LMFDB - Embedded newform 8034.2.a.o.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.1518129839$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 4x^{5} + 14x^{4} + 3x^{3} - 12x^{2} - 3x + 1 $ x^7 - 3x^6 - 4x^5 + 14x^4 + 3x^3 - 12x^2 - 3x + 1
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			1.6
Root			$-0.761570$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.28276 q^{5} +1.00000 q^{6} -3.26302 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.28276 q^{5} +1.00000 q^{6} -3.26302 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.28276 q^{10} +3.43964 q^{11} -1.00000 q^{12} +1.00000 q^{13} +3.26302 q^{14} -3.28276 q^{15} +1.00000 q^{16} -4.30990 q^{17} -1.00000 q^{18} -4.26302 q^{19} +3.28276 q^{20} +3.26302 q^{21} -3.43964 q^{22} +0.898821 q^{23} +1.00000 q^{24} +5.77652 q^{25} -1.00000 q^{26} -1.00000 q^{27} -3.26302 q^{28} +1.85461 q^{29} +3.28276 q^{30} +0.0760444 q^{31} -1.00000 q^{32} -3.43964 q^{33} +4.30990 q^{34} -10.7117 q^{35} +1.00000 q^{36} +6.10764 q^{37} +4.26302 q^{38} -1.00000 q^{39} -3.28276 q^{40} -10.4552 q^{41} -3.26302 q^{42} -4.03388 q^{43} +3.43964 q^{44} +3.28276 q^{45} -0.898821 q^{46} +8.58105 q^{47} -1.00000 q^{48} +3.64729 q^{49} -5.77652 q^{50} +4.30990 q^{51} +1.00000 q^{52} -0.879007 q^{53} +1.00000 q^{54} +11.2915 q^{55} +3.26302 q^{56} +4.26302 q^{57} -1.85461 q^{58} -8.39658 q^{59} -3.28276 q^{60} +6.04443 q^{61} -0.0760444 q^{62} -3.26302 q^{63} +1.00000 q^{64} +3.28276 q^{65} +3.43964 q^{66} +2.20686 q^{67} -4.30990 q^{68} -0.898821 q^{69} +10.7117 q^{70} -9.35352 q^{71} -1.00000 q^{72} +7.76041 q^{73} -6.10764 q^{74} -5.77652 q^{75} -4.26302 q^{76} -11.2236 q^{77} +1.00000 q^{78} -12.7124 q^{79} +3.28276 q^{80} +1.00000 q^{81} +10.4552 q^{82} -5.25414 q^{83} +3.26302 q^{84} -14.1484 q^{85} +4.03388 q^{86} -1.85461 q^{87} -3.43964 q^{88} -13.0095 q^{89} -3.28276 q^{90} -3.26302 q^{91} +0.898821 q^{92} -0.0760444 q^{93} -8.58105 q^{94} -13.9945 q^{95} +1.00000 q^{96} -0.220152 q^{97} -3.64729 q^{98} +3.43964 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9} - 2 q^{10} - 7 q^{12} + 7 q^{13} + 9 q^{14} - 2 q^{15} + 7 q^{16} + 3 q^{17} - 7 q^{18} - 16 q^{19} + 2 q^{20} + 9 q^{21} + 6 q^{23} + 7 q^{24} + 15 q^{25} - 7 q^{26} - 7 q^{27} - 9 q^{28} - 5 q^{29} + 2 q^{30} - 16 q^{31} - 7 q^{32} - 3 q^{34} - 10 q^{35} + 7 q^{36} + 17 q^{37} + 16 q^{38} - 7 q^{39} - 2 q^{40} + 12 q^{41} - 9 q^{42} - 22 q^{43} + 2 q^{45} - 6 q^{46} - 7 q^{48} - 2 q^{49} - 15 q^{50} - 3 q^{51} + 7 q^{52} + 2 q^{53} + 7 q^{54} - 16 q^{55} + 9 q^{56} + 16 q^{57} + 5 q^{58} - 3 q^{59} - 2 q^{60} - 6 q^{61} + 16 q^{62} - 9 q^{63} + 7 q^{64} + 2 q^{65} + q^{67} + 3 q^{68} - 6 q^{69} + 10 q^{70} + 15 q^{71} - 7 q^{72} + 17 q^{73} - 17 q^{74} - 15 q^{75} - 16 q^{76} - 10 q^{77} + 7 q^{78} - 27 q^{79} + 2 q^{80} + 7 q^{81} - 12 q^{82} + 12 q^{83} + 9 q^{84} + 15 q^{85} + 22 q^{86} + 5 q^{87} - 9 q^{89} - 2 q^{90} - 9 q^{91} + 6 q^{92} + 16 q^{93} - 12 q^{95} + 7 q^{96} - 3 q^{97} + 2 q^{98}+O(q^{100}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9 - 2 * q^10 - 7 * q^12 + 7 * q^13 + 9 * q^14 - 2 * q^15 + 7 * q^16 + 3 * q^17 - 7 * q^18 - 16 * q^19 + 2 * q^20 + 9 * q^21 + 6 * q^23 + 7 * q^24 + 15 * q^25 - 7 * q^26 - 7 * q^27 - 9 * q^28 - 5 * q^29 + 2 * q^30 - 16 * q^31 - 7 * q^32 - 3 * q^34 - 10 * q^35 + 7 * q^36 + 17 * q^37 + 16 * q^38 - 7 * q^39 - 2 * q^40 + 12 * q^41 - 9 * q^42 - 22 * q^43 + 2 * q^45 - 6 * q^46 - 7 * q^48 - 2 * q^49 - 15 * q^50 - 3 * q^51 + 7 * q^52 + 2 * q^53 + 7 * q^54 - 16 * q^55 + 9 * q^56 + 16 * q^57 + 5 * q^58 - 3 * q^59 - 2 * q^60 - 6 * q^61 + 16 * q^62 - 9 * q^63 + 7 * q^64 + 2 * q^65 + q^67 + 3 * q^68 - 6 * q^69 + 10 * q^70 + 15 * q^71 - 7 * q^72 + 17 * q^73 - 17 * q^74 - 15 * q^75 - 16 * q^76 - 10 * q^77 + 7 * q^78 - 27 * q^79 + 2 * q^80 + 7 * q^81 - 12 * q^82 + 12 * q^83 + 9 * q^84 + 15 * q^85 + 22 * q^86 + 5 * q^87 - 9 * q^89 - 2 * q^90 - 9 * q^91 + 6 * q^92 + 16 * q^93 - 12 * q^95 + 7 * q^96 - 3 * q^97 + 2 * q^98

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
$5$	3.28276	1.46810	0.734048	−	0.679098i	$-0.237629\pi$
$5$	3.28276	1.46810	0.734048	+	0.679098i	$0.237629\pi$
$6$	1.00000	0.408248
$7$	−3.26302	−1.23331	−0.616653	−	0.787235i	$-0.711512\pi$
$7$	−3.26302	−1.23331	−0.616653	+	0.787235i	$0.711512\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.28276	−1.03810
$11$	3.43964	1.03709	0.518545	−	0.855050i	$-0.326474\pi$
$11$	3.43964	1.03709	0.518545	+	0.855050i	$0.326474\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	3.26302	0.872079
$15$	−3.28276	−0.847605
$16$	1.00000	0.250000
$17$	−4.30990	−1.04530	−0.522652	−	0.852546i	$-0.675057\pi$
$17$	−4.30990	−1.04530	−0.522652	+	0.852546i	$0.675057\pi$
$18$	−1.00000	−0.235702
$19$	−4.26302	−0.978004	−0.489002	−	0.872283i	$-0.662639\pi$
$19$	−4.26302	−0.978004	−0.489002	+	0.872283i	$0.662639\pi$
$20$	3.28276	0.734048
$21$	3.26302	0.712049
$22$	−3.43964	−0.733333
$23$	0.898821	0.187417	0.0937085	−	0.995600i	$-0.470128\pi$
$23$	0.898821	0.187417	0.0937085	+	0.995600i	$0.470128\pi$
$24$	1.00000	0.204124
$25$	5.77652	1.15530
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	−3.26302	−0.616653
$29$	1.85461	0.344392	0.172196	−	0.985063i	$-0.444914\pi$
$29$	1.85461	0.344392	0.172196	+	0.985063i	$0.444914\pi$
$30$	3.28276	0.599347
$31$	0.0760444	0.0136580	0.00682899	−	0.999977i	$-0.497826\pi$
$31$	0.0760444	0.0136580	0.00682899	+	0.999977i	$0.497826\pi$
$32$	−1.00000	−0.176777
$33$	−3.43964	−0.598764
$34$	4.30990	0.739141
$35$	−10.7117	−1.81061
$36$	1.00000	0.166667
$37$	6.10764	1.00409	0.502045	−	0.864841i	$-0.332581\pi$
$37$	6.10764	1.00409	0.502045	+	0.864841i	$0.332581\pi$
$38$	4.26302	0.691553
$39$	−1.00000	−0.160128
$40$	−3.28276	−0.519050
$41$	−10.4552	−1.63283	−0.816417	−	0.577463i	$-0.804043\pi$
$41$	−10.4552	−1.63283	−0.816417	+	0.577463i	$0.804043\pi$
$42$	−3.26302	−0.503495
$43$	−4.03388	−0.615161	−0.307580	−	0.951522i	$-0.599519\pi$
$43$	−4.03388	−0.615161	−0.307580	+	0.951522i	$0.599519\pi$
