LMFDB - Embedded newform 4334.2.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.38598 q^{3} +1.00000 q^{4} -3.46177 q^{5} -2.38598 q^{6} +0.0815889 q^{7} +1.00000 q^{8} +2.69289 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.38598 q^{3} +1.00000 q^{4} -3.46177 q^{5} -2.38598 q^{6} +0.0815889 q^{7} +1.00000 q^{8} +2.69289 q^{9} -3.46177 q^{10} -1.00000 q^{11} -2.38598 q^{12} +3.82373 q^{13} +0.0815889 q^{14} +8.25969 q^{15} +1.00000 q^{16} +3.10202 q^{17} +2.69289 q^{18} -0.518366 q^{19} -3.46177 q^{20} -0.194669 q^{21} -1.00000 q^{22} -5.34838 q^{23} -2.38598 q^{24} +6.98382 q^{25} +3.82373 q^{26} +0.732765 q^{27} +0.0815889 q^{28} -9.87114 q^{29} +8.25969 q^{30} -7.74062 q^{31} +1.00000 q^{32} +2.38598 q^{33} +3.10202 q^{34} -0.282442 q^{35} +2.69289 q^{36} -6.85008 q^{37} -0.518366 q^{38} -9.12333 q^{39} -3.46177 q^{40} -8.22301 q^{41} -0.194669 q^{42} +5.61647 q^{43} -1.00000 q^{44} -9.32214 q^{45} -5.34838 q^{46} +4.71648 q^{47} -2.38598 q^{48} -6.99334 q^{49} +6.98382 q^{50} -7.40136 q^{51} +3.82373 q^{52} +5.19718 q^{53} +0.732765 q^{54} +3.46177 q^{55} +0.0815889 q^{56} +1.23681 q^{57} -9.87114 q^{58} -9.19118 q^{59} +8.25969 q^{60} +8.92181 q^{61} -7.74062 q^{62} +0.219710 q^{63} +1.00000 q^{64} -13.2369 q^{65} +2.38598 q^{66} +12.6438 q^{67} +3.10202 q^{68} +12.7611 q^{69} -0.282442 q^{70} -2.10742 q^{71} +2.69289 q^{72} -6.06931 q^{73} -6.85008 q^{74} -16.6632 q^{75} -0.518366 q^{76} -0.0815889 q^{77} -9.12333 q^{78} +10.1129 q^{79} -3.46177 q^{80} -9.82702 q^{81} -8.22301 q^{82} +14.6015 q^{83} -0.194669 q^{84} -10.7385 q^{85} +5.61647 q^{86} +23.5523 q^{87} -1.00000 q^{88} -3.11482 q^{89} -9.32214 q^{90} +0.311974 q^{91} -5.34838 q^{92} +18.4689 q^{93} +4.71648 q^{94} +1.79446 q^{95} -2.38598 q^{96} +7.84193 q^{97} -6.99334 q^{98} -2.69289 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9}+O(q^{10}) $ 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9} - 24 q^{11} + 8 q^{12} + 9 q^{13} + 11 q^{14} + 6 q^{15} + 24 q^{16} - q^{17} + 28 q^{18} + 35 q^{19} + 21 q^{21} - 24 q^{22} + 13 q^{23} + 8 q^{24} + 38 q^{25} + 9 q^{26} + 23 q^{27} + 11 q^{28} + 15 q^{29} + 6 q^{30} + 31 q^{31} + 24 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 28 q^{36} + 13 q^{37} + 35 q^{38} + 31 q^{39} + 16 q^{41} + 21 q^{42} + 35 q^{43} - 24 q^{44} + 13 q^{45} + 13 q^{46} + 46 q^{47} + 8 q^{48} + 55 q^{49} + 38 q^{50} + 18 q^{51} + 9 q^{52} + 6 q^{53} + 23 q^{54} + 11 q^{56} + 18 q^{57} + 15 q^{58} + 13 q^{59} + 6 q^{60} + 60 q^{61} + 31 q^{62} + 52 q^{63} + 24 q^{64} - 9 q^{65} - 8 q^{66} + 28 q^{67} - q^{68} + 21 q^{69} + 28 q^{70} + 10 q^{71} + 28 q^{72} + 3 q^{73} + 13 q^{74} + 48 q^{75} + 35 q^{76} - 11 q^{77} + 31 q^{78} + 47 q^{79} + 16 q^{81} + 16 q^{82} + 66 q^{83} + 21 q^{84} + 37 q^{85} + 35 q^{86} + 34 q^{87} - 24 q^{88} - 5 q^{89} + 13 q^{90} + q^{91} + 13 q^{92} - 16 q^{93} + 46 q^{94} + 9 q^{95} + 8 q^{96} + 24 q^{97} + 55 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9 - 24 * q^11 + 8 * q^12 + 9 * q^13 + 11 * q^14 + 6 * q^15 + 24 * q^16 - q^17 + 28 * q^18 + 35 * q^19 + 21 * q^21 - 24 * q^22 + 13 * q^23 + 8 * q^24 + 38 * q^25 + 9 * q^26 + 23 * q^27 + 11 * q^28 + 15 * q^29 + 6 * q^30 + 31 * q^31 + 24 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 28 * q^36 + 13 * q^37 + 35 * q^38 + 31 * q^39 + 16 * q^41 + 21 * q^42 + 35 * q^43 - 24 * q^44 + 13 * q^45 + 13 * q^46 + 46 * q^47 + 8 * q^48 + 55 * q^49 + 38 * q^50 + 18 * q^51 + 9 * q^52 + 6 * q^53 + 23 * q^54 + 11 * q^56 + 18 * q^57 + 15 * q^58 + 13 * q^59 + 6 * q^60 + 60 * q^61 + 31 * q^62 + 52 * q^63 + 24 * q^64 - 9 * q^65 - 8 * q^66 + 28 * q^67 - q^68 + 21 * q^69 + 28 * q^70 + 10 * q^71 + 28 * q^72 + 3 * q^73 + 13 * q^74 + 48 * q^75 + 35 * q^76 - 11 * q^77 + 31 * q^78 + 47 * q^79 + 16 * q^81 + 16 * q^82 + 66 * q^83 + 21 * q^84 + 37 * q^85 + 35 * q^86 + 34 * q^87 - 24 * q^88 - 5 * q^89 + 13 * q^90 + q^91 + 13 * q^92 - 16 * q^93 + 46 * q^94 + 9 * q^95 + 8 * q^96 + 24 * q^97 + 55 * q^98 - 28 * 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
$3$	−2.38598	−1.37754	−0.688772	−	0.724978i	$-0.741850\pi$
$3$	−2.38598	−1.37754	−0.688772	+	0.724978i	$0.741850\pi$
$4$	1.00000	0.500000
$5$	−3.46177	−1.54815	−0.774074	−	0.633095i	$-0.781784\pi$
$5$	−3.46177	−1.54815	−0.774074	+	0.633095i	$0.781784\pi$
$6$	−2.38598	−0.974071
$7$	0.0815889	0.0308377	0.0154188	−	0.999881i	$-0.495092\pi$
$7$	0.0815889	0.0308377	0.0154188	+	0.999881i	$0.495092\pi$
$8$	1.00000	0.353553
$9$	2.69289	0.897629
$10$	−3.46177	−1.09471
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.38598	−0.688772
$13$	3.82373	1.06051	0.530256	−	0.847838i	$-0.322096\pi$
$13$	3.82373	1.06051	0.530256	+	0.847838i	$0.322096\pi$
$14$	0.0815889	0.0218055
$15$	8.25969	2.13264
$16$	1.00000	0.250000
$17$	3.10202	0.752351	0.376176	−	0.926548i	$-0.377239\pi$
$17$	3.10202	0.752351	0.376176	+	0.926548i	$0.377239\pi$
$18$	2.69289	0.634719
$19$	−0.518366	−0.118921	−0.0594606	−	0.998231i	$-0.518938\pi$
$19$	−0.518366	−0.118921	−0.0594606	+	0.998231i	$0.518938\pi$
$20$	−3.46177	−0.774074
$21$	−0.194669	−0.0424803
$22$	−1.00000	−0.213201
$23$	−5.34838	−1.11521	−0.557607	−	0.830105i	$-0.688281\pi$
$23$	−5.34838	−1.11521	−0.557607	+	0.830105i	$0.688281\pi$
$24$	−2.38598	−0.487036
$25$	6.98382	1.39676
$26$	3.82373	0.749895
$27$	0.732765	0.141021
$28$	0.0815889	0.0154188
$29$	−9.87114	−1.83302	−0.916512	−	0.400007i	$-0.869008\pi$
$29$	−9.87114	−1.83302	−0.916512	+	0.400007i	$0.869008\pi$
$30$	8.25969	1.50801
$31$	−7.74062	−1.39026	−0.695128	−	0.718886i	$-0.744652\pi$
$31$	−7.74062	−1.39026	−0.695128	+	0.718886i	$0.744652\pi$
$32$	1.00000	0.176777
$33$	2.38598	0.415345
$34$	3.10202	0.531993
$35$	−0.282442	−0.0477413
$36$	2.69289	0.448814
$37$	−6.85008	−1.12615	−0.563073	−	0.826407i	$-0.690381\pi$
$37$	−6.85008	−1.12615	−0.563073	+	0.826407i	$0.690381\pi$
$38$	−0.518366	−0.0840900
$39$	−9.12333	−1.46090
$40$	−3.46177	−0.547353
$41$	−8.22301	−1.28422	−0.642109	−	0.766613i	$-0.721941\pi$
$41$	−8.22301	−1.28422	−0.642109	+	0.766613i	$0.721941\pi$
