LMFDB - Embedded newform 6026.2.a.k.1.4

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:	$35$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.88440 q^{3} +1.00000 q^{4} +3.48712 q^{5} -2.88440 q^{6} +4.69814 q^{7} +1.00000 q^{8} +5.31979 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.88440 q^{3} +1.00000 q^{4} +3.48712 q^{5} -2.88440 q^{6} +4.69814 q^{7} +1.00000 q^{8} +5.31979 q^{9} +3.48712 q^{10} -5.17475 q^{11} -2.88440 q^{12} +5.05135 q^{13} +4.69814 q^{14} -10.0583 q^{15} +1.00000 q^{16} -1.47500 q^{17} +5.31979 q^{18} +7.66641 q^{19} +3.48712 q^{20} -13.5513 q^{21} -5.17475 q^{22} -1.00000 q^{23} -2.88440 q^{24} +7.15999 q^{25} +5.05135 q^{26} -6.69120 q^{27} +4.69814 q^{28} -9.46033 q^{29} -10.0583 q^{30} -7.01808 q^{31} +1.00000 q^{32} +14.9261 q^{33} -1.47500 q^{34} +16.3830 q^{35} +5.31979 q^{36} +9.21797 q^{37} +7.66641 q^{38} -14.5701 q^{39} +3.48712 q^{40} +8.24311 q^{41} -13.5513 q^{42} +3.71808 q^{43} -5.17475 q^{44} +18.5507 q^{45} -1.00000 q^{46} +6.46207 q^{47} -2.88440 q^{48} +15.0725 q^{49} +7.15999 q^{50} +4.25449 q^{51} +5.05135 q^{52} +0.950489 q^{53} -6.69120 q^{54} -18.0450 q^{55} +4.69814 q^{56} -22.1130 q^{57} -9.46033 q^{58} +7.62498 q^{59} -10.0583 q^{60} -4.34554 q^{61} -7.01808 q^{62} +24.9931 q^{63} +1.00000 q^{64} +17.6146 q^{65} +14.9261 q^{66} -9.09574 q^{67} -1.47500 q^{68} +2.88440 q^{69} +16.3830 q^{70} -10.9748 q^{71} +5.31979 q^{72} +8.57358 q^{73} +9.21797 q^{74} -20.6523 q^{75} +7.66641 q^{76} -24.3117 q^{77} -14.5701 q^{78} -13.8098 q^{79} +3.48712 q^{80} +3.34077 q^{81} +8.24311 q^{82} +8.06431 q^{83} -13.5513 q^{84} -5.14350 q^{85} +3.71808 q^{86} +27.2874 q^{87} -5.17475 q^{88} -4.46572 q^{89} +18.5507 q^{90} +23.7319 q^{91} -1.00000 q^{92} +20.2430 q^{93} +6.46207 q^{94} +26.7337 q^{95} -2.88440 q^{96} +1.61289 q^{97} +15.0725 q^{98} -27.5286 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) $ 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * 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
$3$	−2.88440	−1.66531	−0.832656	−	0.553791i	$-0.813181\pi$
$3$	−2.88440	−1.66531	−0.832656	+	0.553791i	$0.813181\pi$
$4$	1.00000	0.500000
$5$	3.48712	1.55949	0.779743	−	0.626100i	$-0.215350\pi$
$5$	3.48712	1.55949	0.779743	+	0.626100i	$0.215350\pi$
$6$	−2.88440	−1.17755
$7$	4.69814	1.77573	0.887865	−	0.460104i	$-0.152188\pi$
$7$	4.69814	1.77573	0.887865	+	0.460104i	$0.152188\pi$
$8$	1.00000	0.353553
$9$	5.31979	1.77326
$10$	3.48712	1.10272
$11$	−5.17475	−1.56025	−0.780123	−	0.625626i	$-0.784844\pi$
$11$	−5.17475	−1.56025	−0.780123	+	0.625626i	$0.784844\pi$
$12$	−2.88440	−0.832656
$13$	5.05135	1.40099	0.700496	−	0.713657i	$-0.252962\pi$
$13$	5.05135	1.40099	0.700496	+	0.713657i	$0.252962\pi$
$14$	4.69814	1.25563
$15$	−10.0583	−2.59703
$16$	1.00000	0.250000
$17$	−1.47500	−0.357740	−0.178870	−	0.983873i	$-0.557244\pi$
$17$	−1.47500	−0.357740	−0.178870	+	0.983873i	$0.557244\pi$
$18$	5.31979	1.25389
$19$	7.66641	1.75880	0.879398	−	0.476088i	$-0.157946\pi$
$19$	7.66641	1.75880	0.879398	+	0.476088i	$0.157946\pi$
$20$	3.48712	0.779743
$21$	−13.5513	−2.95714
$22$	−5.17475	−1.10326
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−2.88440	−0.588777
$25$	7.15999	1.43200
$26$	5.05135	0.990650
$27$	−6.69120	−1.28772
$28$	4.69814	0.887865
$29$	−9.46033	−1.75674	−0.878370	−	0.477981i	$-0.841369\pi$
$29$	−9.46033	−1.75674	−0.878370	+	0.477981i	$0.841369\pi$
$30$	−10.0583	−1.83638
$31$	−7.01808	−1.26048	−0.630242	−	0.776399i	$-0.717044\pi$
$31$	−7.01808	−1.26048	−0.630242	+	0.776399i	$0.717044\pi$
$32$	1.00000	0.176777
$33$	14.9261	2.59830
$34$	−1.47500	−0.252960
$35$	16.3830	2.76923
$36$	5.31979	0.886631
$37$	9.21797	1.51543	0.757713	−	0.652588i	$-0.226317\pi$
$37$	9.21797	1.51543	0.757713	+	0.652588i	$0.226317\pi$
$38$	7.66641	1.24366
$39$	−14.5701	−2.33309
$40$	3.48712	0.551362
$41$	8.24311	1.28736	0.643679	−	0.765296i	$-0.277407\pi$
$41$	8.24311	1.28736	0.643679	+	0.765296i	$0.277407\pi$
$42$	−13.5513	−2.09102
$43$	3.71808	0.567002	0.283501	−	0.958972i	$-0.408504\pi$
$43$	3.71808	0.567002	0.283501	+	0.958972i	$0.408504\pi$
$44$	−5.17475	−0.780123
$45$	18.5507	2.76538
$46$	−1.00000	−0.147442
$47$	6.46207	0.942590	0.471295	−	0.881976i	$-0.343787\pi$
$47$	6.46207	0.942590	0.471295	+	0.881976i	$0.343787\pi$
$48$	−2.88440	−0.416328
$49$	15.0725	2.15322
$50$	7.15999	1.01258
$51$	4.25449	0.595748
$52$	5.05135	0.700496
$53$	0.950489	0.130560	0.0652799	−	0.997867i	$-0.479206\pi$
$53$	0.950489	0.130560	0.0652799	+	0.997867i	$0.479206\pi$
$54$	−6.69120	−0.910557
$55$	−18.0450	−2.43318
$56$	4.69814	0.627815
$57$	−22.1130	−2.92894
$58$	−9.46033	−1.24220
$59$	7.62498	0.992688	0.496344	−	0.868126i	$-0.334676\pi$
$59$	7.62498	0.992688	0.496344	+	0.868126i	$0.334676\pi$
$60$	−10.0583	−1.29852
$61$	−4.34554	−0.556389	−0.278195	−	0.960525i	$-0.589736\pi$
$61$	−4.34554	−0.556389	−0.278195	+	0.960525i	$0.589736\pi$
$62$	−7.01808	−0.891297
$63$	24.9931	3.14883
$64$	1.00000	0.125000
$65$	17.6146	2.18483
$66$	14.9261	1.83727
$67$	−9.09574	−1.11122	−0.555611	−	0.831442i	$-0.687516\pi$
$67$	−9.09574	−1.11122	−0.555611	+	0.831442i	$0.687516\pi$
$68$	−1.47500	−0.178870
$69$	2.88440	0.347241
$70$	16.3830	1.95814
$71$	−10.9748	−1.30246	−0.651232	−	0.758878i	$-0.725748\pi$
$71$	−10.9748	−1.30246	−0.651232	+	0.758878i	$0.725748\pi$
$72$	5.31979	0.626943
$73$	8.57358	1.00346	0.501731	−	0.865024i	$-0.332697\pi$
$73$	8.57358	1.00346	0.501731	+	0.865024i	$0.332697\pi$
$74$	9.21797	1.07157
