LMFDB - Embedded newform 6010.2.a.j.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$0$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.489009 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.489009 q^{6} -2.03673 q^{7} +1.00000 q^{8} -2.76087 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.489009 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.489009 q^{6} -2.03673 q^{7} +1.00000 q^{8} -2.76087 q^{9} +1.00000 q^{10} +3.55613 q^{11} -0.489009 q^{12} -6.34714 q^{13} -2.03673 q^{14} -0.489009 q^{15} +1.00000 q^{16} -0.509753 q^{17} -2.76087 q^{18} +6.21230 q^{19} +1.00000 q^{20} +0.995979 q^{21} +3.55613 q^{22} +0.0973899 q^{23} -0.489009 q^{24} +1.00000 q^{25} -6.34714 q^{26} +2.81712 q^{27} -2.03673 q^{28} +0.202752 q^{29} -0.489009 q^{30} +8.32682 q^{31} +1.00000 q^{32} -1.73898 q^{33} -0.509753 q^{34} -2.03673 q^{35} -2.76087 q^{36} -4.09559 q^{37} +6.21230 q^{38} +3.10381 q^{39} +1.00000 q^{40} -5.06237 q^{41} +0.995979 q^{42} -6.14104 q^{43} +3.55613 q^{44} -2.76087 q^{45} +0.0973899 q^{46} +11.1825 q^{47} -0.489009 q^{48} -2.85173 q^{49} +1.00000 q^{50} +0.249274 q^{51} -6.34714 q^{52} +4.00795 q^{53} +2.81712 q^{54} +3.55613 q^{55} -2.03673 q^{56} -3.03787 q^{57} +0.202752 q^{58} -3.35700 q^{59} -0.489009 q^{60} +11.8722 q^{61} +8.32682 q^{62} +5.62315 q^{63} +1.00000 q^{64} -6.34714 q^{65} -1.73898 q^{66} +0.114675 q^{67} -0.509753 q^{68} -0.0476245 q^{69} -2.03673 q^{70} +5.12951 q^{71} -2.76087 q^{72} -3.80215 q^{73} -4.09559 q^{74} -0.489009 q^{75} +6.21230 q^{76} -7.24288 q^{77} +3.10381 q^{78} +9.23971 q^{79} +1.00000 q^{80} +6.90501 q^{81} -5.06237 q^{82} +2.73026 q^{83} +0.995979 q^{84} -0.509753 q^{85} -6.14104 q^{86} -0.0991477 q^{87} +3.55613 q^{88} +16.2605 q^{89} -2.76087 q^{90} +12.9274 q^{91} +0.0973899 q^{92} -4.07189 q^{93} +11.1825 q^{94} +6.21230 q^{95} -0.489009 q^{96} +5.74013 q^{97} -2.85173 q^{98} -9.81802 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9}+O(q^{10}) $ 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9	\( 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9} + 33 q^{10} + 12 q^{11} + 6 q^{12} + 20 q^{13} + 4 q^{14} + 6 q^{15} + 33 q^{16} + 33 q^{17} + 49 q^{18} + 17 q^{19} + 33 q^{20} + 26 q^{21} + 12 q^{22} + 7 q^{23} + 6 q^{24} + 33 q^{25} + 20 q^{26} + 21 q^{27} + 4 q^{28} + 33 q^{29} + 6 q^{30} + 35 q^{31} + 33 q^{32} + 25 q^{33} + 33 q^{34} + 4 q^{35} + 49 q^{36} + 16 q^{37} + 17 q^{38} + 22 q^{39} + 33 q^{40} + 39 q^{41} + 26 q^{42} - 3 q^{43} + 12 q^{44} + 49 q^{45} + 7 q^{46} + 19 q^{47} + 6 q^{48} + 69 q^{49} + 33 q^{50} + 21 q^{51} + 20 q^{52} + 41 q^{53} + 21 q^{54} + 12 q^{55} + 4 q^{56} + 33 q^{58} + 18 q^{59} + 6 q^{60} + 30 q^{61} + 35 q^{62} - 15 q^{63} + 33 q^{64} + 20 q^{65} + 25 q^{66} - 9 q^{67} + 33 q^{68} + 23 q^{69} + 4 q^{70} + 36 q^{71} + 49 q^{72} + 35 q^{73} + 16 q^{74} + 6 q^{75} + 17 q^{76} + 26 q^{77} + 22 q^{78} + 32 q^{79} + 33 q^{80} + 53 q^{81} + 39 q^{82} + 24 q^{83} + 26 q^{84} + 33 q^{85} - 3 q^{86} + 12 q^{87} + 12 q^{88} + 40 q^{89} + 49 q^{90} + 5 q^{91} + 7 q^{92} + 18 q^{93} + 19 q^{94} + 17 q^{95} + 6 q^{96} + 39 q^{97} + 69 q^{98} + 3 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9 + 33 * q^10 + 12 * q^11 + 6 * q^12 + 20 * q^13 + 4 * q^14 + 6 * q^15 + 33 * q^16 + 33 * q^17 + 49 * q^18 + 17 * q^19 + 33 * q^20 + 26 * q^21 + 12 * q^22 + 7 * q^23 + 6 * q^24 + 33 * q^25 + 20 * q^26 + 21 * q^27 + 4 * q^28 + 33 * q^29 + 6 * q^30 + 35 * q^31 + 33 * q^32 + 25 * q^33 + 33 * q^34 + 4 * q^35 + 49 * q^36 + 16 * q^37 + 17 * q^38 + 22 * q^39 + 33 * q^40 + 39 * q^41 + 26 * q^42 - 3 * q^43 + 12 * q^44 + 49 * q^45 + 7 * q^46 + 19 * q^47 + 6 * q^48 + 69 * q^49 + 33 * q^50 + 21 * q^51 + 20 * q^52 + 41 * q^53 + 21 * q^54 + 12 * q^55 + 4 * q^56 + 33 * q^58 + 18 * q^59 + 6 * q^60 + 30 * q^61 + 35 * q^62 - 15 * q^63 + 33 * q^64 + 20 * q^65 + 25 * q^66 - 9 * q^67 + 33 * q^68 + 23 * q^69 + 4 * q^70 + 36 * q^71 + 49 * q^72 + 35 * q^73 + 16 * q^74 + 6 * q^75 + 17 * q^76 + 26 * q^77 + 22 * q^78 + 32 * q^79 + 33 * q^80 + 53 * q^81 + 39 * q^82 + 24 * q^83 + 26 * q^84 + 33 * q^85 - 3 * q^86 + 12 * q^87 + 12 * q^88 + 40 * q^89 + 49 * q^90 + 5 * q^91 + 7 * q^92 + 18 * q^93 + 19 * q^94 + 17 * q^95 + 6 * q^96 + 39 * q^97 + 69 * q^98 + 3 * 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
$3$	−0.489009	−0.282329	−0.141165	−	0.989986i	$-0.545085\pi$
$3$	−0.489009	−0.282329	−0.141165	+	0.989986i	$0.545085\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.489009	−0.199637
$7$	−2.03673	−0.769811	−0.384906	−	0.922956i	$-0.625766\pi$
$7$	−2.03673	−0.769811	−0.384906	+	0.922956i	$0.625766\pi$
$8$	1.00000	0.353553
$9$	−2.76087	−0.920290
$10$	1.00000	0.316228
$11$	3.55613	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$11$	3.55613	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$12$	−0.489009	−0.141165
$13$	−6.34714	−1.76038	−0.880190	−	0.474622i	$-0.842585\pi$
$13$	−6.34714	−1.76038	−0.880190	+	0.474622i	$0.842585\pi$
$14$	−2.03673	−0.544339
$15$	−0.489009	−0.126262
$16$	1.00000	0.250000
$17$	−0.509753	−0.123633	−0.0618167	−	0.998088i	$-0.519689\pi$
$17$	−0.509753	−0.123633	−0.0618167	+	0.998088i	$0.519689\pi$
$18$	−2.76087	−0.650743
$19$	6.21230	1.42520	0.712599	−	0.701571i	$-0.247518\pi$
$19$	6.21230	1.42520	0.712599	+	0.701571i	$0.247518\pi$
$20$	1.00000	0.223607
$21$	0.995979	0.217340
$22$	3.55613	0.758170
$23$	0.0973899	0.0203072	0.0101536	−	0.999948i	$-0.496768\pi$
$23$	0.0973899	0.0203072	0.0101536	+	0.999948i	$0.496768\pi$
$24$	−0.489009	−0.0998185
$25$	1.00000	0.200000
$26$	−6.34714	−1.24478
$27$	2.81712	0.542154
$28$	−2.03673	−0.384906
$29$	0.202752	0.0376502	0.0188251	−	0.999823i	$-0.494007\pi$
$29$	0.202752	0.0376502	0.0188251	+	0.999823i	$0.494007\pi$
$30$	−0.489009	−0.0892804
$31$	8.32682	1.49554	0.747770	−	0.663957i	$-0.231124\pi$
$31$	8.32682	1.49554	0.747770	+	0.663957i	$0.231124\pi$
$32$	1.00000	0.176777
$33$	−1.73898	−0.302718
$34$	−0.509753	−0.0874220
$35$	−2.03673	−0.344270
$36$	−2.76087	−0.460145
$37$	−4.09559	−0.673310	−0.336655	−	0.941628i	$-0.609296\pi$
$37$	−4.09559	−0.673310	−0.336655	+	0.941628i	$0.609296\pi$
$38$	6.21230	1.00777