$42$	−0.194669	−0.0300381
$43$	5.61647	0.856504	0.428252	−	0.903659i	$-0.359130\pi$
$43$	5.61647	0.856504	0.428252	+	0.903659i	$0.359130\pi$
$44$	−1.00000	−0.150756
$45$	−9.32214	−1.38966
$46$	−5.34838	−0.788576
$47$	4.71648	0.687969	0.343985	−	0.938975i	$-0.388223\pi$
$47$	4.71648	0.687969	0.343985	+	0.938975i	$0.388223\pi$
$48$	−2.38598	−0.344386
$49$	−6.99334	−0.999049
$50$	6.98382	0.987661
$51$	−7.40136	−1.03640
$52$	3.82373	0.530256
$53$	5.19718	0.713888	0.356944	−	0.934126i	$-0.383819\pi$
$53$	5.19718	0.713888	0.356944	+	0.934126i	$0.383819\pi$
$54$	0.732765	0.0997167
$55$	3.46177	0.466784
$56$	0.0815889	0.0109028
$57$	1.23681	0.163819
$58$	−9.87114	−1.29614
$59$	−9.19118	−1.19659	−0.598295	−	0.801276i	$-0.704155\pi$
$59$	−9.19118	−1.19659	−0.598295	+	0.801276i	$0.704155\pi$
$60$	8.25969	1.06632
$61$	8.92181	1.14232	0.571160	−	0.820839i	$-0.306493\pi$
$61$	8.92181	1.14232	0.571160	+	0.820839i	$0.306493\pi$
$62$	−7.74062	−0.983060
$63$	0.219710	0.0276808
$64$	1.00000	0.125000
$65$	−13.2369	−1.64183
$66$	2.38598	0.293693
$67$	12.6438	1.54469	0.772345	−	0.635204i	$-0.219084\pi$
$67$	12.6438	1.54469	0.772345	+	0.635204i	$0.219084\pi$
$68$	3.10202	0.376176
$69$	12.7611	1.53626
$70$	−0.282442	−0.0337582
$71$	−2.10742	−0.250105	−0.125053	−	0.992150i	$-0.539910\pi$
$71$	−2.10742	−0.250105	−0.125053	+	0.992150i	$0.539910\pi$
$72$	2.69289	0.317360
$73$	−6.06931	−0.710359	−0.355179	−	0.934798i	$-0.615580\pi$
$73$	−6.06931	−0.710359	−0.355179	+	0.934798i	$0.615580\pi$
$74$	−6.85008	−0.796306
$75$	−16.6632	−1.92410
$76$	−0.518366	−0.0594606
$77$	−0.0815889	−0.00929792
$78$	−9.12333	−1.03301
$79$	10.1129	1.13779	0.568896	−	0.822409i	$-0.307371\pi$
$79$	10.1129	1.13779	0.568896	+	0.822409i	$0.307371\pi$
$80$	−3.46177	−0.387037
$81$	−9.82702	−1.09189
$82$	−8.22301	−0.908080
$83$	14.6015	1.60273	0.801363	−	0.598179i	$-0.204109\pi$
$83$	14.6015	1.60273	0.801363	+	0.598179i	$0.204109\pi$
$84$	−0.194669	−0.0212402
$85$	−10.7385	−1.16475
$86$	5.61647	0.605640
$87$	23.5523	2.52507
$88$	−1.00000	−0.106600
$89$	−3.11482	−0.330170	−0.165085	−	0.986279i	$-0.552790\pi$
$89$	−3.11482	−0.330170	−0.165085	+	0.986279i	$0.552790\pi$
$90$	−9.32214	−0.982640
$91$	0.311974	0.0327037
$92$	−5.34838	−0.557607
$93$	18.4689	1.91514
$94$	4.71648	0.486468
$95$	1.79446	0.184108
$96$	−2.38598	−0.243518
$97$	7.84193	0.796227	0.398114	−	0.917336i	$-0.369665\pi$
$97$	7.84193	0.796227	0.398114	+	0.917336i	$0.369665\pi$
$98$	−6.99334	−0.706434
$99$	−2.69289	−0.270645
$100$	6.98382	0.698382
$101$	11.6310	1.15732	0.578661	−	0.815568i	$-0.303575\pi$
$101$	11.6310	1.15732	0.578661	+	0.815568i	$0.303575\pi$
$102$	−7.40136	−0.732844
$103$	4.63482	0.456683	0.228341	−	0.973581i	$-0.426670\pi$
$103$	4.63482	0.456683	0.228341	+	0.973581i	$0.426670\pi$
$104$	3.82373	0.374947
$105$	0.673899	0.0657658
$106$	5.19718	0.504795
$107$	−1.33096	−0.128669	−0.0643343	−	0.997928i	$-0.520492\pi$
$107$	−1.33096	−0.128669	−0.0643343	+	0.997928i	$0.520492\pi$
$108$	0.732765	0.0705104
$109$	0.408588	0.0391357	0.0195678	−	0.999809i	$-0.493771\pi$
$109$	0.408588	0.0391357	0.0195678	+	0.999809i	$0.493771\pi$
$110$	3.46177	0.330066
$111$	16.3441	1.55132
$112$	0.0815889	0.00770942
$113$	14.3578	1.35067	0.675334	−	0.737512i	$-0.263999\pi$
$113$	14.3578	1.35067	0.675334	+	0.737512i	$0.263999\pi$
$114$	1.23681	0.115838
$115$	18.5148	1.72652
$116$	−9.87114	−0.916512
$117$	10.2969	0.951946
$118$	−9.19118	−0.846116
$119$	0.253091	0.0232008
$120$	8.25969	0.754003
$121$	1.00000	0.0909091
$122$	8.92181	0.807743
$123$	19.6199	1.76907
$124$	−7.74062	−0.695128
$125$	−6.86752	−0.614249
$126$	0.219710	0.0195733
$127$	2.72481	0.241788	0.120894	−	0.992665i	$-0.461424\pi$
$127$	2.72481	0.241788	0.120894	+	0.992665i	$0.461424\pi$
$128$	1.00000	0.0883883
$129$	−13.4008	−1.17987
$130$	−13.2369	−1.16095
$131$	5.58058	0.487578	0.243789	−	0.969828i	$-0.421610\pi$
$131$	5.58058	0.487578	0.243789	+	0.969828i	$0.421610\pi$
$132$	2.38598	0.207673
$133$	−0.0422929	−0.00366726
$134$	12.6438	1.09226
$135$	−2.53666	−0.218321
$136$	3.10202	0.265996
$137$	−10.6046	−0.906013	−0.453006	−	0.891507i	$-0.649649\pi$
$137$	−10.6046	−0.906013	−0.453006	+	0.891507i	$0.649649\pi$
$138$	12.7611	1.08630
$139$	14.0650	1.19298	0.596488	−	0.802622i	$-0.296562\pi$
$139$	14.0650	1.19298	0.596488	+	0.802622i	$0.296562\pi$
$140$	−0.282442	−0.0238707
$141$	−11.2534	−0.947708
$142$	−2.10742	−0.176851
$143$	−3.82373	−0.319756
$144$	2.69289	0.224407
$145$	34.1716	2.83779
$146$	−6.06931	−0.502300
$147$	16.6860	1.37623
$148$	−6.85008	−0.563073
$149$	6.72224	0.550707	0.275354	−	0.961343i	$-0.411205\pi$
$149$	6.72224	0.550707	0.275354	+	0.961343i	$0.411205\pi$
$150$	−16.6632	−1.36055
$151$	−8.78877	−0.715220	−0.357610	−	0.933871i	$-0.616408\pi$
$151$	−8.78877	−0.715220	−0.357610	+	0.933871i	$0.616408\pi$
$152$	−0.518366	−0.0420450
$153$	8.35340	0.675332
$154$	−0.0815889	−0.00657462
$155$	26.7962	2.15232
$156$	−9.12333	−0.730451
$157$	8.91365	0.711386	0.355693	−	0.934603i	$-0.384245\pi$
$157$	8.91365	0.711386	0.355693	+	0.934603i	$0.384245\pi$
$158$	10.1129	0.804541
$159$	−12.4004	−0.983412
$160$	−3.46177	−0.273677
$161$	−0.436369	−0.0343907
$162$	−9.82702	−0.772084
$163$	4.23045	0.331354	0.165677	−	0.986180i	$-0.447019\pi$
$163$	4.23045	0.331354	0.165677	+	0.986180i	$0.447019\pi$
$164$	−8.22301	−0.642109
$165$	−8.25969	−0.643016
$166$	14.6015	1.13330
$167$	−2.88384	−0.223158	−0.111579	−	0.993756i	$-0.535591\pi$
$167$	−2.88384	−0.223158	−0.111579	+	0.993756i	$0.535591\pi$
$168$	−0.194669	−0.0150191
$169$	1.62090	0.124685
$170$	−10.7385	−0.823604
$171$	−1.39590	−0.106747
$172$	5.61647	0.428252
$173$	−1.11796	−0.0849966	−0.0424983	−	0.999097i	$-0.513532\pi$
$173$	−1.11796	−0.0849966	−0.0424983	+	0.999097i	$0.513532\pi$
$174$	23.5523	1.78550
$175$	0.569802	0.0430730
$176$	−1.00000	−0.0753778
$177$	21.9299	1.64836
$178$	−3.11482	−0.233466
$179$	−25.2017	−1.88366	−0.941830	−	0.336090i	$-0.890896\pi$
$179$	−25.2017	−1.88366	−0.941830	+	0.336090i	$0.890896\pi$
$180$	−9.32214	−0.694831
