LMFDB - Embedded newform 6014.2.a.f.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.79599 q^{3} +1.00000 q^{4} -3.70171 q^{5} +1.79599 q^{6} -3.49561 q^{7} -1.00000 q^{8} +0.225587 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.79599 q^{3} +1.00000 q^{4} -3.70171 q^{5} +1.79599 q^{6} -3.49561 q^{7} -1.00000 q^{8} +0.225587 q^{9} +3.70171 q^{10} -2.91358 q^{11} -1.79599 q^{12} -5.02215 q^{13} +3.49561 q^{14} +6.64824 q^{15} +1.00000 q^{16} -2.33035 q^{17} -0.225587 q^{18} -5.04050 q^{19} -3.70171 q^{20} +6.27809 q^{21} +2.91358 q^{22} +1.87422 q^{23} +1.79599 q^{24} +8.70264 q^{25} +5.02215 q^{26} +4.98282 q^{27} -3.49561 q^{28} -0.320848 q^{29} -6.64824 q^{30} +1.00000 q^{31} -1.00000 q^{32} +5.23276 q^{33} +2.33035 q^{34} +12.9397 q^{35} +0.225587 q^{36} -0.812786 q^{37} +5.04050 q^{38} +9.01973 q^{39} +3.70171 q^{40} -5.50200 q^{41} -6.27809 q^{42} +5.99091 q^{43} -2.91358 q^{44} -0.835057 q^{45} -1.87422 q^{46} +2.07325 q^{47} -1.79599 q^{48} +5.21931 q^{49} -8.70264 q^{50} +4.18528 q^{51} -5.02215 q^{52} +8.65655 q^{53} -4.98282 q^{54} +10.7852 q^{55} +3.49561 q^{56} +9.05270 q^{57} +0.320848 q^{58} +1.65273 q^{59} +6.64824 q^{60} +8.66355 q^{61} -1.00000 q^{62} -0.788565 q^{63} +1.00000 q^{64} +18.5905 q^{65} -5.23276 q^{66} -11.2652 q^{67} -2.33035 q^{68} -3.36609 q^{69} -12.9397 q^{70} -2.21214 q^{71} -0.225587 q^{72} +3.82229 q^{73} +0.812786 q^{74} -15.6299 q^{75} -5.04050 q^{76} +10.1847 q^{77} -9.01973 q^{78} -15.5595 q^{79} -3.70171 q^{80} -9.62587 q^{81} +5.50200 q^{82} -0.286227 q^{83} +6.27809 q^{84} +8.62626 q^{85} -5.99091 q^{86} +0.576241 q^{87} +2.91358 q^{88} -13.3619 q^{89} +0.835057 q^{90} +17.5555 q^{91} +1.87422 q^{92} -1.79599 q^{93} -2.07325 q^{94} +18.6585 q^{95} +1.79599 q^{96} +1.00000 q^{97} -5.21931 q^{98} -0.657265 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9}+O(q^{10}) $ 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9	$ 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9} - 8 q^{13} + 11 q^{14} + q^{15} + 22 q^{16} - 4 q^{17} - 8 q^{18} - 23 q^{19} - 12 q^{21} + 2 q^{23} - 12 q^{25} + 8 q^{26} + 3 q^{27} - 11 q^{28} + 9 q^{29} - q^{30} + 22 q^{31} - 22 q^{32} + 4 q^{34} + 4 q^{35} + 8 q^{36} - 17 q^{37} + 23 q^{38} + 8 q^{39} - 21 q^{41} + 12 q^{42} - 7 q^{43} + 9 q^{45} - 2 q^{46} - 10 q^{47} - 27 q^{49} + 12 q^{50} - q^{51} - 8 q^{52} + 9 q^{53} - 3 q^{54} - 6 q^{55} + 11 q^{56} - q^{57} - 9 q^{58} - 12 q^{59} + q^{60} - 34 q^{61} - 22 q^{62} - 5 q^{63} + 22 q^{64} + 4 q^{65} - 31 q^{67} - 4 q^{68} - 51 q^{69} - 4 q^{70} - 15 q^{71} - 8 q^{72} + 3 q^{73} + 17 q^{74} - 24 q^{75} - 23 q^{76} + 24 q^{77} - 8 q^{78} - 23 q^{79} - 26 q^{81} + 21 q^{82} + 22 q^{83} - 12 q^{84} - 42 q^{85} + 7 q^{86} - 9 q^{87} - 36 q^{89} - 9 q^{90} - 6 q^{91} + 2 q^{92} + 10 q^{94} + 2 q^{95} + 22 q^{97} + 27 q^{98} - 25 q^{99}+O(q^{100}) $ 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9 - 8 * q^13 + 11 * q^14 + q^15 + 22 * q^16 - 4 * q^17 - 8 * q^18 - 23 * q^19 - 12 * q^21 + 2 * q^23 - 12 * q^25 + 8 * q^26 + 3 * q^27 - 11 * q^28 + 9 * q^29 - q^30 + 22 * q^31 - 22 * q^32 + 4 * q^34 + 4 * q^35 + 8 * q^36 - 17 * q^37 + 23 * q^38 + 8 * q^39 - 21 * q^41 + 12 * q^42 - 7 * q^43 + 9 * q^45 - 2 * q^46 - 10 * q^47 - 27 * q^49 + 12 * q^50 - q^51 - 8 * q^52 + 9 * q^53 - 3 * q^54 - 6 * q^55 + 11 * q^56 - q^57 - 9 * q^58 - 12 * q^59 + q^60 - 34 * q^61 - 22 * q^62 - 5 * q^63 + 22 * q^64 + 4 * q^65 - 31 * q^67 - 4 * q^68 - 51 * q^69 - 4 * q^70 - 15 * q^71 - 8 * q^72 + 3 * q^73 + 17 * q^74 - 24 * q^75 - 23 * q^76 + 24 * q^77 - 8 * q^78 - 23 * q^79 - 26 * q^81 + 21 * q^82 + 22 * q^83 - 12 * q^84 - 42 * q^85 + 7 * q^86 - 9 * q^87 - 36 * q^89 - 9 * q^90 - 6 * q^91 + 2 * q^92 + 10 * q^94 + 2 * q^95 + 22 * q^97 + 27 * q^98 - 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.79599	−1.03692	−0.518458	−	0.855103i	$-0.673494\pi$
$3$	−1.79599	−1.03692	−0.518458	+	0.855103i	$0.673494\pi$
$4$	1.00000	0.500000
$5$	−3.70171	−1.65545	−0.827727	−	0.561131i	$-0.810366\pi$
$5$	−3.70171	−1.65545	−0.827727	+	0.561131i	$0.810366\pi$
$6$	1.79599	0.733211
$7$	−3.49561	−1.32122	−0.660609	−	0.750730i	$-0.729702\pi$
$7$	−3.49561	−1.32122	−0.660609	+	0.750730i	$0.729702\pi$
$8$	−1.00000	−0.353553
$9$	0.225587	0.0751957
$10$	3.70171	1.17058
$11$	−2.91358	−0.878477	−0.439238	−	0.898371i	$-0.644752\pi$
$11$	−2.91358	−0.878477	−0.439238	+	0.898371i	$0.644752\pi$
$12$	−1.79599	−0.518458
$13$	−5.02215	−1.39289	−0.696446	−	0.717609i	$-0.745237\pi$
$13$	−5.02215	−1.39289	−0.696446	+	0.717609i	$0.745237\pi$
$14$	3.49561	0.934242
$15$	6.64824	1.71657
$16$	1.00000	0.250000
$17$	−2.33035	−0.565192	−0.282596	−	0.959239i	$-0.591196\pi$
$17$	−2.33035	−0.565192	−0.282596	+	0.959239i	$0.591196\pi$
$18$	−0.225587	−0.0531714
$19$	−5.04050	−1.15637	−0.578185	−	0.815906i	$-0.696239\pi$
$19$	−5.04050	−1.15637	−0.578185	+	0.815906i	$0.696239\pi$
$20$	−3.70171	−0.827727
$21$	6.27809	1.36999
$22$	2.91358	0.621177
$23$	1.87422	0.390802	0.195401	−	0.980723i	$-0.437399\pi$
$23$	1.87422	0.390802	0.195401	+	0.980723i	$0.437399\pi$
$24$	1.79599	0.366605
$25$	8.70264	1.74053
$26$	5.02215	0.984924
$27$	4.98282	0.958945
$28$	−3.49561	−0.660609
$29$	−0.320848	−0.0595800	−0.0297900	−	0.999556i	$-0.509484\pi$
$29$	−0.320848	−0.0595800	−0.0297900	+	0.999556i	$0.509484\pi$
$30$	−6.64824	−1.21380
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	5.23276	0.910907
$34$	2.33035	0.399651
$35$	12.9397	2.18722
$36$	0.225587	0.0375978
$37$	−0.812786	−0.133621	−0.0668106	−	0.997766i	$-0.521282\pi$
$37$	−0.812786	−0.133621	−0.0668106	+	0.997766i	$0.521282\pi$
$38$	5.04050	0.817677
$39$	9.01973	1.44431
$40$	3.70171	0.585291
$41$	−5.50200	−0.859267	−0.429634	−	0.903003i	$-0.641357\pi$
$41$	−5.50200	−0.859267	−0.429634	+	0.903003i	$0.641357\pi$
$42$	−6.27809	−0.968731
$43$	5.99091	0.913606	0.456803	−	0.889568i	$-0.348994\pi$
$43$	5.99091	0.913606	0.456803	+	0.889568i	$0.348994\pi$
$44$	−2.91358	−0.439238
$45$	−0.835057	−0.124483