$44$	3.43964	0.518545
$45$	3.28276	0.489365
$46$	−0.898821	−0.132524
$47$	8.58105	1.25167	0.625837	−	0.779954i	$-0.284757\pi$
$47$	8.58105	1.25167	0.625837	+	0.779954i	$0.284757\pi$
$48$	−1.00000	−0.144338
$49$	3.64729	0.521042
$50$	−5.77652	−0.816923
$51$	4.30990	0.603506
$52$	1.00000	0.138675
$53$	−0.879007	−0.120741	−0.0603704	−	0.998176i	$-0.519228\pi$
$53$	−0.879007	−0.120741	−0.0603704	+	0.998176i	$0.519228\pi$
$54$	1.00000	0.136083
$55$	11.2915	1.52255
$56$	3.26302	0.436039
$57$	4.26302	0.564651
$58$	−1.85461	−0.243522
$59$	−8.39658	−1.09314	−0.546571	−	0.837413i	$-0.684067\pi$
$59$	−8.39658	−1.09314	−0.546571	+	0.837413i	$0.684067\pi$
$60$	−3.28276	−0.423803
$61$	6.04443	0.773910	0.386955	−	0.922099i	$-0.373527\pi$
$61$	6.04443	0.773910	0.386955	+	0.922099i	$0.373527\pi$
$62$	−0.0760444	−0.00965765
$63$	−3.26302	−0.411102
$64$	1.00000	0.125000
$65$	3.28276	0.407176
$66$	3.43964	0.423390
$67$	2.20686	0.269611	0.134805	−	0.990872i	$-0.456959\pi$
$67$	2.20686	0.269611	0.134805	+	0.990872i	$0.456959\pi$
$68$	−4.30990	−0.522652
$69$	−0.898821	−0.108205
$70$	10.7117	1.28029
$71$	−9.35352	−1.11006	−0.555029	−	0.831831i	$-0.687293\pi$
$71$	−9.35352	−1.11006	−0.555029	+	0.831831i	$0.687293\pi$
$72$	−1.00000	−0.117851
$73$	7.76041	0.908287	0.454144	−	0.890929i	$-0.349945\pi$
$73$	7.76041	0.908287	0.454144	+	0.890929i	$0.349945\pi$
$74$	−6.10764	−0.709999
$75$	−5.77652	−0.667015
$76$	−4.26302	−0.489002
$77$	−11.2236	−1.27905
$78$	1.00000	0.113228
$79$	−12.7124	−1.43026	−0.715129	−	0.698993i	$-0.753632\pi$
$79$	−12.7124	−1.43026	−0.715129	+	0.698993i	$0.753632\pi$
$80$	3.28276	0.367024
$81$	1.00000	0.111111
$82$	10.4552	1.15459
$83$	−5.25414	−0.576717	−0.288358	−	0.957523i	$-0.593109\pi$
$83$	−5.25414	−0.576717	−0.288358	+	0.957523i	$0.593109\pi$
$84$	3.26302	0.356025
$85$	−14.1484	−1.53461
$86$	4.03388	0.434985
$87$	−1.85461	−0.198835
$88$	−3.43964	−0.366667
$89$	−13.0095	−1.37900	−0.689501	−	0.724284i	$-0.742170\pi$
$89$	−13.0095	−1.37900	−0.689501	+	0.724284i	$0.742170\pi$
$90$	−3.28276	−0.346033
$91$	−3.26302	−0.342057
$92$	0.898821	0.0937085
$93$	−0.0760444	−0.00788544
$94$	−8.58105	−0.885067
$95$	−13.9945	−1.43580
$96$	1.00000	0.102062
$97$	−0.220152	−0.0223531	−0.0111765	−	0.999938i	$-0.503558\pi$
$97$	−0.220152	−0.0223531	−0.0111765	+	0.999938i	$0.503558\pi$
$98$	−3.64729	−0.368432
$99$	3.43964	0.345697
$100$	5.77652	0.577652
$101$	−6.97473	−0.694011	−0.347006	−	0.937863i	$-0.612801\pi$
$101$	−6.97473	−0.694011	−0.347006	+	0.937863i	$0.612801\pi$
$102$	−4.30990	−0.426744
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	10.7117	1.04536
$106$	0.879007	0.0853767
$107$	12.5778	1.21594	0.607970	−	0.793960i	$-0.291984\pi$
$107$	12.5778	1.21594	0.607970	+	0.793960i	$0.291984\pi$
$108$	−1.00000	−0.0962250
$109$	18.9579	1.81584	0.907920	−	0.419144i	$-0.137670\pi$
$109$	18.9579	1.81584	0.907920	+	0.419144i	$0.137670\pi$
$110$	−11.2915	−1.07660
$111$	−6.10764	−0.579712
$112$	−3.26302	−0.308326
$113$	−3.10165	−0.291779	−0.145890	−	0.989301i	$-0.546604\pi$
$113$	−3.10165	−0.291779	−0.145890	+	0.989301i	$0.546604\pi$
$114$	−4.26302	−0.399268
$115$	2.95061	0.275146
$116$	1.85461	0.172196
$117$	1.00000	0.0924500
$118$	8.39658	0.772968
$119$	14.0633	1.28918
$120$	3.28276	0.299674
$121$	0.831115	0.0755559
$122$	−6.04443	−0.547237
$123$	10.4552	0.942717
$124$	0.0760444	0.00682899
$125$	2.54912	0.228000
$126$	3.26302	0.290693
$127$	−10.7269	−0.951859	−0.475930	−	0.879483i	$-0.657888\pi$
$127$	−10.7269	−0.951859	−0.475930	+	0.879483i	$0.657888\pi$
$128$	−1.00000	−0.0883883
$129$	4.03388	0.355163
$130$	−3.28276	−0.287917
$131$	5.95551	0.520335	0.260168	−	0.965563i	$-0.416222\pi$
$131$	5.95551	0.520335	0.260168	+	0.965563i	$0.416222\pi$
$132$	−3.43964	−0.299382
$133$	13.9103	1.20618
$134$	−2.20686	−0.190644
$135$	−3.28276	−0.282535
$136$	4.30990	0.369571
$137$	20.6100	1.76083	0.880417	−	0.474201i	$-0.157263\pi$
$137$	20.6100	1.76083	0.880417	+	0.474201i	$0.157263\pi$
$138$	0.898821	0.0765127
$139$	−8.49965	−0.720931	−0.360466	−	0.932772i	$-0.617382\pi$
$139$	−8.49965	−0.720931	−0.360466	+	0.932772i	$0.617382\pi$
$140$	−10.7117	−0.905305
$141$	−8.58105	−0.722655
$142$	9.35352	0.784930
$143$	3.43964	0.287637
$144$	1.00000	0.0833333
$145$	6.08824	0.505601
$146$	−7.76041	−0.642256
$147$	−3.64729	−0.300824
$148$	6.10764	0.502045
$149$	−17.4883	−1.43270	−0.716350	−	0.697741i	$-0.754189\pi$
$149$	−17.4883	−1.43270	−0.716350	+	0.697741i	$0.754189\pi$
$150$	5.77652	0.471651
$151$	−12.6784	−1.03176	−0.515879	−	0.856662i	$-0.672534\pi$
$151$	−12.6784	−1.03176	−0.515879	+	0.856662i	$0.672534\pi$
$152$	4.26302	0.345777
$153$	−4.30990	−0.348435
$154$	11.2236	0.904424
$155$	0.249636	0.0200512
$156$	−1.00000	−0.0800641
$157$	−6.28656	−0.501722	−0.250861	−	0.968023i	$-0.580714\pi$
$157$	−6.28656	−0.501722	−0.250861	+	0.968023i	$0.580714\pi$
$158$	12.7124	1.01134
$159$	0.879007	0.0697098
$160$	−3.28276	−0.259525
$161$	−2.93287	−0.231142
$162$	−1.00000	−0.0785674
$163$	−11.1403	−0.872579	−0.436289	−	0.899806i	$-0.643708\pi$
$163$	−11.1403	−0.872579	−0.436289	+	0.899806i	$0.643708\pi$
$164$	−10.4552	−0.816417
$165$	−11.2915	−0.879043
$166$	5.25414	0.407800
$167$	−2.48103	−0.191988	−0.0959938	−	0.995382i	$-0.530603\pi$
$167$	−2.48103	−0.191988	−0.0959938	+	0.995382i	$0.530603\pi$
$168$	−3.26302	−0.251747
$169$	1.00000	0.0769231
$170$	14.1484	1.08513
$171$	−4.26302	−0.326001
$172$	−4.03388	−0.307580
$173$	21.7190	1.65126	0.825632	−	0.564209i	$-0.190819\pi$
$173$	21.7190	1.65126	0.825632	+	0.564209i	$0.190819\pi$
$174$	1.85461	0.140598
$175$	−18.8489	−1.42484
$176$	3.43964	0.259273
$177$	8.39658	0.631126
$178$	13.0095	0.975102
$179$	−2.68391	−0.200605	−0.100303	−	0.994957i	$-0.531981\pi$
$179$	−2.68391	−0.200605	−0.100303	+	0.994957i	$0.531981\pi$
$180$	3.28276	0.244683
$181$	−8.98763	−0.668046	−0.334023	−	0.942565i	$-0.608406\pi$
$181$	−8.98763	−0.668046	−0.334023	+	0.942565i	$0.608406\pi$
$182$	3.26302	0.241871
$183$	−6.04443	−0.446817
