LMFDB - Embedded newform 4970.2.a.z.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4970,2,Mod(1,4970)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4970, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4970.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4970 = 2 \cdot 5 \cdot 7 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4970.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:	$39.6856498046$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4x^{8} - 9x^{7} + 47x^{6} + 6x^{5} - 151x^{4} + 80x^{3} + 79x^{2} - 54x + 8 $ x^9 - 4x^8 - 9x^7 + 47x^6 + 6x^5 - 151x^4 + 80x^3 + 79x^2 - 54x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.07442$ of defining polynomial
Character	$\chi$	$=$	4970.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.07442 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.07442 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.84562 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.07442 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.07442 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.84562 q^{9} -1.00000 q^{10} +5.09568 q^{11} +1.07442 q^{12} +0.914784 q^{13} +1.00000 q^{14} -1.07442 q^{15} +1.00000 q^{16} +4.79497 q^{17} -1.84562 q^{18} +0.565643 q^{19} -1.00000 q^{20} +1.07442 q^{21} +5.09568 q^{22} -5.86704 q^{23} +1.07442 q^{24} +1.00000 q^{25} +0.914784 q^{26} -5.20624 q^{27} +1.00000 q^{28} -2.02045 q^{29} -1.07442 q^{30} -1.64601 q^{31} +1.00000 q^{32} +5.47490 q^{33} +4.79497 q^{34} -1.00000 q^{35} -1.84562 q^{36} +5.69141 q^{37} +0.565643 q^{38} +0.982863 q^{39} -1.00000 q^{40} +10.4886 q^{41} +1.07442 q^{42} +0.900115 q^{43} +5.09568 q^{44} +1.84562 q^{45} -5.86704 q^{46} -0.380031 q^{47} +1.07442 q^{48} +1.00000 q^{49} +1.00000 q^{50} +5.15182 q^{51} +0.914784 q^{52} +12.1778 q^{53} -5.20624 q^{54} -5.09568 q^{55} +1.00000 q^{56} +0.607739 q^{57} -2.02045 q^{58} -5.38187 q^{59} -1.07442 q^{60} +9.30140 q^{61} -1.64601 q^{62} -1.84562 q^{63} +1.00000 q^{64} -0.914784 q^{65} +5.47490 q^{66} +1.39207 q^{67} +4.79497 q^{68} -6.30368 q^{69} -1.00000 q^{70} +1.00000 q^{71} -1.84562 q^{72} -1.42429 q^{73} +5.69141 q^{74} +1.07442 q^{75} +0.565643 q^{76} +5.09568 q^{77} +0.982863 q^{78} -3.86704 q^{79} -1.00000 q^{80} -0.0568350 q^{81} +10.4886 q^{82} +3.86268 q^{83} +1.07442 q^{84} -4.79497 q^{85} +0.900115 q^{86} -2.17082 q^{87} +5.09568 q^{88} +5.14043 q^{89} +1.84562 q^{90} +0.914784 q^{91} -5.86704 q^{92} -1.76851 q^{93} -0.380031 q^{94} -0.565643 q^{95} +1.07442 q^{96} -13.6793 q^{97} +1.00000 q^{98} -9.40468 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 4 q^{3} + 9 q^{4} - 9 q^{5} + 4 q^{6} + 9 q^{7} + 9 q^{8} + 7 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 4 * q^3 + 9 * q^4 - 9 * q^5 + 4 * q^6 + 9 * q^7 + 9 * q^8 + 7 * q^9	\( 9 q + 9 q^{2} + 4 q^{3} + 9 q^{4} - 9 q^{5} + 4 q^{6} + 9 q^{7} + 9 q^{8} + 7 q^{9} - 9 q^{10} - 2 q^{11} + 4 q^{12} + 11 q^{13} + 9 q^{14} - 4 q^{15} + 9 q^{16} + 9 q^{17} + 7 q^{18} + 9 q^{19} - 9 q^{20} + 4 q^{21} - 2 q^{22} + 2 q^{23} + 4 q^{24} + 9 q^{25} + 11 q^{26} + 7 q^{27} + 9 q^{28} + 2 q^{29} - 4 q^{30} + 18 q^{31} + 9 q^{32} + 8 q^{33} + 9 q^{34} - 9 q^{35} + 7 q^{36} + 15 q^{37} + 9 q^{38} - 7 q^{39} - 9 q^{40} + 15 q^{41} + 4 q^{42} + 7 q^{43} - 2 q^{44} - 7 q^{45} + 2 q^{46} + 12 q^{47} + 4 q^{48} + 9 q^{49} + 9 q^{50} + 4 q^{51} + 11 q^{52} + 3 q^{53} + 7 q^{54} + 2 q^{55} + 9 q^{56} + 9 q^{57} + 2 q^{58} + 24 q^{59} - 4 q^{60} + 25 q^{61} + 18 q^{62} + 7 q^{63} + 9 q^{64} - 11 q^{65} + 8 q^{66} - 4 q^{67} + 9 q^{68} + 3 q^{69} - 9 q^{70} + 9 q^{71} + 7 q^{72} + 32 q^{73} + 15 q^{74} + 4 q^{75} + 9 q^{76} - 2 q^{77} - 7 q^{78} + 20 q^{79} - 9 q^{80} - 7 q^{81} + 15 q^{82} + 11 q^{83} + 4 q^{84} - 9 q^{85} + 7 q^{86} + 26 q^{87} - 2 q^{88} + 10 q^{89} - 7 q^{90} + 11 q^{91} + 2 q^{92} + 32 q^{93} + 12 q^{94} - 9 q^{95} + 4 q^{96} + 19 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 4 * q^3 + 9 * q^4 - 9 * q^5 + 4 * q^6 + 9 * q^7 + 9 * q^8 + 7 * q^9 - 9 * q^10 - 2 * q^11 + 4 * q^12 + 11 * q^13 + 9 * q^14 - 4 * q^15 + 9 * q^16 + 9 * q^17 + 7 * q^18 + 9 * q^19 - 9 * q^20 + 4 * q^21 - 2 * q^22 + 2 * q^23 + 4 * q^24 + 9 * q^25 + 11 * q^26 + 7 * q^27 + 9 * q^28 + 2 * q^29 - 4 * q^30 + 18 * q^31 + 9 * q^32 + 8 * q^33 + 9 * q^34 - 9 * q^35 + 7 * q^36 + 15 * q^37 + 9 * q^38 - 7 * q^39 - 9 * q^40 + 15 * q^41 + 4 * q^42 + 7 * q^43 - 2 * q^44 - 7 * q^45 + 2 * q^46 + 12 * q^47 + 4 * q^48 + 9 * q^49 + 9 * q^50 + 4 * q^51 + 11 * q^52 + 3 * q^53 + 7 * q^54 + 2 * q^55 + 9 * q^56 + 9 * q^57 + 2 * q^58 + 24 * q^59 - 4 * q^60 + 25 * q^61 + 18 * q^62 + 7 * q^63 + 9 * q^64 - 11 * q^65 + 8 * q^66 - 4 * q^67 + 9 * q^68 + 3 * q^69 - 9 * q^70 + 9 * q^71 + 7 * q^72 + 32 * q^73 + 15 * q^74 + 4 * q^75 + 9 * q^76 - 2 * q^77 - 7 * q^78 + 20 * q^79 - 9 * q^80 - 7 * q^81 + 15 * q^82 + 11 * q^83 + 4 * q^84 - 9 * q^85 + 7 * q^86 + 26 * q^87 - 2 * q^88 + 10 * q^89 - 7 * q^90 + 11 * q^91 + 2 * q^92 + 32 * q^93 + 12 * q^94 - 9 * q^95 + 4 * q^96 + 19 * q^97 + 9 * q^98 - 7 * 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
$3$	1.07442	0.620317	0.310159	−	0.950685i	$-0.399618\pi$
$3$	1.07442	0.620317	0.310159	+	0.950685i	$0.399618\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.07442	0.438631
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−1.84562	−0.615206
$10$	−1.00000	−0.316228
$11$	5.09568	1.53640	0.768202	−	0.640207i	$-0.221151\pi$
$11$	5.09568	1.53640	0.768202	+	0.640207i	$0.221151\pi$
$12$	1.07442	0.310159
$13$	0.914784	0.253715	0.126858	−	0.991921i	$-0.459511\pi$
$13$	0.914784	0.253715	0.126858	+	0.991921i	$0.459511\pi$
$14$	1.00000	0.267261
$15$	−1.07442	−0.277414
$16$	1.00000	0.250000
$17$	4.79497	1.16295	0.581476	−	0.813563i	$-0.302475\pi$
$17$	4.79497	1.16295	0.581476	+	0.813563i	$0.302475\pi$
$18$	−1.84562	−0.435017
$19$	0.565643	0.129767	0.0648837	−	0.997893i	$-0.479332\pi$
$19$	0.565643	0.129767	0.0648837	+	0.997893i	$0.479332\pi$
$20$	−1.00000	−0.223607
$21$	1.07442	0.234458
$22$	5.09568	1.08640
$23$	−5.86704	−1.22336	−0.611682	−	0.791104i	$-0.709507\pi$
$23$	−5.86704	−1.22336	−0.611682	+	0.791104i	$0.709507\pi$
$24$	1.07442	0.219315
$25$	1.00000	0.200000
$26$	0.914784	0.179404
$27$	−5.20624	−1.00194
$28$	1.00000	0.188982
