LMFDB - Embedded newform 6015.2.a.i.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$43$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53504 q^{2} +1.00000 q^{3} +4.42643 q^{4} +1.00000 q^{5} -2.53504 q^{6} +3.85984 q^{7} -6.15109 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.53504 q^{2} +1.00000 q^{3} +4.42643 q^{4} +1.00000 q^{5} -2.53504 q^{6} +3.85984 q^{7} -6.15109 q^{8} +1.00000 q^{9} -2.53504 q^{10} -4.87454 q^{11} +4.42643 q^{12} +0.512763 q^{13} -9.78484 q^{14} +1.00000 q^{15} +6.74040 q^{16} +5.81185 q^{17} -2.53504 q^{18} -0.722104 q^{19} +4.42643 q^{20} +3.85984 q^{21} +12.3571 q^{22} +9.55090 q^{23} -6.15109 q^{24} +1.00000 q^{25} -1.29987 q^{26} +1.00000 q^{27} +17.0853 q^{28} -7.31662 q^{29} -2.53504 q^{30} +9.61579 q^{31} -4.78501 q^{32} -4.87454 q^{33} -14.7333 q^{34} +3.85984 q^{35} +4.42643 q^{36} +6.63406 q^{37} +1.83056 q^{38} +0.512763 q^{39} -6.15109 q^{40} +5.72142 q^{41} -9.78484 q^{42} -0.643801 q^{43} -21.5768 q^{44} +1.00000 q^{45} -24.2119 q^{46} +1.45962 q^{47} +6.74040 q^{48} +7.89835 q^{49} -2.53504 q^{50} +5.81185 q^{51} +2.26971 q^{52} -10.7445 q^{53} -2.53504 q^{54} -4.87454 q^{55} -23.7422 q^{56} -0.722104 q^{57} +18.5479 q^{58} +3.46661 q^{59} +4.42643 q^{60} -0.197562 q^{61} -24.3764 q^{62} +3.85984 q^{63} -1.35061 q^{64} +0.512763 q^{65} +12.3571 q^{66} -4.46730 q^{67} +25.7257 q^{68} +9.55090 q^{69} -9.78484 q^{70} -7.10326 q^{71} -6.15109 q^{72} +3.43798 q^{73} -16.8176 q^{74} +1.00000 q^{75} -3.19634 q^{76} -18.8149 q^{77} -1.29987 q^{78} +13.8081 q^{79} +6.74040 q^{80} +1.00000 q^{81} -14.5040 q^{82} -15.5452 q^{83} +17.0853 q^{84} +5.81185 q^{85} +1.63206 q^{86} -7.31662 q^{87} +29.9837 q^{88} -17.0418 q^{89} -2.53504 q^{90} +1.97918 q^{91} +42.2764 q^{92} +9.61579 q^{93} -3.70019 q^{94} -0.722104 q^{95} -4.78501 q^{96} -13.6028 q^{97} -20.0226 q^{98} -4.87454 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9}+O(q^{10}) $ 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9} + 3 q^{10} + 19 q^{11} + 61 q^{12} + 8 q^{13} + 6 q^{14} + 43 q^{15} + 85 q^{16} + 40 q^{17} + 3 q^{18} + 43 q^{19} + 61 q^{20} + 14 q^{21} + 19 q^{22} + 12 q^{23} + 18 q^{24} + 43 q^{25} + 43 q^{27} + 36 q^{28} + 41 q^{29} + 3 q^{30} + 33 q^{31} + 4 q^{32} + 19 q^{33} + 20 q^{34} + 14 q^{35} + 61 q^{36} + 12 q^{37} + 10 q^{38} + 8 q^{39} + 18 q^{40} + 47 q^{41} + 6 q^{42} + 73 q^{43} + 5 q^{44} + 43 q^{45} + 21 q^{46} + 32 q^{47} + 85 q^{48} + 87 q^{49} + 3 q^{50} + 40 q^{51} + 18 q^{52} + 17 q^{53} + 3 q^{54} + 19 q^{55} + 15 q^{56} + 43 q^{57} - 16 q^{58} + 21 q^{59} + 61 q^{60} + 77 q^{61} + 15 q^{62} + 14 q^{63} + 112 q^{64} + 8 q^{65} + 19 q^{66} + 26 q^{67} + 50 q^{68} + 12 q^{69} + 6 q^{70} + 2 q^{71} + 18 q^{72} + 49 q^{73} - 34 q^{74} + 43 q^{75} + 50 q^{76} - 2 q^{77} + 59 q^{79} + 85 q^{80} + 43 q^{81} - 45 q^{82} - 3 q^{83} + 36 q^{84} + 40 q^{85} - 35 q^{86} + 41 q^{87} - 13 q^{88} + 57 q^{89} + 3 q^{90} + 11 q^{91} - 9 q^{92} + 33 q^{93} + 52 q^{94} + 43 q^{95} + 4 q^{96} + 7 q^{97} - 32 q^{98} + 19 q^{99}+O(q^{100}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9 + 3 * q^10 + 19 * q^11 + 61 * q^12 + 8 * q^13 + 6 * q^14 + 43 * q^15 + 85 * q^16 + 40 * q^17 + 3 * q^18 + 43 * q^19 + 61 * q^20 + 14 * q^21 + 19 * q^22 + 12 * q^23 + 18 * q^24 + 43 * q^25 + 43 * q^27 + 36 * q^28 + 41 * q^29 + 3 * q^30 + 33 * q^31 + 4 * q^32 + 19 * q^33 + 20 * q^34 + 14 * q^35 + 61 * q^36 + 12 * q^37 + 10 * q^38 + 8 * q^39 + 18 * q^40 + 47 * q^41 + 6 * q^42 + 73 * q^43 + 5 * q^44 + 43 * q^45 + 21 * q^46 + 32 * q^47 + 85 * q^48 + 87 * q^49 + 3 * q^50 + 40 * q^51 + 18 * q^52 + 17 * q^53 + 3 * q^54 + 19 * q^55 + 15 * q^56 + 43 * q^57 - 16 * q^58 + 21 * q^59 + 61 * q^60 + 77 * q^61 + 15 * q^62 + 14 * q^63 + 112 * q^64 + 8 * q^65 + 19 * q^66 + 26 * q^67 + 50 * q^68 + 12 * q^69 + 6 * q^70 + 2 * q^71 + 18 * q^72 + 49 * q^73 - 34 * q^74 + 43 * q^75 + 50 * q^76 - 2 * q^77 + 59 * q^79 + 85 * q^80 + 43 * q^81 - 45 * q^82 - 3 * q^83 + 36 * q^84 + 40 * q^85 - 35 * q^86 + 41 * q^87 - 13 * q^88 + 57 * q^89 + 3 * q^90 + 11 * q^91 - 9 * q^92 + 33 * q^93 + 52 * q^94 + 43 * q^95 + 4 * q^96 + 7 * q^97 - 32 * q^98 + 19 * 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 $

$2$	−2.53504	−1.79254	−0.896272	−	0.443505i	$-0.853735\pi$
$2$	−2.53504	−1.79254	−0.896272	+	0.443505i	$0.853735\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.42643	2.21321
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.53504	−1.03493
$7$	3.85984	1.45888	0.729441	−	0.684044i	$-0.239780\pi$
$7$	3.85984	1.45888	0.729441	+	0.684044i	$0.239780\pi$
$8$	−6.15109	−2.17474
$9$	1.00000	0.333333
$10$	−2.53504	−0.801650
$11$	−4.87454	−1.46973	−0.734864	−	0.678214i	$-0.762754\pi$
$11$	−4.87454	−1.46973	−0.734864	+	0.678214i	$0.762754\pi$
$12$	4.42643	1.27780
$13$	0.512763	0.142215	0.0711074	−	0.997469i	$-0.477347\pi$
$13$	0.512763	0.142215	0.0711074	+	0.997469i	$0.477347\pi$
$14$	−9.78484	−2.61511
$15$	1.00000	0.258199
$16$	6.74040	1.68510
$17$	5.81185	1.40958	0.704790	−	0.709416i	$-0.251041\pi$
$17$	5.81185	1.40958	0.704790	+	0.709416i	$0.251041\pi$
$18$	−2.53504	−0.597515
$19$	−0.722104	−0.165662	−0.0828310	−	0.996564i	$-0.526396\pi$
$19$	−0.722104	−0.165662	−0.0828310	+	0.996564i	$0.526396\pi$
$20$	4.42643	0.989779
$21$	3.85984	0.842286
$22$	12.3571	2.63455
$23$	9.55090	1.99150	0.995750	−	0.0920935i	$-0.0293559\pi$
$23$	9.55090	1.99150	0.995750	+	0.0920935i	$0.0293559\pi$
$24$	−6.15109	−1.25559
$25$	1.00000	0.200000
$26$	−1.29987	−0.254926
$27$	1.00000	0.192450
$28$	17.0853	3.22882
$29$	−7.31662	−1.35866	−0.679331	−	0.733832i	$-0.737730\pi$
$29$	−7.31662	−1.35866	−0.679331	+	0.733832i	$0.737730\pi$
$30$	−2.53504	−0.462833
$31$	9.61579	1.72705	0.863523	−	0.504309i	$-0.168253\pi$
$31$	9.61579	1.72705	0.863523	+	0.504309i	$0.168253\pi$
$32$	−4.78501	−0.845879
$33$	−4.87454	−0.848548
$34$	−14.7333	−2.52673
$35$	3.85984	0.652432
$36$	4.42643	0.737738
$37$	6.63406	1.09063	0.545316	−	0.838230i	$-0.316409\pi$
$37$	6.63406	1.09063	0.545316	+	0.838230i	$0.316409\pi$
$38$	1.83056	0.296957
