LMFDB - Embedded newform 6026.2.a.j.1.9

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:	$33$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.80561 q^{3} +1.00000 q^{4} -1.32735 q^{5} +1.80561 q^{6} -4.32567 q^{7} -1.00000 q^{8} +0.260232 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.80561 q^{3} +1.00000 q^{4} -1.32735 q^{5} +1.80561 q^{6} -4.32567 q^{7} -1.00000 q^{8} +0.260232 q^{9} +1.32735 q^{10} +1.86526 q^{11} -1.80561 q^{12} +3.09123 q^{13} +4.32567 q^{14} +2.39668 q^{15} +1.00000 q^{16} -4.60385 q^{17} -0.260232 q^{18} -5.39557 q^{19} -1.32735 q^{20} +7.81047 q^{21} -1.86526 q^{22} +1.00000 q^{23} +1.80561 q^{24} -3.23814 q^{25} -3.09123 q^{26} +4.94696 q^{27} -4.32567 q^{28} -1.23190 q^{29} -2.39668 q^{30} -2.10534 q^{31} -1.00000 q^{32} -3.36794 q^{33} +4.60385 q^{34} +5.74168 q^{35} +0.260232 q^{36} -5.10501 q^{37} +5.39557 q^{38} -5.58156 q^{39} +1.32735 q^{40} -7.15971 q^{41} -7.81047 q^{42} -12.5688 q^{43} +1.86526 q^{44} -0.345419 q^{45} -1.00000 q^{46} +12.6346 q^{47} -1.80561 q^{48} +11.7114 q^{49} +3.23814 q^{50} +8.31276 q^{51} +3.09123 q^{52} -7.01514 q^{53} -4.94696 q^{54} -2.47586 q^{55} +4.32567 q^{56} +9.74230 q^{57} +1.23190 q^{58} -4.28353 q^{59} +2.39668 q^{60} +5.88838 q^{61} +2.10534 q^{62} -1.12568 q^{63} +1.00000 q^{64} -4.10315 q^{65} +3.36794 q^{66} -1.51476 q^{67} -4.60385 q^{68} -1.80561 q^{69} -5.74168 q^{70} -6.94658 q^{71} -0.260232 q^{72} -6.83151 q^{73} +5.10501 q^{74} +5.84682 q^{75} -5.39557 q^{76} -8.06851 q^{77} +5.58156 q^{78} -1.92356 q^{79} -1.32735 q^{80} -9.71298 q^{81} +7.15971 q^{82} -8.12356 q^{83} +7.81047 q^{84} +6.11093 q^{85} +12.5688 q^{86} +2.22433 q^{87} -1.86526 q^{88} -15.2788 q^{89} +0.345419 q^{90} -13.3716 q^{91} +1.00000 q^{92} +3.80142 q^{93} -12.6346 q^{94} +7.16182 q^{95} +1.80561 q^{96} -14.6172 q^{97} -11.7114 q^{98} +0.485401 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9}+O(q^{10}) $ 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9} + 4 q^{10} + 5 q^{11} + 3 q^{12} + 15 q^{13} - 11 q^{14} + 16 q^{15} + 33 q^{16} + 2 q^{17} - 44 q^{18} + 32 q^{19} - 4 q^{20} + 8 q^{21} - 5 q^{22} + 33 q^{23} - 3 q^{24} + 49 q^{25} - 15 q^{26} + 15 q^{27} + 11 q^{28} + 20 q^{29} - 16 q^{30} + 25 q^{31} - 33 q^{32} - 6 q^{33} - 2 q^{34} + 15 q^{35} + 44 q^{36} + 6 q^{37} - 32 q^{38} + 25 q^{39} + 4 q^{40} + 2 q^{41} - 8 q^{42} + 31 q^{43} + 5 q^{44} + 2 q^{45} - 33 q^{46} + 4 q^{47} + 3 q^{48} + 72 q^{49} - 49 q^{50} + 26 q^{51} + 15 q^{52} - 65 q^{53} - 15 q^{54} - 4 q^{55} - 11 q^{56} + 12 q^{57} - 20 q^{58} + 8 q^{59} + 16 q^{60} + 23 q^{61} - 25 q^{62} - 14 q^{63} + 33 q^{64} + 5 q^{65} + 6 q^{66} + 31 q^{67} + 2 q^{68} + 3 q^{69} - 15 q^{70} + 20 q^{71} - 44 q^{72} + 22 q^{73} - 6 q^{74} - 32 q^{75} + 32 q^{76} + 2 q^{77} - 25 q^{78} + 53 q^{79} - 4 q^{80} + 17 q^{81} - 2 q^{82} + 45 q^{83} + 8 q^{84} + 60 q^{85} - 31 q^{86} + 11 q^{87} - 5 q^{88} - 54 q^{89} - 2 q^{90} + 38 q^{91} + 33 q^{92} + 63 q^{93} - 4 q^{94} + 44 q^{95} - 3 q^{96} - 72 q^{98} + 43 q^{99}+O(q^{100}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9 + 4 * q^10 + 5 * q^11 + 3 * q^12 + 15 * q^13 - 11 * q^14 + 16 * q^15 + 33 * q^16 + 2 * q^17 - 44 * q^18 + 32 * q^19 - 4 * q^20 + 8 * q^21 - 5 * q^22 + 33 * q^23 - 3 * q^24 + 49 * q^25 - 15 * q^26 + 15 * q^27 + 11 * q^28 + 20 * q^29 - 16 * q^30 + 25 * q^31 - 33 * q^32 - 6 * q^33 - 2 * q^34 + 15 * q^35 + 44 * q^36 + 6 * q^37 - 32 * q^38 + 25 * q^39 + 4 * q^40 + 2 * q^41 - 8 * q^42 + 31 * q^43 + 5 * q^44 + 2 * q^45 - 33 * q^46 + 4 * q^47 + 3 * q^48 + 72 * q^49 - 49 * q^50 + 26 * q^51 + 15 * q^52 - 65 * q^53 - 15 * q^54 - 4 * q^55 - 11 * q^56 + 12 * q^57 - 20 * q^58 + 8 * q^59 + 16 * q^60 + 23 * q^61 - 25 * q^62 - 14 * q^63 + 33 * q^64 + 5 * q^65 + 6 * q^66 + 31 * q^67 + 2 * q^68 + 3 * q^69 - 15 * q^70 + 20 * q^71 - 44 * q^72 + 22 * q^73 - 6 * q^74 - 32 * q^75 + 32 * q^76 + 2 * q^77 - 25 * q^78 + 53 * q^79 - 4 * q^80 + 17 * q^81 - 2 * q^82 + 45 * q^83 + 8 * q^84 + 60 * q^85 - 31 * q^86 + 11 * q^87 - 5 * q^88 - 54 * q^89 - 2 * q^90 + 38 * q^91 + 33 * q^92 + 63 * q^93 - 4 * q^94 + 44 * q^95 - 3 * q^96 - 72 * q^98 + 43 * 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
$3$	−1.80561	−1.04247	−0.521235	−	0.853413i	$-0.674529\pi$
$3$	−1.80561	−1.04247	−0.521235	+	0.853413i	$0.674529\pi$
$4$	1.00000	0.500000
$5$	−1.32735	−0.593610	−0.296805	−	0.954938i	$-0.595921\pi$
$5$	−1.32735	−0.593610	−0.296805	+	0.954938i	$0.595921\pi$
$6$	1.80561	0.737138
$7$	−4.32567	−1.63495	−0.817474	−	0.575965i	$-0.804626\pi$
$7$	−4.32567	−1.63495	−0.817474	+	0.575965i	$0.804626\pi$
$8$	−1.00000	−0.353553
$9$	0.260232	0.0867440
$10$	1.32735	0.419745
$11$	1.86526	0.562398	0.281199	−	0.959650i	$-0.409268\pi$
$11$	1.86526	0.562398	0.281199	+	0.959650i	$0.409268\pi$
$12$	−1.80561	−0.521235
$13$	3.09123	0.857353	0.428676	−	0.903458i	$-0.358980\pi$
$13$	3.09123	0.857353	0.428676	+	0.903458i	$0.358980\pi$
$14$	4.32567	1.15608
$15$	2.39668	0.618820
$16$	1.00000	0.250000
$17$	−4.60385	−1.11660	−0.558299	−	0.829640i	$-0.688546\pi$
$17$	−4.60385	−1.11660	−0.558299	+	0.829640i	$0.688546\pi$
$18$	−0.260232	−0.0613372
$19$	−5.39557	−1.23783	−0.618914	−	0.785458i	$-0.712427\pi$
$19$	−5.39557	−1.23783	−0.618914	+	0.785458i	$0.712427\pi$
$20$	−1.32735	−0.296805
$21$	7.81047	1.70439
$22$	−1.86526	−0.397675
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.80561	0.368569
$25$	−3.23814	−0.647627
$26$	−3.09123	−0.606240
$27$	4.94696	0.952042
$28$	−4.32567	−0.817474
$29$	−1.23190	−0.228758	−0.114379	−	0.993437i	$-0.536488\pi$
$29$	−1.23190	−0.228758	−0.114379	+	0.993437i	$0.536488\pi$
$30$	−2.39668	−0.437572
$31$	−2.10534	−0.378130	−0.189065	−	0.981965i	$-0.560546\pi$
$31$	−2.10534	−0.378130	−0.189065	+	0.981965i	$0.560546\pi$
$32$	−1.00000	−0.176777
$33$	−3.36794	−0.586283
$34$	4.60385	0.789554
$35$	5.74168	0.970522
$36$	0.260232	0.0433720
$37$	−5.10501	−0.839259	−0.419629	−	0.907696i	$-0.637840\pi$
$37$	−5.10501	−0.839259	−0.419629	+	0.907696i	$0.637840\pi$
$38$	5.39557	0.875277
$39$	−5.58156	−0.893765
$40$	1.32735	0.209873
