LMFDB - Embedded newform 8034.2.a.x.1.7

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:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - x^{12} - 40 x^{11} + 34 x^{10} + 604 x^{9} - 381 x^{8} - 4352 x^{7} + 1474 x^{6} + 15809 x^{5} + \cdots + 8832 $ x^13 - x^12 - 40x^11 + 34x^10 + 604x^9 - 381x^8 - 4352x^7 + 1474x^6 + 15809x^5 - 368x^4 - 27369x^3 - 7621x^2 + 17300*x + 8832
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.757993$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.757993 q^{5} -1.00000 q^{6} +1.64575 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.757993 q^{5} -1.00000 q^{6} +1.64575 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.757993 q^{10} +1.41377 q^{11} +1.00000 q^{12} +1.00000 q^{13} -1.64575 q^{14} -0.757993 q^{15} +1.00000 q^{16} -1.39354 q^{17} -1.00000 q^{18} +8.50823 q^{19} -0.757993 q^{20} +1.64575 q^{21} -1.41377 q^{22} +2.96384 q^{23} -1.00000 q^{24} -4.42545 q^{25} -1.00000 q^{26} +1.00000 q^{27} +1.64575 q^{28} +8.43062 q^{29} +0.757993 q^{30} +0.646304 q^{31} -1.00000 q^{32} +1.41377 q^{33} +1.39354 q^{34} -1.24747 q^{35} +1.00000 q^{36} -8.78180 q^{37} -8.50823 q^{38} +1.00000 q^{39} +0.757993 q^{40} +12.0433 q^{41} -1.64575 q^{42} -0.841861 q^{43} +1.41377 q^{44} -0.757993 q^{45} -2.96384 q^{46} +2.52267 q^{47} +1.00000 q^{48} -4.29150 q^{49} +4.42545 q^{50} -1.39354 q^{51} +1.00000 q^{52} +5.66691 q^{53} -1.00000 q^{54} -1.07163 q^{55} -1.64575 q^{56} +8.50823 q^{57} -8.43062 q^{58} +2.01248 q^{59} -0.757993 q^{60} -5.39934 q^{61} -0.646304 q^{62} +1.64575 q^{63} +1.00000 q^{64} -0.757993 q^{65} -1.41377 q^{66} +8.33443 q^{67} -1.39354 q^{68} +2.96384 q^{69} +1.24747 q^{70} -3.32627 q^{71} -1.00000 q^{72} -6.98523 q^{73} +8.78180 q^{74} -4.42545 q^{75} +8.50823 q^{76} +2.32671 q^{77} -1.00000 q^{78} -13.2133 q^{79} -0.757993 q^{80} +1.00000 q^{81} -12.0433 q^{82} -3.92742 q^{83} +1.64575 q^{84} +1.05630 q^{85} +0.841861 q^{86} +8.43062 q^{87} -1.41377 q^{88} +16.4159 q^{89} +0.757993 q^{90} +1.64575 q^{91} +2.96384 q^{92} +0.646304 q^{93} -2.52267 q^{94} -6.44918 q^{95} -1.00000 q^{96} -6.37085 q^{97} +4.29150 q^{98} +1.41377 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} + q^{5} - 13 q^{6} - q^{7} - 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 + q^5 - 13 * q^6 - q^7 - 13 * q^8 + 13 * q^9	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} + q^{5} - 13 q^{6} - q^{7} - 13 q^{8} + 13 q^{9} - q^{10} + 6 q^{11} + 13 q^{12} + 13 q^{13} + q^{14} + q^{15} + 13 q^{16} + 18 q^{17} - 13 q^{18} - q^{19} + q^{20} - q^{21} - 6 q^{22} + 20 q^{23} - 13 q^{24} + 16 q^{25} - 13 q^{26} + 13 q^{27} - q^{28} + 25 q^{29} - q^{30} - 5 q^{31} - 13 q^{32} + 6 q^{33} - 18 q^{34} + 26 q^{35} + 13 q^{36} - 6 q^{37} + q^{38} + 13 q^{39} - q^{40} + 13 q^{41} + q^{42} - 2 q^{43} + 6 q^{44} + q^{45} - 20 q^{46} + 5 q^{47} + 13 q^{48} - 16 q^{50} + 18 q^{51} + 13 q^{52} + 21 q^{53} - 13 q^{54} + 2 q^{55} + q^{56} - q^{57} - 25 q^{58} + 22 q^{59} + q^{60} + 2 q^{61} + 5 q^{62} - q^{63} + 13 q^{64} + q^{65} - 6 q^{66} - q^{67} + 18 q^{68} + 20 q^{69} - 26 q^{70} + 32 q^{71} - 13 q^{72} - 13 q^{73} + 6 q^{74} + 16 q^{75} - q^{76} + 33 q^{77} - 13 q^{78} - 7 q^{79} + q^{80} + 13 q^{81} - 13 q^{82} + 17 q^{83} - q^{84} - 25 q^{85} + 2 q^{86} + 25 q^{87} - 6 q^{88} - 12 q^{89} - q^{90} - q^{91} + 20 q^{92} - 5 q^{93} - 5 q^{94} + 36 q^{95} - 13 q^{96} - 42 q^{97} + 6 q^{99}+O(q^{100}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 + q^5 - 13 * q^6 - q^7 - 13 * q^8 + 13 * q^9 - q^10 + 6 * q^11 + 13 * q^12 + 13 * q^13 + q^14 + q^15 + 13 * q^16 + 18 * q^17 - 13 * q^18 - q^19 + q^20 - q^21 - 6 * q^22 + 20 * q^23 - 13 * q^24 + 16 * q^25 - 13 * q^26 + 13 * q^27 - q^28 + 25 * q^29 - q^30 - 5 * q^31 - 13 * q^32 + 6 * q^33 - 18 * q^34 + 26 * q^35 + 13 * q^36 - 6 * q^37 + q^38 + 13 * q^39 - q^40 + 13 * q^41 + q^42 - 2 * q^43 + 6 * q^44 + q^45 - 20 * q^46 + 5 * q^47 + 13 * q^48 - 16 * q^50 + 18 * q^51 + 13 * q^52 + 21 * q^53 - 13 * q^54 + 2 * q^55 + q^56 - q^57 - 25 * q^58 + 22 * q^59 + q^60 + 2 * q^61 + 5 * q^62 - q^63 + 13 * q^64 + q^65 - 6 * q^66 - q^67 + 18 * q^68 + 20 * q^69 - 26 * q^70 + 32 * q^71 - 13 * q^72 - 13 * q^73 + 6 * q^74 + 16 * q^75 - q^76 + 33 * q^77 - 13 * q^78 - 7 * q^79 + q^80 + 13 * q^81 - 13 * q^82 + 17 * q^83 - q^84 - 25 * q^85 + 2 * q^86 + 25 * q^87 - 6 * q^88 - 12 * q^89 - q^90 - q^91 + 20 * q^92 - 5 * q^93 - 5 * q^94 + 36 * q^95 - 13 * q^96 - 42 * q^97 + 6 * 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
$5$	−0.757993	−0.338985	−0.169492	−	0.985531i	$-0.554213\pi$
$5$	−0.757993	−0.338985	−0.169492	+	0.985531i	$0.554213\pi$
$6$	−1.00000	−0.408248
$7$	1.64575	0.622035	0.311018	−	0.950404i	$-0.399330\pi$
$7$	1.64575	0.622035	0.311018	+	0.950404i	$0.399330\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.757993	0.239699
$11$	1.41377	0.426267	0.213134	−	0.977023i	$-0.431633\pi$
$11$	1.41377	0.426267	0.213134	+	0.977023i	$0.431633\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.64575	−0.439845
$15$	−0.757993	−0.195713
$16$	1.00000	0.250000
$17$	−1.39354	−0.337984	−0.168992	−	0.985617i	$-0.554051\pi$
$17$	−1.39354	−0.337984	−0.168992	+	0.985617i	$0.554051\pi$
$18$	−1.00000	−0.235702
$19$	8.50823	1.95192	0.975961	−	0.217946i	$-0.0699356\pi$
$19$	8.50823	1.95192	0.975961	+	0.217946i	$0.0699356\pi$
$20$	−0.757993	−0.169492
$21$	1.64575	0.359132
$22$	−1.41377	−0.301416
$23$	2.96384	0.618004	0.309002	−	0.951061i	$-0.400005\pi$
$23$	2.96384	0.618004	0.309002	+	0.951061i	$0.400005\pi$
$24$	−1.00000	−0.204124
$25$	−4.42545	−0.885089
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	1.64575	0.311018
$29$	8.43062	1.56553	0.782763	−	0.622320i	$-0.213810\pi$
$29$	8.43062	1.56553	0.782763	+	0.622320i	$0.213810\pi$
$30$	0.757993	0.138390
$31$	0.646304	0.116080	0.0580398	−	0.998314i	$-0.481515\pi$
$31$	0.646304	0.116080	0.0580398	+	0.998314i	$0.481515\pi$
$32$	−1.00000	−0.176777
$33$	1.41377	0.246106
$34$	1.39354	0.238991
$35$	−1.24747	−0.210861
$36$	1.00000	0.166667
$37$	−8.78180	−1.44372	−0.721860	−	0.692039i	$-0.756712\pi$
$37$	−8.78180	−1.44372	−0.721860	+	0.692039i	$0.756712\pi$
