LMFDB - Embedded newform 6162.2.a.bj.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6162,2,Mod(1,6162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6162, 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("6162.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6162 = 2 \cdot 3 \cdot 13 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6162.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:	$49.2038177255$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 22x^{8} + 84x^{7} + 149x^{6} - 596x^{5} - 300x^{4} + 1684x^{3} - 228x^{2} - 1520x + 688 $ x^10 - 4x^9 - 22x^8 + 84x^7 + 149x^6 - 596x^5 - 300x^4 + 1684x^3 - 228x^2 - 1520*x + 688
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-1.30197$ of defining polynomial
Character	$\chi$	$=$	6162.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.30197 q^{5} -1.00000 q^{6} -1.48369 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.30197 q^{5} -1.00000 q^{6} -1.48369 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.30197 q^{10} +1.45470 q^{11} -1.00000 q^{12} -1.00000 q^{13} -1.48369 q^{14} -2.30197 q^{15} +1.00000 q^{16} -5.05980 q^{17} +1.00000 q^{18} +1.16141 q^{19} +2.30197 q^{20} +1.48369 q^{21} +1.45470 q^{22} +1.42055 q^{23} -1.00000 q^{24} +0.299075 q^{25} -1.00000 q^{26} -1.00000 q^{27} -1.48369 q^{28} -0.645096 q^{29} -2.30197 q^{30} +5.49508 q^{31} +1.00000 q^{32} -1.45470 q^{33} -5.05980 q^{34} -3.41540 q^{35} +1.00000 q^{36} +9.13743 q^{37} +1.16141 q^{38} +1.00000 q^{39} +2.30197 q^{40} -3.13816 q^{41} +1.48369 q^{42} +9.55158 q^{43} +1.45470 q^{44} +2.30197 q^{45} +1.42055 q^{46} -0.649167 q^{47} -1.00000 q^{48} -4.79868 q^{49} +0.299075 q^{50} +5.05980 q^{51} -1.00000 q^{52} +12.3104 q^{53} -1.00000 q^{54} +3.34868 q^{55} -1.48369 q^{56} -1.16141 q^{57} -0.645096 q^{58} -4.11934 q^{59} -2.30197 q^{60} +6.41227 q^{61} +5.49508 q^{62} -1.48369 q^{63} +1.00000 q^{64} -2.30197 q^{65} -1.45470 q^{66} -8.73905 q^{67} -5.05980 q^{68} -1.42055 q^{69} -3.41540 q^{70} +5.64506 q^{71} +1.00000 q^{72} +13.3593 q^{73} +9.13743 q^{74} -0.299075 q^{75} +1.16141 q^{76} -2.15832 q^{77} +1.00000 q^{78} -1.00000 q^{79} +2.30197 q^{80} +1.00000 q^{81} -3.13816 q^{82} +9.50219 q^{83} +1.48369 q^{84} -11.6475 q^{85} +9.55158 q^{86} +0.645096 q^{87} +1.45470 q^{88} +2.12365 q^{89} +2.30197 q^{90} +1.48369 q^{91} +1.42055 q^{92} -5.49508 q^{93} -0.649167 q^{94} +2.67353 q^{95} -1.00000 q^{96} +12.4889 q^{97} -4.79868 q^{98} +1.45470 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} - 10 q^{6} + 3 q^{7} + 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 - 10 * q^6 + 3 * q^7 + 10 * q^8 + 10 * q^9	\( 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} - 10 q^{6} + 3 q^{7} + 10 q^{8} + 10 q^{9} + 6 q^{10} + 3 q^{11} - 10 q^{12} - 10 q^{13} + 3 q^{14} - 6 q^{15} + 10 q^{16} + 12 q^{17} + 10 q^{18} + 17 q^{19} + 6 q^{20} - 3 q^{21} + 3 q^{22} + 3 q^{23} - 10 q^{24} + 12 q^{25} - 10 q^{26} - 10 q^{27} + 3 q^{28} + 6 q^{29} - 6 q^{30} + 9 q^{31} + 10 q^{32} - 3 q^{33} + 12 q^{34} - 8 q^{35} + 10 q^{36} + 6 q^{37} + 17 q^{38} + 10 q^{39} + 6 q^{40} + 28 q^{41} - 3 q^{42} + 3 q^{43} + 3 q^{44} + 6 q^{45} + 3 q^{46} + 13 q^{47} - 10 q^{48} + 11 q^{49} + 12 q^{50} - 12 q^{51} - 10 q^{52} + 18 q^{53} - 10 q^{54} + 16 q^{55} + 3 q^{56} - 17 q^{57} + 6 q^{58} + 9 q^{59} - 6 q^{60} + 16 q^{61} + 9 q^{62} + 3 q^{63} + 10 q^{64} - 6 q^{65} - 3 q^{66} + 19 q^{67} + 12 q^{68} - 3 q^{69} - 8 q^{70} - 11 q^{71} + 10 q^{72} + 20 q^{73} + 6 q^{74} - 12 q^{75} + 17 q^{76} + 16 q^{77} + 10 q^{78} - 10 q^{79} + 6 q^{80} + 10 q^{81} + 28 q^{82} + 15 q^{83} - 3 q^{84} + 34 q^{85} + 3 q^{86} - 6 q^{87} + 3 q^{88} + 10 q^{89} + 6 q^{90} - 3 q^{91} + 3 q^{92} - 9 q^{93} + 13 q^{94} + 26 q^{95} - 10 q^{96} + 18 q^{97} + 11 q^{98} + 3 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 - 10 * q^6 + 3 * q^7 + 10 * q^8 + 10 * q^9 + 6 * q^10 + 3 * q^11 - 10 * q^12 - 10 * q^13 + 3 * q^14 - 6 * q^15 + 10 * q^16 + 12 * q^17 + 10 * q^18 + 17 * q^19 + 6 * q^20 - 3 * q^21 + 3 * q^22 + 3 * q^23 - 10 * q^24 + 12 * q^25 - 10 * q^26 - 10 * q^27 + 3 * q^28 + 6 * q^29 - 6 * q^30 + 9 * q^31 + 10 * q^32 - 3 * q^33 + 12 * q^34 - 8 * q^35 + 10 * q^36 + 6 * q^37 + 17 * q^38 + 10 * q^39 + 6 * q^40 + 28 * q^41 - 3 * q^42 + 3 * q^43 + 3 * q^44 + 6 * q^45 + 3 * q^46 + 13 * q^47 - 10 * q^48 + 11 * q^49 + 12 * q^50 - 12 * q^51 - 10 * q^52 + 18 * q^53 - 10 * q^54 + 16 * q^55 + 3 * q^56 - 17 * q^57 + 6 * q^58 + 9 * q^59 - 6 * q^60 + 16 * q^61 + 9 * q^62 + 3 * q^63 + 10 * q^64 - 6 * q^65 - 3 * q^66 + 19 * q^67 + 12 * q^68 - 3 * q^69 - 8 * q^70 - 11 * q^71 + 10 * q^72 + 20 * q^73 + 6 * q^74 - 12 * q^75 + 17 * q^76 + 16 * q^77 + 10 * q^78 - 10 * q^79 + 6 * q^80 + 10 * q^81 + 28 * q^82 + 15 * q^83 - 3 * q^84 + 34 * q^85 + 3 * q^86 - 6 * q^87 + 3 * q^88 + 10 * q^89 + 6 * q^90 - 3 * q^91 + 3 * q^92 - 9 * q^93 + 13 * q^94 + 26 * q^95 - 10 * q^96 + 18 * q^97 + 11 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	2.30197	1.02947	0.514737	−	0.857348i	$-0.327890\pi$
$5$	2.30197	1.02947	0.514737	+	0.857348i	$0.327890\pi$
$6$	−1.00000	−0.408248
$7$	−1.48369	−0.560780	−0.280390	−	0.959886i	$-0.590464\pi$
$7$	−1.48369	−0.560780	−0.280390	+	0.959886i	$0.590464\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.30197	0.727947
$11$	1.45470	0.438608	0.219304	−	0.975657i	$-0.429621\pi$
$11$	1.45470	0.438608	0.219304	+	0.975657i	$0.429621\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.48369	−0.396532
$15$	−2.30197	−0.594367
$16$	1.00000	0.250000
$17$	−5.05980	−1.22718	−0.613591	−	0.789624i	$-0.710276\pi$
$17$	−5.05980	−1.22718	−0.613591	+	0.789624i	$0.710276\pi$
$18$	1.00000	0.235702
$19$	1.16141	0.266446	0.133223	−	0.991086i	$-0.457467\pi$
$19$	1.16141	0.266446	0.133223	+	0.991086i	$0.457467\pi$
$20$	2.30197	0.514737
$21$	1.48369	0.323767
$22$	1.45470	0.310143
$23$	1.42055	0.296206	0.148103	−	0.988972i	$-0.452683\pi$
$23$	1.42055	0.296206	0.148103	+	0.988972i	$0.452683\pi$
$24$	−1.00000	−0.204124
$25$	0.299075	0.0598150
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	−1.48369	−0.280390
$29$	−0.645096	−0.119791	−0.0598957	−	0.998205i	$-0.519077\pi$
$29$	−0.645096	−0.119791	−0.0598957	+	0.998205i	$0.519077\pi$