$184$	−0.898821	−0.0662619
$185$	20.0499	1.47410
$186$	0.0760444	0.00557585
$187$	−14.8245	−1.08407
$188$	8.58105	0.625837
$189$	3.26302	0.237350
$190$	13.9945	1.01527
$191$	−20.8937	−1.51181	−0.755906	−	0.654680i	$-0.772803\pi$
$191$	−20.8937	−1.51181	−0.755906	+	0.654680i	$0.772803\pi$
$192$	−1.00000	−0.0721688
$193$	−7.84674	−0.564820	−0.282410	−	0.959294i	$-0.591134\pi$
$193$	−7.84674	−0.564820	−0.282410	+	0.959294i	$0.591134\pi$
$194$	0.220152	0.0158060
$195$	−3.28276	−0.235083
$196$	3.64729	0.260521
$197$	−12.3894	−0.882705	−0.441353	−	0.897334i	$-0.645501\pi$
$197$	−12.3894	−0.882705	−0.441353	+	0.897334i	$0.645501\pi$
$198$	−3.43964	−0.244444
$199$	−4.38042	−0.310520	−0.155260	−	0.987874i	$-0.549622\pi$
$199$	−4.38042	−0.310520	−0.155260	+	0.987874i	$0.549622\pi$
$200$	−5.77652	−0.408461
$201$	−2.20686	−0.155660
$202$	6.97473	0.490740
$203$	−6.05162	−0.424741
$204$	4.30990	0.301753
$205$	−34.3220	−2.39715
$206$	−1.00000	−0.0696733
$207$	0.898821	0.0624723
$208$	1.00000	0.0693375
$209$	−14.6632	−1.01428
$210$	−10.7117	−0.739178
$211$	−9.73052	−0.669876	−0.334938	−	0.942240i	$-0.608715\pi$
$211$	−9.73052	−0.669876	−0.334938	+	0.942240i	$0.608715\pi$
$212$	−0.879007	−0.0603704
$213$	9.35352	0.640892
$214$	−12.5778	−0.859799
$215$	−13.2423	−0.903115
$216$	1.00000	0.0680414
$217$	−0.248134	−0.0168445
$218$	−18.9579	−1.28399
$219$	−7.76041	−0.524400
$220$	11.2915	0.761274
$221$	−4.30990	−0.289915
$222$	6.10764	0.409918
$223$	−1.97961	−0.132564	−0.0662822	−	0.997801i	$-0.521114\pi$
$223$	−1.97961	−0.132564	−0.0662822	+	0.997801i	$0.521114\pi$
$224$	3.26302	0.218020
$225$	5.77652	0.385101
$226$	3.10165	0.206319
$227$	−15.6688	−1.03998	−0.519988	−	0.854173i	$-0.674064\pi$
$227$	−15.6688	−1.03998	−0.519988	+	0.854173i	$0.674064\pi$
$228$	4.26302	0.282325
$229$	25.9643	1.71577	0.857885	−	0.513841i	$-0.171778\pi$
$229$	25.9643	1.71577	0.857885	+	0.513841i	$0.171778\pi$
$230$	−2.95061	−0.194558
$231$	11.2236	0.738459
$232$	−1.85461	−0.121761
$233$	−1.78245	−0.116772	−0.0583860	−	0.998294i	$-0.518595\pi$
$233$	−1.78245	−0.116772	−0.0583860	+	0.998294i	$0.518595\pi$
$234$	−1.00000	−0.0653720
$235$	28.1695	1.83758
$236$	−8.39658	−0.546571
$237$	12.7124	0.825759
$238$	−14.0633	−0.911587
$239$	3.14850	0.203660	0.101830	−	0.994802i	$-0.467530\pi$
$239$	3.14850	0.203660	0.101830	+	0.994802i	$0.467530\pi$
$240$	−3.28276	−0.211901
$241$	−15.0632	−0.970303	−0.485152	−	0.874430i	$-0.661236\pi$
$241$	−15.0632	−0.970303	−0.485152	+	0.874430i	$0.661236\pi$
$242$	−0.831115	−0.0534261
$243$	−1.00000	−0.0641500
$244$	6.04443	0.386955
$245$	11.9732	0.764939
$246$	−10.4552	−0.666601
$247$	−4.26302	−0.271249
$248$	−0.0760444	−0.00482883
$249$	5.25414	0.332968
$250$	−2.54912	−0.161221
$251$	−6.66166	−0.420481	−0.210240	−	0.977650i	$-0.567425\pi$
$251$	−6.66166	−0.420481	−0.210240	+	0.977650i	$0.567425\pi$
$252$	−3.26302	−0.205551
$253$	3.09162	0.194368
$254$	10.7269	0.673066
$255$	14.1484	0.886005
$256$	1.00000	0.0625000
$257$	2.53517	0.158139	0.0790696	−	0.996869i	$-0.474805\pi$
$257$	2.53517	0.158139	0.0790696	+	0.996869i	$0.474805\pi$
$258$	−4.03388	−0.251138
$259$	−19.9294	−1.23835
$260$	3.28276	0.203588
$261$	1.85461	0.114797
$262$	−5.95551	−0.367932
$263$	30.3814	1.87340	0.936698	−	0.350138i	$-0.113865\pi$
$263$	30.3814	1.87340	0.936698	+	0.350138i	$0.113865\pi$
$264$	3.43964	0.211695
$265$	−2.88557	−0.177259
$266$	−13.9103	−0.852896
$267$	13.0095	0.796168
$268$	2.20686	0.134805
$269$	14.9780	0.913222	0.456611	−	0.889666i	$-0.349063\pi$
$269$	14.9780	0.913222	0.456611	+	0.889666i	$0.349063\pi$
$270$	3.28276	0.199782
$271$	22.7307	1.38079	0.690395	−	0.723433i	$-0.257437\pi$
$271$	22.7307	1.38079	0.690395	+	0.723433i	$0.257437\pi$
$272$	−4.30990	−0.261326
$273$	3.26302	0.197487
$274$	−20.6100	−1.24510
$275$	19.8691	1.19815
$276$	−0.898821	−0.0541026
$277$	16.0879	0.966628	0.483314	−	0.875447i	$-0.339433\pi$
$277$	16.0879	0.966628	0.483314	+	0.875447i	$0.339433\pi$
$278$	8.49965	0.509775
$279$	0.0760444	0.00455266
$280$	10.7117	0.640147
$281$	7.59780	0.453246	0.226623	−	0.973983i	$-0.427231\pi$
$281$	7.59780	0.453246	0.226623	+	0.973983i	$0.427231\pi$
$282$	8.58105	0.510994
$283$	−21.7133	−1.29072	−0.645361	−	0.763878i	$-0.723293\pi$
$283$	−21.7133	−1.29072	−0.645361	+	0.763878i	$0.723293\pi$
$284$	−9.35352	−0.555029
$285$	13.9945	0.828961
$286$	−3.43964	−0.203390
$287$	34.1156	2.01378
$288$	−1.00000	−0.0589256
$289$	1.57522	0.0926601
$290$	−6.08824	−0.357514
$291$	0.220152	0.0129055
$292$	7.76041	0.454144
$293$	3.95009	0.230767	0.115383	−	0.993321i	$-0.463190\pi$
$293$	3.95009	0.230767	0.115383	+	0.993321i	$0.463190\pi$
$294$	3.64729	0.212714
$295$	−27.5640	−1.60484
$296$	−6.10764	−0.354999
$297$	−3.43964	−0.199588
$298$	17.4883	1.01307
$299$	0.898821	0.0519801
$300$	−5.77652	−0.333507
$301$	13.1626	0.758681
$302$	12.6784	0.729563
$303$	6.97473	0.400687
$304$	−4.26302	−0.244501
$305$	19.8424	1.13617
$306$	4.30990	0.246380
$307$	−31.6335	−1.80542	−0.902711	−	0.430248i	$-0.858426\pi$
$307$	−31.6335	−1.80542	−0.902711	+	0.430248i	$0.858426\pi$
$308$	−11.2236	−0.639524
$309$	−1.00000	−0.0568880
$310$	−0.249636	−0.0141784
$311$	−4.11144	−0.233138	−0.116569	−	0.993183i	$-0.537190\pi$
$311$	−4.11144	−0.233138	−0.116569	+	0.993183i	$0.537190\pi$
$312$	1.00000	0.0566139
$313$	−1.23314	−0.0697009	−0.0348505	−	0.999393i	$-0.511095\pi$
$313$	−1.23314	−0.0697009	−0.0348505	+	0.999393i	$0.511095\pi$
$314$	6.28656	0.354771
$315$	−10.7117	−0.603537
$316$	−12.7124	−0.715129
$317$	−11.2352	−0.631032	−0.315516	−	0.948920i	$-0.602178\pi$
$317$	−11.2352	−0.631032	−0.315516	+	0.948920i	$0.602178\pi$
$318$	−0.879007	−0.0492922
$319$	6.37919	0.357166
$320$	3.28276	0.183512
$321$	−12.5778	−0.702023
$322$	2.93287	0.163442
$323$	18.3732	1.02231
$324$	1.00000	0.0555556
$325$	5.77652	0.320424
$326$	11.1403	0.617006
$327$	−18.9579	−1.04838
$328$	10.4552	0.577294
$329$	−28.0001	−1.54370
$330$	11.2915	0.621577
$331$	−12.0823	−0.664101	−0.332050	−	0.943262i	$-0.607740\pi$
