LMFDB - Embedded newform 4017.2.a.j.1.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.22
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.45725 q^{2} -1.00000 q^{3} +4.03807 q^{4} +1.82467 q^{5} -2.45725 q^{6} +1.71478 q^{7} +5.00803 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.45725 q^{2} -1.00000 q^{3} +4.03807 q^{4} +1.82467 q^{5} -2.45725 q^{6} +1.71478 q^{7} +5.00803 q^{8} +1.00000 q^{9} +4.48366 q^{10} -2.47217 q^{11} -4.03807 q^{12} +1.00000 q^{13} +4.21365 q^{14} -1.82467 q^{15} +4.22984 q^{16} +2.10209 q^{17} +2.45725 q^{18} +5.03790 q^{19} +7.36812 q^{20} -1.71478 q^{21} -6.07475 q^{22} -4.48018 q^{23} -5.00803 q^{24} -1.67059 q^{25} +2.45725 q^{26} -1.00000 q^{27} +6.92441 q^{28} +2.41624 q^{29} -4.48366 q^{30} +8.42140 q^{31} +0.377710 q^{32} +2.47217 q^{33} +5.16535 q^{34} +3.12891 q^{35} +4.03807 q^{36} +5.69321 q^{37} +12.3794 q^{38} -1.00000 q^{39} +9.13799 q^{40} +11.1071 q^{41} -4.21365 q^{42} -2.64739 q^{43} -9.98280 q^{44} +1.82467 q^{45} -11.0089 q^{46} +6.04114 q^{47} -4.22984 q^{48} -4.05952 q^{49} -4.10506 q^{50} -2.10209 q^{51} +4.03807 q^{52} -1.63456 q^{53} -2.45725 q^{54} -4.51089 q^{55} +8.58769 q^{56} -5.03790 q^{57} +5.93731 q^{58} +2.39601 q^{59} -7.36812 q^{60} -10.8292 q^{61} +20.6935 q^{62} +1.71478 q^{63} -7.53156 q^{64} +1.82467 q^{65} +6.07475 q^{66} -7.49568 q^{67} +8.48837 q^{68} +4.48018 q^{69} +7.68850 q^{70} -1.28480 q^{71} +5.00803 q^{72} +4.77967 q^{73} +13.9896 q^{74} +1.67059 q^{75} +20.3434 q^{76} -4.23924 q^{77} -2.45725 q^{78} +10.3906 q^{79} +7.71805 q^{80} +1.00000 q^{81} +27.2929 q^{82} +5.09703 q^{83} -6.92441 q^{84} +3.83561 q^{85} -6.50529 q^{86} -2.41624 q^{87} -12.3807 q^{88} -5.25191 q^{89} +4.48366 q^{90} +1.71478 q^{91} -18.0913 q^{92} -8.42140 q^{93} +14.8446 q^{94} +9.19248 q^{95} -0.377710 q^{96} -13.6887 q^{97} -9.97524 q^{98} -2.47217 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * 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 $

$2$	2.45725	1.73754	0.868768	−	0.495219i	$-0.164912\pi$
$2$	2.45725	1.73754	0.868768	+	0.495219i	$0.164912\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.03807	2.01903
$5$	1.82467	0.816016	0.408008	−	0.912978i	$-0.366224\pi$
$5$	1.82467	0.816016	0.408008	+	0.912978i	$0.366224\pi$
$6$	−2.45725	−1.00317
$7$	1.71478	0.648127	0.324064	−	0.946035i	$-0.394951\pi$
$7$	1.71478	0.648127	0.324064	+	0.946035i	$0.394951\pi$
$8$	5.00803	1.77061
$9$	1.00000	0.333333
$10$	4.48366	1.41786
$11$	−2.47217	−0.745389	−0.372694	−	0.927954i	$-0.621566\pi$
$11$	−2.47217	−0.745389	−0.372694	+	0.927954i	$0.621566\pi$
$12$	−4.03807	−1.16569
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	4.21365	1.12614
$15$	−1.82467	−0.471127
$16$	4.22984	1.05746
$17$	2.10209	0.509831	0.254916	−	0.966963i	$-0.417952\pi$
$17$	2.10209	0.509831	0.254916	+	0.966963i	$0.417952\pi$
$18$	2.45725	0.579179
$19$	5.03790	1.15577	0.577887	−	0.816117i	$-0.303878\pi$
$19$	5.03790	1.15577	0.577887	+	0.816117i	$0.303878\pi$
$20$	7.36812	1.64756
$21$	−1.71478	−0.374196
$22$	−6.07475	−1.29514
$23$	−4.48018	−0.934183	−0.467091	−	0.884209i	$-0.654698\pi$
$23$	−4.48018	−0.934183	−0.467091	+	0.884209i	$0.654698\pi$
$24$	−5.00803	−1.02226
$25$	−1.67059	−0.334119
$26$	2.45725	0.481906
$27$	−1.00000	−0.192450
$28$	6.92441	1.30859
$29$	2.41624	0.448685	0.224343	−	0.974510i	$-0.427977\pi$
$29$	2.41624	0.448685	0.224343	+	0.974510i	$0.427977\pi$
$30$	−4.48366	−0.818600
$31$	8.42140	1.51253	0.756264	−	0.654266i	$-0.227022\pi$
$31$	8.42140	1.51253	0.756264	+	0.654266i	$0.227022\pi$
$32$	0.377710	0.0667704
$33$	2.47217	0.430350
$34$	5.16535	0.885850
$35$	3.12891	0.528882
$36$	4.03807	0.673011
$37$	5.69321	0.935957	0.467979	−	0.883740i	$-0.344982\pi$
$37$	5.69321	0.935957	0.467979	+	0.883740i	$0.344982\pi$
$38$	12.3794	2.00820
$39$	−1.00000	−0.160128
$40$	9.13799	1.44484
$41$	11.1071	1.73464	0.867319	−	0.497752i	$-0.165841\pi$
$41$	11.1071	1.73464	0.867319	+	0.497752i	$0.165841\pi$
$42$	−4.21365	−0.650180
$43$	−2.64739	−0.403723	−0.201862	−	0.979414i	$-0.564699\pi$
$43$	−2.64739	−0.403723	−0.201862	+	0.979414i	$0.564699\pi$
$44$	−9.98280	−1.50496
$45$	1.82467	0.272005
$46$	−11.0089	−1.62318
$47$	6.04114	0.881190	0.440595	−	0.897706i	$-0.354767\pi$
$47$	6.04114	0.881190	0.440595	+	0.897706i	$0.354767\pi$
$48$	−4.22984	−0.610525
$49$	−4.05952	−0.579931
$50$	−4.10506	−0.580543
$51$	−2.10209	−0.294351
$52$	4.03807	0.559979
$53$	−1.63456	−0.224525	−0.112262	−	0.993679i	$-0.535810\pi$
$53$	−1.63456	−0.224525	−0.112262	+	0.993679i	$0.535810\pi$
$54$	−2.45725	−0.334389
$55$	−4.51089	−0.608249
$56$	8.58769	1.14758
$57$	−5.03790	−0.667286
$58$	5.93731	0.779607
$59$	2.39601	0.311934	0.155967	−	0.987762i	$-0.450151\pi$
$59$	2.39601	0.311934	0.155967	+	0.987762i	$0.450151\pi$
$60$	−7.36812	−0.951221
$61$	−10.8292	−1.38654	−0.693270	−	0.720678i	$-0.743831\pi$
$61$	−10.8292	−1.38654	−0.693270	+	0.720678i	$0.743831\pi$
$62$	20.6935	2.62807
$63$	1.71478	0.216042
$64$	−7.53156	−0.941445
$65$	1.82467	0.226322
$66$	6.07475	0.747749
$67$	−7.49568	−0.915743	−0.457872	−	0.889018i	$-0.651388\pi$
$67$	−7.49568	−0.915743	−0.457872	+	0.889018i	$0.651388\pi$
$68$	8.48837	1.02937
$69$	4.48018	0.539351
$70$	7.68850	0.918952
$71$	−1.28480	−0.152478	−0.0762389	−	0.997090i	$-0.524291\pi$
$71$	−1.28480	−0.152478	−0.0762389	+	0.997090i	$0.524291\pi$
$72$	5.00803	0.590202
$73$	4.77967	0.559418	0.279709	−	0.960085i	$-0.409762\pi$
$73$	4.77967	0.559418	0.279709	+	0.960085i	$0.409762\pi$
$74$	13.9896	1.62626
