LMFDB - Embedded newform 8034.2.a.bd.1.16

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			1.16
Root			$3.81307$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.81307 q^{5} +1.00000 q^{6} +4.46750 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.81307 q^{5} +1.00000 q^{6} +4.46750 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.81307 q^{10} -1.59586 q^{11} +1.00000 q^{12} -1.00000 q^{13} +4.46750 q^{14} +3.81307 q^{15} +1.00000 q^{16} +2.26725 q^{17} +1.00000 q^{18} -7.26486 q^{19} +3.81307 q^{20} +4.46750 q^{21} -1.59586 q^{22} +3.73931 q^{23} +1.00000 q^{24} +9.53949 q^{25} -1.00000 q^{26} +1.00000 q^{27} +4.46750 q^{28} -0.246991 q^{29} +3.81307 q^{30} -4.75143 q^{31} +1.00000 q^{32} -1.59586 q^{33} +2.26725 q^{34} +17.0349 q^{35} +1.00000 q^{36} +3.05081 q^{37} -7.26486 q^{38} -1.00000 q^{39} +3.81307 q^{40} -4.71067 q^{41} +4.46750 q^{42} -7.38226 q^{43} -1.59586 q^{44} +3.81307 q^{45} +3.73931 q^{46} -10.9780 q^{47} +1.00000 q^{48} +12.9586 q^{49} +9.53949 q^{50} +2.26725 q^{51} -1.00000 q^{52} +1.12894 q^{53} +1.00000 q^{54} -6.08512 q^{55} +4.46750 q^{56} -7.26486 q^{57} -0.246991 q^{58} +7.94815 q^{59} +3.81307 q^{60} +2.85929 q^{61} -4.75143 q^{62} +4.46750 q^{63} +1.00000 q^{64} -3.81307 q^{65} -1.59586 q^{66} +7.06089 q^{67} +2.26725 q^{68} +3.73931 q^{69} +17.0349 q^{70} +1.51324 q^{71} +1.00000 q^{72} +15.6393 q^{73} +3.05081 q^{74} +9.53949 q^{75} -7.26486 q^{76} -7.12951 q^{77} -1.00000 q^{78} +11.0249 q^{79} +3.81307 q^{80} +1.00000 q^{81} -4.71067 q^{82} -7.04586 q^{83} +4.46750 q^{84} +8.64517 q^{85} -7.38226 q^{86} -0.246991 q^{87} -1.59586 q^{88} -3.12195 q^{89} +3.81307 q^{90} -4.46750 q^{91} +3.73931 q^{92} -4.75143 q^{93} -10.9780 q^{94} -27.7014 q^{95} +1.00000 q^{96} -8.69500 q^{97} +12.9586 q^{98} -1.59586 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	3.81307	1.70526	0.852628	−	0.522519i	$-0.175007\pi$
$5$	3.81307	1.70526	0.852628	+	0.522519i	$0.175007\pi$
$6$	1.00000	0.408248
$7$	4.46750	1.68856	0.844278	−	0.535905i	$-0.180029\pi$
$7$	4.46750	1.68856	0.844278	+	0.535905i	$0.180029\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.81307	1.20580
$11$	−1.59586	−0.481170	−0.240585	−	0.970628i	$-0.577339\pi$
$11$	−1.59586	−0.481170	−0.240585	+	0.970628i	$0.577339\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	4.46750	1.19399
$15$	3.81307	0.984530
$16$	1.00000	0.250000
$17$	2.26725	0.549888	0.274944	−	0.961460i	$-0.411341\pi$
$17$	2.26725	0.549888	0.274944	+	0.961460i	$0.411341\pi$
$18$	1.00000	0.235702
$19$	−7.26486	−1.66667	−0.833337	−	0.552765i	$-0.813573\pi$
$19$	−7.26486	−1.66667	−0.833337	+	0.552765i	$0.813573\pi$
$20$	3.81307	0.852628
$21$	4.46750	0.974889
$22$	−1.59586	−0.340239
$23$	3.73931	0.779699	0.389850	−	0.920878i	$-0.372527\pi$
$23$	3.73931	0.779699	0.389850	+	0.920878i	$0.372527\pi$
$24$	1.00000	0.204124
$25$	9.53949	1.90790
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	4.46750	0.844278
$29$	−0.246991	−0.0458650	−0.0229325	−	0.999737i	$-0.507300\pi$
$29$	−0.246991	−0.0458650	−0.0229325	+	0.999737i	$0.507300\pi$
$30$	3.81307	0.696168
$31$	−4.75143	−0.853381	−0.426691	−	0.904398i	$-0.640321\pi$
$31$	−4.75143	−0.853381	−0.426691	+	0.904398i	$0.640321\pi$
$32$	1.00000	0.176777
$33$	−1.59586	−0.277804
$34$	2.26725	0.388830
$35$	17.0349	2.87942
$36$	1.00000	0.166667
$37$	3.05081	0.501550	0.250775	−	0.968045i	$-0.419315\pi$
$37$	3.05081	0.501550	0.250775	+	0.968045i	$0.419315\pi$
$38$	−7.26486	−1.17852
$39$	−1.00000	−0.160128
$40$	3.81307	0.602899
$41$	−4.71067	−0.735683	−0.367841	−	0.929889i	$-0.619903\pi$
$41$	−4.71067	−0.735683	−0.367841	+	0.929889i	$0.619903\pi$
$42$	4.46750	0.689350
$43$	−7.38226	−1.12578	−0.562892	−	0.826531i	$-0.690311\pi$
$43$	−7.38226	−1.12578	−0.562892	+	0.826531i	$0.690311\pi$
$44$	−1.59586	−0.240585
$45$	3.81307	0.568419
$46$	3.73931	0.551331
$47$	−10.9780	−1.60130	−0.800652	−	0.599130i	$-0.795513\pi$
$47$	−10.9780	−1.60130	−0.800652	+	0.599130i	$0.795513\pi$
$48$	1.00000	0.144338
$49$	12.9586	1.85122
$50$	9.53949	1.34909
$51$	2.26725	0.317478
$52$	−1.00000	−0.138675
$53$	1.12894	0.155071	0.0775356	−	0.996990i	$-0.475295\pi$
$53$	1.12894	0.155071	0.0775356	+	0.996990i	$0.475295\pi$
$54$	1.00000	0.136083
$55$	−6.08512	−0.820518
$56$	4.46750	0.596995
$57$	−7.26486	−0.962255
$58$	−0.246991	−0.0324315
$59$	7.94815	1.03476	0.517380	−	0.855756i	$-0.326907\pi$
$59$	7.94815	1.03476	0.517380	+	0.855756i	$0.326907\pi$
$60$	3.81307	0.492265
$61$	2.85929	0.366094	0.183047	−	0.983104i	$-0.441404\pi$
$61$	2.85929	0.366094	0.183047	+	0.983104i	$0.441404\pi$
$62$	−4.75143	−0.603432
$63$	4.46750	0.562852
$64$	1.00000	0.125000
$65$	−3.81307	−0.472953
$66$	−1.59586	−0.196437
$67$	7.06089	0.862625	0.431313	−	0.902203i	$-0.358051\pi$
$67$	7.06089	0.862625	0.431313	+	0.902203i	$0.358051\pi$
$68$	2.26725	0.274944
$69$	3.73931	0.450160
$70$	17.0349	2.03606
$71$	1.51324	0.179588	0.0897941	−	0.995960i	$-0.471379\pi$
$71$	1.51324	0.179588	0.0897941	+	0.995960i	$0.471379\pi$
$72$	1.00000	0.117851
$73$	15.6393	1.83044	0.915220	−	0.402953i	$-0.132016\pi$
$73$	15.6393	1.83044	0.915220	+	0.402953i	$0.132016\pi$
$74$	3.05081	0.354650
$75$	9.53949	1.10152
$76$	−7.26486	−0.833337
$77$	−7.12951	−0.812483
$78$	−1.00000	−0.113228
$79$	11.0249	1.24039	0.620197	−	0.784446i	$-0.287053\pi$
$79$	11.0249	1.24039	0.620197	+	0.784446i	$0.287053\pi$
$80$	3.81307	0.426314
$81$	1.00000	0.111111
$82$	−4.71067	−0.520206
