LMFDB - Embedded newform 4011.2.a.j.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.71722 q^{2} -1.00000 q^{3} +0.948829 q^{4} +0.183092 q^{5} -1.71722 q^{6} -1.00000 q^{7} -1.80509 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.71722 q^{2} -1.00000 q^{3} +0.948829 q^{4} +0.183092 q^{5} -1.71722 q^{6} -1.00000 q^{7} -1.80509 q^{8} +1.00000 q^{9} +0.314408 q^{10} +4.71803 q^{11} -0.948829 q^{12} +2.68057 q^{13} -1.71722 q^{14} -0.183092 q^{15} -4.99738 q^{16} +0.0323624 q^{17} +1.71722 q^{18} -3.44341 q^{19} +0.173723 q^{20} +1.00000 q^{21} +8.10187 q^{22} +6.22119 q^{23} +1.80509 q^{24} -4.96648 q^{25} +4.60312 q^{26} -1.00000 q^{27} -0.948829 q^{28} +7.51906 q^{29} -0.314408 q^{30} -6.42671 q^{31} -4.97141 q^{32} -4.71803 q^{33} +0.0555732 q^{34} -0.183092 q^{35} +0.948829 q^{36} -5.12574 q^{37} -5.91308 q^{38} -2.68057 q^{39} -0.330497 q^{40} +6.69305 q^{41} +1.71722 q^{42} -1.78467 q^{43} +4.47660 q^{44} +0.183092 q^{45} +10.6831 q^{46} +4.72390 q^{47} +4.99738 q^{48} +1.00000 q^{49} -8.52851 q^{50} -0.0323624 q^{51} +2.54341 q^{52} +11.6106 q^{53} -1.71722 q^{54} +0.863832 q^{55} +1.80509 q^{56} +3.44341 q^{57} +12.9118 q^{58} +3.45923 q^{59} -0.173723 q^{60} -2.89590 q^{61} -11.0360 q^{62} -1.00000 q^{63} +1.45778 q^{64} +0.490791 q^{65} -8.10187 q^{66} +5.66086 q^{67} +0.0307064 q^{68} -6.22119 q^{69} -0.314408 q^{70} +1.09703 q^{71} -1.80509 q^{72} -0.651871 q^{73} -8.80199 q^{74} +4.96648 q^{75} -3.26721 q^{76} -4.71803 q^{77} -4.60312 q^{78} +4.08066 q^{79} -0.914980 q^{80} +1.00000 q^{81} +11.4934 q^{82} -4.51743 q^{83} +0.948829 q^{84} +0.00592529 q^{85} -3.06467 q^{86} -7.51906 q^{87} -8.51645 q^{88} +11.6975 q^{89} +0.314408 q^{90} -2.68057 q^{91} +5.90285 q^{92} +6.42671 q^{93} +8.11196 q^{94} -0.630461 q^{95} +4.97141 q^{96} +12.8070 q^{97} +1.71722 q^{98} +4.71803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9}+O(q^{10}) $ 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9	$ 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9} - q^{10} + 13 q^{11} - 34 q^{12} - q^{13} - 2 q^{15} + 54 q^{16} + q^{19} - 22 q^{20} + 26 q^{21} + 17 q^{22} - 3 q^{23} + 48 q^{25} + 6 q^{26} - 26 q^{27} - 34 q^{28} + 23 q^{29} + q^{30} + 18 q^{31} + 10 q^{32} - 13 q^{33} - 19 q^{34} - 2 q^{35} + 34 q^{36} + 23 q^{37} - 15 q^{38} + q^{39} + 14 q^{40} - 4 q^{41} + 5 q^{43} + 60 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{47} - 54 q^{48} + 26 q^{49} + 26 q^{50} + 19 q^{52} + 31 q^{53} + 41 q^{55} - q^{57} + 19 q^{58} - 2 q^{59} + 22 q^{60} - 2 q^{61} - 35 q^{62} - 26 q^{63} + 132 q^{64} + 40 q^{65} - 17 q^{66} + 47 q^{67} - 60 q^{68} + 3 q^{69} + q^{70} + 16 q^{71} - 23 q^{73} + 34 q^{74} - 48 q^{75} + 72 q^{76} - 13 q^{77} - 6 q^{78} + 14 q^{79} - 21 q^{80} + 26 q^{81} + 60 q^{82} - 4 q^{83} + 34 q^{84} + 36 q^{85} + 21 q^{86} - 23 q^{87} + 67 q^{88} + 14 q^{89} - q^{90} + q^{91} + 20 q^{92} - 18 q^{93} + 58 q^{94} - 4 q^{95} - 10 q^{96} + 48 q^{97} + 13 q^{99}+O(q^{100}) $ 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9 - q^10 + 13 * q^11 - 34 * q^12 - q^13 - 2 * q^15 + 54 * q^16 + q^19 - 22 * q^20 + 26 * q^21 + 17 * q^22 - 3 * q^23 + 48 * q^25 + 6 * q^26 - 26 * q^27 - 34 * q^28 + 23 * q^29 + q^30 + 18 * q^31 + 10 * q^32 - 13 * q^33 - 19 * q^34 - 2 * q^35 + 34 * q^36 + 23 * q^37 - 15 * q^38 + q^39 + 14 * q^40 - 4 * q^41 + 5 * q^43 + 60 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^47 - 54 * q^48 + 26 * q^49 + 26 * q^50 + 19 * q^52 + 31 * q^53 + 41 * q^55 - q^57 + 19 * q^58 - 2 * q^59 + 22 * q^60 - 2 * q^61 - 35 * q^62 - 26 * q^63 + 132 * q^64 + 40 * q^65 - 17 * q^66 + 47 * q^67 - 60 * q^68 + 3 * q^69 + q^70 + 16 * q^71 - 23 * q^73 + 34 * q^74 - 48 * q^75 + 72 * q^76 - 13 * q^77 - 6 * q^78 + 14 * q^79 - 21 * q^80 + 26 * q^81 + 60 * q^82 - 4 * q^83 + 34 * q^84 + 36 * q^85 + 21 * q^86 - 23 * q^87 + 67 * q^88 + 14 * q^89 - q^90 + q^91 + 20 * q^92 - 18 * q^93 + 58 * q^94 - 4 * q^95 - 10 * q^96 + 48 * q^97 + 13 * 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 $

$2$	1.71722	1.21425	0.607127	−	0.794605i	$-0.292322\pi$
$2$	1.71722	1.21425	0.607127	+	0.794605i	$0.292322\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.948829	0.474415
$5$	0.183092	0.0818811	0.0409406	−	0.999162i	$-0.486965\pi$
$5$	0.183092	0.0818811	0.0409406	+	0.999162i	$0.486965\pi$
$6$	−1.71722	−0.701050
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.80509	−0.638194
$9$	1.00000	0.333333
$10$	0.314408	0.0994246
$11$	4.71803	1.42254	0.711269	−	0.702920i	$-0.248121\pi$
$11$	4.71803	1.42254	0.711269	+	0.702920i	$0.248121\pi$
$12$	−0.948829	−0.273903
$13$	2.68057	0.743457	0.371729	−	0.928341i	$-0.378765\pi$
$13$	2.68057	0.743457	0.371729	+	0.928341i	$0.378765\pi$
$14$	−1.71722	−0.458945
$15$	−0.183092	−0.0472741
$16$	−4.99738	−1.24935
$17$	0.0323624	0.00784903	0.00392452	−	0.999992i	$-0.498751\pi$
$17$	0.0323624	0.00784903	0.00392452	+	0.999992i	$0.498751\pi$
$18$	1.71722	0.404752
$19$	−3.44341	−0.789973	−0.394987	−	0.918687i	$-0.629251\pi$
$19$	−3.44341	−0.789973	−0.394987	+	0.918687i	$0.629251\pi$
$20$	0.173723	0.0388456
$21$	1.00000	0.218218
$22$	8.10187	1.72732
$23$	6.22119	1.29721	0.648604	−	0.761126i	$-0.275353\pi$
$23$	6.22119	1.29721	0.648604	+	0.761126i	$0.275353\pi$
$24$	1.80509	0.368462
$25$	−4.96648	−0.993295
$26$	4.60312	0.902746
$27$	−1.00000	−0.192450
$28$	−0.948829	−0.179312
$29$	7.51906	1.39625	0.698127	−	0.715974i	$-0.254017\pi$
$29$	7.51906	1.39625	0.698127	+	0.715974i	$0.254017\pi$
$30$	−0.314408	−0.0574028
$31$	−6.42671	−1.15427	−0.577135	−	0.816648i	$-0.695830\pi$
$31$	−6.42671	−1.15427	−0.577135	+	0.816648i	$0.695830\pi$
$32$	−4.97141	−0.878829
$33$	−4.71803	−0.821303
$34$	0.0555732	0.00953073
$35$	−0.183092	−0.0309482
$36$	0.948829	0.158138
$37$	−5.12574	−0.842666	−0.421333	−	0.906906i	$-0.638438\pi$
$37$	−5.12574	−0.842666	−0.421333	+	0.906906i	$0.638438\pi$
$38$	−5.91308	−0.959229
$39$	−2.68057	−0.429235
$40$	−0.330497	−0.0522561
$41$	6.69305	1.04528	0.522639	−	0.852554i	$-0.324948\pi$
$41$	6.69305	1.04528	0.522639	+	0.852554i	$0.324948\pi$
$42$	1.71722	0.264972
