LMFDB - Embedded newform 6007.2.a.b.1.12

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			1.12
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)

$f(q)$	$=$	$q-2.68501 q^{2} -2.77509 q^{3} +5.20930 q^{4} +3.15364 q^{5} +7.45116 q^{6} -1.25017 q^{7} -8.61702 q^{8} +4.70113 q^{9} +O(q^{10})$	\(q-2.68501 q^{2} -2.77509 q^{3} +5.20930 q^{4} +3.15364 q^{5} +7.45116 q^{6} -1.25017 q^{7} -8.61702 q^{8} +4.70113 q^{9} -8.46756 q^{10} +2.27115 q^{11} -14.4563 q^{12} +4.14896 q^{13} +3.35672 q^{14} -8.75163 q^{15} +12.7182 q^{16} -7.16250 q^{17} -12.6226 q^{18} +8.09188 q^{19} +16.4282 q^{20} +3.46933 q^{21} -6.09807 q^{22} -3.11964 q^{23} +23.9130 q^{24} +4.94542 q^{25} -11.1400 q^{26} -4.72080 q^{27} -6.51250 q^{28} -9.47302 q^{29} +23.4982 q^{30} +0.931053 q^{31} -16.9145 q^{32} -6.30265 q^{33} +19.2314 q^{34} -3.94258 q^{35} +24.4896 q^{36} +5.20833 q^{37} -21.7268 q^{38} -11.5137 q^{39} -27.1749 q^{40} +4.56850 q^{41} -9.31520 q^{42} -2.07995 q^{43} +11.8311 q^{44} +14.8257 q^{45} +8.37628 q^{46} +5.08655 q^{47} -35.2942 q^{48} -5.43708 q^{49} -13.2785 q^{50} +19.8766 q^{51} +21.6132 q^{52} -7.06493 q^{53} +12.6754 q^{54} +7.16238 q^{55} +10.7727 q^{56} -22.4557 q^{57} +25.4352 q^{58} +13.1505 q^{59} -45.5899 q^{60} +5.56230 q^{61} -2.49989 q^{62} -5.87721 q^{63} +19.9793 q^{64} +13.0843 q^{65} +16.9227 q^{66} -6.19545 q^{67} -37.3116 q^{68} +8.65729 q^{69} +10.5859 q^{70} -16.2256 q^{71} -40.5097 q^{72} -2.28294 q^{73} -13.9845 q^{74} -13.7240 q^{75} +42.1530 q^{76} -2.83932 q^{77} +30.9145 q^{78} +2.61426 q^{79} +40.1086 q^{80} -1.00276 q^{81} -12.2665 q^{82} -12.6101 q^{83} +18.0728 q^{84} -22.5879 q^{85} +5.58470 q^{86} +26.2885 q^{87} -19.5705 q^{88} -2.48077 q^{89} -39.8071 q^{90} -5.18689 q^{91} -16.2512 q^{92} -2.58376 q^{93} -13.6575 q^{94} +25.5188 q^{95} +46.9394 q^{96} -14.8493 q^{97} +14.5986 q^{98} +10.6770 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.68501	−1.89859	−0.949296	−	0.314384i	$-0.898202\pi$
$2$	−2.68501	−1.89859	−0.949296	+	0.314384i	$0.898202\pi$
$3$	−2.77509	−1.60220	−0.801100	−	0.598531i	$-0.795751\pi$
$3$	−2.77509	−1.60220	−0.801100	+	0.598531i	$0.795751\pi$
$4$	5.20930	2.60465
$5$	3.15364	1.41035	0.705175	−	0.709034i	$-0.250869\pi$
$5$	3.15364	1.41035	0.705175	+	0.709034i	$0.250869\pi$
$6$	7.45116	3.04192
$7$	−1.25017	−0.472519	−0.236260	−	0.971690i	$-0.575922\pi$
$7$	−1.25017	−0.472519	−0.236260	+	0.971690i	$0.575922\pi$
$8$	−8.61702	−3.04658
$9$	4.70113	1.56704
$10$	−8.46756	−2.67768
$11$	2.27115	0.684777	0.342389	−	0.939558i	$-0.388764\pi$
$11$	2.27115	0.684777	0.342389	+	0.939558i	$0.388764\pi$
$12$	−14.4563	−4.17317
$13$	4.14896	1.15071	0.575357	−	0.817903i	$-0.304863\pi$
$13$	4.14896	1.15071	0.575357	+	0.817903i	$0.304863\pi$
$14$	3.35672	0.897121
$15$	−8.75163	−2.25966
$16$	12.7182	3.17955
$17$	−7.16250	−1.73716	−0.868581	−	0.495548i	$-0.834967\pi$
$17$	−7.16250	−1.73716	−0.868581	+	0.495548i	$0.834967\pi$
$18$	−12.6226	−2.97518
$19$	8.09188	1.85640	0.928202	−	0.372076i	$-0.121354\pi$
$19$	8.09188	1.85640	0.928202	+	0.372076i	$0.121354\pi$
$20$	16.4282	3.67347
$21$	3.46933	0.757070
$22$	−6.09807	−1.30011
$23$	−3.11964	−0.650490	−0.325245	−	0.945630i	$-0.605447\pi$
$23$	−3.11964	−0.650490	−0.325245	+	0.945630i	$0.605447\pi$
$24$	23.9130	4.88122
$25$	4.94542	0.989085
$26$	−11.1400	−2.18473
$27$	−4.72080	−0.908518
$28$	−6.51250	−1.23075
$29$	−9.47302	−1.75909	−0.879547	−	0.475811i	$-0.842155\pi$
$29$	−9.47302	−1.75909	−0.879547	+	0.475811i	$0.842155\pi$
$30$	23.4982	4.29017
$31$	0.931053	0.167222	0.0836110	−	0.996498i	$-0.473355\pi$
$31$	0.931053	0.167222	0.0836110	+	0.996498i	$0.473355\pi$
$32$	−16.9145	−2.99010
$33$	−6.30265	−1.09715
$34$	19.2314	3.29816
$35$	−3.94258	−0.666417
$36$	24.4896	4.08160
$37$	5.20833	0.856245	0.428122	−	0.903721i	$-0.359175\pi$
$37$	5.20833	0.856245	0.428122	+	0.903721i	$0.359175\pi$
$38$	−21.7268	−3.52455
$39$	−11.5137	−1.84367
$40$	−27.1749	−4.29673
$41$	4.56850	0.713480	0.356740	−	0.934204i	$-0.383888\pi$
$41$	4.56850	0.713480	0.356740	+	0.934204i	$0.383888\pi$
$42$	−9.31520	−1.43737
$43$	−2.07995	−0.317190	−0.158595	−	0.987344i	$-0.550696\pi$
$43$	−2.07995	−0.317190	−0.158595	+	0.987344i	$0.550696\pi$
$44$	11.8311	1.78361
$45$	14.8257	2.21008
$46$	8.37628	1.23502
$47$	5.08655	0.741950	0.370975	−	0.928643i	$-0.379024\pi$
$47$	5.08655	0.741950	0.370975	+	0.928643i	$0.379024\pi$
$48$	−35.2942	−5.09428
$49$	−5.43708	−0.776726
$50$	−13.2785	−1.87787
$51$	19.8766	2.78328
$52$	21.6132	2.99721
$53$	−7.06493	−0.970442	−0.485221	−	0.874392i	$-0.661261\pi$
$53$	−7.06493	−0.970442	−0.485221	+	0.874392i	$0.661261\pi$
$54$	12.6754	1.72490
$55$	7.16238	0.965775
$56$	10.7727	1.43957
$57$	−22.4557	−2.97433
$58$	25.4352	3.33980
$59$	13.1505	1.71205	0.856025	−	0.516934i	$-0.172927\pi$
$59$	13.1505	1.71205	0.856025	+	0.516934i	$0.172927\pi$
$60$	−45.5899	−5.88563
$61$	5.56230	0.712179	0.356090	−	0.934452i	$-0.384110\pi$
$61$	5.56230	0.712179	0.356090	+	0.934452i	$0.384110\pi$
$62$	−2.49989	−0.317486
$63$	−5.87721	−0.740458
$64$	19.9793	2.49742
$65$	13.0843	1.62291
$66$	16.9227	2.08304
$67$	−6.19545	−0.756894	−0.378447	−	0.925623i	$-0.623542\pi$
$67$	−6.19545	−0.756894	−0.378447	+	0.925623i	$0.623542\pi$
$68$	−37.3116	−4.52470
$69$	8.65729	1.04222
$70$	10.5859	1.26525
$71$	−16.2256	−1.92563	−0.962813	−	0.270170i	$-0.912920\pi$
$71$	−16.2256	−1.92563	−0.962813	+	0.270170i	$0.912920\pi$
$72$	−40.5097	−4.77412
$73$	−2.28294	−0.267198	−0.133599	−	0.991035i	$-0.542653\pi$
