LMFDB - Embedded newform 6026.2.a.m.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$41$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.27958 q^{3} +1.00000 q^{4} +2.95127 q^{5} -1.27958 q^{6} +4.74723 q^{7} +1.00000 q^{8} -1.36266 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.27958 q^{3} +1.00000 q^{4} +2.95127 q^{5} -1.27958 q^{6} +4.74723 q^{7} +1.00000 q^{8} -1.36266 q^{9} +2.95127 q^{10} +1.68649 q^{11} -1.27958 q^{12} -1.31820 q^{13} +4.74723 q^{14} -3.77640 q^{15} +1.00000 q^{16} +6.64597 q^{17} -1.36266 q^{18} -5.53342 q^{19} +2.95127 q^{20} -6.07449 q^{21} +1.68649 q^{22} +1.00000 q^{23} -1.27958 q^{24} +3.70999 q^{25} -1.31820 q^{26} +5.58240 q^{27} +4.74723 q^{28} -6.13755 q^{29} -3.77640 q^{30} +3.84417 q^{31} +1.00000 q^{32} -2.15800 q^{33} +6.64597 q^{34} +14.0104 q^{35} -1.36266 q^{36} -5.04546 q^{37} -5.53342 q^{38} +1.68675 q^{39} +2.95127 q^{40} +5.93000 q^{41} -6.07449 q^{42} -2.13776 q^{43} +1.68649 q^{44} -4.02159 q^{45} +1.00000 q^{46} +11.5048 q^{47} -1.27958 q^{48} +15.5362 q^{49} +3.70999 q^{50} -8.50408 q^{51} -1.31820 q^{52} -7.33707 q^{53} +5.58240 q^{54} +4.97727 q^{55} +4.74723 q^{56} +7.08047 q^{57} -6.13755 q^{58} +5.45885 q^{59} -3.77640 q^{60} +2.10475 q^{61} +3.84417 q^{62} -6.46888 q^{63} +1.00000 q^{64} -3.89036 q^{65} -2.15800 q^{66} +3.02281 q^{67} +6.64597 q^{68} -1.27958 q^{69} +14.0104 q^{70} -1.42059 q^{71} -1.36266 q^{72} +3.67386 q^{73} -5.04546 q^{74} -4.74725 q^{75} -5.53342 q^{76} +8.00614 q^{77} +1.68675 q^{78} -10.0013 q^{79} +2.95127 q^{80} -3.05515 q^{81} +5.93000 q^{82} +0.385656 q^{83} -6.07449 q^{84} +19.6140 q^{85} -2.13776 q^{86} +7.85351 q^{87} +1.68649 q^{88} +3.50549 q^{89} -4.02159 q^{90} -6.25780 q^{91} +1.00000 q^{92} -4.91893 q^{93} +11.5048 q^{94} -16.3306 q^{95} -1.27958 q^{96} +15.5694 q^{97} +15.5362 q^{98} -2.29811 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) $ 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * 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
$3$	−1.27958	−0.738768	−0.369384	−	0.929277i	$-0.620431\pi$
$3$	−1.27958	−0.738768	−0.369384	+	0.929277i	$0.620431\pi$
$4$	1.00000	0.500000
$5$	2.95127	1.31985	0.659924	−	0.751332i	$-0.270589\pi$
$5$	2.95127	1.31985	0.659924	+	0.751332i	$0.270589\pi$
$6$	−1.27958	−0.522388
$7$	4.74723	1.79429	0.897143	−	0.441741i	$-0.145639\pi$
$7$	4.74723	1.79429	0.897143	+	0.441741i	$0.145639\pi$
$8$	1.00000	0.353553
$9$	−1.36266	−0.454221
$10$	2.95127	0.933273
$11$	1.68649	0.508494	0.254247	−	0.967139i	$-0.418172\pi$
$11$	1.68649	0.508494	0.254247	+	0.967139i	$0.418172\pi$
$12$	−1.27958	−0.369384
$13$	−1.31820	−0.365603	−0.182802	−	0.983150i	$-0.558517\pi$
$13$	−1.31820	−0.365603	−0.182802	+	0.983150i	$0.558517\pi$
$14$	4.74723	1.26875
$15$	−3.77640	−0.975062
$16$	1.00000	0.250000
$17$	6.64597	1.61188	0.805942	−	0.591994i	$-0.201659\pi$
$17$	6.64597	1.61188	0.805942	+	0.591994i	$0.201659\pi$
$18$	−1.36266	−0.321183
$19$	−5.53342	−1.26945	−0.634727	−	0.772737i	$-0.718887\pi$
$19$	−5.53342	−1.26945	−0.634727	+	0.772737i	$0.718887\pi$
$20$	2.95127	0.659924
$21$	−6.07449	−1.32556
$22$	1.68649	0.359560
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.27958	−0.261194
$25$	3.70999	0.741998
$26$	−1.31820	−0.258520
$27$	5.58240	1.07433
$28$	4.74723	0.897143
$29$	−6.13755	−1.13971	−0.569857	−	0.821744i	$-0.693001\pi$
$29$	−6.13755	−1.13971	−0.569857	+	0.821744i	$0.693001\pi$
$30$	−3.77640	−0.689473
$31$	3.84417	0.690433	0.345216	−	0.938523i	$-0.387806\pi$
$31$	3.84417	0.690433	0.345216	+	0.938523i	$0.387806\pi$
$32$	1.00000	0.176777
$33$	−2.15800	−0.375660
$34$	6.64597	1.13977
$35$	14.0104	2.36818
$36$	−1.36266	−0.227111
$37$	−5.04546	−0.829468	−0.414734	−	0.909943i	$-0.636125\pi$
$37$	−5.04546	−0.829468	−0.414734	+	0.909943i	$0.636125\pi$
$38$	−5.53342	−0.897639
$39$	1.68675	0.270096
$40$	2.95127	0.466637
$41$	5.93000	0.926110	0.463055	−	0.886329i	$-0.346753\pi$
$41$	5.93000	0.926110	0.463055	+	0.886329i	$0.346753\pi$
$42$	−6.07449	−0.937313
$43$	−2.13776	−0.326006	−0.163003	−	0.986626i	$-0.552118\pi$
$43$	−2.13776	−0.326006	−0.163003	+	0.986626i	$0.552118\pi$
$44$	1.68649	0.254247
$45$	−4.02159	−0.599503
$46$	1.00000	0.147442
$47$	11.5048	1.67815	0.839076	−	0.544014i	$-0.183096\pi$
$47$	11.5048	1.67815	0.839076	+	0.544014i	$0.183096\pi$
$48$	−1.27958	−0.184692
$49$	15.5362	2.21946
$50$	3.70999	0.524672
$51$	−8.50408	−1.19081
$52$	−1.31820	−0.182802
$53$	−7.33707	−1.00782	−0.503912	−	0.863755i	$-0.668107\pi$
$53$	−7.33707	−1.00782	−0.503912	+	0.863755i	$0.668107\pi$
$54$	5.58240	0.759668
$55$	4.97727	0.671135
$56$	4.74723	0.634376
$57$	7.08047	0.937832
$58$	−6.13755	−0.805900
$59$	5.45885	0.710681	0.355341	−	0.934737i	$-0.384365\pi$
$59$	5.45885	0.710681	0.355341	+	0.934737i	$0.384365\pi$
$60$	−3.77640	−0.487531
$61$	2.10475	0.269486	0.134743	−	0.990881i	$-0.456979\pi$
$61$	2.10475	0.269486	0.134743	+	0.990881i	$0.456979\pi$
$62$	3.84417	0.488210
$63$	−6.46888	−0.815003
$64$	1.00000	0.125000
$65$	−3.89036	−0.482540
$66$	−2.15800	−0.265631
$67$	3.02281	0.369295	0.184647	−	0.982805i	$-0.440886\pi$
$67$	3.02281	0.369295	0.184647	+	0.982805i	$0.440886\pi$
$68$	6.64597	0.805942
$69$	−1.27958	−0.154044
$70$	14.0104	1.67456
$71$	−1.42059	−0.168593	−0.0842963	−	0.996441i	$-0.526864\pi$
$71$	−1.42059	−0.168593	−0.0842963	+	0.996441i	$0.526864\pi$
$72$	−1.36266	−0.160592
$73$	3.67386	0.429993	0.214996	−	0.976615i	$-0.431026\pi$
$73$	3.67386	0.429993	0.214996	+	0.976615i	$0.431026\pi$
$74$	−5.04546	−0.586523