$75$	−20.6523	−2.38472
$76$	7.66641	0.879398
$77$	−24.3117	−2.77058
$78$	−14.5701	−1.64974
$79$	−13.8098	−1.55372	−0.776862	−	0.629671i	$-0.783190\pi$
$79$	−13.8098	−1.55372	−0.776862	+	0.629671i	$0.783190\pi$
$80$	3.48712	0.389872
$81$	3.34077	0.371196
$82$	8.24311	0.910300
$83$	8.06431	0.885173	0.442587	−	0.896726i	$-0.354061\pi$
$83$	8.06431	0.885173	0.442587	+	0.896726i	$0.354061\pi$
$84$	−13.5513	−1.47857
$85$	−5.14350	−0.557890
$86$	3.71808	0.400931
$87$	27.2874	2.92552
$88$	−5.17475	−0.551630
$89$	−4.46572	−0.473365	−0.236683	−	0.971587i	$-0.576060\pi$
$89$	−4.46572	−0.473365	−0.236683	+	0.971587i	$0.576060\pi$
$90$	18.5507	1.95542
$91$	23.7319	2.48778
$92$	−1.00000	−0.104257
$93$	20.2430	2.09910
$94$	6.46207	0.666512
$95$	26.7337	2.74282
$96$	−2.88440	−0.294388
$97$	1.61289	0.163765	0.0818823	−	0.996642i	$-0.473907\pi$
$97$	1.61289	0.163765	0.0818823	+	0.996642i	$0.473907\pi$
$98$	15.0725	1.52255
$99$	−27.5286	−2.76673
$100$	7.15999	0.715999
$101$	−1.47352	−0.146621	−0.0733104	−	0.997309i	$-0.523356\pi$
$101$	−1.47352	−0.146621	−0.0733104	+	0.997309i	$0.523356\pi$
$102$	4.25449	0.421258
$103$	4.97975	0.490669	0.245335	−	0.969438i	$-0.421102\pi$
$103$	4.97975	0.490669	0.245335	+	0.969438i	$0.421102\pi$
$104$	5.05135	0.495325
$105$	−47.2551	−4.61162
$106$	0.950489	0.0923197
$107$	2.15046	0.207892	0.103946	−	0.994583i	$-0.466853\pi$
$107$	2.15046	0.207892	0.103946	+	0.994583i	$0.466853\pi$
$108$	−6.69120	−0.643861
$109$	−0.0674336	−0.00645897	−0.00322948	−	0.999995i	$-0.501028\pi$
$109$	−0.0674336	−0.00645897	−0.00322948	+	0.999995i	$0.501028\pi$
$110$	−18.0450	−1.72052
$111$	−26.5884	−2.52365
$112$	4.69814	0.443932
$113$	−3.52507	−0.331611	−0.165805	−	0.986159i	$-0.553022\pi$
$113$	−3.52507	−0.331611	−0.165805	+	0.986159i	$0.553022\pi$
$114$	−22.1130	−2.07107
$115$	−3.48712	−0.325175
$116$	−9.46033	−0.878370
$117$	26.8721	2.48432
$118$	7.62498	0.701936
$119$	−6.92975	−0.635249
$120$	−10.0583	−0.918189
$121$	15.7781	1.43437
$122$	−4.34554	−0.393427
$123$	−23.7765	−2.14385
$124$	−7.01808	−0.630242
$125$	7.53213	0.673694
$126$	24.9931	2.22656
$127$	−9.81277	−0.870742	−0.435371	−	0.900251i	$-0.643383\pi$
$127$	−9.81277	−0.870742	−0.435371	+	0.900251i	$0.643383\pi$
$128$	1.00000	0.0883883
$129$	−10.7244	−0.944235
$130$	17.6146	1.54491
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	14.9261	1.29915
$133$	36.0179	3.12315
$134$	−9.09574	−0.785752
$135$	−23.3330	−2.00819
$136$	−1.47500	−0.126480
$137$	18.6735	1.59538	0.797692	−	0.603065i	$-0.206054\pi$
$137$	18.6735	1.59538	0.797692	+	0.603065i	$0.206054\pi$
$138$	2.88440	0.245537
$139$	−12.9517	−1.09855	−0.549273	−	0.835643i	$-0.685095\pi$
$139$	−12.9517	−1.09855	−0.549273	+	0.835643i	$0.685095\pi$
$140$	16.3830	1.38461
$141$	−18.6392	−1.56971
$142$	−10.9748	−0.920982
$143$	−26.1395	−2.18589
$144$	5.31979	0.443316
$145$	−32.9893	−2.73961
$146$	8.57358	0.709555
$147$	−43.4752	−3.58578
$148$	9.21797	0.757713
$149$	−23.3837	−1.91566	−0.957832	−	0.287329i	$-0.907233\pi$
$149$	−23.3837	−1.91566	−0.957832	+	0.287329i	$0.907233\pi$
$150$	−20.6523	−1.68625
$151$	11.6945	0.951685	0.475843	−	0.879530i	$-0.342143\pi$
$151$	11.6945	0.951685	0.475843	+	0.879530i	$0.342143\pi$
$152$	7.66641	0.621828
$153$	−7.84668	−0.634367
$154$	−24.3117	−1.95909
$155$	−24.4729	−1.96571
$156$	−14.5701	−1.16654
$157$	−5.91928	−0.472410	−0.236205	−	0.971703i	$-0.575904\pi$
$157$	−5.91928	−0.472410	−0.236205	+	0.971703i	$0.575904\pi$
$158$	−13.8098	−1.09865
$159$	−2.74160	−0.217423
$160$	3.48712	0.275681
$161$	−4.69814	−0.370265
$162$	3.34077	0.262476
$163$	−6.47775	−0.507377	−0.253688	−	0.967286i	$-0.581644\pi$
$163$	−6.47775	−0.507377	−0.253688	+	0.967286i	$0.581644\pi$
$164$	8.24311	0.643679
$165$	52.0490	4.05201
$166$	8.06431	0.625912
$167$	−24.7385	−1.91432	−0.957162	−	0.289552i	$-0.906494\pi$
$167$	−24.7385	−1.91432	−0.957162	+	0.289552i	$0.906494\pi$
$168$	−13.5513	−1.04551
$169$	12.5161	0.962776
$170$	−5.14350	−0.394488
$171$	40.7837	3.11881
$172$	3.71808	0.283501
$173$	23.6063	1.79475	0.897377	−	0.441265i	$-0.145470\pi$
$173$	23.6063	1.79475	0.897377	+	0.441265i	$0.145470\pi$
$174$	27.2874	2.06865
$175$	33.6386	2.54284
$176$	−5.17475	−0.390062
$177$	−21.9935	−1.65313
$178$	−4.46572	−0.334720
$179$	−25.7858	−1.92732	−0.963662	−	0.267125i	$-0.913926\pi$
$179$	−25.7858	−1.92732	−0.963662	+	0.267125i	$0.913926\pi$
$180$	18.5507	1.38269
$181$	−14.7721	−1.09800	−0.549001	−	0.835822i	$-0.684992\pi$
$181$	−14.7721	−1.09800	−0.549001	+	0.835822i	$0.684992\pi$
$182$	23.7319	1.75913
$183$	12.5343	0.926561
$184$	−1.00000	−0.0737210
$185$	32.1441	2.36328
$186$	20.2430	1.48429
$187$	7.63275	0.558162
$188$	6.46207	0.471295
$189$	−31.4362	−2.28665
$190$	26.7337	1.93946
$191$	−16.1448	−1.16820	−0.584099	−	0.811683i	$-0.698552\pi$
$191$	−16.1448	−1.16820	−0.584099	+	0.811683i	$0.698552\pi$
$192$	−2.88440	−0.208164
$193$	8.53483	0.614351	0.307175	−	0.951653i	$-0.400616\pi$
$193$	8.53483	0.614351	0.307175	+	0.951653i	$0.400616\pi$
$194$	1.61289	0.115799
$195$	−50.8077	−3.63842
$196$	15.0725	1.07661
$197$	19.4198	1.38361	0.691803	−	0.722086i	$-0.256817\pi$
$197$	19.4198	1.38361	0.691803	+	0.722086i	$0.256817\pi$
$198$	−27.5286	−1.95637
$199$	19.4957	1.38202	0.691008	−	0.722847i	$-0.257167\pi$
$199$	19.4957	1.38202	0.691008	+	0.722847i	$0.257167\pi$
$200$	7.15999	0.506288
$201$	26.2358	1.85053
$202$	−1.47352	−0.103677
$203$	−44.4460	−3.11950
$204$	4.25449	0.297874
$205$	28.7447	2.00762
$206$	4.97975	0.346956
