LMFDB - Embedded newform 6013.2.a.f.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, 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("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$0$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.31912 q^{2} -2.74143 q^{3} +3.37834 q^{4} -1.26450 q^{5} +6.35772 q^{6} -1.00000 q^{7} -3.19654 q^{8} +4.51544 q^{9} +O(q^{10})$	\(q-2.31912 q^{2} -2.74143 q^{3} +3.37834 q^{4} -1.26450 q^{5} +6.35772 q^{6} -1.00000 q^{7} -3.19654 q^{8} +4.51544 q^{9} +2.93254 q^{10} -0.680575 q^{11} -9.26148 q^{12} -0.422415 q^{13} +2.31912 q^{14} +3.46654 q^{15} +0.656500 q^{16} +1.16796 q^{17} -10.4719 q^{18} -4.26718 q^{19} -4.27192 q^{20} +2.74143 q^{21} +1.57834 q^{22} -5.26189 q^{23} +8.76309 q^{24} -3.40104 q^{25} +0.979632 q^{26} -4.15446 q^{27} -3.37834 q^{28} -8.71343 q^{29} -8.03934 q^{30} -0.598966 q^{31} +4.87058 q^{32} +1.86575 q^{33} -2.70865 q^{34} +1.26450 q^{35} +15.2547 q^{36} -3.89974 q^{37} +9.89613 q^{38} +1.15802 q^{39} +4.04203 q^{40} -1.21274 q^{41} -6.35772 q^{42} -4.46838 q^{43} -2.29921 q^{44} -5.70977 q^{45} +12.2030 q^{46} +4.98523 q^{47} -1.79975 q^{48} +1.00000 q^{49} +7.88743 q^{50} -3.20188 q^{51} -1.42706 q^{52} +7.71937 q^{53} +9.63471 q^{54} +0.860588 q^{55} +3.19654 q^{56} +11.6982 q^{57} +20.2075 q^{58} -0.672094 q^{59} +11.7112 q^{60} -8.41636 q^{61} +1.38908 q^{62} -4.51544 q^{63} -12.6085 q^{64} +0.534144 q^{65} -4.32690 q^{66} +15.6009 q^{67} +3.94577 q^{68} +14.4251 q^{69} -2.93254 q^{70} -7.08924 q^{71} -14.4338 q^{72} -4.67755 q^{73} +9.04399 q^{74} +9.32370 q^{75} -14.4160 q^{76} +0.680575 q^{77} -2.68559 q^{78} +1.36925 q^{79} -0.830146 q^{80} -2.15715 q^{81} +2.81248 q^{82} -16.6487 q^{83} +9.26148 q^{84} -1.47689 q^{85} +10.3627 q^{86} +23.8873 q^{87} +2.17549 q^{88} -14.0929 q^{89} +13.2417 q^{90} +0.422415 q^{91} -17.7765 q^{92} +1.64202 q^{93} -11.5614 q^{94} +5.39586 q^{95} -13.3523 q^{96} -11.1274 q^{97} -2.31912 q^{98} -3.07309 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) $ 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * 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 $

$2$	−2.31912	−1.63987	−0.819934	−	0.572457i	$-0.805990\pi$
$2$	−2.31912	−1.63987	−0.819934	+	0.572457i	$0.805990\pi$
$3$	−2.74143	−1.58277	−0.791383	−	0.611321i	$-0.790638\pi$
$3$	−2.74143	−1.58277	−0.791383	+	0.611321i	$0.790638\pi$
$4$	3.37834	1.68917
$5$	−1.26450	−0.565502	−0.282751	−	0.959193i	$-0.591247\pi$
$5$	−1.26450	−0.565502	−0.282751	+	0.959193i	$0.591247\pi$
$6$	6.35772	2.59553
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.19654	−1.13015
$9$	4.51544	1.50515
$10$	2.93254	0.927349
$11$	−0.680575	−0.205201	−0.102601	−	0.994723i	$-0.532716\pi$
$11$	−0.680575	−0.205201	−0.102601	+	0.994723i	$0.532716\pi$
$12$	−9.26148	−2.67356
$13$	−0.422415	−0.117157	−0.0585784	−	0.998283i	$-0.518657\pi$
$13$	−0.422415	−0.117157	−0.0585784	+	0.998283i	$0.518657\pi$
$14$	2.31912	0.619812
$15$	3.46654	0.895057
$16$	0.656500	0.164125
$17$	1.16796	0.283272	0.141636	−	0.989919i	$-0.454764\pi$
$17$	1.16796	0.283272	0.141636	+	0.989919i	$0.454764\pi$
$18$	−10.4719	−2.46824
$19$	−4.26718	−0.978959	−0.489479	−	0.872015i	$-0.662813\pi$
$19$	−4.26718	−0.978959	−0.489479	+	0.872015i	$0.662813\pi$
$20$	−4.27192	−0.955229
$21$	2.74143	0.598229
$22$	1.57834	0.336503
$23$	−5.26189	−1.09718	−0.548590	−	0.836091i	$-0.684835\pi$
$23$	−5.26189	−1.09718	−0.548590	+	0.836091i	$0.684835\pi$
$24$	8.76309	1.78876
$25$	−3.40104	−0.680207
$26$	0.979632	0.192122
$27$	−4.15446	−0.799526
$28$	−3.37834	−0.638446
$29$	−8.71343	−1.61804	−0.809022	−	0.587778i	$-0.800003\pi$
$29$	−8.71343	−1.61804	−0.809022	+	0.587778i	$0.800003\pi$
$30$	−8.03934	−1.46778
$31$	−0.598966	−0.107578	−0.0537888	−	0.998552i	$-0.517130\pi$
$31$	−0.598966	−0.107578	−0.0537888	+	0.998552i	$0.517130\pi$
$32$	4.87058	0.861005
$33$	1.86575	0.324785
$34$	−2.70865	−0.464529
$35$	1.26450	0.213740
$36$	15.2547	2.54245
$37$	−3.89974	−0.641114	−0.320557	−	0.947229i	$-0.603870\pi$
$37$	−3.89974	−0.641114	−0.320557	+	0.947229i	$0.603870\pi$
$38$	9.89613	1.60536
$39$	1.15802	0.185432
$40$	4.04203	0.639101
$41$	−1.21274	−0.189397	−0.0946987	−	0.995506i	$-0.530189\pi$
$41$	−1.21274	−0.189397	−0.0946987	+	0.995506i	$0.530189\pi$
$42$	−6.35772	−0.981017
$43$	−4.46838	−0.681422	−0.340711	−	0.940168i	$-0.610668\pi$
$43$	−4.46838	−0.681422	−0.340711	+	0.940168i	$0.610668\pi$
$44$	−2.29921	−0.346619
$45$	−5.70977	−0.851163
$46$	12.2030	1.79923
$47$	4.98523	0.727170	0.363585	−	0.931561i	$-0.381553\pi$
$47$	4.98523	0.727170	0.363585	+	0.931561i	$0.381553\pi$
$48$	−1.79975	−0.259771
$49$	1.00000	0.142857
$50$	7.88743	1.11545
$51$	−3.20188	−0.448353
$52$	−1.42706	−0.197898
$53$	7.71937	1.06034	0.530169	−	0.847892i	$-0.322129\pi$
$53$	7.71937	1.06034	0.530169	+	0.847892i	$0.322129\pi$
$54$	9.63471	1.31112
$55$	0.860588	0.116042
$56$	3.19654	0.427156
$57$	11.6982	1.54946
$58$	20.2075	2.65338
$59$	−0.672094	−0.0874992	−0.0437496	−	0.999043i	$-0.513930\pi$
$59$	−0.672094	−0.0874992	−0.0437496	+	0.999043i	$0.513930\pi$
$60$	11.7112	1.51190
$61$	−8.41636	−1.07760	−0.538802	−	0.842432i	$-0.681123\pi$
$61$	−8.41636	−1.07760	−0.538802	+	0.842432i	$0.681123\pi$
$62$	1.38908	0.176413
$63$	−4.51544	−0.568891
$64$	−12.6085	−1.57606
$65$	0.534144	0.0662524
$66$	−4.32690	−0.532605
$67$	15.6009	1.90595	0.952977	−	0.303043i	$-0.0980027\pi$
$67$	15.6009	1.90595	0.952977	+	0.303043i	$0.0980027\pi$
$68$	3.94577	0.478495
$69$	14.4251	1.73658
$70$	−2.93254	−0.350505
$71$	−7.08924	−0.841338	−0.420669	−	0.907214i	$-0.638205\pi$
