LMFDB - Embedded newform 6031.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$0$
Dimension:	$134$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.77108 q^{2} +1.62557 q^{3} +5.67890 q^{4} -0.123356 q^{5} -4.50458 q^{6} -1.34606 q^{7} -10.1945 q^{8} -0.357536 q^{9} +O(q^{10})$	\(q-2.77108 q^{2} +1.62557 q^{3} +5.67890 q^{4} -0.123356 q^{5} -4.50458 q^{6} -1.34606 q^{7} -10.1945 q^{8} -0.357536 q^{9} +0.341829 q^{10} -2.83787 q^{11} +9.23143 q^{12} -6.71398 q^{13} +3.73005 q^{14} -0.200523 q^{15} +16.8921 q^{16} -5.05529 q^{17} +0.990761 q^{18} -2.99405 q^{19} -0.700525 q^{20} -2.18811 q^{21} +7.86398 q^{22} -1.60826 q^{23} -16.5719 q^{24} -4.98478 q^{25} +18.6050 q^{26} -5.45790 q^{27} -7.64415 q^{28} +8.58981 q^{29} +0.555665 q^{30} -9.87440 q^{31} -26.4204 q^{32} -4.61315 q^{33} +14.0086 q^{34} +0.166044 q^{35} -2.03041 q^{36} +1.00000 q^{37} +8.29677 q^{38} -10.9140 q^{39} +1.25755 q^{40} +5.91841 q^{41} +6.06344 q^{42} +11.0321 q^{43} -16.1160 q^{44} +0.0441040 q^{45} +4.45661 q^{46} +12.2998 q^{47} +27.4592 q^{48} -5.18812 q^{49} +13.8132 q^{50} -8.21771 q^{51} -38.1280 q^{52} -10.9478 q^{53} +15.1243 q^{54} +0.350068 q^{55} +13.7225 q^{56} -4.86703 q^{57} -23.8031 q^{58} -3.97005 q^{59} -1.13875 q^{60} +9.00802 q^{61} +27.3628 q^{62} +0.481265 q^{63} +39.4288 q^{64} +0.828207 q^{65} +12.7834 q^{66} -8.26957 q^{67} -28.7085 q^{68} -2.61433 q^{69} -0.460123 q^{70} -2.09117 q^{71} +3.64491 q^{72} -6.57378 q^{73} -2.77108 q^{74} -8.10309 q^{75} -17.0029 q^{76} +3.81995 q^{77} +30.2436 q^{78} +5.12669 q^{79} -2.08374 q^{80} -7.79956 q^{81} -16.4004 q^{82} +16.9366 q^{83} -12.4261 q^{84} +0.623599 q^{85} -30.5709 q^{86} +13.9633 q^{87} +28.9308 q^{88} -4.94027 q^{89} -0.122216 q^{90} +9.03743 q^{91} -9.13313 q^{92} -16.0515 q^{93} -34.0837 q^{94} +0.369333 q^{95} -42.9481 q^{96} -14.1674 q^{97} +14.3767 q^{98} +1.01464 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9}+O(q^{10}) $ 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9} + 15 q^{10} + 20 q^{11} + 28 q^{12} + 11 q^{13} + 17 q^{14} - 13 q^{15} + 143 q^{16} + 76 q^{17} + 23 q^{18} + 15 q^{19} + 67 q^{20} + 63 q^{21} + 2 q^{22} + 22 q^{23} + 33 q^{24} + 160 q^{25} + 65 q^{26} + 31 q^{27} + 10 q^{28} + 73 q^{29} + 20 q^{30} + 10 q^{31} + 53 q^{32} + 72 q^{33} - 7 q^{34} + 52 q^{35} + 201 q^{36} + 134 q^{37} + 70 q^{38} + 6 q^{39} + 11 q^{40} + 182 q^{41} - 15 q^{42} + 12 q^{43} + 33 q^{44} + 29 q^{45} + 24 q^{46} + 80 q^{47} + 21 q^{48} + 229 q^{49} + 37 q^{50} + 57 q^{51} - 15 q^{52} + 75 q^{53} + 95 q^{54} - 9 q^{55} + 39 q^{56} + 19 q^{57} - 21 q^{58} + 91 q^{59} + 62 q^{60} + 58 q^{61} + 108 q^{62} + 9 q^{63} + 167 q^{64} + 76 q^{65} + 105 q^{66} - 17 q^{67} + 109 q^{68} + 48 q^{69} - 55 q^{70} + 56 q^{71} + 48 q^{72} + 54 q^{73} + 9 q^{74} + 28 q^{75} + 82 q^{76} + 156 q^{77} + 16 q^{78} - 2 q^{79} + 98 q^{80} + 270 q^{81} - 42 q^{82} + 130 q^{83} + 229 q^{84} + 22 q^{85} + 72 q^{86} + 22 q^{87} + 61 q^{88} + 157 q^{89} + 176 q^{90} + 31 q^{91} - 18 q^{92} + 36 q^{93} + 83 q^{94} + 98 q^{95} + 111 q^{96} + 35 q^{97} + 53 q^{98} + 55 q^{99}+O(q^{100}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9 + 15 * q^10 + 20 * q^11 + 28 * q^12 + 11 * q^13 + 17 * q^14 - 13 * q^15 + 143 * q^16 + 76 * q^17 + 23 * q^18 + 15 * q^19 + 67 * q^20 + 63 * q^21 + 2 * q^22 + 22 * q^23 + 33 * q^24 + 160 * q^25 + 65 * q^26 + 31 * q^27 + 10 * q^28 + 73 * q^29 + 20 * q^30 + 10 * q^31 + 53 * q^32 + 72 * q^33 - 7 * q^34 + 52 * q^35 + 201 * q^36 + 134 * q^37 + 70 * q^38 + 6 * q^39 + 11 * q^40 + 182 * q^41 - 15 * q^42 + 12 * q^43 + 33 * q^44 + 29 * q^45 + 24 * q^46 + 80 * q^47 + 21 * q^48 + 229 * q^49 + 37 * q^50 + 57 * q^51 - 15 * q^52 + 75 * q^53 + 95 * q^54 - 9 * q^55 + 39 * q^56 + 19 * q^57 - 21 * q^58 + 91 * q^59 + 62 * q^60 + 58 * q^61 + 108 * q^62 + 9 * q^63 + 167 * q^64 + 76 * q^65 + 105 * q^66 - 17 * q^67 + 109 * q^68 + 48 * q^69 - 55 * q^70 + 56 * q^71 + 48 * q^72 + 54 * q^73 + 9 * q^74 + 28 * q^75 + 82 * q^76 + 156 * q^77 + 16 * q^78 - 2 * q^79 + 98 * q^80 + 270 * q^81 - 42 * q^82 + 130 * q^83 + 229 * q^84 + 22 * q^85 + 72 * q^86 + 22 * q^87 + 61 * q^88 + 157 * q^89 + 176 * q^90 + 31 * q^91 - 18 * q^92 + 36 * q^93 + 83 * q^94 + 98 * q^95 + 111 * q^96 + 35 * q^97 + 53 * q^98 + 55 * 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 $

$2$	−2.77108	−1.95945	−0.979726	−	0.200343i	$-0.935794\pi$
$2$	−2.77108	−1.95945	−0.979726	+	0.200343i	$0.935794\pi$
$3$	1.62557	0.938521	0.469260	−	0.883060i	$-0.344521\pi$
$3$	1.62557	0.938521	0.469260	+	0.883060i	$0.344521\pi$
$4$	5.67890	2.83945
$5$	−0.123356	−0.0551663	−0.0275832	−	0.999620i	$-0.508781\pi$
$5$	−0.123356	−0.0551663	−0.0275832	+	0.999620i	$0.508781\pi$
$6$	−4.50458	−1.83899
$7$	−1.34606	−0.508764	−0.254382	−	0.967104i	$-0.581872\pi$
$7$	−1.34606	−0.508764	−0.254382	+	0.967104i	$0.581872\pi$
$8$	−10.1945	−3.60431
$9$	−0.357536	−0.119179
$10$	0.341829	0.108096
$11$	−2.83787	−0.855650	−0.427825	−	0.903861i	$-0.640720\pi$
$11$	−2.83787	−0.855650	−0.427825	+	0.903861i	$0.640720\pi$
$12$	9.23143	2.66488
$13$	−6.71398	−1.86212	−0.931061	−	0.364864i	$-0.881116\pi$
$13$	−6.71398	−1.86212	−0.931061	+	0.364864i	$0.881116\pi$
$14$	3.73005	0.996898
$15$	−0.200523	−0.0517748
$16$	16.8921	4.22303
$17$	−5.05529	−1.22609	−0.613045	−	0.790048i	$-0.710055\pi$
$17$	−5.05529	−1.22609	−0.613045	+	0.790048i	$0.710055\pi$
$18$	0.990761	0.233525
$19$	−2.99405	−0.686883	−0.343441	−	0.939174i	$-0.611593\pi$
$19$	−2.99405	−0.686883	−0.343441	+	0.939174i	$0.611593\pi$
$20$	−0.700525	−0.156642
$21$	−2.18811	−0.477485
$22$	7.86398	1.67661
$23$	−1.60826	−0.335345	−0.167672	−	0.985843i	$-0.553625\pi$
$23$	−1.60826	−0.335345	−0.167672	+	0.985843i	$0.553625\pi$
$24$	−16.5719	−3.38272
$25$	−4.98478	−0.996957
$26$	18.6050	3.64874
$27$	−5.45790	−1.05037
$28$	−7.64415	−1.44461
$29$	8.58981	1.59509	0.797543	−	0.603261i	$-0.206132\pi$
$29$	8.58981	1.59509	0.797543	+	0.603261i	$0.206132\pi$
$30$	0.555665	0.101450
$31$	−9.87440	−1.77349	−0.886747	−	0.462254i	$-0.847041\pi$
$31$	−9.87440	−1.77349	−0.886747	+	0.462254i	$0.847041\pi$