$207$	−5.31979	−0.369751
$208$	5.05135	0.350248
$209$	−39.6718	−2.74415
$210$	−47.2551	−3.26091
$211$	−10.1841	−0.701101	−0.350550	−	0.936544i	$-0.614005\pi$
$211$	−10.1841	−0.701101	−0.350550	+	0.936544i	$0.614005\pi$
$212$	0.950489	0.0652799
$213$	31.6556	2.16901
$214$	2.15046	0.147002
$215$	12.9654	0.884232
$216$	−6.69120	−0.455279
$217$	−32.9719	−2.23828
$218$	−0.0674336	−0.00456718
$219$	−24.7297	−1.67108
$220$	−18.0450	−1.21659
$221$	−7.45073	−0.501190
$222$	−26.5884	−1.78449
$223$	11.0845	0.742274	0.371137	−	0.928578i	$-0.378968\pi$
$223$	11.0845	0.742274	0.371137	+	0.928578i	$0.378968\pi$
$224$	4.69814	0.313908
$225$	38.0896	2.53931
$226$	−3.52507	−0.234484
$227$	12.0036	0.796708	0.398354	−	0.917232i	$-0.369582\pi$
$227$	12.0036	0.796708	0.398354	+	0.917232i	$0.369582\pi$
$228$	−22.1130	−1.46447
$229$	18.4340	1.21815	0.609075	−	0.793112i	$-0.291541\pi$
$229$	18.4340	1.21815	0.609075	+	0.793112i	$0.291541\pi$
$230$	−3.48712	−0.229934
$231$	70.1248	4.61387
$232$	−9.46033	−0.621101
$233$	−17.1880	−1.12603	−0.563013	−	0.826448i	$-0.690358\pi$
$233$	−17.1880	−1.12603	−0.563013	+	0.826448i	$0.690358\pi$
$234$	26.8721	1.75668
$235$	22.5340	1.46996
$236$	7.62498	0.496344
$237$	39.8330	2.58743
$238$	−6.92975	−0.449189
$239$	−1.65203	−0.106861	−0.0534304	−	0.998572i	$-0.517016\pi$
$239$	−1.65203	−0.106861	−0.0534304	+	0.998572i	$0.517016\pi$
$240$	−10.0583	−0.649258
$241$	4.17573	0.268983	0.134491	−	0.990915i	$-0.457060\pi$
$241$	4.17573	0.268983	0.134491	+	0.990915i	$0.457060\pi$
$242$	15.7781	1.01425
$243$	10.4375	0.669565
$244$	−4.34554	−0.278195
$245$	52.5596	3.35791
$246$	−23.7765	−1.51593
$247$	38.7257	2.46406
$248$	−7.01808	−0.445648
$249$	−23.2607	−1.47409
$250$	7.53213	0.476374
$251$	5.78251	0.364989	0.182494	−	0.983207i	$-0.441583\pi$
$251$	5.78251	0.364989	0.182494	+	0.983207i	$0.441583\pi$
$252$	24.9931	1.57442
$253$	5.17475	0.325334
$254$	−9.81277	−0.615708
$255$	14.8359	0.929061
$256$	1.00000	0.0625000
$257$	23.3185	1.45457	0.727285	−	0.686335i	$-0.240782\pi$
$257$	23.3185	1.45457	0.727285	+	0.686335i	$0.240782\pi$
$258$	−10.7244	−0.667675
$259$	43.3073	2.69099
$260$	17.6146	1.09241
$261$	−50.3270	−3.11516
$262$	−1.00000	−0.0617802
$263$	−3.75989	−0.231845	−0.115922	−	0.993258i	$-0.536982\pi$
$263$	−3.75989	−0.231845	−0.115922	+	0.993258i	$0.536982\pi$
$264$	14.9261	0.918636
$265$	3.31447	0.203606
$266$	36.0179	2.20840
$267$	12.8809	0.788301
$268$	−9.09574	−0.555611
$269$	−14.9400	−0.910909	−0.455454	−	0.890259i	$-0.650523\pi$
$269$	−14.9400	−0.910909	−0.455454	+	0.890259i	$0.650523\pi$
$270$	−23.3330	−1.42000
$271$	12.1012	0.735093	0.367547	−	0.930005i	$-0.380198\pi$
$271$	12.1012	0.735093	0.367547	+	0.930005i	$0.380198\pi$
$272$	−1.47500	−0.0894350
$273$	−68.4525	−4.14293
$274$	18.6735	1.12811
$275$	−37.0512	−2.23427
$276$	2.88440	0.173621
$277$	−10.2890	−0.618207	−0.309103	−	0.951028i	$-0.600029\pi$
$277$	−10.2890	−0.618207	−0.309103	+	0.951028i	$0.600029\pi$
$278$	−12.9517	−0.776789
$279$	−37.3347	−2.23517
$280$	16.3830	0.979069
$281$	25.7684	1.53721	0.768607	−	0.639722i	$-0.220950\pi$
$281$	25.7684	1.53721	0.768607	+	0.639722i	$0.220950\pi$
$282$	−18.6392	−1.10995
$283$	15.3170	0.910504	0.455252	−	0.890363i	$-0.349549\pi$
$283$	15.3170	0.910504	0.455252	+	0.890363i	$0.349549\pi$
$284$	−10.9748	−0.651232
$285$	−77.1107	−4.56765
$286$	−26.1395	−1.54566
$287$	38.7273	2.28600
$288$	5.31979	0.313471
$289$	−14.8244	−0.872022
$290$	−32.9893	−1.93720
$291$	−4.65224	−0.272719
$292$	8.57358	0.501731
$293$	5.65770	0.330527	0.165263	−	0.986249i	$-0.447153\pi$
$293$	5.65770	0.330527	0.165263	+	0.986249i	$0.447153\pi$
$294$	−43.4752	−2.53553
$295$	26.5892	1.54808
$296$	9.21797	0.535784
$297$	34.6253	2.00916
$298$	−23.3837	−1.35458
$299$	−5.05135	−0.292127
$300$	−20.6523	−1.19236
$301$	17.4681	1.00684
$302$	11.6945	0.672943
$303$	4.25023	0.244169
$304$	7.66641	0.439699
$305$	−15.1534	−0.867681
$306$	−7.84668	−0.448565
$307$	7.28552	0.415807	0.207903	−	0.978149i	$-0.433336\pi$
$307$	7.28552	0.415807	0.207903	+	0.978149i	$0.433336\pi$
$308$	−24.3117	−1.38529
$309$	−14.3636	−0.817117
$310$	−24.4729	−1.38996
$311$	−8.22899	−0.466623	−0.233312	−	0.972402i	$-0.574956\pi$
$311$	−8.22899	−0.466623	−0.233312	+	0.972402i	$0.574956\pi$
$312$	−14.5701	−0.824871
$313$	15.3300	0.866502	0.433251	−	0.901273i	$-0.357366\pi$
$313$	15.3300	0.866502	0.433251	+	0.901273i	$0.357366\pi$
$314$	−5.91928	−0.334044
$315$	87.1539	4.91056
$316$	−13.8098	−0.776862
$317$	−32.8047	−1.84250	−0.921249	−	0.388975i	$-0.872829\pi$
$317$	−32.8047	−1.84250	−0.921249	+	0.388975i	$0.872829\pi$
$318$	−2.74160	−0.153741
$319$	48.9549	2.74095
$320$	3.48712	0.194936
$321$	−6.20278	−0.346206
$322$	−4.69814	−0.261817
$323$	−11.3080	−0.629191
$324$	3.34077	0.185598
$325$	36.1676	2.00622
$326$	−6.47775	−0.358770
$327$	0.194506	0.0107562
$328$	8.24311	0.455150
$329$	30.3597	1.67379
$330$	52.0490	2.86520
$331$	−22.6274	−1.24372	−0.621859	−	0.783130i	$-0.713622\pi$
$331$	−22.6274	−1.24372	−0.621859	+	0.783130i	$0.713622\pi$
$332$	8.06431	0.442587
$333$	49.0376	2.68725
$334$	−24.7385	−1.35363
$335$	−31.7179	−1.73293
$336$	−13.5513	−0.739286
$337$	−16.8756	−0.919270	−0.459635	−	0.888108i	$-0.652020\pi$
$337$	−16.8756	−0.919270	−0.459635	+	0.888108i	$0.652020\pi$
$338$	12.5161	0.680785
$339$	10.1677	0.552235
$340$	−5.14350	−0.278945
$341$	36.3168	1.96667
$342$	40.7837	2.20533
$343$	37.9258	2.04780
$344$	3.71808	0.200465
$345$	10.0583	0.541518
$346$	23.6063	1.26908
