LMFDB - Embedded newform 8034.2.a.q.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.1518129839$
Analytic rank:	$1$
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} - 11x^{6} + 21x^{5} + 23x^{4} - 29x^{3} - 27x^{2} + x + 3 $ x^8 - 2x^7 - 11x^6 + 21x^5 + 23x^4 - 29x^3 - 27x^2 + x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.811382$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.81138 q^{5} +1.00000 q^{6} +4.37785 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.81138 q^{5} +1.00000 q^{6} +4.37785 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.81138 q^{10} -5.56647 q^{11} +1.00000 q^{12} -1.00000 q^{13} +4.37785 q^{14} -1.81138 q^{15} +1.00000 q^{16} -5.16511 q^{17} +1.00000 q^{18} +3.80372 q^{19} -1.81138 q^{20} +4.37785 q^{21} -5.56647 q^{22} -0.487660 q^{23} +1.00000 q^{24} -1.71890 q^{25} -1.00000 q^{26} +1.00000 q^{27} +4.37785 q^{28} -9.38955 q^{29} -1.81138 q^{30} -0.944100 q^{31} +1.00000 q^{32} -5.56647 q^{33} -5.16511 q^{34} -7.92996 q^{35} +1.00000 q^{36} -5.87569 q^{37} +3.80372 q^{38} -1.00000 q^{39} -1.81138 q^{40} +0.941958 q^{41} +4.37785 q^{42} -8.57969 q^{43} -5.56647 q^{44} -1.81138 q^{45} -0.487660 q^{46} +3.30130 q^{47} +1.00000 q^{48} +12.1656 q^{49} -1.71890 q^{50} -5.16511 q^{51} -1.00000 q^{52} -0.598639 q^{53} +1.00000 q^{54} +10.0830 q^{55} +4.37785 q^{56} +3.80372 q^{57} -9.38955 q^{58} -8.16678 q^{59} -1.81138 q^{60} -9.67331 q^{61} -0.944100 q^{62} +4.37785 q^{63} +1.00000 q^{64} +1.81138 q^{65} -5.56647 q^{66} +4.48035 q^{67} -5.16511 q^{68} -0.487660 q^{69} -7.92996 q^{70} -3.22682 q^{71} +1.00000 q^{72} +1.48245 q^{73} -5.87569 q^{74} -1.71890 q^{75} +3.80372 q^{76} -24.3692 q^{77} -1.00000 q^{78} +0.265176 q^{79} -1.81138 q^{80} +1.00000 q^{81} +0.941958 q^{82} -5.02677 q^{83} +4.37785 q^{84} +9.35598 q^{85} -8.57969 q^{86} -9.38955 q^{87} -5.56647 q^{88} +4.65275 q^{89} -1.81138 q^{90} -4.37785 q^{91} -0.487660 q^{92} -0.944100 q^{93} +3.30130 q^{94} -6.88999 q^{95} +1.00000 q^{96} -10.6986 q^{97} +12.1656 q^{98} -5.56647 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9} - 6 q^{10} - 15 q^{11} + 8 q^{12} - 8 q^{13} - 3 q^{14} - 6 q^{15} + 8 q^{16} - 11 q^{17} + 8 q^{18} - 15 q^{19} - 6 q^{20} - 3 q^{21} - 15 q^{22} + q^{23} + 8 q^{24} - 10 q^{25} - 8 q^{26} + 8 q^{27} - 3 q^{28} - 10 q^{29} - 6 q^{30} - 3 q^{31} + 8 q^{32} - 15 q^{33} - 11 q^{34} - 12 q^{35} + 8 q^{36} - 26 q^{37} - 15 q^{38} - 8 q^{39} - 6 q^{40} - 12 q^{41} - 3 q^{42} - 4 q^{43} - 15 q^{44} - 6 q^{45} + q^{46} - 6 q^{47} + 8 q^{48} - 5 q^{49} - 10 q^{50} - 11 q^{51} - 8 q^{52} - 4 q^{53} + 8 q^{54} - 3 q^{56} - 15 q^{57} - 10 q^{58} - 19 q^{59} - 6 q^{60} - 14 q^{61} - 3 q^{62} - 3 q^{63} + 8 q^{64} + 6 q^{65} - 15 q^{66} - 13 q^{67} - 11 q^{68} + q^{69} - 12 q^{70} - 31 q^{71} + 8 q^{72} - 27 q^{73} - 26 q^{74} - 10 q^{75} - 15 q^{76} - 30 q^{77} - 8 q^{78} - 13 q^{79} - 6 q^{80} + 8 q^{81} - 12 q^{82} - 28 q^{83} - 3 q^{84} + 15 q^{85} - 4 q^{86} - 10 q^{87} - 15 q^{88} - 2 q^{89} - 6 q^{90} + 3 q^{91} + q^{92} - 3 q^{93} - 6 q^{94} - 18 q^{95} + 8 q^{96} - 30 q^{97} - 5 q^{98} - 15 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9 - 6 * q^10 - 15 * q^11 + 8 * q^12 - 8 * q^13 - 3 * q^14 - 6 * q^15 + 8 * q^16 - 11 * q^17 + 8 * q^18 - 15 * q^19 - 6 * q^20 - 3 * q^21 - 15 * q^22 + q^23 + 8 * q^24 - 10 * q^25 - 8 * q^26 + 8 * q^27 - 3 * q^28 - 10 * q^29 - 6 * q^30 - 3 * q^31 + 8 * q^32 - 15 * q^33 - 11 * q^34 - 12 * q^35 + 8 * q^36 - 26 * q^37 - 15 * q^38 - 8 * q^39 - 6 * q^40 - 12 * q^41 - 3 * q^42 - 4 * q^43 - 15 * q^44 - 6 * q^45 + q^46 - 6 * q^47 + 8 * q^48 - 5 * q^49 - 10 * q^50 - 11 * q^51 - 8 * q^52 - 4 * q^53 + 8 * q^54 - 3 * q^56 - 15 * q^57 - 10 * q^58 - 19 * q^59 - 6 * q^60 - 14 * q^61 - 3 * q^62 - 3 * q^63 + 8 * q^64 + 6 * q^65 - 15 * q^66 - 13 * q^67 - 11 * q^68 + q^69 - 12 * q^70 - 31 * q^71 + 8 * q^72 - 27 * q^73 - 26 * q^74 - 10 * q^75 - 15 * q^76 - 30 * q^77 - 8 * q^78 - 13 * q^79 - 6 * q^80 + 8 * q^81 - 12 * q^82 - 28 * q^83 - 3 * q^84 + 15 * q^85 - 4 * q^86 - 10 * q^87 - 15 * q^88 - 2 * q^89 - 6 * q^90 + 3 * q^91 + q^92 - 3 * q^93 - 6 * q^94 - 18 * q^95 + 8 * q^96 - 30 * q^97 - 5 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.81138	−0.810075	−0.405037	−	0.914300i	$-0.632741\pi$
$5$	−1.81138	−0.810075	−0.405037	+	0.914300i	$0.632741\pi$
$6$	1.00000	0.408248
$7$	4.37785	1.65467	0.827336	−	0.561707i	$-0.189855\pi$
$7$	4.37785	1.65467	0.827336	+	0.561707i	$0.189855\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.81138	−0.572809
$11$	−5.56647	−1.67835	−0.839177	−	0.543859i	$-0.816963\pi$
$11$	−5.56647	−1.67835	−0.839177	+	0.543859i	$0.816963\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	4.37785	1.17003
$15$	−1.81138	−0.467697
$16$	1.00000	0.250000
$17$	−5.16511	−1.25272	−0.626361	−	0.779533i	$-0.715457\pi$
$17$	−5.16511	−1.25272	−0.626361	+	0.779533i	$0.715457\pi$
$18$	1.00000	0.235702
$19$	3.80372	0.872633	0.436317	−	0.899793i	$-0.356283\pi$
$19$	3.80372	0.872633	0.436317	+	0.899793i	$0.356283\pi$
$20$	−1.81138	−0.405037
$21$	4.37785	0.955325
$22$	−5.56647	−1.18678
$23$	−0.487660	−0.101684	−0.0508420	−	0.998707i	$-0.516190\pi$
$23$	−0.487660	−0.101684	−0.0508420	+	0.998707i	$0.516190\pi$
$24$	1.00000	0.204124
$25$	−1.71890	−0.343779
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	4.37785	0.827336
$29$	−9.38955	−1.74360	−0.871798	−	0.489866i	$-0.837046\pi$
$29$	−9.38955	−1.74360	−0.871798	+	0.489866i	$0.837046\pi$
$30$	−1.81138	−0.330712
$31$	−0.944100	−0.169565	−0.0847827	−	0.996399i	$-0.527020\pi$
$31$	−0.944100	−0.169565	−0.0847827	+	0.996399i	$0.527020\pi$
$32$	1.00000	0.176777
$33$	−5.56647	−0.968998
$34$	−5.16511	−0.885809
$35$	−7.92996	−1.34041
$36$	1.00000	0.166667
$37$	−5.87569	−0.965958	−0.482979	−	0.875632i	$-0.660445\pi$
$37$	−5.87569	−0.965958	−0.482979	+	0.875632i	$0.660445\pi$
$38$	3.80372	0.617045
$39$	−1.00000	−0.160128
$40$	−1.81138	−0.286405
$41$	0.941958	0.147109	0.0735546	−	0.997291i	$-0.476566\pi$
$41$	0.941958	0.147109	0.0735546	+	0.997291i	$0.476566\pi$