$181$	3.72573	0.276932	0.138466	−	0.990367i	$-0.455783\pi$
$181$	3.72573	0.276932	0.138466	+	0.990367i	$0.455783\pi$
$182$	0.311974	0.0231250
$183$	−21.2872	−1.57360
$184$	−5.34838	−0.394288
$185$	23.7134	1.74344
$186$	18.4689	1.35421
$187$	−3.10202	−0.226842
$188$	4.71648	0.343985
$189$	0.0597855	0.00434876
$190$	1.79446	0.130184
$191$	17.2173	1.24580	0.622900	−	0.782302i	$-0.285955\pi$
$191$	17.2173	1.24580	0.622900	+	0.782302i	$0.285955\pi$
$192$	−2.38598	−0.172193
$193$	9.46096	0.681015	0.340507	−	0.940242i	$-0.389401\pi$
$193$	9.46096	0.681015	0.340507	+	0.940242i	$0.389401\pi$
$194$	7.84193	0.563018
$195$	31.5828	2.26169
$196$	−6.99334	−0.499525
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	−2.69289	−0.191375
$199$	17.8434	1.26489	0.632443	−	0.774607i	$-0.282052\pi$
$199$	17.8434	1.26489	0.632443	+	0.774607i	$0.282052\pi$
$200$	6.98382	0.493831
$201$	−30.1679	−2.12788
$202$	11.6310	0.818351
$203$	−0.805375	−0.0565263
$204$	−7.40136	−0.518199
$205$	28.4661	1.98816
$206$	4.63482	0.322923
$207$	−14.4026	−1.00105
$208$	3.82373	0.265128
$209$	0.518366	0.0358561
$210$	0.673899	0.0465035
$211$	8.81169	0.606621	0.303311	−	0.952892i	$-0.401908\pi$
$211$	8.81169	0.606621	0.303311	+	0.952892i	$0.401908\pi$
$212$	5.19718	0.356944
$213$	5.02826	0.344531
$214$	−1.33096	−0.0909825
$215$	−19.4429	−1.32600
$216$	0.732765	0.0498584
$217$	−0.631549	−0.0428723
$218$	0.408588	0.0276731
$219$	14.4812	0.978551
$220$	3.46177	0.233392
$221$	11.8613	0.797877
$222$	16.3441	1.09695
$223$	−27.0668	−1.81253	−0.906263	−	0.422714i	$-0.861078\pi$
$223$	−27.0668	−1.81253	−0.906263	+	0.422714i	$0.861078\pi$
$224$	0.0815889	0.00545139
$225$	18.8066	1.25378
$226$	14.3578	0.955067
$227$	1.62502	0.107856	0.0539282	−	0.998545i	$-0.482826\pi$
$227$	1.62502	0.107856	0.0539282	+	0.998545i	$0.482826\pi$
$228$	1.23681	0.0819097
$229$	14.6032	0.965007	0.482503	−	0.875894i	$-0.339728\pi$
$229$	14.6032	0.965007	0.482503	+	0.875894i	$0.339728\pi$
$230$	18.5148	1.22083
$231$	0.194669	0.0128083
$232$	−9.87114	−0.648072
$233$	−27.4739	−1.79988	−0.899939	−	0.436016i	$-0.856389\pi$
$233$	−27.4739	−1.79988	−0.899939	+	0.436016i	$0.856389\pi$
$234$	10.2969	0.673127
$235$	−16.3273	−1.06508
$236$	−9.19118	−0.598295
$237$	−24.1292	−1.56736
$238$	0.253091	0.0164054
$239$	17.3832	1.12443	0.562213	−	0.826993i	$-0.309950\pi$
$239$	17.3832	1.12443	0.562213	+	0.826993i	$0.309950\pi$
$240$	8.25969	0.533161
$241$	−11.0253	−0.710204	−0.355102	−	0.934828i	$-0.615554\pi$
$241$	−11.0253	−0.710204	−0.355102	+	0.934828i	$0.615554\pi$
$242$	1.00000	0.0642824
$243$	21.2488	1.36311
$244$	8.92181	0.571160
$245$	24.2093	1.54668
$246$	19.6199	1.25092
$247$	−1.98209	−0.126117
$248$	−7.74062	−0.491530
$249$	−34.8389	−2.20783
$250$	−6.86752	−0.434340
$251$	−15.2133	−0.960254	−0.480127	−	0.877199i	$-0.659409\pi$
$251$	−15.2133	−0.960254	−0.480127	+	0.877199i	$0.659409\pi$
$252$	0.219710	0.0138404
$253$	5.34838	0.336250
$254$	2.72481	0.170970
$255$	25.6218	1.60450
$256$	1.00000	0.0625000
$257$	−26.1028	−1.62825	−0.814125	−	0.580690i	$-0.802783\pi$
$257$	−26.1028	−1.62825	−0.814125	+	0.580690i	$0.802783\pi$
$258$	−13.4008	−0.834296
$259$	−0.558891	−0.0347278
$260$	−13.2369	−0.820915
$261$	−26.5819	−1.64538
$262$	5.58058	0.344769
$263$	8.98049	0.553760	0.276880	−	0.960904i	$-0.410699\pi$
$263$	8.98049	0.553760	0.276880	+	0.960904i	$0.410699\pi$
$264$	2.38598	0.146847
$265$	−17.9914	−1.10520
$266$	−0.0422929	−0.00259314
$267$	7.43189	0.454824
$268$	12.6438	0.772345
$269$	14.1260	0.861279	0.430640	−	0.902524i	$-0.358288\pi$
$269$	14.1260	0.861279	0.430640	+	0.902524i	$0.358288\pi$
$270$	−2.53666	−0.154376
$271$	11.0822	0.673195	0.336597	−	0.941649i	$-0.390724\pi$
$271$	11.0822	0.673195	0.336597	+	0.941649i	$0.390724\pi$
$272$	3.10202	0.188088
$273$	−0.744362	−0.0450509
$274$	−10.6046	−0.640648
$275$	−6.98382	−0.421140
$276$	12.7611	0.768129
$277$	−29.9652	−1.80044	−0.900218	−	0.435439i	$-0.856593\pi$
$277$	−29.9652	−1.80044	−0.900218	+	0.435439i	$0.856593\pi$
$278$	14.0650	0.843562
$279$	−20.8446	−1.24793
$280$	−0.282442	−0.0168791
$281$	−12.7326	−0.759564	−0.379782	−	0.925076i	$-0.624001\pi$
$281$	−12.7326	−0.759564	−0.379782	+	0.925076i	$0.624001\pi$
$282$	−11.2534	−0.670131
$283$	−13.1451	−0.781395	−0.390698	−	0.920519i	$-0.627766\pi$
$283$	−13.1451	−0.781395	−0.390698	+	0.920519i	$0.627766\pi$
$284$	−2.10742	−0.125053
$285$	−4.28154	−0.253617
$286$	−3.82373	−0.226102
$287$	−0.670907	−0.0396024
$288$	2.69289	0.158680
$289$	−7.37745	−0.433967
$290$	34.1716	2.00662
$291$	−18.7107	−1.09684
$292$	−6.06931	−0.355179
$293$	23.0838	1.34857	0.674285	−	0.738471i	$-0.264452\pi$
$293$	23.0838	1.34857	0.674285	+	0.738471i	$0.264452\pi$
$294$	16.6860	0.973145
$295$	31.8177	1.85250
$296$	−6.85008	−0.398153
$297$	−0.732765	−0.0425194
$298$	6.72224	0.389409
$299$	−20.4508	−1.18270
$300$	−16.6632	−0.962052
$301$	0.458242	0.0264126
$302$	−8.78877	−0.505737
$303$	−27.7512	−1.59426
$304$	−0.518366	−0.0297303
$305$	−30.8852	−1.76848
$306$	8.35340	0.477532
$307$	8.61516	0.491693	0.245846	−	0.969309i	$-0.420934\pi$
$307$	8.61516	0.491693	0.245846	+	0.969309i	$0.420934\pi$
$308$	−0.0815889	−0.00464896
$309$	−11.0586	−0.629101
$310$	26.7962	1.52192
$311$	12.8976	0.731358	0.365679	−	0.930741i	$-0.380837\pi$
$311$	12.8976	0.731358	0.365679	+	0.930741i	$0.380837\pi$
$312$	−9.12333	−0.516507
$313$	26.9171	1.52144	0.760722	−	0.649078i	$-0.224845\pi$
$313$	26.9171	1.52144	0.760722	+	0.649078i	$0.224845\pi$
$314$	8.91365	0.503026
$315$	−0.760583	−0.0428540
$316$	10.1129	0.568896
$317$	−3.60757	−0.202621	−0.101311	−	0.994855i	$-0.532304\pi$
$317$	−3.60757	−0.202621	−0.101311	+	0.994855i	$0.532304\pi$
$318$	−12.4004	−0.695377
$319$	9.87114	0.552678
$320$	−3.46177	−0.193519
$321$	3.17564	0.177247
$322$	−0.436369	−0.0243179
$323$	−1.60798	−0.0894706
$324$	−9.82702	−0.545946
$325$	26.7042	1.48128
$326$	4.23045	0.234303
$327$	−0.974882	−0.0539111
$328$	−8.22301	−0.454040
$329$	0.384812	0.0212154
$330$	−8.25969	−0.454681
$331$	8.08631	0.444464	0.222232	−	0.974994i	$-0.428666\pi$
