LMFDB - Embedded newform 4034.2.a.d.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.36933 q^{3} +1.00000 q^{4} -2.34107 q^{5} -2.36933 q^{6} +4.14004 q^{7} +1.00000 q^{8} +2.61374 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.36933 q^{3} +1.00000 q^{4} -2.34107 q^{5} -2.36933 q^{6} +4.14004 q^{7} +1.00000 q^{8} +2.61374 q^{9} -2.34107 q^{10} +0.755051 q^{11} -2.36933 q^{12} +5.20636 q^{13} +4.14004 q^{14} +5.54677 q^{15} +1.00000 q^{16} -0.343613 q^{17} +2.61374 q^{18} +3.14510 q^{19} -2.34107 q^{20} -9.80914 q^{21} +0.755051 q^{22} +3.00025 q^{23} -2.36933 q^{24} +0.480595 q^{25} +5.20636 q^{26} +0.915175 q^{27} +4.14004 q^{28} +0.0845158 q^{29} +5.54677 q^{30} -1.30032 q^{31} +1.00000 q^{32} -1.78897 q^{33} -0.343613 q^{34} -9.69212 q^{35} +2.61374 q^{36} -3.42817 q^{37} +3.14510 q^{38} -12.3356 q^{39} -2.34107 q^{40} -10.4772 q^{41} -9.80914 q^{42} +1.80280 q^{43} +0.755051 q^{44} -6.11894 q^{45} +3.00025 q^{46} +7.76816 q^{47} -2.36933 q^{48} +10.1399 q^{49} +0.480595 q^{50} +0.814133 q^{51} +5.20636 q^{52} -3.31248 q^{53} +0.915175 q^{54} -1.76762 q^{55} +4.14004 q^{56} -7.45180 q^{57} +0.0845158 q^{58} -6.69383 q^{59} +5.54677 q^{60} +6.64404 q^{61} -1.30032 q^{62} +10.8210 q^{63} +1.00000 q^{64} -12.1884 q^{65} -1.78897 q^{66} +8.31293 q^{67} -0.343613 q^{68} -7.10859 q^{69} -9.69212 q^{70} -6.11170 q^{71} +2.61374 q^{72} -0.836250 q^{73} -3.42817 q^{74} -1.13869 q^{75} +3.14510 q^{76} +3.12594 q^{77} -12.3356 q^{78} -5.99442 q^{79} -2.34107 q^{80} -10.0096 q^{81} -10.4772 q^{82} +4.33584 q^{83} -9.80914 q^{84} +0.804420 q^{85} +1.80280 q^{86} -0.200246 q^{87} +0.755051 q^{88} +8.23783 q^{89} -6.11894 q^{90} +21.5545 q^{91} +3.00025 q^{92} +3.08090 q^{93} +7.76816 q^{94} -7.36290 q^{95} -2.36933 q^{96} +16.4266 q^{97} +10.1399 q^{98} +1.97351 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) $ 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.36933	−1.36794	−0.683968	−	0.729512i	$-0.739747\pi$
$3$	−2.36933	−1.36794	−0.683968	+	0.729512i	$0.739747\pi$
$4$	1.00000	0.500000
$5$	−2.34107	−1.04696	−0.523479	−	0.852039i	$-0.675366\pi$
$5$	−2.34107	−1.04696	−0.523479	+	0.852039i	$0.675366\pi$
$6$	−2.36933	−0.967276
$7$	4.14004	1.56479	0.782394	−	0.622783i	$-0.213998\pi$
$7$	4.14004	1.56479	0.782394	+	0.622783i	$0.213998\pi$
$8$	1.00000	0.353553
$9$	2.61374	0.871247
$10$	−2.34107	−0.740310
$11$	0.755051	0.227656	0.113828	−	0.993500i	$-0.463689\pi$
$11$	0.755051	0.227656	0.113828	+	0.993500i	$0.463689\pi$
$12$	−2.36933	−0.683968
$13$	5.20636	1.44398	0.721992	−	0.691902i	$-0.243227\pi$
$13$	5.20636	1.44398	0.721992	+	0.691902i	$0.243227\pi$
$14$	4.14004	1.10647
$15$	5.54677	1.43217
$16$	1.00000	0.250000
$17$	−0.343613	−0.0833383	−0.0416691	−	0.999131i	$-0.513268\pi$
$17$	−0.343613	−0.0833383	−0.0416691	+	0.999131i	$0.513268\pi$
$18$	2.61374	0.616065
$19$	3.14510	0.721536	0.360768	−	0.932656i	$-0.382515\pi$
$19$	3.14510	0.721536	0.360768	+	0.932656i	$0.382515\pi$
$20$	−2.34107	−0.523479
$21$	−9.80914	−2.14053
$22$	0.755051	0.160977
$23$	3.00025	0.625595	0.312798	−	0.949820i	$-0.398734\pi$
$23$	3.00025	0.625595	0.312798	+	0.949820i	$0.398734\pi$
$24$	−2.36933	−0.483638
$25$	0.480595	0.0961190
$26$	5.20636	1.02105
$27$	0.915175	0.176125
$28$	4.14004	0.782394
$29$	0.0845158	0.0156942	0.00784709	−	0.999969i	$-0.497502\pi$
$29$	0.0845158	0.0156942	0.00784709	+	0.999969i	$0.497502\pi$
$30$	5.54677	1.01270
$31$	−1.30032	−0.233545	−0.116773	−	0.993159i	$-0.537255\pi$
$31$	−1.30032	−0.233545	−0.116773	+	0.993159i	$0.537255\pi$
$32$	1.00000	0.176777
$33$	−1.78897	−0.311419
$34$	−0.343613	−0.0589291
$35$	−9.69212	−1.63827
$36$	2.61374	0.435624
$37$	−3.42817	−0.563588	−0.281794	−	0.959475i	$-0.590929\pi$
$37$	−3.42817	−0.563588	−0.281794	+	0.959475i	$0.590929\pi$
$38$	3.14510	0.510203
$39$	−12.3356	−1.97528
$40$	−2.34107	−0.370155
$41$	−10.4772	−1.63626	−0.818132	−	0.575030i	$-0.804990\pi$
$41$	−10.4772	−1.63626	−0.818132	+	0.575030i	$0.804990\pi$
$42$	−9.80914	−1.51358
$43$	1.80280	0.274924	0.137462	−	0.990507i	$-0.456106\pi$
$43$	1.80280	0.274924	0.137462	+	0.990507i	$0.456106\pi$
$44$	0.755051	0.113828
$45$	−6.11894	−0.912158
$46$	3.00025	0.442363
$47$	7.76816	1.13310	0.566552	−	0.824026i	$-0.308277\pi$
$47$	7.76816	1.13310	0.566552	+	0.824026i	$0.308277\pi$
$48$	−2.36933	−0.341984
$49$	10.1399	1.44856
$50$	0.480595	0.0679664
$51$	0.814133	0.114001
$52$	5.20636	0.721992
$53$	−3.31248	−0.455004	−0.227502	−	0.973778i	$-0.573056\pi$
$53$	−3.31248	−0.455004	−0.227502	+	0.973778i	$0.573056\pi$
$54$	0.915175	0.124540
$55$	−1.76762	−0.238346
$56$	4.14004	0.553236
$57$	−7.45180	−0.987015
$58$	0.0845158	0.0110975
$59$	−6.69383	−0.871463	−0.435731	−	0.900077i	$-0.643510\pi$
$59$	−6.69383	−0.871463	−0.435731	+	0.900077i	$0.643510\pi$
$60$	5.54677	0.716085
$61$	6.64404	0.850682	0.425341	−	0.905033i	$-0.360154\pi$
$61$	6.64404	0.850682	0.425341	+	0.905033i	$0.360154\pi$
$62$	−1.30032	−0.165141
$63$	10.8210	1.36332
$64$	1.00000	0.125000
$65$	−12.1884	−1.51179
$66$	−1.78897	−0.220207
$67$	8.31293	1.01559	0.507793	−	0.861479i	$-0.330461\pi$
$67$	8.31293	1.01559	0.507793	+	0.861479i	$0.330461\pi$
$68$	−0.343613	−0.0416691
$69$	−7.10859	−0.855774
$70$	−9.69212	−1.15843
$71$	−6.11170	−0.725325	−0.362662	−	0.931921i	$-0.618132\pi$
$71$	−6.11170	−0.725325	−0.362662	+	0.931921i	$0.618132\pi$
$72$	2.61374	0.308032
$73$	−0.836250	−0.0978756	−0.0489378	−	0.998802i	$-0.515584\pi$
$73$	−0.836250	−0.0978756	−0.0489378	+	0.998802i	$0.515584\pi$
$74$	−3.42817	−0.398517
$75$	−1.13869	−0.131485