$43$	−1.78467	−0.272160	−0.136080	−	0.990698i	$-0.543450\pi$
$43$	−1.78467	−0.272160	−0.136080	+	0.990698i	$0.543450\pi$
$44$	4.47660	0.674873
$45$	0.183092	0.0272937
$46$	10.6831	1.57514
$47$	4.72390	0.689052	0.344526	−	0.938777i	$-0.388040\pi$
$47$	4.72390	0.689052	0.344526	+	0.938777i	$0.388040\pi$
$48$	4.99738	0.721310
$49$	1.00000	0.142857
$50$	−8.52851	−1.20611
$51$	−0.0323624	−0.00453164
$52$	2.54341	0.352707
$53$	11.6106	1.59484	0.797420	−	0.603425i	$-0.206198\pi$
$53$	11.6106	1.59484	0.797420	+	0.603425i	$0.206198\pi$
$54$	−1.71722	−0.233683
$55$	0.863832	0.116479
$56$	1.80509	0.241215
$57$	3.44341	0.456091
$58$	12.9118	1.69541
$59$	3.45923	0.450353	0.225176	−	0.974318i	$-0.427704\pi$
$59$	3.45923	0.450353	0.225176	+	0.974318i	$0.427704\pi$
$60$	−0.173723	−0.0224275
$61$	−2.89590	−0.370782	−0.185391	−	0.982665i	$-0.559355\pi$
$61$	−2.89590	−0.370782	−0.185391	+	0.982665i	$0.559355\pi$
$62$	−11.0360	−1.40158
$63$	−1.00000	−0.125988
$64$	1.45778	0.182223
$65$	0.490791	0.0608751
$66$	−8.10187	−0.997271
$67$	5.66086	0.691585	0.345792	−	0.938311i	$-0.387610\pi$
$67$	5.66086	0.691585	0.345792	+	0.938311i	$0.387610\pi$
$68$	0.0307064	0.00372370
$69$	−6.22119	−0.748943
$70$	−0.314408	−0.0375790
$71$	1.09703	0.130194	0.0650970	−	0.997879i	$-0.479264\pi$
$71$	1.09703	0.130194	0.0650970	+	0.997879i	$0.479264\pi$
$72$	−1.80509	−0.212731
$73$	−0.651871	−0.0762957	−0.0381479	−	0.999272i	$-0.512146\pi$
$73$	−0.651871	−0.0762957	−0.0381479	+	0.999272i	$0.512146\pi$
$74$	−8.80199	−1.02321
$75$	4.96648	0.573479
$76$	−3.26721	−0.374775
$77$	−4.71803	−0.537669
$78$	−4.60312	−0.521201
$79$	4.08066	0.459110	0.229555	−	0.973296i	$-0.426273\pi$
$79$	4.08066	0.459110	0.229555	+	0.973296i	$0.426273\pi$
$80$	−0.914980	−0.102298
$81$	1.00000	0.111111
$82$	11.4934	1.26923
$83$	−4.51743	−0.495853	−0.247926	−	0.968779i	$-0.579749\pi$
$83$	−4.51743	−0.495853	−0.247926	+	0.968779i	$0.579749\pi$
$84$	0.948829	0.103526
$85$	0.00592529	0.000642688 0
$86$	−3.06467	−0.330472
$87$	−7.51906	−0.806127
$88$	−8.51645	−0.907856
$89$	11.6975	1.23993	0.619965	−	0.784630i	$-0.287147\pi$
$89$	11.6975	1.23993	0.619965	+	0.784630i	$0.287147\pi$
$90$	0.314408	0.0331415
$91$	−2.68057	−0.281000
$92$	5.90285	0.615415
$93$	6.42671	0.666419
$94$	8.11196	0.836685
$95$	−0.630461	−0.0646839
$96$	4.97141	0.507392
$97$	12.8070	1.30036	0.650178	−	0.759782i	$-0.274694\pi$
$97$	12.8070	1.30036	0.650178	+	0.759782i	$0.274694\pi$
$98$	1.71722	0.173465
$99$	4.71803	0.474180
$100$	−4.71234	−0.471234
$101$	11.0060	1.09514	0.547571	−	0.836759i	$-0.315553\pi$
$101$	11.0060	1.09514	0.547571	+	0.836759i	$0.315553\pi$
$102$	−0.0555732	−0.00550257
$103$	0.615149	0.0606124	0.0303062	−	0.999541i	$-0.490352\pi$
$103$	0.615149	0.0606124	0.0303062	+	0.999541i	$0.490352\pi$
$104$	−4.83867	−0.474470
$105$	0.183092	0.0178679
$106$	19.9379	1.93654
$107$	10.3843	1.00388	0.501942	−	0.864901i	$-0.332619\pi$
$107$	10.3843	1.00388	0.501942	+	0.864901i	$0.332619\pi$
$108$	−0.948829	−0.0913012
$109$	13.0645	1.25135	0.625675	−	0.780084i	$-0.284824\pi$
$109$	13.0645	1.25135	0.625675	+	0.780084i	$0.284824\pi$
$110$	1.48339	0.141435
$111$	5.12574	0.486513
$112$	4.99738	0.472208
$113$	2.70642	0.254599	0.127299	−	0.991864i	$-0.459369\pi$
$113$	2.70642	0.254599	0.127299	+	0.991864i	$0.459369\pi$
$114$	5.91308	0.553811
$115$	1.13905	0.106217
$116$	7.13430	0.662403
$117$	2.68057	0.247819
$118$	5.94024	0.546843
$119$	−0.0323624	−0.00296666
$120$	0.330497	0.0301701
$121$	11.2598	1.02362
$122$	−4.97289	−0.450224
$123$	−6.69305	−0.603492
$124$	−6.09785	−0.547603
$125$	−1.82478	−0.163213
$126$	−1.71722	−0.152982
$127$	0.0244773	0.00217201	0.00108601	−	0.999999i	$-0.499654\pi$
$127$	0.0244773	0.00217201	0.00108601	+	0.999999i	$0.499654\pi$
$128$	12.4461	1.10009
$129$	1.78467	0.157132
$130$	0.842794	0.0739179
$131$	−11.7894	−1.03004	−0.515020	−	0.857178i	$-0.672216\pi$
$131$	−11.7894	−1.03004	−0.515020	+	0.857178i	$0.672216\pi$
$132$	−4.47660	−0.389638
$133$	3.44341	0.298582
$134$	9.72092	0.839760
$135$	−0.183092	−0.0157580
$136$	−0.0584169	−0.00500921
$137$	−1.47437	−0.125964	−0.0629819	−	0.998015i	$-0.520061\pi$
$137$	−1.47437	−0.125964	−0.0629819	+	0.998015i	$0.520061\pi$
$138$	−10.6831	−0.909408
$139$	16.1077	1.36624	0.683120	−	0.730306i	$-0.260623\pi$
$139$	16.1077	1.36624	0.683120	+	0.730306i	$0.260623\pi$
$140$	−0.173723	−0.0146823
$141$	−4.72390	−0.397824
$142$	1.88384	0.158089
$143$	12.6470	1.05760
$144$	−4.99738	−0.416448
$145$	1.37668	0.114327
$146$	−1.11940	−0.0926425
$147$	−1.00000	−0.0824786
$148$	−4.86345	−0.399773
$149$	−8.08916	−0.662690	−0.331345	−	0.943510i	$-0.607502\pi$
$149$	−8.08916	−0.662690	−0.331345	+	0.943510i	$0.607502\pi$
$150$	8.52851	0.696350
$151$	20.8330	1.69536	0.847682	−	0.530505i	$-0.177998\pi$
$151$	20.8330	1.69536	0.847682	+	0.530505i	$0.177998\pi$
$152$	6.21566	0.504157
$153$	0.0323624	0.00261634
$154$	−8.10187	−0.652867
$155$	−1.17668	−0.0945130
$156$	−2.54341	−0.203635
$157$	−20.7117	−1.65297	−0.826486	−	0.562957i	$-0.809664\pi$
$157$	−20.7117	−1.65297	−0.826486	+	0.562957i	$0.809664\pi$
$158$	7.00738	0.557477
$159$	−11.6106	−0.920781
$160$	−0.910224	−0.0719595
$161$	−6.22119	−0.490299
$162$	1.71722	0.134917
$163$	−18.2273	−1.42767	−0.713837	−	0.700312i	$-0.753044\pi$
$163$	−18.2273	−1.42767	−0.713837	+	0.700312i	$0.753044\pi$
$164$	6.35056	0.495895
$165$	−0.863832	−0.0672492
$166$	−7.75740	−0.602091
$167$	−2.67188	−0.206756	−0.103378	−	0.994642i	$-0.532965\pi$
$167$	−2.67188	−0.206756	−0.103378	+	0.994642i	$0.532965\pi$
$168$	−1.80509	−0.139265
$169$	−5.81453	−0.447272
$170$	0.0101750	0.000780387 0
$171$	−3.44341	−0.263324
$172$	−1.69335	−0.129117
$173$	2.94799	0.224131	0.112066	−	0.993701i	$-0.464253\pi$
$173$	2.94799	0.224131	0.112066	+	0.993701i	$0.464253\pi$
$174$	−12.9118	−0.978844
$175$	4.96648	0.375430
$176$	−23.5778	−1.77724
$177$	−3.45923	−0.260011
$178$	20.0871	1.50559
$179$	14.5121	1.08469	0.542344	−	0.840156i	$-0.317537\pi$
$179$	14.5121	1.08469	0.542344	+	0.840156i	$0.317537\pi$
$180$	0.173723	0.0129485
$181$	−6.12681	−0.455402	−0.227701	−	0.973731i	$-0.573121\pi$
