LMFDB - Embedded newform 6029.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6029,2,Mod(1,6029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6029, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6029 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6029.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1418073786$
Analytic rank:	$1$
Dimension:	$234$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.80022 q^{2} +1.58457 q^{3} +5.84121 q^{4} +4.15609 q^{5} -4.43714 q^{6} -3.16901 q^{7} -10.7562 q^{8} -0.489138 q^{9} +O(q^{10})$	\(q-2.80022 q^{2} +1.58457 q^{3} +5.84121 q^{4} +4.15609 q^{5} -4.43714 q^{6} -3.16901 q^{7} -10.7562 q^{8} -0.489138 q^{9} -11.6379 q^{10} -2.40992 q^{11} +9.25580 q^{12} -1.53495 q^{13} +8.87392 q^{14} +6.58561 q^{15} +18.4373 q^{16} +2.66666 q^{17} +1.36969 q^{18} -0.944943 q^{19} +24.2766 q^{20} -5.02152 q^{21} +6.74830 q^{22} +3.96705 q^{23} -17.0440 q^{24} +12.2731 q^{25} +4.29820 q^{26} -5.52878 q^{27} -18.5109 q^{28} -4.07587 q^{29} -18.4411 q^{30} -1.89498 q^{31} -30.1160 q^{32} -3.81869 q^{33} -7.46724 q^{34} -13.1707 q^{35} -2.85716 q^{36} +6.09196 q^{37} +2.64605 q^{38} -2.43224 q^{39} -44.7038 q^{40} +7.62325 q^{41} +14.0613 q^{42} -10.2910 q^{43} -14.0768 q^{44} -2.03290 q^{45} -11.1086 q^{46} -4.33913 q^{47} +29.2152 q^{48} +3.04265 q^{49} -34.3672 q^{50} +4.22552 q^{51} -8.96598 q^{52} -8.34417 q^{53} +15.4818 q^{54} -10.0158 q^{55} +34.0866 q^{56} -1.49733 q^{57} +11.4133 q^{58} -10.3895 q^{59} +38.4679 q^{60} -6.02046 q^{61} +5.30635 q^{62} +1.55009 q^{63} +47.4567 q^{64} -6.37940 q^{65} +10.6931 q^{66} +14.1657 q^{67} +15.5765 q^{68} +6.28606 q^{69} +36.8808 q^{70} -12.8144 q^{71} +5.26128 q^{72} -1.30315 q^{73} -17.0588 q^{74} +19.4475 q^{75} -5.51961 q^{76} +7.63707 q^{77} +6.81080 q^{78} -8.54427 q^{79} +76.6270 q^{80} -7.29333 q^{81} -21.3468 q^{82} +2.18827 q^{83} -29.3318 q^{84} +11.0829 q^{85} +28.8170 q^{86} -6.45850 q^{87} +25.9216 q^{88} +4.24721 q^{89} +5.69256 q^{90} +4.86429 q^{91} +23.1723 q^{92} -3.00272 q^{93} +12.1505 q^{94} -3.92727 q^{95} -47.7209 q^{96} -8.88506 q^{97} -8.52007 q^{98} +1.17878 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9}+O(q^{10}) $ 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9} - 89 q^{10} - 55 q^{11} - 75 q^{12} - 49 q^{13} - 42 q^{14} - 43 q^{15} + 142 q^{16} - 40 q^{17} - 30 q^{18} - 235 q^{19} - 62 q^{20} - 62 q^{21} - 63 q^{22} - 30 q^{23} - 108 q^{24} + 170 q^{25} - 44 q^{26} - 160 q^{27} - 147 q^{28} - 76 q^{29} - 15 q^{30} - 175 q^{31} - 49 q^{32} - 43 q^{33} - 104 q^{34} - 87 q^{35} + 124 q^{36} - 77 q^{37} - 18 q^{38} - 104 q^{39} - 247 q^{40} - 60 q^{41} - 6 q^{42} - 201 q^{43} - 89 q^{44} - 102 q^{45} - 128 q^{46} - 27 q^{47} - 130 q^{48} + 123 q^{49} - 33 q^{50} - 220 q^{51} - 125 q^{52} - 34 q^{53} - 126 q^{54} - 176 q^{55} - 125 q^{56} - 17 q^{57} - 46 q^{58} - 172 q^{59} - 61 q^{60} - 243 q^{61} - 37 q^{62} - 137 q^{63} + 39 q^{64} - 31 q^{65} - 142 q^{66} - 132 q^{67} - 106 q^{68} - 115 q^{69} - 60 q^{70} - 68 q^{71} - 66 q^{72} - 109 q^{73} - 74 q^{74} - 256 q^{75} - 412 q^{76} - 32 q^{77} - 38 q^{78} - 297 q^{79} - 111 q^{80} + 142 q^{81} - 94 q^{82} - 100 q^{83} - 134 q^{84} - 90 q^{85} + q^{86} - 103 q^{87} - 143 q^{88} - 77 q^{89} - 181 q^{90} - 418 q^{91} - 19 q^{92} + 5 q^{93} - 231 q^{94} - 92 q^{95} - 189 q^{96} - 141 q^{97} - 25 q^{98} - 244 q^{99}+O(q^{100}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9 - 89 * q^10 - 55 * q^11 - 75 * q^12 - 49 * q^13 - 42 * q^14 - 43 * q^15 + 142 * q^16 - 40 * q^17 - 30 * q^18 - 235 * q^19 - 62 * q^20 - 62 * q^21 - 63 * q^22 - 30 * q^23 - 108 * q^24 + 170 * q^25 - 44 * q^26 - 160 * q^27 - 147 * q^28 - 76 * q^29 - 15 * q^30 - 175 * q^31 - 49 * q^32 - 43 * q^33 - 104 * q^34 - 87 * q^35 + 124 * q^36 - 77 * q^37 - 18 * q^38 - 104 * q^39 - 247 * q^40 - 60 * q^41 - 6 * q^42 - 201 * q^43 - 89 * q^44 - 102 * q^45 - 128 * q^46 - 27 * q^47 - 130 * q^48 + 123 * q^49 - 33 * q^50 - 220 * q^51 - 125 * q^52 - 34 * q^53 - 126 * q^54 - 176 * q^55 - 125 * q^56 - 17 * q^57 - 46 * q^58 - 172 * q^59 - 61 * q^60 - 243 * q^61 - 37 * q^62 - 137 * q^63 + 39 * q^64 - 31 * q^65 - 142 * q^66 - 132 * q^67 - 106 * q^68 - 115 * q^69 - 60 * q^70 - 68 * q^71 - 66 * q^72 - 109 * q^73 - 74 * q^74 - 256 * q^75 - 412 * q^76 - 32 * q^77 - 38 * q^78 - 297 * q^79 - 111 * q^80 + 142 * q^81 - 94 * q^82 - 100 * q^83 - 134 * q^84 - 90 * q^85 + q^86 - 103 * q^87 - 143 * q^88 - 77 * q^89 - 181 * q^90 - 418 * q^91 - 19 * q^92 + 5 * q^93 - 231 * q^94 - 92 * q^95 - 189 * q^96 - 141 * q^97 - 25 * q^98 - 244 * 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 $

$2$	−2.80022	−1.98005	−0.990026	−	0.140886i	$-0.955005\pi$
$2$	−2.80022	−1.98005	−0.990026	+	0.140886i	$0.955005\pi$
$3$	1.58457	0.914852	0.457426	−	0.889248i	$-0.348771\pi$
$3$	1.58457	0.914852	0.457426	+	0.889248i	$0.348771\pi$
$4$	5.84121	2.92060
$5$	4.15609	1.85866	0.929329	−	0.369252i	$-0.120386\pi$
$5$	4.15609	1.85866	0.929329	+	0.369252i	$0.120386\pi$
$6$	−4.43714	−1.81145
$7$	−3.16901	−1.19777	−0.598887	−	0.800833i	$-0.704390\pi$
$7$	−3.16901	−1.19777	−0.598887	+	0.800833i	$0.704390\pi$
$8$	−10.7562	−3.80290
$9$	−0.489138	−0.163046
$10$	−11.6379	−3.68024
$11$	−2.40992	−0.726618	−0.363309	−	0.931669i	$-0.618353\pi$
$11$	−2.40992	−0.726618	−0.363309	+	0.931669i	$0.618353\pi$
$12$	9.25580	2.67192
$13$	−1.53495	−0.425719	−0.212860	−	0.977083i	$-0.568278\pi$
$13$	−1.53495	−0.425719	−0.212860	+	0.977083i	$0.568278\pi$
$14$	8.87392	2.37166
$15$	6.58561	1.70040
$16$	18.4373	4.60932
$17$	2.66666	0.646761	0.323381	−	0.946269i	$-0.395181\pi$
$17$	2.66666	0.646761	0.323381	+	0.946269i	$0.395181\pi$
$18$	1.36969	0.322840
$19$	−0.944943	−0.216785	−0.108392	−	0.994108i	$-0.534570\pi$
$19$	−0.944943	−0.216785	−0.108392	+	0.994108i	$0.534570\pi$
$20$	24.2766	5.42841
$21$	−5.02152	−1.09579
$22$	6.74830	1.43874
$23$	3.96705	0.827186	0.413593	−	0.910462i	$-0.364274\pi$
$23$	3.96705	0.827186	0.413593	+	0.910462i	$0.364274\pi$
$24$	−17.0440	−3.47909
$25$	12.2731	2.45461
$26$	4.29820	0.842946
$27$	−5.52878	−1.06401
$28$	−18.5109	−3.49823
