LMFDB - Embedded newform 4017.2.a.j.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.18299 q^{2} -1.00000 q^{3} +2.76546 q^{4} +2.14752 q^{5} +2.18299 q^{6} +0.603238 q^{7} -1.67100 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.18299 q^{2} -1.00000 q^{3} +2.76546 q^{4} +2.14752 q^{5} +2.18299 q^{6} +0.603238 q^{7} -1.67100 q^{8} +1.00000 q^{9} -4.68803 q^{10} -1.05632 q^{11} -2.76546 q^{12} +1.00000 q^{13} -1.31686 q^{14} -2.14752 q^{15} -1.88315 q^{16} +5.27690 q^{17} -2.18299 q^{18} +6.92975 q^{19} +5.93890 q^{20} -0.603238 q^{21} +2.30593 q^{22} -3.16152 q^{23} +1.67100 q^{24} -0.388137 q^{25} -2.18299 q^{26} -1.00000 q^{27} +1.66823 q^{28} +6.31547 q^{29} +4.68803 q^{30} +1.92623 q^{31} +7.45289 q^{32} +1.05632 q^{33} -11.5194 q^{34} +1.29547 q^{35} +2.76546 q^{36} -7.58967 q^{37} -15.1276 q^{38} -1.00000 q^{39} -3.58851 q^{40} -6.70449 q^{41} +1.31686 q^{42} +3.27034 q^{43} -2.92120 q^{44} +2.14752 q^{45} +6.90157 q^{46} +0.617887 q^{47} +1.88315 q^{48} -6.63610 q^{49} +0.847301 q^{50} -5.27690 q^{51} +2.76546 q^{52} +14.2897 q^{53} +2.18299 q^{54} -2.26847 q^{55} -1.00801 q^{56} -6.92975 q^{57} -13.7866 q^{58} +8.58769 q^{59} -5.93890 q^{60} +2.25155 q^{61} -4.20495 q^{62} +0.603238 q^{63} -12.5033 q^{64} +2.14752 q^{65} -2.30593 q^{66} +6.67280 q^{67} +14.5931 q^{68} +3.16152 q^{69} -2.82800 q^{70} +2.12217 q^{71} -1.67100 q^{72} +11.5346 q^{73} +16.5682 q^{74} +0.388137 q^{75} +19.1640 q^{76} -0.637210 q^{77} +2.18299 q^{78} +3.02621 q^{79} -4.04411 q^{80} +1.00000 q^{81} +14.6359 q^{82} +6.20971 q^{83} -1.66823 q^{84} +11.3323 q^{85} -7.13912 q^{86} -6.31547 q^{87} +1.76510 q^{88} -6.13977 q^{89} -4.68803 q^{90} +0.603238 q^{91} -8.74305 q^{92} -1.92623 q^{93} -1.34884 q^{94} +14.8818 q^{95} -7.45289 q^{96} -5.90264 q^{97} +14.4866 q^{98} -1.05632 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.18299	−1.54361	−0.771805	−	0.635860i	$-0.780646\pi$
$2$	−2.18299	−1.54361	−0.771805	+	0.635860i	$0.780646\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.76546	1.38273
$5$	2.14752	0.960402	0.480201	−	0.877158i	$-0.340564\pi$
$5$	2.14752	0.960402	0.480201	+	0.877158i	$0.340564\pi$
$6$	2.18299	0.891203
$7$	0.603238	0.228002	0.114001	−	0.993481i	$-0.463633\pi$
$7$	0.603238	0.228002	0.114001	+	0.993481i	$0.463633\pi$
$8$	−1.67100	−0.590786
$9$	1.00000	0.333333
$10$	−4.68803	−1.48249
$11$	−1.05632	−0.318492	−0.159246	−	0.987239i	$-0.550906\pi$
$11$	−1.05632	−0.318492	−0.159246	+	0.987239i	$0.550906\pi$
$12$	−2.76546	−0.798320
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.31686	−0.351947
$15$	−2.14752	−0.554489
$16$	−1.88315	−0.470787
$17$	5.27690	1.27984	0.639918	−	0.768443i	$-0.278968\pi$
$17$	5.27690	1.27984	0.639918	+	0.768443i	$0.278968\pi$
$18$	−2.18299	−0.514537
$19$	6.92975	1.58979	0.794897	−	0.606744i	$-0.207525\pi$
$19$	6.92975	1.58979	0.794897	+	0.606744i	$0.207525\pi$
$20$	5.93890	1.32798
$21$	−0.603238	−0.131637
$22$	2.30593	0.491627
$23$	−3.16152	−0.659222	−0.329611	−	0.944117i	$-0.606918\pi$
$23$	−3.16152	−0.659222	−0.329611	+	0.944117i	$0.606918\pi$
$24$	1.67100	0.341091
$25$	−0.388137	−0.0776275
$26$	−2.18299	−0.428120
$27$	−1.00000	−0.192450
$28$	1.66823	0.315266
$29$	6.31547	1.17275	0.586377	−	0.810038i	$-0.300554\pi$
$29$	6.31547	1.17275	0.586377	+	0.810038i	$0.300554\pi$
$30$	4.68803	0.855914
$31$	1.92623	0.345962	0.172981	−	0.984925i	$-0.444660\pi$
$31$	1.92623	0.345962	0.172981	+	0.984925i	$0.444660\pi$
$32$	7.45289	1.31750
$33$	1.05632	0.183881
$34$	−11.5194	−1.97557
$35$	1.29547	0.218974
$36$	2.76546	0.460910
$37$	−7.58967	−1.24773	−0.623867	−	0.781530i	$-0.714439\pi$
$37$	−7.58967	−1.24773	−0.623867	+	0.781530i	$0.714439\pi$
$38$	−15.1276	−2.45402
$39$	−1.00000	−0.160128
$40$	−3.58851	−0.567392
$41$	−6.70449	−1.04707	−0.523533	−	0.852006i	$-0.675386\pi$
$41$	−6.70449	−1.04707	−0.523533	+	0.852006i	$0.675386\pi$
$42$	1.31686	0.203197
$43$	3.27034	0.498721	0.249361	−	0.968411i	$-0.419780\pi$
$43$	3.27034	0.498721	0.249361	+	0.968411i	$0.419780\pi$
$44$	−2.92120	−0.440388
$45$	2.14752	0.320134
$46$	6.90157	1.01758
$47$	0.617887	0.0901281	0.0450641	−	0.998984i	$-0.485651\pi$
$47$	0.617887	0.0901281	0.0450641	+	0.998984i	$0.485651\pi$
$48$	1.88315	0.271809
$49$	−6.63610	−0.948015
$50$	0.847301	0.119827
$51$	−5.27690	−0.738913
$52$	2.76546	0.383500
$53$	14.2897	1.96284	0.981421	−	0.191867i	$-0.0614542\pi$
$53$	14.2897	1.96284	0.981421	+	0.191867i	$0.0614542\pi$
$54$	2.18299	0.297068
$55$	−2.26847	−0.305880
$56$	−1.00801	−0.134701
$57$	−6.92975	−0.917868
$58$	−13.7866	−1.81027
$59$	8.58769	1.11802	0.559011	−	0.829160i	$-0.311181\pi$
$59$	8.58769	1.11802	0.559011	+	0.829160i	$0.311181\pi$
$60$	−5.93890	−0.766708
$61$	2.25155	0.288282	0.144141	−	0.989557i	$-0.453958\pi$
$61$	2.25155	0.288282	0.144141	+	0.989557i	$0.453958\pi$
$62$	−4.20495	−0.534030
$63$	0.603238	0.0760008
$64$	−12.5033	−1.56291
$65$	2.14752	0.266368
$66$	−2.30593	−0.283841
$67$	6.67280	0.815213	0.407606	−	0.913158i	$-0.366364\pi$
$67$	6.67280	0.815213	0.407606	+	0.913158i	$0.366364\pi$
$68$	14.5931	1.76967
$69$	3.16152	0.380602
$70$	−2.82800	−0.338011
$71$	2.12217	0.251855	0.125927	−	0.992039i	$-0.459809\pi$
$71$	2.12217	0.251855	0.125927	+	0.992039i	$0.459809\pi$
$72$	−1.67100	−0.196929
$73$	11.5346	1.35002	0.675010	−	0.737808i	$-0.264139\pi$
$73$	11.5346	1.35002	0.675010	+	0.737808i	$0.264139\pi$
$74$	16.5682	1.92601
$75$	0.388137	0.0448182
$76$	19.1640	2.19826
$77$	−0.637210	−0.0726169
$78$	2.18299	0.247175
