LMFDB - Embedded newform 7942.2.a.bs.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7942,2,Mod(1,7942)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7942, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("7942.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7942 = 2 \cdot 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7942.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:	$63.4171892853$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 21 x^{10} + 59 x^{9} + 162 x^{8} - 408 x^{7} - 581 x^{6} + 1236 x^{5} + 972 x^{4} + \cdots + 81 $ x^12 - 3x^11 - 21x^10 + 59x^9 + 162x^8 - 408x^7 - 581x^6 + 1236x^5 + 972x^4 - 1596x^3 - 621x^2 + 648*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$1.31121$ of defining polynomial
Character	$\chi$	$=$	7942.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.31121 q^{3} +1.00000 q^{4} -3.25078 q^{5} -1.31121 q^{6} +0.670809 q^{7} -1.00000 q^{8} -1.28073 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.31121 q^{3} +1.00000 q^{4} -3.25078 q^{5} -1.31121 q^{6} +0.670809 q^{7} -1.00000 q^{8} -1.28073 q^{9} +3.25078 q^{10} +1.00000 q^{11} +1.31121 q^{12} -2.21747 q^{13} -0.670809 q^{14} -4.26246 q^{15} +1.00000 q^{16} -6.10412 q^{17} +1.28073 q^{18} -3.25078 q^{20} +0.879571 q^{21} -1.00000 q^{22} +8.37229 q^{23} -1.31121 q^{24} +5.56760 q^{25} +2.21747 q^{26} -5.61293 q^{27} +0.670809 q^{28} -1.33081 q^{29} +4.26246 q^{30} +9.63931 q^{31} -1.00000 q^{32} +1.31121 q^{33} +6.10412 q^{34} -2.18065 q^{35} -1.28073 q^{36} +3.75336 q^{37} -2.90756 q^{39} +3.25078 q^{40} -5.10439 q^{41} -0.879571 q^{42} +10.9693 q^{43} +1.00000 q^{44} +4.16338 q^{45} -8.37229 q^{46} +6.15373 q^{47} +1.31121 q^{48} -6.55002 q^{49} -5.56760 q^{50} -8.00378 q^{51} -2.21747 q^{52} +9.75026 q^{53} +5.61293 q^{54} -3.25078 q^{55} -0.670809 q^{56} +1.33081 q^{58} +9.12263 q^{59} -4.26246 q^{60} +7.49741 q^{61} -9.63931 q^{62} -0.859125 q^{63} +1.00000 q^{64} +7.20850 q^{65} -1.31121 q^{66} -4.55258 q^{67} -6.10412 q^{68} +10.9778 q^{69} +2.18065 q^{70} -2.89974 q^{71} +1.28073 q^{72} -2.93991 q^{73} -3.75336 q^{74} +7.30028 q^{75} +0.670809 q^{77} +2.90756 q^{78} -14.9357 q^{79} -3.25078 q^{80} -3.51754 q^{81} +5.10439 q^{82} -2.91398 q^{83} +0.879571 q^{84} +19.8432 q^{85} -10.9693 q^{86} -1.74497 q^{87} -1.00000 q^{88} -7.36234 q^{89} -4.16338 q^{90} -1.48750 q^{91} +8.37229 q^{92} +12.6392 q^{93} -6.15373 q^{94} -1.31121 q^{96} -3.33485 q^{97} +6.55002 q^{98} -1.28073 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 3 q^{3} + 12 q^{4} - 9 q^{5} - 3 q^{6} - 12 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 + 3 * q^3 + 12 * q^4 - 9 * q^5 - 3 * q^6 - 12 * q^7 - 12 * q^8 + 15 * q^9	\( 12 q - 12 q^{2} + 3 q^{3} + 12 q^{4} - 9 q^{5} - 3 q^{6} - 12 q^{7} - 12 q^{8} + 15 q^{9} + 9 q^{10} + 12 q^{11} + 3 q^{12} + 12 q^{14} + 21 q^{15} + 12 q^{16} - 33 q^{17} - 15 q^{18} - 9 q^{20} - 9 q^{21} - 12 q^{22} - 18 q^{23} - 3 q^{24} + 15 q^{25} + 21 q^{27} - 12 q^{28} - 15 q^{29} - 21 q^{30} + 9 q^{31} - 12 q^{32} + 3 q^{33} + 33 q^{34} - 30 q^{35} + 15 q^{36} + 9 q^{37} - 6 q^{39} + 9 q^{40} - 15 q^{41} + 9 q^{42} - 21 q^{43} + 12 q^{44} + 18 q^{46} - 27 q^{47} + 3 q^{48} + 18 q^{49} - 15 q^{50} - 6 q^{51} + 6 q^{53} - 21 q^{54} - 9 q^{55} + 12 q^{56} + 15 q^{58} + 48 q^{59} + 21 q^{60} + 12 q^{61} - 9 q^{62} - 66 q^{63} + 12 q^{64} - 36 q^{65} - 3 q^{66} - 3 q^{67} - 33 q^{68} - 24 q^{69} + 30 q^{70} - 3 q^{71} - 15 q^{72} - 30 q^{73} - 9 q^{74} + 21 q^{75} - 12 q^{77} + 6 q^{78} + 12 q^{79} - 9 q^{80} + 12 q^{81} + 15 q^{82} - 66 q^{83} - 9 q^{84} + 15 q^{85} + 21 q^{86} - 51 q^{87} - 12 q^{88} + 30 q^{89} + 54 q^{91} - 18 q^{92} - 66 q^{93} + 27 q^{94} - 3 q^{96} + 36 q^{97} - 18 q^{98} + 15 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 3 * q^3 + 12 * q^4 - 9 * q^5 - 3 * q^6 - 12 * q^7 - 12 * q^8 + 15 * q^9 + 9 * q^10 + 12 * q^11 + 3 * q^12 + 12 * q^14 + 21 * q^15 + 12 * q^16 - 33 * q^17 - 15 * q^18 - 9 * q^20 - 9 * q^21 - 12 * q^22 - 18 * q^23 - 3 * q^24 + 15 * q^25 + 21 * q^27 - 12 * q^28 - 15 * q^29 - 21 * q^30 + 9 * q^31 - 12 * q^32 + 3 * q^33 + 33 * q^34 - 30 * q^35 + 15 * q^36 + 9 * q^37 - 6 * q^39 + 9 * q^40 - 15 * q^41 + 9 * q^42 - 21 * q^43 + 12 * q^44 + 18 * q^46 - 27 * q^47 + 3 * q^48 + 18 * q^49 - 15 * q^50 - 6 * q^51 + 6 * q^53 - 21 * q^54 - 9 * q^55 + 12 * q^56 + 15 * q^58 + 48 * q^59 + 21 * q^60 + 12 * q^61 - 9 * q^62 - 66 * q^63 + 12 * q^64 - 36 * q^65 - 3 * q^66 - 3 * q^67 - 33 * q^68 - 24 * q^69 + 30 * q^70 - 3 * q^71 - 15 * q^72 - 30 * q^73 - 9 * q^74 + 21 * q^75 - 12 * q^77 + 6 * q^78 + 12 * q^79 - 9 * q^80 + 12 * q^81 + 15 * q^82 - 66 * q^83 - 9 * q^84 + 15 * q^85 + 21 * q^86 - 51 * q^87 - 12 * q^88 + 30 * q^89 + 54 * q^91 - 18 * q^92 - 66 * q^93 + 27 * q^94 - 3 * q^96 + 36 * q^97 - 18 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.31121	0.757027	0.378513	−	0.925596i	$-0.376435\pi$
$3$	1.31121	0.757027	0.378513	+	0.925596i	$0.376435\pi$
$4$	1.00000	0.500000
$5$	−3.25078	−1.45379	−0.726897	−	0.686746i	$-0.759038\pi$
$5$	−3.25078	−1.45379	−0.726897	+	0.686746i	$0.759038\pi$
$6$	−1.31121	−0.535299
$7$	0.670809	0.253542	0.126771	−	0.991932i	$-0.459539\pi$
$7$	0.670809	0.253542	0.126771	+	0.991932i	$0.459539\pi$
$8$	−1.00000	−0.353553
$9$	−1.28073	−0.426910
$10$	3.25078	1.02799
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.31121	0.378513
$13$	−2.21747	−0.615014	−0.307507	−	0.951546i	$-0.599495\pi$
$13$	−2.21747	−0.615014	−0.307507	+	0.951546i	$0.599495\pi$
$14$	−0.670809	−0.179281
$15$	−4.26246	−1.10056
$16$	1.00000	0.250000
$17$	−6.10412	−1.48047	−0.740233	−	0.672350i	$-0.765285\pi$
$17$	−6.10412	−1.48047	−0.740233	+	0.672350i	$0.765285\pi$
$18$	1.28073	0.301871
$19$	0	0
$19$	0	0
$20$	−3.25078	−0.726897
$21$	0.879571	0.191938
$22$	−1.00000	−0.213201
$23$	8.37229	1.74574	0.872872	−	0.487950i	$-0.162255\pi$
$23$	8.37229	1.74574	0.872872	+	0.487950i	$0.162255\pi$
$24$	−1.31121	−0.267649
$25$	5.56760	1.11352
$26$	2.21747	0.434881
$27$	−5.61293	−1.08021
$28$	0.670809	0.126771
$29$	−1.33081	−0.247125	−0.123563	−	0.992337i	$-0.539432\pi$
