152$	−1.34682	−0.109241
$153$	4.87641	0.394234
$154$	0	0
$155$	−1.08839	−0.0874215
$156$	1.53712	0.123068
$157$	−14.4384	−1.15231	−0.576153	−	0.817342i	$-0.695447\pi$
$157$	−14.4384	−1.15231	−0.576153	+	0.817342i	$0.695447\pi$
$158$	−0.0923743	−0.00734890
$159$	−1.27202	−0.100878
$160$	−1.68121	−0.132911
$161$	3.00039	0.236464
$162$	0.629514	0.0494593
$163$	4.26870	0.334351	0.167175	−	0.985927i	$-0.446535\pi$
$163$	4.26870	0.334351	0.167175	+	0.985927i	$0.446535\pi$
$164$	6.65351	0.519552
$165$	0	0
$166$	0.155926	0.0121022
$167$	−16.9182	−1.30917	−0.654586	−	0.755987i	$-0.727157\pi$
$167$	−16.9182	−1.30917	−0.654586	+	0.755987i	$0.727157\pi$
$168$	0.0378452	0.00291982
$169$	11.3841	0.875697
$170$	0.230381	0.0176694
$171$	−13.9943	−1.07017
$172$	14.6012	1.11333
$173$	18.5670	1.41162	0.705811	−	0.708400i	$-0.250583\pi$
$173$	18.5670	1.41162	0.705811	+	0.708400i	$0.250583\pi$
$174$	−0.0910903	−0.00690554
$175$	0.977534	0.0738946
$176$	0	0
$177$	0.475062	0.0357078
$178$	0.930509	0.0697446
$179$	9.74109	0.728084	0.364042	−	0.931383i	$-0.381397\pi$
$179$	9.74109	0.728084	0.364042	+	0.931383i	$0.381397\pi$
$180$	−11.6408	−0.867657
$181$	−4.27273	−0.317589	−0.158795	−	0.987312i	$-0.550761\pi$
$181$	−4.27273	−0.317589	−0.158795	+	0.987312i	$0.550761\pi$
$182$	0.299792	0.0222220
$183$	0.156042	0.0115350
$184$	1.01459	0.0747966
$185$	10.0423	0.738324
$186$	0.00620834	0.000455217 0
$187$	0	0
$188$	12.3085	0.897686
$189$	0.789686	0.0574412
$190$	−0.661146	−0.0479646
$191$	10.6022	0.767145	0.383572	−	0.923511i	$-0.374694\pi$
$191$	10.6022	0.767145	0.383572	+	0.923511i	$0.374694\pi$
$192$	−1.22913	−0.0887051
$193$	22.5737	1.62489	0.812444	−	0.583040i	$-0.198137\pi$
$193$	22.5737	1.62489	0.812444	+	0.583040i	$0.198137\pi$
$194$	−1.09618	−0.0787008
$195$	1.51107	0.108210
$196$	12.5333	0.895233
$197$	20.3056	1.44671	0.723356	−	0.690475i	$-0.242599\pi$
$197$	20.3056	1.44671	0.723356	+	0.690475i	$0.242599\pi$
$198$	0	0
$199$	14.4421	1.02377	0.511887	−	0.859053i	$-0.328946\pi$
$199$	14.4421	1.02377	0.511887	+	0.859053i	$0.328946\pi$
$200$	0.330556	0.0233739
$201$	−1.98821	−0.140238
$202$	−0.108368	−0.00762472
$203$	6.89633	0.484028
$204$	0.510121	0.0357156
$205$	6.54075	0.456826
$206$	1.37274	0.0956435
$207$	10.5422	0.732735
$208$	−19.6000	−1.35901
$209$	0	0
$210$	0.0185780	0.00128200
$211$	−23.4320	−1.61313	−0.806563	−	0.591147i	$-0.798675\pi$
$211$	−23.4320	−1.61313	−0.806563	+	0.591147i	$0.798675\pi$
$212$	16.2617	1.11686
$213$	−2.51147	−0.172083
$214$	0.357458	0.0244354
$215$	14.3538	0.978920
$216$	0.267035	0.0181694
$217$	−0.470026	−0.0319074
$218$	−1.06818	−0.0723460
$219$	−0.333886	−0.0225619
$220$	0	0
$221$	8.09229	0.544346
$222$	−0.0572828	−0.00384457
$223$	−3.58251	−0.239903	−0.119951	−	0.992780i	$-0.538274\pi$
$223$	−3.58251	−0.239903	−0.119951	+	0.992780i	$0.538274\pi$
$224$	−0.726036	−0.0485103
$225$	3.43468	0.228979
$226$	−0.0230240	−0.00153153
$227$	−13.5455	−0.899045	−0.449523	−	0.893269i	$-0.648406\pi$
$227$	−13.5455	−0.899045	−0.449523	+	0.893269i	$0.648406\pi$
$228$	−1.46394	−0.0969517
$229$	27.5255	1.81894	0.909469	−	0.415772i	$-0.136489\pi$
$229$	27.5255	1.81894	0.909469	+	0.415772i	$0.136489\pi$
$230$	0.498057	0.0328409
$231$	0	0
$232$	2.33202	0.153104
$233$	−8.90210	−0.583196	−0.291598	−	0.956541i	$-0.594187\pi$
$233$	−8.90210	−0.583196	−0.291598	+	0.956541i	$0.594187\pi$
$234$	1.05335	0.0688599
$235$	12.0999	0.789309
$236$	−6.07324	−0.395334
$237$	−0.201073	−0.0130611
$238$	0.0994912	0.00644906
$239$	10.8453	0.701524	0.350762	−	0.936465i	$-0.385923\pi$
$239$	10.8453	0.701524	0.350762	+	0.936465i	$0.385923\pi$
$240$	−1.21460	−0.0784022
$241$	3.89833	0.251114	0.125557	−	0.992086i	$-0.459928\pi$
$241$	3.89833	0.251114	0.125557	+	0.992086i	$0.459928\pi$
$242$	0	0
$243$	4.16764	0.267354
$244$	−1.99486	−0.127708
$245$	12.3209	0.787152
$246$	−0.0373095	−0.00237877
$247$	−23.2232	−1.47765
$248$	−0.158941	−0.0100927
$249$	0.339406	0.0215090
$250$	0.865177	0.0547186
$251$	−2.50172	−0.157907	−0.0789537	−	0.996878i	$-0.525158\pi$
$251$	−2.50172	−0.157907	−0.0789537	+	0.996878i	$0.525158\pi$
$252$	−5.02715	−0.316681
$253$	0	0
$254$	−0.859711	−0.0539431
$255$	0.501476	0.0314036
$256$	15.5905	0.974404
$257$	11.9582	0.745934	0.372967	−	0.927845i	$-0.378341\pi$
$257$	11.9582	0.745934	0.372967	+	0.927845i	$0.378341\pi$
$258$	−0.0818763	−0.00509739
$259$	4.33681	0.269476
$260$	−19.3177	−1.19803
$261$	24.2311	1.49987
$262$	−1.10913	−0.0685222
$263$	−14.0670	−0.867409	−0.433705	−	0.901055i	$-0.642794\pi$
$263$	−14.0670	−0.867409	−0.433705	+	0.901055i	$0.642794\pi$
$264$	0	0
$265$	15.9861	0.982019
$266$	−0.285519	−0.0175063
