LMFDB - Embedded newform 4017.2.a.l.1.28

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:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.28
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)

$f(q)$	$=$	$q+2.39333 q^{2} +1.00000 q^{3} +3.72803 q^{4} -1.40202 q^{5} +2.39333 q^{6} +1.96997 q^{7} +4.13575 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.39333 q^{2} +1.00000 q^{3} +3.72803 q^{4} -1.40202 q^{5} +2.39333 q^{6} +1.96997 q^{7} +4.13575 q^{8} +1.00000 q^{9} -3.35549 q^{10} +6.57798 q^{11} +3.72803 q^{12} -1.00000 q^{13} +4.71479 q^{14} -1.40202 q^{15} +2.44215 q^{16} -1.72068 q^{17} +2.39333 q^{18} +2.07272 q^{19} -5.22676 q^{20} +1.96997 q^{21} +15.7433 q^{22} +6.57879 q^{23} +4.13575 q^{24} -3.03435 q^{25} -2.39333 q^{26} +1.00000 q^{27} +7.34411 q^{28} +0.697292 q^{29} -3.35549 q^{30} +1.51915 q^{31} -2.42662 q^{32} +6.57798 q^{33} -4.11816 q^{34} -2.76193 q^{35} +3.72803 q^{36} -8.95694 q^{37} +4.96070 q^{38} -1.00000 q^{39} -5.79839 q^{40} -10.0180 q^{41} +4.71479 q^{42} +7.65800 q^{43} +24.5229 q^{44} -1.40202 q^{45} +15.7452 q^{46} -5.50250 q^{47} +2.44215 q^{48} -3.11922 q^{49} -7.26220 q^{50} -1.72068 q^{51} -3.72803 q^{52} +6.02052 q^{53} +2.39333 q^{54} -9.22245 q^{55} +8.14730 q^{56} +2.07272 q^{57} +1.66885 q^{58} -11.8504 q^{59} -5.22676 q^{60} +5.39639 q^{61} +3.63583 q^{62} +1.96997 q^{63} -10.6920 q^{64} +1.40202 q^{65} +15.7433 q^{66} +4.09403 q^{67} -6.41475 q^{68} +6.57879 q^{69} -6.61022 q^{70} +15.6357 q^{71} +4.13575 q^{72} +12.5085 q^{73} -21.4369 q^{74} -3.03435 q^{75} +7.72715 q^{76} +12.9584 q^{77} -2.39333 q^{78} -7.11099 q^{79} -3.42394 q^{80} +1.00000 q^{81} -23.9763 q^{82} +4.05475 q^{83} +7.34411 q^{84} +2.41242 q^{85} +18.3281 q^{86} +0.697292 q^{87} +27.2049 q^{88} +3.74013 q^{89} -3.35549 q^{90} -1.96997 q^{91} +24.5259 q^{92} +1.51915 q^{93} -13.1693 q^{94} -2.90599 q^{95} -2.42662 q^{96} +2.19386 q^{97} -7.46532 q^{98} +6.57798 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * 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 $

$2$	2.39333	1.69234	0.846170	−	0.532913i	$-0.178903\pi$
$2$	2.39333	1.69234	0.846170	+	0.532913i	$0.178903\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.72803	1.86402
$5$	−1.40202	−0.627001	−0.313501	−	0.949588i	$-0.601502\pi$
$5$	−1.40202	−0.627001	−0.313501	+	0.949588i	$0.601502\pi$
$6$	2.39333	0.977073
$7$	1.96997	0.744579	0.372289	−	0.928117i	$-0.378573\pi$
$7$	1.96997	0.744579	0.372289	+	0.928117i	$0.378573\pi$
$8$	4.13575	1.46221
$9$	1.00000	0.333333
$10$	−3.35549	−1.06110
$11$	6.57798	1.98334	0.991668	−	0.128818i	$-0.0411184\pi$
$11$	6.57798	1.98334	0.991668	+	0.128818i	$0.0411184\pi$
$12$	3.72803	1.07619
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	4.71479	1.26008
$15$	−1.40202	−0.361999
$16$	2.44215	0.610539
$17$	−1.72068	−0.417326	−0.208663	−	0.977988i	$-0.566911\pi$
$17$	−1.72068	−0.417326	−0.208663	+	0.977988i	$0.566911\pi$
$18$	2.39333	0.564113
$19$	2.07272	0.475514	0.237757	−	0.971325i	$-0.423588\pi$
$19$	2.07272	0.475514	0.237757	+	0.971325i	$0.423588\pi$
$20$	−5.22676	−1.16874
$21$	1.96997	0.429883
$22$	15.7433	3.35648
$23$	6.57879	1.37177	0.685886	−	0.727709i	$-0.259415\pi$
$23$	6.57879	1.37177	0.685886	+	0.727709i	$0.259415\pi$
$24$	4.13575	0.844206
$25$	−3.03435	−0.606869
$26$	−2.39333	−0.469371
$27$	1.00000	0.192450
$28$	7.34411	1.38791
$29$	0.697292	0.129484	0.0647419	−	0.997902i	$-0.479378\pi$
$29$	0.697292	0.129484	0.0647419	+	0.997902i	$0.479378\pi$
$30$	−3.35549	−0.612626
$31$	1.51915	0.272848	0.136424	−	0.990651i	$-0.456439\pi$
$31$	1.51915	0.272848	0.136424	+	0.990651i	$0.456439\pi$
$32$	−2.42662	−0.428969
$33$	6.57798	1.14508
$34$	−4.11816	−0.706258
$35$	−2.76193	−0.466852
$36$	3.72803	0.621339
$37$	−8.95694	−1.47251	−0.736256	−	0.676704i	$-0.763408\pi$
$37$	−8.95694	−1.47251	−0.736256	+	0.676704i	$0.763408\pi$
$38$	4.96070	0.804731
$39$	−1.00000	−0.160128
$40$	−5.79839	−0.916807
$41$	−10.0180	−1.56454	−0.782272	−	0.622937i	$-0.785939\pi$
$41$	−10.0180	−1.56454	−0.782272	+	0.622937i	$0.785939\pi$
$42$	4.71479	0.727508
$43$	7.65800	1.16783	0.583917	−	0.811813i	$-0.301519\pi$
$43$	7.65800	1.16783	0.583917	+	0.811813i	$0.301519\pi$
$44$	24.5229	3.69697
$45$	−1.40202	−0.209000
$46$	15.7452	2.32151
$47$	−5.50250	−0.802623	−0.401311	−	0.915942i	$-0.631445\pi$
$47$	−5.50250	−0.802623	−0.401311	+	0.915942i	$0.631445\pi$
$48$	2.44215	0.352495
$49$	−3.11922	−0.445603
$50$	−7.26220	−1.02703
$51$	−1.72068	−0.240944
$52$	−3.72803	−0.516985
$53$	6.02052	0.826983	0.413491	−	0.910508i	$-0.364309\pi$
$53$	6.02052	0.826983	0.413491	+	0.910508i	$0.364309\pi$
$54$	2.39333	0.325691
$55$	−9.22245	−1.24355
$56$	8.14730	1.08873
$57$	2.07272	0.274538
$58$	1.66885	0.219131
$59$	−11.8504	−1.54279	−0.771396	−	0.636355i	$-0.780441\pi$
$59$	−11.8504	−1.54279	−0.771396	+	0.636355i	$0.780441\pi$
$60$	−5.22676	−0.674772
$61$	5.39639	0.690936	0.345468	−	0.938430i	$-0.387720\pi$
$61$	5.39639	0.690936	0.345468	+	0.938430i	$0.387720\pi$
$62$	3.63583	0.461751
$63$	1.96997	0.248193
$64$	−10.6920	−1.33650
$65$	1.40202	0.173899
$66$	15.7433	1.93786
$67$	4.09403	0.500165	0.250082	−	0.968225i	$-0.419542\pi$
$67$	4.09403	0.500165	0.250082	+	0.968225i	$0.419542\pi$
$68$	−6.41475	−0.777903
$69$	6.57879	0.791993
$70$	−6.61022	−0.790072
$71$	15.6357	1.85562	0.927810	−	0.373053i	$-0.121689\pi$
$71$	15.6357	1.85562	0.927810	+	0.373053i	$0.121689\pi$
$72$	4.13575	0.487403
$73$	12.5085	1.46401	0.732003	−	0.681301i	$-0.238586\pi$
