LMFDB - Embedded newform 8034.2.a.bd.1.6

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			1.6
Root			$-1.52621$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.52621 q^{5} +1.00000 q^{6} +4.59536 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.52621 q^{5} +1.00000 q^{6} +4.59536 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.52621 q^{10} +5.46248 q^{11} +1.00000 q^{12} -1.00000 q^{13} +4.59536 q^{14} -1.52621 q^{15} +1.00000 q^{16} -3.99639 q^{17} +1.00000 q^{18} -4.36670 q^{19} -1.52621 q^{20} +4.59536 q^{21} +5.46248 q^{22} -0.656722 q^{23} +1.00000 q^{24} -2.67069 q^{25} -1.00000 q^{26} +1.00000 q^{27} +4.59536 q^{28} +5.77154 q^{29} -1.52621 q^{30} +7.53717 q^{31} +1.00000 q^{32} +5.46248 q^{33} -3.99639 q^{34} -7.01347 q^{35} +1.00000 q^{36} +5.61670 q^{37} -4.36670 q^{38} -1.00000 q^{39} -1.52621 q^{40} +3.17737 q^{41} +4.59536 q^{42} -8.63591 q^{43} +5.46248 q^{44} -1.52621 q^{45} -0.656722 q^{46} +4.76373 q^{47} +1.00000 q^{48} +14.1174 q^{49} -2.67069 q^{50} -3.99639 q^{51} -1.00000 q^{52} +5.30468 q^{53} +1.00000 q^{54} -8.33687 q^{55} +4.59536 q^{56} -4.36670 q^{57} +5.77154 q^{58} +1.34821 q^{59} -1.52621 q^{60} +8.91845 q^{61} +7.53717 q^{62} +4.59536 q^{63} +1.00000 q^{64} +1.52621 q^{65} +5.46248 q^{66} +2.64703 q^{67} -3.99639 q^{68} -0.656722 q^{69} -7.01347 q^{70} +2.04340 q^{71} +1.00000 q^{72} -10.6784 q^{73} +5.61670 q^{74} -2.67069 q^{75} -4.36670 q^{76} +25.1021 q^{77} -1.00000 q^{78} +1.80048 q^{79} -1.52621 q^{80} +1.00000 q^{81} +3.17737 q^{82} -0.725177 q^{83} +4.59536 q^{84} +6.09931 q^{85} -8.63591 q^{86} +5.77154 q^{87} +5.46248 q^{88} -15.6596 q^{89} -1.52621 q^{90} -4.59536 q^{91} -0.656722 q^{92} +7.53717 q^{93} +4.76373 q^{94} +6.66449 q^{95} +1.00000 q^{96} -2.62451 q^{97} +14.1174 q^{98} +5.46248 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.52621	−0.682540	−0.341270	−	0.939965i	$-0.610857\pi$
$5$	−1.52621	−0.682540	−0.341270	+	0.939965i	$0.610857\pi$
$6$	1.00000	0.408248
$7$	4.59536	1.73688	0.868442	−	0.495791i	$-0.165122\pi$
$7$	4.59536	1.73688	0.868442	+	0.495791i	$0.165122\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.52621	−0.482629
$11$	5.46248	1.64700	0.823499	−	0.567317i	$-0.192019\pi$
$11$	5.46248	1.64700	0.823499	+	0.567317i	$0.192019\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	4.59536	1.22816
$15$	−1.52621	−0.394065
$16$	1.00000	0.250000
$17$	−3.99639	−0.969266	−0.484633	−	0.874718i	$-0.661047\pi$
$17$	−3.99639	−0.969266	−0.484633	+	0.874718i	$0.661047\pi$
$18$	1.00000	0.235702
$19$	−4.36670	−1.00179	−0.500895	−	0.865508i	$-0.666996\pi$
$19$	−4.36670	−1.00179	−0.500895	+	0.865508i	$0.666996\pi$
$20$	−1.52621	−0.341270
$21$	4.59536	1.00279
$22$	5.46248	1.16460
$23$	−0.656722	−0.136936	−0.0684680	−	0.997653i	$-0.521811\pi$
$23$	−0.656722	−0.136936	−0.0684680	+	0.997653i	$0.521811\pi$
$24$	1.00000	0.204124
$25$	−2.67069	−0.534139
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	4.59536	0.868442
$29$	5.77154	1.07175	0.535874	−	0.844298i	$-0.319982\pi$
$29$	5.77154	1.07175	0.535874	+	0.844298i	$0.319982\pi$
$30$	−1.52621	−0.278646
$31$	7.53717	1.35372	0.676858	−	0.736114i	$-0.263341\pi$
$31$	7.53717	1.35372	0.676858	+	0.736114i	$0.263341\pi$
$32$	1.00000	0.176777
$33$	5.46248	0.950895
$34$	−3.99639	−0.685375
$35$	−7.01347	−1.18549
$36$	1.00000	0.166667
$37$	5.61670	0.923380	0.461690	−	0.887041i	$-0.347243\pi$
$37$	5.61670	0.923380	0.461690	+	0.887041i	$0.347243\pi$
$38$	−4.36670	−0.708373
$39$	−1.00000	−0.160128
$40$	−1.52621	−0.241314
$41$	3.17737	0.496221	0.248111	−	0.968732i	$-0.420190\pi$
$41$	3.17737	0.496221	0.248111	+	0.968732i	$0.420190\pi$
$42$	4.59536	0.709080
$43$	−8.63591	−1.31696	−0.658482	−	0.752597i	$-0.728801\pi$
$43$	−8.63591	−1.31696	−0.658482	+	0.752597i	$0.728801\pi$
$44$	5.46248	0.823499
$45$	−1.52621	−0.227513
$46$	−0.656722	−0.0968283
$47$	4.76373	0.694862	0.347431	−	0.937706i	$-0.387054\pi$
$47$	4.76373	0.694862	0.347431	+	0.937706i	$0.387054\pi$
$48$	1.00000	0.144338
$49$	14.1174	2.01677
$50$	−2.67069	−0.377693
$51$	−3.99639	−0.559606
$52$	−1.00000	−0.138675
$53$	5.30468	0.728654	0.364327	−	0.931271i	$-0.381299\pi$
$53$	5.30468	0.728654	0.364327	+	0.931271i	$0.381299\pi$
$54$	1.00000	0.136083
$55$	−8.33687	−1.12414
$56$	4.59536	0.614081
$57$	−4.36670	−0.578384
$58$	5.77154	0.757840
$59$	1.34821	0.175523	0.0877613	−	0.996142i	$-0.472029\pi$
$59$	1.34821	0.175523	0.0877613	+	0.996142i	$0.472029\pi$
$60$	−1.52621	−0.197032
$61$	8.91845	1.14189	0.570945	−	0.820988i	$-0.306577\pi$
$61$	8.91845	1.14189	0.570945	+	0.820988i	$0.306577\pi$
$62$	7.53717	0.957222
$63$	4.59536	0.578961
$64$	1.00000	0.125000
$65$	1.52621	0.189303
$66$	5.46248	0.672384
$67$	2.64703	0.323386	0.161693	−	0.986841i	$-0.448304\pi$
$67$	2.64703	0.323386	0.161693	+	0.986841i	$0.448304\pi$
$68$	−3.99639	−0.484633
$69$	−0.656722	−0.0790600
$70$	−7.01347	−0.838270
$71$	2.04340	0.242507	0.121254	−	0.992622i	$-0.461309\pi$
$71$	2.04340	0.242507	0.121254	+	0.992622i	$0.461309\pi$
$72$	1.00000	0.117851
$73$	−10.6784	−1.24982	−0.624909	−	0.780698i	$-0.714864\pi$
$73$	−10.6784	−1.24982	−0.624909	+	0.780698i	$0.714864\pi$
$74$	5.61670	0.652928
$75$	−2.67069	−0.308385
$76$	−4.36670	−0.500895
$77$	25.1021	2.86065
$78$	−1.00000	−0.113228
$79$	1.80048	0.202570	0.101285	−	0.994857i	$-0.467705\pi$
$79$	1.80048	0.202570	0.101285	+	0.994857i	$0.467705\pi$
$80$	−1.52621	−0.170635
$81$	1.00000	0.111111
$82$	3.17737	0.350881
