LMFDB - Embedded newform 8034.2.a.bd.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} - 36 x^{14} + 196 x^{13} + 498 x^{12} - 3101 x^{11} - 3150 x^{10} + 25368 x^{9} + \cdots - 66432 $ x^16 - 5x^15 - 36x^14 + 196x^13 + 498x^12 - 3101x^11 - 3150x^10 + 25368x^9 + 6763x^8 - 113788x^7 + 19731x^6 + 270913x^5 - 122680x^4 - 296326x^3 + 185524x^2 + 94528*x - 66432
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.86082$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.86082 q^{5} +1.00000 q^{6} +2.85228 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.86082 q^{5} +1.00000 q^{6} +2.85228 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.86082 q^{10} +1.19850 q^{11} +1.00000 q^{12} -1.00000 q^{13} +2.85228 q^{14} -2.86082 q^{15} +1.00000 q^{16} +2.96877 q^{17} +1.00000 q^{18} +2.83827 q^{19} -2.86082 q^{20} +2.85228 q^{21} +1.19850 q^{22} +0.625472 q^{23} +1.00000 q^{24} +3.18427 q^{25} -1.00000 q^{26} +1.00000 q^{27} +2.85228 q^{28} -2.58568 q^{29} -2.86082 q^{30} -0.784713 q^{31} +1.00000 q^{32} +1.19850 q^{33} +2.96877 q^{34} -8.15984 q^{35} +1.00000 q^{36} -1.41636 q^{37} +2.83827 q^{38} -1.00000 q^{39} -2.86082 q^{40} -2.32303 q^{41} +2.85228 q^{42} +2.86823 q^{43} +1.19850 q^{44} -2.86082 q^{45} +0.625472 q^{46} +2.92226 q^{47} +1.00000 q^{48} +1.13548 q^{49} +3.18427 q^{50} +2.96877 q^{51} -1.00000 q^{52} +11.0426 q^{53} +1.00000 q^{54} -3.42868 q^{55} +2.85228 q^{56} +2.83827 q^{57} -2.58568 q^{58} +10.7617 q^{59} -2.86082 q^{60} +0.277556 q^{61} -0.784713 q^{62} +2.85228 q^{63} +1.00000 q^{64} +2.86082 q^{65} +1.19850 q^{66} -5.96078 q^{67} +2.96877 q^{68} +0.625472 q^{69} -8.15984 q^{70} +12.9810 q^{71} +1.00000 q^{72} -9.67045 q^{73} -1.41636 q^{74} +3.18427 q^{75} +2.83827 q^{76} +3.41844 q^{77} -1.00000 q^{78} +11.0634 q^{79} -2.86082 q^{80} +1.00000 q^{81} -2.32303 q^{82} +5.10077 q^{83} +2.85228 q^{84} -8.49312 q^{85} +2.86823 q^{86} -2.58568 q^{87} +1.19850 q^{88} +13.6780 q^{89} -2.86082 q^{90} -2.85228 q^{91} +0.625472 q^{92} -0.784713 q^{93} +2.92226 q^{94} -8.11976 q^{95} +1.00000 q^{96} -15.6062 q^{97} +1.13548 q^{98} +1.19850 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9} + 5 q^{10} + 18 q^{11} + 16 q^{12} - 16 q^{13} + 4 q^{14} + 5 q^{15} + 16 q^{16} + 17 q^{17} + 16 q^{18} + 8 q^{19} + 5 q^{20} + 4 q^{21} + 18 q^{22} + 9 q^{23} + 16 q^{24} + 17 q^{25} - 16 q^{26} + 16 q^{27} + 4 q^{28} + 14 q^{29} + 5 q^{30} + 12 q^{31} + 16 q^{32} + 18 q^{33} + 17 q^{34} + 16 q^{35} + 16 q^{36} + 31 q^{37} + 8 q^{38} - 16 q^{39} + 5 q^{40} + 29 q^{41} + 4 q^{42} + 30 q^{43} + 18 q^{44} + 5 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 36 q^{49} + 17 q^{50} + 17 q^{51} - 16 q^{52} + 12 q^{53} + 16 q^{54} + 30 q^{55} + 4 q^{56} + 8 q^{57} + 14 q^{58} + 38 q^{59} + 5 q^{60} + 12 q^{62} + 4 q^{63} + 16 q^{64} - 5 q^{65} + 18 q^{66} + 28 q^{67} + 17 q^{68} + 9 q^{69} + 16 q^{70} + 32 q^{71} + 16 q^{72} + 20 q^{73} + 31 q^{74} + 17 q^{75} + 8 q^{76} + 26 q^{77} - 16 q^{78} + 13 q^{79} + 5 q^{80} + 16 q^{81} + 29 q^{82} + 39 q^{83} + 4 q^{84} + 31 q^{85} + 30 q^{86} + 14 q^{87} + 18 q^{88} + 9 q^{89} + 5 q^{90} - 4 q^{91} + 9 q^{92} + 12 q^{93} - q^{94} - 20 q^{95} + 16 q^{96} + 35 q^{97} + 36 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9 + 5 * q^10 + 18 * q^11 + 16 * q^12 - 16 * q^13 + 4 * q^14 + 5 * q^15 + 16 * q^16 + 17 * q^17 + 16 * q^18 + 8 * q^19 + 5 * q^20 + 4 * q^21 + 18 * q^22 + 9 * q^23 + 16 * q^24 + 17 * q^25 - 16 * q^26 + 16 * q^27 + 4 * q^28 + 14 * q^29 + 5 * q^30 + 12 * q^31 + 16 * q^32 + 18 * q^33 + 17 * q^34 + 16 * q^35 + 16 * q^36 + 31 * q^37 + 8 * q^38 - 16 * q^39 + 5 * q^40 + 29 * q^41 + 4 * q^42 + 30 * q^43 + 18 * q^44 + 5 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 36 * q^49 + 17 * q^50 + 17 * q^51 - 16 * q^52 + 12 * q^53 + 16 * q^54 + 30 * q^55 + 4 * q^56 + 8 * q^57 + 14 * q^58 + 38 * q^59 + 5 * q^60 + 12 * q^62 + 4 * q^63 + 16 * q^64 - 5 * q^65 + 18 * q^66 + 28 * q^67 + 17 * q^68 + 9 * q^69 + 16 * q^70 + 32 * q^71 + 16 * q^72 + 20 * q^73 + 31 * q^74 + 17 * q^75 + 8 * q^76 + 26 * q^77 - 16 * q^78 + 13 * q^79 + 5 * q^80 + 16 * q^81 + 29 * q^82 + 39 * q^83 + 4 * q^84 + 31 * q^85 + 30 * q^86 + 14 * q^87 + 18 * q^88 + 9 * q^89 + 5 * q^90 - 4 * q^91 + 9 * q^92 + 12 * q^93 - q^94 - 20 * q^95 + 16 * q^96 + 35 * q^97 + 36 * q^98 + 18 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−2.86082	−1.27940	−0.639698	−	0.768626i	$-0.720941\pi$
$5$	−2.86082	−1.27940	−0.639698	+	0.768626i	$0.720941\pi$
$6$	1.00000	0.408248
$7$	2.85228	1.07806	0.539030	−	0.842287i	$-0.318791\pi$
$7$	2.85228	1.07806	0.539030	+	0.842287i	$0.318791\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.86082	−0.904669
$11$	1.19850	0.361360	0.180680	−	0.983542i	$-0.442170\pi$
$11$	1.19850	0.361360	0.180680	+	0.983542i	$0.442170\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.85228	0.762303
$15$	−2.86082	−0.738660
$16$	1.00000	0.250000
$17$	2.96877	0.720033	0.360017	−	0.932946i	$-0.382771\pi$
$17$	2.96877	0.720033	0.360017	+	0.932946i	$0.382771\pi$
$18$	1.00000	0.235702
$19$	2.83827	0.651143	0.325572	−	0.945517i	$-0.394443\pi$
$19$	2.83827	0.651143	0.325572	+	0.945517i	$0.394443\pi$
$20$	−2.86082	−0.639698
$21$	2.85228	0.622418
$22$	1.19850	0.255520
$23$	0.625472	0.130420	0.0652099	−	0.997872i	$-0.479228\pi$
$23$	0.625472	0.130420	0.0652099	+	0.997872i	$0.479228\pi$
$24$	1.00000	0.204124
$25$	3.18427	0.636854
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	2.85228	0.539030
$29$	−2.58568	−0.480149	−0.240074	−	0.970755i	$-0.577172\pi$
$29$	−2.58568	−0.480149	−0.240074	+	0.970755i	$0.577172\pi$
$30$	−2.86082	−0.522311
$31$	−0.784713	−0.140939	−0.0704693	−	0.997514i	$-0.522450\pi$
$31$	−0.784713	−0.140939	−0.0704693	+	0.997514i	$0.522450\pi$
$32$	1.00000	0.176777
$33$	1.19850	0.208631
$34$	2.96877	0.509141
$35$	−8.15984	−1.37926
$36$	1.00000	0.166667
$37$	−1.41636	−0.232848	−0.116424	−	0.993200i	$-0.537143\pi$
$37$	−1.41636	−0.232848	−0.116424	+	0.993200i	$0.537143\pi$
$38$	2.83827	0.460428
$39$	−1.00000	−0.160128
$40$	−2.86082	−0.452335
