LMFDB - Embedded newform 6046.2.a.f.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6046,2,Mod(1,6046)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6046, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6046.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6046 = 2 \cdot 3023 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6046.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:	$48.2775530621$
Analytic rank:	$0$
Dimension:	$67$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6046.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.55218 q^{3} +1.00000 q^{4} +3.12516 q^{5} -1.55218 q^{6} +2.04511 q^{7} +1.00000 q^{8} -0.590743 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.55218 q^{3} +1.00000 q^{4} +3.12516 q^{5} -1.55218 q^{6} +2.04511 q^{7} +1.00000 q^{8} -0.590743 q^{9} +3.12516 q^{10} -3.41353 q^{11} -1.55218 q^{12} -0.627560 q^{13} +2.04511 q^{14} -4.85080 q^{15} +1.00000 q^{16} +1.41772 q^{17} -0.590743 q^{18} +2.85358 q^{19} +3.12516 q^{20} -3.17437 q^{21} -3.41353 q^{22} +0.787676 q^{23} -1.55218 q^{24} +4.76660 q^{25} -0.627560 q^{26} +5.57347 q^{27} +2.04511 q^{28} -2.73736 q^{29} -4.85080 q^{30} -4.45516 q^{31} +1.00000 q^{32} +5.29840 q^{33} +1.41772 q^{34} +6.39128 q^{35} -0.590743 q^{36} -3.79545 q^{37} +2.85358 q^{38} +0.974085 q^{39} +3.12516 q^{40} +4.83562 q^{41} -3.17437 q^{42} +10.9835 q^{43} -3.41353 q^{44} -1.84616 q^{45} +0.787676 q^{46} -1.38207 q^{47} -1.55218 q^{48} -2.81753 q^{49} +4.76660 q^{50} -2.20056 q^{51} -0.627560 q^{52} +1.88876 q^{53} +5.57347 q^{54} -10.6678 q^{55} +2.04511 q^{56} -4.42927 q^{57} -2.73736 q^{58} +10.6849 q^{59} -4.85080 q^{60} +14.6947 q^{61} -4.45516 q^{62} -1.20813 q^{63} +1.00000 q^{64} -1.96122 q^{65} +5.29840 q^{66} -1.89631 q^{67} +1.41772 q^{68} -1.22261 q^{69} +6.39128 q^{70} +9.48153 q^{71} -0.590743 q^{72} +6.55511 q^{73} -3.79545 q^{74} -7.39861 q^{75} +2.85358 q^{76} -6.98103 q^{77} +0.974085 q^{78} +0.983107 q^{79} +3.12516 q^{80} -6.87879 q^{81} +4.83562 q^{82} +12.5642 q^{83} -3.17437 q^{84} +4.43061 q^{85} +10.9835 q^{86} +4.24888 q^{87} -3.41353 q^{88} -5.68248 q^{89} -1.84616 q^{90} -1.28343 q^{91} +0.787676 q^{92} +6.91520 q^{93} -1.38207 q^{94} +8.91790 q^{95} -1.55218 q^{96} +7.64530 q^{97} -2.81753 q^{98} +2.01652 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 67 q + 67 q^{2} + 21 q^{3} + 67 q^{4} + 21 q^{5} + 21 q^{6} + 38 q^{7} + 67 q^{8} + 90 q^{9}+O(q^{10}) $ 67 * q + 67 * q^2 + 21 * q^3 + 67 * q^4 + 21 * q^5 + 21 * q^6 + 38 * q^7 + 67 * q^8 + 90 * q^9	\( 67 q + 67 q^{2} + 21 q^{3} + 67 q^{4} + 21 q^{5} + 21 q^{6} + 38 q^{7} + 67 q^{8} + 90 q^{9} + 21 q^{10} + 56 q^{11} + 21 q^{12} + 33 q^{13} + 38 q^{14} + 25 q^{15} + 67 q^{16} + 30 q^{17} + 90 q^{18} + 36 q^{19} + 21 q^{20} + 20 q^{21} + 56 q^{22} + 65 q^{23} + 21 q^{24} + 72 q^{25} + 33 q^{26} + 57 q^{27} + 38 q^{28} + 84 q^{29} + 25 q^{30} + 52 q^{31} + 67 q^{32} - 9 q^{33} + 30 q^{34} + 30 q^{35} + 90 q^{36} + 52 q^{37} + 36 q^{38} + 41 q^{39} + 21 q^{40} + 46 q^{41} + 20 q^{42} + 61 q^{43} + 56 q^{44} + 23 q^{45} + 65 q^{46} + 51 q^{47} + 21 q^{48} + 81 q^{49} + 72 q^{50} + 33 q^{51} + 33 q^{52} + 72 q^{53} + 57 q^{54} + 14 q^{55} + 38 q^{56} - 26 q^{57} + 84 q^{58} + 71 q^{59} + 25 q^{60} + 42 q^{61} + 52 q^{62} + 63 q^{63} + 67 q^{64} - 2 q^{65} - 9 q^{66} + 70 q^{67} + 30 q^{68} + 21 q^{69} + 30 q^{70} + 104 q^{71} + 90 q^{72} - 31 q^{73} + 52 q^{74} + 69 q^{75} + 36 q^{76} + 48 q^{77} + 41 q^{78} + 79 q^{79} + 21 q^{80} + 123 q^{81} + 46 q^{82} + 41 q^{83} + 20 q^{84} + 6 q^{85} + 61 q^{86} + 19 q^{87} + 56 q^{88} + 58 q^{89} + 23 q^{90} + 31 q^{91} + 65 q^{92} + 13 q^{93} + 51 q^{94} + 77 q^{95} + 21 q^{96} - 8 q^{97} + 81 q^{98} + 129 q^{99}+O(q^{100}) \) 67 * q + 67 * q^2 + 21 * q^3 + 67 * q^4 + 21 * q^5 + 21 * q^6 + 38 * q^7 + 67 * q^8 + 90 * q^9 + 21 * q^10 + 56 * q^11 + 21 * q^12 + 33 * q^13 + 38 * q^14 + 25 * q^15 + 67 * q^16 + 30 * q^17 + 90 * q^18 + 36 * q^19 + 21 * q^20 + 20 * q^21 + 56 * q^22 + 65 * q^23 + 21 * q^24 + 72 * q^25 + 33 * q^26 + 57 * q^27 + 38 * q^28 + 84 * q^29 + 25 * q^30 + 52 * q^31 + 67 * q^32 - 9 * q^33 + 30 * q^34 + 30 * q^35 + 90 * q^36 + 52 * q^37 + 36 * q^38 + 41 * q^39 + 21 * q^40 + 46 * q^41 + 20 * q^42 + 61 * q^43 + 56 * q^44 + 23 * q^45 + 65 * q^46 + 51 * q^47 + 21 * q^48 + 81 * q^49 + 72 * q^50 + 33 * q^51 + 33 * q^52 + 72 * q^53 + 57 * q^54 + 14 * q^55 + 38 * q^56 - 26 * q^57 + 84 * q^58 + 71 * q^59 + 25 * q^60 + 42 * q^61 + 52 * q^62 + 63 * q^63 + 67 * q^64 - 2 * q^65 - 9 * q^66 + 70 * q^67 + 30 * q^68 + 21 * q^69 + 30 * q^70 + 104 * q^71 + 90 * q^72 - 31 * q^73 + 52 * q^74 + 69 * q^75 + 36 * q^76 + 48 * q^77 + 41 * q^78 + 79 * q^79 + 21 * q^80 + 123 * q^81 + 46 * q^82 + 41 * q^83 + 20 * q^84 + 6 * q^85 + 61 * q^86 + 19 * q^87 + 56 * q^88 + 58 * q^89 + 23 * q^90 + 31 * q^91 + 65 * q^92 + 13 * q^93 + 51 * q^94 + 77 * q^95 + 21 * q^96 - 8 * q^97 + 81 * q^98 + 129 * 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
$3$	−1.55218	−0.896150	−0.448075	−	0.893996i	$-0.647890\pi$
$3$	−1.55218	−0.896150	−0.448075	+	0.893996i	$0.647890\pi$
$4$	1.00000	0.500000
$5$	3.12516	1.39761	0.698806	−	0.715311i	$-0.253715\pi$
$5$	3.12516	1.39761	0.698806	+	0.715311i	$0.253715\pi$
$6$	−1.55218	−0.633674
$7$	2.04511	0.772978	0.386489	−	0.922294i	$-0.373688\pi$
$7$	2.04511	0.772978	0.386489	+	0.922294i	$0.373688\pi$
$8$	1.00000	0.353553
$9$	−0.590743	−0.196914
$10$	3.12516	0.988261
$11$	−3.41353	−1.02922	−0.514609	−	0.857425i	$-0.672063\pi$
$11$	−3.41353	−1.02922	−0.514609	+	0.857425i	$0.672063\pi$
$12$	−1.55218	−0.448075
$13$	−0.627560	−0.174054	−0.0870269	−	0.996206i	$-0.527737\pi$
$13$	−0.627560	−0.174054	−0.0870269	+	0.996206i	$0.527737\pi$
$14$	2.04511	0.546578
$15$	−4.85080	−1.25247
$16$	1.00000	0.250000
$17$	1.41772	0.343848	0.171924	−	0.985110i	$-0.445002\pi$
$17$	1.41772	0.343848	0.171924	+	0.985110i	$0.445002\pi$
$18$	−0.590743	−0.139239
$19$	2.85358	0.654657	0.327329	−	0.944911i	$-0.393852\pi$
$19$	2.85358	0.654657	0.327329	+	0.944911i	$0.393852\pi$
$20$	3.12516	0.698806
$21$	−3.17437	−0.692705
$22$	−3.41353	−0.727766
$23$	0.787676	0.164242	0.0821209	−	0.996622i	$-0.473831\pi$
$23$	0.787676	0.164242	0.0821209	+	0.996622i	$0.473831\pi$
$24$	−1.55218	−0.316837
