LMFDB - Embedded newform 6026.2.a.i.1.24

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:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.24
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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.63411 q^{3} +1.00000 q^{4} -1.57235 q^{5} -2.63411 q^{6} -2.35190 q^{7} -1.00000 q^{8} +3.93852 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.63411 q^{3} +1.00000 q^{4} -1.57235 q^{5} -2.63411 q^{6} -2.35190 q^{7} -1.00000 q^{8} +3.93852 q^{9} +1.57235 q^{10} +2.96575 q^{11} +2.63411 q^{12} +2.20486 q^{13} +2.35190 q^{14} -4.14174 q^{15} +1.00000 q^{16} -0.149501 q^{17} -3.93852 q^{18} -4.54283 q^{19} -1.57235 q^{20} -6.19515 q^{21} -2.96575 q^{22} +1.00000 q^{23} -2.63411 q^{24} -2.52771 q^{25} -2.20486 q^{26} +2.47215 q^{27} -2.35190 q^{28} -2.19750 q^{29} +4.14174 q^{30} +4.09974 q^{31} -1.00000 q^{32} +7.81209 q^{33} +0.149501 q^{34} +3.69801 q^{35} +3.93852 q^{36} -10.6850 q^{37} +4.54283 q^{38} +5.80785 q^{39} +1.57235 q^{40} -9.66406 q^{41} +6.19515 q^{42} +7.19034 q^{43} +2.96575 q^{44} -6.19273 q^{45} -1.00000 q^{46} -10.4074 q^{47} +2.63411 q^{48} -1.46858 q^{49} +2.52771 q^{50} -0.393801 q^{51} +2.20486 q^{52} +4.11242 q^{53} -2.47215 q^{54} -4.66319 q^{55} +2.35190 q^{56} -11.9663 q^{57} +2.19750 q^{58} -1.51452 q^{59} -4.14174 q^{60} +8.49493 q^{61} -4.09974 q^{62} -9.26298 q^{63} +1.00000 q^{64} -3.46682 q^{65} -7.81209 q^{66} -3.65583 q^{67} -0.149501 q^{68} +2.63411 q^{69} -3.69801 q^{70} +10.0327 q^{71} -3.93852 q^{72} -9.06369 q^{73} +10.6850 q^{74} -6.65827 q^{75} -4.54283 q^{76} -6.97513 q^{77} -5.80785 q^{78} +3.04296 q^{79} -1.57235 q^{80} -5.30364 q^{81} +9.66406 q^{82} -4.50375 q^{83} -6.19515 q^{84} +0.235068 q^{85} -7.19034 q^{86} -5.78846 q^{87} -2.96575 q^{88} -7.58616 q^{89} +6.19273 q^{90} -5.18561 q^{91} +1.00000 q^{92} +10.7991 q^{93} +10.4074 q^{94} +7.14293 q^{95} -2.63411 q^{96} -6.63484 q^{97} +1.46858 q^{98} +11.6806 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) $ 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * 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
$3$	2.63411	1.52080	0.760401	−	0.649454i	$-0.225002\pi$
$3$	2.63411	1.52080	0.760401	+	0.649454i	$0.225002\pi$
$4$	1.00000	0.500000
$5$	−1.57235	−0.703177	−0.351588	−	0.936155i	$-0.614358\pi$
$5$	−1.57235	−0.703177	−0.351588	+	0.936155i	$0.614358\pi$
$6$	−2.63411	−1.07537
$7$	−2.35190	−0.888934	−0.444467	−	0.895795i	$-0.646607\pi$
$7$	−2.35190	−0.888934	−0.444467	+	0.895795i	$0.646607\pi$
$8$	−1.00000	−0.353553
$9$	3.93852	1.31284
$10$	1.57235	0.497221
$11$	2.96575	0.894206	0.447103	−	0.894482i	$-0.352456\pi$
$11$	2.96575	0.894206	0.447103	+	0.894482i	$0.352456\pi$
$12$	2.63411	0.760401
$13$	2.20486	0.611519	0.305760	−	0.952109i	$-0.401090\pi$
$13$	2.20486	0.611519	0.305760	+	0.952109i	$0.401090\pi$
$14$	2.35190	0.628571
$15$	−4.14174	−1.06939
$16$	1.00000	0.250000
$17$	−0.149501	−0.0362593	−0.0181297	−	0.999836i	$-0.505771\pi$
$17$	−0.149501	−0.0362593	−0.0181297	+	0.999836i	$0.505771\pi$
$18$	−3.93852	−0.928317
$19$	−4.54283	−1.04220	−0.521099	−	0.853496i	$-0.674478\pi$
$19$	−4.54283	−1.04220	−0.521099	+	0.853496i	$0.674478\pi$
$20$	−1.57235	−0.351588
$21$	−6.19515	−1.35189
$22$	−2.96575	−0.632299
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.63411	−0.537685
$25$	−2.52771	−0.505543
$26$	−2.20486	−0.432409
$27$	2.47215	0.475765
$28$	−2.35190	−0.444467
$29$	−2.19750	−0.408066	−0.204033	−	0.978964i	$-0.565405\pi$
$29$	−2.19750	−0.408066	−0.204033	+	0.978964i	$0.565405\pi$
$30$	4.14174	0.756175
$31$	4.09974	0.736335	0.368167	−	0.929760i	$-0.379985\pi$
$31$	4.09974	0.736335	0.368167	+	0.929760i	$0.379985\pi$
$32$	−1.00000	−0.176777
$33$	7.81209	1.35991
$34$	0.149501	0.0256392
$35$	3.69801	0.625077
$36$	3.93852	0.656419
$37$	−10.6850	−1.75660	−0.878302	−	0.478105i	$-0.841324\pi$
$37$	−10.6850	−1.75660	−0.878302	+	0.478105i	$0.841324\pi$
$38$	4.54283	0.736945
$39$	5.80785	0.930000
$40$	1.57235	0.248610
$41$	−9.66406	−1.50927	−0.754637	−	0.656143i	$-0.772187\pi$
$41$	−9.66406	−1.50927	−0.754637	+	0.656143i	$0.772187\pi$
$42$	6.19515	0.955932
$43$	7.19034	1.09652	0.548258	−	0.836309i	$-0.315291\pi$
$43$	7.19034	1.09652	0.548258	+	0.836309i	$0.315291\pi$
$44$	2.96575	0.447103
$45$	−6.19273	−0.923157
$46$	−1.00000	−0.147442
$47$	−10.4074	−1.51807	−0.759037	−	0.651048i	$-0.774330\pi$
$47$	−10.4074	−1.51807	−0.759037	+	0.651048i	$0.774330\pi$
$48$	2.63411	0.380200
$49$	−1.46858	−0.209797
$50$	2.52771	0.357473
$51$	−0.393801	−0.0551432
$52$	2.20486	0.305760
$53$	4.11242	0.564885	0.282442	−	0.959284i	$-0.408855\pi$
$53$	4.11242	0.564885	0.282442	+	0.959284i	$0.408855\pi$
$54$	−2.47215	−0.336417
$55$	−4.66319	−0.628785
$56$	2.35190	0.314285
$57$	−11.9663	−1.58498
$58$	2.19750	0.288546
$59$	−1.51452	−0.197173	−0.0985867	−	0.995128i	$-0.531432\pi$
$59$	−1.51452	−0.197173	−0.0985867	+	0.995128i	$0.531432\pi$
$60$	−4.14174	−0.534696
$61$	8.49493	1.08766	0.543832	−	0.839194i	$-0.316973\pi$
$61$	8.49493	1.08766	0.543832	+	0.839194i	$0.316973\pi$
$62$	−4.09974	−0.520667
$63$	−9.26298	−1.16703
$64$	1.00000	0.125000
$65$	−3.46682	−0.430006
$66$	−7.81209	−0.961602
$67$	−3.65583	−0.446631	−0.223315	−	0.974746i	$-0.571688\pi$
$67$	−3.65583	−0.446631	−0.223315	+	0.974746i	$0.571688\pi$
$68$	−0.149501	−0.0181297
$69$	2.63411	0.317109
$70$	−3.69801	−0.441996
$71$	10.0327	1.19066	0.595329	−	0.803482i	$-0.297022\pi$
$71$	10.0327	1.19066	0.595329	+	0.803482i	$0.297022\pi$
$72$	−3.93852	−0.464158