$75$	−4.74725	−0.548165
$76$	−5.53342	−0.634727
$77$	8.00614	0.912384
$78$	1.68675	0.190987
$79$	−10.0013	−1.12524	−0.562619	−	0.826716i	$-0.690206\pi$
$79$	−10.0013	−1.12524	−0.562619	+	0.826716i	$0.690206\pi$
$80$	2.95127	0.329962
$81$	−3.05515	−0.339462
$82$	5.93000	0.654859
$83$	0.385656	0.0423313	0.0211656	−	0.999776i	$-0.493262\pi$
$83$	0.385656	0.0423313	0.0211656	+	0.999776i	$0.493262\pi$
$84$	−6.07449	−0.662781
$85$	19.6140	2.12744
$86$	−2.13776	−0.230521
$87$	7.85351	0.841985
$88$	1.68649	0.179780
$89$	3.50549	0.371581	0.185790	−	0.982589i	$-0.440515\pi$
$89$	3.50549	0.371581	0.185790	+	0.982589i	$0.440515\pi$
$90$	−4.02159	−0.423913
$91$	−6.25780	−0.655996
$92$	1.00000	0.104257
$93$	−4.91893	−0.510070
$94$	11.5048	1.18663
$95$	−16.3306	−1.67548
$96$	−1.27958	−0.130597
$97$	15.5694	1.58084	0.790419	−	0.612567i	$-0.209863\pi$
$97$	15.5694	1.58084	0.790419	+	0.612567i	$0.209863\pi$
$98$	15.5362	1.56940
$99$	−2.29811	−0.230969
$100$	3.70999	0.370999
$101$	13.8983	1.38294	0.691468	−	0.722407i	$-0.256964\pi$
$101$	13.8983	1.38294	0.691468	+	0.722407i	$0.256964\pi$
$102$	−8.50408	−0.842029
$103$	4.21226	0.415046	0.207523	−	0.978230i	$-0.433460\pi$
$103$	4.21226	0.415046	0.207523	+	0.978230i	$0.433460\pi$
$104$	−1.31820	−0.129260
$105$	−17.9274	−1.74954
$106$	−7.33707	−0.712640
$107$	−18.0468	−1.74465	−0.872325	−	0.488927i	$-0.837388\pi$
$107$	−18.0468	−1.74465	−0.872325	+	0.488927i	$0.837388\pi$
$108$	5.58240	0.537166
$109$	−13.7479	−1.31681	−0.658404	−	0.752665i	$-0.728768\pi$
$109$	−13.7479	−1.31681	−0.658404	+	0.752665i	$0.728768\pi$
$110$	4.97727	0.474564
$111$	6.45609	0.612785
$112$	4.74723	0.448571
$113$	−9.84150	−0.925810	−0.462905	−	0.886408i	$-0.653193\pi$
$113$	−9.84150	−0.925810	−0.462905	+	0.886408i	$0.653193\pi$
$114$	7.08047	0.663147
$115$	2.95127	0.275207
$116$	−6.13755	−0.569857
$117$	1.79626	0.166065
$118$	5.45885	0.502528
$119$	31.5500	2.89218
$120$	−3.77640	−0.344736
$121$	−8.15577	−0.741433
$122$	2.10475	0.190555
$123$	−7.58793	−0.684181
$124$	3.84417	0.345216
$125$	−3.80717	−0.340523
$126$	−6.46888	−0.576294
$127$	6.86090	0.608807	0.304403	−	0.952543i	$-0.401543\pi$
$127$	6.86090	0.608807	0.304403	+	0.952543i	$0.401543\pi$
$128$	1.00000	0.0883883
$129$	2.73545	0.240843
$130$	−3.89036	−0.341208
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−2.15800	−0.187830
$133$	−26.2684	−2.27776
$134$	3.02281	0.261131
$135$	16.4752	1.41796
$136$	6.64597	0.569887
$137$	5.40259	0.461575	0.230787	−	0.973004i	$-0.425870\pi$
$137$	5.40259	0.461575	0.230787	+	0.973004i	$0.425870\pi$
$138$	−1.27958	−0.108925
$139$	−6.27702	−0.532410	−0.266205	−	0.963916i	$-0.585770\pi$
$139$	−6.27702	−0.532410	−0.266205	+	0.963916i	$0.585770\pi$
$140$	14.0104	1.18409
$141$	−14.7214	−1.23977
$142$	−1.42059	−0.119213
$143$	−2.22313	−0.185907
$144$	−1.36266	−0.113555
$145$	−18.1136	−1.50425
$146$	3.67386	0.304051
$147$	−19.8799	−1.63967
$148$	−5.04546	−0.414734
$149$	3.16624	0.259388	0.129694	−	0.991554i	$-0.458600\pi$
$149$	3.16624	0.259388	0.129694	+	0.991554i	$0.458600\pi$
$150$	−4.74725	−0.387611
$151$	−20.2522	−1.64810	−0.824050	−	0.566518i	$-0.808290\pi$
$151$	−20.2522	−1.64810	−0.824050	+	0.566518i	$0.808290\pi$
$152$	−5.53342	−0.448819
$153$	−9.05622	−0.732152
$154$	8.00614	0.645153
$155$	11.3452	0.911266
$156$	1.68675	0.135048
$157$	9.69770	0.773961	0.386981	−	0.922088i	$-0.373518\pi$
$157$	9.69770	0.773961	0.386981	+	0.922088i	$0.373518\pi$
$158$	−10.0013	−0.795663
$159$	9.38841	0.744549
$160$	2.95127	0.233318
$161$	4.74723	0.374134
$162$	−3.05515	−0.240036
$163$	9.64251	0.755260	0.377630	−	0.925957i	$-0.376739\pi$
$163$	9.64251	0.755260	0.377630	+	0.925957i	$0.376739\pi$
$164$	5.93000	0.463055
$165$	−6.36884	−0.495814
$166$	0.385656	0.0299327
$167$	12.1386	0.939310	0.469655	−	0.882850i	$-0.344378\pi$
$167$	12.1386	0.939310	0.469655	+	0.882850i	$0.344378\pi$
$168$	−6.07449	−0.468657
$169$	−11.2623	−0.866334
$170$	19.6140	1.50433
$171$	7.54019	0.576613
$172$	−2.13776	−0.163003
$173$	9.76551	0.742458	0.371229	−	0.928541i	$-0.378936\pi$
$173$	9.76551	0.742458	0.371229	+	0.928541i	$0.378936\pi$
$174$	7.85351	0.595373
$175$	17.6122	1.33136
$176$	1.68649	0.127124
$177$	−6.98505	−0.525029
$178$	3.50549	0.262747
$179$	−11.1736	−0.835156	−0.417578	−	0.908641i	$-0.637121\pi$
$179$	−11.1736	−0.835156	−0.417578	+	0.908641i	$0.637121\pi$
$180$	−4.02159	−0.299752
$181$	−17.2511	−1.28227	−0.641133	−	0.767430i	$-0.721535\pi$
$181$	−17.2511	−1.28227	−0.641133	+	0.767430i	$0.721535\pi$
$182$	−6.25780	−0.463859
$183$	−2.69321	−0.199088
$184$	1.00000	0.0737210
$185$	−14.8905	−1.09477
$186$	−4.91893	−0.360674
$187$	11.2083	0.819634
$188$	11.5048	0.839076
$189$	26.5009	1.92766
$190$	−16.3306	−1.18475
$191$	14.3004	1.03474	0.517369	−	0.855763i	$-0.326912\pi$
$191$	14.3004	1.03474	0.517369	+	0.855763i	$0.326912\pi$
$192$	−1.27958	−0.0923460
$193$	−1.54720	−0.111370	−0.0556849	−	0.998448i	$-0.517734\pi$
$193$	−1.54720	−0.111370	−0.0556849	+	0.998448i	$0.517734\pi$
$194$	15.5694	1.11782
$195$	4.97805	0.356485
$196$	15.5362	1.10973
$197$	−8.79837	−0.626858	−0.313429	−	0.949612i	$-0.601478\pi$
$197$	−8.79837	−0.626858	−0.313429	+	0.949612i	$0.601478\pi$
$198$	−2.29811	−0.163320
$199$	−23.1379	−1.64020	−0.820100	−	0.572220i	$-0.806082\pi$
$199$	−23.1379	−1.64020	−0.820100	+	0.572220i	$0.806082\pi$
$200$	3.70999	0.262336
$201$	−3.86793	−0.272823
$202$	13.8983	0.977883
$203$	−29.1364	−2.04497
$204$	−8.50408	−0.595405
$205$	17.5010	1.22232
$206$	4.21226	0.293482
