LMFDB - Embedded newform 8026.2.a.c.1.16

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:	$0$
Dimension:	$86$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.07592 q^{3} +1.00000 q^{4} +1.44155 q^{5} +2.07592 q^{6} -4.11205 q^{7} -1.00000 q^{8} +1.30942 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.07592 q^{3} +1.00000 q^{4} +1.44155 q^{5} +2.07592 q^{6} -4.11205 q^{7} -1.00000 q^{8} +1.30942 q^{9} -1.44155 q^{10} +5.99563 q^{11} -2.07592 q^{12} +3.21129 q^{13} +4.11205 q^{14} -2.99254 q^{15} +1.00000 q^{16} +1.06620 q^{17} -1.30942 q^{18} +5.32863 q^{19} +1.44155 q^{20} +8.53627 q^{21} -5.99563 q^{22} -7.12034 q^{23} +2.07592 q^{24} -2.92193 q^{25} -3.21129 q^{26} +3.50949 q^{27} -4.11205 q^{28} +1.85829 q^{29} +2.99254 q^{30} +3.43368 q^{31} -1.00000 q^{32} -12.4464 q^{33} -1.06620 q^{34} -5.92773 q^{35} +1.30942 q^{36} -3.01695 q^{37} -5.32863 q^{38} -6.66637 q^{39} -1.44155 q^{40} +6.35129 q^{41} -8.53627 q^{42} +9.80529 q^{43} +5.99563 q^{44} +1.88760 q^{45} +7.12034 q^{46} -3.24466 q^{47} -2.07592 q^{48} +9.90898 q^{49} +2.92193 q^{50} -2.21333 q^{51} +3.21129 q^{52} +10.5296 q^{53} -3.50949 q^{54} +8.64301 q^{55} +4.11205 q^{56} -11.0618 q^{57} -1.85829 q^{58} +12.9162 q^{59} -2.99254 q^{60} -5.67762 q^{61} -3.43368 q^{62} -5.38442 q^{63} +1.00000 q^{64} +4.62924 q^{65} +12.4464 q^{66} -4.13256 q^{67} +1.06620 q^{68} +14.7812 q^{69} +5.92773 q^{70} +8.70368 q^{71} -1.30942 q^{72} +2.83064 q^{73} +3.01695 q^{74} +6.06568 q^{75} +5.32863 q^{76} -24.6543 q^{77} +6.66637 q^{78} -1.16497 q^{79} +1.44155 q^{80} -11.2137 q^{81} -6.35129 q^{82} +11.9791 q^{83} +8.53627 q^{84} +1.53698 q^{85} -9.80529 q^{86} -3.85765 q^{87} -5.99563 q^{88} -18.4593 q^{89} -1.88760 q^{90} -13.2050 q^{91} -7.12034 q^{92} -7.12802 q^{93} +3.24466 q^{94} +7.68149 q^{95} +2.07592 q^{96} +4.15044 q^{97} -9.90898 q^{98} +7.85083 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) $ 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * 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
$3$	−2.07592	−1.19853	−0.599265	−	0.800551i	$-0.704540\pi$
$3$	−2.07592	−1.19853	−0.599265	+	0.800551i	$0.704540\pi$
$4$	1.00000	0.500000
$5$	1.44155	0.644681	0.322341	−	0.946624i	$-0.395530\pi$
$5$	1.44155	0.644681	0.322341	+	0.946624i	$0.395530\pi$
$6$	2.07592	0.847489
$7$	−4.11205	−1.55421	−0.777105	−	0.629371i	$-0.783313\pi$
$7$	−4.11205	−1.55421	−0.777105	+	0.629371i	$0.783313\pi$
$8$	−1.00000	−0.353553
$9$	1.30942	0.436475
$10$	−1.44155	−0.455859
$11$	5.99563	1.80775	0.903875	−	0.427796i	$-0.140710\pi$
$11$	5.99563	1.80775	0.903875	+	0.427796i	$0.140710\pi$
$12$	−2.07592	−0.599265
$13$	3.21129	0.890652	0.445326	−	0.895368i	$-0.353088\pi$
$13$	3.21129	0.890652	0.445326	+	0.895368i	$0.353088\pi$
$14$	4.11205	1.09899
$15$	−2.99254	−0.772670
$16$	1.00000	0.250000
$17$	1.06620	0.258590	0.129295	−	0.991606i	$-0.458729\pi$
$17$	1.06620	0.258590	0.129295	+	0.991606i	$0.458729\pi$
$18$	−1.30942	−0.308634
$19$	5.32863	1.22247	0.611235	−	0.791449i	$-0.290673\pi$
$19$	5.32863	1.22247	0.611235	+	0.791449i	$0.290673\pi$
$20$	1.44155	0.322341
$21$	8.53627	1.86277
$22$	−5.99563	−1.27827
$23$	−7.12034	−1.48469	−0.742347	−	0.670016i	$-0.766287\pi$
$23$	−7.12034	−1.48469	−0.742347	+	0.670016i	$0.766287\pi$
$24$	2.07592	0.423744
$25$	−2.92193	−0.584386
$26$	−3.21129	−0.629786
$27$	3.50949	0.675402
$28$	−4.11205	−0.777105
$29$	1.85829	0.345076	0.172538	−	0.985003i	$-0.444803\pi$
$29$	1.85829	0.345076	0.172538	+	0.985003i	$0.444803\pi$
$30$	2.99254	0.546360
$31$	3.43368	0.616706	0.308353	−	0.951272i	$-0.400222\pi$
$31$	3.43368	0.616706	0.308353	+	0.951272i	$0.400222\pi$
$32$	−1.00000	−0.176777
$33$	−12.4464	−2.16664
$34$	−1.06620	−0.182851
$35$	−5.92773	−1.00197
$36$	1.30942	0.218237
$37$	−3.01695	−0.495983	−0.247991	−	0.968762i	$-0.579770\pi$
$37$	−3.01695	−0.495983	−0.247991	+	0.968762i	$0.579770\pi$
$38$	−5.32863	−0.864417
$39$	−6.66637	−1.06747
$40$	−1.44155	−0.227929
$41$	6.35129	0.991905	0.495953	−	0.868350i	$-0.334819\pi$
$41$	6.35129	0.991905	0.495953	+	0.868350i	$0.334819\pi$
$42$	−8.53627	−1.31718
$43$	9.80529	1.49529	0.747646	−	0.664097i	$-0.231184\pi$
$43$	9.80529	1.49529	0.747646	+	0.664097i	$0.231184\pi$
$44$	5.99563	0.903875
$45$	1.88760	0.281387
$46$	7.12034	1.04984
$47$	−3.24466	−0.473282	−0.236641	−	0.971597i	$-0.576046\pi$
$47$	−3.24466	−0.473282	−0.236641	+	0.971597i	$0.576046\pi$
$48$	−2.07592	−0.299633
$49$	9.90898	1.41557
$50$	2.92193	0.413223
$51$	−2.21333	−0.309928
$52$	3.21129	0.445326
$53$	10.5296	1.44635	0.723176	−	0.690664i	$-0.242682\pi$
$53$	10.5296	1.44635	0.723176	+	0.690664i	$0.242682\pi$
$54$	−3.50949	−0.477581
$55$	8.64301	1.16542
$56$	4.11205	0.549496
$57$	−11.0618	−1.46517
$58$	−1.85829	−0.244005
$59$	12.9162	1.68155	0.840775	−	0.541385i	$-0.182100\pi$
$59$	12.9162	1.68155	0.840775	+	0.541385i	$0.182100\pi$
$60$	−2.99254	−0.386335
$61$	−5.67762	−0.726945	−0.363472	−	0.931605i	$-0.618409\pi$
$61$	−5.67762	−0.726945	−0.363472	+	0.931605i	$0.618409\pi$
$62$	−3.43368	−0.436077
$63$	−5.38442	−0.678374
$64$	1.00000	0.125000
$65$	4.62924	0.574187
$66$	12.4464	1.53205
$67$	−4.13256	−0.504872	−0.252436	−	0.967614i	$-0.581232\pi$
$67$	−4.13256	−0.504872	−0.252436	+	0.967614i	$0.581232\pi$
$68$	1.06620	0.129295
$69$	14.7812	1.77945
$70$	5.92773	0.708500
$71$	8.70368	1.03294	0.516468	−	0.856306i	$-0.327246\pi$
$71$	8.70368	1.03294	0.516468	+	0.856306i	$0.327246\pi$
$72$	−1.30942	−0.154317
$73$	2.83064	0.331301	0.165651	−	0.986184i	$-0.447028\pi$
