LMFDB - Embedded newform 6034.2.a.r.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.29198 q^{3} +1.00000 q^{4} -1.58360 q^{5} -3.29198 q^{6} -1.00000 q^{7} +1.00000 q^{8} +7.83715 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.29198 q^{3} +1.00000 q^{4} -1.58360 q^{5} -3.29198 q^{6} -1.00000 q^{7} +1.00000 q^{8} +7.83715 q^{9} -1.58360 q^{10} -1.04429 q^{11} -3.29198 q^{12} +5.91311 q^{13} -1.00000 q^{14} +5.21319 q^{15} +1.00000 q^{16} +6.46407 q^{17} +7.83715 q^{18} +1.93103 q^{19} -1.58360 q^{20} +3.29198 q^{21} -1.04429 q^{22} -6.43182 q^{23} -3.29198 q^{24} -2.49220 q^{25} +5.91311 q^{26} -15.9238 q^{27} -1.00000 q^{28} +7.87631 q^{29} +5.21319 q^{30} +5.52603 q^{31} +1.00000 q^{32} +3.43778 q^{33} +6.46407 q^{34} +1.58360 q^{35} +7.83715 q^{36} -10.2335 q^{37} +1.93103 q^{38} -19.4659 q^{39} -1.58360 q^{40} +6.16217 q^{41} +3.29198 q^{42} +6.15886 q^{43} -1.04429 q^{44} -12.4109 q^{45} -6.43182 q^{46} +1.35515 q^{47} -3.29198 q^{48} +1.00000 q^{49} -2.49220 q^{50} -21.2796 q^{51} +5.91311 q^{52} -6.74266 q^{53} -15.9238 q^{54} +1.65374 q^{55} -1.00000 q^{56} -6.35692 q^{57} +7.87631 q^{58} +2.59978 q^{59} +5.21319 q^{60} +3.85482 q^{61} +5.52603 q^{62} -7.83715 q^{63} +1.00000 q^{64} -9.36402 q^{65} +3.43778 q^{66} +6.13084 q^{67} +6.46407 q^{68} +21.1734 q^{69} +1.58360 q^{70} -10.2969 q^{71} +7.83715 q^{72} -6.83546 q^{73} -10.2335 q^{74} +8.20428 q^{75} +1.93103 q^{76} +1.04429 q^{77} -19.4659 q^{78} -13.6844 q^{79} -1.58360 q^{80} +28.9094 q^{81} +6.16217 q^{82} -17.7353 q^{83} +3.29198 q^{84} -10.2365 q^{85} +6.15886 q^{86} -25.9287 q^{87} -1.04429 q^{88} +11.8742 q^{89} -12.4109 q^{90} -5.91311 q^{91} -6.43182 q^{92} -18.1916 q^{93} +1.35515 q^{94} -3.05798 q^{95} -3.29198 q^{96} -16.8320 q^{97} +1.00000 q^{98} -8.18425 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9} + 15 q^{10} + 12 q^{11} + 7 q^{12} + 26 q^{13} - 31 q^{14} + 6 q^{15} + 31 q^{16} + 33 q^{17} + 42 q^{18} + 34 q^{19} + 15 q^{20} - 7 q^{21} + 12 q^{22} - 14 q^{23} + 7 q^{24} + 58 q^{25} + 26 q^{26} + 28 q^{27} - 31 q^{28} + 11 q^{29} + 6 q^{30} + 19 q^{31} + 31 q^{32} + 43 q^{33} + 33 q^{34} - 15 q^{35} + 42 q^{36} + 2 q^{37} + 34 q^{38} - 16 q^{39} + 15 q^{40} + 53 q^{41} - 7 q^{42} + 22 q^{43} + 12 q^{44} + 43 q^{45} - 14 q^{46} + 27 q^{47} + 7 q^{48} + 31 q^{49} + 58 q^{50} + 17 q^{51} + 26 q^{52} + 11 q^{53} + 28 q^{54} + 19 q^{55} - 31 q^{56} + 45 q^{57} + 11 q^{58} + 54 q^{59} + 6 q^{60} + 41 q^{61} + 19 q^{62} - 42 q^{63} + 31 q^{64} + 30 q^{65} + 43 q^{66} + 13 q^{67} + 33 q^{68} + 17 q^{69} - 15 q^{70} + 43 q^{71} + 42 q^{72} + 42 q^{73} + 2 q^{74} + 62 q^{75} + 34 q^{76} - 12 q^{77} - 16 q^{78} - 12 q^{79} + 15 q^{80} + 63 q^{81} + 53 q^{82} + 35 q^{83} - 7 q^{84} + 16 q^{85} + 22 q^{86} - 4 q^{87} + 12 q^{88} + 115 q^{89} + 43 q^{90} - 26 q^{91} - 14 q^{92} + q^{93} + 27 q^{94} - 13 q^{95} + 7 q^{96} + 32 q^{97} + 31 q^{98} + 34 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9 + 15 * q^10 + 12 * q^11 + 7 * q^12 + 26 * q^13 - 31 * q^14 + 6 * q^15 + 31 * q^16 + 33 * q^17 + 42 * q^18 + 34 * q^19 + 15 * q^20 - 7 * q^21 + 12 * q^22 - 14 * q^23 + 7 * q^24 + 58 * q^25 + 26 * q^26 + 28 * q^27 - 31 * q^28 + 11 * q^29 + 6 * q^30 + 19 * q^31 + 31 * q^32 + 43 * q^33 + 33 * q^34 - 15 * q^35 + 42 * q^36 + 2 * q^37 + 34 * q^38 - 16 * q^39 + 15 * q^40 + 53 * q^41 - 7 * q^42 + 22 * q^43 + 12 * q^44 + 43 * q^45 - 14 * q^46 + 27 * q^47 + 7 * q^48 + 31 * q^49 + 58 * q^50 + 17 * q^51 + 26 * q^52 + 11 * q^53 + 28 * q^54 + 19 * q^55 - 31 * q^56 + 45 * q^57 + 11 * q^58 + 54 * q^59 + 6 * q^60 + 41 * q^61 + 19 * q^62 - 42 * q^63 + 31 * q^64 + 30 * q^65 + 43 * q^66 + 13 * q^67 + 33 * q^68 + 17 * q^69 - 15 * q^70 + 43 * q^71 + 42 * q^72 + 42 * q^73 + 2 * q^74 + 62 * q^75 + 34 * q^76 - 12 * q^77 - 16 * q^78 - 12 * q^79 + 15 * q^80 + 63 * q^81 + 53 * q^82 + 35 * q^83 - 7 * q^84 + 16 * q^85 + 22 * q^86 - 4 * q^87 + 12 * q^88 + 115 * q^89 + 43 * q^90 - 26 * q^91 - 14 * q^92 + q^93 + 27 * q^94 - 13 * q^95 + 7 * q^96 + 32 * q^97 + 31 * q^98 + 34 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.29198	−1.90063	−0.950313	−	0.311295i	$-0.899237\pi$
$3$	−3.29198	−1.90063	−0.950313	+	0.311295i	$0.899237\pi$
$4$	1.00000	0.500000
$5$	−1.58360	−0.708209	−0.354104	−	0.935206i	$-0.615214\pi$
$5$	−1.58360	−0.708209	−0.354104	+	0.935206i	$0.615214\pi$
$6$	−3.29198	−1.34395
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	7.83715	2.61238
$10$	−1.58360	−0.500779
$11$	−1.04429	−0.314865	−0.157433	−	0.987530i	$-0.550322\pi$
$11$	−1.04429	−0.314865	−0.157433	+	0.987530i	$0.550322\pi$
$12$	−3.29198	−0.950313
$13$	5.91311	1.64000	0.820001	−	0.572362i	$-0.193973\pi$
$13$	5.91311	1.64000	0.820001	+	0.572362i	$0.193973\pi$
$14$	−1.00000	−0.267261
$15$	5.21319	1.34604
$16$	1.00000	0.250000
$17$	6.46407	1.56777	0.783884	−	0.620908i	$-0.213236\pi$
$17$	6.46407	1.56777	0.783884	+	0.620908i	$0.213236\pi$
$18$	7.83715	1.84723
$19$	1.93103	0.443009	0.221504	−	0.975159i	$-0.428903\pi$
$19$	1.93103	0.443009	0.221504	+	0.975159i	$0.428903\pi$
$20$	−1.58360	−0.354104
$21$	3.29198	0.718369
$22$	−1.04429	−0.222643
$23$	−6.43182	−1.34113	−0.670563	−	0.741852i	$-0.733947\pi$
$23$	−6.43182	−1.34113	−0.670563	+	0.741852i	$0.733947\pi$
$24$	−3.29198	−0.671973
$25$	−2.49220	−0.498440
$26$	5.91311	1.15966
$27$	−15.9238	−3.06454
$28$	−1.00000	−0.188982
$29$	7.87631	1.46259	0.731297	−	0.682060i	$-0.238916\pi$
$29$	7.87631	1.46259	0.731297	+	0.682060i	$0.238916\pi$
$30$	5.21319	0.951794
$31$	5.52603	0.992504	0.496252	−	0.868178i	$-0.334709\pi$
$31$	5.52603	0.992504	0.496252	+	0.868178i	$0.334709\pi$
$32$	1.00000	0.176777
$33$	3.43778	0.598441
$34$	6.46407	1.10858
$35$	1.58360	0.267678
$36$	7.83715	1.30619
$37$	−10.2335	−1.68238	−0.841190	−	0.540740i	$-0.818144\pi$
$37$	−10.2335	−1.68238	−0.841190	+	0.540740i	$0.818144\pi$
$38$	1.93103	0.313254
$39$	−19.4659	−3.11703
$40$	−1.58360	−0.250390
$41$	6.16217	0.962369	0.481185	−	0.876619i	$-0.340207\pi$
$41$	6.16217	0.962369	0.481185	+	0.876619i	$0.340207\pi$
