LMFDB - Embedded newform 5054.2.a.bg.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, 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("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.8.19520000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 12x^{6} + 16x^{5} + 50x^{4} - 24x^{3} - 72x^{2} - 32x - 4 $ x^8 - 2x^7 - 12x^6 + 16x^5 + 50x^4 - 24x^3 - 72x^2 - 32*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.368905$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.57867 q^{3} +1.00000 q^{4} +0.329540 q^{5} -1.57867 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.507804 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.57867 q^{3} +1.00000 q^{4} +0.329540 q^{5} -1.57867 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.507804 q^{9} -0.329540 q^{10} +3.25194 q^{11} +1.57867 q^{12} +3.60351 q^{13} -1.00000 q^{14} +0.520235 q^{15} +1.00000 q^{16} -2.15017 q^{17} +0.507804 q^{18} +0.329540 q^{20} +1.57867 q^{21} -3.25194 q^{22} +3.48786 q^{23} -1.57867 q^{24} -4.89140 q^{25} -3.60351 q^{26} -5.53766 q^{27} +1.00000 q^{28} +7.27409 q^{29} -0.520235 q^{30} -1.84367 q^{31} -1.00000 q^{32} +5.13373 q^{33} +2.15017 q^{34} +0.329540 q^{35} -0.507804 q^{36} +8.60440 q^{37} +5.68875 q^{39} -0.329540 q^{40} -0.542326 q^{41} -1.57867 q^{42} -5.42210 q^{43} +3.25194 q^{44} -0.167342 q^{45} -3.48786 q^{46} +2.57970 q^{47} +1.57867 q^{48} +1.00000 q^{49} +4.89140 q^{50} -3.39440 q^{51} +3.60351 q^{52} +13.0647 q^{53} +5.53766 q^{54} +1.07164 q^{55} -1.00000 q^{56} -7.27409 q^{58} -9.47596 q^{59} +0.520235 q^{60} +3.17369 q^{61} +1.84367 q^{62} -0.507804 q^{63} +1.00000 q^{64} +1.18750 q^{65} -5.13373 q^{66} +0.375188 q^{67} -2.15017 q^{68} +5.50618 q^{69} -0.329540 q^{70} +6.95851 q^{71} +0.507804 q^{72} +13.9789 q^{73} -8.60440 q^{74} -7.72191 q^{75} +3.25194 q^{77} -5.68875 q^{78} +3.46990 q^{79} +0.329540 q^{80} -7.21872 q^{81} +0.542326 q^{82} -5.46502 q^{83} +1.57867 q^{84} -0.708567 q^{85} +5.42210 q^{86} +11.4834 q^{87} -3.25194 q^{88} +0.179118 q^{89} +0.167342 q^{90} +3.60351 q^{91} +3.48786 q^{92} -2.91054 q^{93} -2.57970 q^{94} -1.57867 q^{96} -11.9566 q^{97} -1.00000 q^{98} -1.65134 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 4 q^{3} + 8 q^{4} - 2 q^{5} - 4 q^{6} + 8 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 4 * q^3 + 8 * q^4 - 2 * q^5 - 4 * q^6 + 8 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} + 4 q^{3} + 8 q^{4} - 2 q^{5} - 4 q^{6} + 8 q^{7} - 8 q^{8} + 8 q^{9} + 2 q^{10} - 12 q^{11} + 4 q^{12} + 10 q^{13} - 8 q^{14} + 24 q^{15} + 8 q^{16} - 6 q^{17} - 8 q^{18} - 2 q^{20} + 4 q^{21} + 12 q^{22} - 20 q^{23} - 4 q^{24} + 8 q^{25} - 10 q^{26} + 22 