LMFDB - Embedded newform 1334.2.a.j.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(1,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.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:	$10.6520436296$
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} - 3x^{8} - 16x^{7} + 44x^{6} + 87x^{5} - 209x^{4} - 160x^{3} + 348x^{2} + 12x - 100 $ x^9 - 3x^8 - 16x^7 + 44x^6 + 87x^5 - 209x^4 - 160x^3 + 348x^2 + 12x - 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.04237$ of defining polynomial
Character	$\chi$	$=$	1334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.04237 q^{3} +1.00000 q^{4} +4.28519 q^{5} +2.04237 q^{6} +0.891555 q^{7} -1.00000 q^{8} +1.17127 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.04237 q^{3} +1.00000 q^{4} +4.28519 q^{5} +2.04237 q^{6} +0.891555 q^{7} -1.00000 q^{8} +1.17127 q^{9} -4.28519 q^{10} +0.374537 q^{11} -2.04237 q^{12} +6.96903 q^{13} -0.891555 q^{14} -8.75193 q^{15} +1.00000 q^{16} +5.42969 q^{17} -1.17127 q^{18} -3.90621 q^{19} +4.28519 q^{20} -1.82088 q^{21} -0.374537 q^{22} -1.00000 q^{23} +2.04237 q^{24} +13.3628 q^{25} -6.96903 q^{26} +3.73495 q^{27} +0.891555 q^{28} +1.00000 q^{29} +8.75193 q^{30} +2.37454 q^{31} -1.00000 q^{32} -0.764943 q^{33} -5.42969 q^{34} +3.82048 q^{35} +1.17127 q^{36} -5.60742 q^{37} +3.90621 q^{38} -14.2333 q^{39} -4.28519 q^{40} -7.60742 q^{41} +1.82088 q^{42} -4.45927 q^{43} +0.374537 q^{44} +5.01909 q^{45} +1.00000 q^{46} -5.56470 q^{47} -2.04237 q^{48} -6.20513 q^{49} -13.3628 q^{50} -11.0894 q^{51} +6.96903 q^{52} -3.94265 q^{53} -3.73495 q^{54} +1.60496 q^{55} -0.891555 q^{56} +7.97792 q^{57} -1.00000 q^{58} +9.38365 q^{59} -8.75193 q^{60} +13.5986 q^{61} -2.37454 q^{62} +1.04425 q^{63} +1.00000 q^{64} +29.8636 q^{65} +0.764943 q^{66} -8.70115 q^{67} +5.42969 q^{68} +2.04237 q^{69} -3.82048 q^{70} +10.4894 q^{71} -1.17127 q^{72} -10.5237 q^{73} +5.60742 q^{74} -27.2918 q^{75} -3.90621 q^{76} +0.333920 q^{77} +14.2333 q^{78} +15.0113 q^{79} +4.28519 q^{80} -11.1419 q^{81} +7.60742 q^{82} -16.1357 q^{83} -1.82088 q^{84} +23.2672 q^{85} +4.45927 q^{86} -2.04237 q^{87} -0.374537 q^{88} -0.519837 q^{89} -5.01909 q^{90} +6.21328 q^{91} -1.00000 q^{92} -4.84968 q^{93} +5.56470 q^{94} -16.7389 q^{95} +2.04237 q^{96} +0.700295 q^{97} +6.20513 q^{98} +0.438683 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 5 q^{5} + 3 q^{6} + 6 q^{7} - 9 q^{8} + 14 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 5 * q^5 + 3 * q^6 + 6 * q^7 - 9 * q^8 + 14 * q^9	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 5 q^{5} + 3 q^{6} + 6 q^{7} - 9 q^{8} + 14 q^{9} - 5 q^{10} - 3 q^{11} - 3 q^{12} + 13 q^{13} - 6 q^{14} - 3 q^{15} + 9 q^{16} + 2 q^{17} - 14 q^{18} + 16 q^{19} + 5 q^{20} + 8 q^{21} + 3 q^{22} - 9 q^{23} + 3 q^{24} + 20 q^{25} - 13 q^{26} - 21 q^{27} + 6 q^{28} + 9 q^{29} + 3 q^{30} + 15 q^{31} - 9 q^{32} + 13 q^{33} - 2 q^{34} + 14 q^{36} + 12 q^{37} - 16 q^{38} - 5 q^{39} - 5 q^{40} - 6 q^{41} - 8 q^{42} - 3 q^{43} - 3 q^{44} + 20 q^{45} + 9 q^{46} - 19 q^{47} - 3 q^{48} + 37 q^{49} - 20 q^{50} + 6 q^{51} + 13 q^{52} + 5 q^{53} + 21 q^{54} + q^{55} - 6 q^{56} - 20 q^{57} - 9 q^{58} + 12 q^{59} - 3 q^{60} + 12 q^{61} - 15 q^{62} + 6 q^{63} + 9 q^{64} + 19 q^{65} - 13 q^{66} - 6 q^{67} + 2 q^{68} + 3 q^{69} + 12 q^{71} - 14 q^{72} - 12 q^{74} + 16 q^{75} + 16 q^{76} + 34 q^{77} + 5 q^{78} + 29 q^{79} + 5 q^{80} + 5 q^{81} + 6 q^{82} + 24 q^{83} + 8 q^{84} + 12 q^{85} + 3 q^{86} - 3 q^{87} + 3 q^{88} - 2 q^{89} - 20 q^{90} + 58 q^{91} - 9 q^{92} + 7 q^{93} + 19 q^{94} + 6 q^{95} + 3 q^{96} + 12 q^{97} - 37 q^{98} - 20 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 5 * q^5 + 3 * q^6 + 6 * q^7 - 9 * q^8 + 14 * q^9 - 5 * q^10 - 3 * q^11 - 3 * q^12 + 13 * q^13 - 6 * q^14 - 3 * q^15 + 9 * q^16 + 2 * q^17 - 14 * q^18 + 16 * q^19 + 5 * q^20 + 8 * q^21 + 3 * q^22 - 9 * q^23 + 3 * q^24 + 20 * q^25 - 13 * q^26 - 21 * q^27 + 6 * q^28 + 9 * q^29 + 3 * q^30 + 15 * q^31 - 9 * q^32 + 13 * q^33 - 2 * q^34 + 14 * q^36 + 12 * q^37 - 16 * q^38 - 5 * q^39 - 5 * q^40 - 6 * q^41 - 8 * q^42 - 3 * q^43 - 3 * q^44 + 20 * q^45 + 9 * q^46 - 19 * q^47 - 3 * q^48 + 37 * q^49 - 20 * q^50 + 6 * q^51 + 13 * q^52 + 5 * q^53 + 21 * q^54 + q^55 - 6 * q^56 - 20 * q^57 - 9 * q^58 + 12 * q^59 - 3 * q^60 + 12 * q^61 - 15 * q^62 + 6 * q^63 + 9 * q^64 + 19 * q^65 - 13 * q^66 - 6 * q^67 + 2 * q^68 + 3 * q^69 + 12 * q^71 - 14 * q^72 - 12 * q^74 + 16 * q^75 + 16 * q^76 + 34 * q^77 + 5 * q^78 + 29 * q^79 + 5 * q^80 + 5 * q^81 + 6 * q^82 + 24 * q^83 + 8 * q^84 + 12 * q^85 + 3 * q^86 - 3 * q^87 + 3 * q^88 - 2 * q^89 - 20 * q^90 + 58 * q^91 - 9 * q^92 + 7 * q^93 + 19 * q^94 + 6 * q^95 + 3 * q^96 + 12 * q^97 - 37 * q^98 - 20 * 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
$3$	−2.04237	−1.17916	−0.589581	−	0.807709i	$-0.700707\pi$
$3$	−2.04237	−1.17916	−0.589581	+	0.807709i	$0.700707\pi$
$4$	1.00000	0.500000
$5$	4.28519	1.91639	0.958197	−	0.286110i	$-0.0923622\pi$
$5$	4.28519	1.91639	0.958197	+	0.286110i	$0.0923622\pi$
$6$	2.04237	0.833793
$7$	0.891555	0.336976	0.168488	−	0.985704i	$-0.446112\pi$
$7$	0.891555	0.336976	0.168488	+	0.985704i	$0.446112\pi$
$8$	−1.00000	−0.353553
$9$	1.17127	0.390422
$10$	−4.28519	−1.35509
$11$	0.374537	0.112927	0.0564636	−	0.998405i	$-0.482018\pi$
$11$	0.374537	0.112927	0.0564636	+	0.998405i	$0.482018\pi$
$12$	−2.04237	−0.589581
$13$	6.96903	1.93286	0.966431	−	0.256926i	$-0.0827096\pi$
$13$	6.96903	1.93286	0.966431	+	0.256926i	$0.0827096\pi$
$14$	−0.891555	−0.238278
$15$	−8.75193	−2.25974
$16$	1.00000	0.250000
$17$	5.42969	1.31689	0.658447	−	0.752627i	$-0.271214\pi$
$17$	5.42969	1.31689	0.658447	+	0.752627i	$0.271214\pi$
$18$	−1.17127	−0.276070
$19$	−3.90621	−0.896147	−0.448073	−	0.893997i	$-0.647890\pi$
$19$	−3.90621	−0.896147	−0.448073	+	0.893997i	$0.647890\pi$
$20$	4.28519	0.958197
$21$	−1.82088	−0.397349
$22$	−0.374537	−0.0798516
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.04237	0.416897
$25$	13.3628	2.67256
$26$	−6.96903	−1.36674
$27$	3.73495	0.718791
$28$	0.891555	0.168488
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	8.75193	1.59788
$31$	2.37454	0.426479	0.213240	−	0.977000i	$-0.431598\pi$