$83$	−0.725177	−0.0795986	−0.0397993	−	0.999208i	$-0.512672\pi$
$83$	−0.725177	−0.0795986	−0.0397993	+	0.999208i	$0.512672\pi$
$84$	4.59536	0.501395
$85$	6.09931	0.661563
$86$	−8.63591	−0.931234
$87$	5.77154	0.618774
$88$	5.46248	0.582302
$89$	−15.6596	−1.65992	−0.829958	−	0.557825i	$-0.811636\pi$
$89$	−15.6596	−1.65992	−0.829958	+	0.557825i	$0.811636\pi$
$90$	−1.52621	−0.160876
$91$	−4.59536	−0.481725
$92$	−0.656722	−0.0684680
$93$	7.53717	0.781568
$94$	4.76373	0.491341
$95$	6.66449	0.683762
$96$	1.00000	0.102062
$97$	−2.62451	−0.266478	−0.133239	−	0.991084i	$-0.542538\pi$
$97$	−2.62451	−0.266478	−0.133239	+	0.991084i	$0.542538\pi$
$98$	14.1174	1.42607
$99$	5.46248	0.549000
$100$	−2.67069	−0.267069
$101$	−1.50847	−0.150098	−0.0750491	−	0.997180i	$-0.523911\pi$
$101$	−1.50847	−0.150098	−0.0750491	+	0.997180i	$0.523911\pi$
$102$	−3.99639	−0.395701
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	−7.01347	−0.684445
$106$	5.30468	0.515236
$107$	−13.9325	−1.34691	−0.673454	−	0.739229i	$-0.735190\pi$
$107$	−13.9325	−1.34691	−0.673454	+	0.739229i	$0.735190\pi$
$108$	1.00000	0.0962250
$109$	−17.7010	−1.69545	−0.847725	−	0.530436i	$-0.822028\pi$
$109$	−17.7010	−1.69545	−0.847725	+	0.530436i	$0.822028\pi$
$110$	−8.33687	−0.794889
$111$	5.61670	0.533114
$112$	4.59536	0.434221
$113$	17.9450	1.68812	0.844061	−	0.536247i	$-0.180158\pi$
$113$	17.9450	1.68812	0.844061	+	0.536247i	$0.180158\pi$
$114$	−4.36670	−0.408979
$115$	1.00229	0.0934643
$116$	5.77154	0.535874
$117$	−1.00000	−0.0924500
$118$	1.34821	0.124113
$119$	−18.3648	−1.68350
$120$	−1.52621	−0.139323
$121$	18.8387	1.71261
$122$	8.91845	0.807438
$123$	3.17737	0.286493
$124$	7.53717	0.676858
$125$	11.7071	1.04711
$126$	4.59536	0.409387
$127$	5.86523	0.520455	0.260228	−	0.965547i	$-0.416202\pi$
$127$	5.86523	0.520455	0.260228	+	0.965547i	$0.416202\pi$
$128$	1.00000	0.0883883
$129$	−8.63591	−0.760349
$130$	1.52621	0.133857
$131$	19.7962	1.72960	0.864802	−	0.502114i	$-0.167444\pi$
$131$	19.7962	1.72960	0.864802	+	0.502114i	$0.167444\pi$
$132$	5.46248	0.475448
$133$	−20.0666	−1.73999
$134$	2.64703	0.228669
$135$	−1.52621	−0.131355
$136$	−3.99639	−0.342687
$137$	−15.6657	−1.33841	−0.669207	−	0.743076i	$-0.733366\pi$
$137$	−15.6657	−1.33841	−0.669207	+	0.743076i	$0.733366\pi$
$138$	−0.656722	−0.0559039
$139$	−11.6480	−0.987969	−0.493985	−	0.869471i	$-0.664460\pi$
$139$	−11.6480	−0.987969	−0.493985	+	0.869471i	$0.664460\pi$
$140$	−7.01347	−0.592747
$141$	4.76373	0.401179
$142$	2.04340	0.171479
$143$	−5.46248	−0.456795
$144$	1.00000	0.0833333
$145$	−8.80856	−0.731511
$146$	−10.6784	−0.883754
$147$	14.1174	1.16438
$148$	5.61670	0.461690
$149$	−0.785905	−0.0643839	−0.0321919	−	0.999482i	$-0.510249\pi$
$149$	−0.785905	−0.0643839	−0.0321919	+	0.999482i	$0.510249\pi$
$150$	−2.67069	−0.218061
$151$	12.5929	1.02480	0.512400	−	0.858747i	$-0.328757\pi$
$151$	12.5929	1.02480	0.512400	+	0.858747i	$0.328757\pi$
$152$	−4.36670	−0.354186
$153$	−3.99639	−0.323089
$154$	25.1021	2.02278
$155$	−11.5033	−0.923966
$156$	−1.00000	−0.0800641
$157$	−9.06618	−0.723560	−0.361780	−	0.932264i	$-0.617831\pi$
$157$	−9.06618	−0.723560	−0.361780	+	0.932264i	$0.617831\pi$
$158$	1.80048	0.143239
$159$	5.30468	0.420689
$160$	−1.52621	−0.120657
$161$	−3.01787	−0.237842
$162$	1.00000	0.0785674
$163$	22.2158	1.74007	0.870037	−	0.492987i	$-0.164095\pi$
$163$	22.2158	1.74007	0.870037	+	0.492987i	$0.164095\pi$
$164$	3.17737	0.248111
$165$	−8.33687	−0.649024
$166$	−0.725177	−0.0562847
$167$	18.3703	1.42154	0.710769	−	0.703425i	$-0.248347\pi$
$167$	18.3703	1.42154	0.710769	+	0.703425i	$0.248347\pi$
$168$	4.59536	0.354540
$169$	1.00000	0.0769231
$170$	6.09931	0.467796
$171$	−4.36670	−0.333930
$172$	−8.63591	−0.658482
$173$	7.39722	0.562400	0.281200	−	0.959649i	$-0.409268\pi$
$173$	7.39722	0.562400	0.281200	+	0.959649i	$0.409268\pi$
$174$	5.77154	0.437539
$175$	−12.2728	−0.927737
$176$	5.46248	0.411750
$177$	1.34821	0.101338
$178$	−15.6596	−1.17374
$179$	5.21907	0.390091	0.195046	−	0.980794i	$-0.437514\pi$
$179$	5.21907	0.390091	0.195046	+	0.980794i	$0.437514\pi$
$180$	−1.52621	−0.113757
$181$	10.7351	0.797936	0.398968	−	0.916965i	$-0.369368\pi$
$181$	10.7351	0.797936	0.398968	+	0.916965i	$0.369368\pi$
$182$	−4.59536	−0.340631
$183$	8.91845	0.659271
$184$	−0.656722	−0.0484142
$185$	−8.57224	−0.630244
$186$	7.53717	0.552652
$187$	−21.8302	−1.59638
$188$	4.76373	0.347431
$189$	4.59536	0.334263
$190$	6.66449	0.483493
$191$	−20.1110	−1.45518	−0.727589	−	0.686013i	$-0.759359\pi$
$191$	−20.1110	−1.45518	−0.727589	+	0.686013i	$0.759359\pi$
$192$	1.00000	0.0721688
$193$	−0.0345970	−0.00249034	−0.00124517	−	0.999999i	$-0.500396\pi$
$193$	−0.0345970	−0.00249034	−0.00124517	+	0.999999i	$0.500396\pi$
$194$	−2.62451	−0.188429
$195$	1.52621	0.109294
$196$	14.1174	1.00838
$197$	−16.9588	−1.20826	−0.604131	−	0.796885i	$-0.706480\pi$
$197$	−16.9588	−1.20826	−0.604131	+	0.796885i	$0.706480\pi$
$198$	5.46248	0.388201
$199$	11.2262	0.795804	0.397902	−	0.917428i	$-0.369738\pi$
$199$	11.2262	0.795804	0.397902	+	0.917428i	$0.369738\pi$
$200$	−2.67069	−0.188847
$201$	2.64703	0.186707
$202$	−1.50847	−0.106136
$203$	26.5223	1.86150
$204$	−3.99639	−0.279803
$205$	−4.84932	−0.338691
$206$	1.00000	0.0696733
$207$	−0.656722	−0.0456453
$208$	−1.00000	−0.0693375
$209$	−23.8530	−1.64995
$210$	−7.01347	−0.483976
$211$	1.61361	0.111086	0.0555428	−	0.998456i	$-0.482311\pi$
$211$	1.61361	0.111086	0.0555428	+	0.998456i	$0.482311\pi$
$212$	5.30468	0.364327
$213$	2.04340	0.140012