$29$	−1.33081	−0.247125	−0.123563	+	0.992337i	$0.539432\pi$
$30$	4.26246	0.778215
$31$	9.63931	1.73127	0.865636	−	0.500674i	$-0.166914\pi$
$31$	9.63931	1.73127	0.865636	+	0.500674i	$0.166914\pi$
$32$	−1.00000	−0.176777
$33$	1.31121	0.228252
$34$	6.10412	1.04685
$35$	−2.18065	−0.368598
$36$	−1.28073	−0.213455
$37$	3.75336	0.617049	0.308524	−	0.951216i	$-0.400165\pi$
$37$	3.75336	0.617049	0.308524	+	0.951216i	$0.400165\pi$
$38$	0	0
$39$	−2.90756	−0.465582
$40$	3.25078	0.513994
$41$	−5.10439	−0.797172	−0.398586	−	0.917131i	$-0.630499\pi$
$41$	−5.10439	−0.797172	−0.398586	+	0.917131i	$0.630499\pi$
$42$	−0.879571	−0.135721
$43$	10.9693	1.67280	0.836402	−	0.548117i	$-0.184655\pi$
$43$	10.9693	1.67280	0.836402	+	0.548117i	$0.184655\pi$
$44$	1.00000	0.150756
$45$	4.16338	0.620640
$46$	−8.37229	−1.23443
$47$	6.15373	0.897613	0.448807	−	0.893629i	$-0.351849\pi$
$47$	6.15373	0.897613	0.448807	+	0.893629i	$0.351849\pi$
$48$	1.31121	0.189257
$49$	−6.55002	−0.935717
$50$	−5.56760	−0.787377
$51$	−8.00378	−1.12075
$52$	−2.21747	−0.307507
$53$	9.75026	1.33930	0.669651	−	0.742676i	$-0.266444\pi$
$53$	9.75026	1.33930	0.669651	+	0.742676i	$0.266444\pi$
$54$	5.61293	0.763823
$55$	−3.25078	−0.438336
$56$	−0.670809	−0.0896406
$57$	0	0
$58$	1.33081	0.174744
$59$	9.12263	1.18767	0.593833	−	0.804589i	$-0.297614\pi$
$59$	9.12263	1.18767	0.593833	+	0.804589i	$0.297614\pi$
$60$	−4.26246	−0.550281
$61$	7.49741	0.959945	0.479972	−	0.877284i	$-0.340647\pi$
$61$	7.49741	0.959945	0.479972	+	0.877284i	$0.340647\pi$
$62$	−9.63931	−1.22419
$63$	−0.859125	−0.108240
$64$	1.00000	0.125000
$65$	7.20850	0.894105
$66$	−1.31121	−0.161399
$67$	−4.55258	−0.556186	−0.278093	−	0.960554i	$-0.589702\pi$
$67$	−4.55258	−0.556186	−0.278093	+	0.960554i	$0.589702\pi$
$68$	−6.10412	−0.740233
$69$	10.9778	1.32157
$70$	2.18065	0.260638
$71$	−2.89974	−0.344136	−0.172068	−	0.985085i	$-0.555045\pi$
$71$	−2.89974	−0.344136	−0.172068	+	0.985085i	$0.555045\pi$
$72$	1.28073	0.150936
$73$	−2.93991	−0.344091	−0.172045	−	0.985089i	$-0.555038\pi$
$73$	−2.93991	−0.344091	−0.172045	+	0.985089i	$0.555038\pi$
$74$	−3.75336	−0.436319
$75$	7.30028	0.842964
$76$	0	0
$77$	0.670809	0.0764458
$78$	2.90756	0.329216
$79$	−14.9357	−1.68040	−0.840199	−	0.542278i	$-0.817562\pi$
$79$	−14.9357	−1.68040	−0.840199	+	0.542278i	$0.817562\pi$
$80$	−3.25078	−0.363449
$81$	−3.51754	−0.390838
$82$	5.10439	0.563686
$83$	−2.91398	−0.319851	−0.159926	−	0.987129i	$-0.551125\pi$
$83$	−2.91398	−0.319851	−0.159926	+	0.987129i	$0.551125\pi$
$84$	0.879571	0.0959690
$85$	19.8432	2.15230
$86$	−10.9693	−1.18285
$87$	−1.74497	−0.187081
$88$	−1.00000	−0.106600
$89$	−7.36234	−0.780406	−0.390203	−	0.920729i	$-0.627595\pi$
$89$	−7.36234	−0.780406	−0.390203	+	0.920729i	$0.627595\pi$
$90$	−4.16338	−0.438859
$91$	−1.48750	−0.155932
$92$	8.37229	0.872872
$93$	12.6392	1.31062
$94$	−6.15373	−0.634709
$95$	0	0
$96$	−1.31121	−0.133825
$97$	−3.33485	−0.338602	−0.169301	−	0.985564i	$-0.554151\pi$
$97$	−3.33485	−0.338602	−0.169301	+	0.985564i	$0.554151\pi$
$98$	6.55002	0.661651
$99$	−1.28073	−0.128718
$100$	5.56760	0.556760
$101$	−17.2807	−1.71949	−0.859745	−	0.510724i	$-0.829377\pi$
$101$	−17.2807	−1.71949	−0.859745	+	0.510724i	$0.829377\pi$
$102$	8.00378	0.792492
$103$	0.414883	0.0408797	0.0204398	−	0.999791i	$-0.493493\pi$
$103$	0.414883	0.0408797	0.0204398	+	0.999791i	$0.493493\pi$
$104$	2.21747	0.217440
$105$	−2.85929	−0.279039
$106$	−9.75026	−0.947029
$107$	−4.37807	−0.423244	−0.211622	−	0.977352i	$-0.567875\pi$
$107$	−4.37807	−0.423244	−0.211622	+	0.977352i	$0.567875\pi$
$108$	−5.61293	−0.540105
$109$	−5.92381	−0.567398	−0.283699	−	0.958913i	$-0.591562\pi$
$109$	−5.92381	−0.567398	−0.283699	+	0.958913i	$0.591562\pi$
$110$	3.25078	0.309950
$111$	4.92144	0.467122
$112$	0.670809	0.0633855
$113$	11.0227	1.03693	0.518463	−	0.855100i	$-0.326504\pi$
$113$	11.0227	1.03693	0.518463	+	0.855100i	$0.326504\pi$
$114$	0	0
$115$	−27.2165	−2.53795
$116$	−1.33081	−0.123563
$117$	2.83998	0.262556
$118$	−9.12263	−0.839806
$119$	−4.09470	−0.375360
$120$	4.26246	0.389107
$121$	1.00000	0.0909091
$122$	−7.49741	−0.678783
$123$	−6.69293	−0.603481
$124$	9.63931	0.865636
$125$	−1.84513	−0.165033
$126$	0.859125	0.0765370
$127$	−4.36682	−0.387493	−0.193746	−	0.981052i	$-0.562064\pi$
$127$	−4.36682	−0.387493	−0.193746	+	0.981052i	$0.562064\pi$
$128$	−1.00000	−0.0883883
$129$	14.3831	1.26636
$130$	−7.20850	−0.632227
$131$	−21.0621	−1.84021	−0.920104	−	0.391674i	$-0.871896\pi$
$131$	−21.0621	−1.84021	−0.920104	+	0.391674i	$0.871896\pi$
$132$	1.31121	0.114126
$133$	0	0
$134$	4.55258	0.393283
$135$	18.2464	1.57040
$136$	6.10412	0.523424
$137$	−21.1070	−1.80329	−0.901646	−	0.432474i	$-0.857641\pi$
$137$	−21.1070	−1.80329	−0.901646	+	0.432474i	$0.857641\pi$
$138$	−10.9778	−0.934494
$139$	12.1711	1.03234	0.516168	−	0.856487i	$-0.327358\pi$
$139$	12.1711	1.03234	0.516168	+	0.856487i	$0.327358\pi$
$140$	−2.18065	−0.184299
$141$	8.06882	0.679518
$142$	2.89974	0.243341
$143$	−2.21747	−0.185434
$144$	−1.28073	−0.106728
$145$	4.32618	0.359270
$146$	2.93991	0.243309
$147$	−8.58844	−0.708363
$148$	3.75336	0.308524
$149$	−19.6594	−1.61056	−0.805279	−	0.592897i	$-0.797984\pi$
$149$	−19.6594	−1.61056	−0.805279	+	0.592897i	$0.797984\pi$
$150$	−7.30028	−0.596066
$151$	2.75510	0.224207	0.112103	−	0.993697i	$-0.464241\pi$
$151$	2.75510	0.224207	0.112103	+	0.993697i	$0.464241\pi$
$152$	0	0
$153$	7.81773	0.632026
$154$	−0.670809	−0.0540553
$155$	−31.3353	−2.51691
$156$	−2.90756	−0.232791
$157$	−18.0855	−1.44338	−0.721689	−	0.692217i	$-0.756634\pi$
$157$	−18.0855	−1.44338	−0.721689	+	0.692217i	$0.756634\pi$
$158$	14.9357	1.18822
$159$	12.7846	1.01389
$160$	3.25078	0.256997
$161$	5.61621	0.442619
$162$	3.51754	0.276364
$163$	0.202708	0.0158773	0.00793865	−	0.999968i	$-0.497473\pi$
$163$	0.202708	0.0158773	0.00793865	+	0.999968i	$0.497473\pi$
$164$	−5.10439	−0.398586
$165$	−4.26246	−0.331832
$166$	2.91398	0.226169
$167$	−16.8141	−1.30111	−0.650557	−	0.759457i	$-0.725465\pi$
$167$	−16.8141	−1.30111	−0.650557	+	0.759457i	$0.725465\pi$
$168$	−0.879571	−0.0678603
$169$	−8.08285	−0.621757
$170$	−19.8432	−1.52190
