LMFDB - Embedded newform 4134.2.a.x.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4134,2,Mod(1,4134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4134, 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("4134.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4134 = 2 \cdot 3 \cdot 13 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4134.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:	$33.0101561956$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 21x^{6} + 43x^{5} + 96x^{4} - 235x^{3} + 136x^{2} - 8x - 8 $ x^8 - 2x^7 - 21x^6 + 43x^5 + 96x^4 - 235x^3 + 136x^2 - 8*x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$2.95264$ of defining polynomial
Character	$\chi$	$=$	4134.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.95264 q^{5} +1.00000 q^{6} +2.84393 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.95264 q^{5} +1.00000 q^{6} +2.84393 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.95264 q^{10} +3.27613 q^{11} +1.00000 q^{12} -1.00000 q^{13} +2.84393 q^{14} +2.95264 q^{15} +1.00000 q^{16} -4.61187 q^{17} +1.00000 q^{18} +2.77905 q^{19} +2.95264 q^{20} +2.84393 q^{21} +3.27613 q^{22} -8.73107 q^{23} +1.00000 q^{24} +3.71806 q^{25} -1.00000 q^{26} +1.00000 q^{27} +2.84393 q^{28} +3.69632 q^{29} +2.95264 q^{30} +4.04675 q^{31} +1.00000 q^{32} +3.27613 q^{33} -4.61187 q^{34} +8.39708 q^{35} +1.00000 q^{36} +6.80850 q^{37} +2.77905 q^{38} -1.00000 q^{39} +2.95264 q^{40} -3.86818 q^{41} +2.84393 q^{42} -7.96045 q^{43} +3.27613 q^{44} +2.95264 q^{45} -8.73107 q^{46} -1.74898 q^{47} +1.00000 q^{48} +1.08792 q^{49} +3.71806 q^{50} -4.61187 q^{51} -1.00000 q^{52} +1.00000 q^{53} +1.00000 q^{54} +9.67321 q^{55} +2.84393 q^{56} +2.77905 q^{57} +3.69632 q^{58} -4.96398 q^{59} +2.95264 q^{60} +0.744532 q^{61} +4.04675 q^{62} +2.84393 q^{63} +1.00000 q^{64} -2.95264 q^{65} +3.27613 q^{66} -5.19687 q^{67} -4.61187 q^{68} -8.73107 q^{69} +8.39708 q^{70} +1.86113 q^{71} +1.00000 q^{72} +0.0164471 q^{73} +6.80850 q^{74} +3.71806 q^{75} +2.77905 q^{76} +9.31707 q^{77} -1.00000 q^{78} +10.3228 q^{79} +2.95264 q^{80} +1.00000 q^{81} -3.86818 q^{82} +0.598010 q^{83} +2.84393 q^{84} -13.6172 q^{85} -7.96045 q^{86} +3.69632 q^{87} +3.27613 q^{88} -18.2102 q^{89} +2.95264 q^{90} -2.84393 q^{91} -8.73107 q^{92} +4.04675 q^{93} -1.74898 q^{94} +8.20551 q^{95} +1.00000 q^{96} -3.71353 q^{97} +1.08792 q^{98} +3.27613 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 2 q^{5} + 8 q^{6} + 7 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 2 * q^5 + 8 * q^6 + 7 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 2 q^{5} + 8 q^{6} + 7 q^{7} + 8 q^{8} + 8 q^{9} + 2 q^{10} + 7 q^{11} + 8 q^{12} - 8 q^{13} + 7 q^{14} + 2 q^{15} + 8 q^{16} + 8 q^{17} + 8 q^{18} + 11 q^{19} + 2 q^{20} + 7 q^{21} + 7 q^{22} + 5 q^{23} + 8 q^{24} + 6 q^{25} - 8 q^{26} + 8 q^{27} + 7 q^{28} + 13 q^{29} + 2 q^{30} + 12 q^{31} + 8 q^{32} + 7 q^{33} + 8 q^{34} + 14 q^{35} + 8 q^{36} + 10 q^{37} + 11 q^{38} - 8 q^{39} + 2 q^{40} + 19 q^{41} + 7 q^{42} + 10 q^{43} + 7 q^{44} + 2 q^{45} + 5 q^{46} + 6 q^{47} + 8 q^{48} + 15 q^{49} + 6 q^{50} + 8 q^{51} - 8 q^{52} + 8 q^{53} + 8 q^{54} + 5 q^{55} + 7 q^{56} + 11 q^{57} + 13 q^{58} + 11 q^{59} + 2 q^{60} + 6 q^{61} + 12 q^{62} + 7 q^{63} + 8 q^{64} - 2 q^{65} + 7 q^{66} + 5 q^{67} + 8 q^{68} + 5 q^{69} + 14 q^{70} - 6 q^{71} + 8 q^{72} + 18 q^{73} + 10 q^{74} + 6 q^{75} + 11 q^{76} - 8 q^{77} - 8 q^{78} + 17 q^{79} + 2 q^{80} + 8 q^{81} + 19 q^{82} + 16 q^{83} + 7 q^{84} + 25 q^{85} + 10 q^{86} + 13 q^{87} + 7 q^{88} - 8 q^{89} + 2 q^{90} - 7 q^{91} + 5 q^{92} + 12 q^{93} + 6 q^{94} - 30 q^{95} + 8 q^{96} + 11 q^{97} + 15 q^{98} + 7 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 2 * q^5 + 8 * q^6 + 7 * q^7 + 8 * q^8 + 8 * q^9 + 2 * q^10 + 7 * q^11 + 8 * q^12 - 8 * q^13 + 7 * q^14 + 2 * q^15 + 8 * q^16 + 8 * q^17 + 8 * q^18 + 11 * q^19 + 2 * q^20 + 7 * q^21 + 7 * q^22 + 5 * q^23 + 8 * q^24 + 6 * q^25 - 8 * q^26 + 8 * q^27 + 7 * q^28 + 13 * q^29 + 2 * q^30 + 12 * q^31 + 8 * q^32 + 7 * q^33 + 8 * q^34 + 14 * q^35 + 8 * q^36 + 10 * q^37 + 11 * q^38 - 8 * q^39 + 2 * q^40 + 19 * q^41 + 7 * q^42 + 10 * q^43 + 7 * q^44 + 2 * q^45 + 5 * q^46 + 6 * q^47 + 8 * q^48 + 15 * q^49 + 6 * q^50 + 8 * q^51 - 8 * q^52 + 8 * q^53 + 8 * q^54 + 5 * q^55 + 7 * q^56 + 11 * q^57 + 13 * q^58 + 11 * q^59 + 2 * q^60 + 6 * q^61 + 12 * q^62 + 7 * q^63 + 8 * q^64 - 2 * q^65 + 7 * q^66 + 5 * q^67 + 8 * q^68 + 5 * q^69 + 14 * q^70 - 6 * q^71 + 8 * q^72 + 18 * q^73 + 10 * q^74 + 6 * q^75 + 11 * q^76 - 8 * q^77 - 8 * q^78 + 17 * q^79 + 2 * q^80 + 8 * q^81 + 19 * q^82 + 16 * q^83 + 7 * q^84 + 25 * q^85 + 10 * q^86 + 13 * q^87 + 7 * q^88 - 8 * q^89 + 2 * q^90 - 7 * q^91 + 5 * q^92 + 12 * q^93 + 6 * q^94 - 30 * q^95 + 8 * q^96 + 11 * q^97 + 15 * q^98 + 7 * 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
$5$	2.95264	1.32046	0.660230	−	0.751064i	$-0.270459\pi$
$5$	2.95264	1.32046	0.660230	+	0.751064i	$0.270459\pi$
$6$	1.00000	0.408248
$7$	2.84393	1.07490	0.537452	−	0.843294i	$-0.319387\pi$
$7$	2.84393	1.07490	0.537452	+	0.843294i	$0.319387\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.95264	0.933706
$11$	3.27613	0.987789	0.493895	−	0.869522i	$-0.335573\pi$
$11$	3.27613	0.987789	0.493895	+	0.869522i	$0.335573\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.84393	0.760072
$15$	2.95264	0.762368
$16$	1.00000	0.250000
$17$	−4.61187	−1.11854	−0.559271	−	0.828985i	$-0.688919\pi$
$17$	−4.61187	−1.11854	−0.559271	+	0.828985i	$0.688919\pi$
$18$	1.00000	0.235702
$19$	2.77905	0.637557	0.318778	−	0.947829i	$-0.396727\pi$
$19$	2.77905	0.637557	0.318778	+	0.947829i	$0.396727\pi$
$20$	2.95264	0.660230
$21$	2.84393	0.620596
$22$	3.27613	0.698472
$23$	−8.73107	−1.82055	−0.910277	−	0.414000i	$-0.864131\pi$
$23$	−8.73107	−1.82055	−0.910277	+	0.414000i	$0.864131\pi$
$24$	1.00000	0.204124
$25$	3.71806	0.743613
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	2.84393	0.537452
$29$	3.69632	0.686389	0.343195	−	0.939264i	$-0.388491\pi$
$29$	3.69632	0.686389	0.343195	+	0.939264i	$0.388491\pi$
$30$	2.95264	0.539075
$31$	4.04675	0.726818	0.363409	−	0.931630i	$-0.381613\pi$
