LMFDB - Embedded newform 8034.2.a.ba.1.8

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:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 44 x^{12} + 36 x^{11} + 722 x^{10} - 451 x^{9} - 5438 x^{8} + 2268 x^{7} + 18441 x^{6} + \cdots - 1492 $ x^14 - x^13 - 44x^12 + 36x^11 + 722x^10 - 451x^9 - 5438x^8 + 2268x^7 + 18441x^6 - 4126x^5 - 22759x^4 + 2997x^3 + 10504x^2 - 506x - 1492
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-0.522326$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.522326 q^{5} +1.00000 q^{6} -2.74868 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.522326 q^{5} +1.00000 q^{6} -2.74868 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.522326 q^{10} -0.360369 q^{11} -1.00000 q^{12} -1.00000 q^{13} +2.74868 q^{14} -0.522326 q^{15} +1.00000 q^{16} +1.93116 q^{17} -1.00000 q^{18} -0.748297 q^{19} +0.522326 q^{20} +2.74868 q^{21} +0.360369 q^{22} -1.23649 q^{23} +1.00000 q^{24} -4.72718 q^{25} +1.00000 q^{26} -1.00000 q^{27} -2.74868 q^{28} -4.90740 q^{29} +0.522326 q^{30} +1.19890 q^{31} -1.00000 q^{32} +0.360369 q^{33} -1.93116 q^{34} -1.43571 q^{35} +1.00000 q^{36} -2.99837 q^{37} +0.748297 q^{38} +1.00000 q^{39} -0.522326 q^{40} +5.55715 q^{41} -2.74868 q^{42} +5.82398 q^{43} -0.360369 q^{44} +0.522326 q^{45} +1.23649 q^{46} -0.902971 q^{47} -1.00000 q^{48} +0.555246 q^{49} +4.72718 q^{50} -1.93116 q^{51} -1.00000 q^{52} -9.38100 q^{53} +1.00000 q^{54} -0.188230 q^{55} +2.74868 q^{56} +0.748297 q^{57} +4.90740 q^{58} +6.21543 q^{59} -0.522326 q^{60} +6.71192 q^{61} -1.19890 q^{62} -2.74868 q^{63} +1.00000 q^{64} -0.522326 q^{65} -0.360369 q^{66} +2.28386 q^{67} +1.93116 q^{68} +1.23649 q^{69} +1.43571 q^{70} -1.41208 q^{71} -1.00000 q^{72} -15.8684 q^{73} +2.99837 q^{74} +4.72718 q^{75} -0.748297 q^{76} +0.990539 q^{77} -1.00000 q^{78} -7.70563 q^{79} +0.522326 q^{80} +1.00000 q^{81} -5.55715 q^{82} -2.77287 q^{83} +2.74868 q^{84} +1.00870 q^{85} -5.82398 q^{86} +4.90740 q^{87} +0.360369 q^{88} +1.03216 q^{89} -0.522326 q^{90} +2.74868 q^{91} -1.23649 q^{92} -1.19890 q^{93} +0.902971 q^{94} -0.390855 q^{95} +1.00000 q^{96} +7.76875 q^{97} -0.555246 q^{98} -0.360369 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9} + q^{10} - q^{11} - 14 q^{12} - 14 q^{13} - 5 q^{14} + q^{15} + 14 q^{16} - 12 q^{17} - 14 q^{18} + 10 q^{19} - q^{20} - 5 q^{21} + q^{22} - q^{23} + 14 q^{24} + 19 q^{25} + 14 q^{26} - 14 q^{27} + 5 q^{28} + 6 q^{29} - q^{30} + 20 q^{31} - 14 q^{32} + q^{33} + 12 q^{34} - 16 q^{35} + 14 q^{36} - 3 q^{37} - 10 q^{38} + 14 q^{39} + q^{40} + q^{41} + 5 q^{42} + 6 q^{43} - q^{44} - q^{45} + q^{46} - 13 q^{47} - 14 q^{48} + 9 q^{49} - 19 q^{50} + 12 q^{51} - 14 q^{52} - 27 q^{53} + 14 q^{54} + 10 q^{55} - 5 q^{56} - 10 q^{57} - 6 q^{58} - 6 q^{59} + q^{60} - 4 q^{61} - 20 q^{62} + 5 q^{63} + 14 q^{64} + q^{65} - q^{66} + 13 q^{67} - 12 q^{68} + q^{69} + 16 q^{70} + 18 q^{71} - 14 q^{72} + 11 q^{73} + 3 q^{74} - 19 q^{75} + 10 q^{76} - 15 q^{77} - 14 q^{78} + 33 q^{79} - q^{80} + 14 q^{81} - q^{82} - 25 q^{83} - 5 q^{84} + 25 q^{85} - 6 q^{86} - 6 q^{87} + q^{88} + 3 q^{89} + q^{90} - 5 q^{91} - q^{92} - 20 q^{93} + 13 q^{94} + 30 q^{95} + 14 q^{96} + 11 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9 + q^10 - q^11 - 14 * q^12 - 14 * q^13 - 5 * q^14 + q^15 + 14 * q^16 - 12 * q^17 - 14 * q^18 + 10 * q^19 - q^20 - 5 * q^21 + q^22 - q^23 + 14 * q^24 + 19 * q^25 + 14 * q^26 - 14 * q^27 + 5 * q^28 + 6 * q^29 - q^30 + 20 * q^31 - 14 * q^32 + q^33 + 12 * q^34 - 16 * q^35 + 14 * q^36 - 3 * q^37 - 10 * q^38 + 14 * q^39 + q^40 + q^41 + 5 * q^42 + 6 * q^43 - q^44 - q^45 + q^46 - 13 * q^47 - 14 * q^48 + 9 * q^49 - 19 * q^50 + 12 * q^51 - 14 * q^52 - 27 * q^53 + 14 * q^54 + 10 * q^55 - 5 * q^56 - 10 * q^57 - 6 * q^58 - 6 * q^59 + q^60 - 4 * q^61 - 20 * q^62 + 5 * q^63 + 14 * q^64 + q^65 - q^66 + 13 * q^67 - 12 * q^68 + q^69 + 16 * q^70 + 18 * q^71 - 14 * q^72 + 11 * q^73 + 3 * q^74 - 19 * q^75 + 10 * q^76 - 15 * q^77 - 14 * q^78 + 33 * q^79 - q^80 + 14 * q^81 - q^82 - 25 * q^83 - 5 * q^84 + 25 * q^85 - 6 * q^86 - 6 * q^87 + q^88 + 3 * q^89 + q^90 - 5 * q^91 - q^92 - 20 * q^93 + 13 * q^94 + 30 * q^95 + 14 * q^96 + 11 * q^97 - 9 * q^98 - 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
$5$	0.522326	0.233591	0.116796	−	0.993156i	$-0.462738\pi$
$5$	0.522326	0.233591	0.116796	+	0.993156i	$0.462738\pi$
$6$	1.00000	0.408248
$7$	−2.74868	−1.03890	−0.519452	−	0.854500i	$-0.673864\pi$
$7$	−2.74868	−1.03890	−0.519452	+	0.854500i	$0.673864\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−0.522326	−0.165174
$11$	−0.360369	−0.108655	−0.0543276	−	0.998523i	$-0.517302\pi$
$11$	−0.360369	−0.108655	−0.0543276	+	0.998523i	$0.517302\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.74868	0.734616
$15$	−0.522326	−0.134864
$16$	1.00000	0.250000
$17$	1.93116	0.468376	0.234188	−	0.972191i	$-0.424757\pi$
$17$	1.93116	0.468376	0.234188	+	0.972191i	$0.424757\pi$
$18$	−1.00000	−0.235702
$19$	−0.748297	−0.171671	−0.0858355	−	0.996309i	$-0.527356\pi$
$19$	−0.748297	−0.171671	−0.0858355	+	0.996309i	$0.527356\pi$
$20$	0.522326	0.116796
$21$	2.74868	0.599811
$22$	0.360369	0.0768309
$23$	−1.23649	−0.257827	−0.128913	−	0.991656i	$-0.541149\pi$
$23$	−1.23649	−0.257827	−0.128913	+	0.991656i	$0.541149\pi$
$24$	1.00000	0.204124
$25$	−4.72718	−0.945435
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	−2.74868	−0.519452
$29$	−4.90740	−0.911281	−0.455640	−	0.890164i	$-0.650590\pi$
$29$	−4.90740	−0.911281	−0.455640	+	0.890164i	$0.650590\pi$
$30$	0.522326	0.0953632
$31$	1.19890	0.215330	0.107665	−	0.994187i	$-0.465663\pi$
$31$	1.19890	0.215330	0.107665	+	0.994187i	$0.465663\pi$
$32$	−1.00000	−0.176777
$33$	0.360369	0.0627321
$34$	−1.93116	−0.331192
$35$	−1.43571	−0.242679
$36$	1.00000	0.166667
$37$	−2.99837	−0.492929	−0.246465	−	0.969152i	$-0.579269\pi$
$37$	−2.99837	−0.492929	−0.246465	+	0.969152i	$0.579269\pi$
$38$	0.748297	0.121390
$39$	1.00000	0.160128
$40$	−0.522326	−0.0825869
$41$	5.55715	0.867882	0.433941	−	0.900941i	$-0.357123\pi$
