LMFDB - Embedded newform 8034.2.a.s.1.9

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 15x^{8} + 72x^{7} - 27x^{6} - 115x^{5} + 54x^{4} + 68x^{3} - 15x^{2} - 15x - 2 $ x^10 - 4x^9 - 15x^8 + 72x^7 - 27x^6 - 115x^5 + 54x^4 + 68x^3 - 15x^2 - 15*x - 2
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			1.9
Root			$1.22324$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.54892 q^{5} +1.00000 q^{6} +0.812393 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.54892 q^{5} +1.00000 q^{6} +0.812393 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.54892 q^{10} -0.499691 q^{11} -1.00000 q^{12} -1.00000 q^{13} -0.812393 q^{14} -3.54892 q^{15} +1.00000 q^{16} -2.03563 q^{17} -1.00000 q^{18} -5.19945 q^{19} +3.54892 q^{20} -0.812393 q^{21} +0.499691 q^{22} -5.38809 q^{23} +1.00000 q^{24} +7.59480 q^{25} +1.00000 q^{26} -1.00000 q^{27} +0.812393 q^{28} +2.20133 q^{29} +3.54892 q^{30} -3.36102 q^{31} -1.00000 q^{32} +0.499691 q^{33} +2.03563 q^{34} +2.88312 q^{35} +1.00000 q^{36} -1.41020 q^{37} +5.19945 q^{38} +1.00000 q^{39} -3.54892 q^{40} +3.63946 q^{41} +0.812393 q^{42} +9.88901 q^{43} -0.499691 q^{44} +3.54892 q^{45} +5.38809 q^{46} -2.07824 q^{47} -1.00000 q^{48} -6.34002 q^{49} -7.59480 q^{50} +2.03563 q^{51} -1.00000 q^{52} +8.30317 q^{53} +1.00000 q^{54} -1.77336 q^{55} -0.812393 q^{56} +5.19945 q^{57} -2.20133 q^{58} -12.9475 q^{59} -3.54892 q^{60} +12.1458 q^{61} +3.36102 q^{62} +0.812393 q^{63} +1.00000 q^{64} -3.54892 q^{65} -0.499691 q^{66} -8.68355 q^{67} -2.03563 q^{68} +5.38809 q^{69} -2.88312 q^{70} -1.09298 q^{71} -1.00000 q^{72} -8.30384 q^{73} +1.41020 q^{74} -7.59480 q^{75} -5.19945 q^{76} -0.405945 q^{77} -1.00000 q^{78} +2.73029 q^{79} +3.54892 q^{80} +1.00000 q^{81} -3.63946 q^{82} +4.12953 q^{83} -0.812393 q^{84} -7.22428 q^{85} -9.88901 q^{86} -2.20133 q^{87} +0.499691 q^{88} -7.94125 q^{89} -3.54892 q^{90} -0.812393 q^{91} -5.38809 q^{92} +3.36102 q^{93} +2.07824 q^{94} -18.4524 q^{95} +1.00000 q^{96} -7.10010 q^{97} +6.34002 q^{98} -0.499691 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 + 10 * q^6 - 9 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9} - 6 q^{10} - q^{11} - 10 q^{12} - 10 q^{13} + 9 q^{14} - 6 q^{15} + 10 q^{16} + 5 q^{17} - 10 q^{18} - 9 q^{19} + 6 q^{20} + 9 q^{21} + q^{22} + q^{23} + 10 q^{24} + 20 q^{25} + 10 q^{26} - 10 q^{27} - 9 q^{28} - 22 q^{29} + 6 q^{30} - 13 q^{31} - 10 q^{32} + q^{33} - 5 q^{34} + 14 q^{35} + 10 q^{36} + 10 q^{37} + 9 q^{38} + 10 q^{39} - 6 q^{40} - 18 q^{41} - 9 q^{42} + 10 q^{43} - q^{44} + 6 q^{45} - q^{46} + 28 q^{47} - 10 q^{48} + 11 q^{49} - 20 q^{50} - 5 q^{51} - 10 q^{52} + 6 q^{53} + 10 q^{54} - 26 q^{55} + 9 q^{56} + 9 q^{57} + 22 q^{58} + 7 q^{59} - 6 q^{60} - 20 q^{61} + 13 q^{62} - 9 q^{63} + 10 q^{64} - 6 q^{65} - q^{66} - 21 q^{67} + 5 q^{68} - q^{69} - 14 q^{70} - 19 q^{71} - 10 q^{72} + 3 q^{73} - 10 q^{74} - 20 q^{75} - 9 q^{76} + 28 q^{77} - 10 q^{78} - 11 q^{79} + 6 q^{80} + 10 q^{81} + 18 q^{82} + 20 q^{83} + 9 q^{84} - q^{85} - 10 q^{86} + 22 q^{87} + q^{88} + 22 q^{89} - 6 q^{90} + 9 q^{91} + q^{92} + 13 q^{93} - 28 q^{94} + 10 q^{96} - 10 q^{97} - 11 q^{98} - q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 + 10 * q^6 - 9 * q^7 - 10 * q^8 + 10 * q^9 - 6 * q^10 - q^11 - 10 * q^12 - 10 * q^13 + 9 * q^14 - 6 * q^15 + 10 * q^16 + 5 * q^17 - 10 * q^18 - 9 * q^19 + 6 * q^20 + 9 * q^21 + q^22 + q^23 + 10 * q^24 + 20 * q^25 + 10 * q^26 - 10 * q^27 - 9 * q^28 - 22 * q^29 + 6 * q^30 - 13 * q^31 - 10 * q^32 + q^33 - 5 * q^34 + 14 * q^35 + 10 * q^36 + 10 * q^37 + 9 * q^38 + 10 * q^39 - 6 * q^40 - 18 * q^41 - 9 * q^42 + 10 * q^43 - q^44 + 6 * q^45 - q^46 + 28 * q^47 - 10 * q^48 + 11 * q^49 - 20 * q^50 - 5 * q^51 - 10 * q^52 + 6 * q^53 + 10 * q^54 - 26 * q^55 + 9 * q^56 + 9 * q^57 + 22 * q^58 + 7 * q^59 - 6 * q^60 - 20 * q^61 + 13 * q^62 - 9 * q^63 + 10 * q^64 - 6 * q^65 - q^66 - 21 * q^67 + 5 * q^68 - q^69 - 14 * q^70 - 19 * q^71 - 10 * q^72 + 3 * q^73 - 10 * q^74 - 20 * q^75 - 9 * q^76 + 28 * q^77 - 10 * q^78 - 11 * q^79 + 6 * q^80 + 10 * q^81 + 18 * q^82 + 20 * q^83 + 9 * q^84 - q^85 - 10 * q^86 + 22 * q^87 + q^88 + 22 * q^89 - 6 * q^90 + 9 * q^91 + q^92 + 13 * q^93 - 28 * q^94 + 10 * q^96 - 10 * q^97 - 11 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	3.54892	1.58712	0.793562	−	0.608490i	$-0.208224\pi$
$5$	3.54892	1.58712	0.793562	+	0.608490i	$0.208224\pi$
$6$	1.00000	0.408248
$7$	0.812393	0.307056	0.153528	−	0.988144i	$-0.450937\pi$
$7$	0.812393	0.307056	0.153528	+	0.988144i	$0.450937\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.54892	−1.12227
$11$	−0.499691	−0.150662	−0.0753312	−	0.997159i	$-0.524001\pi$
$11$	−0.499691	−0.150662	−0.0753312	+	0.997159i	$0.524001\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.812393	−0.217121
$15$	−3.54892	−0.916326
$16$	1.00000	0.250000
$17$	−2.03563	−0.493713	−0.246856	−	0.969052i	$-0.579398\pi$
$17$	−2.03563	−0.493713	−0.246856	+	0.969052i	$0.579398\pi$
$18$	−1.00000	−0.235702
$19$	−5.19945	−1.19284	−0.596418	−	0.802674i	$-0.703410\pi$
$19$	−5.19945	−1.19284	−0.596418	+	0.802674i	$0.703410\pi$
$20$	3.54892	0.793562
$21$	−0.812393	−0.177279
$22$	0.499691	0.106534
$23$	−5.38809	−1.12349	−0.561747	−	0.827309i	$-0.689871\pi$
$23$	−5.38809	−1.12349	−0.561747	+	0.827309i	$0.689871\pi$
$24$	1.00000	0.204124
$25$	7.59480	1.51896
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	0.812393	0.153528
$29$	2.20133	0.408776	0.204388	−	0.978890i	$-0.434480\pi$
$29$	2.20133	0.408776	0.204388	+	0.978890i	$0.434480\pi$
$30$	3.54892	0.647940
$31$	−3.36102	−0.603657	−0.301829	−	0.953362i	$-0.597597\pi$
$31$	−3.36102	−0.603657	−0.301829	+	0.953362i	$0.597597\pi$
$32$	−1.00000	−0.176777
$33$	0.499691	0.0869850
$34$	2.03563	0.349108
$35$	2.88312	0.487335
$36$	1.00000	0.166667
$37$	−1.41020	−0.231836	−0.115918	−	0.993259i	$-0.536981\pi$
$37$	−1.41020	−0.231836	−0.115918	+	0.993259i	$0.536981\pi$
$38$	5.19945	0.843463
$39$	1.00000	0.160128
$40$	−3.54892	−0.561133
$41$	3.63946	0.568388	0.284194	−	0.958767i	$-0.408274\pi$