$30$	−2.30197	−0.420281
$31$	5.49508	0.986945	0.493473	−	0.869761i	$-0.335727\pi$
$31$	5.49508	0.986945	0.493473	+	0.869761i	$0.335727\pi$
$32$	1.00000	0.176777
$33$	−1.45470	−0.253231
$34$	−5.05980	−0.867749
$35$	−3.41540	−0.577308
$36$	1.00000	0.166667
$37$	9.13743	1.50218	0.751092	−	0.660198i	$-0.229527\pi$
$37$	9.13743	1.50218	0.751092	+	0.660198i	$0.229527\pi$
$38$	1.16141	0.188406
$39$	1.00000	0.160128
$40$	2.30197	0.363974
$41$	−3.13816	−0.490099	−0.245049	−	0.969511i	$-0.578804\pi$
$41$	−3.13816	−0.490099	−0.245049	+	0.969511i	$0.578804\pi$
$42$	1.48369	0.228938
$43$	9.55158	1.45660	0.728301	−	0.685257i	$-0.240310\pi$
$43$	9.55158	1.45660	0.728301	+	0.685257i	$0.240310\pi$
$44$	1.45470	0.219304
$45$	2.30197	0.343158
$46$	1.42055	0.209449
$47$	−0.649167	−0.0946908	−0.0473454	−	0.998879i	$-0.515076\pi$
$47$	−0.649167	−0.0946908	−0.0473454	+	0.998879i	$0.515076\pi$
$48$	−1.00000	−0.144338
$49$	−4.79868	−0.685525
$50$	0.299075	0.0422956
$51$	5.05980	0.708514
$52$	−1.00000	−0.138675
$53$	12.3104	1.69096	0.845482	−	0.534004i	$-0.179313\pi$
$53$	12.3104	1.69096	0.845482	+	0.534004i	$0.179313\pi$
$54$	−1.00000	−0.136083
$55$	3.34868	0.451535
$56$	−1.48369	−0.198266
$57$	−1.16141	−0.153833
$58$	−0.645096	−0.0847052
$59$	−4.11934	−0.536292	−0.268146	−	0.963378i	$-0.586411\pi$
$59$	−4.11934	−0.536292	−0.268146	+	0.963378i	$0.586411\pi$
$60$	−2.30197	−0.297183
$61$	6.41227	0.821007	0.410504	−	0.911859i	$-0.365353\pi$
$61$	6.41227	0.821007	0.410504	+	0.911859i	$0.365353\pi$
$62$	5.49508	0.697876
$63$	−1.48369	−0.186927
$64$	1.00000	0.125000
$65$	−2.30197	−0.285524
$66$	−1.45470	−0.179061
$67$	−8.73905	−1.06764	−0.533822	−	0.845597i	$-0.679245\pi$
$67$	−8.73905	−1.06764	−0.533822	+	0.845597i	$0.679245\pi$
$68$	−5.05980	−0.613591
$69$	−1.42055	−0.171014
$70$	−3.41540	−0.408219
$71$	5.64506	0.669945	0.334973	−	0.942228i	$-0.391273\pi$
$71$	5.64506	0.669945	0.334973	+	0.942228i	$0.391273\pi$
$72$	1.00000	0.117851
$73$	13.3593	1.56359	0.781795	−	0.623535i	$-0.214304\pi$
$73$	13.3593	1.56359	0.781795	+	0.623535i	$0.214304\pi$
$74$	9.13743	1.06220
$75$	−0.299075	−0.0345342
$76$	1.16141	0.133223
$77$	−2.15832	−0.245963
$78$	1.00000	0.113228
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	2.30197	0.257368
$81$	1.00000	0.111111
$82$	−3.13816	−0.346552
$83$	9.50219	1.04300	0.521500	−	0.853251i	$-0.325372\pi$
$83$	9.50219	1.04300	0.521500	+	0.853251i	$0.325372\pi$
$84$	1.48369	0.161883
$85$	−11.6475	−1.26335
$86$	9.55158	1.02997
$87$	0.645096	0.0691615
$88$	1.45470	0.155071
$89$	2.12365	0.225107	0.112553	−	0.993646i	$-0.464097\pi$
$89$	2.12365	0.225107	0.112553	+	0.993646i	$0.464097\pi$
$90$	2.30197	0.242649
$91$	1.48369	0.155533
$92$	1.42055	0.148103
$93$	−5.49508	−0.569813
$94$	−0.649167	−0.0669565
$95$	2.67353	0.274299
$96$	−1.00000	−0.102062
$97$	12.4889	1.26805	0.634026	−	0.773312i	$-0.281401\pi$
$97$	12.4889	1.26805	0.634026	+	0.773312i	$0.281401\pi$
$98$	−4.79868	−0.484740
$99$	1.45470	0.146203
$100$	0.299075	0.0299075
$101$	18.7245	1.86316	0.931580	−	0.363537i	$-0.118431\pi$
$101$	18.7245	1.86316	0.931580	+	0.363537i	$0.118431\pi$
$102$	5.05980	0.500995
$103$	−2.93346	−0.289043	−0.144521	−	0.989502i	$-0.546164\pi$
$103$	−2.93346	−0.289043	−0.144521	+	0.989502i	$0.546164\pi$
$104$	−1.00000	−0.0980581
$105$	3.41540	0.333309
$106$	12.3104	1.19569
$107$	−4.87580	−0.471362	−0.235681	−	0.971831i	$-0.575732\pi$
$107$	−4.87580	−0.471362	−0.235681	+	0.971831i	$0.575732\pi$
$108$	−1.00000	−0.0962250
$109$	−4.36952	−0.418524	−0.209262	−	0.977860i	$-0.567106\pi$
$109$	−4.36952	−0.418524	−0.209262	+	0.977860i	$0.567106\pi$
$110$	3.34868	0.319284
$111$	−9.13743	−0.867286
$112$	−1.48369	−0.140195
$113$	10.1291	0.952867	0.476434	−	0.879210i	$-0.341929\pi$
$113$	10.1291	0.952867	0.476434	+	0.879210i	$0.341929\pi$
$114$	−1.16141	−0.108776
$115$	3.27007	0.304936
$116$	−0.645096	−0.0598957
$117$	−1.00000	−0.0924500
$118$	−4.11934	−0.379216
$119$	7.50715	0.688180
$120$	−2.30197	−0.210140
$121$	−8.88385	−0.807623
$122$	6.41227	0.580540
$123$	3.13816	0.282959
$124$	5.49508	0.493473
$125$	−10.8214	−0.967895
$126$	−1.48369	−0.132177
$127$	−11.2206	−0.995667	−0.497834	−	0.867273i	$-0.665871\pi$
$127$	−11.2206	−0.995667	−0.497834	+	0.867273i	$0.665871\pi$
$128$	1.00000	0.0883883
$129$	−9.55158	−0.840970
$130$	−2.30197	−0.201896
$131$	−1.89704	−0.165745	−0.0828726	−	0.996560i	$-0.526409\pi$
$131$	−1.89704	−0.165745	−0.0828726	+	0.996560i	$0.526409\pi$
$132$	−1.45470	−0.126615
$133$	−1.72317	−0.149418
$134$	−8.73905	−0.754939
$135$	−2.30197	−0.198122
$136$	−5.05980	−0.433874
$137$	8.45406	0.722279	0.361139	−	0.932512i	$-0.382388\pi$
$137$	8.45406	0.722279	0.361139	+	0.932512i	$0.382388\pi$
$138$	−1.42055	−0.120925
$139$	−6.96044	−0.590377	−0.295188	−	0.955439i	$-0.595382\pi$
$139$	−6.96044	−0.590377	−0.295188	+	0.955439i	$0.595382\pi$
$140$	−3.41540	−0.288654
$141$	0.649167	0.0546698
$142$	5.64506	0.473723
$143$	−1.45470	−0.121648
$144$	1.00000	0.0833333
$145$	−1.48499	−0.123322
$146$	13.3593	1.10563
$147$	4.79868	0.395788
$148$	9.13743	0.751092
$149$	−6.81810	−0.558560	−0.279280	−	0.960210i	$-0.590096\pi$
$149$	−6.81810	−0.558560	−0.279280	+	0.960210i	$0.590096\pi$
$150$	−0.299075	−0.0244194
$151$	18.2202	1.48274	0.741371	−	0.671096i	$-0.234176\pi$
$151$	18.2202	1.48274	0.741371	+	0.671096i	$0.234176\pi$
$152$	1.16141	0.0942028
$153$	−5.05980	−0.409061
$154$	−2.15832	−0.173922
$155$	12.6495	1.01603
$156$	1.00000	0.0800641
$157$	0.757630	0.0604654	0.0302327	−	0.999543i	$-0.490375\pi$
$157$	0.757630	0.0604654	0.0302327	+	0.999543i	$0.490375\pi$
$158$	−1.00000	−0.0795557
$159$	−12.3104	−0.976278
$160$	2.30197	0.181987
$161$	−2.10765	−0.166106
$162$	1.00000	0.0785674
$163$	−24.6698	−1.93229	−0.966144	−	0.258003i	$-0.916936\pi$
$163$	−24.6698	−1.93229	−0.966144	+	0.258003i	$0.916936\pi$
$164$	−3.13816	−0.245049
$165$	−3.34868	−0.260694
$166$	9.50219	0.737513
$167$	20.8856	1.61618	0.808090	−	0.589059i	$-0.200502\pi$
$167$	20.8856	1.61618	0.808090	+	0.589059i	$0.200502\pi$
$168$	1.48369	0.114469
$169$	1.00000	0.0769231
$170$	−11.6475	−0.893324
$171$	1.16141	0.0888153
$172$	9.55158	0.728301
$173$	−5.10263	−0.387946	−0.193973	−	0.981007i	$-0.562137\pi$