$75$	1.67059	0.192903
$76$	20.3434	2.33354
$77$	−4.23924	−0.483107
$78$	−2.45725	−0.278229
$79$	10.3906	1.16904	0.584519	−	0.811380i	$-0.301283\pi$
$79$	10.3906	1.16904	0.584519	+	0.811380i	$0.301283\pi$
$80$	7.71805	0.862905
$81$	1.00000	0.111111
$82$	27.2929	3.01400
$83$	5.09703	0.559471	0.279736	−	0.960077i	$-0.409753\pi$
$83$	5.09703	0.559471	0.279736	+	0.960077i	$0.409753\pi$
$84$	−6.92441	−0.755515
$85$	3.83561	0.416030
$86$	−6.50529	−0.701484
$87$	−2.41624	−0.259048
$88$	−12.3807	−1.31979
$89$	−5.25191	−0.556702	−0.278351	−	0.960479i	$-0.589788\pi$
$89$	−5.25191	−0.556702	−0.278351	+	0.960479i	$0.589788\pi$
$90$	4.48366	0.472619
$91$	1.71478	0.179758
$92$	−18.0913	−1.88615
$93$	−8.42140	−0.873259
$94$	14.8446	1.53110
$95$	9.19248	0.943129
$96$	−0.377710	−0.0385499
$97$	−13.6887	−1.38988	−0.694940	−	0.719068i	$-0.744569\pi$
$97$	−13.6887	−1.38988	−0.694940	+	0.719068i	$0.744569\pi$
$98$	−9.97524	−1.00765
$99$	−2.47217	−0.248463
$100$	−6.74596	−0.674596
$101$	−1.97292	−0.196313	−0.0981566	−	0.995171i	$-0.531295\pi$
$101$	−1.97292	−0.196313	−0.0981566	+	0.995171i	$0.531295\pi$
$102$	−5.16535	−0.511446
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	5.00803	0.491078
$105$	−3.12891	−0.305350
$106$	−4.01653	−0.390120
$107$	15.1982	1.46927	0.734634	−	0.678463i	$-0.237354\pi$
$107$	15.1982	1.46927	0.734634	+	0.678463i	$0.237354\pi$
$108$	−4.03807	−0.388563
$109$	−18.2958	−1.75242	−0.876208	−	0.481933i	$-0.839935\pi$
$109$	−18.2958	−1.75242	−0.876208	+	0.481933i	$0.839935\pi$
$110$	−11.0844	−1.05685
$111$	−5.69321	−0.540375
$112$	7.25327	0.685369
$113$	−10.9011	−1.02549	−0.512743	−	0.858542i	$-0.671371\pi$
$113$	−10.9011	−1.02549	−0.512743	+	0.858542i	$0.671371\pi$
$114$	−12.3794	−1.15943
$115$	−8.17484	−0.762308
$116$	9.75695	0.905910
$117$	1.00000	0.0924500
$118$	5.88758	0.541996
$119$	3.60463	0.330436
$120$	−9.13799	−0.834180
$121$	−4.88835	−0.444396
$122$	−26.6101	−2.40916
$123$	−11.1071	−1.00149
$124$	34.0062	3.05384
$125$	−12.1716	−1.08866
$126$	4.21365	0.375382
$127$	18.0296	1.59987	0.799934	−	0.600088i	$-0.204868\pi$
$127$	18.0296	1.59987	0.799934	+	0.600088i	$0.204868\pi$
$128$	−19.2623	−1.70257
$129$	2.64739	0.233090
$130$	4.48366	0.393243
$131$	7.05989	0.616826	0.308413	−	0.951253i	$-0.400202\pi$
$131$	7.05989	0.616826	0.308413	+	0.951253i	$0.400202\pi$
$132$	9.98280	0.868892
$133$	8.63891	0.749088
$134$	−18.4187	−1.59114
$135$	−1.82467	−0.157042
$136$	10.5273	0.902711
$137$	18.8311	1.60885	0.804424	−	0.594055i	$-0.202474\pi$
$137$	18.8311	1.60885	0.804424	+	0.594055i	$0.202474\pi$
$138$	11.0089	0.937141
$139$	−15.2404	−1.29268	−0.646339	−	0.763051i	$-0.723701\pi$
$139$	−15.2404	−1.29268	−0.646339	+	0.763051i	$0.723701\pi$
$140$	12.6347	1.06783
$141$	−6.04114	−0.508756
$142$	−3.15707	−0.264936
$143$	−2.47217	−0.206734
$144$	4.22984	0.352487
$145$	4.40884	0.366134
$146$	11.7448	0.972009
$147$	4.05952	0.334823
$148$	22.9895	1.88973
$149$	−9.62177	−0.788246	−0.394123	−	0.919058i	$-0.628952\pi$
$149$	−9.62177	−0.788246	−0.394123	+	0.919058i	$0.628952\pi$
$150$	4.10506	0.335177
$151$	−5.21999	−0.424797	−0.212398	−	0.977183i	$-0.568127\pi$
$151$	−5.21999	−0.424797	−0.212398	+	0.977183i	$0.568127\pi$
$152$	25.2300	2.04642
$153$	2.10209	0.169944
$154$	−10.4169	−0.839416
$155$	15.3662	1.23425
$156$	−4.03807	−0.323304
$157$	2.11215	0.168568	0.0842841	−	0.996442i	$-0.473140\pi$
$157$	2.11215	0.168568	0.0842841	+	0.996442i	$0.473140\pi$
$158$	25.5324	2.03125
$159$	1.63456	0.129629
$160$	0.689195	0.0544856
$161$	−7.68254	−0.605469
$162$	2.45725	0.193060
$163$	−22.7611	−1.78279	−0.891393	−	0.453231i	$-0.850271\pi$
$163$	−22.7611	−1.78279	−0.891393	+	0.453231i	$0.850271\pi$
$164$	44.8512	3.50229
$165$	4.51089	0.351173
$166$	12.5247	0.972102
$167$	6.01129	0.465168	0.232584	−	0.972576i	$-0.425282\pi$
$167$	6.01129	0.465168	0.232584	+	0.972576i	$0.425282\pi$
$168$	−8.58769	−0.662555
$169$	1.00000	0.0769231
$170$	9.42504	0.722868
$171$	5.03790	0.385258
$172$	−10.6903	−0.815131
$173$	2.03881	0.155008	0.0775038	−	0.996992i	$-0.475305\pi$
$173$	2.03881	0.155008	0.0775038	+	0.996992i	$0.475305\pi$
$174$	−5.93731	−0.450106
$175$	−2.86471	−0.216551
$176$	−10.4569	−0.788220
$177$	−2.39601	−0.180095
$178$	−12.9053	−0.967290
$179$	25.5086	1.90661	0.953303	−	0.302016i	$-0.0976596\pi$
$179$	25.5086	1.90661	0.953303	+	0.302016i	$0.0976596\pi$
$180$	7.36812	0.549187
$181$	10.2267	0.760147	0.380073	−	0.924956i	$-0.375899\pi$
$181$	10.2267	0.760147	0.380073	+	0.924956i	$0.375899\pi$
$182$	4.21365	0.312336
$183$	10.8292	0.800519
$184$	−22.4369	−1.65407
$185$	10.3882	0.763756
$186$	−20.6935	−1.51732
$187$	−5.19673	−0.380022
$188$	24.3945	1.77915
$189$	−1.71478	−0.124732
$190$	22.5882	1.63872
$191$	−8.37666	−0.606114	−0.303057	−	0.952972i	$-0.598007\pi$
$191$	−8.37666	−0.606114	−0.303057	+	0.952972i	$0.598007\pi$
$192$	7.53156	0.543544
$193$	−15.6923	−1.12956	−0.564779	−	0.825242i	$-0.691039\pi$
$193$	−15.6923	−1.12956	−0.564779	+	0.825242i	$0.691039\pi$
$194$	−33.6366	−2.41497
$195$	−1.82467	−0.130667
$196$	−16.3926	−1.17090
$197$	−11.2707	−0.803001	−0.401501	−	0.915859i	$-0.631511\pi$
$197$	−11.2707	−0.803001	−0.401501	+	0.915859i	$0.631511\pi$
$198$	−6.07475	−0.431713
$199$	−0.778082	−0.0551567	−0.0275784	−	0.999620i	$-0.508780\pi$
$199$	−0.778082	−0.0551567	−0.0275784	+	0.999620i	$0.508780\pi$
$200$	−8.36638	−0.591593
$201$	7.49568	0.528705
$202$	−4.84796	−0.341101
$203$	4.14333	0.290805
$204$	−8.48837	−0.594305
$205$	20.2668	1.41549