$41$	3.63946	0.568388	0.284194	+	0.958767i	$0.408274\pi$
$42$	0.812393	0.125355
$43$	9.88901	1.50806	0.754030	−	0.656840i	$-0.228107\pi$
$43$	9.88901	1.50806	0.754030	+	0.656840i	$0.228107\pi$
$44$	−0.499691	−0.0753312
$45$	3.54892	0.529041
$46$	5.38809	0.794430
$47$	−2.07824	−0.303143	−0.151572	−	0.988446i	$-0.548433\pi$
$47$	−2.07824	−0.303143	−0.151572	+	0.988446i	$0.548433\pi$
$48$	−1.00000	−0.144338
$49$	−6.34002	−0.905717
$50$	−7.59480	−1.07407
$51$	2.03563	0.285045
$52$	−1.00000	−0.138675
$53$	8.30317	1.14053	0.570264	−	0.821462i	$-0.306841\pi$
$53$	8.30317	1.14053	0.570264	+	0.821462i	$0.306841\pi$
$54$	1.00000	0.136083
$55$	−1.77336	−0.239120
$56$	−0.812393	−0.108561
$57$	5.19945	0.688685
$58$	−2.20133	−0.289048
$59$	−12.9475	−1.68562	−0.842809	−	0.538213i	$-0.819100\pi$
$59$	−12.9475	−1.68562	−0.842809	+	0.538213i	$0.819100\pi$
$60$	−3.54892	−0.458163
$61$	12.1458	1.55511	0.777556	−	0.628813i	$-0.216459\pi$
$61$	12.1458	1.55511	0.777556	+	0.628813i	$0.216459\pi$
$62$	3.36102	0.426850
$63$	0.812393	0.102352
$64$	1.00000	0.125000
$65$	−3.54892	−0.440189
$66$	−0.499691	−0.0615077
$67$	−8.68355	−1.06087	−0.530433	−	0.847727i	$-0.677970\pi$
$67$	−8.68355	−1.06087	−0.530433	+	0.847727i	$0.677970\pi$
$68$	−2.03563	−0.246856
$69$	5.38809	0.648649
$70$	−2.88312	−0.344598
$71$	−1.09298	−0.129712	−0.0648562	−	0.997895i	$-0.520659\pi$
$71$	−1.09298	−0.129712	−0.0648562	+	0.997895i	$0.520659\pi$
$72$	−1.00000	−0.117851
$73$	−8.30384	−0.971891	−0.485945	−	0.873989i	$-0.661525\pi$
$73$	−8.30384	−0.971891	−0.485945	+	0.873989i	$0.661525\pi$
$74$	1.41020	0.163933
$75$	−7.59480	−0.876972
$76$	−5.19945	−0.596418
$77$	−0.405945	−0.0462618
$78$	−1.00000	−0.113228
$79$	2.73029	0.307182	0.153591	−	0.988135i	$-0.450916\pi$
$79$	2.73029	0.307182	0.153591	+	0.988135i	$0.450916\pi$
$80$	3.54892	0.396781
$81$	1.00000	0.111111
$82$	−3.63946	−0.401911
$83$	4.12953	0.453275	0.226637	−	0.973979i	$-0.427227\pi$
$83$	4.12953	0.453275	0.226637	+	0.973979i	$0.427227\pi$
$84$	−0.812393	−0.0886394
$85$	−7.22428	−0.783583
$86$	−9.88901	−1.06636
$87$	−2.20133	−0.236007
$88$	0.499691	0.0532672
$89$	−7.94125	−0.841771	−0.420885	−	0.907114i	$-0.638281\pi$
$89$	−7.94125	−0.841771	−0.420885	+	0.907114i	$0.638281\pi$
$90$	−3.54892	−0.374089
$91$	−0.812393	−0.0851620
$92$	−5.38809	−0.561747
$93$	3.36102	0.348522
$94$	2.07824	0.214354
$95$	−18.4524	−1.89318
$96$	1.00000	0.102062
$97$	−7.10010	−0.720906	−0.360453	−	0.932777i	$-0.617378\pi$
$97$	−7.10010	−0.720906	−0.360453	+	0.932777i	$0.617378\pi$
$98$	6.34002	0.640438
$99$	−0.499691	−0.0502208
$100$	7.59480	0.759480
$101$	6.97303	0.693842	0.346921	−	0.937894i	$-0.387227\pi$
$101$	6.97303	0.693842	0.346921	+	0.937894i	$0.387227\pi$
$102$	−2.03563	−0.201557
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00000	0.0980581
$105$	−2.88312	−0.281363
$106$	−8.30317	−0.806475
$107$	−16.4662	−1.59185	−0.795925	−	0.605396i	$-0.793015\pi$
$107$	−16.4662	−1.59185	−0.795925	+	0.605396i	$0.793015\pi$
$108$	−1.00000	−0.0962250
$109$	−4.10903	−0.393573	−0.196787	−	0.980446i	$-0.563051\pi$
$109$	−4.10903	−0.393573	−0.196787	+	0.980446i	$0.563051\pi$
$110$	1.77336	0.169083
$111$	1.41020	0.133850
$112$	0.812393	0.0767640
$113$	14.8227	1.39440	0.697202	−	0.716875i	$-0.254428\pi$
$113$	14.8227	1.39440	0.697202	+	0.716875i	$0.254428\pi$
$114$	−5.19945	−0.486974
$115$	−19.1219	−1.78312
$116$	2.20133	0.204388
$117$	−1.00000	−0.0924500
$118$	12.9475	1.19191
$119$	−1.65373	−0.151597
$120$	3.54892	0.323970
$121$	−10.7503	−0.977301
$122$	−12.1458	−1.09963
$123$	−3.63946	−0.328159
$124$	−3.36102	−0.301829
$125$	9.20874	0.823654
$126$	−0.812393	−0.0723737
$127$	1.46274	0.129798	0.0648988	−	0.997892i	$-0.479328\pi$
$127$	1.46274	0.129798	0.0648988	+	0.997892i	$0.479328\pi$
$128$	−1.00000	−0.0883883
$129$	−9.88901	−0.870679
$130$	3.54892	0.311260
$131$	−21.8680	−1.91062	−0.955309	−	0.295607i	$-0.904478\pi$
$131$	−21.8680	−1.91062	−0.955309	+	0.295607i	$0.904478\pi$
$132$	0.499691	0.0434925
$133$	−4.22400	−0.366267
$134$	8.68355	0.750145
$135$	−3.54892	−0.305442
$136$	2.03563	0.174554
$137$	2.95340	0.252326	0.126163	−	0.992010i	$-0.459734\pi$
$137$	2.95340	0.252326	0.126163	+	0.992010i	$0.459734\pi$
$138$	−5.38809	−0.458664
$139$	1.80669	0.153241	0.0766205	−	0.997060i	$-0.475587\pi$
$139$	1.80669	0.153241	0.0766205	+	0.997060i	$0.475587\pi$
$140$	2.88312	0.243668
$141$	2.07824	0.175020
$142$	1.09298	0.0917205
$143$	0.499691	0.0417862
$144$	1.00000	0.0833333
$145$	7.81232	0.648778
$146$	8.30384	0.687231
$147$	6.34002	0.522916
$148$	−1.41020	−0.115918
$149$	−23.2504	−1.90475	−0.952374	−	0.304933i	$-0.901366\pi$
$149$	−23.2504	−1.90475	−0.952374	+	0.304933i	$0.901366\pi$
$150$	7.59480	0.620113
$151$	17.4554	1.42050	0.710252	−	0.703947i	$-0.248581\pi$
$151$	17.4554	1.42050	0.710252	+	0.703947i	$0.248581\pi$
$152$	5.19945	0.421731
$153$	−2.03563	−0.164571
$154$	0.405945	0.0327120
$155$	−11.9280	−0.958078
$156$	1.00000	0.0800641
$157$	−18.6902	−1.49164	−0.745822	−	0.666145i	$-0.767943\pi$
$157$	−18.6902	−1.49164	−0.745822	+	0.666145i	$0.767943\pi$
$158$	−2.73029	−0.217211
$159$	−8.30317	−0.658484
$160$	−3.54892	−0.280566
$161$	−4.37725	−0.344975
$162$	−1.00000	−0.0785674
$163$	−6.47633	−0.507265	−0.253633	−	0.967301i	$-0.581625\pi$
$163$	−6.47633	−0.507265	−0.253633	+	0.967301i	$0.581625\pi$
$164$	3.63946	0.284194
$165$	1.77336	0.138056
$166$	−4.12953	−0.320514
$167$	7.71238	0.596802	0.298401	−	0.954441i	$-0.403547\pi$
$167$	7.71238	0.596802	0.298401	+	0.954441i	$0.403547\pi$
$168$	0.812393	0.0626775
$169$	1.00000	0.0769231
$170$	7.22428	0.554077
$171$	−5.19945	−0.397612
$172$	9.88901	0.754030
$173$	10.4697	0.795997	0.397999	−	0.917386i	$-0.369705\pi$
$173$	10.4697	0.795997	0.397999	+	0.917386i	$0.369705\pi$
$174$	2.20133	0.166882
$175$	6.16997	0.466406
$176$	−0.499691	−0.0376656
$177$	12.9475	0.973192
$178$	7.94125	0.595222
$179$	−10.7578	−0.804076	−0.402038	−	0.915623i	$-0.631698\pi$
$179$	−10.7578	−0.804076	−0.402038	+	0.915623i	$0.631698\pi$
$180$	3.54892	0.264521
$181$	10.5978	0.787731	0.393865	−	0.919168i	$-0.371138\pi$