$41$	−2.32303	−0.362796	−0.181398	−	0.983410i	$-0.558062\pi$
$41$	−2.32303	−0.362796	−0.181398	+	0.983410i	$0.558062\pi$
$42$	2.85228	0.440116
$43$	2.86823	0.437400	0.218700	−	0.975792i	$-0.429818\pi$
$43$	2.86823	0.437400	0.218700	+	0.975792i	$0.429818\pi$
$44$	1.19850	0.180680
$45$	−2.86082	−0.426465
$46$	0.625472	0.0922208
$47$	2.92226	0.426256	0.213128	−	0.977024i	$-0.431635\pi$
$47$	2.92226	0.426256	0.213128	+	0.977024i	$0.431635\pi$
$48$	1.00000	0.144338
$49$	1.13548	0.162212
$50$	3.18427	0.450324
$51$	2.96877	0.415712
$52$	−1.00000	−0.138675
$53$	11.0426	1.51682	0.758409	−	0.651779i	$-0.225977\pi$
$53$	11.0426	1.51682	0.758409	+	0.651779i	$0.225977\pi$
$54$	1.00000	0.136083
$55$	−3.42868	−0.462323
$56$	2.85228	0.381152
$57$	2.83827	0.375938
$58$	−2.58568	−0.339516
$59$	10.7617	1.40105	0.700526	−	0.713627i	$-0.252949\pi$
$59$	10.7617	1.40105	0.700526	+	0.713627i	$0.252949\pi$
$60$	−2.86082	−0.369330
$61$	0.277556	0.0355375	0.0177687	−	0.999842i	$-0.494344\pi$
$61$	0.277556	0.0355375	0.0177687	+	0.999842i	$0.494344\pi$
$62$	−0.784713	−0.0996586
$63$	2.85228	0.359353
$64$	1.00000	0.125000
$65$	2.86082	0.354841
$66$	1.19850	0.147525
$67$	−5.96078	−0.728225	−0.364112	−	0.931355i	$-0.618628\pi$
$67$	−5.96078	−0.728225	−0.364112	+	0.931355i	$0.618628\pi$
$68$	2.96877	0.360017
$69$	0.625472	0.0752979
$70$	−8.15984	−0.975287
$71$	12.9810	1.54057	0.770283	−	0.637702i	$-0.220115\pi$
$71$	12.9810	1.54057	0.770283	+	0.637702i	$0.220115\pi$
$72$	1.00000	0.117851
$73$	−9.67045	−1.13184	−0.565920	−	0.824460i	$-0.691479\pi$
$73$	−9.67045	−1.13184	−0.565920	+	0.824460i	$0.691479\pi$
$74$	−1.41636	−0.164648
$75$	3.18427	0.367688
$76$	2.83827	0.325572
$77$	3.41844	0.389568
$78$	−1.00000	−0.113228
$79$	11.0634	1.24473	0.622363	−	0.782729i	$-0.286173\pi$
$79$	11.0634	1.24473	0.622363	+	0.782729i	$0.286173\pi$
$80$	−2.86082	−0.319849
$81$	1.00000	0.111111
$82$	−2.32303	−0.256535
$83$	5.10077	0.559882	0.279941	−	0.960017i	$-0.409685\pi$
$83$	5.10077	0.559882	0.279941	+	0.960017i	$0.409685\pi$
$84$	2.85228	0.311209
$85$	−8.49312	−0.921208
$86$	2.86823	0.309289
$87$	−2.58568	−0.277214
$88$	1.19850	0.127760
$89$	13.6780	1.44986	0.724931	−	0.688822i	$-0.241872\pi$
$89$	13.6780	1.44986	0.724931	+	0.688822i	$0.241872\pi$
$90$	−2.86082	−0.301556
$91$	−2.85228	−0.299000
$92$	0.625472	0.0652099
$93$	−0.784713	−0.0813709
$94$	2.92226	0.301408
$95$	−8.11976	−0.833070
$96$	1.00000	0.102062
$97$	−15.6062	−1.58457	−0.792284	−	0.610153i	$-0.791108\pi$
$97$	−15.6062	−1.58457	−0.792284	+	0.610153i	$0.791108\pi$
$98$	1.13548	0.114701
$99$	1.19850	0.120453
$100$	3.18427	0.318427
$101$	−9.79121	−0.974262	−0.487131	−	0.873329i	$-0.661957\pi$
$101$	−9.79121	−0.974262	−0.487131	+	0.873329i	$0.661957\pi$
$102$	2.96877	0.293952
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	−8.15984	−0.796319
$106$	11.0426	1.07255
$107$	12.7422	1.23184	0.615918	−	0.787811i	$-0.288785\pi$
$107$	12.7422	1.23184	0.615918	+	0.787811i	$0.288785\pi$
$108$	1.00000	0.0962250
$109$	3.98561	0.381752	0.190876	−	0.981614i	$-0.438867\pi$
$109$	3.98561	0.381752	0.190876	+	0.981614i	$0.438867\pi$
$110$	−3.42868	−0.326911
$111$	−1.41636	−0.134435
$112$	2.85228	0.269515
$113$	3.21426	0.302372	0.151186	−	0.988505i	$-0.451691\pi$
$113$	3.21426	0.302372	0.151186	+	0.988505i	$0.451691\pi$
$114$	2.83827	0.265828
$115$	−1.78936	−0.166859
$116$	−2.58568	−0.240074
$117$	−1.00000	−0.0924500
$118$	10.7617	0.990694
$119$	8.46777	0.776239
$120$	−2.86082	−0.261156
$121$	−9.56361	−0.869419
$122$	0.277556	0.0251288
$123$	−2.32303	−0.209460
$124$	−0.784713	−0.0704693
$125$	5.19447	0.464608
$126$	2.85228	0.254101
$127$	−20.2683	−1.79852	−0.899260	−	0.437415i	$-0.855894\pi$
$127$	−20.2683	−1.79852	−0.899260	+	0.437415i	$0.855894\pi$
$128$	1.00000	0.0883883
$129$	2.86823	0.252533
$130$	2.86082	0.250910
$131$	−21.2785	−1.85911	−0.929555	−	0.368684i	$-0.879808\pi$
$131$	−21.2785	−1.85911	−0.929555	+	0.368684i	$0.879808\pi$
$132$	1.19850	0.104316
$133$	8.09552	0.701971
$134$	−5.96078	−0.514933
$135$	−2.86082	−0.246220
$136$	2.96877	0.254570
$137$	8.97192	0.766523	0.383262	−	0.923640i	$-0.374801\pi$
$137$	8.97192	0.766523	0.383262	+	0.923640i	$0.374801\pi$
$138$	0.625472	0.0532437
$139$	10.8246	0.918133	0.459066	−	0.888402i	$-0.348184\pi$
$139$	10.8246	0.918133	0.459066	+	0.888402i	$0.348184\pi$
$140$	−8.15984	−0.689632
$141$	2.92226	0.246099
$142$	12.9810	1.08934
$143$	−1.19850	−0.100223
$144$	1.00000	0.0833333
$145$	7.39715	0.614300
$146$	−9.67045	−0.800332
$147$	1.13548	0.0936531
$148$	−1.41636	−0.116424
$149$	−13.0661	−1.07042	−0.535210	−	0.844719i	$-0.679767\pi$
$149$	−13.0661	−1.07042	−0.535210	+	0.844719i	$0.679767\pi$
$150$	3.18427	0.259994
$151$	−15.6045	−1.26988	−0.634940	−	0.772561i	$-0.718975\pi$
$151$	−15.6045	−1.26988	−0.634940	+	0.772561i	$0.718975\pi$
$152$	2.83827	0.230214
$153$	2.96877	0.240011
$154$	3.41844	0.275466
$155$	2.24492	0.180316
$156$	−1.00000	−0.0800641
$157$	9.80497	0.782522	0.391261	−	0.920280i	$-0.372039\pi$
$157$	9.80497	0.782522	0.391261	+	0.920280i	$0.372039\pi$
$158$	11.0634	0.880154
$159$	11.0426	0.875735
$160$	−2.86082	−0.226167
$161$	1.78402	0.140600
$162$	1.00000	0.0785674
$163$	−0.739601	−0.0579300	−0.0289650	−	0.999580i	$-0.509221\pi$
$163$	−0.739601	−0.0579300	−0.0289650	+	0.999580i	$0.509221\pi$
$164$	−2.32303	−0.181398
$165$	−3.42868	−0.266922
$166$	5.10077	0.395897
$167$	9.43205	0.729874	0.364937	−	0.931032i	$-0.381091\pi$
$167$	9.43205	0.729874	0.364937	+	0.931032i	$0.381091\pi$
$168$	2.85228	0.220058
$169$	1.00000	0.0769231
$170$	−8.49312	−0.651392
$171$	2.83827	0.217048
$172$	2.86823	0.218700
$173$	−8.78926	−0.668235	−0.334118	−	0.942531i	$-0.608438\pi$
$173$	−8.78926	−0.668235	−0.334118	+	0.942531i	$0.608438\pi$
$174$	−2.58568	−0.196020
$175$	9.08241	0.686566
$176$	1.19850	0.0903400
$177$	10.7617	0.808898
$178$	13.6780	1.02521
$179$	3.29520	0.246295	0.123147	−	0.992388i	$-0.460701\pi$
$179$	3.29520	0.246295	0.123147	+	0.992388i	$0.460701\pi$
$180$	−2.86082	−0.213233
$181$	21.6431	1.60872	0.804360	−	0.594142i	$-0.202508\pi$