$39$	3.10381	0.497007
$40$	1.00000	0.158114
$41$	−5.06237	−0.790609	−0.395305	−	0.918550i	$-0.629361\pi$
$41$	−5.06237	−0.790609	−0.395305	+	0.918550i	$0.629361\pi$
$42$	0.995979	0.153683
$43$	−6.14104	−0.936499	−0.468250	−	0.883596i	$-0.655115\pi$
$43$	−6.14104	−0.936499	−0.468250	+	0.883596i	$0.655115\pi$
$44$	3.55613	0.536107
$45$	−2.76087	−0.411566
$46$	0.0973899	0.0143594
$47$	11.1825	1.63114	0.815571	−	0.578657i	$-0.196423\pi$
$47$	11.1825	1.63114	0.815571	+	0.578657i	$0.196423\pi$
$48$	−0.489009	−0.0705824
$49$	−2.85173	−0.407391
$50$	1.00000	0.141421
$51$	0.249274	0.0349053
$52$	−6.34714	−0.880190
$53$	4.00795	0.550534	0.275267	−	0.961368i	$-0.411234\pi$
$53$	4.00795	0.550534	0.275267	+	0.961368i	$0.411234\pi$
$54$	2.81712	0.383361
$55$	3.55613	0.479509
$56$	−2.03673	−0.272169
$57$	−3.03787	−0.402376
$58$	0.202752	0.0266227
$59$	−3.35700	−0.437044	−0.218522	−	0.975832i	$-0.570124\pi$
$59$	−3.35700	−0.437044	−0.218522	+	0.975832i	$0.570124\pi$
$60$	−0.489009	−0.0631308
$61$	11.8722	1.52007	0.760037	−	0.649879i	$-0.225181\pi$
$61$	11.8722	1.52007	0.760037	+	0.649879i	$0.225181\pi$
$62$	8.32682	1.05751
$63$	5.62315	0.708450
$64$	1.00000	0.125000
$65$	−6.34714	−0.787265
$66$	−1.73898	−0.214054
$67$	0.114675	0.0140098	0.00700489	−	0.999975i	$-0.497770\pi$
$67$	0.114675	0.0140098	0.00700489	+	0.999975i	$0.497770\pi$
$68$	−0.509753	−0.0618167
$69$	−0.0476245	−0.00573332
$70$	−2.03673	−0.243436
$71$	5.12951	0.608761	0.304381	−	0.952551i	$-0.401551\pi$
$71$	5.12951	0.608761	0.304381	+	0.952551i	$0.401551\pi$
$72$	−2.76087	−0.325372
$73$	−3.80215	−0.445008	−0.222504	−	0.974932i	$-0.571423\pi$
$73$	−3.80215	−0.445008	−0.222504	+	0.974932i	$0.571423\pi$
$74$	−4.09559	−0.476102
$75$	−0.489009	−0.0564659
$76$	6.21230	0.712599
$77$	−7.24288	−0.825403
$78$	3.10381	0.351437
$79$	9.23971	1.03955	0.519774	−	0.854304i	$-0.326016\pi$
$79$	9.23971	1.03955	0.519774	+	0.854304i	$0.326016\pi$
$80$	1.00000	0.111803
$81$	6.90501	0.767224
$82$	−5.06237	−0.559045
$83$	2.73026	0.299685	0.149842	−	0.988710i	$-0.452123\pi$
$83$	2.73026	0.299685	0.149842	+	0.988710i	$0.452123\pi$
$84$	0.995979	0.108670
$85$	−0.509753	−0.0552905
$86$	−6.14104	−0.662205
$87$	−0.0991477	−0.0106297
$88$	3.55613	0.379085
$89$	16.2605	1.72361	0.861804	−	0.507241i	$-0.169335\pi$
$89$	16.2605	1.72361	0.861804	+	0.507241i	$0.169335\pi$
$90$	−2.76087	−0.291021
$91$	12.9274	1.35516
$92$	0.0973899	0.0101536
$93$	−4.07189	−0.422235
$94$	11.1825	1.15339
$95$	6.21230	0.637368
$96$	−0.489009	−0.0499093
$97$	5.74013	0.582821	0.291411	−	0.956598i	$-0.405875\pi$
$97$	5.74013	0.582821	0.291411	+	0.956598i	$0.405875\pi$
$98$	−2.85173	−0.288069
$99$	−9.81802	−0.986748
$100$	1.00000	0.100000
$101$	−11.8099	−1.17513	−0.587566	−	0.809176i	$-0.699914\pi$
$101$	−11.8099	−1.17513	−0.587566	+	0.809176i	$0.699914\pi$
$102$	0.249274	0.0246818
$103$	−9.14541	−0.901124	−0.450562	−	0.892745i	$-0.648776\pi$
$103$	−9.14541	−0.901124	−0.450562	+	0.892745i	$0.648776\pi$
$104$	−6.34714	−0.622388
$105$	0.995979	0.0971976
$106$	4.00795	0.389287
$107$	11.9421	1.15449	0.577244	−	0.816572i	$-0.304128\pi$
$107$	11.9421	1.15449	0.577244	+	0.816572i	$0.304128\pi$
$108$	2.81712	0.271077
$109$	−1.31504	−0.125958	−0.0629788	−	0.998015i	$-0.520060\pi$
$109$	−1.31504	−0.125958	−0.0629788	+	0.998015i	$0.520060\pi$
$110$	3.55613	0.339064
$111$	2.00278	0.190095
$112$	−2.03673	−0.192453
$113$	−5.62764	−0.529404	−0.264702	−	0.964330i	$-0.585274\pi$
$113$	−5.62764	−0.529404	−0.264702	+	0.964330i	$0.585274\pi$
$114$	−3.03787	−0.284523
$115$	0.0973899	0.00908165
$116$	0.202752	0.0188251
$117$	17.5236	1.62006
$118$	−3.35700	−0.309037
$119$	1.03823	0.0951744
$120$	−0.489009	−0.0446402
$121$	1.64608	0.149644
$122$	11.8722	1.07486
$123$	2.47554	0.223212
$124$	8.32682	0.747770
$125$	1.00000	0.0894427
$126$	5.62315	0.500950
$127$	16.2188	1.43918	0.719591	−	0.694398i	$-0.244329\pi$
$127$	16.2188	1.43918	0.719591	+	0.694398i	$0.244329\pi$
$128$	1.00000	0.0883883
$129$	3.00302	0.264401
$130$	−6.34714	−0.556681
$131$	12.0280	1.05089	0.525446	−	0.850827i	$-0.323899\pi$
$131$	12.0280	1.05089	0.525446	+	0.850827i	$0.323899\pi$
$132$	−1.73898	−0.151359
$133$	−12.6528	−1.09713
$134$	0.114675	0.00990641
$135$	2.81712	0.242459
$136$	−0.509753	−0.0437110
$137$	12.9578	1.10706	0.553530	−	0.832829i	$-0.313281\pi$
$137$	12.9578	1.10706	0.553530	+	0.832829i	$0.313281\pi$
$138$	−0.0476245	−0.00405407
$139$	17.4919	1.48365	0.741824	−	0.670595i	$-0.233961\pi$
$139$	17.4919	1.48365	0.741824	+	0.670595i	$0.233961\pi$
$140$	−2.03673	−0.172135
$141$	−5.46837	−0.460520
$142$	5.12951	0.430459
$143$	−22.5713	−1.88750
$144$	−2.76087	−0.230073
$145$	0.202752	0.0168377
$146$	−3.80215	−0.314668
$147$	1.39452	0.115018
$148$	−4.09559	−0.336655
$149$	16.7327	1.37080	0.685398	−	0.728169i	$-0.259628\pi$
$149$	16.7327	1.37080	0.685398	+	0.728169i	$0.259628\pi$
$150$	−0.489009	−0.0399274
$151$	16.4838	1.34143	0.670715	−	0.741715i	$-0.265987\pi$
$151$	16.4838	1.34143	0.670715	+	0.741715i	$0.265987\pi$
$152$	6.21230	0.503884
$153$	1.40736	0.113779
$154$	−7.24288	−0.583648
$155$	8.32682	0.668826
$156$	3.10381	0.248503
$157$	−16.8831	−1.34742	−0.673708	−	0.738998i	$-0.735299\pi$
$157$	−16.8831	−1.34742	−0.673708	+	0.738998i	$0.735299\pi$
$158$	9.23971	0.735072
$159$	−1.95992	−0.155432
$160$	1.00000	0.0790569
$161$	−0.198357	−0.0156327
$162$	6.90501	0.542509
$163$	0.601022	0.0470757	0.0235378	−	0.999723i	$-0.492507\pi$
$163$	0.601022	0.0470757	0.0235378	+	0.999723i	$0.492507\pi$
$164$	−5.06237	−0.395305
$165$	−1.73898	−0.135379
$166$	2.73026	0.211909
$167$	−21.8605	−1.69161	−0.845807	−	0.533489i	$-0.820881\pi$
$167$	−21.8605	−1.69161	−0.845807	+	0.533489i	$0.820881\pi$
$168$	0.995979	0.0768414
$169$	27.2861	2.09893
$170$	−0.509753	−0.0390963
$171$	−17.1513	−1.31160
$172$	−6.14104	−0.468250
$173$	16.7546	1.27383	0.636913	−	0.770936i	$-0.280211\pi$
$173$	16.7546	1.27383	0.636913	+	0.770936i	$0.280211\pi$
$174$	−0.0991477	−0.00751637
$175$	−2.03673	−0.153962
$176$	3.55613	0.268054
$177$	1.64160	0.123390
$178$	16.2605	1.21877
$179$	−13.6147	−1.01761	−0.508805	−	0.860882i	$-0.669913\pi$