$73$	12.5085	1.46401	0.732003	+	0.681301i	$0.238586\pi$
$74$	−21.4369	−2.49199
$75$	−3.03435	−0.350376
$76$	7.72715	0.886365
$77$	12.9584	1.47675
$78$	−2.39333	−0.270991
$79$	−7.11099	−0.800049	−0.400025	−	0.916504i	$-0.630998\pi$
$79$	−7.11099	−0.800049	−0.400025	+	0.916504i	$0.630998\pi$
$80$	−3.42394	−0.382809
$81$	1.00000	0.111111
$82$	−23.9763	−2.64774
$83$	4.05475	0.445066	0.222533	−	0.974925i	$-0.428567\pi$
$83$	4.05475	0.445066	0.222533	+	0.974925i	$0.428567\pi$
$84$	7.34411	0.801308
$85$	2.41242	0.261664
$86$	18.3281	1.97637
$87$	0.697292	0.0747575
$88$	27.2049	2.90005
$89$	3.74013	0.396453	0.198227	−	0.980156i	$-0.436482\pi$
$89$	3.74013	0.396453	0.198227	+	0.980156i	$0.436482\pi$
$90$	−3.35549	−0.353700
$91$	−1.96997	−0.206509
$92$	24.5259	2.55701
$93$	1.51915	0.157529
$94$	−13.1693	−1.35831
$95$	−2.90599	−0.298148
$96$	−2.42662	−0.247665
$97$	2.19386	0.222753	0.111377	−	0.993778i	$-0.464474\pi$
$97$	2.19386	0.222753	0.111377	+	0.993778i	$0.464474\pi$
$98$	−7.46532	−0.754111
$99$	6.57798	0.661112
$100$	−11.3121	−1.13121
$101$	4.53311	0.451061	0.225530	−	0.974236i	$-0.427588\pi$
$101$	4.53311	0.451061	0.225530	+	0.974236i	$0.427588\pi$
$102$	−4.11816	−0.407758
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−4.13575	−0.405544
$105$	−2.76193	−0.269537
$106$	14.4091	1.39954
$107$	0.309436	0.0299143	0.0149572	−	0.999888i	$-0.495239\pi$
$107$	0.309436	0.0299143	0.0149572	+	0.999888i	$0.495239\pi$
$108$	3.72803	0.358730
$109$	3.16102	0.302770	0.151385	−	0.988475i	$-0.451627\pi$
$109$	3.16102	0.302770	0.151385	+	0.988475i	$0.451627\pi$
$110$	−22.0724	−2.10452
$111$	−8.95694	−0.850155
$112$	4.81097	0.454594
$113$	9.15105	0.860859	0.430429	−	0.902624i	$-0.358362\pi$
$113$	9.15105	0.860859	0.430429	+	0.902624i	$0.358362\pi$
$114$	4.96070	0.464612
$115$	−9.22358	−0.860103
$116$	2.59953	0.241360
$117$	−1.00000	−0.0924500
$118$	−28.3619	−2.61093
$119$	−3.38969	−0.310732
$120$	−5.79839	−0.529318
$121$	32.2699	2.93362
$122$	12.9153	1.16930
$123$	−10.0180	−0.903290
$124$	5.66345	0.508593
$125$	11.2643	1.00751
$126$	4.71479	0.420027
$127$	10.3919	0.922131	0.461066	−	0.887366i	$-0.347467\pi$
$127$	10.3919	0.922131	0.461066	+	0.887366i	$0.347467\pi$
$128$	−20.7363	−1.83284
$129$	7.65800	0.674249
$130$	3.35549	0.294296
$131$	−16.7622	−1.46452	−0.732260	−	0.681025i	$-0.761534\pi$
$131$	−16.7622	−1.46452	−0.732260	+	0.681025i	$0.761534\pi$
$132$	24.5229	2.13445
$133$	4.08319	0.354057
$134$	9.79836	0.846449
$135$	−1.40202	−0.120666
$136$	−7.11631	−0.610218
$137$	0.847367	0.0723954	0.0361977	−	0.999345i	$-0.488475\pi$
$137$	0.847367	0.0723954	0.0361977	+	0.999345i	$0.488475\pi$
$138$	15.7452	1.34032
$139$	−15.6706	−1.32916	−0.664579	−	0.747218i	$-0.731389\pi$
$139$	−15.6706	−1.32916	−0.664579	+	0.747218i	$0.731389\pi$
$140$	−10.2966	−0.870219
$141$	−5.50250	−0.463394
$142$	37.4215	3.14034
$143$	−6.57798	−0.550079
$144$	2.44215	0.203513
$145$	−0.977615	−0.0811865
$146$	29.9369	2.47760
$147$	−3.11922	−0.257269
$148$	−33.3917	−2.74478
$149$	22.1349	1.81336	0.906679	−	0.421820i	$-0.138609\pi$
$149$	22.1349	1.81336	0.906679	+	0.421820i	$0.138609\pi$
$150$	−7.26220	−0.592956
$151$	−19.2801	−1.56899	−0.784496	−	0.620134i	$-0.787078\pi$
$151$	−19.2801	−1.56899	−0.784496	+	0.620134i	$0.787078\pi$
$152$	8.57224	0.695301
$153$	−1.72068	−0.139109
$154$	31.0138	2.49916
$155$	−2.12988	−0.171076
$156$	−3.72803	−0.298481
$157$	−20.6178	−1.64548	−0.822741	−	0.568416i	$-0.807557\pi$
$157$	−20.6178	−1.64548	−0.822741	+	0.568416i	$0.807557\pi$
$158$	−17.0190	−1.35396
$159$	6.02052	0.477459
$160$	3.40216	0.268964
$161$	12.9600	1.02139
$162$	2.39333	0.188038
$163$	−20.6759	−1.61947	−0.809733	−	0.586799i	$-0.800388\pi$
$163$	−20.6759	−1.61947	−0.809733	+	0.586799i	$0.800388\pi$
$164$	−37.3473	−2.91633
$165$	−9.22245	−0.717966
$166$	9.70435	0.753204
$167$	−9.91149	−0.766974	−0.383487	−	0.923546i	$-0.625277\pi$
$167$	−9.91149	−0.766974	−0.383487	+	0.923546i	$0.625277\pi$
$168$	8.14730	0.628578
$169$	1.00000	0.0769231
$170$	5.77373	0.442825
$171$	2.07272	0.158505
$172$	28.5493	2.17686
$173$	−17.7226	−1.34742	−0.673711	−	0.738995i	$-0.735301\pi$
$173$	−17.7226	−1.34742	−0.673711	+	0.738995i	$0.735301\pi$
$174$	1.66885	0.126515
$175$	−5.97757	−0.451862
$176$	16.0645	1.21090
$177$	−11.8504	−0.890731
$178$	8.95137	0.670934
$179$	−17.0965	−1.27785	−0.638927	−	0.769267i	$-0.720621\pi$
$179$	−17.0965	−1.27785	−0.638927	+	0.769267i	$0.720621\pi$
$180$	−5.22676	−0.389580
$181$	−11.9926	−0.891401	−0.445700	−	0.895182i	$-0.647045\pi$
$181$	−11.9926	−0.891401	−0.445700	+	0.895182i	$0.647045\pi$
$182$	−4.71479	−0.349483
$183$	5.39639	0.398912
$184$	27.2082	2.00582
$185$	12.5578	0.923266
$186$	3.63583	0.266592
$187$	−11.3186	−0.827699
$188$	−20.5135	−1.49610
$189$	1.96997	0.143294
$190$	−6.95498	−0.504568
$191$	−19.2489	−1.39280	−0.696401	−	0.717653i	$-0.745216\pi$
$191$	−19.2489	−1.39280	−0.696401	+	0.717653i	$0.745216\pi$
$192$	−10.6920	−0.771629
$193$	−22.7401	−1.63687	−0.818434	−	0.574600i	$-0.805158\pi$
$193$	−22.7401	−1.63687	−0.818434	+	0.574600i	$0.805158\pi$
$194$	5.25064	0.376974
$195$	1.40202	0.100401
$196$	−11.6285	−0.830610
$197$	−27.3503	−1.94863	−0.974316	−	0.225186i	$-0.927701\pi$
$197$	−27.3503	−1.94863	−0.974316	+	0.225186i	$0.927701\pi$
$198$	15.7433	1.11883
$199$	10.4397	0.740050	0.370025	−	0.929022i	$-0.379349\pi$
$199$	10.4397	0.740050	0.370025	+	0.929022i	$0.379349\pi$
$200$	−12.5493	−0.887370
$201$	4.09403	0.288770
$202$	10.8492	0.763349
$203$	1.37364	0.0964109
$204$	−6.41475	−0.449123