$73$	−9.06369	−1.06082	−0.530412	−	0.847740i	$-0.677963\pi$
$73$	−9.06369	−1.06082	−0.530412	+	0.847740i	$0.677963\pi$
$74$	10.6850	1.24211
$75$	−6.65827	−0.768830
$76$	−4.54283	−0.521099
$77$	−6.97513	−0.794890
$78$	−5.80785	−0.657609
$79$	3.04296	0.342360	0.171180	−	0.985240i	$-0.445242\pi$
$79$	3.04296	0.342360	0.171180	+	0.985240i	$0.445242\pi$
$80$	−1.57235	−0.175794
$81$	−5.30364	−0.589294
$82$	9.66406	1.06722
$83$	−4.50375	−0.494351	−0.247175	−	0.968971i	$-0.579502\pi$
$83$	−4.50375	−0.494351	−0.247175	+	0.968971i	$0.579502\pi$
$84$	−6.19515	−0.675946
$85$	0.235068	0.0254967
$86$	−7.19034	−0.775354
$87$	−5.78846	−0.620588
$88$	−2.96575	−0.316150
$89$	−7.58616	−0.804131	−0.402066	−	0.915611i	$-0.631708\pi$
$89$	−7.58616	−0.804131	−0.402066	+	0.915611i	$0.631708\pi$
$90$	6.19273	0.652771
$91$	−5.18561	−0.543600
$92$	1.00000	0.104257
$93$	10.7991	1.11982
$94$	10.4074	1.07344
$95$	7.14293	0.732849
$96$	−2.63411	−0.268842
$97$	−6.63484	−0.673666	−0.336833	−	0.941564i	$-0.609356\pi$
$97$	−6.63484	−0.673666	−0.336833	+	0.941564i	$0.609356\pi$
$98$	1.46858	0.148349
$99$	11.6806	1.17395
$100$	−2.52771	−0.252771
$101$	−16.6115	−1.65291	−0.826454	−	0.563005i	$-0.809645\pi$
$101$	−16.6115	−1.65291	−0.826454	+	0.563005i	$0.809645\pi$
$102$	0.393801	0.0389921
$103$	11.6110	1.14407	0.572035	−	0.820229i	$-0.306154\pi$
$103$	11.6110	1.14407	0.572035	+	0.820229i	$0.306154\pi$
$104$	−2.20486	−0.216205
$105$	9.74094	0.950619
$106$	−4.11242	−0.399434
$107$	9.94017	0.960953	0.480476	−	0.877008i	$-0.340464\pi$
$107$	9.94017	0.960953	0.480476	+	0.877008i	$0.340464\pi$
$108$	2.47215	0.237883
$109$	−1.67937	−0.160854	−0.0804272	−	0.996760i	$-0.525628\pi$
$109$	−1.67937	−0.160854	−0.0804272	+	0.996760i	$0.525628\pi$
$110$	4.66319	0.444618
$111$	−28.1455	−2.67145
$112$	−2.35190	−0.222233
$113$	−2.91261	−0.273995	−0.136998	−	0.990571i	$-0.543745\pi$
$113$	−2.91261	−0.273995	−0.136998	+	0.990571i	$0.543745\pi$
$114$	11.9663	1.12075
$115$	−1.57235	−0.146622
$116$	−2.19750	−0.204033
$117$	8.68389	0.802826
$118$	1.51452	0.139423
$119$	0.351611	0.0322321
$120$	4.14174	0.378087
$121$	−2.20435	−0.200395
$122$	−8.49493	−0.769095
$123$	−25.4562	−2.29531
$124$	4.09974	0.368167
$125$	11.8362	1.05866
$126$	9.26298	0.825212
$127$	17.3960	1.54364	0.771821	−	0.635840i	$-0.219346\pi$
$127$	17.3960	1.54364	0.771821	+	0.635840i	$0.219346\pi$
$128$	−1.00000	−0.0883883
$129$	18.9401	1.66758
$130$	3.46682	0.304060
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	7.81209	0.679955
$133$	10.6843	0.926444
$134$	3.65583	0.315816
$135$	−3.88708	−0.334547
$136$	0.149501	0.0128196
$137$	16.8583	1.44030	0.720150	−	0.693819i	$-0.244073\pi$
$137$	16.8583	1.44030	0.720150	+	0.693819i	$0.244073\pi$
$138$	−2.63411	−0.224230
$139$	0.235857	0.0200051	0.0100026	−	0.999950i	$-0.496816\pi$
$139$	0.235857	0.0200051	0.0100026	+	0.999950i	$0.496816\pi$
$140$	3.69801	0.312539
$141$	−27.4142	−2.30869
$142$	−10.0327	−0.841922
$143$	6.53907	0.546824
$144$	3.93852	0.328210
$145$	3.45525	0.286943
$146$	9.06369	0.750116
$147$	−3.86840	−0.319060
$148$	−10.6850	−0.878302
$149$	9.97660	0.817315	0.408658	−	0.912688i	$-0.365997\pi$
$149$	9.97660	0.817315	0.408658	+	0.912688i	$0.365997\pi$
$150$	6.65827	0.543645
$151$	−11.7483	−0.956060	−0.478030	−	0.878344i	$-0.658649\pi$
$151$	−11.7483	−0.956060	−0.478030	+	0.878344i	$0.658649\pi$
$152$	4.54283	0.368473
$153$	−0.588812	−0.0476026
$154$	6.97513	0.562072
$155$	−6.44623	−0.517773
$156$	5.80785	0.465000
$157$	−6.33027	−0.505210	−0.252605	−	0.967569i	$-0.581287\pi$
$157$	−6.33027	−0.505210	−0.252605	+	0.967569i	$0.581287\pi$
$158$	−3.04296	−0.242085
$159$	10.8326	0.859078
$160$	1.57235	0.124305
$161$	−2.35190	−0.185355
$162$	5.30364	0.416694
$163$	0.935374	0.0732642	0.0366321	−	0.999329i	$-0.488337\pi$
$163$	0.935374	0.0732642	0.0366321	+	0.999329i	$0.488337\pi$
$164$	−9.66406	−0.754637
$165$	−12.2833	−0.956257
$166$	4.50375	0.349559
$167$	0.280520	0.0217073	0.0108537	−	0.999941i	$-0.496545\pi$
$167$	0.280520	0.0217073	0.0108537	+	0.999941i	$0.496545\pi$
$168$	6.19515	0.477966
$169$	−8.13857	−0.626044
$170$	−0.235068	−0.0180289
$171$	−17.8920	−1.36824
$172$	7.19034	0.548258
$173$	13.1834	1.00231	0.501157	−	0.865356i	$-0.332908\pi$
$173$	13.1834	1.00231	0.501157	+	0.865356i	$0.332908\pi$
$174$	5.78846	0.438822
$175$	5.94492	0.449394
$176$	2.96575	0.223552
$177$	−3.98940	−0.299862
$178$	7.58616	0.568607
$179$	−6.23529	−0.466047	−0.233024	−	0.972471i	$-0.574862\pi$
$179$	−6.23529	−0.466047	−0.233024	+	0.972471i	$0.574862\pi$
$180$	−6.19273	−0.461579
$181$	4.70289	0.349563	0.174782	−	0.984607i	$-0.444078\pi$
$181$	4.70289	0.349563	0.174782	+	0.984607i	$0.444078\pi$
$182$	5.18561	0.384383
$183$	22.3766	1.65412
$184$	−1.00000	−0.0737210
$185$	16.8006	1.23520
$186$	−10.7991	−0.791832
$187$	−0.443382	−0.0324233
$188$	−10.4074	−0.759037
$189$	−5.81424	−0.422924
$190$	−7.14293	−0.518203
$191$	−1.09719	−0.0793897	−0.0396948	−	0.999212i	$-0.512639\pi$
$191$	−1.09719	−0.0793897	−0.0396948	+	0.999212i	$0.512639\pi$
$192$	2.63411	0.190100
$193$	−22.1824	−1.59672	−0.798362	−	0.602178i	$-0.794300\pi$
$193$	−22.1824	−1.59672	−0.798362	+	0.602178i	$0.794300\pi$
$194$	6.63484	0.476354
$195$	−9.13197	−0.653954
$196$	−1.46858	−0.104899
$197$	−18.2553	−1.30064	−0.650319	−	0.759661i	$-0.725365\pi$
$197$	−18.2553	−1.30064	−0.650319	+	0.759661i	$0.725365\pi$
$198$	−11.6806	−0.830107
$199$	−24.0493	−1.70481	−0.852405	−	0.522881i	$-0.824857\pi$
$199$	−24.0493	−1.70481	−0.852405	+	0.522881i	$0.824857\pi$
$200$	2.52771	0.178736
$201$	−9.62985	−0.679237