$41$	−7.15971	−1.11816	−0.559080	−	0.829114i	$-0.688845\pi$
$41$	−7.15971	−1.11816	−0.559080	+	0.829114i	$0.688845\pi$
$42$	−7.81047	−1.20518
$43$	−12.5688	−1.91672	−0.958359	−	0.285567i	$-0.907818\pi$
$43$	−12.5688	−1.91672	−0.958359	+	0.285567i	$0.907818\pi$
$44$	1.86526	0.281199
$45$	−0.345419	−0.0514921
$46$	−1.00000	−0.147442
$47$	12.6346	1.84295	0.921474	−	0.388441i	$-0.126986\pi$
$47$	12.6346	1.84295	0.921474	+	0.388441i	$0.126986\pi$
$48$	−1.80561	−0.260618
$49$	11.7114	1.67306
$50$	3.23814	0.457942
$51$	8.31276	1.16402
$52$	3.09123	0.428676
$53$	−7.01514	−0.963603	−0.481801	−	0.876280i	$-0.660017\pi$
$53$	−7.01514	−0.963603	−0.481801	+	0.876280i	$0.660017\pi$
$54$	−4.94696	−0.673195
$55$	−2.47586	−0.333845
$56$	4.32567	0.578042
$57$	9.74230	1.29040
$58$	1.23190	0.161756
$59$	−4.28353	−0.557668	−0.278834	−	0.960339i	$-0.589948\pi$
$59$	−4.28353	−0.557668	−0.278834	+	0.960339i	$0.589948\pi$
$60$	2.39668	0.309410
$61$	5.88838	0.753929	0.376965	−	0.926228i	$-0.376968\pi$
$61$	5.88838	0.753929	0.376965	+	0.926228i	$0.376968\pi$
$62$	2.10534	0.267378
$63$	−1.12568	−0.141822
$64$	1.00000	0.125000
$65$	−4.10315	−0.508933
$66$	3.36794	0.414565
$67$	−1.51476	−0.185058	−0.0925288	−	0.995710i	$-0.529495\pi$
$67$	−1.51476	−0.185058	−0.0925288	+	0.995710i	$0.529495\pi$
$68$	−4.60385	−0.558299
$69$	−1.80561	−0.217370
$70$	−5.74168	−0.686262
$71$	−6.94658	−0.824408	−0.412204	−	0.911092i	$-0.635241\pi$
$71$	−6.94658	−0.824408	−0.412204	+	0.911092i	$0.635241\pi$
$72$	−0.260232	−0.0306686
$73$	−6.83151	−0.799568	−0.399784	−	0.916609i	$-0.630915\pi$
$73$	−6.83151	−0.799568	−0.399784	+	0.916609i	$0.630915\pi$
$74$	5.10501	0.593445
$75$	5.84682	0.675132
$76$	−5.39557	−0.618914
$77$	−8.06851	−0.919491
$78$	5.58156	0.631987
$79$	−1.92356	−0.216418	−0.108209	−	0.994128i	$-0.534512\pi$
$79$	−1.92356	−0.216418	−0.108209	+	0.994128i	$0.534512\pi$
$80$	−1.32735	−0.148402
$81$	−9.71298	−1.07922
$82$	7.15971	0.790658
$83$	−8.12356	−0.891677	−0.445838	−	0.895113i	$-0.647094\pi$
$83$	−8.12356	−0.891677	−0.445838	+	0.895113i	$0.647094\pi$
$84$	7.81047	0.852193
$85$	6.11093	0.662823
$86$	12.5688	1.35532
$87$	2.22433	0.238473
$88$	−1.86526	−0.198838
$89$	−15.2788	−1.61955	−0.809774	−	0.586742i	$-0.800410\pi$
$89$	−15.2788	−1.61955	−0.809774	+	0.586742i	$0.800410\pi$
$90$	0.345419	0.0364104
$91$	−13.3716	−1.40173
$92$	1.00000	0.104257
$93$	3.80142	0.394189
$94$	−12.6346	−1.30316
$95$	7.16182	0.734787
$96$	1.80561	0.184284
$97$	−14.6172	−1.48415	−0.742074	−	0.670318i	$-0.766158\pi$
$97$	−14.6172	−1.48415	−0.742074	+	0.670318i	$0.766158\pi$
$98$	−11.7114	−1.18303
$99$	0.485401	0.0487846
$100$	−3.23814	−0.323814
$101$	0.695099	0.0691650	0.0345825	−	0.999402i	$-0.488990\pi$
$101$	0.695099	0.0691650	0.0345825	+	0.999402i	$0.488990\pi$
$102$	−8.31276	−0.823086
$103$	−8.30467	−0.818284	−0.409142	−	0.912471i	$-0.634172\pi$
$103$	−8.30467	−0.818284	−0.409142	+	0.912471i	$0.634172\pi$
$104$	−3.09123	−0.303120
$105$	−10.3672	−1.01174
$106$	7.01514	0.681370
$107$	−19.5610	−1.89103	−0.945514	−	0.325580i	$-0.894440\pi$
$107$	−19.5610	−1.89103	−0.945514	+	0.325580i	$0.894440\pi$
$108$	4.94696	0.476021
$109$	1.42166	0.136170	0.0680850	−	0.997680i	$-0.478311\pi$
$109$	1.42166	0.136170	0.0680850	+	0.997680i	$0.478311\pi$
$110$	2.47586	0.236064
$111$	9.21766	0.874902
$112$	−4.32567	−0.408737
$113$	−11.8348	−1.11332	−0.556662	−	0.830739i	$-0.687918\pi$
$113$	−11.8348	−1.11332	−0.556662	+	0.830739i	$0.687918\pi$
$114$	−9.74230	−0.912450
$115$	−1.32735	−0.123776
$116$	−1.23190	−0.114379
$117$	0.804436	0.0743702
$118$	4.28353	0.394331
$119$	19.9147	1.82558
$120$	−2.39668	−0.218786
$121$	−7.52080	−0.683709
$122$	−5.88838	−0.533108
$123$	12.9277	1.16565
$124$	−2.10534	−0.189065
$125$	10.9349	0.978048
$126$	1.12568	0.100283
$127$	−5.38940	−0.478232	−0.239116	−	0.970991i	$-0.576858\pi$
$127$	−5.38940	−0.478232	−0.239116	+	0.970991i	$0.576858\pi$
$128$	−1.00000	−0.0883883
$129$	22.6943	1.99812
$130$	4.10315	0.359870
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−3.36794	−0.293141
$133$	23.3395	2.02379
$134$	1.51476	0.130856
$135$	−6.56635	−0.565141
$136$	4.60385	0.394777
$137$	10.1908	0.870660	0.435330	−	0.900271i	$-0.356632\pi$
$137$	10.1908	0.870660	0.435330	+	0.900271i	$0.356632\pi$
$138$	1.80561	0.153704
$139$	17.9403	1.52168	0.760838	−	0.648942i	$-0.224788\pi$
$139$	17.9403	1.52168	0.760838	+	0.648942i	$0.224788\pi$
$140$	5.74168	0.485261
$141$	−22.8132	−1.92122
$142$	6.94658	0.582944
$143$	5.76595	0.482173
$144$	0.260232	0.0216860
$145$	1.63516	0.135793
$146$	6.83151	0.565380
$147$	−21.1462	−1.74411
$148$	−5.10501	−0.419629
$149$	1.23929	0.101527	0.0507633	−	0.998711i	$-0.483835\pi$
$149$	1.23929	0.101527	0.0507633	+	0.998711i	$0.483835\pi$
$150$	−5.84682	−0.477391
$151$	11.4716	0.933547	0.466773	−	0.884377i	$-0.345416\pi$
$151$	11.4716	0.933547	0.466773	+	0.884377i	$0.345416\pi$
$152$	5.39557	0.437639
$153$	−1.19807	−0.0968581
$154$	8.06851	0.650179
$155$	2.79452	0.224461
$156$	−5.58156	−0.446882
$157$	−3.98402	−0.317960	−0.158980	−	0.987282i	$-0.550820\pi$
$157$	−3.98402	−0.317960	−0.158980	+	0.987282i	$0.550820\pi$
$158$	1.92356	0.153031
$159$	12.6666	1.00453
$160$	1.32735	0.104936
$161$	−4.32567	−0.340910
$162$	9.71298	0.763123
$163$	−10.5559	−0.826803	−0.413402	−	0.910549i	$-0.635659\pi$
$163$	−10.5559	−0.826803	−0.413402	+	0.910549i	$0.635659\pi$
$164$	−7.15971	−0.559080
$165$	4.47044	0.348023
$166$	8.12356	0.630511
$167$	8.81067	0.681790	0.340895	−	0.940101i	$-0.389270\pi$
$167$	8.81067	0.681790	0.340895	+	0.940101i	$0.389270\pi$
$168$	−7.81047	−0.602591
$169$	−3.44430	−0.264946
$170$	−6.11093	−0.468687
$171$	−1.40410	−0.107374
$172$	−12.5688	−0.958359
$173$	4.67939	0.355767	0.177884	−	0.984052i	$-0.443075\pi$
$173$	4.67939	0.355767	0.177884	+	0.984052i	$0.443075\pi$
$174$	−2.22433	−0.168626
$175$	14.0071	1.05884
$176$	1.86526	0.140599
$177$	7.73439	0.581352
$178$	15.2788	1.14519
$179$	−9.43241	−0.705011	−0.352506	−	0.935810i	$-0.614670\pi$
$179$	−9.43241	−0.705011	−0.352506	+	0.935810i	$0.614670\pi$
$180$	−0.345419	−0.0257460
