LMFDB - Embedded newform 8041.2.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41177 q^{2} +3.28542 q^{3} +3.81663 q^{4} -1.23247 q^{5} -7.92367 q^{6} +1.42521 q^{7} -4.38130 q^{8} +7.79396 q^{9} +O(q^{10})$	\(q-2.41177 q^{2} +3.28542 q^{3} +3.81663 q^{4} -1.23247 q^{5} -7.92367 q^{6} +1.42521 q^{7} -4.38130 q^{8} +7.79396 q^{9} +2.97244 q^{10} -1.00000 q^{11} +12.5392 q^{12} +4.19562 q^{13} -3.43727 q^{14} -4.04918 q^{15} +2.93341 q^{16} +1.00000 q^{17} -18.7972 q^{18} -2.67994 q^{19} -4.70389 q^{20} +4.68240 q^{21} +2.41177 q^{22} +3.72795 q^{23} -14.3944 q^{24} -3.48101 q^{25} -10.1189 q^{26} +15.7502 q^{27} +5.43949 q^{28} +1.30208 q^{29} +9.76569 q^{30} -4.89145 q^{31} +1.68788 q^{32} -3.28542 q^{33} -2.41177 q^{34} -1.75653 q^{35} +29.7467 q^{36} -0.296109 q^{37} +6.46339 q^{38} +13.7844 q^{39} +5.39982 q^{40} +9.83284 q^{41} -11.2929 q^{42} -1.00000 q^{43} -3.81663 q^{44} -9.60583 q^{45} -8.99095 q^{46} +1.61771 q^{47} +9.63748 q^{48} -4.96879 q^{49} +8.39540 q^{50} +3.28542 q^{51} +16.0131 q^{52} -7.02840 q^{53} -37.9857 q^{54} +1.23247 q^{55} -6.24425 q^{56} -8.80471 q^{57} -3.14032 q^{58} +5.50175 q^{59} -15.4542 q^{60} -3.69937 q^{61} +11.7970 q^{62} +11.1080 q^{63} -9.93760 q^{64} -5.17098 q^{65} +7.92367 q^{66} -12.9547 q^{67} +3.81663 q^{68} +12.2479 q^{69} +4.23634 q^{70} +14.8132 q^{71} -34.1476 q^{72} +16.4239 q^{73} +0.714147 q^{74} -11.4366 q^{75} -10.2283 q^{76} -1.42521 q^{77} -33.2447 q^{78} +4.76420 q^{79} -3.61535 q^{80} +28.3639 q^{81} -23.7145 q^{82} +15.5636 q^{83} +17.8710 q^{84} -1.23247 q^{85} +2.41177 q^{86} +4.27788 q^{87} +4.38130 q^{88} +6.85183 q^{89} +23.1671 q^{90} +5.97963 q^{91} +14.2282 q^{92} -16.0704 q^{93} -3.90154 q^{94} +3.30295 q^{95} +5.54538 q^{96} +1.34613 q^{97} +11.9836 q^{98} -7.79396 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) $ 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * 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 $

$2$	−2.41177	−1.70538	−0.852689	−	0.522418i	$-0.825030\pi$
$2$	−2.41177	−1.70538	−0.852689	+	0.522418i	$0.825030\pi$
$3$	3.28542	1.89684	0.948418	−	0.317022i	$-0.102683\pi$
$3$	3.28542	1.89684	0.948418	+	0.317022i	$0.102683\pi$
$4$	3.81663	1.90832
$5$	−1.23247	−0.551178	−0.275589	−	0.961276i	$-0.588873\pi$
$5$	−1.23247	−0.551178	−0.275589	+	0.961276i	$0.588873\pi$
$6$	−7.92367	−3.23482
$7$	1.42521	0.538678	0.269339	−	0.963045i	$-0.413195\pi$
$7$	1.42521	0.538678	0.269339	+	0.963045i	$0.413195\pi$
$8$	−4.38130	−1.54902
$9$	7.79396	2.59799
$10$	2.97244	0.939967
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	12.5392	3.61976
$13$	4.19562	1.16366	0.581828	−	0.813312i	$-0.302338\pi$
$13$	4.19562	1.16366	0.581828	+	0.813312i	$0.302338\pi$
$14$	−3.43727	−0.918649
$15$	−4.04918	−1.04549
$16$	2.93341	0.733353
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−18.7972	−4.43055
$19$	−2.67994	−0.614820	−0.307410	−	0.951577i	$-0.599462\pi$
$19$	−2.67994	−0.614820	−0.307410	+	0.951577i	$0.599462\pi$
$20$	−4.70389	−1.05182
$21$	4.68240	1.02178
$22$	2.41177	0.514191
$23$	3.72795	0.777331	0.388665	−	0.921379i	$-0.372936\pi$
$23$	3.72795	0.777331	0.388665	+	0.921379i	$0.372936\pi$
$24$	−14.3944	−2.93824
$25$	−3.48101	−0.696203
$26$	−10.1189	−1.98447
$27$	15.7502	3.03112
$28$	5.43949	1.02797
$29$	1.30208	0.241791	0.120895	−	0.992665i	$-0.461423\pi$
$29$	1.30208	0.241791	0.120895	+	0.992665i	$0.461423\pi$
$30$	9.76569	1.78296
$31$	−4.89145	−0.878530	−0.439265	−	0.898358i	$-0.644761\pi$
$31$	−4.89145	−0.878530	−0.439265	+	0.898358i	$0.644761\pi$
$32$	1.68788	0.298378
$33$	−3.28542	−0.571918
$34$	−2.41177	−0.413615
$35$	−1.75653	−0.296907
$36$	29.7467	4.95778
$37$	−0.296109	−0.0486800	−0.0243400	−	0.999704i	$-0.507748\pi$
$37$	−0.296109	−0.0486800	−0.0243400	+	0.999704i	$0.507748\pi$
$38$	6.46339	1.04850
$39$	13.7844	2.20726
$40$	5.39982	0.853787
$41$	9.83284	1.53563	0.767816	−	0.640671i	$-0.221344\pi$
$41$	9.83284	1.53563	0.767816	+	0.640671i	$0.221344\pi$
$42$	−11.2929	−1.74253
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−3.81663	−0.575379
$45$	−9.60583	−1.43195
$46$	−8.99095	−1.32564
$47$	1.61771	0.235967	0.117983	−	0.993016i	$-0.462357\pi$
$47$	1.61771	0.235967	0.117983	+	0.993016i	$0.462357\pi$
$48$	9.63748	1.39105
$49$	−4.96879	−0.709826
$50$	8.39540	1.18729
$51$	3.28542	0.460050
$52$	16.0131	2.22062
$53$	−7.02840	−0.965425	−0.482712	−	0.875779i	$-0.660348\pi$
$53$	−7.02840	−0.965425	−0.482712	+	0.875779i	$0.660348\pi$
$54$	−37.9857	−5.16921
$55$	1.23247	0.166186
$56$	−6.24425	−0.834423
$57$	−8.80471	−1.16621
$58$	−3.14032	−0.412344
$59$	5.50175	0.716266	0.358133	−	0.933671i	$-0.383413\pi$
$59$	5.50175	0.716266	0.358133	+	0.933671i	$0.383413\pi$
$60$	−15.4542	−1.99513
$61$	−3.69937	−0.473656	−0.236828	−	0.971552i	$-0.576108\pi$
$61$	−3.69937	−0.473656	−0.236828	+	0.971552i	$0.576108\pi$
$62$	11.7970	1.49823
$63$	11.1080	1.39948
$64$	−9.93760	−1.24220
$65$	−5.17098	−0.641381
$66$	7.92367	0.975336
$67$	−12.9547	−1.58267	−0.791334	−	0.611384i	$-0.790613\pi$
$67$	−12.9547	−1.58267	−0.791334	+	0.611384i	$0.790613\pi$
$68$	3.81663	0.462835
$69$	12.2479	1.47447
$70$	4.23634	0.506339
$71$	14.8132	1.75800	0.879000	−	0.476821i	$-0.158211\pi$
$71$	14.8132	1.75800	0.879000	+	0.476821i	$0.158211\pi$
$72$	−34.1476	−4.02434
$73$	16.4239	1.92227	0.961133	−	0.276084i	$-0.0890369\pi$
$73$	16.4239	1.92227	0.961133	+	0.276084i	$0.0890369\pi$
$74$	0.714147	0.0830179
$75$	−11.4366	−1.32058
$76$	−10.2283	−1.17327
$77$	−1.42521	−0.162417