$179$	−13.6147	−1.01761	−0.508805	+	0.860882i	$0.669913\pi$
$180$	−2.76087	−0.205783
$181$	6.55399	0.487154	0.243577	−	0.969882i	$-0.421679\pi$
$181$	6.55399	0.487154	0.243577	+	0.969882i	$0.421679\pi$
$182$	12.9274	0.958243
$183$	−5.80559	−0.429162
$184$	0.0973899	0.00717968
$185$	−4.09559	−0.301113
$186$	−4.07189	−0.298565
$187$	−1.81275	−0.132561
$188$	11.1825	0.815571
$189$	−5.73771	−0.417357
$190$	6.21230	0.450687
$191$	−2.84286	−0.205702	−0.102851	−	0.994697i	$-0.532797\pi$
$191$	−2.84286	−0.205702	−0.102851	+	0.994697i	$0.532797\pi$
$192$	−0.489009	−0.0352912
$193$	8.02417	0.577593	0.288796	−	0.957391i	$-0.406745\pi$
$193$	8.02417	0.577593	0.288796	+	0.957391i	$0.406745\pi$
$194$	5.74013	0.412117
$195$	3.10381	0.222268
$196$	−2.85173	−0.203695
$197$	−10.0352	−0.714980	−0.357490	−	0.933917i	$-0.616367\pi$
$197$	−10.0352	−0.714980	−0.357490	+	0.933917i	$0.616367\pi$
$198$	−9.81802	−0.697736
$199$	11.4910	0.814578	0.407289	−	0.913299i	$-0.366474\pi$
$199$	11.4910	0.814578	0.407289	+	0.913299i	$0.366474\pi$
$200$	1.00000	0.0707107
$201$	−0.0560771	−0.00395537
$202$	−11.8099	−0.830944
$203$	−0.412952	−0.0289835
$204$	0.249274	0.0174527
$205$	−5.06237	−0.353571
$206$	−9.14541	−0.637191
$207$	−0.268881	−0.0186885
$208$	−6.34714	−0.440095
$209$	22.0918	1.52812
$210$	0.995979	0.0687291
$211$	8.79413	0.605413	0.302706	−	0.953084i	$-0.402110\pi$
$211$	8.79413	0.605413	0.302706	+	0.953084i	$0.402110\pi$
$212$	4.00795	0.275267
$213$	−2.50838	−0.171871
$214$	11.9421	0.816346
$215$	−6.14104	−0.418815
$216$	2.81712	0.191681
$217$	−16.9595	−1.15128
$218$	−1.31504	−0.0890655
$219$	1.85928	0.125639
$220$	3.55613	0.239754
$221$	3.23547	0.217642
$222$	2.00278	0.134418
$223$	6.77408	0.453626	0.226813	−	0.973938i	$-0.427169\pi$
$223$	6.77408	0.453626	0.226813	+	0.973938i	$0.427169\pi$
$224$	−2.03673	−0.136085
$225$	−2.76087	−0.184058
$226$	−5.62764	−0.374345
$227$	2.42787	0.161143	0.0805717	−	0.996749i	$-0.474325\pi$
$227$	2.42787	0.161143	0.0805717	+	0.996749i	$0.474325\pi$
$228$	−3.03787	−0.201188
$229$	−16.7250	−1.10522	−0.552609	−	0.833440i	$-0.686368\pi$
$229$	−16.7250	−1.10522	−0.552609	+	0.833440i	$0.686368\pi$
$230$	0.0973899	0.00642170
$231$	3.54183	0.233036
$232$	0.202752	0.0133113
$233$	−9.60484	−0.629234	−0.314617	−	0.949219i	$-0.601876\pi$
$233$	−9.60484	−0.629234	−0.314617	+	0.949219i	$0.601876\pi$
$234$	17.5236	1.14555
$235$	11.1825	0.729469
$236$	−3.35700	−0.218522
$237$	−4.51830	−0.293495
$238$	1.03823	0.0672984
$239$	9.01741	0.583288	0.291644	−	0.956527i	$-0.405798\pi$
$239$	9.01741	0.583288	0.291644	+	0.956527i	$0.405798\pi$
$240$	−0.489009	−0.0315654
$241$	2.76512	0.178117	0.0890585	−	0.996026i	$-0.471614\pi$
$241$	2.76512	0.178117	0.0890585	+	0.996026i	$0.471614\pi$
$242$	1.64608	0.105814
$243$	−11.8280	−0.758764
$244$	11.8722	0.760037
$245$	−2.85173	−0.182191
$246$	2.47554	0.157835
$247$	−39.4303	−2.50889
$248$	8.32682	0.528753
$249$	−1.33512	−0.0846098
$250$	1.00000	0.0632456
$251$	−10.3787	−0.655098	−0.327549	−	0.944834i	$-0.606223\pi$
$251$	−10.3787	−0.655098	−0.327549	+	0.944834i	$0.606223\pi$
$252$	5.62315	0.354225
$253$	0.346331	0.0217737
$254$	16.2188	1.01766
$255$	0.249274	0.0156101
$256$	1.00000	0.0625000
$257$	−7.91527	−0.493741	−0.246870	−	0.969048i	$-0.579402\pi$
$257$	−7.91527	−0.493741	−0.246870	+	0.969048i	$0.579402\pi$
$258$	3.00302	0.186960
$259$	8.34160	0.518322
$260$	−6.34714	−0.393633
$261$	−0.559773	−0.0346491
$262$	12.0280	0.743093
$263$	28.1777	1.73751	0.868755	−	0.495242i	$-0.164921\pi$
$263$	28.1777	1.73751	0.868755	+	0.495242i	$0.164921\pi$
$264$	−1.73898	−0.107027
$265$	4.00795	0.246206
$266$	−12.6528	−0.775791
$267$	−7.95152	−0.486625
$268$	0.114675	0.00700489
$269$	−8.10580	−0.494219	−0.247110	−	0.968988i	$-0.579481\pi$
$269$	−8.10580	−0.494219	−0.247110	+	0.968988i	$0.579481\pi$
$270$	2.81712	0.171444
$271$	−18.8480	−1.14493	−0.572467	−	0.819928i	$-0.694013\pi$
$271$	−18.8480	−1.14493	−0.572467	+	0.819928i	$0.694013\pi$
$272$	−0.509753	−0.0309083
$273$	−6.32161	−0.382602
$274$	12.9578	0.782809
$275$	3.55613	0.214443
$276$	−0.0476245	−0.00286666
$277$	8.26193	0.496411	0.248206	−	0.968707i	$-0.420159\pi$
$277$	8.26193	0.496411	0.248206	+	0.968707i	$0.420159\pi$
$278$	17.4919	1.04910
$279$	−22.9893	−1.37633
$280$	−2.03673	−0.121718
$281$	−17.8060	−1.06222	−0.531110	−	0.847303i	$-0.678225\pi$
$281$	−17.8060	−1.06222	−0.531110	+	0.847303i	$0.678225\pi$
$282$	−5.46837	−0.325636
$283$	−2.59060	−0.153995	−0.0769977	−	0.997031i	$-0.524533\pi$
$283$	−2.59060	−0.153995	−0.0769977	+	0.997031i	$0.524533\pi$
$284$	5.12951	0.304381
$285$	−3.03787	−0.179948
$286$	−22.5713	−1.33467
$287$	10.3107	0.608620
$288$	−2.76087	−0.162686
$289$	−16.7402	−0.984715
$290$	0.202752	0.0119060
$291$	−2.80697	−0.164548
$292$	−3.80215	−0.222504
$293$	−33.6373	−1.96511	−0.982556	−	0.185965i	$-0.940459\pi$
$293$	−33.6373	−1.96511	−0.982556	+	0.185965i	$0.940459\pi$
$294$	1.39452	0.0813303
$295$	−3.35700	−0.195452
$296$	−4.09559	−0.238051
$297$	10.0180	0.581306
$298$	16.7327	0.969299
$299$	−0.618147	−0.0357484
$300$	−0.489009	−0.0282329
$301$	12.5076	0.720928
$302$	16.4838	0.948534
$303$	5.77516	0.331774
$304$	6.21230	0.356300
$305$	11.8722	0.679798
$306$	1.40736	0.0804536
$307$	−0.225218	−0.0128539	−0.00642693	−	0.999979i	$-0.502046\pi$
$307$	−0.225218	−0.0128539	−0.00642693	+	0.999979i	$0.502046\pi$
$308$	−7.24288	−0.412701
$309$	4.47219	0.254414
$310$	8.32682	0.472931
$311$	−19.8908	−1.12790	−0.563951	−	0.825809i	$-0.690719\pi$
$311$	−19.8908	−1.12790	−0.563951	+	0.825809i	$0.690719\pi$
$312$	3.10381	0.175718
$313$	−3.18174	−0.179842	−0.0899212	−	0.995949i	$-0.528662\pi$
$313$	−3.18174	−0.179842	−0.0899212	+	0.995949i	$0.528662\pi$
$314$	−16.8831	−0.952766
$315$	5.62315	0.316828
$316$	9.23971	0.519774
$317$	34.3983	1.93200	0.966001	−	0.258538i	$-0.0832407\pi$
$317$	34.3983	1.93200	0.966001	+	0.258538i	$0.0832407\pi$
$318$	−1.95992	−0.109907
$319$	0.721014	0.0403690
$320$	1.00000	0.0559017
$321$	−5.83980	−0.325946
$322$	−0.198357	−0.0110540
$323$	−3.16674	−0.176202
$324$	6.90501	0.383612
$325$	−6.34714	−0.352076
$326$	0.601022	0.0332875
$327$	0.643064	0.0355615
$328$	−5.06237	−0.279523
