LMFDB - Embedded newform 6023.2.a.c.1.41

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$0$
Dimension:	$138$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.41
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.32719 q^{2} -0.802041 q^{3} -0.238573 q^{4} +3.89854 q^{5} +1.06446 q^{6} -4.39346 q^{7} +2.97101 q^{8} -2.35673 q^{9} +O(q^{10})$	\(q-1.32719 q^{2} -0.802041 q^{3} -0.238573 q^{4} +3.89854 q^{5} +1.06446 q^{6} -4.39346 q^{7} +2.97101 q^{8} -2.35673 q^{9} -5.17410 q^{10} +5.32033 q^{11} +0.191346 q^{12} +4.24688 q^{13} +5.83094 q^{14} -3.12679 q^{15} -3.46594 q^{16} -7.17200 q^{17} +3.12782 q^{18} +1.00000 q^{19} -0.930089 q^{20} +3.52373 q^{21} -7.06108 q^{22} -4.68819 q^{23} -2.38287 q^{24} +10.1986 q^{25} -5.63640 q^{26} +4.29632 q^{27} +1.04816 q^{28} -5.61052 q^{29} +4.14984 q^{30} +1.71663 q^{31} -1.34207 q^{32} -4.26713 q^{33} +9.51859 q^{34} -17.1281 q^{35} +0.562253 q^{36} +0.788404 q^{37} -1.32719 q^{38} -3.40617 q^{39} +11.5826 q^{40} -1.24847 q^{41} -4.67666 q^{42} +0.000507817 q^{43} -1.26929 q^{44} -9.18781 q^{45} +6.22211 q^{46} +11.6355 q^{47} +2.77982 q^{48} +12.3025 q^{49} -13.5355 q^{50} +5.75224 q^{51} -1.01319 q^{52} +5.29714 q^{53} -5.70202 q^{54} +20.7416 q^{55} -13.0530 q^{56} -0.802041 q^{57} +7.44621 q^{58} -0.231094 q^{59} +0.745970 q^{60} +11.2379 q^{61} -2.27828 q^{62} +10.3542 q^{63} +8.71305 q^{64} +16.5566 q^{65} +5.66328 q^{66} -10.1142 q^{67} +1.71105 q^{68} +3.76012 q^{69} +22.7322 q^{70} -8.22105 q^{71} -7.00186 q^{72} -3.64442 q^{73} -1.04636 q^{74} -8.17973 q^{75} -0.238573 q^{76} -23.3747 q^{77} +4.52063 q^{78} -8.90945 q^{79} -13.5121 q^{80} +3.62436 q^{81} +1.65695 q^{82} +15.2388 q^{83} -0.840669 q^{84} -27.9604 q^{85} -0.000673968 q^{86} +4.49987 q^{87} +15.8067 q^{88} -14.0205 q^{89} +12.1939 q^{90} -18.6585 q^{91} +1.11848 q^{92} -1.37681 q^{93} -15.4425 q^{94} +3.89854 q^{95} +1.07639 q^{96} -6.91821 q^{97} -16.3277 q^{98} -12.5386 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) $ 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * 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 $

$2$	−1.32719	−0.938463	−0.469232	−	0.883075i	$-0.655469\pi$
$2$	−1.32719	−0.938463	−0.469232	+	0.883075i	$0.655469\pi$
$3$	−0.802041	−0.463059	−0.231529	−	0.972828i	$-0.574373\pi$
$3$	−0.802041	−0.463059	−0.231529	+	0.972828i	$0.574373\pi$
$4$	−0.238573	−0.119287
$5$	3.89854	1.74348	0.871741	−	0.489967i	$-0.162991\pi$
$5$	3.89854	1.74348	0.871741	+	0.489967i	$0.162991\pi$
$6$	1.06446	0.434564
$7$	−4.39346	−1.66057	−0.830285	−	0.557339i	$-0.811822\pi$
$7$	−4.39346	−1.66057	−0.830285	+	0.557339i	$0.811822\pi$
$8$	2.97101	1.05041
$9$	−2.35673	−0.785576
$10$	−5.17410	−1.63619
$11$	5.32033	1.60414	0.802071	−	0.597229i	$-0.203732\pi$
$11$	5.32033	1.60414	0.802071	+	0.597229i	$0.203732\pi$
$12$	0.191346	0.0552368
$13$	4.24688	1.17787	0.588936	−	0.808180i	$-0.299547\pi$
$13$	4.24688	1.17787	0.588936	+	0.808180i	$0.299547\pi$
$14$	5.83094	1.55838
$15$	−3.12679	−0.807335
$16$	−3.46594	−0.866484
$17$	−7.17200	−1.73947	−0.869733	−	0.493523i	$-0.835709\pi$
$17$	−7.17200	−1.73947	−0.869733	+	0.493523i	$0.835709\pi$
$18$	3.12782	0.737235
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−0.930089	−0.207974
$21$	3.52373	0.768942
$22$	−7.06108	−1.50543
$23$	−4.68819	−0.977556	−0.488778	−	0.872408i	$-0.662557\pi$
$23$	−4.68819	−0.977556	−0.488778	+	0.872408i	$0.662557\pi$
$24$	−2.38287	−0.486401
$25$	10.1986	2.03973
$26$	−5.63640	−1.10539
$27$	4.29632	0.826827
$28$	1.04816	0.198084
$29$	−5.61052	−1.04185	−0.520923	−	0.853603i	$-0.674412\pi$
$29$	−5.61052	−1.04185	−0.520923	+	0.853603i	$0.674412\pi$
$30$	4.14984	0.757654
$31$	1.71663	0.308315	0.154158	−	0.988046i	$-0.450734\pi$
$31$	1.71663	0.308315	0.154158	+	0.988046i	$0.450734\pi$
$32$	−1.34207	−0.237246
$33$	−4.26713	−0.742812
$34$	9.51859	1.63242
$35$	−17.1281	−2.89517
$36$	0.562253	0.0937088
$37$	0.788404	0.129613	0.0648064	−	0.997898i	$-0.479357\pi$
$37$	0.788404	0.129613	0.0648064	+	0.997898i	$0.479357\pi$
$38$	−1.32719	−0.215298
$39$	−3.40617	−0.545424
$40$	11.5826	1.83137
$41$	−1.24847	−0.194978	−0.0974890	−	0.995237i	$-0.531081\pi$
$41$	−1.24847	−0.194978	−0.0974890	+	0.995237i	$0.531081\pi$
$42$	−4.67666	−0.721624
$43$	0.000507817 0	7.74414e−5 0	3.87207e−5	−	1.00000i	$-0.499988\pi$
$43$	0.000507817 0	7.74414e−5 0	3.87207e−5		1.00000i	$0.499988\pi$
$44$	−1.26929	−0.191353
$45$	−9.18781	−1.36964
$46$	6.22211	0.917400
$47$	11.6355	1.69722	0.848608	−	0.529022i	$-0.177441\pi$
$47$	11.6355	1.69722	0.848608	+	0.529022i	$0.177441\pi$
$48$	2.77982	0.401233
$49$	12.3025	1.75749
$50$	−13.5355	−1.91421
$51$	5.75224	0.805475
$52$	−1.01319	−0.140504
$53$	5.29714	0.727618	0.363809	−	0.931474i	$-0.381476\pi$
$53$	5.29714	0.727618	0.363809	+	0.931474i	$0.381476\pi$
$54$	−5.70202	−0.775947
$55$	20.7416	2.79679
$56$	−13.0530	−1.74428
$57$	−0.802041	−0.106233
$58$	7.44621	0.977735
$59$	−0.231094	−0.0300859	−0.0150429	−	0.999887i	$-0.504788\pi$
$59$	−0.231094	−0.0300859	−0.0150429	+	0.999887i	$0.504788\pi$
$60$	0.745970	0.0963043
$61$	11.2379	1.43886	0.719431	−	0.694564i	$-0.244403\pi$
$61$	11.2379	1.43886	0.719431	+	0.694564i	$0.244403\pi$
$62$	−2.27828	−0.289342
$63$	10.3542	1.30450
$64$	8.71305	1.08913
$65$	16.5566	2.05360
$66$	5.66328	0.697102
$67$	−10.1142	−1.23564	−0.617820	−	0.786320i	$-0.711984\pi$
$67$	−10.1142	−1.23564	−0.617820	+	0.786320i	$0.711984\pi$
$68$	1.71105	0.207495
$69$	3.76012	0.452666
$70$	22.7322	2.71701
$71$	−8.22105	−0.975659	−0.487830	−	0.872939i	$-0.662211\pi$