$29$	−2.02045	−0.375189	−0.187594	−	0.982247i	$-0.560069\pi$
$29$	−2.02045	−0.375189	−0.187594	+	0.982247i	$0.560069\pi$
$30$	−1.07442	−0.196162
$31$	−1.64601	−0.295632	−0.147816	−	0.989015i	$-0.547224\pi$
$31$	−1.64601	−0.295632	−0.147816	+	0.989015i	$0.547224\pi$
$32$	1.00000	0.176777
$33$	5.47490	0.953059
$34$	4.79497	0.822331
$35$	−1.00000	−0.169031
$36$	−1.84562	−0.307603
$37$	5.69141	0.935662	0.467831	−	0.883818i	$-0.345036\pi$
$37$	5.69141	0.935662	0.467831	+	0.883818i	$0.345036\pi$
$38$	0.565643	0.0917594
$39$	0.982863	0.157384
$40$	−1.00000	−0.158114
$41$	10.4886	1.63804	0.819019	−	0.573767i	$-0.194518\pi$
$41$	10.4886	1.63804	0.819019	+	0.573767i	$0.194518\pi$
$42$	1.07442	0.165787
$43$	0.900115	0.137266	0.0686331	−	0.997642i	$-0.478136\pi$
$43$	0.900115	0.137266	0.0686331	+	0.997642i	$0.478136\pi$
$44$	5.09568	0.768202
$45$	1.84562	0.275129
$46$	−5.86704	−0.865048
$47$	−0.380031	−0.0554332	−0.0277166	−	0.999616i	$-0.508824\pi$
$47$	−0.380031	−0.0554332	−0.0277166	+	0.999616i	$0.508824\pi$
$48$	1.07442	0.155079
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	5.15182	0.721400
$52$	0.914784	0.126858
$53$	12.1778	1.67275	0.836374	−	0.548159i	$-0.184671\pi$
$53$	12.1778	1.67275	0.836374	+	0.548159i	$0.184671\pi$
$54$	−5.20624	−0.708479
$55$	−5.09568	−0.687101
$56$	1.00000	0.133631
$57$	0.607739	0.0804970
$58$	−2.02045	−0.265298
$59$	−5.38187	−0.700660	−0.350330	−	0.936626i	$-0.613931\pi$
$59$	−5.38187	−0.700660	−0.350330	+	0.936626i	$0.613931\pi$
$60$	−1.07442	−0.138707
$61$	9.30140	1.19092	0.595461	−	0.803384i	$-0.296969\pi$
$61$	9.30140	1.19092	0.595461	+	0.803384i	$0.296969\pi$
$62$	−1.64601	−0.209044
$63$	−1.84562	−0.232526
$64$	1.00000	0.125000
$65$	−0.914784	−0.113465
$66$	5.47490	0.673914
$67$	1.39207	0.170068	0.0850342	−	0.996378i	$-0.472900\pi$
$67$	1.39207	0.170068	0.0850342	+	0.996378i	$0.472900\pi$
$68$	4.79497	0.581476
$69$	−6.30368	−0.758874
$70$	−1.00000	−0.119523
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	−1.84562	−0.217508
$73$	−1.42429	−0.166701	−0.0833503	−	0.996520i	$-0.526562\pi$
$73$	−1.42429	−0.166701	−0.0833503	+	0.996520i	$0.526562\pi$
$74$	5.69141	0.661613
$75$	1.07442	0.124063
$76$	0.565643	0.0648837
$77$	5.09568	0.580706
$78$	0.982863	0.111287
$79$	−3.86704	−0.435076	−0.217538	−	0.976052i	$-0.569803\pi$
$79$	−3.86704	−0.435076	−0.217538	+	0.976052i	$0.569803\pi$
$80$	−1.00000	−0.111803
$81$	−0.0568350	−0.00631500
$82$	10.4886	1.15827
$83$	3.86268	0.423984	0.211992	−	0.977271i	$-0.432005\pi$
$83$	3.86268	0.423984	0.211992	+	0.977271i	$0.432005\pi$
$84$	1.07442	0.117229
$85$	−4.79497	−0.520088
$86$	0.900115	0.0970619
$87$	−2.17082	−0.232736
$88$	5.09568	0.543201
$89$	5.14043	0.544885	0.272442	−	0.962172i	$-0.412169\pi$
$89$	5.14043	0.544885	0.272442	+	0.962172i	$0.412169\pi$
$90$	1.84562	0.194545
$91$	0.914784	0.0958954
$92$	−5.86704	−0.611682
$93$	−1.76851	−0.183386
$94$	−0.380031	−0.0391972
$95$	−0.565643	−0.0580337
$96$	1.07442	0.109658
$97$	−13.6793	−1.38892	−0.694460	−	0.719531i	$-0.744357\pi$
$97$	−13.6793	−1.38892	−0.694460	+	0.719531i	$0.744357\pi$
$98$	1.00000	0.101015
$99$	−9.40468	−0.945206
$100$	1.00000	0.100000
$101$	1.10357	0.109809	0.0549046	−	0.998492i	$-0.482515\pi$
$101$	1.10357	0.109809	0.0549046	+	0.998492i	$0.482515\pi$
$102$	5.15182	0.510107
$103$	−3.10960	−0.306398	−0.153199	−	0.988195i	$-0.548958\pi$
$103$	−3.10960	−0.306398	−0.153199	+	0.988195i	$0.548958\pi$
$104$	0.914784	0.0897019
$105$	−1.07442	−0.104853
$106$	12.1778	1.18281
$107$	10.2994	0.995685	0.497843	−	0.867267i	$-0.334126\pi$
$107$	10.2994	0.995685	0.497843	+	0.867267i	$0.334126\pi$
$108$	−5.20624	−0.500970
$109$	−1.86474	−0.178610	−0.0893049	−	0.996004i	$-0.528465\pi$
$109$	−1.86474	−0.178610	−0.0893049	+	0.996004i	$0.528465\pi$
$110$	−5.09568	−0.485854
$111$	6.11497	0.580407
$112$	1.00000	0.0944911
$113$	−18.3923	−1.73020	−0.865100	−	0.501600i	$-0.832745\pi$
$113$	−18.3923	−1.73020	−0.865100	+	0.501600i	$0.832745\pi$
$114$	0.607739	0.0569199
$115$	5.86704	0.547105
$116$	−2.02045	−0.187594
$117$	−1.68834	−0.156087
$118$	−5.38187	−0.495442
$119$	4.79497	0.439555
$120$	−1.07442	−0.0980808
$121$	14.9659	1.36054
$122$	9.30140	0.842109
$123$	11.2691	1.01610
$124$	−1.64601	−0.147816
$125$	−1.00000	−0.0894427
$126$	−1.84562	−0.164421
$127$	−2.13198	−0.189183	−0.0945915	−	0.995516i	$-0.530154\pi$
$127$	−2.13198	−0.189183	−0.0945915	+	0.995516i	$0.530154\pi$
$128$	1.00000	0.0883883
$129$	0.967102	0.0851486
$130$	−0.914784	−0.0802318
$131$	−16.0653	−1.40364	−0.701818	−	0.712357i	$-0.747628\pi$
$131$	−16.0653	−1.40364	−0.701818	+	0.712357i	$0.747628\pi$
$132$	5.47490	0.476529
$133$	0.565643	0.0490474
$134$	1.39207	0.120256
$135$	5.20624	0.448081
$136$	4.79497	0.411166
$137$	−12.4580	−1.06436	−0.532178	−	0.846632i	$-0.678626\pi$
$137$	−12.4580	−1.06436	−0.532178	+	0.846632i	$0.678626\pi$
$138$	−6.30368	−0.536605
$139$	4.02672	0.341542	0.170771	−	0.985311i	$-0.445374\pi$
$139$	4.02672	0.341542	0.170771	+	0.985311i	$0.445374\pi$
$140$	−1.00000	−0.0845154
$141$	−0.408313	−0.0343862
$142$	1.00000	0.0839181
$143$	4.66144	0.389809
$144$	−1.84562	−0.153802
$145$	2.02045	0.167789
$146$	−1.42429	−0.117875
$147$	1.07442	0.0886168
$148$	5.69141	0.467831
$149$	0.616182	0.0504796	0.0252398	−	0.999681i	$-0.491965\pi$
$149$	0.616182	0.0504796	0.0252398	+	0.999681i	$0.491965\pi$
$150$	1.07442	0.0877261
$151$	14.6732	1.19408	0.597042	−	0.802210i	$-0.296343\pi$
$151$	14.6732	1.19408	0.597042	+	0.802210i	$0.296343\pi$
$152$	0.565643	0.0458797
$153$	−8.84970	−0.715455
$154$	5.09568	0.410621
$155$	1.64601	0.132211
$156$	0.982863	0.0786920
$157$	18.8138	1.50151	0.750754	−	0.660582i	$-0.229690\pi$
$157$	18.8138	1.50151	0.750754	+	0.660582i	$0.229690\pi$
$158$	−3.86704	−0.307646
$159$	13.0841	1.03763
$160$	−1.00000	−0.0790569
$161$	−5.86704	−0.462388
$162$	−0.0568350	−0.00446538
$163$	−2.30928	−0.180877	−0.0904385	−	0.995902i	$-0.528827\pi$
$163$	−2.30928	−0.180877	−0.0904385	+	0.995902i	$0.528827\pi$
$164$	10.4886	0.819019
$165$	−5.47490	−0.426221
$166$	3.86268	0.299802
$167$	17.0812	1.32178	0.660892	−	0.750481i	$-0.270178\pi$
$167$	17.0812	1.32178	0.660892	+	0.750481i	$0.270178\pi$
$168$	1.07442	0.0828934
$169$	−12.1632	−0.935629
$170$	−4.79497	−0.367758
$171$	−1.04396	−0.0798337