$78$	−33.2447	−3.76422
$79$	4.76420	0.536014	0.268007	−	0.963417i	$-0.413635\pi$
$79$	4.76420	0.536014	0.268007	+	0.963417i	$0.413635\pi$
$80$	−3.61535	−0.404208
$81$	28.3639	3.15155
$82$	−23.7145	−2.61883
$83$	15.5636	1.70833	0.854166	−	0.520000i	$-0.174068\pi$
$83$	15.5636	1.70833	0.854166	+	0.520000i	$0.174068\pi$
$84$	17.8710	1.94988
$85$	−1.23247	−0.133680
$86$	2.41177	0.260068
$87$	4.27788	0.458637
$88$	4.38130	0.467048
$89$	6.85183	0.726292	0.363146	−	0.931732i	$-0.381703\pi$
$89$	6.85183	0.726292	0.363146	+	0.931732i	$0.381703\pi$
$90$	23.1671	2.44202
$91$	5.97963	0.626835
$92$	14.2282	1.48339
$93$	−16.0704	−1.66643
$94$	−3.90154	−0.402413
$95$	3.30295	0.338875
$96$	5.54538	0.565973
$97$	1.34613	0.136679	0.0683393	−	0.997662i	$-0.478230\pi$
$97$	1.34613	0.136679	0.0683393	+	0.997662i	$0.478230\pi$
$98$	11.9836	1.21052
$99$	−7.79396	−0.783323
$100$	−13.2857	−1.32857
$101$	−0.931187	−0.0926566	−0.0463283	−	0.998926i	$-0.514752\pi$
$101$	−0.931187	−0.0926566	−0.0463283	+	0.998926i	$0.514752\pi$
$102$	−7.92367	−0.784560
$103$	2.10967	0.207872	0.103936	−	0.994584i	$-0.466856\pi$
$103$	2.10967	0.207872	0.103936	+	0.994584i	$0.466856\pi$
$104$	−18.3823	−1.80253
$105$	−5.77092	−0.563184
$106$	16.9509	1.64641
$107$	−5.56821	−0.538299	−0.269150	−	0.963098i	$-0.586743\pi$
$107$	−5.56821	−0.538299	−0.269150	+	0.963098i	$0.586743\pi$
$108$	60.1125	5.78433
$109$	19.3706	1.85536	0.927682	−	0.373370i	$-0.121798\pi$
$109$	19.3706	1.85536	0.927682	+	0.373370i	$0.121798\pi$
$110$	−2.97244	−0.283411
$111$	−0.972842	−0.0923380
$112$	4.18072	0.395041
$113$	−11.3986	−1.07229	−0.536144	−	0.844127i	$-0.680120\pi$
$113$	−11.3986	−1.07229	−0.536144	+	0.844127i	$0.680120\pi$
$114$	21.2349	1.98883
$115$	−4.59459	−0.428447
$116$	4.96957	0.461413
$117$	32.7005	3.02316
$118$	−13.2689	−1.22151
$119$	1.42521	0.130649
$120$	17.7407	1.61949
$121$	1.00000	0.0909091
$122$	8.92203	0.807762
$123$	32.3050	2.91284
$124$	−18.6688	−1.67651
$125$	10.4526	0.934910
$126$	−26.7900	−2.38664
$127$	−0.552522	−0.0490284	−0.0245142	−	0.999699i	$-0.507804\pi$
$127$	−0.552522	−0.0490284	−0.0245142	+	0.999699i	$0.507804\pi$
$128$	20.5914	1.82004
$129$	−3.28542	−0.289265
$130$	12.4712	1.09380
$131$	3.85988	0.337239	0.168620	−	0.985681i	$-0.446069\pi$
$131$	3.85988	0.337239	0.168620	+	0.985681i	$0.446069\pi$
$132$	−12.5392	−1.09140
$133$	−3.81947	−0.331190
$134$	31.2437	2.69905
$135$	−19.4116	−1.67069
$136$	−4.38130	−0.375693
$137$	4.47133	0.382012	0.191006	−	0.981589i	$-0.438825\pi$
$137$	4.47133	0.382012	0.191006	+	0.981589i	$0.438825\pi$
$138$	−29.5390	−2.51453
$139$	1.07340	0.0910446	0.0455223	−	0.998963i	$-0.485505\pi$
$139$	1.07340	0.0910446	0.0455223	+	0.998963i	$0.485505\pi$
$140$	−6.70401	−0.566593
$141$	5.31485	0.447591
$142$	−35.7260	−2.99806
$143$	−4.19562	−0.350855
$144$	22.8629	1.90524
$145$	−1.60478	−0.133270
$146$	−39.6105	−3.27819
$147$	−16.3245	−1.34642
$148$	−1.13014	−0.0928969
$149$	−2.23935	−0.183455	−0.0917274	−	0.995784i	$-0.529239\pi$
$149$	−2.23935	−0.183455	−0.0917274	+	0.995784i	$0.529239\pi$
$150$	27.5824	2.25209
$151$	−19.0344	−1.54900	−0.774498	−	0.632576i	$-0.781998\pi$
$151$	−19.0344	−1.54900	−0.774498	+	0.632576i	$0.781998\pi$
$152$	11.7416	0.952370
$153$	7.79396	0.630104
$154$	3.43727	0.276983
$155$	6.02857	0.484226
$156$	52.6098	4.21216
$157$	7.49129	0.597870	0.298935	−	0.954273i	$-0.403369\pi$
$157$	7.49129	0.597870	0.298935	+	0.954273i	$0.403369\pi$
$158$	−11.4902	−0.914107
$159$	−23.0912	−1.83125
$160$	−2.08026	−0.164459
$161$	5.31310	0.418731
$162$	−68.4073	−5.37458
$163$	−2.96923	−0.232568	−0.116284	−	0.993216i	$-0.537098\pi$
$163$	−2.96923	−0.232568	−0.116284	+	0.993216i	$0.537098\pi$
$164$	37.5283	2.93047
$165$	4.04918	0.315228
$166$	−37.5359	−2.91335
$167$	−4.96048	−0.383853	−0.191927	−	0.981409i	$-0.561474\pi$
$167$	−4.96048	−0.383853	−0.191927	+	0.981409i	$0.561474\pi$
$168$	−20.5150	−1.58276
$169$	4.60323	0.354094
$170$	2.97244	0.227975
$171$	−20.8873	−1.59729
$172$	−3.81663	−0.291015
$173$	3.80667	0.289415	0.144708	−	0.989474i	$-0.453776\pi$
$173$	3.80667	0.289415	0.144708	+	0.989474i	$0.453776\pi$
$174$	−10.3173	−0.782150
$175$	−4.96117	−0.375029
$176$	−2.93341	−0.221114
$177$	18.0755	1.35864
$178$	−16.5250	−1.23860
$179$	3.14456	0.235035	0.117518	−	0.993071i	$-0.462506\pi$
$179$	3.14456	0.235035	0.117518	+	0.993071i	$0.462506\pi$
$180$	−36.6619	−2.73262
$181$	7.68320	0.571088	0.285544	−	0.958366i	$-0.407826\pi$
$181$	7.68320	0.571088	0.285544	+	0.958366i	$0.407826\pi$
$182$	−14.4215	−1.06899
$183$	−12.1540	−0.898447
$184$	−16.3332	−1.20410
$185$	0.364946	0.0268314
$186$	38.7582	2.84189
$187$	−1.00000	−0.0731272
$188$	6.17420	0.450300
$189$	22.4472	1.63280
$190$	−7.96595	−0.577911
$191$	−2.62489	−0.189931	−0.0949653	−	0.995481i	$-0.530274\pi$
$191$	−2.62489	−0.189931	−0.0949653	+	0.995481i	$0.530274\pi$
$192$	−32.6491	−2.35625
$193$	18.1746	1.30824	0.654118	−	0.756392i	$-0.273040\pi$
$193$	18.1746	1.30824	0.654118	+	0.756392i	$0.273040\pi$
$194$	−3.24655	−0.233089
$195$	−16.9888	−1.21660
$196$	−18.9640	−1.35457
$197$	8.56808	0.610451	0.305225	−	0.952280i	$-0.401268\pi$
$197$	8.56808	0.610451	0.305225	+	0.952280i	$0.401268\pi$
$198$	18.7972	1.33586
$199$	−19.7427	−1.39952	−0.699762	−	0.714376i	$-0.746711\pi$
$199$	−19.7427	−1.39952	−0.699762	+	0.714376i	$0.746711\pi$
$200$	15.2514	1.07843
$201$	−42.5616	−3.00206
$202$	2.24581	0.158015
$203$	1.85574	0.130247
$204$	12.5392	0.877921
$205$	−12.1187	−0.846406