$42$	3.29198	0.507964
$43$	6.15886	0.939218	0.469609	−	0.882875i	$-0.344395\pi$
$43$	6.15886	0.939218	0.469609	+	0.882875i	$0.344395\pi$
$44$	−1.04429	−0.157433
$45$	−12.4109	−1.85011
$46$	−6.43182	−0.948320
$47$	1.35515	0.197668	0.0988342	−	0.995104i	$-0.468489\pi$
$47$	1.35515	0.197668	0.0988342	+	0.995104i	$0.468489\pi$
$48$	−3.29198	−0.475157
$49$	1.00000	0.142857
$50$	−2.49220	−0.352451
$51$	−21.2796	−2.97974
$52$	5.91311	0.820001
$53$	−6.74266	−0.926176	−0.463088	−	0.886312i	$-0.653259\pi$
$53$	−6.74266	−0.926176	−0.463088	+	0.886312i	$0.653259\pi$
$54$	−15.9238	−2.16695
$55$	1.65374	0.222990
$56$	−1.00000	−0.133631
$57$	−6.35692	−0.841994
$58$	7.87631	1.03421
$59$	2.59978	0.338462	0.169231	−	0.985576i	$-0.445872\pi$
$59$	2.59978	0.338462	0.169231	+	0.985576i	$0.445872\pi$
$60$	5.21319	0.673020
$61$	3.85482	0.493560	0.246780	−	0.969072i	$-0.420628\pi$
$61$	3.85482	0.493560	0.246780	+	0.969072i	$0.420628\pi$
$62$	5.52603	0.701806
$63$	−7.83715	−0.987388
$64$	1.00000	0.125000
$65$	−9.36402	−1.16146
$66$	3.43778	0.423162
$67$	6.13084	0.749001	0.374500	−	0.927227i	$-0.377814\pi$
$67$	6.13084	0.749001	0.374500	+	0.927227i	$0.377814\pi$
$68$	6.46407	0.783884
$69$	21.1734	2.54898
$70$	1.58360	0.189277
$71$	−10.2969	−1.22201	−0.611006	−	0.791626i	$-0.709235\pi$
$71$	−10.2969	−1.22201	−0.611006	+	0.791626i	$0.709235\pi$
$72$	7.83715	0.923617
$73$	−6.83546	−0.800030	−0.400015	−	0.916509i	$-0.630995\pi$
$73$	−6.83546	−0.800030	−0.400015	+	0.916509i	$0.630995\pi$
$74$	−10.2335	−1.18962
$75$	8.20428	0.947349
$76$	1.93103	0.221504
$77$	1.04429	0.119008
$78$	−19.4659	−2.20407
$79$	−13.6844	−1.53962	−0.769808	−	0.638276i	$-0.779648\pi$
$79$	−13.6844	−1.53962	−0.769808	+	0.638276i	$0.779648\pi$
$80$	−1.58360	−0.177052
$81$	28.9094	3.21216
$82$	6.16217	0.680498
$83$	−17.7353	−1.94670	−0.973352	−	0.229314i	$-0.926352\pi$
$83$	−17.7353	−1.94670	−0.973352	+	0.229314i	$0.926352\pi$
$84$	3.29198	0.359185
$85$	−10.2365	−1.11031
$86$	6.15886	0.664127
$87$	−25.9287	−2.77984
$88$	−1.04429	−0.111322
$89$	11.8742	1.25866	0.629332	−	0.777137i	$-0.283329\pi$
$89$	11.8742	1.25866	0.629332	+	0.777137i	$0.283329\pi$
$90$	−12.4109	−1.30823
$91$	−5.91311	−0.619862
$92$	−6.43182	−0.670563
$93$	−18.1916	−1.88638
$94$	1.35515	0.139773
$95$	−3.05798	−0.313743
$96$	−3.29198	−0.335987
$97$	−16.8320	−1.70903	−0.854515	−	0.519427i	$-0.826145\pi$
$97$	−16.8320	−1.70903	−0.854515	+	0.519427i	$0.826145\pi$
$98$	1.00000	0.101015
$99$	−8.18425	−0.822548
$100$	−2.49220	−0.249220
$101$	15.9596	1.58804	0.794020	−	0.607892i	$-0.207985\pi$
$101$	15.9596	1.58804	0.794020	+	0.607892i	$0.207985\pi$
$102$	−21.2796	−2.10699
$103$	−2.59763	−0.255952	−0.127976	−	0.991777i	$-0.540848\pi$
$103$	−2.59763	−0.255952	−0.127976	+	0.991777i	$0.540848\pi$
$104$	5.91311	0.579828
$105$	−5.21319	−0.508756
$106$	−6.74266	−0.654905
$107$	9.77966	0.945436	0.472718	−	0.881214i	$-0.343273\pi$
$107$	9.77966	0.945436	0.472718	+	0.881214i	$0.343273\pi$
$108$	−15.9238	−1.53227
$109$	14.1494	1.35526	0.677632	−	0.735401i	$-0.263006\pi$
$109$	14.1494	1.35526	0.677632	+	0.735401i	$0.263006\pi$
$110$	1.65374	0.157678
$111$	33.6886	3.19758
$112$	−1.00000	−0.0944911
$113$	7.67897	0.722377	0.361189	−	0.932493i	$-0.382371\pi$
$113$	7.67897	0.722377	0.361189	+	0.932493i	$0.382371\pi$
$114$	−6.35692	−0.595380
$115$	10.1854	0.949797
$116$	7.87631	0.731297
$117$	46.3419	4.28431
$118$	2.59978	0.239329
$119$	−6.46407	−0.592560
$120$	5.21319	0.475897
$121$	−9.90946	−0.900860
$122$	3.85482	0.348999
$123$	−20.2857	−1.82910
$124$	5.52603	0.496252
$125$	11.8647	1.06121
$126$	−7.83715	−0.698188
$127$	8.07114	0.716198	0.358099	−	0.933684i	$-0.383425\pi$
$127$	8.07114	0.716198	0.358099	+	0.933684i	$0.383425\pi$
$128$	1.00000	0.0883883
$129$	−20.2749	−1.78510
$130$	−9.36402	−0.821279
$131$	−9.57144	−0.836260	−0.418130	−	0.908387i	$-0.637314\pi$
$131$	−9.57144	−0.836260	−0.418130	+	0.908387i	$0.637314\pi$
$132$	3.43778	0.299221
$133$	−1.93103	−0.167442
$134$	6.13084	0.529624
$135$	25.2170	2.17033
$136$	6.46407	0.554289
$137$	8.45364	0.722244	0.361122	−	0.932519i	$-0.382394\pi$
$137$	8.45364	0.722244	0.361122	+	0.932519i	$0.382394\pi$
$138$	21.1734	1.80240
$139$	9.32592	0.791014	0.395507	−	0.918463i	$-0.370569\pi$
$139$	9.32592	0.791014	0.395507	+	0.918463i	$0.370569\pi$
$140$	1.58360	0.133839
$141$	−4.46112	−0.375694
$142$	−10.2969	−0.864093
$143$	−6.17500	−0.516379
$144$	7.83715	0.653096
$145$	−12.4729	−1.03582
$146$	−6.83546	−0.565707
$147$	−3.29198	−0.271518
$148$	−10.2335	−0.841190
$149$	−22.8422	−1.87130	−0.935652	−	0.352923i	$-0.885188\pi$
$149$	−22.8422	−1.87130	−0.935652	+	0.352923i	$0.885188\pi$
$150$	8.20428	0.669877
$151$	−8.32283	−0.677302	−0.338651	−	0.940912i	$-0.609971\pi$
$151$	−8.32283	−0.677302	−0.338651	+	0.940912i	$0.609971\pi$
$152$	1.93103	0.156627
$153$	50.6599	4.09561
$154$	1.04429	0.0841513
$155$	−8.75104	−0.702900
$156$	−19.4659	−1.55852
$157$	10.1764	0.812166	0.406083	−	0.913836i	$-0.366894\pi$
$157$	10.1764	0.812166	0.406083	+	0.913836i	$0.366894\pi$
$158$	−13.6844	−1.08867
$159$	22.1967	1.76032
$160$	−1.58360	−0.125195
$161$	6.43182	0.506898
$162$	28.9094	2.27134
$163$	13.2032	1.03415	0.517076	−	0.855940i	$-0.327020\pi$
$163$	13.2032	1.03415	0.517076	+	0.855940i	$0.327020\pi$
$164$	6.16217	0.481185
$165$	−5.44408	−0.423821
$166$	−17.7353	−1.37653
$167$	−1.38903	−0.107486	−0.0537432	−	0.998555i	$-0.517115\pi$
$167$	−1.38903	−0.107486	−0.0537432	+	0.998555i	$0.517115\pi$
$168$	3.29198	0.253982
$169$	21.9649	1.68961
$170$	−10.2365	−0.785105
$171$	15.1338	1.15731
$172$	6.15886	0.469609
$173$	−4.52377	−0.343936	−0.171968	−	0.985103i	$-0.555013\pi$
$173$	−4.52377	−0.343936	−0.171968	+	0.985103i	$0.555013\pi$
$174$	−25.9287	−1.96565
$175$	2.49220	0.188393
$176$	−1.04429	−0.0787163
$177$	−8.55842	−0.643291
$178$	11.8742	0.890010
$179$	24.9209	1.86267	0.931336	−	0.364161i	$-0.118644\pi$
$179$	24.9209	1.86267	0.931336	+	0.364161i	$0.118644\pi$
$180$	−12.4109	−0.925056
$181$	−1.90310	−0.141456	−0.0707281	−	0.997496i	$-0.522532\pi$