$202$	16.6115	1.16878
$203$	5.16830	0.362744
$204$	−0.393801	−0.0275716
$205$	15.1953	1.06129
$206$	−11.6110	−0.808980
$207$	3.93852	0.273746
$208$	2.20486	0.152880
$209$	−13.4729	−0.931940
$210$	−9.74094	−0.672189
$211$	−6.30002	−0.433711	−0.216856	−	0.976204i	$-0.569580\pi$
$211$	−6.30002	−0.433711	−0.216856	+	0.976204i	$0.569580\pi$
$212$	4.11242	0.282442
$213$	26.4271	1.81075
$214$	−9.94017	−0.679496
$215$	−11.3057	−0.771044
$216$	−2.47215	−0.168208
$217$	−9.64216	−0.654553
$218$	1.67937	0.113741
$219$	−23.8747	−1.61330
$220$	−4.66319	−0.314392
$221$	−0.329629	−0.0221733
$222$	28.1455	1.88900
$223$	−0.212280	−0.0142153	−0.00710766	−	0.999975i	$-0.502262\pi$
$223$	−0.212280	−0.0142153	−0.00710766	+	0.999975i	$0.502262\pi$
$224$	2.35190	0.157143
$225$	−9.95544	−0.663696
$226$	2.91261	0.193744
$227$	−26.8775	−1.78392	−0.891962	−	0.452111i	$-0.850671\pi$
$227$	−26.8775	−1.78392	−0.891962	+	0.452111i	$0.850671\pi$
$228$	−11.9663	−0.792488
$229$	−2.34586	−0.155019	−0.0775096	−	0.996992i	$-0.524697\pi$
$229$	−2.34586	−0.155019	−0.0775096	+	0.996992i	$0.524697\pi$
$230$	1.57235	0.103678
$231$	−18.3732	−1.20887
$232$	2.19750	0.144273
$233$	−20.0817	−1.31559	−0.657797	−	0.753196i	$-0.728511\pi$
$233$	−20.0817	−1.31559	−0.657797	+	0.753196i	$0.728511\pi$
$234$	−8.68389	−0.567684
$235$	16.3641	1.06747
$236$	−1.51452	−0.0985867
$237$	8.01548	0.520661
$238$	−0.351611	−0.0227915
$239$	−23.3768	−1.51212	−0.756061	−	0.654502i	$-0.772878\pi$
$239$	−23.3768	−1.51212	−0.756061	+	0.654502i	$0.772878\pi$
$240$	−4.14174	−0.267348
$241$	8.43854	0.543574	0.271787	−	0.962357i	$-0.412385\pi$
$241$	8.43854	0.543574	0.271787	+	0.962357i	$0.412385\pi$
$242$	2.20435	0.141701
$243$	−21.3868	−1.37196
$244$	8.49493	0.543832
$245$	2.30912	0.147524
$246$	25.4562	1.62303
$247$	−10.0163	−0.637324
$248$	−4.09974	−0.260334
$249$	−11.8634	−0.751810
$250$	−11.8362	−0.748587
$251$	13.1897	0.832524	0.416262	−	0.909245i	$-0.363340\pi$
$251$	13.1897	0.832524	0.416262	+	0.909245i	$0.363340\pi$
$252$	−9.26298	−0.583513
$253$	2.96575	0.186455
$254$	−17.3960	−1.09152
$255$	0.619194	0.0387754
$256$	1.00000	0.0625000
$257$	−5.02724	−0.313590	−0.156795	−	0.987631i	$-0.550116\pi$
$257$	−5.02724	−0.313590	−0.156795	+	0.987631i	$0.550116\pi$
$258$	−18.9401	−1.17916
$259$	25.1300	1.56150
$260$	−3.46682	−0.215003
$261$	−8.65490	−0.535725
$262$	−1.00000	−0.0617802
$263$	−28.9737	−1.78660	−0.893298	−	0.449464i	$-0.851615\pi$
$263$	−28.9737	−1.78660	−0.893298	+	0.449464i	$0.851615\pi$
$264$	−7.81209	−0.480801
$265$	−6.46617	−0.397214
$266$	−10.6843	−0.655095
$267$	−19.9828	−1.22292
$268$	−3.65583	−0.223315
$269$	−0.941078	−0.0573786	−0.0286893	−	0.999588i	$-0.509133\pi$
$269$	−0.941078	−0.0573786	−0.0286893	+	0.999588i	$0.509133\pi$
$270$	3.88708	0.236560
$271$	−13.4954	−0.819787	−0.409894	−	0.912133i	$-0.634434\pi$
$271$	−13.4954	−0.819787	−0.409894	+	0.912133i	$0.634434\pi$
$272$	−0.149501	−0.00906483
$273$	−13.6595	−0.826708
$274$	−16.8583	−1.01845
$275$	−7.49656	−0.452059
$276$	2.63411	0.158555
$277$	−2.88384	−0.173273	−0.0866367	−	0.996240i	$-0.527612\pi$
$277$	−2.88384	−0.173273	−0.0866367	+	0.996240i	$0.527612\pi$
$278$	−0.235857	−0.0141458
$279$	16.1469	0.966688
$280$	−3.69801	−0.220998
$281$	−5.98104	−0.356799	−0.178400	−	0.983958i	$-0.557092\pi$
$281$	−5.98104	−0.356799	−0.178400	+	0.983958i	$0.557092\pi$
$282$	27.4142	1.63249
$283$	−9.36485	−0.556682	−0.278341	−	0.960482i	$-0.589785\pi$
$283$	−9.36485	−0.556682	−0.278341	+	0.960482i	$0.589785\pi$
$284$	10.0327	0.595329
$285$	18.8152	1.11452
$286$	−6.53907	−0.386663
$287$	22.7289	1.34164
$288$	−3.93852	−0.232079
$289$	−16.9776	−0.998685
$290$	−3.45525	−0.202899
$291$	−17.4769	−1.02451
$292$	−9.06369	−0.530412
$293$	14.2167	0.830547	0.415273	−	0.909697i	$-0.363686\pi$
$293$	14.2167	0.830547	0.415273	+	0.909697i	$0.363686\pi$
$294$	3.86840	0.225609
$295$	2.38135	0.138648
$296$	10.6850	0.621054
$297$	7.33177	0.425432
$298$	−9.97660	−0.577929
$299$	2.20486	0.127511
$300$	−6.65827	−0.384415
$301$	−16.9109	−0.974730
$302$	11.7483	0.676036
$303$	−43.7565	−2.51374
$304$	−4.54283	−0.260549
$305$	−13.3570	−0.764820
$306$	0.588812	0.0336601
$307$	−31.5468	−1.80047	−0.900235	−	0.435404i	$-0.856606\pi$
$307$	−31.5468	−1.80047	−0.900235	+	0.435404i	$0.856606\pi$
$308$	−6.97513	−0.397445
$309$	30.5847	1.73990
$310$	6.44623	0.366121
$311$	2.59699	0.147262	0.0736309	−	0.997286i	$-0.476541\pi$
$311$	2.59699	0.147262	0.0736309	+	0.997286i	$0.476541\pi$
$312$	−5.80785	−0.328805
$313$	−14.3185	−0.809329	−0.404665	−	0.914465i	$-0.632612\pi$
$313$	−14.3185	−0.809329	−0.404665	+	0.914465i	$0.632612\pi$
$314$	6.33027	0.357238
$315$	14.5647	0.820625
$316$	3.04296	0.171180
$317$	1.77671	0.0997898	0.0498949	−	0.998754i	$-0.484111\pi$
$317$	1.77671	0.0997898	0.0498949	+	0.998754i	$0.484111\pi$
$318$	−10.8326	−0.607460
$319$	−6.51724	−0.364895
$320$	−1.57235	−0.0878971
$321$	26.1835	1.46142
$322$	2.35190	0.131066
$323$	0.679158	0.0377894
$324$	−5.30364	−0.294647
$325$	−5.57326	−0.309149
$326$	−0.935374	−0.0518056
$327$	−4.42363	−0.244628
$328$	9.66406	0.533609
$329$	24.4771	1.34947
$330$	12.2833	0.676176
$331$	−1.68271	−0.0924903	−0.0462452	−	0.998930i	$-0.514726\pi$
$331$	−1.68271	−0.0924903	−0.0462452	+	0.998930i	$0.514726\pi$
$332$	−4.50375	−0.247175
$333$	−42.0831	−2.30614
$334$	−0.280520	−0.0153494
$335$	5.74825	0.314060
$336$	−6.19515	−0.337973
$337$	−19.5940	−1.06735	−0.533675	−	0.845689i	$-0.679190\pi$
$337$	−19.5940	−1.06735	−0.533675	+	0.845689i	$0.679190\pi$
$338$	8.13857	0.442680