$173$	−5.10263	−0.387946	−0.193973	+	0.981007i	$0.562137\pi$
$174$	0.645096	0.0489046
$175$	−0.443733	−0.0335431
$176$	1.45470	0.109652
$177$	4.11934	0.309629
$178$	2.12365	0.159175
$179$	−7.54212	−0.563725	−0.281862	−	0.959455i	$-0.590952\pi$
$179$	−7.54212	−0.563725	−0.281862	+	0.959455i	$0.590952\pi$
$180$	2.30197	0.171579
$181$	6.99392	0.519854	0.259927	−	0.965628i	$-0.416301\pi$
$181$	6.99392	0.519854	0.259927	+	0.965628i	$0.416301\pi$
$182$	1.48369	0.109978
$183$	−6.41227	−0.474009
$184$	1.42055	0.104725
$185$	21.0341	1.54646
$186$	−5.49508	−0.402919
$187$	−7.36049	−0.538252
$188$	−0.649167	−0.0473454
$189$	1.48369	0.107922
$190$	2.67353	0.193959
$191$	4.09683	0.296436	0.148218	−	0.988955i	$-0.452646\pi$
$191$	4.09683	0.296436	0.148218	+	0.988955i	$0.452646\pi$
$192$	−1.00000	−0.0721688
$193$	−13.1156	−0.944078	−0.472039	−	0.881578i	$-0.656482\pi$
$193$	−13.1156	−0.944078	−0.472039	+	0.881578i	$0.656482\pi$
$194$	12.4889	0.896648
$195$	2.30197	0.164848
$196$	−4.79868	−0.342763
$197$	−9.84786	−0.701631	−0.350816	−	0.936445i	$-0.614096\pi$
$197$	−9.84786	−0.701631	−0.350816	+	0.936445i	$0.614096\pi$
$198$	1.45470	0.103381
$199$	27.3916	1.94174	0.970869	−	0.239610i	$-0.0770196\pi$
$199$	27.3916	1.94174	0.970869	+	0.239610i	$0.0770196\pi$
$200$	0.299075	0.0211478
$201$	8.73905	0.616405
$202$	18.7245	1.31745
$203$	0.957120	0.0671766
$204$	5.05980	0.354257
$205$	−7.22396	−0.504543
$206$	−2.93346	−0.204384
$207$	1.42055	0.0987352
$208$	−1.00000	−0.0693375
$209$	1.68950	0.116865
$210$	3.41540	0.235685
$211$	−11.7715	−0.810385	−0.405193	−	0.914231i	$-0.632796\pi$
$211$	−11.7715	−0.810385	−0.405193	+	0.914231i	$0.632796\pi$
$212$	12.3104	0.845482
$213$	−5.64506	−0.386793
$214$	−4.87580	−0.333303
$215$	21.9875	1.49953
$216$	−1.00000	−0.0680414
$217$	−8.15297	−0.553460
$218$	−4.36952	−0.295941
$219$	−13.3593	−0.902739
$220$	3.34868	0.225768
$221$	5.05980	0.340359
$222$	−9.13743	−0.613264
$223$	12.6013	0.843844	0.421922	−	0.906632i	$-0.361356\pi$
$223$	12.6013	0.843844	0.421922	+	0.906632i	$0.361356\pi$
$224$	−1.48369	−0.0991329
$225$	0.299075	0.0199383
$226$	10.1291	0.673779
$227$	−27.0019	−1.79218	−0.896088	−	0.443876i	$-0.853603\pi$
$227$	−27.0019	−1.79218	−0.896088	+	0.443876i	$0.853603\pi$
$228$	−1.16141	−0.0769163
$229$	19.2273	1.27057	0.635287	−	0.772276i	$-0.280882\pi$
$229$	19.2273	1.27057	0.635287	+	0.772276i	$0.280882\pi$
$230$	3.27007	0.215622
$231$	2.15832	0.142007
$232$	−0.645096	−0.0423526
$233$	21.2824	1.39426	0.697129	−	0.716946i	$-0.254461\pi$
$233$	21.2824	1.39426	0.697129	+	0.716946i	$0.254461\pi$
$234$	−1.00000	−0.0653720
$235$	−1.49437	−0.0974816
$236$	−4.11934	−0.268146
$237$	1.00000	0.0649570
$238$	7.50715	0.486617
$239$	−21.0272	−1.36013	−0.680067	−	0.733150i	$-0.738049\pi$
$239$	−21.0272	−1.36013	−0.680067	+	0.733150i	$0.738049\pi$
$240$	−2.30197	−0.148592
$241$	2.57137	0.165636	0.0828182	−	0.996565i	$-0.473608\pi$
$241$	2.57137	0.165636	0.0828182	+	0.996565i	$0.473608\pi$
$242$	−8.88385	−0.571076
$243$	−1.00000	−0.0641500
$244$	6.41227	0.410504
$245$	−11.0464	−0.705730
$246$	3.13816	0.200082
$247$	−1.16141	−0.0738988
$248$	5.49508	0.348938
$249$	−9.50219	−0.602177
$250$	−10.8214	−0.684405
$251$	−11.4065	−0.719969	−0.359985	−	0.932958i	$-0.617218\pi$
$251$	−11.4065	−0.719969	−0.359985	+	0.932958i	$0.617218\pi$
$252$	−1.48369	−0.0934634
$253$	2.06648	0.129918
$254$	−11.2206	−0.704043
$255$	11.6475	0.729396
$256$	1.00000	0.0625000
$257$	7.25709	0.452685	0.226342	−	0.974048i	$-0.427323\pi$
$257$	7.25709	0.452685	0.226342	+	0.974048i	$0.427323\pi$
$258$	−9.55158	−0.594655
$259$	−13.5571	−0.842395
$260$	−2.30197	−0.142762
$261$	−0.645096	−0.0399304
$262$	−1.89704	−0.117200
$263$	−0.363767	−0.0224309	−0.0112154	−	0.999937i	$-0.503570\pi$
$263$	−0.363767	−0.0224309	−0.0112154	+	0.999937i	$0.503570\pi$
$264$	−1.45470	−0.0895305
$265$	28.3382	1.74080
$266$	−1.72317	−0.105654
$267$	−2.12365	−0.129966
$268$	−8.73905	−0.533822
$269$	24.2421	1.47807	0.739033	−	0.673669i	$-0.235283\pi$
$269$	24.2421	1.47807	0.739033	+	0.673669i	$0.235283\pi$
$270$	−2.30197	−0.140094
$271$	−22.4435	−1.36335	−0.681673	−	0.731657i	$-0.738747\pi$
$271$	−22.4435	−1.36335	−0.681673	+	0.731657i	$0.738747\pi$
$272$	−5.05980	−0.306796
$273$	−1.48369	−0.0897967
$274$	8.45406	0.510728
$275$	0.435064	0.0262353
$276$	−1.42055	−0.0855072
$277$	0.0354150	0.00212788	0.00106394	−	0.999999i	$-0.499661\pi$
$277$	0.0354150	0.00212788	0.00106394	+	0.999999i	$0.499661\pi$
$278$	−6.96044	−0.417459
$279$	5.49508	0.328982
$280$	−3.41540	−0.204109
$281$	13.4969	0.805158	0.402579	−	0.915385i	$-0.368114\pi$
$281$	13.4969	0.805158	0.402579	+	0.915385i	$0.368114\pi$
$282$	0.649167	0.0386574
$283$	10.8497	0.644950	0.322475	−	0.946578i	$-0.395485\pi$
$283$	10.8497	0.644950	0.322475	+	0.946578i	$0.395485\pi$
$284$	5.64506	0.334973
$285$	−2.67353	−0.158366
$286$	−1.45470	−0.0860181
$287$	4.65605	0.274838
$288$	1.00000	0.0589256
$289$	8.60159	0.505976
$290$	−1.48499	−0.0872018
$291$	−12.4889	−0.732110
$292$	13.3593	0.781795
$293$	−8.99683	−0.525601	−0.262800	−	0.964850i	$-0.584646\pi$
$293$	−8.99683	−0.525601	−0.262800	+	0.964850i	$0.584646\pi$
$294$	4.79868	0.279865
$295$	−9.48261	−0.552099
$296$	9.13743	0.531102
$297$	−1.45470	−0.0844102
$298$	−6.81810	−0.394962
$299$	−1.42055	−0.0821527
$300$	−0.299075	−0.0172671
$301$	−14.1715	−0.816834
$302$	18.2202	1.04846
$303$	−18.7245	−1.07570
$304$	1.16141	0.0666114
$305$	14.7609	0.845205
$306$	−5.05980	−0.289250
$307$	−12.7618	−0.728356	−0.364178	−	0.931329i	$-0.618650\pi$
$307$	−12.7618	−0.728356	−0.364178	+	0.931329i	$0.618650\pi$
$308$	−2.15832	−0.122981
$309$	2.93346	0.166879
$310$	12.6495	0.718444
$311$	26.1546	1.48309	0.741547	−	0.670901i	$-0.234092\pi$
$311$	26.1546	1.48309	0.741547	+	0.670901i	$0.234092\pi$
$312$	1.00000	0.0566139
$313$	21.7717	1.23061	0.615304	−	0.788290i	$-0.289033\pi$
$313$	21.7717	1.23061	0.615304	+	0.788290i	$0.289033\pi$
$314$	0.757630	0.0427555
$315$	−3.41540	−0.192436
$316$	−1.00000	−0.0562544
$317$	12.7294	0.714953	0.357477	−	0.933922i	$-0.383637\pi$
$317$	12.7294	0.714953	0.357477	+	0.933922i	$0.383637\pi$
$318$	−12.3104	−0.690333
$319$	−0.938420	−0.0525414
$320$	2.30197	0.128684
$321$	4.87580	0.272141