$181$	−1.90310	−0.141456	−0.0707281	+	0.997496i	$0.522532\pi$
$182$	−5.91311	−0.438309
$183$	−12.6900	−0.938072
$184$	−6.43182	−0.474160
$185$	16.2058	1.19148
$186$	−18.1916	−1.33387
$187$	−6.75036	−0.493635
$188$	1.35515	0.0988342
$189$	15.9238	1.15829
$190$	−3.05798	−0.221850
$191$	1.64252	0.118849	0.0594243	−	0.998233i	$-0.481073\pi$
$191$	1.64252	0.118849	0.0594243	+	0.998233i	$0.481073\pi$
$192$	−3.29198	−0.237578
$193$	−3.78037	−0.272117	−0.136058	−	0.990701i	$-0.543443\pi$
$193$	−3.78037	−0.272117	−0.136058	+	0.990701i	$0.543443\pi$
$194$	−16.8320	−1.20847
$195$	30.8262	2.20751
$196$	1.00000	0.0714286
$197$	9.38742	0.668826	0.334413	−	0.942427i	$-0.391462\pi$
$197$	9.38742	0.668826	0.334413	+	0.942427i	$0.391462\pi$
$198$	−8.18425	−0.581629
$199$	5.02451	0.356178	0.178089	−	0.984014i	$-0.443008\pi$
$199$	5.02451	0.356178	0.178089	+	0.984014i	$0.443008\pi$
$200$	−2.49220	−0.176225
$201$	−20.1826	−1.42357
$202$	15.9596	1.12291
$203$	−7.87631	−0.552808
$204$	−21.2796	−1.48987
$205$	−9.75843	−0.681558
$206$	−2.59763	−0.180985
$207$	−50.4071	−3.50353
$208$	5.91311	0.410000
$209$	−2.01655	−0.139488
$210$	−5.21319	−0.359744
$211$	1.52528	0.105005	0.0525023	−	0.998621i	$-0.483280\pi$
$211$	1.52528	0.105005	0.0525023	+	0.998621i	$0.483280\pi$
$212$	−6.74266	−0.463088
$213$	33.8971	2.32259
$214$	9.77966	0.668524
$215$	−9.75319	−0.665162
$216$	−15.9238	−1.08348
$217$	−5.52603	−0.375131
$218$	14.1494	0.958317
$219$	22.5022	1.52056
$220$	1.65374	0.111495
$221$	38.2228	2.57114
$222$	33.6886	2.26103
$223$	9.42133	0.630899	0.315450	−	0.948942i	$-0.397845\pi$
$223$	9.42133	0.630899	0.315450	+	0.948942i	$0.397845\pi$
$224$	−1.00000	−0.0668153
$225$	−19.5317	−1.30212
$226$	7.67897	0.510798
$227$	20.9263	1.38892	0.694462	−	0.719529i	$-0.255642\pi$
$227$	20.9263	1.38892	0.694462	+	0.719529i	$0.255642\pi$
$228$	−6.35692	−0.420997
$229$	−9.97264	−0.659011	−0.329505	−	0.944154i	$-0.606882\pi$
$229$	−9.97264	−0.659011	−0.329505	+	0.944154i	$0.606882\pi$
$230$	10.1854	0.671608
$231$	−3.43778	−0.226189
$232$	7.87631	0.517105
$233$	−3.07790	−0.201640	−0.100820	−	0.994905i	$-0.532147\pi$
$233$	−3.07790	−0.201640	−0.100820	+	0.994905i	$0.532147\pi$
$234$	46.3419	3.02947
$235$	−2.14601	−0.139991
$236$	2.59978	0.169231
$237$	45.0488	2.92623
$238$	−6.46407	−0.419003
$239$	−10.1819	−0.658615	−0.329307	−	0.944223i	$-0.606815\pi$
$239$	−10.1819	−0.658615	−0.329307	+	0.944223i	$0.606815\pi$
$240$	5.21319	0.336510
$241$	20.6539	1.33043	0.665216	−	0.746651i	$-0.268339\pi$
$241$	20.6539	1.33043	0.665216	+	0.746651i	$0.268339\pi$
$242$	−9.90946	−0.637004
$243$	−47.3979	−3.04058
$244$	3.85482	0.246780
$245$	−1.58360	−0.101173
$246$	−20.2857	−1.29337
$247$	11.4184	0.726535
$248$	5.52603	0.350903
$249$	58.3844	3.69996
$250$	11.8647	0.750388
$251$	18.0662	1.14033	0.570163	−	0.821531i	$-0.306880\pi$
$251$	18.0662	1.14033	0.570163	+	0.821531i	$0.306880\pi$
$252$	−7.83715	−0.493694
$253$	6.71668	0.422274
$254$	8.07114	0.506428
$255$	33.6984	2.11028
$256$	1.00000	0.0625000
$257$	22.9396	1.43094	0.715468	−	0.698646i	$-0.246214\pi$
$257$	22.9396	1.43094	0.715468	+	0.698646i	$0.246214\pi$
$258$	−20.2749	−1.26226
$259$	10.2335	0.635880
$260$	−9.36402	−0.580732
$261$	61.7278	3.82085
$262$	−9.57144	−0.591325
$263$	19.7834	1.21990	0.609949	−	0.792441i	$-0.291190\pi$
$263$	19.7834	1.21990	0.609949	+	0.792441i	$0.291190\pi$
$264$	3.43778	0.211581
$265$	10.6777	0.655926
$266$	−1.93103	−0.118399
$267$	−39.0897	−2.39225
$268$	6.13084	0.374500
$269$	8.11747	0.494931	0.247466	−	0.968897i	$-0.420402\pi$
$269$	8.11747	0.494931	0.247466	+	0.968897i	$0.420402\pi$
$270$	25.2170	1.53466
$271$	3.82856	0.232569	0.116284	−	0.993216i	$-0.462902\pi$
$271$	3.82856	0.232569	0.116284	+	0.993216i	$0.462902\pi$
$272$	6.46407	0.391942
$273$	19.4659	1.17813
$274$	8.45364	0.510703
$275$	2.60258	0.156941
$276$	21.1734	1.27449
$277$	−23.3516	−1.40306	−0.701531	−	0.712639i	$-0.747500\pi$
$277$	−23.3516	−1.40306	−0.701531	+	0.712639i	$0.747500\pi$
$278$	9.32592	0.559331
$279$	43.3083	2.59280
$280$	1.58360	0.0946384
$281$	−21.9269	−1.30805	−0.654025	−	0.756473i	$-0.726921\pi$
$281$	−21.9269	−1.30805	−0.654025	+	0.756473i	$0.726921\pi$
$282$	−4.46112	−0.265656
$283$	14.2045	0.844368	0.422184	−	0.906510i	$-0.361264\pi$
$283$	14.2045	0.844368	0.422184	+	0.906510i	$0.361264\pi$
$284$	−10.2969	−0.611006
$285$	10.0668	0.596308
$286$	−6.17500	−0.365135
$287$	−6.16217	−0.363741
$288$	7.83715	0.461808
$289$	24.7842	1.45789
$290$	−12.4729	−0.732436
$291$	55.4106	3.24823
$292$	−6.83546	−0.400015
$293$	7.96349	0.465232	0.232616	−	0.972569i	$-0.425271\pi$
$293$	7.96349	0.465232	0.232616	+	0.972569i	$0.425271\pi$
$294$	−3.29198	−0.191992
$295$	−4.11702	−0.239702
$296$	−10.2335	−0.594811
$297$	16.6291	0.964916
$298$	−22.8422	−1.32321
$299$	−38.0320	−2.19945
$300$	8.20428	0.473674
$301$	−6.15886	−0.354991
$302$	−8.32283	−0.478925
$303$	−52.5387	−3.01827
$304$	1.93103	0.110752
$305$	−6.10451	−0.349543
$306$	50.6599	2.89603
$307$	−9.24768	−0.527793	−0.263897	−	0.964551i	$-0.585008\pi$
$307$	−9.24768	−0.527793	−0.263897	+	0.964551i	$0.585008\pi$
$308$	1.04429	0.0595039
$309$	8.55134	0.486469
$310$	−8.75104	−0.497025
$311$	−19.3756	−1.09869	−0.549346	−	0.835595i	$-0.685123\pi$
$311$	−19.3756	−1.09869	−0.549346	+	0.835595i	$0.685123\pi$
$312$	−19.4659	−1.10204
$313$	−7.08348	−0.400382	−0.200191	−	0.979757i	$-0.564156\pi$
$313$	−7.08348	−0.400382	−0.200191	+	0.979757i	$0.564156\pi$
$314$	10.1764	0.574288
$315$	12.4109	0.699277
$316$	−13.6844	−0.769808
$317$	−13.0506	−0.732992	−0.366496	−	0.930420i	$-0.619443\pi$
$317$	−13.0506	−0.732992	−0.366496	+	0.930420i	$0.619443\pi$
$318$	22.1967	1.24473
$319$	−8.22514	−0.460520
$320$	−1.58360	−0.0885261
$321$	−32.1945	−1.79692
$322$	6.43182	0.358431
$323$	12.4823	0.694534
$324$	28.9094	1.60608
$325$	−14.7367	−0.817443
$326$	13.2032	0.731256
$327$	−46.5795	−2.57585
$328$	6.16217	0.340249
$329$	−1.35515	−0.0747116
$330$	−5.44408	−0.299687