$38$	−8.50823	−1.38022
$39$	1.00000	0.160128
$40$	0.757993	0.119849
$41$	12.0433	1.88084	0.940422	−	0.340010i	$-0.110431\pi$
$41$	12.0433	1.88084	0.940422	+	0.340010i	$0.110431\pi$
$42$	−1.64575	−0.253945
$43$	−0.841861	−0.128383	−0.0641913	−	0.997938i	$-0.520447\pi$
$43$	−0.841861	−0.128383	−0.0641913	+	0.997938i	$0.520447\pi$
$44$	1.41377	0.213134
$45$	−0.757993	−0.112995
$46$	−2.96384	−0.436995
$47$	2.52267	0.367970	0.183985	−	0.982929i	$-0.441100\pi$
$47$	2.52267	0.367970	0.183985	+	0.982929i	$0.441100\pi$
$48$	1.00000	0.144338
$49$	−4.29150	−0.613072
$50$	4.42545	0.625853
$51$	−1.39354	−0.195135
$52$	1.00000	0.138675
$53$	5.66691	0.778410	0.389205	−	0.921151i	$-0.372750\pi$
$53$	5.66691	0.778410	0.389205	+	0.921151i	$0.372750\pi$
$54$	−1.00000	−0.136083
$55$	−1.07163	−0.144498
$56$	−1.64575	−0.219923
$57$	8.50823	1.12694
$58$	−8.43062	−1.10699
$59$	2.01248	0.262002	0.131001	−	0.991382i	$-0.458181\pi$
$59$	2.01248	0.262002	0.131001	+	0.991382i	$0.458181\pi$
$60$	−0.757993	−0.0978565
$61$	−5.39934	−0.691315	−0.345657	−	0.938361i	$-0.612344\pi$
$61$	−5.39934	−0.691315	−0.345657	+	0.938361i	$0.612344\pi$
$62$	−0.646304	−0.0820807
$63$	1.64575	0.207345
$64$	1.00000	0.125000
$65$	−0.757993	−0.0940175
$66$	−1.41377	−0.174023
$67$	8.33443	1.01821	0.509106	−	0.860704i	$-0.329976\pi$
$67$	8.33443	1.01821	0.509106	+	0.860704i	$0.329976\pi$
$68$	−1.39354	−0.168992
$69$	2.96384	0.356805
$70$	1.24747	0.149101
$71$	−3.32627	−0.394756	−0.197378	−	0.980327i	$-0.563243\pi$
$71$	−3.32627	−0.394756	−0.197378	+	0.980327i	$0.563243\pi$
$72$	−1.00000	−0.117851
$73$	−6.98523	−0.817560	−0.408780	−	0.912633i	$-0.634046\pi$
$73$	−6.98523	−0.817560	−0.408780	+	0.912633i	$0.634046\pi$
$74$	8.78180	1.02086
$75$	−4.42545	−0.511007
$76$	8.50823	0.975961
$77$	2.32671	0.265153
$78$	−1.00000	−0.113228
$79$	−13.2133	−1.48661	−0.743307	−	0.668951i	$-0.766744\pi$
$79$	−13.2133	−1.48661	−0.743307	+	0.668951i	$0.766744\pi$
$80$	−0.757993	−0.0847462
$81$	1.00000	0.111111
$82$	−12.0433	−1.32996
$83$	−3.92742	−0.431091	−0.215545	−	0.976494i	$-0.569153\pi$
$83$	−3.92742	−0.431091	−0.215545	+	0.976494i	$0.569153\pi$
$84$	1.64575	0.179566
$85$	1.05630	0.114571
$86$	0.841861	0.0907802
$87$	8.43062	0.903857
$88$	−1.41377	−0.150708
$89$	16.4159	1.74008	0.870039	−	0.492983i	$-0.164094\pi$
$89$	16.4159	1.74008	0.870039	+	0.492983i	$0.164094\pi$
$90$	0.757993	0.0798995
$91$	1.64575	0.172522
$92$	2.96384	0.309002
$93$	0.646304	0.0670186
$94$	−2.52267	−0.260194
$95$	−6.44918	−0.661672
$96$	−1.00000	−0.102062
$97$	−6.37085	−0.646862	−0.323431	−	0.946252i	$-0.604836\pi$
$97$	−6.37085	−0.646862	−0.323431	+	0.946252i	$0.604836\pi$
$98$	4.29150	0.433507
$99$	1.41377	0.142089
$100$	−4.42545	−0.442545
$101$	14.9185	1.48444	0.742222	−	0.670155i	$-0.233772\pi$
$101$	14.9185	1.48444	0.742222	+	0.670155i	$0.233772\pi$
$102$	1.39354	0.137981
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	−1.24747	−0.121740
$106$	−5.66691	−0.550419
$107$	−7.66812	−0.741305	−0.370653	−	0.928772i	$-0.620866\pi$
$107$	−7.66812	−0.741305	−0.370653	+	0.928772i	$0.620866\pi$
$108$	1.00000	0.0962250
$109$	3.54095	0.339162	0.169581	−	0.985516i	$-0.445759\pi$
$109$	3.54095	0.339162	0.169581	+	0.985516i	$0.445759\pi$
$110$	1.07163	0.102176
$111$	−8.78180	−0.833532
$112$	1.64575	0.155509
$113$	−7.99534	−0.752138	−0.376069	−	0.926592i	$-0.622725\pi$
$113$	−7.99534	−0.752138	−0.376069	+	0.926592i	$0.622725\pi$
$114$	−8.50823	−0.796869
$115$	−2.24657	−0.209494
$116$	8.43062	0.782763
$117$	1.00000	0.0924500
$118$	−2.01248	−0.185264
$119$	−2.29342	−0.210238
$120$	0.757993	0.0691950
$121$	−9.00126	−0.818296
$122$	5.39934	0.488833
$123$	12.0433	1.08591
$124$	0.646304	0.0580398
$125$	7.14442	0.639017
$126$	−1.64575	−0.146615
$127$	−6.67441	−0.592258	−0.296129	−	0.955148i	$-0.595696\pi$
$127$	−6.67441	−0.592258	−0.296129	+	0.955148i	$0.595696\pi$
$128$	−1.00000	−0.0883883
$129$	−0.841861	−0.0741217
$130$	0.757993	0.0664804
$131$	21.0923	1.84284	0.921421	−	0.388566i	$-0.127029\pi$
$131$	21.0923	1.84284	0.921421	+	0.388566i	$0.127029\pi$
$132$	1.41377	0.123053
$133$	14.0024	1.21416
$134$	−8.33443	−0.719985
$135$	−0.757993	−0.0652377
$136$	1.39354	0.119495
$137$	−16.8586	−1.44033	−0.720163	−	0.693805i	$-0.755933\pi$
$137$	−16.8586	−1.44033	−0.720163	+	0.693805i	$0.755933\pi$
$138$	−2.96384	−0.252299
$139$	−0.986892	−0.0837071	−0.0418536	−	0.999124i	$-0.513326\pi$
$139$	−0.986892	−0.0837071	−0.0418536	+	0.999124i	$0.513326\pi$
$140$	−1.24747	−0.105430
$141$	2.52267	0.212448
$142$	3.32627	0.279135
$143$	1.41377	0.118225
$144$	1.00000	0.0833333
$145$	−6.39035	−0.530690
$146$	6.98523	0.578102
$147$	−4.29150	−0.353957
$148$	−8.78180	−0.721860
$149$	18.9628	1.55350	0.776748	−	0.629811i	$-0.216868\pi$
$149$	18.9628	1.55350	0.776748	+	0.629811i	$0.216868\pi$
$150$	4.42545	0.361336
$151$	−19.9243	−1.62142	−0.810709	−	0.585450i	$-0.800918\pi$
$151$	−19.9243	−1.62142	−0.810709	+	0.585450i	$0.800918\pi$
$152$	−8.50823	−0.690109
$153$	−1.39354	−0.112661
$154$	−2.32671	−0.187492
$155$	−0.489894	−0.0393492
$156$	1.00000	0.0800641
$157$	18.9110	1.50926	0.754629	−	0.656151i	$-0.227817\pi$
$157$	18.9110	1.50926	0.754629	+	0.656151i	$0.227817\pi$
$158$	13.2133	1.05119
$159$	5.66691	0.449415
$160$	0.757993	0.0599246
$161$	4.87775	0.384420
$162$	−1.00000	−0.0785674
$163$	1.85271	0.145115	0.0725576	−	0.997364i	$-0.476884\pi$
$163$	1.85271	0.145115	0.0725576	+	0.997364i	$0.476884\pi$
$164$	12.0433	0.940422
$165$	−1.07163	−0.0834261
$166$	3.92742	0.304827
$167$	−18.2715	−1.41389	−0.706947	−	0.707266i	$-0.749928\pi$
$167$	−18.2715	−1.41389	−0.706947	+	0.707266i	$0.749928\pi$
$168$	−1.64575	−0.126972
$169$	1.00000	0.0769231
$170$	−1.05630	−0.0810142
$171$	8.50823	0.650641
$172$	−0.841861	−0.0641913
$173$	13.4188	1.02022	0.510108	−	0.860110i	$-0.329605\pi$
$173$	13.4188	1.02022	0.510108	+	0.860110i	$0.329605\pi$
$174$	−8.43062	−0.639123
$175$	−7.28318	−0.550557
$176$	1.41377	0.106567
$177$	2.01248	0.151267
$178$	−16.4159	−1.23042
$179$	−1.99353	−0.149004	−0.0745018	−	0.997221i	$-0.523737\pi$
