LMFDB - Embedded newform 6013.2.a.d.1.9

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			1.9
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)

$f(q)$	$=$	$q-2.50413 q^{2} -2.14527 q^{3} +4.27066 q^{4} -3.15595 q^{5} +5.37203 q^{6} +1.00000 q^{7} -5.68604 q^{8} +1.60217 q^{9} +O(q^{10})$	\(q-2.50413 q^{2} -2.14527 q^{3} +4.27066 q^{4} -3.15595 q^{5} +5.37203 q^{6} +1.00000 q^{7} -5.68604 q^{8} +1.60217 q^{9} +7.90290 q^{10} +4.97909 q^{11} -9.16172 q^{12} +5.78769 q^{13} -2.50413 q^{14} +6.77035 q^{15} +5.69724 q^{16} -3.92818 q^{17} -4.01205 q^{18} +6.50330 q^{19} -13.4780 q^{20} -2.14527 q^{21} -12.4683 q^{22} +0.806841 q^{23} +12.1981 q^{24} +4.96001 q^{25} -14.4931 q^{26} +2.99871 q^{27} +4.27066 q^{28} +2.69062 q^{29} -16.9538 q^{30} -3.83069 q^{31} -2.89456 q^{32} -10.6815 q^{33} +9.83667 q^{34} -3.15595 q^{35} +6.84234 q^{36} -5.87037 q^{37} -16.2851 q^{38} -12.4162 q^{39} +17.9448 q^{40} -7.44318 q^{41} +5.37203 q^{42} +1.34868 q^{43} +21.2640 q^{44} -5.05638 q^{45} -2.02043 q^{46} -4.88333 q^{47} -12.2221 q^{48} +1.00000 q^{49} -12.4205 q^{50} +8.42700 q^{51} +24.7173 q^{52} -3.87750 q^{53} -7.50916 q^{54} -15.7137 q^{55} -5.68604 q^{56} -13.9513 q^{57} -6.73767 q^{58} +4.50511 q^{59} +28.9139 q^{60} -10.6962 q^{61} +9.59255 q^{62} +1.60217 q^{63} -4.14614 q^{64} -18.2657 q^{65} +26.7478 q^{66} +8.43739 q^{67} -16.7759 q^{68} -1.73089 q^{69} +7.90290 q^{70} -0.752810 q^{71} -9.11002 q^{72} -7.88110 q^{73} +14.7002 q^{74} -10.6405 q^{75} +27.7734 q^{76} +4.97909 q^{77} +31.0917 q^{78} +7.86285 q^{79} -17.9802 q^{80} -11.2396 q^{81} +18.6387 q^{82} +8.04987 q^{83} -9.16172 q^{84} +12.3971 q^{85} -3.37727 q^{86} -5.77211 q^{87} -28.3113 q^{88} -13.2558 q^{89} +12.6618 q^{90} +5.78769 q^{91} +3.44575 q^{92} +8.21787 q^{93} +12.2285 q^{94} -20.5241 q^{95} +6.20960 q^{96} -9.28471 q^{97} -2.50413 q^{98} +7.97737 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.50413	−1.77069	−0.885343	−	0.464938i	$-0.846077\pi$
$2$	−2.50413	−1.77069	−0.885343	+	0.464938i	$0.846077\pi$
$3$	−2.14527	−1.23857	−0.619285	−	0.785166i	$-0.712578\pi$
$3$	−2.14527	−1.23857	−0.619285	+	0.785166i	$0.712578\pi$
$4$	4.27066	2.13533
$5$	−3.15595	−1.41138	−0.705691	−	0.708519i	$-0.749363\pi$
$5$	−3.15595	−1.41138	−0.705691	+	0.708519i	$0.749363\pi$
$6$	5.37203	2.19312
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−5.68604	−2.01032
$9$	1.60217	0.534058
$10$	7.90290	2.49912
$11$	4.97909	1.50125	0.750626	−	0.660727i	$-0.229752\pi$
$11$	4.97909	1.50125	0.750626	+	0.660727i	$0.229752\pi$
$12$	−9.16172	−2.64476
$13$	5.78769	1.60522	0.802609	−	0.596506i	$-0.203445\pi$
$13$	5.78769	1.60522	0.802609	+	0.596506i	$0.203445\pi$
$14$	−2.50413	−0.669257
$15$	6.77035	1.74810
$16$	5.69724	1.42431
$17$	−3.92818	−0.952724	−0.476362	−	0.879249i	$-0.658045\pi$
$17$	−3.92818	−0.952724	−0.476362	+	0.879249i	$0.658045\pi$
$18$	−4.01205	−0.945649
$19$	6.50330	1.49196	0.745980	−	0.665968i	$-0.231981\pi$
$19$	6.50330	1.49196	0.745980	+	0.665968i	$0.231981\pi$
$20$	−13.4780	−3.01377
$21$	−2.14527	−0.468136
$22$	−12.4683	−2.65825
$23$	0.806841	0.168238	0.0841190	−	0.996456i	$-0.473192\pi$
$23$	0.806841	0.168238	0.0841190	+	0.996456i	$0.473192\pi$
$24$	12.1981	2.48992
$25$	4.96001	0.992001
$26$	−14.4931	−2.84234
$27$	2.99871	0.577102
$28$	4.27066	0.807080
$29$	2.69062	0.499636	0.249818	−	0.968293i	$-0.419629\pi$
$29$	2.69062	0.499636	0.249818	+	0.968293i	$0.419629\pi$
$30$	−16.9538	−3.09533
$31$	−3.83069	−0.688013	−0.344007	−	0.938967i	$-0.611784\pi$
$31$	−3.83069	−0.688013	−0.344007	+	0.938967i	$0.611784\pi$
$32$	−2.89456	−0.511690
$33$	−10.6815	−1.85941
$34$	9.83667	1.68698
$35$	−3.15595	−0.533453
$36$	6.84234	1.14039
$37$	−5.87037	−0.965082	−0.482541	−	0.875873i	$-0.660286\pi$
$37$	−5.87037	−0.965082	−0.482541	+	0.875873i	$0.660286\pi$
$38$	−16.2851	−2.64179
$39$	−12.4162	−1.98818
$40$	17.9448	2.83733
$41$	−7.44318	−1.16243	−0.581215	−	0.813750i	$-0.697422\pi$
$41$	−7.44318	−1.16243	−0.581215	+	0.813750i	$0.697422\pi$
$42$	5.37203	0.828922
$43$	1.34868	0.205672	0.102836	−	0.994698i	$-0.467208\pi$
$43$	1.34868	0.205672	0.102836	+	0.994698i	$0.467208\pi$
$44$	21.2640	3.20567
$45$	−5.05638	−0.753760
$46$	−2.02043	−0.297897
$47$	−4.88333	−0.712307	−0.356153	−	0.934427i	$-0.615912\pi$
$47$	−4.88333	−0.712307	−0.356153	+	0.934427i	$0.615912\pi$
$48$	−12.2221	−1.76411
$49$	1.00000	0.142857
$50$	−12.4205	−1.75652
$51$	8.42700	1.18002
$52$	24.7173	3.42767
$53$	−3.87750	−0.532615	−0.266307	−	0.963888i	$-0.585804\pi$
$53$	−3.87750	−0.532615	−0.266307	+	0.963888i	$0.585804\pi$
$54$	−7.50916	−1.02187
$55$	−15.7137	−2.11884
$56$	−5.68604	−0.759828
$57$	−13.9513	−1.84790
$58$	−6.73767	−0.884699
$59$	4.50511	0.586515	0.293258	−	0.956033i	$-0.405261\pi$
$59$	4.50511	0.586515	0.293258	+	0.956033i	$0.405261\pi$
$60$	28.9139	3.73277
$61$	−10.6962	−1.36951	−0.684754	−	0.728774i	$-0.740091\pi$
$61$	−10.6962	−1.36951	−0.684754	+	0.728774i	$0.740091\pi$
$62$	9.59255	1.21826
$63$	1.60217	0.201855
$64$	−4.14614	−0.518267
$65$	−18.2657	−2.26558
$66$	26.7478	3.29243
$67$	8.43739	1.03079	0.515395	−	0.856952i	$-0.327645\pi$
$67$	8.43739	1.03079	0.515395	+	0.856952i	$0.327645\pi$
$68$	−16.7759	−2.03438
$69$	−1.73089	−0.208375
$70$	7.90290	0.944577
$71$	−0.752810	−0.0893421	−0.0446710	−	0.999002i	$-0.514224\pi$
$71$	−0.752810	−0.0893421	−0.0446710	+	0.999002i	$0.514224\pi$
$72$	−9.11002	−1.07363
$73$	−7.88110	−0.922413	−0.461206	−	0.887293i	$-0.652583\pi$