$31$	2.37454	0.426479	0.213240	+	0.977000i	$0.431598\pi$
$32$	−1.00000	−0.176777
$33$	−0.764943	−0.133159
$34$	−5.42969	−0.931184
$35$	3.82048	0.645779
$36$	1.17127	0.195211
$37$	−5.60742	−0.921855	−0.460927	−	0.887438i	$-0.652483\pi$
$37$	−5.60742	−0.921855	−0.460927	+	0.887438i	$0.652483\pi$
$38$	3.90621	0.633671
$39$	−14.2333	−2.27916
$40$	−4.28519	−0.677547
$41$	−7.60742	−1.18808	−0.594040	−	0.804435i	$-0.702468\pi$
$41$	−7.60742	−1.18808	−0.594040	+	0.804435i	$0.702468\pi$
$42$	1.82088	0.280968
$43$	−4.45927	−0.680033	−0.340016	−	0.940420i	$-0.610433\pi$
$43$	−4.45927	−0.680033	−0.340016	+	0.940420i	$0.610433\pi$
$44$	0.374537	0.0564636
$45$	5.01909	0.748202
$46$	1.00000	0.147442
$47$	−5.56470	−0.811695	−0.405848	−	0.913941i	$-0.633024\pi$
$47$	−5.56470	−0.811695	−0.405848	+	0.913941i	$0.633024\pi$
$48$	−2.04237	−0.294790
$49$	−6.20513	−0.886447
$50$	−13.3628	−1.88979
$51$	−11.0894	−1.55283
$52$	6.96903	0.966431
$53$	−3.94265	−0.541565	−0.270783	−	0.962641i	$-0.587282\pi$
$53$	−3.94265	−0.541565	−0.270783	+	0.962641i	$0.587282\pi$
$54$	−3.73495	−0.508262
$55$	1.60496	0.216413
$56$	−0.891555	−0.119139
$57$	7.97792	1.05670
$58$	−1.00000	−0.131306
$59$	9.38365	1.22165	0.610824	−	0.791767i	$-0.290838\pi$
$59$	9.38365	1.22165	0.610824	+	0.791767i	$0.290838\pi$
$60$	−8.75193	−1.12987
$61$	13.5986	1.74112	0.870558	−	0.492066i	$-0.163758\pi$
$61$	13.5986	1.74112	0.870558	+	0.492066i	$0.163758\pi$
$62$	−2.37454	−0.301567
$63$	1.04425	0.131563
$64$	1.00000	0.125000
$65$	29.8636	3.70413
$66$	0.764943	0.0941580
$67$	−8.70115	−1.06301	−0.531507	−	0.847054i	$-0.678374\pi$
$67$	−8.70115	−1.06301	−0.531507	+	0.847054i	$0.678374\pi$
$68$	5.42969	0.658447
$69$	2.04237	0.245872
$70$	−3.82048	−0.456635
$71$	10.4894	1.24487	0.622434	−	0.782673i	$-0.286144\pi$
$71$	10.4894	1.24487	0.622434	+	0.782673i	$0.286144\pi$
$72$	−1.17127	−0.138035
$73$	−10.5237	−1.23171	−0.615855	−	0.787860i	$-0.711189\pi$
$73$	−10.5237	−1.23171	−0.615855	+	0.787860i	$0.711189\pi$
$74$	5.60742	0.651850
$75$	−27.2918	−3.15139
$76$	−3.90621	−0.448073
$77$	0.333920	0.0380538
$78$	14.2333	1.61161
$79$	15.0113	1.68891	0.844454	−	0.535628i	$-0.179925\pi$
$79$	15.0113	1.68891	0.844454	+	0.535628i	$0.179925\pi$
$80$	4.28519	0.479098
$81$	−11.1419	−1.23799
$82$	7.60742	0.840099
$83$	−16.1357	−1.77112	−0.885561	−	0.464523i	$-0.846226\pi$
$83$	−16.1357	−1.77112	−0.885561	+	0.464523i	$0.846226\pi$
$84$	−1.82088	−0.198675
$85$	23.2672	2.52369
$86$	4.45927	0.480856
$87$	−2.04237	−0.218965
$88$	−0.374537	−0.0399258
$89$	−0.519837	−0.0551027	−0.0275513	−	0.999620i	$-0.508771\pi$
$89$	−0.519837	−0.0551027	−0.0275513	+	0.999620i	$0.508771\pi$
$90$	−5.01909	−0.529059
$91$	6.21328	0.651328
$92$	−1.00000	−0.104257
$93$	−4.84968	−0.502888
$94$	5.56470	0.573955
$95$	−16.7389	−1.71737
$96$	2.04237	0.208448
$97$	0.700295	0.0711042	0.0355521	−	0.999368i	$-0.488681\pi$
$97$	0.700295	0.0711042	0.0355521	+	0.999368i	$0.488681\pi$
$98$	6.20513	0.626813
$99$	0.438683	0.0440893
$100$	13.3628	1.33628
$101$	0.0231245	0.00230097	0.00115049	−	0.999999i	$-0.499634\pi$
$101$	0.0231245	0.00230097	0.00115049	+	0.999999i	$0.499634\pi$
$102$	11.0894	1.09802
$103$	13.5268	1.33283	0.666416	−	0.745581i	$-0.267828\pi$
$103$	13.5268	1.33283	0.666416	+	0.745581i	$0.267828\pi$
$104$	−6.96903	−0.683370
$105$	−7.80282	−0.761477
$106$	3.94265	0.382944
$107$	15.3591	1.48482	0.742412	−	0.669943i	$-0.233682\pi$
$107$	15.3591	1.48482	0.742412	+	0.669943i	$0.233682\pi$
$108$	3.73495	0.359395
$109$	2.84940	0.272923	0.136462	−	0.990645i	$-0.456427\pi$
$109$	2.84940	0.272923	0.136462	+	0.990645i	$0.456427\pi$
$110$	−1.60496	−0.153027
$111$	11.4524	1.08702
$112$	0.891555	0.0842440
$113$	7.15494	0.673080	0.336540	−	0.941669i	$-0.390743\pi$
$113$	7.15494	0.673080	0.336540	+	0.941669i	$0.390743\pi$
$114$	−7.97792	−0.747201
$115$	−4.28519	−0.399596
$116$	1.00000	0.0928477
$117$	8.16259	0.754632
$118$	−9.38365	−0.863835
$119$	4.84087	0.443761
$120$	8.75193	0.798938
$121$	−10.8597	−0.987247
$122$	−13.5986	−1.23116
$123$	15.5372	1.40094
$124$	2.37454	0.213240
$125$	35.8363	3.20529
$126$	−1.04425	−0.0930290
$127$	5.49168	0.487308	0.243654	−	0.969862i	$-0.421654\pi$
$127$	5.49168	0.487308	0.243654	+	0.969862i	$0.421654\pi$
$128$	−1.00000	−0.0883883
$129$	9.10748	0.801868
$130$	−29.8636	−2.61921
$131$	7.00086	0.611668	0.305834	−	0.952085i	$-0.401065\pi$
$131$	7.00086	0.611668	0.305834	+	0.952085i	$0.401065\pi$
$132$	−0.764943	−0.0665797
$133$	−3.48260	−0.301980
$134$	8.70115	0.751665
$135$	16.0049	1.37749
$136$	−5.42969	−0.465592
$137$	7.99860	0.683367	0.341683	−	0.939815i	$-0.389003\pi$
$137$	7.99860	0.683367	0.341683	+	0.939815i	$0.389003\pi$
$138$	−2.04237	−0.173858
$139$	−14.8456	−1.25919	−0.629593	−	0.776925i	$-0.716778\pi$
$139$	−14.8456	−1.25919	−0.629593	+	0.776925i	$0.716778\pi$
$140$	3.82048	0.322889
$141$	11.3652	0.957120
$142$	−10.4894	−0.880254
$143$	2.61016	0.218273
$144$	1.17127	0.0976055
$145$	4.28519	0.355865
$146$	10.5237	0.870950
$147$	12.6732	1.04526
$148$	−5.60742	−0.460927
$149$	−13.7303	−1.12483	−0.562413	−	0.826856i	$-0.690127\pi$
$149$	−13.7303	−1.12483	−0.562413	+	0.826856i	$0.690127\pi$
$150$	27.2918	2.22837
$151$	13.2107	1.07507	0.537536	−	0.843241i	$-0.319355\pi$
$151$	13.2107	1.07507	0.537536	+	0.843241i	$0.319355\pi$
$152$	3.90621	0.316836
$153$	6.35961	0.514144
$154$	−0.333920	−0.0269081
$155$	10.1753	0.817303
$156$	−14.2333	−1.13958
$157$	−11.6432	−0.929229	−0.464615	−	0.885513i	$-0.653807\pi$
$157$	−11.6432	−0.929229	−0.464615	+	0.885513i	$0.653807\pi$
$158$	−15.0113	−1.19424
$159$	8.05235	0.638593
$160$	−4.28519	−0.338774
$161$	−0.891555	−0.0702644
$162$	11.1419	0.875393
$163$	19.4966	1.52709	0.763546	−	0.645754i	$-0.223457\pi$
$163$	19.4966	1.52709	0.763546	+	0.645754i	$0.223457\pi$
$164$	−7.60742	−0.594040
$165$	−3.27792	−0.255186
$166$	16.1357	1.25237
$167$	−10.2786	−0.795385	−0.397693	−	0.917519i	$-0.630189\pi$
$167$	−10.2786	−0.795385	−0.397693	+	0.917519i	$0.630189\pi$
$168$	1.82088	0.140484
$169$	35.5674	2.73596
$170$	−23.2672	−1.78452
$171$	−4.57522	−0.349875
$172$	−4.45927	−0.340016
$173$	−22.2308	−1.69018	−0.845089	−	0.534626i	$-0.820453\pi$