$331$	−14.1584	−0.778217	−0.389108	−	0.921192i	$-0.627217\pi$
$331$	−14.1584	−0.778217	−0.389108	+	0.921192i	$0.627217\pi$
$332$	−17.7353	−0.973352
$333$	−80.2016	−4.39502
$334$	−1.38903	−0.0760043
$335$	−9.70881	−0.530449
$336$	3.29198	0.179592
$337$	20.8841	1.13763	0.568814	−	0.822466i	$-0.307402\pi$
$337$	20.8841	1.13763	0.568814	+	0.822466i	$0.307402\pi$
$338$	21.9649	1.19473
$339$	−25.2790	−1.37297
$340$	−10.2365	−0.555153
$341$	−5.77077	−0.312505
$342$	15.1338	0.818340
$343$	−1.00000	−0.0539949
$344$	6.15886	0.332064
$345$	−33.5303	−1.80521
$346$	−4.52377	−0.243199
$347$	16.2642	0.873110	0.436555	−	0.899677i	$-0.356198\pi$
$347$	16.2642	0.873110	0.436555	+	0.899677i	$0.356198\pi$
$348$	−25.9287	−1.38992
$349$	14.5526	0.778983	0.389491	−	0.921030i	$-0.372651\pi$
$349$	14.5526	0.778983	0.389491	+	0.921030i	$0.372651\pi$
$350$	2.49220	0.133214
$351$	−94.1592	−5.02585
$352$	−1.04429	−0.0556608
$353$	12.4550	0.662913	0.331456	−	0.943471i	$-0.392460\pi$
$353$	12.4550	0.662913	0.331456	+	0.943471i	$0.392460\pi$
$354$	−8.55842	−0.454875
$355$	16.3061	0.865440
$356$	11.8742	0.629332
$357$	21.2796	1.12624
$358$	24.9209	1.31711
$359$	17.6306	0.930510	0.465255	−	0.885177i	$-0.345963\pi$
$359$	17.6306	0.930510	0.465255	+	0.885177i	$0.345963\pi$
$360$	−12.4109	−0.654113
$361$	−15.2711	−0.803743
$362$	−1.90310	−0.100025
$363$	32.6218	1.71220
$364$	−5.91311	−0.309931
$365$	10.8247	0.566588
$366$	−12.6900	−0.663317
$367$	−3.78521	−0.197586	−0.0987931	−	0.995108i	$-0.531498\pi$
$367$	−3.78521	−0.197586	−0.0987931	+	0.995108i	$0.531498\pi$
$368$	−6.43182	−0.335282
$369$	48.2938	2.51408
$370$	16.2058	0.842501
$371$	6.74266	0.350062
$372$	−18.1916	−0.943190
$373$	−21.2484	−1.10020	−0.550100	−	0.835099i	$-0.685410\pi$
$373$	−21.2484	−1.10020	−0.550100	+	0.835099i	$0.685410\pi$
$374$	−6.75036	−0.349053
$375$	−39.0583	−2.01696
$376$	1.35515	0.0698863
$377$	46.5735	2.39866
$378$	15.9238	0.819032
$379$	6.88934	0.353882	0.176941	−	0.984222i	$-0.443380\pi$
$379$	6.88934	0.353882	0.176941	+	0.984222i	$0.443380\pi$
$380$	−3.05798	−0.156871
$381$	−26.5701	−1.36122
$382$	1.64252	0.0840387
$383$	−3.24799	−0.165964	−0.0829822	−	0.996551i	$-0.526444\pi$
$383$	−3.24799	−0.165964	−0.0829822	+	0.996551i	$0.526444\pi$
$384$	−3.29198	−0.167993
$385$	−1.65374	−0.0842824
$386$	−3.78037	−0.192416
$387$	48.2679	2.45360
$388$	−16.8320	−0.854515
$389$	36.6365	1.85754	0.928771	−	0.370654i	$-0.120866\pi$
$389$	36.6365	1.85754	0.928771	+	0.370654i	$0.120866\pi$
$390$	30.8262	1.56094
$391$	−41.5757	−2.10257
$392$	1.00000	0.0505076
$393$	31.5090	1.58942
$394$	9.38742	0.472931
$395$	21.6707	1.09037
$396$	−8.18425	−0.411274
$397$	−4.30614	−0.216119	−0.108060	−	0.994144i	$-0.534464\pi$
$397$	−4.30614	−0.216119	−0.108060	+	0.994144i	$0.534464\pi$
$398$	5.02451	0.251856
$399$	6.35692	0.318244
$400$	−2.49220	−0.124610
$401$	−9.72496	−0.485641	−0.242821	−	0.970071i	$-0.578073\pi$
$401$	−9.72496	−0.485641	−0.242821	+	0.970071i	$0.578073\pi$
$402$	−20.1826	−1.00662
$403$	32.6760	1.62771
$404$	15.9596	0.794020
$405$	−45.7810	−2.27488
$406$	−7.87631	−0.390894
$407$	10.6868	0.529723
$408$	−21.2796	−1.05350
$409$	−35.7663	−1.76853	−0.884265	−	0.466985i	$-0.845340\pi$
$409$	−35.7663	−1.76853	−0.884265	+	0.466985i	$0.845340\pi$
$410$	−9.75843	−0.481934
$411$	−27.8292	−1.37272
$412$	−2.59763	−0.127976
$413$	−2.59978	−0.127927
$414$	−50.4071	−2.47737
$415$	28.0857	1.37867
$416$	5.91311	0.289914
$417$	−30.7008	−1.50342
$418$	−2.01655	−0.0986329
$419$	11.5896	0.566190	0.283095	−	0.959092i	$-0.408639\pi$
$419$	11.5896	0.566190	0.283095	+	0.959092i	$0.408639\pi$
$420$	−5.21319	−0.254378
$421$	24.6478	1.20126	0.600630	−	0.799527i	$-0.294917\pi$
$421$	24.6478	1.20126	0.600630	+	0.799527i	$0.294917\pi$
$422$	1.52528	0.0742495
$423$	10.6205	0.516385
$424$	−6.74266	−0.327453
$425$	−16.1098	−0.781438
$426$	33.8971	1.64232
$427$	−3.85482	−0.186548
$428$	9.77966	0.472718
$429$	20.3280	0.981445
$430$	−9.75319	−0.470341
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	−15.9238	−0.766134
$433$	−22.6705	−1.08948	−0.544738	−	0.838606i	$-0.683371\pi$
$433$	−22.6705	−1.08948	−0.544738	+	0.838606i	$0.683371\pi$
$434$	−5.52603	−0.265258
$435$	41.0607	1.96871
$436$	14.1494	0.677632
$437$	−12.4200	−0.594131
$438$	22.5022	1.07520
$439$	−10.9560	−0.522899	−0.261450	−	0.965217i	$-0.584201\pi$
$439$	−10.9560	−0.522899	−0.261450	+	0.965217i	$0.584201\pi$
$440$	1.65374	0.0788390
$441$	7.83715	0.373197
$442$	38.2228	1.81807
$443$	−34.2211	−1.62589	−0.812947	−	0.582337i	$-0.802138\pi$
$443$	−34.2211	−1.62589	−0.812947	+	0.582337i	$0.802138\pi$
$444$	33.6886	1.59879
$445$	−18.8040	−0.891397
$446$	9.42133	0.446113
$447$	75.1961	3.55665
$448$	−1.00000	−0.0472456
$449$	8.42266	0.397490	0.198745	−	0.980051i	$-0.436313\pi$
$449$	8.42266	0.397490	0.198745	+	0.980051i	$0.436313\pi$
$450$	−19.5317	−0.920735
$451$	−6.43509	−0.303016
$452$	7.67897	0.361189
$453$	27.3986	1.28730
$454$	20.9263	0.982118
$455$	9.36402	0.438992
$456$	−6.35692	−0.297690
$457$	8.89532	0.416106	0.208053	−	0.978118i	$-0.433287\pi$
$457$	8.89532	0.416106	0.208053	+	0.978118i	$0.433287\pi$
$458$	−9.97264	−0.465991
$459$	−102.933	−4.80448
$460$	10.1854	0.474899
$461$	−8.42714	−0.392491	−0.196246	−	0.980555i	$-0.562875\pi$
$461$	−8.42714	−0.392491	−0.196246	+	0.980555i	$0.562875\pi$
$462$	−3.43778	−0.159940
$463$	13.3927	0.622410	0.311205	−	0.950343i	$-0.399267\pi$
$463$	13.3927	0.622410	0.311205	+	0.950343i	$0.399267\pi$
$464$	7.87631	0.365648
$465$	28.8083	1.33595
$466$	−3.07790	−0.142581
$467$	11.0212	0.510002	0.255001	−	0.966941i	$-0.417924\pi$
$467$	11.0212	0.510002	0.255001	+	0.966941i	$0.417924\pi$
$468$	46.3419	2.14216
$469$	−6.13084	−0.283096
$470$	−2.14601	−0.0989882
$471$	−33.5006	−1.54363
$472$	2.59978	0.119665
$473$	−6.43163	−0.295727
$474$	45.0488	2.06916
$475$	−4.81252	−0.220813
$476$	−6.46407	−0.296280
$477$	−52.8432	−2.41953
$478$	−10.1819	−0.465711
$479$	−19.1823	−0.876461	−0.438230	−	0.898863i	$-0.644395\pi$
$479$	−19.1823	−0.876461	−0.438230	+	0.898863i	$0.644395\pi$