$83$	−7.04586	−0.773384	−0.386692	−	0.922209i	$-0.626382\pi$
$83$	−7.04586	−0.773384	−0.386692	+	0.922209i	$0.626382\pi$
$84$	4.46750	0.487444
$85$	8.64517	0.937700
$86$	−7.38226	−0.796049
$87$	−0.246991	−0.0264802
$88$	−1.59586	−0.170119
$89$	−3.12195	−0.330926	−0.165463	−	0.986216i	$-0.552912\pi$
$89$	−3.12195	−0.330926	−0.165463	+	0.986216i	$0.552912\pi$
$90$	3.81307	0.401933
$91$	−4.46750	−0.468321
$92$	3.73931	0.389850
$93$	−4.75143	−0.492700
$94$	−10.9780	−1.13229
$95$	−27.7014	−2.84211
$96$	1.00000	0.102062
$97$	−8.69500	−0.882844	−0.441422	−	0.897300i	$-0.645526\pi$
$97$	−8.69500	−0.882844	−0.441422	+	0.897300i	$0.645526\pi$
$98$	12.9586	1.30901
$99$	−1.59586	−0.160390
$100$	9.53949	0.953949
$101$	16.8240	1.67405	0.837025	−	0.547164i	$-0.184293\pi$
$101$	16.8240	1.67405	0.837025	+	0.547164i	$0.184293\pi$
$102$	2.26725	0.224491
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	17.0349	1.66243
$106$	1.12894	0.109652
$107$	−8.98739	−0.868844	−0.434422	−	0.900709i	$-0.643047\pi$
$107$	−8.98739	−0.868844	−0.434422	+	0.900709i	$0.643047\pi$
$108$	1.00000	0.0962250
$109$	0.980976	0.0939605	0.0469802	−	0.998896i	$-0.485040\pi$
$109$	0.980976	0.0939605	0.0469802	+	0.998896i	$0.485040\pi$
$110$	−6.08512	−0.580194
$111$	3.05081	0.289570
$112$	4.46750	0.422139
$113$	−2.64165	−0.248505	−0.124253	−	0.992251i	$-0.539653\pi$
$113$	−2.64165	−0.248505	−0.124253	+	0.992251i	$0.539653\pi$
$114$	−7.26486	−0.680417
$115$	14.2582	1.32959
$116$	−0.246991	−0.0229325
$117$	−1.00000	−0.0924500
$118$	7.94815	0.731686
$119$	10.1289	0.928518
$120$	3.81307	0.348084
$121$	−8.45323	−0.768475
$122$	2.85929	0.258868
$123$	−4.71067	−0.424747
$124$	−4.75143	−0.426691
$125$	17.3094	1.54820
$126$	4.46750	0.397997
$127$	−16.6249	−1.47522	−0.737609	−	0.675228i	$-0.764045\pi$
$127$	−16.6249	−1.47522	−0.737609	+	0.675228i	$0.764045\pi$
$128$	1.00000	0.0883883
$129$	−7.38226	−0.649971
$130$	−3.81307	−0.334428
$131$	−17.6247	−1.53987	−0.769937	−	0.638120i	$-0.779712\pi$
$131$	−17.6247	−1.53987	−0.769937	+	0.638120i	$0.779712\pi$
$132$	−1.59586	−0.138902
$133$	−32.4558	−2.81427
$134$	7.06089	0.609968
$135$	3.81307	0.328177
$136$	2.26725	0.194415
$137$	2.86600	0.244859	0.122429	−	0.992477i	$-0.460931\pi$
$137$	2.86600	0.244859	0.122429	+	0.992477i	$0.460931\pi$
$138$	3.73931	0.318311
$139$	12.2423	1.03838	0.519188	−	0.854660i	$-0.326234\pi$
$139$	12.2423	1.03838	0.519188	+	0.854660i	$0.326234\pi$
$140$	17.0349	1.43971
$141$	−10.9780	−0.924513
$142$	1.51324	0.126988
$143$	1.59586	0.133453
$144$	1.00000	0.0833333
$145$	−0.941793	−0.0782116
$146$	15.6393	1.29432
$147$	12.9586	1.06880
$148$	3.05081	0.250775
$149$	17.5022	1.43384	0.716920	−	0.697156i	$-0.245551\pi$
$149$	17.5022	1.43384	0.716920	+	0.697156i	$0.245551\pi$
$150$	9.53949	0.778896
$151$	13.8923	1.13054	0.565272	−	0.824905i	$-0.308771\pi$
$151$	13.8923	1.13054	0.565272	+	0.824905i	$0.308771\pi$
$152$	−7.26486	−0.589258
$153$	2.26725	0.183296
$154$	−7.12951	−0.574512
$155$	−18.1175	−1.45523
$156$	−1.00000	−0.0800641
$157$	−6.01596	−0.480126	−0.240063	−	0.970757i	$-0.577168\pi$
$157$	−6.01596	−0.480126	−0.240063	+	0.970757i	$0.577168\pi$
$158$	11.0249	0.877091
$159$	1.12894	0.0895304
$160$	3.81307	0.301449
$161$	16.7054	1.31657
$162$	1.00000	0.0785674
$163$	−3.48106	−0.272658	−0.136329	−	0.990664i	$-0.543530\pi$
$163$	−3.48106	−0.272658	−0.136329	+	0.990664i	$0.543530\pi$
$164$	−4.71067	−0.367841
$165$	−6.08512	−0.473726
$166$	−7.04586	−0.546865
$167$	−4.16837	−0.322558	−0.161279	−	0.986909i	$-0.551562\pi$
$167$	−4.16837	−0.322558	−0.161279	+	0.986909i	$0.551562\pi$
$168$	4.46750	0.344675
$169$	1.00000	0.0769231
$170$	8.64517	0.663054
$171$	−7.26486	−0.555558
$172$	−7.38226	−0.562892
$173$	−3.26982	−0.248600	−0.124300	−	0.992245i	$-0.539668\pi$
$173$	−3.26982	−0.248600	−0.124300	+	0.992245i	$0.539668\pi$
$174$	−0.246991	−0.0187243
$175$	42.6177	3.22159
$176$	−1.59586	−0.120292
$177$	7.94815	0.597419
$178$	−3.12195	−0.234000
$179$	5.96568	0.445895	0.222948	−	0.974830i	$-0.428432\pi$
$179$	5.96568	0.445895	0.222948	+	0.974830i	$0.428432\pi$
$180$	3.81307	0.284209
$181$	−3.32325	−0.247016	−0.123508	−	0.992344i	$-0.539414\pi$
$181$	−3.32325	−0.247016	−0.123508	+	0.992344i	$0.539414\pi$
$182$	−4.46750	−0.331153
$183$	2.85929	0.211365
$184$	3.73931	0.275665
$185$	11.6329	0.855271
$186$	−4.75143	−0.348391
$187$	−3.61821	−0.264590
$188$	−10.9780	−0.800652
$189$	4.46750	0.324963
$190$	−27.7014	−2.00967
$191$	−3.77447	−0.273111	−0.136555	−	0.990632i	$-0.543603\pi$
$191$	−3.77447	−0.273111	−0.136555	+	0.990632i	$0.543603\pi$
$192$	1.00000	0.0721688
$193$	19.4237	1.39815	0.699073	−	0.715050i	$-0.253596\pi$
$193$	19.4237	1.39815	0.699073	+	0.715050i	$0.253596\pi$
$194$	−8.69500	−0.624265
$195$	−3.81307	−0.273059
$196$	12.9586	0.925612
$197$	−9.47214	−0.674862	−0.337431	−	0.941350i	$-0.609558\pi$
$197$	−9.47214	−0.674862	−0.337431	+	0.941350i	$0.609558\pi$
$198$	−1.59586	−0.113413
$199$	−11.6570	−0.826343	−0.413172	−	0.910653i	$-0.635579\pi$
$199$	−11.6570	−0.826343	−0.413172	+	0.910653i	$0.635579\pi$
$200$	9.53949	0.674544
$201$	7.06089	0.498037
$202$	16.8240	1.18373
$203$	−1.10343	−0.0774457
$204$	2.26725	0.158739
$205$	−17.9621	−1.25453
$206$	1.00000	0.0696733
$207$	3.73931	0.259900
$208$	−1.00000	−0.0693375
$209$	11.5937	0.801953
$210$	17.0349	1.17552
$211$	−8.84899	−0.609189	−0.304595	−	0.952482i	$-0.598521\pi$
$211$	−8.84899	−0.609189	−0.304595	+	0.952482i	$0.598521\pi$
$212$	1.12894	0.0775356