$205$	14.0454	0.980971
$206$	−2.39333	−0.166751
$207$	6.57879	0.457257
$208$	−2.44215	−0.169333
$209$	13.6343	0.943104
$210$	−6.61022	−0.456148
$211$	19.4053	1.33591	0.667956	−	0.744200i	$-0.267169\pi$
$211$	19.4053	1.33591	0.667956	+	0.744200i	$0.267169\pi$
$212$	22.4447	1.54151
$213$	15.6357	1.07134
$214$	0.740583	0.0506252
$215$	−10.7367	−0.732234
$216$	4.13575	0.281402
$217$	2.99268	0.203157
$218$	7.56536	0.512391
$219$	12.5085	0.845244
$220$	−34.3816	−2.31800
$221$	1.72068	0.115746
$222$	−21.4369	−1.43875
$223$	6.29590	0.421604	0.210802	−	0.977529i	$-0.432392\pi$
$223$	6.29590	0.421604	0.210802	+	0.977529i	$0.432392\pi$
$224$	−4.78036	−0.319401
$225$	−3.03435	−0.202290
$226$	21.9015	1.45687
$227$	20.3748	1.35232	0.676161	−	0.736754i	$-0.263643\pi$
$227$	20.3748	1.35232	0.676161	+	0.736754i	$0.263643\pi$
$228$	7.72715	0.511743
$229$	24.5363	1.62140	0.810702	−	0.585460i	$-0.199086\pi$
$229$	24.5363	1.62140	0.810702	+	0.585460i	$0.199086\pi$
$230$	−22.0751	−1.45559
$231$	12.9584	0.852602
$232$	2.88383	0.189332
$233$	−14.6915	−0.962475	−0.481237	−	0.876590i	$-0.659813\pi$
$233$	−14.6915	−0.962475	−0.481237	+	0.876590i	$0.659813\pi$
$234$	−2.39333	−0.156457
$235$	7.71460	0.503245
$236$	−44.1787	−2.87579
$237$	−7.11099	−0.461909
$238$	−8.11265	−0.525865
$239$	−8.86244	−0.573263	−0.286632	−	0.958041i	$-0.592536\pi$
$239$	−8.86244	−0.573263	−0.286632	+	0.958041i	$0.592536\pi$
$240$	−3.42394	−0.221015
$241$	−7.51534	−0.484106	−0.242053	−	0.970263i	$-0.577821\pi$
$241$	−7.51534	−0.484106	−0.242053	+	0.970263i	$0.577821\pi$
$242$	77.2324	4.96469
$243$	1.00000	0.0641500
$244$	20.1179	1.28792
$245$	4.37320	0.279393
$246$	−23.9763	−1.52867
$247$	−2.07272	−0.131884
$248$	6.28284	0.398960
$249$	4.05475	0.256959
$250$	26.9592	1.70505
$251$	−14.5437	−0.917991	−0.458996	−	0.888439i	$-0.651791\pi$
$251$	−14.5437	−0.917991	−0.458996	+	0.888439i	$0.651791\pi$
$252$	7.34411	0.462635
$253$	43.2752	2.72069
$254$	24.8712	1.56056
$255$	2.41242	0.151072
$256$	−28.2447	−1.76530
$257$	−22.7923	−1.42175	−0.710874	−	0.703320i	$-0.751700\pi$
$257$	−22.7923	−1.42175	−0.710874	+	0.703320i	$0.751700\pi$
$258$	18.3281	1.14106
$259$	−17.6449	−1.09640
$260$	5.22676	0.324150
$261$	0.697292	0.0431613
$262$	−40.1175	−2.47847
$263$	−2.72920	−0.168289	−0.0841447	−	0.996454i	$-0.526816\pi$
$263$	−2.72920	−0.168289	−0.0841447	+	0.996454i	$0.526816\pi$
$264$	27.2049	1.67435
$265$	−8.44088	−0.518519
$266$	9.77242	0.599186
$267$	3.74013	0.228892
$268$	15.2627	0.932315
$269$	−13.7805	−0.840214	−0.420107	−	0.907474i	$-0.638008\pi$
$269$	−13.7805	−0.840214	−0.420107	+	0.907474i	$0.638008\pi$
$270$	−3.35549	−0.204209
$271$	−8.95832	−0.544179	−0.272090	−	0.962272i	$-0.587715\pi$
$271$	−8.95832	−0.544179	−0.272090	+	0.962272i	$0.587715\pi$
$272$	−4.20217	−0.254794
$273$	−1.96997	−0.119228
$274$	2.02803	0.122518
$275$	−19.9599	−1.20363
$276$	24.5259	1.47629
$277$	16.8977	1.01528	0.507641	−	0.861568i	$-0.330517\pi$
$277$	16.8977	1.01528	0.507641	+	0.861568i	$0.330517\pi$
$278$	−37.5048	−2.24939
$279$	1.51915	0.0909493
$280$	−11.4227	−0.682635
$281$	−8.90419	−0.531180	−0.265590	−	0.964086i	$-0.585567\pi$
$281$	−8.90419	−0.531180	−0.265590	+	0.964086i	$0.585567\pi$
$282$	−13.1693	−0.784221
$283$	15.3626	0.913211	0.456606	−	0.889669i	$-0.349065\pi$
$283$	15.3626	0.913211	0.456606	+	0.889669i	$0.349065\pi$
$284$	58.2905	3.45891
$285$	−2.90599	−0.172136
$286$	−15.7433	−0.930920
$287$	−19.7351	−1.16493
$288$	−2.42662	−0.142990
$289$	−14.0393	−0.825839
$290$	−2.33976	−0.137395
$291$	2.19386	0.128607
$292$	46.6320	2.72893
$293$	−32.2142	−1.88197	−0.940987	−	0.338442i	$-0.890100\pi$
$293$	−32.2142	−1.88197	−0.940987	+	0.338442i	$0.890100\pi$
$294$	−7.46532	−0.435386
$295$	16.6145	0.967332
$296$	−37.0437	−2.15312
$297$	6.57798	0.381693
$298$	52.9761	3.06882
$299$	−6.57879	−0.380461
$300$	−11.3121	−0.653107
$301$	15.0860	0.869544
$302$	−46.1436	−2.65527
$303$	4.53311	0.260420
$304$	5.06190	0.290320
$305$	−7.56583	−0.433218
$306$	−4.11816	−0.235419
$307$	10.6243	0.606359	0.303179	−	0.952933i	$-0.401952\pi$
$307$	10.6243	0.606359	0.303179	+	0.952933i	$0.401952\pi$
$308$	48.3094	2.75268
$309$	−1.00000	−0.0568880
$310$	−5.09750	−0.289519
$311$	12.9606	0.734929	0.367464	−	0.930038i	$-0.380226\pi$
$311$	12.9606	0.734929	0.367464	+	0.930038i	$0.380226\pi$
$312$	−4.13575	−0.234141
$313$	33.1552	1.87404	0.937022	−	0.349272i	$-0.113571\pi$
$313$	33.1552	1.87404	0.937022	+	0.349272i	$0.113571\pi$
$314$	−49.3453	−2.78472
$315$	−2.76193	−0.155617
$316$	−26.5100	−1.49130
$317$	−2.98155	−0.167460	−0.0837301	−	0.996488i	$-0.526683\pi$
$317$	−2.98155	−0.167460	−0.0837301	+	0.996488i	$0.526683\pi$
$318$	14.4091	0.808022
$319$	4.58677	0.256810
$320$	14.9904	0.837988
$321$	0.309436	0.0172710
$322$	31.0176	1.72854
$323$	−3.56649	−0.198445
$324$	3.72803	0.207113
$325$	3.03435	0.168315
$326$	−49.4844	−2.74069
$327$	3.16102	0.174805
$328$	−41.4318	−2.28769
$329$	−10.8398	−0.597616
$330$	−22.0724	−1.21504
$331$	−9.54196	−0.524474	−0.262237	−	0.965004i	$-0.584460\pi$
$331$	−9.54196	−0.524474	−0.262237	+	0.965004i	$0.584460\pi$
$332$	15.1162	0.829611
$333$	−8.95694	−0.490837
$334$	−23.7215	−1.29798
$335$	−5.73990	−0.313604
$336$	4.81097	0.262460
$337$	−16.0039	−0.871788	−0.435894	−	0.899998i	$-0.643568\pi$
$337$	−16.0039	−0.871788	−0.435894	+	0.899998i	$0.643568\pi$
$338$	2.39333	0.130180
$339$	9.15105	0.497017
$340$	8.99359	0.487746
$341$	9.99296	0.541149
$342$	4.96070	0.268244
$343$	−19.9346	−1.07636
$344$	31.6716	1.70762