$480$	5.21319	0.237949
$481$	−60.5119	−2.75911
$482$	20.6539	0.940758
$483$	−21.1734	−0.963424
$484$	−9.90946	−0.450430
$485$	26.6552	1.21035
$486$	−47.3979	−2.15001
$487$	27.9885	1.26828	0.634140	−	0.773218i	$-0.281354\pi$
$487$	27.9885	1.26828	0.634140	+	0.773218i	$0.281354\pi$
$488$	3.85482	0.174500
$489$	−43.4646	−1.96554
$490$	−1.58360	−0.0715399
$491$	32.1273	1.44989	0.724943	−	0.688809i	$-0.241866\pi$
$491$	32.1273	1.44989	0.724943	+	0.688809i	$0.241866\pi$
$492$	−20.2857	−0.914552
$493$	50.9130	2.29301
$494$	11.4184	0.513738
$495$	12.9606	0.582536
$496$	5.52603	0.248126
$497$	10.2969	0.461877
$498$	58.3844	2.61627
$499$	32.4197	1.45131	0.725653	−	0.688061i	$-0.241538\pi$
$499$	32.4197	1.45131	0.725653	+	0.688061i	$0.241538\pi$
$500$	11.8647	0.530604
$501$	4.57266	0.204291
$502$	18.0662	0.806333
$503$	26.1240	1.16481	0.582405	−	0.812899i	$-0.302112\pi$
$503$	26.1240	1.16481	0.582405	+	0.812899i	$0.302112\pi$
$504$	−7.83715	−0.349094
$505$	−25.2737	−1.12466
$506$	6.71668	0.298593
$507$	−72.3080	−3.21131
$508$	8.07114	0.358099
$509$	34.7712	1.54121	0.770603	−	0.637316i	$-0.219955\pi$
$509$	34.7712	1.54121	0.770603	+	0.637316i	$0.219955\pi$
$510$	33.6984	1.49219
$511$	6.83546	0.302383
$512$	1.00000	0.0441942
$513$	−30.7493	−1.35762
$514$	22.9396	1.01182
$515$	4.11361	0.181267
$516$	−20.2749	−0.892551
$517$	−1.41517	−0.0622389
$518$	10.2335	0.449635
$519$	14.8922	0.653694
$520$	−9.36402	−0.410639
$521$	11.1621	0.489019	0.244509	−	0.969647i	$-0.421373\pi$
$521$	11.1621	0.489019	0.244509	+	0.969647i	$0.421373\pi$
$522$	61.7278	2.70175
$523$	−31.3970	−1.37290	−0.686448	−	0.727178i	$-0.740831\pi$
$523$	−31.3970	−1.37290	−0.686448	+	0.727178i	$0.740831\pi$
$524$	−9.57144	−0.418130
$525$	−8.20428	−0.358064
$526$	19.7834	0.862598
$527$	35.7206	1.55602
$528$	3.43778	0.149610
$529$	18.3683	0.798620
$530$	10.6777	0.463810
$531$	20.3748	0.884193
$532$	−1.93103	−0.0837208
$533$	36.4376	1.57829
$534$	−39.0897	−1.69158
$535$	−15.4871	−0.669566
$536$	6.13084	0.264812
$537$	−82.0390	−3.54024
$538$	8.11747	0.349969
$539$	−1.04429	−0.0449807
$540$	25.2170	1.08517
$541$	−33.0120	−1.41930	−0.709648	−	0.704557i	$-0.751146\pi$
$541$	−33.0120	−1.41930	−0.709648	+	0.704557i	$0.751146\pi$
$542$	3.82856	0.164451
$543$	6.26497	0.268856
$544$	6.46407	0.277145
$545$	−22.4070	−0.959811
$546$	19.4659	0.833062
$547$	−32.4174	−1.38607	−0.693034	−	0.720905i	$-0.743726\pi$
$547$	−32.4174	−1.38607	−0.693034	+	0.720905i	$0.743726\pi$
$548$	8.45364	0.361122
$549$	30.2108	1.28937
$550$	2.60258	0.110974
$551$	15.2094	0.647941
$552$	21.1734	0.901201
$553$	13.6844	0.581920
$554$	−23.3516	−0.992114
$555$	−53.3493	−2.26455
$556$	9.32592	0.395507
$557$	−8.45910	−0.358424	−0.179212	−	0.983811i	$-0.557355\pi$
$557$	−8.45910	−0.358424	−0.179212	+	0.983811i	$0.557355\pi$
$558$	43.3083	1.83339
$559$	36.4180	1.54032
$560$	1.58360	0.0669194
$561$	22.2221	0.938216
$562$	−21.9269	−0.924931
$563$	−2.81162	−0.118496	−0.0592478	−	0.998243i	$-0.518870\pi$
$563$	−2.81162	−0.118496	−0.0592478	+	0.998243i	$0.518870\pi$
$564$	−4.46112	−0.187847
$565$	−12.1604	−0.511594
$566$	14.2045	0.597059
$567$	−28.9094	−1.21408
$568$	−10.2969	−0.432047
$569$	19.2907	0.808708	0.404354	−	0.914603i	$-0.367496\pi$
$569$	19.2907	0.808708	0.404354	+	0.914603i	$0.367496\pi$
$570$	10.0668	0.421653
$571$	−9.33246	−0.390551	−0.195276	−	0.980748i	$-0.562560\pi$
$571$	−9.33246	−0.390551	−0.195276	+	0.980748i	$0.562560\pi$
$572$	−6.17500	−0.258190
$573$	−5.40715	−0.225887
$574$	−6.16217	−0.257204
$575$	16.0294	0.668471
$576$	7.83715	0.326548
$577$	−28.9937	−1.20702	−0.603512	−	0.797354i	$-0.706232\pi$
$577$	−28.9937	−1.20702	−0.603512	+	0.797354i	$0.706232\pi$
$578$	24.7842	1.03089
$579$	12.4449	0.517192
$580$	−12.4729	−0.517911
$581$	17.7353	0.735785
$582$	55.4106	2.29684
$583$	7.04129	0.291621
$584$	−6.83546	−0.282853
$585$	−73.3872	−3.03419
$586$	7.96349	0.328969
$587$	−8.21877	−0.339225	−0.169612	−	0.985511i	$-0.554252\pi$
$587$	−8.21877	−0.339225	−0.169612	+	0.985511i	$0.554252\pi$
$588$	−3.29198	−0.135759
$589$	10.6709	0.439688
$590$	−4.11702	−0.169495
$591$	−30.9032	−1.27119
$592$	−10.2335	−0.420595
$593$	16.0527	0.659207	0.329603	−	0.944119i	$-0.393085\pi$
$593$	16.0527	0.659207	0.329603	+	0.944119i	$0.393085\pi$
$594$	16.6291	0.682298
$595$	10.2365	0.419656
$596$	−22.8422	−0.935652
$597$	−16.5406	−0.676962
$598$	−38.0320	−1.55525
$599$	−43.9194	−1.79450	−0.897250	−	0.441523i	$-0.854438\pi$
$599$	−43.9194	−1.79450	−0.897250	+	0.441523i	$0.854438\pi$
$600$	8.20428	0.334938
$601$	−18.7232	−0.763736	−0.381868	−	0.924217i	$-0.624719\pi$
$601$	−18.7232	−0.763736	−0.381868	+	0.924217i	$0.624719\pi$
$602$	−6.15886	−0.251016
$603$	48.0483	1.95668
$604$	−8.32283	−0.338651
$605$	15.6926	0.637997
$606$	−52.5387	−2.13424
$607$	−3.71406	−0.150749	−0.0753746	−	0.997155i	$-0.524015\pi$
$607$	−3.71406	−0.150749	−0.0753746	+	0.997155i	$0.524015\pi$
$608$	1.93103	0.0783136
$609$	25.9287	1.05068
$610$	−6.10451	−0.247164
$611$	8.01313	0.324177
$612$	50.6599	2.04780
$613$	15.5840	0.629434	0.314717	−	0.949186i	$-0.398090\pi$
$613$	15.5840	0.629434	0.314717	+	0.949186i	$0.398090\pi$
$614$	−9.24768	−0.373206
$615$	32.1246	1.29539
$616$	1.04429	0.0420756
$617$	−4.87802	−0.196382	−0.0981909	−	0.995168i	$-0.531306\pi$
$617$	−4.87802	−0.196382	−0.0981909	+	0.995168i	$0.531306\pi$
$618$	8.55134	0.343986
$619$	36.7109	1.47553	0.737767	−	0.675056i	$-0.235880\pi$
$619$	36.7109	1.47553	0.737767	+	0.675056i	$0.235880\pi$
$620$	−8.75104	−0.351450
$621$	102.419	4.10993
$622$	−19.3756	−0.776892
$623$	−11.8742	−0.475730
$624$	−19.4659	−0.779258
$625$	−6.32792	−0.253117
$626$	−7.08348	−0.283113
$627$	6.63846	0.265115
$628$	10.1764	0.406083
$629$	−66.1502	−2.63758
$630$	12.4109	0.494463
$631$	−18.5782	−0.739587	−0.369794	−	0.929114i	$-0.620572\pi$
$631$	−18.5782	−0.739587	−0.369794	+	0.929114i	$0.620572\pi$
$632$	−13.6844	−0.544336
$633$	−5.02120	−0.199575
$634$	−13.0506	−0.518304
$635$	−12.7815	−0.507218
$636$	22.1967	0.880158
$637$	5.91311	0.234286