$329$	−22.7758	−1.25567
$330$	−1.73898	−0.0957277
$331$	21.7472	1.19534	0.597668	−	0.801743i	$-0.296094\pi$
$331$	21.7472	1.19534	0.597668	+	0.801743i	$0.296094\pi$
$332$	2.73026	0.149842
$333$	11.3074	0.619641
$334$	−21.8605	−1.19615
$335$	0.114675	0.00626536
$336$	0.995979	0.0543351
$337$	13.5392	0.737525	0.368762	−	0.929524i	$-0.379782\pi$
$337$	13.5392	0.737525	0.368762	+	0.929524i	$0.379782\pi$
$338$	27.2861	1.48417
$339$	2.75197	0.149466
$340$	−0.509753	−0.0276453
$341$	29.6113	1.60354
$342$	−17.1513	−0.927439
$343$	20.0653	1.08343
$344$	−6.14104	−0.331102
$345$	−0.0476245	−0.00256402
$346$	16.7546	0.900731
$347$	−5.56562	−0.298778	−0.149389	−	0.988779i	$-0.547731\pi$
$347$	−5.56562	−0.298778	−0.149389	+	0.988779i	$0.547731\pi$
$348$	−0.0991477	−0.00531487
$349$	16.5137	0.883958	0.441979	−	0.897025i	$-0.354277\pi$
$349$	16.5137	0.883958	0.441979	+	0.897025i	$0.354277\pi$
$350$	−2.03673	−0.108868
$351$	−17.8806	−0.954397
$352$	3.55613	0.189543
$353$	−7.20701	−0.383590	−0.191795	−	0.981435i	$-0.561431\pi$
$353$	−7.20701	−0.383590	−0.191795	+	0.981435i	$0.561431\pi$
$354$	1.64160	0.0872501
$355$	5.12951	0.272246
$356$	16.2605	0.861804
$357$	−0.507704	−0.0268705
$358$	−13.6147	−0.719559
$359$	−26.6709	−1.40764	−0.703818	−	0.710381i	$-0.748523\pi$
$359$	−26.6709	−1.40764	−0.703818	+	0.710381i	$0.748523\pi$
$360$	−2.76087	−0.145511
$361$	19.5926	1.03119
$362$	6.55399	0.344470
$363$	−0.804947	−0.0422488
$364$	12.9274	0.677580
$365$	−3.80215	−0.199013
$366$	−5.80559	−0.303463
$367$	7.27368	0.379683	0.189842	−	0.981815i	$-0.439203\pi$
$367$	7.27368	0.379683	0.189842	+	0.981815i	$0.439203\pi$
$368$	0.0973899	0.00507680
$369$	13.9765	0.727590
$370$	−4.09559	−0.212919
$371$	−8.16311	−0.423808
$372$	−4.07189	−0.211118
$373$	−1.44704	−0.0749248	−0.0374624	−	0.999298i	$-0.511927\pi$
$373$	−1.44704	−0.0749248	−0.0374624	+	0.999298i	$0.511927\pi$
$374$	−1.81275	−0.0937351
$375$	−0.489009	−0.0252523
$376$	11.1825	0.576696
$377$	−1.28690	−0.0662786
$378$	−5.73771	−0.295116
$379$	−11.3657	−0.583815	−0.291907	−	0.956447i	$-0.594290\pi$
$379$	−11.3657	−0.583815	−0.291907	+	0.956447i	$0.594290\pi$
$380$	6.21230	0.318684
$381$	−7.93112	−0.406324
$382$	−2.84286	−0.145453
$383$	−16.2134	−0.828468	−0.414234	−	0.910170i	$-0.635950\pi$
$383$	−16.2134	−0.828468	−0.414234	+	0.910170i	$0.635950\pi$
$384$	−0.489009	−0.0249546
$385$	−7.24288	−0.369131
$386$	8.02417	0.408420
$387$	16.9546	0.861851
$388$	5.74013	0.291411
$389$	−8.30762	−0.421213	−0.210606	−	0.977571i	$-0.567544\pi$
$389$	−8.30762	−0.421213	−0.210606	+	0.977571i	$0.567544\pi$
$390$	3.10381	0.157167
$391$	−0.0496448	−0.00251065
$392$	−2.85173	−0.144034
$393$	−5.88180	−0.296698
$394$	−10.0352	−0.505567
$395$	9.23971	0.464900
$396$	−9.81802	−0.493374
$397$	34.2955	1.72124	0.860620	−	0.509248i	$-0.170076\pi$
$397$	34.2955	1.72124	0.860620	+	0.509248i	$0.170076\pi$
$398$	11.4910	0.575993
$399$	6.18732	0.309753
$400$	1.00000	0.0500000
$401$	33.2471	1.66028	0.830141	−	0.557553i	$-0.188260\pi$
$401$	33.2471	1.66028	0.830141	+	0.557553i	$0.188260\pi$
$402$	−0.0560771	−0.00279687
$403$	−52.8515	−2.63272
$404$	−11.8099	−0.587566
$405$	6.90501	0.343113
$406$	−0.412952	−0.0204944
$407$	−14.5644	−0.721933
$408$	0.249274	0.0123409
$409$	7.79119	0.385250	0.192625	−	0.981272i	$-0.438300\pi$
$409$	7.79119	0.385250	0.192625	+	0.981272i	$0.438300\pi$
$410$	−5.06237	−0.250013
$411$	−6.33648	−0.312556
$412$	−9.14541	−0.450562
$413$	6.83729	0.336441
$414$	−0.268881	−0.0132148
$415$	2.73026	0.134023
$416$	−6.34714	−0.311194
$417$	−8.55372	−0.418877
$418$	22.0918	1.08054
$419$	19.6068	0.957854	0.478927	−	0.877855i	$-0.341026\pi$
$419$	19.6068	0.957854	0.478927	+	0.877855i	$0.341026\pi$
$420$	0.995979	0.0485988
$421$	−15.5200	−0.756396	−0.378198	−	0.925725i	$-0.623456\pi$
$421$	−15.5200	−0.756396	−0.378198	+	0.925725i	$0.623456\pi$
$422$	8.79413	0.428092
$423$	−30.8736	−1.50112
$424$	4.00795	0.194643
$425$	−0.509753	−0.0247267
$426$	−2.50838	−0.121531
$427$	−24.1804	−1.17017
$428$	11.9421	0.577244
$429$	11.0375	0.532898
$430$	−6.14104	−0.296147
$431$	−21.5989	−1.04038	−0.520191	−	0.854050i	$-0.674139\pi$
$431$	−21.5989	−1.04038	−0.520191	+	0.854050i	$0.674139\pi$
$432$	2.81712	0.135539
$433$	28.8228	1.38514	0.692568	−	0.721353i	$-0.256479\pi$
$433$	28.8228	1.38514	0.692568	+	0.721353i	$0.256479\pi$
$434$	−16.9595	−0.814081
$435$	−0.0991477	−0.00475377
$436$	−1.31504	−0.0629788
$437$	0.605015	0.0289418
$438$	1.85928	0.0888400
$439$	−2.38883	−0.114013	−0.0570064	−	0.998374i	$-0.518156\pi$
$439$	−2.38883	−0.114013	−0.0570064	+	0.998374i	$0.518156\pi$
$440$	3.55613	0.169532
$441$	7.87327	0.374917
$442$	3.23547	0.153896
$443$	6.62066	0.314557	0.157278	−	0.987554i	$-0.449728\pi$
$443$	6.62066	0.314557	0.157278	+	0.987554i	$0.449728\pi$
$444$	2.00278	0.0950476
$445$	16.2605	0.770821
$446$	6.77408	0.320762
$447$	−8.18244	−0.387016
$448$	−2.03673	−0.0962264
$449$	−22.5769	−1.06547	−0.532736	−	0.846282i	$-0.678836\pi$
$449$	−22.5769	−1.06547	−0.532736	+	0.846282i	$0.678836\pi$
$450$	−2.76087	−0.130149
$451$	−18.0025	−0.847702
$452$	−5.62764	−0.264702
$453$	−8.06071	−0.378725
$454$	2.42787	0.113946
$455$	12.9274	0.606046
$456$	−3.03787	−0.142261
$457$	11.7645	0.550322	0.275161	−	0.961398i	$-0.411269\pi$
$457$	11.7645	0.550322	0.275161	+	0.961398i	$0.411269\pi$
$458$	−16.7250	−0.781508
$459$	−1.43604	−0.0670284
$460$	0.0973899	0.00454083
$461$	−17.2785	−0.804740	−0.402370	−	0.915477i	$-0.631813\pi$
$461$	−17.2785	−0.804740	−0.402370	+	0.915477i	$0.631813\pi$
$462$	3.54183	0.164781
$463$	24.2766	1.12823	0.564115	−	0.825696i	$-0.309217\pi$
$463$	24.2766	1.12823	0.564115	+	0.825696i	$0.309217\pi$
$464$	0.202752	0.00941254
$465$	−4.07189	−0.188829
$466$	−9.60484	−0.444935
$467$	39.2753	1.81744	0.908721	−	0.417404i	$-0.137060\pi$
$467$	39.2753	1.81744	0.908721	+	0.417404i	$0.137060\pi$
$468$	17.5236	0.810030
$469$	−0.233562	−0.0107849
$470$	11.1825	0.515812
$471$	8.25597	0.380415
$472$	−3.35700	−0.154518
$473$	−21.8383	−1.00413
$474$	−4.51830	−0.207532
$475$	6.21230	0.285040
$476$	1.03823	0.0475872
$477$	−11.0654	−0.506651
$478$	9.01741	0.412447
$479$	14.9576	0.683428	0.341714	−	0.939804i	$-0.388993\pi$