$173$	−22.2308	−1.69018	−0.845089	+	0.534626i	$0.820453\pi$
$174$	2.04237	0.154832
$175$	11.9137	0.900590
$176$	0.374537	0.0282318
$177$	−19.1649	−1.44052
$178$	0.519837	0.0389635
$179$	−0.847608	−0.0633532	−0.0316766	−	0.999498i	$-0.510085\pi$
$179$	−0.847608	−0.0633532	−0.0316766	+	0.999498i	$0.510085\pi$
$180$	5.01909	0.374101
$181$	−8.02945	−0.596824	−0.298412	−	0.954437i	$-0.596457\pi$
$181$	−8.02945	−0.596824	−0.298412	+	0.954437i	$0.596457\pi$
$182$	−6.21328	−0.460559
$183$	−27.7732	−2.05306
$184$	1.00000	0.0737210
$185$	−24.0289	−1.76664
$186$	4.84968	0.355596
$187$	2.03362	0.148713
$188$	−5.56470	−0.405848
$189$	3.32991	0.242215
$190$	16.7389	1.21436
$191$	−17.8510	−1.29165	−0.645827	−	0.763484i	$-0.723487\pi$
$191$	−17.8510	−1.29165	−0.645827	+	0.763484i	$0.723487\pi$
$192$	−2.04237	−0.147395
$193$	16.0590	1.15595	0.577977	−	0.816053i	$-0.303842\pi$
$193$	16.0590	1.15595	0.577977	+	0.816053i	$0.303842\pi$
$194$	−0.700295	−0.0502783
$195$	−60.9925	−4.36776
$196$	−6.20513	−0.443224
$197$	3.66892	0.261400	0.130700	−	0.991422i	$-0.458278\pi$
$197$	3.66892	0.261400	0.130700	+	0.991422i	$0.458278\pi$
$198$	−0.438683	−0.0311758
$199$	16.6746	1.18203	0.591016	−	0.806660i	$-0.298727\pi$
$199$	16.6746	1.18203	0.591016	+	0.806660i	$0.298727\pi$
$200$	−13.3628	−0.944894
$201$	17.7709	1.25347
$202$	−0.0231245	−0.00162703
$203$	0.891555	0.0625749
$204$	−11.0894	−0.776415
$205$	−32.5992	−2.27683
$206$	−13.5268	−0.942454
$207$	−1.17127	−0.0814086
$208$	6.96903	0.483216
$209$	−1.46302	−0.101199
$210$	7.80282	0.538446
$211$	22.8516	1.57317	0.786585	−	0.617482i	$-0.211847\pi$
$211$	22.8516	1.57317	0.786585	+	0.617482i	$0.211847\pi$
$212$	−3.94265	−0.270783
$213$	−21.4233	−1.46790
$214$	−15.3591	−1.04993
$215$	−19.1088	−1.30321
$216$	−3.73495	−0.254131
$217$	2.11703	0.143713
$218$	−2.84940	−0.192986
$219$	21.4933	1.45238
$220$	1.60496	0.108207
$221$	37.8397	2.54537
$222$	−11.4524	−0.768636
$223$	−11.2146	−0.750982	−0.375491	−	0.926826i	$-0.622526\pi$
$223$	−11.2146	−0.750982	−0.375491	+	0.926826i	$0.622526\pi$
$224$	−0.891555	−0.0595695
$225$	15.6514	1.04343
$226$	−7.15494	−0.475939
$227$	5.70650	0.378754	0.189377	−	0.981904i	$-0.439353\pi$
$227$	5.70650	0.378754	0.189377	+	0.981904i	$0.439353\pi$
$228$	7.97792	0.528351
$229$	8.21001	0.542533	0.271266	−	0.962504i	$-0.412558\pi$
$229$	8.21001	0.542533	0.271266	+	0.962504i	$0.412558\pi$
$230$	4.28519	0.282557
$231$	−0.681988	−0.0448715
$232$	−1.00000	−0.0656532
$233$	−17.6884	−1.15881	−0.579403	−	0.815041i	$-0.696714\pi$
$233$	−17.6884	−1.15881	−0.579403	+	0.815041i	$0.696714\pi$
$234$	−8.16259	−0.533606
$235$	−23.8458	−1.55553
$236$	9.38365	0.610824
$237$	−30.6587	−1.99150
$238$	−4.84087	−0.313787
$239$	−23.7964	−1.53926	−0.769630	−	0.638490i	$-0.779560\pi$
$239$	−23.7964	−1.53926	−0.769630	+	0.638490i	$0.779560\pi$
$240$	−8.75193	−0.564934
$241$	27.5232	1.77292	0.886462	−	0.462800i	$-0.153155\pi$
$241$	27.5232	1.77292	0.886462	+	0.462800i	$0.153155\pi$
$242$	10.8597	0.698089
$243$	11.5511	0.741003
$244$	13.5986	0.870558
$245$	−26.5901	−1.69878
$246$	−15.5372	−0.990613
$247$	−27.2225	−1.73213
$248$	−2.37454	−0.150783
$249$	32.9550	2.08844
$250$	−35.8363	−2.26648
$251$	−7.61124	−0.480417	−0.240208	−	0.970721i	$-0.577216\pi$
$251$	−7.61124	−0.480417	−0.240208	+	0.970721i	$0.577216\pi$
$252$	1.04425	0.0657814
$253$	−0.374537	−0.0235470
$254$	−5.49168	−0.344579
$255$	−47.5202	−2.97583
$256$	1.00000	0.0625000
$257$	−12.2298	−0.762875	−0.381437	−	0.924395i	$-0.624571\pi$
$257$	−12.2298	−0.762875	−0.381437	+	0.924395i	$0.624571\pi$
$258$	−9.10748	−0.567007
$259$	−4.99933	−0.310643
$260$	29.8636	1.85206
$261$	1.17127	0.0724996
$262$	−7.00086	−0.432515
$263$	−24.6992	−1.52302	−0.761510	−	0.648153i	$-0.775542\pi$
$263$	−24.6992	−1.52302	−0.761510	+	0.648153i	$0.775542\pi$
$264$	0.764943	0.0470790
$265$	−16.8950	−1.03785
$266$	3.48260	0.213532
$267$	1.06170	0.0649749
$268$	−8.70115	−0.531507
$269$	7.59155	0.462865	0.231433	−	0.972851i	$-0.425659\pi$
$269$	7.59155	0.462865	0.231433	+	0.972851i	$0.425659\pi$
$270$	−16.0049	−0.974030
$271$	−13.6684	−0.830298	−0.415149	−	0.909753i	$-0.636271\pi$
$271$	−13.6684	−0.830298	−0.415149	+	0.909753i	$0.636271\pi$
$272$	5.42969	0.329223
$273$	−12.6898	−0.768021
$274$	−7.99860	−0.483213
$275$	5.00488	0.301805
$276$	2.04237	0.122936
$277$	−16.6626	−1.00116	−0.500578	−	0.865691i	$-0.666879\pi$
$277$	−16.6626	−1.00116	−0.500578	+	0.865691i	$0.666879\pi$
$278$	14.8456	0.890379
$279$	2.78122	0.166507
$280$	−3.82048	−0.228317
$281$	20.2319	1.20693	0.603467	−	0.797388i	$-0.293786\pi$
$281$	20.2319	1.20693	0.603467	+	0.797388i	$0.293786\pi$
$282$	−11.3652	−0.676786
$283$	7.44153	0.442353	0.221177	−	0.975234i	$-0.429010\pi$
$283$	7.44153	0.442353	0.221177	+	0.975234i	$0.429010\pi$
$284$	10.4894	0.622434
$285$	34.1869	2.02506
$286$	−2.61016	−0.154342
$287$	−6.78244	−0.400354
$288$	−1.17127	−0.0690175
$289$	12.4815	0.734208
$290$	−4.28519	−0.251635
$291$	−1.43026	−0.0838434
$292$	−10.5237	−0.615855
$293$	−12.9484	−0.756452	−0.378226	−	0.925713i	$-0.623466\pi$
$293$	−12.9484	−0.756452	−0.378226	+	0.925713i	$0.623466\pi$
$294$	−12.6732	−0.739114
$295$	40.2107	2.34116
$296$	5.60742	0.325925
$297$	1.39888	0.0811711
$298$	13.7303	0.795373
$299$	−6.96903	−0.403030
$300$	−27.2918	−1.57569
$301$	−3.97569	−0.229155
$302$	−13.2107	−0.760190
$303$	−0.0472287	−0.00271322
$304$	−3.90621	−0.224037
$305$	58.2723	3.33666
$306$	−6.35961	−0.363555
$307$	−1.05304	−0.0601001	−0.0300500	−	0.999548i	$-0.509567\pi$
$307$	−1.05304	−0.0601001	−0.0300500	+	0.999548i	$0.509567\pi$
$308$	0.333920	0.0190269
$309$	−27.6266	−1.57162
$310$	−10.1753	−0.577920
$311$	20.9402	1.18741	0.593704	−	0.804683i	$-0.297665\pi$
$311$	20.9402	1.18741	0.593704	+	0.804683i	$0.297665\pi$
$312$	14.2333	0.805804
$313$	−29.8561	−1.68757	−0.843784	−	0.536682i	$-0.819677\pi$
$313$	−29.8561	−1.68757	−0.843784	+	0.536682i	$0.819677\pi$
$314$	11.6432	0.657064
$315$	4.47480	0.252126
$316$	15.0113	0.844454
$317$	−2.73637	−0.153690	−0.0768448	−	0.997043i	$-0.524485\pi$
$317$	−2.73637	−0.153690	−0.0768448	+	0.997043i	$0.524485\pi$
$318$	−8.05235	−0.451553
