LMFDB - Embedded newform 6023.2.a.a.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$1$
Dimension:	$98$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.15437 q^{2} -1.80294 q^{3} +2.64131 q^{4} +1.24504 q^{5} +3.88420 q^{6} -4.16426 q^{7} -1.38162 q^{8} +0.250590 q^{9} +O(q^{10})$	\(q-2.15437 q^{2} -1.80294 q^{3} +2.64131 q^{4} +1.24504 q^{5} +3.88420 q^{6} -4.16426 q^{7} -1.38162 q^{8} +0.250590 q^{9} -2.68227 q^{10} -5.02791 q^{11} -4.76213 q^{12} -0.709845 q^{13} +8.97136 q^{14} -2.24473 q^{15} -2.30610 q^{16} -5.44702 q^{17} -0.539864 q^{18} +1.00000 q^{19} +3.28853 q^{20} +7.50791 q^{21} +10.8320 q^{22} +1.16536 q^{23} +2.49098 q^{24} -3.44988 q^{25} +1.52927 q^{26} +4.95702 q^{27} -10.9991 q^{28} -6.88590 q^{29} +4.83597 q^{30} +0.621318 q^{31} +7.73143 q^{32} +9.06502 q^{33} +11.7349 q^{34} -5.18466 q^{35} +0.661887 q^{36} +3.09908 q^{37} -2.15437 q^{38} +1.27981 q^{39} -1.72017 q^{40} +11.5047 q^{41} -16.1748 q^{42} +3.66314 q^{43} -13.2803 q^{44} +0.311994 q^{45} -2.51062 q^{46} +6.68145 q^{47} +4.15775 q^{48} +10.3411 q^{49} +7.43232 q^{50} +9.82064 q^{51} -1.87492 q^{52} +4.58416 q^{53} -10.6793 q^{54} -6.25994 q^{55} +5.75344 q^{56} -1.80294 q^{57} +14.8348 q^{58} +2.45438 q^{59} -5.92903 q^{60} +1.19882 q^{61} -1.33855 q^{62} -1.04352 q^{63} -12.0442 q^{64} -0.883784 q^{65} -19.5294 q^{66} -3.45131 q^{67} -14.3873 q^{68} -2.10108 q^{69} +11.1697 q^{70} +11.0392 q^{71} -0.346221 q^{72} -0.446499 q^{73} -6.67656 q^{74} +6.21993 q^{75} +2.64131 q^{76} +20.9375 q^{77} -2.75718 q^{78} +16.3644 q^{79} -2.87118 q^{80} -9.68898 q^{81} -24.7855 q^{82} -4.44375 q^{83} +19.8307 q^{84} -6.78174 q^{85} -7.89175 q^{86} +12.4149 q^{87} +6.94668 q^{88} -7.04842 q^{89} -0.672151 q^{90} +2.95598 q^{91} +3.07809 q^{92} -1.12020 q^{93} -14.3943 q^{94} +1.24504 q^{95} -13.9393 q^{96} -10.5528 q^{97} -22.2785 q^{98} -1.25995 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9}+O(q^{10}) $ 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9} - 24 q^{10} - 12 q^{11} - 51 q^{12} - 58 q^{13} - 15 q^{14} - 18 q^{15} + 58 q^{16} - 25 q^{17} - 40 q^{18} + 98 q^{19} - 12 q^{20} - 24 q^{21} - 59 q^{22} - 38 q^{23} - 9 q^{24} - 12 q^{25} - 3 q^{26} - 85 q^{27} - 33 q^{28} - 24 q^{29} - 22 q^{30} - 56 q^{31} - 29 q^{32} - 51 q^{33} - 38 q^{34} - 10 q^{35} + 50 q^{36} - 124 q^{37} - 8 q^{38} - 4 q^{39} - 80 q^{40} - 28 q^{41} - 37 q^{42} - 63 q^{43} - 7 q^{44} - 32 q^{45} - 47 q^{46} - 10 q^{47} - 88 q^{48} + 6 q^{49} - 17 q^{50} - 22 q^{51} - 119 q^{52} - 65 q^{53} + 24 q^{54} - 30 q^{55} - 39 q^{56} - 25 q^{57} - 91 q^{58} - 26 q^{59} - 60 q^{60} - 60 q^{61} + 6 q^{62} - 26 q^{63} + 50 q^{64} - 40 q^{65} + 57 q^{66} - 108 q^{67} - 41 q^{68} - 15 q^{69} - 36 q^{70} - 19 q^{71} - 47 q^{72} - 136 q^{73} + 22 q^{74} - 48 q^{75} + 82 q^{76} - 35 q^{77} - 56 q^{78} - 98 q^{79} - 42 q^{80} + 6 q^{81} - 37 q^{82} - 31 q^{83} - 24 q^{84} - 71 q^{85} - 24 q^{86} + 7 q^{87} - 166 q^{88} - 38 q^{89} + 26 q^{90} - 100 q^{91} - 59 q^{92} - 21 q^{93} - 48 q^{94} - 10 q^{95} - 16 q^{96} - 190 q^{97} - 80 q^{98} - 17 q^{99}+O(q^{100}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9 - 24 * q^10 - 12 * q^11 - 51 * q^12 - 58 * q^13 - 15 * q^14 - 18 * q^15 + 58 * q^16 - 25 * q^17 - 40 * q^18 + 98 * q^19 - 12 * q^20 - 24 * q^21 - 59 * q^22 - 38 * q^23 - 9 * q^24 - 12 * q^25 - 3 * q^26 - 85 * q^27 - 33 * q^28 - 24 * q^29 - 22 * q^30 - 56 * q^31 - 29 * q^32 - 51 * q^33 - 38 * q^34 - 10 * q^35 + 50 * q^36 - 124 * q^37 - 8 * q^38 - 4 * q^39 - 80 * q^40 - 28 * q^41 - 37 * q^42 - 63 * q^43 - 7 * q^44 - 32 * q^45 - 47 * q^46 - 10 * q^47 - 88 * q^48 + 6 * q^49 - 17 * q^50 - 22 * q^51 - 119 * q^52 - 65 * q^53 + 24 * q^54 - 30 * q^55 - 39 * q^56 - 25 * q^57 - 91 * q^58 - 26 * q^59 - 60 * q^60 - 60 * q^61 + 6 * q^62 - 26 * q^63 + 50 * q^64 - 40 * q^65 + 57 * q^66 - 108 * q^67 - 41 * q^68 - 15 * q^69 - 36 * q^70 - 19 * q^71 - 47 * q^72 - 136 * q^73 + 22 * q^74 - 48 * q^75 + 82 * q^76 - 35 * q^77 - 56 * q^78 - 98 * q^79 - 42 * q^80 + 6 * q^81 - 37 * q^82 - 31 * q^83 - 24 * q^84 - 71 * q^85 - 24 * q^86 + 7 * q^87 - 166 * q^88 - 38 * q^89 + 26 * q^90 - 100 * q^91 - 59 * q^92 - 21 * q^93 - 48 * q^94 - 10 * q^95 - 16 * q^96 - 190 * q^97 - 80 * q^98 - 17 * 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 $

$2$	−2.15437	−1.52337	−0.761685	−	0.647948i	$-0.775628\pi$
$2$	−2.15437	−1.52337	−0.761685	+	0.647948i	$0.775628\pi$
$3$	−1.80294	−1.04093	−0.520464	−	0.853884i	$-0.674241\pi$
$3$	−1.80294	−1.04093	−0.520464	+	0.853884i	$0.674241\pi$
$4$	2.64131	1.32066
$5$	1.24504	0.556798	0.278399	−	0.960466i	$-0.410196\pi$
$5$	1.24504	0.556798	0.278399	+	0.960466i	$0.410196\pi$
$6$	3.88420	1.58572
$7$	−4.16426	−1.57394	−0.786971	−	0.616990i	$-0.788352\pi$
$7$	−4.16426	−1.57394	−0.786971	+	0.616990i	$0.788352\pi$
$8$	−1.38162	−0.488478
$9$	0.250590	0.0835301
$10$	−2.68227	−0.848209
$11$	−5.02791	−1.51597	−0.757986	−	0.652271i	$-0.773816\pi$
$11$	−5.02791	−1.51597	−0.757986	+	0.652271i	$0.773816\pi$
$12$	−4.76213	−1.37471
$13$	−0.709845	−0.196876	−0.0984379	−	0.995143i	$-0.531385\pi$
$13$	−0.709845	−0.196876	−0.0984379	+	0.995143i	$0.531385\pi$
$14$	8.97136	2.39770
$15$	−2.24473	−0.579586
$16$	−2.30610	−0.576524
$17$	−5.44702	−1.32110	−0.660548	−	0.750784i	$-0.729676\pi$
$17$	−5.44702	−1.32110	−0.660548	+	0.750784i	$0.729676\pi$
$18$	−0.539864	−0.127247
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	3.28853	0.735338
$21$	7.50791	1.63836
$22$	10.8320	2.30939
$23$	1.16536	0.242995	0.121497	−	0.992592i	$-0.461230\pi$
$23$	1.16536	0.242995	0.121497	+	0.992592i	$0.461230\pi$
$24$	2.49098	0.508470
$25$	−3.44988	−0.689976
$26$	1.52927	0.299915
$27$	4.95702	0.953979
$28$	−10.9991	−2.07864
$29$	−6.88590	−1.27868	−0.639340	−	0.768925i	$-0.720792\pi$
$29$	−6.88590	−1.27868	−0.639340	+	0.768925i	$0.720792\pi$
$30$	4.83597	0.882924
$31$	0.621318	0.111592	0.0557960	−	0.998442i	$-0.482230\pi$
$31$	0.621318	0.111592	0.0557960	+	0.998442i	$0.482230\pi$
$32$	7.73143	1.36674
$33$	9.06502	1.57802
$34$	11.7349	2.01252
$35$	−5.18466	−0.876367
$36$	0.661887	0.110314