$331$	8.08631	0.444464	0.222232	+	0.974994i	$0.428666\pi$
$332$	14.6015	0.801363
$333$	−18.4465	−1.01086
$334$	−2.88384	−0.157797
$335$	−43.7700	−2.39141
$336$	−0.194669	−0.0106201
$337$	23.2260	1.26520	0.632599	−	0.774479i	$-0.281988\pi$
$337$	23.2260	1.26520	0.632599	+	0.774479i	$0.281988\pi$
$338$	1.62090	0.0881654
$339$	−34.2574	−1.86061
$340$	−10.7385	−0.582376
$341$	7.74062	0.419178
$342$	−1.39590	−0.0754816
$343$	−1.14170	−0.0616461
$344$	5.61647	0.302820
$345$	−44.1760	−2.37836
$346$	−1.11796	−0.0601017
$347$	4.61215	0.247593	0.123797	−	0.992308i	$-0.460493\pi$
$347$	4.61215	0.247593	0.123797	+	0.992308i	$0.460493\pi$
$348$	23.5523	1.26254
$349$	22.4311	1.20071	0.600354	−	0.799735i	$-0.295026\pi$
$349$	22.4311	1.20071	0.600354	+	0.799735i	$0.295026\pi$
$350$	0.569802	0.0304572
$351$	2.80190	0.149554
$352$	−1.00000	−0.0533002
$353$	20.5492	1.09372	0.546861	−	0.837223i	$-0.315823\pi$
$353$	20.5492	1.09372	0.546861	+	0.837223i	$0.315823\pi$
$354$	21.9299	1.16556
$355$	7.29540	0.387200
$356$	−3.11482	−0.165085
$357$	−0.603869	−0.0319601
$358$	−25.2017	−1.33195
$359$	19.9555	1.05321	0.526604	−	0.850111i	$-0.323465\pi$
$359$	19.9555	1.05321	0.526604	+	0.850111i	$0.323465\pi$
$360$	−9.32214	−0.491320
$361$	−18.7313	−0.985858
$362$	3.72573	0.195820
$363$	−2.38598	−0.125231
$364$	0.311974	0.0163519
$365$	21.0105	1.09974
$366$	−21.2872	−1.11270
$367$	5.73619	0.299427	0.149713	−	0.988729i	$-0.452165\pi$
$367$	5.73619	0.299427	0.149713	+	0.988729i	$0.452165\pi$
$368$	−5.34838	−0.278804
$369$	−22.1436	−1.15275
$370$	23.7134	1.23280
$371$	0.424032	0.0220147
$372$	18.4689	0.957570
$373$	−16.4749	−0.853038	−0.426519	−	0.904479i	$-0.640260\pi$
$373$	−16.4749	−0.853038	−0.426519	+	0.904479i	$0.640260\pi$
$374$	−3.10202	−0.160402
$375$	16.3857	0.846156
$376$	4.71648	0.243234
$377$	−37.7446	−1.94394
$378$	0.0597855	0.00307503
$379$	15.3549	0.788728	0.394364	−	0.918954i	$-0.370965\pi$
$379$	15.3549	0.788728	0.394364	+	0.918954i	$0.370965\pi$
$380$	1.79446	0.0920539
$381$	−6.50133	−0.333073
$382$	17.2173	0.880913
$383$	21.8210	1.11500	0.557499	−	0.830177i	$-0.311761\pi$
$383$	21.8210	1.11500	0.557499	+	0.830177i	$0.311761\pi$
$384$	−2.38598	−0.121759
$385$	0.282442	0.0143946
$386$	9.46096	0.481550
$387$	15.1245	0.768823
$388$	7.84193	0.398114
$389$	−11.1228	−0.563946	−0.281973	−	0.959422i	$-0.590989\pi$
$389$	−11.1228	−0.563946	−0.281973	+	0.959422i	$0.590989\pi$
$390$	31.5828	1.59926
$391$	−16.5908	−0.839034
$392$	−6.99334	−0.353217
$393$	−13.3151	−0.671660
$394$	−1.00000	−0.0503793
$395$	−35.0086	−1.76147
$396$	−2.69289	−0.135323
$397$	30.0429	1.50781	0.753905	−	0.656984i	$-0.228168\pi$
$397$	30.0429	1.50781	0.753905	+	0.656984i	$0.228168\pi$
$398$	17.8434	0.894409
$399$	0.100910	0.00505181
$400$	6.98382	0.349191
$401$	14.9384	0.745987	0.372993	−	0.927834i	$-0.378331\pi$
$401$	14.9384	0.745987	0.372993	+	0.927834i	$0.378331\pi$
$402$	−30.1679	−1.50464
$403$	−29.5980	−1.47438
$404$	11.6310	0.578661
$405$	34.0188	1.69041
$406$	−0.805375	−0.0399701
$407$	6.85008	0.339546
$408$	−7.40136	−0.366422
$409$	36.8812	1.82366	0.911828	−	0.410572i	$-0.134671\pi$
$409$	36.8812	1.82366	0.911828	+	0.410572i	$0.134671\pi$
$410$	28.4661	1.40584
$411$	25.3024	1.24807
$412$	4.63482	0.228341
$413$	−0.749898	−0.0369001
$414$	−14.4026	−0.707849
$415$	−50.5470	−2.48126
$416$	3.82373	0.187474
$417$	−33.5587	−1.64338
$418$	0.518366	0.0253541
$419$	19.1578	0.935920	0.467960	−	0.883750i	$-0.344989\pi$
$419$	19.1578	0.935920	0.467960	+	0.883750i	$0.344989\pi$
$420$	0.673899	0.0328829
$421$	17.3698	0.846552	0.423276	−	0.906001i	$-0.360880\pi$
$421$	17.3698	0.846552	0.423276	+	0.906001i	$0.360880\pi$
$422$	8.81169	0.428946
$423$	12.7009	0.617541
$424$	5.19718	0.252397
$425$	21.6640	1.05086
$426$	5.02826	0.243620
$427$	0.727920	0.0352265
$428$	−1.33096	−0.0643343
$429$	9.12333	0.440478
$430$	−19.4429	−0.937620
$431$	−15.1837	−0.731371	−0.365685	−	0.930738i	$-0.619165\pi$
$431$	−15.1837	−0.731371	−0.365685	+	0.930738i	$0.619165\pi$
$432$	0.732765	0.0352552
$433$	18.0552	0.867676	0.433838	−	0.900991i	$-0.357159\pi$
$433$	18.0552	0.867676	0.433838	+	0.900991i	$0.357159\pi$
$434$	−0.631549	−0.0303153
$435$	−81.5326	−3.90919
$436$	0.408588	0.0195678
$437$	2.77242	0.132623
$438$	14.4812	0.691940
$439$	−21.1408	−1.00899	−0.504497	−	0.863413i	$-0.668322\pi$
$439$	−21.1408	−1.00899	−0.504497	+	0.863413i	$0.668322\pi$
$440$	3.46177	0.165033
$441$	−18.8323	−0.896775
$442$	11.8613	0.564184
$443$	1.88656	0.0896332	0.0448166	−	0.998995i	$-0.485730\pi$
$443$	1.88656	0.0896332	0.0448166	+	0.998995i	$0.485730\pi$
$444$	16.3441	0.775658
$445$	10.7828	0.511153
$446$	−27.0668	−1.28165
$447$	−16.0391	−0.758623
$448$	0.0815889	0.00385471
$449$	−26.2338	−1.23805	−0.619025	−	0.785371i	$-0.712472\pi$
$449$	−26.2338	−1.23805	−0.619025	+	0.785371i	$0.712472\pi$
$450$	18.8066	0.886553
$451$	8.22301	0.387207
$452$	14.3578	0.675334
$453$	20.9698	0.985248
$454$	1.62502	0.0762660
$455$	−1.07998	−0.0506302
$456$	1.23681	0.0579189
$457$	−31.8347	−1.48916	−0.744581	−	0.667532i	$-0.767351\pi$
$457$	−31.8347	−1.48916	−0.744581	+	0.667532i	$0.767351\pi$
$458$	14.6032	0.682363
$459$	2.27306	0.106097
$460$	18.5148	0.863259
$461$	40.0679	1.86615	0.933074	−	0.359685i	$-0.117116\pi$
$461$	40.0679	1.86615	0.933074	+	0.359685i	$0.117116\pi$
$462$	0.194669	0.00905683
$463$	13.6793	0.635729	0.317865	−	0.948136i	$-0.397034\pi$
$463$	13.6793	0.635729	0.317865	+	0.948136i	$0.397034\pi$
$464$	−9.87114	−0.458256
$465$	−63.9352	−2.96492
$466$	−27.4739	−1.27271
$467$	7.72554	0.357495	0.178748	−	0.983895i	$-0.442795\pi$
$467$	7.72554	0.357495	0.178748	+	0.983895i	$0.442795\pi$
$468$	10.2969	0.475973
$469$	1.03160	0.0476347
$470$	−16.3273	−0.753124
$471$	−21.2678	−0.979966
$472$	−9.19118	−0.423058
$473$	−5.61647	−0.258246
$474$	−24.1292	−1.10829
$475$	−3.62017	−0.166105
$476$	0.253091	0.0116004
$477$	13.9954	0.640806
$478$	17.3832	0.795089
$479$	33.7895	1.54388	0.771942	−	0.635693i	$-0.219286\pi$
$479$	33.7895	1.54388	0.771942	+	0.635693i	$0.219286\pi$
