LMFDB - Embedded newform 6007.2.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6007,2,Mod(1,6007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6007.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:	$47.9661364942$
Analytic rank:	$1$
Dimension:	$237$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.73398 q^{2} -2.84716 q^{3} +5.47464 q^{4} -1.36635 q^{5} +7.78406 q^{6} -2.19683 q^{7} -9.49960 q^{8} +5.10630 q^{9} +O(q^{10})$	\(q-2.73398 q^{2} -2.84716 q^{3} +5.47464 q^{4} -1.36635 q^{5} +7.78406 q^{6} -2.19683 q^{7} -9.49960 q^{8} +5.10630 q^{9} +3.73558 q^{10} -0.530110 q^{11} -15.5872 q^{12} -5.57838 q^{13} +6.00608 q^{14} +3.89022 q^{15} +15.0224 q^{16} +0.561443 q^{17} -13.9605 q^{18} -1.50555 q^{19} -7.48030 q^{20} +6.25472 q^{21} +1.44931 q^{22} -4.23432 q^{23} +27.0468 q^{24} -3.13308 q^{25} +15.2512 q^{26} -5.99696 q^{27} -12.0269 q^{28} -4.33611 q^{29} -10.6358 q^{30} +6.07654 q^{31} -22.0718 q^{32} +1.50931 q^{33} -1.53497 q^{34} +3.00165 q^{35} +27.9551 q^{36} +3.16492 q^{37} +4.11614 q^{38} +15.8825 q^{39} +12.9798 q^{40} +3.00093 q^{41} -17.1003 q^{42} +0.316242 q^{43} -2.90216 q^{44} -6.97701 q^{45} +11.5766 q^{46} -9.26219 q^{47} -42.7712 q^{48} -2.17394 q^{49} +8.56576 q^{50} -1.59852 q^{51} -30.5396 q^{52} +3.77723 q^{53} +16.3956 q^{54} +0.724318 q^{55} +20.8690 q^{56} +4.28653 q^{57} +11.8548 q^{58} -5.67915 q^{59} +21.2976 q^{60} +12.3344 q^{61} -16.6131 q^{62} -11.2177 q^{63} +30.2989 q^{64} +7.62205 q^{65} -4.12641 q^{66} +7.32553 q^{67} +3.07370 q^{68} +12.0558 q^{69} -8.20644 q^{70} -1.23240 q^{71} -48.5078 q^{72} -0.847258 q^{73} -8.65284 q^{74} +8.92036 q^{75} -8.24234 q^{76} +1.16456 q^{77} -43.4225 q^{78} -5.72161 q^{79} -20.5259 q^{80} +1.75538 q^{81} -8.20449 q^{82} +10.0568 q^{83} +34.2423 q^{84} -0.767130 q^{85} -0.864599 q^{86} +12.3456 q^{87} +5.03583 q^{88} +0.234856 q^{89} +19.0750 q^{90} +12.2548 q^{91} -23.1814 q^{92} -17.3009 q^{93} +25.3226 q^{94} +2.05711 q^{95} +62.8418 q^{96} -7.98007 q^{97} +5.94351 q^{98} -2.70690 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9}+O(q^{10}) $ 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9} - 39 q^{10} - 38 q^{11} - 67 q^{12} - 52 q^{13} - 54 q^{14} - 24 q^{15} + 208 q^{16} - 255 q^{17} - 71 q^{18} - 24 q^{19} - 154 q^{20} - 60 q^{21} - 39 q^{22} - 118 q^{23} - 85 q^{24} + 170 q^{25} - 61 q^{26} - 87 q^{27} - 99 q^{28} - 87 q^{29} - 30 q^{30} - 28 q^{31} - 156 q^{32} - 173 q^{33} - 4 q^{34} - 113 q^{35} + 152 q^{36} - 49 q^{37} - 145 q^{38} - 49 q^{39} - 91 q^{40} - 197 q^{41} - 61 q^{42} - 63 q^{43} - 106 q^{44} - 181 q^{45} - 2 q^{46} - 119 q^{47} - 142 q^{48} + 150 q^{49} - 89 q^{50} - 40 q^{51} - 97 q^{52} - 190 q^{53} - 97 q^{54} - 55 q^{55} - 154 q^{56} - 202 q^{57} - 27 q^{58} - 86 q^{59} - 48 q^{60} - 96 q^{61} - 239 q^{62} - 149 q^{63} + 183 q^{64} - 259 q^{65} - 72 q^{66} - 28 q^{67} - 482 q^{68} - 83 q^{69} + 20 q^{70} - 63 q^{71} - 193 q^{72} - 206 q^{73} - 132 q^{74} - 89 q^{75} - 11 q^{76} - 179 q^{77} - 58 q^{78} - 32 q^{79} - 320 q^{80} + 57 q^{81} - 77 q^{82} - 245 q^{83} - 133 q^{84} + q^{85} - 39 q^{86} - 179 q^{87} - 104 q^{88} - 227 q^{89} - 146 q^{90} - 36 q^{91} - 315 q^{92} - 87 q^{93} - 48 q^{94} - 111 q^{95} - 134 q^{96} - 221 q^{97} - 161 q^{98} - 68 q^{99}+O(q^{100}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9 - 39 * q^10 - 38 * q^11 - 67 * q^12 - 52 * q^13 - 54 * q^14 - 24 * q^15 + 208 * q^16 - 255 * q^17 - 71 * q^18 - 24 * q^19 - 154 * q^20 - 60 * q^21 - 39 * q^22 - 118 * q^23 - 85 * q^24 + 170 * q^25 - 61 * q^26 - 87 * q^27 - 99 * q^28 - 87 * q^29 - 30 * q^30 - 28 * q^31 - 156 * q^32 - 173 * q^33 - 4 * q^34 - 113 * q^35 + 152 * q^36 - 49 * q^37 - 145 * q^38 - 49 * q^39 - 91 * q^40 - 197 * q^41 - 61 * q^42 - 63 * q^43 - 106 * q^44 - 181 * q^45 - 2 * q^46 - 119 * q^47 - 142 * q^48 + 150 * q^49 - 89 * q^50 - 40 * q^51 - 97 * q^52 - 190 * q^53 - 97 * q^54 - 55 * q^55 - 154 * q^56 - 202 * q^57 - 27 * q^58 - 86 * q^59 - 48 * q^60 - 96 * q^61 - 239 * q^62 - 149 * q^63 + 183 * q^64 - 259 * q^65 - 72 * q^66 - 28 * q^67 - 482 * q^68 - 83 * q^69 + 20 * q^70 - 63 * q^71 - 193 * q^72 - 206 * q^73 - 132 * q^74 - 89 * q^75 - 11 * q^76 - 179 * q^77 - 58 * q^78 - 32 * q^79 - 320 * q^80 + 57 * q^81 - 77 * q^82 - 245 * q^83 - 133 * q^84 + q^85 - 39 * q^86 - 179 * q^87 - 104 * q^88 - 227 * q^89 - 146 * q^90 - 36 * q^91 - 315 * q^92 - 87 * q^93 - 48 * q^94 - 111 * q^95 - 134 * q^96 - 221 * q^97 - 161 * q^98 - 68 * 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 $

$2$	−2.73398	−1.93322	−0.966608	−	0.256261i	$-0.917509\pi$
$2$	−2.73398	−1.93322	−0.966608	+	0.256261i	$0.917509\pi$
$3$	−2.84716	−1.64381	−0.821903	−	0.569627i	$-0.807088\pi$
$3$	−2.84716	−1.64381	−0.821903	+	0.569627i	$0.807088\pi$
$4$	5.47464	2.73732
$5$	−1.36635	−0.611052	−0.305526	−	0.952184i	$-0.598832\pi$
$5$	−1.36635	−0.611052	−0.305526	+	0.952184i	$0.598832\pi$
$6$	7.78406	3.17783
$7$	−2.19683	−0.830323	−0.415162	−	0.909748i	$-0.636275\pi$
$7$	−2.19683	−0.830323	−0.415162	+	0.909748i	$0.636275\pi$
$8$	−9.49960	−3.35861
$9$	5.10630	1.70210
$10$	3.73558	1.18130
$11$	−0.530110	−0.159834	−0.0799171	−	0.996802i	$-0.525466\pi$
$11$	−0.530110	−0.159834	−0.0799171	+	0.996802i	$0.525466\pi$
$12$	−15.5872	−4.49962
$13$	−5.57838	−1.54716	−0.773582	−	0.633696i	$-0.781537\pi$
$13$	−5.57838	−1.54716	−0.773582	+	0.633696i	$0.781537\pi$
$14$	6.00608	1.60519
$15$	3.89022	1.00445
$16$	15.0224	3.75560
$17$	0.561443	0.136170	0.0680849	−	0.997680i	$-0.478311\pi$
$17$	0.561443	0.136170	0.0680849	+	0.997680i	$0.478311\pi$
$18$	−13.9605	−3.29052
$19$	−1.50555	−0.345396	−0.172698	−	0.984975i	$-0.555249\pi$
$19$	−1.50555	−0.345396	−0.172698	+	0.984975i	$0.555249\pi$
$20$	−7.48030	−1.67265
$21$	6.25472	1.36489
$22$	1.44931	0.308994
$23$	−4.23432	−0.882917	−0.441459	−	0.897282i	$-0.645539\pi$
$23$	−4.23432	−0.882917	−0.441459	+	0.897282i	$0.645539\pi$
$24$	27.0468	5.52091
$25$	−3.13308	−0.626615
$26$	15.2512	2.99100
$27$	−5.99696	−1.15412
$28$	−12.0269	−2.27286
$29$	−4.33611	−0.805196	−0.402598	−	0.915377i	$-0.631893\pi$
$29$	−4.33611	−0.805196	−0.402598	+	0.915377i	$0.631893\pi$