$206$	−2.45725	−0.171205
$207$	−4.48018	−0.311394
$208$	4.22984	0.293287
$209$	−12.4546	−0.861500
$210$	−7.68850	−0.530557
$211$	27.4762	1.89154	0.945769	−	0.324840i	$-0.105311\pi$
$211$	27.4762	1.89154	0.945769	+	0.324840i	$0.105311\pi$
$212$	−6.60047	−0.453322
$213$	1.28480	0.0880331
$214$	37.3458	2.55291
$215$	−4.83060	−0.329444
$216$	−5.00803	−0.340753
$217$	14.4409	0.980311
$218$	−44.9572	−3.04489
$219$	−4.77967	−0.322980
$220$	−18.2153	−1.22807
$221$	2.10209	0.141402
$222$	−13.9896	−0.938922
$223$	21.7022	1.45329	0.726643	−	0.687015i	$-0.241079\pi$
$223$	21.7022	1.45329	0.726643	+	0.687015i	$0.241079\pi$
$224$	0.647691	0.0432757
$225$	−1.67059	−0.111373
$226$	−26.7866	−1.78182
$227$	−6.41324	−0.425662	−0.212831	−	0.977089i	$-0.568268\pi$
$227$	−6.41324	−0.425662	−0.212831	+	0.977089i	$0.568268\pi$
$228$	−20.3434	−1.34727
$229$	−18.9532	−1.25247	−0.626233	−	0.779636i	$-0.715404\pi$
$229$	−18.9532	−1.25247	−0.626233	+	0.779636i	$0.715404\pi$
$230$	−20.0876	−1.32454
$231$	4.23924	0.278922
$232$	12.1006	0.794445
$233$	−13.3023	−0.871460	−0.435730	−	0.900077i	$-0.643510\pi$
$233$	−13.3023	−0.871460	−0.435730	+	0.900077i	$0.643510\pi$
$234$	2.45725	0.160635
$235$	11.0231	0.719065
$236$	9.67524	0.629804
$237$	−10.3906	−0.674944
$238$	8.85746	0.574144
$239$	3.37996	0.218631	0.109316	−	0.994007i	$-0.465134\pi$
$239$	3.37996	0.218631	0.109316	+	0.994007i	$0.465134\pi$
$240$	−7.71805	−0.498198
$241$	−6.02414	−0.388049	−0.194025	−	0.980997i	$-0.562154\pi$
$241$	−6.02414	−0.388049	−0.194025	+	0.980997i	$0.562154\pi$
$242$	−12.0119	−0.772154
$243$	−1.00000	−0.0641500
$244$	−43.7291	−2.79947
$245$	−7.40726	−0.473233
$246$	−27.2929	−1.74013
$247$	5.03790	0.320554
$248$	42.1747	2.67809
$249$	−5.09703	−0.323011
$250$	−29.9087	−1.89159
$251$	6.55153	0.413529	0.206764	−	0.978391i	$-0.433707\pi$
$251$	6.55153	0.413529	0.206764	+	0.978391i	$0.433707\pi$
$252$	6.92441	0.436197
$253$	11.0758	0.696329
$254$	44.3032	2.77983
$255$	−3.83561	−0.240195
$256$	−32.2692	−2.01682
$257$	20.5033	1.27896	0.639482	−	0.768806i	$-0.279149\pi$
$257$	20.5033	1.27896	0.639482	+	0.768806i	$0.279149\pi$
$258$	6.50529	0.405002
$259$	9.76262	0.606619
$260$	7.36812	0.456952
$261$	2.41624	0.149562
$262$	17.3479	1.07176
$263$	−17.7020	−1.09155	−0.545775	−	0.837932i	$-0.683765\pi$
$263$	−17.7020	−1.09155	−0.545775	+	0.837932i	$0.683765\pi$
$264$	12.3807	0.761981
$265$	−2.98253	−0.183216
$266$	21.2279	1.30157
$267$	5.25191	0.321412
$268$	−30.2681	−1.84892
$269$	−24.5061	−1.49417	−0.747083	−	0.664731i	$-0.768546\pi$
$269$	−24.5061	−1.49417	−0.747083	+	0.664731i	$0.768546\pi$
$270$	−4.48366	−0.272867
$271$	−26.9728	−1.63848	−0.819240	−	0.573451i	$-0.805604\pi$
$271$	−26.9728	−1.63848	−0.819240	+	0.573451i	$0.805604\pi$
$272$	8.89151	0.539127
$273$	−1.71478	−0.103783
$274$	46.2727	2.79543
$275$	4.13000	0.249048
$276$	18.0913	1.08897
$277$	24.0323	1.44396	0.721980	−	0.691914i	$-0.243232\pi$
$277$	24.0323	1.44396	0.721980	+	0.691914i	$0.243232\pi$
$278$	−37.4495	−2.24607
$279$	8.42140	0.504176
$280$	15.6697	0.936442
$281$	12.5280	0.747359	0.373679	−	0.927558i	$-0.378096\pi$
$281$	12.5280	0.747359	0.373679	+	0.927558i	$0.378096\pi$
$282$	−14.8446	−0.883981
$283$	−30.3643	−1.80497	−0.902485	−	0.430721i	$-0.858259\pi$
$283$	−30.3643	−1.80497	−0.902485	+	0.430721i	$0.858259\pi$
$284$	−5.18811	−0.307858
$285$	−9.19248	−0.544516
$286$	−6.07475	−0.359207
$287$	19.0463	1.12427
$288$	0.377710	0.0222568
$289$	−12.5812	−0.740072
$290$	10.8336	0.636171
$291$	13.6887	0.802448
$292$	19.3006	1.12948
$293$	−29.0186	−1.69529	−0.847644	−	0.530566i	$-0.821979\pi$
$293$	−29.0186	−1.69529	−0.847644	+	0.530566i	$0.821979\pi$
$294$	9.97524	0.581768
$295$	4.37191	0.254543
$296$	28.5118	1.65721
$297$	2.47217	0.143450
$298$	−23.6431	−1.36961
$299$	−4.48018	−0.259096
$300$	6.74596	0.389478
$301$	−4.53970	−0.261664
$302$	−12.8268	−0.738100
$303$	1.97292	0.113341
$304$	21.3095	1.22219
$305$	−19.7597	−1.13144
$306$	5.16535	0.295283
$307$	−30.0178	−1.71321	−0.856603	−	0.515976i	$-0.827429\pi$
$307$	−30.0178	−1.71321	−0.856603	+	0.515976i	$0.827429\pi$
$308$	−17.1183	−0.975409
$309$	1.00000	0.0568880
$310$	37.7587	2.14455
$311$	17.9357	1.01704	0.508521	−	0.861050i	$-0.330192\pi$
$311$	17.9357	1.01704	0.508521	+	0.861050i	$0.330192\pi$
$312$	−5.00803	−0.283524
$313$	5.61280	0.317254	0.158627	−	0.987339i	$-0.449293\pi$
$313$	5.61280	0.317254	0.158627	+	0.987339i	$0.449293\pi$
$314$	5.19009	0.292894
$315$	3.12891	0.176294
$316$	41.9581	2.36033
$317$	21.9236	1.23135	0.615677	−	0.787999i	$-0.288883\pi$
$317$	21.9236	1.23135	0.615677	+	0.787999i	$0.288883\pi$
$318$	4.01653	0.225236
$319$	−5.97338	−0.334445
$320$	−13.7426	−0.768234
$321$	−15.1982	−0.848282
$322$	−18.8779	−1.05202
$323$	10.5901	0.589249
$324$	4.03807	0.224337
$325$	−1.67059	−0.0926678
$326$	−55.9296	−3.09766
$327$	18.2958	1.01176
$328$	55.6247	3.07136
$329$	10.3592	0.571124
$330$	11.0844	0.610175
$331$	−2.09911	−0.115377	−0.0576887	−	0.998335i	$-0.518373\pi$
$331$	−2.09911	−0.115377	−0.0576887	+	0.998335i	$0.518373\pi$
$332$	20.5821	1.12959
$333$	5.69321	0.311986
$334$	14.7712	0.808246
$335$	−13.6771	−0.747261
$336$	−7.25327	−0.395698
$337$	−0.810195	−0.0441342	−0.0220671	−	0.999756i	$-0.507025\pi$
$337$	−0.810195	−0.0441342	−0.0220671	+	0.999756i	$0.507025\pi$
$338$	2.45725	0.133657
$339$	10.9011	0.592065
$340$	15.4884	0.839979
$341$	−20.8192	−1.12742
$342$	12.3794	0.669399
$343$	−18.9647	−1.02400
$344$	−13.2582	−0.714835
$345$	8.17484	0.440118
$346$	5.00986	0.269331