$41$	5.55715	0.867882	0.433941	+	0.900941i	$0.357123\pi$
$42$	−2.74868	−0.424131
$43$	5.82398	0.888148	0.444074	−	0.895990i	$-0.353533\pi$
$43$	5.82398	0.888148	0.444074	+	0.895990i	$0.353533\pi$
$44$	−0.360369	−0.0543276
$45$	0.522326	0.0778637
$46$	1.23649	0.182311
$47$	−0.902971	−0.131712	−0.0658559	−	0.997829i	$-0.520978\pi$
$47$	−0.902971	−0.131712	−0.0658559	+	0.997829i	$0.520978\pi$
$48$	−1.00000	−0.144338
$49$	0.555246	0.0793209
$50$	4.72718	0.668524
$51$	−1.93116	−0.270417
$52$	−1.00000	−0.138675
$53$	−9.38100	−1.28858	−0.644290	−	0.764781i	$-0.722847\pi$
$53$	−9.38100	−1.28858	−0.644290	+	0.764781i	$0.722847\pi$
$54$	1.00000	0.136083
$55$	−0.188230	−0.0253809
$56$	2.74868	0.367308
$57$	0.748297	0.0991143
$58$	4.90740	0.644373
$59$	6.21543	0.809181	0.404590	−	0.914498i	$-0.367414\pi$
$59$	6.21543	0.809181	0.404590	+	0.914498i	$0.367414\pi$
$60$	−0.522326	−0.0674320
$61$	6.71192	0.859374	0.429687	−	0.902978i	$-0.358624\pi$
$61$	6.71192	0.859374	0.429687	+	0.902978i	$0.358624\pi$
$62$	−1.19890	−0.152261
$63$	−2.74868	−0.346301
$64$	1.00000	0.125000
$65$	−0.522326	−0.0647865
$66$	−0.360369	−0.0443583
$67$	2.28386	0.279018	0.139509	−	0.990221i	$-0.455448\pi$
$67$	2.28386	0.279018	0.139509	+	0.990221i	$0.455448\pi$
$68$	1.93116	0.234188
$69$	1.23649	0.148856
$70$	1.43571	0.171600
$71$	−1.41208	−0.167583	−0.0837914	−	0.996483i	$-0.526703\pi$
$71$	−1.41208	−0.167583	−0.0837914	+	0.996483i	$0.526703\pi$
$72$	−1.00000	−0.117851
$73$	−15.8684	−1.85725	−0.928626	−	0.371017i	$-0.879009\pi$
$73$	−15.8684	−1.85725	−0.928626	+	0.371017i	$0.879009\pi$
$74$	2.99837	0.348554
$75$	4.72718	0.545847
$76$	−0.748297	−0.0858355
$77$	0.990539	0.112882
$78$	−1.00000	−0.113228
$79$	−7.70563	−0.866951	−0.433475	−	0.901165i	$-0.642713\pi$
$79$	−7.70563	−0.866951	−0.433475	+	0.901165i	$0.642713\pi$
$80$	0.522326	0.0583978
$81$	1.00000	0.111111
$82$	−5.55715	−0.613685
$83$	−2.77287	−0.304362	−0.152181	−	0.988353i	$-0.548630\pi$
$83$	−2.77287	−0.304362	−0.152181	+	0.988353i	$0.548630\pi$
$84$	2.74868	0.299906
$85$	1.00870	0.109409
$86$	−5.82398	−0.628016
$87$	4.90740	0.526128
$88$	0.360369	0.0384154
$89$	1.03216	0.109409	0.0547045	−	0.998503i	$-0.482578\pi$
$89$	1.03216	0.109409	0.0547045	+	0.998503i	$0.482578\pi$
$90$	−0.522326	−0.0550580
$91$	2.74868	0.288140
$92$	−1.23649	−0.128913
$93$	−1.19890	−0.124321
$94$	0.902971	0.0931344
$95$	−0.390855	−0.0401008
$96$	1.00000	0.102062
$97$	7.76875	0.788797	0.394398	−	0.918940i	$-0.370953\pi$
$97$	7.76875	0.788797	0.394398	+	0.918940i	$0.370953\pi$
$98$	−0.555246	−0.0560883
$99$	−0.360369	−0.0362184
$100$	−4.72718	−0.472718
$101$	8.86370	0.881971	0.440985	−	0.897514i	$-0.354629\pi$
$101$	8.86370	0.881971	0.440985	+	0.897514i	$0.354629\pi$
$102$	1.93116	0.191214
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	1.43571	0.140111
$106$	9.38100	0.911164
$107$	8.57097	0.828587	0.414293	−	0.910143i	$-0.364029\pi$
$107$	8.57097	0.828587	0.414293	+	0.910143i	$0.364029\pi$
$108$	−1.00000	−0.0962250
$109$	6.80669	0.651962	0.325981	−	0.945376i	$-0.394305\pi$
$109$	6.80669	0.651962	0.325981	+	0.945376i	$0.394305\pi$
$110$	0.188230	0.0179470
$111$	2.99837	0.284593
$112$	−2.74868	−0.259726
$113$	−12.4885	−1.17482	−0.587410	−	0.809290i	$-0.699852\pi$
$113$	−12.4885	−1.17482	−0.587410	+	0.809290i	$0.699852\pi$
$114$	−0.748297	−0.0700844
$115$	−0.645852	−0.0602260
$116$	−4.90740	−0.455640
$117$	−1.00000	−0.0924500
$118$	−6.21543	−0.572177
$119$	−5.30816	−0.486598
$120$	0.522326	0.0476816
$121$	−10.8701	−0.988194
$122$	−6.71192	−0.607669
$123$	−5.55715	−0.501072
$124$	1.19890	0.107665
$125$	−5.08075	−0.454436
$126$	2.74868	0.244872
$127$	7.24136	0.642566	0.321283	−	0.946983i	$-0.395886\pi$
$127$	7.24136	0.642566	0.321283	+	0.946983i	$0.395886\pi$
$128$	−1.00000	−0.0883883
$129$	−5.82398	−0.512773
$130$	0.522326	0.0458110
$131$	8.82634	0.771161	0.385580	−	0.922674i	$-0.374001\pi$
$131$	8.82634	0.771161	0.385580	+	0.922674i	$0.374001\pi$
$132$	0.360369	0.0313661
$133$	2.05683	0.178350
$134$	−2.28386	−0.197296
$135$	−0.522326	−0.0449546
$136$	−1.93116	−0.165596
$137$	12.0119	1.02624	0.513122	−	0.858315i	$-0.328489\pi$
$137$	12.0119	1.02624	0.513122	+	0.858315i	$0.328489\pi$
$138$	−1.23649	−0.105257
$139$	−16.0537	−1.36166	−0.680831	−	0.732441i	$-0.738381\pi$
$139$	−16.0537	−1.36166	−0.680831	+	0.732441i	$0.738381\pi$
$140$	−1.43571	−0.121339
$141$	0.902971	0.0760439
$142$	1.41208	0.118499
$143$	0.360369	0.0301355
$144$	1.00000	0.0833333
$145$	−2.56326	−0.212867
$146$	15.8684	1.31328
$147$	−0.555246	−0.0457959
$148$	−2.99837	−0.246465
$149$	−19.4381	−1.59243	−0.796216	−	0.605013i	$-0.793168\pi$
$149$	−19.4381	−1.59243	−0.796216	+	0.605013i	$0.793168\pi$
$150$	−4.72718	−0.385972
$151$	2.58033	0.209984	0.104992	−	0.994473i	$-0.466518\pi$
$151$	2.58033	0.209984	0.104992	+	0.994473i	$0.466518\pi$
$152$	0.748297	0.0606949
$153$	1.93116	0.156125
$154$	−0.990539	−0.0798199
$155$	0.626218	0.0502991
$156$	1.00000	0.0800641
$157$	1.50247	0.119910	0.0599552	−	0.998201i	$-0.480904\pi$
$157$	1.50247	0.119910	0.0599552	+	0.998201i	$0.480904\pi$
$158$	7.70563	0.613027
$159$	9.38100	0.743962
$160$	−0.522326	−0.0412935
$161$	3.39873	0.267857
$162$	−1.00000	−0.0785674
$163$	4.06884	0.318696	0.159348	−	0.987222i	$-0.449061\pi$
$163$	4.06884	0.318696	0.159348	+	0.987222i	$0.449061\pi$
$164$	5.55715	0.433941
$165$	0.188230	0.0146537
$166$	2.77287	0.215216
$167$	−18.3623	−1.42091	−0.710457	−	0.703741i	$-0.751512\pi$
$167$	−18.3623	−1.42091	−0.710457	+	0.703741i	$0.751512\pi$
$168$	−2.74868	−0.212065
$169$	1.00000	0.0769231
$170$	−1.00870	−0.0773635
$171$	−0.748297	−0.0572237
$172$	5.82398	0.444074
$173$	−5.17700	−0.393600	−0.196800	−	0.980444i	$-0.563055\pi$
$173$	−5.17700	−0.393600	−0.196800	+	0.980444i	$0.563055\pi$
$174$	−4.90740	−0.372029
$175$	12.9935	0.982216
$176$	−0.360369	−0.0271638
$177$	−6.21543	−0.467181
$178$	−1.03216	−0.0773639
$179$	−2.12323	−0.158698	−0.0793488	−	0.996847i	$-0.525284\pi$
$179$	−2.12323	−0.158698	−0.0793488	+	0.996847i	$0.525284\pi$
$180$	0.522326	0.0389319
$181$	22.8106	1.69550	0.847750	−	0.530396i	$-0.177957\pi$
