LMFDB - Embedded newform 6013.2.a.d.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:	$1$
Dimension:	$104$
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)

$f(q)$	$=$	$q-2.49952 q^{2} +2.02668 q^{3} +4.24760 q^{4} +1.29364 q^{5} -5.06572 q^{6} +1.00000 q^{7} -5.61792 q^{8} +1.10742 q^{9} +O(q^{10})$	\(q-2.49952 q^{2} +2.02668 q^{3} +4.24760 q^{4} +1.29364 q^{5} -5.06572 q^{6} +1.00000 q^{7} -5.61792 q^{8} +1.10742 q^{9} -3.23348 q^{10} -0.617161 q^{11} +8.60852 q^{12} -4.73175 q^{13} -2.49952 q^{14} +2.62179 q^{15} +5.54691 q^{16} +1.72713 q^{17} -2.76803 q^{18} +3.17315 q^{19} +5.49486 q^{20} +2.02668 q^{21} +1.54261 q^{22} +5.60704 q^{23} -11.3857 q^{24} -3.32650 q^{25} +11.8271 q^{26} -3.83564 q^{27} +4.24760 q^{28} -5.62995 q^{29} -6.55322 q^{30} -3.55306 q^{31} -2.62876 q^{32} -1.25079 q^{33} -4.31699 q^{34} +1.29364 q^{35} +4.70389 q^{36} -7.51419 q^{37} -7.93135 q^{38} -9.58974 q^{39} -7.26757 q^{40} -5.94601 q^{41} -5.06572 q^{42} -2.82476 q^{43} -2.62145 q^{44} +1.43261 q^{45} -14.0149 q^{46} +4.37769 q^{47} +11.2418 q^{48} +1.00000 q^{49} +8.31464 q^{50} +3.50033 q^{51} -20.0986 q^{52} -10.5926 q^{53} +9.58727 q^{54} -0.798384 q^{55} -5.61792 q^{56} +6.43095 q^{57} +14.0722 q^{58} +3.38794 q^{59} +11.1363 q^{60} +9.91504 q^{61} +8.88094 q^{62} +1.10742 q^{63} -4.52318 q^{64} -6.12118 q^{65} +3.12636 q^{66} -6.63027 q^{67} +7.33614 q^{68} +11.3637 q^{69} -3.23348 q^{70} -5.90084 q^{71} -6.22142 q^{72} +13.1726 q^{73} +18.7819 q^{74} -6.74174 q^{75} +13.4783 q^{76} -0.617161 q^{77} +23.9697 q^{78} +2.45441 q^{79} +7.17570 q^{80} -11.0959 q^{81} +14.8622 q^{82} -13.4839 q^{83} +8.60852 q^{84} +2.23428 q^{85} +7.06055 q^{86} -11.4101 q^{87} +3.46716 q^{88} -3.38391 q^{89} -3.58083 q^{90} -4.73175 q^{91} +23.8165 q^{92} -7.20090 q^{93} -10.9421 q^{94} +4.10491 q^{95} -5.32765 q^{96} +7.65661 q^{97} -2.49952 q^{98} -0.683458 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) $ 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9} - 17 q^{10} - 46 q^{11} - 62 q^{12} - 37 q^{13} - 17 q^{14} - 17 q^{15} + 93 q^{16} - 75 q^{17} - 41 q^{18} - 40 q^{19} - 106 q^{20} - 34 q^{21} - 14 q^{22} - 57 q^{23} - 38 q^{24} + 102 q^{25} - 45 q^{26} - 121 q^{27} + 99 q^{28} - 29 q^{29} + 26 q^{30} - 42 q^{31} - 113 q^{32} - 42 q^{33} - 7 q^{34} - 46 q^{35} + 99 q^{36} - 31 q^{37} - 62 q^{38} - 9 q^{39} - 36 q^{40} - 106 q^{41} - 18 q^{42} - 29 q^{43} - 60 q^{44} - 121 q^{45} + 21 q^{46} - 141 q^{47} - 88 q^{48} + 104 q^{49} - 70 q^{50} - 2 q^{51} - 58 q^{52} - 70 q^{53} - 49 q^{54} - 14 q^{55} - 48 q^{56} - 11 q^{57} - 28 q^{58} - 202 q^{59} + 17 q^{60} - 79 q^{61} - 41 q^{62} + 98 q^{63} + 110 q^{64} - 34 q^{65} - 21 q^{66} - 57 q^{67} - 180 q^{68} - 99 q^{69} - 17 q^{70} - 109 q^{71} - 73 q^{72} - 46 q^{73} - 7 q^{74} - 146 q^{75} - 54 q^{76} - 46 q^{77} - 42 q^{78} - 12 q^{79} - 187 q^{80} + 100 q^{81} - 45 q^{82} - 156 q^{83} - 62 q^{84} - 13 q^{85} - 8 q^{86} - 76 q^{87} - 6 q^{88} - 140 q^{89} - 5 q^{90} - 37 q^{91} - 98 q^{92} - q^{93} - 17 q^{94} - 48 q^{95} - 12 q^{96} - 63 q^{97} - 17 q^{98} - 78 q^{99}+O(q^{100}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9 - 17 * q^10 - 46 * q^11 - 62 * q^12 - 37 * q^13 - 17 * q^14 - 17 * q^15 + 93 * q^16 - 75 * q^17 - 41 * q^18 - 40 * q^19 - 106 * q^20 - 34 * q^21 - 14 * q^22 - 57 * q^23 - 38 * q^24 + 102 * q^25 - 45 * q^26 - 121 * q^27 + 99 * q^28 - 29 * q^29 + 26 * q^30 - 42 * q^31 - 113 * q^32 - 42 * q^33 - 7 * q^34 - 46 * q^35 + 99 * q^36 - 31 * q^37 - 62 * q^38 - 9 * q^39 - 36 * q^40 - 106 * q^41 - 18 * q^42 - 29 * q^43 - 60 * q^44 - 121 * q^45 + 21 * q^46 - 141 * q^47 - 88 * q^48 + 104 * q^49 - 70 * q^50 - 2 * q^51 - 58 * q^52 - 70 * q^53 - 49 * q^54 - 14 * q^55 - 48 * q^56 - 11 * q^57 - 28 * q^58 - 202 * q^59 + 17 * q^60 - 79 * q^61 - 41 * q^62 + 98 * q^63 + 110 * q^64 - 34 * q^65 - 21 * q^66 - 57 * q^67 - 180 * q^68 - 99 * q^69 - 17 * q^70 - 109 * q^71 - 73 * q^72 - 46 * q^73 - 7 * q^74 - 146 * q^75 - 54 * q^76 - 46 * q^77 - 42 * q^78 - 12 * q^79 - 187 * q^80 + 100 * q^81 - 45 * q^82 - 156 * q^83 - 62 * q^84 - 13 * q^85 - 8 * q^86 - 76 * q^87 - 6 * q^88 - 140 * q^89 - 5 * q^90 - 37 * q^91 - 98 * q^92 - q^93 - 17 * q^94 - 48 * q^95 - 12 * q^96 - 63 * q^97 - 17 * q^98 - 78 * 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 $

$2$	−2.49952	−1.76743	−0.883714	−	0.468028i	$-0.844965\pi$
$2$	−2.49952	−1.76743	−0.883714	+	0.468028i	$0.844965\pi$
$3$	2.02668	1.17010	0.585052	−	0.810996i	$-0.301074\pi$
$3$	2.02668	1.17010	0.585052	+	0.810996i	$0.301074\pi$
$4$	4.24760	2.12380
$5$	1.29364	0.578533	0.289267	−	0.957249i	$-0.406589\pi$
$5$	1.29364	0.578533	0.289267	+	0.957249i	$0.406589\pi$
$6$	−5.06572	−2.06807
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−5.61792	−1.98623
$9$	1.10742	0.369141
$10$	−3.23348	−1.02252
$11$	−0.617161	−0.186081	−0.0930405	−	0.995662i	$-0.529659\pi$
$11$	−0.617161	−0.186081	−0.0930405	+	0.995662i	$0.529659\pi$
$12$	8.60852	2.48506
$13$	−4.73175	−1.31235	−0.656176	−	0.754608i	$-0.727827\pi$
$13$	−4.73175	−1.31235	−0.656176	+	0.754608i	$0.727827\pi$
$14$	−2.49952	−0.668025
$15$	2.62179	0.676944
$16$	5.54691	1.38673
$17$	1.72713	0.418890	0.209445	−	0.977820i	$-0.432834\pi$
$17$	1.72713	0.418890	0.209445	+	0.977820i	$0.432834\pi$
$18$	−2.76803	−0.652430
$19$	3.17315	0.727970	0.363985	−	0.931405i	$-0.381416\pi$
$19$	3.17315	0.727970	0.363985	+	0.931405i	$0.381416\pi$
$20$	5.49486	1.22869
$21$	2.02668	0.442257
$22$	1.54261	0.328885
$23$	5.60704	1.16915	0.584575	−	0.811340i	$-0.301261\pi$
$23$	5.60704	1.16915	0.584575	+	0.811340i	$0.301261\pi$
$24$	−11.3857	−2.32410
$25$	−3.32650	−0.665299
$26$	11.8271	2.31949
$27$	−3.83564	−0.738170
$28$	4.24760	0.802721
$29$	−5.62995	−1.04546	−0.522728	−	0.852500i	$-0.675086\pi$
$29$	−5.62995	−1.04546	−0.522728	+	0.852500i	$0.675086\pi$
$30$	−6.55322	−1.19645
$31$	−3.55306	−0.638148	−0.319074	−	0.947730i	$-0.603372\pi$
$31$	−3.55306	−0.638148	−0.319074	+	0.947730i	$0.603372\pi$
$32$	−2.62876	−0.464703
$33$	−1.25079	−0.217734
$34$	−4.31699	−0.740357
$35$	1.29364	0.218665