$73$	2.83064	0.331301	0.165651	+	0.986184i	$0.447028\pi$
$74$	3.01695	0.350713
$75$	6.06568	0.700404
$76$	5.32863	0.611235
$77$	−24.6543	−2.80962
$78$	6.66637	0.754818
$79$	−1.16497	−0.131069	−0.0655347	−	0.997850i	$-0.520875\pi$
$79$	−1.16497	−0.131069	−0.0655347	+	0.997850i	$0.520875\pi$
$80$	1.44155	0.161170
$81$	−11.2137	−1.24596
$82$	−6.35129	−0.701383
$83$	11.9791	1.31487	0.657436	−	0.753510i	$-0.271641\pi$
$83$	11.9791	1.31487	0.657436	+	0.753510i	$0.271641\pi$
$84$	8.53627	0.931384
$85$	1.53698	0.166708
$86$	−9.80529	−1.05733
$87$	−3.85765	−0.413584
$88$	−5.99563	−0.639136
$89$	−18.4593	−1.95668	−0.978341	−	0.207002i	$-0.933629\pi$
$89$	−18.4593	−1.95668	−0.978341	+	0.207002i	$0.933629\pi$
$90$	−1.88760	−0.198971
$91$	−13.2050	−1.38426
$92$	−7.12034	−0.742347
$93$	−7.12802	−0.739141
$94$	3.24466	0.334661
$95$	7.68149	0.788104
$96$	2.07592	0.211872
$97$	4.15044	0.421413	0.210707	−	0.977549i	$-0.432424\pi$
$97$	4.15044	0.421413	0.210707	+	0.977549i	$0.432424\pi$
$98$	−9.90898	−1.00096
$99$	7.85083	0.789038
$100$	−2.92193	−0.292193
$101$	−5.32081	−0.529441	−0.264720	−	0.964325i	$-0.585280\pi$
$101$	−5.32081	−0.529441	−0.264720	+	0.964325i	$0.585280\pi$
$102$	2.21333	0.219152
$103$	1.93950	0.191105	0.0955525	−	0.995424i	$-0.469538\pi$
$103$	1.93950	0.191105	0.0955525	+	0.995424i	$0.469538\pi$
$104$	−3.21129	−0.314893
$105$	12.3055	1.20089
$106$	−10.5296	−1.02272
$107$	4.93217	0.476811	0.238405	−	0.971166i	$-0.423375\pi$
$107$	4.93217	0.476811	0.238405	+	0.971166i	$0.423375\pi$
$108$	3.50949	0.337701
$109$	−15.5135	−1.48593	−0.742963	−	0.669332i	$-0.766580\pi$
$109$	−15.5135	−1.48593	−0.742963	+	0.669332i	$0.766580\pi$
$110$	−8.64301	−0.824078
$111$	6.26293	0.594451
$112$	−4.11205	−0.388552
$113$	−16.3194	−1.53520	−0.767599	−	0.640930i	$-0.778549\pi$
$113$	−16.3194	−1.53520	−0.767599	+	0.640930i	$0.778549\pi$
$114$	11.0618	1.03603
$115$	−10.2643	−0.957154
$116$	1.85829	0.172538
$117$	4.20495	0.388747
$118$	−12.9162	−1.18904
$119$	−4.38425	−0.401904
$120$	2.99254	0.273180
$121$	24.9476	2.26796
$122$	5.67762	0.514027
$123$	−13.1847	−1.18883
$124$	3.43368	0.308353
$125$	−11.4199	−1.02142
$126$	5.38442	0.479683
$127$	11.8521	1.05171	0.525853	−	0.850576i	$-0.323746\pi$
$127$	11.8521	1.05171	0.525853	+	0.850576i	$0.323746\pi$
$128$	−1.00000	−0.0883883
$129$	−20.3549	−1.79215
$130$	−4.62924	−0.406011
$131$	−11.1715	−0.976059	−0.488030	−	0.872827i	$-0.662284\pi$
$131$	−11.1715	−0.976059	−0.488030	+	0.872827i	$0.662284\pi$
$132$	−12.4464	−1.08332
$133$	−21.9116	−1.89998
$134$	4.13256	0.356998
$135$	5.05911	0.435419
$136$	−1.06620	−0.0914255
$137$	6.19110	0.528942	0.264471	−	0.964394i	$-0.414803\pi$
$137$	6.19110	0.528942	0.264471	+	0.964394i	$0.414803\pi$
$138$	−14.7812	−1.25826
$139$	1.91022	0.162023	0.0810115	−	0.996713i	$-0.474185\pi$
$139$	1.91022	0.162023	0.0810115	+	0.996713i	$0.474185\pi$
$140$	−5.92773	−0.500985
$141$	6.73563	0.567243
$142$	−8.70368	−0.730397
$143$	19.2537	1.61008
$144$	1.30942	0.109119
$145$	2.67882	0.222464
$146$	−2.83064	−0.234265
$147$	−20.5702	−1.69660
$148$	−3.01695	−0.247991
$149$	−10.5010	−0.860274	−0.430137	−	0.902764i	$-0.641535\pi$
$149$	−10.5010	−0.860274	−0.430137	+	0.902764i	$0.641535\pi$
$150$	−6.06568	−0.495261
$151$	−9.82428	−0.799489	−0.399744	−	0.916627i	$-0.630901\pi$
$151$	−9.82428	−0.799489	−0.399744	+	0.916627i	$0.630901\pi$
$152$	−5.32863	−0.432209
$153$	1.39610	0.112868
$154$	24.6543	1.98670
$155$	4.94982	0.397579
$156$	−6.66637	−0.533737
$157$	−0.0348559	−0.00278181	−0.00139090	−	0.999999i	$-0.500443\pi$
$157$	−0.0348559	−0.00278181	−0.00139090	+	0.999999i	$0.500443\pi$
$158$	1.16497	0.0926800
$159$	−21.8585	−1.73350
$160$	−1.44155	−0.113965
$161$	29.2792	2.30753
$162$	11.2137	0.881030
$163$	−1.13792	−0.0891286	−0.0445643	−	0.999007i	$-0.514190\pi$
$163$	−1.13792	−0.0891286	−0.0445643	+	0.999007i	$0.514190\pi$
$164$	6.35129	0.495953
$165$	−17.9422	−1.39679
$166$	−11.9791	−0.929755
$167$	−14.4080	−1.11492	−0.557461	−	0.830203i	$-0.688224\pi$
$167$	−14.4080	−1.11492	−0.557461	+	0.830203i	$0.688224\pi$
$168$	−8.53627	−0.658588
$169$	−2.68760	−0.206738
$170$	−1.53698	−0.117881
$171$	6.97743	0.533578
$172$	9.80529	0.747646
$173$	−23.6418	−1.79745	−0.898727	−	0.438510i	$-0.855507\pi$
$173$	−23.6418	−1.79745	−0.898727	+	0.438510i	$0.855507\pi$
$174$	3.85765	0.292448
$175$	12.0151	0.908258
$176$	5.99563	0.451938
$177$	−26.8130	−2.01539
$178$	18.4593	1.38358
$179$	12.7988	0.956626	0.478313	−	0.878189i	$-0.341248\pi$
$179$	12.7988	0.956626	0.478313	+	0.878189i	$0.341248\pi$
$180$	1.88760	0.140694
$181$	23.0580	1.71388	0.856942	−	0.515412i	$-0.172361\pi$
$181$	23.0580	1.71388	0.856942	+	0.515412i	$0.172361\pi$
$182$	13.2050	0.978820
$183$	11.7863	0.871265
$184$	7.12034	0.524918
$185$	−4.34908	−0.319751
$186$	7.12802	0.522652
$187$	6.39251	0.467467
$188$	−3.24466	−0.236641
$189$	−14.4312	−1.04972
$190$	−7.68149	−0.557274
$191$	17.5004	1.26628	0.633142	−	0.774036i	$-0.281765\pi$
$191$	17.5004	1.26628	0.633142	+	0.774036i	$0.281765\pi$
$192$	−2.07592	−0.149816
$193$	10.1790	0.732704	0.366352	−	0.930476i	$-0.380607\pi$
$193$	10.1790	0.732704	0.366352	+	0.930476i	$0.380607\pi$
$194$	−4.15044	−0.297984
$195$	−9.60992	−0.688180
$196$	9.90898	0.707784
$197$	−1.58375	−0.112838	−0.0564189	−	0.998407i	$-0.517968\pi$
$197$	−1.58375	−0.112838	−0.0564189	+	0.998407i	$0.517968\pi$
$198$	−7.85083	−0.557934
$199$	25.5416	1.81060	0.905298	−	0.424778i	$-0.139648\pi$
$199$	25.5416	1.81060	0.905298	+	0.424778i	$0.139648\pi$
$200$	2.92193	0.206612