$30$	−10.6358	−1.94182
$31$	6.07654	1.09138	0.545690	−	0.837987i	$-0.316268\pi$
$31$	6.07654	1.09138	0.545690	+	0.837987i	$0.316268\pi$
$32$	−22.0718	−3.90177
$33$	1.50931	0.262736
$34$	−1.53497	−0.263246
$35$	3.00165	0.507371
$36$	27.9551	4.65919
$37$	3.16492	0.520310	0.260155	−	0.965567i	$-0.416226\pi$
$37$	3.16492	0.520310	0.260155	+	0.965567i	$0.416226\pi$
$38$	4.11614	0.667726
$39$	15.8825	2.54324
$40$	12.9798	2.05229
$41$	3.00093	0.468667	0.234333	−	0.972156i	$-0.424709\pi$
$41$	3.00093	0.468667	0.234333	+	0.972156i	$0.424709\pi$
$42$	−17.1003	−2.63863
$43$	0.316242	0.0482265	0.0241132	−	0.999709i	$-0.492324\pi$
$43$	0.316242	0.0482265	0.0241132	+	0.999709i	$0.492324\pi$
$44$	−2.90216	−0.437517
$45$	−6.97701	−1.04007
$46$	11.5766	1.70687
$47$	−9.26219	−1.35103	−0.675515	−	0.737346i	$-0.736079\pi$
$47$	−9.26219	−1.35103	−0.675515	+	0.737346i	$0.736079\pi$
$48$	−42.7712	−6.17348
$49$	−2.17394	−0.310563
$50$	8.56576	1.21138
$51$	−1.59852	−0.223837
$52$	−30.5396	−4.23509
$53$	3.77723	0.518843	0.259421	−	0.965764i	$-0.416468\pi$
$53$	3.77723	0.518843	0.259421	+	0.965764i	$0.416468\pi$
$54$	16.3956	2.23115
$55$	0.724318	0.0976670
$56$	20.8690	2.78874
$57$	4.28653	0.567765
$58$	11.8548	1.55662
$59$	−5.67915	−0.739362	−0.369681	−	0.929159i	$-0.620533\pi$
$59$	−5.67915	−0.739362	−0.369681	+	0.929159i	$0.620533\pi$
$60$	21.2976	2.74951
$61$	12.3344	1.57926	0.789629	−	0.613585i	$-0.210273\pi$
$61$	12.3344	1.57926	0.789629	+	0.613585i	$0.210273\pi$
$62$	−16.6131	−2.10987
$63$	−11.2177	−1.41329
$64$	30.2989	3.78737
$65$	7.62205	0.945398
$66$	−4.12641	−0.507926
$67$	7.32553	0.894955	0.447478	−	0.894295i	$-0.352322\pi$
$67$	7.32553	0.894955	0.447478	+	0.894295i	$0.352322\pi$
$68$	3.07370	0.372741
$69$	12.0558	1.45135
$70$	−8.20644	−0.980857
$71$	−1.23240	−0.146259	−0.0731293	−	0.997322i	$-0.523299\pi$
$71$	−1.23240	−0.146259	−0.0731293	+	0.997322i	$0.523299\pi$
$72$	−48.5078	−5.71669
$73$	−0.847258	−0.0991641	−0.0495820	−	0.998770i	$-0.515789\pi$
$73$	−0.847258	−0.0991641	−0.0495820	+	0.998770i	$0.515789\pi$
$74$	−8.65284	−1.00587
$75$	8.92036	1.03003
$76$	−8.24234	−0.945461
$77$	1.16456	0.132714
$78$	−43.4225	−4.91663
$79$	−5.72161	−0.643732	−0.321866	−	0.946785i	$-0.604310\pi$
$79$	−5.72161	−0.643732	−0.321866	+	0.946785i	$0.604310\pi$
$80$	−20.5259	−2.29487
$81$	1.75538	0.195043
$82$	−8.20449	−0.906034
$83$	10.0568	1.10388	0.551939	−	0.833884i	$-0.313888\pi$
$83$	10.0568	1.10388	0.551939	+	0.833884i	$0.313888\pi$
$84$	34.2423	3.73614
$85$	−0.767130	−0.0832069
$86$	−0.864599	−0.0932322
$87$	12.3456	1.32359
$88$	5.03583	0.536821
$89$	0.234856	0.0248947	0.0124474	−	0.999923i	$-0.496038\pi$
$89$	0.234856	0.0248947	0.0124474	+	0.999923i	$0.496038\pi$
$90$	19.0750	2.01068
$91$	12.2548	1.28465
$92$	−23.1814	−2.41683
$93$	−17.3009	−1.79402
$94$	25.3226	2.61183
$95$	2.05711	0.211055
$96$	62.8418	6.41376
$97$	−7.98007	−0.810253	−0.405127	−	0.914261i	$-0.632773\pi$
$97$	−7.98007	−0.810253	−0.405127	+	0.914261i	$0.632773\pi$
$98$	5.94351	0.600385
$99$	−2.70690	−0.272054
$100$	−17.1525	−1.71525
$101$	−11.4405	−1.13837	−0.569187	−	0.822208i	$-0.692742\pi$
$101$	−11.4405	−1.13837	−0.569187	+	0.822208i	$0.692742\pi$
$102$	4.37031	0.432725
$103$	12.6461	1.24605	0.623027	−	0.782200i	$-0.285903\pi$
$103$	12.6461	1.24605	0.623027	+	0.782200i	$0.285903\pi$
$104$	52.9924	5.19633
$105$	−8.54616	−0.834020
$106$	−10.3269	−1.00303
$107$	0.989585	0.0956668	0.0478334	−	0.998855i	$-0.484768\pi$
$107$	0.989585	0.0956668	0.0478334	+	0.998855i	$0.484768\pi$
$108$	−32.8312	−3.15918
$109$	−1.73286	−0.165978	−0.0829889	−	0.996550i	$-0.526447\pi$
$109$	−1.73286	−0.165978	−0.0829889	+	0.996550i	$0.526447\pi$
$110$	−1.98027	−0.188811
$111$	−9.01104	−0.855290
$112$	−33.0017	−3.11837
$113$	−7.91472	−0.744555	−0.372277	−	0.928122i	$-0.621423\pi$
$113$	−7.91472	−0.744555	−0.372277	+	0.928122i	$0.621423\pi$
$114$	−11.7193	−1.09761
$115$	5.78559	0.539509
$116$	−23.7387	−2.20408
$117$	−28.4849	−2.63343
$118$	15.5267	1.42935
$119$	−1.23339	−0.113065
$120$	−36.9556	−3.37356
$121$	−10.7190	−0.974453
$122$	−33.7220	−3.05304
$123$	−8.54412	−0.770398
$124$	33.2669	2.98745
$125$	11.1127	0.993947
$126$	30.6689	2.73220
$127$	12.2009	1.08266	0.541328	−	0.840811i	$-0.317922\pi$
$127$	12.2009	1.08266	0.541328	+	0.840811i	$0.317922\pi$
$128$	−38.6931	−3.42002
$129$	−0.900391	−0.0792750
$130$	−20.8385	−1.82766
$131$	−11.9780	−1.04652	−0.523260	−	0.852173i	$-0.675285\pi$
$131$	−11.9780	−1.04652	−0.523260	+	0.852173i	$0.675285\pi$
$132$	8.26291	0.719194
$133$	3.30743	0.286791
$134$	−20.0278	−1.73014
$135$	8.19397	0.705225
$136$	−5.33348	−0.457342
$137$	1.82600	0.156006	0.0780028	−	0.996953i	$-0.475146\pi$
$137$	1.82600	0.156006	0.0780028	+	0.996953i	$0.475146\pi$
$138$	−32.9602	−2.80576
$139$	17.0202	1.44363	0.721817	−	0.692084i	$-0.243307\pi$
$139$	17.0202	1.44363	0.721817	+	0.692084i	$0.243307\pi$
$140$	16.4329	1.38884
$141$	26.3709	2.22083
$142$	3.36935	0.282749
$143$	2.95716	0.247290
$144$	76.7089	6.39241
$145$	5.92467	0.492017
$146$	2.31639	0.191705
$147$	6.18955	0.510505
$148$	17.3268	1.42426
$149$	3.59054	0.294148	0.147074	−	0.989125i	$-0.453014\pi$
$149$	3.59054	0.294148	0.147074	+	0.989125i	$0.453014\pi$
$150$	−24.3881	−1.99128
$151$	−0.691522	−0.0562753	−0.0281376	−	0.999604i	$-0.508958\pi$
$151$	−0.691522	−0.0562753	−0.0281376	+	0.999604i	$0.508958\pi$
$152$	14.3021	1.16005
$153$	2.86689	0.231775
$154$	−3.18389	−0.256565
$155$	−8.30271	−0.666890
$156$	86.9511	6.96166
$157$	−4.62693	−0.369269	−0.184634	−	0.982807i	$-0.559110\pi$
$157$	−4.62693	−0.369269	−0.184634	+	0.982807i	$0.559110\pi$
$158$	15.6428	1.24447
$159$	−10.7544	−0.852877
$160$	30.1579	2.38419
$161$	9.30208	0.733107
$162$	−4.79918	−0.377059
$163$	9.61234	0.752896	0.376448	−	0.926438i	$-0.377145\pi$
$163$	9.61234	0.752896	0.376448	+	0.926438i	$0.377145\pi$
$164$	16.4290	1.28289
$165$	−2.06225	−0.160546
$166$	−27.4951	−2.13404
$167$	−4.56343	−0.353129	−0.176564	−	0.984289i	$-0.556498\pi$
$167$	−4.56343	−0.353129	−0.176564	+	0.984289i	$0.556498\pi$
$168$	−59.4173	−4.58414
$169$	18.1183	1.39372
$170$	2.09732	0.160857
$171$	−7.68778	−0.587899