$179$	−1.99353	−0.149004	−0.0745018	+	0.997221i	$0.523737\pi$
$180$	−0.757993	−0.0564975
$181$	18.0165	1.33916	0.669578	−	0.742742i	$-0.266475\pi$
$181$	18.0165	1.33916	0.669578	+	0.742742i	$0.266475\pi$
$182$	−1.64575	−0.121991
$183$	−5.39934	−0.399131
$184$	−2.96384	−0.218497
$185$	6.65655	0.489399
$186$	−0.646304	−0.0473893
$187$	−1.97015	−0.144071
$188$	2.52267	0.183985
$189$	1.64575	0.119711
$190$	6.44918	0.467873
$191$	−10.4402	−0.755429	−0.377715	−	0.925922i	$-0.623290\pi$
$191$	−10.4402	−0.755429	−0.377715	+	0.925922i	$0.623290\pi$
$192$	1.00000	0.0721688
$193$	−20.9658	−1.50915	−0.754574	−	0.656215i	$-0.772156\pi$
$193$	−20.9658	−1.50915	−0.754574	+	0.656215i	$0.772156\pi$
$194$	6.37085	0.457401
$195$	−0.757993	−0.0542810
$196$	−4.29150	−0.306536
$197$	−5.00003	−0.356237	−0.178119	−	0.984009i	$-0.557001\pi$
$197$	−5.00003	−0.356237	−0.178119	+	0.984009i	$0.557001\pi$
$198$	−1.41377	−0.100472
$199$	21.5029	1.52430	0.762149	−	0.647401i	$-0.224144\pi$
$199$	21.5029	1.52430	0.762149	+	0.647401i	$0.224144\pi$
$200$	4.42545	0.312926
$201$	8.33443	0.587865
$202$	−14.9185	−1.04966
$203$	13.8747	0.973813
$204$	−1.39354	−0.0975675
$205$	−9.12872	−0.637578
$206$	−1.00000	−0.0696733
$207$	2.96384	0.206001
$208$	1.00000	0.0693375
$209$	12.0287	0.832040
$210$	1.24747	0.0860835
$211$	5.16654	0.355679	0.177840	−	0.984059i	$-0.443089\pi$
$211$	5.16654	0.355679	0.177840	+	0.984059i	$0.443089\pi$
$212$	5.66691	0.389205
$213$	−3.32627	−0.227913
$214$	7.66812	0.524182
$215$	0.638125	0.0435198
$216$	−1.00000	−0.0680414
$217$	1.06366	0.0722056
$218$	−3.54095	−0.239824
$219$	−6.98523	−0.472018
$220$	−1.07163	−0.0722491
$221$	−1.39354	−0.0937398
$222$	8.78180	0.589396
$223$	23.7710	1.59182	0.795912	−	0.605413i	$-0.206992\pi$
$223$	23.7710	1.59182	0.795912	+	0.605413i	$0.206992\pi$
$224$	−1.64575	−0.109961
$225$	−4.42545	−0.295030
$226$	7.99534	0.531842
$227$	−11.8084	−0.783752	−0.391876	−	0.920018i	$-0.628174\pi$
$227$	−11.8084	−0.783752	−0.391876	+	0.920018i	$0.628174\pi$
$228$	8.50823	0.563471
$229$	−7.42697	−0.490788	−0.245394	−	0.969423i	$-0.578917\pi$
$229$	−7.42697	−0.490788	−0.245394	+	0.969423i	$0.578917\pi$
$230$	2.24657	0.148135
$231$	2.32671	0.153086
$232$	−8.43062	−0.553497
$233$	3.53932	0.231869	0.115934	−	0.993257i	$-0.463014\pi$
$233$	3.53932	0.231869	0.115934	+	0.993257i	$0.463014\pi$
$234$	−1.00000	−0.0653720
$235$	−1.91217	−0.124736
$236$	2.01248	0.131001
$237$	−13.2133	−0.858297
$238$	2.29342	0.148661
$239$	−9.86381	−0.638037	−0.319019	−	0.947748i	$-0.603353\pi$
$239$	−9.86381	−0.638037	−0.319019	+	0.947748i	$0.603353\pi$
$240$	−0.757993	−0.0489283
$241$	15.8070	1.01822	0.509110	−	0.860701i	$-0.329974\pi$
$241$	15.8070	1.01822	0.509110	+	0.860701i	$0.329974\pi$
$242$	9.00126	0.578623
$243$	1.00000	0.0641500
$244$	−5.39934	−0.345657
$245$	3.25293	0.207822
$246$	−12.0433	−0.767851
$247$	8.50823	0.541366
$248$	−0.646304	−0.0410403
$249$	−3.92742	−0.248890
$250$	−7.14442	−0.451853
$251$	−12.8671	−0.812162	−0.406081	−	0.913837i	$-0.633105\pi$
$251$	−12.8671	−0.812162	−0.406081	+	0.913837i	$0.633105\pi$
$252$	1.64575	0.103673
$253$	4.19019	0.263435
$254$	6.67441	0.418790
$255$	1.05630	0.0661478
$256$	1.00000	0.0625000
$257$	7.17252	0.447410	0.223705	−	0.974657i	$-0.428185\pi$
$257$	7.17252	0.447410	0.223705	+	0.974657i	$0.428185\pi$
$258$	0.841861	0.0524120
$259$	−14.4527	−0.898045
$260$	−0.757993	−0.0470087
$261$	8.43062	0.521842
$262$	−21.0923	−1.30309
$263$	4.86330	0.299884	0.149942	−	0.988695i	$-0.452091\pi$
$263$	4.86330	0.299884	0.149942	+	0.988695i	$0.452091\pi$
$264$	−1.41377	−0.0870114
$265$	−4.29548	−0.263869
$266$	−14.0024	−0.858544
$267$	16.4159	1.00463
$268$	8.33443	0.509106
$269$	1.96247	0.119654	0.0598268	−	0.998209i	$-0.480945\pi$
$269$	1.96247	0.119654	0.0598268	+	0.998209i	$0.480945\pi$
$270$	0.757993	0.0461300
$271$	8.58875	0.521729	0.260865	−	0.965375i	$-0.415992\pi$
$271$	8.58875	0.521729	0.260865	+	0.965375i	$0.415992\pi$
$272$	−1.39354	−0.0844959
$273$	1.64575	0.0996054
$274$	16.8586	1.01846
$275$	−6.25656	−0.377285
$276$	2.96384	0.178402
$277$	−9.04141	−0.543246	−0.271623	−	0.962404i	$-0.587560\pi$
$277$	−9.04141	−0.543246	−0.271623	+	0.962404i	$0.587560\pi$
$278$	0.986892	0.0591899
$279$	0.646304	0.0386932
$280$	1.24747	0.0745505
$281$	16.8920	1.00769	0.503845	−	0.863794i	$-0.331918\pi$
$281$	16.8920	1.00769	0.503845	+	0.863794i	$0.331918\pi$
$282$	−2.52267	−0.150223
$283$	31.0520	1.84585	0.922924	−	0.384983i	$-0.125793\pi$
$283$	31.0520	1.84585	0.922924	+	0.384983i	$0.125793\pi$
$284$	−3.32627	−0.197378
$285$	−6.44918	−0.382017
$286$	−1.41377	−0.0835979
$287$	19.8202	1.16995
$288$	−1.00000	−0.0589256
$289$	−15.0580	−0.885767
$290$	6.39035	0.375254
$291$	−6.37085	−0.373466
$292$	−6.98523	−0.408780
$293$	−2.42857	−0.141878	−0.0709392	−	0.997481i	$-0.522600\pi$
$293$	−2.42857	−0.141878	−0.0709392	+	0.997481i	$0.522600\pi$
$294$	4.29150	0.250286
$295$	−1.52545	−0.0888149
$296$	8.78180	0.510432
$297$	1.41377	0.0820352
$298$	−18.9628	−1.09849
$299$	2.96384	0.171403
$300$	−4.42545	−0.255503
$301$	−1.38549	−0.0798585
$302$	19.9243	1.14652
$303$	14.9185	0.857044
$304$	8.50823	0.487980
$305$	4.09266	0.234345
$306$	1.39354	0.0796635
$307$	−15.9272	−0.909014	−0.454507	−	0.890743i	$-0.650185\pi$
$307$	−15.9272	−0.909014	−0.454507	+	0.890743i	$0.650185\pi$
$308$	2.32671	0.132577
$309$	1.00000	0.0568880
$310$	0.489894	0.0278241
$311$	−9.90781	−0.561820	−0.280910	−	0.959734i	$-0.590636\pi$
$311$	−9.90781	−0.561820	−0.280910	+	0.959734i	$0.590636\pi$
$312$	−1.00000	−0.0566139
$313$	24.7917	1.40131	0.700654	−	0.713501i	$-0.252892\pi$
$313$	24.7917	1.40131	0.700654	+	0.713501i	$0.252892\pi$
$314$	−18.9110	−1.06721
$315$	−1.24747	−0.0702869
$316$	−13.2133	−0.743307
$317$	−1.30590	−0.0733466	−0.0366733	−	0.999327i	$-0.511676\pi$
$317$	−1.30590	−0.0733466	−0.0366733	+	0.999327i	$0.511676\pi$
$318$	−5.66691	−0.317784
$319$	11.9189	0.667333
$320$	−0.757993	−0.0423731
$321$	−7.66812	−0.427993
$322$	−4.87775	−0.271826
$323$	−11.8566	−0.659718
$324$	1.00000	0.0555556
$325$	−4.42545	−0.245480
$326$	−1.85271	−0.102612
$327$	3.54095	0.195815
$328$	−12.0433	−0.664979