$71$	−7.08924	−0.841338	−0.420669	+	0.907214i	$0.638205\pi$
$72$	−14.4338	−1.70104
$73$	−4.67755	−0.547465	−0.273733	−	0.961806i	$-0.588258\pi$
$73$	−4.67755	−0.547465	−0.273733	+	0.961806i	$0.588258\pi$
$74$	9.04399	1.05134
$75$	9.32370	1.07661
$76$	−14.4160	−1.65363
$77$	0.680575	0.0775587
$78$	−2.68559	−0.304084
$79$	1.36925	0.154053	0.0770266	−	0.997029i	$-0.475457\pi$
$79$	1.36925	0.154053	0.0770266	+	0.997029i	$0.475457\pi$
$80$	−0.830146	−0.0928131
$81$	−2.15715	−0.239683
$82$	2.81248	0.310587
$83$	−16.6487	−1.82743	−0.913717	−	0.406351i	$-0.866801\pi$
$83$	−16.6487	−1.82743	−0.913717	+	0.406351i	$0.866801\pi$
$84$	9.26148	1.01051
$85$	−1.47689	−0.160191
$86$	10.3627	1.11744
$87$	23.8873	2.56098
$88$	2.17549	0.231908
$89$	−14.0929	−1.49385	−0.746923	−	0.664911i	$-0.768469\pi$
$89$	−14.0929	−1.49385	−0.746923	+	0.664911i	$0.768469\pi$
$90$	13.2417	1.39580
$91$	0.422415	0.0442811
$92$	−17.7765	−1.85332
$93$	1.64202	0.170270
$94$	−11.5614	−1.19246
$95$	5.39586	0.553603
$96$	−13.3523	−1.36277
$97$	−11.1274	−1.12981	−0.564906	−	0.825155i	$-0.691088\pi$
$97$	−11.1274	−1.12981	−0.564906	+	0.825155i	$0.691088\pi$
$98$	−2.31912	−0.234267
$99$	−3.07309	−0.308857
$100$	−11.4899	−1.14899
$101$	−7.75024	−0.771178	−0.385589	−	0.922671i	$-0.626002\pi$
$101$	−7.75024	−0.771178	−0.385589	+	0.922671i	$0.626002\pi$
$102$	7.42557	0.735241
$103$	−8.87887	−0.874861	−0.437431	−	0.899252i	$-0.644111\pi$
$103$	−8.87887	−0.874861	−0.437431	+	0.899252i	$0.644111\pi$
$104$	1.35027	0.132405
$105$	−3.46654	−0.338300
$106$	−17.9022	−1.73881
$107$	18.2206	1.76145	0.880724	−	0.473629i	$-0.157056\pi$
$107$	18.2206	1.76145	0.880724	+	0.473629i	$0.157056\pi$
$108$	−14.0352	−1.35054
$109$	−8.60334	−0.824051	−0.412025	−	0.911172i	$-0.635178\pi$
$109$	−8.60334	−0.824051	−0.412025	+	0.911172i	$0.635178\pi$
$110$	−1.99581	−0.190293
$111$	10.6909	1.01473
$112$	−0.656500	−0.0620335
$113$	8.81575	0.829316	0.414658	−	0.909977i	$-0.363901\pi$
$113$	8.81575	0.829316	0.414658	+	0.909977i	$0.363901\pi$
$114$	−27.1295	−2.54091
$115$	6.65367	0.620458
$116$	−29.4369	−2.73315
$117$	−1.90739	−0.176338
$118$	1.55867	0.143487
$119$	−1.16796	−0.107067
$120$	−11.0809	−1.01155
$121$	−10.5368	−0.957893
$122$	19.5186	1.76713
$123$	3.32463	0.299772
$124$	−2.02351	−0.181717
$125$	10.6231	0.950161
$126$	10.4719	0.932907
$127$	−6.66684	−0.591586	−0.295793	−	0.955252i	$-0.595584\pi$
$127$	−6.66684	−0.591586	−0.295793	+	0.955252i	$0.595584\pi$
$128$	19.4995	1.72353
$129$	12.2497	1.07853
$130$	−1.23875	−0.108645
$131$	7.47336	0.652950	0.326475	−	0.945206i	$-0.394139\pi$
$131$	7.47336	0.652950	0.326475	+	0.945206i	$0.394139\pi$
$132$	6.30313	0.548617
$133$	4.26718	0.370012
$134$	−36.1804	−3.12551
$135$	5.25332	0.452134
$136$	−3.73344	−0.320140
$137$	12.0437	1.02896	0.514480	−	0.857503i	$-0.327985\pi$
$137$	12.0437	1.02896	0.514480	+	0.857503i	$0.327985\pi$
$138$	−33.4536	−2.84776
$139$	19.7835	1.67801	0.839005	−	0.544123i	$-0.183138\pi$
$139$	19.7835	1.67801	0.839005	+	0.544123i	$0.183138\pi$
$140$	4.27192	0.361043
$141$	−13.6666	−1.15094
$142$	16.4408	1.37968
$143$	0.287485	0.0240407
$144$	2.96439	0.247032
$145$	11.0181	0.915007
$146$	10.8478	0.897771
$147$	−2.74143	−0.226109
$148$	−13.1747	−1.08295
$149$	12.8632	1.05379	0.526895	−	0.849930i	$-0.323356\pi$
$149$	12.8632	1.05379	0.526895	+	0.849930i	$0.323356\pi$
$150$	−21.6228	−1.76550
$151$	−9.31390	−0.757954	−0.378977	−	0.925406i	$-0.623724\pi$
$151$	−9.31390	−0.757954	−0.378977	+	0.925406i	$0.623724\pi$
$152$	13.6402	1.10637
$153$	5.27385	0.426366
$154$	−1.57834	−0.127186
$155$	0.757394	0.0608353
$156$	3.91219	0.313226
$157$	−7.39988	−0.590575	−0.295287	−	0.955409i	$-0.595415\pi$
$157$	−7.39988	−0.590575	−0.295287	+	0.955409i	$0.595415\pi$
$158$	−3.17547	−0.252627
$159$	−21.1621	−1.67826
$160$	−6.15885	−0.486900
$161$	5.26189	0.414695
$162$	5.00270	0.393049
$163$	−4.42930	−0.346929	−0.173465	−	0.984840i	$-0.555496\pi$
$163$	−4.42930	−0.346929	−0.173465	+	0.984840i	$0.555496\pi$
$164$	−4.09703	−0.319924
$165$	−2.35924	−0.183667
$166$	38.6105	2.99675
$167$	−25.0927	−1.94173	−0.970866	−	0.239622i	$-0.922976\pi$
$167$	−25.0927	−1.94173	−0.970866	+	0.239622i	$0.922976\pi$
$168$	−8.76309	−0.676087
$169$	−12.8216	−0.986274
$170$	3.42509	0.262692
$171$	−19.2682	−1.47348
$172$	−15.0957	−1.15104
$173$	−11.9443	−0.908109	−0.454055	−	0.890974i	$-0.650023\pi$
$173$	−11.9443	−0.908109	−0.454055	+	0.890974i	$0.650023\pi$
$174$	−55.3975	−4.19968
$175$	3.40104	0.257094
$176$	−0.446798	−0.0336787
$177$	1.84250	0.138491
$178$	32.6832	2.44971
$179$	−20.7694	−1.55238	−0.776189	−	0.630500i	$-0.782850\pi$
$179$	−20.7694	−1.55238	−0.776189	+	0.630500i	$0.782850\pi$
$180$	−19.2896	−1.43776
$181$	−20.1612	−1.49857	−0.749285	−	0.662248i	$-0.769603\pi$
$181$	−20.1612	−1.49857	−0.749285	+	0.662248i	$0.769603\pi$
$182$	−0.979632	−0.0726152
$183$	23.0728	1.70559
$184$	16.8199	1.23998
$185$	4.93123	0.362551
$186$	−3.80806	−0.279220
$187$	−0.794885	−0.0581278
$188$	16.8418	1.22831
$189$	4.15446	0.302192
$190$	−12.5137	−0.907837
$191$	−11.7216	−0.848145	−0.424072	−	0.905628i	$-0.639400\pi$
$191$	−11.7216	−0.848145	−0.424072	+	0.905628i	$0.639400\pi$
$192$	34.5653	2.49453
$193$	−13.4100	−0.965271	−0.482635	−	0.875821i	$-0.660320\pi$
$193$	−13.4100	−0.965271	−0.482635	+	0.875821i	$0.660320\pi$
$194$	25.8057	1.85274
$195$	−1.46432	−0.104862
$196$	3.37834	0.241310
$197$	−6.20827	−0.442321	−0.221161	−	0.975237i	$-0.570984\pi$
$197$	−6.20827	−0.442321	−0.221161	+	0.975237i	$0.570984\pi$