$32$	−26.4204	−4.67051
$33$	−4.61315	−0.803046
$34$	14.0086	2.40246
$35$	0.166044	0.0280666
$36$	−2.03041	−0.338402
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	8.29677	1.34591
$39$	−10.9140	−1.74764
$40$	1.25755	0.198837
$41$	5.91841	0.924301	0.462151	−	0.886802i	$-0.347078\pi$
$41$	5.91841	0.924301	0.462151	+	0.886802i	$0.347078\pi$
$42$	6.06344	0.935609
$43$	11.0321	1.68238	0.841190	−	0.540739i	$-0.181855\pi$
$43$	11.0321	1.68238	0.841190	+	0.540739i	$0.181855\pi$
$44$	−16.1160	−2.42958
$45$	0.0441040	0.00657464
$46$	4.45661	0.657092
$47$	12.2998	1.79410	0.897052	−	0.441924i	$-0.145704\pi$
$47$	12.2998	1.79410	0.897052	+	0.441924i	$0.145704\pi$
$48$	27.4592	3.96340
$49$	−5.18812	−0.741160
$50$	13.8132	1.95349
$51$	−8.21771	−1.15071
$52$	−38.1280	−5.28740
$53$	−10.9478	−1.50380	−0.751899	−	0.659279i	$-0.770862\pi$
$53$	−10.9478	−1.50380	−0.751899	+	0.659279i	$0.770862\pi$
$54$	15.1243	2.05815
$55$	0.350068	0.0472031
$56$	13.7225	1.83374
$57$	−4.86703	−0.644654
$58$	−23.8031	−3.12550
$59$	−3.97005	−0.516857	−0.258429	−	0.966030i	$-0.583205\pi$
$59$	−3.97005	−0.516857	−0.258429	+	0.966030i	$0.583205\pi$
$60$	−1.13875	−0.147012
$61$	9.00802	1.15336	0.576679	−	0.816971i	$-0.304348\pi$
$61$	9.00802	1.15336	0.576679	+	0.816971i	$0.304348\pi$
$62$	27.3628	3.47508
$63$	0.481265	0.0606337
$64$	39.4288	4.92860
$65$	0.828207	0.102726
$66$	12.7834	1.57353
$67$	−8.26957	−1.01029	−0.505145	−	0.863035i	$-0.668561\pi$
$67$	−8.26957	−1.01029	−0.505145	+	0.863035i	$0.668561\pi$
$68$	−28.7085	−3.48142
$69$	−2.61433	−0.314728
$70$	−0.460123	−0.0549952
$71$	−2.09117	−0.248176	−0.124088	−	0.992271i	$-0.539601\pi$
$71$	−2.09117	−0.248176	−0.124088	+	0.992271i	$0.539601\pi$
$72$	3.64491	0.429557
$73$	−6.57378	−0.769403	−0.384701	−	0.923041i	$-0.625696\pi$
$73$	−6.57378	−0.769403	−0.384701	+	0.923041i	$0.625696\pi$
$74$	−2.77108	−0.322132
$75$	−8.10309	−0.935665
$76$	−17.0029	−1.95037
$77$	3.81995	0.435324
$78$	30.2436	3.42442
$79$	5.12669	0.576797	0.288399	−	0.957510i	$-0.406877\pi$
$79$	5.12669	0.576797	0.288399	+	0.957510i	$0.406877\pi$
$80$	−2.08374	−0.232969
$81$	−7.79956	−0.866618
$82$	−16.4004	−1.81112
$83$	16.9366	1.85903	0.929516	−	0.368781i	$-0.120225\pi$
$83$	16.9366	1.85903	0.929516	+	0.368781i	$0.120225\pi$
$84$	−12.4261	−1.35580
$85$	0.623599	0.0676388
$86$	−30.5709	−3.29654
$87$	13.9633	1.49702
$88$	28.9308	3.08403
$89$	−4.94027	−0.523667	−0.261834	−	0.965113i	$-0.584327\pi$
$89$	−4.94027	−0.523667	−0.261834	+	0.965113i	$0.584327\pi$
$90$	−0.122216	−0.0128827
$91$	9.03743	0.947380
$92$	−9.13313	−0.952195
$93$	−16.0515	−1.66446
$94$	−34.0837	−3.51546
$95$	0.369333	0.0378928
$96$	−42.9481	−4.38337
$97$	−14.1674	−1.43849	−0.719243	−	0.694758i	$-0.755511\pi$
$97$	−14.1674	−1.43849	−0.719243	+	0.694758i	$0.755511\pi$
$98$	14.3767	1.45227
$99$	1.01464	0.101975
$100$	−28.3081	−2.83081
$101$	15.5769	1.54996	0.774978	−	0.631988i	$-0.217761\pi$
$101$	15.5769	1.54996	0.774978	+	0.631988i	$0.217761\pi$
$102$	22.7720	2.25476
$103$	−6.32046	−0.622774	−0.311387	−	0.950283i	$-0.600793\pi$
$103$	−6.32046	−0.622774	−0.311387	+	0.950283i	$0.600793\pi$
$104$	68.4459	6.71167
$105$	0.269916	0.0263411
$106$	30.3373	2.94662
$107$	−3.37023	−0.325813	−0.162906	−	0.986642i	$-0.552087\pi$
$107$	−3.37023	−0.325813	−0.162906	+	0.986642i	$0.552087\pi$
$108$	−30.9948	−2.98248
$109$	−9.48702	−0.908692	−0.454346	−	0.890825i	$-0.650127\pi$
$109$	−9.48702	−0.908692	−0.454346	+	0.890825i	$0.650127\pi$
$110$	−0.970066	−0.0924922
$111$	1.62557	0.154292
$112$	−22.7378	−2.14852
$113$	−10.8452	−1.02023	−0.510115	−	0.860106i	$-0.670397\pi$
$113$	−10.8452	−1.02023	−0.510115	+	0.860106i	$0.670397\pi$
$114$	13.4869	1.26317
$115$	0.198388	0.0184997
$116$	48.7807	4.52917
$117$	2.40049	0.221925
$118$	11.0013	1.01276
$119$	6.80474	0.623789
$120$	2.04424	0.186612
$121$	−2.94649	−0.267862
$122$	−24.9620	−2.25995
$123$	9.62077	0.867476
$124$	−56.0757	−5.03575
$125$	1.23168	0.110165
$126$	−1.33363	−0.118809
$127$	−3.68586	−0.327067	−0.163534	−	0.986538i	$-0.552289\pi$
$127$	−3.68586	−0.327067	−0.163534	+	0.986538i	$0.552289\pi$
$128$	−56.4198	−4.98685
$129$	17.9334	1.57895
$130$	−2.29503	−0.201287
$131$	5.65856	0.494391	0.247195	−	0.968966i	$-0.420491\pi$
$131$	5.65856	0.494391	0.247195	+	0.968966i	$0.420491\pi$
$132$	−26.1976	−2.28021
$133$	4.03018	0.349461
$134$	22.9157	1.97961
$135$	0.673262	0.0579452
$136$	51.5364	4.41921
$137$	7.82037	0.668139	0.334070	−	0.942548i	$-0.391578\pi$
$137$	7.82037	0.668139	0.334070	+	0.942548i	$0.391578\pi$
$138$	7.24452	0.616694
$139$	12.6273	1.07104	0.535518	−	0.844524i	$-0.320116\pi$
$139$	12.6273	1.07104	0.535518	+	0.844524i	$0.320116\pi$
$140$	0.942949	0.0796938
$141$	19.9941	1.68381
$142$	5.79480	0.486289
$143$	19.0534	1.59333
$144$	−6.03953	−0.503294
$145$	−1.05960	−0.0879951
$146$	18.2165	1.50761
$147$	−8.43363	−0.695594
$148$	5.67890	0.466803
$149$	10.4528	0.856329	0.428164	−	0.903701i	$-0.359160\pi$
$149$	10.4528	0.856329	0.428164	+	0.903701i	$0.359160\pi$
$150$	22.4543	1.83339
$151$	−2.75130	−0.223897	−0.111949	−	0.993714i	$-0.535709\pi$
$151$	−2.75130	−0.223897	−0.111949	+	0.993714i	$0.535709\pi$
$152$	30.5230	2.47574
$153$	1.80745	0.146124
$154$	−10.5854	−0.852996
$155$	1.21806	0.0978372
$156$	−61.9796	−4.96234
$157$	15.6895	1.25216	0.626080	−	0.779759i	$-0.284658\pi$
$157$	15.6895	1.25216	0.626080	+	0.779759i	$0.284658\pi$
$158$	−14.2065	−1.13021
$159$	−17.7964	−1.41134
$160$	3.25910	0.257655
$161$	2.16481	0.170611
$162$	21.6132	1.69810
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	33.6101	2.62451
$165$	0.569058	0.0443011
$166$	−46.9327	−3.64268
$167$	−13.4129	−1.03792	−0.518961	−	0.854798i	$-0.673681\pi$
$167$	−13.4129	−1.03792	−0.518961	+	0.854798i	$0.673681\pi$
$168$	22.3068	1.72101
$169$	32.0775	2.46750
$170$	−1.72805	−0.132535
$171$	1.07048	0.0818617
$172$	62.6502	4.77704
$173$	2.37655	0.180686	0.0903428	−	0.995911i	$-0.471204\pi$
$173$	2.37655	0.180686	0.0903428	+	0.995911i	$0.471204\pi$
$174$	−38.6935	−2.93334
$175$	6.70983	0.507215
$176$	−47.9376	−3.61344
$177$	−6.45358	−0.485081
$178$	13.6899	1.02610