$322$	−2.10765	−0.117455
$323$	−5.87651	−0.326977
$324$	1.00000	0.0555556
$325$	−0.299075	−0.0165897
$326$	−24.6698	−1.36633
$327$	4.36952	0.241635
$328$	−3.13816	−0.173276
$329$	0.963160	0.0531007
$330$	−3.34868	−0.184339
$331$	5.60613	0.308141	0.154070	−	0.988060i	$-0.450762\pi$
$331$	5.60613	0.308141	0.154070	+	0.988060i	$0.450762\pi$
$332$	9.50219	0.521500
$333$	9.13743	0.500728
$334$	20.8856	1.14281
$335$	−20.1170	−1.09911
$336$	1.48369	0.0809417
$337$	−16.3236	−0.889203	−0.444602	−	0.895728i	$-0.646655\pi$
$337$	−16.3236	−0.889203	−0.444602	+	0.895728i	$0.646655\pi$
$338$	1.00000	0.0543928
$339$	−10.1291	−0.550138
$340$	−11.6475	−0.631675
$341$	7.99368	0.432882
$342$	1.16141	0.0628019
$343$	17.5055	0.945210
$344$	9.55158	0.514987
$345$	−3.27007	−0.176055
$346$	−5.10263	−0.274319
$347$	7.64170	0.410228	0.205114	−	0.978738i	$-0.434244\pi$
$347$	7.64170	0.410228	0.205114	+	0.978738i	$0.434244\pi$
$348$	0.645096	0.0345808
$349$	16.5198	0.884286	0.442143	−	0.896945i	$-0.354218\pi$
$349$	16.5198	0.884286	0.442143	+	0.896945i	$0.354218\pi$
$350$	−0.443733	−0.0237185
$351$	1.00000	0.0533761
$352$	1.45470	0.0775357
$353$	−24.3507	−1.29606	−0.648029	−	0.761616i	$-0.724407\pi$
$353$	−24.3507	−1.29606	−0.648029	+	0.761616i	$0.724407\pi$
$354$	4.11934	0.218940
$355$	12.9948	0.689691
$356$	2.12365	0.112553
$357$	−7.50715	−0.397321
$358$	−7.54212	−0.398613
$359$	−31.0362	−1.63803	−0.819014	−	0.573774i	$-0.805479\pi$
$359$	−31.0362	−1.63803	−0.819014	+	0.573774i	$0.805479\pi$
$360$	2.30197	0.121325
$361$	−17.6511	−0.929007
$362$	6.99392	0.367592
$363$	8.88385	0.466281
$364$	1.48369	0.0777663
$365$	30.7528	1.60967
$366$	−6.41227	−0.335175
$367$	18.2454	0.952400	0.476200	−	0.879337i	$-0.342014\pi$
$367$	18.2454	0.952400	0.476200	+	0.879337i	$0.342014\pi$
$368$	1.42055	0.0740514
$369$	−3.13816	−0.163366
$370$	21.0341	1.09351
$371$	−18.2648	−0.948260
$372$	−5.49508	−0.284907
$373$	15.2593	0.790098	0.395049	−	0.918660i	$-0.370728\pi$
$373$	15.2593	0.790098	0.395049	+	0.918660i	$0.370728\pi$
$374$	−7.36049	−0.380602
$375$	10.8214	0.558815
$376$	−0.649167	−0.0334783
$377$	0.645096	0.0332241
$378$	1.48369	0.0763126
$379$	−36.2255	−1.86078	−0.930389	−	0.366574i	$-0.880531\pi$
$379$	−36.2255	−1.86078	−0.930389	+	0.366574i	$0.880531\pi$
$380$	2.67353	0.137149
$381$	11.2206	0.574849
$382$	4.09683	0.209612
$383$	19.1781	0.979957	0.489978	−	0.871735i	$-0.337005\pi$
$383$	19.1781	0.979957	0.489978	+	0.871735i	$0.337005\pi$
$384$	−1.00000	−0.0510310
$385$	−4.96838	−0.253212
$386$	−13.1156	−0.667564
$387$	9.55158	0.485534
$388$	12.4889	0.634026
$389$	−26.8310	−1.36039	−0.680193	−	0.733033i	$-0.738104\pi$
$389$	−26.8310	−1.36039	−0.680193	+	0.733033i	$0.738104\pi$
$390$	2.30197	0.116565
$391$	−7.18771	−0.363498
$392$	−4.79868	−0.242370
$393$	1.89704	0.0956930
$394$	−9.84786	−0.496128
$395$	−2.30197	−0.115825
$396$	1.45470	0.0731014
$397$	30.5548	1.53350	0.766752	−	0.641944i	$-0.221872\pi$
$397$	30.5548	1.53350	0.766752	+	0.641944i	$0.221872\pi$
$398$	27.3916	1.37302
$399$	1.72317	0.0862663
$400$	0.299075	0.0149537
$401$	2.46636	0.123164	0.0615821	−	0.998102i	$-0.480385\pi$
$401$	2.46636	0.123164	0.0615821	+	0.998102i	$0.480385\pi$
$402$	8.73905	0.435864
$403$	−5.49508	−0.273729
$404$	18.7245	0.931580
$405$	2.30197	0.114386
$406$	0.957120	0.0475010
$407$	13.2922	0.658870
$408$	5.05980	0.250497
$409$	−0.815979	−0.0403476	−0.0201738	−	0.999796i	$-0.506422\pi$
$409$	−0.815979	−0.0403476	−0.0201738	+	0.999796i	$0.506422\pi$
$410$	−7.22396	−0.356766
$411$	−8.45406	−0.417008
$412$	−2.93346	−0.144521
$413$	6.11181	0.300742
$414$	1.42055	0.0698164
$415$	21.8738	1.07374
$416$	−1.00000	−0.0490290
$417$	6.96044	0.340854
$418$	1.68950	0.0826362
$419$	34.3996	1.68053	0.840264	−	0.542177i	$-0.182400\pi$
$419$	34.3996	1.68053	0.840264	+	0.542177i	$0.182400\pi$
$420$	3.41540	0.166655
$421$	14.9486	0.728550	0.364275	−	0.931291i	$-0.381317\pi$
$421$	14.9486	0.728550	0.364275	+	0.931291i	$0.381317\pi$
$422$	−11.7715	−0.573029
$423$	−0.649167	−0.0315636
$424$	12.3104	0.597846
$425$	−1.51326	−0.0734039
$426$	−5.64506	−0.273504
$427$	−9.51379	−0.460405
$428$	−4.87580	−0.235681
$429$	1.45470	0.0702335
$430$	21.9875	1.06033
$431$	13.0932	0.630678	0.315339	−	0.948979i	$-0.397882\pi$
$431$	13.0932	0.630678	0.315339	+	0.948979i	$0.397882\pi$
$432$	−1.00000	−0.0481125
$433$	32.1195	1.54356	0.771782	−	0.635888i	$-0.219366\pi$
$433$	32.1195	1.54356	0.771782	+	0.635888i	$0.219366\pi$
$434$	−8.15297	−0.391355
$435$	1.48499	0.0711999
$436$	−4.36952	−0.209262
$437$	1.64984	0.0789228
$438$	−13.3593	−0.638333
$439$	−19.2393	−0.918240	−0.459120	−	0.888374i	$-0.651835\pi$
$439$	−19.2393	−0.918240	−0.459120	+	0.888374i	$0.651835\pi$
$440$	3.34868	0.159642
$441$	−4.79868	−0.228508
$442$	5.05980	0.240670
$443$	−12.7622	−0.606349	−0.303174	−	0.952935i	$-0.598046\pi$
$443$	−12.7622	−0.606349	−0.303174	+	0.952935i	$0.598046\pi$
$444$	−9.13743	−0.433643
$445$	4.88859	0.231742
$446$	12.6013	0.596688
$447$	6.81810	0.322485
$448$	−1.48369	−0.0700976
$449$	−2.42272	−0.114335	−0.0571676	−	0.998365i	$-0.518207\pi$
$449$	−2.42272	−0.114335	−0.0571676	+	0.998365i	$0.518207\pi$
$450$	0.299075	0.0140985
$451$	−4.56508	−0.214961
$452$	10.1291	0.476434
$453$	−18.2202	−0.856061
$454$	−27.0019	−1.26726
$455$	3.41540	0.160117
$456$	−1.16141	−0.0543880
$457$	−20.8164	−0.973751	−0.486875	−	0.873471i	$-0.661863\pi$
$457$	−20.8164	−0.973751	−0.486875	+	0.873471i	$0.661863\pi$
$458$	19.2273	0.898431
$459$	5.05980	0.236171
$460$	3.27007	0.152468
$461$	1.56625	0.0729475	0.0364738	−	0.999335i	$-0.488387\pi$
$461$	1.56625	0.0729475	0.0364738	+	0.999335i	$0.488387\pi$
$462$	2.15832	0.100414
$463$	27.5241	1.27915	0.639577	−	0.768727i	$-0.279109\pi$
$463$	27.5241	1.27915	0.639577	+	0.768727i	$0.279109\pi$
$464$	−0.645096	−0.0299478
$465$	−12.6495	−0.586607
$466$	21.2824	0.985889
$467$	−16.8995	−0.782017	−0.391008	−	0.920387i	$-0.627874\pi$
$467$	−16.8995	−0.782017	−0.391008	+	0.920387i	$0.627874\pi$
$468$	−1.00000	−0.0462250
$469$	12.9660	0.598714
$470$	−1.49437	−0.0689299
$471$	−0.757630	−0.0349097
$472$	−4.11934	−0.189608
$473$	13.8947	0.638877
$474$	1.00000	0.0459315
$475$	0.347349	0.0159374
$476$	7.50715	0.344090