$198$	7.12688	0.506486
$199$	1.33900	0.0949192	0.0474596	−	0.998873i	$-0.484887\pi$
$199$	1.33900	0.0949192	0.0474596	+	0.998873i	$0.484887\pi$
$200$	10.8716	0.768735
$201$	−42.7688	−3.01668
$202$	17.9738	1.26463
$203$	8.71343	0.611563
$204$	−10.8171	−0.757345
$205$	1.53351	0.107105
$206$	20.5912	1.43466
$207$	−23.7597	−1.65142
$208$	−0.277315	−0.0192284
$209$	2.90414	0.200883
$210$	8.03934	0.554767
$211$	−23.4054	−1.61130	−0.805648	−	0.592395i	$-0.798182\pi$
$211$	−23.4054	−1.61130	−0.805648	+	0.592395i	$0.798182\pi$
$212$	26.0787	1.79109
$213$	19.4347	1.33164
$214$	−42.2558	−2.88854
$215$	5.65027	0.385345
$216$	13.2799	0.903583
$217$	0.598966	0.0406605
$218$	19.9522	1.35134
$219$	12.8232	0.866509
$220$	2.90736	0.196014
$221$	−0.493364	−0.0331873
$222$	−24.7935	−1.66403
$223$	−2.41965	−0.162032	−0.0810159	−	0.996713i	$-0.525816\pi$
$223$	−2.41965	−0.162032	−0.0810159	+	0.996713i	$0.525816\pi$
$224$	−4.87058	−0.325429
$225$	−15.3572	−1.02381
$226$	−20.4448	−1.35997
$227$	22.5817	1.49880	0.749399	−	0.662118i	$-0.230342\pi$
$227$	22.5817	1.49880	0.749399	+	0.662118i	$0.230342\pi$
$228$	39.5204	2.61730
$229$	−4.16736	−0.275387	−0.137693	−	0.990475i	$-0.543969\pi$
$229$	−4.16736	−0.275387	−0.137693	+	0.990475i	$0.543969\pi$
$230$	−15.4307	−1.01747
$231$	−1.86575	−0.122757
$232$	27.8529	1.82863
$233$	−8.67970	−0.568626	−0.284313	−	0.958731i	$-0.591766\pi$
$233$	−8.67970	−0.568626	−0.284313	+	0.958731i	$0.591766\pi$
$234$	4.42347	0.289171
$235$	−6.30383	−0.411216
$236$	−2.27056	−0.147801
$237$	−3.75372	−0.243830
$238$	2.70865	0.175576
$239$	−9.56778	−0.618888	−0.309444	−	0.950918i	$-0.600143\pi$
$239$	−9.56778	−0.618888	−0.309444	+	0.950918i	$0.600143\pi$
$240$	2.27579	0.146901
$241$	−18.4776	−1.19025	−0.595123	−	0.803634i	$-0.702897\pi$
$241$	−18.4776	−1.19025	−0.595123	+	0.803634i	$0.702897\pi$
$242$	24.4362	1.57082
$243$	18.3771	1.17889
$244$	−28.4333	−1.82026
$245$	−1.26450	−0.0807860
$246$	−7.71023	−0.491586
$247$	1.80252	0.114692
$248$	1.91462	0.121579
$249$	45.6413	2.89240
$250$	−24.6363	−1.55814
$251$	−1.81710	−0.114695	−0.0573473	−	0.998354i	$-0.518264\pi$
$251$	−1.81710	−0.114695	−0.0573473	+	0.998354i	$0.518264\pi$
$252$	−15.2547	−0.960954
$253$	3.58111	0.225143
$254$	15.4612	0.970124
$255$	4.04879	0.253545
$256$	−20.0048	−1.25030
$257$	−20.9598	−1.30744	−0.653719	−	0.756737i	$-0.726792\pi$
$257$	−20.9598	−1.30744	−0.653719	+	0.756737i	$0.726792\pi$
$258$	−28.4087	−1.76865
$259$	3.89974	0.242318
$260$	1.80452	0.111912
$261$	−39.3449	−2.43539
$262$	−17.3316	−1.07075
$263$	12.9124	0.796211	0.398105	−	0.917340i	$-0.369668\pi$
$263$	12.9124	0.796211	0.398105	+	0.917340i	$0.369668\pi$
$264$	−5.96394	−0.367055
$265$	−9.76116	−0.599623
$266$	−9.89613	−0.606771
$267$	38.6347	2.36441
$268$	52.7051	3.21948
$269$	−0.216802	−0.0132186	−0.00660932	−	0.999978i	$-0.502104\pi$
$269$	−0.216802	−0.0132186	−0.00660932	+	0.999978i	$0.502104\pi$
$270$	−12.1831	−0.741440
$271$	−19.2708	−1.17062	−0.585309	−	0.810810i	$-0.699027\pi$
$271$	−19.2708	−1.17062	−0.585309	+	0.810810i	$0.699027\pi$
$272$	0.766767	0.0464921
$273$	−1.15802	−0.0700866
$274$	−27.9308	−1.68736
$275$	2.31466	0.139579
$276$	48.7329	2.93338
$277$	−7.27873	−0.437337	−0.218668	−	0.975799i	$-0.570171\pi$
$277$	−7.27873	−0.437337	−0.218668	+	0.975799i	$0.570171\pi$
$278$	−45.8803	−2.75172
$279$	−2.70459	−0.161920
$280$	−4.04203	−0.241558
$281$	−4.19100	−0.250014	−0.125007	−	0.992156i	$-0.539895\pi$
$281$	−4.19100	−0.250014	−0.125007	+	0.992156i	$0.539895\pi$
$282$	31.6947	1.88739
$283$	17.3077	1.02884	0.514419	−	0.857539i	$-0.328008\pi$
$283$	17.3077	1.02884	0.514419	+	0.857539i	$0.328008\pi$
$284$	−23.9499	−1.42116
$285$	−14.7924	−0.876224
$286$	−0.666713	−0.0394236
$287$	1.21274	0.0715855
$288$	21.9928	1.29594
$289$	−15.6359	−0.919757
$290$	−25.5525	−1.50049
$291$	30.5049	1.78823
$292$	−15.8023	−0.924762
$293$	−8.33832	−0.487130	−0.243565	−	0.969885i	$-0.578317\pi$
$293$	−8.33832	−0.487130	−0.243565	+	0.969885i	$0.578317\pi$
$294$	6.35772	0.370790
$295$	0.849864	0.0494810
$296$	12.4657	0.724554
$297$	2.82742	0.164064
$298$	−29.8313	−1.72808
$299$	2.22270	0.128542
$300$	31.4986	1.81857
$301$	4.46838	0.257553
$302$	21.6001	1.24295
$303$	21.2467	1.22059
$304$	−2.80141	−0.160672
$305$	10.6425	0.609387
$306$	−12.2307	−0.699184
$307$	−24.2158	−1.38207	−0.691035	−	0.722821i	$-0.742845\pi$
$307$	−24.2158	−1.38207	−0.691035	+	0.722821i	$0.742845\pi$
$308$	2.29921	0.131010
$309$	24.3408	1.38470
$310$	−1.75649	−0.0997619
$311$	15.6378	0.886736	0.443368	−	0.896340i	$-0.353783\pi$
$311$	15.6378	0.886736	0.443368	+	0.896340i	$0.353783\pi$
$312$	−3.70166	−0.209565
$313$	5.29773	0.299445	0.149723	−	0.988728i	$-0.452162\pi$
$313$	5.29773	0.299445	0.149723	+	0.988728i	$0.452162\pi$
$314$	17.1612	0.968465
$315$	5.70977	0.321709
$316$	4.62581	0.260222
$317$	7.37435	0.414185	0.207092	−	0.978321i	$-0.433600\pi$
$317$	7.37435	0.414185	0.207092	+	0.978321i	$0.433600\pi$
$318$	49.0776	2.75213
$319$	5.93014	0.332024
$320$	15.9434	0.891265
$321$	−49.9504	−2.78796
$322$	−12.2030	−0.680046
$323$	−4.98391	−0.277312
$324$	−7.28759	−0.404866
$325$	1.43665	0.0796909
$326$	10.2721	0.568919
$327$	23.5855	1.30428
$328$	3.87656	0.214047
$329$	−4.98523	−0.274844
$330$	5.47137	0.301189
$331$	−3.01623	−0.165787	−0.0828936	−	0.996558i	$-0.526416\pi$
$331$	−3.01623	−0.165787	−0.0828936	+	0.996558i	$0.526416\pi$
$332$	−56.2450	−3.08685
$333$	−17.6090	−0.964969
$334$	58.1931	3.18419
$335$	−19.7274	−1.07782
$336$	1.79975	0.0981844
$337$	−18.5667	−1.01139	−0.505696	−	0.862712i	$-0.668764\pi$