$331$	−12.0823	−0.664101	−0.332050	+	0.943262i	$0.607740\pi$
$332$	−5.25414	−0.288358
$333$	6.10764	0.334697
$334$	2.48103	0.135756
$335$	7.24459	0.395814
$336$	3.26302	0.178012
$337$	11.5507	0.629206	0.314603	−	0.949223i	$-0.398129\pi$
$337$	11.5507	0.629206	0.314603	+	0.949223i	$0.398129\pi$
$338$	−1.00000	−0.0543928
$339$	3.10165	0.168459
$340$	−14.1484	−0.767303
$341$	0.261565	0.0141646
$342$	4.26302	0.230518
$343$	10.9399	0.590702
$344$	4.03388	0.217492
$345$	−2.95061	−0.158856
$346$	−21.7190	−1.16762
$347$	−1.65725	−0.0889661	−0.0444830	−	0.999010i	$-0.514164\pi$
$347$	−1.65725	−0.0889661	−0.0444830	+	0.999010i	$0.514164\pi$
$348$	−1.85461	−0.0994175
$349$	2.13379	0.114219	0.0571094	−	0.998368i	$-0.481812\pi$
$349$	2.13379	0.114219	0.0571094	+	0.998368i	$0.481812\pi$
$350$	18.8489	1.00752
$351$	−1.00000	−0.0533761
$352$	−3.43964	−0.183333
$353$	2.11532	0.112587	0.0562935	−	0.998414i	$-0.482072\pi$
$353$	2.11532	0.112587	0.0562935	+	0.998414i	$0.482072\pi$
$354$	−8.39658	−0.446273
$355$	−30.7054	−1.62967
$356$	−13.0095	−0.689501
$357$	−14.0633	−0.744308
$358$	2.68391	0.141849
$359$	−24.6758	−1.30234	−0.651169	−	0.758933i	$-0.725721\pi$
$359$	−24.6758	−1.30234	−0.651169	+	0.758933i	$0.725721\pi$
$360$	−3.28276	−0.173017
$361$	−0.826669	−0.0435089
$362$	8.98763	0.472380
$363$	−0.831115	−0.0436222
$364$	−3.26302	−0.171029
$365$	25.4756	1.33345
$366$	6.04443	0.315948
$367$	28.4209	1.48356	0.741780	−	0.670643i	$-0.233982\pi$
$367$	28.4209	1.48356	0.741780	+	0.670643i	$0.233982\pi$
$368$	0.898821	0.0468543
$369$	−10.4552	−0.544278
$370$	−20.0499	−1.04235
$371$	2.86822	0.148910
$372$	−0.0760444	−0.00394272
$373$	−18.1734	−0.940982	−0.470491	−	0.882405i	$-0.655923\pi$
$373$	−18.1734	−0.940982	−0.470491	+	0.882405i	$0.655923\pi$
$374$	14.8245	0.766556
$375$	−2.54912	−0.131636
$376$	−8.58105	−0.442534
$377$	1.85461	0.0955172
$378$	−3.26302	−0.167832
$379$	10.2512	0.526571	0.263285	−	0.964718i	$-0.415194\pi$
$379$	10.2512	0.526571	0.263285	+	0.964718i	$0.415194\pi$
$380$	−13.9945	−0.717901
$381$	10.7269	0.549556
$382$	20.8937	1.06901
$383$	25.1009	1.28259	0.641297	−	0.767293i	$-0.278397\pi$
$383$	25.1009	1.28259	0.641297	+	0.767293i	$0.278397\pi$
$384$	1.00000	0.0510310
$385$	−36.8444	−1.87777
$386$	7.84674	0.399388
$387$	−4.03388	−0.205054
$388$	−0.220152	−0.0111765
$389$	−10.0350	−0.508795	−0.254398	−	0.967100i	$-0.581877\pi$
$389$	−10.0350	−0.508795	−0.254398	+	0.967100i	$0.581877\pi$
$390$	3.28276	0.166229
$391$	−3.87382	−0.195908
$392$	−3.64729	−0.184216
$393$	−5.95551	−0.300416
$394$	12.3894	0.624167
$395$	−41.7318	−2.09975
$396$	3.43964	0.172848
$397$	32.7780	1.64508	0.822540	−	0.568707i	$-0.192556\pi$
$397$	32.7780	1.64508	0.822540	+	0.568707i	$0.192556\pi$
$398$	4.38042	0.219571
$399$	−13.9103	−0.696387
$400$	5.77652	0.288826
$401$	−2.15080	−0.107406	−0.0537029	−	0.998557i	$-0.517102\pi$
$401$	−2.15080	−0.107406	−0.0537029	+	0.998557i	$0.517102\pi$
$402$	2.20686	0.110068
$403$	0.0760444	0.00378804
$404$	−6.97473	−0.347006
$405$	3.28276	0.163122
$406$	6.05162	0.300337
$407$	21.0081	1.04133
$408$	−4.30990	−0.213372
$409$	−24.9692	−1.23465	−0.617324	−	0.786709i	$-0.711783\pi$
$409$	−24.9692	−1.23465	−0.617324	+	0.786709i	$0.711783\pi$
$410$	34.3220	1.69504
$411$	−20.6100	−1.01662
$412$	1.00000	0.0492665
$413$	27.3982	1.34818
$414$	−0.898821	−0.0441746
$415$	−17.2481	−0.846675
$416$	−1.00000	−0.0490290
$417$	8.49965	0.416230
$418$	14.6632	0.717203
$419$	−11.6865	−0.570923	−0.285462	−	0.958390i	$-0.592147\pi$
$419$	−11.6865	−0.570923	−0.285462	+	0.958390i	$0.592147\pi$
$420$	10.7117	0.522678
$421$	10.0040	0.487565	0.243782	−	0.969830i	$-0.421612\pi$
$421$	10.0040	0.487565	0.243782	+	0.969830i	$0.421612\pi$
$422$	9.73052	0.473674
$423$	8.58105	0.417225
$424$	0.879007	0.0426883
$425$	−24.8962	−1.20764
$426$	−9.35352	−0.453179
$427$	−19.7231	−0.954468
$428$	12.5778	0.607970
$429$	−3.43964	−0.166067
$430$	13.2423	0.638599
$431$	7.96361	0.383594	0.191797	−	0.981435i	$-0.438569\pi$
$431$	7.96361	0.383594	0.191797	+	0.981435i	$0.438569\pi$
$432$	−1.00000	−0.0481125
$433$	20.0637	0.964198	0.482099	−	0.876117i	$-0.339875\pi$
$433$	20.0637	0.964198	0.482099	+	0.876117i	$0.339875\pi$
$434$	0.248134	0.0119108
$435$	−6.08824	−0.291909
$436$	18.9579	0.907920
$437$	−3.83169	−0.183295
$438$	7.76041	0.370807
$439$	−24.6906	−1.17842	−0.589208	−	0.807981i	$-0.700560\pi$
$439$	−24.6906	−1.17842	−0.589208	+	0.807981i	$0.700560\pi$
$440$	−11.2915	−0.538302
$441$	3.64729	0.173681
$442$	4.30990	0.205001
$443$	−35.2903	−1.67669	−0.838347	−	0.545136i	$-0.816478\pi$
$443$	−35.2903	−1.67669	−0.838347	+	0.545136i	$0.816478\pi$
$444$	−6.10764	−0.289856
$445$	−42.7070	−2.02451
$446$	1.97961	0.0937372
$447$	17.4883	0.827170
$448$	−3.26302	−0.154163
$449$	−15.5411	−0.733428	−0.366714	−	0.930334i	$-0.619517\pi$
$449$	−15.5411	−0.733428	−0.366714	+	0.930334i	$0.619517\pi$
$450$	−5.77652	−0.272308
$451$	−35.9622	−1.69340
$452$	−3.10165	−0.145890
$453$	12.6784	0.595685
$454$	15.6688	0.735375
$455$	−10.7117	−0.502173
$456$	−4.26302	−0.199634
$457$	−37.2104	−1.74063	−0.870314	−	0.492497i	$-0.836084\pi$
$457$	−37.2104	−1.74063	−0.870314	+	0.492497i	$0.836084\pi$
$458$	−25.9643	−1.21323
$459$	4.30990	0.201169
$460$	2.95061	0.137573
$461$	16.2449	0.756600	0.378300	−	0.925683i	$-0.376509\pi$
$461$	16.2449	0.756600	0.378300	+	0.925683i	$0.376509\pi$
$462$	−11.2236	−0.522169
$463$	32.2809	1.50022	0.750110	−	0.661313i	$-0.230001\pi$
$463$	32.2809	1.50022	0.750110	+	0.661313i	$0.230001\pi$
$464$	1.85461	0.0860981
$465$	−0.249636	−0.0115766
$466$	1.78245	0.0825702
$467$	23.2790	1.07722	0.538611	−	0.842555i	$-0.318949\pi$
$467$	23.2790	1.07722	0.538611	+	0.842555i	$0.318949\pi$
$468$	1.00000	0.0462250
$469$	−7.20103	−0.332512
$470$	−28.1695	−1.29936
$471$	6.28656	0.289669
$472$	8.39658	0.386484
$473$	−13.8751	−0.637977
$474$	−12.7124	−0.583900
$475$	−24.6254	−1.12989
$476$	14.0633	0.644589
$477$	−0.879007	−0.0402470
$478$	−3.14850	−0.144009
$479$	7.50179	0.342766	0.171383	−	0.985205i	$-0.445176\pi$