$206$	−5.08805	−0.354501
$207$	29.0555	2.01949
$208$	12.3075	0.853370
$209$	2.67994	0.185375
$210$	13.9181	0.960442
$211$	−19.8374	−1.36566	−0.682830	−	0.730577i	$-0.739251\pi$
$211$	−19.8374	−1.36566	−0.682830	+	0.730577i	$0.739251\pi$
$212$	−26.8248	−1.84234
$213$	48.6675	3.33464
$214$	13.4292	0.918004
$215$	1.23247	0.0840538
$216$	−69.0061	−4.69527
$217$	−6.97132	−0.473244
$218$	−46.7174	−3.16410
$219$	53.9592	3.64622
$220$	4.70389	0.317136
$221$	4.19562	0.282228
$222$	2.34627	0.157471
$223$	12.5241	0.838677	0.419339	−	0.907830i	$-0.362262\pi$
$223$	12.5241	0.838677	0.419339	+	0.907830i	$0.362262\pi$
$224$	2.40558	0.160729
$225$	−27.1309	−1.80873
$226$	27.4907	1.82866
$227$	19.0042	1.26135	0.630677	−	0.776046i	$-0.282777\pi$
$227$	19.0042	1.26135	0.630677	+	0.776046i	$0.282777\pi$
$228$	−33.6043	−2.22550
$229$	−19.4916	−1.28804	−0.644019	−	0.765009i	$-0.722734\pi$
$229$	−19.4916	−1.28804	−0.644019	+	0.765009i	$0.722734\pi$
$230$	11.0811	0.730665
$231$	−4.68240	−0.308079
$232$	−5.70481	−0.374539
$233$	0.209112	0.0136994	0.00684969	−	0.999977i	$-0.497820\pi$
$233$	0.209112	0.0136994	0.00684969	+	0.999977i	$0.497820\pi$
$234$	−78.8661	−5.15564
$235$	−1.99378	−0.130060
$236$	20.9981	1.36686
$237$	15.6524	1.01673
$238$	−3.43727	−0.222805
$239$	16.0364	1.03731	0.518656	−	0.854983i	$-0.326433\pi$
$239$	16.0364	1.03731	0.518656	+	0.854983i	$0.326433\pi$
$240$	−11.8779	−0.766716
$241$	−26.9844	−1.73822	−0.869109	−	0.494620i	$-0.835307\pi$
$241$	−26.9844	−1.73822	−0.869109	+	0.494620i	$0.835307\pi$
$242$	−2.41177	−0.155034
$243$	45.9369	2.94685
$244$	−14.1191	−0.903885
$245$	6.12388	0.391241
$246$	−77.9122	−4.96750
$247$	−11.2440	−0.715439
$248$	21.4309	1.36086
$249$	51.1331	3.24043
$250$	−25.2093	−1.59437
$251$	4.46297	0.281700	0.140850	−	0.990031i	$-0.455016\pi$
$251$	4.46297	0.281700	0.140850	+	0.990031i	$0.455016\pi$
$252$	42.3952	2.67064
$253$	−3.72795	−0.234374
$254$	1.33256	0.0836120
$255$	−4.04918	−0.253570
$256$	−29.7866	−1.86166
$257$	2.67827	0.167066	0.0835329	−	0.996505i	$-0.473380\pi$
$257$	2.67827	0.167066	0.0835329	+	0.996505i	$0.473380\pi$
$258$	7.92367	0.493306
$259$	−0.422017	−0.0262228
$260$	−19.7357	−1.22396
$261$	10.1484	0.628169
$262$	−9.30914	−0.575121
$263$	17.1684	1.05865	0.529324	−	0.848420i	$-0.322446\pi$
$263$	17.1684	1.05865	0.529324	+	0.848420i	$0.322446\pi$
$264$	14.3944	0.885913
$265$	8.66230	0.532121
$266$	9.21167	0.564804
$267$	22.5111	1.37766
$268$	−49.4433	−3.02023
$269$	−31.3873	−1.91372	−0.956858	−	0.290554i	$-0.906160\pi$
$269$	−31.3873	−1.91372	−0.956858	+	0.290554i	$0.906160\pi$
$270$	46.8163	2.84915
$271$	−23.3978	−1.42132	−0.710659	−	0.703537i	$-0.751603\pi$
$271$	−23.3978	−1.42132	−0.710659	+	0.703537i	$0.751603\pi$
$272$	2.93341	0.177864
$273$	19.6456	1.18900
$274$	−10.7838	−0.651474
$275$	3.48101	0.209913
$276$	46.7456	2.81375
$277$	−8.43854	−0.507023	−0.253511	−	0.967332i	$-0.581586\pi$
$277$	−8.43854	−0.507023	−0.253511	+	0.967332i	$0.581586\pi$
$278$	−2.58879	−0.155265
$279$	−38.1237	−2.28241
$280$	7.69586	0.459916
$281$	−27.7724	−1.65676	−0.828382	−	0.560164i	$-0.810738\pi$
$281$	−27.7724	−1.65676	−0.828382	+	0.560164i	$0.810738\pi$
$282$	−12.8182	−0.763312
$283$	12.1798	0.724011	0.362006	−	0.932176i	$-0.382092\pi$
$283$	12.1798	0.724011	0.362006	+	0.932176i	$0.382092\pi$
$284$	56.5364	3.35482
$285$	10.8516	0.642791
$286$	10.1189	0.598341
$287$	14.0138	0.827210
$288$	13.1553	0.775181
$289$	1.00000	0.0588235
$290$	3.87036	0.227275
$291$	4.42259	0.259257
$292$	62.6838	3.66829
$293$	11.2128	0.655062	0.327531	−	0.944841i	$-0.393783\pi$
$293$	11.2128	0.655062	0.327531	+	0.944841i	$0.393783\pi$
$294$	39.3710	2.29616
$295$	−6.78074	−0.394790
$296$	1.29734	0.0754064
$297$	−15.7502	−0.913917
$298$	5.40080	0.312860
$299$	15.6410	0.904545
$300$	−43.6492	−2.52009
$301$	−1.42521	−0.0821476
$302$	45.9065	2.64162
$303$	−3.05934	−0.175754
$304$	−7.86136	−0.450880
$305$	4.55937	0.261069
$306$	−18.7972	−1.07457
$307$	23.2958	1.32956	0.664781	−	0.747039i	$-0.268525\pi$
$307$	23.2958	1.32956	0.664781	+	0.747039i	$0.268525\pi$
$308$	−5.43949	−0.309944
$309$	6.93116	0.394300
$310$	−14.5395	−0.825789
$311$	11.6961	0.663224	0.331612	−	0.943416i	$-0.392408\pi$
$311$	11.6961	0.663224	0.331612	+	0.943416i	$0.392408\pi$
$312$	−60.3934	−3.41910
$313$	34.6487	1.95846	0.979230	−	0.202754i	$-0.0649893\pi$
$313$	34.6487	1.95846	0.979230	+	0.202754i	$0.0649893\pi$
$314$	−18.0673	−1.01959
$315$	−13.6903	−0.771361
$316$	18.1832	1.02288
$317$	22.2425	1.24926	0.624632	−	0.780919i	$-0.285249\pi$
$317$	22.2425	1.24926	0.624632	+	0.780919i	$0.285249\pi$
$318$	55.6907	3.12298
$319$	−1.30208	−0.0729026
$320$	12.2478	0.684673
$321$	−18.2939	−1.02107
$322$	−12.8140	−0.714094
$323$	−2.67994	−0.149116
$324$	108.255	6.01415
$325$	−14.6050	−0.810140
$326$	7.16110	0.396617
$327$	63.6404	3.51932
$328$	−43.0806	−2.37873
$329$	2.30557	0.127110
$330$	−9.76569	−0.537584
$331$	3.67062	0.201756	0.100878	−	0.994899i	$-0.467835\pi$
$331$	3.67062	0.201756	0.100878	+	0.994899i	$0.467835\pi$
$332$	59.4007	3.26004
$333$	−2.30786	−0.126470
$334$	11.9635	0.654615
$335$	15.9663	0.872332
$336$	13.7354	0.749328
$337$	−15.9107	−0.866712	−0.433356	−	0.901223i	$-0.642671\pi$
$337$	−15.9107	−0.866712	−0.433356	+	0.901223i	$0.642671\pi$
$338$	−11.1019	−0.603865
$339$	−37.4491	−2.03395
$340$	−4.70389	−0.255104
$341$	4.89145	0.264887
$342$	50.3754	2.72399
$343$	−17.0580	−0.921045
$344$	4.38130	0.236224
$345$	−15.0951	−0.812695
