LMFDB - Embedded newform 6014.2.a.k.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.11031 q^{3} +1.00000 q^{4} +2.99950 q^{5} -3.11031 q^{6} +2.46329 q^{7} +1.00000 q^{8} +6.67403 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.11031 q^{3} +1.00000 q^{4} +2.99950 q^{5} -3.11031 q^{6} +2.46329 q^{7} +1.00000 q^{8} +6.67403 q^{9} +2.99950 q^{10} -1.64625 q^{11} -3.11031 q^{12} +3.05612 q^{13} +2.46329 q^{14} -9.32938 q^{15} +1.00000 q^{16} -7.30070 q^{17} +6.67403 q^{18} +5.24743 q^{19} +2.99950 q^{20} -7.66161 q^{21} -1.64625 q^{22} +3.96028 q^{23} -3.11031 q^{24} +3.99701 q^{25} +3.05612 q^{26} -11.4274 q^{27} +2.46329 q^{28} -7.42542 q^{29} -9.32938 q^{30} +1.00000 q^{31} +1.00000 q^{32} +5.12035 q^{33} -7.30070 q^{34} +7.38866 q^{35} +6.67403 q^{36} +10.9467 q^{37} +5.24743 q^{38} -9.50550 q^{39} +2.99950 q^{40} +2.96481 q^{41} -7.66161 q^{42} +6.77924 q^{43} -1.64625 q^{44} +20.0188 q^{45} +3.96028 q^{46} +12.2307 q^{47} -3.11031 q^{48} -0.932182 q^{49} +3.99701 q^{50} +22.7074 q^{51} +3.05612 q^{52} -0.0444449 q^{53} -11.4274 q^{54} -4.93793 q^{55} +2.46329 q^{56} -16.3211 q^{57} -7.42542 q^{58} +2.31645 q^{59} -9.32938 q^{60} -7.95615 q^{61} +1.00000 q^{62} +16.4401 q^{63} +1.00000 q^{64} +9.16685 q^{65} +5.12035 q^{66} +7.01291 q^{67} -7.30070 q^{68} -12.3177 q^{69} +7.38866 q^{70} -10.1525 q^{71} +6.67403 q^{72} -12.7393 q^{73} +10.9467 q^{74} -12.4320 q^{75} +5.24743 q^{76} -4.05520 q^{77} -9.50550 q^{78} +3.73882 q^{79} +2.99950 q^{80} +15.5206 q^{81} +2.96481 q^{82} -5.47840 q^{83} -7.66161 q^{84} -21.8985 q^{85} +6.77924 q^{86} +23.0954 q^{87} -1.64625 q^{88} +16.8996 q^{89} +20.0188 q^{90} +7.52813 q^{91} +3.96028 q^{92} -3.11031 q^{93} +12.2307 q^{94} +15.7397 q^{95} -3.11031 q^{96} +1.00000 q^{97} -0.932182 q^{98} -10.9871 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9}+O(q^{10}) $ 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9} + 9 q^{10} + 5 q^{11} + 9 q^{12} + 16 q^{13} + 19 q^{14} + 22 q^{15} + 37 q^{16} + 3 q^{17} + 52 q^{18} + 36 q^{19} + 9 q^{20} + 6 q^{21} + 5 q^{22} + 11 q^{23} + 9 q^{24} + 58 q^{25} + 16 q^{26} + 24 q^{27} + 19 q^{28} + 5 q^{29} + 22 q^{30} + 37 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 28 q^{35} + 52 q^{36} + 21 q^{37} + 36 q^{38} + 38 q^{39} + 9 q^{40} + 21 q^{41} + 6 q^{42} + 14 q^{43} + 5 q^{44} + 55 q^{45} + 11 q^{46} + 59 q^{47} + 9 q^{48} + 82 q^{49} + 58 q^{50} + 46 q^{51} + 16 q^{52} + 8 q^{53} + 24 q^{54} + 25 q^{55} + 19 q^{56} + 5 q^{58} + 41 q^{59} + 22 q^{60} + 16 q^{61} + 37 q^{62} + 23 q^{63} + 37 q^{64} - 46 q^{65} + q^{66} + 45 q^{67} + 3 q^{68} + 68 q^{69} + 28 q^{70} + 55 q^{71} + 52 q^{72} + 29 q^{73} + 21 q^{74} - 12 q^{75} + 36 q^{76} + 30 q^{77} + 38 q^{78} + 25 q^{79} + 9 q^{80} + 73 q^{81} + 21 q^{82} + 70 q^{83} + 6 q^{84} - 21 q^{85} + 14 q^{86} + 37 q^{87} + 5 q^{88} + 55 q^{90} + 18 q^{91} + 11 q^{92} + 9 q^{93} + 59 q^{94} - 9 q^{95} + 9 q^{96} + 37 q^{97} + 82 q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9 + 9 * q^10 + 5 * q^11 + 9 * q^12 + 16 * q^13 + 19 * q^14 + 22 * q^15 + 37 * q^16 + 3 * q^17 + 52 * q^18 + 36 * q^19 + 9 * q^20 + 6 * q^21 + 5 * q^22 + 11 * q^23 + 9 * q^24 + 58 * q^25 + 16 * q^26 + 24 * q^27 + 19 * q^28 + 5 * q^29 + 22 * q^30 + 37 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 28 * q^35 + 52 * q^36 + 21 * q^37 + 36 * q^38 + 38 * q^39 + 9 * q^40 + 21 * q^41 + 6 * q^42 + 14 * q^43 + 5 * q^44 + 55 * q^45 + 11 * q^46 + 59 * q^47 + 9 * q^48 + 82 * q^49 + 58 * q^50 + 46 * q^51 + 16 * q^52 + 8 * q^53 + 24 * q^54 + 25 * q^55 + 19 * q^56 + 5 * q^58 + 41 * q^59 + 22 * q^60 + 16 * q^61 + 37 * q^62 + 23 * q^63 + 37 * q^64 - 46 * q^65 + q^66 + 45 * q^67 + 3 * q^68 + 68 * q^69 + 28 * q^70 + 55 * q^71 + 52 * q^72 + 29 * q^73 + 21 * q^74 - 12 * q^75 + 36 * q^76 + 30 * q^77 + 38 * q^78 + 25 * q^79 + 9 * q^80 + 73 * q^81 + 21 * q^82 + 70 * q^83 + 6 * q^84 - 21 * q^85 + 14 * q^86 + 37 * q^87 + 5 * q^88 + 55 * q^90 + 18 * q^91 + 11 * q^92 + 9 * q^93 + 59 * q^94 - 9 * q^95 + 9 * q^96 + 37 * q^97 + 82 * q^98 + 33 * 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
$3$	−3.11031	−1.79574	−0.897869	−	0.440262i	$-0.854886\pi$
$3$	−3.11031	−1.79574	−0.897869	+	0.440262i	$0.854886\pi$
$4$	1.00000	0.500000
$5$	2.99950	1.34142	0.670709	−	0.741721i	$-0.265990\pi$
$5$	2.99950	1.34142	0.670709	+	0.741721i	$0.265990\pi$
$6$	−3.11031	−1.26978
$7$	2.46329	0.931038	0.465519	−	0.885038i	$-0.345868\pi$
$7$	2.46329	0.931038	0.465519	+	0.885038i	$0.345868\pi$
$8$	1.00000	0.353553
$9$	6.67403	2.22468
$10$	2.99950	0.948526
$11$	−1.64625	−0.496363	−0.248182	−	0.968714i	$-0.579833\pi$
$11$	−1.64625	−0.496363	−0.248182	+	0.968714i	$0.579833\pi$
$12$	−3.11031	−0.897869
$13$	3.05612	0.847617	0.423808	−	0.905752i	$-0.360693\pi$
$13$	3.05612	0.847617	0.423808	+	0.905752i	$0.360693\pi$
$14$	2.46329	0.658343
$15$	−9.32938	−2.40884
$16$	1.00000	0.250000
$17$	−7.30070	−1.77068	−0.885340	−	0.464945i	$-0.846074\pi$
$17$	−7.30070	−1.77068	−0.885340	+	0.464945i	$0.846074\pi$
$18$	6.67403	1.57309
$19$	5.24743	1.20384	0.601922	−	0.798555i	$-0.294402\pi$
$19$	5.24743	1.20384	0.601922	+	0.798555i	$0.294402\pi$
$20$	2.99950	0.670709
$21$	−7.66161	−1.67190
$22$	−1.64625	−0.350982
$23$	3.96028	0.825776	0.412888	−	0.910782i	$-0.364520\pi$
$23$	3.96028	0.825776	0.412888	+	0.910782i	$0.364520\pi$
$24$	−3.11031	−0.634890
$25$	3.99701	0.799403
$26$	3.05612	0.599355
$27$	−11.4274	−2.19920
$28$	2.46329	0.465519
$29$	−7.42542	−1.37887	−0.689433	−	0.724349i	$-0.742140\pi$
$29$	−7.42542	−1.37887	−0.689433	+	0.724349i	$0.742140\pi$
$30$	−9.32938	−1.70330
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	5.12035	0.891338
$34$	−7.30070	−1.25206
$35$	7.38866	1.24891
$36$	6.67403	1.11234
$37$	10.9467	1.79962	0.899811	−	0.436281i	$-0.143705\pi$
$37$	10.9467	1.79962	0.899811	+	0.436281i	$0.143705\pi$
$38$	5.24743	0.851246
$39$	−9.50550	−1.52210
$40$	2.99950	0.474263
$41$	2.96481	0.463026	0.231513	−	0.972832i	$-0.425632\pi$
$41$	2.96481	0.463026	0.231513	+	0.972832i	$0.425632\pi$