$347$	−20.7820	−1.11564	−0.557818	−	0.829963i	$-0.688361\pi$
$347$	−20.7820	−1.11564	−0.557818	+	0.829963i	$0.688361\pi$
$348$	−9.75695	−0.523027
$349$	11.4654	0.613731	0.306865	−	0.951753i	$-0.400720\pi$
$349$	11.4654	0.613731	0.306865	+	0.951753i	$0.400720\pi$
$350$	−7.03929	−0.376266
$351$	−1.00000	−0.0533761
$352$	−0.933765	−0.0497699
$353$	16.0880	0.856278	0.428139	−	0.903713i	$-0.359169\pi$
$353$	16.0880	0.856278	0.428139	+	0.903713i	$0.359169\pi$
$354$	−5.88758	−0.312922
$355$	−2.34433	−0.124424
$356$	−21.2076	−1.12400
$357$	−3.60463	−0.190777
$358$	62.6811	3.31280
$359$	−9.74393	−0.514265	−0.257133	−	0.966376i	$-0.582778\pi$
$359$	−9.74393	−0.514265	−0.257133	+	0.966376i	$0.582778\pi$
$360$	9.13799	0.481614
$361$	6.38042	0.335811
$362$	25.1296	1.32078
$363$	4.88835	0.256572
$364$	6.92441	0.362938
$365$	8.72130	0.456494
$366$	26.6101	1.39093
$367$	4.49956	0.234875	0.117437	−	0.993080i	$-0.462532\pi$
$367$	4.49956	0.234875	0.117437	+	0.993080i	$0.462532\pi$
$368$	−18.9505	−0.987862
$369$	11.1071	0.578213
$370$	25.5264	1.32705
$371$	−2.80292	−0.145520
$372$	−34.0062	−1.76314
$373$	29.6861	1.53709	0.768543	−	0.639798i	$-0.220982\pi$
$373$	29.6861	1.53709	0.768543	+	0.639798i	$0.220982\pi$
$374$	−12.7696	−0.660303
$375$	12.1716	0.628539
$376$	30.2542	1.56024
$377$	2.41624	0.124443
$378$	−4.21365	−0.216727
$379$	−24.5787	−1.26252	−0.631262	−	0.775569i	$-0.717463\pi$
$379$	−24.5787	−1.26252	−0.631262	+	0.775569i	$0.717463\pi$
$380$	37.1198	1.90421
$381$	−18.0296	−0.923684
$382$	−20.5835	−1.05314
$383$	−18.1584	−0.927849	−0.463925	−	0.885875i	$-0.653559\pi$
$383$	−18.1584	−0.927849	−0.463925	+	0.885875i	$0.653559\pi$
$384$	19.2623	0.982977
$385$	−7.73521	−0.394223
$386$	−38.5599	−1.96265
$387$	−2.64739	−0.134574
$388$	−55.2760	−2.80621
$389$	0.0830578	0.00421120	0.00210560	−	0.999998i	$-0.499330\pi$
$389$	0.0830578	0.00421120	0.00210560	+	0.999998i	$0.499330\pi$
$390$	−4.48366	−0.227039
$391$	−9.41774	−0.476275
$392$	−20.3302	−1.02683
$393$	−7.05989	−0.356125
$394$	−27.6948	−1.39524
$395$	18.9594	0.953953
$396$	−9.98280	−0.501655
$397$	13.2343	0.664212	0.332106	−	0.943242i	$-0.392241\pi$
$397$	13.2343	0.664212	0.332106	+	0.943242i	$0.392241\pi$
$398$	−1.91194	−0.0958368
$399$	−8.63891	−0.432486
$400$	−7.06635	−0.353317
$401$	−9.78535	−0.488657	−0.244329	−	0.969693i	$-0.578568\pi$
$401$	−9.78535	−0.488657	−0.244329	+	0.969693i	$0.578568\pi$
$402$	18.4187	0.918644
$403$	8.42140	0.419500
$404$	−7.96679	−0.396363
$405$	1.82467	0.0906684
$406$	10.1812	0.505284
$407$	−14.0746	−0.697652
$408$	−10.5273	−0.521180
$409$	32.2133	1.59284	0.796422	−	0.604742i	$-0.206724\pi$
$409$	32.2133	1.59284	0.796422	+	0.604742i	$0.206724\pi$
$410$	49.8004	2.45947
$411$	−18.8311	−0.928869
$412$	−4.03807	−0.198941
$413$	4.10863	0.202173
$414$	−11.0089	−0.541059
$415$	9.30037	0.456537
$416$	0.377710	0.0185188
$417$	15.2404	0.746328
$418$	−30.6039	−1.49689
$419$	−20.8448	−1.01833	−0.509167	−	0.860668i	$-0.670046\pi$
$419$	−20.8448	−1.01833	−0.509167	+	0.860668i	$0.670046\pi$
$420$	−12.6347	−0.616512
$421$	−26.9078	−1.31141	−0.655704	−	0.755018i	$-0.727628\pi$
$421$	−26.9078	−1.31141	−0.655704	+	0.755018i	$0.727628\pi$
$422$	67.5158	3.28662
$423$	6.04114	0.293730
$424$	−8.18595	−0.397545
$425$	−3.51173	−0.170344
$426$	3.15707	0.152961
$427$	−18.5698	−0.898654
$428$	61.3715	2.96650
$429$	2.47217	0.119358
$430$	−11.8700	−0.572422
$431$	25.2765	1.21753	0.608763	−	0.793352i	$-0.291666\pi$
$431$	25.2765	1.21753	0.608763	+	0.793352i	$0.291666\pi$
$432$	−4.22984	−0.203508
$433$	−33.2750	−1.59909	−0.799547	−	0.600604i	$-0.794927\pi$
$433$	−33.2750	−1.59909	−0.799547	+	0.600604i	$0.794927\pi$
$434$	35.4848	1.70333
$435$	−4.40884	−0.211388
$436$	−73.8795	−3.53819
$437$	−22.5707	−1.07970
$438$	−11.7448	−0.561190
$439$	−27.8343	−1.32846	−0.664230	−	0.747528i	$-0.731240\pi$
$439$	−27.8343	−1.32846	−0.664230	+	0.747528i	$0.731240\pi$
$440$	−22.5907	−1.07697
$441$	−4.05952	−0.193310
$442$	5.16535	0.245691
$443$	13.4728	0.640114	0.320057	−	0.947398i	$-0.396298\pi$
$443$	13.4728	0.640114	0.320057	+	0.947398i	$0.396298\pi$
$444$	−22.9895	−1.09104
$445$	−9.58299	−0.454277
$446$	53.3276	2.52514
$447$	9.62177	0.455094
$448$	−12.9150	−0.610176
$449$	−27.8246	−1.31312	−0.656561	−	0.754273i	$-0.727990\pi$
$449$	−27.8246	−1.31312	−0.656561	+	0.754273i	$0.727990\pi$
$450$	−4.10506	−0.193514
$451$	−27.4587	−1.29298
$452$	−44.0192	−2.07049
$453$	5.21999	0.245257
$454$	−15.7589	−0.739603
$455$	3.12891	0.146685
$456$	−25.2300	−1.18150
$457$	4.15766	0.194487	0.0972435	−	0.995261i	$-0.468997\pi$
$457$	4.15766	0.194487	0.0972435	+	0.995261i	$0.468997\pi$
$458$	−46.5728	−2.17620
$459$	−2.10209	−0.0981171
$460$	−33.0105	−1.53912
$461$	−28.3340	−1.31964	−0.659822	−	0.751422i	$-0.729368\pi$
$461$	−28.3340	−1.31964	−0.659822	+	0.751422i	$0.729368\pi$
$462$	10.4169	0.484637
$463$	−4.84265	−0.225057	−0.112529	−	0.993648i	$-0.535895\pi$
$463$	−4.84265	−0.225057	−0.112529	+	0.993648i	$0.535895\pi$
$464$	10.2203	0.474467
$465$	−15.3662	−0.712593
$466$	−32.6870	−1.51419
$467$	3.18012	0.147159	0.0735793	−	0.997289i	$-0.476558\pi$
$467$	3.18012	0.147159	0.0735793	+	0.997289i	$0.476558\pi$
$468$	4.03807	0.186660
$469$	−12.8535	−0.593518
$470$	27.0864	1.24940
$471$	−2.11215	−0.0973229
$472$	11.9993	0.552312
$473$	6.54481	0.300931
$474$	−25.5324	−1.17274
$475$	−8.41628	−0.386165
$476$	14.5557	0.667160
$477$	−1.63456	−0.0748415
$478$	8.30540	0.379880
$479$	15.9757	0.729948	0.364974	−	0.931018i	$-0.381078\pi$