$172$	1.73131	0.132011
$173$	5.75542	0.437577	0.218788	−	0.975772i	$-0.429790\pi$
$173$	5.75542	0.437577	0.218788	+	0.975772i	$0.429790\pi$
$174$	−33.7526	−2.55878
$175$	6.88283	0.520293
$176$	−7.96353	−0.600274
$177$	16.1694	1.21537
$178$	−0.642092	−0.0481268
$179$	2.88193	0.215406	0.107703	−	0.994183i	$-0.465651\pi$
$179$	2.88193	0.215406	0.107703	+	0.994183i	$0.465651\pi$
$180$	−38.1966	−2.84701
$181$	−7.65197	−0.568766	−0.284383	−	0.958711i	$-0.591789\pi$
$181$	−7.65197	−0.568766	−0.284383	+	0.958711i	$0.591789\pi$
$182$	−33.5042	−2.48350
$183$	−35.1179	−2.59599
$184$	40.2244	2.96538
$185$	−4.32441	−0.317937
$186$	47.3002	3.46822
$187$	−0.297626	−0.0217646
$188$	−50.7072	−3.69820
$189$	13.1743	0.958289
$190$	−5.62410	−0.408015
$191$	10.4702	0.757594	0.378797	−	0.925480i	$-0.376338\pi$
$191$	10.4702	0.757594	0.378797	+	0.925480i	$0.376338\pi$
$192$	−86.2658	−6.22570
$193$	4.58418	0.329977	0.164988	−	0.986296i	$-0.447241\pi$
$193$	4.58418	0.329977	0.164988	+	0.986296i	$0.447241\pi$
$194$	21.8173	1.56639
$195$	−21.7012	−1.55405
$196$	−11.9015	−0.850111
$197$	−17.6793	−1.25959	−0.629797	−	0.776760i	$-0.716862\pi$
$197$	−17.6793	−1.25959	−0.629797	+	0.776760i	$0.716862\pi$
$198$	7.40061	0.525938
$199$	14.4858	1.02687	0.513436	−	0.858128i	$-0.328372\pi$
$199$	14.4858	1.02687	0.513436	+	0.858128i	$0.328372\pi$
$200$	29.7630	2.10456
$201$	−20.8569	−1.47113
$202$	31.2781	2.20072
$203$	9.52570	0.668573
$204$	−8.75130	−0.612713
$205$	−4.10034	−0.286380
$206$	−34.5741	−2.40889
$207$	−21.6217	−1.50281
$208$	−83.8008	−5.81054
$209$	0.798106	0.0552062
$210$	23.3650	1.61234
$211$	15.8041	1.08800	0.543998	−	0.839086i	$-0.316910\pi$
$211$	15.8041	1.08800	0.543998	+	0.839086i	$0.316910\pi$
$212$	20.6790	1.42024
$213$	3.50883	0.240421
$214$	−2.70550	−0.184944
$215$	−0.432099	−0.0294689
$216$	56.9687	3.87623
$217$	−13.3491	−0.906198
$218$	4.73760	0.320871
$219$	2.41228	0.163007
$220$	3.96538	0.267346
$221$	−3.13194	−0.210677
$222$	24.6360	1.65346
$223$	27.0853	1.81377	0.906884	−	0.421379i	$-0.138454\pi$
$223$	27.0853	1.81377	0.906884	+	0.421379i	$0.138454\pi$
$224$	48.4879	3.23973
$225$	−15.9984	−1.06656
$226$	21.6387	1.43938
$227$	−9.30553	−0.617630	−0.308815	−	0.951122i	$-0.599932\pi$
$227$	−9.30553	−0.617630	−0.308815	+	0.951122i	$0.599932\pi$
$228$	23.4672	1.55415
$229$	15.1551	1.00147	0.500737	−	0.865599i	$-0.333062\pi$
$229$	15.1551	1.00147	0.500737	+	0.865599i	$0.333062\pi$
$230$	−15.8177	−1.04299
$231$	−3.31569	−0.218156
$232$	41.1913	2.70434
$233$	28.1422	1.84366	0.921828	−	0.387599i	$-0.126696\pi$
$233$	28.1422	1.84366	0.921828	+	0.387599i	$0.126696\pi$
$234$	77.8771	5.09098
$235$	12.6554	0.825550
$236$	−31.0913	−2.02387
$237$	16.2903	1.05817
$238$	3.37207	0.218579
$239$	30.0957	1.94673	0.973363	−	0.229268i	$-0.0736331\pi$
$239$	30.0957	1.94673	0.973363	+	0.229268i	$0.0736331\pi$
$240$	58.4405	3.77232
$241$	−17.9258	−1.15470	−0.577352	−	0.816495i	$-0.695914\pi$
$241$	−17.9258	−1.15470	−0.577352	+	0.816495i	$0.695914\pi$
$242$	29.3055	1.88383
$243$	12.9930	0.833503
$244$	67.5264	4.32293
$245$	2.97037	0.189770
$246$	23.3595	1.48934
$247$	8.39852	0.534385
$248$	−57.7247	−3.66552
$249$	−28.6333	−1.81456
$250$	−30.3818	−1.92151
$251$	−21.1301	−1.33372	−0.666860	−	0.745183i	$-0.732362\pi$
$251$	−21.1301	−1.33372	−0.666860	+	0.745183i	$0.732362\pi$
$252$	−61.4127	−3.86864
$253$	2.24466	0.141120
$254$	−33.3571	−2.09301
$255$	2.18414	0.136776
$256$	45.1882	2.82427
$257$	22.9004	1.42849	0.714244	−	0.699897i	$-0.246771\pi$
$257$	22.9004	1.42849	0.714244	+	0.699897i	$0.246771\pi$
$258$	2.46165	0.153256
$259$	−6.95280	−0.432026
$260$	41.7280	2.58786
$261$	−22.1415	−1.37052
$262$	32.7475	2.02315
$263$	−16.1628	−0.996640	−0.498320	−	0.866993i	$-0.666050\pi$
$263$	−16.1628	−0.996640	−0.498320	+	0.866993i	$0.666050\pi$
$264$	−14.3378	−0.882430
$265$	−5.16104	−0.317040
$266$	−9.04245	−0.554428
$267$	−0.668672	−0.0409221
$268$	40.1046	2.44978
$269$	9.38536	0.572236	0.286118	−	0.958194i	$-0.407635\pi$
$269$	9.38536	0.572236	0.286118	+	0.958194i	$0.407635\pi$
$270$	−22.4021	−1.36335
$271$	−4.31078	−0.261861	−0.130931	−	0.991392i	$-0.541797\pi$
$271$	−4.31078	−0.261861	−0.130931	+	0.991392i	$0.541797\pi$
$272$	8.43423	0.511400
$273$	−34.8912	−2.11171
$274$	−4.99224	−0.301592
$275$	1.66087	0.100155
$276$	66.0011	3.97280
$277$	27.6377	1.66059	0.830295	−	0.557324i	$-0.188172\pi$
$277$	27.6377	1.66059	0.830295	+	0.557324i	$0.188172\pi$
$278$	−46.5328	−2.79085
$279$	31.0286	1.85764
$280$	−28.5144	−1.70406
$281$	5.82933	0.347749	0.173874	−	0.984768i	$-0.444371\pi$
$281$	5.82933	0.347749	0.173874	+	0.984768i	$0.444371\pi$
$282$	−72.0975	−4.29334
$283$	13.8094	0.820886	0.410443	−	0.911886i	$-0.365374\pi$
$283$	13.8094	0.820886	0.410443	+	0.911886i	$0.365374\pi$
$284$	−6.74693	−0.400357
$285$	−5.85692	−0.346934
$286$	−8.08480	−0.478064
$287$	−6.59254	−0.389145
$288$	−112.705	−6.64121
$289$	−16.6848	−0.981458
$290$	−16.1979	−0.951175
$291$	22.7205	1.33190
$292$	−4.63843	−0.271444
$293$	11.9256	0.696702	0.348351	−	0.937364i	$-0.386742\pi$
$293$	11.9256	0.696702	0.348351	+	0.937364i	$0.386742\pi$
$294$	−16.9221	−0.986917
$295$	7.75973	0.451789
$296$	−30.0655	−1.74752
$297$	3.17905	0.184467
$298$	−9.81646	−0.568652
$299$	23.6207	1.36602
$300$	48.8358	2.81953
$301$	−0.694730	−0.0400436
$302$	1.89061	0.108792
$303$	32.5729	1.87127
$304$	−22.6170	−1.29717
$305$	−16.8531	−0.965008
$306$	−7.83803	−0.448070
$307$	8.79812	0.502135	0.251068	−	0.967970i	$-0.419218\pi$
$307$	8.79812	0.502135	0.251068	+	0.967970i	$0.419218\pi$
$308$	6.37555	0.363281
$309$	−36.0053	−2.04827
$310$	22.6994	1.28924
$311$	−2.40758	−0.136521	−0.0682606	−	0.997668i	$-0.521745\pi$
$311$	−2.40758	−0.136521	−0.0682606	+	0.997668i	$0.521745\pi$
$312$	−150.878	−8.54176
$313$	8.11346	0.458600	0.229300	−	0.973356i	$-0.426356\pi$
$313$	8.11346	0.458600	0.229300	+	0.973356i	$0.426356\pi$
$314$	12.6499	0.713876
$315$	15.3273	0.863596
$316$	−31.3238	−1.76210
$317$	12.1988	0.685153	0.342576	−	0.939490i	$-0.388700\pi$
$317$	12.1988	0.685153	0.342576	+	0.939490i	$0.388700\pi$
$318$	29.4022	1.64879
$319$	2.29862	0.128698
$320$	−41.3991	−2.31428