$71$	−8.22105	−0.975659	−0.487830	+	0.872939i	$0.662211\pi$
$72$	−7.00186	−0.825177
$73$	−3.64442	−0.426547	−0.213273	−	0.976993i	$-0.568412\pi$
$73$	−3.64442	−0.426547	−0.213273	+	0.976993i	$0.568412\pi$
$74$	−1.04636	−0.121637
$75$	−8.17973	−0.944514
$76$	−0.238573	−0.0273662
$77$	−23.3747	−2.66379
$78$	4.52063	0.511860
$79$	−8.90945	−1.00239	−0.501196	−	0.865334i	$-0.667106\pi$
$79$	−8.90945	−1.00239	−0.501196	+	0.865334i	$0.667106\pi$
$80$	−13.5121	−1.51070
$81$	3.62436	0.402707
$82$	1.65695	0.182980
$83$	15.2388	1.67268	0.836340	−	0.548211i	$-0.184691\pi$
$83$	15.2388	1.67268	0.836340	+	0.548211i	$0.184691\pi$
$84$	−0.840669	−0.0917245
$85$	−27.9604	−3.03273
$86$	−0.000673968 0	−7.26759e−5 0
$87$	4.49987	0.482436
$88$	15.8067	1.68500
$89$	−14.0205	−1.48617	−0.743086	−	0.669196i	$-0.766639\pi$
$89$	−14.0205	−1.48617	−0.743086	+	0.669196i	$0.766639\pi$
$90$	12.1939	1.28536
$91$	−18.6585	−1.95594
$92$	1.11848	0.116609
$93$	−1.37681	−0.142768
$94$	−15.4425	−1.59277
$95$	3.89854	0.399982
$96$	1.07639	0.109859
$97$	−6.91821	−0.702438	−0.351219	−	0.936293i	$-0.614233\pi$
$97$	−6.91821	−0.702438	−0.351219	+	0.936293i	$0.614233\pi$
$98$	−16.3277	−1.64934
$99$	−12.5386	−1.26018
$100$	−2.43312	−0.243312
$101$	−2.33734	−0.232574	−0.116287	−	0.993216i	$-0.537099\pi$
$101$	−2.33734	−0.232574	−0.116287	+	0.993216i	$0.537099\pi$
$102$	−7.63430	−0.755909
$103$	4.77803	0.470794	0.235397	−	0.971899i	$-0.424361\pi$
$103$	4.77803	0.470794	0.235397	+	0.971899i	$0.424361\pi$
$104$	12.6175	1.23725
$105$	13.7374	1.34064
$106$	−7.03029	−0.682842
$107$	−3.52733	−0.341000	−0.170500	−	0.985358i	$-0.554538\pi$
$107$	−3.52733	−0.341000	−0.170500	+	0.985358i	$0.554538\pi$
$108$	−1.02499	−0.0986295
$109$	17.0897	1.63689	0.818447	−	0.574581i	$-0.194835\pi$
$109$	17.0897	1.63689	0.818447	+	0.574581i	$0.194835\pi$
$110$	−27.5279	−2.62469
$111$	−0.632333	−0.0600184
$112$	15.2274	1.43886
$113$	20.7795	1.95477	0.977387	−	0.211458i	$-0.0678210\pi$
$113$	20.7795	1.95477	0.977387	+	0.211458i	$0.0678210\pi$
$114$	1.06446	0.0996958
$115$	−18.2771	−1.70435
$116$	1.33852	0.124278
$117$	−10.0087	−0.925308
$118$	0.306705	0.0282345
$119$	31.5099	2.88850
$120$	−9.28972	−0.848032
$121$	17.3060	1.57327
$122$	−14.9148	−1.35032
$123$	1.00132	0.0902863
$124$	−0.409541	−0.0367779
$125$	20.2671	1.81275
$126$	−13.7419	−1.22423
$127$	8.86258	0.786427	0.393213	−	0.919447i	$-0.371363\pi$
$127$	8.86258	0.786427	0.393213	+	0.919447i	$0.371363\pi$
$128$	−8.87971	−0.784863
$129$	−0.000407290 0	−3.58599e−5 0
$130$	−21.9738	−1.92723
$131$	−12.2026	−1.06614	−0.533072	−	0.846070i	$-0.678963\pi$
$131$	−12.2026	−1.06614	−0.533072	+	0.846070i	$0.678963\pi$
$132$	1.01802	0.0886075
$133$	−4.39346	−0.380961
$134$	13.4234	1.15960
$135$	16.7494	1.44156
$136$	−21.3081	−1.82715
$137$	9.95941	0.850890	0.425445	−	0.904984i	$-0.360118\pi$
$137$	9.95941	0.850890	0.425445	+	0.904984i	$0.360118\pi$
$138$	−4.99039	−0.424810
$139$	−19.1409	−1.62351	−0.811753	−	0.584001i	$-0.801487\pi$
$139$	−19.1409	−1.62351	−0.811753	+	0.584001i	$0.801487\pi$
$140$	4.08630	0.345356
$141$	−9.33217	−0.785911
$142$	10.9109	0.915620
$143$	22.5948	1.88947
$144$	8.16827	0.680689
$145$	−21.8728	−1.81644
$146$	4.83682	0.400298
$147$	−9.86708	−0.813823
$148$	−0.188092	−0.0154611
$149$	−5.96671	−0.488812	−0.244406	−	0.969673i	$-0.578593\pi$
$149$	−5.96671	−0.488812	−0.244406	+	0.969673i	$0.578593\pi$
$150$	10.8560	0.886392
$151$	1.15816	0.0942495	0.0471247	−	0.998889i	$-0.484994\pi$
$151$	1.15816	0.0942495	0.0471247	+	0.998889i	$0.484994\pi$
$152$	2.97101	0.240980
$153$	16.9025	1.36648
$154$	31.0225	2.49987
$155$	6.69234	0.537542
$156$	0.812622	0.0650618
$157$	16.9067	1.34930	0.674651	−	0.738137i	$-0.264294\pi$
$157$	16.9067	1.34930	0.674651	+	0.738137i	$0.264294\pi$
$158$	11.8245	0.940708
$159$	−4.24852	−0.336930
$160$	−5.23210	−0.413634
$161$	20.5974	1.62330
$162$	−4.81021	−0.377926
$163$	−5.29761	−0.414941	−0.207470	−	0.978241i	$-0.566523\pi$
$163$	−5.29761	−0.414941	−0.207470	+	0.978241i	$0.566523\pi$
$164$	0.297851	0.0232583
$165$	−16.6356	−1.29508
$166$	−20.2248	−1.56975
$167$	19.6623	1.52151	0.760756	−	0.649038i	$-0.224828\pi$
$167$	19.6623	1.52151	0.760756	+	0.649038i	$0.224828\pi$
$168$	10.4690	0.807704
$169$	5.03596	0.387381
$170$	37.1086	2.84610
$171$	−2.35673	−0.180224
$172$	−0.000121152 0	−9.23772e−6 0
$173$	17.5650	1.33544	0.667720	−	0.744412i	$-0.267270\pi$
$173$	17.5650	1.33544	0.667720	+	0.744412i	$0.267270\pi$
$174$	−5.97217	−0.452749
$175$	−44.8073	−3.38711
$176$	−18.4399	−1.38996
$177$	0.185347	0.0139315
$178$	18.6079	1.39472
$179$	−16.3470	−1.22183	−0.610916	−	0.791695i	$-0.709199\pi$
$179$	−16.3470	−1.22183	−0.610916	+	0.791695i	$0.709199\pi$
$180$	2.19197	0.163380
$181$	0.449083	0.0333801	0.0166900	−	0.999861i	$-0.494687\pi$
$181$	0.449083	0.0333801	0.0166900	+	0.999861i	$0.494687\pi$
$182$	24.7633	1.83558
$183$	−9.01324	−0.666278
$184$	−13.9287	−1.02683
$185$	3.07363	0.225978
$186$	1.82728	0.133983
$187$	−38.1574	−2.79035
$188$	−2.77593	−0.202455
$189$	−18.8757	−1.37300
$190$	−5.17410	−0.375369
$191$	−6.52130	−0.471865	−0.235932	−	0.971769i	$-0.575814\pi$
$191$	−6.52130	−0.471865	−0.235932	+	0.971769i	$0.575814\pi$
$192$	−6.98822	−0.504332
$193$	4.82387	0.347230	0.173615	−	0.984814i	$-0.444455\pi$
$193$	4.82387	0.347230	0.173615	+	0.984814i	$0.444455\pi$
$194$	9.18176	0.659212
$195$	−13.2791	−0.950936
$196$	−2.93504	−0.209646
$197$	−15.9656	−1.13750	−0.568751	−	0.822510i	$-0.692573\pi$
$197$	−15.9656	−1.13750	−0.568751	+	0.822510i	$0.692573\pi$
$198$	16.6411	1.18263