$36$	4.70389	0.783982
$37$	−7.51419	−1.23533	−0.617663	−	0.786443i	$-0.711920\pi$
$37$	−7.51419	−1.23533	−0.617663	+	0.786443i	$0.711920\pi$
$38$	−7.93135	−1.28663
$39$	−9.58974	−1.53559
$40$	−7.26757	−1.14910
$41$	−5.94601	−0.928610	−0.464305	−	0.885675i	$-0.653696\pi$
$41$	−5.94601	−0.928610	−0.464305	+	0.885675i	$0.653696\pi$
$42$	−5.06572	−0.781658
$43$	−2.82476	−0.430772	−0.215386	−	0.976529i	$-0.569101\pi$
$43$	−2.82476	−0.430772	−0.215386	+	0.976529i	$0.569101\pi$
$44$	−2.62145	−0.395199
$45$	1.43261	0.213560
$46$	−14.0149	−2.06639
$47$	4.37769	0.638551	0.319276	−	0.947662i	$-0.396560\pi$
$47$	4.37769	0.638551	0.319276	+	0.947662i	$0.396560\pi$
$48$	11.2418	1.62261
$49$	1.00000	0.142857
$50$	8.31464	1.17587
$51$	3.50033	0.490144
$52$	−20.0986	−2.78717
$53$	−10.5926	−1.45501	−0.727506	−	0.686102i	$-0.759320\pi$
$53$	−10.5926	−1.45501	−0.727506	+	0.686102i	$0.759320\pi$
$54$	9.58727	1.30466
$55$	−0.798384	−0.107654
$56$	−5.61792	−0.750726
$57$	6.43095	0.851800
$58$	14.0722	1.84777
$59$	3.38794	0.441073	0.220536	−	0.975379i	$-0.429219\pi$
$59$	3.38794	0.441073	0.220536	+	0.975379i	$0.429219\pi$
$60$	11.1363	1.43769
$61$	9.91504	1.26949	0.634745	−	0.772721i	$-0.281105\pi$
$61$	9.91504	1.26949	0.634745	+	0.772721i	$0.281105\pi$
$62$	8.88094	1.12788
$63$	1.10742	0.139522
$64$	−4.52318	−0.565397
$65$	−6.12118	−0.759239
$66$	3.12636	0.384829
$67$	−6.63027	−0.810016	−0.405008	−	0.914313i	$-0.632731\pi$
$67$	−6.63027	−0.810016	−0.405008	+	0.914313i	$0.632731\pi$
$68$	7.33614	0.889638
$69$	11.3637	1.36803
$70$	−3.23348	−0.386475
$71$	−5.90084	−0.700301	−0.350151	−	0.936693i	$-0.613870\pi$
$71$	−5.90084	−0.700301	−0.350151	+	0.936693i	$0.613870\pi$
$72$	−6.22142	−0.733201
$73$	13.1726	1.54173	0.770866	−	0.636998i	$-0.219824\pi$
$73$	13.1726	1.54173	0.770866	+	0.636998i	$0.219824\pi$
$74$	18.7819	2.18335
$75$	−6.74174	−0.778469
$76$	13.4783	1.54606
$77$	−0.617161	−0.0703320
$78$	23.9697	2.71404
$79$	2.45441	0.276143	0.138071	−	0.990422i	$-0.455910\pi$
$79$	2.45441	0.276143	0.138071	+	0.990422i	$0.455910\pi$
$80$	7.17570	0.802267
$81$	−11.0959	−1.23288
$82$	14.8622	1.64125
$83$	−13.4839	−1.48005	−0.740024	−	0.672581i	$-0.765186\pi$
$83$	−13.4839	−1.48005	−0.740024	+	0.672581i	$0.765186\pi$
$84$	8.60852	0.939266
$85$	2.23428	0.242342
$86$	7.06055	0.761358
$87$	−11.4101	−1.22329
$88$	3.46716	0.369600
$89$	−3.38391	−0.358693	−0.179347	−	0.983786i	$-0.557398\pi$
$89$	−3.38391	−0.358693	−0.179347	+	0.983786i	$0.557398\pi$
$90$	−3.58083	−0.377453
$91$	−4.73175	−0.496022
$92$	23.8165	2.48304
$93$	−7.20090	−0.746699
$94$	−10.9421	−1.12859
$95$	4.10491	0.421155
$96$	−5.32765	−0.543751
$97$	7.65661	0.777411	0.388705	−	0.921362i	$-0.372922\pi$
$97$	7.65661	0.777411	0.388705	+	0.921362i	$0.372922\pi$
$98$	−2.49952	−0.252490
$99$	−0.683458	−0.0686901
$100$	−14.1296	−1.41296
$101$	2.80771	0.279378	0.139689	−	0.990195i	$-0.455390\pi$
$101$	2.80771	0.279378	0.139689	+	0.990195i	$0.455390\pi$
$102$	−8.74914	−0.866294
$103$	4.74433	0.467473	0.233736	−	0.972300i	$-0.424905\pi$
$103$	4.74433	0.467473	0.233736	+	0.972300i	$0.424905\pi$
$104$	26.5826	2.60664
$105$	2.62179	0.255861
$106$	26.4765	2.57163
$107$	−3.73897	−0.361460	−0.180730	−	0.983533i	$-0.557846\pi$
$107$	−3.73897	−0.361460	−0.180730	+	0.983533i	$0.557846\pi$
$108$	−16.2923	−1.56773
$109$	−11.3481	−1.08695	−0.543476	−	0.839424i	$-0.682892\pi$
$109$	−11.3481	−1.08695	−0.543476	+	0.839424i	$0.682892\pi$
$110$	1.99558	0.190271
$111$	−15.2289	−1.44546
$112$	5.54691	0.524133
$113$	−18.5626	−1.74622	−0.873111	−	0.487521i	$-0.837901\pi$
$113$	−18.5626	−1.74622	−0.873111	+	0.487521i	$0.837901\pi$
$114$	−16.0743	−1.50550
$115$	7.25350	0.676392
$116$	−23.9138	−2.22034
$117$	−5.24005	−0.484443
$118$	−8.46823	−0.779564
$119$	1.72713	0.158325
$120$	−14.7290	−1.34457
$121$	−10.6191	−0.965374
$122$	−24.7828	−2.24373
$123$	−12.0506	−1.08657
$124$	−15.0920	−1.35530
$125$	−10.7715	−0.963431
$126$	−2.76803	−0.246595
$127$	3.98129	0.353282	0.176641	−	0.984275i	$-0.443477\pi$
$127$	3.98129	0.353282	0.176641	+	0.984275i	$0.443477\pi$
$128$	16.5633	1.46400
$129$	−5.72488	−0.504048
$130$	15.3000	1.34190
$131$	12.9478	1.13125	0.565626	−	0.824662i	$-0.308635\pi$
$131$	12.9478	1.13125	0.565626	+	0.824662i	$0.308635\pi$
$132$	−5.31284	−0.462423
$133$	3.17315	0.275147
$134$	16.5725	1.43164
$135$	−4.96194	−0.427056
$136$	−9.70286	−0.832013
$137$	6.45623	0.551593	0.275796	−	0.961216i	$-0.411058\pi$
$137$	6.45623	0.551593	0.275796	+	0.961216i	$0.411058\pi$
$138$	−28.4037	−2.41789
$139$	2.54627	0.215972	0.107986	−	0.994152i	$-0.465560\pi$
$139$	2.54627	0.215972	0.107986	+	0.994152i	$0.465560\pi$
$140$	5.49486	0.464401
$141$	8.87216	0.747171
$142$	14.7493	1.23773
$143$	2.92025	0.244204
$144$	6.14277	0.511898
$145$	−7.28313	−0.604831
$146$	−32.9251	−2.72490
$147$	2.02668	0.167158
$148$	−31.9173	−2.62359
$149$	−18.9342	−1.55115	−0.775573	−	0.631257i	$-0.782539\pi$
$149$	−18.9342	−1.55115	−0.775573	+	0.631257i	$0.782539\pi$
$150$	16.8511	1.37589
$151$	5.88946	0.479277	0.239639	−	0.970862i	$-0.422971\pi$
$151$	5.88946	0.479277	0.239639	+	0.970862i	$0.422971\pi$
$152$	−17.8265	−1.44592
$153$	1.91266	0.154629
$154$	1.54261	0.124307
$155$	−4.59638	−0.369190
$156$	−40.7334	−3.26128
$157$	2.49497	0.199120	0.0995600	−	0.995032i	$-0.468256\pi$
$157$	2.49497	0.199120	0.0995600	+	0.995032i	$0.468256\pi$
$158$	−6.13484	−0.488062
$159$	−21.4679	−1.70251
$160$	−3.40067	−0.268846
$161$	5.60704	0.441897
$162$	27.7344	2.17902
$163$	9.27728	0.726653	0.363326	−	0.931662i	$-0.381641\pi$
$163$	9.27728	0.726653	0.363326	+	0.931662i	$0.381641\pi$
$164$	−25.2563	−1.97218
$165$	−1.61807	−0.125966
$166$	33.7032	2.61588
$167$	−2.81573	−0.217888	−0.108944	−	0.994048i	$-0.534747\pi$
$167$	−2.81573	−0.217888	−0.108944	+	0.994048i	$0.534747\pi$
$168$	−11.3857	−0.878427
$169$	9.38947	0.722267
$170$	−5.58463	−0.428321
$171$	3.51402	0.268724
$172$	−11.9985	−0.914874
$173$	−8.39093	−0.637951	−0.318975	−	0.947763i	$-0.603339\pi$
$173$	−8.39093	−0.637951	−0.318975	+	0.947763i	$0.603339\pi$
$174$	28.5198	2.16208
$175$	−3.32650	−0.251459