$201$	8.57884	0.605104
$202$	5.32081	0.374371
$203$	−7.64139	−0.536320
$204$	−2.21333	−0.154964
$205$	9.15571	0.639463
$206$	−1.93950	−0.135132
$207$	−9.32355	−0.648031
$208$	3.21129	0.222663
$209$	31.9485	2.20992
$210$	−12.3055	−0.849159
$211$	21.1708	1.45746	0.728729	−	0.684802i	$-0.240111\pi$
$211$	21.1708	1.45746	0.728729	+	0.684802i	$0.240111\pi$
$212$	10.5296	0.723176
$213$	−18.0681	−1.23801
$214$	−4.93217	−0.337156
$215$	14.1348	0.963987
$216$	−3.50949	−0.238791
$217$	−14.1195	−0.958491
$218$	15.5135	1.05071
$219$	−5.87617	−0.397075
$220$	8.64301	0.582711
$221$	3.42386	0.230314
$222$	−6.26293	−0.420340
$223$	−13.1191	−0.878520	−0.439260	−	0.898360i	$-0.644759\pi$
$223$	−13.1191	−0.878520	−0.439260	+	0.898360i	$0.644759\pi$
$224$	4.11205	0.274748
$225$	−3.82605	−0.255070
$226$	16.3194	1.08555
$227$	−15.4021	−1.02228	−0.511138	−	0.859499i	$-0.670776\pi$
$227$	−15.4021	−1.02228	−0.511138	+	0.859499i	$0.670776\pi$
$228$	−11.0618	−0.732584
$229$	−3.50073	−0.231335	−0.115667	−	0.993288i	$-0.536901\pi$
$229$	−3.50073	−0.231335	−0.115667	+	0.993288i	$0.536901\pi$
$230$	10.2643	0.676810
$231$	51.1803	3.36742
$232$	−1.85829	−0.122003
$233$	−4.15039	−0.271901	−0.135950	−	0.990716i	$-0.543409\pi$
$233$	−4.15039	−0.271901	−0.135950	+	0.990716i	$0.543409\pi$
$234$	−4.20495	−0.274886
$235$	−4.67734	−0.305116
$236$	12.9162	0.840775
$237$	2.41838	0.157091
$238$	4.38425	0.284189
$239$	27.3980	1.77223	0.886113	−	0.463469i	$-0.153396\pi$
$239$	27.3980	1.77223	0.886113	+	0.463469i	$0.153396\pi$
$240$	−2.99254	−0.193168
$241$	8.54467	0.550411	0.275205	−	0.961385i	$-0.411254\pi$
$241$	8.54467	0.550411	0.275205	+	0.961385i	$0.411254\pi$
$242$	−24.9476	−1.60369
$243$	12.7502	0.817924
$244$	−5.67762	−0.363472
$245$	14.2843	0.912590
$246$	13.1847	0.840629
$247$	17.1118	1.08880
$248$	−3.43368	−0.218039
$249$	−24.8675	−1.57591
$250$	11.4199	0.722256
$251$	−25.5464	−1.61247	−0.806237	−	0.591593i	$-0.798499\pi$
$251$	−25.5464	−1.61247	−0.806237	+	0.591593i	$0.798499\pi$
$252$	−5.38442	−0.339187
$253$	−42.6909	−2.68396
$254$	−11.8521	−0.743668
$255$	−3.19063	−0.199805
$256$	1.00000	0.0625000
$257$	−24.6658	−1.53861	−0.769306	−	0.638880i	$-0.779398\pi$
$257$	−24.6658	−1.53861	−0.769306	+	0.638880i	$0.779398\pi$
$258$	20.3549	1.26724
$259$	12.4058	0.770862
$260$	4.62924	0.287093
$261$	2.43329	0.150617
$262$	11.1715	0.690178
$263$	−6.96314	−0.429365	−0.214683	−	0.976684i	$-0.568872\pi$
$263$	−6.96314	−0.429365	−0.214683	+	0.976684i	$0.568872\pi$
$264$	12.4464	0.766024
$265$	15.1790	0.932435
$266$	21.9116	1.34349
$267$	38.3199	2.34514
$268$	−4.13256	−0.252436
$269$	−28.9974	−1.76800	−0.884002	−	0.467483i	$-0.845161\pi$
$269$	−28.9974	−1.76800	−0.884002	+	0.467483i	$0.845161\pi$
$270$	−5.05911	−0.307888
$271$	−6.97294	−0.423576	−0.211788	−	0.977316i	$-0.567929\pi$
$271$	−6.97294	−0.423576	−0.211788	+	0.977316i	$0.567929\pi$
$272$	1.06620	0.0646476
$273$	27.4125	1.65908
$274$	−6.19110	−0.374018
$275$	−17.5188	−1.05642
$276$	14.7812	0.889725
$277$	−16.0816	−0.966252	−0.483126	−	0.875551i	$-0.660499\pi$
$277$	−16.0816	−0.966252	−0.483126	+	0.875551i	$0.660499\pi$
$278$	−1.91022	−0.114568
$279$	4.49614	0.269177
$280$	5.92773	0.354250
$281$	27.7683	1.65652	0.828258	−	0.560346i	$-0.189332\pi$
$281$	27.7683	1.65652	0.828258	+	0.560346i	$0.189332\pi$
$282$	−6.73563	−0.401101
$283$	−23.2596	−1.38264	−0.691321	−	0.722548i	$-0.742971\pi$
$283$	−23.2596	−1.38264	−0.691321	+	0.722548i	$0.742971\pi$
$284$	8.70368	0.516468
$285$	−15.9461	−0.944566
$286$	−19.2537	−1.13850
$287$	−26.1169	−1.54163
$288$	−1.30942	−0.0771586
$289$	−15.8632	−0.933131
$290$	−2.67882	−0.157306
$291$	−8.61596	−0.505076
$292$	2.83064	0.165651
$293$	17.4510	1.01950	0.509750	−	0.860323i	$-0.329738\pi$
$293$	17.4510	1.01950	0.509750	+	0.860323i	$0.329738\pi$
$294$	20.5702	1.19968
$295$	18.6194	1.08406
$296$	3.01695	0.175356
$297$	21.0416	1.22096
$298$	10.5010	0.608306
$299$	−22.8655	−1.32235
$300$	6.06568	0.350202
$301$	−40.3199	−2.32400
$302$	9.82428	0.565324
$303$	11.0456	0.634551
$304$	5.32863	0.305618
$305$	−8.18458	−0.468648
$306$	−1.39610	−0.0798099
$307$	17.7396	1.01245	0.506226	−	0.862401i	$-0.331040\pi$
$307$	17.7396	1.01245	0.506226	+	0.862401i	$0.331040\pi$
$308$	−24.6543	−1.40481
$309$	−4.02625	−0.229045
$310$	−4.94982	−0.281131
$311$	−10.1502	−0.575565	−0.287783	−	0.957696i	$-0.592918\pi$
$311$	−10.1502	−0.575565	−0.287783	+	0.957696i	$0.592918\pi$
$312$	6.66637	0.377409
$313$	−3.82420	−0.216156	−0.108078	−	0.994142i	$-0.534470\pi$
$313$	−3.82420	−0.216156	−0.108078	+	0.994142i	$0.534470\pi$
$314$	0.0348559	0.00196703
$315$	−7.76192	−0.437335
$316$	−1.16497	−0.0655347
$317$	12.7887	0.718286	0.359143	−	0.933283i	$-0.383069\pi$
$317$	12.7887	0.718286	0.359143	+	0.933283i	$0.383069\pi$
$318$	21.8585	1.22577
$319$	11.1416	0.623811
$320$	1.44155	0.0805852
$321$	−10.2388	−0.571472
$322$	−29.2792	−1.63167
$323$	5.68135	0.316119
$324$	−11.2137	−0.622982
$325$	−9.38317	−0.520485
$326$	1.13792	0.0630234
$327$	32.2048	1.78093
$328$	−6.35129	−0.350691
$329$	13.3422	0.735579
$330$	17.9422	0.987683
$331$	−0.323841	−0.0177999	−0.00889995	−	0.999960i	$-0.502833\pi$
$331$	−0.323841	−0.0177999	−0.00889995	+	0.999960i	$0.502833\pi$
$332$	11.9791	0.657436
$333$	−3.95046	−0.216484
$334$	14.4080	0.788369
$335$	−5.95729	−0.325482
$336$	8.53627	0.465692
$337$	6.56303	0.357511	0.178755	−	0.983894i	$-0.442793\pi$
$337$	6.56303	0.357511	0.178755	+	0.983894i	$0.442793\pi$
$338$	2.68760	0.146186
$339$	33.8777	1.83998
$340$	1.53698	0.0833542