$479$	7.50179	0.342766	0.171383	+	0.985205i	$0.445176\pi$
$480$	3.28276	0.149837
$481$	6.10764	0.278484
$482$	15.0632	0.686108
$483$	2.93287	0.133450
$484$	0.831115	0.0377780
$485$	−0.722707	−0.0328164
$486$	1.00000	0.0453609
$487$	−18.3043	−0.829448	−0.414724	−	0.909947i	$-0.636122\pi$
$487$	−18.3043	−0.829448	−0.414724	+	0.909947i	$0.636122\pi$
$488$	−6.04443	−0.273619
$489$	11.1403	0.503783
$490$	−11.9732	−0.540894
$491$	30.8152	1.39067	0.695335	−	0.718686i	$-0.255256\pi$
$491$	30.8152	1.39067	0.695335	+	0.718686i	$0.255256\pi$
$492$	10.4552	0.471358
$493$	−7.99318	−0.359995
$494$	4.26302	0.191802
$495$	11.2915	0.507516
$496$	0.0760444	0.00341450
$497$	30.5207	1.36904
$498$	−5.25414	−0.235444
$499$	−29.3153	−1.31234	−0.656168	−	0.754615i	$-0.727824\pi$
$499$	−29.3153	−1.31234	−0.656168	+	0.754615i	$0.727824\pi$
$500$	2.54912	0.114000
$501$	2.48103	0.110844
$502$	6.66166	0.297325
$503$	−11.5573	−0.515315	−0.257658	−	0.966236i	$-0.582951\pi$
$503$	−11.5573	−0.515315	−0.257658	+	0.966236i	$0.582951\pi$
$504$	3.26302	0.145346
$505$	−22.8964	−1.01887
$506$	−3.09162	−0.137439
$507$	−1.00000	−0.0444116
$508$	−10.7269	−0.475930
$509$	10.6860	0.473647	0.236824	−	0.971553i	$-0.423894\pi$
$509$	10.6860	0.473647	0.236824	+	0.971553i	$0.423894\pi$
$510$	−14.1484	−0.626500
$511$	−25.3224	−1.12020
$512$	−1.00000	−0.0441942
$513$	4.26302	0.188217
$514$	−2.53517	−0.111821
$515$	3.28276	0.144656
$516$	4.03388	0.177582
$517$	29.5157	1.29810
$518$	19.9294	0.875645
$519$	−21.7190	−0.953358
$520$	−3.28276	−0.143959
$521$	5.14259	0.225301	0.112651	−	0.993635i	$-0.464066\pi$
$521$	5.14259	0.225301	0.112651	+	0.993635i	$0.464066\pi$
$522$	−1.85461	−0.0811740
$523$	−11.7640	−0.514404	−0.257202	−	0.966358i	$-0.582801\pi$
$523$	−11.7640	−0.514404	−0.257202	+	0.966358i	$0.582801\pi$
$524$	5.95551	0.260168
$525$	18.8489	0.822633
$526$	−30.3814	−1.32469
$527$	−0.327744	−0.0142767
$528$	−3.43964	−0.149691
$529$	−22.1921	−0.964875
$530$	2.88557	0.125341
$531$	−8.39658	−0.364381
$532$	13.9103	0.603089
$533$	−10.4552	−0.452866
$534$	−13.0095	−0.562975
$535$	41.2898	1.78511
$536$	−2.20686	−0.0953218
$537$	2.68391	0.115819
$538$	−14.9780	−0.645745
$539$	12.5454	0.540367
$540$	−3.28276	−0.141268
$541$	−20.5340	−0.882825	−0.441413	−	0.897304i	$-0.645523\pi$
$541$	−20.5340	−0.882825	−0.441413	+	0.897304i	$0.645523\pi$
$542$	−22.7307	−0.976366
$543$	8.98763	0.385696
$544$	4.30990	0.184785
$545$	62.2343	2.66582
$546$	−3.26302	−0.139644
$547$	−23.1411	−0.989441	−0.494721	−	0.869052i	$-0.664730\pi$
$547$	−23.1411	−0.989441	−0.494721	+	0.869052i	$0.664730\pi$
$548$	20.6100	0.880417
$549$	6.04443	0.257970
$550$	−19.8691	−0.847223
$551$	−7.90623	−0.336817
$552$	0.898821	0.0382563
$553$	41.4808	1.76394
$554$	−16.0879	−0.683509
$555$	−20.0499	−0.851072
$556$	−8.49965	−0.360466
$557$	−4.31085	−0.182657	−0.0913284	−	0.995821i	$-0.529111\pi$
$557$	−4.31085	−0.182657	−0.0913284	+	0.995821i	$0.529111\pi$
$558$	−0.0760444	−0.00321922
$559$	−4.03388	−0.170615
$560$	−10.7117	−0.452652
$561$	14.8245	0.625891
$562$	−7.59780	−0.320494
$563$	30.5560	1.28778	0.643891	−	0.765117i	$-0.277319\pi$
$563$	30.5560	1.28778	0.643891	+	0.765117i	$0.277319\pi$
$564$	−8.58105	−0.361327
$565$	−10.1820	−0.428360
$566$	21.7133	0.912678
$567$	−3.26302	−0.137034
$568$	9.35352	0.392465
$569$	17.5992	0.737797	0.368898	−	0.929470i	$-0.379735\pi$
$569$	17.5992	0.737797	0.368898	+	0.929470i	$0.379735\pi$
$570$	−13.9945	−0.586164
$571$	21.3058	0.891621	0.445811	−	0.895127i	$-0.352916\pi$
$571$	21.3058	0.891621	0.445811	+	0.895127i	$0.352916\pi$
$572$	3.43964	0.143819
$573$	20.8937	0.872845
$574$	−34.1156	−1.42396
$575$	5.19205	0.216524
$576$	1.00000	0.0416667
$577$	18.6119	0.774822	0.387411	−	0.921907i	$-0.373370\pi$
$577$	18.6119	0.774822	0.387411	+	0.921907i	$0.373370\pi$
$578$	−1.57522	−0.0655206
$579$	7.84674	0.326099
$580$	6.08824	0.252800
$581$	17.1444	0.711268
$582$	−0.220152	−0.00912560
$583$	−3.02347	−0.125219
$584$	−7.76041	−0.321128
$585$	3.28276	0.135725
$586$	−3.95009	−0.163177
$587$	−33.0387	−1.36365	−0.681827	−	0.731514i	$-0.738814\pi$
$587$	−33.0387	−1.36365	−0.681827	+	0.731514i	$0.738814\pi$
$588$	−3.64729	−0.150412
$589$	−0.324179	−0.0133576
$590$	27.5640	1.13479
$591$	12.3894	0.509630
$592$	6.10764	0.251023
$593$	20.1374	0.826943	0.413471	−	0.910517i	$-0.364316\pi$
$593$	20.1374	0.826943	0.413471	+	0.910517i	$0.364316\pi$
$594$	3.43964	0.141130
$595$	46.1664	1.89264
$596$	−17.4883	−0.716350
$597$	4.38042	0.179279
$598$	−0.898821	−0.0367555
$599$	−34.4796	−1.40880	−0.704399	−	0.709804i	$-0.748783\pi$
$599$	−34.4796	−1.40880	−0.704399	+	0.709804i	$0.748783\pi$
$600$	5.77652	0.235825
$601$	2.31160	0.0942922	0.0471461	−	0.998888i	$-0.484987\pi$
$601$	2.31160	0.0942922	0.0471461	+	0.998888i	$0.484987\pi$
$602$	−13.1626	−0.536469
$603$	2.20686	0.0898703
$604$	−12.6784	−0.515879
$605$	2.72835	0.110923
$606$	−6.97473	−0.283329
$607$	−36.1744	−1.46827	−0.734136	−	0.679002i	$-0.762413\pi$
$607$	−36.1744	−1.46827	−0.734136	+	0.679002i	$0.762413\pi$
$608$	4.26302	0.172888
$609$	6.05162	0.245224
$610$	−19.8424	−0.803397
$611$	8.58105	0.347152
$612$	−4.30990	−0.174217
$613$	−47.4639	−1.91705	−0.958524	−	0.285010i	$-0.908003\pi$
$613$	−47.4639	−1.91705	−0.958524	+	0.285010i	$0.908003\pi$
$614$	31.6335	1.27663
$615$	34.3220	1.38400
$616$	11.2236	0.452212
$617$	−36.5587	−1.47180	−0.735898	−	0.677092i	$-0.763240\pi$
$617$	−36.5587	−1.47180	−0.735898	+	0.677092i	$0.763240\pi$
$618$	1.00000	0.0402259
$619$	−44.8668	−1.80335	−0.901675	−	0.432415i	$-0.857662\pi$
$619$	−44.8668	−1.80335	−0.901675	+	0.432415i	$0.857662\pi$
$620$	0.249636	0.0100256
$621$	−0.898821	−0.0360684
$622$	4.11144	0.164854
$623$	42.4502	1.70073
$624$	−1.00000	−0.0400320
$625$	−20.5144	−0.820577
$626$	1.23314	0.0492860
$627$	14.6632	0.585594
$628$	−6.28656	−0.250861
$629$	−26.3233	−1.04958
$630$	10.7117	0.426765
$631$	−25.8508	−1.02910	−0.514552	−	0.857459i	$-0.672042\pi$
$631$	−25.8508	−1.02910	−0.514552	+	0.857459i	$0.672042\pi$