$267$	2.02546	0.123956
$268$	25.4176	1.55262
$269$	22.7014	1.38413	0.692065	−	0.721836i	$-0.256701\pi$
$269$	22.7014	1.38413	0.692065	+	0.721836i	$0.256701\pi$
$270$	0.131086	0.00797764
$271$	−5.05581	−0.307119	−0.153559	−	0.988139i	$-0.549074\pi$
$271$	−5.05581	−0.307119	−0.153559	+	0.988139i	$0.549074\pi$
$272$	−6.50460	−0.394399
$273$	0.652563	0.0394949
$274$	−0.0264588	−0.00159843
$275$	0	0
$276$	1.10282	0.0663820
$277$	−27.7358	−1.66648	−0.833242	−	0.552909i	$-0.813518\pi$
$277$	−27.7358	−1.66648	−0.833242	+	0.552909i	$0.813518\pi$
$278$	1.04844	0.0628813
$279$	−1.65149	−0.0988722
$280$	−0.475618	−0.0284236
$281$	−17.3498	−1.03501	−0.517503	−	0.855682i	$-0.673138\pi$
$281$	−17.3498	−1.03501	−0.517503	+	0.855682i	$0.673138\pi$
$282$	−0.0690196	−0.00411006
$283$	−1.96477	−0.116793	−0.0583967	−	0.998293i	$-0.518599\pi$
$283$	−1.96477	−0.116793	−0.0583967	+	0.998293i	$0.518599\pi$
$284$	32.1069	1.90520
$285$	−1.43913	−0.0852467
$286$	0	0
$287$	2.82465	0.166734
$288$	−2.55101	−0.150320
$289$	−14.3144	−0.842025
$290$	1.14477	0.0672234
$291$	−2.38607	−0.139874
$292$	4.26844	0.249791
$293$	−26.5349	−1.55019	−0.775093	−	0.631848i	$-0.782297\pi$
$293$	−26.5349	−1.55019	−0.775093	+	0.631848i	$0.782297\pi$
$294$	−0.0702802	−0.00409882
$295$	−5.97032	−0.347605
$296$	1.46651	0.0852390
$297$	0	0
$298$	0.973584	0.0563982
$299$	17.4946	1.01174
$300$	0.359302	0.0207443
$301$	6.19875	0.357290
$302$	−0.472555	−0.0271925
$303$	−0.235886	−0.0135513
$304$	18.6668	1.07062
$305$	−1.96106	−0.112290
$306$	0.349574	0.0199838
$307$	9.68313	0.552645	0.276323	−	0.961065i	$-0.410884\pi$
$307$	9.68313	0.552645	0.276323	+	0.961065i	$0.410884\pi$
$308$	0	0
$309$	2.98808	0.169986
$310$	−0.0780231	−0.00443141
$311$	15.7364	0.892331	0.446166	−	0.894950i	$-0.352789\pi$
$311$	15.7364	0.892331	0.446166	+	0.894950i	$0.352789\pi$
$312$	0.220666	0.0124928
$313$	10.0770	0.569588	0.284794	−	0.958589i	$-0.408075\pi$
$313$	10.0770	0.569588	0.284794	+	0.958589i	$0.408075\pi$
$314$	−1.03504	−0.0584106
$315$	−4.94196	−0.278448
$316$	2.57054	0.144604
$317$	−30.1924	−1.69577	−0.847887	−	0.530177i	$-0.822126\pi$
$317$	−30.1924	−1.69577	−0.847887	+	0.530177i	$0.822126\pi$
$318$	−0.0911873	−0.00511353
$319$	0	0
$320$	15.4471	0.863519
$321$	0.778088	0.0434286
$322$	0.215088	0.0119864
$323$	−7.70702	−0.428830
$324$	−17.5178	−0.973210
$325$	5.69977	0.316167
$326$	0.306010	0.0169483
$327$	−2.32512	−0.128580
$328$	0.955166	0.0527402
$329$	5.22539	0.288085
$330$	0	0
$331$	−22.2692	−1.22403	−0.612013	−	0.790848i	$-0.709640\pi$
$331$	−22.2692	−1.22403	−0.612013	+	0.790848i	$0.709640\pi$
$332$	−4.33901	−0.238134
$333$	15.2379	0.835032
$334$	−1.21281	−0.0663622
$335$	24.9868	1.36518
$336$	−0.524532	−0.0286155
$337$	−8.07402	−0.439820	−0.219910	−	0.975520i	$-0.570576\pi$
$337$	−8.07402	−0.439820	−0.219910	+	0.975520i	$0.570576\pi$
$338$	0.816087	0.0443893
$339$	−0.0501169	−0.00272197
$340$	−6.41093	−0.347681
$341$	0	0
$342$	−1.00320	−0.0542471
$343$	11.2491	0.607392
$344$	2.09613	0.113016
$345$	1.08413	0.0583677
$346$	1.33101	0.0715554
$347$	−16.2986	−0.874955	−0.437477	−	0.899229i	$-0.644128\pi$
$347$	−16.2986	−0.874955	−0.437477	+	0.899229i	$0.644128\pi$
$348$	2.53481	0.135880
$349$	5.96195	0.319136	0.159568	−	0.987187i	$-0.448990\pi$
$349$	5.96195	0.319136	0.159568	+	0.987187i	$0.448990\pi$
$350$	0.0700763	0.00374573
$351$	4.60448	0.245769
$352$	0	0
$353$	6.29795	0.335206	0.167603	−	0.985855i	$-0.446397\pi$
$353$	6.29795	0.335206	0.167603	+	0.985855i	$0.446397\pi$
$354$	0.0340556	0.00181004
$355$	31.5628	1.67518
$356$	−25.8937	−1.37236
$357$	0.216565	0.0114618
$358$	0.698308	0.0369067
$359$	−30.2083	−1.59433	−0.797167	−	0.603758i	$-0.793669\pi$
$359$	−30.2083	−1.59433	−0.797167	+	0.603758i	$0.793669\pi$
$360$	−1.67114	−0.0880768
$361$	3.11753	0.164080
$362$	−0.306298	−0.0160987
$363$	0	0
$364$	−8.34244	−0.437263
$365$	4.19610	0.219634
$366$	0.0111862	0.000584710 0
$367$	−23.3911	−1.22100	−0.610502	−	0.792015i	$-0.709032\pi$
$367$	−23.3911	−1.22100	−0.610502	+	0.792015i	$0.709032\pi$
$368$	−14.0622	−0.733041
$369$	9.92476	0.516662
$370$	0.719900	0.0374258
$371$	6.90367	0.358421
$372$	−0.172762	−0.00895731
$373$	−35.9555	−1.86171	−0.930853	−	0.365393i	$-0.880935\pi$
$373$	−35.9555	−1.86171	−0.930853	+	0.365393i	$0.880935\pi$
$374$	0	0
$375$	1.88325	0.0972506
$376$	1.76698	0.0911251
$377$	40.2109	2.07097
$378$	0.0566101	0.00291171
$379$	20.8768	1.07237	0.536184	−	0.844101i	$-0.319865\pi$
$379$	20.8768	1.07237	0.536184	+	0.844101i	$0.319865\pi$
$380$	18.3980	0.943798
$381$	−1.87135	−0.0958722
$382$	0.760034	0.0388867
$383$	−4.08060	−0.208509	−0.104254	−	0.994551i	$-0.533246\pi$
