LMFDB - Embedded newform 4027.2.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4027,2,Mod(1,4027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4027, 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("4027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4027 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4027.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:	$32.1557568940$
Analytic rank:	$0$
Dimension:	$174$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66961 q^{2} -0.492916 q^{3} +5.12680 q^{4} +2.37281 q^{5} +1.31589 q^{6} +1.32431 q^{7} -8.34733 q^{8} -2.75703 q^{9} +O(q^{10})$	\(q-2.66961 q^{2} -0.492916 q^{3} +5.12680 q^{4} +2.37281 q^{5} +1.31589 q^{6} +1.32431 q^{7} -8.34733 q^{8} -2.75703 q^{9} -6.33447 q^{10} +0.0220541 q^{11} -2.52708 q^{12} -4.40501 q^{13} -3.53539 q^{14} -1.16960 q^{15} +12.0305 q^{16} +1.88399 q^{17} +7.36020 q^{18} +2.05105 q^{19} +12.1649 q^{20} -0.652774 q^{21} -0.0588757 q^{22} +3.94541 q^{23} +4.11453 q^{24} +0.630226 q^{25} +11.7596 q^{26} +2.83773 q^{27} +6.78948 q^{28} -8.40013 q^{29} +3.12236 q^{30} -5.95042 q^{31} -15.4220 q^{32} -0.0108708 q^{33} -5.02952 q^{34} +3.14234 q^{35} -14.1348 q^{36} -6.74280 q^{37} -5.47550 q^{38} +2.17130 q^{39} -19.8066 q^{40} -1.19570 q^{41} +1.74265 q^{42} +9.27473 q^{43} +0.113067 q^{44} -6.54192 q^{45} -10.5327 q^{46} +3.38827 q^{47} -5.93002 q^{48} -5.24620 q^{49} -1.68246 q^{50} -0.928651 q^{51} -22.5836 q^{52} -8.44209 q^{53} -7.57564 q^{54} +0.0523301 q^{55} -11.0545 q^{56} -1.01100 q^{57} +22.4250 q^{58} +8.17842 q^{59} -5.99629 q^{60} +7.87505 q^{61} +15.8853 q^{62} -3.65117 q^{63} +17.1098 q^{64} -10.4523 q^{65} +0.0290208 q^{66} +11.0828 q^{67} +9.65887 q^{68} -1.94475 q^{69} -8.38881 q^{70} +12.4430 q^{71} +23.0139 q^{72} +8.53257 q^{73} +18.0006 q^{74} -0.310649 q^{75} +10.5153 q^{76} +0.0292065 q^{77} -5.79652 q^{78} +2.13340 q^{79} +28.5461 q^{80} +6.87234 q^{81} +3.19206 q^{82} -9.19652 q^{83} -3.34664 q^{84} +4.47036 q^{85} -24.7599 q^{86} +4.14056 q^{87} -0.184093 q^{88} +16.1600 q^{89} +17.4643 q^{90} -5.83360 q^{91} +20.2273 q^{92} +2.93306 q^{93} -9.04535 q^{94} +4.86675 q^{95} +7.60177 q^{96} -10.1958 q^{97} +14.0053 q^{98} -0.0608039 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9}+O(q^{10}) $ 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9} + 20 q^{10} + 35 q^{11} + 23 q^{12} + 91 q^{13} + 18 q^{14} + 16 q^{15} + 201 q^{16} + 148 q^{17} + 39 q^{18} + 36 q^{19} + 128 q^{20} + 57 q^{21} + 17 q^{22} + 96 q^{23} + 24 q^{24} + 226 q^{25} + 44 q^{26} + 62 q^{27} + 32 q^{28} + 122 q^{29} + 25 q^{30} + 23 q^{31} + 104 q^{32} + 91 q^{33} + 6 q^{34} + 80 q^{35} + 222 q^{36} + 71 q^{37} + 125 q^{38} + 16 q^{39} + 53 q^{40} + 97 q^{41} + 14 q^{42} + 38 q^{43} + 70 q^{44} + 185 q^{45} - 23 q^{46} + 110 q^{47} + 36 q^{48} + 210 q^{49} + 51 q^{50} + 33 q^{51} + 118 q^{52} + 214 q^{53} + 8 q^{54} + 37 q^{55} + 41 q^{56} + 76 q^{57} + 2 q^{58} + 66 q^{59} - 12 q^{60} + 114 q^{61} + 175 q^{62} + 62 q^{63} + 190 q^{64} + 128 q^{65} + 12 q^{66} - 6 q^{67} + 348 q^{68} + 115 q^{69} - 38 q^{70} + 54 q^{71} + 101 q^{72} + 107 q^{73} + 71 q^{74} - q^{75} + 31 q^{76} + 368 q^{77} - 14 q^{78} - 14 q^{79} + 205 q^{80} + 222 q^{81} + 26 q^{82} + 246 q^{83} + 41 q^{84} + 87 q^{85} + 33 q^{86} + 100 q^{87} - 6 q^{88} + 147 q^{89} + 50 q^{90} - 23 q^{91} + 189 q^{92} + 117 q^{93} + 23 q^{94} + 42 q^{95} + 38 q^{96} + 52 q^{97} + 148 q^{98} + 38 q^{99}+O(q^{100}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9 + 20 * q^10 + 35 * q^11 + 23 * q^12 + 91 * q^13 + 18 * q^14 + 16 * q^15 + 201 * q^16 + 148 * q^17 + 39 * q^18 + 36 * q^19 + 128 * q^20 + 57 * q^21 + 17 * q^22 + 96 * q^23 + 24 * q^24 + 226 * q^25 + 44 * q^26 + 62 * q^27 + 32 * q^28 + 122 * q^29 + 25 * q^30 + 23 * q^31 + 104 * q^32 + 91 * q^33 + 6 * q^34 + 80 * q^35 + 222 * q^36 + 71 * q^37 + 125 * q^38 + 16 * q^39 + 53 * q^40 + 97 * q^41 + 14 * q^42 + 38 * q^43 + 70 * q^44 + 185 * q^45 - 23 * q^46 + 110 * q^47 + 36 * q^48 + 210 * q^49 + 51 * q^50 + 33 * q^51 + 118 * q^52 + 214 * q^53 + 8 * q^54 + 37 * q^55 + 41 * q^56 + 76 * q^57 + 2 * q^58 + 66 * q^59 - 12 * q^60 + 114 * q^61 + 175 * q^62 + 62 * q^63 + 190 * q^64 + 128 * q^65 + 12 * q^66 - 6 * q^67 + 348 * q^68 + 115 * q^69 - 38 * q^70 + 54 * q^71 + 101 * q^72 + 107 * q^73 + 71 * q^74 - q^75 + 31 * q^76 + 368 * q^77 - 14 * q^78 - 14 * q^79 + 205 * q^80 + 222 * q^81 + 26 * q^82 + 246 * q^83 + 41 * q^84 + 87 * q^85 + 33 * q^86 + 100 * q^87 - 6 * q^88 + 147 * q^89 + 50 * q^90 - 23 * q^91 + 189 * q^92 + 117 * q^93 + 23 * q^94 + 42 * q^95 + 38 * q^96 + 52 * q^97 + 148 * q^98 + 38 * 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 $

$2$	−2.66961	−1.88770	−0.943849	−	0.330378i	$-0.892824\pi$
$2$	−2.66961	−1.88770	−0.943849	+	0.330378i	$0.892824\pi$
$3$	−0.492916	−0.284585	−0.142293	−	0.989825i	$-0.545447\pi$
$3$	−0.492916	−0.284585	−0.142293	+	0.989825i	$0.545447\pi$
$4$	5.12680	2.56340
$5$	2.37281	1.06115	0.530576	−	0.847637i	$-0.321976\pi$
$5$	2.37281	1.06115	0.530576	+	0.847637i	$0.321976\pi$
$6$	1.31589	0.537211
$7$	1.32431	0.500543	0.250271	−	0.968176i	$-0.419480\pi$
$7$	1.32431	0.500543	0.250271	+	0.968176i	$0.419480\pi$
$8$	−8.34733	−2.95123
$9$	−2.75703	−0.919011
$10$	−6.33447	−2.00314
$11$	0.0220541	0.00664956	0.00332478	−	0.999994i	$-0.498942\pi$
$11$	0.0220541	0.00664956	0.00332478	+	0.999994i	$0.498942\pi$
$12$	−2.52708	−0.729506
$13$	−4.40501	−1.22173	−0.610865	−	0.791735i	$-0.709178\pi$
$13$	−4.40501	−1.22173	−0.610865	+	0.791735i	$0.709178\pi$
$14$	−3.53539	−0.944873
$15$	−1.16960	−0.301988
$16$	12.0305	3.00762
$17$	1.88399	0.456936	0.228468	−	0.973551i	$-0.426628\pi$
$17$	1.88399	0.456936	0.228468	+	0.973551i	$0.426628\pi$
$18$	7.36020	1.73482
$19$	2.05105	0.470543	0.235271	−	0.971930i	$-0.424402\pi$
$19$	2.05105	0.470543	0.235271	+	0.971930i	$0.424402\pi$
$20$	12.1649	2.72016
$21$	−0.652774	−0.142447
$22$	−0.0588757	−0.0125524
$23$	3.94541	0.822674	0.411337	−	0.911483i	$-0.365062\pi$
$23$	3.94541	0.822674	0.411337	+	0.911483i	$0.365062\pi$
$24$	4.11453	0.839876
$25$	0.630226	0.126045
$26$	11.7596	2.30626
$27$	2.83773	0.546122
$28$	6.78948	1.28309