$199$	19.2685	1.36591	0.682954	−	0.730461i	$-0.260695\pi$
$199$	19.2685	1.36591	0.682954	+	0.730461i	$0.260695\pi$
$200$	30.3002	2.14255
$201$	8.11197	0.572174
$202$	3.10208	0.218262
$203$	24.6496	1.73006
$204$	−1.37233	−0.0960824
$205$	−4.86721	−0.339941
$206$	−6.34135	−0.441823
$207$	11.0488	0.767945
$208$	−14.7194	−1.02061
$209$	5.32033	0.368015
$210$	−18.2321	−1.25814
$211$	−19.1649	−1.31936	−0.659682	−	0.751545i	$-0.729309\pi$
$211$	−19.1649	−1.31936	−0.659682	+	0.751545i	$0.729309\pi$
$212$	−1.26376	−0.0867951
$213$	6.59362	0.451788
$214$	4.68143	0.320016
$215$	0.00197975	0.000135018 0
$216$	12.7644	0.868507
$217$	−7.54192	−0.511979
$218$	−22.6812	−1.53617
$219$	2.92297	0.197516
$220$	−4.94838	−0.333620
$221$	−30.4586	−2.04887
$222$	0.839224	0.0563250
$223$	7.95334	0.532595	0.266298	−	0.963891i	$-0.414200\pi$
$223$	7.95334	0.532595	0.266298	+	0.963891i	$0.414200\pi$
$224$	5.89631	0.393964
$225$	−24.0354	−1.60236
$226$	−27.5783	−1.83448
$227$	9.48689	0.629667	0.314834	−	0.949147i	$-0.398051\pi$
$227$	9.48689	0.629667	0.314834	+	0.949147i	$0.398051\pi$
$228$	0.191346	0.0126722
$229$	−5.30004	−0.350236	−0.175118	−	0.984547i	$-0.556031\pi$
$229$	−5.30004	−0.350236	−0.175118	+	0.984547i	$0.556031\pi$
$230$	24.2572	1.59947
$231$	18.7474	1.23349
$232$	−16.6689	−1.09437
$233$	−29.4681	−1.93052	−0.965260	−	0.261290i	$-0.915852\pi$
$233$	−29.4681	−1.93052	−0.965260	+	0.261290i	$0.915852\pi$
$234$	13.2835	0.868368
$235$	45.3616	2.95906
$236$	0.0551328	0.00358884
$237$	7.14575	0.464166
$238$	−41.8195	−2.71076
$239$	2.64046	0.170797	0.0853987	−	0.996347i	$-0.472784\pi$
$239$	2.64046	0.170797	0.0853987	+	0.996347i	$0.472784\pi$
$240$	10.8373	0.699543
$241$	2.35883	0.151945	0.0759727	−	0.997110i	$-0.475794\pi$
$241$	2.35883	0.151945	0.0759727	+	0.997110i	$0.475794\pi$
$242$	−22.9682	−1.47645
$243$	−15.7958	−1.01330
$244$	−2.68106	−0.171637
$245$	47.9616	3.06416
$246$	−1.32894	−0.0847304
$247$	4.24688	0.270222
$248$	5.10011	0.323857
$249$	−12.2222	−0.774550
$250$	−26.8983	−1.70120
$251$	17.6676	1.11517	0.557584	−	0.830121i	$-0.311729\pi$
$251$	17.6676	1.11517	0.557584	+	0.830121i	$0.311729\pi$
$252$	−2.47023	−0.155610
$253$	−24.9427	−1.56814
$254$	−11.7623	−0.738032
$255$	22.4254	1.40433
$256$	−5.64105	−0.352565
$257$	13.6464	0.851241	0.425620	−	0.904902i	$-0.360056\pi$
$257$	13.6464	0.851241	0.425620	+	0.904902i	$0.360056\pi$
$258$	0.000540551 0	3.36532e−5 0
$259$	−3.46382	−0.215231
$260$	−3.94997	−0.244967
$261$	13.2225	0.818450
$262$	16.1951	1.00054
$263$	−11.3386	−0.699165	−0.349583	−	0.936906i	$-0.613677\pi$
$263$	−11.3386	−0.699165	−0.349583	+	0.936906i	$0.613677\pi$
$264$	−12.6777	−0.780256
$265$	20.6511	1.26859
$266$	5.83094	0.357518
$267$	11.2450	0.688185
$268$	2.41297	0.147395
$269$	26.1804	1.59625	0.798124	−	0.602494i	$-0.205826\pi$
$269$	26.1804	1.59625	0.798124	+	0.602494i	$0.205826\pi$
$270$	−22.2296	−1.35285
$271$	−20.1524	−1.22417	−0.612087	−	0.790791i	$-0.709670\pi$
$271$	−20.1524	−1.22417	−0.612087	+	0.790791i	$0.709670\pi$
$272$	24.8577	1.50722
$273$	14.9649	0.905715
$274$	−13.2180	−0.798529
$275$	54.2602	3.27201
$276$	−0.897066	−0.0539970
$277$	24.2465	1.45683	0.728417	−	0.685134i	$-0.240257\pi$
$277$	24.2465	1.45683	0.728417	+	0.685134i	$0.240257\pi$
$278$	25.4035	1.52360
$279$	−4.04562	−0.242205
$280$	−50.8876	−3.04112
$281$	−4.87589	−0.290871	−0.145436	−	0.989368i	$-0.546458\pi$
$281$	−4.87589	−0.290871	−0.145436	+	0.989368i	$0.546458\pi$
$282$	12.3855	0.737548
$283$	−0.331863	−0.0197272	−0.00986360	−	0.999951i	$-0.503140\pi$
$283$	−0.331863	−0.0197272	−0.00986360	+	0.999951i	$0.503140\pi$
$284$	1.96132	0.116383
$285$	−3.12679	−0.185215
$286$	−29.9875	−1.77320
$287$	5.48509	0.323775
$288$	3.16289	0.186375
$289$	34.4376	2.02574
$290$	29.0294	1.70466
$291$	5.54869	0.325270
$292$	0.869461	0.0508813
$293$	−3.88261	−0.226825	−0.113412	−	0.993548i	$-0.536178\pi$
$293$	−3.88261	−0.226825	−0.113412	+	0.993548i	$0.536178\pi$
$294$	13.0955	0.763743
$295$	−0.900929	−0.0524541
$296$	2.34235	0.136147
$297$	22.8579	1.32635
$298$	7.91894	0.458732
$299$	−19.9102	−1.15144
$300$	1.95147	0.112668
$301$	−0.00223107	−0.000128597 0
$302$	−1.53709	−0.0884497
$303$	1.87464	0.107695
$304$	−3.46594	−0.198785
$305$	43.8113	2.50863
$306$	−22.4327	−1.28239
$307$	−3.37742	−0.192759	−0.0963797	−	0.995345i	$-0.530726\pi$
$307$	−3.37742	−0.192759	−0.0963797	+	0.995345i	$0.530726\pi$
$308$	5.57657	0.317755
$309$	−3.83218	−0.218005
$310$	−8.88199	−0.504463
$311$	−9.27764	−0.526087	−0.263043	−	0.964784i	$-0.584726\pi$
$311$	−9.27764	−0.526087	−0.263043	+	0.964784i	$0.584726\pi$
$312$	−10.1198	−0.572918
$313$	26.1192	1.47635	0.738173	−	0.674612i	$-0.235689\pi$
$313$	26.1192	1.47635	0.738173	+	0.674612i	$0.235689\pi$
$314$	−22.4384	−1.26627
$315$	40.3662	2.27438
$316$	2.12556	0.119572
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	5.63859	0.316196
$319$	−29.8498	−1.67127
$320$	33.9682	1.89888
$321$	2.82907	0.157903
$322$	−27.3366	−1.52341
$323$	−7.17200	−0.399061
$324$	−0.864676	−0.0480376
$325$	43.3124	2.40254
$326$	7.03092	0.389406
$327$	−13.7066	−0.757979
$328$	−3.70921	−0.204807
$329$	−51.1202	−2.81835
$330$	22.0785	1.21538
$331$	−22.6181	−1.24320	−0.621600	−	0.783335i	$-0.713517\pi$
$331$	−22.6181	−1.24320	−0.621600	+	0.783335i	$0.713517\pi$
$332$	−3.63558	−0.199529
$333$	−1.85806	−0.101821
$334$	−26.0955	−1.42788
$335$	−39.4305	−2.15432
$336$	−12.2130	−0.666276
$337$	2.43276	0.132521	0.0662605	−	0.997802i	$-0.478893\pi$
$337$	2.43276	0.132521	0.0662605	+	0.997802i	$0.478893\pi$
$338$	−6.68366	−0.363543