$480$	8.25969	0.377002
$481$	−26.1929	−1.19429
$482$	−11.0253	−0.502190
$483$	1.04117	0.0473747
$484$	1.00000	0.0454545
$485$	−27.1469	−1.23268
$486$	21.2488	0.963863
$487$	3.78692	0.171602	0.0858009	−	0.996312i	$-0.472655\pi$
$487$	3.78692	0.171602	0.0858009	+	0.996312i	$0.472655\pi$
$488$	8.92181	0.403871
$489$	−10.0938	−0.456456
$490$	24.2093	1.09367
$491$	18.7155	0.844619	0.422309	−	0.906452i	$-0.361220\pi$
$491$	18.7155	0.844619	0.422309	+	0.906452i	$0.361220\pi$
$492$	19.6199	0.884534
$493$	−30.6205	−1.37908
$494$	−1.98209	−0.0891784
$495$	9.32214	0.418999
$496$	−7.74062	−0.347564
$497$	−0.171942	−0.00771267
$498$	−34.8389	−1.56117
$499$	21.5094	0.962892	0.481446	−	0.876476i	$-0.340112\pi$
$499$	21.5094	0.962892	0.481446	+	0.876476i	$0.340112\pi$
$500$	−6.86752	−0.307125
$501$	6.88078	0.307411
$502$	−15.2133	−0.679002
$503$	31.8834	1.42161	0.710805	−	0.703389i	$-0.248331\pi$
$503$	31.8834	1.42161	0.710805	+	0.703389i	$0.248331\pi$
$504$	0.219710	0.00978664
$505$	−40.2636	−1.79171
$506$	5.34838	0.237765
$507$	−3.86743	−0.171759
$508$	2.72481	0.120894
$509$	17.8550	0.791408	0.395704	−	0.918378i	$-0.370501\pi$
$509$	17.8550	0.791408	0.395704	+	0.918378i	$0.370501\pi$
$510$	25.6218	1.13455
$511$	−0.495188	−0.0219058
$512$	1.00000	0.0441942
$513$	−0.379840	−0.0167704
$514$	−26.1028	−1.15135
$515$	−16.0447	−0.707013
$516$	−13.4008	−0.589936
$517$	−4.71648	−0.207431
$518$	−0.558891	−0.0245562
$519$	2.66742	0.117087
$520$	−13.2369	−0.580474
$521$	−26.3190	−1.15306	−0.576528	−	0.817078i	$-0.695593\pi$
$521$	−26.3190	−1.15306	−0.576528	+	0.817078i	$0.695593\pi$
$522$	−26.5819	−1.16346
$523$	4.99632	0.218474	0.109237	−	0.994016i	$-0.465159\pi$
$523$	4.99632	0.218474	0.109237	+	0.994016i	$0.465159\pi$
$524$	5.58058	0.243789
$525$	−1.35953	−0.0593349
$526$	8.98049	0.391568
$527$	−24.0116	−1.04596
$528$	2.38598	0.103836
$529$	5.60520	0.243704
$530$	−17.9914	−0.781497
$531$	−24.7508	−1.07409
$532$	−0.0422929	−0.00183363
$533$	−31.4426	−1.36193
$534$	7.43189	0.321609
$535$	4.60747	0.199198
$536$	12.6438	0.546130
$537$	60.1306	2.59483
$538$	14.1260	0.609016
$539$	6.99334	0.301225
$540$	−2.53666	−0.109161
$541$	27.2645	1.17219	0.586095	−	0.810242i	$-0.300664\pi$
$541$	27.2645	1.17219	0.586095	+	0.810242i	$0.300664\pi$
$542$	11.0822	0.476020
$543$	−8.88951	−0.381486
$544$	3.10202	0.132998
$545$	−1.41444	−0.0605878
$546$	−0.744362	−0.0318558
$547$	−28.4359	−1.21583	−0.607916	−	0.794001i	$-0.707994\pi$
$547$	−28.4359	−1.21583	−0.607916	+	0.794001i	$0.707994\pi$
$548$	−10.6046	−0.453006
$549$	24.0254	1.02538
$550$	−6.98382	−0.297791
$551$	5.11686	0.217986
$552$	12.7611	0.543149
$553$	0.825102	0.0350869
$554$	−29.9652	−1.27310
$555$	−56.5796	−2.40167
$556$	14.0650	0.596488
$557$	−35.1125	−1.48776	−0.743881	−	0.668312i	$-0.767017\pi$
$557$	−35.1125	−1.48776	−0.743881	+	0.668312i	$0.767017\pi$
$558$	−20.8446	−0.882423
$559$	21.4759	0.908332
$560$	−0.282442	−0.0119353
$561$	7.40136	0.312486
$562$	−12.7326	−0.537093
$563$	5.54907	0.233865	0.116933	−	0.993140i	$-0.462694\pi$
$563$	5.54907	0.233865	0.116933	+	0.993140i	$0.462694\pi$
$564$	−11.2534	−0.473854
$565$	−49.7033	−2.09104
$566$	−13.1451	−0.552530
$567$	−0.801776	−0.0336714
$568$	−2.10742	−0.0884255
$569$	−32.0625	−1.34413	−0.672065	−	0.740492i	$-0.734593\pi$
$569$	−32.0625	−1.34413	−0.672065	+	0.740492i	$0.734593\pi$
$570$	−4.28154	−0.179334
$571$	1.56875	0.0656501	0.0328250	−	0.999461i	$-0.489550\pi$
$571$	1.56875	0.0656501	0.0328250	+	0.999461i	$0.489550\pi$
$572$	−3.82373	−0.159878
$573$	−41.0800	−1.71614
$574$	−0.670907	−0.0280031
$575$	−37.3521	−1.55769
$576$	2.69289	0.112204
$577$	−26.3944	−1.09881	−0.549407	−	0.835555i	$-0.685146\pi$
$577$	−26.3944	−1.09881	−0.549407	+	0.835555i	$0.685146\pi$
$578$	−7.37745	−0.306861
$579$	−22.5736	−0.938128
$580$	34.1716	1.41890
$581$	1.19132	0.0494244
$582$	−18.7107	−0.775582
$583$	−5.19718	−0.215245
$584$	−6.06931	−0.251150
$585$	−35.6453	−1.47375
$586$	23.0838	0.953583
$587$	10.6050	0.437716	0.218858	−	0.975757i	$-0.429767\pi$
$587$	10.6050	0.437716	0.218858	+	0.975757i	$0.429767\pi$
$588$	16.6860	0.688117
$589$	4.01247	0.165331
$590$	31.8177	1.30991
$591$	2.38598	0.0981460
$592$	−6.85008	−0.281537
$593$	−33.7714	−1.38682	−0.693412	−	0.720542i	$-0.743893\pi$
$593$	−33.7714	−1.38682	−0.693412	+	0.720542i	$0.743893\pi$
$594$	−0.732765	−0.0300657
$595$	−0.876141	−0.0359183
$596$	6.72224	0.275354
$597$	−42.5740	−1.74244
$598$	−20.4508	−0.836294
$599$	22.2668	0.909798	0.454899	−	0.890543i	$-0.349675\pi$
$599$	22.2668	0.909798	0.454899	+	0.890543i	$0.349675\pi$
$600$	−16.6632	−0.680274
$601$	18.1064	0.738576	0.369288	−	0.929315i	$-0.379602\pi$
$601$	18.1064	0.738576	0.369288	+	0.929315i	$0.379602\pi$
$602$	0.458242	0.0186765
$603$	34.0484	1.38656
$604$	−8.78877	−0.357610
$605$	−3.46177	−0.140741
$606$	−27.7512	−1.12731
$607$	4.84567	0.196680	0.0983398	−	0.995153i	$-0.468647\pi$
$607$	4.84567	0.196680	0.0983398	+	0.995153i	$0.468647\pi$
$608$	−0.518366	−0.0210225
$609$	1.92161	0.0778674
$610$	−30.8852	−1.25051
$611$	18.0345	0.729599
$612$	8.35340	0.337666
$613$	−1.33806	−0.0540438	−0.0270219	−	0.999635i	$-0.508602\pi$
$613$	−1.33806	−0.0540438	−0.0270219	+	0.999635i	$0.508602\pi$
$614$	8.61516	0.347679
$615$	−67.9196	−2.73878
$616$	−0.0815889	−0.00328731
$617$	10.7523	0.432872	0.216436	−	0.976297i	$-0.430557\pi$
$617$	10.7523	0.432872	0.216436	+	0.976297i	$0.430557\pi$
$618$	−11.0586	−0.444841
$619$	14.0176	0.563416	0.281708	−	0.959500i	$-0.409099\pi$
$619$	14.0176	0.563416	0.281708	+	0.959500i	$0.409099\pi$
$620$	26.7962	1.07616
$621$	−3.91911	−0.157268
$622$	12.8976	0.517148
$623$	−0.254135	−0.0101817
$624$	−9.12333	−0.365225
$625$	−11.1454	−0.445815
$626$	26.9171	1.07582
$627$	−1.23681	−0.0493934
$628$	8.91365	0.355693
$629$	−21.2491	−0.847258
$630$	−0.760583	−0.0303024
$631$	27.6470	1.10061	0.550305	−	0.834964i	$-0.314511\pi$
$631$	27.6470	1.10061	0.550305	+	0.834964i	$0.314511\pi$
$632$	10.1129	0.402270
$633$	−21.0245	−0.835648
$634$	−3.60757	−0.143275
$635$	−9.43264	−0.374323