$29$	−8.40013	−1.55986	−0.779932	−	0.625864i	$-0.784747\pi$
$29$	−8.40013	−1.55986	−0.779932	+	0.625864i	$0.784747\pi$
$30$	3.12236	0.570063
$31$	−5.95042	−1.06873	−0.534364	−	0.845255i	$-0.679449\pi$
$31$	−5.95042	−1.06873	−0.534364	+	0.845255i	$0.679449\pi$
$32$	−15.4220	−2.72626
$33$	−0.0108708	−0.00189237
$34$	−5.02952	−0.862556
$35$	3.14234	0.531152
$36$	−14.1348	−2.35579
$37$	−6.74280	−1.10851	−0.554255	−	0.832347i	$-0.686997\pi$
$37$	−6.74280	−1.10851	−0.554255	+	0.832347i	$0.686997\pi$
$38$	−5.47550	−0.888243
$39$	2.17130	0.347686
$40$	−19.8066	−3.13170
$41$	−1.19570	−0.186738	−0.0933688	−	0.995632i	$-0.529764\pi$
$41$	−1.19570	−0.186738	−0.0933688	+	0.995632i	$0.529764\pi$
$42$	1.74265	0.268897
$43$	9.27473	1.41438	0.707192	−	0.707022i	$-0.249962\pi$
$43$	9.27473	1.41438	0.707192	+	0.707022i	$0.249962\pi$
$44$	0.113067	0.0170455
$45$	−6.54192	−0.975211
$46$	−10.5327	−1.55296
$47$	3.38827	0.494230	0.247115	−	0.968986i	$-0.420517\pi$
$47$	3.38827	0.494230	0.247115	+	0.968986i	$0.420517\pi$
$48$	−5.93002	−0.855925
$49$	−5.24620	−0.749457
$50$	−1.68246	−0.237935
$51$	−0.928651	−0.130037
$52$	−22.5836	−3.13178
$53$	−8.44209	−1.15961	−0.579805	−	0.814755i	$-0.696871\pi$
$53$	−8.44209	−1.15961	−0.579805	+	0.814755i	$0.696871\pi$
$54$	−7.57564	−1.03091
$55$	0.0523301	0.00705620
$56$	−11.0545	−1.47722
$57$	−1.01100	−0.133910
$58$	22.4250	2.94455
$59$	8.17842	1.06474	0.532370	−	0.846512i	$-0.321302\pi$
$59$	8.17842	1.06474	0.532370	+	0.846512i	$0.321302\pi$
$60$	−5.99629	−0.774117
$61$	7.87505	1.00830	0.504148	−	0.863617i	$-0.331806\pi$
$61$	7.87505	1.00830	0.504148	+	0.863617i	$0.331806\pi$
$62$	15.8853	2.01743
$63$	−3.65117	−0.460004
$64$	17.1098	2.13872
$65$	−10.4523	−1.29644
$66$	0.0290208	0.00357221
$67$	11.0828	1.35398	0.676992	−	0.735990i	$-0.263283\pi$
$67$	11.0828	1.35398	0.676992	+	0.735990i	$0.263283\pi$
$68$	9.65887	1.17131
$69$	−1.94475	−0.234121
$70$	−8.38881	−1.00265
$71$	12.4430	1.47671	0.738355	−	0.674413i	$-0.235603\pi$
$71$	12.4430	1.47671	0.738355	+	0.674413i	$0.235603\pi$
$72$	23.0139	2.71221
$73$	8.53257	0.998661	0.499331	−	0.866412i	$-0.333579\pi$
$73$	8.53257	0.998661	0.499331	+	0.866412i	$0.333579\pi$
$74$	18.0006	2.09253
$75$	−0.310649	−0.0358706
$76$	10.5153	1.20619
$77$	0.0292065	0.00332839
$78$	−5.79652	−0.656326
$79$	2.13340	0.240027	0.120013	−	0.992772i	$-0.461706\pi$
$79$	2.13340	0.240027	0.120013	+	0.992772i	$0.461706\pi$
$80$	28.5461	3.19155
$81$	6.87234	0.763593
$82$	3.19206	0.352504
$83$	−9.19652	−1.00945	−0.504725	−	0.863280i	$-0.668406\pi$
$83$	−9.19652	−1.00945	−0.504725	+	0.863280i	$0.668406\pi$
$84$	−3.34664	−0.365149
$85$	4.47036	0.484879
$86$	−24.7599	−2.66993
$87$	4.14056	0.443914
$88$	−0.184093	−0.0196244
$89$	16.1600	1.71296	0.856479	−	0.516182i	$-0.172647\pi$
$89$	16.1600	1.71296	0.856479	+	0.516182i	$0.172647\pi$
$90$	17.4643	1.84090
$91$	−5.83360	−0.611528
$92$	20.2273	2.10884
$93$	2.93306	0.304144
$94$	−9.04535	−0.932956
$95$	4.86675	0.499318
$96$	7.60177	0.775852
$97$	−10.1958	−1.03522	−0.517612	−	0.855616i	$-0.673179\pi$
$97$	−10.1958	−1.03522	−0.517612	+	0.855616i	$0.673179\pi$
$98$	14.0053	1.41475
$99$	−0.0608039	−0.00611102
$100$	3.23104	0.323104
$101$	9.17371	0.912818	0.456409	−	0.889770i	$-0.349135\pi$
$101$	9.17371	0.912818	0.456409	+	0.889770i	$0.349135\pi$
$102$	2.47913	0.245471
$103$	−10.2688	−1.01182	−0.505908	−	0.862588i	$-0.668842\pi$
$103$	−10.2688	−1.01182	−0.505908	+	0.862588i	$0.668842\pi$
$104$	36.7701	3.60560
$105$	−1.54891	−0.151158
$106$	22.5371	2.18899
$107$	14.2555	1.37813	0.689065	−	0.724700i	$-0.258022\pi$
$107$	14.2555	1.37813	0.689065	+	0.724700i	$0.258022\pi$
$108$	14.5485	1.39993
$109$	10.0984	0.967255	0.483627	−	0.875274i	$-0.339319\pi$
$109$	10.0984	0.967255	0.483627	+	0.875274i	$0.339319\pi$
$110$	−0.139701	−0.0133200
$111$	3.32363	0.315465
$112$	15.9321	1.50544
$113$	−0.296080	−0.0278528	−0.0139264	−	0.999903i	$-0.504433\pi$
$113$	−0.296080	−0.0278528	−0.0139264	+	0.999903i	$0.504433\pi$
$114$	2.69896	0.252781
$115$	9.36170	0.872983
$116$	−43.0658	−3.99856
$117$	12.1448	1.12278
$118$	−21.8332	−2.00991
$119$	2.49500	0.228716
$120$	9.76301	0.891237
$121$	−10.9995	−0.999956
$122$	−21.0233	−1.90336
$123$	0.589382	0.0531428
$124$	−30.5066	−2.73958
$125$	−10.3686	−0.927400
$126$	9.74719	0.868349
$127$	7.28789	0.646695	0.323348	−	0.946280i	$-0.395192\pi$
$127$	7.28789	0.646695	0.323348	+	0.946280i	$0.395192\pi$
$128$	−14.8323	−1.31100
$129$	−4.57166	−0.402513
$130$	27.9034	2.44729
$131$	20.0345	1.75042	0.875212	−	0.483739i	$-0.160722\pi$
$131$	20.0345	1.75042	0.875212	+	0.483739i	$0.160722\pi$
$132$	−0.0557325	−0.00485089
$133$	2.71623	0.235527
$134$	−29.5868	−2.55591
$135$	6.73340	0.579519
$136$	−15.7263	−1.34852
$137$	20.2975	1.73413	0.867066	−	0.498193i	$-0.166003\pi$
$137$	20.2975	1.73413	0.867066	+	0.498193i	$0.166003\pi$
$138$	5.19173	0.441949
$139$	−13.9576	−1.18387	−0.591933	−	0.805987i	$-0.701635\pi$
$139$	−13.9576	−1.18387	−0.591933	+	0.805987i	$0.701635\pi$
$140$	16.1101	1.36156
$141$	−1.67013	−0.140651
$142$	−33.2178	−2.78758
$143$	−0.0971485	−0.00812396
$144$	−33.1685	−2.76404
$145$	−19.9319	−1.65525
$146$	−22.7786	−1.88517
$147$	2.58594	0.213284
$148$	−34.5690	−2.84155
$149$	−15.9273	−1.30482	−0.652409	−	0.757867i	$-0.726242\pi$
$149$	−15.9273	−1.30482	−0.652409	+	0.757867i	$0.726242\pi$
$150$	0.829310	0.0677128
$151$	−10.0185	−0.815296	−0.407648	−	0.913139i	$-0.633651\pi$
$151$	−10.0185	−0.815296	−0.407648	+	0.913139i	$0.633651\pi$
$152$	−17.1208	−1.38868
$153$	−5.19424	−0.419929
$154$	−0.0779698	−0.00628299
$155$	−14.1192	−1.13408
$156$	11.1318	0.891259
$157$	−2.64432	−0.211040	−0.105520	−	0.994417i	$-0.533651\pi$
$157$	−2.64432	−0.211040	−0.105520	+	0.994417i	$0.533651\pi$
$158$	−5.69535	−0.453098
$159$	4.16124	0.330008
$160$	−36.5935	−2.89297
$161$	5.22495	0.411783
$162$	−18.3464	−1.44143
$163$	20.5807	1.61201	0.806003	−	0.591911i	$-0.201626\pi$
$163$	20.5807	1.61201	0.806003	+	0.591911i	$0.201626\pi$
$164$	−6.13014	−0.478683
$165$	−0.0257944	−0.00200809
$166$	24.5511	1.90554
$167$	24.7481	1.91507	0.957534	−	0.288320i	$-0.0930965\pi$
$167$	24.7481	1.91507	0.957534	+	0.288320i	$0.0930965\pi$
$168$	5.44892	0.420394