$337$	−18.5667	−1.01139	−0.505696	+	0.862712i	$0.668764\pi$
$338$	29.7348	1.61736
$339$	−24.1678	−1.31261
$340$	−4.98943	−0.270590
$341$	0.407641	0.0220750
$342$	44.6853	2.41631
$343$	−1.00000	−0.0539949
$344$	14.2834	0.770108
$345$	−18.2406	−0.982039
$346$	27.7003	1.48918
$347$	13.9823	0.750608	0.375304	−	0.926902i	$-0.377538\pi$
$347$	13.9823	0.750608	0.375304	+	0.926902i	$0.377538\pi$
$348$	80.6993	4.32594
$349$	−11.0203	−0.589906	−0.294953	−	0.955512i	$-0.595304\pi$
$349$	−11.0203	−0.589906	−0.294953	+	0.955512i	$0.595304\pi$
$350$	−7.88743	−0.421601
$351$	1.75490	0.0936699
$352$	−3.31479	−0.176679
$353$	−33.1132	−1.76244	−0.881219	−	0.472708i	$-0.843277\pi$
$353$	−33.1132	−1.76244	−0.881219	+	0.472708i	$0.843277\pi$
$354$	−4.27299	−0.227107
$355$	8.96436	0.475779
$356$	−47.6106	−2.52336
$357$	3.20188	0.169462
$358$	48.1669	2.54570
$359$	−1.38111	−0.0728919	−0.0364460	−	0.999336i	$-0.511604\pi$
$359$	−1.38111	−0.0728919	−0.0364460	+	0.999336i	$0.511604\pi$
$360$	18.2515	0.961940
$361$	−0.791147	−0.0416393
$362$	46.7563	2.45746
$363$	28.8859	1.51612
$364$	1.42706	0.0747983
$365$	5.91476	0.309593
$366$	−53.5088	−2.79695
$367$	−4.83262	−0.252261	−0.126130	−	0.992014i	$-0.540256\pi$
$367$	−4.83262	−0.252261	−0.126130	+	0.992014i	$0.540256\pi$
$368$	−3.45443	−0.180075
$369$	−5.47603	−0.285071
$370$	−11.4361	−0.594537
$371$	−7.71937	−0.400770
$372$	5.54731	0.287615
$373$	−29.2368	−1.51382	−0.756912	−	0.653517i	$-0.773293\pi$
$373$	−29.2368	−1.51382	−0.756912	+	0.653517i	$0.773293\pi$
$374$	1.84344	0.0953219
$375$	−29.1225	−1.50388
$376$	−15.9355	−0.821810
$377$	3.68068	0.189565
$378$	−9.63471	−0.495556
$379$	14.3386	0.736527	0.368263	−	0.929722i	$-0.379952\pi$
$379$	14.3386	0.736527	0.368263	+	0.929722i	$0.379952\pi$
$380$	18.2290	0.935130
$381$	18.2767	0.936342
$382$	27.1838	1.39085
$383$	−0.127568	−0.00651840	−0.00325920	−	0.999995i	$-0.501037\pi$
$383$	−0.127568	−0.00651840	−0.00325920	+	0.999995i	$0.501037\pi$
$384$	−53.4564	−2.72794
$385$	−0.860588	−0.0438596
$386$	31.0994	1.58292
$387$	−20.1767	−1.02564
$388$	−37.5920	−1.90844
$389$	30.0569	1.52394	0.761972	−	0.647610i	$-0.224231\pi$
$389$	30.0569	1.52394	0.761972	+	0.647610i	$0.224231\pi$
$390$	3.39594	0.171960
$391$	−6.14569	−0.310801
$392$	−3.19654	−0.161450
$393$	−20.4877	−1.03347
$394$	14.3978	0.725349
$395$	−1.73142	−0.0871174
$396$	−10.3819	−0.521713
$397$	−11.0988	−0.557031	−0.278516	−	0.960432i	$-0.589842\pi$
$397$	−11.0988	−0.557031	−0.278516	+	0.960432i	$0.589842\pi$
$398$	−3.10531	−0.155655
$399$	−11.6982	−0.585642
$400$	−2.23278	−0.111639
$401$	16.9975	0.848812	0.424406	−	0.905472i	$-0.360483\pi$
$401$	16.9975	0.848812	0.424406	+	0.905472i	$0.360483\pi$
$402$	99.1861	4.94695
$403$	0.253012	0.0126034
$404$	−26.1829	−1.30265
$405$	2.72772	0.135542
$406$	−20.2075	−1.00288
$407$	2.65407	0.131557
$408$	10.2350	0.506706
$409$	9.08339	0.449145	0.224572	−	0.974457i	$-0.427901\pi$
$409$	9.08339	0.449145	0.224572	+	0.974457i	$0.427901\pi$
$410$	−3.55639	−0.175638
$411$	−33.0169	−1.62860
$412$	−29.9959	−1.47779
$413$	0.672094	0.0330716
$414$	55.1018	2.70810
$415$	21.0523	1.03342
$416$	−2.05740	−0.100873
$417$	−54.2349	−2.65590
$418$	−6.73506	−0.329422
$419$	28.3890	1.38690	0.693448	−	0.720507i	$-0.256091\pi$
$419$	28.3890	1.38690	0.693448	+	0.720507i	$0.256091\pi$
$420$	−11.7112	−0.571446
$421$	36.1873	1.76366	0.881830	−	0.471567i	$-0.156311\pi$
$421$	36.1873	1.76366	0.881830	+	0.471567i	$0.156311\pi$
$422$	54.2801	2.64231
$423$	22.5105	1.09450
$424$	−24.6753	−1.19834
$425$	−3.97228	−0.192684
$426$	−45.0714	−2.18372
$427$	8.41636	0.407296
$428$	61.5553	2.97539
$429$	−0.788119	−0.0380508
$430$	−13.1037	−0.631916
$431$	−26.0412	−1.25436	−0.627179	−	0.778875i	$-0.715791\pi$
$431$	−26.0412	−1.25436	−0.627179	+	0.778875i	$0.715791\pi$
$432$	−2.72740	−0.131222
$433$	−17.4962	−0.840815	−0.420408	−	0.907335i	$-0.638113\pi$
$433$	−17.4962	−0.840815	−0.420408	+	0.907335i	$0.638113\pi$
$434$	−1.38908	−0.0666778
$435$	−30.2055	−1.44824
$436$	−29.0650	−1.39196
$437$	22.4535	1.07409
$438$	−29.7385	−1.42096
$439$	−0.271668	−0.0129660	−0.00648301	−	0.999979i	$-0.502064\pi$
$439$	−0.271668	−0.0129660	−0.00648301	+	0.999979i	$0.502064\pi$
$440$	−2.75091	−0.131144
$441$	4.51544	0.215021
$442$	1.14417	0.0544228
$443$	23.0532	1.09529	0.547646	−	0.836710i	$-0.315524\pi$
$443$	23.0532	1.09529	0.547646	+	0.836710i	$0.315524\pi$
$444$	36.1174	1.71406
$445$	17.8205	0.844773
$446$	5.61147	0.265711
$447$	−35.2634	−1.66790
$448$	12.6085	0.595695
$449$	40.8204	1.92643	0.963216	−	0.268728i	$-0.0866034\pi$
$449$	40.8204	1.92643	0.963216	+	0.268728i	$0.0866034\pi$
$450$	35.6152	1.67892
$451$	0.825357	0.0388646
$452$	29.7826	1.40086
$453$	25.5334	1.19966
$454$	−52.3697	−2.45783
$455$	−0.534144	−0.0250411
$456$	−37.3937	−1.75112
$457$	26.1954	1.22537	0.612685	−	0.790327i	$-0.290089\pi$
$457$	26.1954	1.22537	0.612685	+	0.790327i	$0.290089\pi$
$458$	9.66462	0.451598
$459$	−4.85225	−0.226484
$460$	22.4784	1.04806
$461$	−16.9271	−0.788374	−0.394187	−	0.919030i	$-0.628974\pi$
$461$	−16.9271	−0.788374	−0.394187	+	0.919030i	$0.628974\pi$
$462$	4.32690	0.201306
$463$	41.6121	1.93388	0.966939	−	0.255009i	$-0.0820786\pi$
$463$	41.6121	1.93388	0.966939	+	0.255009i	$0.0820786\pi$
$464$	−5.72037	−0.265562
$465$	−2.07634	−0.0962880
$466$	20.1293	0.932473
$467$	2.17141	0.100481	0.0502405	−	0.998737i	$-0.484001\pi$
$467$	2.17141	0.100481	0.0502405	+	0.998737i	$0.484001\pi$
$468$	−6.44380	−0.297865
$469$	−15.6009	−0.720383
$470$	14.6194	0.674341
$471$	20.2862	0.934741