q^{27} + 8 q^{28} + 8 q^{29} - 24 q^{30} + 18 q^{31} - 8 q^{32} - 16 q^{33} + 6 q^{34} - 2 q^{35} + 8 q^{36} + 36 q^{37} + 2 q^{40} + 4 q^{41} - 4 q^{42} - 16 q^{43} - 12 q^{44} + 8 q^{45} + 20 q^{46} - 10 q^{47} + 4 q^{48} + 8 q^{49} - 8 q^{50} + 12 q^{51} + 10 q^{52} + 32 q^{53} - 22 q^{54} - 22 q^{55} - 8 q^{56} - 8 q^{58} - 2 q^{59} + 24 q^{60} + 2 q^{61} - 18 q^{62} + 8 q^{63} + 8 q^{64} + 16 q^{66} + 44 q^{67} - 6 q^{68} + 2 q^{70} + 8 q^{71} - 8 q^{72} + 30 q^{73} - 36 q^{74} - 16 q^{75} - 12 q^{77} + 60 q^{79} - 2 q^{80} + 12 q^{81} - 4 q^{82} - 28 q^{83} + 4 q^{84} - 16 q^{85} + 16 q^{86} + 24 q^{87} + 12 q^{88} - 22 q^{89} - 8 q^{90} + 10 q^{91} - 20 q^{92} - 16 q^{93} + 10 q^{94} - 4 q^{96} - 6 q^{97} - 8 q^{98} - 52 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 4 * q^3 + 8 * q^4 - 2 * q^5 - 4 * q^6 + 8 * q^7 - 8 * q^8 + 8 * q^9 + 2 * q^10 - 12 * q^11 + 4 * q^12 + 10 * q^13 - 8 * q^14 + 24 * q^15 + 8 * q^16 - 6 * q^17 - 8 * q^18 - 2 * q^20 + 4 * q^21 + 12 * q^22 - 20 * q^23 - 4 * q^24 + 8 * q^25 - 10 * q^26 + 22 * q^27 + 8 * q^28 + 8 * q^29 - 24 * q^30 + 18 * q^31 - 8 * q^32 - 16 * q^33 + 6 * q^34 - 2 * q^35 + 8 * q^36 + 36 * q^37 + 2 * q^40 + 4 * q^41 - 4 * q^42 - 16 * q^43 - 12 * q^44 + 8 * q^45 + 20 * q^46 - 10 * q^47 + 4 * q^48 + 8 * q^49 - 8 * q^50 + 12 * q^51 + 10 * q^52 + 32 * q^53 - 22 * q^54 - 22 * q^55 - 8 * q^56 - 8 * q^58 - 2 * q^59 + 24 * q^60 + 2 * q^61 - 18 * q^62 + 8 * q^63 + 8 * q^64 + 16 * q^66 + 44 * q^67 - 6 * q^68 + 2 * q^70 + 8 * q^71 - 8 * q^72 + 30 * q^73 - 36 * q^74 - 16 * q^75 - 12 * q^77 + 60 * q^79 - 2 * q^80 + 12 * q^81 - 4 * q^82 - 28 * q^83 + 4 * q^84 - 16 * q^85 + 16 * q^86 + 24 * q^87 + 12 * q^88 - 22 * q^89 - 8 * q^90 + 10 * q^91 - 20 * q^92 - 16 * q^93 + 10 * q^94 - 4 * q^96 - 6 * q^97 - 8 * q^98 - 52 * 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
$3$	1.57867	0.911445	0.455723	−	0.890122i	$-0.349381\pi$
$3$	1.57867	0.911445	0.455723	+	0.890122i	$0.349381\pi$
$4$	1.00000	0.500000
$5$	0.329540	0.147375	0.0736875	−	0.997281i	$-0.476523\pi$
$5$	0.329540	0.147375	0.0736875	+	0.997281i	$0.476523\pi$
$6$	−1.57867	−0.644489
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−0.507804	−0.169268
$10$	−0.329540	−0.104210
$11$	3.25194	0.980496	0.490248	−	0.871583i	$-0.336906\pi$
$11$	3.25194	0.980496	0.490248	+	0.871583i	$0.336906\pi$
$12$	1.57867	0.455723
$13$	3.60351	0.999434	0.499717	−	0.866189i	$-0.333437\pi$
$13$	3.60351	0.999434	0.499717	+	0.866189i	$0.333437\pi$
$14$	−1.00000	−0.267261
$15$	0.520235	0.134324
$16$	1.00000	0.250000
$17$	−2.15017	−0.521492	−0.260746	−	0.965407i	$-0.583969\pi$
$17$	−2.15017	−0.521492	−0.260746	+	0.965407i	$0.583969\pi$
$18$	0.507804	0.119690