$638$	−8.22514	−0.325637
$639$	−80.6980	−3.19236
$640$	−1.58360	−0.0625974
$641$	1.15763	0.0457238	0.0228619	−	0.999739i	$-0.492722\pi$
$641$	1.15763	0.0457238	0.0228619	+	0.999739i	$0.492722\pi$
$642$	−32.1945	−1.27061
$643$	−1.28949	−0.0508525	−0.0254262	−	0.999677i	$-0.508094\pi$
$643$	−1.28949	−0.0508525	−0.0254262	+	0.999677i	$0.508094\pi$
$644$	6.43182	0.253449
$645$	32.1073	1.26422
$646$	12.4823	0.491110
$647$	−35.0485	−1.37790	−0.688949	−	0.724810i	$-0.741927\pi$
$647$	−35.0485	−1.37790	−0.688949	+	0.724810i	$0.741927\pi$
$648$	28.9094	1.13567
$649$	−2.71492	−0.106570
$650$	−14.7367	−0.578020
$651$	18.1916	0.712985
$652$	13.2032	0.517076
$653$	−7.26183	−0.284177	−0.142089	−	0.989854i	$-0.545382\pi$
$653$	−7.26183	−0.284177	−0.142089	+	0.989854i	$0.545382\pi$
$654$	−46.5795	−1.82140
$655$	15.1574	0.592247
$656$	6.16217	0.240592
$657$	−53.5705	−2.08998
$658$	−1.35515	−0.0528291
$659$	29.5667	1.15176	0.575878	−	0.817536i	$-0.304660\pi$
$659$	29.5667	1.15176	0.575878	+	0.817536i	$0.304660\pi$
$660$	−5.44408	−0.211911
$661$	24.4731	0.951892	0.475946	−	0.879474i	$-0.342106\pi$
$661$	24.4731	0.951892	0.475946	+	0.879474i	$0.342106\pi$
$662$	−14.1584	−0.550283
$663$	−125.829	−4.88678
$664$	−17.7353	−0.688264
$665$	3.05798	0.118584
$666$	−80.2016	−3.10775
$667$	−50.6589	−1.96152
$668$	−1.38903	−0.0537432
$669$	−31.0149	−1.19910
$670$	−9.70881	−0.375084
$671$	−4.02555	−0.155405
$672$	3.29198	0.126991
$673$	−4.42411	−0.170537	−0.0852685	−	0.996358i	$-0.527175\pi$
$673$	−4.42411	−0.170537	−0.0852685	+	0.996358i	$0.527175\pi$
$674$	20.8841	0.804424
$675$	39.6853	1.52749
$676$	21.9649	0.844803
$677$	11.9174	0.458025	0.229012	−	0.973424i	$-0.426450\pi$
$677$	11.9174	0.458025	0.229012	+	0.973424i	$0.426450\pi$
$678$	−25.2790	−0.970836
$679$	16.8320	0.645952
$680$	−10.2365	−0.392553
$681$	−68.8889	−2.63983
$682$	−5.77077	−0.220974
$683$	29.7401	1.13797	0.568987	−	0.822347i	$-0.307336\pi$
$683$	29.7401	1.13797	0.568987	+	0.822347i	$0.307336\pi$
$684$	15.1338	0.578654
$685$	−13.3872	−0.511499
$686$	−1.00000	−0.0381802
$687$	32.8298	1.25253
$688$	6.15886	0.234804
$689$	−39.8701	−1.51893
$690$	−33.5303	−1.27648
$691$	34.3924	1.30835	0.654175	−	0.756343i	$-0.273016\pi$
$691$	34.3924	1.30835	0.654175	+	0.756343i	$0.273016\pi$
$692$	−4.52377	−0.171968
$693$	8.18425	0.310894
$694$	16.2642	0.617382
$695$	−14.7685	−0.560203
$696$	−25.9287	−0.982823
$697$	39.8327	1.50877
$698$	14.5526	0.550824
$699$	10.1324	0.383242
$700$	2.49220	0.0941964
$701$	0.519007	0.0196026	0.00980131	−	0.999952i	$-0.496880\pi$
$701$	0.519007	0.0196026	0.00980131	+	0.999952i	$0.496880\pi$
$702$	−94.1592	−3.55381
$703$	−19.7612	−0.745309
$704$	−1.04429	−0.0393581
$705$	7.06464	0.266070
$706$	12.4550	0.468750
$707$	−15.9596	−0.600222
$708$	−8.55842	−0.321645
$709$	32.6082	1.22463	0.612313	−	0.790615i	$-0.290239\pi$
$709$	32.6082	1.22463	0.612313	+	0.790615i	$0.290239\pi$
$710$	16.3061	0.611958
$711$	−107.247	−4.02206
$712$	11.8742	0.445005
$713$	−35.5424	−1.33107
$714$	21.2796	0.796369
$715$	9.77875	0.365704
$716$	24.9209	0.931336
$717$	33.5188	1.25178
$718$	17.6306	0.657970
$719$	44.4517	1.65777	0.828885	−	0.559419i	$-0.188976\pi$
$719$	44.4517	1.65777	0.828885	+	0.559419i	$0.188976\pi$
$720$	−12.4109	−0.462528
$721$	2.59763	0.0967407
$722$	−15.2711	−0.568332
$723$	−67.9922	−2.52866
$724$	−1.90310	−0.0707281
$725$	−19.6293	−0.729015
$726$	32.6218	1.21071
$727$	42.4213	1.57332	0.786659	−	0.617388i	$-0.211809\pi$
$727$	42.4213	1.57332	0.786659	+	0.617388i	$0.211809\pi$
$728$	−5.91311	−0.219154
$729$	69.3048	2.56684
$730$	10.8247	0.400638
$731$	39.8113	1.47247
$732$	−12.6900	−0.469036
$733$	13.3101	0.491621	0.245810	−	0.969318i	$-0.420946\pi$
$733$	13.3101	0.491621	0.245810	+	0.969318i	$0.420946\pi$
$734$	−3.78521	−0.139715
$735$	5.21319	0.192292
$736$	−6.43182	−0.237080
$737$	−6.40237	−0.235834
$738$	48.2938	1.77772
$739$	34.2252	1.25899	0.629497	−	0.777003i	$-0.283261\pi$
$739$	34.2252	1.25899	0.629497	+	0.777003i	$0.283261\pi$
$740$	16.2058	0.595738
$741$	−37.5891	−1.38087
$742$	6.74266	0.247531
$743$	−21.3991	−0.785056	−0.392528	−	0.919740i	$-0.628399\pi$
$743$	−21.3991	−0.785056	−0.392528	+	0.919740i	$0.628399\pi$
$744$	−18.1916	−0.666936
$745$	36.1730	1.32527
$746$	−21.2484	−0.777959
$747$	−138.994	−5.08554
$748$	−6.75036	−0.246818
$749$	−9.77966	−0.357341
$750$	−39.0583	−1.42621
$751$	15.7138	0.573404	0.286702	−	0.958020i	$-0.407441\pi$
$751$	15.7138	0.573404	0.286702	+	0.958020i	$0.407441\pi$
$752$	1.35515	0.0494171
$753$	−59.4735	−2.16734
$754$	46.5735	1.69611
$755$	13.1801	0.479671
$756$	15.9238	0.579143
$757$	−30.4183	−1.10557	−0.552786	−	0.833323i	$-0.686435\pi$
$757$	−30.4183	−1.10557	−0.552786	+	0.833323i	$0.686435\pi$
$758$	6.88934	0.250232
$759$	−22.1112	−0.802585
$760$	−3.05798	−0.110925
$761$	40.6192	1.47245	0.736223	−	0.676739i	$-0.236608\pi$
$761$	40.6192	1.47245	0.736223	+	0.676739i	$0.236608\pi$
$762$	−26.5701	−0.962531
$763$	−14.1494	−0.512242
$764$	1.64252	0.0594243
$765$	−80.2251	−2.90054
$766$	−3.24799	−0.117355
$767$	15.3728	0.555079
$768$	−3.29198	−0.118789
$769$	−24.8549	−0.896291	−0.448146	−	0.893961i	$-0.647915\pi$
$769$	−24.8549	−0.896291	−0.448146	+	0.893961i	$0.647915\pi$
$770$	−1.65374	−0.0595967
$771$	−75.5169	−2.71968
$772$	−3.78037	−0.136058
$773$	0.941121	0.0338498	0.0169249	−	0.999857i	$-0.494612\pi$
$773$	0.941121	0.0338498	0.0169249	+	0.999857i	$0.494612\pi$
$774$	48.2679	1.73495
$775$	−13.7720	−0.494704
$776$	−16.8320	−0.604233
$777$	−33.6886	−1.20857
$778$	36.6365	1.31348
$779$	11.8993	0.426338
$780$	30.8262	1.10375
$781$	10.7529	0.384769
$782$	−41.5757	−1.48674
$783$	−125.421	−4.48217
$784$	1.00000	0.0357143
$785$	−16.1154	−0.575183
$786$	31.5090	1.12389
$787$	48.1659	1.71693	0.858465	−	0.512873i	$-0.171419\pi$
$787$	48.1659	1.71693	0.858465	+	0.512873i	$0.171419\pi$
$788$	9.38742	0.334413
$789$	−65.1267	−2.31857
$790$	21.6707	0.771008
$791$	−7.67897	−0.273033
$792$	−8.18425	−0.290815
$793$	22.7940	0.809439
$794$	−4.30614	−0.152819