$345$	−9.22358	−0.496581
$346$	−42.4160	−2.28030
$347$	−1.67653	−0.0900009	−0.0450004	−	0.998987i	$-0.514329\pi$
$347$	−1.67653	−0.0900009	−0.0450004	+	0.998987i	$0.514329\pi$
$348$	2.59953	0.139349
$349$	29.0703	1.55610	0.778049	−	0.628203i	$-0.216209\pi$
$349$	29.0703	1.55610	0.778049	+	0.628203i	$0.216209\pi$
$350$	−14.3063	−0.764704
$351$	−1.00000	−0.0533761
$352$	−15.9622	−0.850790
$353$	−0.00454881	−0.000242109 0	−0.000121054	−	1.00000i	$-0.500039\pi$
$353$	−0.00454881	−0.000242109 0	−0.000121054		1.00000i	$0.500039\pi$
$354$	−28.3619	−1.50742
$355$	−21.9216	−1.16348
$356$	13.9433	0.738995
$357$	−3.38969	−0.179401
$358$	−40.9176	−2.16256
$359$	24.8957	1.31395	0.656973	−	0.753914i	$-0.271837\pi$
$359$	24.8957	1.31395	0.656973	+	0.753914i	$0.271837\pi$
$360$	−5.79839	−0.305602
$361$	−14.7038	−0.773887
$362$	−28.7022	−1.50855
$363$	32.2699	1.69373
$364$	−7.34411	−0.384936
$365$	−17.5371	−0.917934
$366$	12.9153	0.675095
$367$	−8.61374	−0.449634	−0.224817	−	0.974401i	$-0.572178\pi$
$367$	−8.61374	−0.449634	−0.224817	+	0.974401i	$0.572178\pi$
$368$	16.0664	0.837520
$369$	−10.0180	−0.521515
$370$	30.0549	1.56248
$371$	11.8603	0.615754
$372$	5.66345	0.293636
$373$	36.6445	1.89738	0.948690	−	0.316208i	$-0.102410\pi$
$373$	36.6445	1.89738	0.948690	+	0.316208i	$0.102410\pi$
$374$	−27.0892	−1.40075
$375$	11.2643	0.581686
$376$	−22.7570	−1.17360
$377$	−0.697292	−0.0359124
$378$	4.71479	0.242503
$379$	−15.9850	−0.821097	−0.410548	−	0.911839i	$-0.634663\pi$
$379$	−15.9850	−0.821097	−0.410548	+	0.911839i	$0.634663\pi$
$380$	−10.8336	−0.555752
$381$	10.3919	0.532393
$382$	−46.0690	−2.35709
$383$	−14.9441	−0.763607	−0.381804	−	0.924244i	$-0.624697\pi$
$383$	−14.9441	−0.763607	−0.381804	+	0.924244i	$0.624697\pi$
$384$	−20.7363	−1.05819
$385$	−18.1679	−0.925924
$386$	−54.4246	−2.77014
$387$	7.65800	0.389278
$388$	8.17880	0.415216
$389$	15.2501	0.773211	0.386606	−	0.922245i	$-0.373648\pi$
$389$	15.2501	0.773211	0.386606	+	0.922245i	$0.373648\pi$
$390$	3.35549	0.169912
$391$	−11.3200	−0.572477
$392$	−12.9003	−0.651564
$393$	−16.7622	−0.845541
$394$	−65.4584	−3.29775
$395$	9.96973	0.501632
$396$	24.5229	1.23232
$397$	−34.8612	−1.74963	−0.874816	−	0.484455i	$-0.839018\pi$
$397$	−34.8612	−1.74963	−0.874816	+	0.484455i	$0.839018\pi$
$398$	24.9856	1.25242
$399$	4.08319	0.204415
$400$	−7.41035	−0.370517
$401$	16.8962	0.843755	0.421878	−	0.906653i	$-0.361371\pi$
$401$	16.8962	0.843755	0.421878	+	0.906653i	$0.361371\pi$
$402$	9.79836	0.488698
$403$	−1.51915	−0.0756744
$404$	16.8996	0.840785
$405$	−1.40202	−0.0696668
$406$	3.28758	0.163160
$407$	−58.9186	−2.92049
$408$	−7.11631	−0.352310
$409$	25.0110	1.23671	0.618356	−	0.785898i	$-0.287799\pi$
$409$	25.0110	1.23671	0.618356	+	0.785898i	$0.287799\pi$
$410$	33.6152	1.66014
$411$	0.847367	0.0417975
$412$	−3.72803	−0.183667
$413$	−23.3450	−1.14873
$414$	15.7452	0.773835
$415$	−5.68483	−0.279057
$416$	2.42662	0.118975
$417$	−15.6706	−0.767390
$418$	32.6314	1.59605
$419$	23.1170	1.12934	0.564669	−	0.825317i	$-0.309004\pi$
$419$	23.1170	1.12934	0.564669	+	0.825317i	$0.309004\pi$
$420$	−10.2966	−0.502421
$421$	21.5315	1.04938	0.524691	−	0.851293i	$-0.324181\pi$
$421$	21.5315	1.04938	0.524691	+	0.851293i	$0.324181\pi$
$422$	46.4432	2.26082
$423$	−5.50250	−0.267541
$424$	24.8994	1.20922
$425$	5.22114	0.253263
$426$	37.4215	1.81308
$427$	10.6307	0.514457
$428$	1.15359	0.0557607
$429$	−6.57798	−0.317588
$430$	−25.6964	−1.23919
$431$	3.19695	0.153992	0.0769959	−	0.997031i	$-0.475467\pi$
$431$	3.19695	0.153992	0.0769959	+	0.997031i	$0.475467\pi$
$432$	2.44215	0.117498
$433$	−3.18997	−0.153300	−0.0766501	−	0.997058i	$-0.524422\pi$
$433$	−3.18997	−0.153300	−0.0766501	+	0.997058i	$0.524422\pi$
$434$	7.16248	0.343810
$435$	−0.977615	−0.0468731
$436$	11.7844	0.564369
$437$	13.6360	0.652297
$438$	29.9369	1.43044
$439$	35.8403	1.71057	0.855283	−	0.518161i	$-0.173383\pi$
$439$	35.8403	1.71057	0.855283	+	0.518161i	$0.173383\pi$
$440$	−38.1417	−1.81834
$441$	−3.11922	−0.148534
$442$	4.11816	0.195881
$443$	21.8064	1.03605	0.518026	−	0.855365i	$-0.326667\pi$
$443$	21.8064	1.03605	0.518026	+	0.855365i	$0.326667\pi$
$444$	−33.3917	−1.58470
$445$	−5.24373	−0.248577
$446$	15.0682	0.713498
$447$	22.1349	1.04694
$448$	−21.0629	−0.995130
$449$	4.63333	0.218660	0.109330	−	0.994005i	$-0.465129\pi$
$449$	4.63333	0.218660	0.109330	+	0.994005i	$0.465129\pi$
$450$	−7.26220	−0.342343
$451$	−65.8980	−3.10302
$452$	34.1154	1.60465
$453$	−19.2801	−0.905858
$454$	48.7636	2.28859
$455$	2.76193	0.129481
$456$	8.57224	0.401432
$457$	−26.2234	−1.22668	−0.613341	−	0.789819i	$-0.710175\pi$
$457$	−26.2234	−1.22668	−0.613341	+	0.789819i	$0.710175\pi$
$458$	58.7234	2.74397
$459$	−1.72068	−0.0803145
$460$	−34.3858	−1.60325
$461$	−21.4423	−0.998666	−0.499333	−	0.866410i	$-0.666422\pi$
$461$	−21.4423	−0.998666	−0.499333	+	0.866410i	$0.666422\pi$
$462$	31.0138	1.44289
$463$	3.85624	0.179215	0.0896074	−	0.995977i	$-0.471439\pi$
$463$	3.85624	0.179215	0.0896074	+	0.995977i	$0.471439\pi$
$464$	1.70290	0.0790549
$465$	−2.12988	−0.0987707
$466$	−35.1617	−1.62884
$467$	−10.5382	−0.487648	−0.243824	−	0.969820i	$-0.578402\pi$
$467$	−10.5382	−0.487648	−0.243824	+	0.969820i	$0.578402\pi$
$468$	−3.72803	−0.172328
$469$	8.06511	0.372412
$470$	18.4636	0.851662
$471$	−20.6178	−0.950020
$472$	−49.0103	−2.25588
$473$	50.3742	2.31621
$474$	−17.0190	−0.781706
$475$	−6.28934	−0.288575
$476$	−12.6369	−0.579210
$477$	6.02052	0.275661
$478$	−21.2107	−0.970157
$479$	−37.5474	−1.71559	−0.857793	−	0.513996i	$-0.828165\pi$