$181$	21.6431	1.60872	0.804360	+	0.594142i	$0.202508\pi$
$182$	−2.85228	−0.211425
$183$	0.277556	0.0205176
$184$	0.625472	0.0461104
$185$	4.05194	0.297905
$186$	−0.784713	−0.0575379
$187$	3.55806	0.260191
$188$	2.92226	0.213128
$189$	2.85228	0.207473
$190$	−8.11976	−0.589069
$191$	7.68710	0.556219	0.278110	−	0.960549i	$-0.410292\pi$
$191$	7.68710	0.556219	0.278110	+	0.960549i	$0.410292\pi$
$192$	1.00000	0.0721688
$193$	7.69396	0.553824	0.276912	−	0.960895i	$-0.410689\pi$
$193$	7.69396	0.553824	0.276912	+	0.960895i	$0.410689\pi$
$194$	−15.6062	−1.12046
$195$	2.86082	0.204867
$196$	1.13548	0.0811060
$197$	1.72631	0.122995	0.0614973	−	0.998107i	$-0.480412\pi$
$197$	1.72631	0.122995	0.0614973	+	0.998107i	$0.480412\pi$
$198$	1.19850	0.0851734
$199$	−20.4133	−1.44706	−0.723529	−	0.690294i	$-0.757481\pi$
$199$	−20.4133	−1.44706	−0.723529	+	0.690294i	$0.757481\pi$
$200$	3.18427	0.225162
$201$	−5.96078	−0.420441
$202$	−9.79121	−0.688907
$203$	−7.37507	−0.517629
$204$	2.96877	0.207856
$205$	6.64575	0.464160
$206$	1.00000	0.0696733
$207$	0.625472	0.0434733
$208$	−1.00000	−0.0693375
$209$	3.40165	0.235297
$210$	−8.15984	−0.563082
$211$	9.15406	0.630191	0.315096	−	0.949060i	$-0.397963\pi$
$211$	9.15406	0.630191	0.315096	+	0.949060i	$0.397963\pi$
$212$	11.0426	0.758409
$213$	12.9810	0.889446
$214$	12.7422	0.871039
$215$	−8.20547	−0.559608
$216$	1.00000	0.0680414
$217$	−2.23822	−0.151940
$218$	3.98561	0.269939
$219$	−9.67045	−0.653468
$220$	−3.42868	−0.231161
$221$	−2.96877	−0.199701
$222$	−1.41636	−0.0950598
$223$	−2.76710	−0.185299	−0.0926494	−	0.995699i	$-0.529534\pi$
$223$	−2.76710	−0.185299	−0.0926494	+	0.995699i	$0.529534\pi$
$224$	2.85228	0.190576
$225$	3.18427	0.212285
$226$	3.21426	0.213809
$227$	17.4139	1.15580	0.577902	−	0.816106i	$-0.303872\pi$
$227$	17.4139	1.15580	0.577902	+	0.816106i	$0.303872\pi$
$228$	2.83827	0.187969
$229$	22.6709	1.49813	0.749067	−	0.662494i	$-0.230502\pi$
$229$	22.6709	1.49813	0.749067	+	0.662494i	$0.230502\pi$
$230$	−1.78936	−0.117987
$231$	3.41844	0.224917
$232$	−2.58568	−0.169758
$233$	29.7069	1.94616	0.973081	−	0.230463i	$-0.0740241\pi$
$233$	29.7069	1.94616	0.973081	+	0.230463i	$0.0740241\pi$
$234$	−1.00000	−0.0653720
$235$	−8.36005	−0.545350
$236$	10.7617	0.700526
$237$	11.0634	0.718642
$238$	8.46777	0.548884
$239$	22.4519	1.45229	0.726147	−	0.687539i	$-0.241309\pi$
$239$	22.4519	1.45229	0.726147	+	0.687539i	$0.241309\pi$
$240$	−2.86082	−0.184665
$241$	9.22740	0.594389	0.297195	−	0.954817i	$-0.403949\pi$
$241$	9.22740	0.594389	0.297195	+	0.954817i	$0.403949\pi$
$242$	−9.56361	−0.614772
$243$	1.00000	0.0641500
$244$	0.277556	0.0177687
$245$	−3.24841	−0.207533
$246$	−2.32303	−0.148111
$247$	−2.83827	−0.180595
$248$	−0.784713	−0.0498293
$249$	5.10077	0.323248
$250$	5.19447	0.328527
$251$	20.3594	1.28507	0.642537	−	0.766255i	$-0.277882\pi$
$251$	20.3594	1.28507	0.642537	+	0.766255i	$0.277882\pi$
$252$	2.85228	0.179677
$253$	0.749625	0.0471285
$254$	−20.2683	−1.27175
$255$	−8.49312	−0.531860
$256$	1.00000	0.0625000
$257$	−23.8138	−1.48546	−0.742732	−	0.669588i	$-0.766471\pi$
$257$	−23.8138	−1.48546	−0.742732	+	0.669588i	$0.766471\pi$
$258$	2.86823	0.178568
$259$	−4.03985	−0.251024
$260$	2.86082	0.177420
$261$	−2.58568	−0.160050
$262$	−21.2785	−1.31459
$263$	19.2080	1.18442	0.592209	−	0.805784i	$-0.298256\pi$
$263$	19.2080	1.18442	0.592209	+	0.805784i	$0.298256\pi$
$264$	1.19850	0.0737623
$265$	−31.5908	−1.94061
$266$	8.09552	0.496368
$267$	13.6780	0.837078
$268$	−5.96078	−0.364112
$269$	−16.6653	−1.01610	−0.508050	−	0.861327i	$-0.669634\pi$
$269$	−16.6653	−1.01610	−0.508050	+	0.861327i	$0.669634\pi$
$270$	−2.86082	−0.174104
$271$	29.3009	1.77990	0.889952	−	0.456054i	$-0.150737\pi$
$271$	29.3009	1.77990	0.889952	+	0.456054i	$0.150737\pi$
$272$	2.96877	0.180008
$273$	−2.85228	−0.172628
$274$	8.97192	0.542014
$275$	3.81633	0.230133
$276$	0.625472	0.0376490
$277$	−8.75114	−0.525805	−0.262902	−	0.964822i	$-0.584680\pi$
$277$	−8.75114	−0.525805	−0.262902	+	0.964822i	$0.584680\pi$
$278$	10.8246	0.649218
$279$	−0.784713	−0.0469795
$280$	−8.15984	−0.487644
$281$	28.5421	1.70268	0.851340	−	0.524615i	$-0.175791\pi$
$281$	28.5421	1.70268	0.851340	+	0.524615i	$0.175791\pi$
$282$	2.92226	0.174018
$283$	18.4172	1.09479	0.547394	−	0.836875i	$-0.315620\pi$
$283$	18.4172	1.09479	0.547394	+	0.836875i	$0.315620\pi$
$284$	12.9810	0.770283
$285$	−8.11976	−0.480973
$286$	−1.19850	−0.0708685
$287$	−6.62592	−0.391115
$288$	1.00000	0.0589256
$289$	−8.18638	−0.481552
$290$	7.39715	0.434376
$291$	−15.6062	−0.914850
$292$	−9.67045	−0.565920
$293$	−26.1437	−1.52733	−0.763665	−	0.645613i	$-0.776602\pi$
$293$	−26.1437	−1.52733	−0.763665	+	0.645613i	$0.776602\pi$
$294$	1.13548	0.0662228
$295$	−30.7872	−1.79250
$296$	−1.41636	−0.0823242
$297$	1.19850	0.0695438
$298$	−13.0661	−0.756901
$299$	−0.625472	−0.0361720
$300$	3.18427	0.183844
$301$	8.18097	0.471544
$302$	−15.6045	−0.897941
$303$	−9.79121	−0.562491
$304$	2.83827	0.162786
$305$	−0.794038	−0.0454665
$306$	2.96877	0.169714
$307$	23.1197	1.31951	0.659757	−	0.751479i	$-0.270659\pi$
$307$	23.1197	1.31951	0.659757	+	0.751479i	$0.270659\pi$
$308$	3.41844	0.194784
$309$	1.00000	0.0568880
$310$	2.24492	0.127503
$311$	0.181499	0.0102919	0.00514593	−	0.999987i	$-0.498362\pi$
$311$	0.181499	0.0102919	0.00514593	+	0.999987i	$0.498362\pi$
$312$	−1.00000	−0.0566139
$313$	−26.2705	−1.48490	−0.742448	−	0.669904i	$-0.766335\pi$
$313$	−26.2705	−1.48490	−0.742448	+	0.669904i	$0.766335\pi$
$314$	9.80497	0.553327
$315$	−8.15984	−0.459755
$316$	11.0634	0.622363
$317$	−21.9172	−1.23099	−0.615497	−	0.788139i	$-0.711045\pi$
$317$	−21.9172	−1.23099	−0.615497	+	0.788139i	$0.711045\pi$
$318$	11.0426	0.619238
$319$	−3.09893	−0.173507
$320$	−2.86082	−0.159924
$321$	12.7422	0.711200
$322$	1.78402	0.0994195
$323$	8.42617	0.468845
$324$	1.00000	0.0555556
$325$	−3.18427	−0.176631
$326$	−0.739601	−0.0409627
$327$	3.98561	0.220404
$328$	−2.32303	−0.128268
$329$	8.33510	0.459529
$330$	−3.42868	−0.188742
$331$	8.20752	0.451126	0.225563	−	0.974229i	$-0.427578\pi$