$19$	0	0
$19$	0	0
$20$	0.329540	0.0736875
$21$	1.57867	0.344494
$22$	−3.25194	−0.693315
$23$	3.48786	0.727269	0.363635	−	0.931542i	$-0.381536\pi$
$23$	3.48786	0.727269	0.363635	+	0.931542i	$0.381536\pi$
$24$	−1.57867	−0.322244
$25$	−4.89140	−0.978281
$26$	−3.60351	−0.706707
$27$	−5.53766	−1.06572
$28$	1.00000	0.188982
$29$	7.27409	1.35076	0.675382	−	0.737468i	$-0.263979\pi$
$29$	7.27409	1.35076	0.675382	+	0.737468i	$0.263979\pi$
$30$	−0.520235	−0.0949816
$31$	−1.84367	−0.331132	−0.165566	−	0.986199i	$-0.552945\pi$
$31$	−1.84367	−0.331132	−0.165566	+	0.986199i	$0.552945\pi$
$32$	−1.00000	−0.176777
$33$	5.13373	0.893668
$34$	2.15017	0.368751
$35$	0.329540	0.0557025
$36$	−0.507804	−0.0846339
$37$	8.60440	1.41455	0.707277	−	0.706936i	$-0.249923\pi$
$37$	8.60440	1.41455	0.707277	+	0.706936i	$0.249923\pi$
$38$	0	0
$39$	5.68875	0.910930
$40$	−0.329540	−0.0521049
$41$	−0.542326	−0.0846971	−0.0423485	−	0.999103i	$-0.513484\pi$
$41$	−0.542326	−0.0846971	−0.0423485	+	0.999103i	$0.513484\pi$
$42$	−1.57867	−0.243594
$43$	−5.42210	−0.826862	−0.413431	−	0.910535i	$-0.635670\pi$
$43$	−5.42210	−0.826862	−0.413431	+	0.910535i	$0.635670\pi$
$44$	3.25194	0.490248
$45$	−0.167342	−0.0249459
$46$	−3.48786	−0.514257
$47$	2.57970	0.376288	0.188144	−	0.982141i	$-0.439753\pi$
$47$	2.57970	0.376288	0.188144	+	0.982141i	$0.439753\pi$
$48$	1.57867	0.227861
$49$	1.00000	0.142857
$50$	4.89140	0.691749
$51$	−3.39440	−0.475311
$52$	3.60351	0.499717
$53$	13.0647	1.79457	0.897284	−	0.441454i	$-0.145537\pi$
$53$	13.0647	1.79457	0.897284	+	0.441454i	$0.145537\pi$
$54$	5.53766	0.753580
$55$	1.07164	0.144501
$56$	−1.00000	−0.133631
$57$	0	0
$58$	−7.27409	−0.955134
$59$	−9.47596	−1.23367	−0.616833	−	0.787094i	$-0.711584\pi$
$59$	−9.47596	−1.23367	−0.616833	+	0.787094i	$0.711584\pi$
$60$	0.520235	0.0671621
$61$	3.17369	0.406350	0.203175	−	0.979142i	$-0.434874\pi$
$61$	3.17369	0.406350	0.203175	+	0.979142i	$0.434874\pi$
$62$	1.84367	0.234146
$63$	−0.507804	−0.0639772
$64$	1.00000	0.125000
$65$	1.18750	0.147292
$66$	−5.13373	−0.631919
$67$	0.375188	0.0458365	0.0229182	−	0.999737i	$-0.492704\pi$
$67$	0.375188	0.0458365	0.0229182	+	0.999737i	$0.492704\pi$
$68$	−2.15017	−0.260746
$69$	5.50618	0.662866
$70$	−0.329540	−0.0393876
$71$	6.95851	0.825823	0.412911	−	0.910771i	$-0.364512\pi$
$71$	6.95851	0.825823	0.412911	+	0.910771i	$0.364512\pi$
$72$	0.507804	0.0598452
$73$	13.9789	1.63610	0.818051	−	0.575146i	$-0.195055\pi$
$73$	13.9789	1.63610	0.818051	+	0.575146i	$0.195055\pi$
$74$	−8.60440	−1.00024
$75$	−7.72191	−0.891649
$76$	0	0
$77$	3.25194	0.370592
$78$	−5.68875	−0.644124
$79$	3.46990	0.390395	0.195197	−	0.980764i	$-0.437465\pi$