$169$	6.40411	0.492624
$170$	−11.9341	−0.915304
$171$	−5.65481	−0.432434
$172$	47.5497	3.62563
$173$	18.9480	1.44059	0.720294	−	0.693668i	$-0.244007\pi$
$173$	18.9480	1.44059	0.720294	+	0.693668i	$0.244007\pi$
$174$	−11.0537	−0.837976
$175$	0.834615	0.0630910
$176$	0.265322	0.0199994
$177$	−4.03127	−0.303009
$178$	−43.1409	−3.23355
$179$	−23.0060	−1.71955	−0.859775	−	0.510672i	$-0.829397\pi$
$179$	−23.0060	−1.71955	−0.859775	+	0.510672i	$0.829397\pi$
$180$	−33.5391	−2.49986
$181$	15.1869	1.12884	0.564418	−	0.825489i	$-0.309101\pi$
$181$	15.1869	1.12884	0.564418	+	0.825489i	$0.309101\pi$
$182$	15.5734	1.15438
$183$	−3.88174	−0.286946
$184$	−32.9336	−2.42790
$185$	−15.9994	−1.17630
$186$	−7.83011	−0.574132
$187$	0.0415498	0.00303842
$188$	17.3710	1.26691
$189$	3.75804	0.273357
$190$	−12.9923	−0.942561
$191$	12.0887	0.874709	0.437354	−	0.899289i	$-0.355916\pi$
$191$	12.0887	0.874709	0.437354	+	0.899289i	$0.355916\pi$
$192$	−8.43368	−0.608649
$193$	−12.5731	−0.905033	−0.452517	−	0.891756i	$-0.649474\pi$
$193$	−12.5731	−0.905033	−0.452517	+	0.891756i	$0.649474\pi$
$194$	27.2187	1.95419
$195$	5.15208	0.368948
$196$	−26.8962	−1.92116
$197$	22.3065	1.58927	0.794635	−	0.607088i	$-0.207662\pi$
$197$	22.3065	1.58927	0.794635	+	0.607088i	$0.207662\pi$
$198$	0.162322	0.0115358
$199$	−6.79573	−0.481737	−0.240868	−	0.970558i	$-0.577432\pi$
$199$	−6.79573	−0.481737	−0.240868	+	0.970558i	$0.577432\pi$
$200$	−5.26071	−0.371988
$201$	−5.46291	−0.385324
$202$	−24.4902	−1.72312
$203$	−11.1244	−0.780779
$204$	−4.76101	−0.333337
$205$	−2.83718	−0.198157
$206$	27.4137	1.91000
$207$	−10.8776	−0.756047
$208$	−52.9945	−3.67450
$209$	0.0452340	0.00312890
$210$	4.13498	0.285341
$211$	−4.85204	−0.334028	−0.167014	−	0.985954i	$-0.553413\pi$
$211$	−4.85204	−0.334028	−0.167014	+	0.985954i	$0.553413\pi$
$212$	−43.2809	−2.97255
$213$	−6.13334	−0.420250
$214$	−38.0565	−2.60149
$215$	22.0072	1.50088
$216$	−23.6875	−1.61173
$217$	−7.88021	−0.534944
$218$	−26.9589	−1.82588
$219$	−4.20584	−0.284204
$220$	0.268286	0.0180879
$221$	−8.29901	−0.558252
$222$	−8.87280	−0.595503
$223$	10.7977	0.723070	0.361535	−	0.932359i	$-0.382253\pi$
$223$	10.7977	0.723070	0.361535	+	0.932359i	$0.382253\pi$
$224$	−20.4236	−1.36461
$225$	−1.73755	−0.115837
$226$	0.790416	0.0525777
$227$	−19.5689	−1.29884	−0.649418	−	0.760432i	$-0.724987\pi$
$227$	−19.5689	−1.29884	−0.649418	+	0.760432i	$0.724987\pi$
$228$	−5.18317	−0.343264
$229$	0.850754	0.0562194	0.0281097	−	0.999605i	$-0.491051\pi$
$229$	0.850754	0.0562194	0.0281097	+	0.999605i	$0.491051\pi$
$230$	−24.9921	−1.64793
$231$	−0.0143963	−0.000947210 0
$232$	70.1187	4.60352
$233$	25.9394	1.69935	0.849673	−	0.527309i	$-0.176799\pi$
$233$	25.9394	1.69935	0.849673	+	0.527309i	$0.176799\pi$
$234$	−32.4217	−2.11948
$235$	8.03972	0.524453
$236$	41.9291	2.72935
$237$	−1.05159	−0.0683081
$238$	−6.66066	−0.431746
$239$	5.87878	0.380267	0.190133	−	0.981758i	$-0.439108\pi$
$239$	5.87878	0.380267	0.190133	+	0.981758i	$0.439108\pi$
$240$	−14.0708	−0.908268
$241$	14.2429	0.917469	0.458734	−	0.888573i	$-0.348303\pi$
$241$	14.2429	0.917469	0.458734	+	0.888573i	$0.348303\pi$
$242$	29.3644	1.88761
$243$	−11.9007	−0.763429
$244$	40.3738	2.58467
$245$	−12.4482	−0.795288
$246$	−1.57342	−0.100317
$247$	−9.03489	−0.574876
$248$	49.6702	3.15406
$249$	4.53311	0.287274
$250$	27.6802	1.75065
$251$	−10.9668	−0.692219	−0.346110	−	0.938194i	$-0.612497\pi$
$251$	−10.9668	−0.692219	−0.346110	+	0.938194i	$0.612497\pi$
$252$	−18.7188	−1.17918
$253$	0.0870123	0.00547042
$254$	−19.4558	−1.22077
$255$	−2.20351	−0.137989
$256$	5.37689	0.336056
$257$	21.3539	1.33202	0.666008	−	0.745944i	$-0.268002\pi$
$257$	21.3539	1.33202	0.666008	+	0.745944i	$0.268002\pi$
$258$	12.2045	0.759822
$259$	−8.92957	−0.554856
$260$	−53.5866	−3.32330
$261$	23.1594	1.43353
$262$	−53.4843	−3.30427
$263$	9.63154	0.593906	0.296953	−	0.954892i	$-0.404029\pi$
$263$	9.63154	0.593906	0.296953	+	0.954892i	$0.404029\pi$
$264$	0.0907423	0.00558480
$265$	−20.0315	−1.23052
$266$	−7.25126	−0.444603
$267$	−7.96553	−0.487482
$268$	56.8195	3.47081
$269$	−2.12980	−0.129856	−0.0649282	−	0.997890i	$-0.520682\pi$
$269$	−2.12980	−0.129856	−0.0649282	+	0.997890i	$0.520682\pi$
$270$	−17.9755	−1.09396
$271$	1.52317	0.0925262	0.0462631	−	0.998929i	$-0.485269\pi$
$271$	1.52317	0.0925262	0.0462631	+	0.998929i	$0.485269\pi$
$272$	22.6654	1.37429
$273$	2.87548	0.174032
$274$	−54.1864	−3.27352
$275$	0.0138991	0.000838145 0
$276$	−9.97037	−0.600146
$277$	−11.6260	−0.698536	−0.349268	−	0.937023i	$-0.613570\pi$
$277$	−11.6260	−0.698536	−0.349268	+	0.937023i	$0.613570\pi$
$278$	37.2613	2.23478
$279$	16.4055	0.982172
$280$	−26.2301	−1.56755
$281$	−24.5100	−1.46215	−0.731073	−	0.682300i	$-0.760980\pi$
$281$	−24.5100	−1.46215	−0.731073	+	0.682300i	$0.760980\pi$
$282$	4.45860	0.265506
$283$	−6.50918	−0.386931	−0.193465	−	0.981107i	$-0.561973\pi$
$283$	−6.50918	−0.386931	−0.193465	+	0.981107i	$0.561973\pi$
$284$	63.7927	3.78540
$285$	−2.39890	−0.142099
$286$	0.259348	0.0153356
$287$	−1.58348	−0.0934701
$288$	42.5191	2.50546
$289$	−13.4506	−0.791210
$290$	53.2104	3.12462
$291$	5.02566	0.294609
$292$	43.7448	2.55997
$293$	11.4226	0.667314	0.333657	−	0.942695i	$-0.391717\pi$
$293$	11.4226	0.667314	0.333657	+	0.942695i	$0.391717\pi$
$294$	−6.90343	−0.402616
$295$	19.4058	1.12985
$296$	56.2844	3.27146
$297$	0.0625836	0.00363147
$298$	42.5197	2.46310
$299$	−17.3796	−1.00509
$300$	−1.59263	−0.0919507
$301$	12.2826	0.707959
$302$	26.7455	1.53903
$303$	−4.52187	−0.259775
$304$	24.6751	1.41522
$305$	18.6860	1.06996
$306$	13.8666	0.792699
$307$	−3.66332	−0.209077	−0.104538	−	0.994521i	$-0.533336\pi$
$307$	−3.66332	−0.209077	−0.104538	+	0.994521i	$0.533336\pi$
$308$	0.149736	0.00853199
$309$	5.06166	0.287948
$310$	37.6928	2.14081
$311$	−18.6634	−1.05830	−0.529152	−	0.848527i	$-0.677490\pi$
$311$	−18.6634	−1.05830	−0.529152	+	0.848527i	$0.677490\pi$
$312$	−18.1246	−1.02610
$313$	21.5401	1.21752	0.608759	−	0.793355i	$-0.291667\pi$
$313$	21.5401	1.21752	0.608759	+	0.793355i	$0.291667\pi$
$314$	7.05930	0.398380
$315$	−8.66353	−0.488135
$316$	10.9375	0.615285
$317$	17.0387	0.956991	0.478495	−	0.878090i	$-0.341182\pi$
