LMFDB - Embedded newform 8013.2.a.d.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8013,2,Mod(1,8013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8013, 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("8013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8013 = 3 \cdot 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8013.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:	$63.9841271397$
Analytic rank:	$0$
Dimension:	$129$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.18651 q^{2} +1.00000 q^{3} +2.78083 q^{4} -0.652555 q^{5} -2.18651 q^{6} +2.68769 q^{7} -1.70730 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.18651 q^{2} +1.00000 q^{3} +2.78083 q^{4} -0.652555 q^{5} -2.18651 q^{6} +2.68769 q^{7} -1.70730 q^{8} +1.00000 q^{9} +1.42682 q^{10} +6.13704 q^{11} +2.78083 q^{12} +2.00005 q^{13} -5.87666 q^{14} -0.652555 q^{15} -1.82864 q^{16} -1.92138 q^{17} -2.18651 q^{18} +8.00888 q^{19} -1.81465 q^{20} +2.68769 q^{21} -13.4187 q^{22} +2.70586 q^{23} -1.70730 q^{24} -4.57417 q^{25} -4.37313 q^{26} +1.00000 q^{27} +7.47400 q^{28} +1.12436 q^{29} +1.42682 q^{30} +8.03868 q^{31} +7.41293 q^{32} +6.13704 q^{33} +4.20113 q^{34} -1.75386 q^{35} +2.78083 q^{36} -2.79404 q^{37} -17.5115 q^{38} +2.00005 q^{39} +1.11411 q^{40} +9.02599 q^{41} -5.87666 q^{42} +6.61674 q^{43} +17.0661 q^{44} -0.652555 q^{45} -5.91639 q^{46} -9.77226 q^{47} -1.82864 q^{48} +0.223654 q^{49} +10.0015 q^{50} -1.92138 q^{51} +5.56181 q^{52} -5.24965 q^{53} -2.18651 q^{54} -4.00476 q^{55} -4.58868 q^{56} +8.00888 q^{57} -2.45843 q^{58} +7.44285 q^{59} -1.81465 q^{60} +1.98726 q^{61} -17.5767 q^{62} +2.68769 q^{63} -12.5512 q^{64} -1.30514 q^{65} -13.4187 q^{66} +14.8687 q^{67} -5.34304 q^{68} +2.70586 q^{69} +3.83484 q^{70} -7.12294 q^{71} -1.70730 q^{72} +0.801682 q^{73} +6.10920 q^{74} -4.57417 q^{75} +22.2714 q^{76} +16.4944 q^{77} -4.37313 q^{78} -3.41932 q^{79} +1.19329 q^{80} +1.00000 q^{81} -19.7354 q^{82} +3.13048 q^{83} +7.47400 q^{84} +1.25381 q^{85} -14.4676 q^{86} +1.12436 q^{87} -10.4778 q^{88} -14.3573 q^{89} +1.42682 q^{90} +5.37551 q^{91} +7.52454 q^{92} +8.03868 q^{93} +21.3672 q^{94} -5.22624 q^{95} +7.41293 q^{96} +18.0263 q^{97} -0.489022 q^{98} +6.13704 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9}+O(q^{10}) $ 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9} + 41 q^{10} + 51 q^{11} + 151 q^{12} + 56 q^{13} + 5 q^{14} + 16 q^{15} + 195 q^{16} + 18 q^{17} + 15 q^{18} + 93 q^{19} + 44 q^{20} + 61 q^{21} + 46 q^{22} + 50 q^{23} + 42 q^{24} + 193 q^{25} + q^{26} + 129 q^{27} + 145 q^{28} + 24 q^{29} + 41 q^{30} + 67 q^{31} + 89 q^{32} + 51 q^{33} + 73 q^{34} + 56 q^{35} + 151 q^{36} + 95 q^{37} + 9 q^{38} + 56 q^{39} + 103 q^{40} + 7 q^{41} + 5 q^{42} + 150 q^{43} + 69 q^{44} + 16 q^{45} + 72 q^{46} + 53 q^{47} + 195 q^{48} + 240 q^{49} + 17 q^{50} + 18 q^{51} + 124 q^{52} + 34 q^{53} + 15 q^{54} + 66 q^{55} - 17 q^{56} + 93 q^{57} + 57 q^{58} + 49 q^{59} + 44 q^{60} + 113 q^{61} + 27 q^{62} + 61 q^{63} + 262 q^{64} + 22 q^{65} + 46 q^{66} + 185 q^{67} + 2 q^{68} + 50 q^{69} + 25 q^{70} + 41 q^{71} + 42 q^{72} + 153 q^{73} - q^{74} + 193 q^{75} + 190 q^{76} + 39 q^{77} + q^{78} + 101 q^{79} + 48 q^{80} + 129 q^{81} + 15 q^{82} + 162 q^{83} + 145 q^{84} + 99 q^{85} + 13 q^{86} + 24 q^{87} + 86 q^{88} - 4 q^{89} + 41 q^{90} + 117 q^{91} + 56 q^{92} + 67 q^{93} + 49 q^{94} + 71 q^{95} + 89 q^{96} + 159 q^{97} + 40 q^{98} + 51 q^{99}+O(q^{100}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9 + 41 * q^10 + 51 * q^11 + 151 * q^12 + 56 * q^13 + 5 * q^14 + 16 * q^15 + 195 * q^16 + 18 * q^17 + 15 * q^18 + 93 * q^19 + 44 * q^20 + 61 * q^21 + 46 * q^22 + 50 * q^23 + 42 * q^24 + 193 * q^25 + q^26 + 129 * q^27 + 145 * q^28 + 24 * q^29 + 41 * q^30 + 67 * q^31 + 89 * q^32 + 51 * q^33 + 73 * q^34 + 56 * q^35 + 151 * q^36 + 95 * q^37 + 9 * q^38 + 56 * q^39 + 103 * q^40 + 7 * q^41 + 5 * q^42 + 150 * q^43 + 69 * q^44 + 16 * q^45 + 72 * q^46 + 53 * q^47 + 195 * q^48 + 240 * q^49 + 17 * q^50 + 18 * q^51 + 124 * q^52 + 34 * q^53 + 15 * q^54 + 66 * q^55 - 17 * q^56 + 93 * q^57 + 57 * q^58 + 49 * q^59 + 44 * q^60 + 113 * q^61 + 27 * q^62 + 61 * q^63 + 262 * q^64 + 22 * q^65 + 46 * q^66 + 185 * q^67 + 2 * q^68 + 50 * q^69 + 25 * q^70 + 41 * q^71 + 42 * q^72 + 153 * q^73 - q^74 + 193 * q^75 + 190 * q^76 + 39 * q^77 + q^78 + 101 * q^79 + 48 * q^80 + 129 * q^81 + 15 * q^82 + 162 * q^83 + 145 * q^84 + 99 * q^85 + 13 * q^86 + 24 * q^87 + 86 * q^88 - 4 * q^89 + 41 * q^90 + 117 * q^91 + 56 * q^92 + 67 * q^93 + 49 * q^94 + 71 * q^95 + 89 * q^96 + 159 * q^97 + 40 * q^98 + 51 * 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 $

$2$	−2.18651	−1.54610	−0.773048	−	0.634347i	$-0.781269\pi$
$2$	−2.18651	−1.54610	−0.773048	+	0.634347i	$0.781269\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.78083	1.39042
$5$	−0.652555	−0.291832	−0.145916	−	0.989297i	$-0.546613\pi$
$5$	−0.652555	−0.291832	−0.145916	+	0.989297i	$0.546613\pi$
$6$	−2.18651	−0.892640
$7$	2.68769	1.01585	0.507925	−	0.861401i	$-0.330413\pi$
$7$	2.68769	1.01585	0.507925	+	0.861401i	$0.330413\pi$
$8$	−1.70730	−0.603621
$9$	1.00000	0.333333
$10$	1.42682	0.451200
$11$	6.13704	1.85039	0.925194	−	0.379495i	$-0.123902\pi$
$11$	6.13704	1.85039	0.925194	+	0.379495i	$0.123902\pi$
$12$	2.78083	0.802757
$13$	2.00005	0.554714	0.277357	−	0.960767i	$-0.410541\pi$
$13$	2.00005	0.554714	0.277357	+	0.960767i	$0.410541\pi$
$14$	−5.87666	−1.57060
$15$	−0.652555	−0.168489
$16$	−1.82864	−0.457159
$17$	−1.92138	−0.466004	−0.233002	−	0.972476i	$-0.574855\pi$
$17$	−1.92138	−0.466004	−0.233002	+	0.972476i	$0.574855\pi$
$18$	−2.18651	−0.515366
$19$	8.00888	1.83736	0.918682	−	0.394998i	$-0.129255\pi$
$19$	8.00888	1.83736	0.918682	+	0.394998i	$0.129255\pi$
$20$	−1.81465	−0.405767
$21$	2.68769	0.586501
$22$	−13.4187	−2.86088
$23$	2.70586	0.564210	0.282105	−	0.959383i	$-0.408967\pi$
$23$	2.70586	0.564210	0.282105	+	0.959383i	$0.408967\pi$
$24$	−1.70730	−0.348501
$25$	−4.57417	−0.914834
$26$	−4.37313	−0.857642
$27$	1.00000	0.192450
$28$	7.47400	1.41245
$29$	1.12436	0.208788	0.104394	−	0.994536i	$-0.466710\pi$