$179$	15.3271	1.14560	0.572799	−	0.819696i	$-0.305858\pi$
$179$	15.3271	1.14560	0.572799	+	0.819696i	$0.305858\pi$
$180$	0.250463	0.0186684
$181$	−4.63455	−0.344484	−0.172242	−	0.985055i	$-0.555101\pi$
$181$	−4.63455	−0.344484	−0.172242	+	0.985055i	$0.555101\pi$
$182$	−25.0435	−1.85634
$183$	14.6431	1.08245
$184$	16.3954	1.20869
$185$	−0.123356	−0.00906929
$186$	44.4800	3.26143
$187$	14.3463	1.04910
$188$	69.8491	5.09427
$189$	7.34666	0.534391
$190$	−1.02345	−0.0742491
$191$	9.13706	0.661135	0.330567	−	0.943782i	$-0.392760\pi$
$191$	9.13706	0.661135	0.330567	+	0.943782i	$0.392760\pi$
$192$	64.0941	4.62560
$193$	18.1906	1.30939	0.654695	−	0.755893i	$-0.272797\pi$
$193$	18.1906	1.30939	0.654695	+	0.755893i	$0.272797\pi$
$194$	39.2592	2.81864
$195$	1.34631	0.0964109
$196$	−29.4628	−2.10449
$197$	−1.72667	−0.123020	−0.0615099	−	0.998106i	$-0.519592\pi$
$197$	−1.72667	−0.123020	−0.0615099	+	0.998106i	$0.519592\pi$
$198$	−2.81165	−0.199815
$199$	−21.1645	−1.50031	−0.750156	−	0.661261i	$-0.770022\pi$
$199$	−21.1645	−1.50031	−0.750156	+	0.661261i	$0.770022\pi$
$200$	50.8176	3.59335
$201$	−13.4427	−0.948177
$202$	−43.1648	−3.03706
$203$	−11.5624	−0.811522
$204$	−46.6676	−3.26738
$205$	−0.730070	−0.0509903
$206$	17.5145	1.22029
$207$	0.575009	0.0399659
$208$	−113.413	−7.86379
$209$	8.49674	0.587732
$210$	−0.747960	−0.0516141
$211$	−2.16229	−0.148858	−0.0744290	−	0.997226i	$-0.523713\pi$
$211$	−2.16229	−0.148858	−0.0744290	+	0.997226i	$0.523713\pi$
$212$	−62.1715	−4.26996
$213$	−3.39933	−0.232918
$214$	9.33919	0.638414
$215$	−1.36087	−0.0928108
$216$	55.6407	3.78587
$217$	13.2916	0.902289
$218$	26.2893	1.78054
$219$	−10.6861	−0.722100
$220$	1.98800	0.134031
$221$	33.9411	2.28313
$222$	−4.50458	−0.302327
$223$	10.3560	0.693486	0.346743	−	0.937960i	$-0.387288\pi$
$223$	10.3560	0.693486	0.346743	+	0.937960i	$0.387288\pi$
$224$	35.5635	2.37618
$225$	1.78224	0.118816
$226$	30.0529	1.99909
$227$	−12.6820	−0.841736	−0.420868	−	0.907122i	$-0.638274\pi$
$227$	−12.6820	−0.841736	−0.420868	+	0.907122i	$0.638274\pi$
$228$	−27.6394	−1.83046
$229$	21.2080	1.40146	0.700732	−	0.713425i	$-0.252857\pi$
$229$	21.2080	1.40146	0.700732	+	0.713425i	$0.252857\pi$
$230$	−0.549749	−0.0362493
$231$	6.20958	0.408560
$232$	−87.5691	−5.74919
$233$	0.313464	0.0205357	0.0102678	−	0.999947i	$-0.496732\pi$
$233$	0.313464	0.0205357	0.0102678	+	0.999947i	$0.496732\pi$
$234$	−6.65194	−0.434851
$235$	−1.51725	−0.0989742
$236$	−22.5455	−1.46759
$237$	8.33376	0.541336
$238$	−18.8565	−1.22229
$239$	−17.3954	−1.12522	−0.562608	−	0.826724i	$-0.690202\pi$
$239$	−17.3954	−1.12522	−0.562608	+	0.826724i	$0.690202\pi$
$240$	−3.38725	−0.218646
$241$	−27.3569	−1.76222	−0.881108	−	0.472915i	$-0.843202\pi$
$241$	−27.3569	−1.76222	−0.881108	+	0.472915i	$0.843202\pi$
$242$	8.16496	0.524863
$243$	3.69499	0.237033
$244$	51.1556	3.27490
$245$	0.639984	0.0408871
$246$	−26.6600	−1.69978
$247$	20.1020	1.27906
$248$	100.665	6.39223
$249$	27.5315	1.74474
$250$	−3.41309	−0.215863
$251$	20.1672	1.27294	0.636471	−	0.771300i	$-0.280393\pi$
$251$	20.1672	1.27294	0.636471	+	0.771300i	$0.280393\pi$
$252$	2.73306	0.172166
$253$	4.56403	0.286938
$254$	10.2138	0.640872
$255$	1.01370	0.0634805
$256$	77.4862	4.84289
$257$	25.4533	1.58773	0.793867	−	0.608091i	$-0.208064\pi$
$257$	25.4533	1.58773	0.793867	+	0.608091i	$0.208064\pi$
$258$	−49.6950	−3.09387
$259$	−1.34606	−0.0836402
$260$	4.70331	0.291687
$261$	−3.07116	−0.190100
$262$	−15.6803	−0.968734
$263$	10.7655	0.663830	0.331915	−	0.943309i	$-0.392305\pi$
$263$	10.7655	0.663830	0.331915	+	0.943309i	$0.392305\pi$
$264$	47.0289	2.89443
$265$	1.35047	0.0829590
$266$	−11.1680	−0.684752
$267$	−8.03073	−0.491473
$268$	−46.9621	−2.86867
$269$	16.1528	0.984856	0.492428	−	0.870353i	$-0.336110\pi$
$269$	16.1528	0.984856	0.492428	+	0.870353i	$0.336110\pi$
$270$	−1.86567	−0.113541
$271$	27.9545	1.69812	0.849059	−	0.528299i	$-0.177170\pi$
$271$	27.9545	1.69812	0.849059	+	0.528299i	$0.177170\pi$
$272$	−85.3946	−5.17781
$273$	14.6909	0.889136
$274$	−21.6709	−1.30919
$275$	14.1462	0.853046
$276$	−14.8465	−0.893655
$277$	−5.11936	−0.307593	−0.153796	−	0.988103i	$-0.549150\pi$
$277$	−5.11936	−0.307593	−0.153796	+	0.988103i	$0.549150\pi$
$278$	−34.9914	−2.09864
$279$	3.53045	0.211363
$280$	−1.69275	−0.101161
$281$	−13.5350	−0.807428	−0.403714	−	0.914885i	$-0.632281\pi$
$281$	−13.5350	−0.807428	−0.403714	+	0.914885i	$0.632281\pi$
$282$	−55.4052	−3.29933
$283$	−18.2976	−1.08768	−0.543839	−	0.839189i	$-0.683030\pi$
$283$	−18.2976	−1.08768	−0.543839	+	0.839189i	$0.683030\pi$
$284$	−11.8755	−0.704683
$285$	0.600376	0.0355632
$286$	−52.7985	−3.12204
$287$	−7.96655	−0.470251
$288$	9.44622	0.556624
$289$	8.55600	0.503294
$290$	2.93624	0.172422
$291$	−23.0301	−1.35005
$292$	−37.3318	−2.18468
$293$	−13.0159	−0.760395	−0.380197	−	0.924905i	$-0.624144\pi$
$293$	−13.0159	−0.760395	−0.380197	+	0.924905i	$0.624144\pi$
$294$	23.3703	1.36298
$295$	0.489729	0.0285131
$296$	−10.1945	−0.592546
$297$	15.4888	0.898752
$298$	−28.9656	−1.67793
$299$	10.7978	0.624453
$300$	−46.0167	−2.65677
$301$	−14.8499	−0.855934
$302$	7.62407	0.438716
$303$	25.3212	1.45467
$304$	−50.5759	−2.90073
$305$	−1.11119	−0.0636266
$306$	−5.00859	−0.286322
$307$	−6.96044	−0.397253	−0.198627	−	0.980075i	$-0.563648\pi$
$307$	−6.96044	−0.397253	−0.198627	+	0.980075i	$0.563648\pi$
$308$	21.6931	1.23608
$309$	−10.2743	−0.584486
$310$	−3.37535	−0.191707
$311$	−5.61111	−0.318177	−0.159088	−	0.987264i	$-0.550855\pi$
$311$	−5.61111	−0.318177	−0.159088	+	0.987264i	$0.550855\pi$
$312$	111.263	6.29904
$313$	12.0187	0.679338	0.339669	−	0.940545i	$-0.389685\pi$
$313$	12.0187	0.679338	0.339669	+	0.940545i	$0.389685\pi$
$314$	−43.4770	−2.45355
$315$	−0.0593668	−0.00334494
$316$	29.1139	1.63779
$317$	−15.4843	−0.869683	−0.434842	−	0.900507i	$-0.643196\pi$
$317$	−15.4843	−0.869683	−0.434842	+	0.900507i	$0.643196\pi$
$318$	49.3153	2.76546
$319$	−24.3768	−1.36484
$320$	−4.86377	−0.271893
$321$	−5.47853	−0.305782
$322$	−5.99888	−0.334304
$323$	15.1358	0.842180
$324$	−44.2929	−2.46072
$325$	33.4677	1.85645
$326$	2.77108	0.153476
$327$	−15.4218	−0.852826