$39$	0.512763	0.0821077
$40$	−6.15109	−0.972573
$41$	5.72142	0.893536	0.446768	−	0.894650i	$-0.352575\pi$
$41$	5.72142	0.893536	0.446768	+	0.894650i	$0.352575\pi$
$42$	−9.78484	−1.50983
$43$	−0.643801	−0.0981788	−0.0490894	−	0.998794i	$-0.515632\pi$
$43$	−0.643801	−0.0981788	−0.0490894	+	0.998794i	$0.515632\pi$
$44$	−21.5768	−3.25282
$45$	1.00000	0.149071
$46$	−24.2119	−3.56985
$47$	1.45962	0.212907	0.106454	−	0.994318i	$-0.466050\pi$
$47$	1.45962	0.212907	0.106454	+	0.994318i	$0.466050\pi$
$48$	6.74040	0.972894
$49$	7.89835	1.12834
$50$	−2.53504	−0.358509
$51$	5.81185	0.813821
$52$	2.26971	0.314752
$53$	−10.7445	−1.47587	−0.737937	−	0.674870i	$-0.764200\pi$
$53$	−10.7445	−1.47587	−0.737937	+	0.674870i	$0.764200\pi$
$54$	−2.53504	−0.344975
$55$	−4.87454	−0.657282
$56$	−23.7422	−3.17269
$57$	−0.722104	−0.0956450
$58$	18.5479	2.43546
$59$	3.46661	0.451314	0.225657	−	0.974207i	$-0.427547\pi$
$59$	3.46661	0.451314	0.225657	+	0.974207i	$0.427547\pi$
$60$	4.42643	0.571449
$61$	−0.197562	−0.0252952	−0.0126476	−	0.999920i	$-0.504026\pi$
$61$	−0.197562	−0.0252952	−0.0126476	+	0.999920i	$0.504026\pi$
$62$	−24.3764	−3.09581
$63$	3.85984	0.486294
$64$	−1.35061	−0.168826
$65$	0.512763	0.0636004
$66$	12.3571	1.52106
$67$	−4.46730	−0.545768	−0.272884	−	0.962047i	$-0.587978\pi$
$67$	−4.46730	−0.545768	−0.272884	+	0.962047i	$0.587978\pi$
$68$	25.7257	3.11970
$69$	9.55090	1.14979
$70$	−9.78484	−1.16951
$71$	−7.10326	−0.843002	−0.421501	−	0.906828i	$-0.638497\pi$
$71$	−7.10326	−0.843002	−0.421501	+	0.906828i	$0.638497\pi$
$72$	−6.15109	−0.724913
$73$	3.43798	0.402385	0.201192	−	0.979552i	$-0.435518\pi$
$73$	3.43798	0.402385	0.201192	+	0.979552i	$0.435518\pi$
$74$	−16.8176	−1.95501
$75$	1.00000	0.115470
$76$	−3.19634	−0.366646
$77$	−18.8149	−2.14416
$78$	−1.29987	−0.147182
$79$	13.8081	1.55353	0.776766	−	0.629789i	$-0.216859\pi$
$79$	13.8081	1.55353	0.776766	+	0.629789i	$0.216859\pi$
$80$	6.74040	0.753600
$81$	1.00000	0.111111
$82$	−14.5040	−1.60170
$83$	−15.5452	−1.70630	−0.853151	−	0.521663i	$-0.825312\pi$
$83$	−15.5452	−1.70630	−0.853151	+	0.521663i	$0.825312\pi$
$84$	17.0853	1.86416
$85$	5.81185	0.630383
$86$	1.63206	0.175990
$87$	−7.31662	−0.784424
$88$	29.9837	3.19627
$89$	−17.0418	−1.80643	−0.903214	−	0.429190i	$-0.858799\pi$
$89$	−17.0418	−1.80643	−0.903214	+	0.429190i	$0.858799\pi$
$90$	−2.53504	−0.267217
$91$	1.97918	0.207475
$92$	42.2764	4.40762
$93$	9.61579	0.997111
$94$	−3.70019	−0.381646
$95$	−0.722104	−0.0740863
$96$	−4.78501	−0.488368
$97$	−13.6028	−1.38116	−0.690578	−	0.723258i	$-0.742644\pi$
$97$	−13.6028	−1.38116	−0.690578	+	0.723258i	$0.742644\pi$
$98$	−20.0226	−2.02259
$99$	−4.87454	−0.489909
$100$	4.42643	0.442643
$101$	4.42276	0.440081	0.220040	−	0.975491i	$-0.429381\pi$
$101$	4.42276	0.440081	0.220040	+	0.975491i	$0.429381\pi$
$102$	−14.7333	−1.45881
$103$	6.63630	0.653894	0.326947	−	0.945043i	$-0.393980\pi$
$103$	6.63630	0.653894	0.326947	+	0.945043i	$0.393980\pi$
$104$	−3.15405	−0.309280
$105$	3.85984	0.376682
$106$	27.2378	2.64557
$107$	3.33206	0.322122	0.161061	−	0.986944i	$-0.448508\pi$
$107$	3.33206	0.322122	0.161061	+	0.986944i	$0.448508\pi$
$108$	4.42643	0.425933
$109$	7.54471	0.722652	0.361326	−	0.932440i	$-0.382324\pi$
$109$	7.54471	0.722652	0.361326	+	0.932440i	$0.382324\pi$
$110$	12.3571	1.17821
$111$	6.63406	0.629677
$112$	26.0169	2.45836
$113$	15.5927	1.46684	0.733420	−	0.679775i	$-0.237923\pi$
$113$	15.5927	1.46684	0.733420	+	0.679775i	$0.237923\pi$
$114$	1.83056	0.171448
$115$	9.55090	0.890626
$116$	−32.3865	−3.00701
$117$	0.512763	0.0474049
$118$	−8.78799	−0.809000
$119$	22.4328	2.05641
$120$	−6.15109	−0.561515
$121$	12.7611	1.16010
$122$	0.500828	0.0453428
$123$	5.72142	0.515883
$124$	42.5636	3.82232
$125$	1.00000	0.0894427
$126$	−9.78484	−0.871703
$127$	9.80059	0.869662	0.434831	−	0.900512i	$-0.356808\pi$
$127$	9.80059	0.869662	0.434831	+	0.900512i	$0.356808\pi$
$128$	12.9939	1.14851
$129$	−0.643801	−0.0566836
$130$	−1.29987	−0.114006
$131$	−9.84967	−0.860570	−0.430285	−	0.902693i	$-0.641587\pi$
$131$	−9.84967	−0.860570	−0.430285	+	0.902693i	$0.641587\pi$
$132$	−21.5768	−1.87802
$133$	−2.78721	−0.241681
$134$	11.3248	0.978313
$135$	1.00000	0.0860663
$136$	−35.7492	−3.06547
$137$	−10.3813	−0.886938	−0.443469	−	0.896290i	$-0.646252\pi$
$137$	−10.3813	−0.886938	−0.443469	+	0.896290i	$0.646252\pi$
$138$	−24.2119	−2.06106
$139$	4.00992	0.340117	0.170058	−	0.985434i	$-0.445604\pi$
$139$	4.00992	0.340117	0.170058	+	0.985434i	$0.445604\pi$
$140$	17.0853	1.44397
$141$	1.45962	0.122922
$142$	18.0071	1.51112
$143$	−2.49948	−0.209017
$144$	6.74040	0.561700
$145$	−7.31662	−0.607612
$146$	−8.71541	−0.721292
$147$	7.89835	0.651445
$148$	29.3652	2.41380
$149$	8.45592	0.692736	0.346368	−	0.938099i	$-0.387415\pi$
$149$	8.45592	0.692736	0.346368	+	0.938099i	$0.387415\pi$
$150$	−2.53504	−0.206985
$151$	12.7744	1.03957	0.519783	−	0.854298i	$-0.326013\pi$
$151$	12.7744	1.03957	0.519783	+	0.854298i	$0.326013\pi$
$152$	4.44173	0.360272
$153$	5.81185	0.469860
$154$	47.6966	3.84350
$155$	9.61579	0.772359
$156$	2.26971	0.181722
$157$	−17.9338	−1.43127	−0.715636	−	0.698473i	$-0.753863\pi$
$157$	−17.9338	−1.43127	−0.715636	+	0.698473i	$0.753863\pi$
$158$	−35.0041	−2.78478
$159$	−10.7445	−0.852096
$160$	−4.78501	−0.378289
$161$	36.8649	2.90536
$162$	−2.53504	−0.199172
$163$	5.91635	0.463404	0.231702	−	0.972787i	$-0.425571\pi$
$163$	5.91635	0.463404	0.231702	+	0.972787i	$0.425571\pi$
$164$	25.3255	1.97759
$165$	−4.87454	−0.379482
$166$	39.4076	3.05862
$167$	3.02610	0.234167	0.117083	−	0.993122i	$-0.462646\pi$
$167$	3.02610	0.234167	0.117083	+	0.993122i	$0.462646\pi$
$168$	−23.7422	−1.83175
$169$	−12.7371	−0.979775
$170$	−14.7333	−1.12999
$171$	−0.722104	−0.0552207
$172$	−2.84974	−0.217291
$173$	5.12244	0.389452	0.194726	−	0.980858i	$-0.437618\pi$
$173$	5.12244	0.389452	0.194726	+	0.980858i	$0.437618\pi$
$174$	18.5479	1.40612
$175$	3.85984	0.291776
$176$	−32.8563	−2.47664
$177$	3.46661	0.260566
$178$	43.2017	3.23810
$179$	0.00454213	0.000339495 0	0.000169747	−	1.00000i	$-0.499946\pi$