$479$	14.9576	0.683428	0.341714	+	0.939804i	$0.388993\pi$
$480$	−0.489009	−0.0223201
$481$	25.9952	1.18528
$482$	2.76512	0.125948
$483$	0.0969983	0.00441357
$484$	1.64608	0.0748218
$485$	5.74013	0.260646
$486$	−11.8280	−0.536527
$487$	11.4068	0.516891	0.258445	−	0.966026i	$-0.416790\pi$
$487$	11.4068	0.516891	0.258445	+	0.966026i	$0.416790\pi$
$488$	11.8722	0.537428
$489$	−0.293905	−0.0132909
$490$	−2.85173	−0.128828
$491$	−11.3773	−0.513452	−0.256726	−	0.966484i	$-0.582644\pi$
$491$	−11.3773	−0.513452	−0.256726	+	0.966484i	$0.582644\pi$
$492$	2.47554	0.111606
$493$	−0.103354	−0.00465482
$494$	−39.4303	−1.77405
$495$	−9.81802	−0.441287
$496$	8.32682	0.373885
$497$	−10.4474	−0.468631
$498$	−1.33512	−0.0598282
$499$	0.706907	0.0316455	0.0158227	−	0.999875i	$-0.494963\pi$
$499$	0.706907	0.0316455	0.0158227	+	0.999875i	$0.494963\pi$
$500$	1.00000	0.0447214
$501$	10.6900	0.477592
$502$	−10.3787	−0.463224
$503$	15.3551	0.684648	0.342324	−	0.939582i	$-0.388786\pi$
$503$	15.3551	0.684648	0.342324	+	0.939582i	$0.388786\pi$
$504$	5.62315	0.250475
$505$	−11.8099	−0.525535
$506$	0.346331	0.0153963
$507$	−13.3432	−0.592591
$508$	16.2188	0.719591
$509$	28.4639	1.26164	0.630819	−	0.775930i	$-0.282719\pi$
$509$	28.4639	1.26164	0.630819	+	0.775930i	$0.282719\pi$
$510$	0.249274	0.0110380
$511$	7.74394	0.342572
$512$	1.00000	0.0441942
$513$	17.5008	0.772678
$514$	−7.91527	−0.349128
$515$	−9.14541	−0.402995
$516$	3.00302	0.132201
$517$	39.7666	1.74893
$518$	8.34160	0.366509
$519$	−8.19313	−0.359638
$520$	−6.34714	−0.278340
$521$	−0.284002	−0.0124424	−0.00622119	−	0.999981i	$-0.501980\pi$
$521$	−0.284002	−0.0124424	−0.00622119	+	0.999981i	$0.501980\pi$
$522$	−0.559773	−0.0245006
$523$	19.1365	0.836780	0.418390	−	0.908267i	$-0.362595\pi$
$523$	19.1365	0.836780	0.418390	+	0.908267i	$0.362595\pi$
$524$	12.0280	0.525446
$525$	0.995979	0.0434681
$526$	28.1777	1.22860
$527$	−4.24462	−0.184899
$528$	−1.73898	−0.0756794
$529$	−22.9905	−0.999588
$530$	4.00795	0.174094
$531$	9.26823	0.402207
$532$	−12.6528	−0.548567
$533$	32.1315	1.39177
$534$	−7.95152	−0.344096
$535$	11.9421	0.516302
$536$	0.114675	0.00495320
$537$	6.65771	0.287301
$538$	−8.10580	−0.349466
$539$	−10.1411	−0.436810
$540$	2.81712	0.121229
$541$	18.3652	0.789582	0.394791	−	0.918771i	$-0.370817\pi$
$541$	18.3652	0.789582	0.394791	+	0.918771i	$0.370817\pi$
$542$	−18.8480	−0.809590
$543$	−3.20496	−0.137538
$544$	−0.509753	−0.0218555
$545$	−1.31504	−0.0563299
$546$	−6.32161	−0.270540
$547$	−43.7800	−1.87190	−0.935949	−	0.352136i	$-0.885455\pi$
$547$	−43.7800	−1.87190	−0.935949	+	0.352136i	$0.885455\pi$
$548$	12.9578	0.553530
$549$	−32.7775	−1.39891
$550$	3.55613	0.151634
$551$	1.25956	0.0536590
$552$	−0.0476245	−0.00202703
$553$	−18.8188	−0.800256
$554$	8.26193	0.351016
$555$	2.00278	0.0850132
$556$	17.4919	0.741824
$557$	−12.1334	−0.514109	−0.257055	−	0.966397i	$-0.582752\pi$
$557$	−12.1334	−0.514109	−0.257055	+	0.966397i	$0.582752\pi$
$558$	−22.9893	−0.973213
$559$	38.9780	1.64859
$560$	−2.03673	−0.0860675
$561$	0.886451	0.0374260
$562$	−17.8060	−0.751103
$563$	−39.2362	−1.65361	−0.826805	−	0.562488i	$-0.809844\pi$
$563$	−39.2362	−1.65361	−0.826805	+	0.562488i	$0.809844\pi$
$564$	−5.46837	−0.230260
$565$	−5.62764	−0.236757
$566$	−2.59060	−0.108891
$567$	−14.0636	−0.590618
$568$	5.12951	0.215230
$569$	−15.6507	−0.656111	−0.328056	−	0.944658i	$-0.606393\pi$
$569$	−15.6507	−0.656111	−0.328056	+	0.944658i	$0.606393\pi$
$570$	−3.03787	−0.127242
$571$	−6.86145	−0.287143	−0.143571	−	0.989640i	$-0.545859\pi$
$571$	−6.86145	−0.287143	−0.143571	+	0.989640i	$0.545859\pi$
$572$	−22.5713	−0.943752
$573$	1.39018	0.0580758
$574$	10.3107	0.430359
$575$	0.0973899	0.00406144
$576$	−2.76087	−0.115036
$577$	−19.0144	−0.791581	−0.395791	−	0.918341i	$-0.629529\pi$
$577$	−19.0144	−0.791581	−0.395791	+	0.918341i	$0.629529\pi$
$578$	−16.7402	−0.696299
$579$	−3.92389	−0.163071
$580$	0.202752	0.00841883
$581$	−5.56079	−0.230701
$582$	−2.80697	−0.116353
$583$	14.2528	0.590291
$584$	−3.80215	−0.157334
$585$	17.5236	0.724513
$586$	−33.6373	−1.38954
$587$	17.3804	0.717367	0.358684	−	0.933459i	$-0.383226\pi$
$587$	17.3804	0.717367	0.358684	+	0.933459i	$0.383226\pi$
$588$	1.39452	0.0575092
$589$	51.7287	2.13144
$590$	−3.35700	−0.138205
$591$	4.90731	0.201860
$592$	−4.09559	−0.168328
$593$	−26.6259	−1.09339	−0.546697	−	0.837330i	$-0.684115\pi$
$593$	−26.6259	−1.09339	−0.546697	+	0.837330i	$0.684115\pi$
$594$	10.0180	0.411045
$595$	1.03823	0.0425633
$596$	16.7327	0.685398
$597$	−5.61922	−0.229979
$598$	−0.618147	−0.0252779
$599$	−37.2025	−1.52005	−0.760027	−	0.649891i	$-0.774814\pi$
$599$	−37.2025	−1.52005	−0.760027	+	0.649891i	$0.774814\pi$
$600$	−0.489009	−0.0199637
$601$	1.00000	0.0407909
$601$	1.00000	0.0407909
$602$	12.5076	0.509773
$603$	−0.316603	−0.0128931
$604$	16.4838	0.670715
$605$	1.64608	0.0669226
$606$	5.77516	0.234600
$607$	20.1137	0.816389	0.408195	−	0.912895i	$-0.366158\pi$
$607$	20.1137	0.816389	0.408195	+	0.912895i	$0.366158\pi$
$608$	6.21230	0.251942
$609$	0.201937	0.00818290
$610$	11.8722	0.480690
$611$	−70.9772	−2.87143
$612$	1.40736	0.0568893
$613$	−36.5549	−1.47644	−0.738218	−	0.674562i	$-0.764333\pi$
$613$	−36.5549	−1.47644	−0.738218	+	0.674562i	$0.764333\pi$
$614$	−0.225218	−0.00908905
$615$	2.47554	0.0998236
$616$	−7.24288	−0.291824
$617$	−23.2107	−0.934429	−0.467214	−	0.884144i	$-0.654742\pi$
$617$	−23.2107	−0.934429	−0.467214	+	0.884144i	$0.654742\pi$
$618$	4.47219	0.179898
$619$	−15.7336	−0.632386	−0.316193	−	0.948695i	$-0.602405\pi$
$619$	−15.7336	−0.632386	−0.316193	+	0.948695i	$0.602405\pi$
$620$	8.32682	0.334413
$621$	0.274359	0.0110096
$622$	−19.8908	−0.797547
$623$	−33.1182	−1.32685
$624$	3.10381	0.124252
$625$	1.00000	0.0400000
$626$	−3.18174	−0.127168
$627$	−10.8031	−0.431433
$628$	−16.8831	−0.673708
$629$	2.08774	0.0832436
$630$	5.62315	0.224031
$631$	−0.535093	−0.0213017	−0.0106509	−	0.999943i	$-0.503390\pi$
$631$	−0.535093	−0.0213017	−0.0106509	+	0.999943i	$0.503390\pi$
$632$	9.23971	0.367536
$633$	−4.30041	−0.170926
$634$	34.3983	1.36613
$635$	16.2188	0.643622
$636$	−1.95992	−0.0777160