$176$	−3.42333	−0.258043
$177$	6.86627	0.516100
$178$	8.45814	0.633965
$179$	−12.3393	−0.922286	−0.461143	−	0.887326i	$-0.652560\pi$
$179$	−12.3393	−0.922286	−0.461143	+	0.887326i	$0.652560\pi$
$180$	6.08514	0.453560
$181$	3.94316	0.293092	0.146546	−	0.989204i	$-0.453184\pi$
$181$	3.94316	0.293092	0.146546	+	0.989204i	$0.453184\pi$
$182$	11.8271	0.876683
$183$	20.0946	1.48544
$184$	−31.4999	−2.32221
$185$	−9.72066	−0.714677
$186$	17.9988	1.31974
$187$	−1.06591	−0.0779474
$188$	18.5947	1.35615
$189$	−3.83564	−0.279002
$190$	−10.2603	−0.744361
$191$	−17.1487	−1.24083	−0.620417	−	0.784272i	$-0.713037\pi$
$191$	−17.1487	−1.24083	−0.620417	+	0.784272i	$0.713037\pi$
$192$	−9.16702	−0.661573
$193$	−4.55225	−0.327678	−0.163839	−	0.986487i	$-0.552388\pi$
$193$	−4.55225	−0.327678	−0.163839	+	0.986487i	$0.552388\pi$
$194$	−19.1378	−1.37402
$195$	−12.4057	−0.888388
$196$	4.24760	0.303400
$197$	−15.0331	−1.07107	−0.535533	−	0.844514i	$-0.679889\pi$
$197$	−15.0331	−1.07107	−0.535533	+	0.844514i	$0.679889\pi$
$198$	1.70832	0.121405
$199$	8.55208	0.606241	0.303120	−	0.952952i	$-0.401972\pi$
$199$	8.55208	0.606241	0.303120	+	0.952952i	$0.401972\pi$
$200$	18.6880	1.32144
$201$	−13.4374	−0.947803
$202$	−7.01793	−0.493780
$203$	−5.62995	−0.395145
$204$	14.8680	1.04097
$205$	−7.69199	−0.537232
$206$	−11.8585	−0.826224
$207$	6.20937	0.431581
$208$	−26.2466	−1.81987
$209$	−1.95834	−0.135461
$210$	−6.55322	−0.452215
$211$	11.2936	0.777486	0.388743	−	0.921346i	$-0.372909\pi$
$211$	11.2936	0.777486	0.388743	+	0.921346i	$0.372909\pi$
$212$	−44.9933	−3.09015
$213$	−11.9591	−0.819424
$214$	9.34563	0.638854
$215$	−3.65422	−0.249216
$216$	21.5483	1.46618
$217$	−3.55306	−0.241197
$218$	28.3649	1.92111
$219$	26.6965	1.80398
$220$	−3.39121	−0.228636
$221$	−8.17233	−0.549731
$222$	38.0648	2.55474
$223$	18.2535	1.22234	0.611172	−	0.791498i	$-0.290699\pi$
$223$	18.2535	1.22234	0.611172	+	0.791498i	$0.290699\pi$
$224$	−2.62876	−0.175641
$225$	−3.68384	−0.245589
$226$	46.3976	3.08632
$227$	−26.8336	−1.78101	−0.890503	−	0.454977i	$-0.849648\pi$
$227$	−26.8336	−1.78101	−0.890503	+	0.454977i	$0.849648\pi$
$228$	27.3161	1.80905
$229$	−20.7969	−1.37430	−0.687149	−	0.726517i	$-0.741138\pi$
$229$	−20.7969	−1.37430	−0.687149	+	0.726517i	$0.741138\pi$
$230$	−18.1303	−1.19547
$231$	−1.25079	−0.0822957
$232$	31.6286	2.07652
$233$	−28.2610	−1.85144	−0.925721	−	0.378206i	$-0.876541\pi$
$233$	−28.2610	−1.85144	−0.925721	+	0.378206i	$0.876541\pi$
$234$	13.0976	0.856218
$235$	5.66315	0.369423
$236$	14.3906	0.936750
$237$	4.97430	0.323115
$238$	−4.31699	−0.279829
$239$	10.8885	0.704320	0.352160	−	0.935940i	$-0.385447\pi$
$239$	10.8885	0.704320	0.352160	+	0.935940i	$0.385447\pi$
$240$	14.5428	0.938735
$241$	2.91740	0.187926	0.0939630	−	0.995576i	$-0.470046\pi$
$241$	2.91740	0.187926	0.0939630	+	0.995576i	$0.470046\pi$
$242$	26.5427	1.70623
$243$	−10.9809	−0.704422
$244$	42.1151	2.69614
$245$	1.29364	0.0826476
$246$	30.1208	1.92043
$247$	−15.0146	−0.955353
$248$	19.9608	1.26751
$249$	−27.3275	−1.73181
$250$	26.9235	1.70279
$251$	−9.40397	−0.593573	−0.296787	−	0.954944i	$-0.595915\pi$
$251$	−9.40397	−0.593573	−0.296787	+	0.954944i	$0.595915\pi$
$252$	4.70389	0.296317
$253$	−3.46045	−0.217556
$254$	−9.95130	−0.624400
$255$	4.52816	0.283565
$256$	−32.3539	−2.02212
$257$	0.108587	0.00677350	0.00338675	−	0.999994i	$-0.498922\pi$
$257$	0.108587	0.00677350	0.00338675	+	0.999994i	$0.498922\pi$
$258$	14.3095	0.890868
$259$	−7.51419	−0.466909
$260$	−26.0003	−1.61247
$261$	−6.23474	−0.385921
$262$	−32.3632	−1.99941
$263$	15.4953	0.955478	0.477739	−	0.878502i	$-0.341456\pi$
$263$	15.4953	0.955478	0.477739	+	0.878502i	$0.341456\pi$
$264$	7.02682	0.432471
$265$	−13.7031	−0.841772
$266$	−7.93135	−0.486302
$267$	−6.85809	−0.419708
$268$	−28.1627	−1.72031
$269$	22.0090	1.34191	0.670957	−	0.741496i	$-0.265883\pi$
$269$	22.0090	1.34191	0.670957	+	0.741496i	$0.265883\pi$
$270$	12.4025	0.754790
$271$	11.2930	0.686001	0.343000	−	0.939335i	$-0.388557\pi$
$271$	11.2930	0.686001	0.343000	+	0.939335i	$0.388557\pi$
$272$	9.58021	0.580885
$273$	−9.58974	−0.580397
$274$	−16.1375	−0.974900
$275$	2.05298	0.123799
$276$	48.2683	2.90541
$277$	−29.9053	−1.79684	−0.898418	−	0.439141i	$-0.855283\pi$
$277$	−29.9053	−1.79684	−0.898418	+	0.439141i	$0.855283\pi$
$278$	−6.36445	−0.381714
$279$	−3.93474	−0.235567
$280$	−7.26757	−0.434320
$281$	5.23889	0.312526	0.156263	−	0.987715i	$-0.450055\pi$
$281$	5.23889	0.312526	0.156263	+	0.987715i	$0.450055\pi$
$282$	−22.1761	−1.32057
$283$	28.1117	1.67106	0.835532	−	0.549441i	$-0.185159\pi$
$283$	28.1117	1.67106	0.835532	+	0.549441i	$0.185159\pi$
$284$	−25.0644	−1.48730
$285$	8.31934	0.492795
$286$	−7.29922	−0.431612
$287$	−5.94601	−0.350982
$288$	−2.91115	−0.171541
$289$	−14.0170	−0.824531
$290$	18.2043	1.06899
$291$	15.5175	0.909651
$292$	55.9518	3.27433
$293$	−10.0334	−0.586159	−0.293080	−	0.956088i	$-0.594680\pi$
$293$	−10.0334	−0.586159	−0.293080	+	0.956088i	$0.594680\pi$
$294$	−5.06572	−0.295439
$295$	4.38278	0.255175
$296$	42.2141	2.45365
$297$	2.36721	0.137359
$298$	47.3263	2.74154
$299$	−26.5311	−1.53434
$300$	−28.6362	−1.65331
$301$	−2.82476	−0.162817
$302$	−14.7208	−0.847088
$303$	5.69033	0.326901
$304$	17.6012	1.00950
$305$	12.8265	0.734443
$306$	−4.78073	−0.273296
$307$	5.53668	0.315995	0.157997	−	0.987440i	$-0.449496\pi$
$307$	5.53668	0.315995	0.157997	+	0.987440i	$0.449496\pi$
$308$	−2.62145	−0.149371
$309$	9.61523	0.546991
$310$	11.4887	0.652516
$311$	7.79136	0.441807	0.220904	−	0.975296i	$-0.429099\pi$
$311$	7.79136	0.441807	0.220904	+	0.975296i	$0.429099\pi$
$312$	53.8744	3.05004
$313$	2.67744	0.151338	0.0756690	−	0.997133i	$-0.475891\pi$
$313$	2.67744	0.151338	0.0756690	+	0.997133i	$0.475891\pi$
$314$	−6.23622	−0.351930
$315$	1.43261	0.0807183
$316$	10.4253	0.586472
$317$	8.51106	0.478029	0.239015	−	0.971016i	$-0.423176\pi$
$317$	8.51106	0.478029	0.239015	+	0.971016i	$0.423176\pi$
$318$	53.6594	3.00907
$319$	3.47458	0.194539
$320$	−5.85136	−0.327101
$321$	−7.57769	−0.422945
$322$	−14.0149	−0.781021
$323$	5.48043	0.304939