$636$	−12.4004	−0.491706
$637$	−26.7406	−1.05950
$638$	9.87114	0.390802
$639$	−5.67505	−0.224502
$640$	−3.46177	−0.136838
$641$	−46.7618	−1.84698	−0.923491	−	0.383621i	$-0.874677\pi$
$641$	−46.7618	−1.84698	−0.923491	+	0.383621i	$0.874677\pi$
$642$	3.17564	0.125332
$643$	32.7287	1.29069	0.645347	−	0.763890i	$-0.276713\pi$
$643$	32.7287	1.29069	0.645347	+	0.763890i	$0.276713\pi$
$644$	−0.436369	−0.0171953
$645$	46.3903	1.82662
$646$	−1.60798	−0.0632652
$647$	27.2420	1.07100	0.535498	−	0.844537i	$-0.320124\pi$
$647$	27.2420	1.07100	0.535498	+	0.844537i	$0.320124\pi$
$648$	−9.82702	−0.386042
$649$	9.19118	0.360785
$650$	26.7042	1.04743
$651$	1.50686	0.0590585
$652$	4.23045	0.165677
$653$	14.6555	0.573514	0.286757	−	0.958003i	$-0.407423\pi$
$653$	14.6555	0.573514	0.286757	+	0.958003i	$0.407423\pi$
$654$	−0.974882	−0.0381209
$655$	−19.3187	−0.754842
$656$	−8.22301	−0.321055
$657$	−16.3440	−0.637639
$658$	0.384812	0.0150015
$659$	−18.9221	−0.737101	−0.368551	−	0.929608i	$-0.620146\pi$
$659$	−18.9221	−0.737101	−0.368551	+	0.929608i	$0.620146\pi$
$660$	−8.25969	−0.321508
$661$	38.4017	1.49365	0.746827	−	0.665018i	$-0.231576\pi$
$661$	38.4017	1.49365	0.746827	+	0.665018i	$0.231576\pi$
$662$	8.08631	0.314284
$663$	−28.3008	−1.09911
$664$	14.6015	0.566649
$665$	0.146408	0.00567746
$666$	−18.4465	−0.714787
$667$	52.7946	2.04422
$668$	−2.88384	−0.111579
$669$	64.5808	2.49684
$670$	−43.7700	−1.69098
$671$	−8.92181	−0.344423
$672$	−0.194669	−0.00750953
$673$	−7.56512	−0.291614	−0.145807	−	0.989313i	$-0.546578\pi$
$673$	−7.56512	−0.291614	−0.145807	+	0.989313i	$0.546578\pi$
$674$	23.2260	0.894630
$675$	5.11750	0.196973
$676$	1.62090	0.0623423
$677$	−13.0490	−0.501514	−0.250757	−	0.968050i	$-0.580680\pi$
$677$	−13.0490	−0.501514	−0.250757	+	0.968050i	$0.580680\pi$
$678$	−34.2574	−1.31565
$679$	0.639814	0.0245538
$680$	−10.7385	−0.411802
$681$	−3.87726	−0.148577
$682$	7.74062	0.296404
$683$	−18.9727	−0.725970	−0.362985	−	0.931795i	$-0.618242\pi$
$683$	−18.9727	−0.725970	−0.362985	+	0.931795i	$0.618242\pi$
$684$	−1.39590	−0.0533736
$685$	36.7107	1.40264
$686$	−1.14170	−0.0435904
$687$	−34.8429	−1.32934
$688$	5.61647	0.214126
$689$	19.8726	0.757086
$690$	−44.1760	−1.68175
$691$	−23.4914	−0.893653	−0.446827	−	0.894621i	$-0.647446\pi$
$691$	−23.4914	−0.893653	−0.446827	+	0.894621i	$0.647446\pi$
$692$	−1.11796	−0.0424983
$693$	−0.219710	−0.00834608
$694$	4.61215	0.175075
$695$	−48.6897	−1.84690
$696$	23.5523	0.892748
$697$	−25.5080	−0.966184
$698$	22.4311	0.849029
$699$	65.5522	2.47941
$700$	0.569802	0.0215365
$701$	−4.53139	−0.171148	−0.0855742	−	0.996332i	$-0.527272\pi$
$701$	−4.53139	−0.171148	−0.0855742	+	0.996332i	$0.527272\pi$
$702$	2.80190	0.105751
$703$	3.55085	0.133923
$704$	−1.00000	−0.0376889
$705$	38.9567	1.46719
$706$	20.5492	0.773379
$707$	0.948956	0.0356892
$708$	21.9299	0.824178
$709$	40.8568	1.53441	0.767205	−	0.641403i	$-0.221647\pi$
$709$	40.8568	1.53441	0.767205	+	0.641403i	$0.221647\pi$
$710$	7.29540	0.273792
$711$	27.2330	1.02132
$712$	−3.11482	−0.116733
$713$	41.3998	1.55044
$714$	−0.603869	−0.0225992
$715$	13.2369	0.495030
$716$	−25.2017	−0.941830
$717$	−41.4759	−1.54895
$718$	19.9555	0.744731
$719$	−25.3847	−0.946689	−0.473345	−	0.880877i	$-0.656953\pi$
$719$	−25.3847	−0.946689	−0.473345	+	0.880877i	$0.656953\pi$
$720$	−9.32214	−0.347416
$721$	0.378150	0.0140830
$722$	−18.7313	−0.697107
$723$	26.3062	0.978337
$724$	3.72573	0.138466
$725$	−68.9382	−2.56030
$726$	−2.38598	−0.0885519
$727$	−31.0957	−1.15327	−0.576637	−	0.817000i	$-0.695635\pi$
$727$	−31.0957	−1.15327	−0.576637	+	0.817000i	$0.695635\pi$
$728$	0.311974	0.0115625
$729$	−21.2180	−0.785851
$730$	21.0105	0.777634
$731$	17.4224	0.644392
$732$	−21.2872	−0.786799
$733$	3.78221	0.139699	0.0698496	−	0.997558i	$-0.477748\pi$
$733$	3.78221	0.139699	0.0698496	+	0.997558i	$0.477748\pi$
$734$	5.73619	0.211727
$735$	−57.7629	−2.13062
$736$	−5.34838	−0.197144
$737$	−12.6438	−0.465741
$738$	−22.1436	−0.815119
$739$	−16.7981	−0.617926	−0.308963	−	0.951074i	$-0.599982\pi$
$739$	−16.7981	−0.617926	−0.308963	+	0.951074i	$0.599982\pi$
$740$	23.7134	0.871721
$741$	4.72922	0.173732
$742$	0.424032	0.0155667
$743$	30.1312	1.10541	0.552704	−	0.833378i	$-0.313596\pi$
$743$	30.1312	1.10541	0.552704	+	0.833378i	$0.313596\pi$
$744$	18.4689	0.677104
$745$	−23.2708	−0.852576
$746$	−16.4749	−0.603189
$747$	39.3202	1.43865
$748$	−3.10202	−0.113421
$749$	−0.108591	−0.00396785
$750$	16.3857	0.598322
$751$	−25.0333	−0.913478	−0.456739	−	0.889601i	$-0.650983\pi$
$751$	−25.0333	−0.913478	−0.456739	+	0.889601i	$0.650983\pi$
$752$	4.71648	0.171992
$753$	36.2985	1.32279
$754$	−37.7446	−1.37458
$755$	30.4247	1.10727
$756$	0.0597855	0.00217438
$757$	5.36955	0.195160	0.0975799	−	0.995228i	$-0.468890\pi$
$757$	5.36955	0.195160	0.0975799	+	0.995228i	$0.468890\pi$
$758$	15.3549	0.557715
$759$	−12.7611	−0.463199
$760$	1.79446	0.0650919
$761$	−14.7516	−0.534746	−0.267373	−	0.963593i	$-0.586156\pi$
$761$	−14.7516	−0.534746	−0.267373	+	0.963593i	$0.586156\pi$
$762$	−6.50133	−0.235518
$763$	0.0333363	0.00120685
$764$	17.2173	0.622900
$765$	−28.9175	−1.04551
$766$	21.8210	0.788423
$767$	−35.1446	−1.26900
$768$	−2.38598	−0.0860965
$769$	13.2634	0.478291	0.239146	−	0.970984i	$-0.423133\pi$
$769$	13.2634	0.478291	0.239146	+	0.970984i	$0.423133\pi$
$770$	0.282442	0.0101785
$771$	62.2807	2.24299
$772$	9.46096	0.340507
$773$	−31.8709	−1.14632	−0.573158	−	0.819445i	$-0.694282\pi$
$773$	−31.8709	−1.14632	−0.573158	+	0.819445i	$0.694282\pi$
$774$	15.1245	0.543640
$775$	−54.0591	−1.94186
$776$	7.84193	0.281509
$777$	1.33350	0.0478390
$778$	−11.1228	−0.398770
$779$	4.26253	0.152721
$780$	31.5828	1.13085
$781$	2.10742	0.0754095
$782$	−16.5908	−0.593286
$783$	−7.23323	−0.258495
$784$	−6.99334	−0.249762
$785$	−30.8570	−1.10133
$786$	−13.3151	−0.474935
$787$	−36.3612	−1.29614	−0.648069	−	0.761582i	$-0.724423\pi$
$787$	−36.3612	−1.29614	−0.648069	+	0.761582i	$0.724423\pi$
$788$	−1.00000	−0.0356235
$789$	−21.4272	−0.762830
$790$	−35.0086	−1.24555
$791$	1.17144	0.0416515