$383$	−4.08060	−0.208509	−0.104254	+	0.994551i	$0.533246\pi$
$384$	−0.355661	−0.0181498
$385$	0	0
$386$	1.61823	0.0823659
$387$	21.7800	1.10714
$388$	30.5038	1.54859
$389$	4.99293	0.253151	0.126576	−	0.991957i	$-0.459601\pi$
$389$	4.99293	0.253151	0.126576	+	0.991957i	$0.459601\pi$
$390$	0.108324	0.00548519
$391$	5.80588	0.293616
$392$	1.79925	0.0908760
$393$	−2.41427	−0.121784
$394$	1.45564	0.0733341
$395$	2.52698	0.127146
$396$	0	0
$397$	13.9218	0.698714	0.349357	−	0.936990i	$-0.386400\pi$
$397$	13.9218	0.698714	0.349357	+	0.936990i	$0.386400\pi$
$398$	1.03531	0.0518954
$399$	−0.621495	−0.0311137
$400$	−4.58149	−0.229074
$401$	−21.6943	−1.08336	−0.541681	−	0.840584i	$-0.682212\pi$
$401$	−21.6943	−1.08336	−0.541681	+	0.840584i	$0.682212\pi$
$402$	−0.142529	−0.00710869
$403$	−2.74061	−0.136519
$404$	3.01559	0.150031
$405$	−17.2209	−0.855714
$406$	0.494376	0.0245355
$407$	0	0
$408$	0.0732321	0.00362553
$409$	5.41535	0.267772	0.133886	−	0.990997i	$-0.457254\pi$
$409$	5.41535	0.267772	0.133886	+	0.990997i	$0.457254\pi$
$410$	0.468886	0.0231566
$411$	−0.0575934	−0.00284087
$412$	−38.1999	−1.88198
$413$	−2.57831	−0.126870
$414$	0.755738	0.0371425
$415$	−4.26548	−0.209384
$416$	−4.23335	−0.207557
$417$	2.28216	0.111758
$418$	0	0
$419$	32.5685	1.59108	0.795538	−	0.605904i	$-0.207188\pi$
$419$	32.5685	1.59108	0.795538	+	0.605904i	$0.207188\pi$
$420$	−0.516978	−0.0252259
$421$	2.24582	0.109455	0.0547274	−	0.998501i	$-0.482571\pi$
$421$	2.24582	0.109455	0.0547274	+	0.998501i	$0.482571\pi$
$422$	−1.67977	−0.0817698
$423$	18.3600	0.892694
$424$	2.33450	0.113373
$425$	1.89157	0.0917547
$426$	−0.180039	−0.00872293
$427$	−0.846891	−0.0409839
$428$	−9.94716	−0.480814
$429$	0	0
$430$	1.02898	0.0496217
$431$	−8.09992	−0.390159	−0.195080	−	0.980787i	$-0.562497\pi$
$431$	−8.09992	−0.390159	−0.195080	+	0.980787i	$0.562497\pi$
$432$	−3.70109	−0.178069
$433$	21.7964	1.04747	0.523734	−	0.851882i	$-0.324538\pi$
$433$	21.7964	1.04747	0.523734	+	0.851882i	$0.324538\pi$
$434$	−0.0336946	−0.00161739
$435$	2.49185	0.119475
$436$	29.7246	1.42355
$437$	−16.6617	−0.797035
$438$	−0.0239352	−0.00114367
$439$	−14.2276	−0.679046	−0.339523	−	0.940598i	$-0.610266\pi$
$439$	−14.2276	−0.679046	−0.339523	+	0.940598i	$0.610266\pi$
$440$	0	0
$441$	18.6953	0.890255
$442$	0.580110	0.0275930
$443$	−30.6250	−1.45504	−0.727518	−	0.686088i	$-0.759326\pi$
$443$	−30.6250	−1.45504	−0.727518	+	0.686088i	$0.759326\pi$
$444$	1.59404	0.0756496
$445$	−25.4549	−1.20668
$446$	−0.256819	−0.0121607
$447$	2.11922	0.100236
$448$	6.67090	0.315170
$449$	31.4403	1.48376	0.741880	−	0.670533i	$-0.233934\pi$
$449$	31.4403	1.48376	0.741880	+	0.670533i	$0.233934\pi$
$450$	0.246221	0.0116070
$451$	0	0
$452$	0.640700	0.0301360
$453$	−1.02862	−0.0483288
$454$	−0.971032	−0.0455728
$455$	−8.20106	−0.384472
$456$	−0.210161	−0.00984167
$457$	16.3816	0.766300	0.383150	−	0.923686i	$-0.374839\pi$
$457$	16.3816	0.766300	0.383150	+	0.923686i	$0.374839\pi$
$458$	1.97322	0.0922023
$459$	1.52808	0.0713246
$460$	−13.8597	−0.646210
$461$	−20.3252	−0.946638	−0.473319	−	0.880891i	$-0.656944\pi$
$461$	−20.3252	−0.946638	−0.473319	+	0.880891i	$0.656944\pi$
$462$	0	0
$463$	−8.00794	−0.372160	−0.186080	−	0.982535i	$-0.559578\pi$
$463$	−8.00794	−0.372160	−0.186080	+	0.982535i	$0.559578\pi$
$464$	−32.3216	−1.50049
$465$	−0.169835	−0.00787589
$466$	−0.638163	−0.0295623
$467$	−10.6675	−0.493632	−0.246816	−	0.969062i	$-0.579384\pi$
$467$	−10.6675	−0.493632	−0.246816	+	0.969062i	$0.579384\pi$
$468$	−29.3121	−1.35495
$469$	10.7907	0.498267
$470$	0.867401	0.0400102
$471$	−2.25299	−0.103812
$472$	−0.871864	−0.0401308
$473$	0	0
$474$	−0.0144143	−0.000662070 0
$475$	−5.42841	−0.249073
$476$	−2.76859	−0.126898
$477$	24.2569	1.11065
$478$	0.777464	0.0355604
$479$	−5.34536	−0.244236	−0.122118	−	0.992516i	$-0.538969\pi$
$479$	−5.34536	−0.244236	−0.122118	+	0.992516i	$0.538969\pi$
$480$	−0.262339	−0.0119741
$481$	25.2869	1.15299
$482$	0.279459	0.0127290
$483$	0.468187	0.0213032
$484$	0	0
$485$	29.9868	1.36163
$486$	0.298765	0.0135522
$487$	−16.3604	−0.741361	−0.370681	−	0.928760i	$-0.620876\pi$
$487$	−16.3604	−0.741361	−0.370681	+	0.928760i	$0.620876\pi$
$488$	−0.286379	−0.0129638
$489$	0.666098	0.0301220
$490$	0.883244	0.0399009
$491$	3.91391	0.176632	0.0883161	−	0.996092i	$-0.471851\pi$
$491$	3.91391	0.176632	0.0883161	+	0.996092i	$0.471851\pi$
$492$	1.03823	0.0468069
$493$	13.3447	0.601015
$494$	−1.66479	−0.0749026
$495$	0	0
$496$	2.20291	0.0989135
$497$	13.6305	0.611414
$498$	0.0243310	0.00109030
$499$	−9.70632	−0.434515	−0.217257	−	0.976114i	$-0.569711\pi$
$499$	−9.70632	−0.434515	−0.217257	+	0.976114i	$0.569711\pi$