$181$	−23.3758	−1.73751	−0.868753	−	0.495245i	$-0.835078\pi$
$181$	−23.3758	−1.73751	−0.868753	+	0.495245i	$0.835078\pi$
$182$	13.3716	0.991171
$183$	−10.6321	−0.785949
$184$	−1.00000	−0.0737210
$185$	6.77614	0.498192
$186$	−3.80142	−0.278734
$187$	−8.58738	−0.627972
$188$	12.6346	0.921474
$189$	−21.3989	−1.55654
$190$	−7.16182	−0.519573
$191$	6.09532	0.441042	0.220521	−	0.975382i	$-0.429224\pi$
$191$	6.09532	0.441042	0.220521	+	0.975382i	$0.429224\pi$
$192$	−1.80561	−0.130309
$193$	−7.79419	−0.561038	−0.280519	−	0.959848i	$-0.590507\pi$
$193$	−7.79419	−0.561038	−0.280519	+	0.959848i	$0.590507\pi$
$194$	14.6172	1.04945
$195$	7.40869	0.530547
$196$	11.7114	0.836529
$197$	−13.9652	−0.994982	−0.497491	−	0.867469i	$-0.665745\pi$
$197$	−13.9652	−0.994982	−0.497491	+	0.867469i	$0.665745\pi$
$198$	−0.485401	−0.0344959
$199$	9.33175	0.661510	0.330755	−	0.943717i	$-0.392697\pi$
$199$	9.33175	0.661510	0.330755	+	0.943717i	$0.392697\pi$
$200$	3.23814	0.228971
$201$	2.73507	0.192917
$202$	−0.695099	−0.0489070
$203$	5.32878	0.374007
$204$	8.31276	0.582010
$205$	9.50346	0.663750
$206$	8.30467	0.578614
$207$	0.260232	0.0180874
$208$	3.09123	0.214338
$209$	−10.0642	−0.696152
$210$	10.3672	0.715408
$211$	8.01622	0.551859	0.275930	−	0.961178i	$-0.411014\pi$
$211$	8.01622	0.551859	0.275930	+	0.961178i	$0.411014\pi$
$212$	−7.01514	−0.481801
$213$	12.5428	0.859420
$214$	19.5610	1.33716
$215$	16.6832	1.13778
$216$	−4.94696	−0.336598
$217$	9.10699	0.618223
$218$	−1.42166	−0.0962867
$219$	12.3351	0.833526
$220$	−2.47586	−0.166922
$221$	−14.2316	−0.957318
$222$	−9.21766	−0.618649
$223$	4.89237	0.327617	0.163809	−	0.986492i	$-0.447622\pi$
$223$	4.89237	0.327617	0.163809	+	0.986492i	$0.447622\pi$
$224$	4.32567	0.289021
$225$	−0.842667	−0.0561778
$226$	11.8348	0.787239
$227$	−26.2011	−1.73903	−0.869514	−	0.493908i	$-0.835568\pi$
$227$	−26.2011	−1.73903	−0.869514	+	0.493908i	$0.835568\pi$
$228$	9.74230	0.645200
$229$	18.3879	1.21511	0.607554	−	0.794279i	$-0.292151\pi$
$229$	18.3879	1.21511	0.607554	+	0.794279i	$0.292151\pi$
$230$	1.32735	0.0875230
$231$	14.5686	0.958542
$232$	1.23190	0.0808781
$233$	14.7959	0.969311	0.484655	−	0.874705i	$-0.338945\pi$
$233$	14.7959	0.969311	0.484655	+	0.874705i	$0.338945\pi$
$234$	−0.804436	−0.0525877
$235$	−16.7706	−1.09399
$236$	−4.28353	−0.278834
$237$	3.47321	0.225609
$238$	−19.9147	−1.29088
$239$	24.4982	1.58466	0.792328	−	0.610096i	$-0.208869\pi$
$239$	24.4982	1.58466	0.792328	+	0.610096i	$0.208869\pi$
$240$	2.39668	0.154705
$241$	−11.3118	−0.728657	−0.364328	−	0.931271i	$-0.618701\pi$
$241$	−11.3118	−0.728657	−0.364328	+	0.931271i	$0.618701\pi$
$242$	7.52080	0.483455
$243$	2.69699	0.173012
$244$	5.88838	0.376965
$245$	−15.5452	−0.993143
$246$	−12.9277	−0.824237
$247$	−16.6789	−1.06126
$248$	2.10534	0.133689
$249$	14.6680	0.929546
$250$	−10.9349	−0.691584
$251$	3.76397	0.237580	0.118790	−	0.992919i	$-0.462098\pi$
$251$	3.76397	0.237580	0.118790	+	0.992919i	$0.462098\pi$
$252$	−1.12568	−0.0709110
$253$	1.86526	0.117268
$254$	5.38940	0.338161
$255$	−11.0340	−0.690973
$256$	1.00000	0.0625000
$257$	8.54403	0.532962	0.266481	−	0.963840i	$-0.414139\pi$
$257$	8.54403	0.532962	0.266481	+	0.963840i	$0.414139\pi$
$258$	−22.6943	−1.41288
$259$	22.0826	1.37214
$260$	−4.10315	−0.254466
$261$	−0.320579	−0.0198434
$262$	1.00000	0.0617802
$263$	−25.4440	−1.56894	−0.784472	−	0.620164i	$-0.787066\pi$
$263$	−25.4440	−1.56894	−0.784472	+	0.620164i	$0.787066\pi$
$264$	3.36794	0.207282
$265$	9.31155	0.572004
$266$	−23.3395	−1.43103
$267$	27.5876	1.68833
$268$	−1.51476	−0.0925288
$269$	−22.4822	−1.37077	−0.685383	−	0.728182i	$-0.740365\pi$
$269$	−22.4822	−1.37077	−0.685383	+	0.728182i	$0.740365\pi$
$270$	6.56635	0.399615
$271$	9.69537	0.588952	0.294476	−	0.955659i	$-0.404855\pi$
$271$	9.69537	0.588952	0.294476	+	0.955659i	$0.404855\pi$
$272$	−4.60385	−0.279149
$273$	24.1440	1.46126
$274$	−10.1908	−0.615649
$275$	−6.03998	−0.364224
$276$	−1.80561	−0.108685
$277$	−10.9550	−0.658220	−0.329110	−	0.944292i	$-0.606749\pi$
$277$	−10.9550	−0.658220	−0.329110	+	0.944292i	$0.606749\pi$
$278$	−17.9403	−1.07599
$279$	−0.547876	−0.0328005
$280$	−5.74168	−0.343131
$281$	−4.00045	−0.238647	−0.119323	−	0.992855i	$-0.538073\pi$
$281$	−4.00045	−0.238647	−0.119323	+	0.992855i	$0.538073\pi$
$282$	22.8132	1.35851
$283$	20.2172	1.20179	0.600895	−	0.799328i	$-0.294811\pi$
$283$	20.2172	1.20179	0.600895	+	0.799328i	$0.294811\pi$
$284$	−6.94658	−0.412204
$285$	−12.9315	−0.765994
$286$	−5.76595	−0.340948
$287$	30.9705	1.82813
$288$	−0.260232	−0.0153343
$289$	4.19542	0.246790
$290$	−1.63516	−0.0960201
$291$	26.3929	1.54718
$292$	−6.83151	−0.399784
$293$	−16.9710	−0.991457	−0.495729	−	0.868478i	$-0.665099\pi$
$293$	−16.9710	−0.991457	−0.495729	+	0.868478i	$0.665099\pi$
$294$	21.1462	1.23327
$295$	5.68575	0.331037
$296$	5.10501	0.296723
$297$	9.22737	0.535426
$298$	−1.23929	−0.0717901
$299$	3.09123	0.178770
$300$	5.84682	0.337566
$301$	54.3683	3.13373
$302$	−11.4716	−0.660117
$303$	−1.25508	−0.0721024
$304$	−5.39557	−0.309457
$305$	−7.81595	−0.447540
$306$	1.19807	0.0684890
$307$	−34.3803	−1.96219	−0.981094	−	0.193533i	$-0.938005\pi$
$307$	−34.3803	−1.96219	−0.981094	+	0.193533i	$0.938005\pi$
$308$	−8.06851	−0.459746
$309$	14.9950	0.853036
$310$	−2.79452	−0.158718
$311$	13.1610	0.746290	0.373145	−	0.927773i	$-0.378279\pi$
$311$	13.1610	0.746290	0.373145	+	0.927773i	$0.378279\pi$
$312$	5.58156	0.315994
$313$	8.12702	0.459366	0.229683	−	0.973265i	$-0.426231\pi$
$313$	8.12702	0.459366	0.229683	+	0.973265i	$0.426231\pi$
$314$	3.98402	0.224831
$315$	1.49417	0.0841869
$316$	−1.92356	−0.108209
$317$	−18.6763	−1.04897	−0.524484	−	0.851420i	$-0.675742\pi$
$317$	−18.6763	−1.04897	−0.524484	+	0.851420i	$0.675742\pi$
$318$	−12.6666	−0.710308
$319$	−2.29781	−0.128653
$320$	−1.32735	−0.0742012
$321$	35.3195	1.97134
$322$	4.32567	0.241060
$323$	24.8404	1.38216
$324$	−9.71298	−0.539610
$325$	−10.0098	−0.555245
$326$	10.5559	0.584638
$327$	−2.56696	−0.141953
$328$	7.15971	0.395329
$329$	−54.6531	−3.01312
$330$	−4.47044	−0.246090