$317$	17.0387	0.956991	0.478495	+	0.878090i	$0.341182\pi$
$318$	−11.1089	−0.622955
$319$	−0.185257	−0.0103724
$320$	40.5982	2.26951
$321$	−7.02676	−0.392195
$322$	−13.9486	−0.777323
$323$	3.86417	0.215008
$324$	35.2331	1.95739
$325$	−2.77615	−0.153993
$326$	−54.9424	−3.04298
$327$	−4.97768	−0.275266
$328$	9.98094	0.551105
$329$	4.48712	0.247383
$330$	0.0688608	0.00379066
$331$	−27.5665	−1.51519	−0.757595	−	0.652725i	$-0.773626\pi$
$331$	−27.5665	−1.51519	−0.757595	+	0.652725i	$0.773626\pi$
$332$	−47.1488	−2.58762
$333$	18.5901	1.01873
$334$	−66.0678	−3.61507
$335$	26.2975	1.43678
$336$	−7.85320	−0.428427
$337$	8.06440	0.439296	0.219648	−	0.975579i	$-0.429509\pi$
$337$	8.06440	0.439296	0.219648	+	0.975579i	$0.429509\pi$
$338$	−17.0965	−0.929925
$339$	0.145942	0.00792650
$340$	22.9187	1.24294
$341$	−0.131231	−0.00710656
$342$	15.0961	0.816305
$343$	−16.2178	−0.875678
$344$	−77.4193	−4.17417
$345$	−4.61453	−0.248438
$346$	−50.5837	−2.71940
$347$	20.8078	1.11702	0.558511	−	0.829497i	$-0.311373\pi$
$347$	20.8078	1.11702	0.558511	+	0.829497i	$0.311373\pi$
$348$	21.2278	1.13793
$349$	1.36090	0.0728471	0.0364236	−	0.999336i	$-0.488403\pi$
$349$	1.36090	0.0728471	0.0364236	+	0.999336i	$0.488403\pi$
$350$	−2.22810	−0.119097
$351$	−12.5002	−0.667214
$352$	−0.340119	−0.0181284
$353$	4.77241	0.254010	0.127005	−	0.991902i	$-0.459464\pi$
$353$	4.77241	0.254010	0.127005	+	0.991902i	$0.459464\pi$
$354$	10.7619	0.571989
$355$	29.5248	1.56701
$356$	82.8492	4.39100
$357$	−1.22982	−0.0650891
$358$	61.4170	3.24599
$359$	−27.8749	−1.47118	−0.735591	−	0.677426i	$-0.763096\pi$
$359$	−27.8749	−1.47118	−0.735591	+	0.677426i	$0.763096\pi$
$360$	54.6076	2.87807
$361$	−14.7932	−0.778589
$362$	−40.5431	−2.13090
$363$	5.42184	0.284573
$364$	−29.9077	−1.56759
$365$	20.2462	1.05973
$366$	10.3627	0.541668
$367$	−7.67869	−0.400825	−0.200412	−	0.979712i	$-0.564228\pi$
$367$	−7.67869	−0.400825	−0.200412	+	0.979712i	$0.564228\pi$
$368$	47.4652	2.47429
$369$	3.29660	0.171614
$370$	42.7121	2.22049
$371$	−11.1800	−0.580435
$372$	15.0372	0.779643
$373$	1.29300	0.0669492	0.0334746	−	0.999440i	$-0.489343\pi$
$373$	1.29300	0.0669492	0.0334746	+	0.999440i	$0.489343\pi$
$374$	−0.110922	−0.00573562
$375$	5.11087	0.263924
$376$	−28.2830	−1.45859
$377$	37.0026	1.90573
$378$	−10.0325	−0.516016
$379$	−16.1562	−0.829889	−0.414944	−	0.909847i	$-0.636199\pi$
$379$	−16.1562	−0.829889	−0.414944	+	0.909847i	$0.636199\pi$
$380$	24.9509	1.27995
$381$	−3.59232	−0.184040
$382$	−32.2721	−1.65119
$383$	6.91868	0.353528	0.176764	−	0.984253i	$-0.443437\pi$
$383$	6.91868	0.353528	0.176764	+	0.984253i	$0.443437\pi$
$384$	7.31108	0.373092
$385$	0.0693014	0.00353193
$386$	33.5653	1.70843
$387$	−25.5708	−1.29983
$388$	−52.2717	−2.65369
$389$	28.0120	1.42027	0.710133	−	0.704067i	$-0.248635\pi$
$389$	28.0120	1.42027	0.710133	+	0.704067i	$0.248635\pi$
$390$	−13.7540	−0.696463
$391$	7.43312	0.375909
$392$	43.7918	2.21182
$393$	−9.87534	−0.498145
$394$	−59.5495	−3.00006
$395$	5.06216	0.254705
$396$	−0.311729	−0.0156650
$397$	8.03898	0.403465	0.201732	−	0.979441i	$-0.435343\pi$
$397$	8.03898	0.403465	0.201732	+	0.979441i	$0.435343\pi$
$398$	18.1419	0.909373
$399$	−1.33887	−0.0670275
$400$	7.58193	0.379097
$401$	−27.1278	−1.35470	−0.677349	−	0.735662i	$-0.736871\pi$
$401$	−27.1278	−1.35470	−0.677349	+	0.735662i	$0.736871\pi$
$402$	14.5838	0.727375
$403$	26.2117	1.30570
$404$	47.0318	2.33992
$405$	16.3067	0.810289
$406$	29.6977	1.47387
$407$	−0.148706	−0.00737110
$408$	7.75176	0.383769
$409$	−38.9578	−1.92634	−0.963169	−	0.268896i	$-0.913341\pi$
$409$	−38.9578	−1.92634	−0.963169	+	0.268896i	$0.913341\pi$
$410$	7.57415	0.374061
$411$	−10.0050	−0.493508
$412$	−52.6461	−2.59369
$413$	10.8308	0.532947
$414$	29.0390	1.42719
$415$	−21.8216	−1.07118
$416$	67.9342	3.33075
$417$	6.87992	0.336911
$418$	−0.120757	−0.00590642
$419$	−0.585367	−0.0285970	−0.0142985	−	0.999898i	$-0.504552\pi$
$419$	−0.585367	−0.0285970	−0.0142985	+	0.999898i	$0.504552\pi$
$420$	−7.94095	−0.387479
$421$	13.8168	0.673389	0.336695	−	0.941614i	$-0.390691\pi$
$421$	13.8168	0.673389	0.336695	+	0.941614i	$0.390691\pi$
$422$	12.9531	0.630545
$423$	−9.34157	−0.454203
$424$	70.4690	3.42228
$425$	1.18734	0.0575946
$426$	16.3736	0.793304
$427$	10.4290	0.504695
$428$	73.0850	3.53270
$429$	0.0478860	0.00231196
$430$	−58.7505	−2.83320
$431$	−6.20793	−0.299026	−0.149513	−	0.988760i	$-0.547771\pi$
$431$	−6.20793	−0.299026	−0.149513	+	0.988760i	$0.547771\pi$
$432$	34.1394	1.64253
$433$	−31.4001	−1.50899	−0.754495	−	0.656306i	$-0.772118\pi$
$433$	−31.4001	−1.50899	−0.754495	+	0.656306i	$0.772118\pi$
$434$	21.0371	1.00981
$435$	9.82476	0.471061
$436$	51.7727	2.47946
$437$	8.09222	0.387103
$438$	11.2279	0.536492
$439$	23.4294	1.11822	0.559111	−	0.829093i	$-0.311142\pi$
$439$	23.4294	1.11822	0.559111	+	0.829093i	$0.311142\pi$
$440$	−0.436817	−0.0208244
$441$	14.4639	0.688759
$442$	22.1551	1.05381
$443$	−18.1083	−0.860349	−0.430175	−	0.902746i	$-0.641548\pi$
$443$	−18.1083	−0.860349	−0.430175	+	0.902746i	$0.641548\pi$
$444$	17.0396	0.808664
$445$	38.3446	1.81771
$446$	−28.8257	−1.36494
$447$	7.85084	0.371332
$448$	22.6587	1.07052
$449$	−5.18463	−0.244678	−0.122339	−	0.992488i	$-0.539039\pi$
$449$	−5.18463	−0.244678	−0.122339	+	0.992488i	$0.539039\pi$
$450$	4.63859	0.218665
$451$	−0.0263702	−0.00124172
$452$	−1.51794	−0.0713980
$453$	4.93829	0.232021
$454$	52.2414	2.45181
$455$	−13.8420	−0.648925
$456$	8.43911	0.395198
$457$	33.6054	1.57200	0.785998	−	0.618229i	$-0.212150\pi$
$457$	33.6054	1.57200	0.785998	+	0.618229i	$0.212150\pi$
$458$	−2.27118	−0.106125
$459$	5.34628	0.249543
$460$	47.9956	2.23781
$461$	10.0720	0.469100	0.234550	−	0.972104i	$-0.424638\pi$
$461$	10.0720	0.469100	0.234550	+	0.972104i	$0.424638\pi$
$462$	0.0384326	0.00178805
$463$	−2.62919	−0.122189	−0.0610945	−	0.998132i	$-0.519459\pi$
$463$	−2.62919	−0.122189	−0.0610945	+	0.998132i	$0.519459\pi$
$464$	−101.058	−4.69149
$465$	6.95959	0.322743
$466$	−69.2480	−3.20785
$467$	−21.1690	−0.979584	−0.489792	−	0.871839i	$-0.662927\pi$
$467$	−21.1690	−0.979584	−0.489792	+	0.871839i	$0.662927\pi$
$468$	62.2638	2.87814
$469$	14.6771	0.677727
$470$	−21.4629	−0.990009
$471$	1.30343	0.0600589