$339$	−7.67212	−0.416693
$340$	0.235068	0.0127483
$341$	12.1588	0.658435
$342$	17.8920	0.967490
$343$	19.9172	1.07543
$344$	−7.19034	−0.387677
$345$	−4.14174	−0.222984
$346$	−13.1834	−0.708743
$347$	17.8468	0.958066	0.479033	−	0.877797i	$-0.340987\pi$
$347$	17.8468	0.958066	0.479033	+	0.877797i	$0.340987\pi$
$348$	−5.78846	−0.310294
$349$	−13.3620	−0.715250	−0.357625	−	0.933865i	$-0.616413\pi$
$349$	−13.3620	−0.715250	−0.357625	+	0.933865i	$0.616413\pi$
$350$	−5.94492	−0.317769
$351$	5.45075	0.290940
$352$	−2.96575	−0.158075
$353$	33.8031	1.79916	0.899579	−	0.436759i	$-0.143874\pi$
$353$	33.8031	1.79916	0.899579	+	0.436759i	$0.143874\pi$
$354$	3.98940	0.212034
$355$	−15.7749	−0.837242
$356$	−7.58616	−0.402066
$357$	0.926180	0.0490187
$358$	6.23529	0.329545
$359$	14.8902	0.785872	0.392936	−	0.919566i	$-0.371459\pi$
$359$	14.8902	0.785872	0.392936	+	0.919566i	$0.371459\pi$
$360$	6.19273	0.326385
$361$	1.63735	0.0861761
$362$	−4.70289	−0.247179
$363$	−5.80649	−0.304761
$364$	−5.18561	−0.271800
$365$	14.2513	0.745947
$366$	−22.3766	−1.16964
$367$	13.3471	0.696714	0.348357	−	0.937362i	$-0.386740\pi$
$367$	13.3471	0.696714	0.348357	+	0.937362i	$0.386740\pi$
$368$	1.00000	0.0521286
$369$	−38.0621	−1.98143
$370$	−16.8006	−0.873421
$371$	−9.67200	−0.502145
$372$	10.7991	0.559910
$373$	−17.8284	−0.923117	−0.461559	−	0.887110i	$-0.652710\pi$
$373$	−17.8284	−0.923117	−0.461559	+	0.887110i	$0.652710\pi$
$374$	0.443382	0.0229267
$375$	31.1778	1.61002
$376$	10.4074	0.536720
$377$	−4.84520	−0.249540
$378$	5.81424	0.299052
$379$	−21.3936	−1.09892	−0.549459	−	0.835521i	$-0.685166\pi$
$379$	−21.3936	−1.09892	−0.549459	+	0.835521i	$0.685166\pi$
$380$	7.14293	0.366425
$381$	45.8228	2.34757
$382$	1.09719	0.0561370
$383$	30.9434	1.58113	0.790566	−	0.612377i	$-0.209786\pi$
$383$	30.9434	1.58113	0.790566	+	0.612377i	$0.209786\pi$
$384$	−2.63411	−0.134421
$385$	10.9674	0.558948
$386$	22.1824	1.12905
$387$	28.3192	1.43955
$388$	−6.63484	−0.336833
$389$	4.42794	0.224505	0.112253	−	0.993680i	$-0.464193\pi$
$389$	4.42794	0.224505	0.112253	+	0.993680i	$0.464193\pi$
$390$	9.13197	0.462415
$391$	−0.149501	−0.00756059
$392$	1.46858	0.0741745
$393$	2.63411	0.132873
$394$	18.2553	0.919690
$395$	−4.78460	−0.240739
$396$	11.6806	0.586974
$397$	27.1286	1.36154	0.680772	−	0.732495i	$-0.261644\pi$
$397$	27.1286	1.36154	0.680772	+	0.732495i	$0.261644\pi$
$398$	24.0493	1.20548
$399$	28.1435	1.40894
$400$	−2.52771	−0.126386
$401$	−23.7341	−1.18523	−0.592613	−	0.805488i	$-0.701903\pi$
$401$	−23.7341	−1.18523	−0.592613	+	0.805488i	$0.701903\pi$
$402$	9.62985	0.480293
$403$	9.03937	0.450283
$404$	−16.6115	−0.826454
$405$	8.33919	0.414378
$406$	−5.16830	−0.256498
$407$	−31.6890	−1.57077
$408$	0.393801	0.0194961
$409$	36.7304	1.81620	0.908101	−	0.418752i	$-0.137532\pi$
$409$	36.7304	1.81620	0.908101	+	0.418752i	$0.137532\pi$
$410$	−15.1953	−0.750442
$411$	44.4065	2.19041
$412$	11.6110	0.572035
$413$	3.56199	0.175274
$414$	−3.93852	−0.193567
$415$	7.08148	0.347616
$416$	−2.20486	−0.108102
$417$	0.621272	0.0304238
$418$	13.4729	0.658981
$419$	27.8594	1.36102	0.680511	−	0.732738i	$-0.261758\pi$
$419$	27.8594	1.36102	0.680511	+	0.732738i	$0.261758\pi$
$420$	9.74094	0.475309
$421$	−30.3618	−1.47974	−0.739871	−	0.672749i	$-0.765113\pi$
$421$	−30.3618	−1.47974	−0.739871	+	0.672749i	$0.765113\pi$
$422$	6.30002	0.306680
$423$	−40.9897	−1.99299
$424$	−4.11242	−0.199717
$425$	0.377896	0.0183306
$426$	−26.4271	−1.28040
$427$	−19.9792	−0.966862
$428$	9.94017	0.480476
$429$	17.2246	0.831612
$430$	11.3057	0.545211
$431$	26.9197	1.29668	0.648338	−	0.761353i	$-0.275464\pi$
$431$	26.9197	1.29668	0.648338	+	0.761353i	$0.275464\pi$
$432$	2.47215	0.118941
$433$	13.5197	0.649715	0.324858	−	0.945763i	$-0.394684\pi$
$433$	13.5197	0.649715	0.324858	+	0.945763i	$0.394684\pi$
$434$	9.64216	0.462839
$435$	9.10148	0.436383
$436$	−1.67937	−0.0804272
$437$	−4.54283	−0.217313
$438$	23.8747	1.14078
$439$	3.59830	0.171737	0.0858687	−	0.996306i	$-0.472633\pi$
$439$	3.59830	0.171737	0.0858687	+	0.996306i	$0.472633\pi$
$440$	4.66319	0.222309
$441$	−5.78403	−0.275430
$442$	0.329629	0.0156789
$443$	−7.58679	−0.360459	−0.180230	−	0.983625i	$-0.557684\pi$
$443$	−7.58679	−0.360459	−0.180230	+	0.983625i	$0.557684\pi$
$444$	−28.1455	−1.33572
$445$	11.9281	0.565446
$446$	0.212280	0.0100518
$447$	26.2794	1.24297
$448$	−2.35190	−0.111117
$449$	11.6351	0.549093	0.274546	−	0.961574i	$-0.411472\pi$
$449$	11.6351	0.549093	0.274546	+	0.961574i	$0.411472\pi$
$450$	9.95544	0.469304
$451$	−28.6612	−1.34960
$452$	−2.91261	−0.136998
$453$	−30.9462	−1.45398
$454$	26.8775	1.26142
$455$	8.15360	0.382247
$456$	11.9663	0.560374
$457$	−13.7403	−0.642744	−0.321372	−	0.946953i	$-0.604144\pi$
$457$	−13.7403	−0.642744	−0.321372	+	0.946953i	$0.604144\pi$
$458$	2.34586	0.109615
$459$	−0.369588	−0.0172509
$460$	−1.57235	−0.0733112
$461$	24.0000	1.11779	0.558897	−	0.829237i	$-0.311225\pi$
$461$	24.0000	1.11779	0.558897	+	0.829237i	$0.311225\pi$
$462$	18.3732	0.854800
$463$	8.72419	0.405448	0.202724	−	0.979236i	$-0.435021\pi$
$463$	8.72419	0.405448	0.202724	+	0.979236i	$0.435021\pi$
$464$	−2.19750	−0.102017
$465$	−16.9800	−0.787431
$466$	20.0817	0.930265
$467$	15.8999	0.735761	0.367881	−	0.929873i	$-0.380084\pi$
$467$	15.8999	0.735761	0.367881	+	0.929873i	$0.380084\pi$
$468$	8.68389	0.401413
$469$	8.59814	0.397025
$470$	−16.3641	−0.754818
$471$	−16.6746	−0.768325
$472$	1.51452	0.0697114
$473$	21.3247	0.980511
$474$	−8.01548	−0.368163
$475$	11.4830	0.526875
$476$	0.351611	0.0161161
$477$	16.1968	0.741602