$214$	−13.9325	−0.952408
$215$	13.1802	0.898880
$216$	1.00000	0.0680414
$217$	34.6360	2.35125
$218$	−17.7010	−1.19886
$219$	−10.6784	−0.721583
$220$	−8.33687	−0.562071
$221$	3.99639	0.268826
$222$	5.61670	0.376968
$223$	−27.2831	−1.82701	−0.913505	−	0.406828i	$-0.866635\pi$
$223$	−27.2831	−1.82701	−0.913505	+	0.406828i	$0.866635\pi$
$224$	4.59536	0.307041
$225$	−2.67069	−0.178046
$226$	17.9450	1.19368
$227$	−11.3248	−0.751655	−0.375827	−	0.926690i	$-0.622641\pi$
$227$	−11.3248	−0.751655	−0.375827	+	0.926690i	$0.622641\pi$
$228$	−4.36670	−0.289192
$229$	−25.8327	−1.70707	−0.853535	−	0.521035i	$-0.825546\pi$
$229$	−25.8327	−1.70707	−0.853535	+	0.521035i	$0.825546\pi$
$230$	1.00229	0.0660892
$231$	25.1021	1.65159
$232$	5.77154	0.378920
$233$	7.13805	0.467629	0.233815	−	0.972281i	$-0.424879\pi$
$233$	7.13805	0.467629	0.233815	+	0.972281i	$0.424879\pi$
$234$	−1.00000	−0.0653720
$235$	−7.27044	−0.474271
$236$	1.34821	0.0877613
$237$	1.80048	0.116954
$238$	−18.3648	−1.19042
$239$	9.00485	0.582475	0.291238	−	0.956651i	$-0.405933\pi$
$239$	9.00485	0.582475	0.291238	+	0.956651i	$0.405933\pi$
$240$	−1.52621	−0.0985162
$241$	−18.4207	−1.18658	−0.593292	−	0.804987i	$-0.702172\pi$
$241$	−18.4207	−1.18658	−0.593292	+	0.804987i	$0.702172\pi$
$242$	18.8387	1.21099
$243$	1.00000	0.0641500
$244$	8.91845	0.570945
$245$	−21.5460	−1.37652
$246$	3.17737	0.202581
$247$	4.36670	0.277847
$248$	7.53717	0.478611
$249$	−0.725177	−0.0459563
$250$	11.7071	0.740420
$251$	11.5031	0.726066	0.363033	−	0.931776i	$-0.381741\pi$
$251$	11.5031	0.726066	0.363033	+	0.931776i	$0.381741\pi$
$252$	4.59536	0.289481
$253$	−3.58733	−0.225533
$254$	5.86523	0.368017
$255$	6.09931	0.381954
$256$	1.00000	0.0625000
$257$	−24.5508	−1.53144	−0.765719	−	0.643175i	$-0.777617\pi$
$257$	−24.5508	−1.53144	−0.765719	+	0.643175i	$0.777617\pi$
$258$	−8.63591	−0.537648
$259$	25.8108	1.60380
$260$	1.52621	0.0946513
$261$	5.77154	0.357249
$262$	19.7962	1.22301
$263$	21.0523	1.29814	0.649070	−	0.760729i	$-0.275158\pi$
$263$	21.0523	1.29814	0.649070	+	0.760729i	$0.275158\pi$
$264$	5.46248	0.336192
$265$	−8.09604	−0.497336
$266$	−20.0666	−1.23036
$267$	−15.6596	−0.958353
$268$	2.64703	0.161693
$269$	7.01865	0.427934	0.213967	−	0.976841i	$-0.431361\pi$
$269$	7.01865	0.427934	0.213967	+	0.976841i	$0.431361\pi$
$270$	−1.52621	−0.0928820
$271$	−0.184502	−0.0112077	−0.00560385	−	0.999984i	$-0.501784\pi$
$271$	−0.184502	−0.0112077	−0.00560385	+	0.999984i	$0.501784\pi$
$272$	−3.99639	−0.242317
$273$	−4.59536	−0.278124
$274$	−15.6657	−0.946401
$275$	−14.5886	−0.879726
$276$	−0.656722	−0.0395300
$277$	−21.2416	−1.27629	−0.638143	−	0.769918i	$-0.720297\pi$
$277$	−21.2416	−1.27629	−0.638143	+	0.769918i	$0.720297\pi$
$278$	−11.6480	−0.698600
$279$	7.53717	0.451239
$280$	−7.01347	−0.419135
$281$	−13.6519	−0.814405	−0.407202	−	0.913338i	$-0.633496\pi$
$281$	−13.6519	−0.814405	−0.407202	+	0.913338i	$0.633496\pi$
$282$	4.76373	0.283676
$283$	−15.5841	−0.926377	−0.463189	−	0.886260i	$-0.653295\pi$
$283$	−15.5841	−0.926377	−0.463189	+	0.886260i	$0.653295\pi$
$284$	2.04340	0.121254
$285$	6.66449	0.394770
$286$	−5.46248	−0.323003
$287$	14.6011	0.861878
$288$	1.00000	0.0589256
$289$	−1.02889	−0.0605231
$290$	−8.80856	−0.517257
$291$	−2.62451	−0.153851
$292$	−10.6784	−0.624909
$293$	14.0141	0.818710	0.409355	−	0.912375i	$-0.365754\pi$
$293$	14.0141	0.818710	0.409355	+	0.912375i	$0.365754\pi$
$294$	14.1174	0.823341
$295$	−2.05765	−0.119801
$296$	5.61670	0.326464
$297$	5.46248	0.316965
$298$	−0.785905	−0.0455263
$299$	0.656722	0.0379792
$300$	−2.67069	−0.154193
$301$	−39.6851	−2.28741
$302$	12.5929	0.724643
$303$	−1.50847	−0.0866593
$304$	−4.36670	−0.250448
$305$	−13.6114	−0.779386
$306$	−3.99639	−0.228458
$307$	−11.4505	−0.653512	−0.326756	−	0.945109i	$-0.605956\pi$
$307$	−11.4505	−0.653512	−0.326756	+	0.945109i	$0.605956\pi$
$308$	25.1021	1.43032
$309$	1.00000	0.0568880
$310$	−11.5033	−0.653342
$311$	26.0673	1.47814	0.739070	−	0.673628i	$-0.235265\pi$
$311$	26.0673	1.47814	0.739070	+	0.673628i	$0.235265\pi$
$312$	−1.00000	−0.0566139
$313$	7.89683	0.446355	0.223178	−	0.974778i	$-0.428357\pi$
$313$	7.89683	0.446355	0.223178	+	0.974778i	$0.428357\pi$
$314$	−9.06618	−0.511634
$315$	−7.01347	−0.395164
$316$	1.80048	0.101285
$317$	−4.33574	−0.243519	−0.121760	−	0.992560i	$-0.538854\pi$
$317$	−4.33574	−0.243519	−0.121760	+	0.992560i	$0.538854\pi$
$318$	5.30468	0.297472
$319$	31.5269	1.76517
$320$	−1.52621	−0.0853175
$321$	−13.9325	−0.777638
$322$	−3.01787	−0.168180
$323$	17.4510	0.971001
$324$	1.00000	0.0555556
$325$	2.67069	0.148143
$326$	22.2158	1.23042
$327$	−17.7010	−0.978868
$328$	3.17737	0.175441
$329$	21.8911	1.20689
$330$	−8.33687	−0.458929
$331$	27.1903	1.49451	0.747256	−	0.664536i	$-0.231371\pi$
$331$	27.1903	1.49451	0.747256	+	0.664536i	$0.231371\pi$
$332$	−0.725177	−0.0397993
$333$	5.61670	0.307793
$334$	18.3703	1.00518
$335$	−4.03992	−0.220724
$336$	4.59536	0.250698
$337$	−33.5408	−1.82709	−0.913543	−	0.406742i	$-0.866665\pi$
$337$	−33.5408	−1.82709	−0.913543	+	0.406742i	$0.866665\pi$
$338$	1.00000	0.0543928
$339$	17.9450	0.974638
$340$	6.09931	0.330782
$341$	41.1716	2.22957
$342$	−4.36670	−0.236124
$343$	32.7068	1.76600
$344$	−8.63591	−0.465617
$345$	1.00229	0.0539616
$346$	7.39722	0.397677
$347$	9.28894	0.498656	0.249328	−	0.968419i	$-0.419790\pi$
$347$	9.28894	0.498656	0.249328	+	0.968419i	$0.419790\pi$
$348$	5.77154	0.309387
$349$	−15.8621	−0.849078	−0.424539	−	0.905410i	$-0.639564\pi$