$331$	25.5270	1.40309	0.701545	−	0.712625i	$-0.252494\pi$
$331$	25.5270	1.40309	0.701545	+	0.712625i	$0.252494\pi$
$332$	−8.12356	−0.445838
$333$	−1.32849	−0.0728006
$334$	−8.81067	−0.482098
$335$	2.01062	0.109852
$336$	7.81047	0.426096
$337$	33.7911	1.84072	0.920360	−	0.391072i	$-0.127895\pi$
$337$	33.7911	1.84072	0.920360	+	0.391072i	$0.127895\pi$
$338$	3.44430	0.187345
$339$	21.3690	1.16061
$340$	6.11093	0.331412
$341$	−3.92700	−0.212659
$342$	1.40410	0.0759250
$343$	−20.3800	−1.10041
$344$	12.5688	0.677662
$345$	2.39668	0.129033
$346$	−4.67939	−0.251566
$347$	−1.10565	−0.0593544	−0.0296772	−	0.999560i	$-0.509448\pi$
$347$	−1.10565	−0.0593544	−0.0296772	+	0.999560i	$0.509448\pi$
$348$	2.22433	0.119237
$349$	18.6252	0.996982	0.498491	−	0.866895i	$-0.333888\pi$
$349$	18.6252	0.996982	0.498491	+	0.866895i	$0.333888\pi$
$350$	−14.0071	−0.748711
$351$	15.2922	0.816236
$352$	−1.86526	−0.0994188
$353$	20.9570	1.11543	0.557714	−	0.830033i	$-0.311678\pi$
$353$	20.9570	1.11543	0.557714	+	0.830033i	$0.311678\pi$
$354$	−7.73439	−0.411078
$355$	9.22056	0.489376
$356$	−15.2788	−0.809774
$357$	−35.9582	−1.90311
$358$	9.43241	0.498518
$359$	8.79519	0.464193	0.232096	−	0.972693i	$-0.425442\pi$
$359$	8.79519	0.464193	0.232096	+	0.972693i	$0.425442\pi$
$360$	0.345419	0.0182052
$361$	10.1122	0.532221
$362$	23.3758	1.22860
$363$	13.5796	0.712746
$364$	−13.3716	−0.700864
$365$	9.06782	0.474631
$366$	10.6321	0.555750
$367$	14.0713	0.734517	0.367259	−	0.930119i	$-0.380296\pi$
$367$	14.0713	0.734517	0.367259	+	0.930119i	$0.380296\pi$
$368$	1.00000	0.0521286
$369$	−1.86319	−0.0969935
$370$	−6.77614	−0.352275
$371$	30.3451	1.57544
$372$	3.80142	0.197094
$373$	−10.6301	−0.550407	−0.275204	−	0.961386i	$-0.588745\pi$
$373$	−10.6301	−0.550407	−0.275204	+	0.961386i	$0.588745\pi$
$374$	8.58738	0.444043
$375$	−19.7442	−1.01959
$376$	−12.6346	−0.651580
$377$	−3.80808	−0.196126
$378$	21.3989	1.10064
$379$	33.8949	1.74106	0.870531	−	0.492113i	$-0.163775\pi$
$379$	33.8949	1.74106	0.870531	+	0.492113i	$0.163775\pi$
$380$	7.16182	0.367394
$381$	9.73116	0.498542
$382$	−6.09532	−0.311864
$383$	17.2663	0.882268	0.441134	−	0.897441i	$-0.354576\pi$
$383$	17.2663	0.882268	0.441134	+	0.897441i	$0.354576\pi$
$384$	1.80561	0.0921422
$385$	10.7097	0.545819
$386$	7.79419	0.396714
$387$	−3.27079	−0.166264
$388$	−14.6172	−0.742074
$389$	−30.4112	−1.54191	−0.770955	−	0.636889i	$-0.780221\pi$
$389$	−30.4112	−1.54191	−0.770955	+	0.636889i	$0.780221\pi$
$390$	−7.40869	−0.375154
$391$	−4.60385	−0.232827
$392$	−11.7114	−0.591515
$393$	1.80561	0.0910810
$394$	13.9652	0.703559
$395$	2.55325	0.128468
$396$	0.485401	0.0243923
$397$	−17.9691	−0.901841	−0.450920	−	0.892564i	$-0.648904\pi$
$397$	−17.9691	−0.901841	−0.450920	+	0.892564i	$0.648904\pi$
$398$	−9.33175	−0.467759
$399$	−42.1420	−2.10974
$400$	−3.23814	−0.161907
$401$	−14.3336	−0.715786	−0.357893	−	0.933763i	$-0.616505\pi$
$401$	−14.3336	−0.715786	−0.357893	+	0.933763i	$0.616505\pi$
$402$	−2.73507	−0.136413
$403$	−6.50808	−0.324190
$404$	0.695099	0.0345825
$405$	12.8925	0.640635
$406$	−5.32878	−0.264463
$407$	−9.52218	−0.471997
$408$	−8.31276	−0.411543
$409$	−18.9955	−0.939265	−0.469633	−	0.882862i	$-0.655614\pi$
$409$	−18.9955	−0.939265	−0.469633	+	0.882862i	$0.655614\pi$
$410$	−9.50346	−0.469342
$411$	−18.4006	−0.907637
$412$	−8.30467	−0.409142
$413$	18.5291	0.911759
$414$	−0.260232	−0.0127897
$415$	10.7828	0.529308
$416$	−3.09123	−0.151560
$417$	−32.3932	−1.58630
$418$	10.0642	0.492254
$419$	−21.4193	−1.04640	−0.523200	−	0.852210i	$-0.675262\pi$
$419$	−21.4193	−1.04640	−0.523200	+	0.852210i	$0.675262\pi$
$420$	−10.3672	−0.505870
$421$	35.7201	1.74089	0.870446	−	0.492263i	$-0.163830\pi$
$421$	35.7201	1.74089	0.870446	+	0.492263i	$0.163830\pi$
$422$	−8.01622	−0.390223
$423$	3.28793	0.159865
$424$	7.01514	0.340685
$425$	14.9079	0.723139
$426$	−12.5428	−0.607702
$427$	−25.4712	−1.23264
$428$	−19.5610	−0.945514
$429$	−10.4111	−0.502651
$430$	−16.6832	−0.804533
$431$	−5.92422	−0.285360	−0.142680	−	0.989769i	$-0.545572\pi$
$431$	−5.92422	−0.285360	−0.142680	+	0.989769i	$0.545572\pi$
$432$	4.94696	0.238011
$433$	−27.6118	−1.32694	−0.663469	−	0.748204i	$-0.730916\pi$
$433$	−27.6118	−1.32694	−0.663469	+	0.748204i	$0.730916\pi$
$434$	−9.10699	−0.437149
$435$	−2.95247	−0.141560
$436$	1.42166	0.0680850
$437$	−5.39557	−0.258105
$438$	−12.3351	−0.589392
$439$	12.9467	0.617913	0.308956	−	0.951076i	$-0.400020\pi$
$439$	12.9467	0.617913	0.308956	+	0.951076i	$0.400020\pi$
$440$	2.47586	0.118032
$441$	3.04768	0.145128
$442$	14.2316	0.676926
$443$	32.0407	1.52230	0.761150	−	0.648576i	$-0.224635\pi$
$443$	32.0407	1.52230	0.761150	+	0.648576i	$0.224635\pi$
$444$	9.21766	0.437451
$445$	20.2803	0.961380
$446$	−4.89237	−0.231660
$447$	−2.23768	−0.105838
$448$	−4.32567	−0.204369
$449$	14.3905	0.679129	0.339565	−	0.940583i	$-0.389720\pi$
$449$	14.3905	0.679129	0.339565	+	0.940583i	$0.389720\pi$
$450$	0.842667	0.0397237
$451$	−13.3547	−0.628850
$452$	−11.8348	−0.556662
$453$	−20.7133	−0.973194
$454$	26.2011	1.22968
$455$	17.7489	0.832079
$456$	−9.74230	−0.456225
$457$	18.9587	0.886852	0.443426	−	0.896311i	$-0.353763\pi$
$457$	18.9587	0.886852	0.443426	+	0.896311i	$0.353763\pi$
$458$	−18.3879	−0.859211
$459$	−22.7750	−1.06305
$460$	−1.32735	−0.0618881
$461$	−12.8900	−0.600348	−0.300174	−	0.953884i	$-0.597045\pi$
$461$	−12.8900	−0.600348	−0.300174	+	0.953884i	$0.597045\pi$
$462$	−14.5686	−0.677792
$463$	6.87915	0.319701	0.159851	−	0.987141i	$-0.448899\pi$
$463$	6.87915	0.319701	0.159851	+	0.987141i	$0.448899\pi$
$464$	−1.23190	−0.0571895
$465$	−5.04582	−0.233994
$466$	−14.7959	−0.685406
$467$	−36.1072	−1.67084	−0.835421	−	0.549610i	$-0.814776\pi$
$467$	−36.1072	−1.67084	−0.835421	+	0.549610i	$0.814776\pi$
$468$	0.804436	0.0371851
$469$	6.55236	0.302560
$470$	16.7706	0.773569
$471$	7.19360	0.331463
$472$	4.28353	0.197165
$473$	−23.4440	−1.07796
$474$	−3.47321	−0.159530
$475$	17.4716	0.801652
$476$	19.9147	0.912790
$477$	−1.82556	−0.0835867
$478$	−24.4982	−1.12052
$479$	−26.0091	−1.18838	−0.594192	−	0.804323i	$-0.702528\pi$