$213$	1.51324	0.103685
$214$	−8.98739	−0.614366
$215$	−28.1490	−1.91975
$216$	1.00000	0.0680414
$217$	−21.2270	−1.44098
$218$	0.980976	0.0664401
$219$	15.6393	1.05681
$220$	−6.08512	−0.410259
$221$	−2.26725	−0.152512
$222$	3.05081	0.204757
$223$	−16.0641	−1.07573	−0.537866	−	0.843030i	$-0.680769\pi$
$223$	−16.0641	−1.07573	−0.537866	+	0.843030i	$0.680769\pi$
$224$	4.46750	0.298497
$225$	9.53949	0.635966
$226$	−2.64165	−0.175720
$227$	16.1341	1.07086	0.535430	−	0.844580i	$-0.320150\pi$
$227$	16.1341	1.07086	0.535430	+	0.844580i	$0.320150\pi$
$228$	−7.26486	−0.481127
$229$	−24.8431	−1.64168	−0.820839	−	0.571159i	$-0.806494\pi$
$229$	−24.8431	−1.64168	−0.820839	+	0.571159i	$0.806494\pi$
$230$	14.2582	0.940160
$231$	−7.12951	−0.469087
$232$	−0.246991	−0.0162157
$233$	−12.1496	−0.795949	−0.397975	−	0.917396i	$-0.630287\pi$
$233$	−12.1496	−0.795949	−0.397975	+	0.917396i	$0.630287\pi$
$234$	−1.00000	−0.0653720
$235$	−41.8598	−2.73063
$236$	7.94815	0.517380
$237$	11.0249	0.716142
$238$	10.1289	0.656561
$239$	0.102602	0.00663680	0.00331840	−	0.999994i	$-0.498944\pi$
$239$	0.102602	0.00663680	0.00331840	+	0.999994i	$0.498944\pi$
$240$	3.81307	0.246132
$241$	2.41780	0.155744	0.0778721	−	0.996963i	$-0.475187\pi$
$241$	2.41780	0.155744	0.0778721	+	0.996963i	$0.475187\pi$
$242$	−8.45323	−0.543394
$243$	1.00000	0.0641500
$244$	2.85929	0.183047
$245$	49.4119	3.15681
$246$	−4.71067	−0.300341
$247$	7.26486	0.462252
$248$	−4.75143	−0.301716
$249$	−7.04586	−0.446513
$250$	17.3094	1.09474
$251$	12.5884	0.794574	0.397287	−	0.917694i	$-0.369952\pi$
$251$	12.5884	0.794574	0.397287	+	0.917694i	$0.369952\pi$
$252$	4.46750	0.281426
$253$	−5.96741	−0.375168
$254$	−16.6249	−1.04314
$255$	8.64517	0.541381
$256$	1.00000	0.0625000
$257$	−22.3358	−1.39327	−0.696635	−	0.717426i	$-0.745320\pi$
$257$	−22.3358	−1.39327	−0.696635	+	0.717426i	$0.745320\pi$
$258$	−7.38226	−0.459599
$259$	13.6295	0.846896
$260$	−3.81307	−0.236476
$261$	−0.246991	−0.0152883
$262$	−17.6247	−1.08886
$263$	−10.7061	−0.660165	−0.330083	−	0.943952i	$-0.607077\pi$
$263$	−10.7061	−0.660165	−0.330083	+	0.943952i	$0.607077\pi$
$264$	−1.59586	−0.0982184
$265$	4.30471	0.264436
$266$	−32.4558	−1.98999
$267$	−3.12195	−0.191060
$268$	7.06089	0.431313
$269$	−5.95721	−0.363217	−0.181609	−	0.983371i	$-0.558130\pi$
$269$	−5.95721	−0.363217	−0.181609	+	0.983371i	$0.558130\pi$
$270$	3.81307	0.232056
$271$	−22.9356	−1.39324	−0.696620	−	0.717440i	$-0.745314\pi$
$271$	−22.9356	−1.39324	−0.696620	+	0.717440i	$0.745314\pi$
$272$	2.26725	0.137472
$273$	−4.46750	−0.270385
$274$	2.86600	0.173141
$275$	−15.2237	−0.918023
$276$	3.73931	0.225080
$277$	4.25730	0.255796	0.127898	−	0.991787i	$-0.459177\pi$
$277$	4.25730	0.255796	0.127898	+	0.991787i	$0.459177\pi$
$278$	12.2423	0.734243
$279$	−4.75143	−0.284460
$280$	17.0349	1.01803
$281$	−15.9367	−0.950702	−0.475351	−	0.879796i	$-0.657679\pi$
$281$	−15.9367	−0.950702	−0.475351	+	0.879796i	$0.657679\pi$
$282$	−10.9780	−0.653730
$283$	−17.1300	−1.01827	−0.509135	−	0.860687i	$-0.670035\pi$
$283$	−17.1300	−1.01827	−0.509135	+	0.860687i	$0.670035\pi$
$284$	1.51324	0.0897941
$285$	−27.7014	−1.64089
$286$	1.59586	0.0943652
$287$	−21.0449	−1.24224
$288$	1.00000	0.0589256
$289$	−11.8596	−0.697623
$290$	−0.941793	−0.0553040
$291$	−8.69500	−0.509710
$292$	15.6393	0.915220
$293$	−9.34148	−0.545735	−0.272868	−	0.962052i	$-0.587972\pi$
$293$	−9.34148	−0.545735	−0.272868	+	0.962052i	$0.587972\pi$
$294$	12.9586	0.755759
$295$	30.3068	1.76453
$296$	3.05081	0.177325
$297$	−1.59586	−0.0926012
$298$	17.5022	1.01388
$299$	−3.73931	−0.216250
$300$	9.53949	0.550762
$301$	−32.9802	−1.90095
$302$	13.8923	0.799415
$303$	16.8240	0.966514
$304$	−7.26486	−0.416668
$305$	10.9027	0.624285
$306$	2.26725	0.129610
$307$	20.1175	1.14817	0.574084	−	0.818797i	$-0.305358\pi$
$307$	20.1175	1.14817	0.574084	+	0.818797i	$0.305358\pi$
$308$	−7.12951	−0.406241
$309$	1.00000	0.0568880
$310$	−18.1175	−1.02901
$311$	−9.05660	−0.513553	−0.256776	−	0.966471i	$-0.582660\pi$
$311$	−9.05660	−0.513553	−0.256776	+	0.966471i	$0.582660\pi$
$312$	−1.00000	−0.0566139
$313$	−19.7267	−1.11502	−0.557510	−	0.830170i	$-0.688243\pi$
$313$	−19.7267	−1.11502	−0.557510	+	0.830170i	$0.688243\pi$
$314$	−6.01596	−0.339500
$315$	17.0349	0.959807
$316$	11.0249	0.620197
$317$	21.9781	1.23441	0.617207	−	0.786801i	$-0.288264\pi$
$317$	21.9781	1.23441	0.617207	+	0.786801i	$0.288264\pi$
$318$	1.12894	0.0633076
$319$	0.394163	0.0220689
$320$	3.81307	0.213157
$321$	−8.98739	−0.501627
$322$	16.7054	0.930953
$323$	−16.4712	−0.916485
$324$	1.00000	0.0555556
$325$	−9.53949	−0.529155
$326$	−3.48106	−0.192798
$327$	0.980976	0.0542481
$328$	−4.71067	−0.260103
$329$	−49.0442	−2.70389
$330$	−6.08512	−0.334975
$331$	−15.8719	−0.872400	−0.436200	−	0.899850i	$-0.643676\pi$
$331$	−15.8719	−0.872400	−0.436200	+	0.899850i	$0.643676\pi$
$332$	−7.04586	−0.386692
$333$	3.05081	0.167183
$334$	−4.16837	−0.228083
$335$	26.9237	1.47100
$336$	4.46750	0.243722
$337$	32.0677	1.74684	0.873418	−	0.486970i	$-0.161898\pi$
$337$	32.0677	1.74684	0.873418	+	0.486970i	$0.161898\pi$
$338$	1.00000	0.0543928
$339$	−2.64165	−0.143475
$340$	8.64517	0.468850
$341$	7.58261	0.410621
$342$	−7.26486	−0.392839
$343$	26.6199	1.43734
$344$	−7.38226	−0.398025
$345$	14.2582	0.767637
$346$	−3.26982	−0.175786
$347$	−26.9359	−1.44600	−0.722998	−	0.690850i	$-0.757237\pi$
$347$	−26.9359	−1.44600	−0.722998	+	0.690850i	$0.757237\pi$
$348$	−0.246991	−0.0132401