$42$	4.37785	0.675517
$43$	−8.57969	−1.30839	−0.654195	−	0.756326i	$-0.726993\pi$
$43$	−8.57969	−1.30839	−0.654195	+	0.756326i	$0.726993\pi$
$44$	−5.56647	−0.839177
$45$	−1.81138	−0.270025
$46$	−0.487660	−0.0719015
$47$	3.30130	0.481545	0.240772	−	0.970582i	$-0.422599\pi$
$47$	3.30130	0.481545	0.240772	+	0.970582i	$0.422599\pi$
$48$	1.00000	0.144338
$49$	12.1656	1.73794
$50$	−1.71890	−0.243089
$51$	−5.16511	−0.723260
$52$	−1.00000	−0.138675
$53$	−0.598639	−0.0822294	−0.0411147	−	0.999154i	$-0.513091\pi$
$53$	−0.598639	−0.0822294	−0.0411147	+	0.999154i	$0.513091\pi$
$54$	1.00000	0.136083
$55$	10.0830	1.35959
$56$	4.37785	0.585015
$57$	3.80372	0.503815
$58$	−9.38955	−1.23291
$59$	−8.16678	−1.06322	−0.531612	−	0.846988i	$-0.678414\pi$
$59$	−8.16678	−1.06322	−0.531612	+	0.846988i	$0.678414\pi$
$60$	−1.81138	−0.233848
$61$	−9.67331	−1.23854	−0.619270	−	0.785178i	$-0.712572\pi$
$61$	−9.67331	−1.23854	−0.619270	+	0.785178i	$0.712572\pi$
$62$	−0.944100	−0.119901
$63$	4.37785	0.551557
$64$	1.00000	0.125000
$65$	1.81138	0.224674
$66$	−5.56647	−0.685185
$67$	4.48035	0.547361	0.273681	−	0.961821i	$-0.411759\pi$
$67$	4.48035	0.547361	0.273681	+	0.961821i	$0.411759\pi$
$68$	−5.16511	−0.626361
$69$	−0.487660	−0.0587073
$70$	−7.92996	−0.947812
$71$	−3.22682	−0.382953	−0.191477	−	0.981497i	$-0.561328\pi$
$71$	−3.22682	−0.382953	−0.191477	+	0.981497i	$0.561328\pi$
$72$	1.00000	0.117851
$73$	1.48245	0.173508	0.0867539	−	0.996230i	$-0.472351\pi$
$73$	1.48245	0.173508	0.0867539	+	0.996230i	$0.472351\pi$
$74$	−5.87569	−0.683035
$75$	−1.71890	−0.198481
$76$	3.80372	0.436317
$77$	−24.3692	−2.77712
$78$	−1.00000	−0.113228
$79$	0.265176	0.0298346	0.0149173	−	0.999889i	$-0.495251\pi$
$79$	0.265176	0.0298346	0.0149173	+	0.999889i	$0.495251\pi$
$80$	−1.81138	−0.202519
$81$	1.00000	0.111111
$82$	0.941958	0.104022
$83$	−5.02677	−0.551760	−0.275880	−	0.961192i	$-0.588969\pi$
$83$	−5.02677	−0.551760	−0.275880	+	0.961192i	$0.588969\pi$
$84$	4.37785	0.477663
$85$	9.35598	1.01480
$86$	−8.57969	−0.925172
$87$	−9.38955	−1.00667
$88$	−5.56647	−0.593388
$89$	4.65275	0.493191	0.246595	−	0.969119i	$-0.420688\pi$
$89$	4.65275	0.493191	0.246595	+	0.969119i	$0.420688\pi$
$90$	−1.81138	−0.190936
$91$	−4.37785	−0.458923
$92$	−0.487660	−0.0508420
$93$	−0.944100	−0.0978986
$94$	3.30130	0.340504
$95$	−6.88999	−0.706898
$96$	1.00000	0.102062
$97$	−10.6986	−1.08628	−0.543140	−	0.839642i	$-0.682765\pi$
$97$	−10.6986	−1.08628	−0.543140	+	0.839642i	$0.682765\pi$
$98$	12.1656	1.22891
$99$	−5.56647	−0.559451
$100$	−1.71890	−0.171890
$101$	7.90390	0.786467	0.393234	−	0.919439i	$-0.371356\pi$
$101$	7.90390	0.786467	0.393234	+	0.919439i	$0.371356\pi$
$102$	−5.16511	−0.511422
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	−7.92996	−0.773885
$106$	−0.598639	−0.0581450
$107$	5.68151	0.549252	0.274626	−	0.961551i	$-0.411446\pi$
$107$	5.68151	0.549252	0.274626	+	0.961551i	$0.411446\pi$
$108$	1.00000	0.0962250
$109$	10.4811	1.00390	0.501952	−	0.864896i	$-0.332616\pi$
$109$	10.4811	1.00390	0.501952	+	0.864896i	$0.332616\pi$
$110$	10.0830	0.961376
$111$	−5.87569	−0.557696
$112$	4.37785	0.413668
$113$	4.21261	0.396289	0.198145	−	0.980173i	$-0.436508\pi$
$113$	4.21261	0.396289	0.198145	+	0.980173i	$0.436508\pi$
$114$	3.80372	0.356251
$115$	0.883338	0.0823717
$116$	−9.38955	−0.871798
$117$	−1.00000	−0.0924500
$118$	−8.16678	−0.751813
$119$	−22.6121	−2.07285
$120$	−1.81138	−0.165356
$121$	19.9856	1.81687
$122$	−9.67331	−0.875781
$123$	0.941958	0.0849335
$124$	−0.944100	−0.0847827
$125$	12.1705	1.08856
$126$	4.37785	0.390010
$127$	−1.94633	−0.172709	−0.0863543	−	0.996264i	$-0.527522\pi$
$127$	−1.94633	−0.172709	−0.0863543	+	0.996264i	$0.527522\pi$
$128$	1.00000	0.0883883
$129$	−8.57969	−0.755400
$130$	1.81138	0.158869
$131$	−9.28623	−0.811342	−0.405671	−	0.914019i	$-0.632962\pi$
$131$	−9.28623	−0.811342	−0.405671	+	0.914019i	$0.632962\pi$
$132$	−5.56647	−0.484499
$133$	16.6521	1.44392
$134$	4.48035	0.387043
$135$	−1.81138	−0.155899
$136$	−5.16511	−0.442904
$137$	−5.64827	−0.482564	−0.241282	−	0.970455i	$-0.577568\pi$
$137$	−5.64827	−0.482564	−0.241282	+	0.970455i	$0.577568\pi$
$138$	−0.487660	−0.0415123
$139$	−21.2985	−1.80651	−0.903256	−	0.429101i	$-0.858830\pi$
$139$	−21.2985	−1.80651	−0.903256	+	0.429101i	$0.858830\pi$
$140$	−7.92996	−0.670204
$141$	3.30130	0.278020
$142$	−3.22682	−0.270789
$143$	5.56647	0.465492
$144$	1.00000	0.0833333
$145$	17.0081	1.41244
$146$	1.48245	0.122689
$147$	12.1656	1.00340
$148$	−5.87569	−0.482979
$149$	10.2997	0.843784	0.421892	−	0.906646i	$-0.361366\pi$
$149$	10.2997	0.843784	0.421892	+	0.906646i	$0.361366\pi$
$150$	−1.71890	−0.140347
$151$	9.58601	0.780098	0.390049	−	0.920794i	$-0.372458\pi$
$151$	9.58601	0.780098	0.390049	+	0.920794i	$0.372458\pi$
$152$	3.80372	0.308522
$153$	−5.16511	−0.417574
$154$	−24.3692	−1.96372
$155$	1.71013	0.137361
$156$	−1.00000	−0.0800641
$157$	17.7343	1.41535	0.707677	−	0.706536i	$-0.249743\pi$
$157$	17.7343	1.41535	0.707677	+	0.706536i	$0.249743\pi$
$158$	0.265176	0.0210963
$159$	−0.598639	−0.0474752
$160$	−1.81138	−0.143202
$161$	−2.13490	−0.168254
$162$	1.00000	0.0785674
$163$	9.61966	0.753470	0.376735	−	0.926321i	$-0.377047\pi$
$163$	9.61966	0.753470	0.376735	+	0.926321i	$0.377047\pi$
$164$	0.941958	0.0735546
$165$	10.0830	0.784961
$166$	−5.02677	−0.390153
$167$	2.80000	0.216670	0.108335	−	0.994114i	$-0.465448\pi$
$167$	2.80000	0.216670	0.108335	+	0.994114i	$0.465448\pi$
$168$	4.37785	0.337759
$169$	1.00000	0.0769231
$170$	9.35598	0.717571
$171$	3.80372	0.290878
$172$	−8.57969	−0.654195
$173$	−23.6784	−1.80024	−0.900118	−	0.435645i	$-0.856520\pi$
$173$	−23.6784	−1.80024	−0.900118	+	0.435645i	$0.856520\pi$
$174$	−9.38955	−0.711820
$175$	−7.52507	−0.568842
$176$	−5.56647	−0.419588
$177$	−8.16678	−0.613853
$178$	4.65275	0.348738
$179$	−9.21549	−0.688798	−0.344399	−	0.938823i	$-0.611917\pi$
$179$	−9.21549	−0.688798	−0.344399	+	0.938823i	$0.611917\pi$
$180$	−1.81138	−0.135012
$181$	−15.3675	−1.14225	−0.571127	−	0.820862i	$-0.693494\pi$
