LMFDB - Embedded newform 6014.2.a.f.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.07834 q^{3} +1.00000 q^{4} -0.312935 q^{5} -2.07834 q^{6} +0.578926 q^{7} -1.00000 q^{8} +1.31950 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.07834 q^{3} +1.00000 q^{4} -0.312935 q^{5} -2.07834 q^{6} +0.578926 q^{7} -1.00000 q^{8} +1.31950 q^{9} +0.312935 q^{10} -1.72607 q^{11} +2.07834 q^{12} -4.32159 q^{13} -0.578926 q^{14} -0.650386 q^{15} +1.00000 q^{16} +1.57691 q^{17} -1.31950 q^{18} +6.45136 q^{19} -0.312935 q^{20} +1.20320 q^{21} +1.72607 q^{22} -0.697590 q^{23} -2.07834 q^{24} -4.90207 q^{25} +4.32159 q^{26} -3.49265 q^{27} +0.578926 q^{28} +1.19134 q^{29} +0.650386 q^{30} +1.00000 q^{31} -1.00000 q^{32} -3.58737 q^{33} -1.57691 q^{34} -0.181166 q^{35} +1.31950 q^{36} +0.997957 q^{37} -6.45136 q^{38} -8.98173 q^{39} +0.312935 q^{40} -1.46432 q^{41} -1.20320 q^{42} -10.4719 q^{43} -1.72607 q^{44} -0.412918 q^{45} +0.697590 q^{46} -1.94370 q^{47} +2.07834 q^{48} -6.66485 q^{49} +4.90207 q^{50} +3.27735 q^{51} -4.32159 q^{52} +0.438164 q^{53} +3.49265 q^{54} +0.540150 q^{55} -0.578926 q^{56} +13.4081 q^{57} -1.19134 q^{58} +3.47699 q^{59} -0.650386 q^{60} -8.60086 q^{61} -1.00000 q^{62} +0.763892 q^{63} +1.00000 q^{64} +1.35238 q^{65} +3.58737 q^{66} -2.64116 q^{67} +1.57691 q^{68} -1.44983 q^{69} +0.181166 q^{70} +0.00609586 q^{71} -1.31950 q^{72} +14.5604 q^{73} -0.997957 q^{74} -10.1882 q^{75} +6.45136 q^{76} -0.999268 q^{77} +8.98173 q^{78} +9.47573 q^{79} -0.312935 q^{80} -11.2174 q^{81} +1.46432 q^{82} -2.75363 q^{83} +1.20320 q^{84} -0.493470 q^{85} +10.4719 q^{86} +2.47600 q^{87} +1.72607 q^{88} -7.60349 q^{89} +0.412918 q^{90} -2.50188 q^{91} -0.697590 q^{92} +2.07834 q^{93} +1.94370 q^{94} -2.01886 q^{95} -2.07834 q^{96} +1.00000 q^{97} +6.66485 q^{98} -2.27755 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9}+O(q^{10}) $ 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9	$ 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9} - 8 q^{13} + 11 q^{14} + q^{15} + 22 q^{16} - 4 q^{17} - 8 q^{18} - 23 q^{19} - 12 q^{21} + 2 q^{23} - 12 q^{25} + 8 q^{26} + 3 q^{27} - 11 q^{28} + 9 q^{29} - q^{30} + 22 q^{31} - 22 q^{32} + 4 q^{34} + 4 q^{35} + 8 q^{36} - 17 q^{37} + 23 q^{38} + 8 q^{39} - 21 q^{41} + 12 q^{42} - 7 q^{43} + 9 q^{45} - 2 q^{46} - 10 q^{47} - 27 q^{49} + 12 q^{50} - q^{51} - 8 q^{52} + 9 q^{53} - 3 q^{54} - 6 q^{55} + 11 q^{56} - q^{57} - 9 q^{58} - 12 q^{59} + q^{60} - 34 q^{61} - 22 q^{62} - 5 q^{63} + 22 q^{64} + 4 q^{65} - 31 q^{67} - 4 q^{68} - 51 q^{69} - 4 q^{70} - 15 q^{71} - 8 q^{72} + 3 q^{73} + 17 q^{74} - 24 q^{75} - 23 q^{76} + 24 q^{77} - 8 q^{78} - 23 q^{79} - 26 q^{81} + 21 q^{82} + 22 q^{83} - 12 q^{84} - 42 q^{85} + 7 q^{86} - 9 q^{87} - 36 q^{89} - 9 q^{90} - 6 q^{91} + 2 q^{92} + 10 q^{94} + 2 q^{95} + 22 q^{97} + 27 q^{98} - 25 q^{99}+O(q^{100}) $ 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9 - 8 * q^13 + 11 * q^14 + q^15 + 22 * q^16 - 4 * q^17 - 8 * q^18 - 23 * q^19 - 12 * q^21 + 2 * q^23 - 12 * q^25 + 8 * q^26 + 3 * q^27 - 11 * q^28 + 9 * q^29 - q^30 + 22 * q^31 - 22 * q^32 + 4 * q^34 + 4 * q^35 + 8 * q^36 - 17 * q^37 + 23 * q^38 + 8 * q^39 - 21 * q^41 + 12 * q^42 - 7 * q^43 + 9 * q^45 - 2 * q^46 - 10 * q^47 - 27 * q^49 + 12 * q^50 - q^51 - 8 * q^52 + 9 * q^53 - 3 * q^54 - 6 * q^55 + 11 * q^56 - q^57 - 9 * q^58 - 12 * q^59 + q^60 - 34 * q^61 - 22 * q^62 - 5 * q^63 + 22 * q^64 + 4 * q^65 - 31 * q^67 - 4 * q^68 - 51 * q^69 - 4 * q^70 - 15 * q^71 - 8 * q^72 + 3 * q^73 + 17 * q^74 - 24 * q^75 - 23 * q^76 + 24 * q^77 - 8 * q^78 - 23 * q^79 - 26 * q^81 + 21 * q^82 + 22 * q^83 - 12 * q^84 - 42 * q^85 + 7 * q^86 - 9 * q^87 - 36 * q^89 - 9 * q^90 - 6 * q^91 + 2 * q^92 + 10 * q^94 + 2 * q^95 + 22 * q^97 + 27 * q^98 - 25 * 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
$3$	2.07834	1.19993	0.599965	−	0.800026i	$-0.295181\pi$
$3$	2.07834	1.19993	0.599965	+	0.800026i	$0.295181\pi$
$4$	1.00000	0.500000
$5$	−0.312935	−0.139949	−0.0699745	−	0.997549i	$-0.522292\pi$
$5$	−0.312935	−0.139949	−0.0699745	+	0.997549i	$0.522292\pi$
$6$	−2.07834	−0.848479
$7$	0.578926	0.218813	0.109407	−	0.993997i	$-0.465105\pi$
$7$	0.578926	0.218813	0.109407	+	0.993997i	$0.465105\pi$
$8$	−1.00000	−0.353553
$9$	1.31950	0.439833
$10$	0.312935	0.0989589
$11$	−1.72607	−0.520431	−0.260215	−	0.965551i	$-0.583794\pi$
$11$	−1.72607	−0.520431	−0.260215	+	0.965551i	$0.583794\pi$
$12$	2.07834	0.599965
$13$	−4.32159	−1.19859	−0.599296	−	0.800527i	$-0.704553\pi$
$13$	−4.32159	−1.19859	−0.599296	+	0.800527i	$0.704553\pi$
$14$	−0.578926	−0.154724
$15$	−0.650386	−0.167929
$16$	1.00000	0.250000
$17$	1.57691	0.382456	0.191228	−	0.981546i	$-0.438753\pi$
$17$	1.57691	0.382456	0.191228	+	0.981546i	$0.438753\pi$
$18$	−1.31950	−0.311009
$19$	6.45136	1.48004	0.740021	−	0.672583i	$-0.234815\pi$
$19$	6.45136	1.48004	0.740021	+	0.672583i	$0.234815\pi$
$20$	−0.312935	−0.0699745
$21$	1.20320	0.262561
$22$	1.72607	0.368000
$23$	−0.697590	−0.145458	−0.0727288	−	0.997352i	$-0.523171\pi$
$23$	−0.697590	−0.145458	−0.0727288	+	0.997352i	$0.523171\pi$
$24$	−2.07834	−0.424239
$25$	−4.90207	−0.980414
$26$	4.32159	0.847533
$27$	−3.49265	−0.672161
$28$	0.578926	0.109407
$29$	1.19134	0.221226	0.110613	−	0.993864i	$-0.464719\pi$
$29$	1.19134	0.221226	0.110613	+	0.993864i	$0.464719\pi$
$30$	0.650386	0.118744
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	−3.58737	−0.624481
$34$	−1.57691	−0.270437
$35$	−0.181166	−0.0306227
$36$	1.31950	0.219917
$37$	0.997957	0.164063	0.0820316	−	0.996630i	$-0.473859\pi$
$37$	0.997957	0.164063	0.0820316	+	0.996630i	$0.473859\pi$
$38$	−6.45136	−1.04655
$39$	−8.98173	−1.43823
$40$	0.312935	0.0494794
$41$	−1.46432	−0.228689	−0.114344	−	0.993441i	$-0.536477\pi$
$41$	−1.46432	−0.228689	−0.114344	+	0.993441i	$0.536477\pi$
$42$	−1.20320	−0.185658
$43$	−10.4719	−1.59695	−0.798477	−	0.602025i	$-0.794361\pi$
$43$	−10.4719	−1.59695	−0.798477	+	0.602025i	$0.794361\pi$
$44$	−1.72607	−0.260215
$45$	−0.412918	−0.0615542
$46$	0.697590	0.102854