$181$	10.5978	0.787731	0.393865	+	0.919168i	$0.371138\pi$
$182$	0.812393	0.0602186
$183$	−12.1458	−0.897845
$184$	5.38809	0.397215
$185$	−5.00469	−0.367952
$186$	−3.36102	−0.246442
$187$	1.01719	0.0743840
$188$	−2.07824	−0.151572
$189$	−0.812393	−0.0590929
$190$	18.4524	1.33868
$191$	6.86981	0.497082	0.248541	−	0.968621i	$-0.420049\pi$
$191$	6.86981	0.497082	0.248541	+	0.968621i	$0.420049\pi$
$192$	−1.00000	−0.0721688
$193$	−22.5474	−1.62300	−0.811499	−	0.584354i	$-0.801348\pi$
$193$	−22.5474	−1.62300	−0.811499	+	0.584354i	$0.801348\pi$
$194$	7.10010	0.509758
$195$	3.54892	0.254143
$196$	−6.34002	−0.452858
$197$	−12.9518	−0.922777	−0.461388	−	0.887198i	$-0.652648\pi$
$197$	−12.9518	−0.922777	−0.461388	+	0.887198i	$0.652648\pi$
$198$	0.499691	0.0355115
$199$	−15.2657	−1.08215	−0.541077	−	0.840973i	$-0.681983\pi$
$199$	−15.2657	−1.08215	−0.541077	+	0.840973i	$0.681983\pi$
$200$	−7.59480	−0.537034
$201$	8.68355	0.612491
$202$	−6.97303	−0.490620
$203$	1.78834	0.125517
$204$	2.03563	0.142523
$205$	12.9161	0.902101
$206$	1.00000	0.0696733
$207$	−5.38809	−0.374498
$208$	−1.00000	−0.0693375
$209$	2.59812	0.179716
$210$	2.88312	0.198954
$211$	−16.5922	−1.14225	−0.571127	−	0.820862i	$-0.693494\pi$
$211$	−16.5922	−1.14225	−0.571127	+	0.820862i	$0.693494\pi$
$212$	8.30317	0.570264
$213$	1.09298	0.0748895
$214$	16.4662	1.12561
$215$	35.0953	2.39348
$216$	1.00000	0.0680414
$217$	−2.73047	−0.185356
$218$	4.10903	0.278298
$219$	8.30384	0.561121
$220$	−1.77336	−0.119560
$221$	2.03563	0.136931
$222$	−1.41020	−0.0946466
$223$	10.8427	0.726078	0.363039	−	0.931774i	$-0.381739\pi$
$223$	10.8427	0.726078	0.363039	+	0.931774i	$0.381739\pi$
$224$	−0.812393	−0.0542803
$225$	7.59480	0.506320
$226$	−14.8227	−0.985992
$227$	−2.73298	−0.181394	−0.0906971	−	0.995879i	$-0.528910\pi$
$227$	−2.73298	−0.181394	−0.0906971	+	0.995879i	$0.528910\pi$
$228$	5.19945	0.344342
$229$	−16.6126	−1.09779	−0.548895	−	0.835891i	$-0.684951\pi$
$229$	−16.6126	−1.09779	−0.548895	+	0.835891i	$0.684951\pi$
$230$	19.1219	1.26086
$231$	0.405945	0.0267093
$232$	−2.20133	−0.144524
$233$	11.2262	0.735454	0.367727	−	0.929934i	$-0.380136\pi$
$233$	11.2262	0.735454	0.367727	+	0.929934i	$0.380136\pi$
$234$	1.00000	0.0653720
$235$	−7.37551	−0.481125
$236$	−12.9475	−0.842809
$237$	−2.73029	−0.177352
$238$	1.65373	0.107195
$239$	17.5931	1.13800	0.569001	−	0.822337i	$-0.307330\pi$
$239$	17.5931	1.13800	0.569001	+	0.822337i	$0.307330\pi$
$240$	−3.54892	−0.229082
$241$	−13.2328	−0.852400	−0.426200	−	0.904629i	$-0.640148\pi$
$241$	−13.2328	−0.852400	−0.426200	+	0.904629i	$0.640148\pi$
$242$	10.7503	0.691056
$243$	−1.00000	−0.0641500
$244$	12.1458	0.777556
$245$	−22.5002	−1.43748
$246$	3.63946	0.232043
$247$	5.19945	0.330833
$248$	3.36102	0.213425
$249$	−4.12953	−0.261698
$250$	−9.20874	−0.582412
$251$	1.63574	0.103247	0.0516235	−	0.998667i	$-0.483560\pi$
$251$	1.63574	0.103247	0.0516235	+	0.998667i	$0.483560\pi$
$252$	0.812393	0.0511760
$253$	2.69238	0.169268
$254$	−1.46274	−0.0917807
$255$	7.22428	0.452402
$256$	1.00000	0.0625000
$257$	−13.7845	−0.859856	−0.429928	−	0.902863i	$-0.641461\pi$
$257$	−13.7845	−0.859856	−0.429928	+	0.902863i	$0.641461\pi$
$258$	9.88901	0.615663
$259$	−1.14564	−0.0711865
$260$	−3.54892	−0.220094
$261$	2.20133	0.136259
$262$	21.8680	1.35101
$263$	−18.6394	−1.14936	−0.574679	−	0.818379i	$-0.694873\pi$
$263$	−18.6394	−1.14936	−0.574679	+	0.818379i	$0.694873\pi$
$264$	−0.499691	−0.0307538
$265$	29.4672	1.81016
$266$	4.22400	0.258990
$267$	7.94125	0.485997
$268$	−8.68355	−0.530433
$269$	23.1317	1.41036	0.705181	−	0.709027i	$-0.250866\pi$
$269$	23.1317	1.41036	0.705181	+	0.709027i	$0.250866\pi$
$270$	3.54892	0.215980
$271$	−9.45858	−0.574568	−0.287284	−	0.957845i	$-0.592752\pi$
$271$	−9.45858	−0.574568	−0.287284	+	0.957845i	$0.592752\pi$
$272$	−2.03563	−0.123428
$273$	0.812393	0.0491683
$274$	−2.95340	−0.178422
$275$	−3.79505	−0.228850
$276$	5.38809	0.324325
$277$	17.7699	1.06769	0.533844	−	0.845583i	$-0.320747\pi$
$277$	17.7699	1.06769	0.533844	+	0.845583i	$0.320747\pi$
$278$	−1.80669	−0.108358
$279$	−3.36102	−0.201219
$280$	−2.88312	−0.172299
$281$	−8.45675	−0.504487	−0.252244	−	0.967664i	$-0.581168\pi$
$281$	−8.45675	−0.504487	−0.252244	+	0.967664i	$0.581168\pi$
$282$	−2.07824	−0.123758
$283$	14.5098	0.862521	0.431260	−	0.902228i	$-0.358069\pi$
$283$	14.5098	0.862521	0.431260	+	0.902228i	$0.358069\pi$
$284$	−1.09298	−0.0648562
$285$	18.4524	1.09303
$286$	−0.499691	−0.0295473
$287$	2.95667	0.174527
$288$	−1.00000	−0.0589256
$289$	−12.8562	−0.756248
$290$	−7.81232	−0.458755
$291$	7.10010	0.416215
$292$	−8.30384	−0.485945
$293$	5.57982	0.325976	0.162988	−	0.986628i	$-0.447887\pi$
$293$	5.57982	0.325976	0.162988	+	0.986628i	$0.447887\pi$
$294$	−6.34002	−0.369757
$295$	−45.9495	−2.67528
$296$	1.41020	0.0819663
$297$	0.499691	0.0289950
$298$	23.2504	1.34686
$299$	5.38809	0.311601
$300$	−7.59480	−0.438486
$301$	8.03376	0.463058
$302$	−17.4554	−1.00445
$303$	−6.97303	−0.400590
$304$	−5.19945	−0.298209
$305$	43.1045	2.46816
$306$	2.03563	0.116369
$307$	−29.7837	−1.69985	−0.849924	−	0.526905i	$-0.823352\pi$
$307$	−29.7837	−1.69985	−0.849924	+	0.526905i	$0.823352\pi$
$308$	−0.405945	−0.0231309
$309$	1.00000	0.0568880
$310$	11.9280	0.677464
$311$	−11.2915	−0.640284	−0.320142	−	0.947370i	$-0.603731\pi$
$311$	−11.2915	−0.640284	−0.320142	+	0.947370i	$0.603731\pi$
$312$	−1.00000	−0.0566139
$313$	29.8641	1.68802	0.844010	−	0.536328i	$-0.180189\pi$
$313$	29.8641	1.68802	0.844010	+	0.536328i	$0.180189\pi$
$314$	18.6902	1.05475
$315$	2.88312	0.162445
$316$	2.73029	0.153591
$317$	16.5466	0.929349	0.464675	−	0.885482i	$-0.346171\pi$
$317$	16.5466	0.929349	0.464675	+	0.885482i	$0.346171\pi$
$318$	8.30317	0.465618
$319$	−1.09998	−0.0615872
$320$	3.54892	0.198390
$321$	16.4662	0.919055
$322$	4.37725	0.243934
$323$	10.5842	0.588919
$324$	1.00000	0.0555556
$325$	−7.59480	−0.421284
$326$	6.47633	0.358691
$327$	4.10903	0.227230
$328$	−3.63946	−0.200955
$329$	−1.68835	−0.0930818
$330$	−1.77336	−0.0976203
$331$	0.373217	0.0205139	0.0102569	−	0.999947i	$-0.496735\pi$