$172$	0.900115	0.0686331
$173$	14.1204	1.07356	0.536778	−	0.843724i	$-0.319641\pi$
$173$	14.1204	1.07356	0.536778	+	0.843724i	$0.319641\pi$
$174$	−2.17082	−0.164569
$175$	1.00000	0.0755929
$176$	5.09568	0.384101
$177$	−5.78240	−0.434632
$178$	5.14043	0.385292
$179$	−2.15075	−0.160755	−0.0803774	−	0.996765i	$-0.525613\pi$
$179$	−2.15075	−0.160755	−0.0803774	+	0.996765i	$0.525613\pi$
$180$	1.84562	0.137564
$181$	6.72664	0.499987	0.249994	−	0.968247i	$-0.419571\pi$
$181$	6.72664	0.499987	0.249994	+	0.968247i	$0.419571\pi$
$182$	0.914784	0.0678083
$183$	9.99362	0.738750
$184$	−5.86704	−0.432524
$185$	−5.69141	−0.418441
$186$	−1.76851	−0.129673
$187$	24.4336	1.78677
$188$	−0.380031	−0.0277166
$189$	−5.20624	−0.378698
$190$	−0.565643	−0.0410360
$191$	21.4910	1.55504	0.777518	−	0.628860i	$-0.216478\pi$
$191$	21.4910	1.55504	0.777518	+	0.628860i	$0.216478\pi$
$192$	1.07442	0.0775397
$193$	10.8607	0.781770	0.390885	−	0.920440i	$-0.372169\pi$
$193$	10.8607	0.781770	0.390885	+	0.920440i	$0.372169\pi$
$194$	−13.6793	−0.982115
$195$	−0.982863	−0.0703843
$196$	1.00000	0.0714286
$197$	14.7532	1.05112	0.525560	−	0.850757i	$-0.323856\pi$
$197$	14.7532	1.05112	0.525560	+	0.850757i	$0.323856\pi$
$198$	−9.40468	−0.668361
$199$	10.3601	0.734410	0.367205	−	0.930140i	$-0.380315\pi$
$199$	10.3601	0.734410	0.367205	+	0.930140i	$0.380315\pi$
$200$	1.00000	0.0707107
$201$	1.49567	0.105496
$202$	1.10357	0.0776468
$203$	−2.02045	−0.141808
$204$	5.15182	0.360700
$205$	−10.4886	−0.732553
$206$	−3.10960	−0.216656
$207$	10.8283	0.752621
$208$	0.914784	0.0634288
$209$	2.88233	0.199375
$210$	−1.07442	−0.0741421
$211$	−13.4584	−0.926512	−0.463256	−	0.886225i	$-0.653319\pi$
$211$	−13.4584	−0.926512	−0.463256	+	0.886225i	$0.653319\pi$
$212$	12.1778	0.836374
$213$	1.07442	0.0736181
$214$	10.2994	0.704056
$215$	−0.900115	−0.0613873
$216$	−5.20624	−0.354240
$217$	−1.64601	−0.111738
$218$	−1.86474	−0.126296
$219$	−1.53029	−0.103407
$220$	−5.09568	−0.343551
$221$	4.38636	0.295059
$222$	6.11497	0.410410
$223$	2.49743	0.167240	0.0836200	−	0.996498i	$-0.473352\pi$
$223$	2.49743	0.167240	0.0836200	+	0.996498i	$0.473352\pi$
$224$	1.00000	0.0668153
$225$	−1.84562	−0.123041
$226$	−18.3923	−1.22344
$227$	7.70860	0.511638	0.255819	−	0.966725i	$-0.417655\pi$
$227$	7.70860	0.511638	0.255819	+	0.966725i	$0.417655\pi$
$228$	0.607739	0.0402485
$229$	13.2813	0.877653	0.438827	−	0.898572i	$-0.355394\pi$
$229$	13.2813	0.877653	0.438827	+	0.898572i	$0.355394\pi$
$230$	5.86704	0.386861
$231$	5.47490	0.360222
$232$	−2.02045	−0.132649
$233$	−29.5341	−1.93484	−0.967421	−	0.253173i	$-0.918526\pi$
$233$	−29.5341	−1.93484	−0.967421	+	0.253173i	$0.918526\pi$
$234$	−1.68834	−0.110370
$235$	0.380031	0.0247905
$236$	−5.38187	−0.350330
$237$	−4.15483	−0.269886
$238$	4.79497	0.310812
$239$	−6.02921	−0.389997	−0.194998	−	0.980804i	$-0.562470\pi$
$239$	−6.02921	−0.389997	−0.194998	+	0.980804i	$0.562470\pi$
$240$	−1.07442	−0.0693536
$241$	−7.12862	−0.459195	−0.229597	−	0.973286i	$-0.573741\pi$
$241$	−7.12862	−0.459195	−0.229597	+	0.973286i	$0.573741\pi$
$242$	14.9659	0.962046
$243$	15.5576	0.998023
$244$	9.30140	0.595461
$245$	−1.00000	−0.0638877
$246$	11.2691	0.718494
$247$	0.517441	0.0329240
$248$	−1.64601	−0.104522
$249$	4.15015	0.263005
$250$	−1.00000	−0.0632456
$251$	−18.6046	−1.17431	−0.587155	−	0.809474i	$-0.699752\pi$
$251$	−18.6046	−1.17431	−0.587155	+	0.809474i	$0.699752\pi$
$252$	−1.84562	−0.116263
$253$	−29.8966	−1.87958
$254$	−2.13198	−0.133773
$255$	−5.15182	−0.322620
$256$	1.00000	0.0625000
$257$	−11.2715	−0.703097	−0.351548	−	0.936170i	$-0.614345\pi$
$257$	−11.2715	−0.703097	−0.351548	+	0.936170i	$0.614345\pi$
$258$	0.967102	0.0602092
$259$	5.69141	0.353647
$260$	−0.914784	−0.0567325
$261$	3.72899	0.230818
$262$	−16.0653	−0.992520
$263$	−14.6145	−0.901167	−0.450584	−	0.892734i	$-0.648784\pi$
$263$	−14.6145	−0.901167	−0.450584	+	0.892734i	$0.648784\pi$
$264$	5.47490	0.336957
$265$	−12.1778	−0.748076
$266$	0.565643	0.0346818
$267$	5.52299	0.338002
$268$	1.39207	0.0850342
$269$	5.30698	0.323573	0.161786	−	0.986826i	$-0.448274\pi$
$269$	5.30698	0.323573	0.161786	+	0.986826i	$0.448274\pi$
$270$	5.20624	0.316841
$271$	−1.01339	−0.0615590	−0.0307795	−	0.999526i	$-0.509799\pi$
$271$	−1.01339	−0.0615590	−0.0307795	+	0.999526i	$0.509799\pi$
$272$	4.79497	0.290738
$273$	0.982863	0.0594856
$274$	−12.4580	−0.752614
$275$	5.09568	0.307281
$276$	−6.30368	−0.379437
$277$	−8.09087	−0.486134	−0.243067	−	0.970010i	$-0.578153\pi$
$277$	−8.09087	−0.486134	−0.243067	+	0.970010i	$0.578153\pi$
$278$	4.02672	0.241507
$279$	3.03791	0.181875
$280$	−1.00000	−0.0597614
$281$	−6.02699	−0.359540	−0.179770	−	0.983709i	$-0.557535\pi$
$281$	−6.02699	−0.359540	−0.179770	+	0.983709i	$0.557535\pi$
$282$	−0.408313	−0.0243147
$283$	11.0840	0.658878	0.329439	−	0.944177i	$-0.393140\pi$
$283$	11.0840	0.658878	0.329439	+	0.944177i	$0.393140\pi$
$284$	1.00000	0.0593391
$285$	−0.607739	−0.0359993
$286$	4.66144	0.275637
$287$	10.4886	0.619120
$288$	−1.84562	−0.108754
$289$	5.99178	0.352458
$290$	2.02045	0.118645
$291$	−14.6973	−0.861572
$292$	−1.42429	−0.0833503
$293$	−6.40359	−0.374102	−0.187051	−	0.982350i	$-0.559893\pi$
$293$	−6.40359	−0.374102	−0.187051	+	0.982350i	$0.559893\pi$
$294$	1.07442	0.0626615
$295$	5.38187	0.313345
$296$	5.69141	0.330806
$297$	−26.5293	−1.53939
$298$	0.616182	0.0356945
$299$	−5.36708	−0.310386
$300$	1.07442	0.0620317
$301$	0.900115	0.0518817
$302$	14.6732	0.844345
$303$	1.18570	0.0681165
$304$	0.565643	0.0324418
$305$	−9.30140	−0.532597
$306$	−8.84970	−0.505903
$307$	−28.7373	−1.64013	−0.820063	−	0.572273i	$-0.806062\pi$
$307$	−28.7373	−1.64013	−0.820063	+	0.572273i	$0.806062\pi$
$308$	5.09568	0.290353
$309$	−3.34102	−0.190064
$310$	1.64601	0.0934871
$311$	19.0633	1.08098	0.540489	−	0.841351i	$-0.318239\pi$
$311$	19.0633	1.08098	0.540489	+	0.841351i	$0.318239\pi$
$312$	0.982863	0.0556437
$313$	15.0198	0.848970	0.424485	−	0.905435i	$-0.360455\pi$
$313$	15.0198	0.848970	0.424485	+	0.905435i	$0.360455\pi$
$314$	18.8138	1.06173
$315$	1.84562	0.103989
$316$	−3.86704	−0.217538
$317$	6.97995	0.392033	0.196017	−	0.980601i	$-0.437199\pi$
$317$	6.97995	0.392033	0.196017	+	0.980601i	$0.437199\pi$
$318$	13.0841	0.733719
$319$	−10.2956	−0.576442
$320$	−1.00000	−0.0559017