$25$	4.76660	0.953320
$26$	−0.627560	−0.123075
$27$	5.57347	1.07262
$28$	2.04511	0.386489
$29$	−2.73736	−0.508316	−0.254158	−	0.967163i	$-0.581798\pi$
$29$	−2.73736	−0.508316	−0.254158	+	0.967163i	$0.581798\pi$
$30$	−4.85080	−0.885631
$31$	−4.45516	−0.800170	−0.400085	−	0.916478i	$-0.631019\pi$
$31$	−4.45516	−0.800170	−0.400085	+	0.916478i	$0.631019\pi$
$32$	1.00000	0.176777
$33$	5.29840	0.922333
$34$	1.41772	0.243137
$35$	6.39128	1.08032
$36$	−0.590743	−0.0984572
$37$	−3.79545	−0.623969	−0.311984	−	0.950087i	$-0.600994\pi$
$37$	−3.79545	−0.623969	−0.311984	+	0.950087i	$0.600994\pi$
$38$	2.85358	0.462913
$39$	0.974085	0.155978
$40$	3.12516	0.494130
$41$	4.83562	0.755196	0.377598	−	0.925970i	$-0.376750\pi$
$41$	4.83562	0.755196	0.377598	+	0.925970i	$0.376750\pi$
$42$	−3.17437	−0.489816
$43$	10.9835	1.67496	0.837481	−	0.546467i	$-0.184028\pi$
$43$	10.9835	1.67496	0.837481	+	0.546467i	$0.184028\pi$
$44$	−3.41353	−0.514609
$45$	−1.84616	−0.275210
$46$	0.787676	0.116136
$47$	−1.38207	−0.201596	−0.100798	−	0.994907i	$-0.532140\pi$
$47$	−1.38207	−0.201596	−0.100798	+	0.994907i	$0.532140\pi$
$48$	−1.55218	−0.224038
$49$	−2.81753	−0.402505
$50$	4.76660	0.674099
$51$	−2.20056	−0.308140
$52$	−0.627560	−0.0870269
$53$	1.88876	0.259441	0.129721	−	0.991551i	$-0.458592\pi$
$53$	1.88876	0.259441	0.129721	+	0.991551i	$0.458592\pi$
$54$	5.57347	0.758454
$55$	−10.6678	−1.43845
$56$	2.04511	0.273289
$57$	−4.42927	−0.586671
$58$	−2.73736	−0.359433
$59$	10.6849	1.39105	0.695526	−	0.718500i	$-0.255171\pi$
$59$	10.6849	1.39105	0.695526	+	0.718500i	$0.255171\pi$
$60$	−4.85080	−0.626235
$61$	14.6947	1.88146	0.940730	−	0.339157i	$-0.110142\pi$
$61$	14.6947	1.88146	0.940730	+	0.339157i	$0.110142\pi$
$62$	−4.45516	−0.565806
$63$	−1.20813	−0.152210
$64$	1.00000	0.125000
$65$	−1.96122	−0.243260
$66$	5.29840	0.652188
$67$	−1.89631	−0.231671	−0.115835	−	0.993268i	$-0.536954\pi$
$67$	−1.89631	−0.231671	−0.115835	+	0.993268i	$0.536954\pi$
$68$	1.41772	0.171924
$69$	−1.22261	−0.147185
$70$	6.39128	0.763904
$71$	9.48153	1.12525	0.562625	−	0.826712i	$-0.309791\pi$
$71$	9.48153	1.12525	0.562625	+	0.826712i	$0.309791\pi$
$72$	−0.590743	−0.0696197
$73$	6.55511	0.767218	0.383609	−	0.923496i	$-0.374681\pi$
$73$	6.55511	0.767218	0.383609	+	0.923496i	$0.374681\pi$
$74$	−3.79545	−0.441213
$75$	−7.39861	−0.854318
$76$	2.85358	0.327329
$77$	−6.98103	−0.795562
$78$	0.974085	0.110293
$79$	0.983107	0.110608	0.0553041	−	0.998470i	$-0.482387\pi$
$79$	0.983107	0.110608	0.0553041	+	0.998470i	$0.482387\pi$
$80$	3.12516	0.349403
$81$	−6.87879	−0.764310
$82$	4.83562	0.534005
$83$	12.5642	1.37910	0.689552	−	0.724236i	$-0.257807\pi$
$83$	12.5642	1.37910	0.689552	+	0.724236i	$0.257807\pi$
$84$	−3.17437	−0.346352
$85$	4.43061	0.480567
$86$	10.9835	1.18438
$87$	4.24888	0.455527
$88$	−3.41353	−0.363883
$89$	−5.68248	−0.602341	−0.301171	−	0.953570i	$-0.597377\pi$
$89$	−5.68248	−0.602341	−0.301171	+	0.953570i	$0.597377\pi$
$90$	−1.84616	−0.194603
$91$	−1.28343	−0.134540
$92$	0.787676	0.0821209
$93$	6.91520	0.717073
$94$	−1.38207	−0.142550
$95$	8.91790	0.914957
$96$	−1.55218	−0.158419
$97$	7.64530	0.776263	0.388131	−	0.921604i	$-0.373121\pi$
$97$	7.64530	0.776263	0.388131	+	0.921604i	$0.373121\pi$
$98$	−2.81753	−0.284614
$99$	2.01652	0.202668
$100$	4.76660	0.476660
$101$	0.457283	0.0455014	0.0227507	−	0.999741i	$-0.492758\pi$
$101$	0.457283	0.0455014	0.0227507	+	0.999741i	$0.492758\pi$
$102$	−2.20056	−0.217888
$103$	19.0745	1.87946	0.939731	−	0.341913i	$-0.111075\pi$
$103$	19.0745	1.87946	0.939731	+	0.341913i	$0.111075\pi$
$104$	−0.627560	−0.0615373
$105$	−9.92041	−0.968132
$106$	1.88876	0.183453
$107$	−11.0264	−1.06596	−0.532982	−	0.846126i	$-0.678929\pi$
$107$	−11.0264	−1.06596	−0.532982	+	0.846126i	$0.678929\pi$
$108$	5.57347	0.536308
$109$	−4.08085	−0.390875	−0.195437	−	0.980716i	$-0.562613\pi$
$109$	−4.08085	−0.390875	−0.195437	+	0.980716i	$0.562613\pi$
$110$	−10.6678	−1.01714
$111$	5.89122	0.559170
$112$	2.04511	0.193245
$113$	4.94619	0.465298	0.232649	−	0.972561i	$-0.425261\pi$
$113$	4.94619	0.465298	0.232649	+	0.972561i	$0.425261\pi$
$114$	−4.42927	−0.414839
$115$	2.46161	0.229546
$116$	−2.73736	−0.254158
$117$	0.370727	0.0342737
$118$	10.6849	0.983623
$119$	2.89940	0.265787
$120$	−4.85080	−0.442815
$121$	0.652168	0.0592880
$122$	14.6947	1.33039
$123$	−7.50574	−0.676770
$124$	−4.45516	−0.400085
$125$	−0.729418	−0.0652411
$126$	−1.20813	−0.107629
$127$	−1.20371	−0.106812	−0.0534059	−	0.998573i	$-0.517008\pi$
$127$	−1.20371	−0.106812	−0.0534059	+	0.998573i	$0.517008\pi$
$128$	1.00000	0.0883883
$129$	−17.0483	−1.50102
$130$	−1.96122	−0.172011
$131$	−4.18545	−0.365684	−0.182842	−	0.983142i	$-0.558530\pi$
$131$	−4.18545	−0.365684	−0.182842	+	0.983142i	$0.558530\pi$
$132$	5.29840	0.461167
$133$	5.83589	0.506036
$134$	−1.89631	−0.163816
$135$	17.4180	1.49910
$136$	1.41772	0.121569
$137$	20.9231	1.78758	0.893792	−	0.448481i	$-0.148035\pi$
$137$	20.9231	1.78758	0.893792	+	0.448481i	$0.148035\pi$
$138$	−1.22261	−0.104076
$139$	−7.84599	−0.665488	−0.332744	−	0.943017i	$-0.607975\pi$
$139$	−7.84599	−0.665488	−0.332744	+	0.943017i	$0.607975\pi$
$140$	6.39128	0.540162
$141$	2.14522	0.180661
$142$	9.48153	0.795672
$143$	2.14219	0.179139
$144$	−0.590743	−0.0492286
$145$	−8.55469	−0.710428
$146$	6.55511	0.542505
$147$	4.37331	0.360705
$148$	−3.79545	−0.311984
$149$	−16.3757	−1.34155	−0.670774	−	0.741662i	$-0.734038\pi$
$149$	−16.3757	−1.34155	−0.670774	+	0.741662i	$0.734038\pi$
$150$	−7.39861	−0.604094
$151$	−2.19946	−0.178990	−0.0894948	−	0.995987i	$-0.528525\pi$
$151$	−2.19946	−0.178990	−0.0894948	+	0.995987i	$0.528525\pi$
$152$	2.85358	0.231456
$153$	−0.837510	−0.0677087
$154$	−6.98103	−0.562548
$155$	−13.9231	−1.11833
$156$	0.974085	0.0779892
$157$	−9.69619	−0.773840	−0.386920	−	0.922113i	$-0.626461\pi$
$157$	−9.69619	−0.773840	−0.386920	+	0.922113i	$0.626461\pi$
$158$	0.983107	0.0782118
$159$	−2.93169	−0.232499
$160$	3.12516	0.247065
$161$	1.61088	0.126955
$162$	−6.87879	−0.540449
$163$	4.92328	0.385621	0.192811	−	0.981236i	$-0.438240\pi$
$163$	4.92328	0.385621	0.192811	+	0.981236i	$0.438240\pi$
$164$	4.83562	0.377598
$165$	16.5583	1.28906
$166$	12.5642	0.975174
$167$	−3.99323	−0.309005	−0.154503	−	0.987992i	$-0.549377\pi$
$167$	−3.99323	−0.309005	−0.154503	+	0.987992i	$0.549377\pi$