$73$	−7.88110	−0.922413	−0.461206	+	0.887293i	$0.652583\pi$
$74$	14.7002	1.70886
$75$	−10.6405	−1.22866
$76$	27.7734	3.18583
$77$	4.97909	0.567420
$78$	31.0917	3.52044
$79$	7.86285	0.884640	0.442320	−	0.896857i	$-0.354156\pi$
$79$	7.86285	0.884640	0.442320	+	0.896857i	$0.354156\pi$
$80$	−17.9802	−2.01025
$81$	−11.2396	−1.24884
$82$	18.6387	2.05830
$83$	8.04987	0.883588	0.441794	−	0.897116i	$-0.354342\pi$
$83$	8.04987	0.883588	0.441794	+	0.897116i	$0.354342\pi$
$84$	−9.16172	−0.999625
$85$	12.3971	1.34466
$86$	−3.37727	−0.364180
$87$	−5.77211	−0.618835
$88$	−28.3113	−3.01799
$89$	−13.2558	−1.40512	−0.702558	−	0.711627i	$-0.747959\pi$
$89$	−13.2558	−1.40512	−0.702558	+	0.711627i	$0.747959\pi$
$90$	12.6618	1.33467
$91$	5.78769	0.606715
$92$	3.44575	0.359244
$93$	8.21787	0.852153
$94$	12.2285	1.26127
$95$	−20.5241	−2.10573
$96$	6.20960	0.633765
$97$	−9.28471	−0.942720	−0.471360	−	0.881941i	$-0.656237\pi$
$97$	−9.28471	−0.942720	−0.471360	+	0.881941i	$0.656237\pi$
$98$	−2.50413	−0.252955
$99$	7.97737	0.801755
$100$	21.1825	2.11825
$101$	−0.384012	−0.0382107	−0.0191053	−	0.999817i	$-0.506082\pi$
$101$	−0.384012	−0.0382107	−0.0191053	+	0.999817i	$0.506082\pi$
$102$	−21.1023	−2.08944
$103$	−1.59612	−0.157270	−0.0786350	−	0.996903i	$-0.525056\pi$
$103$	−1.59612	−0.157270	−0.0786350	+	0.996903i	$0.525056\pi$
$104$	−32.9090	−3.22700
$105$	6.77035	0.660719
$106$	9.70975	0.943094
$107$	−8.74042	−0.844968	−0.422484	−	0.906370i	$-0.638842\pi$
$107$	−8.74042	−0.844968	−0.422484	+	0.906370i	$0.638842\pi$
$108$	12.8065	1.23231
$109$	19.9211	1.90810	0.954049	−	0.299652i	$-0.0968705\pi$
$109$	19.9211	1.90810	0.954049	+	0.299652i	$0.0968705\pi$
$110$	39.3493	3.75180
$111$	12.5935	1.19532
$112$	5.69724	0.538339
$113$	−13.4535	−1.26560	−0.632800	−	0.774315i	$-0.718094\pi$
$113$	−13.4535	−1.26560	−0.632800	+	0.774315i	$0.718094\pi$
$114$	34.9359	3.27205
$115$	−2.54635	−0.237448
$116$	11.4907	1.06689
$117$	9.27289	0.857279
$118$	−11.2814	−1.03853
$119$	−3.92818	−0.360096
$120$	−38.4965	−3.51423
$121$	13.7913	1.25376
$122$	26.7847	2.42497
$123$	15.9676	1.43975
$124$	−16.3596	−1.46914
$125$	0.126219	0.0112894
$126$	−4.01205	−0.357422
$127$	−17.0418	−1.51221	−0.756107	−	0.654448i	$-0.772901\pi$
$127$	−17.0418	−1.51221	−0.756107	+	0.654448i	$0.772901\pi$
$128$	16.1716	1.42938
$129$	−2.89328	−0.254739
$130$	45.7396	4.01163
$131$	−10.6904	−0.934027	−0.467014	−	0.884250i	$-0.654670\pi$
$131$	−10.6904	−0.934027	−0.467014	+	0.884250i	$0.654670\pi$
$132$	−45.6170	−3.97045
$133$	6.50330	0.563908
$134$	−21.1283	−1.82521
$135$	−9.46378	−0.814512
$136$	22.3358	1.91528
$137$	−2.68456	−0.229358	−0.114679	−	0.993403i	$-0.536584\pi$
$137$	−2.68456	−0.229358	−0.114679	+	0.993403i	$0.536584\pi$
$138$	4.33437	0.368966
$139$	13.4235	1.13856	0.569282	−	0.822142i	$-0.307221\pi$
$139$	13.4235	1.13856	0.569282	+	0.822142i	$0.307221\pi$
$140$	−13.4780	−1.13910
$141$	10.4761	0.882243
$142$	1.88513	0.158197
$143$	28.8174	2.40984
$144$	9.12797	0.760664
$145$	−8.49146	−0.705178
$146$	19.7353	1.63330
$147$	−2.14527	−0.176939
$148$	−25.0704	−2.06077
$149$	16.7812	1.37477	0.687384	−	0.726294i	$-0.258759\pi$
$149$	16.7812	1.37477	0.687384	+	0.726294i	$0.258759\pi$
$150$	26.6453	2.17558
$151$	20.5017	1.66841	0.834203	−	0.551457i	$-0.185928\pi$
$151$	20.5017	1.66841	0.834203	+	0.551457i	$0.185928\pi$
$152$	−36.9780	−2.99931
$153$	−6.29363	−0.508810
$154$	−12.4683	−1.00472
$155$	12.0895	0.971050
$156$	−53.0252	−4.24542
$157$	−10.2944	−0.821582	−0.410791	−	0.911730i	$-0.634747\pi$
$157$	−10.2944	−0.821582	−0.410791	+	0.911730i	$0.634747\pi$
$158$	−19.6896	−1.56642
$159$	8.31826	0.659681
$160$	9.13507	0.722191
$161$	0.806841	0.0635880
$162$	28.1453	2.21130
$163$	−8.57012	−0.671264	−0.335632	−	0.941993i	$-0.608950\pi$
$163$	−8.57012	−0.671264	−0.335632	+	0.941993i	$0.608950\pi$
$164$	−31.7873	−2.48217
$165$	33.7102	2.62433
$166$	−20.1579	−1.56456
$167$	−11.2892	−0.873581	−0.436791	−	0.899563i	$-0.643885\pi$
$167$	−11.2892	−0.873581	−0.436791	+	0.899563i	$0.643885\pi$
$168$	12.1981	0.941101
$169$	20.4974	1.57672
$170$	−31.0440	−2.38097
$171$	10.4194	0.796793
$172$	5.75976	0.439178
$173$	−15.7032	−1.19389	−0.596946	−	0.802282i	$-0.703619\pi$
$173$	−15.7032	−1.19389	−0.596946	+	0.802282i	$0.703619\pi$
$174$	14.4541	1.09576
$175$	4.96001	0.374941
$176$	28.3671	2.13825
$177$	−9.66466	−0.726441
$178$	33.1943	2.48802
$179$	3.18412	0.237992	0.118996	−	0.992895i	$-0.462032\pi$
$179$	3.18412	0.237992	0.118996	+	0.992895i	$0.462032\pi$
$180$	−21.5941	−1.60953
$181$	−0.345740	−0.0256987	−0.0128493	−	0.999917i	$-0.504090\pi$
$181$	−0.345740	−0.0256987	−0.0128493	+	0.999917i	$0.504090\pi$
$182$	−14.4931	−1.07430
$183$	22.9462	1.69623
$184$	−4.58773	−0.338212
$185$	18.5266	1.36210
$186$	−20.5786	−1.50890
$187$	−19.5588	−1.43028
$188$	−20.8551	−1.52101
$189$	2.99871	0.218124
$190$	51.3950	3.72858
$191$	−19.5358	−1.41356	−0.706779	−	0.707434i	$-0.749853\pi$
$191$	−19.5358	−1.41356	−0.706779	+	0.707434i	$0.749853\pi$
$192$	8.89457	0.641911
$193$	−8.92829	−0.642673	−0.321336	−	0.946965i	$-0.604132\pi$
$193$	−8.92829	−0.642673	−0.321336	+	0.946965i	$0.604132\pi$
$194$	23.2501	1.66926
$195$	39.1847	2.80608
$196$	4.27066	0.305047
$197$	−17.4057	−1.24010	−0.620051	−	0.784562i	$-0.712888\pi$
$197$	−17.4057	−1.24010	−0.620051	+	0.784562i	$0.712888\pi$
$198$	−19.9764	−1.41966
$199$	25.0823	1.77804	0.889020	−	0.457869i	$-0.151387\pi$
$199$	25.0823	1.77804	0.889020	+	0.457869i	$0.151387\pi$
$200$	−28.2028	−1.99424