$37$	3.09908	0.509485	0.254743	−	0.967009i	$-0.418009\pi$
$37$	3.09908	0.509485	0.254743	+	0.967009i	$0.418009\pi$
$38$	−2.15437	−0.349485
$39$	1.27981	0.204933
$40$	−1.72017	−0.271983
$41$	11.5047	1.79674	0.898369	−	0.439241i	$-0.144753\pi$
$41$	11.5047	1.79674	0.898369	+	0.439241i	$0.144753\pi$
$42$	−16.1748	−2.49583
$43$	3.66314	0.558623	0.279311	−	0.960201i	$-0.409894\pi$
$43$	3.66314	0.558623	0.279311	+	0.960201i	$0.409894\pi$
$44$	−13.2803	−2.00208
$45$	0.311994	0.0465094
$46$	−2.51062	−0.370171
$47$	6.68145	0.974589	0.487295	−	0.873238i	$-0.337984\pi$
$47$	6.68145	0.974589	0.487295	+	0.873238i	$0.337984\pi$
$48$	4.15775	0.600119
$49$	10.3411	1.47729
$50$	7.43232	1.05109
$51$	9.82064	1.37517
$52$	−1.87492	−0.260005
$53$	4.58416	0.629683	0.314841	−	0.949144i	$-0.398049\pi$
$53$	4.58416	0.629683	0.314841	+	0.949144i	$0.398049\pi$
$54$	−10.6793	−1.45326
$55$	−6.25994	−0.844090
$56$	5.75344	0.768835
$57$	−1.80294	−0.238805
$58$	14.8348	1.94790
$59$	2.45438	0.319532	0.159766	−	0.987155i	$-0.448926\pi$
$59$	2.45438	0.319532	0.159766	+	0.987155i	$0.448926\pi$
$60$	−5.92903	−0.765434
$61$	1.19882	0.153493	0.0767466	−	0.997051i	$-0.475547\pi$
$61$	1.19882	0.153493	0.0767466	+	0.997051i	$0.475547\pi$
$62$	−1.33855	−0.169996
$63$	−1.04352	−0.131471
$64$	−12.0442	−1.50552
$65$	−0.883784	−0.109620
$66$	−19.5294	−2.40390
$67$	−3.45131	−0.421644	−0.210822	−	0.977524i	$-0.567614\pi$
$67$	−3.45131	−0.421644	−0.210822	+	0.977524i	$0.567614\pi$
$68$	−14.3873	−1.74471
$69$	−2.10108	−0.252940
$70$	11.1697	1.33503
$71$	11.0392	1.31011	0.655057	−	0.755579i	$-0.272644\pi$
$71$	11.0392	1.31011	0.655057	+	0.755579i	$0.272644\pi$
$72$	−0.346221	−0.0408026
$73$	−0.446499	−0.0522588	−0.0261294	−	0.999659i	$-0.508318\pi$
$73$	−0.446499	−0.0522588	−0.0261294	+	0.999659i	$0.508318\pi$
$74$	−6.67656	−0.776135
$75$	6.21993	0.718215
$76$	2.64131	0.302979
$77$	20.9375	2.38605
$78$	−2.75718	−0.312189
$79$	16.3644	1.84114	0.920572	−	0.390572i	$-0.127723\pi$
$79$	16.3644	1.84114	0.920572	+	0.390572i	$0.127723\pi$
$80$	−2.87118	−0.321007
$81$	−9.68898	−1.07655
$82$	−24.7855	−2.73710
$83$	−4.44375	−0.487765	−0.243882	−	0.969805i	$-0.578421\pi$
$83$	−4.44375	−0.487765	−0.243882	+	0.969805i	$0.578421\pi$
$84$	19.8307	2.16371
$85$	−6.78174	−0.735583
$86$	−7.89175	−0.850989
$87$	12.4149	1.33101
$88$	6.94668	0.740518
$89$	−7.04842	−0.747131	−0.373565	−	0.927604i	$-0.621865\pi$
$89$	−7.04842	−0.747131	−0.373565	+	0.927604i	$0.621865\pi$
$90$	−0.672151	−0.0708510
$91$	2.95598	0.309871
$92$	3.07809	0.320913
$93$	−1.12020	−0.116159
$94$	−14.3943	−1.48466
$95$	1.24504	0.127738
$96$	−13.9393	−1.42267
$97$	−10.5528	−1.07147	−0.535736	−	0.844385i	$-0.679966\pi$
$97$	−10.5528	−1.07147	−0.535736	+	0.844385i	$0.679966\pi$
$98$	−22.2785	−2.25046
$99$	−1.25995	−0.126629
$100$	−9.11221	−0.911221
$101$	4.04497	0.402489	0.201245	−	0.979541i	$-0.435501\pi$
$101$	4.04497	0.402489	0.201245	+	0.979541i	$0.435501\pi$
$102$	−21.1573	−2.09489
$103$	2.75567	0.271524	0.135762	−	0.990741i	$-0.456652\pi$
$103$	2.75567	0.271524	0.135762	+	0.990741i	$0.456652\pi$
$104$	0.980739	0.0961694
$105$	9.34763	0.912235
$106$	−9.87598	−0.959240
$107$	4.64339	0.448893	0.224447	−	0.974486i	$-0.427943\pi$
$107$	4.64339	0.448893	0.224447	+	0.974486i	$0.427943\pi$
$108$	13.0930	1.25988
$109$	1.37458	0.131661	0.0658304	−	0.997831i	$-0.479030\pi$
$109$	1.37458	0.131661	0.0658304	+	0.997831i	$0.479030\pi$
$110$	13.4862	1.28586
$111$	−5.58745	−0.530337
$112$	9.60318	0.907415
$113$	−4.61639	−0.434273	−0.217137	−	0.976141i	$-0.569672\pi$
$113$	−4.61639	−0.434273	−0.217137	+	0.976141i	$0.569672\pi$
$114$	3.88420	0.363789
$115$	1.45092	0.135299
$116$	−18.1878	−1.68870
$117$	−0.177880	−0.0164450
$118$	−5.28763	−0.486766
$119$	22.6828	2.07933
$120$	3.10137	0.283115
$121$	14.2799	1.29817
$122$	−2.58270	−0.233827
$123$	−20.7423	−1.87027
$124$	1.64110	0.147375
$125$	−10.5204	−0.940975
$126$	2.24813	0.200280
$127$	−7.81124	−0.693136	−0.346568	−	0.938025i	$-0.612653\pi$
$127$	−7.81124	−0.693136	−0.346568	+	0.938025i	$0.612653\pi$
$128$	10.4848	0.926730
$129$	−6.60441	−0.581486
$130$	1.90400	0.166992
$131$	3.32174	0.290222	0.145111	−	0.989415i	$-0.453646\pi$
$131$	3.32174	0.290222	0.145111	+	0.989415i	$0.453646\pi$
$132$	23.9435	2.08402
$133$	−4.16426	−0.361087
$134$	7.43540	0.642320
$135$	6.17168	0.531173
$136$	7.52573	0.645326
$137$	−14.9306	−1.27561	−0.637805	−	0.770198i	$-0.720157\pi$
$137$	−14.9306	−1.27561	−0.637805	+	0.770198i	$0.720157\pi$
$138$	4.52650	0.385321
$139$	9.65712	0.819106	0.409553	−	0.912286i	$-0.365685\pi$
$139$	9.65712	0.819106	0.409553	+	0.912286i	$0.365685\pi$
$140$	−13.6943	−1.15738
$141$	−12.0462	−1.01448
$142$	−23.7826	−1.99579
$143$	3.56904	0.298458
$144$	−0.577885	−0.0481571
$145$	−8.57320	−0.711966
$146$	0.961924	0.0796094
$147$	−18.6443	−1.53775
$148$	8.18563	0.672855
$149$	2.60383	0.213314	0.106657	−	0.994296i	$-0.465985\pi$
$149$	2.60383	0.213314	0.106657	+	0.994296i	$0.465985\pi$
$150$	−13.4000	−1.09411
$151$	1.79394	0.145989	0.0729944	−	0.997332i	$-0.476744\pi$
$151$	1.79394	0.145989	0.0729944	+	0.997332i	$0.476744\pi$
$152$	−1.38162	−0.112064
$153$	−1.36497	−0.110351
$154$	−45.1072	−3.63484
$155$	0.773565	0.0621342
$156$	3.38037	0.270646
$157$	−5.66108	−0.451803	−0.225902	−	0.974150i	$-0.572533\pi$
$157$	−5.66108	−0.451803	−0.225902	+	0.974150i	$0.572533\pi$
$158$	−35.2551	−2.80474
$159$	−8.26496	−0.655454
$160$	9.62592	0.760996
$161$	−4.85287	−0.382460
$162$	20.8736	1.63999
$163$	13.1987	1.03380	0.516902	−	0.856044i	$-0.327085\pi$
$163$	13.1987	1.03380	0.516902	+	0.856044i	$0.327085\pi$
$164$	30.3876	2.37287
$165$	11.2863	0.878636
$166$	9.57348	0.743046
$167$	−3.92810	−0.303966	−0.151983	−	0.988383i	$-0.548566\pi$
$167$	−3.92810	−0.303966	−0.151983	+	0.988383i	$0.548566\pi$
$168$	−10.3731	−0.800302
$169$	−12.4961	−0.961240
$170$	14.6104	1.12057
$171$	0.250590	0.0191631
$172$	9.67548	0.737749
$173$	−21.6027	−1.64242	−0.821210	−	0.570627i	$-0.806700\pi$
$173$	−21.6027	−1.64242	−0.821210	+	0.570627i	$0.806700\pi$
$174$	−26.7462	−2.02762
$175$	14.3662	1.08598
$176$	11.5948	0.873994