$47$	−1.94370	−0.283518	−0.141759	−	0.989901i	$-0.545276\pi$
$47$	−1.94370	−0.283518	−0.141759	+	0.989901i	$0.545276\pi$
$48$	2.07834	0.299983
$49$	−6.66485	−0.952121
$50$	4.90207	0.693258
$51$	3.27735	0.458921
$52$	−4.32159	−0.599296
$53$	0.438164	0.0601865	0.0300933	−	0.999547i	$-0.490420\pi$
$53$	0.438164	0.0601865	0.0300933	+	0.999547i	$0.490420\pi$
$54$	3.49265	0.475290
$55$	0.540150	0.0728338
$56$	−0.578926	−0.0773622
$57$	13.4081	1.77595
$58$	−1.19134	−0.156430
$59$	3.47699	0.452665	0.226333	−	0.974050i	$-0.427326\pi$
$59$	3.47699	0.452665	0.226333	+	0.974050i	$0.427326\pi$
$60$	−0.650386	−0.0839645
$61$	−8.60086	−1.10123	−0.550614	−	0.834760i	$-0.685606\pi$
$61$	−8.60086	−1.10123	−0.550614	+	0.834760i	$0.685606\pi$
$62$	−1.00000	−0.127000
$63$	0.763892	0.0962413
$64$	1.00000	0.125000
$65$	1.35238	0.167742
$66$	3.58737	0.441575
$67$	−2.64116	−0.322669	−0.161334	−	0.986900i	$-0.551580\pi$
$67$	−2.64116	−0.322669	−0.161334	+	0.986900i	$0.551580\pi$
$68$	1.57691	0.191228
$69$	−1.44983	−0.174539
$70$	0.181166	0.0216535
$71$	0.00609586	0.000723445 0	0.000361723	−	1.00000i	$-0.499885\pi$
$71$	0.00609586	0.000723445 0	0.000361723		1.00000i	$0.499885\pi$
$72$	−1.31950	−0.155505
$73$	14.5604	1.70417	0.852085	−	0.523404i	$-0.175338\pi$
$73$	14.5604	1.70417	0.852085	+	0.523404i	$0.175338\pi$
$74$	−0.997957	−0.116010
$75$	−10.1882	−1.17643
$76$	6.45136	0.740021
$77$	−0.999268	−0.113877
$78$	8.98173	1.01698
$79$	9.47573	1.06610	0.533051	−	0.846083i	$-0.321045\pi$
$79$	9.47573	1.06610	0.533051	+	0.846083i	$0.321045\pi$
$80$	−0.312935	−0.0349872
$81$	−11.2174	−1.24638
$82$	1.46432	0.161708
$83$	−2.75363	−0.302250	−0.151125	−	0.988515i	$-0.548290\pi$
$83$	−2.75363	−0.302250	−0.151125	+	0.988515i	$0.548290\pi$
$84$	1.20320	0.131280
$85$	−0.493470	−0.0535243
$86$	10.4719	1.12922
$87$	2.47600	0.265455
$88$	1.72607	0.184000
$89$	−7.60349	−0.805969	−0.402984	−	0.915207i	$-0.632027\pi$
$89$	−7.60349	−0.805969	−0.402984	+	0.915207i	$0.632027\pi$
$90$	0.412918	0.0435254
$91$	−2.50188	−0.262268
$92$	−0.697590	−0.0727288
$93$	2.07834	0.215514
$94$	1.94370	0.200478
$95$	−2.01886	−0.207130
$96$	−2.07834	−0.212120
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	6.66485	0.673251
$99$	−2.27755	−0.228903
$100$	−4.90207	−0.490207
$101$	−6.13748	−0.610702	−0.305351	−	0.952240i	$-0.598774\pi$
$101$	−6.13748	−0.610702	−0.305351	+	0.952240i	$0.598774\pi$
$102$	−3.27735	−0.324506
$103$	−5.28037	−0.520291	−0.260145	−	0.965569i	$-0.583770\pi$
$103$	−5.28037	−0.520291	−0.260145	+	0.965569i	$0.583770\pi$
$104$	4.32159	0.423766
$105$	−0.376525	−0.0367451
$106$	−0.438164	−0.0425583
$107$	0.784333	0.0758243	0.0379121	−	0.999281i	$-0.487929\pi$
$107$	0.784333	0.0758243	0.0379121	+	0.999281i	$0.487929\pi$
$108$	−3.49265	−0.336081
$109$	−4.94380	−0.473530	−0.236765	−	0.971567i	$-0.576087\pi$
$109$	−4.94380	−0.473530	−0.236765	+	0.971567i	$0.576087\pi$
$110$	−0.540150	−0.0515013
$111$	2.07409	0.196864
$112$	0.578926	0.0547033
$113$	−7.08767	−0.666752	−0.333376	−	0.942794i	$-0.608188\pi$
$113$	−7.08767	−0.666752	−0.333376	+	0.942794i	$0.608188\pi$
$114$	−13.4081	−1.25579
$115$	0.218301	0.0203566
$116$	1.19134	0.110613
$117$	−5.70233	−0.527181
$118$	−3.47699	−0.320083
$119$	0.912912	0.0836865
$120$	0.650386	0.0593719
$121$	−8.02067	−0.729152
$122$	8.60086	0.778685
$123$	−3.04336	−0.274411
$124$	1.00000	0.0898027
$125$	3.09871	0.277157
$126$	−0.763892	−0.0680529
$127$	−18.7608	−1.66475	−0.832376	−	0.554211i	$-0.813020\pi$
$127$	−18.7608	−1.66475	−0.832376	+	0.554211i	$0.813020\pi$
$128$	−1.00000	−0.0883883
$129$	−21.7642	−1.91623
$130$	−1.35238	−0.118611
$131$	−17.8597	−1.56041	−0.780205	−	0.625524i	$-0.784885\pi$
$131$	−17.8597	−1.56041	−0.780205	+	0.625524i	$0.784885\pi$
$132$	−3.58737	−0.312240
$133$	3.73485	0.323853
$134$	2.64116	0.228161
$135$	1.09297	0.0940683
$136$	−1.57691	−0.135219
$137$	10.1778	0.869546	0.434773	−	0.900540i	$-0.356829\pi$
$137$	10.1778	0.869546	0.434773	+	0.900540i	$0.356829\pi$
$138$	1.44983	0.123418
$139$	−6.84087	−0.580235	−0.290117	−	0.956991i	$-0.593694\pi$
$139$	−6.84087	−0.580235	−0.290117	+	0.956991i	$0.593694\pi$
$140$	−0.181166	−0.0153114
$141$	−4.03968	−0.340202
$142$	−0.00609586	−0.000511553 0
$143$	7.45938	0.623784
$144$	1.31950	0.109958
$145$	−0.372811	−0.0309603
$146$	−14.5604	−1.20503
$147$	−13.8518	−1.14248
$148$	0.997957	0.0820316
$149$	24.0482	1.97011	0.985054	−	0.172245i	$-0.0551022\pi$
$149$	24.0482	1.97011	0.985054	+	0.172245i	$0.0551022\pi$
$150$	10.1882	0.831861
$151$	−5.88232	−0.478697	−0.239348	−	0.970934i	$-0.576934\pi$
$151$	−5.88232	−0.478697	−0.239348	+	0.970934i	$0.576934\pi$
$152$	−6.45136	−0.523274
$153$	2.08073	0.168217
$154$	0.999268	0.0805233
$155$	−0.312935	−0.0251356
$156$	−8.98173	−0.719114
$157$	1.52618	0.121802	0.0609012	−	0.998144i	$-0.480603\pi$
$157$	1.52618	0.121802	0.0609012	+	0.998144i	$0.480603\pi$
$158$	−9.47573	−0.753848
$159$	0.910655	0.0722196
$160$	0.312935	0.0247397
$161$	−0.403853	−0.0318280
$162$	11.2174	0.881324
$163$	2.51420	0.196927	0.0984637	−	0.995141i	$-0.468607\pi$
$163$	2.51420	0.196927	0.0984637	+	0.995141i	$0.468607\pi$
$164$	−1.46432	−0.114344
$165$	1.12262	0.0873955
$166$	2.75363	0.213723
$167$	−24.2794	−1.87879	−0.939397	−	0.342832i	$-0.888614\pi$
$167$	−24.2794	−1.87879	−0.939397	+	0.342832i	$0.888614\pi$
$168$	−1.20320	−0.0928292
$169$	5.67611	0.436624
$170$	0.493470	0.0378474
$171$	8.51256	0.650972
$172$	−10.4719	−0.798477
$173$	3.96621	0.301545	0.150773	−	0.988568i	$-0.451824\pi$
$173$	3.96621	0.301545	0.150773	+	0.988568i	$0.451824\pi$
$174$	−2.47600	−0.187705
$175$	−2.83793	−0.214528
$176$	−1.72607	−0.130108
$177$	7.22636	0.543167
$178$	7.60349	0.569906
$179$	14.4775	1.08210	0.541050	−	0.840990i	$-0.318027\pi$
$179$	14.4775	1.08210	0.541050	+	0.840990i	$0.318027\pi$
$180$	−0.412918	−0.0307771
$181$	−13.2088	−0.981800	−0.490900	−	0.871216i	$-0.663332\pi$
$181$	−13.2088	−0.981800	−0.490900	+	0.871216i	$0.663332\pi$
$182$	2.50188	0.185451
$183$	−17.8755	−1.32140
$184$	0.697590	0.0514270
$185$	−0.312296	−0.0229605
