LMFDB - Embedded newform 6002.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$0$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.34863 q^{3} +1.00000 q^{4} -3.86481 q^{5} -3.34863 q^{6} -0.0235424 q^{7} +1.00000 q^{8} +8.21330 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.34863 q^{3} +1.00000 q^{4} -3.86481 q^{5} -3.34863 q^{6} -0.0235424 q^{7} +1.00000 q^{8} +8.21330 q^{9} -3.86481 q^{10} -1.04192 q^{11} -3.34863 q^{12} +1.10988 q^{13} -0.0235424 q^{14} +12.9418 q^{15} +1.00000 q^{16} -7.22562 q^{17} +8.21330 q^{18} +7.07849 q^{19} -3.86481 q^{20} +0.0788349 q^{21} -1.04192 q^{22} +5.63293 q^{23} -3.34863 q^{24} +9.93676 q^{25} +1.10988 q^{26} -17.4574 q^{27} -0.0235424 q^{28} -3.94444 q^{29} +12.9418 q^{30} -7.89580 q^{31} +1.00000 q^{32} +3.48899 q^{33} -7.22562 q^{34} +0.0909871 q^{35} +8.21330 q^{36} -3.67169 q^{37} +7.07849 q^{38} -3.71657 q^{39} -3.86481 q^{40} -2.82351 q^{41} +0.0788349 q^{42} +5.60277 q^{43} -1.04192 q^{44} -31.7429 q^{45} +5.63293 q^{46} -7.18408 q^{47} -3.34863 q^{48} -6.99945 q^{49} +9.93676 q^{50} +24.1959 q^{51} +1.10988 q^{52} +3.68758 q^{53} -17.4574 q^{54} +4.02681 q^{55} -0.0235424 q^{56} -23.7032 q^{57} -3.94444 q^{58} -11.6276 q^{59} +12.9418 q^{60} +8.83505 q^{61} -7.89580 q^{62} -0.193361 q^{63} +1.00000 q^{64} -4.28947 q^{65} +3.48899 q^{66} +5.31285 q^{67} -7.22562 q^{68} -18.8626 q^{69} +0.0909871 q^{70} -8.40830 q^{71} +8.21330 q^{72} -4.09689 q^{73} -3.67169 q^{74} -33.2745 q^{75} +7.07849 q^{76} +0.0245292 q^{77} -3.71657 q^{78} -15.2286 q^{79} -3.86481 q^{80} +33.8185 q^{81} -2.82351 q^{82} +7.67378 q^{83} +0.0788349 q^{84} +27.9257 q^{85} +5.60277 q^{86} +13.2085 q^{87} -1.04192 q^{88} -7.13039 q^{89} -31.7429 q^{90} -0.0261293 q^{91} +5.63293 q^{92} +26.4401 q^{93} -7.18408 q^{94} -27.3570 q^{95} -3.34863 q^{96} -13.9943 q^{97} -6.99945 q^{98} -8.55757 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9}+O(q^{10}) $ 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9	\( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9} + 18 q^{10} + 28 q^{11} + 17 q^{12} + 47 q^{13} + 19 q^{14} + 14 q^{15} + 79 q^{16} + 36 q^{17} + 118 q^{18} + 29 q^{19} + 18 q^{20} + 45 q^{21} + 28 q^{22} + 23 q^{23} + 17 q^{24} + 161 q^{25} + 47 q^{26} + 50 q^{27} + 19 q^{28} + 53 q^{29} + 14 q^{30} + 29 q^{31} + 79 q^{32} + 34 q^{33} + 36 q^{34} + 33 q^{35} + 118 q^{36} + 89 q^{37} + 29 q^{38} - 7 q^{39} + 18 q^{40} + 58 q^{41} + 45 q^{42} + 88 q^{43} + 28 q^{44} + 45 q^{45} + 23 q^{46} + 3 q^{47} + 17 q^{48} + 162 q^{49} + 161 q^{50} + 29 q^{51} + 47 q^{52} + 88 q^{53} + 50 q^{54} + 37 q^{55} + 19 q^{56} + 54 q^{57} + 53 q^{58} + 37 q^{59} + 14 q^{60} + 55 q^{61} + 29 q^{62} + 21 q^{63} + 79 q^{64} + 55 q^{65} + 34 q^{66} + 107 q^{67} + 36 q^{68} + 39 q^{69} + 33 q^{70} - 5 q^{71} + 118 q^{72} + 71 q^{73} + 89 q^{74} + 37 q^{75} + 29 q^{76} + 61 q^{77} - 7 q^{78} + 29 q^{79} + 18 q^{80} + 215 q^{81} + 58 q^{82} + 42 q^{83} + 45 q^{84} + 84 q^{85} + 88 q^{86} + 15 q^{87} + 28 q^{88} + 72 q^{89} + 45 q^{90} + 70 q^{91} + 23 q^{92} + 97 q^{93} + 3 q^{94} - 18 q^{95} + 17 q^{96} + 93 q^{97} + 162 q^{98} + 49 q^{99}+O(q^{100}) \) 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9 + 18 * q^10 + 28 * q^11 + 17 * q^12 + 47 * q^13 + 19 * q^14 + 14 * q^15 + 79 * q^16 + 36 * q^17 + 118 * q^18 + 29 * q^19 + 18 * q^20 + 45 * q^21 + 28 * q^22 + 23 * q^23 + 17 * q^24 + 161 * q^25 + 47 * q^26 + 50 * q^27 + 19 * q^28 + 53 * q^29 + 14 * q^30 + 29 * q^31 + 79 * q^32 + 34 * q^33 + 36 * q^34 + 33 * q^35 + 118 * q^36 + 89 * q^37 + 29 * q^38 - 7 * q^39 + 18 * q^40 + 58 * q^41 + 45 * q^42 + 88 * q^43 + 28 * q^44 + 45 * q^45 + 23 * q^46 + 3 * q^47 + 17 * q^48 + 162 * q^49 + 161 * q^50 + 29 * q^51 + 47 * q^52 + 88 * q^53 + 50 * q^54 + 37 * q^55 + 19 * q^56 + 54 * q^57 + 53 * q^58 + 37 * q^59 + 14 * q^60 + 55 * q^61 + 29 * q^62 + 21 * q^63 + 79 * q^64 + 55 * q^65 + 34 * q^66 + 107 * q^67 + 36 * q^68 + 39 * q^69 + 33 * q^70 - 5 * q^71 + 118 * q^72 + 71 * q^73 + 89 * q^74 + 37 * q^75 + 29 * q^76 + 61 * q^77 - 7 * q^78 + 29 * q^79 + 18 * q^80 + 215 * q^81 + 58 * q^82 + 42 * q^83 + 45 * q^84 + 84 * q^85 + 88 * q^86 + 15 * q^87 + 28 * q^88 + 72 * q^89 + 45 * q^90 + 70 * q^91 + 23 * q^92 + 97 * q^93 + 3 * q^94 - 18 * q^95 + 17 * q^96 + 93 * q^97 + 162 * q^98 + 49 * 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
$3$	−3.34863	−1.93333	−0.966665	−	0.256043i	$-0.917581\pi$
$3$	−3.34863	−1.93333	−0.966665	+	0.256043i	$0.917581\pi$
$4$	1.00000	0.500000
$5$	−3.86481	−1.72840	−0.864198	−	0.503152i	$-0.832173\pi$
$5$	−3.86481	−1.72840	−0.864198	+	0.503152i	$0.832173\pi$
$6$	−3.34863	−1.36707
$7$	−0.0235424	−0.00889821	−0.00444910	−	0.999990i	$-0.501416\pi$
$7$	−0.0235424	−0.00889821	−0.00444910	+	0.999990i	$0.501416\pi$
$8$	1.00000	0.353553
$9$	8.21330	2.73777
$10$	−3.86481	−1.22216
$11$	−1.04192	−0.314149	−0.157075	−	0.987587i	$-0.550206\pi$
$11$	−1.04192	−0.314149	−0.157075	+	0.987587i	$0.550206\pi$
$12$	−3.34863	−0.966665
$13$	1.10988	0.307825	0.153912	−	0.988084i	$-0.450813\pi$
$13$	1.10988	0.307825	0.153912	+	0.988084i	$0.450813\pi$
$14$	−0.0235424	−0.00629198
$15$	12.9418	3.34156
$16$	1.00000	0.250000
$17$	−7.22562	−1.75247	−0.876235	−	0.481884i	$-0.839953\pi$
$17$	−7.22562	−1.75247	−0.876235	+	0.481884i	$0.839953\pi$
$18$	8.21330	1.93589
$19$	7.07849	1.62392	0.811958	−	0.583716i	$-0.198402\pi$
$19$	7.07849	1.62392	0.811958	+	0.583716i	$0.198402\pi$
$20$	−3.86481	−0.864198
$21$	0.0788349	0.0172032
$22$	−1.04192	−0.222137
$23$	5.63293	1.17455	0.587274	−	0.809388i	$-0.300201\pi$
$23$	5.63293	1.17455	0.587274	+	0.809388i	$0.300201\pi$
$24$	−3.34863	−0.683536
$25$	9.93676	1.98735
$26$	1.10988	0.217665
$27$	−17.4574	−3.35968
$28$	−0.0235424	−0.00444910
$29$	−3.94444	−0.732464	−0.366232	−	0.930524i	$-0.619352\pi$
$29$	−3.94444	−0.732464	−0.366232	+	0.930524i	$0.619352\pi$
$30$	12.9418	2.36284
$31$	−7.89580	−1.41813	−0.709064	−	0.705144i	$-0.750882\pi$
$31$	−7.89580	−1.41813	−0.709064	+	0.705144i	$0.750882\pi$
$32$	1.00000	0.176777
$33$	3.48899	0.607355
$34$	−7.22562	−1.23918
$35$	0.0909871	0.0153796
$36$	8.21330	1.36888
$37$	−3.67169	−0.603623	−0.301811	−	0.953368i	$-0.597591\pi$