$346$	−9.18080	−0.493563
$347$	−25.4539	−1.36643	−0.683217	−	0.730215i	$-0.739420\pi$
$347$	−25.4539	−1.36643	−0.683217	+	0.730215i	$0.739420\pi$
$348$	16.3271	0.875224
$349$	7.72924	0.413737	0.206868	−	0.978369i	$-0.433673\pi$
$349$	7.72924	0.413737	0.206868	+	0.978369i	$0.433673\pi$
$350$	11.9652	0.639566
$351$	66.0817	3.52718
$352$	−1.68788	−0.0899642
$353$	−15.8663	−0.844477	−0.422239	−	0.906485i	$-0.638756\pi$
$353$	−15.8663	−0.844477	−0.422239	+	0.906485i	$0.638756\pi$
$354$	−43.5940	−2.31699
$355$	−18.2568	−0.968971
$356$	26.1509	1.38599
$357$	4.68240	0.247819
$358$	−7.58395	−0.400824
$359$	20.5056	1.08224	0.541121	−	0.840945i	$-0.318000\pi$
$359$	20.5056	1.08224	0.541121	+	0.840945i	$0.318000\pi$
$360$	42.0860	2.21813
$361$	−11.8179	−0.621996
$362$	−18.5301	−0.973921
$363$	3.28542	0.172440
$364$	22.8220	1.19620
$365$	−20.2419	−1.05951
$366$	29.3126	1.53219
$367$	9.87227	0.515329	0.257664	−	0.966235i	$-0.417047\pi$
$367$	9.87227	0.515329	0.257664	+	0.966235i	$0.417047\pi$
$368$	10.9356	0.570058
$369$	76.6368	3.98955
$370$	−0.880165	−0.0457576
$371$	−10.0169	−0.520053
$372$	−61.3349	−3.18007
$373$	31.4685	1.62938	0.814689	−	0.579898i	$-0.196908\pi$
$373$	31.4685	1.62938	0.814689	+	0.579898i	$0.196908\pi$
$374$	2.41177	0.124710
$375$	34.3412	1.77337
$376$	−7.08766	−0.365518
$377$	5.46304	0.281361
$378$	−54.1376	−2.78454
$379$	5.87198	0.301623	0.150812	−	0.988563i	$-0.451811\pi$
$379$	5.87198	0.301623	0.150812	+	0.988563i	$0.451811\pi$
$380$	12.6061	0.646681
$381$	−1.81527	−0.0929989
$382$	6.33064	0.323904
$383$	13.0501	0.666830	0.333415	−	0.942780i	$-0.391799\pi$
$383$	13.0501	0.666830	0.333415	+	0.942780i	$0.391799\pi$
$384$	67.6514	3.45232
$385$	1.75653	0.0895209
$386$	−43.8329	−2.23104
$387$	−7.79396	−0.396189
$388$	5.13767	0.260826
$389$	−26.0808	−1.32235	−0.661175	−	0.750232i	$-0.729942\pi$
$389$	−26.0808	−1.32235	−0.661175	+	0.750232i	$0.729942\pi$
$390$	40.9731	2.07476
$391$	3.72795	0.188530
$392$	21.7697	1.09954
$393$	12.6813	0.639688
$394$	−20.6642	−1.04105
$395$	−5.87174	−0.295439
$396$	−29.7467	−1.49483
$397$	−8.64308	−0.433784	−0.216892	−	0.976196i	$-0.569592\pi$
$397$	−8.64308	−0.433784	−0.216892	+	0.976196i	$0.569592\pi$
$398$	47.6149	2.38672
$399$	−12.5485	−0.628213
$400$	−10.2112	−0.510562
$401$	5.38012	0.268670	0.134335	−	0.990936i	$-0.457110\pi$
$401$	5.38012	0.268670	0.134335	+	0.990936i	$0.457110\pi$
$402$	102.649	5.11965
$403$	−20.5226	−1.02231
$404$	−3.55400	−0.176818
$405$	−34.9577	−1.73706
$406$	−4.47561	−0.222121
$407$	0.296109	0.0146776
$408$	−14.3944	−0.712628
$409$	1.45898	0.0721417	0.0360708	−	0.999349i	$-0.488516\pi$
$409$	1.45898	0.0721417	0.0360708	+	0.999349i	$0.488516\pi$
$410$	29.2275	1.44344
$411$	14.6902	0.724613
$412$	8.05185	0.396686
$413$	7.84113	0.385837
$414$	−70.0751	−3.44400
$415$	−19.1817	−0.941595
$416$	7.08170	0.347209
$417$	3.52656	0.172697
$418$	−6.46339	−0.316135
$419$	27.8333	1.35974	0.679872	−	0.733331i	$-0.262035\pi$
$419$	27.8333	1.35974	0.679872	+	0.733331i	$0.262035\pi$
$420$	−22.0255	−1.07473
$421$	4.99022	0.243209	0.121604	−	0.992579i	$-0.461196\pi$
$421$	4.99022	0.243209	0.121604	+	0.992579i	$0.461196\pi$
$422$	47.8431	2.32897
$423$	12.6084	0.613039
$424$	30.7935	1.49546
$425$	−3.48101	−0.168854
$426$	−117.375	−5.68682
$427$	−5.27237	−0.255148
$428$	−21.2518	−1.02725
$429$	−13.7844	−0.665515
$430$	−2.97244	−0.143344
$431$	10.9500	0.527442	0.263721	−	0.964599i	$-0.415050\pi$
$431$	10.9500	0.527442	0.263721	+	0.964599i	$0.415050\pi$
$432$	46.2017	2.22288
$433$	16.1841	0.777760	0.388880	−	0.921288i	$-0.372862\pi$
$433$	16.1841	0.777760	0.388880	+	0.921288i	$0.372862\pi$
$434$	16.8132	0.807060
$435$	−5.27237	−0.252791
$436$	73.9304	3.54062
$437$	−9.99067	−0.477918
$438$	−130.137	−6.21819
$439$	38.0553	1.81628	0.908140	−	0.418667i	$-0.137503\pi$
$439$	38.0553	1.81628	0.908140	+	0.418667i	$0.137503\pi$
$440$	−5.39982	−0.257426
$441$	−38.7265	−1.84412
$442$	−10.1189	−0.481305
$443$	3.35933	0.159606	0.0798032	−	0.996811i	$-0.474571\pi$
$443$	3.35933	0.159606	0.0798032	+	0.996811i	$0.474571\pi$
$444$	−3.71298	−0.176210
$445$	−8.44468	−0.400316
$446$	−30.2053	−1.43026
$447$	−7.35720	−0.347984
$448$	−14.1631	−0.669145
$449$	−1.79512	−0.0847168	−0.0423584	−	0.999102i	$-0.513487\pi$
$449$	−1.79512	−0.0847168	−0.0423584	+	0.999102i	$0.513487\pi$
$450$	65.4335	3.08456
$451$	−9.83284	−0.463010
$452$	−43.5042	−2.04626
$453$	−62.5359	−2.93819
$454$	−45.8337	−2.15108
$455$	−7.36972	−0.345498
$456$	38.5761	1.80649
$457$	8.46543	0.395996	0.197998	−	0.980202i	$-0.436556\pi$
$457$	8.46543	0.395996	0.197998	+	0.980202i	$0.436556\pi$
$458$	47.0091	2.19659
$459$	15.7502	0.735154
$460$	−17.5358	−0.817613
$461$	−32.3755	−1.50788	−0.753939	−	0.656945i	$-0.771848\pi$
$461$	−32.3755	−1.50788	−0.753939	+	0.656945i	$0.771848\pi$
$462$	11.2929	0.525392
$463$	12.6996	0.590199	0.295100	−	0.955466i	$-0.404647\pi$
$463$	12.6996	0.590199	0.295100	+	0.955466i	$0.404647\pi$
$464$	3.81954	0.177318
$465$	19.8064	0.918498
$466$	−0.504329	−0.0233626
$467$	−32.0534	−1.48325	−0.741626	−	0.670813i	$-0.765945\pi$
$467$	−32.0534	−1.48325	−0.741626	+	0.670813i	$0.765945\pi$
$468$	124.806	5.76915
$469$	−18.4631	−0.852548
$470$	4.80853	0.221801
$471$	24.6120	1.13406
$472$	−24.1048	−1.10951
$473$	1.00000	0.0459800
$474$	−37.7499	−1.73391
$475$	9.32891	0.428040
$476$	5.43949	0.249319
$477$	−54.7791	−2.50816
$478$	−38.6762	−1.76901
$479$	26.3644	1.20462	0.602310	−	0.798262i	$-0.294247\pi$