$181$	−6.12681	−0.455402	−0.227701	+	0.973731i	$0.573121\pi$
$182$	−4.60312	−0.341206
$183$	2.89590	0.214071
$184$	−11.2298	−0.827871
$185$	−0.938480	−0.0689985
$186$	11.0360	0.809202
$187$	0.152687	0.0111656
$188$	4.48218	0.326896
$189$	1.00000	0.0727393
$190$	−1.08264	−0.0785428
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	−1.45778	−0.105206
$193$	6.49620	0.467606	0.233803	−	0.972284i	$-0.424883\pi$
$193$	6.49620	0.467606	0.233803	+	0.972284i	$0.424883\pi$
$194$	21.9924	1.57896
$195$	−0.490791	−0.0351463
$196$	0.948829	0.0677735
$197$	8.18842	0.583401	0.291700	−	0.956510i	$-0.405779\pi$
$197$	8.18842	0.583401	0.291700	+	0.956510i	$0.405779\pi$
$198$	8.10187	0.575775
$199$	2.92719	0.207503	0.103752	−	0.994603i	$-0.466915\pi$
$199$	2.92719	0.207503	0.103752	+	0.994603i	$0.466915\pi$
$200$	8.96492	0.633916
$201$	−5.66086	−0.399287
$202$	18.8997	1.32978
$203$	−7.51906	−0.527734
$204$	−0.0307064	−0.00214988
$205$	1.22544	0.0855886
$206$	1.05634	0.0735989
$207$	6.22119	0.432403
$208$	−13.3958	−0.928835
$209$	−16.2461	−1.12377
$210$	0.314408	0.0216962
$211$	15.9483	1.09793	0.548964	−	0.835846i	$-0.315022\pi$
$211$	15.9483	1.09793	0.548964	+	0.835846i	$0.315022\pi$
$212$	11.0165	0.756615
$213$	−1.09703	−0.0751676
$214$	17.8320	1.21897
$215$	−0.326759	−0.0222848
$216$	1.80509	0.122821
$217$	6.42671	0.436273
$218$	22.4345	1.51946
$219$	0.651871	0.0440494
$220$	0.819629	0.0552594
$221$	0.0867498	0.00583542
$222$	8.80199	0.590751
$223$	−21.3944	−1.43267	−0.716337	−	0.697754i	$-0.754183\pi$
$223$	−21.3944	−1.43267	−0.716337	+	0.697754i	$0.754183\pi$
$224$	4.97141	0.332166
$225$	−4.96648	−0.331098
$226$	4.64751	0.309148
$227$	22.4814	1.49214	0.746072	−	0.665866i	$-0.231938\pi$
$227$	22.4814	1.49214	0.746072	+	0.665866i	$0.231938\pi$
$228$	3.26721	0.216376
$229$	−10.4645	−0.691512	−0.345756	−	0.938324i	$-0.612377\pi$
$229$	−10.4645	−0.691512	−0.345756	+	0.938324i	$0.612377\pi$
$230$	1.95599	0.128974
$231$	4.71803	0.310423
$232$	−13.5725	−0.891081
$233$	5.54139	0.363029	0.181514	−	0.983388i	$-0.441900\pi$
$233$	5.54139	0.363029	0.181514	+	0.983388i	$0.441900\pi$
$234$	4.60312	0.300915
$235$	0.864908	0.0564204
$236$	3.28222	0.213654
$237$	−4.08066	−0.265068
$238$	−0.0555732	−0.00360228
$239$	−12.4843	−0.807543	−0.403771	−	0.914860i	$-0.632301\pi$
$239$	−12.4843	−0.807543	−0.403771	+	0.914860i	$0.632301\pi$
$240$	0.914980	0.0590617
$241$	10.5727	0.681045	0.340523	−	0.940236i	$-0.389396\pi$
$241$	10.5727	0.681045	0.340523	+	0.940236i	$0.389396\pi$
$242$	19.3355	1.24293
$243$	−1.00000	−0.0641500
$244$	−2.74772	−0.175905
$245$	0.183092	0.0116973
$246$	−11.4934	−0.732793
$247$	−9.23032	−0.587311
$248$	11.6008	0.736649
$249$	4.51743	0.286281
$250$	−3.13354	−0.198183
$251$	−15.7595	−0.994734	−0.497367	−	0.867540i	$-0.665700\pi$
$251$	−15.7595	−0.994734	−0.497367	+	0.867540i	$0.665700\pi$
$252$	−0.948829	−0.0597706
$253$	29.3517	1.84533
$254$	0.0420329	0.00263738
$255$	−0.00592529	−0.000371056 0
$256$	18.4571	1.15357
$257$	−4.18653	−0.261148	−0.130574	−	0.991439i	$-0.541682\pi$
$257$	−4.18653	−0.261148	−0.130574	+	0.991439i	$0.541682\pi$
$258$	3.06467	0.190798
$259$	5.12574	0.318498
$260$	0.465677	0.0288801
$261$	7.51906	0.465418
$262$	−20.2449	−1.25073
$263$	1.33947	0.0825953	0.0412977	−	0.999147i	$-0.486851\pi$
$263$	1.33947	0.0825953	0.0412977	+	0.999147i	$0.486851\pi$
$264$	8.51645	0.524151
$265$	2.12581	0.130587
$266$	5.91308	0.362554
$267$	−11.6975	−0.715874
$268$	5.37119	0.328098
$269$	−6.74442	−0.411214	−0.205607	−	0.978635i	$-0.565917\pi$
$269$	−6.74442	−0.411214	−0.205607	+	0.978635i	$0.565917\pi$
$270$	−0.314408	−0.0191343
$271$	13.8097	0.838882	0.419441	−	0.907783i	$-0.362226\pi$
$271$	13.8097	0.838882	0.419441	+	0.907783i	$0.362226\pi$
$272$	−0.161727	−0.00980615
$273$	2.68057	0.162236
$274$	−2.53181	−0.152952
$275$	−23.4320	−1.41300
$276$	−5.90285	−0.355310
$277$	27.3120	1.64102	0.820511	−	0.571631i	$-0.193689\pi$
$277$	27.3120	1.64102	0.820511	+	0.571631i	$0.193689\pi$
$278$	27.6605	1.65896
$279$	−6.42671	−0.384757
$280$	0.330497	0.0197509
$281$	−6.58671	−0.392930	−0.196465	−	0.980511i	$-0.562946\pi$
$281$	−6.58671	−0.392930	−0.196465	+	0.980511i	$0.562946\pi$
$282$	−8.11196	−0.483060
$283$	−8.49850	−0.505183	−0.252592	−	0.967573i	$-0.581283\pi$
$283$	−8.49850	−0.505183	−0.252592	+	0.967573i	$0.581283\pi$
$284$	1.04090	0.0617660
$285$	0.630461	0.0373453
$286$	21.7176	1.28419
$287$	−6.69305	−0.395078
$288$	−4.97141	−0.292943
$289$	−16.9990	−0.999938
$290$	2.36405	0.138822
$291$	−12.8070	−0.750761
$292$	−0.618514	−0.0361958
$293$	−8.66147	−0.506009	−0.253004	−	0.967465i	$-0.581419\pi$
$293$	−8.66147	−0.506009	−0.253004	+	0.967465i	$0.581419\pi$
$294$	−1.71722	−0.100150
$295$	0.633356	0.0368754
$296$	9.25240	0.537785
$297$	−4.71803	−0.273768
$298$	−13.8908	−0.804675
$299$	16.6764	0.964419
$300$	4.71234	0.272067
$301$	1.78467	0.102867
$302$	35.7747	2.05860
$303$	−11.0060	−0.632280
$304$	17.2081	0.986950
$305$	−0.530216	−0.0303601
$306$	0.0555732	0.00317691
$307$	−17.5001	−0.998786	−0.499393	−	0.866376i	$-0.666444\pi$
$307$	−17.5001	−0.998786	−0.499393	+	0.866376i	$0.666444\pi$
$308$	−4.47660	−0.255078
$309$	−0.615149	−0.0349946
$310$	−2.02061	−0.114763
$311$	−29.9182	−1.69651	−0.848253	−	0.529591i	$-0.822346\pi$
$311$	−29.9182	−1.69651	−0.848253	+	0.529591i	$0.822346\pi$
$312$	4.83867	0.273935
$313$	−26.1507	−1.47813	−0.739063	−	0.673637i	$-0.764731\pi$
$313$	−26.1507	−1.47813	−0.739063	+	0.673637i	$0.764731\pi$
$314$	−35.5664	−2.00713
$315$	−0.183092	−0.0103161
$316$	3.87185	0.217809
$317$	3.64417	0.204677	0.102338	−	0.994750i	$-0.467368\pi$
$317$	3.64417	0.204677	0.102338	+	0.994750i	$0.467368\pi$
$318$	−19.9379	−1.11806
$319$	35.4751	1.98622
$320$	0.266908	0.0149206
$321$	−10.3843	−0.579592
$322$	−10.6831	−0.595347
$323$	−0.111437	−0.00620053
$324$	0.948829	0.0527127
$325$	−13.3130	−0.738473
$326$	−31.3002	−1.73356
$327$	−13.0645	−0.722467
$328$	−12.0815	−0.667091
$329$	−4.72390	−0.260437
$330$	−1.48339	−0.0816577
$331$	−19.3670	−1.06451	−0.532253	−	0.846585i	$-0.678655\pi$
$331$	−19.3670	−1.06451	−0.532253	+	0.846585i	$0.678655\pi$