$46$	−1.87422	−0.276339
$47$	2.07325	0.302414	0.151207	−	0.988502i	$-0.451684\pi$
$47$	2.07325	0.302414	0.151207	+	0.988502i	$0.451684\pi$
$48$	−1.79599	−0.259229
$49$	5.21931	0.745616
$50$	−8.70264	−1.23074
$51$	4.18528	0.586057
$52$	−5.02215	−0.696446
$53$	8.65655	1.18907	0.594534	−	0.804070i	$-0.297337\pi$
$53$	8.65655	1.18907	0.594534	+	0.804070i	$0.297337\pi$
$54$	−4.98282	−0.678076
$55$	10.7852	1.45428
$56$	3.49561	0.467121
$57$	9.05270	1.19906
$58$	0.320848	0.0421294
$59$	1.65273	0.215167	0.107583	−	0.994196i	$-0.465689\pi$
$59$	1.65273	0.215167	0.107583	+	0.994196i	$0.465689\pi$
$60$	6.64824	0.858284
$61$	8.66355	1.10925	0.554627	−	0.832099i	$-0.312861\pi$
$61$	8.66355	1.10925	0.554627	+	0.832099i	$0.312861\pi$
$62$	−1.00000	−0.127000
$63$	−0.788565	−0.0993498
$64$	1.00000	0.125000
$65$	18.5905	2.30587
$66$	−5.23276	−0.644108
$67$	−11.2652	−1.37626	−0.688130	−	0.725587i	$-0.741568\pi$
$67$	−11.2652	−1.37626	−0.688130	+	0.725587i	$0.741568\pi$
$68$	−2.33035	−0.282596
$69$	−3.36609	−0.405229
$70$	−12.9397	−1.54659
$71$	−2.21214	−0.262532	−0.131266	−	0.991347i	$-0.541904\pi$
$71$	−2.21214	−0.262532	−0.131266	+	0.991347i	$0.541904\pi$
$72$	−0.225587	−0.0265857
$73$	3.82229	0.447365	0.223683	−	0.974662i	$-0.428192\pi$
$73$	3.82229	0.447365	0.223683	+	0.974662i	$0.428192\pi$
$74$	0.812786	0.0944845
$75$	−15.6299	−1.80478
$76$	−5.04050	−0.578185
$77$	10.1847	1.16066
$78$	−9.01973	−1.02128
$79$	−15.5595	−1.75058	−0.875292	−	0.483595i	$-0.839331\pi$
$79$	−15.5595	−1.75058	−0.875292	+	0.483595i	$0.839331\pi$
$80$	−3.70171	−0.413864
$81$	−9.62587	−1.06954
$82$	5.50200	0.607594
$83$	−0.286227	−0.0314175	−0.0157087	−	0.999877i	$-0.505000\pi$
$83$	−0.286227	−0.0314175	−0.0157087	+	0.999877i	$0.505000\pi$
$84$	6.27809	0.684996
$85$	8.62626	0.935649
$86$	−5.99091	−0.646017
$87$	0.576241	0.0617795
$88$	2.91358	0.310588
$89$	−13.3619	−1.41636	−0.708178	−	0.706034i	$-0.750483\pi$
$89$	−13.3619	−1.41636	−0.708178	+	0.706034i	$0.750483\pi$
$90$	0.835057	0.0880228
$91$	17.5555	1.84031
$92$	1.87422	0.195401
$93$	−1.79599	−0.186236
$94$	−2.07325	−0.213839
$95$	18.6585	1.91432
$96$	1.79599	0.183303
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	−5.21931	−0.527230
$99$	−0.657265	−0.0660576
$100$	8.70264	0.870264
$101$	14.8156	1.47420	0.737102	−	0.675782i	$-0.236194\pi$
$101$	14.8156	1.47420	0.737102	+	0.675782i	$0.236194\pi$
$102$	−4.18528	−0.414405
$103$	−1.49393	−0.147201	−0.0736004	−	0.997288i	$-0.523449\pi$
$103$	−1.49393	−0.147201	−0.0736004	+	0.997288i	$0.523449\pi$
$104$	5.02215	0.492462
$105$	−23.2397	−2.26796
$106$	−8.65655	−0.840798
$107$	10.7656	1.04075	0.520375	−	0.853938i	$-0.325792\pi$
$107$	10.7656	1.04075	0.520375	+	0.853938i	$0.325792\pi$
$108$	4.98282	0.479472
$109$	0.242196	0.0231982	0.0115991	−	0.999933i	$-0.496308\pi$
$109$	0.242196	0.0231982	0.0115991	+	0.999933i	$0.496308\pi$
$110$	−10.7852	−1.02833
$111$	1.45976	0.138554
$112$	−3.49561	−0.330304
$113$	15.0284	1.41375	0.706875	−	0.707338i	$-0.250104\pi$
$113$	15.0284	1.41375	0.706875	+	0.707338i	$0.250104\pi$
$114$	−9.05270	−0.847863
$115$	−6.93782	−0.646955
$116$	−0.320848	−0.0297900
$117$	−1.13293	−0.104739
$118$	−1.65273	−0.152146
$119$	8.14599	0.746741
$120$	−6.64824	−0.606898
$121$	−2.51107	−0.228279
$122$	−8.66355	−0.784361
$123$	9.88154	0.890989
$124$	1.00000	0.0898027
$125$	−13.7061	−1.22591
$126$	0.788565	0.0702510
$127$	1.47730	0.131089	0.0655445	−	0.997850i	$-0.479122\pi$
$127$	1.47730	0.131089	0.0655445	+	0.997850i	$0.479122\pi$
$128$	−1.00000	−0.0883883
$129$	−10.7596	−0.947333
$130$	−18.5905	−1.63050
$131$	−2.18012	−0.190478	−0.0952388	−	0.995454i	$-0.530361\pi$
$131$	−2.18012	−0.190478	−0.0952388	+	0.995454i	$0.530361\pi$
$132$	5.23276	0.455453
$133$	17.6196	1.52782
$134$	11.2652	0.973163
$135$	−18.4450	−1.58749
$136$	2.33035	0.199825
$137$	−16.8956	−1.44349	−0.721746	−	0.692158i	$-0.756660\pi$
$137$	−16.8956	−1.44349	−0.721746	+	0.692158i	$0.756660\pi$
$138$	3.36609	0.286540
$139$	5.72687	0.485747	0.242873	−	0.970058i	$-0.421910\pi$
$139$	5.72687	0.485747	0.242873	+	0.970058i	$0.421910\pi$
$140$	12.9397	1.09361
$141$	−3.72354	−0.313579
$142$	2.21214	0.185638
$143$	14.6324	1.22362
$144$	0.225587	0.0187989
$145$	1.18769	0.0986319
$146$	−3.82229	−0.316335
$147$	−9.37384	−0.773142
$148$	−0.812786	−0.0668106
$149$	5.18336	0.424637	0.212319	−	0.977200i	$-0.431899\pi$
$149$	5.18336	0.424637	0.212319	+	0.977200i	$0.431899\pi$
$150$	15.6299	1.27617
$151$	−21.1260	−1.71921	−0.859605	−	0.510959i	$-0.829290\pi$
$151$	−21.1260	−1.71921	−0.859605	+	0.510959i	$0.829290\pi$
$152$	5.04050	0.408839
$153$	−0.525696	−0.0425000
$154$	−10.1847	−0.820710
$155$	−3.70171	−0.297328
$156$	9.01973	0.722157
$157$	−2.59221	−0.206881	−0.103441	−	0.994636i	$-0.532985\pi$
$157$	−2.59221	−0.206881	−0.103441	+	0.994636i	$0.532985\pi$
$158$	15.5595	1.23785
$159$	−15.5471	−1.23296
$160$	3.70171	0.292646
$161$	−6.55155	−0.516335
$162$	9.62587	0.756280
$163$	8.11000	0.635224	0.317612	−	0.948221i	$-0.397119\pi$
$163$	8.11000	0.635224	0.317612	+	0.948221i	$0.397119\pi$
$164$	−5.50200	−0.429634
$165$	−19.3702	−1.50796
$166$	0.286227	0.0222155
$167$	15.6571	1.21158	0.605791	−	0.795624i	$-0.292857\pi$
$167$	15.6571	1.21158	0.605791	+	0.795624i	$0.292857\pi$
$168$	−6.27809	−0.484365
$169$	12.2219	0.940150
$170$	−8.62626	−0.661604
$171$	−1.13707	−0.0869540
$172$	5.99091	0.456803
$173$	−18.7546	−1.42589	−0.712945	−	0.701220i	$-0.752639\pi$
$173$	−18.7546	−1.42589	−0.712945	+	0.701220i	$0.752639\pi$
$174$	−0.576241	−0.0436847
$175$	−30.4211	−2.29962
$176$	−2.91358	−0.219619
$177$	−2.96828	−0.223110
$178$	13.3619	1.00152
$179$	22.8829	1.71035	0.855175	−	0.518339i	$-0.173449\pi$
$179$	22.8829	1.71035	0.855175	+	0.518339i	$0.173449\pi$
$180$	−0.835057	−0.0622415
$181$	−13.2414	−0.984224	−0.492112	−	0.870532i	$-0.663775\pi$
$181$	−13.2414	−0.984224	−0.492112	+	0.870532i	$0.663775\pi$
$182$	−17.5555	−1.30130
$183$	−15.5597	−1.15020
$184$	−1.87422	−0.138169
$185$	3.00870	0.221204
$186$	1.79599	0.131689