$181$	−15.3675	−1.14225	−0.571127	+	0.820862i	$0.693494\pi$
$182$	−4.37785	−0.324508
$183$	−9.67331	−0.715072
$184$	−0.487660	−0.0359507
$185$	10.6431	0.782498
$186$	−0.944100	−0.0692248
$187$	28.7514	2.10251
$188$	3.30130	0.240772
$189$	4.37785	0.318442
$190$	−6.88999	−0.499852
$191$	−5.85534	−0.423677	−0.211839	−	0.977305i	$-0.567945\pi$
$191$	−5.85534	−0.423677	−0.211839	+	0.977305i	$0.567945\pi$
$192$	1.00000	0.0721688
$193$	11.0520	0.795543	0.397771	−	0.917485i	$-0.369784\pi$
$193$	11.0520	0.795543	0.397771	+	0.917485i	$0.369784\pi$
$194$	−10.6986	−0.768116
$195$	1.81138	0.129716
$196$	12.1656	0.868970
$197$	−23.8570	−1.69974	−0.849869	−	0.526994i	$-0.823319\pi$
$197$	−23.8570	−1.69974	−0.849869	+	0.526994i	$0.823319\pi$
$198$	−5.56647	−0.395592
$199$	13.5544	0.960849	0.480425	−	0.877036i	$-0.340483\pi$
$199$	13.5544	0.960849	0.480425	+	0.877036i	$0.340483\pi$
$200$	−1.71890	−0.121544
$201$	4.48035	0.316019
$202$	7.90390	0.556116
$203$	−41.1060	−2.88508
$204$	−5.16511	−0.361630
$205$	−1.70625	−0.119169
$206$	−1.00000	−0.0696733
$207$	−0.487660	−0.0338947
$208$	−1.00000	−0.0693375
$209$	−21.1733	−1.46459
$210$	−7.92996	−0.547219
$211$	4.74160	0.326425	0.163212	−	0.986591i	$-0.447814\pi$
$211$	4.74160	0.326425	0.163212	+	0.986591i	$0.447814\pi$
$212$	−0.598639	−0.0411147
$213$	−3.22682	−0.221098
$214$	5.68151	0.388380
$215$	15.5411	1.05989
$216$	1.00000	0.0680414
$217$	−4.13313	−0.280575
$218$	10.4811	0.709867
$219$	1.48245	0.100175
$220$	10.0830	0.679796
$221$	5.16511	0.347443
$222$	−5.87569	−0.394351
$223$	4.85412	0.325056	0.162528	−	0.986704i	$-0.448035\pi$
$223$	4.85412	0.325056	0.162528	+	0.986704i	$0.448035\pi$
$224$	4.37785	0.292507
$225$	−1.71890	−0.114593
$226$	4.21261	0.280219
$227$	−21.1215	−1.40188	−0.700942	−	0.713219i	$-0.747237\pi$
$227$	−21.1215	−1.40188	−0.700942	+	0.713219i	$0.747237\pi$
$228$	3.80372	0.251907
$229$	−27.2810	−1.80278	−0.901391	−	0.433007i	$-0.857453\pi$
$229$	−27.2810	−1.80278	−0.901391	+	0.433007i	$0.857453\pi$
$230$	0.883338	0.0582456
$231$	−24.3692	−1.60337
$232$	−9.38955	−0.616454
$233$	−12.8522	−0.841978	−0.420989	−	0.907066i	$-0.638317\pi$
$233$	−12.8522	−0.841978	−0.420989	+	0.907066i	$0.638317\pi$
$234$	−1.00000	−0.0653720
$235$	−5.97992	−0.390087
$236$	−8.16678	−0.531612
$237$	0.265176	0.0172250
$238$	−22.6121	−1.46572
$239$	−0.580598	−0.0375558	−0.0187779	−	0.999824i	$-0.505978\pi$
$239$	−0.580598	−0.0375558	−0.0187779	+	0.999824i	$0.505978\pi$
$240$	−1.81138	−0.116924
$241$	−2.90864	−0.187362	−0.0936810	−	0.995602i	$-0.529863\pi$
$241$	−2.90864	−0.187362	−0.0936810	+	0.995602i	$0.529863\pi$
$242$	19.9856	1.28472
$243$	1.00000	0.0641500
$244$	−9.67331	−0.619270
$245$	−22.0365	−1.40786
$246$	0.941958	0.0600571
$247$	−3.80372	−0.242025
$248$	−0.944100	−0.0599504
$249$	−5.02677	−0.318559
$250$	12.1705	0.769729
$251$	30.4421	1.92149	0.960745	−	0.277434i	$-0.0894841\pi$
$251$	30.4421	1.92149	0.960745	+	0.277434i	$0.0894841\pi$
$252$	4.37785	0.275779
$253$	2.71454	0.170662
$254$	−1.94633	−0.122123
$255$	9.35598	0.585894
$256$	1.00000	0.0625000
$257$	26.2924	1.64007	0.820037	−	0.572310i	$-0.193953\pi$
$257$	26.2924	1.64007	0.820037	+	0.572310i	$0.193953\pi$
$258$	−8.57969	−0.534148
$259$	−25.7229	−1.59834
$260$	1.81138	0.112337
$261$	−9.38955	−0.581198
$262$	−9.28623	−0.573705
$263$	12.4674	0.768772	0.384386	−	0.923172i	$-0.374413\pi$
$263$	12.4674	0.768772	0.384386	+	0.923172i	$0.374413\pi$
$264$	−5.56647	−0.342592
$265$	1.08436	0.0666120
$266$	16.6521	1.02101
$267$	4.65275	0.284744
$268$	4.48035	0.273681
$269$	14.4119	0.878711	0.439356	−	0.898313i	$-0.355207\pi$
$269$	14.4119	0.878711	0.439356	+	0.898313i	$0.355207\pi$
$270$	−1.81138	−0.110237
$271$	−21.5259	−1.30760	−0.653802	−	0.756666i	$-0.726827\pi$
$271$	−21.5259	−1.30760	−0.653802	+	0.756666i	$0.726827\pi$
$272$	−5.16511	−0.313181
$273$	−4.37785	−0.264960
$274$	−5.64827	−0.341224
$275$	9.56818	0.576983
$276$	−0.487660	−0.0293537
$277$	−9.61980	−0.577998	−0.288999	−	0.957329i	$-0.593322\pi$
$277$	−9.61980	−0.577998	−0.288999	+	0.957329i	$0.593322\pi$
$278$	−21.2985	−1.27740
$279$	−0.944100	−0.0565218
$280$	−7.92996	−0.473906
$281$	26.1990	1.56290	0.781452	−	0.623966i	$-0.214479\pi$
$281$	26.1990	1.56290	0.781452	+	0.623966i	$0.214479\pi$
$282$	3.30130	0.196590
$283$	−6.77984	−0.403020	−0.201510	−	0.979486i	$-0.564585\pi$
$283$	−6.77984	−0.403020	−0.201510	+	0.979486i	$0.564585\pi$
$284$	−3.22682	−0.191477
$285$	−6.88999	−0.408128
$286$	5.56647	0.329152
$287$	4.12375	0.243417
$288$	1.00000	0.0589256
$289$	9.67835	0.569314
$290$	17.0081	0.998747
$291$	−10.6986	−0.627164
$292$	1.48245	0.0867539
$293$	−4.73881	−0.276844	−0.138422	−	0.990373i	$-0.544203\pi$
$293$	−4.73881	−0.276844	−0.138422	+	0.990373i	$0.544203\pi$
$294$	12.1656	0.709511
$295$	14.7932	0.861291
$296$	−5.87569	−0.341518
$297$	−5.56647	−0.322999
$298$	10.2997	0.596645
$299$	0.487660	0.0282021
$300$	−1.71890	−0.0992405
$301$	−37.5606	−2.16496
$302$	9.58601	0.551613
$303$	7.90390	0.454067
$304$	3.80372	0.218158
$305$	17.5221	1.00331
$306$	−5.16511	−0.295270
$307$	12.8551	0.733681	0.366840	−	0.930284i	$-0.380440\pi$
$307$	12.8551	0.733681	0.366840	+	0.930284i	$0.380440\pi$
$308$	−24.3692	−1.38856
$309$	−1.00000	−0.0568880
$310$	1.71013	0.0971286
$311$	−30.5174	−1.73048	−0.865242	−	0.501354i	$-0.832836\pi$
$311$	−30.5174	−1.73048	−0.865242	+	0.501354i	$0.832836\pi$
$312$	−1.00000	−0.0566139
$313$	18.8827	1.06731	0.533657	−	0.845701i	$-0.320817\pi$
$313$	18.8827	1.06731	0.533657	+	0.845701i	$0.320817\pi$
$314$	17.7343	1.00081
$315$	−7.92996	−0.446803
$316$	0.265176	0.0149173
$317$	33.5941	1.88683	0.943415	−	0.331613i	$-0.107593\pi$
$317$	33.5941	1.88683	0.943415	+	0.331613i	$0.107593\pi$
$318$	−0.598639	−0.0335700
$319$	52.2666	2.92637
$320$	−1.81138	−0.101259
$321$	5.68151	0.317111
$322$	−2.13490	−0.118973
$323$	−19.6466	−1.09317
$324$	1.00000	0.0555556
$325$	1.71890	0.0953472
$326$	9.61966	0.532784
$327$	10.4811	0.579604
$328$	0.941958	0.0520110
$329$	14.4526	0.796799
$330$	10.0830	0.555051