$37$	−3.67169	−0.603623	−0.301811	+	0.953368i	$0.597591\pi$
$38$	7.07849	1.14828
$39$	−3.71657	−0.595128
$40$	−3.86481	−0.611080
$41$	−2.82351	−0.440959	−0.220479	−	0.975392i	$-0.570762\pi$
$41$	−2.82351	−0.440959	−0.220479	+	0.975392i	$0.570762\pi$
$42$	0.0788349	0.0121645
$43$	5.60277	0.854415	0.427207	−	0.904154i	$-0.359497\pi$
$43$	5.60277	0.854415	0.427207	+	0.904154i	$0.359497\pi$
$44$	−1.04192	−0.157075
$45$	−31.7429	−4.73195
$46$	5.63293	0.830530
$47$	−7.18408	−1.04791	−0.523953	−	0.851747i	$-0.675543\pi$
$47$	−7.18408	−1.04791	−0.523953	+	0.851747i	$0.675543\pi$
$48$	−3.34863	−0.483333
$49$	−6.99945	−0.999921
$50$	9.93676	1.40527
$51$	24.1959	3.38811
$52$	1.10988	0.153912
$53$	3.68758	0.506527	0.253264	−	0.967397i	$-0.418496\pi$
$53$	3.68758	0.506527	0.253264	+	0.967397i	$0.418496\pi$
$54$	−17.4574	−2.37565
$55$	4.02681	0.542975
$56$	−0.0235424	−0.00314599
$57$	−23.7032	−3.13957
$58$	−3.94444	−0.517930
$59$	−11.6276	−1.51379	−0.756894	−	0.653537i	$-0.773284\pi$
$59$	−11.6276	−1.51379	−0.756894	+	0.653537i	$0.773284\pi$
$60$	12.9418	1.67078
$61$	8.83505	1.13121	0.565606	−	0.824675i	$-0.308642\pi$
$61$	8.83505	1.13121	0.565606	+	0.824675i	$0.308642\pi$
$62$	−7.89580	−1.00277
$63$	−0.193361	−0.0243612
$64$	1.00000	0.125000
$65$	−4.28947	−0.532043
$66$	3.48899	0.429465
$67$	5.31285	0.649068	0.324534	−	0.945874i	$-0.394793\pi$
$67$	5.31285	0.649068	0.324534	+	0.945874i	$0.394793\pi$
$68$	−7.22562	−0.876235
$69$	−18.8626	−2.27079
$70$	0.0909871	0.0108750
$71$	−8.40830	−0.997881	−0.498941	−	0.866636i	$-0.666277\pi$
$71$	−8.40830	−0.997881	−0.498941	+	0.866636i	$0.666277\pi$
$72$	8.21330	0.967947
$73$	−4.09689	−0.479505	−0.239752	−	0.970834i	$-0.577066\pi$
$73$	−4.09689	−0.479505	−0.239752	+	0.970834i	$0.577066\pi$
$74$	−3.67169	−0.426826
$75$	−33.2745	−3.84221
$76$	7.07849	0.811958
$77$	0.0245292	0.00279537
$78$	−3.71657	−0.420819
$79$	−15.2286	−1.71335	−0.856674	−	0.515859i	$-0.827473\pi$
$79$	−15.2286	−1.71335	−0.856674	+	0.515859i	$0.827473\pi$
$80$	−3.86481	−0.432099
$81$	33.8185	3.75761
$82$	−2.82351	−0.311805
$83$	7.67378	0.842307	0.421153	−	0.906989i	$-0.361625\pi$
$83$	7.67378	0.842307	0.421153	+	0.906989i	$0.361625\pi$
$84$	0.0788349	0.00860159
$85$	27.9257	3.02896
$86$	5.60277	0.604163
$87$	13.2085	1.41609
$88$	−1.04192	−0.111069
$89$	−7.13039	−0.755820	−0.377910	−	0.925842i	$-0.623357\pi$
$89$	−7.13039	−0.755820	−0.377910	+	0.925842i	$0.623357\pi$
$90$	−31.7429	−3.34599
$91$	−0.0261293	−0.00273909
$92$	5.63293	0.587274
$93$	26.4401	2.74171
$94$	−7.18408	−0.740981
$95$	−27.3570	−2.80677
$96$	−3.34863	−0.341768
$97$	−13.9943	−1.42090	−0.710451	−	0.703747i	$-0.751509\pi$
$97$	−13.9943	−1.42090	−0.710451	+	0.703747i	$0.751509\pi$
$98$	−6.99945	−0.707051
$99$	−8.55757	−0.860068
$100$	9.93676	0.993676
$101$	2.05393	0.204373	0.102187	−	0.994765i	$-0.467416\pi$
$101$	2.05393	0.204373	0.102187	+	0.994765i	$0.467416\pi$
$102$	24.1959	2.39575
$103$	13.1679	1.29747	0.648735	−	0.761014i	$-0.275298\pi$
$103$	13.1679	1.29747	0.648735	+	0.761014i	$0.275298\pi$
$104$	1.10988	0.108833
$105$	−0.304682	−0.0297339
$106$	3.68758	0.358169
$107$	−3.77755	−0.365189	−0.182595	−	0.983188i	$-0.558450\pi$
$107$	−3.77755	−0.365189	−0.182595	+	0.983188i	$0.558450\pi$
$108$	−17.4574	−1.67984
$109$	17.3248	1.65941	0.829707	−	0.558199i	$-0.188507\pi$
$109$	17.3248	1.65941	0.829707	+	0.558199i	$0.188507\pi$
$110$	4.02681	0.383941
$111$	12.2951	1.16700
$112$	−0.0235424	−0.00222455
$113$	−1.33624	−0.125703	−0.0628517	−	0.998023i	$-0.520020\pi$
$113$	−1.33624	−0.125703	−0.0628517	+	0.998023i	$0.520020\pi$
$114$	−23.7032	−2.22001
$115$	−21.7702	−2.03008
$116$	−3.94444	−0.366232
$117$	9.11577	0.842753
$118$	−11.6276	−1.07041
$119$	0.170109	0.0155938
$120$	12.9418	1.18142
$121$	−9.91441	−0.901310
$122$	8.83505	0.799888
$123$	9.45490	0.852519
$124$	−7.89580	−0.709064
$125$	−19.0796	−1.70653
$126$	−0.193361	−0.0172260
$127$	15.8799	1.40911	0.704556	−	0.709648i	$-0.251146\pi$
$127$	15.8799	1.40911	0.704556	+	0.709648i	$0.251146\pi$
$128$	1.00000	0.0883883
$129$	−18.7616	−1.65187
$130$	−4.28947	−0.376211
$131$	7.86929	0.687543	0.343772	−	0.939053i	$-0.388295\pi$
$131$	7.86929	0.687543	0.343772	+	0.939053i	$0.388295\pi$
$132$	3.48899	0.303677
$133$	−0.166645	−0.0144499
$134$	5.31285	0.458960
$135$	67.4696	5.80686
$136$	−7.22562	−0.619592
$137$	7.62274	0.651254	0.325627	−	0.945498i	$-0.394425\pi$
$137$	7.62274	0.651254	0.325627	+	0.945498i	$0.394425\pi$
$138$	−18.8626	−1.60569
$139$	0.0147454	0.00125069	0.000625343	−	1.00000i	$-0.499801\pi$
$139$	0.0147454	0.00125069	0.000625343		1.00000i	$0.499801\pi$
$140$	0.0909871	0.00768981
$141$	24.0568	2.02595
$142$	−8.40830	−0.705609
$143$	−1.15640	−0.0967031
$144$	8.21330	0.684442
$145$	15.2445	1.26599
$146$	−4.09689	−0.339061
$147$	23.4385	1.93318
$148$	−3.67169	−0.301811
$149$	−3.68071	−0.301535	−0.150768	−	0.988569i	$-0.548175\pi$
$149$	−3.68071	−0.301535	−0.150768	+	0.988569i	$0.548175\pi$
$150$	−33.2745	−2.71685
$151$	−13.5110	−1.09951	−0.549754	−	0.835327i	$-0.685278\pi$
$151$	−13.5110	−1.09951	−0.549754	+	0.835327i	$0.685278\pi$
$152$	7.07849	0.574141
$153$	−59.3462	−4.79786
$154$	0.0245292	0.00197662
$155$	30.5158	2.45109
$156$	−3.71657	−0.297564
$157$	12.3679	0.987066	0.493533	−	0.869727i	$-0.335705\pi$
$157$	12.3679	0.987066	0.493533	+	0.869727i	$0.335705\pi$
$158$	−15.2286	−1.21152
$159$	−12.3483	−0.979285
$160$	−3.86481	−0.305540
$161$	−0.132613	−0.0104514
$162$	33.8185	2.65703
$163$	−3.06844	−0.240338	−0.120169	−	0.992753i	$-0.538344\pi$
$163$	−3.06844	−0.240338	−0.120169	+	0.992753i	$0.538344\pi$
$164$	−2.82351	−0.220479
$165$	−13.4843	−1.04975
$166$	7.67378	0.595601
$167$	1.88888	0.146166	0.0730830	−	0.997326i	$-0.476716\pi$
$167$	1.88888	0.146166	0.0730830	+	0.997326i	$0.476716\pi$
$168$	0.0788349	0.00608224
$169$	−11.7682	−0.905244
$170$	27.9257	2.14180
$171$	58.1378	4.44591
$172$	5.60277	0.427207
$173$	16.1956	1.23133	0.615664	−	0.788009i	$-0.288888\pi$
$173$	16.1956	1.23133	0.615664	+	0.788009i	$0.288888\pi$
$174$	13.2085	1.00133
$175$	−0.233935	−0.0176839
$176$	−1.04192	−0.0785374
$177$	38.9366	2.92665