$76$	3.14510	0.360768
$77$	3.12594	0.356234
$78$	−12.3356	−1.39673
$79$	−5.99442	−0.674424	−0.337212	−	0.941429i	$-0.609484\pi$
$79$	−5.99442	−0.674424	−0.337212	+	0.941429i	$0.609484\pi$
$80$	−2.34107	−0.261739
$81$	−10.0096	−1.11218
$82$	−10.4772	−1.15701
$83$	4.33584	0.475921	0.237960	−	0.971275i	$-0.423521\pi$
$83$	4.33584	0.475921	0.237960	+	0.971275i	$0.423521\pi$
$84$	−9.80914	−1.07026
$85$	0.804420	0.0872516
$86$	1.80280	0.194401
$87$	−0.200246	−0.0214686
$88$	0.755051	0.0804887
$89$	8.23783	0.873208	0.436604	−	0.899654i	$-0.356181\pi$
$89$	8.23783	0.873208	0.436604	+	0.899654i	$0.356181\pi$
$90$	−6.11894	−0.644993
$91$	21.5545	2.25953
$92$	3.00025	0.312798
$93$	3.08090	0.319474
$94$	7.76816	0.801225
$95$	−7.36290	−0.755417
$96$	−2.36933	−0.241819
$97$	16.4266	1.66787	0.833936	−	0.551862i	$-0.186082\pi$
$97$	16.4266	1.66787	0.833936	+	0.551862i	$0.186082\pi$
$98$	10.1399	1.02429
$99$	1.97351	0.198345
$100$	0.480595	0.0480595
$101$	−0.616998	−0.0613936	−0.0306968	−	0.999529i	$-0.509773\pi$
$101$	−0.616998	−0.0613936	−0.0306968	+	0.999529i	$0.509773\pi$
$102$	0.814133	0.0806112
$103$	−7.49611	−0.738614	−0.369307	−	0.929307i	$-0.620405\pi$
$103$	−7.49611	−0.738614	−0.369307	+	0.929307i	$0.620405\pi$
$104$	5.20636	0.510525
$105$	22.9639	2.24104
$106$	−3.31248	−0.321736
$107$	13.6226	1.31695	0.658473	−	0.752605i	$-0.271203\pi$
$107$	13.6226	1.31695	0.658473	+	0.752605i	$0.271203\pi$
$108$	0.915175	0.0880627
$109$	8.30128	0.795119	0.397559	−	0.917576i	$-0.369857\pi$
$109$	8.30128	0.795119	0.397559	+	0.917576i	$0.369857\pi$
$110$	−1.76762	−0.168536
$111$	8.12248	0.770952
$112$	4.14004	0.391197
$113$	−1.84052	−0.173141	−0.0865706	−	0.996246i	$-0.527591\pi$
$113$	−1.84052	−0.173141	−0.0865706	+	0.996246i	$0.527591\pi$
$114$	−7.45180	−0.697925
$115$	−7.02379	−0.654971
$116$	0.0845158	0.00784709
$117$	13.6081	1.25807
$118$	−6.69383	−0.616217
$119$	−1.42257	−0.130407
$120$	5.54677	0.506348
$121$	−10.4299	−0.948173
$122$	6.64404	0.601523
$123$	24.8240	2.23830
$124$	−1.30032	−0.116773
$125$	10.5802	0.946325
$126$	10.8210	0.964011
$127$	1.17295	0.104082	0.0520411	−	0.998645i	$-0.483427\pi$
$127$	1.17295	0.104082	0.0520411	+	0.998645i	$0.483427\pi$
$128$	1.00000	0.0883883
$129$	−4.27143	−0.376078
$130$	−12.1884	−1.06900
$131$	−6.58080	−0.574968	−0.287484	−	0.957786i	$-0.592819\pi$
$131$	−6.58080	−0.574968	−0.287484	+	0.957786i	$0.592819\pi$
$132$	−1.78897	−0.155710
$133$	13.0209	1.12905
$134$	8.31293	0.718128
$135$	−2.14249	−0.184396
$136$	−0.343613	−0.0294645
$137$	−4.72294	−0.403508	−0.201754	−	0.979436i	$-0.564664\pi$
$137$	−4.72294	−0.403508	−0.201754	+	0.979436i	$0.564664\pi$
$138$	−7.10859	−0.605124
$139$	16.7008	1.41655	0.708273	−	0.705939i	$-0.249475\pi$
$139$	16.7008	1.41655	0.708273	+	0.705939i	$0.249475\pi$
$140$	−9.69212	−0.819133
$141$	−18.4054	−1.55001
$142$	−6.11170	−0.512882
$143$	3.93106	0.328732
$144$	2.61374	0.217812
$145$	−0.197857	−0.0164311
$146$	−0.836250	−0.0692085
$147$	−24.0249	−1.98154
$148$	−3.42817	−0.281794
$149$	11.5419	0.945546	0.472773	−	0.881184i	$-0.343253\pi$
$149$	11.5419	0.945546	0.472773	+	0.881184i	$0.343253\pi$
$150$	−1.13869	−0.0929736
$151$	−0.545605	−0.0444007	−0.0222004	−	0.999754i	$-0.507067\pi$
$151$	−0.545605	−0.0444007	−0.0222004	+	0.999754i	$0.507067\pi$
$152$	3.14510	0.255102
$153$	−0.898114	−0.0726083
$154$	3.12594	0.251896
$155$	3.04414	0.244512
$156$	−12.3356	−0.987638
$157$	−4.50559	−0.359585	−0.179792	−	0.983705i	$-0.557543\pi$
$157$	−4.50559	−0.359585	−0.179792	+	0.983705i	$0.557543\pi$
$158$	−5.99442	−0.476890
$159$	7.84837	0.622416
$160$	−2.34107	−0.185078
$161$	12.4212	0.978925
$162$	−10.0096	−0.786427
$163$	2.14088	0.167686	0.0838432	−	0.996479i	$-0.473281\pi$
$163$	2.14088	0.167686	0.0838432	+	0.996479i	$0.473281\pi$
$164$	−10.4772	−0.818132
$165$	4.18809	0.326043
$166$	4.33584	0.336527
$167$	15.0791	1.16685	0.583427	−	0.812166i	$-0.301712\pi$
$167$	15.0791	1.16685	0.583427	+	0.812166i	$0.301712\pi$
$168$	−9.80914	−0.756792
$169$	14.1062	1.08509
$170$	0.804420	0.0616962
$171$	8.22049	0.628636
$172$	1.80280	0.137462
$173$	14.1736	1.07760	0.538800	−	0.842433i	$-0.318878\pi$
$173$	14.1736	1.07760	0.538800	+	0.842433i	$0.318878\pi$
$174$	−0.200246	−0.0151806
$175$	1.98968	0.150406
$176$	0.755051	0.0569141
$177$	15.8599	1.19210
$178$	8.23783	0.617451
$179$	−12.3698	−0.924563	−0.462282	−	0.886733i	$-0.652969\pi$
$179$	−12.3698	−0.924563	−0.462282	+	0.886733i	$0.652969\pi$
$180$	−6.11894	−0.456079
$181$	−10.2887	−0.764756	−0.382378	−	0.924006i	$-0.624895\pi$
$181$	−10.2887	−0.764756	−0.382378	+	0.924006i	$0.624895\pi$
$182$	21.5545	1.59773
$183$	−15.7419	−1.16368
$184$	3.00025	0.221181
$185$	8.02558	0.590053
$186$	3.08090	0.225903
$187$	−0.259445	−0.0189725
$188$	7.76816	0.566552
$189$	3.78886	0.275599
$190$	−7.36290	−0.534161
$191$	−8.22711	−0.595293	−0.297647	−	0.954676i	$-0.596202\pi$
$191$	−8.22711	−0.595293	−0.297647	+	0.954676i	$0.596202\pi$
$192$	−2.36933	−0.170992
$193$	−2.60862	−0.187773	−0.0938864	−	0.995583i	$-0.529929\pi$
$193$	−2.60862	−0.187773	−0.0938864	+	0.995583i	$0.529929\pi$
$194$	16.4266	1.17936
$195$	28.8785	2.06803
$196$	10.1399	0.724282
$197$	2.73344	0.194750	0.0973749	−	0.995248i	$-0.468955\pi$
$197$	2.73344	0.194750	0.0973749	+	0.995248i	$0.468955\pi$
$198$	1.97351	0.140251
$199$	23.9101	1.69494	0.847472	−	0.530839i	$-0.178123\pi$
$199$	23.9101	1.69494	0.847472	+	0.530839i	$0.178123\pi$
$200$	0.480595	0.0339832
$201$	−19.6961	−1.38926
$202$	−0.616998	−0.0434118
$203$	0.349899	0.0245581
$204$	0.814133	0.0570007