$341$	20.5871	1.11485
$342$	−6.97743	−0.377296
$343$	−11.9619	−0.645880
$344$	−9.80529	−0.528666
$345$	21.3079	1.14718
$346$	23.6418	1.27099
$347$	−7.83547	−0.420630	−0.210315	−	0.977634i	$-0.567449\pi$
$347$	−7.83547	−0.420630	−0.210315	+	0.977634i	$0.567449\pi$
$348$	−3.85765	−0.206792
$349$	−7.38196	−0.395147	−0.197574	−	0.980288i	$-0.563306\pi$
$349$	−7.38196	−0.395147	−0.197574	+	0.980288i	$0.563306\pi$
$350$	−12.0151	−0.642236
$351$	11.2700	0.601548
$352$	−5.99563	−0.319568
$353$	4.57489	0.243497	0.121749	−	0.992561i	$-0.461150\pi$
$353$	4.57489	0.243497	0.121749	+	0.992561i	$0.461150\pi$
$354$	26.8130	1.42510
$355$	12.5468	0.665915
$356$	−18.4593	−0.978341
$357$	9.10133	0.481694
$358$	−12.7988	−0.676437
$359$	−16.8477	−0.889187	−0.444594	−	0.895732i	$-0.646652\pi$
$359$	−16.8477	−0.889187	−0.444594	+	0.895732i	$0.646652\pi$
$360$	−1.88760	−0.0994854
$361$	9.39425	0.494434
$362$	−23.0580	−1.21190
$363$	−51.7891	−2.71822
$364$	−13.2050	−0.692130
$365$	4.08051	0.213584
$366$	−11.7863	−0.616077
$367$	−25.5439	−1.33338	−0.666691	−	0.745335i	$-0.732290\pi$
$367$	−25.5439	−1.33338	−0.666691	+	0.745335i	$0.732290\pi$
$368$	−7.12034	−0.371173
$369$	8.31654	0.432942
$370$	4.34908	0.226098
$371$	−43.2982	−2.24793
$372$	−7.12802	−0.369571
$373$	33.7897	1.74957	0.874783	−	0.484515i	$-0.161004\pi$
$373$	33.7897	1.74957	0.874783	+	0.484515i	$0.161004\pi$
$374$	−6.39251	−0.330549
$375$	23.7067	1.22421
$376$	3.24466	0.167330
$377$	5.96751	0.307343
$378$	14.4312	0.742261
$379$	27.1181	1.39296	0.696481	−	0.717575i	$-0.254748\pi$
$379$	27.1181	1.39296	0.696481	+	0.717575i	$0.254748\pi$
$380$	7.68149	0.394052
$381$	−24.6040	−1.26050
$382$	−17.5004	−0.895398
$383$	11.2691	0.575826	0.287913	−	0.957657i	$-0.407039\pi$
$383$	11.2691	0.575826	0.287913	+	0.957657i	$0.407039\pi$
$384$	2.07592	0.105936
$385$	−35.5405	−1.81131
$386$	−10.1790	−0.518100
$387$	12.8393	0.652658
$388$	4.15044	0.210707
$389$	17.0583	0.864892	0.432446	−	0.901660i	$-0.357651\pi$
$389$	17.0583	0.864892	0.432446	+	0.901660i	$0.357651\pi$
$390$	9.60992	0.486617
$391$	−7.59167	−0.383927
$392$	−9.90898	−0.500479
$393$	23.1911	1.16984
$394$	1.58375	0.0797884
$395$	−1.67936	−0.0844980
$396$	7.85083	0.394519
$397$	−5.86272	−0.294242	−0.147121	−	0.989119i	$-0.547001\pi$
$397$	−5.86272	−0.294242	−0.147121	+	0.989119i	$0.547001\pi$
$398$	−25.5416	−1.28028
$399$	45.4866	2.27718
$400$	−2.92193	−0.146096
$401$	25.4091	1.26887	0.634435	−	0.772976i	$-0.281233\pi$
$401$	25.4091	1.26887	0.634435	+	0.772976i	$0.281233\pi$
$402$	−8.57884	−0.427873
$403$	11.0265	0.549271
$404$	−5.32081	−0.264720
$405$	−16.1651	−0.803250
$406$	7.64139	0.379236
$407$	−18.0885	−0.896613
$408$	2.21333	0.109576
$409$	37.9278	1.87541	0.937703	−	0.347437i	$-0.112948\pi$
$409$	37.9278	1.87541	0.937703	+	0.347437i	$0.112948\pi$
$410$	−9.15571	−0.452168
$411$	−12.8522	−0.633953
$412$	1.93950	0.0955525
$413$	−53.1122	−2.61348
$414$	9.32355	0.458227
$415$	17.2684	0.847674
$416$	−3.21129	−0.157447
$417$	−3.96546	−0.194190
$418$	−31.9485	−1.56265
$419$	5.24610	0.256289	0.128144	−	0.991756i	$-0.459098\pi$
$419$	5.24610	0.256289	0.128144	+	0.991756i	$0.459098\pi$
$420$	12.3055	0.600446
$421$	−6.49858	−0.316721	−0.158361	−	0.987381i	$-0.550621\pi$
$421$	−6.49858	−0.316721	−0.158361	+	0.987381i	$0.550621\pi$
$422$	−21.1708	−1.03058
$423$	−4.24863	−0.206576
$424$	−10.5296	−0.511362
$425$	−3.11535	−0.151117
$426$	18.0681	0.875403
$427$	23.3467	1.12982
$428$	4.93217	0.238405
$429$	−39.9691	−1.92973
$430$	−14.1348	−0.681642
$431$	−15.4246	−0.742978	−0.371489	−	0.928437i	$-0.621153\pi$
$431$	−15.4246	−0.742978	−0.371489	+	0.928437i	$0.621153\pi$
$432$	3.50949	0.168850
$433$	36.3239	1.74562	0.872809	−	0.488063i	$-0.162296\pi$
$433$	36.3239	1.74562	0.872809	+	0.488063i	$0.162296\pi$
$434$	14.1195	0.677756
$435$	−5.56100	−0.266630
$436$	−15.5135	−0.742963
$437$	−37.9416	−1.81499
$438$	5.87617	0.280774
$439$	18.8872	0.901437	0.450719	−	0.892666i	$-0.351168\pi$
$439$	18.8872	0.901437	0.450719	+	0.892666i	$0.351168\pi$
$440$	−8.64301	−0.412039
$441$	12.9751	0.617860
$442$	−3.42386	−0.162857
$443$	16.6464	0.790895	0.395448	−	0.918488i	$-0.370589\pi$
$443$	16.6464	0.790895	0.395448	+	0.918488i	$0.370589\pi$
$444$	6.26293	0.297225
$445$	−26.6100	−1.26144
$446$	13.1191	0.621207
$447$	21.7992	1.03106
$448$	−4.11205	−0.194276
$449$	0.147606	0.00696598	0.00348299	−	0.999994i	$-0.498891\pi$
$449$	0.147606	0.00696598	0.00348299	+	0.999994i	$0.498891\pi$
$450$	3.82605	0.180362
$451$	38.0800	1.79312
$452$	−16.3194	−0.767599
$453$	20.3944	0.958212
$454$	15.4021	0.722858
$455$	−19.0357	−0.892407
$456$	11.0618	0.518015
$457$	2.00120	0.0936120	0.0468060	−	0.998904i	$-0.485096\pi$
$457$	2.00120	0.0936120	0.0468060	+	0.998904i	$0.485096\pi$
$458$	3.50073	0.163578
$459$	3.74180	0.174652
$460$	−10.2643	−0.478577
$461$	34.0566	1.58618	0.793088	−	0.609107i	$-0.208472\pi$
$461$	34.0566	1.58618	0.793088	+	0.609107i	$0.208472\pi$
$462$	−51.1803	−2.38112
$463$	−14.3063	−0.664868	−0.332434	−	0.943126i	$-0.607870\pi$
$463$	−14.3063	−0.664868	−0.332434	+	0.943126i	$0.607870\pi$
$464$	1.85829	0.0862689
$465$	−10.2754	−0.476511
$466$	4.15039	0.192263
$467$	1.77069	0.0819375	0.0409688	−	0.999160i	$-0.486956\pi$
$467$	1.77069	0.0819375	0.0409688	+	0.999160i	$0.486956\pi$
$468$	4.20495	0.194374
$469$	16.9933	0.784677
$470$	4.67734	0.215750
$471$	0.0723579	0.00333408
$472$	−12.9162	−0.594518
$473$	58.7889	2.70312
$474$	−2.41838	−0.111080
$475$	−15.5699	−0.714395
$476$	−4.38425	−0.200952