$207$	−1.36266	−0.0947117
$208$	−1.31820	−0.0914008
$209$	−9.33203	−0.645510
$210$	−17.9274	−1.23711
$211$	−21.1199	−1.45395	−0.726977	−	0.686662i	$-0.759075\pi$
$211$	−21.1199	−1.45395	−0.726977	+	0.686662i	$0.759075\pi$
$212$	−7.33707	−0.503912
$213$	1.81776	0.124551
$214$	−18.0468	−1.23365
$215$	−6.30911	−0.430278
$216$	5.58240	0.379834
$217$	18.2492	1.23883
$218$	−13.7479	−0.931124
$219$	−4.70101	−0.317665
$220$	4.97727	0.335568
$221$	−8.76072	−0.589310
$222$	6.45609	0.433304
$223$	16.0897	1.07745	0.538724	−	0.842482i	$-0.318907\pi$
$223$	16.0897	1.07745	0.538724	+	0.842482i	$0.318907\pi$
$224$	4.74723	0.317188
$225$	−5.05547	−0.337031
$226$	−9.84150	−0.654647
$227$	−17.2662	−1.14600	−0.572999	−	0.819556i	$-0.694220\pi$
$227$	−17.2662	−1.14600	−0.572999	+	0.819556i	$0.694220\pi$
$228$	7.08047	0.468916
$229$	−21.1484	−1.39753	−0.698764	−	0.715352i	$-0.746266\pi$
$229$	−21.1484	−1.39753	−0.698764	+	0.715352i	$0.746266\pi$
$230$	2.95127	0.194601
$231$	−10.2445	−0.674041
$232$	−6.13755	−0.402950
$233$	21.1957	1.38857	0.694287	−	0.719698i	$-0.255720\pi$
$233$	21.1957	1.38857	0.694287	+	0.719698i	$0.255720\pi$
$234$	1.79626	0.117425
$235$	33.9539	2.21491
$236$	5.45885	0.355341
$237$	12.7976	0.831290
$238$	31.5500	2.04508
$239$	19.8509	1.28405	0.642025	−	0.766684i	$-0.278094\pi$
$239$	19.8509	1.28405	0.642025	+	0.766684i	$0.278094\pi$
$240$	−3.77640	−0.243765
$241$	1.68704	0.108672	0.0543359	−	0.998523i	$-0.482696\pi$
$241$	1.68704	0.108672	0.0543359	+	0.998523i	$0.482696\pi$
$242$	−8.15577	−0.524273
$243$	−12.8379	−0.823549
$244$	2.10475	0.134743
$245$	45.8516	2.92935
$246$	−7.58793	−0.483789
$247$	7.29415	0.464116
$248$	3.84417	0.244105
$249$	−0.493480	−0.0312730
$250$	−3.80717	−0.240786
$251$	−0.897053	−0.0566215	−0.0283107	−	0.999599i	$-0.509013\pi$
$251$	−0.897053	−0.0566215	−0.0283107	+	0.999599i	$0.509013\pi$
$252$	−6.46888	−0.407501
$253$	1.68649	0.106028
$254$	6.86090	0.430491
$255$	−25.0978	−1.57169
$256$	1.00000	0.0625000
$257$	24.1224	1.50472	0.752358	−	0.658754i	$-0.228916\pi$
$257$	24.1224	1.50472	0.752358	+	0.658754i	$0.228916\pi$
$258$	2.73545	0.170302
$259$	−23.9520	−1.48830
$260$	−3.89036	−0.241270
$261$	8.36342	0.517683
$262$	1.00000	0.0617802
$263$	−4.89687	−0.301954	−0.150977	−	0.988537i	$-0.548242\pi$
$263$	−4.89687	−0.301954	−0.150977	+	0.988537i	$0.548242\pi$
$264$	−2.15800	−0.132816
$265$	−21.6537	−1.33018
$266$	−26.2684	−1.61062
$267$	−4.48557	−0.274512
$268$	3.02281	0.184647
$269$	−2.33407	−0.142311	−0.0711554	−	0.997465i	$-0.522669\pi$
$269$	−2.33407	−0.142311	−0.0711554	+	0.997465i	$0.522669\pi$
$270$	16.4752	1.00265
$271$	−2.33567	−0.141882	−0.0709408	−	0.997481i	$-0.522600\pi$
$271$	−2.33567	−0.141882	−0.0709408	+	0.997481i	$0.522600\pi$
$272$	6.64597	0.402971
$273$	8.00739	0.484629
$274$	5.40259	0.326383
$275$	6.25684	0.377302
$276$	−1.27958	−0.0770219
$277$	21.5815	1.29671	0.648355	−	0.761338i	$-0.275457\pi$
$277$	21.5815	1.29671	0.648355	+	0.761338i	$0.275457\pi$
$278$	−6.27702	−0.376471
$279$	−5.23831	−0.313609
$280$	14.0104	0.837279
$281$	21.8913	1.30593	0.652963	−	0.757390i	$-0.273526\pi$
$281$	21.8913	1.30593	0.652963	+	0.757390i	$0.273526\pi$
$282$	−14.7214	−0.876647
$283$	−16.8548	−1.00192	−0.500958	−	0.865472i	$-0.667019\pi$
$283$	−16.8548	−1.00192	−0.500958	+	0.865472i	$0.667019\pi$
$284$	−1.42059	−0.0842963
$285$	20.8964	1.23780
$286$	−2.22313	−0.131456
$287$	28.1511	1.66171
$288$	−1.36266	−0.0802958
$289$	27.1689	1.59817
$290$	−18.1136	−1.06367
$291$	−19.9224	−1.16787
$292$	3.67386	0.214996
$293$	4.61397	0.269551	0.134775	−	0.990876i	$-0.456969\pi$
$293$	4.61397	0.269551	0.134775	+	0.990876i	$0.456969\pi$
$294$	−19.8799	−1.15942
$295$	16.1105	0.937991
$296$	−5.04546	−0.293261
$297$	9.41463	0.546292
$298$	3.16624	0.183415
$299$	−1.31820	−0.0762335
$300$	−4.74725	−0.274082
$301$	−10.1485	−0.584948
$302$	−20.2522	−1.16538
$303$	−17.7841	−1.02167
$304$	−5.53342	−0.317363
$305$	6.21169	0.355680
$306$	−9.05622	−0.517710
$307$	−7.91136	−0.451525	−0.225762	−	0.974182i	$-0.572487\pi$
$307$	−7.91136	−0.451525	−0.225762	+	0.974182i	$0.572487\pi$
$308$	8.00614	0.456192
$309$	−5.38994	−0.306623
$310$	11.3452	0.644362
$311$	−25.5085	−1.44645	−0.723227	−	0.690610i	$-0.757342\pi$
$311$	−25.5085	−1.44645	−0.723227	+	0.690610i	$0.757342\pi$
$312$	1.68675	0.0954933
$313$	−2.34853	−0.132747	−0.0663734	−	0.997795i	$-0.521143\pi$
$313$	−2.34853	−0.132747	−0.0663734	+	0.997795i	$0.521143\pi$
$314$	9.69770	0.547273
$315$	−19.0914	−1.07568
$316$	−10.0013	−0.562619
$317$	14.9311	0.838612	0.419306	−	0.907845i	$-0.362273\pi$
$317$	14.9311	0.838612	0.419306	+	0.907845i	$0.362273\pi$
$318$	9.38841	0.526476
$319$	−10.3509	−0.579538
$320$	2.95127	0.164981
$321$	23.0924	1.28889
$322$	4.74723	0.264553
$323$	−36.7749	−2.04621
$324$	−3.05515	−0.169731
$325$	−4.89051	−0.271277
$326$	9.64251	0.534049
$327$	17.5916	0.972816
$328$	5.93000	0.327429
$329$	54.6161	3.01109
$330$	−6.36884	−0.350593
$331$	21.4838	1.18086	0.590429	−	0.807090i	$-0.298959\pi$
$331$	21.4838	1.18086	0.590429	+	0.807090i	$0.298959\pi$
$332$	0.385656	0.0211656
$333$	6.87527	0.376762
$334$	12.1386	0.664193
$335$	8.92111	0.487413
$336$	−6.07449	−0.331390
$337$	−20.1099	−1.09546	−0.547728	−	0.836656i	$-0.684507\pi$
$337$	−20.1099	−1.09546	−0.547728	+	0.836656i	$0.684507\pi$
$338$	−11.2623	−0.612591
$339$	12.5930	0.683959
$340$	19.6140	1.06372
$341$	6.48313	0.351081
$342$	7.54019	0.407727
$343$	40.5235	2.18806
$344$	−2.13776	−0.115260
$345$	−3.77640	−0.203314
$346$	9.76551	0.524997