$187$	6.78964	0.496508
$188$	2.07325	0.151207
$189$	−17.4180	−1.26697
$190$	−18.6585	−1.35363
$191$	8.82005	0.638197	0.319098	−	0.947722i	$-0.396620\pi$
$191$	8.82005	0.638197	0.319098	+	0.947722i	$0.396620\pi$
$192$	−1.79599	−0.129615
$193$	9.61514	0.692113	0.346056	−	0.938214i	$-0.387521\pi$
$193$	9.61514	0.692113	0.346056	+	0.938214i	$0.387521\pi$
$194$	−1.00000	−0.0717958
$195$	−33.3884	−2.39099
$196$	5.21931	0.372808
$197$	9.03250	0.643539	0.321769	−	0.946818i	$-0.395722\pi$
$197$	9.03250	0.643539	0.321769	+	0.946818i	$0.395722\pi$
$198$	0.657265	0.0467098
$199$	−18.4248	−1.30610	−0.653049	−	0.757316i	$-0.726510\pi$
$199$	−18.4248	−1.30610	−0.653049	+	0.757316i	$0.726510\pi$
$200$	−8.70264	−0.615370
$201$	20.2322	1.42707
$202$	−14.8156	−1.04242
$203$	1.12156	0.0787181
$204$	4.18528	0.293028
$205$	20.3668	1.42248
$206$	1.49393	0.104087
$207$	0.422800	0.0293866
$208$	−5.02215	−0.348223
$209$	14.6859	1.01584
$210$	23.2397	1.60369
$211$	12.3569	0.850686	0.425343	−	0.905032i	$-0.360153\pi$
$211$	12.3569	0.850686	0.425343	+	0.905032i	$0.360153\pi$
$212$	8.65655	0.594534
$213$	3.97298	0.272224
$214$	−10.7656	−0.735921
$215$	−22.1766	−1.51243
$216$	−4.98282	−0.339038
$217$	−3.49561	−0.237298
$218$	−0.242196	−0.0164036
$219$	−6.86480	−0.463880
$220$	10.7852	0.727139
$221$	11.7033	0.787251
$222$	−1.45976	−0.0979725
$223$	13.3743	0.895607	0.447804	−	0.894132i	$-0.352206\pi$
$223$	13.3743	0.895607	0.447804	+	0.894132i	$0.352206\pi$
$224$	3.49561	0.233560
$225$	1.96320	0.130880
$226$	−15.0284	−0.999673
$227$	−8.23725	−0.546725	−0.273363	−	0.961911i	$-0.588136\pi$
$227$	−8.23725	−0.546725	−0.273363	+	0.961911i	$0.588136\pi$
$228$	9.05270	0.599530
$229$	6.10053	0.403134	0.201567	−	0.979475i	$-0.435397\pi$
$229$	6.10053	0.403134	0.201567	+	0.979475i	$0.435397\pi$
$230$	6.93782	0.457466
$231$	−18.2917	−1.20351
$232$	0.320848	0.0210647
$233$	1.94593	0.127482	0.0637409	−	0.997966i	$-0.479697\pi$
$233$	1.94593	0.127482	0.0637409	+	0.997966i	$0.479697\pi$
$234$	1.13293	0.0740620
$235$	−7.67456	−0.500633
$236$	1.65273	0.107583
$237$	27.9448	1.81521
$238$	−8.14599	−0.528026
$239$	−18.1503	−1.17404	−0.587022	−	0.809571i	$-0.699700\pi$
$239$	−18.1503	−1.17404	−0.587022	+	0.809571i	$0.699700\pi$
$240$	6.64824	0.429142
$241$	21.0753	1.35758	0.678790	−	0.734332i	$-0.262505\pi$
$241$	21.0753	1.35758	0.678790	+	0.734332i	$0.262505\pi$
$242$	2.51107	0.161418
$243$	2.33952	0.150080
$244$	8.66355	0.554627
$245$	−19.3204	−1.23433
$246$	−9.88154	−0.630024
$247$	25.3141	1.61070
$248$	−1.00000	−0.0635001
$249$	0.514061	0.0325773
$250$	13.7061	0.866850
$251$	20.8592	1.31662	0.658311	−	0.752746i	$-0.271271\pi$
$251$	20.8592	1.31662	0.658311	+	0.752746i	$0.271271\pi$
$252$	−0.788565	−0.0496749
$253$	−5.46069	−0.343310
$254$	−1.47730	−0.0926939
$255$	−15.4927	−0.970190
$256$	1.00000	0.0625000
$257$	−11.1697	−0.696749	−0.348375	−	0.937355i	$-0.613266\pi$
$257$	−11.1697	−0.696749	−0.348375	+	0.937355i	$0.613266\pi$
$258$	10.7596	0.669866
$259$	2.84119	0.176543
$260$	18.5905	1.15293
$261$	−0.0723792	−0.00448016
$262$	2.18012	0.134688
$263$	22.0767	1.36131	0.680654	−	0.732605i	$-0.261696\pi$
$263$	22.0767	1.36131	0.680654	+	0.732605i	$0.261696\pi$
$264$	−5.23276	−0.322054
$265$	−32.0440	−1.96845
$266$	−17.6196	−1.08033
$267$	23.9978	1.46864
$268$	−11.2652	−0.688130
$269$	−1.98069	−0.120765	−0.0603823	−	0.998175i	$-0.519232\pi$
$269$	−1.98069	−0.120765	−0.0603823	+	0.998175i	$0.519232\pi$
$270$	18.4450	1.12252
$271$	−24.6306	−1.49620	−0.748101	−	0.663585i	$-0.769034\pi$
$271$	−24.6306	−1.49620	−0.748101	+	0.663585i	$0.769034\pi$
$272$	−2.33035	−0.141298
$273$	−31.5295	−1.90825
$274$	16.8956	1.02070
$275$	−25.3558	−1.52901
$276$	−3.36609	−0.202615
$277$	9.35226	0.561923	0.280961	−	0.959719i	$-0.409347\pi$
$277$	9.35226	0.561923	0.280961	+	0.959719i	$0.409347\pi$
$278$	−5.72687	−0.343475
$279$	0.225587	0.0135055
$280$	−12.9397	−0.773297
$281$	−23.2651	−1.38788	−0.693939	−	0.720034i	$-0.744126\pi$
$281$	−23.2651	−1.38788	−0.693939	+	0.720034i	$0.744126\pi$
$282$	3.72354	0.221733
$283$	−11.0134	−0.654677	−0.327339	−	0.944907i	$-0.606152\pi$
$283$	−11.0134	−0.654677	−0.327339	+	0.944907i	$0.606152\pi$
$284$	−2.21214	−0.131266
$285$	−33.5105	−1.98499
$286$	−14.6324	−0.865232
$287$	19.2329	1.13528
$288$	−0.225587	−0.0132928
$289$	−11.5695	−0.680558
$290$	−1.18769	−0.0697433
$291$	−1.79599	−0.105283
$292$	3.82229	0.223683
$293$	7.65828	0.447402	0.223701	−	0.974658i	$-0.428186\pi$
$293$	7.65828	0.447402	0.223701	+	0.974658i	$0.428186\pi$
$294$	9.37384	0.546694
$295$	−6.11791	−0.356199
$296$	0.812786	0.0472422
$297$	−14.5178	−0.842411
$298$	−5.18336	−0.300264
$299$	−9.41261	−0.544345
$300$	−15.6299	−0.902391
$301$	−20.9419	−1.20707
$302$	21.1260	1.21567
$303$	−26.6086	−1.52863
$304$	−5.04050	−0.289093
$305$	−32.0699	−1.83632
$306$	0.525696	0.0300520
$307$	25.6958	1.46654	0.733269	−	0.679939i	$-0.237994\pi$
$307$	25.6958	1.46654	0.733269	+	0.679939i	$0.237994\pi$
$308$	10.1847	0.580329
$309$	2.68308	0.152635
$310$	3.70171	0.210243
$311$	−9.14756	−0.518711	−0.259355	−	0.965782i	$-0.583510\pi$
$311$	−9.14756	−0.518711	−0.259355	+	0.965782i	$0.583510\pi$
$312$	−9.01973	−0.510642
$313$	−21.7149	−1.22740	−0.613700	−	0.789539i	$-0.710320\pi$
$313$	−21.7149	−1.22740	−0.613700	+	0.789539i	$0.710320\pi$
$314$	2.59221	0.146287
$315$	2.91904	0.164469
$316$	−15.5595	−0.875292
$317$	0.719481	0.0404101	0.0202050	−	0.999796i	$-0.493568\pi$
$317$	0.719481	0.0404101	0.0202050	+	0.999796i	$0.493568\pi$
$318$	15.5471	0.871837
$319$	0.934816	0.0523396
$320$	−3.70171	−0.206932
$321$	−19.3349	−1.07917
$322$	6.55155	0.365104
$323$	11.7461	0.653571
$324$	−9.62587	−0.534771
$325$	−43.7059	−2.42437
$326$	−8.11000	−0.449171
$327$	−0.434982	−0.0240546
$328$	5.50200	0.303797
$329$	−7.24728	−0.399555
$330$	19.3702	1.06629
$331$	−1.01726	−0.0559137	−0.0279568	−	0.999609i	$-0.508900\pi$
$331$	−1.01726	−0.0559137	−0.0279568	+	0.999609i	$0.508900\pi$
$332$	−0.286227	−0.0157087