$319$	0.374537	0.0209701
$320$	4.28519	0.239549
$321$	−31.3690	−1.75085
$322$	0.891555	0.0496844
$323$	−21.2095	−1.18013
$324$	−11.1419	−0.618996
$325$	93.1260	5.16570
$326$	−19.4966	−1.07982
$327$	−5.81953	−0.321821
$328$	7.60742	0.420050
$329$	−4.96124	−0.273522
$330$	3.27792	0.180444
$331$	−3.62597	−0.199301	−0.0996506	−	0.995022i	$-0.531773\pi$
$331$	−3.62597	−0.199301	−0.0996506	+	0.995022i	$0.531773\pi$
$332$	−16.1357	−0.885561
$333$	−6.56779	−0.359913
$334$	10.2786	0.562422
$335$	−37.2860	−2.03715
$336$	−1.82088	−0.0993373
$337$	−4.93538	−0.268847	−0.134424	−	0.990924i	$-0.542918\pi$
$337$	−4.93538	−0.268847	−0.134424	+	0.990924i	$0.542918\pi$
$338$	−35.5674	−1.93461
$339$	−14.6130	−0.793670
$340$	23.2672	1.26184
$341$	0.889353	0.0481611
$342$	4.57522	0.247399
$343$	−11.7731	−0.635687
$344$	4.45927	0.240428
$345$	8.75193	0.471188
$346$	22.2308	1.19514
$347$	−1.99010	−0.106834	−0.0534172	−	0.998572i	$-0.517011\pi$
$347$	−1.99010	−0.106834	−0.0534172	+	0.998572i	$0.517011\pi$
$348$	−2.04237	−0.109482
$349$	26.6487	1.42647	0.713235	−	0.700925i	$-0.247229\pi$
$349$	26.6487	1.42647	0.713235	+	0.700925i	$0.247229\pi$
$350$	−11.9137	−0.636813
$351$	26.0290	1.38932
$352$	−0.374537	−0.0199629
$353$	5.41817	0.288380	0.144190	−	0.989550i	$-0.453942\pi$
$353$	5.41817	0.288380	0.144190	+	0.989550i	$0.453942\pi$
$354$	19.1649	1.01860
$355$	44.9492	2.38566
$356$	−0.519837	−0.0275513
$357$	−9.88683	−0.523266
$358$	0.847608	0.0447975
$359$	−8.69274	−0.458785	−0.229393	−	0.973334i	$-0.573674\pi$
$359$	−8.69274	−0.458785	−0.229393	+	0.973334i	$0.573674\pi$
$360$	−5.01909	−0.264530
$361$	−3.74150	−0.196921
$362$	8.02945	0.422019
$363$	22.1795	1.16412
$364$	6.21328	0.325664
$365$	−45.0961	−2.36044
$366$	27.7732	1.45173
$367$	7.10545	0.370902	0.185451	−	0.982654i	$-0.440625\pi$
$367$	7.10545	0.370902	0.185451	+	0.982654i	$0.440625\pi$
$368$	−1.00000	−0.0521286
$369$	−8.91032	−0.463853
$370$	24.0289	1.24920
$371$	−3.51509	−0.182494
$372$	−4.84968	−0.251444
$373$	4.52726	0.234412	0.117206	−	0.993108i	$-0.462606\pi$
$373$	4.52726	0.234412	0.117206	+	0.993108i	$0.462606\pi$
$374$	−2.03362	−0.105156
$375$	−73.1908	−3.77956
$376$	5.56470	0.286978
$377$	6.96903	0.358924
$378$	−3.32991	−0.171272
$379$	−19.0357	−0.977800	−0.488900	−	0.872340i	$-0.662602\pi$
$379$	−19.0357	−0.977800	−0.488900	+	0.872340i	$0.662602\pi$
$380$	−16.7389	−0.858685
$381$	−11.2160	−0.574615
$382$	17.8510	0.913337
$383$	−25.4289	−1.29936	−0.649679	−	0.760209i	$-0.725097\pi$
$383$	−25.4289	−1.29936	−0.649679	+	0.760209i	$0.725097\pi$
$384$	2.04237	0.104224
$385$	1.43091	0.0729260
$386$	−16.0590	−0.817383
$387$	−5.22300	−0.265500
$388$	0.700295	0.0355521
$389$	−16.6467	−0.844024	−0.422012	−	0.906590i	$-0.638676\pi$
$389$	−16.6467	−0.844024	−0.422012	+	0.906590i	$0.638676\pi$
$390$	60.9925	3.08847
$391$	−5.42969	−0.274591
$392$	6.20513	0.313406
$393$	−14.2983	−0.721255
$394$	−3.66892	−0.184837
$395$	64.3264	3.23661
$396$	0.438683	0.0220446
$397$	24.3436	1.22177	0.610886	−	0.791718i	$-0.290813\pi$
$397$	24.3436	1.22177	0.610886	+	0.791718i	$0.290813\pi$
$398$	−16.6746	−0.835823
$399$	7.11276	0.356083
$400$	13.3628	0.668141
$401$	10.5725	0.527964	0.263982	−	0.964528i	$-0.414964\pi$
$401$	10.5725	0.527964	0.263982	+	0.964528i	$0.414964\pi$
$402$	−17.7709	−0.886334
$403$	16.5482	0.824326
$404$	0.0231245	0.00115049
$405$	−47.7453	−2.37248
$406$	−0.891555	−0.0442471
$407$	−2.10019	−0.104103
$408$	11.0894	0.549008
$409$	20.4852	1.01293	0.506463	−	0.862261i	$-0.330952\pi$
$409$	20.4852	1.01293	0.506463	+	0.862261i	$0.330952\pi$
$410$	32.5992	1.60996
$411$	−16.3361	−0.805800
$412$	13.5268	0.666416
$413$	8.36604	0.411666
$414$	1.17127	0.0575646
$415$	−69.1444	−3.39417
$416$	−6.96903	−0.341685
$417$	30.3201	1.48478
$418$	1.46302	0.0715588
$419$	−7.14907	−0.349255	−0.174628	−	0.984635i	$-0.555872\pi$
$419$	−7.14907	−0.349255	−0.174628	+	0.984635i	$0.555872\pi$
$420$	−7.80282	−0.380739
$421$	0.652897	0.0318203	0.0159101	−	0.999873i	$-0.494935\pi$
$421$	0.652897	0.0318203	0.0159101	+	0.999873i	$0.494935\pi$
$422$	−22.8516	−1.11240
$423$	−6.51775	−0.316904
$424$	3.94265	0.191472
$425$	72.5560	3.51948
$426$	21.4233	1.03796
$427$	12.1239	0.586714
$428$	15.3591	0.742412
$429$	−5.33091	−0.257379
$430$	19.1088	0.921509
$431$	19.3633	0.932698	0.466349	−	0.884601i	$-0.345569\pi$
$431$	19.3633	0.932698	0.466349	+	0.884601i	$0.345569\pi$
$432$	3.73495	0.179698
$433$	−2.44692	−0.117592	−0.0587958	−	0.998270i	$-0.518726\pi$
$433$	−2.44692	−0.117592	−0.0587958	+	0.998270i	$0.518726\pi$
$434$	−2.11703	−0.101621
$435$	−8.75193	−0.419623
$436$	2.84940	0.136462
$437$	3.90621	0.186860
$438$	−21.4933	−1.02699
$439$	−28.2209	−1.34691	−0.673456	−	0.739228i	$-0.735191\pi$
$439$	−28.2209	−1.34691	−0.673456	+	0.739228i	$0.735191\pi$
$440$	−1.60496	−0.0765136
$441$	−7.26786	−0.346089
$442$	−37.8397	−1.79985
$443$	−12.8562	−0.610818	−0.305409	−	0.952221i	$-0.598793\pi$
$443$	−12.8562	−0.610818	−0.305409	+	0.952221i	$0.598793\pi$
$444$	11.4524	0.543508
$445$	−2.22760	−0.105598
$446$	11.2146	0.531025
$447$	28.0422	1.32635
$448$	0.891555	0.0421220
$449$	−38.2462	−1.80495	−0.902475	−	0.430741i	$-0.858252\pi$
$449$	−38.2462	−1.80495	−0.902475	+	0.430741i	$0.858252\pi$
$450$	−15.6514	−0.737815
$451$	−2.84926	−0.134167
$452$	7.15494	0.336540
$453$	−26.9811	−1.26768
$454$	−5.70650	−0.267819
$455$	26.6250	1.24820
$456$	−7.97792	−0.373601
$457$	6.61509	0.309441	0.154720	−	0.987958i	$-0.450552\pi$
$457$	6.61509	0.309441	0.154720	+	0.987958i	$0.450552\pi$
$458$	−8.21001	−0.383629
$459$	20.2796	0.946571
$460$	−4.28519	−0.199798
$461$	12.2758	0.571743	0.285872	−	0.958268i	$-0.407717\pi$
$461$	12.2758	0.571743	0.285872	+	0.958268i	$0.407717\pi$
$462$	0.681988	0.0317290
$463$	16.4863	0.766184	0.383092	−	0.923710i	$-0.374859\pi$
$463$	16.4863	0.766184	0.383092	+	0.923710i	$0.374859\pi$
$464$	1.00000	0.0464238
$465$	−20.7818	−0.963732
$466$	17.6884	0.819400
$467$	−2.56115	−0.118516	−0.0592579	−	0.998243i	$-0.518873\pi$
$467$	−2.56115	−0.118516	−0.0592579	+	0.998243i	$0.518873\pi$
$468$	8.16259	0.377316
$469$	−7.75755	−0.358210
$470$	23.8458	1.09992
$471$	23.7797	1.09571
$472$	−9.38365	−0.431918