$179$	0.00454213	0.000339495 0	0.000169747		1.00000i	$0.499946\pi$
$180$	4.42643	0.329926
$181$	−4.76830	−0.354425	−0.177212	−	0.984173i	$-0.556708\pi$
$181$	−4.76830	−0.354425	−0.177212	+	0.984173i	$0.556708\pi$
$182$	−5.01730	−0.371907
$183$	−0.197562	−0.0146042
$184$	−58.7485	−4.33099
$185$	6.63406	0.487746
$186$	−24.3764	−1.78737
$187$	−28.3301	−2.07170
$188$	6.46090	0.471210
$189$	3.85984	0.280762
$190$	1.83056	0.132803
$191$	−7.99940	−0.578816	−0.289408	−	0.957206i	$-0.593458\pi$
$191$	−7.99940	−0.578816	−0.289408	+	0.957206i	$0.593458\pi$
$192$	−1.35061	−0.0974718
$193$	−19.8197	−1.42665	−0.713327	−	0.700831i	$-0.752813\pi$
$193$	−19.8197	−1.42665	−0.713327	+	0.700831i	$0.752813\pi$
$194$	34.4837	2.47578
$195$	0.512763	0.0367197
$196$	34.9615	2.49725
$197$	−10.4728	−0.746155	−0.373078	−	0.927800i	$-0.621697\pi$
$197$	−10.4728	−0.746155	−0.373078	+	0.927800i	$0.621697\pi$
$198$	12.3571	0.878184
$199$	−8.41969	−0.596856	−0.298428	−	0.954432i	$-0.596462\pi$
$199$	−8.41969	−0.596856	−0.298428	+	0.954432i	$0.596462\pi$
$200$	−6.15109	−0.434948
$201$	−4.46730	−0.315099
$202$	−11.2119	−0.788864
$203$	−28.2410	−1.98213
$204$	25.7257	1.80116
$205$	5.72142	0.399602
$206$	−16.8233	−1.17213
$207$	9.55090	0.663834
$208$	3.45623	0.239646
$209$	3.51992	0.243478
$210$	−9.78484	−0.675218
$211$	−8.58956	−0.591330	−0.295665	−	0.955292i	$-0.595541\pi$
$211$	−8.58956	−0.591330	−0.295665	+	0.955292i	$0.595541\pi$
$212$	−47.5599	−3.26642
$213$	−7.10326	−0.486707
$214$	−8.44690	−0.577418
$215$	−0.643801	−0.0439069
$216$	−6.15109	−0.418529
$217$	37.1154	2.51956
$218$	−19.1261	−1.29539
$219$	3.43798	0.232317
$220$	−21.5768	−1.45471
$221$	2.98010	0.200463
$222$	−16.8176	−1.12872
$223$	−13.4387	−0.899925	−0.449963	−	0.893047i	$-0.648563\pi$
$223$	−13.4387	−0.899925	−0.449963	+	0.893047i	$0.648563\pi$
$224$	−18.4694	−1.23404
$225$	1.00000	0.0666667
$226$	−39.5282	−2.62938
$227$	25.9726	1.72386	0.861932	−	0.507024i	$-0.169254\pi$
$227$	25.9726	1.72386	0.861932	+	0.507024i	$0.169254\pi$
$228$	−3.19634	−0.211683
$229$	25.7690	1.70287	0.851433	−	0.524464i	$-0.175734\pi$
$229$	25.7690	1.70287	0.851433	+	0.524464i	$0.175734\pi$
$230$	−24.2119	−1.59649
$231$	−18.8149	−1.23793
$232$	45.0052	2.95474
$233$	−7.42940	−0.486716	−0.243358	−	0.969937i	$-0.578249\pi$
$233$	−7.42940	−0.486716	−0.243358	+	0.969937i	$0.578249\pi$
$234$	−1.29987	−0.0849754
$235$	1.45962	0.0952151
$236$	15.3447	0.998854
$237$	13.8081	0.896932
$238$	−56.8680	−3.68621
$239$	12.0779	0.781255	0.390627	−	0.920549i	$-0.372258\pi$
$239$	12.0779	0.781255	0.390627	+	0.920549i	$0.372258\pi$
$240$	6.74040	0.435091
$241$	28.4154	1.83040	0.915198	−	0.403004i	$-0.132034\pi$
$241$	28.4154	1.83040	0.915198	+	0.403004i	$0.132034\pi$
$242$	−32.3499	−2.07953
$243$	1.00000	0.0641500
$244$	−0.874494	−0.0559838
$245$	7.89835	0.504607
$246$	−14.5040	−0.924744
$247$	−0.370268	−0.0235596
$248$	−59.1476	−3.75588
$249$	−15.5452	−0.985134
$250$	−2.53504	−0.160330
$251$	24.5305	1.54835	0.774177	−	0.632970i	$-0.218164\pi$
$251$	24.5305	1.54835	0.774177	+	0.632970i	$0.218164\pi$
$252$	17.0853	1.07627
$253$	−46.5562	−2.92696
$254$	−24.8449	−1.55891
$255$	5.81185	0.363952
$256$	−30.2388	−1.88992
$257$	9.68397	0.604069	0.302035	−	0.953297i	$-0.402334\pi$
$257$	9.68397	0.604069	0.302035	+	0.953297i	$0.402334\pi$
$258$	1.63206	0.101608
$259$	25.6064	1.59110
$260$	2.26971	0.140761
$261$	−7.31662	−0.452888
$262$	24.9693	1.54261
$263$	−10.2400	−0.631425	−0.315712	−	0.948855i	$-0.602243\pi$
$263$	−10.2400	−0.631425	−0.315712	+	0.948855i	$0.602243\pi$
$264$	29.9837	1.84537
$265$	−10.7445	−0.660031
$266$	7.06568	0.433225
$267$	−17.0418	−1.04294
$268$	−19.7742	−1.20790
$269$	11.9210	0.726838	0.363419	−	0.931626i	$-0.381609\pi$
$269$	11.9210	0.726838	0.363419	+	0.931626i	$0.381609\pi$
$270$	−2.53504	−0.154278
$271$	−11.2460	−0.683148	−0.341574	−	0.939855i	$-0.610960\pi$
$271$	−11.2460	−0.683148	−0.341574	+	0.939855i	$0.610960\pi$
$272$	39.1742	2.37528
$273$	1.97918	0.119785
$274$	26.3171	1.58987
$275$	−4.87454	−0.293946
$276$	42.2764	2.54474
$277$	−0.406642	−0.0244328	−0.0122164	−	0.999925i	$-0.503889\pi$
$277$	−0.406642	−0.0244328	−0.0122164	+	0.999925i	$0.503889\pi$
$278$	−10.1653	−0.609674
$279$	9.61579	0.575682
$280$	−23.7422	−1.41887
$281$	2.51594	0.150089	0.0750443	−	0.997180i	$-0.476090\pi$
$281$	2.51594	0.150089	0.0750443	+	0.997180i	$0.476090\pi$
$282$	−3.70019	−0.220343
$283$	−3.33705	−0.198367	−0.0991835	−	0.995069i	$-0.531623\pi$
$283$	−3.33705	−0.198367	−0.0991835	+	0.995069i	$0.531623\pi$
$284$	−31.4421	−1.86574
$285$	−0.722104	−0.0427738
$286$	6.33628	0.374672
$287$	22.0838	1.30356
$288$	−4.78501	−0.281960
$289$	16.7776	0.986916
$290$	18.5479	1.08917
$291$	−13.6028	−0.797411
$292$	15.2180	0.890564
$293$	16.3868	0.957328	0.478664	−	0.877998i	$-0.341121\pi$
$293$	16.3868	0.957328	0.478664	+	0.877998i	$0.341121\pi$
$294$	−20.0226	−1.16774
$295$	3.46661	0.201834
$296$	−40.8067	−2.37184
$297$	−4.87454	−0.282849
$298$	−21.4361	−1.24176
$299$	4.89735	0.283221
$300$	4.42643	0.255560
$301$	−2.48497	−0.143231
$302$	−32.3836	−1.86347
$303$	4.42276	0.254081
$304$	−4.86727	−0.279157
$305$	−0.197562	−0.0113124
$306$	−14.7333	−0.842245
$307$	2.71821	0.155137	0.0775683	−	0.996987i	$-0.475284\pi$
$307$	2.71821	0.155137	0.0775683	+	0.996987i	$0.475284\pi$
$308$	−83.2829	−4.74548
$309$	6.63630	0.377526
$310$	−24.3764	−1.38449
$311$	22.2122	1.25954	0.629768	−	0.776783i	$-0.283150\pi$
$311$	22.2122	1.25954	0.629768	+	0.776783i	$0.283150\pi$
$312$	−3.15405	−0.178563
$313$	9.47180	0.535378	0.267689	−	0.963505i	$-0.413740\pi$
$313$	9.47180	0.535378	0.267689	+	0.963505i	$0.413740\pi$
$314$	45.4629	2.56562
$315$	3.85984	0.217477
$316$	61.1205	3.43830
$317$	17.5826	0.987537	0.493769	−	0.869593i	$-0.335619\pi$
$317$	17.5826	0.987537	0.493769	+	0.869593i	$0.335619\pi$
$318$	27.2378	1.52742
$319$	35.6651	1.99686
$320$	−1.35061	−0.0755013
$321$	3.33206	0.185977
$322$	−93.4541	−5.20799
$323$	−4.19676	−0.233514
$324$	4.42643	0.245913
$325$	0.512763	0.0284430
$326$	−14.9982	−0.830672