$331$	9.48800	0.521508	0.260754	−	0.965405i	$-0.416029\pi$
$331$	9.48800	0.521508	0.260754	+	0.965405i	$0.416029\pi$
$332$	−5.02677	−0.275880
$333$	−5.87569	−0.321986
$334$	2.80000	0.153209
$335$	−8.11562	−0.443404
$336$	4.37785	0.238831
$337$	12.5707	0.684767	0.342384	−	0.939560i	$-0.388766\pi$
$337$	12.5707	0.684767	0.342384	+	0.939560i	$0.388766\pi$
$338$	1.00000	0.0543928
$339$	4.21261	0.228798
$340$	9.35598	0.507399
$341$	5.25530	0.284591
$342$	3.80372	0.205682
$343$	22.6141	1.22105
$344$	−8.57969	−0.462586
$345$	0.883338	0.0475573
$346$	−23.6784	−1.27296
$347$	7.58431	0.407147	0.203574	−	0.979060i	$-0.434744\pi$
$347$	7.58431	0.407147	0.203574	+	0.979060i	$0.434744\pi$
$348$	−9.38955	−0.503333
$349$	10.2740	0.549955	0.274977	−	0.961451i	$-0.411330\pi$
$349$	10.2740	0.549955	0.274977	+	0.961451i	$0.411330\pi$
$350$	−7.52507	−0.402232
$351$	−1.00000	−0.0533761
$352$	−5.56647	−0.296694
$353$	−23.2135	−1.23553	−0.617766	−	0.786362i	$-0.711962\pi$
$353$	−23.2135	−1.23553	−0.617766	+	0.786362i	$0.711962\pi$
$354$	−8.16678	−0.434059
$355$	5.84500	0.310221
$356$	4.65275	0.246595
$357$	−22.6121	−1.19676
$358$	−9.21549	−0.487054
$359$	−22.5062	−1.18783	−0.593916	−	0.804527i	$-0.702419\pi$
$359$	−22.5062	−1.18783	−0.593916	+	0.804527i	$0.702419\pi$
$360$	−1.81138	−0.0954682
$361$	−4.53172	−0.238512
$362$	−15.3675	−0.807696
$363$	19.9856	1.04897
$364$	−4.37785	−0.229462
$365$	−2.68529	−0.140554
$366$	−9.67331	−0.505632
$367$	17.1243	0.893881	0.446941	−	0.894564i	$-0.352514\pi$
$367$	17.1243	0.893881	0.446941	+	0.894564i	$0.352514\pi$
$368$	−0.487660	−0.0254210
$369$	0.941958	0.0490364
$370$	10.6431	0.553309
$371$	−2.62075	−0.136063
$372$	−0.944100	−0.0489493
$373$	13.4598	0.696920	0.348460	−	0.937324i	$-0.386705\pi$
$373$	13.4598	0.696920	0.348460	+	0.937324i	$0.386705\pi$
$374$	28.7514	1.48670
$375$	12.1705	0.628481
$376$	3.30130	0.170252
$377$	9.38955	0.483586
$378$	4.37785	0.225172
$379$	4.65242	0.238979	0.119489	−	0.992835i	$-0.461874\pi$
$379$	4.65242	0.238979	0.119489	+	0.992835i	$0.461874\pi$
$380$	−6.88999	−0.353449
$381$	−1.94633	−0.0997134
$382$	−5.85534	−0.299585
$383$	0.934727	0.0477623	0.0238812	−	0.999715i	$-0.492398\pi$
$383$	0.934727	0.0477623	0.0238812	+	0.999715i	$0.492398\pi$
$384$	1.00000	0.0510310
$385$	44.1419	2.24968
$386$	11.0520	0.562534
$387$	−8.57969	−0.436130
$388$	−10.6986	−0.543140
$389$	−29.0606	−1.47343	−0.736715	−	0.676203i	$-0.763624\pi$
$389$	−29.0606	−1.47343	−0.736715	+	0.676203i	$0.763624\pi$
$390$	1.81138	0.0917229
$391$	2.51881	0.127382
$392$	12.1656	0.614455
$393$	−9.28623	−0.468428
$394$	−23.8570	−1.20190
$395$	−0.480335	−0.0241683
$396$	−5.56647	−0.279726
$397$	0.323229	0.0162224	0.00811120	−	0.999967i	$-0.497418\pi$
$397$	0.323229	0.0162224	0.00811120	+	0.999967i	$0.497418\pi$
$398$	13.5544	0.679423
$399$	16.6521	0.833649
$400$	−1.71890	−0.0859448
$401$	−17.3492	−0.866377	−0.433189	−	0.901303i	$-0.642612\pi$
$401$	−17.3492	−0.866377	−0.433189	+	0.901303i	$0.642612\pi$
$402$	4.48035	0.223459
$403$	0.944100	0.0470290
$404$	7.90390	0.393234
$405$	−1.81138	−0.0900083
$406$	−41.1060	−2.04006
$407$	32.7069	1.62122
$408$	−5.16511	−0.255711
$409$	8.63479	0.426963	0.213481	−	0.976947i	$-0.431520\pi$
$409$	8.63479	0.426963	0.213481	+	0.976947i	$0.431520\pi$
$410$	−1.70625	−0.0842655
$411$	−5.64827	−0.278609
$412$	−1.00000	−0.0492665
$413$	−35.7529	−1.75929
$414$	−0.487660	−0.0239672
$415$	9.10540	0.446966
$416$	−1.00000	−0.0490290
$417$	−21.2985	−1.04299
$418$	−21.1733	−1.03562
$419$	−22.7542	−1.11162	−0.555808	−	0.831311i	$-0.687591\pi$
$419$	−22.7542	−1.11162	−0.555808	+	0.831311i	$0.687591\pi$
$420$	−7.92996	−0.386942
$421$	−2.70603	−0.131884	−0.0659420	−	0.997823i	$-0.521005\pi$
$421$	−2.70603	−0.131884	−0.0659420	+	0.997823i	$0.521005\pi$
$422$	4.74160	0.230817
$423$	3.30130	0.160515
$424$	−0.598639	−0.0290725
$425$	8.87828	0.430660
$426$	−3.22682	−0.156340
$427$	−42.3483	−2.04938
$428$	5.68151	0.274626
$429$	5.56647	0.268752
$430$	15.5411	0.749458
$431$	23.1697	1.11605	0.558023	−	0.829825i	$-0.311560\pi$
$431$	23.1697	1.11605	0.558023	+	0.829825i	$0.311560\pi$
$432$	1.00000	0.0481125
$433$	24.5834	1.18140	0.590702	−	0.806890i	$-0.298851\pi$
$433$	24.5834	1.18140	0.590702	+	0.806890i	$0.298851\pi$
$434$	−4.13313	−0.198397
$435$	17.0081	0.815474
$436$	10.4811	0.501952
$437$	−1.85492	−0.0887329
$438$	1.48245	0.0708343
$439$	−20.5109	−0.978934	−0.489467	−	0.872022i	$-0.662809\pi$
$439$	−20.5109	−0.978934	−0.489467	+	0.872022i	$0.662809\pi$
$440$	10.0830	0.480688
$441$	12.1656	0.579313
$442$	5.16511	0.245679
$443$	−12.4724	−0.592581	−0.296290	−	0.955098i	$-0.595750\pi$
$443$	−12.4724	−0.592581	−0.296290	+	0.955098i	$0.595750\pi$
$444$	−5.87569	−0.278848
$445$	−8.42791	−0.399521
$446$	4.85412	0.229849
$447$	10.2997	0.487159
$448$	4.37785	0.206834
$449$	24.6318	1.16245	0.581224	−	0.813744i	$-0.302574\pi$
$449$	24.6318	1.16245	0.581224	+	0.813744i	$0.302574\pi$
$450$	−1.71890	−0.0810295
$451$	−5.24338	−0.246901
$452$	4.21261	0.198145
$453$	9.58601	0.450390
$454$	−21.1215	−0.991281
$455$	7.92996	0.371762
$456$	3.80372	0.178125
$457$	−20.7717	−0.971660	−0.485830	−	0.874053i	$-0.661483\pi$
$457$	−20.7717	−0.971660	−0.485830	+	0.874053i	$0.661483\pi$
$458$	−27.2810	−1.27476
$459$	−5.16511	−0.241087
$460$	0.883338	0.0411858
$461$	16.6568	0.775784	0.387892	−	0.921705i	$-0.373203\pi$
$461$	16.6568	0.775784	0.387892	+	0.921705i	$0.373203\pi$
$462$	−24.3692	−1.13376
$463$	−34.8615	−1.62015	−0.810075	−	0.586327i	$-0.800573\pi$
$463$	−34.8615	−1.62015	−0.810075	+	0.586327i	$0.800573\pi$
$464$	−9.38955	−0.435899
$465$	1.71013	0.0793052
$466$	−12.8522	−0.595368
$467$	−31.7256	−1.46809	−0.734044	−	0.679102i	$-0.762369\pi$
$467$	−31.7256	−1.46809	−0.734044	+	0.679102i	$0.762369\pi$
$468$	−1.00000	−0.0462250
$469$	19.6143	0.905704
$470$	−5.97992	−0.275833
$471$	17.7343	0.817156
$472$	−8.16678	−0.375907
$473$	47.7586	2.19594
$474$	0.265176	0.0121799
$475$	−6.53820	−0.299993
$476$	−22.6121	−1.03642
$477$	−0.598639	−0.0274098
$478$	−0.580598	−0.0265559