$332$	−4.28627	−0.235240
$333$	−5.12574	−0.280889
$334$	−4.58820	−0.251055
$335$	1.03646	0.0566277
$336$	−4.99738	−0.272630
$337$	10.4010	0.566579	0.283290	−	0.959034i	$-0.408574\pi$
$337$	10.4010	0.566579	0.283290	+	0.959034i	$0.408574\pi$
$338$	−9.98480	−0.543102
$339$	−2.70642	−0.146993
$340$	0.00562209	0.000304901 0
$341$	−30.3214	−1.64199
$342$	−5.91308	−0.319743
$343$	−1.00000	−0.0539949
$344$	3.22149	0.173691
$345$	−1.13905	−0.0613243
$346$	5.06233	0.272152
$347$	−10.3442	−0.555305	−0.277653	−	0.960682i	$-0.589556\pi$
$347$	−10.3442	−0.555305	−0.277653	+	0.960682i	$0.589556\pi$
$348$	−7.13430	−0.382439
$349$	−9.28407	−0.496965	−0.248482	−	0.968636i	$-0.579932\pi$
$349$	−9.28407	−0.496965	−0.248482	+	0.968636i	$0.579932\pi$
$350$	8.52851	0.455868
$351$	−2.68057	−0.143078
$352$	−23.4552	−1.25017
$353$	34.0564	1.81264	0.906320	−	0.422593i	$-0.138880\pi$
$353$	34.0564	1.81264	0.906320	+	0.422593i	$0.138880\pi$
$354$	−5.94024	−0.315720
$355$	0.200858	0.0106604
$356$	11.0989	0.588241
$357$	0.0323624	0.00171280
$358$	24.9205	1.31709
$359$	−5.15763	−0.272209	−0.136105	−	0.990694i	$-0.543458\pi$
$359$	−5.15763	−0.272209	−0.136105	+	0.990694i	$0.543458\pi$
$360$	−0.330497	−0.0174187
$361$	−7.14290	−0.375942
$362$	−10.5210	−0.552974
$363$	−11.2598	−0.590985
$364$	−2.54341	−0.133311
$365$	−0.119352	−0.00624718
$366$	4.97289	0.259937
$367$	−22.3302	−1.16563	−0.582814	−	0.812606i	$-0.698048\pi$
$367$	−22.3302	−1.16563	−0.582814	+	0.812606i	$0.698048\pi$
$368$	−31.0897	−1.62066
$369$	6.69305	0.348426
$370$	−1.61157	−0.0837817
$371$	−11.6106	−0.602793
$372$	6.09785	0.316159
$373$	9.27921	0.480459	0.240230	−	0.970716i	$-0.422777\pi$
$373$	9.27921	0.480459	0.240230	+	0.970716i	$0.422777\pi$
$374$	0.262196	0.0135578
$375$	1.82478	0.0942313
$376$	−8.52705	−0.439749
$377$	20.1554	1.03805
$378$	1.71722	0.0883240
$379$	−3.01182	−0.154707	−0.0773535	−	0.997004i	$-0.524647\pi$
$379$	−3.01182	−0.154707	−0.0773535	+	0.997004i	$0.524647\pi$
$380$	−0.598200	−0.0306870
$381$	−0.0244773	−0.00125401
$382$	1.71722	0.0878604
$383$	−33.4713	−1.71030	−0.855152	−	0.518378i	$-0.826536\pi$
$383$	−33.4713	−1.71030	−0.855152	+	0.518378i	$0.826536\pi$
$384$	−12.4461	−0.635140
$385$	−0.863832	−0.0440250
$386$	11.1554	0.567793
$387$	−1.78467	−0.0907200
$388$	12.1517	0.616908
$389$	0.965832	0.0489696	0.0244848	−	0.999700i	$-0.492205\pi$
$389$	0.965832	0.0489696	0.0244848	+	0.999700i	$0.492205\pi$
$390$	−0.842794	−0.0426765
$391$	0.201333	0.0101818
$392$	−1.80509	−0.0911706
$393$	11.7894	0.594694
$394$	14.0613	0.708397
$395$	0.747136	0.0375925
$396$	4.47660	0.224958
$397$	−16.5766	−0.831957	−0.415978	−	0.909375i	$-0.636561\pi$
$397$	−16.5766	−0.831957	−0.415978	+	0.909375i	$0.636561\pi$
$398$	5.02662	0.251962
$399$	−3.44341	−0.172386
$400$	24.8194	1.24097
$401$	29.8698	1.49163	0.745814	−	0.666154i	$-0.232061\pi$
$401$	29.8698	1.49163	0.745814	+	0.666154i	$0.232061\pi$
$402$	−9.72092	−0.484836
$403$	−17.2273	−0.858151
$404$	10.4429	0.519551
$405$	0.183092	0.00909791
$406$	−12.9118	−0.640804
$407$	−24.1834	−1.19872
$408$	0.0584169	0.00289207
$409$	−28.4795	−1.40822	−0.704111	−	0.710090i	$-0.748654\pi$
$409$	−28.4795	−1.40822	−0.704111	+	0.710090i	$0.748654\pi$
$410$	2.10435	0.103926
$411$	1.47437	0.0727252
$412$	0.583672	0.0287554
$413$	−3.45923	−0.170217
$414$	10.6831	0.525047
$415$	−0.827105	−0.0406010
$416$	−13.3262	−0.653372
$417$	−16.1077	−0.788799
$418$	−27.8981	−1.36454
$419$	19.2462	0.940241	0.470120	−	0.882602i	$-0.344210\pi$
$419$	19.2462	0.940241	0.470120	+	0.882602i	$0.344210\pi$
$420$	0.173723	0.00847681
$421$	−16.4583	−0.802129	−0.401064	−	0.916050i	$-0.631360\pi$
$421$	−16.4583	−0.802129	−0.401064	+	0.916050i	$0.631360\pi$
$422$	27.3867	1.33317
$423$	4.72390	0.229684
$424$	−20.9582	−1.01782
$425$	−0.160727	−0.00779641
$426$	−1.88384	−0.0912726
$427$	2.89590	0.140143
$428$	9.85288	0.476257
$429$	−12.6470	−0.610604
$430$	−0.561115	−0.0270594
$431$	4.75397	0.228991	0.114495	−	0.993424i	$-0.463475\pi$
$431$	4.75397	0.228991	0.114495	+	0.993424i	$0.463475\pi$
$432$	4.99738	0.240437
$433$	32.0534	1.54039	0.770194	−	0.637810i	$-0.220160\pi$
$433$	32.0534	1.54039	0.770194	+	0.637810i	$0.220160\pi$
$434$	11.0360	0.529747
$435$	−1.37668	−0.0660066
$436$	12.3960	0.593659
$437$	−21.4221	−1.02476
$438$	1.11940	0.0534871
$439$	10.1310	0.483528	0.241764	−	0.970335i	$-0.422274\pi$
$439$	10.1310	0.483528	0.241764	+	0.970335i	$0.422274\pi$
$440$	−1.55929	−0.0743363
$441$	1.00000	0.0476190
$442$	0.148968	0.00708569
$443$	−31.3609	−1.49000	−0.745001	−	0.667063i	$-0.767551\pi$
$443$	−31.3609	−1.49000	−0.745001	+	0.667063i	$0.767551\pi$
$444$	4.86345	0.230809
$445$	2.14171	0.101527
$446$	−36.7388	−1.73963
$447$	8.08916	0.382604
$448$	−1.45778	−0.0688737
$449$	14.3149	0.675560	0.337780	−	0.941225i	$-0.390324\pi$
$449$	14.3149	0.675560	0.337780	+	0.941225i	$0.390324\pi$
$450$	−8.52851	−0.402038
$451$	31.5780	1.48695
$452$	2.56794	0.120786
$453$	−20.8330	−0.978819
$454$	38.6054	1.81184
$455$	−0.490791	−0.0230086
$456$	−6.21566	−0.291075
$457$	12.1189	0.566899	0.283450	−	0.958987i	$-0.408521\pi$
$457$	12.1189	0.566899	0.283450	+	0.958987i	$0.408521\pi$
$458$	−17.9698	−0.839672
$459$	−0.0323624	−0.00151055
$460$	1.08076	0.0503909
$461$	14.7252	0.685823	0.342911	−	0.939368i	$-0.388587\pi$
$461$	14.7252	0.685823	0.342911	+	0.939368i	$0.388587\pi$
$462$	8.10187	0.376933
$463$	11.4042	0.529999	0.264999	−	0.964249i	$-0.414628\pi$
$463$	11.4042	0.529999	0.264999	+	0.964249i	$0.414628\pi$
$464$	−37.5756	−1.74440
$465$	1.17668	0.0545671
$466$	9.51576	0.440809
$467$	14.8934	0.689183	0.344592	−	0.938753i	$-0.388017\pi$
$467$	14.8934	0.689183	0.344592	+	0.938753i	$0.388017\pi$
$468$	2.54341	0.117569
$469$	−5.66086	−0.261394
$470$	1.48523	0.0685087
$471$	20.7117	0.954344
$472$	−6.24420	−0.287413
$473$	−8.42013	−0.387158
$474$	−7.00738	−0.321859
$475$	17.1016	0.784677
$476$	−0.0307064	−0.00140743
$477$	11.6106	0.531613
$478$	−21.4382	−0.980563
$479$	7.90130	0.361020	0.180510	−	0.983573i	$-0.442225\pi$
$479$	7.90130	0.361020	0.180510	+	0.983573i	$0.442225\pi$