$178$	−7.13039	−0.534445
$179$	−6.43794	−0.481194	−0.240597	−	0.970625i	$-0.577343\pi$
$179$	−6.43794	−0.481194	−0.240597	+	0.970625i	$0.577343\pi$
$180$	−31.7429	−2.36597
$181$	0.514630	0.0382522	0.0191261	−	0.999817i	$-0.493912\pi$
$181$	0.514630	0.0382522	0.0191261	+	0.999817i	$0.493912\pi$
$182$	−0.0261293	−0.00193683
$183$	−29.5853	−2.18701
$184$	5.63293	0.415265
$185$	14.1904	1.04330
$186$	26.4401	1.93868
$187$	7.52849	0.550538
$188$	−7.18408	−0.523953
$189$	0.410990	0.0298951
$190$	−27.3570	−1.98469
$191$	0.684344	0.0495174	0.0247587	−	0.999693i	$-0.492118\pi$
$191$	0.684344	0.0495174	0.0247587	+	0.999693i	$0.492118\pi$
$192$	−3.34863	−0.241666
$193$	1.53534	0.110516	0.0552581	−	0.998472i	$-0.482402\pi$
$193$	1.53534	0.110516	0.0552581	+	0.998472i	$0.482402\pi$
$194$	−13.9943	−1.00473
$195$	14.3638	1.02862
$196$	−6.99945	−0.499960
$197$	5.75420	0.409970	0.204985	−	0.978765i	$-0.434285\pi$
$197$	5.75420	0.409970	0.204985	+	0.978765i	$0.434285\pi$
$198$	−8.55757	−0.608160
$199$	20.1461	1.42812	0.714060	−	0.700085i	$-0.246855\pi$
$199$	20.1461	1.42812	0.714060	+	0.700085i	$0.246855\pi$
$200$	9.93676	0.702635
$201$	−17.7908	−1.25486
$202$	2.05393	0.144514
$203$	0.0928617	0.00651761
$204$	24.1959	1.69405
$205$	10.9123	0.762151
$206$	13.1679	0.917450
$207$	46.2650	3.21564
$208$	1.10988	0.0769562
$209$	−7.37519	−0.510152
$210$	−0.304682	−0.0210250
$211$	−14.8632	−1.02323	−0.511613	−	0.859216i	$-0.670952\pi$
$211$	−14.8632	−1.02323	−0.511613	+	0.859216i	$0.670952\pi$
$212$	3.68758	0.253264
$213$	28.1563	1.92923
$214$	−3.77755	−0.258228
$215$	−21.6537	−1.47677
$216$	−17.4574	−1.18783
$217$	0.185886	0.0126188
$218$	17.3248	1.17338
$219$	13.7190	0.927041
$220$	4.02681	0.271487
$221$	−8.01956	−0.539454
$222$	12.2951	0.825195
$223$	10.4540	0.700054	0.350027	−	0.936740i	$-0.386172\pi$
$223$	10.4540	0.700054	0.350027	+	0.936740i	$0.386172\pi$
$224$	−0.0235424	−0.00157300
$225$	81.6136	5.44091
$226$	−1.33624	−0.0888857
$227$	−19.6105	−1.30159	−0.650796	−	0.759252i	$-0.725565\pi$
$227$	−19.6105	−1.30159	−0.650796	+	0.759252i	$0.725565\pi$
$228$	−23.7032	−1.56978
$229$	−9.20334	−0.608174	−0.304087	−	0.952644i	$-0.598351\pi$
$229$	−9.20334	−0.608174	−0.304087	+	0.952644i	$0.598351\pi$
$230$	−21.7702	−1.43548
$231$	−0.0821393	−0.00540437
$232$	−3.94444	−0.258965
$233$	28.2627	1.85155	0.925774	−	0.378077i	$-0.123414\pi$
$233$	28.2627	1.85155	0.925774	+	0.378077i	$0.123414\pi$
$234$	9.11577	0.595917
$235$	27.7651	1.81120
$236$	−11.6276	−0.756894
$237$	50.9948	3.31247
$238$	0.170109	0.0110265
$239$	−12.7503	−0.824748	−0.412374	−	0.911015i	$-0.635300\pi$
$239$	−12.7503	−0.824748	−0.412374	+	0.911015i	$0.635300\pi$
$240$	12.9418	0.835390
$241$	24.6569	1.58829	0.794144	−	0.607730i	$-0.207920\pi$
$241$	24.6569	1.58829	0.794144	+	0.607730i	$0.207920\pi$
$242$	−9.91441	−0.637322
$243$	−60.8732	−3.90501
$244$	8.83505	0.565606
$245$	27.0515	1.72826
$246$	9.45490	0.602822
$247$	7.85626	0.499882
$248$	−7.89580	−0.501384
$249$	−25.6966	−1.62846
$250$	−19.0796	−1.20670
$251$	20.4984	1.29385	0.646923	−	0.762555i	$-0.276056\pi$
$251$	20.4984	1.29385	0.646923	+	0.762555i	$0.276056\pi$
$252$	−0.193361	−0.0121806
$253$	−5.86904	−0.368983
$254$	15.8799	0.996393
$255$	−93.5126	−5.85599
$256$	1.00000	0.0625000
$257$	1.31093	0.0817733	0.0408867	−	0.999164i	$-0.486982\pi$
$257$	1.31093	0.0817733	0.0408867	+	0.999164i	$0.486982\pi$
$258$	−18.7616	−1.16805
$259$	0.0864406	0.00537116
$260$	−4.28947	−0.266022
$261$	−32.3969	−2.00532
$262$	7.86929	0.486166
$263$	−29.4107	−1.81354	−0.906771	−	0.421624i	$-0.861460\pi$
$263$	−29.4107	−1.81354	−0.906771	+	0.421624i	$0.861460\pi$
$264$	3.48899	0.214732
$265$	−14.2518	−0.875480
$266$	−0.166645	−0.0102176
$267$	23.8770	1.46125
$268$	5.31285	0.324534
$269$	6.13271	0.373918	0.186959	−	0.982368i	$-0.440137\pi$
$269$	6.13271	0.373918	0.186959	+	0.982368i	$0.440137\pi$
$270$	67.4696	4.10607
$271$	1.46966	0.0892756	0.0446378	−	0.999003i	$-0.485787\pi$
$271$	1.46966	0.0892756	0.0446378	+	0.999003i	$0.485787\pi$
$272$	−7.22562	−0.438118
$273$	0.0874971	0.00529557
$274$	7.62274	0.460506
$275$	−10.3533	−0.624325
$276$	−18.8626	−1.13539
$277$	11.0949	0.666626	0.333313	−	0.942816i	$-0.391833\pi$
$277$	11.0949	0.666626	0.333313	+	0.942816i	$0.391833\pi$
$278$	0.0147454	0.000884368 0
$279$	−64.8506	−3.88250
$280$	0.0909871	0.00543752
$281$	−8.05695	−0.480637	−0.240319	−	0.970694i	$-0.577252\pi$
$281$	−8.05695	−0.480637	−0.240319	+	0.970694i	$0.577252\pi$
$282$	24.0568	1.43256
$283$	15.1627	0.901330	0.450665	−	0.892693i	$-0.351187\pi$
$283$	15.1627	0.901330	0.450665	+	0.892693i	$0.351187\pi$
$284$	−8.40830	−0.498941
$285$	91.6084	5.42641
$286$	−1.15640	−0.0683794
$287$	0.0664724	0.00392374
$288$	8.21330	0.483974
$289$	35.2096	2.07115
$290$	15.2445	0.895188
$291$	46.8616	2.74707
$292$	−4.09689	−0.239752
$293$	27.3144	1.59573	0.797864	−	0.602838i	$-0.205964\pi$
$293$	27.3144	1.59573	0.797864	+	0.602838i	$0.205964\pi$
$294$	23.4385	1.36696
$295$	44.9386	2.61643
$296$	−3.67169	−0.213413
$297$	18.1892	1.05544
$298$	−3.68071	−0.213218
$299$	6.25187	0.361555
$300$	−33.2745	−1.92110
$301$	−0.131903	−0.00760276
$302$	−13.5110	−0.777469
$303$	−6.87783	−0.395121
$304$	7.07849	0.405979
$305$	−34.1458	−1.95518
$306$	−59.3462	−3.39260
$307$	10.3930	0.593158	0.296579	−	0.955008i	$-0.404154\pi$
$307$	10.3930	0.593158	0.296579	+	0.955008i	$0.404154\pi$
$308$	0.0245292	0.00139768
$309$	−44.0943	−2.50844
$310$	30.5158	1.73318
$311$	−30.3335	−1.72006	−0.860029	−	0.510246i	$-0.829554\pi$
$311$	−30.3335	−1.72006	−0.860029	+	0.510246i	$0.829554\pi$
$312$	−3.71657	−0.210409
$313$	10.7703	0.608774	0.304387	−	0.952548i	$-0.401548\pi$
$313$	10.7703	0.608774	0.304387	+	0.952548i	$0.401548\pi$
$314$	12.3679	0.697961
$315$	0.747304	0.0421058
$316$	−15.2286	−0.856674
$317$	20.5995	1.15698	0.578491	−	0.815689i	$-0.303642\pi$
$317$	20.5995	1.15698	0.578491	+	0.815689i	$0.303642\pi$
$318$	−12.3483	−0.692459
$319$	4.10977	0.230103
$320$	−3.86481	−0.216049
$321$	12.6496	0.706032
$322$	−0.132613	−0.00739023
$323$	−51.1465	−2.84586
$324$	33.8185	1.87880
$325$	11.0286	0.611756
$326$	−3.06844	−0.169945
$327$	−58.0143	−3.20820