$321$	−2.81750	−0.157258
$322$	−25.4317	−1.41725
$323$	−0.845279	−0.0470326
$324$	9.61009	0.533894
$325$	17.4775	0.969477
$326$	−26.2799	−1.45551
$327$	4.93372	0.272835
$328$	−28.5076	−1.57407
$329$	20.3475	1.12179
$330$	5.63814	0.310369
$331$	28.0804	1.54344	0.771720	−	0.635963i	$-0.219397\pi$
$331$	28.0804	1.54344	0.771720	+	0.635963i	$0.219397\pi$
$332$	55.0575	3.02167
$333$	16.1610	0.885620
$334$	12.4763	0.682674
$335$	−10.0093	−0.546864
$336$	93.9609	5.12599
$337$	−23.7207	−1.29215	−0.646075	−	0.763274i	$-0.723590\pi$
$337$	−23.7207	−1.29215	−0.646075	+	0.763274i	$0.723590\pi$
$338$	−49.5352	−2.69436
$339$	22.5345	1.22390
$340$	−4.19976	−0.227764
$341$	−3.22124	−0.174440
$342$	21.0182	1.13654
$343$	20.1536	1.08819
$344$	−3.00417	−0.161974
$345$	−16.4725	−0.886848
$346$	−15.7352	−0.845930
$347$	16.2114	0.870276	0.435138	−	0.900364i	$-0.356700\pi$
$347$	16.2114	0.870276	0.435138	+	0.900364i	$0.356700\pi$
$348$	67.5877	3.62308
$349$	−3.12283	−0.167161	−0.0835805	−	0.996501i	$-0.526636\pi$
$349$	−3.12283	−0.167161	−0.0835805	+	0.996501i	$0.526636\pi$
$350$	−18.8175	−1.00584
$351$	33.4533	1.78561
$352$	11.7005	0.623637
$353$	−4.45280	−0.236999	−0.118499	−	0.992954i	$-0.537808\pi$
$353$	−4.45280	−0.236999	−0.118499	+	0.992954i	$0.537808\pi$
$354$	−44.2068	−2.34957
$355$	1.68389	0.0893717
$356$	1.28575	0.0681448
$357$	3.51167	0.185857
$358$	−7.87913	−0.416425
$359$	2.28622	0.120662	0.0603309	−	0.998178i	$-0.480784\pi$
$359$	2.28622	0.120662	0.0603309	+	0.998178i	$0.480784\pi$
$360$	66.2788	3.49320
$361$	−16.7333	−0.880701
$362$	20.9203	1.09955
$363$	30.5186	1.60181
$364$	67.0904	3.51649
$365$	1.15765	0.0605944
$366$	96.0117	5.01861
$367$	0.471409	0.0246073	0.0123037	−	0.999924i	$-0.496084\pi$
$367$	0.471409	0.0246073	0.0123037	+	0.999924i	$0.496084\pi$
$368$	−63.6097	−3.31589
$369$	15.3237	0.797718
$370$	11.8228	0.614640
$371$	−8.29793	−0.430807
$372$	−94.7160	−4.91080
$373$	32.5131	1.68347	0.841733	−	0.539894i	$-0.181536\pi$
$373$	32.5131	1.68347	0.841733	+	0.539894i	$0.181536\pi$
$374$	0.813704	0.0420757
$375$	−31.6395	−1.63386
$376$	87.9871	4.53759
$377$	24.1885	1.24577
$378$	−36.0182	−1.85258
$379$	12.7850	0.656721	0.328360	−	0.944552i	$-0.393504\pi$
$379$	12.7850	0.656721	0.328360	+	0.944552i	$0.393504\pi$
$380$	11.2620	0.577726
$381$	−34.7379	−1.77968
$382$	−28.6252	−1.46459
$383$	−37.3214	−1.90704	−0.953518	−	0.301337i	$-0.902567\pi$
$383$	−37.3214	−1.90704	−0.953518	+	0.301337i	$0.902567\pi$
$384$	110.165	5.62185
$385$	−1.59120	−0.0810952
$386$	−12.5331	−0.637916
$387$	1.61483	0.0820863
$388$	−43.6880	−2.21792
$389$	−25.2868	−1.28209	−0.641045	−	0.767503i	$-0.721499\pi$
$389$	−25.2868	−1.28209	−0.641045	+	0.767503i	$0.721499\pi$
$390$	59.3305	3.00432
$391$	−2.37733	−0.120227
$392$	20.6516	1.04306
$393$	34.1032	1.72028
$394$	48.3347	2.43507
$395$	7.81775	0.393354
$396$	−14.8193	−0.744698
$397$	36.1299	1.81331	0.906654	−	0.421876i	$-0.138628\pi$
$397$	36.1299	1.81331	0.906654	+	0.421876i	$0.138628\pi$
$398$	−39.6039	−1.98517
$399$	−9.41678	−0.471428
$400$	−47.0664	−2.35332
$401$	2.55701	0.127691	0.0638455	−	0.997960i	$-0.479663\pi$
$401$	2.55701	0.127691	0.0638455	+	0.997960i	$0.479663\pi$
$402$	57.0224	2.84402
$403$	−33.8973	−1.68854
$404$	−62.6327	−3.11610
$405$	−2.39848	−0.119181
$406$	−26.0431	−1.29250
$407$	−1.67776	−0.0831634
$408$	15.1852	0.751782
$409$	−0.674408	−0.0333473	−0.0166737	−	0.999861i	$-0.505308\pi$
$409$	−0.674408	−0.0333473	−0.0166737	+	0.999861i	$0.505308\pi$
$410$	11.2102	0.553634
$411$	−5.19890	−0.256443
$412$	69.2327	3.41085
$413$	12.4761	0.613909
$414$	59.1133	2.90526
$415$	−13.7412	−0.674528
$416$	123.125	6.03669
$417$	−48.4591	−2.37305
$418$	−2.18201	−0.106725
$419$	−24.2197	−1.18321	−0.591606	−	0.806227i	$-0.701506\pi$
$419$	−24.2197	−1.18321	−0.591606	+	0.806227i	$0.701506\pi$
$420$	−46.7871	−2.28298
$421$	−0.459781	−0.0224083	−0.0112042	−	0.999937i	$-0.503566\pi$
$421$	−0.459781	−0.0224083	−0.0112042	+	0.999937i	$0.503566\pi$
$422$	−43.2080	−2.10333
$423$	−47.2955	−2.29959
$424$	−35.8822	−1.74259
$425$	−1.75904	−0.0853261
$426$	−9.59306	−0.464785
$427$	−27.0966	−1.31129
$428$	5.41762	0.261871
$429$	−8.41948	−0.406497
$430$	1.18135	0.0569697
$431$	11.3921	0.548740	0.274370	−	0.961624i	$-0.411531\pi$
$431$	11.3921	0.548740	0.274370	+	0.961624i	$0.411531\pi$
$432$	−90.0888	−4.33440
$433$	−18.7389	−0.900533	−0.450267	−	0.892894i	$-0.648671\pi$
$433$	−18.7389	−0.900533	−0.450267	+	0.892894i	$0.648671\pi$
$434$	36.4962	1.75188
$435$	−16.8685	−0.808781
$436$	−9.48678	−0.454335
$437$	6.37498	0.304957
$438$	−6.59511	−0.315127
$439$	−8.43199	−0.402437	−0.201219	−	0.979546i	$-0.564490\pi$
$439$	−8.43199	−0.402437	−0.201219	+	0.979546i	$0.564490\pi$
$440$	−6.88073	−0.328026
$441$	−11.1008	−0.528609
$442$	8.56267	0.407284
$443$	8.42203	0.400143	0.200071	−	0.979781i	$-0.435883\pi$
$443$	8.42203	0.400143	0.200071	+	0.979781i	$0.435883\pi$
$444$	−49.3322	−2.34120
$445$	−0.320897	−0.0152120
$446$	−74.0508	−3.50641
$447$	−10.2228	−0.483523
$448$	−66.5616	−3.14474
$449$	35.5958	1.67987	0.839936	−	0.542686i	$-0.182593\pi$
$449$	35.5958	1.67987	0.839936	+	0.542686i	$0.182593\pi$
$450$	43.7393	2.06189
$451$	−1.59082	−0.0749090
$452$	−43.3303	−2.03808
$453$	1.96887	0.0925057
$454$	25.4411	1.19401
$455$	−16.7443	−0.784986
$456$	−40.7203	−1.90690
$457$	−5.86785	−0.274487	−0.137243	−	0.990537i	$-0.543824\pi$
$457$	−5.86785	−0.274487	−0.137243	+	0.990537i	$0.543824\pi$
$458$	−41.4336	−1.93607
$459$	−3.36695	−0.157156
$460$	31.6740	1.47681
$461$	−5.47719	−0.255098	−0.127549	−	0.991832i	$-0.540711\pi$
$461$	−5.47719	−0.255098	−0.127549	+	0.991832i	$0.540711\pi$
$462$	9.06502	0.421743
$463$	−15.6482	−0.727233	−0.363617	−	0.931549i	$-0.618458\pi$
$463$	−15.6482	−0.727233	−0.363617	+	0.931549i	$0.618458\pi$
$464$	−65.1389	−3.02400
$465$	23.6391	1.09624
$466$	−76.9402	−3.56418
$467$	−4.80041	−0.222137	−0.111068	−	0.993813i	$-0.535427\pi$
$467$	−4.80041	−0.222137	−0.111068	+	0.993813i	$0.535427\pi$
$468$	−155.944	−7.20854
$469$	−16.0929	−0.743102
$470$	−34.5997	−1.59597
$471$	13.1736	0.607007
$472$	53.9496	2.48323
$473$	−0.167643	−0.00770824
$474$	−44.5374	−2.04567