$79$	3.02621	0.340475	0.170237	−	0.985403i	$-0.445547\pi$
$79$	3.02621	0.340475	0.170237	+	0.985403i	$0.445547\pi$
$80$	−4.04411	−0.452145
$81$	1.00000	0.111111
$82$	14.6359	1.61626
$83$	6.20971	0.681604	0.340802	−	0.940135i	$-0.389301\pi$
$83$	6.20971	0.681604	0.340802	+	0.940135i	$0.389301\pi$
$84$	−1.66823	−0.182019
$85$	11.3323	1.22916
$86$	−7.13912	−0.769831
$87$	−6.31547	−0.677090
$88$	1.76510	0.188160
$89$	−6.13977	−0.650815	−0.325407	−	0.945574i	$-0.605501\pi$
$89$	−6.13977	−0.650815	−0.325407	+	0.945574i	$0.605501\pi$
$90$	−4.68803	−0.494162
$91$	0.603238	0.0632365
$92$	−8.74305	−0.911526
$93$	−1.92623	−0.199741
$94$	−1.34884	−0.139123
$95$	14.8818	1.52684
$96$	−7.45289	−0.760658
$97$	−5.90264	−0.599323	−0.299661	−	0.954046i	$-0.596874\pi$
$97$	−5.90264	−0.599323	−0.299661	+	0.954046i	$0.596874\pi$
$98$	14.4866	1.46336
$99$	−1.05632	−0.106164
$100$	−1.07338	−0.107338
$101$	7.67214	0.763407	0.381703	−	0.924285i	$-0.375338\pi$
$101$	7.67214	0.763407	0.381703	+	0.924285i	$0.375338\pi$
$102$	11.5194	1.14059
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.67100	−0.163855
$105$	−1.29547	−0.126425
$106$	−31.1943	−3.02986
$107$	14.0593	1.35916	0.679582	−	0.733599i	$-0.262161\pi$
$107$	14.0593	1.35916	0.679582	+	0.733599i	$0.262161\pi$
$108$	−2.76546	−0.266107
$109$	−14.1233	−1.35276	−0.676381	−	0.736552i	$-0.736453\pi$
$109$	−14.1233	−1.35276	−0.676381	+	0.736552i	$0.736453\pi$
$110$	4.95205	0.472159
$111$	7.58967	0.720380
$112$	−1.13599	−0.107341
$113$	−19.9292	−1.87478	−0.937392	−	0.348276i	$-0.886767\pi$
$113$	−19.9292	−1.87478	−0.937392	+	0.348276i	$0.886767\pi$
$114$	15.1276	1.41683
$115$	−6.78943	−0.633118
$116$	17.4652	1.62160
$117$	1.00000	0.0924500
$118$	−18.7469	−1.72579
$119$	3.18322	0.291806
$120$	3.58851	0.327584
$121$	−9.88419	−0.898563
$122$	−4.91512	−0.444994
$123$	6.70449	0.604523
$124$	5.32692	0.478372
$125$	−11.5712	−1.03496
$126$	−1.31686	−0.117316
$127$	−7.73839	−0.686671	−0.343336	−	0.939213i	$-0.611557\pi$
$127$	−7.73839	−0.686671	−0.343336	+	0.939213i	$0.611557\pi$
$128$	12.3889	1.09503
$129$	−3.27034	−0.287937
$130$	−4.68803	−0.411168
$131$	5.61500	0.490585	0.245293	−	0.969449i	$-0.421116\pi$
$131$	5.61500	0.490585	0.245293	+	0.969449i	$0.421116\pi$
$132$	2.92120	0.254258
$133$	4.18029	0.362477
$134$	−14.5667	−1.25837
$135$	−2.14752	−0.184830
$136$	−8.81767	−0.756109
$137$	−11.3859	−0.972766	−0.486383	−	0.873746i	$-0.661684\pi$
$137$	−11.3859	−0.972766	−0.486383	+	0.873746i	$0.661684\pi$
$138$	−6.90157	−0.587501
$139$	12.3445	1.04704	0.523522	−	0.852012i	$-0.324618\pi$
$139$	12.3445	1.04704	0.523522	+	0.852012i	$0.324618\pi$
$140$	3.58257	0.302782
$141$	−0.617887	−0.0520355
$142$	−4.63267	−0.388765
$143$	−1.05632	−0.0883337
$144$	−1.88315	−0.156929
$145$	13.5626	1.12632
$146$	−25.1799	−2.08391
$147$	6.63610	0.547337
$148$	−20.9889	−1.72528
$149$	5.16781	0.423364	0.211682	−	0.977339i	$-0.432106\pi$
$149$	5.16781	0.423364	0.211682	+	0.977339i	$0.432106\pi$
$150$	−0.847301	−0.0691819
$151$	−9.03652	−0.735382	−0.367691	−	0.929948i	$-0.619852\pi$
$151$	−9.03652	−0.735382	−0.367691	+	0.929948i	$0.619852\pi$
$152$	−11.5796	−0.939228
$153$	5.27690	0.426612
$154$	1.39103	0.112092
$155$	4.13663	0.332262
$156$	−2.76546	−0.221414
$157$	−7.10949	−0.567399	−0.283700	−	0.958913i	$-0.591562\pi$
$157$	−7.10949	−0.567399	−0.283700	+	0.958913i	$0.591562\pi$
$158$	−6.60619	−0.525560
$159$	−14.2897	−1.13325
$160$	16.0053	1.26533
$161$	−1.90715	−0.150304
$162$	−2.18299	−0.171512
$163$	−2.59103	−0.202945	−0.101472	−	0.994838i	$-0.532355\pi$
$163$	−2.59103	−0.202945	−0.101472	+	0.994838i	$0.532355\pi$
$164$	−18.5410	−1.44781
$165$	2.26847	0.176600
$166$	−13.5558	−1.05213
$167$	14.1263	1.09312	0.546562	−	0.837418i	$-0.315936\pi$
$167$	14.1263	1.09312	0.546562	+	0.837418i	$0.315936\pi$
$168$	1.00801	0.0777695
$169$	1.00000	0.0769231
$170$	−24.7383	−1.89734
$171$	6.92975	0.529931
$172$	9.04398	0.689597
$173$	20.8676	1.58654	0.793269	−	0.608872i	$-0.208378\pi$
$173$	20.8676	1.58654	0.793269	+	0.608872i	$0.208378\pi$
$174$	13.7866	1.04516
$175$	−0.234139	−0.0176993
$176$	1.98920	0.149942
$177$	−8.58769	−0.645490
$178$	13.4031	1.00460
$179$	3.05765	0.228540	0.114270	−	0.993450i	$-0.463547\pi$
$179$	3.05765	0.228540	0.114270	+	0.993450i	$0.463547\pi$
$180$	5.93890	0.442659
$181$	−18.0793	−1.34382	−0.671912	−	0.740631i	$-0.734527\pi$
$181$	−18.0793	−1.34382	−0.671912	+	0.740631i	$0.734527\pi$
$182$	−1.31686	−0.0976125
$183$	−2.25155	−0.166440
$184$	5.28288	0.389459
$185$	−16.2990	−1.19833
$186$	4.20495	0.308322
$187$	−5.57408	−0.407617
$188$	1.70874	0.124623
$189$	−0.603238	−0.0438791
$190$	−32.4869	−2.35685
$191$	−11.8236	−0.855525	−0.427763	−	0.903891i	$-0.640698\pi$
$191$	−11.8236	−0.855525	−0.427763	+	0.903891i	$0.640698\pi$
$192$	12.5033	0.902349
$193$	7.57274	0.545098	0.272549	−	0.962142i	$-0.412133\pi$
$193$	7.57274	0.545098	0.272549	+	0.962142i	$0.412133\pi$
$194$	12.8854	0.925120
$195$	−2.14752	−0.153787
$196$	−18.3519	−1.31085
$197$	−20.4137	−1.45442	−0.727208	−	0.686418i	$-0.759182\pi$
$197$	−20.4137	−1.45442	−0.727208	+	0.686418i	$0.759182\pi$
$198$	2.30593	0.163876
$199$	−20.4533	−1.44990	−0.724948	−	0.688803i	$-0.758136\pi$
$199$	−20.4533	−1.44990	−0.724948	+	0.688803i	$0.758136\pi$
$200$	0.648576	0.0458612
$201$	−6.67280	−0.470663
$202$	−16.7482	−1.17840
$203$	3.80973	0.267391
$204$	−14.5931	−1.02172
$205$	−14.3981	−1.00560
$206$	2.18299	0.152096
$207$	−3.16152	−0.219741
$208$	−1.88315	−0.130573
$209$	−7.32001	−0.506336
$210$	2.82800	0.195150