$347$	−27.5683	−1.47994	−0.739971	−	0.672639i	$-0.765161\pi$
$347$	−27.5683	−1.47994	−0.739971	+	0.672639i	$0.765161\pi$
$348$	7.85351	0.420992
$349$	25.8432	1.38336	0.691678	−	0.722206i	$-0.256872\pi$
$349$	25.8432	1.38336	0.691678	+	0.722206i	$0.256872\pi$
$350$	17.6122	0.941411
$351$	−7.35872	−0.392779
$352$	1.68649	0.0898900
$353$	20.1449	1.07221	0.536103	−	0.844152i	$-0.319896\pi$
$353$	20.1449	1.07221	0.536103	+	0.844152i	$0.319896\pi$
$354$	−6.98505	−0.371251
$355$	−4.19253	−0.222516
$356$	3.50549	0.185790
$357$	−40.3708	−2.13665
$358$	−11.1736	−0.590544
$359$	3.16446	0.167014	0.0835070	−	0.996507i	$-0.473388\pi$
$359$	3.16446	0.167014	0.0835070	+	0.996507i	$0.473388\pi$
$360$	−4.02159	−0.211956
$361$	11.6187	0.611511
$362$	−17.2511	−0.906699
$363$	10.4360	0.547747
$364$	−6.25780	−0.327998
$365$	10.8426	0.567525
$366$	−2.69321	−0.140776
$367$	31.2229	1.62982	0.814912	−	0.579585i	$-0.196785\pi$
$367$	31.2229	1.62982	0.814912	+	0.579585i	$0.196785\pi$
$368$	1.00000	0.0521286
$369$	−8.08060	−0.420659
$370$	−14.8905	−0.774121
$371$	−34.8308	−1.80833
$372$	−4.91893	−0.255035
$373$	5.45277	0.282334	0.141167	−	0.989986i	$-0.454915\pi$
$373$	5.45277	0.282334	0.141167	+	0.989986i	$0.454915\pi$
$374$	11.2083	0.579569
$375$	4.87159	0.251568
$376$	11.5048	0.593317
$377$	8.09052	0.416683
$378$	26.5009	1.36306
$379$	1.47584	0.0758087	0.0379044	−	0.999281i	$-0.487932\pi$
$379$	1.47584	0.0758087	0.0379044	+	0.999281i	$0.487932\pi$
$380$	−16.3306	−0.837742
$381$	−8.77910	−0.449767
$382$	14.3004	0.731670
$383$	16.3685	0.836392	0.418196	−	0.908357i	$-0.362663\pi$
$383$	16.3685	0.836392	0.418196	+	0.908357i	$0.362663\pi$
$384$	−1.27958	−0.0652985
$385$	23.6283	1.20421
$386$	−1.54720	−0.0787504
$387$	2.91305	0.148079
$388$	15.5694	0.790419
$389$	−14.1903	−0.719477	−0.359738	−	0.933053i	$-0.617134\pi$
$389$	−14.1903	−0.719477	−0.359738	+	0.933053i	$0.617134\pi$
$390$	4.97805	0.252073
$391$	6.64597	0.336101
$392$	15.5362	0.784698
$393$	−1.27958	−0.0645465
$394$	−8.79837	−0.443255
$395$	−29.5166	−1.48514
$396$	−2.29811	−0.115485
$397$	−13.8874	−0.696990	−0.348495	−	0.937311i	$-0.613307\pi$
$397$	−13.8874	−0.696990	−0.348495	+	0.937311i	$0.613307\pi$
$398$	−23.1379	−1.15980
$399$	33.6127	1.68274
$400$	3.70999	0.185500
$401$	−36.8887	−1.84213	−0.921067	−	0.389405i	$-0.872681\pi$
$401$	−36.8887	−1.84213	−0.921067	+	0.389405i	$0.872681\pi$
$402$	−3.86793	−0.192915
$403$	−5.06738	−0.252424
$404$	13.8983	0.691468
$405$	−9.01658	−0.448038
$406$	−29.1364	−1.44601
$407$	−8.50909	−0.421780
$408$	−8.50408	−0.421015
$409$	−13.6119	−0.673063	−0.336532	−	0.941672i	$-0.609254\pi$
$409$	−13.6119	−0.673063	−0.336532	+	0.941672i	$0.609254\pi$
$410$	17.5010	0.864314
$411$	−6.91307	−0.340997
$412$	4.21226	0.207523
$413$	25.9144	1.27517
$414$	−1.36266	−0.0669713
$415$	1.13818	0.0558708
$416$	−1.31820	−0.0646301
$417$	8.03198	0.393328
$418$	−9.33203	−0.456444
$419$	−7.83625	−0.382826	−0.191413	−	0.981510i	$-0.561307\pi$
$419$	−7.83625	−0.382826	−0.191413	+	0.981510i	$0.561307\pi$
$420$	−17.9274	−0.874770
$421$	2.02966	0.0989197	0.0494599	−	0.998776i	$-0.484250\pi$
$421$	2.02966	0.0989197	0.0494599	+	0.998776i	$0.484250\pi$
$422$	−21.1199	−1.02810
$423$	−15.6772	−0.762253
$424$	−7.33707	−0.356320
$425$	24.6565	1.19602
$426$	1.81776	0.0880707
$427$	9.99175	0.483535
$428$	−18.0468	−0.872325
$429$	2.84468	0.137342
$430$	−6.30911	−0.304253
$431$	−2.21359	−0.106625	−0.0533123	−	0.998578i	$-0.516978\pi$
$431$	−2.21359	−0.106625	−0.0533123	+	0.998578i	$0.516978\pi$
$432$	5.58240	0.268583
$433$	−12.5343	−0.602359	−0.301180	−	0.953567i	$-0.597380\pi$
$433$	−12.5343	−0.602359	−0.301180	+	0.953567i	$0.597380\pi$
$434$	18.2492	0.875988
$435$	23.1778	1.11129
$436$	−13.7479	−0.658404
$437$	−5.53342	−0.264699
$438$	−4.70101	−0.224623
$439$	0.106187	0.00506804	0.00253402	−	0.999997i	$-0.499193\pi$
$439$	0.106187	0.00506804	0.00253402	+	0.999997i	$0.499193\pi$
$440$	4.97727	0.237282
$441$	−21.1707	−1.00813
$442$	−8.76072	−0.416705
$443$	4.76653	0.226465	0.113232	−	0.993569i	$-0.463880\pi$
$443$	4.76653	0.226465	0.113232	+	0.993569i	$0.463880\pi$
$444$	6.45609	0.306392
$445$	10.3456	0.490430
$446$	16.0897	0.761871
$447$	−4.05147	−0.191628
$448$	4.74723	0.224286
$449$	−30.5001	−1.43939	−0.719695	−	0.694290i	$-0.755719\pi$
$449$	−30.5001	−1.43939	−0.719695	+	0.694290i	$0.755719\pi$
$450$	−5.05547	−0.238317
$451$	10.0009	0.470922
$452$	−9.84150	−0.462905
$453$	25.9144	1.21756
$454$	−17.2662	−0.810343
$455$	−18.4685	−0.865815
$456$	7.08047	0.331574
$457$	27.8433	1.30245	0.651227	−	0.758883i	$-0.274255\pi$
$457$	27.8433	1.30245	0.651227	+	0.758883i	$0.274255\pi$
$458$	−21.1484	−0.988201
$459$	37.1004	1.73170
$460$	2.95127	0.137604
$461$	−16.4811	−0.767603	−0.383802	−	0.923416i	$-0.625385\pi$
$461$	−16.4811	−0.767603	−0.383802	+	0.923416i	$0.625385\pi$
$462$	−10.2445	−0.476619
$463$	21.4363	0.996230	0.498115	−	0.867111i	$-0.334026\pi$
$463$	21.4363	0.996230	0.498115	+	0.867111i	$0.334026\pi$
$464$	−6.13755	−0.284929
$465$	−14.5171	−0.673214
$466$	21.1957	0.981871
$467$	−0.583846	−0.0270172	−0.0135086	−	0.999909i	$-0.504300\pi$
$467$	−0.583846	−0.0270172	−0.0135086	+	0.999909i	$0.504300\pi$
$468$	1.79626	0.0830324
$469$	14.3500	0.662620
$470$	33.9539	1.56618
$471$	−12.4090	−0.571778
$472$	5.45885	0.251264
$473$	−3.60531	−0.165772
$474$	12.7976	0.587811
$475$	−20.5289	−0.941932
$476$	31.5500	1.44609
$477$	9.99797	0.457776
$478$	19.8509	0.907961
$479$	−17.7737	−0.812100	−0.406050	−	0.913851i	$-0.633094\pi$