$177$	−4.42509	−0.332610
$178$	15.1849	1.13816
$179$	1.44995	0.108374	0.0541871	−	0.998531i	$-0.482743\pi$
$179$	1.44995	0.108374	0.0541871	+	0.998531i	$0.482743\pi$
$180$	0.824074	0.0614229
$181$	−0.838236	−0.0623056	−0.0311528	−	0.999515i	$-0.509918\pi$
$181$	−0.838236	−0.0623056	−0.0311528	+	0.999515i	$0.509918\pi$
$182$	−6.36828	−0.472048
$183$	−2.16140	−0.159775
$184$	−1.61009	−0.118698
$185$	3.85847	0.283680
$186$	2.41332	0.176953
$187$	27.3871	2.00274
$188$	17.6478	1.28710
$189$	−20.6423	−1.50151
$190$	−2.68227	−0.194592
$191$	−0.730339	−0.0528455	−0.0264227	−	0.999651i	$-0.508412\pi$
$191$	−0.730339	−0.0528455	−0.0264227	+	0.999651i	$0.508412\pi$
$192$	21.7149	1.56714
$193$	−17.0338	−1.22612	−0.613060	−	0.790036i	$-0.710062\pi$
$193$	−17.0338	−1.22612	−0.613060	+	0.790036i	$0.710062\pi$
$194$	22.7346	1.63225
$195$	1.59341	0.114106
$196$	27.3139	1.95100
$197$	−6.12004	−0.436035	−0.218017	−	0.975945i	$-0.569959\pi$
$197$	−6.12004	−0.436035	−0.218017	+	0.975945i	$0.569959\pi$
$198$	2.71439	0.192903
$199$	11.9498	0.847096	0.423548	−	0.905874i	$-0.360784\pi$
$199$	11.9498	0.847096	0.423548	+	0.905874i	$0.360784\pi$
$200$	4.76644	0.337038
$201$	6.22250	0.438901
$202$	−8.71436	−0.613140
$203$	28.6747	2.01257
$204$	25.9394	1.81612
$205$	14.3238	1.00042
$206$	−5.93673	−0.413632
$207$	0.292029	0.0202974
$208$	1.63697	0.113504
$209$	−5.02791	−0.347788
$210$	−20.1382	−1.38967
$211$	11.3968	0.784588	0.392294	−	0.919840i	$-0.371682\pi$
$211$	11.3968	0.784588	0.392294	+	0.919840i	$0.371682\pi$
$212$	12.1082	0.831594
$213$	−19.9031	−1.36373
$214$	−10.0036	−0.683830
$215$	4.56074	0.311040
$216$	−6.84873	−0.465997
$217$	−2.58733	−0.175639
$218$	−2.96135	−0.200568
$219$	0.805011	0.0543976
$220$	−16.5344	−1.11475
$221$	3.86654	0.260092
$222$	12.0374	0.807900
$223$	−26.5404	−1.77728	−0.888638	−	0.458610i	$-0.848348\pi$
$223$	−26.5404	−1.77728	−0.888638	+	0.458610i	$0.848348\pi$
$224$	−32.1957	−2.15116
$225$	−0.864506	−0.0576338
$226$	9.94541	0.661559
$227$	15.9179	1.05651	0.528253	−	0.849087i	$-0.322847\pi$
$227$	15.9179	1.05651	0.528253	+	0.849087i	$0.322847\pi$
$228$	−4.76213	−0.315379
$229$	24.4253	1.61407	0.807036	−	0.590503i	$-0.201071\pi$
$229$	24.4253	1.61407	0.807036	+	0.590503i	$0.201071\pi$
$230$	−3.12582	−0.206111
$231$	−37.7491	−2.48371
$232$	9.51372	0.624606
$233$	6.30280	0.412910	0.206455	−	0.978456i	$-0.433807\pi$
$233$	6.30280	0.412910	0.206455	+	0.978456i	$0.433807\pi$
$234$	0.383220	0.0250519
$235$	8.31865	0.542649
$236$	6.48277	0.421992
$237$	−29.5041	−1.91650
$238$	−48.8671	−3.16759
$239$	1.16758	0.0755245	0.0377622	−	0.999287i	$-0.487977\pi$
$239$	1.16758	0.0755245	0.0377622	+	0.999287i	$0.487977\pi$
$240$	5.17656	0.334145
$241$	12.0082	0.773518	0.386759	−	0.922181i	$-0.373594\pi$
$241$	12.0082	0.773518	0.386759	+	0.922181i	$0.373594\pi$
$242$	−30.7642	−1.97759
$243$	2.59758	0.166635
$244$	3.16646	0.202712
$245$	12.8750	0.822553
$246$	44.6867	2.84912
$247$	−0.709845	−0.0451664
$248$	−0.858428	−0.0545102
$249$	8.01181	0.507728
$250$	22.6649	1.43345
$251$	−9.89310	−0.624447	−0.312224	−	0.950009i	$-0.601074\pi$
$251$	−9.89310	−0.624447	−0.312224	+	0.950009i	$0.601074\pi$
$252$	−2.75627	−0.173629
$253$	−5.85934	−0.368374
$254$	16.8283	1.05590
$255$	12.2271	0.765689
$256$	1.50031	0.0937692
$257$	31.8141	1.98451	0.992253	−	0.124233i	$-0.0396469\pi$
$257$	31.8141	1.98451	0.992253	+	0.124233i	$0.0396469\pi$
$258$	14.2283	0.885818
$259$	−12.9054	−0.801900
$260$	−2.33435	−0.144770
$261$	−1.72554	−0.106808
$262$	−7.15626	−0.442115
$263$	6.43224	0.396629	0.198314	−	0.980138i	$-0.436453\pi$
$263$	6.43224	0.396629	0.198314	+	0.980138i	$0.436453\pi$
$264$	−12.5244	−0.770826
$265$	5.70745	0.350606
$266$	8.97136	0.550069
$267$	12.7079	0.777709
$268$	−9.11598	−0.556847
$269$	−1.75433	−0.106963	−0.0534817	−	0.998569i	$-0.517032\pi$
$269$	−1.75433	−0.106963	−0.0534817	+	0.998569i	$0.517032\pi$
$270$	−13.2961	−0.809173
$271$	−1.32140	−0.0802696	−0.0401348	−	0.999194i	$-0.512779\pi$
$271$	−1.32140	−0.0802696	−0.0401348	+	0.999194i	$0.512779\pi$
$272$	12.5613	0.761643
$273$	−5.32945	−0.322553
$274$	32.1661	1.94323
$275$	17.3457	1.04598
$276$	−5.54960	−0.334047
$277$	6.69722	0.402397	0.201199	−	0.979550i	$-0.435516\pi$
$277$	6.69722	0.402397	0.201199	+	0.979550i	$0.435516\pi$
$278$	−20.8050	−1.24780
$279$	0.155696	0.00932129
$280$	7.16325	0.428086
$281$	30.3039	1.80778	0.903889	−	0.427768i	$-0.140700\pi$
$281$	30.3039	1.80778	0.903889	+	0.427768i	$0.140700\pi$
$282$	25.9521	1.54542
$283$	8.19969	0.487421	0.243711	−	0.969848i	$-0.421635\pi$
$283$	8.19969	0.487421	0.243711	+	0.969848i	$0.421635\pi$
$284$	29.1580	1.73021
$285$	−2.24473	−0.132966
$286$	−7.68903	−0.454662
$287$	−47.9087	−2.82796
$288$	1.93742	0.114164
$289$	12.6700	0.745295
$290$	18.4699	1.08459
$291$	19.0260	1.11532
$292$	−1.17934	−0.0690159
$293$	−10.6312	−0.621082	−0.310541	−	0.950560i	$-0.600510\pi$
$293$	−10.6312	−0.621082	−0.310541	+	0.950560i	$0.600510\pi$
$294$	40.1667	2.34257
$295$	3.05579	0.177915
$296$	−4.28176	−0.248872
$297$	−24.9234	−1.44621
$298$	−5.60962	−0.324957
$299$	−0.827228	−0.0478398
$300$	16.4288	0.948515
$301$	−15.2542	−0.879240
$302$	−3.86481	−0.222395
$303$	−7.29283	−0.418962
$304$	−2.30610	−0.132264
$305$	1.49258	0.0854647
$306$	2.94065	0.168106
$307$	8.89657	0.507754	0.253877	−	0.967236i	$-0.418294\pi$
$307$	8.89657	0.507754	0.253877	+	0.967236i	$0.418294\pi$
$308$	55.3025	3.15115
$309$	−4.96830	−0.282637
$310$	−1.66654	−0.0946534
$311$	−2.61409	−0.148231	−0.0741157	−	0.997250i	$-0.523613\pi$
$311$	−2.61409	−0.148231	−0.0741157	+	0.997250i	$0.523613\pi$
$312$	−1.76821	−0.100105
$313$	11.1213	0.628615	0.314308	−	0.949321i	$-0.398228\pi$
$313$	11.1213	0.628615	0.314308	+	0.949321i	$0.398228\pi$
$314$	12.1961	0.688264
$315$	−1.29922	−0.0732030
$316$	43.2236	2.43152
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	17.8058	0.998499
$319$	34.6217	1.93844
$320$	−14.9955	−0.838271
$321$	−8.37175	−0.467265
$322$	10.4549	0.582628
$323$	−5.44702	−0.303080
$324$	−25.5916	−1.42176
$325$	2.44888	0.135840
$326$	−28.4350	−1.57487
$327$	−2.47828	−0.137049