$324$	−47.1309	−2.61838
$325$	15.7402	0.873107
$326$	−23.1888	−1.28431
$327$	−22.9990	−1.27185
$328$	33.4042	1.84444
$329$	4.37769	0.241350
$330$	4.04439	0.222636
$331$	−8.36062	−0.459541	−0.229771	−	0.973245i	$-0.573798\pi$
$331$	−8.36062	−0.459541	−0.229771	+	0.973245i	$0.573798\pi$
$332$	−57.2741	−3.14333
$333$	−8.32140	−0.456010
$334$	7.03797	0.385101
$335$	−8.57718	−0.468621
$336$	11.2418	0.613290
$337$	−2.55793	−0.139339	−0.0696695	−	0.997570i	$-0.522194\pi$
$337$	−2.55793	−0.139339	−0.0696695	+	0.997570i	$0.522194\pi$
$338$	−23.4692	−1.27655
$339$	−37.6204	−2.04326
$340$	9.49032	0.514685
$341$	2.19281	0.118747
$342$	−8.78336	−0.474950
$343$	1.00000	0.0539949
$344$	15.8693	0.855615
$345$	14.7005	0.791448
$346$	20.9733	1.12753
$347$	30.2980	1.62648	0.813240	−	0.581928i	$-0.197701\pi$
$347$	30.2980	1.62648	0.813240	+	0.581928i	$0.197701\pi$
$348$	−48.4655	−2.59803
$349$	−7.03116	−0.376369	−0.188185	−	0.982134i	$-0.560260\pi$
$349$	−7.03116	−0.376369	−0.188185	+	0.982134i	$0.560260\pi$
$350$	8.31464	0.444436
$351$	18.1493	0.968738
$352$	1.62237	0.0864724
$353$	−23.7214	−1.26256	−0.631282	−	0.775553i	$-0.717471\pi$
$353$	−23.7214	−1.26256	−0.631282	+	0.775553i	$0.717471\pi$
$354$	−17.1624	−0.912170
$355$	−7.63356	−0.405148
$356$	−14.3735	−0.761793
$357$	3.50033	0.185257
$358$	30.8424	1.63007
$359$	33.8044	1.78413	0.892065	−	0.451907i	$-0.149256\pi$
$359$	33.8044	1.78413	0.892065	+	0.451907i	$0.149256\pi$
$360$	−8.04827	−0.424181
$361$	−8.93112	−0.470059
$362$	−9.85600	−0.518020
$363$	−21.5215	−1.12959
$364$	−20.0986	−1.05345
$365$	17.0405	0.891943
$366$	−50.2268	−2.62540
$367$	1.02649	0.0535825	0.0267913	−	0.999641i	$-0.491471\pi$
$367$	1.02649	0.0535825	0.0267913	+	0.999641i	$0.491471\pi$
$368$	31.1017	1.62129
$369$	−6.58475	−0.342788
$370$	24.2970	1.26314
$371$	−10.5926	−0.549943
$372$	−30.5866	−1.58584
$373$	−7.96742	−0.412538	−0.206269	−	0.978495i	$-0.566132\pi$
$373$	−7.96742	−0.412538	−0.206269	+	0.978495i	$0.566132\pi$
$374$	2.66427	0.137766
$375$	−21.8303	−1.12731
$376$	−24.5935	−1.26831
$377$	26.6395	1.37201
$378$	9.58727	0.493116
$379$	25.9307	1.33197	0.665986	−	0.745964i	$-0.268011\pi$
$379$	25.9307	1.33197	0.665986	+	0.745964i	$0.268011\pi$
$380$	17.4360	0.894449
$381$	8.06878	0.413376
$382$	42.8634	2.19308
$383$	5.69375	0.290937	0.145469	−	0.989363i	$-0.453531\pi$
$383$	5.69375	0.290937	0.145469	+	0.989363i	$0.453531\pi$
$384$	33.5684	1.71303
$385$	−0.798384	−0.0406894
$386$	11.3784	0.579147
$387$	−3.12821	−0.159016
$388$	32.5222	1.65106
$389$	7.90126	0.400610	0.200305	−	0.979734i	$-0.435807\pi$
$389$	7.90126	0.400610	0.200305	+	0.979734i	$0.435807\pi$
$390$	31.0082	1.57016
$391$	9.68407	0.489745
$392$	−5.61792	−0.283748
$393$	26.2410	1.32368
$394$	37.5756	1.89303
$395$	3.17512	0.159758
$396$	−2.90306	−0.145884
$397$	−18.3231	−0.919611	−0.459806	−	0.888020i	$-0.652081\pi$
$397$	−18.3231	−0.919611	−0.459806	+	0.888020i	$0.652081\pi$
$398$	−21.3761	−1.07149
$399$	6.43095	0.321950
$400$	−18.4518	−0.922588
$401$	−16.2661	−0.812290	−0.406145	−	0.913809i	$-0.633127\pi$
$401$	−16.2661	−0.812290	−0.406145	+	0.913809i	$0.633127\pi$
$402$	33.5871	1.67517
$403$	16.8122	0.837474
$404$	11.9260	0.593342
$405$	−14.3541	−0.713260
$406$	14.0722	0.698390
$407$	4.63746	0.229871
$408$	−19.6646	−0.973541
$409$	−4.52362	−0.223679	−0.111839	−	0.993726i	$-0.535674\pi$
$409$	−4.52362	−0.223679	−0.111839	+	0.993726i	$0.535674\pi$
$410$	19.2263	0.949518
$411$	13.0847	0.645420
$412$	20.1520	0.992818
$413$	3.38794	0.166710
$414$	−15.5205	−0.762789
$415$	−17.4433	−0.856257
$416$	12.4386	0.609854
$417$	5.16047	0.252709
$418$	4.89492	0.239418
$419$	−9.39915	−0.459178	−0.229589	−	0.973288i	$-0.573738\pi$
$419$	−9.39915	−0.459178	−0.229589	+	0.973288i	$0.573738\pi$
$420$	11.1363	0.543397
$421$	27.2623	1.32868	0.664342	−	0.747429i	$-0.268712\pi$
$421$	27.2623	1.32868	0.664342	+	0.747429i	$0.268712\pi$
$422$	−28.2287	−1.37415
$423$	4.84795	0.235716
$424$	59.5086	2.88999
$425$	−5.74528	−0.278687
$426$	29.8920	1.44827
$427$	9.91504	0.479822
$428$	−15.8817	−0.767669
$429$	5.91841	0.285743
$430$	9.13381	0.440471
$431$	6.20202	0.298741	0.149370	−	0.988781i	$-0.452275\pi$
$431$	6.20202	0.298741	0.149370	+	0.988781i	$0.452275\pi$
$432$	−21.2759	−1.02364
$433$	22.2835	1.07088	0.535438	−	0.844575i	$-0.320147\pi$
$433$	22.2835	1.07088	0.535438	+	0.844575i	$0.320147\pi$
$434$	8.88094	0.426299
$435$	−14.7606	−0.707715
$436$	−48.2023	−2.30847
$437$	17.7920	0.851106
$438$	−66.7285	−3.18841
$439$	7.41196	0.353753	0.176877	−	0.984233i	$-0.443401\pi$
$439$	7.41196	0.353753	0.176877	+	0.984233i	$0.443401\pi$
$440$	4.48526	0.213826
$441$	1.10742	0.0527345
$442$	20.4269	0.971609
$443$	−26.7988	−1.27325	−0.636624	−	0.771174i	$-0.719670\pi$
$443$	−26.7988	−1.27325	−0.636624	+	0.771174i	$0.719670\pi$
$444$	−64.6861	−3.06987
$445$	−4.37756	−0.207516
$446$	−45.6249	−2.16040
$447$	−38.3734	−1.81500
$448$	−4.52318	−0.213700
$449$	−25.8779	−1.22125	−0.610627	−	0.791919i	$-0.709082\pi$
$449$	−25.8779	−1.22125	−0.610627	+	0.791919i	$0.709082\pi$
$450$	9.20783	0.434061
$451$	3.66964	0.172797
$452$	−78.8465	−3.70863
$453$	11.9360	0.560804
$454$	67.0711	3.14780
$455$	−6.12118	−0.286965
$456$	−36.1286	−1.69188
$457$	15.8453	0.741211	0.370605	−	0.928790i	$-0.379150\pi$
$457$	15.8453	0.741211	0.370605	+	0.928790i	$0.379150\pi$
$458$	51.9822	2.42897
$459$	−6.62464	−0.309212
$460$	30.8099	1.43652
$461$	16.5894	0.772647	0.386324	−	0.922363i	$-0.373745\pi$
$461$	16.5894	0.772647	0.386324	+	0.922363i	$0.373745\pi$
$462$	3.12636	0.145452
$463$	16.3248	0.758675	0.379338	−	0.925258i	$-0.376152\pi$
$463$	16.3248	0.758675	0.379338	+	0.925258i	$0.376152\pi$
$464$	−31.2288	−1.44976
$465$	−9.31537	−0.431990
$466$	70.6390	3.27229
$467$	10.8257	0.500954	0.250477	−	0.968123i	$-0.419413\pi$
$467$	10.8257	0.500954	0.250477	+	0.968123i	$0.419413\pi$
$468$	−22.2576	−1.02886
$469$	−6.63027	−0.306157
$470$	−14.1552	−0.652929
$471$	5.05650	0.232991
$472$	−19.0332	−0.876074
$473$	1.74333	0.0801585
$474$	−12.4334	−0.571083
$475$	−10.5555	−0.484318
$476$	7.33614	0.336252