$339$	−16.6661	−0.905176
$340$	6.67060	0.361764
$341$	9.13302	0.494581
$342$	3.12782	0.169133
$343$	−23.2961	−1.25787
$344$	0.00150873	8.13452e−5 0
$345$	14.6590	0.789215
$346$	−23.3120	−1.25326
$347$	−7.50757	−0.403028	−0.201514	−	0.979486i	$-0.564586\pi$
$347$	−7.50757	−0.403028	−0.201514	+	0.979486i	$0.564586\pi$
$348$	−1.07355	−0.0575482
$349$	5.60161	0.299847	0.149924	−	0.988698i	$-0.452097\pi$
$349$	5.60161	0.299847	0.149924	+	0.988698i	$0.452097\pi$
$350$	59.4677	3.17868
$351$	18.2459	0.973896
$352$	−7.14024	−0.380576
$353$	13.4722	0.717053	0.358527	−	0.933519i	$-0.383279\pi$
$353$	13.4722	0.717053	0.358527	+	0.933519i	$0.383279\pi$
$354$	−0.245990	−0.0130742
$355$	−32.0501	−1.70104
$356$	3.34492	0.177281
$357$	−25.2722	−1.33755
$358$	21.6955	1.14664
$359$	3.35270	0.176949	0.0884745	−	0.996078i	$-0.471801\pi$
$359$	3.35270	0.176949	0.0884745	+	0.996078i	$0.471801\pi$
$360$	−27.2971	−1.43868
$361$	1.00000	0.0526316
$362$	−0.596017	−0.0313260
$363$	−13.8801	−0.728516
$364$	4.45141	0.233317
$365$	−14.2079	−0.743676
$366$	11.9623	0.625277
$367$	4.17729	0.218053	0.109026	−	0.994039i	$-0.465227\pi$
$367$	4.17729	0.218053	0.109026	+	0.994039i	$0.465227\pi$
$368$	16.2490	0.847036
$369$	2.94230	0.153170
$370$	−4.07928	−0.212072
$371$	−23.2727	−1.20826
$372$	0.328469	0.0170303
$373$	19.3061	0.999631	0.499815	−	0.866132i	$-0.333401\pi$
$373$	19.3061	0.999631	0.499815	+	0.866132i	$0.333401\pi$
$374$	50.6421	2.61864
$375$	−16.2551	−0.839409
$376$	34.5692	1.78277
$377$	−23.8272	−1.22716
$378$	25.0516	1.28851
$379$	1.51605	0.0778745	0.0389372	−	0.999242i	$-0.487603\pi$
$379$	1.51605	0.0778745	0.0389372	+	0.999242i	$0.487603\pi$
$380$	−0.930089	−0.0477125
$381$	−7.10815	−0.364162
$382$	8.65499	0.442828
$383$	−33.4690	−1.71018	−0.855092	−	0.518476i	$-0.826499\pi$
$383$	−33.4690	−1.71018	−0.855092	+	0.518476i	$0.826499\pi$
$384$	7.12190	0.363438
$385$	−91.1271	−4.64427
$386$	−6.40218	−0.325862
$387$	−0.00119679	−6.08361e−5 0
$388$	1.65050	0.0837915
$389$	37.8959	1.92140	0.960700	−	0.277589i	$-0.0895353\pi$
$389$	37.8959	1.92140	0.960700	+	0.277589i	$0.0895353\pi$
$390$	17.6239	0.892419
$391$	33.6237	1.70042
$392$	36.5507	1.84609
$393$	9.78697	0.493688
$394$	21.1893	1.06750
$395$	−34.7339	−1.74765
$396$	2.99137	0.150322
$397$	25.3230	1.27092	0.635462	−	0.772132i	$-0.280810\pi$
$397$	25.3230	1.27092	0.635462	+	0.772132i	$0.280810\pi$
$398$	−25.5729	−1.28186
$399$	3.52373	0.176407
$400$	−35.3478	−1.76739
$401$	18.5192	0.924803	0.462401	−	0.886671i	$-0.346988\pi$
$401$	18.5192	0.924803	0.462401	+	0.886671i	$0.346988\pi$
$402$	−10.7661	−0.536964
$403$	7.29030	0.363156
$404$	0.557626	0.0277429
$405$	14.1297	0.702112
$406$	−32.7146	−1.62360
$407$	4.19457	0.207917
$408$	17.0899	0.846078
$409$	18.4712	0.913341	0.456671	−	0.889636i	$-0.349042\pi$
$409$	18.4712	0.913341	0.456671	+	0.889636i	$0.349042\pi$
$410$	6.45970	0.319022
$411$	−7.98786	−0.394012
$412$	−1.13991	−0.0561594
$413$	1.01530	0.0499597
$414$	−14.6638	−0.720688
$415$	59.4093	2.91629
$416$	−5.69959	−0.279445
$417$	15.3518	0.751779
$418$	−7.06108	−0.345369
$419$	5.89618	0.288047	0.144024	−	0.989574i	$-0.453996\pi$
$419$	5.89618	0.288047	0.144024	+	0.989574i	$0.453996\pi$
$420$	−3.27738	−0.159920
$421$	−14.0733	−0.685889	−0.342944	−	0.939356i	$-0.611424\pi$
$421$	−14.0733	−0.685889	−0.342944	+	0.939356i	$0.611424\pi$
$422$	25.4354	1.23817
$423$	−27.4218	−1.33329
$424$	15.7378	0.764297
$425$	−73.1447	−3.54804
$426$	−8.75098	−0.423986
$427$	−49.3731	−2.38933
$428$	0.841528	0.0406768
$429$	−18.1220	−0.874937
$430$	−0.00262750	−0.000126709 0
$431$	31.5286	1.51868	0.759340	−	0.650694i	$-0.225522\pi$
$431$	31.5286	1.51868	0.759340	+	0.650694i	$0.225522\pi$
$432$	−14.8908	−0.716432
$433$	32.7394	1.57336	0.786678	−	0.617363i	$-0.211799\pi$
$433$	32.7394	1.57336	0.786678	+	0.617363i	$0.211799\pi$
$434$	10.0095	0.480473
$435$	17.5429	0.841119
$436$	−4.07714	−0.195260
$437$	−4.68819	−0.224267
$438$	−3.87933	−0.185362
$439$	20.5599	0.981270	0.490635	−	0.871365i	$-0.336765\pi$
$439$	20.5599	0.981270	0.490635	+	0.871365i	$0.336765\pi$
$440$	61.6233	2.93778
$441$	−28.9936	−1.38065
$442$	40.4243	1.92279
$443$	37.9544	1.80327	0.901633	−	0.432502i	$-0.142369\pi$
$443$	37.9544	1.80327	0.901633	+	0.432502i	$0.142369\pi$
$444$	0.150858	0.00715939
$445$	−54.6596	−2.59111
$446$	−10.5556	−0.499821
$447$	4.78555	0.226349
$448$	−38.2804	−1.80858
$449$	−6.43261	−0.303574	−0.151787	−	0.988413i	$-0.548503\pi$
$449$	−6.43261	−0.303574	−0.151787	+	0.988413i	$0.548503\pi$
$450$	31.8995	1.50376
$451$	−6.64227	−0.312772
$452$	−4.95744	−0.233179
$453$	−0.928890	−0.0436431
$454$	−12.5909	−0.590920
$455$	−72.7408	−3.41014
$456$	−2.38287	−0.111588
$457$	0.151329	0.00707890	0.00353945	−	0.999994i	$-0.498873\pi$
$457$	0.151329	0.00707890	0.00353945	+	0.999994i	$0.498873\pi$
$458$	7.03414	0.328684
$459$	−30.8132	−1.43824
$460$	4.36043	0.203306
$461$	23.4415	1.09178	0.545890	−	0.837857i	$-0.316192\pi$
$461$	23.4415	1.09178	0.545890	+	0.837857i	$0.316192\pi$
$462$	−24.8814	−1.15759
$463$	15.0811	0.700879	0.350440	−	0.936585i	$-0.386032\pi$
$463$	15.0811	0.700879	0.350440	+	0.936585i	$0.386032\pi$
$464$	19.4457	0.902743
$465$	−5.36753	−0.248913
$466$	39.1097	1.81172
$467$	3.22571	0.149268	0.0746341	−	0.997211i	$-0.476221\pi$
$467$	3.22571	0.149268	0.0746341	+	0.997211i	$0.476221\pi$
$468$	2.38782	0.110377
$469$	44.4361	2.05187
$470$	−60.2033	−2.77697
$471$	−13.5599	−0.624806
$472$	−0.686581	−0.0316025
$473$	0.00270176	0.000124227 0
$474$	−9.48375	−0.435603
$475$	10.1986	0.467946
$476$	−7.51741	−0.344560