$479$	−26.0091	−1.18838	−0.594192	+	0.804323i	$0.702528\pi$
$480$	−2.39668	−0.109393
$481$	−15.7808	−0.719541
$482$	11.3118	0.515238
$483$	7.81047	0.355389
$484$	−7.52080	−0.341854
$485$	19.4021	0.881005
$486$	−2.69699	−0.122338
$487$	−9.30524	−0.421661	−0.210830	−	0.977523i	$-0.567617\pi$
$487$	−9.30524	−0.421661	−0.210830	+	0.977523i	$0.567617\pi$
$488$	−5.88838	−0.266554
$489$	19.0599	0.861918
$490$	15.5452	0.702258
$491$	38.4944	1.73723	0.868615	−	0.495488i	$-0.165011\pi$
$491$	38.4944	1.73723	0.868615	+	0.495488i	$0.165011\pi$
$492$	12.9277	0.582824
$493$	5.67147	0.255430
$494$	16.6789	0.750421
$495$	−0.644297	−0.0289590
$496$	−2.10534	−0.0945324
$497$	30.0486	1.34786
$498$	−14.6680	−0.657289
$499$	31.4539	1.40807	0.704036	−	0.710164i	$-0.251379\pi$
$499$	31.4539	1.40807	0.704036	+	0.710164i	$0.251379\pi$
$500$	10.9349	0.489024
$501$	−15.9086	−0.710745
$502$	−3.76397	−0.167994
$503$	34.8745	1.55498	0.777489	−	0.628896i	$-0.216493\pi$
$503$	34.8745	1.55498	0.777489	+	0.628896i	$0.216493\pi$
$504$	1.12568	0.0501416
$505$	−0.922641	−0.0410570
$506$	−1.86526	−0.0829210
$507$	6.21907	0.276199
$508$	−5.38940	−0.239116
$509$	−43.6575	−1.93508	−0.967542	−	0.252709i	$-0.918679\pi$
$509$	−43.6575	−1.93508	−0.967542	+	0.252709i	$0.918679\pi$
$510$	11.0340	0.488592
$511$	29.5509	1.30725
$512$	−1.00000	−0.0441942
$513$	−26.6917	−1.17847
$514$	−8.54403	−0.376861
$515$	11.0232	0.485741
$516$	22.6943	0.999060
$517$	23.5669	1.03647
$518$	−22.0826	−0.970253
$519$	−8.44916	−0.370877
$520$	4.10315	0.179935
$521$	−24.3122	−1.06514	−0.532568	−	0.846387i	$-0.678773\pi$
$521$	−24.3122	−1.06514	−0.532568	+	0.846387i	$0.678773\pi$
$522$	0.320579	0.0140314
$523$	1.61571	0.0706502	0.0353251	−	0.999376i	$-0.488753\pi$
$523$	1.61571	0.0706502	0.0353251	+	0.999376i	$0.488753\pi$
$524$	−1.00000	−0.0436852
$525$	−25.2914	−1.10381
$526$	25.4440	1.10941
$527$	9.69265	0.422219
$528$	−3.36794	−0.146571
$529$	1.00000	0.0434783
$530$	−9.31155	−0.404468
$531$	−1.11471	−0.0483743
$532$	23.3395	1.01189
$533$	−22.1323	−0.958657
$534$	−27.5876	−1.19383
$535$	25.9643	1.12253
$536$	1.51476	0.0654278
$537$	17.0313	0.734953
$538$	22.4822	0.969279
$539$	21.8448	0.940924
$540$	−6.56635	−0.282571
$541$	40.9612	1.76106	0.880529	−	0.473992i	$-0.157188\pi$
$541$	40.9612	1.76106	0.880529	+	0.473992i	$0.157188\pi$
$542$	−9.69537	−0.416452
$543$	42.2075	1.81130
$544$	4.60385	0.197388
$545$	−1.88704	−0.0808318
$546$	−24.1440	−1.03327
$547$	−15.0983	−0.645559	−0.322779	−	0.946474i	$-0.604617\pi$
$547$	−15.0983	−0.645559	−0.322779	+	0.946474i	$0.604617\pi$
$548$	10.1908	0.435330
$549$	1.53234	0.0653988
$550$	6.03998	0.257545
$551$	6.64680	0.283163
$552$	1.80561	0.0768519
$553$	8.32070	0.353832
$554$	10.9550	0.465432
$555$	−12.2351	−0.519350
$556$	17.9403	0.760838
$557$	9.02869	0.382558	0.191279	−	0.981536i	$-0.438737\pi$
$557$	9.02869	0.382558	0.191279	+	0.981536i	$0.438737\pi$
$558$	0.547876	0.0231934
$559$	−38.8529	−1.64330
$560$	5.74168	0.242630
$561$	15.5055	0.654642
$562$	4.00045	0.168749
$563$	12.9216	0.544580	0.272290	−	0.962215i	$-0.412219\pi$
$563$	12.9216	0.544580	0.272290	+	0.962215i	$0.412219\pi$
$564$	−22.8132	−0.960609
$565$	15.7089	0.660880
$566$	−20.2172	−0.849793
$567$	42.0151	1.76447
$568$	6.94658	0.291472
$569$	−29.4576	−1.23493	−0.617464	−	0.786599i	$-0.711840\pi$
$569$	−29.4576	−1.23493	−0.617464	+	0.786599i	$0.711840\pi$
$570$	12.9315	0.541639
$571$	30.0998	1.25964	0.629818	−	0.776743i	$-0.283129\pi$
$571$	30.0998	1.25964	0.629818	+	0.776743i	$0.283129\pi$
$572$	5.76595	0.241087
$573$	−11.0058	−0.459773
$574$	−30.9705	−1.29269
$575$	−3.23814	−0.135040
$576$	0.260232	0.0108430
$577$	−26.2419	−1.09246	−0.546232	−	0.837634i	$-0.683938\pi$
$577$	−26.2419	−1.09246	−0.546232	+	0.837634i	$0.683938\pi$
$578$	−4.19542	−0.174507
$579$	14.0733	0.584866
$580$	1.63516	0.0678964
$581$	35.1398	1.45785
$582$	−26.3929	−1.09402
$583$	−13.0851	−0.541928
$584$	6.83151	0.282690
$585$	−1.06777	−0.0441469
$586$	16.9710	0.701066
$587$	−23.9371	−0.987992	−0.493996	−	0.869464i	$-0.664464\pi$
$587$	−23.9371	−0.987992	−0.493996	+	0.869464i	$0.664464\pi$
$588$	−21.1462	−0.872056
$589$	11.3595	0.468060
$590$	−5.68575	−0.234079
$591$	25.2158	1.03724
$592$	−5.10501	−0.209815
$593$	13.8220	0.567600	0.283800	−	0.958884i	$-0.408405\pi$
$593$	13.8220	0.567600	0.283800	+	0.958884i	$0.408405\pi$
$594$	−9.22737	−0.378604
$595$	−26.4338	−1.08368
$596$	1.23929	0.0507633
$597$	−16.8495	−0.689605
$598$	−3.09123	−0.126410
$599$	−8.67973	−0.354644	−0.177322	−	0.984153i	$-0.556743\pi$
$599$	−8.67973	−0.354644	−0.177322	+	0.984153i	$0.556743\pi$
$600$	−5.84682	−0.238695
$601$	18.9876	0.774521	0.387261	−	0.921970i	$-0.373421\pi$
$601$	18.9876	0.774521	0.387261	+	0.921970i	$0.373421\pi$
$602$	−54.3683	−2.21588
$603$	−0.394189	−0.0160526
$604$	11.4716	0.466773
$605$	9.98274	0.405856
$606$	1.25508	0.0509841
$607$	−45.6586	−1.85323	−0.926613	−	0.376016i	$-0.877294\pi$
$607$	−45.6586	−1.85323	−0.926613	+	0.376016i	$0.877294\pi$
$608$	5.39557	0.218819
$609$	−9.62171	−0.389891
$610$	7.81595	0.316458
$611$	39.0565	1.58006
$612$	−1.19807	−0.0484290
$613$	40.7373	1.64536	0.822681	−	0.568503i	$-0.192477\pi$
$613$	40.7373	1.64536	0.822681	+	0.568503i	$0.192477\pi$
$614$	34.3803	1.38748
$615$	−17.1595	−0.691940
$616$	8.06851	0.325089
$617$	−26.6199	−1.07168	−0.535839	−	0.844320i	$-0.680005\pi$
$617$	−26.6199	−1.07168	−0.535839	+	0.844320i	$0.680005\pi$
$618$	−14.9950	−0.603188
$619$	0.230345	0.00925836	0.00462918	−	0.999989i	$-0.498526\pi$
$619$	0.230345	0.00925836	0.00462918	+	0.999989i	$0.498526\pi$
$620$	2.79452	0.112231
$621$	4.94696	0.198515
$622$	−13.1610	−0.527706
$623$	66.0910	2.64788
$624$	−5.58156	−0.223441
$625$	1.67622	0.0670488
$626$	−8.12702	−0.324821
$627$	18.1720	0.725718
$628$	−3.98402	−0.158980
$629$	23.5027	0.937114
$630$	−1.49417	−0.0595291
$631$	18.7253	0.745444	0.372722	−	0.927943i	$-0.378424\pi$
$631$	18.7253	0.745444	0.372722	+	0.927943i	$0.378424\pi$
$632$	1.92356	0.0765153
$633$	−14.4742	−0.575297
$634$	18.6763	0.741732
$635$	7.15363	0.283883
$636$	12.6666	0.502264