$472$	−68.2680	−3.14229
$473$	0.204546	0.00940502
$474$	2.80733	0.128945
$475$	1.29262	0.0593097
$476$	12.7913	0.586290
$477$	23.2751	1.06570
$478$	−15.6940	−0.717829
$479$	22.3250	1.02005	0.510027	−	0.860159i	$-0.329635\pi$
$479$	22.3250	1.02005	0.510027	+	0.860159i	$0.329635\pi$
$480$	18.0375	0.823298
$481$	29.7021	1.35430
$482$	−38.0231	−1.73190
$483$	−2.57546	−0.117187
$484$	−56.3923	−2.56329
$485$	−24.1926	−1.09853
$486$	31.7702	1.44112
$487$	−12.3971	−0.561765	−0.280882	−	0.959742i	$-0.590627\pi$
$487$	−12.3971	−0.561765	−0.280882	+	0.959742i	$0.590627\pi$
$488$	−65.7357	−2.97571
$489$	−10.1446	−0.458753
$490$	33.2319	1.50126
$491$	21.6477	0.976948	0.488474	−	0.872578i	$-0.337554\pi$
$491$	21.6477	0.976948	0.488474	+	0.872578i	$0.337554\pi$
$492$	3.02164	0.136226
$493$	−15.8258	−0.712758
$494$	24.1196	1.08519
$495$	−0.144276	−0.00648472
$496$	−71.5865	−3.21433
$497$	16.4784	0.739156
$498$	−12.1016	−0.542287
$499$	36.3551	1.62748	0.813739	−	0.581230i	$-0.197428\pi$
$499$	36.3551	1.62748	0.813739	+	0.581230i	$0.197428\pi$
$500$	−53.1580	−2.37730
$501$	−12.1988	−0.545000
$502$	29.2771	1.30670
$503$	5.55810	0.247823	0.123912	−	0.992293i	$-0.460456\pi$
$503$	5.55810	0.247823	0.123912	+	0.992293i	$0.460456\pi$
$504$	30.4775	1.35758
$505$	21.7675	0.968640
$506$	−0.232289	−0.0103265
$507$	−3.15669	−0.140194
$508$	37.3636	1.65774
$509$	4.79382	0.212483	0.106241	−	0.994340i	$-0.466118\pi$
$509$	4.79382	0.212483	0.106241	+	0.994340i	$0.466118\pi$
$510$	5.88251	0.260482
$511$	11.2998	0.499873
$512$	15.3104	0.676632
$513$	5.82033	0.256974
$514$	−57.0064	−2.51444
$515$	−24.3659	−1.07369
$516$	−23.4380	−1.03180
$517$	0.0747252	0.00328641
$518$	23.8384	1.04740
$519$	−9.33977	−0.409970
$520$	87.2484	3.82610
$521$	7.89807	0.346021	0.173010	−	0.984920i	$-0.444651\pi$
$521$	7.89807	0.346021	0.173010	+	0.984920i	$0.444651\pi$
$522$	−61.8266	−2.70608
$523$	−7.69827	−0.336622	−0.168311	−	0.985734i	$-0.553831\pi$
$523$	−7.69827	−0.336622	−0.168311	+	0.985734i	$0.553831\pi$
$524$	102.713	4.48704
$525$	−0.411395	−0.0179548
$526$	−25.7124	−1.12112
$527$	−11.2106	−0.488340
$528$	−0.130781	−0.00569152
$529$	−7.43377	−0.323207
$530$	53.4762	2.32286
$531$	−22.5482	−0.978507
$532$	13.9256	0.603750
$533$	5.26709	0.228143
$534$	21.2648	0.920219
$535$	33.8255	1.46241
$536$	−92.5122	−3.99592
$537$	11.3400	0.489359
$538$	5.68573	0.245129
$539$	−0.115700	−0.00498356
$540$	34.5208	1.48554
$541$	−9.72119	−0.417947	−0.208973	−	0.977921i	$-0.567012\pi$
$541$	−9.72119	−0.417947	−0.208973	+	0.977921i	$0.567012\pi$
$542$	−4.06627	−0.174661
$543$	−7.48588	−0.321250
$544$	−29.0550	−1.24572
$545$	23.9617	1.02641
$546$	−7.67640	−0.328519
$547$	44.4771	1.90170	0.950851	−	0.309649i	$-0.100212\pi$
$547$	44.4771	1.90170	0.950851	+	0.309649i	$0.100212\pi$
$548$	104.061	4.44528
$549$	−21.7118	−0.926636
$550$	−0.0371050	−0.00158216
$551$	−17.2291	−0.733983
$552$	16.2335	0.690944
$553$	2.82529	0.120144
$554$	31.0367	1.31862
$555$	7.88635	0.334757
$556$	−71.5578	−3.03473
$557$	13.1352	0.556558	0.278279	−	0.960500i	$-0.410236\pi$
$557$	13.1352	0.556558	0.278279	+	0.960500i	$0.410236\pi$
$558$	−43.7963	−1.85404
$559$	−40.8553	−1.72799
$560$	37.8039	1.59751
$561$	−0.0204805	−0.000864689 0
$562$	65.4321	2.76009
$563$	25.1592	1.06033	0.530167	−	0.847893i	$-0.322129\pi$
$563$	25.1592	1.06033	0.530167	+	0.847893i	$0.322129\pi$
$564$	−8.56244	−0.360544
$565$	−0.702541	−0.0295561
$566$	17.3770	0.730408
$567$	9.10111	0.382211
$568$	−103.866	−4.35811
$569$	−13.6901	−0.573919	−0.286960	−	0.957943i	$-0.592645\pi$
$569$	−13.6901	−0.573919	−0.286960	+	0.957943i	$0.592645\pi$
$570$	6.40412	0.268239
$571$	35.9345	1.50381	0.751907	−	0.659269i	$-0.229134\pi$
$571$	35.9345	1.50381	0.751907	+	0.659269i	$0.229134\pi$
$572$	−0.498061	−0.0208250
$573$	−5.95872	−0.248929
$574$	4.22728	0.176443
$575$	2.48650	0.103694
$576$	−47.1722	−1.96551
$577$	−24.9740	−1.03968	−0.519840	−	0.854264i	$-0.674008\pi$
$577$	−24.9740	−1.03968	−0.519840	+	0.854264i	$0.674008\pi$
$578$	35.9077	1.49356
$579$	6.19749	0.257559
$580$	−102.187	−4.24308
$581$	−12.1791	−0.505273
$582$	−13.4165	−0.556133
$583$	−0.186183	−0.00771090
$584$	−71.2242	−2.94728
$585$	28.8172	1.19144
$586$	−30.4938	−1.25969
$587$	−11.5977	−0.478689	−0.239344	−	0.970935i	$-0.576933\pi$
$587$	−11.5977	−0.478689	−0.239344	+	0.970935i	$0.576933\pi$
$588$	13.2576	0.546733
$589$	−12.2046	−0.502882
$590$	−51.8059	−2.13282
$591$	−10.9952	−0.452283
$592$	−81.1192	−3.33398
$593$	1.85002	0.0759711	0.0379856	−	0.999278i	$-0.487906\pi$
$593$	1.85002	0.0759711	0.0379856	+	0.999278i	$0.487906\pi$
$594$	−0.167074	−0.00685512
$595$	5.92015	0.242702
$596$	−81.6563	−3.34477
$597$	3.34973	0.137095
$598$	46.3966	1.89730
$599$	20.0959	0.821098	0.410549	−	0.911839i	$-0.365337\pi$
$599$	20.0959	0.821098	0.410549	+	0.911839i	$0.365337\pi$
$600$	2.59309	0.105862
$601$	43.0798	1.75726	0.878631	−	0.477501i	$-0.158457\pi$
$601$	43.0798	1.75726	0.878631	+	0.477501i	$0.158457\pi$
$602$	−32.7898	−1.33641
$603$	−30.5558	−1.24433
$604$	−51.3630	−2.08993
$605$	−26.0998	−1.06111
$606$	12.0716	0.490376
$607$	9.31075	0.377912	0.188956	−	0.981986i	$-0.439490\pi$
$607$	9.31075	0.377912	0.188956	+	0.981986i	$0.439490\pi$
$608$	−31.6313	−1.28282
$609$	5.48339	0.222198
$610$	−49.8843	−2.01975
$611$	−14.9254	−0.603815
$612$	−26.6298	−1.07645
$613$	23.7679	0.959978	0.479989	−	0.877274i	$-0.340641\pi$
$613$	23.7679	0.959978	0.479989	+	0.877274i	$0.340641\pi$
$614$	9.77962	0.394673
$615$	1.39849	0.0563926
$616$	−0.243796	−0.00982283
$617$	−30.2247	−1.21680	−0.608400	−	0.793630i	$-0.708188\pi$
$617$	−30.2247	−1.21680	−0.608400	+	0.793630i	$0.708188\pi$
$618$	−13.5126	−0.543558
$619$	19.0637	0.766234	0.383117	−	0.923700i	$-0.374851\pi$
$619$	19.0637	0.766234	0.383117	+	0.923700i	$0.374851\pi$
$620$	−72.3864	−2.90711
$621$	11.1960	0.449281
$622$	49.8240	1.99776
$623$	21.4009	0.857408
$624$	26.1218	1.04571
$625$	−27.7539	−1.11016
$626$	−57.5036	−2.29831
$627$	−0.0222966	−0.000890439 0
$628$	−13.5569	−0.540980
$629$	−12.7034	−0.506518
$630$	23.1282	0.921451
$631$	36.3233	1.44601	0.723005	−	0.690843i	$-0.242761\pi$
$631$	36.3233	1.44601	0.723005	+	0.690843i	$0.242761\pi$