$321$	11.0659	0.617641
$322$	−5.86704	−0.326958
$323$	2.71224	0.150913
$324$	−0.0568350	−0.00315750
$325$	0.914784	0.0507431
$326$	−2.30928	−0.127899
$327$	−2.00352	−0.110795
$328$	10.4886	0.579134
$329$	−0.380031	−0.0209518
$330$	−5.47490	−0.301384
$331$	−3.84687	−0.211443	−0.105721	−	0.994396i	$-0.533715\pi$
$331$	−3.84687	−0.211443	−0.105721	+	0.994396i	$0.533715\pi$
$332$	3.86268	0.211992
$333$	−10.5042	−0.575625
$334$	17.0812	0.934642
$335$	−1.39207	−0.0760569
$336$	1.07442	0.0586145
$337$	−5.77664	−0.314673	−0.157337	−	0.987545i	$-0.550291\pi$
$337$	−5.77664	−0.314673	−0.157337	+	0.987545i	$0.550291\pi$
$338$	−12.1632	−0.661589
$339$	−19.7610	−1.07327
$340$	−4.79497	−0.260044
$341$	−8.38754	−0.454211
$342$	−1.04396	−0.0564509
$343$	1.00000	0.0539949
$344$	0.900115	0.0485309
$345$	6.30368	0.339379
$346$	14.1204	0.759118
$347$	−9.99236	−0.536418	−0.268209	−	0.963361i	$-0.586432\pi$
$347$	−9.99236	−0.536418	−0.268209	+	0.963361i	$0.586432\pi$
$348$	−2.17082	−0.116368
$349$	−0.466656	−0.0249795	−0.0124897	−	0.999922i	$-0.503976\pi$
$349$	−0.466656	−0.0249795	−0.0124897	+	0.999922i	$0.503976\pi$
$350$	1.00000	0.0534522
$351$	−4.76258	−0.254208
$352$	5.09568	0.271601
$353$	8.30028	0.441779	0.220890	−	0.975299i	$-0.429104\pi$
$353$	8.30028	0.441779	0.220890	+	0.975299i	$0.429104\pi$
$354$	−5.78240	−0.307331
$355$	−1.00000	−0.0530745
$356$	5.14043	0.272442
$357$	5.15182	0.272663
$358$	−2.15075	−0.113671
$359$	11.7028	0.617651	0.308825	−	0.951119i	$-0.400064\pi$
$359$	11.7028	0.617651	0.308825	+	0.951119i	$0.400064\pi$
$360$	1.84562	0.0972727
$361$	−18.6800	−0.983160
$362$	6.72664	0.353544
$363$	16.0797	0.843966
$364$	0.914784	0.0479477
$365$	1.42429	0.0745507
$366$	9.99362	0.522375
$367$	−7.59712	−0.396566	−0.198283	−	0.980145i	$-0.563537\pi$
$367$	−7.59712	−0.396566	−0.198283	+	0.980145i	$0.563537\pi$
$368$	−5.86704	−0.305841
$369$	−19.3579	−1.00773
$370$	−5.69141	−0.295882
$371$	12.1778	0.632239
$372$	−1.76851	−0.0916929
$373$	−2.39483	−0.124000	−0.0619999	−	0.998076i	$-0.519748\pi$
$373$	−2.39483	−0.124000	−0.0619999	+	0.998076i	$0.519748\pi$
$374$	24.4336	1.26343
$375$	−1.07442	−0.0554829
$376$	−0.380031	−0.0195986
$377$	−1.84828	−0.0951911
$378$	−5.20624	−0.267780
$379$	−20.1300	−1.03401	−0.517005	−	0.855982i	$-0.672953\pi$
$379$	−20.1300	−1.03401	−0.517005	+	0.855982i	$0.672953\pi$
$380$	−0.565643	−0.0290169
$381$	−2.29065	−0.117354
$382$	21.4910	1.09958
$383$	−10.8186	−0.552805	−0.276403	−	0.961042i	$-0.589142\pi$
$383$	−10.8186	−0.552805	−0.276403	+	0.961042i	$0.589142\pi$
$384$	1.07442	0.0548288
$385$	−5.09568	−0.259700
$386$	10.8607	0.552795
$387$	−1.66127	−0.0844470
$388$	−13.6793	−0.694460
$389$	−27.2862	−1.38347	−0.691733	−	0.722153i	$-0.743153\pi$
$389$	−27.2862	−1.38347	−0.691733	+	0.722153i	$0.743153\pi$
$390$	−0.982863	−0.0497692
$391$	−28.1323	−1.42271
$392$	1.00000	0.0505076
$393$	−17.2609	−0.870699
$394$	14.7532	0.743254
$395$	3.86704	0.194572
$396$	−9.40468	−0.472603
$397$	−6.00067	−0.301165	−0.150583	−	0.988597i	$-0.548115\pi$
$397$	−6.00067	−0.301165	−0.150583	+	0.988597i	$0.548115\pi$
$398$	10.3601	0.519306
$399$	0.607739	0.0304250
$400$	1.00000	0.0500000
$401$	12.3083	0.614648	0.307324	−	0.951605i	$-0.400566\pi$
$401$	12.3083	0.614648	0.307324	+	0.951605i	$0.400566\pi$
$402$	1.49567	0.0745972
$403$	−1.50574	−0.0750064
$404$	1.10357	0.0549046
$405$	0.0568350	0.00282415
$406$	−2.02045	−0.100273
$407$	29.0016	1.43755
$408$	5.15182	0.255053
$409$	39.9349	1.97466	0.987328	−	0.158696i	$-0.0507289\pi$
$409$	39.9349	1.97466	0.987328	+	0.158696i	$0.0507289\pi$
$410$	−10.4886	−0.517993
$411$	−13.3851	−0.660239
$412$	−3.10960	−0.153199
$413$	−5.38187	−0.264825
$414$	10.8283	0.532183
$415$	−3.86268	−0.189612
$416$	0.914784	0.0448510
$417$	4.32639	0.211864
$418$	2.88233	0.140980
$419$	−17.3888	−0.849496	−0.424748	−	0.905312i	$-0.639637\pi$
$419$	−17.3888	−0.849496	−0.424748	+	0.905312i	$0.639637\pi$
$420$	−1.07442	−0.0524264
$421$	−15.5418	−0.757460	−0.378730	−	0.925507i	$-0.623639\pi$
$421$	−15.5418	−0.757460	−0.378730	+	0.925507i	$0.623639\pi$
$422$	−13.4584	−0.655143
$423$	0.701392	0.0341028
$424$	12.1778	0.591406
$425$	4.79497	0.232590
$426$	1.07442	0.0520559
$427$	9.30140	0.450126
$428$	10.2994	0.497843
$429$	5.00835	0.241806
$430$	−0.900115	−0.0434074
$431$	−33.5217	−1.61469	−0.807343	−	0.590083i	$-0.799095\pi$
$431$	−33.5217	−1.61469	−0.807343	+	0.590083i	$0.799095\pi$
$432$	−5.20624	−0.250485
$433$	9.06228	0.435505	0.217753	−	0.976004i	$-0.430127\pi$
$433$	9.06228	0.435505	0.217753	+	0.976004i	$0.430127\pi$
$434$	−1.64601	−0.0790110
$435$	2.17082	0.104083
$436$	−1.86474	−0.0893049
$437$	−3.31865	−0.158753
$438$	−1.53029	−0.0731200
$439$	−1.42534	−0.0680278	−0.0340139	−	0.999421i	$-0.510829\pi$
$439$	−1.42534	−0.0680278	−0.0340139	+	0.999421i	$0.510829\pi$
$440$	−5.09568	−0.242927
$441$	−1.84562	−0.0878866
$442$	4.38636	0.208638
$443$	9.40454	0.446823	0.223412	−	0.974724i	$-0.428281\pi$
$443$	9.40454	0.446823	0.223412	+	0.974724i	$0.428281\pi$
$444$	6.11497	0.290204
$445$	−5.14043	−0.243680
$446$	2.49743	0.118257
$447$	0.662039	0.0313134
$448$	1.00000	0.0472456
$449$	−9.21427	−0.434848	−0.217424	−	0.976077i	$-0.569765\pi$
$449$	−9.21427	−0.434848	−0.217424	+	0.976077i	$0.569765\pi$
$450$	−1.84562	−0.0870033
$451$	53.4463	2.51669
$452$	−18.3923	−0.865100
$453$	15.7651	0.740711
$454$	7.70860	0.361783
$455$	−0.914784	−0.0428857
$456$	0.607739	0.0284600
$457$	−34.4258	−1.61037	−0.805186	−	0.593023i	$-0.797935\pi$
$457$	−34.4258	−1.61037	−0.805186	+	0.593023i	$0.797935\pi$
$458$	13.2813	0.620595
$459$	−24.9638	−1.16521
$460$	5.86704	0.273552
$461$	13.6401	0.635285	0.317642	−	0.948211i	$-0.397109\pi$
$461$	13.6401	0.635285	0.317642	+	0.948211i	$0.397109\pi$
$462$	5.47490	0.254716
$463$	7.27555	0.338123	0.169062	−	0.985605i	$-0.445926\pi$
$463$	7.27555	0.338123	0.169062	+	0.985605i	$0.445926\pi$
$464$	−2.02045	−0.0937972
$465$	1.76851	0.0820126
$466$	−29.5341	−1.36814
$467$	26.9219	1.24580	0.622900	−	0.782302i	$-0.285955\pi$
$467$	26.9219	1.24580	0.622900	+	0.782302i	$0.285955\pi$
$468$	−1.68834	−0.0780436
$469$	1.39207	0.0642798
$470$	0.380031	0.0175295
$471$	20.2140	0.931411
$472$	−5.38187	−0.247721
$473$	4.58669	0.210896
$474$	−4.15483	−0.190838
$475$	0.565643	0.0259535