$171$	0	0
$172$	10.9693	0.836402
$173$	7.45306	0.566646	0.283323	−	0.959025i	$-0.408563\pi$
$173$	7.45306	0.566646	0.283323	+	0.959025i	$0.408563\pi$
$174$	1.74497	0.132286
$175$	3.73479	0.282324
$176$	1.00000	0.0753778
$177$	11.9617	0.899095
$178$	7.36234	0.551831
$179$	−17.2985	−1.29295	−0.646475	−	0.762936i	$-0.723757\pi$
$179$	−17.2985	−1.29295	−0.646475	+	0.762936i	$0.723757\pi$
$180$	4.16338	0.310320
$181$	19.5944	1.45644	0.728221	−	0.685342i	$-0.240347\pi$
$181$	19.5944	1.45644	0.728221	+	0.685342i	$0.240347\pi$
$182$	1.48750	0.110260
$183$	9.83067	0.726704
$184$	−8.37229	−0.617213
$185$	−12.2014	−0.897062
$186$	−12.6392	−0.926748
$187$	−6.10412	−0.446378
$188$	6.15373	0.448807
$189$	−3.76520	−0.273878
$190$	0	0
$191$	−9.26240	−0.670204	−0.335102	−	0.942182i	$-0.608771\pi$
$191$	−9.26240	−0.670204	−0.335102	+	0.942182i	$0.608771\pi$
$192$	1.31121	0.0946284
$193$	9.25574	0.666243	0.333122	−	0.942884i	$-0.391898\pi$
$193$	9.25574	0.666243	0.333122	+	0.942884i	$0.391898\pi$
$194$	3.33485	0.239428
$195$	9.45185	0.676861
$196$	−6.55002	−0.467858
$197$	4.85358	0.345803	0.172902	−	0.984939i	$-0.444686\pi$
$197$	4.85358	0.345803	0.172902	+	0.984939i	$0.444686\pi$
$198$	1.28073	0.0910175
$199$	0.352088	0.0249589	0.0124794	−	0.999922i	$-0.496028\pi$
$199$	0.352088	0.0249589	0.0124794	+	0.999922i	$0.496028\pi$
$200$	−5.56760	−0.393688
$201$	−5.96938	−0.421048
$202$	17.2807	1.21586
$203$	−0.892720	−0.0626566
$204$	−8.00378	−0.560377
$205$	16.5933	1.15892
$206$	−0.414883	−0.0289063
$207$	−10.7226	−0.745275
$208$	−2.21747	−0.153754
$209$	0	0
$210$	2.85929	0.197310
$211$	13.4525	0.926111	0.463055	−	0.886329i	$-0.346753\pi$
$211$	13.4525	0.926111	0.463055	+	0.886329i	$0.346753\pi$
$212$	9.75026	0.669651
$213$	−3.80217	−0.260520
$214$	4.37807	0.299279
$215$	−35.6588	−2.43191
$216$	5.61293	0.381912
$217$	6.46614	0.438950
$218$	5.92381	0.401211
$219$	−3.85484	−0.260486
$220$	−3.25078	−0.219168
$221$	13.5357	0.910508
$222$	−4.92144	−0.330305
$223$	15.2495	1.02118	0.510591	−	0.859824i	$-0.329427\pi$
$223$	15.2495	1.02118	0.510591	+	0.859824i	$0.329427\pi$
$224$	−0.670809	−0.0448203
$225$	−7.13059	−0.475373
$226$	−11.0227	−0.733217
$227$	−12.4192	−0.824289	−0.412145	−	0.911118i	$-0.635220\pi$
$227$	−12.4192	−0.824289	−0.412145	+	0.911118i	$0.635220\pi$
$228$	0	0
$229$	−25.0447	−1.65500	−0.827502	−	0.561463i	$-0.810239\pi$
$229$	−25.0447	−1.65500	−0.827502	+	0.561463i	$0.810239\pi$
$230$	27.2165	1.79460
$231$	0.879571	0.0578715
$232$	1.33081	0.0873720
$233$	3.24468	0.212566	0.106283	−	0.994336i	$-0.466105\pi$
$233$	3.24468	0.212566	0.106283	+	0.994336i	$0.466105\pi$
$234$	−2.83998	−0.185655
$235$	−20.0044	−1.30495
$236$	9.12263	0.593833
$237$	−19.5838	−1.27211
$238$	4.09470	0.265420
$239$	7.39516	0.478353	0.239177	−	0.970976i	$-0.423123\pi$
$239$	7.39516	0.478353	0.239177	+	0.970976i	$0.423123\pi$
$240$	−4.26246	−0.275140
$241$	24.2077	1.55936	0.779678	−	0.626180i	$-0.215383\pi$
$241$	24.2077	1.55936	0.779678	+	0.626180i	$0.215383\pi$
$242$	−1.00000	−0.0642824
$243$	12.2266	0.784335
$244$	7.49741	0.479972
$245$	21.2927	1.36034
$246$	6.69293	0.426725
$247$	0	0
$248$	−9.63931	−0.612097
$249$	−3.82084	−0.242136
$250$	1.84513	0.116696
$251$	0.758269	0.0478615	0.0239308	−	0.999714i	$-0.492382\pi$
$251$	0.758269	0.0478615	0.0239308	+	0.999714i	$0.492382\pi$
$252$	−0.859125	−0.0541198
$253$	8.37229	0.526361
$254$	4.36682	0.273999
$255$	26.0186	1.62935
$256$	1.00000	0.0625000
$257$	−15.2391	−0.950589	−0.475294	−	0.879827i	$-0.657658\pi$
$257$	−15.2391	−0.950589	−0.475294	+	0.879827i	$0.657658\pi$
$258$	−14.3831	−0.895450
$259$	2.51779	0.156448
$260$	7.20850	0.447052
$261$	1.70441	0.105500
$262$	21.0621	1.30122
$263$	−25.1587	−1.55135	−0.775675	−	0.631133i	$-0.782590\pi$
$263$	−25.1587	−1.55135	−0.775675	+	0.631133i	$0.782590\pi$
$264$	−1.31121	−0.0806993
$265$	−31.6960	−1.94707
$266$	0	0
$267$	−9.65357	−0.590789
$268$	−4.55258	−0.278093
$269$	5.45507	0.332601	0.166301	−	0.986075i	$-0.446818\pi$
$269$	5.45507	0.332601	0.166301	+	0.986075i	$0.446818\pi$
$270$	−18.2464	−1.11044
$271$	−6.02787	−0.366167	−0.183083	−	0.983097i	$-0.558608\pi$
$271$	−6.02787	−0.366167	−0.183083	+	0.983097i	$0.558608\pi$
$272$	−6.10412	−0.370117
$273$	−1.95042	−0.118045
$274$	21.1070	1.27512
$275$	5.56760	0.335739
$276$	10.9778	0.660787
$277$	11.9513	0.718086	0.359043	−	0.933321i	$-0.383103\pi$
$277$	11.9513	0.718086	0.359043	+	0.933321i	$0.383103\pi$
$278$	−12.1711	−0.729972
$279$	−12.3454	−0.739098
$280$	2.18065	0.130319
$281$	15.6262	0.932179	0.466090	−	0.884737i	$-0.345662\pi$
$281$	15.6262	0.932179	0.466090	+	0.884737i	$0.345662\pi$
$282$	−8.06882	−0.480491
$283$	29.0147	1.72475	0.862373	−	0.506274i	$-0.168978\pi$
$283$	29.0147	1.72475	0.862373	+	0.506274i	$0.168978\pi$
$284$	−2.89974	−0.172068
$285$	0	0
$286$	2.21747	0.131121
$287$	−3.42407	−0.202117
$288$	1.28073	0.0754678
$289$	20.2603	1.19178
$290$	−4.32618	−0.254042
$291$	−4.37268	−0.256331
$292$	−2.93991	−0.172045
$293$	7.39860	0.432231	0.216115	−	0.976368i	$-0.430661\pi$
$293$	7.39860	0.432231	0.216115	+	0.976368i	$0.430661\pi$
$294$	8.58844	0.500888
$295$	−29.6557	−1.72662
$296$	−3.75336	−0.218160
$297$	−5.61293	−0.325695
$298$	19.6594	1.13884
$299$	−18.5653	−1.07366
$300$	7.30028	0.421482
$301$	7.35831	0.424126
$302$	−2.75510	−0.158538
$303$	−22.6585	−1.30170
$304$	0	0
$305$	−24.3724	−1.39556
$306$	−7.81773	−0.446910
$307$	−9.56584	−0.545951	−0.272976	−	0.962021i	$-0.588008\pi$
$307$	−9.56584	−0.545951	−0.272976	+	0.962021i	$0.588008\pi$
$308$	0.670809	0.0382229
$309$	0.543999	0.0309470
$310$	31.3353	1.77973
$311$	−11.6288	−0.659410	−0.329705	−	0.944084i	$-0.606949\pi$
$311$	−11.6288	−0.659410	−0.329705	+	0.944084i	$0.606949\pi$
$312$	2.90756	0.164608
$313$	−22.4931	−1.27139	−0.635693	−	0.771942i	$-0.719285\pi$
$313$	−22.4931	−1.27139	−0.635693	+	0.771942i	$0.719285\pi$
$314$	18.0855	1.02062
$315$	2.79283	0.157358
$316$	−14.9357	−0.840199
$317$	12.7818	0.717897	0.358948	−	0.933357i	$-0.383135\pi$
$317$	12.7818	0.717897	0.358948	+	0.933357i	$0.383135\pi$
$318$	−12.7846	−0.716927
$319$	−1.33081	−0.0745111