$479$	15.9757	0.729948	0.364974	+	0.931018i	$0.381078\pi$
$480$	−0.689195	−0.0314573
$481$	5.69321	0.259588
$482$	−14.8028	−0.674250
$483$	7.68254	0.349568
$484$	−19.7395	−0.897250
$485$	−24.9774	−1.13416
$486$	−2.45725	−0.111463
$487$	6.70437	0.303804	0.151902	−	0.988396i	$-0.451460\pi$
$487$	6.70437	0.303804	0.151902	+	0.988396i	$0.451460\pi$
$488$	−54.2331	−2.45502
$489$	22.7611	1.02929
$490$	−18.2015	−0.822259
$491$	20.3061	0.916402	0.458201	−	0.888849i	$-0.348494\pi$
$491$	20.3061	0.916402	0.458201	+	0.888849i	$0.348494\pi$
$492$	−44.8512	−2.02205
$493$	5.07916	0.228754
$494$	12.3794	0.556974
$495$	−4.51089	−0.202750
$496$	35.6212	1.59944
$497$	−2.20315	−0.0988250
$498$	−12.5247	−0.561243
$499$	6.47947	0.290061	0.145030	−	0.989427i	$-0.453672\pi$
$499$	6.47947	0.290061	0.145030	+	0.989427i	$0.453672\pi$
$500$	−49.1497	−2.19804
$501$	−6.01129	−0.268565
$502$	16.0987	0.718521
$503$	−23.7928	−1.06087	−0.530434	−	0.847726i	$-0.677971\pi$
$503$	−23.7928	−1.06087	−0.530434	+	0.847726i	$0.677971\pi$
$504$	8.58769	0.382526
$505$	−3.59992	−0.160195
$506$	27.2160	1.20990
$507$	−1.00000	−0.0444116
$508$	72.8047	3.23019
$509$	28.2482	1.25208	0.626040	−	0.779791i	$-0.284675\pi$
$509$	28.2482	1.25208	0.626040	+	0.779791i	$0.284675\pi$
$510$	−9.42504	−0.417348
$511$	8.19610	0.362574
$512$	−40.7687	−1.80174
$513$	−5.03790	−0.222429
$514$	50.3818	2.22225
$515$	−1.82467	−0.0804044
$516$	10.6903	0.470616
$517$	−14.9347	−0.656829
$518$	23.9892	1.05402
$519$	−2.03881	−0.0894937
$520$	9.13799	0.400727
$521$	−44.1567	−1.93454	−0.967271	−	0.253746i	$-0.918337\pi$
$521$	−44.1567	−1.93454	−0.967271	+	0.253746i	$0.918337\pi$
$522$	5.93731	0.259869
$523$	31.6452	1.38375	0.691875	−	0.722017i	$-0.256785\pi$
$523$	31.6452	1.38375	0.691875	+	0.722017i	$0.256785\pi$
$524$	28.5083	1.24539
$525$	2.86471	0.125026
$526$	−43.4981	−1.89661
$527$	17.7025	0.771134
$528$	10.4569	0.455079
$529$	−2.92797	−0.127303
$530$	−7.32882	−0.318344
$531$	2.39601	0.103978
$532$	34.8845	1.51243
$533$	11.1071	0.481102
$534$	12.9053	0.558465
$535$	27.7317	1.19895
$536$	−37.5386	−1.62142
$537$	−25.5086	−1.10078
$538$	−60.2176	−2.59617
$539$	10.0358	0.432274
$540$	−7.36812	−0.317074
$541$	−42.7803	−1.83927	−0.919634	−	0.392775i	$-0.871515\pi$
$541$	−42.7803	−1.83927	−0.919634	+	0.392775i	$0.871515\pi$
$542$	−66.2788	−2.84692
$543$	−10.2267	−0.438871
$544$	0.793980	0.0340416
$545$	−33.3837	−1.43000
$546$	−4.21365	−0.180327
$547$	16.3747	0.700131	0.350066	−	0.936725i	$-0.386159\pi$
$547$	16.3747	0.700131	0.350066	+	0.936725i	$0.386159\pi$
$548$	76.0412	3.24832
$549$	−10.8292	−0.462180
$550$	10.1484	0.432730
$551$	12.1728	0.518578
$552$	22.4369	0.954978
$553$	17.8177	0.757685
$554$	59.0533	2.50893
$555$	−10.3882	−0.440955
$556$	−61.5419	−2.60996
$557$	33.3832	1.41449	0.707245	−	0.706969i	$-0.249938\pi$
$557$	33.3832	1.41449	0.707245	+	0.706969i	$0.249938\pi$
$558$	20.6935	0.876024
$559$	−2.64739	−0.111973
$560$	13.2348	0.559272
$561$	5.19673	0.219406
$562$	30.7844	1.29856
$563$	14.3656	0.605439	0.302719	−	0.953080i	$-0.402105\pi$
$563$	14.3656	0.605439	0.302719	+	0.953080i	$0.402105\pi$
$564$	−24.3945	−1.02719
$565$	−19.8908	−0.836813
$566$	−74.6126	−3.13620
$567$	1.71478	0.0720141
$568$	−6.43432	−0.269978
$569$	12.0211	0.503949	0.251975	−	0.967734i	$-0.418920\pi$
$569$	12.0211	0.503949	0.251975	+	0.967734i	$0.418920\pi$
$570$	−22.5882	−0.946116
$571$	18.0344	0.754718	0.377359	−	0.926067i	$-0.376832\pi$
$571$	18.0344	0.754718	0.377359	+	0.926067i	$0.376832\pi$
$572$	−9.98280	−0.417402
$573$	8.37666	0.349940
$574$	46.8014	1.95345
$575$	7.48456	0.312128
$576$	−7.53156	−0.313815
$577$	10.8638	0.452266	0.226133	−	0.974096i	$-0.427392\pi$
$577$	10.8638	0.452266	0.226133	+	0.974096i	$0.427392\pi$
$578$	−30.9152	−1.28590
$579$	15.6923	0.652151
$580$	17.8032	0.739237
$581$	8.74030	0.362609
$582$	33.6366	1.39428
$583$	4.04093	0.167358
$584$	23.9367	0.990509
$585$	1.82467	0.0754407
$586$	−71.3060	−2.94562
$587$	4.52036	0.186575	0.0932877	−	0.995639i	$-0.470262\pi$
$587$	4.52036	0.186575	0.0932877	+	0.995639i	$0.470262\pi$
$588$	16.3926	0.676019
$589$	42.4262	1.74814
$590$	10.7429	0.442277
$591$	11.2707	0.463613
$592$	24.0814	0.989738
$593$	−31.7623	−1.30432	−0.652160	−	0.758081i	$-0.726137\pi$
$593$	−31.7623	−1.30432	−0.652160	+	0.758081i	$0.726137\pi$
$594$	6.07475	0.249250
$595$	6.57724	0.269641
$596$	−38.8534	−1.59150
$597$	0.778082	0.0318448
$598$	−11.0089	−0.450188
$599$	−22.3684	−0.913948	−0.456974	−	0.889480i	$-0.651067\pi$
$599$	−22.3684	−0.913948	−0.456974	+	0.889480i	$0.651067\pi$
$600$	8.36638	0.341556
$601$	−12.7059	−0.518284	−0.259142	−	0.965839i	$-0.583440\pi$
$601$	−12.7059	−0.518284	−0.259142	+	0.965839i	$0.583440\pi$
$602$	−11.1552	−0.454651
$603$	−7.49568	−0.305248
$604$	−21.0787	−0.857679
$605$	−8.91961	−0.362634
$606$	4.84796	0.196935
$607$	13.8752	0.563176	0.281588	−	0.959535i	$-0.409139\pi$
$607$	13.8752	0.563176	0.281588	+	0.959535i	$0.409139\pi$
$608$	1.90287	0.0771714
$609$	−4.14333	−0.167896
$610$	−48.5545	−1.96591
$611$	6.04114	0.244398
$612$	8.48837	0.343122
$613$	20.2055	0.816094	0.408047	−	0.912961i	$-0.366210\pi$
$613$	20.2055	0.816094	0.408047	+	0.912961i	$0.366210\pi$
$614$	−73.7612	−2.97676
$615$	−20.2668	−0.817235
$616$	−21.2303	−0.855392
$617$	−25.7238	−1.03560	−0.517802	−	0.855501i	$-0.673249\pi$
$617$	−25.7238	−1.03560	−0.517802	+	0.855501i	$0.673249\pi$
$618$	2.45725	0.0988450
$619$	−19.3588	−0.778094	−0.389047	−	0.921218i	$-0.627196\pi$