$347$	4.82688	0.259121	0.129560	−	0.991572i	$-0.458643\pi$
$347$	4.82688	0.259121	0.129560	+	0.991572i	$0.458643\pi$
$348$	27.2874	1.46276
$349$	22.6374	1.21175	0.605875	−	0.795560i	$-0.292823\pi$
$349$	22.6374	1.21175	0.605875	+	0.795560i	$0.292823\pi$
$350$	33.6386	1.79806
$351$	−33.7996	−1.80409
$352$	−5.17475	−0.275815
$353$	−9.27487	−0.493652	−0.246826	−	0.969060i	$-0.579388\pi$
$353$	−9.27487	−0.493652	−0.246826	+	0.969060i	$0.579388\pi$
$354$	−21.9935	−1.16894
$355$	−38.2703	−2.03118
$356$	−4.46572	−0.236683
$357$	19.9882	1.05789
$358$	−25.7858	−1.36282
$359$	−12.8102	−0.676098	−0.338049	−	0.941128i	$-0.609767\pi$
$359$	−12.8102	−0.676098	−0.338049	+	0.941128i	$0.609767\pi$
$360$	18.5507	0.977709
$361$	39.7739	2.09336
$362$	−14.7721	−0.776404
$363$	−45.5103	−2.38867
$364$	23.7319	1.24389
$365$	29.8971	1.56488
$366$	12.5343	0.655178
$367$	10.5468	0.550537	0.275268	−	0.961367i	$-0.411233\pi$
$367$	10.5468	0.550537	0.275268	+	0.961367i	$0.411233\pi$
$368$	−1.00000	−0.0521286
$369$	43.8516	2.28282
$370$	32.1441	1.67109
$371$	4.46553	0.231839
$372$	20.2430	1.04955
$373$	−30.3417	−1.57103	−0.785517	−	0.618840i	$-0.787603\pi$
$373$	−30.3417	−1.57103	−0.785517	+	0.618840i	$0.787603\pi$
$374$	7.63275	0.394680
$375$	−21.7257	−1.12191
$376$	6.46207	0.333256
$377$	−47.7874	−2.46118
$378$	−31.4362	−1.61690
$379$	−6.44165	−0.330885	−0.165443	−	0.986219i	$-0.552905\pi$
$379$	−6.44165	−0.330885	−0.165443	+	0.986219i	$0.552905\pi$
$380$	26.7337	1.37141
$381$	28.3040	1.45006
$382$	−16.1448	−0.826040
$383$	1.85812	0.0949455	0.0474728	−	0.998873i	$-0.484883\pi$
$383$	1.85812	0.0949455	0.0474728	+	0.998873i	$0.484883\pi$
$384$	−2.88440	−0.147194
$385$	−84.7778	−4.32068
$386$	8.53483	0.434412
$387$	19.7794	1.00544
$388$	1.61289	0.0818823
$389$	−9.17898	−0.465393	−0.232696	−	0.972549i	$-0.574755\pi$
$389$	−9.17898	−0.465393	−0.232696	+	0.972549i	$0.574755\pi$
$390$	−50.8077	−2.57275
$391$	1.47500	0.0745939
$392$	15.0725	0.761277
$393$	2.88440	0.145499
$394$	19.4198	0.978357
$395$	−48.1564	−2.42301
$396$	−27.5286	−1.38336
$397$	14.6507	0.735299	0.367650	−	0.929964i	$-0.380163\pi$
$397$	14.6507	0.735299	0.367650	+	0.929964i	$0.380163\pi$
$398$	19.4957	0.977233
$399$	−103.890	−5.20101
$400$	7.15999	0.357999
$401$	27.4417	1.37037	0.685187	−	0.728367i	$-0.259720\pi$
$401$	27.4417	1.37037	0.685187	+	0.728367i	$0.259720\pi$
$402$	26.2358	1.30852
$403$	−35.4507	−1.76593
$404$	−1.47352	−0.0733104
$405$	11.6497	0.578876
$406$	−44.4460	−2.20582
$407$	−47.7007	−2.36444
$408$	4.25449	0.210629
$409$	−0.608772	−0.0301018	−0.0150509	−	0.999887i	$-0.504791\pi$
$409$	−0.608772	−0.0301018	−0.0150509	+	0.999887i	$0.504791\pi$
$410$	28.7447	1.41960
$411$	−53.8619	−2.65681
$412$	4.97975	0.245335
$413$	35.8232	1.76274
$414$	−5.31979	−0.261453
$415$	28.1212	1.38042
$416$	5.05135	0.247663
$417$	37.3578	1.82942
$418$	−39.6718	−1.94041
$419$	−7.97892	−0.389796	−0.194898	−	0.980824i	$-0.562438\pi$
$419$	−7.97892	−0.389796	−0.194898	+	0.980824i	$0.562438\pi$
$420$	−47.2551	−2.30581
$421$	−7.09547	−0.345812	−0.172906	−	0.984938i	$-0.555316\pi$
$421$	−7.09547	−0.345812	−0.172906	+	0.984938i	$0.555316\pi$
$422$	−10.1841	−0.495753
$423$	34.3768	1.67146
$424$	0.950489	0.0461598
$425$	−10.5610	−0.512283
$426$	31.6556	1.53372
$427$	−20.4159	−0.987997
$428$	2.15046	0.103946
$429$	75.3968	3.64019
$430$	12.9654	0.625246
$431$	18.8478	0.907867	0.453933	−	0.891036i	$-0.350020\pi$
$431$	18.8478	0.907867	0.453933	+	0.891036i	$0.350020\pi$
$432$	−6.69120	−0.321931
$433$	20.9324	1.00595	0.502974	−	0.864302i	$-0.332239\pi$
$433$	20.9324	1.00595	0.502974	+	0.864302i	$0.332239\pi$
$434$	−32.9719	−1.58270
$435$	95.1545	4.56231
$436$	−0.0674336	−0.00322948
$437$	−7.66641	−0.366734
$438$	−24.7297	−1.18163
$439$	3.62798	0.173154	0.0865771	−	0.996245i	$-0.472407\pi$
$439$	3.62798	0.173154	0.0865771	+	0.996245i	$0.472407\pi$
$440$	−18.0450	−0.860260
$441$	80.1826	3.81822
$442$	−7.45073	−0.354395
$443$	−17.0529	−0.810208	−0.405104	−	0.914271i	$-0.632765\pi$
$443$	−17.0529	−0.810208	−0.405104	+	0.914271i	$0.632765\pi$
$444$	−26.5884	−1.26183
$445$	−15.5725	−0.738207
$446$	11.0845	0.524867
$447$	67.4479	3.19018
$448$	4.69814	0.221966
$449$	3.35788	0.158468	0.0792342	−	0.996856i	$-0.474753\pi$
$449$	3.35788	0.158468	0.0792342	+	0.996856i	$0.474753\pi$
$450$	38.0896	1.79556
$451$	−42.6561	−2.00860
$452$	−3.52507	−0.165805
$453$	−33.7317	−1.58485
$454$	12.0036	0.563358
$455$	82.7560	3.87966
$456$	−22.1130	−1.03554
$457$	16.5243	0.772972	0.386486	−	0.922295i	$-0.373689\pi$
$457$	16.5243	0.772972	0.386486	+	0.922295i	$0.373689\pi$
$458$	18.4340	0.861363
$459$	9.86952	0.460670
$460$	−3.48712	−0.162588
$461$	2.99792	0.139627	0.0698136	−	0.997560i	$-0.477760\pi$
$461$	2.99792	0.139627	0.0698136	+	0.997560i	$0.477760\pi$
$462$	70.1248	3.26250
$463$	12.7839	0.594117	0.297058	−	0.954859i	$-0.403994\pi$
$463$	12.7839	0.594117	0.297058	+	0.954859i	$0.403994\pi$
$464$	−9.46033	−0.439185
$465$	70.5896	3.27351
$466$	−17.1880	−0.796221
$467$	17.3021	0.800646	0.400323	−	0.916374i	$-0.368898\pi$
$467$	17.3021	0.800646	0.400323	+	0.916374i	$0.368898\pi$
$468$	26.8721	1.24216
$469$	−42.7331	−1.97323
$470$	22.5340	1.03942
$471$	17.0736	0.786710
$472$	7.62498	0.350968
$473$	−19.2401	−0.884663
$474$	39.8330	1.82959
$475$	54.8914	2.51859
$476$	−6.92975	−0.317625
$477$	5.05640	0.231517
$478$	−1.65203	−0.0755620
$479$	23.1313	1.05690	0.528449	−	0.848965i	$-0.322774\pi$
$479$	23.1313	1.05690	0.528449	+	0.848965i	$0.322774\pi$