$29$	−4.07587	−0.756870	−0.378435	−	0.925628i	$-0.623538\pi$
$29$	−4.07587	−0.756870	−0.378435	+	0.925628i	$0.623538\pi$
$30$	−18.4411	−3.36687
$31$	−1.89498	−0.340348	−0.170174	−	0.985414i	$-0.554433\pi$
$31$	−1.89498	−0.340348	−0.170174	+	0.985414i	$0.554433\pi$
$32$	−30.1160	−5.32380
$33$	−3.81869	−0.664748
$34$	−7.46724	−1.28062
$35$	−13.1707	−2.22625
$36$	−2.85716	−0.476193
$37$	6.09196	1.00151	0.500756	−	0.865589i	$-0.333055\pi$
$37$	6.09196	1.00151	0.500756	+	0.865589i	$0.333055\pi$
$38$	2.64605	0.429245
$39$	−2.43224	−0.389470
$40$	−44.7038	−7.06828
$41$	7.62325	1.19055	0.595276	−	0.803521i	$-0.297043\pi$
$41$	7.62325	1.19055	0.595276	+	0.803521i	$0.297043\pi$
$42$	14.0613	2.16971
$43$	−10.2910	−1.56936	−0.784680	−	0.619901i	$-0.787173\pi$
$43$	−10.2910	−1.56936	−0.784680	+	0.619901i	$0.787173\pi$
$44$	−14.0768	−2.12216
$45$	−2.03290	−0.303047
$46$	−11.1086	−1.63787
$47$	−4.33913	−0.632927	−0.316463	−	0.948605i	$-0.602495\pi$
$47$	−4.33913	−0.632927	−0.316463	+	0.948605i	$0.602495\pi$
$48$	29.2152	4.21685
$49$	3.04265	0.434664
$50$	−34.3672	−4.86026
$51$	4.22552	0.591691
$52$	−8.96598	−1.24336
$53$	−8.34417	−1.14616	−0.573080	−	0.819500i	$-0.694251\pi$
$53$	−8.34417	−1.14616	−0.573080	+	0.819500i	$0.694251\pi$
$54$	15.4818	2.10680
$55$	−10.0158	−1.35054
$56$	34.0866	4.55501
$57$	−1.49733	−0.198326
$58$	11.4133	1.49864
$59$	−10.3895	−1.35260	−0.676299	−	0.736627i	$-0.736417\pi$
$59$	−10.3895	−1.35260	−0.676299	+	0.736627i	$0.736417\pi$
$60$	38.4679	4.96619
$61$	−6.02046	−0.770841	−0.385420	−	0.922741i	$-0.625944\pi$
$61$	−6.02046	−0.770841	−0.385420	+	0.922741i	$0.625944\pi$
$62$	5.30635	0.673907
$63$	1.55009	0.195292
$64$	47.4567	5.93208
$65$	−6.37940	−0.791267
$66$	10.6931	1.31624
$67$	14.1657	1.73061	0.865306	−	0.501244i	$-0.167124\pi$
$67$	14.1657	1.73061	0.865306	+	0.501244i	$0.167124\pi$
$68$	15.5765	1.88893
$69$	6.28606	0.756753
$70$	36.8808	4.40810
$71$	−12.8144	−1.52079	−0.760394	−	0.649461i	$-0.774994\pi$
$71$	−12.8144	−1.52079	−0.760394	+	0.649461i	$0.774994\pi$
$72$	5.26128	0.620047
$73$	−1.30315	−0.152523	−0.0762614	−	0.997088i	$-0.524298\pi$
$73$	−1.30315	−0.152523	−0.0762614	+	0.997088i	$0.524298\pi$
$74$	−17.0588	−1.98304
$75$	19.4475	2.24561
$76$	−5.51961	−0.633143
$77$	7.63707	0.870325
$78$	6.81080	0.771171
$79$	−8.54427	−0.961306	−0.480653	−	0.876911i	$-0.659600\pi$
$79$	−8.54427	−0.961306	−0.480653	+	0.876911i	$0.659600\pi$
$80$	76.6270	8.56716
$81$	−7.29333	−0.810370
$82$	−21.3468	−2.35736
$83$	2.18827	0.240194	0.120097	−	0.992762i	$-0.461679\pi$
$83$	2.18827	0.240194	0.120097	+	0.992762i	$0.461679\pi$
$84$	−29.3318	−3.20036
$85$	11.0829	1.20211
$86$	28.8170	3.10741
$87$	−6.45850	−0.692424
$88$	25.9216	2.76325
$89$	4.24721	0.450204	0.225102	−	0.974335i	$-0.427729\pi$
$89$	4.24721	0.450204	0.225102	+	0.974335i	$0.427729\pi$
$90$	5.69256	0.600049
$91$	4.86429	0.509916
$92$	23.1723	2.41588
$93$	−3.00272	−0.311368
$94$	12.1505	1.25323
$95$	−3.92727	−0.402929
$96$	−47.7209	−4.87049
$97$	−8.88506	−0.902141	−0.451071	−	0.892488i	$-0.648958\pi$
$97$	−8.88506	−0.902141	−0.451071	+	0.892488i	$0.648958\pi$
$98$	−8.52007	−0.860657
$99$	1.17878	0.118472
$100$	71.6895	7.16895
$101$	−2.08529	−0.207494	−0.103747	−	0.994604i	$-0.533083\pi$
$101$	−2.08529	−0.207494	−0.103747	+	0.994604i	$0.533083\pi$
$102$	−11.8324	−1.17158
$103$	9.16272	0.902829	0.451415	−	0.892314i	$-0.350920\pi$
$103$	9.16272	0.902829	0.451415	+	0.892314i	$0.350920\pi$
$104$	16.5103	1.61897
$105$	−20.8699	−2.03669
$106$	23.3655	2.26945
$107$	−8.28976	−0.801402	−0.400701	−	0.916209i	$-0.631233\pi$
$107$	−8.28976	−0.801402	−0.400701	+	0.916209i	$0.631233\pi$
$108$	−32.2948	−3.10757
$109$	−9.63887	−0.923236	−0.461618	−	0.887079i	$-0.652731\pi$
$109$	−9.63887	−0.923236	−0.461618	+	0.887079i	$0.652731\pi$
$110$	28.0465	2.67413
$111$	9.65313	0.916235
$112$	−58.4280	−5.52093
$113$	1.36810	0.128700	0.0643498	−	0.997927i	$-0.479503\pi$
$113$	1.36810	0.128700	0.0643498	+	0.997927i	$0.479503\pi$
$114$	4.19284	0.392696
$115$	16.4874	1.53746
$116$	−23.8080	−2.21052
$117$	0.750804	0.0694119
$118$	29.0928	2.67821
$119$	−8.45070	−0.774674
$120$	−70.8362	−6.46643
$121$	−5.19228	−0.472026
$122$	16.8586	1.52630
$123$	12.0796	1.08918
$124$	−11.0690	−0.994022
$125$	30.2275	2.70363
$126$	−4.34058	−0.386689
$127$	3.54613	0.314668	0.157334	−	0.987545i	$-0.449710\pi$
$127$	3.54613	0.314668	0.157334	+	0.987545i	$0.449710\pi$
$128$	−72.6569	−6.42203
$129$	−16.3068	−1.43573
$130$	17.8637	1.56675
$131$	−11.0650	−0.966753	−0.483376	−	0.875413i	$-0.660590\pi$
$131$	−11.0650	−0.966753	−0.483376	+	0.875413i	$0.660590\pi$
$132$	−22.3057	−1.94147
$133$	2.99454	0.259659
$134$	−39.6669	−3.42670
$135$	−22.9781	−1.97764
$136$	−28.6832	−2.45956
$137$	14.9137	1.27417	0.637083	−	0.770795i	$-0.280141\pi$
$137$	14.9137	1.27417	0.637083	+	0.770795i	$0.280141\pi$
$138$	−17.6023	−1.49841
$139$	0.889659	0.0754599	0.0377300	−	0.999288i	$-0.487987\pi$
$139$	0.889659	0.0754599	0.0377300	+	0.999288i	$0.487987\pi$
$140$	−76.9328	−6.50201
$141$	−6.87565	−0.579034
$142$	35.8831	3.01124
$143$	3.69911	0.309335
$144$	−9.01839	−0.751532
$145$	−16.9397	−1.40676
$146$	3.64911	0.302003
$147$	4.82129	0.397653
$148$	35.5844	2.92502
$149$	23.9969	1.96591	0.982953	−	0.183855i	$-0.0588578\pi$
$149$	23.9969	1.96591	0.982953	+	0.183855i	$0.0588578\pi$
$150$	−54.4573	−4.44642
$151$	−16.2702	−1.32405	−0.662023	−	0.749483i	$-0.730302\pi$
$151$	−16.2702	−1.32405	−0.662023	+	0.749483i	$0.730302\pi$
$152$	10.1640	0.824410
$153$	−1.30437	−0.105452
$154$	−21.3854	−1.72329
$155$	−7.87569	−0.632591
$156$	−14.2072	−1.13749
$157$	−5.33212	−0.425550	−0.212775	−	0.977101i	$-0.568250\pi$
$157$	−5.33212	−0.425550	−0.212775	+	0.977101i	$0.568250\pi$
$158$	23.9258	1.90344
$159$	−13.2219	−1.04857
$160$	−125.165	−9.89513
$161$	−12.5716	−0.990783
$162$	20.4229	1.60457
$163$	−13.6210	−1.06688	−0.533439	−	0.845838i	$-0.679101\pi$
$163$	−13.6210	−1.06688	−0.533439	+	0.845838i	$0.679101\pi$
$164$	44.5290	3.47713
$165$	−15.8708	−1.23554
$166$	−6.12762	−0.475596
$167$	6.17812	0.478078	0.239039	−	0.971010i	$-0.423168\pi$
$167$	6.17812	0.478078	0.239039	+	0.971010i	$0.423168\pi$