$29$	1.12436	0.208788	0.104394	+	0.994536i	$0.466710\pi$
$30$	1.42682	0.260500
$31$	8.03868	1.44379	0.721895	−	0.692003i	$-0.243272\pi$
$31$	8.03868	1.44379	0.721895	+	0.692003i	$0.243272\pi$
$32$	7.41293	1.31043
$33$	6.13704	1.06832
$34$	4.20113	0.720487
$35$	−1.75386	−0.296457
$36$	2.78083	0.463472
$37$	−2.79404	−0.459337	−0.229669	−	0.973269i	$-0.573764\pi$
$37$	−2.79404	−0.459337	−0.229669	+	0.973269i	$0.573764\pi$
$38$	−17.5115	−2.84074
$39$	2.00005	0.320265
$40$	1.11411	0.176156
$41$	9.02599	1.40962	0.704811	−	0.709395i	$-0.251032\pi$
$41$	9.02599	1.40962	0.704811	+	0.709395i	$0.251032\pi$
$42$	−5.87666	−0.906788
$43$	6.61674	1.00904	0.504521	−	0.863399i	$-0.331669\pi$
$43$	6.61674	1.00904	0.504521	+	0.863399i	$0.331669\pi$
$44$	17.0661	2.57281
$45$	−0.652555	−0.0972772
$46$	−5.91639	−0.872324
$47$	−9.77226	−1.42543	−0.712715	−	0.701453i	$-0.752535\pi$
$47$	−9.77226	−1.42543	−0.712715	+	0.701453i	$0.752535\pi$
$48$	−1.82864	−0.263941
$49$	0.223654	0.0319506
$50$	10.0015	1.41442
$51$	−1.92138	−0.269047
$52$	5.56181	0.771284
$53$	−5.24965	−0.721095	−0.360547	−	0.932741i	$-0.617410\pi$
$53$	−5.24965	−0.721095	−0.360547	+	0.932741i	$0.617410\pi$
$54$	−2.18651	−0.297547
$55$	−4.00476	−0.540001
$56$	−4.58868	−0.613188
$57$	8.00888	1.06080
$58$	−2.45843	−0.322807
$59$	7.44285	0.968977	0.484488	−	0.874798i	$-0.339006\pi$
$59$	7.44285	0.968977	0.484488	+	0.874798i	$0.339006\pi$
$60$	−1.81465	−0.234270
$61$	1.98726	0.254442	0.127221	−	0.991874i	$-0.459394\pi$
$61$	1.98726	0.254442	0.127221	+	0.991874i	$0.459394\pi$
$62$	−17.5767	−2.23224
$63$	2.68769	0.338617
$64$	−12.5512	−1.56890
$65$	−1.30514	−0.161883
$66$	−13.4187	−1.65173
$67$	14.8687	1.81649	0.908247	−	0.418433i	$-0.137421\pi$
$67$	14.8687	1.81649	0.908247	+	0.418433i	$0.137421\pi$
$68$	−5.34304	−0.647939
$69$	2.70586	0.325747
$70$	3.83484	0.458351
$71$	−7.12294	−0.845338	−0.422669	−	0.906284i	$-0.638907\pi$
$71$	−7.12294	−0.845338	−0.422669	+	0.906284i	$0.638907\pi$
$72$	−1.70730	−0.201207
$73$	0.801682	0.0938297	0.0469149	−	0.998899i	$-0.485061\pi$
$73$	0.801682	0.0938297	0.0469149	+	0.998899i	$0.485061\pi$
$74$	6.10920	0.710180
$75$	−4.57417	−0.528180
$76$	22.2714	2.55470
$77$	16.4944	1.87972
$78$	−4.37313	−0.495160
$79$	−3.41932	−0.384704	−0.192352	−	0.981326i	$-0.561611\pi$
$79$	−3.41932	−0.384704	−0.192352	+	0.981326i	$0.561611\pi$
$80$	1.19329	0.133414
$81$	1.00000	0.111111
$82$	−19.7354	−2.17941
$83$	3.13048	0.343615	0.171808	−	0.985131i	$-0.445039\pi$
$83$	3.13048	0.343615	0.171808	+	0.985131i	$0.445039\pi$
$84$	7.47400	0.815480
$85$	1.25381	0.135995
$86$	−14.4676	−1.56008
$87$	1.12436	0.120544
$88$	−10.4778	−1.11693
$89$	−14.3573	−1.52187	−0.760936	−	0.648826i	$-0.775260\pi$
$89$	−14.3573	−1.52187	−0.760936	+	0.648826i	$0.775260\pi$
$90$	1.42682	0.150400
$91$	5.37551	0.563506
$92$	7.52454	0.784487
$93$	8.03868	0.833572
$94$	21.3672	2.20385
$95$	−5.22624	−0.536201
$96$	7.41293	0.756579
$97$	18.0263	1.83029	0.915146	−	0.403123i	$-0.132075\pi$
$97$	18.0263	1.83029	0.915146	+	0.403123i	$0.132075\pi$
$98$	−0.489022	−0.0493987
$99$	6.13704	0.616796
$100$	−12.7200	−1.27200
$101$	−10.2115	−1.01608	−0.508040	−	0.861333i	$-0.669630\pi$
$101$	−10.2115	−1.01608	−0.508040	+	0.861333i	$0.669630\pi$
$102$	4.20113	0.415973
$103$	14.8657	1.46476	0.732380	−	0.680896i	$-0.238409\pi$
$103$	14.8657	1.46476	0.732380	+	0.680896i	$0.238409\pi$
$104$	−3.41468	−0.334837
$105$	−1.75386	−0.171160
$106$	11.4784	1.11488
$107$	3.90660	0.377665	0.188832	−	0.982009i	$-0.439530\pi$
$107$	3.90660	0.377665	0.188832	+	0.982009i	$0.439530\pi$
$108$	2.78083	0.267586
$109$	−3.91532	−0.375020	−0.187510	−	0.982263i	$-0.560042\pi$
$109$	−3.91532	−0.375020	−0.187510	+	0.982263i	$0.560042\pi$
$110$	8.75645	0.834895
$111$	−2.79404	−0.265198
$112$	−4.91480	−0.464405
$113$	6.95742	0.654499	0.327250	−	0.944938i	$-0.393878\pi$
$113$	6.95742	0.654499	0.327250	+	0.944938i	$0.393878\pi$
$114$	−17.5115	−1.64010
$115$	−1.76572	−0.164654
$116$	3.12666	0.290303
$117$	2.00005	0.184905
$118$	−16.2739	−1.49813
$119$	−5.16407	−0.473390
$120$	1.11411	0.101703
$121$	26.6633	2.42393
$122$	−4.34516	−0.393392
$123$	9.02599	0.813846
$124$	22.3542	2.00747
$125$	6.24768	0.558809
$126$	−5.87666	−0.523534
$127$	1.39821	0.124071	0.0620355	−	0.998074i	$-0.480241\pi$
$127$	1.39821	0.124071	0.0620355	+	0.998074i	$0.480241\pi$
$128$	12.6174	1.11524
$129$	6.61674	0.582571
$130$	2.85371	0.250287
$131$	−8.78537	−0.767582	−0.383791	−	0.923420i	$-0.625382\pi$
$131$	−8.78537	−0.767582	−0.383791	+	0.923420i	$0.625382\pi$
$132$	17.0661	1.48541
$133$	21.5254	1.86649
$134$	−32.5105	−2.80848
$135$	−0.652555	−0.0561630
$136$	3.28037	0.281290
$137$	−13.5144	−1.15462	−0.577308	−	0.816527i	$-0.695897\pi$
$137$	−13.5144	−1.15462	−0.577308	+	0.816527i	$0.695897\pi$
$138$	−5.91639	−0.503637
$139$	−9.85284	−0.835707	−0.417854	−	0.908514i	$-0.637218\pi$
$139$	−9.85284	−0.835707	−0.417854	+	0.908514i	$0.637218\pi$
$140$	−4.87720	−0.412199
$141$	−9.77226	−0.822973
$142$	15.5744	1.30697
$143$	12.2744	1.02644
$144$	−1.82864	−0.152386
$145$	−0.733707	−0.0609310
$146$	−1.75289	−0.145070
$147$	0.223654	0.0184467
$148$	−7.76975	−0.638670
$149$	−17.0386	−1.39585	−0.697927	−	0.716169i	$-0.745894\pi$
$149$	−17.0386	−1.39585	−0.697927	+	0.716169i	$0.745894\pi$
$150$	10.0015	0.816617
$151$	−18.1673	−1.47844	−0.739218	−	0.673466i	$-0.764805\pi$
$151$	−18.1673	−1.47844	−0.739218	+	0.673466i	$0.764805\pi$
$152$	−13.6735	−1.10907
$153$	−1.92138	−0.155335
$154$	−36.0653	−2.90622
$155$	−5.24568	−0.421343
$156$	5.56181	0.445301
$157$	12.7630	1.01860	0.509299	−	0.860590i	$-0.329905\pi$
$157$	12.7630	1.01860	0.509299	+	0.860590i	$0.329905\pi$
$158$	7.47638	0.594789
$159$	−5.24965	−0.416324
$160$	−4.83735	−0.382426
$161$	7.27250	0.573153
$162$	−2.18651	−0.171789
$163$	−7.50977	−0.588211	−0.294105	−	0.955773i	$-0.595022\pi$
$163$	−7.50977	−0.588211	−0.294105	+	0.955773i	$0.595022\pi$
$164$	25.0998	1.95996
$165$	−4.00476	−0.311770
$166$	−6.84483	−0.531262
$167$	−13.0431	−1.00931	−0.504654	−	0.863322i	$-0.668380\pi$
$167$	−13.0431	−1.00931	−0.504654	+	0.863322i	$0.668380\pi$
$168$	−4.58868	−0.354024
$169$	−8.99980	−0.692292
$170$	−2.74147	−0.210261