$328$	−2.82351	−0.155903
$329$	0.169131	0.00932448
$330$	−13.4843	−0.742285
$331$	21.2558	1.16833	0.584164	−	0.811636i	$-0.301423\pi$
$331$	21.2558	1.16833	0.584164	+	0.811636i	$0.301423\pi$
$332$	7.67378	0.421153
$333$	−30.1567	−1.65258
$334$	1.88888	0.103355
$335$	−20.5332	−1.12185
$336$	0.0788349	0.00430079
$337$	17.4539	0.950773	0.475386	−	0.879777i	$-0.342308\pi$
$337$	17.4539	0.950773	0.475386	+	0.879777i	$0.342308\pi$
$338$	−11.7682	−0.640104
$339$	4.47459	0.243026
$340$	27.9257	1.51448
$341$	8.22676	0.445504
$342$	58.1378	3.14373
$343$	0.329581	0.0177957
$344$	5.60277	0.302081
$345$	72.9003	3.92482
$346$	16.1956	0.870680
$347$	−25.5946	−1.37399	−0.686996	−	0.726661i	$-0.741071\pi$
$347$	−25.5946	−1.37399	−0.686996	+	0.726661i	$0.741071\pi$
$348$	13.2085	0.708047
$349$	−34.4502	−1.84408	−0.922040	−	0.387096i	$-0.873478\pi$
$349$	−34.4502	−1.84408	−0.922040	+	0.387096i	$0.873478\pi$
$350$	−0.233935	−0.0125044
$351$	−19.3756	−1.03419
$352$	−1.04192	−0.0555343
$353$	19.2320	1.02362	0.511808	−	0.859100i	$-0.328976\pi$
$353$	19.2320	1.02362	0.511808	+	0.859100i	$0.328976\pi$
$354$	38.9366	2.06946
$355$	32.4965	1.72473
$356$	−7.13039	−0.377910
$357$	−0.569631	−0.0301481
$358$	−6.43794	−0.340256
$359$	1.21207	0.0639707	0.0319854	−	0.999488i	$-0.489817\pi$
$359$	1.21207	0.0639707	0.0319854	+	0.999488i	$0.489817\pi$
$360$	−31.7429	−1.67300
$361$	31.1050	1.63710
$362$	0.514630	0.0270484
$363$	33.1997	1.74253
$364$	−0.0261293	−0.00136955
$365$	15.8337	0.828774
$366$	−29.5853	−1.54645
$367$	−17.1388	−0.894641	−0.447320	−	0.894374i	$-0.647622\pi$
$367$	−17.1388	−0.894641	−0.447320	+	0.894374i	$0.647622\pi$
$368$	5.63293	0.293637
$369$	−23.1904	−1.20724
$370$	14.1904	0.737724
$371$	−0.0868145	−0.00450719
$372$	26.4401	1.37085
$373$	25.0442	1.29674	0.648370	−	0.761326i	$-0.275451\pi$
$373$	25.0442	1.29674	0.648370	+	0.761326i	$0.275451\pi$
$374$	7.52849	0.389289
$375$	63.8905	3.29929
$376$	−7.18408	−0.370491
$377$	−4.37785	−0.225471
$378$	0.410990	0.0211390
$379$	−35.0633	−1.80108	−0.900542	−	0.434770i	$-0.856830\pi$
$379$	−35.0633	−1.80108	−0.900542	+	0.434770i	$0.856830\pi$
$380$	−27.3570	−1.40338
$381$	−53.1758	−2.72428
$382$	0.684344	0.0350141
$383$	25.0548	1.28024	0.640120	−	0.768275i	$-0.278885\pi$
$383$	25.0548	1.28024	0.640120	+	0.768275i	$0.278885\pi$
$384$	−3.34863	−0.170884
$385$	−0.0948009	−0.00483150
$386$	1.53534	0.0781467
$387$	46.0173	2.33919
$388$	−13.9943	−0.710451
$389$	−3.79217	−0.192271	−0.0961354	−	0.995368i	$-0.530648\pi$
$389$	−3.79217	−0.192271	−0.0961354	+	0.995368i	$0.530648\pi$
$390$	14.3638	0.727341
$391$	−40.7014	−2.05836
$392$	−6.99945	−0.353525
$393$	−26.3513	−1.32925
$394$	5.75420	0.289893
$395$	58.8555	2.96134
$396$	−8.55757	−0.430034
$397$	−24.4714	−1.22818	−0.614091	−	0.789235i	$-0.710477\pi$
$397$	−24.4714	−1.22818	−0.614091	+	0.789235i	$0.710477\pi$
$398$	20.1461	1.00983
$399$	0.558031	0.0279365
$400$	9.93676	0.496838
$401$	35.8142	1.78847	0.894237	−	0.447594i	$-0.147719\pi$
$401$	35.8142	1.78847	0.894237	+	0.447594i	$0.147719\pi$
$402$	−17.7908	−0.887322
$403$	−8.76338	−0.436535
$404$	2.05393	0.102187
$405$	−130.702	−6.49463
$406$	0.0928617	0.00460865
$407$	3.82560	0.189628
$408$	24.1959	1.19788
$409$	−20.9237	−1.03461	−0.517306	−	0.855800i	$-0.673065\pi$
$409$	−20.9237	−1.03461	−0.517306	+	0.855800i	$0.673065\pi$
$410$	10.9123	0.538922
$411$	−25.5257	−1.25909
$412$	13.1679	0.648735
$413$	0.273743	0.0134700
$414$	46.2650	2.27380
$415$	−29.6577	−1.45584
$416$	1.10988	0.0544163
$417$	−0.0493767	−0.00241799
$418$	−7.37519	−0.360732
$419$	35.2155	1.72039	0.860195	−	0.509965i	$-0.170341\pi$
$419$	35.2155	1.72039	0.860195	+	0.509965i	$0.170341\pi$
$420$	−0.304682	−0.0148669
$421$	−28.6958	−1.39855	−0.699273	−	0.714855i	$-0.746493\pi$
$421$	−28.6958	−1.39855	−0.699273	+	0.714855i	$0.746493\pi$
$422$	−14.8632	−0.723530
$423$	−59.0050	−2.86892
$424$	3.68758	0.179085
$425$	−71.7992	−3.48277
$426$	28.1563	1.36418
$427$	−0.207999	−0.0100658
$428$	−3.77755	−0.182595
$429$	3.87235	0.186959
$430$	−21.6537	−1.04423
$431$	−27.2890	−1.31447	−0.657233	−	0.753687i	$-0.728273\pi$
$431$	−27.2890	−1.31447	−0.657233	+	0.753687i	$0.728273\pi$
$432$	−17.4574	−0.839920
$433$	19.1891	0.922168	0.461084	−	0.887356i	$-0.347461\pi$
$433$	19.1891	0.922168	0.461084	+	0.887356i	$0.347461\pi$
$434$	0.185886	0.00892283
$435$	−51.0482	−2.44757
$436$	17.3248	0.829707
$437$	39.8726	1.90737
$438$	13.7190	0.655517
$439$	5.89054	0.281140	0.140570	−	0.990071i	$-0.455106\pi$
$439$	5.89054	0.281140	0.140570	+	0.990071i	$0.455106\pi$
$440$	4.02681	0.191970
$441$	−57.4886	−2.73755
$442$	−8.01956	−0.381452
$443$	−1.31190	−0.0623303	−0.0311652	−	0.999514i	$-0.509922\pi$
$443$	−1.31190	−0.0623303	−0.0311652	+	0.999514i	$0.509922\pi$
$444$	12.2951	0.583501
$445$	27.5576	1.30636
$446$	10.4540	0.495013
$447$	12.3253	0.582967
$448$	−0.0235424	−0.00111228
$449$	−0.355750	−0.0167889	−0.00839445	−	0.999965i	$-0.502672\pi$
$449$	−0.355750	−0.0167889	−0.00839445	+	0.999965i	$0.502672\pi$
$450$	81.6136	3.84730
$451$	2.94186	0.138527
$452$	−1.33624	−0.0628517
$453$	45.2432	2.12571
$454$	−19.6105	−0.920365
$455$	0.100985	0.00473423
$456$	−23.7032	−1.11000
$457$	30.1693	1.41126	0.705630	−	0.708580i	$-0.250664\pi$
$457$	30.1693	1.41126	0.705630	+	0.708580i	$0.250664\pi$
$458$	−9.20334	−0.430044
$459$	126.141	5.88774
$460$	−21.7702	−1.01504
$461$	4.33400	0.201855	0.100927	−	0.994894i	$-0.467819\pi$
$461$	4.33400	0.201855	0.100927	+	0.994894i	$0.467819\pi$
$462$	−0.0821393	−0.00382147
$463$	27.6466	1.28485	0.642423	−	0.766350i	$-0.277929\pi$
$463$	27.6466	1.28485	0.642423	+	0.766350i	$0.277929\pi$
$464$	−3.94444	−0.183116
$465$	−102.186	−4.73876
$466$	28.2627	1.30924
$467$	−23.3173	−1.07899	−0.539497	−	0.841987i	$-0.681386\pi$
$467$	−23.3173	−1.07899	−0.539497	+	0.841987i	$0.681386\pi$
$468$	9.11577	0.421377
$469$	−0.125077	−0.00577554
$470$	27.7651	1.28071
$471$	−41.4155	−1.90833
$472$	−11.6276	−0.535205
$473$	−5.83762	−0.268414
$474$	50.9948	2.34227
$475$	70.3372	3.22729
$476$	0.170109	0.00779692
$477$	30.2872	1.38675
$478$	−12.7503	−0.583185
$479$	25.6389	1.17147	0.585735	−	0.810503i	$-0.300806\pi$