$477$	−11.7305	−0.537105
$478$	−27.2161	−1.24483
$479$	33.8030	1.54450	0.772250	−	0.635318i	$-0.219131\pi$
$479$	33.8030	1.54450	0.772250	+	0.635318i	$0.219131\pi$
$480$	−6.89206	−0.314578
$481$	35.5553	1.62118
$482$	−7.29209	−0.332146
$483$	11.3637	0.517065
$484$	−45.1057	−2.05026
$485$	9.90489	0.449758
$486$	27.4469	1.24502
$487$	−37.4612	−1.69753	−0.848765	−	0.528770i	$-0.822653\pi$
$487$	−37.4612	−1.69753	−0.848765	+	0.528770i	$0.822653\pi$
$488$	−55.7019	−2.52151
$489$	18.8021	0.850259
$490$	−3.23348	−0.146074
$491$	−19.5660	−0.883000	−0.441500	−	0.897261i	$-0.645553\pi$
$491$	−19.5660	−0.883000	−0.441500	+	0.897261i	$0.645553\pi$
$492$	−51.1863	−2.30766
$493$	−9.72364	−0.437931
$494$	37.5292	1.68852
$495$	−0.884149	−0.0397395
$496$	−19.7085	−0.884936
$497$	−5.90084	−0.264689
$498$	68.3056	3.06085
$499$	12.6160	0.564768	0.282384	−	0.959302i	$-0.408875\pi$
$499$	12.6160	0.564768	0.282384	+	0.959302i	$0.408875\pi$
$500$	−45.7530	−2.04613
$501$	−5.70658	−0.254951
$502$	23.5054	1.04910
$503$	16.2901	0.726342	0.363171	−	0.931723i	$-0.381694\pi$
$503$	16.2901	0.726342	0.363171	+	0.931723i	$0.381694\pi$
$504$	−6.22142	−0.277124
$505$	3.63217	0.161629
$506$	8.64946	0.384515
$507$	19.0294	0.845127
$508$	16.9109	0.750300
$509$	−27.0239	−1.19781	−0.598906	−	0.800820i	$-0.704398\pi$
$509$	−27.0239	−1.19781	−0.598906	+	0.800820i	$0.704398\pi$
$510$	−11.3182	−0.501180
$511$	13.1726	0.582720
$512$	47.7427	2.10995
$513$	−12.1711	−0.537366
$514$	−0.271416	−0.0119717
$515$	6.13745	0.270448
$516$	−24.3170	−1.07050
$517$	−2.70174	−0.118822
$518$	18.7819	0.825228
$519$	−17.0057	−0.746468
$520$	34.3883	1.50803
$521$	−8.80083	−0.385571	−0.192786	−	0.981241i	$-0.561752\pi$
$521$	−8.80083	−0.385571	−0.192786	+	0.981241i	$0.561752\pi$
$522$	15.5839	0.682087
$523$	41.8762	1.83112	0.915558	−	0.402186i	$-0.131749\pi$
$523$	41.8762	1.83112	0.915558	+	0.402186i	$0.131749\pi$
$524$	54.9970	2.40255
$525$	−6.74174	−0.294233
$526$	−38.7307	−1.68874
$527$	−6.13658	−0.267314
$528$	−6.93799	−0.301937
$529$	8.43895	0.366911
$530$	34.2511	1.48777
$531$	3.75189	0.162818
$532$	13.4783	0.584357
$533$	28.1350	1.21866
$534$	17.1419	0.741804
$535$	−4.83688	−0.209117
$536$	37.2483	1.60888
$537$	−25.0079	−1.07917
$538$	−55.0120	−2.37174
$539$	−0.617161	−0.0265830
$540$	−21.0763	−0.906981
$541$	−8.97285	−0.385773	−0.192887	−	0.981221i	$-0.561785\pi$
$541$	−8.97285	−0.385773	−0.192887	+	0.981221i	$0.561785\pi$
$542$	−28.2271	−1.21246
$543$	7.99151	0.342948
$544$	−4.54020	−0.194659
$545$	−14.6804	−0.628838
$546$	23.9697	1.02581
$547$	−30.3243	−1.29657	−0.648286	−	0.761397i	$-0.724514\pi$
$547$	−30.3243	−1.29657	−0.648286	+	0.761397i	$0.724514\pi$
$548$	27.4235	1.17147
$549$	10.9801	0.468621
$550$	−5.13147	−0.218807
$551$	−17.8647	−0.761061
$552$	−63.8402	−2.71722
$553$	2.45441	0.104372
$554$	74.7489	3.17578
$555$	−19.7006	−0.836246
$556$	10.8155	0.458681
$557$	−16.4788	−0.698229	−0.349114	−	0.937080i	$-0.613518\pi$
$557$	−16.4788	−0.698229	−0.349114	+	0.937080i	$0.613518\pi$
$558$	9.83496	0.416347
$559$	13.3661	0.565324
$560$	7.17570	0.303229
$561$	−2.16027	−0.0912065
$562$	−13.0947	−0.552367
$563$	16.0329	0.675707	0.337853	−	0.941199i	$-0.390299\pi$
$563$	16.0329	0.675707	0.337853	+	0.941199i	$0.390299\pi$
$564$	37.6854	1.58684
$565$	−24.0133	−1.01025
$566$	−70.2656	−2.95349
$567$	−11.0959	−0.465983
$568$	33.1505	1.39096
$569$	−16.1904	−0.678736	−0.339368	−	0.940654i	$-0.610213\pi$
$569$	−16.1904	−0.678736	−0.339368	+	0.940654i	$0.610213\pi$
$570$	−20.7943	−0.870979
$571$	6.87267	0.287612	0.143806	−	0.989606i	$-0.454066\pi$
$571$	6.87267	0.287612	0.143806	+	0.989606i	$0.454066\pi$
$572$	12.4041	0.518640
$573$	−34.7548	−1.45190
$574$	14.8622	0.620334
$575$	−18.6518	−0.777834
$576$	−5.00907	−0.208711
$577$	7.06855	0.294267	0.147134	−	0.989117i	$-0.452995\pi$
$577$	7.06855	0.294267	0.147134	+	0.989117i	$0.452995\pi$
$578$	35.0359	1.45730
$579$	−9.22594	−0.383417
$580$	−30.9358	−1.28454
$581$	−13.4839	−0.559405
$582$	−38.7862	−1.60774
$583$	6.53736	0.270750
$584$	−74.0024	−3.06224
$585$	−6.77874	−0.280266
$586$	25.0788	1.03599
$587$	−32.3049	−1.33337	−0.666684	−	0.745341i	$-0.732287\pi$
$587$	−32.3049	−1.33337	−0.666684	+	0.745341i	$0.732287\pi$
$588$	8.60852	0.355009
$589$	−11.2744	−0.464553
$590$	−10.9548	−0.451004
$591$	−30.4673	−1.25326
$592$	−41.6805	−1.71306
$593$	−27.4103	−1.12561	−0.562803	−	0.826591i	$-0.690277\pi$
$593$	−27.4103	−1.12561	−0.562803	+	0.826591i	$0.690277\pi$
$594$	−5.91688	−0.242773
$595$	2.23428	0.0915965
$596$	−80.4247	−3.29433
$597$	17.3323	0.709364
$598$	66.3151	2.71183
$599$	22.3688	0.913965	0.456983	−	0.889476i	$-0.348930\pi$
$599$	22.3688	0.913965	0.456983	+	0.889476i	$0.348930\pi$
$600$	37.8745	1.54622
$601$	−0.646354	−0.0263653	−0.0131827	−	0.999913i	$-0.504196\pi$
$601$	−0.646354	−0.0263653	−0.0131827	+	0.999913i	$0.504196\pi$
$602$	7.06055	0.287766
$603$	−7.34252	−0.299010
$604$	25.0161	1.01789
$605$	−13.7373	−0.558501
$606$	−14.2231	−0.577773
$607$	−11.4561	−0.464988	−0.232494	−	0.972598i	$-0.574689\pi$
$607$	−11.4561	−0.464988	−0.232494	+	0.972598i	$0.574689\pi$
$608$	−8.34144	−0.338290
$609$	−11.4101	−0.462361
$610$	−32.0601	−1.29807
$611$	−20.7141	−0.838004
$612$	8.12422	0.328402
$613$	28.1781	1.13810	0.569050	−	0.822303i	$-0.307311\pi$
$613$	28.1781	1.13810	0.569050	+	0.822303i	$0.307311\pi$
$614$	−13.8390	−0.558498
$615$	−15.5892	−0.628617
$616$	3.46716	0.139696
$617$	43.6940	1.75906	0.879528	−	0.475847i	$-0.157859\pi$
$617$	43.6940	1.75906	0.879528	+	0.475847i	$0.157859\pi$
$618$	−24.0335	−0.966767
$619$	13.9418	0.560369	0.280185	−	0.959946i	$-0.409604\pi$
$619$	13.9418	0.560369	0.280185	+	0.959946i	$0.409604\pi$
$620$	−19.5236	−0.784085
$621$	−21.5066	−0.863031
$622$	−19.4747	−0.780863
$623$	−3.38391	−0.135573
$624$	−53.1934	−2.12944
$625$	2.69806	0.107922
$626$	−6.69232	−0.267479
$627$	−3.96893	−0.158504
$628$	10.5976	0.422891
$629$	−12.9780	−0.517465
$630$	−3.58083	−0.142664
$631$	−10.5709	−0.420823	−0.210411	−	0.977613i	$-0.567480\pi$
$631$	−10.5709	−0.420823	−0.210411	+	0.977613i	$0.567480\pi$