$500$	−24.0757	−1.07670
$501$	−2.63996	−0.117945
$502$	−0.179341	−0.00800436
$503$	−36.1257	−1.61076	−0.805382	−	0.592756i	$-0.798040\pi$
$503$	−36.1257	−1.61076	−0.805382	+	0.592756i	$0.798040\pi$
$504$	−0.721689	−0.0321466
$505$	2.96449	0.131918
$506$	0	0
$507$	1.77639	0.0788925
$508$	23.9236	1.06144
$509$	6.90750	0.306169	0.153085	−	0.988213i	$-0.451079\pi$
$509$	6.90750	0.306169	0.153085	+	0.988213i	$0.451079\pi$
$510$	0.0359492	0.00159186
$511$	1.81211	0.0801628
$512$	5.67616	0.250853
$513$	−4.38526	−0.193614
$514$	0.857247	0.0378115
$515$	−37.5526	−1.65477
$516$	2.27841	0.100301
$517$	0	0
$518$	0.310892	0.0136598
$519$	2.89723	0.127174
$520$	−2.77322	−0.121614
$521$	26.3028	1.15234	0.576172	−	0.817328i	$-0.304546\pi$
$521$	26.3028	1.15234	0.576172	+	0.817328i	$0.304546\pi$
$522$	1.73705	0.0760285
$523$	25.3425	1.10815	0.554075	−	0.832467i	$-0.313072\pi$
$523$	25.3425	1.10815	0.554075	+	0.832467i	$0.313072\pi$
$524$	30.8642	1.34831
$525$	0.152537	0.00665724
$526$	−1.00842	−0.0439692
$527$	−0.909520	−0.0396193
$528$	0	0
$529$	−10.4484	−0.454278
$530$	1.14599	0.0497788
$531$	−9.05920	−0.393136
$532$	7.94526	0.344471
$533$	16.4699	0.713391
$534$	0.145199	0.00628336
$535$	−9.77859	−0.422765
$536$	3.64890	0.157608
$537$	1.52002	0.0655938
$538$	1.62739	0.0701618
$539$	0	0
$540$	−3.64779	−0.156976
$541$	43.9319	1.88878	0.944391	−	0.328825i	$-0.106653\pi$
$541$	43.9319	1.88878	0.944391	+	0.328825i	$0.106653\pi$
$542$	−0.362435	−0.0155679
$543$	−0.666726	−0.0286119
$544$	−1.40491	−0.0602351
$545$	29.2209	1.25169
$546$	0.0467802	0.00200201
$547$	11.4769	0.490717	0.245359	−	0.969432i	$-0.421094\pi$
$547$	11.4769	0.490717	0.245359	+	0.969432i	$0.421094\pi$
$548$	0.736280	0.0314523
$549$	−2.97565	−0.126998
$550$	0	0
$551$	−38.2965	−1.63149
$552$	0.158319	0.00673850
$553$	1.09129	0.0464063
$554$	−1.98829	−0.0844744
$555$	1.56702	0.0665164
$556$	−29.1754	−1.23731
$557$	−15.3352	−0.649773	−0.324887	−	0.945753i	$-0.605326\pi$
$557$	−15.3352	−0.649773	−0.324887	+	0.945753i	$0.605326\pi$
$558$	−0.118390	−0.00501185
$559$	36.1435	1.52871
$560$	6.59203	0.278564
$561$	0	0
$562$	−1.24376	−0.0524646
$563$	18.3000	0.771252	0.385626	−	0.922655i	$-0.373985\pi$
$563$	18.3000	0.771252	0.385626	+	0.922655i	$0.373985\pi$
$564$	1.92064	0.0808735
$565$	0.629842	0.0264977
$566$	−0.140848	−0.00592029
$567$	−7.43693	−0.312322
$568$	4.60921	0.193398
$569$	−25.2040	−1.05660	−0.528302	−	0.849056i	$-0.677171\pi$
$569$	−25.2040	−1.05660	−0.528302	+	0.849056i	$0.677171\pi$
$570$	−0.103167	−0.00432118
$571$	−23.9750	−1.00332	−0.501662	−	0.865064i	$-0.667278\pi$
$571$	−23.9750	−1.00332	−0.501662	+	0.865064i	$0.667278\pi$
$572$	0	0
$573$	1.65438	0.0691129
$574$	0.202490	0.00845179
$575$	4.08935	0.170538
$576$	23.4390	0.976624
$577$	4.24625	0.176774	0.0883868	−	0.996086i	$-0.471829\pi$
$577$	4.24625	0.176774	0.0883868	+	0.996086i	$0.471829\pi$
$578$	−1.02616	−0.0426824
$579$	3.52244	0.146388
$580$	−31.8561	−1.32275
$581$	−1.84207	−0.0764218
$582$	−0.171050	−0.00709024
$583$	0	0
$584$	0.612769	0.0253566
$585$	−28.8154	−1.19137
$586$	−1.90220	−0.0785792
$587$	23.7825	0.981608	0.490804	−	0.871270i	$-0.336703\pi$
$587$	23.7825	0.981608	0.490804	+	0.871270i	$0.336703\pi$
$588$	1.95572	0.0806525
$589$	2.61013	0.107549
$590$	−0.427993	−0.0176202
$591$	3.16853	0.130336
$592$	−20.3257	−0.835381
$593$	36.0502	1.48040	0.740201	−	0.672385i	$-0.234730\pi$
$593$	36.0502	1.48040	0.740201	+	0.672385i	$0.234730\pi$
$594$	0	0
$595$	−2.72167	−0.111578
$596$	−27.0924	−1.10975
$597$	2.25358	0.0922329
$598$	1.25413	0.0512851
$599$	18.4521	0.753933	0.376966	−	0.926227i	$-0.376967\pi$
$599$	18.4521	0.753933	0.376966	+	0.926227i	$0.376967\pi$
$600$	0.0515807	0.00210577
$601$	39.5402	1.61288	0.806440	−	0.591317i	$-0.201392\pi$
$601$	39.5402	1.61288	0.806440	+	0.591317i	$0.201392\pi$
$602$	0.444369	0.0181111
$603$	37.9143	1.54399
$604$	13.1500	0.535065
$605$	0	0
$606$	−0.0169099	−0.000686918 0
$607$	−36.0568	−1.46350	−0.731750	−	0.681573i	$-0.761296\pi$
$607$	−36.0568	−1.46350	−0.731750	+	0.681573i	$0.761296\pi$
$608$	4.03180	0.163511
$609$	1.07612	0.0436065
$610$	−0.140582	−0.00569199
$611$	30.4680	1.23260
$612$	−9.72776	−0.393221
$613$	−3.13719	−0.126710	−0.0633550	−	0.997991i	$-0.520180\pi$
$613$	−3.13719	−0.126710	−0.0633550	+	0.997991i	$0.520180\pi$
$614$	0.694152	0.0280137
$615$	1.02063	0.0411559
$616$	0	0
$617$	−7.78976	−0.313604	−0.156802	−	0.987630i	$-0.550118\pi$
$617$	−7.78976	−0.313604	−0.156802	+	0.987630i	$0.550118\pi$
$618$	0.214206	0.00861662
$619$	4.02747	0.161878	0.0809389	−	0.996719i	$-0.474208\pi$
$619$	4.02747	0.161878	0.0809389	+	0.996719i	$0.474208\pi$