$479$	−37.5474	−1.71559	−0.857793	+	0.513996i	$0.828165\pi$
$480$	3.40216	0.155287
$481$	8.95694	0.408401
$482$	−17.9867	−0.819271
$483$	12.9600	0.589701
$484$	120.303	5.46832
$485$	−3.07584	−0.139667
$486$	2.39333	0.108564
$487$	−34.2698	−1.55291	−0.776457	−	0.630170i	$-0.782985\pi$
$487$	−34.2698	−1.55291	−0.776457	+	0.630170i	$0.782985\pi$
$488$	22.3181	1.01029
$489$	−20.6759	−0.934999
$490$	10.4665	0.472829
$491$	4.81346	0.217228	0.108614	−	0.994084i	$-0.465359\pi$
$491$	4.81346	0.217228	0.108614	+	0.994084i	$0.465359\pi$
$492$	−37.3473	−1.68375
$493$	−1.19982	−0.0540370
$494$	−4.96070	−0.223192
$495$	−9.22245	−0.414518
$496$	3.71001	0.166584
$497$	30.8019	1.38166
$498$	9.70435	0.434862
$499$	9.73682	0.435880	0.217940	−	0.975962i	$-0.430066\pi$
$499$	9.73682	0.435880	0.217940	+	0.975962i	$0.430066\pi$
$500$	41.9936	1.87801
$501$	−9.91149	−0.442813
$502$	−34.8079	−1.55355
$503$	−25.4110	−1.13302	−0.566511	−	0.824054i	$-0.691707\pi$
$503$	−25.4110	−1.13302	−0.566511	+	0.824054i	$0.691707\pi$
$504$	8.14730	0.362910
$505$	−6.35549	−0.282816
$506$	103.572	4.60433
$507$	1.00000	0.0444116
$508$	38.7413	1.71887
$509$	14.8081	0.656357	0.328179	−	0.944616i	$-0.393565\pi$
$509$	14.8081	0.656357	0.328179	+	0.944616i	$0.393565\pi$
$510$	5.77373	0.255665
$511$	24.6413	1.09007
$512$	−26.1265	−1.15464
$513$	2.07272	0.0915127
$514$	−54.5496	−2.40608
$515$	1.40202	0.0617803
$516$	28.5493	1.25681
$517$	−36.1954	−1.59187
$518$	−42.2301	−1.85548
$519$	−17.7226	−0.777935
$520$	5.79839	0.254276
$521$	−12.6812	−0.555576	−0.277788	−	0.960642i	$-0.589601\pi$
$521$	−12.6812	−0.555576	−0.277788	+	0.960642i	$0.589601\pi$
$522$	1.66885	0.0730436
$523$	−11.3759	−0.497432	−0.248716	−	0.968576i	$-0.580009\pi$
$523$	−11.3759	−0.497432	−0.248716	+	0.968576i	$0.580009\pi$
$524$	−62.4900	−2.72989
$525$	−5.97757	−0.260883
$526$	−6.53187	−0.284803
$527$	−2.61398	−0.113867
$528$	16.0645	0.699116
$529$	20.2805	0.881759
$530$	−20.2018	−0.877511
$531$	−11.8504	−0.514264
$532$	15.2223	0.659969
$533$	10.0180	0.433926
$534$	8.95137	0.387364
$535$	−0.433835	−0.0187563
$536$	16.9319	0.731345
$537$	−17.0965	−0.737769
$538$	−32.9814	−1.42193
$539$	−20.5182	−0.883780
$540$	−5.22676	−0.224924
$541$	16.3771	0.704107	0.352054	−	0.935980i	$-0.385483\pi$
$541$	16.3771	0.704107	0.352054	+	0.935980i	$0.385483\pi$
$542$	−21.4402	−0.920937
$543$	−11.9926	−0.514651
$544$	4.17543	0.179020
$545$	−4.43180	−0.189837
$546$	−4.71479	−0.201774
$547$	24.3646	1.04176	0.520878	−	0.853631i	$-0.325604\pi$
$547$	24.3646	1.04176	0.520878	+	0.853631i	$0.325604\pi$
$548$	3.15901	0.134946
$549$	5.39639	0.230312
$550$	−47.7706	−2.03695
$551$	1.44529	0.0615714
$552$	27.2082	1.15806
$553$	−14.0084	−0.595699
$554$	40.4417	1.71820
$555$	12.5578	0.533048
$556$	−58.4203	−2.47757
$557$	27.0486	1.14609	0.573044	−	0.819525i	$-0.305762\pi$
$557$	27.0486	1.14609	0.573044	+	0.819525i	$0.305762\pi$
$558$	3.63583	0.153917
$559$	−7.65800	−0.323899
$560$	−6.74507	−0.285031
$561$	−11.3186	−0.477872
$562$	−21.3107	−0.898937
$563$	−26.4163	−1.11331	−0.556657	−	0.830742i	$-0.687916\pi$
$563$	−26.4163	−1.11331	−0.556657	+	0.830742i	$0.687916\pi$
$564$	−20.5135	−0.863774
$565$	−12.8299	−0.539759
$566$	36.7678	1.54546
$567$	1.96997	0.0827310
$568$	64.6655	2.71330
$569$	−35.8171	−1.50153	−0.750766	−	0.660569i	$-0.770315\pi$
$569$	−35.8171	−1.50153	−0.750766	+	0.660569i	$0.770315\pi$
$570$	−6.95498	−0.291312
$571$	18.6546	0.780669	0.390334	−	0.920673i	$-0.372359\pi$
$571$	18.6546	0.780669	0.390334	+	0.920673i	$0.372359\pi$
$572$	−24.5229	−1.02536
$573$	−19.2489	−0.804134
$574$	−47.2326	−1.97145
$575$	−19.9623	−0.832487
$576$	−10.6920	−0.445500
$577$	20.1123	0.837288	0.418644	−	0.908151i	$-0.362506\pi$
$577$	20.1123	0.837288	0.418644	+	0.908151i	$0.362506\pi$
$578$	−33.6006	−1.39760
$579$	−22.7401	−0.945047
$580$	−3.64458	−0.151333
$581$	7.98773	0.331387
$582$	5.25064	0.217646
$583$	39.6029	1.64018
$584$	51.7319	2.14068
$585$	1.40202	0.0579663
$586$	−77.0993	−3.18494
$587$	16.7804	0.692602	0.346301	−	0.938124i	$-0.387438\pi$
$587$	16.7804	0.692602	0.346301	+	0.938124i	$0.387438\pi$
$588$	−11.6285	−0.479553
$589$	3.14877	0.129743
$590$	39.7639	1.63706
$591$	−27.3503	−1.12504
$592$	−21.8742	−0.899025
$593$	7.76849	0.319014	0.159507	−	0.987197i	$-0.449010\pi$
$593$	7.76849	0.319014	0.159507	+	0.987197i	$0.449010\pi$
$594$	15.7433	0.645955
$595$	4.75240	0.194830
$596$	82.5195	3.38013
$597$	10.4397	0.427268
$598$	−15.7452	−0.643870
$599$	−1.73615	−0.0709371	−0.0354685	−	0.999371i	$-0.511292\pi$
$599$	−1.73615	−0.0709371	−0.0354685	+	0.999371i	$0.511292\pi$
$600$	−12.5493	−0.512323
$601$	−9.81766	−0.400471	−0.200235	−	0.979748i	$-0.564171\pi$
$601$	−9.81766	−0.400471	−0.200235	+	0.979748i	$0.564171\pi$
$602$	36.1059	1.47157
$603$	4.09403	0.166722
$604$	−71.8768	−2.92462
$605$	−45.2429	−1.83939
$606$	10.8492	0.440720
$607$	34.0658	1.38269	0.691344	−	0.722526i	$-0.257019\pi$
$607$	34.0658	1.38269	0.691344	+	0.722526i	$0.257019\pi$
$608$	−5.02969	−0.203981
$609$	1.37364	0.0556629
$610$	−18.1075	−0.733152
$611$	5.50250	0.222607
$612$	−6.41475	−0.259301
$613$	24.0149	0.969951	0.484976	−	0.874528i	$-0.338828\pi$
$613$	24.0149	0.969951	0.484976	+	0.874528i	$0.338828\pi$
$614$	25.4274	1.02617
$615$	14.0454	0.566364
$616$	53.5928	2.15932
$617$	6.66177	0.268193	0.134096	−	0.990968i	$-0.457187\pi$
$617$	6.66177	0.268193	0.134096	+	0.990968i	$0.457187\pi$
$618$	−2.39333	−0.0962739
$619$	37.9680	1.52606	0.763032	−	0.646360i	$-0.223710\pi$