$479$	−17.7737	−0.812100	−0.406050	+	0.913851i	$0.633094\pi$
$480$	−3.77640	−0.172368
$481$	6.65093	0.303256
$482$	1.68704	0.0768426
$483$	−6.07449	−0.276399
$484$	−8.15577	−0.370717
$485$	45.9496	2.08646
$486$	−12.8379	−0.582337
$487$	−26.8170	−1.21520	−0.607598	−	0.794245i	$-0.707867\pi$
$487$	−26.8170	−1.21520	−0.607598	+	0.794245i	$0.707867\pi$
$488$	2.10475	0.0952777
$489$	−12.3384	−0.557962
$490$	45.8516	2.07136
$491$	23.5407	1.06238	0.531189	−	0.847254i	$-0.321746\pi$
$491$	23.5407	1.06238	0.531189	+	0.847254i	$0.321746\pi$
$492$	−7.58793	−0.342090
$493$	−40.7900	−1.83709
$494$	7.29415	0.328180
$495$	−6.78235	−0.304844
$496$	3.84417	0.172608
$497$	−6.74385	−0.302503
$498$	−0.493480	−0.0221133
$499$	−21.6552	−0.969420	−0.484710	−	0.874675i	$-0.661075\pi$
$499$	−21.6552	−0.969420	−0.484710	+	0.874675i	$0.661075\pi$
$500$	−3.80717	−0.170262
$501$	−15.5323	−0.693933
$502$	−0.897053	−0.0400374
$503$	16.0716	0.716596	0.358298	−	0.933607i	$-0.383357\pi$
$503$	16.0716	0.716596	0.358298	+	0.933607i	$0.383357\pi$
$504$	−6.46888	−0.288147
$505$	41.0177	1.82526
$506$	1.68649	0.0749734
$507$	14.4111	0.640020
$508$	6.86090	0.304403
$509$	25.8919	1.14764	0.573820	−	0.818981i	$-0.305461\pi$
$509$	25.8919	1.14764	0.573820	+	0.818981i	$0.305461\pi$
$510$	−25.0978	−1.11135
$511$	17.4407	0.771530
$512$	1.00000	0.0441942
$513$	−30.8897	−1.36382
$514$	24.1224	1.06399
$515$	12.4315	0.547798
$516$	2.73545	0.120421
$517$	19.4027	0.853332
$518$	−23.9520	−1.05239
$519$	−12.4958	−0.548505
$520$	−3.89036	−0.170604
$521$	25.7051	1.12616	0.563081	−	0.826401i	$-0.309616\pi$
$521$	25.7051	1.12616	0.563081	+	0.826401i	$0.309616\pi$
$522$	8.36342	0.366057
$523$	5.89661	0.257841	0.128920	−	0.991655i	$-0.458849\pi$
$523$	5.89661	0.257841	0.128920	+	0.991655i	$0.458849\pi$
$524$	1.00000	0.0436852
$525$	−22.5363	−0.983564
$526$	−4.89687	−0.213513
$527$	25.5482	1.11290
$528$	−2.15800	−0.0939149
$529$	1.00000	0.0434783
$530$	−21.6537	−0.940576
$531$	−7.43857	−0.322807
$532$	−26.2684	−1.13888
$533$	−7.81693	−0.338589
$534$	−4.48557	−0.194109
$535$	−53.2610	−2.30267
$536$	3.02281	0.130565
$537$	14.2976	0.616986
$538$	−2.33407	−0.100629
$539$	26.2016	1.12858
$540$	16.4752	0.708978
$541$	1.65317	0.0710755	0.0355377	−	0.999368i	$-0.488686\pi$
$541$	1.65317	0.0710755	0.0355377	+	0.999368i	$0.488686\pi$
$542$	−2.33567	−0.100325
$543$	22.0743	0.947297
$544$	6.64597	0.284944
$545$	−40.5737	−1.73799
$546$	8.00739	0.342685
$547$	3.81571	0.163148	0.0815741	−	0.996667i	$-0.474005\pi$
$547$	3.81571	0.163148	0.0815741	+	0.996667i	$0.474005\pi$
$548$	5.40259	0.230787
$549$	−2.86807	−0.122406
$550$	6.25684	0.266793
$551$	33.9616	1.44681
$552$	−1.27958	−0.0544627
$553$	−47.4787	−2.01900
$554$	21.5815	0.916912
$555$	19.0537	0.808783
$556$	−6.27702	−0.266205
$557$	23.0485	0.976598	0.488299	−	0.872676i	$-0.337617\pi$
$557$	23.0485	0.976598	0.488299	+	0.872676i	$0.337617\pi$
$558$	−5.23831	−0.221755
$559$	2.81800	0.119189
$560$	14.0104	0.592046
$561$	−14.3420	−0.605520
$562$	21.8913	0.923429
$563$	6.92779	0.291971	0.145986	−	0.989287i	$-0.453365\pi$
$563$	6.92779	0.291971	0.145986	+	0.989287i	$0.453365\pi$
$564$	−14.7214	−0.619883
$565$	−29.0449	−1.22193
$566$	−16.8548	−0.708461
$567$	−14.5035	−0.609091
$568$	−1.42059	−0.0596065
$569$	10.2091	0.427987	0.213994	−	0.976835i	$-0.431353\pi$
$569$	10.2091	0.427987	0.213994	+	0.976835i	$0.431353\pi$
$570$	20.8964	0.875253
$571$	−7.64768	−0.320045	−0.160023	−	0.987113i	$-0.551157\pi$
$571$	−7.64768	−0.320045	−0.160023	+	0.987113i	$0.551157\pi$
$572$	−2.22313	−0.0929536
$573$	−18.2985	−0.764431
$574$	28.1511	1.17500
$575$	3.70999	0.154717
$576$	−1.36266	−0.0567777
$577$	4.69825	0.195591	0.0977953	−	0.995207i	$-0.468821\pi$
$577$	4.69825	0.195591	0.0977953	+	0.995207i	$0.468821\pi$
$578$	27.1689	1.13008
$579$	1.97977	0.0822765
$580$	−18.1136	−0.752125
$581$	1.83080	0.0759544
$582$	−19.9224	−0.825811
$583$	−12.3739	−0.512473
$584$	3.67386	0.152025
$585$	5.30126	0.219180
$586$	4.61397	0.190601
$587$	33.5656	1.38540	0.692700	−	0.721226i	$-0.256421\pi$
$587$	33.5656	1.38540	0.692700	+	0.721226i	$0.256421\pi$
$588$	−19.8799	−0.819834
$589$	−21.2714	−0.876472
$590$	16.1105	0.663260
$591$	11.2583	0.463103
$592$	−5.04546	−0.207367
$593$	−1.13797	−0.0467308	−0.0233654	−	0.999727i	$-0.507438\pi$
$593$	−1.13797	−0.0467308	−0.0233654	+	0.999727i	$0.507438\pi$
$594$	9.41463	0.386287
$595$	93.1125	3.81724
$596$	3.16624	0.129694
$597$	29.6069	1.21173
$598$	−1.31820	−0.0539052
$599$	−26.6206	−1.08769	−0.543845	−	0.839186i	$-0.683032\pi$
$599$	−26.6206	−1.08769	−0.543845	+	0.839186i	$0.683032\pi$
$600$	−4.74725	−0.193805
$601$	3.95546	0.161347	0.0806733	−	0.996741i	$-0.474293\pi$
$601$	3.95546	0.161347	0.0806733	+	0.996741i	$0.474293\pi$
$602$	−10.1485	−0.413620
$603$	−4.11907	−0.167741
$604$	−20.2522	−0.824050
$605$	−24.0699	−0.978579
$606$	−17.7841	−0.722429
$607$	−5.20694	−0.211343	−0.105672	−	0.994401i	$-0.533699\pi$
$607$	−5.20694	−0.211343	−0.105672	+	0.994401i	$0.533699\pi$
$608$	−5.53342	−0.224410
$609$	37.2825	1.51076
$610$	6.21169	0.251504
$611$	−15.1657	−0.613538
$612$	−9.05622	−0.366076
$613$	33.0564	1.33513	0.667567	−	0.744550i	$-0.267336\pi$
$613$	33.0564	1.33513	0.667567	+	0.744550i	$0.267336\pi$
$614$	−7.91136	−0.319276
$615$	−22.3940	−0.903015
$616$	8.00614	0.322577
$617$	−22.4957	−0.905641	−0.452820	−	0.891602i	$-0.649582\pi$
$617$	−22.4957	−0.905641	−0.452820	+	0.891602i	$0.649582\pi$
$618$	−5.38994	−0.216815
$619$	−30.3211	−1.21871	−0.609354	−	0.792898i	$-0.708571\pi$