$42$	−7.66161	−1.18221
$43$	6.77924	1.03382	0.516912	−	0.856039i	$-0.327081\pi$
$43$	6.77924	1.03382	0.516912	+	0.856039i	$0.327081\pi$
$44$	−1.64625	−0.248182
$45$	20.0188	2.98422
$46$	3.96028	0.583911
$47$	12.2307	1.78403	0.892015	−	0.452005i	$-0.149291\pi$
$47$	12.2307	1.78403	0.892015	+	0.452005i	$0.149291\pi$
$48$	−3.11031	−0.448935
$49$	−0.932182	−0.133169
$50$	3.99701	0.565263
$51$	22.7074	3.17968
$52$	3.05612	0.423808
$53$	−0.0444449	−0.00610498	−0.00305249	−	0.999995i	$-0.500972\pi$
$53$	−0.0444449	−0.00610498	−0.00305249	+	0.999995i	$0.500972\pi$
$54$	−11.4274	−1.55507
$55$	−4.93793	−0.665830
$56$	2.46329	0.329172
$57$	−16.3211	−2.16179
$58$	−7.42542	−0.975006
$59$	2.31645	0.301576	0.150788	−	0.988566i	$-0.451819\pi$
$59$	2.31645	0.301576	0.150788	+	0.988566i	$0.451819\pi$
$60$	−9.32938	−1.20442
$61$	−7.95615	−1.01868	−0.509340	−	0.860565i	$-0.670111\pi$
$61$	−7.95615	−1.01868	−0.509340	+	0.860565i	$0.670111\pi$
$62$	1.00000	0.127000
$63$	16.4401	2.07126
$64$	1.00000	0.125000
$65$	9.16685	1.13701
$66$	5.12035	0.630271
$67$	7.01291	0.856763	0.428381	−	0.903598i	$-0.359084\pi$
$67$	7.01291	0.856763	0.428381	+	0.903598i	$0.359084\pi$
$68$	−7.30070	−0.885340
$69$	−12.3177	−1.48288
$70$	7.38866	0.883113
$71$	−10.1525	−1.20488	−0.602442	−	0.798163i	$-0.705806\pi$
$71$	−10.1525	−1.20488	−0.602442	+	0.798163i	$0.705806\pi$
$72$	6.67403	0.786543
$73$	−12.7393	−1.49102	−0.745510	−	0.666494i	$-0.767794\pi$
$73$	−12.7393	−1.49102	−0.745510	+	0.666494i	$0.767794\pi$
$74$	10.9467	1.27252
$75$	−12.4320	−1.43552
$76$	5.24743	0.601922
$77$	−4.05520	−0.462133
$78$	−9.50550	−1.07629
$79$	3.73882	0.420650	0.210325	−	0.977632i	$-0.432548\pi$
$79$	3.73882	0.420650	0.210325	+	0.977632i	$0.432548\pi$
$80$	2.99950	0.335355
$81$	15.5206	1.72451
$82$	2.96481	0.327409
$83$	−5.47840	−0.601332	−0.300666	−	0.953729i	$-0.597209\pi$
$83$	−5.47840	−0.601332	−0.300666	+	0.953729i	$0.597209\pi$
$84$	−7.66161	−0.835950
$85$	−21.8985	−2.37522
$86$	6.77924	0.731024
$87$	23.0954	2.47608
$88$	−1.64625	−0.175491
$89$	16.8996	1.79136	0.895680	−	0.444700i	$-0.146690\pi$
$89$	16.8996	1.79136	0.895680	+	0.444700i	$0.146690\pi$
$90$	20.0188	2.11016
$91$	7.52813	0.789163
$92$	3.96028	0.412888
$93$	−3.11031	−0.322524
$94$	12.2307	1.26150
$95$	15.7397	1.61486
$96$	−3.11031	−0.317445
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	−0.932182	−0.0941646
$99$	−10.9871	−1.10425
$100$	3.99701	0.399701
$101$	6.75915	0.672560	0.336280	−	0.941762i	$-0.390831\pi$
$101$	6.75915	0.672560	0.336280	+	0.941762i	$0.390831\pi$
$102$	22.7074	2.24837
$103$	9.59532	0.945455	0.472728	−	0.881209i	$-0.343269\pi$
$103$	9.59532	0.945455	0.472728	+	0.881209i	$0.343269\pi$
$104$	3.05612	0.299678
$105$	−22.9810	−2.24272
$106$	−0.0444449	−0.00431687
$107$	−3.12399	−0.302007	−0.151004	−	0.988533i	$-0.548250\pi$
$107$	−3.12399	−0.302007	−0.151004	+	0.988533i	$0.548250\pi$
$108$	−11.4274	−1.09960
$109$	−4.72870	−0.452927	−0.226464	−	0.974020i	$-0.572716\pi$
$109$	−4.72870	−0.452927	−0.226464	+	0.974020i	$0.572716\pi$
$110$	−4.93793	−0.470813
$111$	−34.0475	−3.23165
$112$	2.46329	0.232759
$113$	−13.1096	−1.23325	−0.616626	−	0.787257i	$-0.711501\pi$
$113$	−13.1096	−1.23325	−0.616626	+	0.787257i	$0.711501\pi$
$114$	−16.3211	−1.52862
$115$	11.8789	1.10771
$116$	−7.42542	−0.689433
$117$	20.3967	1.88567
$118$	2.31645	0.213247
$119$	−17.9838	−1.64857
$120$	−9.32938	−0.851652
$121$	−8.28986	−0.753624
$122$	−7.95615	−0.720316
$123$	−9.22150	−0.831474
$124$	1.00000	0.0898027
$125$	−3.00846	−0.269085
$126$	16.4401	1.46460
$127$	11.2065	0.994414	0.497207	−	0.867632i	$-0.334359\pi$
$127$	11.2065	0.994414	0.497207	+	0.867632i	$0.334359\pi$
$128$	1.00000	0.0883883
$129$	−21.0855	−1.85648
$130$	9.16685	0.803986
$131$	−21.1504	−1.84792	−0.923958	−	0.382495i	$-0.875065\pi$
$131$	−21.1504	−1.84792	−0.923958	+	0.382495i	$0.875065\pi$
$132$	5.12035	0.445669
$133$	12.9260	1.12082
$134$	7.01291	0.605823
$135$	−34.2765	−2.95005
$136$	−7.30070	−0.626030
$137$	7.53105	0.643421	0.321711	−	0.946838i	$-0.395742\pi$
$137$	7.53105	0.643421	0.321711	+	0.946838i	$0.395742\pi$
$138$	−12.3177	−1.04855
$139$	19.1150	1.62132	0.810658	−	0.585520i	$-0.199109\pi$
$139$	19.1150	1.62132	0.810658	+	0.585520i	$0.199109\pi$
$140$	7.38866	0.624455
$141$	−38.0413	−3.20365
$142$	−10.1525	−0.851982
$143$	−5.03115	−0.420726
$144$	6.67403	0.556170
$145$	−22.2726	−1.84964
$146$	−12.7393	−1.05431
$147$	2.89938	0.239136
$148$	10.9467	0.899811
$149$	−11.3352	−0.928614	−0.464307	−	0.885674i	$-0.653697\pi$
$149$	−11.3352	−0.928614	−0.464307	+	0.885674i	$0.653697\pi$
$150$	−12.4320	−1.01506
$151$	13.1376	1.06912	0.534562	−	0.845129i	$-0.320476\pi$
$151$	13.1376	1.06912	0.534562	+	0.845129i	$0.320476\pi$
$152$	5.24743	0.425623
$153$	−48.7251	−3.93919
$154$	−4.05520	−0.326777
$155$	2.99950	0.240926
$156$	−9.50550	−0.761049
$157$	6.67826	0.532983	0.266491	−	0.963837i	$-0.414136\pi$
$157$	6.67826	0.532983	0.266491	+	0.963837i	$0.414136\pi$
$158$	3.73882	0.297444
$159$	0.138238	0.0109630
$160$	2.99950	0.237131
$161$	9.75534	0.768828
$162$	15.5206	1.21942
$163$	1.04238	0.0816458	0.0408229	−	0.999166i	$-0.487002\pi$
$163$	1.04238	0.0816458	0.0408229	+	0.999166i	$0.487002\pi$
$164$	2.96481	0.231513
$165$	15.3585	1.19566
$166$	−5.47840	−0.425206
$167$	0.0474407	0.00367107	0.00183554	−	0.999998i	$-0.499416\pi$
$167$	0.0474407	0.00367107	0.00183554	+	0.999998i	$0.499416\pi$
$168$	−7.66161	−0.591106
$169$	−3.66010	−0.281546
$170$	−21.8985	−1.67954
$171$	35.0215	2.67816
$172$	6.77924	0.516912
$173$	−8.55194	−0.650192	−0.325096	−	0.945681i	$-0.605397\pi$
$173$	−8.55194	−0.650192	−0.325096	+	0.945681i	$0.605397\pi$
$174$	23.0954	1.75086
$175$	9.84582	0.744274
$176$	−1.64625	−0.124091
$177$	−7.20489	−0.541553
$178$	16.8996	1.26668
$179$	−14.8669	−1.11120	−0.555601	−	0.831449i	$-0.687512\pi$
$179$	−14.8669	−1.11120	−0.555601	+	0.831449i	$0.687512\pi$
$180$	20.0188	1.49211
$181$	5.84833	0.434703	0.217352	−	0.976093i	$-0.430258\pi$