$632$	12.7124	0.505672
$633$	9.73052	0.386753
$634$	11.2352	0.446207
$635$	−35.2139	−1.39742
$636$	0.879007	0.0348549
$637$	3.64729	0.144511
$638$	−6.37919	−0.252554
$639$	−9.35352	−0.370019
$640$	−3.28276	−0.129763
$641$	−44.7299	−1.76673	−0.883363	−	0.468690i	$-0.844726\pi$
$641$	−44.7299	−1.76673	−0.883363	+	0.468690i	$0.844726\pi$
$642$	12.5778	0.496405
$643$	11.7784	0.464493	0.232247	−	0.972657i	$-0.425392\pi$
$643$	11.7784	0.464493	0.232247	+	0.972657i	$0.425392\pi$
$644$	−2.93287	−0.115571
$645$	13.2423	0.521414
$646$	−18.3732	−0.722883
$647$	9.23873	0.363212	0.181606	−	0.983371i	$-0.441870\pi$
$647$	9.23873	0.363212	0.181606	+	0.983371i	$0.441870\pi$
$648$	−1.00000	−0.0392837
$649$	−28.8812	−1.13369
$650$	−5.77652	−0.226574
$651$	0.248134	0.00972515
$652$	−11.1403	−0.436289
$653$	−0.764358	−0.0299116	−0.0149558	−	0.999888i	$-0.504761\pi$
$653$	−0.764358	−0.0299116	−0.0149558	+	0.999888i	$0.504761\pi$
$654$	18.9579	0.741313
$655$	19.5505	0.763901
$656$	−10.4552	−0.408208
$657$	7.76041	0.302762
$658$	28.0001	1.09156
$659$	−34.4761	−1.34300	−0.671499	−	0.741006i	$-0.734349\pi$
$659$	−34.4761	−1.34300	−0.671499	+	0.741006i	$0.734349\pi$
$660$	−11.2915	−0.439521
$661$	29.1626	1.13429	0.567146	−	0.823617i	$-0.308047\pi$
$661$	29.1626	1.13429	0.567146	+	0.823617i	$0.308047\pi$
$662$	12.0823	0.469590
$663$	4.30990	0.167383
$664$	5.25414	0.203900
$665$	45.6642	1.77078
$666$	−6.10764	−0.236666
$667$	1.66696	0.0645450
$668$	−2.48103	−0.0959938
$669$	1.97961	0.0765361
$670$	−7.24459	−0.279883
$671$	20.7907	0.802615
$672$	−3.26302	−0.125874
$673$	10.4580	0.403125	0.201562	−	0.979476i	$-0.435398\pi$
$673$	10.4580	0.403125	0.201562	+	0.979476i	$0.435398\pi$
$674$	−11.5507	−0.444916
$675$	−5.77652	−0.222338
$676$	1.00000	0.0384615
$677$	−31.7092	−1.21869	−0.609343	−	0.792907i	$-0.708567\pi$
$677$	−31.7092	−1.21869	−0.609343	+	0.792907i	$0.708567\pi$
$678$	−3.10165	−0.119118
$679$	0.718360	0.0275681
$680$	14.1484	0.542565
$681$	15.6688	0.600431
$682$	−0.261565	−0.0100159
$683$	−12.2425	−0.468448	−0.234224	−	0.972183i	$-0.575255\pi$
$683$	−12.2425	−0.468448	−0.234224	+	0.972183i	$0.575255\pi$
$684$	−4.26302	−0.163001
$685$	67.6578	2.58507
$686$	−10.9399	−0.417689
$687$	−25.9643	−0.990601
$688$	−4.03388	−0.153790
$689$	−0.879007	−0.0334875
$690$	2.95061	0.112328
$691$	30.0734	1.14405	0.572023	−	0.820238i	$-0.306159\pi$
$691$	30.0734	1.14405	0.572023	+	0.820238i	$0.306159\pi$
$692$	21.7190	0.825632
$693$	−11.2236	−0.426350
$694$	1.65725	0.0629085
$695$	−27.9023	−1.05840
$696$	1.85461	0.0702988
$697$	45.0610	1.70681
$698$	−2.13379	−0.0807650
$699$	1.78245	0.0674183
$700$	−18.8489	−0.712421
$701$	−28.4612	−1.07497	−0.537483	−	0.843275i	$-0.680625\pi$
$701$	−28.4612	−1.07497	−0.537483	+	0.843275i	$0.680625\pi$
$702$	1.00000	0.0377426
$703$	−26.0370	−0.982004
$704$	3.43964	0.129636
$705$	−28.1695	−1.06093
$706$	−2.11532	−0.0796110
$707$	22.7587	0.855928
$708$	8.39658	0.315563
$709$	8.65120	0.324903	0.162451	−	0.986717i	$-0.448060\pi$
$709$	8.65120	0.324903	0.162451	+	0.986717i	$0.448060\pi$
$710$	30.7054	1.15235
$711$	−12.7124	−0.476752
$712$	13.0095	0.487551
$713$	0.0683503	0.00255974
$714$	14.0633	0.526305
$715$	11.2915	0.422279
$716$	−2.68391	−0.100303
$717$	−3.14850	−0.117583
$718$	24.6758	0.920892
$719$	22.8200	0.851043	0.425522	−	0.904948i	$-0.360091\pi$
$719$	22.8200	0.851043	0.425522	+	0.904948i	$0.360091\pi$
$720$	3.28276	0.122341
$721$	−3.26302	−0.121521
$722$	0.826669	0.0307654
$723$	15.0632	0.560205
$724$	−8.98763	−0.334023
$725$	10.7132	0.397878
$726$	0.831115	0.0308456
$727$	−47.1790	−1.74977	−0.874886	−	0.484329i	$-0.839064\pi$
$727$	−47.1790	−1.74977	−0.874886	+	0.484329i	$0.839064\pi$
$728$	3.26302	0.120936
$729$	1.00000	0.0370370
$730$	−25.4756	−0.942893
$731$	17.3856	0.643030
$732$	−6.04443	−0.223409
$733$	9.75884	0.360451	0.180225	−	0.983625i	$-0.442317\pi$
$733$	9.75884	0.360451	0.180225	+	0.983625i	$0.442317\pi$
$734$	−28.4209	−1.04904
$735$	−11.9732	−0.441638
$736$	−0.898821	−0.0331310
$737$	7.59080	0.279611
$738$	10.4552	0.384862
$739$	−38.3408	−1.41039	−0.705195	−	0.709013i	$-0.749141\pi$
$739$	−38.3408	−1.41039	−0.705195	+	0.709013i	$0.749141\pi$
$740$	20.0499	0.737050
$741$	4.26302	0.156606
$742$	−2.86822	−0.105296
$743$	−1.14474	−0.0419964	−0.0209982	−	0.999780i	$-0.506684\pi$
$743$	−1.14474	−0.0419964	−0.0209982	+	0.999780i	$0.506684\pi$
$744$	0.0760444	0.00278792
$745$	−57.4100	−2.10334
$746$	18.1734	0.665375
$747$	−5.25414	−0.192239
$748$	−14.8245	−0.542037
$749$	−41.0415	−1.49962
$750$	2.54912	0.0930808
$751$	12.4653	0.454865	0.227433	−	0.973794i	$-0.426967\pi$
$751$	12.4653	0.454865	0.227433	+	0.973794i	$0.426967\pi$
$752$	8.58105	0.312919
$753$	6.66166	0.242765
$754$	−1.85461	−0.0675409
$755$	−41.6203	−1.51472
$756$	3.26302	0.118675
$757$	0.935711	0.0340090	0.0170045	−	0.999855i	$-0.494587\pi$
$757$	0.935711	0.0340090	0.0170045	+	0.999855i	$0.494587\pi$
$758$	−10.2512	−0.372342
$759$	−3.09162	−0.112219
$760$	13.9945	0.507633
$761$	7.60000	0.275500	0.137750	−	0.990467i	$-0.456013\pi$
$761$	7.60000	0.275500	0.137750	+	0.990467i	$0.456013\pi$
$762$	−10.7269	−0.388595
$763$	−61.8600	−2.23948
$764$	−20.8937	−0.755906
$765$	−14.1484	−0.511535
$766$	−25.1009	−0.906931
$767$	−8.39658	−0.303183
$768$	−1.00000	−0.0360844
$769$	−48.9605	−1.76556	−0.882780	−	0.469786i	$-0.844331\pi$
$769$	−48.9605	−1.76556	−0.882780	+	0.469786i	$0.844331\pi$
$770$	36.8444	1.32778
$771$	−2.53517	−0.0913018
$772$	−7.84674	−0.282410
$773$	−4.51395	−0.162356	−0.0811778	−	0.996700i	$-0.525868\pi$
$773$	−4.51395	−0.162356	−0.0811778	+	0.996700i	$0.525868\pi$
$774$	4.03388	0.144995
$775$	0.439272	0.0157791
$776$	0.220152	0.00790300
$777$	19.9294	0.714961
$778$	10.0350	0.359773
$779$	44.5709	1.59692
$780$	−3.28276	−0.117542
$781$	−32.1727	−1.15123
$782$	3.87382	0.138528
$783$	−1.85461	−0.0662783
$784$	3.64729	0.130260
$785$	−20.6373	−0.736576
$786$	5.95551	0.212426
$787$	−8.70267	−0.310217	−0.155108	−	0.987897i	$-0.549573\pi$