$331$	8.20752	0.451126	0.225563	+	0.974229i	$0.427578\pi$
$332$	5.10077	0.279941
$333$	−1.41636	−0.0776160
$334$	9.43205	0.516099
$335$	17.0527	0.931688
$336$	2.85228	0.155604
$337$	−6.11072	−0.332872	−0.166436	−	0.986052i	$-0.553226\pi$
$337$	−6.11072	−0.332872	−0.166436	+	0.986052i	$0.553226\pi$
$338$	1.00000	0.0543928
$339$	3.21426	0.174574
$340$	−8.49312	−0.460604
$341$	−0.940475	−0.0509296
$342$	2.83827	0.153476
$343$	−16.7272	−0.903185
$344$	2.86823	0.154644
$345$	−1.78936	−0.0963359
$346$	−8.78926	−0.472514
$347$	10.3267	0.554366	0.277183	−	0.960817i	$-0.410599\pi$
$347$	10.3267	0.554366	0.277183	+	0.960817i	$0.410599\pi$
$348$	−2.58568	−0.138607
$349$	−16.9721	−0.908494	−0.454247	−	0.890876i	$-0.650092\pi$
$349$	−16.9721	−0.908494	−0.454247	+	0.890876i	$0.650092\pi$
$350$	9.08241	0.485475
$351$	−1.00000	−0.0533761
$352$	1.19850	0.0638800
$353$	−26.0421	−1.38608	−0.693040	−	0.720900i	$-0.743729\pi$
$353$	−26.0421	−1.38608	−0.693040	+	0.720900i	$0.743729\pi$
$354$	10.7617	0.571977
$355$	−37.1364	−1.97099
$356$	13.6780	0.724931
$357$	8.46777	0.448162
$358$	3.29520	0.174157
$359$	5.50478	0.290531	0.145266	−	0.989393i	$-0.453596\pi$
$359$	5.50478	0.290531	0.145266	+	0.989393i	$0.453596\pi$
$360$	−2.86082	−0.150778
$361$	−10.9442	−0.576013
$362$	21.6431	1.13754
$363$	−9.56361	−0.501959
$364$	−2.85228	−0.149500
$365$	27.6654	1.44807
$366$	0.277556	0.0145081
$367$	11.1371	0.581353	0.290677	−	0.956821i	$-0.406120\pi$
$367$	11.1371	0.581353	0.290677	+	0.956821i	$0.406120\pi$
$368$	0.625472	0.0326050
$369$	−2.32303	−0.120932
$370$	4.05194	0.210650
$371$	31.4965	1.63522
$372$	−0.784713	−0.0406855
$373$	−8.70720	−0.450842	−0.225421	−	0.974261i	$-0.572376\pi$
$373$	−8.70720	−0.450842	−0.225421	+	0.974261i	$0.572376\pi$
$374$	3.55806	0.183983
$375$	5.19447	0.268242
$376$	2.92226	0.150704
$377$	2.58568	0.133169
$378$	2.85228	0.146705
$379$	25.3071	1.29994	0.649969	−	0.759961i	$-0.274782\pi$
$379$	25.3071	1.29994	0.649969	+	0.759961i	$0.274782\pi$
$380$	−8.11976	−0.416535
$381$	−20.2683	−1.03838
$382$	7.68710	0.393306
$383$	−4.02289	−0.205560	−0.102780	−	0.994704i	$-0.532774\pi$
$383$	−4.02289	−0.205560	−0.102780	+	0.994704i	$0.532774\pi$
$384$	1.00000	0.0510310
$385$	−9.77953	−0.498411
$386$	7.69396	0.391612
$387$	2.86823	0.145800
$388$	−15.6062	−0.792284
$389$	14.0322	0.711459	0.355729	−	0.934589i	$-0.384232\pi$
$389$	14.0322	0.711459	0.355729	+	0.934589i	$0.384232\pi$
$390$	2.86082	0.144863
$391$	1.85688	0.0939067
$392$	1.13548	0.0573506
$393$	−21.2785	−1.07336
$394$	1.72631	0.0869703
$395$	−31.6502	−1.59250
$396$	1.19850	0.0602267
$397$	−5.96104	−0.299176	−0.149588	−	0.988748i	$-0.547795\pi$
$397$	−5.96104	−0.299176	−0.149588	+	0.988748i	$0.547795\pi$
$398$	−20.4133	−1.02322
$399$	8.09552	0.405283
$400$	3.18427	0.159213
$401$	4.14882	0.207182	0.103591	−	0.994620i	$-0.466967\pi$
$401$	4.14882	0.207182	0.103591	+	0.994620i	$0.466967\pi$
$402$	−5.96078	−0.297297
$403$	0.784713	0.0390893
$404$	−9.79121	−0.487131
$405$	−2.86082	−0.142155
$406$	−7.37507	−0.366019
$407$	−1.69750	−0.0841420
$408$	2.96877	0.146976
$409$	−9.33705	−0.461688	−0.230844	−	0.972991i	$-0.574149\pi$
$409$	−9.33705	−0.461688	−0.230844	+	0.972991i	$0.574149\pi$
$410$	6.64575	0.328210
$411$	8.97192	0.442552
$412$	1.00000	0.0492665
$413$	30.6953	1.51042
$414$	0.625472	0.0307403
$415$	−14.5924	−0.716311
$416$	−1.00000	−0.0490290
$417$	10.8246	0.530084
$418$	3.40165	0.166380
$419$	−3.15521	−0.154142	−0.0770709	−	0.997026i	$-0.524557\pi$
$419$	−3.15521	−0.154142	−0.0770709	+	0.997026i	$0.524557\pi$
$420$	−8.15984	−0.398159
$421$	−26.1807	−1.27597	−0.637984	−	0.770049i	$-0.720232\pi$
$421$	−26.1807	−1.27597	−0.637984	+	0.770049i	$0.720232\pi$
$422$	9.15406	0.445613
$423$	2.92226	0.142085
$424$	11.0426	0.536276
$425$	9.45337	0.458556
$426$	12.9810	0.628933
$427$	0.791668	0.0383115
$428$	12.7422	0.615918
$429$	−1.19850	−0.0578639
$430$	−8.20547	−0.395703
$431$	−15.0601	−0.725418	−0.362709	−	0.931902i	$-0.618148\pi$
$431$	−15.0601	−0.725418	−0.362709	+	0.931902i	$0.618148\pi$
$432$	1.00000	0.0481125
$433$	−9.53858	−0.458395	−0.229197	−	0.973380i	$-0.573610\pi$
$433$	−9.53858	−0.458395	−0.229197	+	0.973380i	$0.573610\pi$
$434$	−2.23822	−0.107438
$435$	7.39715	0.354666
$436$	3.98561	0.190876
$437$	1.77526	0.0849220
$438$	−9.67045	−0.462072
$439$	9.30792	0.444243	0.222121	−	0.975019i	$-0.428702\pi$
$439$	9.30792	0.444243	0.222121	+	0.975019i	$0.428702\pi$
$440$	−3.42868	−0.163456
$441$	1.13548	0.0540707
$442$	−2.96877	−0.141210
$443$	17.0382	0.809511	0.404755	−	0.914425i	$-0.367357\pi$
$443$	17.0382	0.809511	0.404755	+	0.914425i	$0.367357\pi$
$444$	−1.41636	−0.0672174
$445$	−39.1301	−1.85495
$446$	−2.76710	−0.131026
$447$	−13.0661	−0.618007
$448$	2.85228	0.134757
$449$	3.53749	0.166944	0.0834722	−	0.996510i	$-0.473399\pi$
$449$	3.53749	0.166944	0.0834722	+	0.996510i	$0.473399\pi$
$450$	3.18427	0.150108
$451$	−2.78414	−0.131100
$452$	3.21426	0.151186
$453$	−15.6045	−0.733166
$454$	17.4139	0.817277
$455$	8.15984	0.382539
$456$	2.83827	0.132914
$457$	−26.9509	−1.26071	−0.630355	−	0.776307i	$-0.717090\pi$
$457$	−26.9509	−1.26071	−0.630355	+	0.776307i	$0.717090\pi$
$458$	22.6709	1.05934
$459$	2.96877	0.138571
$460$	−1.78936	−0.0834293
$461$	−27.4475	−1.27836	−0.639179	−	0.769058i	$-0.720726\pi$
$461$	−27.4475	−1.27836	−0.639179	+	0.769058i	$0.720726\pi$
$462$	3.41844	0.159040
$463$	15.0972	0.701626	0.350813	−	0.936446i	$-0.385905\pi$
$463$	15.0972	0.701626	0.350813	+	0.936446i	$0.385905\pi$
$464$	−2.58568	−0.120037
$465$	2.24492	0.104106
$466$	29.7069	1.37614
$467$	41.3324	1.91264	0.956319	−	0.292326i	$-0.0944292\pi$
$467$	41.3324	1.91264	0.956319	+	0.292326i	$0.0944292\pi$
$468$	−1.00000	−0.0462250
$469$	−17.0018	−0.785070
$470$	−8.36005	−0.385620
$471$	9.80497	0.451789
$472$	10.7617	0.495347
$473$	3.43756	0.158059
$474$	11.0634	0.508157
$475$	9.03780	0.414683
$476$	8.46777	0.388119
$477$	11.0426	0.505606
$478$	22.4519	1.02693
$479$	−1.84771	−0.0844241	−0.0422121	−	0.999109i	$-0.513441\pi$