$73$	−2.28294	−0.267198	−0.133599	+	0.991035i	$0.542653\pi$
$74$	−13.9845	−1.62566
$75$	−13.7240	−1.58471
$76$	42.1530	4.83528
$77$	−2.83932	−0.323570
$78$	30.9145	3.50038
$79$	2.61426	0.294128	0.147064	−	0.989127i	$-0.453018\pi$
$79$	2.61426	0.294128	0.147064	+	0.989127i	$0.453018\pi$
$80$	40.1086	4.48428
$81$	−1.00276	−0.111417
$82$	−12.2665	−1.35461
$83$	−12.6101	−1.38414	−0.692070	−	0.721830i	$-0.743301\pi$
$83$	−12.6101	−1.38414	−0.692070	+	0.721830i	$0.743301\pi$
$84$	18.0728	1.97190
$85$	−22.5879	−2.45000
$86$	5.58470	0.602214
$87$	26.2885	2.81842
$88$	−19.5705	−2.08623
$89$	−2.48077	−0.262961	−0.131481	−	0.991319i	$-0.541973\pi$
$89$	−2.48077	−0.262961	−0.131481	+	0.991319i	$0.541973\pi$
$90$	−39.8071	−4.19604
$91$	−5.18689	−0.543734
$92$	−16.2512	−1.69430
$93$	−2.58376	−0.267923
$94$	−13.6575	−1.40866
$95$	25.5188	2.61818
$96$	46.9394	4.79073
$97$	−14.8493	−1.50772	−0.753860	−	0.657036i	$-0.771810\pi$
$97$	−14.8493	−1.50772	−0.753860	+	0.657036i	$0.771810\pi$
$98$	14.5986	1.47468
$99$	10.6770	1.07308
$100$	25.7622	2.57622
$101$	−17.5966	−1.75092	−0.875462	−	0.483287i	$-0.839443\pi$
$101$	−17.5966	−1.75092	−0.875462	+	0.483287i	$0.839443\pi$
$102$	−53.3689	−5.28431
$103$	−2.52010	−0.248313	−0.124156	−	0.992263i	$-0.539622\pi$
$103$	−2.52010	−0.248313	−0.124156	+	0.992263i	$0.539622\pi$
$104$	−35.7516	−3.50573
$105$	10.9410	1.06773
$106$	18.9694	1.84247
$107$	17.1003	1.65315	0.826575	−	0.562826i	$-0.190286\pi$
$107$	17.1003	1.65315	0.826575	+	0.562826i	$0.190286\pi$
$108$	−24.5920	−2.36637
$109$	−7.29215	−0.698461	−0.349231	−	0.937037i	$-0.613557\pi$
$109$	−7.29215	−0.698461	−0.349231	+	0.937037i	$0.613557\pi$
$110$	−19.2311	−1.83361
$111$	−14.4536	−1.37188
$112$	−15.8999	−1.50240
$113$	−2.67118	−0.251284	−0.125642	−	0.992076i	$-0.540099\pi$
$113$	−2.67118	−0.251284	−0.125642	+	0.992076i	$0.540099\pi$
$114$	60.2939	5.64704
$115$	−9.83822	−0.917418
$116$	−49.3478	−4.58183
$117$	19.5048	1.80322
$118$	−35.3093	−3.25048
$119$	8.95433	0.820842
$120$	75.4129	6.88423
$121$	−5.84188	−0.531080
$122$	−14.9348	−1.35214
$123$	−12.6780	−1.14314
$124$	4.85013	0.435555
$125$	−0.172113	−0.0153943
$126$	15.7804	1.40583
$127$	−14.9578	−1.32729	−0.663645	−	0.748048i	$-0.730991\pi$
$127$	−14.9578	−1.32729	−0.663645	+	0.748048i	$0.730991\pi$
$128$	−19.8158	−1.75148
$129$	5.77206	0.508201
$130$	−35.1315	−3.08124
$131$	−16.2372	−1.41865	−0.709324	−	0.704883i	$-0.751000\pi$
$131$	−16.2372	−1.41865	−0.709324	+	0.704883i	$0.751000\pi$
$132$	−32.8324	−2.85769
$133$	−10.1162	−0.877187
$134$	16.6349	1.43703
$135$	−14.8877	−1.28133
$136$	61.7194	5.29239
$137$	6.65484	0.568561	0.284281	−	0.958741i	$-0.408245\pi$
$137$	6.65484	0.568561	0.284281	+	0.958741i	$0.408245\pi$
$138$	−23.2449	−1.97874
$139$	−9.38305	−0.795860	−0.397930	−	0.917416i	$-0.630271\pi$
$139$	−9.38305	−0.795860	−0.397930	+	0.917416i	$0.630271\pi$
$140$	−20.5381	−1.73578
$141$	−14.1156	−1.18875
$142$	43.5660	3.65598
$143$	9.42290	0.787982
$144$	59.7900	4.98250
$145$	−29.8745	−2.48094
$146$	6.12972	0.507300
$147$	15.0884	1.24447
$148$	27.1318	2.23022
$149$	−18.8920	−1.54770	−0.773848	−	0.633371i	$-0.781671\pi$
$149$	−18.8920	−1.54770	−0.773848	+	0.633371i	$0.781671\pi$
$150$	36.8491	3.00872
$151$	−7.32914	−0.596437	−0.298219	−	0.954498i	$-0.596392\pi$
$151$	−7.32914	−0.596437	−0.298219	+	0.954498i	$0.596392\pi$
$152$	−69.7278	−5.65567
$153$	−33.6719	−2.72221
$154$	7.62361	0.614328
$155$	2.93620	0.235841
$156$	−59.9785	−4.80212
$157$	8.49234	0.677763	0.338881	−	0.940829i	$-0.389951\pi$
$157$	8.49234	0.677763	0.338881	+	0.940829i	$0.389951\pi$
$158$	−7.01934	−0.558428
$159$	19.6058	1.55484
$160$	−53.3423	−4.21708
$161$	3.90008	0.307369
$162$	2.69241	0.211536
$163$	−5.20146	−0.407410	−0.203705	−	0.979032i	$-0.565298\pi$
$163$	−5.20146	−0.407410	−0.203705	+	0.979032i	$0.565298\pi$
$164$	23.7987	1.85837
$165$	−19.8763	−1.54736
$166$	33.8583	2.62792
$167$	15.1997	1.17619	0.588096	−	0.808791i	$-0.299878\pi$
$167$	15.1997	1.17619	0.588096	+	0.808791i	$0.299878\pi$
$168$	−29.8953	−2.30647
$169$	4.21383	0.324141
$170$	60.6489	4.65156
$171$	38.0410	2.90907
$172$	−10.8351	−0.826168
$173$	4.93902	0.375507	0.187753	−	0.982216i	$-0.439879\pi$
$173$	4.93902	0.375507	0.187753	+	0.982216i	$0.439879\pi$
$174$	−70.5849	−5.35103
$175$	−6.18261	−0.467362
$176$	28.8850	2.17729
$177$	−36.4939	−2.74305
$178$	6.66091	0.499256
$179$	12.4743	0.932371	0.466186	−	0.884687i	$-0.345628\pi$
$179$	12.4743	0.932371	0.466186	+	0.884687i	$0.345628\pi$
$180$	77.2313	5.75648
$181$	17.0764	1.26928	0.634641	−	0.772807i	$-0.281148\pi$
$181$	17.0764	1.26928	0.634641	+	0.772807i	$0.281148\pi$
$182$	13.9269	1.03233
$183$	−15.4359	−1.14105
$184$	26.8820	1.98177
$185$	16.4252	1.20760
$186$	6.93742	0.508676
$187$	−16.2671	−1.18957
$188$	26.4974	1.93252
$189$	5.90179	0.429292
$190$	−68.5185	−4.97085
$191$	14.8714	1.07606	0.538029	−	0.842927i	$-0.319169\pi$
$191$	14.8714	1.07606	0.538029	+	0.842927i	$0.319169\pi$
$192$	−55.4445	−4.00136
$193$	23.4323	1.68669	0.843346	−	0.537372i	$-0.180583\pi$
$193$	23.4323	1.68669	0.843346	+	0.537372i	$0.180583\pi$
$194$	39.8706	2.86254
$195$	−36.3101	−2.60022
$196$	−28.3234	−2.02310
$197$	−27.8066	−1.98114	−0.990570	−	0.137006i	$-0.956252\pi$
$197$	−27.8066	−1.98114	−0.990570	+	0.137006i	$0.956252\pi$
$198$	−28.6678	−2.03733
$199$	−11.0438	−0.782875	−0.391437	−	0.920205i	$-0.628022\pi$
$199$	−11.0438	−0.782875	−0.391437	+	0.920205i	$0.628022\pi$
$200$	−42.6148	−3.01332