$328$	−15.8952	−0.877667
$329$	−27.8233	−1.53395
$330$	−24.3148	−1.33849
$331$	−35.5258	−1.95267	−0.976336	−	0.216258i	$-0.930615\pi$
$331$	−35.5258	−1.95267	−0.976336	+	0.216258i	$0.930615\pi$
$332$	−11.7373	−0.644169
$333$	0.776599	0.0425573
$334$	8.46259	0.463052
$335$	−4.29701	−0.234771
$336$	−17.3139	−0.944553
$337$	−24.7961	−1.35073	−0.675366	−	0.737483i	$-0.736014\pi$
$337$	−24.7961	−1.35073	−0.675366	+	0.737483i	$0.736014\pi$
$338$	26.9213	1.46432
$339$	8.32307	0.452047
$340$	−17.9127	−0.971453
$341$	−3.12393	−0.169170
$342$	−0.539864	−0.0291925
$343$	−13.9130	−0.751231
$344$	−5.06107	−0.272875
$345$	−2.61592	−0.140837
$346$	46.5401	2.50201
$347$	26.0738	1.39971	0.699857	−	0.714283i	$-0.253247\pi$
$347$	26.0738	1.39971	0.699857	+	0.714283i	$0.253247\pi$
$348$	32.7915	1.75781
$349$	18.2907	0.979078	0.489539	−	0.871982i	$-0.337165\pi$
$349$	18.2907	0.979078	0.489539	+	0.871982i	$0.337165\pi$
$350$	−30.9501	−1.65435
$351$	−3.51872	−0.187815
$352$	−38.8729	−2.07193
$353$	−11.3358	−0.603343	−0.301672	−	0.953412i	$-0.597545\pi$
$353$	−11.3358	−0.603343	−0.301672	+	0.953412i	$0.597545\pi$
$354$	9.53328	0.506688
$355$	13.7443	0.729469
$356$	−18.6171	−0.986703
$357$	−40.8957	−2.16443
$358$	−3.12372	−0.165094
$359$	−7.79247	−0.411271	−0.205635	−	0.978629i	$-0.565926\pi$
$359$	−7.79247	−0.411271	−0.205635	+	0.978629i	$0.565926\pi$
$360$	−0.431059	−0.0227188
$361$	1.00000	0.0526316
$362$	1.80587	0.0949145
$363$	−25.7458	−1.35130
$364$	7.80767	0.409233
$365$	−0.555908	−0.0290976
$366$	4.65646	0.243397
$367$	−21.3207	−1.11293	−0.556466	−	0.830870i	$-0.687843\pi$
$367$	−21.3207	−1.11293	−0.556466	+	0.830870i	$0.687843\pi$
$368$	−2.68744	−0.140092
$369$	2.88297	0.150082
$370$	−8.31257	−0.432150
$371$	−19.0896	−0.991084
$372$	−2.95880	−0.153406
$373$	−28.2146	−1.46090	−0.730449	−	0.682967i	$-0.760689\pi$
$373$	−28.2146	−1.46090	−0.730449	+	0.682967i	$0.760689\pi$
$374$	−59.0020	−3.05092
$375$	18.9677	0.979487
$376$	−9.23124	−0.476065
$377$	4.88792	0.251741
$378$	44.4712	2.28735
$379$	16.5006	0.847578	0.423789	−	0.905761i	$-0.360700\pi$
$379$	16.5006	0.847578	0.423789	+	0.905761i	$0.360700\pi$
$380$	3.28853	0.168698
$381$	14.0832	0.721504
$382$	1.57342	0.0805032
$383$	15.1396	0.773597	0.386798	−	0.922164i	$-0.373581\pi$
$383$	15.1396	0.773597	0.386798	+	0.922164i	$0.373581\pi$
$384$	−18.9034	−0.964659
$385$	26.0680	1.32855
$386$	36.6971	1.86784
$387$	0.917946	0.0466618
$388$	−27.8732	−1.41505
$389$	2.48317	0.125901	0.0629507	−	0.998017i	$-0.479949\pi$
$389$	2.48317	0.125901	0.0629507	+	0.998017i	$0.479949\pi$
$390$	−3.43279	−0.173826
$391$	−6.34775	−0.321020
$392$	−14.2874	−0.721625
$393$	−5.98890	−0.302100
$394$	13.1848	0.664242
$395$	20.3744	1.02515
$396$	−3.32791	−0.167234
$397$	−33.4469	−1.67865	−0.839327	−	0.543627i	$-0.817051\pi$
$397$	−33.4469	−1.67865	−0.839327	+	0.543627i	$0.817051\pi$
$398$	−25.7442	−1.29044
$399$	7.50791	0.375865
$400$	7.95575	0.397788
$401$	36.3323	1.81435	0.907175	−	0.420754i	$-0.138235\pi$
$401$	36.3323	1.81435	0.907175	+	0.420754i	$0.138235\pi$
$402$	−13.4056	−0.668609
$403$	−0.441040	−0.0219698
$404$	10.6840	0.531550
$405$	−12.0631	−0.599422
$406$	−61.7758	−3.06588
$407$	−15.5819	−0.772365
$408$	−13.5684	−0.671738
$409$	3.82048	0.188911	0.0944554	−	0.995529i	$-0.469889\pi$
$409$	3.82048	0.188911	0.0944554	+	0.995529i	$0.469889\pi$
$410$	−30.8588	−1.52401
$411$	26.9190	1.32782
$412$	7.27858	0.358590
$413$	−10.2207	−0.502925
$414$	−0.629138	−0.0309204
$415$	−5.53263	−0.271586
$416$	−5.48812	−0.269077
$417$	−17.4112	−0.852630
$418$	10.8320	0.529810
$419$	11.7240	0.572757	0.286379	−	0.958117i	$-0.407548\pi$
$419$	11.7240	0.572757	0.286379	+	0.958117i	$0.407548\pi$
$420$	24.6900	1.20475
$421$	−39.3824	−1.91938	−0.959690	−	0.281059i	$-0.909314\pi$
$421$	−39.3824	−1.91938	−0.959690	+	0.281059i	$0.909314\pi$
$422$	−24.5529	−1.19522
$423$	1.67431	0.0814075
$424$	−6.33358	−0.307586
$425$	18.7916	0.911525
$426$	42.8785	2.07747
$427$	−4.99220	−0.241589
$428$	12.2646	0.592834
$429$	−6.43476	−0.310673
$430$	−9.82553	−0.473829
$431$	−6.60267	−0.318039	−0.159020	−	0.987275i	$-0.550833\pi$
$431$	−6.60267	−0.318039	−0.159020	+	0.987275i	$0.550833\pi$
$432$	−11.4314	−0.549991
$433$	−4.64459	−0.223205	−0.111602	−	0.993753i	$-0.535598\pi$
$433$	−4.64459	−0.223205	−0.111602	+	0.993753i	$0.535598\pi$
$434$	5.57407	0.267564
$435$	15.4570	0.741105
$436$	3.63069	0.173879
$437$	1.16536	0.0557469
$438$	−1.73429	−0.0828677
$439$	2.73648	0.130605	0.0653024	−	0.997866i	$-0.479199\pi$
$439$	2.73648	0.130605	0.0653024	+	0.997866i	$0.479199\pi$
$440$	8.64888	0.412319
$441$	2.59137	0.123398
$442$	−8.32996	−0.396216
$443$	−12.6897	−0.602906	−0.301453	−	0.953481i	$-0.597472\pi$
$443$	−12.6897	−0.602906	−0.301453	+	0.953481i	$0.597472\pi$
$444$	−14.7582	−0.700393
$445$	−8.77555	−0.416001
$446$	57.1778	2.70745
$447$	−4.69455	−0.222045
$448$	50.1551	2.36960
$449$	−8.96103	−0.422897	−0.211448	−	0.977389i	$-0.567818\pi$
$449$	−8.96103	−0.422897	−0.211448	+	0.977389i	$0.567818\pi$
$450$	1.86247	0.0877975
$451$	−57.8448	−2.72381
$452$	−12.1933	−0.573526
$453$	−3.23437	−0.151964
$454$	−34.2930	−1.60945
$455$	3.68031	0.172535
$456$	2.49098	0.116651
$457$	21.6395	1.01225	0.506126	−	0.862460i	$-0.331077\pi$
$457$	21.6395	1.01225	0.506126	+	0.862460i	$0.331077\pi$
$458$	−52.6212	−2.45883
$459$	−27.0010	−1.26030
$460$	3.83233	0.178684
$461$	0.0771956	0.00359536	0.00179768	−	0.999998i	$-0.499428\pi$
$461$	0.0771956	0.00359536	0.00179768	+	0.999998i	$0.499428\pi$
$462$	81.3255	3.78360
$463$	−33.0823	−1.53746	−0.768731	−	0.639572i	$-0.779112\pi$
$463$	−33.0823	−1.53746	−0.768731	+	0.639572i	$0.779112\pi$
$464$	15.8795	0.737189
$465$	−1.39469	−0.0646772
$466$	−13.5786	−0.629015
$467$	36.1941	1.67486	0.837431	−	0.546543i	$-0.184056\pi$
$467$	36.1941	1.67486	0.837431	+	0.546543i	$0.184056\pi$
$468$	−0.469837	−0.0217182
$469$	14.3721	0.663644
$470$	−17.9215	−0.826655
$471$	10.2066	0.470295
$472$	−3.39102	−0.156084
$473$	−18.4179	−0.846857
$474$	63.5628	2.91954
$475$	−3.44988	−0.158291
$476$	59.9123	2.74608
$477$	1.14875	0.0525974
$478$	−2.51540	−0.115052