$171$	8.00888	0.612455
$172$	18.4000	1.40299
$173$	19.8639	1.51022	0.755111	−	0.655596i	$-0.227583\pi$
$173$	19.8639	1.51022	0.755111	+	0.655596i	$0.227583\pi$
$174$	−2.45843	−0.186373
$175$	−12.2939	−0.929334
$176$	−11.2224	−0.845922
$177$	7.44285	0.559439
$178$	31.3924	2.35296
$179$	−13.2540	−0.990647	−0.495324	−	0.868709i	$-0.664950\pi$
$179$	−13.2540	−0.990647	−0.495324	+	0.868709i	$0.664950\pi$
$180$	−1.81465	−0.135256
$181$	20.0835	1.49279	0.746397	−	0.665501i	$-0.231782\pi$
$181$	20.0835	1.49279	0.746397	+	0.665501i	$0.231782\pi$
$182$	−11.7536	−0.871236
$183$	1.98726	0.146902
$184$	−4.61971	−0.340569
$185$	1.82326	0.134049
$186$	−17.5767	−1.28878
$187$	−11.7916	−0.862287
$188$	−27.1750	−1.98194
$189$	2.68769	0.195500
$190$	11.4272	0.829018
$191$	−6.87606	−0.497534	−0.248767	−	0.968563i	$-0.580025\pi$
$191$	−6.87606	−0.497534	−0.248767	+	0.968563i	$0.580025\pi$
$192$	−12.5512	−0.905804
$193$	−10.9795	−0.790322	−0.395161	−	0.918612i	$-0.629311\pi$
$193$	−10.9795	−0.790322	−0.395161	+	0.918612i	$0.629311\pi$
$194$	−39.4147	−2.82981
$195$	−1.30514	−0.0934633
$196$	0.621944	0.0444246
$197$	−4.66023	−0.332027	−0.166014	−	0.986123i	$-0.553090\pi$
$197$	−4.66023	−0.332027	−0.166014	+	0.986123i	$0.553090\pi$
$198$	−13.4187	−0.953626
$199$	3.82920	0.271445	0.135723	−	0.990747i	$-0.456664\pi$
$199$	3.82920	0.271445	0.135723	+	0.990747i	$0.456664\pi$
$200$	7.80947	0.552213
$201$	14.8687	1.04875
$202$	22.3275	1.57096
$203$	3.02193	0.212098
$204$	−5.34304	−0.374088
$205$	−5.88995	−0.411372
$206$	−32.5040	−2.26466
$207$	2.70586	0.188070
$208$	−3.65737	−0.253593
$209$	49.1508	3.39983
$210$	3.83484	0.264629
$211$	−18.5482	−1.27691	−0.638455	−	0.769659i	$-0.720426\pi$
$211$	−18.5482	−1.27691	−0.638455	+	0.769659i	$0.720426\pi$
$212$	−14.5984	−1.00262
$213$	−7.12294	−0.488056
$214$	−8.54182	−0.583907
$215$	−4.31778	−0.294470
$216$	−1.70730	−0.116167
$217$	21.6054	1.46667
$218$	8.56089	0.579817
$219$	0.801682	0.0541726
$220$	−11.1366	−0.750827
$221$	−3.84286	−0.258499
$222$	6.10920	0.410023
$223$	1.92216	0.128717	0.0643586	−	0.997927i	$-0.479500\pi$
$223$	1.92216	0.128717	0.0643586	+	0.997927i	$0.479500\pi$
$224$	19.9236	1.33120
$225$	−4.57417	−0.304945
$226$	−15.2125	−1.01192
$227$	16.8012	1.11513	0.557567	−	0.830132i	$-0.311735\pi$
$227$	16.8012	1.11513	0.557567	+	0.830132i	$0.311735\pi$
$228$	22.2714	1.47496
$229$	−24.5007	−1.61905	−0.809525	−	0.587085i	$-0.800275\pi$
$229$	−24.5007	−1.61905	−0.809525	+	0.587085i	$0.800275\pi$
$230$	3.86077	0.254572
$231$	16.4944	1.08525
$232$	−1.91962	−0.126029
$233$	−17.0879	−1.11946	−0.559732	−	0.828674i	$-0.689096\pi$
$233$	−17.0879	−1.11946	−0.559732	+	0.828674i	$0.689096\pi$
$234$	−4.37313	−0.285881
$235$	6.37694	0.415986
$236$	20.6973	1.34728
$237$	−3.41932	−0.222109
$238$	11.2913	0.731907
$239$	−15.4605	−1.00006	−0.500028	−	0.866009i	$-0.666677\pi$
$239$	−15.4605	−1.00006	−0.500028	+	0.866009i	$0.666677\pi$
$240$	1.19329	0.0770264
$241$	−18.8038	−1.21126	−0.605631	−	0.795746i	$-0.707079\pi$
$241$	−18.8038	−1.21126	−0.605631	+	0.795746i	$0.707079\pi$
$242$	−58.2995	−3.74764
$243$	1.00000	0.0641500
$244$	5.52623	0.353780
$245$	−0.145946	−0.00932418
$246$	−19.7354	−1.25828
$247$	16.0182	1.01921
$248$	−13.7244	−0.871501
$249$	3.13048	0.198386
$250$	−13.6606	−0.863973
$251$	−3.37724	−0.213170	−0.106585	−	0.994304i	$-0.533992\pi$
$251$	−3.37724	−0.213170	−0.106585	+	0.994304i	$0.533992\pi$
$252$	7.47400	0.470818
$253$	16.6060	1.04401
$254$	−3.05720	−0.191826
$255$	1.25381	0.0785165
$256$	−2.48581	−0.155363
$257$	19.3182	1.20503	0.602517	−	0.798106i	$-0.294165\pi$
$257$	19.3182	1.20503	0.602517	+	0.798106i	$0.294165\pi$
$258$	−14.4676	−0.900711
$259$	−7.50950	−0.466618
$260$	−3.62939	−0.225085
$261$	1.12436	0.0695961
$262$	19.2093	1.18676
$263$	0.619074	0.0381737	0.0190869	−	0.999818i	$-0.493924\pi$
$263$	0.619074	0.0381737	0.0190869	+	0.999818i	$0.493924\pi$
$264$	−10.4778	−0.644861
$265$	3.42569	0.210438
$266$	−47.0654	−2.88577
$267$	−14.3573	−0.878654
$268$	41.3472	2.52568
$269$	7.64782	0.466296	0.233148	−	0.972441i	$-0.425097\pi$
$269$	7.64782	0.466296	0.233148	+	0.972441i	$0.425097\pi$
$270$	1.42682	0.0868335
$271$	1.12885	0.0685729	0.0342864	−	0.999412i	$-0.489084\pi$
$271$	1.12885	0.0685729	0.0342864	+	0.999412i	$0.489084\pi$
$272$	3.51351	0.213038
$273$	5.37551	0.325341
$274$	29.5494	1.78515
$275$	−28.0719	−1.69280
$276$	7.52454	0.452924
$277$	−31.2374	−1.87687	−0.938437	−	0.345452i	$-0.887726\pi$
$277$	−31.2374	−1.87687	−0.938437	+	0.345452i	$0.887726\pi$
$278$	21.5434	1.29208
$279$	8.03868	0.481263
$280$	2.99437	0.178948
$281$	17.8540	1.06508	0.532539	−	0.846405i	$-0.321238\pi$
$281$	17.8540	1.06508	0.532539	+	0.846405i	$0.321238\pi$
$282$	21.3672	1.27240
$283$	−0.972284	−0.0577963	−0.0288982	−	0.999582i	$-0.509200\pi$
$283$	−0.972284	−0.0577963	−0.0288982	+	0.999582i	$0.509200\pi$
$284$	−19.8077	−1.17537
$285$	−5.22624	−0.309576
$286$	−26.8381	−1.58697
$287$	24.2590	1.43196
$288$	7.41293	0.436811
$289$	−13.3083	−0.782840
$290$	1.60426	0.0942053
$291$	18.0263	1.05672
$292$	2.22934	0.130462
$293$	−26.8200	−1.56684	−0.783420	−	0.621492i	$-0.786527\pi$
$293$	−26.8200	−1.56684	−0.783420	+	0.621492i	$0.786527\pi$
$294$	−0.489022	−0.0285203
$295$	−4.85687	−0.282778
$296$	4.77026	0.277266
$297$	6.13704	0.356107
$298$	37.2550	2.15813
$299$	5.41186	0.312976
$300$	−12.7200	−0.734390
$301$	17.7837	1.02504
$302$	39.7231	2.28581
$303$	−10.2115	−0.586634
$304$	−14.6453	−0.839968
$305$	−1.29679	−0.0742543
$306$	4.20113	0.240162
$307$	0.676932	0.0386345	0.0193173	−	0.999813i	$-0.493851\pi$
$307$	0.676932	0.0386345	0.0193173	+	0.999813i	$0.493851\pi$
$308$	45.8682	2.61359
$309$	14.8657	0.845680
$310$	11.4697	0.651437
$311$	−21.1307	−1.19821	−0.599107	−	0.800669i	$-0.704478\pi$
$311$	−21.1307	−1.19821	−0.599107	+	0.800669i	$0.704478\pi$
$312$	−3.41468	−0.193318
$313$	27.7779	1.57010	0.785049	−	0.619433i	$-0.212638\pi$
$313$	27.7779	1.57010	0.785049	+	0.619433i	$0.212638\pi$
$314$	−27.9064	−1.57485
$315$	−1.75386	−0.0988190
$316$	−9.50855	−0.534898
$317$	−33.5260	−1.88301	−0.941503	−	0.337004i	$-0.890587\pi$
$317$	−33.5260	−1.88301	−0.941503	+	0.337004i	$0.890587\pi$