$479$	25.6389	1.17147	0.585735	+	0.810503i	$0.300806\pi$
$480$	12.9418	0.590710
$481$	−4.07513	−0.185810
$482$	24.6569	1.12309
$483$	0.444071	0.0202059
$484$	−9.91441	−0.450655
$485$	54.0851	2.45588
$486$	−60.8732	−2.76126
$487$	14.9329	0.676675	0.338337	−	0.941025i	$-0.390135\pi$
$487$	14.9329	0.676675	0.338337	+	0.941025i	$0.390135\pi$
$488$	8.83505	0.399944
$489$	10.2750	0.464654
$490$	27.0515	1.22206
$491$	−20.2530	−0.914005	−0.457003	−	0.889465i	$-0.651077\pi$
$491$	−20.2530	−0.914005	−0.457003	+	0.889465i	$0.651077\pi$
$492$	9.45490	0.426260
$493$	28.5010	1.28362
$494$	7.85626	0.353470
$495$	33.0734	1.48654
$496$	−7.89580	−0.354532
$497$	0.197952	0.00887935
$498$	−25.6966	−1.15149
$499$	37.5404	1.68054	0.840269	−	0.542169i	$-0.182397\pi$
$499$	37.5404	1.68054	0.840269	+	0.542169i	$0.182397\pi$
$500$	−19.0796	−0.853267
$501$	−6.32516	−0.282587
$502$	20.4984	0.914887
$503$	13.4992	0.601901	0.300951	−	0.953640i	$-0.402696\pi$
$503$	13.4992	0.601901	0.300951	+	0.953640i	$0.402696\pi$
$504$	−0.193361	−0.00861299
$505$	−7.93803	−0.353238
$506$	−5.86904	−0.260911
$507$	39.4072	1.75014
$508$	15.8799	0.704556
$509$	20.0231	0.887509	0.443755	−	0.896148i	$-0.353646\pi$
$509$	20.0231	0.887509	0.443755	+	0.896148i	$0.353646\pi$
$510$	−93.5126	−4.14081
$511$	0.0964508	0.00426673
$512$	1.00000	0.0441942
$513$	−123.572	−5.45584
$514$	1.31093	0.0578225
$515$	−50.8914	−2.24254
$516$	−18.7616	−0.825933
$517$	7.48521	0.329199
$518$	0.0864406	0.00379798
$519$	−54.2330	−2.38056
$520$	−4.28947	−0.188106
$521$	27.5373	1.20643	0.603215	−	0.797578i	$-0.293886\pi$
$521$	27.5373	1.20643	0.603215	+	0.797578i	$0.293886\pi$
$522$	−32.3969	−1.41797
$523$	27.7303	1.21256	0.606281	−	0.795250i	$-0.292661\pi$
$523$	27.7303	1.21256	0.606281	+	0.795250i	$0.292661\pi$
$524$	7.86929	0.343772
$525$	0.783363	0.0341888
$526$	−29.4107	−1.28237
$527$	57.0521	2.48523
$528$	3.48899	0.151839
$529$	8.72991	0.379561
$530$	−14.2518	−0.619058
$531$	−95.5013	−4.14440
$532$	−0.166645	−0.00722497
$533$	−3.13376	−0.135738
$534$	23.8770	1.03326
$535$	14.5995	0.631192
$536$	5.31285	0.229480
$537$	21.5583	0.930308
$538$	6.13271	0.264400
$539$	7.29283	0.314125
$540$	67.4696	2.90343
$541$	33.7805	1.45234	0.726168	−	0.687517i	$-0.241299\pi$
$541$	33.7805	1.45234	0.726168	+	0.687517i	$0.241299\pi$
$542$	1.46966	0.0631274
$543$	−1.72331	−0.0739541
$544$	−7.22562	−0.309796
$545$	−66.9570	−2.86812
$546$	0.0874971	0.00374453
$547$	−0.119116	−0.00509304	−0.00254652	−	0.999997i	$-0.500811\pi$
$547$	−0.119116	−0.00509304	−0.00254652	+	0.999997i	$0.500811\pi$
$548$	7.62274	0.325627
$549$	72.5650	3.09700
$550$	−10.3533	−0.441465
$551$	−27.9206	−1.18946
$552$	−18.8626	−0.802845
$553$	0.358518	0.0152457
$554$	11.0949	0.471375
$555$	−47.5183	−2.01704
$556$	0.0147454	0.000625343 0
$557$	−39.8353	−1.68787	−0.843937	−	0.536442i	$-0.819768\pi$
$557$	−39.8353	−1.68787	−0.843937	+	0.536442i	$0.819768\pi$
$558$	−64.8506	−2.74534
$559$	6.21840	0.263010
$560$	0.0909871	0.00384490
$561$	−25.2101	−1.06437
$562$	−8.05695	−0.339862
$563$	14.4336	0.608305	0.304153	−	0.952623i	$-0.401627\pi$
$563$	14.4336	0.608305	0.304153	+	0.952623i	$0.401627\pi$
$564$	24.0568	1.01297
$565$	5.16433	0.217265
$566$	15.1627	0.637336
$567$	−0.796169	−0.0334360
$568$	−8.40830	−0.352804
$569$	−2.66727	−0.111818	−0.0559089	−	0.998436i	$-0.517806\pi$
$569$	−2.66727	−0.111818	−0.0559089	+	0.998436i	$0.517806\pi$
$570$	91.6084	3.83705
$571$	39.9784	1.67304	0.836522	−	0.547933i	$-0.184585\pi$
$571$	39.9784	1.67304	0.836522	+	0.547933i	$0.184585\pi$
$572$	−1.15640	−0.0483515
$573$	−2.29161	−0.0957335
$574$	0.0664724	0.00277451
$575$	55.9731	2.33424
$576$	8.21330	0.342221
$577$	−36.5528	−1.52171	−0.760855	−	0.648921i	$-0.775220\pi$
$577$	−36.5528	−1.52171	−0.760855	+	0.648921i	$0.775220\pi$
$578$	35.2096	1.46453
$579$	−5.14128	−0.213664
$580$	15.2445	0.632994
$581$	−0.180659	−0.00749502
$582$	46.8616	1.94247
$583$	−3.84214	−0.159125
$584$	−4.09689	−0.169531
$585$	−35.2307	−1.45661
$586$	27.3144	1.12835
$587$	−19.6734	−0.812009	−0.406005	−	0.913871i	$-0.633078\pi$
$587$	−19.6734	−0.812009	−0.406005	+	0.913871i	$0.633078\pi$
$588$	23.4385	0.966589
$589$	−55.8903	−2.30292
$590$	44.9386	1.85009
$591$	−19.2687	−0.792608
$592$	−3.67169	−0.150906
$593$	7.53128	0.309273	0.154636	−	0.987971i	$-0.450579\pi$
$593$	7.53128	0.309273	0.154636	+	0.987971i	$0.450579\pi$
$594$	18.1892	0.746310
$595$	−0.657438	−0.0269523
$596$	−3.68071	−0.150768
$597$	−67.4618	−2.76103
$598$	6.25187	0.255658
$599$	9.37370	0.382999	0.191500	−	0.981493i	$-0.438665\pi$
$599$	9.37370	0.382999	0.191500	+	0.981493i	$0.438665\pi$
$600$	−33.2745	−1.35843
$601$	−0.00917741	−0.000374354 0	−0.000187177	−	1.00000i	$-0.500060\pi$
$601$	−0.00917741	−0.000374354 0	−0.000187177		1.00000i	$0.500060\pi$
$602$	−0.131903	−0.00537596
$603$	43.6360	1.77700
$604$	−13.5110	−0.549754
$605$	38.3173	1.55782
$606$	−6.87783	−0.279393
$607$	2.27029	0.0921482	0.0460741	−	0.998938i	$-0.485329\pi$
$607$	2.27029	0.0921482	0.0460741	+	0.998938i	$0.485329\pi$
$608$	7.07849	0.287070
$609$	−0.310959	−0.0126007
$610$	−34.1458	−1.38252
$611$	−7.97346	−0.322572
$612$	−59.3462	−2.39893
$613$	−2.80575	−0.113323	−0.0566616	−	0.998393i	$-0.518046\pi$
$613$	−2.80575	−0.113323	−0.0566616	+	0.998393i	$0.518046\pi$
$614$	10.3930	0.419426
$615$	−36.5414	−1.47349
$616$	0.0245292	0.000988311 0
$617$	13.2042	0.531582	0.265791	−	0.964031i	$-0.414367\pi$
$617$	13.2042	0.531582	0.265791	+	0.964031i	$0.414367\pi$
$618$	−44.0943	−1.77373
$619$	−25.5044	−1.02511	−0.512555	−	0.858655i	$-0.671301\pi$
$619$	−25.5044	−1.02511	−0.512555	+	0.858655i	$0.671301\pi$
$620$	30.5158	1.22554
$621$	−98.3364	−3.94610
$622$	−30.3335	−1.21626
$623$	0.167867	0.00672544
$624$	−3.71657	−0.148782
$625$	24.0553	0.962213
$626$	10.7703	0.430468
$627$	24.6968	0.986293
$628$	12.3679	0.493533
$629$	26.5303	1.05783
$630$	0.747304	0.0297733
$631$	−21.1183	−0.840707	−0.420354	−	0.907360i	$-0.638094\pi$
$631$	−21.1183	−0.840707	−0.420354	+	0.907360i	$0.638094\pi$
$632$	−15.2286	−0.605760
$633$	49.7714	1.97823
$634$	20.5995	0.818110
$635$	−61.3728	−2.43550
$636$	−12.3483	−0.489643
$637$	−7.76854	−0.307801