$201$	17.1929	1.21270
$202$	47.2470	3.32429
$203$	11.8429	0.831206
$204$	103.543	7.24947
$205$	14.4074	1.00626
$206$	6.76651	0.471445
$207$	−14.6658	−1.01935
$208$	52.7673	3.65875
$209$	18.3779	1.27122
$210$	−29.3768	−2.02719
$211$	−16.9987	−1.17024	−0.585119	−	0.810947i	$-0.698952\pi$
$211$	−16.9987	−1.17024	−0.585119	+	0.810947i	$0.698952\pi$
$212$	−36.8033	−2.52766
$213$	45.0275	3.08524
$214$	−45.9146	−3.13866
$215$	−6.55941	−0.447348
$216$	40.6792	2.76787
$217$	−1.16397	−0.0790156
$218$	19.5795	1.32609
$219$	6.33536	0.428104
$220$	37.3110	2.51551
$221$	−29.7169	−1.99897
$222$	38.8081	2.60463
$223$	0.280372	0.0187751	0.00938754	−	0.999956i	$-0.497012\pi$
$223$	0.280372	0.0187751	0.00938754	+	0.999956i	$0.497012\pi$
$224$	21.1460	1.41288
$225$	23.2491	1.54994
$226$	7.17216	0.477085
$227$	13.2556	0.879804	0.439902	−	0.898046i	$-0.355013\pi$
$227$	13.2556	0.879804	0.439902	+	0.898046i	$0.355013\pi$
$228$	−116.978	−7.74709
$229$	−1.17990	−0.0779702	−0.0389851	−	0.999240i	$-0.512412\pi$
$229$	−1.17990	−0.0779702	−0.0389851	+	0.999240i	$0.512412\pi$
$230$	26.4158	1.74180
$231$	7.87937	0.518424
$232$	81.6291	5.35921
$233$	−5.60379	−0.367116	−0.183558	−	0.983009i	$-0.558762\pi$
$233$	−5.60379	−0.367116	−0.183558	+	0.983009i	$0.558762\pi$
$234$	−52.3706	−3.42357
$235$	16.0411	1.04641
$236$	68.5049	4.45929
$237$	−7.25482	−0.471251
$238$	−24.0425	−1.55844
$239$	8.44381	0.546185	0.273092	−	0.961988i	$-0.411954\pi$
$239$	8.44381	0.546185	0.273092	+	0.961988i	$0.411954\pi$
$240$	−111.305	−7.18471
$241$	6.73077	0.433567	0.216784	−	0.976220i	$-0.430443\pi$
$241$	6.73077	0.433567	0.216784	+	0.976220i	$0.430443\pi$
$242$	15.6855	1.00830
$243$	16.9451	1.08703
$244$	28.9757	1.85498
$245$	−17.1466	−1.09545
$246$	34.0406	2.17035
$247$	33.5728	2.13619
$248$	−8.02290	−0.509454
$249$	34.9942	2.21767
$250$	0.462127	0.0292275
$251$	24.6818	1.55790	0.778951	−	0.627085i	$-0.215752\pi$
$251$	24.6818	1.55790	0.778951	+	0.627085i	$0.215752\pi$
$252$	−30.6161	−1.92864
$253$	−7.08517	−0.445441
$254$	40.1619	2.51998
$255$	62.6835	3.92540
$256$	13.2469	0.827931
$257$	−21.5542	−1.34451	−0.672256	−	0.740318i	$-0.734675\pi$
$257$	−21.5542	−1.34451	−0.672256	+	0.740318i	$0.734675\pi$
$258$	−15.4980	−0.964866
$259$	−6.51130	−0.404592
$260$	68.1600	4.22711
$261$	−44.5339	−2.75658
$262$	43.5970	2.69343
$263$	13.8119	0.851679	0.425840	−	0.904799i	$-0.359979\pi$
$263$	13.8119	0.851679	0.425840	+	0.904799i	$0.359979\pi$
$264$	54.3100	3.34255
$265$	−22.2802	−1.36866
$266$	27.1622	1.66542
$267$	6.88437	0.421317
$268$	−32.2739	−1.97144
$269$	−17.1375	−1.04489	−0.522446	−	0.852672i	$-0.674981\pi$
$269$	−17.1375	−1.04489	−0.522446	+	0.852672i	$0.674981\pi$
$270$	39.9736	2.43272
$271$	3.88126	0.235770	0.117885	−	0.993027i	$-0.462389\pi$
$271$	3.88126	0.235770	0.117885	+	0.993027i	$0.462389\pi$
$272$	−91.0942	−5.52339
$273$	14.3941	0.871171
$274$	−17.8683	−1.07947
$275$	11.2318	0.677303
$276$	45.0984	2.71461
$277$	17.3914	1.04495	0.522475	−	0.852655i	$-0.325009\pi$
$277$	17.3914	1.04495	0.522475	+	0.852655i	$0.325009\pi$
$278$	25.1936	1.51101
$279$	4.37700	0.262044
$280$	33.9732	2.03029
$281$	5.30274	0.316335	0.158167	−	0.987412i	$-0.449441\pi$
$281$	5.30274	0.316335	0.158167	+	0.987412i	$0.449441\pi$
$282$	37.9007	2.25695
$283$	−14.3714	−0.854291	−0.427145	−	0.904183i	$-0.640481\pi$
$283$	−14.3714	−0.854291	−0.427145	+	0.904183i	$0.640481\pi$
$284$	−84.5241	−5.01558
$285$	−70.8171	−4.19484
$286$	−25.3006	−1.49606
$287$	−5.71139	−0.337133
$288$	−79.5175	−4.68561
$289$	34.3014	2.01773
$290$	80.2133	4.71029
$291$	41.2082	2.41567
$292$	−11.8925	−0.695957
$293$	−16.9299	−0.989054	−0.494527	−	0.869162i	$-0.664659\pi$
$293$	−16.9299	−0.989054	−0.494527	+	0.869162i	$0.664659\pi$
$294$	−40.5125	−2.36274
$295$	41.4719	2.41459
$296$	−44.8803	−2.60861
$297$	−10.7216	−0.622132
$298$	50.7254	2.93844
$299$	−12.9433	−0.748528
$300$	−71.4924	−4.12762
$301$	2.60029	0.149878
$302$	19.6788	1.13239
$303$	48.8321	2.80533
$304$	102.914	5.90253
$305$	17.5415	1.00442
$306$	90.4094	5.16836
$307$	29.6620	1.69290	0.846451	−	0.532466i	$-0.178735\pi$
$307$	29.6620	1.69290	0.846451	+	0.532466i	$0.178735\pi$
$308$	−14.7909	−0.842788
$309$	6.99351	0.397847
$310$	−7.88374	−0.447767
$311$	−7.82586	−0.443764	−0.221882	−	0.975074i	$-0.571220\pi$
$311$	−7.82586	−0.443764	−0.221882	+	0.975074i	$0.571220\pi$
$312$	99.2140	5.61689
$313$	−22.0797	−1.24802	−0.624010	−	0.781416i	$-0.714498\pi$
$313$	−22.0797	−1.24802	−0.624010	+	0.781416i	$0.714498\pi$
$314$	−22.8021	−1.28679
$315$	−18.5346	−1.04430
$316$	13.6185	0.766100
$317$	−24.6186	−1.38272	−0.691358	−	0.722512i	$-0.742987\pi$
$317$	−24.6186	−1.38272	−0.691358	+	0.722512i	$0.742987\pi$
$318$	−52.6419	−2.95201
$319$	−21.5146	−1.20459
$320$	63.0076	3.52223
$321$	−47.4550	−2.64868
$322$	−10.4718	−0.583569
$323$	−57.9581	−3.22487
$324$	−5.22365	−0.290203
$325$	20.5183	1.13815
$326$	13.9660	0.773505
$327$	20.2364	1.11907
$328$	−39.3668	−2.17367
$329$	−6.35904	−0.350585
$330$	53.3680	2.93781
$331$	0.331155	0.0182019	0.00910097	−	0.999959i	$-0.497103\pi$
$331$	0.331155	0.0182019	0.00910097	+	0.999959i	$0.497103\pi$
$332$	−65.6899	−3.60520
$333$	24.4851	1.34177
$334$	−40.8115	−2.23311
$335$	−19.5382	−1.06749
$336$	44.1237	2.40714
$337$	−11.4376	−0.623048	−0.311524	−	0.950238i	$-0.600840\pi$
$337$	−11.4376	−0.623048	−0.311524	+	0.950238i	$0.600840\pi$
$338$	−11.3142	−0.615411
$339$	7.41277	0.402606
$340$	−117.667	−6.38140
$341$	2.11456	0.114510
$342$	−102.141	−5.52313