$479$	−35.1413	−1.60565	−0.802823	−	0.596217i	$-0.796670\pi$
$479$	−35.1413	−1.60565	−0.802823	+	0.596217i	$0.796670\pi$
$480$	−1.81138	−0.0826779
$481$	5.87569	0.267908
$482$	−2.90864	−0.132485
$483$	−2.13490	−0.0971413
$484$	19.9856	0.908435
$485$	19.3793	0.879967
$486$	1.00000	0.0453609
$487$	17.7859	0.805956	0.402978	−	0.915210i	$-0.367975\pi$
$487$	17.7859	0.805956	0.402978	+	0.915210i	$0.367975\pi$
$488$	−9.67331	−0.437890
$489$	9.61966	0.435016
$490$	−22.0365	−0.995508
$491$	8.27351	0.373378	0.186689	−	0.982419i	$-0.440224\pi$
$491$	8.27351	0.373378	0.186689	+	0.982419i	$0.440224\pi$
$492$	0.941958	0.0424668
$493$	48.4980	2.18424
$494$	−3.80372	−0.171137
$495$	10.0830	0.453197
$496$	−0.944100	−0.0423914
$497$	−14.1265	−0.633662
$498$	−5.02677	−0.225255
$499$	−30.6191	−1.37070	−0.685350	−	0.728214i	$-0.740351\pi$
$499$	−30.6191	−1.37070	−0.685350	+	0.728214i	$0.740351\pi$
$500$	12.1705	0.544281
$501$	2.80000	0.125095
$502$	30.4421	1.35870
$503$	−22.7930	−1.01629	−0.508144	−	0.861272i	$-0.669668\pi$
$503$	−22.7930	−1.01629	−0.508144	+	0.861272i	$0.669668\pi$
$504$	4.37785	0.195005
$505$	−14.3170	−0.637097
$506$	2.71454	0.120676
$507$	1.00000	0.0444116
$508$	−1.94633	−0.0863543
$509$	36.6861	1.62608	0.813042	−	0.582205i	$-0.197810\pi$
$509$	36.6861	1.62608	0.813042	+	0.582205i	$0.197810\pi$
$510$	9.35598	0.414290
$511$	6.48995	0.287099
$512$	1.00000	0.0441942
$513$	3.80372	0.167938
$514$	26.2924	1.15971
$515$	1.81138	0.0798190
$516$	−8.57969	−0.377700
$517$	−18.3766	−0.808202
$518$	−25.7229	−1.13020
$519$	−23.6784	−1.03937
$520$	1.81138	0.0794343
$521$	2.38421	0.104454	0.0522271	−	0.998635i	$-0.483368\pi$
$521$	2.38421	0.104454	0.0522271	+	0.998635i	$0.483368\pi$
$522$	−9.38955	−0.410969
$523$	−18.1159	−0.792152	−0.396076	−	0.918218i	$-0.629628\pi$
$523$	−18.1159	−0.792152	−0.396076	+	0.918218i	$0.629628\pi$
$524$	−9.28623	−0.405671
$525$	−7.52507	−0.328421
$526$	12.4674	0.543604
$527$	4.87638	0.212418
$528$	−5.56647	−0.242249
$529$	−22.7622	−0.989660
$530$	1.08436	0.0471018
$531$	−8.16678	−0.354408
$532$	16.6521	0.721961
$533$	−0.941958	−0.0408007
$534$	4.65275	0.201344
$535$	−10.2914	−0.444935
$536$	4.48035	0.193521
$537$	−9.21549	−0.397678
$538$	14.4119	0.621343
$539$	−67.7193	−2.91688
$540$	−1.81138	−0.0779495
$541$	−12.9925	−0.558592	−0.279296	−	0.960205i	$-0.590101\pi$
$541$	−12.9925	−0.558592	−0.279296	+	0.960205i	$0.590101\pi$
$542$	−21.5259	−0.924616
$543$	−15.3675	−0.659481
$544$	−5.16511	−0.221452
$545$	−18.9852	−0.813236
$546$	−4.37785	−0.187355
$547$	2.86119	0.122336	0.0611678	−	0.998127i	$-0.480518\pi$
$547$	2.86119	0.122336	0.0611678	+	0.998127i	$0.480518\pi$
$548$	−5.64827	−0.241282
$549$	−9.67331	−0.412847
$550$	9.56818	0.407989
$551$	−35.7152	−1.52152
$552$	−0.487660	−0.0207562
$553$	1.16090	0.0493665
$554$	−9.61980	−0.408706
$555$	10.6431	0.451775
$556$	−21.2985	−0.903256
$557$	−14.8839	−0.630649	−0.315324	−	0.948984i	$-0.602113\pi$
$557$	−14.8839	−0.630649	−0.315324	+	0.948984i	$0.602113\pi$
$558$	−0.944100	−0.0399669
$559$	8.57969	0.362882
$560$	−7.92996	−0.335102
$561$	28.7514	1.21389
$562$	26.1990	1.10514
$563$	−10.8563	−0.457540	−0.228770	−	0.973481i	$-0.573470\pi$
$563$	−10.8563	−0.457540	−0.228770	+	0.973481i	$0.573470\pi$
$564$	3.30130	0.139010
$565$	−7.63065	−0.321024
$566$	−6.77984	−0.284978
$567$	4.37785	0.183852
$568$	−3.22682	−0.135394
$569$	30.8487	1.29324	0.646622	−	0.762810i	$-0.276181\pi$
$569$	30.8487	1.29324	0.646622	+	0.762810i	$0.276181\pi$
$570$	−6.88999	−0.288590
$571$	0.636296	0.0266282	0.0133141	−	0.999911i	$-0.495762\pi$
$571$	0.636296	0.0266282	0.0133141	+	0.999911i	$0.495762\pi$
$572$	5.56647	0.232746
$573$	−5.85534	−0.244610
$574$	4.12375	0.172122
$575$	0.838236	0.0349569
$576$	1.00000	0.0416667
$577$	−5.64259	−0.234904	−0.117452	−	0.993079i	$-0.537473\pi$
$577$	−5.64259	−0.234904	−0.117452	+	0.993079i	$0.537473\pi$
$578$	9.67835	0.402566
$579$	11.0520	0.459307
$580$	17.0081	0.706221
$581$	−22.0064	−0.912981
$582$	−10.6986	−0.443472
$583$	3.33231	0.138010
$584$	1.48245	0.0613443
$585$	1.81138	0.0748914
$586$	−4.73881	−0.195758
$587$	33.5860	1.38624	0.693121	−	0.720821i	$-0.256235\pi$
$587$	33.5860	1.38624	0.693121	+	0.720821i	$0.256235\pi$
$588$	12.1656	0.501700
$589$	−3.59109	−0.147968
$590$	14.7932	0.609025
$591$	−23.8570	−0.981344
$592$	−5.87569	−0.241489
$593$	−43.6575	−1.79280	−0.896399	−	0.443249i	$-0.853826\pi$
$593$	−43.6575	−1.79280	−0.896399	+	0.443249i	$0.853826\pi$
$594$	−5.56647	−0.228395
$595$	40.9591	1.67916
$596$	10.2997	0.421892
$597$	13.5544	0.554747
$598$	0.487660	0.0199419
$599$	43.8126	1.79013	0.895067	−	0.445931i	$-0.147127\pi$
$599$	43.8126	1.79013	0.895067	+	0.445931i	$0.147127\pi$
$600$	−1.71890	−0.0701736
$601$	18.5859	0.758133	0.379066	−	0.925370i	$-0.376245\pi$
$601$	18.5859	0.758133	0.379066	+	0.925370i	$0.376245\pi$
$602$	−37.5606	−1.53086
$603$	4.48035	0.182454
$604$	9.58601	0.390049
$605$	−36.2015	−1.47180
$606$	7.90390	0.321074
$607$	2.58005	0.104721	0.0523605	−	0.998628i	$-0.483326\pi$
$607$	2.58005	0.104721	0.0523605	+	0.998628i	$0.483326\pi$
$608$	3.80372	0.154261
$609$	−41.1060	−1.66570
$610$	17.5221	0.709448
$611$	−3.30130	−0.133557
$612$	−5.16511	−0.208787
$613$	−5.83795	−0.235793	−0.117896	−	0.993026i	$-0.537615\pi$
$613$	−5.83795	−0.235793	−0.117896	+	0.993026i	$0.537615\pi$
$614$	12.8551	0.518791
$615$	−1.70625	−0.0688025
$616$	−24.3692	−0.981862
$617$	11.9361	0.480530	0.240265	−	0.970707i	$-0.422766\pi$
$617$	11.9361	0.480530	0.240265	+	0.970707i	$0.422766\pi$
$618$	−1.00000	−0.0402259
$619$	25.9889	1.04458	0.522291	−	0.852767i	$-0.325077\pi$
$619$	25.9889	1.04458	0.522291	+	0.852767i	$0.325077\pi$
$620$	1.71013	0.0686803
$621$	−0.487660	−0.0195691
$622$	−30.5174	−1.22364
$623$	20.3690	0.816069
$624$	−1.00000	−0.0400320
$625$	−13.4509	−0.538037
$626$	18.8827	0.754705
$627$	−21.1733	−0.845580
$628$	17.7343	0.707677
$629$	30.3486	1.21008
$630$	−7.92996	−0.315937
$631$	−13.5519	−0.539493	−0.269747	−	0.962931i	$-0.586940\pi$
$631$	−13.5519	−0.539493	−0.269747	+	0.962931i	$0.586940\pi$