$480$	−10.0583	−0.459094
$481$	46.5632	2.12310
$482$	4.17573	0.190199
$483$	13.5513	0.616607
$484$	15.7781	0.717184
$485$	5.62435	0.255389
$486$	10.4375	0.473454
$487$	4.17670	0.189265	0.0946323	−	0.995512i	$-0.469832\pi$
$487$	4.17670	0.189265	0.0946323	+	0.995512i	$0.469832\pi$
$488$	−4.34554	−0.196713
$489$	18.6845	0.844940
$490$	52.5596	2.37440
$491$	−9.79872	−0.442210	−0.221105	−	0.975250i	$-0.570966\pi$
$491$	−9.79872	−0.442210	−0.221105	+	0.975250i	$0.570966\pi$
$492$	−23.7765	−1.07193
$493$	13.9540	0.628456
$494$	38.7257	1.74235
$495$	−95.9954	−4.31467
$496$	−7.01808	−0.315121
$497$	−51.5610	−2.31283
$498$	−23.2607	−1.04234
$499$	−15.0016	−0.671565	−0.335783	−	0.941940i	$-0.609001\pi$
$499$	−15.0016	−0.671565	−0.335783	+	0.941940i	$0.609001\pi$
$500$	7.53213	0.336847
$501$	71.3559	3.18795
$502$	5.78251	0.258086
$503$	−12.6818	−0.565455	−0.282728	−	0.959200i	$-0.591239\pi$
$503$	−12.6818	−0.565455	−0.282728	+	0.959200i	$0.591239\pi$
$504$	24.9931	1.11328
$505$	−5.13834	−0.228653
$506$	5.17475	0.230046
$507$	−36.1015	−1.60332
$508$	−9.81277	−0.435371
$509$	17.9547	0.795827	0.397913	−	0.917423i	$-0.369734\pi$
$509$	17.9547	0.795827	0.397913	+	0.917423i	$0.369734\pi$
$510$	14.8359	0.656945
$511$	40.2799	1.78188
$512$	1.00000	0.0441942
$513$	−51.2975	−2.26484
$514$	23.3185	1.02854
$515$	17.3650	0.765192
$516$	−10.7244	−0.472117
$517$	−33.4396	−1.47067
$518$	43.3073	1.90281
$519$	−68.0901	−2.98882
$520$	17.6146	0.772453
$521$	−7.88500	−0.345448	−0.172724	−	0.984970i	$-0.555257\pi$
$521$	−7.88500	−0.345448	−0.172724	+	0.984970i	$0.555257\pi$
$522$	−50.3270	−2.20275
$523$	14.5674	0.636989	0.318494	−	0.947925i	$-0.396823\pi$
$523$	14.5674	0.636989	0.318494	+	0.947925i	$0.396823\pi$
$524$	−1.00000	−0.0436852
$525$	−97.0274	−4.23462
$526$	−3.75989	−0.163939
$527$	10.3517	0.450925
$528$	14.9261	0.649574
$529$	1.00000	0.0434783
$530$	3.31447	0.143971
$531$	40.5633	1.76030
$532$	36.0179	1.56157
$533$	41.6388	1.80358
$534$	12.8809	0.557413
$535$	7.49889	0.324205
$536$	−9.09574	−0.392876
$537$	74.3768	3.20959
$538$	−14.9400	−0.644110
$539$	−77.9965	−3.35955
$540$	−23.3330	−1.00409
$541$	9.82818	0.422547	0.211273	−	0.977427i	$-0.432239\pi$
$541$	9.82818	0.422547	0.211273	+	0.977427i	$0.432239\pi$
$542$	12.1012	0.519789
$543$	42.6087	1.82851
$544$	−1.47500	−0.0632401
$545$	−0.235149	−0.0100727
$546$	−68.4525	−2.92949
$547$	38.1586	1.63154	0.815772	−	0.578374i	$-0.196313\pi$
$547$	38.1586	1.63154	0.815772	+	0.578374i	$0.196313\pi$
$548$	18.6735	0.797692
$549$	−23.1173	−0.986624
$550$	−37.0512	−1.57987
$551$	−72.5268	−3.08975
$552$	2.88440	0.122768
$553$	−64.8803	−2.75899
$554$	−10.2890	−0.437138
$555$	−92.7167	−3.93560
$556$	−12.9517	−0.549273
$557$	−3.43045	−0.145353	−0.0726765	−	0.997356i	$-0.523154\pi$
$557$	−3.43045	−0.145353	−0.0726765	+	0.997356i	$0.523154\pi$
$558$	−37.3347	−1.58050
$559$	18.7813	0.794365
$560$	16.3830	0.692307
$561$	−22.0159	−0.929514
$562$	25.7684	1.08697
$563$	−40.1191	−1.69082	−0.845409	−	0.534119i	$-0.820643\pi$
$563$	−40.1191	−1.69082	−0.845409	+	0.534119i	$0.820643\pi$
$564$	−18.6392	−0.784853
$565$	−12.2923	−0.517142
$566$	15.3170	0.643824
$567$	15.6954	0.659145
$568$	−10.9748	−0.460491
$569$	−32.1013	−1.34575	−0.672877	−	0.739754i	$-0.734942\pi$
$569$	−32.1013	−1.34575	−0.672877	+	0.739754i	$0.734942\pi$
$570$	−77.1107	−3.22981
$571$	−21.3778	−0.894633	−0.447316	−	0.894376i	$-0.647620\pi$
$571$	−21.3778	−0.894633	−0.447316	+	0.894376i	$0.647620\pi$
$572$	−26.1395	−1.09295
$573$	46.5682	1.94541
$574$	38.7273	1.61645
$575$	−7.15999	−0.298592
$576$	5.31979	0.221658
$577$	−24.3048	−1.01182	−0.505911	−	0.862586i	$-0.668843\pi$
$577$	−24.3048	−1.01182	−0.505911	+	0.862586i	$0.668843\pi$
$578$	−14.8244	−0.616613
$579$	−24.6179	−1.02309
$580$	−32.9893	−1.36981
$581$	37.8873	1.57183
$582$	−4.65224	−0.192842
$583$	−4.91855	−0.203705
$584$	8.57358	0.354777
$585$	93.7061	3.87427
$586$	5.65770	0.233718
$587$	36.2893	1.49782	0.748911	−	0.662671i	$-0.230577\pi$
$587$	36.2893	1.49782	0.748911	+	0.662671i	$0.230577\pi$
$588$	−43.4752	−1.79289
$589$	−53.8035	−2.21693
$590$	26.5892	1.09466
$591$	−56.0147	−2.30413
$592$	9.21797	0.378856
$593$	−4.08887	−0.167910	−0.0839549	−	0.996470i	$-0.526755\pi$
$593$	−4.08887	−0.167910	−0.0839549	+	0.996470i	$0.526755\pi$
$594$	34.6253	1.42069
$595$	−24.1649	−0.990663
$596$	−23.3837	−0.957832
$597$	−56.2336	−2.30149
$598$	−5.05135	−0.206565
$599$	12.8439	0.524787	0.262394	−	0.964961i	$-0.415488\pi$
$599$	12.8439	0.524787	0.262394	+	0.964961i	$0.415488\pi$
$600$	−20.6523	−0.843126
$601$	−2.80479	−0.114410	−0.0572048	−	0.998362i	$-0.518219\pi$
$601$	−2.80479	−0.114410	−0.0572048	+	0.998362i	$0.518219\pi$
$602$	17.4681	0.711945
$603$	−48.3874	−1.97049
$604$	11.6945	0.475843
$605$	55.0199	2.23688
$606$	4.25023	0.172654
$607$	−7.62978	−0.309683	−0.154842	−	0.987939i	$-0.549487\pi$
$607$	−7.62978	−0.309683	−0.154842	+	0.987939i	$0.549487\pi$
$608$	7.66641	0.310914
$609$	128.200	5.19493
$610$	−15.1534	−0.613543
$611$	32.6422	1.32056
$612$	−7.84668	−0.317183
$613$	26.0357	1.05157	0.525786	−	0.850617i	$-0.323771\pi$
$613$	26.0357	1.05157	0.525786	+	0.850617i	$0.323771\pi$
$614$	7.28552	0.294020
$615$	−82.9113	−3.34331
$616$	−24.3117	−0.979547
$617$	47.5545	1.91447	0.957235	−	0.289311i	$-0.0934261\pi$
$617$	47.5545	1.91447	0.957235	+	0.289311i	$0.0934261\pi$
$618$	−14.3636	−0.577789
$619$	−5.75794	−0.231431	−0.115716	−	0.993282i	$-0.536916\pi$
