LMFDB - Embedded newform 8026.2.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.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:	$64.0879326623$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.91430 q^{3} +1.00000 q^{4} -0.167675 q^{5} -2.91430 q^{6} +0.471775 q^{7} +1.00000 q^{8} +5.49314 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.91430 q^{3} +1.00000 q^{4} -0.167675 q^{5} -2.91430 q^{6} +0.471775 q^{7} +1.00000 q^{8} +5.49314 q^{9} -0.167675 q^{10} +3.72184 q^{11} -2.91430 q^{12} +4.10256 q^{13} +0.471775 q^{14} +0.488654 q^{15} +1.00000 q^{16} -3.33349 q^{17} +5.49314 q^{18} -1.99949 q^{19} -0.167675 q^{20} -1.37489 q^{21} +3.72184 q^{22} -0.626646 q^{23} -2.91430 q^{24} -4.97189 q^{25} +4.10256 q^{26} -7.26576 q^{27} +0.471775 q^{28} -4.42225 q^{29} +0.488654 q^{30} -4.37926 q^{31} +1.00000 q^{32} -10.8465 q^{33} -3.33349 q^{34} -0.0791047 q^{35} +5.49314 q^{36} -8.13245 q^{37} -1.99949 q^{38} -11.9561 q^{39} -0.167675 q^{40} +7.95605 q^{41} -1.37489 q^{42} +2.12097 q^{43} +3.72184 q^{44} -0.921060 q^{45} -0.626646 q^{46} +0.489990 q^{47} -2.91430 q^{48} -6.77743 q^{49} -4.97189 q^{50} +9.71479 q^{51} +4.10256 q^{52} -1.65426 q^{53} -7.26576 q^{54} -0.624057 q^{55} +0.471775 q^{56} +5.82712 q^{57} -4.42225 q^{58} -13.0508 q^{59} +0.488654 q^{60} -0.248867 q^{61} -4.37926 q^{62} +2.59153 q^{63} +1.00000 q^{64} -0.687896 q^{65} -10.8465 q^{66} -2.36886 q^{67} -3.33349 q^{68} +1.82623 q^{69} -0.0791047 q^{70} +12.4156 q^{71} +5.49314 q^{72} +7.26273 q^{73} -8.13245 q^{74} +14.4896 q^{75} -1.99949 q^{76} +1.75587 q^{77} -11.9561 q^{78} -11.6253 q^{79} -0.167675 q^{80} +4.69517 q^{81} +7.95605 q^{82} +5.81448 q^{83} -1.37489 q^{84} +0.558942 q^{85} +2.12097 q^{86} +12.8877 q^{87} +3.72184 q^{88} -14.1827 q^{89} -0.921060 q^{90} +1.93549 q^{91} -0.626646 q^{92} +12.7625 q^{93} +0.489990 q^{94} +0.335264 q^{95} -2.91430 q^{96} -7.02417 q^{97} -6.77743 q^{98} +20.4446 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9}+O(q^{10}) $ 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9} - 34 q^{10} - 37 q^{11} - 9 q^{12} - 62 q^{13} - 19 q^{14} - 29 q^{15} + 71 q^{16} - 52 q^{17} + 34 q^{18} - 30 q^{19} - 34 q^{20} - 51 q^{21} - 37 q^{22} - 45 q^{23} - 9 q^{24} + 27 q^{25} - 62 q^{26} - 27 q^{27} - 19 q^{28} - 55 q^{29} - 29 q^{30} - 61 q^{31} + 71 q^{32} - 73 q^{33} - 52 q^{34} - 33 q^{35} + 34 q^{36} - 43 q^{37} - 30 q^{38} - 40 q^{39} - 34 q^{40} - 87 q^{41} - 51 q^{42} - 4 q^{43} - 37 q^{44} - 81 q^{45} - 45 q^{46} - 89 q^{47} - 9 q^{48} - 2 q^{49} + 27 q^{50} - 19 q^{51} - 62 q^{52} - 50 q^{53} - 27 q^{54} - 66 q^{55} - 19 q^{56} - 45 q^{57} - 55 q^{58} - 118 q^{59} - 29 q^{60} - 92 q^{61} - 61 q^{62} - 54 q^{63} + 71 q^{64} - 51 q^{65} - 73 q^{66} - 17 q^{67} - 52 q^{68} - 89 q^{69} - 33 q^{70} - 95 q^{71} + 34 q^{72} - 114 q^{73} - 43 q^{74} - 38 q^{75} - 30 q^{76} - 73 q^{77} - 40 q^{78} - 47 q^{79} - 34 q^{80} - 57 q^{81} - 87 q^{82} - 68 q^{83} - 51 q^{84} - 67 q^{85} - 4 q^{86} - 55 q^{87} - 37 q^{88} - 150 q^{89} - 81 q^{90} - 23 q^{91} - 45 q^{92} - 59 q^{93} - 89 q^{94} - 47 q^{95} - 9 q^{96} - 97 q^{97} - 2 q^{98} - 57 q^{99}+O(q^{100}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9 - 34 * q^10 - 37 * q^11 - 9 * q^12 - 62 * q^13 - 19 * q^14 - 29 * q^15 + 71 * q^16 - 52 * q^17 + 34 * q^18 - 30 * q^19 - 34 * q^20 - 51 * q^21 - 37 * q^22 - 45 * q^23 - 9 * q^24 + 27 * q^25 - 62 * q^26 - 27 * q^27 - 19 * q^28 - 55 * q^29 - 29 * q^30 - 61 * q^31 + 71 * q^32 - 73 * q^33 - 52 * q^34 - 33 * q^35 + 34 * q^36 - 43 * q^37 - 30 * q^38 - 40 * q^39 - 34 * q^40 - 87 * q^41 - 51 * q^42 - 4 * q^43 - 37 * q^44 - 81 * q^45 - 45 * q^46 - 89 * q^47 - 9 * q^48 - 2 * q^49 + 27 * q^50 - 19 * q^51 - 62 * q^52 - 50 * q^53 - 27 * q^54 - 66 * q^55 - 19 * q^56 - 45 * q^57 - 55 * q^58 - 118 * q^59 - 29 * q^60 - 92 * q^61 - 61 * q^62 - 54 * q^63 + 71 * q^64 - 51 * q^65 - 73 * q^66 - 17 * q^67 - 52 * q^68 - 89 * q^69 - 33 * q^70 - 95 * q^71 + 34 * q^72 - 114 * q^73 - 43 * q^74 - 38 * q^75 - 30 * q^76 - 73 * q^77 - 40 * q^78 - 47 * q^79 - 34 * q^80 - 57 * q^81 - 87 * q^82 - 68 * q^83 - 51 * q^84 - 67 * q^85 - 4 * q^86 - 55 * q^87 - 37 * q^88 - 150 * q^89 - 81 * q^90 - 23 * q^91 - 45 * q^92 - 59 * q^93 - 89 * q^94 - 47 * q^95 - 9 * q^96 - 97 * q^97 - 2 * q^98 - 57 * 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
$3$	−2.91430	−1.68257	−0.841286	−	0.540591i	$-0.818201\pi$
$3$	−2.91430	−1.68257	−0.841286	+	0.540591i	$0.818201\pi$
$4$	1.00000	0.500000
$5$	−0.167675	−0.0749864	−0.0374932	−	0.999297i	$-0.511937\pi$
$5$	−0.167675	−0.0749864	−0.0374932	+	0.999297i	$0.511937\pi$
$6$	−2.91430	−1.18976
$7$	0.471775	0.178314	0.0891571	−	0.996018i	$-0.471583\pi$
$7$	0.471775	0.178314	0.0891571	+	0.996018i	$0.471583\pi$
$8$	1.00000	0.353553
$9$	5.49314	1.83105
$10$	−0.167675	−0.0530234
$11$	3.72184	1.12218	0.561088	−	0.827756i	$-0.310383\pi$
$11$	3.72184	1.12218	0.561088	+	0.827756i	$0.310383\pi$
$12$	−2.91430	−0.841286
$13$	4.10256	1.13785	0.568923	−	0.822391i	$-0.307360\pi$
$13$	4.10256	1.13785	0.568923	+	0.822391i	$0.307360\pi$
$14$	0.471775	0.126087
$15$	0.488654	0.126170
$16$	1.00000	0.250000
$17$	−3.33349	−0.808490	−0.404245	−	0.914651i	$-0.632466\pi$
$17$	−3.33349	−0.808490	−0.404245	+	0.914651i	$0.632466\pi$
$18$	5.49314	1.29475
$19$	−1.99949	−0.458715	−0.229357	−	0.973342i	$-0.573662\pi$
$19$	−1.99949	−0.458715	−0.229357	+	0.973342i	$0.573662\pi$
$20$	−0.167675	−0.0374932
$21$	−1.37489	−0.300026
$22$	3.72184	0.793498
$23$	−0.626646	−0.130665	−0.0653324	−	0.997864i	$-0.520811\pi$
$23$	−0.626646	−0.130665	−0.0653324	+	0.997864i	$0.520811\pi$
$24$	−2.91430	−0.594879
$25$	−4.97189	−0.994377
$26$	4.10256	0.804579
$27$	−7.26576	−1.39830
$28$	0.471775	0.0891571
$29$	−4.42225	−0.821190	−0.410595	−	0.911818i	$-0.634679\pi$
$29$	−4.42225	−0.821190	−0.410595	+	0.911818i	$0.634679\pi$
$30$	0.488654	0.0892156
$31$	−4.37926	−0.786539	−0.393269	−	0.919423i	$-0.628656\pi$
$31$	−4.37926	−0.786539	−0.393269	+	0.919423i	$0.628656\pi$
$32$	1.00000	0.176777
$33$	−10.8465	−1.88814
$34$	−3.33349	−0.571689
$35$	−0.0791047	−0.0133711
$36$	5.49314	0.915523