$619$	−19.3588	−0.778094	−0.389047	+	0.921218i	$0.627196\pi$
$620$	62.0499	2.49198
$621$	4.48018	0.179784
$622$	44.0725	1.76715
$623$	−9.00590	−0.360814
$624$	−4.22984	−0.169329
$625$	−13.8562	−0.554246
$626$	13.7920	0.551241
$627$	12.4546	0.497387
$628$	8.52902	0.340345
$629$	11.9676	0.477180
$630$	7.68850	0.306317
$631$	−30.4519	−1.21227	−0.606136	−	0.795361i	$-0.707281\pi$
$631$	−30.4519	−1.21227	−0.606136	+	0.795361i	$0.707281\pi$
$632$	52.0366	2.06991
$633$	−27.4762	−1.09208
$634$	53.8718	2.13952
$635$	32.8980	1.30552
$636$	6.60047	0.261726
$637$	−4.05952	−0.160844
$638$	−14.6781	−0.581110
$639$	−1.28480	−0.0508259
$640$	−35.1473	−1.38932
$641$	8.91397	0.352081	0.176040	−	0.984383i	$-0.443671\pi$
$641$	8.91397	0.352081	0.176040	+	0.984383i	$0.443671\pi$
$642$	−37.3458	−1.47392
$643$	11.9688	0.472005	0.236002	−	0.971752i	$-0.424163\pi$
$643$	11.9688	0.472005	0.236002	+	0.971752i	$0.424163\pi$
$644$	−31.0226	−1.22246
$645$	4.83060	0.190205
$646$	26.0225	1.02384
$647$	−4.78523	−0.188127	−0.0940634	−	0.995566i	$-0.529986\pi$
$647$	−4.78523	−0.188127	−0.0940634	+	0.995566i	$0.529986\pi$
$648$	5.00803	0.196734
$649$	−5.92335	−0.232512
$650$	−4.10506	−0.161014
$651$	−14.4409	−0.565983
$652$	−91.9108	−3.59950
$653$	−24.9769	−0.977422	−0.488711	−	0.872446i	$-0.662533\pi$
$653$	−24.9769	−0.977422	−0.488711	+	0.872446i	$0.662533\pi$
$654$	44.9572	1.75797
$655$	12.8820	0.503339
$656$	46.9813	1.83431
$657$	4.77967	0.186473
$658$	25.4552	0.992348
$659$	10.8201	0.421490	0.210745	−	0.977541i	$-0.432411\pi$
$659$	10.8201	0.421490	0.210745	+	0.977541i	$0.432411\pi$
$660$	18.2153	0.709029
$661$	−7.22917	−0.281182	−0.140591	−	0.990068i	$-0.544900\pi$
$661$	−7.22917	−0.281182	−0.140591	+	0.990068i	$0.544900\pi$
$662$	−5.15802	−0.200472
$663$	−2.10209	−0.0816383
$664$	25.5261	0.990604
$665$	15.7631	0.611268
$666$	13.9896	0.542087
$667$	−10.8252	−0.419154
$668$	24.2740	0.939189
$669$	−21.7022	−0.839055
$670$	−33.6081	−1.29839
$671$	26.7717	1.03351
$672$	−0.647691	−0.0249852
$673$	26.7146	1.02977	0.514886	−	0.857259i	$-0.327834\pi$
$673$	26.7146	1.02977	0.514886	+	0.857259i	$0.327834\pi$
$674$	−1.99085	−0.0766847
$675$	1.67059	0.0643012
$676$	4.03807	0.155310
$677$	17.6487	0.678294	0.339147	−	0.940733i	$-0.389862\pi$
$677$	17.6487	0.678294	0.339147	+	0.940733i	$0.389862\pi$
$678$	26.7866	1.02873
$679$	−23.4732	−0.900819
$680$	19.2089	0.736626
$681$	6.41324	0.245756
$682$	−51.1579	−1.95894
$683$	−22.1422	−0.847247	−0.423623	−	0.905838i	$-0.639242\pi$
$683$	−22.1422	−0.847247	−0.423623	+	0.905838i	$0.639242\pi$
$684$	20.3434	0.777848
$685$	34.3605	1.31285
$686$	−46.6009	−1.77923
$687$	18.9532	0.723111
$688$	−11.1981	−0.426922
$689$	−1.63456	−0.0622719
$690$	20.0876	0.764722
$691$	26.0769	0.992011	0.496006	−	0.868319i	$-0.334800\pi$
$691$	26.0769	0.992011	0.496006	+	0.868319i	$0.334800\pi$
$692$	8.23284	0.312966
$693$	−4.23924	−0.161036
$694$	−51.0665	−1.93846
$695$	−27.8087	−1.05484
$696$	−12.1006	−0.458673
$697$	23.3481	0.884373
$698$	28.1734	1.06638
$699$	13.3023	0.503138
$700$	−11.5679	−0.437224
$701$	−13.9609	−0.527297	−0.263648	−	0.964619i	$-0.584926\pi$
$701$	−13.9609	−0.527297	−0.263648	+	0.964619i	$0.584926\pi$
$702$	−2.45725	−0.0927428
$703$	28.6818	1.08175
$704$	18.6193	0.701743
$705$	−11.0231	−0.415152
$706$	39.5322	1.48781
$707$	−3.38313	−0.127236
$708$	−9.67524	−0.363618
$709$	−16.0197	−0.601632	−0.300816	−	0.953682i	$-0.597259\pi$
$709$	−16.0197	−0.601632	−0.300816	+	0.953682i	$0.597259\pi$
$710$	−5.76060	−0.216192
$711$	10.3906	0.389679
$712$	−26.3018	−0.985700
$713$	−37.7294	−1.41298
$714$	−8.85746	−0.331482
$715$	−4.51089	−0.168698
$716$	103.006	3.84950
$717$	−3.37996	−0.126227
$718$	−23.9433	−0.893555
$719$	−8.82899	−0.329266	−0.164633	−	0.986355i	$-0.552644\pi$
$719$	−8.82899	−0.329266	−0.164633	+	0.986355i	$0.552644\pi$
$720$	7.71805	0.287635
$721$	−1.71478	−0.0638619
$722$	15.6783	0.583484
$723$	6.02414	0.224040
$724$	41.2962	1.53476
$725$	−4.03656	−0.149914
$726$	12.0119	0.445803
$727$	19.1342	0.709649	0.354825	−	0.934933i	$-0.384541\pi$
$727$	19.1342	0.709649	0.354825	+	0.934933i	$0.384541\pi$
$728$	8.58769	0.318281
$729$	1.00000	0.0370370
$730$	21.4304	0.793174
$731$	−5.56505	−0.205831
$732$	43.7291	1.61627
$733$	−11.8488	−0.437644	−0.218822	−	0.975765i	$-0.570221\pi$
$733$	−11.8488	−0.437644	−0.218822	+	0.975765i	$0.570221\pi$
$734$	11.0565	0.408104
$735$	7.40726	0.273221
$736$	−1.69221	−0.0623757
$737$	18.5306	0.682585
$738$	27.2929	1.00467
$739$	35.6420	1.31111	0.655555	−	0.755147i	$-0.272435\pi$
$739$	35.6420	1.31111	0.655555	+	0.755147i	$0.272435\pi$
$740$	41.9482	1.54205
$741$	−5.03790	−0.185072
$742$	−6.88748	−0.252847
$743$	32.2067	1.18155	0.590774	−	0.806837i	$-0.298823\pi$
$743$	32.2067	1.18155	0.590774	+	0.806837i	$0.298823\pi$
$744$	−42.1747	−1.54620
$745$	−17.5565	−0.643221
$746$	72.9460	2.67074
$747$	5.09703	0.186490
$748$	−20.9847	−0.767278
$749$	26.0617	0.952273
$750$	29.9087	1.09211
$751$	24.8419	0.906494	0.453247	−	0.891385i	$-0.350266\pi$
$751$	24.8419	0.906494	0.453247	+	0.891385i	$0.350266\pi$
$752$	25.5531	0.931825
$753$	−6.55153	−0.238751
$754$	5.93731	0.216224
$755$	−9.52474	−0.346641
$756$	−6.92441	−0.251838
$757$	−15.3497	−0.557893	−0.278946	−	0.960307i	$-0.589985\pi$
$757$	−15.3497	−0.557893	−0.278946	+	0.960307i	$0.589985\pi$
$758$	−60.3960	−2.19368
$759$	−11.0758	−0.402026
$760$	46.0363	1.66991
$761$	6.52172	0.236412	0.118206	−	0.992989i	$-0.462286\pi$
$761$	6.52172	0.236412	0.118206	+	0.992989i	$0.462286\pi$