$329$	4.15169	0.228890
$330$	1.07163	0.0589911
$331$	0.166194	0.00913483	0.00456742	−	0.999990i	$-0.498546\pi$
$331$	0.166194	0.00913483	0.00456742	+	0.999990i	$0.498546\pi$
$332$	−3.92742	−0.215545
$333$	−8.78180	−0.481240
$334$	18.2715	0.999775
$335$	−6.31744	−0.345159
$336$	1.64575	0.0897831
$337$	6.00123	0.326908	0.163454	−	0.986551i	$-0.447736\pi$
$337$	6.00123	0.326908	0.163454	+	0.986551i	$0.447736\pi$
$338$	−1.00000	−0.0543928
$339$	−7.99534	−0.434247
$340$	1.05630	0.0572857
$341$	0.913724	0.0494809
$342$	−8.50823	−0.460072
$343$	−18.5830	−1.00339
$344$	0.841861	0.0453901
$345$	−2.24657	−0.120951
$346$	−13.4188	−0.721401
$347$	−25.9529	−1.39322	−0.696612	−	0.717448i	$-0.745310\pi$
$347$	−25.9529	−1.39322	−0.696612	+	0.717448i	$0.745310\pi$
$348$	8.43062	0.451928
$349$	−23.2277	−1.24335	−0.621676	−	0.783274i	$-0.713548\pi$
$349$	−23.2277	−1.24335	−0.621676	+	0.783274i	$0.713548\pi$
$350$	7.28318	0.389302
$351$	1.00000	0.0533761
$352$	−1.41377	−0.0753541
$353$	−13.7280	−0.730670	−0.365335	−	0.930876i	$-0.619046\pi$
$353$	−13.7280	−0.730670	−0.365335	+	0.930876i	$0.619046\pi$
$354$	−2.01248	−0.106962
$355$	2.52129	0.133816
$356$	16.4159	0.870039
$357$	−2.29342	−0.121381
$358$	1.99353	0.105362
$359$	10.3683	0.547217	0.273609	−	0.961841i	$-0.411783\pi$
$359$	10.3683	0.547217	0.273609	+	0.961841i	$0.411783\pi$
$360$	0.757993	0.0399498
$361$	53.3900	2.81000
$362$	−18.0165	−0.946927
$363$	−9.00126	−0.472444
$364$	1.64575	0.0862608
$365$	5.29476	0.277140
$366$	5.39934	0.282228
$367$	29.5295	1.54143	0.770713	−	0.637182i	$-0.219900\pi$
$367$	29.5295	1.54143	0.770713	+	0.637182i	$0.219900\pi$
$368$	2.96384	0.154501
$369$	12.0433	0.626948
$370$	−6.65655	−0.346057
$371$	9.32632	0.484198
$372$	0.646304	0.0335093
$373$	−6.91324	−0.357954	−0.178977	−	0.983853i	$-0.557279\pi$
$373$	−6.91324	−0.357954	−0.178977	+	0.983853i	$0.557279\pi$
$374$	1.97015	0.101874
$375$	7.14442	0.368937
$376$	−2.52267	−0.130097
$377$	8.43062	0.434199
$378$	−1.64575	−0.0846483
$379$	−18.5888	−0.954841	−0.477421	−	0.878675i	$-0.658428\pi$
$379$	−18.5888	−0.954841	−0.477421	+	0.878675i	$0.658428\pi$
$380$	−6.44918	−0.330836
$381$	−6.67441	−0.341941
$382$	10.4402	0.534169
$383$	−8.83321	−0.451356	−0.225678	−	0.974202i	$-0.572460\pi$
$383$	−8.83321	−0.451356	−0.225678	+	0.974202i	$0.572460\pi$
$384$	−1.00000	−0.0510310
$385$	−1.76363	−0.0898830
$386$	20.9658	1.06713
$387$	−0.841861	−0.0427942
$388$	−6.37085	−0.323431
$389$	34.3240	1.74030	0.870148	−	0.492790i	$-0.164023\pi$
$389$	34.3240	1.74030	0.870148	+	0.492790i	$0.164023\pi$
$390$	0.757993	0.0383825
$391$	−4.13024	−0.208875
$392$	4.29150	0.216754
$393$	21.0923	1.06397
$394$	5.00003	0.251898
$395$	10.0156	0.503939
$396$	1.41377	0.0710445
$397$	7.34364	0.368567	0.184283	−	0.982873i	$-0.441004\pi$
$397$	7.34364	0.368567	0.184283	+	0.982873i	$0.441004\pi$
$398$	−21.5029	−1.07784
$399$	14.0024	0.700998
$400$	−4.42545	−0.221272
$401$	−9.51687	−0.475250	−0.237625	−	0.971357i	$-0.576369\pi$
$401$	−9.51687	−0.475250	−0.237625	+	0.971357i	$0.576369\pi$
$402$	−8.33443	−0.415683
$403$	0.646304	0.0321947
$404$	14.9185	0.742222
$405$	−0.757993	−0.0376650
$406$	−13.8747	−0.688590
$407$	−12.4154	−0.615410
$408$	1.39354	0.0689906
$409$	28.9455	1.43127	0.715633	−	0.698477i	$-0.246138\pi$
$409$	28.9455	1.43127	0.715633	+	0.698477i	$0.246138\pi$
$410$	9.12872	0.450835
$411$	−16.8586	−0.831572
$412$	1.00000	0.0492665
$413$	3.31204	0.162975
$414$	−2.96384	−0.145665
$415$	2.97696	0.146133
$416$	−1.00000	−0.0490290
$417$	−0.986892	−0.0483283
$418$	−12.0287	−0.588341
$419$	1.46454	0.0715475	0.0357737	−	0.999360i	$-0.488610\pi$
$419$	1.46454	0.0715475	0.0357737	+	0.999360i	$0.488610\pi$
$420$	−1.24747	−0.0608702
$421$	−0.372758	−0.0181671	−0.00908355	−	0.999959i	$-0.502891\pi$
$421$	−0.372758	−0.0181671	−0.00908355	+	0.999959i	$0.502891\pi$
$422$	−5.16654	−0.251503
$423$	2.52267	0.122657
$424$	−5.66691	−0.275209
$425$	6.16705	0.299146
$426$	3.32627	0.161159
$427$	−8.88597	−0.430022
$428$	−7.66812	−0.370653
$429$	1.41377	0.0682574
$430$	−0.638125	−0.0307731
$431$	−16.1733	−0.779042	−0.389521	−	0.921018i	$-0.627359\pi$
$431$	−16.1733	−0.779042	−0.389521	+	0.921018i	$0.627359\pi$
$432$	1.00000	0.0481125
$433$	13.7440	0.660492	0.330246	−	0.943895i	$-0.392868\pi$
$433$	13.7440	0.660492	0.330246	+	0.943895i	$0.392868\pi$
$434$	−1.06366	−0.0510571
$435$	−6.39035	−0.306394
$436$	3.54095	0.169581
$437$	25.2171	1.20630
$438$	6.98523	0.333767
$439$	18.5868	0.887099	0.443549	−	0.896250i	$-0.353719\pi$
$439$	18.5868	0.887099	0.443549	+	0.896250i	$0.353719\pi$
$440$	1.07163	0.0510878
$441$	−4.29150	−0.204357
$442$	1.39354	0.0662841
$443$	4.58156	0.217677	0.108838	−	0.994059i	$-0.465287\pi$
$443$	4.58156	0.217677	0.108838	+	0.994059i	$0.465287\pi$
$444$	−8.78180	−0.416766
$445$	−12.4431	−0.589860
$446$	−23.7710	−1.12559
$447$	18.9628	0.896912
$448$	1.64575	0.0777544
$449$	−5.03342	−0.237542	−0.118771	−	0.992922i	$-0.537895\pi$
$449$	−5.03342	−0.237542	−0.118771	+	0.992922i	$0.537895\pi$
$450$	4.42545	0.208618
$451$	17.0264	0.801742
$452$	−7.99534	−0.376069
$453$	−19.9243	−0.936126
$454$	11.8084	0.554197
$455$	−1.24747	−0.0584822
$456$	−8.50823	−0.398434
$457$	−23.7501	−1.11098	−0.555491	−	0.831523i	$-0.687469\pi$
$457$	−23.7501	−1.11098	−0.555491	+	0.831523i	$0.687469\pi$
$458$	7.42697	0.347040
$459$	−1.39354	−0.0650450
$460$	−2.24657	−0.104747
$461$	−1.33515	−0.0621841	−0.0310920	−	0.999517i	$-0.509898\pi$
$461$	−1.33515	−0.0621841	−0.0310920	+	0.999517i	$0.509898\pi$
$462$	−2.32671	−0.108248
$463$	9.70299	0.450936	0.225468	−	0.974251i	$-0.427609\pi$
$463$	9.70299	0.450936	0.225468	+	0.974251i	$0.427609\pi$
$464$	8.43062	0.391382
$465$	−0.489894	−0.0227183
$466$	−3.53932	−0.163956
$467$	25.6598	1.18740	0.593698	−	0.804688i	$-0.297667\pi$
$467$	25.6598	1.18740	0.593698	+	0.804688i	$0.297667\pi$
$468$	1.00000	0.0462250
$469$	13.7164	0.633364
$470$	1.91217	0.0882018
$471$	18.9110	0.871371
$472$	−2.01248	−0.0926319
$473$	−1.19020	−0.0547253
$474$	13.2133	0.606907
$475$	−37.6527	−1.72763
$476$	−2.29342	−0.105119
$477$	5.66691	0.259470
$478$	9.86381	0.451160