$637$	36.2026	1.43440
$638$	2.29781	0.0909713
$639$	−1.80772	−0.0715124
$640$	1.32735	0.0524682
$641$	44.5802	1.76081	0.880406	−	0.474220i	$-0.157270\pi$
$641$	44.5802	1.76081	0.880406	+	0.474220i	$0.157270\pi$
$642$	−35.3195	−1.39395
$643$	−3.84811	−0.151755	−0.0758773	−	0.997117i	$-0.524176\pi$
$643$	−3.84811	−0.151755	−0.0758773	+	0.997117i	$0.524176\pi$
$644$	−4.32567	−0.170455
$645$	−30.1233	−1.18610
$646$	−24.8404	−0.977332
$647$	−20.6529	−0.811951	−0.405976	−	0.913884i	$-0.633068\pi$
$647$	−20.6529	−0.811951	−0.405976	+	0.913884i	$0.633068\pi$
$648$	9.71298	0.381562
$649$	−7.98991	−0.313631
$650$	10.0098	0.392618
$651$	−16.4437	−0.644479
$652$	−10.5559	−0.413402
$653$	−5.73340	−0.224365	−0.112183	−	0.993688i	$-0.535784\pi$
$653$	−5.73340	−0.224365	−0.112183	+	0.993688i	$0.535784\pi$
$654$	2.56696	0.100376
$655$	1.32735	0.0518639
$656$	−7.15971	−0.279540
$657$	−1.77778	−0.0693577
$658$	54.6531	2.13060
$659$	14.8658	0.579091	0.289545	−	0.957164i	$-0.406496\pi$
$659$	14.8658	0.579091	0.289545	+	0.957164i	$0.406496\pi$
$660$	4.47044	0.174012
$661$	7.57387	0.294590	0.147295	−	0.989093i	$-0.452943\pi$
$661$	7.57387	0.294590	0.147295	+	0.989093i	$0.452943\pi$
$662$	−25.5270	−0.992134
$663$	25.6967	0.997975
$664$	8.12356	0.315255
$665$	−30.9797	−1.20134
$666$	1.32849	0.0514778
$667$	−1.23190	−0.0476993
$668$	8.81067	0.340895
$669$	−8.83371	−0.341531
$670$	−2.01062	−0.0776771
$671$	10.9834	0.424008
$672$	−7.81047	−0.301296
$673$	−1.14253	−0.0440412	−0.0220206	−	0.999758i	$-0.507010\pi$
$673$	−1.14253	−0.0440412	−0.0220206	+	0.999758i	$0.507010\pi$
$674$	−33.7911	−1.30159
$675$	−16.0189	−0.616569
$676$	−3.44430	−0.132473
$677$	19.7553	0.759258	0.379629	−	0.925139i	$-0.376052\pi$
$677$	19.7553	0.759258	0.379629	+	0.925139i	$0.376052\pi$
$678$	−21.3690	−0.820673
$679$	63.2290	2.42651
$680$	−6.11093	−0.234343
$681$	47.3090	1.81289
$682$	3.92700	0.150373
$683$	−11.2425	−0.430181	−0.215090	−	0.976594i	$-0.569005\pi$
$683$	−11.2425	−0.430181	−0.215090	+	0.976594i	$0.569005\pi$
$684$	−1.40410	−0.0536871
$685$	−13.5268	−0.516832
$686$	20.3800	0.778111
$687$	−33.2014	−1.26671
$688$	−12.5688	−0.479179
$689$	−21.6854	−0.826148
$690$	−2.39668	−0.0912401
$691$	15.5094	0.590005	0.295003	−	0.955496i	$-0.404679\pi$
$691$	15.5094	0.590005	0.295003	+	0.955496i	$0.404679\pi$
$692$	4.67939	0.177884
$693$	−2.09968	−0.0797603
$694$	1.10565	0.0419699
$695$	−23.8131	−0.903282
$696$	−2.22433	−0.0843130
$697$	32.9622	1.24853
$698$	−18.6252	−0.704973
$699$	−26.7156	−1.01048
$700$	14.0071	0.529419
$701$	8.20626	0.309946	0.154973	−	0.987919i	$-0.450471\pi$
$701$	8.20626	0.309946	0.154973	+	0.987919i	$0.450471\pi$
$702$	−15.2922	−0.577166
$703$	27.5444	1.03886
$704$	1.86526	0.0702997
$705$	30.2811	1.14045
$706$	−20.9570	−0.788727
$707$	−3.00677	−0.113081
$708$	7.73439	0.290676
$709$	−23.7026	−0.890169	−0.445085	−	0.895489i	$-0.646826\pi$
$709$	−23.7026	−0.890169	−0.445085	+	0.895489i	$0.646826\pi$
$710$	−9.22056	−0.346041
$711$	−0.500573	−0.0187729
$712$	15.2788	0.572597
$713$	−2.10534	−0.0788455
$714$	35.9582	1.34570
$715$	−7.65345	−0.286223
$716$	−9.43241	−0.352506
$717$	−44.2342	−1.65196
$718$	−8.79519	−0.328234
$719$	−2.73616	−0.102041	−0.0510207	−	0.998698i	$-0.516247\pi$
$719$	−2.73616	−0.102041	−0.0510207	+	0.998698i	$0.516247\pi$
$720$	−0.345419	−0.0128730
$721$	35.9232	1.33785
$722$	−10.1122	−0.376337
$723$	20.4247	0.759603
$724$	−23.3758	−0.868753
$725$	3.98906	0.148150
$726$	−13.5796	−0.503988
$727$	−33.0449	−1.22557	−0.612783	−	0.790251i	$-0.709950\pi$
$727$	−33.0449	−1.22557	−0.612783	+	0.790251i	$0.709950\pi$
$728$	13.3716	0.495586
$729$	24.2692	0.898860
$730$	−9.06782	−0.335615
$731$	57.8646	2.14020
$732$	−10.6321	−0.392974
$733$	50.8481	1.87812	0.939059	−	0.343757i	$-0.111700\pi$
$733$	50.8481	1.87812	0.939059	+	0.343757i	$0.111700\pi$
$734$	−14.0713	−0.519382
$735$	28.0685	1.03532
$736$	−1.00000	−0.0368605
$737$	−2.82543	−0.104076
$738$	1.86319	0.0685848
$739$	−35.3951	−1.30203	−0.651015	−	0.759065i	$-0.725657\pi$
$739$	−35.3951	−1.30203	−0.651015	+	0.759065i	$0.725657\pi$
$740$	6.77614	0.249096
$741$	30.1157	1.10633
$742$	−30.3451	−1.11401
$743$	42.6682	1.56534	0.782672	−	0.622434i	$-0.213856\pi$
$743$	42.6682	1.56534	0.782672	+	0.622434i	$0.213856\pi$
$744$	−3.80142	−0.139367
$745$	−1.64497	−0.0602672
$746$	10.6301	0.389197
$747$	−2.11401	−0.0773476
$748$	−8.58738	−0.313986
$749$	84.6142	3.09174
$750$	19.7442	0.720956
$751$	−39.3070	−1.43433	−0.717166	−	0.696902i	$-0.754561\pi$
$751$	−39.3070	−1.43433	−0.717166	+	0.696902i	$0.754561\pi$
$752$	12.6346	0.460737
$753$	−6.79627	−0.247670
$754$	3.80808	0.138682
$755$	−15.2269	−0.554162
$756$	−21.3989	−0.778270
$757$	4.41370	0.160419	0.0802094	−	0.996778i	$-0.474441\pi$
$757$	4.41370	0.160419	0.0802094	+	0.996778i	$0.474441\pi$
$758$	−33.8949	−1.23112
$759$	−3.36794	−0.122248
$760$	−7.16182	−0.259787
$761$	−1.03158	−0.0373948	−0.0186974	−	0.999825i	$-0.505952\pi$
$761$	−1.03158	−0.0373948	−0.0186974	+	0.999825i	$0.505952\pi$
$762$	−9.73116	−0.352523
$763$	−6.14961	−0.222631
$764$	6.09532	0.220521
$765$	1.59026	0.0574959
$766$	−17.2663	−0.623857
$767$	−13.2414	−0.478118
$768$	−1.80561	−0.0651544
$769$	−1.97869	−0.0713535	−0.0356767	−	0.999363i	$-0.511359\pi$
$769$	−1.97869	−0.0713535	−0.0356767	+	0.999363i	$0.511359\pi$
$770$	−10.7097	−0.385952
$771$	−15.4272	−0.555597
$772$	−7.79419	−0.280519
$773$	−15.0376	−0.540864	−0.270432	−	0.962739i	$-0.587167\pi$
$773$	−15.0376	−0.540864	−0.270432	+	0.962739i	$0.587167\pi$
$774$	3.27079	0.117566
$775$	6.81737	0.244887
$776$	14.6172	0.524726
$777$	−39.8726	−1.43042
$778$	30.4112	1.09030
$779$	38.6307	1.38409
$780$	7.40869	0.265274
$781$	−12.9572	−0.463645
$782$	4.60385	0.164633
$783$	−6.09415	−0.217787
$784$	11.7114	0.418264
$785$	5.28820	0.188744
$786$	−1.80561	−0.0644040
$787$	−19.6755	−0.701355	−0.350677	−	0.936496i	$-0.614049\pi$
$787$	−19.6755	−0.701355	−0.350677	+	0.936496i	$0.614049\pi$
$788$	−13.9652	−0.497491
$789$	45.9420	1.63558
$790$	−2.55325	−0.0908404
$791$	51.1934	1.82023
$792$	−0.485401	−0.0172480
$793$	18.2023	0.646383