$349$	−15.8621	−0.849078	−0.424539	+	0.905410i	$0.639564\pi$
$350$	−12.2728	−0.656009
$351$	−1.00000	−0.0533761
$352$	5.46248	0.291151
$353$	−20.3134	−1.08117	−0.540586	−	0.841289i	$-0.681798\pi$
$353$	−20.3134	−1.08117	−0.540586	+	0.841289i	$0.681798\pi$
$354$	1.34821	0.0716568
$355$	−3.11866	−0.165521
$356$	−15.6596	−0.829958
$357$	−18.3648	−0.971971
$358$	5.21907	0.275836
$359$	−25.3784	−1.33942	−0.669711	−	0.742622i	$-0.733582\pi$
$359$	−25.3784	−1.33942	−0.669711	+	0.742622i	$0.733582\pi$
$360$	−1.52621	−0.0804381
$361$	0.0680923	0.00358381
$362$	10.7351	0.564226
$363$	18.8387	0.988773
$364$	−4.59536	−0.240862
$365$	16.2975	0.853051
$366$	8.91845	0.466175
$367$	15.5018	0.809188	0.404594	−	0.914496i	$-0.367413\pi$
$367$	15.5018	0.809188	0.404594	+	0.914496i	$0.367413\pi$
$368$	−0.656722	−0.0342340
$369$	3.17737	0.165407
$370$	−8.57224	−0.445650
$371$	24.3769	1.26559
$372$	7.53717	0.390784
$373$	−1.68273	−0.0871283	−0.0435642	−	0.999051i	$-0.513871\pi$
$373$	−1.68273	−0.0871283	−0.0435642	+	0.999051i	$0.513871\pi$
$374$	−21.8302	−1.12881
$375$	11.7071	0.604550
$376$	4.76373	0.245671
$377$	−5.77154	−0.297249
$378$	4.59536	0.236360
$379$	−23.0464	−1.18381	−0.591906	−	0.806007i	$-0.701624\pi$
$379$	−23.0464	−1.18381	−0.591906	+	0.806007i	$0.701624\pi$
$380$	6.66449	0.341881
$381$	5.86523	0.300485
$382$	−20.1110	−1.02897
$383$	4.65948	0.238088	0.119044	−	0.992889i	$-0.462017\pi$
$383$	4.65948	0.238088	0.119044	+	0.992889i	$0.462017\pi$
$384$	1.00000	0.0510310
$385$	−38.3109	−1.95251
$386$	−0.0345970	−0.00176094
$387$	−8.63591	−0.438988
$388$	−2.62451	−0.133239
$389$	32.6143	1.65361	0.826805	−	0.562488i	$-0.190156\pi$
$389$	32.6143	1.65361	0.826805	+	0.562488i	$0.190156\pi$
$390$	1.52621	0.0772825
$391$	2.62451	0.132727
$392$	14.1174	0.713034
$393$	19.7962	0.998587
$394$	−16.9588	−0.854371
$395$	−2.74791	−0.138262
$396$	5.46248	0.274500
$397$	12.6379	0.634276	0.317138	−	0.948379i	$-0.397278\pi$
$397$	12.6379	0.634276	0.317138	+	0.948379i	$0.397278\pi$
$398$	11.2262	0.562718
$399$	−20.0666	−1.00459
$400$	−2.67069	−0.133535
$401$	31.2042	1.55826	0.779131	−	0.626861i	$-0.215660\pi$
$401$	31.2042	1.55826	0.779131	+	0.626861i	$0.215660\pi$
$402$	2.64703	0.132022
$403$	−7.53717	−0.375453
$404$	−1.50847	−0.0750491
$405$	−1.52621	−0.0758378
$406$	26.5223	1.31628
$407$	30.6811	1.52081
$408$	−3.99639	−0.197851
$409$	−9.66693	−0.477999	−0.239000	−	0.971020i	$-0.576819\pi$
$409$	−9.66693	−0.477999	−0.239000	+	0.971020i	$0.576819\pi$
$410$	−4.84932	−0.239491
$411$	−15.6657	−0.772733
$412$	1.00000	0.0492665
$413$	6.19553	0.304862
$414$	−0.656722	−0.0322761
$415$	1.10677	0.0543292
$416$	−1.00000	−0.0490290
$417$	−11.6480	−0.570404
$418$	−23.8530	−1.16669
$419$	−4.05490	−0.198095	−0.0990474	−	0.995083i	$-0.531580\pi$
$419$	−4.05490	−0.198095	−0.0990474	+	0.995083i	$0.531580\pi$
$420$	−7.01347	−0.342222
$421$	−4.35497	−0.212248	−0.106124	−	0.994353i	$-0.533844\pi$
$421$	−4.35497	−0.212248	−0.106124	+	0.994353i	$0.533844\pi$
$422$	1.61361	0.0785493
$423$	4.76373	0.231621
$424$	5.30468	0.257618
$425$	10.6731	0.517723
$426$	2.04340	0.0990032
$427$	40.9835	1.98333
$428$	−13.9325	−0.673454
$429$	−5.46248	−0.263731
$430$	13.1802	0.635604
$431$	28.7105	1.38294	0.691468	−	0.722407i	$-0.256964\pi$
$431$	28.7105	1.38294	0.691468	+	0.722407i	$0.256964\pi$
$432$	1.00000	0.0481125
$433$	−32.9383	−1.58292	−0.791458	−	0.611224i	$-0.790678\pi$
$433$	−32.9383	−1.58292	−0.791458	+	0.611224i	$0.790678\pi$
$434$	34.6360	1.66258
$435$	−8.80856	−0.422338
$436$	−17.7010	−0.847725
$437$	2.86771	0.137181
$438$	−10.6784	−0.510236
$439$	24.1380	1.15205	0.576023	−	0.817434i	$-0.304604\pi$
$439$	24.1380	1.15205	0.576023	+	0.817434i	$0.304604\pi$
$440$	−8.33687	−0.397445
$441$	14.1174	0.672255
$442$	3.99639	0.190089
$443$	−3.44383	−0.163621	−0.0818107	−	0.996648i	$-0.526070\pi$
$443$	−3.44383	−0.163621	−0.0818107	+	0.996648i	$0.526070\pi$
$444$	5.61670	0.266557
$445$	23.8998	1.13296
$446$	−27.2831	−1.29189
$447$	−0.785905	−0.0371720
$448$	4.59536	0.217110
$449$	15.0910	0.712187	0.356094	−	0.934450i	$-0.384108\pi$
$449$	15.0910	0.712187	0.356094	+	0.934450i	$0.384108\pi$
$450$	−2.67069	−0.125898
$451$	17.3563	0.817276
$452$	17.9450	0.844061
$453$	12.5929	0.591668
$454$	−11.3248	−0.531500
$455$	7.01347	0.328797
$456$	−4.36670	−0.204490
$457$	18.1545	0.849233	0.424617	−	0.905373i	$-0.360409\pi$
$457$	18.1545	0.849233	0.424617	+	0.905373i	$0.360409\pi$
$458$	−25.8327	−1.20708
$459$	−3.99639	−0.186535
$460$	1.00229	0.0467321
$461$	38.5958	1.79758	0.898792	−	0.438376i	$-0.144446\pi$
$461$	38.5958	1.79758	0.898792	+	0.438376i	$0.144446\pi$
$462$	25.1021	1.16785
$463$	36.0814	1.67684	0.838422	−	0.545021i	$-0.183478\pi$
$463$	36.0814	1.67684	0.838422	+	0.545021i	$0.183478\pi$
$464$	5.77154	0.267937
$465$	−11.5033	−0.533452
$466$	7.13805	0.330664
$467$	−6.01897	−0.278525	−0.139262	−	0.990256i	$-0.544473\pi$
$467$	−6.01897	−0.278525	−0.139262	+	0.990256i	$0.544473\pi$
$468$	−1.00000	−0.0462250
$469$	12.1641	0.561685
$470$	−7.27044	−0.335360
$471$	−9.06618	−0.417747
$472$	1.34821	0.0620566
$473$	−47.1734	−2.16904
$474$	1.80048	0.0826990
$475$	11.6621	0.535095
$476$	−18.3648	−0.841751
$477$	5.30468	0.242885
$478$	9.00485	0.411872
$479$	40.3075	1.84170	0.920848	−	0.389922i	$-0.127498\pi$
$479$	40.3075	1.84170	0.920848	+	0.389922i	$0.127498\pi$
$480$	−1.52621	−0.0696615
$481$	−5.61670	−0.256099
$482$	−18.4207	−0.839042
$483$	−3.01787	−0.137318
$484$	18.8387	0.856303