$632$	−17.8082	−0.708374
$633$	2.39165	0.0950596
$634$	−45.4867	−1.80651
$635$	17.2928	0.686243
$636$	21.3339	0.845943
$637$	23.1096	0.915634
$638$	0.494564	0.0195800
$639$	−34.3057	−1.35711
$640$	−35.1942	−1.39117
$641$	−23.0023	−0.908537	−0.454269	−	0.890865i	$-0.650099\pi$
$641$	−23.0023	−0.908537	−0.454269	+	0.890865i	$0.650099\pi$
$642$	18.7587	0.740346
$643$	39.3735	1.55274	0.776369	−	0.630279i	$-0.217059\pi$
$643$	39.3735	1.55274	0.776369	+	0.630279i	$0.217059\pi$
$644$	26.7873	1.05557
$645$	−10.8477	−0.427127
$646$	−10.3158	−0.405870
$647$	11.3424	0.445915	0.222958	−	0.974828i	$-0.428429\pi$
$647$	11.3424	0.445915	0.222958	+	0.974828i	$0.428429\pi$
$648$	−57.3657	−2.25354
$649$	0.180368	0.00708004
$650$	7.41124	0.290693
$651$	3.88428	0.152237
$652$	105.513	4.13222
$653$	33.8088	1.32304	0.661519	−	0.749928i	$-0.269912\pi$
$653$	33.8088	1.32304	0.661519	+	0.749928i	$0.269912\pi$
$654$	13.2885	0.519620
$655$	47.5381	1.85747
$656$	−14.3849	−0.561637
$657$	−23.5246	−0.917781
$658$	−11.9789	−0.466984
$659$	38.8880	1.51486	0.757430	−	0.652916i	$-0.226455\pi$
$659$	38.8880	1.51486	0.757430	+	0.652916i	$0.226455\pi$
$660$	−0.132243	−0.00514754
$661$	48.7096	1.89458	0.947292	−	0.320371i	$-0.103808\pi$
$661$	48.7096	1.89458	0.947292	+	0.320371i	$0.103808\pi$
$662$	73.5917	2.86022
$663$	4.09072	0.158870
$664$	76.7665	2.97912
$665$	6.44509	0.249930
$666$	−49.6283	−1.92306
$667$	−33.1419	−1.28326
$668$	126.879	4.90909
$669$	−5.32238	−0.205775
$670$	−70.2039	−2.71221
$671$	0.173677	0.00670473
$672$	10.0671	0.388347
$673$	11.3809	0.438702	0.219351	−	0.975646i	$-0.429606\pi$
$673$	11.3809	0.438702	0.219351	+	0.975646i	$0.429606\pi$
$674$	−21.5288	−0.829258
$675$	1.78841	0.0688361
$676$	32.8326	1.26279
$677$	−24.3824	−0.937093	−0.468546	−	0.883439i	$-0.655222\pi$
$677$	−24.3824	−0.937093	−0.468546	+	0.883439i	$0.655222\pi$
$678$	−0.389609	−0.0149628
$679$	−13.5024	−0.518173
$680$	−37.3156	−1.43099
$681$	9.64584	0.369630
$682$	0.350335	0.0134150
$683$	14.6937	0.562240	0.281120	−	0.959673i	$-0.409294\pi$
$683$	14.6937	0.562240	0.281120	+	0.959673i	$0.409294\pi$
$684$	−28.9911	−1.10850
$685$	48.1621	1.84018
$686$	43.2951	1.65301
$687$	−0.419350	−0.0159992
$688$	111.580	4.25393
$689$	37.1875	1.41673
$690$	12.3190	0.468976
$691$	5.65759	0.215225	0.107612	−	0.994193i	$-0.465679\pi$
$691$	5.65759	0.215225	0.107612	+	0.994193i	$0.465679\pi$
$692$	97.1426	3.69281
$693$	−0.0805232	−0.00305882
$694$	−55.5487	−2.10860
$695$	−33.1187	−1.25626
$696$	−34.5626	−1.31009
$697$	−2.25270	−0.0853271
$698$	−3.63306	−0.137513
$699$	−12.7859	−0.483609
$700$	4.27891	0.161728
$701$	−25.4597	−0.961600	−0.480800	−	0.876830i	$-0.659654\pi$
$701$	−25.4597	−0.961600	−0.480800	+	0.876830i	$0.659654\pi$
$702$	33.3708	1.25950
$703$	−13.8298	−0.521601
$704$	0.377340	0.0142216
$705$	−3.96291	−0.149252
$706$	−12.7405	−0.479494
$707$	12.1488	0.456905
$708$	−20.6675	−0.776734
$709$	43.0961	1.61851	0.809254	−	0.587459i	$-0.199872\pi$
$709$	43.0961	1.61851	0.809254	+	0.587459i	$0.199872\pi$
$710$	−78.8196	−2.95805
$711$	−5.88187	−0.220587
$712$	−134.893	−5.05533
$713$	−23.4768	−0.879214
$714$	3.28314	0.122869
$715$	−0.230515	−0.00862077
$716$	−117.947	−4.40790
$717$	−2.89775	−0.108218
$718$	74.4151	2.77715
$719$	−14.5383	−0.542186	−0.271093	−	0.962553i	$-0.587385\pi$
$719$	−14.5383	−0.542186	−0.271093	+	0.962553i	$0.587385\pi$
$720$	−78.7025	−2.93307
$721$	−13.5991	−0.506457
$722$	39.4920	1.46974
$723$	−7.02058	−0.261098
$724$	77.8603	2.89366
$725$	−5.29398	−0.196613
$726$	−14.4742	−0.537187
$727$	−19.3707	−0.718420	−0.359210	−	0.933257i	$-0.616954\pi$
$727$	−19.3707	−0.718420	−0.359210	+	0.933257i	$0.616954\pi$
$728$	48.6950	1.80476
$729$	−14.7510	−0.546332
$730$	−54.0493	−2.00045
$731$	17.4735	0.646282
$732$	−19.9009	−0.735559
$733$	11.1626	0.412301	0.206150	−	0.978520i	$-0.433906\pi$
$733$	11.1626	0.412301	0.206150	+	0.978520i	$0.433906\pi$
$734$	20.4991	0.756635
$735$	6.13593	0.226327
$736$	−60.8462	−2.24282
$737$	0.244422	0.00900340
$738$	−8.80062	−0.323955
$739$	−4.41772	−0.162509	−0.0812543	−	0.996693i	$-0.525893\pi$
$739$	−4.41772	−0.162509	−0.0812543	+	0.996693i	$0.525893\pi$
$740$	−82.0257	−3.01532
$741$	4.45344	0.163601
$742$	29.8461	1.09568
$743$	30.8234	1.13080	0.565400	−	0.824817i	$-0.308722\pi$
$743$	30.8234	1.13080	0.565400	+	0.824817i	$0.308722\pi$
$744$	−24.4832	−0.897598
$745$	−37.7925	−1.38461
$746$	−3.45181	−0.126380
$747$	25.3551	0.927696
$748$	0.213017	0.00778869
$749$	18.8787	0.689813
$750$	−13.6440	−0.498209
$751$	15.9352	0.581483	0.290742	−	0.956802i	$-0.406098\pi$
$751$	15.9352	0.581483	0.290742	+	0.956802i	$0.406098\pi$
$752$	40.7626	1.48646
$753$	5.40572	0.196995
$754$	−98.7825	−3.59745
$755$	−23.7720	−0.865153
$756$	19.2667	0.700725
$757$	−30.7460	−1.11748	−0.558741	−	0.829342i	$-0.688716\pi$
$757$	−30.7460	−1.11748	−0.558741	+	0.829342i	$0.688716\pi$
$758$	43.1307	1.56658
$759$	−0.0428898	−0.00155680
$760$	−40.6244	−1.47360
$761$	0.105709	0.00383195	0.00191598	−	0.999998i	$-0.499390\pi$
$761$	0.105709	0.00383195	0.00191598	+	0.999998i	$0.499390\pi$
$762$	9.59007	0.347412
$763$	13.3735	0.484152
$764$	61.9765	2.24223
$765$	−12.3249	−0.445609
$766$	−18.4701	−0.667354
$767$	−36.0260	−1.30082
$768$	−2.65035	−0.0956364
$769$	−44.3309	−1.59861	−0.799306	−	0.600924i	$-0.794800\pi$
$769$	−44.3309	−1.59861	−0.799306	+	0.600924i	$0.794800\pi$
$770$	−0.185008	−0.00666721
$771$	−10.5257	−0.379072
$772$	−64.4599	−2.31996
$773$	−1.75128	−0.0629892	−0.0314946	−	0.999504i	$-0.510027\pi$
$773$	−1.75128	−0.0629892	−0.0314946	+	0.999504i	$0.510027\pi$
$774$	68.2639	2.45369
$775$	−3.75011	−0.134708
$776$	85.1075	3.05518
$777$	4.40153	0.157904
$778$	−74.7811	−2.68103
$779$	−2.45245	−0.0878681
$780$	26.4137	0.945762
$781$	0.274418	0.00981946
$782$	−19.8435	−0.709603
$783$	−23.8373	−0.851877
$784$	−63.1144	−2.25409
$785$	−6.27448	−0.223946
$786$	26.3633	0.940347
$787$	−25.1571	−0.896754	−0.448377	−	0.893845i	$-0.647998\pi$
$787$	−25.1571	−0.896754	−0.448377	+	0.893845i	$0.647998\pi$
$788$	114.361	4.07393
$789$	−4.74754	−0.169017
$790$	−13.5140	−0.480806
$791$	−0.392102	−0.0139415
$792$	0.507550	0.0180350
$793$	−34.6897	−1.23187
$794$	−21.4609	−0.761620