$186$	−2.07834	−0.152391
$187$	−2.72186	−0.199042
$188$	−1.94370	−0.141759
$189$	−2.02199	−0.147078
$190$	2.01886	0.146463
$191$	−8.38615	−0.606800	−0.303400	−	0.952863i	$-0.598122\pi$
$191$	−8.38615	−0.606800	−0.303400	+	0.952863i	$0.598122\pi$
$192$	2.07834	0.149991
$193$	−23.1185	−1.66411	−0.832053	−	0.554696i	$-0.812835\pi$
$193$	−23.1185	−1.66411	−0.832053	+	0.554696i	$0.812835\pi$
$194$	−1.00000	−0.0717958
$195$	2.81070	0.201279
$196$	−6.66485	−0.476060
$197$	−4.08605	−0.291119	−0.145560	−	0.989349i	$-0.546498\pi$
$197$	−4.08605	−0.291119	−0.145560	+	0.989349i	$0.546498\pi$
$198$	2.27755	0.161859
$199$	−4.21555	−0.298833	−0.149416	−	0.988774i	$-0.547739\pi$
$199$	−4.21555	−0.298833	−0.149416	+	0.988774i	$0.547739\pi$
$200$	4.90207	0.346629
$201$	−5.48922	−0.387180
$202$	6.13748	0.431831
$203$	0.689695	0.0484071
$204$	3.27735	0.229460
$205$	0.458239	0.0320048
$206$	5.28037	0.367901
$207$	−0.920470	−0.0639771
$208$	−4.32159	−0.299648
$209$	−11.1355	−0.770260
$210$	0.376525	0.0259827
$211$	4.85780	0.334425	0.167212	−	0.985921i	$-0.446523\pi$
$211$	4.85780	0.334425	0.167212	+	0.985921i	$0.446523\pi$
$212$	0.438164	0.0300933
$213$	0.0126693	0.000868084 0
$214$	−0.784333	−0.0536159
$215$	3.27704	0.223492
$216$	3.49265	0.237645
$217$	0.578926	0.0393000
$218$	4.94380	0.334836
$219$	30.2615	2.04489
$220$	0.540150	0.0364169
$221$	−6.81474	−0.458409
$222$	−2.07409	−0.139204
$223$	29.4479	1.97198	0.985989	−	0.166813i	$-0.0533476\pi$
$223$	29.4479	1.97198	0.985989	+	0.166813i	$0.0533476\pi$
$224$	−0.578926	−0.0386811
$225$	−6.46828	−0.431219
$226$	7.08767	0.471465
$227$	3.54148	0.235056	0.117528	−	0.993070i	$-0.462503\pi$
$227$	3.54148	0.235056	0.117528	+	0.993070i	$0.462503\pi$
$228$	13.4081	0.887974
$229$	−16.7123	−1.10438	−0.552191	−	0.833717i	$-0.686208\pi$
$229$	−16.7123	−1.10438	−0.552191	+	0.833717i	$0.686208\pi$
$230$	−0.218301	−0.0143943
$231$	−2.07682	−0.136645
$232$	−1.19134	−0.0782151
$233$	13.9707	0.915251	0.457625	−	0.889145i	$-0.348700\pi$
$233$	13.9707	0.915251	0.457625	+	0.889145i	$0.348700\pi$
$234$	5.70233	0.372773
$235$	0.608254	0.0396781
$236$	3.47699	0.226333
$237$	19.6938	1.27925
$238$	−0.912912	−0.0591753
$239$	−6.84308	−0.442642	−0.221321	−	0.975201i	$-0.571037\pi$
$239$	−6.84308	−0.442642	−0.221321	+	0.975201i	$0.571037\pi$
$240$	−0.650386	−0.0419823
$241$	−9.11288	−0.587012	−0.293506	−	0.955957i	$-0.594822\pi$
$241$	−9.11288	−0.587012	−0.293506	+	0.955957i	$0.594822\pi$
$242$	8.02067	0.515588
$243$	−12.8357	−0.823408
$244$	−8.60086	−0.550614
$245$	2.08567	0.133248
$246$	3.04336	0.194038
$247$	−27.8801	−1.77397
$248$	−1.00000	−0.0635001
$249$	−5.72299	−0.362680
$250$	−3.09871	−0.195980
$251$	−16.6536	−1.05117	−0.525584	−	0.850742i	$-0.676153\pi$
$251$	−16.6536	−1.05117	−0.525584	+	0.850742i	$0.676153\pi$
$252$	0.763892	0.0481207
$253$	1.20409	0.0757006
$254$	18.7608	1.17716
$255$	−1.02560	−0.0642255
$256$	1.00000	0.0625000
$257$	27.1002	1.69047	0.845233	−	0.534398i	$-0.179462\pi$
$257$	27.1002	1.69047	0.845233	+	0.534398i	$0.179462\pi$
$258$	21.7642	1.35498
$259$	0.577743	0.0358992
$260$	1.35238	0.0838709
$261$	1.57197	0.0973024
$262$	17.8597	1.10338
$263$	5.03703	0.310597	0.155298	−	0.987868i	$-0.450366\pi$
$263$	5.03703	0.310597	0.155298	+	0.987868i	$0.450366\pi$
$264$	3.58737	0.220787
$265$	−0.137117	−0.00842304
$266$	−3.73485	−0.228999
$267$	−15.8026	−0.967106
$268$	−2.64116	−0.161334
$269$	13.9943	0.853245	0.426623	−	0.904430i	$-0.359703\pi$
$269$	13.9943	0.853245	0.426623	+	0.904430i	$0.359703\pi$
$270$	−1.09297	−0.0665163
$271$	−20.1189	−1.22214	−0.611069	−	0.791577i	$-0.709260\pi$
$271$	−20.1189	−1.22214	−0.611069	+	0.791577i	$0.709260\pi$
$272$	1.57691	0.0956140
$273$	−5.19975	−0.314703
$274$	−10.1778	−0.614862
$275$	8.46134	0.510238
$276$	−1.44983	−0.0872695
$277$	20.6939	1.24338	0.621689	−	0.783264i	$-0.286447\pi$
$277$	20.6939	1.24338	0.621689	+	0.783264i	$0.286447\pi$
$278$	6.84087	0.410288
$279$	1.31950	0.0789964
$280$	0.181166	0.0108268
$281$	−22.7676	−1.35820	−0.679100	−	0.734046i	$-0.737630\pi$
$281$	−22.7676	−1.35820	−0.679100	+	0.734046i	$0.737630\pi$
$282$	4.03968	0.240559
$283$	−21.1519	−1.25735	−0.628675	−	0.777668i	$-0.716402\pi$
$283$	−21.1519	−1.25735	−0.628675	+	0.777668i	$0.716402\pi$
$284$	0.00609586	0.000361723 0
$285$	−4.19587	−0.248542
$286$	−7.45938	−0.441082
$287$	−0.847735	−0.0500402
$288$	−1.31950	−0.0777523
$289$	−14.5134	−0.853727
$290$	0.372811	0.0218922
$291$	2.07834	0.121834
$292$	14.5604	0.852085
$293$	−15.2950	−0.893545	−0.446772	−	0.894648i	$-0.647427\pi$
$293$	−15.2950	−0.893545	−0.446772	+	0.894648i	$0.647427\pi$
$294$	13.8518	0.807854
$295$	−1.08807	−0.0633500
$296$	−0.997957	−0.0580051
$297$	6.02858	0.349813
$298$	−24.0482	−1.39308
$299$	3.01470	0.174344
$300$	−10.1882	−0.588214
$301$	−6.06247	−0.349435
$302$	5.88232	0.338490
$303$	−12.7558	−0.732799
$304$	6.45136	0.370011
$305$	2.69151	0.154116
$306$	−2.08073	−0.118947
$307$	14.5542	0.830651	0.415325	−	0.909673i	$-0.363668\pi$
$307$	14.5542	0.830651	0.415325	+	0.909673i	$0.363668\pi$
$308$	−0.999268	−0.0569386
$309$	−10.9744	−0.624313
$310$	0.312935	0.0177735
$311$	−14.2361	−0.807258	−0.403629	−	0.914923i	$-0.632251\pi$
$311$	−14.2361	−0.807258	−0.403629	+	0.914923i	$0.632251\pi$
$312$	8.98173	0.508490
$313$	9.28440	0.524786	0.262393	−	0.964961i	$-0.415488\pi$
$313$	9.28440	0.524786	0.262393	+	0.964961i	$0.415488\pi$
$314$	−1.52618	−0.0861273
$315$	−0.239049	−0.0134689
$316$	9.47573	0.533051
$317$	28.0181	1.57365	0.786826	−	0.617175i	$-0.211723\pi$
$317$	28.0181	1.57365	0.786826	+	0.617175i	$0.211723\pi$
$318$	−0.910655	−0.0510670
$319$	−2.05633	−0.115133
$320$	−0.312935	−0.0174936
$321$	1.63011	0.0909839
$322$	0.403853	0.0225058
$323$	10.1732	0.566051
$324$	−11.2174	−0.623190
$325$	21.1847	1.17512
$326$	−2.51420	−0.139249
$327$	−10.2749	−0.568203
$328$	1.46432	0.0808538
$329$	−1.12526	−0.0620376
$330$	−1.12262	−0.0617979
$331$	−10.8803	−0.598034	−0.299017	−	0.954248i	$-0.596659\pi$
$331$	−10.8803	−0.598034	−0.299017	+	0.954248i	$0.596659\pi$