$632$	−13.7887	−0.548484
$633$	22.8886	0.909739
$634$	−21.2736	−0.844882
$635$	5.15035	0.204385
$636$	−91.1869	−3.61580
$637$	−4.73175	−0.187479
$638$	−8.68479	−0.343834
$639$	−6.53473	−0.258510
$640$	21.4269	0.846974
$641$	7.18624	0.283839	0.141920	−	0.989878i	$-0.454673\pi$
$641$	7.18624	0.283839	0.141920	+	0.989878i	$0.454673\pi$
$642$	18.9406	0.747525
$643$	−29.1217	−1.14845	−0.574223	−	0.818699i	$-0.694696\pi$
$643$	−29.1217	−1.14845	−0.574223	+	0.818699i	$0.694696\pi$
$644$	23.8165	0.938501
$645$	−7.40594	−0.291608
$646$	−13.6984	−0.538958
$647$	−44.9080	−1.76552	−0.882759	−	0.469827i	$-0.844316\pi$
$647$	−44.9080	−1.76552	−0.882759	+	0.469827i	$0.844316\pi$
$648$	62.3358	2.44878
$649$	−2.09090	−0.0820752
$650$	−39.3428	−1.54315
$651$	−7.20090	−0.282226
$652$	39.4062	1.54327
$653$	−5.35826	−0.209685	−0.104843	−	0.994489i	$-0.533434\pi$
$653$	−5.35826	−0.209685	−0.104843	+	0.994489i	$0.533434\pi$
$654$	57.4864	2.24790
$655$	16.7498	0.654467
$656$	−32.9819	−1.28773
$657$	14.5876	0.569117
$658$	−10.9421	−0.426568
$659$	−6.17168	−0.240414	−0.120207	−	0.992749i	$-0.538356\pi$
$659$	−6.17168	−0.240414	−0.120207	+	0.992749i	$0.538356\pi$
$660$	−6.87290	−0.267527
$661$	−33.3505	−1.29718	−0.648592	−	0.761137i	$-0.724642\pi$
$661$	−33.3505	−1.29718	−0.648592	+	0.761137i	$0.724642\pi$
$662$	20.8975	0.812206
$663$	−16.5627	−0.643241
$664$	75.7513	2.93972
$665$	4.10491	0.159182
$666$	20.7995	0.805964
$667$	−31.5674	−1.22229
$668$	−11.9601	−0.462750
$669$	36.9939	1.43027
$670$	21.4388	0.828254
$671$	−6.11917	−0.236228
$672$	−5.32765	−0.205518
$673$	−0.468547	−0.0180611	−0.00903057	−	0.999959i	$-0.502875\pi$
$673$	−0.468547	−0.0180611	−0.00903057	+	0.999959i	$0.502875\pi$
$674$	6.39359	0.246272
$675$	12.7593	0.491104
$676$	39.8827	1.53395
$677$	−11.7398	−0.451198	−0.225599	−	0.974220i	$-0.572434\pi$
$677$	−11.7398	−0.451198	−0.225599	+	0.974220i	$0.572434\pi$
$678$	94.0329	3.61131
$679$	7.65661	0.293834
$680$	−12.5520	−0.481347
$681$	−54.3830	−2.08396
$682$	−5.48096	−0.209877
$683$	21.8049	0.834341	0.417170	−	0.908828i	$-0.363022\pi$
$683$	21.8049	0.834341	0.417170	+	0.908828i	$0.363022\pi$
$684$	14.9262	0.570716
$685$	8.35203	0.319115
$686$	−2.49952	−0.0954321
$687$	−42.1486	−1.60807
$688$	−15.6687	−0.597363
$689$	50.1217	1.90949
$690$	−36.7442	−1.39883
$691$	−32.6199	−1.24092	−0.620459	−	0.784239i	$-0.713054\pi$
$691$	−32.6199	−1.24092	−0.620459	+	0.784239i	$0.713054\pi$
$692$	−35.6413	−1.35488
$693$	−0.683458	−0.0259624
$694$	−75.7304	−2.87469
$695$	3.29396	0.124947
$696$	64.1010	2.42974
$697$	−10.2695	−0.388985
$698$	17.5745	0.665205
$699$	−57.2760	−2.16638
$700$	−14.1296	−0.534050
$701$	40.7172	1.53787	0.768934	−	0.639329i	$-0.220788\pi$
$701$	40.7172	1.53787	0.768934	+	0.639329i	$0.220788\pi$
$702$	−45.3646	−1.71217
$703$	−23.8437	−0.899281
$704$	2.79153	0.105210
$705$	11.4774	0.432263
$706$	59.2922	2.23149
$707$	2.80771	0.105595
$708$	29.1652	1.09609
$709$	−11.5052	−0.432087	−0.216043	−	0.976384i	$-0.569315\pi$
$709$	−11.5052	−0.432087	−0.216043	+	0.976384i	$0.569315\pi$
$710$	19.0802	0.716069
$711$	2.71807	0.101936
$712$	19.0105	0.712450
$713$	−19.9221	−0.746090
$714$	−8.74914	−0.327428
$715$	3.77775	0.141280
$716$	−52.4126	−1.95875
$717$	22.0675	0.824127
$718$	−84.4949	−3.15332
$719$	28.8436	1.07569	0.537843	−	0.843045i	$-0.319239\pi$
$719$	28.8436	1.07569	0.537843	+	0.843045i	$0.319239\pi$
$720$	7.94654	0.296150
$721$	4.74433	0.176688
$722$	22.3235	0.830795
$723$	5.91262	0.219893
$724$	16.7490	0.622470
$725$	18.7280	0.695541
$726$	53.7935	1.99646
$727$	52.1125	1.93275	0.966373	−	0.257146i	$-0.0827821\pi$
$727$	52.1125	1.93275	0.966373	+	0.257146i	$0.0827821\pi$
$728$	26.5826	0.985217
$729$	11.0330	0.408629
$730$	−42.5932	−1.57644
$731$	−4.87872	−0.180446
$732$	85.3538	3.15477
$733$	2.24288	0.0828427	0.0414214	−	0.999142i	$-0.486811\pi$
$733$	2.24288	0.0828427	0.0414214	+	0.999142i	$0.486811\pi$
$734$	−2.56574	−0.0947032
$735$	2.62179	0.0967062
$736$	−14.7396	−0.543308
$737$	4.09194	0.150729
$738$	16.4587	0.605853
$739$	3.21369	0.118218	0.0591088	−	0.998252i	$-0.481174\pi$
$739$	3.21369	0.118218	0.0591088	+	0.998252i	$0.481174\pi$
$740$	−41.2895	−1.51783
$741$	−30.4297	−1.11786
$742$	26.4765	0.971984
$743$	−24.1187	−0.884828	−0.442414	−	0.896811i	$-0.645878\pi$
$743$	−24.1187	−0.884828	−0.442414	+	0.896811i	$0.645878\pi$
$744$	40.4541	1.48312
$745$	−24.4940	−0.897390
$746$	19.9147	0.729130
$747$	−14.9324	−0.546347
$748$	−4.52758	−0.165545
$749$	−3.73897	−0.136619
$750$	54.5654	1.99245
$751$	−28.4884	−1.03955	−0.519777	−	0.854302i	$-0.673985\pi$
$751$	−28.4884	−1.03955	−0.519777	+	0.854302i	$0.673985\pi$
$752$	24.2826	0.885496
$753$	−19.0588	−0.694542
$754$	−66.5860	−2.42492
$755$	7.61884	0.277278
$756$	−16.2923	−0.592544
$757$	−43.7063	−1.58853	−0.794267	−	0.607569i	$-0.792145\pi$
$757$	−43.7063	−1.58853	−0.794267	+	0.607569i	$0.792145\pi$
$758$	−64.8144	−2.35416
$759$	−7.01321	−0.254563
$760$	−23.0611	−0.836513
$761$	19.0984	0.692318	0.346159	−	0.938176i	$-0.387486\pi$
$761$	19.0984	0.692318	0.346159	+	0.938176i	$0.387486\pi$
$762$	−20.1681	−0.730613
$763$	−11.3481	−0.410829
$764$	−72.8406	−2.63528
$765$	2.47429	0.0894583
$766$	−14.2317	−0.514210
$767$	−16.0309	−0.578842
$768$	−65.5710	−2.36609
$769$	−0.635467	−0.0229155	−0.0114578	−	0.999934i	$-0.503647\pi$
$769$	−0.635467	−0.0229155	−0.0114578	+	0.999934i	$0.503647\pi$
$770$	1.99558	0.0719156
$771$	0.220072	0.00792569
$772$	−19.3361	−0.695923
$773$	−41.7198	−1.50056	−0.750279	−	0.661121i	$-0.770081\pi$
$773$	−41.7198	−1.50056	−0.750279	+	0.661121i	$0.770081\pi$
$774$	7.81902	0.281049
$775$	11.8192	0.424559
$776$	−43.0142	−1.54412
$777$	−15.2289	−0.546332
$778$	−19.7493	−0.708048
$779$	−18.8676	−0.676001
$780$	−52.6943	−1.88676
$781$	3.64177	0.130313
$782$	−24.2055	−0.865588
$783$	21.5945	0.771724
$784$	5.54691	0.198104
$785$	3.22759	0.115198
$786$	−65.5898	−2.33951
$787$	−11.5158	−0.410494	−0.205247	−	0.978710i	$-0.565800\pi$
$787$	−11.5158	−0.410494	−0.205247	+	0.978710i	$0.565800\pi$
$788$	−63.8547	−2.27473
$789$	31.4039	1.11801
$790$	−7.93628	−0.282360