$477$	−12.4839	−0.571599
$478$	−3.50439	−0.160287
$479$	−5.98491	−0.273458	−0.136729	−	0.990609i	$-0.543659\pi$
$479$	−5.98491	−0.273458	−0.136729	+	0.990609i	$0.543659\pi$
$480$	4.19636	0.191537
$481$	3.34825	0.152667
$482$	−3.13061	−0.142595
$483$	−16.5199	−0.751683
$484$	−4.12874	−0.187670
$485$	−26.9709	−1.22469
$486$	20.9640	0.950949
$487$	−22.3686	−1.01362	−0.506808	−	0.862059i	$-0.669175\pi$
$487$	−22.3686	−1.01362	−0.506808	+	0.862059i	$0.669175\pi$
$488$	33.3878	1.51139
$489$	4.24890	0.192142
$490$	−63.6541	−2.87560
$491$	26.6323	1.20190	0.600950	−	0.799287i	$-0.294789\pi$
$491$	26.6323	1.20190	0.600950	+	0.799287i	$0.294789\pi$
$492$	−0.238889	−0.0107700
$493$	40.2386	1.81226
$494$	−5.63640	−0.253594
$495$	−48.8822	−2.19709
$496$	−5.94971	−0.267150
$497$	36.1188	1.62015
$498$	16.2211	0.726886
$499$	−21.7102	−0.971884	−0.485942	−	0.873991i	$-0.661523\pi$
$499$	−21.7102	−0.971884	−0.485942	+	0.873991i	$0.661523\pi$
$500$	−4.83520	−0.216237
$501$	−15.7700	−0.704550
$502$	−23.4482	−1.04654
$503$	−2.48890	−0.110974	−0.0554872	−	0.998459i	$-0.517671\pi$
$503$	−2.48890	−0.110974	−0.0554872	+	0.998459i	$0.517671\pi$
$504$	30.7624	1.37026
$505$	−9.11221	−0.405488
$506$	33.1037	1.47164
$507$	−4.03905	−0.179380
$508$	−2.11437	−0.0938102
$509$	22.1252	0.980681	0.490341	−	0.871531i	$-0.336872\pi$
$509$	22.1252	0.980681	0.490341	+	0.871531i	$0.336872\pi$
$510$	−29.7627	−1.31791
$511$	16.0116	0.708311
$512$	25.2462	1.11573
$513$	4.29632	0.189687
$514$	−18.1114	−0.798858
$515$	18.6274	0.820820
$516$	9.71686e−5 0	4.27761e−6 0
$517$	61.9049	2.72257
$518$	4.59714	0.201987
$519$	−14.0878	−0.618388
$520$	49.1899	2.15712
$521$	32.2474	1.41278	0.706391	−	0.707822i	$-0.250322\pi$
$521$	32.2474	1.41278	0.706391	+	0.707822i	$0.250322\pi$
$522$	−17.5487	−0.768085
$523$	18.2905	0.799789	0.399895	−	0.916561i	$-0.369047\pi$
$523$	18.2905	0.799789	0.399895	+	0.916561i	$0.369047\pi$
$524$	2.91121	0.127177
$525$	35.9373	1.56843
$526$	15.0484	0.656141
$527$	−12.3116	−0.536303
$528$	14.7896	0.643634
$529$	−1.02085	−0.0443848
$530$	−27.4079	−1.19052
$531$	0.544626	0.0236347
$532$	1.04816	0.0454436
$533$	−5.30209	−0.229659
$534$	−14.9243	−0.645837
$535$	−13.7515	−0.594528
$536$	−30.0492	−1.29793
$537$	13.1110	0.565780
$538$	−34.7463	−1.49802
$539$	65.4532	2.81927
$540$	−3.99596	−0.171959
$541$	−11.1780	−0.480581	−0.240291	−	0.970701i	$-0.577243\pi$
$541$	−11.1780	−0.480581	−0.240291	+	0.970701i	$0.577243\pi$
$542$	26.7461	1.14884
$543$	−0.360183	−0.0154569
$544$	9.62530	0.412681
$545$	66.6249	2.85390
$546$	−19.8612	−0.849980
$547$	35.6659	1.52496	0.762482	−	0.647010i	$-0.223981\pi$
$547$	35.6659	1.52496	0.762482	+	0.647010i	$0.223981\pi$
$548$	−2.37605	−0.101500
$549$	−26.4846	−1.13034
$550$	−72.0134	−3.07066
$551$	−5.61052	−0.239016
$552$	11.1714	0.475484
$553$	39.1433	1.66454
$554$	−32.1797	−1.36718
$555$	−2.46518	−0.104641
$556$	4.56650	0.193663
$557$	−12.4759	−0.528621	−0.264311	−	0.964438i	$-0.585144\pi$
$557$	−12.4759	−0.528621	−0.264311	+	0.964438i	$0.585144\pi$
$558$	5.36930	0.227301
$559$	0.00215664	9.12160e−5 0
$560$	59.3648	2.50862
$561$	30.6038	1.29210
$562$	6.47122	0.272972
$563$	36.0271	1.51836	0.759181	−	0.650879i	$-0.225600\pi$
$563$	36.0271	1.51836	0.759181	+	0.650879i	$0.225600\pi$
$564$	2.22641	0.0937487
$565$	81.0099	3.40811
$566$	0.440444	0.0185133
$567$	−15.9235	−0.668723
$568$	−24.4248	−1.02484
$569$	−23.9225	−1.00288	−0.501442	−	0.865191i	$-0.667197\pi$
$569$	−23.9225	−1.00288	−0.501442	+	0.865191i	$0.667197\pi$
$570$	4.14984	0.173818
$571$	−6.43553	−0.269319	−0.134659	−	0.990892i	$-0.542994\pi$
$571$	−6.43553	−0.269319	−0.134659	+	0.990892i	$0.542994\pi$
$572$	−5.39052	−0.225389
$573$	5.23035	0.218501
$574$	−7.27975	−0.303851
$575$	−47.8132	−1.99395
$576$	−20.5343	−0.855595
$577$	−23.4951	−0.978114	−0.489057	−	0.872252i	$-0.662659\pi$
$577$	−23.4951	−0.978114	−0.489057	+	0.872252i	$0.662659\pi$
$578$	−45.7051	−1.90108
$579$	−3.86894	−0.160788
$580$	5.21828	0.216677
$581$	−66.9512	−2.77760
$582$	−7.36415	−0.305254
$583$	28.1825	1.16720
$584$	−10.8276	−0.448049
$585$	−39.0195	−1.61326
$586$	5.15296	0.212867
$587$	−15.9261	−0.657339	−0.328670	−	0.944445i	$-0.606600\pi$
$587$	−15.9261	−0.657339	−0.328670	+	0.944445i	$0.606600\pi$
$588$	2.35402	0.0970782
$589$	1.71663	0.0707323
$590$	1.19570	0.0492263
$591$	12.8051	0.526730
$592$	−2.73256	−0.112307
$593$	7.52200	0.308891	0.154446	−	0.988001i	$-0.450641\pi$
$593$	7.52200	0.308891	0.154446	+	0.988001i	$0.450641\pi$
$594$	−30.3367	−1.24473
$595$	122.843	5.03605
$596$	1.42350	0.0583088
$597$	−15.4541	−0.632496
$598$	26.4245	1.08058
$599$	24.2875	0.992361	0.496180	−	0.868220i	$-0.334735\pi$
$599$	24.2875	0.992361	0.496180	+	0.868220i	$0.334735\pi$
$600$	−24.3020	−0.992127
$601$	−24.4655	−0.997969	−0.498984	−	0.866611i	$-0.666293\pi$
$601$	−24.4655	−0.997969	−0.498984	+	0.866611i	$0.666293\pi$
$602$	0.00296105	0.000120683 0
$603$	23.8363	0.970690
$604$	−0.276305	−0.0112427
$605$	67.4680	2.74296
$606$	−2.48800	−0.101068
$607$	21.8321	0.886139	0.443070	−	0.896487i	$-0.353889\pi$
$607$	21.8321	0.886139	0.443070	+	0.896487i	$0.353889\pi$
$608$	−1.34207	−0.0544280
$609$	−19.7700	−0.801119
$610$	−58.1459	−2.35426
$611$	49.4146	1.99910
$612$	−4.03248	−0.163003
$613$	27.7819	1.12210	0.561051	−	0.827781i	$-0.310397\pi$
$613$	27.7819	1.12210	0.561051	+	0.827781i	$0.310397\pi$
$614$	4.48247	0.180898
$615$	3.90370	0.157413
$616$	−69.4462	−2.79807
$617$	−8.31150	−0.334608	−0.167304	−	0.985905i	$-0.553506\pi$
$617$	−8.31150	−0.334608	−0.167304	+	0.985905i	$0.553506\pi$