$31$	4.04675	0.726818	0.363409	+	0.931630i	$0.381613\pi$
$32$	1.00000	0.176777
$33$	3.27613	0.570300
$34$	−4.61187	−0.790928
$35$	8.39708	1.41937
$36$	1.00000	0.166667
$37$	6.80850	1.11931	0.559655	−	0.828726i	$-0.310934\pi$
$37$	6.80850	1.11931	0.559655	+	0.828726i	$0.310934\pi$
$38$	2.77905	0.450821
$39$	−1.00000	−0.160128
$40$	2.95264	0.466853
$41$	−3.86818	−0.604109	−0.302054	−	0.953291i	$-0.597672\pi$
$41$	−3.86818	−0.604109	−0.302054	+	0.953291i	$0.597672\pi$
$42$	2.84393	0.438828
$43$	−7.96045	−1.21396	−0.606978	−	0.794718i	$-0.707619\pi$
$43$	−7.96045	−1.21396	−0.606978	+	0.794718i	$0.707619\pi$
$44$	3.27613	0.493895
$45$	2.95264	0.440153
$46$	−8.73107	−1.28733
$47$	−1.74898	−0.255115	−0.127557	−	0.991831i	$-0.540714\pi$
$47$	−1.74898	−0.255115	−0.127557	+	0.991831i	$0.540714\pi$
$48$	1.00000	0.144338
$49$	1.08792	0.155418
$50$	3.71806	0.525814
$51$	−4.61187	−0.645790
$52$	−1.00000	−0.138675
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	1.00000	0.136083
$55$	9.67321	1.30434
$56$	2.84393	0.380036
$57$	2.77905	0.368094
$58$	3.69632	0.485350
$59$	−4.96398	−0.646255	−0.323128	−	0.946355i	$-0.604734\pi$
$59$	−4.96398	−0.646255	−0.323128	+	0.946355i	$0.604734\pi$
$60$	2.95264	0.381184
$61$	0.744532	0.0953275	0.0476638	−	0.998863i	$-0.484822\pi$
$61$	0.744532	0.0953275	0.0476638	+	0.998863i	$0.484822\pi$
$62$	4.04675	0.513938
$63$	2.84393	0.358301
$64$	1.00000	0.125000
$65$	−2.95264	−0.366230
$66$	3.27613	0.403263
$67$	−5.19687	−0.634899	−0.317449	−	0.948275i	$-0.602826\pi$
$67$	−5.19687	−0.634899	−0.317449	+	0.948275i	$0.602826\pi$
$68$	−4.61187	−0.559271
$69$	−8.73107	−1.05110
$70$	8.39708	1.00364
$71$	1.86113	0.220876	0.110438	−	0.993883i	$-0.464775\pi$
$71$	1.86113	0.220876	0.110438	+	0.993883i	$0.464775\pi$
$72$	1.00000	0.117851
$73$	0.0164471	0.00192498	0.000962491	−	1.00000i	$-0.499694\pi$
$73$	0.0164471	0.00192498	0.000962491		1.00000i	$0.499694\pi$
$74$	6.80850	0.791472
$75$	3.71806	0.429325
$76$	2.77905	0.318778
$77$	9.31707	1.06178
$78$	−1.00000	−0.113228
$79$	10.3228	1.16140	0.580701	−	0.814117i	$-0.302779\pi$
$79$	10.3228	1.16140	0.580701	+	0.814117i	$0.302779\pi$
$80$	2.95264	0.330115
$81$	1.00000	0.111111
$82$	−3.86818	−0.427169
$83$	0.598010	0.0656401	0.0328201	−	0.999461i	$-0.489551\pi$
$83$	0.598010	0.0656401	0.0328201	+	0.999461i	$0.489551\pi$
$84$	2.84393	0.310298
$85$	−13.6172	−1.47699
$86$	−7.96045	−0.858397
$87$	3.69632	0.396287
$88$	3.27613	0.349236
$89$	−18.2102	−1.93028	−0.965141	−	0.261732i	$-0.915706\pi$
$89$	−18.2102	−1.93028	−0.965141	+	0.261732i	$0.915706\pi$
$90$	2.95264	0.311235
$91$	−2.84393	−0.298125
$92$	−8.73107	−0.910277
$93$	4.04675	0.419628
$94$	−1.74898	−0.180394
$95$	8.20551	0.841868
$96$	1.00000	0.102062
$97$	−3.71353	−0.377052	−0.188526	−	0.982068i	$-0.560371\pi$
$97$	−3.71353	−0.377052	−0.188526	+	0.982068i	$0.560371\pi$
$98$	1.08792	0.109897
$99$	3.27613	0.329263
$100$	3.71806	0.371806
$101$	7.85142	0.781246	0.390623	−	0.920551i	$-0.372260\pi$
$101$	7.85142	0.781246	0.390623	+	0.920551i	$0.372260\pi$
$102$	−4.61187	−0.456643
$103$	7.81548	0.770082	0.385041	−	0.922899i	$-0.374187\pi$
$103$	7.81548	0.770082	0.385041	+	0.922899i	$0.374187\pi$
$104$	−1.00000	−0.0980581
$105$	8.39708	0.819472
$106$	1.00000	0.0971286
$107$	−11.1579	−1.07867	−0.539335	−	0.842091i	$-0.681324\pi$
$107$	−11.1579	−1.07867	−0.539335	+	0.842091i	$0.681324\pi$
$108$	1.00000	0.0962250
$109$	−14.4182	−1.38101	−0.690507	−	0.723325i	$-0.742613\pi$
$109$	−14.4182	−1.38101	−0.690507	+	0.723325i	$0.742613\pi$
$110$	9.67321	0.922304
$111$	6.80850	0.646234
$112$	2.84393	0.268726
$113$	6.60572	0.621414	0.310707	−	0.950506i	$-0.399434\pi$
$113$	6.60572	0.621414	0.310707	+	0.950506i	$0.399434\pi$
$114$	2.77905	0.260281
$115$	−25.7797	−2.40397
$116$	3.69632	0.343195
$117$	−1.00000	−0.0924500
$118$	−4.96398	−0.456972
$119$	−13.1158	−1.20232
$120$	2.95264	0.269538
$121$	−0.266996	−0.0242724
$122$	0.744532	0.0674067
$123$	−3.86818	−0.348782
$124$	4.04675	0.363409
$125$	−3.78509	−0.338549
$126$	2.84393	0.253357
$127$	−21.7829	−1.93292	−0.966460	−	0.256819i	$-0.917326\pi$
$127$	−21.7829	−1.93292	−0.966460	+	0.256819i	$0.917326\pi$
$128$	1.00000	0.0883883
$129$	−7.96045	−0.700878
$130$	−2.95264	−0.258963
$131$	10.1364	0.885624	0.442812	−	0.896614i	$-0.353981\pi$
$131$	10.1364	0.885624	0.442812	+	0.896614i	$0.353981\pi$
$132$	3.27613	0.285150
$133$	7.90340	0.685312
$134$	−5.19687	−0.448941
$135$	2.95264	0.254123
$136$	−4.61187	−0.395464
$137$	−0.968941	−0.0827822	−0.0413911	−	0.999143i	$-0.513179\pi$
$137$	−0.968941	−0.0827822	−0.0413911	+	0.999143i	$0.513179\pi$
$138$	−8.73107	−0.743238
$139$	−6.05549	−0.513620	−0.256810	−	0.966462i	$-0.582671\pi$
$139$	−6.05549	−0.513620	−0.256810	+	0.966462i	$0.582671\pi$
$140$	8.39708	0.709683
$141$	−1.74898	−0.147291
$142$	1.86113	0.156183
$143$	−3.27613	−0.273963
$144$	1.00000	0.0833333
$145$	10.9139	0.906349
$146$	0.0164471	0.00136117
$147$	1.08792	0.0897304
$148$	6.80850	0.559655
$149$	5.34941	0.438240	0.219120	−	0.975698i	$-0.429681\pi$
$149$	5.34941	0.438240	0.219120	+	0.975698i	$0.429681\pi$
$150$	3.71806	0.303579
$151$	−10.1818	−0.828585	−0.414292	−	0.910144i	$-0.635971\pi$
$151$	−10.1818	−0.828585	−0.414292	+	0.910144i	$0.635971\pi$
$152$	2.77905	0.225410
$153$	−4.61187	−0.372847
$154$	9.31707	0.750791
$155$	11.9486	0.959733
$156$	−1.00000	−0.0800641
$157$	−6.19431	−0.494360	−0.247180	−	0.968970i	$-0.579504\pi$
$157$	−6.19431	−0.494360	−0.247180	+	0.968970i	$0.579504\pi$
$158$	10.3228	0.821235
$159$	1.00000	0.0793052
$160$	2.95264	0.233426
$161$	−24.8305	−1.95692
$162$	1.00000	0.0785674
$163$	−1.96681	−0.154052	−0.0770262	−	0.997029i	$-0.524543\pi$
$163$	−1.96681	−0.154052	−0.0770262	+	0.997029i	$0.524543\pi$
$164$	−3.86818	−0.302054
$165$	9.67321	0.753058
$166$	0.598010	0.0464146
$167$	−13.0377	−1.00889	−0.504443	−	0.863445i	$-0.668302\pi$
$167$	−13.0377	−1.00889	−0.504443	+	0.863445i	$0.668302\pi$
$168$	2.84393	0.219414
$169$	1.00000	0.0769231
$170$	−13.6172	−1.04439
$171$	2.77905	0.212519
$172$	−7.96045	−0.606978
$173$	12.2974	0.934954	0.467477	−	0.884005i	$-0.345163\pi$
$173$	12.2974	0.934954	0.467477	+	0.884005i	$0.345163\pi$