$168$	−3.17437	−0.244908
$169$	−12.6062	−0.969705
$170$	4.43061	0.339812
$171$	−1.68574	−0.128911
$172$	10.9835	0.837481
$173$	−3.65121	−0.277596	−0.138798	−	0.990321i	$-0.544324\pi$
$173$	−3.65121	−0.277596	−0.138798	+	0.990321i	$0.544324\pi$
$174$	4.24888	0.322106
$175$	9.74821	0.736895
$176$	−3.41353	−0.257304
$177$	−16.5848	−1.24659
$178$	−5.68248	−0.425920
$179$	4.08218	0.305116	0.152558	−	0.988295i	$-0.451249\pi$
$179$	4.08218	0.305116	0.152558	+	0.988295i	$0.451249\pi$
$180$	−1.84616	−0.137605
$181$	−9.65145	−0.717387	−0.358693	−	0.933455i	$-0.616778\pi$
$181$	−9.65145	−0.717387	−0.358693	+	0.933455i	$0.616778\pi$
$182$	−1.28343	−0.0951340
$183$	−22.8087	−1.68607
$184$	0.787676	0.0580682
$185$	−11.8614	−0.872067
$186$	6.91520	0.507047
$187$	−4.83944	−0.353895
$188$	−1.38207	−0.100798
$189$	11.3984	0.829108
$190$	8.91790	0.646972
$191$	−11.4925	−0.831571	−0.415786	−	0.909463i	$-0.636493\pi$
$191$	−11.4925	−0.831571	−0.415786	+	0.909463i	$0.636493\pi$
$192$	−1.55218	−0.112019
$193$	−5.76266	−0.414805	−0.207403	−	0.978256i	$-0.566501\pi$
$193$	−5.76266	−0.414805	−0.207403	+	0.978256i	$0.566501\pi$
$194$	7.64530	0.548901
$195$	3.04417	0.217997
$196$	−2.81753	−0.201252
$197$	8.41305	0.599405	0.299702	−	0.954033i	$-0.403113\pi$
$197$	8.41305	0.599405	0.299702	+	0.954033i	$0.403113\pi$
$198$	2.01652	0.143308
$199$	28.1006	1.99200	0.996001	−	0.0893462i	$-0.0284778\pi$
$199$	28.1006	1.99200	0.996001	+	0.0893462i	$0.0284778\pi$
$200$	4.76660	0.337049
$201$	2.94340	0.207612
$202$	0.457283	0.0321744
$203$	−5.59820	−0.392917
$204$	−2.20056	−0.154070
$205$	15.1121	1.05547
$206$	19.0745	1.32898
$207$	−0.465314	−0.0323416
$208$	−0.627560	−0.0435134
$209$	−9.74079	−0.673784
$210$	−9.92041	−0.684573
$211$	−15.3093	−1.05394	−0.526968	−	0.849885i	$-0.676671\pi$
$211$	−15.3093	−1.05394	−0.526968	+	0.849885i	$0.676671\pi$
$212$	1.88876	0.129721
$213$	−14.7170	−1.00839
$214$	−11.0264	−0.753751
$215$	34.3250	2.34095
$216$	5.57347	0.379227
$217$	−9.11128	−0.618514
$218$	−4.08085	−0.276390
$219$	−10.1747	−0.687543
$220$	−10.6678	−0.719223
$221$	−0.889706	−0.0598481
$222$	5.89122	0.395393
$223$	14.5154	0.972026	0.486013	−	0.873952i	$-0.338451\pi$
$223$	14.5154	0.972026	0.486013	+	0.873952i	$0.338451\pi$
$224$	2.04511	0.136645
$225$	−2.81583	−0.187722
$226$	4.94619	0.329016
$227$	13.5709	0.900735	0.450367	−	0.892843i	$-0.351293\pi$
$227$	13.5709	0.900735	0.450367	+	0.892843i	$0.351293\pi$
$228$	−4.42927	−0.293336
$229$	−27.1374	−1.79329	−0.896645	−	0.442750i	$-0.854003\pi$
$229$	−27.1374	−1.79329	−0.896645	+	0.442750i	$0.854003\pi$
$230$	2.46161	0.162314
$231$	10.8358	0.712944
$232$	−2.73736	−0.179717
$233$	7.41482	0.485761	0.242881	−	0.970056i	$-0.421908\pi$
$233$	7.41482	0.485761	0.242881	+	0.970056i	$0.421908\pi$
$234$	0.370727	0.0242352
$235$	−4.31920	−0.281753
$236$	10.6849	0.695526
$237$	−1.52596	−0.0991216
$238$	2.89940	0.187940
$239$	27.5707	1.78340	0.891699	−	0.452629i	$-0.149514\pi$
$239$	27.5707	1.78340	0.891699	+	0.452629i	$0.149514\pi$
$240$	−4.85080	−0.313118
$241$	6.38331	0.411185	0.205593	−	0.978638i	$-0.434088\pi$
$241$	6.38331	0.411185	0.205593	+	0.978638i	$0.434088\pi$
$242$	0.652168	0.0419230
$243$	−6.04331	−0.387678
$244$	14.6947	0.940730
$245$	−8.80523	−0.562546
$246$	−7.50574	−0.478548
$247$	−1.79080	−0.113946
$248$	−4.45516	−0.282903
$249$	−19.5019	−1.23588
$250$	−0.729418	−0.0461325
$251$	−4.40293	−0.277911	−0.138955	−	0.990299i	$-0.544374\pi$
$251$	−4.40293	−0.277911	−0.138955	+	0.990299i	$0.544374\pi$
$252$	−1.20813	−0.0761052
$253$	−2.68875	−0.169040
$254$	−1.20371	−0.0755273
$255$	−6.87709	−0.430660
$256$	1.00000	0.0625000
$257$	21.7783	1.35849	0.679245	−	0.733911i	$-0.262307\pi$
$257$	21.7783	1.35849	0.679245	+	0.733911i	$0.262307\pi$
$258$	−17.0483	−1.06138
$259$	−7.76211	−0.482314
$260$	−1.96122	−0.121630
$261$	1.61708	0.100095
$262$	−4.18545	−0.258578
$263$	−30.5143	−1.88159	−0.940796	−	0.338973i	$-0.889921\pi$
$263$	−30.5143	−1.88159	−0.940796	+	0.338973i	$0.889921\pi$
$264$	5.29840	0.326094
$265$	5.90267	0.362598
$266$	5.83589	0.357821
$267$	8.82022	0.539789
$268$	−1.89631	−0.115835
$269$	27.0947	1.65199	0.825997	−	0.563675i	$-0.190613\pi$
$269$	27.0947	1.65199	0.825997	+	0.563675i	$0.190613\pi$
$270$	17.4180	1.06002
$271$	7.48389	0.454614	0.227307	−	0.973823i	$-0.427008\pi$
$271$	7.48389	0.454614	0.227307	+	0.973823i	$0.427008\pi$
$272$	1.41772	0.0859621
$273$	1.99211	0.120568
$274$	20.9231	1.26401
$275$	−16.2709	−0.981173
$276$	−1.22261	−0.0735927
$277$	−18.0226	−1.08287	−0.541437	−	0.840742i	$-0.682119\pi$
$277$	−18.0226	−1.08287	−0.541437	+	0.840742i	$0.682119\pi$
$278$	−7.84599	−0.470571
$279$	2.63185	0.157565
$280$	6.39128	0.381952
$281$	−21.4132	−1.27740	−0.638701	−	0.769455i	$-0.720528\pi$
$281$	−21.4132	−1.27740	−0.638701	+	0.769455i	$0.720528\pi$
$282$	2.14522	0.127746
$283$	1.46415	0.0870348	0.0435174	−	0.999053i	$-0.486144\pi$
$283$	1.46415	0.0870348	0.0435174	+	0.999053i	$0.486144\pi$
$284$	9.48153	0.562625
$285$	−13.8422	−0.819939
$286$	2.14219	0.126671
$287$	9.88936	0.583750
$288$	−0.590743	−0.0348099
$289$	−14.9901	−0.881768
$290$	−8.55469	−0.502349
$291$	−11.8669	−0.695648
$292$	6.55511	0.383609
$293$	13.3899	0.782248	0.391124	−	0.920338i	$-0.372086\pi$
$293$	13.3899	0.782248	0.391124	+	0.920338i	$0.372086\pi$
$294$	4.37331	0.255057
$295$	33.3919	1.94415
$296$	−3.79545	−0.220606
$297$	−19.0252	−1.10395
$298$	−16.3757	−0.948618
$299$	−0.494314	−0.0285869
$300$	−7.39861	−0.427159
$301$	22.4624	1.29471
$302$	−2.19946	−0.126565
$303$	−0.709785	−0.0407761
$304$	2.85358	0.163664
$305$	45.9231	2.62955
$306$	−0.837510	−0.0478773
$307$	−1.22039	−0.0696512	−0.0348256	−	0.999393i	$-0.511088\pi$
$307$	−1.22039	−0.0696512	−0.0348256	+	0.999393i	$0.511088\pi$
$308$	−6.98103	−0.397781
$309$	−29.6070	−1.68428
$310$	−13.9231	−0.790777
$311$	−5.10488	−0.289471	−0.144736	−	0.989470i	$-0.546233\pi$
$311$	−5.10488	−0.289471	−0.144736	+	0.989470i	$0.546233\pi$
$312$	0.974085	0.0551467
$313$	−6.84707	−0.387019	−0.193510	−	0.981098i	$-0.561987\pi$
$313$	−6.84707	−0.387019	−0.193510	+	0.981098i	$0.561987\pi$
$314$	−9.69619	−0.547188
$315$	−3.77560	−0.212731
$316$	0.983107	0.0553041
$317$	2.95723	0.166095	0.0830474	−	0.996546i	$-0.473535\pi$