$327$	7.54471	0.417223
$328$	−35.1930	−1.94321
$329$	5.63390	0.310607
$330$	12.3571	0.680238
$331$	−18.8824	−1.03787	−0.518934	−	0.854814i	$-0.673671\pi$
$331$	−18.8824	−1.03787	−0.518934	+	0.854814i	$0.673671\pi$
$332$	−68.8095	−3.77641
$333$	6.63406	0.363544
$334$	−7.67129	−0.419754
$335$	−4.46730	−0.244075
$336$	26.0169	1.41934
$337$	−14.1703	−0.771907	−0.385953	−	0.922518i	$-0.626127\pi$
$337$	−14.1703	−0.771907	−0.385953	+	0.922518i	$0.626127\pi$
$338$	32.2890	1.75629
$339$	15.5927	0.846881
$340$	25.7257	1.39517
$341$	−46.8725	−2.53829
$342$	1.83056	0.0989855
$343$	3.46750	0.187227
$344$	3.96008	0.213513
$345$	9.55090	0.514203
$346$	−12.9856	−0.698110
$347$	2.38148	0.127845	0.0639224	−	0.997955i	$-0.479639\pi$
$347$	2.38148	0.127845	0.0639224	+	0.997955i	$0.479639\pi$
$348$	−32.3865	−1.73610
$349$	−9.46381	−0.506586	−0.253293	−	0.967390i	$-0.581514\pi$
$349$	−9.46381	−0.506586	−0.253293	+	0.967390i	$0.581514\pi$
$350$	−9.78484	−0.523022
$351$	0.512763	0.0273692
$352$	23.3247	1.24321
$353$	−15.6072	−0.830685	−0.415343	−	0.909665i	$-0.636338\pi$
$353$	−15.6072	−0.830685	−0.415343	+	0.909665i	$0.636338\pi$
$354$	−8.78799	−0.467076
$355$	−7.10326	−0.377002
$356$	−75.4344	−3.99801
$357$	22.4328	1.18727
$358$	−0.0115145	−0.000608559 0
$359$	−11.3237	−0.597640	−0.298820	−	0.954309i	$-0.596593\pi$
$359$	−11.3237	−0.597640	−0.298820	+	0.954309i	$0.596593\pi$
$360$	−6.15109	−0.324191
$361$	−18.4786	−0.972556
$362$	12.0878	0.635322
$363$	12.7611	0.669784
$364$	8.76070	0.459186
$365$	3.43798	0.179952
$366$	0.500828	0.0261787
$367$	−12.2946	−0.641772	−0.320886	−	0.947118i	$-0.603981\pi$
$367$	−12.2946	−0.641772	−0.320886	+	0.947118i	$0.603981\pi$
$368$	64.3769	3.35588
$369$	5.72142	0.297845
$370$	−16.8176	−0.874306
$371$	−41.4721	−2.15313
$372$	42.5636	2.20682
$373$	30.1907	1.56321	0.781607	−	0.623772i	$-0.214400\pi$
$373$	30.1907	1.56321	0.781607	+	0.623772i	$0.214400\pi$
$374$	71.8178	3.71361
$375$	1.00000	0.0516398
$376$	−8.97825	−0.463018
$377$	−3.75169	−0.193222
$378$	−9.78484	−0.503278
$379$	−37.5118	−1.92685	−0.963425	−	0.267978i	$-0.913645\pi$
$379$	−37.5118	−1.92685	−0.963425	+	0.267978i	$0.913645\pi$
$380$	−3.19634	−0.163969
$381$	9.80059	0.502099
$382$	20.2788	1.03755
$383$	7.28987	0.372495	0.186247	−	0.982503i	$-0.440367\pi$
$383$	7.28987	0.372495	0.186247	+	0.982503i	$0.440367\pi$
$384$	12.9939	0.663091
$385$	−18.8149	−0.958897
$386$	50.2438	2.55734
$387$	−0.643801	−0.0327263
$388$	−60.2118	−3.05679
$389$	−9.58794	−0.486128	−0.243064	−	0.970010i	$-0.578153\pi$
$389$	−9.58794	−0.486128	−0.243064	+	0.970010i	$0.578153\pi$
$390$	−1.29987	−0.0658217
$391$	55.5084	2.80718
$392$	−48.5835	−2.45384
$393$	−9.84967	−0.496850
$394$	26.5489	1.33752
$395$	13.8081	0.694761
$396$	−21.5768	−1.08427
$397$	15.1172	0.758708	0.379354	−	0.925252i	$-0.376146\pi$
$397$	15.1172	0.758708	0.379354	+	0.925252i	$0.376146\pi$
$398$	21.3443	1.06989
$399$	−2.78721	−0.139535
$400$	6.74040	0.337020
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	11.3248	0.564829
$403$	4.93062	0.245612
$404$	19.5770	0.973993
$405$	1.00000	0.0496904
$406$	71.5920	3.55305
$407$	−32.3380	−1.60293
$408$	−35.7492	−1.76985
$409$	19.7000	0.974102	0.487051	−	0.873373i	$-0.338073\pi$
$409$	19.7000	0.974102	0.487051	+	0.873373i	$0.338073\pi$
$410$	−14.5040	−0.716303
$411$	−10.3813	−0.512074
$412$	29.3751	1.44721
$413$	13.3805	0.658414
$414$	−24.2119	−1.18995
$415$	−15.5452	−0.763082
$416$	−2.45358	−0.120296
$417$	4.00992	0.196367
$418$	−8.92315	−0.436445
$419$	−36.5148	−1.78386	−0.891932	−	0.452170i	$-0.850650\pi$
$419$	−36.5148	−1.78386	−0.891932	+	0.452170i	$0.850650\pi$
$420$	17.0853	0.833677
$421$	−22.1397	−1.07902	−0.539512	−	0.841978i	$-0.681391\pi$
$421$	−22.1397	−1.07902	−0.539512	+	0.841978i	$0.681391\pi$
$422$	21.7749	1.05998
$423$	1.45962	0.0709691
$424$	66.0905	3.20964
$425$	5.81185	0.281916
$426$	18.0071	0.872445
$427$	−0.762558	−0.0369028
$428$	14.7491	0.712925
$429$	−2.49948	−0.120676
$430$	1.63206	0.0787050
$431$	−29.0302	−1.39833	−0.699167	−	0.714958i	$-0.746446\pi$
$431$	−29.0302	−1.39833	−0.699167	+	0.714958i	$0.746446\pi$
$432$	6.74040	0.324298
$433$	11.5295	0.554073	0.277036	−	0.960859i	$-0.410648\pi$
$433$	11.5295	0.554073	0.277036	+	0.960859i	$0.410648\pi$
$434$	−94.0890	−4.51642
$435$	−7.31662	−0.350805
$436$	33.3961	1.59938
$437$	−6.89675	−0.329916
$438$	−8.71541	−0.416438
$439$	18.9994	0.906792	0.453396	−	0.891309i	$-0.350212\pi$
$439$	18.9994	0.906792	0.453396	+	0.891309i	$0.350212\pi$
$440$	29.9837	1.42942
$441$	7.89835	0.376112
$442$	−7.55467	−0.359339
$443$	−37.3964	−1.77676	−0.888379	−	0.459110i	$-0.848168\pi$
$443$	−37.3964	−1.77676	−0.888379	+	0.459110i	$0.848168\pi$
$444$	29.3652	1.39361
$445$	−17.0418	−0.807860
$446$	34.0678	1.61316
$447$	8.45592	0.399951
$448$	−5.21313	−0.246297
$449$	−11.0546	−0.521698	−0.260849	−	0.965380i	$-0.584002\pi$
$449$	−11.0546	−0.521698	−0.260849	+	0.965380i	$0.584002\pi$
$450$	−2.53504	−0.119503
$451$	−27.8893	−1.31326
$452$	69.0201	3.24643
$453$	12.7744	0.600193
$454$	−65.8417	−3.09010
$455$	1.97918	0.0927854
$456$	4.44173	0.208003
$457$	−30.8270	−1.44203	−0.721013	−	0.692922i	$-0.756323\pi$
$457$	−30.8270	−1.44203	−0.721013	+	0.692922i	$0.756323\pi$
$458$	−65.3255	−3.05246
$459$	5.81185	0.271274
$460$	42.2764	1.97115
$461$	−0.743479	−0.0346273	−0.0173136	−	0.999850i	$-0.505511\pi$
$461$	−0.743479	−0.0346273	−0.0173136	+	0.999850i	$0.505511\pi$
$462$	47.6966	2.21905
$463$	11.9906	0.557250	0.278625	−	0.960400i	$-0.410121\pi$
$463$	11.9906	0.557250	0.278625	+	0.960400i	$0.410121\pi$
$464$	−49.3170	−2.28948
$465$	9.61579	0.445922
$466$	18.8338	0.872460
$467$	37.2457	1.72352	0.861762	−	0.507312i	$-0.169361\pi$
$467$	37.2457	1.72352	0.861762	+	0.507312i	$0.169361\pi$
$468$	2.26971	0.104917
$469$	−17.2431	−0.796211
$470$	−3.70019	−0.170677
$471$	−17.9338	−0.826346
$472$	−21.3234	−0.981490
$473$	3.13823	0.144296
$474$	−35.0041	−1.60779
$475$	−0.722104	−0.0331324
$476$	99.2971	4.55128
$477$	−10.7445	−0.491958
$478$	−30.6180	−1.40043
$479$	−20.9020	−0.955038	−0.477519	−	0.878621i	$-0.658464\pi$