$333$	−0.183354	−0.0100477
$334$	−15.6571	−0.856718
$335$	41.7004	2.27834
$336$	6.27809	0.342498
$337$	−16.4230	−0.894615	−0.447308	−	0.894380i	$-0.647617\pi$
$337$	−16.4230	−0.894615	−0.447308	+	0.894380i	$0.647617\pi$
$338$	−12.2219	−0.664786
$339$	−26.9908	−1.46594
$340$	8.62626	0.467824
$341$	−2.91358	−0.157779
$342$	1.13707	0.0614858
$343$	6.22459	0.336097
$344$	−5.99091	−0.323008
$345$	12.4603	0.670838
$346$	18.7546	1.00826
$347$	2.51057	0.134775	0.0673873	−	0.997727i	$-0.478534\pi$
$347$	2.51057	0.134775	0.0673873	+	0.997727i	$0.478534\pi$
$348$	0.576241	0.0308897
$349$	−6.71552	−0.359473	−0.179737	−	0.983715i	$-0.557525\pi$
$349$	−6.71552	−0.359473	−0.179737	+	0.983715i	$0.557525\pi$
$350$	30.4211	1.62607
$351$	−25.0245	−1.33571
$352$	2.91358	0.155294
$353$	−22.3498	−1.18956	−0.594779	−	0.803889i	$-0.702760\pi$
$353$	−22.3498	−1.18956	−0.594779	+	0.803889i	$0.702760\pi$
$354$	2.96828	0.157763
$355$	8.18868	0.434610
$356$	−13.3619	−0.708178
$357$	−14.6301	−0.774308
$358$	−22.8829	−1.20940
$359$	29.6922	1.56709	0.783546	−	0.621333i	$-0.213409\pi$
$359$	29.6922	1.56709	0.783546	+	0.621333i	$0.213409\pi$
$360$	0.835057	0.0440114
$361$	6.40666	0.337192
$362$	13.2414	0.695952
$363$	4.50986	0.236706
$364$	17.5555	0.920157
$365$	−14.1490	−0.740592
$366$	15.5597	0.813317
$367$	−12.8230	−0.669355	−0.334677	−	0.942333i	$-0.608627\pi$
$367$	−12.8230	−0.669355	−0.334677	+	0.942333i	$0.608627\pi$
$368$	1.87422	0.0977005
$369$	−1.24118	−0.0646132
$370$	−3.00870	−0.156415
$371$	−30.2599	−1.57102
$372$	−1.79599	−0.0931178
$373$	10.5220	0.544809	0.272404	−	0.962183i	$-0.412181\pi$
$373$	10.5220	0.544809	0.272404	+	0.962183i	$0.412181\pi$
$374$	−6.78964	−0.351084
$375$	24.6160	1.27117
$376$	−2.07325	−0.106920
$377$	1.61135	0.0829885
$378$	17.4180	0.895886
$379$	35.2442	1.81037	0.905187	−	0.425013i	$-0.139730\pi$
$379$	35.2442	1.81037	0.905187	+	0.425013i	$0.139730\pi$
$380$	18.6585	0.957159
$381$	−2.65321	−0.135928
$382$	−8.82005	−0.451273
$383$	33.9472	1.73462	0.867310	−	0.497768i	$-0.165847\pi$
$383$	33.9472	1.73462	0.867310	+	0.497768i	$0.165847\pi$
$384$	1.79599	0.0916513
$385$	−37.7009	−1.92142
$386$	−9.61514	−0.489398
$387$	1.35147	0.0686992
$388$	1.00000	0.0507673
$389$	18.9115	0.958852	0.479426	−	0.877582i	$-0.340845\pi$
$389$	18.9115	0.958852	0.479426	+	0.877582i	$0.340845\pi$
$390$	33.3884	1.69069
$391$	−4.36758	−0.220878
$392$	−5.21931	−0.263615
$393$	3.91547	0.197509
$394$	−9.03250	−0.455051
$395$	57.5968	2.89801
$396$	−0.657265	−0.0330288
$397$	6.20572	0.311456	0.155728	−	0.987800i	$-0.450228\pi$
$397$	6.20572	0.311456	0.155728	+	0.987800i	$0.450228\pi$
$398$	18.4248	0.923550
$399$	−31.6447	−1.58422
$400$	8.70264	0.435132
$401$	13.1044	0.654403	0.327202	−	0.944955i	$-0.393894\pi$
$401$	13.1044	0.654403	0.327202	+	0.944955i	$0.393894\pi$
$402$	−20.2322	−1.00909
$403$	−5.02215	−0.250171
$404$	14.8156	0.737102
$405$	35.6322	1.77058
$406$	−1.12156	−0.0556621
$407$	2.36812	0.117383
$408$	−4.18528	−0.207202
$409$	−29.4637	−1.45688	−0.728442	−	0.685108i	$-0.759755\pi$
$409$	−29.4637	−1.45688	−0.728442	+	0.685108i	$0.759755\pi$
$410$	−20.3668	−1.00584
$411$	30.3444	1.49678
$412$	−1.49393	−0.0736004
$413$	−5.77729	−0.284282
$414$	−0.422800	−0.0207795
$415$	1.05953	0.0520102
$416$	5.02215	0.246231
$417$	−10.2854	−0.503679
$418$	−14.6859	−0.718310
$419$	−18.7991	−0.918396	−0.459198	−	0.888334i	$-0.651863\pi$
$419$	−18.7991	−0.918396	−0.459198	+	0.888334i	$0.651863\pi$
$420$	−23.2397	−1.13398
$421$	−25.6665	−1.25091	−0.625455	−	0.780260i	$-0.715087\pi$
$421$	−25.6665	−1.25091	−0.625455	+	0.780260i	$0.715087\pi$
$422$	−12.3569	−0.601526
$423$	0.467698	0.0227403
$424$	−8.65655	−0.420399
$425$	−20.2802	−0.983732
$426$	−3.97298	−0.192491
$427$	−30.2844	−1.46557
$428$	10.7656	0.520375
$429$	−26.2797	−1.26880
$430$	22.1766	1.06945
$431$	6.25883	0.301477	0.150739	−	0.988574i	$-0.451835\pi$
$431$	6.25883	0.301477	0.150739	+	0.988574i	$0.451835\pi$
$432$	4.98282	0.239736
$433$	18.7460	0.900877	0.450439	−	0.892807i	$-0.351268\pi$
$433$	18.7460	0.900877	0.450439	+	0.892807i	$0.351268\pi$
$434$	3.49561	0.167795
$435$	−2.13307	−0.102273
$436$	0.242196	0.0115991
$437$	−9.44701	−0.451912
$438$	6.86480	0.328013
$439$	−11.8724	−0.566641	−0.283320	−	0.959025i	$-0.591436\pi$
$439$	−11.8724	−0.566641	−0.283320	+	0.959025i	$0.591436\pi$
$440$	−10.7852	−0.514165
$441$	1.17741	0.0560671
$442$	−11.7033	−0.556671
$443$	4.14894	0.197122	0.0985610	−	0.995131i	$-0.468576\pi$
$443$	4.14894	0.197122	0.0985610	+	0.995131i	$0.468576\pi$
$444$	1.45976	0.0692770
$445$	49.4618	2.34471
$446$	−13.3743	−0.633290
$447$	−9.30927	−0.440313
$448$	−3.49561	−0.165152
$449$	−9.25746	−0.436887	−0.218443	−	0.975850i	$-0.570098\pi$
$449$	−9.25746	−0.436887	−0.218443	+	0.975850i	$0.570098\pi$
$450$	−1.96320	−0.0925463
$451$	16.0305	0.754846
$452$	15.0284	0.706875
$453$	37.9421	1.78268
$454$	8.23725	0.386593
$455$	−64.9853	−3.04656
$456$	−9.05270	−0.423932
$457$	6.52813	0.305373	0.152686	−	0.988275i	$-0.451208\pi$
$457$	6.52813	0.305373	0.152686	+	0.988275i	$0.451208\pi$
$458$	−6.10053	−0.285059
$459$	−11.6117	−0.541988
$460$	−6.93782	−0.323477
$461$	4.87135	0.226881	0.113441	−	0.993545i	$-0.463813\pi$
$461$	4.87135	0.226881	0.113441	+	0.993545i	$0.463813\pi$
$462$	18.2917	0.851007
$463$	4.28779	0.199271	0.0996353	−	0.995024i	$-0.468232\pi$
$463$	4.28779	0.199271	0.0996353	+	0.995024i	$0.468232\pi$
$464$	−0.320848	−0.0148950
$465$	6.64824	0.308305
$466$	−1.94593	−0.0901433
$467$	−0.100521	−0.00465154	−0.00232577	−	0.999997i	$-0.500740\pi$
$467$	−0.100521	−0.00465154	−0.00232577	+	0.999997i	$0.500740\pi$
$468$	−1.13293	−0.0523697
$469$	39.3787	1.81834
$470$	7.67456	0.354001
$471$	4.65560	0.214519
$472$	−1.65273	−0.0760729
$473$	−17.4550	−0.802581
$474$	−27.9448	−1.28355
$475$	−43.8657	−2.01270
$476$	8.14599	0.373371
$477$	1.95280	0.0894128
$478$	18.1503	0.830175
$479$	−28.9254	−1.32163	−0.660817	−	0.750547i	$-0.729790\pi$
$479$	−28.9254	−1.32163	−0.660817	+	0.750547i	$0.729790\pi$