$181$	22.8106	1.69550	0.847750	+	0.530396i	$0.177957\pi$
$182$	−2.74868	−0.203746
$183$	−6.71192	−0.496160
$184$	1.23649	0.0911555
$185$	−1.56613	−0.115144
$186$	1.19890	0.0879079
$187$	−0.695931	−0.0508915
$188$	−0.902971	−0.0658559
$189$	2.74868	0.199937
$190$	0.390855	0.0283556
$191$	8.47503	0.613232	0.306616	−	0.951833i	$-0.400803\pi$
$191$	8.47503	0.613232	0.306616	+	0.951833i	$0.400803\pi$
$192$	−1.00000	−0.0721688
$193$	−19.8592	−1.42949	−0.714747	−	0.699383i	$-0.753458\pi$
$193$	−19.8592	−1.42949	−0.714747	+	0.699383i	$0.753458\pi$
$194$	−7.76875	−0.557764
$195$	0.522326	0.0374045
$196$	0.555246	0.0396604
$197$	−9.82460	−0.699974	−0.349987	−	0.936755i	$-0.613814\pi$
$197$	−9.82460	−0.699974	−0.349987	+	0.936755i	$0.613814\pi$
$198$	0.360369	0.0256103
$199$	12.1513	0.861381	0.430690	−	0.902500i	$-0.358270\pi$
$199$	12.1513	0.861381	0.430690	+	0.902500i	$0.358270\pi$
$200$	4.72718	0.334262
$201$	−2.28386	−0.161091
$202$	−8.86370	−0.623647
$203$	13.4889	0.946733
$204$	−1.93116	−0.135209
$205$	2.90264	0.202729
$206$	−1.00000	−0.0696733
$207$	−1.23649	−0.0859422
$208$	−1.00000	−0.0693375
$209$	0.269663	0.0186530
$210$	−1.43571	−0.0990732
$211$	−2.76064	−0.190050	−0.0950250	−	0.995475i	$-0.530293\pi$
$211$	−2.76064	−0.190050	−0.0950250	+	0.995475i	$0.530293\pi$
$212$	−9.38100	−0.644290
$213$	1.41208	0.0967539
$214$	−8.57097	−0.585899
$215$	3.04201	0.207464
$216$	1.00000	0.0680414
$217$	−3.29540	−0.223707
$218$	−6.80669	−0.461007
$219$	15.8684	1.07229
$220$	−0.188230	−0.0126905
$221$	−1.93116	−0.129904
$222$	−2.99837	−0.201238
$223$	18.8473	1.26211	0.631055	−	0.775738i	$-0.282622\pi$
$223$	18.8473	1.26211	0.631055	+	0.775738i	$0.282622\pi$
$224$	2.74868	0.183654
$225$	−4.72718	−0.315145
$226$	12.4885	0.830723
$227$	9.80664	0.650889	0.325445	−	0.945561i	$-0.394486\pi$
$227$	9.80664	0.650889	0.325445	+	0.945561i	$0.394486\pi$
$228$	0.748297	0.0495572
$229$	22.6867	1.49918	0.749590	−	0.661902i	$-0.230251\pi$
$229$	22.6867	1.49918	0.749590	+	0.661902i	$0.230251\pi$
$230$	0.645852	0.0425862
$231$	−0.990539	−0.0651727
$232$	4.90740	0.322186
$233$	−0.545768	−0.0357544	−0.0178772	−	0.999840i	$-0.505691\pi$
$233$	−0.545768	−0.0357544	−0.0178772	+	0.999840i	$0.505691\pi$
$234$	1.00000	0.0653720
$235$	−0.471645	−0.0307667
$236$	6.21543	0.404590
$237$	7.70563	0.500534
$238$	5.30816	0.344077
$239$	19.9894	1.29300	0.646502	−	0.762912i	$-0.276231\pi$
$239$	19.9894	1.29300	0.646502	+	0.762912i	$0.276231\pi$
$240$	−0.522326	−0.0337160
$241$	23.8871	1.53870	0.769350	−	0.638827i	$-0.220580\pi$
$241$	23.8871	1.53870	0.769350	+	0.638827i	$0.220580\pi$
$242$	10.8701	0.698759
$243$	−1.00000	−0.0641500
$244$	6.71192	0.429687
$245$	0.290019	0.0185287
$246$	5.55715	0.354311
$247$	0.748297	0.0476130
$248$	−1.19890	−0.0761305
$249$	2.77287	0.175723
$250$	5.08075	0.321335
$251$	−27.8402	−1.75726	−0.878628	−	0.477508i	$-0.841540\pi$
$251$	−27.8402	−1.75726	−0.878628	+	0.477508i	$0.841540\pi$
$252$	−2.74868	−0.173151
$253$	0.445594	0.0280142
$254$	−7.24136	−0.454363
$255$	−1.00870	−0.0631670
$256$	1.00000	0.0625000
$257$	0.573865	0.0357967	0.0178983	−	0.999840i	$-0.494302\pi$
$257$	0.573865	0.0357967	0.0178983	+	0.999840i	$0.494302\pi$
$258$	5.82398	0.362585
$259$	8.24157	0.512106
$260$	−0.522326	−0.0323933
$261$	−4.90740	−0.303760
$262$	−8.82634	−0.545293
$263$	31.1711	1.92209	0.961045	−	0.276391i	$-0.0891385\pi$
$263$	31.1711	1.92209	0.961045	+	0.276391i	$0.0891385\pi$
$264$	−0.360369	−0.0221792
$265$	−4.89994	−0.301001
$266$	−2.05683	−0.126112
$267$	−1.03216	−0.0631673
$268$	2.28386	0.139509
$269$	4.14299	0.252602	0.126301	−	0.991992i	$-0.459689\pi$
$269$	4.14299	0.252602	0.126301	+	0.991992i	$0.459689\pi$
$270$	0.522326	0.0317877
$271$	25.0410	1.52113	0.760566	−	0.649261i	$-0.224922\pi$
$271$	25.0410	1.52113	0.760566	+	0.649261i	$0.224922\pi$
$272$	1.93116	0.117094
$273$	−2.74868	−0.166358
$274$	−12.0119	−0.725665
$275$	1.70353	0.102727
$276$	1.23649	0.0744282
$277$	−3.29484	−0.197968	−0.0989839	−	0.995089i	$-0.531559\pi$
$277$	−3.29484	−0.197968	−0.0989839	+	0.995089i	$0.531559\pi$
$278$	16.0537	0.962840
$279$	1.19890	0.0717765
$280$	1.43571	0.0857999
$281$	−20.3656	−1.21491	−0.607456	−	0.794354i	$-0.707810\pi$
$281$	−20.3656	−1.21491	−0.607456	+	0.794354i	$0.707810\pi$
$282$	−0.902971	−0.0537711
$283$	13.6604	0.812024	0.406012	−	0.913868i	$-0.366919\pi$
$283$	13.6604	0.812024	0.406012	+	0.913868i	$0.366919\pi$
$284$	−1.41208	−0.0837914
$285$	0.390855	0.0231522
$286$	−0.360369	−0.0213091
$287$	−15.2748	−0.901646
$288$	−1.00000	−0.0589256
$289$	−13.2706	−0.780624
$290$	2.56326	0.150520
$291$	−7.76875	−0.455412
$292$	−15.8684	−0.928626
$293$	−22.1368	−1.29325	−0.646624	−	0.762809i	$-0.723820\pi$
$293$	−22.1368	−1.29325	−0.646624	+	0.762809i	$0.723820\pi$
$294$	0.555246	0.0323826
$295$	3.24648	0.189017
$296$	2.99837	0.174277
$297$	0.360369	0.0209107
$298$	19.4381	1.12602
$299$	1.23649	0.0715083
$300$	4.72718	0.272924
$301$	−16.0083	−0.922701
$302$	−2.58033	−0.148481
$303$	−8.86370	−0.509206
$304$	−0.748297	−0.0429178
$305$	3.50581	0.200742
$306$	−1.93116	−0.110397
$307$	13.5244	0.771877	0.385939	−	0.922524i	$-0.373878\pi$
$307$	13.5244	0.771877	0.385939	+	0.922524i	$0.373878\pi$
$308$	0.990539	0.0564412
$309$	−1.00000	−0.0568880
$310$	−0.626218	−0.0355668
$311$	−0.984074	−0.0558017	−0.0279009	−	0.999611i	$-0.508882\pi$
$311$	−0.984074	−0.0558017	−0.0279009	+	0.999611i	$0.508882\pi$
$312$	−1.00000	−0.0566139
$313$	−8.44322	−0.477239	−0.238620	−	0.971113i	$-0.576695\pi$
$313$	−8.44322	−0.477239	−0.238620	+	0.971113i	$0.576695\pi$
$314$	−1.50247	−0.0847895
$315$	−1.43571	−0.0808929
$316$	−7.70563	−0.433475
$317$	2.32174	0.130402	0.0652010	−	0.997872i	$-0.479231\pi$
$317$	2.32174	0.130402	0.0652010	+	0.997872i	$0.479231\pi$
$318$	−9.38100	−0.526061
$319$	1.76847	0.0990155
$320$	0.522326	0.0291989
$321$	−8.57097	−0.478385
$322$	−3.39873	−0.189404
$323$	−1.44508	−0.0804066
$324$	1.00000	0.0555556
$325$	4.72718	0.262217
$326$	−4.06884	−0.225352
$327$	−6.80669	−0.376411
$328$	−5.55715	−0.306843
$329$	2.48198	0.136836