$317$	2.95723	0.166095	0.0830474	+	0.996546i	$0.473535\pi$
$318$	−2.93169	−0.164401
$319$	9.34406	0.523167
$320$	3.12516	0.174702
$321$	17.1150	0.955265
$322$	1.61088	0.0897709
$323$	4.04559	0.225103
$324$	−6.87879	−0.382155
$325$	−2.99133	−0.165929
$326$	4.92328	0.272675
$327$	6.33421	0.350283
$328$	4.83562	0.267002
$329$	−2.82649	−0.155829
$330$	16.5583	0.911506
$331$	30.2239	1.66126	0.830628	−	0.556828i	$-0.187982\pi$
$331$	30.2239	1.66126	0.830628	+	0.556828i	$0.187982\pi$
$332$	12.5642	0.689552
$333$	2.24214	0.122868
$334$	−3.99323	−0.218500
$335$	−5.92625	−0.323786
$336$	−3.17437	−0.173176
$337$	−7.93881	−0.432455	−0.216227	−	0.976343i	$-0.569375\pi$
$337$	−7.93881	−0.432455	−0.216227	+	0.976343i	$0.569375\pi$
$338$	−12.6062	−0.685685
$339$	−7.67736	−0.416977
$340$	4.43061	0.240283
$341$	15.2078	0.823549
$342$	−1.68574	−0.0911541
$343$	−20.0779	−1.08411
$344$	10.9835	0.592188
$345$	−3.82086	−0.205708
$346$	−3.65121	−0.196290
$347$	12.9273	0.693976	0.346988	−	0.937870i	$-0.387204\pi$
$347$	12.9273	0.693976	0.346988	+	0.937870i	$0.387204\pi$
$348$	4.24888	0.227764
$349$	10.6296	0.568988	0.284494	−	0.958678i	$-0.408174\pi$
$349$	10.6296	0.568988	0.284494	+	0.958678i	$0.408174\pi$
$350$	9.74821	0.521064
$351$	−3.49769	−0.186693
$352$	−3.41353	−0.181942
$353$	−17.3165	−0.921663	−0.460831	−	0.887488i	$-0.652449\pi$
$353$	−17.3165	−0.921663	−0.460831	+	0.887488i	$0.652449\pi$
$354$	−16.5848	−0.881474
$355$	29.6313	1.57266
$356$	−5.68248	−0.301171
$357$	−4.50038	−0.238185
$358$	4.08218	0.215750
$359$	5.39874	0.284935	0.142467	−	0.989800i	$-0.454496\pi$
$359$	5.39874	0.284935	0.142467	+	0.989800i	$0.454496\pi$
$360$	−1.84616	−0.0973014
$361$	−10.8571	−0.571424
$362$	−9.65145	−0.507269
$363$	−1.01228	−0.0531310
$364$	−1.28343	−0.0672699
$365$	20.4857	1.07227
$366$	−22.8087	−1.19223
$367$	−18.6066	−0.971256	−0.485628	−	0.874166i	$-0.661409\pi$
$367$	−18.6066	−0.971256	−0.485628	+	0.874166i	$0.661409\pi$
$368$	0.787676	0.0410604
$369$	−2.85661	−0.148709
$370$	−11.8614	−0.616644
$371$	3.86272	0.200543
$372$	6.91520	0.358537
$373$	−19.9619	−1.03359	−0.516793	−	0.856110i	$-0.672874\pi$
$373$	−19.9619	−1.03359	−0.516793	+	0.856110i	$0.672874\pi$
$374$	−4.83944	−0.250241
$375$	1.13219	0.0584659
$376$	−1.38207	−0.0712750
$377$	1.71786	0.0884743
$378$	11.3984	0.586268
$379$	8.18521	0.420446	0.210223	−	0.977653i	$-0.432581\pi$
$379$	8.18521	0.420446	0.210223	+	0.977653i	$0.432581\pi$
$380$	8.91790	0.457478
$381$	1.86837	0.0957194
$382$	−11.4925	−0.588010
$383$	27.4074	1.40045	0.700226	−	0.713921i	$-0.253083\pi$
$383$	27.4074	1.40045	0.700226	+	0.713921i	$0.253083\pi$
$384$	−1.55218	−0.0792093
$385$	−21.8168	−1.11189
$386$	−5.76266	−0.293312
$387$	−6.48840	−0.329824
$388$	7.64530	0.388131
$389$	20.8903	1.05918	0.529590	−	0.848254i	$-0.322346\pi$
$389$	20.8903	1.05918	0.529590	+	0.848254i	$0.322346\pi$
$390$	3.04417	0.154147
$391$	1.11671	0.0564743
$392$	−2.81753	−0.142307
$393$	6.49656	0.327708
$394$	8.41305	0.423843
$395$	3.07236	0.154587
$396$	2.01652	0.101334
$397$	23.6586	1.18739	0.593695	−	0.804690i	$-0.297669\pi$
$397$	23.6586	1.18739	0.593695	+	0.804690i	$0.297669\pi$
$398$	28.1006	1.40856
$399$	−9.05834	−0.453484
$400$	4.76660	0.238330
$401$	−37.0152	−1.84845	−0.924225	−	0.381849i	$-0.875287\pi$
$401$	−37.0152	−1.84845	−0.924225	+	0.381849i	$0.875287\pi$
$402$	2.94340	0.146804
$403$	2.79588	0.139273
$404$	0.457283	0.0227507
$405$	−21.4973	−1.06821
$406$	−5.59820	−0.277834
$407$	12.9559	0.642200
$408$	−2.20056	−0.108944
$409$	4.22387	0.208857	0.104428	−	0.994532i	$-0.466699\pi$
$409$	4.22387	0.208857	0.104428	+	0.994532i	$0.466699\pi$
$410$	15.1121	0.746331
$411$	−32.4764	−1.60194
$412$	19.0745	0.939731
$413$	21.8517	1.07525
$414$	−0.465314	−0.0228689
$415$	39.2652	1.92745
$416$	−0.627560	−0.0307687
$417$	12.1784	0.596378
$418$	−9.74079	−0.476438
$419$	−7.50624	−0.366704	−0.183352	−	0.983047i	$-0.558695\pi$
$419$	−7.50624	−0.366704	−0.183352	+	0.983047i	$0.558695\pi$
$420$	−9.92041	−0.484066
$421$	17.6163	0.858566	0.429283	−	0.903170i	$-0.358766\pi$
$421$	17.6163	0.858566	0.429283	+	0.903170i	$0.358766\pi$
$422$	−15.3093	−0.745246
$423$	0.816450	0.0396972
$424$	1.88876	0.0917264
$425$	6.75772	0.327797
$426$	−14.7170	−0.713042
$427$	30.0522	1.45433
$428$	−11.0264	−0.532982
$429$	−3.32506	−0.160536
$430$	34.3250	1.65530
$431$	22.3139	1.07482	0.537412	−	0.843320i	$-0.319402\pi$
$431$	22.3139	1.07482	0.537412	+	0.843320i	$0.319402\pi$
$432$	5.57347	0.268154
$433$	−38.9290	−1.87081	−0.935404	−	0.353581i	$-0.884964\pi$
$433$	−38.9290	−1.87081	−0.935404	+	0.353581i	$0.884964\pi$
$434$	−9.11128	−0.437356
$435$	13.2784	0.636650
$436$	−4.08085	−0.195437
$437$	2.24770	0.107522
$438$	−10.1747	−0.486166
$439$	26.3294	1.25663	0.628317	−	0.777957i	$-0.283744\pi$
$439$	26.3294	1.25663	0.628317	+	0.777957i	$0.283744\pi$
$440$	−10.6678	−0.508568
$441$	1.66444	0.0792590
$442$	−0.889706	−0.0423190
$443$	−19.1751	−0.911038	−0.455519	−	0.890226i	$-0.650546\pi$
$443$	−19.1751	−0.911038	−0.455519	+	0.890226i	$0.650546\pi$
$444$	5.89122	0.279585
$445$	−17.7586	−0.841840
$446$	14.5154	0.687326
$447$	25.4180	1.20223
$448$	2.04511	0.0966223
$449$	−7.80518	−0.368349	−0.184175	−	0.982894i	$-0.558961\pi$
$449$	−7.80518	−0.368349	−0.184175	+	0.982894i	$0.558961\pi$
$450$	−2.81583	−0.132740
$451$	−16.5065	−0.777261
$452$	4.94619	0.232649
$453$	3.41395	0.160402
$454$	13.5709	0.636916
$455$	−4.01091	−0.188034
$456$	−4.42927	−0.207420
$457$	38.8686	1.81819	0.909097	−	0.416584i	$-0.136773\pi$
$457$	38.8686	1.81819	0.909097	+	0.416584i	$0.136773\pi$
$458$	−27.1374	−1.26805
$459$	7.90164	0.368817
$460$	2.46161	0.114773
$461$	−8.14130	−0.379178	−0.189589	−	0.981864i	$-0.560716\pi$
$461$	−8.14130	−0.379178	−0.189589	+	0.981864i	$0.560716\pi$
$462$	10.8358	0.504127
$463$	−5.60120	−0.260310	−0.130155	−	0.991494i	$-0.541547\pi$
$463$	−5.60120	−0.260310	−0.130155	+	0.991494i	$0.541547\pi$
$464$	−2.73736	−0.127079
$465$	21.6111	1.00219
$466$	7.41482	0.343485
$467$	33.9279	1.56999	0.784997	−	0.619500i	$-0.212664\pi$
$467$	33.9279	1.56999	0.784997	+	0.619500i	$0.212664\pi$
$468$	0.370727	0.0171368
$469$	−3.87815	−0.179076
$470$	−4.31920	−0.199230
$471$	15.0502	0.693477
$472$	10.6849	0.491811
$473$	−37.4923	−1.72390
$474$	−1.52596	−0.0700896