$638$	4.10977	0.162707
$639$	−69.0599	−2.73197
$640$	−3.86481	−0.152770
$641$	25.4079	1.00355	0.501776	−	0.864998i	$-0.332680\pi$
$641$	25.4079	1.00355	0.501776	+	0.864998i	$0.332680\pi$
$642$	12.6496	0.499240
$643$	−39.2829	−1.54916	−0.774582	−	0.632473i	$-0.782040\pi$
$643$	−39.2829	−1.54916	−0.774582	+	0.632473i	$0.782040\pi$
$644$	−0.132613	−0.00522568
$645$	72.5100	2.85508
$646$	−51.1465	−2.01233
$647$	−29.2823	−1.15121	−0.575604	−	0.817729i	$-0.695233\pi$
$647$	−29.2823	−1.15121	−0.575604	+	0.817729i	$0.695233\pi$
$648$	33.8185	1.32851
$649$	12.1150	0.475556
$650$	11.0286	0.432577
$651$	−0.622464	−0.0243963
$652$	−3.06844	−0.120169
$653$	−33.4536	−1.30914	−0.654570	−	0.756001i	$-0.727150\pi$
$653$	−33.4536	−1.30914	−0.654570	+	0.756001i	$0.727150\pi$
$654$	−58.0143	−2.26854
$655$	−30.4133	−1.18835
$656$	−2.82351	−0.110240
$657$	−33.6490	−1.31277
$658$	0.169131	0.00659340
$659$	−15.1563	−0.590407	−0.295204	−	0.955434i	$-0.595388\pi$
$659$	−15.1563	−0.590407	−0.295204	+	0.955434i	$0.595388\pi$
$660$	−13.4843	−0.524875
$661$	34.4725	1.34082	0.670412	−	0.741989i	$-0.266117\pi$
$661$	34.4725	1.34082	0.670412	+	0.741989i	$0.266117\pi$
$662$	21.2558	0.826132
$663$	26.8545	1.04294
$664$	7.67378	0.297800
$665$	0.644051	0.0249752
$666$	−30.1567	−1.16855
$667$	−22.2187	−0.860313
$668$	1.88888	0.0730830
$669$	−35.0066	−1.35344
$670$	−20.5332	−0.793265
$671$	−9.20538	−0.355370
$672$	0.0788349	0.00304112
$673$	−39.6828	−1.52966	−0.764830	−	0.644232i	$-0.777177\pi$
$673$	−39.6828	−1.52966	−0.764830	+	0.644232i	$0.777177\pi$
$674$	17.4539	0.672298
$675$	−173.470	−6.67686
$676$	−11.7682	−0.452622
$677$	−11.7251	−0.450633	−0.225317	−	0.974286i	$-0.572342\pi$
$677$	−11.7251	−0.450633	−0.225317	+	0.974286i	$0.572342\pi$
$678$	4.47459	0.171845
$679$	0.329459	0.0126435
$680$	27.9257	1.07090
$681$	65.6681	2.51641
$682$	8.22676	0.315019
$683$	29.8166	1.14090	0.570451	−	0.821332i	$-0.306768\pi$
$683$	29.8166	1.14090	0.570451	+	0.821332i	$0.306768\pi$
$684$	58.1378	2.22295
$685$	−29.4604	−1.12563
$686$	0.329581	0.0125835
$687$	30.8185	1.17580
$688$	5.60277	0.213604
$689$	4.09276	0.155922
$690$	72.9003	2.77527
$691$	18.5696	0.706421	0.353211	−	0.935544i	$-0.385090\pi$
$691$	18.5696	0.706421	0.353211	+	0.935544i	$0.385090\pi$
$692$	16.1956	0.615664
$693$	0.201466	0.00765307
$694$	−25.5946	−0.971559
$695$	−0.0569880	−0.00216168
$696$	13.2085	0.500665
$697$	20.4016	0.772767
$698$	−34.4502	−1.30396
$699$	−94.6411	−3.57966
$700$	−0.233935	−0.00884193
$701$	11.9982	0.453165	0.226583	−	0.973992i	$-0.427245\pi$
$701$	11.9982	0.453165	0.226583	+	0.973992i	$0.427245\pi$
$702$	−19.3756	−0.731285
$703$	−25.9900	−0.980232
$704$	−1.04192	−0.0392687
$705$	−92.9750	−3.50164
$706$	19.2320	0.723806
$707$	−0.0483544	−0.00181855
$708$	38.9366	1.46333
$709$	−18.4544	−0.693069	−0.346535	−	0.938037i	$-0.612642\pi$
$709$	−18.4544	−0.693069	−0.346535	+	0.938037i	$0.612642\pi$
$710$	32.4965	1.21957
$711$	−125.077	−4.69075
$712$	−7.13039	−0.267223
$713$	−44.4765	−1.66566
$714$	−0.569631	−0.0213179
$715$	4.46927	0.167141
$716$	−6.43794	−0.240597
$717$	42.6960	1.59451
$718$	1.21207	0.0452341
$719$	−6.16610	−0.229957	−0.114978	−	0.993368i	$-0.536680\pi$
$719$	−6.16610	−0.229957	−0.114978	+	0.993368i	$0.536680\pi$
$720$	−31.7429	−1.18299
$721$	−0.310004	−0.0115452
$722$	31.1050	1.15761
$723$	−82.5666	−3.07069
$724$	0.514630	0.0191261
$725$	−39.1949	−1.45566
$726$	33.1997	1.23216
$727$	−12.3960	−0.459741	−0.229870	−	0.973221i	$-0.573830\pi$
$727$	−12.3960	−0.459741	−0.229870	+	0.973221i	$0.573830\pi$
$728$	−0.0261293	−0.000968415 0
$729$	102.386	3.79208
$730$	15.8337	0.586032
$731$	−40.4835	−1.49734
$732$	−29.5853	−1.09350
$733$	−14.6618	−0.541545	−0.270772	−	0.962643i	$-0.587279\pi$
$733$	−14.6618	−0.541545	−0.270772	+	0.962643i	$0.587279\pi$
$734$	−17.1388	−0.632606
$735$	−90.5855	−3.34130
$736$	5.63293	0.207633
$737$	−5.53554	−0.203904
$738$	−23.1904	−0.853650
$739$	−45.5532	−1.67570	−0.837851	−	0.545899i	$-0.816188\pi$
$739$	−45.5532	−1.67570	−0.837851	+	0.545899i	$0.816188\pi$
$740$	14.1904	0.521649
$741$	−26.3077	−0.966437
$742$	−0.0868145	−0.00318706
$743$	14.3306	0.525737	0.262868	−	0.964832i	$-0.415331\pi$
$743$	14.3306	0.525737	0.262868	+	0.964832i	$0.415331\pi$
$744$	26.4401	0.969341
$745$	14.2252	0.521172
$746$	25.0442	0.916933
$747$	63.0271	2.30604
$748$	7.52849	0.275269
$749$	0.0889327	0.00324953
$750$	63.8905	2.33295
$751$	−37.9571	−1.38508	−0.692538	−	0.721382i	$-0.743507\pi$
$751$	−37.9571	−1.38508	−0.692538	+	0.721382i	$0.743507\pi$
$752$	−7.18408	−0.261976
$753$	−68.6414	−2.50143
$754$	−4.37785	−0.159432
$755$	52.2173	1.90038
$756$	0.410990	0.0149476
$757$	−5.07900	−0.184599	−0.0922996	−	0.995731i	$-0.529422\pi$
$757$	−5.07900	−0.184599	−0.0922996	+	0.995731i	$0.529422\pi$
$758$	−35.0633	−1.27356
$759$	19.6532	0.713367
$760$	−27.3570	−0.992343
$761$	−2.63434	−0.0954946	−0.0477473	−	0.998859i	$-0.515204\pi$
$761$	−2.63434	−0.0954946	−0.0477473	+	0.998859i	$0.515204\pi$
$762$	−53.1758	−1.92636
$763$	−0.407868	−0.0147658
$764$	0.684344	0.0247587
$765$	229.362	8.29260
$766$	25.0548	0.905266
$767$	−12.9053	−0.465982
$768$	−3.34863	−0.120833
$769$	26.8736	0.969088	0.484544	−	0.874767i	$-0.338986\pi$
$769$	26.8736	0.969088	0.484544	+	0.874767i	$0.338986\pi$
$770$	−0.0948009	−0.00341639
$771$	−4.38980	−0.158095
$772$	1.53534	0.0552581
$773$	26.0775	0.937943	0.468972	−	0.883213i	$-0.344625\pi$
$773$	26.0775	0.937943	0.468972	+	0.883213i	$0.344625\pi$
$774$	46.0173	1.65406
$775$	−78.4586	−2.81832
$776$	−13.9943	−0.502365
$777$	−0.289457	−0.0103842
$778$	−3.79217	−0.135956
$779$	−19.9862	−0.716080
$780$	14.3638	0.514308
$781$	8.76074	0.313484
$782$	−40.7014	−1.45548
$783$	68.8597	2.46084
$784$	−6.99945	−0.249980
$785$	−47.7996	−1.70604
$786$	−26.3513	−0.939920
$787$	26.8950	0.958704	0.479352	−	0.877623i	$-0.340872\pi$
$787$	26.8950	0.958704	0.479352	+	0.877623i	$0.340872\pi$
$788$	5.75420	0.204985
$789$	98.4855	3.50618
$790$	58.8555	2.09399
$791$	0.0314585	0.00111853
$792$	−8.55757	−0.304080
$793$	9.80584	0.348215
$794$	−24.4714	−0.868456
$795$	47.7239	1.69259
$796$	20.1461	0.714060