$479$	−20.9020	−0.955038	−0.477519	+	0.878621i	$0.658464\pi$
$480$	−4.78501	−0.218405
$481$	3.40170	0.155104
$482$	−72.0342	−3.28107
$483$	36.8649	1.67741
$484$	56.4861	2.56755
$485$	−13.6028	−0.617672
$486$	−2.53504	−0.114992
$487$	29.1538	1.32109	0.660543	−	0.750789i	$-0.270326\pi$
$487$	29.1538	1.32109	0.660543	+	0.750789i	$0.270326\pi$
$488$	1.21522	0.0550105
$489$	5.91635	0.267546
$490$	−20.0226	−0.904531
$491$	11.3524	0.512328	0.256164	−	0.966633i	$-0.417541\pi$
$491$	11.3524	0.512328	0.256164	+	0.966633i	$0.417541\pi$
$492$	25.3255	1.14176
$493$	−42.5231	−1.91514
$494$	0.938645	0.0422316
$495$	−4.87454	−0.219094
$496$	64.8143	2.91025
$497$	−27.4174	−1.22984
$498$	39.4076	1.76590
$499$	16.6293	0.744431	0.372216	−	0.928146i	$-0.378598\pi$
$499$	16.6293	0.744431	0.372216	+	0.928146i	$0.378598\pi$
$500$	4.42643	0.197956
$501$	3.02610	0.135196
$502$	−62.1859	−2.77549
$503$	26.6105	1.18650	0.593252	−	0.805017i	$-0.297844\pi$
$503$	26.6105	1.18650	0.593252	+	0.805017i	$0.297844\pi$
$504$	−23.7422	−1.05756
$505$	4.42276	0.196810
$506$	118.022	5.24671
$507$	−12.7371	−0.565673
$508$	43.3816	1.92475
$509$	27.7162	1.22850	0.614250	−	0.789111i	$-0.289459\pi$
$509$	27.7162	1.22850	0.614250	+	0.789111i	$0.289459\pi$
$510$	−14.7333	−0.652400
$511$	13.2700	0.587032
$512$	50.6687	2.23926
$513$	−0.722104	−0.0318817
$514$	−24.5492	−1.08282
$515$	6.63630	0.292430
$516$	−2.84974	−0.125453
$517$	−7.11497	−0.312916
$518$	−64.9133	−2.85212
$519$	5.12244	0.224850
$520$	−3.15405	−0.138314
$521$	21.0636	0.922815	0.461407	−	0.887188i	$-0.347345\pi$
$521$	21.0636	0.922815	0.461407	+	0.887188i	$0.347345\pi$
$522$	18.5479	0.811821
$523$	−23.8054	−1.04094	−0.520470	−	0.853880i	$-0.674243\pi$
$523$	−23.8054	−1.04094	−0.520470	+	0.853880i	$0.674243\pi$
$524$	−43.5989	−1.90463
$525$	3.85984	0.168457
$526$	25.9588	1.13186
$527$	55.8855	2.43441
$528$	−32.8563	−1.42989
$529$	68.2197	2.96608
$530$	27.2378	1.18313
$531$	3.46661	0.150438
$532$	−12.3374	−0.534893
$533$	2.93373	0.127074
$534$	43.2017	1.86952
$535$	3.33206	0.144057
$536$	27.4788	1.18690
$537$	0.00454213	0.000196007 0
$538$	−30.2203	−1.30289
$539$	−38.5008	−1.65835
$540$	4.42643	0.190483
$541$	44.3589	1.90714	0.953568	−	0.301176i	$-0.0973793\pi$
$541$	44.3589	1.90714	0.953568	+	0.301176i	$0.0973793\pi$
$542$	28.5092	1.22457
$543$	−4.76830	−0.204627
$544$	−27.8098	−1.19233
$545$	7.54471	0.323180
$546$	−5.01730	−0.214721
$547$	13.5813	0.580693	0.290347	−	0.956922i	$-0.406229\pi$
$547$	13.5813	0.580693	0.290347	+	0.956922i	$0.406229\pi$
$548$	−45.9523	−1.96298
$549$	−0.197562	−0.00843175
$550$	12.3571	0.526910
$551$	5.28336	0.225079
$552$	−58.7485	−2.50050
$553$	53.2970	2.26642
$554$	1.03085	0.0437968
$555$	6.63406	0.281600
$556$	17.7496	0.752751
$557$	37.2210	1.57711	0.788553	−	0.614967i	$-0.210831\pi$
$557$	37.2210	1.57711	0.788553	+	0.614967i	$0.210831\pi$
$558$	−24.3764	−1.03194
$559$	−0.330117	−0.0139625
$560$	26.0169	1.09941
$561$	−28.3301	−1.19610
$562$	−6.37802	−0.269041
$563$	14.5146	0.611716	0.305858	−	0.952077i	$-0.401057\pi$
$563$	14.5146	0.611716	0.305858	+	0.952077i	$0.401057\pi$
$564$	6.46090	0.272053
$565$	15.5927	0.655991
$566$	8.45955	0.355581
$567$	3.85984	0.162098
$568$	43.6928	1.83331
$569$	−30.1311	−1.26316	−0.631581	−	0.775310i	$-0.717594\pi$
$569$	−30.1311	−1.26316	−0.631581	+	0.775310i	$0.717594\pi$
$570$	1.83056	0.0766739
$571$	−3.43482	−0.143743	−0.0718714	−	0.997414i	$-0.522897\pi$
$571$	−3.43482	−0.143743	−0.0718714	+	0.997414i	$0.522897\pi$
$572$	−11.0638	−0.462599
$573$	−7.99940	−0.334180
$574$	−55.9832	−2.33670
$575$	9.55090	0.398300
$576$	−1.35061	−0.0562754
$577$	−31.6905	−1.31929	−0.659647	−	0.751576i	$-0.729294\pi$
$577$	−31.6905	−1.31929	−0.659647	+	0.751576i	$0.729294\pi$
$578$	−42.5318	−1.76909
$579$	−19.8197	−0.823679
$580$	−32.3865	−1.34478
$581$	−60.0018	−2.48929
$582$	34.4837	1.42939
$583$	52.3746	2.16913
$584$	−21.1473	−0.875082
$585$	0.512763	0.0212001
$586$	−41.5412	−1.71605
$587$	−15.8119	−0.652628	−0.326314	−	0.945261i	$-0.605807\pi$
$587$	−15.8119	−0.652628	−0.326314	+	0.945261i	$0.605807\pi$
$588$	34.9615	1.44179
$589$	−6.94360	−0.286106
$590$	−8.78799	−0.361796
$591$	−10.4728	−0.430793
$592$	44.7163	1.83783
$593$	32.4573	1.33286	0.666430	−	0.745568i	$-0.267822\pi$
$593$	32.4573	1.33286	0.666430	+	0.745568i	$0.267822\pi$
$594$	12.3571	0.507020
$595$	22.4328	0.919655
$596$	37.4295	1.53317
$597$	−8.41969	−0.344595
$598$	−12.4150	−0.507686
$599$	−21.8683	−0.893514	−0.446757	−	0.894655i	$-0.647421\pi$
$599$	−21.8683	−0.893514	−0.446757	+	0.894655i	$0.647421\pi$
$600$	−6.15109	−0.251117
$601$	−12.7763	−0.521157	−0.260578	−	0.965453i	$-0.583913\pi$
$601$	−12.7763	−0.521157	−0.260578	+	0.965453i	$0.583913\pi$
$602$	6.29950	0.256748
$603$	−4.46730	−0.181923
$604$	56.5449	2.30078
$605$	12.7611	0.518813
$606$	−11.2119	−0.455451
$607$	−3.65229	−0.148242	−0.0741210	−	0.997249i	$-0.523615\pi$
$607$	−3.65229	−0.148242	−0.0741210	+	0.997249i	$0.523615\pi$
$608$	3.45528	0.140130
$609$	−28.2410	−1.14438
$610$	0.500828	0.0202779
$611$	0.748439	0.0302786
$612$	25.7257	1.03990
$613$	−18.9988	−0.767353	−0.383676	−	0.923468i	$-0.625342\pi$
$613$	−18.9988	−0.767353	−0.383676	+	0.923468i	$0.625342\pi$
$614$	−6.89078	−0.278089
$615$	5.72142	0.230710
$616$	115.732	4.66299
$617$	17.8972	0.720515	0.360258	−	0.932853i	$-0.382689\pi$
$617$	17.8972	0.720515	0.360258	+	0.932853i	$0.382689\pi$
$618$	−16.8233	−0.676732
$619$	−24.8201	−0.997603	−0.498802	−	0.866716i	$-0.666226\pi$
$619$	−24.8201	−0.997603	−0.498802	+	0.866716i	$0.666226\pi$
$620$	42.5636	1.70940
$621$	9.55090	0.383264
$622$	−56.3087	−2.25777
$623$	−65.7787	−2.63537
$624$	3.45623	0.138360
$625$	1.00000	0.0400000
$626$	−24.0114	−0.959688
$627$	3.51992	0.140572
$628$	−79.3826	−3.16771
$629$	38.5561	1.53733
$630$	−9.78484	−0.389838
$631$	−19.6634	−0.782786	−0.391393	−	0.920224i	$-0.628007\pi$
$631$	−19.6634	−0.782786	−0.391393	+	0.920224i	$0.628007\pi$
$632$	−84.9349	−3.37853
$633$	−8.58956	−0.341404
$634$	−44.5726	−1.77020
$635$	9.80059	0.388925