$480$	−6.64824	−0.303449
$481$	4.08193	0.186120
$482$	−21.0753	−0.959954
$483$	11.7665	0.535396
$484$	−2.51107	−0.114139
$485$	−3.70171	−0.168086
$486$	−2.33952	−0.106123
$487$	25.0538	1.13530	0.567649	−	0.823271i	$-0.307853\pi$
$487$	25.0538	1.13530	0.567649	+	0.823271i	$0.307853\pi$
$488$	−8.66355	−0.392181
$489$	−14.5655	−0.658675
$490$	19.3204	0.872805
$491$	11.2407	0.507284	0.253642	−	0.967298i	$-0.418372\pi$
$491$	11.2407	0.507284	0.253642	+	0.967298i	$0.418372\pi$
$492$	9.88154	0.445494
$493$	0.747687	0.0336741
$494$	−25.3141	−1.13894
$495$	2.43300	0.109355
$496$	1.00000	0.0449013
$497$	7.73277	0.346862
$498$	−0.514061	−0.0230356
$499$	−32.4949	−1.45467	−0.727336	−	0.686281i	$-0.759242\pi$
$499$	−32.4949	−1.45467	−0.727336	+	0.686281i	$0.759242\pi$
$500$	−13.7061	−0.612956
$501$	−28.1200	−1.25631
$502$	−20.8592	−0.930992
$503$	−9.70085	−0.432539	−0.216270	−	0.976334i	$-0.569389\pi$
$503$	−9.70085	−0.432539	−0.216270	+	0.976334i	$0.569389\pi$
$504$	0.788565	0.0351255
$505$	−54.8429	−2.44048
$506$	5.46069	0.242757
$507$	−21.9505	−0.974857
$508$	1.47730	0.0655445
$509$	0.267339	0.0118496	0.00592480	−	0.999982i	$-0.498114\pi$
$509$	0.267339	0.0118496	0.00592480	+	0.999982i	$0.498114\pi$
$510$	15.4927	0.686028
$511$	−13.3612	−0.591067
$512$	−1.00000	−0.0441942
$513$	−25.1159	−1.10890
$514$	11.1697	0.492676
$515$	5.53007	0.243684
$516$	−10.7596	−0.473667
$517$	−6.04057	−0.265664
$518$	−2.84119	−0.124835
$519$	33.6832	1.47853
$520$	−18.5905	−0.815248
$521$	−0.830022	−0.0363639	−0.0181820	−	0.999835i	$-0.505788\pi$
$521$	−0.830022	−0.0363639	−0.0181820	+	0.999835i	$0.505788\pi$
$522$	0.0723792	0.00316795
$523$	−5.62153	−0.245812	−0.122906	−	0.992418i	$-0.539221\pi$
$523$	−5.62153	−0.245812	−0.122906	+	0.992418i	$0.539221\pi$
$524$	−2.18012	−0.0952388
$525$	54.6360	2.38451
$526$	−22.0767	−0.962591
$527$	−2.33035	−0.101511
$528$	5.23276	0.227727
$529$	−19.4873	−0.847274
$530$	32.0440	1.39190
$531$	0.372834	0.0161796
$532$	17.6196	0.763908
$533$	27.6318	1.19687
$534$	−23.9978	−1.03849
$535$	−39.8511	−1.72291
$536$	11.2652	0.486581
$537$	−41.0976	−1.77349
$538$	1.98069	0.0853935
$539$	−15.2069	−0.655006
$540$	−18.4450	−0.793745
$541$	−30.5546	−1.31365	−0.656823	−	0.754045i	$-0.728100\pi$
$541$	−30.5546	−1.31365	−0.656823	+	0.754045i	$0.728100\pi$
$542$	24.6306	1.05797
$543$	23.7814	1.02056
$544$	2.33035	0.0999127
$545$	−0.896539	−0.0384035
$546$	31.5295	1.34934
$547$	24.8103	1.06081	0.530406	−	0.847744i	$-0.322040\pi$
$547$	24.8103	1.06081	0.530406	+	0.847744i	$0.322040\pi$
$548$	−16.8956	−0.721746
$549$	1.95438	0.0834111
$550$	25.3558	1.08118
$551$	1.61724	0.0688965
$552$	3.36609	0.143270
$553$	54.3901	2.31290
$554$	−9.35226	−0.397339
$555$	−5.40360	−0.229370
$556$	5.72687	0.242873
$557$	10.6299	0.450402	0.225201	−	0.974312i	$-0.427696\pi$
$557$	10.6299	0.450402	0.225201	+	0.974312i	$0.427696\pi$
$558$	−0.225587	−0.00954986
$559$	−30.0872	−1.27255
$560$	12.9397	0.546804
$561$	−12.1941	−0.514837
$562$	23.2651	0.981377
$563$	22.4827	0.947533	0.473767	−	0.880650i	$-0.342894\pi$
$563$	22.4827	0.947533	0.473767	+	0.880650i	$0.342894\pi$
$564$	−3.72354	−0.156789
$565$	−55.6307	−2.34040
$566$	11.0134	0.462927
$567$	33.6483	1.41310
$568$	2.21214	0.0928192
$569$	45.9090	1.92461	0.962304	−	0.271977i	$-0.0876775\pi$
$569$	45.9090	1.92461	0.962304	+	0.271977i	$0.0876775\pi$
$570$	33.5105	1.40360
$571$	38.6605	1.61789	0.808945	−	0.587884i	$-0.200039\pi$
$571$	38.6605	1.61789	0.808945	+	0.587884i	$0.200039\pi$
$572$	14.6324	0.611812
$573$	−15.8407	−0.661757
$574$	−19.2329	−0.802764
$575$	16.3107	0.680202
$576$	0.225587	0.00939946
$577$	−16.2487	−0.676441	−0.338221	−	0.941067i	$-0.609825\pi$
$577$	−16.2487	−0.676441	−0.338221	+	0.941067i	$0.609825\pi$
$578$	11.5695	0.481227
$579$	−17.2687	−0.717663
$580$	1.18769	0.0493160
$581$	1.00054	0.0415093
$582$	1.79599	0.0744463
$583$	−25.2215	−1.04457
$584$	−3.82229	−0.158167
$585$	4.19378	0.173391
$586$	−7.65828	−0.316361
$587$	−41.7599	−1.72362	−0.861808	−	0.507235i	$-0.830668\pi$
$587$	−41.7599	−1.72362	−0.861808	+	0.507235i	$0.830668\pi$
$588$	−9.37384	−0.386571
$589$	−5.04050	−0.207690
$590$	6.11791	0.251870
$591$	−16.2223	−0.667296
$592$	−0.812786	−0.0334053
$593$	7.51708	0.308690	0.154345	−	0.988017i	$-0.450673\pi$
$593$	7.51708	0.308690	0.154345	+	0.988017i	$0.450673\pi$
$594$	14.5178	0.595674
$595$	−30.1541	−1.23620
$596$	5.18336	0.212319
$597$	33.0907	1.35431
$598$	9.41261	0.384910
$599$	41.8506	1.70997	0.854984	−	0.518655i	$-0.173567\pi$
$599$	41.8506	1.70997	0.854984	+	0.518655i	$0.173567\pi$
$600$	15.6299	0.638087
$601$	−14.4295	−0.588591	−0.294296	−	0.955714i	$-0.595085\pi$
$601$	−14.4295	−0.588591	−0.294296	+	0.955714i	$0.595085\pi$
$602$	20.9419	0.853529
$603$	−2.54128	−0.103489
$604$	−21.1260	−0.859605
$605$	9.29524	0.377905
$606$	26.6086	1.08090
$607$	−8.03586	−0.326166	−0.163083	−	0.986612i	$-0.552144\pi$
$607$	−8.03586	−0.326166	−0.163083	+	0.986612i	$0.552144\pi$
$608$	5.04050	0.204419
$609$	−2.01431	−0.0816241
$610$	32.0699	1.29847
$611$	−10.4122	−0.421231
$612$	−0.525696	−0.0212500
$613$	28.4317	1.14834	0.574172	−	0.818734i	$-0.305324\pi$
$613$	28.4317	1.14834	0.574172	+	0.818734i	$0.305324\pi$
$614$	−25.6958	−1.03700
$615$	−36.5786	−1.47499
$616$	−10.1847	−0.410355
$617$	46.7260	1.88112	0.940559	−	0.339630i	$-0.110302\pi$
$617$	46.7260	1.88112	0.940559	+	0.339630i	$0.110302\pi$
$618$	−2.68308	−0.107929
$619$	43.3755	1.74341	0.871703	−	0.490034i	$-0.163016\pi$
$619$	43.3755	1.74341	0.871703	+	0.490034i	$0.163016\pi$
$620$	−3.70171	−0.148664
$621$	9.33891	0.374758
$622$	9.14756	0.366784
$623$	46.7080	1.87131
$624$	9.01973	0.361078
$625$	7.22278	0.288911
$626$	21.7149	0.867904
$627$	−26.3757	−1.05335
$628$	−2.59221	−0.103441
$629$	1.89407	0.0755216
$630$	−2.91904	−0.116297
$631$	−16.7767	−0.667872	−0.333936	−	0.942596i	$-0.608377\pi$
$631$	−16.7767	−0.667872	−0.333936	+	0.942596i	$0.608377\pi$
$632$	15.5595	0.618925
$633$	−22.1929	−0.882090
$634$	−0.719481	−0.0285742