$349$	−19.1811	−1.02674	−0.513369	−	0.858168i	$-0.671603\pi$
$349$	−19.1811	−1.02674	−0.513369	+	0.858168i	$0.671603\pi$
$350$	42.6177	2.27801
$351$	−1.00000	−0.0533761
$352$	−1.59586	−0.0850596
$353$	30.1259	1.60344	0.801721	−	0.597699i	$-0.203918\pi$
$353$	30.1259	1.60344	0.801721	+	0.597699i	$0.203918\pi$
$354$	7.94815	0.422439
$355$	5.77007	0.306244
$356$	−3.12195	−0.165463
$357$	10.1289	0.536080
$358$	5.96568	0.315296
$359$	−24.0036	−1.26686	−0.633432	−	0.773798i	$-0.718354\pi$
$359$	−24.0036	−1.26686	−0.633432	+	0.773798i	$0.718354\pi$
$360$	3.81307	0.200966
$361$	33.7782	1.77780
$362$	−3.32325	−0.174666
$363$	−8.45323	−0.443680
$364$	−4.46750	−0.234161
$365$	59.6337	3.12137
$366$	2.85929	0.149457
$367$	−28.6267	−1.49430	−0.747150	−	0.664655i	$-0.768579\pi$
$367$	−28.6267	−1.49430	−0.747150	+	0.664655i	$0.768579\pi$
$368$	3.73931	0.194925
$369$	−4.71067	−0.245228
$370$	11.6329	0.604768
$371$	5.04352	0.261847
$372$	−4.75143	−0.246350
$373$	22.0872	1.14363	0.571816	−	0.820382i	$-0.306239\pi$
$373$	22.0872	1.14363	0.571816	+	0.820382i	$0.306239\pi$
$374$	−3.61821	−0.187093
$375$	17.3094	0.893852
$376$	−10.9780	−0.566146
$377$	0.246991	0.0127207
$378$	4.46750	0.229783
$379$	−11.7744	−0.604813	−0.302406	−	0.953179i	$-0.597790\pi$
$379$	−11.7744	−0.604813	−0.302406	+	0.953179i	$0.597790\pi$
$380$	−27.7014	−1.42105
$381$	−16.6249	−0.851718
$382$	−3.77447	−0.193119
$383$	5.26266	0.268909	0.134455	−	0.990920i	$-0.457072\pi$
$383$	5.26266	0.268909	0.134455	+	0.990920i	$0.457072\pi$
$384$	1.00000	0.0510310
$385$	−27.1853	−1.38549
$386$	19.4237	0.988639
$387$	−7.38226	−0.375261
$388$	−8.69500	−0.441422
$389$	9.50462	0.481903	0.240952	−	0.970537i	$-0.422540\pi$
$389$	9.50462	0.481903	0.240952	+	0.970537i	$0.422540\pi$
$390$	−3.81307	−0.193082
$391$	8.47794	0.428748
$392$	12.9586	0.654506
$393$	−17.6247	−0.889047
$394$	−9.47214	−0.477199
$395$	42.0386	2.11519
$396$	−1.59586	−0.0801950
$397$	−33.1473	−1.66361	−0.831807	−	0.555065i	$-0.812693\pi$
$397$	−33.1473	−1.66361	−0.831807	+	0.555065i	$0.812693\pi$
$398$	−11.6570	−0.584313
$399$	−32.4558	−1.62482
$400$	9.53949	0.476974
$401$	19.6209	0.979822	0.489911	−	0.871772i	$-0.337029\pi$
$401$	19.6209	0.979822	0.489911	+	0.871772i	$0.337029\pi$
$402$	7.06089	0.352165
$403$	4.75143	0.236685
$404$	16.8240	0.837025
$405$	3.81307	0.189473
$406$	−1.10343	−0.0547624
$407$	−4.86867	−0.241331
$408$	2.26725	0.112245
$409$	−39.4468	−1.95052	−0.975260	−	0.221063i	$-0.929047\pi$
$409$	−39.4468	−1.95052	−0.975260	+	0.221063i	$0.929047\pi$
$410$	−17.9621	−0.887085
$411$	2.86600	0.141369
$412$	1.00000	0.0492665
$413$	35.5084	1.74725
$414$	3.73931	0.183777
$415$	−26.8663	−1.31882
$416$	−1.00000	−0.0490290
$417$	12.2423	0.599507
$418$	11.5937	0.567067
$419$	−19.8115	−0.967853	−0.483927	−	0.875109i	$-0.660790\pi$
$419$	−19.8115	−0.967853	−0.483927	+	0.875109i	$0.660790\pi$
$420$	17.0349	0.831217
$421$	9.45934	0.461020	0.230510	−	0.973070i	$-0.425961\pi$
$421$	9.45934	0.461020	0.230510	+	0.973070i	$0.425961\pi$
$422$	−8.84899	−0.430762
$423$	−10.9780	−0.533768
$424$	1.12894	0.0548260
$425$	21.6284	1.04913
$426$	1.51324	0.0733166
$427$	12.7739	0.618171
$428$	−8.98739	−0.434422
$429$	1.59586	0.0770489
$430$	−28.1490	−1.35747
$431$	33.7764	1.62695	0.813477	−	0.581597i	$-0.197572\pi$
$431$	33.7764	1.62695	0.813477	+	0.581597i	$0.197572\pi$
$432$	1.00000	0.0481125
$433$	−33.4766	−1.60878	−0.804392	−	0.594099i	$-0.797509\pi$
$433$	−33.4766	−1.60878	−0.804392	+	0.594099i	$0.797509\pi$
$434$	−21.2270	−1.01893
$435$	−0.941793	−0.0451555
$436$	0.980976	0.0469802
$437$	−27.1656	−1.29950
$438$	15.6393	0.747274
$439$	25.8749	1.23494	0.617471	−	0.786594i	$-0.288157\pi$
$439$	25.8749	1.23494	0.617471	+	0.786594i	$0.288157\pi$
$440$	−6.08512	−0.290097
$441$	12.9586	0.617075
$442$	−2.26725	−0.107842
$443$	13.5986	0.646089	0.323045	−	0.946384i	$-0.395294\pi$
$443$	13.5986	0.646089	0.323045	+	0.946384i	$0.395294\pi$
$444$	3.05081	0.144785
$445$	−11.9042	−0.564314
$446$	−16.0641	−0.760658
$447$	17.5022	0.827828
$448$	4.46750	0.211070
$449$	11.8898	0.561116	0.280558	−	0.959837i	$-0.409480\pi$
$449$	11.8898	0.561116	0.280558	+	0.959837i	$0.409480\pi$
$450$	9.53949	0.449696
$451$	7.51757	0.353989
$452$	−2.64165	−0.124253
$453$	13.8923	0.652719
$454$	16.1341	0.757212
$455$	−17.0349	−0.798608
$456$	−7.26486	−0.340208
$457$	−20.9708	−0.980971	−0.490485	−	0.871449i	$-0.663180\pi$
$457$	−20.9708	−0.980971	−0.490485	+	0.871449i	$0.663180\pi$
$458$	−24.8431	−1.16084
$459$	2.26725	0.105826
$460$	14.2582	0.664793
$461$	−41.7923	−1.94646	−0.973231	−	0.229831i	$-0.926183\pi$
$461$	−41.7923	−1.94646	−0.973231	+	0.229831i	$0.926183\pi$
$462$	−7.12951	−0.331695
$463$	26.1791	1.21665	0.608324	−	0.793689i	$-0.291842\pi$
$463$	26.1791	1.21665	0.608324	+	0.793689i	$0.291842\pi$
$464$	−0.246991	−0.0114663
$465$	−18.1175	−0.840179
$466$	−12.1496	−0.562821
$467$	−15.3852	−0.711943	−0.355972	−	0.934497i	$-0.615850\pi$
$467$	−15.3852	−0.711943	−0.355972	+	0.934497i	$0.615850\pi$
$468$	−1.00000	−0.0462250
$469$	31.5445	1.45659
$470$	−41.8598	−1.93085
$471$	−6.01596	−0.277201
$472$	7.94815	0.365843
$473$	11.7810	0.541693
$474$	11.0249	0.506389
$475$	−69.3031	−3.17984
$476$	10.1289	0.464259
$477$	1.12894	0.0516904
$478$	0.102602	0.00469292
$479$	−9.98323	−0.456145	−0.228073	−	0.973644i	$-0.573242\pi$
$479$	−9.98323	−0.456145	−0.228073	+	0.973644i	$0.573242\pi$
$480$	3.81307	0.174042
$481$	−3.05081	−0.139105
$482$	2.41780	0.110128