$343$	15.5484	0.839537
$344$	17.9230	0.966342
$345$	27.3020	1.46989
$346$	−13.2613	−0.712934
$347$	−33.8612	−1.81777	−0.908883	−	0.417051i	$-0.863064\pi$
$347$	−33.8612	−1.81777	−0.908883	+	0.417051i	$0.863064\pi$
$348$	136.945	7.34100
$349$	−16.3304	−0.874149	−0.437074	−	0.899425i	$-0.643985\pi$
$349$	−16.3304	−0.874149	−0.437074	+	0.899425i	$0.643985\pi$
$350$	16.6004	0.887329
$351$	−19.5864	−1.04544
$352$	−38.4154	−2.04755
$353$	29.9857	1.59598	0.797989	−	0.602671i	$-0.205897\pi$
$353$	29.9857	1.59598	0.797989	+	0.602671i	$0.205897\pi$
$354$	97.9865	5.20793
$355$	−51.1697	−2.71580
$356$	−12.9231	−0.684922
$357$	−24.8491	−1.31515
$358$	−33.4936	−1.77019
$359$	−11.5894	−0.611668	−0.305834	−	0.952085i	$-0.598935\pi$
$359$	−11.5894	−0.611668	−0.305834	+	0.952085i	$0.598935\pi$
$360$	−127.753	−6.73317
$361$	46.4785	2.44624
$362$	−45.8505	−2.40985
$363$	16.2118	0.850896
$364$	−27.0201	−1.41624
$365$	−7.19956	−0.376842
$366$	41.4456	2.16639
$367$	20.5132	1.07078	0.535389	−	0.844605i	$-0.320165\pi$
$367$	20.5132	1.07078	0.535389	+	0.844605i	$0.320165\pi$
$368$	−39.6763	−2.06827
$369$	21.4771	1.11805
$370$	−44.1019	−2.29275
$371$	8.83235	0.458553
$372$	−13.4596	−0.697846
$373$	−16.9524	−0.877761	−0.438880	−	0.898546i	$-0.644625\pi$
$373$	−16.9524	−0.877761	−0.438880	+	0.898546i	$0.644625\pi$
$374$	43.6774	2.25851
$375$	0.477630	0.0246647
$376$	−43.8309	−2.26041
$377$	−39.3031	−2.02421
$378$	−15.8464	−0.815050
$379$	−0.365747	−0.0187872	−0.00939358	−	0.999956i	$-0.502990\pi$
$379$	−0.365747	−0.0187872	−0.00939358	+	0.999956i	$0.502990\pi$
$380$	132.935	6.81944
$381$	41.5093	2.12658
$382$	−39.9299	−2.04299
$383$	26.5924	1.35881	0.679405	−	0.733763i	$-0.262238\pi$
$383$	26.5924	1.35881	0.679405	+	0.733763i	$0.262238\pi$
$384$	54.9905	2.80622
$385$	−8.95418	−0.456347
$386$	−62.9160	−3.20234
$387$	−9.77813	−0.497050
$388$	−77.3545	−3.92708
$389$	−15.4043	−0.781030	−0.390515	−	0.920597i	$-0.627703\pi$
$389$	−15.4043	−0.781030	−0.390515	+	0.920597i	$0.627703\pi$
$390$	97.4932	4.93676
$391$	22.3444	1.13001
$392$	46.8514	2.36635
$393$	45.0596	2.27296
$394$	74.6612	3.76138
$395$	8.24444	0.414823
$396$	55.6196	2.79499
$397$	32.3231	1.62225	0.811126	−	0.584872i	$-0.198855\pi$
$397$	32.3231	1.62225	0.811126	+	0.584872i	$0.198855\pi$
$398$	29.6528	1.48636
$399$	28.0734	1.40543
$400$	62.8969	3.14485
$401$	−5.16077	−0.257716	−0.128858	−	0.991663i	$-0.541131\pi$
$401$	−5.16077	−0.257716	−0.128858	+	0.991663i	$0.541131\pi$
$402$	−46.1633	−2.30241
$403$	3.86290	0.192425
$404$	−91.6658	−4.56055
$405$	−3.16232	−0.157137
$406$	−31.7983	−1.57812
$407$	11.8289	0.586337
$408$	−171.277	−8.47947
$409$	−19.2749	−0.953082	−0.476541	−	0.879152i	$-0.658110\pi$
$409$	−19.2749	−0.953082	−0.476541	+	0.879152i	$0.658110\pi$
$410$	−38.6840	−1.91047
$411$	−18.4678	−0.910949
$412$	−13.1280	−0.646768
$413$	−16.4403	−0.808977
$414$	39.3780	1.93532
$415$	−39.7677	−1.95212
$416$	−70.1777	−3.44074
$417$	26.0388	1.27513
$418$	−49.3448	−2.41353
$419$	−6.19779	−0.302782	−0.151391	−	0.988474i	$-0.548375\pi$
$419$	−6.19779	−0.302782	−0.151391	+	0.988474i	$0.548375\pi$
$420$	56.9950	2.78107
$421$	−9.48191	−0.462120	−0.231060	−	0.972940i	$-0.574219\pi$
$421$	−9.48191	−0.462120	−0.231060	+	0.972940i	$0.574219\pi$
$422$	45.6417	2.22181
$423$	23.9125	1.16267
$424$	60.8786	2.95652
$425$	−35.4216	−1.71820
$426$	−120.900	−5.85760
$427$	−6.95381	−0.336518
$428$	89.0807	4.30588
$429$	−26.1494	−1.26251
$430$	17.6121	0.849331
$431$	−7.73566	−0.372614	−0.186307	−	0.982492i	$-0.559652\pi$
$431$	−7.73566	−0.372614	−0.186307	+	0.982492i	$0.559652\pi$
$432$	−60.0401	−2.88868
$433$	29.2389	1.40513	0.702566	−	0.711619i	$-0.252038\pi$
$433$	29.2389	1.40513	0.702566	+	0.711619i	$0.252038\pi$
$434$	3.12528	0.150018
$435$	82.9043	3.97496
$436$	−37.9870	−1.81925
$437$	−25.2438	−1.20757
$438$	−17.0105	−0.812795
$439$	29.9791	1.43083	0.715413	−	0.698702i	$-0.246239\pi$
$439$	29.9791	1.43083	0.715413	+	0.698702i	$0.246239\pi$
$440$	−61.7183	−2.94231
$441$	−25.5604	−1.21716
$442$	79.7903	3.79524
$443$	−17.3406	−0.823878	−0.411939	−	0.911212i	$-0.635148\pi$
$443$	−17.3406	−0.823878	−0.411939	+	0.911212i	$0.635148\pi$
$444$	−75.2932	−3.57326
$445$	−7.82346	−0.370867
$446$	−0.752802	−0.0356462
$447$	52.4271	2.47972
$448$	−24.9775	−1.18008
$449$	28.6520	1.35217	0.676086	−	0.736823i	$-0.263675\pi$
$449$	28.6520	1.35217	0.676086	+	0.736823i	$0.263675\pi$
$450$	−62.4241	−2.94270
$451$	10.3757	0.488575
$452$	−13.9150	−0.654506
$453$	20.3390	0.955611
$454$	−35.5914	−1.67039
$455$	−16.3576	−0.766855
$456$	193.501	9.06152
$457$	−7.80071	−0.364902	−0.182451	−	0.983215i	$-0.558403\pi$
$457$	−7.80071	−0.364902	−0.182451	+	0.983215i	$0.558403\pi$
$458$	3.16806	0.148034
$459$	33.8127	1.57824
$460$	−51.2502	−2.38955
$461$	22.5442	1.04999	0.524994	−	0.851106i	$-0.324068\pi$
$461$	22.5442	1.04999	0.524994	+	0.851106i	$0.324068\pi$
$462$	−21.1562	−0.984276
$463$	−12.6446	−0.587644	−0.293822	−	0.955860i	$-0.594927\pi$
$463$	−12.6446	−0.587644	−0.293822	+	0.955860i	$0.594927\pi$
$464$	−120.480	−5.59313
$465$	−8.14823	−0.377865
$466$	15.0462	0.697004
$467$	4.50583	0.208505	0.104253	−	0.994551i	$-0.466755\pi$
$467$	4.50583	0.208505	0.104253	+	0.994551i	$0.466755\pi$
$468$	101.606	4.69675
$469$	7.74535	0.357647
$470$	−43.0707	−1.98670
$471$	−23.5670	−1.08591
$472$	−113.318	−5.21589
$473$	−4.72388	−0.217204
$474$	19.4793	0.894714
$475$	40.0178	1.83614
$476$	46.6458	2.13801
$477$	−33.2131	−1.52073
$478$	−22.6717	−1.03698