$473$	−1.67016	−0.0767942
$474$	30.6587	1.40820
$475$	−52.1980	−2.39501
$476$	4.84087	0.221881
$477$	−4.61790	−0.211439
$478$	23.7964	1.08842
$479$	−22.0144	−1.00586	−0.502931	−	0.864327i	$-0.667745\pi$
$479$	−22.0144	−1.00586	−0.502931	+	0.864327i	$0.667745\pi$
$480$	8.75193	0.399469
$481$	−39.0783	−1.78182
$482$	−27.5232	−1.25365
$483$	1.82088	0.0828530
$484$	−10.8597	−0.493624
$485$	3.00090	0.136264
$486$	−11.5511	−0.523968
$487$	5.62372	0.254835	0.127418	−	0.991849i	$-0.459331\pi$
$487$	5.62372	0.254835	0.127418	+	0.991849i	$0.459331\pi$
$488$	−13.5986	−0.615578
$489$	−39.8192	−1.80069
$490$	26.5901	1.20122
$491$	−8.86601	−0.400118	−0.200059	−	0.979784i	$-0.564113\pi$
$491$	−8.86601	−0.400118	−0.200059	+	0.979784i	$0.564113\pi$
$492$	15.5372	0.700469
$493$	5.42969	0.244541
$494$	27.2225	1.22480
$495$	1.87984	0.0844924
$496$	2.37454	0.106620
$497$	9.35191	0.419490
$498$	−32.9550	−1.47675
$499$	16.9590	0.759188	0.379594	−	0.925153i	$-0.376064\pi$
$499$	16.9590	0.759188	0.379594	+	0.925153i	$0.376064\pi$
$500$	35.8363	1.60265
$501$	20.9928	0.937888
$502$	7.61124	0.339706
$503$	13.5789	0.605454	0.302727	−	0.953077i	$-0.402103\pi$
$503$	13.5789	0.605454	0.302727	+	0.953077i	$0.402103\pi$
$504$	−1.04425	−0.0465145
$505$	0.0990928	0.00440957
$506$	0.374537	0.0166502
$507$	−72.6418	−3.22614
$508$	5.49168	0.243654
$509$	−30.5170	−1.35264	−0.676321	−	0.736607i	$-0.736427\pi$
$509$	−30.5170	−1.35264	−0.676321	+	0.736607i	$0.736427\pi$
$510$	47.5202	2.10423
$511$	−9.38248	−0.415056
$512$	−1.00000	−0.0441942
$513$	−14.5895	−0.644142
$514$	12.2298	0.539434
$515$	57.9647	2.55423
$516$	9.10748	0.400934
$517$	−2.08419	−0.0916625
$518$	4.99933	0.219658
$519$	45.4035	1.99299
$520$	−29.8636	−1.30961
$521$	−16.4294	−0.719785	−0.359893	−	0.932994i	$-0.617187\pi$
$521$	−16.4294	−0.719785	−0.359893	+	0.932994i	$0.617187\pi$
$522$	−1.17127	−0.0512649
$523$	10.7893	0.471785	0.235892	−	0.971779i	$-0.424199\pi$
$523$	10.7893	0.471785	0.235892	+	0.971779i	$0.424199\pi$
$524$	7.00086	0.305834
$525$	−24.3321	−1.06194
$526$	24.6992	1.07694
$527$	12.8930	0.561628
$528$	−0.764943	−0.0332899
$529$	1.00000	0.0434783
$530$	16.8950	0.733872
$531$	10.9908	0.476958
$532$	−3.48260	−0.150990
$533$	−53.0164	−2.29640
$534$	−1.06170	−0.0459442
$535$	65.8168	2.84551
$536$	8.70115	0.375832
$537$	1.73113	0.0747037
$538$	−7.59155	−0.327295
$539$	−2.32405	−0.100104
$540$	16.0049	0.688743
$541$	20.9420	0.900367	0.450183	−	0.892936i	$-0.351359\pi$
$541$	20.9420	0.900367	0.450183	+	0.892936i	$0.351359\pi$
$542$	13.6684	0.587110
$543$	16.3991	0.703752
$544$	−5.42969	−0.232796
$545$	12.2102	0.523029
$546$	12.6898	0.543073
$547$	−16.4436	−0.703076	−0.351538	−	0.936174i	$-0.614341\pi$
$547$	−16.4436	−0.703076	−0.351538	+	0.936174i	$0.614341\pi$
$548$	7.99860	0.341683
$549$	15.9275	0.679770
$550$	−5.00488	−0.213409
$551$	−3.90621	−0.166410
$552$	−2.04237	−0.0869289
$553$	13.3834	0.569122
$554$	16.6626	0.707925
$555$	49.0758	2.08315
$556$	−14.8456	−0.629593
$557$	20.0188	0.848224	0.424112	−	0.905610i	$-0.360586\pi$
$557$	20.0188	0.848224	0.424112	+	0.905610i	$0.360586\pi$
$558$	−2.78122	−0.117738
$559$	−31.0768	−1.31441
$560$	3.82048	0.161445
$561$	−4.15340	−0.175357
$562$	−20.2319	−0.853431
$563$	−28.7306	−1.21085	−0.605426	−	0.795902i	$-0.706997\pi$
$563$	−28.7306	−1.21085	−0.605426	+	0.795902i	$0.706997\pi$
$564$	11.3652	0.478560
$565$	30.6602	1.28989
$566$	−7.44153	−0.312791
$567$	−9.93364	−0.417174
$568$	−10.4894	−0.440127
$569$	−16.0749	−0.673895	−0.336948	−	0.941523i	$-0.609395\pi$
$569$	−16.0749	−0.673895	−0.336948	+	0.941523i	$0.609395\pi$
$570$	−34.1869	−1.43193
$571$	−4.75606	−0.199035	−0.0995175	−	0.995036i	$-0.531730\pi$
$571$	−4.75606	−0.199035	−0.0995175	+	0.995036i	$0.531730\pi$
$572$	2.61016	0.109136
$573$	36.4583	1.52307
$574$	6.78244	0.283093
$575$	−13.3628	−0.557268
$576$	1.17127	0.0488028
$577$	13.3879	0.557348	0.278674	−	0.960386i	$-0.410105\pi$
$577$	13.3879	0.557348	0.278674	+	0.960386i	$0.410105\pi$
$578$	−12.4815	−0.519163
$579$	−32.7985	−1.36306
$580$	4.28519	0.177933
$581$	−14.3858	−0.596826
$582$	1.43026	0.0592862
$583$	−1.47667	−0.0611575
$584$	10.5237	0.435475
$585$	34.9782	1.44617
$586$	12.9484	0.534892
$587$	−37.8595	−1.56263	−0.781315	−	0.624137i	$-0.785451\pi$
$587$	−37.8595	−1.56263	−0.781315	+	0.624137i	$0.785451\pi$
$588$	12.6732	0.522632
$589$	−9.27545	−0.382188
$590$	−40.2107	−1.65545
$591$	−7.49328	−0.308232
$592$	−5.60742	−0.230464
$593$	−6.88125	−0.282579	−0.141290	−	0.989968i	$-0.545125\pi$
$593$	−6.88125	−0.282579	−0.141290	+	0.989968i	$0.545125\pi$
$594$	−1.39888	−0.0573966
$595$	20.7440	0.850422
$596$	−13.7303	−0.562413
$597$	−34.0557	−1.39381
$598$	6.96903	0.284985
$599$	−3.18359	−0.130078	−0.0650390	−	0.997883i	$-0.520717\pi$
$599$	−3.18359	−0.130078	−0.0650390	+	0.997883i	$0.520717\pi$
$600$	27.2918	1.11418
$601$	17.4448	0.711590	0.355795	−	0.934564i	$-0.384210\pi$
$601$	17.4448	0.711590	0.355795	+	0.934564i	$0.384210\pi$
$602$	3.97569	0.162037
$603$	−10.1914	−0.415024
$604$	13.2107	0.537536
$605$	−46.5359	−1.89195
$606$	0.0472287	0.00191854
$607$	−28.1612	−1.14303	−0.571514	−	0.820593i	$-0.693644\pi$
$607$	−28.1612	−1.14303	−0.571514	+	0.820593i	$0.693644\pi$
$608$	3.90621	0.158418
$609$	−1.82088	−0.0737859
$610$	−58.2723	−2.35938
$611$	−38.7806	−1.56890
$612$	6.35961	0.257072
$613$	−19.9646	−0.806362	−0.403181	−	0.915120i	$-0.632095\pi$
$613$	−19.9646	−0.806362	−0.403181	+	0.915120i	$0.632095\pi$
$614$	1.05304	0.0424972
$615$	66.5796	2.68475
$616$	−0.333920	−0.0134540
$617$	2.35261	0.0947127	0.0473564	−	0.998878i	$-0.484920\pi$
$617$	2.35261	0.0947127	0.0473564	+	0.998878i	$0.484920\pi$
$618$	27.6266	1.11131
$619$	7.30791	0.293730	0.146865	−	0.989157i	$-0.453082\pi$
$619$	7.30791	0.293730	0.146865	+	0.989157i	$0.453082\pi$
$620$	10.1753	0.408651
$621$	−3.73495	−0.149878
$622$	−20.9402	−0.839625
$623$	−0.463464	−0.0185683
$624$	−14.2333	−0.569789
$625$	86.7510	3.47004
$626$	29.8561	1.19329
$627$	2.98803	0.119330
$628$	−11.6432	−0.464615
$629$	−30.4466	−1.21398
$630$	−4.47480	−0.178280
$631$	−2.27129	−0.0904185	−0.0452093	−	0.998978i	$-0.514395\pi$
$631$	−2.27129	−0.0904185	−0.0452093	+	0.998978i	$0.514395\pi$