$480$	0.910224	0.0415459
$481$	−13.7399	−0.626486
$482$	18.1555	0.826962
$483$	6.22119	0.283074
$484$	10.6836	0.485618
$485$	2.34486	0.106475
$486$	−1.71722	−0.0778945
$487$	18.6210	0.843800	0.421900	−	0.906642i	$-0.361363\pi$
$487$	18.6210	0.843800	0.421900	+	0.906642i	$0.361363\pi$
$488$	5.22735	0.236631
$489$	18.2273	0.824268
$490$	0.314408	0.0142035
$491$	−28.5791	−1.28976	−0.644878	−	0.764286i	$-0.723092\pi$
$491$	−28.5791	−1.28976	−0.644878	+	0.764286i	$0.723092\pi$
$492$	−6.35056	−0.286305
$493$	0.243335	0.0109592
$494$	−15.8505	−0.713146
$495$	0.863832	0.0388264
$496$	32.1167	1.44208
$497$	−1.09703	−0.0492087
$498$	7.75740	0.347618
$499$	16.8000	0.752070	0.376035	−	0.926606i	$-0.377287\pi$
$499$	16.8000	0.752070	0.376035	+	0.926606i	$0.377287\pi$
$500$	−1.73141	−0.0774308
$501$	2.67188	0.119371
$502$	−27.0625	−1.20786
$503$	14.1085	0.629067	0.314533	−	0.949246i	$-0.398152\pi$
$503$	14.1085	0.629067	0.314533	+	0.949246i	$0.398152\pi$
$504$	1.80509	0.0804049
$505$	2.01512	0.0896715
$506$	50.4033	2.24070
$507$	5.81453	0.258232
$508$	0.0232248	0.00103043
$509$	0.0689706	0.00305707	0.00152853	−	0.999999i	$-0.499513\pi$
$509$	0.0689706	0.00305707	0.00152853	+	0.999999i	$0.499513\pi$
$510$	−0.0101750	−0.000450557 0
$511$	0.651871	0.0288371
$512$	6.80261	0.300636
$513$	3.44341	0.152030
$514$	−7.18917	−0.317101
$515$	0.112629	0.00496302
$516$	1.69335	0.0745456
$517$	22.2875	0.980203
$518$	8.80199	0.386737
$519$	−2.94799	−0.129402
$520$	−0.885920	−0.0388502
$521$	−8.87691	−0.388904	−0.194452	−	0.980912i	$-0.562293\pi$
$521$	−8.87691	−0.388904	−0.194452	+	0.980912i	$0.562293\pi$
$522$	12.9118	0.565136
$523$	−37.4581	−1.63793	−0.818964	−	0.573845i	$-0.805451\pi$
$523$	−37.4581	−1.63793	−0.818964	+	0.573845i	$0.805451\pi$
$524$	−11.1861	−0.488666
$525$	−4.96648	−0.216755
$526$	2.30016	0.100292
$527$	−0.207984	−0.00905991
$528$	23.5778	1.02609
$529$	15.7032	0.682749
$530$	3.65047	0.158566
$531$	3.45923	0.150118
$532$	3.26721	0.141652
$533$	17.9412	0.777120
$534$	−20.0871	−0.869253
$535$	1.90127	0.0821991
$536$	−10.2183	−0.441365
$537$	−14.5121	−0.626245
$538$	−11.5816	−0.499319
$539$	4.71803	0.203220
$540$	−0.173723	−0.00747584
$541$	−17.3921	−0.747745	−0.373872	−	0.927480i	$-0.621970\pi$
$541$	−17.3921	−0.747745	−0.373872	+	0.927480i	$0.621970\pi$
$542$	23.7143	1.01862
$543$	6.12681	0.262926
$544$	−0.160887	−0.00689796
$545$	2.39200	0.102462
$546$	4.60312	0.196995
$547$	21.3392	0.912398	0.456199	−	0.889878i	$-0.349211\pi$
$547$	21.3392	0.912398	0.456199	+	0.889878i	$0.349211\pi$
$548$	−1.39892	−0.0597591
$549$	−2.89590	−0.123594
$550$	−40.2377	−1.71574
$551$	−25.8912	−1.10300
$552$	11.2298	0.477972
$553$	−4.08066	−0.173527
$554$	46.9007	1.99262
$555$	0.938480	0.0398363
$556$	15.2835	0.648165
$557$	−30.5689	−1.29525	−0.647623	−	0.761961i	$-0.724237\pi$
$557$	−30.5689	−1.29525	−0.647623	+	0.761961i	$0.724237\pi$
$558$	−11.0360	−0.467193
$559$	−4.78394	−0.202339
$560$	0.914980	0.0386649
$561$	−0.152687	−0.00644644
$562$	−11.3108	−0.477117
$563$	−19.4667	−0.820423	−0.410212	−	0.911990i	$-0.634545\pi$
$563$	−19.4667	−0.820423	−0.410212	+	0.911990i	$0.634545\pi$
$564$	−4.48218	−0.188734
$565$	0.495524	0.0208469
$566$	−14.5938	−0.613421
$567$	−1.00000	−0.0419961
$568$	−1.98024	−0.0830891
$569$	32.1647	1.34842	0.674208	−	0.738542i	$-0.264485\pi$
$569$	32.1647	1.34842	0.674208	+	0.738542i	$0.264485\pi$
$570$	1.08264	0.0453467
$571$	−7.66647	−0.320832	−0.160416	−	0.987050i	$-0.551284\pi$
$571$	−7.66647	−0.320832	−0.160416	+	0.987050i	$0.551284\pi$
$572$	11.9999	0.501739
$573$	−1.00000	−0.0417756
$574$	−11.4934	−0.479725
$575$	−30.8974	−1.28851
$576$	1.45778	0.0607409
$577$	−7.92105	−0.329758	−0.164879	−	0.986314i	$-0.552723\pi$
$577$	−7.92105	−0.329758	−0.164879	+	0.986314i	$0.552723\pi$
$578$	−29.1909	−1.21418
$579$	−6.49620	−0.269973
$580$	1.30623	0.0542383
$581$	4.51743	0.187415
$582$	−21.9924	−0.911615
$583$	54.7792	2.26872
$584$	1.17668	0.0486915
$585$	0.490791	0.0202917
$586$	−14.8736	−0.614423
$587$	13.2745	0.547899	0.273949	−	0.961744i	$-0.411670\pi$
$587$	13.2745	0.547899	0.273949	+	0.961744i	$0.411670\pi$
$588$	−0.948829	−0.0391291
$589$	22.1298	0.911843
$590$	1.08761	0.0447761
$591$	−8.18842	−0.336827
$592$	25.6153	1.05278
$593$	−7.66763	−0.314872	−0.157436	−	0.987529i	$-0.550323\pi$
$593$	−7.66763	−0.314872	−0.157436	+	0.987529i	$0.550323\pi$
$594$	−8.10187	−0.332424
$595$	−0.00592529	−0.000242913 0
$596$	−7.67524	−0.314390
$597$	−2.92719	−0.119802
$598$	28.6369	1.17105
$599$	25.8622	1.05670	0.528351	−	0.849026i	$-0.322811\pi$
$599$	25.8622	1.05670	0.528351	+	0.849026i	$0.322811\pi$
$600$	−8.96492	−0.365991
$601$	−7.59663	−0.309873	−0.154936	−	0.987924i	$-0.549517\pi$
$601$	−7.59663	−0.309873	−0.154936	+	0.987924i	$0.549517\pi$
$602$	3.06467	0.124907
$603$	5.66086	0.230528
$604$	19.7669	0.804306
$605$	2.06157	0.0838148
$606$	−18.8997	−0.767750
$607$	−24.8450	−1.00843	−0.504213	−	0.863579i	$-0.668217\pi$
$607$	−24.8450	−1.00843	−0.504213	+	0.863579i	$0.668217\pi$
$608$	17.1186	0.694252
$609$	7.51906	0.304688
$610$	−0.910495	−0.0368649
$611$	12.6628	0.512281
$612$	0.0307064	0.00124123
$613$	−39.8712	−1.61038	−0.805192	−	0.593014i	$-0.797938\pi$
$613$	−39.8712	−1.61038	−0.805192	+	0.593014i	$0.797938\pi$
$614$	−30.0515	−1.21278
$615$	−1.22544	−0.0494146
$616$	8.51645	0.343137
$617$	32.7016	1.31652	0.658259	−	0.752792i	$-0.271293\pi$
$617$	32.7016	1.31652	0.658259	+	0.752792i	$0.271293\pi$
$618$	−1.05634	−0.0424924
$619$	22.5517	0.906427	0.453214	−	0.891402i	$-0.350277\pi$
$619$	22.5517	0.906427	0.453214	+	0.891402i	$0.350277\pi$
$620$	−1.11647	−0.0448384
$621$	−6.22119	−0.249648
$622$	−51.3760	−2.05999
$623$	−11.6975	−0.468649
$624$	13.3958	0.536263
$625$	24.4983	0.979931
$626$	−44.9064	−1.79482
$627$	16.2461	0.648807
$628$	−19.6519	−0.784194
$629$	−0.165881	−0.00661411
$630$	−0.314408	−0.0125263
$631$	−4.02793	−0.160349	−0.0801746	−	0.996781i	$-0.525548\pi$
$631$	−4.02793	−0.160349	−0.0801746	+	0.996781i	$0.525548\pi$
$632$	−7.36595	−0.293002
$633$	−15.9483	−0.633889
$634$	6.25782	0.248530
$635$	0.00448160	0.000177847 0