$168$	54.0126	4.16716
$169$	−10.6439	−0.818763
$170$	−31.0345	−2.38024
$171$	0.462208	0.0353459
$172$	−60.1118	−4.58348
$173$	19.8825	1.51164	0.755818	−	0.654782i	$-0.227240\pi$
$173$	19.8825	1.51164	0.755818	+	0.654782i	$0.227240\pi$
$174$	18.0852	1.37103
$175$	−38.8935	−2.94007
$176$	−44.4324	−3.34922
$177$	−16.4629	−1.23743
$178$	−11.8931	−0.891426
$179$	−23.7272	−1.77345	−0.886727	−	0.462294i	$-0.847026\pi$
$179$	−23.7272	−1.77345	−0.886727	+	0.462294i	$0.847026\pi$
$180$	−11.8746	−0.885080
$181$	−17.0985	−1.27092	−0.635462	−	0.772132i	$-0.719191\pi$
$181$	−17.0985	−1.27092	−0.635462	+	0.772132i	$0.719191\pi$
$182$	−13.6210	−1.00966
$183$	−9.53984	−0.705205
$184$	−42.6704	−3.14570
$185$	25.3187	1.86147
$186$	8.40828	0.616525
$187$	−6.42645	−0.469949
$188$	−25.3458	−1.84853
$189$	17.5208	1.27445
$190$	10.9972	0.797820
$191$	−18.0860	−1.30866	−0.654328	−	0.756211i	$-0.727048\pi$
$191$	−18.0860	−1.30866	−0.654328	+	0.756211i	$0.727048\pi$
$192$	75.1984	5.42698
$193$	1.42737	0.102745	0.0513723	−	0.998680i	$-0.483641\pi$
$193$	1.42737	0.102745	0.0513723	+	0.998680i	$0.483641\pi$
$194$	24.8801	1.78629
$195$	−10.1086	−0.723892
$196$	17.7727	1.26948
$197$	1.19023	0.0848006	0.0424003	−	0.999101i	$-0.486500\pi$
$197$	1.19023	0.0848006	0.0424003	+	0.999101i	$0.486500\pi$
$198$	−3.30085	−0.234581
$199$	14.6131	1.03589	0.517947	−	0.855413i	$-0.326697\pi$
$199$	14.6131	1.03589	0.517947	+	0.855413i	$0.326697\pi$
$200$	−132.012	−9.33463
$201$	22.4465	1.58325
$202$	5.83926	0.410849
$203$	12.9165	0.906560
$204$	24.6821	1.72809
$205$	31.6829	2.21283
$206$	−25.6576	−1.78765
$207$	−1.94043	−0.134870
$208$	−28.3004	−1.96228
$209$	2.27724	0.157520
$210$	58.4402	4.03276
$211$	4.10287	0.282453	0.141227	−	0.989977i	$-0.454895\pi$
$211$	4.10287	0.282453	0.141227	+	0.989977i	$0.454895\pi$
$212$	−48.7400	−3.34748
$213$	−20.3053	−1.39130
$214$	23.2131	1.58682
$215$	−42.7702	−2.91690
$216$	59.4688	4.04634
$217$	6.00521	0.407660
$218$	26.9909	1.82806
$219$	−2.06494	−0.139536
$220$	−58.5046	−3.94438
$221$	−4.09320	−0.275339
$222$	−27.0309	−1.81419
$223$	2.45016	0.164075	0.0820375	−	0.996629i	$-0.473857\pi$
$223$	2.45016	0.164075	0.0820375	+	0.996629i	$0.473857\pi$
$224$	95.4380	6.37672
$225$	−6.00322	−0.400215
$226$	−3.83097	−0.254832
$227$	10.0421	0.666517	0.333258	−	0.942836i	$-0.391852\pi$
$227$	10.0421	0.666517	0.333258	+	0.942836i	$0.391852\pi$
$228$	−8.74621	−0.579232
$229$	14.2599	0.942323	0.471162	−	0.882047i	$-0.343835\pi$
$229$	14.2599	0.942323	0.471162	+	0.882047i	$0.343835\pi$
$230$	−46.1683	−3.04424
$231$	12.1015	0.796219
$232$	43.8409	2.87830
$233$	28.1392	1.84346	0.921730	−	0.387833i	$-0.126776\pi$
$233$	28.1392	1.84346	0.921730	+	0.387833i	$0.126776\pi$
$234$	−2.10241	−0.137439
$235$	−18.0338	−1.17640
$236$	−60.6872	−3.95040
$237$	−13.5390	−0.879452
$238$	23.6638	1.53389
$239$	23.3841	1.51259	0.756295	−	0.654231i	$-0.227007\pi$
$239$	23.3841	1.51259	0.756295	+	0.654231i	$0.227007\pi$
$240$	121.421	7.83768
$241$	−12.4228	−0.800224	−0.400112	−	0.916466i	$-0.631029\pi$
$241$	−12.4228	−0.800224	−0.400112	+	0.916466i	$0.631029\pi$
$242$	14.5395	0.934635
$243$	5.02956	0.322647
$244$	−35.1668	−2.25132
$245$	12.6455	0.807892
$246$	−33.8254	−2.15663
$247$	1.45044	0.0922895
$248$	20.3828	1.29431
$249$	3.46746	0.219742
$250$	−84.6434	−5.35332
$251$	−4.61670	−0.291404	−0.145702	−	0.989329i	$-0.546544\pi$
$251$	−4.61670	−0.291404	−0.145702	+	0.989329i	$0.546544\pi$
$252$	9.05437	0.570372
$253$	−9.56027	−0.601049
$254$	−9.92993	−0.623059
$255$	17.5616	1.09975
$256$	108.542	6.78386
$257$	−24.7242	−1.54225	−0.771126	−	0.636682i	$-0.780306\pi$
$257$	−24.7242	−1.54225	−0.771126	+	0.636682i	$0.780306\pi$
$258$	45.6625	2.84282
$259$	−19.3055	−1.19959
$260$	−37.2634	−2.31098
$261$	1.99366	0.123405
$262$	30.9844	1.91422
$263$	−8.62048	−0.531562	−0.265781	−	0.964033i	$-0.585630\pi$
$263$	−8.62048	−0.531562	−0.265781	+	0.964033i	$0.585630\pi$
$264$	41.0746	2.52797
$265$	−34.6791	−2.13032
$266$	−8.38535	−0.514139
$267$	6.73000	0.411870
$268$	82.7446	5.05443
$269$	2.08517	0.127135	0.0635674	−	0.997978i	$-0.479752\pi$
$269$	2.08517	0.127135	0.0635674	+	0.997978i	$0.479752\pi$
$270$	64.3437	3.91583
$271$	0.910909	0.0553338	0.0276669	−	0.999617i	$-0.491192\pi$
$271$	0.910909	0.0553338	0.0276669	+	0.999617i	$0.491192\pi$
$272$	49.1661	2.98113
$273$	7.70780	0.466497
$274$	−41.7617	−2.52291
$275$	−29.5771	−1.78357
$276$	36.7182	2.21018
$277$	−27.9806	−1.68119	−0.840595	−	0.541664i	$-0.817794\pi$
$277$	−27.9806	−1.68119	−0.840595	+	0.541664i	$0.817794\pi$
$278$	−2.49124	−0.149415
$279$	0.926906	0.0554924
$280$	141.667	8.46621
$281$	8.36709	0.499139	0.249569	−	0.968357i	$-0.419711\pi$
$281$	8.36709	0.499139	0.249569	+	0.968357i	$0.419711\pi$
$282$	19.2533	1.14652
$283$	2.03596	0.121025	0.0605126	−	0.998167i	$-0.480726\pi$
$283$	2.03596	0.121025	0.0605126	+	0.998167i	$0.480726\pi$
$284$	−74.8516	−4.44162
$285$	−6.22303	−0.368620
$286$	−10.3583	−0.612500
$287$	−24.1582	−1.42601
$288$	14.7309	0.868026
$289$	−9.88890	−0.581700
$290$	47.4347	2.78546
$291$	−14.0790	−0.825326
$292$	−7.61200	−0.445458
$293$	19.1136	1.11663	0.558315	−	0.829629i	$-0.311448\pi$
$293$	19.1136	1.11663	0.558315	+	0.829629i	$0.311448\pi$
$294$	−13.5006	−0.787374
$295$	−43.1797	−2.51402
$296$	−65.5264	−3.80864
$297$	13.3239	0.773133
$298$	−67.1966	−3.89260
$299$	−6.08923	−0.352149
$300$	113.597	6.55853
$301$	32.6123	1.87974
$302$	45.5599	2.62168
$303$	−3.30429	−0.189826
$304$	−17.4222	−0.999232
$305$	−25.0216	−1.43273
$306$	3.65251	0.208800
$307$	−7.56381	−0.431690	−0.215845	−	0.976428i	$-0.569251\pi$
$307$	−7.56381	−0.431690	−0.215845	+	0.976428i	$0.569251\pi$
$308$	44.6097	2.54188
$309$	14.5190	0.825955
$310$	22.0536	1.25256
$311$	13.6171	0.772156	0.386078	−	0.922466i	$-0.373830\pi$
$311$	13.6171	0.772156	0.386078	+	0.922466i	$0.373830\pi$
$312$	26.1617	1.48111
$313$	−5.07688	−0.286962	−0.143481	−	0.989653i	$-0.545830\pi$
$313$	−5.07688	−0.286962	−0.143481	+	0.989653i	$0.545830\pi$
$314$	14.9311	0.842610
$315$	6.44229	0.362982
$316$	−49.9089	−2.80759
$317$	−19.3200	−1.08512	−0.542561	−	0.840017i	$-0.682545\pi$