$79$	3.46990	0.390395	0.195197	+	0.980764i	$0.437465\pi$
$80$	0.329540	0.0368437
$81$	−7.21872	−0.802081
$82$	0.542326	0.0598899
$83$	−5.46502	−0.599864	−0.299932	−	0.953961i	$-0.596964\pi$
$83$	−5.46502	−0.599864	−0.299932	+	0.953961i	$0.596964\pi$
$84$	1.57867	0.172247
$85$	−0.708567	−0.0768549
$86$	5.42210	0.584680
$87$	11.4834	1.23115
$88$	−3.25194	−0.346658
$89$	0.179118	0.0189865	0.00949325	−	0.999955i	$-0.496978\pi$
$89$	0.179118	0.0189865	0.00949325	+	0.999955i	$0.496978\pi$
$90$	0.167342	0.0176394
$91$	3.60351	0.377751
$92$	3.48786	0.363635
$93$	−2.91054	−0.301809
$94$	−2.57970	−0.266076
$95$	0	0
$96$	−1.57867	−0.161122
$97$	−11.9566	−1.21401	−0.607006	−	0.794697i	$-0.707630\pi$
$97$	−11.9566	−1.21401	−0.607006	+	0.794697i	$0.707630\pi$
$98$	−1.00000	−0.101015
$99$	−1.65134	−0.165966
$100$	−4.89140	−0.489140
$101$	−14.4122	−1.43406	−0.717032	−	0.697040i	$-0.754500\pi$
$101$	−14.4122	−1.43406	−0.717032	+	0.697040i	$0.754500\pi$
$102$	3.39440	0.336096
$103$	4.51595	0.444969	0.222485	−	0.974936i	$-0.428583\pi$
$103$	4.51595	0.444969	0.222485	+	0.974936i	$0.428583\pi$
$104$	−3.60351	−0.353353
$105$	0.520235	0.0507698
$106$	−13.0647	−1.26895
$107$	4.41527	0.426840	0.213420	−	0.976961i	$-0.431540\pi$
$107$	4.41527	0.426840	0.213420	+	0.976961i	$0.431540\pi$
$108$	−5.53766	−0.532862
$109$	12.4100	1.18866	0.594330	−	0.804221i	$-0.297417\pi$
$109$	12.4100	1.18866	0.594330	+	0.804221i	$0.297417\pi$
$110$	−1.07164	−0.102177
$111$	13.5835	1.28929
$112$	1.00000	0.0944911
$113$	2.66085	0.250312	0.125156	−	0.992137i	$-0.460057\pi$
$113$	2.66085	0.250312	0.125156	+	0.992137i	$0.460057\pi$
$114$	0	0
$115$	1.14939	0.107181
$116$	7.27409	0.675382
$117$	−1.82988	−0.169172
$118$	9.47596	0.872333
$119$	−2.15017	−0.197105
$120$	−0.520235	−0.0474908
$121$	−0.424913	−0.0386285
$122$	−3.17369	−0.287333
$123$	−0.856153	−0.0771967
$124$	−1.84367	−0.165566
$125$	−3.25962	−0.291549
$126$	0.507804	0.0452387
$127$	1.71904	0.152540	0.0762701	−	0.997087i	$-0.475699\pi$
$127$	1.71904	0.152540	0.0762701	+	0.997087i	$0.475699\pi$
$128$	−1.00000	−0.0883883
$129$	−8.55970	−0.753640
$130$	−1.18750	−0.104151
$131$	−9.79836	−0.856086	−0.428043	−	0.903758i	$-0.640797\pi$
$131$	−9.79836	−0.856086	−0.428043	+	0.903758i	$0.640797\pi$
$132$	5.13373	0.446834
$133$	0	0
$134$	−0.375188	−0.0324113
$135$	−1.82488	−0.157061
$136$	2.15017	0.184375
$137$	1.29590	0.110716	0.0553580	−	0.998467i	$-0.482370\pi$
$137$	1.29590	0.110716	0.0553580	+	0.998467i	$0.482370\pi$
$138$	−5.50618	−0.468717
$139$	9.63992	0.817647	0.408824	−	0.912613i	$-0.365939\pi$
$139$	9.63992	0.817647	0.408824	+	0.912613i	$0.365939\pi$
$140$	0.329540	0.0278513
$141$	4.07250	0.342966
$142$	−6.95851	−0.583945