$479$	26.3644	1.20462	0.602310	+	0.798262i	$0.294247\pi$
$480$	−6.83453	−0.311952
$481$	−1.24236	−0.0566468
$482$	65.0802	2.96432
$483$	17.4557	0.794263
$484$	3.81663	0.173483
$485$	−1.65906	−0.0753342
$486$	−110.789	−5.02550
$487$	−7.61680	−0.345150	−0.172575	−	0.984996i	$-0.555209\pi$
$487$	−7.61680	−0.345150	−0.172575	+	0.984996i	$0.555209\pi$
$488$	16.2080	0.733703
$489$	−9.75516	−0.441144
$490$	−14.7694	−0.667213
$491$	−34.6580	−1.56409	−0.782046	−	0.623220i	$-0.785824\pi$
$491$	−34.6580	−1.56409	−0.782046	+	0.623220i	$0.785824\pi$
$492$	123.296	5.55862
$493$	1.30208	0.0586428
$494$	27.1179	1.22009
$495$	9.60583	0.431750
$496$	−14.3486	−0.644272
$497$	21.1118	0.946996
$498$	−123.321	−5.52615
$499$	−24.2755	−1.08672	−0.543361	−	0.839499i	$-0.682849\pi$
$499$	−24.2755	−1.08672	−0.543361	+	0.839499i	$0.682849\pi$
$500$	39.8937	1.78410
$501$	−16.2972	−0.728107
$502$	−10.7637	−0.480405
$503$	−11.2061	−0.499657	−0.249829	−	0.968290i	$-0.580374\pi$
$503$	−11.2061	−0.499657	−0.249829	+	0.968290i	$0.580374\pi$
$504$	−48.6675	−2.16782
$505$	1.14766	0.0510703
$506$	8.99095	0.399696
$507$	15.1235	0.671659
$508$	−2.10877	−0.0935617
$509$	−34.9803	−1.55047	−0.775237	−	0.631671i	$-0.782369\pi$
$509$	−34.9803	−1.55047	−0.775237	+	0.631671i	$0.782369\pi$
$510$	9.76569	0.432432
$511$	23.4074	1.03548
$512$	30.6555	1.35480
$513$	−42.2095	−1.86359
$514$	−6.45937	−0.284911
$515$	−2.60011	−0.114575
$516$	−12.5392	−0.552009
$517$	−1.61771	−0.0711467
$518$	1.01781	0.0447199
$519$	12.5065	0.548974
$520$	22.6556	0.993514
$521$	−20.1024	−0.880700	−0.440350	−	0.897826i	$-0.645146\pi$
$521$	−20.1024	−0.880700	−0.440350	+	0.897826i	$0.645146\pi$
$522$	−24.4755	−1.07127
$523$	−33.8208	−1.47888	−0.739440	−	0.673223i	$-0.764909\pi$
$523$	−33.8208	−1.47888	−0.739440	+	0.673223i	$0.764909\pi$
$524$	14.7317	0.643559
$525$	−16.2995	−0.711368
$526$	−41.4062	−1.80540
$527$	−4.89145	−0.213075
$528$	−9.63748	−0.419417
$529$	−9.10241	−0.395757
$530$	−20.8915	−0.907467
$531$	42.8804	1.86085
$532$	−14.5775	−0.632015
$533$	41.2549	1.78695
$534$	−54.2916	−2.34943
$535$	6.86266	0.296699
$536$	56.7584	2.45159
$537$	10.3312	0.445823
$538$	75.6989	3.26361
$539$	4.96879	0.214021
$540$	−74.0870	−3.18820
$541$	−17.6242	−0.757722	−0.378861	−	0.925454i	$-0.623684\pi$
$541$	−17.6242	−0.757722	−0.378861	+	0.925454i	$0.623684\pi$
$542$	56.4302	2.42388
$543$	25.2425	1.08326
$544$	1.68788	0.0723672
$545$	−23.8737	−1.02264
$546$	−47.3806	−2.02770
$547$	−12.7887	−0.546805	−0.273403	−	0.961900i	$-0.588149\pi$
$547$	−12.7887	−0.546805	−0.273403	+	0.961900i	$0.588149\pi$
$548$	17.0654	0.728999
$549$	−28.8327	−1.23055
$550$	−8.39540	−0.357981
$551$	−3.48950	−0.148658
$552$	−53.6615	−2.28398
$553$	6.78997	0.288739
$554$	20.3518	0.864666
$555$	1.19900	0.0508947
$556$	4.09677	0.173742
$557$	0.846942	0.0358861	0.0179431	−	0.999839i	$-0.494288\pi$
$557$	0.846942	0.0358861	0.0179431	+	0.999839i	$0.494288\pi$
$558$	91.9457	3.89237
$559$	−4.19562	−0.177456
$560$	−5.15262	−0.217738
$561$	−3.28542	−0.138710
$562$	66.9807	2.82541
$563$	−42.1861	−1.77793	−0.888966	−	0.457974i	$-0.848575\pi$
$563$	−42.1861	−1.77793	−0.888966	+	0.457974i	$0.848575\pi$
$564$	20.2848	0.854144
$565$	14.0484	0.591021
$566$	−29.3748	−1.23471
$567$	40.4245	1.69767
$568$	−64.9009	−2.72318
$569$	−33.3973	−1.40009	−0.700044	−	0.714100i	$-0.746836\pi$
$569$	−33.3973	−1.40009	−0.700044	+	0.714100i	$0.746836\pi$
$570$	−26.1715	−1.09620
$571$	24.1234	1.00953	0.504766	−	0.863256i	$-0.331579\pi$
$571$	24.1234	1.00953	0.504766	+	0.863256i	$0.331579\pi$
$572$	−16.0131	−0.669543
$573$	−8.62387	−0.360267
$574$	−33.7981	−1.41071
$575$	−12.9770	−0.541180
$576$	−77.4532	−3.22722
$577$	−9.37007	−0.390081	−0.195040	−	0.980795i	$-0.562484\pi$
$577$	−9.37007	−0.390081	−0.195040	+	0.980795i	$0.562484\pi$
$578$	−2.41177	−0.100316
$579$	59.7111	2.48151
$580$	−6.12485	−0.254321
$581$	22.1814	0.920240
$582$	−10.6663	−0.442131
$583$	7.02840	0.291087
$584$	−71.9578	−2.97763
$585$	−40.3024	−1.66630
$586$	−27.0428	−1.11713
$587$	30.6607	1.26550	0.632751	−	0.774355i	$-0.281926\pi$
$587$	30.6607	1.26550	0.632751	+	0.774355i	$0.281926\pi$
$588$	−62.3047	−2.56940
$589$	13.1088	0.540138
$590$	16.3536	0.673267
$591$	28.1497	1.15792
$592$	−0.868610	−0.0356996
$593$	−5.32957	−0.218859	−0.109430	−	0.993995i	$-0.534902\pi$
$593$	−5.32957	−0.218859	−0.109430	+	0.993995i	$0.534902\pi$
$594$	37.9857	1.55857
$595$	−1.75653	−0.0720106
$596$	−8.54678	−0.350090
$597$	−64.8631	−2.65467
$598$	−37.7226	−1.54259
$599$	−32.2794	−1.31890	−0.659450	−	0.751748i	$-0.729211\pi$
$599$	−32.2794	−1.31890	−0.659450	+	0.751748i	$0.729211\pi$
$600$	50.1070	2.04561
$601$	40.8548	1.66650	0.833251	−	0.552896i	$-0.186477\pi$
$601$	40.8548	1.66650	0.833251	+	0.552896i	$0.186477\pi$
$602$	3.43727	0.140093
$603$	−100.968	−4.11175
$604$	−72.6472	−2.95597
$605$	−1.23247	−0.0501071
$606$	7.37842	0.299728
$607$	11.0159	0.447121	0.223560	−	0.974690i	$-0.428232\pi$
$607$	11.0159	0.447121	0.223560	+	0.974690i	$0.428232\pi$
$608$	−4.52341	−0.183448
$609$	6.09687	0.247058
$610$	−10.9961	−0.445221
$611$	6.78729	0.274584
$612$	29.7467	1.20244
$613$	−9.83633	−0.397286	−0.198643	−	0.980072i	$-0.563653\pi$
$613$	−9.83633	−0.397286	−0.198643	+	0.980072i	$0.563653\pi$
$614$	−56.1841	−2.26741
$615$	−39.8150	−1.60549
$616$	6.24425	0.251588
$617$	12.5258	0.504269	0.252135	−	0.967692i	$-0.418867\pi$
$617$	12.5258	0.504269	0.252135	+	0.967692i	$0.418867\pi$
$618$	−16.7164	−0.672430
$619$	25.3504	1.01892	0.509459	−	0.860495i	$-0.329846\pi$