$637$	18.1003	0.717162
$638$	0.721014	0.0285452
$639$	−14.1619	−0.560237
$640$	1.00000	0.0395285
$641$	−9.02242	−0.356364	−0.178182	−	0.983998i	$-0.557022\pi$
$641$	−9.02242	−0.356364	−0.178182	+	0.983998i	$0.557022\pi$
$642$	−5.83980	−0.230478
$643$	11.3243	0.446588	0.223294	−	0.974751i	$-0.428319\pi$
$643$	11.3243	0.446588	0.223294	+	0.974751i	$0.428319\pi$
$644$	−0.198357	−0.00781635
$645$	3.00302	0.118244
$646$	−3.16674	−0.124594
$647$	−28.0141	−1.10135	−0.550674	−	0.834721i	$-0.685629\pi$
$647$	−28.0141	−1.10135	−0.550674	+	0.834721i	$0.685629\pi$
$648$	6.90501	0.271255
$649$	−11.9379	−0.468605
$650$	−6.34714	−0.248955
$651$	8.29334	0.325041
$652$	0.601022	0.0235378
$653$	−31.6136	−1.23714	−0.618568	−	0.785731i	$-0.712287\pi$
$653$	−31.6136	−1.23714	−0.618568	+	0.785731i	$0.712287\pi$
$654$	0.643064	0.0251458
$655$	12.0280	0.469973
$656$	−5.06237	−0.197652
$657$	10.4972	0.409536
$658$	−22.7758	−0.887894
$659$	0.795765	0.0309986	0.0154993	−	0.999880i	$-0.495066\pi$
$659$	0.795765	0.0309986	0.0154993	+	0.999880i	$0.495066\pi$
$660$	−1.73898	−0.0676897
$661$	26.9067	1.04655	0.523275	−	0.852164i	$-0.324710\pi$
$661$	26.9067	1.04655	0.523275	+	0.852164i	$0.324710\pi$
$662$	21.7472	0.845231
$663$	−1.58218	−0.0614466
$664$	2.73026	0.105955
$665$	−12.6528	−0.490653
$666$	11.3074	0.438152
$667$	0.0197460	0.000764569 0
$668$	−21.8605	−0.845807
$669$	−3.31258	−0.128072
$670$	0.114675	0.00443028
$671$	42.2190	1.62985
$672$	0.995979	0.0384207
$673$	−21.3815	−0.824197	−0.412098	−	0.911139i	$-0.635204\pi$
$673$	−21.3815	−0.824197	−0.412098	+	0.911139i	$0.635204\pi$
$674$	13.5392	0.521509
$675$	2.81712	0.108431
$676$	27.2861	1.04947
$677$	0.0444560	0.00170858	0.000854291	−	1.00000i	$-0.499728\pi$
$677$	0.0444560	0.00170858	0.000854291		1.00000i	$0.499728\pi$
$678$	2.75197	0.105689
$679$	−11.6911	−0.448663
$680$	−0.509753	−0.0195482
$681$	−1.18725	−0.0454955
$682$	29.6113	1.13387
$683$	−45.8355	−1.75385	−0.876924	−	0.480629i	$-0.840408\pi$
$683$	−45.8355	−1.75385	−0.876924	+	0.480629i	$0.840408\pi$
$684$	−17.1513	−0.655798
$685$	12.9578	0.495092
$686$	20.0653	0.766097
$687$	8.17867	0.312036
$688$	−6.14104	−0.234125
$689$	−25.4390	−0.969149
$690$	−0.0476245	−0.00181303
$691$	−24.8519	−0.945411	−0.472706	−	0.881220i	$-0.656723\pi$
$691$	−24.8519	−0.945411	−0.472706	+	0.881220i	$0.656723\pi$
$692$	16.7546	0.636913
$693$	19.9967	0.759610
$694$	−5.56562	−0.211268
$695$	17.4919	0.663507
$696$	−0.0991477	−0.00375818
$697$	2.58056	0.0977457
$698$	16.5137	0.625052
$699$	4.69685	0.177651
$700$	−2.03673	−0.0769811
$701$	15.4738	0.584436	0.292218	−	0.956352i	$-0.405607\pi$
$701$	15.4738	0.584436	0.292218	+	0.956352i	$0.405607\pi$
$702$	−17.8806	−0.674861
$703$	−25.4430	−0.959601
$704$	3.55613	0.134027
$705$	−5.46837	−0.205951
$706$	−7.20701	−0.271239
$707$	24.0536	0.904630
$708$	1.64160	0.0616952
$709$	12.6745	0.476001	0.238001	−	0.971265i	$-0.423508\pi$
$709$	12.6745	0.476001	0.238001	+	0.971265i	$0.423508\pi$
$710$	5.12951	0.192507
$711$	−25.5096	−0.956686
$712$	16.2605	0.609387
$713$	0.810948	0.0303702
$714$	−0.507704	−0.0190003
$715$	−22.5713	−0.844117
$716$	−13.6147	−0.508805
$717$	−4.40959	−0.164679
$718$	−26.6709	−0.995348
$719$	−18.9344	−0.706134	−0.353067	−	0.935598i	$-0.614861\pi$
$719$	−18.9344	−0.706134	−0.353067	+	0.935598i	$0.614861\pi$
$720$	−2.76087	−0.102892
$721$	18.6267	0.693696
$722$	19.5926	0.729162
$723$	−1.35217	−0.0502877
$724$	6.55399	0.243577
$725$	0.202752	0.00753003
$726$	−0.804947	−0.0298744
$727$	6.71810	0.249161	0.124580	−	0.992210i	$-0.460242\pi$
$727$	6.71810	0.249161	0.124580	+	0.992210i	$0.460242\pi$
$728$	12.9274	0.479121
$729$	−14.9311	−0.553002
$730$	−3.80215	−0.140724
$731$	3.13041	0.115783
$732$	−5.80559	−0.214581
$733$	26.5804	0.981768	0.490884	−	0.871225i	$-0.336674\pi$
$733$	26.5804	0.981768	0.490884	+	0.871225i	$0.336674\pi$
$734$	7.27368	0.268477
$735$	1.39452	0.0514378
$736$	0.0973899	0.00358984
$737$	0.407799	0.0150215
$738$	13.9765	0.514484
$739$	−42.3024	−1.55612	−0.778059	−	0.628192i	$-0.783795\pi$
$739$	−42.3024	−1.55612	−0.778059	+	0.628192i	$0.783795\pi$
$740$	−4.09559	−0.150557
$741$	19.2818	0.708334
$742$	−8.16311	−0.299677
$743$	10.8708	0.398811	0.199405	−	0.979917i	$-0.436099\pi$
$743$	10.8708	0.398811	0.199405	+	0.979917i	$0.436099\pi$
$744$	−4.07189	−0.149283
$745$	16.7327	0.613039
$746$	−1.44704	−0.0529798
$747$	−7.53788	−0.275797
$748$	−1.81275	−0.0662807
$749$	−24.3228	−0.888737
$750$	−0.489009	−0.0178561
$751$	−48.2818	−1.76183	−0.880914	−	0.473277i	$-0.843071\pi$
$751$	−48.2818	−1.76183	−0.880914	+	0.473277i	$0.843071\pi$
$752$	11.1825	0.407786
$753$	5.07528	0.184953
$754$	−1.28690	−0.0468660
$755$	16.4838	0.599906
$756$	−5.73771	−0.208678
$757$	47.7119	1.73412	0.867059	−	0.498205i	$-0.166007\pi$
$757$	47.7119	1.73412	0.867059	+	0.498205i	$0.166007\pi$
$758$	−11.3657	−0.412820
$759$	−0.169359	−0.00614735
$760$	6.21230	0.225344
$761$	−8.53883	−0.309532	−0.154766	−	0.987951i	$-0.549462\pi$
$761$	−8.53883	−0.309532	−0.154766	+	0.987951i	$0.549462\pi$
$762$	−7.93112	−0.287314
$763$	2.67837	0.0969636
$764$	−2.84286	−0.102851
$765$	1.40736	0.0508833
$766$	−16.2134	−0.585815
$767$	21.3073	0.769363
$768$	−0.489009	−0.0176456
$769$	36.1175	1.30243	0.651215	−	0.758894i	$-0.274260\pi$
$769$	36.1175	1.30243	0.651215	+	0.758894i	$0.274260\pi$
$770$	−7.24288	−0.261015
$771$	3.87064	0.139398
$772$	8.02417	0.288796
$773$	−7.34514	−0.264186	−0.132093	−	0.991237i	$-0.542170\pi$
$773$	−7.34514	−0.264186	−0.132093	+	0.991237i	$0.542170\pi$
$774$	16.9546	0.609421
$775$	8.32682	0.299108
$776$	5.74013	0.206058
$777$	−4.07912	−0.146338
$778$	−8.30762	−0.297842
$779$	−31.4489	−1.12678
$780$	3.10381	0.111134
$781$	18.2412	0.652722
$782$	−0.0496448	−0.00177529
$783$	0.571177	0.0204122
$784$	−2.85173	−0.101848
$785$	−16.8831	−0.602582
$786$	−5.88180	−0.209797
$787$	44.9982	1.60401	0.802005	−	0.597317i	$-0.203766\pi$
$787$	44.9982	1.60401	0.802005	+	0.597317i	$0.203766\pi$
$788$	−10.0352	−0.357490
$789$	−13.7791	−0.490550
$790$	9.23971	0.328734
$791$	11.4620	0.407541
$792$	−9.81802	−0.348868
$793$	−75.3542	−2.67591
$794$	34.2955	1.21710
$795$	−1.95992	−0.0695113