$479$	−2.13878	−0.0977233	−0.0488616	−	0.998806i	$-0.515559\pi$
$479$	−2.13878	−0.0977233	−0.0488616	+	0.998806i	$0.515559\pi$
$480$	−17.3550	−0.792142
$481$	−2.19987	−0.100305
$482$	−25.8702	−1.17835
$483$	8.74943	0.398113
$484$	37.7176	1.71444
$485$	−13.1386	−0.596593
$486$	−5.59614	−0.253846
$487$	−15.9643	−0.723411	−0.361706	−	0.932292i	$-0.617805\pi$
$487$	−15.9643	−0.723411	−0.361706	+	0.932292i	$0.617805\pi$
$488$	−1.65632	−0.0749780
$489$	−23.7965	−1.07612
$490$	−27.7375	−1.25305
$491$	−22.8981	−1.03338	−0.516689	−	0.856173i	$-0.672836\pi$
$491$	−22.8981	−1.03338	−0.516689	+	0.856173i	$0.672836\pi$
$492$	−54.7870	−2.46999
$493$	37.5076	1.68926
$494$	1.52927	0.0688051
$495$	−1.56868	−0.0705069
$496$	−1.43282	−0.0643355
$497$	−45.9702	−2.06204
$498$	−17.2604	−0.773457
$499$	2.22449	0.0995819	0.0497909	−	0.998760i	$-0.484144\pi$
$499$	2.22449	0.0995819	0.0497909	+	0.998760i	$0.484144\pi$
$500$	−27.7877	−1.24270
$501$	7.08213	0.316406
$502$	21.3134	0.951264
$503$	−2.14264	−0.0955356	−0.0477678	−	0.998858i	$-0.515211\pi$
$503$	−2.14264	−0.0955356	−0.0477678	+	0.998858i	$0.515211\pi$
$504$	1.44176	0.0642209
$505$	5.03614	0.224105
$506$	12.6232	0.561169
$507$	22.5297	1.00058
$508$	−20.6319	−0.915394
$509$	18.9434	0.839652	0.419826	−	0.907605i	$-0.362091\pi$
$509$	18.9434	0.839652	0.419826	+	0.907605i	$0.362091\pi$
$510$	−26.3416	−1.16643
$511$	1.85934	0.0822523
$512$	−24.2017	−1.06958
$513$	4.95702	0.218858
$514$	−68.5393	−3.02314
$515$	3.43091	0.151184
$516$	−17.4443	−0.767943
$517$	−33.5937	−1.47745
$518$	27.8029	1.22159
$519$	38.9483	1.70964
$520$	1.22106	0.0535469
$521$	−21.1672	−0.927350	−0.463675	−	0.886005i	$-0.653469\pi$
$521$	−21.1672	−0.927350	−0.463675	+	0.886005i	$0.653469\pi$
$522$	3.71745	0.162708
$523$	−42.2275	−1.84648	−0.923241	−	0.384222i	$-0.874470\pi$
$523$	−42.2275	−1.84648	−0.923241	+	0.384222i	$0.874470\pi$
$524$	8.77375	0.383283
$525$	−25.9014	−1.13043
$526$	−13.8574	−0.604212
$527$	−3.38433	−0.147424
$528$	−20.9048	−0.909764
$529$	−21.6419	−0.940953
$530$	−12.2960	−0.534102
$531$	0.615042	0.0266906
$532$	−10.9991	−0.476872
$533$	−8.16659	−0.353734
$534$	−27.3775	−1.18474
$535$	5.78119	0.249943
$536$	4.76841	0.205964
$537$	−2.61417	−0.112810
$538$	3.77948	0.162945
$539$	−51.9939	−2.23953
$540$	16.3013	0.701497
$541$	21.4657	0.922883	0.461441	−	0.887171i	$-0.347332\pi$
$541$	21.4657	0.922883	0.461441	+	0.887171i	$0.347332\pi$
$542$	2.84679	0.122280
$543$	1.51129	0.0648556
$544$	−42.1132	−1.80559
$545$	1.71140	0.0733084
$546$	11.4816	0.491368
$547$	1.14487	0.0489511	0.0244755	−	0.999700i	$-0.492208\pi$
$547$	1.14487	0.0489511	0.0244755	+	0.999700i	$0.492208\pi$
$548$	−39.4365	−1.68464
$549$	0.300413	0.0128213
$550$	−37.3690	−1.59342
$551$	−6.88590	−0.293349
$552$	2.90290	0.123556
$553$	−68.1458	−2.89785
$554$	−14.4283	−0.613000
$555$	−6.95659	−0.295291
$556$	25.5075	1.08176
$557$	31.8816	1.35087	0.675434	−	0.737420i	$-0.263956\pi$
$557$	31.8816	1.35087	0.675434	+	0.737420i	$0.263956\pi$
$558$	−0.335427	−0.0141998
$559$	−2.60026	−0.109979
$560$	11.9563	0.505247
$561$	−49.3773	−2.08471
$562$	−65.2858	−2.75391
$563$	26.4741	1.11575	0.557875	−	0.829925i	$-0.311617\pi$
$563$	26.4741	1.11575	0.557875	+	0.829925i	$0.311617\pi$
$564$	−31.8179	−1.33977
$565$	−5.74758	−0.241802
$566$	−17.6652	−0.742523
$567$	40.3474	1.69443
$568$	−15.2521	−0.639962
$569$	11.7137	0.491062	0.245531	−	0.969389i	$-0.421038\pi$
$569$	11.7137	0.491062	0.245531	+	0.969389i	$0.421038\pi$
$570$	4.83597	0.202557
$571$	−23.4049	−0.979464	−0.489732	−	0.871873i	$-0.662905\pi$
$571$	−23.4049	−0.979464	−0.489732	+	0.871873i	$0.662905\pi$
$572$	9.42695	0.394160
$573$	1.31676	0.0550083
$574$	103.213	4.30803
$575$	−4.02036	−0.167661
$576$	−3.01815	−0.125756
$577$	−9.56610	−0.398242	−0.199121	−	0.979975i	$-0.563809\pi$
$577$	−9.56610	−0.398242	−0.199121	+	0.979975i	$0.563809\pi$
$578$	−27.2959	−1.13536
$579$	30.7109	1.27630
$580$	−22.6445	−0.940262
$581$	18.5049	0.767713
$582$	−40.9891	−1.69905
$583$	−23.0487	−0.954581
$584$	0.616894	0.0255272
$585$	−0.221468	−0.00915656
$586$	22.9036	0.946137
$587$	−16.4407	−0.678580	−0.339290	−	0.940682i	$-0.610187\pi$
$587$	−16.4407	−0.678580	−0.339290	+	0.940682i	$0.610187\pi$
$588$	−49.2454	−2.03085
$589$	0.621318	0.0256010
$590$	−6.58330	−0.271030
$591$	11.0341	0.453881
$592$	−7.14677	−0.293730
$593$	−22.2917	−0.915409	−0.457704	−	0.889104i	$-0.651328\pi$
$593$	−22.2917	−0.915409	−0.457704	+	0.889104i	$0.651328\pi$
$594$	53.6943	2.20311
$595$	28.2409	1.15777
$596$	6.87753	0.281715
$597$	−21.5447	−0.881766
$598$	1.78215	0.0728777
$599$	31.4561	1.28526	0.642630	−	0.766176i	$-0.277843\pi$
$599$	31.4561	1.28526	0.642630	+	0.766176i	$0.277843\pi$
$600$	−8.59360	−0.350832
$601$	−27.3705	−1.11647	−0.558234	−	0.829684i	$-0.688521\pi$
$601$	−27.3705	−1.11647	−0.558234	+	0.829684i	$0.688521\pi$
$602$	32.8633	1.33941
$603$	−0.864864	−0.0352200
$604$	4.73836	0.192801
$605$	17.7790	0.722819
$606$	15.7115	0.638235
$607$	29.6965	1.20534	0.602672	−	0.797989i	$-0.294103\pi$
$607$	29.6965	1.20534	0.602672	+	0.797989i	$0.294103\pi$
$608$	7.73143	0.313551
$609$	−51.6987	−2.09494
$610$	−3.21556	−0.130194
$611$	−4.74279	−0.191873
$612$	−3.60531	−0.145736
$613$	−35.5322	−1.43513	−0.717565	−	0.696491i	$-0.754743\pi$
$613$	−35.5322	−1.43513	−0.717565	+	0.696491i	$0.754743\pi$
$614$	−19.1665	−0.773497
$615$	−25.8250	−1.04136
$616$	−28.9278	−1.16553
$617$	32.7967	1.32035	0.660173	−	0.751114i	$-0.270483\pi$
$617$	32.7967	1.32035	0.660173	+	0.751114i	$0.270483\pi$
$618$	10.7036	0.430560
$619$	6.13454	0.246568	0.123284	−	0.992371i	$-0.460657\pi$
$619$	6.13454	0.246568	0.123284	+	0.992371i	$0.460657\pi$
$620$	2.04323	0.0820579
$621$	5.77673	0.231812
$622$	5.63172	0.225811
$623$	29.3514	1.17594
$624$	−2.95136	−0.118149
$625$	4.15108	0.166043
$626$	−23.9595	−0.957613
$627$	9.06502	0.362022
$628$	−14.9527	−0.596677
$629$	−16.8807	−0.673079
$630$	2.79901	0.111515
$631$	47.7349	1.90029	0.950147	−	0.311801i	$-0.100932\pi$
$631$	47.7349	1.90029	0.950147	+	0.311801i	$0.100932\pi$
$632$	−22.6095	−0.899358
$633$	−20.5477	−0.816699