$37$	−8.13245	−1.33697	−0.668483	−	0.743727i	$-0.733056\pi$
$37$	−8.13245	−1.33697	−0.668483	+	0.743727i	$0.733056\pi$
$38$	−1.99949	−0.324360
$39$	−11.9561	−1.91451
$40$	−0.167675	−0.0265117
$41$	7.95605	1.24253	0.621263	−	0.783602i	$-0.286620\pi$
$41$	7.95605	1.24253	0.621263	+	0.783602i	$0.286620\pi$
$42$	−1.37489	−0.212151
$43$	2.12097	0.323444	0.161722	−	0.986836i	$-0.448295\pi$
$43$	2.12097	0.323444	0.161722	+	0.986836i	$0.448295\pi$
$44$	3.72184	0.561088
$45$	−0.921060	−0.137304
$46$	−0.626646	−0.0923939
$47$	0.489990	0.0714724	0.0357362	−	0.999361i	$-0.488622\pi$
$47$	0.489990	0.0714724	0.0357362	+	0.999361i	$0.488622\pi$
$48$	−2.91430	−0.420643
$49$	−6.77743	−0.968204
$50$	−4.97189	−0.703131
$51$	9.71479	1.36034
$52$	4.10256	0.568923
$53$	−1.65426	−0.227231	−0.113615	−	0.993525i	$-0.536243\pi$
$53$	−1.65426	−0.227231	−0.113615	+	0.993525i	$0.536243\pi$
$54$	−7.26576	−0.988745
$55$	−0.624057	−0.0841479
$56$	0.471775	0.0630436
$57$	5.82712	0.771820
$58$	−4.42225	−0.580669
$59$	−13.0508	−1.69907	−0.849536	−	0.527530i	$-0.823118\pi$
$59$	−13.0508	−1.69907	−0.849536	+	0.527530i	$0.823118\pi$
$60$	0.488654	0.0630850
$61$	−0.248867	−0.0318642	−0.0159321	−	0.999873i	$-0.505072\pi$
$61$	−0.248867	−0.0318642	−0.0159321	+	0.999873i	$0.505072\pi$
$62$	−4.37926	−0.556167
$63$	2.59153	0.326502
$64$	1.00000	0.125000
$65$	−0.687896	−0.0853229
$66$	−10.8465	−1.33512
$67$	−2.36886	−0.289403	−0.144701	−	0.989475i	$-0.546222\pi$
$67$	−2.36886	−0.289403	−0.144701	+	0.989475i	$0.546222\pi$
$68$	−3.33349	−0.404245
$69$	1.82623	0.219853
$70$	−0.0791047	−0.00945482
$71$	12.4156	1.47346	0.736728	−	0.676190i	$-0.236370\pi$
$71$	12.4156	1.47346	0.736728	+	0.676190i	$0.236370\pi$
$72$	5.49314	0.647373
$73$	7.26273	0.850038	0.425019	−	0.905184i	$-0.360267\pi$
$73$	7.26273	0.850038	0.425019	+	0.905184i	$0.360267\pi$
$74$	−8.13245	−0.945378
$75$	14.4896	1.67311
$76$	−1.99949	−0.229357
$77$	1.75587	0.200100
$78$	−11.9561	−1.35376
$79$	−11.6253	−1.30795	−0.653973	−	0.756518i	$-0.726899\pi$
$79$	−11.6253	−1.30795	−0.653973	+	0.756518i	$0.726899\pi$
$80$	−0.167675	−0.0187466
$81$	4.69517	0.521686
$82$	7.95605	0.878599
$83$	5.81448	0.638222	0.319111	−	0.947717i	$-0.396616\pi$
$83$	5.81448	0.638222	0.319111	+	0.947717i	$0.396616\pi$
$84$	−1.37489	−0.150013
$85$	0.558942	0.0606257
$86$	2.12097	0.228710
$87$	12.8877	1.38171
$88$	3.72184	0.396749
$89$	−14.1827	−1.50336	−0.751680	−	0.659527i	$-0.770756\pi$
$89$	−14.1827	−1.50336	−0.751680	+	0.659527i	$0.770756\pi$
$90$	−0.921060	−0.0970883
$91$	1.93549	0.202894
$92$	−0.626646	−0.0653324
$93$	12.7625	1.32341
$94$	0.489990	0.0505386
$95$	0.335264	0.0343974
$96$	−2.91430	−0.297439
$97$	−7.02417	−0.713196	−0.356598	−	0.934258i	$-0.616063\pi$
$97$	−7.02417	−0.713196	−0.356598	+	0.934258i	$0.616063\pi$
$98$	−6.77743	−0.684624
$99$	20.4446	2.05476
$100$	−4.97189	−0.497189
$101$	5.54241	0.551491	0.275745	−	0.961231i	$-0.411075\pi$
$101$	5.54241	0.551491	0.275745	+	0.961231i	$0.411075\pi$
$102$	9.71479	0.961908
$103$	5.70320	0.561953	0.280977	−	0.959715i	$-0.409342\pi$
$103$	5.70320	0.561953	0.280977	+	0.959715i	$0.409342\pi$
$104$	4.10256	0.402289
$105$	0.230535	0.0224979
$106$	−1.65426	−0.160676
$107$	−12.7802	−1.23551	−0.617756	−	0.786370i	$-0.711958\pi$
$107$	−12.7802	−1.23551	−0.617756	+	0.786370i	$0.711958\pi$
$108$	−7.26576	−0.699148
$109$	15.8397	1.51717	0.758585	−	0.651574i	$-0.225891\pi$
$109$	15.8397	1.51717	0.758585	+	0.651574i	$0.225891\pi$
$110$	−0.624057	−0.0595015
$111$	23.7004	2.24954
$112$	0.471775	0.0445786
$113$	2.36837	0.222797	0.111399	−	0.993776i	$-0.464467\pi$
$113$	2.36837	0.222797	0.111399	+	0.993776i	$0.464467\pi$
$114$	5.82712	0.545759
$115$	0.105073	0.00979807
$116$	−4.42225	−0.410595
$117$	22.5360	2.08345
$118$	−13.0508	−1.20143
$119$	−1.57266	−0.144165
$120$	0.488654	0.0446078
$121$	2.85206	0.259278
$122$	−0.248867	−0.0225314
$123$	−23.1863	−2.09064
$124$	−4.37926	−0.393269
$125$	1.67203	0.149551
$126$	2.59153	0.230872
$127$	15.1311	1.34266	0.671332	−	0.741157i	$-0.265722\pi$
$127$	15.1311	1.34266	0.671332	+	0.741157i	$0.265722\pi$
$128$	1.00000	0.0883883
$129$	−6.18113	−0.544218
$130$	−0.687896	−0.0603324
$131$	−9.55394	−0.834732	−0.417366	−	0.908739i	$-0.637047\pi$
$131$	−9.55394	−0.834732	−0.417366	+	0.908739i	$0.637047\pi$
$132$	−10.8465	−0.944070
$133$	−0.943310	−0.0817954
$134$	−2.36886	−0.204639
$135$	1.21828	0.104853
$136$	−3.33349	−0.285845
$137$	−12.8216	−1.09542	−0.547710	−	0.836668i	$-0.684500\pi$
$137$	−12.8216	−1.09542	−0.547710	+	0.836668i	$0.684500\pi$
$138$	1.82623	0.155459
$139$	−19.4117	−1.64648	−0.823238	−	0.567697i	$-0.807835\pi$
$139$	−19.4117	−1.64648	−0.823238	+	0.567697i	$0.807835\pi$
$140$	−0.0791047	−0.00668557
$141$	−1.42798	−0.120257
$142$	12.4156	1.04189
$143$	15.2691	1.27686
$144$	5.49314	0.457762
$145$	0.741498	0.0615781
$146$	7.26273	0.601068
$147$	19.7515	1.62907
$148$	−8.13245	−0.668483
$149$	16.4466	1.34736	0.673680	−	0.739023i	$-0.264713\pi$
$149$	16.4466	1.34736	0.673680	+	0.739023i	$0.264713\pi$
$150$	14.4896	1.18307
$151$	13.2186	1.07571	0.537855	−	0.843037i	$-0.319235\pi$
$151$	13.2186	1.07571	0.537855	+	0.843037i	$0.319235\pi$
$152$	−1.99949	−0.162180
$153$	−18.3113	−1.48038
$154$	1.75587	0.141492
$155$	0.734291	0.0589797
$156$	−11.9561	−0.957254
$157$	−10.6647	−0.851136	−0.425568	−	0.904926i	$-0.639926\pi$
$157$	−10.6647	−0.851136	−0.425568	+	0.904926i	$0.639926\pi$
$158$	−11.6253	−0.924857
$159$	4.82102	0.382332
$160$	−0.167675	−0.0132558
$161$	−0.295636	−0.0232994
$162$	4.69517	0.368888
$163$	−0.862319	−0.0675420	−0.0337710	−	0.999430i	$-0.510752\pi$
$163$	−0.862319	−0.0675420	−0.0337710	+	0.999430i	$0.510752\pi$
$164$	7.95605	0.621263
$165$	1.81869	0.141585
$166$	5.81448	0.451291
$167$	11.5467	0.893512	0.446756	−	0.894656i	$-0.352579\pi$
$167$	11.5467	0.893512	0.446756	+	0.894656i	$0.352579\pi$
$168$	−1.37489	−0.106075
$169$	3.83102	0.294694
$170$	0.558942	0.0428689
$171$	−10.9835	−0.839928
$172$	2.12097	0.161722
$173$	15.0345	1.14305	0.571525	−	0.820585i	$-0.306352\pi$
$173$	15.0345	1.14305	0.571525	+	0.820585i	$0.306352\pi$
$174$	12.8877	0.977018
$175$	−2.34561	−0.177312
$176$	3.72184	0.280544
$177$	38.0340	2.85881