$472$	2.14838	0.0988871
$473$	3.04107	0.139828
$474$	8.70533	0.399849
$475$	14.5128	0.665895
$476$	−3.94577	−0.180854
$477$	34.8563	1.59596
$478$	22.1889	1.01490
$479$	−15.5050	−0.708442	−0.354221	−	0.935162i	$-0.615254\pi$
$479$	−15.5050	−0.708442	−0.354221	+	0.935162i	$0.615254\pi$
$480$	16.8841	0.770648
$481$	1.64731	0.0751108
$482$	42.8518	1.95185
$483$	−14.4251	−0.656365
$484$	−35.5970	−1.61804
$485$	14.0706	0.638911
$486$	−42.6187	−1.93322
$487$	−2.22775	−0.100949	−0.0504745	−	0.998725i	$-0.516073\pi$
$487$	−2.22775	−0.100949	−0.0504745	+	0.998725i	$0.516073\pi$
$488$	26.9032	1.21785
$489$	12.1426	0.549108
$490$	2.93254	0.132478
$491$	39.3837	1.77736	0.888680	−	0.458528i	$-0.151623\pi$
$491$	39.3837	1.77736	0.888680	+	0.458528i	$0.151623\pi$
$492$	11.2317	0.506365
$493$	−10.1770	−0.458347
$494$	−4.18027	−0.188079
$495$	3.88593	0.174660
$496$	−0.393222	−0.0176562
$497$	7.08924	0.317996
$498$	−105.848	−4.74316
$499$	−32.3962	−1.45025	−0.725127	−	0.688615i	$-0.758219\pi$
$499$	−32.3962	−1.45025	−0.725127	+	0.688615i	$0.758219\pi$
$500$	35.8885	1.60498
$501$	68.7899	3.07331
$502$	4.21409	0.188084
$503$	−23.9978	−1.07001	−0.535004	−	0.844849i	$-0.679690\pi$
$503$	−23.9978	−1.07001	−0.535004	+	0.844849i	$0.679690\pi$
$504$	14.4338	0.642932
$505$	9.80019	0.436103
$506$	−8.30505	−0.369204
$507$	35.1494	1.56104
$508$	−22.5229	−0.999290
$509$	−26.7713	−1.18662	−0.593308	−	0.804976i	$-0.702178\pi$
$509$	−26.7713	−1.18662	−0.593308	+	0.804976i	$0.702178\pi$
$510$	−9.38964	−0.415780
$511$	4.67755	0.206922
$512$	7.39460	0.326798
$513$	17.7278	0.782703
$514$	48.6085	2.14403
$515$	11.2273	0.494736
$516$	41.3838	1.82182
$517$	−3.39282	−0.149216
$518$	−9.04399	−0.397370
$519$	32.7445	1.43732
$520$	−1.70741	−0.0748750
$521$	36.7070	1.60816	0.804081	−	0.594519i	$-0.202658\pi$
$521$	36.7070	1.60816	0.804081	+	0.594519i	$0.202658\pi$
$522$	91.2458	3.99372
$523$	−36.7405	−1.60655	−0.803274	−	0.595610i	$-0.796911\pi$
$523$	−36.7405	−1.60655	−0.803274	+	0.595610i	$0.796911\pi$
$524$	25.2475	1.10294
$525$	−9.32370	−0.406920
$526$	−29.9454	−1.30568
$527$	−0.699570	−0.0304737
$528$	1.22486	0.0533054
$529$	4.68751	0.203805
$530$	22.6373	0.983303
$531$	−3.03480	−0.131699
$532$	14.4160	0.625013
$533$	0.512277	0.0221892
$534$	−89.5987	−3.87732
$535$	−23.0399	−0.996103
$536$	−49.8689	−2.15401
$537$	56.9379	2.45705
$538$	0.502790	0.0216768
$539$	−0.680575	−0.0293144
$540$	17.7475	0.763731
$541$	−18.5884	−0.799177	−0.399588	−	0.916695i	$-0.630847\pi$
$541$	−18.5884	−0.799177	−0.399588	+	0.916695i	$0.630847\pi$
$542$	44.6914	1.91966
$543$	55.2705	2.37188
$544$	5.68865	0.243899
$545$	10.8789	0.466002
$546$	2.68559	0.114933
$547$	17.5611	0.750859	0.375429	−	0.926851i	$-0.377495\pi$
$547$	17.5611	0.750859	0.375429	+	0.926851i	$0.377495\pi$
$548$	40.6876	1.73809
$549$	−38.0035	−1.62195
$550$	−5.36799	−0.228892
$551$	37.1818	1.58400
$552$	−46.1105	−1.96259
$553$	−1.36925	−0.0582266
$554$	16.8803	0.717175
$555$	−13.5186	−0.573834
$556$	66.8352	2.83445
$557$	32.4891	1.37661	0.688304	−	0.725422i	$-0.258355\pi$
$557$	32.4891	1.37661	0.688304	+	0.725422i	$0.258355\pi$
$558$	6.27229	0.265527
$559$	1.88751	0.0798331
$560$	0.830146	0.0350801
$561$	2.17912	0.0920026
$562$	9.71946	0.409991
$563$	−1.80808	−0.0762016	−0.0381008	−	0.999274i	$-0.512131\pi$
$563$	−1.80808	−0.0762016	−0.0381008	+	0.999274i	$0.512131\pi$
$564$	−46.1706	−1.94413
$565$	−11.1475	−0.468980
$566$	−40.1388	−1.68716
$567$	2.15715	0.0905918
$568$	22.6611	0.950837
$569$	−32.8722	−1.37808	−0.689038	−	0.724725i	$-0.741967\pi$
$569$	−32.8722	−1.37808	−0.689038	+	0.724725i	$0.741967\pi$
$570$	34.3053	1.43689
$571$	−12.3827	−0.518198	−0.259099	−	0.965851i	$-0.583426\pi$
$571$	−12.3827	−0.518198	−0.259099	+	0.965851i	$0.583426\pi$
$572$	0.971222	0.0406088
$573$	32.1339	1.34241
$574$	−2.81248	−0.117391
$575$	17.8959	0.746310
$576$	−56.9328	−2.37220
$577$	18.8947	0.786597	0.393299	−	0.919411i	$-0.371334\pi$
$577$	18.8947	0.786597	0.393299	+	0.919411i	$0.371334\pi$
$578$	36.2615	1.50828
$579$	36.7625	1.52780
$580$	37.2230	1.54560
$581$	16.6487	0.690705
$582$	−70.7446	−2.93246
$583$	−5.25361	−0.217582
$584$	14.9520	0.618717
$585$	2.41189	0.0997195
$586$	19.3376	0.798829
$587$	−26.3021	−1.08561	−0.542803	−	0.839860i	$-0.682637\pi$
$587$	−26.3021	−1.08561	−0.542803	+	0.839860i	$0.682637\pi$
$588$	−9.26148	−0.381937
$589$	2.55590	0.105314
$590$	−1.97094	−0.0811424
$591$	17.0195	0.700090
$592$	−2.56018	−0.105223
$593$	−28.6904	−1.17817	−0.589087	−	0.808069i	$-0.700513\pi$
$593$	−28.6904	−1.17817	−0.589087	+	0.808069i	$0.700513\pi$
$594$	−6.55714	−0.269043
$595$	1.47689	0.0605465
$596$	43.4561	1.78003
$597$	−3.67077	−0.150235
$598$	−5.15472	−0.210792
$599$	−16.2369	−0.663420	−0.331710	−	0.943381i	$-0.607626\pi$
$599$	−16.2369	−0.663420	−0.331710	+	0.943381i	$0.607626\pi$
$600$	−29.8036	−1.21673
$601$	−15.5794	−0.635496	−0.317748	−	0.948175i	$-0.602927\pi$
$601$	−15.5794	−0.635496	−0.317748	+	0.948175i	$0.602927\pi$
$602$	−10.3627	−0.422353
$603$	70.4449	2.86874
$604$	−31.4655	−1.28031
$605$	13.3238	0.541690
$606$	−49.2738	−2.00161
$607$	−7.74866	−0.314508	−0.157254	−	0.987558i	$-0.550264\pi$
$607$	−7.74866	−0.314508	−0.157254	+	0.987558i	$0.550264\pi$
$608$	−20.7836	−0.842888
$609$	−23.8873	−0.967961
$610$	−24.6813	−0.999315
$611$	−2.10583	−0.0851929
$612$	17.8169	0.720204
$613$	−2.00348	−0.0809197	−0.0404598	−	0.999181i	$-0.512882\pi$
$613$	−2.00348	−0.0809197	−0.0404598	+	0.999181i	$0.512882\pi$
$614$	56.1595	2.26641
$615$	−4.20400	−0.169522
$616$	−2.17549	−0.0876529