$330$	−0.188230	−0.0103617
$331$	−8.39888	−0.461644	−0.230822	−	0.972996i	$-0.574141\pi$
$331$	−8.39888	−0.461644	−0.230822	+	0.972996i	$0.574141\pi$
$332$	−2.77287	−0.152181
$333$	−2.99837	−0.164310
$334$	18.3623	1.00474
$335$	1.19292	0.0651762
$336$	2.74868	0.149953
$337$	30.6516	1.66970	0.834850	−	0.550477i	$-0.185554\pi$
$337$	30.6516	1.66970	0.834850	+	0.550477i	$0.185554\pi$
$338$	−1.00000	−0.0543928
$339$	12.4885	0.678282
$340$	1.00870	0.0547043
$341$	−0.432048	−0.0233967
$342$	0.748297	0.0404633
$343$	17.7146	0.956497
$344$	−5.82398	−0.314008
$345$	0.645852	0.0347715
$346$	5.17700	0.278317
$347$	−26.7991	−1.43865	−0.719326	−	0.694673i	$-0.755549\pi$
$347$	−26.7991	−1.43865	−0.719326	+	0.694673i	$0.755549\pi$
$348$	4.90740	0.263064
$349$	36.0370	1.92902	0.964509	−	0.264051i	$-0.0850587\pi$
$349$	36.0370	1.92902	0.964509	+	0.264051i	$0.0850587\pi$
$350$	−12.9935	−0.694532
$351$	1.00000	0.0533761
$352$	0.360369	0.0192077
$353$	−27.9712	−1.48875	−0.744377	−	0.667759i	$-0.767254\pi$
$353$	−27.9712	−1.48875	−0.744377	+	0.667759i	$0.767254\pi$
$354$	6.21543	0.330347
$355$	−0.737564	−0.0391458
$356$	1.03216	0.0547045
$357$	5.30816	0.280937
$358$	2.12323	0.112216
$359$	12.1286	0.640122	0.320061	−	0.947397i	$-0.396297\pi$
$359$	12.1286	0.640122	0.320061	+	0.947397i	$0.396297\pi$
$360$	−0.522326	−0.0275290
$361$	−18.4401	−0.970529
$362$	−22.8106	−1.19890
$363$	10.8701	0.570534
$364$	2.74868	0.144070
$365$	−8.28846	−0.433838
$366$	6.71192	0.350838
$367$	−6.87499	−0.358871	−0.179436	−	0.983770i	$-0.557427\pi$
$367$	−6.87499	−0.358871	−0.179436	+	0.983770i	$0.557427\pi$
$368$	−1.23649	−0.0644567
$369$	5.55715	0.289294
$370$	1.56613	0.0814190
$371$	25.7854	1.33871
$372$	−1.19890	−0.0621603
$373$	−10.2960	−0.533104	−0.266552	−	0.963820i	$-0.585884\pi$
$373$	−10.2960	−0.533104	−0.266552	+	0.963820i	$0.585884\pi$
$374$	0.695931	0.0359858
$375$	5.08075	0.262369
$376$	0.902971	0.0465672
$377$	4.90740	0.252744
$378$	−2.74868	−0.141377
$379$	19.9240	1.02342	0.511712	−	0.859157i	$-0.329011\pi$
$379$	19.9240	1.02342	0.511712	+	0.859157i	$0.329011\pi$
$380$	−0.390855	−0.0200504
$381$	−7.24136	−0.370986
$382$	−8.47503	−0.433620
$383$	−19.6327	−1.00318	−0.501591	−	0.865105i	$-0.667252\pi$
$383$	−19.6327	−1.00318	−0.501591	+	0.865105i	$0.667252\pi$
$384$	1.00000	0.0510310
$385$	0.517384	0.0263683
$386$	19.8592	1.01081
$387$	5.82398	0.296049
$388$	7.76875	0.394398
$389$	−4.93870	−0.250402	−0.125201	−	0.992131i	$-0.539958\pi$
$389$	−4.93870	−0.250402	−0.125201	+	0.992131i	$0.539958\pi$
$390$	−0.522326	−0.0264490
$391$	−2.38787	−0.120760
$392$	−0.555246	−0.0280442
$393$	−8.82634	−0.445230
$394$	9.82460	0.494956
$395$	−4.02485	−0.202512
$396$	−0.360369	−0.0181092
$397$	12.0504	0.604791	0.302396	−	0.953182i	$-0.402214\pi$
$397$	12.0504	0.604791	0.302396	+	0.953182i	$0.402214\pi$
$398$	−12.1513	−0.609088
$399$	−2.05683	−0.102970
$400$	−4.72718	−0.236359
$401$	12.3082	0.614640	0.307320	−	0.951606i	$-0.400568\pi$
$401$	12.3082	0.614640	0.307320	+	0.951606i	$0.400568\pi$
$402$	2.28386	0.113909
$403$	−1.19890	−0.0597217
$404$	8.86370	0.440985
$405$	0.522326	0.0259546
$406$	−13.4889	−0.669441
$407$	1.08052	0.0535594
$408$	1.93116	0.0956069
$409$	−7.93754	−0.392486	−0.196243	−	0.980555i	$-0.562874\pi$
$409$	−7.93754	−0.392486	−0.196243	+	0.980555i	$0.562874\pi$
$410$	−2.90264	−0.143351
$411$	−12.0119	−0.592503
$412$	1.00000	0.0492665
$413$	−17.0842	−0.840661
$414$	1.23649	0.0607703
$415$	−1.44834	−0.0710963
$416$	1.00000	0.0490290
$417$	16.0537	0.786155
$418$	−0.269663	−0.0131896
$419$	8.38895	0.409827	0.204913	−	0.978780i	$-0.434309\pi$
$419$	8.38895	0.409827	0.204913	+	0.978780i	$0.434309\pi$
$420$	1.43571	0.0700553
$421$	10.8439	0.528501	0.264250	−	0.964454i	$-0.414875\pi$
$421$	10.8439	0.528501	0.264250	+	0.964454i	$0.414875\pi$
$422$	2.76064	0.134386
$423$	−0.902971	−0.0439040
$424$	9.38100	0.455582
$425$	−9.12896	−0.442819
$426$	−1.41208	−0.0684154
$427$	−18.4489	−0.892807
$428$	8.57097	0.414293
$429$	−0.360369	−0.0173988
$430$	−3.04201	−0.146699
$431$	15.4234	0.742920	0.371460	−	0.928449i	$-0.378857\pi$
$431$	15.4234	0.742920	0.371460	+	0.928449i	$0.378857\pi$
$432$	−1.00000	−0.0481125
$433$	−27.4292	−1.31816	−0.659082	−	0.752071i	$-0.729055\pi$
$433$	−27.4292	−1.31816	−0.659082	+	0.752071i	$0.729055\pi$
$434$	3.29540	0.158184
$435$	2.56326	0.122899
$436$	6.80669	0.325981
$437$	0.925264	0.0442614
$438$	−15.8684	−0.758220
$439$	9.13157	0.435826	0.217913	−	0.975968i	$-0.430075\pi$
$439$	9.13157	0.435826	0.217913	+	0.975968i	$0.430075\pi$
$440$	0.188230	0.00897351
$441$	0.555246	0.0264403
$442$	1.93116	0.0918561
$443$	11.0611	0.525527	0.262763	−	0.964860i	$-0.415366\pi$
$443$	11.0611	0.525527	0.262763	+	0.964860i	$0.415366\pi$
$444$	2.99837	0.142296
$445$	0.539125	0.0255570
$446$	−18.8473	−0.892446
$447$	19.4381	0.919391
$448$	−2.74868	−0.129863
$449$	15.6357	0.737892	0.368946	−	0.929451i	$-0.379719\pi$
$449$	15.6357	0.737892	0.368946	+	0.929451i	$0.379719\pi$
$450$	4.72718	0.222841
$451$	−2.00262	−0.0942999
$452$	−12.4885	−0.587410
$453$	−2.58033	−0.121235
$454$	−9.80664	−0.460248
$455$	1.43571	0.0673070
$456$	−0.748297	−0.0350422
$457$	16.3840	0.766412	0.383206	−	0.923663i	$-0.374820\pi$
$457$	16.3840	0.766412	0.383206	+	0.923663i	$0.374820\pi$
$458$	−22.6867	−1.06008
$459$	−1.93116	−0.0901390
$460$	−0.645852	−0.0301130
$461$	−10.9385	−0.509457	−0.254728	−	0.967013i	$-0.581986\pi$
$461$	−10.9385	−0.509457	−0.254728	+	0.967013i	$0.581986\pi$
$462$	0.990539	0.0460840
$463$	−9.38112	−0.435977	−0.217989	−	0.975951i	$-0.569950\pi$
$463$	−9.38112	−0.435977	−0.217989	+	0.975951i	$0.569950\pi$
$464$	−4.90740	−0.227820
$465$	−0.626218	−0.0290402
$466$	0.545768	0.0252822
$467$	29.8882	1.38306	0.691532	−	0.722346i	$-0.256936\pi$
$467$	29.8882	1.38306	0.691532	+	0.722346i	$0.256936\pi$
$468$	−1.00000	−0.0462250
$469$	−6.27762	−0.289873
$470$	0.471645	0.0217554
$471$	−1.50247	−0.0692303
$472$	−6.21543	−0.286089
$473$	−2.09878	−0.0965020
$474$	−7.70563	−0.353931
$475$	3.53733	0.162304
$476$	−5.30816	−0.243299
$477$	−9.38100	−0.429527