$178$	−14.1827	−1.06304
$179$	12.2906	0.918645	0.459322	−	0.888270i	$-0.348092\pi$
$179$	12.2906	0.918645	0.459322	+	0.888270i	$0.348092\pi$
$180$	−0.921060	−0.0686518
$181$	−26.1232	−1.94173	−0.970863	−	0.239636i	$-0.922972\pi$
$181$	−26.1232	−1.94173	−0.970863	+	0.239636i	$0.922972\pi$
$182$	1.93549	0.143468
$183$	0.725274	0.0536138
$184$	−0.626646	−0.0461970
$185$	1.36360	0.100254
$186$	12.7625	0.935790
$187$	−12.4067	−0.907268
$188$	0.489990	0.0357362
$189$	−3.42780	−0.249336
$190$	0.335264	0.0243226
$191$	−4.08787	−0.295788	−0.147894	−	0.989003i	$-0.547249\pi$
$191$	−4.08787	−0.295788	−0.147894	+	0.989003i	$0.547249\pi$
$192$	−2.91430	−0.210321
$193$	−9.23482	−0.664737	−0.332368	−	0.943150i	$-0.607848\pi$
$193$	−9.23482	−0.664737	−0.332368	+	0.943150i	$0.607848\pi$
$194$	−7.02417	−0.504306
$195$	2.00473	0.143562
$196$	−6.77743	−0.484102
$197$	1.10197	0.0785120	0.0392560	−	0.999229i	$-0.487501\pi$
$197$	1.10197	0.0785120	0.0392560	+	0.999229i	$0.487501\pi$
$198$	20.4446	1.45293
$199$	3.23851	0.229572	0.114786	−	0.993390i	$-0.463382\pi$
$199$	3.23851	0.229572	0.114786	+	0.993390i	$0.463382\pi$
$200$	−4.97189	−0.351565
$201$	6.90358	0.486941
$202$	5.54241	0.389963
$203$	−2.08631	−0.146430
$204$	9.71479	0.680171
$205$	−1.33403	−0.0931725
$206$	5.70320	0.397361
$207$	−3.44226	−0.239253
$208$	4.10256	0.284462
$209$	−7.44178	−0.514759
$210$	0.230535	0.0159084
$211$	8.00164	0.550856	0.275428	−	0.961322i	$-0.411180\pi$
$211$	8.00164	0.550856	0.275428	+	0.961322i	$0.411180\pi$
$212$	−1.65426	−0.113615
$213$	−36.1826	−2.47919
$214$	−12.7802	−0.873639
$215$	−0.355632	−0.0242539
$216$	−7.26576	−0.494372
$217$	−2.06603	−0.140251
$218$	15.8397	1.07280
$219$	−21.1658	−1.43025
$220$	−0.624057	−0.0420739
$221$	−13.6759	−0.919938
$222$	23.7004	1.59067
$223$	−16.3720	−1.09635	−0.548177	−	0.836363i	$-0.684678\pi$
$223$	−16.3720	−1.09635	−0.548177	+	0.836363i	$0.684678\pi$
$224$	0.471775	0.0315218
$225$	−27.3113	−1.82075
$226$	2.36837	0.157542
$227$	−25.9074	−1.71954	−0.859768	−	0.510684i	$-0.829392\pi$
$227$	−25.9074	−1.71954	−0.859768	+	0.510684i	$0.829392\pi$
$228$	5.82712	0.385910
$229$	−20.9780	−1.38627	−0.693133	−	0.720810i	$-0.743770\pi$
$229$	−20.9780	−1.38627	−0.693133	+	0.720810i	$0.743770\pi$
$230$	0.105073	0.00692828
$231$	−5.11713	−0.336682
$232$	−4.42225	−0.290335
$233$	−9.11482	−0.597132	−0.298566	−	0.954389i	$-0.596508\pi$
$233$	−9.11482	−0.597132	−0.298566	+	0.954389i	$0.596508\pi$
$234$	22.5360	1.47322
$235$	−0.0821589	−0.00535946
$236$	−13.0508	−0.849536
$237$	33.8795	2.20071
$238$	−1.57266	−0.101940
$239$	20.4235	1.32109	0.660543	−	0.750788i	$-0.270326\pi$
$239$	20.4235	1.32109	0.660543	+	0.750788i	$0.270326\pi$
$240$	0.488654	0.0315425
$241$	−16.6065	−1.06972	−0.534860	−	0.844941i	$-0.679636\pi$
$241$	−16.6065	−1.06972	−0.534860	+	0.844941i	$0.679636\pi$
$242$	2.85206	0.183338
$243$	8.11413	0.520522
$244$	−0.248867	−0.0159321
$245$	1.13640	0.0726021
$246$	−23.1863	−1.47831
$247$	−8.20304	−0.521947
$248$	−4.37926	−0.278083
$249$	−16.9451	−1.07385
$250$	1.67203	0.105749
$251$	3.37699	0.213154	0.106577	−	0.994304i	$-0.466011\pi$
$251$	3.37699	0.213154	0.106577	+	0.994304i	$0.466011\pi$
$252$	2.59153	0.163251
$253$	−2.33227	−0.146629
$254$	15.1311	0.949407
$255$	−1.62892	−0.102007
$256$	1.00000	0.0625000
$257$	−6.24245	−0.389393	−0.194697	−	0.980864i	$-0.562372\pi$
$257$	−6.24245	−0.389393	−0.194697	+	0.980864i	$0.562372\pi$
$258$	−6.18113	−0.384820
$259$	−3.83669	−0.238400
$260$	−0.687896	−0.0426615
$261$	−24.2920	−1.50364
$262$	−9.55394	−0.590245
$263$	−22.6424	−1.39619	−0.698096	−	0.716004i	$-0.745969\pi$
$263$	−22.6424	−1.39619	−0.698096	+	0.716004i	$0.745969\pi$
$264$	−10.8465	−0.667559
$265$	0.277378	0.0170392
$266$	−0.943310	−0.0578381
$267$	41.3326	2.52951
$268$	−2.36886	−0.144701
$269$	−22.8556	−1.39353	−0.696764	−	0.717300i	$-0.745378\pi$
$269$	−22.8556	−1.39353	−0.696764	+	0.717300i	$0.745378\pi$
$270$	1.21828	0.0741424
$271$	10.7256	0.651536	0.325768	−	0.945450i	$-0.394377\pi$
$271$	10.7256	0.651536	0.325768	+	0.945450i	$0.394377\pi$
$272$	−3.33349	−0.202123
$273$	−5.64059	−0.341384
$274$	−12.8216	−0.774579
$275$	−18.5045	−1.11587
$276$	1.82623	0.109926
$277$	6.52380	0.391977	0.195988	−	0.980606i	$-0.437208\pi$
$277$	6.52380	0.391977	0.195988	+	0.980606i	$0.437208\pi$
$278$	−19.4117	−1.16423
$279$	−24.0559	−1.44019
$280$	−0.0791047	−0.00472741
$281$	−22.1089	−1.31891	−0.659454	−	0.751745i	$-0.729213\pi$
$281$	−22.1089	−1.31891	−0.659454	+	0.751745i	$0.729213\pi$
$282$	−1.42798	−0.0850349
$283$	5.98609	0.355836	0.177918	−	0.984045i	$-0.443064\pi$
$283$	5.98609	0.355836	0.177918	+	0.984045i	$0.443064\pi$
$284$	12.4156	0.736728
$285$	−0.977059	−0.0578760
$286$	15.2691	0.902879
$287$	3.75347	0.221560
$288$	5.49314	0.323686
$289$	−5.88784	−0.346343
$290$	0.741498	0.0435423
$291$	20.4705	1.20000
$292$	7.26273	0.425019
$293$	−12.3677	−0.722531	−0.361265	−	0.932463i	$-0.617655\pi$
$293$	−12.3677	−0.722531	−0.361265	+	0.932463i	$0.617655\pi$
$294$	19.7515	1.15193
$295$	2.18829	0.127407
$296$	−8.13245	−0.472689
$297$	−27.0420	−1.56913
$298$	16.4466	0.952727
$299$	−2.57086	−0.148676
$300$	14.4896	0.836555
$301$	1.00062	0.0576747
$302$	13.2186	0.760642
$303$	−16.1523	−0.927923
$304$	−1.99949	−0.114679
$305$	0.0417287	0.00238938
$306$	−18.3113	−1.04679
$307$	10.5029	0.599432	0.299716	−	0.954029i	$-0.403108\pi$
$307$	10.5029	0.599432	0.299716	+	0.954029i	$0.403108\pi$
$308$	1.75587	0.100050
$309$	−16.6208	−0.945526
$310$	0.734291	0.0417049
$311$	1.48839	0.0843988	0.0421994	−	0.999109i	$-0.486564\pi$
$311$	1.48839	0.0843988	0.0421994	+	0.999109i	$0.486564\pi$
$312$	−11.9561	−0.676881
$313$	3.12573	0.176677	0.0883384	−	0.996091i	$-0.471844\pi$
$313$	3.12573	0.176677	0.0883384	+	0.996091i	$0.471844\pi$
$314$	−10.6647	−0.601844
$315$	−0.434533	−0.0244832
$316$	−11.6253	−0.653973
$317$	17.5755	0.987140	0.493570	−	0.869706i	$-0.335692\pi$
$317$	17.5755	0.987140	0.493570	+	0.869706i	$0.335692\pi$
$318$	4.82102	0.270349
$319$	−16.4589	−0.921520
$320$	−0.167675	−0.00937329
$321$	37.2454	2.07884
$322$	−0.295636	−0.0164752
$323$	6.66529	0.370866
$324$	4.69517	0.260843
$325$	−20.3975	−1.13145