$475$	13.6019	0.624098
$476$	2.89940	0.132894
$477$	−1.11577	−0.0510877
$478$	27.5707	1.26105
$479$	30.5642	1.39651	0.698256	−	0.715848i	$-0.253960\pi$
$479$	30.5642	1.39651	0.698256	+	0.715848i	$0.253960\pi$
$480$	−4.85080	−0.221408
$481$	2.38188	0.108604
$482$	6.38331	0.290752
$483$	−2.50038	−0.113771
$484$	0.652168	0.0296440
$485$	23.8928	1.08491
$486$	−6.04331	−0.274130
$487$	19.5778	0.887157	0.443578	−	0.896236i	$-0.353709\pi$
$487$	19.5778	0.887157	0.443578	+	0.896236i	$0.353709\pi$
$488$	14.6947	0.665196
$489$	−7.64181	−0.345574
$490$	−8.80523	−0.397780
$491$	−18.7417	−0.845801	−0.422901	−	0.906176i	$-0.638988\pi$
$491$	−18.7417	−0.845801	−0.422901	+	0.906176i	$0.638988\pi$
$492$	−7.50574	−0.338385
$493$	−3.88082	−0.174783
$494$	−1.79080	−0.0805717
$495$	6.30193	0.283251
$496$	−4.45516	−0.200043
$497$	19.3908	0.869794
$498$	−19.5019	−0.873902
$499$	−28.8181	−1.29007	−0.645037	−	0.764151i	$-0.723158\pi$
$499$	−28.8181	−1.29007	−0.645037	+	0.764151i	$0.723158\pi$
$500$	−0.729418	−0.0326206
$501$	6.19820	0.276915
$502$	−4.40293	−0.196512
$503$	−16.5217	−0.736668	−0.368334	−	0.929694i	$-0.620072\pi$
$503$	−16.5217	−0.736668	−0.368334	+	0.929694i	$0.620072\pi$
$504$	−1.20813	−0.0538145
$505$	1.42908	0.0635933
$506$	−2.68875	−0.119530
$507$	19.5670	0.869002
$508$	−1.20371	−0.0534059
$509$	30.2822	1.34223	0.671117	−	0.741352i	$-0.265815\pi$
$509$	30.2822	1.34223	0.671117	+	0.741352i	$0.265815\pi$
$510$	−6.87709	−0.304523
$511$	13.4059	0.593043
$512$	1.00000	0.0441942
$513$	15.9044	0.702195
$514$	21.7783	0.960598
$515$	59.6107	2.62676
$516$	−17.0483	−0.750509
$517$	4.71775	0.207486
$518$	−7.76211	−0.341048
$519$	5.66733	0.248768
$520$	−1.96122	−0.0860053
$521$	−29.4681	−1.29102	−0.645510	−	0.763751i	$-0.723355\pi$
$521$	−29.4681	−1.29102	−0.645510	+	0.763751i	$0.723355\pi$
$522$	1.61708	0.0707776
$523$	−8.37540	−0.366231	−0.183115	−	0.983091i	$-0.558618\pi$
$523$	−8.37540	−0.366231	−0.183115	+	0.983091i	$0.558618\pi$
$524$	−4.18545	−0.182842
$525$	−15.1310	−0.660369
$526$	−30.5143	−1.33049
$527$	−6.31618	−0.275137
$528$	5.29840	0.230583
$529$	−22.3796	−0.973025
$530$	5.90267	0.256396
$531$	−6.31202	−0.273918
$532$	5.83589	0.253018
$533$	−3.03464	−0.131445
$534$	8.82022	0.381688
$535$	−34.4593	−1.48981
$536$	−1.89631	−0.0819079
$537$	−6.33626	−0.273430
$538$	27.0947	1.16814
$539$	9.61773	0.414265
$540$	17.4180	0.749550
$541$	−32.7565	−1.40831	−0.704155	−	0.710046i	$-0.748674\pi$
$541$	−32.7565	−1.40831	−0.704155	+	0.710046i	$0.748674\pi$
$542$	7.48389	0.321461
$543$	14.9808	0.642886
$544$	1.41772	0.0607844
$545$	−12.7533	−0.546291
$546$	1.99211	0.0852544
$547$	23.6677	1.01196	0.505978	−	0.862546i	$-0.331132\pi$
$547$	23.6677	1.01196	0.505978	+	0.862546i	$0.331132\pi$
$548$	20.9231	0.893792
$549$	−8.68077	−0.370486
$550$	−16.2709	−0.693794
$551$	−7.81130	−0.332773
$552$	−1.22261	−0.0520379
$553$	2.01056	0.0854977
$554$	−18.0226	−0.765707
$555$	18.4110	0.781503
$556$	−7.84599	−0.332744
$557$	−41.1289	−1.74269	−0.871345	−	0.490671i	$-0.836752\pi$
$557$	−41.1289	−1.74269	−0.871345	+	0.490671i	$0.836752\pi$
$558$	2.63185	0.111415
$559$	−6.89278	−0.291533
$560$	6.39128	0.270081
$561$	7.51167	0.317143
$562$	−21.4132	−0.903259
$563$	−31.1382	−1.31232	−0.656159	−	0.754623i	$-0.727820\pi$
$563$	−31.1382	−1.31232	−0.656159	+	0.754623i	$0.727820\pi$
$564$	2.14522	0.0903303
$565$	15.4576	0.650306
$566$	1.46415	0.0615429
$567$	−14.0679	−0.590795
$568$	9.48153	0.397836
$569$	−29.5840	−1.24023	−0.620113	−	0.784513i	$-0.712913\pi$
$569$	−29.5840	−1.24023	−0.620113	+	0.784513i	$0.712913\pi$
$570$	−13.8422	−0.579784
$571$	−24.1971	−1.01262	−0.506308	−	0.862352i	$-0.668990\pi$
$571$	−24.1971	−1.01262	−0.506308	+	0.862352i	$0.668990\pi$
$572$	2.14219	0.0895696
$573$	17.8385	0.745213
$574$	9.88936	0.412774
$575$	3.75453	0.156575
$576$	−0.590743	−0.0246143
$577$	31.4691	1.31008	0.655038	−	0.755596i	$-0.272653\pi$
$577$	31.4691	1.31008	0.655038	+	0.755596i	$0.272653\pi$
$578$	−14.9901	−0.623504
$579$	8.94468	0.371728
$580$	−8.55469	−0.355214
$581$	25.6952	1.06602
$582$	−11.8669	−0.491898
$583$	−6.44734	−0.267022
$584$	6.55511	0.271252
$585$	1.15858	0.0479013
$586$	13.3899	0.553133
$587$	15.8930	0.655975	0.327987	−	0.944682i	$-0.393630\pi$
$587$	15.8930	0.655975	0.327987	+	0.944682i	$0.393630\pi$
$588$	4.37331	0.180352
$589$	−12.7132	−0.523837
$590$	33.3919	1.37472
$591$	−13.0585	−0.537157
$592$	−3.79545	−0.155992
$593$	10.0203	0.411483	0.205741	−	0.978606i	$-0.434039\pi$
$593$	10.0203	0.411483	0.205741	+	0.978606i	$0.434039\pi$
$594$	−19.0252	−0.780613
$595$	9.06107	0.371467
$596$	−16.3757	−0.670774
$597$	−43.6172	−1.78513
$598$	−0.494314	−0.0202140
$599$	−18.5704	−0.758765	−0.379383	−	0.925240i	$-0.623864\pi$
$599$	−18.5704	−0.758765	−0.379383	+	0.925240i	$0.623864\pi$
$600$	−7.39861	−0.302047
$601$	28.9794	1.18209	0.591047	−	0.806637i	$-0.298715\pi$
$601$	28.9794	1.18209	0.591047	+	0.806637i	$0.298715\pi$
$602$	22.4624	0.915497
$603$	1.12023	0.0456193
$604$	−2.19946	−0.0894948
$605$	2.03813	0.0828616
$606$	−0.709785	−0.0288331
$607$	−21.3131	−0.865071	−0.432535	−	0.901617i	$-0.642381\pi$
$607$	−21.3131	−0.865071	−0.432535	+	0.901617i	$0.642381\pi$
$608$	2.85358	0.115728
$609$	8.68941	0.352113
$610$	45.9231	1.85937
$611$	0.867334	0.0350886
$612$	−0.837510	−0.0338543
$613$	20.3433	0.821659	0.410830	−	0.911712i	$-0.365239\pi$
$613$	20.3433	0.821659	0.410830	+	0.911712i	$0.365239\pi$
$614$	−1.22039	−0.0492509
$615$	−23.4566	−0.945861
$616$	−6.98103	−0.281274
$617$	3.03383	0.122137	0.0610686	−	0.998134i	$-0.480549\pi$
$617$	3.03383	0.122137	0.0610686	+	0.998134i	$0.480549\pi$
$618$	−29.6070	−1.19097
$619$	19.0766	0.766752	0.383376	−	0.923592i	$-0.374761\pi$
$619$	19.0766	0.766752	0.383376	+	0.923592i	$0.374761\pi$
$620$	−13.9231	−0.559164
$621$	4.39009	0.176168
$622$	−5.10488	−0.204687
$623$	−11.6213	−0.465597
$624$	0.974085	0.0389946
$625$	−26.1125	−1.04450
$626$	−6.84707	−0.273664
$627$	15.1194	0.603812
$628$	−9.69619	−0.386920
$629$	−5.38090	−0.214551
$630$	−3.77560	−0.150424
$631$	−17.8937	−0.712336	−0.356168	−	0.934422i	$-0.615917\pi$
$631$	−17.8937	−0.712336	−0.356168	+	0.934422i	$0.615917\pi$
$632$	0.983107	0.0391059
$633$	23.7628	0.944486
$634$	2.95723	0.117447
$635$	−3.76177	−0.149281
$636$	−2.93169	−0.116249