$331$	0.373217	0.0205139	0.0102569	+	0.999947i	$0.496735\pi$
$332$	4.12953	0.226637
$333$	−1.41020	−0.0772786
$334$	−7.71238	−0.422003
$335$	−30.8172	−1.68372
$336$	−0.812393	−0.0443197
$337$	18.8949	1.02927	0.514635	−	0.857409i	$-0.327927\pi$
$337$	18.8949	1.02927	0.514635	+	0.857409i	$0.327927\pi$
$338$	−1.00000	−0.0543928
$339$	−14.8227	−0.805059
$340$	−7.22428	−0.391791
$341$	1.67947	0.0909485
$342$	5.19945	0.281154
$343$	−10.8373	−0.585161
$344$	−9.88901	−0.533180
$345$	19.1219	1.02949
$346$	−10.4697	−0.562855
$347$	−3.51822	−0.188868	−0.0944339	−	0.995531i	$-0.530104\pi$
$347$	−3.51822	−0.188868	−0.0944339	+	0.995531i	$0.530104\pi$
$348$	−2.20133	−0.118003
$349$	7.25939	0.388586	0.194293	−	0.980944i	$-0.437759\pi$
$349$	7.25939	0.388586	0.194293	+	0.980944i	$0.437759\pi$
$350$	−6.16997	−0.329799
$351$	1.00000	0.0533761
$352$	0.499691	0.0266336
$353$	32.5403	1.73195	0.865973	−	0.500090i	$-0.166700\pi$
$353$	32.5403	1.73195	0.865973	+	0.500090i	$0.166700\pi$
$354$	−12.9475	−0.688151
$355$	−3.87888	−0.205870
$356$	−7.94125	−0.420885
$357$	1.65373	0.0875248
$358$	10.7578	0.568567
$359$	−5.75472	−0.303722	−0.151861	−	0.988402i	$-0.548527\pi$
$359$	−5.75472	−0.303722	−0.151861	+	0.988402i	$0.548527\pi$
$360$	−3.54892	−0.187044
$361$	8.03433	0.422859
$362$	−10.5978	−0.557010
$363$	10.7503	0.564245
$364$	−0.812393	−0.0425810
$365$	−29.4696	−1.54251
$366$	12.1458	0.634872
$367$	−3.37104	−0.175967	−0.0879834	−	0.996122i	$-0.528042\pi$
$367$	−3.37104	−0.175967	−0.0879834	+	0.996122i	$0.528042\pi$
$368$	−5.38809	−0.280873
$369$	3.63946	0.189463
$370$	5.00469	0.260181
$371$	6.74544	0.350206
$372$	3.36102	0.174261
$373$	−28.5538	−1.47846	−0.739231	−	0.673452i	$-0.764811\pi$
$373$	−28.5538	−1.47846	−0.739231	+	0.673452i	$0.764811\pi$
$374$	−1.01719	−0.0525974
$375$	−9.20874	−0.475537
$376$	2.07824	0.107177
$377$	−2.20133	−0.113374
$378$	0.812393	0.0417850
$379$	−1.35050	−0.0693707	−0.0346853	−	0.999398i	$-0.511043\pi$
$379$	−1.35050	−0.0693707	−0.0346853	+	0.999398i	$0.511043\pi$
$380$	−18.4524	−0.946590
$381$	−1.46274	−0.0749387
$382$	−6.86981	−0.351490
$383$	14.0443	0.717630	0.358815	−	0.933409i	$-0.383181\pi$
$383$	14.0443	0.717630	0.358815	+	0.933409i	$0.383181\pi$
$384$	1.00000	0.0510310
$385$	−1.44067	−0.0734231
$386$	22.5474	1.14763
$387$	9.88901	0.502687
$388$	−7.10010	−0.360453
$389$	−16.5767	−0.840471	−0.420235	−	0.907415i	$-0.638053\pi$
$389$	−16.5767	−0.840471	−0.420235	+	0.907415i	$0.638053\pi$
$390$	−3.54892	−0.179706
$391$	10.9681	0.554683
$392$	6.34002	0.320219
$393$	21.8680	1.10310
$394$	12.9518	0.652502
$395$	9.68958	0.487536
$396$	−0.499691	−0.0251104
$397$	−18.8173	−0.944415	−0.472208	−	0.881487i	$-0.656543\pi$
$397$	−18.8173	−0.944415	−0.472208	+	0.881487i	$0.656543\pi$
$398$	15.2657	0.765199
$399$	4.22400	0.211465
$400$	7.59480	0.379740
$401$	−25.1966	−1.25826	−0.629130	−	0.777300i	$-0.716589\pi$
$401$	−25.1966	−1.25826	−0.629130	+	0.777300i	$0.716589\pi$
$402$	−8.68355	−0.433096
$403$	3.36102	0.167424
$404$	6.97303	0.346921
$405$	3.54892	0.176347
$406$	−1.78834	−0.0887539
$407$	0.704665	0.0349289
$408$	−2.03563	−0.100779
$409$	17.8758	0.883899	0.441950	−	0.897040i	$-0.354287\pi$
$409$	17.8758	0.883899	0.441950	+	0.897040i	$0.354287\pi$
$410$	−12.9161	−0.637882
$411$	−2.95340	−0.145681
$412$	−1.00000	−0.0492665
$413$	−10.5184	−0.517579
$414$	5.38809	0.264810
$415$	14.6554	0.719403
$416$	1.00000	0.0490290
$417$	−1.80669	−0.0884738
$418$	−2.59812	−0.127078
$419$	39.0321	1.90685	0.953423	−	0.301638i	$-0.0975333\pi$
$419$	39.0321	1.90685	0.953423	+	0.301638i	$0.0975333\pi$
$420$	−2.88312	−0.140682
$421$	3.28999	0.160344	0.0801722	−	0.996781i	$-0.474453\pi$
$421$	3.28999	0.160344	0.0801722	+	0.996781i	$0.474453\pi$
$422$	16.5922	0.807696
$423$	−2.07824	−0.101048
$424$	−8.30317	−0.403237
$425$	−15.4602	−0.749930
$426$	−1.09298	−0.0529549
$427$	9.86718	0.477506
$428$	−16.4662	−0.795925
$429$	−0.499691	−0.0241253
$430$	−35.0953	−1.69244
$431$	−6.70463	−0.322951	−0.161475	−	0.986877i	$-0.551625\pi$
$431$	−6.70463	−0.322951	−0.161475	+	0.986877i	$0.551625\pi$
$432$	−1.00000	−0.0481125
$433$	−24.6410	−1.18417	−0.592085	−	0.805875i	$-0.701695\pi$
$433$	−24.6410	−1.18417	−0.592085	+	0.805875i	$0.701695\pi$
$434$	2.73047	0.131067
$435$	−7.81232	−0.374572
$436$	−4.10903	−0.196787
$437$	28.0151	1.34014
$438$	−8.30384	−0.396773
$439$	−13.1741	−0.628764	−0.314382	−	0.949297i	$-0.601797\pi$
$439$	−13.1741	−0.628764	−0.314382	+	0.949297i	$0.601797\pi$
$440$	1.77336	0.0845416
$441$	−6.34002	−0.301906
$442$	−2.03563	−0.0968250
$443$	1.54575	0.0734410	0.0367205	−	0.999326i	$-0.488309\pi$
$443$	1.54575	0.0734410	0.0367205	+	0.999326i	$0.488309\pi$
$444$	1.41020	0.0669252
$445$	−28.1828	−1.33599
$446$	−10.8427	−0.513415
$447$	23.2504	1.09971
$448$	0.812393	0.0383820
$449$	18.3702	0.866943	0.433472	−	0.901167i	$-0.357288\pi$
$449$	18.3702	0.866943	0.433472	+	0.901167i	$0.357288\pi$
$450$	−7.59480	−0.358022
$451$	−1.81860	−0.0856347
$452$	14.8227	0.697202
$453$	−17.4554	−0.820129
$454$	2.73298	0.128265
$455$	−2.88312	−0.135163
$456$	−5.19945	−0.243487
$457$	−15.7142	−0.735079	−0.367540	−	0.930008i	$-0.619800\pi$
$457$	−15.7142	−0.735079	−0.367540	+	0.930008i	$0.619800\pi$
$458$	16.6126	0.776255
$459$	2.03563	0.0950150
$460$	−19.1219	−0.891562
$461$	−11.2251	−0.522805	−0.261402	−	0.965230i	$-0.584185\pi$
$461$	−11.2251	−0.522805	−0.261402	+	0.965230i	$0.584185\pi$
$462$	−0.405945	−0.0188863
$463$	10.6807	0.496375	0.248187	−	0.968712i	$-0.420165\pi$
$463$	10.6807	0.496375	0.248187	+	0.968712i	$0.420165\pi$
$464$	2.20133	0.102194
$465$	11.9280	0.553147
$466$	−11.2262	−0.520045
$467$	15.5030	0.717392	0.358696	−	0.933454i	$-0.383221\pi$
$467$	15.5030	0.717392	0.358696	+	0.933454i	$0.383221\pi$
$468$	−1.00000	−0.0462250
$469$	−7.05446	−0.325745
$470$	7.37551	0.340207
$471$	18.6902	0.861201
$472$	12.9475	0.595956
$473$	−4.94145	−0.227208
$474$	2.73029	0.125407
$475$	−39.4888	−1.81187
$476$	−1.65373	−0.0757987
$477$	8.30317	0.380176
$478$	−17.5931	−0.804689
$479$	26.0238	1.18906	0.594528	−	0.804075i	$-0.297339\pi$