$181$	5.84833	0.434703	0.217352	+	0.976093i	$0.430258\pi$
$182$	7.52813	0.558022
$183$	24.7461	1.82928
$184$	3.96028	0.291956
$185$	32.8346	2.41404
$186$	−3.11031	−0.228059
$187$	12.0188	0.878900
$188$	12.2307	0.892015
$189$	−28.1490	−2.04754
$190$	15.7397	1.14188
$191$	13.1493	0.951453	0.475727	−	0.879593i	$-0.342185\pi$
$191$	13.1493	0.951453	0.475727	+	0.879593i	$0.342185\pi$
$192$	−3.11031	−0.224467
$193$	16.0838	1.15774	0.578868	−	0.815422i	$-0.303495\pi$
$193$	16.0838	1.15774	0.578868	+	0.815422i	$0.303495\pi$
$194$	1.00000	0.0717958
$195$	−28.5118	−2.04177
$196$	−0.932182	−0.0665844
$197$	−23.5101	−1.67503	−0.837514	−	0.546416i	$-0.815992\pi$
$197$	−23.5101	−1.67503	−0.837514	+	0.546416i	$0.815992\pi$
$198$	−10.9871	−0.780821
$199$	20.3651	1.44364	0.721822	−	0.692079i	$-0.243305\pi$
$199$	20.3651	1.44364	0.721822	+	0.692079i	$0.243305\pi$
$200$	3.99701	0.282632
$201$	−21.8123	−1.53852
$202$	6.75915	0.475572
$203$	−18.2910	−1.28378
$204$	22.7074	1.58984
$205$	8.89297	0.621112
$206$	9.59532	0.668538
$207$	26.4310	1.83708
$208$	3.05612	0.211904
$209$	−8.63858	−0.597543
$210$	−22.9810	−1.58584
$211$	−10.8849	−0.749348	−0.374674	−	0.927157i	$-0.622245\pi$
$211$	−10.8849	−0.749348	−0.374674	+	0.927157i	$0.622245\pi$
$212$	−0.0444449	−0.00305249
$213$	31.5775	2.16366
$214$	−3.12399	−0.213551
$215$	20.3343	1.38679
$216$	−11.4274	−0.777535
$217$	2.46329	0.167219
$218$	−4.72870	−0.320268
$219$	39.6231	2.67748
$220$	−4.93793	−0.332915
$221$	−22.3118	−1.50086
$222$	−34.0475	−2.28512
$223$	−9.76292	−0.653774	−0.326887	−	0.945063i	$-0.606000\pi$
$223$	−9.76292	−0.653774	−0.326887	+	0.945063i	$0.606000\pi$
$224$	2.46329	0.164586
$225$	26.6762	1.77841
$226$	−13.1096	−0.872040
$227$	−17.9660	−1.19245	−0.596224	−	0.802818i	$-0.703333\pi$
$227$	−17.9660	−1.19245	−0.596224	+	0.802818i	$0.703333\pi$
$228$	−16.3211	−1.08089
$229$	14.8025	0.978174	0.489087	−	0.872235i	$-0.337330\pi$
$229$	14.8025	0.978174	0.489087	+	0.872235i	$0.337330\pi$
$230$	11.8789	0.783269
$231$	12.6129	0.829870
$232$	−7.42542	−0.487503
$233$	15.9758	1.04661	0.523304	−	0.852146i	$-0.324699\pi$
$233$	15.9758	1.04661	0.523304	+	0.852146i	$0.324699\pi$
$234$	20.3967	1.33337
$235$	36.6860	2.39313
$236$	2.31645	0.150788
$237$	−11.6289	−0.755377
$238$	−17.9838	−1.16571
$239$	−3.05880	−0.197858	−0.0989288	−	0.995095i	$-0.531542\pi$
$239$	−3.05880	−0.197858	−0.0989288	+	0.995095i	$0.531542\pi$
$240$	−9.32938	−0.602209
$241$	−10.7958	−0.695419	−0.347710	−	0.937602i	$-0.613041\pi$
$241$	−10.7958	−0.695419	−0.347710	+	0.937602i	$0.613041\pi$
$242$	−8.28986	−0.532892
$243$	−13.9918	−0.897576
$244$	−7.95615	−0.509340
$245$	−2.79608	−0.178635
$246$	−9.22150	−0.587941
$247$	16.0368	1.02040
$248$	1.00000	0.0635001
$249$	17.0395	1.07984
$250$	−3.00846	−0.190272
$251$	15.0834	0.952057	0.476029	−	0.879430i	$-0.342076\pi$
$251$	15.0834	0.952057	0.476029	+	0.879430i	$0.342076\pi$
$252$	16.4401	1.03563
$253$	−6.51961	−0.409884
$254$	11.2065	0.703157
$255$	68.1110	4.26528
$256$	1.00000	0.0625000
$257$	2.62316	0.163628	0.0818142	−	0.996648i	$-0.473929\pi$
$257$	2.62316	0.163628	0.0818142	+	0.996648i	$0.473929\pi$
$258$	−21.0855	−1.31273
$259$	26.9649	1.67552
$260$	9.16685	0.568504
$261$	−49.5575	−3.06753
$262$	−21.1504	−1.30667
$263$	−21.4672	−1.32372	−0.661862	−	0.749626i	$-0.730233\pi$
$263$	−21.4672	−1.32372	−0.661862	+	0.749626i	$0.730233\pi$
$264$	5.12035	0.315136
$265$	−0.133313	−0.00818933
$266$	12.9260	0.792542
$267$	−52.5632	−3.21681
$268$	7.01291	0.428381
$269$	18.5171	1.12901	0.564503	−	0.825431i	$-0.309068\pi$
$269$	18.5171	1.12901	0.564503	+	0.825431i	$0.309068\pi$
$270$	−34.2765	−2.08600
$271$	21.6657	1.31610	0.658049	−	0.752975i	$-0.271382\pi$
$271$	21.6657	1.31610	0.658049	+	0.752975i	$0.271382\pi$
$272$	−7.30070	−0.442670
$273$	−23.4148	−1.41713
$274$	7.53105	0.454968
$275$	−6.58008	−0.396794
$276$	−12.3177	−0.741439
$277$	15.7455	0.946056	0.473028	−	0.881047i	$-0.343161\pi$
$277$	15.7455	0.946056	0.473028	+	0.881047i	$0.343161\pi$
$278$	19.1150	1.14644
$279$	6.67403	0.399564
$280$	7.38866	0.441557
$281$	23.6186	1.40897	0.704483	−	0.709720i	$-0.251179\pi$
$281$	23.6186	1.40897	0.704483	+	0.709720i	$0.251179\pi$
$282$	−38.0413	−2.26532
$283$	−20.7001	−1.23049	−0.615245	−	0.788336i	$-0.710943\pi$
$283$	−20.7001	−1.23049	−0.615245	+	0.788336i	$0.710943\pi$
$284$	−10.1525	−0.602442
$285$	−48.9553	−2.89986
$286$	−5.03115	−0.297498
$287$	7.30321	0.431095
$288$	6.67403	0.393271
$289$	36.3002	2.13531
$290$	−22.2726	−1.30789
$291$	−3.11031	−0.182330
$292$	−12.7393	−0.745510
$293$	16.0366	0.936868	0.468434	−	0.883499i	$-0.344818\pi$
$293$	16.0366	0.936868	0.468434	+	0.883499i	$0.344818\pi$
$294$	2.89938	0.169095
$295$	6.94820	0.404540
$296$	10.9467	0.636262
$297$	18.8123	1.09160
$298$	−11.3352	−0.656629
$299$	12.1031	0.699941
$300$	−12.4320	−0.717759
$301$	16.6993	0.962529
$302$	13.1376	0.755985
$303$	−21.0230	−1.20774
$304$	5.24743	0.300961
$305$	−23.8645	−1.36648
$306$	−48.7251	−2.78543
$307$	24.1619	1.37899	0.689496	−	0.724290i	$-0.257832\pi$
$307$	24.1619	1.37899	0.689496	+	0.724290i	$0.257832\pi$
$308$	−4.05520	−0.231066
$309$	−29.8444	−1.69779
$310$	2.99950	0.170360
$311$	−2.84205	−0.161158	−0.0805790	−	0.996748i	$-0.525677\pi$
$311$	−2.84205	−0.161158	−0.0805790	+	0.996748i	$0.525677\pi$
$312$	−9.50550	−0.538143
$313$	−12.0953	−0.683667	−0.341833	−	0.939761i	$-0.611048\pi$
$313$	−12.0953	−0.683667	−0.341833	+	0.939761i	$0.611048\pi$
$314$	6.67826	0.376876
$315$	49.3121	2.77842
$316$	3.73882	0.210325
$317$	0.708162	0.0397743	0.0198872	−	0.999802i	$-0.493669\pi$
$317$	0.708162	0.0397743	0.0198872	+	0.999802i	$0.493669\pi$
$318$	0.138238	0.00775198
$319$	12.2241	0.684418
$320$	2.99950	0.167677
$321$	9.71657	0.542326
$322$	9.75534	0.543644
$323$	−38.3099	−2.13162
$324$	15.5206	0.862257
$325$	12.2154	0.677587
$326$	1.04238	0.0577323
$327$	14.7077	0.813339
$328$	2.96481	0.163705
$329$	30.1278	1.66100
$330$	15.3585	0.845458
$331$	21.6097	1.18778	0.593889	−	0.804547i	$-0.297592\pi$
$331$	21.6097	1.18778	0.593889	+	0.804547i	$0.297592\pi$