$636$	−11.0165	−0.436832
$637$	2.68057	0.106208
$638$	60.9184	2.41178
$639$	1.09703	0.0433980
$640$	2.27879	0.0900770
$641$	−10.0440	−0.396713	−0.198357	−	0.980130i	$-0.563560\pi$
$641$	−10.0440	−0.396713	−0.198357	+	0.980130i	$0.563560\pi$
$642$	−17.8320	−0.703773
$643$	−14.2689	−0.562711	−0.281356	−	0.959604i	$-0.590784\pi$
$643$	−14.2689	−0.562711	−0.281356	+	0.959604i	$0.590784\pi$
$644$	−5.90285	−0.232605
$645$	0.326759	0.0128661
$646$	−0.191362	−0.00752902
$647$	11.6362	0.457466	0.228733	−	0.973489i	$-0.426542\pi$
$647$	11.6362	0.457466	0.228733	+	0.973489i	$0.426542\pi$
$648$	−1.80509	−0.0709105
$649$	16.3207	0.640644
$650$	−22.8613	−0.896694
$651$	−6.42671	−0.251883
$652$	−17.2946	−0.677309
$653$	−12.1438	−0.475222	−0.237611	−	0.971360i	$-0.576364\pi$
$653$	−12.1438	−0.475222	−0.237611	+	0.971360i	$0.576364\pi$
$654$	−22.4345	−0.877259
$655$	−2.15853	−0.0843409
$656$	−33.4477	−1.30591
$657$	−0.651871	−0.0254319
$658$	−8.11196	−0.316237
$659$	0.985525	0.0383906	0.0191953	−	0.999816i	$-0.493890\pi$
$659$	0.985525	0.0383906	0.0191953	+	0.999816i	$0.493890\pi$
$660$	−0.819629	−0.0319040
$661$	−31.2839	−1.21680	−0.608401	−	0.793629i	$-0.708189\pi$
$661$	−31.2839	−1.21680	−0.608401	+	0.793629i	$0.708189\pi$
$662$	−33.2573	−1.29258
$663$	−0.0867498	−0.00336908
$664$	8.15436	0.316450
$665$	0.630461	0.0244482
$666$	−8.80199	−0.341070
$667$	46.7775	1.81123
$668$	−2.53516	−0.0980883
$669$	21.3944	0.827155
$670$	1.77982	0.0687605
$671$	−13.6629	−0.527452
$672$	−4.97141	−0.191776
$673$	35.0750	1.35204	0.676020	−	0.736883i	$-0.263703\pi$
$673$	35.0750	1.35204	0.676020	+	0.736883i	$0.263703\pi$
$674$	17.8608	0.687971
$675$	4.96648	0.191160
$676$	−5.51700	−0.212192
$677$	−5.69139	−0.218738	−0.109369	−	0.994001i	$-0.534883\pi$
$677$	−5.69139	−0.218738	−0.109369	+	0.994001i	$0.534883\pi$
$678$	−4.64751	−0.178487
$679$	−12.8070	−0.491489
$680$	−0.0106957	−0.000410160 0
$681$	−22.4814	−0.861489
$682$	−52.0683	−1.99380
$683$	14.9479	0.571965	0.285982	−	0.958235i	$-0.407680\pi$
$683$	14.9479	0.571965	0.285982	+	0.958235i	$0.407680\pi$
$684$	−3.26721	−0.124925
$685$	−0.269945	−0.0103141
$686$	−1.71722	−0.0655636
$687$	10.4645	0.399245
$688$	8.91869	0.340022
$689$	31.1231	1.18569
$690$	−1.95599	−0.0744634
$691$	−30.7390	−1.16937	−0.584683	−	0.811262i	$-0.698781\pi$
$691$	−30.7390	−1.16937	−0.584683	+	0.811262i	$0.698781\pi$
$692$	2.79714	0.106331
$693$	−4.71803	−0.179223
$694$	−17.7632	−0.674282
$695$	2.94919	0.111869
$696$	13.5725	0.514466
$697$	0.216603	0.00820443
$698$	−15.9428	−0.603442
$699$	−5.54139	−0.209595
$700$	4.71234	0.178110
$701$	49.2086	1.85858	0.929291	−	0.369347i	$-0.120419\pi$
$701$	49.2086	1.85858	0.929291	+	0.369347i	$0.120419\pi$
$702$	−4.60312	−0.173734
$703$	17.6500	0.665684
$704$	6.87786	0.259219
$705$	−0.864908	−0.0325743
$706$	58.4822	2.20101
$707$	−11.0060	−0.413925
$708$	−3.28222	−0.123353
$709$	−31.2818	−1.17481	−0.587407	−	0.809292i	$-0.699851\pi$
$709$	−31.2818	−1.17481	−0.587407	+	0.809292i	$0.699851\pi$
$710$	0.344917	0.0129445
$711$	4.08066	0.153037
$712$	−21.1150	−0.791316
$713$	−39.9818	−1.49733
$714$	0.0555732	0.00207978
$715$	2.31556	0.0865972
$716$	13.7696	0.514592
$717$	12.4843	0.466235
$718$	−8.85675	−0.330531
$719$	−27.4705	−1.02448	−0.512238	−	0.858843i	$-0.671184\pi$
$719$	−27.4705	−1.02448	−0.512238	+	0.858843i	$0.671184\pi$
$720$	−0.914980	−0.0340993
$721$	−0.615149	−0.0229093
$722$	−12.2659	−0.456490
$723$	−10.5727	−0.393202
$724$	−5.81329	−0.216049
$725$	−37.3432	−1.38689
$726$	−19.3355	−0.717606
$727$	1.28335	0.0475969	0.0237985	−	0.999717i	$-0.492424\pi$
$727$	1.28335	0.0475969	0.0237985	+	0.999717i	$0.492424\pi$
$728$	4.83867	0.179333
$729$	1.00000	0.0370370
$730$	−0.204954	−0.00758567
$731$	−0.0577563	−0.00213619
$732$	2.74772	0.101559
$733$	28.3029	1.04539	0.522695	−	0.852520i	$-0.324927\pi$
$733$	28.3029	1.04539	0.522695	+	0.852520i	$0.324927\pi$
$734$	−38.3458	−1.41537
$735$	−0.183092	−0.00675344
$736$	−30.9281	−1.14002
$737$	26.7081	0.983806
$738$	11.4934	0.423078
$739$	−35.1131	−1.29166	−0.645829	−	0.763482i	$-0.723488\pi$
$739$	−35.1131	−1.29166	−0.645829	+	0.763482i	$0.723488\pi$
$740$	−0.890458	−0.0327339
$741$	9.23032	0.339084
$742$	−19.9379	−0.731944
$743$	−1.12395	−0.0412338	−0.0206169	−	0.999787i	$-0.506563\pi$
$743$	−1.12395	−0.0412338	−0.0206169	+	0.999787i	$0.506563\pi$
$744$	−11.6008	−0.425305
$745$	−1.48106	−0.0542618
$746$	15.9344	0.583400
$747$	−4.51743	−0.165284
$748$	0.144874	0.00529710
$749$	−10.3843	−0.379432
$750$	3.13354	0.114421
$751$	5.37391	0.196097	0.0980484	−	0.995182i	$-0.468740\pi$
$751$	5.37391	0.196097	0.0980484	+	0.995182i	$0.468740\pi$
$752$	−23.6071	−0.860864
$753$	15.7595	0.574310
$754$	34.6111	1.26046
$755$	3.81435	0.138818
$756$	0.948829	0.0345086
$757$	24.4926	0.890198	0.445099	−	0.895481i	$-0.353168\pi$
$757$	24.4926	0.890198	0.445099	+	0.895481i	$0.353168\pi$
$758$	−5.17195	−0.187854
$759$	−29.3517	−1.06540
$760$	1.13804	0.0412809
$761$	33.7005	1.22164	0.610821	−	0.791769i	$-0.290839\pi$
$761$	33.7005	1.22164	0.610821	+	0.791769i	$0.290839\pi$
$762$	−0.0420329	−0.00152269
$763$	−13.0645	−0.472966
$764$	0.948829	0.0343274
$765$	0.00592529	0.000214229 0
$766$	−57.4774	−2.07674
$767$	9.27271	0.334818
$768$	−18.4571	−0.666015
$769$	−27.3127	−0.984920	−0.492460	−	0.870335i	$-0.663902\pi$
$769$	−27.3127	−0.984920	−0.492460	+	0.870335i	$0.663902\pi$
$770$	−1.48339	−0.0534575
$771$	4.18653	0.150774
$772$	6.16378	0.221839
$773$	1.97291	0.0709607	0.0354803	−	0.999370i	$-0.488704\pi$
$773$	1.97291	0.0709607	0.0354803	+	0.999370i	$0.488704\pi$
$774$	−3.06467	−0.110157
$775$	31.9181	1.14653
$776$	−23.1178	−0.829880
$777$	−5.12574	−0.183885
$778$	1.65854	0.0594616
$779$	−23.0469	−0.825742
$780$	−0.465677	−0.0166739
$781$	5.17584	0.185206
$782$	0.345732	0.0123633
$783$	−7.51906	−0.268709
$784$	−4.99738	−0.178478
$785$	−3.79214	−0.135347
$786$	20.2449	0.722110
$787$	2.16259	0.0770880	0.0385440	−	0.999257i	$-0.487728\pi$
$787$	2.16259	0.0770880	0.0385440	+	0.999257i	$0.487728\pi$
$788$	7.76941	0.276774
$789$	−1.33947	−0.0476864
$790$	1.28299	0.0456469