$483$	16.7054	0.760120
$484$	−8.45323	−0.384238
$485$	−33.1546	−1.50547
$486$	1.00000	0.0453609
$487$	9.76763	0.442614	0.221307	−	0.975204i	$-0.428968\pi$
$487$	9.76763	0.442614	0.221307	+	0.975204i	$0.428968\pi$
$488$	2.85929	0.129434
$489$	−3.48106	−0.157419
$490$	49.4119	2.23220
$491$	2.66651	0.120338	0.0601689	−	0.998188i	$-0.480836\pi$
$491$	2.66651	0.120338	0.0601689	+	0.998188i	$0.480836\pi$
$492$	−4.71067	−0.212373
$493$	−0.559989	−0.0252207
$494$	7.26486	0.326862
$495$	−6.08512	−0.273506
$496$	−4.75143	−0.213345
$497$	6.76039	0.303245
$498$	−7.04586	−0.315733
$499$	3.22023	0.144157	0.0720786	−	0.997399i	$-0.477037\pi$
$499$	3.22023	0.144157	0.0720786	+	0.997399i	$0.477037\pi$
$500$	17.3094	0.774099
$501$	−4.16837	−0.186229
$502$	12.5884	0.561849
$503$	3.19738	0.142564	0.0712820	−	0.997456i	$-0.477291\pi$
$503$	3.19738	0.142564	0.0712820	+	0.997456i	$0.477291\pi$
$504$	4.46750	0.198998
$505$	64.1511	2.85468
$506$	−5.96741	−0.265284
$507$	1.00000	0.0444116
$508$	−16.6249	−0.737609
$509$	−16.4801	−0.730469	−0.365235	−	0.930916i	$-0.619011\pi$
$509$	−16.4801	−0.730469	−0.365235	+	0.930916i	$0.619011\pi$
$510$	8.64517	0.382815
$511$	69.8686	3.09080
$512$	1.00000	0.0441942
$513$	−7.26486	−0.320752
$514$	−22.3358	−0.985190
$515$	3.81307	0.168024
$516$	−7.38226	−0.324986
$517$	17.5193	0.770499
$518$	13.6295	0.598846
$519$	−3.26982	−0.143529
$520$	−3.81307	−0.167214
$521$	35.9379	1.57447	0.787234	−	0.616655i	$-0.211513\pi$
$521$	35.9379	1.57447	0.787234	+	0.616655i	$0.211513\pi$
$522$	−0.246991	−0.0108105
$523$	−9.53111	−0.416766	−0.208383	−	0.978047i	$-0.566820\pi$
$523$	−9.53111	−0.416766	−0.208383	+	0.978047i	$0.566820\pi$
$524$	−17.6247	−0.769937
$525$	42.6177	1.85999
$526$	−10.7061	−0.466807
$527$	−10.7727	−0.469264
$528$	−1.59586	−0.0694509
$529$	−9.01758	−0.392069
$530$	4.30471	0.186985
$531$	7.94815	0.344920
$532$	−32.4558	−1.40714
$533$	4.71067	0.204042
$534$	−3.12195	−0.135100
$535$	−34.2695	−1.48160
$536$	7.06089	0.304984
$537$	5.96568	0.257438
$538$	−5.95721	−0.256834
$539$	−20.6801	−0.890753
$540$	3.81307	0.164088
$541$	25.4045	1.09222	0.546112	−	0.837712i	$-0.316107\pi$
$541$	25.4045	1.09222	0.546112	+	0.837712i	$0.316107\pi$
$542$	−22.9356	−0.985170
$543$	−3.32325	−0.142615
$544$	2.26725	0.0972074
$545$	3.74053	0.160227
$546$	−4.46750	−0.191191
$547$	7.28803	0.311614	0.155807	−	0.987788i	$-0.450202\pi$
$547$	7.28803	0.311614	0.155807	+	0.987788i	$0.450202\pi$
$548$	2.86600	0.122429
$549$	2.85929	0.122031
$550$	−15.2237	−0.649140
$551$	1.79435	0.0764421
$552$	3.73931	0.159155
$553$	49.2536	2.09448
$554$	4.25730	0.180875
$555$	11.6329	0.493791
$556$	12.2423	0.519188
$557$	38.7139	1.64036	0.820179	−	0.572106i	$-0.193874\pi$
$557$	38.7139	1.64036	0.820179	+	0.572106i	$0.193874\pi$
$558$	−4.75143	−0.201144
$559$	7.38226	0.312236
$560$	17.0349	0.719855
$561$	−3.61821	−0.152761
$562$	−15.9367	−0.672248
$563$	33.4789	1.41097	0.705484	−	0.708726i	$-0.250730\pi$
$563$	33.4789	1.41097	0.705484	+	0.708726i	$0.250730\pi$
$564$	−10.9780	−0.462257
$565$	−10.0728	−0.423765
$566$	−17.1300	−0.720026
$567$	4.46750	0.187617
$568$	1.51324	0.0634940
$569$	−44.6323	−1.87108	−0.935541	−	0.353217i	$-0.885088\pi$
$569$	−44.6323	−1.87108	−0.935541	+	0.353217i	$0.885088\pi$
$570$	−27.7014	−1.16028
$571$	28.3539	1.18657	0.593287	−	0.804991i	$-0.297830\pi$
$571$	28.3539	1.18657	0.593287	+	0.804991i	$0.297830\pi$
$572$	1.59586	0.0667263
$573$	−3.77447	−0.157681
$574$	−21.0449	−0.878398
$575$	35.6711	1.48759
$576$	1.00000	0.0416667
$577$	16.3216	0.679475	0.339738	−	0.940520i	$-0.389662\pi$
$577$	16.3216	0.679475	0.339738	+	0.940520i	$0.389662\pi$
$578$	−11.8596	−0.493294
$579$	19.4237	0.807220
$580$	−0.941793	−0.0391058
$581$	−31.4774	−1.30590
$582$	−8.69500	−0.360419
$583$	−1.80162	−0.0746156
$584$	15.6393	0.647159
$585$	−3.81307	−0.157651
$586$	−9.34148	−0.385893
$587$	30.0515	1.24036	0.620179	−	0.784460i	$-0.287060\pi$
$587$	30.0515	1.24036	0.620179	+	0.784460i	$0.287060\pi$
$588$	12.9586	0.534402
$589$	34.5185	1.42231
$590$	30.3068	1.24771
$591$	−9.47214	−0.389632
$592$	3.05081	0.125388
$593$	−31.4461	−1.29134	−0.645668	−	0.763619i	$-0.723421\pi$
$593$	−31.4461	−1.29134	−0.645668	+	0.763619i	$0.723421\pi$
$594$	−1.59586	−0.0654789
$595$	38.6223	1.58336
$596$	17.5022	0.716920
$597$	−11.6570	−0.477090
$598$	−3.73931	−0.152912
$599$	14.3772	0.587435	0.293717	−	0.955892i	$-0.405108\pi$
$599$	14.3772	0.587435	0.293717	+	0.955892i	$0.405108\pi$
$600$	9.53949	0.389448
$601$	−14.5198	−0.592277	−0.296138	−	0.955145i	$-0.595699\pi$
$601$	−14.5198	−0.592277	−0.296138	+	0.955145i	$0.595699\pi$
$602$	−32.9802	−1.34417
$603$	7.06089	0.287542
$604$	13.8923	0.565272
$605$	−32.2327	−1.31045
$606$	16.8240	0.683428
$607$	42.6914	1.73279	0.866396	−	0.499357i	$-0.166430\pi$
$607$	42.6914	1.73279	0.866396	+	0.499357i	$0.166430\pi$
$608$	−7.26486	−0.294629
$609$	−1.10343	−0.0447133
$610$	10.9027	0.441436
$611$	10.9780	0.444122
$612$	2.26725	0.0916481
$613$	35.3379	1.42728	0.713641	−	0.700511i	$-0.247045\pi$
$613$	35.3379	1.42728	0.713641	+	0.700511i	$0.247045\pi$
$614$	20.1175	0.811877
$615$	−17.9621	−0.724302
$616$	−7.12951	−0.287256
$617$	−34.7496	−1.39897	−0.699483	−	0.714649i	$-0.746586\pi$
$617$	−34.7496	−1.39897	−0.699483	+	0.714649i	$0.746586\pi$
$618$	1.00000	0.0402259
$619$	26.1704	1.05188	0.525938	−	0.850523i	$-0.323714\pi$
$619$	26.1704	1.05188	0.525938	+	0.850523i	$0.323714\pi$
$620$	−18.1175	−0.727617
$621$	3.73931	0.150053