$794$	17.9691	0.637698
$795$	−16.8130	−0.596297
$796$	9.33175	0.330755
$797$	−45.3541	−1.60652	−0.803262	−	0.595626i	$-0.796904\pi$
$797$	−45.3541	−1.60652	−0.803262	+	0.595626i	$0.796904\pi$
$798$	42.1420	1.49181
$799$	−58.1678	−2.05783
$800$	3.23814	0.114485
$801$	−3.97603	−0.140486
$802$	14.3336	0.506137
$803$	−12.7426	−0.449675
$804$	2.73507	0.0964585
$805$	5.74168	0.202368
$806$	6.50808	0.229237
$807$	40.5942	1.42898
$808$	−0.695099	−0.0244535
$809$	42.9213	1.50903	0.754517	−	0.656281i	$-0.227871\pi$
$809$	42.9213	1.50903	0.754517	+	0.656281i	$0.227871\pi$
$810$	−12.8925	−0.452997
$811$	−16.2139	−0.569347	−0.284674	−	0.958625i	$-0.591885\pi$
$811$	−16.2139	−0.569347	−0.284674	+	0.958625i	$0.591885\pi$
$812$	5.32878	0.187004
$813$	−17.5061	−0.613965
$814$	9.52218	0.333752
$815$	14.0114	0.490799
$816$	8.31276	0.291005
$817$	67.8156	2.37257
$818$	18.9955	0.664161
$819$	−3.47973	−0.121591
$820$	9.50346	0.331875
$821$	−33.4633	−1.16788	−0.583939	−	0.811797i	$-0.698489\pi$
$821$	−33.4633	−1.16788	−0.583939	+	0.811797i	$0.698489\pi$
$822$	18.4006	0.641796
$823$	6.83737	0.238336	0.119168	−	0.992874i	$-0.461977\pi$
$823$	6.83737	0.238336	0.119168	+	0.992874i	$0.461977\pi$
$824$	8.30467	0.289307
$825$	10.9058	0.379693
$826$	−18.5291	−0.644711
$827$	17.7194	0.616163	0.308081	−	0.951360i	$-0.400313\pi$
$827$	17.7194	0.616163	0.308081	+	0.951360i	$0.400313\pi$
$828$	0.260232	0.00904368
$829$	23.4735	0.815268	0.407634	−	0.913145i	$-0.366354\pi$
$829$	23.4735	0.815268	0.407634	+	0.913145i	$0.366354\pi$
$830$	−10.7828	−0.374277
$831$	19.7804	0.686175
$832$	3.09123	0.107169
$833$	−53.9175	−1.86813
$834$	32.3932	1.12168
$835$	−11.6949	−0.404717
$836$	−10.0642	−0.348076
$837$	−10.4150	−0.359995
$838$	21.4193	0.739916
$839$	−29.4810	−1.01780	−0.508899	−	0.860826i	$-0.669947\pi$
$839$	−29.4810	−1.01780	−0.508899	+	0.860826i	$0.669947\pi$
$840$	10.3672	0.357704
$841$	−27.4824	−0.947670
$842$	−35.7201	−1.23100
$843$	7.22326	0.248782
$844$	8.01622	0.275930
$845$	4.57180	0.157275
$846$	−3.28793	−0.113041
$847$	32.5325	1.11783
$848$	−7.01514	−0.240901
$849$	−36.5044	−1.25283
$850$	−14.9079	−0.511337
$851$	−5.10501	−0.174998
$852$	12.5428	0.429710
$853$	1.41702	0.0485178	0.0242589	−	0.999706i	$-0.492277\pi$
$853$	1.41702	0.0485178	0.0242589	+	0.999706i	$0.492277\pi$
$854$	25.4712	0.871605
$855$	1.86373	0.0637384
$856$	19.5610	0.668580
$857$	−56.0332	−1.91406	−0.957029	−	0.289993i	$-0.906347\pi$
$857$	−56.0332	−1.91406	−0.957029	+	0.289993i	$0.906347\pi$
$858$	10.4111	0.355428
$859$	7.04163	0.240257	0.120129	−	0.992758i	$-0.461669\pi$
$859$	7.04163	0.240257	0.120129	+	0.992758i	$0.461669\pi$
$860$	16.6832	0.568891
$861$	−55.9207	−1.90577
$862$	5.92422	0.201780
$863$	23.1308	0.787382	0.393691	−	0.919243i	$-0.371198\pi$
$863$	23.1308	0.787382	0.393691	+	0.919243i	$0.371198\pi$
$864$	−4.94696	−0.168299
$865$	−6.21120	−0.211187
$866$	27.6118	0.938286
$867$	−7.57530	−0.257271
$868$	9.10699	0.309111
$869$	−3.58795	−0.121713
$870$	2.95247	0.100098
$871$	−4.68248	−0.158660
$872$	−1.42166	−0.0481434
$873$	−3.80385	−0.128741
$874$	5.39557	0.182508
$875$	−47.3008	−1.59906
$876$	12.3351	0.416763
$877$	−16.8562	−0.569193	−0.284597	−	0.958647i	$-0.591860\pi$
$877$	−16.8562	−0.569193	−0.284597	+	0.958647i	$0.591860\pi$
$878$	−12.9467	−0.436930
$879$	30.6431	1.03356
$880$	−2.47586	−0.0834612
$881$	−21.9186	−0.738455	−0.369228	−	0.929339i	$-0.620378\pi$
$881$	−21.9186	−0.738455	−0.369228	+	0.929339i	$0.620378\pi$
$882$	−3.04768	−0.102621
$883$	4.35752	0.146642	0.0733212	−	0.997308i	$-0.476640\pi$
$883$	4.35752	0.146642	0.0733212	+	0.997308i	$0.476640\pi$
$884$	−14.2316	−0.478659
$885$	−10.2663	−0.345096
$886$	−32.0407	−1.07643
$887$	27.2783	0.915915	0.457957	−	0.888974i	$-0.348581\pi$
$887$	27.2783	0.915915	0.457957	+	0.888974i	$0.348581\pi$
$888$	−9.21766	−0.309325
$889$	23.3127	0.781884
$890$	−20.2803	−0.679798
$891$	−18.1172	−0.606951
$892$	4.89237	0.163809
$893$	−68.1709	−2.28125
$894$	2.23768	0.0748391
$895$	12.5201	0.418502
$896$	4.32567	0.144510
$897$	−5.58156	−0.186363
$898$	−14.3905	−0.480217
$899$	2.59356	0.0865001
$900$	−0.842667	−0.0280889
$901$	32.2966	1.07596
$902$	13.3547	0.444664
$903$	−98.1679	−3.26682
$904$	11.8348	0.393619
$905$	31.0278	1.03140
$906$	20.7133	0.688152
$907$	−21.6796	−0.719860	−0.359930	−	0.932979i	$-0.617199\pi$
$907$	−21.6796	−0.719860	−0.359930	+	0.932979i	$0.617199\pi$
$908$	−26.2011	−0.869514
$909$	0.180887	0.00599964
$910$	−17.7489	−0.588369
$911$	5.85292	0.193916	0.0969580	−	0.995288i	$-0.469089\pi$
$911$	5.85292	0.193916	0.0969580	+	0.995288i	$0.469089\pi$
$912$	9.74230	0.322600
$913$	−15.1526	−0.501477
$914$	−18.9587	−0.627099
$915$	14.1126	0.466547
$916$	18.3879	0.607554
$917$	4.32567	0.142846
$918$	22.7750	0.751688
$919$	33.3285	1.09941	0.549703	−	0.835360i	$-0.314741\pi$
$919$	33.3285	1.09941	0.549703	+	0.835360i	$0.314741\pi$
$920$	1.32735	0.0437615
$921$	62.0775	2.04552
$922$	12.8900	0.424510
$923$	−21.4735	−0.706808
$924$	14.5686	0.479271
$925$	16.5307	0.543527
$926$	−6.87915	−0.226063
$927$	−2.16114	−0.0709812
$928$	1.23190	0.0404391
$929$	3.80199	0.124739	0.0623697	−	0.998053i	$-0.480134\pi$
$929$	3.80199	0.124739	0.0623697	+	0.998053i	$0.480134\pi$
$930$	5.04582	0.165459
$931$	−63.1897	−2.07096
$932$	14.7959	0.484655
$933$	−23.7636	−0.777985
$934$	36.1072	1.18146
$935$	11.3985	0.372770
$936$	−0.804436	−0.0262938
$937$	5.73284	0.187284	0.0936418	−	0.995606i	$-0.470149\pi$
$937$	5.73284	0.187284	0.0936418	+	0.995606i	$0.470149\pi$
$938$	−6.55236	−0.213942
$939$	−14.6742	−0.478876
$940$	−16.7706	−0.546996
$941$	3.58081	0.116731	0.0583656	−	0.998295i	$-0.481411\pi$
$941$	3.58081	0.116731	0.0583656	+	0.998295i	$0.481411\pi$
$942$	−7.19360	−0.234380
$943$	−7.15971	−0.233152
$944$	−4.28353	−0.139417
$945$	28.4039	0.923977
$946$	23.4440	0.762231
$947$	−2.86742	−0.0931786	−0.0465893	−	0.998914i	$-0.514835\pi$
$947$	−2.86742	−0.0931786	−0.0465893	+	0.998914i	$0.514835\pi$
$948$	3.47321	0.112805
$949$	−21.1178	−0.685512
$950$	−17.4716	−0.566854
$951$	33.7222	1.09352