$762$	−44.3032	−1.60493
$763$	−31.3733	−1.13579
$764$	−33.8255	−1.22376
$765$	3.83561	0.138677
$766$	−44.6196	−1.61217
$767$	2.39601	0.0865148
$768$	32.2692	1.16441
$769$	−21.7203	−0.783252	−0.391626	−	0.920124i	$-0.628087\pi$
$769$	−21.7203	−0.783252	−0.391626	+	0.920124i	$0.628087\pi$
$770$	−19.0073	−0.684976
$771$	−20.5033	−0.738410
$772$	−63.3667	−2.28062
$773$	−4.58871	−0.165045	−0.0825223	−	0.996589i	$-0.526298\pi$
$773$	−4.58871	−0.165045	−0.0825223	+	0.996589i	$0.526298\pi$
$774$	−6.50529	−0.233828
$775$	−14.0687	−0.505364
$776$	−68.5536	−2.46093
$777$	−9.76262	−0.350232
$778$	0.204094	0.00731711
$779$	55.9565	2.00485
$780$	−7.36812	−0.263821
$781$	3.17625	0.113655
$782$	−23.1417	−0.827546
$783$	−2.41624	−0.0863495
$784$	−17.1711	−0.613254
$785$	3.85398	0.137554
$786$	−17.3479	−0.618779
$787$	10.4885	0.373873	0.186937	−	0.982372i	$-0.440144\pi$
$787$	10.4885	0.373873	0.186937	+	0.982372i	$0.440144\pi$
$788$	−45.5117	−1.62129
$789$	17.7020	0.630207
$790$	46.5880	1.65753
$791$	−18.6930	−0.664646
$792$	−12.3807	−0.439930
$793$	−10.8292	−0.384557
$794$	32.5200	1.15409
$795$	2.98253	0.105780
$796$	−3.14194	−0.111363
$797$	−19.4563	−0.689178	−0.344589	−	0.938754i	$-0.611982\pi$
$797$	−19.4563	−0.689178	−0.344589	+	0.938754i	$0.611982\pi$
$798$	−21.2279	−0.751461
$799$	12.6990	0.449258
$800$	−0.631000	−0.0223092
$801$	−5.25191	−0.185567
$802$	−24.0450	−0.849059
$803$	−11.8162	−0.416984
$804$	30.2681	1.06747
$805$	−14.0181	−0.494072
$806$	20.6935	0.728896
$807$	24.5061	0.862657
$808$	−9.88046	−0.347593
$809$	−33.2176	−1.16787	−0.583935	−	0.811800i	$-0.698488\pi$
$809$	−33.2176	−1.16787	−0.583935	+	0.811800i	$0.698488\pi$
$810$	4.48366	0.157540
$811$	20.0974	0.705715	0.352857	−	0.935677i	$-0.385210\pi$
$811$	20.0974	0.705715	0.352857	+	0.935677i	$0.385210\pi$
$812$	16.7311	0.587145
$813$	26.9728	0.945977
$814$	−34.5848	−1.21220
$815$	−41.5314	−1.45478
$816$	−8.89151	−0.311265
$817$	−13.3373	−0.466613
$818$	79.1560	2.76762
$819$	1.71478	0.0599194
$820$	81.8385	2.85792
$821$	−9.75001	−0.340278	−0.170139	−	0.985420i	$-0.554422\pi$
$821$	−9.75001	−0.340278	−0.170139	+	0.985420i	$0.554422\pi$
$822$	−46.2727	−1.61394
$823$	−33.2226	−1.15807	−0.579033	−	0.815304i	$-0.696570\pi$
$823$	−33.2226	−1.15807	−0.579033	+	0.815304i	$0.696570\pi$
$824$	−5.00803	−0.174463
$825$	−4.13000	−0.143788
$826$	10.0959	0.351282
$827$	−37.6560	−1.30943	−0.654714	−	0.755877i	$-0.727211\pi$
$827$	−37.6560	−1.30943	−0.654714	+	0.755877i	$0.727211\pi$
$828$	−18.0913	−0.628715
$829$	28.5745	0.992433	0.496217	−	0.868199i	$-0.334722\pi$
$829$	28.5745	0.992433	0.496217	+	0.868199i	$0.334722\pi$
$830$	22.8533	0.793250
$831$	−24.0323	−0.833670
$832$	−7.53156	−0.261110
$833$	−8.53346	−0.295667
$834$	37.4495	1.29677
$835$	10.9686	0.379584
$836$	−50.2923	−1.73940
$837$	−8.42140	−0.291086
$838$	−51.2207	−1.76939
$839$	35.7276	1.23346	0.616728	−	0.787177i	$-0.288458\pi$
$839$	35.7276	1.23346	0.616728	+	0.787177i	$0.288458\pi$
$840$	−15.6697	−0.540655
$841$	−23.1618	−0.798682
$842$	−66.1192	−2.27862
$843$	−12.5280	−0.431488
$844$	110.951	3.81908
$845$	1.82467	0.0627704
$846$	14.8446	0.510367
$847$	−8.38247	−0.288025
$848$	−6.91395	−0.237426
$849$	30.3643	1.04210
$850$	−8.62920	−0.295979
$851$	−25.5066	−0.874355
$852$	5.18811	0.177742
$853$	−44.9199	−1.53803	−0.769015	−	0.639231i	$-0.779253\pi$
$853$	−44.9199	−1.53803	−0.769015	+	0.639231i	$0.779253\pi$
$854$	−45.6305	−1.56144
$855$	9.19248	0.314376
$856$	76.1132	2.60150
$857$	41.0855	1.40345	0.701726	−	0.712447i	$-0.252413\pi$
$857$	41.0855	1.40345	0.701726	+	0.712447i	$0.252413\pi$
$858$	6.07475	0.207388
$859$	−50.4833	−1.72247	−0.861234	−	0.508209i	$-0.830308\pi$
$859$	−50.4833	−1.72247	−0.861234	+	0.508209i	$0.830308\pi$
$860$	−19.5063	−0.665159
$861$	−19.0463	−0.649096
$862$	62.1106	2.11550
$863$	−36.8528	−1.25448	−0.627241	−	0.778825i	$-0.715816\pi$
$863$	−36.8528	−1.25448	−0.627241	+	0.778825i	$0.715816\pi$
$864$	−0.377710	−0.0128500
$865$	3.72014	0.126489
$866$	−81.7649	−2.77848
$867$	12.5812	0.427281
$868$	58.3132	1.97928
$869$	−25.6875	−0.871387
$870$	−10.8336	−0.367294
$871$	−7.49568	−0.253982
$872$	−91.6258	−3.10284
$873$	−13.6887	−0.463293
$874$	−55.4618	−1.87602
$875$	−20.8717	−0.705591
$876$	−19.3006	−0.652107
$877$	7.42795	0.250824	0.125412	−	0.992105i	$-0.459975\pi$
$877$	7.42795	0.250824	0.125412	+	0.992105i	$0.459975\pi$
$878$	−68.3958	−2.30825
$879$	29.0186	0.978775
$880$	−19.0804	−0.643199
$881$	−23.2794	−0.784302	−0.392151	−	0.919901i	$-0.628269\pi$
$881$	−23.2794	−0.784302	−0.392151	+	0.919901i	$0.628269\pi$
$882$	−9.97524	−0.335884
$883$	3.87577	0.130430	0.0652149	−	0.997871i	$-0.479227\pi$
$883$	3.87577	0.130430	0.0652149	+	0.997871i	$0.479227\pi$
$884$	8.48837	0.285495
$885$	−4.37191	−0.146960
$886$	33.1061	1.11222
$887$	47.3370	1.58942	0.794711	−	0.606988i	$-0.207623\pi$
$887$	47.3370	1.58942	0.794711	+	0.606988i	$0.207623\pi$
$888$	−28.5118	−0.956792
$889$	30.9168	1.03692
$890$	−23.5478	−0.789323
$891$	−2.47217	−0.0828210
$892$	87.6349	2.93423
$893$	30.4346	1.01846
$894$	23.6431	0.790743
$895$	46.5448	1.55582
$896$	−33.0307	−1.10348
$897$	4.48018	0.149589
$898$	−68.3719	−2.28160
$899$	20.3482	0.678649
$900$	−6.74596	−0.224865
$901$	−3.43600	−0.114470
$902$	−67.4728	−2.24660
$903$	4.53970	0.151072
$904$	−54.5929	−1.81573
$905$	18.6604	0.620292
$906$	12.8268	0.426142
$907$	−33.1774	−1.10164	−0.550818	−	0.834625i	$-0.685684\pi$
$907$	−33.1774	−1.10164	−0.550818	+	0.834625i	$0.685684\pi$