$476$	4.79497	0.219777
$477$	−22.4756	−1.02908
$478$	−6.02921	−0.275769
$479$	−22.3358	−1.02055	−0.510275	−	0.860011i	$-0.670456\pi$
$479$	−22.3358	−1.02055	−0.510275	+	0.860011i	$0.670456\pi$
$480$	−1.07442	−0.0490404
$481$	5.20641	0.237392
$482$	−7.12862	−0.324700
$483$	−6.30368	−0.286827
$484$	14.9659	0.680270
$485$	13.6793	0.621144
$486$	15.5576	0.705709
$487$	−24.2199	−1.09751	−0.548754	−	0.835984i	$-0.684898\pi$
$487$	−24.2199	−1.09751	−0.548754	+	0.835984i	$0.684898\pi$
$488$	9.30140	0.421055
$489$	−2.48114	−0.112201
$490$	−1.00000	−0.0451754
$491$	−27.9134	−1.25972	−0.629858	−	0.776710i	$-0.716887\pi$
$491$	−27.9134	−1.25972	−0.629858	+	0.776710i	$0.716887\pi$
$492$	11.2691	0.508052
$493$	−9.68802	−0.436327
$494$	0.517441	0.0232808
$495$	9.40468	0.422709
$496$	−1.64601	−0.0739080
$497$	1.00000	0.0448561
$498$	4.15015	0.185972
$499$	9.77527	0.437601	0.218801	−	0.975770i	$-0.429786\pi$
$499$	9.77527	0.437601	0.218801	+	0.975770i	$0.429786\pi$
$500$	−1.00000	−0.0447214
$501$	18.3524	0.819926
$502$	−18.6046	−0.830363
$503$	−11.9895	−0.534586	−0.267293	−	0.963615i	$-0.586129\pi$
$503$	−11.9895	−0.534586	−0.267293	+	0.963615i	$0.586129\pi$
$504$	−1.84562	−0.0822104
$505$	−1.10357	−0.0491081
$506$	−29.8966	−1.32906
$507$	−13.0684	−0.580387
$508$	−2.13198	−0.0945915
$509$	−18.0497	−0.800037	−0.400019	−	0.916507i	$-0.630996\pi$
$509$	−18.0497	−0.800037	−0.400019	+	0.916507i	$0.630996\pi$
$510$	−5.15182	−0.228127
$511$	−1.42429	−0.0630069
$512$	1.00000	0.0441942
$513$	−2.94487	−0.130019
$514$	−11.2715	−0.497165
$515$	3.10960	0.137025
$516$	0.967102	0.0425743
$517$	−1.93651	−0.0851678
$518$	5.69141	0.250066
$519$	15.1713	0.665945
$520$	−0.914784	−0.0401159
$521$	−8.12753	−0.356073	−0.178037	−	0.984024i	$-0.556975\pi$
$521$	−8.12753	−0.356073	−0.178037	+	0.984024i	$0.556975\pi$
$522$	3.72899	0.163213
$523$	−32.0993	−1.40360	−0.701802	−	0.712372i	$-0.747621\pi$
$523$	−32.0993	−1.40360	−0.701802	+	0.712372i	$0.747621\pi$
$524$	−16.0653	−0.701818
$525$	1.07442	0.0468916
$526$	−14.6145	−0.637221
$527$	−7.89258	−0.343806
$528$	5.47490	0.238265
$529$	11.4222	0.496618
$530$	−12.1778	−0.528969
$531$	9.93289	0.431051
$532$	0.565643	0.0245237
$533$	9.59476	0.415595
$534$	5.52299	0.239003
$535$	−10.2994	−0.445284
$536$	1.39207	0.0601282
$537$	−2.31081	−0.0997190
$538$	5.30698	0.228800
$539$	5.09568	0.219486
$540$	5.20624	0.224041
$541$	17.8136	0.765866	0.382933	−	0.923776i	$-0.374914\pi$
$541$	17.8136	0.765866	0.382933	+	0.923776i	$0.374914\pi$
$542$	−1.01339	−0.0435288
$543$	7.22725	0.310151
$544$	4.79497	0.205583
$545$	1.86474	0.0798767
$546$	0.982863	0.0420627
$547$	11.8760	0.507779	0.253890	−	0.967233i	$-0.418290\pi$
$547$	11.8760	0.507779	0.253890	+	0.967233i	$0.418290\pi$
$548$	−12.4580	−0.532178
$549$	−17.1668	−0.732663
$550$	5.09568	0.217280
$551$	−1.14285	−0.0486872
$552$	−6.30368	−0.268302
$553$	−3.86704	−0.164443
$554$	−8.09087	−0.343748
$555$	−6.11497	−0.259566
$556$	4.02672	0.170771
$557$	−4.43945	−0.188106	−0.0940528	−	0.995567i	$-0.529982\pi$
$557$	−4.43945	−0.188106	−0.0940528	+	0.995567i	$0.529982\pi$
$558$	3.03791	0.128605
$559$	0.823410	0.0348265
$560$	−1.00000	−0.0422577
$561$	26.2520	1.10836
$562$	−6.02699	−0.254233
$563$	−40.7622	−1.71792	−0.858960	−	0.512043i	$-0.828889\pi$
$563$	−40.7622	−1.71792	−0.858960	+	0.512043i	$0.828889\pi$
$564$	−0.408313	−0.0171931
$565$	18.3923	0.773769
$566$	11.0840	0.465897
$567$	−0.0568350	−0.00238685
$568$	1.00000	0.0419591
$569$	−21.8841	−0.917429	−0.458714	−	0.888584i	$-0.651690\pi$
$569$	−21.8841	−0.917429	−0.458714	+	0.888584i	$0.651690\pi$
$570$	−0.607739	−0.0254554
$571$	−36.2917	−1.51876	−0.759381	−	0.650647i	$-0.774498\pi$
$571$	−36.2917	−1.51876	−0.759381	+	0.650647i	$0.774498\pi$
$572$	4.66144	0.194905
$573$	23.0904	0.964616
$574$	10.4886	0.437784
$575$	−5.86704	−0.244673
$576$	−1.84562	−0.0769008
$577$	−9.92779	−0.413299	−0.206650	−	0.978415i	$-0.566256\pi$
$577$	−9.92779	−0.413299	−0.206650	+	0.978415i	$0.566256\pi$
$578$	5.99178	0.249225
$579$	11.6690	0.484945
$580$	2.02045	0.0838947
$581$	3.86268	0.160251
$582$	−14.6973	−0.609223
$583$	62.0541	2.57002
$584$	−1.42429	−0.0589375
$585$	1.68834	0.0698043
$586$	−6.40359	−0.264530
$587$	30.0213	1.23911	0.619557	−	0.784952i	$-0.287312\pi$
$587$	30.0213	1.23911	0.619557	+	0.784952i	$0.287312\pi$
$588$	1.07442	0.0443084
$589$	−0.931054	−0.0383634
$590$	5.38187	0.221568
$591$	15.8511	0.652028
$592$	5.69141	0.233915
$593$	−40.5723	−1.66610	−0.833052	−	0.553195i	$-0.813408\pi$
$593$	−40.5723	−1.66610	−0.833052	+	0.553195i	$0.813408\pi$
$594$	−26.5293	−1.08851
$595$	−4.79497	−0.196575
$596$	0.616182	0.0252398
$597$	11.1311	0.455567
$598$	−5.36708	−0.219476
$599$	0.910636	0.0372076	0.0186038	−	0.999827i	$-0.494078\pi$
$599$	0.910636	0.0372076	0.0186038	+	0.999827i	$0.494078\pi$
$600$	1.07442	0.0438631
$601$	9.38192	0.382696	0.191348	−	0.981522i	$-0.438714\pi$
$601$	9.38192	0.382696	0.191348	+	0.981522i	$0.438714\pi$
$602$	0.900115	0.0366859
$603$	−2.56923	−0.104627
$604$	14.6732	0.597042
$605$	−14.9659	−0.608452
$606$	1.18570	0.0481656
$607$	−14.7119	−0.597137	−0.298569	−	0.954388i	$-0.596509\pi$
$607$	−14.7119	−0.597137	−0.298569	+	0.954388i	$0.596509\pi$
$608$	0.565643	0.0229398
$609$	−2.17082	−0.0879660
$610$	−9.30140	−0.376603
$611$	−0.347646	−0.0140642
$612$	−8.84970	−0.357728
$613$	−4.09857	−0.165540	−0.0827699	−	0.996569i	$-0.526377\pi$
$613$	−4.09857	−0.165540	−0.0827699	+	0.996569i	$0.526377\pi$
$614$	−28.7373	−1.15974
$615$	−11.2691	−0.454415
$616$	5.09568	0.205311
$617$	33.5664	1.35133	0.675666	−	0.737208i	$-0.263856\pi$
$617$	33.5664	1.35133	0.675666	+	0.737208i	$0.263856\pi$
$618$	−3.34102	−0.134396
$619$	−11.1696	−0.448946	−0.224473	−	0.974480i	$-0.572066\pi$
$619$	−11.1696	−0.448946	−0.224473	+	0.974480i	$0.572066\pi$
$620$	1.64601	0.0661054
$621$	30.5452	1.22574
$622$	19.0633	0.764367
$623$	5.14043	0.205947
$624$	0.982863	0.0393460
$625$	1.00000	0.0400000
$626$	15.0198	0.600312
$627$	3.09684	0.123676
$628$	18.8138	0.750754
$629$	27.2902	1.08813
$630$	1.84562	0.0735312
$631$	−40.8446	−1.62600	−0.812998	−	0.582266i	$-0.802166\pi$
$631$	−40.8446	−1.62600	−0.812998	+	0.582266i	$0.802166\pi$
$632$	−3.86704	−0.153823
$633$	−14.4599	−0.574731
$634$	6.97995	0.277209
$635$	2.13198	0.0846052