$618$	5.08602	0.204590
$619$	−17.3719	−0.698237	−0.349119	−	0.937079i	$-0.613519\pi$
$619$	−17.3719	−0.698237	−0.349119	+	0.937079i	$0.613519\pi$
$620$	−1.59661	−0.0641216
$621$	−20.1420	−0.808269
$622$	12.3132	0.493713
$623$	61.5986	2.46789
$624$	11.8056	0.472601
$625$	28.0191	1.12076
$626$	−34.6651	−1.38550
$627$	−4.26713	−0.170413
$628$	−4.03349	−0.160954
$629$	−5.65443	−0.225457
$630$	−53.5736	−2.13442
$631$	3.88167	0.154527	0.0772634	−	0.997011i	$-0.475382\pi$
$631$	3.88167	0.154527	0.0772634	+	0.997011i	$0.475382\pi$
$632$	−26.4700	−1.05292
$633$	15.3710	0.610943
$634$	1.32719	0.0527093
$635$	34.5511	1.37112
$636$	1.01358	0.0401912
$637$	52.2470	2.07010
$638$	39.6163	1.56842
$639$	19.3748	0.766455
$640$	−34.6179	−1.36839
$641$	4.51592	0.178368	0.0891840	−	0.996015i	$-0.471574\pi$
$641$	4.51592	0.178368	0.0891840	+	0.996015i	$0.471574\pi$
$642$	−3.75470	−0.148186
$643$	3.60818	0.142293	0.0711464	−	0.997466i	$-0.477334\pi$
$643$	3.60818	0.142293	0.0711464	+	0.997466i	$0.477334\pi$
$644$	−4.91398	−0.193638
$645$	−0.00158784	−6.25211e−5 0
$646$	9.51859	0.374504
$647$	−37.4835	−1.47363	−0.736814	−	0.676096i	$-0.763670\pi$
$647$	−37.4835	−1.47363	−0.736814	+	0.676096i	$0.763670\pi$
$648$	10.7680	0.423007
$649$	−1.22950	−0.0482620
$650$	−57.4836	−2.25469
$651$	6.04893	0.237076
$652$	1.26387	0.0494969
$653$	2.41413	0.0944722	0.0472361	−	0.998884i	$-0.484959\pi$
$653$	2.41413	0.0944722	0.0472361	+	0.998884i	$0.484959\pi$
$654$	18.1913	0.711335
$655$	−47.5723	−1.85880
$656$	4.32711	0.168945
$657$	8.58890	0.335085
$658$	67.8460	2.64491
$659$	32.2494	1.25626	0.628130	−	0.778109i	$-0.283821\pi$
$659$	32.2494	1.25626	0.628130	+	0.778109i	$0.283821\pi$
$660$	3.96881	0.154486
$661$	42.8552	1.66687	0.833437	−	0.552614i	$-0.186370\pi$
$661$	42.8552	1.66687	0.833437	+	0.552614i	$0.186370\pi$
$662$	30.0184	1.16670
$663$	24.4291	0.948746
$664$	45.2747	1.75700
$665$	−17.1281	−0.664198
$666$	2.46599	0.0955551
$667$	26.3032	1.01846
$668$	−4.69089	−0.181496
$669$	−6.37891	−0.246623
$670$	52.3316	2.02175
$671$	59.7892	2.30814
$672$	−4.72908	−0.182428
$673$	2.27404	0.0876576	0.0438288	−	0.999039i	$-0.486044\pi$
$673$	2.27404	0.0876576	0.0438288	+	0.999039i	$0.486044\pi$
$674$	−3.22873	−0.124366
$675$	43.8166	1.68650
$676$	−1.20145	−0.0462094
$677$	35.3010	1.35673	0.678363	−	0.734726i	$-0.262689\pi$
$677$	35.3010	1.35673	0.678363	+	0.734726i	$0.262689\pi$
$678$	22.1190	0.849474
$679$	30.3949	1.16645
$680$	−83.0704	−3.18560
$681$	−7.60888	−0.291573
$682$	−12.1212	−0.464146
$683$	−23.3075	−0.891836	−0.445918	−	0.895074i	$-0.647123\pi$
$683$	−23.3075	−0.891836	−0.445918	+	0.895074i	$0.647123\pi$
$684$	0.562253	0.0214983
$685$	38.8272	1.48351
$686$	30.9183	1.18047
$687$	4.25085	0.162180
$688$	−0.00176006	−6.71017e−5 0
$689$	22.4963	0.857040
$690$	−19.4553	−0.740649
$691$	20.3373	0.773668	0.386834	−	0.922149i	$-0.373569\pi$
$691$	20.3373	0.773668	0.386834	+	0.922149i	$0.373569\pi$
$692$	−4.19054	−0.159300
$693$	55.0877	2.09261
$694$	9.96396	0.378227
$695$	−74.6215	−2.83055
$696$	13.3691	0.506756
$697$	8.95402	0.339158
$698$	−7.43438	−0.281396
$699$	23.6347	0.893945
$700$	10.6898	0.404037
$701$	−1.39377	−0.0526421	−0.0263211	−	0.999654i	$-0.508379\pi$
$701$	−1.39377	−0.0526421	−0.0263211	+	0.999654i	$0.508379\pi$
$702$	−24.2158	−0.913966
$703$	0.788404	0.0297352
$704$	46.3563	1.74712
$705$	−36.3819	−1.37022
$706$	−17.8801	−0.672928
$707$	10.2690	0.386205
$708$	−0.0442188	−0.00166184
$709$	−23.7670	−0.892587	−0.446293	−	0.894887i	$-0.647256\pi$
$709$	−23.7670	−0.892587	−0.446293	+	0.894887i	$0.647256\pi$
$710$	42.5365	1.59637
$711$	20.9972	0.787455
$712$	−41.6551	−1.56109
$713$	−8.04787	−0.301395
$714$	33.5410	1.25524
$715$	88.0868	3.29426
$716$	3.89996	0.145748
$717$	−2.11776	−0.0790893
$718$	−4.44967	−0.166060
$719$	41.2463	1.53823	0.769115	−	0.639111i	$-0.220698\pi$
$719$	41.2463	1.53823	0.769115	+	0.639111i	$0.220698\pi$
$720$	31.8444	1.18677
$721$	−20.9921	−0.781786
$722$	−1.32719	−0.0493928
$723$	−1.89188	−0.0703597
$724$	−0.107139	−0.00398180
$725$	−57.2196	−2.12508
$726$	18.4215	0.683685
$727$	37.4203	1.38784	0.693922	−	0.720051i	$-0.255881\pi$
$727$	37.4203	1.38784	0.693922	+	0.720051i	$0.255881\pi$
$728$	−55.4344	−2.05454
$729$	1.79584	0.0665125
$730$	18.8566	0.697913
$731$	−0.00364206	−0.000134707 0
$732$	2.15032	0.0794781
$733$	−6.39055	−0.236040	−0.118020	−	0.993011i	$-0.537655\pi$
$733$	−6.39055	−0.236040	−0.118020	+	0.993011i	$0.537655\pi$
$734$	−5.54405	−0.204635
$735$	−38.4672	−1.41889
$736$	6.29186	0.231921
$737$	−53.8107	−1.98214
$738$	−3.90499	−0.143745
$739$	38.7264	1.42457	0.712287	−	0.701889i	$-0.247660\pi$
$739$	38.7264	1.42457	0.712287	+	0.701889i	$0.247660\pi$
$740$	−0.733286	−0.0269561
$741$	−3.40617	−0.125129
$742$	30.8873	1.13391
$743$	29.1115	1.06800	0.533998	−	0.845486i	$-0.320689\pi$
$743$	29.1115	1.06800	0.533998	+	0.845486i	$0.320689\pi$
$744$	−4.09050	−0.149965
$745$	−23.2615	−0.852235
$746$	−25.6228	−0.938117
$747$	−35.9138	−1.31402
$748$	9.10335	0.332851
$749$	15.4972	0.566255
$750$	21.5735	0.787754
$751$	−10.7817	−0.393431	−0.196716	−	0.980461i	$-0.563028\pi$
$751$	−10.7817	−0.393431	−0.196716	+	0.980461i	$0.563028\pi$
$752$	−40.3280	−1.47061
$753$	−14.1701	−0.516388
$754$	31.6231	1.15165
$755$	4.51513	0.164322
$756$	4.50324	0.163781
$757$	6.39361	0.232380	0.116190	−	0.993227i	$-0.462932\pi$
$757$	6.39361	0.232380	0.116190	+	0.993227i	$0.462932\pi$
$758$	−2.01209	−0.0730823
$759$	20.0051	0.726140
$760$	11.5826	0.420145
$761$	−34.0651	−1.23486	−0.617430	−	0.786626i	$-0.711826\pi$