$332$	−5.47840	−0.300666
$333$	73.0584	4.00358
$334$	0.0474407	0.00259584
$335$	21.0352	1.14928
$336$	−7.66161	−0.417975
$337$	−16.5535	−0.901724	−0.450862	−	0.892594i	$-0.648883\pi$
$337$	−16.5535	−0.901724	−0.450862	+	0.892594i	$0.648883\pi$
$338$	−3.66010	−0.199083
$339$	40.7751	2.21460
$340$	−21.8985	−1.18761
$341$	−1.64625	−0.0891494
$342$	35.0215	1.89375
$343$	−19.5393	−1.05502
$344$	6.77924	0.365512
$345$	−36.9470	−1.98916
$346$	−8.55194	−0.459755
$347$	9.79843	0.526007	0.263004	−	0.964795i	$-0.415287\pi$
$347$	9.79843	0.526007	0.263004	+	0.964795i	$0.415287\pi$
$348$	23.0954	1.23804
$349$	27.4990	1.47199	0.735994	−	0.676988i	$-0.236715\pi$
$349$	27.4990	1.47199	0.735994	+	0.676988i	$0.236715\pi$
$350$	9.84582	0.526281
$351$	−34.9235	−1.86408
$352$	−1.64625	−0.0877454
$353$	−23.9804	−1.27635	−0.638173	−	0.769893i	$-0.720310\pi$
$353$	−23.9804	−1.27635	−0.638173	+	0.769893i	$0.720310\pi$
$354$	−7.20489	−0.382935
$355$	−30.4526	−1.61625
$356$	16.8996	0.895680
$357$	55.9351	2.96040
$358$	−14.8669	−0.785738
$359$	17.9160	0.945572	0.472786	−	0.881177i	$-0.343248\pi$
$359$	17.9160	0.945572	0.472786	+	0.881177i	$0.343248\pi$
$360$	20.0188	1.05508
$361$	8.53554	0.449239
$362$	5.84833	0.307382
$363$	25.7840	1.35331
$364$	7.52813	0.394581
$365$	−38.2115	−2.00008
$366$	24.7461	1.29350
$367$	−26.3679	−1.37639	−0.688197	−	0.725524i	$-0.741597\pi$
$367$	−26.3679	−1.37639	−0.688197	+	0.725524i	$0.741597\pi$
$368$	3.96028	0.206444
$369$	19.7873	1.03008
$370$	32.8346	1.70699
$371$	−0.109481	−0.00568397
$372$	−3.11031	−0.161262
$373$	−24.0220	−1.24381	−0.621906	−	0.783092i	$-0.713641\pi$
$373$	−24.0220	−1.24381	−0.621906	+	0.783092i	$0.713641\pi$
$374$	12.0188	0.621476
$375$	9.35725	0.483206
$376$	12.2307	0.630750
$377$	−22.6930	−1.16875
$378$	−28.1490	−1.44783
$379$	−14.6222	−0.751093	−0.375546	−	0.926804i	$-0.622545\pi$
$379$	−14.6222	−0.751093	−0.375546	+	0.926804i	$0.622545\pi$
$380$	15.7397	0.807429
$381$	−34.8556	−1.78571
$382$	13.1493	0.672779
$383$	16.3080	0.833301	0.416651	−	0.909067i	$-0.363204\pi$
$383$	16.3080	0.833301	0.416651	+	0.909067i	$0.363204\pi$
$384$	−3.11031	−0.158722
$385$	−12.1636	−0.619913
$386$	16.0838	0.818642
$387$	45.2449	2.29993
$388$	1.00000	0.0507673
$389$	28.4595	1.44295	0.721477	−	0.692438i	$-0.243464\pi$
$389$	28.4595	1.44295	0.721477	+	0.692438i	$0.243464\pi$
$390$	−28.5118	−1.44375
$391$	−28.9128	−1.46218
$392$	−0.932182	−0.0470823
$393$	65.7842	3.31837
$394$	−23.5101	−1.18442
$395$	11.2146	0.564267
$396$	−10.9871	−0.552124
$397$	38.6259	1.93858	0.969289	−	0.245924i	$-0.0790913\pi$
$397$	38.6259	1.93858	0.969289	+	0.245924i	$0.0790913\pi$
$398$	20.3651	1.02081
$399$	−40.2038	−2.01271
$400$	3.99701	0.199851
$401$	−19.0370	−0.950660	−0.475330	−	0.879808i	$-0.657671\pi$
$401$	−19.0370	−0.950660	−0.475330	+	0.879808i	$0.657671\pi$
$402$	−21.8123	−1.08790
$403$	3.05612	0.152236
$404$	6.75915	0.336280
$405$	46.5542	2.31330
$406$	−18.2910	−0.907767
$407$	−18.0210	−0.893266
$408$	22.7074	1.12419
$409$	−31.3635	−1.55082	−0.775412	−	0.631455i	$-0.782458\pi$
$409$	−31.3635	−1.55082	−0.775412	+	0.631455i	$0.782458\pi$
$410$	8.89297	0.439192
$411$	−23.4239	−1.15542
$412$	9.59532	0.472728
$413$	5.70610	0.280779
$414$	26.4310	1.29902
$415$	−16.4325	−0.806638
$416$	3.05612	0.149839
$417$	−59.4537	−2.91146
$418$	−8.63858	−0.422527
$419$	10.8263	0.528902	0.264451	−	0.964399i	$-0.414809\pi$
$419$	10.8263	0.528902	0.264451	+	0.964399i	$0.414809\pi$
$420$	−22.9810	−1.12136
$421$	−23.8556	−1.16265	−0.581325	−	0.813672i	$-0.697465\pi$
$421$	−23.8556	−1.16265	−0.581325	+	0.813672i	$0.697465\pi$
$422$	−10.8849	−0.529869
$423$	81.6281	3.96889
$424$	−0.0444449	−0.00215844
$425$	−29.1810	−1.41549
$426$	31.5775	1.52994
$427$	−19.5983	−0.948430
$428$	−3.12399	−0.151004
$429$	15.6484	0.755513
$430$	20.3343	0.980609
$431$	−6.88720	−0.331745	−0.165872	−	0.986147i	$-0.553044\pi$
$431$	−6.88720	−0.331745	−0.165872	+	0.986147i	$0.553044\pi$
$432$	−11.4274	−0.549801
$433$	17.4472	0.838459	0.419229	−	0.907880i	$-0.362300\pi$
$433$	17.4472	0.838459	0.419229	+	0.907880i	$0.362300\pi$
$434$	2.46329	0.118242
$435$	69.2746	3.32146
$436$	−4.72870	−0.226464
$437$	20.7813	0.994104
$438$	39.6231	1.89327
$439$	−24.3872	−1.16394	−0.581968	−	0.813212i	$-0.697717\pi$
$439$	−24.3872	−1.16394	−0.581968	+	0.813212i	$0.697717\pi$
$440$	−4.93793	−0.235407
$441$	−6.22141	−0.296258
$442$	−22.3118	−1.06127
$443$	33.8184	1.60676	0.803381	−	0.595466i	$-0.203033\pi$
$443$	33.8184	1.60676	0.803381	+	0.595466i	$0.203033\pi$
$444$	−34.0475	−1.61582
$445$	50.6905	2.40296
$446$	−9.76292	−0.462288
$447$	35.2559	1.66755
$448$	2.46329	0.116380
$449$	24.4342	1.15312	0.576561	−	0.817054i	$-0.304394\pi$
$449$	24.4342	1.15312	0.576561	+	0.817054i	$0.304394\pi$
$450$	26.6762	1.25753
$451$	−4.88083	−0.229829
$452$	−13.1096	−0.616626
$453$	−40.8621	−1.91987
$454$	−17.9660	−0.843188
$455$	22.5807	1.05860
$456$	−16.3211	−0.764308
$457$	−19.3425	−0.904806	−0.452403	−	0.891814i	$-0.649433\pi$
$457$	−19.3425	−0.904806	−0.452403	+	0.891814i	$0.649433\pi$
$458$	14.8025	0.691673
$459$	83.4279	3.89408
$460$	11.8789	0.553855
$461$	25.5738	1.19109	0.595546	−	0.803321i	$-0.296936\pi$
$461$	25.5738	1.19109	0.595546	+	0.803321i	$0.296936\pi$
$462$	12.6129	0.586806
$463$	−16.8559	−0.783359	−0.391679	−	0.920102i	$-0.628106\pi$
$463$	−16.8559	−0.783359	−0.391679	+	0.920102i	$0.628106\pi$
$464$	−7.42542	−0.344717
$465$	−9.32938	−0.432640
$466$	15.9758	0.740063
$467$	−33.9220	−1.56972	−0.784862	−	0.619670i	$-0.787266\pi$
$467$	−33.9220	−1.56972	−0.784862	+	0.619670i	$0.787266\pi$
$468$	20.3967	0.942837
$469$	17.2749	0.797679
$470$	36.6860	1.69220
$471$	−20.7715	−0.957098
$472$	2.31645	0.106623
$473$	−11.1603	−0.513152
$474$	−11.6289	−0.534133
$475$	20.9741	0.962356
$476$	−17.9838	−0.824285
$477$	−0.296627	−0.0135816
$478$	−3.05880	−0.139906
$479$	37.6647	1.72094	0.860471	−	0.509499i	$-0.170169\pi$
$479$	37.6647	1.72094	0.860471	+	0.509499i	$0.170169\pi$
$480$	−9.32938	−0.425826