$475$	4.71700	0.216431
$476$	−6.75239	−0.309495
$477$	19.2877	0.883122
$478$	−82.2809	−3.76344
$479$	−20.6889	−0.945298	−0.472649	−	0.881251i	$-0.656702\pi$
$479$	−20.6889	−0.945298	−0.472649	+	0.881251i	$0.656702\pi$
$480$	−85.8641	−3.91914
$481$	−17.6552	−0.805006
$482$	49.0088	2.23229
$483$	−26.4845	−1.20509
$484$	−58.6826	−2.66739
$485$	10.9036	0.495107
$486$	−35.5227	−1.61134
$487$	−34.3260	−1.55546	−0.777731	−	0.628598i	$-0.783629\pi$
$487$	−34.3260	−1.55546	−0.777731	+	0.628598i	$0.783629\pi$
$488$	−117.172	−5.30412
$489$	−27.3678	−1.23762
$490$	−8.12094	−0.366867
$491$	−25.9048	−1.16907	−0.584533	−	0.811370i	$-0.698722\pi$
$491$	−25.9048	−1.16907	−0.584533	+	0.811370i	$0.698722\pi$
$492$	−46.7760	−2.10883
$493$	−2.43448	−0.109643
$494$	−22.9614	−1.03308
$495$	3.69858	0.166239
$496$	91.2843	4.09879
$497$	2.70737	0.121442
$498$	78.2829	3.50794
$499$	26.7328	1.19672	0.598362	−	0.801226i	$-0.295818\pi$
$499$	26.7328	1.19672	0.598362	+	0.801226i	$0.295818\pi$
$500$	60.8378	2.72075
$501$	12.9928	0.580476
$502$	57.7692	2.57837
$503$	−37.5514	−1.67433	−0.837166	−	0.546949i	$-0.815789\pi$
$503$	−37.5514	−1.67433	−0.837166	+	0.546949i	$0.815789\pi$
$504$	106.563	4.74671
$505$	15.6318	0.695606
$506$	−6.13684	−0.272816
$507$	−51.5858	−2.29100
$508$	66.7957	2.96358
$509$	−12.2217	−0.541718	−0.270859	−	0.962619i	$-0.587308\pi$
$509$	−12.2217	−0.541718	−0.270859	+	0.962619i	$0.587308\pi$
$510$	−5.97139	−0.264418
$511$	1.86128	0.0823383
$512$	−46.1575	−2.03989
$513$	9.02871	0.398627
$514$	−62.6092	−2.76157
$515$	−17.2790	−0.761404
$516$	−4.92932	−0.217001
$517$	4.90998	0.215941
$518$	19.0088	0.835199
$519$	−16.3866	−0.719291
$520$	−72.4064	−3.17523
$521$	19.3374	0.847188	0.423594	−	0.905852i	$-0.360768\pi$
$521$	19.3374	0.847188	0.423594	+	0.905852i	$0.360768\pi$
$522$	60.5344	2.64952
$523$	−29.5797	−1.29343	−0.646715	−	0.762732i	$-0.723858\pi$
$523$	−29.5797	−1.29343	−0.646715	+	0.762732i	$0.723858\pi$
$524$	−65.5751	−2.86466
$525$	−19.5965	−0.855261
$526$	44.1887	1.92672
$527$	3.41163	0.148613
$528$	22.6734	0.986734
$529$	−5.07051	−0.220457
$530$	14.1102	0.612906
$531$	−28.9994	−1.25847
$532$	18.1070	0.785038
$533$	−16.7404	−0.725105
$534$	1.82814	0.0791112
$535$	−1.35212	−0.0584574
$536$	−69.5895	−3.00581
$537$	−8.20530	−0.354085
$538$	−25.6594	−1.10625
$539$	1.15243	0.0496386
$540$	44.8590	1.93043
$541$	−13.8836	−0.596902	−0.298451	−	0.954425i	$-0.596470\pi$
$541$	−13.8836	−0.596902	−0.298451	+	0.954425i	$0.596470\pi$
$542$	11.7856	0.506234
$543$	21.7863	0.934942
$544$	−12.3920	−0.531304
$545$	2.36770	0.101421
$546$	95.3918	4.08239
$547$	−6.01754	−0.257292	−0.128646	−	0.991691i	$-0.541063\pi$
$547$	−6.01754	−0.257292	−0.128646	+	0.991691i	$0.541063\pi$
$548$	9.99668	0.427037
$549$	62.9831	2.68805
$550$	−4.54080	−0.193620
$551$	6.52823	0.278112
$552$	−114.525	−4.87451
$553$	12.5694	0.534506
$554$	−75.5610	−3.21028
$555$	12.3123	0.522627
$556$	93.1794	3.95169
$557$	−38.2212	−1.61949	−0.809743	−	0.586785i	$-0.800393\pi$
$557$	−38.2212	−1.61949	−0.809743	+	0.586785i	$0.800393\pi$
$558$	−84.8316	−3.59121
$559$	−1.76412	−0.0746143
$560$	45.0920	1.90548
$561$	0.847389	0.0357768
$562$	−15.9373	−0.672273
$563$	−3.40099	−0.143335	−0.0716673	−	0.997429i	$-0.522832\pi$
$563$	−3.40099	−0.143335	−0.0716673	+	0.997429i	$0.522832\pi$
$564$	144.371	6.07913
$565$	10.8143	0.454962
$566$	−37.7547	−1.58695
$567$	−3.85628	−0.161948
$568$	11.7073	0.491226
$569$	−38.0937	−1.59697	−0.798486	−	0.602013i	$-0.794366\pi$
$569$	−38.0937	−1.59697	−0.798486	+	0.602013i	$0.794366\pi$
$570$	16.0127	0.670698
$571$	16.0608	0.672126	0.336063	−	0.941840i	$-0.390905\pi$
$571$	16.0608	0.672126	0.336063	+	0.941840i	$0.390905\pi$
$572$	16.1894	0.676911
$573$	−29.8102	−1.24534
$574$	18.0239	0.752301
$575$	13.2665	0.553249
$576$	154.715	6.44647
$577$	13.0255	0.542259	0.271130	−	0.962543i	$-0.412603\pi$
$577$	13.0255	0.542259	0.271130	+	0.962543i	$0.412603\pi$
$578$	45.6158	1.89737
$579$	−13.0519	−0.542418
$580$	32.4354	1.34681
$581$	−22.0931	−0.916577
$582$	−62.1174	−2.57485
$583$	−2.00235	−0.0829288
$584$	8.04861	0.333054
$585$	38.9204	1.60916
$586$	−32.6044	−1.34688
$587$	5.18931	0.214186	0.107093	−	0.994249i	$-0.465846\pi$
$587$	5.18931	0.214186	0.107093	+	0.994249i	$0.465846\pi$
$588$	33.8856	1.39742
$589$	−9.14853	−0.376958
$590$	−21.2149	−0.873405
$591$	50.3356	2.07053
$592$	47.5448	1.95408
$593$	−27.4618	−1.12772	−0.563860	−	0.825871i	$-0.690684\pi$
$593$	−27.4618	−1.12772	−0.563860	+	0.825871i	$0.690684\pi$
$594$	−8.69145	−0.356614
$595$	1.68525	0.0690886
$596$	19.6569	0.805178
$597$	−41.2434	−1.68798
$598$	−64.5784	−2.64081
$599$	34.7739	1.42082	0.710411	−	0.703787i	$-0.248509\pi$
$599$	34.7739	1.42082	0.710411	+	0.703787i	$0.248509\pi$
$600$	−84.7398	−3.45949
$601$	−29.3124	−1.19568	−0.597839	−	0.801616i	$-0.703974\pi$
$601$	−29.3124	−1.19568	−0.597839	+	0.801616i	$0.703974\pi$
$602$	1.89938	0.0774128
$603$	37.4063	1.52330
$604$	−3.78584	−0.154043
$605$	14.6459	0.595442
$606$	−89.0538	−3.61756
$607$	8.52574	0.346049	0.173025	−	0.984918i	$-0.444646\pi$
$607$	8.52574	0.346049	0.173025	+	0.984918i	$0.444646\pi$
$608$	33.2301	1.34766
$609$	−27.1212	−1.09901
$610$	46.0762	1.86557
$611$	51.6681	2.09027
$612$	15.6952	0.634442
$613$	−5.07534	−0.204991	−0.102496	−	0.994733i	$-0.532683\pi$
$613$	−5.07534	−0.204991	−0.102496	+	0.994733i	$0.532683\pi$
$614$	−24.0539	−0.970735
$615$	11.6743	0.470753
$616$	−11.0629	−0.445735
$617$	−9.29590	−0.374239	−0.187119	−	0.982337i	$-0.559915\pi$
$617$	−9.29590	−0.374239	−0.187119	+	0.982337i	$0.559915\pi$
$618$	98.4379	3.95975
$619$	4.40231	0.176944	0.0884720	−	0.996079i	$-0.471802\pi$
$619$	4.40231	0.176944	0.0884720	+	0.996079i	$0.471802\pi$
$620$	−45.4544	−1.82549
$621$	25.3931	1.01899
$622$	6.58227	0.263925
$623$	−0.515939	−0.0206707
$624$	238.594	9.55140
$625$	0.481547	0.0192619
$626$	−22.1820	−0.886572
$627$	−2.27233	−0.0907482
$628$	−25.3308	−1.01081
$629$	1.77692	0.0708506
$630$	−41.9045	−1.66952
$631$	35.5105	1.41365	0.706825	−	0.707389i	$-0.250127\pi$
$631$	35.5105	1.41365	0.706825	+	0.707389i	$0.250127\pi$
$632$	54.3530	2.16205
$633$	−44.9966	−1.78845