$326$	−0.862319	−0.0477594
$327$	−46.1617	−2.55275
$328$	7.95605	0.439299
$329$	0.231165	0.0127446
$330$	1.81869	0.100116
$331$	17.8052	0.978662	0.489331	−	0.872098i	$-0.337241\pi$
$331$	17.8052	0.978662	0.489331	+	0.872098i	$0.337241\pi$
$332$	5.81448	0.319111
$333$	−44.6727	−2.44805
$334$	11.5467	0.631808
$335$	0.397198	0.0217013
$336$	−1.37489	−0.0750066
$337$	12.3399	0.672198	0.336099	−	0.941827i	$-0.390892\pi$
$337$	12.3399	0.672198	0.336099	+	0.941827i	$0.390892\pi$
$338$	3.83102	0.208380
$339$	−6.90214	−0.374873
$340$	0.558942	0.0303129
$341$	−16.2989	−0.882635
$342$	−10.9835	−0.593919
$343$	−6.49985	−0.350959
$344$	2.12097	0.114355
$345$	−0.306213	−0.0164860
$346$	15.0345	0.808259
$347$	−7.40836	−0.397702	−0.198851	−	0.980030i	$-0.563721\pi$
$347$	−7.40836	−0.397702	−0.198851	+	0.980030i	$0.563721\pi$
$348$	12.8877	0.690856
$349$	−3.90986	−0.209290	−0.104645	−	0.994510i	$-0.533371\pi$
$349$	−3.90986	−0.209290	−0.104645	+	0.994510i	$0.533371\pi$
$350$	−2.34561	−0.125378
$351$	−29.8082	−1.59105
$352$	3.72184	0.198375
$353$	−26.2786	−1.39867	−0.699334	−	0.714795i	$-0.746520\pi$
$353$	−26.2786	−1.39867	−0.699334	+	0.714795i	$0.746520\pi$
$354$	38.0340	2.02148
$355$	−2.08177	−0.110489
$356$	−14.1827	−0.751680
$357$	4.58320	0.242568
$358$	12.2906	0.649580
$359$	−25.9628	−1.37026	−0.685131	−	0.728420i	$-0.740255\pi$
$359$	−25.9628	−1.37026	−0.685131	+	0.728420i	$0.740255\pi$
$360$	−0.921060	−0.0485441
$361$	−15.0020	−0.789581
$362$	−26.1232	−1.37301
$363$	−8.31176	−0.436254
$364$	1.93549	0.101447
$365$	−1.21777	−0.0637412
$366$	0.725274	0.0379107
$367$	31.9179	1.66610	0.833051	−	0.553196i	$-0.186592\pi$
$367$	31.9179	1.66610	0.833051	+	0.553196i	$0.186592\pi$
$368$	−0.626646	−0.0326662
$369$	43.7037	2.27512
$370$	1.36360	0.0708904
$371$	−0.780441	−0.0405185
$372$	12.7625	0.661704
$373$	−5.03015	−0.260452	−0.130226	−	0.991484i	$-0.541570\pi$
$373$	−5.03015	−0.260452	−0.130226	+	0.991484i	$0.541570\pi$
$374$	−12.4067	−0.641536
$375$	−4.87280	−0.251630
$376$	0.489990	0.0252693
$377$	−18.1425	−0.934388
$378$	−3.42780	−0.176307
$379$	−9.31527	−0.478493	−0.239247	−	0.970959i	$-0.576900\pi$
$379$	−9.31527	−0.478493	−0.239247	+	0.970959i	$0.576900\pi$
$380$	0.335264	0.0171987
$381$	−44.0964	−2.25913
$382$	−4.08787	−0.209154
$383$	−16.3017	−0.832980	−0.416490	−	0.909140i	$-0.636740\pi$
$383$	−16.3017	−0.832980	−0.416490	+	0.909140i	$0.636740\pi$
$384$	−2.91430	−0.148720
$385$	−0.294415	−0.0150048
$386$	−9.23482	−0.470040
$387$	11.6508	0.592242
$388$	−7.02417	−0.356598
$389$	−1.97000	−0.0998830	−0.0499415	−	0.998752i	$-0.515903\pi$
$389$	−1.97000	−0.0998830	−0.0499415	+	0.998752i	$0.515903\pi$
$390$	2.00473	0.101514
$391$	2.08892	0.105641
$392$	−6.77743	−0.342312
$393$	27.8430	1.40450
$394$	1.10197	0.0555164
$395$	1.94926	0.0980781
$396$	20.4446	1.02738
$397$	−26.6331	−1.33668	−0.668338	−	0.743857i	$-0.732994\pi$
$397$	−26.6331	−1.33668	−0.668338	+	0.743857i	$0.732994\pi$
$398$	3.23851	0.162332
$399$	2.74909	0.137627
$400$	−4.97189	−0.248594
$401$	1.83126	0.0914489	0.0457244	−	0.998954i	$-0.485440\pi$
$401$	1.83126	0.0914489	0.0457244	+	0.998954i	$0.485440\pi$
$402$	6.90358	0.344319
$403$	−17.9662	−0.894960
$404$	5.54241	0.275745
$405$	−0.787261	−0.0391193
$406$	−2.08631	−0.103542
$407$	−30.2676	−1.50031
$408$	9.71479	0.480954
$409$	23.1014	1.14229	0.571144	−	0.820850i	$-0.306500\pi$
$409$	23.1014	1.14229	0.571144	+	0.820850i	$0.306500\pi$
$410$	−1.33403	−0.0658829
$411$	37.3659	1.84312
$412$	5.70320	0.280977
$413$	−6.15705	−0.302969
$414$	−3.44226	−0.169178
$415$	−0.974940	−0.0478579
$416$	4.10256	0.201145
$417$	56.5714	2.77031
$418$	−7.44178	−0.363989
$419$	−3.66020	−0.178812	−0.0894062	−	0.995995i	$-0.528497\pi$
$419$	−3.66020	−0.178812	−0.0894062	+	0.995995i	$0.528497\pi$
$420$	0.230535	0.0112489
$421$	27.3149	1.33125	0.665623	−	0.746288i	$-0.268166\pi$
$421$	27.3149	1.33125	0.665623	+	0.746288i	$0.268166\pi$
$422$	8.00164	0.389514
$423$	2.69159	0.130869
$424$	−1.65426	−0.0803382
$425$	16.5737	0.803944
$426$	−36.1826	−1.75305
$427$	−0.117409	−0.00568184
$428$	−12.7802	−0.617756
$429$	−44.4986	−2.14841
$430$	−0.355632	−0.0171501
$431$	35.9840	1.73329	0.866643	−	0.498929i	$-0.166273\pi$
$431$	35.9840	1.73329	0.866643	+	0.498929i	$0.166273\pi$
$432$	−7.26576	−0.349574
$433$	21.9189	1.05335	0.526677	−	0.850065i	$-0.323438\pi$
$433$	21.9189	1.05335	0.526677	+	0.850065i	$0.323438\pi$
$434$	−2.06603	−0.0991724
$435$	−2.16095	−0.103610
$436$	15.8397	0.758585
$437$	1.25297	0.0599379
$438$	−21.1658	−1.01134
$439$	−27.7178	−1.32290	−0.661449	−	0.749990i	$-0.730058\pi$
$439$	−27.7178	−1.32290	−0.661449	+	0.749990i	$0.730058\pi$
$440$	−0.624057	−0.0297508
$441$	−37.2294	−1.77283
$442$	−13.6759	−0.650494
$443$	17.1067	0.812764	0.406382	−	0.913703i	$-0.366790\pi$
$443$	17.1067	0.812764	0.406382	+	0.913703i	$0.366790\pi$
$444$	23.7004	1.12477
$445$	2.37808	0.112732
$446$	−16.3720	−0.775239
$447$	−47.9304	−2.26703
$448$	0.471775	0.0222893
$449$	10.9074	0.514750	0.257375	−	0.966312i	$-0.417142\pi$
$449$	10.9074	0.514750	0.257375	+	0.966312i	$0.417142\pi$
$450$	−27.3113	−1.28747
$451$	29.6111	1.39433
$452$	2.36837	0.111399
$453$	−38.5228	−1.80996
$454$	−25.9074	−1.21590
$455$	−0.324532	−0.0152143
$456$	5.82712	0.272880
$457$	−8.10631	−0.379197	−0.189599	−	0.981862i	$-0.560719\pi$
$457$	−8.10631	−0.379197	−0.189599	+	0.981862i	$0.560719\pi$
$458$	−20.9780	−0.980238
$459$	24.2203	1.13051
$460$	0.105073	0.00489904
$461$	−37.5983	−1.75113	−0.875564	−	0.483103i	$-0.839510\pi$
$461$	−37.5983	−1.75113	−0.875564	+	0.483103i	$0.839510\pi$
$462$	−5.11713	−0.238070
$463$	−22.8723	−1.06297	−0.531484	−	0.847068i	$-0.678365\pi$
$463$	−22.8723	−1.06297	−0.531484	+	0.847068i	$0.678365\pi$
$464$	−4.42225	−0.205298
$465$	−2.13994	−0.0992375
$466$	−9.11482	−0.422236
$467$	17.3038	0.800725	0.400363	−	0.916357i	$-0.368884\pi$
$467$	17.3038	0.800725	0.400363	+	0.916357i	$0.368884\pi$
$468$	22.5360	1.04172
$469$	−1.11757	−0.0516046
$470$	−0.0821589	−0.00378971
$471$	31.0802	1.43210
$472$	−13.0508	−0.600713
$473$	7.89389	0.362961
$474$	33.8795	1.55614
$475$	9.94124	0.456135
$476$	−1.57266	−0.0720827
$477$	−9.08711	−0.416070