$636$	−47.5599	−1.88587
$637$	4.04998	0.160466
$638$	−90.4126	−3.57947
$639$	−7.10326	−0.281001
$640$	12.9939	0.513628
$641$	39.1608	1.54676	0.773379	−	0.633944i	$-0.218565\pi$
$641$	39.1608	1.54676	0.773379	+	0.633944i	$0.218565\pi$
$642$	−8.44690	−0.333373
$643$	−28.0609	−1.10662	−0.553308	−	0.832977i	$-0.686635\pi$
$643$	−28.0609	−1.10662	−0.553308	+	0.832977i	$0.686635\pi$
$644$	163.180	6.43019
$645$	−0.643801	−0.0253497
$646$	10.6390	0.418584
$647$	19.3023	0.758850	0.379425	−	0.925223i	$-0.376122\pi$
$647$	19.3023	0.758850	0.379425	+	0.925223i	$0.376122\pi$
$648$	−6.15109	−0.241638
$649$	−16.8981	−0.663309
$650$	−1.29987	−0.0509853
$651$	37.1154	1.45467
$652$	26.1883	1.02561
$653$	11.4746	0.449036	0.224518	−	0.974470i	$-0.427919\pi$
$653$	11.4746	0.449036	0.224518	+	0.974470i	$0.427919\pi$
$654$	−19.1261	−0.747891
$655$	−9.84967	−0.384859
$656$	38.5647	1.50570
$657$	3.43798	0.134128
$658$	−14.2822	−0.556776
$659$	26.3597	1.02683	0.513415	−	0.858141i	$-0.328380\pi$
$659$	26.3597	1.02683	0.513415	+	0.858141i	$0.328380\pi$
$660$	−21.5768	−0.839875
$661$	33.1071	1.28772	0.643859	−	0.765144i	$-0.277332\pi$
$661$	33.1071	1.28772	0.643859	+	0.765144i	$0.277332\pi$
$662$	47.8676	1.86043
$663$	2.98010	0.115737
$664$	95.6197	3.71076
$665$	−2.78721	−0.108083
$666$	−16.8176	−0.651669
$667$	−69.8803	−2.70578
$668$	13.3948	0.518261
$669$	−13.4387	−0.519572
$670$	11.3248	0.437515
$671$	0.963024	0.0371771
$672$	−18.4694	−0.712472
$673$	−7.67852	−0.295985	−0.147993	−	0.988988i	$-0.547281\pi$
$673$	−7.67852	−0.295985	−0.147993	+	0.988988i	$0.547281\pi$
$674$	35.9223	1.38368
$675$	1.00000	0.0384900
$676$	−56.3797	−2.16845
$677$	21.9735	0.844509	0.422254	−	0.906477i	$-0.361239\pi$
$677$	21.9735	0.844509	0.422254	+	0.906477i	$0.361239\pi$
$678$	−39.5282	−1.51807
$679$	−52.5046	−2.01494
$680$	−35.7492	−1.37092
$681$	25.9726	0.995273
$682$	118.824	4.54999
$683$	−25.6119	−0.980013	−0.490006	−	0.871719i	$-0.663006\pi$
$683$	−25.6119	−0.980013	−0.490006	+	0.871719i	$0.663006\pi$
$684$	−3.19634	−0.122215
$685$	−10.3813	−0.396651
$686$	−8.79024	−0.335613
$687$	25.7690	0.983150
$688$	−4.33948	−0.165441
$689$	−5.50939	−0.209891
$690$	−24.2119	−0.921732
$691$	−14.5875	−0.554935	−0.277467	−	0.960735i	$-0.589495\pi$
$691$	−14.5875	−0.554935	−0.277467	+	0.960735i	$0.589495\pi$
$692$	22.6741	0.861940
$693$	−18.8149	−0.714720
$694$	−6.03716	−0.229167
$695$	4.00992	0.152105
$696$	45.0052	1.70592
$697$	33.2520	1.25951
$698$	23.9911	0.908078
$699$	−7.42940	−0.281006
$700$	17.0853	0.645763
$701$	33.2231	1.25482	0.627409	−	0.778690i	$-0.284115\pi$
$701$	33.2231	1.25482	0.627409	+	0.778690i	$0.284115\pi$
$702$	−1.29987	−0.0490606
$703$	−4.79048	−0.180677
$704$	6.58359	0.248128
$705$	1.45962	0.0549725
$706$	39.5648	1.48904
$707$	17.0711	0.642026
$708$	15.3447	0.576689
$709$	38.8199	1.45791	0.728957	−	0.684560i	$-0.240006\pi$
$709$	38.8199	1.45791	0.728957	+	0.684560i	$0.240006\pi$
$710$	18.0071	0.675793
$711$	13.8081	0.517844
$712$	104.826	3.92851
$713$	91.8395	3.43942
$714$	−56.8680	−2.12823
$715$	−2.49948	−0.0934753
$716$	0.0201054	0.000751375 0
$717$	12.0779	0.451058
$718$	28.7059	1.07130
$719$	3.86868	0.144277	0.0721387	−	0.997395i	$-0.477018\pi$
$719$	3.86868	0.144277	0.0721387	+	0.997395i	$0.477018\pi$
$720$	6.74040	0.251200
$721$	25.6150	0.953954
$722$	46.8439	1.74335
$723$	28.4154	1.05678
$724$	−21.1065	−0.784418
$725$	−7.31662	−0.271733
$726$	−32.3499	−1.20062
$727$	9.65238	0.357987	0.178994	−	0.983850i	$-0.442716\pi$
$727$	9.65238	0.357987	0.178994	+	0.983850i	$0.442716\pi$
$728$	−12.1741	−0.451203
$729$	1.00000	0.0370370
$730$	−8.71541	−0.322572
$731$	−3.74168	−0.138391
$732$	−0.874494	−0.0323222
$733$	5.90194	0.217993	0.108996	−	0.994042i	$-0.465236\pi$
$733$	5.90194	0.217993	0.108996	+	0.994042i	$0.465236\pi$
$734$	31.1673	1.15041
$735$	7.89835	0.291335
$736$	−45.7012	−1.68457
$737$	21.7760	0.802130
$738$	−14.5040	−0.533901
$739$	−11.4781	−0.422229	−0.211115	−	0.977461i	$-0.567709\pi$
$739$	−11.4781	−0.422229	−0.211115	+	0.977461i	$0.567709\pi$
$740$	29.3652	1.07949
$741$	−0.370268	−0.0136021
$742$	105.133	3.85957
$743$	−46.3732	−1.70127	−0.850633	−	0.525760i	$-0.823781\pi$
$743$	−46.3732	−1.70127	−0.850633	+	0.525760i	$0.823781\pi$
$744$	−59.1476	−2.16846
$745$	8.45592	0.309801
$746$	−76.5345	−2.80213
$747$	−15.5452	−0.568768
$748$	−125.401	−4.58511
$749$	12.8612	0.469938
$750$	−2.53504	−0.0925666
$751$	51.5341	1.88050	0.940252	−	0.340479i	$-0.110589\pi$
$751$	51.5341	1.88050	0.940252	+	0.340479i	$0.110589\pi$
$752$	9.83843	0.358771
$753$	24.5305	0.893942
$754$	9.51069	0.346359
$755$	12.7744	0.464908
$756$	17.0853	0.621386
$757$	38.5403	1.40077	0.700386	−	0.713764i	$-0.253011\pi$
$757$	38.5403	1.40077	0.700386	+	0.713764i	$0.253011\pi$
$758$	95.0938	3.45396
$759$	−46.5562	−1.68988
$760$	4.44173	0.161118
$761$	−33.5699	−1.21691	−0.608454	−	0.793589i	$-0.708210\pi$
$761$	−33.5699	−1.21691	−0.608454	+	0.793589i	$0.708210\pi$
$762$	−24.8449	−0.900035
$763$	29.1214	1.05426
$764$	−35.4088	−1.28104
$765$	5.81185	0.210128
$766$	−18.4801	−0.667713
$767$	1.77755	0.0641835
$768$	−30.2388	−1.09115
$769$	−34.8392	−1.25633	−0.628166	−	0.778079i	$-0.716194\pi$
$769$	−34.8392	−1.25633	−0.628166	+	0.778079i	$0.716194\pi$
$770$	47.6966	1.71887
$771$	9.68397	0.348760
$772$	−87.7305	−3.15749
$773$	−9.19964	−0.330888	−0.165444	−	0.986219i	$-0.552906\pi$
$773$	−9.19964	−0.330888	−0.165444	+	0.986219i	$0.552906\pi$
$774$	1.63206	0.0586633
$775$	9.61579	0.345409
$776$	83.6721	3.00365
$777$	25.6064	0.918625
$778$	24.3058	0.871406
$779$	−4.13147	−0.148025
$780$	2.26971	0.0812685
$781$	34.6251	1.23898
$782$	−140.716	−5.03199
$783$	−7.31662	−0.261475
$784$	53.2381	1.90136
$785$	−17.9338	−0.640084
$786$	24.9693	0.890626
$787$	−21.1231	−0.752958	−0.376479	−	0.926425i	$-0.622865\pi$
$787$	−21.1231	−0.752958	−0.376479	+	0.926425i	$0.622865\pi$
$788$	−46.3570	−1.65140
$789$	−10.2400	−0.364553
$790$	−35.0041	−1.24539
$791$	60.1854	2.13995
$792$	29.9837	1.06542
$793$	−0.101303	−0.00359736
$794$	−38.3226	−1.36002