$634$	−33.3513	−1.32455
$635$	−16.6708	−0.661560
$636$	−58.8763	−2.33460
$637$	12.1271	0.480492
$638$	−6.28437	−0.248801
$639$	−6.29299	−0.248947
$640$	52.8685	2.08981
$641$	12.9750	0.512481	0.256241	−	0.966613i	$-0.417516\pi$
$641$	12.9750	0.512481	0.256241	+	0.966613i	$0.417516\pi$
$642$	7.70299	0.304013
$643$	−13.0919	−0.516295	−0.258147	−	0.966106i	$-0.583112\pi$
$643$	−13.0919	−0.516295	−0.258147	+	0.966106i	$0.583112\pi$
$644$	50.9256	2.00675
$645$	1.23025	0.0484412
$646$	2.31098	0.0909241
$647$	−7.91178	−0.311044	−0.155522	−	0.987832i	$-0.549706\pi$
$647$	−7.91178	−0.311044	−0.155522	+	0.987832i	$0.549706\pi$
$648$	−16.6754	−0.655073
$649$	3.01057	0.118175
$650$	−47.7831	−1.87421
$651$	38.0070	1.48961
$652$	52.6241	2.06092
$653$	−9.34667	−0.365764	−0.182882	−	0.983135i	$-0.558543\pi$
$653$	−9.34667	−0.365764	−0.182882	+	0.983135i	$0.558543\pi$
$654$	−13.4887	−0.527450
$655$	16.3662	0.639479
$656$	45.0813	1.76013
$657$	−4.32635	−0.168787
$658$	−55.6295	−2.16866
$659$	31.6432	1.23264	0.616322	−	0.787494i	$-0.288622\pi$
$659$	31.6432	1.23264	0.616322	+	0.787494i	$0.288622\pi$
$660$	−11.2901	−0.439465
$661$	36.7130	1.42797	0.713984	−	0.700162i	$-0.246889\pi$
$661$	36.7130	1.42797	0.713984	+	0.700162i	$0.246889\pi$
$662$	−76.7713	−2.98380
$663$	8.91713	0.346313
$664$	−95.5357	−3.70750
$665$	−4.51912	−0.175244
$666$	−44.1840	−1.71209
$667$	18.3605	0.710922
$668$	−24.9831	−0.966627
$669$	−77.1162	−2.98148
$670$	27.3651	1.05721
$671$	−6.53858	−0.252419
$672$	−138.053	−5.32550
$673$	−12.1147	−0.466986	−0.233493	−	0.972358i	$-0.575016\pi$
$673$	−12.1147	−0.466986	−0.233493	+	0.972358i	$0.575016\pi$
$674$	64.8519	2.49800
$675$	18.7889	0.723186
$676$	99.1914	3.81506
$677$	−19.5625	−0.751849	−0.375924	−	0.926650i	$-0.622675\pi$
$677$	−19.5625	−0.751849	−0.375924	+	0.926650i	$0.622675\pi$
$678$	−61.6087	−2.36607
$679$	17.5309	0.672772
$680$	7.28742	0.279460
$681$	26.4943	1.01526
$682$	8.80679	0.337229
$683$	28.5852	1.09378	0.546891	−	0.837204i	$-0.315811\pi$
$683$	28.5852	1.09378	0.546891	+	0.837204i	$0.315811\pi$
$684$	−42.0878	−1.60927
$685$	−2.49496	−0.0953275
$686$	−55.0995	−2.10371
$687$	−43.1488	−1.64623
$688$	4.75072	0.181120
$689$	−21.0708	−0.802735
$690$	45.0354	1.71447
$691$	−11.7032	−0.445210	−0.222605	−	0.974909i	$-0.571456\pi$
$691$	−11.7032	−0.445210	−0.222605	+	0.974909i	$0.571456\pi$
$692$	31.5089	1.19779
$693$	5.94660	0.225892
$694$	−44.3217	−1.68243
$695$	−23.2556	−0.882135
$696$	−117.278	−4.44542
$697$	1.68485	0.0638183
$698$	8.53774	0.323158
$699$	−80.1252	−3.03061
$700$	37.6810	1.42421
$701$	−33.0041	−1.24655	−0.623273	−	0.782004i	$-0.714197\pi$
$701$	−33.0041	−1.24655	−0.623273	+	0.782004i	$0.714197\pi$
$702$	−91.4607	−3.45196
$703$	−4.76495	−0.179713
$704$	−16.0618	−0.605351
$705$	−36.0320	−1.35704
$706$	12.1739	0.458169
$707$	25.1329	0.945219
$708$	88.5217	3.32685
$709$	3.05854	0.114866	0.0574330	−	0.998349i	$-0.481708\pi$
$709$	3.05854	0.114866	0.0574330	+	0.998349i	$0.481708\pi$
$710$	−4.60372	−0.172775
$711$	−29.2163	−1.09570
$712$	−2.23104	−0.0836117
$713$	−25.7300	−0.963598
$714$	−9.60082	−0.359302
$715$	−4.04052	−0.151107
$716$	15.7775	0.589634
$717$	−85.6871	−3.20004
$718$	−6.25047	−0.233265
$719$	−25.7557	−0.960525	−0.480263	−	0.877125i	$-0.659459\pi$
$719$	−25.7557	−0.960525	−0.480263	+	0.877125i	$0.659459\pi$
$720$	−104.812	−3.90610
$721$	−27.7813	−1.03463
$722$	45.7486	1.70259
$723$	51.0376	1.89811
$724$	−41.8918	−1.55690
$725$	13.5854	0.504548
$726$	−83.4373	−3.09665
$727$	−44.1955	−1.63912	−0.819561	−	0.572992i	$-0.805783\pi$
$727$	−44.1955	−1.63912	−0.819561	+	0.572992i	$0.805783\pi$
$728$	−116.415	−4.31463
$729$	−42.2593	−1.56516
$730$	−3.16500	−0.117142
$731$	0.177552	0.00656699
$732$	−192.258	−7.10606
$733$	−3.29508	−0.121707	−0.0608533	−	0.998147i	$-0.519382\pi$
$733$	−3.29508	−0.121707	−0.0608533	+	0.998147i	$0.519382\pi$
$734$	−1.28882	−0.0475713
$735$	−8.45712	−0.311945
$736$	93.4590	3.44494
$737$	−3.88333	−0.143044
$738$	−41.8946	−1.54216
$739$	−3.13462	−0.115309	−0.0576544	−	0.998337i	$-0.518362\pi$
$739$	−3.13462	−0.115309	−0.0576544	+	0.998337i	$0.518362\pi$
$740$	−23.6746	−0.870295
$741$	−23.9119	−0.878426
$742$	22.6864	0.832843
$743$	43.5317	1.59702	0.798512	−	0.601978i	$-0.205621\pi$
$743$	43.5317	1.59702	0.798512	+	0.601978i	$0.205621\pi$
$744$	164.351	6.02541
$745$	−4.90595	−0.179740
$746$	−88.8902	−3.25450
$747$	51.3531	1.87891
$748$	−1.62940	−0.0595767
$749$	−2.17395	−0.0794344
$750$	86.5017	3.15860
$751$	−34.5444	−1.26054	−0.630271	−	0.776375i	$-0.717056\pi$
$751$	−34.5444	−1.26054	−0.630271	+	0.776375i	$0.717056\pi$
$752$	−139.140	−5.07393
$753$	60.1607	2.19238
$754$	−66.1309	−2.40834
$755$	0.944864	0.0343871
$756$	72.1245	2.62314
$757$	23.1284	0.840616	0.420308	−	0.907382i	$-0.361922\pi$
$757$	23.1284	0.840616	0.420308	+	0.907382i	$0.361922\pi$
$758$	−34.9539	−1.26958
$759$	−6.39089	−0.231975
$760$	−19.5417	−0.708853
$761$	−39.3241	−1.42550	−0.712748	−	0.701420i	$-0.752550\pi$
$761$	−39.3241	−1.42550	−0.712748	+	0.701420i	$0.752550\pi$
$762$	94.9728	3.44050
$763$	3.80680	0.137815
$764$	57.3204	2.07378
$765$	−3.91719	−0.141626
$766$	102.036	3.68671
$767$	31.6804	1.14391
$768$	−128.658	−4.64255
$769$	29.5811	1.06672	0.533361	−	0.845888i	$-0.320929\pi$
$769$	29.5811	1.06672	0.533361	+	0.845888i	$0.320929\pi$
$770$	4.35032	0.156774
$771$	−65.2010	−2.34816
$772$	25.0967	0.903252
$773$	27.0637	0.973413	0.486707	−	0.873565i	$-0.338198\pi$
$773$	27.0637	0.973413	0.486707	+	0.873565i	$0.338198\pi$
$774$	−4.41490	−0.158690
$775$	−19.0383	−0.683875
$776$	75.8074	2.72133
$777$	19.7957	0.710167
$778$	69.1335	2.47856
$779$	−4.51805	−0.161876
$780$	−118.806	−4.25394
$781$	0.653306	0.0233771
$782$	6.49957	0.232424
$783$	26.0035	0.929289
$784$	−32.6578	−1.16635
$785$	6.32202	0.225643
$786$	−93.2374	−3.32567
$787$	−15.0327	−0.535857	−0.267928	−	0.963439i	$-0.586339\pi$
$787$	−15.0327	−0.535857	−0.267928	+	0.963439i	$0.586339\pi$
$788$	−96.7876	−3.44791
$789$	46.0180	1.63828
$790$	−21.3736	−0.760437
$791$	17.3873	0.618221
$792$	25.7144	0.913723
$793$	−68.8060	−2.44337
$794$	−98.7784	−3.50551
$795$	14.6943	0.521152