$477$	12.3104	0.563655
$478$	−21.0272	−0.961760
$479$	−27.9916	−1.27897	−0.639483	−	0.768805i	$-0.720852\pi$
$479$	−27.9916	−1.27897	−0.639483	+	0.768805i	$0.720852\pi$
$480$	−2.30197	−0.105070
$481$	−9.13743	−0.416631
$482$	2.57137	0.117123
$483$	2.10765	0.0959016
$484$	−8.88385	−0.403811
$485$	28.7490	1.30542
$486$	−1.00000	−0.0453609
$487$	−35.0710	−1.58922	−0.794610	−	0.607121i	$-0.792324\pi$
$487$	−35.0710	−1.58922	−0.794610	+	0.607121i	$0.792324\pi$
$488$	6.41227	0.290270
$489$	24.6698	1.11561
$490$	−11.0464	−0.499026
$491$	12.2653	0.553527	0.276764	−	0.960938i	$-0.410738\pi$
$491$	12.2653	0.553527	0.276764	+	0.960938i	$0.410738\pi$
$492$	3.13816	0.141479
$493$	3.26406	0.147006
$494$	−1.16141	−0.0522543
$495$	3.34868	0.150512
$496$	5.49508	0.246736
$497$	−8.37549	−0.375692
$498$	−9.50219	−0.425803
$499$	11.7808	0.527379	0.263689	−	0.964608i	$-0.415061\pi$
$499$	11.7808	0.527379	0.263689	+	0.964608i	$0.415061\pi$
$500$	−10.8214	−0.483948
$501$	−20.8856	−0.933102
$502$	−11.4065	−0.509095
$503$	−42.4425	−1.89242	−0.946208	−	0.323559i	$-0.895121\pi$
$503$	−42.4425	−1.89242	−0.946208	+	0.323559i	$0.895121\pi$
$504$	−1.48369	−0.0660886
$505$	43.1033	1.91807
$506$	2.06648	0.0918661
$507$	−1.00000	−0.0444116
$508$	−11.2206	−0.497834
$509$	−23.2304	−1.02967	−0.514835	−	0.857290i	$-0.672147\pi$
$509$	−23.2304	−1.02967	−0.514835	+	0.857290i	$0.672147\pi$
$510$	11.6475	0.515761
$511$	−19.8210	−0.876831
$512$	1.00000	0.0441942
$513$	−1.16141	−0.0512775
$514$	7.25709	0.320096
$515$	−6.75275	−0.297562
$516$	−9.55158	−0.420485
$517$	−0.944343	−0.0415322
$518$	−13.5571	−0.595663
$519$	5.10263	0.223981
$520$	−2.30197	−0.100948
$521$	−17.5034	−0.766839	−0.383419	−	0.923574i	$-0.625254\pi$
$521$	−17.5034	−0.766839	−0.383419	+	0.923574i	$0.625254\pi$
$522$	−0.645096	−0.0282351
$523$	24.7944	1.08418	0.542091	−	0.840320i	$-0.317633\pi$
$523$	24.7944	1.08418	0.542091	+	0.840320i	$0.317633\pi$
$524$	−1.89704	−0.0828726
$525$	0.443733	0.0193661
$526$	−0.363767	−0.0158610
$527$	−27.8040	−1.21116
$528$	−1.45470	−0.0633076
$529$	−20.9820	−0.912262
$530$	28.3382	1.23093
$531$	−4.11934	−0.178764
$532$	−1.72317	−0.0747088
$533$	3.13816	0.135929
$534$	−2.12365	−0.0918995
$535$	−11.2240	−0.485254
$536$	−8.73905	−0.377469
$537$	7.54212	0.325467
$538$	24.2421	1.04515
$539$	−6.98063	−0.300677
$540$	−2.30197	−0.0990611
$541$	35.3754	1.52091	0.760454	−	0.649392i	$-0.224977\pi$
$541$	35.3754	1.52091	0.760454	+	0.649392i	$0.224977\pi$
$542$	−22.4435	−0.964031
$543$	−6.99392	−0.300138
$544$	−5.05980	−0.216937
$545$	−10.0585	−0.430860
$546$	−1.48369	−0.0634959
$547$	−0.647125	−0.0276691	−0.0138345	−	0.999904i	$-0.504404\pi$
$547$	−0.647125	−0.0276691	−0.0138345	+	0.999904i	$0.504404\pi$
$548$	8.45406	0.361139
$549$	6.41227	0.273669
$550$	0.435064	0.0185512
$551$	−0.749221	−0.0319179
$552$	−1.42055	−0.0604627
$553$	1.48369	0.0630927
$554$	0.0354150	0.00150464
$555$	−21.0341	−0.892848
$556$	−6.96044	−0.295188
$557$	−18.6489	−0.790181	−0.395090	−	0.918642i	$-0.629287\pi$
$557$	−18.6489	−0.790181	−0.395090	+	0.918642i	$0.629287\pi$
$558$	5.49508	0.232625
$559$	−9.55158	−0.403989
$560$	−3.41540	−0.144327
$561$	7.36049	0.310760
$562$	13.4969	0.569333
$563$	−31.0815	−1.30993	−0.654964	−	0.755660i	$-0.727316\pi$
$563$	−31.0815	−1.30993	−0.654964	+	0.755660i	$0.727316\pi$
$564$	0.649167	0.0273349
$565$	23.3169	0.980951
$566$	10.8497	0.456049
$567$	−1.48369	−0.0623089
$568$	5.64506	0.236861
$569$	31.1041	1.30395	0.651977	−	0.758239i	$-0.273940\pi$
$569$	31.1041	1.30395	0.651977	+	0.758239i	$0.273940\pi$
$570$	−2.67353	−0.111982
$571$	−20.2921	−0.849197	−0.424598	−	0.905382i	$-0.639585\pi$
$571$	−20.2921	−0.849197	−0.424598	+	0.905382i	$0.639585\pi$
$572$	−1.45470	−0.0608240
$573$	−4.09683	−0.171147
$574$	4.65605	0.194340
$575$	0.424852	0.0177175
$576$	1.00000	0.0416667
$577$	−11.0741	−0.461019	−0.230510	−	0.973070i	$-0.574039\pi$
$577$	−11.0741	−0.461019	−0.230510	+	0.973070i	$0.574039\pi$
$578$	8.60159	0.357779
$579$	13.1156	0.545064
$580$	−1.48499	−0.0616610
$581$	−14.0983	−0.584894
$582$	−12.4889	−0.517680
$583$	17.9079	0.741671
$584$	13.3593	0.552813
$585$	−2.30197	−0.0951748
$586$	−8.99683	−0.371656
$587$	20.3364	0.839373	0.419686	−	0.907669i	$-0.362140\pi$
$587$	20.3364	0.839373	0.419686	+	0.907669i	$0.362140\pi$
$588$	4.79868	0.197894
$589$	6.38204	0.262967
$590$	−9.48261	−0.390393
$591$	9.84786	0.405087
$592$	9.13743	0.375546
$593$	6.87519	0.282330	0.141165	−	0.989986i	$-0.454915\pi$
$593$	6.87519	0.282330	0.141165	+	0.989986i	$0.454915\pi$
$594$	−1.45470	−0.0596870
$595$	17.2813	0.708463
$596$	−6.81810	−0.279280
$597$	−27.3916	−1.12106
$598$	−1.42055	−0.0580907
$599$	−3.40322	−0.139052	−0.0695258	−	0.997580i	$-0.522149\pi$
$599$	−3.40322	−0.139052	−0.0695258	+	0.997580i	$0.522149\pi$
$600$	−0.299075	−0.0122097
$601$	−3.76888	−0.153736	−0.0768679	−	0.997041i	$-0.524492\pi$
$601$	−3.76888	−0.153736	−0.0768679	+	0.997041i	$0.524492\pi$
$602$	−14.1715	−0.577589
$603$	−8.73905	−0.355882
$604$	18.2202	0.741371
$605$	−20.4504	−0.831426
$606$	−18.7245	−0.760632
$607$	−45.5526	−1.84892	−0.924461	−	0.381276i	$-0.875485\pi$
$607$	−45.5526	−1.84892	−0.924461	+	0.381276i	$0.875485\pi$
$608$	1.16141	0.0471014
$609$	−0.957120	−0.0387844
$610$	14.7609	0.597650
$611$	0.649167	0.0262625
$612$	−5.05980	−0.204530
$613$	28.4843	1.15047	0.575236	−	0.817988i	$-0.304910\pi$
$613$	28.4843	1.15047	0.575236	+	0.817988i	$0.304910\pi$
$614$	−12.7618	−0.515025
$615$	7.22396	0.291298
$616$	−2.15832	−0.0869610
$617$	22.7000	0.913868	0.456934	−	0.889501i	$-0.348948\pi$
$617$	22.7000	0.913868	0.456934	+	0.889501i	$0.348948\pi$
$618$	2.93346	0.118001
$619$	−1.37535	−0.0552800	−0.0276400	−	0.999618i	$-0.508799\pi$
$619$	−1.37535	−0.0552800	−0.0276400	+	0.999618i	$0.508799\pi$
$620$	12.6495	0.508017
$621$	−1.42055	−0.0570048
$622$	26.1546	1.04871
$623$	−3.15084	−0.126236
$624$	1.00000	0.0400320
$625$	−26.4059	−1.05624
$626$	21.7717	0.870171
$627$	−1.68950	−0.0674722
$628$	0.757630	0.0302327
$629$	−46.2336	−1.84345
$630$	−3.41540	−0.136073
$631$	30.1305	1.19948	0.599738	−	0.800196i	$-0.295271\pi$
$631$	30.1305	1.19948	0.599738	+	0.800196i	$0.295271\pi$
$632$	−1.00000	−0.0397779
$633$	11.7715	0.467876