$619$	37.9680	1.52606	0.763032	+	0.646360i	$0.223710\pi$
$620$	−7.94025	−0.318888
$621$	6.57879	0.263998
$622$	31.0190	1.24375
$623$	7.36795	0.295191
$624$	−2.44215	−0.0977644
$625$	−0.620999	−0.0248399
$626$	79.3514	3.17152
$627$	13.6343	0.544501
$628$	−76.8640	−3.06721
$629$	15.4120	0.614518
$630$	−6.61022	−0.263357
$631$	−14.7677	−0.587894	−0.293947	−	0.955822i	$-0.594969\pi$
$631$	−14.7677	−0.587894	−0.293947	+	0.955822i	$0.594969\pi$
$632$	−29.4093	−1.16984
$633$	19.4053	0.771290
$634$	−7.13582	−0.283400
$635$	−14.5696	−0.578177
$636$	22.4447	0.889990
$637$	3.11922	0.123588
$638$	10.9777	0.434610
$639$	15.6357	0.618540
$640$	29.0726	1.14920
$641$	−10.5131	−0.415244	−0.207622	−	0.978209i	$-0.566572\pi$
$641$	−10.5131	−0.415244	−0.207622	+	0.978209i	$0.566572\pi$
$642$	0.740583	0.0292285
$643$	15.2864	0.602836	0.301418	−	0.953492i	$-0.402540\pi$
$643$	15.2864	0.602836	0.301418	+	0.953492i	$0.402540\pi$
$644$	48.3153	1.90389
$645$	−10.7367	−0.422755
$646$	−8.53578	−0.335836
$647$	27.1963	1.06920	0.534598	−	0.845107i	$-0.320463\pi$
$647$	27.1963	1.06920	0.534598	+	0.845107i	$0.320463\pi$
$648$	4.13575	0.162468
$649$	−77.9518	−3.05988
$650$	7.26220	0.284847
$651$	2.99268	0.117293
$652$	−77.0806	−3.01871
$653$	9.22026	0.360817	0.180408	−	0.983592i	$-0.442258\pi$
$653$	9.22026	0.360817	0.180408	+	0.983592i	$0.442258\pi$
$654$	7.56536	0.295829
$655$	23.5009	0.918256
$656$	−24.4654	−0.955215
$657$	12.5085	0.488002
$658$	−25.9431	−1.01137
$659$	40.4699	1.57648	0.788242	−	0.615366i	$-0.210992\pi$
$659$	40.4699	1.57648	0.788242	+	0.615366i	$0.210992\pi$
$660$	−34.3816	−1.33830
$661$	0.625564	0.0243316	0.0121658	−	0.999926i	$-0.496127\pi$
$661$	0.625564	0.0243316	0.0121658	+	0.999926i	$0.496127\pi$
$662$	−22.8371	−0.887588
$663$	1.72068	0.0668257
$664$	16.7694	0.650780
$665$	−5.72470	−0.221994
$666$	−21.4369	−0.830663
$667$	4.58734	0.177622
$668$	−36.9504	−1.42965
$669$	6.29590	0.243413
$670$	−13.7375	−0.530725
$671$	35.4973	1.37036
$672$	−4.78036	−0.184406
$673$	0.191479	0.00738099	0.00369050	−	0.999993i	$-0.498825\pi$
$673$	0.191479	0.00738099	0.00369050	+	0.999993i	$0.498825\pi$
$674$	−38.3026	−1.47536
$675$	−3.03435	−0.116792
$676$	3.72803	0.143386
$677$	−43.2058	−1.66053	−0.830266	−	0.557367i	$-0.811812\pi$
$677$	−43.2058	−1.66053	−0.830266	+	0.557367i	$0.811812\pi$
$678$	21.9015	0.841122
$679$	4.32185	0.165857
$680$	9.97719	0.382608
$681$	20.3748	0.780763
$682$	23.9165	0.915808
$683$	1.98340	0.0758926	0.0379463	−	0.999280i	$-0.487918\pi$
$683$	1.98340	0.0758926	0.0379463	+	0.999280i	$0.487918\pi$
$684$	7.72715	0.295455
$685$	−1.18802	−0.0453920
$686$	−47.7100	−1.82158
$687$	24.5363	0.936118
$688$	18.7020	0.713008
$689$	−6.02052	−0.229364
$690$	−22.0751	−0.840383
$691$	−29.4304	−1.11958	−0.559792	−	0.828633i	$-0.689119\pi$
$691$	−29.4304	−1.11958	−0.559792	+	0.828633i	$0.689119\pi$
$692$	−66.0703	−2.51162
$693$	12.9584	0.492250
$694$	−4.01249	−0.152312
$695$	21.9704	0.833384
$696$	2.88383	0.109311
$697$	17.2377	0.652926
$698$	69.5749	2.63345
$699$	−14.6915	−0.555685
$700$	−22.2846	−0.842278
$701$	−13.8461	−0.522958	−0.261479	−	0.965209i	$-0.584210\pi$
$701$	−13.8461	−0.522958	−0.261479	+	0.965209i	$0.584210\pi$
$702$	−2.39333	−0.0903304
$703$	−18.5652	−0.700200
$704$	−70.3318	−2.65073
$705$	7.71460	0.290549
$706$	−0.0108868	−0.000409730 0
$707$	8.93008	0.335850
$708$	−44.1787	−1.66034
$709$	39.0064	1.46492	0.732458	−	0.680812i	$-0.238373\pi$
$709$	39.0064	1.46492	0.732458	+	0.680812i	$0.238373\pi$
$710$	−52.4656	−1.96900
$711$	−7.11099	−0.266683
$712$	15.4682	0.579697
$713$	9.99418	0.374285
$714$	−8.11265	−0.303608
$715$	9.22245	0.344900
$716$	−63.7364	−2.38194
$717$	−8.86244	−0.330974
$718$	59.5837	2.22364
$719$	−28.5523	−1.06482	−0.532410	−	0.846487i	$-0.678714\pi$
$719$	−28.5523	−1.06482	−0.532410	+	0.846487i	$0.678714\pi$
$720$	−3.42394	−0.127603
$721$	−1.96997	−0.0733655
$722$	−35.1912	−1.30968
$723$	−7.51534	−0.279499
$724$	−44.7087	−1.66159
$725$	−2.11583	−0.0785798
$726$	77.2324	2.86636
$727$	33.2187	1.23201	0.616006	−	0.787741i	$-0.288750\pi$
$727$	33.2187	1.23201	0.616006	+	0.787741i	$0.288750\pi$
$728$	−8.14730	−0.301959
$729$	1.00000	0.0370370
$730$	−41.9721	−1.55346
$731$	−13.1770	−0.487368
$732$	20.1179	0.743579
$733$	48.4551	1.78973	0.894864	−	0.446338i	$-0.147272\pi$
$733$	48.4551	1.78973	0.894864	+	0.446338i	$0.147272\pi$
$734$	−20.6155	−0.760933
$735$	4.37320	0.161308
$736$	−15.9642	−0.588448
$737$	26.9304	0.991995
$738$	−23.9763	−0.882580
$739$	−30.5567	−1.12405	−0.562024	−	0.827121i	$-0.689977\pi$
$739$	−30.5567	−1.12405	−0.562024	+	0.827121i	$0.689977\pi$
$740$	46.8158	1.72098
$741$	−2.07272	−0.0761432
$742$	28.3855	1.04206
$743$	48.9834	1.79703	0.898513	−	0.438947i	$-0.144648\pi$
$743$	48.9834	1.79703	0.898513	+	0.438947i	$0.144648\pi$
$744$	6.28284	0.230340
$745$	−31.0335	−1.13698
$746$	87.7024	3.21101
$747$	4.05475	0.148355
$748$	−42.1961	−1.54284
$749$	0.609580	0.0222736
$750$	26.9592	0.984410
$751$	18.8810	0.688979	0.344489	−	0.938790i	$-0.388052\pi$
$751$	18.8810	0.688979	0.344489	+	0.938790i	$0.388052\pi$
$752$	−13.4380	−0.490032
$753$	−14.5437	−0.530002
$754$	−1.66885	−0.0607759
$755$	27.0310	0.983759
$756$	7.34411	0.267103
$757$	37.6388	1.36801	0.684003	−	0.729479i	$-0.260238\pi$
$757$	37.6388	1.36801	0.684003	+	0.729479i	$0.260238\pi$
$758$	−38.2575	−1.38957
$759$	43.2752	1.57079
$760$	−12.0184	−0.435954
$761$	−19.3933	−0.703008	−0.351504	−	0.936186i	$-0.614330\pi$
$761$	−19.3933	−0.703008	−0.351504	+	0.936186i	$0.614330\pi$