$211$	−10.0266	−0.690263	−0.345132	−	0.938554i	$-0.612166\pi$
$211$	−10.0266	−0.690263	−0.345132	+	0.938554i	$0.612166\pi$
$212$	39.5176	2.71408
$213$	−2.12217	−0.145408
$214$	−30.6914	−2.09802
$215$	7.02313	0.478973
$216$	1.67100	0.113697
$217$	1.16198	0.0788801
$218$	30.8310	2.08814
$219$	−11.5346	−0.779435
$220$	−6.27336	−0.422950
$221$	5.27690	0.354963
$222$	−16.5682	−1.11199
$223$	−7.81693	−0.523460	−0.261730	−	0.965141i	$-0.584293\pi$
$223$	−7.81693	−0.523460	−0.261730	+	0.965141i	$0.584293\pi$
$224$	4.49587	0.300393
$225$	−0.388137	−0.0258758
$226$	43.5054	2.89393
$227$	17.4432	1.15774	0.578872	−	0.815418i	$-0.303493\pi$
$227$	17.4432	1.15774	0.578872	+	0.815418i	$0.303493\pi$
$228$	−19.1640	−1.26916
$229$	8.39787	0.554947	0.277473	−	0.960733i	$-0.410503\pi$
$229$	8.39787	0.554947	0.277473	+	0.960733i	$0.410503\pi$
$230$	14.8213	0.977287
$231$	0.637210	0.0419254
$232$	−10.5531	−0.692847
$233$	27.1373	1.77782	0.888911	−	0.458080i	$-0.151463\pi$
$233$	27.1373	1.77782	0.888911	+	0.458080i	$0.151463\pi$
$234$	−2.18299	−0.142707
$235$	1.32693	0.0865593
$236$	23.7489	1.54592
$237$	−3.02621	−0.196573
$238$	−6.94896	−0.450434
$239$	17.3407	1.12168	0.560839	−	0.827925i	$-0.310479\pi$
$239$	17.3407	1.12168	0.560839	+	0.827925i	$0.310479\pi$
$240$	4.04411	0.261046
$241$	−11.9353	−0.768822	−0.384411	−	0.923162i	$-0.625595\pi$
$241$	−11.9353	−0.768822	−0.384411	+	0.923162i	$0.625595\pi$
$242$	21.5771	1.38703
$243$	−1.00000	−0.0641500
$244$	6.22658	0.398616
$245$	−14.2512	−0.910476
$246$	−14.6359	−0.933148
$247$	6.92975	0.440929
$248$	−3.21873	−0.204389
$249$	−6.20971	−0.393524
$250$	25.2598	1.59757
$251$	14.6678	0.925823	0.462911	−	0.886405i	$-0.346805\pi$
$251$	14.6678	0.925823	0.462911	+	0.886405i	$0.346805\pi$
$252$	1.66823	0.105089
$253$	3.33956	0.209957
$254$	16.8929	1.05995
$255$	−11.3323	−0.709654
$256$	−2.03821	−0.127388
$257$	−12.1143	−0.755669	−0.377835	−	0.925873i	$-0.623331\pi$
$257$	−12.1143	−0.755669	−0.377835	+	0.925873i	$0.623331\pi$
$258$	7.13912	0.444462
$259$	−4.57838	−0.284487
$260$	5.93890	0.368315
$261$	6.31547	0.390918
$262$	−12.2575	−0.757272
$263$	14.7217	0.907779	0.453889	−	0.891058i	$-0.350036\pi$
$263$	14.7217	0.907779	0.453889	+	0.891058i	$0.350036\pi$
$264$	−1.76510	−0.108634
$265$	30.6875	1.88512
$266$	−9.12554	−0.559523
$267$	6.13977	0.375748
$268$	18.4534	1.12722
$269$	26.8565	1.63747	0.818733	−	0.574174i	$-0.194677\pi$
$269$	26.8565	1.63747	0.818733	+	0.574174i	$0.194677\pi$
$270$	4.68803	0.285305
$271$	18.3421	1.11420	0.557101	−	0.830445i	$-0.311914\pi$
$271$	18.3421	1.11420	0.557101	+	0.830445i	$0.311914\pi$
$272$	−9.93718	−0.602530
$273$	−0.603238	−0.0365096
$274$	24.8554	1.50157
$275$	0.409996	0.0247237
$276$	8.74305	0.526270
$277$	−21.2918	−1.27930	−0.639651	−	0.768666i	$-0.720921\pi$
$277$	−21.2918	−1.27930	−0.639651	+	0.768666i	$0.720921\pi$
$278$	−26.9479	−1.61623
$279$	1.92623	0.115321
$280$	−2.16472	−0.129367
$281$	−32.8578	−1.96013	−0.980067	−	0.198668i	$-0.936339\pi$
$281$	−32.8578	−1.96013	−0.980067	+	0.198668i	$0.936339\pi$
$282$	1.34884	0.0803225
$283$	−14.5898	−0.867276	−0.433638	−	0.901087i	$-0.642770\pi$
$283$	−14.5898	−0.867276	−0.433638	+	0.901087i	$0.642770\pi$
$284$	5.86876	0.348247
$285$	−14.8818	−0.881522
$286$	2.30593	0.136353
$287$	−4.04440	−0.238733
$288$	7.45289	0.439166
$289$	10.8456	0.637979
$290$	−29.6071	−1.73859
$291$	5.90264	0.346019
$292$	31.8984	1.86671
$293$	22.6706	1.32443	0.662215	−	0.749314i	$-0.269617\pi$
$293$	22.6706	1.32443	0.662215	+	0.749314i	$0.269617\pi$
$294$	−14.4866	−0.844874
$295$	18.4423	1.07375
$296$	12.6823	0.737144
$297$	1.05632	0.0612937
$298$	−11.2813	−0.653508
$299$	−3.16152	−0.182835
$300$	1.07338	0.0619716
$301$	1.97279	0.113710
$302$	19.7267	1.13514
$303$	−7.67214	−0.440753
$304$	−13.0497	−0.748454
$305$	4.83526	0.276866
$306$	−11.5194	−0.658522
$307$	18.6881	1.06659	0.533293	−	0.845930i	$-0.320954\pi$
$307$	18.6881	1.06659	0.533293	+	0.845930i	$0.320954\pi$
$308$	−1.76218	−0.100410
$309$	1.00000	0.0568880
$310$	−9.03024	−0.512883
$311$	−10.0778	−0.571460	−0.285730	−	0.958310i	$-0.592236\pi$
$311$	−10.0778	−0.571460	−0.285730	+	0.958310i	$0.592236\pi$
$312$	1.67100	0.0946015
$313$	3.34692	0.189179	0.0945895	−	0.995516i	$-0.469846\pi$
$313$	3.34692	0.189179	0.0945895	+	0.995516i	$0.469846\pi$
$314$	15.5200	0.875843
$315$	1.29547	0.0729914
$316$	8.36886	0.470785
$317$	−1.89021	−0.106165	−0.0530824	−	0.998590i	$-0.516905\pi$
$317$	−1.89021	−0.106165	−0.0530824	+	0.998590i	$0.516905\pi$
$318$	31.1943	1.74929
$319$	−6.67114	−0.373512
$320$	−26.8512	−1.50103
$321$	−14.0593	−0.784714
$322$	4.16329	0.232011
$323$	36.5676	2.03467
$324$	2.76546	0.153637
$325$	−0.388137	−0.0215300
$326$	5.65620	0.313268
$327$	14.1233	0.781018
$328$	11.2032	0.618592
$329$	0.372733	0.0205494
$330$	−4.95205	−0.272601
$331$	−22.6947	−1.24741	−0.623706	−	0.781659i	$-0.714374\pi$
$331$	−22.6947	−1.24741	−0.623706	+	0.781659i	$0.714374\pi$
$332$	17.1727	0.942475
$333$	−7.58967	−0.415911
$334$	−30.8376	−1.68736
$335$	14.3300	0.782932
$336$	1.13599	0.0619731
$337$	34.4444	1.87631	0.938153	−	0.346220i	$-0.112535\pi$
$337$	34.4444	1.87631	0.938153	+	0.346220i	$0.112535\pi$
$338$	−2.18299	−0.118739
$339$	19.9292	1.08241
$340$	31.3389	1.69959
$341$	−2.03471	−0.110186
$342$	−15.1276	−0.818007
$343$	−8.22581	−0.444152
$344$	−5.46472	−0.294638
$345$	6.78943	0.365531
$346$	−45.5539	−2.44899
$347$	−19.0816	−1.02435	−0.512176	−	0.858881i	$-0.671160\pi$
$347$	−19.0816	−1.02435	−0.512176	+	0.858881i	$0.671160\pi$