$481$	33.4544	1.52539
$482$	−10.7958	−0.491736
$483$	−30.3421	−1.38061
$484$	−8.28986	−0.376812
$485$	2.99950	0.136200
$486$	−13.9918	−0.634682
$487$	7.90068	0.358014	0.179007	−	0.983848i	$-0.442712\pi$
$487$	7.90068	0.358014	0.179007	+	0.983848i	$0.442712\pi$
$488$	−7.95615	−0.360158
$489$	−3.24214	−0.146615
$490$	−2.79608	−0.126314
$491$	14.2217	0.641815	0.320907	−	0.947111i	$-0.396012\pi$
$491$	14.2217	0.641815	0.320907	+	0.947111i	$0.396012\pi$
$492$	−9.22150	−0.415737
$493$	54.2108	2.44153
$494$	16.0368	0.721530
$495$	−32.9559	−1.48126
$496$	1.00000	0.0449013
$497$	−25.0087	−1.12179
$498$	17.0395	0.763559
$499$	36.1805	1.61966	0.809832	−	0.586662i	$-0.199558\pi$
$499$	36.1805	1.61966	0.809832	+	0.586662i	$0.199558\pi$
$500$	−3.00846	−0.134542
$501$	−0.147555	−0.00659229
$502$	15.0834	0.673206
$503$	−27.7622	−1.23785	−0.618927	−	0.785449i	$-0.712432\pi$
$503$	−27.7622	−1.23785	−0.618927	+	0.785449i	$0.712432\pi$
$504$	16.4401	0.732301
$505$	20.2741	0.902184
$506$	−6.51961	−0.289832
$507$	11.3840	0.505583
$508$	11.2065	0.497207
$509$	−6.37748	−0.282677	−0.141338	−	0.989961i	$-0.545141\pi$
$509$	−6.37748	−0.282677	−0.141338	+	0.989961i	$0.545141\pi$
$510$	68.1110	3.01601
$511$	−31.3806	−1.38820
$512$	1.00000	0.0441942
$513$	−59.9645	−2.64750
$514$	2.62316	0.115703
$515$	28.7812	1.26825
$516$	−21.0855	−0.928239
$517$	−20.1348	−0.885527
$518$	26.9649	1.18477
$519$	26.5992	1.16757
$520$	9.16685	0.401993
$521$	−18.3255	−0.802854	−0.401427	−	0.915891i	$-0.631486\pi$
$521$	−18.3255	−0.802854	−0.401427	+	0.915891i	$0.631486\pi$
$522$	−49.5575	−2.16907
$523$	−20.9936	−0.917985	−0.458993	−	0.888440i	$-0.651790\pi$
$523$	−20.9936	−0.917985	−0.458993	+	0.888440i	$0.651790\pi$
$524$	−21.1504	−0.923958
$525$	−30.6236	−1.33652
$526$	−21.4672	−0.936014
$527$	−7.30070	−0.318023
$528$	5.12035	0.222835
$529$	−7.31618	−0.318095
$530$	−0.133313	−0.00579073
$531$	15.4601	0.670911
$532$	12.9260	0.560412
$533$	9.06084	0.392469
$534$	−52.5632	−2.27463
$535$	−9.37040	−0.405118
$536$	7.01291	0.302911
$537$	46.2406	1.99543
$538$	18.5171	0.798327
$539$	1.53460	0.0661001
$540$	−34.2765	−1.47502
$541$	7.77550	0.334295	0.167147	−	0.985932i	$-0.446544\pi$
$541$	7.77550	0.334295	0.167147	+	0.985932i	$0.446544\pi$
$542$	21.6657	0.930621
$543$	−18.1901	−0.780613
$544$	−7.30070	−0.313015
$545$	−14.1837	−0.607565
$546$	−23.4148	−1.00206
$547$	3.65969	0.156477	0.0782385	−	0.996935i	$-0.475070\pi$
$547$	3.65969	0.156477	0.0782385	+	0.996935i	$0.475070\pi$
$548$	7.53105	0.321711
$549$	−53.0996	−2.26624
$550$	−6.58008	−0.280576
$551$	−38.9644	−1.65994
$552$	−12.3177	−0.524276
$553$	9.20981	0.391641
$554$	15.7455	0.668963
$555$	−102.126	−4.33499
$556$	19.1150	0.810658
$557$	18.3711	0.778410	0.389205	−	0.921151i	$-0.372750\pi$
$557$	18.3711	0.778410	0.389205	+	0.921151i	$0.372750\pi$
$558$	6.67403	0.282534
$559$	20.7182	0.876286
$560$	7.38866	0.312228
$561$	−37.3821	−1.57827
$562$	23.6186	0.996290
$563$	3.80739	0.160462	0.0802311	−	0.996776i	$-0.474434\pi$
$563$	3.80739	0.160462	0.0802311	+	0.996776i	$0.474434\pi$
$564$	−38.0413	−1.60183
$565$	−39.3224	−1.65431
$566$	−20.7001	−0.870088
$567$	38.2319	1.60559
$568$	−10.1525	−0.425991
$569$	−43.6728	−1.83086	−0.915430	−	0.402477i	$-0.868149\pi$
$569$	−43.6728	−1.83086	−0.915430	+	0.402477i	$0.868149\pi$
$570$	−48.9553	−2.05051
$571$	−36.6110	−1.53212	−0.766061	−	0.642768i	$-0.777786\pi$
$571$	−36.6110	−1.53212	−0.766061	+	0.642768i	$0.777786\pi$
$572$	−5.03115	−0.210363
$573$	−40.8986	−1.70856
$574$	7.30321	0.304830
$575$	15.8293	0.660127
$576$	6.67403	0.278085
$577$	−37.2758	−1.55181	−0.775906	−	0.630849i	$-0.782707\pi$
$577$	−37.2758	−1.55181	−0.775906	+	0.630849i	$0.782707\pi$
$578$	36.3002	1.50989
$579$	−50.0255	−2.07899
$580$	−22.2726	−0.924818
$581$	−13.4949	−0.559863
$582$	−3.11031	−0.128927
$583$	0.0731675	0.00303029
$584$	−12.7393	−0.527155
$585$	61.1799	2.52948
$586$	16.0366	0.662465
$587$	−5.67114	−0.234073	−0.117037	−	0.993128i	$-0.537339\pi$
$587$	−5.67114	−0.234073	−0.117037	+	0.993128i	$0.537339\pi$
$588$	2.89938	0.119568
$589$	5.24743	0.216217
$590$	6.94820	0.286053
$591$	73.1238	3.00791
$592$	10.9467	0.449905
$593$	−2.39409	−0.0983134	−0.0491567	−	0.998791i	$-0.515653\pi$
$593$	−2.39409	−0.0983134	−0.0491567	+	0.998791i	$0.515653\pi$
$594$	18.8123	0.771880
$595$	−53.9424	−2.21142
$596$	−11.3352	−0.464307
$597$	−63.3418	−2.59241
$598$	12.1031	0.494933
$599$	−0.947030	−0.0386946	−0.0193473	−	0.999813i	$-0.506159\pi$
$599$	−0.947030	−0.0386946	−0.0193473	+	0.999813i	$0.506159\pi$
$600$	−12.4320	−0.507532
$601$	24.8122	1.01211	0.506056	−	0.862501i	$-0.331103\pi$
$601$	24.8122	1.01211	0.506056	+	0.862501i	$0.331103\pi$
$602$	16.6993	0.680611
$603$	46.8044	1.90602
$604$	13.1376	0.534562
$605$	−24.8655	−1.01092
$606$	−21.0230	−0.854003
$607$	20.4513	0.830094	0.415047	−	0.909800i	$-0.363765\pi$
$607$	20.4513	0.830094	0.415047	+	0.909800i	$0.363765\pi$
$608$	5.24743	0.212811
$609$	56.8907	2.30533
$610$	−23.8645	−0.966245
$611$	37.3785	1.51217
$612$	−48.7251	−1.96960
$613$	−24.1129	−0.973910	−0.486955	−	0.873427i	$-0.661892\pi$
$613$	−24.1129	−0.973910	−0.486955	+	0.873427i	$0.661892\pi$
$614$	24.1619	0.975094
$615$	−27.6599	−1.11535
$616$	−4.05520	−0.163389
$617$	16.3954	0.660052	0.330026	−	0.943972i	$-0.392942\pi$
$617$	16.3954	0.660052	0.330026	+	0.943972i	$0.392942\pi$
$618$	−29.8444	−1.20052
$619$	39.1629	1.57409	0.787046	−	0.616895i	$-0.211610\pi$
$619$	39.1629	1.57409	0.787046	+	0.616895i	$0.211610\pi$
$620$	2.99950	0.120463
$621$	−45.2557	−1.81605
$622$	−2.84205	−0.113956
$623$	41.6288	1.66782
$624$	−9.50550	−0.380525
$625$	−29.0090	−1.16036
$626$	−12.0953	−0.483425
$627$	26.8687	1.07303
$628$	6.67826	0.266491
$629$	−79.9183	−3.18655
$630$	49.3121	1.96464
$631$	40.4515	1.61035	0.805174	−	0.593039i	$-0.202072\pi$
$631$	40.4515	1.61035	0.805174	+	0.593039i	$0.202072\pi$
$632$	3.73882	0.148722
$633$	33.8554	1.34563
$634$	0.708162	0.0281247
$635$	33.6138	1.33392
$636$	0.138238	0.00548148
$637$	−2.84886	−0.112876
$638$	12.2241	0.483957