$478$	23.3768	1.06923
$479$	−10.1866	−0.465440	−0.232720	−	0.972544i	$-0.574762\pi$
$479$	−10.1866	−0.465440	−0.232720	+	0.972544i	$0.574762\pi$
$480$	4.14174	0.189044
$481$	−23.5590	−1.07420
$482$	−8.43854	−0.384365
$483$	−6.19515	−0.281889
$484$	−2.20435	−0.100198
$485$	10.4323	0.473706
$486$	21.3868	0.970125
$487$	−14.7922	−0.670299	−0.335150	−	0.942165i	$-0.608787\pi$
$487$	−14.7922	−0.670299	−0.335150	+	0.942165i	$0.608787\pi$
$488$	−8.49493	−0.384548
$489$	2.46387	0.111420
$490$	−2.30912	−0.104316
$491$	−36.3943	−1.64245	−0.821225	−	0.570604i	$-0.806709\pi$
$491$	−36.3943	−1.64245	−0.821225	+	0.570604i	$0.806709\pi$
$492$	−25.4562	−1.14765
$493$	0.328529	0.0147962
$494$	10.0163	0.450656
$495$	−18.3661	−0.825493
$496$	4.09974	0.184084
$497$	−23.5958	−1.05842
$498$	11.8634	0.531610
$499$	−3.37451	−0.151064	−0.0755320	−	0.997143i	$-0.524065\pi$
$499$	−3.37451	−0.151064	−0.0755320	+	0.997143i	$0.524065\pi$
$500$	11.8362	0.529331
$501$	0.738920	0.0330125
$502$	−13.1897	−0.588684
$503$	17.6893	0.788729	0.394364	−	0.918954i	$-0.370965\pi$
$503$	17.6893	0.788729	0.394364	+	0.918954i	$0.370965\pi$
$504$	9.26298	0.412606
$505$	26.1191	1.16229
$506$	−2.96575	−0.131844
$507$	−21.4379	−0.952089
$508$	17.3960	0.771821
$509$	32.2075	1.42757	0.713785	−	0.700365i	$-0.246979\pi$
$509$	32.2075	1.42757	0.713785	+	0.700365i	$0.246979\pi$
$510$	−0.619194	−0.0274184
$511$	21.3169	0.943003
$512$	−1.00000	−0.0441942
$513$	−11.2306	−0.495841
$514$	5.02724	0.221742
$515$	−18.2566	−0.804484
$516$	18.9401	0.833792
$517$	−30.8657	−1.35747
$518$	−25.1300	−1.10415
$519$	34.7264	1.52432
$520$	3.46682	0.152030
$521$	11.8813	0.520531	0.260266	−	0.965537i	$-0.416190\pi$
$521$	11.8813	0.520531	0.260266	+	0.965537i	$0.416190\pi$
$522$	8.65490	0.378815
$523$	0.347525	0.0151962	0.00759810	−	0.999971i	$-0.497581\pi$
$523$	0.347525	0.0151962	0.00759810	+	0.999971i	$0.497581\pi$
$524$	1.00000	0.0436852
$525$	15.6596	0.683439
$526$	28.9737	1.26331
$527$	−0.612915	−0.0266990
$528$	7.81209	0.339978
$529$	1.00000	0.0434783
$530$	6.46617	0.280873
$531$	−5.96495	−0.258857
$532$	10.6843	0.463222
$533$	−21.3079	−0.922950
$534$	19.9828	0.864738
$535$	−15.6294	−0.675720
$536$	3.65583	0.157908
$537$	−16.4244	−0.708765
$538$	0.941078	0.0405728
$539$	−4.35544	−0.187602
$540$	−3.88708	−0.167273
$541$	17.7639	0.763731	0.381866	−	0.924218i	$-0.375282\pi$
$541$	17.7639	0.763731	0.381866	+	0.924218i	$0.375282\pi$
$542$	13.4954	0.579677
$543$	12.3879	0.531617
$544$	0.149501	0.00640980
$545$	2.64056	0.113109
$546$	13.6595	0.584571
$547$	32.2743	1.37995	0.689974	−	0.723834i	$-0.257622\pi$
$547$	32.2743	1.37995	0.689974	+	0.723834i	$0.257622\pi$
$548$	16.8583	0.720150
$549$	33.4574	1.42793
$550$	7.49656	0.319654
$551$	9.98289	0.425286
$552$	−2.63411	−0.112115
$553$	−7.15673	−0.304335
$554$	2.88384	0.122523
$555$	44.2545	1.87850
$556$	0.235857	0.0100026
$557$	−15.7236	−0.666232	−0.333116	−	0.942886i	$-0.608100\pi$
$557$	−15.7236	−0.666232	−0.333116	+	0.942886i	$0.608100\pi$
$558$	−16.1469	−0.683552
$559$	15.8537	0.670541
$560$	3.69801	0.156269
$561$	−1.16791	−0.0493094
$562$	5.98104	0.252295
$563$	8.05528	0.339490	0.169745	−	0.985488i	$-0.445706\pi$
$563$	8.05528	0.339490	0.169745	+	0.985488i	$0.445706\pi$
$564$	−27.4142	−1.15434
$565$	4.57964	0.192667
$566$	9.36485	0.393634
$567$	12.4736	0.523843
$568$	−10.0327	−0.420961
$569$	16.1557	0.677282	0.338641	−	0.940916i	$-0.390033\pi$
$569$	16.1557	0.677282	0.338641	+	0.940916i	$0.390033\pi$
$570$	−18.8152	−0.788083
$571$	5.00119	0.209293	0.104647	−	0.994509i	$-0.466629\pi$
$571$	5.00119	0.209293	0.104647	+	0.994509i	$0.466629\pi$
$572$	6.53907	0.273412
$573$	−2.89011	−0.120736
$574$	−22.7289	−0.948685
$575$	−2.52771	−0.105413
$576$	3.93852	0.164105
$577$	−45.7965	−1.90653	−0.953266	−	0.302132i	$-0.902302\pi$
$577$	−45.7965	−1.90653	−0.953266	+	0.302132i	$0.902302\pi$
$578$	16.9776	0.706177
$579$	−58.4308	−2.42830
$580$	3.45525	0.143471
$581$	10.5924	0.439445
$582$	17.4769	0.724440
$583$	12.1964	0.505124
$584$	9.06369	0.375058
$585$	−13.6541	−0.564528
$586$	−14.2167	−0.587285
$587$	19.7056	0.813336	0.406668	−	0.913576i	$-0.366691\pi$
$587$	19.7056	0.813336	0.406668	+	0.913576i	$0.366691\pi$
$588$	−3.86840	−0.159530
$589$	−18.6244	−0.767406
$590$	−2.38135	−0.0980388
$591$	−48.0864	−1.97801
$592$	−10.6850	−0.439151
$593$	9.62668	0.395321	0.197660	−	0.980271i	$-0.436666\pi$
$593$	9.62668	0.395321	0.197660	+	0.980271i	$0.436666\pi$
$594$	−7.33177	−0.300826
$595$	−0.552856	−0.0226649
$596$	9.97660	0.408658
$597$	−63.3485	−2.59268
$598$	−2.20486	−0.0901636
$599$	−35.6451	−1.45642	−0.728209	−	0.685355i	$-0.759647\pi$
$599$	−35.6451	−1.45642	−0.728209	+	0.685355i	$0.759647\pi$
$600$	6.65827	0.271823
$601$	−37.5404	−1.53130	−0.765652	−	0.643255i	$-0.777584\pi$
$601$	−37.5404	−1.53130	−0.765652	+	0.643255i	$0.777584\pi$
$602$	16.9109	0.689238
$603$	−14.3985	−0.586354
$604$	−11.7483	−0.478030
$605$	3.46601	0.140913
$606$	43.7565	1.77749
$607$	−32.8697	−1.33414	−0.667069	−	0.744996i	$-0.732452\pi$
$607$	−32.8697	−1.33414	−0.667069	+	0.744996i	$0.732452\pi$
$608$	4.54283	0.184236
$609$	13.6139	0.551661
$610$	13.3570	0.540810
$611$	−22.9469	−0.928331
$612$	−0.588812	−0.0238013
$613$	37.5438	1.51638	0.758191	−	0.652033i	$-0.226084\pi$
$613$	37.5438	1.51638	0.758191	+	0.652033i	$0.226084\pi$
$614$	31.5468	1.27313
$615$	40.0260	1.61401
$616$	6.97513	0.281036
$617$	11.3175	0.455626	0.227813	−	0.973705i	$-0.426842\pi$
$617$	11.3175	0.455626	0.227813	+	0.973705i	$0.426842\pi$
$618$	−30.5847	−1.23030