$795$	9.87384	0.350189
$796$	−34.8404	−1.23488
$797$	16.2960	0.577235	0.288617	−	0.957445i	$-0.406804\pi$
$797$	16.2960	0.577235	0.288617	+	0.957445i	$0.406804\pi$
$798$	3.57426	0.126528
$799$	6.38348	0.225831
$800$	−9.71937	−0.343631
$801$	−44.5537	−1.57423
$802$	72.4206	2.55726
$803$	0.188178	0.00664065
$804$	−28.0073	−0.987740
$805$	12.3978	0.436965
$806$	−69.9749	−2.46476
$807$	1.04981	0.0369552
$808$	−76.5760	−2.69394
$809$	−21.8305	−0.767518	−0.383759	−	0.923433i	$-0.625371\pi$
$809$	−21.8305	−0.767518	−0.383759	+	0.923433i	$0.625371\pi$
$810$	−43.5326	−1.52958
$811$	−49.5710	−1.74067	−0.870337	−	0.492456i	$-0.836099\pi$
$811$	−49.5710	−1.74067	−0.870337	+	0.492456i	$0.836099\pi$
$812$	−57.0325	−2.00145
$813$	−0.750797	−0.0263316
$814$	0.396987	0.0139144
$815$	48.8341	1.71058
$816$	−11.1721	−0.391103
$817$	19.0229	0.665528
$818$	104.002	3.63634
$819$	16.0834	0.562001
$820$	−14.5457	−0.507956
$821$	−28.7693	−1.00405	−0.502027	−	0.864852i	$-0.667412\pi$
$821$	−28.7693	−1.00405	−0.502027	+	0.864852i	$0.667412\pi$
$822$	26.7093	0.931595
$823$	28.2424	0.984468	0.492234	−	0.870463i	$-0.336180\pi$
$823$	28.2424	0.984468	0.492234	+	0.870463i	$0.336180\pi$
$824$	85.7171	2.98610
$825$	−0.00685107	−0.000238524 0
$826$	−28.9139	−1.00604
$827$	−22.4252	−0.779801	−0.389901	−	0.920857i	$-0.627491\pi$
$827$	−22.4252	−0.779801	−0.389901	+	0.920857i	$0.627491\pi$
$828$	−55.7674	−1.93805
$829$	−44.5840	−1.54847	−0.774233	−	0.632901i	$-0.781864\pi$
$829$	−44.5840	−1.54847	−0.774233	+	0.632901i	$0.781864\pi$
$830$	58.2551	2.02206
$831$	5.73062	0.198793
$832$	−75.3687	−2.61294
$833$	−9.88381	−0.342454
$834$	−18.3667	−0.635986
$835$	58.7226	2.03218
$836$	0.231906	0.00802063
$837$	−16.8857	−0.583656
$838$	1.56270	0.0539826
$839$	−8.59628	−0.296777	−0.148388	−	0.988929i	$-0.547409\pi$
$839$	−8.59628	−0.296777	−0.148388	+	0.988929i	$0.547409\pi$
$840$	12.9293	0.446102
$841$	41.5621	1.43318
$842$	−36.8854	−1.27116
$843$	12.0814	0.416105
$844$	−24.8755	−0.856249
$845$	15.1957	0.522749
$846$	24.9383	0.857397
$847$	−14.5668	−0.500521
$848$	−101.563	−3.48767
$849$	3.20848	0.110115
$850$	−3.16974	−0.108721
$851$	−26.6031	−0.911942
$852$	−31.4444	−1.07727
$853$	3.97518	0.136108	0.0680538	−	0.997682i	$-0.478321\pi$
$853$	3.97518	0.136108	0.0680538	+	0.997682i	$0.478321\pi$
$854$	−27.8414	−0.952712
$855$	−13.4178	−0.458879
$856$	−118.995	−4.06717
$857$	−35.9946	−1.22955	−0.614776	−	0.788701i	$-0.710754\pi$
$857$	−35.9946	−1.22955	−0.614776	+	0.788701i	$0.710754\pi$
$858$	−0.127837	−0.00436428
$859$	−40.1751	−1.37076	−0.685379	−	0.728186i	$-0.740363\pi$
$859$	−40.1751	−1.37076	−0.685379	+	0.728186i	$0.740363\pi$
$860$	112.826	3.84735
$861$	0.780525	0.0266002
$862$	16.5727	0.564470
$863$	−22.6578	−0.771282	−0.385641	−	0.922649i	$-0.626020\pi$
$863$	−22.6578	−0.771282	−0.385641	+	0.922649i	$0.626020\pi$
$864$	−43.7636	−1.48887
$865$	44.9600	1.52868
$866$	83.8258	2.84852
$867$	6.63000	0.225167
$868$	−40.4003	−1.37127
$869$	0.0470503	0.00159607
$870$	−26.2282	−0.889220
$871$	−48.8200	−1.65420
$872$	−84.2950	−2.85459
$873$	28.1101	0.951382
$874$	−21.6031	−0.730734
$875$	−13.7313	−0.464203
$876$	−21.5625	−0.728529
$877$	12.1004	0.408602	0.204301	−	0.978908i	$-0.434508\pi$
$877$	12.1004	0.408602	0.204301	+	0.978908i	$0.434508\pi$
$878$	−62.5472	−2.11087
$879$	−5.63037	−0.189908
$880$	0.629558	0.0212224
$881$	−14.9641	−0.504153	−0.252077	−	0.967707i	$-0.581113\pi$
$881$	−14.9641	−0.504153	−0.252077	+	0.967707i	$0.581113\pi$
$882$	−38.6131	−1.30017
$883$	4.27924	0.144008	0.0720039	−	0.997404i	$-0.477061\pi$
$883$	4.27924	0.144008	0.0720039	+	0.997404i	$0.477061\pi$
$884$	−42.5474	−1.43102
$885$	−9.56544	−0.321539
$886$	48.3419	1.62408
$887$	14.5774	0.489462	0.244731	−	0.969591i	$-0.421300\pi$
$887$	14.5774	0.489462	0.244731	+	0.969591i	$0.421300\pi$
$888$	−27.7435	−0.931010
$889$	9.65143	0.323699
$890$	−102.365	−3.43129
$891$	0.151563	0.00507755
$892$	55.3578	1.85352
$893$	6.94951	0.232556
$894$	−20.9587	−0.700962
$895$	−54.5889	−1.82471
$896$	−19.6426	−0.656213
$897$	8.56666	0.286032
$898$	13.8409	0.461878
$899$	49.9843	1.66707
$900$	−8.90810	−0.296937
$901$	−15.9049	−0.529868
$902$	0.0703980	0.00234400
$903$	−6.05431	−0.201475
$904$	2.47148	0.0822001
$905$	36.0357	1.19787
$906$	−13.1833	−0.437986
$907$	4.14976	0.137791	0.0688953	−	0.997624i	$-0.478053\pi$
$907$	4.14976	0.137791	0.0688953	+	0.997624i	$0.478053\pi$
$908$	−100.326	−3.32944
$909$	−25.2922	−0.838890
$910$	36.9528	1.22497
$911$	16.3301	0.541041	0.270520	−	0.962714i	$-0.412804\pi$
$911$	16.3301	0.541041	0.270520	+	0.962714i	$0.412804\pi$
$912$	−12.1628	−0.402750
$913$	−0.202821	−0.00671239
$914$	−89.7133	−2.96745
$915$	−9.21063	−0.304494
$916$	4.36165	0.144113
$917$	26.5319	0.876162
$918$	−14.2725	−0.471061
$919$	25.3757	0.837067	0.418533	−	0.908201i	$-0.362544\pi$
$919$	25.3757	0.837067	0.418533	+	0.908201i	$0.362544\pi$
$920$	−78.1452	−2.57637
$921$	1.80571	0.0595001
$922$	−26.8883	−0.885520
$923$	−54.8114	−1.80414
$924$	−0.0738072	−0.00242808
$925$	−4.24949	−0.139722
$926$	7.01891	0.230656
$927$	28.3114	0.929870
$928$	129.547	4.25259
$929$	30.1512	0.989228	0.494614	−	0.869113i	$-0.335309\pi$
$929$	30.1512	0.989228	0.494614	+	0.869113i	$0.335309\pi$
$930$	−18.5794	−0.609241
$931$	−10.7602	−0.352652
$932$	132.986	4.35611
$933$	9.19949	0.301178
$934$	56.5129	1.84916
$935$	0.0985897	0.00322423
$936$	−101.376	−3.31359
$937$	7.63452	0.249409	0.124704	−	0.992194i	$-0.460202\pi$
$937$	7.63452	0.249409	0.124704	+	0.992194i	$0.460202\pi$
$938$	−39.1822	−1.27934
$939$	−10.6175	−0.346488
$940$	41.2180	1.34438
$941$	35.0964	1.14411	0.572055	−	0.820215i	$-0.306146\pi$
$941$	35.0964	1.14411	0.572055	+	0.820215i	$0.306146\pi$
$942$	−3.47964	−0.113373
$943$	−4.71754	−0.153624
$944$	98.3904	3.20234
$945$	8.91712	0.290074
$946$	−0.546057	−0.0177538
$947$	−7.54860	−0.245297	−0.122648	−	0.992450i	$-0.539139\pi$
$947$	−7.54860	−0.245297	−0.122648	+	0.992450i	$0.539139\pi$
$948$	−5.39129	−0.175101
$949$	−37.5860	−1.22009
$950$	−3.45080	−0.111959
$951$	−8.39867	−0.272345
$952$	−20.8266	−0.674993
$953$	43.1692	1.39839	0.699194	−	0.714932i	$-0.253542\pi$
$953$	43.1692	1.39839	0.699194	+	0.714932i	$0.253542\pi$