$952$	−19.9147	−0.645440
$953$	48.6769	1.57680	0.788400	−	0.615163i	$-0.210910\pi$
$953$	48.6769	1.57680	0.788400	+	0.615163i	$0.210910\pi$
$954$	1.82556	0.0591047
$955$	−8.09064	−0.261807
$956$	24.4982	0.792328
$957$	4.14896	0.134117
$958$	26.0091	0.840314
$959$	−44.0821	−1.42348
$960$	2.39668	0.0773526
$961$	−26.5676	−0.857018
$962$	15.7808	0.508792
$963$	−5.09038	−0.164035
$964$	−11.3118	−0.364328
$965$	10.3456	0.333038
$966$	−7.81047	−0.251298
$967$	−30.6244	−0.984815	−0.492408	−	0.870365i	$-0.663883\pi$
$967$	−30.6244	−0.984815	−0.492408	+	0.870365i	$0.663883\pi$
$968$	7.52080	0.241728
$969$	−44.8521	−1.44086
$970$	−19.4021	−0.622965
$971$	33.7515	1.08314	0.541568	−	0.840657i	$-0.317831\pi$
$971$	33.7515	1.08314	0.541568	+	0.840657i	$0.317831\pi$
$972$	2.69699	0.0865059
$973$	−77.6038	−2.48786
$974$	9.30524	0.298159
$975$	18.0739	0.578827
$976$	5.88838	0.188482
$977$	−13.2095	−0.422609	−0.211304	−	0.977420i	$-0.567771\pi$
$977$	−13.2095	−0.422609	−0.211304	+	0.977420i	$0.567771\pi$
$978$	−19.0599	−0.609468
$979$	−28.4990	−0.910830
$980$	−15.5452	−0.496572
$981$	0.369960	0.0118119
$982$	−38.4944	−1.22841
$983$	−24.8987	−0.794144	−0.397072	−	0.917788i	$-0.629974\pi$
$983$	−24.8987	−0.794144	−0.397072	+	0.917788i	$0.629974\pi$
$984$	−12.9277	−0.412119
$985$	18.5368	0.590631
$986$	−5.67147	−0.180617
$987$	98.6823	3.14109
$988$	−16.6789	−0.530628
$989$	−12.5688	−0.399663
$990$	0.644297	0.0204771
$991$	−11.4892	−0.364965	−0.182483	−	0.983209i	$-0.558413\pi$
$991$	−11.4892	−0.364965	−0.182483	+	0.983209i	$0.558413\pi$
$992$	2.10534	0.0668445
$993$	−46.0918	−1.46268
$994$	−30.0486	−0.953084
$995$	−12.3865	−0.392679
$996$	14.6680	0.464773
$997$	−44.7377	−1.41686	−0.708428	−	0.705783i	$-0.750595\pi$
$997$	−44.7377	−1.41686	−0.708428	+	0.705783i	$0.750595\pi$
$998$	−31.4539	−0.995657
$999$	−25.2543	−0.799010

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.j.1.9	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.j.1.9	✓	33	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.80561 q^{3} +1.00000 q^{4} -1.32735 q^{5} +1.80561 q^{6} -4.32567 q^{7} -1.00000 q^{8} +0.260232 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.80561 q^{3} +1.00000 q^{4} -1.32735 q^{5} +1.80561 q^{6} -4.32567 q^{7} -1.00000 q^{8} +0.260232 q^{9} +1.32735 q^{10} +1.86526 q^{11} -1.80561 q^{12} +3.09123 q^{13} +4.32567 q^{14} +2.39668 q^{15} +1.00000 q^{16} -4.60385 q^{17} -0.260232 q^{18} -5.39557 q^{19} -1.32735 q^{20} +7.81047 q^{21} -1.86526 q^{22} +1.00000 q^{23} +1.80561 q^{24} -3.23814 q^{25} -3.09123 q^{26} +4.94696 q^{27} -4.32567 q^{28} -1.23190 q^{29} -2.39668 q^{30} -2.10534 q^{31} -1.00000 q^{32} -3.36794 q^{33} +4.60385 q^{34} +5.74168 q^{35} +0.260232 q^{36} -5.10501 q^{37} +5.39557 q^{38} -5.58156 q^{39} +1.32735 q^{40} -7.15971 q^{41} -7.81047 q^{42} -12.5688 q^{43} +1.86526 q^{44} -0.345419 q^{45} -1.00000 q^{46} +12.6346 q^{47} -1.80561 q^{48} +11.7114 q^{49} +3.23814 q^{50} +8.31276 q^{51} +3.09123 q^{52} -7.01514 q^{53} -4.94696 q^{54} -2.47586 q^{55} +4.32567 q^{56} +9.74230 q^{57} +1.23190 q^{58} -4.28353 q^{59} +2.39668 q^{60} +5.88838 q^{61} +2.10534 q^{62} -1.12568 q^{63} +1.00000 q^{64} -4.10315 q^{65} +3.36794 q^{66} -1.51476 q^{67} -4.60385 q^{68} -1.80561 q^{69} -5.74168 q^{70} -6.94658 q^{71} -0.260232 q^{72} -6.83151 q^{73} +5.10501 q^{74} +5.84682 q^{75} -5.39557 q^{76} -8.06851 q^{77} +5.58156 q^{78} -1.92356 q^{79} -1.32735 q^{80} -9.71298 q^{81} +7.15971 q^{82} -8.12356 q^{83} +7.81047 q^{84} +6.11093 q^{85} +12.5688 q^{86} +2.22433 q^{87} -1.86526 q^{88} -15.2788 q^{89} +0.345419 q^{90} -13.3716 q^{91} +1.00000 q^{92} +3.80142 q^{93} -12.6346 q^{94} +7.16182 q^{95} +1.80561 q^{96} -14.6172 q^{97} -11.7114 q^{98} +0.485401 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9}+O(q^{10}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9} + 4 q^{10} + 5 q^{11} + 3 q^{12} + 15 q^{13} - 11 q^{14} + 16 q^{15} + 33 q^{16} + 2 q^{17} - 44 q^{18} + 32 q^{19} - 4 q^{20} + 8 q^{21} - 5 q^{22} + 33 q^{23} - 3 q^{24} + 49 q^{25} - 15 q^{26} + 15 q^{27} + 11 q^{28} + 20 q^{29} - 16 q^{30} + 25 q^{31} - 33 q^{32} - 6 q^{33} - 2 q^{34} + 15 q^{35} + 44 q^{36} + 6 q^{37} - 32 q^{38} + 25 q^{39} + 4 q^{40} + 2 q^{41} - 8 q^{42} + 31 q^{43} + 5 q^{44} + 2 q^{45} - 33 q^{46} + 4 q^{47} + 3 q^{48} + 72 q^{49} - 49 q^{50} + 26 q^{51} + 15 q^{52} - 65 q^{53} - 15 q^{54} - 4 q^{55} - 11 q^{56} + 12 q^{57} - 20 q^{58} + 8 q^{59} + 16 q^{60} + 23 q^{61} - 25 q^{62} - 14 q^{63} + 33 q^{64} + 5 q^{65} + 6 q^{66} + 31 q^{67} + 2 q^{68} + 3 q^{69} - 15 q^{70} + 20 q^{71} - 44 q^{72} + 22 q^{73} - 6 q^{74} - 32 q^{75} + 32 q^{76} + 2 q^{77} - 25 q^{78} + 53 q^{79} - 4 q^{80} + 17 q^{81} - 2 q^{82} + 45 q^{83} + 8 q^{84} + 60 q^{85} - 31 q^{86} + 11 q^{87} - 5 q^{88} - 54 q^{89} - 2 q^{90} + 38 q^{91} + 33 q^{92} + 63 q^{93} - 4 q^{94} + 44 q^{95} - 3 q^{96} - 72 q^{98} + 43 q^{99}+O(q^{100}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9 + 4 * q^10 + 5 * q^11 + 3 * q^12 + 15 * q^13 - 11 * q^14 + 16 * q^15 + 33 * q^16 + 2 * q^17 - 44 * q^18 + 32 * q^19 - 4 * q^20 + 8 * q^21 - 5 * q^22 + 33 * q^23 - 3 * q^24 + 49 * q^25 - 15 * q^26 + 15 * q^27 + 11 * q^28 + 20 * q^29 - 16 * q^30 + 25 * q^31 - 33 * q^32 - 6 * q^33 - 2 * q^34 + 15 * q^35 + 44 * q^36 + 6 * q^37 - 32 * q^38 + 25 * q^39 + 4 * q^40 + 2 * q^41 - 8 * q^42 + 31 * q^43 + 5 * q^44 + 2 * q^45 - 33 * q^46 + 4 * q^47 + 3 * q^48 + 72 * q^49 - 49 * q^50 + 26 * q^51 + 15 * q^52 - 65 * q^53 - 15 * q^54 - 4 * q^55 - 11 * q^56 + 12 * q^57 - 20 * q^58 + 8 * q^59 + 16 * q^60 + 23 * q^61 - 25 * q^62 - 14 * q^63 + 33 * q^64 + 5 * q^65 + 6 * q^66 + 31 * q^67 + 2 * q^68 + 3 * q^69 - 15 * q^70 + 20 * q^71 - 44 * q^72 + 22 * q^73 - 6 * q^74 - 32 * q^75 + 32 * q^76 + 2 * q^77 - 25 * q^78 + 53 * q^79 - 4 * q^80 + 17 * q^81 - 2 * q^82 + 45 * q^83 + 8 * q^84 + 60 * q^85 - 31 * q^86 + 11 * q^87 - 5 * q^88 - 54 * q^89 - 2 * q^90 + 38 * q^91 + 33 * q^92 + 63 * q^93 - 4 * q^94 + 44 * q^95 - 3 * q^96 - 72 * q^98 + 43 * q^99

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