$762$	24.8712	0.900990
$763$	6.22711	0.225436
$764$	−71.7605	−2.59620
$765$	2.41242	0.0872214
$766$	−35.7661	−1.29228
$767$	11.8504	0.427894
$768$	−28.2447	−1.01919
$769$	25.2397	0.910166	0.455083	−	0.890449i	$-0.349610\pi$
$769$	25.2397	0.910166	0.455083	+	0.890449i	$0.349610\pi$
$770$	−43.4819	−1.56698
$771$	−22.7923	−0.820846
$772$	−84.7758	−3.05115
$773$	−10.0563	−0.361700	−0.180850	−	0.983511i	$-0.557885\pi$
$773$	−10.0563	−0.361700	−0.180850	+	0.983511i	$0.557885\pi$
$774$	18.3281	0.658791
$775$	−4.60964	−0.165583
$776$	9.07328	0.325712
$777$	−17.6449	−0.633007
$778$	36.4985	1.30854
$779$	−20.7644	−0.743962
$780$	5.22676	0.187148
$781$	102.852	3.68032
$782$	−27.0925	−0.968826
$783$	0.697292	0.0249192
$784$	−7.61762	−0.272058
$785$	28.9066	1.03172
$786$	−40.1175	−1.43094
$787$	−39.6445	−1.41317	−0.706586	−	0.707627i	$-0.749766\pi$
$787$	−39.6445	−1.41317	−0.706586	+	0.707627i	$0.749766\pi$
$788$	−101.963	−3.63228
$789$	−2.72920	−0.0971620
$790$	23.8609	0.848932
$791$	18.0273	0.640977
$792$	27.2049	0.966684
$793$	−5.39639	−0.191631
$794$	−83.4343	−2.96097
$795$	−8.44088	−0.299367
$796$	38.9195	1.37946
$797$	2.50007	0.0885569	0.0442784	−	0.999019i	$-0.485901\pi$
$797$	2.50007	0.0885569	0.0442784	+	0.999019i	$0.485901\pi$
$798$	9.77242	0.345940
$799$	9.46805	0.334956
$800$	7.36320	0.260328
$801$	3.74013	0.132151
$802$	40.4382	1.42792
$803$	82.2805	2.90362
$804$	15.2627	0.538272
$805$	−18.1702	−0.640414
$806$	−3.63583	−0.128067
$807$	−13.7805	−0.485098
$808$	18.7478	0.659545
$809$	−10.7324	−0.377332	−0.188666	−	0.982041i	$-0.560416\pi$
$809$	−10.7324	−0.377332	−0.188666	+	0.982041i	$0.560416\pi$
$810$	−3.35549	−0.117900
$811$	−18.9480	−0.665354	−0.332677	−	0.943041i	$-0.607952\pi$
$811$	−18.9480	−0.665354	−0.332677	+	0.943041i	$0.607952\pi$
$812$	5.12099	0.179711
$813$	−8.95832	−0.314182
$814$	−141.012	−4.94245
$815$	28.9880	1.01541
$816$	−4.20217	−0.147105
$817$	15.8729	0.555321
$818$	59.8595	2.09294
$819$	−1.96997	−0.0688363
$820$	52.3616	1.82855
$821$	12.8088	0.447030	0.223515	−	0.974700i	$-0.428247\pi$
$821$	12.8088	0.447030	0.223515	+	0.974700i	$0.428247\pi$
$822$	2.02803	0.0707356
$823$	−29.5627	−1.03049	−0.515246	−	0.857043i	$-0.672299\pi$
$823$	−29.5627	−1.03049	−0.515246	+	0.857043i	$0.672299\pi$
$824$	−4.13575	−0.144076
$825$	−19.9599	−0.694914
$826$	−55.8722	−1.94404
$827$	−29.9252	−1.04060	−0.520300	−	0.853983i	$-0.674180\pi$
$827$	−29.9252	−1.04060	−0.520300	+	0.853983i	$0.674180\pi$
$828$	24.5259	0.852335
$829$	−0.595191	−0.0206718	−0.0103359	−	0.999947i	$-0.503290\pi$
$829$	−0.595191	−0.0206718	−0.0103359	+	0.999947i	$0.503290\pi$
$830$	−13.6057	−0.472260
$831$	16.8977	0.586174
$832$	10.6920	0.370679
$833$	5.36718	0.185962
$834$	−37.5048	−1.29869
$835$	13.8961	0.480894
$836$	50.8291	1.75796
$837$	1.51915	0.0525096
$838$	55.3266	1.91123
$839$	26.2642	0.906739	0.453370	−	0.891323i	$-0.350222\pi$
$839$	26.2642	0.906739	0.453370	+	0.891323i	$0.350222\pi$
$840$	−11.4227	−0.394119
$841$	−28.5138	−0.983234
$842$	51.5321	1.77591
$843$	−8.90419	−0.306677
$844$	72.3434	2.49016
$845$	−1.40202	−0.0482309
$846$	−13.1693	−0.452770
$847$	63.5706	2.18431
$848$	14.7031	0.504905
$849$	15.3626	0.527243
$850$	12.4959	0.428607
$851$	−58.9258	−2.01995
$852$	58.2905	1.99700
$853$	−15.0010	−0.513624	−0.256812	−	0.966461i	$-0.582672\pi$
$853$	−15.0010	−0.513624	−0.256812	+	0.966461i	$0.582672\pi$
$854$	25.4428	0.870635
$855$	−2.90599	−0.0993826
$856$	1.27975	0.0437410
$857$	−14.1049	−0.481813	−0.240907	−	0.970548i	$-0.577445\pi$
$857$	−14.1049	−0.481813	−0.240907	+	0.970548i	$0.577445\pi$
$858$	−15.7433	−0.537467
$859$	−27.3185	−0.932095	−0.466047	−	0.884760i	$-0.654322\pi$
$859$	−27.3185	−0.932095	−0.466047	+	0.884760i	$0.654322\pi$
$860$	−40.0266	−1.36489
$861$	−19.7351	−0.672570
$862$	7.65136	0.260606
$863$	23.7194	0.807418	0.403709	−	0.914887i	$-0.367721\pi$
$863$	23.7194	0.807418	0.403709	+	0.914887i	$0.367721\pi$
$864$	−2.42662	−0.0825552
$865$	24.8474	0.844835
$866$	−7.63465	−0.259436
$867$	−14.0393	−0.476798
$868$	11.1568	0.378687
$869$	−46.7760	−1.58677
$870$	−2.33976	−0.0793252
$871$	−4.09403	−0.138721
$872$	13.0732	0.442714
$873$	2.19386	0.0742511
$874$	32.6354	1.10391
$875$	22.1903	0.750170
$876$	46.6320	1.57555
$877$	20.3693	0.687823	0.343912	−	0.939002i	$-0.388248\pi$
$877$	20.3693	0.687823	0.343912	+	0.939002i	$0.388248\pi$
$878$	85.7778	2.89486
$879$	−32.2142	−1.08656
$880$	−22.5226	−0.759238
$881$	−39.2551	−1.32254	−0.661269	−	0.750149i	$-0.729982\pi$
$881$	−39.2551	−1.32254	−0.661269	+	0.750149i	$0.729982\pi$
$882$	−7.46532	−0.251370
$883$	−26.3435	−0.886531	−0.443265	−	0.896390i	$-0.646180\pi$
$883$	−26.3435	−0.886531	−0.443265	+	0.896390i	$0.646180\pi$
$884$	6.41475	0.215751
$885$	16.6145	0.558490
$886$	52.1898	1.75335
$887$	39.8770	1.33894	0.669470	−	0.742839i	$-0.266521\pi$
$887$	39.8770	1.33894	0.669470	+	0.742839i	$0.266521\pi$
$888$	−37.0437	−1.24310
$889$	20.4717	0.686599
$890$	−12.5500	−0.420676
$891$	6.57798	0.220371
$892$	23.4713	0.785877
$893$	−11.4051	−0.381658
$894$	52.9761	1.77178
$895$	23.9696	0.801216
$896$	−40.8498	−1.36470
$897$	−6.57879	−0.219659
$898$	11.0891	0.370048
$899$	1.05929	0.0353294
$900$	−11.3121	−0.377071
$901$	−10.3594	−0.345122
$902$	−157.716	−5.25136
$903$	15.0860	0.502032
$904$	37.8465	1.25875
$905$	16.8138	0.558909
$906$	−46.1436	−1.53302
$907$	3.86966	0.128490	0.0642450	−	0.997934i	$-0.479536\pi$
$907$	3.86966	0.128490	0.0642450	+	0.997934i	$0.479536\pi$
$908$	75.9578	2.52075