$634$	−2.15437	−0.0855610
$635$	−9.72529	−0.385937
$636$	−21.8303	−0.865629
$637$	−7.34055	−0.290843
$638$	−74.5879	−2.95296
$639$	2.76632	0.109434
$640$	13.0539	0.516001
$641$	14.0392	0.554517	0.277258	−	0.960795i	$-0.410574\pi$
$641$	14.0392	0.554517	0.277258	+	0.960795i	$0.410574\pi$
$642$	18.0358	0.711818
$643$	−34.0070	−1.34111	−0.670554	−	0.741861i	$-0.733943\pi$
$643$	−34.0070	−1.34111	−0.670554	+	0.741861i	$0.733943\pi$
$644$	−12.8180	−0.505098
$645$	−8.22274	−0.323770
$646$	11.7349	0.461703
$647$	−1.36869	−0.0538087	−0.0269043	−	0.999638i	$-0.508565\pi$
$647$	−1.36869	−0.0538087	−0.0269043	+	0.999638i	$0.508565\pi$
$648$	13.3865	0.525872
$649$	−12.3404	−0.484402
$650$	−5.27580	−0.206934
$651$	4.66480	0.182828
$652$	34.8620	1.36530
$653$	−44.8400	−1.75473	−0.877363	−	0.479827i	$-0.840700\pi$
$653$	−44.8400	−1.75473	−0.877363	+	0.479827i	$0.840700\pi$
$654$	5.33914	0.208777
$655$	4.13569	0.161595
$656$	−26.5310	−1.03586
$657$	−0.111888	−0.00436518
$658$	59.9416	2.33677
$659$	31.0456	1.20937	0.604683	−	0.796466i	$-0.293300\pi$
$659$	31.0456	1.20937	0.604683	+	0.796466i	$0.293300\pi$
$660$	29.8106	1.16038
$661$	4.26023	0.165704	0.0828519	−	0.996562i	$-0.473597\pi$
$661$	4.26023	0.165704	0.0828519	+	0.996562i	$0.473597\pi$
$662$	76.5357	2.97464
$663$	−6.97114	−0.270737
$664$	6.13959	0.238262
$665$	−5.18466	−0.201052
$666$	−1.67308	−0.0648306
$667$	−8.02457	−0.310713
$668$	−10.3753	−0.401434
$669$	47.8507	1.85001
$670$	9.25735	0.357643
$671$	−6.02756	−0.232691
$672$	58.0468	2.23921
$673$	−9.70112	−0.373951	−0.186975	−	0.982365i	$-0.559868\pi$
$673$	−9.70112	−0.373951	−0.186975	+	0.982365i	$0.559868\pi$
$674$	53.4201	2.05766
$675$	−17.1011	−0.658223
$676$	−33.0061	−1.26947
$677$	45.3925	1.74457	0.872287	−	0.488994i	$-0.162636\pi$
$677$	45.3925	1.74457	0.872287	+	0.488994i	$0.162636\pi$
$678$	−17.9310	−0.688635
$679$	43.9445	1.68643
$680$	9.36982	0.359316
$681$	−28.6989	−1.09975
$682$	6.73011	0.257709
$683$	13.0354	0.498786	0.249393	−	0.968402i	$-0.419769\pi$
$683$	13.0354	0.498786	0.249393	+	0.968402i	$0.419769\pi$
$684$	0.661887	0.0253079
$685$	−18.5892	−0.710257
$686$	29.9738	1.14440
$687$	−44.0374	−1.68013
$688$	−8.44754	−0.322059
$689$	−3.25404	−0.123969
$690$	5.63567	0.214546
$691$	−48.6737	−1.85164	−0.925818	−	0.377970i	$-0.876622\pi$
$691$	−48.6737	−1.85164	−0.925818	+	0.377970i	$0.876622\pi$
$692$	−57.0593	−2.16907
$693$	5.24674	0.199307
$694$	−56.1726	−2.13228
$695$	12.0235	0.456077
$696$	−17.1527	−0.650170
$697$	−62.6665	−2.37366
$698$	−39.4049	−1.49150
$699$	−11.3636	−0.429810
$700$	37.9456	1.43421
$701$	42.8785	1.61950	0.809750	−	0.586775i	$-0.199603\pi$
$701$	42.8785	1.61950	0.809750	+	0.586775i	$0.199603\pi$
$702$	7.58062	0.286112
$703$	3.09908	0.116884
$704$	60.5570	2.28233
$705$	−14.9980	−0.564858
$706$	24.4215	0.919115
$707$	−16.8443	−0.633495
$708$	−11.6880	−0.439263
$709$	34.1037	1.28079	0.640395	−	0.768046i	$-0.278771\pi$
$709$	34.1037	1.28079	0.640395	+	0.768046i	$0.278771\pi$
$710$	−29.6102	−1.11125
$711$	4.10077	0.153791
$712$	9.73826	0.364957
$713$	0.724061	0.0271163
$714$	88.1045	3.29723
$715$	4.44359	0.166181
$716$	3.82976	0.143125
$717$	−2.10508	−0.0786155
$718$	16.7879	0.626517
$719$	−1.59254	−0.0593916	−0.0296958	−	0.999559i	$-0.509454\pi$
$719$	−1.59254	−0.0593916	−0.0296958	+	0.999559i	$0.509454\pi$
$720$	−0.719488	−0.0268138
$721$	−11.4753	−0.427363
$722$	−2.15437	−0.0801774
$723$	−21.6501	−0.805176
$724$	−2.21404	−0.0822842
$725$	23.7555	0.882258
$726$	55.4659	2.05853
$727$	44.1806	1.63857	0.819284	−	0.573387i	$-0.194371\pi$
$727$	44.1806	1.63857	0.819284	+	0.573387i	$0.194371\pi$
$728$	−4.08405	−0.151365
$729$	24.3837	0.903098
$730$	1.19763	0.0443264
$731$	−19.9532	−0.737995
$732$	−5.70893	−0.211008
$733$	−17.8095	−0.657809	−0.328905	−	0.944363i	$-0.606680\pi$
$733$	−17.8095	−0.657809	−0.328905	+	0.944363i	$0.606680\pi$
$734$	45.9327	1.69541
$735$	−23.2128	−0.856218
$736$	9.00992	0.332110
$737$	17.3529	0.639201
$738$	−6.21100	−0.228630
$739$	−18.9060	−0.695467	−0.347733	−	0.937593i	$-0.613049\pi$
$739$	−18.9060	−0.695467	−0.347733	+	0.937593i	$0.613049\pi$
$740$	10.1914	0.374644
$741$	1.27981	0.0470149
$742$	41.1261	1.50979
$743$	21.5779	0.791617	0.395809	−	0.918333i	$-0.370464\pi$
$743$	21.5779	0.791617	0.395809	+	0.918333i	$0.370464\pi$
$744$	1.54769	0.0567412
$745$	3.24187	0.118773
$746$	60.7848	2.22549
$747$	−1.11356	−0.0407430
$748$	72.3379	2.64494
$749$	−19.3363	−0.706532
$750$	−40.8634	−1.49212
$751$	−44.2983	−1.61647	−0.808234	−	0.588861i	$-0.799577\pi$
$751$	−44.2983	−1.61647	−0.808234	+	0.588861i	$0.799577\pi$
$752$	−15.4081	−0.561874
$753$	17.8367	0.650004
$754$	−10.5304	−0.383494
$755$	2.23352	0.0812862
$756$	−54.5228	−1.98297
$757$	−17.3868	−0.631933	−0.315967	−	0.948770i	$-0.602329\pi$
$757$	−17.3868	−0.631933	−0.315967	+	0.948770i	$0.602329\pi$
$758$	−35.5484	−1.29118
$759$	10.5640	0.383450
$760$	−1.72017	−0.0623972
$761$	−14.8099	−0.536859	−0.268429	−	0.963299i	$-0.586505\pi$
$761$	−14.8099	−0.536859	−0.268429	+	0.963299i	$0.586505\pi$
$762$	−30.3404	−1.09912
$763$	−5.72410	−0.207226
$764$	−1.92905	−0.0697907
$765$	−1.69944	−0.0614433
$766$	−32.6163	−1.17847
$767$	−1.74223	−0.0629082
$768$	−2.70496	−0.0976070
$769$	8.08473	0.291543	0.145771	−	0.989318i	$-0.453434\pi$
$769$	8.08473	0.291543	0.145771	+	0.989318i	$0.453434\pi$
$770$	−56.1601	−2.02387
$771$	−57.3588	−2.06573
$772$	−44.9916	−1.61928
$773$	−29.6420	−1.06615	−0.533074	−	0.846068i	$-0.678963\pi$
$773$	−29.6420	−1.06615	−0.533074	+	0.846068i	$0.678963\pi$
$774$	−1.97760	−0.0710832
$775$	−2.14347	−0.0769959
$776$	14.5800	0.523390
$777$	23.2676	0.834720
$778$	−5.34966	−0.191795
$779$	11.5047	0.412200
$780$	4.20869	0.150695
$781$	−55.5042	−1.98610
$782$	13.6754	0.489032
$783$	−34.1335	−1.21983
$784$	−23.8474	−0.851694
$785$	−7.04826	−0.251563
$786$	12.9023	0.460210
$787$	−38.5571	−1.37441	−0.687205	−	0.726463i	$-0.741163\pi$
$787$	−38.5571	−1.37441	−0.687205	+	0.726463i	$0.741163\pi$
$788$	−16.1649	−0.575852
$789$	−11.5969	−0.412862
$790$	−43.8939	−1.56168
$791$	19.2238	0.683521
$792$	1.74077	0.0618556