$479$	−1.84771	−0.0844241	−0.0422121	+	0.999109i	$0.513441\pi$
$480$	−2.86082	−0.130578
$481$	1.41636	0.0645804
$482$	9.22740	0.420297
$483$	1.78402	0.0811757
$484$	−9.56361	−0.434709
$485$	44.6464	2.02729
$486$	1.00000	0.0453609
$487$	33.8269	1.53284	0.766422	−	0.642337i	$-0.222035\pi$
$487$	33.8269	1.53284	0.766422	+	0.642337i	$0.222035\pi$
$488$	0.277556	0.0125644
$489$	−0.739601	−0.0334459
$490$	−3.24841	−0.146748
$491$	−19.2802	−0.870105	−0.435052	−	0.900405i	$-0.643270\pi$
$491$	−19.2802	−0.870105	−0.435052	+	0.900405i	$0.643270\pi$
$492$	−2.32303	−0.104730
$493$	−7.67630	−0.345723
$494$	−2.83827	−0.127700
$495$	−3.42868	−0.154108
$496$	−0.784713	−0.0352347
$497$	37.0255	1.66082
$498$	5.10077	0.228571
$499$	−2.81918	−0.126204	−0.0631019	−	0.998007i	$-0.520099\pi$
$499$	−2.81918	−0.126204	−0.0631019	+	0.998007i	$0.520099\pi$
$500$	5.19447	0.232304
$501$	9.43205	0.421393
$502$	20.3594	0.908684
$503$	−16.7557	−0.747099	−0.373550	−	0.927610i	$-0.621859\pi$
$503$	−16.7557	−0.747099	−0.373550	+	0.927610i	$0.621859\pi$
$504$	2.85228	0.127051
$505$	28.0109	1.24647
$506$	0.749625	0.0333249
$507$	1.00000	0.0444116
$508$	−20.2683	−0.899260
$509$	−25.9689	−1.15105	−0.575525	−	0.817784i	$-0.695202\pi$
$509$	−25.9689	−1.15105	−0.575525	+	0.817784i	$0.695202\pi$
$510$	−8.49312	−0.376082
$511$	−27.5828	−1.22019
$512$	1.00000	0.0441942
$513$	2.83827	0.125313
$514$	−23.8138	−1.05038
$515$	−2.86082	−0.126063
$516$	2.86823	0.126267
$517$	3.50232	0.154032
$518$	−4.03985	−0.177501
$519$	−8.78926	−0.385806
$520$	2.86082	0.125455
$521$	3.81915	0.167320	0.0836599	−	0.996494i	$-0.473339\pi$
$521$	3.81915	0.167320	0.0836599	+	0.996494i	$0.473339\pi$
$522$	−2.58568	−0.113172
$523$	39.6237	1.73263	0.866313	−	0.499502i	$-0.166484\pi$
$523$	39.6237	1.73263	0.866313	+	0.499502i	$0.166484\pi$
$524$	−21.2785	−0.929555
$525$	9.08241	0.396389
$526$	19.2080	0.837511
$527$	−2.32964	−0.101481
$528$	1.19850	0.0521578
$529$	−22.6088	−0.982991
$530$	−31.5908	−1.37222
$531$	10.7617	0.467018
$532$	8.09552	0.350985
$533$	2.32303	0.100621
$534$	13.6780	0.591904
$535$	−36.4531	−1.57600
$536$	−5.96078	−0.257466
$537$	3.29520	0.142198
$538$	−16.6653	−0.718492
$539$	1.36087	0.0586169
$540$	−2.86082	−0.123110
$541$	−20.0093	−0.860268	−0.430134	−	0.902765i	$-0.641534\pi$
$541$	−20.0093	−0.860268	−0.430134	+	0.902765i	$0.641534\pi$
$542$	29.3009	1.25858
$543$	21.6431	0.928795
$544$	2.96877	0.127285
$545$	−11.4021	−0.488412
$546$	−2.85228	−0.122066
$547$	−0.998176	−0.0426789	−0.0213395	−	0.999772i	$-0.506793\pi$
$547$	−0.998176	−0.0426789	−0.0213395	+	0.999772i	$0.506793\pi$
$548$	8.97192	0.383262
$549$	0.277556	0.0118458
$550$	3.81633	0.162729
$551$	−7.33885	−0.312645
$552$	0.625472	0.0266218
$553$	31.5558	1.34189
$554$	−8.75114	−0.371800
$555$	4.05194	0.171995
$556$	10.8246	0.459066
$557$	24.9543	1.05735	0.528674	−	0.848825i	$-0.322689\pi$
$557$	24.9543	1.05735	0.528674	+	0.848825i	$0.322689\pi$
$558$	−0.784713	−0.0332195
$559$	−2.86823	−0.121313
$560$	−8.15984	−0.344816
$561$	3.55806	0.150222
$562$	28.5421	1.20398
$563$	29.4171	1.23978	0.619891	−	0.784688i	$-0.287177\pi$
$563$	29.4171	1.23978	0.619891	+	0.784688i	$0.287177\pi$
$564$	2.92226	0.123049
$565$	−9.19540	−0.386853
$566$	18.4172	0.774133
$567$	2.85228	0.119784
$568$	12.9810	0.544672
$569$	−41.8457	−1.75426	−0.877131	−	0.480251i	$-0.840546\pi$
$569$	−41.8457	−1.75426	−0.877131	+	0.480251i	$0.840546\pi$
$570$	−8.11976	−0.340099
$571$	−6.09411	−0.255031	−0.127515	−	0.991837i	$-0.540700\pi$
$571$	−6.09411	−0.255031	−0.127515	+	0.991837i	$0.540700\pi$
$572$	−1.19850	−0.0501116
$573$	7.68710	0.321133
$574$	−6.62592	−0.276560
$575$	1.99167	0.0830584
$576$	1.00000	0.0416667
$577$	−14.2184	−0.591921	−0.295961	−	0.955200i	$-0.595640\pi$
$577$	−14.2184	−0.591921	−0.295961	+	0.955200i	$0.595640\pi$
$578$	−8.18638	−0.340509
$579$	7.69396	0.319750
$580$	7.39715	0.307150
$581$	14.5488	0.603586
$582$	−15.6062	−0.646897
$583$	13.2345	0.548117
$584$	−9.67045	−0.400166
$585$	2.86082	0.118280
$586$	−26.1437	−1.07999
$587$	−21.8606	−0.902284	−0.451142	−	0.892452i	$-0.648983\pi$
$587$	−21.8606	−0.902284	−0.451142	+	0.892452i	$0.648983\pi$
$588$	1.13548	0.0468266
$589$	−2.22723	−0.0917712
$590$	−30.7872	−1.26749
$591$	1.72631	0.0710110
$592$	−1.41636	−0.0582120
$593$	−32.4108	−1.33095	−0.665477	−	0.746418i	$-0.731772\pi$
$593$	−32.4108	−1.33095	−0.665477	+	0.746418i	$0.731772\pi$
$594$	1.19850	0.0491749
$595$	−24.2247	−0.993117
$596$	−13.0661	−0.535210
$597$	−20.4133	−0.835459
$598$	−0.625472	−0.0255774
$599$	−30.4677	−1.24488	−0.622439	−	0.782668i	$-0.713858\pi$
$599$	−30.4677	−1.24488	−0.622439	+	0.782668i	$0.713858\pi$
$600$	3.18427	0.129997
$601$	22.1835	0.904885	0.452443	−	0.891793i	$-0.350553\pi$
$601$	22.1835	0.904885	0.452443	+	0.891793i	$0.350553\pi$
$602$	8.18097	0.333432
$603$	−5.96078	−0.242742
$604$	−15.6045	−0.634940
$605$	27.3597	1.11233
$606$	−9.79121	−0.397741
$607$	−30.1816	−1.22504	−0.612518	−	0.790457i	$-0.709843\pi$
$607$	−30.1816	−1.22504	−0.612518	+	0.790457i	$0.709843\pi$
$608$	2.83827	0.115107
$609$	−7.37507	−0.298853
$610$	−0.794038	−0.0321496
$611$	−2.92226	−0.118222
$612$	2.96877	0.120006
$613$	39.4016	1.59142	0.795708	−	0.605681i	$-0.207099\pi$
$613$	39.4016	1.59142	0.795708	+	0.605681i	$0.207099\pi$
$614$	23.1197	0.933037
$615$	6.64575	0.267983
$616$	3.41844	0.137733
$617$	31.3994	1.26409	0.632046	−	0.774930i	$-0.282215\pi$
$617$	31.3994	1.26409	0.632046	+	0.774930i	$0.282215\pi$
$618$	1.00000	0.0402259
$619$	1.72232	0.0692260	0.0346130	−	0.999401i	$-0.488980\pi$
$619$	1.72232	0.0692260	0.0346130	+	0.999401i	$0.488980\pi$
$620$	2.24492	0.0901581
$621$	0.625472	0.0250993
$622$	0.181499	0.00727744
$623$	39.0134	1.56304
$624$	−1.00000	−0.0400320
$625$	−30.7818	−1.23127
$626$	−26.2705	−1.04998
$627$	3.40165	0.135849
$628$	9.80497	0.391261
$629$	−4.20485	−0.167658
$630$	−8.15984	−0.325096
$631$	−11.0869	−0.441361	−0.220681	−	0.975346i	$-0.570828\pi$
$631$	−11.0869	−0.441361	−0.220681	+	0.975346i	$0.570828\pi$
$632$	11.0634	0.440077
$633$	9.15406	0.363841