$477$	13.7877	0.631296
$478$	−27.3980	−1.25315
$479$	38.4803	1.75821	0.879105	−	0.476629i	$-0.158141\pi$
$479$	38.4803	1.75821	0.879105	+	0.476629i	$0.158141\pi$
$480$	2.99254	0.136590
$481$	−9.68830	−0.441748
$482$	−8.54467	−0.389199
$483$	−60.7812	−2.76564
$484$	24.9476	1.13398
$485$	5.98307	0.271677
$486$	−12.7502	−0.578360
$487$	−33.5449	−1.52006	−0.760032	−	0.649886i	$-0.774817\pi$
$487$	−33.5449	−1.52006	−0.760032	+	0.649886i	$0.774817\pi$
$488$	5.67762	0.257014
$489$	2.36222	0.106823
$490$	−14.2843	−0.645299
$491$	1.37731	0.0621570	0.0310785	−	0.999517i	$-0.490106\pi$
$491$	1.37731	0.0621570	0.0310785	+	0.999517i	$0.490106\pi$
$492$	−13.1847	−0.594414
$493$	1.98130	0.0892332
$494$	−17.1118	−0.769895
$495$	11.3174	0.508678
$496$	3.43368	0.154177
$497$	−35.7900	−1.60540
$498$	24.8675	1.11434
$499$	−27.8989	−1.24893	−0.624463	−	0.781054i	$-0.714682\pi$
$499$	−27.8989	−1.24893	−0.624463	+	0.781054i	$0.714682\pi$
$500$	−11.4199	−0.510712
$501$	29.9097	1.33627
$502$	25.5464	1.14019
$503$	41.5295	1.85171	0.925855	−	0.377878i	$-0.123346\pi$
$503$	41.5295	1.85171	0.925855	+	0.377878i	$0.123346\pi$
$504$	5.38442	0.239841
$505$	−7.67023	−0.341321
$506$	42.6909	1.89784
$507$	5.57923	0.247782
$508$	11.8521	0.525853
$509$	19.5799	0.867863	0.433931	−	0.900946i	$-0.357126\pi$
$509$	19.5799	0.867863	0.433931	+	0.900946i	$0.357126\pi$
$510$	3.19063	0.141283
$511$	−11.6397	−0.514912
$512$	−1.00000	−0.0441942
$513$	18.7008	0.825659
$514$	24.6658	1.08796
$515$	2.79590	0.123202
$516$	−20.3549	−0.896077
$517$	−19.4538	−0.855575
$518$	−12.4058	−0.545081
$519$	49.0784	2.15430
$520$	−4.62924	−0.203006
$521$	7.18235	0.314664	0.157332	−	0.987546i	$-0.449711\pi$
$521$	7.18235	0.314664	0.157332	+	0.987546i	$0.449711\pi$
$522$	−2.43329	−0.106502
$523$	2.61100	0.114171	0.0570855	−	0.998369i	$-0.481819\pi$
$523$	2.61100	0.114171	0.0570855	+	0.998369i	$0.481819\pi$
$524$	−11.1715	−0.488030
$525$	−24.9424	−1.08858
$526$	6.96314	0.303607
$527$	3.66097	0.159474
$528$	−12.4464	−0.541661
$529$	27.6992	1.20431
$530$	−15.1790	−0.659331
$531$	16.9128	0.733954
$532$	−21.9116	−0.949988
$533$	20.3959	0.883443
$534$	−38.3199	−1.65827
$535$	7.10997	0.307391
$536$	4.13256	0.178499
$537$	−26.5692	−1.14655
$538$	28.9974	1.25017
$539$	59.4106	2.55899
$540$	5.05911	0.217709
$541$	44.2869	1.90404	0.952022	−	0.306031i	$-0.0990010\pi$
$541$	44.2869	1.90404	0.952022	+	0.306031i	$0.0990010\pi$
$542$	6.97294	0.299513
$543$	−47.8664	−2.05414
$544$	−1.06620	−0.0457127
$545$	−22.3635	−0.957949
$546$	−27.4125	−1.17315
$547$	33.8135	1.44576	0.722881	−	0.690973i	$-0.242818\pi$
$547$	33.8135	1.44576	0.722881	+	0.690973i	$0.242818\pi$
$548$	6.19110	0.264471
$549$	−7.43441	−0.317293
$550$	17.5188	0.747005
$551$	9.90213	0.421845
$552$	−14.7812	−0.629131
$553$	4.79042	0.203709
$554$	16.0816	0.683244
$555$	9.02833	0.383231
$556$	1.91022	0.0810115
$557$	27.4987	1.16516	0.582578	−	0.812775i	$-0.302044\pi$
$557$	27.4987	1.16516	0.582578	+	0.812775i	$0.302044\pi$
$558$	−4.49614	−0.190337
$559$	31.4877	1.33179
$560$	−5.92773	−0.250493
$561$	−13.2703	−0.560273
$562$	−27.7683	−1.17133
$563$	−18.5773	−0.782939	−0.391469	−	0.920191i	$-0.628033\pi$
$563$	−18.5773	−0.782939	−0.391469	+	0.920191i	$0.628033\pi$
$564$	6.73563	0.283621
$565$	−23.5252	−0.989714
$566$	23.2596	0.977675
$567$	46.1112	1.93649
$568$	−8.70368	−0.365198
$569$	20.4075	0.855528	0.427764	−	0.903891i	$-0.359301\pi$
$569$	20.4075	0.855528	0.427764	+	0.903891i	$0.359301\pi$
$570$	15.9461	0.667909
$571$	30.1749	1.26278	0.631391	−	0.775465i	$-0.282484\pi$
$571$	30.1749	1.26278	0.631391	+	0.775465i	$0.282484\pi$
$572$	19.2537	0.805039
$573$	−36.3293	−1.51768
$574$	26.1169	1.09010
$575$	20.8051	0.867634
$576$	1.30942	0.0545594
$577$	−28.4206	−1.18317	−0.591583	−	0.806244i	$-0.701497\pi$
$577$	−28.4206	−1.18317	−0.591583	+	0.806244i	$0.701497\pi$
$578$	15.8632	0.659823
$579$	−21.1308	−0.878168
$580$	2.67882	0.111232
$581$	−49.2585	−2.04359
$582$	8.61596	0.357143
$583$	63.1316	2.61464
$584$	−2.83064	−0.117133
$585$	6.06165	0.250618
$586$	−17.4510	−0.720895
$587$	11.1014	0.458206	0.229103	−	0.973402i	$-0.426421\pi$
$587$	11.1014	0.458206	0.229103	+	0.973402i	$0.426421\pi$
$588$	−20.5702	−0.848301
$589$	18.2968	0.753905
$590$	−18.6194	−0.766549
$591$	3.28774	0.135240
$592$	−3.01695	−0.123996
$593$	3.92649	0.161242	0.0806209	−	0.996745i	$-0.474310\pi$
$593$	3.92649	0.161242	0.0806209	+	0.996745i	$0.474310\pi$
$594$	−21.0416	−0.863348
$595$	−6.32012	−0.259100
$596$	−10.5010	−0.430137
$597$	−53.0222	−2.17005
$598$	22.8655	0.935040
$599$	−26.0503	−1.06439	−0.532193	−	0.846623i	$-0.678632\pi$
$599$	−26.0503	−1.06439	−0.532193	+	0.846623i	$0.678632\pi$
$600$	−6.06568	−0.247630
$601$	−6.18483	−0.252285	−0.126142	−	0.992012i	$-0.540260\pi$
$601$	−6.18483	−0.252285	−0.126142	+	0.992012i	$0.540260\pi$
$602$	40.3199	1.64331
$603$	−5.41127	−0.220364
$604$	−9.82428	−0.399744
$605$	35.9632	1.46211
$606$	−11.0456	−0.448695
$607$	−13.5813	−0.551246	−0.275623	−	0.961266i	$-0.588884\pi$
$607$	−13.5813	−0.551246	−0.275623	+	0.961266i	$0.588884\pi$
$608$	−5.32863	−0.216104
$609$	15.8629	0.642796
$610$	8.18458	0.331384
$611$	−10.4195	−0.421530
$612$	1.39610	0.0564341
$613$	−43.4926	−1.75665	−0.878324	−	0.478065i	$-0.841338\pi$
$613$	−43.4926	−1.75665	−0.878324	+	0.478065i	$0.841338\pi$
$614$	−17.7396	−0.715911
$615$	−19.0065	−0.766416
$616$	24.6543	0.993352
$617$	−33.8468	−1.36262	−0.681311	−	0.731994i	$-0.738590\pi$
$617$	−33.8468	−1.36262	−0.681311	+	0.731994i	$0.738590\pi$