$205$	24.5278	1.71310
$206$	−7.49611	−0.522279
$207$	7.84188	0.545048
$208$	5.20636	0.360996
$209$	2.37471	0.164262
$210$	22.9639	1.58466
$211$	11.5749	0.796846	0.398423	−	0.917202i	$-0.369558\pi$
$211$	11.5749	0.796846	0.398423	+	0.917202i	$0.369558\pi$
$212$	−3.31248	−0.227502
$213$	14.4806	0.992198
$214$	13.6226	0.931221
$215$	−4.22047	−0.287834
$216$	0.915175	0.0622698
$217$	−5.38339	−0.365449
$218$	8.30128	0.562234
$219$	1.98135	0.133888
$220$	−1.76762	−0.119173
$221$	−1.78897	−0.120339
$222$	8.12248	0.545145
$223$	16.4678	1.10276	0.551382	−	0.834253i	$-0.314101\pi$
$223$	16.4678	1.10276	0.551382	+	0.834253i	$0.314101\pi$
$224$	4.14004	0.276618
$225$	1.25615	0.0837434
$226$	−1.84052	−0.122429
$227$	−2.29445	−0.152288	−0.0761438	−	0.997097i	$-0.524261\pi$
$227$	−2.29445	−0.152288	−0.0761438	+	0.997097i	$0.524261\pi$
$228$	−7.45180	−0.493507
$229$	2.55902	0.169105	0.0845525	−	0.996419i	$-0.473054\pi$
$229$	2.55902	0.169105	0.0845525	+	0.996419i	$0.473054\pi$
$230$	−7.02379	−0.463135
$231$	−7.40640	−0.487305
$232$	0.0845158	0.00554873
$233$	9.25024	0.606003	0.303002	−	0.952990i	$-0.402011\pi$
$233$	9.25024	0.606003	0.303002	+	0.952990i	$0.402011\pi$
$234$	13.6081	0.889588
$235$	−18.1858	−1.18631
$236$	−6.69383	−0.435731
$237$	14.2028	0.922569
$238$	−1.42257	−0.0922115
$239$	−25.7318	−1.66445	−0.832226	−	0.554437i	$-0.812934\pi$
$239$	−25.7318	−1.66445	−0.832226	+	0.554437i	$0.812934\pi$
$240$	5.54677	0.358042
$241$	1.06429	0.0685572	0.0342786	−	0.999412i	$-0.489087\pi$
$241$	1.06429	0.0685572	0.0342786	+	0.999412i	$0.489087\pi$
$242$	−10.4299	−0.670459
$243$	20.9705	1.34526
$244$	6.64404	0.425341
$245$	−23.7383	−1.51658
$246$	24.8240	1.58272
$247$	16.3745	1.04189
$248$	−1.30032	−0.0825706
$249$	−10.2731	−0.651029
$250$	10.5802	0.669153
$251$	0.401328	0.0253316	0.0126658	−	0.999920i	$-0.495968\pi$
$251$	0.401328	0.0253316	0.0126658	+	0.999920i	$0.495968\pi$
$252$	10.8210	0.681659
$253$	2.26534	0.142421
$254$	1.17295	0.0735973
$255$	−1.90594	−0.119355
$256$	1.00000	0.0625000
$257$	−21.6886	−1.35290	−0.676448	−	0.736490i	$-0.736482\pi$
$257$	−21.6886	−1.35290	−0.676448	+	0.736490i	$0.736482\pi$
$258$	−4.27143	−0.265927
$259$	−14.1928	−0.881896
$260$	−12.1884	−0.755894
$261$	0.220902	0.0136735
$262$	−6.58080	−0.406563
$263$	−8.24604	−0.508473	−0.254236	−	0.967142i	$-0.581824\pi$
$263$	−8.24604	−0.508473	−0.254236	+	0.967142i	$0.581824\pi$
$264$	−1.78897	−0.110103
$265$	7.75474	0.476370
$266$	13.0209	0.798360
$267$	−19.5182	−1.19449
$268$	8.31293	0.507793
$269$	18.2646	1.11361	0.556807	−	0.830642i	$-0.312026\pi$
$269$	18.2646	1.11361	0.556807	+	0.830642i	$0.312026\pi$
$270$	−2.14249	−0.130388
$271$	22.8042	1.38526	0.692629	−	0.721294i	$-0.256453\pi$
$271$	22.8042	1.38526	0.692629	+	0.721294i	$0.256453\pi$
$272$	−0.343613	−0.0208346
$273$	−51.0699	−3.09089
$274$	−4.72294	−0.285323
$275$	0.362873	0.0218821
$276$	−7.10859	−0.427887
$277$	−4.27071	−0.256602	−0.128301	−	0.991735i	$-0.540952\pi$
$277$	−4.27071	−0.256602	−0.128301	+	0.991735i	$0.540952\pi$
$278$	16.7008	1.00165
$279$	−3.39871	−0.203475
$280$	−9.69212	−0.579215
$281$	−5.93422	−0.354006	−0.177003	−	0.984210i	$-0.556640\pi$
$281$	−5.93422	−0.354006	−0.177003	+	0.984210i	$0.556640\pi$
$282$	−18.4054	−1.09602
$283$	16.9149	1.00549	0.502743	−	0.864436i	$-0.332324\pi$
$283$	16.9149	1.00549	0.502743	+	0.864436i	$0.332324\pi$
$284$	−6.11170	−0.362662
$285$	17.4452	1.03336
$286$	3.93106	0.232449
$287$	−43.3761	−2.56041
$288$	2.61374	0.154016
$289$	−16.8819	−0.993055
$290$	−0.197857	−0.0116186
$291$	−38.9202	−2.28154
$292$	−0.836250	−0.0489378
$293$	23.5952	1.37845	0.689223	−	0.724550i	$-0.257952\pi$
$293$	23.5952	1.37845	0.689223	+	0.724550i	$0.257952\pi$
$294$	−24.0249	−1.40116
$295$	15.6707	0.912384
$296$	−3.42817	−0.199258
$297$	0.691004	0.0400961
$298$	11.5419	0.668602
$299$	15.6204	0.903350
$300$	−1.13869	−0.0657423
$301$	7.46365	0.430198
$302$	−0.545605	−0.0313961
$303$	1.46187	0.0839825
$304$	3.14510	0.180384
$305$	−15.5541	−0.890628
$306$	−0.898114	−0.0513418
$307$	−17.3589	−0.990727	−0.495364	−	0.868686i	$-0.664965\pi$
$307$	−17.3589	−0.990727	−0.495364	+	0.868686i	$0.664965\pi$
$308$	3.12594	0.178117
$309$	17.7608	1.01038
$310$	3.04414	0.172896
$311$	10.4240	0.591089	0.295545	−	0.955329i	$-0.404499\pi$
$311$	10.4240	0.591089	0.295545	+	0.955329i	$0.404499\pi$
$312$	−12.3356	−0.698366
$313$	3.48391	0.196922	0.0984612	−	0.995141i	$-0.468608\pi$
$313$	3.48391	0.196922	0.0984612	+	0.995141i	$0.468608\pi$
$314$	−4.50559	−0.254265
$315$	−25.3327	−1.42734
$316$	−5.99442	−0.337212
$317$	26.2911	1.47666	0.738329	−	0.674441i	$-0.235615\pi$
$317$	26.2911	1.47666	0.738329	+	0.674441i	$0.235615\pi$
$318$	7.84837	0.440115
$319$	0.0638137	0.00357288
$320$	−2.34107	−0.130870
$321$	−32.2765	−1.80150
$322$	12.4212	0.692204
$323$	−1.08070	−0.0601316
$324$	−10.0096	−0.556088
$325$	2.50215	0.138794
$326$	2.14088	0.118572
$327$	−19.6685	−1.08767
$328$	−10.4772	−0.578507
$329$	32.1605	1.77307
$330$	4.18809	0.230547
$331$	2.86964	0.157730	0.0788648	−	0.996885i	$-0.474870\pi$
$331$	2.86964	0.157730	0.0788648	+	0.996885i	$0.474870\pi$
$332$	4.33584	0.237960
$333$	−8.96036	−0.491025
$334$	15.0791	0.825090
$335$	−19.4611	−1.06328
$336$	−9.80914	−0.535132
$337$	−9.68411	−0.527527	−0.263763	−	0.964587i	$-0.584964\pi$
$337$	−9.68411	−0.527527	−0.263763	+	0.964587i	$0.584964\pi$
$338$	14.1062	0.767274
$339$	4.36080	0.236846
$340$	0.804420	0.0436258
$341$	−0.981810	−0.0531680
$342$	8.22049	0.444513
$343$	12.9995	0.701908
$344$	1.80280	0.0972003