$479$	26.0238	1.18906	0.594528	+	0.804075i	$0.297339\pi$
$480$	3.54892	0.161985
$481$	1.41020	0.0642997
$482$	13.2328	0.602738
$483$	4.37725	0.199172
$484$	−10.7503	−0.488650
$485$	−25.1977	−1.14417
$486$	1.00000	0.0453609
$487$	−8.33767	−0.377816	−0.188908	−	0.981995i	$-0.560495\pi$
$487$	−8.33767	−0.377816	−0.188908	+	0.981995i	$0.560495\pi$
$488$	−12.1458	−0.549815
$489$	6.47633	0.292870
$490$	22.5002	1.01645
$491$	−14.2679	−0.643901	−0.321950	−	0.946757i	$-0.604338\pi$
$491$	−14.2679	−0.643901	−0.321950	+	0.946757i	$0.604338\pi$
$492$	−3.63946	−0.164079
$493$	−4.48108	−0.201818
$494$	−5.19945	−0.233935
$495$	−1.77336	−0.0797066
$496$	−3.36102	−0.150914
$497$	−0.887927	−0.0398290
$498$	4.12953	0.185049
$499$	−5.36546	−0.240191	−0.120095	−	0.992762i	$-0.538320\pi$
$499$	−5.36546	−0.240191	−0.120095	+	0.992762i	$0.538320\pi$
$500$	9.20874	0.411827
$501$	−7.71238	−0.344564
$502$	−1.63574	−0.0730066
$503$	20.7354	0.924545	0.462273	−	0.886738i	$-0.347034\pi$
$503$	20.7354	0.924545	0.462273	+	0.886738i	$0.347034\pi$
$504$	−0.812393	−0.0361869
$505$	24.7467	1.10121
$506$	−2.69238	−0.119691
$507$	−1.00000	−0.0444116
$508$	1.46274	0.0648988
$509$	−3.26354	−0.144654	−0.0723269	−	0.997381i	$-0.523042\pi$
$509$	−3.26354	−0.144654	−0.0723269	+	0.997381i	$0.523042\pi$
$510$	−7.22428	−0.319896
$511$	−6.74598	−0.298425
$512$	−1.00000	−0.0441942
$513$	5.19945	0.229562
$514$	13.7845	0.608010
$515$	−3.54892	−0.156384
$516$	−9.88901	−0.435339
$517$	1.03848	0.0456723
$518$	1.14564	0.0503365
$519$	−10.4697	−0.459569
$520$	3.54892	0.155630
$521$	1.16693	0.0511241	0.0255621	−	0.999673i	$-0.491862\pi$
$521$	1.16693	0.0511241	0.0255621	+	0.999673i	$0.491862\pi$
$522$	−2.20133	−0.0963494
$523$	1.13661	0.0497006	0.0248503	−	0.999691i	$-0.492089\pi$
$523$	1.13661	0.0497006	0.0248503	+	0.999691i	$0.492089\pi$
$524$	−21.8680	−0.955309
$525$	−6.16997	−0.269279
$526$	18.6394	0.812718
$527$	6.84179	0.298033
$528$	0.499691	0.0217463
$529$	6.03148	0.262238
$530$	−29.4672	−1.27997
$531$	−12.9475	−0.561873
$532$	−4.22400	−0.183134
$533$	−3.63946	−0.157642
$534$	−7.94125	−0.343651
$535$	−58.4372	−2.52646
$536$	8.68355	0.375072
$537$	10.7578	0.464233
$538$	−23.1317	−0.997277
$539$	3.16805	0.136457
$540$	−3.54892	−0.152721
$541$	2.55180	0.109711	0.0548553	−	0.998494i	$-0.482530\pi$
$541$	2.55180	0.109711	0.0548553	+	0.998494i	$0.482530\pi$
$542$	9.45858	0.406281
$543$	−10.5978	−0.454797
$544$	2.03563	0.0872769
$545$	−14.5826	−0.624650
$546$	−0.812393	−0.0347672
$547$	−16.8417	−0.720101	−0.360050	−	0.932933i	$-0.617241\pi$
$547$	−16.8417	−0.720101	−0.360050	+	0.932933i	$0.617241\pi$
$548$	2.95340	0.126163
$549$	12.1458	0.518371
$550$	3.79505	0.161822
$551$	−11.4457	−0.487603
$552$	−5.38809	−0.229332
$553$	2.21807	0.0943220
$554$	−17.7699	−0.754970
$555$	5.00469	0.212437
$556$	1.80669	0.0766205
$557$	33.3989	1.41516	0.707579	−	0.706634i	$-0.249787\pi$
$557$	33.3989	1.41516	0.707579	+	0.706634i	$0.249787\pi$
$558$	3.36102	0.142283
$559$	−9.88901	−0.418261
$560$	2.88312	0.121834
$561$	−1.01719	−0.0429456
$562$	8.45675	0.356726
$563$	−42.7565	−1.80197	−0.900986	−	0.433849i	$-0.857155\pi$
$563$	−42.7565	−1.80197	−0.900986	+	0.433849i	$0.857155\pi$
$564$	2.07824	0.0875098
$565$	52.6046	2.21309
$566$	−14.5098	−0.609894
$567$	0.812393	0.0341173
$568$	1.09298	0.0458603
$569$	−31.1795	−1.30711	−0.653557	−	0.756877i	$-0.726724\pi$
$569$	−31.1795	−1.30711	−0.653557	+	0.756877i	$0.726724\pi$
$570$	−18.4524	−0.772887
$571$	−15.7027	−0.657137	−0.328568	−	0.944480i	$-0.606566\pi$
$571$	−15.7027	−0.657137	−0.328568	+	0.944480i	$0.606566\pi$
$572$	0.499691	0.0208931
$573$	−6.86981	−0.286990
$574$	−2.95667	−0.123409
$575$	−40.9215	−1.70654
$576$	1.00000	0.0416667
$577$	−28.1508	−1.17193	−0.585967	−	0.810335i	$-0.699285\pi$
$577$	−28.1508	−1.17193	−0.585967	+	0.810335i	$0.699285\pi$
$578$	12.8562	0.534748
$579$	22.5474	0.937039
$580$	7.81232	0.324389
$581$	3.35480	0.139181
$582$	−7.10010	−0.294309
$583$	−4.14902	−0.171835
$584$	8.30384	0.343615
$585$	−3.54892	−0.146730
$586$	−5.57982	−0.230500
$587$	−19.4447	−0.802567	−0.401283	−	0.915954i	$-0.631436\pi$
$587$	−19.4447	−0.802567	−0.401283	+	0.915954i	$0.631436\pi$
$588$	6.34002	0.261458
$589$	17.4755	0.720064
$590$	45.9495	1.89171
$591$	12.9518	0.532765
$592$	−1.41020	−0.0579589
$593$	47.8144	1.96350	0.981751	−	0.190169i	$-0.0609036\pi$
$593$	47.8144	1.96350	0.981751	+	0.190169i	$0.0609036\pi$
$594$	−0.499691	−0.0205026
$595$	−5.86895	−0.240604
$596$	−23.2504	−0.952374
$597$	15.2657	0.624782
$598$	−5.38809	−0.220335
$599$	6.05363	0.247345	0.123672	−	0.992323i	$-0.460533\pi$
$599$	6.05363	0.247345	0.123672	+	0.992323i	$0.460533\pi$
$600$	7.59480	0.310057
$601$	−39.7244	−1.62039	−0.810195	−	0.586160i	$-0.800639\pi$
$601$	−39.7244	−1.62039	−0.810195	+	0.586160i	$0.800639\pi$
$602$	−8.03376	−0.327432
$603$	−8.68355	−0.353622
$604$	17.4554	0.710252
$605$	−38.1519	−1.55110
$606$	6.97303	0.283260
$607$	30.2119	1.22626	0.613132	−	0.789980i	$-0.289909\pi$
$607$	30.2119	1.22626	0.613132	+	0.789980i	$0.289909\pi$
$608$	5.19945	0.210866
$609$	−1.78834	−0.0724673
$610$	−43.1045	−1.74525
$611$	2.07824	0.0840767
$612$	−2.03563	−0.0822854
$613$	−33.3455	−1.34681	−0.673405	−	0.739273i	$-0.735169\pi$
$613$	−33.3455	−1.34681	−0.673405	+	0.739273i	$0.735169\pi$
$614$	29.7837	1.20197
$615$	−12.9161	−0.520829
$616$	0.405945	0.0163560
$617$	13.2142	0.531984	0.265992	−	0.963975i	$-0.414301\pi$
$617$	13.2142	0.531984	0.265992	+	0.963975i	$0.414301\pi$
$618$	−1.00000	−0.0402259
$619$	−12.3150	−0.494980	−0.247490	−	0.968890i	$-0.579606\pi$
$619$	−12.3150	−0.494980	−0.247490	+	0.968890i	$0.579606\pi$
$620$	−11.9280	−0.479039
$621$	5.38809	0.216216
$622$	11.2915	0.452749
$623$	−6.45142	−0.258471
$624$	1.00000	0.0400320
$625$	−5.29298	−0.211719
$626$	−29.8641	−1.19361
$627$	−2.59812	−0.103759
$628$	−18.6902	−0.745822
$629$	2.87065	0.114460
$630$	−2.88312	−0.114866
$631$	−39.6617	−1.57891	−0.789454	−	0.613810i	$-0.789636\pi$
$631$	−39.6617	−1.57891	−0.789454	+	0.613810i	$0.789636\pi$
$632$	−2.73029	−0.108605