$637$	1.76817	0.0700575
$638$	9.34406	0.369935
$639$	−5.60115	−0.221578
$640$	3.12516	0.123533
$641$	−17.2550	−0.681533	−0.340766	−	0.940148i	$-0.610686\pi$
$641$	−17.2550	−0.681533	−0.340766	+	0.940148i	$0.610686\pi$
$642$	17.1150	0.675474
$643$	16.3635	0.645314	0.322657	−	0.946516i	$-0.395424\pi$
$643$	16.3635	0.645314	0.322657	+	0.946516i	$0.395424\pi$
$644$	1.61088	0.0634776
$645$	−53.2785	−2.09784
$646$	4.04559	0.159172
$647$	1.25157	0.0492044	0.0246022	−	0.999697i	$-0.492168\pi$
$647$	1.25157	0.0492044	0.0246022	+	0.999697i	$0.492168\pi$
$648$	−6.87879	−0.270225
$649$	−36.4731	−1.43170
$650$	−2.99133	−0.117329
$651$	14.1423	0.554282
$652$	4.92328	0.192811
$653$	42.7371	1.67243	0.836215	−	0.548401i	$-0.184763\pi$
$653$	42.7371	1.67243	0.836215	+	0.548401i	$0.184763\pi$
$654$	6.33421	0.247687
$655$	−13.0802	−0.511085
$656$	4.83562	0.188799
$657$	−3.87239	−0.151076
$658$	−2.82649	−0.110188
$659$	1.66961	0.0650387	0.0325194	−	0.999471i	$-0.489647\pi$
$659$	1.66961	0.0650387	0.0325194	+	0.999471i	$0.489647\pi$
$660$	16.5583	0.644532
$661$	−5.59707	−0.217701	−0.108850	−	0.994058i	$-0.534717\pi$
$661$	−5.59707	−0.217701	−0.108850	+	0.994058i	$0.534717\pi$
$662$	30.2239	1.17468
$663$	1.38098	0.0536329
$664$	12.5642	0.487587
$665$	18.2381	0.707242
$666$	2.24214	0.0868811
$667$	−2.15615	−0.0834866
$668$	−3.99323	−0.154503
$669$	−22.5305	−0.871081
$670$	−5.92625	−0.228951
$671$	−50.1606	−1.93643
$672$	−3.17437	−0.122454
$673$	−9.79948	−0.377742	−0.188871	−	0.982002i	$-0.560483\pi$
$673$	−9.79948	−0.377742	−0.188871	+	0.982002i	$0.560483\pi$
$674$	−7.93881	−0.305792
$675$	26.5665	1.02255
$676$	−12.6062	−0.484853
$677$	−18.7735	−0.721525	−0.360762	−	0.932658i	$-0.617483\pi$
$677$	−18.7735	−0.721525	−0.360762	+	0.932658i	$0.617483\pi$
$678$	−7.67736	−0.294847
$679$	15.6355	0.600034
$680$	4.43061	0.169906
$681$	−21.0645	−0.807194
$682$	15.2078	0.582337
$683$	15.3758	0.588340	0.294170	−	0.955753i	$-0.404957\pi$
$683$	15.3758	0.588340	0.294170	+	0.955753i	$0.404957\pi$
$684$	−1.68574	−0.0644557
$685$	65.3881	2.49835
$686$	−20.0779	−0.766578
$687$	42.1221	1.60706
$688$	10.9835	0.418740
$689$	−1.18531	−0.0451568
$690$	−3.82086	−0.145458
$691$	−5.77346	−0.219633	−0.109816	−	0.993952i	$-0.535026\pi$
$691$	−5.77346	−0.219633	−0.109816	+	0.993952i	$0.535026\pi$
$692$	−3.65121	−0.138798
$693$	4.12400	0.156658
$694$	12.9273	0.490715
$695$	−24.5199	−0.930094
$696$	4.24888	0.161053
$697$	6.85557	0.259673
$698$	10.6296	0.402336
$699$	−11.5091	−0.435315
$700$	9.74821	0.368448
$701$	−6.81009	−0.257213	−0.128607	−	0.991696i	$-0.541050\pi$
$701$	−6.81009	−0.257213	−0.128607	+	0.991696i	$0.541050\pi$
$702$	−3.49769	−0.132012
$703$	−10.8307	−0.408486
$704$	−3.41353	−0.128652
$705$	6.70416	0.252493
$706$	−17.3165	−0.651714
$707$	0.935194	0.0351716
$708$	−16.5848	−0.623296
$709$	4.67409	0.175539	0.0877695	−	0.996141i	$-0.472026\pi$
$709$	4.67409	0.175539	0.0877695	+	0.996141i	$0.472026\pi$
$710$	29.6313	1.11204
$711$	−0.580764	−0.0217803
$712$	−5.68248	−0.212960
$713$	−3.50922	−0.131421
$714$	−4.50038	−0.168422
$715$	6.69469	0.250367
$716$	4.08218	0.152558
$717$	−42.7946	−1.59819
$718$	5.39874	0.201479
$719$	−28.2634	−1.05405	−0.527023	−	0.849851i	$-0.676692\pi$
$719$	−28.2634	−1.05405	−0.527023	+	0.849851i	$0.676692\pi$
$720$	−1.84616	−0.0688025
$721$	39.0093	1.45278
$722$	−10.8571	−0.404058
$723$	−9.90803	−0.368484
$724$	−9.65145	−0.358693
$725$	−13.0479	−0.484587
$726$	−1.01228	−0.0375693
$727$	−31.9499	−1.18496	−0.592478	−	0.805587i	$-0.701850\pi$
$727$	−31.9499	−1.18496	−0.592478	+	0.805587i	$0.701850\pi$
$728$	−1.28343	−0.0475670
$729$	30.0167	1.11173
$730$	20.4857	0.758211
$731$	15.5715	0.575933
$732$	−22.8087	−0.843035
$733$	−2.06319	−0.0762056	−0.0381028	−	0.999274i	$-0.512131\pi$
$733$	−2.06319	−0.0762056	−0.0381028	+	0.999274i	$0.512131\pi$
$734$	−18.6066	−0.686781
$735$	13.6673	0.504125
$736$	0.787676	0.0290341
$737$	6.47309	0.238439
$738$	−2.85661	−0.105153
$739$	−25.9395	−0.954199	−0.477100	−	0.878849i	$-0.658312\pi$
$739$	−25.9395	−0.954199	−0.477100	+	0.878849i	$0.658312\pi$
$740$	−11.8614	−0.436033
$741$	2.77963	0.102112
$742$	3.86272	0.141805
$743$	33.1776	1.21717	0.608584	−	0.793489i	$-0.291738\pi$
$743$	33.1776	1.21717	0.608584	+	0.793489i	$0.291738\pi$
$744$	6.91520	0.253524
$745$	−51.1765	−1.87496
$746$	−19.9619	−0.730856
$747$	−7.42223	−0.271565
$748$	−4.83944	−0.176947
$749$	−22.5502	−0.823967
$750$	1.13219	0.0413416
$751$	−12.5679	−0.458610	−0.229305	−	0.973355i	$-0.573645\pi$
$751$	−12.5679	−0.458610	−0.229305	+	0.973355i	$0.573645\pi$
$752$	−1.38207	−0.0503990
$753$	6.83414	0.249050
$754$	1.71786	0.0625607
$755$	−6.87365	−0.250158
$756$	11.3984	0.414554
$757$	50.5109	1.83585	0.917925	−	0.396755i	$-0.129864\pi$
$757$	50.5109	1.83585	0.917925	+	0.396755i	$0.129864\pi$
$758$	8.18521	0.297300
$759$	4.17342	0.151486
$760$	8.91790	0.323486
$761$	−18.0664	−0.654906	−0.327453	−	0.944867i	$-0.606190\pi$
$761$	−18.0664	−0.654906	−0.327453	+	0.944867i	$0.606190\pi$
$762$	1.86837	0.0676838
$763$	−8.34579	−0.302138
$764$	−11.4925	−0.415786
$765$	−2.61735	−0.0946305
$766$	27.4074	0.990269
$767$	−6.70540	−0.242118
$768$	−1.55218	−0.0560094
$769$	22.4044	0.807925	0.403962	−	0.914776i	$-0.367633\pi$
$769$	22.4044	0.807925	0.403962	+	0.914776i	$0.367633\pi$
$770$	−21.8168	−0.786223
$771$	−33.8037	−1.21741
$772$	−5.76266	−0.207403
$773$	−19.6767	−0.707723	−0.353862	−	0.935298i	$-0.615132\pi$
$773$	−19.6767	−0.707723	−0.353862	+	0.935298i	$0.615132\pi$
$774$	−6.48840	−0.233221
$775$	−21.2360	−0.762818
$776$	7.64530	0.274450
$777$	12.0482	0.432226
$778$	20.8903	0.748954
$779$	13.7988	0.494395
$780$	3.04417	0.108999
$781$	−32.3655	−1.15813
$782$	1.11671	0.0399333
$783$	−15.2566	−0.545227
$784$	−2.81753	−0.100626
$785$	−30.3021	−1.08153
$786$	6.49656	0.231725
$787$	−2.59184	−0.0923892	−0.0461946	−	0.998932i	$-0.514709\pi$
$787$	−2.59184	−0.0923892	−0.0461946	+	0.998932i	$0.514709\pi$
$788$	8.41305	0.299702
$789$	47.3636	1.68619
$790$	3.07236	0.109310
$791$	10.1155	0.359665
$792$	2.01652	0.0716538
$793$	−9.22178	−0.327475
$794$	23.6586	0.839612
$795$	−9.16200	−0.324943
$796$	28.1006	0.996001
$797$	22.2968	0.789794	0.394897	−	0.918725i	$-0.370780\pi$
$797$	22.2968	0.789794	0.394897	+	0.918725i	$0.370780\pi$