$201$	−18.1005	−1.27671
$202$	0.961616	0.0676591
$203$	2.69062	0.188845
$204$	35.9889	2.51973
$205$	23.4903	1.64063
$206$	3.99688	0.278476
$207$	1.29270	0.0898489
$208$	32.9739	2.28633
$209$	32.3805	2.23981
$210$	−16.9538	−1.16993
$211$	7.84264	0.539910	0.269955	−	0.962873i	$-0.412991\pi$
$211$	7.84264	0.539910	0.269955	+	0.962873i	$0.412991\pi$
$212$	−16.5595	−1.13731
$213$	1.61498	0.110656
$214$	21.8871	1.49617
$215$	−4.25636	−0.290282
$216$	−17.0508	−1.16016
$217$	−3.83069	−0.260044
$218$	−49.8851	−3.37864
$219$	16.9071	1.14247
$220$	−67.1081	−4.52443
$221$	−22.7351	−1.52933
$222$	−31.5358	−2.11654
$223$	13.2581	0.887829	0.443914	−	0.896069i	$-0.353589\pi$
$223$	13.2581	0.887829	0.443914	+	0.896069i	$0.353589\pi$
$224$	−2.89456	−0.193401
$225$	7.94679	0.529786
$226$	33.6893	2.24098
$227$	10.7748	0.715149	0.357574	−	0.933885i	$-0.383604\pi$
$227$	10.7748	0.715149	0.357574	+	0.933885i	$0.383604\pi$
$228$	−59.5814	−3.94588
$229$	−28.9338	−1.91200	−0.956000	−	0.293366i	$-0.905224\pi$
$229$	−28.9338	−1.91200	−0.956000	+	0.293366i	$0.905224\pi$
$230$	6.37639	0.420447
$231$	−10.6815	−0.702790
$232$	−15.2990	−1.00443
$233$	−12.1637	−0.796872	−0.398436	−	0.917196i	$-0.630447\pi$
$233$	−12.1637	−0.796872	−0.398436	+	0.917196i	$0.630447\pi$
$234$	−23.2205	−1.51797
$235$	15.4115	1.00534
$236$	19.2398	1.25240
$237$	−16.8679	−1.09569
$238$	9.83667	0.637617
$239$	6.21313	0.401894	0.200947	−	0.979602i	$-0.435598\pi$
$239$	6.21313	0.401894	0.200947	+	0.979602i	$0.435598\pi$
$240$	38.5723	2.48983
$241$	−23.1444	−1.49086	−0.745432	−	0.666582i	$-0.767757\pi$
$241$	−23.1444	−1.49086	−0.745432	+	0.666582i	$0.767757\pi$
$242$	−34.5353	−2.22001
$243$	15.1157	0.969675
$244$	−45.6799	−2.92436
$245$	−3.15595	−0.201626
$246$	−39.9850	−2.54935
$247$	37.6391	2.39492
$248$	21.7815	1.38312
$249$	−17.2691	−1.09439
$250$	−0.316069	−0.0199899
$251$	13.1104	0.827523	0.413762	−	0.910385i	$-0.364215\pi$
$251$	13.1104	0.827523	0.413762	+	0.910385i	$0.364215\pi$
$252$	6.84234	0.431027
$253$	4.01734	0.252568
$254$	42.6748	2.67766
$255$	−26.5952	−1.66545
$256$	−32.2034	−2.01272
$257$	17.2881	1.07840	0.539202	−	0.842176i	$-0.318726\pi$
$257$	17.2881	1.07840	0.539202	+	0.842176i	$0.318726\pi$
$258$	7.24515	0.451063
$259$	−5.87037	−0.364767
$260$	−78.0065	−4.83776
$261$	4.31084	0.266835
$262$	26.7702	1.65387
$263$	−13.3507	−0.823237	−0.411619	−	0.911356i	$-0.635036\pi$
$263$	−13.3507	−0.823237	−0.411619	+	0.911356i	$0.635036\pi$
$264$	60.7353	3.73800
$265$	12.2372	0.751723
$266$	−16.2851	−0.998504
$267$	28.4373	1.74033
$268$	36.0332	2.20108
$269$	−2.59642	−0.158306	−0.0791532	−	0.996862i	$-0.525222\pi$
$269$	−2.59642	−0.158306	−0.0791532	+	0.996862i	$0.525222\pi$
$270$	23.6985	1.44225
$271$	−10.1860	−0.618755	−0.309377	−	0.950939i	$-0.600121\pi$
$271$	−10.1860	−0.618755	−0.309377	+	0.950939i	$0.600121\pi$
$272$	−22.3798	−1.35697
$273$	−12.4162	−0.751460
$274$	6.72249	0.406120
$275$	24.6963	1.48924
$276$	−7.39205	−0.444949
$277$	3.93936	0.236693	0.118347	−	0.992972i	$-0.462241\pi$
$277$	3.93936	0.236693	0.118347	+	0.992972i	$0.462241\pi$
$278$	−33.6141	−2.01604
$279$	−6.13744	−0.367439
$280$	17.9448	1.07241
$281$	30.9648	1.84720	0.923602	−	0.383352i	$-0.125230\pi$
$281$	30.9648	1.84720	0.923602	+	0.383352i	$0.125230\pi$
$282$	−26.2334	−1.56218
$283$	8.59850	0.511128	0.255564	−	0.966792i	$-0.417739\pi$
$283$	8.59850	0.511128	0.255564	+	0.966792i	$0.417739\pi$
$284$	−3.21500	−0.190775
$285$	44.0297	2.60809
$286$	−72.1626	−4.26707
$287$	−7.44318	−0.439357
$288$	−4.63758	−0.273272
$289$	−1.56940	−0.0923177
$290$	21.2637	1.24865
$291$	19.9182	1.16763
$292$	−33.6575	−1.96966
$293$	−25.9397	−1.51541	−0.757706	−	0.652596i	$-0.773680\pi$
$293$	−25.9397	−1.51541	−0.757706	+	0.652596i	$0.773680\pi$
$294$	5.37203	0.313303
$295$	−14.2179	−0.827797
$296$	33.3791	1.94012
$297$	14.9309	0.866376
$298$	−42.0223	−2.43428
$299$	4.66975	0.270059
$300$	−45.4422	−2.62360
$301$	1.34868	0.0777366
$302$	−51.3390	−2.95422
$303$	0.823809	0.0473266
$304$	37.0509	2.12501
$305$	33.7567	1.93290
$306$	15.7601	0.900942
$307$	6.00378	0.342654	0.171327	−	0.985214i	$-0.445195\pi$
$307$	6.00378	0.342654	0.171327	+	0.985214i	$0.445195\pi$
$308$	21.2640	1.21163
$309$	3.42410	0.194790
$310$	−30.2736	−1.71942
$311$	1.36491	0.0773969	0.0386984	−	0.999251i	$-0.487679\pi$
$311$	1.36491	0.0773969	0.0386984	+	0.999251i	$0.487679\pi$
$312$	70.5987	3.99686
$313$	−18.9829	−1.07298	−0.536490	−	0.843907i	$-0.680250\pi$
$313$	−18.9829	−1.07298	−0.536490	+	0.843907i	$0.680250\pi$
$314$	25.7785	1.45476
$315$	−5.05638	−0.284895
$316$	33.5796	1.88900
$317$	20.1102	1.12950	0.564750	−	0.825262i	$-0.308973\pi$
$317$	20.1102	1.12950	0.564750	+	0.825262i	$0.308973\pi$
$318$	−20.8300	−1.16809
$319$	13.3969	0.750080
$320$	13.0850	0.731473
$321$	18.7505	1.04655
$322$	−2.02043	−0.112594
$323$	−25.5462	−1.42143
$324$	−48.0004	−2.66669
$325$	28.7070	1.59238
$326$	21.4607	1.18860
$327$	−42.7361	−2.36331
$328$	42.3222	2.33685
$329$	−4.88333	−0.269227
$330$	−84.4147	−4.64688
$331$	−21.5873	−1.18655	−0.593273	−	0.805002i	$-0.702164\pi$
$331$	−21.5873	−1.18655	−0.593273	+	0.805002i	$0.702164\pi$
$332$	34.3783	1.88675
$333$	−9.40535	−0.515410
$334$	28.2695	1.54684
$335$	−26.6280	−1.45484
$336$	−12.2221	−0.666771
$337$	−9.89230	−0.538868	−0.269434	−	0.963019i	$-0.586837\pi$
$337$	−9.89230	−0.538868	−0.269434	+	0.963019i	$0.586837\pi$
$338$	−51.3282	−2.79188
$339$	28.8614	1.56754
$340$	52.9440	2.87129
$341$	−19.0734	−1.03288