$345$	16.6417	0.895959
$346$	14.1736	0.761979
$347$	5.83173	0.313064	0.156532	−	0.987673i	$-0.449969\pi$
$347$	5.83173	0.313064	0.156532	+	0.987673i	$0.449969\pi$
$348$	−0.200246	−0.0107343
$349$	−8.77677	−0.469810	−0.234905	−	0.972018i	$-0.575478\pi$
$349$	−8.77677	−0.469810	−0.234905	+	0.972018i	$0.575478\pi$
$350$	1.98968	0.106353
$351$	4.76473	0.254322
$352$	0.755051	0.0402443
$353$	−0.0838628	−0.00446357	−0.00223178	−	0.999998i	$-0.500710\pi$
$353$	−0.0838628	−0.00446357	−0.00223178	+	0.999998i	$0.500710\pi$
$354$	15.8599	0.842945
$355$	14.3079	0.759384
$356$	8.23783	0.436604
$357$	3.37054	0.178388
$358$	−12.3698	−0.653765
$359$	−4.99511	−0.263632	−0.131816	−	0.991274i	$-0.542081\pi$
$359$	−4.99511	−0.263632	−0.131816	+	0.991274i	$0.542081\pi$
$360$	−6.11894	−0.322497
$361$	−9.10832	−0.479386
$362$	−10.2887	−0.540764
$363$	24.7119	1.29704
$364$	21.5545	1.12976
$365$	1.95772	0.102472
$366$	−15.7419	−0.822845
$367$	−35.6347	−1.86012	−0.930059	−	0.367409i	$-0.880245\pi$
$367$	−35.6347	−1.86012	−0.930059	+	0.367409i	$0.880245\pi$
$368$	3.00025	0.156399
$369$	−27.3847	−1.42559
$370$	8.02558	0.417230
$371$	−13.7138	−0.711985
$372$	3.08090	0.159737
$373$	9.03274	0.467697	0.233849	−	0.972273i	$-0.424868\pi$
$373$	9.03274	0.467697	0.233849	+	0.972273i	$0.424868\pi$
$374$	−0.259445	−0.0134156
$375$	−25.0681	−1.29451
$376$	7.76816	0.400612
$377$	0.440019	0.0226621
$378$	3.78886	0.194878
$379$	27.2329	1.39886	0.699429	−	0.714702i	$-0.253438\pi$
$379$	27.2329	1.39886	0.699429	+	0.714702i	$0.253438\pi$
$380$	−7.36290	−0.377709
$381$	−2.77910	−0.142378
$382$	−8.22711	−0.420936
$383$	−21.1512	−1.08078	−0.540389	−	0.841415i	$-0.681723\pi$
$383$	−21.1512	−1.08078	−0.540389	+	0.841415i	$0.681723\pi$
$384$	−2.36933	−0.120910
$385$	−7.31804	−0.372962
$386$	−2.60862	−0.132775
$387$	4.71204	0.239527
$388$	16.4266	0.833936
$389$	2.69212	0.136496	0.0682478	−	0.997668i	$-0.478259\pi$
$389$	2.69212	0.136496	0.0682478	+	0.997668i	$0.478259\pi$
$390$	28.8785	1.46232
$391$	−1.03092	−0.0521360
$392$	10.1399	0.512145
$393$	15.5921	0.786519
$394$	2.73344	0.137709
$395$	14.0333	0.706093
$396$	1.97351	0.0991725
$397$	32.2819	1.62018	0.810092	−	0.586303i	$-0.199417\pi$
$397$	32.2819	1.62018	0.810092	+	0.586303i	$0.199417\pi$
$398$	23.9101	1.19851
$399$	−30.8508	−1.54447
$400$	0.480595	0.0240297
$401$	−6.63858	−0.331515	−0.165757	−	0.986167i	$-0.553007\pi$
$401$	−6.63858	−0.331515	−0.165757	+	0.986167i	$0.553007\pi$
$402$	−19.6961	−0.982353
$403$	−6.76995	−0.337235
$404$	−0.616998	−0.0306968
$405$	23.4331	1.16440
$406$	0.349899	0.0173652
$407$	−2.58844	−0.128304
$408$	0.814133	0.0403056
$409$	2.28005	0.112741	0.0563705	−	0.998410i	$-0.482047\pi$
$409$	2.28005	0.112741	0.0563705	+	0.998410i	$0.482047\pi$
$410$	24.5278	1.21134
$411$	11.1902	0.551973
$412$	−7.49611	−0.369307
$413$	−27.7127	−1.36365
$414$	7.84188	0.385407
$415$	−10.1505	−0.498268
$416$	5.20636	0.255263
$417$	−39.5698	−1.93774
$418$	2.37471	0.116151
$419$	−35.3845	−1.72864	−0.864322	−	0.502939i	$-0.832252\pi$
$419$	−35.3845	−1.72864	−0.864322	+	0.502939i	$0.832252\pi$
$420$	22.9639	1.12052
$421$	25.3165	1.23385	0.616924	−	0.787022i	$-0.288378\pi$
$421$	25.3165	1.23385	0.616924	+	0.787022i	$0.288378\pi$
$422$	11.5749	0.563455
$423$	20.3040	0.987213
$424$	−3.31248	−0.160868
$425$	−0.165138	−0.00801039
$426$	14.4806	0.701590
$427$	27.5066	1.33114
$428$	13.6226	0.658473
$429$	−9.31400	−0.449684
$430$	−4.22047	−0.203529
$431$	−2.94430	−0.141822	−0.0709111	−	0.997483i	$-0.522591\pi$
$431$	−2.94430	−0.141822	−0.0709111	+	0.997483i	$0.522591\pi$
$432$	0.915175	0.0440314
$433$	41.1769	1.97883	0.989417	−	0.145101i	$-0.0463508\pi$
$433$	41.1769	1.97883	0.989417	+	0.145101i	$0.0463508\pi$
$434$	−5.38339	−0.258411
$435$	0.468789	0.0224767
$436$	8.30128	0.397559
$437$	9.43610	0.451390
$438$	1.98135	0.0946728
$439$	20.0910	0.958889	0.479444	−	0.877572i	$-0.340838\pi$
$439$	20.0910	0.958889	0.479444	+	0.877572i	$0.340838\pi$
$440$	−1.76762	−0.0842682
$441$	26.5032	1.26206
$442$	−1.78897	−0.0850926
$443$	25.9539	1.23311	0.616554	−	0.787313i	$-0.288528\pi$
$443$	25.9539	1.23311	0.616554	+	0.787313i	$0.288528\pi$
$444$	8.12248	0.385476
$445$	−19.2853	−0.914211
$446$	16.4678	0.779772
$447$	−27.3465	−1.29345
$448$	4.14004	0.195599
$449$	29.0725	1.37202	0.686008	−	0.727594i	$-0.259362\pi$
$449$	29.0725	1.37202	0.686008	+	0.727594i	$0.259362\pi$
$450$	1.25615	0.0592155
$451$	−7.91082	−0.372506
$452$	−1.84052	−0.0865706
$453$	1.29272	0.0607373
$454$	−2.29445	−0.107684
$455$	−50.4606	−2.36563
$456$	−7.45180	−0.348962
$457$	−0.918963	−0.0429873	−0.0214936	−	0.999769i	$-0.506842\pi$
$457$	−0.918963	−0.0429873	−0.0214936	+	0.999769i	$0.506842\pi$
$458$	2.55902	0.119575
$459$	−0.314466	−0.0146780
$460$	−7.02379	−0.327486
$461$	−25.9230	−1.20735	−0.603677	−	0.797229i	$-0.706298\pi$
$461$	−25.9230	−1.20735	−0.603677	+	0.797229i	$0.706298\pi$
$462$	−7.40640	−0.344577
$463$	−30.5937	−1.42181	−0.710905	−	0.703288i	$-0.751714\pi$
$463$	−30.5937	−1.42181	−0.710905	+	0.703288i	$0.751714\pi$
$464$	0.0845158	0.00392355
$465$	−7.21259	−0.334476
$466$	9.25024	0.428509
$467$	1.42500	0.0659412	0.0329706	−	0.999456i	$-0.489503\pi$
$467$	1.42500	0.0659412	0.0329706	+	0.999456i	$0.489503\pi$
$468$	13.6081	0.629033
$469$	34.4159	1.58918
$470$	−18.1858	−0.838848
$471$	10.6752	0.491889
$472$	−6.69383	−0.308109
$473$	1.36120	0.0625882
$474$	14.2028	0.652355
$475$	1.51152	0.0693533
$476$	−1.42257	−0.0652034
$477$	−8.65797	−0.396421
$478$	−25.7318	−1.17695
$479$	−34.1758	−1.56153	−0.780765	−	0.624824i	$-0.785171\pi$