$633$	16.5922	0.659481
$634$	−16.5466	−0.657149
$635$	5.19116	0.206005
$636$	−8.30317	−0.329242
$637$	6.34002	0.251201
$638$	1.09998	0.0435487
$639$	−1.09298	−0.0432375
$640$	−3.54892	−0.140283
$641$	47.2949	1.86803	0.934017	−	0.357228i	$-0.116278\pi$
$641$	47.2949	1.86803	0.934017	+	0.357228i	$0.116278\pi$
$642$	−16.4662	−0.649870
$643$	15.8351	0.624474	0.312237	−	0.950004i	$-0.398922\pi$
$643$	15.8351	0.624474	0.312237	+	0.950004i	$0.398922\pi$
$644$	−4.37725	−0.172488
$645$	−35.0953	−1.38187
$646$	−10.5842	−0.416428
$647$	20.8480	0.819618	0.409809	−	0.912171i	$-0.365595\pi$
$647$	20.8480	0.819618	0.409809	+	0.912171i	$0.365595\pi$
$648$	−1.00000	−0.0392837
$649$	6.46973	0.253959
$650$	7.59480	0.297893
$651$	2.73047	0.107016
$652$	−6.47633	−0.253633
$653$	28.8463	1.12884	0.564422	−	0.825486i	$-0.309099\pi$
$653$	28.8463	1.12884	0.564422	+	0.825486i	$0.309099\pi$
$654$	−4.10903	−0.160676
$655$	−77.6078	−3.03239
$656$	3.63946	0.142097
$657$	−8.30384	−0.323964
$658$	1.68835	0.0658188
$659$	23.9344	0.932353	0.466177	−	0.884692i	$-0.345631\pi$
$659$	23.9344	0.932353	0.466177	+	0.884692i	$0.345631\pi$
$660$	1.77336	0.0690280
$661$	−25.3905	−0.987576	−0.493788	−	0.869582i	$-0.664388\pi$
$661$	−25.3905	−0.987576	−0.493788	+	0.869582i	$0.664388\pi$
$662$	−0.373217	−0.0145055
$663$	−2.03563	−0.0790573
$664$	−4.12953	−0.160257
$665$	−14.9906	−0.581312
$666$	1.41020	0.0546442
$667$	−11.8609	−0.459257
$668$	7.71238	0.298401
$669$	−10.8427	−0.419201
$670$	30.8172	1.19057
$671$	−6.06915	−0.234297
$672$	0.812393	0.0313388
$673$	−42.2446	−1.62841	−0.814205	−	0.580577i	$-0.802827\pi$
$673$	−42.2446	−1.62841	−0.814205	+	0.580577i	$0.802827\pi$
$674$	−18.8949	−0.727804
$675$	−7.59480	−0.292324
$676$	1.00000	0.0384615
$677$	18.8419	0.724151	0.362076	−	0.932149i	$-0.382068\pi$
$677$	18.8419	0.724151	0.362076	+	0.932149i	$0.382068\pi$
$678$	14.8227	0.569263
$679$	−5.76807	−0.221358
$680$	7.22428	0.277038
$681$	2.73298	0.104728
$682$	−1.67947	−0.0643103
$683$	−35.1385	−1.34454	−0.672268	−	0.740308i	$-0.734680\pi$
$683$	−35.1385	−1.34454	−0.672268	+	0.740308i	$0.734680\pi$
$684$	−5.19945	−0.198806
$685$	10.4814	0.400473
$686$	10.8373	0.413772
$687$	16.6126	0.633809
$688$	9.88901	0.377015
$689$	−8.30317	−0.316325
$690$	−19.1219	−0.727957
$691$	4.57868	0.174181	0.0870907	−	0.996200i	$-0.472243\pi$
$691$	4.57868	0.174181	0.0870907	+	0.996200i	$0.472243\pi$
$692$	10.4697	0.397999
$693$	−0.405945	−0.0154206
$694$	3.51822	0.133550
$695$	6.41177	0.243212
$696$	2.20133	0.0834410
$697$	−7.40859	−0.280620
$698$	−7.25939	−0.274772
$699$	−11.2262	−0.424615
$700$	6.16997	0.233203
$701$	4.43577	0.167537	0.0837684	−	0.996485i	$-0.473304\pi$
$701$	4.43577	0.167537	0.0837684	+	0.996485i	$0.473304\pi$
$702$	−1.00000	−0.0377426
$703$	7.33228	0.276542
$704$	−0.499691	−0.0188328
$705$	7.37551	0.277778
$706$	−32.5403	−1.22467
$707$	5.66484	0.213048
$708$	12.9475	0.486596
$709$	1.55655	0.0584576	0.0292288	−	0.999573i	$-0.490695\pi$
$709$	1.55655	0.0584576	0.0292288	+	0.999573i	$0.490695\pi$
$710$	3.87888	0.145572
$711$	2.73029	0.102394
$712$	7.94125	0.297611
$713$	18.1095	0.678205
$714$	−1.65373	−0.0618894
$715$	1.77336	0.0663199
$716$	−10.7578	−0.402038
$717$	−17.5931	−0.657026
$718$	5.75472	0.214764
$719$	−13.8662	−0.517124	−0.258562	−	0.965995i	$-0.583249\pi$
$719$	−13.8662	−0.517124	−0.258562	+	0.965995i	$0.583249\pi$
$720$	3.54892	0.132260
$721$	−0.812393	−0.0302551
$722$	−8.03433	−0.299007
$723$	13.2328	0.492133
$724$	10.5978	0.393865
$725$	16.7186	0.620915
$726$	−10.7503	−0.398981
$727$	34.6396	1.28471	0.642356	−	0.766406i	$-0.277957\pi$
$727$	34.6396	1.28471	0.642356	+	0.766406i	$0.277957\pi$
$728$	0.812393	0.0301093
$729$	1.00000	0.0370370
$730$	29.4696	1.09072
$731$	−20.1304	−0.744548
$732$	−12.1458	−0.448922
$733$	−19.8531	−0.733293	−0.366646	−	0.930360i	$-0.619494\pi$
$733$	−19.8531	−0.733293	−0.366646	+	0.930360i	$0.619494\pi$
$734$	3.37104	0.124427
$735$	22.5002	0.829932
$736$	5.38809	0.198608
$737$	4.33909	0.159833
$738$	−3.63946	−0.133970
$739$	38.7738	1.42632	0.713159	−	0.701002i	$-0.247264\pi$
$739$	38.7738	1.42632	0.713159	+	0.701002i	$0.247264\pi$
$740$	−5.00469	−0.183976
$741$	−5.19945	−0.191007
$742$	−6.74544	−0.247633
$743$	−15.8298	−0.580740	−0.290370	−	0.956914i	$-0.593778\pi$
$743$	−15.8298	−0.580740	−0.290370	+	0.956914i	$0.593778\pi$
$744$	−3.36102	−0.123221
$745$	−82.5137	−3.02307
$746$	28.5538	1.04543
$747$	4.12953	0.151092
$748$	1.01719	0.0371920
$749$	−13.3770	−0.488787
$750$	9.20874	0.336256
$751$	−47.5112	−1.73371	−0.866855	−	0.498561i	$-0.833862\pi$
$751$	−47.5112	−1.73371	−0.866855	+	0.498561i	$0.833862\pi$
$752$	−2.07824	−0.0757858
$753$	−1.63574	−0.0596096
$754$	2.20133	0.0801676
$755$	61.9479	2.25452
$756$	−0.812393	−0.0295465
$757$	3.55221	0.129107	0.0645537	−	0.997914i	$-0.479438\pi$
$757$	3.55221	0.129107	0.0645537	+	0.997914i	$0.479438\pi$
$758$	1.35050	0.0490525
$759$	−2.69238	−0.0977271
$760$	18.4524	0.669340
$761$	17.4972	0.634272	0.317136	−	0.948380i	$-0.397279\pi$
$761$	17.4972	0.634272	0.317136	+	0.948380i	$0.397279\pi$
$762$	1.46274	0.0529896
$763$	−3.33815	−0.120849
$764$	6.86981	0.248541
$765$	−7.22428	−0.261194
$766$	−14.0443	−0.507441
$767$	12.9475	0.467506
$768$	−1.00000	−0.0360844
$769$	6.43567	0.232076	0.116038	−	0.993245i	$-0.462981\pi$
$769$	6.43567	0.232076	0.116038	+	0.993245i	$0.462981\pi$
$770$	1.44067	0.0519180
$771$	13.7845	0.496438
$772$	−22.5474	−0.811499
$773$	24.7134	0.888878	0.444439	−	0.895809i	$-0.353403\pi$
$773$	24.7134	0.888878	0.444439	+	0.895809i	$0.353403\pi$
$774$	−9.88901	−0.355453
$775$	−25.5263	−0.916931
$776$	7.10010	0.254879
$777$	1.14564	0.0410996
$778$	16.5767	0.594303
$779$	−18.9232	−0.677994
$780$	3.54892	0.127072
$781$	0.546150	0.0195428
$782$	−10.9681	−0.392220
$783$	−2.20133	−0.0786690
$784$	−6.34002	−0.226429
$785$	−66.3301	−2.36742
$786$	−21.8680	−0.780007
$787$	−29.5263	−1.05250	−0.526249	−	0.850330i	$-0.676402\pi$
$787$	−29.5263	−1.05250	−0.526249	+	0.850330i	$0.676402\pi$
$788$	−12.9518	−0.461388
$789$	18.6394	0.663582
$790$	−9.68958	−0.344740