$485$	4.00554	0.181882
$486$	1.00000	0.0453609
$487$	−34.0634	−1.54356	−0.771780	−	0.635890i	$-0.780633\pi$
$487$	−34.0634	−1.54356	−0.771780	+	0.635890i	$0.780633\pi$
$488$	8.91845	0.403719
$489$	22.2158	1.00463
$490$	−21.5460	−0.973349
$491$	22.7366	1.02609	0.513044	−	0.858362i	$-0.328518\pi$
$491$	22.7366	1.02609	0.513044	+	0.858362i	$0.328518\pi$
$492$	3.17737	0.143247
$493$	−23.0653	−1.03881
$494$	4.36670	0.196467
$495$	−8.33687	−0.374714
$496$	7.53717	0.338429
$497$	9.39018	0.421207
$498$	−0.725177	−0.0324960
$499$	−8.61905	−0.385842	−0.192921	−	0.981214i	$-0.561796\pi$
$499$	−8.61905	−0.385842	−0.192921	+	0.981214i	$0.561796\pi$
$500$	11.7071	0.523556
$501$	18.3703	0.820726
$502$	11.5031	0.513406
$503$	−23.8915	−1.06527	−0.532635	−	0.846345i	$-0.678798\pi$
$503$	−23.8915	−1.06527	−0.532635	+	0.846345i	$0.678798\pi$
$504$	4.59536	0.204694
$505$	2.30224	0.102448
$506$	−3.58733	−0.159476
$507$	1.00000	0.0444116
$508$	5.86523	0.260228
$509$	9.49832	0.421006	0.210503	−	0.977593i	$-0.432490\pi$
$509$	9.49832	0.421006	0.210503	+	0.977593i	$0.432490\pi$
$510$	6.09931	0.270082
$511$	−49.0713	−2.17079
$512$	1.00000	0.0441942
$513$	−4.36670	−0.192795
$514$	−24.5508	−1.08289
$515$	−1.52621	−0.0672527
$516$	−8.63591	−0.380175
$517$	26.0218	1.14444
$518$	25.8108	1.13406
$519$	7.39722	0.324702
$520$	1.52621	0.0669286
$521$	2.91387	0.127659	0.0638295	−	0.997961i	$-0.479669\pi$
$521$	2.91387	0.127659	0.0638295	+	0.997961i	$0.479669\pi$
$522$	5.77154	0.252613
$523$	−40.6486	−1.77744	−0.888720	−	0.458450i	$-0.848405\pi$
$523$	−40.6486	−1.77744	−0.888720	+	0.458450i	$0.848405\pi$
$524$	19.7962	0.864802
$525$	−12.2728	−0.535629
$526$	21.0523	0.917924
$527$	−30.1215	−1.31211
$528$	5.46248	0.237724
$529$	−22.5687	−0.981249
$530$	−8.09604	−0.351670
$531$	1.34821	0.0585075
$532$	−20.0666	−0.869997
$533$	−3.17737	−0.137627
$534$	−15.6596	−0.677658
$535$	21.2639	0.919319
$536$	2.64703	0.114334
$537$	5.21907	0.225219
$538$	7.01865	0.302595
$539$	77.1157	3.32161
$540$	−1.52621	−0.0656775
$541$	−4.77930	−0.205478	−0.102739	−	0.994708i	$-0.532761\pi$
$541$	−4.77930	−0.205478	−0.102739	+	0.994708i	$0.532761\pi$
$542$	−0.184502	−0.00792504
$543$	10.7351	0.460689
$544$	−3.99639	−0.171344
$545$	27.0154	1.15721
$546$	−4.59536	−0.196663
$547$	32.0352	1.36973	0.684863	−	0.728672i	$-0.259862\pi$
$547$	32.0352	1.36973	0.684863	+	0.728672i	$0.259862\pi$
$548$	−15.6657	−0.669207
$549$	8.91845	0.380630
$550$	−14.5886	−0.622060
$551$	−25.2026	−1.07367
$552$	−0.656722	−0.0279519
$553$	8.27388	0.351841
$554$	−21.2416	−0.902470
$555$	−8.57224	−0.363871
$556$	−11.6480	−0.493985
$557$	−4.87355	−0.206499	−0.103249	−	0.994655i	$-0.532924\pi$
$557$	−4.87355	−0.206499	−0.103249	+	0.994655i	$0.532924\pi$
$558$	7.53717	0.319074
$559$	8.63591	0.365260
$560$	−7.01347	−0.296373
$561$	−21.8302	−0.921671
$562$	−13.6519	−0.575871
$563$	14.3117	0.603166	0.301583	−	0.953440i	$-0.402485\pi$
$563$	14.3117	0.603166	0.301583	+	0.953440i	$0.402485\pi$
$564$	4.76373	0.200589
$565$	−27.3878	−1.15221
$566$	−15.5841	−0.655048
$567$	4.59536	0.192987
$568$	2.04340	0.0857393
$569$	−27.3288	−1.14568	−0.572841	−	0.819666i	$-0.694159\pi$
$569$	−27.3288	−1.14568	−0.572841	+	0.819666i	$0.694159\pi$
$570$	6.66449	0.279145
$571$	9.14430	0.382677	0.191338	−	0.981524i	$-0.438717\pi$
$571$	9.14430	0.382677	0.191338	+	0.981524i	$0.438717\pi$
$572$	−5.46248	−0.228398
$573$	−20.1110	−0.840148
$574$	14.6011	0.609440
$575$	1.75390	0.0731428
$576$	1.00000	0.0416667
$577$	−35.2619	−1.46797	−0.733986	−	0.679164i	$-0.762342\pi$
$577$	−35.2619	−1.46797	−0.733986	+	0.679164i	$0.762342\pi$
$578$	−1.02889	−0.0427963
$579$	−0.0345970	−0.00143780
$580$	−8.80856	−0.365756
$581$	−3.33245	−0.138253
$582$	−2.62451	−0.108789
$583$	28.9767	1.20009
$584$	−10.6784	−0.441877
$585$	1.52621	0.0631009
$586$	14.0141	0.578915
$587$	17.4867	0.721755	0.360878	−	0.932613i	$-0.382477\pi$
$587$	17.4867	0.721755	0.360878	+	0.932613i	$0.382477\pi$
$588$	14.1174	0.582190
$589$	−32.9126	−1.35614
$590$	−2.05765	−0.0847122
$591$	−16.9588	−0.697591
$592$	5.61670	0.230845
$593$	7.27949	0.298933	0.149466	−	0.988767i	$-0.452244\pi$
$593$	7.27949	0.298933	0.149466	+	0.988767i	$0.452244\pi$
$594$	5.46248	0.224128
$595$	28.0285	1.14906
$596$	−0.785905	−0.0321919
$597$	11.2262	0.459458
$598$	0.656722	0.0268553
$599$	−42.6597	−1.74303	−0.871514	−	0.490370i	$-0.836862\pi$
$599$	−42.6597	−1.74303	−0.871514	+	0.490370i	$0.836862\pi$
$600$	−2.67069	−0.109031
$601$	−20.0055	−0.816042	−0.408021	−	0.912973i	$-0.633781\pi$
$601$	−20.0055	−0.816042	−0.408021	+	0.912973i	$0.633781\pi$
$602$	−39.6851	−1.61744
$603$	2.64703	0.107795
$604$	12.5929	0.512400
$605$	−28.7517	−1.16892
$606$	−1.50847	−0.0612774
$607$	−10.0239	−0.406857	−0.203429	−	0.979090i	$-0.565208\pi$
$607$	−10.0239	−0.406857	−0.203429	+	0.979090i	$0.565208\pi$
$608$	−4.36670	−0.177093
$609$	26.5223	1.07474
$610$	−13.6114	−0.551109
$611$	−4.76373	−0.192720
$612$	−3.99639	−0.161544
$613$	4.86171	0.196363	0.0981814	−	0.995169i	$-0.468697\pi$
$613$	4.86171	0.196363	0.0981814	+	0.995169i	$0.468697\pi$
$614$	−11.4505	−0.462103
$615$	−4.84932	−0.195543
$616$	25.1021	1.01139
$617$	25.2779	1.01765	0.508825	−	0.860870i	$-0.330080\pi$
$617$	25.2779	1.01765	0.508825	+	0.860870i	$0.330080\pi$
$618$	1.00000	0.0402259
$619$	−34.1686	−1.37335	−0.686676	−	0.726964i	$-0.740931\pi$
$619$	−34.1686	−1.37335	−0.686676	+	0.726964i	$0.740931\pi$
$620$	−11.5033	−0.461983
$621$	−0.656722	−0.0263533