$791$	−2.70642	−0.0962294
$792$	−8.51645	−0.302619
$793$	−7.76268	−0.275661
$794$	−28.4656	−1.01021
$795$	−2.12581	−0.0753946
$796$	2.77741	0.0984426
$797$	24.9032	0.882117	0.441059	−	0.897478i	$-0.354603\pi$
$797$	24.9032	0.882117	0.441059	+	0.897478i	$0.354603\pi$
$798$	−5.91308	−0.209321
$799$	0.152877	0.00540839
$800$	24.6904	0.872937
$801$	11.6975	0.413310
$802$	51.2929	1.81122
$803$	−3.07554	−0.108534
$804$	−5.37119	−0.189427
$805$	−1.13905	−0.0401462
$806$	−29.5829	−1.04201
$807$	6.74442	0.237415
$808$	−19.8669	−0.698913
$809$	0.794168	0.0279215	0.0139607	−	0.999903i	$-0.495556\pi$
$809$	0.794168	0.0279215	0.0139607	+	0.999903i	$0.495556\pi$
$810$	0.314408	0.0110472
$811$	−10.5327	−0.369852	−0.184926	−	0.982752i	$-0.559204\pi$
$811$	−10.5327	−0.369852	−0.184926	+	0.982752i	$0.559204\pi$
$812$	−7.13430	−0.250365
$813$	−13.8097	−0.484329
$814$	−41.5280	−1.45556
$815$	−3.33727	−0.116900
$816$	0.161727	0.00566159
$817$	6.14537	0.214999
$818$	−48.9055	−1.70994
$819$	−2.68057	−0.0936668
$820$	1.16274	0.0406045
$821$	17.7002	0.617742	0.308871	−	0.951104i	$-0.400049\pi$
$821$	17.7002	0.617742	0.308871	+	0.951104i	$0.400049\pi$
$822$	2.53181	0.0883070
$823$	−49.7535	−1.73430	−0.867149	−	0.498049i	$-0.834050\pi$
$823$	−49.7535	−1.73430	−0.867149	+	0.498049i	$0.834050\pi$
$824$	−1.11040	−0.0386825
$825$	23.4320	0.815797
$826$	−5.94024	−0.206687
$827$	−43.1892	−1.50184	−0.750918	−	0.660395i	$-0.770389\pi$
$827$	−43.1892	−1.50184	−0.750918	+	0.660395i	$0.770389\pi$
$828$	5.90285	0.205138
$829$	52.6435	1.82838	0.914192	−	0.405282i	$-0.132827\pi$
$829$	52.6435	1.82838	0.914192	+	0.405282i	$0.132827\pi$
$830$	−1.42032	−0.0492999
$831$	−27.3120	−0.947444
$832$	3.90769	0.135475
$833$	0.0323624	0.00112129
$834$	−27.6605	−0.957803
$835$	−0.489199	−0.0169294
$836$	−15.4148	−0.533132
$837$	6.42671	0.222140
$838$	33.0500	1.14169
$839$	−32.0590	−1.10680	−0.553399	−	0.832916i	$-0.686670\pi$
$839$	−32.0590	−1.10680	−0.553399	+	0.832916i	$0.686670\pi$
$840$	−0.330497	−0.0114032
$841$	27.5362	0.949524
$842$	−28.2625	−0.973989
$843$	6.58671	0.226858
$844$	15.1322	0.520874
$845$	−1.06459	−0.0366231
$846$	8.11196	0.278895
$847$	−11.2598	−0.386890
$848$	−58.0226	−1.99251
$849$	8.49850	0.291668
$850$	−0.276003	−0.00946683
$851$	−31.8882	−1.09311
$852$	−1.04090	−0.0356606
$853$	−8.80033	−0.301318	−0.150659	−	0.988586i	$-0.548139\pi$
$853$	−8.80033	−0.301318	−0.150659	+	0.988586i	$0.548139\pi$
$854$	4.97289	0.170169
$855$	−0.630461	−0.0215613
$856$	−18.7445	−0.640673
$857$	2.27617	0.0777525	0.0388763	−	0.999244i	$-0.487622\pi$
$857$	2.27617	0.0777525	0.0388763	+	0.999244i	$0.487622\pi$
$858$	−21.7176	−0.741428
$859$	28.9392	0.987394	0.493697	−	0.869634i	$-0.335645\pi$
$859$	28.9392	0.987394	0.493697	+	0.869634i	$0.335645\pi$
$860$	−0.310038	−0.0105722
$861$	6.69305	0.228098
$862$	8.16360	0.278053
$863$	−20.9975	−0.714763	−0.357381	−	0.933959i	$-0.616330\pi$
$863$	−20.9975	−0.714763	−0.357381	+	0.933959i	$0.616330\pi$
$864$	4.97141	0.169131
$865$	0.539752	0.0183521
$866$	55.0426	1.87042
$867$	16.9990	0.577315
$868$	6.09785	0.206975
$869$	19.2527	0.653102
$870$	−2.36405	−0.0801489
$871$	15.1744	0.514164
$872$	−23.5825	−0.798604
$873$	12.8070	0.433452
$874$	−36.7864	−1.24432
$875$	1.82478	0.0616888
$876$	0.618514	0.0208977
$877$	36.4305	1.23017	0.615086	−	0.788460i	$-0.289121\pi$
$877$	36.4305	1.23017	0.615086	+	0.788460i	$0.289121\pi$
$878$	17.3972	0.587126
$879$	8.66147	0.292144
$880$	−4.31690	−0.145523
$881$	11.7783	0.396822	0.198411	−	0.980119i	$-0.436422\pi$
$881$	11.7783	0.396822	0.198411	+	0.980119i	$0.436422\pi$
$882$	1.71722	0.0578217
$883$	2.75277	0.0926382	0.0463191	−	0.998927i	$-0.485251\pi$
$883$	2.75277	0.0926382	0.0463191	+	0.998927i	$0.485251\pi$
$884$	0.0823107	0.00276841
$885$	−0.633356	−0.0212900
$886$	−53.8535	−1.80924
$887$	−7.54015	−0.253173	−0.126587	−	0.991956i	$-0.540402\pi$
$887$	−7.54015	−0.253173	−0.126587	+	0.991956i	$0.540402\pi$
$888$	−9.25240	−0.310490
$889$	−0.0244773	−0.000820944 0
$890$	3.67778	0.123279
$891$	4.71803	0.158060
$892$	−20.2996	−0.679682
$893$	−16.2664	−0.544333
$894$	13.8908	0.464579
$895$	2.65706	0.0888156
$896$	−12.4461	−0.415796
$897$	−16.6764	−0.556807
$898$	24.5817	0.820302
$899$	−48.3228	−1.61165
$900$	−4.71234	−0.157078
$901$	0.375747	0.0125180
$902$	54.2262	1.80553
$903$	−1.78467	−0.0593902
$904$	−4.88533	−0.162484
$905$	−1.12177	−0.0372888
$906$	−35.7747	−1.18854
$907$	47.2320	1.56831	0.784156	−	0.620564i	$-0.213096\pi$
$907$	47.2320	1.56831	0.784156	+	0.620564i	$0.213096\pi$
$908$	21.3310	0.707895
$909$	11.0060	0.365047
$910$	−0.842794	−0.0279383
$911$	−18.7961	−0.622741	−0.311371	−	0.950289i	$-0.600788\pi$
$911$	−18.7961	−0.622741	−0.311371	+	0.950289i	$0.600788\pi$
$912$	−17.2081	−0.569816
$913$	−21.3134	−0.705369
$914$	20.8108	0.688360
$915$	0.530216	0.0175284
$916$	−9.92900	−0.328063
$917$	11.7894	0.389319
$918$	−0.0555732	−0.00183419
$919$	−6.92400	−0.228402	−0.114201	−	0.993458i	$-0.536431\pi$
$919$	−6.92400	−0.228402	−0.114201	+	0.993458i	$0.536431\pi$
$920$	−2.05608	−0.0677870
$921$	17.5001	0.576649
$922$	25.2864	0.832764
$923$	2.94068	0.0967937
$924$	4.47660	0.147269
$925$	25.4569	0.837016
$926$	19.5835	0.643554
$927$	0.615149	0.0202041
$928$	−37.3803	−1.22707
$929$	−22.2367	−0.729562	−0.364781	−	0.931093i	$-0.618856\pi$
$929$	−22.2367	−0.729562	−0.364781	+	0.931093i	$0.618856\pi$
$930$	2.02061	0.0662584
$931$	−3.44341	−0.112853
$932$	5.25783	0.172226
$933$	29.9182	0.979479
$934$	25.5751	0.836844
$935$	0.0279557	0.000914248 0
$936$	−4.83867	−0.158157
$937$	−24.3000	−0.793846	−0.396923	−	0.917852i	$-0.629922\pi$
$937$	−24.3000	−0.793846	−0.396923	+	0.917852i	$0.629922\pi$
$938$	−9.72092	−0.317399
$939$	26.1507	0.853396
$940$	0.820650	0.0267667
$941$	41.2192	1.34371	0.671854	−	0.740684i	$-0.265498\pi$
$941$	41.2192	1.34371	0.671854	+	0.740684i	$0.265498\pi$
$942$	35.5664	1.15882
$943$	41.6387	1.35594
$944$	−17.2871	−0.562646
$945$	0.183092	0.00595598
$946$	−14.4592	−0.470109
$947$	1.80386	0.0586174	0.0293087	−	0.999570i	$-0.490669\pi$
$947$	1.80386	0.0586174	0.0293087	+	0.999570i	$0.490669\pi$