$620$	2.17118	0.0871968
$621$	3.30352	0.132566
$622$	1.12809	0.0452325
$623$	−10.9928	−0.440418
$624$	−3.05842	−0.122435
$625$	−17.8964	−0.715855
$626$	0.722390	0.0288725
$627$	0	0
$628$	28.8025	1.14934
$629$	8.39192	0.334608
$630$	−0.354273	−0.0141146
$631$	13.9637	0.555887	0.277944	−	0.960597i	$-0.410347\pi$
$631$	13.9637	0.555887	0.277944	+	0.960597i	$0.410347\pi$
$632$	0.369022	0.0146789
$633$	−3.65638	−0.145328
$634$	−2.16440	−0.0859592
$635$	23.5181	0.933289
$636$	2.53751	0.100619
$637$	31.0245	1.22924
$638$	0	0
$639$	47.8925	1.89460
$640$	4.46976	0.176683
$641$	7.95220	0.314093	0.157047	−	0.987591i	$-0.449803\pi$
$641$	7.95220	0.314093	0.157047	+	0.987591i	$0.449803\pi$
$642$	0.0557786	0.00220141
$643$	19.3565	0.763345	0.381673	−	0.924298i	$-0.375348\pi$
$643$	19.3565	0.763345	0.381673	+	0.924298i	$0.375348\pi$
$644$	−5.98535	−0.235856
$645$	2.23980	0.0881919
$646$	−0.552492	−0.0217375
$647$	−9.35792	−0.367898	−0.183949	−	0.982936i	$-0.558888\pi$
$647$	−9.35792	−0.367898	−0.183949	+	0.982936i	$0.558888\pi$
$648$	−2.51482	−0.0987915
$649$	0	0
$650$	0.408598	0.0160266
$651$	−0.0733438	−0.00287457
$652$	−8.51547	−0.333492
$653$	6.77277	0.265039	0.132519	−	0.991180i	$-0.457693\pi$
$653$	6.77277	0.265039	0.132519	+	0.991180i	$0.457693\pi$
$654$	−0.166681	−0.00651772
$655$	30.3412	1.18553
$656$	−13.2385	−0.516878
$657$	6.36705	0.248402
$658$	0.374591	0.0146031
$659$	−25.5385	−0.994839	−0.497420	−	0.867510i	$-0.665719\pi$
$659$	−25.5385	−0.994839	−0.497420	+	0.867510i	$0.665719\pi$
$660$	0	0
$661$	−40.5252	−1.57625	−0.788124	−	0.615517i	$-0.788947\pi$
$661$	−40.5252	−1.57625	−0.788124	+	0.615517i	$0.788947\pi$
$662$	−1.59641	−0.0620461
$663$	1.26274	0.0490407
$664$	−0.622901	−0.0241732
$665$	7.81062	0.302883
$666$	1.09236	0.0423280
$667$	28.8497	1.11706
$668$	33.7495	1.30581
$669$	−0.559023	−0.0216131
$670$	1.79122	0.0692010
$671$	0	0
$672$	−0.113292	−0.00437035
$673$	−10.1803	−0.392420	−0.196210	−	0.980562i	$-0.562863\pi$
$673$	−10.1803	−0.392420	−0.196210	+	0.980562i	$0.562863\pi$
$674$	−0.578800	−0.0222946
$675$	1.07630	0.0414267
$676$	−22.7096	−0.873447
$677$	21.3189	0.819353	0.409676	−	0.912231i	$-0.365642\pi$
$677$	21.3189	0.819353	0.409676	+	0.912231i	$0.365642\pi$
$678$	−0.00359272	−0.000137977 0
$679$	12.9500	0.496974
$680$	−0.920341	−0.0352935
$681$	−2.11367	−0.0809959
$682$	0	0
$683$	−4.79732	−0.183564	−0.0917822	−	0.995779i	$-0.529256\pi$
$683$	−4.79732	−0.183564	−0.0917822	+	0.995779i	$0.529256\pi$
$684$	27.9166	1.06742
$685$	0.723803	0.0276551
$686$	0.806409	0.0307888
$687$	4.29514	0.163870
$688$	−29.0522	−1.10760
$689$	40.2537	1.53354
$690$	0.0777179	0.00295867
$691$	14.2912	0.543661	0.271831	−	0.962345i	$-0.412371\pi$
$691$	14.2912	0.543661	0.271831	+	0.962345i	$0.412371\pi$
$692$	−37.0385	−1.40799
$693$	0	0
$694$	−1.16839	−0.0443517
$695$	−28.6810	−1.08793
$696$	0.363893	0.0137933
$697$	5.46583	0.207033
$698$	0.427393	0.0161771
$699$	−1.38910	−0.0525407
$700$	−1.95004	−0.0737048
$701$	2.13120	0.0804943	0.0402472	−	0.999190i	$-0.487185\pi$
$701$	2.13120	0.0804943	0.0402472	+	0.999190i	$0.487185\pi$
$702$	0.330080	0.0124581
$703$	−24.0831	−0.908309
$704$	0	0
$705$	1.88809	0.0711096
$706$	0.451480	0.0169917
$707$	1.28023	0.0481480
$708$	−0.947682	−0.0356161
$709$	−19.5091	−0.732679	−0.366340	−	0.930481i	$-0.619389\pi$
$709$	−19.5091	−0.732679	−0.366340	+	0.930481i	$0.619389\pi$
$710$	2.26264	0.0849153
$711$	3.83437	0.143800
$712$	−3.71725	−0.139310
$713$	−1.96627	−0.0736375
$714$	0.0155248	0.000581002 0
$715$	0	0
$716$	−19.4321	−0.726213
$717$	1.69232	0.0632010
$718$	−2.16554	−0.0808172
$719$	−38.3808	−1.43136	−0.715680	−	0.698428i	$-0.753883\pi$
$719$	−38.3808	−1.43136	−0.715680	+	0.698428i	$0.753883\pi$
$720$	23.1619	0.863193
$721$	−16.2173	−0.603962
$722$	0.223486	0.00831727
$723$	0.608304	0.0226231
$724$	8.52350	0.316773
$725$	9.39930	0.349081
$726$	0	0
$727$	30.4523	1.12941	0.564707	−	0.825292i	$-0.308989\pi$
$727$	30.4523	1.12941	0.564707	+	0.825292i	$0.308989\pi$
$728$	−1.19763	−0.0443870
$729$	−25.6940	−0.951631
$730$	0.300805	0.0111333
$731$	11.9949	0.443646
$732$	−0.311283	−0.0115053
$733$	−43.0022	−1.58832	−0.794162	−	0.607706i	$-0.792090\pi$
$733$	−43.0022	−1.58832	−0.794162	+	0.607706i	$0.792090\pi$
$734$	−1.67683	−0.0618930
$735$	1.92258	0.0709153
$736$	−3.03725	−0.111955
$737$	0	0
$738$	0.711474	0.0261897
$739$	−0.287712	−0.0105836	−0.00529182	−	0.999986i	$-0.501684\pi$
$739$	−0.287712	−0.0105836	−0.00529182	+	0.999986i	$0.501684\pi$
$740$	−20.0330	−0.736427
$741$	−3.62379	−0.133123
$742$	0.494902	0.0181684
$743$	−0.450373	−0.0165226	−0.00826129	−	0.999966i	$-0.502630\pi$