$478$	−19.9894	−0.914292
$479$	−1.85725	−0.0848597	−0.0424298	−	0.999099i	$-0.513510\pi$
$479$	−1.85725	−0.0848597	−0.0424298	+	0.999099i	$0.513510\pi$
$480$	0.522326	0.0238408
$481$	2.99837	0.136714
$482$	−23.8871	−1.08803
$483$	−3.39873	−0.154647
$484$	−10.8701	−0.494097
$485$	4.05782	0.184256
$486$	1.00000	0.0453609
$487$	22.4287	1.01634	0.508171	−	0.861256i	$-0.330322\pi$
$487$	22.4287	1.01634	0.508171	+	0.861256i	$0.330322\pi$
$488$	−6.71192	−0.303835
$489$	−4.06884	−0.183999
$490$	−0.290019	−0.0131017
$491$	−42.4005	−1.91351	−0.956753	−	0.290900i	$-0.906045\pi$
$491$	−42.4005	−1.91351	−0.956753	+	0.290900i	$0.906045\pi$
$492$	−5.55715	−0.250536
$493$	−9.47699	−0.426822
$494$	−0.748297	−0.0336675
$495$	−0.188230	−0.00846030
$496$	1.19890	0.0538324
$497$	3.88135	0.174102
$498$	−2.77287	−0.124255
$499$	5.80163	0.259717	0.129858	−	0.991533i	$-0.458548\pi$
$499$	5.80163	0.259717	0.129858	+	0.991533i	$0.458548\pi$
$500$	−5.08075	−0.227218
$501$	18.3623	0.820365
$502$	27.8402	1.24257
$503$	24.9902	1.11426	0.557129	−	0.830426i	$-0.311903\pi$
$503$	24.9902	1.11426	0.557129	+	0.830426i	$0.311903\pi$
$504$	2.74868	0.122436
$505$	4.62974	0.206021
$506$	−0.445594	−0.0198091
$507$	−1.00000	−0.0444116
$508$	7.24136	0.321283
$509$	3.33723	0.147920	0.0739601	−	0.997261i	$-0.476436\pi$
$509$	3.33723	0.147920	0.0739601	+	0.997261i	$0.476436\pi$
$510$	1.00870	0.0446658
$511$	43.6171	1.92951
$512$	−1.00000	−0.0441942
$513$	0.748297	0.0330381
$514$	−0.573865	−0.0253121
$515$	0.522326	0.0230164
$516$	−5.82398	−0.256386
$517$	0.325403	0.0143112
$518$	−8.24157	−0.362114
$519$	5.17700	0.227245
$520$	0.522326	0.0229055
$521$	−31.5427	−1.38191	−0.690956	−	0.722897i	$-0.742810\pi$
$521$	−31.5427	−1.38191	−0.690956	+	0.722897i	$0.742810\pi$
$522$	4.90740	0.214791
$523$	15.5475	0.679843	0.339921	−	0.940454i	$-0.389600\pi$
$523$	15.5475	0.679843	0.339921	+	0.940454i	$0.389600\pi$
$524$	8.82634	0.385580
$525$	−12.9935	−0.567083
$526$	−31.1711	−1.35912
$527$	2.31528	0.100855
$528$	0.360369	0.0156830
$529$	−21.4711	−0.933525
$530$	4.89994	0.212840
$531$	6.21543	0.269727
$532$	2.05683	0.0891748
$533$	−5.55715	−0.240707
$534$	1.03216	0.0446660
$535$	4.47684	0.193550
$536$	−2.28386	−0.0986479
$537$	2.12323	0.0916241
$538$	−4.14299	−0.178617
$539$	−0.200093	−0.00861863
$540$	−0.522326	−0.0224773
$541$	20.5163	0.882066	0.441033	−	0.897491i	$-0.354612\pi$
$541$	20.5163	0.882066	0.441033	+	0.897491i	$0.354612\pi$
$542$	−25.0410	−1.07560
$543$	−22.8106	−0.978897
$544$	−1.93116	−0.0827980
$545$	3.55531	0.152293
$546$	2.74868	0.117633
$547$	−19.0763	−0.815645	−0.407823	−	0.913061i	$-0.633712\pi$
$547$	−19.0763	−0.815645	−0.407823	+	0.913061i	$0.633712\pi$
$548$	12.0119	0.513122
$549$	6.71192	0.286458
$550$	−1.70353	−0.0726386
$551$	3.67219	0.156441
$552$	−1.23649	−0.0526287
$553$	21.1803	0.900678
$554$	3.29484	0.139984
$555$	1.56613	0.0664784
$556$	−16.0537	−0.680831
$557$	7.58335	0.321317	0.160659	−	0.987010i	$-0.448638\pi$
$557$	7.58335	0.321317	0.160659	+	0.987010i	$0.448638\pi$
$558$	−1.19890	−0.0507537
$559$	−5.82398	−0.246328
$560$	−1.43571	−0.0606697
$561$	0.695931	0.0293822
$562$	20.3656	0.859072
$563$	22.8927	0.964814	0.482407	−	0.875947i	$-0.339763\pi$
$563$	22.8927	0.964814	0.482407	+	0.875947i	$0.339763\pi$
$564$	0.902971	0.0380219
$565$	−6.52306	−0.274427
$566$	−13.6604	−0.574188
$567$	−2.74868	−0.115434
$568$	1.41208	0.0592494
$569$	46.6115	1.95406	0.977029	−	0.213108i	$-0.0683586\pi$
$569$	46.6115	1.95406	0.977029	+	0.213108i	$0.0683586\pi$
$570$	−0.390855	−0.0163711
$571$	−1.60969	−0.0673636	−0.0336818	−	0.999433i	$-0.510723\pi$
$571$	−1.60969	−0.0673636	−0.0336818	+	0.999433i	$0.510723\pi$
$572$	0.360369	0.0150678
$573$	−8.47503	−0.354050
$574$	15.2748	0.637560
$575$	5.84512	0.243758
$576$	1.00000	0.0416667
$577$	5.73655	0.238816	0.119408	−	0.992845i	$-0.461900\pi$
$577$	5.73655	0.238816	0.119408	+	0.992845i	$0.461900\pi$
$578$	13.2706	0.551984
$579$	19.8592	0.825319
$580$	−2.56326	−0.106434
$581$	7.62173	0.316203
$582$	7.76875	0.322025
$583$	3.38062	0.140011
$584$	15.8684	0.656638
$585$	−0.522326	−0.0215955
$586$	22.1368	0.914464
$587$	−5.36219	−0.221321	−0.110661	−	0.993858i	$-0.535297\pi$
$587$	−5.36219	−0.221321	−0.110661	+	0.993858i	$0.535297\pi$
$588$	−0.555246	−0.0228980
$589$	−0.897136	−0.0369658
$590$	−3.24648	−0.133656
$591$	9.82460	0.404130
$592$	−2.99837	−0.123232
$593$	0.564040	0.0231623	0.0115812	−	0.999933i	$-0.496314\pi$
$593$	0.564040	0.0231623	0.0115812	+	0.999933i	$0.496314\pi$
$594$	−0.360369	−0.0147861
$595$	−2.77259	−0.113665
$596$	−19.4381	−0.796216
$597$	−12.1513	−0.497319
$598$	−1.23649	−0.0505640
$599$	12.6688	0.517633	0.258817	−	0.965927i	$-0.416668\pi$
$599$	12.6688	0.517633	0.258817	+	0.965927i	$0.416668\pi$
$600$	−4.72718	−0.192986
$601$	24.1607	0.985534	0.492767	−	0.870161i	$-0.335985\pi$
$601$	24.1607	0.985534	0.492767	+	0.870161i	$0.335985\pi$
$602$	16.0083	0.652448
$603$	2.28386	0.0930062
$604$	2.58033	0.104992
$605$	−5.67775	−0.230833
$606$	8.86370	0.360063
$607$	28.1195	1.14133	0.570667	−	0.821182i	$-0.306685\pi$
$607$	28.1195	1.14133	0.570667	+	0.821182i	$0.306685\pi$
$608$	0.748297	0.0303474
$609$	−13.4889	−0.546597
$610$	−3.50581	−0.141946
$611$	0.902971	0.0365303
$612$	1.93116	0.0780627
$613$	2.51093	0.101415	0.0507077	−	0.998714i	$-0.483852\pi$
$613$	2.51093	0.101415	0.0507077	+	0.998714i	$0.483852\pi$
$614$	−13.5244	−0.545800
$615$	−2.90264	−0.117046
$616$	−0.990539	−0.0399099
$617$	9.97891	0.401736	0.200868	−	0.979618i	$-0.435624\pi$
$617$	9.97891	0.401736	0.200868	+	0.979618i	$0.435624\pi$
$618$	1.00000	0.0402259
$619$	18.2603	0.733944	0.366972	−	0.930232i	$-0.380395\pi$
$619$	18.2603	0.733944	0.366972	+	0.930232i	$0.380395\pi$
$620$	0.626218	0.0251495
$621$	1.23649	0.0496188
$622$	0.984074	0.0394578
$623$	−2.83709	−0.113665
$624$	1.00000	0.0400320
$625$	20.9821	0.839283
$626$	8.44322	0.337459
$627$	−0.269663	−0.0107693
$628$	1.50247	0.0599552
$629$	−5.79035	−0.230876
$630$	1.43571	0.0571999
$631$	28.8571	1.14878	0.574391	−	0.818581i	$-0.305239\pi$