$174$	3.69632	0.280217
$175$	10.5739	0.799312
$176$	3.27613	0.246947
$177$	−4.96398	−0.373116
$178$	−18.2102	−1.36492
$179$	15.9934	1.19540	0.597701	−	0.801719i	$-0.296081\pi$
$179$	15.9934	1.19540	0.597701	+	0.801719i	$0.296081\pi$
$180$	2.95264	0.220077
$181$	18.9180	1.40616	0.703082	−	0.711109i	$-0.251807\pi$
$181$	18.9180	1.40616	0.703082	+	0.711109i	$0.251807\pi$
$182$	−2.84393	−0.210806
$183$	0.744532	0.0550374
$184$	−8.73107	−0.643663
$185$	20.1030	1.47800
$186$	4.04675	0.296722
$187$	−15.1091	−1.10488
$188$	−1.74898	−0.127557
$189$	2.84393	0.206865
$190$	8.20551	0.595290
$191$	11.6429	0.842451	0.421226	−	0.906956i	$-0.361600\pi$
$191$	11.6429	0.842451	0.421226	+	0.906956i	$0.361600\pi$
$192$	1.00000	0.0721688
$193$	11.8002	0.849399	0.424700	−	0.905334i	$-0.360380\pi$
$193$	11.8002	0.849399	0.424700	+	0.905334i	$0.360380\pi$
$194$	−3.71353	−0.266616
$195$	−2.95264	−0.211443
$196$	1.08792	0.0777088
$197$	15.5562	1.10833	0.554167	−	0.832406i	$-0.313037\pi$
$197$	15.5562	1.10833	0.554167	+	0.832406i	$0.313037\pi$
$198$	3.27613	0.232824
$199$	−0.957556	−0.0678793	−0.0339397	−	0.999424i	$-0.510805\pi$
$199$	−0.957556	−0.0678793	−0.0339397	+	0.999424i	$0.510805\pi$
$200$	3.71806	0.262907
$201$	−5.19687	−0.366559
$202$	7.85142	0.552424
$203$	10.5121	0.737802
$204$	−4.61187	−0.322895
$205$	−11.4213	−0.797701
$206$	7.81548	0.544530
$207$	−8.73107	−0.606851
$208$	−1.00000	−0.0693375
$209$	9.10451	0.629772
$210$	8.39708	0.579454
$211$	13.6803	0.941788	0.470894	−	0.882190i	$-0.343931\pi$
$211$	13.6803	0.941788	0.470894	+	0.882190i	$0.343931\pi$
$212$	1.00000	0.0686803
$213$	1.86113	0.127523
$214$	−11.1579	−0.762735
$215$	−23.5043	−1.60298
$216$	1.00000	0.0680414
$217$	11.5087	0.781259
$218$	−14.4182	−0.976525
$219$	0.0164471	0.00111139
$220$	9.67321	0.652168
$221$	4.61187	0.310228
$222$	6.80850	0.456956
$223$	8.05388	0.539328	0.269664	−	0.962954i	$-0.413087\pi$
$223$	8.05388	0.539328	0.269664	+	0.962954i	$0.413087\pi$
$224$	2.84393	0.190018
$225$	3.71806	0.247871
$226$	6.60572	0.439406
$227$	−12.7907	−0.848946	−0.424473	−	0.905441i	$-0.639541\pi$
$227$	−12.7907	−0.848946	−0.424473	+	0.905441i	$0.639541\pi$
$228$	2.77905	0.184047
$229$	12.2201	0.807525	0.403763	−	0.914864i	$-0.367702\pi$
$229$	12.2201	0.807525	0.403763	+	0.914864i	$0.367702\pi$
$230$	−25.7797	−1.69986
$231$	9.31707	0.613018
$232$	3.69632	0.242675
$233$	−18.3744	−1.20374	−0.601872	−	0.798592i	$-0.705578\pi$
$233$	−18.3744	−1.20374	−0.601872	+	0.798592i	$0.705578\pi$
$234$	−1.00000	−0.0653720
$235$	−5.16410	−0.336869
$236$	−4.96398	−0.323128
$237$	10.3228	0.670535
$238$	−13.1158	−0.850172
$239$	−20.6989	−1.33890	−0.669450	−	0.742857i	$-0.733470\pi$
$239$	−20.6989	−1.33890	−0.669450	+	0.742857i	$0.733470\pi$
$240$	2.95264	0.190592
$241$	26.1603	1.68513	0.842566	−	0.538593i	$-0.181044\pi$
$241$	26.1603	1.68513	0.842566	+	0.538593i	$0.181044\pi$
$242$	−0.266996	−0.0171632
$243$	1.00000	0.0641500
$244$	0.744532	0.0476638
$245$	3.21224	0.205223
$246$	−3.86818	−0.246626
$247$	−2.77905	−0.176826
$248$	4.04675	0.256969
$249$	0.598010	0.0378973
$250$	−3.78509	−0.239390
$251$	6.94432	0.438321	0.219161	−	0.975689i	$-0.429668\pi$
$251$	6.94432	0.438321	0.219161	+	0.975689i	$0.429668\pi$
$252$	2.84393	0.179151
$253$	−28.6041	−1.79832
$254$	−21.7829	−1.36678
$255$	−13.6172	−0.852740
$256$	1.00000	0.0625000
$257$	−22.0543	−1.37571	−0.687853	−	0.725850i	$-0.741447\pi$
$257$	−22.0543	−1.37571	−0.687853	+	0.725850i	$0.741447\pi$
$258$	−7.96045	−0.495596
$259$	19.3629	1.20315
$260$	−2.95264	−0.183115
$261$	3.69632	0.228796
$262$	10.1364	0.626231
$263$	12.8686	0.793511	0.396756	−	0.917924i	$-0.370136\pi$
$263$	12.8686	0.793511	0.396756	+	0.917924i	$0.370136\pi$
$264$	3.27613	0.201632
$265$	2.95264	0.181379
$266$	7.90340	0.484589
$267$	−18.2102	−1.11445
$268$	−5.19687	−0.317449
$269$	−8.95740	−0.546142	−0.273071	−	0.961994i	$-0.588039\pi$
$269$	−8.95740	−0.546142	−0.273071	+	0.961994i	$0.588039\pi$
$270$	2.95264	0.179692
$271$	5.13369	0.311849	0.155925	−	0.987769i	$-0.450164\pi$
$271$	5.13369	0.311849	0.155925	+	0.987769i	$0.450164\pi$
$272$	−4.61187	−0.279635
$273$	−2.84393	−0.172122
$274$	−0.968941	−0.0585359
$275$	12.1808	0.734533
$276$	−8.73107	−0.525549
$277$	2.17268	0.130543	0.0652717	−	0.997868i	$-0.479209\pi$
$277$	2.17268	0.130543	0.0652717	+	0.997868i	$0.479209\pi$
$278$	−6.05549	−0.363184
$279$	4.04675	0.242273
$280$	8.39708	0.501822
$281$	4.58911	0.273764	0.136882	−	0.990587i	$-0.456292\pi$
$281$	4.58911	0.273764	0.136882	+	0.990587i	$0.456292\pi$
$282$	−1.74898	−0.104150
$283$	14.8125	0.880513	0.440257	−	0.897872i	$-0.354887\pi$
$283$	14.8125	0.880513	0.440257	+	0.897872i	$0.354887\pi$
$284$	1.86113	0.110438
$285$	8.20551	0.486053
$286$	−3.27613	−0.193721
$287$	−11.0008	−0.649359
$288$	1.00000	0.0589256
$289$	4.26930	0.251135
$290$	10.9139	0.640885
$291$	−3.71353	−0.217691
$292$	0.0164471	0.000962491 0
$293$	−12.0571	−0.704386	−0.352193	−	0.935927i	$-0.614564\pi$
$293$	−12.0571	−0.704386	−0.352193	+	0.935927i	$0.614564\pi$
$294$	1.08792	0.0634490
$295$	−14.6568	−0.853354
$296$	6.80850	0.395736
$297$	3.27613	0.190100
$298$	5.34941	0.309883
$299$	8.73107	0.504931
$300$	3.71806	0.214663
$301$	−22.6389	−1.30489
$302$	−10.1818	−0.585898
$303$	7.85142	0.451052
$304$	2.77905	0.159389
$305$	2.19833	0.125876
$306$	−4.61187	−0.263643
$307$	27.8541	1.58972	0.794858	−	0.606796i	$-0.207546\pi$
$307$	27.8541	1.58972	0.794858	+	0.606796i	$0.207546\pi$
$308$	9.31707	0.530889
$309$	7.81548	0.444607
$310$	11.9486	0.678634
$311$	−17.1346	−0.971615	−0.485808	−	0.874066i	$-0.661474\pi$
$311$	−17.1346	−0.971615	−0.485808	+	0.874066i	$0.661474\pi$
$312$	−1.00000	−0.0566139
$313$	−7.31890	−0.413689	−0.206844	−	0.978374i	$-0.566319\pi$
$313$	−7.31890	−0.413689	−0.206844	+	0.978374i	$0.566319\pi$
$314$	−6.19431	−0.349565
$315$	8.39708	0.473122
$316$	10.3228	0.580701
$317$	10.2670	0.576650	0.288325	−	0.957533i	$-0.406902\pi$
$317$	10.2670	0.576650	0.288325	+	0.957533i	$0.406902\pi$
$318$	1.00000	0.0560772
$319$	12.1096	0.678008
$320$	2.95264	0.165057
$321$	−11.1579	−0.622771
$322$	−24.8305	−1.38375
$323$	−12.8166	−0.713134