$348$	−17.4652	−0.936232
$349$	21.9421	1.17453	0.587267	−	0.809393i	$-0.300204\pi$
$349$	21.9421	1.17453	0.587267	+	0.809393i	$0.300204\pi$
$350$	0.511124	0.0273207
$351$	−1.00000	−0.0533761
$352$	−7.87262	−0.419612
$353$	−5.60304	−0.298220	−0.149110	−	0.988821i	$-0.547641\pi$
$353$	−5.60304	−0.298220	−0.149110	+	0.988821i	$0.547641\pi$
$354$	18.7469	0.996384
$355$	4.55740	0.241882
$356$	−16.9793	−0.899901
$357$	−3.18322	−0.168474
$358$	−6.67484	−0.352776
$359$	13.9845	0.738075	0.369038	−	0.929414i	$-0.379687\pi$
$359$	13.9845	0.738075	0.369038	+	0.929414i	$0.379687\pi$
$360$	−3.58851	−0.189131
$361$	29.0214	1.52744
$362$	39.4670	2.07434
$363$	9.88419	0.518786
$364$	1.66823	0.0874390
$365$	24.7708	1.29656
$366$	4.91512	0.256918
$367$	−7.73232	−0.403624	−0.201812	−	0.979424i	$-0.564683\pi$
$367$	−7.73232	−0.403624	−0.201812	+	0.979424i	$0.564683\pi$
$368$	5.95360	0.310353
$369$	−6.70449	−0.349022
$370$	35.5806	1.84975
$371$	8.62009	0.447533
$372$	−5.32692	−0.276188
$373$	−24.1629	−1.25111	−0.625555	−	0.780180i	$-0.715127\pi$
$373$	−24.1629	−1.25111	−0.625555	+	0.780180i	$0.715127\pi$
$374$	12.1682	0.629201
$375$	11.5712	0.597532
$376$	−1.03249	−0.0532465
$377$	6.31547	0.325263
$378$	1.31686	0.0677322
$379$	8.27854	0.425240	0.212620	−	0.977135i	$-0.431800\pi$
$379$	8.27854	0.425240	0.212620	+	0.977135i	$0.431800\pi$
$380$	41.1551	2.11121
$381$	7.73839	0.396450
$382$	25.8108	1.32060
$383$	14.0812	0.719516	0.359758	−	0.933046i	$-0.382859\pi$
$383$	14.0812	0.719516	0.359758	+	0.933046i	$0.382859\pi$
$384$	−12.3889	−0.632217
$385$	−1.36843	−0.0697414
$386$	−16.5313	−0.841418
$387$	3.27034	0.166240
$388$	−16.3235	−0.828702
$389$	−1.09755	−0.0556480	−0.0278240	−	0.999613i	$-0.508858\pi$
$389$	−1.09755	−0.0556480	−0.0278240	+	0.999613i	$0.508858\pi$
$390$	4.68803	0.237388
$391$	−16.6830	−0.843695
$392$	11.0889	0.560074
$393$	−5.61500	−0.283240
$394$	44.5629	2.24505
$395$	6.49885	0.326993
$396$	−2.92120	−0.146796
$397$	30.4637	1.52893	0.764464	−	0.644667i	$-0.223004\pi$
$397$	30.4637	1.52893	0.764464	+	0.644667i	$0.223004\pi$
$398$	44.6494	2.23807
$399$	−4.18029	−0.209276
$400$	0.730920	0.0365460
$401$	6.94279	0.346706	0.173353	−	0.984860i	$-0.444540\pi$
$401$	6.94279	0.346706	0.173353	+	0.984860i	$0.444540\pi$
$402$	14.5667	0.726520
$403$	1.92623	0.0959525
$404$	21.2170	1.05559
$405$	2.14752	0.106711
$406$	−8.31662	−0.412747
$407$	8.01710	0.397393
$408$	8.81767	0.436540
$409$	−0.773582	−0.0382512	−0.0191256	−	0.999817i	$-0.506088\pi$
$409$	−0.773582	−0.0382512	−0.0191256	+	0.999817i	$0.506088\pi$
$410$	31.4309	1.55226
$411$	11.3859	0.561627
$412$	−2.76546	−0.136244
$413$	5.18042	0.254912
$414$	6.90157	0.339194
$415$	13.3355	0.654614
$416$	7.45289	0.365408
$417$	−12.3445	−0.604511
$418$	15.9795	0.781585
$419$	27.6118	1.34892	0.674462	−	0.738310i	$-0.264376\pi$
$419$	27.6118	1.34892	0.674462	+	0.738310i	$0.264376\pi$
$420$	−3.58257	−0.174811
$421$	26.8931	1.31069	0.655344	−	0.755330i	$-0.272524\pi$
$421$	26.8931	1.31069	0.655344	+	0.755330i	$0.272524\pi$
$422$	21.8881	1.06550
$423$	0.617887	0.0300427
$424$	−23.8780	−1.15962
$425$	−2.04816	−0.0993504
$426$	4.63267	0.224454
$427$	1.35822	0.0657289
$428$	38.8805	1.87936
$429$	1.05632	0.0509995
$430$	−15.3314	−0.739348
$431$	20.8097	1.00237	0.501185	−	0.865340i	$-0.332898\pi$
$431$	20.8097	1.00237	0.501185	+	0.865340i	$0.332898\pi$
$432$	1.88315	0.0906030
$433$	4.03399	0.193861	0.0969305	−	0.995291i	$-0.469098\pi$
$433$	4.03399	0.193861	0.0969305	+	0.995291i	$0.469098\pi$
$434$	−2.53659	−0.121760
$435$	−13.5626	−0.650278
$436$	−39.0573	−1.87051
$437$	−21.9085	−1.04803
$438$	25.1799	1.20314
$439$	−8.85604	−0.422676	−0.211338	−	0.977413i	$-0.567782\pi$
$439$	−8.85604	−0.422676	−0.211338	+	0.977413i	$0.567782\pi$
$440$	3.79060	0.180710
$441$	−6.63610	−0.316005
$442$	−11.5194	−0.547923
$443$	35.3295	1.67855	0.839277	−	0.543704i	$-0.182979\pi$
$443$	35.3295	1.67855	0.839277	+	0.543704i	$0.182979\pi$
$444$	20.9889	0.996091
$445$	−13.1853	−0.625044
$446$	17.0643	0.808018
$447$	−5.16781	−0.244429
$448$	−7.54248	−0.356348
$449$	−13.7652	−0.649619	−0.324810	−	0.945779i	$-0.605300\pi$
$449$	−13.7652	−0.649619	−0.324810	+	0.945779i	$0.605300\pi$
$450$	0.847301	0.0399422
$451$	7.08207	0.333481
$452$	−55.1135	−2.59232
$453$	9.03652	0.424573
$454$	−38.0783	−1.78710
$455$	1.29547	0.0607325
$456$	11.5796	0.542264
$457$	−5.99230	−0.280308	−0.140154	−	0.990130i	$-0.544760\pi$
$457$	−5.99230	−0.280308	−0.140154	+	0.990130i	$0.544760\pi$
$458$	−18.3325	−0.856621
$459$	−5.27690	−0.246304
$460$	−18.7759	−0.875431
$461$	−30.2105	−1.40704	−0.703521	−	0.710675i	$-0.748390\pi$
$461$	−30.2105	−1.40704	−0.703521	+	0.710675i	$0.748390\pi$
$462$	−1.39103	−0.0647164
$463$	−3.79915	−0.176561	−0.0882807	−	0.996096i	$-0.528137\pi$
$463$	−3.79915	−0.176561	−0.0882807	+	0.996096i	$0.528137\pi$
$464$	−11.8930	−0.552117
$465$	−4.13663	−0.191832
$466$	−59.2405	−2.74426
$467$	0.327390	0.0151498	0.00757489	−	0.999971i	$-0.497589\pi$
$467$	0.327390	0.0151498	0.00757489	+	0.999971i	$0.497589\pi$
$468$	2.76546	0.127833
$469$	4.02529	0.185871
$470$	−2.89668	−0.133614
$471$	7.10949	0.327588
$472$	−14.3500	−0.660512
$473$	−3.45451	−0.158839
$474$	6.60619	0.303432
$475$	−2.68970	−0.123412
$476$	8.80308	0.403489
$477$	14.2897	0.654281
$478$	−37.8547	−1.73143
$479$	28.1466	1.28605	0.643024	−	0.765846i	$-0.277679\pi$
$479$	28.1466	1.28605	0.643024	+	0.765846i	$0.277679\pi$
$480$	−16.0053	−0.730537
$481$	−7.58967	−0.346059