$617$	−47.1689	−1.89895	−0.949473	−	0.313848i	$-0.898382\pi$
$617$	−47.1689	−1.89895	−0.949473	+	0.313848i	$0.898382\pi$
$618$	−56.4494	−2.27073
$619$	−5.01393	−0.201527	−0.100763	−	0.994910i	$-0.532129\pi$
$619$	−5.01393	−0.201527	−0.100763	+	0.994910i	$0.532129\pi$
$620$	2.55873	0.102761
$621$	21.8603	0.877224
$622$	−36.2659	−1.45413
$623$	14.0929	0.564620
$624$	0.760241	0.0304340
$625$	3.57223	0.142889
$626$	−12.2861	−0.491051
$627$	−7.96149	−0.317951
$628$	−24.9993	−0.997581
$629$	−4.55475	−0.181610
$630$	−13.2417	−0.527561
$631$	4.18629	0.166654	0.0833269	−	0.996522i	$-0.473445\pi$
$631$	4.18629	0.166654	0.0833269	+	0.996522i	$0.473445\pi$
$632$	−4.37688	−0.174103
$633$	64.1643	2.55030
$634$	−17.1020	−0.679209
$635$	8.43023	0.334543
$636$	−71.4928	−2.83487
$637$	−0.422415	−0.0167367
$638$	−13.7527	−0.544476
$639$	−32.0110	−1.26634
$640$	−24.6571	−0.974658
$641$	−6.65903	−0.263016	−0.131508	−	0.991315i	$-0.541982\pi$
$641$	−6.65903	−0.263016	−0.131508	+	0.991315i	$0.541982\pi$
$642$	115.841	4.57189
$643$	11.2247	0.442658	0.221329	−	0.975199i	$-0.428961\pi$
$643$	11.2247	0.442658	0.221329	+	0.975199i	$0.428961\pi$
$644$	17.7765	0.700491
$645$	−15.4898	−0.609911
$646$	11.5583	0.454755
$647$	1.96116	0.0771010	0.0385505	−	0.999257i	$-0.487726\pi$
$647$	1.96116	0.0771010	0.0385505	+	0.999257i	$0.487726\pi$
$648$	6.89542	0.270878
$649$	0.457411	0.0179549
$650$	−3.33177	−0.130683
$651$	−1.64202	−0.0643560
$652$	−14.9637	−0.586023
$653$	−7.41095	−0.290013	−0.145007	−	0.989431i	$-0.546320\pi$
$653$	−7.41095	−0.290013	−0.145007	+	0.989431i	$0.546320\pi$
$654$	−54.6976	−2.13885
$655$	−9.45007	−0.369245
$656$	−0.796161	−0.0310849
$657$	−21.1212	−0.824015
$658$	11.5614	0.450709
$659$	−25.5928	−0.996955	−0.498477	−	0.866903i	$-0.666107\pi$
$659$	−25.5928	−0.996955	−0.498477	+	0.866903i	$0.666107\pi$
$660$	−7.97032	−0.310244
$661$	−5.37356	−0.209007	−0.104504	−	0.994524i	$-0.533325\pi$
$661$	−5.37356	−0.209007	−0.104504	+	0.994524i	$0.533325\pi$
$662$	6.99502	0.271869
$663$	1.35252	0.0525276
$664$	53.2183	2.06527
$665$	−5.39586	−0.209242
$666$	40.8376	1.58242
$667$	45.8491	1.77529
$668$	−84.7717	−3.27992
$669$	6.63330	0.256458
$670$	45.7502	1.76748
$671$	5.72796	0.221125
$672$	13.3523	0.515078
$673$	33.3251	1.28459	0.642294	−	0.766458i	$-0.277983\pi$
$673$	33.3251	1.28459	0.642294	+	0.766458i	$0.277983\pi$
$674$	43.0584	1.65855
$675$	14.1295	0.543843
$676$	−43.3156	−1.66598
$677$	23.2769	0.894603	0.447302	−	0.894383i	$-0.352385\pi$
$677$	23.2769	0.894603	0.447302	+	0.894383i	$0.352385\pi$
$678$	56.0480	2.15251
$679$	11.1274	0.427029
$680$	4.72094	0.181040
$681$	−61.9061	−2.37225
$682$	−0.945371	−0.0362001
$683$	49.2886	1.88598	0.942988	−	0.332827i	$-0.108003\pi$
$683$	49.2886	1.88598	0.942988	+	0.332827i	$0.108003\pi$
$684$	−65.0945	−2.48895
$685$	−15.2292	−0.581879
$686$	2.31912	0.0885446
$687$	11.4245	0.435872
$688$	−2.93349	−0.111838
$689$	−3.26078	−0.124226
$690$	42.3021	1.61042
$691$	14.8113	0.563450	0.281725	−	0.959495i	$-0.409093\pi$
$691$	14.8113	0.563450	0.281725	+	0.959495i	$0.409093\pi$
$692$	−40.3519	−1.53395
$693$	3.07309	0.116737
$694$	−32.4266	−1.23090
$695$	−25.0162	−0.948919
$696$	−76.3566	−2.89429
$697$	−1.41643	−0.0536510
$698$	25.5576	0.967368
$699$	23.7948	0.900002
$700$	11.4899	0.434276
$701$	12.3254	0.465524	0.232762	−	0.972534i	$-0.425224\pi$
$701$	12.3254	0.465524	0.232762	+	0.972534i	$0.425224\pi$
$702$	−4.06984	−0.153606
$703$	16.6409	0.627624
$704$	8.58102	0.323409
$705$	17.2815	0.650859
$706$	76.7937	2.89017
$707$	7.75024	0.291478
$708$	6.22459	0.233934
$709$	45.6343	1.71383	0.856915	−	0.515457i	$-0.172378\pi$
$709$	45.6343	1.71383	0.856915	+	0.515457i	$0.172378\pi$
$710$	−20.7895	−0.780215
$711$	6.18278	0.231872
$712$	45.0486	1.68827
$713$	3.15170	0.118032
$714$	−7.42557	−0.277895
$715$	−0.363525	−0.0135951
$716$	−70.1661	−2.62223
$717$	26.2294	0.979554
$718$	3.20296	0.119533
$719$	−37.6507	−1.40413	−0.702067	−	0.712111i	$-0.747739\pi$
$719$	−37.6507	−1.40413	−0.702067	+	0.712111i	$0.747739\pi$
$720$	−3.74847	−0.139697
$721$	8.87887	0.330667
$722$	1.83477	0.0682830
$723$	50.6550	1.88388
$724$	−68.1114	−2.53134
$725$	29.6347	1.10061
$726$	−66.9901	−2.48624
$727$	0.968114	0.0359054	0.0179527	−	0.999839i	$-0.494285\pi$
$727$	0.968114	0.0359054	0.0179527	+	0.999839i	$0.494285\pi$
$728$	−1.35027	−0.0500442
$729$	−43.9079	−1.62622
$730$	−13.7171	−0.507692
$731$	−5.21890	−0.193028
$732$	77.9479	2.88104
$733$	−0.140566	−0.00519192	−0.00259596	−	0.999997i	$-0.500826\pi$
$733$	−0.140566	−0.00519192	−0.00259596	+	0.999997i	$0.500826\pi$
$734$	11.2075	0.413675
$735$	3.46654	0.127865
$736$	−25.6285	−0.944677
$737$	−10.6176	−0.391104
$738$	12.6996	0.467478
$739$	33.4940	1.23210	0.616048	−	0.787708i	$-0.288733\pi$
$739$	33.4940	1.23210	0.616048	+	0.787708i	$0.288733\pi$
$740$	16.6594	0.612411
$741$	−4.94148	−0.181530
$742$	17.9022	0.657210
$743$	34.5763	1.26848	0.634241	−	0.773135i	$-0.281313\pi$
$743$	34.5763	1.26848	0.634241	+	0.773135i	$0.281313\pi$
$744$	−5.24880	−0.192430
$745$	−16.2655	−0.595921
$746$	67.8038	2.48247
$747$	−75.1762	−2.75055
$748$	−2.68539	−0.0981877
$749$	−18.2206	−0.665765
$750$	67.5388	2.46617
$751$	11.4887	0.419230	0.209615	−	0.977784i	$-0.432779\pi$
$751$	11.4887	0.419230	0.209615	+	0.977784i	$0.432779\pi$
$752$	3.27280	0.119347
$753$	4.98146	0.181535
$754$	−8.53596	−0.310861
$755$	11.7774	0.428625
$756$	14.0352	0.510454
$757$	−20.1737	−0.733227	−0.366614	−	0.930373i	$-0.619483\pi$
$757$	−20.1737	−0.733227	−0.366614	+	0.930373i	$0.619483\pi$