$324$	1.00000	0.0555556
$325$	−3.71806	−0.206241
$326$	−1.96681	−0.108932
$327$	−14.4182	−0.797329
$328$	−3.86818	−0.213585
$329$	−4.97397	−0.274224
$330$	9.67321	0.532493
$331$	24.8604	1.36645	0.683225	−	0.730208i	$-0.260577\pi$
$331$	24.8604	1.36645	0.683225	+	0.730208i	$0.260577\pi$
$332$	0.598010	0.0328201
$333$	6.80850	0.373103
$334$	−13.0377	−0.713390
$335$	−15.3445	−0.838358
$336$	2.84393	0.155149
$337$	−9.23715	−0.503179	−0.251590	−	0.967834i	$-0.580953\pi$
$337$	−9.23715	−0.503179	−0.251590	+	0.967834i	$0.580953\pi$
$338$	1.00000	0.0543928
$339$	6.60572	0.358774
$340$	−13.6172	−0.738494
$341$	13.2577	0.717943
$342$	2.77905	0.150274
$343$	−16.8135	−0.907845
$344$	−7.96045	−0.429198
$345$	−25.7797	−1.38793
$346$	12.2974	0.661112
$347$	7.86180	0.422044	0.211022	−	0.977481i	$-0.432321\pi$
$347$	7.86180	0.422044	0.211022	+	0.977481i	$0.432321\pi$
$348$	3.69632	0.198143
$349$	4.23604	0.226750	0.113375	−	0.993552i	$-0.463834\pi$
$349$	4.23604	0.226750	0.113375	+	0.993552i	$0.463834\pi$
$350$	10.5739	0.565199
$351$	−1.00000	−0.0533761
$352$	3.27613	0.174618
$353$	6.51019	0.346502	0.173251	−	0.984878i	$-0.444573\pi$
$353$	6.51019	0.346502	0.173251	+	0.984878i	$0.444573\pi$
$354$	−4.96398	−0.263833
$355$	5.49524	0.291657
$356$	−18.2102	−0.965141
$357$	−13.1158	−0.694162
$358$	15.9934	0.845278
$359$	25.8980	1.36684	0.683422	−	0.730023i	$-0.260491\pi$
$359$	25.8980	1.36684	0.683422	+	0.730023i	$0.260491\pi$
$360$	2.95264	0.155618
$361$	−11.2769	−0.593521
$362$	18.9180	0.994308
$363$	−0.266996	−0.0140137
$364$	−2.84393	−0.149062
$365$	0.0485622	0.00254186
$366$	0.744532	0.0389173
$367$	−32.2042	−1.68105	−0.840524	−	0.541775i	$-0.817753\pi$
$367$	−32.2042	−1.68105	−0.840524	+	0.541775i	$0.817753\pi$
$368$	−8.73107	−0.455138
$369$	−3.86818	−0.201370
$370$	20.1030	1.04511
$371$	2.84393	0.147649
$372$	4.04675	0.209814
$373$	21.2372	1.09962	0.549810	−	0.835290i	$-0.314700\pi$
$373$	21.2372	1.09962	0.549810	+	0.835290i	$0.314700\pi$
$374$	−15.1091	−0.781271
$375$	−3.78509	−0.195461
$376$	−1.74898	−0.0901968
$377$	−3.69632	−0.190370
$378$	2.84393	0.146276
$379$	−2.55494	−0.131238	−0.0656192	−	0.997845i	$-0.520902\pi$
$379$	−2.55494	−0.131238	−0.0656192	+	0.997845i	$0.520902\pi$
$380$	8.20551	0.420934
$381$	−21.7829	−1.11597
$382$	11.6429	0.595703
$383$	−15.4573	−0.789831	−0.394916	−	0.918717i	$-0.629226\pi$
$383$	−15.4573	−0.789831	−0.394916	+	0.918717i	$0.629226\pi$
$384$	1.00000	0.0510310
$385$	27.5099	1.40203
$386$	11.8002	0.600616
$387$	−7.96045	−0.404652
$388$	−3.71353	−0.188526
$389$	6.43431	0.326233	0.163116	−	0.986607i	$-0.447845\pi$
$389$	6.43431	0.326233	0.163116	+	0.986607i	$0.447845\pi$
$390$	−2.95264	−0.149513
$391$	40.2665	2.03636
$392$	1.08792	0.0549484
$393$	10.1364	0.511316
$394$	15.5562	0.783710
$395$	30.4794	1.53358
$396$	3.27613	0.164632
$397$	14.0436	0.704828	0.352414	−	0.935844i	$-0.385361\pi$
$397$	14.0436	0.704828	0.352414	+	0.935844i	$0.385361\pi$
$398$	−0.957556	−0.0479979
$399$	7.90340	0.395665
$400$	3.71806	0.185903
$401$	−27.6387	−1.38021	−0.690105	−	0.723709i	$-0.742436\pi$
$401$	−27.6387	−1.38021	−0.690105	+	0.723709i	$0.742436\pi$
$402$	−5.19687	−0.259196
$403$	−4.04675	−0.201583
$404$	7.85142	0.390623
$405$	2.95264	0.146718
$406$	10.5121	0.521705
$407$	22.3055	1.10564
$408$	−4.61187	−0.228321
$409$	−16.3826	−0.810069	−0.405034	−	0.914301i	$-0.632740\pi$
$409$	−16.3826	−0.810069	−0.405034	+	0.914301i	$0.632740\pi$
$410$	−11.4213	−0.564060
$411$	−0.968941	−0.0477943
$412$	7.81548	0.385041
$413$	−14.1172	−0.694662
$414$	−8.73107	−0.429109
$415$	1.76571	0.0866751
$416$	−1.00000	−0.0490290
$417$	−6.05549	−0.296539
$418$	9.10451	0.445316
$419$	10.5466	0.515234	0.257617	−	0.966247i	$-0.417063\pi$
$419$	10.5466	0.515234	0.257617	+	0.966247i	$0.417063\pi$
$420$	8.39708	0.409736
$421$	2.22913	0.108641	0.0543207	−	0.998524i	$-0.482701\pi$
$421$	2.22913	0.108641	0.0543207	+	0.998524i	$0.482701\pi$
$422$	13.6803	0.665945
$423$	−1.74898	−0.0850383
$424$	1.00000	0.0485643
$425$	−17.1472	−0.831762
$426$	1.86113	0.0901721
$427$	2.11739	0.102468
$428$	−11.1579	−0.539335
$429$	−3.27613	−0.158173
$430$	−23.5043	−1.13348
$431$	−13.2429	−0.637887	−0.318944	−	0.947774i	$-0.603328\pi$
$431$	−13.2429	−0.637887	−0.318944	+	0.947774i	$0.603328\pi$
$432$	1.00000	0.0481125
$433$	−12.7436	−0.612419	−0.306210	−	0.951964i	$-0.599061\pi$
$433$	−12.7436	−0.612419	−0.306210	+	0.951964i	$0.599061\pi$
$434$	11.5087	0.552433
$435$	10.9139	0.523281
$436$	−14.4182	−0.690507
$437$	−24.2640	−1.16071
$438$	0.0164471	0.000785871 0
$439$	28.7032	1.36993	0.684965	−	0.728576i	$-0.259817\pi$
$439$	28.7032	1.36993	0.684965	+	0.728576i	$0.259817\pi$
$440$	9.67321	0.461152
$441$	1.08792	0.0518059
$442$	4.61187	0.219364
$443$	−6.89706	−0.327689	−0.163845	−	0.986486i	$-0.552390\pi$
$443$	−6.89706	−0.327689	−0.163845	+	0.986486i	$0.552390\pi$
$444$	6.80850	0.323117
$445$	−53.7682	−2.54886
$446$	8.05388	0.381362
$447$	5.34941	0.253018
$448$	2.84393	0.134363
$449$	−28.8797	−1.36292	−0.681459	−	0.731856i	$-0.738654\pi$
$449$	−28.8797	−1.36292	−0.681459	+	0.731856i	$0.738654\pi$
$450$	3.71806	0.175271
$451$	−12.6727	−0.596732
$452$	6.60572	0.310707
$453$	−10.1818	−0.478384
$454$	−12.7907	−0.600295
$455$	−8.39708	−0.393661
$456$	2.77905	0.130141
$457$	−26.2039	−1.22577	−0.612884	−	0.790173i	$-0.709991\pi$
$457$	−26.2039	−1.22577	−0.612884	+	0.790173i	$0.709991\pi$
$458$	12.2201	0.571007
$459$	−4.61187	−0.215263
$460$	−25.7797	−1.20198
$461$	10.2595	0.477834	0.238917	−	0.971040i	$-0.423208\pi$
$461$	10.2595	0.477834	0.238917	+	0.971040i	$0.423208\pi$
$462$	9.31707	0.433469
$463$	−4.64413	−0.215831	−0.107916	−	0.994160i	$-0.534418\pi$
$463$	−4.64413	−0.215831	−0.107916	+	0.994160i	$0.534418\pi$
$464$	3.69632	0.171597
$465$	11.9486	0.554102
$466$	−18.3744	−0.851176
$467$	26.5096	1.22672	0.613360	−	0.789803i	$-0.289817\pi$
$467$	26.5096	1.22672	0.613360	+	0.789803i	$0.289817\pi$
$468$	−1.00000	−0.0462250
$469$	−14.7795	−0.682455
$470$	−5.16410	−0.238202
$471$	−6.19431	−0.285419
$472$	−4.96398	−0.228486
$473$	−26.0794	−1.19913
$474$	10.3228	0.474140
$475$	10.3327	0.474095
$476$	−13.1158	−0.601162
$477$	1.00000	0.0457869