$636$	13.0841	0.518817
$637$	0.914784	0.0362450
$638$	−10.2956	−0.407606
$639$	−1.84562	−0.0730116
$640$	−1.00000	−0.0395285
$641$	5.65568	0.223386	0.111693	−	0.993743i	$-0.464373\pi$
$641$	5.65568	0.223386	0.111693	+	0.993743i	$0.464373\pi$
$642$	11.0659	0.436738
$643$	−17.7509	−0.700026	−0.350013	−	0.936745i	$-0.613823\pi$
$643$	−17.7509	−0.700026	−0.350013	+	0.936745i	$0.613823\pi$
$644$	−5.86704	−0.231194
$645$	−0.967102	−0.0380796
$646$	2.71224	0.106712
$647$	−32.9555	−1.29561	−0.647806	−	0.761805i	$-0.724313\pi$
$647$	−32.9555	−1.29561	−0.647806	+	0.761805i	$0.724313\pi$
$648$	−0.0568350	−0.00223269
$649$	−27.4243	−1.07650
$650$	0.914784	0.0358808
$651$	−1.76851	−0.0693133
$652$	−2.30928	−0.0904385
$653$	−32.7317	−1.28089	−0.640444	−	0.768004i	$-0.721250\pi$
$653$	−32.7317	−1.28089	−0.640444	+	0.768004i	$0.721250\pi$
$654$	−2.00352	−0.0783437
$655$	16.0653	0.627725
$656$	10.4886	0.409509
$657$	2.62870	0.102555
$658$	−0.380031	−0.0148151
$659$	−20.3524	−0.792816	−0.396408	−	0.918074i	$-0.629744\pi$
$659$	−20.3524	−0.792816	−0.396408	+	0.918074i	$0.629744\pi$
$660$	−5.47490	−0.213110
$661$	6.40276	0.249039	0.124519	−	0.992217i	$-0.460261\pi$
$661$	6.40276	0.249039	0.124519	+	0.992217i	$0.460261\pi$
$662$	−3.84687	−0.149513
$663$	4.71280	0.183030
$664$	3.86268	0.149901
$665$	−0.565643	−0.0219347
$666$	−10.5042	−0.407028
$667$	11.8541	0.458992
$668$	17.0812	0.660892
$669$	2.68329	0.103742
$670$	−1.39207	−0.0537803
$671$	47.3969	1.82974
$672$	1.07442	0.0414467
$673$	−7.75566	−0.298959	−0.149479	−	0.988765i	$-0.547760\pi$
$673$	−7.75566	−0.298959	−0.149479	+	0.988765i	$0.547760\pi$
$674$	−5.77664	−0.222508
$675$	−5.20624	−0.200388
$676$	−12.1632	−0.467814
$677$	−32.0881	−1.23324	−0.616622	−	0.787259i	$-0.711499\pi$
$677$	−32.0881	−1.23324	−0.616622	+	0.787259i	$0.711499\pi$
$678$	−19.7610	−0.758918
$679$	−13.6793	−0.524963
$680$	−4.79497	−0.183879
$681$	8.28228	0.317378
$682$	−8.38754	−0.321175
$683$	14.8269	0.567335	0.283667	−	0.958923i	$-0.408449\pi$
$683$	14.8269	0.567335	0.283667	+	0.958923i	$0.408449\pi$
$684$	−1.04396	−0.0399168
$685$	12.4580	0.475995
$686$	1.00000	0.0381802
$687$	14.2697	0.544424
$688$	0.900115	0.0343166
$689$	11.1400	0.424402
$690$	6.30368	0.239977
$691$	19.3152	0.734783	0.367392	−	0.930066i	$-0.380251\pi$
$691$	19.3152	0.734783	0.367392	+	0.930066i	$0.380251\pi$
$692$	14.1204	0.536778
$693$	−9.40468	−0.357254
$694$	−9.99236	−0.379305
$695$	−4.02672	−0.152742
$696$	−2.17082	−0.0822846
$697$	50.2924	1.90496
$698$	−0.466656	−0.0176632
$699$	−31.7320	−1.20022
$700$	1.00000	0.0377964
$701$	21.8291	0.824472	0.412236	−	0.911077i	$-0.364748\pi$
$701$	21.8291	0.824472	0.412236	+	0.911077i	$0.364748\pi$
$702$	−4.76258	−0.179752
$703$	3.21930	0.121418
$704$	5.09568	0.192051
$705$	0.408313	0.0153780
$706$	8.30028	0.312385
$707$	1.10357	0.0415039
$708$	−5.78240	−0.217316
$709$	−15.8228	−0.594237	−0.297118	−	0.954841i	$-0.596026\pi$
$709$	−15.8228	−0.594237	−0.297118	+	0.954841i	$0.596026\pi$
$710$	−1.00000	−0.0375293
$711$	7.13709	0.267662
$712$	5.14043	0.192646
$713$	9.65721	0.361666
$714$	5.15182	0.192802
$715$	−4.66144	−0.174328
$716$	−2.15075	−0.0803774
$717$	−6.47791	−0.241922
$718$	11.7028	0.436745
$719$	12.2977	0.458626	0.229313	−	0.973353i	$-0.426352\pi$
$719$	12.2977	0.458626	0.229313	+	0.973353i	$0.426352\pi$
$720$	1.84562	0.0687822
$721$	−3.10960	−0.115808
$722$	−18.6800	−0.695199
$723$	−7.65914	−0.284847
$724$	6.72664	0.249994
$725$	−2.02045	−0.0750377
$726$	16.0797	0.596774
$727$	−16.4285	−0.609300	−0.304650	−	0.952464i	$-0.598540\pi$
$727$	−16.4285	−0.609300	−0.304650	+	0.952464i	$0.598540\pi$
$728$	0.914784	0.0339041
$729$	16.8860	0.625406
$730$	1.42429	0.0527153
$731$	4.31603	0.159634
$732$	9.99362	0.369375
$733$	−5.46119	−0.201713	−0.100857	−	0.994901i	$-0.532158\pi$
$733$	−5.46119	−0.201713	−0.100857	+	0.994901i	$0.532158\pi$
$734$	−7.59712	−0.280415
$735$	−1.07442	−0.0396306
$736$	−5.86704	−0.216262
$737$	7.09354	0.261294
$738$	−19.3579	−0.712573
$739$	−4.44502	−0.163513	−0.0817564	−	0.996652i	$-0.526053\pi$
$739$	−4.44502	−0.163513	−0.0817564	+	0.996652i	$0.526053\pi$
$740$	−5.69141	−0.209220
$741$	0.555949	0.0204233
$742$	12.1778	0.447061
$743$	−40.3031	−1.47858	−0.739288	−	0.673390i	$-0.764838\pi$
$743$	−40.3031	−1.47858	−0.739288	+	0.673390i	$0.764838\pi$
$744$	−1.76851	−0.0648367
$745$	−0.616182	−0.0225752
$746$	−2.39483	−0.0876811
$747$	−7.12904	−0.260838
$748$	24.4336	0.893383
$749$	10.2994	0.376334
$750$	−1.07442	−0.0392323
$751$	52.6564	1.92146	0.960730	−	0.277485i	$-0.0895007\pi$
$751$	52.6564	1.92146	0.960730	+	0.277485i	$0.0895007\pi$
$752$	−0.380031	−0.0138583
$753$	−19.9892	−0.728446
$754$	−1.84828	−0.0673103
$755$	−14.6732	−0.534011
$756$	−5.20624	−0.189349
$757$	−11.2163	−0.407663	−0.203832	−	0.979006i	$-0.565340\pi$
$757$	−11.2163	−0.407663	−0.203832	+	0.979006i	$0.565340\pi$
$758$	−20.1300	−0.731156
$759$	−32.1215	−1.16594
$760$	−0.565643	−0.0205180
$761$	−14.6295	−0.530321	−0.265160	−	0.964204i	$-0.585425\pi$
$761$	−14.6295	−0.530321	−0.265160	+	0.964204i	$0.585425\pi$
$762$	−2.29065	−0.0829815
$763$	−1.86474	−0.0675082
$764$	21.4910	0.777518
$765$	8.84970	0.319961
$766$	−10.8186	−0.390892
$767$	−4.92325	−0.177768
$768$	1.07442	0.0387698
$769$	1.14981	0.0414631	0.0207315	−	0.999785i	$-0.493400\pi$
$769$	1.14981	0.0414631	0.0207315	+	0.999785i	$0.493400\pi$
$770$	−5.09568	−0.183635
$771$	−12.1103	−0.436143
$772$	10.8607	0.390885
$773$	19.4010	0.697805	0.348902	−	0.937159i	$-0.386554\pi$
$773$	19.4010	0.697805	0.348902	+	0.937159i	$0.386554\pi$
$774$	−1.66127	−0.0597131
$775$	−1.64601	−0.0591264
$776$	−13.6793	−0.491058
$777$	6.11497	0.219373
$778$	−27.2862	−0.978259
$779$	5.93278	0.212564
$780$	−0.982863	−0.0351921
$781$	5.09568	0.182338
$782$	−28.1323	−1.00601
$783$	10.5190	0.375917
$784$	1.00000	0.0357143
$785$	−18.8138	−0.671495
$786$	−17.2609	−0.615677
$787$	15.9044	0.566930	0.283465	−	0.958983i	$-0.408516\pi$
$787$	15.9044	0.566930	0.283465	+	0.958983i	$0.408516\pi$
$788$	14.7532	0.525560
$789$	−15.7021	−0.559010
$790$	3.86704	0.137583
$791$	−18.3923	−0.653954
$792$	−9.40468	−0.334181
$793$	8.50877	0.302155
$794$	−6.00067	−0.212956
$795$	−13.0841	−0.464044
$796$	10.3601	0.367205
$797$	−0.656655	−0.0232599	−0.0116300	−	0.999932i	$-0.503702\pi$