$793$	−0.850977	−0.0302191
$794$	72.0571	2.55721
$795$	−10.2902	−0.364955
$796$	31.5630	1.11872
$797$	−17.0600	−0.604296	−0.302148	−	0.953261i	$-0.597704\pi$
$797$	−17.0600	−0.604296	−0.302148	+	0.953261i	$0.597704\pi$
$798$	−16.1748	−0.572582
$799$	−36.3940	−1.28753
$800$	−26.6725	−0.943016
$801$	−1.76626	−0.0624079
$802$	−78.2733	−2.76392
$803$	2.24496	0.0792228
$804$	16.4356	0.579638
$805$	−6.04201	−0.212953
$806$	0.950163	0.0334681
$807$	3.16295	0.111341
$808$	−5.58862	−0.196607
$809$	19.2155	0.675579	0.337790	−	0.941222i	$-0.390321\pi$
$809$	19.2155	0.675579	0.337790	+	0.941222i	$0.390321\pi$
$810$	25.9885	0.913142
$811$	2.89661	0.101714	0.0508568	−	0.998706i	$-0.483805\pi$
$811$	2.89661	0.101714	0.0508568	+	0.998706i	$0.483805\pi$
$812$	75.7387	2.65791
$813$	2.38241	0.0835548
$814$	33.5692	1.17660
$815$	16.4329	0.575620
$816$	−22.6473	−0.792816
$817$	3.66314	0.128157
$818$	−8.23073	−0.287781
$819$	0.740740	0.0258835
$820$	37.8337	1.32121
$821$	−33.5853	−1.17214	−0.586068	−	0.810262i	$-0.699325\pi$
$821$	−33.5853	−1.17214	−0.586068	+	0.810262i	$0.699325\pi$
$822$	−57.9936	−2.02276
$823$	−39.3337	−1.37109	−0.685544	−	0.728031i	$-0.740436\pi$
$823$	−39.3337	−1.37109	−0.685544	+	0.728031i	$0.740436\pi$
$824$	−3.80730	−0.132633
$825$	−31.2732	−1.08879
$826$	22.0191	0.766142
$827$	−32.0464	−1.11436	−0.557182	−	0.830391i	$-0.688117\pi$
$827$	−32.0464	−1.11436	−0.557182	+	0.830391i	$0.688117\pi$
$828$	0.771338	0.0268059
$829$	−31.5813	−1.09686	−0.548432	−	0.836195i	$-0.684775\pi$
$829$	−31.5813	−1.09686	−0.548432	+	0.836195i	$0.684775\pi$
$830$	11.9193	0.413726
$831$	−12.0747	−0.418866
$832$	8.54950	0.296401
$833$	−56.3279	−1.95165
$834$	37.5102	1.29887
$835$	−4.89064	−0.169247
$836$	−13.2803	−0.459308
$837$	3.07989	0.106456
$838$	−25.2579	−0.872521
$839$	−19.7550	−0.682019	−0.341009	−	0.940060i	$-0.610769\pi$
$839$	−19.7550	−0.682019	−0.341009	+	0.940060i	$0.610769\pi$
$840$	−12.9149	−0.445606
$841$	18.4156	0.635020
$842$	84.8443	2.92393
$843$	−54.6360	−1.88177
$844$	30.1025	1.03617
$845$	−15.5581	−0.535216
$846$	−3.60707	−0.124014
$847$	−59.4651	−2.04325
$848$	−10.5715	−0.363027
$849$	−14.7835	−0.507370
$850$	−40.4840	−1.38859
$851$	3.61155	0.123802
$852$	−52.5702	−1.80102
$853$	3.92386	0.134350	0.0671752	−	0.997741i	$-0.478601\pi$
$853$	3.92386	0.134350	0.0671752	+	0.997741i	$0.478601\pi$
$854$	10.7550	0.368030
$855$	0.311994	0.0106700
$856$	−6.41541	−0.219274
$857$	45.9583	1.56991	0.784953	−	0.619555i	$-0.212687\pi$
$857$	45.9583	1.56991	0.784953	+	0.619555i	$0.212687\pi$
$858$	13.8629	0.473270
$859$	−9.17457	−0.313032	−0.156516	−	0.987675i	$-0.550026\pi$
$859$	−9.17457	−0.313032	−0.156516	+	0.987675i	$0.550026\pi$
$860$	12.0463	0.410777
$861$	86.3765	2.94370
$862$	14.2246	0.484491
$863$	−19.1413	−0.651579	−0.325790	−	0.945442i	$-0.605630\pi$
$863$	−19.1413	−0.651579	−0.325790	+	0.945442i	$0.605630\pi$
$864$	38.3248	1.30384
$865$	−26.8961	−0.914495
$866$	10.0062	0.340024
$867$	−22.8433	−0.775798
$868$	−6.83394	−0.231959
$869$	−82.2790	−2.79112
$870$	−33.3000	−1.12898
$871$	2.44990	0.0830115
$872$	−1.89915	−0.0643133
$873$	−2.64442	−0.0895001
$874$	−2.51062	−0.0849231
$875$	43.8098	1.48104
$876$	2.12628	0.0718405
$877$	17.1002	0.577432	0.288716	−	0.957415i	$-0.406772\pi$
$877$	17.1002	0.577432	0.288716	+	0.957415i	$0.406772\pi$
$878$	−5.89538	−0.198959
$879$	19.1674	0.646501
$880$	14.4360	0.486638
$881$	−35.3981	−1.19259	−0.596296	−	0.802765i	$-0.703362\pi$
$881$	−35.3981	−1.19259	−0.596296	+	0.802765i	$0.703362\pi$
$882$	−5.58276	−0.187981
$883$	17.4055	0.585743	0.292872	−	0.956152i	$-0.405389\pi$
$883$	17.4055	0.585743	0.292872	+	0.956152i	$0.405389\pi$
$884$	10.2127	0.343492
$885$	−5.50940	−0.185197
$886$	27.3383	0.918448
$887$	1.18258	0.0397072	0.0198536	−	0.999803i	$-0.493680\pi$
$887$	1.18258	0.0397072	0.0198536	+	0.999803i	$0.493680\pi$
$888$	7.71975	0.259058
$889$	32.5280	1.09096
$890$	18.9058	0.633723
$891$	48.7153	1.63202
$892$	−70.1014	−2.34717
$893$	6.68145	0.223586
$894$	10.1138	0.338256
$895$	1.80524	0.0603425
$896$	−43.6612	−1.45862
$897$	1.49144	0.0497978
$898$	19.3054	0.644229
$899$	−4.27833	−0.142690
$900$	−2.28343	−0.0761144
$901$	−24.9700	−0.831871
$902$	124.619	4.14936
$903$	27.5025	0.915225
$904$	6.37811	0.212133
$905$	−1.04364	−0.0346916
$906$	6.96802	0.231497
$907$	12.7765	0.424236	0.212118	−	0.977244i	$-0.431964\pi$
$907$	12.7765	0.424236	0.212118	+	0.977244i	$0.431964\pi$
$908$	42.0440	1.39528
$909$	1.01363	0.0336200
$910$	−7.92874	−0.262835
$911$	57.2754	1.89762	0.948810	−	0.315848i	$-0.102289\pi$
$911$	57.2754	1.89762	0.948810	+	0.315848i	$0.102289\pi$
$912$	4.15775	0.137677
$913$	22.3428	0.739438
$914$	−46.6194	−1.54203
$915$	−2.69102	−0.0889625
$916$	64.5149	2.13163
$917$	−13.8326	−0.456792
$918$	58.1701	1.91990
$919$	48.7278	1.60738	0.803691	−	0.595047i	$-0.202867\pi$
$919$	48.7278	1.60738	0.803691	+	0.595047i	$0.202867\pi$
$920$	−2.00463	−0.0660906
$921$	−16.0400	−0.528535
$922$	−0.166308	−0.00547706
$923$	−7.83614	−0.257930
$924$	−99.7071	−3.28012
$925$	−10.6914	−0.351533
$926$	71.2714	2.34212
$927$	0.690543	0.0226804
$928$	−53.2378	−1.74762
$929$	38.7567	1.27156	0.635782	−	0.771868i	$-0.280678\pi$
$929$	38.7567	1.27156	0.635782	+	0.771868i	$0.280678\pi$
$930$	3.00468	0.0985273
$931$	10.3411	0.338914
$932$	16.6477	0.545312
$933$	4.71304	0.154298
$934$	−77.9755	−2.55144
$935$	34.0980	1.11512
$936$	0.245764	0.00803304
$937$	−42.0300	−1.37306	−0.686529	−	0.727102i	$-0.740867\pi$
$937$	−42.0300	−1.37306	−0.686529	+	0.727102i	$0.740867\pi$
$938$	−30.9629	−1.01097
$939$	−20.0511	−0.654343
$940$	21.9722	0.716653
$941$	14.3884	0.469047	0.234524	−	0.972110i	$-0.424647\pi$
$941$	14.3884	0.469047	0.234524	+	0.972110i	$0.424647\pi$
$942$	−21.9888	−0.716433
$943$	13.4072	0.436598
$944$	−5.66002	−0.184218
$945$	−25.7005	−0.836036
$946$	39.6790	1.29008
$947$	17.7782	0.577712	0.288856	−	0.957373i	$-0.406725\pi$
$947$	17.7782	0.577712	0.288856	+	0.957373i	$0.406725\pi$
$948$	−77.9296	−2.53103
$949$	0.316945	0.0102885
$950$	7.43232	0.241136
$951$	−1.80294	−0.0584643
$952$	−31.3391	−1.01571