$479$	−18.7424	−0.856360	−0.428180	−	0.903693i	$-0.640845\pi$
$479$	−18.7424	−0.856360	−0.428180	+	0.903693i	$0.640845\pi$
$480$	148.030	6.75660
$481$	21.6091	0.985292
$482$	−18.0722	−0.823167
$483$	−10.8231	−0.492467
$484$	−30.4321	−1.38328
$485$	−46.8293	−2.12641
$486$	−45.4979	−2.06383
$487$	4.73313	0.214478	0.107239	−	0.994233i	$-0.465799\pi$
$487$	4.73313	0.214478	0.107239	+	0.994233i	$0.465799\pi$
$488$	−47.9304	−2.16971
$489$	14.4345	0.652752
$490$	46.0388	2.07982
$491$	4.06649	0.183518	0.0917591	−	0.995781i	$-0.470751\pi$
$491$	4.06649	0.183518	0.0917591	+	0.995781i	$0.470751\pi$
$492$	−66.0435	−2.97747
$493$	67.8505	3.05583
$494$	−90.1436	−4.05575
$495$	33.6713	1.51341
$496$	11.8413	0.531691
$497$	20.2847	0.909895
$498$	−93.9600	−4.21045
$499$	−20.9149	−0.936280	−0.468140	−	0.883654i	$-0.655076\pi$
$499$	−20.9149	−0.936280	−0.468140	+	0.883654i	$0.655076\pi$
$500$	−0.896590	−0.0400967
$501$	−42.1807	−1.88449
$502$	−66.2710	−2.95782
$503$	32.6741	1.45687	0.728433	−	0.685117i	$-0.240249\pi$
$503$	32.6741	1.45687	0.728433	+	0.685117i	$0.240249\pi$
$504$	50.6440	2.25586
$505$	−55.4932	−2.46941
$506$	19.0238	0.845711
$507$	−11.6938	−0.519339
$508$	−77.9197	−3.45713
$509$	12.2959	0.545006	0.272503	−	0.962155i	$-0.412149\pi$
$509$	12.2959	0.545006	0.272503	+	0.962155i	$0.412149\pi$
$510$	−168.306	−7.45272
$511$	2.85406	0.126256
$512$	4.06343	0.179580
$513$	−38.2001	−1.68658
$514$	57.8733	2.55268
$515$	−7.94748	−0.350208
$516$	30.0684	1.32369
$517$	11.5523	0.508070
$518$	17.4829	0.768155
$519$	−13.7062	−0.601637
$520$	−112.748	−4.94431
$521$	−7.52768	−0.329794	−0.164897	−	0.986311i	$-0.552729\pi$
$521$	−7.52768	−0.329794	−0.164897	+	0.986311i	$0.552729\pi$
$522$	119.574	5.23362
$523$	18.4721	0.807730	0.403865	−	0.914819i	$-0.367667\pi$
$523$	18.4721	0.807730	0.403865	+	0.914819i	$0.367667\pi$
$524$	−84.5843	−3.69508
$525$	17.1573	0.748807
$526$	−37.0852	−1.61699
$527$	−6.66866	−0.290492
$528$	−80.1584	−3.48845
$529$	−13.2678	−0.576862
$530$	59.8227	2.59853
$531$	61.8223	2.68286
$532$	−52.6984	−2.28476
$533$	18.9545	0.821011
$534$	−18.4846	−0.799908
$535$	53.9282	2.33152
$536$	53.3863	2.30594
$537$	−34.6173	−1.49385
$538$	46.0145	1.98382
$539$	−12.3484	−0.531884
$540$	−77.5544	−3.33741
$541$	−11.1594	−0.479782	−0.239891	−	0.970800i	$-0.577112\pi$
$541$	−11.1594	−0.479782	−0.239891	+	0.970800i	$0.577112\pi$
$542$	−10.4212	−0.447630
$543$	−47.3887	−2.03364
$544$	121.150	5.19428
$545$	−22.9968	−0.985074
$546$	−38.6484	−1.65400
$547$	−33.6273	−1.43780	−0.718900	−	0.695114i	$-0.755354\pi$
$547$	−33.6273	−1.43780	−0.718900	+	0.695114i	$0.755354\pi$
$548$	34.6670	1.48090
$549$	26.1491	1.11602
$550$	−30.1575	−1.28592
$551$	−76.6545	−3.26559
$552$	−74.6000	−3.17519
$553$	−3.26827	−0.138981
$554$	−46.6962	−1.98393
$555$	−45.5814	−1.93482
$556$	−48.8791	−2.07294
$557$	−19.4584	−0.824479	−0.412240	−	0.911076i	$-0.635253\pi$
$557$	−19.4584	−0.824479	−0.412240	+	0.911076i	$0.635253\pi$
$558$	−11.7523	−0.497515
$559$	−8.62963	−0.364994
$560$	−50.1425	−2.11891
$561$	45.1427	1.90593
$562$	−14.2379	−0.600591
$563$	−5.96404	−0.251354	−0.125677	−	0.992071i	$-0.540110\pi$
$563$	−5.96404	−0.251354	−0.125677	+	0.992071i	$0.540110\pi$
$564$	−73.5326	−3.09628
$565$	−8.42393	−0.354398
$566$	38.5874	1.62195
$567$	1.25361	0.0526468
$568$	139.816	5.86656
$569$	23.8361	0.999260	0.499630	−	0.866239i	$-0.333469\pi$
$569$	23.8361	0.999260	0.499630	+	0.866239i	$0.333469\pi$
$570$	190.145	7.96430
$571$	18.7496	0.784647	0.392324	−	0.919827i	$-0.371671\pi$
$571$	18.7496	0.784647	0.392324	+	0.919827i	$0.371671\pi$
$572$	49.0867	2.05242
$573$	−41.2695	−1.72406
$574$	15.3352	0.640078
$575$	−15.4280	−0.643390
$576$	93.9255	3.91356
$577$	−38.7935	−1.61500	−0.807498	−	0.589870i	$-0.799179\pi$
$577$	−38.7935	−1.61500	−0.807498	+	0.589870i	$0.799179\pi$
$578$	−92.0997	−3.83084
$579$	−65.0267	−2.70242
$580$	−155.625	−6.46198
$581$	15.7648	0.654033
$582$	−110.645	−4.58637
$583$	−16.0455	−0.664537
$584$	19.6721	0.814038
$585$	61.5110	2.54317
$586$	45.4569	1.87781
$587$	−13.0437	−0.538370	−0.269185	−	0.963089i	$-0.586754\pi$
$587$	−13.0437	−0.538370	−0.269185	+	0.963089i	$0.586754\pi$
$588$	78.6000	3.24141
$589$	7.53396	0.310432
$590$	−111.353	−4.58432
$591$	77.1659	3.17418
$592$	66.2407	2.72248
$593$	12.2477	0.502954	0.251477	−	0.967863i	$-0.419084\pi$
$593$	12.2477	0.502954	0.251477	+	0.967863i	$0.419084\pi$
$594$	28.7877	1.18118
$595$	28.2387	1.15767
$596$	−98.4143	−4.03121
$597$	30.6476	1.25432
$598$	34.7528	1.42115
$599$	−15.0068	−0.613160	−0.306580	−	0.951845i	$-0.599185\pi$
$599$	−15.0068	−0.613160	−0.306580	+	0.951845i	$0.599185\pi$
$600$	118.260	4.82794
$601$	40.4310	1.64922	0.824608	−	0.565705i	$-0.191396\pi$
$601$	40.4310	1.64922	0.824608	+	0.565705i	$0.191396\pi$
$602$	−6.98181	−0.284557
$603$	−29.1256	−1.18609
$604$	−38.1797	−1.55351
$605$	−18.4232	−0.749008
$606$	−131.115	−5.32618
$607$	22.6606	0.919765	0.459882	−	0.887980i	$-0.347892\pi$
$607$	22.6606	0.919765	0.459882	+	0.887980i	$0.347892\pi$
$608$	−136.870	−5.55083
$609$	−32.8650	−1.33176
$610$	−47.0991	−1.90699
$611$	21.1039	0.853771
$612$	−175.407	−7.09040
$613$	−7.27316	−0.293760	−0.146880	−	0.989154i	$-0.546923\pi$
$613$	−7.27316	−0.293760	−0.146880	+	0.989154i	$0.546923\pi$
$614$	−79.6430	−3.21413
$615$	−39.9818	−1.61222
$616$	24.4665	0.985782
$617$	−23.6808	−0.953352	−0.476676	−	0.879079i	$-0.658158\pi$
$617$	−23.6808	−0.953352	−0.476676	+	0.879079i	$0.658158\pi$
$618$	−18.7777	−0.755349