$317$	−19.3200	−1.08512	−0.542561	+	0.840017i	$0.682545\pi$
$318$	37.0242	2.07621
$319$	9.82252	0.549956
$320$	197.234	11.0257
$321$	−13.1357	−0.733164
$322$	35.2033	1.96180
$323$	−2.51985	−0.140208
$324$	−42.6019	−2.36677
$325$	−18.8386	−1.04498
$326$	38.1417	2.11247
$327$	−15.2735	−0.844624
$328$	−81.9973	−4.52755
$329$	13.7508	0.758104
$330$	44.4417	2.44643
$331$	−25.4491	−1.39881	−0.699404	−	0.714726i	$-0.746551\pi$
$331$	−25.4491	−1.39881	−0.699404	+	0.714726i	$0.746551\pi$
$332$	12.7821	0.701510
$333$	−2.97981	−0.163293
$334$	−17.3001	−0.946618
$335$	58.8737	3.21662
$336$	−92.5833	−5.05083
$337$	−31.1263	−1.69556	−0.847778	−	0.530352i	$-0.822060\pi$
$337$	−31.1263	−1.69556	−0.847778	+	0.530352i	$0.822060\pi$
$338$	29.8053	1.62119
$339$	2.16784	0.117741
$340$	64.7375	3.51088
$341$	4.56675	0.247303
$342$	−1.29428	−0.0699868
$343$	12.5409	0.677145
$344$	110.692	5.96811
$345$	26.1254	1.40655
$346$	−55.6752	−2.99312
$347$	−2.83749	−0.152324	−0.0761622	−	0.997095i	$-0.524267\pi$
$347$	−2.83749	−0.152324	−0.0761622	+	0.997095i	$0.524267\pi$
$348$	−37.7254	−2.02230
$349$	34.0585	1.82311	0.911554	−	0.411181i	$-0.134883\pi$
$349$	34.0585	1.82311	0.911554	+	0.411181i	$0.134883\pi$
$350$	108.910	5.82149
$351$	8.48642	0.452972
$352$	72.5771	3.86837
$353$	20.2474	1.07766	0.538831	−	0.842414i	$-0.318866\pi$
$353$	20.2474	1.07766	0.538831	+	0.842414i	$0.318866\pi$
$354$	46.0996	2.45017
$355$	−53.2577	−2.82663
$356$	24.8089	1.31487
$357$	−13.3907	−0.708712
$358$	66.4412	3.51153
$359$	−17.8457	−0.941857	−0.470929	−	0.882171i	$-0.656081\pi$
$359$	−17.8457	−0.941857	−0.470929	+	0.882171i	$0.656081\pi$
$360$	21.8663	1.15246
$361$	−18.1071	−0.953004
$362$	47.8796	2.51650
$363$	−8.22753	−0.431834
$364$	28.4133	1.48926
$365$	−5.41602	−0.283488
$366$	26.7136	1.39634
$367$	0.0381163	0.00198966	0.000994828	−	1.00000i	$-0.499683\pi$
$367$	0.0381163	0.00198966	0.000994828		1.00000i	$0.499683\pi$
$368$	73.1416	3.81277
$369$	−3.72883	−0.194115
$370$	−70.8978	−3.68580
$371$	26.4428	1.37284
$372$	−17.5395	−0.909383
$373$	−21.3659	−1.10629	−0.553143	−	0.833087i	$-0.686572\pi$
$373$	−21.3659	−1.10629	−0.553143	+	0.833087i	$0.686572\pi$
$374$	17.9954	0.930522
$375$	47.8975	2.47342
$376$	46.6726	2.40695
$377$	6.25627	0.322214
$378$	−49.0620	−2.52348
$379$	18.1989	0.934813	0.467407	−	0.884043i	$-0.345188\pi$
$379$	18.1989	0.934813	0.467407	+	0.884043i	$0.345188\pi$
$380$	−22.9400	−1.17680
$381$	5.61909	0.287875
$382$	50.6446	2.59121
$383$	−2.63328	−0.134554	−0.0672771	−	0.997734i	$-0.521431\pi$
$383$	−2.63328	−0.134554	−0.0672771	+	0.997734i	$0.521431\pi$
$384$	−115.130	−5.87520
$385$	31.7403	1.61764
$386$	−3.99695	−0.203439
$387$	5.03371	0.255878
$388$	−51.8995	−2.63480
$389$	−16.4654	−0.834828	−0.417414	−	0.908716i	$-0.637064\pi$
$389$	−16.4654	−0.834828	−0.417414	+	0.908716i	$0.637064\pi$
$390$	28.3063	1.43334
$391$	10.5788	0.534992
$392$	−32.7274	−1.65298
$393$	−17.5333	−0.884436
$394$	−3.33291	−0.167909
$395$	−35.5107	−1.78674
$396$	6.88553	0.346011
$397$	−16.0457	−0.805312	−0.402656	−	0.915351i	$-0.631913\pi$
$397$	−16.0457	−0.805312	−0.402656	+	0.915351i	$0.631913\pi$
$398$	−40.9198	−2.05112
$399$	4.74506	0.237550
$400$	226.282	11.3141
$401$	36.5715	1.82629	0.913147	−	0.407631i	$-0.133645\pi$
$401$	36.5715	1.82629	0.913147	+	0.407631i	$0.133645\pi$
$402$	−62.8550	−3.13492
$403$	2.90870	0.144893
$404$	−12.1806	−0.606008
$405$	−30.3117	−1.50620
$406$	−36.1689	−1.79503
$407$	−14.6811	−0.727717
$408$	−45.4505	−2.25014
$409$	−26.9493	−1.33255	−0.666277	−	0.745704i	$-0.732113\pi$
$409$	−26.9493	−1.33255	−0.666277	+	0.745704i	$0.732113\pi$
$410$	−88.7190	−4.38152
$411$	23.6318	1.16567
$412$	53.5213	2.63681
$413$	32.9245	1.62011
$414$	5.43363	0.267049
$415$	9.09463	0.446438
$416$	46.2266	2.26645
$417$	1.40973	0.0690346
$418$	−6.37676	−0.311897
$419$	−24.2233	−1.18338	−0.591692	−	0.806164i	$-0.701540\pi$
$419$	−24.2233	−1.18338	−0.591692	+	0.806164i	$0.701540\pi$
$420$	−121.905	−5.94837
$421$	−31.2057	−1.52087	−0.760437	−	0.649412i	$-0.775015\pi$
$421$	−31.2057	−1.52087	−0.760437	+	0.649412i	$0.775015\pi$
$422$	−11.4889	−0.559272
$423$	2.12243	0.103196
$424$	89.7516	4.35872
$425$	32.7281	1.58755
$426$	56.8592	2.75484
$427$	19.0789	0.923293
$428$	−48.4222	−2.34058
$429$	5.86150	0.282996
$430$	119.766	5.77562
$431$	−7.63410	−0.367722	−0.183861	−	0.982952i	$-0.558860\pi$
$431$	−7.63410	−0.367722	−0.183861	+	0.982952i	$0.558860\pi$
$432$	−101.936	−4.90439
$433$	14.3854	0.691319	0.345659	−	0.938360i	$-0.387655\pi$
$433$	14.3854	0.691319	0.345659	+	0.938360i	$0.387655\pi$
$434$	−16.8159	−0.807188
$435$	−26.8421	−1.28698
$436$	−56.3026	−2.69641
$437$	−3.74863	−0.179321
$438$	5.78228	0.276288
$439$	−16.0142	−0.764314	−0.382157	−	0.924097i	$-0.624819\pi$
$439$	−16.0142	−0.764314	−0.382157	+	0.924097i	$0.624819\pi$
$440$	107.732	5.13595
$441$	−1.48828	−0.0708703
$442$	11.4619	0.545185
$443$	−25.3818	−1.20593	−0.602963	−	0.797769i	$-0.706013\pi$
$443$	−25.3818	−1.20593	−0.602963	+	0.797769i	$0.706013\pi$
$444$	56.3860	2.67596
$445$	17.6518	0.836775
$446$	−6.86099	−0.324877
$447$	38.0248	1.79851
$448$	−150.391	−7.10530
$449$	−18.6471	−0.880012	−0.440006	−	0.897995i	$-0.645024\pi$
$449$	−18.6471	−0.880012	−0.440006	+	0.897995i	$0.645024\pi$
$450$	16.8103	0.792446
$451$	−18.3714	−0.865077
$452$	7.99134	0.375881
$453$	−25.7812	−1.21131
$454$	−28.1200	−1.31974
$455$	20.2164	0.947759
$456$	16.1056	0.754213
$457$	−8.02070	−0.375193	−0.187596	−	0.982246i	$-0.560070\pi$
$457$	−8.02070	−0.375193	−0.187596	+	0.982246i	$0.560070\pi$
$458$	−39.9309	−1.86585
$459$	−14.7434	−0.688163
$460$	96.3063	4.49030
$461$	−37.1778	−1.73154	−0.865772	−	0.500439i	$-0.833172\pi$
$461$	−37.1778	−1.73154	−0.865772	+	0.500439i	$0.833172\pi$
$462$	−33.8867	−1.57655
$463$	29.2413	1.35896	0.679480	−	0.733694i	$-0.262205\pi$
$463$	29.2413	1.35896	0.679480	+	0.733694i	$0.262205\pi$
$464$	−75.1480	−3.48866
$465$	−12.4796	−0.578727
$466$	−78.7958	−3.65015
$467$	−7.67520	−0.355166	−0.177583	−	0.984106i	$-0.556828\pi$
$467$	−7.67520	−0.355166	−0.177583	+	0.984106i	$0.556828\pi$
$468$	4.38560	0.202725
$469$	−44.8912	−2.07288
$470$	50.4985	2.32932