$478$	−20.6989	−0.946745
$479$	−3.35501	−0.153294	−0.0766471	−	0.997058i	$-0.524421\pi$
$479$	−3.35501	−0.153294	−0.0766471	+	0.997058i	$0.524421\pi$
$480$	2.95264	0.134769
$481$	−6.80850	−0.310441
$482$	26.1603	1.19157
$483$	−24.8305	−1.12983
$484$	−0.266996	−0.0121362
$485$	−10.9647	−0.497882
$486$	1.00000	0.0453609
$487$	−13.8138	−0.625962	−0.312981	−	0.949759i	$-0.601328\pi$
$487$	−13.8138	−0.625962	−0.312981	+	0.949759i	$0.601328\pi$
$488$	0.744532	0.0337034
$489$	−1.96681	−0.0889422
$490$	3.21224	0.145114
$491$	25.7090	1.16023	0.580115	−	0.814535i	$-0.303008\pi$
$491$	25.7090	1.16023	0.580115	+	0.814535i	$0.303008\pi$
$492$	−3.86818	−0.174391
$493$	−17.0469	−0.767755
$494$	−2.77905	−0.125035
$495$	9.67321	0.434779
$496$	4.04675	0.181704
$497$	5.29292	0.237420
$498$	0.598010	0.0267975
$499$	−2.51342	−0.112516	−0.0562582	−	0.998416i	$-0.517917\pi$
$499$	−2.51342	−0.112516	−0.0562582	+	0.998416i	$0.517917\pi$
$500$	−3.78509	−0.169274
$501$	−13.0377	−0.582480
$502$	6.94432	0.309940
$503$	12.7499	0.568490	0.284245	−	0.958752i	$-0.408257\pi$
$503$	12.7499	0.568490	0.284245	+	0.958752i	$0.408257\pi$
$504$	2.84393	0.126679
$505$	23.1824	1.03160
$506$	−28.6041	−1.27161
$507$	1.00000	0.0444116
$508$	−21.7829	−0.966460
$509$	16.7075	0.740548	0.370274	−	0.928923i	$-0.379264\pi$
$509$	16.7075	0.740548	0.370274	+	0.928923i	$0.379264\pi$
$510$	−13.6172	−0.602978
$511$	0.0467742	0.00206917
$512$	1.00000	0.0441942
$513$	2.77905	0.122698
$514$	−22.0543	−0.972772
$515$	23.0763	1.01686
$516$	−7.96045	−0.350439
$517$	−5.72988	−0.252000
$518$	19.3629	0.850756
$519$	12.2974	0.539796
$520$	−2.95264	−0.129482
$521$	3.38293	0.148209	0.0741045	−	0.997250i	$-0.476390\pi$
$521$	3.38293	0.148209	0.0741045	+	0.997250i	$0.476390\pi$
$522$	3.69632	0.161783
$523$	−30.2443	−1.32249	−0.661246	−	0.750169i	$-0.729972\pi$
$523$	−30.2443	−1.32249	−0.661246	+	0.750169i	$0.729972\pi$
$524$	10.1364	0.442812
$525$	10.5739	0.461483
$526$	12.8686	0.561097
$527$	−18.6631	−0.812976
$528$	3.27613	0.142575
$529$	53.2316	2.31442
$530$	2.95264	0.128254
$531$	−4.96398	−0.215418
$532$	7.90340	0.342656
$533$	3.86818	0.167550
$534$	−18.2102	−0.788034
$535$	−32.9451	−1.42434
$536$	−5.19687	−0.224471
$537$	15.9934	0.690166
$538$	−8.95740	−0.386181
$539$	3.56417	0.153520
$540$	2.95264	0.127061
$541$	38.8481	1.67021	0.835106	−	0.550089i	$-0.185406\pi$
$541$	38.8481	1.67021	0.835106	+	0.550089i	$0.185406\pi$
$542$	5.13369	0.220511
$543$	18.9180	0.811849
$544$	−4.61187	−0.197732
$545$	−42.5718	−1.82357
$546$	−2.84393	−0.121709
$547$	11.1603	0.477179	0.238590	−	0.971121i	$-0.423315\pi$
$547$	11.1603	0.477179	0.238590	+	0.971121i	$0.423315\pi$
$548$	−0.968941	−0.0413911
$549$	0.744532	0.0317758
$550$	12.1808	0.519393
$551$	10.2722	0.437612
$552$	−8.73107	−0.371619
$553$	29.3572	1.24839
$554$	2.17268	0.0923081
$555$	20.1030	0.853326
$556$	−6.05549	−0.256810
$557$	11.0050	0.466295	0.233147	−	0.972441i	$-0.425098\pi$
$557$	11.0050	0.466295	0.233147	+	0.972441i	$0.425098\pi$
$558$	4.04675	0.171313
$559$	7.96045	0.336691
$560$	8.39708	0.354842
$561$	−15.1091	−0.637905
$562$	4.58911	0.193580
$563$	−35.8234	−1.50978	−0.754889	−	0.655852i	$-0.772309\pi$
$563$	−35.8234	−1.50978	−0.754889	+	0.655852i	$0.772309\pi$
$564$	−1.74898	−0.0736453
$565$	19.5043	0.820552
$566$	14.8125	0.622617
$567$	2.84393	0.119434
$568$	1.86113	0.0780913
$569$	−24.7952	−1.03947	−0.519734	−	0.854328i	$-0.673969\pi$
$569$	−24.7952	−1.03947	−0.519734	+	0.854328i	$0.673969\pi$
$570$	8.20551	0.343691
$571$	31.6327	1.32379	0.661894	−	0.749598i	$-0.269753\pi$
$571$	31.6327	1.32379	0.661894	+	0.749598i	$0.269753\pi$
$572$	−3.27613	−0.136982
$573$	11.6429	0.486389
$574$	−11.0008	−0.459166
$575$	−32.4627	−1.35379
$576$	1.00000	0.0416667
$577$	−27.3922	−1.14035	−0.570176	−	0.821523i	$-0.693125\pi$
$577$	−27.3922	−1.14035	−0.570176	+	0.821523i	$0.693125\pi$
$578$	4.26930	0.177579
$579$	11.8002	0.490401
$580$	10.9139	0.453174
$581$	1.70070	0.0705568
$582$	−3.71353	−0.153931
$583$	3.27613	0.135683
$584$	0.0164471	0.000680584 0
$585$	−2.95264	−0.122077
$586$	−12.0571	−0.498076
$587$	40.4010	1.66753	0.833763	−	0.552122i	$-0.186182\pi$
$587$	40.4010	1.66753	0.833763	+	0.552122i	$0.186182\pi$
$588$	1.08792	0.0448652
$589$	11.2461	0.463388
$590$	−14.6568	−0.603412
$591$	15.5562	0.639897
$592$	6.80850	0.279828
$593$	2.84699	0.116912	0.0584559	−	0.998290i	$-0.481382\pi$
$593$	2.84699	0.116912	0.0584559	+	0.998290i	$0.481382\pi$
$594$	3.27613	0.134421
$595$	−38.7262	−1.58762
$596$	5.34941	0.219120
$597$	−0.957556	−0.0391902
$598$	8.73107	0.357040
$599$	10.0851	0.412068	0.206034	−	0.978545i	$-0.433944\pi$
$599$	10.0851	0.412068	0.206034	+	0.978545i	$0.433944\pi$
$600$	3.71806	0.151789
$601$	35.0571	1.43001	0.715005	−	0.699119i	$-0.246424\pi$
$601$	35.0571	1.43001	0.715005	+	0.699119i	$0.246424\pi$
$602$	−22.6389	−0.922694
$603$	−5.19687	−0.211633
$604$	−10.1818	−0.414292
$605$	−0.788342	−0.0320507
$606$	7.85142	0.318942
$607$	−6.74002	−0.273569	−0.136784	−	0.990601i	$-0.543677\pi$
$607$	−6.74002	−0.273569	−0.136784	+	0.990601i	$0.543677\pi$
$608$	2.77905	0.112705
$609$	10.5121	0.425970
$610$	2.19833	0.0890079
$611$	1.74898	0.0707562
$612$	−4.61187	−0.186424
$613$	18.1510	0.733111	0.366556	−	0.930396i	$-0.380537\pi$
$613$	18.1510	0.733111	0.366556	+	0.930396i	$0.380537\pi$
$614$	27.8541	1.12410
$615$	−11.4213	−0.460553
$616$	9.31707	0.375395
$617$	−23.4994	−0.946052	−0.473026	−	0.881049i	$-0.656838\pi$
$617$	−23.4994	−0.946052	−0.473026	+	0.881049i	$0.656838\pi$
$618$	7.81548	0.314385
$619$	6.45697	0.259527	0.129764	−	0.991545i	$-0.458578\pi$
$619$	6.45697	0.259527	0.129764	+	0.991545i	$0.458578\pi$
$620$	11.9486	0.479867
$621$	−8.73107	−0.350366
$622$	−17.1346	−0.687036
$623$	−51.7886	−2.07487
$624$	−1.00000	−0.0400320
$625$	−29.7663	−1.19065
$626$	−7.31890	−0.292522
$627$	9.10451	0.363599
$628$	−6.19431	−0.247180
$629$	−31.3999	−1.25199
$630$	8.39708	0.334548
$631$	−29.7971	−1.18620	−0.593101	−	0.805128i	$-0.702097\pi$
$631$	−29.7971	−1.18620	−0.593101	+	0.805128i	$0.702097\pi$
$632$	10.3228	0.410617
$633$	13.6803	0.543742
$634$	10.2670	0.407753
$635$	−64.3170	−2.55234
$636$	1.00000	0.0396526