$791$	−18.5626	−0.660010
$792$	3.83961	0.136435
$793$	−46.9155	−1.66602
$794$	45.7990	1.62535
$795$	−27.7717	−0.984961
$796$	36.3258	1.28753
$797$	0.313735	0.0111131	0.00555654	−	0.999985i	$-0.498231\pi$
$797$	0.313735	0.0111131	0.00555654	+	0.999985i	$0.498231\pi$
$798$	−16.0743	−0.569024
$799$	7.56082	0.267482
$800$	8.74455	0.309167
$801$	−3.74742	−0.132409
$802$	40.6574	1.43566
$803$	−8.12958	−0.286887
$804$	−57.0768	−2.01294
$805$	7.25350	0.255652
$806$	−42.0224	−1.48018
$807$	44.6052	1.57018
$808$	−15.7735	−0.554910
$809$	52.0882	1.83132	0.915662	−	0.401949i	$-0.131667\pi$
$809$	52.0882	1.83132	0.915662	+	0.401949i	$0.131667\pi$
$810$	35.8783	1.26064
$811$	−4.77589	−0.167704	−0.0838521	−	0.996478i	$-0.526722\pi$
$811$	−4.77589	−0.167704	−0.0838521	+	0.996478i	$0.526722\pi$
$812$	−23.9138	−0.839209
$813$	22.8873	0.802692
$814$	−11.5914	−0.406280
$815$	12.0015	0.420393
$816$	19.4160	0.679696
$817$	−8.96339	−0.313589
$818$	11.3069	0.395336
$819$	−5.24005	−0.183102
$820$	−32.6725	−1.14097
$821$	15.4201	0.538167	0.269083	−	0.963117i	$-0.413279\pi$
$821$	15.4201	0.538167	0.269083	+	0.963117i	$0.413279\pi$
$822$	−32.7055	−1.14073
$823$	−17.1500	−0.597810	−0.298905	−	0.954283i	$-0.596621\pi$
$823$	−17.1500	−0.597810	−0.298905	+	0.954283i	$0.596621\pi$
$824$	−26.6533	−0.928510
$825$	4.16073	0.144858
$826$	−8.46823	−0.294647
$827$	11.8453	0.411900	0.205950	−	0.978563i	$-0.433972\pi$
$827$	11.8453	0.411900	0.205950	+	0.978563i	$0.433972\pi$
$828$	26.3749	0.916592
$829$	−11.7098	−0.406697	−0.203348	−	0.979106i	$-0.565182\pi$
$829$	−11.7098	−0.406697	−0.203348	+	0.979106i	$0.565182\pi$
$830$	43.5998	1.51337
$831$	−60.6085	−2.10248
$832$	21.4025	0.742000
$833$	1.72713	0.0598414
$834$	−12.8987	−0.446645
$835$	−3.64254	−0.126055
$836$	−8.31826	−0.287693
$837$	13.6283	0.471062
$838$	23.4934	0.811564
$839$	−31.9734	−1.10385	−0.551923	−	0.833895i	$-0.686106\pi$
$839$	−31.9734	−1.10385	−0.551923	+	0.833895i	$0.686106\pi$
$840$	−14.7290	−0.508199
$841$	2.69636	0.0929779
$842$	−68.1427	−2.34835
$843$	10.6175	0.365687
$844$	47.9709	1.65123
$845$	12.1466	0.417855
$846$	−12.1176	−0.416610
$847$	−10.6191	−0.364877
$848$	−58.7564	−2.01770
$849$	56.9733	1.95532
$850$	14.3604	0.492559
$851$	−42.1324	−1.44428
$852$	−50.7975	−1.74029
$853$	−16.0746	−0.550385	−0.275193	−	0.961389i	$-0.588742\pi$
$853$	−16.0746	−0.550385	−0.275193	+	0.961389i	$0.588742\pi$
$854$	−24.7828	−0.848051
$855$	4.54588	0.155466
$856$	21.0052	0.717945
$857$	44.0827	1.50584	0.752918	−	0.658114i	$-0.228646\pi$
$857$	44.0827	1.50584	0.752918	+	0.658114i	$0.228646\pi$
$858$	−14.7932	−0.505031
$859$	1.00000	0.0341196
$859$	1.00000	0.0341196
$860$	−15.5217	−0.529285
$861$	−12.0506	−0.410685
$862$	−15.5021	−0.528002
$863$	−55.9821	−1.90565	−0.952827	−	0.303513i	$-0.901840\pi$
$863$	−55.9821	−1.90565	−0.952827	+	0.303513i	$0.901840\pi$
$864$	10.0830	0.343030
$865$	−10.8548	−0.369076
$866$	−55.6980	−1.89269
$867$	−28.4080	−0.964787
$868$	−15.0920	−0.512255
$869$	−1.51476	−0.0513849
$870$	36.8943	1.25083
$871$	31.3728	1.06303
$872$	63.7528	2.15894
$873$	8.47911	0.286974
$874$	−44.4714	−1.50427
$875$	−10.7715	−0.364143
$876$	113.396	3.83130
$877$	−49.3574	−1.66668	−0.833341	−	0.552759i	$-0.813575\pi$
$877$	−49.3574	−1.66668	−0.833341	+	0.552759i	$0.813575\pi$
$878$	−18.5263	−0.625234
$879$	−20.3345	−0.685867
$880$	−4.42856	−0.149287
$881$	−33.8992	−1.14209	−0.571047	−	0.820917i	$-0.693463\pi$
$881$	−33.8992	−1.14209	−0.571047	+	0.820917i	$0.693463\pi$
$882$	−2.76803	−0.0932043
$883$	−20.9624	−0.705440	−0.352720	−	0.935729i	$-0.614743\pi$
$883$	−20.9624	−0.705440	−0.352720	+	0.935729i	$0.614743\pi$
$884$	−34.7128	−1.16752
$885$	8.88248	0.298581
$886$	66.9841	2.25037
$887$	47.5400	1.59624	0.798119	−	0.602499i	$-0.205828\pi$
$887$	47.5400	1.59624	0.798119	+	0.602499i	$0.205828\pi$
$888$	85.5545	2.87102
$889$	3.98129	0.133528
$890$	10.9418	0.366770
$891$	6.84794	0.229415
$892$	77.5335	2.59601
$893$	13.8911	0.464846
$894$	95.9152	3.20788
$895$	−15.9627	−0.533573
$896$	16.5633	0.553341
$897$	−53.7701	−1.79533
$898$	64.6823	2.15848
$899$	20.0035	0.667155
$900$	−15.6475	−0.521583
$901$	−18.2948	−0.609489
$902$	−9.17234	−0.305405
$903$	−5.72488	−0.190512
$904$	104.283	3.46841
$905$	5.10102	0.169564
$906$	−29.8343	−0.991180
$907$	−3.18667	−0.105812	−0.0529059	−	0.998600i	$-0.516848\pi$
$907$	−3.18667	−0.105812	−0.0529059	+	0.998600i	$0.516848\pi$
$908$	−113.978	−3.78250
$909$	3.10932	0.103130
$910$	15.3000	0.507191
$911$	12.8998	0.427389	0.213694	−	0.976901i	$-0.431450\pi$
$911$	12.8998	0.427389	0.213694	+	0.976901i	$0.431450\pi$
$912$	35.6719	1.18121
$913$	8.32172	0.275409
$914$	−39.6056	−1.31004
$915$	25.9952	0.859374
$916$	−88.3369	−2.91873
$917$	12.9478	0.427573
$918$	16.5584	0.546509
$919$	20.6766	0.682058	0.341029	−	0.940053i	$-0.389225\pi$
$919$	20.6766	0.682058	0.341029	+	0.940053i	$0.389225\pi$
$920$	−40.7496	−1.34347
$921$	11.2211	0.369747
$922$	−41.4656	−1.36560
$923$	27.9213	0.919041
$924$	−5.31284	−0.174780
$925$	24.9959	0.821861
$926$	−40.8040	−1.34090
$927$	5.25398	0.172563
$928$	14.7998	0.485827
$929$	37.0979	1.21714	0.608571	−	0.793500i	$-0.291743\pi$
$929$	37.0979	1.21714	0.608571	+	0.793500i	$0.291743\pi$
$930$	23.2840	0.763511
$931$	3.17315	0.103996
$932$	−120.042	−3.93209
$933$	15.7906	0.516960
$934$	−27.0591	−0.885400
$935$	−1.37891	−0.0450952
$936$	29.4382	0.962218
$937$	38.6629	1.26306	0.631531	−	0.775351i	$-0.282427\pi$
$937$	38.6629	1.26306	0.631531	+	0.775351i	$0.282427\pi$
$938$	16.5725	0.541111
$939$	5.42632	0.177081
$940$	24.0548	0.784581
$941$	35.6965	1.16367	0.581836	−	0.813306i	$-0.302335\pi$
$941$	35.6965	1.16367	0.581836	+	0.813306i	$0.302335\pi$
$942$	−12.6388	−0.411795
$943$	−33.3395	−1.08568
$944$	18.7926	0.611647
$945$	−4.96194	−0.161412
$946$	−4.35749	−0.141674
$947$	−18.8846	−0.613668	−0.306834	−	0.951763i	$-0.599270\pi$
$947$	−18.8846	−0.613668	−0.306834	+	0.951763i	$0.599270\pi$
$948$	21.1288	0.686232
$949$	−62.3293	−2.02329
$950$	26.3836	0.855997
$951$	17.2492	0.559343
$952$	−9.70286	−0.314471