$953$	44.2608	1.43375	0.716874	−	0.697203i	$-0.245572\pi$
$953$	44.2608	1.43375	0.716874	+	0.697203i	$0.245572\pi$
$954$	−2.47482	−0.0801253
$955$	−0.909300	−0.0294242
$956$	3.08394	0.0997418
$957$	−62.4208	−2.01778
$958$	4.60772	0.148869
$959$	62.1750	2.00774
$960$	27.0359	0.872580
$961$	−30.6140	−0.987547
$962$	4.73933	0.152802
$963$	1.16359	0.0374961
$964$	31.7175	1.02155
$965$	−21.2077	−0.682701
$966$	−18.8495	−0.606473
$967$	20.7630	0.667692	0.333846	−	0.942628i	$-0.391653\pi$
$967$	20.7630	0.667692	0.333846	+	0.942628i	$0.391653\pi$
$968$	−19.7294	−0.634128
$969$	9.82064	0.315485
$970$	28.3054	0.908832
$971$	18.1237	0.581618	0.290809	−	0.956781i	$-0.406076\pi$
$971$	18.1237	0.581618	0.290809	+	0.956781i	$0.406076\pi$
$972$	6.86101	0.220067
$973$	−40.2148	−1.28923
$974$	34.3930	1.10202
$975$	−4.41519	−0.141399
$976$	−2.76459	−0.0884925
$977$	8.52423	0.272714	0.136357	−	0.990660i	$-0.456461\pi$
$977$	8.52423	0.272714	0.136357	+	0.990660i	$0.456461\pi$
$978$	51.2665	1.63932
$979$	35.4388	1.13263
$980$	34.0069	1.08631
$981$	0.344456	0.0109976
$982$	49.3310	1.57422
$983$	−41.6592	−1.32872	−0.664362	−	0.747411i	$-0.731297\pi$
$983$	−41.6592	−1.32872	−0.664362	+	0.747411i	$0.731297\pi$
$984$	28.6581	0.913587
$985$	−7.61968	−0.242783
$986$	−80.8053	−2.57337
$987$	50.1637	1.59673
$988$	−1.87492	−0.0596493
$989$	4.26888	0.135743
$990$	3.37952	0.107408
$991$	−1.63739	−0.0520134	−0.0260067	−	0.999662i	$-0.508279\pi$
$991$	−1.63739	−0.0520134	−0.0260067	+	0.999662i	$0.508279\pi$
$992$	4.80368	0.152517
$993$	64.0508	2.03259
$994$	99.0368	3.14126
$995$	14.8779	0.471661
$996$	21.1617	0.670534
$997$	10.3964	0.329258	0.164629	−	0.986356i	$-0.447357\pi$
$997$	10.3964	0.329258	0.164629	+	0.986356i	$0.447357\pi$
$998$	−4.79238	−0.151700
$999$	15.3622	0.486038

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.a.1.15	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.a.1.15	✓	98	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.15437 q^{2} -1.80294 q^{3} +2.64131 q^{4} +1.24504 q^{5} +3.88420 q^{6} -4.16426 q^{7} -1.38162 q^{8} +0.250590 q^{9} +O(q^{10})\)	\(q-2.15437 q^{2} -1.80294 q^{3} +2.64131 q^{4} +1.24504 q^{5} +3.88420 q^{6} -4.16426 q^{7} -1.38162 q^{8} +0.250590 q^{9} -2.68227 q^{10} -5.02791 q^{11} -4.76213 q^{12} -0.709845 q^{13} +8.97136 q^{14} -2.24473 q^{15} -2.30610 q^{16} -5.44702 q^{17} -0.539864 q^{18} +1.00000 q^{19} +3.28853 q^{20} +7.50791 q^{21} +10.8320 q^{22} +1.16536 q^{23} +2.49098 q^{24} -3.44988 q^{25} +1.52927 q^{26} +4.95702 q^{27} -10.9991 q^{28} -6.88590 q^{29} +4.83597 q^{30} +0.621318 q^{31} +7.73143 q^{32} +9.06502 q^{33} +11.7349 q^{34} -5.18466 q^{35} +0.661887 q^{36} +3.09908 q^{37} -2.15437 q^{38} +1.27981 q^{39} -1.72017 q^{40} +11.5047 q^{41} -16.1748 q^{42} +3.66314 q^{43} -13.2803 q^{44} +0.311994 q^{45} -2.51062 q^{46} +6.68145 q^{47} +4.15775 q^{48} +10.3411 q^{49} +7.43232 q^{50} +9.82064 q^{51} -1.87492 q^{52} +4.58416 q^{53} -10.6793 q^{54} -6.25994 q^{55} +5.75344 q^{56} -1.80294 q^{57} +14.8348 q^{58} +2.45438 q^{59} -5.92903 q^{60} +1.19882 q^{61} -1.33855 q^{62} -1.04352 q^{63} -12.0442 q^{64} -0.883784 q^{65} -19.5294 q^{66} -3.45131 q^{67} -14.3873 q^{68} -2.10108 q^{69} +11.1697 q^{70} +11.0392 q^{71} -0.346221 q^{72} -0.446499 q^{73} -6.67656 q^{74} +6.21993 q^{75} +2.64131 q^{76} +20.9375 q^{77} -2.75718 q^{78} +16.3644 q^{79} -2.87118 q^{80} -9.68898 q^{81} -24.7855 q^{82} -4.44375 q^{83} +19.8307 q^{84} -6.78174 q^{85} -7.89175 q^{86} +12.4149 q^{87} +6.94668 q^{88} -7.04842 q^{89} -0.672151 q^{90} +2.95598 q^{91} +3.07809 q^{92} -1.12020 q^{93} -14.3943 q^{94} +1.24504 q^{95} -13.9393 q^{96} -10.5528 q^{97} -22.2785 q^{98} -1.25995 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9}+O(q^{10}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9} - 24 q^{10} - 12 q^{11} - 51 q^{12} - 58 q^{13} - 15 q^{14} - 18 q^{15} + 58 q^{16} - 25 q^{17} - 40 q^{18} + 98 q^{19} - 12 q^{20} - 24 q^{21} - 59 q^{22} - 38 q^{23} - 9 q^{24} - 12 q^{25} - 3 q^{26} - 85 q^{27} - 33 q^{28} - 24 q^{29} - 22 q^{30} - 56 q^{31} - 29 q^{32} - 51 q^{33} - 38 q^{34} - 10 q^{35} + 50 q^{36} - 124 q^{37} - 8 q^{38} - 4 q^{39} - 80 q^{40} - 28 q^{41} - 37 q^{42} - 63 q^{43} - 7 q^{44} - 32 q^{45} - 47 q^{46} - 10 q^{47} - 88 q^{48} + 6 q^{49} - 17 q^{50} - 22 q^{51} - 119 q^{52} - 65 q^{53} + 24 q^{54} - 30 q^{55} - 39 q^{56} - 25 q^{57} - 91 q^{58} - 26 q^{59} - 60 q^{60} - 60 q^{61} + 6 q^{62} - 26 q^{63} + 50 q^{64} - 40 q^{65} + 57 q^{66} - 108 q^{67} - 41 q^{68} - 15 q^{69} - 36 q^{70} - 19 q^{71} - 47 q^{72} - 136 q^{73} + 22 q^{74} - 48 q^{75} + 82 q^{76} - 35 q^{77} - 56 q^{78} - 98 q^{79} - 42 q^{80} + 6 q^{81} - 37 q^{82} - 31 q^{83} - 24 q^{84} - 71 q^{85} - 24 q^{86} + 7 q^{87} - 166 q^{88} - 38 q^{89} + 26 q^{90} - 100 q^{91} - 59 q^{92} - 21 q^{93} - 48 q^{94} - 10 q^{95} - 16 q^{96} - 190 q^{97} - 80 q^{98} - 17 q^{99}+O(q^{100}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9 - 24 * q^10 - 12 * q^11 - 51 * q^12 - 58 * q^13 - 15 * q^14 - 18 * q^15 + 58 * q^16 - 25 * q^17 - 40 * q^18 + 98 * q^19 - 12 * q^20 - 24 * q^21 - 59 * q^22 - 38 * q^23 - 9 * q^24 - 12 * q^25 - 3 * q^26 - 85 * q^27 - 33 * q^28 - 24 * q^29 - 22 * q^30 - 56 * q^31 - 29 * q^32 - 51 * q^33 - 38 * q^34 - 10 * q^35 + 50 * q^36 - 124 * q^37 - 8 * q^38 - 4 * q^39 - 80 * q^40 - 28 * q^41 - 37 * q^42 - 63 * q^43 - 7 * q^44 - 32 * q^45 - 47 * q^46 - 10 * q^47 - 88 * q^48 + 6 * q^49 - 17 * q^50 - 22 * q^51 - 119 * q^52 - 65 * q^53 + 24 * q^54 - 30 * q^55 - 39 * q^56 - 25 * q^57 - 91 * q^58 - 26 * q^59 - 60 * q^60 - 60 * q^61 + 6 * q^62 - 26 * q^63 + 50 * q^64 - 40 * q^65 + 57 * q^66 - 108 * q^67 - 41 * q^68 - 15 * q^69 - 36 * q^70 - 19 * q^71 - 47 * q^72 - 136 * q^73 + 22 * q^74 - 48 * q^75 + 82 * q^76 - 35 * q^77 - 56 * q^78 - 98 * q^79 - 42 * q^80 + 6 * q^81 - 37 * q^82 - 31 * q^83 - 24 * q^84 - 71 * q^85 - 24 * q^86 + 7 * q^87 - 166 * q^88 - 38 * q^89 + 26 * q^90 - 100 * q^91 - 59 * q^92 - 21 * q^93 - 48 * q^94 - 10 * q^95 - 16 * q^96 - 190 * q^97 - 80 * q^98 - 17 * q^99

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