$619$	−30.3211	−1.21871	−0.609354	+	0.792898i	$0.708571\pi$
$620$	11.3452	0.455633
$621$	5.58240	0.224014
$622$	−25.5085	−1.02280
$623$	16.6414	0.666722
$624$	1.68675	0.0675240
$625$	−29.7859	−1.19144
$626$	−2.34853	−0.0938662
$627$	11.9411	0.476882
$628$	9.69770	0.386981
$629$	−33.5320	−1.33701
$630$	−19.0914	−0.760620
$631$	11.1207	0.442709	0.221354	−	0.975193i	$-0.428952\pi$
$631$	11.1207	0.442709	0.221354	+	0.975193i	$0.428952\pi$
$632$	−10.0013	−0.397832
$633$	27.0247	1.07413
$634$	14.9311	0.592988
$635$	20.2484	0.803532
$636$	9.38841	0.372274
$637$	−20.4799	−0.811441
$638$	−10.3509	−0.409796
$639$	1.93578	0.0765783
$640$	2.95127	0.116659
$641$	9.30805	0.367646	0.183823	−	0.982959i	$-0.441153\pi$
$641$	9.30805	0.367646	0.183823	+	0.982959i	$0.441153\pi$
$642$	23.0924	0.911384
$643$	−15.8328	−0.624385	−0.312192	−	0.950019i	$-0.601063\pi$
$643$	−15.8328	−0.624385	−0.312192	+	0.950019i	$0.601063\pi$
$644$	4.74723	0.187067
$645$	8.07304	0.317876
$646$	−36.7749	−1.44689
$647$	−46.5985	−1.83197	−0.915987	−	0.401208i	$-0.868591\pi$
$647$	−46.5985	−1.83197	−0.915987	+	0.401208i	$0.868591\pi$
$648$	−3.05515	−0.120018
$649$	9.20626	0.361378
$650$	−4.89051	−0.191822
$651$	−23.3513	−0.915211
$652$	9.64251	0.377630
$653$	6.71144	0.262639	0.131320	−	0.991340i	$-0.458079\pi$
$653$	6.71144	0.262639	0.131320	+	0.991340i	$0.458079\pi$
$654$	17.5916	0.687885
$655$	2.95127	0.115316
$656$	5.93000	0.231528
$657$	−5.00624	−0.195312
$658$	54.6161	2.12916
$659$	−12.8224	−0.499491	−0.249746	−	0.968311i	$-0.580347\pi$
$659$	−12.8224	−0.499491	−0.249746	+	0.968311i	$0.580347\pi$
$660$	−6.36884	−0.247907
$661$	−36.9387	−1.43675	−0.718374	−	0.695657i	$-0.755113\pi$
$661$	−36.9387	−1.43675	−0.718374	+	0.695657i	$0.755113\pi$
$662$	21.4838	0.834992
$663$	11.2101	0.435363
$664$	0.385656	0.0149664
$665$	−77.5252	−3.00630
$666$	6.87527	0.266411
$667$	−6.13755	−0.237647
$668$	12.1386	0.469655
$669$	−20.5882	−0.795985
$670$	8.92111	0.344653
$671$	3.54964	0.137032
$672$	−6.07449	−0.234328
$673$	24.3096	0.937064	0.468532	−	0.883446i	$-0.344783\pi$
$673$	24.3096	0.937064	0.468532	+	0.883446i	$0.344783\pi$
$674$	−20.1099	−0.774605
$675$	20.7106	0.797153
$676$	−11.2623	−0.433167
$677$	37.6887	1.44850	0.724248	−	0.689540i	$-0.242187\pi$
$677$	37.6887	1.44850	0.724248	+	0.689540i	$0.242187\pi$
$678$	12.5930	0.483632
$679$	73.9118	2.83647
$680$	19.6140	0.752164
$681$	22.0935	0.846627
$682$	6.48313	0.248252
$683$	−16.2151	−0.620454	−0.310227	−	0.950662i	$-0.600405\pi$
$683$	−16.2151	−0.620454	−0.310227	+	0.950662i	$0.600405\pi$
$684$	7.54019	0.288306
$685$	15.9445	0.609208
$686$	40.5235	1.54719
$687$	27.0612	1.03245
$688$	−2.13776	−0.0815015
$689$	9.67173	0.368464
$690$	−3.77640	−0.143765
$691$	−44.0969	−1.67752	−0.838762	−	0.544498i	$-0.816720\pi$
$691$	−44.0969	−1.67752	−0.838762	+	0.544498i	$0.816720\pi$
$692$	9.76551	0.371229
$693$	−10.9097	−0.414424
$694$	−27.5683	−1.04648
$695$	−18.5252	−0.702700
$696$	7.85351	0.297687
$697$	39.4106	1.49278
$698$	25.8432	0.978180
$699$	−27.1216	−1.02583
$700$	17.6122	0.665678
$701$	−6.36550	−0.240422	−0.120211	−	0.992748i	$-0.538357\pi$
$701$	−6.36550	−0.240422	−0.120211	+	0.992748i	$0.538357\pi$
$702$	−7.35872	−0.277737
$703$	27.9186	1.05297
$704$	1.68649	0.0635618
$705$	−43.4468	−1.63630
$706$	20.1449	0.758165
$707$	65.9786	2.48138
$708$	−6.98505	−0.262514
$709$	−19.4462	−0.730316	−0.365158	−	0.930946i	$-0.618985\pi$
$709$	−19.4462	−0.730316	−0.365158	+	0.930946i	$0.618985\pi$
$710$	−4.19253	−0.157343
$711$	13.6285	0.511107
$712$	3.50549	0.131374
$713$	3.84417	0.143965
$714$	−40.3708	−1.51084
$715$	−6.56104	−0.245369
$716$	−11.1736	−0.417578
$717$	−25.4009	−0.948616
$718$	3.16446	0.118097
$719$	−45.4479	−1.69492	−0.847461	−	0.530858i	$-0.821870\pi$
$719$	−45.4479	−1.69492	−0.847461	+	0.530858i	$0.821870\pi$
$720$	−4.02159	−0.149876
$721$	19.9966	0.744711
$722$	11.6187	0.432404
$723$	−2.15871	−0.0802833
$724$	−17.2511	−0.641133
$725$	−22.7703	−0.845666
$726$	10.4360	0.387316
$727$	−21.2551	−0.788309	−0.394155	−	0.919044i	$-0.628963\pi$
$727$	−21.2551	−0.788309	−0.394155	+	0.919044i	$0.628963\pi$
$728$	−6.25780	−0.231930
$729$	25.5926	0.947874
$730$	10.8426	0.401301
$731$	−14.2075	−0.525484
$732$	−2.69321	−0.0995439
$733$	1.73464	0.0640703	0.0320351	−	0.999487i	$-0.489801\pi$
$733$	1.73464	0.0640703	0.0320351	+	0.999487i	$0.489801\pi$
$734$	31.2229	1.15246
$735$	−58.6710	−2.16411
$736$	1.00000	0.0368605
$737$	5.09792	0.187784
$738$	−8.08060	−0.297451
$739$	34.4412	1.26694	0.633470	−	0.773767i	$-0.281630\pi$
$739$	34.4412	1.26694	0.633470	+	0.773767i	$0.281630\pi$
$740$	−14.8905	−0.547386
$741$	−9.33348	−0.342874
$742$	−34.8308	−1.27868
$743$	−37.7041	−1.38323	−0.691615	−	0.722266i	$-0.743101\pi$
$743$	−37.7041	−1.38323	−0.691615	+	0.722266i	$0.743101\pi$
$744$	−4.91893	−0.180337
$745$	9.34442	0.342353
$746$	5.45277	0.199640
$747$	−0.525520	−0.0192278
$748$	11.2083	0.409817
$749$	−85.6723	−3.13040
$750$	4.87159	0.177885
$751$	−50.5347	−1.84404	−0.922018	−	0.387147i	$-0.873461\pi$
$751$	−50.5347	−1.84404	−0.922018	+	0.387147i	$0.873461\pi$
$752$	11.5048	0.419538
$753$	1.14786	0.0418302
$754$	8.09052	0.294639
$755$	−59.7696	−2.17524
$756$	26.5009	0.963830
$757$	16.6381	0.604721	0.302360	−	0.953194i	$-0.402225\pi$
$757$	16.6381	0.604721	0.302360	+	0.953194i	$0.402225\pi$
$758$	1.47584	0.0536049
$759$	−2.15800	−0.0783304
$760$	−16.3306	−0.592373
$761$	−35.5159	−1.28745	−0.643725	−	0.765257i	$-0.722612\pi$