$332$	−2.75363	−0.151125
$333$	1.31680	0.0721604
$334$	24.2794	1.32851
$335$	0.826512	0.0451572
$336$	1.20320	0.0656402
$337$	−13.5609	−0.738711	−0.369356	−	0.929288i	$-0.620422\pi$
$337$	−13.5609	−0.738711	−0.369356	+	0.929288i	$0.620422\pi$
$338$	−5.67611	−0.308740
$339$	−14.7306	−0.800056
$340$	−0.493470	−0.0267622
$341$	−1.72607	−0.0934721
$342$	−8.51256	−0.460307
$343$	−7.91093	−0.427150
$344$	10.4719	0.564609
$345$	0.453703	0.0244266
$346$	−3.96621	−0.213225
$347$	−34.7350	−1.86467	−0.932336	−	0.361594i	$-0.882233\pi$
$347$	−34.7350	−1.86467	−0.932336	+	0.361594i	$0.882233\pi$
$348$	2.47600	0.132728
$349$	−9.31074	−0.498393	−0.249196	−	0.968453i	$-0.580166\pi$
$349$	−9.31074	−0.498393	−0.249196	+	0.968453i	$0.580166\pi$
$350$	2.83793	0.151694
$351$	15.0938	0.805647
$352$	1.72607	0.0920001
$353$	15.6447	0.832686	0.416343	−	0.909208i	$-0.363312\pi$
$353$	15.6447	0.832686	0.416343	+	0.909208i	$0.363312\pi$
$354$	−7.22636	−0.384077
$355$	−0.00190761	−0.000101245 0
$356$	−7.60349	−0.402984
$357$	1.89734	0.100418
$358$	−14.4775	−0.765160
$359$	18.8153	0.993035	0.496517	−	0.868027i	$-0.334612\pi$
$359$	18.8153	0.993035	0.496517	+	0.868027i	$0.334612\pi$
$360$	0.412918	0.0217627
$361$	22.6200	1.19053
$362$	13.2088	0.694237
$363$	−16.6697	−0.874931
$364$	−2.50188	−0.131134
$365$	−4.55648	−0.238497
$366$	17.8755	0.934368
$367$	20.8679	1.08930	0.544648	−	0.838664i	$-0.316663\pi$
$367$	20.8679	1.08930	0.544648	+	0.838664i	$0.316663\pi$
$368$	−0.697590	−0.0363644
$369$	−1.93217	−0.100585
$370$	0.312296	0.0162355
$371$	0.253665	0.0131696
$372$	2.07834	0.107757
$373$	−14.2509	−0.737882	−0.368941	−	0.929453i	$-0.620280\pi$
$373$	−14.2509	−0.737882	−0.368941	+	0.929453i	$0.620280\pi$
$374$	2.72186	0.140744
$375$	6.44017	0.332569
$376$	1.94370	0.100239
$377$	−5.14846	−0.265159
$378$	2.02199	0.104000
$379$	−34.6255	−1.77859	−0.889297	−	0.457331i	$-0.848806\pi$
$379$	−34.6255	−1.77859	−0.889297	+	0.457331i	$0.848806\pi$
$380$	−2.01886	−0.103565
$381$	−38.9914	−1.99759
$382$	8.38615	0.429073
$383$	18.2824	0.934188	0.467094	−	0.884208i	$-0.345301\pi$
$383$	18.2824	0.934188	0.467094	+	0.884208i	$0.345301\pi$
$384$	−2.07834	−0.106060
$385$	0.312706	0.0159370
$386$	23.1185	1.17670
$387$	−13.8177	−0.702394
$388$	1.00000	0.0507673
$389$	22.3836	1.13489	0.567447	−	0.823410i	$-0.307931\pi$
$389$	22.3836	1.13489	0.567447	+	0.823410i	$0.307931\pi$
$390$	−2.81070	−0.142325
$391$	−1.10003	−0.0556311
$392$	6.66485	0.336626
$393$	−37.1186	−1.87238
$394$	4.08605	0.205852
$395$	−2.96529	−0.149200
$396$	−2.27755	−0.114451
$397$	−8.31134	−0.417134	−0.208567	−	0.978008i	$-0.566880\pi$
$397$	−8.31134	−0.417134	−0.208567	+	0.978008i	$0.566880\pi$
$398$	4.21555	0.211306
$399$	7.76230	0.388601
$400$	−4.90207	−0.245104
$401$	34.1044	1.70309	0.851547	−	0.524279i	$-0.175665\pi$
$401$	34.1044	1.70309	0.851547	+	0.524279i	$0.175665\pi$
$402$	5.48922	0.273778
$403$	−4.32159	−0.215274
$404$	−6.13748	−0.305351
$405$	3.51033	0.174430
$406$	−0.689695	−0.0342290
$407$	−1.72255	−0.0853835
$408$	−3.27735	−0.162253
$409$	−14.9322	−0.738350	−0.369175	−	0.929360i	$-0.620360\pi$
$409$	−14.9322	−0.738350	−0.369175	+	0.929360i	$0.620360\pi$
$410$	−0.458239	−0.0226308
$411$	21.1529	1.04339
$412$	−5.28037	−0.260145
$413$	2.01292	0.0990491
$414$	0.920470	0.0452386
$415$	0.861709	0.0422996
$416$	4.32159	0.211883
$417$	−14.2177	−0.696241
$418$	11.1355	0.544656
$419$	3.48102	0.170059	0.0850296	−	0.996378i	$-0.472902\pi$
$419$	3.48102	0.170059	0.0850296	+	0.996378i	$0.472902\pi$
$420$	−0.376525	−0.0183726
$421$	−3.46896	−0.169067	−0.0845333	−	0.996421i	$-0.526940\pi$
$421$	−3.46896	−0.169067	−0.0845333	+	0.996421i	$0.526940\pi$
$422$	−4.85780	−0.236474
$423$	−2.56472	−0.124701
$424$	−0.438164	−0.0212791
$425$	−7.73011	−0.374965
$426$	−0.0126693	−0.000613828 0
$427$	−4.97926	−0.240963
$428$	0.784333	0.0379121
$429$	15.5031	0.748498
$430$	−3.27704	−0.158033
$431$	17.6028	0.847897	0.423948	−	0.905686i	$-0.360644\pi$
$431$	17.6028	0.847897	0.423948	+	0.905686i	$0.360644\pi$
$432$	−3.49265	−0.168040
$433$	17.0381	0.818798	0.409399	−	0.912355i	$-0.365738\pi$
$433$	17.0381	0.818798	0.409399	+	0.912355i	$0.365738\pi$
$434$	−0.578926	−0.0277893
$435$	−0.774829	−0.0371502
$436$	−4.94380	−0.236765
$437$	−4.50040	−0.215283
$438$	−30.2615	−1.44595
$439$	32.0357	1.52898	0.764489	−	0.644637i	$-0.222991\pi$
$439$	32.0357	1.52898	0.764489	+	0.644637i	$0.222991\pi$
$440$	−0.540150	−0.0257506
$441$	−8.79426	−0.418774
$442$	6.81474	0.324144
$443$	29.2811	1.39119	0.695593	−	0.718436i	$-0.255142\pi$
$443$	29.2811	1.39119	0.695593	+	0.718436i	$0.255142\pi$
$444$	2.07409	0.0984322
$445$	2.37940	0.112794
$446$	−29.4479	−1.39440
$447$	49.9804	2.36399
$448$	0.578926	0.0273517
$449$	−29.1142	−1.37398	−0.686991	−	0.726666i	$-0.741069\pi$
$449$	−29.1142	−1.37398	−0.686991	+	0.726666i	$0.741069\pi$
$450$	6.46828	0.304918
$451$	2.52753	0.119017
$452$	−7.08767	−0.333376
$453$	−12.2255	−0.574403
$454$	−3.54148	−0.166210
$455$	0.782926	0.0367041
$456$	−13.4081	−0.627893
$457$	23.1410	1.08249	0.541245	−	0.840865i	$-0.317953\pi$
$457$	23.1410	1.08249	0.541245	+	0.840865i	$0.317953\pi$
$458$	16.7123	0.780917
$459$	−5.50759	−0.257072
$460$	0.218301	0.0101783
$461$	36.8469	1.71613	0.858067	−	0.513538i	$-0.171666\pi$
$461$	36.8469	1.71613	0.858067	+	0.513538i	$0.171666\pi$
$462$	2.07682	0.0966224
$463$	12.8881	0.598961	0.299480	−	0.954102i	$-0.403187\pi$
$463$	12.8881	0.598961	0.299480	+	0.954102i	$0.403187\pi$
$464$	1.19134	0.0553064
$465$	−0.650386	−0.0301610
$466$	−13.9707	−0.647180
$467$	−13.4363	−0.621756	−0.310878	−	0.950450i	$-0.600623\pi$
$467$	−13.4363	−0.621756	−0.310878	+	0.950450i	$0.600623\pi$
$468$	−5.70233	−0.263590
$469$	−1.52903	−0.0706042
$470$	−0.608254	−0.0280567
$471$	3.17192	0.146154
$472$	−3.47699	−0.160041
$473$	18.0753	0.831105
$474$	−19.6938	−0.904566
$475$	−31.6250	−1.45105
$476$	0.912912	0.0418432
$477$	0.578158	0.0264720
$478$	6.84308	0.312995
$479$	4.47078	0.204275	0.102138	−	0.994770i	$-0.467432\pi$
$479$	4.47078	0.204275	0.102138	+	0.994770i	$0.467432\pi$