$622$	−9.05660	−0.363137
$623$	−13.9473	−0.558788
$624$	−1.00000	−0.0400320
$625$	18.3044	0.732175
$626$	−19.7267	−0.788439
$627$	11.5937	0.463008
$628$	−6.01596	−0.240063
$629$	6.91694	0.275797
$630$	17.0349	0.678686
$631$	−42.0523	−1.67408	−0.837038	−	0.547145i	$-0.815715\pi$
$631$	−42.0523	−1.67408	−0.837038	+	0.547145i	$0.815715\pi$
$632$	11.0249	0.438546
$633$	−8.84899	−0.351716
$634$	21.9781	0.872863
$635$	−63.3918	−2.51563
$636$	1.12894	0.0447652
$637$	−12.9586	−0.513437
$638$	0.394163	0.0156051
$639$	1.51324	0.0598627
$640$	3.81307	0.150725
$641$	−12.3917	−0.489441	−0.244721	−	0.969594i	$-0.578696\pi$
$641$	−12.3917	−0.489441	−0.244721	+	0.969594i	$0.578696\pi$
$642$	−8.98739	−0.354704
$643$	−31.9464	−1.25984	−0.629922	−	0.776659i	$-0.716913\pi$
$643$	−31.9464	−1.25984	−0.629922	+	0.776659i	$0.716913\pi$
$644$	16.7054	0.658283
$645$	−28.1490	−1.10837
$646$	−16.4712	−0.648052
$647$	11.9548	0.469991	0.234995	−	0.971996i	$-0.424492\pi$
$647$	11.9548	0.469991	0.234995	+	0.971996i	$0.424492\pi$
$648$	1.00000	0.0392837
$649$	−12.6841	−0.497896
$650$	−9.53949	−0.374169
$651$	−21.2270	−0.831952
$652$	−3.48106	−0.136329
$653$	40.4032	1.58110	0.790549	−	0.612399i	$-0.209795\pi$
$653$	40.4032	1.58110	0.790549	+	0.612399i	$0.209795\pi$
$654$	0.980976	0.0383592
$655$	−67.2041	−2.62588
$656$	−4.71067	−0.183921
$657$	15.6393	0.610147
$658$	−49.0442	−1.91194
$659$	−11.5177	−0.448668	−0.224334	−	0.974512i	$-0.572021\pi$
$659$	−11.5177	−0.448668	−0.224334	+	0.974512i	$0.572021\pi$
$660$	−6.08512	−0.236863
$661$	14.8567	0.577859	0.288929	−	0.957350i	$-0.406701\pi$
$661$	14.8567	0.577859	0.288929	+	0.957350i	$0.406701\pi$
$662$	−15.8719	−0.616880
$663$	−2.26725	−0.0880526
$664$	−7.04586	−0.273432
$665$	−123.756	−4.79906
$666$	3.05081	0.118217
$667$	−0.923575	−0.0357610
$668$	−4.16837	−0.161279
$669$	−16.0641	−0.621074
$670$	26.9237	1.04015
$671$	−4.56302	−0.176154
$672$	4.46750	0.172338
$673$	−22.4985	−0.867255	−0.433628	−	0.901092i	$-0.642767\pi$
$673$	−22.4985	−0.867255	−0.433628	+	0.901092i	$0.642767\pi$
$674$	32.0677	1.23520
$675$	9.53949	0.367175
$676$	1.00000	0.0384615
$677$	14.9884	0.576049	0.288025	−	0.957623i	$-0.407001\pi$
$677$	14.9884	0.576049	0.288025	+	0.957623i	$0.407001\pi$
$678$	−2.64165	−0.101452
$679$	−38.8449	−1.49073
$680$	8.64517	0.331527
$681$	16.1341	0.618261
$682$	7.58261	0.290353
$683$	31.1041	1.19017	0.595084	−	0.803664i	$-0.297119\pi$
$683$	31.1041	1.19017	0.595084	+	0.803664i	$0.297119\pi$
$684$	−7.26486	−0.277779
$685$	10.9282	0.417547
$686$	26.6199	1.01635
$687$	−24.8431	−0.947823
$688$	−7.38226	−0.281446
$689$	−1.12894	−0.0430090
$690$	14.2582	0.542802
$691$	7.95175	0.302499	0.151249	−	0.988496i	$-0.451670\pi$
$691$	7.95175	0.302499	0.151249	+	0.988496i	$0.451670\pi$
$692$	−3.26982	−0.124300
$693$	−7.12951	−0.270828
$694$	−26.9359	−1.02247
$695$	46.6806	1.77070
$696$	−0.246991	−0.00936216
$697$	−10.6803	−0.404543
$698$	−19.1811	−0.726014
$699$	−12.1496	−0.459542
$700$	42.6177	1.61080
$701$	6.53007	0.246637	0.123319	−	0.992367i	$-0.460646\pi$
$701$	6.53007	0.246637	0.123319	+	0.992367i	$0.460646\pi$
$702$	−1.00000	−0.0377426
$703$	−22.1637	−0.835921
$704$	−1.59586	−0.0601462
$705$	−41.8598	−1.57653
$706$	30.1259	1.13380
$707$	75.1612	2.82673
$708$	7.94815	0.298710
$709$	−36.1214	−1.35657	−0.678284	−	0.734799i	$-0.737276\pi$
$709$	−36.1214	−1.35657	−0.678284	+	0.734799i	$0.737276\pi$
$710$	5.77007	0.216547
$711$	11.0249	0.413465
$712$	−3.12195	−0.117000
$713$	−17.7670	−0.665381
$714$	10.1289	0.379066
$715$	6.08512	0.227571
$716$	5.96568	0.222948
$717$	0.102602	0.00383176
$718$	−24.0036	−0.895808
$719$	29.5528	1.10213	0.551066	−	0.834461i	$-0.314221\pi$
$719$	29.5528	1.10213	0.551066	+	0.834461i	$0.314221\pi$
$720$	3.81307	0.142105
$721$	4.46750	0.166378
$722$	33.7782	1.25710
$723$	2.41780	0.0899190
$724$	−3.32325	−0.123508
$725$	−2.35617	−0.0875058
$726$	−8.45323	−0.313729
$727$	12.7601	0.473245	0.236623	−	0.971602i	$-0.423959\pi$
$727$	12.7601	0.473245	0.236623	+	0.971602i	$0.423959\pi$
$728$	−4.46750	−0.165577
$729$	1.00000	0.0370370
$730$	59.6337	2.20714
$731$	−16.7374	−0.619055
$732$	2.85929	0.105682
$733$	43.4534	1.60499	0.802495	−	0.596659i	$-0.203506\pi$
$733$	43.4534	1.60499	0.802495	+	0.596659i	$0.203506\pi$
$734$	−28.6267	−1.05663
$735$	49.4119	1.82258
$736$	3.73931	0.137833
$737$	−11.2682	−0.415069
$738$	−4.71067	−0.173402
$739$	−5.51930	−0.203031	−0.101515	−	0.994834i	$-0.532369\pi$
$739$	−5.51930	−0.203031	−0.101515	+	0.994834i	$0.532369\pi$
$740$	11.6329	0.427636
$741$	7.26486	0.266881
$742$	5.04352	0.185154
$743$	26.9330	0.988077	0.494038	−	0.869440i	$-0.335520\pi$
$743$	26.9330	0.988077	0.494038	+	0.869440i	$0.335520\pi$
$744$	−4.75143	−0.174196
$745$	66.7373	2.44506
$746$	22.0872	0.808669
$747$	−7.04586	−0.257795
$748$	−3.61821	−0.132295
$749$	−40.1512	−1.46709
$750$	17.3094	0.632049
$751$	18.6079	0.679010	0.339505	−	0.940604i	$-0.389740\pi$
$751$	18.6079	0.679010	0.339505	+	0.940604i	$0.389740\pi$
$752$	−10.9780	−0.400326
$753$	12.5884	0.458748
$754$	0.246991	0.00899488
$755$	52.9725	1.92787
$756$	4.46750	0.162481
$757$	49.9205	1.81439	0.907196	−	0.420709i	$-0.138219\pi$
$757$	49.9205	1.81439	0.907196	+	0.420709i	$0.138219\pi$
$758$	−11.7744	−0.427667
$759$	−5.96741	−0.216603
$760$	−27.7014	−1.00484
$761$	8.17020	0.296170	0.148085	−	0.988975i	$-0.452689\pi$
$761$	8.17020	0.296170	0.148085	+	0.988975i	$0.452689\pi$
$762$	−16.6249	−0.602256
$763$	4.38251	0.158658