$618$	4.02625	0.161959
$619$	−12.6957	−0.510282	−0.255141	−	0.966904i	$-0.582122\pi$
$619$	−12.6957	−0.510282	−0.255141	+	0.966904i	$0.582122\pi$
$620$	4.94982	0.198790
$621$	−24.9888	−1.00276
$622$	10.1502	0.406986
$623$	75.9056	3.04109
$624$	−6.66637	−0.266868
$625$	−1.85268	−0.0741070
$626$	3.82420	0.152846
$627$	−66.3223	−2.64866
$628$	−0.0348559	−0.00139090
$629$	−3.21665	−0.128256
$630$	7.76192	0.309242
$631$	39.5718	1.57533	0.787665	−	0.616104i	$-0.211290\pi$
$631$	39.5718	1.57533	0.787665	+	0.616104i	$0.211290\pi$
$632$	1.16497	0.0463400
$633$	−43.9488	−1.74681
$634$	−12.7887	−0.507905
$635$	17.0854	0.678015
$636$	−21.8585	−0.866748
$637$	31.8206	1.26078
$638$	−11.1416	−0.441101
$639$	11.3968	0.450851
$640$	−1.44155	−0.0569823
$641$	−7.99850	−0.315922	−0.157961	−	0.987445i	$-0.550492\pi$
$641$	−7.99850	−0.315922	−0.157961	+	0.987445i	$0.550492\pi$
$642$	10.2388	0.404092
$643$	−13.8835	−0.547512	−0.273756	−	0.961799i	$-0.588266\pi$
$643$	−13.8835	−0.547512	−0.273756	+	0.961799i	$0.588266\pi$
$644$	29.2792	1.15376
$645$	−29.3427	−1.15537
$646$	−5.68135	−0.223530
$647$	16.5966	0.652478	0.326239	−	0.945287i	$-0.394219\pi$
$647$	16.5966	0.652478	0.326239	+	0.945287i	$0.394219\pi$
$648$	11.2137	0.440515
$649$	77.4409	3.03982
$650$	9.38317	0.368038
$651$	29.3108	1.14878
$652$	−1.13792	−0.0445643
$653$	7.91079	0.309573	0.154787	−	0.987948i	$-0.450531\pi$
$653$	7.91079	0.309573	0.154787	+	0.987948i	$0.450531\pi$
$654$	−32.2048	−1.25931
$655$	−16.1043	−0.629247
$656$	6.35129	0.247976
$657$	3.70651	0.144605
$658$	−13.3422	−0.520133
$659$	−13.1363	−0.511716	−0.255858	−	0.966714i	$-0.582358\pi$
$659$	−13.1363	−0.511716	−0.255858	+	0.966714i	$0.582358\pi$
$660$	−17.9422	−0.698397
$661$	25.9863	1.01075	0.505376	−	0.862899i	$-0.331354\pi$
$661$	25.9863	1.01075	0.505376	+	0.862899i	$0.331354\pi$
$662$	0.323841	0.0125864
$663$	−7.10765	−0.276038
$664$	−11.9791	−0.464878
$665$	−31.5867	−1.22488
$666$	3.95046	0.153077
$667$	−13.2317	−0.512332
$668$	−14.4080	−0.557461
$669$	27.2341	1.05293
$670$	5.95729	0.230150
$671$	−34.0409	−1.31413
$672$	−8.53627	−0.329294
$673$	−26.2958	−1.01363	−0.506814	−	0.862055i	$-0.669177\pi$
$673$	−26.2958	−1.01363	−0.506814	+	0.862055i	$0.669177\pi$
$674$	−6.56303	−0.252798
$675$	−10.2545	−0.394695
$676$	−2.68760	−0.103369
$677$	−10.9160	−0.419536	−0.209768	−	0.977751i	$-0.567271\pi$
$677$	−10.9160	−0.419536	−0.209768	+	0.977751i	$0.567271\pi$
$678$	−33.8777	−1.30106
$679$	−17.0668	−0.654964
$680$	−1.53698	−0.0589403
$681$	31.9735	1.22523
$682$	−20.5871	−0.788319
$683$	39.4955	1.51125	0.755627	−	0.655002i	$-0.227332\pi$
$683$	39.4955	1.51125	0.755627	+	0.655002i	$0.227332\pi$
$684$	6.97743	0.266789
$685$	8.92479	0.340999
$686$	11.9619	0.456706
$687$	7.26722	0.277262
$688$	9.80529	0.373823
$689$	33.8136	1.28820
$690$	−21.3079	−0.811178
$691$	14.9476	0.568633	0.284317	−	0.958730i	$-0.408233\pi$
$691$	14.9476	0.568633	0.284317	+	0.958730i	$0.408233\pi$
$692$	−23.6418	−0.898727
$693$	−32.2830	−1.22633
$694$	7.83547	0.297430
$695$	2.75368	0.104453
$696$	3.85765	0.146224
$697$	6.77172	0.256497
$698$	7.38196	0.279411
$699$	8.61585	0.325881
$700$	12.0151	0.454129
$701$	−2.70945	−0.102334	−0.0511672	−	0.998690i	$-0.516294\pi$
$701$	−2.70945	−0.102334	−0.0511672	+	0.998690i	$0.516294\pi$
$702$	−11.2700	−0.425359
$703$	−16.0762	−0.606324
$704$	5.99563	0.225969
$705$	9.70976	0.365691
$706$	−4.57489	−0.172178
$707$	21.8795	0.822862
$708$	−26.8130	−1.00769
$709$	−36.1221	−1.35659	−0.678297	−	0.734788i	$-0.737282\pi$
$709$	−36.1221	−1.35659	−0.678297	+	0.734788i	$0.737282\pi$
$710$	−12.5468	−0.470873
$711$	−1.52544	−0.0572085
$712$	18.4593	0.691791
$713$	−24.4489	−0.915620
$714$	−9.10133	−0.340609
$715$	27.7552	1.03799
$716$	12.7988	0.478313
$717$	−56.8758	−2.12407
$718$	16.8477	0.628750
$719$	−21.3608	−0.796624	−0.398312	−	0.917250i	$-0.630404\pi$
$719$	−21.3608	−0.796624	−0.398312	+	0.917250i	$0.630404\pi$
$720$	1.88760	0.0703468
$721$	−7.97534	−0.297017
$722$	−9.39425	−0.349618
$723$	−17.7380	−0.659684
$724$	23.0580	0.856942
$725$	−5.42979	−0.201657
$726$	51.7891	1.92207
$727$	−10.5640	−0.391798	−0.195899	−	0.980624i	$-0.562762\pi$
$727$	−10.5640	−0.391798	−0.195899	+	0.980624i	$0.562762\pi$
$728$	13.2050	0.489410
$729$	7.17275	0.265657
$730$	−4.08051	−0.151027
$731$	10.4544	0.386668
$732$	11.7863	0.435633
$733$	9.00194	0.332494	0.166247	−	0.986084i	$-0.446835\pi$
$733$	9.00194	0.332494	0.166247	+	0.986084i	$0.446835\pi$
$734$	25.5439	0.942843
$735$	−29.6530	−1.09377
$736$	7.12034	0.262459
$737$	−24.7773	−0.912683
$738$	−8.31654	−0.306136
$739$	14.0902	0.518318	0.259159	−	0.965835i	$-0.416555\pi$
$739$	14.0902	0.518318	0.259159	+	0.965835i	$0.416555\pi$
$740$	−4.34908	−0.159875
$741$	−35.5226	−1.30496
$742$	43.2982	1.58953
$743$	9.25927	0.339690	0.169845	−	0.985471i	$-0.445673\pi$
$743$	9.25927	0.339690	0.169845	+	0.985471i	$0.445673\pi$
$744$	7.12802	0.261326
$745$	−15.1377	−0.554603
$746$	−33.7897	−1.23713
$747$	15.6857	0.573909
$748$	6.39251	0.233733
$749$	−20.2813	−0.741064
$750$	−23.7067	−0.865646
$751$	−45.5881	−1.66353	−0.831766	−	0.555126i	$-0.812670\pi$
$751$	−45.5881	−1.66353	−0.831766	+	0.555126i	$0.812670\pi$
$752$	−3.24466	−0.118320
$753$	53.0321	1.93260
$754$	−5.96751	−0.217324
$755$	−14.1622	−0.515416
$756$	−14.4312	−0.524858
$757$	22.3596	0.812672	0.406336	−	0.913724i	$-0.366806\pi$
$757$	22.3596	0.812672	0.406336	+	0.913724i	$0.366806\pi$
$758$	−27.1181	−0.984973
$759$	88.6228	3.21680
$760$	−7.68149	−0.278637