$791$	12.0419	0.428160
$792$	0.499691	0.0177557
$793$	−12.1458	−0.431311
$794$	18.8173	0.667803
$795$	−29.4672	−1.04510
$796$	−15.2657	−0.541077
$797$	21.3683	0.756904	0.378452	−	0.925621i	$-0.376457\pi$
$797$	21.3683	0.756904	0.378452	+	0.925621i	$0.376457\pi$
$798$	−4.22400	−0.149528
$799$	4.23053	0.149666
$800$	−7.59480	−0.268517
$801$	−7.94125	−0.280590
$802$	25.1966	0.889724
$803$	4.14935	0.146427
$804$	8.68355	0.306245
$805$	−15.5345	−0.547518
$806$	−3.36102	−0.118387
$807$	−23.1317	−0.814273
$808$	−6.97303	−0.245310
$809$	−49.9916	−1.75761	−0.878805	−	0.477180i	$-0.841659\pi$
$809$	−49.9916	−1.75761	−0.878805	+	0.477180i	$0.841659\pi$
$810$	−3.54892	−0.124696
$811$	−1.54672	−0.0543126	−0.0271563	−	0.999631i	$-0.508645\pi$
$811$	−1.54672	−0.0543126	−0.0271563	+	0.999631i	$0.508645\pi$
$812$	1.78834	0.0627585
$813$	9.45858	0.331727
$814$	−0.704665	−0.0246985
$815$	−22.9839	−0.805092
$816$	2.03563	0.0712613
$817$	−51.4175	−1.79887
$818$	−17.8758	−0.625011
$819$	−0.812393	−0.0283873
$820$	12.9161	0.451051
$821$	−48.1037	−1.67883	−0.839416	−	0.543489i	$-0.817103\pi$
$821$	−48.1037	−1.67883	−0.839416	+	0.543489i	$0.817103\pi$
$822$	2.95340	0.103012
$823$	49.6785	1.73168	0.865842	−	0.500317i	$-0.166783\pi$
$823$	49.6785	1.73168	0.865842	+	0.500317i	$0.166783\pi$
$824$	1.00000	0.0348367
$825$	3.79505	0.132127
$826$	10.5184	0.365983
$827$	−24.4408	−0.849891	−0.424945	−	0.905219i	$-0.639707\pi$
$827$	−24.4408	−0.849891	−0.424945	+	0.905219i	$0.639707\pi$
$828$	−5.38809	−0.187249
$829$	−17.3716	−0.603339	−0.301670	−	0.953413i	$-0.597544\pi$
$829$	−17.3716	−0.603339	−0.301670	+	0.953413i	$0.597544\pi$
$830$	−14.6554	−0.508695
$831$	−17.7699	−0.616431
$832$	−1.00000	−0.0346688
$833$	12.9059	0.447164
$834$	1.80669	0.0625604
$835$	27.3706	0.947198
$836$	2.59812	0.0898578
$837$	3.36102	0.116174
$838$	−39.0321	−1.34834
$839$	−3.54028	−0.122224	−0.0611120	−	0.998131i	$-0.519465\pi$
$839$	−3.54028	−0.122224	−0.0611120	+	0.998131i	$0.519465\pi$
$840$	2.88312	0.0994769
$841$	−24.1542	−0.832902
$842$	−3.28999	−0.113381
$843$	8.45675	0.291266
$844$	−16.5922	−0.571127
$845$	3.54892	0.122086
$846$	2.07824	0.0714515
$847$	−8.73348	−0.300086
$848$	8.30317	0.285132
$849$	−14.5098	−0.497977
$850$	15.4602	0.530281
$851$	7.59829	0.260466
$852$	1.09298	0.0374448
$853$	53.0507	1.81642	0.908210	−	0.418515i	$-0.137449\pi$
$853$	53.0507	1.81642	0.908210	+	0.418515i	$0.137449\pi$
$854$	−9.86718	−0.337648
$855$	−18.4524	−0.631060
$856$	16.4662	0.562804
$857$	−43.1264	−1.47317	−0.736586	−	0.676344i	$-0.763563\pi$
$857$	−43.1264	−1.47317	−0.736586	+	0.676344i	$0.763563\pi$
$858$	0.499691	0.0170592
$859$	−18.5943	−0.634428	−0.317214	−	0.948354i	$-0.602747\pi$
$859$	−18.5943	−0.634428	−0.317214	+	0.948354i	$0.602747\pi$
$860$	35.0953	1.19674
$861$	−2.95667	−0.100763
$862$	6.70463	0.228361
$863$	−33.7151	−1.14768	−0.573838	−	0.818969i	$-0.694546\pi$
$863$	−33.7151	−1.14768	−0.573838	+	0.818969i	$0.694546\pi$
$864$	1.00000	0.0340207
$865$	37.1561	1.26335
$866$	24.6410	0.837335
$867$	12.8562	0.436620
$868$	−2.73047	−0.0926782
$869$	−1.36430	−0.0462808
$870$	7.81232	0.264862
$871$	8.68355	0.294231
$872$	4.10903	0.139149
$873$	−7.10010	−0.240302
$874$	−28.0151	−0.947625
$875$	7.48112	0.252908
$876$	8.30384	0.280561
$877$	18.1730	0.613659	0.306830	−	0.951764i	$-0.400732\pi$
$877$	18.1730	0.613659	0.306830	+	0.951764i	$0.400732\pi$
$878$	13.1741	0.444603
$879$	−5.57982	−0.188203
$880$	−1.77336	−0.0597800
$881$	2.86482	0.0965183	0.0482591	−	0.998835i	$-0.484633\pi$
$881$	2.86482	0.0965183	0.0482591	+	0.998835i	$0.484633\pi$
$882$	6.34002	0.213479
$883$	−5.30033	−0.178370	−0.0891852	−	0.996015i	$-0.528426\pi$
$883$	−5.30033	−0.178370	−0.0891852	+	0.996015i	$0.528426\pi$
$884$	2.03563	0.0684656
$885$	45.9495	1.54458
$886$	−1.54575	−0.0519306
$887$	−39.8268	−1.33725	−0.668626	−	0.743599i	$-0.733117\pi$
$887$	−39.8268	−1.33725	−0.668626	+	0.743599i	$0.733117\pi$
$888$	−1.41020	−0.0473233
$889$	1.18832	0.0398551
$890$	28.1828	0.944690
$891$	−0.499691	−0.0167403
$892$	10.8427	0.363039
$893$	10.8057	0.361600
$894$	−23.2504	−0.777610
$895$	−38.1785	−1.27617
$896$	−0.812393	−0.0271402
$897$	−5.38809	−0.179903
$898$	−18.3702	−0.613022
$899$	−7.39870	−0.246760
$900$	7.59480	0.253160
$901$	−16.9022	−0.563093
$902$	1.81860	0.0605529
$903$	−8.03376	−0.267347
$904$	−14.8227	−0.492996
$905$	37.6108	1.25023
$906$	17.4554	0.579918
$907$	22.4974	0.747015	0.373508	−	0.927627i	$-0.378155\pi$
$907$	22.4974	0.747015	0.373508	+	0.927627i	$0.378155\pi$
$908$	−2.73298	−0.0906971
$909$	6.97303	0.231281
$910$	2.88312	0.0955743
$911$	12.2306	0.405217	0.202609	−	0.979260i	$-0.435058\pi$
$911$	12.2306	0.405217	0.202609	+	0.979260i	$0.435058\pi$
$912$	5.19945	0.172171
$913$	−2.06349	−0.0682915
$914$	15.7142	0.519779
$915$	−43.1045	−1.42499
$916$	−16.6126	−0.548895
$917$	−17.7654	−0.586667
$918$	−2.03563	−0.0671858
$919$	19.1553	0.631876	0.315938	−	0.948780i	$-0.397681\pi$
$919$	19.1553	0.631876	0.315938	+	0.948780i	$0.397681\pi$
$920$	19.1219	0.630429
$921$	29.7837	0.981408
$922$	11.2251	0.369679
$923$	1.09298	0.0359758
$924$	0.405945	0.0133546
$925$	−10.7102	−0.352149
$926$	−10.6807	−0.350990
$927$	−1.00000	−0.0328443
$928$	−2.20133	−0.0722621
$929$	43.3712	1.42296	0.711482	−	0.702705i	$-0.248025\pi$
$929$	43.3712	1.42296	0.711482	+	0.702705i	$0.248025\pi$
$930$	−11.9280	−0.391134
$931$	32.9646	1.08037
$932$	11.2262	0.367727
$933$	11.2915	0.369668
$934$	−15.5030	−0.507273
$935$	3.60990	0.118057
$936$	1.00000	0.0326860
$937$	−10.4740	−0.342169	−0.171085	−	0.985256i	$-0.554727\pi$
$937$	−10.4740	−0.342169	−0.171085	+	0.985256i	$0.554727\pi$
$938$	7.05446	0.230336
$939$	−29.8641	−0.974579
$940$	−7.37551	−0.240563
$941$	55.8764	1.82152	0.910759	−	0.412939i	$-0.135498\pi$
$941$	55.8764	1.82152	0.910759	+	0.412939i	$0.135498\pi$
$942$	−18.6902	−0.608961
$943$	−19.6097	−0.638580
$944$	−12.9475	−0.421404
$945$	−2.88312	−0.0937877
$946$	4.94145	0.160660
$947$	−22.6306	−0.735395	−0.367698	−	0.929945i	$-0.619854\pi$
$947$	−22.6306	−0.735395	−0.367698	+	0.929945i	$0.619854\pi$