$342$	−26.0916	−1.41087
$343$	1.00000	0.0539949
$344$	−7.66864	−0.413466
$345$	5.46260	0.294097
$346$	39.3228	2.11401
$347$	16.0351	0.860812	0.430406	−	0.902636i	$-0.358370\pi$
$347$	16.0351	0.860812	0.430406	+	0.902636i	$0.358370\pi$
$348$	−24.6507	−1.32142
$349$	−11.9828	−0.641424	−0.320712	−	0.947177i	$-0.603922\pi$
$349$	−11.9828	−0.641424	−0.320712	+	0.947177i	$0.603922\pi$
$350$	−12.4205	−0.663903
$351$	17.3556	0.926375
$352$	−14.4123	−0.768176
$353$	2.86753	0.152623	0.0763117	−	0.997084i	$-0.475686\pi$
$353$	2.86753	0.152623	0.0763117	+	0.997084i	$0.475686\pi$
$354$	24.2016	1.28630
$355$	2.37583	0.126096
$356$	−56.6112	−3.00039
$357$	8.42700	0.446004
$358$	−7.97344	−0.421409
$359$	−14.0540	−0.741743	−0.370871	−	0.928684i	$-0.620941\pi$
$359$	−14.0540	−0.741743	−0.370871	+	0.928684i	$0.620941\pi$
$360$	28.7507	1.51530
$361$	23.2930	1.22595
$362$	0.865778	0.0455043
$363$	−29.5861	−1.55287
$364$	24.7173	1.29554
$365$	24.8723	1.30188
$366$	−57.4603	−3.00350
$367$	20.3956	1.06464	0.532320	−	0.846543i	$-0.321320\pi$
$367$	20.3956	1.06464	0.532320	+	0.846543i	$0.321320\pi$
$368$	4.59677	0.239623
$369$	−11.9253	−0.620805
$370$	−46.3929	−2.41185
$371$	−3.87750	−0.201310
$372$	35.0957	1.81963
$373$	10.5533	0.546429	0.273214	−	0.961953i	$-0.411913\pi$
$373$	10.5533	0.546429	0.273214	+	0.961953i	$0.411913\pi$
$374$	48.9777	2.53257
$375$	−0.270774	−0.0139827
$376$	27.7668	1.43196
$377$	15.5725	0.802025
$378$	−7.50916	−0.386230
$379$	11.3483	0.582922	0.291461	−	0.956583i	$-0.405859\pi$
$379$	11.3483	0.582922	0.291461	+	0.956583i	$0.405859\pi$
$380$	−87.6515	−4.49643
$381$	36.5592	1.87298
$382$	48.9201	2.50297
$383$	25.1546	1.28534	0.642671	−	0.766143i	$-0.277826\pi$
$383$	25.1546	1.28534	0.642671	+	0.766143i	$0.277826\pi$
$384$	−34.6924	−1.77039
$385$	−15.7137	−0.800847
$386$	22.3576	1.13797
$387$	2.16082	0.109841
$388$	−39.6519	−2.01302
$389$	−8.92964	−0.452750	−0.226375	−	0.974040i	$-0.572688\pi$
$389$	−8.92964	−0.452750	−0.226375	+	0.974040i	$0.572688\pi$
$390$	−98.1236	−4.96868
$391$	−3.16942	−0.160284
$392$	−5.68604	−0.287188
$393$	22.9338	1.15686
$394$	43.5860	2.19583
$395$	−24.8148	−1.24857
$396$	34.0686	1.71201
$397$	14.9109	0.748356	0.374178	−	0.927357i	$-0.377925\pi$
$397$	14.9109	0.748356	0.374178	+	0.927357i	$0.377925\pi$
$398$	−62.8094	−3.14835
$399$	−13.9513	−0.698440
$400$	28.2583	1.41292
$401$	15.6884	0.783442	0.391721	−	0.920084i	$-0.371880\pi$
$401$	15.6884	0.783442	0.391721	+	0.920084i	$0.371880\pi$
$402$	45.3259	2.26065
$403$	−22.1709	−1.10441
$404$	−1.63999	−0.0815924
$405$	35.4715	1.76259
$406$	−6.73767	−0.334385
$407$	−29.2291	−1.44883
$408$	−47.9162	−2.37221
$409$	−10.5770	−0.523000	−0.261500	−	0.965204i	$-0.584217\pi$
$409$	−10.5770	−0.523000	−0.261500	+	0.965204i	$0.584217\pi$
$410$	−58.8227	−2.90505
$411$	5.75910	0.284076
$412$	−6.81648	−0.335824
$413$	4.50511	0.221682
$414$	−3.23709	−0.159094
$415$	−25.4050	−1.24708
$416$	−16.7528	−0.821374
$417$	−28.7969	−1.41019
$418$	−81.0850	−3.96600
$419$	−5.46217	−0.266844	−0.133422	−	0.991059i	$-0.542597\pi$
$419$	−5.46217	−0.266844	−0.133422	+	0.991059i	$0.542597\pi$
$420$	28.9139	1.41085
$421$	3.39170	0.165302	0.0826508	−	0.996579i	$-0.473661\pi$
$421$	3.39170	0.165302	0.0826508	+	0.996579i	$0.473661\pi$
$422$	−19.6390	−0.956011
$423$	−7.82394	−0.380413
$424$	22.0476	1.07072
$425$	−19.4838	−0.945103
$426$	−4.04411	−0.195938
$427$	−10.6962	−0.517626
$428$	−37.3274	−1.80429
$429$	−61.8211	−2.98475
$430$	10.6585	0.513998
$431$	−30.2509	−1.45714	−0.728568	−	0.684974i	$-0.759814\pi$
$431$	−30.2509	−1.45714	−0.728568	+	0.684974i	$0.759814\pi$
$432$	17.0844	0.821973
$433$	−16.5967	−0.797586	−0.398793	−	0.917041i	$-0.630571\pi$
$433$	−16.5967	−0.797586	−0.398793	+	0.917041i	$0.630571\pi$
$434$	9.59255	0.460457
$435$	18.2165	0.873413
$436$	85.0764	4.07442
$437$	5.24713	0.251004
$438$	−42.3375	−2.02296
$439$	11.2284	0.535901	0.267950	−	0.963433i	$-0.413654\pi$
$439$	11.2284	0.535901	0.267950	+	0.963433i	$0.413654\pi$
$440$	89.3489	4.25954
$441$	1.60217	0.0762940
$442$	56.9316	2.70796
$443$	16.4253	0.780388	0.390194	−	0.920733i	$-0.372408\pi$
$443$	16.4253	0.780388	0.390194	+	0.920733i	$0.372408\pi$
$444$	53.7826	2.55241
$445$	41.8347	1.98316
$446$	−33.2000	−1.57207
$447$	−36.0001	−1.70275
$448$	−4.14614	−0.195887
$449$	−10.8908	−0.513969	−0.256984	−	0.966416i	$-0.582729\pi$
$449$	−10.8908	−0.513969	−0.256984	+	0.966416i	$0.582729\pi$
$450$	−19.8998	−0.938085
$451$	−37.0603	−1.74510
$452$	−57.4554	−2.70248
$453$	−43.9817	−2.06644
$454$	−26.9815	−1.26630
$455$	−18.2657	−0.856307
$456$	79.3278	3.71486
$457$	−6.45143	−0.301785	−0.150892	−	0.988550i	$-0.548215\pi$
$457$	−6.45143	−0.301785	−0.150892	+	0.988550i	$0.548215\pi$
$458$	72.4540	3.38555
$459$	−11.7795	−0.549819
$460$	−10.8746	−0.507031
$461$	29.5223	1.37499	0.687495	−	0.726189i	$-0.258710\pi$
$461$	29.5223	1.37499	0.687495	+	0.726189i	$0.258710\pi$
$462$	26.7478	1.24442
$463$	−23.0461	−1.07104	−0.535522	−	0.844521i	$-0.679885\pi$
$463$	−23.0461	−1.07104	−0.535522	+	0.844521i	$0.679885\pi$
$464$	15.3291	0.711637
$465$	−25.9352	−1.20271
$466$	30.4595	1.41101
$467$	−21.9577	−1.01608	−0.508041	−	0.861333i	$-0.669630\pi$
$467$	−21.9577	−1.01608	−0.508041	+	0.861333i	$0.669630\pi$
$468$	39.6014	1.83058
$469$	8.43739	0.389602
$470$	−38.5925	−1.78014
$471$	22.0842	1.01759
$472$	−25.6162	−1.17908
$473$	6.71520	0.308765
$474$	42.2395	1.94012
$475$	32.2564	1.48003
$476$	−16.7759	−0.768924
$477$	−6.21242	−0.284447