$634$	12.7294	0.505548
$635$	−25.8295	−1.02501
$636$	−12.3104	−0.488139
$637$	4.79868	0.190131
$638$	−0.938420	−0.0371524
$639$	5.64506	0.223315
$640$	2.30197	0.0909934
$641$	−45.0137	−1.77794	−0.888968	−	0.457970i	$-0.848577\pi$
$641$	−45.0137	−1.77794	−0.888968	+	0.457970i	$0.848577\pi$
$642$	4.87580	0.192433
$643$	−44.7871	−1.76623	−0.883115	−	0.469157i	$-0.844558\pi$
$643$	−44.7871	−1.76623	−0.883115	+	0.469157i	$0.844558\pi$
$644$	−2.10765	−0.0830532
$645$	−21.9875	−0.865756
$646$	−5.87651	−0.231208
$647$	−19.4056	−0.762913	−0.381456	−	0.924387i	$-0.624577\pi$
$647$	−19.4056	−0.762913	−0.381456	+	0.924387i	$0.624577\pi$
$648$	1.00000	0.0392837
$649$	−5.99240	−0.235222
$650$	−0.299075	−0.0117307
$651$	8.15297	0.319540
$652$	−24.6698	−0.966144
$653$	−3.92665	−0.153662	−0.0768309	−	0.997044i	$-0.524480\pi$
$653$	−3.92665	−0.153662	−0.0768309	+	0.997044i	$0.524480\pi$
$654$	4.36952	0.170862
$655$	−4.36693	−0.170630
$656$	−3.13816	−0.122525
$657$	13.3593	0.521197
$658$	0.963160	0.0375479
$659$	−22.2076	−0.865085	−0.432543	−	0.901613i	$-0.642384\pi$
$659$	−22.2076	−0.865085	−0.432543	+	0.901613i	$0.642384\pi$
$660$	−3.34868	−0.130347
$661$	−10.0502	−0.390906	−0.195453	−	0.980713i	$-0.562618\pi$
$661$	−10.0502	−0.390906	−0.195453	+	0.980713i	$0.562618\pi$
$662$	5.60613	0.217888
$663$	−5.05980	−0.196506
$664$	9.50219	0.368756
$665$	−3.96668	−0.153821
$666$	9.13743	0.354068
$667$	−0.916393	−0.0354829
$668$	20.8856	0.808090
$669$	−12.6013	−0.487194
$670$	−20.1170	−0.777189
$671$	9.32792	0.360100
$672$	1.48369	0.0572344
$673$	14.7754	0.569550	0.284775	−	0.958594i	$-0.408081\pi$
$673$	14.7754	0.569550	0.284775	+	0.958594i	$0.408081\pi$
$674$	−16.3236	−0.628762
$675$	−0.299075	−0.0115114
$676$	1.00000	0.0384615
$677$	39.6311	1.52315	0.761574	−	0.648078i	$-0.224427\pi$
$677$	39.6311	1.52315	0.761574	+	0.648078i	$0.224427\pi$
$678$	−10.1291	−0.389006
$679$	−18.5295	−0.711098
$680$	−11.6475	−0.446662
$681$	27.0019	1.03471
$682$	7.99368	0.306094
$683$	22.6411	0.866339	0.433170	−	0.901312i	$-0.357395\pi$
$683$	22.6411	0.866339	0.433170	+	0.901312i	$0.357395\pi$
$684$	1.16141	0.0444076
$685$	19.4610	0.743567
$686$	17.5055	0.668364
$687$	−19.2273	−0.733566
$688$	9.55158	0.364150
$689$	−12.3104	−0.468989
$690$	−3.27007	−0.124490
$691$	−40.7768	−1.55122	−0.775610	−	0.631212i	$-0.782558\pi$
$691$	−40.7768	−1.55122	−0.775610	+	0.631212i	$0.782558\pi$
$692$	−5.10263	−0.193973
$693$	−2.15832	−0.0819876
$694$	7.64170	0.290075
$695$	−16.0227	−0.607777
$696$	0.645096	0.0244523
$697$	15.8785	0.601440
$698$	16.5198	0.625285
$699$	−21.2824	−0.804975
$700$	−0.443733	−0.0167715
$701$	−39.3364	−1.48571	−0.742857	−	0.669450i	$-0.766530\pi$
$701$	−39.3364	−1.48571	−0.742857	+	0.669450i	$0.766530\pi$
$702$	1.00000	0.0377426
$703$	10.6123	0.400251
$704$	1.45470	0.0548260
$705$	1.49437	0.0562810
$706$	−24.3507	−0.916452
$707$	−27.7813	−1.04482
$708$	4.11934	0.154814
$709$	−14.3109	−0.537458	−0.268729	−	0.963216i	$-0.586604\pi$
$709$	−14.3109	−0.537458	−0.268729	+	0.963216i	$0.586604\pi$
$710$	12.9948	0.487685
$711$	−1.00000	−0.0375029
$712$	2.12365	0.0795873
$713$	7.80605	0.292339
$714$	−7.50715	−0.280948
$715$	−3.34868	−0.125233
$716$	−7.54212	−0.281862
$717$	21.0272	0.785274
$718$	−31.0362	−1.15826
$719$	32.2993	1.20456	0.602280	−	0.798285i	$-0.294259\pi$
$719$	32.2993	1.20456	0.602280	+	0.798285i	$0.294259\pi$
$720$	2.30197	0.0857894
$721$	4.35233	0.162089
$722$	−17.6511	−0.656907
$723$	−2.57137	−0.0956302
$724$	6.99392	0.259927
$725$	−0.192932	−0.00716531
$726$	8.88385	0.329711
$727$	23.5937	0.875041	0.437521	−	0.899208i	$-0.355857\pi$
$727$	23.5937	0.875041	0.437521	+	0.899208i	$0.355857\pi$
$728$	1.48369	0.0549890
$729$	1.00000	0.0370370
$730$	30.7528	1.13821
$731$	−48.3291	−1.78752
$732$	−6.41227	−0.237004
$733$	3.95608	0.146121	0.0730606	−	0.997328i	$-0.476723\pi$
$733$	3.95608	0.146121	0.0730606	+	0.997328i	$0.476723\pi$
$734$	18.2454	0.673449
$735$	11.0464	0.407453
$736$	1.42055	0.0523623
$737$	−12.7127	−0.468278
$738$	−3.13816	−0.115517
$739$	13.0338	0.479456	0.239728	−	0.970840i	$-0.422942\pi$
$739$	13.0338	0.479456	0.239728	+	0.970840i	$0.422942\pi$
$740$	21.0341	0.773229
$741$	1.16141	0.0426655
$742$	−18.2648	−0.670521
$743$	−40.1994	−1.47477	−0.737387	−	0.675470i	$-0.763941\pi$
$743$	−40.1994	−1.47477	−0.737387	+	0.675470i	$0.763941\pi$
$744$	−5.49508	−0.201459
$745$	−15.6951	−0.575023
$746$	15.2593	0.558684
$747$	9.50219	0.347667
$748$	−7.36049	−0.269126
$749$	7.23416	0.264330
$750$	10.8214	0.395142
$751$	19.3427	0.705825	0.352912	−	0.935656i	$-0.385191\pi$
$751$	19.3427	0.705825	0.352912	+	0.935656i	$0.385191\pi$
$752$	−0.649167	−0.0236727
$753$	11.4065	0.415675
$754$	0.645096	0.0234930
$755$	41.9425	1.52644
$756$	1.48369	0.0539611
$757$	42.1224	1.53097	0.765483	−	0.643456i	$-0.222500\pi$
$757$	42.1224	1.53097	0.765483	+	0.643456i	$0.222500\pi$
$758$	−36.2255	−1.31577
$759$	−2.06648	−0.0750083
$760$	2.67353	0.0969793
$761$	−26.1817	−0.949086	−0.474543	−	0.880232i	$-0.657387\pi$
$761$	−26.1817	−0.949086	−0.474543	+	0.880232i	$0.657387\pi$
$762$	11.2206	0.406479
$763$	6.48300	0.234700
$764$	4.09683	0.148218
$765$	−11.6475	−0.421117
$766$	19.1781	0.692934
$767$	4.11934	0.148741
$768$	−1.00000	−0.0360844
$769$	41.5183	1.49719	0.748593	−	0.663029i	$-0.230730\pi$
$769$	41.5183	1.49719	0.748593	+	0.663029i	$0.230730\pi$
$770$	−4.96838	−0.179048
$771$	−7.25709	−0.261358
$772$	−13.1156	−0.472039
$773$	−0.652280	−0.0234609	−0.0117304	−	0.999931i	$-0.503734\pi$
$773$	−0.652280	−0.0234609	−0.0117304	+	0.999931i	$0.503734\pi$
$774$	9.55158	0.343324
$775$	1.64344	0.0590341
$776$	12.4889	0.448324
$777$	13.5571	0.486357
$778$	−26.8310	−0.961939
$779$	−3.64469	−0.130585
$780$	2.30197	0.0824238
$781$	8.21186	0.293843
$782$	−7.18771	−0.257032
$783$	0.645096	0.0230538
$784$	−4.79868	−0.171381
$785$	1.74404	0.0622475
$786$	1.89704	0.0676652
$787$	55.4068	1.97504	0.987520	−	0.157492i	$-0.0503409\pi$
$787$	55.4068	1.97504	0.987520	+	0.157492i	$0.0503409\pi$
$788$	−9.84786	−0.350816
$789$	0.363767	0.0129505
$790$	−2.30197	−0.0819005
$791$	−15.0284	−0.534349
$792$	1.45470	0.0516905
$793$	−6.41227	−0.227706
$794$	30.5548	1.08435
$795$	−28.3382	−1.00505
$796$	27.3916	0.970869