$761$	−18.9509	−0.686968	−0.343484	−	0.939159i	$-0.611607\pi$
$761$	−18.9509	−0.686968	−0.343484	+	0.939159i	$0.611607\pi$
$762$	24.6040	0.891309
$763$	63.7924	2.30944
$764$	17.5004	0.633142
$765$	2.01255	0.0727640
$766$	−11.2691	−0.407171
$767$	41.4778	1.49768
$768$	−2.07592	−0.0749081
$769$	11.7125	0.422364	0.211182	−	0.977447i	$-0.432269\pi$
$769$	11.7125	0.422364	0.211182	+	0.977447i	$0.432269\pi$
$770$	35.5405	1.28079
$771$	51.2042	1.84407
$772$	10.1790	0.366352
$773$	18.1788	0.653844	0.326922	−	0.945051i	$-0.393989\pi$
$773$	18.1788	0.653844	0.326922	+	0.945051i	$0.393989\pi$
$774$	−12.8393	−0.461499
$775$	−10.0330	−0.360395
$776$	−4.15044	−0.148992
$777$	−25.7535	−0.923901
$778$	−17.0583	−0.611571
$779$	33.8437	1.21257
$780$	−9.60992	−0.344090
$781$	52.1840	1.86729
$782$	7.59167	0.271478
$783$	6.52165	0.233065
$784$	9.90898	0.353892
$785$	−0.0502466	−0.00179338
$786$	−23.1911	−0.827200
$787$	26.7883	0.954900	0.477450	−	0.878659i	$-0.341561\pi$
$787$	26.7883	0.954900	0.477450	+	0.878659i	$0.341561\pi$
$788$	−1.58375	−0.0564189
$789$	14.4549	0.514608
$790$	1.67936	0.0597491
$791$	67.1062	2.38602
$792$	−7.85083	−0.278967
$793$	−18.2325	−0.647455
$794$	5.86272	0.208060
$795$	−31.5102	−1.11755
$796$	25.5416	0.905298
$797$	36.2285	1.28328	0.641640	−	0.767006i	$-0.278255\pi$
$797$	36.2285	1.28328	0.641640	+	0.767006i	$0.278255\pi$
$798$	−45.4866	−1.61021
$799$	−3.45944	−0.122386
$800$	2.92193	0.103306
$801$	−24.1711	−0.854042
$802$	−25.4091	−0.897227
$803$	16.9715	0.598910
$804$	8.57884	0.302552
$805$	42.2075	1.48762
$806$	−11.0265	−0.388393
$807$	60.1962	2.11901
$808$	5.32081	0.187186
$809$	48.6335	1.70986	0.854932	−	0.518740i	$-0.173599\pi$
$809$	48.6335	1.70986	0.854932	+	0.518740i	$0.173599\pi$
$810$	16.1651	0.567984
$811$	−37.0639	−1.30149	−0.650745	−	0.759296i	$-0.725543\pi$
$811$	−37.0639	−1.30149	−0.650745	+	0.759296i	$0.725543\pi$
$812$	−7.64139	−0.268160
$813$	14.4752	0.507669
$814$	18.0885	0.634001
$815$	−1.64037	−0.0574595
$816$	−2.21333	−0.0774821
$817$	52.2487	1.82795
$818$	−37.9278	−1.32611
$819$	−17.2910	−0.604195
$820$	9.15571	0.319731
$821$	−12.4307	−0.433833	−0.216917	−	0.976190i	$-0.569600\pi$
$821$	−12.4307	−0.433833	−0.216917	+	0.976190i	$0.569600\pi$
$822$	12.8522	0.448272
$823$	43.2880	1.50892	0.754462	−	0.656344i	$-0.227898\pi$
$823$	43.2880	1.50892	0.754462	+	0.656344i	$0.227898\pi$
$824$	−1.93950	−0.0675658
$825$	36.3676	1.26616
$826$	53.1122	1.84801
$827$	14.1892	0.493407	0.246703	−	0.969091i	$-0.420653\pi$
$827$	14.1892	0.493407	0.246703	+	0.969091i	$0.420653\pi$
$828$	−9.32355	−0.324016
$829$	−33.3618	−1.15870	−0.579352	−	0.815078i	$-0.696694\pi$
$829$	−33.3618	−1.15870	−0.579352	+	0.815078i	$0.696694\pi$
$830$	−17.2684	−0.599396
$831$	33.3841	1.15808
$832$	3.21129	0.111332
$833$	10.5649	0.366052
$834$	3.96546	0.137313
$835$	−20.7698	−0.718770
$836$	31.9485	1.10496
$837$	12.0505	0.416525
$838$	−5.24610	−0.181224
$839$	−44.1248	−1.52336	−0.761679	−	0.647955i	$-0.775624\pi$
$839$	−44.1248	−1.52336	−0.761679	+	0.647955i	$0.775624\pi$
$840$	−12.3055	−0.424579
$841$	−25.5468	−0.880923
$842$	6.49858	0.223956
$843$	−57.6446	−1.98539
$844$	21.1708	0.728729
$845$	−3.87431	−0.133280
$846$	4.24863	0.146071
$847$	−102.586	−3.52489
$848$	10.5296	0.361588
$849$	48.2850	1.65714
$850$	3.11535	0.106856
$851$	21.4817	0.736383
$852$	−18.0681	−0.619003
$853$	7.35164	0.251715	0.125858	−	0.992048i	$-0.459832\pi$
$853$	7.35164	0.251715	0.125858	+	0.992048i	$0.459832\pi$
$854$	−23.3467	−0.798907
$855$	10.0583	0.343988
$856$	−4.93217	−0.168578
$857$	27.2076	0.929393	0.464697	−	0.885470i	$-0.346163\pi$
$857$	27.2076	0.929393	0.464697	+	0.885470i	$0.346163\pi$
$858$	39.9691	1.36452
$859$	−11.8647	−0.404817	−0.202409	−	0.979301i	$-0.564877\pi$
$859$	−11.8647	−0.404817	−0.202409	+	0.979301i	$0.564877\pi$
$860$	14.1348	0.481994
$861$	54.2164	1.84769
$862$	15.4246	0.525365
$863$	44.9141	1.52889	0.764446	−	0.644688i	$-0.223013\pi$
$863$	44.9141	1.52889	0.764446	+	0.644688i	$0.223013\pi$
$864$	−3.50949	−0.119395
$865$	−34.0809	−1.15878
$866$	−36.3239	−1.23434
$867$	32.9307	1.11839
$868$	−14.1195	−0.479246
$869$	−6.98473	−0.236941
$870$	5.56100	0.188536
$871$	−13.2708	−0.449665
$872$	15.5135	0.525354
$873$	5.43469	0.183936
$874$	37.9416	1.28339
$875$	46.9591	1.58751
$876$	−5.87617	−0.198537
$877$	−35.3290	−1.19297	−0.596487	−	0.802623i	$-0.703437\pi$
$877$	−35.3290	−1.19297	−0.596487	+	0.802623i	$0.703437\pi$
$878$	−18.8872	−0.637412
$879$	−36.2269	−1.22190
$880$	8.64301	0.291356
$881$	26.2405	0.884063	0.442032	−	0.896999i	$-0.354258\pi$
$881$	26.2405	0.884063	0.442032	+	0.896999i	$0.354258\pi$
$882$	−12.9751	−0.436893
$883$	−54.1862	−1.82351	−0.911756	−	0.410732i	$-0.865273\pi$
$883$	−54.1862	−1.82351	−0.911756	+	0.410732i	$0.865273\pi$
$884$	3.42386	0.115157
$885$	−38.6523	−1.29928
$886$	−16.6464	−0.559248
$887$	27.3551	0.918496	0.459248	−	0.888308i	$-0.348119\pi$
$887$	27.3551	0.918496	0.459248	+	0.888308i	$0.348119\pi$
$888$	−6.26293	−0.210170
$889$	−48.7365	−1.63457
$890$	26.6100	0.891970
$891$	−67.2331	−2.25239
$892$	−13.1191	−0.439260
$893$	−17.2896	−0.578573
$894$	−21.7992	−0.729073
$895$	18.4501	0.616719
$896$	4.11205	0.137374
$897$	47.4668	1.58487
$898$	−0.147606	−0.00492569
$899$	6.38076	0.212810
$900$	−3.82605	−0.127535
$901$	11.2266	0.374012
$902$	−38.0800	−1.26793
$903$	83.7006	2.78538
$904$	16.3194	0.542775
$905$	33.2392	1.10491
$906$	−20.3944	−0.677558
$907$	39.0075	1.29522	0.647612	−	0.761970i	$-0.275768\pi$
$907$	39.0075	1.29522	0.647612	+	0.761970i	$0.275768\pi$