$622$	26.0673	1.04520
$623$	−71.9616	−2.88308
$624$	−1.00000	−0.0400320
$625$	−4.51392	−0.180557
$626$	7.89683	0.315621
$627$	−23.8530	−0.952598
$628$	−9.06618	−0.361780
$629$	−22.4465	−0.895001
$630$	−7.01347	−0.279423
$631$	−14.8691	−0.591931	−0.295965	−	0.955199i	$-0.595641\pi$
$631$	−14.8691	−0.591931	−0.295965	+	0.955199i	$0.595641\pi$
$632$	1.80048	0.0716194
$633$	1.61361	0.0641353
$634$	−4.33574	−0.172194
$635$	−8.95155	−0.355232
$636$	5.30468	0.210344
$637$	−14.1174	−0.559350
$638$	31.5269	1.24816
$639$	2.04340	0.0808358
$640$	−1.52621	−0.0603286
$641$	25.3556	1.00149	0.500743	−	0.865596i	$-0.333060\pi$
$641$	25.3556	1.00149	0.500743	+	0.865596i	$0.333060\pi$
$642$	−13.9325	−0.549873
$643$	21.2448	0.837814	0.418907	−	0.908029i	$-0.362413\pi$
$643$	21.2448	0.837814	0.418907	+	0.908029i	$0.362413\pi$
$644$	−3.01787	−0.118921
$645$	13.1802	0.518969
$646$	17.4510	0.686602
$647$	−43.0485	−1.69241	−0.846205	−	0.532857i	$-0.821118\pi$
$647$	−43.0485	−1.69241	−0.846205	+	0.532857i	$0.821118\pi$
$648$	1.00000	0.0392837
$649$	7.36459	0.289085
$650$	2.67069	0.104753
$651$	34.6360	1.35749
$652$	22.2158	0.870037
$653$	−27.0099	−1.05698	−0.528489	−	0.848940i	$-0.677241\pi$
$653$	−27.0099	−1.05698	−0.528489	+	0.848940i	$0.677241\pi$
$654$	−17.7010	−0.692165
$655$	−30.2131	−1.18052
$656$	3.17737	0.124055
$657$	−10.6784	−0.416606
$658$	21.8911	0.853403
$659$	6.48804	0.252738	0.126369	−	0.991983i	$-0.459668\pi$
$659$	6.48804	0.252738	0.126369	+	0.991983i	$0.459668\pi$
$660$	−8.33687	−0.324512
$661$	−21.2881	−0.828010	−0.414005	−	0.910275i	$-0.635870\pi$
$661$	−21.2881	−0.828010	−0.414005	+	0.910275i	$0.635870\pi$
$662$	27.1903	1.05678
$663$	3.99639	0.155207
$664$	−0.725177	−0.0281423
$665$	30.6257	1.18762
$666$	5.61670	0.217643
$667$	−3.79029	−0.146761
$668$	18.3703	0.710769
$669$	−27.2831	−1.05482
$670$	−4.03992	−0.156076
$671$	48.7168	1.88069
$672$	4.59536	0.177270
$673$	42.6718	1.64488	0.822439	−	0.568853i	$-0.192613\pi$
$673$	42.6718	1.64488	0.822439	+	0.568853i	$0.192613\pi$
$674$	−33.5408	−1.29194
$675$	−2.67069	−0.102795
$676$	1.00000	0.0384615
$677$	−35.3790	−1.35973	−0.679864	−	0.733339i	$-0.737961\pi$
$677$	−35.3790	−1.35973	−0.679864	+	0.733339i	$0.737961\pi$
$678$	17.9450	0.689173
$679$	−12.0606	−0.462842
$680$	6.09931	0.233898
$681$	−11.3248	−0.433968
$682$	41.1716	1.57654
$683$	38.0681	1.45664	0.728318	−	0.685240i	$-0.240303\pi$
$683$	38.0681	1.45664	0.728318	+	0.685240i	$0.240303\pi$
$684$	−4.36670	−0.166965
$685$	23.9091	0.913521
$686$	32.7068	1.24875
$687$	−25.8327	−0.985578
$688$	−8.63591	−0.329241
$689$	−5.30468	−0.202092
$690$	1.00229	0.0381566
$691$	−19.3196	−0.734951	−0.367475	−	0.930033i	$-0.619778\pi$
$691$	−19.3196	−0.734951	−0.367475	+	0.930033i	$0.619778\pi$
$692$	7.39722	0.281200
$693$	25.1021	0.953548
$694$	9.28894	0.352603
$695$	17.7772	0.674329
$696$	5.77154	0.218770
$697$	−12.6980	−0.480970
$698$	−15.8621	−0.600389
$699$	7.13805	0.269986
$700$	−12.2728	−0.463869
$701$	−11.8834	−0.448831	−0.224415	−	0.974494i	$-0.572047\pi$
$701$	−11.8834	−0.448831	−0.224415	+	0.974494i	$0.572047\pi$
$702$	−1.00000	−0.0377426
$703$	−24.5265	−0.925033
$704$	5.46248	0.205875
$705$	−7.27044	−0.273821
$706$	−20.3134	−0.764504
$707$	−6.93196	−0.260703
$708$	1.34821	0.0506690
$709$	26.4272	0.992496	0.496248	−	0.868181i	$-0.334711\pi$
$709$	26.4272	0.992496	0.496248	+	0.868181i	$0.334711\pi$
$710$	−3.11866	−0.117041
$711$	1.80048	0.0675234
$712$	−15.6596	−0.586869
$713$	−4.94982	−0.185372
$714$	−18.3648	−0.687287
$715$	8.33687	0.311781
$716$	5.21907	0.195046
$717$	9.00485	0.336292
$718$	−25.3784	−0.947114
$719$	20.0720	0.748561	0.374281	−	0.927316i	$-0.377890\pi$
$719$	20.0720	0.748561	0.374281	+	0.927316i	$0.377890\pi$
$720$	−1.52621	−0.0568784
$721$	4.59536	0.171140
$722$	0.0680923	0.00253413
$723$	−18.4207	−0.685075
$724$	10.7351	0.398968
$725$	−15.4140	−0.572462
$726$	18.8387	0.699168
$727$	0.742049	0.0275211	0.0137605	−	0.999905i	$-0.495620\pi$
$727$	0.742049	0.0275211	0.0137605	+	0.999905i	$0.495620\pi$
$728$	−4.59536	−0.170315
$729$	1.00000	0.0370370
$730$	16.2975	0.603198
$731$	34.5124	1.27649
$732$	8.91845	0.329635
$733$	−40.5482	−1.49768	−0.748841	−	0.662750i	$-0.769389\pi$
$733$	−40.5482	−1.49768	−0.748841	+	0.662750i	$0.769389\pi$
$734$	15.5018	0.572182
$735$	−21.5460	−0.794736
$736$	−0.656722	−0.0242071
$737$	14.4594	0.532617
$738$	3.17737	0.116960
$739$	21.3264	0.784505	0.392252	−	0.919858i	$-0.371696\pi$
$739$	21.3264	0.784505	0.392252	+	0.919858i	$0.371696\pi$
$740$	−8.57224	−0.315122
$741$	4.36670	0.160415
$742$	24.3769	0.894906
$743$	−5.97335	−0.219141	−0.109570	−	0.993979i	$-0.534948\pi$
$743$	−5.97335	−0.219141	−0.109570	+	0.993979i	$0.534948\pi$
$744$	7.53717	0.276326
$745$	1.19945	0.0439446
$746$	−1.68273	−0.0616090
$747$	−0.725177	−0.0265329
$748$	−21.8302	−0.798190
$749$	−64.0250	−2.33942
$750$	11.7071	0.427481
$751$	−33.8886	−1.23661	−0.618306	−	0.785937i	$-0.712181\pi$
$751$	−33.8886	−1.23661	−0.618306	+	0.785937i	$0.712181\pi$
$752$	4.76373	0.173715
$753$	11.5031	0.419194
$754$	−5.77154	−0.210187
$755$	−19.2194	−0.699467
$756$	4.59536	0.167132
$757$	−6.64445	−0.241496	−0.120748	−	0.992683i	$-0.538529\pi$
$757$	−6.64445	−0.241496	−0.120748	+	0.992683i	$0.538529\pi$
$758$	−23.0464	−0.837082
$759$	−3.58733	−0.130212
$760$	6.66449	0.241746
$761$	17.8634	0.647547	0.323774	−	0.946135i	$-0.395048\pi$
$761$	17.8634	0.647547	0.323774	+	0.946135i	$0.395048\pi$
$762$	5.86523	0.212475
$763$	−81.3426	−2.94480