$634$	−21.9172	−0.870444
$635$	57.9838	2.30102
$636$	11.0426	0.437868
$637$	−1.13548	−0.0449895
$638$	−3.09893	−0.122688
$639$	12.9810	0.513522
$640$	−2.86082	−0.113084
$641$	−29.7970	−1.17691	−0.588454	−	0.808530i	$-0.700263\pi$
$641$	−29.7970	−1.17691	−0.588454	+	0.808530i	$0.700263\pi$
$642$	12.7422	0.502895
$643$	−32.6477	−1.28750	−0.643750	−	0.765236i	$-0.722622\pi$
$643$	−32.6477	−1.28750	−0.643750	+	0.765236i	$0.722622\pi$
$644$	1.78402	0.0703002
$645$	−8.20547	−0.323090
$646$	8.42617	0.331523
$647$	−16.7780	−0.659613	−0.329807	−	0.944049i	$-0.606984\pi$
$647$	−16.7780	−0.659613	−0.329807	+	0.944049i	$0.606984\pi$
$648$	1.00000	0.0392837
$649$	12.8978	0.506284
$650$	−3.18427	−0.124897
$651$	−2.23822	−0.0877227
$652$	−0.739601	−0.0289650
$653$	−16.3195	−0.638629	−0.319315	−	0.947649i	$-0.603453\pi$
$653$	−16.3195	−0.638629	−0.319315	+	0.947649i	$0.603453\pi$
$654$	3.98561	0.155849
$655$	60.8738	2.37854
$656$	−2.32303	−0.0906990
$657$	−9.67045	−0.377280
$658$	8.33510	0.324936
$659$	−28.9586	−1.12807	−0.564033	−	0.825753i	$-0.690751\pi$
$659$	−28.9586	−1.12807	−0.564033	+	0.825753i	$0.690751\pi$
$660$	−3.42868	−0.133461
$661$	11.0305	0.429036	0.214518	−	0.976720i	$-0.431182\pi$
$661$	11.0305	0.429036	0.214518	+	0.976720i	$0.431182\pi$
$662$	8.20752	0.318994
$663$	−2.96877	−0.115298
$664$	5.10077	0.197948
$665$	−23.1598	−0.898099
$666$	−1.41636	−0.0548828
$667$	−1.61727	−0.0626209
$668$	9.43205	0.364937
$669$	−2.76710	−0.106982
$670$	17.0527	0.658803
$671$	0.332650	0.0128418
$672$	2.85228	0.110029
$673$	8.00462	0.308555	0.154278	−	0.988028i	$-0.450695\pi$
$673$	8.00462	0.308555	0.154278	+	0.988028i	$0.450695\pi$
$674$	−6.11072	−0.235376
$675$	3.18427	0.122563
$676$	1.00000	0.0384615
$677$	−46.9181	−1.80321	−0.901604	−	0.432562i	$-0.857610\pi$
$677$	−46.9181	−1.80321	−0.901604	+	0.432562i	$0.857610\pi$
$678$	3.21426	0.123443
$679$	−44.5131	−1.70826
$680$	−8.49312	−0.325696
$681$	17.4139	0.667304
$682$	−0.940475	−0.0360127
$683$	34.7651	1.33025	0.665125	−	0.746732i	$-0.268378\pi$
$683$	34.7651	1.33025	0.665125	+	0.746732i	$0.268378\pi$
$684$	2.83827	0.108524
$685$	−25.6670	−0.980686
$686$	−16.7272	−0.638648
$687$	22.6709	0.864948
$688$	2.86823	0.109350
$689$	−11.0426	−0.420690
$690$	−1.78936	−0.0681198
$691$	12.9620	0.493099	0.246550	−	0.969130i	$-0.420703\pi$
$691$	12.9620	0.493099	0.246550	+	0.969130i	$0.420703\pi$
$692$	−8.78926	−0.334118
$693$	3.41844	0.129856
$694$	10.3267	0.391996
$695$	−30.9673	−1.17466
$696$	−2.58568	−0.0980099
$697$	−6.89654	−0.261225
$698$	−16.9721	−0.642402
$699$	29.7069	1.12362
$700$	9.08241	0.343283
$701$	15.4128	0.582133	0.291067	−	0.956703i	$-0.405990\pi$
$701$	15.4128	0.582133	0.291067	+	0.956703i	$0.405990\pi$
$702$	−1.00000	−0.0377426
$703$	−4.02001	−0.151617
$704$	1.19850	0.0451700
$705$	−8.36005	−0.314858
$706$	−26.0421	−0.980106
$707$	−27.9273	−1.05031
$708$	10.7617	0.404449
$709$	−50.9659	−1.91407	−0.957033	−	0.289980i	$-0.906351\pi$
$709$	−50.9659	−1.91407	−0.957033	+	0.289980i	$0.906351\pi$
$710$	−37.1364	−1.39370
$711$	11.0634	0.414908
$712$	13.6780	0.512603
$713$	−0.490816	−0.0183812
$714$	8.46777	0.316898
$715$	3.42868	0.128225
$716$	3.29520	0.123147
$717$	22.4519	0.838482
$718$	5.50478	0.205437
$719$	−32.4745	−1.21109	−0.605547	−	0.795809i	$-0.707046\pi$
$719$	−32.4745	−1.21109	−0.605547	+	0.795809i	$0.707046\pi$
$720$	−2.86082	−0.106616
$721$	2.85228	0.106224
$722$	−10.9442	−0.407302
$723$	9.22740	0.343171
$724$	21.6431	0.804360
$725$	−8.23350	−0.305784
$726$	−9.56361	−0.354939
$727$	−50.4887	−1.87252	−0.936262	−	0.351304i	$-0.885738\pi$
$727$	−50.4887	−1.87252	−0.936262	+	0.351304i	$0.885738\pi$
$728$	−2.85228	−0.105712
$729$	1.00000	0.0370370
$730$	27.6654	1.02394
$731$	8.51512	0.314943
$732$	0.277556	0.0102588
$733$	−36.6653	−1.35426	−0.677132	−	0.735861i	$-0.736778\pi$
$733$	−36.6653	−1.35426	−0.677132	+	0.735861i	$0.736778\pi$
$734$	11.1371	0.411079
$735$	−3.24841	−0.119819
$736$	0.625472	0.0230552
$737$	−7.14397	−0.263151
$738$	−2.32303	−0.0855118
$739$	−15.0076	−0.552065	−0.276032	−	0.961148i	$-0.589020\pi$
$739$	−15.0076	−0.552065	−0.276032	+	0.961148i	$0.589020\pi$
$740$	4.05194	0.148952
$741$	−2.83827	−0.104266
$742$	31.4965	1.15627
$743$	22.3468	0.819826	0.409913	−	0.912125i	$-0.365559\pi$
$743$	22.3468	0.819826	0.409913	+	0.912125i	$0.365559\pi$
$744$	−0.784713	−0.0287690
$745$	37.3798	1.36949
$746$	−8.70720	−0.318793
$747$	5.10077	0.186627
$748$	3.55806	0.130096
$749$	36.3443	1.32799
$750$	5.19447	0.189675
$751$	41.6782	1.52086	0.760429	−	0.649421i	$-0.224989\pi$
$751$	41.6782	1.52086	0.760429	+	0.649421i	$0.224989\pi$
$752$	2.92226	0.106564
$753$	20.3594	0.741938
$754$	2.58568	0.0941649
$755$	44.6417	1.62468
$756$	2.85228	0.103736
$757$	−33.3997	−1.21393	−0.606967	−	0.794727i	$-0.707614\pi$
$757$	−33.3997	−1.21393	−0.606967	+	0.794727i	$0.707614\pi$
$758$	25.3071	0.919195
$759$	0.749625	0.0272097
$760$	−8.11976	−0.294535
$761$	3.64277	0.132050	0.0660251	−	0.997818i	$-0.478968\pi$
$761$	3.64277	0.132050	0.0660251	+	0.997818i	$0.478968\pi$
$762$	−20.2683	−0.734242
$763$	11.3681	0.411551
$764$	7.68710	0.278110
$765$	−8.49312	−0.307069
$766$	−4.02289	−0.145353
$767$	−10.7617	−0.388582
$768$	1.00000	0.0360844
$769$	38.8854	1.40225	0.701123	−	0.713041i	$-0.252683\pi$
$769$	38.8854	1.40225	0.701123	+	0.713041i	$0.252683\pi$
$770$	−9.77953	−0.352430
$771$	−23.8138	−0.857633
$772$	7.69396	0.276912
$773$	3.14817	0.113232	0.0566159	−	0.998396i	$-0.481969\pi$
$773$	3.14817	0.113232	0.0566159	+	0.998396i	$0.481969\pi$
$774$	2.86823	0.103096
$775$	−2.49874	−0.0897573
$776$	−15.6062	−0.560229
$777$	−4.03985	−0.144929
$778$	14.0322	0.503077
$779$	−6.59337	−0.236232
$780$	2.86082	0.102434
$781$	15.5577	0.556699
$782$	1.85688	0.0664020
$783$	−2.58568	−0.0924046
$784$	1.13548	0.0405530
$785$	−28.0502	−1.00116
$786$	−21.2785	−0.758978
$787$	20.2668	0.722434	0.361217	−	0.932482i	$-0.382361\pi$
$787$	20.2668	0.722434	0.361217	+	0.932482i	$0.382361\pi$
$788$	1.72631	0.0614973
$789$	19.2080	0.683825
$790$	−31.6502	−1.12606
$791$	9.16795	0.325975