$320$	−3.25078	−0.181724
$321$	−5.74057	−0.320407
$322$	−5.61621	−0.312979
$323$	0	0
$324$	−3.51754	−0.195419
$325$	−12.3460	−0.684830
$326$	−0.202708	−0.0112269
$327$	−7.76736	−0.429536
$328$	5.10439	0.281843
$329$	4.12797	0.227583
$330$	4.26246	0.234641
$331$	−7.71237	−0.423910	−0.211955	−	0.977279i	$-0.567983\pi$
$331$	−7.71237	−0.423910	−0.211955	+	0.977279i	$0.567983\pi$
$332$	−2.91398	−0.159926
$333$	−4.80704	−0.263424
$334$	16.8141	0.920027
$335$	14.7994	0.808580
$336$	0.879571	0.0479845
$337$	7.93441	0.432215	0.216108	−	0.976370i	$-0.430664\pi$
$337$	7.93441	0.432215	0.216108	+	0.976370i	$0.430664\pi$
$338$	8.08285	0.439649
$339$	14.4530	0.784981
$340$	19.8432	1.07615
$341$	9.63931	0.521998
$342$	0	0
$343$	−9.08947	−0.490785
$344$	−10.9693	−0.591425
$345$	−35.6865	−1.92130
$346$	−7.45306	−0.400679
$347$	−15.2630	−0.819359	−0.409680	−	0.912229i	$-0.634360\pi$
$347$	−15.2630	−0.819359	−0.409680	+	0.912229i	$0.634360\pi$
$348$	−1.74497	−0.0935403
$349$	−17.9656	−0.961675	−0.480838	−	0.876810i	$-0.659667\pi$
$349$	−17.9656	−0.961675	−0.480838	+	0.876810i	$0.659667\pi$
$350$	−3.73479	−0.199633
$351$	12.4465	0.664344
$352$	−1.00000	−0.0533002
$353$	−16.4839	−0.877348	−0.438674	−	0.898646i	$-0.644552\pi$
$353$	−16.4839	−0.877348	−0.438674	+	0.898646i	$0.644552\pi$
$354$	−11.9617	−0.635756
$355$	9.42643	0.500303
$356$	−7.36234	−0.390203
$357$	−5.36901	−0.284158
$358$	17.2985	0.914253
$359$	−10.8313	−0.571655	−0.285828	−	0.958281i	$-0.592268\pi$
$359$	−10.8313	−0.571655	−0.285828	+	0.958281i	$0.592268\pi$
$360$	−4.16338	−0.219429
$361$	0	0
$362$	−19.5944	−1.02986
$363$	1.31121	0.0688206
$364$	−1.48750	−0.0779659
$365$	9.55702	0.500237
$366$	−9.83067	−0.513857
$367$	8.58108	0.447929	0.223964	−	0.974597i	$-0.428100\pi$
$367$	8.58108	0.447929	0.223964	+	0.974597i	$0.428100\pi$
$368$	8.37229	0.436436
$369$	6.53735	0.340321
$370$	12.2014	0.634319
$371$	6.54056	0.339569
$372$	12.6392	0.655310
$373$	−28.5466	−1.47809	−0.739044	−	0.673657i	$-0.764722\pi$
$373$	−28.5466	−1.47809	−0.739044	+	0.673657i	$0.764722\pi$
$374$	6.10412	0.315637
$375$	−2.41935	−0.124935
$376$	−6.15373	−0.317354
$377$	2.95103	0.151986
$378$	3.76520	0.193661
$379$	17.7270	0.910576	0.455288	−	0.890344i	$-0.349536\pi$
$379$	17.7270	0.910576	0.455288	+	0.890344i	$0.349536\pi$
$380$	0	0
$381$	−5.72582	−0.293342
$382$	9.26240	0.473906
$383$	−9.71073	−0.496195	−0.248098	−	0.968735i	$-0.579805\pi$
$383$	−9.71073	−0.496195	−0.248098	+	0.968735i	$0.579805\pi$
$384$	−1.31121	−0.0669124
$385$	−2.18065	−0.111136
$386$	−9.25574	−0.471105
$387$	−14.0487	−0.714137
$388$	−3.33485	−0.169301
$389$	15.2721	0.774328	0.387164	−	0.922011i	$-0.373455\pi$
$389$	15.2721	0.774328	0.387164	+	0.922011i	$0.373455\pi$
$390$	−9.45185	−0.478613
$391$	−51.1055	−2.58452
$392$	6.55002	0.330826
$393$	−27.6169	−1.39309
$394$	−4.85358	−0.244520
$395$	48.5527	2.44295
$396$	−1.28073	−0.0643591
$397$	−11.9204	−0.598267	−0.299134	−	0.954211i	$-0.596698\pi$
$397$	−11.9204	−0.598267	−0.299134	+	0.954211i	$0.596698\pi$
$398$	−0.352088	−0.0176486
$399$	0	0
$400$	5.56760	0.278380
$401$	−13.6988	−0.684088	−0.342044	−	0.939684i	$-0.611119\pi$
$401$	−13.6988	−0.684088	−0.342044	+	0.939684i	$0.611119\pi$
$402$	5.96938	0.297726
$403$	−21.3748	−1.06476
$404$	−17.2807	−0.859745
$405$	11.4348	0.568198
$406$	0.892720	0.0443049
$407$	3.75336	0.186047
$408$	8.00378	0.396246
$409$	−4.60043	−0.227477	−0.113738	−	0.993511i	$-0.536283\pi$
$409$	−4.60043	−0.227477	−0.113738	+	0.993511i	$0.536283\pi$
$410$	−16.5933	−0.819483
$411$	−27.6757	−1.36514
$412$	0.414883	0.0204398
$413$	6.11954	0.301123
$414$	10.7226	0.526989
$415$	9.47273	0.464998
$416$	2.21747	0.108720
$417$	15.9588	0.781506
$418$	0	0
$419$	−12.9653	−0.633397	−0.316699	−	0.948526i	$-0.602574\pi$
$419$	−12.9653	−0.633397	−0.316699	+	0.948526i	$0.602574\pi$
$420$	−2.85929	−0.139519
$421$	−38.1067	−1.85721	−0.928603	−	0.371074i	$-0.878990\pi$
$421$	−38.1067	−1.85721	−0.928603	+	0.371074i	$0.878990\pi$
$422$	−13.4525	−0.654859
$423$	−7.88127	−0.383200
$424$	−9.75026	−0.473515
$425$	−33.9853	−1.64853
$426$	3.80217	0.184216
$427$	5.02933	0.243386
$428$	−4.37807	−0.211622
$429$	−2.90756	−0.140378
$430$	35.6588	1.71962
$431$	−15.3186	−0.737871	−0.368936	−	0.929455i	$-0.620278\pi$
$431$	−15.3186	−0.737871	−0.368936	+	0.929455i	$0.620278\pi$
$432$	−5.61293	−0.270052
$433$	−22.4007	−1.07651	−0.538255	−	0.842782i	$-0.680916\pi$
$433$	−22.4007	−1.07651	−0.538255	+	0.842782i	$0.680916\pi$
$434$	−6.46614	−0.310384
$435$	5.67253	0.271977
$436$	−5.92381	−0.283699
$437$	0	0
$438$	3.85484	0.184191
$439$	14.7208	0.702587	0.351293	−	0.936265i	$-0.385742\pi$
$439$	14.7208	0.702587	0.351293	+	0.936265i	$0.385742\pi$
$440$	3.25078	0.154975
$441$	8.38880	0.399467
$442$	−13.5357	−0.643827
$443$	−14.0323	−0.666693	−0.333347	−	0.942804i	$-0.608178\pi$
$443$	−14.0323	−0.666693	−0.333347	+	0.942804i	$0.608178\pi$
$444$	4.92144	0.233561
$445$	23.9334	1.13455
$446$	−15.2495	−0.722084
$447$	−25.7775	−1.21924
$448$	0.670809	0.0316927
$449$	20.2903	0.957561	0.478780	−	0.877935i	$-0.341079\pi$
$449$	20.2903	0.957561	0.478780	+	0.877935i	$0.341079\pi$
$450$	7.13059	0.336139
$451$	−5.10439	−0.240356
$452$	11.0227	0.518463
$453$	3.61251	0.169731
$454$	12.4192	0.582861
$455$	4.83553	0.226693
$456$	0	0
$457$	−4.00708	−0.187443	−0.0937217	−	0.995598i	$-0.529876\pi$
$457$	−4.00708	−0.187443	−0.0937217	+	0.995598i	$0.529876\pi$
$458$	25.0447	1.17026
$459$	34.2620	1.59921
$460$	−27.2165	−1.26898
$461$	−23.9251	−1.11430	−0.557151	−	0.830411i	$-0.688106\pi$
$461$	−23.9251	−1.11430	−0.557151	+	0.830411i	$0.688106\pi$
$462$	−0.879571	−0.0409213
$463$	−6.18485	−0.287434	−0.143717	−	0.989619i	$-0.545906\pi$
$463$	−6.18485	−0.287434	−0.143717	+	0.989619i	$0.545906\pi$
$464$	−1.33081	−0.0617813
$465$	−41.0872	−1.90537
$466$	−3.24468	−0.150307
$467$	0.958537	0.0443558	0.0221779	−	0.999754i	$-0.492940\pi$
$467$	0.958537	0.0443558	0.0221779	+	0.999754i	$0.492940\pi$
$468$	2.83998	0.131278
$469$	−3.05391	−0.141016
$470$	20.0044	0.922736
$471$	−23.7139	−1.09268
$472$	−9.12263	−0.419903
$473$	10.9693	0.504369