$797$	−6.42604	−0.227622	−0.113811	−	0.993502i	$-0.536306\pi$
$797$	−6.42604	−0.227622	−0.113811	+	0.993502i	$0.536306\pi$
$798$	1.72317	0.0609995
$799$	3.28466	0.116203
$800$	0.299075	0.0105739
$801$	2.12365	0.0750357
$802$	2.46636	0.0870902
$803$	19.4338	0.685803
$804$	8.73905	0.308203
$805$	−4.85176	−0.171002
$806$	−5.49508	−0.193556
$807$	−24.2421	−0.853362
$808$	18.7245	0.658726
$809$	−26.0313	−0.915213	−0.457607	−	0.889155i	$-0.651293\pi$
$809$	−26.0313	−0.915213	−0.457607	+	0.889155i	$0.651293\pi$
$810$	2.30197	0.0808830
$811$	−9.63357	−0.338280	−0.169140	−	0.985592i	$-0.554099\pi$
$811$	−9.63357	−0.338280	−0.169140	+	0.985592i	$0.554099\pi$
$812$	0.957120	0.0335883
$813$	22.4435	0.787128
$814$	13.2922	0.465891
$815$	−56.7892	−1.98924
$816$	5.05980	0.177128
$817$	11.0933	0.388105
$818$	−0.815979	−0.0285301
$819$	1.48369	0.0518442
$820$	−7.22396	−0.252272
$821$	−30.8580	−1.07695	−0.538475	−	0.842641i	$-0.681000\pi$
$821$	−30.8580	−1.07695	−0.538475	+	0.842641i	$0.681000\pi$
$822$	−8.45406	−0.294869
$823$	−8.38167	−0.292167	−0.146083	−	0.989272i	$-0.546667\pi$
$823$	−8.38167	−0.292167	−0.146083	+	0.989272i	$0.546667\pi$
$824$	−2.93346	−0.102192
$825$	−0.435064	−0.0151470
$826$	6.11181	0.212657
$827$	14.1204	0.491014	0.245507	−	0.969395i	$-0.421046\pi$
$827$	14.1204	0.491014	0.245507	+	0.969395i	$0.421046\pi$
$828$	1.42055	0.0493676
$829$	−57.4619	−1.99574	−0.997868	−	0.0652707i	$-0.979209\pi$
$829$	−57.4619	−1.99574	−0.997868	+	0.0652707i	$0.979209\pi$
$830$	21.8738	0.759250
$831$	−0.0354150	−0.00122853
$832$	−1.00000	−0.0346688
$833$	24.2804	0.841264
$834$	6.96044	0.241020
$835$	48.0782	1.66381
$836$	1.68950	0.0584326
$837$	−5.49508	−0.189938
$838$	34.3996	1.18831
$839$	−31.1607	−1.07579	−0.537893	−	0.843013i	$-0.680780\pi$
$839$	−31.1607	−1.07579	−0.537893	+	0.843013i	$0.680780\pi$
$840$	3.41540	0.117843
$841$	−28.5839	−0.985650
$842$	14.9486	0.515163
$843$	−13.4969	−0.464858
$844$	−11.7715	−0.405193
$845$	2.30197	0.0791902
$846$	−0.649167	−0.0223188
$847$	13.1808	0.452899
$848$	12.3104	0.422741
$849$	−10.8497	−0.372362
$850$	−1.51326	−0.0519044
$851$	12.9802	0.444955
$852$	−5.64506	−0.193397
$853$	44.6981	1.53043	0.765217	−	0.643773i	$-0.222632\pi$
$853$	44.6981	1.53043	0.765217	+	0.643773i	$0.222632\pi$
$854$	−9.51379	−0.325555
$855$	2.67353	0.0914329
$856$	−4.87580	−0.166652
$857$	47.0832	1.60833	0.804166	−	0.594405i	$-0.202613\pi$
$857$	47.0832	1.60833	0.804166	+	0.594405i	$0.202613\pi$
$858$	1.45470	0.0496626
$859$	1.01030	0.0344710	0.0172355	−	0.999851i	$-0.494513\pi$
$859$	1.01030	0.0344710	0.0172355	+	0.999851i	$0.494513\pi$
$860$	21.9875	0.749766
$861$	−4.65605	−0.158678
$862$	13.0932	0.445957
$863$	−14.9703	−0.509595	−0.254797	−	0.966994i	$-0.582009\pi$
$863$	−14.9703	−0.509595	−0.254797	+	0.966994i	$0.582009\pi$
$864$	−1.00000	−0.0340207
$865$	−11.7461	−0.399380
$866$	32.1195	1.09146
$867$	−8.60159	−0.292125
$868$	−8.15297	−0.276730
$869$	−1.45470	−0.0493473
$870$	1.48499	0.0503460
$871$	8.73905	0.296111
$872$	−4.36952	−0.147971
$873$	12.4889	0.422684
$874$	1.64984	0.0558068
$875$	16.0556	0.542777
$876$	−13.3593	−0.451370
$877$	41.9923	1.41798	0.708989	−	0.705219i	$-0.249152\pi$
$877$	41.9923	1.41798	0.708989	+	0.705219i	$0.249152\pi$
$878$	−19.2393	−0.649294
$879$	8.99683	0.303456
$880$	3.34868	0.112884
$881$	−25.4477	−0.857354	−0.428677	−	0.903458i	$-0.641020\pi$
$881$	−25.4477	−0.857354	−0.428677	+	0.903458i	$0.641020\pi$
$882$	−4.79868	−0.161580
$883$	−23.7953	−0.800777	−0.400388	−	0.916346i	$-0.631125\pi$
$883$	−23.7953	−0.800777	−0.400388	+	0.916346i	$0.631125\pi$
$884$	5.05980	0.170180
$885$	9.48261	0.318754
$886$	−12.7622	−0.428753
$887$	45.2655	1.51987	0.759934	−	0.650001i	$-0.225231\pi$
$887$	45.2655	1.51987	0.759934	+	0.650001i	$0.225231\pi$
$888$	−9.13743	−0.306632
$889$	16.6478	0.558351
$890$	4.88859	0.163866
$891$	1.45470	0.0487342
$892$	12.6013	0.421922
$893$	−0.753950	−0.0252300
$894$	6.81810	0.228031
$895$	−17.3618	−0.580339
$896$	−1.48369	−0.0495665
$897$	1.42055	0.0474309
$898$	−2.42272	−0.0808472
$899$	−3.54485	−0.118227
$900$	0.299075	0.00996916
$901$	−62.2882	−2.07512
$902$	−4.56508	−0.152001
$903$	14.1715	0.471599
$904$	10.1291	0.336889
$905$	16.0998	0.535176
$906$	−18.2202	−0.605327
$907$	11.2355	0.373067	0.186534	−	0.982449i	$-0.440275\pi$
$907$	11.2355	0.373067	0.186534	+	0.982449i	$0.440275\pi$
$908$	−27.0019	−0.896088
$909$	18.7245	0.621053
$910$	3.41540	0.113219
$911$	23.9390	0.793133	0.396567	−	0.918006i	$-0.370202\pi$
$911$	23.9390	0.793133	0.396567	+	0.918006i	$0.370202\pi$
$912$	−1.16141	−0.0384581
$913$	13.8228	0.457469
$914$	−20.8164	−0.688546
$915$	−14.7609	−0.487979
$916$	19.2273	0.635287
$917$	2.81461	0.0929467
$918$	5.05980	0.166998
$919$	−11.2065	−0.369669	−0.184835	−	0.982770i	$-0.559175\pi$
$919$	−11.2065	−0.369669	−0.184835	+	0.982770i	$0.559175\pi$
$920$	3.27007	0.107811
$921$	12.7618	0.420516
$922$	1.56625	0.0515817
$923$	−5.64506	−0.185809
$924$	2.15832	0.0710034
$925$	2.73277	0.0898531
$926$	27.5241	0.904499
$927$	−2.93346	−0.0963475
$928$	−0.645096	−0.0211763
$929$	−27.9760	−0.917862	−0.458931	−	0.888472i	$-0.651768\pi$
$929$	−27.9760	−0.917862	−0.458931	+	0.888472i	$0.651768\pi$
$930$	−12.6495	−0.414794
$931$	−5.57323	−0.182655
$932$	21.2824	0.697129
$933$	−26.1546	−0.856265
$934$	−16.8995	−0.552969
$935$	−16.9436	−0.554116
$936$	−1.00000	−0.0326860
$937$	58.0040	1.89491	0.947454	−	0.319891i	$-0.103646\pi$
$937$	58.0040	1.89491	0.947454	+	0.319891i	$0.103646\pi$
$938$	12.9660	0.423355
$939$	−21.7717	−0.710492
$940$	−1.49437	−0.0487408
$941$	−37.5826	−1.22516	−0.612580	−	0.790409i	$-0.709868\pi$
$941$	−37.5826	−1.22516	−0.612580	+	0.790409i	$0.709868\pi$
$942$	−0.757630	−0.0246849
$943$	−4.45793	−0.145170
$944$	−4.11934	−0.134073
$945$	3.41540	0.111103
$946$	13.8947	0.451755
$947$	−12.0068	−0.390167	−0.195083	−	0.980787i	$-0.562498\pi$
$947$	−12.0068	−0.390167	−0.195083	+	0.980787i	$0.562498\pi$
$948$	1.00000	0.0324785
$949$	−13.3593	−0.433662
$950$	0.347349	0.0112695
$951$	−12.7294	−0.412778
$952$	7.50715	0.243308
$953$	25.6971	0.832410	0.416205	−	0.909271i	$-0.363360\pi$
$953$	25.6971	0.832410	0.416205	+	0.909271i	$0.363360\pi$
$954$	12.3104	0.398564