$471$	−8.44912	−0.389315
$472$	111.752	5.14379
$473$	24.8004	1.14033
$474$	37.9121	1.74136
$475$	−11.5973	−0.532123
$476$	−49.3623	−2.26252
$477$	4.08145	0.186877
$478$	−65.4805	−2.99501
$479$	−4.49479	−0.205372	−0.102686	−	0.994714i	$-0.532744\pi$
$479$	−4.49479	−0.205372	−0.102686	+	0.994714i	$0.532744\pi$
$480$	−198.332	−9.05258
$481$	−9.35086	−0.426363
$482$	34.7866	1.58448
$483$	−19.9206	−0.906420
$484$	−30.3292	−1.37860
$485$	−36.9271	−1.67677
$486$	−14.0839	−0.638857
$487$	4.45775	0.202000	0.101000	−	0.994886i	$-0.467796\pi$
$487$	4.45775	0.202000	0.101000	+	0.994886i	$0.467796\pi$
$488$	64.7573	2.93143
$489$	−21.5834	−0.976035
$490$	−35.4102	−1.59967
$491$	22.4757	1.01431	0.507157	−	0.861854i	$-0.330697\pi$
$491$	22.4757	1.01431	0.507157	+	0.861854i	$0.330697\pi$
$492$	70.5593	3.18106
$493$	−10.8690	−0.489514
$494$	−4.06155	−0.182738
$495$	4.89913	0.220200
$496$	−34.9383	−1.56877
$497$	40.6090	1.82156
$498$	−9.70965	−0.435100
$499$	−11.5710	−0.517988	−0.258994	−	0.965879i	$-0.583391\pi$
$499$	−11.5710	−0.517988	−0.258994	+	0.965879i	$0.583391\pi$
$500$	176.565	7.89622
$501$	9.78967	0.437370
$502$	12.9278	0.576994
$503$	31.2981	1.39551	0.697756	−	0.716336i	$-0.254182\pi$
$503$	31.2981	1.39551	0.697756	+	0.716336i	$0.254182\pi$
$504$	−16.6731	−0.742677
$505$	−8.66664	−0.385661
$506$	26.7708	1.19011
$507$	−16.8660	−0.749047
$508$	20.7137	0.919022
$509$	15.9515	0.707039	0.353520	−	0.935427i	$-0.384985\pi$
$509$	15.9515	0.707039	0.353520	+	0.935427i	$0.384985\pi$
$510$	−49.1763	−2.17756
$511$	4.12971	0.182688
$512$	−158.626	−7.01036
$513$	5.22439	0.230662
$514$	69.2331	3.05374
$515$	38.0811	1.67805
$516$	−95.2513	−4.19320
$517$	10.4570	0.459896
$518$	54.0596	2.37524
$519$	31.5051	1.38292
$520$	68.6181	3.00910
$521$	11.8797	0.520458	0.260229	−	0.965547i	$-0.416202\pi$
$521$	11.8797	0.520458	0.260229	+	0.965547i	$0.416202\pi$
$522$	−5.58269	−0.244348
$523$	−40.5952	−1.77510	−0.887552	−	0.460707i	$-0.847596\pi$
$523$	−40.5952	−1.77510	−0.887552	+	0.460707i	$0.847596\pi$
$524$	−64.6329	−2.82350
$525$	−61.6295	−2.68973
$526$	24.1392	1.05252
$527$	−5.05327	−0.220124
$528$	−70.4063	−3.06404
$529$	−7.26254	−0.315763
$530$	97.1089	4.21814
$531$	5.08190	0.220536
$532$	17.4917	0.758362
$533$	−11.7013	−0.506841
$534$	−18.8455	−0.815523
$535$	−34.4530	−1.48953
$536$	−152.369	−6.58133
$537$	−37.5974	−1.62245
$538$	−5.83891	−0.251734
$539$	−7.33254	−0.315835
$540$	−134.220	−5.77590
$541$	−17.2817	−0.742999	−0.371500	−	0.928433i	$-0.621156\pi$
$541$	−17.2817	−0.742999	−0.371500	+	0.928433i	$0.621156\pi$
$542$	−2.55074	−0.109564
$543$	−27.0938	−1.16271
$544$	−80.3092	−3.44323
$545$	−40.0600	−1.71598
$546$	−21.5835	−0.923689
$547$	36.1947	1.54757	0.773786	−	0.633447i	$-0.218361\pi$
$547$	36.1947	1.54757	0.773786	+	0.633447i	$0.218361\pi$
$548$	87.1142	3.72133
$549$	2.94484	0.125683
$550$	82.8223	3.53155
$551$	3.85147	0.164078
$552$	−67.6142	−2.87785
$553$	27.0769	1.15143
$554$	78.3516	3.32884
$555$	40.1193	1.70297
$556$	5.19669	0.220389
$557$	−33.0969	−1.40236	−0.701180	−	0.712985i	$-0.747343\pi$
$557$	−33.0969	−1.40236	−0.701180	+	0.712985i	$0.747343\pi$
$558$	−2.59554	−0.109878
$559$	15.7962	0.668107
$560$	−242.832	−10.2615
$561$	−10.1832	−0.429933
$562$	−23.4297	−0.988321
$563$	−3.67137	−0.154730	−0.0773648	−	0.997003i	$-0.524651\pi$
$563$	−3.67137	−0.154730	−0.0773648	+	0.997003i	$0.524651\pi$
$564$	−40.1621	−1.69113
$565$	5.68593	0.239209
$566$	−5.70113	−0.239636
$567$	23.1127	0.970640
$568$	137.834	5.78340
$569$	33.9810	1.42456	0.712279	−	0.701896i	$-0.247663\pi$
$569$	33.9810	1.42456	0.712279	+	0.701896i	$0.247663\pi$
$570$	17.4258	0.729887
$571$	31.7629	1.32923	0.664617	−	0.747184i	$-0.268595\pi$
$571$	31.7629	1.32923	0.664617	+	0.747184i	$0.268595\pi$
$572$	21.6073	0.903446
$573$	−28.6585	−1.19723
$574$	67.6482	2.82358
$575$	48.6878	2.03042
$576$	−23.2129	−0.967203
$577$	5.10203	0.212400	0.106200	−	0.994345i	$-0.466132\pi$
$577$	5.10203	0.212400	0.106200	+	0.994345i	$0.466132\pi$
$578$	27.6911	1.15180
$579$	2.26177	0.0939960
$580$	−98.9481	−4.10860
$581$	−6.93465	−0.287698
$582$	39.4242	1.63419
$583$	20.1088	0.832821
$584$	14.0170	0.580028
$585$	3.12041	0.129013
$586$	−53.5223	−2.21099
$587$	0.917702	0.0378776	0.0189388	−	0.999821i	$-0.493971\pi$
$587$	0.917702	0.0378776	0.0189388	+	0.999821i	$0.493971\pi$
$588$	28.1621	1.16139
$589$	1.79065	0.0737823
$590$	120.912	4.97788
$591$	1.88601	0.0775800
$592$	112.319	4.61629
$593$	−28.4587	−1.16866	−0.584329	−	0.811517i	$-0.698642\pi$
$593$	−28.4587	−1.16866	−0.584329	+	0.811517i	$0.698642\pi$
$594$	−37.3099	−1.53084
$595$	−35.1218	−1.43985
$596$	140.171	5.74163
$597$	23.1554	0.947689
$598$	17.0512	0.697273
$599$	−42.1401	−1.72180	−0.860899	−	0.508776i	$-0.830098\pi$
$599$	−42.1401	−1.72180	−0.860899	+	0.508776i	$0.830098\pi$
$600$	−209.182	−8.53980
$601$	−7.85375	−0.320361	−0.160181	−	0.987088i	$-0.551208\pi$
$601$	−7.85375	−0.320361	−0.160181	+	0.987088i	$0.551208\pi$
$602$	−91.3214	−3.72198
$603$	−6.92897	−0.282169
$604$	−95.0374	−3.86702
$605$	−21.5796	−0.877335
$606$	9.25271	0.375866
$607$	−20.9818	−0.851627	−0.425813	−	0.904811i	$-0.640012\pi$
$607$	−20.9818	−0.851627	−0.425813	+	0.904811i	$0.640012\pi$
$608$	28.4579	1.15412
$609$	20.4671	0.829368
$610$	70.0657	2.83688
$611$	6.66036	0.269449
$612$	−7.61908	−0.307983
$613$	−21.3216	−0.861170	−0.430585	−	0.902550i	$-0.641693\pi$
$613$	−21.3216	−0.861170	−0.430585	+	0.902550i	$0.641693\pi$
$614$	21.1803	0.854768
$615$	50.2038	2.02441
$616$	−82.1460	−3.30976
$617$	26.3587	1.06116	0.530580	−	0.847635i	$-0.321974\pi$
$617$	26.3587	1.06116	0.530580	+	0.847635i	$0.321974\pi$
$618$	−40.6562	−1.63543
$619$	48.1962	1.93717	0.968585	−	0.248683i	$-0.0799976\pi$
$619$	48.1962	1.93717	0.968585	+	0.248683i	$0.0799976\pi$
$620$	−46.0036	−1.84755
$621$	−21.9329	−0.880139
$622$	−38.1308	−1.52891
$623$	−13.4595	−0.539242
$624$	−44.8439	−1.79519
$625$	64.2627	2.57051
$626$	14.2164	0.568200
$627$	3.60844	0.144107
$628$	−31.1460	−1.24286
$629$	16.2452	0.647739
$630$	−18.0398	−0.718723
$631$	−24.4686	−0.974078	−0.487039	−	0.873380i	$-0.661923\pi$