$328$	−60.3355	−3.33147
$329$	−16.5562	−0.912775
$330$	−1.57691	−0.0868058
$331$	−21.2125	−1.16594	−0.582972	−	0.812493i	$-0.698110\pi$
$331$	−21.2125	−1.16594	−0.582972	+	0.812493i	$0.698110\pi$
$332$	96.1812	5.27863
$333$	−0.357536	−0.0195928
$334$	37.1683	2.03376
$335$	1.02010	0.0557339
$336$	−36.9618	−2.01643
$337$	−19.0023	−1.03512	−0.517561	−	0.855646i	$-0.673160\pi$
$337$	−19.0023	−1.03512	−0.517561	+	0.855646i	$0.673160\pi$
$338$	−88.8893	−4.83494
$339$	−17.6296	−0.957507
$340$	3.54136	0.192057
$341$	28.0223	1.51749
$342$	−2.96639	−0.160404
$343$	16.4060	0.885839
$344$	−112.467	−6.06383
$345$	0.322492	0.0173624
$346$	−6.58561	−0.354045
$347$	11.1966	0.601067	0.300534	−	0.953771i	$-0.402835\pi$
$347$	11.1966	0.601067	0.300534	+	0.953771i	$0.402835\pi$
$348$	79.2962	4.25072
$349$	−4.05811	−0.217226	−0.108613	−	0.994084i	$-0.534641\pi$
$349$	−4.05811	−0.217226	−0.108613	+	0.994084i	$0.534641\pi$
$350$	−18.5935	−0.993864
$351$	36.6442	1.95592
$352$	74.9776	3.99632
$353$	−15.3428	−0.816616	−0.408308	−	0.912844i	$-0.633881\pi$
$353$	−15.3428	−0.816616	−0.408308	+	0.912844i	$0.633881\pi$
$354$	17.8834	0.950493
$355$	0.257957	0.0136910
$356$	−28.0553	−1.48693
$357$	11.0616	0.585439
$358$	−42.4726	−2.24474
$359$	−20.0988	−1.06077	−0.530387	−	0.847755i	$-0.677954\pi$
$359$	−20.0988	−1.06077	−0.530387	+	0.847755i	$0.677954\pi$
$360$	−0.449620	−0.0236971
$361$	−10.0356	−0.528192
$362$	12.8427	0.674999
$363$	−4.78971	−0.251394
$364$	51.3226	2.69004
$365$	0.810913	0.0424451
$366$	−40.5773	−2.12101
$367$	−24.0023	−1.25291	−0.626455	−	0.779457i	$-0.715495\pi$
$367$	−24.0023	−1.25291	−0.626455	+	0.779457i	$0.715495\pi$
$368$	−27.1669	−1.41617
$369$	−2.11604	−0.110157
$370$	0.341829	0.0177708
$371$	14.7364	0.765077
$372$	−91.1548	−4.72616
$373$	−11.4973	−0.595305	−0.297653	−	0.954674i	$-0.596204\pi$
$373$	−11.4973	−0.595305	−0.297653	+	0.954674i	$0.596204\pi$
$374$	−39.7547	−2.05567
$375$	2.00218	0.103392
$376$	−125.390	−6.46652
$377$	−57.6717	−2.97025
$378$	−20.3582	−1.04711
$379$	33.4664	1.71906	0.859528	−	0.511089i	$-0.170758\pi$
$379$	33.4664	1.71906	0.859528	+	0.511089i	$0.170758\pi$
$380$	2.09741	0.107595
$381$	−5.99161	−0.306959
$382$	−25.3196	−1.29546
$383$	−26.1891	−1.33820	−0.669100	−	0.743173i	$-0.733320\pi$
$383$	−26.1891	−1.33820	−0.669100	+	0.743173i	$0.733320\pi$
$384$	−91.7141	−4.68026
$385$	−0.471213	−0.0240152
$386$	−50.4078	−2.56569
$387$	−3.94437	−0.200504
$388$	−80.4555	−4.08451
$389$	5.86181	0.297206	0.148603	−	0.988897i	$-0.452522\pi$
$389$	5.86181	0.297206	0.148603	+	0.988897i	$0.452522\pi$
$390$	−3.73072	−0.188913
$391$	8.13021	0.411163
$392$	52.8905	2.67137
$393$	9.19836	0.463996
$394$	4.78474	0.241052
$395$	−0.632406	−0.0318198
$396$	5.76204	0.289553
$397$	−2.58708	−0.129842	−0.0649208	−	0.997890i	$-0.520679\pi$
$397$	−2.58708	−0.129842	−0.0649208	+	0.997890i	$0.520679\pi$
$398$	58.6486	2.93979
$399$	6.55132	0.327976
$400$	−84.2035	−4.21018
$401$	19.8764	0.992579	0.496289	−	0.868157i	$-0.334695\pi$
$401$	19.8764	0.992579	0.496289	+	0.868157i	$0.334695\pi$
$402$	37.2509	1.85791
$403$	66.2965	3.30246
$404$	88.4595	4.40102
$405$	0.962120	0.0478081
$406$	32.0404	1.59014
$407$	−2.83787	−0.140668
$408$	83.7758	4.14752
$409$	−9.09422	−0.449680	−0.224840	−	0.974396i	$-0.572186\pi$
$409$	−9.09422	−0.449680	−0.224840	+	0.974396i	$0.572186\pi$
$410$	2.02308	0.0999130
$411$	12.7125	0.627063
$412$	−35.8933	−1.76833
$413$	5.34394	0.262958
$414$	−1.59340	−0.0783112
$415$	−2.08922	−0.102556
$416$	177.386	8.69705
$417$	20.5266	1.00519
$418$	−23.5452	−1.15163
$419$	−2.39942	−0.117219	−0.0586097	−	0.998281i	$-0.518667\pi$
$419$	−2.39942	−0.117219	−0.0586097	+	0.998281i	$0.518667\pi$
$420$	1.53283	0.0747943
$421$	25.9092	1.26274	0.631369	−	0.775482i	$-0.282493\pi$
$421$	25.9092	1.26274	0.631369	+	0.775482i	$0.282493\pi$
$422$	5.99188	0.291680
$423$	−4.39760	−0.213819
$424$	111.608	5.42016
$425$	25.1995	1.22236
$426$	9.41983	0.456392
$427$	−12.1253	−0.586787
$428$	−19.1392	−0.925129
$429$	30.9726	1.49537
$430$	3.77109	0.181858
$431$	−34.6731	−1.67014	−0.835071	−	0.550141i	$-0.814574\pi$
$431$	−34.6731	−1.67014	−0.835071	+	0.550141i	$0.814574\pi$
$432$	−92.1954	−4.43575
$433$	−16.4014	−0.788203	−0.394102	−	0.919067i	$-0.628944\pi$
$433$	−16.4014	−0.788203	−0.394102	+	0.919067i	$0.628944\pi$
$434$	−36.8320	−1.76799
$435$	−1.72245	−0.0825852
$436$	−53.8758	−2.58018
$437$	4.81521	0.230343
$438$	29.6121	1.41492
$439$	24.3206	1.16076	0.580379	−	0.814347i	$-0.302905\pi$
$439$	24.3206	1.16076	0.580379	+	0.814347i	$0.302905\pi$
$440$	−3.56878	−0.170135
$441$	1.85494	0.0883303
$442$	−94.0537	−4.47368
$443$	10.5623	0.501829	0.250915	−	0.968009i	$-0.419269\pi$
$443$	10.5623	0.501829	0.250915	+	0.968009i	$0.419269\pi$
$444$	9.23143	0.438104
$445$	0.609410	0.0288888
$446$	−28.6972	−1.35885
$447$	16.9918	0.803682
$448$	−53.0736	−2.50749
$449$	6.40078	0.302072	0.151036	−	0.988528i	$-0.451739\pi$
$449$	6.40078	0.302072	0.151036	+	0.988528i	$0.451739\pi$
$450$	−4.93873	−0.232814
$451$	−16.7957	−0.790879
$452$	−61.5888	−2.89689
$453$	−4.47241	−0.210132
$454$	35.1429	1.64934
$455$	−1.11482	−0.0522635
$456$	49.6171	2.32354
$457$	12.6462	0.591563	0.295781	−	0.955256i	$-0.404420\pi$
$457$	12.6462	0.591563	0.295781	+	0.955256i	$0.404420\pi$
$458$	−58.7691	−2.74610
$459$	27.5913	1.28785
$460$	1.12662	0.0525291
$461$	0.349657	0.0162851	0.00814256	−	0.999967i	$-0.497408\pi$
$461$	0.349657	0.0162851	0.00814256	+	0.999967i	$0.497408\pi$
$462$	−17.2073	−0.800554
$463$	−20.9165	−0.972072	−0.486036	−	0.873939i	$-0.661558\pi$
$463$	−20.9165	−0.972072	−0.486036	+	0.873939i	$0.661558\pi$
$464$	145.100	6.73610
$465$	1.98004	0.0918223
$466$	−0.868634	−0.0402387
$467$	−17.4265	−0.806400	−0.403200	−	0.915112i	$-0.632102\pi$
$467$	−17.4265	−0.806400	−0.403200	+	0.915112i	$0.632102\pi$
$468$	13.6321	0.630145
$469$	11.1314	0.513998
$470$	4.20441	0.193935
$471$	25.5044	1.17518
$472$	40.4729	1.86292
$473$	−31.3077	−1.43953
$474$	−23.0936	−1.06072
$475$	14.9247	0.684792
$476$	38.6434	1.77122
$477$	3.91423	0.179220
$478$	48.2042	2.20481