$619$	25.3504	1.01892	0.509459	+	0.860495i	$0.329846\pi$
$620$	23.0088	0.924056
$621$	58.7157	2.35618
$622$	−28.2082	−1.13105
$623$	9.76527	0.391237
$624$	40.4352	1.61870
$625$	4.52253	0.180901
$626$	−83.5646	−3.33991
$627$	8.80471	0.351626
$628$	28.5915	1.14092
$629$	−0.296109	−0.0118066
$630$	33.0178	1.31546
$631$	−9.52158	−0.379048	−0.189524	−	0.981876i	$-0.560694\pi$
$631$	−9.52158	−0.379048	−0.189524	+	0.981876i	$0.560694\pi$
$632$	−20.8734	−0.830298
$633$	−65.1740	−2.59043
$634$	−53.6438	−2.13047
$635$	0.680968	0.0270234
$636$	−88.1307	−3.49461
$637$	−20.8471	−0.825994
$638$	3.14032	0.124327
$639$	115.453	4.56726
$640$	−25.3784	−1.00317
$641$	−13.8726	−0.547934	−0.273967	−	0.961739i	$-0.588336\pi$
$641$	−13.8726	−0.547934	−0.273967	+	0.961739i	$0.588336\pi$
$642$	44.1207	1.74130
$643$	28.1170	1.10883	0.554414	−	0.832241i	$-0.312943\pi$
$643$	28.1170	1.10883	0.554414	+	0.832241i	$0.312943\pi$
$644$	20.2781	0.799070
$645$	4.04918	0.159436
$646$	6.46339	0.254299
$647$	18.9154	0.743642	0.371821	−	0.928304i	$-0.378734\pi$
$647$	18.9154	0.743642	0.371821	+	0.928304i	$0.378734\pi$
$648$	−124.271	−4.88182
$649$	−5.50175	−0.215962
$650$	35.2239	1.38160
$651$	−22.9037	−0.897667
$652$	−11.3325	−0.443814
$653$	−3.33368	−0.130457	−0.0652284	−	0.997870i	$-0.520778\pi$
$653$	−3.33368	−0.130457	−0.0652284	+	0.997870i	$0.520778\pi$
$654$	−153.486	−6.00178
$655$	−4.75719	−0.185879
$656$	28.8438	1.12616
$657$	128.007	4.99402
$658$	−5.56050	−0.216771
$659$	47.2092	1.83901	0.919504	−	0.393081i	$-0.128591\pi$
$659$	47.2092	1.83901	0.919504	+	0.393081i	$0.128591\pi$
$660$	15.4542	0.601555
$661$	−17.5355	−0.682051	−0.341025	−	0.940054i	$-0.610774\pi$
$661$	−17.5355	−0.682051	−0.341025	+	0.940054i	$0.610774\pi$
$662$	−8.85270	−0.344070
$663$	13.7844	0.535340
$664$	−68.1889	−2.64624
$665$	4.70738	0.182545
$666$	5.56603	0.215679
$667$	4.85409	0.187951
$668$	−18.9323	−0.732514
$669$	41.1470	1.59083
$670$	−38.5070	−1.48766
$671$	3.69937	0.142813
$672$	7.90332	0.304877
$673$	34.7901	1.34106	0.670530	−	0.741883i	$-0.266067\pi$
$673$	34.7901	1.34106	0.670530	+	0.741883i	$0.266067\pi$
$674$	38.3730	1.47807
$675$	−54.8265	−2.11027
$676$	17.5688	0.675724
$677$	34.0244	1.30766	0.653831	−	0.756641i	$-0.273161\pi$
$677$	34.0244	1.30766	0.653831	+	0.756641i	$0.273161\pi$
$678$	90.3185	3.46866
$679$	1.91851	0.0736257
$680$	5.39982	0.207074
$681$	62.4367	2.39258
$682$	−11.7970	−0.451732
$683$	−42.8694	−1.64035	−0.820175	−	0.572112i	$-0.806124\pi$
$683$	−42.8694	−1.64035	−0.820175	+	0.572112i	$0.806124\pi$
$684$	−79.7193	−3.04814
$685$	−5.51079	−0.210556
$686$	41.1400	1.57073
$687$	−64.0379	−2.44320
$688$	−2.93341	−0.111835
$689$	−29.4885	−1.12342
$690$	36.4060	1.38595
$691$	24.3302	0.925565	0.462782	−	0.886472i	$-0.346851\pi$
$691$	24.3302	0.925565	0.462782	+	0.886472i	$0.346851\pi$
$692$	14.5286	0.552296
$693$	−11.1080	−0.421958
$694$	61.3888	2.33029
$695$	−1.32293	−0.0501818
$696$	−18.7427	−0.710439
$697$	9.83284	0.372445
$698$	−18.6411	−0.705577
$699$	0.687019	0.0259855
$700$	−18.9349	−0.715674
$701$	−9.07344	−0.342699	−0.171350	−	0.985210i	$-0.554813\pi$
$701$	−9.07344	−0.342699	−0.171350	+	0.985210i	$0.554813\pi$
$702$	−159.374	−6.01518
$703$	0.793554	0.0299295
$704$	9.93760	0.374537
$705$	−6.55039	−0.246702
$706$	38.2658	1.44015
$707$	−1.32713	−0.0499120
$708$	68.9876	2.59271
$709$	16.4226	0.616764	0.308382	−	0.951263i	$-0.400212\pi$
$709$	16.4226	0.616764	0.308382	+	0.951263i	$0.400212\pi$
$710$	44.0312	1.65246
$711$	37.1320	1.39256
$712$	−30.0199	−1.12504
$713$	−18.2350	−0.682908
$714$	−11.2929	−0.422625
$715$	5.17098	0.193384
$716$	12.0016	0.448521
$717$	52.6864	1.96761
$718$	−49.4547	−1.84563
$719$	−11.6145	−0.433148	−0.216574	−	0.976266i	$-0.569488\pi$
$719$	−11.6145	−0.433148	−0.216574	+	0.976266i	$0.569488\pi$
$720$	−28.1779	−1.05013
$721$	3.00672	0.111976
$722$	28.5021	1.06074
$723$	−88.6550	−3.29712
$724$	29.3239	1.08982
$725$	−4.53257	−0.168335
$726$	−7.92367	−0.294075
$727$	−16.7893	−0.622680	−0.311340	−	0.950299i	$-0.600778\pi$
$727$	−16.7893	−0.622680	−0.311340	+	0.950299i	$0.600778\pi$
$728$	−26.1985	−0.970982
$729$	65.8300	2.43815
$730$	48.8189	1.80687
$731$	−1.00000	−0.0369863
$732$	−46.3872	−1.71452
$733$	41.3020	1.52552	0.762762	−	0.646680i	$-0.223843\pi$
$733$	41.3020	1.52552	0.762762	+	0.646680i	$0.223843\pi$
$734$	−23.8096	−0.878830
$735$	20.1195	0.742119
$736$	6.29232	0.231938
$737$	12.9547	0.477192
$738$	−184.830	−6.80369
$739$	−24.9377	−0.917349	−0.458675	−	0.888604i	$-0.651676\pi$
$739$	−24.9377	−0.917349	−0.458675	+	0.888604i	$0.651676\pi$
$740$	1.39286	0.0512027
$741$	−36.9412	−1.35707
$742$	24.1585	0.886887
$743$	−27.8176	−1.02053	−0.510265	−	0.860017i	$-0.670453\pi$
$743$	−27.8176	−1.02053	−0.510265	+	0.860017i	$0.670453\pi$
$744$	70.4093	2.58133
$745$	2.75994	0.101116
$746$	−75.8948	−2.77871
$747$	121.302	4.43822
$748$	−3.81663	−0.139550
$749$	−7.93585	−0.289970
$750$	−82.8230	−3.02427
$751$	−8.50367	−0.310303	−0.155152	−	0.987891i	$-0.549587\pi$
$751$	−8.50367	−0.310303	−0.155152	+	0.987891i	$0.549587\pi$
$752$	4.74540	0.173047
$753$	14.6627	0.534339
$754$	−13.1756	−0.479827
$755$	23.4593	0.853773
$756$	85.6728	3.11589
$757$	−10.4675	−0.380447	−0.190223	−	0.981741i	$-0.560921\pi$
$757$	−10.4675	−0.380447	−0.190223	+	0.981741i	$0.560921\pi$
$758$	−14.1619	−0.514382
$759$	−12.2479	−0.444569
$760$	−14.4712	−0.524925
$761$	−13.0379	−0.472624	−0.236312	−	0.971677i	$-0.575939\pi$