$632$	0.265176	0.0105481
$633$	4.74160	0.188461
$634$	33.5941	1.33419
$635$	3.52554	0.139907
$636$	−0.598639	−0.0237376
$637$	−12.1656	−0.482018
$638$	52.2666	2.06926
$639$	−3.22682	−0.127651
$640$	−1.81138	−0.0716012
$641$	−8.10768	−0.320234	−0.160117	−	0.987098i	$-0.551187\pi$
$641$	−8.10768	−0.320234	−0.160117	+	0.987098i	$0.551187\pi$
$642$	5.68151	0.224231
$643$	7.02199	0.276920	0.138460	−	0.990368i	$-0.455785\pi$
$643$	7.02199	0.276920	0.138460	+	0.990368i	$0.455785\pi$
$644$	−2.13490	−0.0841269
$645$	15.5411	0.611930
$646$	−19.6466	−0.772986
$647$	−47.0959	−1.85153	−0.925765	−	0.378100i	$-0.876578\pi$
$647$	−47.0959	−1.85153	−0.925765	+	0.378100i	$0.876578\pi$
$648$	1.00000	0.0392837
$649$	45.4601	1.78447
$650$	1.71890	0.0674206
$651$	−4.13313	−0.161990
$652$	9.61966	0.376735
$653$	−13.9840	−0.547235	−0.273618	−	0.961839i	$-0.588220\pi$
$653$	−13.9840	−0.547235	−0.273618	+	0.961839i	$0.588220\pi$
$654$	10.4811	0.409842
$655$	16.8209	0.657247
$656$	0.941958	0.0367773
$657$	1.48245	0.0578360
$658$	14.4526	0.563422
$659$	12.4604	0.485388	0.242694	−	0.970103i	$-0.421969\pi$
$659$	12.4604	0.485388	0.242694	+	0.970103i	$0.421969\pi$
$660$	10.0830	0.392480
$661$	−32.4263	−1.26124	−0.630618	−	0.776093i	$-0.717199\pi$
$661$	−32.4263	−1.26124	−0.630618	+	0.776093i	$0.717199\pi$
$662$	9.48800	0.368762
$663$	5.16511	0.200596
$664$	−5.02677	−0.195076
$665$	−30.1633	−1.16968
$666$	−5.87569	−0.227678
$667$	4.57890	0.177296
$668$	2.80000	0.108335
$669$	4.85412	0.187671
$670$	−8.11562	−0.313534
$671$	53.8462	2.07871
$672$	4.37785	0.168879
$673$	−34.2779	−1.32132	−0.660659	−	0.750687i	$-0.729723\pi$
$673$	−34.2779	−1.32132	−0.660659	+	0.750687i	$0.729723\pi$
$674$	12.5707	0.484204
$675$	−1.71890	−0.0661603
$676$	1.00000	0.0384615
$677$	−34.0811	−1.30984	−0.654921	−	0.755697i	$-0.727298\pi$
$677$	−34.0811	−1.30984	−0.654921	+	0.755697i	$0.727298\pi$
$678$	4.21261	0.161784
$679$	−46.8369	−1.79744
$680$	9.35598	0.358786
$681$	−21.1215	−0.809378
$682$	5.25530	0.201236
$683$	34.8796	1.33463	0.667315	−	0.744775i	$-0.267443\pi$
$683$	34.8796	1.33463	0.667315	+	0.744775i	$0.267443\pi$
$684$	3.80372	0.145439
$685$	10.2312	0.390913
$686$	22.6141	0.863412
$687$	−27.2810	−1.04084
$688$	−8.57969	−0.327098
$689$	0.598639	0.0228063
$690$	0.883338	0.0336281
$691$	12.4419	0.473314	0.236657	−	0.971593i	$-0.423948\pi$
$691$	12.4419	0.473314	0.236657	+	0.971593i	$0.423948\pi$
$692$	−23.6784	−0.900118
$693$	−24.3692	−0.925708
$694$	7.58431	0.287897
$695$	38.5797	1.46341
$696$	−9.38955	−0.355910
$697$	−4.86532	−0.184287
$698$	10.2740	0.388877
$699$	−12.8522	−0.486116
$700$	−7.52507	−0.284421
$701$	−15.4831	−0.584787	−0.292394	−	0.956298i	$-0.594452\pi$
$701$	−15.4831	−0.584787	−0.292394	+	0.956298i	$0.594452\pi$
$702$	−1.00000	−0.0377426
$703$	−22.3495	−0.842927
$704$	−5.56647	−0.209794
$705$	−5.97992	−0.225217
$706$	−23.2135	−0.873653
$707$	34.6021	1.30135
$708$	−8.16678	−0.306926
$709$	−37.4072	−1.40486	−0.702428	−	0.711755i	$-0.747901\pi$
$709$	−37.4072	−1.40486	−0.702428	+	0.711755i	$0.747901\pi$
$710$	5.84500	0.219359
$711$	0.265176	0.00994488
$712$	4.65275	0.174369
$713$	0.460399	0.0172421
$714$	−22.6121	−0.846236
$715$	−10.0830	−0.377083
$716$	−9.21549	−0.344399
$717$	−0.580598	−0.0216828
$718$	−22.5062	−0.839923
$719$	−27.5344	−1.02686	−0.513431	−	0.858131i	$-0.671626\pi$
$719$	−27.5344	−1.02686	−0.513431	+	0.858131i	$0.671626\pi$
$720$	−1.81138	−0.0675062
$721$	−4.37785	−0.163040
$722$	−4.53172	−0.168653
$723$	−2.90864	−0.108174
$724$	−15.3675	−0.571127
$725$	16.1397	0.599412
$726$	19.9856	0.741734
$727$	27.6481	1.02541	0.512706	−	0.858564i	$-0.328643\pi$
$727$	27.6481	1.02541	0.512706	+	0.858564i	$0.328643\pi$
$728$	−4.37785	−0.162254
$729$	1.00000	0.0370370
$730$	−2.68529	−0.0993869
$731$	44.3150	1.63905
$732$	−9.67331	−0.357536
$733$	13.2415	0.489085	0.244542	−	0.969639i	$-0.421362\pi$
$733$	13.2415	0.489085	0.244542	+	0.969639i	$0.421362\pi$
$734$	17.1243	0.632069
$735$	−22.0365	−0.812829
$736$	−0.487660	−0.0179754
$737$	−24.9397	−0.918666
$738$	0.941958	0.0346740
$739$	−28.6866	−1.05525	−0.527627	−	0.849476i	$-0.676918\pi$
$739$	−28.6866	−1.05525	−0.527627	+	0.849476i	$0.676918\pi$
$740$	10.6431	0.391249
$741$	−3.80372	−0.139733
$742$	−2.62075	−0.0962109
$743$	−10.8669	−0.398670	−0.199335	−	0.979931i	$-0.563878\pi$
$743$	−10.8669	−0.398670	−0.199335	+	0.979931i	$0.563878\pi$
$744$	−0.944100	−0.0346124
$745$	−18.6567	−0.683528
$746$	13.4598	0.492797
$747$	−5.02677	−0.183920
$748$	28.7514	1.05126
$749$	24.8728	0.908832
$750$	12.1705	0.444403
$751$	−29.5429	−1.07804	−0.539018	−	0.842294i	$-0.681204\pi$
$751$	−29.5429	−1.07804	−0.539018	+	0.842294i	$0.681204\pi$
$752$	3.30130	0.120386
$753$	30.4421	1.10937
$754$	9.38955	0.341947
$755$	−17.3639	−0.631938
$756$	4.37785	0.159221
$757$	30.2692	1.10015	0.550076	−	0.835115i	$-0.314599\pi$
$757$	30.2692	1.10015	0.550076	+	0.835115i	$0.314599\pi$
$758$	4.65242	0.168984
$759$	2.71454	0.0985316
$760$	−6.88999	−0.249926
$761$	36.1585	1.31074	0.655372	−	0.755306i	$-0.272512\pi$
$761$	36.1585	1.31074	0.655372	+	0.755306i	$0.272512\pi$
$762$	−1.94633	−0.0705080
$763$	45.8845	1.66113
$764$	−5.85534	−0.211839
$765$	9.35598	0.338266
$766$	0.934727	0.0337731
$767$	8.16678	0.294885
$768$	1.00000	0.0360844
$769$	−24.4039	−0.880026	−0.440013	−	0.897991i	$-0.645026\pi$
$769$	−24.4039	−0.880026	−0.440013	+	0.897991i	$0.645026\pi$
$770$	44.1419	1.59076
$771$	26.2924	0.946897
$772$	11.0520	0.397771
$773$	24.7129	0.888860	0.444430	−	0.895814i	$-0.353406\pi$
$773$	24.7129	0.888860	0.444430	+	0.895814i	$0.353406\pi$
$774$	−8.57969	−0.308391
$775$	1.62281	0.0582930
$776$	−10.6986	−0.384058
$777$	−25.7229	−0.922804
$778$	−29.0606	−1.04187
$779$	3.58295	0.128372
$780$	1.81138	0.0648579
$781$	17.9620	0.642731
$782$	2.51881	0.0900726
$783$	−9.38955	−0.335555
$784$	12.1656	0.434485
$785$	−32.1237	−1.14654
$786$	−9.28623	−0.331229
$787$	−36.6040	−1.30479	−0.652396	−	0.757878i	$-0.726236\pi$
$787$	−36.6040	−1.30479	−0.652396	+	0.757878i	$0.726236\pi$