$479$	35.4066	1.61777	0.808884	−	0.587969i	$-0.200072\pi$
$479$	35.4066	1.61777	0.808884	+	0.587969i	$0.200072\pi$
$480$	5.29789	0.241814
$481$	−6.71398	−0.306131
$482$	75.8084	3.45298
$483$	3.51905	0.160122
$484$	−16.7328	−0.760582
$485$	1.74763	0.0793560
$486$	−10.2391	−0.464455
$487$	−19.2843	−0.873855	−0.436927	−	0.899497i	$-0.643933\pi$
$487$	−19.2843	−0.873855	−0.436927	+	0.899497i	$0.643933\pi$
$488$	−91.8326	−4.15707
$489$	−1.62557	−0.0735106
$490$	−1.77345	−0.0801162
$491$	25.8024	1.16445	0.582224	−	0.813028i	$-0.302183\pi$
$491$	25.8024	1.16445	0.582224	+	0.813028i	$0.302183\pi$
$492$	54.6354	2.46315
$493$	−43.4240	−1.95572
$494$	−55.7043	−2.50626
$495$	−0.125162	−0.00562560
$496$	−166.800	−7.48952
$497$	2.81484	0.126263
$498$	−76.2922	−3.41874
$499$	−4.66922	−0.209023	−0.104511	−	0.994524i	$-0.533328\pi$
$499$	−4.66922	−0.209023	−0.104511	+	0.994524i	$0.533328\pi$
$500$	6.99459	0.312807
$501$	−21.8036	−0.974111
$502$	−55.8850	−2.49427
$503$	28.1408	1.25473	0.627367	−	0.778723i	$-0.284132\pi$
$503$	28.1408	1.25473	0.627367	+	0.778723i	$0.284132\pi$
$504$	−4.90628	−0.218543
$505$	−1.92149	−0.0855054
$506$	−12.6473	−0.562241
$507$	52.1440	2.31580
$508$	−20.9316	−0.928691
$509$	−18.1361	−0.803869	−0.401935	−	0.915668i	$-0.631662\pi$
$509$	−18.1361	−0.803869	−0.401935	+	0.915668i	$0.631662\pi$
$510$	−2.80905	−0.124387
$511$	8.84871	0.391444
$512$	−101.881	−4.50256
$513$	16.3412	0.721483
$514$	−70.5333	−3.11109
$515$	0.779665	0.0343561
$516$	101.842	4.48335
$517$	−34.9051	−1.53513
$518$	3.73005	0.163889
$519$	3.86323	0.169577
$520$	−8.44319	−0.370258
$521$	−29.8905	−1.30953	−0.654763	−	0.755834i	$-0.727232\pi$
$521$	−29.8905	−1.30953	−0.654763	+	0.755834i	$0.727232\pi$
$522$	8.51044	0.372492
$523$	4.92167	0.215210	0.107605	−	0.994194i	$-0.465682\pi$
$523$	4.92167	0.215210	0.107605	+	0.994194i	$0.465682\pi$
$524$	32.1344	1.40380
$525$	10.9073	0.476032
$526$	−29.8321	−1.30074
$527$	49.9180	2.17446
$528$	−77.9258	−3.39129
$529$	−20.4135	−0.887544
$530$	−3.74228	−0.162554
$531$	1.41944	0.0615983
$532$	22.8870	0.992277
$533$	−39.7361	−1.72116
$534$	22.2538	0.963017
$535$	0.415737	0.0179739
$536$	84.3045	3.64140
$537$	24.9151	1.07517
$538$	−44.7608	−1.92978
$539$	14.7232	0.634174
$540$	3.82339	0.164533
$541$	−3.61926	−0.155604	−0.0778020	−	0.996969i	$-0.524790\pi$
$541$	−3.61926	−0.155604	−0.0778020	+	0.996969i	$0.524790\pi$
$542$	−77.4643	−3.32738
$543$	−7.53377	−0.323305
$544$	133.563	5.72646
$545$	1.17028	0.0501292
$546$	−40.7098	−1.74222
$547$	−17.3050	−0.739909	−0.369955	−	0.929050i	$-0.620627\pi$
$547$	−17.3050	−0.739909	−0.369955	+	0.929050i	$0.620627\pi$
$548$	44.4111	1.89715
$549$	−3.22069	−0.137456
$550$	−39.2002	−1.67150
$551$	−25.7183	−1.09564
$552$	26.6519	1.13438
$553$	−6.90083	−0.293453
$554$	14.1862	0.602713
$555$	−0.200523	−0.00851172
$556$	71.7093	3.04115
$557$	34.0241	1.44165	0.720823	−	0.693119i	$-0.243764\pi$
$557$	34.0241	1.44165	0.720823	+	0.693119i	$0.243764\pi$
$558$	−9.78317	−0.414155
$559$	−74.0693	−3.13280
$560$	2.80484	0.118526
$561$	23.3208	0.984606
$562$	37.5065	1.58212
$563$	−5.70068	−0.240255	−0.120128	−	0.992758i	$-0.538330\pi$
$563$	−5.70068	−0.240255	−0.120128	+	0.992758i	$0.538330\pi$
$564$	113.544	4.78108
$565$	1.33782	0.0562823
$566$	50.7041	2.13125
$567$	10.4987	0.440904
$568$	21.3185	0.894504
$569$	−33.3947	−1.39998	−0.699989	−	0.714154i	$-0.746812\pi$
$569$	−33.3947	−1.39998	−0.699989	+	0.714154i	$0.746812\pi$
$570$	−1.66369	−0.0696844
$571$	−6.01824	−0.251855	−0.125928	−	0.992039i	$-0.540191\pi$
$571$	−6.01824	−0.251855	−0.125928	+	0.992039i	$0.540191\pi$
$572$	108.202	4.52417
$573$	14.8529	0.620489
$574$	22.0760	0.921433
$575$	8.01681	0.334324
$576$	−14.0972	−0.587384
$577$	−17.3873	−0.723841	−0.361921	−	0.932209i	$-0.617879\pi$
$577$	−17.3873	−0.723841	−0.361921	+	0.932209i	$0.617879\pi$
$578$	−23.7094	−0.986181
$579$	29.5701	1.22889
$580$	−6.01737	−0.249858
$581$	−22.7977	−0.945808
$582$	63.8184	2.64536
$583$	31.0685	1.28672
$584$	67.0167	2.77317
$585$	−0.296114	−0.0122428
$586$	36.0680	1.48996
$587$	0.574053	0.0236937	0.0118468	−	0.999930i	$-0.496229\pi$
$587$	0.574053	0.0236937	0.0118468	+	0.999930i	$0.496229\pi$
$588$	−47.8937	−1.97510
$589$	29.5645	1.21818
$590$	−1.35708	−0.0558701
$591$	−2.80681	−0.115457
$592$	16.8921	0.694262
$593$	−7.04736	−0.289400	−0.144700	−	0.989476i	$-0.546222\pi$
$593$	−7.04736	−0.289400	−0.144700	+	0.989476i	$0.546222\pi$
$594$	−42.9208	−1.76106
$595$	−0.839403	−0.0344122
$596$	59.3606	2.43150
$597$	−34.4043	−1.40807
$598$	−29.9216	−1.22359
$599$	−17.6305	−0.720361	−0.360181	−	0.932883i	$-0.617285\pi$
$599$	−17.6305	−0.720361	−0.360181	+	0.932883i	$0.617285\pi$
$600$	82.6073	3.37243
$601$	−16.7711	−0.684106	−0.342053	−	0.939681i	$-0.611122\pi$
$601$	−16.7711	−0.684106	−0.342053	+	0.939681i	$0.611122\pi$
$602$	41.1503	1.67716
$603$	2.95667	0.120405
$604$	−15.6243	−0.635745
$605$	0.363466	0.0147770
$606$	−70.1672	−2.85035
$607$	4.17130	0.169308	0.0846540	−	0.996410i	$-0.473022\pi$
$607$	4.17130	0.169308	0.0846540	+	0.996410i	$0.473022\pi$
$608$	79.1040	3.20809
$609$	−18.7955	−0.761630
$610$	3.07920	0.124673
$611$	−82.5803	−3.34084
$612$	10.2643	0.414910
$613$	2.93237	0.118437	0.0592186	−	0.998245i	$-0.481139\pi$
$613$	2.93237	0.118437	0.0592186	+	0.998245i	$0.481139\pi$
$614$	19.2880	0.778399
$615$	−1.18678	−0.0478555
$616$	−38.9426	−1.56904
$617$	−5.75708	−0.231771	−0.115886	−	0.993263i	$-0.536971\pi$
$617$	−5.75708	−0.231771	−0.115886	+	0.993263i	$0.536971\pi$
$618$	28.4710	1.14527
$619$	20.1092	0.808258	0.404129	−	0.914702i	$-0.367575\pi$
$619$	20.1092	0.808258	0.404129	+	0.914702i	$0.367575\pi$
$620$	6.91726	0.277804
$621$	8.77770	0.352237
$622$	15.5488	0.623452
$623$	6.64991	0.266423
$624$	−184.361	−7.38033
$625$	24.7720	0.990879
$626$	−33.3048	−1.33113
$627$	13.8120	0.551598
$628$	89.0993	3.55545
$629$	−5.05529	−0.201568
$630$	0.164510	0.00655425
$631$	20.2222	0.805032	0.402516	−	0.915413i	$-0.368136\pi$
$631$	20.2222	0.805032	0.402516	+	0.915413i	$0.368136\pi$
$632$	−52.2642	−2.07896
$633$	−3.51494	−0.139706
$634$	42.9082	1.70410
$635$	0.454672	0.0180431