$761$	−13.0379	−0.472624	−0.236312	+	0.971677i	$0.575939\pi$
$762$	4.37800	0.158598
$763$	27.6071	0.999444
$764$	−10.0182	−0.362447
$765$	−9.60583	−0.347300
$766$	−31.4739	−1.13720
$767$	23.0832	0.833487
$768$	−97.8614	−3.53127
$769$	1.67357	0.0603504	0.0301752	−	0.999545i	$-0.490393\pi$
$769$	1.67357	0.0603504	0.0301752	+	0.999545i	$0.490393\pi$
$770$	−4.23634	−0.152667
$771$	8.79923	0.316897
$772$	69.3657	2.49653
$773$	−10.4843	−0.377095	−0.188548	−	0.982064i	$-0.560378\pi$
$773$	−10.4843	−0.377095	−0.188548	+	0.982064i	$0.560378\pi$
$774$	18.7972	0.675653
$775$	17.0272	0.611635
$776$	−5.89778	−0.211718
$777$	−1.38650	−0.0497404
$778$	62.9009	2.25511
$779$	−26.3514	−0.944137
$780$	−64.8401	−2.32165
$781$	−14.8132	−0.530057
$782$	−8.99095	−0.321516
$783$	20.5080	0.732896
$784$	−14.5755	−0.520553
$785$	−9.23280	−0.329533
$786$	−30.5844	−1.09091
$787$	−19.1967	−0.684289	−0.342144	−	0.939647i	$-0.611153\pi$
$787$	−19.1967	−0.684289	−0.342144	+	0.939647i	$0.611153\pi$
$788$	32.7012	1.16493
$789$	56.4053	2.00808
$790$	14.1613	0.503836
$791$	−16.2453	−0.577617
$792$	34.1476	1.21338
$793$	−15.5212	−0.551172
$794$	20.8451	0.739765
$795$	28.4593	1.00935
$796$	−75.3507	−2.67074
$797$	−45.3909	−1.60783	−0.803914	−	0.594745i	$-0.797253\pi$
$797$	−45.3909	−1.60783	−0.803914	+	0.594745i	$0.797253\pi$
$798$	30.2642	1.07134
$799$	1.61771	0.0572304
$800$	−5.87553	−0.207731
$801$	53.4029	1.88690
$802$	−12.9756	−0.458184
$803$	−16.4239	−0.579585
$804$	−162.442	−5.72888
$805$	−6.54824	−0.230795
$806$	49.4959	1.74342
$807$	−103.120	−3.63001
$808$	4.07981	0.143527
$809$	−12.2401	−0.430339	−0.215169	−	0.976577i	$-0.569030\pi$
$809$	−12.2401	−0.430339	−0.215169	+	0.976577i	$0.569030\pi$
$810$	84.3100	2.96235
$811$	−16.2561	−0.570830	−0.285415	−	0.958404i	$-0.592131\pi$
$811$	−16.2561	−0.570830	−0.285415	+	0.958404i	$0.592131\pi$
$812$	7.08266	0.248553
$813$	−76.8717	−2.69601
$814$	−0.714147	−0.0250308
$815$	3.65949	0.128186
$816$	9.63748	0.337379
$817$	2.67994	0.0937592
$818$	−3.51871	−0.123029
$819$	46.6050	1.62851
$820$	−46.2526	−1.61521
$821$	16.8899	0.589460	0.294730	−	0.955581i	$-0.404770\pi$
$821$	16.8899	0.589460	0.294730	+	0.955581i	$0.404770\pi$
$822$	−35.4293	−1.23574
$823$	−32.3503	−1.12766	−0.563830	−	0.825891i	$-0.690673\pi$
$823$	−32.3503	−1.12766	−0.563830	+	0.825891i	$0.690673\pi$
$824$	−9.24311	−0.321999
$825$	11.4366	0.398171
$826$	−18.9110	−0.657997
$827$	−16.3371	−0.568098	−0.284049	−	0.958810i	$-0.591678\pi$
$827$	−16.3371	−0.568098	−0.284049	+	0.958810i	$0.591678\pi$
$828$	110.894	3.85383
$829$	33.1318	1.15072	0.575358	−	0.817902i	$-0.304863\pi$
$829$	33.1318	1.15072	0.575358	+	0.817902i	$0.304863\pi$
$830$	46.2619	1.60578
$831$	−27.7241	−0.961739
$832$	−41.6944	−1.44549
$833$	−4.96879	−0.172158
$834$	−8.50526	−0.294513
$835$	6.11365	0.211572
$836$	10.2283	0.353754
$837$	−77.0410	−2.66293
$838$	−67.1274	−2.31888
$839$	−19.3944	−0.669571	−0.334785	−	0.942294i	$-0.608664\pi$
$839$	−19.3944	−0.669571	−0.334785	+	0.942294i	$0.608664\pi$
$840$	25.2841	0.872385
$841$	−27.3046	−0.941537
$842$	−12.0353	−0.414763
$843$	−91.2440	−3.14261
$844$	−75.7119	−2.60611
$845$	−5.67335	−0.195169
$846$	−30.4084	−1.04546
$847$	1.42521	0.0489707
$848$	−20.6172	−0.707997
$849$	40.0156	1.37333
$850$	8.39540	0.287960
$851$	−1.10388	−0.0378405
$852$	185.746	6.36354
$853$	−40.9881	−1.40341	−0.701703	−	0.712470i	$-0.747576\pi$
$853$	−40.9881	−1.40341	−0.701703	+	0.712470i	$0.747576\pi$
$854$	12.7157	0.435124
$855$	25.7430	0.880393
$856$	24.3960	0.833838
$857$	12.3222	0.420917	0.210458	−	0.977603i	$-0.432504\pi$
$857$	12.3222	0.420917	0.210458	+	0.977603i	$0.432504\pi$
$858$	33.2447	1.13496
$859$	51.0280	1.74105	0.870526	−	0.492123i	$-0.163779\pi$
$859$	51.0280	1.74105	0.870526	+	0.492123i	$0.163779\pi$
$860$	4.70389	0.160401
$861$	46.0413	1.56908
$862$	−26.4088	−0.899487
$863$	34.3023	1.16766	0.583831	−	0.811875i	$-0.301553\pi$
$863$	34.3023	1.16766	0.583831	+	0.811875i	$0.301553\pi$
$864$	26.5843	0.904418
$865$	−4.69161	−0.159519
$866$	−39.0324	−1.32638
$867$	3.28542	0.111579
$868$	−26.6070	−0.903099
$869$	−4.76420	−0.161614
$870$	12.7157	0.431104
$871$	−54.3530	−1.84168
$872$	−84.8682	−2.87400
$873$	10.4917	0.355089
$874$	24.0952	0.815032
$875$	14.8971	0.503615
$876$	205.942	6.95815
$877$	11.5521	0.390088	0.195044	−	0.980794i	$-0.437515\pi$
$877$	11.5521	0.390088	0.195044	+	0.980794i	$0.437515\pi$
$878$	−91.7805	−3.09744
$879$	36.8389	1.24254
$880$	3.61535	0.121873
$881$	36.7910	1.23952	0.619759	−	0.784792i	$-0.287230\pi$
$881$	36.7910	1.23952	0.619759	+	0.784792i	$0.287230\pi$
$882$	93.3994	3.14492
$883$	−35.4481	−1.19292	−0.596462	−	0.802642i	$-0.703427\pi$
$883$	−35.4481	−1.19292	−0.596462	+	0.802642i	$0.703427\pi$
$884$	16.0131	0.538580
$885$	−22.2776	−0.748852
$886$	−8.10192	−0.272189
$887$	31.3152	1.05146	0.525731	−	0.850651i	$-0.323792\pi$
$887$	31.3152	1.05146	0.525731	+	0.850651i	$0.323792\pi$
$888$	4.26231	0.143034
$889$	−0.787459	−0.0264105
$890$	20.3666	0.682691
$891$	−28.3639	−0.950228
$892$	47.8000	1.60046
$893$	−4.33536	−0.145077
$894$	17.7439	0.593444
$895$	−3.87558	−0.129546
$896$	29.3471	0.980416
$897$	51.3874	1.71577
$898$	4.32941	0.144474
$899$	−6.36906	−0.212420
$900$	−103.549	−3.45162
$901$	−7.02840	−0.234150
$902$	23.7145	0.789608
$903$	−4.68240	−0.155820
$904$	49.9405	1.66100
$905$	−9.46932	−0.314771
$906$	150.822	5.01073
$907$	−14.7734	−0.490543	−0.245271	−	0.969454i	$-0.578877\pi$
$907$	−14.7734	−0.490543	−0.245271	+	0.969454i	$0.578877\pi$