$788$	−23.8570	−0.849869
$789$	12.4674	0.443851
$790$	−0.480335	−0.0170896
$791$	18.4422	0.655729
$792$	−5.56647	−0.197796
$793$	9.67331	0.343509
$794$	0.323229	0.0114710
$795$	1.08436	0.0384584
$796$	13.5544	0.480425
$797$	36.8100	1.30388	0.651938	−	0.758272i	$-0.273956\pi$
$797$	36.8100	1.30388	0.651938	+	0.758272i	$0.273956\pi$
$798$	16.6521	0.589479
$799$	−17.0516	−0.603242
$800$	−1.71890	−0.0607721
$801$	4.65275	0.164397
$802$	−17.3492	−0.612621
$803$	−8.25202	−0.291208
$804$	4.48035	0.158010
$805$	3.86712	0.136298
$806$	0.944100	0.0332545
$807$	14.4119	0.507324
$808$	7.90390	0.278058
$809$	48.7300	1.71326	0.856628	−	0.515934i	$-0.172555\pi$
$809$	48.7300	1.71326	0.856628	+	0.515934i	$0.172555\pi$
$810$	−1.81138	−0.0636455
$811$	−8.06656	−0.283255	−0.141628	−	0.989920i	$-0.545234\pi$
$811$	−8.06656	−0.283255	−0.141628	+	0.989920i	$0.545234\pi$
$812$	−41.1060	−1.44254
$813$	−21.5259	−0.754945
$814$	32.7069	1.14637
$815$	−17.4249	−0.610367
$816$	−5.16511	−0.180815
$817$	−32.6347	−1.14174
$818$	8.63479	0.301908
$819$	−4.37785	−0.152974
$820$	−1.70625	−0.0595847
$821$	9.63778	0.336361	0.168180	−	0.985756i	$-0.446211\pi$
$821$	9.63778	0.336361	0.168180	+	0.985756i	$0.446211\pi$
$822$	−5.64827	−0.197006
$823$	15.4284	0.537800	0.268900	−	0.963168i	$-0.413340\pi$
$823$	15.4284	0.537800	0.268900	+	0.963168i	$0.413340\pi$
$824$	−1.00000	−0.0348367
$825$	9.56818	0.333121
$826$	−35.7529	−1.24400
$827$	−9.07574	−0.315594	−0.157797	−	0.987472i	$-0.550439\pi$
$827$	−9.07574	−0.315594	−0.157797	+	0.987472i	$0.550439\pi$
$828$	−0.487660	−0.0169473
$829$	−12.5557	−0.436078	−0.218039	−	0.975940i	$-0.569966\pi$
$829$	−12.5557	−0.436078	−0.218039	+	0.975940i	$0.569966\pi$
$830$	9.10540	0.316053
$831$	−9.61980	−0.333707
$832$	−1.00000	−0.0346688
$833$	−62.8365	−2.17716
$834$	−21.2985	−0.737506
$835$	−5.07187	−0.175519
$836$	−21.1733	−0.732293
$837$	−0.944100	−0.0326329
$838$	−22.7542	−0.786031
$839$	−34.8333	−1.20258	−0.601290	−	0.799031i	$-0.705346\pi$
$839$	−34.8333	−1.20258	−0.601290	+	0.799031i	$0.705346\pi$
$840$	−7.92996	−0.273610
$841$	59.1636	2.04012
$842$	−2.70603	−0.0932561
$843$	26.1990	0.902343
$844$	4.74160	0.163212
$845$	−1.81138	−0.0623134
$846$	3.30130	0.113501
$847$	87.4939	3.00633
$848$	−0.598639	−0.0205574
$849$	−6.77984	−0.232683
$850$	8.87828	0.304523
$851$	2.86534	0.0982225
$852$	−3.22682	−0.110549
$853$	−57.0762	−1.95425	−0.977126	−	0.212662i	$-0.931787\pi$
$853$	−57.0762	−1.95425	−0.977126	+	0.212662i	$0.931787\pi$
$854$	−42.3483	−1.44913
$855$	−6.88999	−0.235633
$856$	5.68151	0.194190
$857$	−9.34204	−0.319118	−0.159559	−	0.987188i	$-0.551007\pi$
$857$	−9.34204	−0.319118	−0.159559	+	0.987188i	$0.551007\pi$
$858$	5.56647	0.190036
$859$	−23.7710	−0.811055	−0.405527	−	0.914083i	$-0.632912\pi$
$859$	−23.7710	−0.811055	−0.405527	+	0.914083i	$0.632912\pi$
$860$	15.5411	0.529947
$861$	4.12375	0.140537
$862$	23.1697	0.789164
$863$	4.02455	0.136997	0.0684986	−	0.997651i	$-0.478179\pi$
$863$	4.02455	0.136997	0.0684986	+	0.997651i	$0.478179\pi$
$864$	1.00000	0.0340207
$865$	42.8907	1.45833
$866$	24.5834	0.835378
$867$	9.67835	0.328694
$868$	−4.13313	−0.140288
$869$	−1.47609	−0.0500731
$870$	17.0081	0.576627
$871$	−4.48035	−0.151811
$872$	10.4811	0.354933
$873$	−10.6986	−0.362093
$874$	−1.85492	−0.0627436
$875$	53.2806	1.80121
$876$	1.48245	0.0500874
$877$	12.9643	0.437773	0.218886	−	0.975750i	$-0.429758\pi$
$877$	12.9643	0.437773	0.218886	+	0.975750i	$0.429758\pi$
$878$	−20.5109	−0.692211
$879$	−4.73881	−0.159836
$880$	10.0830	0.339898
$881$	55.7404	1.87794	0.938970	−	0.343998i	$-0.111781\pi$
$881$	55.7404	1.87794	0.938970	+	0.343998i	$0.111781\pi$
$882$	12.1656	0.409636
$883$	−4.81700	−0.162105	−0.0810525	−	0.996710i	$-0.525828\pi$
$883$	−4.81700	−0.162105	−0.0810525	+	0.996710i	$0.525828\pi$
$884$	5.16511	0.173721
$885$	14.7932	0.497267
$886$	−12.4724	−0.419018
$887$	49.1138	1.64908	0.824539	−	0.565805i	$-0.191434\pi$
$887$	49.1138	1.64908	0.824539	+	0.565805i	$0.191434\pi$
$888$	−5.87569	−0.197175
$889$	−8.52073	−0.285776
$890$	−8.42791	−0.282504
$891$	−5.56647	−0.186484
$892$	4.85412	0.162528
$893$	12.5572	0.420212
$894$	10.2997	0.344473
$895$	16.6928	0.557978
$896$	4.37785	0.146254
$897$	0.487660	0.0162825
$898$	24.6318	0.821974
$899$	8.86467	0.295653
$900$	−1.71890	−0.0572965
$901$	3.09204	0.103011
$902$	−5.24338	−0.174586
$903$	−37.5606	−1.24994
$904$	4.21261	0.140109
$905$	27.8363	0.925311
$906$	9.58601	0.318474
$907$	38.0044	1.26192	0.630958	−	0.775817i	$-0.282662\pi$
$907$	38.0044	1.26192	0.630958	+	0.775817i	$0.282662\pi$
$908$	−21.1215	−0.700942
$909$	7.90390	0.262156
$910$	7.92996	0.262876
$911$	−3.97665	−0.131752	−0.0658762	−	0.997828i	$-0.520984\pi$
$911$	−3.97665	−0.131752	−0.0658762	+	0.997828i	$0.520984\pi$
$912$	3.80372	0.125954
$913$	27.9814	0.926048
$914$	−20.7717	−0.687067
$915$	17.5221	0.579262
$916$	−27.2810	−0.901391
$917$	−40.6537	−1.34250
$918$	−5.16511	−0.170474
$919$	17.7103	0.584208	0.292104	−	0.956387i	$-0.405645\pi$
$919$	17.7103	0.584208	0.292104	+	0.956387i	$0.405645\pi$
$920$	0.883338	0.0291228
$921$	12.8551	0.423591
$922$	16.6568	0.548562
$923$	3.22682	0.106212
$924$	−24.3692	−0.801687
$925$	10.0997	0.332076
$926$	−34.8615	−1.14562
$927$	−1.00000	−0.0328443
$928$	−9.38955	−0.308227
$929$	−14.6561	−0.480850	−0.240425	−	0.970668i	$-0.577287\pi$
$929$	−14.6561	−0.480850	−0.240425	+	0.970668i	$0.577287\pi$
$930$	1.71013	0.0560772
$931$	46.2745	1.51658
$932$	−12.8522	−0.420989
$933$	−30.5174	−0.999096
$934$	−31.7256	−1.03809
$935$	−52.0798	−1.70319
$936$	−1.00000	−0.0326860
$937$	15.3053	0.500001	0.250000	−	0.968246i	$-0.419569\pi$
$937$	15.3053	0.500001	0.250000	+	0.968246i	$0.419569\pi$
$938$	19.6143	0.640429
$939$	18.8827	0.616214
$940$	−5.97992	−0.195044
$941$	11.1823	0.364532	0.182266	−	0.983249i	$-0.441657\pi$
$941$	11.1823	0.364532	0.182266	+	0.983249i	$0.441657\pi$
$942$	17.7343	0.577816
$943$	−0.459355	−0.0149587
$944$	−8.16678	−0.265806
$945$	−7.92996	−0.257962
$946$	47.7586	1.55277
$947$	−19.1548	−0.622447	−0.311224	−	0.950337i	$-0.600739\pi$