$909$	4.53311	0.150354
$910$	6.61022	0.219127
$911$	−39.7419	−1.31671	−0.658354	−	0.752709i	$-0.728747\pi$
$911$	−39.7419	−1.31671	−0.658354	+	0.752709i	$0.728747\pi$
$912$	5.06190	0.167616
$913$	26.6721	0.882716
$914$	−62.7614	−2.07596
$915$	−7.56583	−0.250119
$916$	91.4720	3.02232
$917$	−33.0210	−1.09045
$918$	−4.11816	−0.135919
$919$	56.2813	1.85655	0.928275	−	0.371895i	$-0.121292\pi$
$919$	56.2813	1.85655	0.928275	+	0.371895i	$0.121292\pi$
$920$	−38.1464	−1.25765
$921$	10.6243	0.350082
$922$	−51.3184	−1.69008
$923$	−15.6357	−0.514656
$924$	48.3094	1.58926
$925$	27.1785	0.893622
$926$	9.22927	0.303293
$927$	−1.00000	−0.0328443
$928$	−1.69206	−0.0555446
$929$	23.1522	0.759598	0.379799	−	0.925069i	$-0.375993\pi$
$929$	23.1522	0.759598	0.379799	+	0.925069i	$0.375993\pi$
$930$	−5.09750	−0.167154
$931$	−6.46526	−0.211890
$932$	−54.7705	−1.79407
$933$	12.9606	0.424311
$934$	−25.2213	−0.825266
$935$	15.8689	0.518968
$936$	−4.13575	−0.135181
$937$	24.5599	0.802336	0.401168	−	0.916005i	$-0.368604\pi$
$937$	24.5599	0.802336	0.401168	+	0.916005i	$0.368604\pi$
$938$	19.3025	0.630248
$939$	33.1552	1.08198
$940$	28.7603	0.938057
$941$	9.14925	0.298257	0.149129	−	0.988818i	$-0.452353\pi$
$941$	9.14925	0.298257	0.149129	+	0.988818i	$0.452353\pi$
$942$	−49.3453	−1.60776
$943$	−65.9061	−2.14620
$944$	−28.9405	−0.941934
$945$	−2.76193	−0.0898456
$946$	120.562	3.91981
$947$	−4.05012	−0.131611	−0.0658056	−	0.997832i	$-0.520962\pi$
$947$	−4.05012	−0.131611	−0.0658056	+	0.997832i	$0.520962\pi$
$948$	−26.5100	−0.861005
$949$	−12.5085	−0.406042
$950$	−15.0525	−0.488367
$951$	−2.98155	−0.0966832
$952$	−14.0189	−0.454355
$953$	44.9117	1.45483	0.727417	−	0.686196i	$-0.240721\pi$
$953$	44.9117	1.45483	0.727417	+	0.686196i	$0.240721\pi$
$954$	14.4091	0.466512
$955$	26.9873	0.873288
$956$	−33.0394	−1.06857
$957$	4.58677	0.148269
$958$	−89.8634	−2.90335
$959$	1.66929	0.0539041
$960$	14.9904	0.483812
$961$	−28.6922	−0.925554
$962$	21.4369	0.691154
$963$	0.309436	0.00997144
$964$	−28.0174	−0.902380
$965$	31.8820	1.02632
$966$	31.0176	0.997975
$967$	−28.2801	−0.909428	−0.454714	−	0.890638i	$-0.650259\pi$
$967$	−28.2801	−0.909428	−0.454714	+	0.890638i	$0.650259\pi$
$968$	133.460	4.28957
$969$	−3.56649	−0.114572
$970$	−7.36149	−0.236363
$971$	35.6652	1.14455	0.572275	−	0.820062i	$-0.306061\pi$
$971$	35.6652	1.14455	0.572275	+	0.820062i	$0.306061\pi$
$972$	3.72803	0.119577
$973$	−30.8705	−0.989663
$974$	−82.0190	−2.62806
$975$	3.03435	0.0971769
$976$	13.1788	0.421843
$977$	−1.02333	−0.0327391	−0.0163696	−	0.999866i	$-0.505211\pi$
$977$	−1.02333	−0.0327391	−0.0163696	+	0.999866i	$0.505211\pi$
$978$	−49.4844	−1.58234
$979$	24.6025	0.786300
$980$	16.3034	0.520794
$981$	3.16102	0.100923
$982$	11.5202	0.367624
$983$	11.9059	0.379740	0.189870	−	0.981809i	$-0.439193\pi$
$983$	11.9059	0.379740	0.189870	+	0.981809i	$0.439193\pi$
$984$	−41.4318	−1.32080
$985$	38.3457	1.22179
$986$	−2.87156	−0.0914491
$987$	−10.8398	−0.345034
$988$	−7.72715	−0.245834
$989$	50.3804	1.60200
$990$	−22.0724	−0.701506
$991$	−40.6099	−1.29002	−0.645009	−	0.764175i	$-0.723146\pi$
$991$	−40.6099	−1.29002	−0.645009	+	0.764175i	$0.723146\pi$
$992$	−3.68640	−0.117043
$993$	−9.54196	−0.302805
$994$	73.7192	2.33823
$995$	−14.6366	−0.464012
$996$	15.1162	0.478976
$997$	−23.8641	−0.755784	−0.377892	−	0.925850i	$-0.623351\pi$
$997$	−23.8641	−0.755784	−0.377892	+	0.925850i	$0.623351\pi$
$998$	23.3034	0.737657
$999$	−8.95694	−0.283385

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.l.1.28	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.l.1.28	✓	32	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)

\(f(q)\)	\(=\)	\(q+2.39333 q^{2} +1.00000 q^{3} +3.72803 q^{4} -1.40202 q^{5} +2.39333 q^{6} +1.96997 q^{7} +4.13575 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.39333 q^{2} +1.00000 q^{3} +3.72803 q^{4} -1.40202 q^{5} +2.39333 q^{6} +1.96997 q^{7} +4.13575 q^{8} +1.00000 q^{9} -3.35549 q^{10} +6.57798 q^{11} +3.72803 q^{12} -1.00000 q^{13} +4.71479 q^{14} -1.40202 q^{15} +2.44215 q^{16} -1.72068 q^{17} +2.39333 q^{18} +2.07272 q^{19} -5.22676 q^{20} +1.96997 q^{21} +15.7433 q^{22} +6.57879 q^{23} +4.13575 q^{24} -3.03435 q^{25} -2.39333 q^{26} +1.00000 q^{27} +7.34411 q^{28} +0.697292 q^{29} -3.35549 q^{30} +1.51915 q^{31} -2.42662 q^{32} +6.57798 q^{33} -4.11816 q^{34} -2.76193 q^{35} +3.72803 q^{36} -8.95694 q^{37} +4.96070 q^{38} -1.00000 q^{39} -5.79839 q^{40} -10.0180 q^{41} +4.71479 q^{42} +7.65800 q^{43} +24.5229 q^{44} -1.40202 q^{45} +15.7452 q^{46} -5.50250 q^{47} +2.44215 q^{48} -3.11922 q^{49} -7.26220 q^{50} -1.72068 q^{51} -3.72803 q^{52} +6.02052 q^{53} +2.39333 q^{54} -9.22245 q^{55} +8.14730 q^{56} +2.07272 q^{57} +1.66885 q^{58} -11.8504 q^{59} -5.22676 q^{60} +5.39639 q^{61} +3.63583 q^{62} +1.96997 q^{63} -10.6920 q^{64} +1.40202 q^{65} +15.7433 q^{66} +4.09403 q^{67} -6.41475 q^{68} +6.57879 q^{69} -6.61022 q^{70} +15.6357 q^{71} +4.13575 q^{72} +12.5085 q^{73} -21.4369 q^{74} -3.03435 q^{75} +7.72715 q^{76} +12.9584 q^{77} -2.39333 q^{78} -7.11099 q^{79} -3.42394 q^{80} +1.00000 q^{81} -23.9763 q^{82} +4.05475 q^{83} +7.34411 q^{84} +2.41242 q^{85} +18.3281 q^{86} +0.697292 q^{87} +27.2049 q^{88} +3.74013 q^{89} -3.35549 q^{90} -1.96997 q^{91} +24.5259 q^{92} +1.51915 q^{93} -13.1693 q^{94} -2.90599 q^{95} -2.42662 q^{96} +2.19386 q^{97} -7.46532 q^{98} +6.57798 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * q^99

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