$761$	−34.0651	−1.23486	−0.617430	+	0.786626i	$0.711826\pi$
$762$	9.43385	0.341752
$763$	−75.0828	−2.71818
$764$	1.55581	0.0562872
$765$	65.8950	2.38244
$766$	44.4196	1.60494
$767$	−0.981427	−0.0354373
$768$	4.52435	0.163259
$769$	1.98811	0.0716931	0.0358466	−	0.999357i	$-0.488587\pi$
$769$	1.98811	0.0716931	0.0358466	+	0.999357i	$0.488587\pi$
$770$	120.943	4.35847
$771$	−10.9450	−0.394175
$772$	−1.15085	−0.0414199
$773$	8.08005	0.290619	0.145310	−	0.989386i	$-0.453582\pi$
$773$	8.08005	0.290619	0.145310	+	0.989386i	$0.453582\pi$
$774$	0.00158836	5.70925e−5 0
$775$	17.5073	0.628879
$776$	−20.5541	−0.737847
$777$	2.77813	0.0996647
$778$	−50.2950	−1.80316
$779$	−1.24847	−0.0447310
$780$	3.16804	0.113434
$781$	−43.7387	−1.56510
$782$	−44.6250	−1.59579
$783$	−24.1046	−0.861427
$784$	−42.6395	−1.52284
$785$	65.9115	2.35248
$786$	−12.9892	−0.463308
$787$	−26.8087	−0.955627	−0.477814	−	0.878461i	$-0.658571\pi$
$787$	−26.8087	−0.955627	−0.477814	+	0.878461i	$0.658571\pi$
$788$	3.80897	0.135689
$789$	9.09399	0.323755
$790$	46.0984	1.64011
$791$	−91.2940	−3.24604
$792$	−37.2522	−1.32370
$793$	47.7259	1.69480
$794$	−33.6084	−1.19272
$795$	−16.5631	−0.587431
$796$	−4.59695	−0.162935
$797$	36.6990	1.29994	0.649972	−	0.759958i	$-0.274781\pi$
$797$	36.6990	1.29994	0.649972	+	0.759958i	$0.274781\pi$
$798$	−4.67666	−0.165552
$799$	−83.4500	−2.95225
$800$	−13.6873	−0.483917
$801$	33.0426	1.16750
$802$	−24.5784	−0.867893
$803$	−19.3895	−0.684241
$804$	−1.93530	−0.0682528
$805$	80.2997	2.83019
$806$	−9.67559	−0.340808
$807$	−20.9978	−0.739157
$808$	−6.94424	−0.244298
$809$	−6.94883	−0.244308	−0.122154	−	0.992511i	$-0.538980\pi$
$809$	−6.94883	−0.244308	−0.122154	+	0.992511i	$0.538980\pi$
$810$	−18.7528	−0.658906
$811$	34.2667	1.20327	0.601634	−	0.798772i	$-0.294517\pi$
$811$	34.2667	1.20327	0.601634	+	0.798772i	$0.294517\pi$
$812$	−5.88073	−0.206373
$813$	16.1631	0.566864
$814$	−5.56698	−0.195123
$815$	−20.6529	−0.723441
$816$	−19.9369	−0.697931
$817$	0.000507817 0	1.77663e−5 0
$818$	−24.5147	−0.857137
$819$	43.9729	1.53654
$820$	1.16119	0.0405504
$821$	−13.1783	−0.459924	−0.229962	−	0.973200i	$-0.573860\pi$
$821$	−13.1783	−0.459924	−0.229962	+	0.973200i	$0.573860\pi$
$822$	10.6014	0.369766
$823$	−4.55687	−0.158842	−0.0794212	−	0.996841i	$-0.525307\pi$
$823$	−4.55687	−0.158842	−0.0794212	+	0.996841i	$0.525307\pi$
$824$	14.1956	0.494526
$825$	−43.5189	−1.51513
$826$	−1.34749	−0.0468853
$827$	3.20270	0.111369	0.0556845	−	0.998448i	$-0.482266\pi$
$827$	3.20270	0.111369	0.0556845	+	0.998448i	$0.482266\pi$
$828$	−2.63595	−0.0916056
$829$	8.43149	0.292838	0.146419	−	0.989223i	$-0.453225\pi$
$829$	8.43149	0.292838	0.146419	+	0.989223i	$0.453225\pi$
$830$	−78.8473	−2.73683
$831$	−19.4467	−0.674600
$832$	37.0032	1.28286
$833$	−88.2332	−3.05710
$834$	−20.3747	−0.705517
$835$	76.6542	2.65273
$836$	−1.26929	−0.0438993
$837$	7.37517	0.254923
$838$	−7.82534	−0.270322
$839$	−17.7279	−0.612034	−0.306017	−	0.952026i	$-0.598996\pi$
$839$	−17.7279	−0.612034	−0.306017	+	0.952026i	$0.598996\pi$
$840$	40.8140	1.40822
$841$	2.47789	0.0854444
$842$	18.6779	0.643682
$843$	3.91067	0.134691
$844$	4.57222	0.157382
$845$	19.6329	0.675392
$846$	36.3938	1.25125
$847$	−76.0329	−2.61252
$848$	−18.3595	−0.630469
$849$	0.266168	0.00913486
$850$	97.0767	3.32970
$851$	−3.69619	−0.126704
$852$	−1.57306	−0.0538923
$853$	−29.8704	−1.02274	−0.511371	−	0.859360i	$-0.670862\pi$
$853$	−29.8704	−1.02274	−0.511371	+	0.859360i	$0.670862\pi$
$854$	65.5274	2.24230
$855$	−9.18781	−0.314217
$856$	−10.4797	−0.358190
$857$	−25.4137	−0.868114	−0.434057	−	0.900885i	$-0.642918\pi$
$857$	−25.4137	−0.868114	−0.434057	+	0.900885i	$0.642918\pi$
$858$	24.0512	0.821096
$859$	1.29589	0.0442151	0.0221075	−	0.999756i	$-0.492962\pi$
$859$	1.29589	0.0442151	0.0221075	+	0.999756i	$0.492962\pi$
$860$	−0.000472315 0	−1.61058e−5 0
$861$	−4.39927	−0.149927
$862$	−41.8444	−1.42523
$863$	30.8263	1.04934	0.524670	−	0.851306i	$-0.324189\pi$
$863$	30.8263	1.04934	0.524670	+	0.851306i	$0.324189\pi$
$864$	−5.76594	−0.196161
$865$	68.4778	2.32832
$866$	−43.4513	−1.47654
$867$	−27.6204	−0.938037
$868$	1.79930	0.0610723
$869$	−47.4013	−1.60798
$870$	−23.2828	−0.789359
$871$	−42.9535	−1.45543
$872$	50.7736	1.71941
$873$	16.3044	0.551819
$874$	6.22211	0.210466
$875$	−89.0427	−3.01019
$876$	−0.697344	−0.0235611
$877$	−42.9169	−1.44920	−0.724601	−	0.689168i	$-0.757976\pi$
$877$	−42.9169	−1.44920	−0.724601	+	0.689168i	$0.757976\pi$
$878$	−27.2868	−0.920886
$879$	3.11402	0.105033
$880$	−71.8889	−2.42337
$881$	−22.8839	−0.770977	−0.385489	−	0.922713i	$-0.625967\pi$
$881$	−22.8839	−0.770977	−0.385489	+	0.922713i	$0.625967\pi$
$882$	38.4799	1.29569
$883$	−55.5315	−1.86878	−0.934391	−	0.356248i	$-0.884056\pi$
$883$	−55.5315	−1.86878	−0.934391	+	0.356248i	$0.884056\pi$
$884$	7.26661	0.244403
$885$	0.722583	0.0242894
$886$	−50.3725	−1.69230
$887$	−1.56799	−0.0526481	−0.0263241	−	0.999653i	$-0.508380\pi$
$887$	−1.56799	−0.0526481	−0.0263241	+	0.999653i	$0.508380\pi$
$888$	−1.87866	−0.0630439
$889$	−38.9373	−1.30592
$890$	72.5436	2.43167
$891$	19.2828	0.645999
$892$	−1.89746	−0.0635315
$893$	11.6355	0.389368
$894$	−6.35132	−0.212420
$895$	−63.7295	−2.13024
$896$	39.0126	1.30332
$897$	15.9688	0.533182
$898$	8.53728	0.284893
$899$	−9.63116	−0.321217
$900$	5.73422	0.191141
$901$	−37.9911	−1.26567
$902$	8.81554	0.293525
$903$	0.00178941	5.95479e−5 0
$904$	61.7361	2.05331
$905$	1.75077	0.0581975
$906$	1.23281	0.0409574
$907$	27.4203	0.910475	0.455237	−	0.890370i	$-0.349554\pi$