$474$	19.5838	0.899515
$475$	0	0
$476$	−4.09470	−0.187680
$477$	−12.4875	−0.571762
$478$	−7.39516	−0.338247
$479$	13.0143	0.594638	0.297319	−	0.954778i	$-0.403908\pi$
$479$	13.0143	0.594638	0.297319	+	0.954778i	$0.403908\pi$
$480$	4.26246	0.194554
$481$	−8.32295	−0.379494
$482$	−24.2077	−1.10263
$483$	7.36402	0.335075
$484$	1.00000	0.0454545
$485$	10.8409	0.492258
$486$	−12.2266	−0.554609
$487$	24.3237	1.10221	0.551105	−	0.834436i	$-0.314206\pi$
$487$	24.3237	1.10221	0.551105	+	0.834436i	$0.314206\pi$
$488$	−7.49741	−0.339392
$489$	0.265792	0.0120195
$490$	−21.2927	−0.961905
$491$	1.87591	0.0846586	0.0423293	−	0.999104i	$-0.486522\pi$
$491$	1.87591	0.0846586	0.0423293	+	0.999104i	$0.486522\pi$
$492$	−6.69293	−0.301740
$493$	8.12343	0.365861
$494$	0	0
$495$	4.16338	0.187130
$496$	9.63931	0.432818
$497$	−1.94517	−0.0872529
$498$	3.82084	0.171216
$499$	−6.58150	−0.294629	−0.147314	−	0.989090i	$-0.547063\pi$
$499$	−6.58150	−0.294629	−0.147314	+	0.989090i	$0.547063\pi$
$500$	−1.84513	−0.0825167
$501$	−22.0468	−0.984979
$502$	−0.758269	−0.0338432
$503$	−17.4337	−0.777328	−0.388664	−	0.921380i	$-0.627063\pi$
$503$	−17.4337	−0.777328	−0.388664	+	0.921380i	$0.627063\pi$
$504$	0.859125	0.0382685
$505$	56.1757	2.49978
$506$	−8.37229	−0.372194
$507$	−10.5983	−0.470687
$508$	−4.36682	−0.193746
$509$	31.0553	1.37650	0.688251	−	0.725473i	$-0.258379\pi$
$509$	31.0553	1.37650	0.688251	+	0.725473i	$0.258379\pi$
$510$	−26.0186	−1.15212
$511$	−1.97212	−0.0872414
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	15.2391	0.672168
$515$	−1.34870	−0.0594306
$516$	14.3831	0.633179
$517$	6.15373	0.270641
$518$	−2.51779	−0.110625
$519$	9.77252	0.428966
$520$	−7.20850	−0.316114
$521$	41.5693	1.82119	0.910593	−	0.413304i	$-0.135625\pi$
$521$	41.5693	1.82119	0.910593	+	0.413304i	$0.135625\pi$
$522$	−1.70441	−0.0746000
$523$	14.4320	0.631069	0.315535	−	0.948914i	$-0.397816\pi$
$523$	14.4320	0.631069	0.315535	+	0.948914i	$0.397816\pi$
$524$	−21.0621	−0.920104
$525$	4.89709	0.213727
$526$	25.1587	1.09697
$527$	−58.8395	−2.56309
$528$	1.31121	0.0570631
$529$	47.0952	2.04762
$530$	31.6960	1.37679
$531$	−11.6836	−0.507026
$532$	0	0
$533$	11.3188	0.490272
$534$	9.65357	0.417751
$535$	14.2322	0.615310
$536$	4.55258	0.196641
$537$	−22.6819	−0.978797
$538$	−5.45507	−0.235185
$539$	−6.55002	−0.282129
$540$	18.2464	0.785201
$541$	14.1455	0.608163	0.304082	−	0.952646i	$-0.401650\pi$
$541$	14.1455	0.608163	0.304082	+	0.952646i	$0.401650\pi$
$542$	6.02787	0.258919
$543$	25.6924	1.10257
$544$	6.10412	0.261712
$545$	19.2570	0.824881
$546$	1.95042	0.0834702
$547$	−8.53953	−0.365124	−0.182562	−	0.983194i	$-0.558439\pi$
$547$	−8.53953	−0.365124	−0.182562	+	0.983194i	$0.558439\pi$
$548$	−21.1070	−0.901646
$549$	−9.60216	−0.409810
$550$	−5.56760	−0.237403
$551$	0	0
$552$	−10.9778	−0.467247
$553$	−10.0190	−0.426051
$554$	−11.9513	−0.507763
$555$	−15.9985	−0.679100
$556$	12.1711	0.516168
$557$	4.84057	0.205102	0.102551	−	0.994728i	$-0.467300\pi$
$557$	4.84057	0.205102	0.102551	+	0.994728i	$0.467300\pi$
$558$	12.3454	0.522621
$559$	−24.3241	−1.02880
$560$	−2.18065	−0.0921495
$561$	−8.00378	−0.337920
$562$	−15.6262	−0.659150
$563$	−26.8361	−1.13101	−0.565504	−	0.824745i	$-0.691318\pi$
$563$	−26.8361	−1.13101	−0.565504	+	0.824745i	$0.691318\pi$
$564$	8.06882	0.339759
$565$	−35.8323	−1.50748
$566$	−29.0147	−1.21958
$567$	−2.35960	−0.0990937
$568$	2.89974	0.121670
$569$	30.0364	1.25919	0.629595	−	0.776923i	$-0.283221\pi$
$569$	30.0364	1.25919	0.629595	+	0.776923i	$0.283221\pi$
$570$	0	0
$571$	−6.27606	−0.262645	−0.131322	−	0.991340i	$-0.541922\pi$
$571$	−6.27606	−0.262645	−0.131322	+	0.991340i	$0.541922\pi$
$572$	−2.21747	−0.0927169
$573$	−12.1449	−0.507362
$574$	3.42407	0.142918
$575$	46.6135	1.94392
$576$	−1.28073	−0.0533638
$577$	13.4577	0.560252	0.280126	−	0.959963i	$-0.409624\pi$
$577$	13.4577	0.560252	0.280126	+	0.959963i	$0.409624\pi$
$578$	−20.2603	−0.842717
$579$	12.1362	0.504364
$580$	4.32618	0.179635
$581$	−1.95473	−0.0810957
$582$	4.37268	0.181253
$583$	9.75026	0.403815
$584$	2.93991	0.121654
$585$	−9.23215	−0.381702
$586$	−7.39860	−0.305633
$587$	4.98338	0.205686	0.102843	−	0.994698i	$-0.467206\pi$
$587$	4.98338	0.205686	0.102843	+	0.994698i	$0.467206\pi$
$588$	−8.58844	−0.354181
$589$	0	0
$590$	29.6557	1.22091
$591$	6.36405	0.261782
$592$	3.75336	0.154262
$593$	3.11357	0.127859	0.0639294	−	0.997954i	$-0.479637\pi$
$593$	3.11357	0.127859	0.0639294	+	0.997954i	$0.479637\pi$
$594$	5.61293	0.230301
$595$	13.3110	0.545697
$596$	−19.6594	−0.805279
$597$	0.461662	0.0188945
$598$	18.5653	0.759190
$599$	1.20145	0.0490897	0.0245449	−	0.999699i	$-0.492186\pi$
$599$	1.20145	0.0490897	0.0245449	+	0.999699i	$0.492186\pi$
$600$	−7.30028	−0.298033
$601$	−15.6644	−0.638964	−0.319482	−	0.947592i	$-0.603509\pi$
$601$	−15.6644	−0.638964	−0.319482	+	0.947592i	$0.603509\pi$
$602$	−7.35831	−0.299902
$603$	5.83062	0.237441
$604$	2.75510	0.112103
$605$	−3.25078	−0.132163
$606$	22.6585	0.920441
$607$	1.01514	0.0412032	0.0206016	−	0.999788i	$-0.493442\pi$
$607$	1.01514	0.0412032	0.0206016	+	0.999788i	$0.493442\pi$
$608$	0	0
$609$	−1.17054	−0.0474328
$610$	24.3724	0.986812
$611$	−13.6457	−0.552045
$612$	7.81773	0.316013
$613$	−37.7150	−1.52329	−0.761647	−	0.647992i	$-0.775609\pi$
$613$	−37.7150	−1.52329	−0.761647	+	0.647992i	$0.775609\pi$
$614$	9.56584	0.386046
$615$	21.7573	0.877337
$616$	−0.670809	−0.0270277
$617$	−35.1548	−1.41528	−0.707640	−	0.706573i	$-0.750240\pi$
$617$	−35.1548	−1.41528	−0.707640	+	0.706573i	$0.750240\pi$
$618$	−0.543999	−0.0218828
$619$	−23.4970	−0.944424	−0.472212	−	0.881485i	$-0.656544\pi$
$619$	−23.4970	−0.944424	−0.472212	+	0.881485i	$0.656544\pi$
$620$	−31.3353	−1.25846
$621$	−46.9931	−1.88577
$622$	11.6288	0.466273
$623$	−4.93872	−0.197866
$624$	−2.90756	−0.116396
$625$	−21.8399	−0.873594
$626$	22.4931	0.899005
$627$	0	0
$628$	−18.0855	−0.721689
$629$	−22.9110	−0.913520
$630$	−2.79283	−0.111269
$631$	25.5458	1.01696	0.508481	−	0.861073i	$-0.330207\pi$
$631$	25.5458	1.01696	0.508481	+	0.861073i	$0.330207\pi$
$632$	14.9357	0.594110
$633$	17.6391	0.701091