$478$	20.4235	0.934149
$479$	21.6462	0.989040	0.494520	−	0.869166i	$-0.335344\pi$
$479$	21.6462	0.989040	0.494520	+	0.869166i	$0.335344\pi$
$480$	0.488654	0.0223039
$481$	−33.3639	−1.52126
$482$	−16.6065	−0.756406
$483$	0.861572	0.0392029
$484$	2.85206	0.129639
$485$	1.17777	0.0534800
$486$	8.11413	0.368065
$487$	19.1398	0.867308	0.433654	−	0.901079i	$-0.357224\pi$
$487$	19.1398	0.867308	0.433654	+	0.901079i	$0.357224\pi$
$488$	−0.248867	−0.0112657
$489$	2.51306	0.113644
$490$	1.13640	0.0513374
$491$	−1.87953	−0.0848220	−0.0424110	−	0.999100i	$-0.513504\pi$
$491$	−1.87953	−0.0848220	−0.0424110	+	0.999100i	$0.513504\pi$
$492$	−23.1863	−1.04532
$493$	14.7415	0.663925
$494$	−8.20304	−0.369072
$495$	−3.42803	−0.154079
$496$	−4.37926	−0.196635
$497$	5.85735	0.262738
$498$	−16.9451	−0.759330
$499$	15.1732	0.679246	0.339623	−	0.940562i	$-0.389701\pi$
$499$	15.1732	0.679246	0.339623	+	0.940562i	$0.389701\pi$
$500$	1.67203	0.0747755
$501$	−33.6506	−1.50340
$502$	3.37699	0.150722
$503$	12.5186	0.558176	0.279088	−	0.960266i	$-0.409968\pi$
$503$	12.5186	0.558176	0.279088	+	0.960266i	$0.409968\pi$
$504$	2.59153	0.115436
$505$	−0.929322	−0.0413543
$506$	−2.33227	−0.103682
$507$	−11.1648	−0.495844
$508$	15.1311	0.671332
$509$	−19.5990	−0.868712	−0.434356	−	0.900741i	$-0.643024\pi$
$509$	−19.5990	−0.868712	−0.434356	+	0.900741i	$0.643024\pi$
$510$	−1.62892	−0.0721300
$511$	3.42637	0.151574
$512$	1.00000	0.0441942
$513$	14.5278	0.641419
$514$	−6.24245	−0.275342
$515$	−0.956282	−0.0421388
$516$	−6.18113	−0.272109
$517$	1.82366	0.0802046
$518$	−3.83669	−0.168574
$519$	−43.8150	−1.92326
$520$	−0.687896	−0.0301662
$521$	−38.2320	−1.67498	−0.837488	−	0.546456i	$-0.815977\pi$
$521$	−38.2320	−1.67498	−0.837488	+	0.546456i	$0.815977\pi$
$522$	−24.2920	−1.06323
$523$	27.5717	1.20563	0.602814	−	0.797882i	$-0.294046\pi$
$523$	27.5717	1.20563	0.602814	+	0.797882i	$0.294046\pi$
$524$	−9.55394	−0.417366
$525$	6.83581	0.298339
$526$	−22.6424	−0.987257
$527$	14.5982	0.635909
$528$	−10.8465	−0.472035
$529$	−22.6073	−0.982927
$530$	0.277378	0.0120485
$531$	−71.6900	−3.11108
$532$	−0.943310	−0.0408977
$533$	32.6402	1.41380
$534$	41.3326	1.78864
$535$	2.14292	0.0926466
$536$	−2.36886	−0.102319
$537$	−35.8186	−1.54569
$538$	−22.8556	−0.985373
$539$	−25.2245	−1.08650
$540$	1.21828	0.0524266
$541$	−32.4152	−1.39364	−0.696818	−	0.717248i	$-0.745402\pi$
$541$	−32.4152	−1.39364	−0.696818	+	0.717248i	$0.745402\pi$
$542$	10.7256	0.460705
$543$	76.1310	3.26709
$544$	−3.33349	−0.142922
$545$	−2.65592	−0.113767
$546$	−5.64059	−0.241395
$547$	23.1562	0.990086	0.495043	−	0.868869i	$-0.335152\pi$
$547$	23.1562	0.990086	0.495043	+	0.868869i	$0.335152\pi$
$548$	−12.8216	−0.547710
$549$	−1.36706	−0.0583448
$550$	−18.5045	−0.789036
$551$	8.84224	0.376692
$552$	1.82623	0.0777297
$553$	−5.48452	−0.233225
$554$	6.52380	0.277170
$555$	−3.97395	−0.168685
$556$	−19.4117	−0.823238
$557$	−12.9132	−0.547148	−0.273574	−	0.961851i	$-0.588206\pi$
$557$	−12.9132	−0.547148	−0.273574	+	0.961851i	$0.588206\pi$
$558$	−24.0559	−1.01837
$559$	8.70140	0.368030
$560$	−0.0791047	−0.00334278
$561$	36.1569	1.52654
$562$	−22.1089	−0.932609
$563$	−30.9210	−1.30316	−0.651581	−	0.758579i	$-0.725894\pi$
$563$	−30.9210	−1.30316	−0.651581	+	0.758579i	$0.725894\pi$
$564$	−1.42798	−0.0601287
$565$	−0.397115	−0.0167068
$566$	5.98609	0.251614
$567$	2.21507	0.0930240
$568$	12.4156	0.520945
$569$	−18.1727	−0.761841	−0.380920	−	0.924608i	$-0.624393\pi$
$569$	−18.1727	−0.761841	−0.380920	+	0.924608i	$0.624393\pi$
$570$	−0.977059	−0.0409245
$571$	−38.0654	−1.59299	−0.796494	−	0.604647i	$-0.793314\pi$
$571$	−38.0654	−1.59299	−0.796494	+	0.604647i	$0.793314\pi$
$572$	15.2691	0.638432
$573$	11.9133	0.497685
$574$	3.75347	0.156667
$575$	3.11561	0.129930
$576$	5.49314	0.228881
$577$	−13.3665	−0.556456	−0.278228	−	0.960515i	$-0.589747\pi$
$577$	−13.3665	−0.556456	−0.278228	+	0.960515i	$0.589747\pi$
$578$	−5.88784	−0.244902
$579$	26.9130	1.11847
$580$	0.741498	0.0307890
$581$	2.74313	0.113804
$582$	20.4705	0.848531
$583$	−6.15690	−0.254993
$584$	7.26273	0.300534
$585$	−3.77871	−0.156230
$586$	−12.3677	−0.510906
$587$	−14.5141	−0.599063	−0.299531	−	0.954086i	$-0.596830\pi$
$587$	−14.5141	−0.599063	−0.299531	+	0.954086i	$0.596830\pi$
$588$	19.7515	0.814536
$589$	8.75630	0.360797
$590$	2.18829	0.0900905
$591$	−3.21147	−0.132102
$592$	−8.13245	−0.334242
$593$	−7.67542	−0.315192	−0.157596	−	0.987504i	$-0.550374\pi$
$593$	−7.67542	−0.315192	−0.157596	+	0.987504i	$0.550374\pi$
$594$	−27.0420	−1.10955
$595$	0.263695	0.0108104
$596$	16.4466	0.673680
$597$	−9.43799	−0.386271
$598$	−2.57086	−0.105130
$599$	14.1611	0.578607	0.289303	−	0.957237i	$-0.406576\pi$
$599$	14.1611	0.578607	0.289303	+	0.957237i	$0.406576\pi$
$600$	14.4896	0.591534
$601$	4.64985	0.189672	0.0948358	−	0.995493i	$-0.469767\pi$
$601$	4.64985	0.189672	0.0948358	+	0.995493i	$0.469767\pi$
$602$	1.00062	0.0407822
$603$	−13.0125	−0.529910
$604$	13.2186	0.537855
$605$	−0.478218	−0.0194423
$606$	−16.1523	−0.656140
$607$	−2.47264	−0.100361	−0.0501806	−	0.998740i	$-0.515980\pi$
$607$	−2.47264	−0.100361	−0.0501806	+	0.998740i	$0.515980\pi$
$608$	−1.99949	−0.0810901
$609$	6.08012	0.246379
$610$	0.0417287	0.00168955
$611$	2.01022	0.0813246
$612$	−18.3113	−0.740192
$613$	47.8350	1.93204	0.966018	−	0.258473i	$-0.0832195\pi$
$613$	47.8350	1.93204	0.966018	+	0.258473i	$0.0832195\pi$
$614$	10.5029	0.423862
$615$	3.88776	0.156769
$616$	1.75587	0.0707460
$617$	−28.0953	−1.13107	−0.565537	−	0.824723i	$-0.691331\pi$
$617$	−28.0953	−1.13107	−0.565537	+	0.824723i	$0.691331\pi$
$618$	−16.6208	−0.668588
$619$	−22.2887	−0.895859	−0.447929	−	0.894069i	$-0.647838\pi$
$619$	−22.2887	−0.895859	−0.447929	+	0.894069i	$0.647838\pi$
$620$	0.734291	0.0294898
$621$	4.55306	0.182708
$622$	1.48839	0.0596790
$623$	−6.69104	−0.268071
$624$	−11.9561	−0.478627
$625$	24.5791	0.983163
$626$	3.12573	0.124929
$627$	21.6876	0.866118
$628$	−10.6647	−0.425568
$629$	27.1094	1.08092
$630$	−0.434533	−0.0173122
$631$	7.28351	0.289952	0.144976	−	0.989435i	$-0.453689\pi$
$631$	7.28351	0.289952	0.144976	+	0.989435i	$0.453689\pi$
$632$	−11.6253	−0.462429