$636$	−101.064	−4.00744
$637$	34.8329	1.38013
$638$	67.5500	2.67433
$639$	0.747667	0.0295773
$640$	6.95970	0.275106
$641$	2.79031	0.110211	0.0551054	−	0.998481i	$-0.482451\pi$
$641$	2.79031	0.110211	0.0551054	+	0.998481i	$0.482451\pi$
$642$	15.1815	0.599165
$643$	−16.9101	−0.666868	−0.333434	−	0.942774i	$-0.608207\pi$
$643$	−16.9101	−0.666868	−0.333434	+	0.942774i	$0.608207\pi$
$644$	12.2938	0.484442
$645$	−2.21219	−0.0871048
$646$	−41.9426	−1.65021
$647$	5.66380	0.222667	0.111333	−	0.993783i	$-0.464488\pi$
$647$	5.66380	0.222667	0.111333	+	0.993783i	$0.464488\pi$
$648$	79.5129	3.12356
$649$	11.2665	0.442249
$650$	−92.7418	−3.63763
$651$	21.6063	0.846818
$652$	−5.67890	−0.222403
$653$	−5.57977	−0.218353	−0.109177	−	0.994022i	$-0.534821\pi$
$653$	−5.57977	−0.218353	−0.109177	+	0.994022i	$0.534821\pi$
$654$	42.7350	1.67107
$655$	−0.698015	−0.0272737
$656$	99.9745	3.90335
$657$	2.35036	0.0916963
$658$	45.8787	1.78854
$659$	47.7129	1.85863	0.929315	−	0.369288i	$-0.120398\pi$
$659$	47.7129	1.85863	0.929315	+	0.369288i	$0.120398\pi$
$660$	3.23162	0.125791
$661$	−12.3002	−0.478423	−0.239212	−	0.970967i	$-0.576889\pi$
$661$	−12.3002	−0.478423	−0.239212	+	0.970967i	$0.576889\pi$
$662$	58.7815	2.28461
$663$	55.1735	2.14276
$664$	−172.661	−6.70054
$665$	−0.497146	−0.0192785
$666$	0.990761	0.0383912
$667$	−13.8146	−0.534904
$668$	−76.1706	−2.94713
$669$	16.8343	0.650851
$670$	−2.82678	−0.109208
$671$	−25.5636	−0.986872
$672$	57.8107	2.23010
$673$	2.95705	0.113986	0.0569929	−	0.998375i	$-0.481849\pi$
$673$	2.95705	0.113986	0.0569929	+	0.998375i	$0.481849\pi$
$674$	52.6570	2.02827
$675$	27.2064	1.04718
$676$	182.165	7.00634
$677$	9.99695	0.384214	0.192107	−	0.981374i	$-0.438468\pi$
$677$	9.99695	0.384214	0.192107	+	0.981374i	$0.438468\pi$
$678$	48.8530	1.87619
$679$	19.0703	0.731849
$680$	−6.35731	−0.243792
$681$	−20.6155	−0.789986
$682$	−77.6521	−2.97345
$683$	19.7920	0.757322	0.378661	−	0.925536i	$-0.376385\pi$
$683$	19.7920	0.757322	0.378661	+	0.925536i	$0.376385\pi$
$684$	6.07915	0.232442
$685$	−0.964687	−0.0368588
$686$	−45.4623	−1.73576
$687$	34.4750	1.31530
$688$	186.356	7.10474
$689$	73.5033	2.80025
$690$	−0.893653	−0.0340208
$691$	−21.7037	−0.825648	−0.412824	−	0.910811i	$-0.635458\pi$
$691$	−21.7037	−0.825648	−0.412824	+	0.910811i	$0.635458\pi$
$692$	13.4962	0.513048
$693$	−1.36577	−0.0518812
$694$	−31.0268	−1.17776
$695$	−1.55765	−0.0590851
$696$	−142.349	−5.39574
$697$	−29.9193	−1.13328
$698$	11.2454	0.425643
$699$	0.509556	0.0192732
$700$	38.1044	1.44021
$701$	−1.43842	−0.0543282	−0.0271641	−	0.999631i	$-0.508648\pi$
$701$	−1.43842	−0.0543282	−0.0271641	+	0.999631i	$0.508648\pi$
$702$	−101.544	−3.83253
$703$	−2.99405	−0.112923
$704$	−111.894	−4.21716
$705$	−2.46638	−0.0928894
$706$	42.5162	1.60012
$707$	−20.9674	−0.788561
$708$	−36.6493	−1.37736
$709$	19.3589	0.727038	0.363519	−	0.931587i	$-0.381575\pi$
$709$	19.3589	0.727038	0.363519	+	0.931587i	$0.381575\pi$
$710$	−0.714821	−0.0268268
$711$	−1.83297	−0.0687418
$712$	50.3638	1.88746
$713$	15.8806	0.594732
$714$	−30.6525	−1.14714
$715$	−2.35034	−0.0878979
$716$	87.0409	3.25287
$717$	−28.2774	−1.05604
$718$	55.6955	2.07854
$719$	2.09891	0.0782762	0.0391381	−	0.999234i	$-0.487539\pi$
$719$	2.09891	0.0782762	0.0391381	+	0.999234i	$0.487539\pi$
$720$	0.745011	0.0277649
$721$	8.50773	0.316844
$722$	27.8096	1.03497
$723$	−44.4705	−1.65388
$724$	−26.3192	−0.978144
$725$	−42.8183	−1.59023
$726$	13.2727	0.492595
$727$	18.9069	0.701217	0.350609	−	0.936522i	$-0.385975\pi$
$727$	18.9069	0.701217	0.350609	+	0.936522i	$0.385975\pi$
$728$	−92.1324	−3.41465
$729$	29.4051	1.08908
$730$	−2.24711	−0.0831692
$731$	−55.7705	−2.06275
$732$	83.1569	3.07357
$733$	−6.52270	−0.240922	−0.120461	−	0.992718i	$-0.538437\pi$
$733$	−6.52270	−0.240922	−0.120461	+	0.992718i	$0.538437\pi$
$734$	66.5124	2.45502
$735$	1.04034	0.0383734
$736$	42.4907	1.56623
$737$	23.4680	0.864454
$738$	5.86373	0.215847
$739$	−7.20745	−0.265130	−0.132565	−	0.991174i	$-0.542321\pi$
$739$	−7.20745	−0.265130	−0.132565	+	0.991174i	$0.542321\pi$
$740$	−0.700525	−0.0257518
$741$	32.6771	1.20042
$742$	−40.8359	−1.49913
$743$	0.550414	0.0201927	0.0100964	−	0.999949i	$-0.496786\pi$
$743$	0.550414	0.0201927	0.0100964	+	0.999949i	$0.496786\pi$
$744$	163.638	5.99924
$745$	−1.28942	−0.0472405
$746$	31.8599	1.16647
$747$	−6.05544	−0.221557
$748$	81.4711	2.97888
$749$	4.53654	0.165762
$750$	−5.54820	−0.202592
$751$	40.1865	1.46643	0.733213	−	0.679999i	$-0.238020\pi$
$751$	40.1865	1.46643	0.733213	+	0.679999i	$0.238020\pi$
$752$	207.769	7.57656
$753$	32.7831	1.19468
$754$	159.813	5.82005
$755$	0.339388	0.0123516
$756$	41.7210	1.51738
$757$	5.65084	0.205383	0.102692	−	0.994713i	$-0.467255\pi$
$757$	5.65084	0.205383	0.102692	+	0.994713i	$0.467255\pi$
$758$	−92.7383	−3.36841
$759$	7.41913	0.269297
$760$	−3.76518	−0.136578
$761$	−43.5271	−1.57786	−0.788929	−	0.614485i	$-0.789364\pi$
$761$	−43.5271	−1.57786	−0.788929	+	0.614485i	$0.789364\pi$
$762$	16.6032	0.601472
$763$	12.7701	0.462309
$764$	51.8885	1.87726
$765$	−0.222959	−0.00806110
$766$	72.5721	2.62214
$767$	26.6548	0.962451
$768$	125.959	4.54515
$769$	41.2281	1.48672	0.743361	−	0.668890i	$-0.233230\pi$
$769$	41.2281	1.48672	0.743361	+	0.668890i	$0.233230\pi$
$770$	1.30577	0.0470566
$771$	41.3760	1.49012
$772$	103.303	3.71795
$773$	−14.1926	−0.510473	−0.255237	−	0.966879i	$-0.582153\pi$
$773$	−14.1926	−0.510473	−0.255237	+	0.966879i	$0.582153\pi$
$774$	10.9302	0.392877
$775$	49.2218	1.76810
$776$	144.431	5.18476
$777$	−2.18811	−0.0784981
$778$	−16.2436	−0.582360
$779$	−17.7200	−0.634886
$780$	7.64553	0.273754
$781$	5.93447	0.212352
$782$	−22.5295	−0.805653
$783$	−46.8823	−1.67544
$784$	−87.6383	−3.12994
$785$	−1.93539	−0.0690771
$786$	−25.4894	−0.909178
$787$	31.5397	1.12427	0.562135	−	0.827045i	$-0.309980\pi$
$787$	31.5397	1.12427	0.562135	+	0.827045i	$0.309980\pi$
$788$	−9.80557	−0.349309
$789$	17.5001	0.623018
$790$	1.75245	0.0623493
$791$	14.5983	0.519056
$792$	−10.3438	−0.367551
$793$	−60.4796	−2.14769
$794$	7.16900	0.254418
$795$	2.19528	0.0778587
$796$	−120.191	−4.26006