$764$	−3.77447	−0.136555
$765$	8.64517	0.312567
$766$	5.26266	0.190148
$767$	−7.94815	−0.286991
$768$	1.00000	0.0360844
$769$	22.5895	0.814598	0.407299	−	0.913295i	$-0.366471\pi$
$769$	22.5895	0.814598	0.407299	+	0.913295i	$0.366471\pi$
$770$	−27.1853	−0.979690
$771$	−22.3358	−0.804405
$772$	19.4237	0.699073
$773$	23.7494	0.854206	0.427103	−	0.904203i	$-0.359534\pi$
$773$	23.7494	0.854206	0.427103	+	0.904203i	$0.359534\pi$
$774$	−7.38226	−0.265350
$775$	−45.3262	−1.62816
$776$	−8.69500	−0.312132
$777$	13.6295	0.488956
$778$	9.50462	0.340757
$779$	34.2224	1.22614
$780$	−3.81307	−0.136530
$781$	−2.41491	−0.0864124
$782$	8.47794	0.303170
$783$	−0.246991	−0.00882673
$784$	12.9586	0.462806
$785$	−22.9392	−0.818737
$786$	−17.6247	−0.628651
$787$	−32.8977	−1.17268	−0.586338	−	0.810066i	$-0.699431\pi$
$787$	−32.8977	−1.17268	−0.586338	+	0.810066i	$0.699431\pi$
$788$	−9.47214	−0.337431
$789$	−10.7061	−0.381147
$790$	42.0386	1.49566
$791$	−11.8016	−0.419615
$792$	−1.59586	−0.0567064
$793$	−2.85929	−0.101536
$794$	−33.1473	−1.17635
$795$	4.30471	0.152672
$796$	−11.6570	−0.413172
$797$	22.1574	0.784854	0.392427	−	0.919783i	$-0.371636\pi$
$797$	22.1574	0.784854	0.392427	+	0.919783i	$0.371636\pi$
$798$	−32.4558	−1.14892
$799$	−24.8898	−0.880538
$800$	9.53949	0.337272
$801$	−3.12195	−0.110309
$802$	19.6209	0.692839
$803$	−24.9581	−0.880753
$804$	7.06089	0.249018
$805$	63.6987	2.24508
$806$	4.75143	0.167362
$807$	−5.95721	−0.209704
$808$	16.8240	0.591866
$809$	−21.0338	−0.739508	−0.369754	−	0.929130i	$-0.620558\pi$
$809$	−21.0338	−0.739508	−0.369754	+	0.929130i	$0.620558\pi$
$810$	3.81307	0.133978
$811$	15.5444	0.545838	0.272919	−	0.962037i	$-0.412011\pi$
$811$	15.5444	0.545838	0.272919	+	0.962037i	$0.412011\pi$
$812$	−1.10343	−0.0387229
$813$	−22.9356	−0.804388
$814$	−4.86867	−0.170647
$815$	−13.2735	−0.464951
$816$	2.26725	0.0793695
$817$	53.6311	1.87631
$818$	−39.4468	−1.37923
$819$	−4.46750	−0.156107
$820$	−17.9621	−0.627264
$821$	13.5064	0.471376	0.235688	−	0.971829i	$-0.424266\pi$
$821$	13.5064	0.471376	0.235688	+	0.971829i	$0.424266\pi$
$822$	2.86600	0.0999632
$823$	41.4443	1.44466	0.722329	−	0.691549i	$-0.243071\pi$
$823$	41.4443	1.44466	0.722329	+	0.691549i	$0.243071\pi$
$824$	1.00000	0.0348367
$825$	−15.2237	−0.530021
$826$	35.5084	1.23549
$827$	16.7467	0.582340	0.291170	−	0.956671i	$-0.405955\pi$
$827$	16.7467	0.582340	0.291170	+	0.956671i	$0.405955\pi$
$828$	3.73931	0.129950
$829$	28.2746	0.982018	0.491009	−	0.871155i	$-0.336628\pi$
$829$	28.2746	0.982018	0.491009	+	0.871155i	$0.336628\pi$
$830$	−26.8663	−0.932545
$831$	4.25730	0.147684
$832$	−1.00000	−0.0346688
$833$	29.3803	1.01797
$834$	12.2423	0.423915
$835$	−15.8943	−0.550044
$836$	11.5937	0.400977
$837$	−4.75143	−0.164233
$838$	−19.8115	−0.684375
$839$	5.08045	0.175397	0.0876984	−	0.996147i	$-0.472049\pi$
$839$	5.08045	0.175397	0.0876984	+	0.996147i	$0.472049\pi$
$840$	17.0349	0.587759
$841$	−28.9390	−0.997896
$842$	9.45934	0.325990
$843$	−15.9367	−0.548888
$844$	−8.84899	−0.304595
$845$	3.81307	0.131174
$846$	−10.9780	−0.377431
$847$	−37.7648	−1.29761
$848$	1.12894	0.0387678
$849$	−17.1300	−0.587898
$850$	21.6284	0.741847
$851$	11.4079	0.391058
$852$	1.51324	0.0518426
$853$	21.0688	0.721382	0.360691	−	0.932685i	$-0.382541\pi$
$853$	21.0688	0.721382	0.360691	+	0.932685i	$0.382541\pi$
$854$	12.7739	0.437113
$855$	−27.7014	−0.947368
$856$	−8.98739	−0.307183
$857$	43.4591	1.48453	0.742267	−	0.670104i	$-0.233750\pi$
$857$	43.4591	1.48453	0.742267	+	0.670104i	$0.233750\pi$
$858$	1.59586	0.0544818
$859$	−16.5921	−0.566116	−0.283058	−	0.959103i	$-0.591349\pi$
$859$	−16.5921	−0.566116	−0.283058	+	0.959103i	$0.591349\pi$
$860$	−28.1490	−0.959874
$861$	−21.0449	−0.717209
$862$	33.7764	1.15043
$863$	−15.9334	−0.542380	−0.271190	−	0.962526i	$-0.587417\pi$
$863$	−15.9334	−0.542380	−0.271190	+	0.962526i	$0.587417\pi$
$864$	1.00000	0.0340207
$865$	−12.4680	−0.423926
$866$	−33.4766	−1.13758
$867$	−11.8596	−0.402773
$868$	−21.2270	−0.720491
$869$	−17.5941	−0.596840
$870$	−0.941793	−0.0319298
$871$	−7.06089	−0.239249
$872$	0.980976	0.0332200
$873$	−8.69500	−0.294281
$874$	−27.1656	−0.918889
$875$	77.3296	2.61422
$876$	15.6393	0.528403
$877$	39.8697	1.34630	0.673152	−	0.739504i	$-0.264940\pi$
$877$	39.8697	1.34630	0.673152	+	0.739504i	$0.264940\pi$
$878$	25.8749	0.873236
$879$	−9.34148	−0.315080
$880$	−6.08512	−0.205129
$881$	−11.3662	−0.382938	−0.191469	−	0.981499i	$-0.561325\pi$
$881$	−11.3662	−0.382938	−0.191469	+	0.981499i	$0.561325\pi$
$882$	12.9586	0.436338
$883$	19.0405	0.640764	0.320382	−	0.947288i	$-0.396189\pi$
$883$	19.0405	0.640764	0.320382	+	0.947288i	$0.396189\pi$
$884$	−2.26725	−0.0762558
$885$	30.3068	1.01875
$886$	13.5986	0.456854
$887$	−29.6275	−0.994794	−0.497397	−	0.867523i	$-0.665711\pi$
$887$	−29.6275	−0.994794	−0.497397	+	0.867523i	$0.665711\pi$
$888$	3.05081	0.102378
$889$	−74.2716	−2.49099
$890$	−11.9042	−0.399030
$891$	−1.59586	−0.0534633
$892$	−16.0641	−0.537866
$893$	79.7536	2.66885
$894$	17.5022	0.585363
$895$	22.7475	0.760366
$896$	4.46750	0.149249
$897$	−3.73931	−0.124852
$898$	11.8898	0.396769
$899$	1.17356	0.0391404
$900$	9.53949	0.317983
$901$	2.55958	0.0852719
$902$	7.51757	0.250308
$903$	−32.9802	−1.09751
$904$	−2.64165	−0.0878599
$905$	−12.6718	−0.421225
$906$	13.8923	0.461542
$907$	−49.6204	−1.64762	−0.823808	−	0.566868i	$-0.808155\pi$
$907$	−49.6204	−1.64762	−0.823808	+	0.566868i	$0.808155\pi$
$908$	16.1341	0.535430
$909$	16.8240	0.558017