$479$	36.5468	1.66986	0.834932	−	0.550353i	$-0.185507\pi$
$479$	36.5468	1.66986	0.834932	+	0.550353i	$0.185507\pi$
$480$	0.757993	0.0345975
$481$	−8.78180	−0.400416
$482$	−15.8070	−0.719991
$483$	4.87775	0.221945
$484$	−9.00126	−0.409148
$485$	4.82906	0.219276
$486$	−1.00000	−0.0453609
$487$	40.7877	1.84827	0.924133	−	0.382072i	$-0.124789\pi$
$487$	40.7877	1.84827	0.924133	+	0.382072i	$0.124789\pi$
$488$	5.39934	0.244417
$489$	1.85271	0.0837823
$490$	−3.25293	−0.146952
$491$	32.9060	1.48503	0.742514	−	0.669830i	$-0.233633\pi$
$491$	32.9060	1.48503	0.742514	+	0.669830i	$0.233633\pi$
$492$	12.0433	0.542953
$493$	−11.7484	−0.529122
$494$	−8.50823	−0.382803
$495$	−1.07163	−0.0481661
$496$	0.646304	0.0290199
$497$	−5.47422	−0.245552
$498$	3.92742	0.175992
$499$	−22.9667	−1.02813	−0.514066	−	0.857751i	$-0.671861\pi$
$499$	−22.9667	−1.02813	−0.514066	+	0.857751i	$0.671861\pi$
$500$	7.14442	0.319508
$501$	−18.2715	−0.816313
$502$	12.8671	0.574285
$503$	−3.31628	−0.147866	−0.0739329	−	0.997263i	$-0.523555\pi$
$503$	−3.31628	−0.147866	−0.0739329	+	0.997263i	$0.523555\pi$
$504$	−1.64575	−0.0733076
$505$	−11.3081	−0.503204
$506$	−4.19019	−0.186277
$507$	1.00000	0.0444116
$508$	−6.67441	−0.296129
$509$	19.3261	0.856614	0.428307	−	0.903633i	$-0.359110\pi$
$509$	19.3261	0.856614	0.428307	+	0.903633i	$0.359110\pi$
$510$	−1.05630	−0.0467736
$511$	−11.4960	−0.508551
$512$	−1.00000	−0.0441942
$513$	8.50823	0.375648
$514$	−7.17252	−0.316366
$515$	−0.757993	−0.0334012
$516$	−0.841861	−0.0370609
$517$	3.56648	0.156854
$518$	14.4527	0.635013
$519$	13.4188	0.589022
$520$	0.757993	0.0332402
$521$	−20.2817	−0.888559	−0.444280	−	0.895888i	$-0.646540\pi$
$521$	−20.2817	−0.888559	−0.444280	+	0.895888i	$0.646540\pi$
$522$	−8.43062	−0.368998
$523$	−5.69980	−0.249235	−0.124617	−	0.992205i	$-0.539770\pi$
$523$	−5.69980	−0.249235	−0.124617	+	0.992205i	$0.539770\pi$
$524$	21.0923	0.921421
$525$	−7.28318	−0.317864
$526$	−4.86330	−0.212050
$527$	−0.900652	−0.0392330
$528$	1.41377	0.0615264
$529$	−14.2156	−0.618071
$530$	4.29548	0.186584
$531$	2.01248	0.0873342
$532$	14.0024	0.607082
$533$	12.0433	0.521652
$534$	−16.4159	−0.710384
$535$	5.81238	0.251291
$536$	−8.33443	−0.359992
$537$	−1.99353	−0.0860273
$538$	−1.96247	−0.0846079
$539$	−6.06719	−0.261333
$540$	−0.757993	−0.0326188
$541$	−19.1208	−0.822066	−0.411033	−	0.911620i	$-0.634832\pi$
$541$	−19.1208	−0.822066	−0.411033	+	0.911620i	$0.634832\pi$
$542$	−8.58875	−0.368918
$543$	18.0165	0.773162
$544$	1.39354	0.0597476
$545$	−2.68402	−0.114971
$546$	−1.64575	−0.0704316
$547$	−26.3347	−1.12599	−0.562995	−	0.826460i	$-0.690351\pi$
$547$	−26.3347	−1.12599	−0.562995	+	0.826460i	$0.690351\pi$
$548$	−16.8586	−0.720163
$549$	−5.39934	−0.230438
$550$	6.25656	0.266780
$551$	71.7296	3.05578
$552$	−2.96384	−0.126150
$553$	−21.7458	−0.924726
$554$	9.04141	0.384133
$555$	6.65655	0.282555
$556$	−0.986892	−0.0418536
$557$	8.53579	0.361673	0.180837	−	0.983513i	$-0.442119\pi$
$557$	8.53579	0.361673	0.180837	+	0.983513i	$0.442119\pi$
$558$	−0.646304	−0.0273602
$559$	−0.841861	−0.0356069
$560$	−1.24747	−0.0527151
$561$	−1.97015	−0.0831797
$562$	−16.8920	−0.712545
$563$	−30.6279	−1.29081	−0.645405	−	0.763840i	$-0.723311\pi$
$563$	−30.6279	−1.29081	−0.645405	+	0.763840i	$0.723311\pi$
$564$	2.52267	0.106224
$565$	6.06042	0.254964
$566$	−31.0520	−1.30521
$567$	1.64575	0.0691150
$568$	3.32627	0.139567
$569$	25.8065	1.08186	0.540931	−	0.841067i	$-0.318072\pi$
$569$	25.8065	1.08186	0.540931	+	0.841067i	$0.318072\pi$
$570$	6.44918	0.270126
$571$	21.8876	0.915968	0.457984	−	0.888960i	$-0.348572\pi$
$571$	21.8876	0.915968	0.457984	+	0.888960i	$0.348572\pi$
$572$	1.41377	0.0591126
$573$	−10.4402	−0.436147
$574$	−19.8202	−0.827280
$575$	−13.1163	−0.546989
$576$	1.00000	0.0416667
$577$	15.9441	0.663762	0.331881	−	0.943321i	$-0.392317\pi$
$577$	15.9441	0.663762	0.331881	+	0.943321i	$0.392317\pi$
$578$	15.0580	0.626332
$579$	−20.9658	−0.871307
$580$	−6.39035	−0.265345
$581$	−6.46356	−0.268154
$582$	6.37085	0.264080
$583$	8.01169	0.331810
$584$	6.98523	0.289051
$585$	−0.757993	−0.0313392
$586$	2.42857	0.100323
$587$	8.80205	0.363299	0.181650	−	0.983363i	$-0.441856\pi$
$587$	8.80205	0.363299	0.181650	+	0.983363i	$0.441856\pi$
$588$	−4.29150	−0.176979
$589$	5.49890	0.226578
$590$	1.52545	0.0628016
$591$	−5.00003	−0.205674
$592$	−8.78180	−0.360930
$593$	−25.9002	−1.06359	−0.531797	−	0.846872i	$-0.678483\pi$
$593$	−25.9002	−1.06359	−0.531797	+	0.846872i	$0.678483\pi$
$594$	−1.41377	−0.0580076
$595$	1.73840	0.0712674
$596$	18.9628	0.776748
$597$	21.5029	0.880054
$598$	−2.96384	−0.121201
$599$	−17.0117	−0.695081	−0.347540	−	0.937665i	$-0.612983\pi$
$599$	−17.0117	−0.695081	−0.347540	+	0.937665i	$0.612983\pi$
$600$	4.42545	0.180668
$601$	−44.3262	−1.80810	−0.904052	−	0.427422i	$-0.859422\pi$
$601$	−44.3262	−1.80810	−0.904052	+	0.427422i	$0.859422\pi$
$602$	1.38549	0.0564685
$603$	8.33443	0.339404
$604$	−19.9243	−0.810709
$605$	6.82289	0.277390
$606$	−14.9185	−0.606021
$607$	−21.5343	−0.874050	−0.437025	−	0.899449i	$-0.643968\pi$
$607$	−21.5343	−0.874050	−0.437025	+	0.899449i	$0.643968\pi$
$608$	−8.50823	−0.345054
$609$	13.8747	0.562231
$610$	−4.09266	−0.165707
$611$	2.52267	0.102056
$612$	−1.39354	−0.0563306
$613$	32.8489	1.32676	0.663378	−	0.748284i	$-0.269122\pi$
$613$	32.8489	1.32676	0.663378	+	0.748284i	$0.269122\pi$
$614$	15.9272	0.642770
$615$	−9.12872	−0.368106
$616$	−2.32671	−0.0937458
$617$	−20.5805	−0.828541	−0.414271	−	0.910154i	$-0.635963\pi$
$617$	−20.5805	−0.828541	−0.414271	+	0.910154i	$0.635963\pi$
$618$	−1.00000	−0.0402259
$619$	−5.33335	−0.214365	−0.107183	−	0.994239i	$-0.534183\pi$
$619$	−5.33335	−0.214365	−0.107183	+	0.994239i	$0.534183\pi$
$620$	−0.489894	−0.0196746
$621$	2.96384	0.118935
$622$	9.90781	0.397267
$623$	27.0164	1.08239
$624$	1.00000	0.0400320
$625$	16.7118	0.668472
$626$	−24.7917	−0.990874
$627$	12.0287	0.480379
$628$	18.9110	0.754629
$629$	12.2378	0.487954
$630$	1.24747	0.0497003
$631$	−23.3332	−0.928880	−0.464440	−	0.885605i	$-0.653744\pi$
$631$	−23.3332	−0.928880	−0.464440	+	0.885605i	$0.653744\pi$
$632$	13.2133	0.525597