$478$	−15.5585	−0.711628
$479$	11.3516	0.518667	0.259334	−	0.965788i	$-0.416497\pi$
$479$	11.3516	0.518667	0.259334	+	0.965788i	$0.416497\pi$
$480$	−19.5972	−0.894484
$481$	−33.9759	−1.54917
$482$	57.9566	2.63985
$483$	−1.73089	−0.0787583
$484$	58.8981	2.67719
$485$	29.3021	1.33054
$486$	−37.8517	−1.71699
$487$	27.8445	1.26176	0.630878	−	0.775882i	$-0.282695\pi$
$487$	27.8445	1.26176	0.630878	+	0.775882i	$0.282695\pi$
$488$	60.8190	2.75315
$489$	18.3852	0.831408
$490$	7.90290	0.357017
$491$	39.7233	1.79269	0.896345	−	0.443358i	$-0.146213\pi$
$491$	39.7233	1.79269	0.896345	+	0.443358i	$0.146213\pi$
$492$	68.1923	3.07435
$493$	−10.5693	−0.476015
$494$	−94.2533	−4.24066
$495$	−25.1761	−1.13158
$496$	−21.8244	−0.979944
$497$	−0.752810	−0.0337681
$498$	43.2441	1.93782
$499$	−36.4114	−1.63000	−0.814999	−	0.579463i	$-0.803262\pi$
$499$	−36.4114	−1.63000	−0.814999	+	0.579463i	$0.803262\pi$
$500$	0.539039	0.0241066
$501$	24.2183	1.08199
$502$	−32.8302	−1.46528
$503$	−9.38373	−0.418400	−0.209200	−	0.977873i	$-0.567086\pi$
$503$	−9.38373	−0.418400	−0.209200	+	0.977873i	$0.567086\pi$
$504$	−9.11002	−0.405792
$505$	1.21192	0.0539299
$506$	−10.0599	−0.447218
$507$	−43.9724	−1.95288
$508$	−72.7797	−3.22908
$509$	24.7933	1.09894	0.549471	−	0.835512i	$-0.314829\pi$
$509$	24.7933	1.09894	0.549471	+	0.835512i	$0.314829\pi$
$510$	66.5977	2.94900
$511$	−7.88110	−0.348639
$512$	48.2984	2.13451
$513$	19.5015	0.861014
$514$	−43.2917	−1.90952
$515$	5.03726	0.221968
$516$	−12.3562	−0.543953
$517$	−24.3145	−1.06935
$518$	14.7002	0.645888
$519$	33.6876	1.47872
$520$	103.859	4.55453
$521$	−30.3768	−1.33083	−0.665417	−	0.746472i	$-0.731746\pi$
$521$	−30.3768	−1.33083	−0.665417	+	0.746472i	$0.731746\pi$
$522$	−10.7949	−0.472480
$523$	13.0957	0.572636	0.286318	−	0.958135i	$-0.407569\pi$
$523$	13.0957	0.572636	0.286318	+	0.958135i	$0.407569\pi$
$524$	−45.6552	−1.99446
$525$	−10.6405	−0.464391
$526$	33.4318	1.45770
$527$	15.0477	0.655486
$528$	−60.8550	−2.64837
$529$	−22.3490	−0.971696
$530$	−30.6435	−1.33107
$531$	7.21797	0.313233
$532$	27.7734	1.20413
$533$	−43.0788	−1.86595
$534$	−71.2107	−3.08159
$535$	27.5843	1.19257
$536$	−47.9753	−2.07222
$537$	−6.83078	−0.294770
$538$	6.50176	0.280311
$539$	4.97909	0.214465
$540$	−40.4166	−1.73925
$541$	0.917225	0.0394346	0.0197173	−	0.999806i	$-0.493723\pi$
$541$	0.917225	0.0394346	0.0197173	+	0.999806i	$0.493723\pi$
$542$	25.5070	1.09562
$543$	0.741705	0.0318296
$544$	11.3703	0.487499
$545$	−62.8700	−2.69306
$546$	31.0917	1.33060
$547$	−38.1629	−1.63173	−0.815864	−	0.578245i	$-0.803738\pi$
$547$	−38.1629	−1.63173	−0.815864	+	0.578245i	$0.803738\pi$
$548$	−11.4649	−0.489755
$549$	−17.1372	−0.731397
$550$	−61.8428	−2.63698
$551$	17.4979	0.745437
$552$	9.84191	0.418899
$553$	7.86285	0.334363
$554$	−9.86467	−0.419110
$555$	−39.7445	−1.68706
$556$	57.3271	2.43121
$557$	27.8173	1.17866	0.589328	−	0.807894i	$-0.299393\pi$
$557$	27.8173	1.17866	0.589328	+	0.807894i	$0.299393\pi$
$558$	15.3689	0.650619
$559$	7.80575	0.330148
$560$	−17.9802	−0.759802
$561$	41.9588	1.77150
$562$	−77.5398	−3.27082
$563$	−20.1995	−0.851306	−0.425653	−	0.904886i	$-0.639956\pi$
$563$	−20.1995	−0.851306	−0.425653	+	0.904886i	$0.639956\pi$
$564$	44.7397	1.88388
$565$	42.4586	1.78625
$566$	−21.5318	−0.905047
$567$	−11.2396	−0.472017
$568$	4.28050	0.179606
$569$	−7.99058	−0.334983	−0.167491	−	0.985874i	$-0.553567\pi$
$569$	−7.99058	−0.334983	−0.167491	+	0.985874i	$0.553567\pi$
$570$	−110.256	−4.61811
$571$	33.2642	1.39206	0.696032	−	0.718011i	$-0.254947\pi$
$571$	33.2642	1.39206	0.696032	+	0.718011i	$0.254947\pi$
$572$	123.070	5.14580
$573$	41.9095	1.75079
$574$	18.6387	0.777964
$575$	4.00194	0.166892
$576$	−6.64283	−0.276785
$577$	−45.3251	−1.88691	−0.943453	−	0.331505i	$-0.892444\pi$
$577$	−45.3251	−1.88691	−0.943453	+	0.331505i	$0.892444\pi$
$578$	3.92998	0.163466
$579$	19.1536	0.795996
$580$	−36.2642	−1.50579
$581$	8.04987	0.333965
$582$	−49.8777	−2.06750
$583$	−19.3064	−0.799589
$584$	44.8122	1.85434
$585$	−29.2648	−1.20995
$586$	64.9563	2.68332
$587$	−33.9063	−1.39946	−0.699732	−	0.714405i	$-0.746697\pi$
$587$	−33.9063	−1.39946	−0.699732	+	0.714405i	$0.746697\pi$
$588$	−9.16172	−0.377823
$589$	−24.9122	−1.02649
$590$	35.6034	1.46577
$591$	37.3398	1.53595
$592$	−33.4449	−1.37458
$593$	2.41007	0.0989697	0.0494848	−	0.998775i	$-0.484242\pi$
$593$	2.41007	0.0989697	0.0494848	+	0.998775i	$0.484242\pi$
$594$	−37.3888	−1.53408
$595$	12.3971	0.508233
$596$	71.6668	2.93559
$597$	−53.8083	−2.20223
$598$	−11.6937	−0.478189
$599$	−10.5387	−0.430600	−0.215300	−	0.976548i	$-0.569073\pi$
$599$	−10.5387	−0.430600	−0.215300	+	0.976548i	$0.569073\pi$
$600$	60.5025	2.47000
$601$	−27.9364	−1.13955	−0.569775	−	0.821801i	$-0.692970\pi$
$601$	−27.9364	−1.13955	−0.569775	+	0.821801i	$0.692970\pi$
$602$	−3.37727	−0.137647
$603$	13.5182	0.550502
$604$	87.5559	3.56260
$605$	−43.5247	−1.76953
$606$	−2.06292	−0.0838006
$607$	−29.6402	−1.20306	−0.601530	−	0.798851i	$-0.705442\pi$
$607$	−29.6402	−1.20306	−0.601530	+	0.798851i	$0.705442\pi$
$608$	−18.8242	−0.763421
$609$	−5.77211	−0.233898
$610$	−84.5311	−3.42256
$611$	−28.2632	−1.14341
$612$	−26.8780	−1.08648
$613$	−45.3519	−1.83174	−0.915872	−	0.401470i	$-0.868500\pi$
$613$	−45.3519	−1.83174	−0.915872	+	0.401470i	$0.868500\pi$
$614$	−15.0342	−0.606732
$615$	−50.3929	−2.03204
$616$	−28.3113	−1.14069
$617$	31.5810	1.27140	0.635701	−	0.771936i	$-0.280711\pi$
$617$	31.5810	1.27140	0.635701	+	0.771936i	$0.280711\pi$