$758$	−33.2531	−1.20781
$759$	−9.81737	−0.356348
$760$	−17.2481	−0.625654
$761$	24.4770	0.887290	0.443645	−	0.896203i	$-0.353685\pi$
$761$	24.4770	0.887290	0.443645	+	0.896203i	$0.353685\pi$
$762$	−42.3859	−1.53548
$763$	8.60334	0.311462
$764$	−39.5995	−1.43266
$765$	−6.66880	−0.241111
$766$	0.295845	0.0106893
$767$	0.283902	0.0102511
$768$	54.8417	1.97893
$769$	−4.44037	−0.160124	−0.0800618	−	0.996790i	$-0.525512\pi$
$769$	−4.44037	−0.160124	−0.0800618	+	0.996790i	$0.525512\pi$
$770$	1.99581	0.0719240
$771$	57.4599	2.06937
$772$	−45.3034	−1.63051
$773$	30.4717	1.09599	0.547995	−	0.836481i	$-0.315391\pi$
$773$	30.4717	1.09599	0.547995	+	0.836481i	$0.315391\pi$
$774$	46.7922	1.68191
$775$	2.03711	0.0731750
$776$	35.5691	1.27685
$777$	−10.6909	−0.383533
$778$	−69.7056	−2.49907
$779$	5.17496	0.185412
$780$	−4.94696	−0.177130
$781$	4.82476	0.172644
$782$	14.2526	0.509673
$783$	36.1996	1.29367
$784$	0.656500	0.0234464
$785$	9.35716	0.333971
$786$	47.5135	1.69475
$787$	49.0350	1.74791	0.873955	−	0.486006i	$-0.161547\pi$
$787$	49.0350	1.74791	0.873955	+	0.486006i	$0.161547\pi$
$788$	−20.9737	−0.747156
$789$	−35.3984	−1.26021
$790$	4.01539	0.142861
$791$	−8.81575	−0.313452
$792$	9.82327	0.349055
$793$	3.55519	0.126249
$794$	25.7394	0.913458
$795$	26.7595	0.949062
$796$	4.52360	0.160335
$797$	−4.59675	−0.162825	−0.0814126	−	0.996680i	$-0.525943\pi$
$797$	−4.59675	−0.162825	−0.0814126	+	0.996680i	$0.525943\pi$
$798$	27.1295	0.960375
$799$	5.82255	0.205987
$800$	−16.5650	−0.585662
$801$	−63.6356	−2.24845
$802$	−39.4192	−1.39194
$803$	3.18342	0.112340
$804$	−144.487	−5.09568
$805$	−6.65367	−0.234511
$806$	−0.586767	−0.0206680
$807$	0.594347	0.0209220
$808$	24.7740	0.871545
$809$	48.8603	1.71784	0.858919	−	0.512112i	$-0.171137\pi$
$809$	48.8603	1.71784	0.858919	+	0.512112i	$0.171137\pi$
$810$	−6.32592	−0.222270
$811$	−13.1718	−0.462526	−0.231263	−	0.972891i	$-0.574286\pi$
$811$	−13.1718	−0.462526	−0.231263	+	0.972891i	$0.574286\pi$
$812$	29.4369	1.03303
$813$	52.8295	1.85281
$814$	−6.15511	−0.215737
$815$	5.60085	0.196189
$816$	−2.10204	−0.0735861
$817$	19.0674	0.667084
$818$	−21.0655	−0.736539
$819$	1.90739	0.0666495
$820$	5.18070	0.180918
$821$	−15.2998	−0.533966	−0.266983	−	0.963701i	$-0.586027\pi$
$821$	−15.2998	−0.533966	−0.266983	+	0.963701i	$0.586027\pi$
$822$	76.5702	2.67069
$823$	−16.9992	−0.592556	−0.296278	−	0.955102i	$-0.595745\pi$
$823$	−16.9992	−0.592556	−0.296278	+	0.955102i	$0.595745\pi$
$824$	28.3817	0.988723
$825$	−6.34548	−0.220921
$826$	−1.55867	−0.0542331
$827$	−46.3011	−1.61005	−0.805023	−	0.593244i	$-0.797847\pi$
$827$	−46.3011	−1.61005	−0.805023	+	0.593244i	$0.797847\pi$
$828$	−80.2685	−2.78952
$829$	−19.0139	−0.660380	−0.330190	−	0.943914i	$-0.607113\pi$
$829$	−19.0139	−0.660380	−0.330190	+	0.943914i	$0.607113\pi$
$830$	−48.8230	−1.69467
$831$	19.9541	0.692201
$832$	5.32601	0.184646
$833$	1.16796	0.0404675
$834$	125.778	4.35532
$835$	31.7298	1.09805
$836$	9.81117	0.339326
$837$	2.48838	0.0860110
$838$	−65.8377	−2.27433
$839$	−19.7583	−0.682131	−0.341065	−	0.940040i	$-0.610788\pi$
$839$	−19.7583	−0.682131	−0.341065	+	0.940040i	$0.610788\pi$
$840$	11.0809	0.382329
$841$	46.9239	1.61807
$842$	−83.9228	−2.89217
$843$	11.4893	0.395714
$844$	−79.0714	−2.72175
$845$	16.2129	0.557740
$846$	−52.2046	−1.79483
$847$	10.5368	0.362049
$848$	5.06777	0.174028
$849$	−47.4479	−1.62841
$850$	9.21221	0.315976
$851$	20.5200	0.703418
$852$	65.6569	2.24937
$853$	−41.9344	−1.43581	−0.717903	−	0.696143i	$-0.754898\pi$
$853$	−41.9344	−1.43581	−0.717903	+	0.696143i	$0.754898\pi$
$854$	−19.5186	−0.667912
$855$	24.3647	0.833254
$856$	−58.2428	−1.99070
$857$	56.8457	1.94181	0.970906	−	0.239462i	$-0.0769711\pi$
$857$	56.8457	1.94181	0.970906	+	0.239462i	$0.0769711\pi$
$858$	1.82775	0.0623983
$859$	1.00000	0.0341196
$859$	1.00000	0.0341196
$860$	19.0885	0.650914
$861$	−3.32463	−0.113303
$862$	60.3927	2.05698
$863$	58.6174	1.99536	0.997680	−	0.0680747i	$-0.0216856\pi$
$863$	58.6174	1.99536	0.997680	+	0.0680747i	$0.0216856\pi$
$864$	−20.2346	−0.688396
$865$	15.1036	0.513538
$866$	40.5759	1.37883
$867$	42.8646	1.45576
$868$	2.02351	0.0686825
$869$	−0.931881	−0.0316119
$870$	70.0503	2.37493
$871$	−6.59005	−0.223295
$872$	27.5009	0.931299
$873$	−50.2449	−1.70053
$874$	−52.0724	−1.76137
$875$	−10.6231	−0.359127
$876$	43.3210	1.46368
$877$	57.5447	1.94315	0.971573	−	0.236738i	$-0.0760784\pi$
$877$	57.5447	1.94315	0.971573	+	0.236738i	$0.0760784\pi$
$878$	0.630033	0.0212626
$879$	22.8589	0.771012
$880$	0.564976	0.0190454
$881$	−19.7052	−0.663885	−0.331943	−	0.943300i	$-0.607704\pi$
$881$	−19.7052	−0.663885	−0.331943	+	0.943300i	$0.607704\pi$
$882$	−10.4719	−0.352606
$883$	−27.0310	−0.909665	−0.454832	−	0.890577i	$-0.650301\pi$
$883$	−27.0310	−0.909665	−0.454832	+	0.890577i	$0.650301\pi$
$884$	−1.66675	−0.0560589
$885$	−2.32984	−0.0783168
$886$	−53.4633	−1.79613
$887$	42.8934	1.44022	0.720110	−	0.693860i	$-0.244091\pi$
$887$	42.8934	1.44022	0.720110	+	0.693860i	$0.244091\pi$
$888$	−34.1738	−1.14680
$889$	6.66684	0.223599
$890$	−41.3280	−1.38532
$891$	1.46810	0.0491833
$892$	−8.17440	−0.273699
$893$	−21.2729	−0.711870
$894$	81.7803	2.73514
$895$	26.2630	0.877874
$896$	−19.4995	−0.651432
$897$	−6.09338	−0.203452
$898$	−94.6675	−3.15910
$899$	5.21905	0.174065
$900$	−51.8817	−1.72939
$901$	9.01593	0.300364
$902$	−1.91411	−0.0637328
$903$	−12.2497	−0.407646
$904$	−28.1799	−0.937250
$905$	25.4939	0.847445
$906$	−59.2151	−1.96729
$907$	−32.1517	−1.06758	−0.533789	−	0.845618i	$-0.679232\pi$