$761$	−35.5159	−1.28745	−0.643725	+	0.765257i	$0.722612\pi$
$762$	−8.77910	−0.318033
$763$	−65.2644	−2.36273
$764$	14.3004	0.517369
$765$	−26.7274	−0.966330
$766$	16.3685	0.591418
$767$	−7.19585	−0.259827
$768$	−1.27958	−0.0461730
$769$	−29.3960	−1.06005	−0.530024	−	0.847983i	$-0.677817\pi$
$769$	−29.3960	−1.06005	−0.530024	+	0.847983i	$0.677817\pi$
$770$	23.6283	0.851504
$771$	−30.8667	−1.11164
$772$	−1.54720	−0.0556849
$773$	−35.2940	−1.26944	−0.634719	−	0.772743i	$-0.718884\pi$
$773$	−35.2940	−1.26944	−0.634719	+	0.772743i	$0.718884\pi$
$774$	2.91305	0.104708
$775$	14.2618	0.512300
$776$	15.5694	0.558910
$777$	30.6486	1.09951
$778$	−14.1903	−0.508747
$779$	−32.8132	−1.17565
$780$	4.97805	0.178243
$781$	−2.39580	−0.0857284
$782$	6.64597	0.237659
$783$	−34.2622	−1.22443
$784$	15.5362	0.554865
$785$	28.6205	1.02151
$786$	−1.27958	−0.0456413
$787$	−25.1139	−0.895215	−0.447607	−	0.894230i	$-0.647724\pi$
$787$	−25.1139	−0.895215	−0.447607	+	0.894230i	$0.647724\pi$
$788$	−8.79837	−0.313429
$789$	6.26595	0.223074
$790$	−29.5166	−1.05015
$791$	−46.7199	−1.66117
$792$	−2.29811	−0.0816599
$793$	−2.77449	−0.0985249
$794$	−13.8874	−0.492846
$795$	27.7077	0.982691
$796$	−23.1379	−0.820100
$797$	6.48083	0.229563	0.114781	−	0.993391i	$-0.463383\pi$
$797$	6.48083	0.229563	0.114781	+	0.993391i	$0.463383\pi$
$798$	33.6127	1.18988
$799$	76.4608	2.70499
$800$	3.70999	0.131168
$801$	−4.77680	−0.168780
$802$	−36.8887	−1.30258
$803$	6.19591	0.218649
$804$	−3.86793	−0.136412
$805$	14.0104	0.493800
$806$	−5.06738	−0.178491
$807$	2.98664	0.105135
$808$	13.8983	0.488942
$809$	19.3684	0.680956	0.340478	−	0.940253i	$-0.389411\pi$
$809$	19.3684	0.680956	0.340478	+	0.940253i	$0.389411\pi$
$810$	−9.01658	−0.316810
$811$	48.3201	1.69675	0.848375	−	0.529396i	$-0.177581\pi$
$811$	48.3201	1.69675	0.848375	+	0.529396i	$0.177581\pi$
$812$	−29.1364	−1.02249
$813$	2.98868	0.104818
$814$	−8.50909	−0.298244
$815$	28.4576	0.996828
$816$	−8.50408	−0.297702
$817$	11.8291	0.413849
$818$	−13.6119	−0.475928
$819$	8.52729	0.297968
$820$	17.5010	0.611162
$821$	−16.3000	−0.568873	−0.284436	−	0.958695i	$-0.591806\pi$
$821$	−16.3000	−0.568873	−0.284436	+	0.958695i	$0.591806\pi$
$822$	−6.91307	−0.241121
$823$	12.1141	0.422270	0.211135	−	0.977457i	$-0.432284\pi$
$823$	12.1141	0.422270	0.211135	+	0.977457i	$0.432284\pi$
$824$	4.21226	0.146741
$825$	−8.00616	−0.278739
$826$	25.9144	0.901678
$827$	3.96905	0.138017	0.0690086	−	0.997616i	$-0.478016\pi$
$827$	3.96905	0.138017	0.0690086	+	0.997616i	$0.478016\pi$
$828$	−1.36266	−0.0473559
$829$	48.3761	1.68017	0.840085	−	0.542454i	$-0.182505\pi$
$829$	48.3761	1.68017	0.840085	+	0.542454i	$0.182505\pi$
$830$	1.13818	0.0395066
$831$	−27.6154	−0.957968
$832$	−1.31820	−0.0457004
$833$	103.253	3.57751
$834$	8.03198	0.278125
$835$	35.8242	1.23975
$836$	−9.33203	−0.322755
$837$	21.4597	0.741754
$838$	−7.83625	−0.270699
$839$	−29.0691	−1.00358	−0.501788	−	0.864991i	$-0.667324\pi$
$839$	−29.0691	−1.00358	−0.501788	+	0.864991i	$0.667324\pi$
$840$	−17.9274	−0.618555
$841$	8.66952	0.298949
$842$	2.02966	0.0699468
$843$	−28.0118	−0.964777
$844$	−21.1199	−0.726977
$845$	−33.2382	−1.14343
$846$	−15.6772	−0.538994
$847$	−38.7173	−1.33034
$848$	−7.33707	−0.251956
$849$	21.5672	0.740184
$850$	24.6565	0.845710
$851$	−5.04546	−0.172956
$852$	1.81776	0.0622754
$853$	26.2417	0.898499	0.449249	−	0.893406i	$-0.351692\pi$
$853$	26.2417	0.898499	0.449249	+	0.893406i	$0.351692\pi$
$854$	9.99175	0.341911
$855$	22.2531	0.761041
$856$	−18.0468	−0.616827
$857$	5.97523	0.204110	0.102055	−	0.994779i	$-0.467458\pi$
$857$	5.97523	0.204110	0.102055	+	0.994779i	$0.467458\pi$
$858$	2.84468	0.0971157
$859$	12.0148	0.409939	0.204969	−	0.978768i	$-0.434291\pi$
$859$	12.0148	0.409939	0.204969	+	0.978768i	$0.434291\pi$
$860$	−6.30911	−0.215139
$861$	−36.0217	−1.22762
$862$	−2.21359	−0.0753950
$863$	−23.6361	−0.804582	−0.402291	−	0.915512i	$-0.631786\pi$
$863$	−23.6361	−0.804582	−0.402291	+	0.915512i	$0.631786\pi$
$864$	5.58240	0.189917
$865$	28.8207	0.979932
$866$	−12.5343	−0.425932
$867$	−34.7649	−1.18068
$868$	18.2492	0.619417
$869$	−16.8671	−0.572177
$870$	23.1778	0.785802
$871$	−3.98466	−0.135015
$872$	−13.7479	−0.465562
$873$	−21.2159	−0.718050
$874$	−5.53342	−0.187171
$875$	−18.0735	−0.610996
$876$	−4.70101	−0.158833
$877$	46.6420	1.57499	0.787494	−	0.616323i	$-0.211378\pi$
$877$	46.6420	1.57499	0.787494	+	0.616323i	$0.211378\pi$
$878$	0.106187	0.00358364
$879$	−5.90396	−0.199136
$880$	4.97727	0.167784
$881$	−56.3965	−1.90005	−0.950024	−	0.312178i	$-0.898941\pi$
$881$	−56.3965	−1.90005	−0.950024	+	0.312178i	$0.898941\pi$
$882$	−21.1707	−0.712853
$883$	30.3720	1.02210	0.511049	−	0.859552i	$-0.329257\pi$
$883$	30.3720	1.02210	0.511049	+	0.859552i	$0.329257\pi$
$884$	−8.76072	−0.294655
$885$	−20.6148	−0.692958
$886$	4.76653	0.160135
$887$	−6.09066	−0.204504	−0.102252	−	0.994759i	$-0.532605\pi$
$887$	−6.09066	−0.204504	−0.102252	+	0.994759i	$0.532605\pi$
$888$	6.45609	0.216652
$889$	32.5703	1.09237
$890$	10.3456	0.346787
$891$	−5.15247	−0.172614
$892$	16.0897	0.538724
$893$	−63.6611	−2.13034
$894$	−4.05147	−0.135501
$895$	−32.9764	−1.10228
$896$	4.74723	0.158594
$897$	1.68675	0.0563189
$898$	−30.5001	−1.01780
$899$	−23.5938	−0.786896
$900$	−5.05547	−0.168516
$901$	−48.7620	−1.62450
$902$	10.0009	0.332992
$903$	12.9858	0.432141
$904$	−9.84150	−0.327323
$905$	−50.9127	−1.69240
$906$	25.9144	0.860947
$907$	42.7434	1.41927	0.709635	−	0.704570i	$-0.248860\pi$
$907$	42.7434	1.41927	0.709635	+	0.704570i	$0.248860\pi$