$619$	24.7921	0.996480	0.498240	−	0.867039i	$-0.333980\pi$
$619$	24.7921	0.996480	0.498240	+	0.867039i	$0.333980\pi$
$620$	−6.44623	−0.258887
$621$	2.47215	0.0992039
$622$	−2.59699	−0.104130
$623$	17.8419	0.714819
$624$	5.80785	0.232500
$625$	−5.97210	−0.238884
$626$	14.3185	0.572282
$627$	−35.4890	−1.41730
$628$	−6.33027	−0.252605
$629$	1.59742	0.0636933
$630$	−14.5647	−0.580270
$631$	2.04998	0.0816083	0.0408041	−	0.999167i	$-0.487008\pi$
$631$	2.04998	0.0816083	0.0408041	+	0.999167i	$0.487008\pi$
$632$	−3.04296	−0.121042
$633$	−16.5949	−0.659589
$634$	−1.77671	−0.0705621
$635$	−27.3526	−1.08545
$636$	10.8326	0.429539
$637$	−3.23802	−0.128295
$638$	6.51724	0.258020
$639$	39.5138	1.56314
$640$	1.57235	0.0621526
$641$	−9.89163	−0.390696	−0.195348	−	0.980734i	$-0.562584\pi$
$641$	−9.89163	−0.390696	−0.195348	+	0.980734i	$0.562584\pi$
$642$	−26.1835	−1.03338
$643$	4.01927	0.158504	0.0792522	−	0.996855i	$-0.474747\pi$
$643$	4.01927	0.158504	0.0792522	+	0.996855i	$0.474747\pi$
$644$	−2.35190	−0.0926777
$645$	−29.7805	−1.17261
$646$	−0.679158	−0.0267211
$647$	−6.33897	−0.249211	−0.124605	−	0.992206i	$-0.539766\pi$
$647$	−6.33897	−0.249211	−0.124605	+	0.992206i	$0.539766\pi$
$648$	5.30364	0.208347
$649$	−4.49168	−0.176314
$650$	5.57326	0.218601
$651$	−25.3985	−0.995445
$652$	0.935374	0.0366321
$653$	17.3441	0.678729	0.339364	−	0.940655i	$-0.389788\pi$
$653$	17.3441	0.678729	0.339364	+	0.940655i	$0.389788\pi$
$654$	4.42363	0.172978
$655$	−1.57235	−0.0614368
$656$	−9.66406	−0.377318
$657$	−35.6975	−1.39269
$658$	−24.4771	−0.954217
$659$	−11.8402	−0.461227	−0.230613	−	0.973045i	$-0.574073\pi$
$659$	−11.8402	−0.461227	−0.230613	+	0.973045i	$0.574073\pi$
$660$	−12.2833	−0.478129
$661$	−34.6115	−1.34623	−0.673116	−	0.739537i	$-0.735044\pi$
$661$	−34.6115	−1.34623	−0.673116	+	0.739537i	$0.735044\pi$
$662$	1.68271	0.0654005
$663$	−0.868279	−0.0337211
$664$	4.50375	0.174779
$665$	−16.7994	−0.651454
$666$	42.0831	1.63069
$667$	−2.19750	−0.0850877
$668$	0.280520	0.0108537
$669$	−0.559168	−0.0216187
$670$	−5.74825	−0.222074
$671$	25.1938	0.972597
$672$	6.19515	0.238983
$673$	28.3474	1.09271	0.546355	−	0.837553i	$-0.316015\pi$
$673$	28.3474	1.09271	0.546355	+	0.837553i	$0.316015\pi$
$674$	19.5940	0.754731
$675$	−6.24888	−0.240520
$676$	−8.13857	−0.313022
$677$	14.8028	0.568916	0.284458	−	0.958688i	$-0.408186\pi$
$677$	14.8028	0.568916	0.284458	+	0.958688i	$0.408186\pi$
$678$	7.67212	0.294646
$679$	15.6045	0.598845
$680$	−0.235068	−0.00901444
$681$	−70.7982	−2.71299
$682$	−12.1588	−0.465584
$683$	34.2560	1.31077	0.655386	−	0.755295i	$-0.272506\pi$
$683$	34.2560	1.31077	0.655386	+	0.755295i	$0.272506\pi$
$684$	−17.8920	−0.684119
$685$	−26.5071	−1.01278
$686$	−19.9172	−0.760443
$687$	−6.17926	−0.235753
$688$	7.19034	0.274129
$689$	9.06734	0.345438
$690$	4.14174	0.157673
$691$	−31.7673	−1.20849	−0.604243	−	0.796800i	$-0.706525\pi$
$691$	−31.7673	−1.20849	−0.604243	+	0.796800i	$0.706525\pi$
$692$	13.1834	0.501157
$693$	−27.4717	−1.04356
$694$	−17.8468	−0.677455
$695$	−0.370850	−0.0140671
$696$	5.78846	0.219411
$697$	1.44479	0.0547252
$698$	13.3620	0.505758
$699$	−52.8972	−2.00076
$700$	5.94492	0.224697
$701$	33.9375	1.28180	0.640900	−	0.767624i	$-0.278561\pi$
$701$	33.9375	1.28180	0.640900	+	0.767624i	$0.278561\pi$
$702$	−5.45075	−0.205725
$703$	48.5402	1.83073
$704$	2.96575	0.111776
$705$	43.1047	1.62342
$706$	−33.8031	−1.27220
$707$	39.0686	1.46932
$708$	−3.98940	−0.149931
$709$	−15.4459	−0.580084	−0.290042	−	0.957014i	$-0.593669\pi$
$709$	−15.4459	−0.580084	−0.290042	+	0.957014i	$0.593669\pi$
$710$	15.7749	0.592020
$711$	11.9847	0.449463
$712$	7.58616	0.284303
$713$	4.09974	0.153536
$714$	−0.926180	−0.0346614
$715$	−10.2817	−0.384514
$716$	−6.23529	−0.233024
$717$	−61.5770	−2.29964
$718$	−14.8902	−0.555696
$719$	47.3695	1.76658	0.883292	−	0.468823i	$-0.155322\pi$
$719$	47.3695	1.76658	0.883292	+	0.468823i	$0.155322\pi$
$720$	−6.19273	−0.230789
$721$	−27.3080	−1.01700
$722$	−1.63735	−0.0609357
$723$	22.2280	0.826668
$724$	4.70289	0.174782
$725$	5.55466	0.206295
$726$	5.80649	0.215499
$727$	49.1015	1.82107	0.910537	−	0.413427i	$-0.135668\pi$
$727$	49.1015	1.82107	0.910537	+	0.413427i	$0.135668\pi$
$728$	5.18561	0.192192
$729$	−40.4242	−1.49719
$730$	−14.2513	−0.527464
$731$	−1.07496	−0.0397589
$732$	22.3766	0.827061
$733$	26.7633	0.988526	0.494263	−	0.869312i	$-0.335438\pi$
$733$	26.7633	0.988526	0.494263	+	0.869312i	$0.335438\pi$
$734$	−13.3471	−0.492651
$735$	6.08248	0.224356
$736$	−1.00000	−0.0368605
$737$	−10.8423	−0.399380
$738$	38.0621	1.40108
$739$	−31.9593	−1.17564	−0.587821	−	0.808991i	$-0.700014\pi$
$739$	−31.9593	−1.17564	−0.587821	+	0.808991i	$0.700014\pi$
$740$	16.8006	0.617602
$741$	−26.3841	−0.969244
$742$	9.67200	0.355070
$743$	13.1087	0.480911	0.240456	−	0.970660i	$-0.422703\pi$
$743$	13.1087	0.480911	0.240456	+	0.970660i	$0.422703\pi$
$744$	−10.7991	−0.395916
$745$	−15.6867	−0.574717
$746$	17.8284	0.652742
$747$	−17.7381	−0.649003
$748$	−0.443382	−0.0162116
$749$	−23.3783	−0.854223
$750$	−31.1778	−1.13845
$751$	12.0092	0.438222	0.219111	−	0.975700i	$-0.429684\pi$
$751$	12.0092	0.438222	0.219111	+	0.975700i	$0.429684\pi$
$752$	−10.4074	−0.379518
$753$	34.7430	1.26610
$754$	4.84520	0.176452
$755$	18.4724	0.672279
$756$	−5.81424	−0.211462
$757$	−35.6676	−1.29636	−0.648180	−	0.761487i	$-0.724469\pi$
$757$	−35.6676	−1.29636	−0.648180	+	0.761487i	$0.724469\pi$
$758$	21.3936	0.777052
$759$	7.81209	0.283561
$760$	−7.14293	−0.259101
$761$	52.5557	1.90514	0.952572	−	0.304313i	$-0.0984269\pi$