$795$	−10.7445	−0.381069
$796$	−37.2692	−1.32097
$797$	−20.1057	−0.712180	−0.356090	−	0.934452i	$-0.615890\pi$
$797$	−20.1057	−0.712180	−0.356090	+	0.934452i	$0.615890\pi$
$798$	7.06568	0.250122
$799$	8.48309	0.300110
$800$	−4.78501	−0.169176
$801$	−17.0418	−0.602143
$802$	−2.53504	−0.0895154
$803$	−16.7585	−0.591396
$804$	−19.7742	−0.697382
$805$	36.8649	1.29932
$806$	−12.4993	−0.440270
$807$	11.9210	0.419640
$808$	−27.2048	−0.957061
$809$	34.5173	1.21356	0.606782	−	0.794868i	$-0.292460\pi$
$809$	34.5173	1.21356	0.606782	+	0.794868i	$0.292460\pi$
$810$	−2.53504	−0.0890722
$811$	−3.52914	−0.123925	−0.0619624	−	0.998078i	$-0.519736\pi$
$811$	−3.52914	−0.123925	−0.0619624	+	0.998078i	$0.519736\pi$
$812$	−125.007	−4.38687
$813$	−11.2460	−0.394416
$814$	81.9781	2.87333
$815$	5.91635	0.207241
$816$	39.1742	1.37137
$817$	0.464892	0.0162645
$818$	−49.9403	−1.74612
$819$	1.97918	0.0691582
$820$	25.3255	0.884404
$821$	−34.6275	−1.20851	−0.604253	−	0.796792i	$-0.706528\pi$
$821$	−34.6275	−1.20851	−0.604253	+	0.796792i	$0.706528\pi$
$822$	26.3171	0.917915
$823$	−35.0722	−1.22254	−0.611270	−	0.791422i	$-0.709341\pi$
$823$	−35.0722	−1.22254	−0.611270	+	0.791422i	$0.709341\pi$
$824$	−40.8205	−1.42205
$825$	−4.87454	−0.169710
$826$	−33.9202	−1.18024
$827$	47.5467	1.65336	0.826681	−	0.562671i	$-0.190226\pi$
$827$	47.5467	1.65336	0.826681	+	0.562671i	$0.190226\pi$
$828$	42.2764	1.46921
$829$	8.20534	0.284983	0.142492	−	0.989796i	$-0.454489\pi$
$829$	8.20534	0.284983	0.142492	+	0.989796i	$0.454489\pi$
$830$	39.4076	1.36786
$831$	−0.406642	−0.0141063
$832$	−0.692542	−0.0240096
$833$	45.9040	1.59048
$834$	−10.1653	−0.351996
$835$	3.02610	0.104723
$836$	15.5807	0.538869
$837$	9.61579	0.332370
$838$	92.5664	3.19765
$839$	50.0058	1.72639	0.863196	−	0.504869i	$-0.168459\pi$
$839$	50.0058	1.72639	0.863196	+	0.504869i	$0.168459\pi$
$840$	−23.7422	−0.819184
$841$	24.5330	0.845965
$842$	56.1251	1.93420
$843$	2.51594	0.0866537
$844$	−38.0211	−1.30874
$845$	−12.7371	−0.438169
$846$	−3.70019	−0.127215
$847$	49.2558	1.69245
$848$	−72.4224	−2.48700
$849$	−3.33705	−0.114527
$850$	−14.7333	−0.505347
$851$	63.3613	2.17200
$852$	−31.4421	−1.07719
$853$	5.78806	0.198179	0.0990897	−	0.995079i	$-0.468407\pi$
$853$	5.78806	0.198179	0.0990897	+	0.995079i	$0.468407\pi$
$854$	1.93311	0.0661498
$855$	−0.722104	−0.0246954
$856$	−20.4958	−0.700532
$857$	−31.7511	−1.08460	−0.542299	−	0.840186i	$-0.682446\pi$
$857$	−31.7511	−1.08460	−0.542299	+	0.840186i	$0.682446\pi$
$858$	6.33628	0.216317
$859$	6.13392	0.209287	0.104643	−	0.994510i	$-0.466630\pi$
$859$	6.13392	0.209287	0.104643	+	0.994510i	$0.466630\pi$
$860$	−2.84974	−0.0971753
$861$	22.0838	0.752613
$862$	73.5926	2.50658
$863$	−12.0179	−0.409095	−0.204547	−	0.978857i	$-0.565572\pi$
$863$	−12.0179	−0.409095	−0.204547	+	0.978857i	$0.565572\pi$
$864$	−4.78501	−0.162789
$865$	5.12244	0.174168
$866$	−29.2278	−0.993200
$867$	16.7776	0.569796
$868$	164.289	5.57632
$869$	−67.3081	−2.28327
$870$	18.5479	0.628834
$871$	−2.29067	−0.0776163
$872$	−46.4082	−1.57158
$873$	−13.6028	−0.460385
$874$	17.4835	0.591389
$875$	3.85984	0.130486
$876$	15.2180	0.514167
$877$	−34.2996	−1.15821	−0.579107	−	0.815252i	$-0.696599\pi$
$877$	−34.2996	−1.15821	−0.579107	+	0.815252i	$0.696599\pi$
$878$	−48.1642	−1.62546
$879$	16.3868	0.552713
$880$	−32.8563	−1.10759
$881$	−0.881219	−0.0296890	−0.0148445	−	0.999890i	$-0.504725\pi$
$881$	−0.881219	−0.0296890	−0.0148445	+	0.999890i	$0.504725\pi$
$882$	−20.0226	−0.674197
$883$	−34.9380	−1.17576	−0.587879	−	0.808949i	$-0.700037\pi$
$883$	−34.9380	−1.17576	−0.587879	+	0.808949i	$0.700037\pi$
$884$	13.1912	0.443668
$885$	3.46661	0.116529
$886$	94.8015	3.18492
$887$	49.5120	1.66245	0.831225	−	0.555937i	$-0.187640\pi$
$887$	49.5120	1.66245	0.831225	+	0.555937i	$0.187640\pi$
$888$	−40.8067	−1.36938
$889$	37.8287	1.26873
$890$	43.2017	1.44812
$891$	−4.87454	−0.163303
$892$	−59.4856	−1.99173
$893$	−1.05400	−0.0352707
$894$	−21.4361	−0.716930
$895$	0.00454213	0.000151827 0
$896$	50.1543	1.67554
$897$	4.89735	0.163518
$898$	28.0238	0.935166
$899$	−70.3551	−2.34647
$900$	4.42643	0.147548
$901$	−62.4455	−2.08036
$902$	70.7005	2.35407
$903$	−2.48497	−0.0826946
$904$	−95.9123	−3.19000
$905$	−4.76830	−0.158504
$906$	−32.3836	−1.07587
$907$	−53.9299	−1.79071	−0.895356	−	0.445350i	$-0.853079\pi$
$907$	−53.9299	−1.79071	−0.895356	+	0.445350i	$0.853079\pi$
$908$	114.966	3.81528
$909$	4.42276	0.146694
$910$	−5.01730	−0.166322
$911$	−44.0832	−1.46054	−0.730271	−	0.683157i	$-0.760606\pi$
$911$	−44.0832	−1.46054	−0.730271	+	0.683157i	$0.760606\pi$
$912$	−4.86727	−0.161172
$913$	75.7754	2.50780
$914$	78.1476	2.58489
$915$	−0.197562	−0.00653120
$916$	114.065	3.76881
$917$	−38.0181	−1.25547
$918$	−14.7333	−0.486270
$919$	−14.0066	−0.462034	−0.231017	−	0.972950i	$-0.574205\pi$
$919$	−14.0066	−0.462034	−0.231017	+	0.972950i	$0.574205\pi$
$920$	−58.7485	−1.93688
$921$	2.71821	0.0895682
$922$	1.88475	0.0620709
$923$	−3.64229	−0.119887
$924$	−83.2829	−2.73981
$925$	6.63406	0.218127
$926$	−30.3966	−0.998895
$927$	6.63630	0.217965
$928$	35.0101	1.14926
$929$	−37.6895	−1.23655	−0.618276	−	0.785961i	$-0.712169\pi$
$929$	−37.6895	−1.23655	−0.618276	+	0.785961i	$0.712169\pi$
$930$	−24.3764	−0.799334
$931$	−5.70343	−0.186923
$932$	−32.8857	−1.07721
$933$	22.2122	0.727193
$934$	−94.4193	−3.08949
$935$	−28.3301	−0.926492
$936$	−3.15405	−0.103093
$937$	−37.0003	−1.20875	−0.604373	−	0.796701i	$-0.706577\pi$
$937$	−37.0003	−1.20875	−0.604373	+	0.796701i	$0.706577\pi$
$938$	43.7119	1.42724
$939$	9.47180	0.309101
$940$	6.46090	0.210731
$941$	−1.03885	−0.0338656	−0.0169328	−	0.999857i	$-0.505390\pi$
$941$	−1.03885	−0.0338656	−0.0169328	+	0.999857i	$0.505390\pi$
$942$	45.4629	1.48126
$943$	54.6448	1.77948
$944$	23.3663	0.760510
$945$	3.85984	0.125561
$946$	−7.95555	−0.258657
$947$	60.6742	1.97165	0.985823	−	0.167790i	$-0.0536630\pi$
$947$	60.6742	1.97165	0.985823	+	0.167790i	$0.0536630\pi$
$948$	61.1205	1.98510
$949$	1.76287	0.0572251
$950$	1.83056	0.0593913
$951$	17.5826	0.570155
$952$	−137.986	−4.47216