$633$	5.16654	0.205352
$634$	1.30590	0.0518639
$635$	5.05916	0.200767
$636$	5.66691	0.224707
$637$	−4.29150	−0.170036
$638$	−11.9189	−0.471875
$639$	−3.32627	−0.131585
$640$	0.757993	0.0299623
$641$	48.3100	1.90813	0.954065	−	0.299600i	$-0.0968534\pi$
$641$	48.3100	1.90813	0.954065	+	0.299600i	$0.0968534\pi$
$642$	7.66812	0.302637
$643$	11.3335	0.446951	0.223475	−	0.974710i	$-0.428260\pi$
$643$	11.3335	0.446951	0.223475	+	0.974710i	$0.428260\pi$
$644$	4.87775	0.192210
$645$	0.638125	0.0251262
$646$	11.8566	0.466491
$647$	−39.7161	−1.56140	−0.780700	−	0.624906i	$-0.785137\pi$
$647$	−39.7161	−1.56140	−0.780700	+	0.624906i	$0.785137\pi$
$648$	−1.00000	−0.0392837
$649$	2.84518	0.111683
$650$	4.42545	0.173580
$651$	1.06366	0.0416879
$652$	1.85271	0.0725576
$653$	−33.7589	−1.32109	−0.660544	−	0.750787i	$-0.729675\pi$
$653$	−33.7589	−1.32109	−0.660544	+	0.750787i	$0.729675\pi$
$654$	−3.54095	−0.138462
$655$	−15.9878	−0.624696
$656$	12.0433	0.470211
$657$	−6.98523	−0.272520
$658$	−4.15169	−0.161850
$659$	16.4795	0.641949	0.320974	−	0.947088i	$-0.395990\pi$
$659$	16.4795	0.641949	0.320974	+	0.947088i	$0.395990\pi$
$660$	−1.07163	−0.0417130
$661$	−22.2435	−0.865173	−0.432586	−	0.901593i	$-0.642399\pi$
$661$	−22.2435	−0.865173	−0.432586	+	0.901593i	$0.642399\pi$
$662$	−0.166194	−0.00645930
$663$	−1.39354	−0.0541207
$664$	3.92742	0.152414
$665$	−10.6137	−0.411583
$666$	8.78180	0.340288
$667$	24.9870	0.967501
$668$	−18.2715	−0.706947
$669$	23.7710	0.919040
$670$	6.31744	0.244064
$671$	−7.63342	−0.294685
$672$	−1.64575	−0.0634862
$673$	15.9077	0.613195	0.306598	−	0.951839i	$-0.400809\pi$
$673$	15.9077	0.613195	0.306598	+	0.951839i	$0.400809\pi$
$674$	−6.00123	−0.231159
$675$	−4.42545	−0.170336
$676$	1.00000	0.0384615
$677$	−14.3797	−0.552658	−0.276329	−	0.961063i	$-0.589118\pi$
$677$	−14.3797	−0.552658	−0.276329	+	0.961063i	$0.589118\pi$
$678$	7.99534	0.307059
$679$	−10.4848	−0.402371
$680$	−1.05630	−0.0405071
$681$	−11.8084	−0.452500
$682$	−0.913724	−0.0349883
$683$	31.2803	1.19691	0.598454	−	0.801157i	$-0.295782\pi$
$683$	31.2803	1.19691	0.598454	+	0.801157i	$0.295782\pi$
$684$	8.50823	0.325320
$685$	12.7787	0.488248
$686$	18.5830	0.709502
$687$	−7.42697	−0.283357
$688$	−0.841861	−0.0320957
$689$	5.66691	0.215892
$690$	2.24657	0.0855256
$691$	−11.7816	−0.448194	−0.224097	−	0.974567i	$-0.571943\pi$
$691$	−11.7816	−0.448194	−0.224097	+	0.974567i	$0.571943\pi$
$692$	13.4188	0.510108
$693$	2.32671	0.0883844
$694$	25.9529	0.985159
$695$	0.748058	0.0283754
$696$	−8.43062	−0.319562
$697$	−16.7828	−0.635694
$698$	23.2277	0.879183
$699$	3.53932	0.133869
$700$	−7.28318	−0.275278
$701$	17.5664	0.663473	0.331737	−	0.943372i	$-0.392365\pi$
$701$	17.5664	0.663473	0.331737	+	0.943372i	$0.392365\pi$
$702$	−1.00000	−0.0377426
$703$	−74.7176	−2.81803
$704$	1.41377	0.0532834
$705$	−1.91217	−0.0720165
$706$	13.7280	0.516662
$707$	24.5521	0.923376
$708$	2.01248	0.0756336
$709$	45.4844	1.70820	0.854101	−	0.520107i	$-0.174108\pi$
$709$	45.4844	1.70820	0.854101	+	0.520107i	$0.174108\pi$
$710$	−2.52129	−0.0946225
$711$	−13.2133	−0.495538
$712$	−16.4159	−0.615210
$713$	1.91554	0.0717377
$714$	2.29342	0.0858292
$715$	−1.07163	−0.0400766
$716$	−1.99353	−0.0745018
$717$	−9.86381	−0.368371
$718$	−10.3683	−0.386941
$719$	−24.0487	−0.896867	−0.448433	−	0.893816i	$-0.648018\pi$
$719$	−24.0487	−0.896867	−0.448433	+	0.893816i	$0.648018\pi$
$720$	−0.757993	−0.0282487
$721$	1.64575	0.0612910
$722$	−53.3900	−1.98697
$723$	15.8070	0.587870
$724$	18.0165	0.669578
$725$	−37.3092	−1.38563
$726$	9.00126	0.334068
$727$	6.53193	0.242256	0.121128	−	0.992637i	$-0.461349\pi$
$727$	6.53193	0.242256	0.121128	+	0.992637i	$0.461349\pi$
$728$	−1.64575	−0.0609956
$729$	1.00000	0.0370370
$730$	−5.29476	−0.195968
$731$	1.17317	0.0433912
$732$	−5.39934	−0.199565
$733$	9.71416	0.358801	0.179400	−	0.983776i	$-0.442584\pi$
$733$	9.71416	0.358801	0.179400	+	0.983776i	$0.442584\pi$
$734$	−29.5295	−1.08995
$735$	3.25293	0.119986
$736$	−2.96384	−0.109249
$737$	11.7830	0.434031
$738$	−12.0433	−0.443319
$739$	−30.4883	−1.12153	−0.560764	−	0.827975i	$-0.689493\pi$
$739$	−30.4883	−1.12153	−0.560764	+	0.827975i	$0.689493\pi$
$740$	6.65655	0.244700
$741$	8.50823	0.312558
$742$	−9.32632	−0.342380
$743$	43.3068	1.58877	0.794387	−	0.607412i	$-0.207792\pi$
$743$	43.3068	1.58877	0.794387	+	0.607412i	$0.207792\pi$
$744$	−0.646304	−0.0236947
$745$	−14.3737	−0.526612
$746$	6.91324	0.253112
$747$	−3.92742	−0.143697
$748$	−1.97015	−0.0720357
$749$	−12.6198	−0.461118
$750$	−7.14442	−0.260878
$751$	10.4348	0.380772	0.190386	−	0.981709i	$-0.439026\pi$
$751$	10.4348	0.380772	0.190386	+	0.981709i	$0.439026\pi$
$752$	2.52267	0.0919925
$753$	−12.8671	−0.468902
$754$	−8.43062	−0.307025
$755$	15.1025	0.549636
$756$	1.64575	0.0598554
$757$	−34.3775	−1.24947	−0.624736	−	0.780836i	$-0.714793\pi$
$757$	−34.3775	−1.24947	−0.624736	+	0.780836i	$0.714793\pi$
$758$	18.5888	0.675175
$759$	4.19019	0.152094
$760$	6.44918	0.233936
$761$	−3.55350	−0.128814	−0.0644071	−	0.997924i	$-0.520516\pi$
$761$	−3.55350	−0.128814	−0.0644071	+	0.997924i	$0.520516\pi$
$762$	6.67441	0.241788
$763$	5.82753	0.210971
$764$	−10.4402	−0.377715
$765$	1.05630	0.0381905
$766$	8.83321	0.319157
$767$	2.01248	0.0726664
$768$	1.00000	0.0360844
$769$	17.2899	0.623490	0.311745	−	0.950166i	$-0.399086\pi$
$769$	17.2899	0.623490	0.311745	+	0.950166i	$0.399086\pi$
$770$	1.76363	0.0635569
$771$	7.17252	0.258312
$772$	−20.9658	−0.754574
$773$	−44.3854	−1.59643	−0.798216	−	0.602371i	$-0.794223\pi$
$773$	−44.3854	−1.59643	−0.798216	+	0.602371i	$0.794223\pi$
$774$	0.841861	0.0302601
$775$	−2.86018	−0.102741
$776$	6.37085	0.228700
$777$	−14.4527	−0.518486
$778$	−34.3240	−1.23058
$779$	102.467	3.67126
$780$	−0.757993	−0.0271405
$781$	−4.70258	−0.168272
$782$	4.13024	0.147697
$783$	8.43062	0.301286
$784$	−4.29150	−0.153268
$785$	−14.3344	−0.511616
$786$	−21.0923	−0.752337
$787$	−5.50111	−0.196093	−0.0980467	−	0.995182i	$-0.531259\pi$
$787$	−5.50111	−0.196093	−0.0980467	+	0.995182i	$0.531259\pi$
$788$	−5.00003	−0.178119
$789$	4.86330	0.173138
$790$	−10.0156	−0.356339