$792$	−2.69289	−0.0956876
$793$	34.1146	1.21144
$794$	30.0429	1.06618
$795$	42.9271	1.52247
$796$	17.8434	0.632443
$797$	−17.9248	−0.634929	−0.317465	−	0.948270i	$-0.602831\pi$
$797$	−17.9248	−0.634929	−0.317465	+	0.948270i	$0.602831\pi$
$798$	0.100910	0.00357217
$799$	14.6306	0.517595
$800$	6.98382	0.246915
$801$	−8.38786	−0.296370
$802$	14.9384	0.527492
$803$	6.06931	0.214181
$804$	−30.1679	−1.06394
$805$	1.51061	0.0532419
$806$	−29.5980	−1.04255
$807$	−33.7044	−1.18645
$808$	11.6310	0.409175
$809$	−7.16592	−0.251940	−0.125970	−	0.992034i	$-0.540204\pi$
$809$	−7.16592	−0.251940	−0.125970	+	0.992034i	$0.540204\pi$
$810$	34.0188	1.19530
$811$	32.7850	1.15124	0.575619	−	0.817718i	$-0.304761\pi$
$811$	32.7850	1.15124	0.575619	+	0.817718i	$0.304761\pi$
$812$	−0.805375	−0.0282631
$813$	−26.4418	−0.927355
$814$	6.85008	0.240095
$815$	−14.6448	−0.512986
$816$	−7.40136	−0.259099
$817$	−2.91139	−0.101857
$818$	36.8812	1.28952
$819$	0.840110	0.0293558
$820$	28.4661	0.994081
$821$	−15.4838	−0.540387	−0.270193	−	0.962806i	$-0.587088\pi$
$821$	−15.4838	−0.540387	−0.270193	+	0.962806i	$0.587088\pi$
$822$	25.3024	0.882521
$823$	38.3965	1.33842	0.669209	−	0.743074i	$-0.266633\pi$
$823$	38.3965	1.33842	0.669209	+	0.743074i	$0.266633\pi$
$824$	4.63482	0.161462
$825$	16.6632	0.580139
$826$	−0.749898	−0.0260923
$827$	40.8778	1.42146	0.710730	−	0.703465i	$-0.248365\pi$
$827$	40.8778	1.42146	0.710730	+	0.703465i	$0.248365\pi$
$828$	−14.4026	−0.500525
$829$	−13.3848	−0.464873	−0.232436	−	0.972612i	$-0.574670\pi$
$829$	−13.3848	−0.464873	−0.232436	+	0.972612i	$0.574670\pi$
$830$	−50.5470	−1.75451
$831$	71.4964	2.48018
$832$	3.82373	0.132564
$833$	−21.6935	−0.751636
$834$	−33.5587	−1.16204
$835$	9.98318	0.345482
$836$	0.518366	0.0179281
$837$	−5.67206	−0.196055
$838$	19.1578	0.661796
$839$	15.8374	0.546768	0.273384	−	0.961905i	$-0.411857\pi$
$839$	15.8374	0.546768	0.273384	+	0.961905i	$0.411857\pi$
$840$	0.673899	0.0232517
$841$	68.4394	2.35998
$842$	17.3698	0.598603
$843$	30.3797	1.04633
$844$	8.81169	0.303311
$845$	−5.61118	−0.193030
$846$	12.7009	0.436667
$847$	0.0815889	0.00280343
$848$	5.19718	0.178472
$849$	31.3639	1.07641
$850$	21.6640	0.743068
$851$	36.6369	1.25590
$852$	5.02826	0.172265
$853$	33.2218	1.13749	0.568746	−	0.822513i	$-0.307429\pi$
$853$	33.2218	1.13749	0.568746	+	0.822513i	$0.307429\pi$
$854$	0.727920	0.0249089
$855$	4.83228	0.165260
$856$	−1.33096	−0.0454913
$857$	−41.8916	−1.43099	−0.715495	−	0.698618i	$-0.753799\pi$
$857$	−41.8916	−1.43099	−0.715495	+	0.698618i	$0.753799\pi$
$858$	9.12333	0.311465
$859$	−31.1346	−1.06230	−0.531149	−	0.847279i	$-0.678239\pi$
$859$	−31.1346	−1.06230	−0.531149	+	0.847279i	$0.678239\pi$
$860$	−19.4429	−0.662998
$861$	1.60077	0.0545540
$862$	−15.1837	−0.517157
$863$	23.9940	0.816766	0.408383	−	0.912811i	$-0.366093\pi$
$863$	23.9940	0.816766	0.408383	+	0.912811i	$0.366093\pi$
$864$	0.732765	0.0249292
$865$	3.87010	0.131587
$866$	18.0552	0.613539
$867$	17.6024	0.597809
$868$	−0.631549	−0.0214362
$869$	−10.1129	−0.343057
$870$	−81.5326	−2.76421
$871$	48.3466	1.63816
$872$	0.408588	0.0138365
$873$	21.1174	0.714716
$874$	2.77242	0.0937785
$875$	−0.560313	−0.0189420
$876$	14.4812	0.489275
$877$	−32.0497	−1.08224	−0.541121	−	0.840945i	$-0.682000\pi$
$877$	−32.0497	−1.08224	−0.541121	+	0.840945i	$0.682000\pi$
$878$	−21.1408	−0.713467
$879$	−55.0774	−1.85771
$880$	3.46177	0.116696
$881$	26.7736	0.902027	0.451013	−	0.892517i	$-0.351063\pi$
$881$	26.7736	0.902027	0.451013	+	0.892517i	$0.351063\pi$
$882$	−18.8323	−0.634116
$883$	9.09396	0.306036	0.153018	−	0.988223i	$-0.451101\pi$
$883$	9.09396	0.306036	0.153018	+	0.988223i	$0.451101\pi$
$884$	11.8613	0.398939
$885$	−75.9163	−2.55190
$886$	1.88656	0.0633803
$887$	−53.9825	−1.81255	−0.906277	−	0.422685i	$-0.861088\pi$
$887$	−53.9825	−1.81255	−0.906277	+	0.422685i	$0.861088\pi$
$888$	16.3441	0.548473
$889$	0.222314	0.00745617
$890$	10.7828	0.361439
$891$	9.82702	0.329218
$892$	−27.0668	−0.906263
$893$	−2.44486	−0.0818142
$894$	−16.0391	−0.536428
$895$	87.2422	2.91619
$896$	0.0815889	0.00272569
$897$	48.7951	1.62922
$898$	−26.2338	−0.875434
$899$	76.4088	2.54837
$900$	18.8066	0.626888
$901$	16.1218	0.537094
$902$	8.22301	0.273796
$903$	−1.09335	−0.0363846
$904$	14.3578	0.477533
$905$	−12.8976	−0.428731
$906$	20.9698	0.696675
$907$	57.4387	1.90722	0.953610	−	0.301046i	$-0.0973357\pi$
$907$	57.4387	1.90722	0.953610	+	0.301046i	$0.0973357\pi$
$908$	1.62502	0.0539282
$909$	31.3208	1.03885
$910$	−1.07998	−0.0358010
$911$	−16.0350	−0.531263	−0.265631	−	0.964075i	$-0.585580\pi$
$911$	−16.0350	−0.531263	−0.265631	+	0.964075i	$0.585580\pi$
$912$	1.23681	0.0409548
$913$	−14.6015	−0.483240
$914$	−31.8347	−1.05300
$915$	73.6914	2.43616
$916$	14.6032	0.482503
$917$	0.455313	0.0150358
$918$	2.27306	0.0750220
$919$	−38.8408	−1.28124	−0.640620	−	0.767858i	$-0.721323\pi$
$919$	−38.8408	−1.28124	−0.640620	+	0.767858i	$0.721323\pi$
$920$	18.5148	0.610416
$921$	−20.5556	−0.677329
$922$	40.0679	1.31957
$923$	−8.05821	−0.265239
$924$	0.194669	0.00640415
$925$	−47.8397	−1.57296
$926$	13.6793	0.449528
$927$	12.4811	0.409932
$928$	−9.87114	−0.324036
$929$	28.3612	0.930501	0.465251	−	0.885179i	$-0.345964\pi$
$929$	28.3612	0.930501	0.465251	+	0.885179i	$0.345964\pi$
$930$	−63.9352	−2.09652
$931$	3.62511	0.118808
$932$	−27.4739	−0.899939
$933$	−30.7735	−1.00748
$934$	7.72554	0.252787
$935$	10.7385	0.351186
$936$	10.2969	0.336564
$937$	−12.3063	−0.402030	−0.201015	−	0.979588i	$-0.564424\pi$
$937$	−12.3063	−0.402030	−0.201015	+	0.979588i	$0.564424\pi$
$938$	1.03160	0.0336828
$939$	−64.2236	−2.09586
$940$	−16.3273	−0.532539
$941$	6.56206	0.213917	0.106959	−	0.994263i	$-0.465889\pi$
$941$	6.56206	0.213917	0.106959	+	0.994263i	$0.465889\pi$
$942$	−21.2678	−0.692941
$943$	43.9798	1.43218
$944$	−9.19118	−0.299147
$945$	−0.206963	−0.00673252
$946$	−5.61647	−0.182607
$947$	16.2486	0.528007	0.264004	−	0.964522i	$-0.414957\pi$
$947$	16.2486	0.528007	0.264004	+	0.964522i	$0.414957\pi$
$948$	−24.1292	−0.783680
$949$	−23.2074	−0.753344