$743$	−0.450373	−0.0165226	−0.00826129	+	0.999966i	$0.502630\pi$
$744$	−0.0248015	−0.000909265 0
$745$	−26.6332	−0.975766
$746$	−2.57754	−0.0943703
$747$	−6.47232	−0.236810
$748$	0	0
$749$	−4.22293	−0.154302
$750$	0.135004	0.00492965
$751$	−37.5963	−1.37191	−0.685955	−	0.727644i	$-0.740615\pi$
$751$	−37.5963	−1.37191	−0.685955	+	0.727644i	$0.740615\pi$
$752$	−24.4902	−0.893067
$753$	−0.390375	−0.0142260
$754$	2.88259	0.104978
$755$	12.9271	0.470467
$756$	−1.57531	−0.0572936
$757$	−17.7464	−0.645005	−0.322502	−	0.946569i	$-0.604524\pi$
$757$	−17.7464	−0.645005	−0.322502	+	0.946569i	$0.604524\pi$
$758$	1.49659	0.0543585
$759$	0	0
$760$	2.64119	0.0958059
$761$	5.75878	0.208756	0.104378	−	0.994538i	$-0.466715\pi$
$761$	5.75878	0.208756	0.104378	+	0.994538i	$0.466715\pi$
$762$	−0.134151	−0.00485978
$763$	12.6192	0.456845
$764$	−21.1498	−0.765174
$765$	−9.56291	−0.345748
$766$	−0.292525	−0.0105694
$767$	−15.0335	−0.542829
$768$	2.43277	0.0877850
$769$	−38.5635	−1.39064	−0.695318	−	0.718702i	$-0.744737\pi$
$769$	−38.5635	−1.39064	−0.695318	+	0.718702i	$0.744737\pi$
$770$	0	0
$771$	1.86599	0.0672019
$772$	−45.0313	−1.62071
$773$	33.6743	1.21118	0.605590	−	0.795777i	$-0.292937\pi$
$773$	33.6743	1.21118	0.605590	+	0.795777i	$0.292937\pi$
$774$	1.56134	0.0561213
$775$	−0.640617	−0.0230117
$776$	4.37907	0.157199
$777$	0.676726	0.0242774
$778$	0.357927	0.0128323
$779$	−15.6858	−0.562002
$780$	−3.01438	−0.107932
$781$	0	0
$782$	0.416205	0.0148835
$783$	7.59308	0.271355
$784$	−24.9375	−0.890627
$785$	28.3144	1.01058
$786$	−0.173071	−0.00617324
$787$	−27.6279	−0.984830	−0.492415	−	0.870361i	$-0.663886\pi$
$787$	−27.6279	−0.984830	−0.492415	+	0.870361i	$0.663886\pi$
$788$	−40.5068	−1.44299
$789$	−2.19505	−0.0781458
$790$	0.181151	0.00644507
$791$	0.272000	0.00967121
$792$	0	0
$793$	−4.93802	−0.175354
$794$	0.998008	0.0354180
$795$	2.49451	0.0884711
$796$	−28.8100	−1.02114
$797$	−15.8778	−0.562420	−0.281210	−	0.959646i	$-0.590736\pi$
$797$	−15.8778	−0.562420	−0.281210	+	0.959646i	$0.590736\pi$
$798$	−0.0445530	−0.00157716
$799$	10.1114	0.357714
$800$	−0.989545	−0.0349857
$801$	−38.6245	−1.36473
$802$	−1.55520	−0.0549159
$803$	0	0
$804$	3.96621	0.139877
$805$	−5.88392	−0.207381
$806$	−0.196466	−0.00692020
$807$	3.54238	0.124698
$808$	0.432913	0.0152298
$809$	−33.8580	−1.19038	−0.595191	−	0.803584i	$-0.702924\pi$
$809$	−33.8580	−1.19038	−0.595191	+	0.803584i	$0.702924\pi$
$810$	−1.23451	−0.0433763
$811$	−11.8040	−0.414496	−0.207248	−	0.978288i	$-0.566451\pi$
$811$	−11.8040	−0.414496	−0.207248	+	0.978288i	$0.566451\pi$
$812$	−13.7572	−0.482784
$813$	−0.788920	−0.0276686
$814$	0	0
$815$	−8.37116	−0.293229
$816$	−1.01499	−0.0355318
$817$	−34.4227	−1.20430
$818$	0.388209	0.0135734
$819$	−12.4441	−0.434831
$820$	−13.0479	−0.455652
$821$	30.8091	1.07525	0.537623	−	0.843185i	$-0.319322\pi$
$821$	30.8091	1.07525	0.537623	+	0.843185i	$0.319322\pi$
$822$	−0.00412868	−0.000144004 0
$823$	10.0467	0.350207	0.175104	−	0.984550i	$-0.443974\pi$
$823$	10.0467	0.350207	0.175104	+	0.984550i	$0.443974\pi$
$824$	−5.48392	−0.191041
$825$	0	0
$826$	−0.184831	−0.00643109
$827$	−14.8987	−0.518079	−0.259040	−	0.965867i	$-0.583406\pi$
$827$	−14.8987	−0.518079	−0.259040	+	0.965867i	$0.583406\pi$
$828$	−21.0303	−0.730852
$829$	−36.2115	−1.25768	−0.628839	−	0.777536i	$-0.716469\pi$
$829$	−36.2115	−1.25768	−0.628839	+	0.777536i	$0.716469\pi$
$830$	−0.305779	−0.0106137
$831$	−4.32796	−0.150135
$832$	38.8964	1.34849
$833$	10.2960	0.356736
$834$	0.163601	0.00566504
$835$	33.1776	1.14816
$836$	0	0
$837$	−0.517513	−0.0178879
$838$	2.33473	0.0806520
$839$	30.8654	1.06559	0.532795	−	0.846244i	$-0.321142\pi$
$839$	30.8654	1.06559	0.532795	+	0.846244i	$0.321142\pi$
$840$	−0.0742164	−0.00256071
$841$	37.3104	1.28657
$842$	0.160996	0.00554829
$843$	−2.70731	−0.0932447
$844$	46.7436	1.60898
$845$	−22.3248	−0.767996
$846$	1.31617	0.0452509
$847$	0	0
$848$	−32.3560	−1.11111
$849$	−0.306587	−0.0105220
$850$	0.135601	0.00465107
$851$	18.1423	0.621911
$852$	5.01003	0.171641
$853$	−32.7171	−1.12021	−0.560106	−	0.828421i	$-0.689240\pi$
$853$	−32.7171	−1.12021	−0.560106	+	0.828421i	$0.689240\pi$
$854$	−0.0607109	−0.00207748
$855$	27.4435	0.938549
$856$	−1.42800	−0.0488079
$857$	−35.3555	−1.20772	−0.603860	−	0.797091i	$-0.706371\pi$
$857$	−35.3555	−1.20772	−0.603860	+	0.797091i	$0.706371\pi$
$858$	0	0
$859$	−43.4182	−1.48141	−0.740706	−	0.671830i	$-0.765509\pi$
$859$	−43.4182	−1.48141	−0.740706	+	0.671830i	$0.765509\pi$
$860$	−28.6338	−0.976405
$861$	0.440765	0.0150212
$862$	−0.580657	−0.0197773
$863$	0.708140	0.0241054	0.0120527	−	0.999927i	$-0.496163\pi$
$863$	0.708140	0.0241054	0.0120527	+	0.999927i	$0.496163\pi$