$631$	−24.4686	−0.974078	−0.487039	+	0.873380i	$0.661923\pi$
$632$	91.9040	3.65575
$633$	6.50129	0.258403
$634$	54.1003	2.14860
$635$	14.7380	0.584861
$636$	−77.2320	−3.06245
$637$	−4.67032	−0.185045
$638$	−27.5052	−1.08894
$639$	6.26801	0.247959
$640$	−301.968	−11.9364
$641$	25.0756	0.990425	0.495213	−	0.868772i	$-0.335090\pi$
$641$	25.0756	0.990425	0.495213	+	0.868772i	$0.335090\pi$
$642$	36.7828	1.45170
$643$	−26.4733	−1.04400	−0.522002	−	0.852944i	$-0.674815\pi$
$643$	−26.4733	−1.04400	−0.522002	+	0.852944i	$0.674815\pi$
$644$	−73.4335	−2.89368
$645$	−67.7724	−2.66854
$646$	7.05611	0.277619
$647$	40.1364	1.57792	0.788961	−	0.614443i	$-0.210619\pi$
$647$	40.1364	1.57792	0.788961	+	0.614443i	$0.210619\pi$
$648$	78.4486	3.08175
$649$	25.0379	0.982823
$650$	52.7520	2.06911
$651$	9.51568	0.372949
$652$	−79.5630	−3.11593
$653$	−38.5453	−1.50840	−0.754198	−	0.656647i	$-0.771974\pi$
$653$	−38.5453	−1.50840	−0.754198	+	0.656647i	$0.771974\pi$
$654$	42.7690	1.67240
$655$	−45.9871	−1.79686
$656$	140.552	5.48764
$657$	0.637423	0.0248682
$658$	−38.5051	−1.50108
$659$	9.13115	0.355699	0.177850	−	0.984058i	$-0.443086\pi$
$659$	9.13115	0.355699	0.177850	+	0.984058i	$0.443086\pi$
$660$	−92.7046	−3.60852
$661$	45.4593	1.76816	0.884082	−	0.467333i	$-0.154785\pi$
$661$	45.4593	1.76816	0.884082	+	0.467333i	$0.154785\pi$
$662$	71.2629	2.76971
$663$	−6.48597	−0.251894
$664$	−23.5375	−0.913431
$665$	12.4456	0.482618
$666$	8.34411	0.323328
$667$	−16.1692	−0.626073
$668$	36.0877	1.39628
$669$	3.88245	0.150104
$670$	−164.859	−6.36907
$671$	14.5088	0.560107
$672$	151.228	5.83375
$673$	27.5067	1.06031	0.530153	−	0.847902i	$-0.322135\pi$
$673$	27.5067	1.06031	0.530153	+	0.847902i	$0.322135\pi$
$674$	87.1602	3.35729
$675$	−67.8551	−2.61174
$676$	−62.1734	−2.39128
$677$	35.9310	1.38094	0.690470	−	0.723361i	$-0.257404\pi$
$677$	35.9310	1.38094	0.690470	+	0.723361i	$0.257404\pi$
$678$	−6.07043	−0.233134
$679$	28.1569	1.08056
$680$	−119.210	−4.57149
$681$	15.9124	0.609764
$682$	−12.7879	−0.489673
$683$	−34.6240	−1.32485	−0.662426	−	0.749128i	$-0.730473\pi$
$683$	−34.6240	−1.32485	−0.662426	+	0.749128i	$0.730473\pi$
$684$	2.69985	0.103231
$685$	61.9828	2.36824
$686$	−35.1172	−1.34078
$687$	22.5959	0.862086
$688$	−189.738	−7.23369
$689$	12.8079	0.487942
$690$	−73.1568	−2.78503
$691$	−39.9579	−1.52007	−0.760034	−	0.649883i	$-0.774818\pi$
$691$	−39.9579	−1.52007	−0.760034	+	0.649883i	$0.774818\pi$
$692$	116.138	4.41489
$693$	−3.73558	−0.141903
$694$	7.94558	0.301610
$695$	3.69750	0.140254
$696$	69.4690	2.63322
$697$	20.3287	0.770003
$698$	−95.3710	−3.60985
$699$	44.5885	1.68649
$700$	−227.185	−8.58679
$701$	14.7487	0.557051	0.278525	−	0.960429i	$-0.410154\pi$
$701$	14.7487	0.557051	0.278525	+	0.960429i	$0.410154\pi$
$702$	−23.7638	−0.896907
$703$	−5.75655	−0.217113
$704$	−114.367	−4.31036
$705$	−28.5758	−1.07623
$706$	−56.6971	−2.13383
$707$	6.60831	0.248531
$708$	−96.1632	−3.61403
$709$	−21.6850	−0.814398	−0.407199	−	0.913340i	$-0.633494\pi$
$709$	−21.6850	−0.814398	−0.407199	+	0.913340i	$0.633494\pi$
$710$	149.133	5.59687
$711$	4.17933	0.156737
$712$	−45.6839	−1.71208
$713$	−7.51746	−0.281531
$714$	37.4969	1.40329
$715$	15.3738	0.574949
$716$	−138.595	−5.17955
$717$	37.0537	1.38380
$718$	49.9717	1.86493
$719$	−12.8348	−0.478659	−0.239329	−	0.970938i	$-0.576928\pi$
$719$	−12.8348	−0.478659	−0.239329	+	0.970938i	$0.576928\pi$
$720$	−37.4812	−1.39684
$721$	−29.0368	−1.08139
$722$	50.7037	1.88700
$723$	−19.6848	−0.732086
$724$	−99.8762	−3.71187
$725$	−50.0234	−1.85782
$726$	23.0389	0.855053
$727$	4.45180	0.165108	0.0825541	−	0.996587i	$-0.473692\pi$
$727$	4.45180	0.165108	0.0825541	+	0.996587i	$0.473692\pi$
$728$	−52.3213	−1.93916
$729$	29.8497	1.10554
$730$	15.1660	0.561320
$731$	−27.4426	−1.01500
$732$	−55.7242	−2.05962
$733$	39.0592	1.44269	0.721343	−	0.692578i	$-0.243525\pi$
$733$	39.0592	1.44269	0.721343	+	0.692578i	$0.243525\pi$
$734$	−0.106734	−0.00393962
$735$	20.0377	0.739101
$736$	−119.472	−4.40378
$737$	−34.1381	−1.25749
$738$	10.4415	0.384358
$739$	−5.96033	−0.219254	−0.109627	−	0.993973i	$-0.534966\pi$
$739$	−5.96033	−0.219254	−0.109627	+	0.993973i	$0.534966\pi$
$740$	147.892	5.43661
$741$	2.29833	0.0844312
$742$	−74.0455	−2.71830
$743$	−24.5069	−0.899071	−0.449536	−	0.893262i	$-0.648411\pi$
$743$	−24.5069	−0.899071	−0.449536	+	0.893262i	$0.648411\pi$
$744$	32.2979	1.18410
$745$	99.7334	3.65395
$746$	59.8292	2.19050
$747$	−1.07037	−0.0391626
$748$	−37.5382	−1.37253
$749$	26.2704	0.959899
$750$	−134.123	−4.89750
$751$	−20.9152	−0.763208	−0.381604	−	0.924326i	$-0.624628\pi$
$751$	−20.9152	−0.763208	−0.381604	+	0.924326i	$0.624628\pi$
$752$	−80.0018	−2.91737
$753$	−7.31549	−0.266591
$754$	−17.5189	−0.638000
$755$	−67.6202	−2.46095
$756$	102.343	3.72216
$757$	−52.5682	−1.91062	−0.955311	−	0.295602i	$-0.904480\pi$
$757$	−52.5682	−1.91062	−0.955311	+	0.295602i	$0.904480\pi$
$758$	−50.9608	−1.85098
$759$	−15.1489	−0.549871
$760$	42.2425	1.53230
$761$	12.9860	0.470743	0.235371	−	0.971905i	$-0.424369\pi$
$761$	12.9860	0.470743	0.235371	+	0.971905i	$0.424369\pi$
$762$	−15.7347	−0.570007
$763$	30.5457	1.10583
$764$	−105.644	−3.82206
$765$	−5.42107	−0.195999
$766$	7.37375	0.266424
$767$	15.9474	0.575827
$768$	171.992	6.20623
$769$	−17.4010	−0.627495	−0.313747	−	0.949507i	$-0.601584\pi$
$769$	−17.4010	−0.627495	−0.313747	+	0.949507i	$0.601584\pi$
$770$	−88.8798	−3.20301
$771$	−39.1772	−1.41093
$772$	8.33758	0.300076
$773$	35.3180	1.27030	0.635151	−	0.772388i	$-0.280938\pi$
$773$	35.3180	1.27030	0.635151	+	0.772388i	$0.280938\pi$
$774$	−14.0955	−0.506652
$775$	−23.2572	−0.835422
$776$	95.5696	3.43075
$777$	−30.5909	−1.09744
$778$	46.1066	1.65300
$779$	−7.20354	−0.258094
$780$	−59.0464	−2.11420
$781$	30.8817	1.10503
$782$	−29.6229	−1.05931
$783$	22.5346	0.805321
$784$	56.0982	2.00351
$785$	−22.1608	−0.790951
$786$	49.0969	1.75123
$787$	45.9012	1.63620	0.818100	−	0.575076i	$-0.195027\pi$
$787$	45.9012	1.63620	0.818100	+	0.575076i	$0.195027\pi$
$788$	6.95240	0.247669
$789$	−13.6598	−0.486300
$790$	99.4377	3.53784
$791$	−4.33552	−0.154153
$792$	−12.6793	−0.450538
$793$	9.24112	0.328162
$794$	44.9315	1.59456