$910$	−17.0349	−0.564701
$911$	−26.4909	−0.877682	−0.438841	−	0.898565i	$-0.644611\pi$
$911$	−26.4909	−0.877682	−0.438841	+	0.898565i	$0.644611\pi$
$912$	−7.26486	−0.240564
$913$	11.2442	0.372129
$914$	−20.9708	−0.693651
$915$	10.9027	0.360431
$916$	−24.8431	−0.820839
$917$	−78.7382	−2.60017
$918$	2.26725	0.0748303
$919$	−13.4291	−0.442984	−0.221492	−	0.975162i	$-0.571093\pi$
$919$	−13.4291	−0.442984	−0.221492	+	0.975162i	$0.571093\pi$
$920$	14.2582	0.470080
$921$	20.1175	0.662895
$922$	−41.7923	−1.37636
$923$	−1.51324	−0.0498088
$924$	−7.12951	−0.234544
$925$	29.1032	0.956906
$926$	26.1791	0.860300
$927$	1.00000	0.0328443
$928$	−0.246991	−0.00810787
$929$	50.0478	1.64202	0.821008	−	0.570917i	$-0.193412\pi$
$929$	50.0478	1.64202	0.821008	+	0.570917i	$0.193412\pi$
$930$	−18.1175	−0.594096
$931$	−94.1422	−3.08539
$932$	−12.1496	−0.397975
$933$	−9.05660	−0.296500
$934$	−15.3852	−0.503420
$935$	−13.7965	−0.451193
$936$	−1.00000	−0.0326860
$937$	−11.3746	−0.371590	−0.185795	−	0.982588i	$-0.559486\pi$
$937$	−11.3746	−0.371590	−0.185795	+	0.982588i	$0.559486\pi$
$938$	31.5445	1.02997
$939$	−19.7267	−0.643758
$940$	−41.8598	−1.36532
$941$	12.4848	0.406992	0.203496	−	0.979076i	$-0.434770\pi$
$941$	12.4848	0.406992	0.203496	+	0.979076i	$0.434770\pi$
$942$	−6.01596	−0.196010
$943$	−17.6146	−0.573612
$944$	7.94815	0.258690
$945$	17.0349	0.554145
$946$	11.7810	0.383035
$947$	47.0980	1.53048	0.765239	−	0.643746i	$-0.222621\pi$
$947$	47.0980	1.53048	0.765239	+	0.643746i	$0.222621\pi$
$948$	11.0249	0.358071
$949$	−15.6393	−0.507673
$950$	−69.3031	−2.24849
$951$	21.9781	0.712689
$952$	10.1289	0.328281
$953$	−20.6992	−0.670514	−0.335257	−	0.942127i	$-0.608823\pi$
$953$	−20.6992	−0.670514	−0.335257	+	0.942127i	$0.608823\pi$
$954$	1.12894	0.0365506
$955$	−14.3923	−0.465724
$956$	0.102602	0.00331840
$957$	0.394163	0.0127415
$958$	−9.98323	−0.322543
$959$	12.8039	0.413458
$960$	3.81307	0.123066
$961$	−8.42396	−0.271741
$962$	−3.05081	−0.0983621
$963$	−8.98739	−0.289615
$964$	2.41780	0.0778721
$965$	74.0638	2.38420
$966$	16.7054	0.537486
$967$	14.9670	0.481307	0.240653	−	0.970611i	$-0.422638\pi$
$967$	14.9670	0.481307	0.240653	+	0.970611i	$0.422638\pi$
$968$	−8.45323	−0.271697
$969$	−16.4712	−0.529133
$970$	−33.1546	−1.06453
$971$	−8.32582	−0.267188	−0.133594	−	0.991036i	$-0.542652\pi$
$971$	−8.32582	−0.267188	−0.133594	+	0.991036i	$0.542652\pi$
$972$	1.00000	0.0320750
$973$	54.6924	1.75336
$974$	9.76763	0.312975
$975$	−9.53949	−0.305508
$976$	2.85929	0.0915236
$977$	−44.1257	−1.41171	−0.705853	−	0.708359i	$-0.749436\pi$
$977$	−44.1257	−1.41171	−0.705853	+	0.708359i	$0.749436\pi$
$978$	−3.48106	−0.111312
$979$	4.98220	0.159232
$980$	49.4119	1.57840
$981$	0.980976	0.0313202
$982$	2.66651	0.0850917
$983$	−9.95145	−0.317402	−0.158701	−	0.987327i	$-0.550731\pi$
$983$	−9.95145	−0.317402	−0.158701	+	0.987327i	$0.550731\pi$
$984$	−4.71067	−0.150171
$985$	−36.1179	−1.15081
$986$	−0.559989	−0.0178337
$987$	−49.0442	−1.56109
$988$	7.26486	0.231126
$989$	−27.6045	−0.877773
$990$	−6.08512	−0.193398
$991$	−33.7123	−1.07091	−0.535453	−	0.844565i	$-0.679859\pi$
$991$	−33.7123	−1.07091	−0.535453	+	0.844565i	$0.679859\pi$
$992$	−4.75143	−0.150858
$993$	−15.8719	−0.503680
$994$	6.76039	0.214426
$995$	−44.4490	−1.40913
$996$	−7.04586	−0.223257
$997$	−10.0853	−0.319405	−0.159702	−	0.987165i	$-0.551053\pi$
$997$	−10.0853	−0.319405	−0.159702	+	0.987165i	$0.551053\pi$
$998$	3.22023	0.101935
$999$	3.05081	0.0965234

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bd.1.16	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bd.1.16	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.81307 q^{5} +1.00000 q^{6} +4.46750 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.81307 q^{5} +1.00000 q^{6} +4.46750 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.81307 q^{10} -1.59586 q^{11} +1.00000 q^{12} -1.00000 q^{13} +4.46750 q^{14} +3.81307 q^{15} +1.00000 q^{16} +2.26725 q^{17} +1.00000 q^{18} -7.26486 q^{19} +3.81307 q^{20} +4.46750 q^{21} -1.59586 q^{22} +3.73931 q^{23} +1.00000 q^{24} +9.53949 q^{25} -1.00000 q^{26} +1.00000 q^{27} +4.46750 q^{28} -0.246991 q^{29} +3.81307 q^{30} -4.75143 q^{31} +1.00000 q^{32} -1.59586 q^{33} +2.26725 q^{34} +17.0349 q^{35} +1.00000 q^{36} +3.05081 q^{37} -7.26486 q^{38} -1.00000 q^{39} +3.81307 q^{40} -4.71067 q^{41} +4.46750 q^{42} -7.38226 q^{43} -1.59586 q^{44} +3.81307 q^{45} +3.73931 q^{46} -10.9780 q^{47} +1.00000 q^{48} +12.9586 q^{49} +9.53949 q^{50} +2.26725 q^{51} -1.00000 q^{52} +1.12894 q^{53} +1.00000 q^{54} -6.08512 q^{55} +4.46750 q^{56} -7.26486 q^{57} -0.246991 q^{58} +7.94815 q^{59} +3.81307 q^{60} +2.85929 q^{61} -4.75143 q^{62} +4.46750 q^{63} +1.00000 q^{64} -3.81307 q^{65} -1.59586 q^{66} +7.06089 q^{67} +2.26725 q^{68} +3.73931 q^{69} +17.0349 q^{70} +1.51324 q^{71} +1.00000 q^{72} +15.6393 q^{73} +3.05081 q^{74} +9.53949 q^{75} -7.26486 q^{76} -7.12951 q^{77} -1.00000 q^{78} +11.0249 q^{79} +3.81307 q^{80} +1.00000 q^{81} -4.71067 q^{82} -7.04586 q^{83} +4.46750 q^{84} +8.64517 q^{85} -7.38226 q^{86} -0.246991 q^{87} -1.59586 q^{88} -3.12195 q^{89} +3.81307 q^{90} -4.46750 q^{91} +3.73931 q^{92} -4.75143 q^{93} -10.9780 q^{94} -27.7014 q^{95} +1.00000 q^{96} -8.69500 q^{97} +12.9586 q^{98} -1.59586 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) \) 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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