$480$	0.650386	0.0296859
$481$	−4.31276	−0.196645
$482$	9.11288	0.415080
$483$	−0.839343	−0.0381914
$484$	−8.02067	−0.364576
$485$	−0.312935	−0.0142097
$486$	12.8357	0.582237
$487$	−29.3740	−1.33106	−0.665531	−	0.746370i	$-0.731795\pi$
$487$	−29.3740	−1.33106	−0.665531	+	0.746370i	$0.731795\pi$
$488$	8.60086	0.389343
$489$	5.22537	0.236299
$490$	−2.08567	−0.0942208
$491$	−15.2364	−0.687609	−0.343805	−	0.939041i	$-0.611716\pi$
$491$	−15.2364	−0.687609	−0.343805	+	0.939041i	$0.611716\pi$
$492$	−3.04336	−0.137205
$493$	1.87863	0.0846091
$494$	27.8801	1.25438
$495$	0.712727	0.0320347
$496$	1.00000	0.0449013
$497$	0.00352905	0.000158299 0
$498$	5.72299	0.256453
$499$	11.5106	0.515286	0.257643	−	0.966240i	$-0.417054\pi$
$499$	11.5106	0.515286	0.257643	+	0.966240i	$0.417054\pi$
$500$	3.09871	0.138578
$501$	−50.4608	−2.25442
$502$	16.6536	0.743288
$503$	33.8112	1.50757	0.753785	−	0.657122i	$-0.228226\pi$
$503$	33.8112	1.50757	0.753785	+	0.657122i	$0.228226\pi$
$504$	−0.763892	−0.0340265
$505$	1.92063	0.0854671
$506$	−1.20409	−0.0535284
$507$	11.7969	0.523918
$508$	−18.7608	−0.832376
$509$	−35.3168	−1.56539	−0.782694	−	0.622406i	$-0.786155\pi$
$509$	−35.3168	−1.56539	−0.782694	+	0.622406i	$0.786155\pi$
$510$	1.02560	0.0454143
$511$	8.42941	0.372895
$512$	−1.00000	−0.0441942
$513$	−22.5323	−0.994827
$514$	−27.1002	−1.19534
$515$	1.65242	0.0728142
$516$	−21.7642	−0.958117
$517$	3.35498	0.147552
$518$	−0.577743	−0.0253846
$519$	8.24313	0.361833
$520$	−1.35238	−0.0593057
$521$	−19.4922	−0.853968	−0.426984	−	0.904259i	$-0.640424\pi$
$521$	−19.4922	−0.853968	−0.426984	+	0.904259i	$0.640424\pi$
$522$	−1.57197	−0.0688032
$523$	2.43875	0.106639	0.0533196	−	0.998577i	$-0.483020\pi$
$523$	2.43875	0.106639	0.0533196	+	0.998577i	$0.483020\pi$
$524$	−17.8597	−0.780205
$525$	−5.89819	−0.257418
$526$	−5.03703	−0.219625
$527$	1.57691	0.0686911
$528$	−3.58737	−0.156120
$529$	−22.5134	−0.978842
$530$	0.137117	0.00595599
$531$	4.58788	0.199097
$532$	3.73485	0.161926
$533$	6.32820	0.274105
$534$	15.8026	0.683847
$535$	−0.245445	−0.0106115
$536$	2.64116	0.114081
$537$	30.0892	1.29844
$538$	−13.9943	−0.603336
$539$	11.5040	0.495513
$540$	1.09297	0.0470341
$541$	−10.2752	−0.441766	−0.220883	−	0.975300i	$-0.570894\pi$
$541$	−10.2752	−0.441766	−0.220883	+	0.975300i	$0.570894\pi$
$542$	20.1189	0.864182
$543$	−27.4523	−1.17809
$544$	−1.57691	−0.0676093
$545$	1.54709	0.0662701
$546$	5.19975	0.222529
$547$	25.0238	1.06994	0.534969	−	0.844871i	$-0.320323\pi$
$547$	25.0238	1.06994	0.534969	+	0.844871i	$0.320323\pi$
$548$	10.1778	0.434773
$549$	−11.3488	−0.484356
$550$	−8.46134	−0.360793
$551$	7.68573	0.327423
$552$	1.44983	0.0617088
$553$	5.48574	0.233277
$554$	−20.6939	−0.879201
$555$	−0.649058	−0.0275510
$556$	−6.84087	−0.290117
$557$	2.56562	0.108709	0.0543544	−	0.998522i	$-0.482690\pi$
$557$	2.56562	0.108709	0.0543544	+	0.998522i	$0.482690\pi$
$558$	−1.31950	−0.0558589
$559$	45.2554	1.91410
$560$	−0.181166	−0.00765568
$561$	−5.65695	−0.238836
$562$	22.7676	0.960392
$563$	−35.5412	−1.49788	−0.748941	−	0.662636i	$-0.769438\pi$
$563$	−35.5412	−1.49788	−0.748941	+	0.662636i	$0.769438\pi$
$564$	−4.03968	−0.170101
$565$	2.21798	0.0933112
$566$	21.1519	0.889080
$567$	−6.49405	−0.272724
$568$	−0.00609586	−0.000255777 0
$569$	−17.0585	−0.715128	−0.357564	−	0.933889i	$-0.616393\pi$
$569$	−17.0585	−0.715128	−0.357564	+	0.933889i	$0.616393\pi$
$570$	4.19587	0.175746
$571$	34.1844	1.43057	0.715286	−	0.698832i	$-0.246297\pi$
$571$	34.1844	1.43057	0.715286	+	0.698832i	$0.246297\pi$
$572$	7.45938	0.311892
$573$	−17.4293	−0.728118
$574$	0.847735	0.0353838
$575$	3.41964	0.142609
$576$	1.31950	0.0549791
$577$	−39.4542	−1.64250	−0.821250	−	0.570569i	$-0.806723\pi$
$577$	−39.4542	−1.64250	−0.821250	+	0.570569i	$0.806723\pi$
$578$	14.5134	0.603676
$579$	−48.0481	−1.99681
$580$	−0.372811	−0.0154802
$581$	−1.59415	−0.0661364
$582$	−2.07834	−0.0861500
$583$	−0.756304	−0.0313229
$584$	−14.5604	−0.602515
$585$	1.78446	0.0737784
$586$	15.2950	0.631832
$587$	−23.1021	−0.953526	−0.476763	−	0.879032i	$-0.658190\pi$
$587$	−23.1021	−0.953526	−0.476763	+	0.879032i	$0.658190\pi$
$588$	−13.8518	−0.571239
$589$	6.45136	0.265824
$590$	1.08807	0.0447952
$591$	−8.49220	−0.349323
$592$	0.997957	0.0410158
$593$	15.0852	0.619476	0.309738	−	0.950822i	$-0.399759\pi$
$593$	15.0852	0.619476	0.309738	+	0.950822i	$0.399759\pi$
$594$	−6.02858	−0.247355
$595$	−0.285682	−0.0117118
$596$	24.0482	0.985054
$597$	−8.76135	−0.358578
$598$	−3.01470	−0.123280
$599$	−28.9461	−1.18270	−0.591352	−	0.806413i	$-0.701406\pi$
$599$	−28.9461	−1.18270	−0.591352	+	0.806413i	$0.701406\pi$
$600$	10.1882	0.415930
$601$	8.79947	0.358938	0.179469	−	0.983764i	$-0.442562\pi$
$601$	8.79947	0.358938	0.179469	+	0.983764i	$0.442562\pi$
$602$	6.06247	0.247088
$603$	−3.48501	−0.141920
$604$	−5.88232	−0.239348
$605$	2.50995	0.102044
$606$	12.7558	0.518167
$607$	26.4912	1.07525	0.537623	−	0.843185i	$-0.319322\pi$
$607$	26.4912	1.07525	0.537623	+	0.843185i	$0.319322\pi$
$608$	−6.45136	−0.261637
$609$	1.43342	0.0580852
$610$	−2.69151	−0.108976
$611$	8.39989	0.339823
$612$	2.08073	0.0841084
$613$	0.454355	0.0183512	0.00917561	−	0.999958i	$-0.497079\pi$
$613$	0.454355	0.0183512	0.00917561	+	0.999958i	$0.497079\pi$
$614$	−14.5542	−0.587359
$615$	0.952377	0.0384035
$616$	0.999268	0.0402617
$617$	−21.8329	−0.878961	−0.439480	−	0.898252i	$-0.644837\pi$
$617$	−21.8329	−0.878961	−0.439480	+	0.898252i	$0.644837\pi$
$618$	10.9744	0.441456
$619$	−8.17869	−0.328729	−0.164365	−	0.986400i	$-0.552557\pi$
$619$	−8.17869	−0.328729	−0.164365	+	0.986400i	$0.552557\pi$
$620$	−0.312935	−0.0125678
$621$	2.43644	0.0977709
$622$	14.2361	0.570818
$623$	−4.40186	−0.176357
$624$	−8.98173	−0.359557
$625$	23.5407	0.941626
$626$	−9.28440	−0.371079
$627$	−23.1434	−0.924258
$628$	1.52618	0.0609012
$629$	1.57369	0.0627469
$630$	0.239049	0.00952394
$631$	−39.2162	−1.56117	−0.780586	−	0.625048i	$-0.785079\pi$
$631$	−39.2162	−1.56117	−0.780586	+	0.625048i	$0.785079\pi$
$632$	−9.47573	−0.376924
$633$	10.0962	0.401286