$633$	−23.3192	−0.926854
$634$	17.5755	0.698013
$635$	−2.53709	−0.100682
$636$	4.82102	0.191166
$637$	−27.8048	−1.10167
$638$	−16.4589	−0.651613
$639$	68.2004	2.69797
$640$	−0.167675	−0.00662792
$641$	−22.3364	−0.882236	−0.441118	−	0.897449i	$-0.645418\pi$
$641$	−22.3364	−0.882236	−0.441118	+	0.897449i	$0.645418\pi$
$642$	37.2454	1.46996
$643$	49.8394	1.96547	0.982737	−	0.185010i	$-0.0592318\pi$
$643$	49.8394	1.96547	0.982737	+	0.185010i	$0.0592318\pi$
$644$	−0.295636	−0.0116497
$645$	1.03642	0.0408089
$646$	6.66529	0.262242
$647$	−11.5894	−0.455626	−0.227813	−	0.973705i	$-0.573157\pi$
$647$	−11.5894	−0.455626	−0.227813	+	0.973705i	$0.573157\pi$
$648$	4.69517	0.184444
$649$	−48.5730	−1.90666
$650$	−20.3975	−0.800055
$651$	6.02102	0.235982
$652$	−0.862319	−0.0337710
$653$	35.7535	1.39914	0.699571	−	0.714563i	$-0.253374\pi$
$653$	35.7535	1.39914	0.699571	+	0.714563i	$0.253374\pi$
$654$	−46.1617	−1.80506
$655$	1.60195	0.0625935
$656$	7.95605	0.310632
$657$	39.8952	1.55646
$658$	0.231165	0.00901176
$659$	−17.7984	−0.693326	−0.346663	−	0.937990i	$-0.612685\pi$
$659$	−17.7984	−0.693326	−0.346663	+	0.937990i	$0.612685\pi$
$660$	1.81869	0.0707924
$661$	2.02173	0.0786361	0.0393180	−	0.999227i	$-0.487481\pi$
$661$	2.02173	0.0786361	0.0393180	+	0.999227i	$0.487481\pi$
$662$	17.8052	0.692019
$663$	39.8555	1.54786
$664$	5.81448	0.225646
$665$	0.158169	0.00613354
$666$	−44.6727	−1.73103
$667$	2.77118	0.107301
$668$	11.5467	0.446756
$669$	47.7130	1.84469
$670$	0.397198	0.0153451
$671$	−0.926243	−0.0357572
$672$	−1.37489	−0.0530377
$673$	−7.36485	−0.283894	−0.141947	−	0.989874i	$-0.545336\pi$
$673$	−7.36485	−0.283894	−0.141947	+	0.989874i	$0.545336\pi$
$674$	12.3399	0.475316
$675$	36.1245	1.39043
$676$	3.83102	0.147347
$677$	−3.55833	−0.136758	−0.0683788	−	0.997659i	$-0.521783\pi$
$677$	−3.55833	−0.136758	−0.0683788	+	0.997659i	$0.521783\pi$
$678$	−6.90214	−0.265075
$679$	−3.31383	−0.127173
$680$	0.558942	0.0214344
$681$	75.5020	2.89324
$682$	−16.2989	−0.624117
$683$	11.5145	0.440591	0.220295	−	0.975433i	$-0.429298\pi$
$683$	11.5145	0.440591	0.220295	+	0.975433i	$0.429298\pi$
$684$	−10.9835	−0.419964
$685$	2.14985	0.0821416
$686$	−6.49985	−0.248165
$687$	61.1362	2.33249
$688$	2.12097	0.0808611
$689$	−6.78672	−0.258554
$690$	−0.306213	−0.0116573
$691$	26.6059	1.01213	0.506067	−	0.862494i	$-0.331099\pi$
$691$	26.6059	1.01213	0.506067	+	0.862494i	$0.331099\pi$
$692$	15.0345	0.571525
$693$	9.64524	0.366392
$694$	−7.40836	−0.281218
$695$	3.25484	0.123463
$696$	12.8877	0.488509
$697$	−26.5214	−1.00457
$698$	−3.90986	−0.147990
$699$	26.5633	1.00472
$700$	−2.34561	−0.0886558
$701$	31.9057	1.20506	0.602531	−	0.798096i	$-0.294159\pi$
$701$	31.9057	1.20506	0.602531	+	0.798096i	$0.294159\pi$
$702$	−29.8082	−1.12504
$703$	16.2608	0.613286
$704$	3.72184	0.140272
$705$	0.239436	0.00901767
$706$	−26.2786	−0.989008
$707$	2.61477	0.0983386
$708$	38.0340	1.42941
$709$	23.1774	0.870445	0.435222	−	0.900323i	$-0.356670\pi$
$709$	23.1774	0.870445	0.435222	+	0.900323i	$0.356670\pi$
$710$	−2.08177	−0.0781275
$711$	−63.8593	−2.39491
$712$	−14.1827	−0.531518
$713$	2.74425	0.102773
$714$	4.58320	0.171522
$715$	−2.56023	−0.0957473
$716$	12.2906	0.459322
$717$	−59.5202	−2.22282
$718$	−25.9628	−0.968922
$719$	−29.6026	−1.10399	−0.551996	−	0.833847i	$-0.686134\pi$
$719$	−29.6026	−1.10399	−0.551996	+	0.833847i	$0.686134\pi$
$720$	−0.921060	−0.0343259
$721$	2.69063	0.100204
$722$	−15.0020	−0.558318
$723$	48.3963	1.79988
$724$	−26.1232	−0.970863
$725$	21.9869	0.816573
$726$	−8.31176	−0.308478
$727$	−8.61122	−0.319373	−0.159686	−	0.987168i	$-0.551048\pi$
$727$	−8.61122	−0.319373	−0.159686	+	0.987168i	$0.551048\pi$
$728$	1.93549	0.0717339
$729$	−37.7325	−1.39750
$730$	−1.21777	−0.0450719
$731$	−7.07022	−0.261502
$732$	0.725274	0.0268069
$733$	38.9109	1.43721	0.718603	−	0.695421i	$-0.244782\pi$
$733$	38.9109	1.43721	0.718603	+	0.695421i	$0.244782\pi$
$734$	31.9179	1.17811
$735$	−3.31182	−0.122158
$736$	−0.626646	−0.0230985
$737$	−8.81652	−0.324761
$738$	43.7037	1.60876
$739$	−4.79396	−0.176349	−0.0881744	−	0.996105i	$-0.528103\pi$
$739$	−4.79396	−0.176349	−0.0881744	+	0.996105i	$0.528103\pi$
$740$	1.36360	0.0501271
$741$	23.9061	0.878213
$742$	−0.780441	−0.0286509
$743$	−49.6208	−1.82041	−0.910206	−	0.414157i	$-0.864077\pi$
$743$	−49.6208	−1.82041	−0.910206	+	0.414157i	$0.864077\pi$
$744$	12.7625	0.467895
$745$	−2.75768	−0.101034
$746$	−5.03015	−0.184167
$747$	31.9398	1.16861
$748$	−12.4067	−0.453634
$749$	−6.02940	−0.220309
$750$	−4.87280	−0.177930
$751$	−20.4246	−0.745303	−0.372651	−	0.927971i	$-0.621551\pi$
$751$	−20.4246	−0.745303	−0.372651	+	0.927971i	$0.621551\pi$
$752$	0.489990	0.0178681
$753$	−9.84155	−0.358646
$754$	−18.1425	−0.660712
$755$	−2.21642	−0.0806636
$756$	−3.42780	−0.124668
$757$	−48.0786	−1.74745	−0.873723	−	0.486423i	$-0.838301\pi$
$757$	−48.0786	−1.74745	−0.873723	+	0.486423i	$0.838301\pi$
$758$	−9.31527	−0.338346
$759$	6.79694	0.246713
$760$	0.335264	0.0121613
$761$	−33.1049	−1.20005	−0.600026	−	0.799981i	$-0.704843\pi$
$761$	−33.1049	−1.20005	−0.600026	+	0.799981i	$0.704843\pi$
$762$	−44.0964	−1.59745
$763$	7.47278	0.270533
$764$	−4.08787	−0.147894
$765$	3.07035	0.111009
$766$	−16.3017	−0.589006
$767$	−53.5418	−1.93328
$768$	−2.91430	−0.105161
$769$	−3.96271	−0.142899	−0.0714494	−	0.997444i	$-0.522762\pi$
$769$	−3.96271	−0.142899	−0.0714494	+	0.997444i	$0.522762\pi$
$770$	−0.294415	−0.0106100
$771$	18.1924	0.655182
$772$	−9.23482	−0.332368
$773$	24.8986	0.895540	0.447770	−	0.894149i	$-0.352218\pi$
$773$	24.8986	0.895540	0.447770	+	0.894149i	$0.352218\pi$
$774$	11.6508	0.418778
$775$	21.7732	0.782116
$776$	−7.02417	−0.252153
$777$	11.1813	0.401125
$778$	−1.97000	−0.0706279
$779$	−15.9081	−0.569965
$780$	2.00473	0.0717810
$781$	46.2087	1.65348
$782$	2.08892	0.0746996
$783$	32.1310	1.14827
$784$	−6.77743	−0.242051
$785$	1.78820	0.0638236
$786$	27.8430	0.993129
$787$	35.0751	1.25029	0.625147	−	0.780507i	$-0.285039\pi$
$787$	35.0751	1.25029	0.625147	+	0.780507i	$0.285039\pi$
$788$	1.10197	0.0392560
$789$	65.9868	2.34919
$790$	1.94926	0.0693517
$791$	1.11734	0.0397280
$792$	20.4446	0.726466
$793$	−1.02099	−0.0362565