$479$	−34.1758	−1.56153	−0.780765	+	0.624824i	$0.785171\pi$
$480$	5.54677	0.253174
$481$	−17.8483	−0.813812
$482$	1.06429	0.0484773
$483$	−29.4299	−1.33911
$484$	−10.4299	−0.474086
$485$	−38.4558	−1.74619
$486$	20.9705	0.951242
$487$	−19.6962	−0.892519	−0.446260	−	0.894904i	$-0.647244\pi$
$487$	−19.6962	−0.892519	−0.446260	+	0.894904i	$0.647244\pi$
$488$	6.64404	0.300762
$489$	−5.07245	−0.229384
$490$	−23.7383	−1.07239
$491$	−43.0249	−1.94169	−0.970844	−	0.239711i	$-0.922947\pi$
$491$	−43.0249	−1.94169	−0.970844	+	0.239711i	$0.922947\pi$
$492$	24.8240	1.11915
$493$	−0.0290407	−0.00130793
$494$	16.3745	0.736725
$495$	−4.62011	−0.207659
$496$	−1.30032	−0.0583863
$497$	−25.3027	−1.13498
$498$	−10.2731	−0.460347
$499$	−31.1367	−1.39387	−0.696936	−	0.717133i	$-0.745454\pi$
$499$	−31.1367	−1.39387	−0.696936	+	0.717133i	$0.745454\pi$
$500$	10.5802	0.473162
$501$	−35.7273	−1.59618
$502$	0.401328	0.0179122
$503$	−0.810356	−0.0361320	−0.0180660	−	0.999837i	$-0.505751\pi$
$503$	−0.810356	−0.0361320	−0.0180660	+	0.999837i	$0.505751\pi$
$504$	10.8210	0.482006
$505$	1.44443	0.0642764
$506$	2.26534	0.100707
$507$	−33.4222	−1.48433
$508$	1.17295	0.0520411
$509$	2.55006	0.113030	0.0565148	−	0.998402i	$-0.482001\pi$
$509$	2.55006	0.113030	0.0565148	+	0.998402i	$0.482001\pi$
$510$	−1.90594	−0.0843964
$511$	−3.46211	−0.153155
$512$	1.00000	0.0441942
$513$	2.87832	0.127081
$514$	−21.6886	−0.956642
$515$	17.5489	0.773297
$516$	−4.27143	−0.188039
$517$	5.86536	0.257958
$518$	−14.1928	−0.623595
$519$	−33.5820	−1.47409
$520$	−12.1884	−0.534498
$521$	6.87970	0.301405	0.150703	−	0.988579i	$-0.451846\pi$
$521$	6.87970	0.301405	0.150703	+	0.988579i	$0.451846\pi$
$522$	0.220902	0.00966863
$523$	−24.2282	−1.05943	−0.529713	−	0.848177i	$-0.677700\pi$
$523$	−24.2282	−1.05943	−0.529713	+	0.848177i	$0.677700\pi$
$524$	−6.58080	−0.287484
$525$	−4.71422	−0.205746
$526$	−8.24604	−0.359544
$527$	0.446808	0.0194632
$528$	−1.78897	−0.0778548
$529$	−13.9985	−0.608630
$530$	7.75474	0.336844
$531$	−17.4959	−0.759259
$532$	13.0209	0.564526
$533$	−54.5481	−2.36274
$534$	−19.5182	−0.844633
$535$	−31.8914	−1.37879
$536$	8.31293	0.359064
$537$	29.3082	1.26474
$538$	18.2646	0.787444
$539$	7.65617	0.329775
$540$	−2.14249	−0.0921979
$541$	23.3047	1.00195	0.500973	−	0.865463i	$-0.332976\pi$
$541$	23.3047	1.00195	0.500973	+	0.865463i	$0.332976\pi$
$542$	22.8042	0.979525
$543$	24.3775	1.04614
$544$	−0.343613	−0.0147323
$545$	−19.4339	−0.832455
$546$	−51.0699	−2.18559
$547$	8.77239	0.375080	0.187540	−	0.982257i	$-0.439949\pi$
$547$	8.77239	0.375080	0.187540	+	0.982257i	$0.439949\pi$
$548$	−4.72294	−0.201754
$549$	17.3658	0.741155
$550$	0.362873	0.0154730
$551$	0.265811	0.0113239
$552$	−7.10859	−0.302562
$553$	−24.8171	−1.05533
$554$	−4.27071	−0.181445
$555$	−19.0153	−0.807154
$556$	16.7008	0.708273
$557$	3.00754	0.127433	0.0637167	−	0.997968i	$-0.479705\pi$
$557$	3.00754	0.127433	0.0637167	+	0.997968i	$0.479705\pi$
$558$	−3.39871	−0.143879
$559$	9.38600	0.396986
$560$	−9.69212	−0.409567
$561$	0.614712	0.0259531
$562$	−5.93422	−0.250320
$563$	−35.8924	−1.51268	−0.756342	−	0.654176i	$-0.773016\pi$
$563$	−35.8924	−1.51268	−0.756342	+	0.654176i	$0.773016\pi$
$564$	−18.4054	−0.775006
$565$	4.30877	0.181271
$566$	16.9149	0.710986
$567$	−41.4401	−1.74032
$568$	−6.11170	−0.256441
$569$	−27.5584	−1.15531	−0.577654	−	0.816282i	$-0.696032\pi$
$569$	−27.5584	−1.15531	−0.577654	+	0.816282i	$0.696032\pi$
$570$	17.4452	0.730697
$571$	−21.1901	−0.886780	−0.443390	−	0.896329i	$-0.646224\pi$
$571$	−21.1901	−0.886780	−0.443390	+	0.896329i	$0.646224\pi$
$572$	3.93106	0.164366
$573$	19.4928	0.814322
$574$	−43.3761	−1.81048
$575$	1.44190	0.0601316
$576$	2.61374	0.108906
$577$	8.62459	0.359047	0.179523	−	0.983754i	$-0.442544\pi$
$577$	8.62459	0.359047	0.179523	+	0.983754i	$0.442544\pi$
$578$	−16.8819	−0.702196
$579$	6.18070	0.256861
$580$	−0.197857	−0.00821557
$581$	17.9506	0.744715
$582$	−38.9202	−1.61329
$583$	−2.50109	−0.103585
$584$	−0.836250	−0.0346043
$585$	−31.8574	−1.31714
$586$	23.5952	0.974708
$587$	−5.63720	−0.232672	−0.116336	−	0.993210i	$-0.537115\pi$
$587$	−5.63720	−0.232672	−0.116336	+	0.993210i	$0.537115\pi$
$588$	−24.0249	−0.990771
$589$	−4.08965	−0.168511
$590$	15.6707	0.645153
$591$	−6.47644	−0.266405
$592$	−3.42817	−0.140897
$593$	35.2054	1.44571	0.722855	−	0.690999i	$-0.242829\pi$
$593$	35.2054	1.44571	0.722855	+	0.690999i	$0.242829\pi$
$594$	0.691004	0.0283522
$595$	3.33033	0.136530
$596$	11.5419	0.472773
$597$	−56.6511	−2.31858
$598$	15.6204	0.638765
$599$	30.1767	1.23299	0.616493	−	0.787360i	$-0.288553\pi$
$599$	30.1767	1.23299	0.616493	+	0.787360i	$0.288553\pi$
$600$	−1.13869	−0.0464868
$601$	17.1839	0.700946	0.350473	−	0.936573i	$-0.386021\pi$
$601$	17.1839	0.700946	0.350473	+	0.936573i	$0.386021\pi$
$602$	7.46365	0.304196
$603$	21.7279	0.884827
$604$	−0.545605	−0.0222004
$605$	24.4171	0.992696
$606$	1.46187	0.0593846
$607$	−12.7735	−0.518461	−0.259231	−	0.965815i	$-0.583469\pi$
$607$	−12.7735	−0.518461	−0.259231	+	0.965815i	$0.583469\pi$
$608$	3.14510	0.127551
$609$	−0.829027	−0.0335939
$610$	−15.5541	−0.629769
$611$	40.4438	1.63618
$612$	−0.898114	−0.0363041
$613$	19.3065	0.779781	0.389891	−	0.920861i	$-0.372513\pi$
$613$	19.3065	0.779781	0.389891	+	0.920861i	$0.372513\pi$
$614$	−17.3589	−0.700550
$615$	−58.1146	−2.34341
$616$	3.12594	0.125948
$617$	−4.37062	−0.175954	−0.0879772	−	0.996122i	$-0.528040\pi$
$617$	−4.37062	−0.175954	−0.0879772	+	0.996122i	$0.528040\pi$
$618$	17.7608	0.714444