$637$	−1.08792	−0.0431051
$638$	12.1096	0.479424
$639$	1.86113	0.0736252
$640$	2.95264	0.116713
$641$	17.8466	0.704898	0.352449	−	0.935831i	$-0.385349\pi$
$641$	17.8466	0.704898	0.352449	+	0.935831i	$0.385349\pi$
$642$	−11.1579	−0.440365
$643$	20.8329	0.821570	0.410785	−	0.911732i	$-0.365255\pi$
$643$	20.8329	0.821570	0.410785	+	0.911732i	$0.365255\pi$
$644$	−24.8305	−0.978460
$645$	−23.5043	−0.925481
$646$	−12.8166	−0.504262
$647$	36.3994	1.43101	0.715505	−	0.698608i	$-0.246197\pi$
$647$	36.3994	1.43101	0.715505	+	0.698608i	$0.246197\pi$
$648$	1.00000	0.0392837
$649$	−16.2626	−0.638364
$650$	−3.71806	−0.145834
$651$	11.5087	0.451060
$652$	−1.96681	−0.0770262
$653$	−44.8501	−1.75512	−0.877560	−	0.479467i	$-0.840830\pi$
$653$	−44.8501	−1.75512	−0.877560	+	0.479467i	$0.840830\pi$
$654$	−14.4182	−0.563797
$655$	29.9292	1.16943
$656$	−3.86818	−0.151027
$657$	0.0164471	0.000641661 0
$658$	−4.97397	−0.193906
$659$	−38.5491	−1.50166	−0.750829	−	0.660497i	$-0.770346\pi$
$659$	−38.5491	−1.50166	−0.750829	+	0.660497i	$0.770346\pi$
$660$	9.67321	0.376529
$661$	−20.8891	−0.812490	−0.406245	−	0.913764i	$-0.633162\pi$
$661$	−20.8891	−0.812490	−0.406245	+	0.913764i	$0.633162\pi$
$662$	24.8604	0.966226
$663$	4.61187	0.179110
$664$	0.598010	0.0232073
$665$	23.3359	0.904927
$666$	6.80850	0.263824
$667$	−32.2728	−1.24961
$668$	−13.0377	−0.504443
$669$	8.05388	0.311381
$670$	−15.3445	−0.592808
$671$	2.43918	0.0941635
$672$	2.84393	0.109707
$673$	−39.7092	−1.53068	−0.765339	−	0.643627i	$-0.777429\pi$
$673$	−39.7092	−1.53068	−0.765339	+	0.643627i	$0.777429\pi$
$674$	−9.23715	−0.355802
$675$	3.71806	0.143108
$676$	1.00000	0.0384615
$677$	−15.7415	−0.604995	−0.302497	−	0.953150i	$-0.597820\pi$
$677$	−15.7415	−0.604995	−0.302497	+	0.953150i	$0.597820\pi$
$678$	6.60572	0.253691
$679$	−10.5610	−0.405295
$680$	−13.6172	−0.522194
$681$	−12.7907	−0.490139
$682$	13.2577	0.507662
$683$	5.24960	0.200870	0.100435	−	0.994944i	$-0.467977\pi$
$683$	5.24960	0.200870	0.100435	+	0.994944i	$0.467977\pi$
$684$	2.77905	0.106259
$685$	−2.86093	−0.109311
$686$	−16.8135	−0.641943
$687$	12.2201	0.466225
$688$	−7.96045	−0.303489
$689$	−1.00000	−0.0380970
$690$	−25.7797	−0.981415
$691$	30.9131	1.17599	0.587995	−	0.808865i	$-0.299918\pi$
$691$	30.9131	1.17599	0.587995	+	0.808865i	$0.299918\pi$
$692$	12.2974	0.467477
$693$	9.31707	0.353926
$694$	7.86180	0.298430
$695$	−17.8797	−0.678214
$696$	3.69632	0.140109
$697$	17.8395	0.675721
$698$	4.23604	0.160337
$699$	−18.3744	−0.694982
$700$	10.5739	0.399656
$701$	−21.0536	−0.795184	−0.397592	−	0.917562i	$-0.630154\pi$
$701$	−21.0536	−0.795184	−0.397592	+	0.917562i	$0.630154\pi$
$702$	−1.00000	−0.0377426
$703$	18.9211	0.713624
$704$	3.27613	0.123474
$705$	−5.16410	−0.194491
$706$	6.51019	0.245014
$707$	22.3289	0.839764
$708$	−4.96398	−0.186558
$709$	9.13516	0.343078	0.171539	−	0.985177i	$-0.445126\pi$
$709$	9.13516	0.343078	0.171539	+	0.985177i	$0.445126\pi$
$710$	5.49524	0.206233
$711$	10.3228	0.387134
$712$	−18.2102	−0.682458
$713$	−35.3324	−1.32321
$714$	−13.1158	−0.490847
$715$	−9.67321	−0.361758
$716$	15.9934	0.597701
$717$	−20.6989	−0.773014
$718$	25.8980	0.966505
$719$	−5.32214	−0.198482	−0.0992411	−	0.995063i	$-0.531641\pi$
$719$	−5.32214	−0.198482	−0.0992411	+	0.995063i	$0.531641\pi$
$720$	2.95264	0.110038
$721$	22.2267	0.827764
$722$	−11.2769	−0.419683
$723$	26.1603	0.972911
$724$	18.9180	0.703082
$725$	13.7431	0.510408
$726$	−0.266996	−0.00990915
$727$	23.0376	0.854418	0.427209	−	0.904153i	$-0.359497\pi$
$727$	23.0376	0.854418	0.427209	+	0.904153i	$0.359497\pi$
$728$	−2.84393	−0.105403
$729$	1.00000	0.0370370
$730$	0.0485622	0.00179737
$731$	36.7125	1.35786
$732$	0.744532	0.0275187
$733$	10.2996	0.380423	0.190211	−	0.981743i	$-0.439083\pi$
$733$	10.2996	0.380423	0.190211	+	0.981743i	$0.439083\pi$
$734$	−32.2042	−1.18868
$735$	3.21224	0.118485
$736$	−8.73107	−0.321831
$737$	−17.0256	−0.627146
$738$	−3.86818	−0.142390
$739$	−4.75424	−0.174888	−0.0874438	−	0.996169i	$-0.527870\pi$
$739$	−4.75424	−0.174888	−0.0874438	+	0.996169i	$0.527870\pi$
$740$	20.1030	0.739002
$741$	−2.77905	−0.102091
$742$	2.84393	0.104404
$743$	2.33000	0.0854794	0.0427397	−	0.999086i	$-0.486391\pi$
$743$	2.33000	0.0854794	0.0427397	+	0.999086i	$0.486391\pi$
$744$	4.04675	0.148361
$745$	15.7949	0.578679
$746$	21.2372	0.777549
$747$	0.598010	0.0218800
$748$	−15.1091	−0.552442
$749$	−31.7321	−1.15947
$750$	−3.78509	−0.138212
$751$	22.1546	0.808432	0.404216	−	0.914664i	$-0.367544\pi$
$751$	22.1546	0.808432	0.404216	+	0.914664i	$0.367544\pi$
$752$	−1.74898	−0.0637787
$753$	6.94432	0.253065
$754$	−3.69632	−0.134612
$755$	−30.0632	−1.09411
$756$	2.84393	0.103433
$757$	1.98901	0.0722918	0.0361459	−	0.999347i	$-0.488492\pi$
$757$	1.98901	0.0722918	0.0361459	+	0.999347i	$0.488492\pi$
$758$	−2.55494	−0.0927995
$759$	−28.6041	−1.03826
$760$	8.20551	0.297645
$761$	−25.7628	−0.933902	−0.466951	−	0.884283i	$-0.654648\pi$
$761$	−25.7628	−0.933902	−0.466951	+	0.884283i	$0.654648\pi$
$762$	−21.7829	−0.789111
$763$	−41.0044	−1.48446
$764$	11.6429	0.421226
$765$	−13.6172	−0.492330
$766$	−15.4573	−0.558495
$767$	4.96398	0.179239
$768$	1.00000	0.0360844
$769$	35.8600	1.29315	0.646573	−	0.762853i	$-0.276202\pi$
$769$	35.8600	1.29315	0.646573	+	0.762853i	$0.276202\pi$
$770$	27.5099	0.991388
$771$	−22.0543	−0.794265
$772$	11.8002	0.424700
$773$	−16.4956	−0.593305	−0.296653	−	0.954985i	$-0.595870\pi$
$773$	−16.4956	−0.593305	−0.296653	+	0.954985i	$0.595870\pi$
$774$	−7.96045	−0.286132
$775$	15.0461	0.540471
$776$	−3.71353	−0.133308
$777$	19.3629	0.694639
$778$	6.43431	0.230681
$779$	−10.7499	−0.385154
$780$	−2.95264	−0.105721
$781$	6.09730	0.218178
$782$	40.2665	1.43993
$783$	3.69632	0.132096
$784$	1.08792	0.0388544
$785$	−18.2896	−0.652782
$786$	10.1364	0.361555
$787$	26.7945	0.955122	0.477561	−	0.878598i	$-0.341521\pi$
$787$	26.7945	0.955122	0.477561	+	0.878598i	$0.341521\pi$
$788$	15.5562	0.554167
$789$	12.8686	0.458134
$790$	30.4794	1.08441
$791$	18.7862	0.667960
$792$	3.27613	0.116412
$793$	−0.744532	−0.0264391
$794$	14.0436	0.498389
$795$	2.95264	0.104719
$796$	−0.957556	−0.0339397