$798$	−9.05834	−0.320662
$799$	−1.95940	−0.0693185
$800$	4.76660	0.168525
$801$	3.35688	0.118610
$802$	−37.0152	−1.30705
$803$	−22.3761	−0.789634
$804$	2.94340	0.103806
$805$	5.03426	0.177434
$806$	2.79588	0.0984807
$807$	−42.0558	−1.48044
$808$	0.457283	0.0160872
$809$	−24.8005	−0.871940	−0.435970	−	0.899961i	$-0.643595\pi$
$809$	−24.8005	−0.871940	−0.435970	+	0.899961i	$0.643595\pi$
$810$	−21.4973	−0.755338
$811$	35.5806	1.24941	0.624703	−	0.780863i	$-0.285220\pi$
$811$	35.5806	1.24941	0.624703	+	0.780863i	$0.285220\pi$
$812$	−5.59820	−0.196458
$813$	−11.6163	−0.407402
$814$	12.9559	0.454104
$815$	15.3860	0.538949
$816$	−2.20056	−0.0770350
$817$	31.3422	1.09653
$818$	4.22387	0.147684
$819$	0.758176	0.0264928
$820$	15.1121	0.527736
$821$	−15.5140	−0.541443	−0.270721	−	0.962658i	$-0.587262\pi$
$821$	−15.5140	−0.541443	−0.270721	+	0.962658i	$0.587262\pi$
$822$	−32.4764	−1.13275
$823$	−32.6527	−1.13820	−0.569100	−	0.822268i	$-0.692708\pi$
$823$	−32.6527	−1.13820	−0.569100	+	0.822268i	$0.692708\pi$
$824$	19.0745	0.664490
$825$	25.2554	0.879279
$826$	21.8517	0.760319
$827$	45.4529	1.58055	0.790277	−	0.612750i	$-0.209937\pi$
$827$	45.4529	1.58055	0.790277	+	0.612750i	$0.209937\pi$
$828$	−0.465314	−0.0161708
$829$	−37.9887	−1.31940	−0.659701	−	0.751528i	$-0.729317\pi$
$829$	−37.9887	−1.31940	−0.659701	+	0.751528i	$0.729317\pi$
$830$	39.2652	1.36291
$831$	27.9743	0.970418
$832$	−0.627560	−0.0217567
$833$	−3.99448	−0.138401
$834$	12.1784	0.421703
$835$	−12.4795	−0.431869
$836$	−9.74079	−0.336892
$837$	−24.8307	−0.858275
$838$	−7.50624	−0.259299
$839$	−12.8826	−0.444757	−0.222379	−	0.974960i	$-0.571382\pi$
$839$	−12.8826	−0.444757	−0.222379	+	0.974960i	$0.571382\pi$
$840$	−9.92041	−0.342287
$841$	−21.5068	−0.741615
$842$	17.6163	0.607098
$843$	33.2370	1.14474
$844$	−15.3093	−0.526968
$845$	−39.3962	−1.35527
$846$	0.816450	0.0280701
$847$	1.33375	0.0458283
$848$	1.88876	0.0648603
$849$	−2.27262	−0.0779963
$850$	6.75772	0.231788
$851$	−2.98959	−0.102482
$852$	−14.7170	−0.504197
$853$	−43.6486	−1.49450	−0.747250	−	0.664543i	$-0.768626\pi$
$853$	−43.6486	−1.49450	−0.747250	+	0.664543i	$0.768626\pi$
$854$	30.0522	1.02836
$855$	−5.26818	−0.180168
$856$	−11.0264	−0.376875
$857$	−12.2279	−0.417698	−0.208849	−	0.977948i	$-0.566972\pi$
$857$	−12.2279	−0.417698	−0.208849	+	0.977948i	$0.566972\pi$
$858$	−3.32506	−0.113516
$859$	−9.66214	−0.329668	−0.164834	−	0.986321i	$-0.552709\pi$
$859$	−9.66214	−0.329668	−0.164834	+	0.986321i	$0.552709\pi$
$860$	34.3250	1.17047
$861$	−15.3500	−0.523128
$862$	22.3139	0.760015
$863$	−14.7337	−0.501543	−0.250771	−	0.968046i	$-0.580684\pi$
$863$	−14.7337	−0.501543	−0.250771	+	0.968046i	$0.580684\pi$
$864$	5.57347	0.189613
$865$	−11.4106	−0.387972
$866$	−38.9290	−1.32286
$867$	23.2672	0.790197
$868$	−9.11128	−0.309257
$869$	−3.35586	−0.113840
$870$	13.2784	0.450180
$871$	1.19005	0.0403231
$872$	−4.08085	−0.138195
$873$	−4.51641	−0.152857
$874$	2.24770	0.0760296
$875$	−1.49174	−0.0504300
$876$	−10.1747	−0.343771
$877$	3.52672	0.119089	0.0595444	−	0.998226i	$-0.481035\pi$
$877$	3.52672	0.119089	0.0595444	+	0.998226i	$0.481035\pi$
$878$	26.3294	0.888575
$879$	−20.7835	−0.701012
$880$	−10.6678	−0.359612
$881$	7.99021	0.269197	0.134598	−	0.990900i	$-0.457026\pi$
$881$	7.99021	0.269197	0.134598	+	0.990900i	$0.457026\pi$
$882$	1.66444	0.0560445
$883$	−19.1947	−0.645954	−0.322977	−	0.946407i	$-0.604684\pi$
$883$	−19.1947	−0.645954	−0.322977	+	0.946407i	$0.604684\pi$
$884$	−0.889706	−0.0299241
$885$	−51.8302	−1.74225
$886$	−19.1751	−0.644201
$887$	−3.01893	−0.101366	−0.0506829	−	0.998715i	$-0.516140\pi$
$887$	−3.01893	−0.101366	−0.0506829	+	0.998715i	$0.516140\pi$
$888$	5.89122	0.197696
$889$	−2.46171	−0.0825631
$890$	−17.7586	−0.595271
$891$	23.4809	0.786641
$892$	14.5154	0.486013
$893$	−3.94386	−0.131976
$894$	25.4180	0.850104
$895$	12.7574	0.426434
$896$	2.04511	0.0683223
$897$	0.767263	0.0256182
$898$	−7.80518	−0.260462
$899$	12.1954	0.406739
$900$	−2.81583	−0.0938611
$901$	2.67774	0.0892085
$902$	−16.5065	−0.549607
$903$	−34.8656	−1.16025
$904$	4.94619	0.164508
$905$	−30.1623	−1.00263
$906$	3.41395	0.113421
$907$	−41.2090	−1.36832	−0.684161	−	0.729331i	$-0.739831\pi$
$907$	−41.2090	−1.36832	−0.684161	+	0.729331i	$0.739831\pi$
$908$	13.5709	0.450367
$909$	−0.270137	−0.00895988
$910$	−4.01091	−0.132960
$911$	−13.7190	−0.454531	−0.227265	−	0.973833i	$-0.572978\pi$
$911$	−13.7190	−0.454531	−0.227265	+	0.973833i	$0.572978\pi$
$912$	−4.42927	−0.146668
$913$	−42.8884	−1.41940
$914$	38.8686	1.28566
$915$	−71.2809	−2.35647
$916$	−27.1374	−0.896645
$917$	−8.55969	−0.282666
$918$	7.90164	0.260793
$919$	−21.9066	−0.722630	−0.361315	−	0.932444i	$-0.617672\pi$
$919$	−21.9066	−0.722630	−0.361315	+	0.932444i	$0.617672\pi$
$920$	2.46161	0.0811569
$921$	1.89426	0.0624180
$922$	−8.14130	−0.268119
$923$	−5.95023	−0.195854
$924$	10.8358	0.356472
$925$	−18.0914	−0.594842
$926$	−5.60120	−0.184067
$927$	−11.2681	−0.370093
$928$	−2.73736	−0.0898584
$929$	−42.3889	−1.39073	−0.695367	−	0.718655i	$-0.744758\pi$
$929$	−42.3889	−1.39073	−0.695367	+	0.718655i	$0.744758\pi$
$930$	21.6111	0.708655
$931$	−8.04007	−0.263503
$932$	7.41482	0.242881
$933$	7.92369	0.259410
$934$	33.9279	1.11015
$935$	−15.1240	−0.494607
$936$	0.370727	0.0121176
$937$	3.29390	0.107607	0.0538036	−	0.998552i	$-0.482866\pi$
$937$	3.29390	0.107607	0.0538036	+	0.998552i	$0.482866\pi$
$938$	−3.87815	−0.126626
$939$	10.6279	0.346827
$940$	−4.31920	−0.140877
$941$	40.5667	1.32244	0.661218	−	0.750194i	$-0.270040\pi$
$941$	40.5667	1.32244	0.661218	+	0.750194i	$0.270040\pi$
$942$	15.0502	0.490363
$943$	3.80890	0.124035
$944$	10.6849	0.347763
$945$	35.6216	1.15877
$946$	−37.4923	−1.21898
$947$	12.5558	0.408007	0.204004	−	0.978970i	$-0.434605\pi$
$947$	12.5558	0.408007	0.204004	+	0.978970i	$0.434605\pi$
$948$	−1.52596	−0.0495608
$949$	−4.11372	−0.133537
$950$	13.6019	0.441304
$951$	−4.59015	−0.148846
$952$	2.89940	0.0939700
$953$	1.39625	0.0452289	0.0226144	−	0.999744i	$-0.492801\pi$
$953$	1.39625	0.0452289	0.0226144	+	0.999744i	$0.492801\pi$
$954$	−1.11577	−0.0361245
$955$	−35.9160	−1.16221
$956$	27.5707	0.891699
$957$	−14.5037	−0.468837
$958$	30.5642	0.987484
$959$	42.7901	1.38176
$960$	−4.85080	−0.156559
$961$	−11.1515	−0.359727