$634$	−12.7818	−0.507630
$635$	14.1956	0.563335
$636$	12.7846	0.506944
$637$	14.5244	0.575479
$638$	1.33081	0.0526873
$639$	3.71379	0.146915
$640$	3.25078	0.128499
$641$	45.2272	1.78637	0.893183	−	0.449693i	$-0.148467\pi$
$641$	45.2272	1.78637	0.893183	+	0.449693i	$0.148467\pi$
$642$	5.74057	0.226562
$643$	15.3169	0.604038	0.302019	−	0.953302i	$-0.402339\pi$
$643$	15.3169	0.604038	0.302019	+	0.953302i	$0.402339\pi$
$644$	5.61621	0.221310
$645$	−46.7562	−1.84102
$646$	0	0
$647$	18.9473	0.744897	0.372449	−	0.928053i	$-0.378518\pi$
$647$	18.9473	0.744897	0.372449	+	0.928053i	$0.378518\pi$
$648$	3.51754	0.138182
$649$	9.12263	0.358095
$650$	12.3460	0.484248
$651$	8.47846	0.332297
$652$	0.202708	0.00793865
$653$	−1.28704	−0.0503659	−0.0251829	−	0.999683i	$-0.508017\pi$
$653$	−1.28704	−0.0503659	−0.0251829	+	0.999683i	$0.508017\pi$
$654$	7.76736	0.303728
$655$	68.4685	2.67528
$656$	−5.10439	−0.199293
$657$	3.76523	0.146896
$658$	−4.12797	−0.160925
$659$	−16.8727	−0.657267	−0.328634	−	0.944457i	$-0.606588\pi$
$659$	−16.8727	−0.657267	−0.328634	+	0.944457i	$0.606588\pi$
$660$	−4.26246	−0.165916
$661$	17.5275	0.681742	0.340871	−	0.940110i	$-0.389278\pi$
$661$	17.5275	0.681742	0.340871	+	0.940110i	$0.389278\pi$
$662$	7.71237	0.299750
$663$	17.7481	0.689279
$664$	2.91398	0.113084
$665$	0	0
$666$	4.80704	0.186269
$667$	−11.1419	−0.431417
$668$	−16.8141	−0.650557
$669$	19.9953	0.773062
$670$	−14.7994	−0.571752
$671$	7.49741	0.289434
$672$	−0.879571	−0.0339302
$673$	−23.1734	−0.893268	−0.446634	−	0.894717i	$-0.647377\pi$
$673$	−23.1734	−0.893268	−0.446634	+	0.894717i	$0.647377\pi$
$674$	−7.93441	−0.305622
$675$	−31.2505	−1.20283
$676$	−8.08285	−0.310879
$677$	17.7551	0.682384	0.341192	−	0.939994i	$-0.389169\pi$
$677$	17.7551	0.682384	0.341192	+	0.939994i	$0.389169\pi$
$678$	−14.4530	−0.555065
$679$	−2.23704	−0.0858499
$680$	−19.8432	−0.760951
$681$	−16.2841	−0.624009
$682$	−9.63931	−0.369108
$683$	1.89794	0.0726228	0.0363114	−	0.999341i	$-0.488439\pi$
$683$	1.89794	0.0726228	0.0363114	+	0.999341i	$0.488439\pi$
$684$	0	0
$685$	68.6143	2.62162
$686$	9.08947	0.347038
$687$	−32.8389	−1.25288
$688$	10.9693	0.418201
$689$	−21.6209	−0.823690
$690$	35.6865	1.35856
$691$	25.7724	0.980427	0.490213	−	0.871602i	$-0.336919\pi$
$691$	25.7724	0.980427	0.490213	+	0.871602i	$0.336919\pi$
$692$	7.45306	0.283323
$693$	−0.859125	−0.0326355
$694$	15.2630	0.579374
$695$	−39.5655	−1.50080
$696$	1.74497	0.0661430
$697$	31.1578	1.18019
$698$	17.9656	0.680007
$699$	4.25445	0.160918
$700$	3.73479	0.141162
$701$	−15.2517	−0.576047	−0.288024	−	0.957623i	$-0.592998\pi$
$701$	−15.2517	−0.576047	−0.288024	+	0.957623i	$0.592998\pi$
$702$	−12.4465	−0.469762
$703$	0	0
$704$	1.00000	0.0376889
$705$	−26.2300	−0.987879
$706$	16.4839	0.620378
$707$	−11.5920	−0.435962
$708$	11.9617	0.449547
$709$	−6.21153	−0.233279	−0.116639	−	0.993174i	$-0.537212\pi$
$709$	−6.21153	−0.233279	−0.116639	+	0.993174i	$0.537212\pi$
$710$	−9.42643	−0.353768
$711$	19.1286	0.717379
$712$	7.36234	0.275915
$713$	80.7031	3.02236
$714$	5.36901	0.200930
$715$	7.20850	0.269583
$716$	−17.2985	−0.646475
$717$	9.69660	0.362126
$718$	10.8313	0.404221
$719$	−47.8543	−1.78467	−0.892333	−	0.451378i	$-0.850933\pi$
$719$	−47.8543	−1.78467	−0.892333	+	0.451378i	$0.850933\pi$
$720$	4.16338	0.155160
$721$	0.278307	0.0103647
$722$	0	0
$723$	31.7414	1.18048
$724$	19.5944	0.728221
$725$	−7.40942	−0.275179
$726$	−1.31121	−0.0486635
$727$	−23.3235	−0.865021	−0.432511	−	0.901629i	$-0.642372\pi$
$727$	−23.3235	−0.865021	−0.432511	+	0.901629i	$0.642372\pi$
$728$	1.48750	0.0551302
$729$	26.5842	0.984600
$730$	−9.55702	−0.353721
$731$	−66.9580	−2.47653
$732$	9.83067	0.363352
$733$	34.5273	1.27529	0.637647	−	0.770329i	$-0.279908\pi$
$733$	34.5273	1.27529	0.637647	+	0.770329i	$0.279908\pi$
$734$	−8.58108	−0.316734
$735$	27.9192	1.02981
$736$	−8.37229	−0.308607
$737$	−4.55258	−0.167696
$738$	−6.53735	−0.240643
$739$	48.7492	1.79327	0.896634	−	0.442773i	$-0.146005\pi$
$739$	48.7492	1.79327	0.896634	+	0.442773i	$0.146005\pi$
$740$	−12.2014	−0.448531
$741$	0	0
$742$	−6.54056	−0.240112
$743$	1.42826	0.0523979	0.0261990	−	0.999657i	$-0.491660\pi$
$743$	1.42826	0.0523979	0.0261990	+	0.999657i	$0.491660\pi$
$744$	−12.6392	−0.463374
$745$	63.9083	2.34142
$746$	28.5466	1.04517
$747$	3.73203	0.136548
$748$	−6.10412	−0.223189
$749$	−2.93685	−0.107310
$750$	2.41935	0.0883422
$751$	−22.2866	−0.813250	−0.406625	−	0.913595i	$-0.633295\pi$
$751$	−22.2866	−0.813250	−0.406625	+	0.913595i	$0.633295\pi$
$752$	6.15373	0.224403
$753$	0.994249	0.0362325
$754$	−2.95103	−0.107470
$755$	−8.95623	−0.325951
$756$	−3.76520	−0.136939
$757$	51.2727	1.86354	0.931769	−	0.363053i	$-0.118265\pi$
$757$	51.2727	1.86354	0.931769	+	0.363053i	$0.118265\pi$
$758$	−17.7270	−0.643874
$759$	10.9778	0.398470
$760$	0	0
$761$	28.1042	1.01878	0.509389	−	0.860537i	$-0.329872\pi$
$761$	28.1042	1.01878	0.509389	+	0.860537i	$0.329872\pi$
$762$	5.72582	0.207424
$763$	−3.97375	−0.143859
$764$	−9.26240	−0.335102
$765$	−25.4138	−0.918837
$766$	9.71073	0.350863
$767$	−20.2291	−0.730431
$768$	1.31121	0.0473142
$769$	35.4752	1.27927	0.639634	−	0.768680i	$-0.279086\pi$
$769$	35.4752	1.27927	0.639634	+	0.768680i	$0.279086\pi$
$770$	2.18065	0.0785853
$771$	−19.9816	−0.719621
$772$	9.25574	0.333122
$773$	−43.0138	−1.54710	−0.773549	−	0.633736i	$-0.781520\pi$
$773$	−43.0138	−1.54710	−0.773549	+	0.633736i	$0.781520\pi$
$774$	14.0487	0.504971
$775$	53.6678	1.92780
$776$	3.33485	0.119714
$777$	3.30135	0.118435
$778$	−15.2721	−0.547532
$779$	0	0
$780$	9.45185	0.338431
$781$	−2.89974	−0.103761
$782$	51.1055	1.82753
$783$	7.46975	0.266947
$784$	−6.55002	−0.233929
$785$	58.7920	2.09838
$786$	27.6169	0.985061
$787$	−45.9147	−1.63668	−0.818340	−	0.574734i	$-0.805106\pi$
$787$	−45.9147	−1.63668	−0.818340	+	0.574734i	$0.805106\pi$
$788$	4.85358	0.172902
$789$	−32.9883	−1.17441
$790$	−48.5527	−1.72743
$791$	7.39410	0.262904
$792$	1.28073	0.0455088
$793$	−16.6252	−0.590380
$794$	11.9204	0.423039
$795$	−41.5601	−1.47398
$796$	0.352088	0.0124794
$797$	−17.0304	−0.603248	−0.301624	−	0.953427i	$-0.597529\pi$