$796$	11.4910	0.407289
$797$	9.47760	0.335714	0.167857	−	0.985811i	$-0.446315\pi$
$797$	9.47760	0.335714	0.167857	+	0.985811i	$0.446315\pi$
$798$	6.18732	0.219029
$799$	−5.70034	−0.201664
$800$	1.00000	0.0353553
$801$	−44.8931	−1.58622
$802$	33.2471	1.17400
$803$	−13.5209	−0.477143
$804$	−0.0560771	−0.00197769
$805$	−0.198357	−0.00699116
$806$	−52.8515	−1.86161
$807$	3.96381	0.139533
$808$	−11.8099	−0.415472
$809$	50.8716	1.78855	0.894275	−	0.447519i	$-0.147692\pi$
$809$	50.8716	1.78855	0.894275	+	0.447519i	$0.147692\pi$
$810$	6.90501	0.242617
$811$	0.660729	0.0232013	0.0116007	−	0.999933i	$-0.496307\pi$
$811$	0.660729	0.0232013	0.0116007	+	0.999933i	$0.496307\pi$
$812$	−0.412952	−0.0144918
$813$	9.21683	0.323248
$814$	−14.5644	−0.510484
$815$	0.601022	0.0210529
$816$	0.249274	0.00872633
$817$	−38.1499	−1.33470
$818$	7.79119	0.272413
$819$	−35.6909	−1.24714
$820$	−5.06237	−0.176786
$821$	43.4481	1.51635	0.758174	−	0.652052i	$-0.226092\pi$
$821$	43.4481	1.51635	0.758174	+	0.652052i	$0.226092\pi$
$822$	−6.33648	−0.221010
$823$	−28.4950	−0.993275	−0.496637	−	0.867958i	$-0.665432\pi$
$823$	−28.4950	−0.993275	−0.496637	+	0.867958i	$0.665432\pi$
$824$	−9.14541	−0.318596
$825$	−1.73898	−0.0605435
$826$	6.83729	0.237900
$827$	−39.9787	−1.39019	−0.695097	−	0.718916i	$-0.744639\pi$
$827$	−39.9787	−1.39019	−0.695097	+	0.718916i	$0.744639\pi$
$828$	−0.268881	−0.00934425
$829$	−13.1182	−0.455613	−0.227807	−	0.973706i	$-0.573155\pi$
$829$	−13.1182	−0.455613	−0.227807	+	0.973706i	$0.573155\pi$
$830$	2.73026	0.0947686
$831$	−4.04016	−0.140152
$832$	−6.34714	−0.220047
$833$	1.45368	0.0503671
$834$	−8.55372	−0.296191
$835$	−21.8605	−0.756513
$836$	22.0918	0.764059
$837$	23.4576	0.810814
$838$	19.6068	0.677305
$839$	−23.5708	−0.813754	−0.406877	−	0.913483i	$-0.633382\pi$
$839$	−23.5708	−0.813754	−0.406877	+	0.913483i	$0.633382\pi$
$840$	0.995979	0.0343645
$841$	−28.9589	−0.998582
$842$	−15.5200	−0.534853
$843$	8.70731	0.299896
$844$	8.79413	0.302706
$845$	27.2861	0.938672
$846$	−30.8736	−1.06146
$847$	−3.35262	−0.115197
$848$	4.00795	0.137634
$849$	1.26683	0.0434774
$850$	−0.509753	−0.0174844
$851$	−0.398869	−0.0136730
$852$	−2.50838	−0.0859356
$853$	34.3660	1.17667	0.588335	−	0.808618i	$-0.299784\pi$
$853$	34.3660	1.17667	0.588335	+	0.808618i	$0.299784\pi$
$854$	−24.1804	−0.827436
$855$	−17.1513	−0.586564
$856$	11.9421	0.408173
$857$	55.7754	1.90525	0.952626	−	0.304144i	$-0.0983704\pi$
$857$	55.7754	1.90525	0.952626	+	0.304144i	$0.0983704\pi$
$858$	11.0375	0.376816
$859$	−1.43295	−0.0488918	−0.0244459	−	0.999701i	$-0.507782\pi$
$859$	−1.43295	−0.0488918	−0.0244459	+	0.999701i	$0.507782\pi$
$860$	−6.14104	−0.209408
$861$	−5.04201	−0.171831
$862$	−21.5989	−0.735661
$863$	42.7018	1.45359	0.726794	−	0.686856i	$-0.241010\pi$
$863$	42.7018	1.45359	0.726794	+	0.686856i	$0.241010\pi$
$864$	2.81712	0.0958403
$865$	16.7546	0.569672
$866$	28.8228	0.979439
$867$	8.18608	0.278014
$868$	−16.9595	−0.575642
$869$	32.8576	1.11462
$870$	−0.0991477	−0.00336142
$871$	−0.727858	−0.0246625
$872$	−1.31504	−0.0445327
$873$	−15.8477	−0.536365
$874$	0.605015	0.0204649
$875$	−2.03673	−0.0688540
$876$	1.85928	0.0628194
$877$	35.3967	1.19526	0.597630	−	0.801772i	$-0.296109\pi$
$877$	35.3967	1.19526	0.597630	+	0.801772i	$0.296109\pi$
$878$	−2.38883	−0.0806192
$879$	16.4489	0.554809
$880$	3.55613	0.119877
$881$	37.9703	1.27925	0.639625	−	0.768687i	$-0.279090\pi$
$881$	37.9703	1.27925	0.639625	+	0.768687i	$0.279090\pi$
$882$	7.87327	0.265107
$883$	−2.02542	−0.0681610	−0.0340805	−	0.999419i	$-0.510850\pi$
$883$	−2.02542	−0.0681610	−0.0340805	+	0.999419i	$0.510850\pi$
$884$	3.23547	0.108821
$885$	1.64160	0.0551818
$886$	6.62066	0.222425
$887$	40.8076	1.37018	0.685092	−	0.728456i	$-0.259762\pi$
$887$	40.8076	1.37018	0.685092	+	0.728456i	$0.259762\pi$
$888$	2.00278	0.0672088
$889$	−33.0332	−1.10790
$890$	16.2605	0.545053
$891$	24.5551	0.822628
$892$	6.77408	0.226813
$893$	69.4693	2.32470
$894$	−8.18244	−0.273662
$895$	−13.6147	−0.455089
$896$	−2.03673	−0.0680424
$897$	0.302279	0.0100928
$898$	−22.5769	−0.753402
$899$	1.68828	0.0563073
$900$	−2.76087	−0.0920290
$901$	−2.04307	−0.0680644
$902$	−18.0025	−0.599416
$903$	−6.11634	−0.203539
$904$	−5.62764	−0.187173
$905$	6.55399	0.217862
$906$	−8.06071	−0.267799
$907$	−43.2141	−1.43490	−0.717450	−	0.696610i	$-0.754691\pi$
$907$	−43.2141	−1.43490	−0.717450	+	0.696610i	$0.754691\pi$
$908$	2.42787	0.0805717
$909$	32.6057	1.08146
$910$	12.9274	0.428539
$911$	−0.754262	−0.0249898	−0.0124949	−	0.999922i	$-0.503977\pi$
$911$	−0.754262	−0.0249898	−0.0124949	+	0.999922i	$0.503977\pi$
$912$	−3.03787	−0.100594
$913$	9.70915	0.321326
$914$	11.7645	0.389136
$915$	−5.80559	−0.191927
$916$	−16.7250	−0.552609
$917$	−24.4978	−0.808988
$918$	−1.43604	−0.0473962
$919$	10.1572	0.335055	0.167527	−	0.985867i	$-0.446422\pi$
$919$	10.1572	0.335055	0.167527	+	0.985867i	$0.446422\pi$
$920$	0.0973899	0.00321085
$921$	0.110133	0.00362902
$922$	−17.2785	−0.569037
$923$	−32.5577	−1.07165
$924$	3.54183	0.116518
$925$	−4.09559	−0.134662
$926$	24.2766	0.797779
$927$	25.2493	0.829296
$928$	0.202752	0.00665567
$929$	21.8239	0.716020	0.358010	−	0.933718i	$-0.383455\pi$
$929$	21.8239	0.716020	0.358010	+	0.933718i	$0.383455\pi$
$930$	−4.07189	−0.133522
$931$	−17.7158	−0.580612
$932$	−9.60484	−0.314617
$933$	9.72676	0.318440
$934$	39.2753	1.28513
$935$	−1.81275	−0.0592833
$936$	17.5236	0.572777
$937$	−38.0511	−1.24307	−0.621537	−	0.783385i	$-0.713492\pi$
$937$	−38.0511	−1.24307	−0.621537	+	0.783385i	$0.713492\pi$
$938$	−0.233562	−0.00762606
$939$	1.55590	0.0507748
$940$	11.1825	0.364735
$941$	9.62439	0.313746	0.156873	−	0.987619i	$-0.449859\pi$
$941$	9.62439	0.313746	0.156873	+	0.987619i	$0.449859\pi$
$942$	8.25597	0.268994
$943$	−0.493023	−0.0160551
$944$	−3.35700	−0.109261
$945$	−5.73771	−0.186648
$946$	−21.8383	−0.710026
$947$	11.1642	0.362787	0.181394	−	0.983411i	$-0.441939\pi$
$947$	11.1642	0.362787	0.181394	+	0.983411i	$0.441939\pi$
$948$	−4.51830	−0.146748
$949$	24.1327	0.783382
$950$	6.21230	0.201554
$951$	−16.8211	−0.545461
$952$	1.03823	0.0336492
$953$	−6.05796	−0.196236	−0.0981182	−	0.995175i	$-0.531282\pi$