$791$	−13.1583	−0.467857
$792$	−1.41377	−0.0502361
$793$	−5.39934	−0.191736
$794$	−7.34364	−0.260616
$795$	−4.29548	−0.152345
$796$	21.5029	0.762149
$797$	−23.7052	−0.839681	−0.419841	−	0.907598i	$-0.637914\pi$
$797$	−23.7052	−0.839681	−0.419841	+	0.907598i	$0.637914\pi$
$798$	−14.0024	−0.495681
$799$	−3.51545	−0.124368
$800$	4.42545	0.156463
$801$	16.4159	0.580026
$802$	9.51687	0.336053
$803$	−9.87550	−0.348499
$804$	8.33443	0.293933
$805$	−3.69730	−0.130313
$806$	−0.646304	−0.0227651
$807$	1.96247	0.0690820
$808$	−14.9185	−0.524830
$809$	−48.1540	−1.69301	−0.846503	−	0.532384i	$-0.821296\pi$
$809$	−48.1540	−1.69301	−0.846503	+	0.532384i	$0.821296\pi$
$810$	0.757993	0.0266332
$811$	−6.48704	−0.227791	−0.113895	−	0.993493i	$-0.536333\pi$
$811$	−6.48704	−0.227791	−0.113895	+	0.993493i	$0.536333\pi$
$812$	13.8747	0.486906
$813$	8.58875	0.301220
$814$	12.4154	0.435161
$815$	−1.40434	−0.0491919
$816$	−1.39354	−0.0487837
$817$	−7.16275	−0.250593
$818$	−28.9455	−1.01206
$819$	1.64575	0.0575072
$820$	−9.12872	−0.318789
$821$	23.9540	0.835999	0.418000	−	0.908447i	$-0.362731\pi$
$821$	23.9540	0.835999	0.418000	+	0.908447i	$0.362731\pi$
$822$	16.8586	0.588010
$823$	5.59527	0.195039	0.0975194	−	0.995234i	$-0.468909\pi$
$823$	5.59527	0.195039	0.0975194	+	0.995234i	$0.468909\pi$
$824$	−1.00000	−0.0348367
$825$	−6.25656	−0.217825
$826$	−3.31204	−0.115241
$827$	47.0969	1.63772	0.818860	−	0.573993i	$-0.194606\pi$
$827$	47.0969	1.63772	0.818860	+	0.573993i	$0.194606\pi$
$828$	2.96384	0.103001
$829$	55.5111	1.92798	0.963989	−	0.265941i	$-0.0856826\pi$
$829$	55.5111	1.92798	0.963989	+	0.265941i	$0.0856826\pi$
$830$	−2.97696	−0.103332
$831$	−9.04141	−0.313643
$832$	1.00000	0.0346688
$833$	5.98039	0.207208
$834$	0.986892	0.0341733
$835$	13.8497	0.479289
$836$	12.0287	0.416020
$837$	0.646304	0.0223395
$838$	−1.46454	−0.0505917
$839$	−19.5062	−0.673427	−0.336714	−	0.941607i	$-0.609315\pi$
$839$	−19.5062	−0.673427	−0.336714	+	0.941607i	$0.609315\pi$
$840$	1.24747	0.0430417
$841$	42.0753	1.45087
$842$	0.372758	0.0128461
$843$	16.8920	0.581791
$844$	5.16654	0.177840
$845$	−0.757993	−0.0260758
$846$	−2.52267	−0.0867313
$847$	−14.8138	−0.509009
$848$	5.66691	0.194602
$849$	31.0520	1.06570
$850$	−6.16705	−0.211528
$851$	−26.0279	−0.892224
$852$	−3.32627	−0.113956
$853$	26.5769	0.909975	0.454987	−	0.890498i	$-0.349644\pi$
$853$	26.5769	0.909975	0.454987	+	0.890498i	$0.349644\pi$
$854$	8.88597	0.304072
$855$	−6.44918	−0.220557
$856$	7.66812	0.262091
$857$	32.4976	1.11010	0.555048	−	0.831818i	$-0.312700\pi$
$857$	32.4976	1.11010	0.555048	+	0.831818i	$0.312700\pi$
$858$	−1.41377	−0.0482653
$859$	9.18079	0.313244	0.156622	−	0.987659i	$-0.449939\pi$
$859$	9.18079	0.313244	0.156622	+	0.987659i	$0.449939\pi$
$860$	0.638125	0.0217599
$861$	19.8202	0.675472
$862$	16.1733	0.550866
$863$	−15.5770	−0.530248	−0.265124	−	0.964214i	$-0.585413\pi$
$863$	−15.5770	−0.530248	−0.265124	+	0.964214i	$0.585413\pi$
$864$	−1.00000	−0.0340207
$865$	−10.1714	−0.345838
$866$	−13.7440	−0.467039
$867$	−15.0580	−0.511398
$868$	1.06366	0.0361028
$869$	−18.6806	−0.633695
$870$	6.39035	0.216653
$871$	8.33443	0.282401
$872$	−3.54095	−0.119912
$873$	−6.37085	−0.215621
$874$	−25.2171	−0.852980
$875$	11.7579	0.397491
$876$	−6.98523	−0.236009
$877$	−9.73966	−0.328885	−0.164443	−	0.986387i	$-0.552583\pi$
$877$	−9.73966	−0.328885	−0.164443	+	0.986387i	$0.552583\pi$
$878$	−18.5868	−0.627274
$879$	−2.42857	−0.0819135
$880$	−1.07163	−0.0361245
$881$	52.7502	1.77720	0.888600	−	0.458682i	$-0.151678\pi$
$881$	52.7502	1.77720	0.888600	+	0.458682i	$0.151678\pi$
$882$	4.29150	0.144502
$883$	−3.83878	−0.129185	−0.0645927	−	0.997912i	$-0.520575\pi$
$883$	−3.83878	−0.129185	−0.0645927	+	0.997912i	$0.520575\pi$
$884$	−1.39354	−0.0468699
$885$	−1.52545	−0.0512773
$886$	−4.58156	−0.153921
$887$	38.2983	1.28593	0.642966	−	0.765895i	$-0.277704\pi$
$887$	38.2983	1.28593	0.642966	+	0.765895i	$0.277704\pi$
$888$	8.78180	0.294698
$889$	−10.9844	−0.368406
$890$	12.4431	0.417094
$891$	1.41377	0.0473630
$892$	23.7710	0.795912
$893$	21.4635	0.718248
$894$	−18.9628	−0.634212
$895$	1.51108	0.0505100
$896$	−1.64575	−0.0549807
$897$	2.96384	0.0989598
$898$	5.03342	0.167968
$899$	5.44874	0.181726
$900$	−4.42545	−0.147515
$901$	−7.89708	−0.263090
$902$	−17.0264	−0.566917
$903$	−1.38549	−0.0461063
$904$	7.99534	0.265921
$905$	−13.6564	−0.453954
$906$	19.9243	0.661941
$907$	2.91657	0.0968430	0.0484215	−	0.998827i	$-0.484581\pi$
$907$	2.91657	0.0968430	0.0484215	+	0.998827i	$0.484581\pi$
$908$	−11.8084	−0.391876
$909$	14.9185	0.494814
$910$	1.24747	0.0413532
$911$	−24.6233	−0.815805	−0.407902	−	0.913026i	$-0.633740\pi$
$911$	−24.6233	−0.815805	−0.407902	+	0.913026i	$0.633740\pi$
$912$	8.50823	0.281736
$913$	−5.55247	−0.183760
$914$	23.7501	0.785582
$915$	4.09266	0.135299
$916$	−7.42697	−0.245394
$917$	34.7127	1.14631
$918$	1.39354	0.0459938
$919$	27.1490	0.895562	0.447781	−	0.894143i	$-0.352214\pi$
$919$	27.1490	0.895562	0.447781	+	0.894143i	$0.352214\pi$
$920$	2.24657	0.0740673
$921$	−15.9272	−0.524819
$922$	1.33515	0.0439708
$923$	−3.32627	−0.109486
$924$	2.32671	0.0765432
$925$	38.8634	1.27782
$926$	−9.70299	−0.318860
$927$	1.00000	0.0328443
$928$	−8.43062	−0.276749
$929$	−8.49245	−0.278628	−0.139314	−	0.990248i	$-0.544490\pi$
$929$	−8.49245	−0.278628	−0.139314	+	0.990248i	$0.544490\pi$
$930$	0.489894	0.0160643
$931$	−36.5131	−1.19667
$932$	3.53932	0.115934
$933$	−9.90781	−0.324367
$934$	−25.6598	−0.839615
$935$	1.49336	0.0488380
$936$	−1.00000	−0.0326860
$937$	−25.7715	−0.841917	−0.420959	−	0.907080i	$-0.638306\pi$
$937$	−25.7715	−0.841917	−0.420959	+	0.907080i	$0.638306\pi$
$938$	−13.7164	−0.447856
$939$	24.7917	0.809045
$940$	−1.91217	−0.0623681
$941$	−38.8323	−1.26590	−0.632949	−	0.774194i	$-0.718156\pi$
$941$	−38.8323	−1.26590	−0.632949	+	0.774194i	$0.718156\pi$
$942$	−18.9110	−0.616152
$943$	35.6944	1.16237
$944$	2.01248	0.0655006
$945$	−1.24747	−0.0405801
$946$	1.19020	0.0386966
$947$	30.1503	0.979752	0.489876	−	0.871792i	$-0.337042\pi$
$947$	30.1503	0.979752	0.489876	+	0.871792i	$0.337042\pi$
$948$	−13.2133	−0.429148