$794$	−26.6331	−0.945173
$795$	−0.808363	−0.0286697
$796$	3.23851	0.114786
$797$	37.0342	1.31182	0.655910	−	0.754839i	$-0.272285\pi$
$797$	37.0342	1.31182	0.655910	+	0.754839i	$0.272285\pi$
$798$	2.74909	0.0973167
$799$	−1.63338	−0.0577848
$800$	−4.97189	−0.175783
$801$	−77.9075	−2.75272
$802$	1.83126	0.0646641
$803$	27.0307	0.953892
$804$	6.90358	0.243470
$805$	0.0495707	0.00174714
$806$	−17.9662	−0.632832
$807$	66.6080	2.34471
$808$	5.54241	0.194981
$809$	0.766858	0.0269613	0.0134806	−	0.999909i	$-0.495709\pi$
$809$	0.766858	0.0269613	0.0134806	+	0.999909i	$0.495709\pi$
$810$	−0.787261	−0.0276615
$811$	−29.8786	−1.04918	−0.524590	−	0.851355i	$-0.675782\pi$
$811$	−29.8786	−1.04918	−0.524590	+	0.851355i	$0.675782\pi$
$812$	−2.08631	−0.0732150
$813$	−31.2577	−1.09626
$814$	−30.2676	−1.06088
$815$	0.144589	0.00506473
$816$	9.71479	0.340086
$817$	−4.24085	−0.148369
$818$	23.1014	0.807720
$819$	10.6319	0.371509
$820$	−1.33403	−0.0465863
$821$	−17.8173	−0.621827	−0.310914	−	0.950438i	$-0.600635\pi$
$821$	−17.8173	−0.621827	−0.310914	+	0.950438i	$0.600635\pi$
$822$	37.3659	1.30328
$823$	26.0269	0.907242	0.453621	−	0.891195i	$-0.350132\pi$
$823$	26.0269	0.907242	0.453621	+	0.891195i	$0.350132\pi$
$824$	5.70320	0.198680
$825$	53.9278	1.87752
$826$	−6.15705	−0.214231
$827$	−16.3040	−0.566947	−0.283474	−	0.958980i	$-0.591487\pi$
$827$	−16.3040	−0.566947	−0.283474	+	0.958980i	$0.591487\pi$
$828$	−3.44226	−0.119627
$829$	−41.8449	−1.45334	−0.726668	−	0.686989i	$-0.758932\pi$
$829$	−41.8449	−1.45334	−0.726668	+	0.686989i	$0.758932\pi$
$830$	−0.974940	−0.0338407
$831$	−19.0123	−0.659529
$832$	4.10256	0.142231
$833$	22.5925	0.782784
$834$	56.5714	1.95891
$835$	−1.93609	−0.0670012
$836$	−7.44178	−0.257379
$837$	31.8187	1.09981
$838$	−3.66020	−0.126439
$839$	1.43127	0.0494130	0.0247065	−	0.999695i	$-0.492135\pi$
$839$	1.43127	0.0494130	0.0247065	+	0.999695i	$0.492135\pi$
$840$	0.230535	0.00795421
$841$	−9.44374	−0.325646
$842$	27.3149	0.941333
$843$	64.4321	2.21916
$844$	8.00164	0.275428
$845$	−0.642365	−0.0220980
$846$	2.69159	0.0925386
$847$	1.34553	0.0462330
$848$	−1.65426	−0.0568077
$849$	−17.4453	−0.598720
$850$	16.5737	0.568474
$851$	5.09617	0.174694
$852$	−36.1826	−1.23960
$853$	12.0040	0.411009	0.205505	−	0.978656i	$-0.434116\pi$
$853$	12.0040	0.411009	0.205505	+	0.978656i	$0.434116\pi$
$854$	−0.117409	−0.00401767
$855$	1.84165	0.0629832
$856$	−12.7802	−0.436820
$857$	−17.6052	−0.601382	−0.300691	−	0.953722i	$-0.597217\pi$
$857$	−17.6052	−0.601382	−0.300691	+	0.953722i	$0.597217\pi$
$858$	−44.4986	−1.51916
$859$	−31.6841	−1.08105	−0.540523	−	0.841329i	$-0.681774\pi$
$859$	−31.6841	−1.08105	−0.540523	+	0.841329i	$0.681774\pi$
$860$	−0.355632	−0.0121270
$861$	−10.9387	−0.372791
$862$	35.9840	1.22562
$863$	23.1236	0.787135	0.393568	−	0.919296i	$-0.371241\pi$
$863$	23.1236	0.787135	0.393568	+	0.919296i	$0.371241\pi$
$864$	−7.26576	−0.247186
$865$	−2.52090	−0.0857132
$866$	21.9189	0.744834
$867$	17.1589	0.582747
$868$	−2.06603	−0.0701255
$869$	−43.2674	−1.46774
$870$	−2.16095	−0.0732630
$871$	−9.71841	−0.329296
$872$	15.8397	0.536401
$873$	−38.5847	−1.30590
$874$	1.25297	0.0423825
$875$	0.788823	0.0266671
$876$	−21.1658	−0.715125
$877$	−19.8698	−0.670956	−0.335478	−	0.942048i	$-0.608898\pi$
$877$	−19.8698	−0.670956	−0.335478	+	0.942048i	$0.608898\pi$
$878$	−27.7178	−0.935430
$879$	36.0433	1.21571
$880$	−0.624057	−0.0210370
$881$	−5.59911	−0.188639	−0.0943195	−	0.995542i	$-0.530068\pi$
$881$	−5.59911	−0.188639	−0.0943195	+	0.995542i	$0.530068\pi$
$882$	−37.2294	−1.25358
$883$	25.4143	0.855261	0.427630	−	0.903954i	$-0.359348\pi$
$883$	25.4143	0.855261	0.427630	+	0.903954i	$0.359348\pi$
$884$	−13.6759	−0.459969
$885$	−6.37734	−0.214372
$886$	17.1067	0.574711
$887$	−0.837361	−0.0281158	−0.0140579	−	0.999901i	$-0.504475\pi$
$887$	−0.837361	−0.0281158	−0.0140579	+	0.999901i	$0.504475\pi$
$888$	23.7004	0.795333
$889$	7.13846	0.239416
$890$	2.37808	0.0797133
$891$	17.4747	0.585423
$892$	−16.3720	−0.548177
$893$	−0.979731	−0.0327855
$894$	−47.9304	−1.60303
$895$	−2.06083	−0.0688858
$896$	0.471775	0.0157609
$897$	7.49224	0.250159
$898$	10.9074	0.363983
$899$	19.3662	0.645898
$900$	−27.3113	−0.910376
$901$	5.51447	0.183714
$902$	29.6111	0.985942
$903$	−2.91610	−0.0970418
$904$	2.36837	0.0787708
$905$	4.38020	0.145603
$906$	−38.5228	−1.27984
$907$	31.7589	1.05454	0.527268	−	0.849699i	$-0.323216\pi$
$907$	31.7589	1.05454	0.527268	+	0.849699i	$0.323216\pi$
$908$	−25.9074	−0.859768
$909$	30.4453	1.00981
$910$	−0.324532	−0.0107581
$911$	15.7206	0.520846	0.260423	−	0.965495i	$-0.416138\pi$
$911$	15.7206	0.520846	0.260423	+	0.965495i	$0.416138\pi$
$912$	5.82712	0.192955
$913$	21.6405	0.716197
$914$	−8.10631	−0.268133
$915$	−0.121610	−0.00402030
$916$	−20.9780	−0.693133
$917$	−4.50731	−0.148845
$918$	24.2203	0.799390
$919$	51.6783	1.70471	0.852356	−	0.522962i	$-0.175173\pi$
$919$	51.6783	1.70471	0.852356	+	0.522962i	$0.175173\pi$
$920$	0.105073	0.00346414
$921$	−30.6086	−1.00859
$922$	−37.5983	−1.23823
$923$	50.9356	1.67657
$924$	−5.11713	−0.168341
$925$	40.4336	1.32945
$926$	−22.8723	−0.751632
$927$	31.3285	1.02896
$928$	−4.42225	−0.145167
$929$	−21.7521	−0.713664	−0.356832	−	0.934169i	$-0.616143\pi$
$929$	−21.7521	−0.713664	−0.356832	+	0.934169i	$0.616143\pi$
$930$	−2.13994	−0.0701715
$931$	13.5514	0.444130
$932$	−9.11482	−0.298566
$933$	−4.33761	−0.142007
$934$	17.3038	0.566198
$935$	2.08029	0.0680327
$936$	22.5360	0.736611
$937$	−10.6803	−0.348909	−0.174454	−	0.984665i	$-0.555816\pi$
$937$	−10.6803	−0.348909	−0.174454	+	0.984665i	$0.555816\pi$
$938$	−1.11757	−0.0364900
$939$	−9.10932	−0.297271
$940$	−0.0821589	−0.00267973
$941$	2.25801	0.0736090	0.0368045	−	0.999322i	$-0.488282\pi$
$941$	2.25801	0.0736090	0.0368045	+	0.999322i	$0.488282\pi$
$942$	31.0802	1.01265
$943$	−4.98563	−0.162354
$944$	−13.0508	−0.424768
$945$	0.574756	0.0186968
$946$	7.89389	0.256652
$947$	23.2417	0.755253	0.377626	−	0.925958i	$-0.376740\pi$
$947$	23.2417	0.755253	0.377626	+	0.925958i	$0.376740\pi$
$948$	33.8795	1.10036
$949$	29.7958	0.967212
$950$	9.94124	0.322536
$951$	−51.2203	−1.66093
$952$	−1.57266	−0.0509701