$482$	26.0548	1.18676
$483$	1.90715	0.0867782
$484$	−27.3344	−1.24247
$485$	−12.6761	−0.575591
$486$	2.18299	0.0990226
$487$	34.7053	1.57265	0.786323	−	0.617815i	$-0.211982\pi$
$487$	34.7053	1.57265	0.786323	+	0.617815i	$0.211982\pi$
$488$	−3.76233	−0.170313
$489$	2.59103	0.117170
$490$	31.1103	1.40542
$491$	−30.6696	−1.38410	−0.692049	−	0.721851i	$-0.743292\pi$
$491$	−30.6696	−1.38410	−0.692049	+	0.721851i	$0.743292\pi$
$492$	18.5410	0.835893
$493$	33.3261	1.50093
$494$	−15.1276	−0.680623
$495$	−2.26847	−0.101960
$496$	−3.62738	−0.162874
$497$	1.28017	0.0574235
$498$	13.5558	0.607448
$499$	−11.0663	−0.495394	−0.247697	−	0.968838i	$-0.579674\pi$
$499$	−11.0663	−0.495394	−0.247697	+	0.968838i	$0.579674\pi$
$500$	−31.9996	−1.43106
$501$	−14.1263	−0.631116
$502$	−32.0197	−1.42911
$503$	5.48152	0.244409	0.122204	−	0.992505i	$-0.461004\pi$
$503$	5.48152	0.244409	0.122204	+	0.992505i	$0.461004\pi$
$504$	−1.00801	−0.0449002
$505$	16.4761	0.733177
$506$	−7.29024	−0.324091
$507$	−1.00000	−0.0444116
$508$	−21.4002	−0.949481
$509$	−7.49438	−0.332183	−0.166091	−	0.986110i	$-0.553115\pi$
$509$	−7.49438	−0.332183	−0.166091	+	0.986110i	$0.553115\pi$
$510$	24.7383	1.09543
$511$	6.95810	0.307808
$512$	−20.3284	−0.898395
$513$	−6.92975	−0.305956
$514$	26.4454	1.16646
$515$	−2.14752	−0.0946312
$516$	−9.04398	−0.398139
$517$	−0.652685	−0.0287050
$518$	9.99457	0.439136
$519$	−20.8676	−0.915988
$520$	−3.58851	−0.157366
$521$	−28.3150	−1.24050	−0.620251	−	0.784403i	$-0.712969\pi$
$521$	−28.3150	−1.24050	−0.620251	+	0.784403i	$0.712969\pi$
$522$	−13.7866	−0.603425
$523$	33.1848	1.45107	0.725535	−	0.688186i	$-0.241593\pi$
$523$	33.1848	1.45107	0.725535	+	0.688186i	$0.241593\pi$
$524$	15.5281	0.678347
$525$	0.234139	0.0102187
$526$	−32.1374	−1.40126
$527$	10.1645	0.442774
$528$	−1.98920	−0.0865689
$529$	−13.0048	−0.565427
$530$	−66.9906	−2.90989
$531$	8.58769	0.372674
$532$	11.5604	0.501208
$533$	−6.70449	−0.290404
$534$	−13.4031	−0.580008
$535$	30.1927	1.30534
$536$	−11.1502	−0.481616
$537$	−3.05765	−0.131948
$538$	−58.6275	−2.52761
$539$	7.00983	0.301935
$540$	−5.93890	−0.255569
$541$	5.17839	0.222636	0.111318	−	0.993785i	$-0.464493\pi$
$541$	5.17839	0.222636	0.111318	+	0.993785i	$0.464493\pi$
$542$	−40.0406	−1.71989
$543$	18.0793	0.775858
$544$	39.3281	1.68618
$545$	−30.3300	−1.29920
$546$	1.31686	0.0563566
$547$	19.9967	0.854997	0.427498	−	0.904016i	$-0.359395\pi$
$547$	19.9967	0.854997	0.427498	+	0.904016i	$0.359395\pi$
$548$	−31.4874	−1.34507
$549$	2.25155	0.0960939
$550$	−0.895019	−0.0381637
$551$	43.7646	1.86444
$552$	−5.28288	−0.224854
$553$	1.82552	0.0776291
$554$	46.4799	1.97474
$555$	16.2990	0.691854
$556$	34.1381	1.44778
$557$	−28.0503	−1.18853	−0.594265	−	0.804269i	$-0.702557\pi$
$557$	−28.0503	−1.18853	−0.594265	+	0.804269i	$0.702557\pi$
$558$	−4.20495	−0.178010
$559$	3.27034	0.138320
$560$	−2.43956	−0.103090
$561$	5.57408	0.235338
$562$	71.7284	3.02568
$563$	−35.5708	−1.49913	−0.749565	−	0.661930i	$-0.769737\pi$
$563$	−35.5708	−1.49913	−0.749565	+	0.661930i	$0.769737\pi$
$564$	−1.70874	−0.0719511
$565$	−42.7985	−1.80055
$566$	31.8495	1.33873
$567$	0.603238	0.0253336
$568$	−3.54613	−0.148792
$569$	−12.8128	−0.537142	−0.268571	−	0.963260i	$-0.586551\pi$
$569$	−12.8128	−0.537142	−0.268571	+	0.963260i	$0.586551\pi$
$570$	32.4869	1.36073
$571$	−2.65151	−0.110962	−0.0554811	−	0.998460i	$-0.517669\pi$
$571$	−2.65151	−0.110962	−0.0554811	+	0.998460i	$0.517669\pi$
$572$	−2.92120	−0.122142
$573$	11.8236	0.493938
$574$	8.82890	0.368511
$575$	1.22710	0.0511737
$576$	−12.5033	−0.520972
$577$	33.7490	1.40499	0.702495	−	0.711689i	$-0.252069\pi$
$577$	33.7490	1.40499	0.702495	+	0.711689i	$0.252069\pi$
$578$	−23.6760	−0.984790
$579$	−7.57274	−0.314712
$580$	37.5069	1.55739
$581$	3.74593	0.155407
$582$	−12.8854	−0.534118
$583$	−15.0945	−0.625149
$584$	−19.2742	−0.797574
$585$	2.14752	0.0887892
$586$	−49.4897	−2.04440
$587$	3.72873	0.153901	0.0769505	−	0.997035i	$-0.475482\pi$
$587$	3.72873	0.153901	0.0769505	+	0.997035i	$0.475482\pi$
$588$	18.3519	0.756819
$589$	13.3483	0.550008
$590$	−40.2593	−1.65745
$591$	20.4137	0.839707
$592$	14.2925	0.587417
$593$	32.6347	1.34015	0.670074	−	0.742294i	$-0.266262\pi$
$593$	32.6347	1.34015	0.670074	+	0.742294i	$0.266262\pi$
$594$	−2.30593	−0.0946136
$595$	6.83605	0.280251
$596$	14.2914	0.585398
$597$	20.4533	0.837098
$598$	6.90157	0.282226
$599$	−37.1180	−1.51660	−0.758300	−	0.651905i	$-0.773970\pi$
$599$	−37.1180	−1.51660	−0.758300	+	0.651905i	$0.773970\pi$
$600$	−0.648576	−0.0264780
$601$	−1.54003	−0.0628192	−0.0314096	−	0.999507i	$-0.510000\pi$
$601$	−1.54003	−0.0628192	−0.0314096	+	0.999507i	$0.510000\pi$
$602$	−4.30659	−0.175523
$603$	6.67280	0.271738
$604$	−24.9901	−1.01683
$605$	−21.2266	−0.862982
$606$	16.7482	0.680351
$607$	33.7817	1.37116	0.685578	−	0.727999i	$-0.259550\pi$
$607$	33.7817	1.37116	0.685578	+	0.727999i	$0.259550\pi$
$608$	51.6467	2.09455
$609$	−3.80973	−0.154378
$610$	−10.5553	−0.427374
$611$	0.617887	0.0249970
$612$	14.5931	0.589889
$613$	32.0731	1.29542	0.647710	−	0.761887i	$-0.275727\pi$
$613$	32.0731	1.29542	0.647710	+	0.761887i	$0.275727\pi$
$614$	−40.7960	−1.64639
$615$	14.3981	0.580586
$616$	1.06478	0.0429010
$617$	42.7972	1.72295	0.861475	−	0.507799i	$-0.169541\pi$
$617$	42.7972	1.72295	0.861475	+	0.507799i	$0.169541\pi$
$618$	−2.18299	−0.0878129
$619$	−38.6834	−1.55482	−0.777409	−	0.628995i	$-0.783467\pi$
$619$	−38.6834	−1.55482	−0.777409	+	0.628995i	$0.783467\pi$
$620$	11.4397	0.459429
$621$	3.16152	0.126867