$318$	11.4784	0.643678
$319$	6.90024	0.386339
$320$	8.19034	0.457854
$321$	3.90660	0.218045
$322$	−15.9014	−0.886150
$323$	−15.3881	−0.856219
$324$	2.78083	0.154491
$325$	−9.14858	−0.507472
$326$	16.4202	0.909431
$327$	−3.91532	−0.216518
$328$	−15.4100	−0.850877
$329$	−26.2648	−1.44802
$330$	8.75645	0.482027
$331$	14.2425	0.782838	0.391419	−	0.920213i	$-0.371984\pi$
$331$	14.2425	0.782838	0.391419	+	0.920213i	$0.371984\pi$
$332$	8.70534	0.477768
$333$	−2.79404	−0.153112
$334$	28.5190	1.56049
$335$	−9.70262	−0.530111
$336$	−4.91480	−0.268125
$337$	24.8892	1.35580	0.677901	−	0.735153i	$-0.262890\pi$
$337$	24.8892	1.35580	0.677901	+	0.735153i	$0.262890\pi$
$338$	19.6782	1.07035
$339$	6.95742	0.377875
$340$	3.48663	0.189089
$341$	49.3337	2.67157
$342$	−17.5115	−0.946914
$343$	−18.2127	−0.983393
$344$	−11.2967	−0.609079
$345$	−1.76572	−0.0950633
$346$	−43.4326	−2.33495
$347$	−25.7231	−1.38089	−0.690443	−	0.723387i	$-0.742584\pi$
$347$	−25.7231	−1.38089	−0.690443	+	0.723387i	$0.742584\pi$
$348$	3.12666	0.167606
$349$	10.5942	0.567094	0.283547	−	0.958958i	$-0.408489\pi$
$349$	10.5942	0.567094	0.283547	+	0.958958i	$0.408489\pi$
$350$	26.8808	1.43684
$351$	2.00005	0.106755
$352$	45.4935	2.42481
$353$	12.4870	0.664616	0.332308	−	0.943171i	$-0.392173\pi$
$353$	12.4870	0.664616	0.332308	+	0.943171i	$0.392173\pi$
$354$	−16.2739	−0.864947
$355$	4.64811	0.246696
$356$	−39.9253	−2.11604
$357$	−5.16407	−0.273312
$358$	28.9799	1.53164
$359$	11.2207	0.592203	0.296102	−	0.955156i	$-0.404313\pi$
$359$	11.2207	0.592203	0.296102	+	0.955156i	$0.404313\pi$
$360$	1.11411	0.0587185
$361$	45.1422	2.37591
$362$	−43.9128	−2.30800
$363$	26.6633	1.39946
$364$	14.9484	0.783508
$365$	−0.523141	−0.0273825
$366$	−4.34516	−0.227125
$367$	−5.64357	−0.294592	−0.147296	−	0.989092i	$-0.547057\pi$
$367$	−5.64357	−0.294592	−0.147296	+	0.989092i	$0.547057\pi$
$368$	−4.94804	−0.257934
$369$	9.02599	0.469874
$370$	−3.98659	−0.207253
$371$	−14.1094	−0.732524
$372$	22.3542	1.15901
$373$	−11.9364	−0.618043	−0.309021	−	0.951055i	$-0.600001\pi$
$373$	−11.9364	−0.618043	−0.309021	+	0.951055i	$0.600001\pi$
$374$	25.7825	1.33318
$375$	6.24768	0.322629
$376$	16.6842	0.860420
$377$	2.24878	0.115818
$378$	−5.87666	−0.302263
$379$	−14.7330	−0.756785	−0.378392	−	0.925645i	$-0.623523\pi$
$379$	−14.7330	−0.756785	−0.378392	+	0.925645i	$0.623523\pi$
$380$	−14.5333	−0.745542
$381$	1.39821	0.0716324
$382$	15.0346	0.769236
$383$	14.4450	0.738103	0.369051	−	0.929409i	$-0.379683\pi$
$383$	14.4450	0.738103	0.369051	+	0.929409i	$0.379683\pi$
$384$	12.6174	0.643881
$385$	−10.7635	−0.548560
$386$	24.0068	1.22191
$387$	6.61674	0.336348
$388$	50.1281	2.54487
$389$	−23.9944	−1.21657	−0.608283	−	0.793721i	$-0.708141\pi$
$389$	−23.9944	−1.21657	−0.608283	+	0.793721i	$0.708141\pi$
$390$	2.85371	0.144503
$391$	−5.19899	−0.262924
$392$	−0.381844	−0.0192860
$393$	−8.78537	−0.443163
$394$	10.1896	0.513347
$395$	2.23129	0.112269
$396$	17.0661	0.857603
$397$	−30.2401	−1.51771	−0.758854	−	0.651261i	$-0.774240\pi$
$397$	−30.2401	−1.51771	−0.758854	+	0.651261i	$0.774240\pi$
$398$	−8.37260	−0.419680
$399$	21.5254	1.07762
$400$	8.36450	0.418225
$401$	21.9369	1.09548	0.547738	−	0.836650i	$-0.315489\pi$
$401$	21.9369	1.09548	0.547738	+	0.836650i	$0.315489\pi$
$402$	−32.5105	−1.62148
$403$	16.0778	0.800891
$404$	−28.3964	−1.41277
$405$	−0.652555	−0.0324257
$406$	−6.60747	−0.327923
$407$	−17.1471	−0.849952
$408$	3.28037	0.162403
$409$	−21.5971	−1.06791	−0.533954	−	0.845514i	$-0.679294\pi$
$409$	−21.5971	−1.06791	−0.533954	+	0.845514i	$0.679294\pi$
$410$	12.8785	0.636021
$411$	−13.5144	−0.666617
$412$	41.3390	2.03663
$413$	20.0040	0.984335
$414$	−5.91639	−0.290775
$415$	−2.04281	−0.100278
$416$	14.8262	0.726916
$417$	−9.85284	−0.482496
$418$	−107.469	−5.25647
$419$	−10.6821	−0.521855	−0.260927	−	0.965358i	$-0.584028\pi$
$419$	−10.6821	−0.521855	−0.260927	+	0.965358i	$0.584028\pi$
$420$	−4.87720	−0.237983
$421$	−7.04420	−0.343314	−0.171657	−	0.985157i	$-0.554912\pi$
$421$	−7.04420	−0.343314	−0.171657	+	0.985157i	$0.554912\pi$
$422$	40.5558	1.97423
$423$	−9.77226	−0.475144
$424$	8.96271	0.435268
$425$	8.78873	0.426316
$426$	15.5744	0.754582
$427$	5.34112	0.258475
$428$	10.8636	0.525111
$429$	12.2744	0.592613
$430$	9.44089	0.455280
$431$	−34.8480	−1.67857	−0.839285	−	0.543691i	$-0.817026\pi$
$431$	−34.8480	−1.67857	−0.839285	+	0.543691i	$0.817026\pi$
$432$	−1.82864	−0.0879804
$433$	20.7170	0.995598	0.497799	−	0.867292i	$-0.334142\pi$
$433$	20.7170	0.995598	0.497799	+	0.867292i	$0.334142\pi$
$434$	−47.2405	−2.26762
$435$	−0.733707	−0.0351786
$436$	−10.8878	−0.521433
$437$	21.6709	1.03666
$438$	−1.75289	−0.0837561
$439$	5.80589	0.277100	0.138550	−	0.990355i	$-0.455756\pi$
$439$	5.80589	0.277100	0.138550	+	0.990355i	$0.455756\pi$
$440$	6.83731	0.325956
$441$	0.223654	0.0106502
$442$	8.40247	0.399665
$443$	−37.5687	−1.78494	−0.892470	−	0.451106i	$-0.851030\pi$
$443$	−37.5687	−1.78494	−0.892470	+	0.451106i	$0.851030\pi$
$444$	−7.76975	−0.368736
$445$	9.36894	0.444130
$446$	−4.20282	−0.199009
$447$	−17.0386	−0.805897
$448$	−33.7336	−1.59376
$449$	−0.143300	−0.00676274	−0.00338137	−	0.999994i	$-0.501076\pi$
$449$	−0.143300	−0.00676274	−0.00338137	+	0.999994i	$0.501076\pi$
$450$	10.0015	0.471474
$451$	55.3928	2.60835
$452$	19.3474	0.910026
$453$	−18.1673	−0.853576
$454$	−36.7360	−1.72411
$455$	−3.50782	−0.164449
$456$	−13.6735	−0.640323
$457$	9.71023	0.454225	0.227113	−	0.973868i	$-0.427071\pi$
$457$	9.71023	0.454225	0.227113	+	0.973868i	$0.427071\pi$
$458$	53.5710	2.50321
$459$	−1.92138	−0.0896825
$460$	−4.91018	−0.228938
$461$	−0.134998	−0.00628749	−0.00314374	−	0.999995i	$-0.501001\pi$
$461$	−0.134998	−0.00628749	−0.00314374	+	0.999995i	$0.501001\pi$
$462$	−36.0653	−1.67791
$463$	28.2002	1.31057	0.655287	−	0.755380i	$-0.272548\pi$
$463$	28.2002	1.31057	0.655287	+	0.755380i	$0.272548\pi$
$464$	−2.05605	−0.0954496
$465$	−5.24568	−0.243263
$466$	37.3629	1.73080
$467$	−19.1322	−0.885331	−0.442665	−	0.896687i	$-0.645967\pi$
$467$	−19.1322	−0.885331	−0.442665	+	0.896687i	$0.645967\pi$
$468$	5.56181	0.257095
$469$	39.9623	1.84529
$470$	−13.9433	−0.643154