$954$	−62.1355	−2.01171
$955$	28.6842	0.928200
$956$	30.1394	0.974776
$957$	0.0913162	0.00295183
$958$	−59.5989	−1.92555
$959$	26.8802	0.868007
$960$	−20.0115	−0.645869
$961$	4.40752	0.142178
$962$	−79.2929	−2.55651
$963$	−39.3028	−1.26652
$964$	73.0208	2.35184
$965$	−29.8336	−0.960378
$966$	6.87547	0.221214
$967$	−53.3958	−1.71709	−0.858547	−	0.512735i	$-0.828632\pi$
$967$	−53.3958	−1.71709	−0.858547	+	0.512735i	$0.828632\pi$
$968$	91.8166	2.95110
$969$	−1.90471	−0.0611881
$970$	64.5848	2.07369
$971$	−59.1605	−1.89855	−0.949276	−	0.314445i	$-0.898182\pi$
$971$	−59.1605	−1.89855	−0.949276	+	0.314445i	$0.898182\pi$
$972$	−61.0125	−1.95698
$973$	−18.4842	−0.592576
$974$	33.0953	1.06044
$975$	1.36841	0.0438242
$976$	94.7407	3.03258
$977$	54.9861	1.75916	0.879580	−	0.475750i	$-0.157823\pi$
$977$	54.9861	1.75916	0.879580	+	0.475750i	$0.157823\pi$
$978$	27.0820	0.865987
$979$	0.356394	0.0113904
$980$	−63.8196	−2.03864
$981$	−27.8417	−0.888918
$982$	−57.7909	−1.84418
$983$	8.21767	0.262103	0.131051	−	0.991376i	$-0.458165\pi$
$983$	8.21767	0.262103	0.131051	+	0.991376i	$0.458165\pi$
$984$	−4.91977	−0.156836
$985$	52.9290	1.68646
$986$	42.2486	1.34547
$987$	−2.21178	−0.0704016
$988$	−46.3201	−1.47364
$989$	36.5926	1.16358
$990$	0.385160	0.0122412
$991$	−11.8354	−0.375964	−0.187982	−	0.982173i	$-0.560195\pi$
$991$	−11.8354	−0.375964	−0.187982	+	0.982173i	$0.560195\pi$
$992$	91.7676	2.91362
$993$	13.5880	0.431201
$994$	−43.9908	−1.39530
$995$	−16.1250	−0.511196
$996$	23.2404	0.736400
$997$	21.6250	0.684872	0.342436	−	0.939541i	$-0.388748\pi$
$997$	21.6250	0.684872	0.342436	+	0.939541i	$0.388748\pi$
$998$	−97.0539	−3.07219
$999$	−19.1343	−0.605382

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4027.2.a.c.1.4	✓	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4027.2.a.c.1.4	✓	174	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:	\( N \)	\(=\)	\( 4027 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66961 q^{2} -0.492916 q^{3} +5.12680 q^{4} +2.37281 q^{5} +1.31589 q^{6} +1.32431 q^{7} -8.34733 q^{8} -2.75703 q^{9} +O(q^{10})\)	\(q-2.66961 q^{2} -0.492916 q^{3} +5.12680 q^{4} +2.37281 q^{5} +1.31589 q^{6} +1.32431 q^{7} -8.34733 q^{8} -2.75703 q^{9} -6.33447 q^{10} +0.0220541 q^{11} -2.52708 q^{12} -4.40501 q^{13} -3.53539 q^{14} -1.16960 q^{15} +12.0305 q^{16} +1.88399 q^{17} +7.36020 q^{18} +2.05105 q^{19} +12.1649 q^{20} -0.652774 q^{21} -0.0588757 q^{22} +3.94541 q^{23} +4.11453 q^{24} +0.630226 q^{25} +11.7596 q^{26} +2.83773 q^{27} +6.78948 q^{28} -8.40013 q^{29} +3.12236 q^{30} -5.95042 q^{31} -15.4220 q^{32} -0.0108708 q^{33} -5.02952 q^{34} +3.14234 q^{35} -14.1348 q^{36} -6.74280 q^{37} -5.47550 q^{38} +2.17130 q^{39} -19.8066 q^{40} -1.19570 q^{41} +1.74265 q^{42} +9.27473 q^{43} +0.113067 q^{44} -6.54192 q^{45} -10.5327 q^{46} +3.38827 q^{47} -5.93002 q^{48} -5.24620 q^{49} -1.68246 q^{50} -0.928651 q^{51} -22.5836 q^{52} -8.44209 q^{53} -7.57564 q^{54} +0.0523301 q^{55} -11.0545 q^{56} -1.01100 q^{57} +22.4250 q^{58} +8.17842 q^{59} -5.99629 q^{60} +7.87505 q^{61} +15.8853 q^{62} -3.65117 q^{63} +17.1098 q^{64} -10.4523 q^{65} +0.0290208 q^{66} +11.0828 q^{67} +9.65887 q^{68} -1.94475 q^{69} -8.38881 q^{70} +12.4430 q^{71} +23.0139 q^{72} +8.53257 q^{73} +18.0006 q^{74} -0.310649 q^{75} +10.5153 q^{76} +0.0292065 q^{77} -5.79652 q^{78} +2.13340 q^{79} +28.5461 q^{80} +6.87234 q^{81} +3.19206 q^{82} -9.19652 q^{83} -3.34664 q^{84} +4.47036 q^{85} -24.7599 q^{86} +4.14056 q^{87} -0.184093 q^{88} +16.1600 q^{89} +17.4643 q^{90} -5.83360 q^{91} +20.2273 q^{92} +2.93306 q^{93} -9.04535 q^{94} +4.86675 q^{95} +7.60177 q^{96} -10.1958 q^{97} +14.0053 q^{98} -0.0608039 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9}+O(q^{10}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9} + 20 q^{10} + 35 q^{11} + 23 q^{12} + 91 q^{13} + 18 q^{14} + 16 q^{15} + 201 q^{16} + 148 q^{17} + 39 q^{18} + 36 q^{19} + 128 q^{20} + 57 q^{21} + 17 q^{22} + 96 q^{23} + 24 q^{24} + 226 q^{25} + 44 q^{26} + 62 q^{27} + 32 q^{28} + 122 q^{29} + 25 q^{30} + 23 q^{31} + 104 q^{32} + 91 q^{33} + 6 q^{34} + 80 q^{35} + 222 q^{36} + 71 q^{37} + 125 q^{38} + 16 q^{39} + 53 q^{40} + 97 q^{41} + 14 q^{42} + 38 q^{43} + 70 q^{44} + 185 q^{45} - 23 q^{46} + 110 q^{47} + 36 q^{48} + 210 q^{49} + 51 q^{50} + 33 q^{51} + 118 q^{52} + 214 q^{53} + 8 q^{54} + 37 q^{55} + 41 q^{56} + 76 q^{57} + 2 q^{58} + 66 q^{59} - 12 q^{60} + 114 q^{61} + 175 q^{62} + 62 q^{63} + 190 q^{64} + 128 q^{65} + 12 q^{66} - 6 q^{67} + 348 q^{68} + 115 q^{69} - 38 q^{70} + 54 q^{71} + 101 q^{72} + 107 q^{73} + 71 q^{74} - q^{75} + 31 q^{76} + 368 q^{77} - 14 q^{78} - 14 q^{79} + 205 q^{80} + 222 q^{81} + 26 q^{82} + 246 q^{83} + 41 q^{84} + 87 q^{85} + 33 q^{86} + 100 q^{87} - 6 q^{88} + 147 q^{89} + 50 q^{90} - 23 q^{91} + 189 q^{92} + 117 q^{93} + 23 q^{94} + 42 q^{95} + 38 q^{96} + 52 q^{97} + 148 q^{98} + 38 q^{99}+O(q^{100}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9 + 20 * q^10 + 35 * q^11 + 23 * q^12 + 91 * q^13 + 18 * q^14 + 16 * q^15 + 201 * q^16 + 148 * q^17 + 39 * q^18 + 36 * q^19 + 128 * q^20 + 57 * q^21 + 17 * q^22 + 96 * q^23 + 24 * q^24 + 226 * q^25 + 44 * q^26 + 62 * q^27 + 32 * q^28 + 122 * q^29 + 25 * q^30 + 23 * q^31 + 104 * q^32 + 91 * q^33 + 6 * q^34 + 80 * q^35 + 222 * q^36 + 71 * q^37 + 125 * q^38 + 16 * q^39 + 53 * q^40 + 97 * q^41 + 14 * q^42 + 38 * q^43 + 70 * q^44 + 185 * q^45 - 23 * q^46 + 110 * q^47 + 36 * q^48 + 210 * q^49 + 51 * q^50 + 33 * q^51 + 118 * q^52 + 214 * q^53 + 8 * q^54 + 37 * q^55 + 41 * q^56 + 76 * q^57 + 2 * q^58 + 66 * q^59 - 12 * q^60 + 114 * q^61 + 175 * q^62 + 62 * q^63 + 190 * q^64 + 128 * q^65 + 12 * q^66 - 6 * q^67 + 348 * q^68 + 115 * q^69 - 38 * q^70 + 54 * q^71 + 101 * q^72 + 107 * q^73 + 71 * q^74 - q^75 + 31 * q^76 + 368 * q^77 - 14 * q^78 - 14 * q^79 + 205 * q^80 + 222 * q^81 + 26 * q^82 + 246 * q^83 + 41 * q^84 + 87 * q^85 + 33 * q^86 + 100 * q^87 - 6 * q^88 + 147 * q^89 + 50 * q^90 - 23 * q^91 + 189 * q^92 + 117 * q^93 + 23 * q^94 + 42 * q^95 + 38 * q^96 + 52 * q^97 + 148 * q^98 + 38 * q^99

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