$618$	−8.57439	−0.344912
$619$	−9.47290	−0.380748	−0.190374	−	0.981712i	$-0.560970\pi$
$619$	−9.47290	−0.380748	−0.190374	+	0.981712i	$0.560970\pi$
$620$	51.6301	2.07351
$621$	2.41948	0.0970906
$622$	−3.41791	−0.137046
$623$	−13.2558	−0.531084
$624$	−70.7378	−2.83178
$625$	−25.1984	−1.00793
$626$	47.5357	1.89991
$627$	−69.4649	−2.77416
$628$	−43.9639	−1.75435
$629$	23.0599	0.919457
$630$	12.6618	0.504459
$631$	5.26792	0.209712	0.104856	−	0.994487i	$-0.466562\pi$
$631$	5.26792	0.209712	0.104856	+	0.994487i	$0.466562\pi$
$632$	−44.7085	−1.77841
$633$	−16.8246	−0.668717
$634$	−50.3585	−1.99999
$635$	53.7830	2.13431
$636$	35.5245	1.40864
$637$	5.78769	0.229317
$638$	−33.5474	−1.32816
$639$	−1.20613	−0.0477138
$640$	−51.0367	−2.01740
$641$	13.4414	0.530904	0.265452	−	0.964124i	$-0.414479\pi$
$641$	13.4414	0.530904	0.265452	+	0.964124i	$0.414479\pi$
$642$	−46.9538	−1.85312
$643$	−14.9024	−0.587692	−0.293846	−	0.955853i	$-0.594935\pi$
$643$	−14.9024	−0.587692	−0.293846	+	0.955853i	$0.594935\pi$
$644$	3.44575	0.135781
$645$	9.13104	0.359534
$646$	63.9709	2.51690
$647$	1.09313	0.0429754	0.0214877	−	0.999769i	$-0.493160\pi$
$647$	1.09313	0.0429754	0.0214877	+	0.999769i	$0.493160\pi$
$648$	63.9085	2.51056
$649$	22.4313	0.880507
$650$	−71.8860	−2.81960
$651$	8.21787	0.322084
$652$	−36.6001	−1.43337
$653$	−23.7586	−0.929746	−0.464873	−	0.885377i	$-0.653900\pi$
$653$	−23.7586	−0.929746	−0.464873	+	0.885377i	$0.653900\pi$
$654$	107.017	4.18469
$655$	33.7384	1.31827
$656$	−42.4056	−1.65566
$657$	−12.6269	−0.492622
$658$	12.2285	0.476716
$659$	−12.0340	−0.468779	−0.234390	−	0.972143i	$-0.575309\pi$
$659$	−12.0340	−0.468779	−0.234390	+	0.972143i	$0.575309\pi$
$660$	143.965	5.60383
$661$	−18.8412	−0.732839	−0.366419	−	0.930450i	$-0.619416\pi$
$661$	−18.8412	−0.732839	−0.366419	+	0.930450i	$0.619416\pi$
$662$	54.0574	2.10100
$663$	48.7729	1.89418
$664$	−45.7719	−1.77629
$665$	−20.5241	−0.795890
$666$	23.5522	0.912629
$667$	2.17091	0.0840578
$668$	−48.2122	−1.86539
$669$	−28.4422	−1.09964
$670$	66.6798	2.57607
$671$	−53.2574	−2.05598
$672$	6.20960	0.239540
$673$	−40.6424	−1.56665	−0.783324	−	0.621613i	$-0.786478\pi$
$673$	−40.6424	−1.56665	−0.783324	+	0.621613i	$0.786478\pi$
$674$	24.7716	0.954166
$675$	14.8736	0.572486
$676$	87.5375	3.36683
$677$	−41.3353	−1.58864	−0.794322	−	0.607497i	$-0.792174\pi$
$677$	−41.3353	−1.58864	−0.794322	+	0.607497i	$0.792174\pi$
$678$	−72.2726	−2.77561
$679$	−9.28471	−0.356315
$680$	−70.4905	−2.70319
$681$	−23.1148	−0.885763
$682$	47.7622	1.82891
$683$	−16.4332	−0.628801	−0.314400	−	0.949290i	$-0.601803\pi$
$683$	−16.4332	−0.628801	−0.314400	+	0.949290i	$0.601803\pi$
$684$	44.4979	1.70142
$685$	8.47234	0.323711
$686$	−2.50413	−0.0956081
$687$	62.0708	2.36815
$688$	7.68376	0.292940
$689$	−22.4418	−0.854963
$690$	−13.6791	−0.520753
$691$	−4.32626	−0.164579	−0.0822894	−	0.996608i	$-0.526223\pi$
$691$	−4.32626	−0.164579	−0.0822894	+	0.996608i	$0.526223\pi$
$692$	−67.0630	−2.54935
$693$	7.97737	0.303035
$694$	−40.1541	−1.52423
$695$	−42.3638	−1.60695
$696$	32.8204	1.24405
$697$	29.2381	1.10747
$698$	30.0064	1.13576
$699$	26.0944	0.986982
$700$	21.1825	0.800624
$701$	−41.2769	−1.55901	−0.779504	−	0.626397i	$-0.784529\pi$
$701$	−41.2769	−1.55901	−0.779504	+	0.626397i	$0.784529\pi$
$702$	−43.4607	−1.64032
$703$	−38.1768	−1.43986
$704$	−20.6440	−0.778050
$705$	−33.0619	−1.24518
$706$	−7.18067	−0.270248
$707$	−0.384012	−0.0144423
$708$	−41.2745	−1.55119
$709$	−51.2696	−1.92547	−0.962735	−	0.270448i	$-0.912828\pi$
$709$	−51.2696	−1.92547	−0.962735	+	0.270448i	$0.912828\pi$
$710$	−5.94938	−0.223276
$711$	12.5977	0.472449
$712$	75.3731	2.82473
$713$	−3.09076	−0.115750
$714$	−21.1023	−0.789733
$715$	−90.9464	−3.40120
$716$	13.5983	0.508192
$717$	−13.3288	−0.497774
$718$	35.1931	1.31339
$719$	25.3149	0.944088	0.472044	−	0.881575i	$-0.343516\pi$
$719$	25.3149	0.944088	0.472044	+	0.881575i	$0.343516\pi$
$720$	−28.8074	−1.07359
$721$	−1.59612	−0.0594425
$722$	−58.3286	−2.17077
$723$	49.6510	1.84654
$724$	−1.47654	−0.0548752
$725$	13.3455	0.495640
$726$	74.0874	2.74964
$727$	−1.86749	−0.0692614	−0.0346307	−	0.999400i	$-0.511025\pi$
$727$	−1.86749	−0.0692614	−0.0346307	+	0.999400i	$0.511025\pi$
$728$	−32.9090	−1.21969
$729$	1.29139	0.0478293
$730$	−62.2835	−2.30522
$731$	−5.29786	−0.195948
$732$	97.9956	3.62202
$733$	32.6726	1.20679	0.603395	−	0.797442i	$-0.293814\pi$
$733$	32.6726	1.20679	0.603395	+	0.797442i	$0.293814\pi$
$734$	−51.0732	−1.88515
$735$	6.77035	0.249728
$736$	−2.33545	−0.0860857
$737$	42.0105	1.54748
$738$	29.8624	1.09925
$739$	−20.2474	−0.744814	−0.372407	−	0.928070i	$-0.621467\pi$
$739$	−20.2474	−0.744814	−0.372407	+	0.928070i	$0.621467\pi$
$740$	79.1207	2.90854
$741$	−80.7460	−2.96628
$742$	9.70975	0.356456
$743$	−0.696977	−0.0255696	−0.0127848	−	0.999918i	$-0.504070\pi$
$743$	−0.696977	−0.0255696	−0.0127848	+	0.999918i	$0.504070\pi$
$744$	−46.7271	−1.71310
$745$	−52.9605	−1.94032
$746$	−26.4268	−0.967555
$747$	12.8973	0.471887
$748$	−83.5289	−3.05412
$749$	−8.74042	−0.319368
$750$	0.678052	0.0247590
$751$	33.8572	1.23547	0.617733	−	0.786388i	$-0.288051\pi$
$751$	33.8572	1.23547	0.617733	+	0.786388i	$0.288051\pi$
$752$	−27.8215	−1.01455
$753$	−28.1254	−1.02495
$754$	−38.9956	−1.42013
$755$	−64.7023	−2.35476
$756$	12.8065	0.465768
$757$	1.79979	0.0654145	0.0327072	−	0.999465i	$-0.489587\pi$
$757$	1.79979	0.0654145	0.0327072	+	0.999465i	$0.489587\pi$
$758$	−28.4176	−1.03217
$759$	−8.61826	−0.312823