$619$	24.5140	0.985299	0.492650	−	0.870228i	$-0.336028\pi$
$619$	24.5140	0.985299	0.492650	+	0.870228i	$0.336028\pi$
$620$	15.2956	0.614284
$621$	14.7272	0.590982
$622$	21.0125	0.842526
$623$	3.10138	0.124254
$624$	−146.434	−5.86205
$625$	−25.2699	−1.01080
$626$	59.2844	2.36948
$627$	−51.0003	−2.03675
$628$	44.2392	1.76533
$629$	−37.3047	−1.48744
$630$	49.7656	1.98271
$631$	−23.1803	−0.922794	−0.461397	−	0.887194i	$-0.652652\pi$
$631$	−23.1803	−0.922794	−0.461397	+	0.887194i	$0.652652\pi$
$632$	−22.5272	−0.896082
$633$	47.1729	1.87496
$634$	66.1012	2.62521
$635$	−47.1715	−1.87194
$636$	102.133	4.04982
$637$	−22.5582	−0.893788
$638$	57.7671	2.28702
$639$	−76.2787	−3.01754
$640$	−62.4917	−2.47020
$641$	−4.90193	−0.193614	−0.0968072	−	0.995303i	$-0.530863\pi$
$641$	−4.90193	−0.193614	−0.0968072	+	0.995303i	$0.530863\pi$
$642$	127.417	5.02876
$643$	17.4329	0.687487	0.343744	−	0.939064i	$-0.388305\pi$
$643$	17.4329	0.687487	0.343744	+	0.939064i	$0.388305\pi$
$644$	20.3167	0.800589
$645$	18.2030	0.716741
$646$	155.618	6.12272
$647$	5.83321	0.229327	0.114664	−	0.993404i	$-0.463421\pi$
$647$	5.83321	0.229327	0.114664	+	0.993404i	$0.463421\pi$
$648$	8.64076	0.339441
$649$	29.8668	1.17237
$650$	−55.0920	−2.16089
$651$	3.23013	0.126599
$652$	−27.0960	−1.06116
$653$	22.5513	0.882502	0.441251	−	0.897384i	$-0.354535\pi$
$653$	22.5513	0.882502	0.441251	+	0.897384i	$0.354535\pi$
$654$	−54.3350	−2.12467
$655$	−51.2061	−2.00079
$656$	58.1031	2.26855
$657$	−10.7324	−0.418711
$658$	17.0741	0.665619
$659$	−25.9976	−1.01272	−0.506361	−	0.862322i	$-0.669010\pi$
$659$	−25.9976	−1.01272	−0.506361	+	0.862322i	$0.669010\pi$
$660$	−103.541	−4.03034
$661$	4.21797	0.164060	0.0820301	−	0.996630i	$-0.473860\pi$
$661$	4.21797	0.164060	0.0820301	+	0.996630i	$0.473860\pi$
$662$	−0.889156	−0.0345580
$663$	82.4671	3.20276
$664$	108.662	4.21689
$665$	−31.9029	−1.23714
$666$	−65.7428	−2.54748
$667$	29.5524	1.14427
$668$	79.1800	3.06357
$669$	−0.778057	−0.0300814
$670$	52.4603	2.02672
$671$	12.6328	0.487684
$672$	−58.6821	−2.26371
$673$	−35.8757	−1.38291	−0.691454	−	0.722420i	$-0.743030\pi$
$673$	−35.8757	−1.38291	−0.691454	+	0.722420i	$0.743030\pi$
$674$	30.7102	1.18291
$675$	−23.3463	−0.898601
$676$	21.9511	0.844274
$677$	−39.8339	−1.53094	−0.765471	−	0.643471i	$-0.777494\pi$
$677$	−39.8339	−1.53094	−0.765471	+	0.643471i	$0.777494\pi$
$678$	−19.9034	−0.764385
$679$	18.5641	0.712426
$680$	194.640	7.46412
$681$	−36.7855	−1.40962
$682$	−5.67762	−0.217407
$683$	15.4085	0.589588	0.294794	−	0.955561i	$-0.404749\pi$
$683$	15.4085	0.589588	0.294794	+	0.955561i	$0.404749\pi$
$684$	198.167	7.57710
$685$	20.9869	0.801870
$686$	−41.7478	−1.59394
$687$	3.27434	0.124924
$688$	−26.4533	−1.00852
$689$	−29.3121	−1.11670
$690$	−73.3061	−2.79072
$691$	−28.7089	−1.09214	−0.546070	−	0.837740i	$-0.683877\pi$
$691$	−28.7089	−1.09214	−0.546070	+	0.837740i	$0.683877\pi$
$692$	25.7288	0.978064
$693$	−13.3480	−0.507049
$694$	90.9179	3.45120
$695$	−29.5907	−1.12244
$696$	−226.528	−8.58653
$697$	−32.7219	−1.23943
$698$	43.8475	1.65965
$699$	15.5510	0.588194
$700$	−32.2071	−1.21731
$701$	4.68137	0.176813	0.0884065	−	0.996084i	$-0.471823\pi$
$701$	4.68137	0.176813	0.0884065	+	0.996084i	$0.471823\pi$
$702$	52.5897	1.98487
$703$	42.1452	1.58954
$704$	45.3761	1.71018
$705$	−44.5156	−1.67655
$706$	−80.5121	−3.03011
$707$	21.9987	0.827345
$708$	−190.107	−7.14468
$709$	6.41121	0.240778	0.120389	−	0.992727i	$-0.461586\pi$
$709$	6.41121	0.240778	0.120389	+	0.992727i	$0.461586\pi$
$710$	137.391	5.15620
$711$	12.2900	0.460911
$712$	21.3769	0.801132
$713$	−2.90455	−0.108776
$714$	66.7201	2.49694
$715$	29.7164	1.11133
$716$	64.9823	2.42850
$717$	−23.4323	−0.875097
$718$	31.1178	1.16131
$719$	20.9645	0.781845	0.390922	−	0.920424i	$-0.372156\pi$
$719$	20.9645	0.781845	0.390922	+	0.920424i	$0.372156\pi$
$720$	188.556	7.02706
$721$	3.15055	0.117333
$722$	−124.795	−4.64440
$723$	−18.6785	−0.694661
$724$	88.9563	3.30604
$725$	−46.8481	−1.73989
$726$	−43.5288	−1.61550
$727$	−33.6256	−1.24711	−0.623553	−	0.781781i	$-0.714311\pi$
$727$	−33.6256	−1.24711	−0.623553	+	0.781781i	$0.714311\pi$
$728$	44.6955	1.65653
$729$	−44.0160	−1.63022
$730$	19.3309	0.715470
$731$	14.8977	0.551010
$732$	−80.4102	−2.97205
$733$	−3.34954	−0.123718	−0.0618591	−	0.998085i	$-0.519703\pi$
$733$	−3.34954	−0.123718	−0.0618591	+	0.998085i	$0.519703\pi$
$734$	−55.0782	−2.03297
$735$	47.5833	1.75514
$736$	52.7673	1.94503
$737$	−14.0708	−0.518304
$738$	−57.6664	−2.12273
$739$	−4.87577	−0.179358	−0.0896790	−	0.995971i	$-0.528584\pi$
$739$	−4.87577	−0.179358	−0.0896790	+	0.995971i	$0.528584\pi$
$740$	85.5638	3.14539
$741$	−93.1677	−3.42260
$742$	−23.7150	−0.870604
$743$	−38.9796	−1.43002	−0.715011	−	0.699113i	$-0.753578\pi$
$743$	−38.9796	−1.43002	−0.715011	+	0.699113i	$0.753578\pi$
$744$	22.2643	0.816248
$745$	−59.5786	−2.18279
$746$	45.5174	1.66651
$747$	−59.2818	−2.16901
$748$	−84.7402	−3.09841
$749$	−21.3783	−0.781146
$750$	−1.28244	−0.0468282
$751$	−32.5133	−1.18643	−0.593214	−	0.805044i	$-0.702141\pi$
$751$	−32.5133	−1.18643	−0.593214	+	0.805044i	$0.702141\pi$
$752$	64.6918	2.35907
$753$	−68.4943	−2.49607
$754$	105.529	3.84316
$755$	−23.1134	−0.841184
$756$	30.7442	1.11816
$757$	42.1401	1.53161	0.765804	−	0.643074i	$-0.222341\pi$
$757$	42.1401	1.53161	0.765804	+	0.643074i	$0.222341\pi$
$758$	0.982036	0.0356691
$759$	19.6620	0.713685
$760$	−219.896	−7.97648
$761$	−35.9959	−1.30485	−0.652424	−	0.757854i	$-0.726248\pi$