$639$	−67.7584	−2.68048
$640$	2.99950	0.118566
$641$	−4.64308	−0.183391	−0.0916954	−	0.995787i	$-0.529229\pi$
$641$	−4.64308	−0.183391	−0.0916954	+	0.995787i	$0.529229\pi$
$642$	9.71657	0.383482
$643$	49.2635	1.94276	0.971381	−	0.237526i	$-0.0763364\pi$
$643$	49.2635	1.94276	0.971381	+	0.237526i	$0.0763364\pi$
$644$	9.75534	0.384414
$645$	−63.2461	−2.49031
$646$	−38.3099	−1.50728
$647$	−23.5929	−0.927533	−0.463766	−	0.885958i	$-0.653502\pi$
$647$	−23.5929	−0.927533	−0.463766	+	0.885958i	$0.653502\pi$
$648$	15.5206	0.609708
$649$	−3.81346	−0.149691
$650$	12.2154	0.479126
$651$	−7.66161	−0.300282
$652$	1.04238	0.0408229
$653$	4.75718	0.186163	0.0930814	−	0.995658i	$-0.470328\pi$
$653$	4.75718	0.186163	0.0930814	+	0.995658i	$0.470328\pi$
$654$	14.7077	0.575117
$655$	−63.4405	−2.47883
$656$	2.96481	0.115757
$657$	−85.0224	−3.31704
$658$	30.1278	1.17450
$659$	15.0377	0.585786	0.292893	−	0.956145i	$-0.405382\pi$
$659$	15.0377	0.585786	0.292893	+	0.956145i	$0.405382\pi$
$660$	15.3585	0.597829
$661$	8.19027	0.318565	0.159282	−	0.987233i	$-0.449082\pi$
$661$	8.19027	0.318565	0.159282	+	0.987233i	$0.449082\pi$
$662$	21.6097	0.839886
$663$	69.3968	2.69515
$664$	−5.47840	−0.212603
$665$	38.7715	1.50349
$666$	73.0584	2.83096
$667$	−29.4068	−1.13863
$668$	0.0474407	0.00183554
$669$	30.3657	1.17401
$670$	21.0352	0.812662
$671$	13.0978	0.505635
$672$	−7.66161	−0.295553
$673$	−12.5026	−0.481939	−0.240970	−	0.970533i	$-0.577465\pi$
$673$	−12.5026	−0.481939	−0.240970	+	0.970533i	$0.577465\pi$
$674$	−16.5535	−0.637615
$675$	−45.6754	−1.75805
$676$	−3.66010	−0.140773
$677$	−36.2919	−1.39481	−0.697406	−	0.716677i	$-0.745662\pi$
$677$	−36.2919	−1.39481	−0.697406	+	0.716677i	$0.745662\pi$
$678$	40.7751	1.56596
$679$	2.46329	0.0945326
$680$	−21.8985	−0.839768
$681$	55.8800	2.14133
$682$	−1.64625	−0.0630382
$683$	−25.2580	−0.966469	−0.483235	−	0.875491i	$-0.660538\pi$
$683$	−25.2580	−0.966469	−0.483235	+	0.875491i	$0.660538\pi$
$684$	35.0215	1.33908
$685$	22.5894	0.863097
$686$	−19.5393	−0.746014
$687$	−46.0402	−1.75654
$688$	6.77924	0.258456
$689$	−0.135829	−0.00517468
$690$	−36.9470	−1.40655
$691$	−22.0152	−0.837498	−0.418749	−	0.908102i	$-0.637531\pi$
$691$	−22.0152	−0.837498	−0.418749	+	0.908102i	$0.637531\pi$
$692$	−8.55194	−0.325096
$693$	−27.0645	−1.02810
$694$	9.79843	0.371943
$695$	57.3356	2.17486
$696$	23.0954	0.875428
$697$	−21.6452	−0.819871
$698$	27.4990	1.04085
$699$	−49.6896	−1.87943
$700$	9.84582	0.372137
$701$	5.13844	0.194076	0.0970381	−	0.995281i	$-0.469063\pi$
$701$	5.13844	0.194076	0.0970381	+	0.995281i	$0.469063\pi$
$702$	−34.9235	−1.31810
$703$	57.4419	2.16646
$704$	−1.64625	−0.0620454
$705$	−114.105	−4.29744
$706$	−23.9804	−0.902513
$707$	16.6498	0.626179
$708$	−7.20489	−0.270776
$709$	−10.6852	−0.401292	−0.200646	−	0.979664i	$-0.564304\pi$
$709$	−10.6852	−0.401292	−0.200646	+	0.979664i	$0.564304\pi$
$710$	−30.4526	−1.14286
$711$	24.9530	0.935811
$712$	16.8996	0.633341
$713$	3.96028	0.148314
$714$	55.9351	2.09332
$715$	−15.0909	−0.564369
$716$	−14.8669	−0.555601
$717$	9.51383	0.355300
$718$	17.9160	0.668620
$719$	−10.7456	−0.400745	−0.200372	−	0.979720i	$-0.564215\pi$
$719$	−10.7456	−0.400745	−0.200372	+	0.979720i	$0.564215\pi$
$720$	20.0188	0.746056
$721$	23.6361	0.880255
$722$	8.53554	0.317660
$723$	33.5783	1.24879
$724$	5.84833	0.217352
$725$	−29.6795	−1.10227
$726$	25.7840	0.956936
$727$	−53.0655	−1.96809	−0.984046	−	0.177915i	$-0.943065\pi$
$727$	−53.0655	−1.96809	−0.984046	+	0.177915i	$0.943065\pi$
$728$	7.52813	0.279011
$729$	−3.04297	−0.112703
$730$	−38.2115	−1.41427
$731$	−49.4932	−1.83057
$732$	24.7461	0.914642
$733$	−5.90196	−0.217994	−0.108997	−	0.994042i	$-0.534764\pi$
$733$	−5.90196	−0.217994	−0.108997	+	0.994042i	$0.534764\pi$
$734$	−26.3679	−0.973257
$735$	8.69668	0.320782
$736$	3.96028	0.145978
$737$	−11.5450	−0.425265
$738$	19.7873	0.728380
$739$	−12.1199	−0.445839	−0.222919	−	0.974837i	$-0.571559\pi$
$739$	−12.1199	−0.445839	−0.222919	+	0.974837i	$0.571559\pi$
$740$	32.8346	1.20702
$741$	−49.8795	−1.83237
$742$	−0.109481	−0.00401917
$743$	4.19260	0.153811	0.0769057	−	0.997038i	$-0.475496\pi$
$743$	4.19260	0.153811	0.0769057	+	0.997038i	$0.475496\pi$
$744$	−3.11031	−0.114030
$745$	−33.9999	−1.24566
$746$	−24.0220	−0.879508
$747$	−36.5630	−1.33777
$748$	12.0188	0.439450
$749$	−7.69529	−0.281180
$750$	9.35725	0.341678
$751$	−46.4074	−1.69343	−0.846715	−	0.532047i	$-0.821423\pi$
$751$	−46.4074	−1.69343	−0.846715	+	0.532047i	$0.821423\pi$
$752$	12.2307	0.446008
$753$	−46.9141	−1.70965
$754$	−22.6930	−0.826431
$755$	39.4063	1.43414
$756$	−28.1490	−1.02377
$757$	−3.16675	−0.115098	−0.0575488	−	0.998343i	$-0.518328\pi$
$757$	−3.16675	−0.115098	−0.0575488	+	0.998343i	$0.518328\pi$
$758$	−14.6222	−0.531103
$759$	20.2780	0.736045
$760$	15.7397	0.570938
$761$	45.5713	1.65196	0.825978	−	0.563702i	$-0.190623\pi$
$761$	45.5713	1.65196	0.825978	+	0.563702i	$0.190623\pi$
$762$	−34.8556	−1.26269
$763$	−11.6482	−0.421692
$764$	13.1493	0.475727
$765$	−146.151	−5.28410
$766$	16.3080	0.589233
$767$	7.07937	0.255621
$768$	−3.11031	−0.112234
$769$	−36.7379	−1.32480	−0.662400	−	0.749150i	$-0.730462\pi$
$769$	−36.7379	−1.32480	−0.662400	+	0.749150i	$0.730462\pi$
$770$	−12.1636	−0.438345
$771$	−8.15886	−0.293834
$772$	16.0838	0.578868
$773$	−16.4700	−0.592385	−0.296193	−	0.955128i	$-0.595717\pi$
$773$	−16.4700	−0.592385	−0.296193	+	0.955128i	$0.595717\pi$
$774$	45.2449	1.62629
$775$	3.99701	0.143577
$776$	1.00000	0.0358979
$777$	−83.8691	−3.00879
$778$	28.4595	1.02032
$779$	15.5577	0.557411
$780$	−28.5118	−1.02088
$781$	16.7136	0.598060
$782$	−28.9128	−1.03392
$783$	84.8532	3.03241
$784$	−0.932182	−0.0332922
$785$	20.0314	0.714953
$786$	65.7842	2.34644
$787$	−8.38405	−0.298859	−0.149430	−	0.988772i	$-0.547744\pi$
$787$	−8.38405	−0.298859	−0.149430	+	0.988772i	$0.547744\pi$
$788$	−23.5101	−0.837514
$789$	66.7696	2.37706
$790$	11.2146	0.398997
$791$	−32.2929	−1.14820
$792$	−10.9871	−0.390411
$793$	−24.3150	−0.863451
$794$	38.6259	1.37078