$622$	21.9998	0.882112
$623$	−3.70374	−0.148387
$624$	1.88315	0.0753863
$625$	−22.9087	−0.916346
$626$	−7.30630	−0.292018
$627$	7.32001	0.292333
$628$	−19.6610	−0.784560
$629$	−40.0499	−1.59689
$630$	−2.82800	−0.112670
$631$	32.0582	1.27622	0.638109	−	0.769946i	$-0.279717\pi$
$631$	32.0582	1.27622	0.638109	+	0.769946i	$0.279717\pi$
$632$	−5.05678	−0.201148
$633$	10.0266	0.398524
$634$	4.12632	0.163877
$635$	−16.6184	−0.659481
$636$	−39.5176	−1.56698
$637$	−6.63610	−0.262932
$638$	14.5631	0.576557
$639$	2.12217	0.0839516
$640$	26.6054	1.05167
$641$	−1.75709	−0.0694010	−0.0347005	−	0.999398i	$-0.511048\pi$
$641$	−1.75709	−0.0694010	−0.0347005	+	0.999398i	$0.511048\pi$
$642$	30.6914	1.21129
$643$	13.5640	0.534913	0.267457	−	0.963570i	$-0.413817\pi$
$643$	13.5640	0.534913	0.267457	+	0.963570i	$0.413817\pi$
$644$	−5.27414	−0.207830
$645$	−7.02313	−0.276535
$646$	−79.8268	−3.14074
$647$	10.4286	0.409991	0.204996	−	0.978763i	$-0.434282\pi$
$647$	10.4286	0.409991	0.204996	+	0.978763i	$0.434282\pi$
$648$	−1.67100	−0.0656429
$649$	−9.07132	−0.356080
$650$	0.847301	0.0332339
$651$	−1.16198	−0.0455414
$652$	−7.16538	−0.280618
$653$	16.4692	0.644491	0.322246	−	0.946656i	$-0.395562\pi$
$653$	16.4692	0.644491	0.322246	+	0.946656i	$0.395562\pi$
$654$	−30.8310	−1.20559
$655$	12.0584	0.471159
$656$	12.6255	0.492945
$657$	11.5346	0.450007
$658$	−0.813674	−0.0317203
$659$	−39.2008	−1.52704	−0.763522	−	0.645781i	$-0.776532\pi$
$659$	−39.2008	−1.52704	−0.763522	+	0.645781i	$0.776532\pi$
$660$	6.27336	0.244190
$661$	9.94678	0.386885	0.193442	−	0.981112i	$-0.438035\pi$
$661$	9.94678	0.386885	0.193442	+	0.981112i	$0.438035\pi$
$662$	49.5423	1.92552
$663$	−5.27690	−0.204938
$664$	−10.3764	−0.402682
$665$	8.97727	0.348124
$666$	16.5682	0.642005
$667$	−19.9665	−0.773105
$668$	39.0657	1.51150
$669$	7.81693	0.302220
$670$	−31.2823	−1.20854
$671$	−2.37835	−0.0918153
$672$	−4.49587	−0.173432
$673$	23.5980	0.909637	0.454819	−	0.890584i	$-0.349704\pi$
$673$	23.5980	0.909637	0.454819	+	0.890584i	$0.349704\pi$
$674$	−75.1919	−2.89628
$675$	0.388137	0.0149394
$676$	2.76546	0.106364
$677$	1.96251	0.0754254	0.0377127	−	0.999289i	$-0.487993\pi$
$677$	1.96251	0.0754254	0.0377127	+	0.999289i	$0.487993\pi$
$678$	−43.5054	−1.67081
$679$	−3.56070	−0.136647
$680$	−18.9362	−0.726169
$681$	−17.4432	−0.668424
$682$	4.44176	0.170084
$683$	−11.7025	−0.447785	−0.223893	−	0.974614i	$-0.571877\pi$
$683$	−11.7025	−0.447785	−0.223893	+	0.974614i	$0.571877\pi$
$684$	19.1640	0.732752
$685$	−24.4516	−0.934247
$686$	17.9569	0.685598
$687$	−8.39787	−0.320399
$688$	−6.15853	−0.234792
$689$	14.2897	0.544394
$690$	−14.8213	−0.564237
$691$	23.7265	0.902598	0.451299	−	0.892373i	$-0.350961\pi$
$691$	23.7265	0.902598	0.451299	+	0.892373i	$0.350961\pi$
$692$	57.7086	2.19375
$693$	−0.637210	−0.0242056
$694$	41.6549	1.58120
$695$	26.5100	1.00558
$696$	10.5531	0.400015
$697$	−35.3789	−1.34007
$698$	−47.8995	−1.81302
$699$	−27.1373	−1.02643
$700$	−0.647503	−0.0244733
$701$	28.7248	1.08492	0.542460	−	0.840082i	$-0.317493\pi$
$701$	28.7248	1.08492	0.542460	+	0.840082i	$0.317493\pi$
$702$	2.18299	0.0823918
$703$	−52.5945	−1.98364
$704$	13.2075	0.497775
$705$	−1.32693	−0.0499750
$706$	12.2314	0.460335
$707$	4.62813	0.174059
$708$	−23.7489	−0.892539
$709$	8.87649	0.333364	0.166682	−	0.986011i	$-0.446695\pi$
$709$	8.87649	0.333364	0.166682	+	0.986011i	$0.446695\pi$
$710$	−9.94878	−0.373371
$711$	3.02621	0.113492
$712$	10.2595	0.384492
$713$	−6.08981	−0.228065
$714$	6.94896	0.260058
$715$	−2.26847	−0.0848358
$716$	8.45582	0.316009
$717$	−17.3407	−0.647601
$718$	−30.5281	−1.13930
$719$	46.4119	1.73087	0.865437	−	0.501018i	$-0.167041\pi$
$719$	46.4119	1.73087	0.865437	+	0.501018i	$0.167041\pi$
$720$	−4.04411	−0.150715
$721$	−0.603238	−0.0224658
$722$	−63.3536	−2.35778
$723$	11.9353	0.443880
$724$	−49.9976	−1.85815
$725$	−2.45127	−0.0910379
$726$	−21.5771	−0.800803
$727$	−1.13202	−0.0419844	−0.0209922	−	0.999780i	$-0.506683\pi$
$727$	−1.13202	−0.0419844	−0.0209922	+	0.999780i	$0.506683\pi$
$728$	−1.00801	−0.0373593
$729$	1.00000	0.0370370
$730$	−54.0745	−2.00139
$731$	17.2572	0.638281
$732$	−6.22658	−0.230141
$733$	44.7170	1.65166	0.825829	−	0.563920i	$-0.190707\pi$
$733$	44.7170	1.65166	0.825829	+	0.563920i	$0.190707\pi$
$734$	16.8796	0.623038
$735$	14.2512	0.525663
$736$	−23.5624	−0.868523
$737$	−7.04860	−0.259638
$738$	14.6359	0.538753
$739$	35.9114	1.32102	0.660512	−	0.750816i	$-0.270339\pi$
$739$	35.9114	1.32102	0.660512	+	0.750816i	$0.270339\pi$
$740$	−45.0743	−1.65696
$741$	−6.92975	−0.254571
$742$	−18.8176	−0.690816
$743$	−5.46113	−0.200349	−0.100175	−	0.994970i	$-0.531940\pi$
$743$	−5.46113	−0.200349	−0.100175	+	0.994970i	$0.531940\pi$
$744$	3.21873	0.118004
$745$	11.0980	0.406600
$746$	52.7475	1.93122
$747$	6.20971	0.227201
$748$	−15.4149	−0.563624
$749$	8.48111	0.309893
$750$	−25.2598	−0.922356
$751$	−6.65506	−0.242847	−0.121423	−	0.992601i	$-0.538746\pi$
$751$	−6.65506	−0.242847	−0.121423	+	0.992601i	$0.538746\pi$
$752$	−1.16357	−0.0424312
$753$	−14.6678	−0.534524
$754$	−13.7866	−0.502080
$755$	−19.4062	−0.706262
$756$	−1.66823	−0.0606730
$757$	−37.9946	−1.38094	−0.690468	−	0.723363i	$-0.742595\pi$
$757$	−37.9946	−1.38094	−0.690468	+	0.723363i	$0.742595\pi$
$758$	−18.0720	−0.656404
$759$	−3.33956	−0.121218
$760$	−24.8674	−0.902037
$761$	47.7901	1.73239	0.866196	−	0.499705i	$-0.166558\pi$
$761$	47.7901	1.73239	0.866196	+	0.499705i	$0.166558\pi$
$762$	−16.8929	−0.611964
$763$	−8.51968	−0.308433