$796$	79.3047	2.81088
$797$	−22.1186	−0.783483	−0.391741	−	0.920075i	$-0.628127\pi$
$797$	−22.1186	−0.783483	−0.391741	+	0.920075i	$0.628127\pi$
$798$	25.7453	0.911373
$799$	−5.20019	−0.183970
$800$	69.1525	2.44491
$801$	1.19925	0.0423733
$802$	−6.99082	−0.246854
$803$	0.449140	0.0158498
$804$	−114.184	−4.02696
$805$	−12.7099	−0.447967
$806$	92.6744	3.26432
$807$	−26.7216	−0.940644
$808$	108.680	3.82336
$809$	−6.74558	−0.237162	−0.118581	−	0.992944i	$-0.537834\pi$
$809$	−6.74558	−0.237162	−0.118581	+	0.992944i	$0.537834\pi$
$810$	6.55738	0.230403
$811$	−39.4289	−1.38454	−0.692268	−	0.721641i	$-0.743388\pi$
$811$	−39.4289	−1.38454	−0.692268	+	0.721641i	$0.743388\pi$
$812$	52.1498	1.83010
$813$	12.2735	0.430449
$814$	4.58696	0.160773
$815$	−13.1339	−0.460059
$816$	−24.0136	−0.840643
$817$	−0.476118	−0.0166573
$818$	1.84382	0.0644675
$819$	62.5764	2.18660
$820$	−22.4479	−0.783914
$821$	−28.2438	−0.985715	−0.492857	−	0.870110i	$-0.664048\pi$
$821$	−28.2438	−0.985715	−0.492857	+	0.870110i	$0.664048\pi$
$822$	14.2137	0.495759
$823$	45.6009	1.58955	0.794775	−	0.606905i	$-0.207589\pi$
$823$	45.6009	1.58955	0.794775	+	0.606905i	$0.207589\pi$
$824$	−120.133	−4.18502
$825$	−4.72877	−0.164635
$826$	−34.1094	−1.18682
$827$	53.7777	1.87003	0.935017	−	0.354604i	$-0.115384\pi$
$827$	53.7777	1.87003	0.935017	+	0.354604i	$0.115384\pi$
$828$	−118.371	−4.11368
$829$	−20.9987	−0.729314	−0.364657	−	0.931142i	$-0.618814\pi$
$829$	−20.9987	−0.729314	−0.364657	+	0.931142i	$0.618814\pi$
$830$	37.5681	1.30401
$831$	−78.6889	−2.72969
$832$	−169.019	−5.85968
$833$	−1.22054	−0.0422893
$834$	132.486	4.58762
$835$	6.23526	0.215780
$836$	4.36934	0.151117
$837$	−36.4408	−1.25958
$838$	66.2162	2.28740
$839$	55.4940	1.91587	0.957933	−	0.286991i	$-0.0926550\pi$
$839$	55.4940	1.91587	0.957933	+	0.286991i	$0.0926550\pi$
$840$	81.1850	2.80115
$841$	−10.1981	−0.351659
$842$	1.25703	0.0433201
$843$	−16.5970	−0.571632
$844$	86.5215	2.97819
$845$	−24.7561	−0.851635
$846$	129.305	4.44560
$847$	23.5478	0.809111
$848$	56.7431	1.94857
$849$	−39.3176	−1.34938
$850$	4.80919	0.164954
$851$	−13.4013	−0.459391
$852$	19.2096	0.658109
$853$	−29.8226	−1.02111	−0.510553	−	0.859847i	$-0.670559\pi$
$853$	−29.8226	−1.02111	−0.510553	+	0.859847i	$0.670559\pi$
$854$	74.0814	2.53501
$855$	10.5042	0.359237
$856$	−9.40066	−0.321308
$857$	2.22974	0.0761664	0.0380832	−	0.999275i	$-0.487875\pi$
$857$	2.22974	0.0761664	0.0380832	+	0.999275i	$0.487875\pi$
$858$	23.0187	0.785845
$859$	−33.7445	−1.15135	−0.575675	−	0.817679i	$-0.695260\pi$
$859$	−33.7445	−1.15135	−0.575675	+	0.817679i	$0.695260\pi$
$860$	−2.36559	−0.0806658
$861$	18.7700	0.639679
$862$	−31.1458	−1.06083
$863$	−26.1295	−0.889460	−0.444730	−	0.895665i	$-0.646700\pi$
$863$	−26.1295	−0.889460	−0.444730	+	0.895665i	$0.646700\pi$
$864$	132.363	4.50310
$865$	−7.86395	−0.267382
$866$	51.2317	1.74092
$867$	47.5042	1.61333
$868$	−73.0817	−2.48055
$869$	3.03308	0.102890
$870$	46.1180	1.56355
$871$	−40.8646	−1.38464
$872$	16.4615	0.557456
$873$	−40.7486	−1.37913
$874$	−17.4291	−0.589547
$875$	−24.4126	−0.825297
$876$	13.2063	0.446201
$877$	−29.5983	−0.999464	−0.499732	−	0.866180i	$-0.666568\pi$
$877$	−29.5983	−0.999464	−0.499732	+	0.866180i	$0.666568\pi$
$878$	23.0529	0.777998
$879$	−33.9541	−1.14524
$880$	10.8810	0.366799
$881$	−12.9573	−0.436543	−0.218271	−	0.975888i	$-0.570042\pi$
$881$	−12.9573	−0.436543	−0.218271	+	0.975888i	$0.570042\pi$
$882$	30.3493	1.02192
$883$	25.4898	0.857801	0.428900	−	0.903352i	$-0.358901\pi$
$883$	25.4898	0.857801	0.428900	+	0.903352i	$0.358901\pi$
$884$	−17.1463	−0.576691
$885$	−22.0931	−0.742653
$886$	−23.0257	−0.773562
$887$	−18.8139	−0.631709	−0.315854	−	0.948808i	$-0.602291\pi$
$887$	−18.8139	−0.631709	−0.315854	+	0.948808i	$0.602291\pi$
$888$	85.6012	2.87259
$889$	−26.8033	−0.898955
$890$	0.877325	0.0294080
$891$	−0.930546	−0.0311745
$892$	148.283	4.96487
$893$	13.9447	0.466641
$894$	27.9490	0.934754
$895$	−3.93774	−0.131624
$896$	85.0021	2.83972
$897$	−67.2517	−2.24547
$898$	−97.3183	−3.24755
$899$	−26.3486	−0.878774
$900$	−87.5856	−2.91952
$901$	2.12070	0.0706508
$902$	4.34928	0.144815
$903$	1.97800	0.0658239
$904$	75.1867	2.50067
$905$	10.4553	0.347546
$906$	−5.38285	−0.178833
$907$	19.3999	0.644163	0.322081	−	0.946712i	$-0.395618\pi$
$907$	19.3999	0.644163	0.322081	+	0.946712i	$0.395618\pi$
$908$	−50.9445	−1.69065
$909$	−58.4187	−1.93763
$910$	45.7787	1.51755
$911$	24.2958	0.804957	0.402478	−	0.915429i	$-0.368149\pi$
$911$	24.2958	0.804957	0.402478	+	0.915429i	$0.368149\pi$
$912$	64.3940	2.13230
$913$	−5.33122	−0.176438
$914$	16.0426	0.530642
$915$	47.9835	1.58629
$916$	82.9685	2.74136
$917$	26.3136	0.868951
$918$	9.20517	0.303816
$919$	39.3478	1.29796	0.648982	−	0.760803i	$-0.275195\pi$
$919$	39.3478	1.29796	0.648982	+	0.760803i	$0.275195\pi$
$920$	−54.9607	−1.81200
$921$	−25.0496	−0.825413
$922$	14.9745	0.493160
$923$	6.87478	0.226286
$924$	−18.1522	−0.597163
$925$	−9.91595	−0.326034
$926$	42.7818	1.40590
$927$	64.5746	2.12091
$928$	95.7057	3.14169
$929$	−7.83812	−0.257160	−0.128580	−	0.991699i	$-0.541042\pi$
$929$	−7.83812	−0.257160	−0.128580	+	0.991699i	$0.541042\pi$
$930$	−64.6288	−2.11926
$931$	3.27297	0.107267
$932$	154.068	5.04668
$933$	6.85475	0.224414
$934$	13.1242	0.429438
$935$	0.406663	0.0132993
$936$	270.595	8.84467
$937$	−38.9259	−1.27166	−0.635828	−	0.771831i	$-0.719341\pi$
$937$	−38.9259	−1.27166	−0.635828	+	0.771831i	$0.719341\pi$
$938$	43.9977	1.43658
$939$	−23.1003	−0.753849
$940$	69.2840	2.25979
$941$	−51.1849	−1.66858	−0.834291	−	0.551325i	$-0.814123\pi$
$941$	−51.1849	−1.66858	−0.834291	+	0.551325i	$0.814123\pi$
$942$	−36.0163	−1.17347
$943$	−12.7069	−0.413794
$944$	−85.3145	−2.77675
$945$	−18.0008	−0.585564
$946$	0.458333	0.0149017
$947$	27.6566	0.898720	0.449360	−	0.893351i	$-0.351652\pi$
$947$	27.6566	0.898720	0.449360	+	0.893351i	$0.351652\pi$
$948$	89.1837	2.89655
$949$	4.72633	0.153423
$950$	−12.8962	−0.418407
$951$	−34.7319	−1.12626
$952$	11.7167	0.379742
$953$	29.6809	0.961460	0.480730	−	0.876869i	$-0.340372\pi$
$953$	29.6809	0.961460	0.480730	+	0.876869i	$0.340372\pi$
$954$	−52.7321	−1.70726