$908$	72.5320	2.40706
$909$	−7.25764	−0.240721
$910$	17.7741	0.589204
$911$	−7.61471	−0.252287	−0.126143	−	0.992012i	$-0.540260\pi$
$911$	−7.61471	−0.252287	−0.126143	+	0.992012i	$0.540260\pi$
$912$	−25.8279	−0.855246
$913$	−15.5636	−0.515081
$914$	−20.4167	−0.675323
$915$	14.9794	0.495204
$916$	−74.3921	−2.45798
$917$	5.50113	0.181663
$918$	−37.9857	−1.25372
$919$	47.4546	1.56538	0.782691	−	0.622410i	$-0.213846\pi$
$919$	47.4546	1.56538	0.782691	+	0.622410i	$0.213846\pi$
$920$	20.1302	0.663675
$921$	76.5364	2.52196
$922$	78.0822	2.57150
$923$	62.1505	2.04571
$924$	−17.8710	−0.587912
$925$	1.03076	0.0338912
$926$	−30.6284	−1.00651
$927$	16.4427	0.540050
$928$	2.19776	0.0721449
$929$	−6.30585	−0.206888	−0.103444	−	0.994635i	$-0.532986\pi$
$929$	−6.30585	−0.206888	−0.103444	+	0.994635i	$0.532986\pi$
$930$	−47.7683	−1.56639
$931$	13.3160	0.436416
$932$	0.798103	0.0261427
$933$	38.4265	1.25803
$934$	77.3053	2.52951
$935$	1.23247	0.0403061
$936$	−143.271	−4.68294
$937$	−48.6564	−1.58953	−0.794767	−	0.606914i	$-0.792407\pi$
$937$	−48.6564	−1.58953	−0.794767	+	0.606914i	$0.792407\pi$
$938$	44.5288	1.45392
$939$	113.835	3.71488
$940$	−7.60952	−0.248195
$941$	22.2468	0.725223	0.362612	−	0.931940i	$-0.381885\pi$
$941$	22.2468	0.725223	0.362612	+	0.931940i	$0.381885\pi$
$942$	−59.3585	−1.93400
$943$	36.6563	1.19369
$944$	16.1389	0.525276
$945$	−27.6656	−0.899961
$946$	−2.41177	−0.0784134
$947$	31.2145	1.01433	0.507167	−	0.861848i	$-0.330693\pi$
$947$	31.2145	1.01433	0.507167	+	0.861848i	$0.330693\pi$
$948$	59.7394	1.94024
$949$	68.9083	2.23686
$950$	−22.4992	−0.729969
$951$	73.0759	2.36965
$952$	−6.24425	−0.202377
$953$	30.8141	0.998168	0.499084	−	0.866554i	$-0.333670\pi$
$953$	30.8141	0.998168	0.499084	+	0.866554i	$0.333670\pi$
$954$	132.114	4.27736
$955$	3.23511	0.104686
$956$	61.2052	1.97952
$957$	−4.27788	−0.138284
$958$	−63.5849	−2.05433
$959$	6.37257	0.205781
$960$	40.2391	1.29871
$961$	−7.07376	−0.228186
$962$	2.99629	0.0966042
$963$	−43.3984	−1.39849
$964$	−102.990	−3.31707
$965$	−22.3997	−0.721071
$966$	−42.0992	−1.35452
$967$	48.0931	1.54657	0.773285	−	0.634059i	$-0.218612\pi$
$967$	48.0931	1.54657	0.773285	+	0.634059i	$0.218612\pi$
$968$	−4.38130	−0.140820
$969$	−8.80471	−0.282848
$970$	4.00128	0.128473
$971$	−25.0105	−0.802624	−0.401312	−	0.915941i	$-0.631446\pi$
$971$	−25.0105	−0.802624	−0.401312	+	0.915941i	$0.631446\pi$
$972$	175.324	5.62353
$973$	1.52982	0.0490437
$974$	18.3700	0.588611
$975$	−47.9836	−1.53670
$976$	−10.8518	−0.347357
$977$	−18.0638	−0.577913	−0.288957	−	0.957342i	$-0.593308\pi$
$977$	−18.0638	−0.577913	−0.288957	+	0.957342i	$0.593308\pi$
$978$	23.5272	0.752317
$979$	−6.85183	−0.218985
$980$	23.3726	0.746611
$981$	150.974	4.82021
$982$	83.5871	2.66737
$983$	35.7429	1.14002	0.570010	−	0.821638i	$-0.306939\pi$
$983$	35.7429	1.14002	0.570010	+	0.821638i	$0.306939\pi$
$984$	−141.538	−4.51206
$985$	−10.5599	−0.336467
$986$	−3.14032	−0.100008
$987$	7.57475	0.241107
$988$	−42.9142	−1.36528
$989$	−3.72795	−0.118542
$990$	−23.1671	−0.736297
$991$	30.2705	0.961575	0.480788	−	0.876837i	$-0.340351\pi$
$991$	30.2705	0.961575	0.480788	+	0.876837i	$0.340351\pi$
$992$	−8.25616	−0.262133
$993$	12.0595	0.382697
$994$	−50.9169	−1.61499
$995$	24.3323	0.771387
$996$	195.156	6.18375
$997$	−31.0823	−0.984388	−0.492194	−	0.870486i	$-0.663805\pi$
$997$	−31.0823	−0.984388	−0.492194	+	0.870486i	$0.663805\pi$
$998$	58.5470	1.85327
$999$	−4.66376	−0.147555

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.f.1.4	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.f.1.4	✓	66	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41177 q^{2} +3.28542 q^{3} +3.81663 q^{4} -1.23247 q^{5} -7.92367 q^{6} +1.42521 q^{7} -4.38130 q^{8} +7.79396 q^{9} +O(q^{10})\)	\(q-2.41177 q^{2} +3.28542 q^{3} +3.81663 q^{4} -1.23247 q^{5} -7.92367 q^{6} +1.42521 q^{7} -4.38130 q^{8} +7.79396 q^{9} +2.97244 q^{10} -1.00000 q^{11} +12.5392 q^{12} +4.19562 q^{13} -3.43727 q^{14} -4.04918 q^{15} +2.93341 q^{16} +1.00000 q^{17} -18.7972 q^{18} -2.67994 q^{19} -4.70389 q^{20} +4.68240 q^{21} +2.41177 q^{22} +3.72795 q^{23} -14.3944 q^{24} -3.48101 q^{25} -10.1189 q^{26} +15.7502 q^{27} +5.43949 q^{28} +1.30208 q^{29} +9.76569 q^{30} -4.89145 q^{31} +1.68788 q^{32} -3.28542 q^{33} -2.41177 q^{34} -1.75653 q^{35} +29.7467 q^{36} -0.296109 q^{37} +6.46339 q^{38} +13.7844 q^{39} +5.39982 q^{40} +9.83284 q^{41} -11.2929 q^{42} -1.00000 q^{43} -3.81663 q^{44} -9.60583 q^{45} -8.99095 q^{46} +1.61771 q^{47} +9.63748 q^{48} -4.96879 q^{49} +8.39540 q^{50} +3.28542 q^{51} +16.0131 q^{52} -7.02840 q^{53} -37.9857 q^{54} +1.23247 q^{55} -6.24425 q^{56} -8.80471 q^{57} -3.14032 q^{58} +5.50175 q^{59} -15.4542 q^{60} -3.69937 q^{61} +11.7970 q^{62} +11.1080 q^{63} -9.93760 q^{64} -5.17098 q^{65} +7.92367 q^{66} -12.9547 q^{67} +3.81663 q^{68} +12.2479 q^{69} +4.23634 q^{70} +14.8132 q^{71} -34.1476 q^{72} +16.4239 q^{73} +0.714147 q^{74} -11.4366 q^{75} -10.2283 q^{76} -1.42521 q^{77} -33.2447 q^{78} +4.76420 q^{79} -3.61535 q^{80} +28.3639 q^{81} -23.7145 q^{82} +15.5636 q^{83} +17.8710 q^{84} -1.23247 q^{85} +2.41177 q^{86} +4.27788 q^{87} +4.38130 q^{88} +6.85183 q^{89} +23.1671 q^{90} +5.97963 q^{91} +14.2282 q^{92} -16.0704 q^{93} -3.90154 q^{94} +3.30295 q^{95} +5.54538 q^{96} +1.34613 q^{97} +11.9836 q^{98} -7.79396 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * q^99

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