$143$	11.7184	0.979941
$144$	−0.507804	−0.0423170
$145$	2.39711	0.199069
$146$	−13.9789	−1.15690
$147$	1.57867	0.130206
$148$	8.60440	0.707277
$149$	−10.2034	−0.835894	−0.417947	−	0.908471i	$-0.637250\pi$
$149$	−10.2034	−0.835894	−0.417947	+	0.908471i	$0.637250\pi$
$150$	7.72191	0.630491
$151$	6.67071	0.542855	0.271427	−	0.962459i	$-0.412504\pi$
$151$	6.67071	0.542855	0.271427	+	0.962459i	$0.412504\pi$
$152$	0	0
$153$	1.09186	0.0882718
$154$	−3.25194	−0.262048
$155$	−0.607563	−0.0488006
$156$	5.68875	0.455465
$157$	−14.4348	−1.15202	−0.576009	−	0.817443i	$-0.695391\pi$
$157$	−14.4348	−1.15202	−0.576009	+	0.817443i	$0.695391\pi$
$158$	−3.46990	−0.276051
$159$	20.6248	1.63565
$160$	−0.329540	−0.0260525
$161$	3.48786	0.274882
$162$	7.21872	0.567157
$163$	19.3303	1.51406	0.757032	−	0.653378i	$-0.226649\pi$
$163$	19.3303	1.51406	0.757032	+	0.653378i	$0.226649\pi$
$164$	−0.542326	−0.0423485
$165$	1.69177	0.131704
$166$	5.46502	0.424168
$167$	15.5520	1.20345	0.601726	−	0.798702i	$-0.294480\pi$
$167$	15.5520	1.20345	0.601726	+	0.798702i	$0.294480\pi$
$168$	−1.57867	−0.121797
$169$	−0.0147006	−0.00113081
$170$	0.708567	0.0543446
$171$	0	0
$172$	−5.42210	−0.413431
$173$	−12.9845	−0.987193	−0.493597	−	0.869691i	$-0.664318\pi$
$173$	−12.9845	−0.987193	−0.493597	+	0.869691i	$0.664318\pi$
$174$	−11.4834	−0.870552
$175$	−4.89140	−0.369755
$176$	3.25194	0.245124
$177$	−14.9594	−1.12442
$178$	−0.179118	−0.0134255
$179$	22.3945	1.67385	0.836923	−	0.547321i	$-0.184352\pi$
$179$	22.3945	1.67385	0.836923	+	0.547321i	$0.184352\pi$
$180$	−0.167342	−0.0124729
$181$	20.7177	1.53993	0.769967	−	0.638084i	$-0.220273\pi$
$181$	20.7177	1.53993	0.769967	+	0.638084i	$0.220273\pi$
$182$	−3.60351	−0.267110
$183$	5.01021	0.370365
$184$	−3.48786	−0.257129
$185$	2.83550	0.208470
$186$	2.91054	0.213411
$187$	−6.99220	−0.511321
$188$	2.57970	0.188144
$189$	−5.53766	−0.402806
$190$	0	0
$191$	−14.0674	−1.01788	−0.508939	−	0.860802i	$-0.669962\pi$
$191$	−14.0674	−1.01788	−0.508939	+	0.860802i	$0.669962\pi$
$192$	1.57867	0.113931
$193$	−15.0982	−1.08679	−0.543397	−	0.839476i	$-0.682862\pi$
$193$	−15.0982	−1.08679	−0.543397	+	0.839476i	$0.682862\pi$
$194$	11.9566	0.858437
$195$	1.87467	0.134248
$196$	1.00000	0.0714286
$197$	23.9075	1.70334	0.851670	−	0.524078i	$-0.175590\pi$
$197$	23.9075	1.70334	0.851670	+	0.524078i	$0.175590\pi$
$198$	1.65134	0.117356
$199$	19.5919	1.38883	0.694417	−	0.719573i	$-0.255662\pi$
$199$	19.5919	1.38883	0.694417	+	0.719573i	$0.255662\pi$
$200$	4.89140	0.345874
$201$	0.592298	0.0417775
$202$	14.4122	1.01404
$203$	7.27409	0.510541
$204$	−3.39440	−0.237656
$205$	−0.178718	−0.0124822
$206$	−4.51595	−0.314641
$207$	−1.77115	−0.123103