$795$	−54.9514	−1.94893
$796$	85.3580	3.02544
$797$	−8.50110	−0.301125	−0.150562	−	0.988601i	$-0.548108\pi$
$797$	−8.50110	−0.301125	−0.150562	+	0.988601i	$0.548108\pi$
$798$	−13.2872	−0.470361
$799$	−11.5710	−0.409353
$800$	−369.615	−13.0679
$801$	−2.07747	−0.0734039
$802$	−102.408	−3.61615
$803$	3.14050	0.110826
$804$	131.115	4.62406
$805$	−52.2488	−1.84153
$806$	−8.14499	−0.286895
$807$	3.30409	0.116310
$808$	22.4298	0.789078
$809$	−15.3275	−0.538888	−0.269444	−	0.963016i	$-0.586840\pi$
$809$	−15.3275	−0.538888	−0.269444	+	0.963016i	$0.586840\pi$
$810$	84.8793	2.98236
$811$	13.9925	0.491342	0.245671	−	0.969353i	$-0.420992\pi$
$811$	13.9925	0.491342	0.245671	+	0.969353i	$0.420992\pi$
$812$	75.4479	2.64770
$813$	1.44340	0.0506222
$814$	41.1103	1.44092
$815$	−56.6100	−1.98296
$816$	77.9071	2.72729
$817$	9.72439	0.340213
$818$	75.4637	2.63853
$819$	−2.37931	−0.0831398
$820$	185.066	6.46280
$821$	35.9363	1.25418	0.627092	−	0.778945i	$-0.284245\pi$
$821$	35.9363	1.25418	0.627092	+	0.778945i	$0.284245\pi$
$822$	−66.1743	−2.30809
$823$	28.7272	1.00137	0.500684	−	0.865630i	$-0.333082\pi$
$823$	28.7272	1.00137	0.500684	+	0.865630i	$0.333082\pi$
$824$	−98.5561	−3.43337
$825$	−46.8670	−1.63170
$826$	−92.1956	−3.20790
$827$	−10.6041	−0.368741	−0.184370	−	0.982857i	$-0.559025\pi$
$827$	−10.6041	−0.368741	−0.184370	+	0.982857i	$0.559025\pi$
$828$	−11.3345	−0.393900
$829$	−8.66659	−0.301003	−0.150502	−	0.988610i	$-0.548089\pi$
$829$	−8.66659	−0.301003	−0.150502	+	0.988610i	$0.548089\pi$
$830$	−25.4669	−0.883970
$831$	−44.3372	−1.53804
$832$	−72.8437	−2.52540
$833$	8.11372	0.281124
$834$	−3.94754	−0.136692
$835$	25.6768	0.888583
$836$	13.3018	0.460053
$837$	10.4769	0.362135
$838$	67.8304	2.34316
$839$	38.8286	1.34051	0.670256	−	0.742130i	$-0.266185\pi$
$839$	38.8286	1.34051	0.670256	+	0.742130i	$0.266185\pi$
$840$	224.481	7.74533
$841$	−12.3873	−0.427148
$842$	87.3827	3.01141
$843$	13.2582	0.456638
$844$	23.9657	0.824935
$845$	−44.2371	−1.52180
$846$	−5.94327	−0.204334
$847$	16.4544	0.565380
$848$	−153.844	−5.28302
$849$	3.22612	0.110720
$850$	−91.6458	−3.14343
$851$	24.1671	0.828437
$852$	−118.608	−4.06343
$853$	−41.0465	−1.40540	−0.702702	−	0.711484i	$-0.748023\pi$
$853$	−41.0465	−1.40540	−0.702702	+	0.711484i	$0.748023\pi$
$854$	−53.4251	−1.82817
$855$	1.92098	0.0656960
$856$	89.1664	3.04765
$857$	24.2998	0.830066	0.415033	−	0.909806i	$-0.363770\pi$
$857$	24.2998	0.830066	0.415033	+	0.909806i	$0.363770\pi$
$858$	−16.4135	−0.560347
$859$	−14.5945	−0.497959	−0.248979	−	0.968509i	$-0.580095\pi$
$859$	−14.5945	−0.497959	−0.248979	+	0.968509i	$0.580095\pi$
$860$	−249.830	−8.51912
$861$	−38.2804	−1.30459
$862$	21.3771	0.728108
$863$	−10.8256	−0.368507	−0.184253	−	0.982879i	$-0.558987\pi$
$863$	−10.8256	−0.368507	−0.184253	+	0.982879i	$0.558987\pi$
$864$	166.505	5.66461
$865$	82.6332	2.80961
$866$	−40.2822	−1.36885
$867$	−15.6697	−0.532169
$868$	35.0777	1.19061
$869$	20.5910	0.698503
$870$	75.1636	2.54829
$871$	−21.7436	−0.736755
$872$	103.678	3.51097
$873$	4.34602	0.147091
$874$	10.4970	0.355066
$875$	−95.7913	−3.23834
$876$	−12.0617	−0.407528
$877$	26.9718	0.910772	0.455386	−	0.890294i	$-0.349501\pi$
$877$	26.9718	0.910772	0.455386	+	0.890294i	$0.349501\pi$
$878$	44.8431	1.51338
$879$	30.2869	1.02155
$880$	−184.665	−6.22506
$881$	54.1135	1.82313	0.911565	−	0.411155i	$-0.134874\pi$
$881$	54.1135	1.82313	0.911565	+	0.411155i	$0.134874\pi$
$882$	4.16749	0.140327
$883$	−23.2584	−0.782709	−0.391355	−	0.920240i	$-0.627993\pi$
$883$	−23.2584	−0.782709	−0.391355	+	0.920240i	$0.627993\pi$
$884$	−23.9093	−0.804155
$885$	−68.4212	−2.29995
$886$	71.0745	2.38779
$887$	7.35789	0.247054	0.123527	−	0.992341i	$-0.460579\pi$
$887$	7.35789	0.247054	0.123527	+	0.992341i	$0.460579\pi$
$888$	−103.831	−3.48434
$889$	−11.2377	−0.376902
$890$	−49.4288	−1.65686
$891$	17.5763	0.588830
$892$	14.3119	0.479198
$893$	4.10023	0.137209
$894$	−106.478	−3.56115
$895$	−98.6122	−3.29624
$896$	230.251	7.69214
$897$	−9.64881	−0.322164
$898$	52.2160	1.74247
$899$	7.72368	0.257599
$900$	−35.0661	−1.16887
$901$	−22.2511	−0.741291
$902$	51.4440	1.71290
$903$	51.6764	1.71968
$904$	−14.7155	−0.489431
$905$	−71.0630	−2.36222
$906$	72.1929	2.39845
$907$	27.4997	0.913112	0.456556	−	0.889695i	$-0.349083\pi$
$907$	27.4997	0.913112	0.456556	+	0.889695i	$0.349083\pi$
$908$	58.6579	1.94663
$909$	1.01999	0.0338311
$910$	−56.6103	−1.87661
$911$	18.1112	0.600052	0.300026	−	0.953931i	$-0.403005\pi$
$911$	18.1112	0.600052	0.300026	+	0.953931i	$0.403005\pi$
$912$	−27.6067	−0.914149
$913$	−5.27355	−0.174529
$914$	22.4597	0.742901
$915$	−39.6484	−1.31074
$916$	83.2953	2.75215
$917$	35.0651	1.15795
$918$	41.2847	1.36260
$919$	−22.8862	−0.754944	−0.377472	−	0.926021i	$-0.623207\pi$
$919$	−22.8862	−0.754944	−0.377472	+	0.926021i	$0.623207\pi$
$920$	−177.342	−5.84679
$921$	−11.9854	−0.394932
$922$	104.106	3.42855
$923$	19.6695	0.647429
$924$	70.6872	2.32544
$925$	74.7670	2.45832
$926$	−81.8821	−2.69081
$927$	−4.48184	−0.147203
$928$	122.749	4.02943
$929$	27.5905	0.905215	0.452607	−	0.891710i	$-0.350494\pi$
$929$	27.5905	0.905215	0.452607	+	0.891710i	$0.350494\pi$
$930$	34.9455	1.14591
$931$	−2.87513	−0.0942286
$932$	164.367	5.38402
$933$	21.5773	0.706408
$934$	21.4922	0.703246
$935$	−26.7089	−0.873474
$936$	−8.07581	−0.263966
$937$	1.20405	0.0393347	0.0196673	−	0.999807i	$-0.493739\pi$
$937$	1.20405	0.0393347	0.0196673	+	0.999807i	$0.493739\pi$
$938$	125.705	4.10441
$939$	−8.04467	−0.262528
$940$	−105.339	−3.43578
$941$	−20.0826	−0.654674	−0.327337	−	0.944908i	$-0.606151\pi$
$941$	−20.0826	−0.654674	−0.327337	+	0.944908i	$0.606151\pi$
$942$	23.6594	0.770863
$943$	30.2418	0.984809
$944$	−191.554	−6.23456
$945$	72.8179	2.36877
$946$	−69.4466	−2.25790
$947$	25.0019	0.812453	0.406226	−	0.913772i	$-0.366844\pi$
$947$	25.0019	0.812453	0.406226	+	0.913772i	$0.366844\pi$
$948$	−79.0841	−2.56853
$949$	2.00028	0.0649318
$950$	32.4751	1.05363
$951$	−30.6140	−0.992726
$952$	90.8975	2.94600
$953$	−4.66080	−0.150978	−0.0754890	−	0.997147i	$-0.524052\pi$
$953$	−4.66080	−0.150978	−0.0754890	+	0.997147i	$0.524052\pi$
$954$	−11.4289	−0.370026