$619$	−17.9263	−0.720519	−0.360259	−	0.932852i	$-0.617312\pi$
$619$	−17.9263	−0.720519	−0.360259	+	0.932852i	$0.617312\pi$
$620$	3.04414	0.122256
$621$	2.74575	0.110183
$622$	10.4240	0.417963
$623$	34.1049	1.36639
$624$	−12.3356	−0.493819
$625$	−27.1720	−1.08688
$626$	3.48391	0.139245
$627$	−5.62649	−0.224700
$628$	−4.50559	−0.179792
$629$	1.17796	0.0469685
$630$	−25.3327	−1.00928
$631$	33.0923	1.31738	0.658692	−	0.752413i	$-0.271110\pi$
$631$	33.0923	1.31738	0.658692	+	0.752413i	$0.271110\pi$
$632$	−5.99442	−0.238445
$633$	−27.4247	−1.09003
$634$	26.2911	1.04415
$635$	−2.74595	−0.108970
$636$	7.84837	0.311208
$637$	52.7922	2.09170
$638$	0.0638137	0.00252641
$639$	−15.9744	−0.631937
$640$	−2.34107	−0.0925388
$641$	35.1585	1.38868	0.694339	−	0.719648i	$-0.255697\pi$
$641$	35.1585	1.38868	0.694339	+	0.719648i	$0.255697\pi$
$642$	−32.2765	−1.27385
$643$	−12.5694	−0.495689	−0.247845	−	0.968800i	$-0.579722\pi$
$643$	−12.5694	−0.495689	−0.247845	+	0.968800i	$0.579722\pi$
$644$	12.4212	0.489462
$645$	9.99970	0.393738
$646$	−1.08070	−0.0425195
$647$	26.3334	1.03527	0.517637	−	0.855600i	$-0.326812\pi$
$647$	26.3334	1.03527	0.517637	+	0.855600i	$0.326812\pi$
$648$	−10.0096	−0.393213
$649$	−5.05418	−0.198394
$650$	2.50215	0.0981423
$651$	12.7551	0.499910
$652$	2.14088	0.0838432
$653$	−8.19309	−0.320620	−0.160310	−	0.987067i	$-0.551249\pi$
$653$	−8.19309	−0.320620	−0.160310	+	0.987067i	$0.551249\pi$
$654$	−19.6685	−0.769100
$655$	15.4061	0.601966
$656$	−10.4772	−0.409066
$657$	−2.18574	−0.0852739
$658$	32.1605	1.25375
$659$	−40.0175	−1.55886	−0.779431	−	0.626489i	$-0.784491\pi$
$659$	−40.0175	−1.55886	−0.779431	+	0.626489i	$0.784491\pi$
$660$	4.18809	0.163021
$661$	−31.2296	−1.21469	−0.607345	−	0.794438i	$-0.707765\pi$
$661$	−31.2296	−1.21469	−0.607345	+	0.794438i	$0.707765\pi$
$662$	2.86964	0.111532
$663$	4.23867	0.164616
$664$	4.33584	0.168263
$665$	−30.4827	−1.18207
$666$	−8.96036	−0.347207
$667$	0.253568	0.00981821
$668$	15.0791	0.583427
$669$	−39.0177	−1.50851
$670$	−19.4611	−0.751849
$671$	5.01659	0.193663
$672$	−9.80914	−0.378396
$673$	−32.5444	−1.25449	−0.627247	−	0.778820i	$-0.715818\pi$
$673$	−32.5444	−1.25449	−0.627247	+	0.778820i	$0.715818\pi$
$674$	−9.68411	−0.373018
$675$	0.439828	0.0169290
$676$	14.1062	0.542545
$677$	−17.5420	−0.674192	−0.337096	−	0.941470i	$-0.609445\pi$
$677$	−17.5420	−0.674192	−0.337096	+	0.941470i	$0.609445\pi$
$678$	4.36080	0.167475
$679$	68.0069	2.60987
$680$	0.804420	0.0308481
$681$	5.43631	0.208320
$682$	−0.981810	−0.0375955
$683$	31.7755	1.21586	0.607928	−	0.793992i	$-0.292001\pi$
$683$	31.7755	1.21586	0.607928	+	0.793992i	$0.292001\pi$
$684$	8.22049	0.314318
$685$	11.0567	0.422455
$686$	12.9995	0.496324
$687$	−6.06318	−0.231325
$688$	1.80280	0.0687310
$689$	−17.2460	−0.657019
$690$	16.6417	0.633538
$691$	51.0411	1.94169	0.970847	−	0.239701i	$-0.0770495\pi$
$691$	51.0411	1.94169	0.970847	+	0.239701i	$0.0770495\pi$
$692$	14.1736	0.538800
$693$	8.17040	0.310368
$694$	5.83173	0.221370
$695$	−39.0977	−1.48306
$696$	−0.200246	−0.00759031
$697$	3.60010	0.136363
$698$	−8.77677	−0.332206
$699$	−21.9169	−0.828974
$700$	1.98968	0.0752029
$701$	−20.0337	−0.756661	−0.378330	−	0.925671i	$-0.623502\pi$
$701$	−20.0337	−0.756661	−0.378330	+	0.925671i	$0.623502\pi$
$702$	4.76473	0.179833
$703$	−10.7820	−0.406649
$704$	0.755051	0.0284570
$705$	43.0882	1.62280
$706$	−0.0838628	−0.00315622
$707$	−2.55440	−0.0960680
$708$	15.8599	0.596052
$709$	−1.49693	−0.0562184	−0.0281092	−	0.999605i	$-0.508949\pi$
$709$	−1.49693	−0.0562184	−0.0281092	+	0.999605i	$0.508949\pi$
$710$	14.3079	0.536966
$711$	−15.6679	−0.587590
$712$	8.23783	0.308726
$713$	−3.90130	−0.146105
$714$	3.37054	0.126139
$715$	−9.20289	−0.344168
$716$	−12.3698	−0.462282
$717$	60.9672	2.27686
$718$	−4.99511	−0.186416
$719$	27.1554	1.01273	0.506363	−	0.862321i	$-0.330990\pi$
$719$	27.1554	1.01273	0.506363	+	0.862321i	$0.330990\pi$
$720$	−6.11894	−0.228040
$721$	−31.0342	−1.15577
$722$	−9.10832	−0.338977
$723$	−2.52167	−0.0937819
$724$	−10.2887	−0.382378
$725$	0.0406178	0.00150851
$726$	24.7119	0.917145
$727$	−35.1681	−1.30431	−0.652156	−	0.758084i	$-0.726135\pi$
$727$	−35.1681	−1.30431	−0.652156	+	0.758084i	$0.726135\pi$
$728$	21.5545	0.798864
$729$	−19.6574	−0.728052
$730$	1.95772	0.0724583
$731$	−0.619464	−0.0229117
$732$	−15.7419	−0.581839
$733$	12.8903	0.476114	0.238057	−	0.971251i	$-0.423490\pi$
$733$	12.8903	0.476114	0.238057	+	0.971251i	$0.423490\pi$
$734$	−35.6347	−1.31530
$735$	56.2439	2.07459
$736$	3.00025	0.110591
$737$	6.27669	0.231205
$738$	−27.3847	−1.00805
$739$	−36.9302	−1.35850	−0.679249	−	0.733908i	$-0.737694\pi$
$739$	−36.9302	−1.35850	−0.679249	+	0.733908i	$0.737694\pi$
$740$	8.02558	0.295026
$741$	−38.7967	−1.42523
$742$	−13.7138	−0.503450
$743$	−18.5321	−0.679876	−0.339938	−	0.940448i	$-0.610406\pi$
$743$	−18.5321	−0.679876	−0.339938	+	0.940448i	$0.610406\pi$
$744$	3.08090	0.112951
$745$	−27.0203	−0.989946
$746$	9.03274	0.330712
$747$	11.3328	0.414644
$748$	−0.259445	−0.00948625
$749$	56.3981	2.06074
$750$	−25.0681	−0.915357
$751$	25.3340	0.924451	0.462226	−	0.886762i	$-0.347051\pi$
$751$	25.3340	0.924451	0.462226	+	0.886762i	$0.347051\pi$
$752$	7.76816	0.283276
$753$	−0.950881	−0.0346520
$754$	0.440019	0.0160246
$755$	1.27730	0.0464857
$756$	3.78886	0.137800
$757$	6.97120	0.253373	0.126686	−	0.991943i	$-0.459566\pi$
$757$	6.97120	0.253373	0.126686	+	0.991943i	$0.459566\pi$
$758$	27.2329	0.989142
$759$	−5.36735	−0.194822
$760$	−7.36290	−0.267080
$761$	−13.3353	−0.483406	−0.241703	−	0.970350i	$-0.577706\pi$