$471$	12.7630	0.588088
$472$	−12.7072	−0.584895
$473$	40.6072	1.86712
$474$	7.47638	0.343402
$475$	−36.6340	−1.68088
$476$	−14.3604	−0.658209
$477$	−5.24965	−0.240365
$478$	33.8045	1.54618
$479$	23.4978	1.07364	0.536821	−	0.843696i	$-0.319625\pi$
$479$	23.4978	1.07364	0.536821	+	0.843696i	$0.319625\pi$
$480$	−4.83735	−0.220794
$481$	−5.58822	−0.254801
$482$	41.1148	1.87273
$483$	7.27250	0.330910
$484$	74.1461	3.37028
$485$	−11.7631	−0.534137
$486$	−2.18651	−0.0991822
$487$	21.9006	0.992411	0.496206	−	0.868205i	$-0.334726\pi$
$487$	21.9006	0.992411	0.496206	+	0.868205i	$0.334726\pi$
$488$	−3.39284	−0.153587
$489$	−7.50977	−0.339604
$490$	0.319114	0.0144161
$491$	18.6524	0.841772	0.420886	−	0.907114i	$-0.361719\pi$
$491$	18.6524	0.841772	0.420886	+	0.907114i	$0.361719\pi$
$492$	25.0998	1.13158
$493$	−2.16033	−0.0972962
$494$	−35.0239	−1.57580
$495$	−4.00476	−0.180000
$496$	−14.6998	−0.660042
$497$	−19.1442	−0.858736
$498$	−6.84483	−0.306724
$499$	25.0170	1.11991	0.559957	−	0.828522i	$-0.310818\pi$
$499$	25.0170	1.11991	0.559957	+	0.828522i	$0.310818\pi$
$500$	17.3737	0.776977
$501$	−13.0431	−0.582724
$502$	7.38438	0.329581
$503$	−0.146721	−0.00654198	−0.00327099	−	0.999995i	$-0.501041\pi$
$503$	−0.146721	−0.00654198	−0.00327099	+	0.999995i	$0.501041\pi$
$504$	−4.58868	−0.204396
$505$	6.66356	0.296524
$506$	−36.3091	−1.61414
$507$	−8.99980	−0.399695
$508$	3.88818	0.172510
$509$	−7.09949	−0.314679	−0.157340	−	0.987545i	$-0.550292\pi$
$509$	−7.09949	−0.314679	−0.157340	+	0.987545i	$0.550292\pi$
$510$	−2.74147	−0.121394
$511$	2.15467	0.0953169
$512$	−19.7996	−0.875028
$513$	8.00888	0.353601
$514$	−42.2394	−1.86310
$515$	−9.70069	−0.427463
$516$	18.4000	0.810016
$517$	−59.9728	−2.63760
$518$	16.4196	0.721436
$519$	19.8639	0.871928
$520$	2.22827	0.0977161
$521$	8.65426	0.379150	0.189575	−	0.981866i	$-0.439289\pi$
$521$	8.65426	0.379150	0.189575	+	0.981866i	$0.439289\pi$
$522$	−2.45843	−0.107602
$523$	−2.51679	−0.110052	−0.0550258	−	0.998485i	$-0.517524\pi$
$523$	−2.51679	−0.110052	−0.0550258	+	0.998485i	$0.517524\pi$
$524$	−24.4306	−1.06726
$525$	−12.2939	−0.536551
$526$	−1.35361	−0.0590203
$527$	−15.4454	−0.672811
$528$	−11.2224	−0.488393
$529$	−15.6783	−0.681667
$530$	−7.49030	−0.325358
$531$	7.44285	0.322992
$532$	59.8584	2.59519
$533$	18.0524	0.781938
$534$	31.3924	1.35848
$535$	−2.54927	−0.110215
$536$	−25.3852	−1.09647
$537$	−13.2540	−0.571950
$538$	−16.7220	−0.720938
$539$	1.37257	0.0591209
$540$	−1.81465	−0.0780899
$541$	23.8170	1.02397	0.511987	−	0.858993i	$-0.328910\pi$
$541$	23.8170	1.02397	0.511987	+	0.858993i	$0.328910\pi$
$542$	−2.46825	−0.106020
$543$	20.0835	0.861865
$544$	−14.2431	−0.610667
$545$	2.55496	0.109443
$546$	−11.7536	−0.503008
$547$	−32.0708	−1.37125	−0.685624	−	0.727956i	$-0.740471\pi$
$547$	−32.0708	−1.37125	−0.685624	+	0.727956i	$0.740471\pi$
$548$	−37.5813	−1.60540
$549$	1.98726	0.0848141
$550$	61.3795	2.61723
$551$	9.00487	0.383620
$552$	−4.61971	−0.196628
$553$	−9.19006	−0.390801
$554$	68.3009	2.90183
$555$	1.82326	0.0773933
$556$	−27.3991	−1.16198
$557$	−40.7966	−1.72861	−0.864303	−	0.502971i	$-0.832240\pi$
$557$	−40.7966	−1.72861	−0.864303	+	0.502971i	$0.832240\pi$
$558$	−17.5767	−0.744079
$559$	13.2338	0.559730
$560$	3.20718	0.135528
$561$	−11.7916	−0.497842
$562$	−39.0379	−1.64672
$563$	−28.4638	−1.19960	−0.599802	−	0.800148i	$-0.704754\pi$
$563$	−28.4638	−1.19960	−0.599802	+	0.800148i	$0.704754\pi$
$564$	−27.1750	−1.14427
$565$	−4.54010	−0.191003
$566$	2.12591	0.0893587
$567$	2.68769	0.112872
$568$	12.1610	0.510263
$569$	−23.4160	−0.981650	−0.490825	−	0.871258i	$-0.663305\pi$
$569$	−23.4160	−0.981650	−0.490825	+	0.871258i	$0.663305\pi$
$570$	11.4272	0.478634
$571$	−27.7694	−1.16211	−0.581056	−	0.813864i	$-0.697360\pi$
$571$	−27.7694	−1.16211	−0.581056	+	0.813864i	$0.697360\pi$
$572$	34.1330	1.42717
$573$	−6.87606	−0.287251
$574$	−53.0426	−2.21396
$575$	−12.3771	−0.516159
$576$	−12.5512	−0.522966
$577$	−21.3672	−0.889528	−0.444764	−	0.895648i	$-0.646712\pi$
$577$	−21.3672	−0.889528	−0.444764	+	0.895648i	$0.646712\pi$
$578$	29.0987	1.21035
$579$	−10.9795	−0.456292
$580$	−2.04032	−0.0847195
$581$	8.41375	0.349061
$582$	−39.4147	−1.63379
$583$	−32.2173	−1.33430
$584$	−1.36871	−0.0566376
$585$	−1.30514	−0.0539611
$586$	58.6422	2.42249
$587$	23.8070	0.982619	0.491309	−	0.870985i	$-0.336518\pi$
$587$	23.8070	0.982619	0.491309	+	0.870985i	$0.336518\pi$
$588$	0.621944	0.0256485
$589$	64.3808	2.65277
$590$	10.6196	0.437202
$591$	−4.66023	−0.191696
$592$	5.10929	0.209990
$593$	14.3937	0.591078	0.295539	−	0.955331i	$-0.404501\pi$
$593$	14.3937	0.591078	0.295539	+	0.955331i	$0.404501\pi$
$594$	−13.4187	−0.550576
$595$	3.36984	0.138150
$596$	−47.3814	−1.94082
$597$	3.82920	0.156719
$598$	−11.8331	−0.483891
$599$	−27.3054	−1.11567	−0.557835	−	0.829952i	$-0.688368\pi$
$599$	−27.3054	−1.11567	−0.557835	+	0.829952i	$0.688368\pi$
$600$	7.80947	0.318820
$601$	−25.4834	−1.03949	−0.519745	−	0.854322i	$-0.673973\pi$
$601$	−25.4834	−1.03949	−0.519745	+	0.854322i	$0.673973\pi$
$602$	−38.8843	−1.58480
$603$	14.8687	0.605498
$604$	−50.5203	−2.05564
$605$	−17.3993	−0.707380
$606$	22.3275	0.906994
$607$	23.4614	0.952269	0.476134	−	0.879372i	$-0.342038\pi$
$607$	23.4614	0.952269	0.476134	+	0.879372i	$0.342038\pi$
$608$	59.3693	2.40774
$609$	3.02193	0.122455
$610$	2.83546	0.114804
$611$	−19.5450	−0.790707
$612$	−5.34304	−0.215980
$613$	−26.1108	−1.05461	−0.527303	−	0.849677i	$-0.676797\pi$
$613$	−26.1108	−1.05461	−0.527303	+	0.849677i	$0.676797\pi$
$614$	−1.48012	−0.0597328
$615$	−5.88995	−0.237506
$616$	−28.1609	−1.13464
$617$	41.7210	1.67962	0.839811	−	0.542879i	$-0.182666\pi$
$617$	41.7210	1.67962	0.839811	+	0.542879i	$0.182666\pi$
$618$	−32.5040	−1.30750
$619$	4.44877	0.178811	0.0894055	−	0.995995i	$-0.471503\pi$
$619$	4.44877	0.178811	0.0894055	+	0.995995i	$0.471503\pi$
$620$	−14.5874	−0.585842
$621$	2.70586	0.108582
$622$	46.2026	1.85256
$623$	−38.5880	−1.54599
$624$	−3.65737	−0.146412
$625$	18.7939	0.751756
$626$	−60.7367	−2.42753
$627$	49.1508	1.96290
$628$	35.4917	1.41627
$629$	5.36842	0.214053
$630$	3.83484	0.152784
$631$	−21.3634	−0.850464	−0.425232	−	0.905084i	$-0.639807\pi$