$761$	52.5557	1.90514	0.952572	+	0.304313i	$0.0984269\pi$
$762$	−45.8228	−1.65999
$763$	3.94970	0.142989
$764$	−1.09719	−0.0396948
$765$	0.925818	0.0334730
$766$	−30.9434	−1.11803
$767$	−3.33931	−0.120575
$768$	2.63411	0.0950501
$769$	29.3428	1.05813	0.529065	−	0.848581i	$-0.322543\pi$
$769$	29.3428	1.05813	0.529065	+	0.848581i	$0.322543\pi$
$770$	−10.9674	−0.395236
$771$	−13.2423	−0.476909
$772$	−22.1824	−0.798362
$773$	3.29086	0.118364	0.0591821	−	0.998247i	$-0.481151\pi$
$773$	3.29086	0.118364	0.0591821	+	0.998247i	$0.481151\pi$
$774$	−28.3192	−1.01791
$775$	−10.3630	−0.372249
$776$	6.63484	0.238177
$777$	66.1952	2.37474
$778$	−4.42794	−0.158749
$779$	43.9022	1.57296
$780$	−9.13197	−0.326977
$781$	29.7543	1.06469
$782$	0.149501	0.00534614
$783$	−5.43255	−0.194144
$784$	−1.46858	−0.0524493
$785$	9.95340	0.355252
$786$	−2.63411	−0.0939555
$787$	−18.9293	−0.674757	−0.337379	−	0.941369i	$-0.609540\pi$
$787$	−18.9293	−0.674757	−0.337379	+	0.941369i	$0.609540\pi$
$788$	−18.2553	−0.650319
$789$	−76.3199	−2.71706
$790$	4.78460	0.170228
$791$	6.85016	0.243564
$792$	−11.6806	−0.415053
$793$	18.7302	0.665128
$794$	−27.1286	−0.962757
$795$	−17.0326	−0.604083
$796$	−24.0493	−0.852405
$797$	−1.93783	−0.0686413	−0.0343207	−	0.999411i	$-0.510927\pi$
$797$	−1.93783	−0.0686413	−0.0343207	+	0.999411i	$0.510927\pi$
$798$	−28.1435	−0.996270
$799$	1.55591	0.0550443
$800$	2.52771	0.0893682
$801$	−29.8782	−1.05569
$802$	23.7341	0.838081
$803$	−26.8806	−0.948596
$804$	−9.62985	−0.339618
$805$	3.69801	0.130338
$806$	−9.03937	−0.318398
$807$	−2.47890	−0.0872614
$808$	16.6115	0.584391
$809$	−47.7742	−1.67965	−0.839826	−	0.542855i	$-0.817343\pi$
$809$	−47.7742	−1.67965	−0.839826	+	0.542855i	$0.817343\pi$
$810$	−8.33919	−0.293009
$811$	35.6555	1.25203	0.626017	−	0.779810i	$-0.284684\pi$
$811$	35.6555	1.25203	0.626017	+	0.779810i	$0.284684\pi$
$812$	5.16830	0.181372
$813$	−35.5483	−1.24673
$814$	31.6890	1.11070
$815$	−1.47074	−0.0515176
$816$	−0.393801	−0.0137858
$817$	−32.6645	−1.14279
$818$	−36.7304	−1.28425
$819$	−20.4236	−0.713659
$820$	15.1953	0.530643
$821$	−50.7308	−1.77052	−0.885259	−	0.465098i	$-0.846019\pi$
$821$	−50.7308	−1.77052	−0.885259	+	0.465098i	$0.846019\pi$
$822$	−44.4065	−1.54885
$823$	34.8422	1.21452	0.607261	−	0.794502i	$-0.292268\pi$
$823$	34.8422	1.21452	0.607261	+	0.794502i	$0.292268\pi$
$824$	−11.6110	−0.404490
$825$	−19.7467	−0.687493
$826$	−3.56199	−0.123938
$827$	15.5282	0.539969	0.269984	−	0.962865i	$-0.412981\pi$
$827$	15.5282	0.539969	0.269984	+	0.962865i	$0.412981\pi$
$828$	3.93852	0.136873
$829$	−7.85646	−0.272866	−0.136433	−	0.990649i	$-0.543564\pi$
$829$	−7.85646	−0.272866	−0.136433	+	0.990649i	$0.543564\pi$
$830$	−7.08148	−0.245802
$831$	−7.59635	−0.263514
$832$	2.20486	0.0764399
$833$	0.219554	0.00760710
$834$	−0.621272	−0.0215129
$835$	−0.441076	−0.0152641
$836$	−13.4729	−0.465970
$837$	10.1352	0.350322
$838$	−27.8594	−0.962388
$839$	−2.99712	−0.103472	−0.0517360	−	0.998661i	$-0.516475\pi$
$839$	−2.99712	−0.103472	−0.0517360	+	0.998661i	$0.516475\pi$
$840$	−9.74094	−0.336094
$841$	−24.1710	−0.833482
$842$	30.3618	1.04634
$843$	−15.7547	−0.542621
$844$	−6.30002	−0.216856
$845$	12.7967	0.440220
$846$	40.9897	1.40925
$847$	5.18440	0.178138
$848$	4.11242	0.141221
$849$	−24.6680	−0.846604
$850$	−0.377896	−0.0129617
$851$	−10.6850	−0.366277
$852$	26.4271	0.905377
$853$	23.5896	0.807691	0.403846	−	0.914827i	$-0.367673\pi$
$853$	23.5896	0.807691	0.403846	+	0.914827i	$0.367673\pi$
$854$	19.9792	0.683674
$855$	28.1325	0.962112
$856$	−9.94017	−0.339748
$857$	−55.5222	−1.89660	−0.948302	−	0.317371i	$-0.897200\pi$
$857$	−55.5222	−1.89660	−0.948302	+	0.317371i	$0.897200\pi$
$858$	−17.2246	−0.588038
$859$	19.3592	0.660528	0.330264	−	0.943889i	$-0.392862\pi$
$859$	19.3592	0.660528	0.330264	+	0.943889i	$0.392862\pi$
$860$	−11.3057	−0.385522
$861$	59.8703	2.04037
$862$	−26.9197	−0.916888
$863$	50.5397	1.72039	0.860195	−	0.509965i	$-0.170342\pi$
$863$	50.5397	1.72039	0.860195	+	0.509965i	$0.170342\pi$
$864$	−2.47215	−0.0841042
$865$	−20.7289	−0.704804
$866$	−13.5197	−0.459418
$867$	−44.7209	−1.51880
$868$	−9.64216	−0.327276
$869$	9.02465	0.306140
$870$	−9.10148	−0.308569
$871$	−8.06061	−0.273123
$872$	1.67937	0.0568706
$873$	−26.1314	−0.884415
$874$	4.54283	0.153664
$875$	−27.8375	−0.941080
$876$	−23.8747	−0.806652
$877$	0.958308	0.0323598	0.0161799	−	0.999869i	$-0.494850\pi$
$877$	0.958308	0.0323598	0.0161799	+	0.999869i	$0.494850\pi$
$878$	−3.59830	−0.121437
$879$	37.4482	1.26310
$880$	−4.66319	−0.157196
$881$	32.7270	1.10260	0.551300	−	0.834307i	$-0.314132\pi$
$881$	32.7270	1.10260	0.551300	+	0.834307i	$0.314132\pi$
$882$	5.78403	0.194758
$883$	3.26872	0.110001	0.0550006	−	0.998486i	$-0.482484\pi$
$883$	3.26872	0.110001	0.0550006	+	0.998486i	$0.482484\pi$
$884$	−0.329629	−0.0110866
$885$	6.27274	0.210856
$886$	7.58679	0.254883
$887$	27.7848	0.932924	0.466462	−	0.884541i	$-0.345528\pi$
$887$	27.7848	0.932924	0.466462	+	0.884541i	$0.345528\pi$
$888$	28.1455	0.944499
$889$	−40.9135	−1.37220
$890$	−11.9281	−0.399831
$891$	−15.7293	−0.526950
$892$	−0.212280	−0.00710766
$893$	47.2791	1.58213
$894$	−26.2794	−0.878916
$895$	9.80406	0.327713
$896$	2.35190	0.0785714
$897$	5.80785	0.193918
$898$	−11.6351	−0.388267
$899$	−9.00919	−0.300473
$900$	−9.95544	−0.331848
$901$	−0.614811	−0.0204823
$902$	28.6612	0.954312
$903$	−44.5452	−1.48237
$904$	2.91261	0.0968720
$905$	−7.39460	−0.245805
$906$	30.9462	1.02812
$907$	−2.55076	−0.0846967	−0.0423484	−	0.999103i	$-0.513484\pi$