$907$	27.4203	0.910475	0.455237	+	0.890370i	$0.349554\pi$
$908$	−2.26332	−0.0751109
$909$	5.50847	0.182704
$910$	96.5407	3.20029
$911$	−45.2940	−1.50066	−0.750329	−	0.661065i	$-0.770105\pi$
$911$	−45.2940	−1.50066	−0.750329	+	0.661065i	$0.770105\pi$
$912$	2.77982	0.0920492
$913$	81.0758	2.68322
$914$	−0.200843	−0.00664328
$915$	−35.1385	−1.16164
$916$	1.26445	0.0417785
$917$	53.6115	1.77041
$918$	40.8949	1.34973
$919$	−10.2785	−0.339057	−0.169528	−	0.985525i	$-0.554224\pi$
$919$	−10.2785	−0.339057	−0.169528	+	0.985525i	$0.554224\pi$
$920$	−54.3015	−1.79027
$921$	2.70883	0.0892590
$922$	−31.1113	−1.02459
$923$	−34.9138	−1.14920
$924$	−4.47264	−0.147139
$925$	8.04065	0.264375
$926$	−20.0155	−0.657749
$927$	−11.2605	−0.369844
$928$	7.52968	0.247174
$929$	13.0794	0.429123	0.214561	−	0.976711i	$-0.431168\pi$
$929$	13.0794	0.429123	0.214561	+	0.976711i	$0.431168\pi$
$930$	7.12372	0.233596
$931$	12.3025	0.403197
$932$	7.03031	0.230285
$933$	7.44105	0.243609
$934$	−4.28112	−0.140083
$935$	−148.758	−4.86492
$936$	−29.7360	−0.971952
$937$	18.3702	0.600127	0.300063	−	0.953919i	$-0.402992\pi$
$937$	18.3702	0.600127	0.300063	+	0.953919i	$0.402992\pi$
$938$	−58.9750	−1.92560
$939$	−20.9487	−0.683635
$940$	−10.8221	−0.352977
$941$	11.1723	0.364207	0.182104	−	0.983279i	$-0.441709\pi$
$941$	11.1723	0.364207	0.182104	+	0.983279i	$0.441709\pi$
$942$	17.9965	0.586357
$943$	5.85306	0.190602
$944$	0.800956	0.0260689
$945$	−73.5877	−2.39381
$946$	−0.00358574	−0.000116582 0
$947$	34.5522	1.12279	0.561397	−	0.827547i	$-0.310264\pi$
$947$	34.5522	1.12279	0.561397	+	0.827547i	$0.310264\pi$
$948$	−1.70479	−0.0553689
$949$	−15.4774	−0.502417
$950$	−13.5355	−0.439150
$951$	0.802041	0.0260080
$952$	93.6160	3.03411
$953$	55.6922	1.80405	0.902023	−	0.431688i	$-0.142082\pi$
$953$	55.6922	1.80405	0.902023	+	0.431688i	$0.142082\pi$
$954$	16.5685	0.536425
$955$	−25.4236	−0.822687
$956$	−0.629944	−0.0203739
$957$	23.9408	0.773896
$958$	7.94310	0.256630
$959$	−43.7562	−1.41296
$960$	−27.2439	−0.879293
$961$	−28.0532	−0.904942
$962$	−4.44376	−0.143273
$963$	8.31297	0.267882
$964$	−0.562753	−0.0181251
$965$	18.8061	0.605388
$966$	21.9251	0.705427
$967$	−48.0884	−1.54642	−0.773210	−	0.634150i	$-0.781350\pi$
$967$	−48.0884	−1.54642	−0.773210	+	0.634150i	$0.781350\pi$
$968$	51.4161	1.65258
$969$	5.75224	0.184789
$970$	35.7955	1.14932
$971$	9.03144	0.289833	0.144916	−	0.989444i	$-0.453709\pi$
$971$	9.03144	0.289833	0.144916	+	0.989444i	$0.453709\pi$
$972$	3.76847	0.120874
$973$	84.0945	2.69595
$974$	29.6873	0.951242
$975$	−34.7383	−1.11252
$976$	−38.9498	−1.24675
$977$	53.5026	1.71170	0.855850	−	0.517225i	$-0.173035\pi$
$977$	53.5026	1.71170	0.855850	+	0.517225i	$0.173035\pi$
$978$	−5.63909	−0.180318
$979$	−74.5939	−2.38403
$980$	−11.4424	−0.365513
$981$	−40.2758	−1.28591
$982$	−35.3461	−1.12794
$983$	6.64002	0.211784	0.105892	−	0.994378i	$-0.466230\pi$
$983$	6.64002	0.211784	0.105892	+	0.994378i	$0.466230\pi$
$984$	2.97494	0.0948376
$985$	−62.2426	−1.98321
$986$	−53.4042	−1.70074
$987$	41.0005	1.30506
$988$	−1.01319	−0.0322339
$989$	−0.00238074	−7.57033e−5 0
$990$	64.8759	2.06189
$991$	57.6393	1.83097	0.915486	−	0.402350i	$-0.131806\pi$
$991$	57.6393	1.83097	0.915486	+	0.402350i	$0.131806\pi$
$992$	−2.30383	−0.0731465
$993$	18.1406	0.575675
$994$	−47.9365	−1.52045
$995$	75.1191	2.38144
$996$	2.91589	0.0923935
$997$	−20.7289	−0.656492	−0.328246	−	0.944592i	$-0.606457\pi$
$997$	−20.7289	−0.656492	−0.328246	+	0.944592i	$0.606457\pi$
$998$	28.8136	0.912078
$999$	3.38724	0.107167

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.c.1.41	✓	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.c.1.41	✓	138	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-1.32719 q^{2} -0.802041 q^{3} -0.238573 q^{4} +3.89854 q^{5} +1.06446 q^{6} -4.39346 q^{7} +2.97101 q^{8} -2.35673 q^{9} +O(q^{10})\)	\(q-1.32719 q^{2} -0.802041 q^{3} -0.238573 q^{4} +3.89854 q^{5} +1.06446 q^{6} -4.39346 q^{7} +2.97101 q^{8} -2.35673 q^{9} -5.17410 q^{10} +5.32033 q^{11} +0.191346 q^{12} +4.24688 q^{13} +5.83094 q^{14} -3.12679 q^{15} -3.46594 q^{16} -7.17200 q^{17} +3.12782 q^{18} +1.00000 q^{19} -0.930089 q^{20} +3.52373 q^{21} -7.06108 q^{22} -4.68819 q^{23} -2.38287 q^{24} +10.1986 q^{25} -5.63640 q^{26} +4.29632 q^{27} +1.04816 q^{28} -5.61052 q^{29} +4.14984 q^{30} +1.71663 q^{31} -1.34207 q^{32} -4.26713 q^{33} +9.51859 q^{34} -17.1281 q^{35} +0.562253 q^{36} +0.788404 q^{37} -1.32719 q^{38} -3.40617 q^{39} +11.5826 q^{40} -1.24847 q^{41} -4.67666 q^{42} +0.000507817 q^{43} -1.26929 q^{44} -9.18781 q^{45} +6.22211 q^{46} +11.6355 q^{47} +2.77982 q^{48} +12.3025 q^{49} -13.5355 q^{50} +5.75224 q^{51} -1.01319 q^{52} +5.29714 q^{53} -5.70202 q^{54} +20.7416 q^{55} -13.0530 q^{56} -0.802041 q^{57} +7.44621 q^{58} -0.231094 q^{59} +0.745970 q^{60} +11.2379 q^{61} -2.27828 q^{62} +10.3542 q^{63} +8.71305 q^{64} +16.5566 q^{65} +5.66328 q^{66} -10.1142 q^{67} +1.71105 q^{68} +3.76012 q^{69} +22.7322 q^{70} -8.22105 q^{71} -7.00186 q^{72} -3.64442 q^{73} -1.04636 q^{74} -8.17973 q^{75} -0.238573 q^{76} -23.3747 q^{77} +4.52063 q^{78} -8.90945 q^{79} -13.5121 q^{80} +3.62436 q^{81} +1.65695 q^{82} +15.2388 q^{83} -0.840669 q^{84} -27.9604 q^{85} -0.000673968 q^{86} +4.49987 q^{87} +15.8067 q^{88} -14.0205 q^{89} +12.1939 q^{90} -18.6585 q^{91} +1.11848 q^{92} -1.37681 q^{93} -15.4425 q^{94} +3.89854 q^{95} +1.07639 q^{96} -6.91821 q^{97} -16.3277 q^{98} -12.5386 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * q^99

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