$797$	−0.656655	−0.0232599	−0.0116300	+	0.999932i	$0.503702\pi$
$798$	0.607739	0.0215137
$799$	−1.82224	−0.0644661
$800$	1.00000	0.0353553
$801$	−9.48728	−0.335217
$802$	12.3083	0.434622
$803$	−7.25772	−0.256119
$804$	1.49567	0.0527482
$805$	5.86704	0.206786
$806$	−1.50574	−0.0530375
$807$	5.70194	0.200718
$808$	1.10357	0.0388234
$809$	−4.90029	−0.172285	−0.0861426	−	0.996283i	$-0.527454\pi$
$809$	−4.90029	−0.172285	−0.0861426	+	0.996283i	$0.527454\pi$
$810$	0.0568350	0.00199698
$811$	28.8621	1.01349	0.506743	−	0.862097i	$-0.330849\pi$
$811$	28.8621	1.01349	0.506743	+	0.862097i	$0.330849\pi$
$812$	−2.02045	−0.0709040
$813$	−1.08881	−0.0381861
$814$	29.0016	1.01650
$815$	2.30928	0.0808907
$816$	5.15182	0.180350
$817$	0.509143	0.0178127
$818$	39.9349	1.39629
$819$	−1.68834	−0.0589954
$820$	−10.4886	−0.366276
$821$	3.02271	0.105493	0.0527466	−	0.998608i	$-0.483202\pi$
$821$	3.02271	0.105493	0.0527466	+	0.998608i	$0.483202\pi$
$822$	−13.3851	−0.466859
$823$	−10.6294	−0.370518	−0.185259	−	0.982690i	$-0.559312\pi$
$823$	−10.6294	−0.370518	−0.185259	+	0.982690i	$0.559312\pi$
$824$	−3.10960	−0.108328
$825$	5.47490	0.190612
$826$	−5.38187	−0.187259
$827$	−40.7011	−1.41532	−0.707658	−	0.706556i	$-0.750248\pi$
$827$	−40.7011	−1.41532	−0.707658	+	0.706556i	$0.750248\pi$
$828$	10.8283	0.376310
$829$	44.7872	1.55552	0.777762	−	0.628559i	$-0.216355\pi$
$829$	44.7872	1.55552	0.777762	+	0.628559i	$0.216355\pi$
$830$	−3.86268	−0.134076
$831$	−8.69301	−0.301557
$832$	0.914784	0.0317144
$833$	4.79497	0.166136
$834$	4.32639	0.149811
$835$	−17.0812	−0.591120
$836$	2.88233	0.0996876
$837$	8.56952	0.296206
$838$	−17.3888	−0.600685
$839$	1.14586	0.0395593	0.0197797	−	0.999804i	$-0.493704\pi$
$839$	1.14586	0.0395593	0.0197797	+	0.999804i	$0.493704\pi$
$840$	−1.07442	−0.0370711
$841$	−24.9178	−0.859233
$842$	−15.5418	−0.535605
$843$	−6.47553	−0.223029
$844$	−13.4584	−0.463256
$845$	12.1632	0.418426
$846$	0.701392	0.0241143
$847$	14.9659	0.514235
$848$	12.1778	0.418187
$849$	11.9089	0.408714
$850$	4.79497	0.164466
$851$	−33.3917	−1.14465
$852$	1.07442	0.0368091
$853$	35.9254	1.23006	0.615030	−	0.788503i	$-0.289144\pi$
$853$	35.9254	1.23006	0.615030	+	0.788503i	$0.289144\pi$
$854$	9.30140	0.318287
$855$	1.04396	0.0357027
$856$	10.2994	0.352028
$857$	−27.3881	−0.935561	−0.467781	−	0.883845i	$-0.654946\pi$
$857$	−27.3881	−0.935561	−0.467781	+	0.883845i	$0.654946\pi$
$858$	5.00835	0.170982
$859$	−38.3785	−1.30946	−0.654729	−	0.755864i	$-0.727217\pi$
$859$	−38.3785	−1.30946	−0.654729	+	0.755864i	$0.727217\pi$
$860$	−0.900115	−0.0306937
$861$	11.2691	0.384051
$862$	−33.5217	−1.14175
$863$	−33.3826	−1.13636	−0.568179	−	0.822905i	$-0.692352\pi$
$863$	−33.3826	−1.13636	−0.568179	+	0.822905i	$0.692352\pi$
$864$	−5.20624	−0.177120
$865$	−14.1204	−0.480108
$866$	9.06228	0.307949
$867$	6.43770	0.218636
$868$	−1.64601	−0.0558692
$869$	−19.7052	−0.668454
$870$	2.17082	0.0735976
$871$	1.27344	0.0431489
$872$	−1.86474	−0.0631481
$873$	25.2467	0.854473
$874$	−3.31865	−0.112255
$875$	−1.00000	−0.0338062
$876$	−1.53029	−0.0517036
$877$	−7.37831	−0.249148	−0.124574	−	0.992210i	$-0.539756\pi$
$877$	−7.37831	−0.249148	−0.124574	+	0.992210i	$0.539756\pi$
$878$	−1.42534	−0.0481029
$879$	−6.88016	−0.232062
$880$	−5.09568	−0.171775
$881$	−43.3075	−1.45907	−0.729534	−	0.683945i	$-0.760263\pi$
$881$	−43.3075	−1.45907	−0.729534	+	0.683945i	$0.760263\pi$
$882$	−1.84562	−0.0621452
$883$	3.24012	0.109039	0.0545194	−	0.998513i	$-0.482637\pi$
$883$	3.24012	0.109039	0.0545194	+	0.998513i	$0.482637\pi$
$884$	4.38636	0.147529
$885$	5.78240	0.194373
$886$	9.40454	0.315952
$887$	−45.1389	−1.51562	−0.757808	−	0.652477i	$-0.773730\pi$
$887$	−45.1389	−1.51562	−0.757808	+	0.652477i	$0.773730\pi$
$888$	6.11497	0.205205
$889$	−2.13198	−0.0715045
$890$	−5.14043	−0.172308
$891$	−0.289613	−0.00970239
$892$	2.49743	0.0836200
$893$	−0.214962	−0.00719341
$894$	0.662039	0.0221419
$895$	2.15075	0.0718917
$896$	1.00000	0.0334077
$897$	−5.76650	−0.192538
$898$	−9.21427	−0.307484
$899$	3.32569	0.110918
$900$	−1.84562	−0.0615206
$901$	58.3922	1.94533
$902$	53.4463	1.77957
$903$	0.967102	0.0321832
$904$	−18.3923	−0.611718
$905$	−6.72664	−0.223601
$906$	15.7651	0.523762
$907$	23.4671	0.779212	0.389606	−	0.920982i	$-0.372611\pi$
$907$	23.4671	0.779212	0.389606	+	0.920982i	$0.372611\pi$
$908$	7.70860	0.255819
$909$	−2.03677	−0.0675552
$910$	−0.914784	−0.0303248
$911$	−32.2878	−1.06974	−0.534872	−	0.844933i	$-0.679640\pi$
$911$	−32.2878	−1.06974	−0.534872	+	0.844933i	$0.679640\pi$
$912$	0.607739	0.0201242
$913$	19.6830	0.651411
$914$	−34.4258	−1.13870
$915$	−9.99362	−0.330379
$916$	13.2813	0.438827
$917$	−16.0653	−0.530524
$918$	−24.9638	−0.823927
$919$	−2.35120	−0.0775590	−0.0387795	−	0.999248i	$-0.512347\pi$
$919$	−2.35120	−0.0775590	−0.0387795	+	0.999248i	$0.512347\pi$
$920$	5.86704	0.193431
$921$	−30.8760	−1.01740
$922$	13.6401	0.449214
$923$	0.914784	0.0301105
$924$	5.47490	0.180111
$925$	5.69141	0.187132
$926$	7.27555	0.239089
$927$	5.73914	0.188498
$928$	−2.02045	−0.0663246
$929$	24.1858	0.793511	0.396755	−	0.917924i	$-0.370136\pi$
$929$	24.1858	0.793511	0.396755	+	0.917924i	$0.370136\pi$
$930$	1.76851	0.0579917
$931$	0.565643	0.0185382
$932$	−29.5341	−0.967421
$933$	20.4820	0.670550
$934$	26.9219	0.880913
$935$	−24.4336	−0.799066
$936$	−1.68834	−0.0551852
$937$	28.4362	0.928971	0.464485	−	0.885581i	$-0.346239\pi$
$937$	28.4362	0.928971	0.464485	+	0.885581i	$0.346239\pi$
$938$	1.39207	0.0454527
$939$	16.1376	0.526631
$940$	0.380031	0.0123952
$941$	−0.153629	−0.00500815	−0.00250407	−	0.999997i	$-0.500797\pi$
$941$	−0.153629	−0.00500815	−0.00250407	+	0.999997i	$0.500797\pi$
$942$	20.2140	0.658607
$943$	−61.5368	−2.00392
$944$	−5.38187	−0.175165
$945$	5.20624	0.169359
$946$	4.58669	0.149126
$947$	31.3860	1.01991	0.509954	−	0.860202i	$-0.329662\pi$
$947$	31.3860	1.01991	0.509954	+	0.860202i	$0.329662\pi$
$948$	−4.15483	−0.134943
$949$	−1.30292	−0.0422945
$950$	0.565643	0.0183519
$951$	7.49941	0.243185
$952$	4.79497	0.155406
$953$	−7.83935	−0.253941	−0.126971	−	0.991906i	$-0.540525\pi$
$953$	−7.83935	−0.253941	−0.126971	+	0.991906i	$0.540525\pi$
$954$	−22.4756	−0.727673
$955$	−21.4910	−0.695433
$956$	−6.02921	−0.194998
$957$	−11.0618	−0.357577