$795$	−35.1508	−1.24667
$796$	5.02451	0.178089
$797$	45.0349	1.59522	0.797609	−	0.603175i	$-0.206098\pi$
$797$	45.0349	1.59522	0.797609	+	0.603175i	$0.206098\pi$
$798$	6.35692	0.225032
$799$	8.75976	0.309898
$800$	−2.49220	−0.0881126
$801$	93.0599	3.28811
$802$	−9.72496	−0.343400
$803$	7.13820	0.251902
$804$	−20.1826	−0.711786
$805$	−10.1854	−0.358990
$806$	32.6760	1.15096
$807$	−26.7226	−0.940679
$808$	15.9596	0.561457
$809$	−23.6353	−0.830972	−0.415486	−	0.909599i	$-0.636389\pi$
$809$	−23.6353	−0.830972	−0.415486	+	0.909599i	$0.636389\pi$
$810$	−45.7810	−1.60858
$811$	46.9935	1.65016	0.825082	−	0.565013i	$-0.191129\pi$
$811$	46.9935	1.65016	0.825082	+	0.565013i	$0.191129\pi$
$812$	−7.87631	−0.276404
$813$	−12.6036	−0.442026
$814$	10.6868	0.374571
$815$	−20.9086	−0.732395
$816$	−21.2796	−0.744935
$817$	11.8929	0.416081
$818$	−35.7663	−1.25054
$819$	−46.3419	−1.61932
$820$	−9.75843	−0.340779
$821$	−15.0341	−0.524692	−0.262346	−	0.964974i	$-0.584496\pi$
$821$	−15.0341	−0.524692	−0.262346	+	0.964974i	$0.584496\pi$
$822$	−27.8292	−0.970656
$823$	−25.3244	−0.882752	−0.441376	−	0.897322i	$-0.645509\pi$
$823$	−25.3244	−0.882752	−0.441376	+	0.897322i	$0.645509\pi$
$824$	−2.59763	−0.0904926
$825$	−8.56765	−0.298287
$826$	−2.59978	−0.0904579
$827$	−37.2826	−1.29644	−0.648221	−	0.761452i	$-0.724487\pi$
$827$	−37.2826	−1.29644	−0.648221	+	0.761452i	$0.724487\pi$
$828$	−50.4071	−1.75177
$829$	32.6013	1.13229	0.566145	−	0.824306i	$-0.308434\pi$
$829$	32.6013	1.13229	0.566145	+	0.824306i	$0.308434\pi$
$830$	28.0857	0.974869
$831$	76.8730	2.66670
$832$	5.91311	0.205000
$833$	6.46407	0.223967
$834$	−30.7008	−1.06308
$835$	2.19967	0.0761228
$836$	−2.01655	−0.0697440
$837$	−87.9954	−3.04156
$838$	11.5896	0.400357
$839$	−22.4220	−0.774094	−0.387047	−	0.922060i	$-0.626505\pi$
$839$	−22.4220	−0.774094	−0.387047	+	0.922060i	$0.626505\pi$
$840$	−5.21319	−0.179872
$841$	33.0362	1.13918
$842$	24.6478	0.849419
$843$	72.1830	2.48611
$844$	1.52528	0.0525023
$845$	−34.7837	−1.19659
$846$	10.6205	0.365140
$847$	9.90946	0.340493
$848$	−6.74266	−0.231544
$849$	−46.7609	−1.60483
$850$	−16.1098	−0.552560
$851$	65.8201	2.25628
$852$	33.8971	1.16129
$853$	−12.5214	−0.428723	−0.214362	−	0.976754i	$-0.568767\pi$
$853$	−12.5214	−0.428723	−0.214362	+	0.976754i	$0.568767\pi$
$854$	−3.85482	−0.131909
$855$	−23.9659	−0.819616
$856$	9.77966	0.334262
$857$	−50.5653	−1.72728	−0.863639	−	0.504111i	$-0.831820\pi$
$857$	−50.5653	−1.72728	−0.863639	+	0.504111i	$0.831820\pi$
$858$	20.3280	0.693986
$859$	−28.6311	−0.976882	−0.488441	−	0.872597i	$-0.662434\pi$
$859$	−28.6311	−0.976882	−0.488441	+	0.872597i	$0.662434\pi$
$860$	−9.75319	−0.332581
$861$	20.2857	0.691336
$862$	−1.00000	−0.0340601
$863$	56.0660	1.90851	0.954255	−	0.298994i	$-0.0966509\pi$
$863$	56.0660	1.90851	0.954255	+	0.298994i	$0.0966509\pi$
$864$	−15.9238	−0.541739
$865$	7.16386	0.243578
$866$	−22.6705	−0.770376
$867$	−81.5891	−2.77091
$868$	−5.52603	−0.187566
$869$	14.2905	0.484771
$870$	41.0607	1.39209
$871$	36.2523	1.22836
$872$	14.1494	0.479159
$873$	−131.915	−4.46464
$874$	−12.4200	−0.420114
$875$	−11.8647	−0.401099
$876$	22.5022	0.760279
$877$	12.6998	0.428841	0.214420	−	0.976741i	$-0.431214\pi$
$877$	12.6998	0.428841	0.214420	+	0.976741i	$0.431214\pi$
$878$	−10.9560	−0.369746
$879$	−26.2157	−0.884232
$880$	1.65374	0.0557476
$881$	5.11737	0.172409	0.0862043	−	0.996277i	$-0.472526\pi$
$881$	5.11737	0.172409	0.0862043	+	0.996277i	$0.472526\pi$
$882$	7.83715	0.263890
$883$	−36.0095	−1.21182	−0.605908	−	0.795535i	$-0.707190\pi$
$883$	−36.0095	−1.21182	−0.605908	+	0.795535i	$0.707190\pi$
$884$	38.2228	1.28557
$885$	13.5531	0.455584
$886$	−34.2211	−1.14968
$887$	−36.5185	−1.22617	−0.613086	−	0.790016i	$-0.710072\pi$
$887$	−36.5185	−1.22617	−0.613086	+	0.790016i	$0.710072\pi$
$888$	33.6886	1.13051
$889$	−8.07114	−0.270697
$890$	−18.8040	−0.630313
$891$	−30.1898	−1.01140
$892$	9.42133	0.315450
$893$	2.61683	0.0875688
$894$	75.1961	2.51493
$895$	−39.4647	−1.31916
$896$	−1.00000	−0.0334077
$897$	125.201	4.18033
$898$	8.42266	0.281068
$899$	43.5247	1.45163
$900$	−19.5317	−0.651058
$901$	−43.5850	−1.45203
$902$	−6.43509	−0.214265
$903$	20.2749	0.674705
$904$	7.67897	0.255399
$905$	3.01375	0.100181
$906$	27.3986	0.910257
$907$	−35.9000	−1.19204	−0.596020	−	0.802970i	$-0.703252\pi$
$907$	−35.9000	−1.19204	−0.596020	+	0.802970i	$0.703252\pi$
$908$	20.9263	0.694462
$909$	125.078	4.14857
$910$	9.36402	0.310414
$911$	5.86691	0.194379	0.0971897	−	0.995266i	$-0.469015\pi$
$911$	5.86691	0.194379	0.0971897	+	0.995266i	$0.469015\pi$
$912$	−6.35692	−0.210499
$913$	18.5208	0.612950
$914$	8.89532	0.294231
$915$	20.0959	0.664351
$916$	−9.97264	−0.329505
$917$	9.57144	0.316077
$918$	−102.933	−3.39728
$919$	−29.0096	−0.956937	−0.478468	−	0.878105i	$-0.658808\pi$
$919$	−29.0096	−0.956937	−0.478468	+	0.878105i	$0.658808\pi$
$920$	10.1854	0.335804
$921$	30.4432	1.00314
$922$	−8.42714	−0.277533
$923$	−60.8865	−2.00410
$924$	−3.43778	−0.113095
$925$	25.5040	0.838566
$926$	13.3927	0.440110
$927$	−20.3580	−0.668644
$928$	7.87631	0.258552
$929$	55.5189	1.82152	0.910758	−	0.412941i	$-0.135498\pi$
$929$	55.5189	1.82152	0.910758	+	0.412941i	$0.135498\pi$
$930$	28.8083	0.944660
$931$	1.93103	0.0632869
$932$	−3.07790	−0.100820
$933$	63.7842	2.08820
$934$	11.0212	0.360626
$935$	10.6899	0.349597
$936$	46.3419	1.51473
$937$	47.7260	1.55914	0.779569	−	0.626316i	$-0.215438\pi$
$937$	47.7260	1.55914	0.779569	+	0.626316i	$0.215438\pi$
$938$	−6.13084	−0.200179
$939$	23.3187	0.760977
$940$	−2.14601	−0.0699953
$941$	27.0451	0.881646	0.440823	−	0.897594i	$-0.354687\pi$
$941$	27.0451	0.881646	0.440823	+	0.897594i	$0.354687\pi$
$942$	−33.5006	−1.09151
$943$	−39.6339	−1.29066
$944$	2.59978	0.0846156
$945$	−25.2170	−0.820308
$946$	−6.43163	−0.209110
$947$	19.8709	0.645719	0.322859	−	0.946447i	$-0.395356\pi$
$947$	19.8709	0.645719	0.322859	+	0.946447i	$0.395356\pi$
$948$	45.0488	1.46312
$949$	−40.4188	−1.31205
$950$	−4.81252	−0.156139
$951$	42.9622	1.39314
$952$	−6.46407	−0.209502