$797$	−16.1311	−0.571391	−0.285696	−	0.958320i	$-0.592225\pi$
$797$	−16.1311	−0.571391	−0.285696	+	0.958320i	$0.592225\pi$
$798$	0.558031	0.0197541
$799$	51.9094	1.83642
$800$	9.93676	0.351317
$801$	−58.5641	−2.06926
$802$	35.8142	1.26464
$803$	4.26862	0.150636
$804$	−17.7908	−0.627431
$805$	0.512524	0.0180641
$806$	−8.76338	−0.308677
$807$	−20.5361	−0.722906
$808$	2.05393	0.0722568
$809$	29.4060	1.03386	0.516930	−	0.856028i	$-0.327075\pi$
$809$	29.4060	1.03386	0.516930	+	0.856028i	$0.327075\pi$
$810$	−130.702	−4.59240
$811$	25.7247	0.903315	0.451657	−	0.892191i	$-0.350833\pi$
$811$	25.7247	0.903315	0.451657	+	0.892191i	$0.350833\pi$
$812$	0.0928617	0.00325881
$813$	−4.92135	−0.172599
$814$	3.82560	0.134087
$815$	11.8589	0.415400
$816$	24.1959	0.847026
$817$	39.6591	1.38750
$818$	−20.9237	−0.731581
$819$	−0.214608	−0.00749899
$820$	10.9123	0.381076
$821$	21.6086	0.754145	0.377072	−	0.926184i	$-0.376931\pi$
$821$	21.6086	0.754145	0.377072	+	0.926184i	$0.376931\pi$
$822$	−25.5257	−0.890311
$823$	−43.2227	−1.50665	−0.753325	−	0.657648i	$-0.771551\pi$
$823$	−43.2227	−1.50665	−0.753325	+	0.657648i	$0.771551\pi$
$824$	13.1679	0.458725
$825$	34.6692	1.20703
$826$	0.273743	0.00952473
$827$	−17.2273	−0.599052	−0.299526	−	0.954088i	$-0.596828\pi$
$827$	−17.2273	−0.599052	−0.299526	+	0.954088i	$0.596828\pi$
$828$	46.2650	1.60782
$829$	40.7132	1.41403	0.707014	−	0.707199i	$-0.250042\pi$
$829$	40.7132	1.41403	0.707014	+	0.707199i	$0.250042\pi$
$830$	−29.6577	−1.02943
$831$	−37.1526	−1.28881
$832$	1.10988	0.0384781
$833$	50.5753	1.75233
$834$	−0.0493767	−0.00170978
$835$	−7.30017	−0.252633
$836$	−7.37519	−0.255076
$837$	137.840	4.76446
$838$	35.2155	1.21650
$839$	−3.01960	−0.104248	−0.0521241	−	0.998641i	$-0.516599\pi$
$839$	−3.01960	−0.104248	−0.0521241	+	0.998641i	$0.516599\pi$
$840$	−0.304682	−0.0105125
$841$	−13.4414	−0.463497
$842$	−28.6958	−0.988921
$843$	26.9797	0.929231
$844$	−14.8632	−0.511613
$845$	45.4817	1.56462
$846$	−59.0050	−2.02863
$847$	0.233409	0.00802004
$848$	3.68758	0.126632
$849$	−50.7743	−1.74257
$850$	−71.7992	−2.46269
$851$	−20.6824	−0.708983
$852$	28.1563	0.964617
$853$	33.4078	1.14386	0.571930	−	0.820302i	$-0.306195\pi$
$853$	33.4078	1.14386	0.571930	+	0.820302i	$0.306195\pi$
$854$	−0.207999	−0.00711757
$855$	−224.691	−7.68428
$856$	−3.77755	−0.129114
$857$	24.4304	0.834527	0.417264	−	0.908785i	$-0.362989\pi$
$857$	24.4304	0.834527	0.417264	+	0.908785i	$0.362989\pi$
$858$	3.87235	0.132200
$859$	−34.9582	−1.19276	−0.596379	−	0.802703i	$-0.703394\pi$
$859$	−34.9582	−1.19276	−0.596379	+	0.802703i	$0.703394\pi$
$860$	−21.6537	−0.738383
$861$	−0.222591	−0.00758589
$862$	−27.2890	−0.929468
$863$	−23.8166	−0.810727	−0.405364	−	0.914156i	$-0.632855\pi$
$863$	−23.8166	−0.810727	−0.405364	+	0.914156i	$0.632855\pi$
$864$	−17.4574	−0.593913
$865$	−62.5928	−2.12822
$866$	19.1891	0.652071
$867$	−117.904	−4.00422
$868$	0.185886	0.00630939
$869$	15.8669	0.538247
$870$	−51.0482	−1.73069
$871$	5.89662	0.199799
$872$	17.3248	0.586692
$873$	−114.939	−3.89010
$874$	39.8726	1.34871
$875$	0.449181	0.0151851
$876$	13.7190	0.463521
$877$	49.5571	1.67342	0.836712	−	0.547643i	$-0.184475\pi$
$877$	49.5571	1.67342	0.836712	+	0.547643i	$0.184475\pi$
$878$	5.89054	0.198796
$879$	−91.4659	−3.08507
$880$	4.02681	0.135744
$881$	11.1348	0.375141	0.187570	−	0.982251i	$-0.439939\pi$
$881$	11.1348	0.375141	0.187570	+	0.982251i	$0.439939\pi$
$882$	−57.4886	−1.93574
$883$	41.1926	1.38624	0.693120	−	0.720822i	$-0.256236\pi$
$883$	41.1926	1.38624	0.693120	+	0.720822i	$0.256236\pi$
$884$	−8.01956	−0.269727
$885$	−150.483	−5.05842
$886$	−1.31190	−0.0440742
$887$	−1.74442	−0.0585720	−0.0292860	−	0.999571i	$-0.509323\pi$
$887$	−1.74442	−0.0585720	−0.0292860	+	0.999571i	$0.509323\pi$
$888$	12.2951	0.412598
$889$	−0.373851	−0.0125386
$890$	27.5576	0.923733
$891$	−35.2360	−1.18045
$892$	10.4540	0.350027
$893$	−50.8524	−1.70171
$894$	12.3253	0.412220
$895$	24.8814	0.831694
$896$	−0.0235424	−0.000786498 0
$897$	−20.9352	−0.699005
$898$	−0.355750	−0.0118715
$899$	31.1445	1.03873
$900$	81.6136	2.72045
$901$	−26.6450	−0.887674
$902$	2.94186	0.0979534
$903$	0.441694	0.0146986
$904$	−1.33624	−0.0444428
$905$	−1.98895	−0.0661149
$906$	45.2432	1.50310
$907$	55.5871	1.84574	0.922869	−	0.385114i	$-0.125838\pi$
$907$	55.5871	1.84574	0.922869	+	0.385114i	$0.125838\pi$
$908$	−19.6105	−0.650796
$909$	16.8695	0.559526
$910$	0.100985	0.00334761
$911$	−1.25128	−0.0414566	−0.0207283	−	0.999785i	$-0.506599\pi$
$911$	−1.25128	−0.0414566	−0.0207283	+	0.999785i	$0.506599\pi$
$912$	−23.7032	−0.784892
$913$	−7.99543	−0.264610
$914$	30.1693	0.997912
$915$	114.342	3.78002
$916$	−9.20334	−0.304087
$917$	−0.185262	−0.00611790
$918$	126.141	4.16326
$919$	−2.69302	−0.0888345	−0.0444172	−	0.999013i	$-0.514143\pi$
$919$	−2.69302	−0.0888345	−0.0444172	+	0.999013i	$0.514143\pi$
$920$	−21.7702	−0.717742
$921$	−34.8022	−1.14677
$922$	4.33400	0.142733
$923$	−9.33219	−0.307173
$924$	−0.0821393	−0.00270218
$925$	−36.4847	−1.19961
$926$	27.6466	0.908524
$927$	108.152	3.55217
$928$	−3.94444	−0.129483
$929$	−18.9366	−0.621291	−0.310645	−	0.950526i	$-0.600545\pi$
$929$	−18.9366	−0.621291	−0.310645	+	0.950526i	$0.600545\pi$
$930$	−102.186	−3.35081
$931$	−49.5455	−1.62379
$932$	28.2627	0.925774
$933$	101.576	3.32544
$934$	−23.3173	−0.762964
$935$	−29.0962	−0.951547
$936$	9.11577	0.297958
$937$	−25.6178	−0.836898	−0.418449	−	0.908240i	$-0.637426\pi$
$937$	−25.6178	−0.836898	−0.418449	+	0.908240i	$0.637426\pi$
$938$	−0.125077	−0.00408392
$939$	−36.0658	−1.17696
$940$	27.7651	0.905598
$941$	−30.3977	−0.990936	−0.495468	−	0.868626i	$-0.665003\pi$
$941$	−30.3977	−0.990936	−0.495468	+	0.868626i	$0.665003\pi$
$942$	−41.4155	−1.34939
$943$	−15.9047	−0.517927
$944$	−11.6276	−0.378447
$945$	−1.58840	−0.0516706
$946$	−5.83762	−0.189797
$947$	27.4586	0.892284	0.446142	−	0.894962i	$-0.352798\pi$
$947$	27.4586	0.892284	0.446142	+	0.894962i	$0.352798\pi$
$948$	50.9948	1.65623
$949$	−4.54705	−0.147604
$950$	70.3372	2.28204
$951$	−68.9800	−2.23683
$952$	0.170109	0.00551326
$953$	30.4753	0.987193	0.493597	−	0.869691i	$-0.335682\pi$
$953$	30.4753	0.987193	0.493597	+	0.869691i	$0.335682\pi$