$797$	−17.0304	−0.603248	−0.301624	+	0.953427i	$0.597529\pi$
$798$	0	0
$799$	−37.5631	−1.32889
$800$	−5.56760	−0.196844
$801$	9.42917	0.333163
$802$	13.6988	0.483723
$803$	−2.93991	−0.103747
$804$	−5.96938	−0.210524
$805$	−18.2571	−0.643477
$806$	21.3748	0.752897
$807$	7.15273	0.251788
$808$	17.2807	0.607931
$809$	4.31502	0.151708	0.0758540	−	0.997119i	$-0.475832\pi$
$809$	4.31502	0.151708	0.0758540	+	0.997119i	$0.475832\pi$
$810$	−11.4348	−0.401776
$811$	−22.5286	−0.791086	−0.395543	−	0.918447i	$-0.629444\pi$
$811$	−22.5286	−0.791086	−0.395543	+	0.918447i	$0.629444\pi$
$812$	−0.892720	−0.0313283
$813$	−7.90380	−0.277198
$814$	−3.75336	−0.131555
$815$	−0.658959	−0.0230823
$816$	−8.00378	−0.280188
$817$	0	0
$818$	4.60043	0.160850
$819$	1.90508	0.0665689
$820$	16.5933	0.579462
$821$	21.0387	0.734255	0.367128	−	0.930171i	$-0.380341\pi$
$821$	21.0387	0.734255	0.367128	+	0.930171i	$0.380341\pi$
$822$	27.6757	0.965300
$823$	−17.0771	−0.595271	−0.297635	−	0.954680i	$-0.596198\pi$
$823$	−17.0771	−0.595271	−0.297635	+	0.954680i	$0.596198\pi$
$824$	−0.414883	−0.0144531
$825$	7.30028	0.254163
$826$	−6.11954	−0.212926
$827$	−47.9825	−1.66851	−0.834257	−	0.551376i	$-0.814103\pi$
$827$	−47.9825	−1.66851	−0.834257	+	0.551376i	$0.814103\pi$
$828$	−10.7226	−0.372638
$829$	−27.6449	−0.960148	−0.480074	−	0.877228i	$-0.659390\pi$
$829$	−27.6449	−0.960148	−0.480074	+	0.877228i	$0.659390\pi$
$830$	−9.47273	−0.328803
$831$	15.6707	0.543610
$832$	−2.21747	−0.0768768
$833$	39.9821	1.38530
$834$	−15.9588	−0.552608
$835$	54.6590	1.89155
$836$	0	0
$837$	−54.1048	−1.87014
$838$	12.9653	0.447880
$839$	23.7994	0.821646	0.410823	−	0.911715i	$-0.365241\pi$
$839$	23.7994	0.821646	0.410823	+	0.911715i	$0.365241\pi$
$840$	2.85929	0.0986550
$841$	−27.2289	−0.938929
$842$	38.1067	1.31324
$843$	20.4892	0.705685
$844$	13.4525	0.463055
$845$	26.2756	0.903908
$846$	7.88127	0.270964
$847$	0.670809	0.0230493
$848$	9.75026	0.334825
$849$	38.0444	1.30568
$850$	33.9853	1.16569
$851$	31.4242	1.07721
$852$	−3.80217	−0.130260
$853$	−19.6855	−0.674020	−0.337010	−	0.941501i	$-0.609416\pi$
$853$	−19.6855	−0.674020	−0.337010	+	0.941501i	$0.609416\pi$
$854$	−5.02933	−0.172100
$855$	0	0
$856$	4.37807	0.149639
$857$	−11.5545	−0.394695	−0.197347	−	0.980334i	$-0.563233\pi$
$857$	−11.5545	−0.394695	−0.197347	+	0.980334i	$0.563233\pi$
$858$	2.90756	0.0992625
$859$	−39.4149	−1.34482	−0.672410	−	0.740179i	$-0.734741\pi$
$859$	−39.4149	−1.34482	−0.672410	+	0.740179i	$0.734741\pi$
$860$	−35.6588	−1.21596
$861$	−4.48967	−0.153008
$862$	15.3186	0.521754
$863$	−35.8828	−1.22146	−0.610732	−	0.791838i	$-0.709125\pi$
$863$	−35.8828	−1.22146	−0.610732	+	0.791838i	$0.709125\pi$
$864$	5.61293	0.190956
$865$	−24.2283	−0.823786
$866$	22.4007	0.761207
$867$	26.5655	0.902211
$868$	6.46614	0.219475
$869$	−14.9357	−0.506659
$870$	−5.67253	−0.192317
$871$	10.0952	0.342062
$872$	5.92381	0.200606
$873$	4.27104	0.144553
$874$	0	0
$875$	−1.23773	−0.0418429
$876$	−3.85484	−0.130243
$877$	−4.73774	−0.159982	−0.0799910	−	0.996796i	$-0.525489\pi$
$877$	−4.73774	−0.159982	−0.0799910	+	0.996796i	$0.525489\pi$
$878$	−14.7208	−0.496804
$879$	9.70111	0.327210
$880$	−3.25078	−0.109584
$881$	13.3859	0.450983	0.225492	−	0.974245i	$-0.427601\pi$
$881$	13.3859	0.450983	0.225492	+	0.974245i	$0.427601\pi$
$882$	−8.38880	−0.282466
$883$	−43.6839	−1.47008	−0.735039	−	0.678024i	$-0.762836\pi$
$883$	−43.6839	−1.47008	−0.735039	+	0.678024i	$0.762836\pi$
$884$	13.5357	0.455254
$885$	−38.8848	−1.30710
$886$	14.0323	0.471423
$887$	−1.30912	−0.0439559	−0.0219779	−	0.999758i	$-0.506996\pi$
$887$	−1.30912	−0.0439559	−0.0219779	+	0.999758i	$0.506996\pi$
$888$	−4.92144	−0.165153
$889$	−2.92930	−0.0982456
$890$	−23.9334	−0.802249
$891$	−3.51754	−0.117842
$892$	15.2495	0.510591
$893$	0	0
$894$	25.7775	0.862130
$895$	56.2336	1.87968
$896$	−0.670809	−0.0224101
$897$	−24.3429	−0.812787
$898$	−20.2903	−0.677098
$899$	−12.8281	−0.427841
$900$	−7.13059	−0.237686
$901$	−59.5168	−1.98279
$902$	5.10439	0.169958
$903$	9.64828	0.321075
$904$	−11.0227	−0.366609
$905$	−63.6973	−2.11737
$906$	−3.61251	−0.120018
$907$	36.7997	1.22191	0.610957	−	0.791663i	$-0.290785\pi$
$907$	36.7997	1.22191	0.610957	+	0.791663i	$0.290785\pi$
$908$	−12.4192	−0.412145
$909$	22.1319	0.734067
$910$	−4.83553	−0.160296
$911$	48.5998	1.61018	0.805092	−	0.593151i	$-0.202116\pi$
$911$	48.5998	1.61018	0.805092	+	0.593151i	$0.202116\pi$
$912$	0	0
$913$	−2.91398	−0.0964388
$914$	4.00708	0.132542
$915$	−31.9574	−1.05648
$916$	−25.0447	−0.827502
$917$	−14.1287	−0.466570
$918$	−34.2620	−1.13082
$919$	−38.4898	−1.26966	−0.634830	−	0.772652i	$-0.718930\pi$
$919$	−38.4898	−1.26966	−0.634830	+	0.772652i	$0.718930\pi$
$920$	27.2165	0.897302
$921$	−12.5428	−0.413300
$922$	23.9251	0.787931
$923$	6.43008	0.211649
$924$	0.879571	0.0289358
$925$	20.8972	0.687095
$926$	6.18485	0.203247
$927$	−0.531354	−0.0174519
$928$	1.33081	0.0436860
$929$	−23.6835	−0.777030	−0.388515	−	0.921442i	$-0.627012\pi$
$929$	−23.6835	−0.777030	−0.388515	+	0.921442i	$0.627012\pi$
$930$	41.0872	1.34730
$931$	0	0
$932$	3.24468	0.106283
$933$	−15.2478	−0.499191
$934$	−0.958537	−0.0313643
$935$	19.8432	0.648941
$936$	−2.83998	−0.0928275
$937$	0.729477	0.0238310	0.0119155	−	0.999929i	$-0.496207\pi$
$937$	0.729477	0.0238310	0.0119155	+	0.999929i	$0.496207\pi$
$938$	3.05391	0.0997137
$939$	−29.4932	−0.962473
$940$	−20.0044	−0.652473
$941$	−33.9291	−1.10606	−0.553028	−	0.833163i	$-0.686528\pi$
$941$	−33.9291	−1.10606	−0.553028	+	0.833163i	$0.686528\pi$
$942$	23.7139	0.772639
$943$	−42.7355	−1.39166
$944$	9.12263	0.296916
$945$	12.2399	0.398163
$946$	−10.9693	−0.356643
$947$	−36.9590	−1.20100	−0.600502	−	0.799623i	$-0.705033\pi$
$947$	−36.9590	−1.20100	−0.600502	+	0.799623i	$0.705033\pi$
$948$	−19.5838	−0.636053
$949$	6.51915	0.211621
$950$	0	0
$951$	16.7596	0.543467
$952$	4.09470	0.132710
$953$	21.0456	0.681735	0.340868	−	0.940111i	$-0.389279\pi$
$953$	21.0456	0.681735	0.340868	+	0.940111i	$0.389279\pi$
$954$	12.4875	0.404296
$955$	30.1101	0.974339
$956$	7.39516	0.239177
$957$	−1.74497	−0.0564069
$958$	−13.0143	−0.420472