$949$	−6.98523	−0.226750
$950$	37.6527	1.22162
$951$	−1.30590	−0.0423467
$952$	2.29342	0.0743303
$953$	−8.69714	−0.281728	−0.140864	−	0.990029i	$-0.544988\pi$
$953$	−8.69714	−0.281728	−0.140864	+	0.990029i	$0.544988\pi$
$954$	−5.66691	−0.183473
$955$	7.91363	0.256079
$956$	−9.86381	−0.319019
$957$	11.9189	0.385285
$958$	−36.5468	−1.18077
$959$	−27.7450	−0.895933
$960$	−0.757993	−0.0244641
$961$	−30.5823	−0.986526
$962$	8.78180	0.283137
$963$	−7.66812	−0.247102
$964$	15.8070	0.509110
$965$	15.8919	0.511578
$966$	−4.87775	−0.156939
$967$	−52.7628	−1.69674	−0.848368	−	0.529406i	$-0.822415\pi$
$967$	−52.7628	−1.69674	−0.848368	+	0.529406i	$0.822415\pi$
$968$	9.00126	0.289311
$969$	−11.8566	−0.380888
$970$	−4.82906	−0.155052
$971$	9.76359	0.313329	0.156664	−	0.987652i	$-0.449926\pi$
$971$	9.76359	0.313329	0.156664	+	0.987652i	$0.449926\pi$
$972$	1.00000	0.0320750
$973$	−1.62418	−0.0520688
$974$	−40.7877	−1.30692
$975$	−4.42545	−0.141728
$976$	−5.39934	−0.172829
$977$	18.9902	0.607550	0.303775	−	0.952744i	$-0.401753\pi$
$977$	18.9902	0.607550	0.303775	+	0.952744i	$0.401753\pi$
$978$	−1.85271	−0.0592430
$979$	23.2082	0.741738
$980$	3.25293	0.103911
$981$	3.54095	0.113054
$982$	−32.9060	−1.05007
$983$	20.0882	0.640716	0.320358	−	0.947297i	$-0.396197\pi$
$983$	20.0882	0.640716	0.320358	+	0.947297i	$0.396197\pi$
$984$	−12.0433	−0.383926
$985$	3.78999	0.120759
$986$	11.7484	0.374146
$987$	4.15169	0.132150
$988$	8.50823	0.270683
$989$	−2.49514	−0.0793410
$990$	1.07163	0.0340585
$991$	−7.17737	−0.227997	−0.113998	−	0.993481i	$-0.536366\pi$
$991$	−7.17737	−0.227997	−0.113998	+	0.993481i	$0.536366\pi$
$992$	−0.646304	−0.0205202
$993$	0.166194	0.00527400
$994$	5.47422	0.173632
$995$	−16.2990	−0.516714
$996$	−3.92742	−0.124445
$997$	12.1672	0.385338	0.192669	−	0.981264i	$-0.438286\pi$
$997$	12.1672	0.385338	0.192669	+	0.981264i	$0.438286\pi$
$998$	22.9667	0.726998
$999$	−8.78180	−0.277844

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.x.1.7	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.x.1.7	✓	13	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.757993 q^{5} -1.00000 q^{6} +1.64575 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.757993 q^{5} -1.00000 q^{6} +1.64575 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.757993 q^{10} +1.41377 q^{11} +1.00000 q^{12} +1.00000 q^{13} -1.64575 q^{14} -0.757993 q^{15} +1.00000 q^{16} -1.39354 q^{17} -1.00000 q^{18} +8.50823 q^{19} -0.757993 q^{20} +1.64575 q^{21} -1.41377 q^{22} +2.96384 q^{23} -1.00000 q^{24} -4.42545 q^{25} -1.00000 q^{26} +1.00000 q^{27} +1.64575 q^{28} +8.43062 q^{29} +0.757993 q^{30} +0.646304 q^{31} -1.00000 q^{32} +1.41377 q^{33} +1.39354 q^{34} -1.24747 q^{35} +1.00000 q^{36} -8.78180 q^{37} -8.50823 q^{38} +1.00000 q^{39} +0.757993 q^{40} +12.0433 q^{41} -1.64575 q^{42} -0.841861 q^{43} +1.41377 q^{44} -0.757993 q^{45} -2.96384 q^{46} +2.52267 q^{47} +1.00000 q^{48} -4.29150 q^{49} +4.42545 q^{50} -1.39354 q^{51} +1.00000 q^{52} +5.66691 q^{53} -1.00000 q^{54} -1.07163 q^{55} -1.64575 q^{56} +8.50823 q^{57} -8.43062 q^{58} +2.01248 q^{59} -0.757993 q^{60} -5.39934 q^{61} -0.646304 q^{62} +1.64575 q^{63} +1.00000 q^{64} -0.757993 q^{65} -1.41377 q^{66} +8.33443 q^{67} -1.39354 q^{68} +2.96384 q^{69} +1.24747 q^{70} -3.32627 q^{71} -1.00000 q^{72} -6.98523 q^{73} +8.78180 q^{74} -4.42545 q^{75} +8.50823 q^{76} +2.32671 q^{77} -1.00000 q^{78} -13.2133 q^{79} -0.757993 q^{80} +1.00000 q^{81} -12.0433 q^{82} -3.92742 q^{83} +1.64575 q^{84} +1.05630 q^{85} +0.841861 q^{86} +8.43062 q^{87} -1.41377 q^{88} +16.4159 q^{89} +0.757993 q^{90} +1.64575 q^{91} +2.96384 q^{92} +0.646304 q^{93} -2.52267 q^{94} -6.44918 q^{95} -1.00000 q^{96} -6.37085 q^{97} +4.29150 q^{98} +1.41377 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} + q^{5} - 13 q^{6} - q^{7} - 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 + q^5 - 13 * q^6 - q^7 - 13 * q^8 + 13 * q^9	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} + q^{5} - 13 q^{6} - q^{7} - 13 q^{8} + 13 q^{9} - q^{10} + 6 q^{11} + 13 q^{12} + 13 q^{13} + q^{14} + q^{15} + 13 q^{16} + 18 q^{17} - 13 q^{18} - q^{19} + q^{20} - q^{21} - 6 q^{22} + 20 q^{23} - 13 q^{24} + 16 q^{25} - 13 q^{26} + 13 q^{27} - q^{28} + 25 q^{29} - q^{30} - 5 q^{31} - 13 q^{32} + 6 q^{33} - 18 q^{34} + 26 q^{35} + 13 q^{36} - 6 q^{37} + q^{38} + 13 q^{39} - q^{40} + 13 q^{41} + q^{42} - 2 q^{43} + 6 q^{44} + q^{45} - 20 q^{46} + 5 q^{47} + 13 q^{48} - 16 q^{50} + 18 q^{51} + 13 q^{52} + 21 q^{53} - 13 q^{54} + 2 q^{55} + q^{56} - q^{57} - 25 q^{58} + 22 q^{59} + q^{60} + 2 q^{61} + 5 q^{62} - q^{63} + 13 q^{64} + q^{65} - 6 q^{66} - q^{67} + 18 q^{68} + 20 q^{69} - 26 q^{70} + 32 q^{71} - 13 q^{72} - 13 q^{73} + 6 q^{74} + 16 q^{75} - q^{76} + 33 q^{77} - 13 q^{78} - 7 q^{79} + q^{80} + 13 q^{81} - 13 q^{82} + 17 q^{83} - q^{84} - 25 q^{85} + 2 q^{86} + 25 q^{87} - 6 q^{88} - 12 q^{89} - q^{90} - q^{91} + 20 q^{92} - 5 q^{93} - 5 q^{94} + 36 q^{95} - 13 q^{96} - 42 q^{97} + 6 q^{99}+O(q^{100}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 + q^5 - 13 * q^6 - q^7 - 13 * q^8 + 13 * q^9 - q^10 + 6 * q^11 + 13 * q^12 + 13 * q^13 + q^14 + q^15 + 13 * q^16 + 18 * q^17 - 13 * q^18 - q^19 + q^20 - q^21 - 6 * q^22 + 20 * q^23 - 13 * q^24 + 16 * q^25 - 13 * q^26 + 13 * q^27 - q^28 + 25 * q^29 - q^30 - 5 * q^31 - 13 * q^32 + 6 * q^33 - 18 * q^34 + 26 * q^35 + 13 * q^36 - 6 * q^37 + q^38 + 13 * q^39 - q^40 + 13 * q^41 + q^42 - 2 * q^43 + 6 * q^44 + q^45 - 20 * q^46 + 5 * q^47 + 13 * q^48 - 16 * q^50 + 18 * q^51 + 13 * q^52 + 21 * q^53 - 13 * q^54 + 2 * q^55 + q^56 - q^57 - 25 * q^58 + 22 * q^59 + q^60 + 2 * q^61 + 5 * q^62 - q^63 + 13 * q^64 + q^65 - 6 * q^66 - q^67 + 18 * q^68 + 20 * q^69 - 26 * q^70 + 32 * q^71 - 13 * q^72 - 13 * q^73 + 6 * q^74 + 16 * q^75 - q^76 + 33 * q^77 - 13 * q^78 - 7 * q^79 + q^80 + 13 * q^81 - 13 * q^82 + 17 * q^83 - q^84 - 25 * q^85 + 2 * q^86 + 25 * q^87 - 6 * q^88 - 12 * q^89 - q^90 - q^91 + 20 * q^92 - 5 * q^93 - 5 * q^94 + 36 * q^95 - 13 * q^96 - 42 * q^97 + 6 * q^99

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