$792$	1.19850	0.0425867
$793$	−0.277556	−0.00985632
$794$	−5.96104	−0.211549
$795$	−31.5908	−1.12041
$796$	−20.4133	−0.723529
$797$	−12.1140	−0.429101	−0.214550	−	0.976713i	$-0.568829\pi$
$797$	−12.1140	−0.429101	−0.214550	+	0.976713i	$0.568829\pi$
$798$	8.09552	0.286578
$799$	8.67553	0.306918
$800$	3.18427	0.112581
$801$	13.6780	0.483287
$802$	4.14882	0.146500
$803$	−11.5900	−0.409002
$804$	−5.96078	−0.210220
$805$	−5.10375	−0.179884
$806$	0.784713	0.0276403
$807$	−16.6653	−0.586646
$808$	−9.79121	−0.344454
$809$	0.584174	0.0205385	0.0102692	−	0.999947i	$-0.496731\pi$
$809$	0.584174	0.0205385	0.0102692	+	0.999947i	$0.496731\pi$
$810$	−2.86082	−0.100519
$811$	15.9743	0.560934	0.280467	−	0.959864i	$-0.409511\pi$
$811$	15.9743	0.560934	0.280467	+	0.959864i	$0.409511\pi$
$812$	−7.37507	−0.258814
$813$	29.3009	1.02763
$814$	−1.69750	−0.0594974
$815$	2.11586	0.0741154
$816$	2.96877	0.103928
$817$	8.14079	0.284810
$818$	−9.33705	−0.326462
$819$	−2.85228	−0.0996666
$820$	6.64575	0.232080
$821$	41.3834	1.44429	0.722145	−	0.691742i	$-0.243156\pi$
$821$	41.3834	1.44429	0.722145	+	0.691742i	$0.243156\pi$
$822$	8.97192	0.312932
$823$	−24.1306	−0.841138	−0.420569	−	0.907260i	$-0.638170\pi$
$823$	−24.1306	−0.841138	−0.420569	+	0.907260i	$0.638170\pi$
$824$	1.00000	0.0348367
$825$	3.81633	0.132868
$826$	30.6953	1.06803
$827$	−44.3599	−1.54255	−0.771273	−	0.636505i	$-0.780379\pi$
$827$	−44.3599	−1.54255	−0.771273	+	0.636505i	$0.780379\pi$
$828$	0.625472	0.0217366
$829$	−45.0087	−1.56322	−0.781609	−	0.623769i	$-0.785601\pi$
$829$	−45.0087	−1.56322	−0.781609	+	0.623769i	$0.785601\pi$
$830$	−14.5924	−0.506509
$831$	−8.75114	−0.303574
$832$	−1.00000	−0.0346688
$833$	3.37100	0.116798
$834$	10.8246	0.374826
$835$	−26.9834	−0.933798
$836$	3.40165	0.117649
$837$	−0.784713	−0.0271236
$838$	−3.15521	−0.108995
$839$	20.9803	0.724319	0.362160	−	0.932116i	$-0.382040\pi$
$839$	20.9803	0.724319	0.362160	+	0.932116i	$0.382040\pi$
$840$	−8.15984	−0.281541
$841$	−22.3143	−0.769457
$842$	−26.1807	−0.902246
$843$	28.5421	0.983043
$844$	9.15406	0.315096
$845$	−2.86082	−0.0984151
$846$	2.92226	0.100469
$847$	−27.2781	−0.937285
$848$	11.0426	0.379204
$849$	18.4172	0.632077
$850$	9.45337	0.324248
$851$	−0.885893	−0.0303680
$852$	12.9810	0.444723
$853$	−27.6062	−0.945218	−0.472609	−	0.881272i	$-0.656688\pi$
$853$	−27.6062	−0.945218	−0.472609	+	0.881272i	$0.656688\pi$
$854$	0.791668	0.0270903
$855$	−8.11976	−0.277690
$856$	12.7422	0.435520
$857$	−38.4790	−1.31442	−0.657209	−	0.753709i	$-0.728263\pi$
$857$	−38.4790	−1.31442	−0.657209	+	0.753709i	$0.728263\pi$
$858$	−1.19850	−0.0409160
$859$	−43.6850	−1.49051	−0.745257	−	0.666777i	$-0.767673\pi$
$859$	−43.6850	−1.49051	−0.745257	+	0.666777i	$0.767673\pi$
$860$	−8.20547	−0.279804
$861$	−6.62592	−0.225811
$862$	−15.0601	−0.512948
$863$	−39.6515	−1.34975	−0.674876	−	0.737931i	$-0.735803\pi$
$863$	−39.6515	−1.34975	−0.674876	+	0.737931i	$0.735803\pi$
$864$	1.00000	0.0340207
$865$	25.1445	0.854937
$866$	−9.53858	−0.324134
$867$	−8.18638	−0.278024
$868$	−2.23822	−0.0759701
$869$	13.2594	0.449794
$870$	7.39715	0.250787
$871$	5.96078	0.201973
$872$	3.98561	0.134970
$873$	−15.6062	−0.528189
$874$	1.77526	0.0600489
$875$	14.8161	0.500875
$876$	−9.67045	−0.326734
$877$	−11.0830	−0.374246	−0.187123	−	0.982336i	$-0.559916\pi$
$877$	−11.0830	−0.374246	−0.187123	+	0.982336i	$0.559916\pi$
$878$	9.30792	0.314127
$879$	−26.1437	−0.881804
$880$	−3.42868	−0.115581
$881$	43.5840	1.46838	0.734190	−	0.678944i	$-0.237562\pi$
$881$	43.5840	1.46838	0.734190	+	0.678944i	$0.237562\pi$
$882$	1.13548	0.0382337
$883$	−3.10816	−0.104598	−0.0522989	−	0.998631i	$-0.516655\pi$
$883$	−3.10816	−0.104598	−0.0522989	+	0.998631i	$0.516655\pi$
$884$	−2.96877	−0.0998507
$885$	−30.7872	−1.03490
$886$	17.0382	0.572410
$887$	−31.2794	−1.05026	−0.525130	−	0.851022i	$-0.675983\pi$
$887$	−31.2794	−1.05026	−0.525130	+	0.851022i	$0.675983\pi$
$888$	−1.41636	−0.0475299
$889$	−57.8108	−1.93891
$890$	−39.1301	−1.31165
$891$	1.19850	0.0401511
$892$	−2.76710	−0.0926494
$893$	8.29416	0.277553
$894$	−13.0661	−0.436997
$895$	−9.42697	−0.315109
$896$	2.85228	0.0952879
$897$	−0.625472	−0.0208839
$898$	3.53749	0.118048
$899$	2.02902	0.0676715
$900$	3.18427	0.106142
$901$	32.7830	1.09216
$902$	−2.78414	−0.0927017
$903$	8.18097	0.272246
$904$	3.21426	0.106905
$905$	−61.9170	−2.05819
$906$	−15.6045	−0.518426
$907$	21.3356	0.708436	0.354218	−	0.935163i	$-0.384747\pi$
$907$	21.3356	0.708436	0.354218	+	0.935163i	$0.384747\pi$
$908$	17.4139	0.577902
$909$	−9.79121	−0.324754
$910$	8.15984	0.270496
$911$	−57.3141	−1.89890	−0.949450	−	0.313919i	$-0.898358\pi$
$911$	−57.3141	−1.89890	−0.949450	+	0.313919i	$0.898358\pi$
$912$	2.83827	0.0939844
$913$	6.11325	0.202319
$914$	−26.9509	−0.891456
$915$	−0.794038	−0.0262501
$916$	22.6709	0.749067
$917$	−60.6921	−2.00423
$918$	2.96877	0.0979841
$919$	−20.5289	−0.677187	−0.338593	−	0.940933i	$-0.609951\pi$
$919$	−20.5289	−0.677187	−0.338593	+	0.940933i	$0.609951\pi$
$920$	−1.78936	−0.0589934
$921$	23.1197	0.761821
$922$	−27.4475	−0.903935
$923$	−12.9810	−0.427276
$924$	3.41844	0.112458
$925$	−4.51007	−0.148290
$926$	15.0972	0.496124
$927$	1.00000	0.0328443
$928$	−2.58568	−0.0848791
$929$	9.72135	0.318947	0.159474	−	0.987202i	$-0.449020\pi$
$929$	9.72135	0.318947	0.159474	+	0.987202i	$0.449020\pi$
$930$	2.24492	0.0736138
$931$	3.22281	0.105623
$932$	29.7069	0.973081
$933$	0.181499	0.00594200
$934$	41.3324	1.35244
$935$	−10.1790	−0.332888
$936$	−1.00000	−0.0326860
$937$	33.7167	1.10148	0.550738	−	0.834678i	$-0.314347\pi$
$937$	33.7167	1.10148	0.550738	+	0.834678i	$0.314347\pi$
$938$	−17.0018	−0.555128
$939$	−26.2705	−0.857305
$940$	−8.36005	−0.272675
$941$	−25.7657	−0.839938	−0.419969	−	0.907538i	$-0.637959\pi$
$941$	−25.7657	−0.839938	−0.419969	+	0.907538i	$0.637959\pi$
$942$	9.80497	0.319463
$943$	−1.45299	−0.0473158
$944$	10.7617	0.350263
$945$	−8.15984	−0.265440
$946$	3.43756	0.111765
$947$	9.01972	0.293101	0.146551	−	0.989203i	$-0.453183\pi$
$947$	9.01972	0.293101	0.146551	+	0.989203i	$0.453183\pi$