$760$	116.701	4.23318
$761$	−8.12047	−0.294367	−0.147183	−	0.989109i	$-0.547021\pi$
$761$	−8.12047	−0.294367	−0.147183	+	0.989109i	$0.547021\pi$
$762$	−91.5489	−3.31647
$763$	19.9211	0.721193
$764$	−83.4307	−3.01842
$765$	19.8624	0.718125
$766$	−62.9904	−2.27594
$767$	26.0742	0.941485
$768$	69.0850	2.49289
$769$	14.8490	0.535469	0.267735	−	0.963493i	$-0.413725\pi$
$769$	14.8490	0.535469	0.267735	+	0.963493i	$0.413725\pi$
$770$	39.3493	1.41805
$771$	−37.0877	−1.33568
$772$	−38.1297	−1.37232
$773$	−3.98451	−0.143313	−0.0716565	−	0.997429i	$-0.522829\pi$
$773$	−3.98451	−0.143313	−0.0716565	+	0.997429i	$0.522829\pi$
$774$	−5.41097	−0.194493
$775$	−19.0003	−0.682510
$776$	52.7932	1.89517
$777$	12.5935	0.451790
$778$	22.3610	0.801679
$779$	−48.4053	−1.73430
$780$	167.345	5.99191
$781$	−3.74831	−0.134125
$782$	7.93663	0.283813
$783$	8.06840	0.288341
$784$	5.69724	0.203473
$785$	32.4886	1.15957
$786$	−57.4293	−2.04843
$787$	−33.5105	−1.19452	−0.597261	−	0.802047i	$-0.703744\pi$
$787$	−33.5105	−1.19452	−0.597261	+	0.802047i	$0.703744\pi$
$788$	−74.3337	−2.64803
$789$	28.6408	1.01964
$790$	62.1394	2.21082
$791$	−13.4535	−0.478352
$792$	−45.3596	−1.61178
$793$	−61.9064	−2.19836
$794$	−37.3388	−1.32510
$795$	−26.2520	−0.931063
$796$	107.118	3.79670
$797$	35.9520	1.27348	0.636742	−	0.771077i	$-0.280282\pi$
$797$	35.9520	1.27348	0.636742	+	0.771077i	$0.280282\pi$
$798$	34.9359	1.23672
$799$	19.1826	0.678632
$800$	−14.3570	−0.507597
$801$	−21.2381	−0.750413
$802$	−39.2858	−1.38723
$803$	−39.2407	−1.38477
$804$	−77.3009	−2.72619
$805$	−2.54635	−0.0897470
$806$	55.5188	1.95557
$807$	5.57001	0.196074
$808$	2.18351	0.0768155
$809$	−18.4939	−0.650209	−0.325105	−	0.945678i	$-0.605400\pi$
$809$	−18.4939	−0.650209	−0.325105	+	0.945678i	$0.605400\pi$
$810$	−88.8251	−3.12100
$811$	−33.8489	−1.18860	−0.594298	−	0.804245i	$-0.702570\pi$
$811$	−33.8489	−1.18860	−0.594298	+	0.804245i	$0.702570\pi$
$812$	11.4907	0.403246
$813$	21.8517	0.766371
$814$	73.1934	2.56543
$815$	27.0469	0.947410
$816$	48.0106	1.68071
$817$	8.77088	0.306854
$818$	26.4862	0.926069
$819$	9.27289	0.324021
$820$	100.319	3.50330
$821$	40.3610	1.40861	0.704305	−	0.709897i	$-0.251259\pi$
$821$	40.3610	1.40861	0.704305	+	0.709897i	$0.251259\pi$
$822$	−14.4215	−0.503009
$823$	13.7241	0.478393	0.239197	−	0.970971i	$-0.423116\pi$
$823$	13.7241	0.478393	0.239197	+	0.970971i	$0.423116\pi$
$824$	9.07558	0.316163
$825$	−52.9802	−1.84453
$826$	−11.2814	−0.392529
$827$	−27.7398	−0.964607	−0.482303	−	0.876004i	$-0.660200\pi$
$827$	−27.7398	−0.964607	−0.482303	+	0.876004i	$0.660200\pi$
$828$	5.52069	0.191857
$829$	−10.4224	−0.361986	−0.180993	−	0.983484i	$-0.557931\pi$
$829$	−10.4224	−0.361986	−0.180993	+	0.983484i	$0.557931\pi$
$830$	63.6174	2.20819
$831$	−8.45099	−0.293162
$832$	−23.9966	−0.831932
$833$	−3.92818	−0.136103
$834$	72.1113	2.49701
$835$	35.6280	1.23296
$836$	138.286	4.78273
$837$	−11.4871	−0.397054
$838$	13.6780	0.472498
$839$	−40.9582	−1.41403	−0.707017	−	0.707196i	$-0.749960\pi$
$839$	−40.9582	−1.41403	−0.707017	+	0.707196i	$0.749960\pi$
$840$	−38.4965	−1.32825
$841$	−21.7605	−0.750364
$842$	−8.49327	−0.292697
$843$	−66.4278	−2.28789
$844$	33.4933	1.15289
$845$	−64.6888	−2.22536
$846$	19.5922	0.673593
$847$	13.7913	0.473876
$848$	−22.0910	−0.758609
$849$	−18.4461	−0.633068
$850$	48.7899	1.67348
$851$	−4.73645	−0.162364
$852$	6.89703	0.236288
$853$	38.7547	1.32694	0.663468	−	0.748204i	$-0.269084\pi$
$853$	38.7547	1.32694	0.663468	+	0.748204i	$0.269084\pi$
$854$	26.7847	0.916553
$855$	−32.8832	−1.12458
$856$	49.6983	1.69865
$857$	3.57298	0.122051	0.0610253	−	0.998136i	$-0.480563\pi$
$857$	3.57298	0.122051	0.0610253	+	0.998136i	$0.480563\pi$
$858$	154.808	5.28506
$859$	1.00000	0.0341196
$859$	1.00000	0.0341196
$860$	−18.1775	−0.619848
$861$	15.9676	0.544175
$862$	75.7522	2.58013
$863$	25.9642	0.883833	0.441917	−	0.897056i	$-0.354299\pi$
$863$	25.9642	0.883833	0.441917	+	0.897056i	$0.354299\pi$
$864$	−8.67994	−0.295298
$865$	49.5585	1.68504
$866$	41.5602	1.41227
$867$	3.36679	0.114342
$868$	−16.3596	−0.555281
$869$	39.1499	1.32807
$870$	−45.6164	−1.54654
$871$	48.8330	1.65464
$872$	−113.272	−3.83588
$873$	−14.8757	−0.503467
$874$	−13.1395	−0.444450
$875$	0.126219	0.00426698
$876$	72.2044	2.43956
$877$	40.2722	1.35989	0.679947	−	0.733261i	$-0.262003\pi$
$877$	40.2722	1.35989	0.679947	+	0.733261i	$0.262003\pi$
$878$	−28.1173	−0.948912
$879$	55.6475	1.87694
$880$	−89.5250	−3.01789
$881$	55.2590	1.86172	0.930862	−	0.365371i	$-0.119058\pi$
$881$	55.2590	1.86172	0.930862	+	0.365371i	$0.119058\pi$
$882$	−4.01205	−0.135093
$883$	19.4003	0.652873	0.326437	−	0.945219i	$-0.394152\pi$
$883$	19.4003	0.652873	0.326437	+	0.945219i	$0.394152\pi$
$884$	−97.0940	−3.26562
$885$	30.5012	1.02529
$886$	−41.1310	−1.38182
$887$	−5.80635	−0.194958	−0.0974790	−	0.995238i	$-0.531078\pi$
$887$	−5.80635	−0.194958	−0.0974790	+	0.995238i	$0.531078\pi$
$888$	−71.6071	−2.40298
$889$	−17.0418	−0.571563
$890$	−104.760	−3.51155
$891$	−55.9628	−1.87482
$892$	56.6209	1.89581
$893$	−31.7578	−1.06273
$894$	90.1490	3.01503
$895$	−10.0489	−0.335898
$896$	16.1716	0.540254
$897$	−10.0179	−0.334487
$898$	27.2720	0.910078
$899$	−10.3070	−0.343756
$900$	33.9381	1.13127
$901$	15.2315	0.507435
$902$	92.8037	3.09002
$903$	−2.89328	−0.0962823
$904$	76.4971	2.54426
$905$	1.09114	0.0362707
$906$	110.136	3.65902
$907$	45.4440	1.50894	0.754472	−	0.656332i	$-0.227893\pi$
$907$	45.4440	1.50894	0.754472	+	0.656332i	$0.227893\pi$