$764$	−32.6977	−1.18296
$765$	11.3323	0.409719
$766$	−30.7392	−1.11065
$767$	8.58769	0.310083
$768$	2.03821	0.0735475
$769$	−33.6790	−1.21449	−0.607247	−	0.794513i	$-0.707726\pi$
$769$	−33.6790	−1.21449	−0.607247	+	0.794513i	$0.707726\pi$
$770$	2.98726	0.107653
$771$	12.1143	0.436286
$772$	20.9421	0.753724
$773$	−4.76372	−0.171339	−0.0856696	−	0.996324i	$-0.527303\pi$
$773$	−4.76372	−0.171339	−0.0856696	+	0.996324i	$0.527303\pi$
$774$	−7.13912	−0.256610
$775$	−0.747643	−0.0268561
$776$	9.86329	0.354072
$777$	4.57838	0.164248
$778$	2.39595	0.0858988
$779$	−46.4604	−1.66462
$780$	−5.93890	−0.212647
$781$	−2.24168	−0.0802136
$782$	36.4189	1.30234
$783$	−6.31547	−0.225697
$784$	12.4968	0.446313
$785$	−15.2678	−0.544931
$786$	12.2575	0.437211
$787$	−7.39989	−0.263778	−0.131889	−	0.991265i	$-0.542104\pi$
$787$	−7.39989	−0.263778	−0.131889	+	0.991265i	$0.542104\pi$
$788$	−56.4533	−2.01106
$789$	−14.7217	−0.524106
$790$	−14.1870	−0.504749
$791$	−12.0221	−0.427455
$792$	1.76510	0.0627201
$793$	2.25155	0.0799550
$794$	−66.5020	−2.36007
$795$	−30.6875	−1.08837
$796$	−56.5628	−2.00482
$797$	22.3261	0.790832	0.395416	−	0.918502i	$-0.370600\pi$
$797$	22.3261	0.790832	0.395416	+	0.918502i	$0.370600\pi$
$798$	9.12554	0.323041
$799$	3.26053	0.115349
$800$	−2.89275	−0.102274
$801$	−6.13977	−0.216938
$802$	−15.1561	−0.535179
$803$	−12.1842	−0.429970
$804$	−18.4534	−0.650800
$805$	−4.09564	−0.144352
$806$	−4.20495	−0.148113
$807$	−26.8565	−0.945392
$808$	−12.8201	−0.451010
$809$	40.3047	1.41704	0.708519	−	0.705691i	$-0.249363\pi$
$809$	40.3047	1.41704	0.708519	+	0.705691i	$0.249363\pi$
$810$	−4.68803	−0.164721
$811$	9.23529	0.324295	0.162147	−	0.986767i	$-0.448158\pi$
$811$	9.23529	0.324295	0.162147	+	0.986767i	$0.448158\pi$
$812$	10.5357	0.369729
$813$	−18.3421	−0.643284
$814$	−17.5013	−0.613419
$815$	−5.56429	−0.194909
$816$	9.93718	0.347871
$817$	22.6626	0.792864
$818$	1.68873	0.0590449
$819$	0.603238	0.0210788
$820$	−39.8173	−1.39048
$821$	−13.1297	−0.458230	−0.229115	−	0.973399i	$-0.573583\pi$
$821$	−13.1297	−0.458230	−0.229115	+	0.973399i	$0.573583\pi$
$822$	−24.8554	−0.866933
$823$	3.44974	0.120250	0.0601251	−	0.998191i	$-0.480850\pi$
$823$	3.44974	0.120250	0.0601251	+	0.998191i	$0.480850\pi$
$824$	1.67100	0.0582119
$825$	−0.409996	−0.0142742
$826$	−11.3088	−0.393484
$827$	39.2823	1.36598	0.682990	−	0.730427i	$-0.260679\pi$
$827$	39.2823	1.36598	0.682990	+	0.730427i	$0.260679\pi$
$828$	−8.74305	−0.303842
$829$	−9.59393	−0.333211	−0.166605	−	0.986024i	$-0.553281\pi$
$829$	−9.59393	−0.333211	−0.166605	+	0.986024i	$0.553281\pi$
$830$	−29.1113	−1.01047
$831$	21.2918	0.738605
$832$	−12.5033	−0.433475
$833$	−35.0180	−1.21330
$834$	26.9479	0.933129
$835$	30.3365	1.04984
$836$	−20.2432	−0.700126
$837$	−1.92623	−0.0665803
$838$	−60.2763	−2.08221
$839$	−32.9251	−1.13670	−0.568351	−	0.822786i	$-0.692418\pi$
$839$	−32.9251	−1.13670	−0.568351	+	0.822786i	$0.692418\pi$
$840$	2.16472	0.0746900
$841$	10.8852	0.375351
$842$	−58.7074	−2.02319
$843$	32.8578	1.13168
$844$	−27.7283	−0.954448
$845$	2.14752	0.0738771
$846$	−1.34884	−0.0463742
$847$	−5.96252	−0.204875
$848$	−26.9096	−0.924081
$849$	14.5898	0.500722
$850$	4.47112	0.153358
$851$	23.9949	0.822534
$852$	−5.86876	−0.201061
$853$	3.45990	0.118465	0.0592323	−	0.998244i	$-0.481135\pi$
$853$	3.45990	0.118465	0.0592323	+	0.998244i	$0.481135\pi$
$854$	−2.96499	−0.101460
$855$	14.8818	0.508947
$856$	−23.4930	−0.802976
$857$	−33.5096	−1.14467	−0.572333	−	0.820021i	$-0.693962\pi$
$857$	−33.5096	−1.14467	−0.572333	+	0.820021i	$0.693962\pi$
$858$	−2.30593	−0.0787233
$859$	−32.1134	−1.09569	−0.547847	−	0.836579i	$-0.684552\pi$
$859$	−32.1134	−1.09569	−0.547847	+	0.836579i	$0.684552\pi$
$860$	19.4222	0.662291
$861$	4.04440	0.137833
$862$	−45.4275	−1.54727
$863$	−55.9802	−1.90559	−0.952793	−	0.303620i	$-0.901805\pi$
$863$	−55.9802	−1.90559	−0.952793	+	0.303620i	$0.901805\pi$
$864$	−7.45289	−0.253553
$865$	44.8138	1.52371
$866$	−8.80617	−0.299246
$867$	−10.8456	−0.368337
$868$	3.21340	0.109070
$869$	−3.19663	−0.108438
$870$	29.6071	1.00378
$871$	6.67280	0.226099
$872$	23.5999	0.799194
$873$	−5.90264	−0.199774
$874$	47.8262	1.61774
$875$	−6.98016	−0.235973
$876$	−31.8984	−1.07775
$877$	36.0850	1.21850	0.609252	−	0.792977i	$-0.291470\pi$
$877$	36.0850	1.21850	0.609252	+	0.792977i	$0.291470\pi$
$878$	19.3327	0.652446
$879$	−22.6706	−0.764660
$880$	4.27186	0.144004
$881$	−35.2781	−1.18855	−0.594274	−	0.804262i	$-0.702561\pi$
$881$	−35.2781	−1.18855	−0.594274	+	0.804262i	$0.702561\pi$
$882$	14.4866	0.487788
$883$	10.7259	0.360954	0.180477	−	0.983579i	$-0.442236\pi$
$883$	10.7259	0.360954	0.180477	+	0.983579i	$0.442236\pi$
$884$	14.5931	0.490817
$885$	−18.4423	−0.619930
$886$	−77.1240	−2.59103
$887$	−21.0020	−0.705179	−0.352590	−	0.935778i	$-0.614699\pi$
$887$	−21.0020	−0.705179	−0.352590	+	0.935778i	$0.614699\pi$
$888$	−12.6823	−0.425591
$889$	−4.66809	−0.156563
$890$	28.7835	0.964824
$891$	−1.05632	−0.0353879
$892$	−21.6174	−0.723805
$893$	4.28181	0.143285
$894$	11.2813	0.377303
$895$	6.56639	0.219490
$896$	7.47344	0.249670
$897$	3.16152	0.105560
$898$	30.0493	1.00276
$899$	12.1651	0.405728
$900$	−1.07338	−0.0357793
$901$	75.4053	2.51211
$902$	−15.4601	−0.514765
$903$	−1.97279	−0.0656503
$904$	33.3017	1.10760
$905$	−38.8258	−1.29061
$906$	−19.7267	−0.655375
$907$	−52.4356	−1.74110	−0.870549	−	0.492082i	$-0.836236\pi$
$907$	−52.4356	−1.74110	−0.870549	+	0.492082i	$0.836236\pi$
$908$	48.2384	1.60085
$909$	7.67214	0.254469
$910$	−2.82800	−0.0937473