$948$	11.0634	0.359321
$949$	9.67045	0.313916
$950$	9.03780	0.293225
$951$	−21.9172	−0.710715
$952$	8.46777	0.274442
$953$	−12.0421	−0.390081	−0.195040	−	0.980795i	$-0.562484\pi$
$953$	−12.0421	−0.390081	−0.195040	+	0.980795i	$0.562484\pi$
$954$	11.0426	0.357517
$955$	−21.9914	−0.711625
$956$	22.4519	0.726147
$957$	−3.09893	−0.100174
$958$	−1.84771	−0.0596969
$959$	25.5904	0.826357
$960$	−2.86082	−0.0923324
$961$	−30.3842	−0.980136
$962$	1.41636	0.0456652
$963$	12.7422	0.410612
$964$	9.22740	0.297195
$965$	−22.0110	−0.708560
$966$	1.78402	0.0573999
$967$	−12.0959	−0.388977	−0.194489	−	0.980905i	$-0.562305\pi$
$967$	−12.0959	−0.388977	−0.194489	+	0.980905i	$0.562305\pi$
$968$	−9.56361	−0.307386
$969$	8.42617	0.270688
$970$	44.6464	1.43351
$971$	8.66106	0.277947	0.138973	−	0.990296i	$-0.455620\pi$
$971$	8.66106	0.277947	0.138973	+	0.990296i	$0.455620\pi$
$972$	1.00000	0.0320750
$973$	30.8748	0.989802
$974$	33.8269	1.08388
$975$	−3.18427	−0.101978
$976$	0.277556	0.00888436
$977$	−18.7524	−0.599944	−0.299972	−	0.953948i	$-0.596977\pi$
$977$	−18.7524	−0.599944	−0.299972	+	0.953948i	$0.596977\pi$
$978$	−0.739601	−0.0236498
$979$	16.3930	0.523922
$980$	−3.24841	−0.103767
$981$	3.98561	0.127251
$982$	−19.2802	−0.615257
$983$	−13.6387	−0.435006	−0.217503	−	0.976060i	$-0.569791\pi$
$983$	−13.6387	−0.435006	−0.217503	+	0.976060i	$0.569791\pi$
$984$	−2.32303	−0.0740554
$985$	−4.93866	−0.157359
$986$	−7.67630	−0.244463
$987$	8.33510	0.265309
$988$	−2.83827	−0.0902973
$989$	1.79399	0.0570457
$990$	−3.42868	−0.108970
$991$	5.31241	0.168754	0.0843772	−	0.996434i	$-0.473110\pi$
$991$	5.31241	0.168754	0.0843772	+	0.996434i	$0.473110\pi$
$992$	−0.784713	−0.0249147
$993$	8.20752	0.260458
$994$	37.0255	1.17438
$995$	58.3986	1.85136
$996$	5.10077	0.161624
$997$	28.8428	0.913460	0.456730	−	0.889605i	$-0.349020\pi$
$997$	28.8428	0.913460	0.456730	+	0.889605i	$0.349020\pi$
$998$	−2.81918	−0.0892396
$999$	−1.41636	−0.0448116

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bd.1.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bd.1.2	✓	16	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.86082 q^{5} +1.00000 q^{6} +2.85228 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.86082 q^{5} +1.00000 q^{6} +2.85228 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.86082 q^{10} +1.19850 q^{11} +1.00000 q^{12} -1.00000 q^{13} +2.85228 q^{14} -2.86082 q^{15} +1.00000 q^{16} +2.96877 q^{17} +1.00000 q^{18} +2.83827 q^{19} -2.86082 q^{20} +2.85228 q^{21} +1.19850 q^{22} +0.625472 q^{23} +1.00000 q^{24} +3.18427 q^{25} -1.00000 q^{26} +1.00000 q^{27} +2.85228 q^{28} -2.58568 q^{29} -2.86082 q^{30} -0.784713 q^{31} +1.00000 q^{32} +1.19850 q^{33} +2.96877 q^{34} -8.15984 q^{35} +1.00000 q^{36} -1.41636 q^{37} +2.83827 q^{38} -1.00000 q^{39} -2.86082 q^{40} -2.32303 q^{41} +2.85228 q^{42} +2.86823 q^{43} +1.19850 q^{44} -2.86082 q^{45} +0.625472 q^{46} +2.92226 q^{47} +1.00000 q^{48} +1.13548 q^{49} +3.18427 q^{50} +2.96877 q^{51} -1.00000 q^{52} +11.0426 q^{53} +1.00000 q^{54} -3.42868 q^{55} +2.85228 q^{56} +2.83827 q^{57} -2.58568 q^{58} +10.7617 q^{59} -2.86082 q^{60} +0.277556 q^{61} -0.784713 q^{62} +2.85228 q^{63} +1.00000 q^{64} +2.86082 q^{65} +1.19850 q^{66} -5.96078 q^{67} +2.96877 q^{68} +0.625472 q^{69} -8.15984 q^{70} +12.9810 q^{71} +1.00000 q^{72} -9.67045 q^{73} -1.41636 q^{74} +3.18427 q^{75} +2.83827 q^{76} +3.41844 q^{77} -1.00000 q^{78} +11.0634 q^{79} -2.86082 q^{80} +1.00000 q^{81} -2.32303 q^{82} +5.10077 q^{83} +2.85228 q^{84} -8.49312 q^{85} +2.86823 q^{86} -2.58568 q^{87} +1.19850 q^{88} +13.6780 q^{89} -2.86082 q^{90} -2.85228 q^{91} +0.625472 q^{92} -0.784713 q^{93} +2.92226 q^{94} -8.11976 q^{95} +1.00000 q^{96} -15.6062 q^{97} +1.13548 q^{98} +1.19850 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9} + 5 q^{10} + 18 q^{11} + 16 q^{12} - 16 q^{13} + 4 q^{14} + 5 q^{15} + 16 q^{16} + 17 q^{17} + 16 q^{18} + 8 q^{19} + 5 q^{20} + 4 q^{21} + 18 q^{22} + 9 q^{23} + 16 q^{24} + 17 q^{25} - 16 q^{26} + 16 q^{27} + 4 q^{28} + 14 q^{29} + 5 q^{30} + 12 q^{31} + 16 q^{32} + 18 q^{33} + 17 q^{34} + 16 q^{35} + 16 q^{36} + 31 q^{37} + 8 q^{38} - 16 q^{39} + 5 q^{40} + 29 q^{41} + 4 q^{42} + 30 q^{43} + 18 q^{44} + 5 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 36 q^{49} + 17 q^{50} + 17 q^{51} - 16 q^{52} + 12 q^{53} + 16 q^{54} + 30 q^{55} + 4 q^{56} + 8 q^{57} + 14 q^{58} + 38 q^{59} + 5 q^{60} + 12 q^{62} + 4 q^{63} + 16 q^{64} - 5 q^{65} + 18 q^{66} + 28 q^{67} + 17 q^{68} + 9 q^{69} + 16 q^{70} + 32 q^{71} + 16 q^{72} + 20 q^{73} + 31 q^{74} + 17 q^{75} + 8 q^{76} + 26 q^{77} - 16 q^{78} + 13 q^{79} + 5 q^{80} + 16 q^{81} + 29 q^{82} + 39 q^{83} + 4 q^{84} + 31 q^{85} + 30 q^{86} + 14 q^{87} + 18 q^{88} + 9 q^{89} + 5 q^{90} - 4 q^{91} + 9 q^{92} + 12 q^{93} - q^{94} - 20 q^{95} + 16 q^{96} + 35 q^{97} + 36 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9 + 5 * q^10 + 18 * q^11 + 16 * q^12 - 16 * q^13 + 4 * q^14 + 5 * q^15 + 16 * q^16 + 17 * q^17 + 16 * q^18 + 8 * q^19 + 5 * q^20 + 4 * q^21 + 18 * q^22 + 9 * q^23 + 16 * q^24 + 17 * q^25 - 16 * q^26 + 16 * q^27 + 4 * q^28 + 14 * q^29 + 5 * q^30 + 12 * q^31 + 16 * q^32 + 18 * q^33 + 17 * q^34 + 16 * q^35 + 16 * q^36 + 31 * q^37 + 8 * q^38 - 16 * q^39 + 5 * q^40 + 29 * q^41 + 4 * q^42 + 30 * q^43 + 18 * q^44 + 5 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 36 * q^49 + 17 * q^50 + 17 * q^51 - 16 * q^52 + 12 * q^53 + 16 * q^54 + 30 * q^55 + 4 * q^56 + 8 * q^57 + 14 * q^58 + 38 * q^59 + 5 * q^60 + 12 * q^62 + 4 * q^63 + 16 * q^64 - 5 * q^65 + 18 * q^66 + 28 * q^67 + 17 * q^68 + 9 * q^69 + 16 * q^70 + 32 * q^71 + 16 * q^72 + 20 * q^73 + 31 * q^74 + 17 * q^75 + 8 * q^76 + 26 * q^77 - 16 * q^78 + 13 * q^79 + 5 * q^80 + 16 * q^81 + 29 * q^82 + 39 * q^83 + 4 * q^84 + 31 * q^85 + 30 * q^86 + 14 * q^87 + 18 * q^88 + 9 * q^89 + 5 * q^90 - 4 * q^91 + 9 * q^92 + 12 * q^93 - q^94 - 20 * q^95 + 16 * q^96 + 35 * q^97 + 36 * q^98 + 18 * q^99

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