$797$	−37.1774	−1.31689	−0.658445	−	0.752628i	$-0.728786\pi$
$797$	−37.1774	−1.31689	−0.658445	+	0.752628i	$0.728786\pi$
$798$	7.90340	0.279778
$799$	8.06606	0.285357
$800$	3.71806	0.131453
$801$	−18.2102	−0.643427
$802$	−27.6387	−0.975956
$803$	0.0538826	0.00190148
$804$	−5.19687	−0.183279
$805$	−73.3155	−2.58403
$806$	−4.04675	−0.142541
$807$	−8.95740	−0.315315
$808$	7.85142	0.276212
$809$	−33.1107	−1.16411	−0.582056	−	0.813149i	$-0.697751\pi$
$809$	−33.1107	−1.16411	−0.582056	+	0.813149i	$0.697751\pi$
$810$	2.95264	0.103745
$811$	3.74128	0.131374	0.0656870	−	0.997840i	$-0.479076\pi$
$811$	3.74128	0.131374	0.0656870	+	0.997840i	$0.479076\pi$
$812$	10.5121	0.368901
$813$	5.13369	0.180046
$814$	22.3055	0.781807
$815$	−5.80727	−0.203420
$816$	−4.61187	−0.161448
$817$	−22.1224	−0.773966
$818$	−16.3826	−0.572805
$819$	−2.84393	−0.0993749
$820$	−11.4213	−0.398851
$821$	−50.0621	−1.74718	−0.873589	−	0.486664i	$-0.838214\pi$
$821$	−50.0621	−1.74718	−0.873589	+	0.486664i	$0.838214\pi$
$822$	−0.968941	−0.0337957
$823$	−10.7192	−0.373649	−0.186824	−	0.982393i	$-0.559820\pi$
$823$	−10.7192	−0.373649	−0.186824	+	0.982393i	$0.559820\pi$
$824$	7.81548	0.272265
$825$	12.1808	0.424083
$826$	−14.1172	−0.491200
$827$	−25.8657	−0.899439	−0.449719	−	0.893170i	$-0.648476\pi$
$827$	−25.8657	−0.899439	−0.449719	+	0.893170i	$0.648476\pi$
$828$	−8.73107	−0.303426
$829$	−28.8270	−1.00120	−0.500601	−	0.865678i	$-0.666888\pi$
$829$	−28.8270	−1.00120	−0.500601	+	0.865678i	$0.666888\pi$
$830$	1.76571	0.0612886
$831$	2.17268	0.0753693
$832$	−1.00000	−0.0346688
$833$	−5.01736	−0.173841
$834$	−6.05549	−0.209684
$835$	−38.4955	−1.33219
$836$	9.10451	0.314886
$837$	4.04675	0.139876
$838$	10.5466	0.364325
$839$	4.90856	0.169462	0.0847312	−	0.996404i	$-0.472997\pi$
$839$	4.90856	0.169462	0.0847312	+	0.996404i	$0.472997\pi$
$840$	8.39708	0.289727
$841$	−15.3372	−0.528870
$842$	2.22913	0.0768210
$843$	4.58911	0.158057
$844$	13.6803	0.470894
$845$	2.95264	0.101574
$846$	−1.74898	−0.0601312
$847$	−0.759317	−0.0260905
$848$	1.00000	0.0343401
$849$	14.8125	0.508365
$850$	−17.1472	−0.588144
$851$	−59.4455	−2.03776
$852$	1.86113	0.0637613
$853$	20.3289	0.696048	0.348024	−	0.937486i	$-0.386853\pi$
$853$	20.3289	0.696048	0.348024	+	0.937486i	$0.386853\pi$
$854$	2.11739	0.0724558
$855$	8.20551	0.280623
$856$	−11.1579	−0.381368
$857$	−39.3960	−1.34574	−0.672870	−	0.739761i	$-0.734939\pi$
$857$	−39.3960	−1.34574	−0.672870	+	0.739761i	$0.734939\pi$
$858$	−3.27613	−0.111845
$859$	−2.00677	−0.0684702	−0.0342351	−	0.999414i	$-0.510900\pi$
$859$	−2.00677	−0.0684702	−0.0342351	+	0.999414i	$0.510900\pi$
$860$	−23.5043	−0.801490
$861$	−11.0008	−0.374907
$862$	−13.2429	−0.451054
$863$	−2.58756	−0.0880816	−0.0440408	−	0.999030i	$-0.514023\pi$
$863$	−2.58756	−0.0880816	−0.0440408	+	0.999030i	$0.514023\pi$
$864$	1.00000	0.0340207
$865$	36.3098	1.23457
$866$	−12.7436	−0.433046
$867$	4.26930	0.144993
$868$	11.5087	0.390629
$869$	33.8187	1.14722
$870$	10.9139	0.370015
$871$	5.19687	0.176089
$872$	−14.4182	−0.488262
$873$	−3.71353	−0.125684
$874$	−24.2640	−0.820743
$875$	−10.7645	−0.363907
$876$	0.0164471	0.000555694 0
$877$	−13.9377	−0.470644	−0.235322	−	0.971917i	$-0.575614\pi$
$877$	−13.9377	−0.470644	−0.235322	+	0.971917i	$0.575614\pi$
$878$	28.7032	0.968687
$879$	−12.0571	−0.406678
$880$	9.67321	0.326084
$881$	−29.3835	−0.989956	−0.494978	−	0.868905i	$-0.664824\pi$
$881$	−29.3835	−0.989956	−0.494978	+	0.868905i	$0.664824\pi$
$882$	1.08792	0.0366323
$883$	52.8509	1.77858	0.889288	−	0.457348i	$-0.151201\pi$
$883$	52.8509	1.77858	0.889288	+	0.457348i	$0.151201\pi$
$884$	4.61187	0.155114
$885$	−14.6568	−0.492684
$886$	−6.89706	−0.231711
$887$	53.1972	1.78619	0.893094	−	0.449871i	$-0.148530\pi$
$887$	53.1972	1.78619	0.893094	+	0.449871i	$0.148530\pi$
$888$	6.80850	0.228478
$889$	−61.9490	−2.07770
$890$	−53.7682	−1.80231
$891$	3.27613	0.109754
$892$	8.05388	0.269664
$893$	−4.86050	−0.162650
$894$	5.34941	0.178911
$895$	47.2227	1.57848
$896$	2.84393	0.0950089
$897$	8.73107	0.291522
$898$	−28.8797	−0.963728
$899$	14.9581	0.498880
$900$	3.71806	0.123935
$901$	−4.61187	−0.153644
$902$	−12.6727	−0.421953
$903$	−22.6389	−0.753376
$904$	6.60572	0.219703
$905$	55.8580	1.85678
$906$	−10.1818	−0.338268
$907$	−14.5224	−0.482208	−0.241104	−	0.970499i	$-0.577509\pi$
$907$	−14.5224	−0.482208	−0.241104	+	0.970499i	$0.577509\pi$
$908$	−12.7907	−0.424473
$909$	7.85142	0.260415
$910$	−8.39708	−0.278361
$911$	38.9308	1.28983	0.644917	−	0.764252i	$-0.276892\pi$
$911$	38.9308	1.28983	0.644917	+	0.764252i	$0.276892\pi$
$912$	2.77905	0.0920234
$913$	1.95916	0.0648386
$914$	−26.2039	−0.866748
$915$	2.19833	0.0726746
$916$	12.2201	0.403763
$917$	28.8273	0.951961
$918$	−4.61187	−0.152214
$919$	10.4354	0.344232	0.172116	−	0.985077i	$-0.444940\pi$
$919$	10.4354	0.344232	0.172116	+	0.985077i	$0.444940\pi$
$920$	−25.7797	−0.849931
$921$	27.8541	0.917822
$922$	10.2595	0.337880
$923$	−1.86113	−0.0612598
$924$	9.31707	0.306509
$925$	25.3144	0.832333
$926$	−4.64413	−0.152616
$927$	7.81548	0.256694
$928$	3.69632	0.121338
$929$	13.5264	0.443788	0.221894	−	0.975071i	$-0.428776\pi$
$929$	13.5264	0.443788	0.221894	+	0.975071i	$0.428776\pi$
$930$	11.9486	0.391809
$931$	3.02339	0.0990876
$932$	−18.3744	−0.601872
$933$	−17.1346	−0.560962
$934$	26.5096	0.867422
$935$	−44.6115	−1.45895
$936$	−1.00000	−0.0326860
$937$	−17.9506	−0.586420	−0.293210	−	0.956048i	$-0.594724\pi$
$937$	−17.9506	−0.586420	−0.293210	+	0.956048i	$0.594724\pi$
$938$	−14.7795	−0.482568
$939$	−7.31890	−0.238843
$940$	−5.16410	−0.168434
$941$	−48.4220	−1.57851	−0.789255	−	0.614065i	$-0.789533\pi$
$941$	−48.4220	−1.57851	−0.789255	+	0.614065i	$0.789533\pi$
$942$	−6.19431	−0.201822
$943$	33.7734	1.09981
$944$	−4.96398	−0.161564
$945$	8.39708	0.273157
$946$	−26.0794	−0.847915
$947$	−5.18862	−0.168608	−0.0843038	−	0.996440i	$-0.526867\pi$
$947$	−5.18862	−0.168608	−0.0843038	+	0.996440i	$0.526867\pi$
$948$	10.3228	0.335268
$949$	−0.0164471	−0.000533894 0
$950$	10.3327	0.335236
$951$	10.2670	0.332929
$952$	−13.1158	−0.425086
$953$	36.8588	1.19397	0.596987	−	0.802251i	$-0.296365\pi$
$953$	36.8588	1.19397	0.596987	+	0.802251i	$0.296365\pi$