$761$	−13.3353	−0.483406	−0.241703	+	0.970350i	$0.577706\pi$
$762$	−2.77910	−0.100676
$763$	34.3677	1.24419
$764$	−8.22711	−0.297647
$765$	2.10255	0.0760177
$766$	−21.1512	−0.764226
$767$	−34.8505	−1.25838
$768$	−2.36933	−0.0854960
$769$	19.5668	0.705598	0.352799	−	0.935699i	$-0.385230\pi$
$769$	19.5668	0.705598	0.352799	+	0.935699i	$0.385230\pi$
$770$	−7.31804	−0.263724
$771$	51.3875	1.85067
$772$	−2.60862	−0.0938864
$773$	−21.0374	−0.756664	−0.378332	−	0.925670i	$-0.623502\pi$
$773$	−21.0374	−0.756664	−0.378332	+	0.925670i	$0.623502\pi$
$774$	4.71204	0.169371
$775$	−0.624929	−0.0224481
$776$	16.4266	0.589682
$777$	33.6274	1.20638
$778$	2.69212	0.0965170
$779$	−32.9519	−1.18062
$780$	28.8785	1.03401
$781$	−4.61464	−0.165125
$782$	−1.03092	−0.0368658
$783$	0.0773467	0.00276415
$784$	10.1399	0.362141
$785$	10.5479	0.376470
$786$	15.5921	0.556153
$787$	36.6619	1.30686	0.653428	−	0.756989i	$-0.273330\pi$
$787$	36.6619	1.30686	0.653428	+	0.756989i	$0.273330\pi$
$788$	2.73344	0.0973749
$789$	19.5376	0.695558
$790$	14.0333	0.499283
$791$	−7.61981	−0.270929
$792$	1.97351	0.0701255
$793$	34.5913	1.22837
$794$	32.2819	1.14564
$795$	−18.3736	−0.651643
$796$	23.9101	0.847472
$797$	5.38270	0.190665	0.0953325	−	0.995445i	$-0.469609\pi$
$797$	5.38270	0.190665	0.0953325	+	0.995445i	$0.469609\pi$
$798$	−30.8508	−1.09211
$799$	−2.66924	−0.0944309
$800$	0.480595	0.0169916
$801$	21.5315	0.760780
$802$	−6.63858	−0.234416
$803$	−0.631411	−0.0222820
$804$	−19.6961	−0.694628
$805$	−29.0788	−1.02489
$806$	−6.76995	−0.238461
$807$	−43.2750	−1.52335
$808$	−0.616998	−0.0217059
$809$	−14.1124	−0.496164	−0.248082	−	0.968739i	$-0.579800\pi$
$809$	−14.1124	−0.496164	−0.248082	+	0.968739i	$0.579800\pi$
$810$	23.4331	0.823355
$811$	−8.53214	−0.299604	−0.149802	−	0.988716i	$-0.547864\pi$
$811$	−8.53214	−0.299604	−0.149802	+	0.988716i	$0.547864\pi$
$812$	0.349899	0.0122790
$813$	−54.0308	−1.89494
$814$	−2.58844	−0.0907249
$815$	−5.01194	−0.175561
$816$	0.814133	0.0285003
$817$	5.66998	0.198368
$818$	2.28005	0.0797200
$819$	56.3380	1.96861
$820$	24.5278	0.856549
$821$	16.3855	0.571858	0.285929	−	0.958251i	$-0.407698\pi$
$821$	16.3855	0.571858	0.285929	+	0.958251i	$0.407698\pi$
$822$	11.1902	0.390304
$823$	43.3833	1.51225	0.756123	−	0.654430i	$-0.227091\pi$
$823$	43.3833	1.51225	0.756123	+	0.654430i	$0.227091\pi$
$824$	−7.49611	−0.261139
$825$	−0.859768	−0.0299333
$826$	−27.7127	−0.964250
$827$	−26.6757	−0.927606	−0.463803	−	0.885938i	$-0.653515\pi$
$827$	−26.6757	−0.927606	−0.463803	+	0.885938i	$0.653515\pi$
$828$	7.84188	0.272524
$829$	14.9818	0.520338	0.260169	−	0.965563i	$-0.416222\pi$
$829$	14.9818	0.520338	0.260169	+	0.965563i	$0.416222\pi$
$830$	−10.1505	−0.352329
$831$	10.1187	0.351015
$832$	5.20636	0.180498
$833$	−3.48421	−0.120721
$834$	−39.5698	−1.37019
$835$	−35.3011	−1.22165
$836$	2.37471	0.0821312
$837$	−1.19002	−0.0411332
$838$	−35.3845	−1.22234
$839$	24.2894	0.838564	0.419282	−	0.907856i	$-0.362282\pi$
$839$	24.2894	0.838564	0.419282	+	0.907856i	$0.362282\pi$
$840$	22.9639	0.792328
$841$	−28.9929	−0.999754
$842$	25.3165	0.872463
$843$	14.0601	0.484257
$844$	11.5749	0.398423
$845$	−33.0235	−1.13604
$846$	20.3040	0.698065
$847$	−43.1802	−1.48369
$848$	−3.31248	−0.113751
$849$	−40.0770	−1.37544
$850$	−0.165138	−0.00566420
$851$	−10.2854	−0.352578
$852$	14.4806	0.496099
$853$	28.4467	0.973996	0.486998	−	0.873403i	$-0.338092\pi$
$853$	28.4467	0.973996	0.486998	+	0.873403i	$0.338092\pi$
$854$	27.5066	0.941257
$855$	−19.2447	−0.658155
$856$	13.6226	0.465610
$857$	−20.8145	−0.711010	−0.355505	−	0.934674i	$-0.615691\pi$
$857$	−20.8145	−0.711010	−0.355505	+	0.934674i	$0.615691\pi$
$858$	−9.31400	−0.317975
$859$	17.3985	0.593629	0.296815	−	0.954935i	$-0.404076\pi$
$859$	17.3985	0.593629	0.296815	+	0.954935i	$0.404076\pi$
$860$	−4.22047	−0.143917
$861$	102.772	3.50247
$862$	−2.94430	−0.100283
$863$	0.280666	0.00955397	0.00477699	−	0.999989i	$-0.498479\pi$
$863$	0.280666	0.00955397	0.00477699	+	0.999989i	$0.498479\pi$
$864$	0.915175	0.0311349
$865$	−33.1814	−1.12820
$866$	41.1769	1.39925
$867$	39.9989	1.35843
$868$	−5.38339	−0.182724
$869$	−4.52609	−0.153537
$870$	0.468789	0.0158934
$871$	43.2801	1.46649
$872$	8.30128	0.281117
$873$	42.9350	1.45313
$874$	9.43610	0.319181
$875$	43.8026	1.48080
$876$	1.98135	0.0669438
$877$	−13.9796	−0.472058	−0.236029	−	0.971746i	$-0.575846\pi$
$877$	−13.9796	−0.472058	−0.236029	+	0.971746i	$0.575846\pi$
$878$	20.0910	0.678037
$879$	−55.9049	−1.88562
$880$	−1.76762	−0.0595866
$881$	−4.46270	−0.150352	−0.0751761	−	0.997170i	$-0.523952\pi$
$881$	−4.46270	−0.150352	−0.0751761	+	0.997170i	$0.523952\pi$
$882$	26.5032	0.892409
$883$	−52.1843	−1.75614	−0.878070	−	0.478532i	$-0.841169\pi$
$883$	−52.1843	−1.75614	−0.878070	+	0.478532i	$0.841169\pi$
$884$	−1.78897	−0.0601696
$885$	−37.1291	−1.24808
$886$	25.9539	0.871938
$887$	−14.9018	−0.500354	−0.250177	−	0.968200i	$-0.580489\pi$
$887$	−14.9018	−0.500354	−0.250177	+	0.968200i	$0.580489\pi$
$888$	8.12248	0.272573
$889$	4.85605	0.162867
$890$	−19.2853	−0.646445
$891$	−7.55774	−0.253194
$892$	16.4678	0.551382
$893$	24.4317	0.817575
$894$	−27.3465	−0.914604
$895$	28.9586	0.967978
$896$	4.14004	0.138309
$897$	−37.0099	−1.23572
$898$	29.0725	0.970161
$899$	−0.109898	−0.00366530
$900$	1.25615	0.0418717
$901$	1.13821	0.0379193
$902$	−7.91082	−0.263402
$903$	−17.6839	−0.588483
$904$	−1.84052	−0.0612146
$905$	24.0866	0.800667
$906$	1.29272	0.0429478
$907$	−49.9055	−1.65709	−0.828543	−	0.559926i	$-0.810830\pi$
$907$	−49.9055	−1.65709	−0.828543	+	0.559926i	$0.810830\pi$