$908$	−15.4021	−0.511138
$909$	−6.96721	−0.231088
$910$	19.0357	0.631027
$911$	−41.1706	−1.36404	−0.682021	−	0.731332i	$-0.738899\pi$
$911$	−41.1706	−1.36404	−0.682021	+	0.731332i	$0.738899\pi$
$912$	−11.0618	−0.366292
$913$	71.8220	2.37696
$914$	−2.00120	−0.0661937
$915$	16.9905	0.561688
$916$	−3.50073	−0.115667
$917$	45.9378	1.51700
$918$	−3.74180	−0.123498
$919$	36.9908	1.22022	0.610108	−	0.792319i	$-0.291126\pi$
$919$	36.9908	1.22022	0.610108	+	0.792319i	$0.291126\pi$
$920$	10.2643	0.338405
$921$	−36.8259	−1.21345
$922$	−34.0566	−1.12160
$923$	27.9501	0.919988
$924$	51.1803	1.68371
$925$	8.81531	0.289845
$926$	14.3063	0.470133
$927$	2.53964	0.0834126
$928$	−1.85829	−0.0610013
$929$	−14.1454	−0.464096	−0.232048	−	0.972704i	$-0.574543\pi$
$929$	−14.1454	−0.464096	−0.232048	+	0.972704i	$0.574543\pi$
$930$	10.2754	0.336944
$931$	52.8012	1.73049
$932$	−4.15039	−0.135950
$933$	21.0710	0.689833
$934$	−1.77069	−0.0579386
$935$	9.21513	0.301367
$936$	−4.20495	−0.137443
$937$	6.06325	0.198078	0.0990389	−	0.995084i	$-0.468423\pi$
$937$	6.06325	0.198078	0.0990389	+	0.995084i	$0.468423\pi$
$938$	−16.9933	−0.554850
$939$	7.93871	0.259070
$940$	−4.67734	−0.152558
$941$	−32.2736	−1.05209	−0.526044	−	0.850457i	$-0.676325\pi$
$941$	−32.2736	−1.05209	−0.526044	+	0.850457i	$0.676325\pi$
$942$	−0.0723579	−0.00235755
$943$	−45.2234	−1.47268
$944$	12.9162	0.420388
$945$	−20.8033	−0.676732
$946$	−58.7889	−1.91139
$947$	55.4974	1.80342	0.901711	−	0.432339i	$-0.142311\pi$
$947$	55.4974	1.80342	0.901711	+	0.432339i	$0.142311\pi$
$948$	2.41838	0.0785453
$949$	9.09001	0.295074
$950$	15.5699	0.505153
$951$	−26.5483	−0.860888
$952$	4.38425	0.142094
$953$	44.2593	1.43370	0.716850	−	0.697227i	$-0.245583\pi$
$953$	44.2593	1.43370	0.716850	+	0.697227i	$0.245583\pi$
$954$	−13.7877	−0.446394
$955$	25.2277	0.816349
$956$	27.3980	0.886113
$957$	−23.1291	−0.747656
$958$	−38.4803	−1.24324
$959$	−25.4581	−0.822086
$960$	−2.99254	−0.0965838
$961$	−19.2099	−0.619673
$962$	9.68830	0.312363
$963$	6.45830	0.208116
$964$	8.54467	0.275205
$965$	14.6736	0.472360
$966$	60.7812	1.95560
$967$	−18.2057	−0.585457	−0.292728	−	0.956196i	$-0.594563\pi$
$967$	−18.2057	−0.585457	−0.292728	+	0.956196i	$0.594563\pi$
$968$	−24.9476	−0.801846
$969$	−11.7940	−0.378878
$970$	−5.98307	−0.192105
$971$	9.33567	0.299596	0.149798	−	0.988717i	$-0.452138\pi$
$971$	9.33567	0.299596	0.149798	+	0.988717i	$0.452138\pi$
$972$	12.7502	0.408962
$973$	−7.85494	−0.251818
$974$	33.5449	1.07485
$975$	19.4787	0.623817
$976$	−5.67762	−0.181736
$977$	−36.0629	−1.15375	−0.576877	−	0.816831i	$-0.695729\pi$
$977$	−36.0629	−1.15375	−0.576877	+	0.816831i	$0.695729\pi$
$978$	−2.36222	−0.0755355
$979$	−110.675	−3.53719
$980$	14.2843	0.456295
$981$	−20.3138	−0.648569
$982$	−1.37731	−0.0439516
$983$	−2.97905	−0.0950170	−0.0475085	−	0.998871i	$-0.515128\pi$
$983$	−2.97905	−0.0950170	−0.0475085	+	0.998871i	$0.515128\pi$
$984$	13.1847	0.420314
$985$	−2.28306	−0.0727445
$986$	−1.98130	−0.0630974
$987$	−27.6973	−0.881614
$988$	17.1118	0.544398
$989$	−69.8170	−2.22005
$990$	−11.3174	−0.359690
$991$	31.6796	1.00633	0.503167	−	0.864189i	$-0.332168\pi$
$991$	31.6796	1.00633	0.503167	+	0.864189i	$0.332168\pi$
$992$	−3.43368	−0.109019
$993$	0.672266	0.0213337
$994$	35.7900	1.13519
$995$	36.8195	1.16726
$996$	−24.8675	−0.787957
$997$	39.1745	1.24067	0.620335	−	0.784337i	$-0.286997\pi$
$997$	39.1745	1.24067	0.620335	+	0.784337i	$0.286997\pi$
$998$	27.8989	0.883124
$999$	−10.5879	−0.334988

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.c.1.16	✓	86

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.c.1.16	✓	86	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.07592 q^{3} +1.00000 q^{4} +1.44155 q^{5} +2.07592 q^{6} -4.11205 q^{7} -1.00000 q^{8} +1.30942 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.07592 q^{3} +1.00000 q^{4} +1.44155 q^{5} +2.07592 q^{6} -4.11205 q^{7} -1.00000 q^{8} +1.30942 q^{9} -1.44155 q^{10} +5.99563 q^{11} -2.07592 q^{12} +3.21129 q^{13} +4.11205 q^{14} -2.99254 q^{15} +1.00000 q^{16} +1.06620 q^{17} -1.30942 q^{18} +5.32863 q^{19} +1.44155 q^{20} +8.53627 q^{21} -5.99563 q^{22} -7.12034 q^{23} +2.07592 q^{24} -2.92193 q^{25} -3.21129 q^{26} +3.50949 q^{27} -4.11205 q^{28} +1.85829 q^{29} +2.99254 q^{30} +3.43368 q^{31} -1.00000 q^{32} -12.4464 q^{33} -1.06620 q^{34} -5.92773 q^{35} +1.30942 q^{36} -3.01695 q^{37} -5.32863 q^{38} -6.66637 q^{39} -1.44155 q^{40} +6.35129 q^{41} -8.53627 q^{42} +9.80529 q^{43} +5.99563 q^{44} +1.88760 q^{45} +7.12034 q^{46} -3.24466 q^{47} -2.07592 q^{48} +9.90898 q^{49} +2.92193 q^{50} -2.21333 q^{51} +3.21129 q^{52} +10.5296 q^{53} -3.50949 q^{54} +8.64301 q^{55} +4.11205 q^{56} -11.0618 q^{57} -1.85829 q^{58} +12.9162 q^{59} -2.99254 q^{60} -5.67762 q^{61} -3.43368 q^{62} -5.38442 q^{63} +1.00000 q^{64} +4.62924 q^{65} +12.4464 q^{66} -4.13256 q^{67} +1.06620 q^{68} +14.7812 q^{69} +5.92773 q^{70} +8.70368 q^{71} -1.30942 q^{72} +2.83064 q^{73} +3.01695 q^{74} +6.06568 q^{75} +5.32863 q^{76} -24.6543 q^{77} +6.66637 q^{78} -1.16497 q^{79} +1.44155 q^{80} -11.2137 q^{81} -6.35129 q^{82} +11.9791 q^{83} +8.53627 q^{84} +1.53698 q^{85} -9.80529 q^{86} -3.85765 q^{87} -5.99563 q^{88} -18.4593 q^{89} -1.88760 q^{90} -13.2050 q^{91} -7.12034 q^{92} -7.12802 q^{93} +3.24466 q^{94} +7.68149 q^{95} +2.07592 q^{96} +4.15044 q^{97} -9.90898 q^{98} +7.85083 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * q^99

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