$962$	2.38188	0.0767947
$963$	6.51378	0.209904
$964$	6.38331	0.205593
$965$	−18.0092	−0.579737
$966$	−2.50038	−0.0804483
$967$	35.7367	1.14922	0.574608	−	0.818429i	$-0.305155\pi$
$967$	35.7367	1.14922	0.574608	+	0.818429i	$0.305155\pi$
$968$	0.652168	0.0209615
$969$	−6.27948	−0.201726
$970$	23.8928	0.767150
$971$	−25.7607	−0.826699	−0.413349	−	0.910573i	$-0.635641\pi$
$971$	−25.7607	−0.826699	−0.413349	+	0.910573i	$0.635641\pi$
$972$	−6.04331	−0.193839
$973$	−16.0459	−0.514408
$974$	19.5778	0.627314
$975$	4.64307	0.148697
$976$	14.6947	0.470365
$977$	−3.12340	−0.0999265	−0.0499633	−	0.998751i	$-0.515910\pi$
$977$	−3.12340	−0.0999265	−0.0499633	+	0.998751i	$0.515910\pi$
$978$	−7.64181	−0.244358
$979$	19.3973	0.619940
$980$	−8.80523	−0.281273
$981$	2.41074	0.0769689
$982$	−18.7417	−0.598072
$983$	6.58653	0.210078	0.105039	−	0.994468i	$-0.466503\pi$
$983$	6.58653	0.210078	0.105039	+	0.994468i	$0.466503\pi$
$984$	−7.50574	−0.239274
$985$	26.2921	0.837735
$986$	−3.88082	−0.123591
$987$	4.38722	0.139647
$988$	−1.79080	−0.0569728
$989$	8.65140	0.275099
$990$	6.30193	0.200288
$991$	−33.2121	−1.05502	−0.527509	−	0.849549i	$-0.676874\pi$
$991$	−33.2121	−1.05502	−0.527509	+	0.849549i	$0.676874\pi$
$992$	−4.45516	−0.141451
$993$	−46.9129	−1.48873
$994$	19.3908	0.615037
$995$	87.8189	2.78405
$996$	−19.5019	−0.617942
$997$	32.5677	1.03143	0.515715	−	0.856760i	$-0.327526\pi$
$997$	32.5677	1.03143	0.515715	+	0.856760i	$0.327526\pi$
$998$	−28.8181	−0.912221
$999$	−21.1539	−0.669279

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.f.1.15	✓	67

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.f.1.15	✓	67	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:	\( N \)	\(=\)	\( 6046 = 2 \cdot 3023 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6046.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.55218 q^{3} +1.00000 q^{4} +3.12516 q^{5} -1.55218 q^{6} +2.04511 q^{7} +1.00000 q^{8} -0.590743 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.55218 q^{3} +1.00000 q^{4} +3.12516 q^{5} -1.55218 q^{6} +2.04511 q^{7} +1.00000 q^{8} -0.590743 q^{9} +3.12516 q^{10} -3.41353 q^{11} -1.55218 q^{12} -0.627560 q^{13} +2.04511 q^{14} -4.85080 q^{15} +1.00000 q^{16} +1.41772 q^{17} -0.590743 q^{18} +2.85358 q^{19} +3.12516 q^{20} -3.17437 q^{21} -3.41353 q^{22} +0.787676 q^{23} -1.55218 q^{24} +4.76660 q^{25} -0.627560 q^{26} +5.57347 q^{27} +2.04511 q^{28} -2.73736 q^{29} -4.85080 q^{30} -4.45516 q^{31} +1.00000 q^{32} +5.29840 q^{33} +1.41772 q^{34} +6.39128 q^{35} -0.590743 q^{36} -3.79545 q^{37} +2.85358 q^{38} +0.974085 q^{39} +3.12516 q^{40} +4.83562 q^{41} -3.17437 q^{42} +10.9835 q^{43} -3.41353 q^{44} -1.84616 q^{45} +0.787676 q^{46} -1.38207 q^{47} -1.55218 q^{48} -2.81753 q^{49} +4.76660 q^{50} -2.20056 q^{51} -0.627560 q^{52} +1.88876 q^{53} +5.57347 q^{54} -10.6678 q^{55} +2.04511 q^{56} -4.42927 q^{57} -2.73736 q^{58} +10.6849 q^{59} -4.85080 q^{60} +14.6947 q^{61} -4.45516 q^{62} -1.20813 q^{63} +1.00000 q^{64} -1.96122 q^{65} +5.29840 q^{66} -1.89631 q^{67} +1.41772 q^{68} -1.22261 q^{69} +6.39128 q^{70} +9.48153 q^{71} -0.590743 q^{72} +6.55511 q^{73} -3.79545 q^{74} -7.39861 q^{75} +2.85358 q^{76} -6.98103 q^{77} +0.974085 q^{78} +0.983107 q^{79} +3.12516 q^{80} -6.87879 q^{81} +4.83562 q^{82} +12.5642 q^{83} -3.17437 q^{84} +4.43061 q^{85} +10.9835 q^{86} +4.24888 q^{87} -3.41353 q^{88} -5.68248 q^{89} -1.84616 q^{90} -1.28343 q^{91} +0.787676 q^{92} +6.91520 q^{93} -1.38207 q^{94} +8.91790 q^{95} -1.55218 q^{96} +7.64530 q^{97} -2.81753 q^{98} +2.01652 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 67 q + 67 q^{2} + 21 q^{3} + 67 q^{4} + 21 q^{5} + 21 q^{6} + 38 q^{7} + 67 q^{8} + 90 q^{9}+O(q^{10}) \) 67 * q + 67 * q^2 + 21 * q^3 + 67 * q^4 + 21 * q^5 + 21 * q^6 + 38 * q^7 + 67 * q^8 + 90 * q^9	\( 67 q + 67 q^{2} + 21 q^{3} + 67 q^{4} + 21 q^{5} + 21 q^{6} + 38 q^{7} + 67 q^{8} + 90 q^{9} + 21 q^{10} + 56 q^{11} + 21 q^{12} + 33 q^{13} + 38 q^{14} + 25 q^{15} + 67 q^{16} + 30 q^{17} + 90 q^{18} + 36 q^{19} + 21 q^{20} + 20 q^{21} + 56 q^{22} + 65 q^{23} + 21 q^{24} + 72 q^{25} + 33 q^{26} + 57 q^{27} + 38 q^{28} + 84 q^{29} + 25 q^{30} + 52 q^{31} + 67 q^{32} - 9 q^{33} + 30 q^{34} + 30 q^{35} + 90 q^{36} + 52 q^{37} + 36 q^{38} + 41 q^{39} + 21 q^{40} + 46 q^{41} + 20 q^{42} + 61 q^{43} + 56 q^{44} + 23 q^{45} + 65 q^{46} + 51 q^{47} + 21 q^{48} + 81 q^{49} + 72 q^{50} + 33 q^{51} + 33 q^{52} + 72 q^{53} + 57 q^{54} + 14 q^{55} + 38 q^{56} - 26 q^{57} + 84 q^{58} + 71 q^{59} + 25 q^{60} + 42 q^{61} + 52 q^{62} + 63 q^{63} + 67 q^{64} - 2 q^{65} - 9 q^{66} + 70 q^{67} + 30 q^{68} + 21 q^{69} + 30 q^{70} + 104 q^{71} + 90 q^{72} - 31 q^{73} + 52 q^{74} + 69 q^{75} + 36 q^{76} + 48 q^{77} + 41 q^{78} + 79 q^{79} + 21 q^{80} + 123 q^{81} + 46 q^{82} + 41 q^{83} + 20 q^{84} + 6 q^{85} + 61 q^{86} + 19 q^{87} + 56 q^{88} + 58 q^{89} + 23 q^{90} + 31 q^{91} + 65 q^{92} + 13 q^{93} + 51 q^{94} + 77 q^{95} + 21 q^{96} - 8 q^{97} + 81 q^{98} + 129 q^{99}+O(q^{100}) \) 67 * q + 67 * q^2 + 21 * q^3 + 67 * q^4 + 21 * q^5 + 21 * q^6 + 38 * q^7 + 67 * q^8 + 90 * q^9 + 21 * q^10 + 56 * q^11 + 21 * q^12 + 33 * q^13 + 38 * q^14 + 25 * q^15 + 67 * q^16 + 30 * q^17 + 90 * q^18 + 36 * q^19 + 21 * q^20 + 20 * q^21 + 56 * q^22 + 65 * q^23 + 21 * q^24 + 72 * q^25 + 33 * q^26 + 57 * q^27 + 38 * q^28 + 84 * q^29 + 25 * q^30 + 52 * q^31 + 67 * q^32 - 9 * q^33 + 30 * q^34 + 30 * q^35 + 90 * q^36 + 52 * q^37 + 36 * q^38 + 41 * q^39 + 21 * q^40 + 46 * q^41 + 20 * q^42 + 61 * q^43 + 56 * q^44 + 23 * q^45 + 65 * q^46 + 51 * q^47 + 21 * q^48 + 81 * q^49 + 72 * q^50 + 33 * q^51 + 33 * q^52 + 72 * q^53 + 57 * q^54 + 14 * q^55 + 38 * q^56 - 26 * q^57 + 84 * q^58 + 71 * q^59 + 25 * q^60 + 42 * q^61 + 52 * q^62 + 63 * q^63 + 67 * q^64 - 2 * q^65 - 9 * q^66 + 70 * q^67 + 30 * q^68 + 21 * q^69 + 30 * q^70 + 104 * q^71 + 90 * q^72 - 31 * q^73 + 52 * q^74 + 69 * q^75 + 36 * q^76 + 48 * q^77 + 41 * q^78 + 79 * q^79 + 21 * q^80 + 123 * q^81 + 46 * q^82 + 41 * q^83 + 20 * q^84 + 6 * q^85 + 61 * q^86 + 19 * q^87 + 56 * q^88 + 58 * q^89 + 23 * q^90 + 31 * q^91 + 65 * q^92 + 13 * q^93 + 51 * q^94 + 77 * q^95 + 21 * q^96 - 8 * q^97 + 81 * q^98 + 129 * q^99

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