$631$	28.8571	1.14878	0.574391	+	0.818581i	$0.305239\pi$
$632$	7.70563	0.306513
$633$	2.76064	0.109725
$634$	−2.32174	−0.0922081
$635$	3.78235	0.150098
$636$	9.38100	0.371981
$637$	−0.555246	−0.0219997
$638$	−1.76847	−0.0700145
$639$	−1.41208	−0.0558609
$640$	−0.522326	−0.0206467
$641$	17.7597	0.701467	0.350734	−	0.936475i	$-0.385932\pi$
$641$	17.7597	0.701467	0.350734	+	0.936475i	$0.385932\pi$
$642$	8.57097	0.338269
$643$	44.8959	1.77052	0.885260	−	0.465096i	$-0.153980\pi$
$643$	44.8959	1.77052	0.885260	+	0.465096i	$0.153980\pi$
$644$	3.39873	0.133929
$645$	−3.04201	−0.119779
$646$	1.44508	0.0568561
$647$	32.9478	1.29531	0.647655	−	0.761934i	$-0.275750\pi$
$647$	32.9478	1.29531	0.647655	+	0.761934i	$0.275750\pi$
$648$	−1.00000	−0.0392837
$649$	−2.23985	−0.0879217
$650$	−4.72718	−0.185415
$651$	3.29540	0.129157
$652$	4.06884	0.159348
$653$	3.03062	0.118597	0.0592987	−	0.998240i	$-0.481114\pi$
$653$	3.03062	0.118597	0.0592987	+	0.998240i	$0.481114\pi$
$654$	6.80669	0.266163
$655$	4.61022	0.180136
$656$	5.55715	0.216970
$657$	−15.8684	−0.619084
$658$	−2.48198	−0.0967576
$659$	−44.6671	−1.73998	−0.869991	−	0.493068i	$-0.835875\pi$
$659$	−44.6671	−1.73998	−0.869991	+	0.493068i	$0.835875\pi$
$660$	0.188230	0.00732684
$661$	28.3968	1.10451	0.552254	−	0.833676i	$-0.313768\pi$
$661$	28.3968	1.10451	0.552254	+	0.833676i	$0.313768\pi$
$662$	8.39888	0.326432
$663$	1.93116	0.0750002
$664$	2.77287	0.107608
$665$	1.07433	0.0416609
$666$	2.99837	0.116185
$667$	6.06797	0.234953
$668$	−18.3623	−0.710457
$669$	−18.8473	−0.728679
$670$	−1.19292	−0.0460866
$671$	−2.41877	−0.0933755
$672$	−2.74868	−0.106033
$673$	1.87967	0.0724559	0.0362279	−	0.999344i	$-0.488466\pi$
$673$	1.87967	0.0724559	0.0362279	+	0.999344i	$0.488466\pi$
$674$	−30.6516	−1.18066
$675$	4.72718	0.181949
$676$	1.00000	0.0384615
$677$	−11.0758	−0.425679	−0.212840	−	0.977087i	$-0.568271\pi$
$677$	−11.0758	−0.425679	−0.212840	+	0.977087i	$0.568271\pi$
$678$	−12.4885	−0.479618
$679$	−21.3538	−0.819484
$680$	−1.00870	−0.0386818
$681$	−9.80664	−0.375791
$682$	0.432048	0.0165440
$683$	−0.794064	−0.0303840	−0.0151920	−	0.999885i	$-0.504836\pi$
$683$	−0.794064	−0.0303840	−0.0151920	+	0.999885i	$0.504836\pi$
$684$	−0.748297	−0.0286118
$685$	6.27412	0.239722
$686$	−17.7146	−0.676345
$687$	−22.6867	−0.865552
$688$	5.82398	0.222037
$689$	9.38100	0.357388
$690$	−0.645852	−0.0245872
$691$	43.5172	1.65547	0.827736	−	0.561117i	$-0.189628\pi$
$691$	43.5172	1.65547	0.827736	+	0.561117i	$0.189628\pi$
$692$	−5.17700	−0.196800
$693$	0.990539	0.0376275
$694$	26.7991	1.01728
$695$	−8.38529	−0.318072
$696$	−4.90740	−0.186014
$697$	10.7318	0.406495
$698$	−36.0370	−1.36402
$699$	0.545768	0.0206428
$700$	12.9935	0.491108
$701$	15.7089	0.593318	0.296659	−	0.954983i	$-0.404127\pi$
$701$	15.7089	0.593318	0.296659	+	0.954983i	$0.404127\pi$
$702$	−1.00000	−0.0377426
$703$	2.24367	0.0846217
$704$	−0.360369	−0.0135819
$705$	0.471645	0.0177632
$706$	27.9712	1.05271
$707$	−24.3635	−0.916283
$708$	−6.21543	−0.233590
$709$	−1.72192	−0.0646682	−0.0323341	−	0.999477i	$-0.510294\pi$
$709$	−1.72192	−0.0646682	−0.0323341	+	0.999477i	$0.510294\pi$
$710$	0.737564	0.0276803
$711$	−7.70563	−0.288984
$712$	−1.03216	−0.0386819
$713$	−1.48244	−0.0555177
$714$	−5.30816	−0.198653
$715$	0.188230	0.00703940
$716$	−2.12323	−0.0793488
$717$	−19.9894	−0.746517
$718$	−12.1286	−0.452634
$719$	−11.1623	−0.416285	−0.208142	−	0.978099i	$-0.566742\pi$
$719$	−11.1623	−0.416285	−0.208142	+	0.978099i	$0.566742\pi$
$720$	0.522326	0.0194659
$721$	−2.74868	−0.102366
$722$	18.4401	0.686268
$723$	−23.8871	−0.888369
$724$	22.8106	0.847750
$725$	23.1981	0.861557
$726$	−10.8701	−0.403429
$727$	−0.284917	−0.0105670	−0.00528349	−	0.999986i	$-0.501682\pi$
$727$	−0.284917	−0.0105670	−0.00528349	+	0.999986i	$0.501682\pi$
$728$	−2.74868	−0.101873
$729$	1.00000	0.0370370
$730$	8.28846	0.306770
$731$	11.2471	0.415988
$732$	−6.71192	−0.248080
$733$	3.90487	0.144230	0.0721148	−	0.997396i	$-0.477025\pi$
$733$	3.90487	0.144230	0.0721148	+	0.997396i	$0.477025\pi$
$734$	6.87499	0.253760
$735$	−0.290019	−0.0106975
$736$	1.23649	0.0455778
$737$	−0.823034	−0.0303168
$738$	−5.55715	−0.204562
$739$	10.5454	0.387918	0.193959	−	0.981010i	$-0.437867\pi$
$739$	10.5454	0.387918	0.193959	+	0.981010i	$0.437867\pi$
$740$	−1.56613	−0.0575720
$741$	−0.748297	−0.0274894
$742$	−25.7854	−0.946611
$743$	34.6724	1.27201	0.636004	−	0.771686i	$-0.280586\pi$
$743$	34.6724	1.27201	0.636004	+	0.771686i	$0.280586\pi$
$744$	1.19890	0.0439540
$745$	−10.1530	−0.371978
$746$	10.2960	0.376962
$747$	−2.77287	−0.101454
$748$	−0.695931	−0.0254458
$749$	−23.5589	−0.860822
$750$	−5.08075	−0.185523
$751$	28.7573	1.04937	0.524684	−	0.851297i	$-0.324184\pi$
$751$	28.7573	1.04937	0.524684	+	0.851297i	$0.324184\pi$
$752$	−0.902971	−0.0329280
$753$	27.8402	1.01455
$754$	−4.90740	−0.178717
$755$	1.34777	0.0490505
$756$	2.74868	0.0999686
$757$	−19.2177	−0.698478	−0.349239	−	0.937034i	$-0.613560\pi$
$757$	−19.2177	−0.698478	−0.349239	+	0.937034i	$0.613560\pi$
$758$	−19.9240	−0.723670
$759$	−0.445594	−0.0161740
$760$	0.390855	0.0141778
$761$	−20.4907	−0.742787	−0.371394	−	0.928476i	$-0.621120\pi$
$761$	−20.4907	−0.742787	−0.371394	+	0.928476i	$0.621120\pi$
$762$	7.24136	0.262327
$763$	−18.7094	−0.677326
$764$	8.47503	0.306616
$765$	1.00870	0.0364695
$766$	19.6327	0.709357
$767$	−6.21543	−0.224426
$768$	−1.00000	−0.0360844
$769$	44.3911	1.60078	0.800392	−	0.599476i	$-0.204624\pi$
$769$	44.3911	1.60078	0.800392	+	0.599476i	$0.204624\pi$
$770$	−0.517384	−0.0186452
$771$	−0.573865	−0.0206672
$772$	−19.8592	−0.714747
$773$	6.45905	0.232316	0.116158	−	0.993231i	$-0.462942\pi$
$773$	6.45905	0.232316	0.116158	+	0.993231i	$0.462942\pi$
$774$	−5.82398	−0.209339
$775$	−5.66743	−0.203580
$776$	−7.76875	−0.278882
$777$	−8.24157	−0.295665
$778$	4.93870	0.177061
$779$	−4.15840	−0.148990
$780$	0.522326	0.0187023
$781$	0.508868	0.0182087
$782$	2.38787	0.0853902
$783$	4.90740	0.175376
$784$	0.555246	0.0198302
$785$	0.784780	0.0280100
$786$	8.82634	0.314825
$787$	19.5577	0.697157	0.348579	−	0.937280i	$-0.386664\pi$