$908$	−25.8971	−0.859426
$909$	−1.97292	−0.0654377
$910$	7.68850	0.254871
$911$	38.9751	1.29130	0.645651	−	0.763633i	$-0.276586\pi$
$911$	38.9751	1.29130	0.645651	+	0.763633i	$0.276586\pi$
$912$	−21.3095	−0.705629
$913$	−12.6007	−0.417024
$914$	10.2164	0.337928
$915$	19.7597	0.653236
$916$	−76.5344	−2.52877
$917$	12.1062	0.399782
$918$	−5.16535	−0.170482
$919$	−33.4095	−1.10208	−0.551038	−	0.834480i	$-0.685768\pi$
$919$	−33.4095	−1.10208	−0.551038	+	0.834480i	$0.685768\pi$
$920$	−40.9399	−1.34975
$921$	30.0178	0.989120
$922$	−69.6236	−2.29293
$923$	−1.28480	−0.0422897
$924$	17.1183	0.563152
$925$	−9.51103	−0.312721
$926$	−11.8996	−0.391045
$927$	−1.00000	−0.0328443
$928$	0.912640	0.0299589
$929$	40.9112	1.34225	0.671126	−	0.741344i	$-0.265811\pi$
$929$	40.9112	1.34225	0.671126	+	0.741344i	$0.265811\pi$
$930$	−37.7587	−1.23816
$931$	−20.4514	−0.670269
$932$	−53.7154	−1.75951
$933$	−17.9357	−0.587189
$934$	7.81435	0.255693
$935$	−9.48230	−0.310104
$936$	5.00803	0.163693
$937$	32.3748	1.05764	0.528820	−	0.848734i	$-0.322635\pi$
$937$	32.3748	1.05764	0.528820	+	0.848734i	$0.322635\pi$
$938$	−31.5842	−1.03126
$939$	−5.61280	−0.183167
$940$	44.5118	1.45182
$941$	2.27246	0.0740801	0.0370401	−	0.999314i	$-0.488207\pi$
$941$	2.27246	0.0740801	0.0370401	+	0.999314i	$0.488207\pi$
$942$	−5.19009	−0.169102
$943$	−49.7619	−1.62047
$944$	10.1347	0.329858
$945$	−3.12891	−0.101783
$946$	16.0822	0.522878
$947$	35.5665	1.15575	0.577877	−	0.816124i	$-0.303881\pi$
$947$	35.5665	1.15575	0.577877	+	0.816124i	$0.303881\pi$
$948$	−41.9581	−1.36273
$949$	4.77967	0.155155
$950$	−20.6809	−0.670976
$951$	−21.9236	−0.710922
$952$	18.0521	0.585071
$953$	58.0872	1.88163	0.940814	−	0.338924i	$-0.110063\pi$
$953$	58.0872	1.88163	0.940814	+	0.338924i	$0.110063\pi$
$954$	−4.01653	−0.130040
$955$	−15.2846	−0.494598
$956$	13.6485	0.441424
$957$	5.97338	0.193092
$958$	39.2562	1.26831
$959$	32.2912	1.04274
$960$	13.7426	0.443540
$961$	39.9200	1.28774
$962$	13.9896	0.451043
$963$	15.1982	0.489756
$964$	−24.3259	−0.783484
$965$	−28.6333	−0.921737
$966$	18.8779	0.607387
$967$	−31.2378	−1.00454	−0.502269	−	0.864711i	$-0.667501\pi$
$967$	−31.2378	−1.00454	−0.502269	+	0.864711i	$0.667501\pi$
$968$	−24.4810	−0.786850
$969$	−10.5901	−0.340203
$970$	−61.3756	−1.97065
$971$	−23.6040	−0.757487	−0.378743	−	0.925502i	$-0.623644\pi$
$971$	−23.6040	−0.757487	−0.378743	+	0.925502i	$0.623644\pi$
$972$	−4.03807	−0.129521
$973$	−26.1341	−0.837820
$974$	16.4743	0.527871
$975$	1.67059	0.0535018
$976$	−45.8059	−1.46621
$977$	−21.7135	−0.694678	−0.347339	−	0.937740i	$-0.612915\pi$
$977$	−21.7135	−0.694678	−0.347339	+	0.937740i	$0.612915\pi$
$978$	55.9296	1.78843
$979$	12.9836	0.414959
$980$	−29.9110	−0.955472
$981$	−18.2958	−0.584139
$982$	49.8971	1.59228
$983$	48.1433	1.53553	0.767766	−	0.640730i	$-0.221368\pi$
$983$	48.1433	1.53553	0.767766	+	0.640730i	$0.221368\pi$
$984$	−55.6247	−1.77325
$985$	−20.5652	−0.655262
$986$	12.4807	0.397468
$987$	−10.3592	−0.329738
$988$	20.3434	0.647209
$989$	11.8608	0.377151
$990$	−11.0844	−0.352285
$991$	12.3184	0.391308	0.195654	−	0.980673i	$-0.437317\pi$
$991$	12.3184	0.391308	0.195654	+	0.980673i	$0.437317\pi$
$992$	3.18085	0.100992
$993$	2.09911	0.0666131
$994$	−5.41370	−0.171712
$995$	−1.41974	−0.0450088
$996$	−20.5821	−0.652170
$997$	−9.40592	−0.297889	−0.148944	−	0.988846i	$-0.547588\pi$
$997$	−9.40592	−0.297889	−0.148944	+	0.988846i	$0.547588\pi$
$998$	15.9217	0.503991
$999$	−5.69321	−0.180125

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.j.1.22	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.j.1.22	✓	25	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+2.45725 q^{2} -1.00000 q^{3} +4.03807 q^{4} +1.82467 q^{5} -2.45725 q^{6} +1.71478 q^{7} +5.00803 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.45725 q^{2} -1.00000 q^{3} +4.03807 q^{4} +1.82467 q^{5} -2.45725 q^{6} +1.71478 q^{7} +5.00803 q^{8} +1.00000 q^{9} +4.48366 q^{10} -2.47217 q^{11} -4.03807 q^{12} +1.00000 q^{13} +4.21365 q^{14} -1.82467 q^{15} +4.22984 q^{16} +2.10209 q^{17} +2.45725 q^{18} +5.03790 q^{19} +7.36812 q^{20} -1.71478 q^{21} -6.07475 q^{22} -4.48018 q^{23} -5.00803 q^{24} -1.67059 q^{25} +2.45725 q^{26} -1.00000 q^{27} +6.92441 q^{28} +2.41624 q^{29} -4.48366 q^{30} +8.42140 q^{31} +0.377710 q^{32} +2.47217 q^{33} +5.16535 q^{34} +3.12891 q^{35} +4.03807 q^{36} +5.69321 q^{37} +12.3794 q^{38} -1.00000 q^{39} +9.13799 q^{40} +11.1071 q^{41} -4.21365 q^{42} -2.64739 q^{43} -9.98280 q^{44} +1.82467 q^{45} -11.0089 q^{46} +6.04114 q^{47} -4.22984 q^{48} -4.05952 q^{49} -4.10506 q^{50} -2.10209 q^{51} +4.03807 q^{52} -1.63456 q^{53} -2.45725 q^{54} -4.51089 q^{55} +8.58769 q^{56} -5.03790 q^{57} +5.93731 q^{58} +2.39601 q^{59} -7.36812 q^{60} -10.8292 q^{61} +20.6935 q^{62} +1.71478 q^{63} -7.53156 q^{64} +1.82467 q^{65} +6.07475 q^{66} -7.49568 q^{67} +8.48837 q^{68} +4.48018 q^{69} +7.68850 q^{70} -1.28480 q^{71} +5.00803 q^{72} +4.77967 q^{73} +13.9896 q^{74} +1.67059 q^{75} +20.3434 q^{76} -4.23924 q^{77} -2.45725 q^{78} +10.3906 q^{79} +7.71805 q^{80} +1.00000 q^{81} +27.2929 q^{82} +5.09703 q^{83} -6.92441 q^{84} +3.83561 q^{85} -6.50529 q^{86} -2.41624 q^{87} -12.3807 q^{88} -5.25191 q^{89} +4.48366 q^{90} +1.71478 q^{91} -18.0913 q^{92} -8.42140 q^{93} +14.8446 q^{94} +9.19248 q^{95} -0.377710 q^{96} -13.6887 q^{97} -9.97524 q^{98} -2.47217 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * q^99

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