$797$	−31.0364	−1.09936	−0.549682	−	0.835374i	$-0.685251\pi$
$797$	−31.0364	−1.09936	−0.549682	+	0.835374i	$0.685251\pi$
$798$	−18.1543	−0.642654
$799$	−62.1789	−2.19973
$800$	131.700	4.65629
$801$	1.76632	0.0624099
$802$	−55.0791	−1.94491
$803$	18.6555	0.658340
$804$	−76.3400	−2.69230
$805$	−0.267042	−0.00941199
$806$	−183.713	−6.47102
$807$	26.2575	0.924308
$808$	−158.799	−5.58653
$809$	14.3500	0.504520	0.252260	−	0.967659i	$-0.418826\pi$
$809$	14.3500	0.504520	0.252260	+	0.967659i	$0.418826\pi$
$810$	−2.66611	−0.0936777
$811$	29.4631	1.03459	0.517294	−	0.855808i	$-0.326939\pi$
$811$	29.4631	1.03459	0.517294	+	0.855808i	$0.326939\pi$
$812$	−65.6618	−2.30428
$813$	45.4419	1.59372
$814$	7.86398	0.275632
$815$	0.123356	0.00432096
$816$	−138.815	−4.85948
$817$	−33.0307	−1.15560
$818$	25.2008	0.881127
$819$	−3.23120	−0.112907
$820$	−4.14600	−0.144784
$821$	−25.0717	−0.875010	−0.437505	−	0.899216i	$-0.644138\pi$
$821$	−25.0717	−0.875010	−0.437505	+	0.899216i	$0.644138\pi$
$822$	−35.2275	−1.22870
$823$	−37.8055	−1.31782	−0.658908	−	0.752224i	$-0.728981\pi$
$823$	−37.8055	−1.31782	−0.658908	+	0.752224i	$0.728981\pi$
$824$	64.4342	2.24467
$825$	22.9955	0.800602
$826$	−14.8085	−0.515253
$827$	−1.68819	−0.0587042	−0.0293521	−	0.999569i	$-0.509344\pi$
$827$	−1.68819	−0.0587042	−0.0293521	+	0.999569i	$0.509344\pi$
$828$	3.26542	0.113481
$829$	57.3110	1.99049	0.995246	−	0.0973884i	$-0.0310489\pi$
$829$	57.3110	1.99049	0.995246	+	0.0973884i	$0.0310489\pi$
$830$	5.78942	0.200954
$831$	−8.32186	−0.288682
$832$	−264.724	−9.17766
$833$	26.2275	0.908728
$834$	−56.8808	−1.96962
$835$	1.65456	0.0572584
$836$	48.2521	1.66883
$837$	53.8934	1.86283
$838$	6.64900	0.229686
$839$	12.9105	0.445719	0.222859	−	0.974851i	$-0.428461\pi$
$839$	12.9105	0.445719	0.222859	+	0.974851i	$0.428461\pi$
$840$	−2.75167	−0.0949416
$841$	44.7848	1.54430
$842$	−71.7966	−2.47427
$843$	−22.0020	−0.757789
$844$	−12.2794	−0.422675
$845$	−3.95694	−0.136123
$846$	12.1861	0.418968
$847$	3.96615	0.136279
$848$	−184.932	−6.35058
$849$	−29.7439	−1.02081
$850$	−69.8300	−2.39515
$851$	−1.60826	−0.0551303
$852$	−19.3045	−0.661360
$853$	−57.1394	−1.95642	−0.978208	−	0.207627i	$-0.933426\pi$
$853$	−57.1394	−1.95642	−0.978208	+	0.207627i	$0.933426\pi$
$854$	33.6003	1.14978
$855$	−0.132050	−0.00451601
$856$	34.3580	1.17433
$857$	44.5018	1.52015	0.760076	−	0.649834i	$-0.225162\pi$
$857$	44.5018	1.52015	0.760076	+	0.649834i	$0.225162\pi$
$858$	−85.8275	−2.93010
$859$	−32.5026	−1.10898	−0.554488	−	0.832192i	$-0.687086\pi$
$859$	−32.5026	−1.10898	−0.554488	+	0.832192i	$0.687086\pi$
$860$	−7.72826	−0.263532
$861$	−12.9502	−0.441340
$862$	96.0820	3.27256
$863$	−20.6885	−0.704245	−0.352123	−	0.935954i	$-0.614540\pi$
$863$	−20.6885	−0.704245	−0.352123	+	0.935954i	$0.614540\pi$
$864$	144.200	4.90577
$865$	−0.293161	−0.00996776
$866$	45.4498	1.54445
$867$	13.9083	0.472352
$868$	75.4814	2.56201
$869$	−14.5489	−0.493537
$870$	4.77306	0.161822
$871$	55.5217	1.88128
$872$	96.7158	3.27521
$873$	5.06537	0.171437
$874$	−13.3433	−0.451345
$875$	−1.65792	−0.0560478
$876$	−60.6854	−2.05037
$877$	23.6237	0.797717	0.398859	−	0.917012i	$-0.369406\pi$
$877$	23.6237	0.797717	0.398859	+	0.917012i	$0.369406\pi$
$878$	−67.3943	−2.27445
$879$	−21.1581	−0.713647
$880$	5.91338	0.199340
$881$	−38.4640	−1.29589	−0.647943	−	0.761689i	$-0.724370\pi$
$881$	−38.4640	−1.29589	−0.647943	+	0.761689i	$0.724370\pi$
$882$	−5.14018	−0.173079
$883$	50.7721	1.70862	0.854309	−	0.519765i	$-0.173980\pi$
$883$	50.7721	1.70862	0.854309	+	0.519765i	$0.173980\pi$
$884$	192.748	6.48283
$885$	0.796086	0.0267601
$886$	−29.2690	−0.983310
$887$	−16.9104	−0.567796	−0.283898	−	0.958855i	$-0.591628\pi$
$887$	−16.9104	−0.567796	−0.283898	+	0.958855i	$0.591628\pi$
$888$	−16.5719	−0.556116
$889$	4.96140	0.166400
$890$	−1.68873	−0.0566062
$891$	22.1342	0.741522
$892$	58.8104	1.96912
$893$	−36.8261	−1.23234
$894$	−47.0856	−1.57478
$895$	−1.89068	−0.0631985
$896$	75.9445	2.53713
$897$	17.5525	0.586062
$898$	−17.7371	−0.591895
$899$	−84.8192	−2.82888
$900$	10.1212	0.337372
$901$	55.3444	1.84379
$902$	46.5423	1.54969
$903$	−24.1395	−0.803312
$904$	110.562	3.67723
$905$	0.571698	0.0190039
$906$	12.3934	0.411744
$907$	−16.8985	−0.561106	−0.280553	−	0.959838i	$-0.590518\pi$
$907$	−16.8985	−0.561106	−0.280553	+	0.959838i	$0.590518\pi$
$908$	−72.0200	−2.39007
$909$	−5.56928	−0.184722
$910$	3.08925	0.102408
$911$	4.68282	0.155149	0.0775744	−	0.996987i	$-0.475282\pi$
$911$	4.68282	0.155149	0.0775744	+	0.996987i	$0.475282\pi$
$912$	−82.2144	−2.72239
$913$	−48.0639	−1.59068
$914$	−35.0436	−1.15914
$915$	−1.80631	−0.0597149
$916$	120.438	3.97939
$917$	−7.61677	−0.251528
$918$	−76.4577	−2.52348
$919$	25.1874	0.830856	0.415428	−	0.909626i	$-0.363632\pi$
$919$	25.1874	0.830856	0.415428	+	0.909626i	$0.363632\pi$
$920$	−2.02247	−0.0666789
$921$	−11.3147	−0.372831
$922$	−0.968927	−0.0319099
$923$	14.0401	0.462134
$924$	35.2636	1.16009
$925$	−4.98478	−0.163899
$926$	57.9613	1.90473
$927$	2.25979	0.0742212
$928$	−226.946	−7.44986
$929$	38.5669	1.26534	0.632670	−	0.774422i	$-0.281959\pi$
$929$	38.5669	1.26534	0.632670	+	0.774422i	$0.281959\pi$
$930$	−5.48686	−0.179921
$931$	15.5335	0.509090
$932$	1.78013	0.0583100
$933$	−9.12122	−0.298615
$934$	48.2902	1.58010
$935$	−1.76969	−0.0578752
$936$	−24.4718	−0.799887
$937$	24.3747	0.796286	0.398143	−	0.917323i	$-0.369655\pi$
$937$	24.3747	0.796286	0.398143	+	0.917323i	$0.369655\pi$
$938$	−30.8459	−1.00715
$939$	19.5372	0.637573
$940$	−8.61629	−0.281032
$941$	31.2626	1.01913	0.509567	−	0.860431i	$-0.329806\pi$
$941$	31.2626	1.01913	0.509567	+	0.860431i	$0.329806\pi$
$942$	−70.6747	−2.30271
$943$	−9.51833	−0.309960
$944$	−67.0626	−2.18270
$945$	−0.906253	−0.0294804
$946$	86.7562	2.82069
$947$	41.2298	1.33979	0.669894	−	0.742457i	$-0.266340\pi$
$947$	41.2298	1.33979	0.669894	+	0.742457i	$0.266340\pi$
$948$	47.3266	1.53710
$949$	44.1362	1.43272
$950$	−41.3576	−1.34182
$951$	−25.1707	−0.816216
$952$	−69.3712	−2.24833
$953$	19.4125	0.628831	0.314416	−	0.949285i	$-0.398191\pi$
$953$	19.4125	0.628831	0.314416	+	0.949285i	$0.398191\pi$