$787$	19.5577	0.697157	0.348579	+	0.937280i	$0.386664\pi$
$788$	−9.82460	−0.349987
$789$	−31.1711	−1.10972
$790$	4.02485	0.143198
$791$	34.3269	1.22052
$792$	0.360369	0.0128051
$793$	−6.71192	−0.238347
$794$	−12.0504	−0.427652
$795$	4.89994	0.173783
$796$	12.1513	0.430690
$797$	22.0929	0.782571	0.391285	−	0.920269i	$-0.372031\pi$
$797$	22.0929	0.782571	0.391285	+	0.920269i	$0.372031\pi$
$798$	2.05683	0.0728110
$799$	−1.74379	−0.0616907
$800$	4.72718	0.167131
$801$	1.03216	0.0364697
$802$	−12.3082	−0.434616
$803$	5.71846	0.201800
$804$	−2.28386	−0.0805457
$805$	1.77524	0.0625691
$806$	1.19890	0.0422296
$807$	−4.14299	−0.145840
$808$	−8.86370	−0.311824
$809$	48.2741	1.69723	0.848614	−	0.529013i	$-0.177438\pi$
$809$	48.2741	1.69723	0.848614	+	0.529013i	$0.177438\pi$
$810$	−0.522326	−0.0183527
$811$	11.3494	0.398531	0.199266	−	0.979946i	$-0.436144\pi$
$811$	11.3494	0.398531	0.199266	+	0.979946i	$0.436144\pi$
$812$	13.4889	0.473367
$813$	−25.0410	−0.878226
$814$	−1.08052	−0.0378722
$815$	2.12526	0.0744447
$816$	−1.93116	−0.0676043
$817$	−4.35806	−0.152469
$818$	7.93754	0.277530
$819$	2.74868	0.0960467
$820$	2.90264	0.101365
$821$	20.2922	0.708204	0.354102	−	0.935207i	$-0.384787\pi$
$821$	20.2922	0.708204	0.354102	+	0.935207i	$0.384787\pi$
$822$	12.0119	0.418963
$823$	−31.7986	−1.10843	−0.554215	−	0.832374i	$-0.686981\pi$
$823$	−31.7986	−1.10843	−0.554215	+	0.832374i	$0.686981\pi$
$824$	−1.00000	−0.0348367
$825$	−1.70353	−0.0593092
$826$	17.0842	0.594437
$827$	−21.1750	−0.736326	−0.368163	−	0.929761i	$-0.620013\pi$
$827$	−21.1750	−0.736326	−0.368163	+	0.929761i	$0.620013\pi$
$828$	−1.23649	−0.0429711
$829$	55.0767	1.91289	0.956446	−	0.291908i	$-0.0942901\pi$
$829$	55.0767	1.91289	0.956446	+	0.291908i	$0.0942901\pi$
$830$	1.44834	0.0502726
$831$	3.29484	0.114297
$832$	−1.00000	−0.0346688
$833$	1.07227	0.0371520
$834$	−16.0537	−0.555896
$835$	−9.59107	−0.331913
$836$	0.269663	0.00932648
$837$	−1.19890	−0.0414402
$838$	−8.38895	−0.289791
$839$	20.3412	0.702255	0.351127	−	0.936328i	$-0.385798\pi$
$839$	20.3412	0.702255	0.351127	+	0.936328i	$0.385798\pi$
$840$	−1.43571	−0.0495366
$841$	−4.91744	−0.169567
$842$	−10.8439	−0.373707
$843$	20.3656	0.701429
$844$	−2.76064	−0.0950250
$845$	0.522326	0.0179685
$846$	0.902971	0.0310448
$847$	29.8785	1.02664
$848$	−9.38100	−0.322145
$849$	−13.6604	−0.468822
$850$	9.12896	0.313121
$851$	3.70747	0.127090
$852$	1.41208	0.0483770
$853$	−2.80668	−0.0960988	−0.0480494	−	0.998845i	$-0.515300\pi$
$853$	−2.80668	−0.0960988	−0.0480494	+	0.998845i	$0.515300\pi$
$854$	18.4489	0.631310
$855$	−0.390855	−0.0133669
$856$	−8.57097	−0.292950
$857$	−47.3635	−1.61791	−0.808953	−	0.587873i	$-0.799965\pi$
$857$	−47.3635	−1.61791	−0.808953	+	0.587873i	$0.799965\pi$
$858$	0.360369	0.0123028
$859$	−11.5391	−0.393710	−0.196855	−	0.980433i	$-0.563073\pi$
$859$	−11.5391	−0.393710	−0.196855	+	0.980433i	$0.563073\pi$
$860$	3.04201	0.103732
$861$	15.2748	0.520565
$862$	−15.4234	−0.525324
$863$	4.17586	0.142148	0.0710740	−	0.997471i	$-0.477357\pi$
$863$	4.17586	0.142148	0.0710740	+	0.997471i	$0.477357\pi$
$864$	1.00000	0.0340207
$865$	−2.70408	−0.0919415
$866$	27.4292	0.932083
$867$	13.2706	0.450693
$868$	−3.29540	−0.111853
$869$	2.77687	0.0941987
$870$	−2.56326	−0.0869026
$871$	−2.28386	−0.0773858
$872$	−6.80669	−0.230504
$873$	7.76875	0.262932
$874$	−0.925264	−0.0312975
$875$	13.9654	0.472116
$876$	15.8684	0.536143
$877$	−48.9089	−1.65154	−0.825769	−	0.564009i	$-0.809258\pi$
$877$	−48.9089	−1.65154	−0.825769	+	0.564009i	$0.809258\pi$
$878$	−9.13157	−0.308175
$879$	22.1368	0.746657
$880$	−0.188230	−0.00634523
$881$	−11.0560	−0.372485	−0.186243	−	0.982504i	$-0.559631\pi$
$881$	−11.0560	−0.372485	−0.186243	+	0.982504i	$0.559631\pi$
$882$	−0.555246	−0.0186961
$883$	−23.3797	−0.786789	−0.393394	−	0.919370i	$-0.628699\pi$
$883$	−23.3797	−0.786789	−0.393394	+	0.919370i	$0.628699\pi$
$884$	−1.93116	−0.0649521
$885$	−3.24648	−0.109129
$886$	−11.0611	−0.371603
$887$	19.2982	0.647970	0.323985	−	0.946062i	$-0.394977\pi$
$887$	19.2982	0.647970	0.323985	+	0.946062i	$0.394977\pi$
$888$	−2.99837	−0.100619
$889$	−19.9042	−0.667565
$890$	−0.539125	−0.0180715
$891$	−0.360369	−0.0120728
$892$	18.8473	0.631055
$893$	0.675690	0.0226111
$894$	−19.4381	−0.650107
$895$	−1.10902	−0.0370704
$896$	2.74868	0.0918270
$897$	−1.23649	−0.0412853
$898$	−15.6357	−0.521769
$899$	−5.88350	−0.196226
$900$	−4.72718	−0.157573
$901$	−18.1163	−0.603540
$902$	2.00262	0.0666801
$903$	16.0083	0.532721
$904$	12.4885	0.415361
$905$	11.9146	0.396054
$906$	2.58033	0.0857257
$907$	20.6555	0.685854	0.342927	−	0.939362i	$-0.388582\pi$
$907$	20.6555	0.685854	0.342927	+	0.939362i	$0.388582\pi$
$908$	9.80664	0.325445
$909$	8.86370	0.293990
$910$	−1.43571	−0.0475932
$911$	−30.7241	−1.01793	−0.508967	−	0.860786i	$-0.669972\pi$
$911$	−30.7241	−1.01793	−0.508967	+	0.860786i	$0.669972\pi$
$912$	0.748297	0.0247786
$913$	0.999256	0.0330705
$914$	−16.3840	−0.541935
$915$	−3.50581	−0.115898
$916$	22.6867	0.749590
$917$	−24.2608	−0.801162
$918$	1.93116	0.0637379
$919$	−8.56740	−0.282612	−0.141306	−	0.989966i	$-0.545130\pi$
$919$	−8.56740	−0.282612	−0.141306	+	0.989966i	$0.545130\pi$
$920$	0.645852	0.0212931
$921$	−13.5244	−0.445644
$922$	10.9385	0.360240
$923$	1.41208	0.0464791
$924$	−0.990539	−0.0325863
$925$	14.1738	0.466033
$926$	9.38112	0.308283
$927$	1.00000	0.0328443
$928$	4.90740	0.161093
$929$	32.8528	1.07786	0.538932	−	0.842349i	$-0.318828\pi$
$929$	32.8528	1.07786	0.538932	+	0.842349i	$0.318828\pi$
$930$	0.626218	0.0205345
$931$	−0.415489	−0.0136171
$932$	−0.545768	−0.0178772
$933$	0.984074	0.0322171
$934$	−29.8882	−0.977973
$935$	−0.363503	−0.0118878
$936$	1.00000	0.0326860
$937$	26.5121	0.866113	0.433057	−	0.901367i	$-0.357435\pi$
$937$	26.5121	0.866113	0.433057	+	0.901367i	$0.357435\pi$
$938$	6.27762	0.204971
$939$	8.44322	0.275534
$940$	−0.471645	−0.0153834
$941$	21.1200	0.688493	0.344246	−	0.938879i	$-0.388134\pi$
$941$	21.1200	0.688493	0.344246	+	0.938879i	$0.388134\pi$
$942$	1.50247	0.0489532
$943$	−6.87139	−0.223763