$907$	−32.1517	−1.06758	−0.533789	+	0.845618i	$0.679232\pi$
$908$	76.2886	2.53173
$909$	−34.9957	−1.16073
$910$	1.23875	0.0410640
$911$	52.6709	1.74507	0.872533	−	0.488556i	$-0.162476\pi$
$911$	52.6709	1.74507	0.872533	+	0.488556i	$0.162476\pi$
$912$	7.67986	0.254306
$913$	11.3307	0.374992
$914$	−60.7505	−2.00945
$915$	−29.1756	−0.964517
$916$	−14.0787	−0.465175
$917$	−7.47336	−0.246792
$918$	11.2530	0.371403
$919$	27.9261	0.921198	0.460599	−	0.887608i	$-0.347635\pi$
$919$	27.9261	0.921198	0.460599	+	0.887608i	$0.347635\pi$
$920$	−21.2687	−0.701209
$921$	66.3860	2.18749
$922$	39.2561	1.29283
$923$	2.99460	0.0985685
$924$	−6.30313	−0.207358
$925$	13.2632	0.436090
$926$	−96.5036	−3.17130
$927$	−40.0920	−1.31679
$928$	−42.4395	−1.39314
$929$	−38.3686	−1.25883	−0.629416	−	0.777068i	$-0.716706\pi$
$929$	−38.3686	−1.25883	−0.629416	+	0.777068i	$0.716706\pi$
$930$	4.81529	0.157900
$931$	−4.26718	−0.139851
$932$	−29.3230	−0.960507
$933$	−42.8698	−1.40349
$934$	−5.03578	−0.164776
$935$	1.00513	0.0328714
$936$	6.09704	0.199288
$937$	8.93159	0.291782	0.145891	−	0.989301i	$-0.453395\pi$
$937$	8.93159	0.291782	0.145891	+	0.989301i	$0.453395\pi$
$938$	36.1804	1.18133
$939$	−14.5233	−0.473952
$940$	−21.2965	−0.694614
$941$	−46.1111	−1.50318	−0.751589	−	0.659632i	$-0.770712\pi$
$941$	−46.1111	−1.50318	−0.751589	+	0.659632i	$0.770712\pi$
$942$	−47.0463	−1.53285
$943$	6.38128	0.207803
$944$	−0.441230	−0.0143608
$945$	−5.25332	−0.170890
$946$	−7.05262	−0.229300
$947$	−33.4053	−1.08553	−0.542764	−	0.839885i	$-0.682622\pi$
$947$	−33.4053	−1.08553	−0.542764	+	0.839885i	$0.682622\pi$
$948$	−12.6813	−0.411870
$949$	1.97586	0.0641393
$950$	−33.6571	−1.09198
$951$	−20.2163	−0.655557
$952$	3.73344	0.121001
$953$	−34.7573	−1.12590	−0.562949	−	0.826491i	$-0.690333\pi$
$953$	−34.7573	−1.12590	−0.562949	+	0.826491i	$0.690333\pi$
$954$	−80.8362	−2.61717
$955$	14.8220	0.479628
$956$	−32.3232	−1.04541
$957$	−16.2571	−0.525517
$958$	35.9580	1.16175
$959$	−12.0437	−0.388910
$960$	−43.7078	−1.41066
$961$	−30.6412	−0.988427
$962$	−3.82031	−0.123172
$963$	82.2738	2.65124
$964$	−62.4236	−2.01053
$965$	16.9569	0.545863
$966$	33.4536	1.07635
$967$	−47.2715	−1.52015	−0.760074	−	0.649837i	$-0.774837\pi$
$967$	−47.2715	−1.52015	−0.760074	+	0.649837i	$0.774837\pi$
$968$	33.6814	1.08256
$969$	13.6630	0.438920
$970$	−32.6314	−1.04773
$971$	5.21113	0.167233	0.0836165	−	0.996498i	$-0.473353\pi$
$971$	5.21113	0.167233	0.0836165	+	0.996498i	$0.473353\pi$
$972$	62.0839	1.99134
$973$	−19.7835	−0.634228
$974$	5.16643	0.165543
$975$	−3.93847	−0.126132
$976$	−5.52534	−0.176862
$977$	−43.9095	−1.40479	−0.702395	−	0.711787i	$-0.747886\pi$
$977$	−43.9095	−1.40479	−0.702395	+	0.711787i	$0.747886\pi$
$978$	−28.1602	−0.900464
$979$	9.59128	0.306539
$980$	−4.27192	−0.136461
$981$	−38.8478	−1.24032
$982$	−91.3356	−2.91464
$983$	40.0609	1.27774	0.638872	−	0.769313i	$-0.279401\pi$
$983$	40.0609	1.27774	0.638872	+	0.769313i	$0.279401\pi$
$984$	−10.6273	−0.338786
$985$	7.85037	0.250134
$986$	23.6016	0.751629
$987$	13.6666	0.435014
$988$	6.08953	0.193734
$989$	23.5121	0.747642
$990$	−9.01196	−0.286419
$991$	−53.1263	−1.68761	−0.843806	−	0.536648i	$-0.819690\pi$
$991$	−53.1263	−1.68761	−0.843806	+	0.536648i	$0.819690\pi$
$992$	−2.91731	−0.0926247
$993$	8.26879	0.262402
$994$	−16.4408	−0.521472
$995$	−1.69317	−0.0536770
$996$	154.192	4.88575
$997$	−36.0235	−1.14088	−0.570438	−	0.821340i	$-0.693227\pi$
$997$	−36.0235	−1.14088	−0.570438	+	0.821340i	$0.693227\pi$
$998$	75.1309	2.37823
$999$	16.2013	0.512587

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.f.1.10	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.f.1.10	✓	110	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.31912 q^{2} -2.74143 q^{3} +3.37834 q^{4} -1.26450 q^{5} +6.35772 q^{6} -1.00000 q^{7} -3.19654 q^{8} +4.51544 q^{9} +O(q^{10})\)	\(q-2.31912 q^{2} -2.74143 q^{3} +3.37834 q^{4} -1.26450 q^{5} +6.35772 q^{6} -1.00000 q^{7} -3.19654 q^{8} +4.51544 q^{9} +2.93254 q^{10} -0.680575 q^{11} -9.26148 q^{12} -0.422415 q^{13} +2.31912 q^{14} +3.46654 q^{15} +0.656500 q^{16} +1.16796 q^{17} -10.4719 q^{18} -4.26718 q^{19} -4.27192 q^{20} +2.74143 q^{21} +1.57834 q^{22} -5.26189 q^{23} +8.76309 q^{24} -3.40104 q^{25} +0.979632 q^{26} -4.15446 q^{27} -3.37834 q^{28} -8.71343 q^{29} -8.03934 q^{30} -0.598966 q^{31} +4.87058 q^{32} +1.86575 q^{33} -2.70865 q^{34} +1.26450 q^{35} +15.2547 q^{36} -3.89974 q^{37} +9.89613 q^{38} +1.15802 q^{39} +4.04203 q^{40} -1.21274 q^{41} -6.35772 q^{42} -4.46838 q^{43} -2.29921 q^{44} -5.70977 q^{45} +12.2030 q^{46} +4.98523 q^{47} -1.79975 q^{48} +1.00000 q^{49} +7.88743 q^{50} -3.20188 q^{51} -1.42706 q^{52} +7.71937 q^{53} +9.63471 q^{54} +0.860588 q^{55} +3.19654 q^{56} +11.6982 q^{57} +20.2075 q^{58} -0.672094 q^{59} +11.7112 q^{60} -8.41636 q^{61} +1.38908 q^{62} -4.51544 q^{63} -12.6085 q^{64} +0.534144 q^{65} -4.32690 q^{66} +15.6009 q^{67} +3.94577 q^{68} +14.4251 q^{69} -2.93254 q^{70} -7.08924 q^{71} -14.4338 q^{72} -4.67755 q^{73} +9.04399 q^{74} +9.32370 q^{75} -14.4160 q^{76} +0.680575 q^{77} -2.68559 q^{78} +1.36925 q^{79} -0.830146 q^{80} -2.15715 q^{81} +2.81248 q^{82} -16.6487 q^{83} +9.26148 q^{84} -1.47689 q^{85} +10.3627 q^{86} +23.8873 q^{87} +2.17549 q^{88} -14.0929 q^{89} +13.2417 q^{90} +0.422415 q^{91} -17.7765 q^{92} +1.64202 q^{93} -11.5614 q^{94} +5.39586 q^{95} -13.3523 q^{96} -11.1274 q^{97} -2.31912 q^{98} -3.07309 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * q^99

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