$953$	−6.05796	−0.196236	−0.0981182	+	0.995175i	$0.531282\pi$
$954$	−11.0654	−0.358257
$955$	−2.84286	−0.0919928
$956$	9.01741	0.291644
$957$	−0.352582	−0.0113974
$958$	14.9576	0.483257
$959$	−26.3915	−0.852227
$960$	−0.489009	−0.0157827
$961$	38.3359	1.23664
$962$	25.9952	0.838120
$963$	−32.9706	−1.06246
$964$	2.76512	0.0890585
$965$	8.02417	0.258307
$966$	0.0969983	0.00312087
$967$	16.6010	0.533853	0.266927	−	0.963717i	$-0.413992\pi$
$967$	16.6010	0.533853	0.266927	+	0.963717i	$0.413992\pi$
$968$	1.64608	0.0529070
$969$	1.54856	0.0497470
$970$	5.74013	0.184304
$971$	21.4472	0.688272	0.344136	−	0.938920i	$-0.388172\pi$
$971$	21.4472	0.688272	0.344136	+	0.938920i	$0.388172\pi$
$972$	−11.8280	−0.379382
$973$	−35.6264	−1.14213
$974$	11.4068	0.365497
$975$	3.10381	0.0994014
$976$	11.8722	0.380019
$977$	−35.7411	−1.14346	−0.571730	−	0.820442i	$-0.693727\pi$
$977$	−35.7411	−1.14346	−0.571730	+	0.820442i	$0.693727\pi$
$978$	−0.293905	−0.00939806
$979$	57.8244	1.84808
$980$	−2.85173	−0.0910953
$981$	3.63064	0.115918
$982$	−11.3773	−0.363065
$983$	−50.2499	−1.60272	−0.801361	−	0.598180i	$-0.795891\pi$
$983$	−50.2499	−1.60272	−0.801361	+	0.598180i	$0.795891\pi$
$984$	2.47554	0.0789175
$985$	−10.0352	−0.319749
$986$	−0.103354	−0.00329145
$987$	11.1376	0.354513
$988$	−39.4303	−1.25444
$989$	−0.598075	−0.0190177
$990$	−9.81802	−0.312037
$991$	−45.4630	−1.44418	−0.722090	−	0.691799i	$-0.756819\pi$
$991$	−45.4630	−1.44418	−0.722090	+	0.691799i	$0.756819\pi$
$992$	8.32682	0.264377
$993$	−10.6346	−0.337479
$994$	−10.4474	−0.331372
$995$	11.4910	0.364290
$996$	−1.33512	−0.0423049
$997$	−40.8474	−1.29365	−0.646825	−	0.762639i	$-0.723903\pi$
$997$	−40.8474	−1.29365	−0.646825	+	0.762639i	$0.723903\pi$
$998$	0.706907	0.0223767
$999$	−11.5377	−0.365038

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.j.1.15	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.j.1.15	✓	33	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.489009 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.489009 q^{6} -2.03673 q^{7} +1.00000 q^{8} -2.76087 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.489009 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.489009 q^{6} -2.03673 q^{7} +1.00000 q^{8} -2.76087 q^{9} +1.00000 q^{10} +3.55613 q^{11} -0.489009 q^{12} -6.34714 q^{13} -2.03673 q^{14} -0.489009 q^{15} +1.00000 q^{16} -0.509753 q^{17} -2.76087 q^{18} +6.21230 q^{19} +1.00000 q^{20} +0.995979 q^{21} +3.55613 q^{22} +0.0973899 q^{23} -0.489009 q^{24} +1.00000 q^{25} -6.34714 q^{26} +2.81712 q^{27} -2.03673 q^{28} +0.202752 q^{29} -0.489009 q^{30} +8.32682 q^{31} +1.00000 q^{32} -1.73898 q^{33} -0.509753 q^{34} -2.03673 q^{35} -2.76087 q^{36} -4.09559 q^{37} +6.21230 q^{38} +3.10381 q^{39} +1.00000 q^{40} -5.06237 q^{41} +0.995979 q^{42} -6.14104 q^{43} +3.55613 q^{44} -2.76087 q^{45} +0.0973899 q^{46} +11.1825 q^{47} -0.489009 q^{48} -2.85173 q^{49} +1.00000 q^{50} +0.249274 q^{51} -6.34714 q^{52} +4.00795 q^{53} +2.81712 q^{54} +3.55613 q^{55} -2.03673 q^{56} -3.03787 q^{57} +0.202752 q^{58} -3.35700 q^{59} -0.489009 q^{60} +11.8722 q^{61} +8.32682 q^{62} +5.62315 q^{63} +1.00000 q^{64} -6.34714 q^{65} -1.73898 q^{66} +0.114675 q^{67} -0.509753 q^{68} -0.0476245 q^{69} -2.03673 q^{70} +5.12951 q^{71} -2.76087 q^{72} -3.80215 q^{73} -4.09559 q^{74} -0.489009 q^{75} +6.21230 q^{76} -7.24288 q^{77} +3.10381 q^{78} +9.23971 q^{79} +1.00000 q^{80} +6.90501 q^{81} -5.06237 q^{82} +2.73026 q^{83} +0.995979 q^{84} -0.509753 q^{85} -6.14104 q^{86} -0.0991477 q^{87} +3.55613 q^{88} +16.2605 q^{89} -2.76087 q^{90} +12.9274 q^{91} +0.0973899 q^{92} -4.07189 q^{93} +11.1825 q^{94} +6.21230 q^{95} -0.489009 q^{96} +5.74013 q^{97} -2.85173 q^{98} -9.81802 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9}+O(q^{10}) \) 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9	\( 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9} + 33 q^{10} + 12 q^{11} + 6 q^{12} + 20 q^{13} + 4 q^{14} + 6 q^{15} + 33 q^{16} + 33 q^{17} + 49 q^{18} + 17 q^{19} + 33 q^{20} + 26 q^{21} + 12 q^{22} + 7 q^{23} + 6 q^{24} + 33 q^{25} + 20 q^{26} + 21 q^{27} + 4 q^{28} + 33 q^{29} + 6 q^{30} + 35 q^{31} + 33 q^{32} + 25 q^{33} + 33 q^{34} + 4 q^{35} + 49 q^{36} + 16 q^{37} + 17 q^{38} + 22 q^{39} + 33 q^{40} + 39 q^{41} + 26 q^{42} - 3 q^{43} + 12 q^{44} + 49 q^{45} + 7 q^{46} + 19 q^{47} + 6 q^{48} + 69 q^{49} + 33 q^{50} + 21 q^{51} + 20 q^{52} + 41 q^{53} + 21 q^{54} + 12 q^{55} + 4 q^{56} + 33 q^{58} + 18 q^{59} + 6 q^{60} + 30 q^{61} + 35 q^{62} - 15 q^{63} + 33 q^{64} + 20 q^{65} + 25 q^{66} - 9 q^{67} + 33 q^{68} + 23 q^{69} + 4 q^{70} + 36 q^{71} + 49 q^{72} + 35 q^{73} + 16 q^{74} + 6 q^{75} + 17 q^{76} + 26 q^{77} + 22 q^{78} + 32 q^{79} + 33 q^{80} + 53 q^{81} + 39 q^{82} + 24 q^{83} + 26 q^{84} + 33 q^{85} - 3 q^{86} + 12 q^{87} + 12 q^{88} + 40 q^{89} + 49 q^{90} + 5 q^{91} + 7 q^{92} + 18 q^{93} + 19 q^{94} + 17 q^{95} + 6 q^{96} + 39 q^{97} + 69 q^{98} + 3 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9 + 33 * q^10 + 12 * q^11 + 6 * q^12 + 20 * q^13 + 4 * q^14 + 6 * q^15 + 33 * q^16 + 33 * q^17 + 49 * q^18 + 17 * q^19 + 33 * q^20 + 26 * q^21 + 12 * q^22 + 7 * q^23 + 6 * q^24 + 33 * q^25 + 20 * q^26 + 21 * q^27 + 4 * q^28 + 33 * q^29 + 6 * q^30 + 35 * q^31 + 33 * q^32 + 25 * q^33 + 33 * q^34 + 4 * q^35 + 49 * q^36 + 16 * q^37 + 17 * q^38 + 22 * q^39 + 33 * q^40 + 39 * q^41 + 26 * q^42 - 3 * q^43 + 12 * q^44 + 49 * q^45 + 7 * q^46 + 19 * q^47 + 6 * q^48 + 69 * q^49 + 33 * q^50 + 21 * q^51 + 20 * q^52 + 41 * q^53 + 21 * q^54 + 12 * q^55 + 4 * q^56 + 33 * q^58 + 18 * q^59 + 6 * q^60 + 30 * q^61 + 35 * q^62 - 15 * q^63 + 33 * q^64 + 20 * q^65 + 25 * q^66 - 9 * q^67 + 33 * q^68 + 23 * q^69 + 4 * q^70 + 36 * q^71 + 49 * q^72 + 35 * q^73 + 16 * q^74 + 6 * q^75 + 17 * q^76 + 26 * q^77 + 22 * q^78 + 32 * q^79 + 33 * q^80 + 53 * q^81 + 39 * q^82 + 24 * q^83 + 26 * q^84 + 33 * q^85 - 3 * q^86 + 12 * q^87 + 12 * q^88 + 40 * q^89 + 49 * q^90 + 5 * q^91 + 7 * q^92 + 18 * q^93 + 19 * q^94 + 17 * q^95 + 6 * q^96 + 39 * q^97 + 69 * q^98 + 3 * q^99

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