$787$	−8.70267	−0.310217	−0.155108	+	0.987897i	$0.549573\pi$
$788$	−12.3894	−0.441353
$789$	−30.3814	−1.08161
$790$	41.7318	1.48475
$791$	10.1208	0.359853
$792$	−3.43964	−0.122222
$793$	6.04443	0.214644
$794$	−32.7780	−1.16325
$795$	2.88557	0.102341
$796$	−4.38042	−0.155260
$797$	−36.5177	−1.29352	−0.646762	−	0.762692i	$-0.723877\pi$
$797$	−36.5177	−1.29352	−0.646762	+	0.762692i	$0.723877\pi$
$798$	13.9103	0.492420
$799$	−36.9834	−1.30838
$800$	−5.77652	−0.204231
$801$	−13.0095	−0.459668
$802$	2.15080	0.0759473
$803$	26.6930	0.941976
$804$	−2.20686	−0.0778300
$805$	−9.62791	−0.339339
$806$	−0.0760444	−0.00267855
$807$	−14.9780	−0.527249
$808$	6.97473	0.245370
$809$	7.20570	0.253339	0.126669	−	0.991945i	$-0.459571\pi$
$809$	7.20570	0.253339	0.126669	+	0.991945i	$0.459571\pi$
$810$	−3.28276	−0.115344
$811$	−24.8192	−0.871519	−0.435759	−	0.900063i	$-0.643520\pi$
$811$	−24.8192	−0.871519	−0.435759	+	0.900063i	$0.643520\pi$
$812$	−6.05162	−0.212370
$813$	−22.7307	−0.797199
$814$	−21.0081	−0.736333
$815$	−36.5711	−1.28103
$816$	4.30990	0.150877
$817$	17.1965	0.601630
$818$	24.9692	0.873028
$819$	−3.26302	−0.114019
$820$	−34.3220	−1.19858
$821$	43.0666	1.50303	0.751517	−	0.659714i	$-0.229323\pi$
$821$	43.0666	1.50303	0.751517	+	0.659714i	$0.229323\pi$
$822$	20.6100	0.718857
$823$	28.3312	0.987562	0.493781	−	0.869586i	$-0.335614\pi$
$823$	28.3312	0.987562	0.493781	+	0.869586i	$0.335614\pi$
$824$	−1.00000	−0.0348367
$825$	−19.8691	−0.691754
$826$	−27.3982	−0.953306
$827$	5.69940	0.198188	0.0990938	−	0.995078i	$-0.468406\pi$
$827$	5.69940	0.198188	0.0990938	+	0.995078i	$0.468406\pi$
$828$	0.898821	0.0312362
$829$	11.8320	0.410941	0.205470	−	0.978663i	$-0.434128\pi$
$829$	11.8320	0.410941	0.205470	+	0.978663i	$0.434128\pi$
$830$	17.2481	0.598690
$831$	−16.0879	−0.558083
$832$	1.00000	0.0346688
$833$	−15.7195	−0.544647
$834$	−8.49965	−0.294319
$835$	−8.14462	−0.281856
$836$	−14.6632	−0.507139
$837$	−0.0760444	−0.00262848
$838$	11.6865	0.403704
$839$	30.6643	1.05865	0.529325	−	0.848419i	$-0.322445\pi$
$839$	30.6643	1.05865	0.529325	+	0.848419i	$0.322445\pi$
$840$	−10.7117	−0.369589
$841$	−25.5604	−0.881394
$842$	−10.0040	−0.344760
$843$	−7.59780	−0.261682
$844$	−9.73052	−0.334938
$845$	3.28276	0.112930
$846$	−8.58105	−0.295022
$847$	−2.71194	−0.0931835
$848$	−0.879007	−0.0301852
$849$	21.7133	0.745198
$850$	24.8962	0.853933
$851$	5.48967	0.188184
$852$	9.35352	0.320446
$853$	−39.6843	−1.35876	−0.679381	−	0.733785i	$-0.737752\pi$
$853$	−39.6843	−1.35876	−0.679381	+	0.733785i	$0.737752\pi$
$854$	19.7231	0.674911
$855$	−13.9945	−0.478601
$856$	−12.5778	−0.429899
$857$	−16.1198	−0.550643	−0.275322	−	0.961352i	$-0.588784\pi$
$857$	−16.1198	−0.550643	−0.275322	+	0.961352i	$0.588784\pi$
$858$	3.43964	0.117427
$859$	28.2736	0.964682	0.482341	−	0.875984i	$-0.339787\pi$
$859$	28.2736	0.964682	0.482341	+	0.875984i	$0.339787\pi$
$860$	−13.2423	−0.451557
$861$	−34.1156	−1.16266
$862$	−7.96361	−0.271242
$863$	20.4429	0.695885	0.347942	−	0.937516i	$-0.386880\pi$
$863$	20.4429	0.695885	0.347942	+	0.937516i	$0.386880\pi$
$864$	1.00000	0.0340207
$865$	71.2982	2.42421
$866$	−20.0637	−0.681791
$867$	−1.57522	−0.0534974
$868$	−0.248134	−0.00842223
$869$	−43.7261	−1.48331
$870$	6.08824	0.206411
$871$	2.20686	0.0747766
$872$	−18.9579	−0.641996
$873$	−0.220152	−0.00745102
$874$	3.83169	0.129609
$875$	−8.31783	−0.281194
$876$	−7.76041	−0.262200
$877$	−35.9441	−1.21375	−0.606874	−	0.794798i	$-0.707577\pi$
$877$	−35.9441	−1.21375	−0.606874	+	0.794798i	$0.707577\pi$
$878$	24.6906	0.833266
$879$	−3.95009	−0.133233
$880$	11.2915	0.380637
$881$	15.9209	0.536389	0.268195	−	0.963365i	$-0.413573\pi$
$881$	15.9209	0.536389	0.268195	+	0.963365i	$0.413573\pi$
$882$	−3.64729	−0.122811
$883$	−34.9059	−1.17468	−0.587339	−	0.809341i	$-0.699825\pi$
$883$	−34.9059	−1.17468	−0.587339	+	0.809341i	$0.699825\pi$
$884$	−4.30990	−0.144958
$885$	27.5640	0.926553
$886$	35.2903	1.18560
$887$	−3.37682	−0.113383	−0.0566913	−	0.998392i	$-0.518055\pi$
$887$	−3.37682	−0.113383	−0.0566913	+	0.998392i	$0.518055\pi$
$888$	6.10764	0.204959
$889$	35.0021	1.17393
$890$	42.7070	1.43154
$891$	3.43964	0.115232
$892$	−1.97961	−0.0662822
$893$	−36.5812	−1.22414
$894$	−17.4883	−0.584897
$895$	−8.81065	−0.294507
$896$	3.26302	0.109010
$897$	−0.898821	−0.0300107
$898$	15.5411	0.518612
$899$	0.141033	0.00470370
$900$	5.77652	0.192551
$901$	3.78843	0.126211
$902$	35.9622	1.19741
$903$	−13.1626	−0.438025
$904$	3.10165	0.103160
$905$	−29.5042	−0.980754
$906$	−12.6784	−0.421213
$907$	−38.8367	−1.28955	−0.644776	−	0.764371i	$-0.723050\pi$
$907$	−38.8367	−1.28955	−0.644776	+	0.764371i	$0.723050\pi$
$908$	−15.6688	−0.519988
$909$	−6.97473	−0.231337
$910$	10.7117	0.355090
$911$	12.6984	0.420717	0.210358	−	0.977624i	$-0.432537\pi$
$911$	12.6984	0.420717	0.210358	+	0.977624i	$0.432537\pi$
$912$	4.26302	0.141163
$913$	−18.0723	−0.598107
$914$	37.2104	1.23081
$915$	−19.8424	−0.655971
$916$	25.9643	0.857885
$917$	−19.4329	−0.641732
$918$	−4.30990	−0.142248
$919$	−39.0797	−1.28912	−0.644560	−	0.764554i	$-0.722959\pi$
$919$	−39.0797	−1.28912	−0.644560	+	0.764554i	$0.722959\pi$
$920$	−2.95061	−0.0972788
$921$	31.6335	1.04236
$922$	−16.2449	−0.534997
$923$	−9.35352	−0.307875
$924$	11.2236	0.369230
$925$	35.2809	1.16003
$926$	−32.2809	−1.06082
$927$	1.00000	0.0328443
$928$	−1.85461	−0.0608805
$929$	50.9887	1.67288	0.836442	−	0.548056i	$-0.184632\pi$
$929$	50.9887	1.67288	0.836442	+	0.548056i	$0.184632\pi$
$930$	0.249636	0.00818588
$931$	−15.5485	−0.509581
$932$	−1.78245	−0.0583860
$933$	4.11144	0.134602
$934$	−23.2790	−0.761711
$935$	−48.6653	−1.59152
$936$	−1.00000	−0.0326860
$937$	−19.8224	−0.647569	−0.323785	−	0.946131i	$-0.604955\pi$
$937$	−19.8224	−0.647569	−0.323785	+	0.946131i	$0.604955\pi$
$938$	7.20103	0.235122
$939$	1.23314	0.0402419
$940$	28.1695	0.918789
$941$	−37.7454	−1.23046	−0.615232	−	0.788346i	$-0.710938\pi$
$941$	−37.7454	−1.23046	−0.615232	+	0.788346i	$0.710938\pi$
$942$	−6.28656	−0.204827
$943$	−9.39738	−0.306021