$631$	−21.3634	−0.850464	−0.425232	+	0.905084i	$0.639807\pi$
$632$	5.83780	0.232215
$633$	−18.5482	−0.737224
$634$	73.3049	2.91131
$635$	−0.912408	−0.0362078
$636$	−14.5984	−0.578864
$637$	0.447319	0.0177234
$638$	−15.0875	−0.597318
$639$	−7.12294	−0.281779
$640$	−8.23358	−0.325461
$641$	21.8440	0.862785	0.431393	−	0.902164i	$-0.358022\pi$
$641$	21.8440	0.862785	0.431393	+	0.902164i	$0.358022\pi$
$642$	−8.54182	−0.337119
$643$	−22.9196	−0.903860	−0.451930	−	0.892053i	$-0.649264\pi$
$643$	−22.9196	−0.903860	−0.451930	+	0.892053i	$0.649264\pi$
$644$	20.2236	0.796921
$645$	−4.31778	−0.170013
$646$	33.6463	1.32380
$647$	6.73789	0.264894	0.132447	−	0.991190i	$-0.457717\pi$
$647$	6.73789	0.264894	0.132447	+	0.991190i	$0.457717\pi$
$648$	−1.70730	−0.0670690
$649$	45.6771	1.79298
$650$	20.0035	0.784601
$651$	21.6054	0.846784
$652$	−20.8834	−0.817857
$653$	26.3951	1.03292	0.516461	−	0.856311i	$-0.327249\pi$
$653$	26.3951	1.03292	0.516461	+	0.856311i	$0.327249\pi$
$654$	8.56089	0.334757
$655$	5.73294	0.224005
$656$	−16.5053	−0.644422
$657$	0.801682	0.0312766
$658$	57.4282	2.23878
$659$	29.4785	1.14832	0.574159	−	0.818744i	$-0.305329\pi$
$659$	29.4785	1.14832	0.574159	+	0.818744i	$0.305329\pi$
$660$	−11.1366	−0.433490
$661$	−44.0953	−1.71511	−0.857554	−	0.514394i	$-0.828017\pi$
$661$	−44.0953	−1.71511	−0.857554	+	0.514394i	$0.828017\pi$
$662$	−31.1414	−1.21034
$663$	−3.84286	−0.149244
$664$	−5.34466	−0.207413
$665$	−14.0465	−0.544699
$666$	6.10920	0.236727
$667$	3.04236	0.117801
$668$	−36.2708	−1.40336
$669$	1.92216	0.0743149
$670$	21.2149	0.819602
$671$	12.1959	0.470817
$672$	19.9236	0.768571
$673$	40.6645	1.56750	0.783752	−	0.621074i	$-0.213304\pi$
$673$	40.6645	1.56750	0.783752	+	0.621074i	$0.213304\pi$
$674$	−54.4206	−2.09620
$675$	−4.57417	−0.176060
$676$	−25.0269	−0.962574
$677$	40.2436	1.54669	0.773344	−	0.633987i	$-0.218583\pi$
$677$	40.2436	1.54669	0.773344	+	0.633987i	$0.218583\pi$
$678$	−15.2125	−0.584232
$679$	48.4490	1.85930
$680$	−2.14062	−0.0820892
$681$	16.8012	0.643823
$682$	−107.869	−4.13050
$683$	13.1245	0.502196	0.251098	−	0.967962i	$-0.419208\pi$
$683$	13.1245	0.502196	0.251098	+	0.967962i	$0.419208\pi$
$684$	22.2714	0.851567
$685$	8.81891	0.336953
$686$	39.8222	1.52042
$687$	−24.5007	−0.934759
$688$	−12.0996	−0.461293
$689$	−10.4996	−0.400002
$690$	3.86077	0.146977
$691$	−49.2232	−1.87254	−0.936269	−	0.351285i	$-0.885745\pi$
$691$	−49.2232	−1.87254	−0.936269	+	0.351285i	$0.885745\pi$
$692$	55.2381	2.09984
$693$	16.4944	0.626572
$694$	56.2438	2.13498
$695$	6.42952	0.243886
$696$	−1.91962	−0.0727629
$697$	−17.3424	−0.656889
$698$	−23.1643	−0.876782
$699$	−17.0879	−0.646323
$700$	−34.1874	−1.29216
$701$	48.4682	1.83062	0.915310	−	0.402749i	$-0.131945\pi$
$701$	48.4682	1.83062	0.915310	+	0.402749i	$0.131945\pi$
$702$	−4.37313	−0.165053
$703$	−22.3771	−0.843970
$704$	−77.0271	−2.90307
$705$	6.37694	0.240169
$706$	−27.3030	−1.02756
$707$	−27.4453	−1.03219
$708$	20.6973	0.777853
$709$	−1.36550	−0.0512825	−0.0256413	−	0.999671i	$-0.508163\pi$
$709$	−1.36550	−0.0512825	−0.0256413	+	0.999671i	$0.508163\pi$
$710$	−10.1631	−0.381416
$711$	−3.41932	−0.128235
$712$	24.5122	0.918634
$713$	21.7515	0.814601
$714$	11.2913	0.422566
$715$	−8.00972	−0.299547
$716$	−36.8570	−1.37741
$717$	−15.4605	−0.577382
$718$	−24.5341	−0.915604
$719$	−14.8131	−0.552437	−0.276218	−	0.961095i	$-0.589081\pi$
$719$	−14.8131	−0.552437	−0.276218	+	0.961095i	$0.589081\pi$
$720$	1.19329	0.0444712
$721$	39.9543	1.48798
$722$	−98.7040	−3.67338
$723$	−18.8038	−0.699322
$724$	55.8488	2.07561
$725$	−5.14301	−0.191007
$726$	−58.2995	−2.16370
$727$	30.5074	1.13146	0.565729	−	0.824591i	$-0.308595\pi$
$727$	30.5074	1.13146	0.565729	+	0.824591i	$0.308595\pi$
$728$	−9.17759	−0.340144
$729$	1.00000	0.0370370
$730$	1.14385	0.0423360
$731$	−12.7133	−0.470218
$732$	5.52623	0.204255
$733$	−3.44415	−0.127212	−0.0636062	−	0.997975i	$-0.520260\pi$
$733$	−3.44415	−0.127212	−0.0636062	+	0.997975i	$0.520260\pi$
$734$	12.3397	0.455468
$735$	−0.145946	−0.00538332
$736$	20.0583	0.739361
$737$	91.2495	3.36122
$738$	−19.7354	−0.726471
$739$	13.8353	0.508940	0.254470	−	0.967081i	$-0.418099\pi$
$739$	13.8353	0.508940	0.254470	+	0.967081i	$0.418099\pi$
$740$	5.07019	0.186384
$741$	16.0182	0.588442
$742$	30.8504	1.13255
$743$	−32.7485	−1.20143	−0.600713	−	0.799465i	$-0.705116\pi$
$743$	−32.7485	−1.20143	−0.600713	+	0.799465i	$0.705116\pi$
$744$	−13.7244	−0.503161
$745$	11.1186	0.407354
$746$	26.0990	0.955554
$747$	3.13048	0.114538
$748$	−32.7905	−1.19894
$749$	10.4997	0.383651
$750$	−13.6606	−0.498815
$751$	−47.7375	−1.74197	−0.870983	−	0.491314i	$-0.836517\pi$
$751$	−47.7375	−1.74197	−0.870983	+	0.491314i	$0.836517\pi$
$752$	17.8699	0.651649
$753$	−3.37724	−0.123074
$754$	−4.91698	−0.179066
$755$	11.8552	0.431454
$756$	7.47400	0.271827
$757$	6.55990	0.238423	0.119212	−	0.992869i	$-0.461963\pi$
$757$	6.55990	0.238423	0.119212	+	0.992869i	$0.461963\pi$
$758$	32.2139	1.17006
$759$	16.6060	0.602758
$760$	8.92274	0.323662
$761$	10.7896	0.391123	0.195561	−	0.980691i	$-0.437347\pi$
$761$	10.7896	0.391123	0.195561	+	0.980691i	$0.437347\pi$
$762$	−3.05720	−0.110751
$763$	−10.5232	−0.380964
$764$	−19.1212	−0.691779
$765$	1.25381	0.0453315
$766$	−31.5841	−1.14118
$767$	14.8861	0.537505
$768$	−2.48581	−0.0896991
$769$	−18.7574	−0.676408	−0.338204	−	0.941073i	$-0.609819\pi$
$769$	−18.7574	−0.676408	−0.338204	+	0.941073i	$0.609819\pi$
$770$	23.5346	0.848127
$771$	19.3182	0.695727
$772$	−30.5321	−1.09888
$773$	16.7113	0.601062	0.300531	−	0.953772i	$-0.402836\pi$
$773$	16.7113	0.601062	0.300531	+	0.953772i	$0.402836\pi$
$774$	−14.4676	−0.520026
$775$	−36.7703	−1.32083
$776$	−30.7762	−1.10480
$777$	−7.50950	−0.269402
$778$	52.4641	1.88093
$779$	72.2881	2.58999
$780$	−3.62939	−0.129953
$781$	−43.7138	−1.56420
$782$	11.3677	0.406506
$783$	1.12436	0.0401813
$784$	−0.408982	−0.0146065
$785$	−8.32856	−0.297259
$786$	19.2093	0.685174
$787$	34.2776	1.22186	0.610932	−	0.791683i	$-0.290795\pi$
$787$	34.2776	1.22186	0.610932	+	0.791683i	$0.290795\pi$
$788$	−12.9593	−0.461656
$789$	0.619074	0.0220396
$790$	−4.87875	−0.173578
$791$	18.6994	0.664873