$953$	5.11975	0.165845	0.0829224	−	0.996556i	$-0.473575\pi$
$953$	5.11975	0.165845	0.0829224	+	0.996556i	$0.473575\pi$
$954$	29.3207	0.949293
$955$	−22.1842	−0.717863
$956$	46.2501	1.49583
$957$	7.04186	0.227631
$958$	−84.4914	−2.72979
$959$	6.45623	0.208482
$960$	−11.8588	−0.382742
$961$	−18.3758	−0.592767
$962$	−88.8712	−2.86532
$963$	−4.14063	−0.133430
$964$	12.3919	0.399117
$965$	−5.88897	−0.189573
$966$	−28.4037	−0.913875
$967$	21.2729	0.684091	0.342045	−	0.939683i	$-0.388880\pi$
$967$	21.2729	0.684091	0.342045	+	0.939683i	$0.388880\pi$
$968$	59.6573	1.91746
$969$	11.1071	0.356810
$970$	−24.7575	−0.794915
$971$	−58.1234	−1.86527	−0.932634	−	0.360823i	$-0.882496\pi$
$971$	−58.1234	−1.86527	−0.932634	+	0.360823i	$0.882496\pi$
$972$	−46.6423	−1.49605
$973$	2.54627	0.0816297
$974$	93.6351	3.00026
$975$	31.9002	1.02162
$976$	54.9978	1.76044
$977$	−57.7010	−1.84602	−0.923010	−	0.384777i	$-0.874278\pi$
$977$	−57.7010	−1.84602	−0.923010	+	0.384777i	$0.874278\pi$
$978$	−46.9961	−1.50277
$979$	2.08841	0.0667460
$980$	5.49486	0.175527
$981$	−12.5672	−0.401239
$982$	48.9055	1.56064
$983$	−21.3570	−0.681181	−0.340591	−	0.940212i	$-0.610627\pi$
$983$	−21.3570	−0.681181	−0.340591	+	0.940212i	$0.610627\pi$
$984$	67.6995	2.15818
$985$	−19.4475	−0.619648
$986$	24.3044	0.774011
$987$	8.87216	0.282404
$988$	−63.7758	−2.02898
$989$	−15.8386	−0.503637
$990$	2.20995	0.0702367
$991$	40.0192	1.27125	0.635625	−	0.771998i	$-0.280742\pi$
$991$	40.0192	1.27125	0.635625	+	0.771998i	$0.280742\pi$
$992$	9.34013	0.296549
$993$	−16.9443	−0.537710
$994$	14.7493	0.467819
$995$	11.0633	0.350731
$996$	−116.076	−3.67801
$997$	−7.88642	−0.249765	−0.124883	−	0.992172i	$-0.539855\pi$
$997$	−7.88642	−0.249765	−0.124883	+	0.992172i	$0.539855\pi$
$998$	−31.5338	−0.998186
$999$	28.8218	0.911880

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.d.1.10	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.d.1.10	✓	104	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)

\(f(q)\)	\(=\)	\(q-2.49952 q^{2} +2.02668 q^{3} +4.24760 q^{4} +1.29364 q^{5} -5.06572 q^{6} +1.00000 q^{7} -5.61792 q^{8} +1.10742 q^{9} +O(q^{10})\)	\(q-2.49952 q^{2} +2.02668 q^{3} +4.24760 q^{4} +1.29364 q^{5} -5.06572 q^{6} +1.00000 q^{7} -5.61792 q^{8} +1.10742 q^{9} -3.23348 q^{10} -0.617161 q^{11} +8.60852 q^{12} -4.73175 q^{13} -2.49952 q^{14} +2.62179 q^{15} +5.54691 q^{16} +1.72713 q^{17} -2.76803 q^{18} +3.17315 q^{19} +5.49486 q^{20} +2.02668 q^{21} +1.54261 q^{22} +5.60704 q^{23} -11.3857 q^{24} -3.32650 q^{25} +11.8271 q^{26} -3.83564 q^{27} +4.24760 q^{28} -5.62995 q^{29} -6.55322 q^{30} -3.55306 q^{31} -2.62876 q^{32} -1.25079 q^{33} -4.31699 q^{34} +1.29364 q^{35} +4.70389 q^{36} -7.51419 q^{37} -7.93135 q^{38} -9.58974 q^{39} -7.26757 q^{40} -5.94601 q^{41} -5.06572 q^{42} -2.82476 q^{43} -2.62145 q^{44} +1.43261 q^{45} -14.0149 q^{46} +4.37769 q^{47} +11.2418 q^{48} +1.00000 q^{49} +8.31464 q^{50} +3.50033 q^{51} -20.0986 q^{52} -10.5926 q^{53} +9.58727 q^{54} -0.798384 q^{55} -5.61792 q^{56} +6.43095 q^{57} +14.0722 q^{58} +3.38794 q^{59} +11.1363 q^{60} +9.91504 q^{61} +8.88094 q^{62} +1.10742 q^{63} -4.52318 q^{64} -6.12118 q^{65} +3.12636 q^{66} -6.63027 q^{67} +7.33614 q^{68} +11.3637 q^{69} -3.23348 q^{70} -5.90084 q^{71} -6.22142 q^{72} +13.1726 q^{73} +18.7819 q^{74} -6.74174 q^{75} +13.4783 q^{76} -0.617161 q^{77} +23.9697 q^{78} +2.45441 q^{79} +7.17570 q^{80} -11.0959 q^{81} +14.8622 q^{82} -13.4839 q^{83} +8.60852 q^{84} +2.23428 q^{85} +7.06055 q^{86} -11.4101 q^{87} +3.46716 q^{88} -3.38391 q^{89} -3.58083 q^{90} -4.73175 q^{91} +23.8165 q^{92} -7.20090 q^{93} -10.9421 q^{94} +4.10491 q^{95} -5.32765 q^{96} +7.65661 q^{97} -2.49952 q^{98} -0.683458 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9} - 17 q^{10} - 46 q^{11} - 62 q^{12} - 37 q^{13} - 17 q^{14} - 17 q^{15} + 93 q^{16} - 75 q^{17} - 41 q^{18} - 40 q^{19} - 106 q^{20} - 34 q^{21} - 14 q^{22} - 57 q^{23} - 38 q^{24} + 102 q^{25} - 45 q^{26} - 121 q^{27} + 99 q^{28} - 29 q^{29} + 26 q^{30} - 42 q^{31} - 113 q^{32} - 42 q^{33} - 7 q^{34} - 46 q^{35} + 99 q^{36} - 31 q^{37} - 62 q^{38} - 9 q^{39} - 36 q^{40} - 106 q^{41} - 18 q^{42} - 29 q^{43} - 60 q^{44} - 121 q^{45} + 21 q^{46} - 141 q^{47} - 88 q^{48} + 104 q^{49} - 70 q^{50} - 2 q^{51} - 58 q^{52} - 70 q^{53} - 49 q^{54} - 14 q^{55} - 48 q^{56} - 11 q^{57} - 28 q^{58} - 202 q^{59} + 17 q^{60} - 79 q^{61} - 41 q^{62} + 98 q^{63} + 110 q^{64} - 34 q^{65} - 21 q^{66} - 57 q^{67} - 180 q^{68} - 99 q^{69} - 17 q^{70} - 109 q^{71} - 73 q^{72} - 46 q^{73} - 7 q^{74} - 146 q^{75} - 54 q^{76} - 46 q^{77} - 42 q^{78} - 12 q^{79} - 187 q^{80} + 100 q^{81} - 45 q^{82} - 156 q^{83} - 62 q^{84} - 13 q^{85} - 8 q^{86} - 76 q^{87} - 6 q^{88} - 140 q^{89} - 5 q^{90} - 37 q^{91} - 98 q^{92} - q^{93} - 17 q^{94} - 48 q^{95} - 12 q^{96} - 63 q^{97} - 17 q^{98} - 78 q^{99}+O(q^{100}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9 - 17 * q^10 - 46 * q^11 - 62 * q^12 - 37 * q^13 - 17 * q^14 - 17 * q^15 + 93 * q^16 - 75 * q^17 - 41 * q^18 - 40 * q^19 - 106 * q^20 - 34 * q^21 - 14 * q^22 - 57 * q^23 - 38 * q^24 + 102 * q^25 - 45 * q^26 - 121 * q^27 + 99 * q^28 - 29 * q^29 + 26 * q^30 - 42 * q^31 - 113 * q^32 - 42 * q^33 - 7 * q^34 - 46 * q^35 + 99 * q^36 - 31 * q^37 - 62 * q^38 - 9 * q^39 - 36 * q^40 - 106 * q^41 - 18 * q^42 - 29 * q^43 - 60 * q^44 - 121 * q^45 + 21 * q^46 - 141 * q^47 - 88 * q^48 + 104 * q^49 - 70 * q^50 - 2 * q^51 - 58 * q^52 - 70 * q^53 - 49 * q^54 - 14 * q^55 - 48 * q^56 - 11 * q^57 - 28 * q^58 - 202 * q^59 + 17 * q^60 - 79 * q^61 - 41 * q^62 + 98 * q^63 + 110 * q^64 - 34 * q^65 - 21 * q^66 - 57 * q^67 - 180 * q^68 - 99 * q^69 - 17 * q^70 - 109 * q^71 - 73 * q^72 - 46 * q^73 - 7 * q^74 - 146 * q^75 - 54 * q^76 - 46 * q^77 - 42 * q^78 - 12 * q^79 - 187 * q^80 + 100 * q^81 - 45 * q^82 - 156 * q^83 - 62 * q^84 - 13 * q^85 - 8 * q^86 - 76 * q^87 - 6 * q^88 - 140 * q^89 - 5 * q^90 - 37 * q^91 - 98 * q^92 - q^93 - 17 * q^94 - 48 * q^95 - 12 * q^96 - 63 * q^97 - 17 * q^98 - 78 * q^99

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