$911$	−9.84115	−0.326052	−0.163026	−	0.986622i	$-0.552125\pi$
$911$	−9.84115	−0.326052	−0.163026	+	0.986622i	$0.552125\pi$
$912$	13.0497	0.432120
$913$	−6.55942	−0.217085
$914$	13.0812	0.432686
$915$	−4.83526	−0.159849
$916$	23.2240	0.767342
$917$	3.38718	0.111855
$918$	11.5194	0.380198
$919$	−27.0275	−0.891556	−0.445778	−	0.895144i	$-0.647073\pi$
$919$	−27.0275	−0.891556	−0.445778	+	0.895144i	$0.647073\pi$
$920$	11.3451	0.374037
$921$	−18.6881	−0.615794
$922$	65.9492	2.17192
$923$	2.12217	0.0698519
$924$	1.76218	0.0579715
$925$	2.94584	0.0968585
$926$	8.29351	0.272542
$927$	−1.00000	−0.0328443
$928$	47.0685	1.54510
$929$	3.35293	0.110006	0.0550031	−	0.998486i	$-0.482483\pi$
$929$	3.35293	0.110006	0.0550031	+	0.998486i	$0.482483\pi$
$930$	9.03024	0.296113
$931$	−45.9865	−1.50715
$932$	75.0471	2.45825
$933$	10.0778	0.329933
$934$	−0.714689	−0.0233853
$935$	−11.9705	−0.391476
$936$	−1.67100	−0.0546182
$937$	−1.87747	−0.0613342	−0.0306671	−	0.999530i	$-0.509763\pi$
$937$	−1.87747	−0.0613342	−0.0306671	+	0.999530i	$0.509763\pi$
$938$	−8.78718	−0.286912
$939$	−3.34692	−0.109223
$940$	3.66957	0.119688
$941$	7.46359	0.243306	0.121653	−	0.992573i	$-0.461180\pi$
$941$	7.46359	0.243306	0.121653	+	0.992573i	$0.461180\pi$
$942$	−15.5200	−0.505668
$943$	21.1963	0.690248
$944$	−16.1719	−0.526350
$945$	−1.29547	−0.0421416
$946$	7.54117	0.245185
$947$	−26.2180	−0.851970	−0.425985	−	0.904730i	$-0.640072\pi$
$947$	−26.2180	−0.851970	−0.425985	+	0.904730i	$0.640072\pi$
$948$	−8.36886	−0.271808
$949$	11.5346	0.374428
$950$	5.87159	0.190499
$951$	1.89021	0.0612943
$952$	−5.31915	−0.172395
$953$	−44.6207	−1.44541	−0.722703	−	0.691159i	$-0.757100\pi$
$953$	−44.6207	−1.44541	−0.722703	+	0.691159i	$0.757100\pi$
$954$	−31.1943	−1.00995
$955$	−25.3915	−0.821648
$956$	47.9551	1.55098
$957$	6.67114	0.215647
$958$	−61.4437	−1.98516
$959$	−6.86843	−0.221793
$960$	26.8512	0.866618
$961$	−27.2896	−0.880311
$962$	16.5682	0.534180
$963$	14.0593	0.453055
$964$	−33.0067	−1.06307
$965$	16.2627	0.523513
$966$	−4.16329	−0.133952
$967$	53.2215	1.71149	0.855744	−	0.517400i	$-0.173100\pi$
$967$	53.2215	1.71149	0.855744	+	0.517400i	$0.173100\pi$
$968$	16.5164	0.530859
$969$	−36.5676	−1.17472
$970$	27.6718	0.888488
$971$	15.3042	0.491135	0.245568	−	0.969379i	$-0.421026\pi$
$971$	15.3042	0.491135	0.245568	+	0.969379i	$0.421026\pi$
$972$	−2.76546	−0.0887022
$973$	7.44665	0.238729
$974$	−75.7614	−2.42755
$975$	0.388137	0.0124303
$976$	−4.24001	−0.135719
$977$	4.73103	0.151359	0.0756795	−	0.997132i	$-0.475887\pi$
$977$	4.73103	0.151359	0.0756795	+	0.997132i	$0.475887\pi$
$978$	−5.65620	−0.180865
$979$	6.48555	0.207279
$980$	−39.4111	−1.25894
$981$	−14.1233	−0.450921
$982$	66.9515	2.13651
$983$	2.48434	0.0792382	0.0396191	−	0.999215i	$-0.487386\pi$
$983$	2.48434	0.0792382	0.0396191	+	0.999215i	$0.487386\pi$
$984$	−11.2032	−0.357144
$985$	−43.8389	−1.39682
$986$	−72.7506	−2.31685
$987$	−0.372733	−0.0118642
$988$	19.1640	0.609687
$989$	−10.3392	−0.328768
$990$	4.95205	0.157386
$991$	31.9034	1.01344	0.506722	−	0.862109i	$-0.330857\pi$
$991$	31.9034	1.01344	0.506722	+	0.862109i	$0.330857\pi$
$992$	14.3560	0.455804
$993$	22.6947	0.720194
$994$	−2.79460	−0.0886394
$995$	−43.9240	−1.39248
$996$	−17.1727	−0.544138
$997$	−7.36795	−0.233345	−0.116673	−	0.993170i	$-0.537223\pi$
$997$	−7.36795	−0.233345	−0.116673	+	0.993170i	$0.537223\pi$
$998$	24.1576	0.764695
$999$	7.58967	0.240127

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.j.1.3	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.j.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.18299 q^{2} -1.00000 q^{3} +2.76546 q^{4} +2.14752 q^{5} +2.18299 q^{6} +0.603238 q^{7} -1.67100 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.18299 q^{2} -1.00000 q^{3} +2.76546 q^{4} +2.14752 q^{5} +2.18299 q^{6} +0.603238 q^{7} -1.67100 q^{8} +1.00000 q^{9} -4.68803 q^{10} -1.05632 q^{11} -2.76546 q^{12} +1.00000 q^{13} -1.31686 q^{14} -2.14752 q^{15} -1.88315 q^{16} +5.27690 q^{17} -2.18299 q^{18} +6.92975 q^{19} +5.93890 q^{20} -0.603238 q^{21} +2.30593 q^{22} -3.16152 q^{23} +1.67100 q^{24} -0.388137 q^{25} -2.18299 q^{26} -1.00000 q^{27} +1.66823 q^{28} +6.31547 q^{29} +4.68803 q^{30} +1.92623 q^{31} +7.45289 q^{32} +1.05632 q^{33} -11.5194 q^{34} +1.29547 q^{35} +2.76546 q^{36} -7.58967 q^{37} -15.1276 q^{38} -1.00000 q^{39} -3.58851 q^{40} -6.70449 q^{41} +1.31686 q^{42} +3.27034 q^{43} -2.92120 q^{44} +2.14752 q^{45} +6.90157 q^{46} +0.617887 q^{47} +1.88315 q^{48} -6.63610 q^{49} +0.847301 q^{50} -5.27690 q^{51} +2.76546 q^{52} +14.2897 q^{53} +2.18299 q^{54} -2.26847 q^{55} -1.00801 q^{56} -6.92975 q^{57} -13.7866 q^{58} +8.58769 q^{59} -5.93890 q^{60} +2.25155 q^{61} -4.20495 q^{62} +0.603238 q^{63} -12.5033 q^{64} +2.14752 q^{65} -2.30593 q^{66} +6.67280 q^{67} +14.5931 q^{68} +3.16152 q^{69} -2.82800 q^{70} +2.12217 q^{71} -1.67100 q^{72} +11.5346 q^{73} +16.5682 q^{74} +0.388137 q^{75} +19.1640 q^{76} -0.637210 q^{77} +2.18299 q^{78} +3.02621 q^{79} -4.04411 q^{80} +1.00000 q^{81} +14.6359 q^{82} +6.20971 q^{83} -1.66823 q^{84} +11.3323 q^{85} -7.13912 q^{86} -6.31547 q^{87} +1.76510 q^{88} -6.13977 q^{89} -4.68803 q^{90} +0.603238 q^{91} -8.74305 q^{92} -1.92623 q^{93} -1.34884 q^{94} +14.8818 q^{95} -7.45289 q^{96} -5.90264 q^{97} +14.4866 q^{98} -1.05632 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) \) 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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