$634$	−28.0181	−1.11274
$635$	5.87092	0.232980
$636$	0.910655	0.0361098
$637$	28.8027	1.14120
$638$	2.05633	0.0814111
$639$	0.00804348	0.000318195 0
$640$	0.312935	0.0123699
$641$	19.1393	0.755956	0.377978	−	0.925815i	$-0.376619\pi$
$641$	19.1393	0.755956	0.377978	+	0.925815i	$0.376619\pi$
$642$	−1.63011	−0.0643353
$643$	11.7956	0.465173	0.232586	−	0.972576i	$-0.425281\pi$
$643$	11.7956	0.465173	0.232586	+	0.972576i	$0.425281\pi$
$644$	−0.403853	−0.0159140
$645$	6.81080	0.268175
$646$	−10.1732	−0.400259
$647$	14.4164	0.566766	0.283383	−	0.959007i	$-0.408543\pi$
$647$	14.4164	0.566766	0.283383	+	0.959007i	$0.408543\pi$
$648$	11.2174	0.440662
$649$	−6.00154	−0.235581
$650$	−21.1847	−0.830933
$651$	1.20320	0.0471573
$652$	2.51420	0.0984637
$653$	−2.33798	−0.0914922	−0.0457461	−	0.998953i	$-0.514567\pi$
$653$	−2.33798	−0.0914922	−0.0457461	+	0.998953i	$0.514567\pi$
$654$	10.2749	0.401780
$655$	5.58894	0.218378
$656$	−1.46432	−0.0571722
$657$	19.2125	0.749550
$658$	1.12526	0.0438672
$659$	−5.65461	−0.220272	−0.110136	−	0.993917i	$-0.535129\pi$
$659$	−5.65461	−0.220272	−0.110136	+	0.993917i	$0.535129\pi$
$660$	1.12262	0.0436977
$661$	10.1586	0.395124	0.197562	−	0.980290i	$-0.436698\pi$
$661$	10.1586	0.395124	0.197562	+	0.980290i	$0.436698\pi$
$662$	10.8803	0.422874
$663$	−14.1633	−0.550059
$664$	2.75363	0.106862
$665$	−1.16877	−0.0453229
$666$	−1.31680	−0.0510251
$667$	−0.831064	−0.0321789
$668$	−24.2794	−0.939397
$669$	61.2028	2.36624
$670$	−0.826512	−0.0319309
$671$	14.8457	0.573113
$672$	−1.20320	−0.0464146
$673$	11.2665	0.434293	0.217147	−	0.976139i	$-0.430325\pi$
$673$	11.2665	0.434293	0.217147	+	0.976139i	$0.430325\pi$
$674$	13.5609	0.522348
$675$	17.1212	0.658997
$676$	5.67611	0.218312
$677$	41.3456	1.58904	0.794520	−	0.607238i	$-0.207723\pi$
$677$	41.3456	1.58904	0.794520	+	0.607238i	$0.207723\pi$
$678$	14.7306	0.565725
$679$	0.578926	0.0222171
$680$	0.493470	0.0189237
$681$	7.36040	0.282051
$682$	1.72607	0.0660948
$683$	28.2342	1.08035	0.540176	−	0.841552i	$-0.318358\pi$
$683$	28.2342	1.08035	0.540176	+	0.841552i	$0.318358\pi$
$684$	8.51256	0.325486
$685$	−3.18499	−0.121692
$686$	7.91093	0.302041
$687$	−34.7339	−1.32518
$688$	−10.4719	−0.399239
$689$	−1.89357	−0.0721391
$690$	−0.453703	−0.0172722
$691$	−2.22542	−0.0846588	−0.0423294	−	0.999104i	$-0.513478\pi$
$691$	−2.22542	−0.0846588	−0.0423294	+	0.999104i	$0.513478\pi$
$692$	3.96621	0.150773
$693$	−1.31853	−0.0500870
$694$	34.7350	1.31852
$695$	2.14075	0.0812033
$696$	−2.47600	−0.0938526
$697$	−2.30910	−0.0874635
$698$	9.31074	0.352417
$699$	29.0359	1.09824
$700$	−2.83793	−0.107264
$701$	13.8097	0.521584	0.260792	−	0.965395i	$-0.416016\pi$
$701$	13.8097	0.521584	0.260792	+	0.965395i	$0.416016\pi$
$702$	−15.0938	−0.569679
$703$	6.43818	0.242820
$704$	−1.72607	−0.0650539
$705$	1.26416	0.0476110
$706$	−15.6447	−0.588798
$707$	−3.55314	−0.133630
$708$	7.22636	0.271583
$709$	28.9325	1.08658	0.543292	−	0.839544i	$-0.317178\pi$
$709$	28.9325	1.08658	0.543292	+	0.839544i	$0.317178\pi$
$710$	0.00190761	7.15913e−5 0
$711$	12.5032	0.468907
$712$	7.60349	0.284953
$713$	−0.697590	−0.0261250
$714$	−1.89734	−0.0710062
$715$	−2.33430	−0.0872980
$716$	14.4775	0.541050
$717$	−14.2223	−0.531140
$718$	−18.8153	−0.702182
$719$	0.0762707	0.00284442	0.00142221	−	0.999999i	$-0.499547\pi$
$719$	0.0762707	0.00284442	0.00142221	+	0.999999i	$0.499547\pi$
$720$	−0.412918	−0.0153886
$721$	−3.05694	−0.113847
$722$	−22.6200	−0.841829
$723$	−18.9397	−0.704374
$724$	−13.2088	−0.490900
$725$	−5.84002	−0.216893
$726$	16.6697	0.618670
$727$	32.9259	1.22115	0.610577	−	0.791957i	$-0.290938\pi$
$727$	32.9259	1.22115	0.610577	+	0.791957i	$0.290938\pi$
$728$	2.50188	0.0927257
$729$	6.97538	0.258348
$730$	4.55648	0.168643
$731$	−16.5133	−0.610765
$732$	−17.8755	−0.660698
$733$	20.2466	0.747824	0.373912	−	0.927464i	$-0.378016\pi$
$733$	20.2466	0.747824	0.373912	+	0.927464i	$0.378016\pi$
$734$	−20.8679	−0.770249
$735$	4.33473	0.159889
$736$	0.697590	0.0257135
$737$	4.55883	0.167927
$738$	1.93217	0.0711243
$739$	−8.51039	−0.313060	−0.156530	−	0.987673i	$-0.550031\pi$
$739$	−8.51039	−0.313060	−0.156530	+	0.987673i	$0.550031\pi$
$740$	−0.312296	−0.0114802
$741$	−57.9443	−2.12864
$742$	−0.253665	−0.00931232
$743$	−47.0007	−1.72429	−0.862144	−	0.506664i	$-0.830879\pi$
$743$	−47.0007	−1.72429	−0.862144	+	0.506664i	$0.830879\pi$
$744$	−2.07834	−0.0761957
$745$	−7.52555	−0.275715
$746$	14.2509	0.521761
$747$	−3.63342	−0.132940
$748$	−2.72186	−0.0995210
$749$	0.454070	0.0165914
$750$	−6.44017	−0.235162
$751$	−23.1778	−0.845770	−0.422885	−	0.906183i	$-0.638983\pi$
$751$	−23.1778	−0.845770	−0.422885	+	0.906183i	$0.638983\pi$
$752$	−1.94370	−0.0708796
$753$	−34.6119	−1.26133
$754$	5.14846	0.187496
$755$	1.84079	0.0669931
$756$	−2.02199	−0.0735389
$757$	−18.9090	−0.687257	−0.343629	−	0.939106i	$-0.611656\pi$
$757$	−18.9090	−0.687257	−0.343629	+	0.939106i	$0.611656\pi$
$758$	34.6255	1.25766
$759$	2.50251	0.0908355
$760$	2.01886	0.0732317
$761$	−36.4775	−1.32231	−0.661154	−	0.750250i	$-0.729933\pi$
$761$	−36.4775	−1.32231	−0.661154	+	0.750250i	$0.729933\pi$
$762$	38.9914	1.41251
$763$	−2.86209	−0.103615
$764$	−8.38615	−0.303400
$765$	−0.651133	−0.0235418
$766$	−18.2824	−0.660571
$767$	−15.0261	−0.542561
$768$	2.07834	0.0749957
$769$	20.7333	0.747663	0.373831	−	0.927497i	$-0.378044\pi$
$769$	20.7333	0.747663	0.373831	+	0.927497i	$0.378044\pi$
$770$	−0.312706	−0.0112692
$771$	56.3235	2.02844
$772$	−23.1185	−0.832053
$773$	13.7605	0.494932	0.247466	−	0.968897i	$-0.420402\pi$
$773$	13.7605	0.494932	0.247466	+	0.968897i	$0.420402\pi$
$774$	13.8177	0.496667
$775$	−4.90207	−0.176088
$776$	−1.00000	−0.0358979
$777$	1.20075	0.0430765
$778$	−22.3836	−0.802491
$779$	−9.44688	−0.338469
$780$	2.81070	0.100639
$781$	−0.0105219	−0.000376503 0
$782$	1.10003	0.0393371
$783$	−4.16092	−0.148699
$784$	−6.66485	−0.238030
$785$	−0.477596	−0.0170461
$786$	37.1186	1.32398
$787$	0.465483	0.0165927	0.00829633	−	0.999966i	$-0.497359\pi$
$787$	0.465483	0.0165927	0.00829633	+	0.999966i	$0.497359\pi$