$947$	−19.1548	−0.622447	−0.311224	+	0.950337i	$0.600739\pi$
$948$	0.265176	0.00861252
$949$	−1.48245	−0.0481224
$950$	−6.53820	−0.212127
$951$	33.5941	1.08936
$952$	−22.6121	−0.732862
$953$	33.6296	1.08937	0.544684	−	0.838641i	$-0.316649\pi$
$953$	33.6296	1.08937	0.544684	+	0.838641i	$0.316649\pi$
$954$	−0.598639	−0.0193817
$955$	10.6063	0.343210
$956$	−0.580598	−0.0187779
$957$	52.2666	1.68954
$958$	−35.1413	−1.13536
$959$	−24.7273	−0.798486
$960$	−1.81138	−0.0584621
$961$	−30.1087	−0.971248
$962$	5.87569	0.189440
$963$	5.68151	0.183084
$964$	−2.90864	−0.0936810
$965$	−20.0195	−0.644449
$966$	−2.13490	−0.0686893
$967$	−43.0722	−1.38511	−0.692554	−	0.721366i	$-0.743514\pi$
$967$	−43.0722	−1.38511	−0.692554	+	0.721366i	$0.743514\pi$
$968$	19.9856	0.642361
$969$	−19.6466	−0.631140
$970$	19.3793	0.622231
$971$	13.4010	0.430059	0.215029	−	0.976608i	$-0.431015\pi$
$971$	13.4010	0.430059	0.215029	+	0.976608i	$0.431015\pi$
$972$	1.00000	0.0320750
$973$	−93.2415	−2.98919
$974$	17.7859	0.569897
$975$	1.71890	0.0550487
$976$	−9.67331	−0.309635
$977$	13.4087	0.428983	0.214492	−	0.976726i	$-0.431191\pi$
$977$	13.4087	0.428983	0.214492	+	0.976726i	$0.431191\pi$
$978$	9.61966	0.307603
$979$	−25.8994	−0.827748
$980$	−22.0365	−0.703930
$981$	10.4811	0.334634
$982$	8.27351	0.264018
$983$	−18.9867	−0.605581	−0.302791	−	0.953057i	$-0.597918\pi$
$983$	−18.9867	−0.605581	−0.302791	+	0.953057i	$0.597918\pi$
$984$	0.941958	0.0300285
$985$	43.2141	1.37691
$986$	48.4980	1.54449
$987$	14.4526	0.460032
$988$	−3.80372	−0.121012
$989$	4.18397	0.133042
$990$	10.0830	0.320459
$991$	2.88673	0.0916999	0.0458500	−	0.998948i	$-0.485400\pi$
$991$	2.88673	0.0916999	0.0458500	+	0.998948i	$0.485400\pi$
$992$	−0.944100	−0.0299752
$993$	9.48800	0.301093
$994$	−14.1265	−0.448066
$995$	−24.5523	−0.778359
$996$	−5.02677	−0.159279
$997$	46.7589	1.48087	0.740434	−	0.672129i	$-0.234620\pi$
$997$	46.7589	1.48087	0.740434	+	0.672129i	$0.234620\pi$
$998$	−30.6191	−0.969231
$999$	−5.87569	−0.185899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.q.1.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.q.1.2	✓	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.81138 q^{5} +1.00000 q^{6} +4.37785 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.81138 q^{5} +1.00000 q^{6} +4.37785 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.81138 q^{10} -5.56647 q^{11} +1.00000 q^{12} -1.00000 q^{13} +4.37785 q^{14} -1.81138 q^{15} +1.00000 q^{16} -5.16511 q^{17} +1.00000 q^{18} +3.80372 q^{19} -1.81138 q^{20} +4.37785 q^{21} -5.56647 q^{22} -0.487660 q^{23} +1.00000 q^{24} -1.71890 q^{25} -1.00000 q^{26} +1.00000 q^{27} +4.37785 q^{28} -9.38955 q^{29} -1.81138 q^{30} -0.944100 q^{31} +1.00000 q^{32} -5.56647 q^{33} -5.16511 q^{34} -7.92996 q^{35} +1.00000 q^{36} -5.87569 q^{37} +3.80372 q^{38} -1.00000 q^{39} -1.81138 q^{40} +0.941958 q^{41} +4.37785 q^{42} -8.57969 q^{43} -5.56647 q^{44} -1.81138 q^{45} -0.487660 q^{46} +3.30130 q^{47} +1.00000 q^{48} +12.1656 q^{49} -1.71890 q^{50} -5.16511 q^{51} -1.00000 q^{52} -0.598639 q^{53} +1.00000 q^{54} +10.0830 q^{55} +4.37785 q^{56} +3.80372 q^{57} -9.38955 q^{58} -8.16678 q^{59} -1.81138 q^{60} -9.67331 q^{61} -0.944100 q^{62} +4.37785 q^{63} +1.00000 q^{64} +1.81138 q^{65} -5.56647 q^{66} +4.48035 q^{67} -5.16511 q^{68} -0.487660 q^{69} -7.92996 q^{70} -3.22682 q^{71} +1.00000 q^{72} +1.48245 q^{73} -5.87569 q^{74} -1.71890 q^{75} +3.80372 q^{76} -24.3692 q^{77} -1.00000 q^{78} +0.265176 q^{79} -1.81138 q^{80} +1.00000 q^{81} +0.941958 q^{82} -5.02677 q^{83} +4.37785 q^{84} +9.35598 q^{85} -8.57969 q^{86} -9.38955 q^{87} -5.56647 q^{88} +4.65275 q^{89} -1.81138 q^{90} -4.37785 q^{91} -0.487660 q^{92} -0.944100 q^{93} +3.30130 q^{94} -6.88999 q^{95} +1.00000 q^{96} -10.6986 q^{97} +12.1656 q^{98} -5.56647 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9} - 6 q^{10} - 15 q^{11} + 8 q^{12} - 8 q^{13} - 3 q^{14} - 6 q^{15} + 8 q^{16} - 11 q^{17} + 8 q^{18} - 15 q^{19} - 6 q^{20} - 3 q^{21} - 15 q^{22} + q^{23} + 8 q^{24} - 10 q^{25} - 8 q^{26} + 8 q^{27} - 3 q^{28} - 10 q^{29} - 6 q^{30} - 3 q^{31} + 8 q^{32} - 15 q^{33} - 11 q^{34} - 12 q^{35} + 8 q^{36} - 26 q^{37} - 15 q^{38} - 8 q^{39} - 6 q^{40} - 12 q^{41} - 3 q^{42} - 4 q^{43} - 15 q^{44} - 6 q^{45} + q^{46} - 6 q^{47} + 8 q^{48} - 5 q^{49} - 10 q^{50} - 11 q^{51} - 8 q^{52} - 4 q^{53} + 8 q^{54} - 3 q^{56} - 15 q^{57} - 10 q^{58} - 19 q^{59} - 6 q^{60} - 14 q^{61} - 3 q^{62} - 3 q^{63} + 8 q^{64} + 6 q^{65} - 15 q^{66} - 13 q^{67} - 11 q^{68} + q^{69} - 12 q^{70} - 31 q^{71} + 8 q^{72} - 27 q^{73} - 26 q^{74} - 10 q^{75} - 15 q^{76} - 30 q^{77} - 8 q^{78} - 13 q^{79} - 6 q^{80} + 8 q^{81} - 12 q^{82} - 28 q^{83} - 3 q^{84} + 15 q^{85} - 4 q^{86} - 10 q^{87} - 15 q^{88} - 2 q^{89} - 6 q^{90} + 3 q^{91} + q^{92} - 3 q^{93} - 6 q^{94} - 18 q^{95} + 8 q^{96} - 30 q^{97} - 5 q^{98} - 15 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9 - 6 * q^10 - 15 * q^11 + 8 * q^12 - 8 * q^13 - 3 * q^14 - 6 * q^15 + 8 * q^16 - 11 * q^17 + 8 * q^18 - 15 * q^19 - 6 * q^20 - 3 * q^21 - 15 * q^22 + q^23 + 8 * q^24 - 10 * q^25 - 8 * q^26 + 8 * q^27 - 3 * q^28 - 10 * q^29 - 6 * q^30 - 3 * q^31 + 8 * q^32 - 15 * q^33 - 11 * q^34 - 12 * q^35 + 8 * q^36 - 26 * q^37 - 15 * q^38 - 8 * q^39 - 6 * q^40 - 12 * q^41 - 3 * q^42 - 4 * q^43 - 15 * q^44 - 6 * q^45 + q^46 - 6 * q^47 + 8 * q^48 - 5 * q^49 - 10 * q^50 - 11 * q^51 - 8 * q^52 - 4 * q^53 + 8 * q^54 - 3 * q^56 - 15 * q^57 - 10 * q^58 - 19 * q^59 - 6 * q^60 - 14 * q^61 - 3 * q^62 - 3 * q^63 + 8 * q^64 + 6 * q^65 - 15 * q^66 - 13 * q^67 - 11 * q^68 + q^69 - 12 * q^70 - 31 * q^71 + 8 * q^72 - 27 * q^73 - 26 * q^74 - 10 * q^75 - 15 * q^76 - 30 * q^77 - 8 * q^78 - 13 * q^79 - 6 * q^80 + 8 * q^81 - 12 * q^82 - 28 * q^83 - 3 * q^84 + 15 * q^85 - 4 * q^86 - 10 * q^87 - 15 * q^88 - 2 * q^89 - 6 * q^90 + 3 * q^91 + q^92 - 3 * q^93 - 6 * q^94 - 18 * q^95 + 8 * q^96 - 30 * q^97 - 5 * q^98 - 15 * q^99

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