$953$	−0.614849	−0.0199169	−0.00995845	−	0.999950i	$-0.503170\pi$
$953$	−0.614849	−0.0199169	−0.00995845	+	0.999950i	$0.503170\pi$
$954$	27.2378	0.881856
$955$	−7.99940	−0.258854
$956$	53.4620	1.72908
$957$	35.6651	1.15289
$958$	52.9875	1.71195
$959$	−40.0703	−1.29394
$960$	−1.35061	−0.0435907
$961$	61.4634	1.98269
$962$	−8.62344	−0.278031
$963$	3.33206	0.107374
$964$	125.779	4.05106
$965$	−19.8197	−0.638019
$966$	−93.4541	−3.00684
$967$	53.8730	1.73244	0.866220	−	0.499663i	$-0.166543\pi$
$967$	53.8730	1.73244	0.866220	+	0.499663i	$0.166543\pi$
$968$	−78.4947	−2.52292
$969$	−4.19676	−0.134819
$970$	34.4837	1.10720
$971$	11.4047	0.365996	0.182998	−	0.983113i	$-0.441420\pi$
$971$	11.4047	0.365996	0.182998	+	0.983113i	$0.441420\pi$
$972$	4.42643	0.141978
$973$	15.4776	0.496190
$974$	−73.9061	−2.36810
$975$	0.512763	0.0164215
$976$	−1.33165	−0.0426250
$977$	−34.5035	−1.10386	−0.551932	−	0.833889i	$-0.686109\pi$
$977$	−34.5035	−1.10386	−0.551932	+	0.833889i	$0.686109\pi$
$978$	−14.9982	−0.479589
$979$	83.0710	2.65496
$980$	34.9615	1.11680
$981$	7.54471	0.240884
$982$	−28.7788	−0.918370
$983$	−26.5879	−0.848021	−0.424011	−	0.905657i	$-0.639378\pi$
$983$	−26.5879	−0.848021	−0.424011	+	0.905657i	$0.639378\pi$
$984$	−35.1930	−1.12191
$985$	−10.4728	−0.333691
$986$	107.798	3.43298
$987$	5.63390	0.179329
$988$	−1.63897	−0.0521424
$989$	−6.14888	−0.195523
$990$	12.3571	0.392736
$991$	25.2713	0.802770	0.401385	−	0.915909i	$-0.368529\pi$
$991$	25.2713	0.802770	0.401385	+	0.915909i	$0.368529\pi$
$992$	−46.0117	−1.46087
$993$	−18.8824	−0.599214
$994$	69.5043	2.20454
$995$	−8.41969	−0.266922
$996$	−68.8095	−2.18031
$997$	29.3020	0.928002	0.464001	−	0.885835i	$-0.346413\pi$
$997$	29.3020	0.928002	0.464001	+	0.885835i	$0.346413\pi$
$998$	−42.1560	−1.33443
$999$	6.63406	0.209892

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.i.1.4	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.i.1.4	✓	43	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53504 q^{2} +1.00000 q^{3} +4.42643 q^{4} +1.00000 q^{5} -2.53504 q^{6} +3.85984 q^{7} -6.15109 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.53504 q^{2} +1.00000 q^{3} +4.42643 q^{4} +1.00000 q^{5} -2.53504 q^{6} +3.85984 q^{7} -6.15109 q^{8} +1.00000 q^{9} -2.53504 q^{10} -4.87454 q^{11} +4.42643 q^{12} +0.512763 q^{13} -9.78484 q^{14} +1.00000 q^{15} +6.74040 q^{16} +5.81185 q^{17} -2.53504 q^{18} -0.722104 q^{19} +4.42643 q^{20} +3.85984 q^{21} +12.3571 q^{22} +9.55090 q^{23} -6.15109 q^{24} +1.00000 q^{25} -1.29987 q^{26} +1.00000 q^{27} +17.0853 q^{28} -7.31662 q^{29} -2.53504 q^{30} +9.61579 q^{31} -4.78501 q^{32} -4.87454 q^{33} -14.7333 q^{34} +3.85984 q^{35} +4.42643 q^{36} +6.63406 q^{37} +1.83056 q^{38} +0.512763 q^{39} -6.15109 q^{40} +5.72142 q^{41} -9.78484 q^{42} -0.643801 q^{43} -21.5768 q^{44} +1.00000 q^{45} -24.2119 q^{46} +1.45962 q^{47} +6.74040 q^{48} +7.89835 q^{49} -2.53504 q^{50} +5.81185 q^{51} +2.26971 q^{52} -10.7445 q^{53} -2.53504 q^{54} -4.87454 q^{55} -23.7422 q^{56} -0.722104 q^{57} +18.5479 q^{58} +3.46661 q^{59} +4.42643 q^{60} -0.197562 q^{61} -24.3764 q^{62} +3.85984 q^{63} -1.35061 q^{64} +0.512763 q^{65} +12.3571 q^{66} -4.46730 q^{67} +25.7257 q^{68} +9.55090 q^{69} -9.78484 q^{70} -7.10326 q^{71} -6.15109 q^{72} +3.43798 q^{73} -16.8176 q^{74} +1.00000 q^{75} -3.19634 q^{76} -18.8149 q^{77} -1.29987 q^{78} +13.8081 q^{79} +6.74040 q^{80} +1.00000 q^{81} -14.5040 q^{82} -15.5452 q^{83} +17.0853 q^{84} +5.81185 q^{85} +1.63206 q^{86} -7.31662 q^{87} +29.9837 q^{88} -17.0418 q^{89} -2.53504 q^{90} +1.97918 q^{91} +42.2764 q^{92} +9.61579 q^{93} -3.70019 q^{94} -0.722104 q^{95} -4.78501 q^{96} -13.6028 q^{97} -20.0226 q^{98} -4.87454 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9}+O(q^{10}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9} + 3 q^{10} + 19 q^{11} + 61 q^{12} + 8 q^{13} + 6 q^{14} + 43 q^{15} + 85 q^{16} + 40 q^{17} + 3 q^{18} + 43 q^{19} + 61 q^{20} + 14 q^{21} + 19 q^{22} + 12 q^{23} + 18 q^{24} + 43 q^{25} + 43 q^{27} + 36 q^{28} + 41 q^{29} + 3 q^{30} + 33 q^{31} + 4 q^{32} + 19 q^{33} + 20 q^{34} + 14 q^{35} + 61 q^{36} + 12 q^{37} + 10 q^{38} + 8 q^{39} + 18 q^{40} + 47 q^{41} + 6 q^{42} + 73 q^{43} + 5 q^{44} + 43 q^{45} + 21 q^{46} + 32 q^{47} + 85 q^{48} + 87 q^{49} + 3 q^{50} + 40 q^{51} + 18 q^{52} + 17 q^{53} + 3 q^{54} + 19 q^{55} + 15 q^{56} + 43 q^{57} - 16 q^{58} + 21 q^{59} + 61 q^{60} + 77 q^{61} + 15 q^{62} + 14 q^{63} + 112 q^{64} + 8 q^{65} + 19 q^{66} + 26 q^{67} + 50 q^{68} + 12 q^{69} + 6 q^{70} + 2 q^{71} + 18 q^{72} + 49 q^{73} - 34 q^{74} + 43 q^{75} + 50 q^{76} - 2 q^{77} + 59 q^{79} + 85 q^{80} + 43 q^{81} - 45 q^{82} - 3 q^{83} + 36 q^{84} + 40 q^{85} - 35 q^{86} + 41 q^{87} - 13 q^{88} + 57 q^{89} + 3 q^{90} + 11 q^{91} - 9 q^{92} + 33 q^{93} + 52 q^{94} + 43 q^{95} + 4 q^{96} + 7 q^{97} - 32 q^{98} + 19 q^{99}+O(q^{100}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9 + 3 * q^10 + 19 * q^11 + 61 * q^12 + 8 * q^13 + 6 * q^14 + 43 * q^15 + 85 * q^16 + 40 * q^17 + 3 * q^18 + 43 * q^19 + 61 * q^20 + 14 * q^21 + 19 * q^22 + 12 * q^23 + 18 * q^24 + 43 * q^25 + 43 * q^27 + 36 * q^28 + 41 * q^29 + 3 * q^30 + 33 * q^31 + 4 * q^32 + 19 * q^33 + 20 * q^34 + 14 * q^35 + 61 * q^36 + 12 * q^37 + 10 * q^38 + 8 * q^39 + 18 * q^40 + 47 * q^41 + 6 * q^42 + 73 * q^43 + 5 * q^44 + 43 * q^45 + 21 * q^46 + 32 * q^47 + 85 * q^48 + 87 * q^49 + 3 * q^50 + 40 * q^51 + 18 * q^52 + 17 * q^53 + 3 * q^54 + 19 * q^55 + 15 * q^56 + 43 * q^57 - 16 * q^58 + 21 * q^59 + 61 * q^60 + 77 * q^61 + 15 * q^62 + 14 * q^63 + 112 * q^64 + 8 * q^65 + 19 * q^66 + 26 * q^67 + 50 * q^68 + 12 * q^69 + 6 * q^70 + 2 * q^71 + 18 * q^72 + 49 * q^73 - 34 * q^74 + 43 * q^75 + 50 * q^76 - 2 * q^77 + 59 * q^79 + 85 * q^80 + 43 * q^81 - 45 * q^82 - 3 * q^83 + 36 * q^84 + 40 * q^85 - 35 * q^86 + 41 * q^87 - 13 * q^88 + 57 * q^89 + 3 * q^90 + 11 * q^91 - 9 * q^92 + 33 * q^93 + 52 * q^94 + 43 * q^95 + 4 * q^96 + 7 * q^97 - 32 * q^98 + 19 * q^99

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