$635$	−5.46852	−0.217012
$636$	−15.5471	−0.616482
$637$	−26.2121	−1.03856
$638$	−0.934816	−0.0370097
$639$	−0.499029	−0.0197413
$640$	3.70171	0.146323
$641$	−29.4238	−1.16217	−0.581085	−	0.813843i	$-0.697372\pi$
$641$	−29.4238	−1.16217	−0.581085	+	0.813843i	$0.697372\pi$
$642$	19.3349	0.763089
$643$	−34.8181	−1.37309	−0.686546	−	0.727087i	$-0.740874\pi$
$643$	−34.8181	−1.37309	−0.686546	+	0.727087i	$0.740874\pi$
$644$	−6.55155	−0.258167
$645$	39.8290	1.56827
$646$	−11.7461	−0.462144
$647$	−16.5182	−0.649398	−0.324699	−	0.945817i	$-0.605263\pi$
$647$	−16.5182	−0.649398	−0.324699	+	0.945817i	$0.605263\pi$
$648$	9.62587	0.378140
$649$	−4.81535	−0.189019
$650$	43.7059	1.71429
$651$	6.27809	0.246058
$652$	8.11000	0.317612
$653$	17.1428	0.670851	0.335425	−	0.942067i	$-0.391120\pi$
$653$	17.1428	0.670851	0.335425	+	0.942067i	$0.391120\pi$
$654$	0.434982	0.0170091
$655$	8.07015	0.315327
$656$	−5.50200	−0.214817
$657$	0.862259	0.0336399
$658$	7.24728	0.282528
$659$	−7.52840	−0.293265	−0.146633	−	0.989191i	$-0.546843\pi$
$659$	−7.52840	−0.293265	−0.146633	+	0.989191i	$0.546843\pi$
$660$	−19.3702	−0.753982
$661$	−10.3537	−0.402714	−0.201357	−	0.979518i	$-0.564535\pi$
$661$	−10.3537	−0.402714	−0.201357	+	0.979518i	$0.564535\pi$
$662$	1.01726	0.0395369
$663$	−21.0191	−0.816314
$664$	0.286227	0.0111078
$665$	−65.2228	−2.52923
$666$	0.183354	0.00710482
$667$	−0.601340	−0.0232840
$668$	15.6571	0.605791
$669$	−24.0201	−0.928670
$670$	−41.7004	−1.61103
$671$	−25.2419	−0.974454
$672$	−6.27809	−0.242183
$673$	−10.9680	−0.422785	−0.211393	−	0.977401i	$-0.567800\pi$
$673$	−10.9680	−0.422785	−0.211393	+	0.977401i	$0.567800\pi$
$674$	16.4230	0.632589
$675$	43.3637	1.66907
$676$	12.2219	0.470075
$677$	15.6599	0.601857	0.300929	−	0.953647i	$-0.402703\pi$
$677$	15.6599	0.601857	0.300929	+	0.953647i	$0.402703\pi$
$678$	26.9908	1.03658
$679$	−3.49561	−0.134149
$680$	−8.62626	−0.330802
$681$	14.7940	0.566909
$682$	2.91358	0.111567
$683$	−18.9094	−0.723549	−0.361774	−	0.932266i	$-0.617829\pi$
$683$	−18.9094	−0.723549	−0.361774	+	0.932266i	$0.617829\pi$
$684$	−1.13707	−0.0434770
$685$	62.5427	2.38963
$686$	−6.22459	−0.237656
$687$	−10.9565	−0.418017
$688$	5.99091	0.228401
$689$	−43.4744	−1.65624
$690$	−12.4603	−0.474354
$691$	−12.2375	−0.465537	−0.232769	−	0.972532i	$-0.574779\pi$
$691$	−12.2375	−0.465537	−0.232769	+	0.972532i	$0.574779\pi$
$692$	−18.7546	−0.712945
$693$	2.29754	0.0872765
$694$	−2.51057	−0.0953001
$695$	−21.1992	−0.804132
$696$	−0.576241	−0.0218423
$697$	12.8216	0.485651
$698$	6.71552	0.254186
$699$	−3.49487	−0.132188
$700$	−30.4211	−1.14981
$701$	21.2048	0.800893	0.400446	−	0.916320i	$-0.368855\pi$
$701$	21.2048	0.800893	0.400446	+	0.916320i	$0.368855\pi$
$702$	25.0245	0.944488
$703$	4.09685	0.154516
$704$	−2.91358	−0.109810
$705$	13.7835	0.519115
$706$	22.3498	0.841144
$707$	−51.7895	−1.94774
$708$	−2.96828	−0.111555
$709$	−27.4239	−1.02992	−0.514962	−	0.857213i	$-0.672194\pi$
$709$	−27.4239	−1.02992	−0.514962	+	0.857213i	$0.672194\pi$
$710$	−8.18868	−0.307316
$711$	−3.51003	−0.131636
$712$	13.3619	0.500758
$713$	1.87422	0.0701901
$714$	14.6301	0.547519
$715$	−54.1649	−2.02565
$716$	22.8829	0.855175
$717$	32.5978	1.21739
$718$	−29.6922	−1.10810
$719$	32.4646	1.21073	0.605363	−	0.795950i	$-0.293028\pi$
$719$	32.4646	1.21073	0.605363	+	0.795950i	$0.293028\pi$
$720$	−0.835057	−0.0311207
$721$	5.22218	0.194484
$722$	−6.40666	−0.238431
$723$	−37.8511	−1.40770
$724$	−13.2414	−0.492112
$725$	−2.79223	−0.103701
$726$	−4.50986	−0.167377
$727$	18.7934	0.697007	0.348503	−	0.937308i	$-0.386690\pi$
$727$	18.7934	0.697007	0.348503	+	0.937308i	$0.386690\pi$
$728$	−17.5555	−0.650649
$729$	24.6759	0.913921
$730$	14.1490	0.523678
$731$	−13.9609	−0.516363
$732$	−15.5597	−0.575102
$733$	−23.0683	−0.852048	−0.426024	−	0.904712i	$-0.640086\pi$
$733$	−23.0683	−0.852048	−0.426024	+	0.904712i	$0.640086\pi$
$734$	12.8230	0.473305
$735$	34.6992	1.27990
$736$	−1.87422	−0.0690847
$737$	32.8220	1.20901
$738$	1.24118	0.0456884
$739$	11.8525	0.435999	0.218000	−	0.975949i	$-0.430047\pi$
$739$	11.8525	0.435999	0.218000	+	0.975949i	$0.430047\pi$
$740$	3.00870	0.110602
$741$	−45.4640	−1.67016
$742$	30.2599	1.11088
$743$	−6.95499	−0.255154	−0.127577	−	0.991829i	$-0.540720\pi$
$743$	−6.95499	−0.255154	−0.127577	+	0.991829i	$0.540720\pi$
$744$	1.79599	0.0658443
$745$	−19.1873	−0.702967
$746$	−10.5220	−0.385238
$747$	−0.0645691	−0.00236246
$748$	6.78964	0.248254
$749$	−37.6324	−1.37506
$750$	−24.6160	−0.898851
$751$	−26.2721	−0.958683	−0.479341	−	0.877629i	$-0.659124\pi$
$751$	−26.2721	−0.958683	−0.479341	+	0.877629i	$0.659124\pi$
$752$	2.07325	0.0756036
$753$	−37.4630	−1.36523
$754$	−1.61135	−0.0586817
$755$	78.2023	2.84607
$756$	−17.4180	−0.633487
$757$	−34.8463	−1.26651	−0.633256	−	0.773943i	$-0.718282\pi$
$757$	−34.8463	−1.26651	−0.633256	+	0.773943i	$0.718282\pi$
$758$	−35.2442	−1.28013
$759$	9.80735	0.355984
$760$	−18.6585	−0.676814
$761$	−20.0475	−0.726723	−0.363361	−	0.931648i	$-0.618371\pi$
$761$	−20.0475	−0.726723	−0.363361	+	0.931648i	$0.618371\pi$
$762$	2.65321	0.0961158
$763$	−0.846624	−0.0306498
$764$	8.82005	0.319098
$765$	1.94597	0.0703568
$766$	−33.9472	−1.22656
$767$	−8.30023	−0.299704
$768$	−1.79599	−0.0648073
$769$	40.0874	1.44559	0.722795	−	0.691063i	$-0.242857\pi$
$769$	40.0874	1.44559	0.722795	+	0.691063i	$0.242857\pi$
$770$	37.7009	1.35865
$771$	20.0608	0.722471
$772$	9.61514	0.346056
$773$	−2.71852	−0.0977785	−0.0488892	−	0.998804i	$-0.515568\pi$
$773$	−2.71852	−0.0977785	−0.0488892	+	0.998804i	$0.515568\pi$
$774$	−1.35147	−0.0485777
$775$	8.70264	0.312608
$776$	−1.00000	−0.0358979
$777$	−5.10275	−0.183060
$778$	−18.9115	−0.678011
$779$	27.7328	0.993631
$780$	−33.3884	−1.19550
$781$	6.44523	0.230628
$782$	4.36758	0.156184
$783$	−1.59873	−0.0571339
$784$	5.21931	0.186404
$785$	9.59562	0.342482
$786$	−3.91547	−0.139660
$787$	−6.11763	−0.218070	−0.109035	−	0.994038i	$-0.534776\pi$
$787$	−6.11763	−0.218070	−0.109035	+	0.994038i	$0.534776\pi$