$764$	−20.1110	−0.727589
$765$	6.09931	0.220521
$766$	4.65948	0.168354
$767$	−1.34821	−0.0486812
$768$	1.00000	0.0360844
$769$	−53.5571	−1.93132	−0.965659	−	0.259813i	$-0.916339\pi$
$769$	−53.5571	−1.93132	−0.965659	+	0.259813i	$0.916339\pi$
$770$	−38.3109	−1.38063
$771$	−24.5508	−0.884176
$772$	−0.0345970	−0.00124517
$773$	−24.7373	−0.889740	−0.444870	−	0.895595i	$-0.646750\pi$
$773$	−24.7373	−0.889740	−0.444870	+	0.895595i	$0.646750\pi$
$774$	−8.63591	−0.310411
$775$	−20.1295	−0.723072
$776$	−2.62451	−0.0942143
$777$	25.8108	0.925956
$778$	32.6143	1.16928
$779$	−13.8746	−0.497109
$780$	1.52621	0.0546470
$781$	11.1620	0.399409
$782$	2.62451	0.0938524
$783$	5.77154	0.206258
$784$	14.1174	0.504191
$785$	13.8369	0.493859
$786$	19.7962	0.706107
$787$	−8.08650	−0.288253	−0.144126	−	0.989559i	$-0.546037\pi$
$787$	−8.08650	−0.288253	−0.144126	+	0.989559i	$0.546037\pi$
$788$	−16.9588	−0.604131
$789$	21.0523	0.749481
$790$	−2.74791	−0.0977663
$791$	82.4637	2.93207
$792$	5.46248	0.194101
$793$	−8.91845	−0.316703
$794$	12.6379	0.448501
$795$	−8.09604	−0.287137
$796$	11.2262	0.397902
$797$	−41.7592	−1.47919	−0.739593	−	0.673055i	$-0.764982\pi$
$797$	−41.7592	−1.47919	−0.739593	+	0.673055i	$0.764982\pi$
$798$	−20.0666	−0.710349
$799$	−19.0377	−0.673506
$800$	−2.67069	−0.0944233
$801$	−15.6596	−0.553306
$802$	31.2042	1.10186
$803$	−58.3308	−2.05845
$804$	2.64703	0.0933536
$805$	4.60590	0.162337
$806$	−7.53717	−0.265486
$807$	7.01865	0.247068
$808$	−1.50847	−0.0530678
$809$	10.5666	0.371503	0.185752	−	0.982597i	$-0.440528\pi$
$809$	10.5666	0.371503	0.185752	+	0.982597i	$0.440528\pi$
$810$	−1.52621	−0.0536254
$811$	13.6799	0.480368	0.240184	−	0.970727i	$-0.422792\pi$
$811$	13.6799	0.480368	0.240184	+	0.970727i	$0.422792\pi$
$812$	26.5223	0.930751
$813$	−0.184502	−0.00647076
$814$	30.6811	1.07537
$815$	−33.9059	−1.18767
$816$	−3.99639	−0.139902
$817$	37.7104	1.31932
$818$	−9.66693	−0.337996
$819$	−4.59536	−0.160575
$820$	−4.84932	−0.169345
$821$	12.8494	0.448448	0.224224	−	0.974538i	$-0.428015\pi$
$821$	12.8494	0.448448	0.224224	+	0.974538i	$0.428015\pi$
$822$	−15.6657	−0.546405
$823$	−22.0620	−0.769033	−0.384517	−	0.923118i	$-0.625632\pi$
$823$	−22.0620	−0.769033	−0.384517	+	0.923118i	$0.625632\pi$
$824$	1.00000	0.0348367
$825$	−14.5886	−0.507910
$826$	6.19553	0.215570
$827$	−11.8996	−0.413789	−0.206895	−	0.978363i	$-0.566336\pi$
$827$	−11.8996	−0.413789	−0.206895	+	0.978363i	$0.566336\pi$
$828$	−0.656722	−0.0228227
$829$	39.5759	1.37453	0.687264	−	0.726407i	$-0.258811\pi$
$829$	39.5759	1.37453	0.687264	+	0.726407i	$0.258811\pi$
$830$	1.10677	0.0384166
$831$	−21.2416	−0.736864
$832$	−1.00000	−0.0346688
$833$	−56.4184	−1.95478
$834$	−11.6480	−0.403337
$835$	−28.0369	−0.970257
$836$	−23.8530	−0.824974
$837$	7.53717	0.260523
$838$	−4.05490	−0.140074
$839$	−26.0187	−0.898264	−0.449132	−	0.893465i	$-0.648267\pi$
$839$	−26.0187	−0.898264	−0.449132	+	0.893465i	$0.648267\pi$
$840$	−7.01347	−0.241988
$841$	4.31067	0.148644
$842$	−4.35497	−0.150082
$843$	−13.6519	−0.470197
$844$	1.61361	0.0555428
$845$	−1.52621	−0.0525031
$846$	4.76373	0.163780
$847$	86.5705	2.97460
$848$	5.30468	0.182164
$849$	−15.5841	−0.534844
$850$	10.6731	0.366085
$851$	−3.68861	−0.126444
$852$	2.04340	0.0700059
$853$	−2.44557	−0.0837348	−0.0418674	−	0.999123i	$-0.513331\pi$
$853$	−2.44557	−0.0837348	−0.0418674	+	0.999123i	$0.513331\pi$
$854$	40.9835	1.40243
$855$	6.66449	0.227921
$856$	−13.9325	−0.476204
$857$	35.6632	1.21823	0.609117	−	0.793081i	$-0.291524\pi$
$857$	35.6632	1.21823	0.609117	+	0.793081i	$0.291524\pi$
$858$	−5.46248	−0.186486
$859$	12.5091	0.426805	0.213402	−	0.976964i	$-0.431545\pi$
$859$	12.5091	0.426805	0.213402	+	0.976964i	$0.431545\pi$
$860$	13.1802	0.449440
$861$	14.6011	0.497606
$862$	28.7105	0.977884
$863$	−31.1064	−1.05887	−0.529437	−	0.848349i	$-0.677597\pi$
$863$	−31.1064	−1.05887	−0.529437	+	0.848349i	$0.677597\pi$
$864$	1.00000	0.0340207
$865$	−11.2897	−0.383861
$866$	−32.9383	−1.11929
$867$	−1.02889	−0.0349430
$868$	34.6360	1.17562
$869$	9.83510	0.333633
$870$	−8.80856	−0.298638
$871$	−2.64703	−0.0896913
$872$	−17.7010	−0.599432
$873$	−2.62451	−0.0888261
$874$	2.86771	0.0970017
$875$	53.7982	1.81871
$876$	−10.6784	−0.360791
$877$	37.2036	1.25628	0.628139	−	0.778101i	$-0.283817\pi$
$877$	37.2036	1.25628	0.628139	+	0.778101i	$0.283817\pi$
$878$	24.1380	0.814619
$879$	14.0141	0.472682
$880$	−8.33687	−0.281036
$881$	−59.1672	−1.99339	−0.996697	−	0.0812107i	$-0.974121\pi$
$881$	−59.1672	−1.99339	−0.996697	+	0.0812107i	$0.974121\pi$
$882$	14.1174	0.475356
$883$	23.5839	0.793662	0.396831	−	0.917892i	$-0.370110\pi$
$883$	23.5839	0.793662	0.396831	+	0.917892i	$0.370110\pi$
$884$	3.99639	0.134413
$885$	−2.05765	−0.0691673
$886$	−3.44383	−0.115698
$887$	7.62368	0.255978	0.127989	−	0.991776i	$-0.459148\pi$
$887$	7.62368	0.255978	0.127989	+	0.991776i	$0.459148\pi$
$888$	5.61670	0.188484
$889$	26.9529	0.903970
$890$	23.8998	0.801124
$891$	5.46248	0.183000
$892$	−27.2831	−0.913505
$893$	−20.8018	−0.696106
$894$	−0.785905	−0.0262846
$895$	−7.96537	−0.266253
$896$	4.59536	0.153520
$897$	0.656722	0.0219273
$898$	15.0910	0.503592
$899$	43.5011	1.45084
$900$	−2.67069	−0.0890231
$901$	−21.1996	−0.706260
$902$	17.3563	0.577901
$903$	−39.6851	−1.32064
$904$	17.9450	0.596841
$905$	−16.3840	−0.544624
$906$	12.5929	0.418373
$907$	−21.1866	−0.703488	−0.351744	−	0.936096i	$-0.614411\pi$
$907$	−21.1866	−0.703488	−0.351744	+	0.936096i	$0.614411\pi$
$908$	−11.3248	−0.375827