$864$	−0.799389	−0.0271958
$865$	−36.4109	−1.23801
$866$	1.56251	0.0530964
$867$	−2.23366	−0.0758589
$868$	0.937636	0.0318254
$869$	0	0
$870$	0.178633	0.00605623
$871$	62.9179	2.13189
$872$	4.26721	0.144506
$873$	45.5012	1.53998
$874$	−1.19442	−0.0404019
$875$	−10.2210	−0.345533
$876$	0.666056	0.0225040
$877$	35.5015	1.19880	0.599401	−	0.800449i	$-0.295406\pi$
$877$	35.5015	1.19880	0.599401	+	0.800449i	$0.295406\pi$
$878$	−1.01993	−0.0344210
$879$	−4.14056	−0.139658
$880$	0	0
$881$	3.04221	0.102495	0.0512473	−	0.998686i	$-0.483680\pi$
$881$	3.04221	0.102495	0.0512473	+	0.998686i	$0.483680\pi$
$882$	1.34021	0.0451272
$883$	24.2116	0.814786	0.407393	−	0.913253i	$-0.366438\pi$
$883$	24.2116	0.814786	0.407393	+	0.913253i	$0.366438\pi$
$884$	−16.1430	−0.542948
$885$	−0.931622	−0.0313161
$886$	−2.19541	−0.0737561
$887$	−44.6086	−1.49781	−0.748905	−	0.662678i	$-0.769420\pi$
$887$	−44.6086	−1.49781	−0.748905	+	0.662678i	$0.769420\pi$
$888$	0.228837	0.00767927
$889$	10.1564	0.340635
$890$	−1.82478	−0.0611667
$891$	0	0
$892$	7.14662	0.239286
$893$	−29.0175	−0.971032
$894$	0.151920	0.00508097
$895$	−19.1028	−0.638537
$896$	1.93029	0.0644864
$897$	2.72989	0.0911483
$898$	2.25386	0.0752121
$899$	−4.51944	−0.150732
$900$	−6.85171	−0.228390
$901$	13.3589	0.445050
$902$	0	0
$903$	0.967267	0.0321886
$904$	0.0919777	0.00305913
$905$	8.37905	0.278529
$906$	−0.0737385	−0.00244980
$907$	22.0470	0.732057	0.366029	−	0.930604i	$-0.380717\pi$
$907$	22.0470	0.732057	0.366029	+	0.930604i	$0.380717\pi$
$908$	27.0214	0.896735
$909$	4.49823	0.149197
$910$	−0.587908	−0.0194890
$911$	21.0306	0.696775	0.348387	−	0.937351i	$-0.386729\pi$
$911$	21.0306	0.696775	0.348387	+	0.937351i	$0.386729\pi$
$912$	2.91281	0.0964529
$913$	0	0
$914$	1.17435	0.0388439
$915$	−0.306007	−0.0101163
$916$	−54.9096	−1.81426
$917$	13.1030	0.432699
$918$	0.109543	0.00361546
$919$	15.5659	0.513471	0.256736	−	0.966482i	$-0.417353\pi$
$919$	15.5659	0.513471	0.256736	+	0.966482i	$0.417353\pi$
$920$	−1.98967	−0.0655974
$921$	1.51098	0.0497884
$922$	−1.45705	−0.0479853
$923$	79.4766	2.61600
$924$	0	0
$925$	5.91082	0.194347
$926$	−0.574063	−0.0188649
$927$	−56.9813	−1.87151
$928$	−6.98107	−0.229165
$929$	20.8189	0.683047	0.341523	−	0.939873i	$-0.389057\pi$
$929$	20.8189	0.683047	0.341523	+	0.939873i	$0.389057\pi$
$930$	−0.0121749	−0.000399231 0
$931$	−29.5474	−0.968378
$932$	17.7584	0.581697
$933$	2.45555	0.0803910
$934$	−0.764717	−0.0250223
$935$	0	0
$936$	−4.20800	−0.137543
$937$	15.7223	0.513624	0.256812	−	0.966461i	$-0.417328\pi$
$937$	15.7223	0.513624	0.256812	+	0.966461i	$0.417328\pi$
$938$	0.773549	0.0252573
$939$	1.57244	0.0513147
$940$	−24.1376	−0.787281
$941$	0.0857753	0.00279620	0.00139810	−	0.999999i	$-0.499555\pi$
$941$	0.0857753	0.00279620	0.00139810	+	0.999999i	$0.499555\pi$
$942$	−0.161510	−0.00526227
$943$	11.8165	0.384797
$944$	12.0840	0.393300
$945$	−1.54862	−0.0503766
$946$	0	0
$947$	−23.9895	−0.779553	−0.389777	−	0.920909i	$-0.627448\pi$
$947$	−23.9895	−0.779553	−0.389777	+	0.920909i	$0.627448\pi$
$948$	0.401113	0.0130275
$949$	10.5660	0.342986
$950$	−0.389145	−0.0126255
$951$	−4.71129	−0.152774
$952$	−0.397454	−0.0128815
$953$	−53.0548	−1.71861	−0.859307	−	0.511461i	$-0.829105\pi$
$953$	−53.0548	−1.71861	−0.859307	+	0.511461i	$0.829105\pi$
$954$	1.73890	0.0562989
$955$	−20.7914	−0.672794
$956$	−21.6349	−0.699721
$957$	0	0
$958$	−0.383192	−0.0123804
$959$	0.312577	0.0100937
$960$	2.41040	0.0777953
$961$	−30.6920	−0.990064
$962$	1.81274	0.0584451
$963$	−14.8378	−0.478140
$964$	−7.77663	−0.250468
$965$	−44.2682	−1.42504
$966$	0.0335628	0.00107987
$967$	26.1167	0.839855	0.419927	−	0.907558i	$-0.362056\pi$
$967$	26.1167	0.839855	0.419927	+	0.907558i	$0.362056\pi$
$968$	0	0
$969$	−1.20262	−0.0386337
$970$	2.14966	0.0690215
$971$	−31.7691	−1.01952	−0.509759	−	0.860317i	$-0.670265\pi$
$971$	−31.7691	−1.01952	−0.509759	+	0.860317i	$0.670265\pi$
$972$	−8.31386	−0.266667
$973$	−12.3860	−0.397078
$974$	−1.17283	−0.0375798
$975$	0.889405	0.0284838
$976$	3.96919	0.127051
$977$	34.5644	1.10581	0.552906	−	0.833244i	$-0.313519\pi$
$977$	34.5644	1.10581	0.552906	+	0.833244i	$0.313519\pi$
$978$	0.0477504	0.00152689
$979$	0	0
$980$	−24.5784	−0.785129
$981$	44.3390	1.41563
$982$	0.280576	0.00895353
$983$	−41.4709	−1.32271	−0.661357	−	0.750071i	$-0.730019\pi$
$983$	−41.4709	−1.32271	−0.661357	+	0.750071i	$0.730019\pi$
$984$	0.149046	0.00475142
$985$	−39.8203	−1.26878
$986$	0.956639	0.0304656
$987$	0.815381	0.0259539
$988$	46.3270	1.47386
$989$	25.9314	0.824572
$990$	0	0
$991$	42.0231	1.33491	0.667454	−	0.744651i	$-0.267384\pi$