$908$	−17.2662	−0.572999
$909$	−18.9388	−0.628159
$910$	−18.4685	−0.612224
$911$	−6.46941	−0.214341	−0.107171	−	0.994241i	$-0.534179\pi$
$911$	−6.46941	−0.214341	−0.107171	+	0.994241i	$0.534179\pi$
$912$	7.08047	0.234458
$913$	0.650404	0.0215252
$914$	27.8433	0.920974
$915$	−7.94838	−0.262765
$916$	−21.1484	−0.698764
$917$	4.74723	0.156767
$918$	37.1004	1.22450
$919$	−27.9567	−0.922205	−0.461103	−	0.887347i	$-0.652546\pi$
$919$	−27.9567	−0.922205	−0.461103	+	0.887347i	$0.652546\pi$
$920$	2.95127	0.0973005
$921$	10.1232	0.333572
$922$	−16.4811	−0.542778
$923$	1.87262	0.0616379
$924$	−10.2445	−0.337020
$925$	−18.7186	−0.615464
$926$	21.4363	0.704441
$927$	−5.73989	−0.188523
$928$	−6.13755	−0.201475
$929$	−21.4483	−0.703695	−0.351848	−	0.936057i	$-0.614447\pi$
$929$	−21.4483	−0.703695	−0.351848	+	0.936057i	$0.614447\pi$
$930$	−14.5171	−0.476035
$931$	−85.9684	−2.81750
$932$	21.1957	0.694287
$933$	32.6403	1.06859
$934$	−0.583846	−0.0191040
$935$	33.0788	1.08179
$936$	1.79626	0.0587127
$937$	19.6864	0.643127	0.321563	−	0.946888i	$-0.395792\pi$
$937$	19.6864	0.643127	0.321563	+	0.946888i	$0.395792\pi$
$938$	14.3500	0.468543
$939$	3.00514	0.0980691
$940$	33.9539	1.10745
$941$	−31.0093	−1.01088	−0.505438	−	0.862863i	$-0.668669\pi$
$941$	−31.0093	−1.01088	−0.505438	+	0.862863i	$0.668669\pi$
$942$	−12.4090	−0.404308
$943$	5.93000	0.193107
$944$	5.45885	0.177670
$945$	78.2114	2.54422
$946$	−3.60531	−0.117219
$947$	−32.1468	−1.04463	−0.522316	−	0.852752i	$-0.674932\pi$
$947$	−32.1468	−1.04463	−0.522316	+	0.852752i	$0.674932\pi$
$948$	12.7976	0.415645
$949$	−4.84288	−0.157207
$950$	−20.5289	−0.666046
$951$	−19.1055	−0.619540
$952$	31.5500	1.02254
$953$	−36.1637	−1.17146	−0.585728	−	0.810508i	$-0.699191\pi$
$953$	−36.1637	−1.17146	−0.585728	+	0.810508i	$0.699191\pi$
$954$	9.99797	0.323696
$955$	42.2042	1.36570
$956$	19.8509	0.642025
$957$	13.2448	0.428145
$958$	−17.7737	−0.574241
$959$	25.6474	0.828197
$960$	−3.77640	−0.121883
$961$	−16.2224	−0.523303
$962$	6.65093	0.214434
$963$	24.5917	0.792457
$964$	1.68704	0.0543359
$965$	−4.56620	−0.146991
$966$	−6.07449	−0.195443
$967$	−28.6509	−0.921351	−0.460676	−	0.887569i	$-0.652393\pi$
$967$	−28.6509	−0.921351	−0.460676	+	0.887569i	$0.652393\pi$
$968$	−8.15577	−0.262136
$969$	47.0566	1.51168
$970$	45.9496	1.47535
$971$	55.6085	1.78456	0.892280	−	0.451482i	$-0.149105\pi$
$971$	55.6085	1.78456	0.892280	+	0.451482i	$0.149105\pi$
$972$	−12.8379	−0.411775
$973$	−29.7985	−0.955295
$974$	−26.8170	−0.859273
$975$	6.25782	0.200411
$976$	2.10475	0.0673715
$977$	−20.9566	−0.670462	−0.335231	−	0.942136i	$-0.608814\pi$
$977$	−20.9566	−0.670462	−0.335231	+	0.942136i	$0.608814\pi$
$978$	−12.3384	−0.394539
$979$	5.91195	0.188947
$980$	45.8516	1.46468
$981$	18.7337	0.598122
$982$	23.5407	0.751214
$983$	54.1192	1.72613	0.863067	−	0.505090i	$-0.168541\pi$
$983$	54.1192	1.72613	0.863067	+	0.505090i	$0.168541\pi$
$984$	−7.58793	−0.241894
$985$	−25.9663	−0.827357
$986$	−40.7900	−1.29902
$987$	−69.8860	−2.22449
$988$	7.29415	0.232058
$989$	−2.13776	−0.0679769
$990$	−6.78235	−0.215557
$991$	−58.4577	−1.85697	−0.928485	−	0.371370i	$-0.878888\pi$
$991$	−58.4577	−1.85697	−0.928485	+	0.371370i	$0.878888\pi$
$992$	3.84417	0.122052
$993$	−27.4904	−0.872380
$994$	−6.74385	−0.213902
$995$	−68.2861	−2.16481
$996$	−0.493480	−0.0156365
$997$	−6.99559	−0.221553	−0.110776	−	0.993845i	$-0.535334\pi$
$997$	−6.99559	−0.221553	−0.110776	+	0.993845i	$0.535334\pi$
$998$	−21.6552	−0.685483
$999$	−28.1658	−0.891125

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.m.1.13	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.m.1.13	✓	41	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.27958 q^{3} +1.00000 q^{4} +2.95127 q^{5} -1.27958 q^{6} +4.74723 q^{7} +1.00000 q^{8} -1.36266 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.27958 q^{3} +1.00000 q^{4} +2.95127 q^{5} -1.27958 q^{6} +4.74723 q^{7} +1.00000 q^{8} -1.36266 q^{9} +2.95127 q^{10} +1.68649 q^{11} -1.27958 q^{12} -1.31820 q^{13} +4.74723 q^{14} -3.77640 q^{15} +1.00000 q^{16} +6.64597 q^{17} -1.36266 q^{18} -5.53342 q^{19} +2.95127 q^{20} -6.07449 q^{21} +1.68649 q^{22} +1.00000 q^{23} -1.27958 q^{24} +3.70999 q^{25} -1.31820 q^{26} +5.58240 q^{27} +4.74723 q^{28} -6.13755 q^{29} -3.77640 q^{30} +3.84417 q^{31} +1.00000 q^{32} -2.15800 q^{33} +6.64597 q^{34} +14.0104 q^{35} -1.36266 q^{36} -5.04546 q^{37} -5.53342 q^{38} +1.68675 q^{39} +2.95127 q^{40} +5.93000 q^{41} -6.07449 q^{42} -2.13776 q^{43} +1.68649 q^{44} -4.02159 q^{45} +1.00000 q^{46} +11.5048 q^{47} -1.27958 q^{48} +15.5362 q^{49} +3.70999 q^{50} -8.50408 q^{51} -1.31820 q^{52} -7.33707 q^{53} +5.58240 q^{54} +4.97727 q^{55} +4.74723 q^{56} +7.08047 q^{57} -6.13755 q^{58} +5.45885 q^{59} -3.77640 q^{60} +2.10475 q^{61} +3.84417 q^{62} -6.46888 q^{63} +1.00000 q^{64} -3.89036 q^{65} -2.15800 q^{66} +3.02281 q^{67} +6.64597 q^{68} -1.27958 q^{69} +14.0104 q^{70} -1.42059 q^{71} -1.36266 q^{72} +3.67386 q^{73} -5.04546 q^{74} -4.74725 q^{75} -5.53342 q^{76} +8.00614 q^{77} +1.68675 q^{78} -10.0013 q^{79} +2.95127 q^{80} -3.05515 q^{81} +5.93000 q^{82} +0.385656 q^{83} -6.07449 q^{84} +19.6140 q^{85} -2.13776 q^{86} +7.85351 q^{87} +1.68649 q^{88} +3.50549 q^{89} -4.02159 q^{90} -6.25780 q^{91} +1.00000 q^{92} -4.91893 q^{93} +11.5048 q^{94} -16.3306 q^{95} -1.27958 q^{96} +15.5694 q^{97} +15.5362 q^{98} -2.29811 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * q^99

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