$948$	−3.87185	−0.125752
$949$	−1.74739	−0.0567226
$950$	29.3672	0.952798
$951$	−3.64417	−0.118170
$952$	0.0584169	0.00189330
$953$	35.8588	1.16158	0.580791	−	0.814053i	$-0.302744\pi$
$953$	35.8588	1.16158	0.580791	+	0.814053i	$0.302744\pi$
$954$	19.9379	0.645514
$955$	0.183092	0.00592471
$956$	−11.8455	−0.383110
$957$	−35.4751	−1.14675
$958$	13.5682	0.438370
$959$	1.47437	0.0476098
$960$	−0.266908	−0.00861442
$961$	10.3026	0.332341
$962$	−23.5944	−0.760714
$963$	10.3843	0.334628
$964$	10.0317	0.323098
$965$	1.18940	0.0382882
$966$	10.6831	0.343724
$967$	−48.2461	−1.55149	−0.775745	−	0.631046i	$-0.782626\pi$
$967$	−48.2461	−1.55149	−0.775745	+	0.631046i	$0.782626\pi$
$968$	−20.3249	−0.653266
$969$	0.111437	0.00357988
$970$	4.02663	0.129287
$971$	−53.5866	−1.71968	−0.859838	−	0.510566i	$-0.829436\pi$
$971$	−53.5866	−1.71968	−0.859838	+	0.510566i	$0.829436\pi$
$972$	−0.948829	−0.0304337
$973$	−16.1077	−0.516390
$974$	31.9764	1.02459
$975$	13.3130	0.426357
$976$	14.4719	0.463235
$977$	−21.6599	−0.692960	−0.346480	−	0.938057i	$-0.612623\pi$
$977$	−21.6599	−0.692960	−0.346480	+	0.938057i	$0.612623\pi$
$978$	31.3002	1.00087
$979$	55.1890	1.76385
$980$	0.173723	0.00554937
$981$	13.0645	0.417116
$982$	−49.0764	−1.56609
$983$	43.3917	1.38398	0.691990	−	0.721907i	$-0.256734\pi$
$983$	43.3917	1.38398	0.691990	+	0.721907i	$0.256734\pi$
$984$	12.0815	0.385145
$985$	1.49923	0.0477695
$986$	0.417858	0.0133073
$987$	4.72390	0.150363
$988$	−8.75800	−0.278629
$989$	−11.1028	−0.353048
$990$	1.48339	0.0471451
$991$	4.59039	0.145818	0.0729092	−	0.997339i	$-0.476772\pi$
$991$	4.59039	0.145818	0.0729092	+	0.997339i	$0.476772\pi$
$992$	31.9498	1.01441
$993$	19.3670	0.614593
$994$	−1.88384	−0.0597519
$995$	0.535945	0.0169906
$996$	4.28627	0.135816
$997$	−14.9187	−0.472480	−0.236240	−	0.971695i	$-0.575915\pi$
$997$	−14.9187	−0.472480	−0.236240	+	0.971695i	$0.575915\pi$
$998$	28.8492	0.913204
$999$	5.12574	0.162171

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.j.1.20	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.j.1.20	✓	26	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q+1.71722 q^{2} -1.00000 q^{3} +0.948829 q^{4} +0.183092 q^{5} -1.71722 q^{6} -1.00000 q^{7} -1.80509 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.71722 q^{2} -1.00000 q^{3} +0.948829 q^{4} +0.183092 q^{5} -1.71722 q^{6} -1.00000 q^{7} -1.80509 q^{8} +1.00000 q^{9} +0.314408 q^{10} +4.71803 q^{11} -0.948829 q^{12} +2.68057 q^{13} -1.71722 q^{14} -0.183092 q^{15} -4.99738 q^{16} +0.0323624 q^{17} +1.71722 q^{18} -3.44341 q^{19} +0.173723 q^{20} +1.00000 q^{21} +8.10187 q^{22} +6.22119 q^{23} +1.80509 q^{24} -4.96648 q^{25} +4.60312 q^{26} -1.00000 q^{27} -0.948829 q^{28} +7.51906 q^{29} -0.314408 q^{30} -6.42671 q^{31} -4.97141 q^{32} -4.71803 q^{33} +0.0555732 q^{34} -0.183092 q^{35} +0.948829 q^{36} -5.12574 q^{37} -5.91308 q^{38} -2.68057 q^{39} -0.330497 q^{40} +6.69305 q^{41} +1.71722 q^{42} -1.78467 q^{43} +4.47660 q^{44} +0.183092 q^{45} +10.6831 q^{46} +4.72390 q^{47} +4.99738 q^{48} +1.00000 q^{49} -8.52851 q^{50} -0.0323624 q^{51} +2.54341 q^{52} +11.6106 q^{53} -1.71722 q^{54} +0.863832 q^{55} +1.80509 q^{56} +3.44341 q^{57} +12.9118 q^{58} +3.45923 q^{59} -0.173723 q^{60} -2.89590 q^{61} -11.0360 q^{62} -1.00000 q^{63} +1.45778 q^{64} +0.490791 q^{65} -8.10187 q^{66} +5.66086 q^{67} +0.0307064 q^{68} -6.22119 q^{69} -0.314408 q^{70} +1.09703 q^{71} -1.80509 q^{72} -0.651871 q^{73} -8.80199 q^{74} +4.96648 q^{75} -3.26721 q^{76} -4.71803 q^{77} -4.60312 q^{78} +4.08066 q^{79} -0.914980 q^{80} +1.00000 q^{81} +11.4934 q^{82} -4.51743 q^{83} +0.948829 q^{84} +0.00592529 q^{85} -3.06467 q^{86} -7.51906 q^{87} -8.51645 q^{88} +11.6975 q^{89} +0.314408 q^{90} -2.68057 q^{91} +5.90285 q^{92} +6.42671 q^{93} +8.11196 q^{94} -0.630461 q^{95} +4.97141 q^{96} +12.8070 q^{97} +1.71722 q^{98} +4.71803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9}+O(q^{10}) \) 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9	\( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9} - q^{10} + 13 q^{11} - 34 q^{12} - q^{13} - 2 q^{15} + 54 q^{16} + q^{19} - 22 q^{20} + 26 q^{21} + 17 q^{22} - 3 q^{23} + 48 q^{25} + 6 q^{26} - 26 q^{27} - 34 q^{28} + 23 q^{29} + q^{30} + 18 q^{31} + 10 q^{32} - 13 q^{33} - 19 q^{34} - 2 q^{35} + 34 q^{36} + 23 q^{37} - 15 q^{38} + q^{39} + 14 q^{40} - 4 q^{41} + 5 q^{43} + 60 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{47} - 54 q^{48} + 26 q^{49} + 26 q^{50} + 19 q^{52} + 31 q^{53} + 41 q^{55} - q^{57} + 19 q^{58} - 2 q^{59} + 22 q^{60} - 2 q^{61} - 35 q^{62} - 26 q^{63} + 132 q^{64} + 40 q^{65} - 17 q^{66} + 47 q^{67} - 60 q^{68} + 3 q^{69} + q^{70} + 16 q^{71} - 23 q^{73} + 34 q^{74} - 48 q^{75} + 72 q^{76} - 13 q^{77} - 6 q^{78} + 14 q^{79} - 21 q^{80} + 26 q^{81} + 60 q^{82} - 4 q^{83} + 34 q^{84} + 36 q^{85} + 21 q^{86} - 23 q^{87} + 67 q^{88} + 14 q^{89} - q^{90} + q^{91} + 20 q^{92} - 18 q^{93} + 58 q^{94} - 4 q^{95} - 10 q^{96} + 48 q^{97} + 13 q^{99}+O(q^{100}) \) 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9 - q^10 + 13 * q^11 - 34 * q^12 - q^13 - 2 * q^15 + 54 * q^16 + q^19 - 22 * q^20 + 26 * q^21 + 17 * q^22 - 3 * q^23 + 48 * q^25 + 6 * q^26 - 26 * q^27 - 34 * q^28 + 23 * q^29 + q^30 + 18 * q^31 + 10 * q^32 - 13 * q^33 - 19 * q^34 - 2 * q^35 + 34 * q^36 + 23 * q^37 - 15 * q^38 + q^39 + 14 * q^40 - 4 * q^41 + 5 * q^43 + 60 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^47 - 54 * q^48 + 26 * q^49 + 26 * q^50 + 19 * q^52 + 31 * q^53 + 41 * q^55 - q^57 + 19 * q^58 - 2 * q^59 + 22 * q^60 - 2 * q^61 - 35 * q^62 - 26 * q^63 + 132 * q^64 + 40 * q^65 - 17 * q^66 + 47 * q^67 - 60 * q^68 + 3 * q^69 + q^70 + 16 * q^71 - 23 * q^73 + 34 * q^74 - 48 * q^75 + 72 * q^76 - 13 * q^77 - 6 * q^78 + 14 * q^79 - 21 * q^80 + 26 * q^81 + 60 * q^82 - 4 * q^83 + 34 * q^84 + 36 * q^85 + 21 * q^86 - 23 * q^87 + 67 * q^88 + 14 * q^89 - q^90 + q^91 + 20 * q^92 - 18 * q^93 + 58 * q^94 - 4 * q^95 - 10 * q^96 + 48 * q^97 + 13 * q^99

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