$955$	9.43078	0.305173
$956$	−21.0272	−0.680067
$957$	0.938420	0.0303348
$958$	−27.9916	−0.904366
$959$	−12.5432	−0.405040
$960$	−2.30197	−0.0742958
$961$	−0.804122	−0.0259394
$962$	−9.13743	−0.294602
$963$	−4.87580	−0.157121
$964$	2.57137	0.0828182
$965$	−30.1916	−0.971903
$966$	2.10765	0.0678126
$967$	−58.1085	−1.86864	−0.934322	−	0.356430i	$-0.883994\pi$
$967$	−58.1085	−1.86864	−0.934322	+	0.356430i	$0.883994\pi$
$968$	−8.88385	−0.285538
$969$	5.87651	0.188781
$970$	28.7490	0.923075
$971$	−17.1974	−0.551892	−0.275946	−	0.961173i	$-0.588991\pi$
$971$	−17.1974	−0.551892	−0.275946	+	0.961173i	$0.588991\pi$
$972$	−1.00000	−0.0320750
$973$	10.3271	0.331072
$974$	−35.0710	−1.12375
$975$	0.299075	0.00957806
$976$	6.41227	0.205252
$977$	45.3160	1.44979	0.724894	−	0.688861i	$-0.241889\pi$
$977$	45.3160	1.44979	0.724894	+	0.688861i	$0.241889\pi$
$978$	24.6698	0.788853
$979$	3.08928	0.0987337
$980$	−11.0464	−0.352865
$981$	−4.36952	−0.139508
$982$	12.2653	0.391403
$983$	−22.9205	−0.731049	−0.365524	−	0.930802i	$-0.619110\pi$
$983$	−22.9205	−0.731049	−0.365524	+	0.930802i	$0.619110\pi$
$984$	3.13816	0.100041
$985$	−22.6695	−0.722310
$986$	3.26406	0.103949
$987$	−0.963160	−0.0306577
$988$	−1.16141	−0.0369494
$989$	13.5685	0.431454
$990$	3.34868	0.106428
$991$	−42.0829	−1.33681	−0.668404	−	0.743798i	$-0.733022\pi$
$991$	−42.0829	−1.33681	−0.668404	+	0.743798i	$0.733022\pi$
$992$	5.49508	0.174469
$993$	−5.60613	−0.177905
$994$	−8.37549	−0.265654
$995$	63.0547	1.99897
$996$	−9.50219	−0.301088
$997$	−19.1999	−0.608068	−0.304034	−	0.952661i	$-0.598334\pi$
$997$	−19.1999	−0.608068	−0.304034	+	0.952661i	$0.598334\pi$
$998$	11.7808	0.372913
$999$	−9.13743	−0.289095

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6162.2.a.bj.1.7	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6162.2.a.bj.1.7	✓	10	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:	\( N \)	\(=\)	\( 6162 = 2 \cdot 3 \cdot 13 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6162.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.30197 q^{5} -1.00000 q^{6} -1.48369 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.30197 q^{5} -1.00000 q^{6} -1.48369 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.30197 q^{10} +1.45470 q^{11} -1.00000 q^{12} -1.00000 q^{13} -1.48369 q^{14} -2.30197 q^{15} +1.00000 q^{16} -5.05980 q^{17} +1.00000 q^{18} +1.16141 q^{19} +2.30197 q^{20} +1.48369 q^{21} +1.45470 q^{22} +1.42055 q^{23} -1.00000 q^{24} +0.299075 q^{25} -1.00000 q^{26} -1.00000 q^{27} -1.48369 q^{28} -0.645096 q^{29} -2.30197 q^{30} +5.49508 q^{31} +1.00000 q^{32} -1.45470 q^{33} -5.05980 q^{34} -3.41540 q^{35} +1.00000 q^{36} +9.13743 q^{37} +1.16141 q^{38} +1.00000 q^{39} +2.30197 q^{40} -3.13816 q^{41} +1.48369 q^{42} +9.55158 q^{43} +1.45470 q^{44} +2.30197 q^{45} +1.42055 q^{46} -0.649167 q^{47} -1.00000 q^{48} -4.79868 q^{49} +0.299075 q^{50} +5.05980 q^{51} -1.00000 q^{52} +12.3104 q^{53} -1.00000 q^{54} +3.34868 q^{55} -1.48369 q^{56} -1.16141 q^{57} -0.645096 q^{58} -4.11934 q^{59} -2.30197 q^{60} +6.41227 q^{61} +5.49508 q^{62} -1.48369 q^{63} +1.00000 q^{64} -2.30197 q^{65} -1.45470 q^{66} -8.73905 q^{67} -5.05980 q^{68} -1.42055 q^{69} -3.41540 q^{70} +5.64506 q^{71} +1.00000 q^{72} +13.3593 q^{73} +9.13743 q^{74} -0.299075 q^{75} +1.16141 q^{76} -2.15832 q^{77} +1.00000 q^{78} -1.00000 q^{79} +2.30197 q^{80} +1.00000 q^{81} -3.13816 q^{82} +9.50219 q^{83} +1.48369 q^{84} -11.6475 q^{85} +9.55158 q^{86} +0.645096 q^{87} +1.45470 q^{88} +2.12365 q^{89} +2.30197 q^{90} +1.48369 q^{91} +1.42055 q^{92} -5.49508 q^{93} -0.649167 q^{94} +2.67353 q^{95} -1.00000 q^{96} +12.4889 q^{97} -4.79868 q^{98} +1.45470 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} - 10 q^{6} + 3 q^{7} + 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 - 10 * q^6 + 3 * q^7 + 10 * q^8 + 10 * q^9	\( 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} - 10 q^{6} + 3 q^{7} + 10 q^{8} + 10 q^{9} + 6 q^{10} + 3 q^{11} - 10 q^{12} - 10 q^{13} + 3 q^{14} - 6 q^{15} + 10 q^{16} + 12 q^{17} + 10 q^{18} + 17 q^{19} + 6 q^{20} - 3 q^{21} + 3 q^{22} + 3 q^{23} - 10 q^{24} + 12 q^{25} - 10 q^{26} - 10 q^{27} + 3 q^{28} + 6 q^{29} - 6 q^{30} + 9 q^{31} + 10 q^{32} - 3 q^{33} + 12 q^{34} - 8 q^{35} + 10 q^{36} + 6 q^{37} + 17 q^{38} + 10 q^{39} + 6 q^{40} + 28 q^{41} - 3 q^{42} + 3 q^{43} + 3 q^{44} + 6 q^{45} + 3 q^{46} + 13 q^{47} - 10 q^{48} + 11 q^{49} + 12 q^{50} - 12 q^{51} - 10 q^{52} + 18 q^{53} - 10 q^{54} + 16 q^{55} + 3 q^{56} - 17 q^{57} + 6 q^{58} + 9 q^{59} - 6 q^{60} + 16 q^{61} + 9 q^{62} + 3 q^{63} + 10 q^{64} - 6 q^{65} - 3 q^{66} + 19 q^{67} + 12 q^{68} - 3 q^{69} - 8 q^{70} - 11 q^{71} + 10 q^{72} + 20 q^{73} + 6 q^{74} - 12 q^{75} + 17 q^{76} + 16 q^{77} + 10 q^{78} - 10 q^{79} + 6 q^{80} + 10 q^{81} + 28 q^{82} + 15 q^{83} - 3 q^{84} + 34 q^{85} + 3 q^{86} - 6 q^{87} + 3 q^{88} + 10 q^{89} + 6 q^{90} - 3 q^{91} + 3 q^{92} - 9 q^{93} + 13 q^{94} + 26 q^{95} - 10 q^{96} + 18 q^{97} + 11 q^{98} + 3 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 - 10 * q^6 + 3 * q^7 + 10 * q^8 + 10 * q^9 + 6 * q^10 + 3 * q^11 - 10 * q^12 - 10 * q^13 + 3 * q^14 - 6 * q^15 + 10 * q^16 + 12 * q^17 + 10 * q^18 + 17 * q^19 + 6 * q^20 - 3 * q^21 + 3 * q^22 + 3 * q^23 - 10 * q^24 + 12 * q^25 - 10 * q^26 - 10 * q^27 + 3 * q^28 + 6 * q^29 - 6 * q^30 + 9 * q^31 + 10 * q^32 - 3 * q^33 + 12 * q^34 - 8 * q^35 + 10 * q^36 + 6 * q^37 + 17 * q^38 + 10 * q^39 + 6 * q^40 + 28 * q^41 - 3 * q^42 + 3 * q^43 + 3 * q^44 + 6 * q^45 + 3 * q^46 + 13 * q^47 - 10 * q^48 + 11 * q^49 + 12 * q^50 - 12 * q^51 - 10 * q^52 + 18 * q^53 - 10 * q^54 + 16 * q^55 + 3 * q^56 - 17 * q^57 + 6 * q^58 + 9 * q^59 - 6 * q^60 + 16 * q^61 + 9 * q^62 + 3 * q^63 + 10 * q^64 - 6 * q^65 - 3 * q^66 + 19 * q^67 + 12 * q^68 - 3 * q^69 - 8 * q^70 - 11 * q^71 + 10 * q^72 + 20 * q^73 + 6 * q^74 - 12 * q^75 + 17 * q^76 + 16 * q^77 + 10 * q^78 - 10 * q^79 + 6 * q^80 + 10 * q^81 + 28 * q^82 + 15 * q^83 - 3 * q^84 + 34 * q^85 + 3 * q^86 - 6 * q^87 + 3 * q^88 + 10 * q^89 + 6 * q^90 - 3 * q^91 + 3 * q^92 - 9 * q^93 + 13 * q^94 + 26 * q^95 - 10 * q^96 + 18 * q^97 + 11 * q^98 + 3 * q^99

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