$619$	−5.75794	−0.231431	−0.115716	+	0.993282i	$0.536916\pi$
$620$	−24.4729	−0.982854
$621$	6.69120	0.268509
$622$	−8.22899	−0.329953
$623$	−20.9806	−0.840569
$624$	−14.5701	−0.583272
$625$	−9.53452	−0.381381
$626$	15.3300	0.612709
$627$	114.429	4.56987
$628$	−5.91928	−0.236205
$629$	−13.5965	−0.542128
$630$	87.1539	3.47229
$631$	−33.2493	−1.32363	−0.661817	−	0.749665i	$-0.730214\pi$
$631$	−33.2493	−1.32363	−0.661817	+	0.749665i	$0.730214\pi$
$632$	−13.8098	−0.549324
$633$	29.3750	1.16755
$634$	−32.8047	−1.30284
$635$	−34.2183	−1.35791
$636$	−2.74160	−0.108711
$637$	76.1365	3.01664
$638$	48.9549	1.93814
$639$	−58.3834	−2.30961
$640$	3.48712	0.137840
$641$	−29.3538	−1.15940	−0.579702	−	0.814828i	$-0.696831\pi$
$641$	−29.3538	−1.15940	−0.579702	+	0.814828i	$0.696831\pi$
$642$	−6.20278	−0.244804
$643$	−43.8045	−1.72748	−0.863740	−	0.503937i	$-0.831884\pi$
$643$	−43.8045	−1.72748	−0.863740	+	0.503937i	$0.831884\pi$
$644$	−4.69814	−0.185133
$645$	−37.3974	−1.47252
$646$	−11.3080	−0.444905
$647$	35.3008	1.38782	0.693909	−	0.720063i	$-0.255887\pi$
$647$	35.3008	1.38782	0.693909	+	0.720063i	$0.255887\pi$
$648$	3.34077	0.131238
$649$	−39.4574	−1.54884
$650$	36.1676	1.41861
$651$	95.1043	3.72743
$652$	−6.47775	−0.253688
$653$	26.9151	1.05327	0.526635	−	0.850092i	$-0.323454\pi$
$653$	26.9151	1.05327	0.526635	+	0.850092i	$0.323454\pi$
$654$	0.194506	0.00760578
$655$	−3.48712	−0.136253
$656$	8.24311	0.321840
$657$	45.6096	1.77940
$658$	30.3597	1.18354
$659$	−11.2559	−0.438466	−0.219233	−	0.975673i	$-0.570355\pi$
$659$	−11.2559	−0.438466	−0.219233	+	0.975673i	$0.570355\pi$
$660$	52.0490	2.02600
$661$	−27.2674	−1.06058	−0.530290	−	0.847816i	$-0.677917\pi$
$661$	−27.2674	−1.06058	−0.530290	+	0.847816i	$0.677917\pi$
$662$	−22.6274	−0.879441
$663$	21.4909	0.834638
$664$	8.06431	0.312956
$665$	125.599	4.87050
$666$	49.0376	1.90017
$667$	9.46033	0.366306
$668$	−24.7385	−0.957162
$669$	−31.9722	−1.23612
$670$	−31.7179	−1.22537
$671$	22.4871	0.868104
$672$	−13.5513	−0.522754
$673$	21.0651	0.812000	0.406000	−	0.913873i	$-0.366923\pi$
$673$	21.0651	0.812000	0.406000	+	0.913873i	$0.366923\pi$
$674$	−16.8756	−0.650022
$675$	−47.9089	−1.84401
$676$	12.5161	0.481388
$677$	−27.0660	−1.04023	−0.520116	−	0.854096i	$-0.674111\pi$
$677$	−27.0660	−1.04023	−0.520116	+	0.854096i	$0.674111\pi$
$678$	10.1677	0.390489
$679$	7.57760	0.290802
$680$	−5.14350	−0.197244
$681$	−34.6233	−1.32677
$682$	36.3168	1.39064
$683$	3.46039	0.132408	0.0662041	−	0.997806i	$-0.478911\pi$
$683$	3.46039	0.132408	0.0662041	+	0.997806i	$0.478911\pi$
$684$	40.7837	1.55940
$685$	65.1167	2.48798
$686$	37.9258	1.44801
$687$	−53.1710	−2.02860
$688$	3.71808	0.141750
$689$	4.80125	0.182913
$690$	10.0583	0.382911
$691$	−21.5670	−0.820449	−0.410224	−	0.911985i	$-0.634550\pi$
$691$	−21.5670	−0.820449	−0.410224	+	0.911985i	$0.634550\pi$
$692$	23.6063	0.897377
$693$	−129.333	−4.91296
$694$	4.82688	0.183226
$695$	−45.1640	−1.71317
$696$	27.2874	1.03433
$697$	−12.1586	−0.460539
$698$	22.6374	0.856837
$699$	49.5773	1.87518
$700$	33.6386	1.27142
$701$	−4.59154	−0.173420	−0.0867101	−	0.996234i	$-0.527635\pi$
$701$	−4.59154	−0.173420	−0.0867101	+	0.996234i	$0.527635\pi$
$702$	−33.7996	−1.27568
$703$	70.6688	2.66532
$704$	−5.17475	−0.195031
$705$	−64.9972	−2.44793
$706$	−9.27487	−0.349064
$707$	−6.92280	−0.260359
$708$	−21.9935	−0.826567
$709$	−19.8631	−0.745975	−0.372987	−	0.927836i	$-0.621667\pi$
$709$	−19.8631	−0.745975	−0.372987	+	0.927836i	$0.621667\pi$
$710$	−38.2703	−1.43626
$711$	−73.4651	−2.75516
$712$	−4.46572	−0.167360
$713$	7.01808	0.262829
$714$	19.9882	0.748040
$715$	−91.1514	−3.40887
$716$	−25.7858	−0.963662
$717$	4.76512	0.177956
$718$	−12.8102	−0.478074
$719$	−0.826990	−0.0308415	−0.0154208	−	0.999881i	$-0.504909\pi$
$719$	−0.826990	−0.0308415	−0.0154208	+	0.999881i	$0.504909\pi$
$720$	18.5507	0.691344
$721$	23.3956	0.871296
$722$	39.7739	1.48023
$723$	−12.0445	−0.447940
$724$	−14.7721	−0.549001
$725$	−67.7359	−2.51565
$726$	−45.5103	−1.68905
$727$	−2.42101	−0.0897904	−0.0448952	−	0.998992i	$-0.514295\pi$
$727$	−2.42101	−0.0897904	−0.0448952	+	0.998992i	$0.514295\pi$
$728$	23.7319	0.879564
$729$	−40.1282	−1.48623
$730$	29.8971	1.10654
$731$	−5.48417	−0.202839
$732$	12.5343	0.463281
$733$	−15.8208	−0.584353	−0.292176	−	0.956364i	$-0.594379\pi$
$733$	−15.8208	−0.584353	−0.292176	+	0.956364i	$0.594379\pi$
$734$	10.5468	0.389288
$735$	−151.603	−5.59197
$736$	−1.00000	−0.0368605
$737$	47.0682	1.73378
$738$	43.8516	1.61420
$739$	16.7530	0.616271	0.308135	−	0.951343i	$-0.400295\pi$
$739$	16.7530	0.616271	0.308135	+	0.951343i	$0.400295\pi$
$740$	32.1441	1.18164
$741$	−111.701	−4.10342
$742$	4.46553	0.163935
$743$	−45.3587	−1.66405	−0.832025	−	0.554738i	$-0.812819\pi$
$743$	−45.3587	−1.66405	−0.832025	+	0.554738i	$0.812819\pi$
$744$	20.2430	0.742143
$745$	−81.5415	−2.98745
$746$	−30.3417	−1.11089
$747$	42.9004	1.56964
$748$	7.63275	0.279081
$749$	10.1031	0.369161
$750$	−21.7257	−0.793310
$751$	41.6639	1.52034	0.760168	−	0.649726i	$-0.225116\pi$
$751$	41.6639	1.52034	0.760168	+	0.649726i	$0.225116\pi$
$752$	6.46207	0.235648
$753$	−16.6791	−0.607820
$754$	−47.7874	−1.74031
$755$	40.7801	1.48414
$756$	−31.4362	−1.14332
$757$	14.4148	0.523914	0.261957	−	0.965080i	$-0.415632\pi$
$757$	14.4148	0.523914	0.261957	+	0.965080i	$0.415632\pi$
$758$	−6.44165	−0.233971
$759$	−14.9261	−0.541782
$760$	26.7337	0.969732
$761$	−4.40144	−0.159552	−0.0797760	−	0.996813i	$-0.525421\pi$
$761$	−4.40144	−0.159552	−0.0797760	+	0.996813i	$0.525421\pi$