$955$	−14.3059	−0.462929
$956$	164.763	5.32882
$957$	−6.54452	−0.211554
$958$	56.5629	1.82747
$959$	−4.01140	−0.129535
$960$	117.870	3.80423
$961$	5.92436	0.191109
$962$	48.2688	1.55625
$963$	5.05311	0.162834
$964$	−98.1375	−3.16079
$965$	−6.26361	−0.201633
$966$	72.4080	2.32969
$967$	21.4296	0.689128	0.344564	−	0.938763i	$-0.388027\pi$
$967$	21.4296	0.689128	0.344564	+	0.938763i	$0.388027\pi$
$968$	101.826	3.27281
$969$	2.40664	0.0773125
$970$	−29.8102	−0.957148
$971$	54.7354	1.75654	0.878272	−	0.478162i	$-0.158697\pi$
$971$	54.7354	1.75654	0.878272	+	0.478162i	$0.158697\pi$
$972$	71.1321	2.28156
$973$	−37.3904	−1.19868
$974$	93.8467	3.00704
$975$	−49.7612	−1.59363
$976$	185.292	5.93106
$977$	−38.2264	−1.22297	−0.611485	−	0.791256i	$-0.709427\pi$
$977$	−38.2264	−1.22297	−0.611485	+	0.791256i	$0.709427\pi$
$978$	74.8231	2.39258
$979$	−0.124500	−0.00397903
$980$	16.2617	0.519462
$981$	−8.84850	−0.282511
$982$	70.8231	2.26005
$983$	−7.19037	−0.229337	−0.114669	−	0.993404i	$-0.536581\pi$
$983$	−7.19037	−0.229337	−0.114669	+	0.993404i	$0.536581\pi$
$984$	81.1657	2.58747
$985$	24.1561	0.769678
$986$	6.65582	0.211964
$987$	−57.9324	−1.84401
$988$	45.9789	1.46278
$989$	−1.33907	−0.0425800
$990$	−10.1118	−0.321376
$991$	−25.7247	−0.817172	−0.408586	−	0.912720i	$-0.633978\pi$
$991$	−25.7247	−0.817172	−0.408586	+	0.912720i	$0.633978\pi$
$992$	−134.120	−4.25832
$993$	−79.9493	−2.53712
$994$	−7.40188	−0.234773
$995$	−19.7928	−0.627473
$996$	−156.757	−4.96704
$997$	27.0521	0.856749	0.428374	−	0.903601i	$-0.359086\pi$
$997$	27.0521	0.856749	0.428374	+	0.903601i	$0.359086\pi$
$998$	−73.0869	−2.31353
$999$	−18.9799	−0.600498

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6007.2.a.b.1.4	✓	237

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6007.2.a.b.1.4	✓	237	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:	\( N \)	\(=\)	\( 6007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.73398 q^{2} -2.84716 q^{3} +5.47464 q^{4} -1.36635 q^{5} +7.78406 q^{6} -2.19683 q^{7} -9.49960 q^{8} +5.10630 q^{9} +O(q^{10})\)	\(q-2.73398 q^{2} -2.84716 q^{3} +5.47464 q^{4} -1.36635 q^{5} +7.78406 q^{6} -2.19683 q^{7} -9.49960 q^{8} +5.10630 q^{9} +3.73558 q^{10} -0.530110 q^{11} -15.5872 q^{12} -5.57838 q^{13} +6.00608 q^{14} +3.89022 q^{15} +15.0224 q^{16} +0.561443 q^{17} -13.9605 q^{18} -1.50555 q^{19} -7.48030 q^{20} +6.25472 q^{21} +1.44931 q^{22} -4.23432 q^{23} +27.0468 q^{24} -3.13308 q^{25} +15.2512 q^{26} -5.99696 q^{27} -12.0269 q^{28} -4.33611 q^{29} -10.6358 q^{30} +6.07654 q^{31} -22.0718 q^{32} +1.50931 q^{33} -1.53497 q^{34} +3.00165 q^{35} +27.9551 q^{36} +3.16492 q^{37} +4.11614 q^{38} +15.8825 q^{39} +12.9798 q^{40} +3.00093 q^{41} -17.1003 q^{42} +0.316242 q^{43} -2.90216 q^{44} -6.97701 q^{45} +11.5766 q^{46} -9.26219 q^{47} -42.7712 q^{48} -2.17394 q^{49} +8.56576 q^{50} -1.59852 q^{51} -30.5396 q^{52} +3.77723 q^{53} +16.3956 q^{54} +0.724318 q^{55} +20.8690 q^{56} +4.28653 q^{57} +11.8548 q^{58} -5.67915 q^{59} +21.2976 q^{60} +12.3344 q^{61} -16.6131 q^{62} -11.2177 q^{63} +30.2989 q^{64} +7.62205 q^{65} -4.12641 q^{66} +7.32553 q^{67} +3.07370 q^{68} +12.0558 q^{69} -8.20644 q^{70} -1.23240 q^{71} -48.5078 q^{72} -0.847258 q^{73} -8.65284 q^{74} +8.92036 q^{75} -8.24234 q^{76} +1.16456 q^{77} -43.4225 q^{78} -5.72161 q^{79} -20.5259 q^{80} +1.75538 q^{81} -8.20449 q^{82} +10.0568 q^{83} +34.2423 q^{84} -0.767130 q^{85} -0.864599 q^{86} +12.3456 q^{87} +5.03583 q^{88} +0.234856 q^{89} +19.0750 q^{90} +12.2548 q^{91} -23.1814 q^{92} -17.3009 q^{93} +25.3226 q^{94} +2.05711 q^{95} +62.8418 q^{96} -7.98007 q^{97} +5.94351 q^{98} -2.70690 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9}+O(q^{10}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9} - 39 q^{10} - 38 q^{11} - 67 q^{12} - 52 q^{13} - 54 q^{14} - 24 q^{15} + 208 q^{16} - 255 q^{17} - 71 q^{18} - 24 q^{19} - 154 q^{20} - 60 q^{21} - 39 q^{22} - 118 q^{23} - 85 q^{24} + 170 q^{25} - 61 q^{26} - 87 q^{27} - 99 q^{28} - 87 q^{29} - 30 q^{30} - 28 q^{31} - 156 q^{32} - 173 q^{33} - 4 q^{34} - 113 q^{35} + 152 q^{36} - 49 q^{37} - 145 q^{38} - 49 q^{39} - 91 q^{40} - 197 q^{41} - 61 q^{42} - 63 q^{43} - 106 q^{44} - 181 q^{45} - 2 q^{46} - 119 q^{47} - 142 q^{48} + 150 q^{49} - 89 q^{50} - 40 q^{51} - 97 q^{52} - 190 q^{53} - 97 q^{54} - 55 q^{55} - 154 q^{56} - 202 q^{57} - 27 q^{58} - 86 q^{59} - 48 q^{60} - 96 q^{61} - 239 q^{62} - 149 q^{63} + 183 q^{64} - 259 q^{65} - 72 q^{66} - 28 q^{67} - 482 q^{68} - 83 q^{69} + 20 q^{70} - 63 q^{71} - 193 q^{72} - 206 q^{73} - 132 q^{74} - 89 q^{75} - 11 q^{76} - 179 q^{77} - 58 q^{78} - 32 q^{79} - 320 q^{80} + 57 q^{81} - 77 q^{82} - 245 q^{83} - 133 q^{84} + q^{85} - 39 q^{86} - 179 q^{87} - 104 q^{88} - 227 q^{89} - 146 q^{90} - 36 q^{91} - 315 q^{92} - 87 q^{93} - 48 q^{94} - 111 q^{95} - 134 q^{96} - 221 q^{97} - 161 q^{98} - 68 q^{99}+O(q^{100}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9 - 39 * q^10 - 38 * q^11 - 67 * q^12 - 52 * q^13 - 54 * q^14 - 24 * q^15 + 208 * q^16 - 255 * q^17 - 71 * q^18 - 24 * q^19 - 154 * q^20 - 60 * q^21 - 39 * q^22 - 118 * q^23 - 85 * q^24 + 170 * q^25 - 61 * q^26 - 87 * q^27 - 99 * q^28 - 87 * q^29 - 30 * q^30 - 28 * q^31 - 156 * q^32 - 173 * q^33 - 4 * q^34 - 113 * q^35 + 152 * q^36 - 49 * q^37 - 145 * q^38 - 49 * q^39 - 91 * q^40 - 197 * q^41 - 61 * q^42 - 63 * q^43 - 106 * q^44 - 181 * q^45 - 2 * q^46 - 119 * q^47 - 142 * q^48 + 150 * q^49 - 89 * q^50 - 40 * q^51 - 97 * q^52 - 190 * q^53 - 97 * q^54 - 55 * q^55 - 154 * q^56 - 202 * q^57 - 27 * q^58 - 86 * q^59 - 48 * q^60 - 96 * q^61 - 239 * q^62 - 149 * q^63 + 183 * q^64 - 259 * q^65 - 72 * q^66 - 28 * q^67 - 482 * q^68 - 83 * q^69 + 20 * q^70 - 63 * q^71 - 193 * q^72 - 206 * q^73 - 132 * q^74 - 89 * q^75 - 11 * q^76 - 179 * q^77 - 58 * q^78 - 32 * q^79 - 320 * q^80 + 57 * q^81 - 77 * q^82 - 245 * q^83 - 133 * q^84 + q^85 - 39 * q^86 - 179 * q^87 - 104 * q^88 - 227 * q^89 - 146 * q^90 - 36 * q^91 - 315 * q^92 - 87 * q^93 - 48 * q^94 - 111 * q^95 - 134 * q^96 - 221 * q^97 - 161 * q^98 - 68 * q^99

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