$954$	1.00000	0.0323762
$955$	34.3773	1.11242
$956$	−20.6989	−0.669450
$957$	12.1096	0.391448
$958$	−3.35501	−0.108395
$959$	−2.75560	−0.0889829
$960$	2.95264	0.0952959
$961$	−14.6238	−0.471736
$962$	−6.80850	−0.219515
$963$	−11.1579	−0.359557
$964$	26.1603	0.842566
$965$	34.8418	1.12160
$966$	−24.8305	−0.798909
$967$	12.7947	0.411450	0.205725	−	0.978610i	$-0.434045\pi$
$967$	12.7947	0.411450	0.205725	+	0.978610i	$0.434045\pi$
$968$	−0.266996	−0.00858158
$969$	−12.8166	−0.411728
$970$	−10.9647	−0.352056
$971$	20.7806	0.666883	0.333441	−	0.942771i	$-0.391790\pi$
$971$	20.7806	0.666883	0.333441	+	0.942771i	$0.391790\pi$
$972$	1.00000	0.0320750
$973$	−17.2214	−0.552092
$974$	−13.8138	−0.442622
$975$	−3.71806	−0.119073
$976$	0.744532	0.0238319
$977$	−14.9588	−0.478575	−0.239287	−	0.970949i	$-0.576914\pi$
$977$	−14.9588	−0.478575	−0.239287	+	0.970949i	$0.576914\pi$
$978$	−1.96681	−0.0628916
$979$	−59.6590	−1.90671
$980$	3.21224	0.102611
$981$	−14.4182	−0.460338
$982$	25.7090	0.820406
$983$	−11.4605	−0.365533	−0.182766	−	0.983156i	$-0.558505\pi$
$983$	−11.4605	−0.365533	−0.182766	+	0.983156i	$0.558505\pi$
$984$	−3.86818	−0.123313
$985$	45.9318	1.46351
$986$	−17.0469	−0.542885
$987$	−4.97397	−0.158323
$988$	−2.77905	−0.0884132
$989$	69.5032	2.21007
$990$	9.67321	0.307435
$991$	48.4077	1.53772	0.768861	−	0.639416i	$-0.220824\pi$
$991$	48.4077	1.53772	0.768861	+	0.639416i	$0.220824\pi$
$992$	4.04675	0.128484
$993$	24.8604	0.788920
$994$	5.29292	0.167881
$995$	−2.82731	−0.0896319
$996$	0.598010	0.0189487
$997$	−2.88851	−0.0914799	−0.0457400	−	0.998953i	$-0.514565\pi$
$997$	−2.88851	−0.0914799	−0.0457400	+	0.998953i	$0.514565\pi$
$998$	−2.51342	−0.0795611
$999$	6.80850	0.215411

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4134.2.a.x.1.7	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4134.2.a.x.1.7	✓	8	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:	\( N \)	\(=\)	\( 4134 = 2 \cdot 3 \cdot 13 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4134.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.95264 q^{5} +1.00000 q^{6} +2.84393 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.95264 q^{5} +1.00000 q^{6} +2.84393 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.95264 q^{10} +3.27613 q^{11} +1.00000 q^{12} -1.00000 q^{13} +2.84393 q^{14} +2.95264 q^{15} +1.00000 q^{16} -4.61187 q^{17} +1.00000 q^{18} +2.77905 q^{19} +2.95264 q^{20} +2.84393 q^{21} +3.27613 q^{22} -8.73107 q^{23} +1.00000 q^{24} +3.71806 q^{25} -1.00000 q^{26} +1.00000 q^{27} +2.84393 q^{28} +3.69632 q^{29} +2.95264 q^{30} +4.04675 q^{31} +1.00000 q^{32} +3.27613 q^{33} -4.61187 q^{34} +8.39708 q^{35} +1.00000 q^{36} +6.80850 q^{37} +2.77905 q^{38} -1.00000 q^{39} +2.95264 q^{40} -3.86818 q^{41} +2.84393 q^{42} -7.96045 q^{43} +3.27613 q^{44} +2.95264 q^{45} -8.73107 q^{46} -1.74898 q^{47} +1.00000 q^{48} +1.08792 q^{49} +3.71806 q^{50} -4.61187 q^{51} -1.00000 q^{52} +1.00000 q^{53} +1.00000 q^{54} +9.67321 q^{55} +2.84393 q^{56} +2.77905 q^{57} +3.69632 q^{58} -4.96398 q^{59} +2.95264 q^{60} +0.744532 q^{61} +4.04675 q^{62} +2.84393 q^{63} +1.00000 q^{64} -2.95264 q^{65} +3.27613 q^{66} -5.19687 q^{67} -4.61187 q^{68} -8.73107 q^{69} +8.39708 q^{70} +1.86113 q^{71} +1.00000 q^{72} +0.0164471 q^{73} +6.80850 q^{74} +3.71806 q^{75} +2.77905 q^{76} +9.31707 q^{77} -1.00000 q^{78} +10.3228 q^{79} +2.95264 q^{80} +1.00000 q^{81} -3.86818 q^{82} +0.598010 q^{83} +2.84393 q^{84} -13.6172 q^{85} -7.96045 q^{86} +3.69632 q^{87} +3.27613 q^{88} -18.2102 q^{89} +2.95264 q^{90} -2.84393 q^{91} -8.73107 q^{92} +4.04675 q^{93} -1.74898 q^{94} +8.20551 q^{95} +1.00000 q^{96} -3.71353 q^{97} +1.08792 q^{98} +3.27613 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 2 q^{5} + 8 q^{6} + 7 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 2 * q^5 + 8 * q^6 + 7 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 2 q^{5} + 8 q^{6} + 7 q^{7} + 8 q^{8} + 8 q^{9} + 2 q^{10} + 7 q^{11} + 8 q^{12} - 8 q^{13} + 7 q^{14} + 2 q^{15} + 8 q^{16} + 8 q^{17} + 8 q^{18} + 11 q^{19} + 2 q^{20} + 7 q^{21} + 7 q^{22} + 5 q^{23} + 8 q^{24} + 6 q^{25} - 8 q^{26} + 8 q^{27} + 7 q^{28} + 13 q^{29} + 2 q^{30} + 12 q^{31} + 8 q^{32} + 7 q^{33} + 8 q^{34} + 14 q^{35} + 8 q^{36} + 10 q^{37} + 11 q^{38} - 8 q^{39} + 2 q^{40} + 19 q^{41} + 7 q^{42} + 10 q^{43} + 7 q^{44} + 2 q^{45} + 5 q^{46} + 6 q^{47} + 8 q^{48} + 15 q^{49} + 6 q^{50} + 8 q^{51} - 8 q^{52} + 8 q^{53} + 8 q^{54} + 5 q^{55} + 7 q^{56} + 11 q^{57} + 13 q^{58} + 11 q^{59} + 2 q^{60} + 6 q^{61} + 12 q^{62} + 7 q^{63} + 8 q^{64} - 2 q^{65} + 7 q^{66} + 5 q^{67} + 8 q^{68} + 5 q^{69} + 14 q^{70} - 6 q^{71} + 8 q^{72} + 18 q^{73} + 10 q^{74} + 6 q^{75} + 11 q^{76} - 8 q^{77} - 8 q^{78} + 17 q^{79} + 2 q^{80} + 8 q^{81} + 19 q^{82} + 16 q^{83} + 7 q^{84} + 25 q^{85} + 10 q^{86} + 13 q^{87} + 7 q^{88} - 8 q^{89} + 2 q^{90} - 7 q^{91} + 5 q^{92} + 12 q^{93} + 6 q^{94} - 30 q^{95} + 8 q^{96} + 11 q^{97} + 15 q^{98} + 7 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 2 * q^5 + 8 * q^6 + 7 * q^7 + 8 * q^8 + 8 * q^9 + 2 * q^10 + 7 * q^11 + 8 * q^12 - 8 * q^13 + 7 * q^14 + 2 * q^15 + 8 * q^16 + 8 * q^17 + 8 * q^18 + 11 * q^19 + 2 * q^20 + 7 * q^21 + 7 * q^22 + 5 * q^23 + 8 * q^24 + 6 * q^25 - 8 * q^26 + 8 * q^27 + 7 * q^28 + 13 * q^29 + 2 * q^30 + 12 * q^31 + 8 * q^32 + 7 * q^33 + 8 * q^34 + 14 * q^35 + 8 * q^36 + 10 * q^37 + 11 * q^38 - 8 * q^39 + 2 * q^40 + 19 * q^41 + 7 * q^42 + 10 * q^43 + 7 * q^44 + 2 * q^45 + 5 * q^46 + 6 * q^47 + 8 * q^48 + 15 * q^49 + 6 * q^50 + 8 * q^51 - 8 * q^52 + 8 * q^53 + 8 * q^54 + 5 * q^55 + 7 * q^56 + 11 * q^57 + 13 * q^58 + 11 * q^59 + 2 * q^60 + 6 * q^61 + 12 * q^62 + 7 * q^63 + 8 * q^64 - 2 * q^65 + 7 * q^66 + 5 * q^67 + 8 * q^68 + 5 * q^69 + 14 * q^70 - 6 * q^71 + 8 * q^72 + 18 * q^73 + 10 * q^74 + 6 * q^75 + 11 * q^76 - 8 * q^77 - 8 * q^78 + 17 * q^79 + 2 * q^80 + 8 * q^81 + 19 * q^82 + 16 * q^83 + 7 * q^84 + 25 * q^85 + 10 * q^86 + 13 * q^87 + 7 * q^88 - 8 * q^89 + 2 * q^90 - 7 * q^91 + 5 * q^92 + 12 * q^93 + 6 * q^94 - 30 * q^95 + 8 * q^96 + 11 * q^97 + 15 * q^98 + 7 * q^99

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