$948$	−2.73029	−0.0886758
$949$	8.30384	0.269554
$950$	39.4888	1.28119
$951$	−16.5466	−0.536560
$952$	1.65373	0.0535977
$953$	−55.2101	−1.78843	−0.894215	−	0.447639i	$-0.852265\pi$
$953$	−55.2101	−1.78843	−0.894215	+	0.447639i	$0.852265\pi$
$954$	−8.30317	−0.268825
$955$	24.3804	0.788930
$956$	17.5931	0.569001
$957$	1.09998	0.0355574
$958$	−26.0238	−0.840790
$959$	2.39932	0.0774782
$960$	−3.54892	−0.114541
$961$	−19.7035	−0.635598
$962$	−1.41020	−0.0454667
$963$	−16.4662	−0.530616
$964$	−13.2328	−0.426200
$965$	−80.0189	−2.57590
$966$	−4.37725	−0.140836
$967$	−39.2690	−1.26281	−0.631403	−	0.775455i	$-0.717521\pi$
$967$	−39.2690	−1.26281	−0.631403	+	0.775455i	$0.717521\pi$
$968$	10.7503	0.345528
$969$	−10.5842	−0.340012
$970$	25.1977	0.809048
$971$	−8.69646	−0.279083	−0.139541	−	0.990216i	$-0.544563\pi$
$971$	−8.69646	−0.279083	−0.139541	+	0.990216i	$0.544563\pi$
$972$	−1.00000	−0.0320750
$973$	1.46774	0.0470536
$974$	8.33767	0.267156
$975$	7.59480	0.243228
$976$	12.1458	0.388778
$977$	45.2688	1.44828	0.724138	−	0.689655i	$-0.242238\pi$
$977$	45.2688	1.44828	0.724138	+	0.689655i	$0.242238\pi$
$978$	−6.47633	−0.207090
$979$	3.96817	0.126823
$980$	−22.5002	−0.718742
$981$	−4.10903	−0.131191
$982$	14.2679	0.455307
$983$	−9.01100	−0.287406	−0.143703	−	0.989621i	$-0.545901\pi$
$983$	−9.01100	−0.287406	−0.143703	+	0.989621i	$0.545901\pi$
$984$	3.63946	0.116022
$985$	−45.9648	−1.46456
$986$	4.48108	0.142707
$987$	1.68835	0.0537408
$988$	5.19945	0.165417
$989$	−53.2828	−1.69430
$990$	1.77336	0.0563611
$991$	−17.5523	−0.557568	−0.278784	−	0.960354i	$-0.589931\pi$
$991$	−17.5523	−0.557568	−0.278784	+	0.960354i	$0.589931\pi$
$992$	3.36102	0.106713
$993$	−0.373217	−0.0118437
$994$	0.887927	0.0281633
$995$	−54.1766	−1.71751
$996$	−4.12953	−0.130849
$997$	13.0451	0.413142	0.206571	−	0.978432i	$-0.433770\pi$
$997$	13.0451	0.413142	0.206571	+	0.978432i	$0.433770\pi$
$998$	5.36546	0.169841
$999$	1.41020	0.0446168

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.s.1.9	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.s.1.9	✓	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.54892 q^{5} +1.00000 q^{6} +0.812393 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.54892 q^{5} +1.00000 q^{6} +0.812393 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.54892 q^{10} -0.499691 q^{11} -1.00000 q^{12} -1.00000 q^{13} -0.812393 q^{14} -3.54892 q^{15} +1.00000 q^{16} -2.03563 q^{17} -1.00000 q^{18} -5.19945 q^{19} +3.54892 q^{20} -0.812393 q^{21} +0.499691 q^{22} -5.38809 q^{23} +1.00000 q^{24} +7.59480 q^{25} +1.00000 q^{26} -1.00000 q^{27} +0.812393 q^{28} +2.20133 q^{29} +3.54892 q^{30} -3.36102 q^{31} -1.00000 q^{32} +0.499691 q^{33} +2.03563 q^{34} +2.88312 q^{35} +1.00000 q^{36} -1.41020 q^{37} +5.19945 q^{38} +1.00000 q^{39} -3.54892 q^{40} +3.63946 q^{41} +0.812393 q^{42} +9.88901 q^{43} -0.499691 q^{44} +3.54892 q^{45} +5.38809 q^{46} -2.07824 q^{47} -1.00000 q^{48} -6.34002 q^{49} -7.59480 q^{50} +2.03563 q^{51} -1.00000 q^{52} +8.30317 q^{53} +1.00000 q^{54} -1.77336 q^{55} -0.812393 q^{56} +5.19945 q^{57} -2.20133 q^{58} -12.9475 q^{59} -3.54892 q^{60} +12.1458 q^{61} +3.36102 q^{62} +0.812393 q^{63} +1.00000 q^{64} -3.54892 q^{65} -0.499691 q^{66} -8.68355 q^{67} -2.03563 q^{68} +5.38809 q^{69} -2.88312 q^{70} -1.09298 q^{71} -1.00000 q^{72} -8.30384 q^{73} +1.41020 q^{74} -7.59480 q^{75} -5.19945 q^{76} -0.405945 q^{77} -1.00000 q^{78} +2.73029 q^{79} +3.54892 q^{80} +1.00000 q^{81} -3.63946 q^{82} +4.12953 q^{83} -0.812393 q^{84} -7.22428 q^{85} -9.88901 q^{86} -2.20133 q^{87} +0.499691 q^{88} -7.94125 q^{89} -3.54892 q^{90} -0.812393 q^{91} -5.38809 q^{92} +3.36102 q^{93} +2.07824 q^{94} -18.4524 q^{95} +1.00000 q^{96} -7.10010 q^{97} +6.34002 q^{98} -0.499691 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 + 10 * q^6 - 9 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9} - 6 q^{10} - q^{11} - 10 q^{12} - 10 q^{13} + 9 q^{14} - 6 q^{15} + 10 q^{16} + 5 q^{17} - 10 q^{18} - 9 q^{19} + 6 q^{20} + 9 q^{21} + q^{22} + q^{23} + 10 q^{24} + 20 q^{25} + 10 q^{26} - 10 q^{27} - 9 q^{28} - 22 q^{29} + 6 q^{30} - 13 q^{31} - 10 q^{32} + q^{33} - 5 q^{34} + 14 q^{35} + 10 q^{36} + 10 q^{37} + 9 q^{38} + 10 q^{39} - 6 q^{40} - 18 q^{41} - 9 q^{42} + 10 q^{43} - q^{44} + 6 q^{45} - q^{46} + 28 q^{47} - 10 q^{48} + 11 q^{49} - 20 q^{50} - 5 q^{51} - 10 q^{52} + 6 q^{53} + 10 q^{54} - 26 q^{55} + 9 q^{56} + 9 q^{57} + 22 q^{58} + 7 q^{59} - 6 q^{60} - 20 q^{61} + 13 q^{62} - 9 q^{63} + 10 q^{64} - 6 q^{65} - q^{66} - 21 q^{67} + 5 q^{68} - q^{69} - 14 q^{70} - 19 q^{71} - 10 q^{72} + 3 q^{73} - 10 q^{74} - 20 q^{75} - 9 q^{76} + 28 q^{77} - 10 q^{78} - 11 q^{79} + 6 q^{80} + 10 q^{81} + 18 q^{82} + 20 q^{83} + 9 q^{84} - q^{85} - 10 q^{86} + 22 q^{87} + q^{88} + 22 q^{89} - 6 q^{90} + 9 q^{91} + q^{92} + 13 q^{93} - 28 q^{94} + 10 q^{96} - 10 q^{97} - 11 q^{98} - q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 + 10 * q^6 - 9 * q^7 - 10 * q^8 + 10 * q^9 - 6 * q^10 - q^11 - 10 * q^12 - 10 * q^13 + 9 * q^14 - 6 * q^15 + 10 * q^16 + 5 * q^17 - 10 * q^18 - 9 * q^19 + 6 * q^20 + 9 * q^21 + q^22 + q^23 + 10 * q^24 + 20 * q^25 + 10 * q^26 - 10 * q^27 - 9 * q^28 - 22 * q^29 + 6 * q^30 - 13 * q^31 - 10 * q^32 + q^33 - 5 * q^34 + 14 * q^35 + 10 * q^36 + 10 * q^37 + 9 * q^38 + 10 * q^39 - 6 * q^40 - 18 * q^41 - 9 * q^42 + 10 * q^43 - q^44 + 6 * q^45 - q^46 + 28 * q^47 - 10 * q^48 + 11 * q^49 - 20 * q^50 - 5 * q^51 - 10 * q^52 + 6 * q^53 + 10 * q^54 - 26 * q^55 + 9 * q^56 + 9 * q^57 + 22 * q^58 + 7 * q^59 - 6 * q^60 - 20 * q^61 + 13 * q^62 - 9 * q^63 + 10 * q^64 - 6 * q^65 - q^66 - 21 * q^67 + 5 * q^68 - q^69 - 14 * q^70 - 19 * q^71 - 10 * q^72 + 3 * q^73 - 10 * q^74 - 20 * q^75 - 9 * q^76 + 28 * q^77 - 10 * q^78 - 11 * q^79 + 6 * q^80 + 10 * q^81 + 18 * q^82 + 20 * q^83 + 9 * q^84 - q^85 - 10 * q^86 + 22 * q^87 + q^88 + 22 * q^89 - 6 * q^90 + 9 * q^91 + q^92 + 13 * q^93 - 28 * q^94 + 10 * q^96 - 10 * q^97 - 11 * q^98 - q^99

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