$955$	−75.1669	−2.43234
$956$	136.591	4.41768
$957$	15.5645	0.503128
$958$	12.5864	0.406648
$959$	−47.2618	−1.52616
$960$	312.531	10.0869
$961$	−27.4091	−0.884163
$962$	26.1844	0.844220
$963$	4.05484	0.130665
$964$	−72.5642	−2.33714
$965$	5.93228	0.190967
$966$	55.7820	1.79476
$967$	25.5256	0.820848	0.410424	−	0.911895i	$-0.365381\pi$
$967$	25.5256	0.820848	0.410424	+	0.911895i	$0.365381\pi$
$968$	55.8493	1.79506
$969$	−3.99287	−0.128270
$970$	103.404	3.32010
$971$	25.0419	0.803634	0.401817	−	0.915720i	$-0.368379\pi$
$971$	25.0419	0.803634	0.401817	+	0.915720i	$0.368379\pi$
$972$	29.3787	0.942323
$973$	−2.81934	−0.0903840
$974$	−12.4827	−0.399970
$975$	−29.8510	−0.955998
$976$	−111.001	−3.55305
$977$	18.4826	0.591310	0.295655	−	0.955295i	$-0.404462\pi$
$977$	18.4826	0.591310	0.295655	+	0.955295i	$0.404462\pi$
$978$	60.4382	1.93260
$979$	−10.2354	−0.327126
$980$	73.8651	2.35953
$981$	4.71474	0.150530
$982$	−62.9368	−2.00839
$983$	10.8244	0.345243	0.172622	−	0.984988i	$-0.444776\pi$
$983$	10.8244	0.345243	0.172622	+	0.984988i	$0.444776\pi$
$984$	−129.931	−4.14203
$985$	4.94671	0.157615
$986$	30.4355	0.969263
$987$	21.7890	0.693553
$988$	8.47234	0.269541
$989$	−40.8248	−1.29815
$990$	−13.7186	−0.436006
$991$	−4.43497	−0.140882	−0.0704408	−	0.997516i	$-0.522441\pi$
$991$	−4.43497	−0.140882	−0.0704408	+	0.997516i	$0.522441\pi$
$992$	57.0691	1.81195
$993$	−40.3259	−1.27970
$994$	−113.714	−3.60679
$995$	60.7332	1.92537
$996$	20.2542	0.641778
$997$	23.1085	0.731852	0.365926	−	0.930644i	$-0.380752\pi$
$997$	23.1085	0.731852	0.365926	+	0.930644i	$0.380752\pi$
$998$	32.4012	1.02564
$999$	−33.6811	−1.06562

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6029.2.a.a.1.1	✓	234

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6029.2.a.a.1.1	✓	234	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:	\( N \)	\(=\)	\( 6029 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.80022 q^{2} +1.58457 q^{3} +5.84121 q^{4} +4.15609 q^{5} -4.43714 q^{6} -3.16901 q^{7} -10.7562 q^{8} -0.489138 q^{9} +O(q^{10})\)	\(q-2.80022 q^{2} +1.58457 q^{3} +5.84121 q^{4} +4.15609 q^{5} -4.43714 q^{6} -3.16901 q^{7} -10.7562 q^{8} -0.489138 q^{9} -11.6379 q^{10} -2.40992 q^{11} +9.25580 q^{12} -1.53495 q^{13} +8.87392 q^{14} +6.58561 q^{15} +18.4373 q^{16} +2.66666 q^{17} +1.36969 q^{18} -0.944943 q^{19} +24.2766 q^{20} -5.02152 q^{21} +6.74830 q^{22} +3.96705 q^{23} -17.0440 q^{24} +12.2731 q^{25} +4.29820 q^{26} -5.52878 q^{27} -18.5109 q^{28} -4.07587 q^{29} -18.4411 q^{30} -1.89498 q^{31} -30.1160 q^{32} -3.81869 q^{33} -7.46724 q^{34} -13.1707 q^{35} -2.85716 q^{36} +6.09196 q^{37} +2.64605 q^{38} -2.43224 q^{39} -44.7038 q^{40} +7.62325 q^{41} +14.0613 q^{42} -10.2910 q^{43} -14.0768 q^{44} -2.03290 q^{45} -11.1086 q^{46} -4.33913 q^{47} +29.2152 q^{48} +3.04265 q^{49} -34.3672 q^{50} +4.22552 q^{51} -8.96598 q^{52} -8.34417 q^{53} +15.4818 q^{54} -10.0158 q^{55} +34.0866 q^{56} -1.49733 q^{57} +11.4133 q^{58} -10.3895 q^{59} +38.4679 q^{60} -6.02046 q^{61} +5.30635 q^{62} +1.55009 q^{63} +47.4567 q^{64} -6.37940 q^{65} +10.6931 q^{66} +14.1657 q^{67} +15.5765 q^{68} +6.28606 q^{69} +36.8808 q^{70} -12.8144 q^{71} +5.26128 q^{72} -1.30315 q^{73} -17.0588 q^{74} +19.4475 q^{75} -5.51961 q^{76} +7.63707 q^{77} +6.81080 q^{78} -8.54427 q^{79} +76.6270 q^{80} -7.29333 q^{81} -21.3468 q^{82} +2.18827 q^{83} -29.3318 q^{84} +11.0829 q^{85} +28.8170 q^{86} -6.45850 q^{87} +25.9216 q^{88} +4.24721 q^{89} +5.69256 q^{90} +4.86429 q^{91} +23.1723 q^{92} -3.00272 q^{93} +12.1505 q^{94} -3.92727 q^{95} -47.7209 q^{96} -8.88506 q^{97} -8.52007 q^{98} +1.17878 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9}+O(q^{10}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9} - 89 q^{10} - 55 q^{11} - 75 q^{12} - 49 q^{13} - 42 q^{14} - 43 q^{15} + 142 q^{16} - 40 q^{17} - 30 q^{18} - 235 q^{19} - 62 q^{20} - 62 q^{21} - 63 q^{22} - 30 q^{23} - 108 q^{24} + 170 q^{25} - 44 q^{26} - 160 q^{27} - 147 q^{28} - 76 q^{29} - 15 q^{30} - 175 q^{31} - 49 q^{32} - 43 q^{33} - 104 q^{34} - 87 q^{35} + 124 q^{36} - 77 q^{37} - 18 q^{38} - 104 q^{39} - 247 q^{40} - 60 q^{41} - 6 q^{42} - 201 q^{43} - 89 q^{44} - 102 q^{45} - 128 q^{46} - 27 q^{47} - 130 q^{48} + 123 q^{49} - 33 q^{50} - 220 q^{51} - 125 q^{52} - 34 q^{53} - 126 q^{54} - 176 q^{55} - 125 q^{56} - 17 q^{57} - 46 q^{58} - 172 q^{59} - 61 q^{60} - 243 q^{61} - 37 q^{62} - 137 q^{63} + 39 q^{64} - 31 q^{65} - 142 q^{66} - 132 q^{67} - 106 q^{68} - 115 q^{69} - 60 q^{70} - 68 q^{71} - 66 q^{72} - 109 q^{73} - 74 q^{74} - 256 q^{75} - 412 q^{76} - 32 q^{77} - 38 q^{78} - 297 q^{79} - 111 q^{80} + 142 q^{81} - 94 q^{82} - 100 q^{83} - 134 q^{84} - 90 q^{85} + q^{86} - 103 q^{87} - 143 q^{88} - 77 q^{89} - 181 q^{90} - 418 q^{91} - 19 q^{92} + 5 q^{93} - 231 q^{94} - 92 q^{95} - 189 q^{96} - 141 q^{97} - 25 q^{98} - 244 q^{99}+O(q^{100}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9 - 89 * q^10 - 55 * q^11 - 75 * q^12 - 49 * q^13 - 42 * q^14 - 43 * q^15 + 142 * q^16 - 40 * q^17 - 30 * q^18 - 235 * q^19 - 62 * q^20 - 62 * q^21 - 63 * q^22 - 30 * q^23 - 108 * q^24 + 170 * q^25 - 44 * q^26 - 160 * q^27 - 147 * q^28 - 76 * q^29 - 15 * q^30 - 175 * q^31 - 49 * q^32 - 43 * q^33 - 104 * q^34 - 87 * q^35 + 124 * q^36 - 77 * q^37 - 18 * q^38 - 104 * q^39 - 247 * q^40 - 60 * q^41 - 6 * q^42 - 201 * q^43 - 89 * q^44 - 102 * q^45 - 128 * q^46 - 27 * q^47 - 130 * q^48 + 123 * q^49 - 33 * q^50 - 220 * q^51 - 125 * q^52 - 34 * q^53 - 126 * q^54 - 176 * q^55 - 125 * q^56 - 17 * q^57 - 46 * q^58 - 172 * q^59 - 61 * q^60 - 243 * q^61 - 37 * q^62 - 137 * q^63 + 39 * q^64 - 31 * q^65 - 142 * q^66 - 132 * q^67 - 106 * q^68 - 115 * q^69 - 60 * q^70 - 68 * q^71 - 66 * q^72 - 109 * q^73 - 74 * q^74 - 256 * q^75 - 412 * q^76 - 32 * q^77 - 38 * q^78 - 297 * q^79 - 111 * q^80 + 142 * q^81 - 94 * q^82 - 100 * q^83 - 134 * q^84 - 90 * q^85 + q^86 - 103 * q^87 - 143 * q^88 - 77 * q^89 - 181 * q^90 - 418 * q^91 - 19 * q^92 + 5 * q^93 - 231 * q^94 - 92 * q^95 - 189 * q^96 - 141 * q^97 - 25 * q^98 - 244 * q^99

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