$788$	−4.08605	−0.145560
$789$	10.4687	0.372694
$790$	2.96529	0.105500
$791$	−4.10323	−0.145894
$792$	2.27755	0.0809293
$793$	37.1694	1.31992
$794$	8.31134	0.294958
$795$	−0.284976	−0.0101071
$796$	−4.21555	−0.149416
$797$	7.44292	0.263642	0.131821	−	0.991274i	$-0.457918\pi$
$797$	7.44292	0.263642	0.131821	+	0.991274i	$0.457918\pi$
$798$	−7.76230	−0.274782
$799$	−3.06504	−0.108433
$800$	4.90207	0.173314
$801$	−10.0328	−0.354492
$802$	−34.1044	−1.20427
$803$	−25.1324	−0.886902
$804$	−5.48922	−0.193590
$805$	0.126380	0.00445430
$806$	4.32159	0.152221
$807$	29.0848	1.02384
$808$	6.13748	0.215916
$809$	35.1316	1.23516	0.617581	−	0.786507i	$-0.288113\pi$
$809$	35.1316	1.23516	0.617581	+	0.786507i	$0.288113\pi$
$810$	−3.51033	−0.123340
$811$	1.52177	0.0534367	0.0267184	−	0.999643i	$-0.491494\pi$
$811$	1.52177	0.0534367	0.0267184	+	0.999643i	$0.491494\pi$
$812$	0.689695	0.0242036
$813$	−41.8140	−1.46648
$814$	1.72255	0.0603753
$815$	−0.786783	−0.0275598
$816$	3.27735	0.114730
$817$	−67.5582	−2.36356
$818$	14.9322	0.522092
$819$	−3.30122	−0.115354
$820$	0.458239	0.0160024
$821$	55.8502	1.94919	0.974593	−	0.223983i	$-0.0719060\pi$
$821$	55.8502	1.94919	0.974593	+	0.223983i	$0.0719060\pi$
$822$	−21.1529	−0.737791
$823$	−27.3941	−0.954899	−0.477450	−	0.878659i	$-0.658439\pi$
$823$	−27.3941	−0.954899	−0.477450	+	0.878659i	$0.658439\pi$
$824$	5.28037	0.183951
$825$	17.5855	0.612250
$826$	−2.01292	−0.0700383
$827$	48.9074	1.70068	0.850339	−	0.526235i	$-0.176397\pi$
$827$	48.9074	1.70068	0.850339	+	0.526235i	$0.176397\pi$
$828$	−0.920470	−0.0319885
$829$	−10.4792	−0.363956	−0.181978	−	0.983303i	$-0.558250\pi$
$829$	−10.4792	−0.363956	−0.181978	+	0.983303i	$0.558250\pi$
$830$	−0.861709	−0.0299104
$831$	43.0091	1.49197
$832$	−4.32159	−0.149824
$833$	−10.5098	−0.364144
$834$	14.2177	0.492317
$835$	7.59787	0.262935
$836$	−11.1355	−0.385130
$837$	−3.49265	−0.120724
$838$	−3.48102	−0.120250
$839$	−1.94724	−0.0672263	−0.0336132	−	0.999435i	$-0.510701\pi$
$839$	−1.94724	−0.0672263	−0.0336132	+	0.999435i	$0.510701\pi$
$840$	0.376525	0.0129914
$841$	−27.5807	−0.951059
$842$	3.46896	0.119548
$843$	−47.3188	−1.62974
$844$	4.85780	0.167212
$845$	−1.77626	−0.0611050
$846$	2.56472	0.0881768
$847$	−4.64337	−0.159548
$848$	0.438164	0.0150466
$849$	−43.9608	−1.50873
$850$	7.73011	0.265141
$851$	−0.696165	−0.0238642
$852$	0.0126693	0.000434042 0
$853$	−44.1674	−1.51226	−0.756131	−	0.654421i	$-0.772913\pi$
$853$	−44.1674	−1.51226	−0.756131	+	0.654421i	$0.772913\pi$
$854$	4.97926	0.170387
$855$	−2.66388	−0.0911029
$856$	−0.784333	−0.0268079
$857$	19.4323	0.663795	0.331898	−	0.943315i	$-0.392311\pi$
$857$	19.4323	0.663795	0.331898	+	0.943315i	$0.392311\pi$
$858$	−15.5031	−0.529268
$859$	7.19809	0.245596	0.122798	−	0.992432i	$-0.460813\pi$
$859$	7.19809	0.245596	0.122798	+	0.992432i	$0.460813\pi$
$860$	3.27704	0.111746
$861$	−1.76188	−0.0600447
$862$	−17.6028	−0.599554
$863$	−33.0272	−1.12426	−0.562129	−	0.827050i	$-0.690017\pi$
$863$	−33.0272	−1.12426	−0.562129	+	0.827050i	$0.690017\pi$
$864$	3.49265	0.118822
$865$	−1.24117	−0.0422010
$866$	−17.0381	−0.578978
$867$	−30.1637	−1.02441
$868$	0.578926	0.0196500
$869$	−16.3558	−0.554833
$870$	0.774829	0.0262692
$871$	11.4140	0.386748
$872$	4.94380	0.167418
$873$	1.31950	0.0446583
$874$	4.50040	0.152228
$875$	1.79392	0.0606456
$876$	30.2615	1.02244
$877$	−48.9149	−1.65174	−0.825869	−	0.563862i	$-0.809315\pi$
$877$	−48.9149	−1.65174	−0.825869	+	0.563862i	$0.809315\pi$
$878$	−32.0357	−1.08115
$879$	−31.7883	−1.07219
$880$	0.540150	0.0182084
$881$	30.0267	1.01163	0.505813	−	0.862643i	$-0.331193\pi$
$881$	30.0267	1.01163	0.505813	+	0.862643i	$0.331193\pi$
$882$	8.79426	0.296118
$883$	4.73472	0.159336	0.0796680	−	0.996821i	$-0.474614\pi$
$883$	4.73472	0.159336	0.0796680	+	0.996821i	$0.474614\pi$
$884$	−6.81474	−0.229204
$885$	−2.26138	−0.0760156
$886$	−29.2811	−0.983717
$887$	23.9721	0.804905	0.402453	−	0.915441i	$-0.368158\pi$
$887$	23.9721	0.804905	0.402453	+	0.915441i	$0.368158\pi$
$888$	−2.07409	−0.0696021
$889$	−10.8611	−0.364270
$890$	−2.37940	−0.0797577
$891$	19.3621	0.648655
$892$	29.4479	0.985989
$893$	−12.5395	−0.419619
$894$	−49.9804	−1.67160
$895$	−4.53053	−0.151439
$896$	−0.578926	−0.0193405
$897$	6.26556	0.209201
$898$	29.1142	0.971552
$899$	1.19134	0.0397333
$900$	−6.46828	−0.215609
$901$	0.690944	0.0230187
$902$	−2.52753	−0.0841576
$903$	−12.5999	−0.419298
$904$	7.08767	0.235732
$905$	4.13349	0.137402
$906$	12.2255	0.406164
$907$	−33.9887	−1.12858	−0.564288	−	0.825578i	$-0.690849\pi$
$907$	−33.9887	−1.12858	−0.564288	+	0.825578i	$0.690849\pi$
$908$	3.54148	0.117528
$909$	−8.09840	−0.268607
$910$	−0.782926	−0.0259537
$911$	−43.5115	−1.44160	−0.720800	−	0.693143i	$-0.756225\pi$
$911$	−43.5115	−1.44160	−0.720800	+	0.693143i	$0.756225\pi$
$912$	13.4081	0.443987
$913$	4.75297	0.157300
$914$	−23.1410	−0.765436
$915$	5.59388	0.184928
$916$	−16.7123	−0.552191
$917$	−10.3394	−0.341439
$918$	5.50759	0.181777
$919$	−13.7873	−0.454802	−0.227401	−	0.973801i	$-0.573023\pi$
$919$	−13.7873	−0.454802	−0.227401	+	0.973801i	$0.573023\pi$
$920$	−0.218301	−0.00719716
$921$	30.2485	0.996723
$922$	−36.8469	−1.21349
$923$	−0.0263438	−0.000867116 0
$924$	−2.07682	−0.0683224
$925$	−4.89206	−0.160850
$926$	−12.8881	−0.423529
$927$	−6.96745	−0.228841
$928$	−1.19134	−0.0391075
$929$	−10.1381	−0.332619	−0.166309	−	0.986074i	$-0.553185\pi$
$929$	−10.1381	−0.332619	−0.166309	+	0.986074i	$0.553185\pi$
$930$	0.650386	0.0213270
$931$	−42.9973	−1.40918
$932$	13.9707	0.457625
$933$	−29.5876	−0.968653
$934$	13.4363	0.439648
$935$	0.851766	0.0278557
$936$	5.70233	0.186387
$937$	−28.5892	−0.933969	−0.466984	−	0.884266i	$-0.654660\pi$
$937$	−28.5892	−0.933969	−0.466984	+	0.884266i	$0.654660\pi$
$938$	1.52903	0.0499247
$939$	19.2962	0.629706
$940$	0.608254	0.0198391
$941$	44.7425	1.45857	0.729283	−	0.684213i	$-0.239854\pi$
$941$	44.7425	1.45857	0.729283	+	0.684213i	$0.239854\pi$
$942$	−3.17192	−0.103347
$943$	1.02150	0.0332645
$944$	3.47699	0.113166
$945$	0.632751	0.0205834