$788$	9.03250	0.321769
$789$	−39.6496	−1.41156
$790$	−57.5968	−2.04920
$791$	−52.5334	−1.86787
$792$	0.657265	0.0233549
$793$	−43.5096	−1.54507
$794$	−6.20572	−0.220233
$795$	57.5508	2.04112
$796$	−18.4248	−0.653049
$797$	−31.9270	−1.13091	−0.565456	−	0.824779i	$-0.691300\pi$
$797$	−31.9270	−1.13091	−0.565456	+	0.824779i	$0.691300\pi$
$798$	31.6447	1.12021
$799$	−4.83139	−0.170922
$800$	−8.70264	−0.307685
$801$	−3.01427	−0.106504
$802$	−13.1044	−0.462733
$803$	−11.1365	−0.393000
$804$	20.2322	0.713533
$805$	24.2519	0.854768
$806$	5.02215	0.176898
$807$	3.55730	0.125223
$808$	−14.8156	−0.521210
$809$	−4.21890	−0.148329	−0.0741644	−	0.997246i	$-0.523629\pi$
$809$	−4.21890	−0.148329	−0.0741644	+	0.997246i	$0.523629\pi$
$810$	−35.6322	−1.25199
$811$	26.0131	0.913445	0.456723	−	0.889609i	$-0.349023\pi$
$811$	26.0131	0.913445	0.456723	+	0.889609i	$0.349023\pi$
$812$	1.12156	0.0393591
$813$	44.2363	1.55144
$814$	−2.36812	−0.0830024
$815$	−30.0209	−1.05158
$816$	4.18528	0.146514
$817$	−30.1972	−1.05647
$818$	29.4637	1.03017
$819$	3.96029	0.138384
$820$	20.3668	0.711239
$821$	45.8208	1.59916	0.799578	−	0.600563i	$-0.205057\pi$
$821$	45.8208	1.59916	0.799578	+	0.600563i	$0.205057\pi$
$822$	−30.3444	−1.05838
$823$	−37.1862	−1.29623	−0.648114	−	0.761543i	$-0.724442\pi$
$823$	−37.1862	−1.29623	−0.648114	+	0.761543i	$0.724442\pi$
$824$	1.49393	0.0520433
$825$	45.5389	1.58546
$826$	5.77729	0.201018
$827$	−8.44505	−0.293663	−0.146832	−	0.989161i	$-0.546908\pi$
$827$	−8.44505	−0.293663	−0.146832	+	0.989161i	$0.546908\pi$
$828$	0.422800	0.0146933
$829$	−4.86433	−0.168945	−0.0844726	−	0.996426i	$-0.526921\pi$
$829$	−4.86433	−0.168945	−0.0844726	+	0.996426i	$0.526921\pi$
$830$	−1.05953	−0.0367768
$831$	−16.7966	−0.582667
$832$	−5.02215	−0.174112
$833$	−12.1628	−0.421416
$834$	10.2854	0.356155
$835$	−57.9580	−2.00572
$836$	14.6859	0.507922
$837$	4.98282	0.172232
$838$	18.7991	0.649404
$839$	33.2201	1.14688	0.573442	−	0.819246i	$-0.305608\pi$
$839$	33.2201	1.14688	0.573442	+	0.819246i	$0.305608\pi$
$840$	23.2397	0.801845
$841$	−28.8971	−0.996450
$842$	25.6665	0.884527
$843$	41.7839	1.43911
$844$	12.3569	0.425343
$845$	−45.2421	−1.55637
$846$	−0.467698	−0.0160798
$847$	8.77772	0.301606
$848$	8.65655	0.297267
$849$	19.7799	0.678846
$850$	20.2802	0.695604
$851$	−1.52334	−0.0522195
$852$	3.97298	0.136112
$853$	11.8546	0.405894	0.202947	−	0.979190i	$-0.434948\pi$
$853$	11.8546	0.405894	0.202947	+	0.979190i	$0.434948\pi$
$854$	30.2844	1.03631
$855$	4.20911	0.143948
$856$	−10.7656	−0.367961
$857$	45.3419	1.54885	0.774425	−	0.632666i	$-0.218039\pi$
$857$	45.3419	1.54885	0.774425	+	0.632666i	$0.218039\pi$
$858$	26.2797	0.897174
$859$	−43.1667	−1.47283	−0.736414	−	0.676531i	$-0.763482\pi$
$859$	−43.1667	−1.47283	−0.736414	+	0.676531i	$0.763482\pi$
$860$	−22.1766	−0.756216
$861$	−34.5420	−1.17719
$862$	−6.25883	−0.213176
$863$	14.3514	0.488527	0.244263	−	0.969709i	$-0.421454\pi$
$863$	14.3514	0.488527	0.244263	+	0.969709i	$0.421454\pi$
$864$	−4.98282	−0.169519
$865$	69.4242	2.36049
$866$	−18.7460	−0.637016
$867$	20.7787	0.705682
$868$	−3.49561	−0.118649
$869$	45.3339	1.53785
$870$	2.13307	0.0723180
$871$	56.5753	1.91698
$872$	−0.242196	−0.00820179
$873$	0.225587	0.00763496
$874$	9.44701	0.319550
$875$	47.9112	1.61970
$876$	−6.86480	−0.231940
$877$	16.7618	0.566005	0.283003	−	0.959119i	$-0.408669\pi$
$877$	16.7618	0.566005	0.283003	+	0.959119i	$0.408669\pi$
$878$	11.8724	0.400675
$879$	−13.7542	−0.463918
$880$	10.7852	0.363569
$881$	−33.6917	−1.13510	−0.567552	−	0.823338i	$-0.692109\pi$
$881$	−33.6917	−1.13510	−0.567552	+	0.823338i	$0.692109\pi$
$882$	−1.17741	−0.0396454
$883$	11.3365	0.381503	0.190752	−	0.981638i	$-0.438907\pi$
$883$	11.3365	0.381503	0.190752	+	0.981638i	$0.438907\pi$
$884$	11.7033	0.393626
$885$	10.9877	0.369348
$886$	−4.14894	−0.139386
$887$	−19.0122	−0.638369	−0.319184	−	0.947693i	$-0.603409\pi$
$887$	−19.0122	−0.638369	−0.319184	+	0.947693i	$0.603409\pi$
$888$	−1.45976	−0.0489863
$889$	−5.16406	−0.173197
$890$	−49.4618	−1.65796
$891$	28.0457	0.939567
$892$	13.3743	0.447804
$893$	−10.4502	−0.349703
$894$	9.30927	0.311349
$895$	−84.7059	−2.83141
$896$	3.49561	0.116780
$897$	16.9050	0.564441
$898$	9.25746	0.308925
$899$	−0.320848	−0.0107009
$900$	1.96320	0.0654401
$901$	−20.1727	−0.672051
$902$	−16.0305	−0.533757
$903$	37.6115	1.25163
$904$	−15.0284	−0.499836
$905$	49.0157	1.62934
$906$	−37.9421	−1.26054
$907$	2.39630	0.0795678	0.0397839	−	0.999208i	$-0.487333\pi$
$907$	2.39630	0.0795678	0.0397839	+	0.999208i	$0.487333\pi$
$908$	−8.23725	−0.273363
$909$	3.34220	0.110854
$910$	64.9853	2.15424
$911$	−5.53200	−0.183283	−0.0916417	−	0.995792i	$-0.529211\pi$
$911$	−5.53200	−0.183283	−0.0916417	+	0.995792i	$0.529211\pi$
$912$	9.05270	0.299765
$913$	0.833944	0.0275995
$914$	−6.52813	−0.215931
$915$	57.5974	1.90411
$916$	6.10053	0.201567
$917$	7.62084	0.251662
$918$	11.6117	0.383243
$919$	−42.8406	−1.41318	−0.706591	−	0.707622i	$-0.749768\pi$
$919$	−42.8406	−1.41318	−0.706591	+	0.707622i	$0.749768\pi$
$920$	6.93782	0.228733
$921$	−46.1495	−1.52068
$922$	−4.87135	−0.160429
$923$	11.1097	0.365679
$924$	−18.2917	−0.601753
$925$	−7.07339	−0.232572
$926$	−4.28779	−0.140906
$927$	−0.337010	−0.0110689
$928$	0.320848	0.0105324
$929$	−19.5419	−0.641147	−0.320574	−	0.947224i	$-0.603876\pi$
$929$	−19.5419	−0.641147	−0.320574	+	0.947224i	$0.603876\pi$
$930$	−6.64824	−0.218004
$931$	−26.3080	−0.862208
$932$	1.94593	0.0637409
$933$	16.4289	0.537860
$934$	0.100521	0.00328913
$935$	−25.1333	−0.821946
$936$	1.13293	0.0370310
$937$	16.3253	0.533325	0.266663	−	0.963790i	$-0.414079\pi$
$937$	16.3253	0.533325	0.266663	+	0.963790i	$0.414079\pi$
$938$	−39.3787	−1.28576
$939$	38.9999	1.27271
$940$	−7.67456	−0.250317
$941$	7.13260	0.232516	0.116258	−	0.993219i	$-0.462910\pi$
$941$	7.13260	0.232516	0.116258	+	0.993219i	$0.462910\pi$
$942$	−4.65560	−0.151688
$943$	−10.3120	−0.335803
$944$	1.65273	0.0537917
$945$	64.4764	2.09742
$946$	17.4550	0.567511