$944$	6.21543	0.202295
$945$	1.43571	0.0467035
$946$	2.09878	0.0682372
$947$	31.2612	1.01585	0.507926	−	0.861401i	$-0.330412\pi$
$947$	31.2612	1.01585	0.507926	+	0.861401i	$0.330412\pi$
$948$	7.70563	0.250267
$949$	15.8684	0.515109
$950$	−3.53733	−0.114766
$951$	−2.32174	−0.0752876
$952$	5.30816	0.172038
$953$	27.6348	0.895180	0.447590	−	0.894239i	$-0.352282\pi$
$953$	27.6348	0.895180	0.447590	+	0.894239i	$0.352282\pi$
$954$	9.38100	0.303721
$955$	4.42673	0.143246
$956$	19.9894	0.646502
$957$	−1.76847	−0.0571666
$958$	1.85725	0.0600049
$959$	−33.0168	−1.06617
$960$	−0.522326	−0.0168580
$961$	−29.5626	−0.953633
$962$	−2.99837	−0.0966714
$963$	8.57097	0.276196
$964$	23.8871	0.769350
$965$	−10.3730	−0.333917
$966$	3.39873	0.109352
$967$	42.4643	1.36556	0.682780	−	0.730624i	$-0.260771\pi$
$967$	42.4643	1.36556	0.682780	+	0.730624i	$0.260771\pi$
$968$	10.8701	0.349379
$969$	1.44508	0.0464228
$970$	−4.05782	−0.130289
$971$	−41.4928	−1.33157	−0.665784	−	0.746144i	$-0.731903\pi$
$971$	−41.4928	−1.33157	−0.665784	+	0.746144i	$0.731903\pi$
$972$	−1.00000	−0.0320750
$973$	44.1266	1.41463
$974$	−22.4287	−0.718662
$975$	−4.72718	−0.151391
$976$	6.71192	0.214843
$977$	−8.75460	−0.280084	−0.140042	−	0.990146i	$-0.544724\pi$
$977$	−8.75460	−0.280084	−0.140042	+	0.990146i	$0.544724\pi$
$978$	4.06884	0.130107
$979$	−0.371959	−0.0118879
$980$	0.290019	0.00926433
$981$	6.80669	0.217321
$982$	42.4005	1.35305
$983$	21.7911	0.695029	0.347515	−	0.937675i	$-0.387026\pi$
$983$	21.7911	0.695029	0.347515	+	0.937675i	$0.387026\pi$
$984$	5.55715	0.177156
$985$	−5.13164	−0.163508
$986$	9.47699	0.301809
$987$	−2.48198	−0.0790023
$988$	0.748297	0.0238065
$989$	−7.20131	−0.228988
$990$	0.188230	0.00598234
$991$	−26.0086	−0.826191	−0.413096	−	0.910688i	$-0.635552\pi$
$991$	−26.0086	−0.826191	−0.413096	+	0.910688i	$0.635552\pi$
$992$	−1.19890	−0.0380652
$993$	8.39888	0.266530
$994$	−3.88135	−0.123109
$995$	6.34692	0.201211
$996$	2.77287	0.0878617
$997$	−31.0258	−0.982597	−0.491299	−	0.870991i	$-0.663478\pi$
$997$	−31.0258	−0.982597	−0.491299	+	0.870991i	$0.663478\pi$
$998$	−5.80163	−0.183647
$999$	2.99837	0.0948643

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.ba.1.8	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.ba.1.8	✓	14	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.522326 q^{5} +1.00000 q^{6} -2.74868 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.522326 q^{5} +1.00000 q^{6} -2.74868 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.522326 q^{10} -0.360369 q^{11} -1.00000 q^{12} -1.00000 q^{13} +2.74868 q^{14} -0.522326 q^{15} +1.00000 q^{16} +1.93116 q^{17} -1.00000 q^{18} -0.748297 q^{19} +0.522326 q^{20} +2.74868 q^{21} +0.360369 q^{22} -1.23649 q^{23} +1.00000 q^{24} -4.72718 q^{25} +1.00000 q^{26} -1.00000 q^{27} -2.74868 q^{28} -4.90740 q^{29} +0.522326 q^{30} +1.19890 q^{31} -1.00000 q^{32} +0.360369 q^{33} -1.93116 q^{34} -1.43571 q^{35} +1.00000 q^{36} -2.99837 q^{37} +0.748297 q^{38} +1.00000 q^{39} -0.522326 q^{40} +5.55715 q^{41} -2.74868 q^{42} +5.82398 q^{43} -0.360369 q^{44} +0.522326 q^{45} +1.23649 q^{46} -0.902971 q^{47} -1.00000 q^{48} +0.555246 q^{49} +4.72718 q^{50} -1.93116 q^{51} -1.00000 q^{52} -9.38100 q^{53} +1.00000 q^{54} -0.188230 q^{55} +2.74868 q^{56} +0.748297 q^{57} +4.90740 q^{58} +6.21543 q^{59} -0.522326 q^{60} +6.71192 q^{61} -1.19890 q^{62} -2.74868 q^{63} +1.00000 q^{64} -0.522326 q^{65} -0.360369 q^{66} +2.28386 q^{67} +1.93116 q^{68} +1.23649 q^{69} +1.43571 q^{70} -1.41208 q^{71} -1.00000 q^{72} -15.8684 q^{73} +2.99837 q^{74} +4.72718 q^{75} -0.748297 q^{76} +0.990539 q^{77} -1.00000 q^{78} -7.70563 q^{79} +0.522326 q^{80} +1.00000 q^{81} -5.55715 q^{82} -2.77287 q^{83} +2.74868 q^{84} +1.00870 q^{85} -5.82398 q^{86} +4.90740 q^{87} +0.360369 q^{88} +1.03216 q^{89} -0.522326 q^{90} +2.74868 q^{91} -1.23649 q^{92} -1.19890 q^{93} +0.902971 q^{94} -0.390855 q^{95} +1.00000 q^{96} +7.76875 q^{97} -0.555246 q^{98} -0.360369 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9} + q^{10} - q^{11} - 14 q^{12} - 14 q^{13} - 5 q^{14} + q^{15} + 14 q^{16} - 12 q^{17} - 14 q^{18} + 10 q^{19} - q^{20} - 5 q^{21} + q^{22} - q^{23} + 14 q^{24} + 19 q^{25} + 14 q^{26} - 14 q^{27} + 5 q^{28} + 6 q^{29} - q^{30} + 20 q^{31} - 14 q^{32} + q^{33} + 12 q^{34} - 16 q^{35} + 14 q^{36} - 3 q^{37} - 10 q^{38} + 14 q^{39} + q^{40} + q^{41} + 5 q^{42} + 6 q^{43} - q^{44} - q^{45} + q^{46} - 13 q^{47} - 14 q^{48} + 9 q^{49} - 19 q^{50} + 12 q^{51} - 14 q^{52} - 27 q^{53} + 14 q^{54} + 10 q^{55} - 5 q^{56} - 10 q^{57} - 6 q^{58} - 6 q^{59} + q^{60} - 4 q^{61} - 20 q^{62} + 5 q^{63} + 14 q^{64} + q^{65} - q^{66} + 13 q^{67} - 12 q^{68} + q^{69} + 16 q^{70} + 18 q^{71} - 14 q^{72} + 11 q^{73} + 3 q^{74} - 19 q^{75} + 10 q^{76} - 15 q^{77} - 14 q^{78} + 33 q^{79} - q^{80} + 14 q^{81} - q^{82} - 25 q^{83} - 5 q^{84} + 25 q^{85} - 6 q^{86} - 6 q^{87} + q^{88} + 3 q^{89} + q^{90} - 5 q^{91} - q^{92} - 20 q^{93} + 13 q^{94} + 30 q^{95} + 14 q^{96} + 11 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9 + q^10 - q^11 - 14 * q^12 - 14 * q^13 - 5 * q^14 + q^15 + 14 * q^16 - 12 * q^17 - 14 * q^18 + 10 * q^19 - q^20 - 5 * q^21 + q^22 - q^23 + 14 * q^24 + 19 * q^25 + 14 * q^26 - 14 * q^27 + 5 * q^28 + 6 * q^29 - q^30 + 20 * q^31 - 14 * q^32 + q^33 + 12 * q^34 - 16 * q^35 + 14 * q^36 - 3 * q^37 - 10 * q^38 + 14 * q^39 + q^40 + q^41 + 5 * q^42 + 6 * q^43 - q^44 - q^45 + q^46 - 13 * q^47 - 14 * q^48 + 9 * q^49 - 19 * q^50 + 12 * q^51 - 14 * q^52 - 27 * q^53 + 14 * q^54 + 10 * q^55 - 5 * q^56 - 10 * q^57 - 6 * q^58 - 6 * q^59 + q^60 - 4 * q^61 - 20 * q^62 + 5 * q^63 + 14 * q^64 + q^65 - q^66 + 13 * q^67 - 12 * q^68 + q^69 + 16 * q^70 + 18 * q^71 - 14 * q^72 + 11 * q^73 + 3 * q^74 - 19 * q^75 + 10 * q^76 - 15 * q^77 - 14 * q^78 + 33 * q^79 - q^80 + 14 * q^81 - q^82 - 25 * q^83 - 5 * q^84 + 25 * q^85 - 6 * q^86 - 6 * q^87 + q^88 + 3 * q^89 + q^90 - 5 * q^91 - q^92 - 20 * q^93 + 13 * q^94 + 30 * q^95 + 14 * q^96 + 11 * q^97 - 9 * q^98 - q^99

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