$959$	−14.1588	−0.457210
$960$	−4.26246	−0.137570
$961$	61.9164	1.99730
$962$	8.32295	0.268343
$963$	5.60713	0.180687
$964$	24.2077	0.779678
$965$	−30.0884	−0.968581
$966$	−7.36402	−0.236933
$967$	−7.72202	−0.248323	−0.124162	−	0.992262i	$-0.539624\pi$
$967$	−7.72202	−0.248323	−0.124162	+	0.992262i	$0.539624\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	−10.8409	−0.348079
$971$	3.50441	0.112462	0.0562310	−	0.998418i	$-0.482092\pi$
$971$	3.50441	0.112462	0.0562310	+	0.998418i	$0.482092\pi$
$972$	12.2266	0.392167
$973$	8.16446	0.261740
$974$	−24.3237	−0.779380
$975$	−16.1881	−0.518435
$976$	7.49741	0.239986
$977$	3.17675	0.101633	0.0508167	−	0.998708i	$-0.483818\pi$
$977$	3.17675	0.101633	0.0508167	+	0.998708i	$0.483818\pi$
$978$	−0.265792	−0.00849910
$979$	−7.36234	−0.235301
$980$	21.2927	0.680170
$981$	7.58681	0.242228
$982$	−1.87591	−0.0598627
$983$	38.1663	1.21732	0.608658	−	0.793433i	$-0.291708\pi$
$983$	38.1663	1.21732	0.608658	+	0.793433i	$0.291708\pi$
$984$	6.69293	0.213363
$985$	−15.7779	−0.502727
$986$	−8.12343	−0.258703
$987$	5.41264	0.172286
$988$	0	0
$989$	91.8382	2.92029
$990$	−4.16338	−0.132321
$991$	−16.1113	−0.511792	−0.255896	−	0.966704i	$-0.582371\pi$
$991$	−16.1113	−0.511792	−0.255896	+	0.966704i	$0.582371\pi$
$992$	−9.63931	−0.306049
$993$	−10.1125	−0.320912
$994$	1.94517	0.0616971
$995$	−1.14456	−0.0362851
$996$	−3.82084	−0.121068
$997$	−27.1550	−0.860006	−0.430003	−	0.902827i	$-0.641488\pi$
$997$	−27.1550	−0.860006	−0.430003	+	0.902827i	$0.641488\pi$
$998$	6.58150	0.208334
$999$	−21.0674	−0.666542

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.bs.1.8		12
19.2	odd	18		418.2.j.b.23.2	✓	24
19.10	odd	18		418.2.j.b.309.2	yes	24
19.18	odd	2		7942.2.a.bw.1.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.j.b.23.2	✓	24	19.2	odd	18
418.2.j.b.309.2	yes	24	19.10	odd	18
7942.2.a.bs.1.8		12	1.1	even	1	trivial
7942.2.a.bw.1.5		12	19.18	odd	2

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:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7942.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.31121 q^{3} +1.00000 q^{4} -3.25078 q^{5} -1.31121 q^{6} +0.670809 q^{7} -1.00000 q^{8} -1.28073 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.31121 q^{3} +1.00000 q^{4} -3.25078 q^{5} -1.31121 q^{6} +0.670809 q^{7} -1.00000 q^{8} -1.28073 q^{9} +3.25078 q^{10} +1.00000 q^{11} +1.31121 q^{12} -2.21747 q^{13} -0.670809 q^{14} -4.26246 q^{15} +1.00000 q^{16} -6.10412 q^{17} +1.28073 q^{18} -3.25078 q^{20} +0.879571 q^{21} -1.00000 q^{22} +8.37229 q^{23} -1.31121 q^{24} +5.56760 q^{25} +2.21747 q^{26} -5.61293 q^{27} +0.670809 q^{28} -1.33081 q^{29} +4.26246 q^{30} +9.63931 q^{31} -1.00000 q^{32} +1.31121 q^{33} +6.10412 q^{34} -2.18065 q^{35} -1.28073 q^{36} +3.75336 q^{37} -2.90756 q^{39} +3.25078 q^{40} -5.10439 q^{41} -0.879571 q^{42} +10.9693 q^{43} +1.00000 q^{44} +4.16338 q^{45} -8.37229 q^{46} +6.15373 q^{47} +1.31121 q^{48} -6.55002 q^{49} -5.56760 q^{50} -8.00378 q^{51} -2.21747 q^{52} +9.75026 q^{53} +5.61293 q^{54} -3.25078 q^{55} -0.670809 q^{56} +1.33081 q^{58} +9.12263 q^{59} -4.26246 q^{60} +7.49741 q^{61} -9.63931 q^{62} -0.859125 q^{63} +1.00000 q^{64} +7.20850 q^{65} -1.31121 q^{66} -4.55258 q^{67} -6.10412 q^{68} +10.9778 q^{69} +2.18065 q^{70} -2.89974 q^{71} +1.28073 q^{72} -2.93991 q^{73} -3.75336 q^{74} +7.30028 q^{75} +0.670809 q^{77} +2.90756 q^{78} -14.9357 q^{79} -3.25078 q^{80} -3.51754 q^{81} +5.10439 q^{82} -2.91398 q^{83} +0.879571 q^{84} +19.8432 q^{85} -10.9693 q^{86} -1.74497 q^{87} -1.00000 q^{88} -7.36234 q^{89} -4.16338 q^{90} -1.48750 q^{91} +8.37229 q^{92} +12.6392 q^{93} -6.15373 q^{94} -1.31121 q^{96} -3.33485 q^{97} +6.55002 q^{98} -1.28073 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 3 q^{3} + 12 q^{4} - 9 q^{5} - 3 q^{6} - 12 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 + 3 * q^3 + 12 * q^4 - 9 * q^5 - 3 * q^6 - 12 * q^7 - 12 * q^8 + 15 * q^9	\( 12 q - 12 q^{2} + 3 q^{3} + 12 q^{4} - 9 q^{5} - 3 q^{6} - 12 q^{7} - 12 q^{8} + 15 q^{9} + 9 q^{10} + 12 q^{11} + 3 q^{12} + 12 q^{14} + 21 q^{15} + 12 q^{16} - 33 q^{17} - 15 q^{18} - 9 q^{20} - 9 q^{21} - 12 q^{22} - 18 q^{23} - 3 q^{24} + 15 q^{25} + 21 q^{27} - 12 q^{28} - 15 q^{29} - 21 q^{30} + 9 q^{31} - 12 q^{32} + 3 q^{33} + 33 q^{34} - 30 q^{35} + 15 q^{36} + 9 q^{37} - 6 q^{39} + 9 q^{40} - 15 q^{41} + 9 q^{42} - 21 q^{43} + 12 q^{44} + 18 q^{46} - 27 q^{47} + 3 q^{48} + 18 q^{49} - 15 q^{50} - 6 q^{51} + 6 q^{53} - 21 q^{54} - 9 q^{55} + 12 q^{56} + 15 q^{58} + 48 q^{59} + 21 q^{60} + 12 q^{61} - 9 q^{62} - 66 q^{63} + 12 q^{64} - 36 q^{65} - 3 q^{66} - 3 q^{67} - 33 q^{68} - 24 q^{69} + 30 q^{70} - 3 q^{71} - 15 q^{72} - 30 q^{73} - 9 q^{74} + 21 q^{75} - 12 q^{77} + 6 q^{78} + 12 q^{79} - 9 q^{80} + 12 q^{81} + 15 q^{82} - 66 q^{83} - 9 q^{84} + 15 q^{85} + 21 q^{86} - 51 q^{87} - 12 q^{88} + 30 q^{89} + 54 q^{91} - 18 q^{92} - 66 q^{93} + 27 q^{94} - 3 q^{96} + 36 q^{97} - 18 q^{98} + 15 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 3 * q^3 + 12 * q^4 - 9 * q^5 - 3 * q^6 - 12 * q^7 - 12 * q^8 + 15 * q^9 + 9 * q^10 + 12 * q^11 + 3 * q^12 + 12 * q^14 + 21 * q^15 + 12 * q^16 - 33 * q^17 - 15 * q^18 - 9 * q^20 - 9 * q^21 - 12 * q^22 - 18 * q^23 - 3 * q^24 + 15 * q^25 + 21 * q^27 - 12 * q^28 - 15 * q^29 - 21 * q^30 + 9 * q^31 - 12 * q^32 + 3 * q^33 + 33 * q^34 - 30 * q^35 + 15 * q^36 + 9 * q^37 - 6 * q^39 + 9 * q^40 - 15 * q^41 + 9 * q^42 - 21 * q^43 + 12 * q^44 + 18 * q^46 - 27 * q^47 + 3 * q^48 + 18 * q^49 - 15 * q^50 - 6 * q^51 + 6 * q^53 - 21 * q^54 - 9 * q^55 + 12 * q^56 + 15 * q^58 + 48 * q^59 + 21 * q^60 + 12 * q^61 - 9 * q^62 - 66 * q^63 + 12 * q^64 - 36 * q^65 - 3 * q^66 - 3 * q^67 - 33 * q^68 - 24 * q^69 + 30 * q^70 - 3 * q^71 - 15 * q^72 - 30 * q^73 - 9 * q^74 + 21 * q^75 - 12 * q^77 + 6 * q^78 + 12 * q^79 - 9 * q^80 + 12 * q^81 + 15 * q^82 - 66 * q^83 - 9 * q^84 + 15 * q^85 + 21 * q^86 - 51 * q^87 - 12 * q^88 + 30 * q^89 + 54 * q^91 - 18 * q^92 - 66 * q^93 + 27 * q^94 - 3 * q^96 + 36 * q^97 - 18 * q^98 + 15 * q^99

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