$958$	−22.3358	−0.721638
$959$	−12.4580	−0.402289
$960$	−1.07442	−0.0346768
$961$	−28.2907	−0.912602
$962$	5.20641	0.167861
$963$	−19.0089	−0.612552
$964$	−7.12862	−0.229597
$965$	−10.8607	−0.349618
$966$	−6.30368	−0.202818
$967$	28.6044	0.919856	0.459928	−	0.887956i	$-0.347875\pi$
$967$	28.6044	0.919856	0.459928	+	0.887956i	$0.347875\pi$
$968$	14.9659	0.481023
$969$	2.91409	0.0936141
$970$	13.6793	0.439215
$971$	17.4385	0.559629	0.279814	−	0.960054i	$-0.409727\pi$
$971$	17.4385	0.559629	0.279814	+	0.960054i	$0.409727\pi$
$972$	15.5576	0.499012
$973$	4.02672	0.129091
$974$	−24.2199	−0.776055
$975$	0.982863	0.0314768
$976$	9.30140	0.297731
$977$	−31.9016	−1.02062	−0.510311	−	0.859990i	$-0.670470\pi$
$977$	−31.9016	−1.02062	−0.510311	+	0.859990i	$0.670470\pi$
$978$	−2.48114	−0.0793382
$979$	26.1940	0.837164
$980$	−1.00000	−0.0319438
$981$	3.44160	0.109882
$982$	−27.9134	−0.890753
$983$	−23.0255	−0.734399	−0.367199	−	0.930142i	$-0.619683\pi$
$983$	−23.0255	−0.734399	−0.367199	+	0.930142i	$0.619683\pi$
$984$	11.2691	0.359247
$985$	−14.7532	−0.470075
$986$	−9.68802	−0.308529
$987$	−0.408313	−0.0129967
$988$	0.517441	0.0164620
$989$	−5.28101	−0.167926
$990$	9.40468	0.298900
$991$	−10.4652	−0.332438	−0.166219	−	0.986089i	$-0.553156\pi$
$991$	−10.4652	−0.332438	−0.166219	+	0.986089i	$0.553156\pi$
$992$	−1.64601	−0.0522609
$993$	−4.13316	−0.131162
$994$	1.00000	0.0317181
$995$	−10.3601	−0.328438
$996$	4.15015	0.131502
$997$	35.6567	1.12926	0.564629	−	0.825345i	$-0.309019\pi$
$997$	35.6567	1.12926	0.564629	+	0.825345i	$0.309019\pi$
$998$	9.77527	0.309431
$999$	−29.6308	−0.937477

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4970.2.a.z.1.6	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4970.2.a.z.1.6	✓	9	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:	\( N \)	\(=\)	\( 4970 = 2 \cdot 5 \cdot 7 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4970.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.07442 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.07442 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.84562 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.07442 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.07442 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.84562 q^{9} -1.00000 q^{10} +5.09568 q^{11} +1.07442 q^{12} +0.914784 q^{13} +1.00000 q^{14} -1.07442 q^{15} +1.00000 q^{16} +4.79497 q^{17} -1.84562 q^{18} +0.565643 q^{19} -1.00000 q^{20} +1.07442 q^{21} +5.09568 q^{22} -5.86704 q^{23} +1.07442 q^{24} +1.00000 q^{25} +0.914784 q^{26} -5.20624 q^{27} +1.00000 q^{28} -2.02045 q^{29} -1.07442 q^{30} -1.64601 q^{31} +1.00000 q^{32} +5.47490 q^{33} +4.79497 q^{34} -1.00000 q^{35} -1.84562 q^{36} +5.69141 q^{37} +0.565643 q^{38} +0.982863 q^{39} -1.00000 q^{40} +10.4886 q^{41} +1.07442 q^{42} +0.900115 q^{43} +5.09568 q^{44} +1.84562 q^{45} -5.86704 q^{46} -0.380031 q^{47} +1.07442 q^{48} +1.00000 q^{49} +1.00000 q^{50} +5.15182 q^{51} +0.914784 q^{52} +12.1778 q^{53} -5.20624 q^{54} -5.09568 q^{55} +1.00000 q^{56} +0.607739 q^{57} -2.02045 q^{58} -5.38187 q^{59} -1.07442 q^{60} +9.30140 q^{61} -1.64601 q^{62} -1.84562 q^{63} +1.00000 q^{64} -0.914784 q^{65} +5.47490 q^{66} +1.39207 q^{67} +4.79497 q^{68} -6.30368 q^{69} -1.00000 q^{70} +1.00000 q^{71} -1.84562 q^{72} -1.42429 q^{73} +5.69141 q^{74} +1.07442 q^{75} +0.565643 q^{76} +5.09568 q^{77} +0.982863 q^{78} -3.86704 q^{79} -1.00000 q^{80} -0.0568350 q^{81} +10.4886 q^{82} +3.86268 q^{83} +1.07442 q^{84} -4.79497 q^{85} +0.900115 q^{86} -2.17082 q^{87} +5.09568 q^{88} +5.14043 q^{89} +1.84562 q^{90} +0.914784 q^{91} -5.86704 q^{92} -1.76851 q^{93} -0.380031 q^{94} -0.565643 q^{95} +1.07442 q^{96} -13.6793 q^{97} +1.00000 q^{98} -9.40468 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 4 q^{3} + 9 q^{4} - 9 q^{5} + 4 q^{6} + 9 q^{7} + 9 q^{8} + 7 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 4 * q^3 + 9 * q^4 - 9 * q^5 + 4 * q^6 + 9 * q^7 + 9 * q^8 + 7 * q^9	\( 9 q + 9 q^{2} + 4 q^{3} + 9 q^{4} - 9 q^{5} + 4 q^{6} + 9 q^{7} + 9 q^{8} + 7 q^{9} - 9 q^{10} - 2 q^{11} + 4 q^{12} + 11 q^{13} + 9 q^{14} - 4 q^{15} + 9 q^{16} + 9 q^{17} + 7 q^{18} + 9 q^{19} - 9 q^{20} + 4 q^{21} - 2 q^{22} + 2 q^{23} + 4 q^{24} + 9 q^{25} + 11 q^{26} + 7 q^{27} + 9 q^{28} + 2 q^{29} - 4 q^{30} + 18 q^{31} + 9 q^{32} + 8 q^{33} + 9 q^{34} - 9 q^{35} + 7 q^{36} + 15 q^{37} + 9 q^{38} - 7 q^{39} - 9 q^{40} + 15 q^{41} + 4 q^{42} + 7 q^{43} - 2 q^{44} - 7 q^{45} + 2 q^{46} + 12 q^{47} + 4 q^{48} + 9 q^{49} + 9 q^{50} + 4 q^{51} + 11 q^{52} + 3 q^{53} + 7 q^{54} + 2 q^{55} + 9 q^{56} + 9 q^{57} + 2 q^{58} + 24 q^{59} - 4 q^{60} + 25 q^{61} + 18 q^{62} + 7 q^{63} + 9 q^{64} - 11 q^{65} + 8 q^{66} - 4 q^{67} + 9 q^{68} + 3 q^{69} - 9 q^{70} + 9 q^{71} + 7 q^{72} + 32 q^{73} + 15 q^{74} + 4 q^{75} + 9 q^{76} - 2 q^{77} - 7 q^{78} + 20 q^{79} - 9 q^{80} - 7 q^{81} + 15 q^{82} + 11 q^{83} + 4 q^{84} - 9 q^{85} + 7 q^{86} + 26 q^{87} - 2 q^{88} + 10 q^{89} - 7 q^{90} + 11 q^{91} + 2 q^{92} + 32 q^{93} + 12 q^{94} - 9 q^{95} + 4 q^{96} + 19 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 4 * q^3 + 9 * q^4 - 9 * q^5 + 4 * q^6 + 9 * q^7 + 9 * q^8 + 7 * q^9 - 9 * q^10 - 2 * q^11 + 4 * q^12 + 11 * q^13 + 9 * q^14 - 4 * q^15 + 9 * q^16 + 9 * q^17 + 7 * q^18 + 9 * q^19 - 9 * q^20 + 4 * q^21 - 2 * q^22 + 2 * q^23 + 4 * q^24 + 9 * q^25 + 11 * q^26 + 7 * q^27 + 9 * q^28 + 2 * q^29 - 4 * q^30 + 18 * q^31 + 9 * q^32 + 8 * q^33 + 9 * q^34 - 9 * q^35 + 7 * q^36 + 15 * q^37 + 9 * q^38 - 7 * q^39 - 9 * q^40 + 15 * q^41 + 4 * q^42 + 7 * q^43 - 2 * q^44 - 7 * q^45 + 2 * q^46 + 12 * q^47 + 4 * q^48 + 9 * q^49 + 9 * q^50 + 4 * q^51 + 11 * q^52 + 3 * q^53 + 7 * q^54 + 2 * q^55 + 9 * q^56 + 9 * q^57 + 2 * q^58 + 24 * q^59 - 4 * q^60 + 25 * q^61 + 18 * q^62 + 7 * q^63 + 9 * q^64 - 11 * q^65 + 8 * q^66 - 4 * q^67 + 9 * q^68 + 3 * q^69 - 9 * q^70 + 9 * q^71 + 7 * q^72 + 32 * q^73 + 15 * q^74 + 4 * q^75 + 9 * q^76 - 2 * q^77 - 7 * q^78 + 20 * q^79 - 9 * q^80 - 7 * q^81 + 15 * q^82 + 11 * q^83 + 4 * q^84 - 9 * q^85 + 7 * q^86 + 26 * q^87 - 2 * q^88 + 10 * q^89 - 7 * q^90 + 11 * q^91 + 2 * q^92 + 32 * q^93 + 12 * q^94 - 9 * q^95 + 4 * q^96 + 19 * q^97 + 9 * q^98 - 7 * q^99

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