$953$	20.3948	0.660652	0.330326	−	0.943867i	$-0.392841\pi$
$953$	20.3948	0.660652	0.330326	+	0.943867i	$0.392841\pi$
$954$	−9.08711	−0.294206
$955$	0.685432	0.0221801
$956$	20.4235	0.660543
$957$	47.9661	1.55052
$958$	21.6462	0.699357
$959$	−6.04890	−0.195329
$960$	0.488654	0.0157712
$961$	−11.8221	−0.381357
$962$	−33.3639	−1.07569
$963$	−70.2037	−2.26228
$964$	−16.6065	−0.534860
$965$	1.54844	0.0498462
$966$	0.861572	0.0277206
$967$	−5.74191	−0.184647	−0.0923237	−	0.995729i	$-0.529429\pi$
$967$	−5.74191	−0.184647	−0.0923237	+	0.995729i	$0.529429\pi$
$968$	2.85206	0.0916688
$969$	−19.4246	−0.624009
$970$	1.17777	0.0378161
$971$	5.72120	0.183602	0.0918010	−	0.995777i	$-0.470738\pi$
$971$	5.72120	0.183602	0.0918010	+	0.995777i	$0.470738\pi$
$972$	8.11413	0.260261
$973$	−9.15794	−0.293590
$974$	19.1398	0.613280
$975$	59.4443	1.90374
$976$	−0.248867	−0.00796605
$977$	31.4116	1.00495	0.502473	−	0.864593i	$-0.332424\pi$
$977$	31.4116	1.00495	0.502473	+	0.864593i	$0.332424\pi$
$978$	2.51306	0.0803587
$979$	−52.7856	−1.68704
$980$	1.13640	0.0363010
$981$	87.0098	2.77801
$982$	−1.87953	−0.0599782
$983$	−38.1409	−1.21651	−0.608254	−	0.793743i	$-0.708130\pi$
$983$	−38.1409	−1.21651	−0.608254	+	0.793743i	$0.708130\pi$
$984$	−23.1863	−0.739153
$985$	−0.184772	−0.00588733
$986$	14.7415	0.469466
$987$	−0.673685	−0.0214436
$988$	−8.20304	−0.260973
$989$	−1.32910	−0.0422628
$990$	−3.42803	−0.108950
$991$	−35.7644	−1.13609	−0.568046	−	0.822997i	$-0.692300\pi$
$991$	−35.7644	−1.13609	−0.568046	+	0.822997i	$0.692300\pi$
$992$	−4.37926	−0.139042
$993$	−51.8897	−1.64667
$994$	5.85735	0.185784
$995$	−0.543016	−0.0172148
$996$	−16.9451	−0.536927
$997$	−27.2861	−0.864161	−0.432080	−	0.901835i	$-0.642220\pi$
$997$	−27.2861	−0.864161	−0.432080	+	0.901835i	$0.642220\pi$
$998$	15.1732	0.480299
$999$	59.0884	1.86947

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.a.1.5	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.a.1.5	✓	71	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.91430 q^{3} +1.00000 q^{4} -0.167675 q^{5} -2.91430 q^{6} +0.471775 q^{7} +1.00000 q^{8} +5.49314 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.91430 q^{3} +1.00000 q^{4} -0.167675 q^{5} -2.91430 q^{6} +0.471775 q^{7} +1.00000 q^{8} +5.49314 q^{9} -0.167675 q^{10} +3.72184 q^{11} -2.91430 q^{12} +4.10256 q^{13} +0.471775 q^{14} +0.488654 q^{15} +1.00000 q^{16} -3.33349 q^{17} +5.49314 q^{18} -1.99949 q^{19} -0.167675 q^{20} -1.37489 q^{21} +3.72184 q^{22} -0.626646 q^{23} -2.91430 q^{24} -4.97189 q^{25} +4.10256 q^{26} -7.26576 q^{27} +0.471775 q^{28} -4.42225 q^{29} +0.488654 q^{30} -4.37926 q^{31} +1.00000 q^{32} -10.8465 q^{33} -3.33349 q^{34} -0.0791047 q^{35} +5.49314 q^{36} -8.13245 q^{37} -1.99949 q^{38} -11.9561 q^{39} -0.167675 q^{40} +7.95605 q^{41} -1.37489 q^{42} +2.12097 q^{43} +3.72184 q^{44} -0.921060 q^{45} -0.626646 q^{46} +0.489990 q^{47} -2.91430 q^{48} -6.77743 q^{49} -4.97189 q^{50} +9.71479 q^{51} +4.10256 q^{52} -1.65426 q^{53} -7.26576 q^{54} -0.624057 q^{55} +0.471775 q^{56} +5.82712 q^{57} -4.42225 q^{58} -13.0508 q^{59} +0.488654 q^{60} -0.248867 q^{61} -4.37926 q^{62} +2.59153 q^{63} +1.00000 q^{64} -0.687896 q^{65} -10.8465 q^{66} -2.36886 q^{67} -3.33349 q^{68} +1.82623 q^{69} -0.0791047 q^{70} +12.4156 q^{71} +5.49314 q^{72} +7.26273 q^{73} -8.13245 q^{74} +14.4896 q^{75} -1.99949 q^{76} +1.75587 q^{77} -11.9561 q^{78} -11.6253 q^{79} -0.167675 q^{80} +4.69517 q^{81} +7.95605 q^{82} +5.81448 q^{83} -1.37489 q^{84} +0.558942 q^{85} +2.12097 q^{86} +12.8877 q^{87} +3.72184 q^{88} -14.1827 q^{89} -0.921060 q^{90} +1.93549 q^{91} -0.626646 q^{92} +12.7625 q^{93} +0.489990 q^{94} +0.335264 q^{95} -2.91430 q^{96} -7.02417 q^{97} -6.77743 q^{98} +20.4446 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9}+O(q^{10}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9} - 34 q^{10} - 37 q^{11} - 9 q^{12} - 62 q^{13} - 19 q^{14} - 29 q^{15} + 71 q^{16} - 52 q^{17} + 34 q^{18} - 30 q^{19} - 34 q^{20} - 51 q^{21} - 37 q^{22} - 45 q^{23} - 9 q^{24} + 27 q^{25} - 62 q^{26} - 27 q^{27} - 19 q^{28} - 55 q^{29} - 29 q^{30} - 61 q^{31} + 71 q^{32} - 73 q^{33} - 52 q^{34} - 33 q^{35} + 34 q^{36} - 43 q^{37} - 30 q^{38} - 40 q^{39} - 34 q^{40} - 87 q^{41} - 51 q^{42} - 4 q^{43} - 37 q^{44} - 81 q^{45} - 45 q^{46} - 89 q^{47} - 9 q^{48} - 2 q^{49} + 27 q^{50} - 19 q^{51} - 62 q^{52} - 50 q^{53} - 27 q^{54} - 66 q^{55} - 19 q^{56} - 45 q^{57} - 55 q^{58} - 118 q^{59} - 29 q^{60} - 92 q^{61} - 61 q^{62} - 54 q^{63} + 71 q^{64} - 51 q^{65} - 73 q^{66} - 17 q^{67} - 52 q^{68} - 89 q^{69} - 33 q^{70} - 95 q^{71} + 34 q^{72} - 114 q^{73} - 43 q^{74} - 38 q^{75} - 30 q^{76} - 73 q^{77} - 40 q^{78} - 47 q^{79} - 34 q^{80} - 57 q^{81} - 87 q^{82} - 68 q^{83} - 51 q^{84} - 67 q^{85} - 4 q^{86} - 55 q^{87} - 37 q^{88} - 150 q^{89} - 81 q^{90} - 23 q^{91} - 45 q^{92} - 59 q^{93} - 89 q^{94} - 47 q^{95} - 9 q^{96} - 97 q^{97} - 2 q^{98} - 57 q^{99}+O(q^{100}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9 - 34 * q^10 - 37 * q^11 - 9 * q^12 - 62 * q^13 - 19 * q^14 - 29 * q^15 + 71 * q^16 - 52 * q^17 + 34 * q^18 - 30 * q^19 - 34 * q^20 - 51 * q^21 - 37 * q^22 - 45 * q^23 - 9 * q^24 + 27 * q^25 - 62 * q^26 - 27 * q^27 - 19 * q^28 - 55 * q^29 - 29 * q^30 - 61 * q^31 + 71 * q^32 - 73 * q^33 - 52 * q^34 - 33 * q^35 + 34 * q^36 - 43 * q^37 - 30 * q^38 - 40 * q^39 - 34 * q^40 - 87 * q^41 - 51 * q^42 - 4 * q^43 - 37 * q^44 - 81 * q^45 - 45 * q^46 - 89 * q^47 - 9 * q^48 - 2 * q^49 + 27 * q^50 - 19 * q^51 - 62 * q^52 - 50 * q^53 - 27 * q^54 - 66 * q^55 - 19 * q^56 - 45 * q^57 - 55 * q^58 - 118 * q^59 - 29 * q^60 - 92 * q^61 - 61 * q^62 - 54 * q^63 + 71 * q^64 - 51 * q^65 - 73 * q^66 - 17 * q^67 - 52 * q^68 - 89 * q^69 - 33 * q^70 - 95 * q^71 + 34 * q^72 - 114 * q^73 - 43 * q^74 - 38 * q^75 - 30 * q^76 - 73 * q^77 - 40 * q^78 - 47 * q^79 - 34 * q^80 - 57 * q^81 - 87 * q^82 - 68 * q^83 - 51 * q^84 - 67 * q^85 - 4 * q^86 - 55 * q^87 - 37 * q^88 - 150 * q^89 - 81 * q^90 - 23 * q^91 - 45 * q^92 - 59 * q^93 - 89 * q^94 - 47 * q^95 - 9 * q^96 - 97 * q^97 - 2 * q^98 - 57 * q^99

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