$762$	28.3040	1.02535
$763$	−0.316813	−0.0114694
$764$	−16.1448	−0.584099
$765$	−27.3623	−0.989286
$766$	1.85812	0.0671366
$767$	38.5164	1.39075
$768$	−2.88440	−0.104082
$769$	−13.8104	−0.498014	−0.249007	−	0.968502i	$-0.580104\pi$
$769$	−13.8104	−0.498014	−0.249007	+	0.968502i	$0.580104\pi$
$770$	−84.7778	−3.05518
$771$	−67.2601	−2.42231
$772$	8.53483	0.307175
$773$	−0.456147	−0.0164065	−0.00820323	−	0.999966i	$-0.502611\pi$
$773$	−0.456147	−0.0164065	−0.00820323	+	0.999966i	$0.502611\pi$
$774$	19.7794	0.710956
$775$	−50.2493	−1.80501
$776$	1.61289	0.0578995
$777$	−124.916	−4.48133
$778$	−9.17898	−0.329082
$779$	63.1951	2.26420
$780$	−50.8077	−1.81921
$781$	56.7917	2.03217
$782$	1.47500	0.0527459
$783$	63.3010	2.26219
$784$	15.0725	0.538304
$785$	−20.6412	−0.736717
$786$	2.88440	0.102883
$787$	47.4855	1.69267	0.846337	−	0.532647i	$-0.178803\pi$
$787$	47.4855	1.69267	0.846337	+	0.532647i	$0.178803\pi$
$788$	19.4198	0.691803
$789$	10.8450	0.386094
$790$	−48.1564	−1.71333
$791$	−16.5613	−0.588851
$792$	−27.5286	−0.978185
$793$	−21.9508	−0.779496
$794$	14.6507	0.519935
$795$	−9.56026	−0.339068
$796$	19.4957	0.691008
$797$	−29.0544	−1.02916	−0.514579	−	0.857443i	$-0.672052\pi$
$797$	−29.0544	−1.02916	−0.514579	+	0.857443i	$0.672052\pi$
$798$	−103.890	−3.67767
$799$	−9.53155	−0.337202
$800$	7.15999	0.253144
$801$	−23.7567	−0.839401
$802$	27.4417	0.969001
$803$	−44.3662	−1.56565
$804$	26.2358	0.925265
$805$	−16.3830	−0.577424
$806$	−35.4507	−1.24870
$807$	43.0930	1.51695
$808$	−1.47352	−0.0518383
$809$	−20.5713	−0.723250	−0.361625	−	0.932324i	$-0.617778\pi$
$809$	−20.5713	−0.723250	−0.361625	+	0.932324i	$0.617778\pi$
$810$	11.6497	0.409327
$811$	−8.17224	−0.286966	−0.143483	−	0.989653i	$-0.545830\pi$
$811$	−8.17224	−0.286966	−0.143483	+	0.989653i	$0.545830\pi$
$812$	−44.4460	−1.55975
$813$	−34.9046	−1.22416
$814$	−47.7007	−1.67191
$815$	−22.5887	−0.791247
$816$	4.25449	0.148937
$817$	28.5043	0.997241
$818$	−0.608772	−0.0212852
$819$	126.249	4.41149
$820$	28.7447	1.00381
$821$	10.3338	0.360651	0.180325	−	0.983607i	$-0.442285\pi$
$821$	10.3338	0.360651	0.180325	+	0.983607i	$0.442285\pi$
$822$	−53.8619	−1.87865
$823$	−19.6714	−0.685703	−0.342852	−	0.939390i	$-0.611393\pi$
$823$	−19.6714	−0.685703	−0.342852	+	0.939390i	$0.611393\pi$
$824$	4.97975	0.173478
$825$	106.871	3.72075
$826$	35.8232	1.24645
$827$	−30.5618	−1.06274	−0.531369	−	0.847141i	$-0.678322\pi$
$827$	−30.5618	−1.06274	−0.531369	+	0.847141i	$0.678322\pi$
$828$	−5.31979	−0.184875
$829$	−16.3843	−0.569050	−0.284525	−	0.958669i	$-0.591836\pi$
$829$	−16.3843	−0.569050	−0.284525	+	0.958669i	$0.591836\pi$
$830$	28.1212	0.976101
$831$	29.6777	1.02951
$832$	5.05135	0.175124
$833$	−22.2319	−0.770291
$834$	37.3578	1.29360
$835$	−86.2661	−2.98536
$836$	−39.6718	−1.37208
$837$	46.9594	1.62315
$838$	−7.97892	−0.275627
$839$	−40.6087	−1.40197	−0.700984	−	0.713177i	$-0.747256\pi$
$839$	−40.6087	−1.40197	−0.700984	+	0.713177i	$0.747256\pi$
$840$	−47.2551	−1.63046
$841$	60.4979	2.08614
$842$	−7.09547	−0.244526
$843$	−74.3264	−2.55994
$844$	−10.1841	−0.350550
$845$	43.6451	1.50144
$846$	34.3768	1.18190
$847$	74.1275	2.54705
$848$	0.950489	0.0326399
$849$	−44.1806	−1.51627
$850$	−10.5610	−0.362238
$851$	−9.21797	−0.315988
$852$	31.6556	1.08450
$853$	−28.6773	−0.981893	−0.490947	−	0.871190i	$-0.663349\pi$
$853$	−28.6773	−0.981893	−0.490947	+	0.871190i	$0.663349\pi$
$854$	−20.4159	−0.698619
$855$	142.217	4.86373
$856$	2.15046	0.0735011
$857$	−32.2858	−1.10286	−0.551432	−	0.834220i	$-0.685918\pi$
$857$	−32.2858	−1.10286	−0.551432	+	0.834220i	$0.685918\pi$
$858$	75.3968	2.57400
$859$	−0.994827	−0.0339431	−0.0169715	−	0.999856i	$-0.505402\pi$
$859$	−0.994827	−0.0339431	−0.0169715	+	0.999856i	$0.505402\pi$
$860$	12.9654	0.442116
$861$	−111.705	−3.80690
$862$	18.8478	0.641959
$863$	27.2008	0.925926	0.462963	−	0.886378i	$-0.346786\pi$
$863$	27.2008	0.925926	0.462963	+	0.886378i	$0.346786\pi$
$864$	−6.69120	−0.227639
$865$	82.3179	2.79889
$866$	20.9324	0.711312
$867$	42.7595	1.45219
$868$	−32.9719	−1.11914
$869$	71.4623	2.42419
$870$	95.1545	3.22604
$871$	−45.9457	−1.55681
$872$	−0.0674336	−0.00228359
$873$	8.58026	0.290398
$874$	−7.66641	−0.259320
$875$	35.3870	1.19630
$876$	−24.7297	−0.835538
$877$	38.3777	1.29592	0.647962	−	0.761673i	$-0.275622\pi$
$877$	38.3777	1.29592	0.647962	+	0.761673i	$0.275622\pi$
$878$	3.62798	0.122439
$879$	−16.3191	−0.550430
$880$	−18.0450	−0.608296
$881$	−45.5450	−1.53445	−0.767225	−	0.641378i	$-0.778363\pi$
$881$	−45.5450	−1.53445	−0.767225	+	0.641378i	$0.778363\pi$
$882$	80.1826	2.69989
$883$	−40.1236	−1.35027	−0.675133	−	0.737696i	$-0.735914\pi$
$883$	−40.1236	−1.35027	−0.675133	+	0.737696i	$0.735914\pi$
$884$	−7.45073	−0.250595
$885$	−76.6940	−2.57804
$886$	−17.0529	−0.572904
$887$	29.8135	1.00104	0.500520	−	0.865725i	$-0.333142\pi$
$887$	29.8135	1.00104	0.500520	+	0.865725i	$0.333142\pi$
$888$	−26.5884	−0.892247
$889$	−46.1018	−1.54620
$890$	−15.5725	−0.521991
$891$	−17.2876	−0.579158
$892$	11.0845	0.371137
$893$	49.5409	1.65782
$894$	67.4479	2.25580
$895$	−89.9182	−3.00563
$896$	4.69814	0.156954
$897$	14.5701	0.486482
$898$	3.35788	0.112054
$899$	66.3933	2.21434
$900$	38.0896	1.26965
$901$	−1.40197	−0.0467064
$902$	−42.6561	−1.42029
$903$	−50.3849	−1.67671
$904$	−3.52507	−0.117242
$905$	−51.5120	−1.71232
$906$	−33.7317	−1.12066
$907$	−19.8247	−0.658268	−0.329134	−	0.944283i	$-0.606757\pi$
$907$	−19.8247	−0.658268	−0.329134	+	0.944283i	$0.606757\pi$