$954$	−10.8467	−0.351174
$955$	−1.12711	−0.0364724
$956$	−98.7869	−3.19500
$957$	−39.6260	−1.28093
$958$	−98.1145	−3.16994
$959$	−10.5267	−0.339925
$960$	−7.90638	−0.255177
$961$	66.5038	2.14528
$962$	18.6050	0.599849
$963$	1.20498	0.0388299
$964$	−155.357	−5.00372
$965$	−2.24392	−0.0722343
$966$	−9.75157	−0.313752
$967$	−28.2047	−0.907001	−0.453501	−	0.891256i	$-0.649825\pi$
$967$	−28.2047	−0.907001	−0.453501	+	0.891256i	$0.649825\pi$
$968$	30.0381	0.965460
$969$	24.6043	0.790403
$970$	−4.84284	−0.155494
$971$	−0.302679	−0.00971343	−0.00485672	−	0.999988i	$-0.501546\pi$
$971$	−0.302679	−0.00971343	−0.00485672	+	0.999988i	$0.501546\pi$
$972$	20.9835	0.673045
$973$	−16.9972	−0.544904
$974$	53.4384	1.71228
$975$	54.4040	1.74232
$976$	152.164	4.87067
$977$	49.6566	1.58866	0.794328	−	0.607489i	$-0.207823\pi$
$977$	49.6566	1.58866	0.794328	+	0.607489i	$0.207823\pi$
$978$	4.50458	0.144041
$979$	14.0198	0.448076
$980$	3.63440	0.116097
$981$	3.39195	0.108297
$982$	−71.5007	−2.28168
$983$	27.8306	0.887657	0.443829	−	0.896112i	$-0.353620\pi$
$983$	27.8306	0.887657	0.443829	+	0.896112i	$0.353620\pi$
$984$	−98.0793	−3.12666
$985$	0.212994	0.00678656
$986$	120.332	3.83214
$987$	−26.9133	−0.856659
$988$	114.157	3.63183
$989$	−17.7425	−0.564177
$990$	0.346833	0.0110231
$991$	−19.3353	−0.614206	−0.307103	−	0.951676i	$-0.599360\pi$
$991$	−19.3353	−0.614206	−0.307103	+	0.951676i	$0.599360\pi$
$992$	260.885	8.28312
$993$	−34.4823	−1.09426
$994$	−7.80016	−0.247406
$995$	2.61076	0.0827667
$996$	156.349	4.95411
$997$	18.4934	0.585693	0.292846	−	0.956160i	$-0.405398\pi$
$997$	18.4934	0.585693	0.292846	+	0.956160i	$0.405398\pi$
$998$	12.9388	0.409570
$999$	−5.45790	−0.172680

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.e.1.2	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.e.1.2	✓	134	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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.77108 q^{2} +1.62557 q^{3} +5.67890 q^{4} -0.123356 q^{5} -4.50458 q^{6} -1.34606 q^{7} -10.1945 q^{8} -0.357536 q^{9} +O(q^{10})\)	\(q-2.77108 q^{2} +1.62557 q^{3} +5.67890 q^{4} -0.123356 q^{5} -4.50458 q^{6} -1.34606 q^{7} -10.1945 q^{8} -0.357536 q^{9} +0.341829 q^{10} -2.83787 q^{11} +9.23143 q^{12} -6.71398 q^{13} +3.73005 q^{14} -0.200523 q^{15} +16.8921 q^{16} -5.05529 q^{17} +0.990761 q^{18} -2.99405 q^{19} -0.700525 q^{20} -2.18811 q^{21} +7.86398 q^{22} -1.60826 q^{23} -16.5719 q^{24} -4.98478 q^{25} +18.6050 q^{26} -5.45790 q^{27} -7.64415 q^{28} +8.58981 q^{29} +0.555665 q^{30} -9.87440 q^{31} -26.4204 q^{32} -4.61315 q^{33} +14.0086 q^{34} +0.166044 q^{35} -2.03041 q^{36} +1.00000 q^{37} +8.29677 q^{38} -10.9140 q^{39} +1.25755 q^{40} +5.91841 q^{41} +6.06344 q^{42} +11.0321 q^{43} -16.1160 q^{44} +0.0441040 q^{45} +4.45661 q^{46} +12.2998 q^{47} +27.4592 q^{48} -5.18812 q^{49} +13.8132 q^{50} -8.21771 q^{51} -38.1280 q^{52} -10.9478 q^{53} +15.1243 q^{54} +0.350068 q^{55} +13.7225 q^{56} -4.86703 q^{57} -23.8031 q^{58} -3.97005 q^{59} -1.13875 q^{60} +9.00802 q^{61} +27.3628 q^{62} +0.481265 q^{63} +39.4288 q^{64} +0.828207 q^{65} +12.7834 q^{66} -8.26957 q^{67} -28.7085 q^{68} -2.61433 q^{69} -0.460123 q^{70} -2.09117 q^{71} +3.64491 q^{72} -6.57378 q^{73} -2.77108 q^{74} -8.10309 q^{75} -17.0029 q^{76} +3.81995 q^{77} +30.2436 q^{78} +5.12669 q^{79} -2.08374 q^{80} -7.79956 q^{81} -16.4004 q^{82} +16.9366 q^{83} -12.4261 q^{84} +0.623599 q^{85} -30.5709 q^{86} +13.9633 q^{87} +28.9308 q^{88} -4.94027 q^{89} -0.122216 q^{90} +9.03743 q^{91} -9.13313 q^{92} -16.0515 q^{93} -34.0837 q^{94} +0.369333 q^{95} -42.9481 q^{96} -14.1674 q^{97} +14.3767 q^{98} +1.01464 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9}+O(q^{10}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9} + 15 q^{10} + 20 q^{11} + 28 q^{12} + 11 q^{13} + 17 q^{14} - 13 q^{15} + 143 q^{16} + 76 q^{17} + 23 q^{18} + 15 q^{19} + 67 q^{20} + 63 q^{21} + 2 q^{22} + 22 q^{23} + 33 q^{24} + 160 q^{25} + 65 q^{26} + 31 q^{27} + 10 q^{28} + 73 q^{29} + 20 q^{30} + 10 q^{31} + 53 q^{32} + 72 q^{33} - 7 q^{34} + 52 q^{35} + 201 q^{36} + 134 q^{37} + 70 q^{38} + 6 q^{39} + 11 q^{40} + 182 q^{41} - 15 q^{42} + 12 q^{43} + 33 q^{44} + 29 q^{45} + 24 q^{46} + 80 q^{47} + 21 q^{48} + 229 q^{49} + 37 q^{50} + 57 q^{51} - 15 q^{52} + 75 q^{53} + 95 q^{54} - 9 q^{55} + 39 q^{56} + 19 q^{57} - 21 q^{58} + 91 q^{59} + 62 q^{60} + 58 q^{61} + 108 q^{62} + 9 q^{63} + 167 q^{64} + 76 q^{65} + 105 q^{66} - 17 q^{67} + 109 q^{68} + 48 q^{69} - 55 q^{70} + 56 q^{71} + 48 q^{72} + 54 q^{73} + 9 q^{74} + 28 q^{75} + 82 q^{76} + 156 q^{77} + 16 q^{78} - 2 q^{79} + 98 q^{80} + 270 q^{81} - 42 q^{82} + 130 q^{83} + 229 q^{84} + 22 q^{85} + 72 q^{86} + 22 q^{87} + 61 q^{88} + 157 q^{89} + 176 q^{90} + 31 q^{91} - 18 q^{92} + 36 q^{93} + 83 q^{94} + 98 q^{95} + 111 q^{96} + 35 q^{97} + 53 q^{98} + 55 q^{99}+O(q^{100}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9 + 15 * q^10 + 20 * q^11 + 28 * q^12 + 11 * q^13 + 17 * q^14 - 13 * q^15 + 143 * q^16 + 76 * q^17 + 23 * q^18 + 15 * q^19 + 67 * q^20 + 63 * q^21 + 2 * q^22 + 22 * q^23 + 33 * q^24 + 160 * q^25 + 65 * q^26 + 31 * q^27 + 10 * q^28 + 73 * q^29 + 20 * q^30 + 10 * q^31 + 53 * q^32 + 72 * q^33 - 7 * q^34 + 52 * q^35 + 201 * q^36 + 134 * q^37 + 70 * q^38 + 6 * q^39 + 11 * q^40 + 182 * q^41 - 15 * q^42 + 12 * q^43 + 33 * q^44 + 29 * q^45 + 24 * q^46 + 80 * q^47 + 21 * q^48 + 229 * q^49 + 37 * q^50 + 57 * q^51 - 15 * q^52 + 75 * q^53 + 95 * q^54 - 9 * q^55 + 39 * q^56 + 19 * q^57 - 21 * q^58 + 91 * q^59 + 62 * q^60 + 58 * q^61 + 108 * q^62 + 9 * q^63 + 167 * q^64 + 76 * q^65 + 105 * q^66 - 17 * q^67 + 109 * q^68 + 48 * q^69 - 55 * q^70 + 56 * q^71 + 48 * q^72 + 54 * q^73 + 9 * q^74 + 28 * q^75 + 82 * q^76 + 156 * q^77 + 16 * q^78 - 2 * q^79 + 98 * q^80 + 270 * q^81 - 42 * q^82 + 130 * q^83 + 229 * q^84 + 22 * q^85 + 72 * q^86 + 22 * q^87 + 61 * q^88 + 157 * q^89 + 176 * q^90 + 31 * q^91 - 18 * q^92 + 36 * q^93 + 83 * q^94 + 98 * q^95 + 111 * q^96 + 35 * q^97 + 53 * q^98 + 55 * q^99

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