$909$	−1.50847	−0.0500328
$910$	7.01347	0.232494
$911$	−24.5337	−0.812837	−0.406418	−	0.913687i	$-0.633222\pi$
$911$	−24.5337	−0.812837	−0.406418	+	0.913687i	$0.633222\pi$
$912$	−4.36670	−0.144596
$913$	−3.96126	−0.131099
$914$	18.1545	0.600499
$915$	−13.6114	−0.449979
$916$	−25.8327	−0.853535
$917$	90.9708	3.00412
$918$	−3.99639	−0.131900
$919$	19.6887	0.649469	0.324735	−	0.945805i	$-0.394725\pi$
$919$	19.6887	0.649469	0.324735	+	0.945805i	$0.394725\pi$
$920$	1.00229	0.0330446
$921$	−11.4505	−0.377305
$922$	38.5958	1.27108
$923$	−2.04340	−0.0672595
$924$	25.1021	0.825797
$925$	−15.0005	−0.493213
$926$	36.0814	1.18571
$927$	1.00000	0.0328443
$928$	5.77154	0.189460
$929$	−39.9492	−1.31069	−0.655345	−	0.755329i	$-0.727477\pi$
$929$	−39.9492	−1.31069	−0.655345	+	0.755329i	$0.727477\pi$
$930$	−11.5033	−0.377207
$931$	−61.6463	−2.02038
$932$	7.13805	0.233815
$933$	26.0673	0.853405
$934$	−6.01897	−0.196947
$935$	33.3173	1.08959
$936$	−1.00000	−0.0326860
$937$	51.0365	1.66729	0.833644	−	0.552302i	$-0.186250\pi$
$937$	51.0365	1.66729	0.833644	+	0.552302i	$0.186250\pi$
$938$	12.1641	0.397171
$939$	7.89683	0.257703
$940$	−7.27044	−0.237136
$941$	−2.51021	−0.0818306	−0.0409153	−	0.999163i	$-0.513027\pi$
$941$	−2.51021	−0.0818306	−0.0409153	+	0.999163i	$0.513027\pi$
$942$	−9.06618	−0.295392
$943$	−2.08664	−0.0679505
$944$	1.34821	0.0438806
$945$	−7.01347	−0.228148
$946$	−47.1734	−1.53374
$947$	−29.7843	−0.967860	−0.483930	−	0.875107i	$-0.660791\pi$
$947$	−29.7843	−0.967860	−0.483930	+	0.875107i	$0.660791\pi$
$948$	1.80048	0.0584770
$949$	10.6784	0.346637
$950$	11.6621	0.378369
$951$	−4.33574	−0.140596
$952$	−18.3648	−0.595208
$953$	9.81443	0.317921	0.158960	−	0.987285i	$-0.449186\pi$
$953$	9.81443	0.317921	0.158960	+	0.987285i	$0.449186\pi$
$954$	5.30468	0.171745
$955$	30.6935	0.993218
$956$	9.00485	0.291238
$957$	31.5269	1.01912
$958$	40.3075	1.30228
$959$	−71.9897	−2.32467
$960$	−1.52621	−0.0492581
$961$	25.8089	0.832547
$962$	−5.61670	−0.181090
$963$	−13.9325	−0.448969
$964$	−18.4207	−0.593292
$965$	0.0528021	0.00169976
$966$	−3.01787	−0.0970985
$967$	−44.9311	−1.44489	−0.722443	−	0.691431i	$-0.756981\pi$
$967$	−44.9311	−1.44489	−0.722443	+	0.691431i	$0.756981\pi$
$968$	18.8387	0.605497
$969$	17.4510	0.560608
$970$	4.00554	0.128610
$971$	−18.8947	−0.606361	−0.303180	−	0.952933i	$-0.598048\pi$
$971$	−18.8947	−0.606361	−0.303180	+	0.952933i	$0.598048\pi$
$972$	1.00000	0.0320750
$973$	−53.5267	−1.71599
$974$	−34.0634	−1.09146
$975$	2.67069	0.0855307
$976$	8.91845	0.285473
$977$	−56.1561	−1.79659	−0.898296	−	0.439391i	$-0.855194\pi$
$977$	−56.1561	−1.79659	−0.898296	+	0.439391i	$0.855194\pi$
$978$	22.2158	0.710382
$979$	−85.5403	−2.73388
$980$	−21.5460	−0.688262
$981$	−17.7010	−0.565150
$982$	22.7366	0.725554
$983$	−26.1836	−0.835127	−0.417563	−	0.908648i	$-0.637116\pi$
$983$	−26.1836	−0.835127	−0.417563	+	0.908648i	$0.637116\pi$
$984$	3.17737	0.101291
$985$	25.8826	0.824688
$986$	−23.0653	−0.734549
$987$	21.8911	0.696801
$988$	4.36670	0.138923
$989$	5.67139	0.180340
$990$	−8.33687	−0.264963
$991$	27.9431	0.887642	0.443821	−	0.896115i	$-0.353623\pi$
$991$	27.9431	0.887642	0.443821	+	0.896115i	$0.353623\pi$
$992$	7.53717	0.239305
$993$	27.1903	0.862857
$994$	9.39018	0.297838
$995$	−17.1335	−0.543168
$996$	−0.725177	−0.0229781
$997$	−3.70889	−0.117462	−0.0587308	−	0.998274i	$-0.518705\pi$
$997$	−3.70889	−0.117462	−0.0587308	+	0.998274i	$0.518705\pi$
$998$	−8.61905	−0.272831
$999$	5.61670	0.177705

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bd.1.6	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bd.1.6	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.52621 q^{5} +1.00000 q^{6} +4.59536 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.52621 q^{5} +1.00000 q^{6} +4.59536 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.52621 q^{10} +5.46248 q^{11} +1.00000 q^{12} -1.00000 q^{13} +4.59536 q^{14} -1.52621 q^{15} +1.00000 q^{16} -3.99639 q^{17} +1.00000 q^{18} -4.36670 q^{19} -1.52621 q^{20} +4.59536 q^{21} +5.46248 q^{22} -0.656722 q^{23} +1.00000 q^{24} -2.67069 q^{25} -1.00000 q^{26} +1.00000 q^{27} +4.59536 q^{28} +5.77154 q^{29} -1.52621 q^{30} +7.53717 q^{31} +1.00000 q^{32} +5.46248 q^{33} -3.99639 q^{34} -7.01347 q^{35} +1.00000 q^{36} +5.61670 q^{37} -4.36670 q^{38} -1.00000 q^{39} -1.52621 q^{40} +3.17737 q^{41} +4.59536 q^{42} -8.63591 q^{43} +5.46248 q^{44} -1.52621 q^{45} -0.656722 q^{46} +4.76373 q^{47} +1.00000 q^{48} +14.1174 q^{49} -2.67069 q^{50} -3.99639 q^{51} -1.00000 q^{52} +5.30468 q^{53} +1.00000 q^{54} -8.33687 q^{55} +4.59536 q^{56} -4.36670 q^{57} +5.77154 q^{58} +1.34821 q^{59} -1.52621 q^{60} +8.91845 q^{61} +7.53717 q^{62} +4.59536 q^{63} +1.00000 q^{64} +1.52621 q^{65} +5.46248 q^{66} +2.64703 q^{67} -3.99639 q^{68} -0.656722 q^{69} -7.01347 q^{70} +2.04340 q^{71} +1.00000 q^{72} -10.6784 q^{73} +5.61670 q^{74} -2.67069 q^{75} -4.36670 q^{76} +25.1021 q^{77} -1.00000 q^{78} +1.80048 q^{79} -1.52621 q^{80} +1.00000 q^{81} +3.17737 q^{82} -0.725177 q^{83} +4.59536 q^{84} +6.09931 q^{85} -8.63591 q^{86} +5.77154 q^{87} +5.46248 q^{88} -15.6596 q^{89} -1.52621 q^{90} -4.59536 q^{91} -0.656722 q^{92} +7.53717 q^{93} +4.76373 q^{94} +6.66449 q^{95} +1.00000 q^{96} -2.62451 q^{97} +14.1174 q^{98} +5.46248 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) \) 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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