$632$	−15.0113	−0.597119
$633$	−46.6714	−1.85502
$634$	2.73637	0.108675
$635$	23.5329	0.933874
$636$	8.05235	0.319296
$637$	−43.2438	−1.71338
$638$	−0.374537	−0.0148281
$639$	12.2859	0.486024
$640$	−4.28519	−0.169387
$641$	−24.3754	−0.962772	−0.481386	−	0.876509i	$-0.659866\pi$
$641$	−24.3754	−0.962772	−0.481386	+	0.876509i	$0.659866\pi$
$642$	31.3690	1.23804
$643$	22.1345	0.872898	0.436449	−	0.899729i	$-0.356236\pi$
$643$	22.1345	0.872898	0.436449	+	0.899729i	$0.356236\pi$
$644$	−0.891555	−0.0351322
$645$	39.0272	1.53670
$646$	21.2095	0.834478
$647$	−16.5362	−0.650105	−0.325053	−	0.945696i	$-0.605382\pi$
$647$	−16.5362	−0.650105	−0.325053	+	0.945696i	$0.605382\pi$
$648$	11.1419	0.437697
$649$	3.51453	0.137957
$650$	−93.1260	−3.65270
$651$	−4.32375	−0.169461
$652$	19.4966	0.763546
$653$	−33.7546	−1.32092	−0.660460	−	0.750861i	$-0.729639\pi$
$653$	−33.7546	−1.32092	−0.660460	+	0.750861i	$0.729639\pi$
$654$	5.81953	0.227562
$655$	30.0000	1.17220
$656$	−7.60742	−0.297020
$657$	−12.3261	−0.480886
$658$	4.96124	0.193409
$659$	46.1140	1.79635	0.898173	−	0.439643i	$-0.144895\pi$
$659$	46.1140	1.79635	0.898173	+	0.439643i	$0.144895\pi$
$660$	−3.27792	−0.127593
$661$	−7.25345	−0.282126	−0.141063	−	0.990001i	$-0.545052\pi$
$661$	−7.25345	−0.282126	−0.141063	+	0.990001i	$0.545052\pi$
$662$	3.62597	0.140927
$663$	−77.2826	−3.00141
$664$	16.1357	0.626186
$665$	−14.9236	−0.578712
$666$	6.56779	0.254497
$667$	−1.00000	−0.0387202
$668$	−10.2786	−0.397693
$669$	22.9042	0.885529
$670$	37.2860	1.44049
$671$	5.09316	0.196619
$672$	1.82088	0.0702421
$673$	−18.1519	−0.699705	−0.349853	−	0.936805i	$-0.613768\pi$
$673$	−18.1519	−0.699705	−0.349853	+	0.936805i	$0.613768\pi$
$674$	4.93538	0.190104
$675$	49.9094	1.92102
$676$	35.5674	1.36798
$677$	−13.2499	−0.509235	−0.254617	−	0.967042i	$-0.581950\pi$
$677$	−13.2499	−0.509235	−0.254617	+	0.967042i	$0.581950\pi$
$678$	14.6130	0.561209
$679$	0.624352	0.0239604
$680$	−23.2672	−0.892258
$681$	−11.6548	−0.446612
$682$	−0.889353	−0.0340551
$683$	35.9850	1.37693	0.688464	−	0.725270i	$-0.258285\pi$
$683$	35.9850	1.37693	0.688464	+	0.725270i	$0.258285\pi$
$684$	−4.57522	−0.174938
$685$	34.2755	1.30960
$686$	11.7731	0.449499
$687$	−16.7679	−0.639734
$688$	−4.45927	−0.170008
$689$	−27.4765	−1.04677
$690$	−8.75193	−0.333180
$691$	39.3467	1.49682	0.748410	−	0.663237i	$-0.230818\pi$
$691$	39.3467	1.49682	0.748410	+	0.663237i	$0.230818\pi$
$692$	−22.2308	−0.845089
$693$	0.391110	0.0148570
$694$	1.99010	0.0755433
$695$	−63.6161	−2.41310
$696$	2.04237	0.0774158
$697$	−41.3060	−1.56457
$698$	−26.6487	−1.00867
$699$	36.1262	1.36642
$700$	11.9137	0.450295
$701$	12.2820	0.463886	0.231943	−	0.972729i	$-0.425492\pi$
$701$	12.2820	0.463886	0.231943	+	0.972729i	$0.425492\pi$
$702$	−26.0290	−0.982400
$703$	21.9038	0.826117
$704$	0.374537	0.0141159
$705$	48.7019	1.83422
$706$	−5.41817	−0.203915
$707$	0.0206168	0.000775373 0
$708$	−19.1649	−0.720260
$709$	−38.4410	−1.44368	−0.721841	−	0.692059i	$-0.756704\pi$
$709$	−38.4410	−1.44368	−0.721841	+	0.692059i	$0.756704\pi$
$710$	−44.9492	−1.68691
$711$	17.5823	0.659387
$712$	0.519837	0.0194817
$713$	−2.37454	−0.0889271
$714$	9.88683	0.370005
$715$	11.1850	0.418297
$716$	−0.847608	−0.0316766
$717$	48.6010	1.81504
$718$	8.69274	0.324410
$719$	−22.9317	−0.855210	−0.427605	−	0.903966i	$-0.640643\pi$
$719$	−22.9317	−0.855210	−0.427605	+	0.903966i	$0.640643\pi$
$720$	5.01909	0.187051
$721$	12.0598	0.449132
$722$	3.74150	0.139244
$723$	−56.2125	−2.09057
$724$	−8.02945	−0.298412
$725$	13.3628	0.496283
$726$	−22.1795	−0.823160
$727$	−19.3986	−0.719455	−0.359728	−	0.933057i	$-0.617130\pi$
$727$	−19.3986	−0.719455	−0.359728	+	0.933057i	$0.617130\pi$
$728$	−6.21328	−0.230279
$729$	9.83423	0.364231
$730$	45.0961	1.66908
$731$	−24.2125	−0.895530
$732$	−27.7732	−1.02653
$733$	−28.3188	−1.04598	−0.522988	−	0.852340i	$-0.675183\pi$
$733$	−28.3188	−1.04598	−0.522988	+	0.852340i	$0.675183\pi$
$734$	−7.10545	−0.262267
$735$	54.3068	2.00314
$736$	1.00000	0.0368605
$737$	−3.25890	−0.120043
$738$	8.91032	0.327993
$739$	19.2948	0.709770	0.354885	−	0.934910i	$-0.384520\pi$
$739$	19.2948	0.709770	0.354885	+	0.934910i	$0.384520\pi$
$740$	−24.0289	−0.883318
$741$	55.5984	2.04246
$742$	3.51509	0.129043
$743$	3.49816	0.128335	0.0641675	−	0.997939i	$-0.479561\pi$
$743$	3.49816	0.128335	0.0641675	+	0.997939i	$0.479561\pi$
$744$	4.84968	0.177798
$745$	−58.8367	−2.15561
$746$	−4.52726	−0.165755
$747$	−18.8992	−0.691485
$748$	2.03362	0.0743565
$749$	13.6935	0.500350
$750$	73.1908	2.67255
$751$	−20.3420	−0.742290	−0.371145	−	0.928575i	$-0.621035\pi$
$751$	−20.3420	−0.742290	−0.371145	+	0.928575i	$0.621035\pi$
$752$	−5.56470	−0.202924
$753$	15.5449	0.566489
$754$	−6.96903	−0.253797
$755$	56.6103	2.06026
$756$	3.32991	0.121108
$757$	30.8540	1.12141	0.560704	−	0.828016i	$-0.310531\pi$
$757$	30.8540	1.12141	0.560704	+	0.828016i	$0.310531\pi$
$758$	19.0357	0.691409
$759$	0.764943	0.0277657
$760$	16.7389	0.607182
$761$	−22.8509	−0.828343	−0.414172	−	0.910199i	$-0.635929\pi$
$761$	−22.8509	−0.828343	−0.414172	+	0.910199i	$0.635929\pi$
$762$	11.2160	0.406314
$763$	2.54040	0.0919686
$764$	−17.8510	−0.645827
$765$	27.2521	0.985303
$766$	25.4289	0.918784
$767$	65.3950	2.36128
$768$	−2.04237	−0.0736976
$769$	−34.3315	−1.23802	−0.619012	−	0.785381i	$-0.712467\pi$
$769$	−34.3315	−1.23802	−0.619012	+	0.785381i	$0.712467\pi$
$770$	−1.43091	−0.0515665
$771$	24.9778	0.899553
$772$	16.0590	0.577977
$773$	20.8555	0.750119	0.375059	−	0.927001i	$-0.377622\pi$
$773$	20.8555	0.750119	0.375059	+	0.927001i	$0.377622\pi$
$774$	5.22300	0.187737
$775$	31.7305	1.13979
$776$	−0.700295	−0.0251391
$777$	10.2105	0.366298
$778$	16.6467	0.596815
$779$	29.7162	1.06469
$780$	−60.9925	−2.18388
$781$	3.92868	0.140579
$782$	5.42969	0.194165
$783$	3.73495	0.133476
$784$	−6.20513	−0.221612
$785$	−49.8933	−1.78077
$786$	14.2983	0.510005
$787$	2.03963	0.0727049	0.0363525	−	0.999339i	$-0.488426\pi$
$787$	2.03963	0.0727049	0.0363525	+	0.999339i	$0.488426\pi$
$788$	3.66892	0.130700
$789$	50.4449	1.79589
$790$	−64.3264	−2.28863
$791$	6.37902	0.226812
$792$	−0.438683	−0.0155879
$793$	94.7688	3.36534