$954$	30.2872	0.980584
$955$	−2.64486	−0.0855856
$956$	−12.7503	−0.412374
$957$	−13.7621	−0.444865
$958$	25.6389	0.828355
$959$	−0.179458	−0.00579500
$960$	12.9418	0.417695
$961$	31.3436	1.01109
$962$	−4.07513	−0.131388
$963$	−31.0262	−0.999804
$964$	24.6569	0.794144
$965$	−5.93379	−0.191016
$966$	0.444071	0.0142878
$967$	−45.5373	−1.46438	−0.732190	−	0.681101i	$-0.761502\pi$
$967$	−45.5373	−1.46438	−0.732190	+	0.681101i	$0.761502\pi$
$968$	−9.91441	−0.318661
$969$	171.270	5.50200
$970$	54.0851	1.73657
$971$	48.0136	1.54083	0.770415	−	0.637543i	$-0.220049\pi$
$971$	48.0136	1.54083	0.770415	+	0.637543i	$0.220049\pi$
$972$	−60.8732	−1.95251
$973$	−0.000347142 0	−1.11289e−5 0
$974$	14.9329	0.478481
$975$	−36.9306	−1.18273
$976$	8.83505	0.282803
$977$	15.1476	0.484614	0.242307	−	0.970200i	$-0.422096\pi$
$977$	15.1476	0.484614	0.242307	+	0.970200i	$0.422096\pi$
$978$	10.2750	0.328560
$979$	7.42927	0.237440
$980$	27.0515	0.864129
$981$	142.294	4.54309
$982$	−20.2530	−0.646299
$983$	−6.24723	−0.199256	−0.0996278	−	0.995025i	$-0.531765\pi$
$983$	−6.24723	−0.199256	−0.0996278	+	0.995025i	$0.531765\pi$
$984$	9.45490	0.301411
$985$	−22.2389	−0.708590
$986$	28.5010	0.907657
$987$	−0.566356	−0.0180273
$988$	7.85626	0.249941
$989$	31.5600	1.00355
$990$	33.0734	1.05114
$991$	27.3856	0.869932	0.434966	−	0.900447i	$-0.356760\pi$
$991$	27.3856	0.869932	0.434966	+	0.900447i	$0.356760\pi$
$992$	−7.89580	−0.250692
$993$	−71.1779	−2.25876
$994$	0.197952	0.00627865
$995$	−77.8608	−2.46835
$996$	−25.6966	−0.814229
$997$	41.0092	1.29877	0.649387	−	0.760458i	$-0.275025\pi$
$997$	41.0092	1.29877	0.649387	+	0.760458i	$0.275025\pi$
$998$	37.5404	1.18832
$999$	64.0983	2.02798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.d.1.2	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.d.1.2	✓	79	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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.34863 q^{3} +1.00000 q^{4} -3.86481 q^{5} -3.34863 q^{6} -0.0235424 q^{7} +1.00000 q^{8} +8.21330 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.34863 q^{3} +1.00000 q^{4} -3.86481 q^{5} -3.34863 q^{6} -0.0235424 q^{7} +1.00000 q^{8} +8.21330 q^{9} -3.86481 q^{10} -1.04192 q^{11} -3.34863 q^{12} +1.10988 q^{13} -0.0235424 q^{14} +12.9418 q^{15} +1.00000 q^{16} -7.22562 q^{17} +8.21330 q^{18} +7.07849 q^{19} -3.86481 q^{20} +0.0788349 q^{21} -1.04192 q^{22} +5.63293 q^{23} -3.34863 q^{24} +9.93676 q^{25} +1.10988 q^{26} -17.4574 q^{27} -0.0235424 q^{28} -3.94444 q^{29} +12.9418 q^{30} -7.89580 q^{31} +1.00000 q^{32} +3.48899 q^{33} -7.22562 q^{34} +0.0909871 q^{35} +8.21330 q^{36} -3.67169 q^{37} +7.07849 q^{38} -3.71657 q^{39} -3.86481 q^{40} -2.82351 q^{41} +0.0788349 q^{42} +5.60277 q^{43} -1.04192 q^{44} -31.7429 q^{45} +5.63293 q^{46} -7.18408 q^{47} -3.34863 q^{48} -6.99945 q^{49} +9.93676 q^{50} +24.1959 q^{51} +1.10988 q^{52} +3.68758 q^{53} -17.4574 q^{54} +4.02681 q^{55} -0.0235424 q^{56} -23.7032 q^{57} -3.94444 q^{58} -11.6276 q^{59} +12.9418 q^{60} +8.83505 q^{61} -7.89580 q^{62} -0.193361 q^{63} +1.00000 q^{64} -4.28947 q^{65} +3.48899 q^{66} +5.31285 q^{67} -7.22562 q^{68} -18.8626 q^{69} +0.0909871 q^{70} -8.40830 q^{71} +8.21330 q^{72} -4.09689 q^{73} -3.67169 q^{74} -33.2745 q^{75} +7.07849 q^{76} +0.0245292 q^{77} -3.71657 q^{78} -15.2286 q^{79} -3.86481 q^{80} +33.8185 q^{81} -2.82351 q^{82} +7.67378 q^{83} +0.0788349 q^{84} +27.9257 q^{85} +5.60277 q^{86} +13.2085 q^{87} -1.04192 q^{88} -7.13039 q^{89} -31.7429 q^{90} -0.0261293 q^{91} +5.63293 q^{92} +26.4401 q^{93} -7.18408 q^{94} -27.3570 q^{95} -3.34863 q^{96} -13.9943 q^{97} -6.99945 q^{98} -8.55757 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9}+O(q^{10}) \) 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9	\( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9} + 18 q^{10} + 28 q^{11} + 17 q^{12} + 47 q^{13} + 19 q^{14} + 14 q^{15} + 79 q^{16} + 36 q^{17} + 118 q^{18} + 29 q^{19} + 18 q^{20} + 45 q^{21} + 28 q^{22} + 23 q^{23} + 17 q^{24} + 161 q^{25} + 47 q^{26} + 50 q^{27} + 19 q^{28} + 53 q^{29} + 14 q^{30} + 29 q^{31} + 79 q^{32} + 34 q^{33} + 36 q^{34} + 33 q^{35} + 118 q^{36} + 89 q^{37} + 29 q^{38} - 7 q^{39} + 18 q^{40} + 58 q^{41} + 45 q^{42} + 88 q^{43} + 28 q^{44} + 45 q^{45} + 23 q^{46} + 3 q^{47} + 17 q^{48} + 162 q^{49} + 161 q^{50} + 29 q^{51} + 47 q^{52} + 88 q^{53} + 50 q^{54} + 37 q^{55} + 19 q^{56} + 54 q^{57} + 53 q^{58} + 37 q^{59} + 14 q^{60} + 55 q^{61} + 29 q^{62} + 21 q^{63} + 79 q^{64} + 55 q^{65} + 34 q^{66} + 107 q^{67} + 36 q^{68} + 39 q^{69} + 33 q^{70} - 5 q^{71} + 118 q^{72} + 71 q^{73} + 89 q^{74} + 37 q^{75} + 29 q^{76} + 61 q^{77} - 7 q^{78} + 29 q^{79} + 18 q^{80} + 215 q^{81} + 58 q^{82} + 42 q^{83} + 45 q^{84} + 84 q^{85} + 88 q^{86} + 15 q^{87} + 28 q^{88} + 72 q^{89} + 45 q^{90} + 70 q^{91} + 23 q^{92} + 97 q^{93} + 3 q^{94} - 18 q^{95} + 17 q^{96} + 93 q^{97} + 162 q^{98} + 49 q^{99}+O(q^{100}) \) 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9 + 18 * q^10 + 28 * q^11 + 17 * q^12 + 47 * q^13 + 19 * q^14 + 14 * q^15 + 79 * q^16 + 36 * q^17 + 118 * q^18 + 29 * q^19 + 18 * q^20 + 45 * q^21 + 28 * q^22 + 23 * q^23 + 17 * q^24 + 161 * q^25 + 47 * q^26 + 50 * q^27 + 19 * q^28 + 53 * q^29 + 14 * q^30 + 29 * q^31 + 79 * q^32 + 34 * q^33 + 36 * q^34 + 33 * q^35 + 118 * q^36 + 89 * q^37 + 29 * q^38 - 7 * q^39 + 18 * q^40 + 58 * q^41 + 45 * q^42 + 88 * q^43 + 28 * q^44 + 45 * q^45 + 23 * q^46 + 3 * q^47 + 17 * q^48 + 162 * q^49 + 161 * q^50 + 29 * q^51 + 47 * q^52 + 88 * q^53 + 50 * q^54 + 37 * q^55 + 19 * q^56 + 54 * q^57 + 53 * q^58 + 37 * q^59 + 14 * q^60 + 55 * q^61 + 29 * q^62 + 21 * q^63 + 79 * q^64 + 55 * q^65 + 34 * q^66 + 107 * q^67 + 36 * q^68 + 39 * q^69 + 33 * q^70 - 5 * q^71 + 118 * q^72 + 71 * q^73 + 89 * q^74 + 37 * q^75 + 29 * q^76 + 61 * q^77 - 7 * q^78 + 29 * q^79 + 18 * q^80 + 215 * q^81 + 58 * q^82 + 42 * q^83 + 45 * q^84 + 84 * q^85 + 88 * q^86 + 15 * q^87 + 28 * q^88 + 72 * q^89 + 45 * q^90 + 70 * q^91 + 23 * q^92 + 97 * q^93 + 3 * q^94 - 18 * q^95 + 17 * q^96 + 93 * q^97 + 162 * q^98 + 49 * q^99

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