$761$	−35.9959	−1.30485	−0.652424	+	0.757854i	$0.726248\pi$
$762$	−111.453	−4.03751
$763$	9.11642	0.330036
$764$	77.4696	2.80275
$765$	−106.189	−3.83926
$766$	−71.4011	−2.57983
$767$	54.5609	1.97008
$768$	−36.7613	−1.32651
$769$	−35.2755	−1.27207	−0.636033	−	0.771662i	$-0.719426\pi$
$769$	−35.2755	−1.27207	−0.636033	+	0.771662i	$0.719426\pi$
$770$	24.0421	0.866417
$771$	59.8148	2.15418
$772$	122.066	4.39324
$773$	28.4052	1.02166	0.510832	−	0.859681i	$-0.329337\pi$
$773$	28.4052	1.02166	0.510832	+	0.859681i	$0.329337\pi$
$774$	26.2544	0.943695
$775$	4.60445	0.165397
$776$	127.957	4.59338
$777$	18.0694	0.648238
$778$	41.3608	1.48286
$779$	36.9677	1.32451
$780$	−189.150	−6.77267
$781$	−36.8508	−1.31862
$782$	−59.9951	−2.14542
$783$	44.7202	1.59817
$784$	−69.1499	−2.46964
$785$	26.7818	0.955882
$786$	−120.986	−4.31542
$787$	−47.8508	−1.70570	−0.852849	−	0.522157i	$-0.825127\pi$
$787$	−47.8508	−1.70570	−0.852849	+	0.522157i	$0.825127\pi$
$788$	−144.853	−5.16018
$789$	−38.3293	−1.36456
$790$	−22.1364	−0.787579
$791$	3.33943	0.118736
$792$	−92.0036	−3.26921
$793$	23.0777	0.819514
$794$	−86.7880	−3.07999
$795$	61.8296	2.19287
$796$	−57.5305	−2.03911
$797$	30.3723	1.07584	0.537921	−	0.842995i	$-0.319210\pi$
$797$	30.3723	1.07584	0.537921	+	0.842995i	$0.319210\pi$
$798$	−75.3775	−2.66833
$799$	−36.4324	−1.28889
$800$	−83.6495	−2.95746
$801$	−11.6624	−0.412072
$802$	13.8567	0.489298
$803$	−5.18490	−0.182971
$804$	89.5631	3.15865
$805$	12.2994	0.433498
$806$	−10.3719	−0.365336
$807$	47.5582	1.67413
$808$	151.630	5.33432
$809$	−22.7046	−0.798250	−0.399125	−	0.916897i	$-0.630686\pi$
$809$	−22.7046	−0.798250	−0.399125	+	0.916897i	$0.630686\pi$
$810$	8.49089	0.298339
$811$	−11.4355	−0.401554	−0.200777	−	0.979637i	$-0.564347\pi$
$811$	−11.4355	−0.401554	−0.200777	+	0.979637i	$0.564347\pi$
$812$	61.6930	2.16500
$813$	−10.7708	−0.377750
$814$	−31.7608	−1.11321
$815$	−16.4035	−0.574590
$816$	252.795	8.84958
$817$	−16.8307	−0.588832
$818$	51.7534	1.80951
$819$	−24.3843	−0.852055
$820$	75.0524	2.62094
$821$	−25.8520	−0.902241	−0.451121	−	0.892463i	$-0.648976\pi$
$821$	−25.8520	−0.902241	−0.451121	+	0.892463i	$0.648976\pi$
$822$	49.5863	1.72952
$823$	−26.8231	−0.934993	−0.467496	−	0.883995i	$-0.654844\pi$
$823$	−26.8231	−0.934993	−0.467496	+	0.883995i	$0.654844\pi$
$824$	21.7158	0.756504
$825$	−31.1693	−1.08517
$826$	44.1426	1.53592
$827$	23.1129	0.803713	0.401856	−	0.915703i	$-0.368365\pi$
$827$	23.1129	0.803713	0.401856	+	0.915703i	$0.368365\pi$
$828$	−76.3988	−2.65504
$829$	20.1184	0.698740	0.349370	−	0.936985i	$-0.386396\pi$
$829$	20.1184	0.698740	0.349370	+	0.936985i	$0.386396\pi$
$830$	106.777	3.70628
$831$	−48.2628	−1.67422
$832$	82.8934	2.87381
$833$	38.9431	1.34930
$834$	−69.9146	−2.42094
$835$	47.9345	1.65884
$836$	95.7358	3.31109
$837$	−4.39531	−0.151924
$838$	16.6412	0.574859
$839$	5.33869	0.184312	0.0921560	−	0.995745i	$-0.470624\pi$
$839$	5.33869	0.184312	0.0921560	+	0.995745i	$0.470624\pi$
$840$	−94.2789	−3.25293
$841$	60.7380	2.09441
$842$	25.4591	0.877377
$843$	−14.7156	−0.506832
$844$	−88.5513	−3.04806
$845$	13.2889	0.457152
$846$	−64.2055	−2.20743
$847$	7.30333	0.250946
$848$	−89.8532	−3.08557
$849$	39.8819	1.36874
$850$	95.1075	3.26216
$851$	−16.2481	−0.556979
$852$	234.562	8.03596
$853$	−10.1798	−0.348550	−0.174275	−	0.984697i	$-0.555758\pi$
$853$	−10.1798	−0.348550	−0.174275	+	0.984697i	$0.555758\pi$
$854$	18.6711	0.638911
$855$	119.967	4.10280
$856$	−147.354	−5.03645
$857$	−32.0694	−1.09547	−0.547735	−	0.836652i	$-0.684510\pi$
$857$	−32.0694	−1.09547	−0.547735	+	0.836652i	$0.684510\pi$
$858$	70.2115	2.39698
$859$	4.57081	0.155954	0.0779770	−	0.996955i	$-0.475154\pi$
$859$	4.57081	0.155954	0.0779770	+	0.996955i	$0.475154\pi$
$860$	−34.1699	−1.16519
$861$	15.8496	0.540154
$862$	20.7704	0.707441
$863$	2.83148	0.0963846	0.0481923	−	0.998838i	$-0.484654\pi$
$863$	2.83148	0.0963846	0.0481923	+	0.998838i	$0.484654\pi$
$864$	79.8501	2.71655
$865$	15.5759	0.529596
$866$	−78.5068	−2.66777
$867$	−95.1895	−3.23281
$868$	−6.06348	−0.205808
$869$	5.93738	0.201412
$870$	−222.599	−7.54682
$871$	−25.7046	−0.870968
$872$	62.8366	2.12791
$873$	−69.8086	−2.36266
$874$	67.7799	2.29269
$875$	0.215171	0.00727410
$876$	33.0028	1.11506
$877$	−48.1922	−1.62733	−0.813667	−	0.581332i	$-0.802532\pi$
$877$	−48.1922	−1.62733	−0.813667	+	0.581332i	$0.802532\pi$
$878$	−80.4944	−2.71655
$879$	46.9819	1.58466
$880$	91.0926	3.07073
$881$	−20.0653	−0.676016	−0.338008	−	0.941143i	$-0.609753\pi$
$881$	−20.0653	−0.676016	−0.338008	+	0.941143i	$0.609753\pi$
$882$	68.6301	2.31090
$883$	−14.9704	−0.503795	−0.251897	−	0.967754i	$-0.581055\pi$
$883$	−14.9704	−0.503795	−0.251897	+	0.967754i	$0.581055\pi$
$884$	−154.804	−5.20663
$885$	−115.088	−3.86865
$886$	46.5598	1.56421
$887$	47.4650	1.59372	0.796859	−	0.604166i	$-0.206494\pi$
$887$	47.4650	1.59372	0.796859	+	0.604166i	$0.206494\pi$
$888$	124.547	4.17952
$889$	18.6998	0.627170
$890$	21.0061	0.704126
$891$	−2.27741	−0.0762960
$892$	1.46054	0.0489025
$893$	41.1597	1.37736
$894$	−140.768	−4.70797
$895$	39.3393	1.31497
$896$	24.7730	0.827609
$897$	35.9187	1.19929
$898$	−76.9310	−2.56722
$899$	−8.81988	−0.294159
$900$	121.111	4.03705
$901$	50.6025	1.68581
$902$	−27.8590	−0.927604
$903$	−7.21604	−0.240135
$904$	23.0176	0.765554
$905$	53.8529	1.79013
$906$	−54.6106	−1.81432
$907$	18.9164	0.628109	0.314055	−	0.949405i	$-0.398312\pi$
$907$	18.9164	0.628109	0.314055	+	0.949405i	$0.398312\pi$
$908$	69.0523	2.29158