$991$	42.0231	1.33491	0.667454	+	0.744651i	$0.267384\pi$
$992$	0.475801	0.0151067
$993$	−3.47494	−0.110274
$994$	0.977130	0.0309927
$995$	−28.3218	−0.897861
$996$	−0.677069	−0.0214537
$997$	−51.8948	−1.64352	−0.821762	−	0.569831i	$-0.807009\pi$
$997$	−51.8948	−1.64352	−0.821762	+	0.569831i	$0.807009\pi$
$998$	−0.695815	−0.0220256
$999$	4.77497	0.151073

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.v.1.32		64
11.5	even	5		671.2.j.c.245.17	✓	128
11.9	even	5		671.2.j.c.367.17	yes	128
11.10	odd	2		7381.2.a.u.1.33		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.j.c.245.17	✓	128	11.5	even	5
671.2.j.c.367.17	yes	128	11.9	even	5
7381.2.a.u.1.33		64	11.10	odd	2
7381.2.a.v.1.32		64	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:	\( N \)	\(=\)	\( 7381 = 11^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7381.a (trivial)

\(f(q)\)	\(=\)	\(q+0.0716868 q^{2} +0.156042 q^{3} -1.99486 q^{4} -1.96106 q^{5} +0.0111862 q^{6} -0.846891 q^{7} -0.286379 q^{8} -2.97565 q^{9} +O(q^{10})\)	\(q+0.0716868 q^{2} +0.156042 q^{3} -1.99486 q^{4} -1.96106 q^{5} +0.0111862 q^{6} -0.846891 q^{7} -0.286379 q^{8} -2.97565 q^{9} -0.140582 q^{10} -0.311283 q^{12} -4.93802 q^{13} -0.0607109 q^{14} -0.306007 q^{15} +3.96919 q^{16} -1.63877 q^{17} -0.213315 q^{18} +4.70293 q^{19} +3.91203 q^{20} -0.132151 q^{21} -3.54283 q^{23} -0.0446872 q^{24} -1.15426 q^{25} -0.353991 q^{26} -0.932454 q^{27} +1.68943 q^{28} -8.14312 q^{29} -0.0219367 q^{30} +0.555001 q^{31} +0.857296 q^{32} -0.117478 q^{34} +1.66080 q^{35} +5.93601 q^{36} -5.12086 q^{37} +0.337138 q^{38} -0.770540 q^{39} +0.561605 q^{40} -3.33532 q^{41} -0.00947346 q^{42} -7.31942 q^{43} +5.83542 q^{45} -0.253974 q^{46} -6.17008 q^{47} +0.619362 q^{48} -6.28278 q^{49} -0.0827454 q^{50} -0.255717 q^{51} +9.85067 q^{52} -8.15179 q^{53} -0.0668446 q^{54} +0.242532 q^{56} +0.733855 q^{57} -0.583754 q^{58} +3.04444 q^{59} +0.610442 q^{60} +1.00000 q^{61} +0.0397863 q^{62} +2.52005 q^{63} -7.87693 q^{64} +9.68373 q^{65} -12.7415 q^{67} +3.26912 q^{68} -0.552830 q^{69} +0.119057 q^{70} -16.0948 q^{71} +0.852163 q^{72} -2.13972 q^{73} -0.367098 q^{74} -0.180114 q^{75} -9.38169 q^{76} -0.0552375 q^{78} -1.28858 q^{79} -7.78381 q^{80} +8.78145 q^{81} -0.239099 q^{82} +2.17509 q^{83} +0.263622 q^{84} +3.21372 q^{85} -0.524706 q^{86} -1.27067 q^{87} +12.9802 q^{89} +0.418322 q^{90} +4.18197 q^{91} +7.06745 q^{92} +0.0866037 q^{93} -0.442313 q^{94} -9.22270 q^{95} +0.133774 q^{96} -15.2912 q^{97} -0.450392 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9	\( 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9} - 4 q^{10} + 41 q^{12} - q^{13} + 41 q^{14} + 28 q^{15} + 107 q^{16} + 13 q^{17} + 38 q^{18} - q^{19} + 65 q^{20} + q^{21} + 52 q^{23} + 3 q^{24} + 87 q^{25} + 37 q^{26} + 88 q^{27} - q^{28} + 19 q^{29} - 19 q^{30} + 45 q^{31} - 24 q^{32} - 23 q^{34} + 10 q^{35} + 146 q^{36} + 26 q^{37} - 4 q^{38} - 6 q^{39} + 84 q^{40} - 12 q^{41} + 28 q^{42} + 5 q^{43} + 71 q^{45} - 5 q^{46} + 63 q^{47} + 85 q^{48} + 78 q^{49} + 14 q^{50} + 22 q^{51} - 24 q^{52} + 86 q^{53} - 114 q^{54} + 119 q^{56} - 29 q^{57} + q^{58} + 119 q^{59} - 22 q^{60} + 64 q^{61} + 13 q^{62} - 28 q^{63} + 135 q^{64} - 30 q^{65} + 2 q^{67} + 59 q^{68} + 63 q^{69} - 2 q^{70} + 126 q^{71} + 48 q^{72} + 8 q^{73} - 27 q^{74} + 107 q^{75} - 82 q^{76} - 13 q^{78} - 5 q^{79} + 119 q^{80} + 96 q^{81} - 27 q^{82} + 14 q^{83} + 182 q^{84} - 52 q^{85} + 60 q^{86} - 8 q^{87} + 59 q^{89} - 45 q^{90} + 83 q^{91} + 111 q^{92} - 7 q^{93} + 21 q^{94} - 26 q^{95} - 86 q^{96} - 39 q^{97} - 57 q^{98}+O(q^{100}) \) 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9 - 4 * q^10 + 41 * q^12 - q^13 + 41 * q^14 + 28 * q^15 + 107 * q^16 + 13 * q^17 + 38 * q^18 - q^19 + 65 * q^20 + q^21 + 52 * q^23 + 3 * q^24 + 87 * q^25 + 37 * q^26 + 88 * q^27 - q^28 + 19 * q^29 - 19 * q^30 + 45 * q^31 - 24 * q^32 - 23 * q^34 + 10 * q^35 + 146 * q^36 + 26 * q^37 - 4 * q^38 - 6 * q^39 + 84 * q^40 - 12 * q^41 + 28 * q^42 + 5 * q^43 + 71 * q^45 - 5 * q^46 + 63 * q^47 + 85 * q^48 + 78 * q^49 + 14 * q^50 + 22 * q^51 - 24 * q^52 + 86 * q^53 - 114 * q^54 + 119 * q^56 - 29 * q^57 + q^58 + 119 * q^59 - 22 * q^60 + 64 * q^61 + 13 * q^62 - 28 * q^63 + 135 * q^64 - 30 * q^65 + 2 * q^67 + 59 * q^68 + 63 * q^69 - 2 * q^70 + 126 * q^71 + 48 * q^72 + 8 * q^73 - 27 * q^74 + 107 * q^75 - 82 * q^76 - 13 * q^78 - 5 * q^79 + 119 * q^80 + 96 * q^81 - 27 * q^82 + 14 * q^83 + 182 * q^84 - 52 * q^85 + 60 * q^86 - 8 * q^87 + 59 * q^89 - 45 * q^90 + 83 * q^91 + 111 * q^92 - 7 * q^93 + 21 * q^94 - 26 * q^95 - 86 * q^96 - 39 * q^97 - 57 * q^98

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