$794$	−24.3436	−0.863924
$795$	34.5058	1.22380
$796$	16.6746	0.591016
$797$	21.7674	0.771042	0.385521	−	0.922699i	$-0.374022\pi$
$797$	21.7674	0.771042	0.385521	+	0.922699i	$0.374022\pi$
$798$	−7.11276	−0.251789
$799$	−30.2146	−1.06892
$800$	−13.3628	−0.472447
$801$	−0.608868	−0.0215133
$802$	−10.5725	−0.373327
$803$	−3.94153	−0.139093
$804$	17.7709	0.626733
$805$	−3.82048	−0.134654
$806$	−16.5482	−0.582887
$807$	−15.5047	−0.545793
$808$	−0.0231245	−0.000813517 0
$809$	52.5500	1.84756	0.923781	−	0.382922i	$-0.125082\pi$
$809$	52.5500	1.84756	0.923781	+	0.382922i	$0.125082\pi$
$810$	47.7453	1.67760
$811$	21.4661	0.753778	0.376889	−	0.926259i	$-0.376994\pi$
$811$	21.4661	0.753778	0.376889	+	0.926259i	$0.376994\pi$
$812$	0.891555	0.0312874
$813$	27.9160	0.979056
$814$	2.10019	0.0736116
$815$	83.5466	2.92651
$816$	−11.0894	−0.388207
$817$	17.4189	0.609409
$818$	−20.4852	−0.716248
$819$	7.27740	0.254293
$820$	−32.5992	−1.13841
$821$	−9.48228	−0.330934	−0.165467	−	0.986215i	$-0.552913\pi$
$821$	−9.48228	−0.330934	−0.165467	+	0.986215i	$0.552913\pi$
$822$	16.3361	0.569787
$823$	−11.9806	−0.417619	−0.208809	−	0.977956i	$-0.566959\pi$
$823$	−11.9806	−0.417619	−0.208809	+	0.977956i	$0.566959\pi$
$824$	−13.5268	−0.471227
$825$	−10.2218	−0.355877
$826$	−8.36604	−0.291092
$827$	35.0000	1.21707	0.608534	−	0.793528i	$-0.291758\pi$
$827$	35.0000	1.21707	0.608534	+	0.793528i	$0.291758\pi$
$828$	−1.17127	−0.0407043
$829$	37.5641	1.30466	0.652328	−	0.757937i	$-0.273793\pi$
$829$	37.5641	1.30466	0.652328	+	0.757937i	$0.273793\pi$
$830$	69.1444	2.40004
$831$	34.0311	1.18053
$832$	6.96903	0.241608
$833$	−33.6919	−1.16736
$834$	−30.3201	−1.04990
$835$	−44.0459	−1.52427
$836$	−1.46302	−0.0505997
$837$	8.86877	0.306550
$838$	7.14907	0.246961
$839$	−54.5784	−1.88426	−0.942128	−	0.335254i	$-0.891178\pi$
$839$	−54.5784	−1.88426	−0.942128	+	0.335254i	$0.891178\pi$
$840$	7.80282	0.269223
$841$	1.00000	0.0344828
$842$	−0.652897	−0.0225003
$843$	−41.3210	−1.42317
$844$	22.8516	0.786585
$845$	152.413	5.24317
$846$	6.51775	0.224085
$847$	−9.68204	−0.332679
$848$	−3.94265	−0.135391
$849$	−15.1983	−0.521606
$850$	−72.5560	−2.48865
$851$	5.60742	0.192220
$852$	−21.4233	−0.733950
$853$	−42.0099	−1.43839	−0.719197	−	0.694807i	$-0.755490\pi$
$853$	−42.0099	−1.43839	−0.719197	+	0.694807i	$0.755490\pi$
$854$	−12.1239	−0.414870
$855$	−19.6057	−0.670499
$856$	−15.3591	−0.524965
$857$	−15.5526	−0.531267	−0.265634	−	0.964074i	$-0.585581\pi$
$857$	−15.5526	−0.531267	−0.265634	+	0.964074i	$0.585581\pi$
$858$	5.33091	0.181994
$859$	−35.6508	−1.21639	−0.608195	−	0.793788i	$-0.708106\pi$
$859$	−35.6508	−1.21639	−0.608195	+	0.793788i	$0.708106\pi$
$860$	−19.1088	−0.651605
$861$	13.8522	0.472083
$862$	−19.3633	−0.659517
$863$	3.39020	0.115404	0.0577019	−	0.998334i	$-0.481623\pi$
$863$	3.39020	0.115404	0.0577019	+	0.998334i	$0.481623\pi$
$864$	−3.73495	−0.127065
$865$	−95.2632	−3.23905
$866$	2.44692	0.0831498
$867$	−25.4919	−0.865749
$868$	2.11703	0.0718567
$869$	5.62231	0.190724
$870$	8.75193	0.296718
$871$	−60.6386	−2.05466
$872$	−2.84940	−0.0964930
$873$	0.820232	0.0277607
$874$	−3.90621	−0.132130
$875$	31.9500	1.08011
$876$	21.4933	0.726192
$877$	16.1420	0.545075	0.272538	−	0.962145i	$-0.412137\pi$
$877$	16.1420	0.545075	0.272538	+	0.962145i	$0.412137\pi$
$878$	28.2209	0.952410
$879$	26.4453	0.891979
$880$	1.60496	0.0541033
$881$	−18.1826	−0.612588	−0.306294	−	0.951937i	$-0.599089\pi$
$881$	−18.1826	−0.612588	−0.306294	+	0.951937i	$0.599089\pi$
$882$	7.26786	0.244722
$883$	35.0464	1.17941	0.589703	−	0.807620i	$-0.299245\pi$
$883$	35.0464	1.17941	0.589703	+	0.807620i	$0.299245\pi$
$884$	37.8397	1.27269
$885$	−82.1250	−2.76060
$886$	12.8562	0.431914
$887$	−41.4267	−1.39097	−0.695485	−	0.718540i	$-0.744811\pi$
$887$	−41.4267	−1.39097	−0.695485	+	0.718540i	$0.744811\pi$
$888$	−11.4524	−0.384318
$889$	4.89614	0.164211
$890$	2.22760	0.0746693
$891$	−4.17307	−0.139803
$892$	−11.2146	−0.375491
$893$	21.7369	0.727398
$894$	−28.0422	−0.937873
$895$	−3.63216	−0.121410
$896$	−0.891555	−0.0297848
$897$	14.2333	0.475237
$898$	38.2462	1.27629
$899$	2.37454	0.0791953
$900$	15.6514	0.521714
$901$	−21.4074	−0.713183
$902$	2.84926	0.0948701
$903$	8.11981	0.270210
$904$	−7.15494	−0.237970
$905$	−34.4077	−1.14375
$906$	26.9811	0.896387
$907$	−7.67801	−0.254944	−0.127472	−	0.991842i	$-0.540686\pi$
$907$	−7.67801	−0.254944	−0.127472	+	0.991842i	$0.540686\pi$
$908$	5.70650	0.189377
$909$	0.0270850	0.000898351 0
$910$	−26.6250	−0.882612
$911$	−13.9871	−0.463413	−0.231706	−	0.972786i	$-0.574431\pi$
$911$	−13.9871	−0.463413	−0.231706	+	0.972786i	$0.574431\pi$
$912$	7.97792	0.264175
$913$	−6.04342	−0.200008
$914$	−6.61509	−0.218808
$915$	−119.014	−3.93447
$916$	8.21001	0.271266
$917$	6.24165	0.206117
$918$	−20.2796	−0.669327
$919$	−38.2116	−1.26048	−0.630242	−	0.776399i	$-0.717044\pi$
$919$	−38.2116	−1.26048	−0.630242	+	0.776399i	$0.717044\pi$
$920$	4.28519	0.141278
$921$	2.15069	0.0708677
$922$	−12.2758	−0.404284
$923$	73.1012	2.40616
$924$	−0.681988	−0.0224358
$925$	−74.9310	−2.46372
$926$	−16.4863	−0.541774
$927$	15.8434	0.520367
$928$	−1.00000	−0.0328266
$929$	14.0135	0.459769	0.229885	−	0.973218i	$-0.426165\pi$
$929$	14.0135	0.459769	0.229885	+	0.973218i	$0.426165\pi$
$930$	20.7818	0.681461
$931$	24.2386	0.794387
$932$	−17.6884	−0.579403
$933$	−42.7675	−1.40015
$934$	2.56115	0.0838033
$935$	8.71445	0.284993
$936$	−8.16259	−0.266803
$937$	34.1668	1.11618	0.558090	−	0.829780i	$-0.311534\pi$
$937$	34.1668	1.11618	0.558090	+	0.829780i	$0.311534\pi$
$938$	7.75755	0.253293
$939$	60.9772	1.98992
$940$	−23.8458	−0.777764
$941$	36.7407	1.19771	0.598857	−	0.800856i	$-0.295622\pi$
$941$	36.7407	1.19771	0.598857	+	0.800856i	$0.295622\pi$
$942$	−23.7797	−0.774785
$943$	7.60742	0.247732
$944$	9.38365	0.305412
$945$	14.2693	0.464180
$946$	1.67016	0.0543017
$947$	9.27128	0.301276	0.150638	−	0.988589i	$-0.451867\pi$
$947$	9.27128	0.301276	0.150638	+	0.988589i	$0.451867\pi$
$948$	−30.6587	−0.995748
$949$	−73.3402	−2.38072
$950$	52.1980	1.69353
$951$	5.58867	0.181225
$952$	−4.84087	−0.156893
$953$	−59.4530	−1.92587	−0.962936	−	0.269728i	$-0.913066\pi$