$950$	−3.62017	−0.117454
$951$	8.60757	0.279120
$952$	0.253091	0.00820272
$953$	−45.7357	−1.48152	−0.740762	−	0.671767i	$-0.765535\pi$
$953$	−45.7357	−1.48152	−0.740762	+	0.671767i	$0.765535\pi$
$954$	13.9954	0.453118
$955$	−59.6022	−1.92868
$956$	17.3832	0.562213
$957$	−23.5523	−0.761338
$958$	33.7895	1.09169
$959$	−0.865218	−0.0279394
$960$	8.25969	0.266580
$961$	28.9172	0.932814
$962$	−26.1929	−0.844492
$963$	−3.58412	−0.115497
$964$	−11.0253	−0.355102
$965$	−32.7516	−1.05431
$966$	1.04117	0.0334990
$967$	−47.0810	−1.51402	−0.757011	−	0.653402i	$-0.773341\pi$
$967$	−47.0810	−1.51402	−0.757011	+	0.653402i	$0.773341\pi$
$968$	1.00000	0.0321412
$969$	3.83661	0.123250
$970$	−27.1469	−0.871635
$971$	−27.4335	−0.880384	−0.440192	−	0.897904i	$-0.645090\pi$
$971$	−27.4335	−0.880384	−0.440192	+	0.897904i	$0.645090\pi$
$972$	21.2488	0.681554
$973$	1.14755	0.0367887
$974$	3.78692	0.121341
$975$	−63.7157	−2.04053
$976$	8.92181	0.285580
$977$	12.6310	0.404100	0.202050	−	0.979375i	$-0.435240\pi$
$977$	12.6310	0.404100	0.202050	+	0.979375i	$0.435240\pi$
$978$	−10.0938	−0.322763
$979$	3.11482	0.0995501
$980$	24.2093	0.773338
$981$	1.10028	0.0351293
$982$	18.7155	0.597236
$983$	32.0940	1.02364	0.511820	−	0.859093i	$-0.328971\pi$
$983$	32.0940	1.02364	0.511820	+	0.859093i	$0.328971\pi$
$984$	19.6199	0.625460
$985$	3.46177	0.110301
$986$	−30.6205	−0.975156
$987$	−0.918153	−0.0292251
$988$	−1.98209	−0.0630587
$989$	−30.0390	−0.955186
$990$	9.32214	0.296277
$991$	31.8904	1.01303	0.506516	−	0.862231i	$-0.330933\pi$
$991$	31.8904	1.01303	0.506516	+	0.862231i	$0.330933\pi$
$992$	−7.74062	−0.245765
$993$	−19.2938	−0.612269
$994$	−0.171942	−0.00545368
$995$	−61.7697	−1.95823
$996$	−34.8389	−1.10391
$997$	−9.36749	−0.296671	−0.148336	−	0.988937i	$-0.547392\pi$
$997$	−9.36749	−0.296671	−0.148336	+	0.988937i	$0.547392\pi$
$998$	21.5094	0.680867
$999$	−5.01950	−0.158810

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.f.1.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.f.1.4	✓	24	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.38598 q^{3} +1.00000 q^{4} -3.46177 q^{5} -2.38598 q^{6} +0.0815889 q^{7} +1.00000 q^{8} +2.69289 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.38598 q^{3} +1.00000 q^{4} -3.46177 q^{5} -2.38598 q^{6} +0.0815889 q^{7} +1.00000 q^{8} +2.69289 q^{9} -3.46177 q^{10} -1.00000 q^{11} -2.38598 q^{12} +3.82373 q^{13} +0.0815889 q^{14} +8.25969 q^{15} +1.00000 q^{16} +3.10202 q^{17} +2.69289 q^{18} -0.518366 q^{19} -3.46177 q^{20} -0.194669 q^{21} -1.00000 q^{22} -5.34838 q^{23} -2.38598 q^{24} +6.98382 q^{25} +3.82373 q^{26} +0.732765 q^{27} +0.0815889 q^{28} -9.87114 q^{29} +8.25969 q^{30} -7.74062 q^{31} +1.00000 q^{32} +2.38598 q^{33} +3.10202 q^{34} -0.282442 q^{35} +2.69289 q^{36} -6.85008 q^{37} -0.518366 q^{38} -9.12333 q^{39} -3.46177 q^{40} -8.22301 q^{41} -0.194669 q^{42} +5.61647 q^{43} -1.00000 q^{44} -9.32214 q^{45} -5.34838 q^{46} +4.71648 q^{47} -2.38598 q^{48} -6.99334 q^{49} +6.98382 q^{50} -7.40136 q^{51} +3.82373 q^{52} +5.19718 q^{53} +0.732765 q^{54} +3.46177 q^{55} +0.0815889 q^{56} +1.23681 q^{57} -9.87114 q^{58} -9.19118 q^{59} +8.25969 q^{60} +8.92181 q^{61} -7.74062 q^{62} +0.219710 q^{63} +1.00000 q^{64} -13.2369 q^{65} +2.38598 q^{66} +12.6438 q^{67} +3.10202 q^{68} +12.7611 q^{69} -0.282442 q^{70} -2.10742 q^{71} +2.69289 q^{72} -6.06931 q^{73} -6.85008 q^{74} -16.6632 q^{75} -0.518366 q^{76} -0.0815889 q^{77} -9.12333 q^{78} +10.1129 q^{79} -3.46177 q^{80} -9.82702 q^{81} -8.22301 q^{82} +14.6015 q^{83} -0.194669 q^{84} -10.7385 q^{85} +5.61647 q^{86} +23.5523 q^{87} -1.00000 q^{88} -3.11482 q^{89} -9.32214 q^{90} +0.311974 q^{91} -5.34838 q^{92} +18.4689 q^{93} +4.71648 q^{94} +1.79446 q^{95} -2.38598 q^{96} +7.84193 q^{97} -6.99334 q^{98} -2.69289 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9}+O(q^{10}) \) 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9} - 24 q^{11} + 8 q^{12} + 9 q^{13} + 11 q^{14} + 6 q^{15} + 24 q^{16} - q^{17} + 28 q^{18} + 35 q^{19} + 21 q^{21} - 24 q^{22} + 13 q^{23} + 8 q^{24} + 38 q^{25} + 9 q^{26} + 23 q^{27} + 11 q^{28} + 15 q^{29} + 6 q^{30} + 31 q^{31} + 24 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 28 q^{36} + 13 q^{37} + 35 q^{38} + 31 q^{39} + 16 q^{41} + 21 q^{42} + 35 q^{43} - 24 q^{44} + 13 q^{45} + 13 q^{46} + 46 q^{47} + 8 q^{48} + 55 q^{49} + 38 q^{50} + 18 q^{51} + 9 q^{52} + 6 q^{53} + 23 q^{54} + 11 q^{56} + 18 q^{57} + 15 q^{58} + 13 q^{59} + 6 q^{60} + 60 q^{61} + 31 q^{62} + 52 q^{63} + 24 q^{64} - 9 q^{65} - 8 q^{66} + 28 q^{67} - q^{68} + 21 q^{69} + 28 q^{70} + 10 q^{71} + 28 q^{72} + 3 q^{73} + 13 q^{74} + 48 q^{75} + 35 q^{76} - 11 q^{77} + 31 q^{78} + 47 q^{79} + 16 q^{81} + 16 q^{82} + 66 q^{83} + 21 q^{84} + 37 q^{85} + 35 q^{86} + 34 q^{87} - 24 q^{88} - 5 q^{89} + 13 q^{90} + q^{91} + 13 q^{92} - 16 q^{93} + 46 q^{94} + 9 q^{95} + 8 q^{96} + 24 q^{97} + 55 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9 - 24 * q^11 + 8 * q^12 + 9 * q^13 + 11 * q^14 + 6 * q^15 + 24 * q^16 - q^17 + 28 * q^18 + 35 * q^19 + 21 * q^21 - 24 * q^22 + 13 * q^23 + 8 * q^24 + 38 * q^25 + 9 * q^26 + 23 * q^27 + 11 * q^28 + 15 * q^29 + 6 * q^30 + 31 * q^31 + 24 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 28 * q^36 + 13 * q^37 + 35 * q^38 + 31 * q^39 + 16 * q^41 + 21 * q^42 + 35 * q^43 - 24 * q^44 + 13 * q^45 + 13 * q^46 + 46 * q^47 + 8 * q^48 + 55 * q^49 + 38 * q^50 + 18 * q^51 + 9 * q^52 + 6 * q^53 + 23 * q^54 + 11 * q^56 + 18 * q^57 + 15 * q^58 + 13 * q^59 + 6 * q^60 + 60 * q^61 + 31 * q^62 + 52 * q^63 + 24 * q^64 - 9 * q^65 - 8 * q^66 + 28 * q^67 - q^68 + 21 * q^69 + 28 * q^70 + 10 * q^71 + 28 * q^72 + 3 * q^73 + 13 * q^74 + 48 * q^75 + 35 * q^76 - 11 * q^77 + 31 * q^78 + 47 * q^79 + 16 * q^81 + 16 * q^82 + 66 * q^83 + 21 * q^84 + 37 * q^85 + 35 * q^86 + 34 * q^87 - 24 * q^88 - 5 * q^89 + 13 * q^90 + q^91 + 13 * q^92 - 16 * q^93 + 46 * q^94 + 9 * q^95 + 8 * q^96 + 24 * q^97 + 55 * q^98 - 28 * q^99

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