$908$	46.0156	1.52708
$909$	−0.615254	−0.0204067
$910$	45.7396	1.51625
$911$	12.7518	0.422486	0.211243	−	0.977434i	$-0.432249\pi$
$911$	12.7518	0.422486	0.211243	+	0.977434i	$0.432249\pi$
$912$	−79.4841	−2.63198
$913$	40.0810	1.32649
$914$	16.1552	0.534367
$915$	−72.4171	−2.39404
$916$	−123.567	−4.08275
$917$	−10.6904	−0.353029
$918$	29.4973	0.973557
$919$	27.1191	0.894577	0.447289	−	0.894390i	$-0.352390\pi$
$919$	27.1191	0.894577	0.447289	+	0.894390i	$0.352390\pi$
$920$	14.4786	0.477346
$921$	−12.8797	−0.424401
$922$	−73.9276	−2.43468
$923$	−4.35703	−0.143413
$924$	−45.6170	−1.50069
$925$	−29.1171	−0.957363
$926$	57.7105	1.89648
$927$	−2.55726	−0.0839913
$928$	−7.78816	−0.255659
$929$	42.8773	1.40676	0.703380	−	0.710814i	$-0.251673\pi$
$929$	42.8773	1.40676	0.703380	+	0.710814i	$0.251673\pi$
$930$	64.9450	2.12963
$931$	6.50330	0.213137
$932$	−51.9472	−1.70159
$933$	−2.92809	−0.0958615
$934$	54.9850	1.79916
$935$	61.7264	2.01867
$936$	−52.7260	−1.72340
$937$	16.6706	0.544605	0.272303	−	0.962212i	$-0.412215\pi$
$937$	16.6706	0.544605	0.272303	+	0.962212i	$0.412215\pi$
$938$	−21.1283	−0.689864
$939$	40.7235	1.32896
$940$	65.8175	2.14673
$941$	−27.0832	−0.882887	−0.441444	−	0.897289i	$-0.645533\pi$
$941$	−27.0832	−0.882887	−0.441444	+	0.897289i	$0.645533\pi$
$942$	−55.3017	−1.80183
$943$	−6.00546	−0.195565
$944$	25.6667	0.835380
$945$	−9.46378	−0.307857
$946$	−16.8157	−0.546727
$947$	49.2594	1.60072	0.800358	−	0.599522i	$-0.204643\pi$
$947$	49.2594	1.60072	0.800358	+	0.599522i	$0.204643\pi$
$948$	−72.0372	−2.33966
$949$	−45.6134	−1.48067
$950$	−80.7743	−2.62066
$951$	−43.1417	−1.39897
$952$	22.3358	0.723907
$953$	49.2013	1.59379	0.796893	−	0.604120i	$-0.206475\pi$
$953$	49.2013	1.59379	0.796893	+	0.604120i	$0.206475\pi$
$954$	15.5567	0.503667
$955$	61.6539	1.99507
$956$	26.5342	0.858177
$957$	−28.7398	−0.929027
$958$	−28.4259	−0.918398
$959$	−2.68456	−0.0866890
$960$	−28.0708	−0.905982
$961$	−16.3258	−0.526638
$962$	85.0800	2.74309
$963$	−14.0037	−0.451262
$964$	−98.8421	−3.18349
$965$	28.1772	0.907057
$966$	4.33437	0.139456
$967$	39.5200	1.27088	0.635439	−	0.772151i	$-0.280819\pi$
$967$	39.5200	1.27088	0.635439	+	0.772151i	$0.280819\pi$
$968$	−78.4180	−2.52045
$969$	54.8033	1.76054
$970$	−73.3762	−2.35597
$971$	34.6198	1.11100	0.555501	−	0.831516i	$-0.312527\pi$
$971$	34.6198	1.11100	0.555501	+	0.831516i	$0.312527\pi$
$972$	64.5542	2.07058
$973$	13.4235	0.430337
$974$	−69.7263	−2.23417
$975$	−61.5842	−1.97227
$976$	−60.9389	−1.95061
$977$	−8.04176	−0.257279	−0.128639	−	0.991691i	$-0.541061\pi$
$977$	−8.04176	−0.257279	−0.128639	+	0.991691i	$0.541061\pi$
$978$	−46.0389	−1.47216
$979$	−66.0020	−2.10943
$980$	−13.4780	−0.430539
$981$	31.9171	1.01903
$982$	−99.4724	−3.17429
$983$	−28.8436	−0.919968	−0.459984	−	0.887927i	$-0.652145\pi$
$983$	−28.8436	−0.919968	−0.459984	+	0.887927i	$0.652145\pi$
$984$	−90.7924	−2.89436
$985$	54.9313	1.75026
$986$	26.4668	0.842874
$987$	10.4761	0.333456
$988$	160.744	5.11395
$989$	1.08817	0.0346018
$990$	63.0443	2.00368
$991$	10.9776	0.348716	0.174358	−	0.984682i	$-0.444215\pi$
$991$	10.9776	0.348716	0.174358	+	0.984682i	$0.444215\pi$
$992$	11.0882	0.352049
$993$	46.3105	1.46962
$994$	1.88513	0.0597928
$995$	−79.1585	−2.50949
$996$	−73.7507	−2.33688
$997$	13.8036	0.437165	0.218582	−	0.975818i	$-0.429857\pi$
$997$	13.8036	0.437165	0.218582	+	0.975818i	$0.429857\pi$
$998$	91.1788	2.88621
$999$	−17.6035	−0.556951

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.d.1.9	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.d.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-2.50413 q^{2} -2.14527 q^{3} +4.27066 q^{4} -3.15595 q^{5} +5.37203 q^{6} +1.00000 q^{7} -5.68604 q^{8} +1.60217 q^{9} +O(q^{10})\)	\(q-2.50413 q^{2} -2.14527 q^{3} +4.27066 q^{4} -3.15595 q^{5} +5.37203 q^{6} +1.00000 q^{7} -5.68604 q^{8} +1.60217 q^{9} +7.90290 q^{10} +4.97909 q^{11} -9.16172 q^{12} +5.78769 q^{13} -2.50413 q^{14} +6.77035 q^{15} +5.69724 q^{16} -3.92818 q^{17} -4.01205 q^{18} +6.50330 q^{19} -13.4780 q^{20} -2.14527 q^{21} -12.4683 q^{22} +0.806841 q^{23} +12.1981 q^{24} +4.96001 q^{25} -14.4931 q^{26} +2.99871 q^{27} +4.27066 q^{28} +2.69062 q^{29} -16.9538 q^{30} -3.83069 q^{31} -2.89456 q^{32} -10.6815 q^{33} +9.83667 q^{34} -3.15595 q^{35} +6.84234 q^{36} -5.87037 q^{37} -16.2851 q^{38} -12.4162 q^{39} +17.9448 q^{40} -7.44318 q^{41} +5.37203 q^{42} +1.34868 q^{43} +21.2640 q^{44} -5.05638 q^{45} -2.02043 q^{46} -4.88333 q^{47} -12.2221 q^{48} +1.00000 q^{49} -12.4205 q^{50} +8.42700 q^{51} +24.7173 q^{52} -3.87750 q^{53} -7.50916 q^{54} -15.7137 q^{55} -5.68604 q^{56} -13.9513 q^{57} -6.73767 q^{58} +4.50511 q^{59} +28.9139 q^{60} -10.6962 q^{61} +9.59255 q^{62} +1.60217 q^{63} -4.14614 q^{64} -18.2657 q^{65} +26.7478 q^{66} +8.43739 q^{67} -16.7759 q^{68} -1.73089 q^{69} +7.90290 q^{70} -0.752810 q^{71} -9.11002 q^{72} -7.88110 q^{73} +14.7002 q^{74} -10.6405 q^{75} +27.7734 q^{76} +4.97909 q^{77} +31.0917 q^{78} +7.86285 q^{79} -17.9802 q^{80} -11.2396 q^{81} +18.6387 q^{82} +8.04987 q^{83} -9.16172 q^{84} +12.3971 q^{85} -3.37727 q^{86} -5.77211 q^{87} -28.3113 q^{88} -13.2558 q^{89} +12.6618 q^{90} +5.78769 q^{91} +3.44575 q^{92} +8.21787 q^{93} +12.2285 q^{94} -20.5241 q^{95} +6.20960 q^{96} -9.28471 q^{97} -2.50413 q^{98} +7.97737 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) \) 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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