$795$	0.414644	0.0147059
$796$	20.3651	0.721822
$797$	3.30647	0.117121	0.0585606	−	0.998284i	$-0.481349\pi$
$797$	3.30647	0.117121	0.0585606	+	0.998284i	$0.481349\pi$
$798$	−40.2038	−1.42320
$799$	−89.2926	−3.15895
$800$	3.99701	0.141316
$801$	112.789	3.98520
$802$	−19.0370	−0.672218
$803$	20.9720	0.740087
$804$	−21.8123	−0.769261
$805$	29.2611	1.03132
$806$	3.05612	0.107647
$807$	−57.5938	−2.02740
$808$	6.75915	0.237786
$809$	−36.1767	−1.27190	−0.635952	−	0.771728i	$-0.719393\pi$
$809$	−36.1767	−1.27190	−0.635952	+	0.771728i	$0.719393\pi$
$810$	46.5542	1.63575
$811$	36.1212	1.26839	0.634193	−	0.773174i	$-0.281332\pi$
$811$	36.1212	1.26839	0.634193	+	0.773174i	$0.281332\pi$
$812$	−18.2910	−0.641888
$813$	−67.3870	−2.36337
$814$	−18.0210	−0.631634
$815$	3.12663	0.109521
$816$	22.7074	0.794919
$817$	35.5736	1.24456
$818$	−31.3635	−1.09660
$819$	50.2430	1.75563
$820$	8.89297	0.310556
$821$	23.6326	0.824785	0.412393	−	0.911006i	$-0.364693\pi$
$821$	23.6326	0.824785	0.412393	+	0.911006i	$0.364693\pi$
$822$	−23.4239	−0.817003
$823$	12.4782	0.434963	0.217481	−	0.976064i	$-0.430216\pi$
$823$	12.4782	0.434963	0.217481	+	0.976064i	$0.430216\pi$
$824$	9.59532	0.334269
$825$	20.4661	0.712538
$826$	5.70610	0.198541
$827$	−21.1436	−0.735237	−0.367618	−	0.929977i	$-0.619827\pi$
$827$	−21.1436	−0.735237	−0.367618	+	0.929977i	$0.619827\pi$
$828$	26.4310	0.918542
$829$	25.4650	0.884436	0.442218	−	0.896908i	$-0.354192\pi$
$829$	25.4650	0.884436	0.442218	+	0.896908i	$0.354192\pi$
$830$	−16.4325	−0.570379
$831$	−48.9734	−1.69887
$832$	3.05612	0.105952
$833$	6.80558	0.235799
$834$	−59.4537	−2.05871
$835$	0.142299	0.00492444
$836$	−8.63858	−0.298772
$837$	−11.4274	−0.394988
$838$	10.8263	0.373990
$839$	−24.6363	−0.850539	−0.425269	−	0.905067i	$-0.639821\pi$
$839$	−24.6363	−0.850539	−0.425269	+	0.905067i	$0.639821\pi$
$840$	−22.9810	−0.792920
$841$	26.1369	0.901273
$842$	−23.8556	−0.822117
$843$	−73.4612	−2.53014
$844$	−10.8849	−0.374674
$845$	−10.9785	−0.377671
$846$	81.6281	2.80643
$847$	−20.4204	−0.701652
$848$	−0.0444449	−0.00152625
$849$	64.3836	2.20964
$850$	−29.1810	−1.00090
$851$	43.3519	1.48608
$852$	31.5775	1.08183
$853$	52.6078	1.80126	0.900629	−	0.434589i	$-0.143106\pi$
$853$	52.6078	1.80126	0.900629	+	0.434589i	$0.143106\pi$
$854$	−19.5983	−0.670641
$855$	105.047	3.59254
$856$	−3.12399	−0.106776
$857$	−20.8235	−0.711316	−0.355658	−	0.934616i	$-0.615743\pi$
$857$	−20.8235	−0.711316	−0.355658	+	0.934616i	$0.615743\pi$
$858$	15.6484	0.534229
$859$	11.7874	0.402180	0.201090	−	0.979573i	$-0.435552\pi$
$859$	11.7874	0.402180	0.201090	+	0.979573i	$0.435552\pi$
$860$	20.3343	0.693395
$861$	−22.7153	−0.774134
$862$	−6.88720	−0.234579
$863$	49.6358	1.68962	0.844811	−	0.535065i	$-0.179713\pi$
$863$	49.6358	1.68962	0.844811	+	0.535065i	$0.179713\pi$
$864$	−11.4274	−0.388768
$865$	−25.6516	−0.872179
$866$	17.4472	0.592880
$867$	−112.905	−3.83445
$868$	2.46329	0.0836097
$869$	−6.15503	−0.208795
$870$	69.2746	2.34863
$871$	21.4323	0.726206
$872$	−4.72870	−0.160134
$873$	6.67403	0.225882
$874$	20.7813	0.702938
$875$	−7.41072	−0.250528
$876$	39.6231	1.33874
$877$	−2.81321	−0.0949955	−0.0474977	−	0.998871i	$-0.515125\pi$
$877$	−2.81321	−0.0949955	−0.0474977	+	0.998871i	$0.515125\pi$
$878$	−24.3872	−0.823027
$879$	−49.8788	−1.68237
$880$	−4.93793	−0.166458
$881$	17.3995	0.586205	0.293103	−	0.956081i	$-0.405312\pi$
$881$	17.3995	0.586205	0.293103	+	0.956081i	$0.405312\pi$
$882$	−6.22141	−0.209486
$883$	11.3470	0.381855	0.190928	−	0.981604i	$-0.438850\pi$
$883$	11.3470	0.381855	0.190928	+	0.981604i	$0.438850\pi$
$884$	−22.3118	−0.750429
$885$	−21.6111	−0.726448
$886$	33.8184	1.13615
$887$	31.0479	1.04249	0.521244	−	0.853408i	$-0.325468\pi$
$887$	31.0479	1.04249	0.521244	+	0.853408i	$0.325468\pi$
$888$	−34.0475	−1.14256
$889$	27.6048	0.925837
$890$	50.6905	1.69915
$891$	−25.5508	−0.855985
$892$	−9.76292	−0.326887
$893$	64.1798	2.14769
$894$	35.2559	1.17913
$895$	−44.5932	−1.49059
$896$	2.46329	0.0822929
$897$	−37.6444	−1.25691
$898$	24.4342	0.815381
$899$	−7.42542	−0.247652
$900$	26.6762	0.889207
$901$	0.324479	0.0108100
$902$	−4.88083	−0.162514
$903$	−51.9399	−1.72845
$904$	−13.1096	−0.436020
$905$	17.5421	0.583119
$906$	−40.8621	−1.35755
$907$	14.0982	0.468124	0.234062	−	0.972222i	$-0.424798\pi$
$907$	14.0982	0.468124	0.234062	+	0.972222i	$0.424798\pi$
$908$	−17.9660	−0.596224
$909$	45.1108	1.49623
$910$	22.5807	0.748541
$911$	10.6176	0.351776	0.175888	−	0.984410i	$-0.443720\pi$
$911$	10.6176	0.351776	0.175888	+	0.984410i	$0.443720\pi$
$912$	−16.3211	−0.540447
$913$	9.01881	0.298479
$914$	−19.3425	−0.639795
$915$	74.2260	2.45384
$916$	14.8025	0.489087
$917$	−52.0996	−1.72048
$918$	83.4279	2.75353
$919$	−12.3168	−0.406292	−0.203146	−	0.979148i	$-0.565117\pi$
$919$	−12.3168	−0.406292	−0.203146	+	0.979148i	$0.565117\pi$
$920$	11.8789	0.391635
$921$	−75.1510	−2.47631
$922$	25.5738	0.842229
$923$	−31.0274	−1.02128
$924$	12.6129	0.414935
$925$	43.7540	1.43862
$926$	−16.8559	−0.553918
$927$	64.0395	2.10333
$928$	−7.42542	−0.243751
$929$	41.6281	1.36577	0.682886	−	0.730525i	$-0.260724\pi$
$929$	41.6281	1.36577	0.682886	+	0.730525i	$0.260724\pi$
$930$	−9.32938	−0.305923
$931$	−4.89156	−0.160314
$932$	15.9758	0.523304
$933$	8.83966	0.289398
$934$	−33.9220	−1.10996
$935$	36.0503	1.17897
$936$	20.3967	0.666686
$937$	22.8191	0.745469	0.372734	−	0.927938i	$-0.378420\pi$
$937$	22.8191	0.745469	0.372734	+	0.927938i	$0.378420\pi$
$938$	17.2749	0.564044
$939$	37.6201	1.22769
$940$	36.6860	1.19657
$941$	41.2079	1.34334	0.671669	−	0.740851i	$-0.265578\pi$
$941$	41.2079	1.34334	0.671669	+	0.740851i	$0.265578\pi$
$942$	−20.7715	−0.676770
$943$	11.7415	0.382356
$944$	2.31645	0.0753941
$945$	−84.4331	−2.74661
$946$	−11.1603	−0.362853
$947$	41.8310	1.35932	0.679662	−	0.733525i	$-0.262126\pi$
$947$	41.8310	1.35932	0.679662	+	0.733525i	$0.262126\pi$
$948$	−11.6289	−0.377689
$949$	−38.9328	−1.26381
$950$	20.9741	0.680488
$951$	−2.20260	−0.0714243
$952$	−17.9838	−0.582857