$944$	−8.39658	−0.273286
$945$	10.7117	0.348452
$946$	13.8751	0.451118
$947$	−32.8061	−1.06606	−0.533028	−	0.846098i	$-0.678946\pi$
$947$	−32.8061	−1.06606	−0.533028	+	0.846098i	$0.678946\pi$
$948$	12.7124	0.412880
$949$	7.76041	0.251914
$950$	24.6254	0.798954
$951$	11.2352	0.364326
$952$	−14.0633	−0.455794
$953$	46.6766	1.51200	0.756001	−	0.654570i	$-0.227150\pi$
$953$	46.6766	1.51200	0.756001	+	0.654570i	$0.227150\pi$
$954$	0.879007	0.0284589
$955$	−68.5889	−2.21948
$956$	3.14850	0.101830
$957$	−6.37919	−0.206210
$958$	−7.50179	−0.242372
$959$	−67.2509	−2.17164
$960$	−3.28276	−0.105951
$961$	−30.9942	−0.999813
$962$	−6.10764	−0.196918
$963$	12.5778	0.405313
$964$	−15.0632	−0.485152
$965$	−25.7590	−0.829210
$966$	−2.93287	−0.0943635
$967$	13.1433	0.422662	0.211331	−	0.977415i	$-0.432220\pi$
$967$	13.1433	0.422662	0.211331	+	0.977415i	$0.432220\pi$
$968$	−0.831115	−0.0267131
$969$	−18.3732	−0.590232
$970$	0.722707	0.0232047
$971$	6.83327	0.219290	0.109645	−	0.993971i	$-0.465029\pi$
$971$	6.83327	0.219290	0.109645	+	0.993971i	$0.465029\pi$
$972$	−1.00000	−0.0320750
$973$	27.7345	0.889128
$974$	18.3043	0.586509
$975$	−5.77652	−0.184997
$976$	6.04443	0.193478
$977$	−7.28983	−0.233222	−0.116611	−	0.993178i	$-0.537203\pi$
$977$	−7.28983	−0.233222	−0.116611	+	0.993178i	$0.537203\pi$
$978$	−11.1403	−0.356229
$979$	−44.7479	−1.43015
$980$	11.9732	0.382470
$981$	18.9579	0.605280
$982$	−30.8152	−0.983352
$983$	11.9172	0.380098	0.190049	−	0.981775i	$-0.439135\pi$
$983$	11.9172	0.380098	0.190049	+	0.981775i	$0.439135\pi$
$984$	−10.4552	−0.333301
$985$	−40.6713	−1.29590
$986$	7.99318	0.254555
$987$	28.0001	0.891254
$988$	−4.26302	−0.135625
$989$	−3.62573	−0.115292
$990$	−11.2915	−0.358868
$991$	2.39520	0.0760861	0.0380431	−	0.999276i	$-0.487888\pi$
$991$	2.39520	0.0760861	0.0380431	+	0.999276i	$0.487888\pi$
$992$	−0.0760444	−0.00241441
$993$	12.0823	0.383419
$994$	−30.5207	−0.968058
$995$	−14.3799	−0.455873
$996$	5.25414	0.166484
$997$	3.65690	0.115815	0.0579076	−	0.998322i	$-0.481557\pi$
$997$	3.65690	0.115815	0.0579076	+	0.998322i	$0.481557\pi$
$998$	29.3153	0.927961
$999$	−6.10764	−0.193237

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.o.1.6	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.o.1.6	✓	7	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.28276 q^{5} +1.00000 q^{6} -3.26302 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.28276 q^{5} +1.00000 q^{6} -3.26302 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.28276 q^{10} +3.43964 q^{11} -1.00000 q^{12} +1.00000 q^{13} +3.26302 q^{14} -3.28276 q^{15} +1.00000 q^{16} -4.30990 q^{17} -1.00000 q^{18} -4.26302 q^{19} +3.28276 q^{20} +3.26302 q^{21} -3.43964 q^{22} +0.898821 q^{23} +1.00000 q^{24} +5.77652 q^{25} -1.00000 q^{26} -1.00000 q^{27} -3.26302 q^{28} +1.85461 q^{29} +3.28276 q^{30} +0.0760444 q^{31} -1.00000 q^{32} -3.43964 q^{33} +4.30990 q^{34} -10.7117 q^{35} +1.00000 q^{36} +6.10764 q^{37} +4.26302 q^{38} -1.00000 q^{39} -3.28276 q^{40} -10.4552 q^{41} -3.26302 q^{42} -4.03388 q^{43} +3.43964 q^{44} +3.28276 q^{45} -0.898821 q^{46} +8.58105 q^{47} -1.00000 q^{48} +3.64729 q^{49} -5.77652 q^{50} +4.30990 q^{51} +1.00000 q^{52} -0.879007 q^{53} +1.00000 q^{54} +11.2915 q^{55} +3.26302 q^{56} +4.26302 q^{57} -1.85461 q^{58} -8.39658 q^{59} -3.28276 q^{60} +6.04443 q^{61} -0.0760444 q^{62} -3.26302 q^{63} +1.00000 q^{64} +3.28276 q^{65} +3.43964 q^{66} +2.20686 q^{67} -4.30990 q^{68} -0.898821 q^{69} +10.7117 q^{70} -9.35352 q^{71} -1.00000 q^{72} +7.76041 q^{73} -6.10764 q^{74} -5.77652 q^{75} -4.26302 q^{76} -11.2236 q^{77} +1.00000 q^{78} -12.7124 q^{79} +3.28276 q^{80} +1.00000 q^{81} +10.4552 q^{82} -5.25414 q^{83} +3.26302 q^{84} -14.1484 q^{85} +4.03388 q^{86} -1.85461 q^{87} -3.43964 q^{88} -13.0095 q^{89} -3.28276 q^{90} -3.26302 q^{91} +0.898821 q^{92} -0.0760444 q^{93} -8.58105 q^{94} -13.9945 q^{95} +1.00000 q^{96} -0.220152 q^{97} -3.64729 q^{98} +3.43964 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9} - 2 q^{10} - 7 q^{12} + 7 q^{13} + 9 q^{14} - 2 q^{15} + 7 q^{16} + 3 q^{17} - 7 q^{18} - 16 q^{19} + 2 q^{20} + 9 q^{21} + 6 q^{23} + 7 q^{24} + 15 q^{25} - 7 q^{26} - 7 q^{27} - 9 q^{28} - 5 q^{29} + 2 q^{30} - 16 q^{31} - 7 q^{32} - 3 q^{34} - 10 q^{35} + 7 q^{36} + 17 q^{37} + 16 q^{38} - 7 q^{39} - 2 q^{40} + 12 q^{41} - 9 q^{42} - 22 q^{43} + 2 q^{45} - 6 q^{46} - 7 q^{48} - 2 q^{49} - 15 q^{50} - 3 q^{51} + 7 q^{52} + 2 q^{53} + 7 q^{54} - 16 q^{55} + 9 q^{56} + 16 q^{57} + 5 q^{58} - 3 q^{59} - 2 q^{60} - 6 q^{61} + 16 q^{62} - 9 q^{63} + 7 q^{64} + 2 q^{65} + q^{67} + 3 q^{68} - 6 q^{69} + 10 q^{70} + 15 q^{71} - 7 q^{72} + 17 q^{73} - 17 q^{74} - 15 q^{75} - 16 q^{76} - 10 q^{77} + 7 q^{78} - 27 q^{79} + 2 q^{80} + 7 q^{81} - 12 q^{82} + 12 q^{83} + 9 q^{84} + 15 q^{85} + 22 q^{86} + 5 q^{87} - 9 q^{89} - 2 q^{90} - 9 q^{91} + 6 q^{92} + 16 q^{93} - 12 q^{95} + 7 q^{96} - 3 q^{97} + 2 q^{98}+O(q^{100}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9 - 2 * q^10 - 7 * q^12 + 7 * q^13 + 9 * q^14 - 2 * q^15 + 7 * q^16 + 3 * q^17 - 7 * q^18 - 16 * q^19 + 2 * q^20 + 9 * q^21 + 6 * q^23 + 7 * q^24 + 15 * q^25 - 7 * q^26 - 7 * q^27 - 9 * q^28 - 5 * q^29 + 2 * q^30 - 16 * q^31 - 7 * q^32 - 3 * q^34 - 10 * q^35 + 7 * q^36 + 17 * q^37 + 16 * q^38 - 7 * q^39 - 2 * q^40 + 12 * q^41 - 9 * q^42 - 22 * q^43 + 2 * q^45 - 6 * q^46 - 7 * q^48 - 2 * q^49 - 15 * q^50 - 3 * q^51 + 7 * q^52 + 2 * q^53 + 7 * q^54 - 16 * q^55 + 9 * q^56 + 16 * q^57 + 5 * q^58 - 3 * q^59 - 2 * q^60 - 6 * q^61 + 16 * q^62 - 9 * q^63 + 7 * q^64 + 2 * q^65 + q^67 + 3 * q^68 - 6 * q^69 + 10 * q^70 + 15 * q^71 - 7 * q^72 + 17 * q^73 - 17 * q^74 - 15 * q^75 - 16 * q^76 - 10 * q^77 + 7 * q^78 - 27 * q^79 + 2 * q^80 + 7 * q^81 - 12 * q^82 + 12 * q^83 + 9 * q^84 + 15 * q^85 + 22 * q^86 + 5 * q^87 - 9 * q^89 - 2 * q^90 - 9 * q^91 + 6 * q^92 + 16 * q^93 - 12 * q^95 + 7 * q^96 - 3 * q^97 + 2 * q^98

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