$792$	−10.4778	−0.372311
$793$	3.97462	0.141143
$794$	66.1203	2.34652
$795$	3.42569	0.121497
$796$	10.6484	0.377422
$797$	28.1692	0.997804	0.498902	−	0.866658i	$-0.333737\pi$
$797$	28.1692	0.997804	0.498902	+	0.866658i	$0.333737\pi$
$798$	−47.0654	−1.66610
$799$	18.7763	0.664256
$800$	−33.9080	−1.19883
$801$	−14.3573	−0.507291
$802$	−47.9652	−1.69371
$803$	4.91995	0.173621
$804$	41.3472	1.45820
$805$	−4.74571	−0.167264
$806$	−35.1542	−1.23825
$807$	7.64782	0.269216
$808$	17.4340	0.613327
$809$	52.6841	1.85228	0.926138	−	0.377186i	$-0.123108\pi$
$809$	52.6841	1.85228	0.926138	+	0.377186i	$0.123108\pi$
$810$	1.42682	0.0501333
$811$	39.2479	1.37818	0.689090	−	0.724676i	$-0.258011\pi$
$811$	39.2479	1.37818	0.689090	+	0.724676i	$0.258011\pi$
$812$	8.40347	0.294904
$813$	1.12885	0.0395906
$814$	37.4924	1.31411
$815$	4.90054	0.171658
$816$	3.51351	0.122998
$817$	52.9927	1.85398
$818$	47.2223	1.65109
$819$	5.37551	0.187835
$820$	−16.3790	−0.571979
$821$	41.0399	1.43230	0.716152	−	0.697944i	$-0.245902\pi$
$821$	41.0399	1.43230	0.716152	+	0.697944i	$0.245902\pi$
$822$	29.5494	1.03066
$823$	−34.5116	−1.20300	−0.601499	−	0.798873i	$-0.705430\pi$
$823$	−34.5116	−1.20300	−0.601499	+	0.798873i	$0.705430\pi$
$824$	−25.3802	−0.884160
$825$	−28.0719	−0.977337
$826$	−43.7391	−1.52188
$827$	8.41939	0.292771	0.146386	−	0.989228i	$-0.453236\pi$
$827$	8.41939	0.292771	0.146386	+	0.989228i	$0.453236\pi$
$828$	7.52454	0.261496
$829$	40.6329	1.41124	0.705620	−	0.708590i	$-0.250669\pi$
$829$	40.6329	1.41124	0.705620	+	0.708590i	$0.250669\pi$
$830$	4.46663	0.155039
$831$	−31.2374	−1.08361
$832$	−25.1030	−0.870290
$833$	−0.429725	−0.0148891
$834$	21.5434	0.745985
$835$	8.51136	0.294548
$836$	136.680	4.72718
$837$	8.03868	0.277857
$838$	23.3565	0.806838
$839$	34.5638	1.19327	0.596637	−	0.802511i	$-0.296503\pi$
$839$	34.5638	1.19327	0.596637	+	0.802511i	$0.296503\pi$
$840$	2.99437	0.103315
$841$	−27.7358	−0.956407
$842$	15.4022	0.530796
$843$	17.8540	0.614924
$844$	−51.5794	−1.77544
$845$	5.87286	0.202033
$846$	21.3672	0.734618
$847$	71.6625	2.46235
$848$	9.59971	0.329655
$849$	−0.972284	−0.0333687
$850$	−19.2167	−0.659126
$851$	−7.56028	−0.259163
$852$	−19.8077	−0.678601
$853$	37.9728	1.30016	0.650082	−	0.759864i	$-0.274735\pi$
$853$	37.9728	1.30016	0.650082	+	0.759864i	$0.274735\pi$
$854$	−11.6784	−0.399627
$855$	−5.22624	−0.178734
$856$	−6.66972	−0.227966
$857$	−41.7626	−1.42658	−0.713291	−	0.700868i	$-0.752796\pi$
$857$	−41.7626	−1.42658	−0.713291	+	0.700868i	$0.752796\pi$
$858$	−26.8381	−0.916238
$859$	0.450663	0.0153764	0.00768822	−	0.999970i	$-0.497553\pi$
$859$	0.450663	0.0153764	0.00768822	+	0.999970i	$0.497553\pi$
$860$	−12.0070	−0.409436
$861$	24.2590	0.826745
$862$	76.1956	2.59523
$863$	−39.0769	−1.33019	−0.665097	−	0.746757i	$-0.731610\pi$
$863$	−39.0769	−1.33019	−0.665097	+	0.746757i	$0.731610\pi$
$864$	7.41293	0.252193
$865$	−12.9623	−0.440731
$866$	−45.2981	−1.53929
$867$	−13.3083	−0.451973
$868$	60.0811	2.03929
$869$	−20.9845	−0.711850
$870$	1.60426	0.0543895
$871$	29.7381	1.00764
$872$	6.68462	0.226370
$873$	18.0263	0.610097
$874$	−47.3837	−1.60278
$875$	16.7918	0.567666
$876$	2.22934	0.0753225
$877$	6.02916	0.203590	0.101795	−	0.994805i	$-0.467541\pi$
$877$	6.02916	0.203590	0.101795	+	0.994805i	$0.467541\pi$
$878$	−12.6946	−0.428423
$879$	−26.8200	−0.904616
$880$	7.32325	0.246867
$881$	8.76369	0.295256	0.147628	−	0.989043i	$-0.452836\pi$
$881$	8.76369	0.295256	0.147628	+	0.989043i	$0.452836\pi$
$882$	−0.489022	−0.0164662
$883$	55.2541	1.85945	0.929725	−	0.368255i	$-0.120045\pi$
$883$	55.2541	1.85945	0.929725	+	0.368255i	$0.120045\pi$
$884$	−10.6864	−0.359421
$885$	−4.85687	−0.163262
$886$	82.1443	2.75969
$887$	0.260653	0.00875187	0.00437594	−	0.999990i	$-0.498607\pi$
$887$	0.260653	0.00875187	0.00437594	+	0.999990i	$0.498607\pi$
$888$	4.77026	0.160079
$889$	3.75794	0.126037
$890$	−20.4853	−0.686669
$891$	6.13704	0.205599
$892$	5.34519	0.178970
$893$	−78.2649	−2.61904
$894$	37.2550	1.24599
$895$	8.64894	0.289102
$896$	33.9117	1.13291
$897$	5.41186	0.180697
$898$	0.313327	0.0104558
$899$	9.03837	0.301446
$900$	−12.7200	−0.424000
$901$	10.0866	0.336033
$902$	−121.117	−4.03276
$903$	17.7837	0.591805
$904$	−11.8784	−0.395069
$905$	−13.1056	−0.435645
$906$	39.7231	1.31971
$907$	−42.6676	−1.41675	−0.708377	−	0.705834i	$-0.750572\pi$
$907$	−42.6676	−1.41675	−0.708377	+	0.705834i	$0.750572\pi$
$908$	46.7213	1.55050
$909$	−10.2115	−0.338694
$910$	7.66988	0.254254
$911$	41.5197	1.37561	0.687804	−	0.725896i	$-0.258575\pi$
$911$	41.5197	1.37561	0.687804	+	0.725896i	$0.258575\pi$
$912$	−14.6453	−0.484956
$913$	19.2119	0.635821
$914$	−21.2315	−0.702277
$915$	−1.29679	−0.0428707
$916$	−68.1323	−2.25115
$917$	−23.6123	−0.779747
$918$	4.20113	0.138658
$919$	−35.2159	−1.16167	−0.580833	−	0.814023i	$-0.697273\pi$
$919$	−35.2159	−1.16167	−0.580833	+	0.814023i	$0.697273\pi$
$920$	3.01461	0.0993888
$921$	0.676932	0.0223057
$922$	0.295175	0.00972107
$923$	−14.2462	−0.468921
$924$	45.8682	1.50895
$925$	12.7804	0.420217
$926$	−61.6600	−2.02627
$927$	14.8657	0.488253
$928$	8.33480	0.273603
$929$	−18.3817	−0.603083	−0.301542	−	0.953453i	$-0.597501\pi$
$929$	−18.3817	−0.603083	−0.301542	+	0.953453i	$0.597501\pi$
$930$	11.4697	0.376108
$931$	1.79122	0.0587048
$932$	−47.5185	−1.55652
$933$	−21.1307	−0.691789
$934$	41.8327	1.36881
$935$	7.69467	0.251643
$936$	−3.41468	−0.111612
$937$	−32.7210	−1.06895	−0.534474	−	0.845185i	$-0.679490\pi$
$937$	−32.7210	−1.06895	−0.534474	+	0.845185i	$0.679490\pi$
$938$	−87.3779	−2.85299
$939$	27.7779	0.906497
$940$	17.7332	0.578393
$941$	−21.7375	−0.708623	−0.354311	−	0.935128i	$-0.615285\pi$
$941$	−21.7375	−0.708623	−0.354311	+	0.935128i	$0.615285\pi$
$942$	−27.9064	−0.909241
$943$	24.4230	0.795324
$944$	−13.6103	−0.442977
$945$	−1.75386	−0.0570532
$946$	−88.7880	−2.88675
$947$	10.0913	0.327923	0.163962	−	0.986467i	$-0.447573\pi$
$947$	10.0913	0.327923	0.163962	+	0.986467i	$0.447573\pi$
$948$	−9.50855	−0.308823
$949$	1.60340	0.0520487
$950$	80.1007	2.59881
$951$	−33.5260	−1.08715
$952$	8.81661	0.285748
$953$	20.2619	0.656349	0.328174	−	0.944617i	$-0.393567\pi$