$953$	−32.4222	−1.05026	−0.525128	−	0.851023i	$-0.675983\pi$
$953$	−32.4222	−1.05026	−0.525128	+	0.851023i	$0.675983\pi$
$954$	−0.296627	−0.00960365
$955$	39.4415	1.27630
$956$	−3.05880	−0.0989288
$957$	−38.0208	−1.22904
$958$	37.6647	1.21689
$959$	18.5512	0.599049
$960$	−9.32938	−0.301105
$961$	1.00000	0.0322581
$962$	33.4544	1.07861
$963$	−20.8496	−0.671868
$964$	−10.7958	−0.347710
$965$	48.2433	1.55301
$966$	−30.3421	−0.976242
$967$	−22.2120	−0.714291	−0.357145	−	0.934049i	$-0.616250\pi$
$967$	−22.2120	−0.714291	−0.357145	+	0.934049i	$0.616250\pi$
$968$	−8.28986	−0.266446
$969$	119.156	3.82783
$970$	2.99950	0.0963082
$971$	−16.4412	−0.527623	−0.263811	−	0.964574i	$-0.584980\pi$
$971$	−16.4412	−0.527623	−0.263811	+	0.964574i	$0.584980\pi$
$972$	−13.9918	−0.448788
$973$	47.0860	1.50951
$974$	7.90068	0.253154
$975$	−37.9936	−1.21677
$976$	−7.95615	−0.254670
$977$	−7.25084	−0.231975	−0.115987	−	0.993251i	$-0.537003\pi$
$977$	−7.25084	−0.231975	−0.115987	+	0.993251i	$0.537003\pi$
$978$	−3.24214	−0.103672
$979$	−27.8210	−0.889164
$980$	−2.79608	−0.0893175
$981$	−31.5595	−1.00762
$982$	14.2217	0.453832
$983$	−40.2099	−1.28250	−0.641248	−	0.767334i	$-0.721583\pi$
$983$	−40.2099	−1.28250	−0.641248	+	0.767334i	$0.721583\pi$
$984$	−9.22150	−0.293971
$985$	−70.5187	−2.24691
$986$	54.2108	1.72642
$987$	−93.7068	−2.98272
$988$	16.0368	0.510199
$989$	26.8477	0.853707
$990$	−32.9559	−1.04741
$991$	−58.3914	−1.85486	−0.927432	−	0.373992i	$-0.877989\pi$
$991$	−58.3914	−1.85486	−0.927432	+	0.373992i	$0.877989\pi$
$992$	1.00000	0.0317500
$993$	−67.2130	−2.13294
$994$	−25.0087	−0.793227
$995$	61.0852	1.93653
$996$	17.0395	0.539918
$997$	−50.1842	−1.58935	−0.794675	−	0.607036i	$-0.792359\pi$
$997$	−50.1842	−1.58935	−0.794675	+	0.607036i	$0.792359\pi$
$998$	36.1805	1.14528
$999$	−125.092	−3.95773

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.k.1.2	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.k.1.2	✓	37	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.11031 q^{3} +1.00000 q^{4} +2.99950 q^{5} -3.11031 q^{6} +2.46329 q^{7} +1.00000 q^{8} +6.67403 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.11031 q^{3} +1.00000 q^{4} +2.99950 q^{5} -3.11031 q^{6} +2.46329 q^{7} +1.00000 q^{8} +6.67403 q^{9} +2.99950 q^{10} -1.64625 q^{11} -3.11031 q^{12} +3.05612 q^{13} +2.46329 q^{14} -9.32938 q^{15} +1.00000 q^{16} -7.30070 q^{17} +6.67403 q^{18} +5.24743 q^{19} +2.99950 q^{20} -7.66161 q^{21} -1.64625 q^{22} +3.96028 q^{23} -3.11031 q^{24} +3.99701 q^{25} +3.05612 q^{26} -11.4274 q^{27} +2.46329 q^{28} -7.42542 q^{29} -9.32938 q^{30} +1.00000 q^{31} +1.00000 q^{32} +5.12035 q^{33} -7.30070 q^{34} +7.38866 q^{35} +6.67403 q^{36} +10.9467 q^{37} +5.24743 q^{38} -9.50550 q^{39} +2.99950 q^{40} +2.96481 q^{41} -7.66161 q^{42} +6.77924 q^{43} -1.64625 q^{44} +20.0188 q^{45} +3.96028 q^{46} +12.2307 q^{47} -3.11031 q^{48} -0.932182 q^{49} +3.99701 q^{50} +22.7074 q^{51} +3.05612 q^{52} -0.0444449 q^{53} -11.4274 q^{54} -4.93793 q^{55} +2.46329 q^{56} -16.3211 q^{57} -7.42542 q^{58} +2.31645 q^{59} -9.32938 q^{60} -7.95615 q^{61} +1.00000 q^{62} +16.4401 q^{63} +1.00000 q^{64} +9.16685 q^{65} +5.12035 q^{66} +7.01291 q^{67} -7.30070 q^{68} -12.3177 q^{69} +7.38866 q^{70} -10.1525 q^{71} +6.67403 q^{72} -12.7393 q^{73} +10.9467 q^{74} -12.4320 q^{75} +5.24743 q^{76} -4.05520 q^{77} -9.50550 q^{78} +3.73882 q^{79} +2.99950 q^{80} +15.5206 q^{81} +2.96481 q^{82} -5.47840 q^{83} -7.66161 q^{84} -21.8985 q^{85} +6.77924 q^{86} +23.0954 q^{87} -1.64625 q^{88} +16.8996 q^{89} +20.0188 q^{90} +7.52813 q^{91} +3.96028 q^{92} -3.11031 q^{93} +12.2307 q^{94} +15.7397 q^{95} -3.11031 q^{96} +1.00000 q^{97} -0.932182 q^{98} -10.9871 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9}+O(q^{10}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9} + 9 q^{10} + 5 q^{11} + 9 q^{12} + 16 q^{13} + 19 q^{14} + 22 q^{15} + 37 q^{16} + 3 q^{17} + 52 q^{18} + 36 q^{19} + 9 q^{20} + 6 q^{21} + 5 q^{22} + 11 q^{23} + 9 q^{24} + 58 q^{25} + 16 q^{26} + 24 q^{27} + 19 q^{28} + 5 q^{29} + 22 q^{30} + 37 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 28 q^{35} + 52 q^{36} + 21 q^{37} + 36 q^{38} + 38 q^{39} + 9 q^{40} + 21 q^{41} + 6 q^{42} + 14 q^{43} + 5 q^{44} + 55 q^{45} + 11 q^{46} + 59 q^{47} + 9 q^{48} + 82 q^{49} + 58 q^{50} + 46 q^{51} + 16 q^{52} + 8 q^{53} + 24 q^{54} + 25 q^{55} + 19 q^{56} + 5 q^{58} + 41 q^{59} + 22 q^{60} + 16 q^{61} + 37 q^{62} + 23 q^{63} + 37 q^{64} - 46 q^{65} + q^{66} + 45 q^{67} + 3 q^{68} + 68 q^{69} + 28 q^{70} + 55 q^{71} + 52 q^{72} + 29 q^{73} + 21 q^{74} - 12 q^{75} + 36 q^{76} + 30 q^{77} + 38 q^{78} + 25 q^{79} + 9 q^{80} + 73 q^{81} + 21 q^{82} + 70 q^{83} + 6 q^{84} - 21 q^{85} + 14 q^{86} + 37 q^{87} + 5 q^{88} + 55 q^{90} + 18 q^{91} + 11 q^{92} + 9 q^{93} + 59 q^{94} - 9 q^{95} + 9 q^{96} + 37 q^{97} + 82 q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9 + 9 * q^10 + 5 * q^11 + 9 * q^12 + 16 * q^13 + 19 * q^14 + 22 * q^15 + 37 * q^16 + 3 * q^17 + 52 * q^18 + 36 * q^19 + 9 * q^20 + 6 * q^21 + 5 * q^22 + 11 * q^23 + 9 * q^24 + 58 * q^25 + 16 * q^26 + 24 * q^27 + 19 * q^28 + 5 * q^29 + 22 * q^30 + 37 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 28 * q^35 + 52 * q^36 + 21 * q^37 + 36 * q^38 + 38 * q^39 + 9 * q^40 + 21 * q^41 + 6 * q^42 + 14 * q^43 + 5 * q^44 + 55 * q^45 + 11 * q^46 + 59 * q^47 + 9 * q^48 + 82 * q^49 + 58 * q^50 + 46 * q^51 + 16 * q^52 + 8 * q^53 + 24 * q^54 + 25 * q^55 + 19 * q^56 + 5 * q^58 + 41 * q^59 + 22 * q^60 + 16 * q^61 + 37 * q^62 + 23 * q^63 + 37 * q^64 - 46 * q^65 + q^66 + 45 * q^67 + 3 * q^68 + 68 * q^69 + 28 * q^70 + 55 * q^71 + 52 * q^72 + 29 * q^73 + 21 * q^74 - 12 * q^75 + 36 * q^76 + 30 * q^77 + 38 * q^78 + 25 * q^79 + 9 * q^80 + 73 * q^81 + 21 * q^82 + 70 * q^83 + 6 * q^84 - 21 * q^85 + 14 * q^86 + 37 * q^87 + 5 * q^88 + 55 * q^90 + 18 * q^91 + 11 * q^92 + 9 * q^93 + 59 * q^94 - 9 * q^95 + 9 * q^96 + 37 * q^97 + 82 * q^98 + 33 * q^99

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