$953$	−59.4530	−1.92587	−0.962936	+	0.269728i	$0.913066\pi$
$954$	4.61790	0.149510
$955$	−76.4949	−2.47532
$956$	−23.7964	−0.769630
$957$	−0.764943	−0.0247271
$958$	22.0144	0.711251
$959$	7.13119	0.230278
$960$	−8.75193	−0.282467
$961$	−25.3616	−0.818115
$962$	39.0783	1.25994
$963$	17.9896	0.579708
$964$	27.5232	0.886462
$965$	68.8160	2.21526
$966$	−1.82088	−0.0585859
$967$	8.39147	0.269852	0.134926	−	0.990856i	$-0.456920\pi$
$967$	8.39147	0.269852	0.134926	+	0.990856i	$0.456920\pi$
$968$	10.8597	0.349045
$969$	43.3177	1.39156
$970$	−3.00090	−0.0963530
$971$	−20.0595	−0.643739	−0.321869	−	0.946784i	$-0.604311\pi$
$971$	−20.0595	−0.643739	−0.321869	+	0.946784i	$0.604311\pi$
$972$	11.5511	0.370501
$973$	−13.2356	−0.424315
$974$	−5.62372	−0.180196
$975$	−190.198	−6.09120
$976$	13.5986	0.435279
$977$	−23.5941	−0.754842	−0.377421	−	0.926042i	$-0.623189\pi$
$977$	−23.5941	−0.754842	−0.377421	+	0.926042i	$0.623189\pi$
$978$	39.8192	1.27328
$979$	−0.194698	−0.00622259
$980$	−26.5901	−0.849391
$981$	3.33741	0.106555
$982$	8.86601	0.282926
$983$	−8.34797	−0.266259	−0.133129	−	0.991099i	$-0.542503\pi$
$983$	−8.34797	−0.266259	−0.133129	+	0.991099i	$0.542503\pi$
$984$	−15.5372	−0.495307
$985$	15.7220	0.500944
$986$	−5.42969	−0.172917
$987$	10.1327	0.322526
$988$	−27.2225	−0.866064
$989$	4.45927	0.141797
$990$	−1.87984	−0.0597452
$991$	−21.4461	−0.681258	−0.340629	−	0.940198i	$-0.610640\pi$
$991$	−21.4461	−0.681258	−0.340629	+	0.940198i	$0.610640\pi$
$992$	−2.37454	−0.0753916
$993$	7.40556	0.235008
$994$	−9.35191	−0.296624
$995$	71.4538	2.26524
$996$	32.9550	1.04422
$997$	35.0663	1.11056	0.555281	−	0.831663i	$-0.312611\pi$
$997$	35.0663	1.11056	0.555281	+	0.831663i	$0.312611\pi$
$998$	−16.9590	−0.536827
$999$	−20.9434	−0.662621

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.j.1.3	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.j.1.3	✓	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:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.04237 q^{3} +1.00000 q^{4} +4.28519 q^{5} +2.04237 q^{6} +0.891555 q^{7} -1.00000 q^{8} +1.17127 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.04237 q^{3} +1.00000 q^{4} +4.28519 q^{5} +2.04237 q^{6} +0.891555 q^{7} -1.00000 q^{8} +1.17127 q^{9} -4.28519 q^{10} +0.374537 q^{11} -2.04237 q^{12} +6.96903 q^{13} -0.891555 q^{14} -8.75193 q^{15} +1.00000 q^{16} +5.42969 q^{17} -1.17127 q^{18} -3.90621 q^{19} +4.28519 q^{20} -1.82088 q^{21} -0.374537 q^{22} -1.00000 q^{23} +2.04237 q^{24} +13.3628 q^{25} -6.96903 q^{26} +3.73495 q^{27} +0.891555 q^{28} +1.00000 q^{29} +8.75193 q^{30} +2.37454 q^{31} -1.00000 q^{32} -0.764943 q^{33} -5.42969 q^{34} +3.82048 q^{35} +1.17127 q^{36} -5.60742 q^{37} +3.90621 q^{38} -14.2333 q^{39} -4.28519 q^{40} -7.60742 q^{41} +1.82088 q^{42} -4.45927 q^{43} +0.374537 q^{44} +5.01909 q^{45} +1.00000 q^{46} -5.56470 q^{47} -2.04237 q^{48} -6.20513 q^{49} -13.3628 q^{50} -11.0894 q^{51} +6.96903 q^{52} -3.94265 q^{53} -3.73495 q^{54} +1.60496 q^{55} -0.891555 q^{56} +7.97792 q^{57} -1.00000 q^{58} +9.38365 q^{59} -8.75193 q^{60} +13.5986 q^{61} -2.37454 q^{62} +1.04425 q^{63} +1.00000 q^{64} +29.8636 q^{65} +0.764943 q^{66} -8.70115 q^{67} +5.42969 q^{68} +2.04237 q^{69} -3.82048 q^{70} +10.4894 q^{71} -1.17127 q^{72} -10.5237 q^{73} +5.60742 q^{74} -27.2918 q^{75} -3.90621 q^{76} +0.333920 q^{77} +14.2333 q^{78} +15.0113 q^{79} +4.28519 q^{80} -11.1419 q^{81} +7.60742 q^{82} -16.1357 q^{83} -1.82088 q^{84} +23.2672 q^{85} +4.45927 q^{86} -2.04237 q^{87} -0.374537 q^{88} -0.519837 q^{89} -5.01909 q^{90} +6.21328 q^{91} -1.00000 q^{92} -4.84968 q^{93} +5.56470 q^{94} -16.7389 q^{95} +2.04237 q^{96} +0.700295 q^{97} +6.20513 q^{98} +0.438683 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 5 q^{5} + 3 q^{6} + 6 q^{7} - 9 q^{8} + 14 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 5 * q^5 + 3 * q^6 + 6 * q^7 - 9 * q^8 + 14 * q^9	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 5 q^{5} + 3 q^{6} + 6 q^{7} - 9 q^{8} + 14 q^{9} - 5 q^{10} - 3 q^{11} - 3 q^{12} + 13 q^{13} - 6 q^{14} - 3 q^{15} + 9 q^{16} + 2 q^{17} - 14 q^{18} + 16 q^{19} + 5 q^{20} + 8 q^{21} + 3 q^{22} - 9 q^{23} + 3 q^{24} + 20 q^{25} - 13 q^{26} - 21 q^{27} + 6 q^{28} + 9 q^{29} + 3 q^{30} + 15 q^{31} - 9 q^{32} + 13 q^{33} - 2 q^{34} + 14 q^{36} + 12 q^{37} - 16 q^{38} - 5 q^{39} - 5 q^{40} - 6 q^{41} - 8 q^{42} - 3 q^{43} - 3 q^{44} + 20 q^{45} + 9 q^{46} - 19 q^{47} - 3 q^{48} + 37 q^{49} - 20 q^{50} + 6 q^{51} + 13 q^{52} + 5 q^{53} + 21 q^{54} + q^{55} - 6 q^{56} - 20 q^{57} - 9 q^{58} + 12 q^{59} - 3 q^{60} + 12 q^{61} - 15 q^{62} + 6 q^{63} + 9 q^{64} + 19 q^{65} - 13 q^{66} - 6 q^{67} + 2 q^{68} + 3 q^{69} + 12 q^{71} - 14 q^{72} - 12 q^{74} + 16 q^{75} + 16 q^{76} + 34 q^{77} + 5 q^{78} + 29 q^{79} + 5 q^{80} + 5 q^{81} + 6 q^{82} + 24 q^{83} + 8 q^{84} + 12 q^{85} + 3 q^{86} - 3 q^{87} + 3 q^{88} - 2 q^{89} - 20 q^{90} + 58 q^{91} - 9 q^{92} + 7 q^{93} + 19 q^{94} + 6 q^{95} + 3 q^{96} + 12 q^{97} - 37 q^{98} - 20 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 5 * q^5 + 3 * q^6 + 6 * q^7 - 9 * q^8 + 14 * q^9 - 5 * q^10 - 3 * q^11 - 3 * q^12 + 13 * q^13 - 6 * q^14 - 3 * q^15 + 9 * q^16 + 2 * q^17 - 14 * q^18 + 16 * q^19 + 5 * q^20 + 8 * q^21 + 3 * q^22 - 9 * q^23 + 3 * q^24 + 20 * q^25 - 13 * q^26 - 21 * q^27 + 6 * q^28 + 9 * q^29 + 3 * q^30 + 15 * q^31 - 9 * q^32 + 13 * q^33 - 2 * q^34 + 14 * q^36 + 12 * q^37 - 16 * q^38 - 5 * q^39 - 5 * q^40 - 6 * q^41 - 8 * q^42 - 3 * q^43 - 3 * q^44 + 20 * q^45 + 9 * q^46 - 19 * q^47 - 3 * q^48 + 37 * q^49 - 20 * q^50 + 6 * q^51 + 13 * q^52 + 5 * q^53 + 21 * q^54 + q^55 - 6 * q^56 - 20 * q^57 - 9 * q^58 + 12 * q^59 - 3 * q^60 + 12 * q^61 - 15 * q^62 + 6 * q^63 + 9 * q^64 + 19 * q^65 - 13 * q^66 - 6 * q^67 + 2 * q^68 + 3 * q^69 + 12 * q^71 - 14 * q^72 - 12 * q^74 + 16 * q^75 + 16 * q^76 + 34 * q^77 + 5 * q^78 + 29 * q^79 + 5 * q^80 + 5 * q^81 + 6 * q^82 + 24 * q^83 + 8 * q^84 + 12 * q^85 + 3 * q^86 - 3 * q^87 + 3 * q^88 - 2 * q^89 - 20 * q^90 + 58 * q^91 - 9 * q^92 + 7 * q^93 + 19 * q^94 + 6 * q^95 + 3 * q^96 + 12 * q^97 - 37 * q^98 - 20 * q^99

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