$953$	20.2619	0.656349	0.328174	+	0.944617i	$0.393567\pi$
$954$	11.4784	0.371627
$955$	4.48701	0.145196
$956$	−42.9930	−1.39049
$957$	6.90024	0.223053
$958$	−51.3783	−1.65996
$959$	−36.3225	−1.17292
$960$	8.19034	0.264342
$961$	33.6203	1.08453
$962$	12.2187	0.393947
$963$	3.90660	0.125888
$964$	−52.2903	−1.68416
$965$	7.16473	0.230641
$966$	−15.9014	−0.511619
$967$	49.8507	1.60309	0.801546	−	0.597933i	$-0.204011\pi$
$967$	49.8507	1.60309	0.801546	+	0.597933i	$0.204011\pi$
$968$	−45.5221	−1.46314
$969$	−15.3881	−0.494338
$970$	25.7203	0.825828
$971$	10.2722	0.329650	0.164825	−	0.986323i	$-0.447294\pi$
$971$	10.2722	0.329650	0.164825	+	0.986323i	$0.447294\pi$
$972$	2.78083	0.0891952
$973$	−26.4813	−0.848953
$974$	−47.8859	−1.53436
$975$	−9.14858	−0.292989
$976$	−3.63397	−0.116321
$977$	−15.7281	−0.503187	−0.251593	−	0.967833i	$-0.580955\pi$
$977$	−15.7281	−0.503187	−0.251593	+	0.967833i	$0.580955\pi$
$978$	16.4202	0.525060
$979$	−88.1114	−2.81605
$980$	−0.405853	−0.0129645
$981$	−3.91532	−0.125007
$982$	−40.7837	−1.30146
$983$	9.91869	0.316357	0.158179	−	0.987411i	$-0.449438\pi$
$983$	9.91869	0.316357	0.158179	+	0.987411i	$0.449438\pi$
$984$	−15.4100	−0.491254
$985$	3.04105	0.0968961
$986$	4.72358	0.150429
$987$	−26.2648	−0.836017
$988$	44.5439	1.41713
$989$	17.9039	0.569312
$990$	8.75645	0.278298
$991$	45.9476	1.45957	0.729786	−	0.683675i	$-0.239619\pi$
$991$	45.9476	1.45957	0.729786	+	0.683675i	$0.239619\pi$
$992$	59.5902	1.89199
$993$	14.2425	0.451972
$994$	41.8591	1.32769
$995$	−2.49877	−0.0792163
$996$	8.70534	0.275839
$997$	−7.02739	−0.222560	−0.111280	−	0.993789i	$-0.535495\pi$
$997$	−7.02739	−0.222560	−0.111280	+	0.993789i	$0.535495\pi$
$998$	−54.6999	−1.73150
$999$	−2.79404	−0.0883995

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.d.1.17	✓	129

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.d.1.17	✓	129	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:	\( N \)	\(=\)	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.18651 q^{2} +1.00000 q^{3} +2.78083 q^{4} -0.652555 q^{5} -2.18651 q^{6} +2.68769 q^{7} -1.70730 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.18651 q^{2} +1.00000 q^{3} +2.78083 q^{4} -0.652555 q^{5} -2.18651 q^{6} +2.68769 q^{7} -1.70730 q^{8} +1.00000 q^{9} +1.42682 q^{10} +6.13704 q^{11} +2.78083 q^{12} +2.00005 q^{13} -5.87666 q^{14} -0.652555 q^{15} -1.82864 q^{16} -1.92138 q^{17} -2.18651 q^{18} +8.00888 q^{19} -1.81465 q^{20} +2.68769 q^{21} -13.4187 q^{22} +2.70586 q^{23} -1.70730 q^{24} -4.57417 q^{25} -4.37313 q^{26} +1.00000 q^{27} +7.47400 q^{28} +1.12436 q^{29} +1.42682 q^{30} +8.03868 q^{31} +7.41293 q^{32} +6.13704 q^{33} +4.20113 q^{34} -1.75386 q^{35} +2.78083 q^{36} -2.79404 q^{37} -17.5115 q^{38} +2.00005 q^{39} +1.11411 q^{40} +9.02599 q^{41} -5.87666 q^{42} +6.61674 q^{43} +17.0661 q^{44} -0.652555 q^{45} -5.91639 q^{46} -9.77226 q^{47} -1.82864 q^{48} +0.223654 q^{49} +10.0015 q^{50} -1.92138 q^{51} +5.56181 q^{52} -5.24965 q^{53} -2.18651 q^{54} -4.00476 q^{55} -4.58868 q^{56} +8.00888 q^{57} -2.45843 q^{58} +7.44285 q^{59} -1.81465 q^{60} +1.98726 q^{61} -17.5767 q^{62} +2.68769 q^{63} -12.5512 q^{64} -1.30514 q^{65} -13.4187 q^{66} +14.8687 q^{67} -5.34304 q^{68} +2.70586 q^{69} +3.83484 q^{70} -7.12294 q^{71} -1.70730 q^{72} +0.801682 q^{73} +6.10920 q^{74} -4.57417 q^{75} +22.2714 q^{76} +16.4944 q^{77} -4.37313 q^{78} -3.41932 q^{79} +1.19329 q^{80} +1.00000 q^{81} -19.7354 q^{82} +3.13048 q^{83} +7.47400 q^{84} +1.25381 q^{85} -14.4676 q^{86} +1.12436 q^{87} -10.4778 q^{88} -14.3573 q^{89} +1.42682 q^{90} +5.37551 q^{91} +7.52454 q^{92} +8.03868 q^{93} +21.3672 q^{94} -5.22624 q^{95} +7.41293 q^{96} +18.0263 q^{97} -0.489022 q^{98} +6.13704 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9}+O(q^{10}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9} + 41 q^{10} + 51 q^{11} + 151 q^{12} + 56 q^{13} + 5 q^{14} + 16 q^{15} + 195 q^{16} + 18 q^{17} + 15 q^{18} + 93 q^{19} + 44 q^{20} + 61 q^{21} + 46 q^{22} + 50 q^{23} + 42 q^{24} + 193 q^{25} + q^{26} + 129 q^{27} + 145 q^{28} + 24 q^{29} + 41 q^{30} + 67 q^{31} + 89 q^{32} + 51 q^{33} + 73 q^{34} + 56 q^{35} + 151 q^{36} + 95 q^{37} + 9 q^{38} + 56 q^{39} + 103 q^{40} + 7 q^{41} + 5 q^{42} + 150 q^{43} + 69 q^{44} + 16 q^{45} + 72 q^{46} + 53 q^{47} + 195 q^{48} + 240 q^{49} + 17 q^{50} + 18 q^{51} + 124 q^{52} + 34 q^{53} + 15 q^{54} + 66 q^{55} - 17 q^{56} + 93 q^{57} + 57 q^{58} + 49 q^{59} + 44 q^{60} + 113 q^{61} + 27 q^{62} + 61 q^{63} + 262 q^{64} + 22 q^{65} + 46 q^{66} + 185 q^{67} + 2 q^{68} + 50 q^{69} + 25 q^{70} + 41 q^{71} + 42 q^{72} + 153 q^{73} - q^{74} + 193 q^{75} + 190 q^{76} + 39 q^{77} + q^{78} + 101 q^{79} + 48 q^{80} + 129 q^{81} + 15 q^{82} + 162 q^{83} + 145 q^{84} + 99 q^{85} + 13 q^{86} + 24 q^{87} + 86 q^{88} - 4 q^{89} + 41 q^{90} + 117 q^{91} + 56 q^{92} + 67 q^{93} + 49 q^{94} + 71 q^{95} + 89 q^{96} + 159 q^{97} + 40 q^{98} + 51 q^{99}+O(q^{100}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9 + 41 * q^10 + 51 * q^11 + 151 * q^12 + 56 * q^13 + 5 * q^14 + 16 * q^15 + 195 * q^16 + 18 * q^17 + 15 * q^18 + 93 * q^19 + 44 * q^20 + 61 * q^21 + 46 * q^22 + 50 * q^23 + 42 * q^24 + 193 * q^25 + q^26 + 129 * q^27 + 145 * q^28 + 24 * q^29 + 41 * q^30 + 67 * q^31 + 89 * q^32 + 51 * q^33 + 73 * q^34 + 56 * q^35 + 151 * q^36 + 95 * q^37 + 9 * q^38 + 56 * q^39 + 103 * q^40 + 7 * q^41 + 5 * q^42 + 150 * q^43 + 69 * q^44 + 16 * q^45 + 72 * q^46 + 53 * q^47 + 195 * q^48 + 240 * q^49 + 17 * q^50 + 18 * q^51 + 124 * q^52 + 34 * q^53 + 15 * q^54 + 66 * q^55 - 17 * q^56 + 93 * q^57 + 57 * q^58 + 49 * q^59 + 44 * q^60 + 113 * q^61 + 27 * q^62 + 61 * q^63 + 262 * q^64 + 22 * q^65 + 46 * q^66 + 185 * q^67 + 2 * q^68 + 50 * q^69 + 25 * q^70 + 41 * q^71 + 42 * q^72 + 153 * q^73 - q^74 + 193 * q^75 + 190 * q^76 + 39 * q^77 + q^78 + 101 * q^79 + 48 * q^80 + 129 * q^81 + 15 * q^82 + 162 * q^83 + 145 * q^84 + 99 * q^85 + 13 * q^86 + 24 * q^87 + 86 * q^88 - 4 * q^89 + 41 * q^90 + 117 * q^91 + 56 * q^92 + 67 * q^93 + 49 * q^94 + 71 * q^95 + 89 * q^96 + 159 * q^97 + 40 * q^98 + 51 * q^99

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