$908$	12.0036	0.398354
$909$	−7.83881	−0.259997
$910$	82.7560	2.74333
$911$	25.8153	0.855300	0.427650	−	0.903944i	$-0.359342\pi$
$911$	25.8153	0.855300	0.427650	+	0.903944i	$0.359342\pi$
$912$	−22.1130	−0.732236
$913$	−41.7308	−1.38109
$914$	16.5243	0.546574
$915$	43.7085	1.44496
$916$	18.4340	0.609075
$917$	−4.69814	−0.155146
$918$	9.86952	0.325743
$919$	−12.7713	−0.421287	−0.210644	−	0.977563i	$-0.567556\pi$
$919$	−12.7713	−0.421287	−0.210644	+	0.977563i	$0.567556\pi$
$920$	−3.48712	−0.114967
$921$	−21.0144	−0.692448
$922$	2.99792	0.0987314
$923$	−55.4373	−1.82474
$924$	70.1248	2.30694
$925$	66.0005	2.17008
$926$	12.7839	0.420104
$927$	26.4912	0.870085
$928$	−9.46033	−0.310551
$929$	−26.2203	−0.860260	−0.430130	−	0.902767i	$-0.641532\pi$
$929$	−26.2203	−0.860260	−0.430130	+	0.902767i	$0.641532\pi$
$930$	70.5896	2.31472
$931$	115.552	3.78707
$932$	−17.1880	−0.563013
$933$	23.7357	0.777073
$934$	17.3021	0.566142
$935$	26.6163	0.870446
$936$	26.8721	0.878341
$937$	−22.9879	−0.750983	−0.375492	−	0.926826i	$-0.622526\pi$
$937$	−22.9879	−0.750983	−0.375492	+	0.926826i	$0.622526\pi$
$938$	−42.7331	−1.39528
$939$	−44.2179	−1.44300
$940$	22.5340	0.734978
$941$	−44.2891	−1.44378	−0.721892	−	0.692005i	$-0.756727\pi$
$941$	−44.2891	−1.44378	−0.721892	+	0.692005i	$0.756727\pi$
$942$	17.0736	0.556288
$943$	−8.24311	−0.268433
$944$	7.62498	0.248172
$945$	−109.622	−3.56599
$946$	−19.2401	−0.625551
$947$	11.2261	0.364801	0.182400	−	0.983224i	$-0.441613\pi$
$947$	11.2261	0.364801	0.182400	+	0.983224i	$0.441613\pi$
$948$	39.8330	1.29372
$949$	43.3081	1.40584
$950$	54.8914	1.78091
$951$	94.6221	3.06833
$952$	−6.92975	−0.224595
$953$	−29.6536	−0.960574	−0.480287	−	0.877111i	$-0.659468\pi$
$953$	−29.6536	−0.960574	−0.480287	+	0.877111i	$0.659468\pi$
$954$	5.05640	0.163707
$955$	−56.2989	−1.82179
$956$	−1.65203	−0.0534304
$957$	−141.206	−4.56453
$958$	23.1313	0.747340
$959$	87.7307	2.83297
$960$	−10.0583	−0.324629
$961$	18.2534	0.588819
$962$	46.5632	1.50126
$963$	11.4400	0.368648
$964$	4.17573	0.134491
$965$	29.7620	0.958072
$966$	13.5513	0.436007
$967$	35.3241	1.13595	0.567973	−	0.823047i	$-0.307728\pi$
$967$	35.3241	1.13595	0.567973	+	0.823047i	$0.307728\pi$
$968$	15.7781	0.507126
$969$	32.6167	1.04780
$970$	5.62435	0.180587
$971$	16.9548	0.544107	0.272053	−	0.962282i	$-0.412297\pi$
$971$	16.9548	0.544107	0.272053	+	0.962282i	$0.412297\pi$
$972$	10.4375	0.334782
$973$	−60.8487	−1.95072
$974$	4.17670	0.133830
$975$	−104.322	−3.34097
$976$	−4.34554	−0.139097
$977$	35.6163	1.13947	0.569733	−	0.821830i	$-0.307047\pi$
$977$	35.6163	1.13947	0.569733	+	0.821830i	$0.307047\pi$
$978$	18.6845	0.597463
$979$	23.1090	0.738567
$980$	52.5596	1.67896
$981$	−0.358732	−0.0114534
$982$	−9.79872	−0.312690
$983$	25.1535	0.802272	0.401136	−	0.916018i	$-0.368615\pi$
$983$	25.1535	0.802272	0.401136	+	0.916018i	$0.368615\pi$
$984$	−23.7765	−0.757966
$985$	67.7192	2.15771
$986$	13.9540	0.444385
$987$	−87.5697	−2.78737
$988$	38.7257	1.23203
$989$	−3.71808	−0.118228
$990$	−95.9954	−3.05093
$991$	−29.3056	−0.930922	−0.465461	−	0.885068i	$-0.654111\pi$
$991$	−29.3056	−0.930922	−0.465461	+	0.885068i	$0.654111\pi$
$992$	−7.01808	−0.222824
$993$	65.2667	2.07118
$994$	−51.5610	−1.63541
$995$	67.9839	2.15524
$996$	−23.2607	−0.737045
$997$	−45.0721	−1.42745	−0.713723	−	0.700428i	$-0.752993\pi$
$997$	−45.0721	−1.42745	−0.713723	+	0.700428i	$0.752993\pi$
$998$	−15.0016	−0.474868
$999$	−61.6793	−1.95145

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.k.1.4	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.k.1.4	✓	35	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.88440 q^{3} +1.00000 q^{4} +3.48712 q^{5} -2.88440 q^{6} +4.69814 q^{7} +1.00000 q^{8} +5.31979 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.88440 q^{3} +1.00000 q^{4} +3.48712 q^{5} -2.88440 q^{6} +4.69814 q^{7} +1.00000 q^{8} +5.31979 q^{9} +3.48712 q^{10} -5.17475 q^{11} -2.88440 q^{12} +5.05135 q^{13} +4.69814 q^{14} -10.0583 q^{15} +1.00000 q^{16} -1.47500 q^{17} +5.31979 q^{18} +7.66641 q^{19} +3.48712 q^{20} -13.5513 q^{21} -5.17475 q^{22} -1.00000 q^{23} -2.88440 q^{24} +7.15999 q^{25} +5.05135 q^{26} -6.69120 q^{27} +4.69814 q^{28} -9.46033 q^{29} -10.0583 q^{30} -7.01808 q^{31} +1.00000 q^{32} +14.9261 q^{33} -1.47500 q^{34} +16.3830 q^{35} +5.31979 q^{36} +9.21797 q^{37} +7.66641 q^{38} -14.5701 q^{39} +3.48712 q^{40} +8.24311 q^{41} -13.5513 q^{42} +3.71808 q^{43} -5.17475 q^{44} +18.5507 q^{45} -1.00000 q^{46} +6.46207 q^{47} -2.88440 q^{48} +15.0725 q^{49} +7.15999 q^{50} +4.25449 q^{51} +5.05135 q^{52} +0.950489 q^{53} -6.69120 q^{54} -18.0450 q^{55} +4.69814 q^{56} -22.1130 q^{57} -9.46033 q^{58} +7.62498 q^{59} -10.0583 q^{60} -4.34554 q^{61} -7.01808 q^{62} +24.9931 q^{63} +1.00000 q^{64} +17.6146 q^{65} +14.9261 q^{66} -9.09574 q^{67} -1.47500 q^{68} +2.88440 q^{69} +16.3830 q^{70} -10.9748 q^{71} +5.31979 q^{72} +8.57358 q^{73} +9.21797 q^{74} -20.6523 q^{75} +7.66641 q^{76} -24.3117 q^{77} -14.5701 q^{78} -13.8098 q^{79} +3.48712 q^{80} +3.34077 q^{81} +8.24311 q^{82} +8.06431 q^{83} -13.5513 q^{84} -5.14350 q^{85} +3.71808 q^{86} +27.2874 q^{87} -5.17475 q^{88} -4.46572 q^{89} +18.5507 q^{90} +23.7319 q^{91} -1.00000 q^{92} +20.2430 q^{93} +6.46207 q^{94} +26.7337 q^{95} -2.88440 q^{96} +1.61289 q^{97} +15.0725 q^{98} -27.5286 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * q^99

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