$947$	27.1297	0.881597	0.440798	−	0.897606i	$-0.354695\pi$
$947$	27.1297	0.881597	0.440798	+	0.897606i	$0.354695\pi$
$948$	27.9448	0.907605
$949$	−19.1961	−0.623131
$950$	43.8657	1.42319
$951$	−1.29218	−0.0419019
$952$	−8.14599	−0.264013
$953$	14.7368	0.477373	0.238686	−	0.971097i	$-0.423283\pi$
$953$	14.7368	0.477373	0.238686	+	0.971097i	$0.423283\pi$
$954$	−1.95280	−0.0632244
$955$	−32.6493	−1.05651
$956$	−18.1503	−0.587022
$957$	−1.67892	−0.0542718
$958$	28.9254	0.934536
$959$	59.0606	1.90717
$960$	6.64824	0.214571
$961$	1.00000	0.0322581
$962$	−4.08193	−0.131607
$963$	2.42858	0.0782599
$964$	21.0753	0.678790
$965$	−35.5924	−1.14576
$966$	−11.7665	−0.378582
$967$	35.6618	1.14681	0.573403	−	0.819274i	$-0.305623\pi$
$967$	35.6618	1.14681	0.573403	+	0.819274i	$0.305623\pi$
$968$	2.51107	0.0807088
$969$	−21.0959	−0.677698
$970$	3.70171	0.118855
$971$	28.8469	0.925742	0.462871	−	0.886426i	$-0.346819\pi$
$971$	28.8469	0.925742	0.462871	+	0.886426i	$0.346819\pi$
$972$	2.33952	0.0750401
$973$	−20.0189	−0.641777
$974$	−25.0538	−0.802777
$975$	78.4955	2.51387
$976$	8.66355	0.277314
$977$	−23.5654	−0.753923	−0.376961	−	0.926229i	$-0.623031\pi$
$977$	−23.5654	−0.753923	−0.376961	+	0.926229i	$0.623031\pi$
$978$	14.5655	0.465753
$979$	38.9309	1.24424
$980$	−19.3204	−0.617167
$981$	0.0546363	0.00174440
$982$	−11.2407	−0.358704
$983$	38.0404	1.21330	0.606651	−	0.794968i	$-0.292513\pi$
$983$	38.0404	1.21330	0.606651	+	0.794968i	$0.292513\pi$
$984$	−9.88154	−0.315012
$985$	−33.4357	−1.06535
$986$	−0.747687	−0.0238112
$987$	13.0161	0.414305
$988$	25.3141	0.805350
$989$	11.2283	0.357039
$990$	−2.43300	−0.0773259
$991$	58.6262	1.86232	0.931161	−	0.364609i	$-0.118797\pi$
$991$	58.6262	1.86232	0.931161	+	0.364609i	$0.118797\pi$
$992$	−1.00000	−0.0317500
$993$	1.82699	0.0579778
$994$	−7.73277	−0.245269
$995$	68.2031	2.16218
$996$	0.514061	0.0162887
$997$	−13.7115	−0.434249	−0.217125	−	0.976144i	$-0.569668\pi$
$997$	−13.7115	−0.434249	−0.217125	+	0.976144i	$0.569668\pi$
$998$	32.4949	1.02861
$999$	−4.04997	−0.128135

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.f.1.5	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.f.1.5	✓	22	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.79599 q^{3} +1.00000 q^{4} -3.70171 q^{5} +1.79599 q^{6} -3.49561 q^{7} -1.00000 q^{8} +0.225587 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.79599 q^{3} +1.00000 q^{4} -3.70171 q^{5} +1.79599 q^{6} -3.49561 q^{7} -1.00000 q^{8} +0.225587 q^{9} +3.70171 q^{10} -2.91358 q^{11} -1.79599 q^{12} -5.02215 q^{13} +3.49561 q^{14} +6.64824 q^{15} +1.00000 q^{16} -2.33035 q^{17} -0.225587 q^{18} -5.04050 q^{19} -3.70171 q^{20} +6.27809 q^{21} +2.91358 q^{22} +1.87422 q^{23} +1.79599 q^{24} +8.70264 q^{25} +5.02215 q^{26} +4.98282 q^{27} -3.49561 q^{28} -0.320848 q^{29} -6.64824 q^{30} +1.00000 q^{31} -1.00000 q^{32} +5.23276 q^{33} +2.33035 q^{34} +12.9397 q^{35} +0.225587 q^{36} -0.812786 q^{37} +5.04050 q^{38} +9.01973 q^{39} +3.70171 q^{40} -5.50200 q^{41} -6.27809 q^{42} +5.99091 q^{43} -2.91358 q^{44} -0.835057 q^{45} -1.87422 q^{46} +2.07325 q^{47} -1.79599 q^{48} +5.21931 q^{49} -8.70264 q^{50} +4.18528 q^{51} -5.02215 q^{52} +8.65655 q^{53} -4.98282 q^{54} +10.7852 q^{55} +3.49561 q^{56} +9.05270 q^{57} +0.320848 q^{58} +1.65273 q^{59} +6.64824 q^{60} +8.66355 q^{61} -1.00000 q^{62} -0.788565 q^{63} +1.00000 q^{64} +18.5905 q^{65} -5.23276 q^{66} -11.2652 q^{67} -2.33035 q^{68} -3.36609 q^{69} -12.9397 q^{70} -2.21214 q^{71} -0.225587 q^{72} +3.82229 q^{73} +0.812786 q^{74} -15.6299 q^{75} -5.04050 q^{76} +10.1847 q^{77} -9.01973 q^{78} -15.5595 q^{79} -3.70171 q^{80} -9.62587 q^{81} +5.50200 q^{82} -0.286227 q^{83} +6.27809 q^{84} +8.62626 q^{85} -5.99091 q^{86} +0.576241 q^{87} +2.91358 q^{88} -13.3619 q^{89} +0.835057 q^{90} +17.5555 q^{91} +1.87422 q^{92} -1.79599 q^{93} -2.07325 q^{94} +18.6585 q^{95} +1.79599 q^{96} +1.00000 q^{97} -5.21931 q^{98} -0.657265 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9}+O(q^{10}) \) 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9	\( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9} - 8 q^{13} + 11 q^{14} + q^{15} + 22 q^{16} - 4 q^{17} - 8 q^{18} - 23 q^{19} - 12 q^{21} + 2 q^{23} - 12 q^{25} + 8 q^{26} + 3 q^{27} - 11 q^{28} + 9 q^{29} - q^{30} + 22 q^{31} - 22 q^{32} + 4 q^{34} + 4 q^{35} + 8 q^{36} - 17 q^{37} + 23 q^{38} + 8 q^{39} - 21 q^{41} + 12 q^{42} - 7 q^{43} + 9 q^{45} - 2 q^{46} - 10 q^{47} - 27 q^{49} + 12 q^{50} - q^{51} - 8 q^{52} + 9 q^{53} - 3 q^{54} - 6 q^{55} + 11 q^{56} - q^{57} - 9 q^{58} - 12 q^{59} + q^{60} - 34 q^{61} - 22 q^{62} - 5 q^{63} + 22 q^{64} + 4 q^{65} - 31 q^{67} - 4 q^{68} - 51 q^{69} - 4 q^{70} - 15 q^{71} - 8 q^{72} + 3 q^{73} + 17 q^{74} - 24 q^{75} - 23 q^{76} + 24 q^{77} - 8 q^{78} - 23 q^{79} - 26 q^{81} + 21 q^{82} + 22 q^{83} - 12 q^{84} - 42 q^{85} + 7 q^{86} - 9 q^{87} - 36 q^{89} - 9 q^{90} - 6 q^{91} + 2 q^{92} + 10 q^{94} + 2 q^{95} + 22 q^{97} + 27 q^{98} - 25 q^{99}+O(q^{100}) \) 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9 - 8 * q^13 + 11 * q^14 + q^15 + 22 * q^16 - 4 * q^17 - 8 * q^18 - 23 * q^19 - 12 * q^21 + 2 * q^23 - 12 * q^25 + 8 * q^26 + 3 * q^27 - 11 * q^28 + 9 * q^29 - q^30 + 22 * q^31 - 22 * q^32 + 4 * q^34 + 4 * q^35 + 8 * q^36 - 17 * q^37 + 23 * q^38 + 8 * q^39 - 21 * q^41 + 12 * q^42 - 7 * q^43 + 9 * q^45 - 2 * q^46 - 10 * q^47 - 27 * q^49 + 12 * q^50 - q^51 - 8 * q^52 + 9 * q^53 - 3 * q^54 - 6 * q^55 + 11 * q^56 - q^57 - 9 * q^58 - 12 * q^59 + q^60 - 34 * q^61 - 22 * q^62 - 5 * q^63 + 22 * q^64 + 4 * q^65 - 31 * q^67 - 4 * q^68 - 51 * q^69 - 4 * q^70 - 15 * q^71 - 8 * q^72 + 3 * q^73 + 17 * q^74 - 24 * q^75 - 23 * q^76 + 24 * q^77 - 8 * q^78 - 23 * q^79 - 26 * q^81 + 21 * q^82 + 22 * q^83 - 12 * q^84 - 42 * q^85 + 7 * q^86 - 9 * q^87 - 36 * q^89 - 9 * q^90 - 6 * q^91 + 2 * q^92 + 10 * q^94 + 2 * q^95 + 22 * q^97 + 27 * q^98 - 25 * q^99

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