$908$	−2.29445	−0.0761438
$909$	−1.61267	−0.0534890
$910$	−50.4606	−1.67275
$911$	−1.87290	−0.0620518	−0.0310259	−	0.999519i	$-0.509877\pi$
$911$	−1.87290	−0.0620518	−0.0310259	+	0.999519i	$0.509877\pi$
$912$	−7.45180	−0.246754
$913$	3.27378	0.108346
$914$	−0.918963	−0.0303966
$915$	36.8530	1.21832
$916$	2.55902	0.0845525
$917$	−27.2448	−0.899703
$918$	−0.314466	−0.0103789
$919$	10.3422	0.341156	0.170578	−	0.985344i	$-0.445436\pi$
$919$	10.3422	0.341156	0.170578	+	0.985344i	$0.445436\pi$
$920$	−7.02379	−0.231567
$921$	41.1291	1.35525
$922$	−25.9230	−0.853728
$923$	−31.8197	−1.04736
$924$	−7.40640	−0.243653
$925$	−1.64756	−0.0541715
$926$	−30.5937	−1.00537
$927$	−19.5929	−0.643515
$928$	0.0845158	0.00277437
$929$	26.8316	0.880316	0.440158	−	0.897920i	$-0.354922\pi$
$929$	26.8316	0.880316	0.440158	+	0.897920i	$0.354922\pi$
$930$	−7.21259	−0.236510
$931$	31.8912	1.04519
$932$	9.25024	0.303002
$933$	−24.6979	−0.808572
$934$	1.42500	0.0466275
$935$	0.607378	0.0198634
$936$	13.6081	0.444794
$937$	9.70369	0.317006	0.158503	−	0.987359i	$-0.449333\pi$
$937$	9.70369	0.317006	0.158503	+	0.987359i	$0.449333\pi$
$938$	34.4159	1.12372
$939$	−8.25455	−0.269377
$940$	−18.1858	−0.593155
$941$	−36.7138	−1.19684	−0.598419	−	0.801184i	$-0.704204\pi$
$941$	−36.7138	−1.19684	−0.598419	+	0.801184i	$0.704204\pi$
$942$	10.6752	0.347818
$943$	−31.4342	−1.02364
$944$	−6.69383	−0.217866
$945$	−8.86998	−0.288540
$946$	1.36120	0.0442565
$947$	−32.6468	−1.06088	−0.530440	−	0.847723i	$-0.677973\pi$
$947$	−32.6468	−1.06088	−0.530440	+	0.847723i	$0.677973\pi$
$948$	14.2028	0.461285
$949$	−4.35381	−0.141331
$950$	1.51152	0.0490402
$951$	−62.2925	−2.01997
$952$	−1.42257	−0.0461058
$953$	18.0463	0.584577	0.292289	−	0.956330i	$-0.405583\pi$
$953$	18.0463	0.584577	0.292289	+	0.956330i	$0.405583\pi$
$954$	−8.65797	−0.280312
$955$	19.2602	0.623246
$956$	−25.7318	−0.832226
$957$	−0.151196	−0.00488747
$958$	−34.1758	−1.10417
$959$	−19.5532	−0.631405
$960$	5.54677	0.179021
$961$	−29.3092	−0.945457
$962$	−17.8483	−0.575452
$963$	35.6059	1.14738
$964$	1.06429	0.0342786
$965$	6.10696	0.196590
$966$	−29.4299	−0.946891
$967$	22.1558	0.712483	0.356241	−	0.934394i	$-0.384058\pi$
$967$	22.1558	0.712483	0.356241	+	0.934394i	$0.384058\pi$
$968$	−10.4299	−0.335230
$969$	2.56053	0.0822561
$970$	−38.4558	−1.23474
$971$	24.4008	0.783058	0.391529	−	0.920166i	$-0.371946\pi$
$971$	24.4008	0.783058	0.391529	+	0.920166i	$0.371946\pi$
$972$	20.9705	0.672629
$973$	69.1421	2.21659
$974$	−19.6962	−0.631107
$975$	−5.92842	−0.189862
$976$	6.64404	0.212671
$977$	41.3608	1.32325	0.661624	−	0.749836i	$-0.269867\pi$
$977$	41.3608	1.32325	0.661624	+	0.749836i	$0.269867\pi$
$978$	−5.07245	−0.162199
$979$	6.21998	0.198791
$980$	−23.7383	−0.758292
$981$	21.6974	0.692745
$982$	−43.0249	−1.37298
$983$	8.38652	0.267489	0.133744	−	0.991016i	$-0.457300\pi$
$983$	8.38652	0.267489	0.133744	+	0.991016i	$0.457300\pi$
$984$	24.8240	0.791360
$985$	−6.39917	−0.203895
$986$	−0.0290407	−0.000924844 0
$987$	−76.1990	−2.42544
$988$	16.3745	0.520943
$989$	5.40884	0.171991
$990$	−4.62011	−0.146837
$991$	5.57407	0.177066	0.0885331	−	0.996073i	$-0.471782\pi$
$991$	5.57407	0.177066	0.0885331	+	0.996073i	$0.471782\pi$
$992$	−1.30032	−0.0412853
$993$	−6.79913	−0.215764
$994$	−25.3027	−0.802552
$995$	−55.9752	−1.77453
$996$	−10.2731	−0.325514
$997$	37.0654	1.17387	0.586937	−	0.809633i	$-0.300334\pi$
$997$	37.0654	1.17387	0.586937	+	0.809633i	$0.300334\pi$
$998$	−31.1367	−0.985616
$999$	−3.13738	−0.0992622

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.d.1.9	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.d.1.9	✓	52	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.36933 q^{3} +1.00000 q^{4} -2.34107 q^{5} -2.36933 q^{6} +4.14004 q^{7} +1.00000 q^{8} +2.61374 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.36933 q^{3} +1.00000 q^{4} -2.34107 q^{5} -2.36933 q^{6} +4.14004 q^{7} +1.00000 q^{8} +2.61374 q^{9} -2.34107 q^{10} +0.755051 q^{11} -2.36933 q^{12} +5.20636 q^{13} +4.14004 q^{14} +5.54677 q^{15} +1.00000 q^{16} -0.343613 q^{17} +2.61374 q^{18} +3.14510 q^{19} -2.34107 q^{20} -9.80914 q^{21} +0.755051 q^{22} +3.00025 q^{23} -2.36933 q^{24} +0.480595 q^{25} +5.20636 q^{26} +0.915175 q^{27} +4.14004 q^{28} +0.0845158 q^{29} +5.54677 q^{30} -1.30032 q^{31} +1.00000 q^{32} -1.78897 q^{33} -0.343613 q^{34} -9.69212 q^{35} +2.61374 q^{36} -3.42817 q^{37} +3.14510 q^{38} -12.3356 q^{39} -2.34107 q^{40} -10.4772 q^{41} -9.80914 q^{42} +1.80280 q^{43} +0.755051 q^{44} -6.11894 q^{45} +3.00025 q^{46} +7.76816 q^{47} -2.36933 q^{48} +10.1399 q^{49} +0.480595 q^{50} +0.814133 q^{51} +5.20636 q^{52} -3.31248 q^{53} +0.915175 q^{54} -1.76762 q^{55} +4.14004 q^{56} -7.45180 q^{57} +0.0845158 q^{58} -6.69383 q^{59} +5.54677 q^{60} +6.64404 q^{61} -1.30032 q^{62} +10.8210 q^{63} +1.00000 q^{64} -12.1884 q^{65} -1.78897 q^{66} +8.31293 q^{67} -0.343613 q^{68} -7.10859 q^{69} -9.69212 q^{70} -6.11170 q^{71} +2.61374 q^{72} -0.836250 q^{73} -3.42817 q^{74} -1.13869 q^{75} +3.14510 q^{76} +3.12594 q^{77} -12.3356 q^{78} -5.99442 q^{79} -2.34107 q^{80} -10.0096 q^{81} -10.4772 q^{82} +4.33584 q^{83} -9.80914 q^{84} +0.804420 q^{85} +1.80280 q^{86} -0.200246 q^{87} +0.755051 q^{88} +8.23783 q^{89} -6.11894 q^{90} +21.5545 q^{91} +3.00025 q^{92} +3.08090 q^{93} +7.76816 q^{94} -7.36290 q^{95} -2.36933 q^{96} +16.4266 q^{97} +10.1399 q^{98} +1.97351 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * q^99

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