$909$	−82.7238	−2.74378
$910$	43.9203	1.45594
$911$	−37.3119	−1.23620	−0.618100	−	0.786100i	$-0.712097\pi$
$911$	−37.3119	−1.23620	−0.618100	+	0.786100i	$0.712097\pi$
$912$	−285.596	−9.45704
$913$	−28.6395	−0.947828
$914$	20.9450	0.692799
$915$	−48.6792	−1.60928
$916$	−6.14647	−0.203085
$917$	20.2992	0.670338
$918$	−90.7876	−2.99644
$919$	21.9212	0.723114	0.361557	−	0.932350i	$-0.382245\pi$
$919$	21.9212	0.723114	0.361557	+	0.932350i	$0.382245\pi$
$920$	84.7761	2.79498
$921$	−82.3149	−2.71237
$922$	−60.5315	−1.99350
$923$	−67.3193	−2.21584
$924$	41.0460	1.35031
$925$	25.7574	0.846899
$926$	33.9509	1.11570
$927$	−11.8473	−0.389117
$928$	160.232	5.25986
$929$	52.1040	1.70948	0.854739	−	0.519058i	$-0.173717\pi$
$929$	52.1040	1.70948	0.854739	+	0.519058i	$0.173717\pi$
$930$	21.8781	0.717411
$931$	−43.9962	−1.44192
$932$	−29.1918	−0.956210
$933$	21.7175	0.710998
$934$	−12.0982	−0.395866
$935$	−51.3005	−1.67771
$936$	−168.073	−5.49364
$937$	42.4652	1.38728	0.693640	−	0.720322i	$-0.256006\pi$
$937$	42.4652	1.38728	0.693640	+	0.720322i	$0.256006\pi$
$938$	−20.7964	−0.679026
$939$	61.2733	1.99958
$940$	83.5631	2.72553
$941$	−36.2533	−1.18182	−0.590912	−	0.806736i	$-0.701232\pi$
$941$	−36.2533	−1.18182	−0.590912	+	0.806736i	$0.701232\pi$
$942$	63.2778	2.06170
$943$	−14.2521	−0.464112
$944$	167.251	5.44355
$945$	18.6121	0.605452
$946$	12.6837	0.412382
$947$	−10.5720	−0.343544	−0.171772	−	0.985137i	$-0.554949\pi$
$947$	−10.5720	−0.343544	−0.171772	+	0.985137i	$0.554949\pi$
$948$	−37.7925	−1.22744
$949$	−9.47181	−0.307468
$950$	−107.448	−3.48608
$951$	68.3188	2.21539
$952$	−77.1596	−2.50076
$953$	−41.6962	−1.35067	−0.675336	−	0.737510i	$-0.736001\pi$
$953$	−41.6962	−1.35067	−0.675336	+	0.737510i	$0.736001\pi$
$954$	89.1778	2.88724
$955$	46.8990	1.51762
$956$	43.9863	1.42262
$957$	59.7051	1.92999
$958$	50.3235	1.62588
$959$	−8.31967	−0.268656
$960$	−174.852	−5.64332
$961$	−30.1331	−0.972037
$962$	−58.0209	−1.87067
$963$	80.3909	2.59056
$964$	35.0626	1.12929
$965$	73.8968	2.37882
$966$	29.0601	0.934993
$967$	6.92839	0.222802	0.111401	−	0.993776i	$-0.464466\pi$
$967$	6.92839	0.222802	0.111401	+	0.993776i	$0.464466\pi$
$968$	50.3396	1.61798
$969$	160.839	5.16689
$970$	125.737	4.03719
$971$	6.17573	0.198189	0.0990943	−	0.995078i	$-0.468405\pi$
$971$	6.17573	0.198189	0.0990943	+	0.995078i	$0.468405\pi$
$972$	88.2722	2.83133
$973$	11.7304	0.376059
$974$	−12.7085	−0.407207
$975$	−56.9403	−1.82355
$976$	70.7425	2.26441
$977$	14.3860	0.460249	0.230125	−	0.973161i	$-0.426087\pi$
$977$	14.3860	0.460249	0.230125	+	0.973161i	$0.426087\pi$
$978$	−38.7569	−1.23931
$979$	−5.63421	−0.180070
$980$	−89.3216	−2.85328
$981$	−34.2814	−1.09452
$982$	−10.9186	−0.348426
$983$	30.2323	0.964261	0.482130	−	0.876099i	$-0.339863\pi$
$983$	30.2323	0.964261	0.482130	+	0.876099i	$0.339863\pi$
$984$	109.247	3.48265
$985$	−87.6920	−2.79410
$986$	−182.179	−5.80178
$987$	17.6469	0.561708
$988$	174.891	5.56402
$989$	6.48870	0.206329
$990$	−90.4079	−2.87335
$991$	48.4804	1.54003	0.770015	−	0.638026i	$-0.220249\pi$
$991$	48.4804	1.54003	0.770015	+	0.638026i	$0.220249\pi$
$992$	−15.7483	−0.500010
$993$	−0.918986	−0.0291631
$994$	−54.4648	−1.72752
$995$	−34.8282	−1.10413
$996$	182.295	5.77625
$997$	24.8044	0.785564	0.392782	−	0.919632i	$-0.371513\pi$
$997$	24.8044	0.785564	0.392782	+	0.919632i	$0.371513\pi$
$998$	56.1569	1.77761
$999$	−24.5875	−0.777914

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6007.2.a.b.1.12	✓	237

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6007.2.a.b.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-2.68501 q^{2} -2.77509 q^{3} +5.20930 q^{4} +3.15364 q^{5} +7.45116 q^{6} -1.25017 q^{7} -8.61702 q^{8} +4.70113 q^{9} +O(q^{10})\)	\(q-2.68501 q^{2} -2.77509 q^{3} +5.20930 q^{4} +3.15364 q^{5} +7.45116 q^{6} -1.25017 q^{7} -8.61702 q^{8} +4.70113 q^{9} -8.46756 q^{10} +2.27115 q^{11} -14.4563 q^{12} +4.14896 q^{13} +3.35672 q^{14} -8.75163 q^{15} +12.7182 q^{16} -7.16250 q^{17} -12.6226 q^{18} +8.09188 q^{19} +16.4282 q^{20} +3.46933 q^{21} -6.09807 q^{22} -3.11964 q^{23} +23.9130 q^{24} +4.94542 q^{25} -11.1400 q^{26} -4.72080 q^{27} -6.51250 q^{28} -9.47302 q^{29} +23.4982 q^{30} +0.931053 q^{31} -16.9145 q^{32} -6.30265 q^{33} +19.2314 q^{34} -3.94258 q^{35} +24.4896 q^{36} +5.20833 q^{37} -21.7268 q^{38} -11.5137 q^{39} -27.1749 q^{40} +4.56850 q^{41} -9.31520 q^{42} -2.07995 q^{43} +11.8311 q^{44} +14.8257 q^{45} +8.37628 q^{46} +5.08655 q^{47} -35.2942 q^{48} -5.43708 q^{49} -13.2785 q^{50} +19.8766 q^{51} +21.6132 q^{52} -7.06493 q^{53} +12.6754 q^{54} +7.16238 q^{55} +10.7727 q^{56} -22.4557 q^{57} +25.4352 q^{58} +13.1505 q^{59} -45.5899 q^{60} +5.56230 q^{61} -2.49989 q^{62} -5.87721 q^{63} +19.9793 q^{64} +13.0843 q^{65} +16.9227 q^{66} -6.19545 q^{67} -37.3116 q^{68} +8.65729 q^{69} +10.5859 q^{70} -16.2256 q^{71} -40.5097 q^{72} -2.28294 q^{73} -13.9845 q^{74} -13.7240 q^{75} +42.1530 q^{76} -2.83932 q^{77} +30.9145 q^{78} +2.61426 q^{79} +40.1086 q^{80} -1.00276 q^{81} -12.2665 q^{82} -12.6101 q^{83} +18.0728 q^{84} -22.5879 q^{85} +5.58470 q^{86} +26.2885 q^{87} -19.5705 q^{88} -2.48077 q^{89} -39.8071 q^{90} -5.18689 q^{91} -16.2512 q^{92} -2.58376 q^{93} -13.6575 q^{94} +25.5188 q^{95} +46.9394 q^{96} -14.8493 q^{97} +14.5986 q^{98} +10.6770 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9}+O(q^{10}) \) 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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