$953$	31.5532	1.02211	0.511054	−	0.859548i	$-0.329255\pi$
$953$	31.5532	1.02211	0.511054	+	0.859548i	$0.329255\pi$
$954$	−52.8432	−1.71086
$955$	−2.60110	−0.0841697
$956$	−10.1819	−0.329307
$957$	27.0770	0.875276
$958$	−19.1823	−0.619751
$959$	−8.45364	−0.272982
$960$	5.21319	0.168255
$961$	−0.463004	−0.0149356
$962$	−60.5119	−1.95098
$963$	76.6446	2.46984
$964$	20.6539	0.665216
$965$	5.98660	0.192715
$966$	−21.1734	−0.681244
$967$	−13.3363	−0.428865	−0.214433	−	0.976739i	$-0.568790\pi$
$967$	−13.3363	−0.428865	−0.214433	+	0.976739i	$0.568790\pi$
$968$	−9.90946	−0.318502
$969$	−41.0915	−1.32005
$970$	26.6552	0.855846
$971$	−16.4700	−0.528548	−0.264274	−	0.964448i	$-0.585132\pi$
$971$	−16.4700	−0.528548	−0.264274	+	0.964448i	$0.585132\pi$
$972$	−47.3979	−1.52029
$973$	−9.32592	−0.298975
$974$	27.9885	0.896809
$975$	48.5128	1.55365
$976$	3.85482	0.123390
$977$	34.5459	1.10522	0.552611	−	0.833439i	$-0.313632\pi$
$977$	34.5459	1.10522	0.552611	+	0.833439i	$0.313632\pi$
$978$	−43.4646	−1.38984
$979$	−12.4001	−0.396309
$980$	−1.58360	−0.0505863
$981$	110.891	3.54047
$982$	32.1273	1.02522
$983$	−43.5652	−1.38951	−0.694757	−	0.719245i	$-0.744488\pi$
$983$	−43.5652	−1.38951	−0.694757	+	0.719245i	$0.744488\pi$
$984$	−20.2857	−0.646686
$985$	−14.8659	−0.473668
$986$	50.9130	1.62140
$987$	4.46112	0.141999
$988$	11.4184	0.363268
$989$	−39.6127	−1.25961
$990$	12.9606	0.411915
$991$	−1.88260	−0.0598027	−0.0299013	−	0.999553i	$-0.509519\pi$
$991$	−1.88260	−0.0598027	−0.0299013	+	0.999553i	$0.509519\pi$
$992$	5.52603	0.175452
$993$	46.6093	1.47910
$994$	10.2969	0.326597
$995$	−7.95683	−0.252248
$996$	58.3844	1.84998
$997$	−18.8409	−0.596696	−0.298348	−	0.954457i	$-0.596436\pi$
$997$	−18.8409	−0.596696	−0.298348	+	0.954457i	$0.596436\pi$
$998$	32.4197	1.02623
$999$	162.956	5.15572

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.r.1.1	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.r.1.1	✓	31	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.29198 q^{3} +1.00000 q^{4} -1.58360 q^{5} -3.29198 q^{6} -1.00000 q^{7} +1.00000 q^{8} +7.83715 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.29198 q^{3} +1.00000 q^{4} -1.58360 q^{5} -3.29198 q^{6} -1.00000 q^{7} +1.00000 q^{8} +7.83715 q^{9} -1.58360 q^{10} -1.04429 q^{11} -3.29198 q^{12} +5.91311 q^{13} -1.00000 q^{14} +5.21319 q^{15} +1.00000 q^{16} +6.46407 q^{17} +7.83715 q^{18} +1.93103 q^{19} -1.58360 q^{20} +3.29198 q^{21} -1.04429 q^{22} -6.43182 q^{23} -3.29198 q^{24} -2.49220 q^{25} +5.91311 q^{26} -15.9238 q^{27} -1.00000 q^{28} +7.87631 q^{29} +5.21319 q^{30} +5.52603 q^{31} +1.00000 q^{32} +3.43778 q^{33} +6.46407 q^{34} +1.58360 q^{35} +7.83715 q^{36} -10.2335 q^{37} +1.93103 q^{38} -19.4659 q^{39} -1.58360 q^{40} +6.16217 q^{41} +3.29198 q^{42} +6.15886 q^{43} -1.04429 q^{44} -12.4109 q^{45} -6.43182 q^{46} +1.35515 q^{47} -3.29198 q^{48} +1.00000 q^{49} -2.49220 q^{50} -21.2796 q^{51} +5.91311 q^{52} -6.74266 q^{53} -15.9238 q^{54} +1.65374 q^{55} -1.00000 q^{56} -6.35692 q^{57} +7.87631 q^{58} +2.59978 q^{59} +5.21319 q^{60} +3.85482 q^{61} +5.52603 q^{62} -7.83715 q^{63} +1.00000 q^{64} -9.36402 q^{65} +3.43778 q^{66} +6.13084 q^{67} +6.46407 q^{68} +21.1734 q^{69} +1.58360 q^{70} -10.2969 q^{71} +7.83715 q^{72} -6.83546 q^{73} -10.2335 q^{74} +8.20428 q^{75} +1.93103 q^{76} +1.04429 q^{77} -19.4659 q^{78} -13.6844 q^{79} -1.58360 q^{80} +28.9094 q^{81} +6.16217 q^{82} -17.7353 q^{83} +3.29198 q^{84} -10.2365 q^{85} +6.15886 q^{86} -25.9287 q^{87} -1.04429 q^{88} +11.8742 q^{89} -12.4109 q^{90} -5.91311 q^{91} -6.43182 q^{92} -18.1916 q^{93} +1.35515 q^{94} -3.05798 q^{95} -3.29198 q^{96} -16.8320 q^{97} +1.00000 q^{98} -8.18425 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9} + 15 q^{10} + 12 q^{11} + 7 q^{12} + 26 q^{13} - 31 q^{14} + 6 q^{15} + 31 q^{16} + 33 q^{17} + 42 q^{18} + 34 q^{19} + 15 q^{20} - 7 q^{21} + 12 q^{22} - 14 q^{23} + 7 q^{24} + 58 q^{25} + 26 q^{26} + 28 q^{27} - 31 q^{28} + 11 q^{29} + 6 q^{30} + 19 q^{31} + 31 q^{32} + 43 q^{33} + 33 q^{34} - 15 q^{35} + 42 q^{36} + 2 q^{37} + 34 q^{38} - 16 q^{39} + 15 q^{40} + 53 q^{41} - 7 q^{42} + 22 q^{43} + 12 q^{44} + 43 q^{45} - 14 q^{46} + 27 q^{47} + 7 q^{48} + 31 q^{49} + 58 q^{50} + 17 q^{51} + 26 q^{52} + 11 q^{53} + 28 q^{54} + 19 q^{55} - 31 q^{56} + 45 q^{57} + 11 q^{58} + 54 q^{59} + 6 q^{60} + 41 q^{61} + 19 q^{62} - 42 q^{63} + 31 q^{64} + 30 q^{65} + 43 q^{66} + 13 q^{67} + 33 q^{68} + 17 q^{69} - 15 q^{70} + 43 q^{71} + 42 q^{72} + 42 q^{73} + 2 q^{74} + 62 q^{75} + 34 q^{76} - 12 q^{77} - 16 q^{78} - 12 q^{79} + 15 q^{80} + 63 q^{81} + 53 q^{82} + 35 q^{83} - 7 q^{84} + 16 q^{85} + 22 q^{86} - 4 q^{87} + 12 q^{88} + 115 q^{89} + 43 q^{90} - 26 q^{91} - 14 q^{92} + q^{93} + 27 q^{94} - 13 q^{95} + 7 q^{96} + 32 q^{97} + 31 q^{98} + 34 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9 + 15 * q^10 + 12 * q^11 + 7 * q^12 + 26 * q^13 - 31 * q^14 + 6 * q^15 + 31 * q^16 + 33 * q^17 + 42 * q^18 + 34 * q^19 + 15 * q^20 - 7 * q^21 + 12 * q^22 - 14 * q^23 + 7 * q^24 + 58 * q^25 + 26 * q^26 + 28 * q^27 - 31 * q^28 + 11 * q^29 + 6 * q^30 + 19 * q^31 + 31 * q^32 + 43 * q^33 + 33 * q^34 - 15 * q^35 + 42 * q^36 + 2 * q^37 + 34 * q^38 - 16 * q^39 + 15 * q^40 + 53 * q^41 - 7 * q^42 + 22 * q^43 + 12 * q^44 + 43 * q^45 - 14 * q^46 + 27 * q^47 + 7 * q^48 + 31 * q^49 + 58 * q^50 + 17 * q^51 + 26 * q^52 + 11 * q^53 + 28 * q^54 + 19 * q^55 - 31 * q^56 + 45 * q^57 + 11 * q^58 + 54 * q^59 + 6 * q^60 + 41 * q^61 + 19 * q^62 - 42 * q^63 + 31 * q^64 + 30 * q^65 + 43 * q^66 + 13 * q^67 + 33 * q^68 + 17 * q^69 - 15 * q^70 + 43 * q^71 + 42 * q^72 + 42 * q^73 + 2 * q^74 + 62 * q^75 + 34 * q^76 - 12 * q^77 - 16 * q^78 - 12 * q^79 + 15 * q^80 + 63 * q^81 + 53 * q^82 + 35 * q^83 - 7 * q^84 + 16 * q^85 + 22 * q^86 - 4 * q^87 + 12 * q^88 + 115 * q^89 + 43 * q^90 - 26 * q^91 - 14 * q^92 + q^93 + 27 * q^94 - 13 * q^95 + 7 * q^96 + 32 * q^97 + 31 * q^98 + 34 * q^99

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