$946$	−18.0753	−0.587680
$947$	−26.9835	−0.876846	−0.438423	−	0.898769i	$-0.644463\pi$
$947$	−26.9835	−0.876846	−0.438423	+	0.898769i	$0.644463\pi$
$948$	19.6938	0.639624
$949$	−62.9242	−2.04260
$950$	31.6250	1.02605
$951$	58.2311	1.88827
$952$	−0.912912	−0.0295876
$953$	2.69757	0.0873830	0.0436915	−	0.999045i	$-0.486088\pi$
$953$	2.69757	0.0873830	0.0436915	+	0.999045i	$0.486088\pi$
$954$	−0.578158	−0.0187185
$955$	2.62432	0.0849211
$956$	−6.84308	−0.221321
$957$	−4.27376	−0.138151
$958$	−4.47078	−0.144444
$959$	5.89217	0.190268
$960$	−0.650386	−0.0209911
$961$	1.00000	0.0322581
$962$	4.31276	0.139049
$963$	1.03493	0.0333500
$964$	−9.11288	−0.293506
$965$	7.23460	0.232890
$966$	0.839343	0.0270054
$967$	10.3054	0.331400	0.165700	−	0.986176i	$-0.447012\pi$
$967$	10.3054	0.331400	0.165700	+	0.986176i	$0.447012\pi$
$968$	8.02067	0.257794
$969$	21.1433	0.679222
$970$	0.312935	0.0100478
$971$	19.7728	0.634540	0.317270	−	0.948335i	$-0.397234\pi$
$971$	19.7728	0.634540	0.317270	+	0.948335i	$0.397234\pi$
$972$	−12.8357	−0.411704
$973$	−3.96035	−0.126963
$974$	29.3740	0.941203
$975$	44.0291	1.41006
$976$	−8.60086	−0.275307
$977$	−44.7616	−1.43205	−0.716025	−	0.698074i	$-0.754040\pi$
$977$	−44.7616	−1.43205	−0.716025	+	0.698074i	$0.754040\pi$
$978$	−5.22537	−0.167089
$979$	13.1242	0.419451
$980$	2.08567	0.0666242
$981$	−6.52334	−0.208274
$982$	15.2364	0.486213
$983$	−54.9649	−1.75311	−0.876553	−	0.481305i	$-0.840163\pi$
$983$	−54.9649	−1.75311	−0.876553	+	0.481305i	$0.840163\pi$
$984$	3.04336	0.0970189
$985$	1.27867	0.0407418
$986$	−1.87863	−0.0598276
$987$	−2.33867	−0.0744408
$988$	−27.8801	−0.886984
$989$	7.30512	0.232289
$990$	−0.712727	−0.0226520
$991$	30.4321	0.966709	0.483355	−	0.875425i	$-0.339418\pi$
$991$	30.4321	0.966709	0.483355	+	0.875425i	$0.339418\pi$
$992$	−1.00000	−0.0317500
$993$	−22.6129	−0.717600
$994$	−0.00352905	−0.000111935 0
$995$	1.31920	0.0418213
$996$	−5.72299	−0.181340
$997$	−27.3108	−0.864943	−0.432471	−	0.901648i	$-0.642358\pi$
$997$	−27.3108	−0.864943	−0.432471	+	0.901648i	$0.642358\pi$
$998$	−11.5106	−0.364362
$999$	−3.48552	−0.110277

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.f.1.18	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.f.1.18	✓	22	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.07834 q^{3} +1.00000 q^{4} -0.312935 q^{5} -2.07834 q^{6} +0.578926 q^{7} -1.00000 q^{8} +1.31950 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.07834 q^{3} +1.00000 q^{4} -0.312935 q^{5} -2.07834 q^{6} +0.578926 q^{7} -1.00000 q^{8} +1.31950 q^{9} +0.312935 q^{10} -1.72607 q^{11} +2.07834 q^{12} -4.32159 q^{13} -0.578926 q^{14} -0.650386 q^{15} +1.00000 q^{16} +1.57691 q^{17} -1.31950 q^{18} +6.45136 q^{19} -0.312935 q^{20} +1.20320 q^{21} +1.72607 q^{22} -0.697590 q^{23} -2.07834 q^{24} -4.90207 q^{25} +4.32159 q^{26} -3.49265 q^{27} +0.578926 q^{28} +1.19134 q^{29} +0.650386 q^{30} +1.00000 q^{31} -1.00000 q^{32} -3.58737 q^{33} -1.57691 q^{34} -0.181166 q^{35} +1.31950 q^{36} +0.997957 q^{37} -6.45136 q^{38} -8.98173 q^{39} +0.312935 q^{40} -1.46432 q^{41} -1.20320 q^{42} -10.4719 q^{43} -1.72607 q^{44} -0.412918 q^{45} +0.697590 q^{46} -1.94370 q^{47} +2.07834 q^{48} -6.66485 q^{49} +4.90207 q^{50} +3.27735 q^{51} -4.32159 q^{52} +0.438164 q^{53} +3.49265 q^{54} +0.540150 q^{55} -0.578926 q^{56} +13.4081 q^{57} -1.19134 q^{58} +3.47699 q^{59} -0.650386 q^{60} -8.60086 q^{61} -1.00000 q^{62} +0.763892 q^{63} +1.00000 q^{64} +1.35238 q^{65} +3.58737 q^{66} -2.64116 q^{67} +1.57691 q^{68} -1.44983 q^{69} +0.181166 q^{70} +0.00609586 q^{71} -1.31950 q^{72} +14.5604 q^{73} -0.997957 q^{74} -10.1882 q^{75} +6.45136 q^{76} -0.999268 q^{77} +8.98173 q^{78} +9.47573 q^{79} -0.312935 q^{80} -11.2174 q^{81} +1.46432 q^{82} -2.75363 q^{83} +1.20320 q^{84} -0.493470 q^{85} +10.4719 q^{86} +2.47600 q^{87} +1.72607 q^{88} -7.60349 q^{89} +0.412918 q^{90} -2.50188 q^{91} -0.697590 q^{92} +2.07834 q^{93} +1.94370 q^{94} -2.01886 q^{95} -2.07834 q^{96} +1.00000 q^{97} +6.66485 q^{98} -2.27755 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9}+O(q^{10}) \) 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9	\( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9} - 8 q^{13} + 11 q^{14} + q^{15} + 22 q^{16} - 4 q^{17} - 8 q^{18} - 23 q^{19} - 12 q^{21} + 2 q^{23} - 12 q^{25} + 8 q^{26} + 3 q^{27} - 11 q^{28} + 9 q^{29} - q^{30} + 22 q^{31} - 22 q^{32} + 4 q^{34} + 4 q^{35} + 8 q^{36} - 17 q^{37} + 23 q^{38} + 8 q^{39} - 21 q^{41} + 12 q^{42} - 7 q^{43} + 9 q^{45} - 2 q^{46} - 10 q^{47} - 27 q^{49} + 12 q^{50} - q^{51} - 8 q^{52} + 9 q^{53} - 3 q^{54} - 6 q^{55} + 11 q^{56} - q^{57} - 9 q^{58} - 12 q^{59} + q^{60} - 34 q^{61} - 22 q^{62} - 5 q^{63} + 22 q^{64} + 4 q^{65} - 31 q^{67} - 4 q^{68} - 51 q^{69} - 4 q^{70} - 15 q^{71} - 8 q^{72} + 3 q^{73} + 17 q^{74} - 24 q^{75} - 23 q^{76} + 24 q^{77} - 8 q^{78} - 23 q^{79} - 26 q^{81} + 21 q^{82} + 22 q^{83} - 12 q^{84} - 42 q^{85} + 7 q^{86} - 9 q^{87} - 36 q^{89} - 9 q^{90} - 6 q^{91} + 2 q^{92} + 10 q^{94} + 2 q^{95} + 22 q^{97} + 27 q^{98} - 25 q^{99}+O(q^{100}) \) 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9 - 8 * q^13 + 11 * q^14 + q^15 + 22 * q^16 - 4 * q^17 - 8 * q^18 - 23 * q^19 - 12 * q^21 + 2 * q^23 - 12 * q^25 + 8 * q^26 + 3 * q^27 - 11 * q^28 + 9 * q^29 - q^30 + 22 * q^31 - 22 * q^32 + 4 * q^34 + 4 * q^35 + 8 * q^36 - 17 * q^37 + 23 * q^38 + 8 * q^39 - 21 * q^41 + 12 * q^42 - 7 * q^43 + 9 * q^45 - 2 * q^46 - 10 * q^47 - 27 * q^49 + 12 * q^50 - q^51 - 8 * q^52 + 9 * q^53 - 3 * q^54 - 6 * q^55 + 11 * q^56 - q^57 - 9 * q^58 - 12 * q^59 + q^60 - 34 * q^61 - 22 * q^62 - 5 * q^63 + 22 * q^64 + 4 * q^65 - 31 * q^67 - 4 * q^68 - 51 * q^69 - 4 * q^70 - 15 * q^71 - 8 * q^72 + 3 * q^73 + 17 * q^74 - 24 * q^75 - 23 * q^76 + 24 * q^77 - 8 * q^78 - 23 * q^79 - 26 * q^81 + 21 * q^82 + 22 * q^83 - 12 * q^84 - 42 * q^85 + 7 * q^86 - 9 * q^87 - 36 * q^89 - 9 * q^90 - 6 * q^91 + 2 * q^92 + 10 * q^94 + 2 * q^95 + 22 * q^97 + 27 * q^98 - 25 * q^99

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