$907$	−2.55076	−0.0846967	−0.0423484	+	0.999103i	$0.513484\pi$
$908$	−26.8775	−0.891962
$909$	−65.4247	−2.17000
$910$	−8.15360	−0.270289
$911$	−1.85508	−0.0614614	−0.0307307	−	0.999528i	$-0.509783\pi$
$911$	−1.85508	−0.0614614	−0.0307307	+	0.999528i	$0.509783\pi$
$912$	−11.9663	−0.396244
$913$	−13.3570	−0.442052
$914$	13.7403	0.454488
$915$	−35.1838	−1.16314
$916$	−2.34586	−0.0775096
$917$	−2.35190	−0.0776665
$918$	0.369588	0.0121982
$919$	31.3149	1.03298	0.516492	−	0.856292i	$-0.327237\pi$
$919$	31.3149	1.03298	0.516492	+	0.856292i	$0.327237\pi$
$920$	1.57235	0.0518389
$921$	−83.0976	−2.73816
$922$	−24.0000	−0.790399
$923$	22.1206	0.728110
$924$	−18.3732	−0.604435
$925$	27.0086	0.888039
$926$	−8.72419	−0.286695
$927$	45.7303	1.50198
$928$	2.19750	0.0721366
$929$	16.7703	0.550217	0.275108	−	0.961413i	$-0.411286\pi$
$929$	16.7703	0.550217	0.275108	+	0.961413i	$0.411286\pi$
$930$	16.9800	0.556798
$931$	6.67152	0.218650
$932$	−20.0817	−0.657797
$933$	6.84075	0.223956
$934$	−15.8999	−0.520262
$935$	0.697152	0.0227993
$936$	−8.68389	−0.283842
$937$	10.4396	0.341045	0.170523	−	0.985354i	$-0.445454\pi$
$937$	10.4396	0.341045	0.170523	+	0.985354i	$0.445454\pi$
$938$	−8.59814	−0.280739
$939$	−37.7164	−1.23083
$940$	16.3641	0.533737
$941$	−44.5288	−1.45160	−0.725799	−	0.687906i	$-0.758530\pi$
$941$	−44.5288	−1.45160	−0.725799	+	0.687906i	$0.758530\pi$
$942$	16.6746	0.543288
$943$	−9.66406	−0.314705
$944$	−1.51452	−0.0492934
$945$	9.14202	0.297390
$946$	−21.3247	−0.693326
$947$	47.1500	1.53217	0.766084	−	0.642741i	$-0.222203\pi$
$947$	47.1500	1.53217	0.766084	+	0.642741i	$0.222203\pi$
$948$	8.01548	0.260331
$949$	−19.9842	−0.648715
$950$	−11.4830	−0.372557
$951$	4.68004	0.151761
$952$	−0.351611	−0.0113958
$953$	8.13599	0.263551	0.131775	−	0.991280i	$-0.457932\pi$
$953$	8.13599	0.263551	0.131775	+	0.991280i	$0.457932\pi$
$954$	−16.1968	−0.524392
$955$	1.72516	0.0558250
$956$	−23.3768	−0.756061
$957$	−17.1671	−0.554933
$958$	10.1866	0.329115
$959$	−39.6489	−1.28033
$960$	−4.14174	−0.133674
$961$	−14.1921	−0.457811
$962$	23.5590	0.759573
$963$	39.1495	1.26158
$964$	8.43854	0.271787
$965$	34.8785	1.12278
$966$	6.19515	0.199326
$967$	19.9712	0.642231	0.321115	−	0.947040i	$-0.395942\pi$
$967$	19.9712	0.642231	0.321115	+	0.947040i	$0.395942\pi$
$968$	2.20435	0.0708504
$969$	1.78897	0.0574701
$970$	−10.4323	−0.334961
$971$	31.7818	1.01993	0.509964	−	0.860196i	$-0.329659\pi$
$971$	31.7818	1.01993	0.509964	+	0.860196i	$0.329659\pi$
$972$	−21.3868	−0.685982
$973$	−0.554711	−0.0177832
$974$	14.7922	0.473973
$975$	−14.6806	−0.470155
$976$	8.49493	0.271916
$977$	−8.97663	−0.287188	−0.143594	−	0.989637i	$-0.545866\pi$
$977$	−8.97663	−0.287188	−0.143594	+	0.989637i	$0.545866\pi$
$978$	−2.46387	−0.0787860
$979$	−22.4986	−0.719059
$980$	2.30912	0.0737622
$981$	−6.61422	−0.211176
$982$	36.3943	1.16139
$983$	−39.4043	−1.25680	−0.628401	−	0.777890i	$-0.716290\pi$
$983$	−39.4043	−1.25680	−0.628401	+	0.777890i	$0.716290\pi$
$984$	25.4562	0.811513
$985$	28.7038	0.914578
$986$	−0.328529	−0.0104625
$987$	64.4753	2.05227
$988$	−10.0163	−0.318662
$989$	7.19034	0.228639
$990$	18.3661	0.583712
$991$	−20.0936	−0.638293	−0.319146	−	0.947705i	$-0.603396\pi$
$991$	−20.0936	−0.638293	−0.319146	+	0.947705i	$0.603396\pi$
$992$	−4.09974	−0.130167
$993$	−4.43245	−0.140659
$994$	23.5958	0.748413
$995$	37.8140	1.19878
$996$	−11.8634	−0.375905
$997$	26.5094	0.839560	0.419780	−	0.907626i	$-0.362107\pi$
$997$	26.5094	0.839560	0.419780	+	0.907626i	$0.362107\pi$
$998$	3.37451	0.106818
$999$	−26.4149	−0.835731

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.i.1.24	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.i.1.24	✓	25	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.63411 q^{3} +1.00000 q^{4} -1.57235 q^{5} -2.63411 q^{6} -2.35190 q^{7} -1.00000 q^{8} +3.93852 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.63411 q^{3} +1.00000 q^{4} -1.57235 q^{5} -2.63411 q^{6} -2.35190 q^{7} -1.00000 q^{8} +3.93852 q^{9} +1.57235 q^{10} +2.96575 q^{11} +2.63411 q^{12} +2.20486 q^{13} +2.35190 q^{14} -4.14174 q^{15} +1.00000 q^{16} -0.149501 q^{17} -3.93852 q^{18} -4.54283 q^{19} -1.57235 q^{20} -6.19515 q^{21} -2.96575 q^{22} +1.00000 q^{23} -2.63411 q^{24} -2.52771 q^{25} -2.20486 q^{26} +2.47215 q^{27} -2.35190 q^{28} -2.19750 q^{29} +4.14174 q^{30} +4.09974 q^{31} -1.00000 q^{32} +7.81209 q^{33} +0.149501 q^{34} +3.69801 q^{35} +3.93852 q^{36} -10.6850 q^{37} +4.54283 q^{38} +5.80785 q^{39} +1.57235 q^{40} -9.66406 q^{41} +6.19515 q^{42} +7.19034 q^{43} +2.96575 q^{44} -6.19273 q^{45} -1.00000 q^{46} -10.4074 q^{47} +2.63411 q^{48} -1.46858 q^{49} +2.52771 q^{50} -0.393801 q^{51} +2.20486 q^{52} +4.11242 q^{53} -2.47215 q^{54} -4.66319 q^{55} +2.35190 q^{56} -11.9663 q^{57} +2.19750 q^{58} -1.51452 q^{59} -4.14174 q^{60} +8.49493 q^{61} -4.09974 q^{62} -9.26298 q^{63} +1.00000 q^{64} -3.46682 q^{65} -7.81209 q^{66} -3.65583 q^{67} -0.149501 q^{68} +2.63411 q^{69} -3.69801 q^{70} +10.0327 q^{71} -3.93852 q^{72} -9.06369 q^{73} +10.6850 q^{74} -6.65827 q^{75} -4.54283 q^{76} -6.97513 q^{77} -5.80785 q^{78} +3.04296 q^{79} -1.57235 q^{80} -5.30364 q^{81} +9.66406 q^{82} -4.50375 q^{83} -6.19515 q^{84} +0.235068 q^{85} -7.19034 q^{86} -5.78846 q^{87} -2.96575 q^{88} -7.58616 q^{89} +6.19273 q^{90} -5.18561 q^{91} +1.00000 q^{92} +10.7991 q^{93} +10.4074 q^{94} +7.14293 q^{95} -2.63411 q^{96} -6.63484 q^{97} +1.46858 q^{98} +11.6806 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * q^99

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