$208$	3.60351	0.249859
$209$	0	0
$210$	−0.520235	−0.0358997
$211$	−1.27051	−0.0874659	−0.0437329	−	0.999043i	$-0.513925\pi$
$211$	−1.27051	−0.0874659	−0.0437329	+	0.999043i	$0.513925\pi$
$212$	13.0647	0.897284
$213$	10.9852	0.752692
$214$	−4.41527	−0.301822
$215$	−1.78680	−0.121859
$216$	5.53766	0.376790
$217$	−1.84367	−0.125156
$218$	−12.4100	−0.840509
$219$	22.0680	1.49122
$220$	1.07164	0.0722503
$221$	−7.74815	−0.521197
$222$	−13.5835	−0.911665
$223$	15.3761	1.02966	0.514831	−	0.857292i	$-0.327855\pi$
$223$	15.3761	1.02966	0.514831	+	0.857292i	$0.327855\pi$
$224$	−1.00000	−0.0668153
$225$	2.48387	0.165591
$226$	−2.66085	−0.176997
$227$	−24.6193	−1.63404	−0.817021	−	0.576608i	$-0.804376\pi$
$227$	−24.6193	−1.63404	−0.817021	+	0.576608i	$0.804376\pi$
$228$	0	0
$229$	8.99878	0.594656	0.297328	−	0.954775i	$-0.403904\pi$
$229$	8.99878	0.594656	0.297328	+	0.954775i	$0.403904\pi$
$230$	−1.14939	−0.0757886
$231$	5.13373	0.337775
$232$	−7.27409	−0.477567
$233$	−8.54664	−0.559909	−0.279954	−	0.960013i	$-0.590319\pi$
$233$	−8.54664	−0.559909	−0.279954	+	0.960013i	$0.590319\pi$
$234$	1.82988	0.119623
$235$	0.850116	0.0554555
$236$	−9.47596	−0.616833
$237$	5.47783	0.355823
$238$	2.15017	0.139375
$239$	−2.44971	−0.158459	−0.0792293	−	0.996856i	$-0.525246\pi$
$239$	−2.44971	−0.158459	−0.0792293	+	0.996856i	$0.525246\pi$
$240$	0.520235	0.0335811
$241$	23.6441	1.52305	0.761526	−	0.648135i	$-0.224451\pi$
$241$	23.6441	1.52305	0.761526	+	0.648135i	$0.224451\pi$
$242$	0.424913	0.0273144
$243$	5.21701	0.334671
$244$	3.17369	0.203175
$245$	0.329540	0.0210536
$246$	0.856153	0.0545863
$247$	0	0
$248$	1.84367	0.117073
$249$	−8.62745	−0.546743
$250$	3.25962	0.206156
$251$	−10.5052	−0.663082	−0.331541	−	0.943441i	$-0.607569\pi$
$251$	−10.5052	−0.663082	−0.331541	+	0.943441i	$0.607569\pi$
$252$	−0.507804	−0.0319886
$253$	11.3423	0.713084
$254$	−1.71904	−0.107862
$255$	−1.11859	−0.0700490
$256$	1.00000	0.0625000
$257$	−20.2657	−1.26414	−0.632071	−	0.774911i	$-0.717795\pi$
$257$	−20.2657	−1.26414	−0.632071	+	0.774911i	$0.717795\pi$
$258$	8.55970	0.532904
$259$	8.60440	0.534652
$260$	1.18750	0.0736458
$261$	−3.69381	−0.228641
$262$	9.79836	0.605344
$263$	−12.1640	−0.750067	−0.375034	−	0.927011i	$-0.622369\pi$
$263$	−12.1640	−0.750067	−0.375034	+	0.927011i	$0.622369\pi$
$264$	−5.13373	−0.315959
$265$	4.30533	0.264474
$266$	0	0
$267$	0.282769	0.0173052
$268$	0.375188	0.0229182
$269$	9.58961	0.584689	0.292344	−	0.956313i	$-0.405565\pi$
$269$	9.58961	0.584689	0.292344	+	0.956313i	$0.405565\pi$
$270$	1.82488	0.111059
$271$	−23.1109	−1.40389	−0.701943	−	0.712233i	$-0.747684\pi$
$271$	−23.1109	−1.40389	−0.701943	+	0.712233i	$0.747684\pi$
$272$	−2.15017	−0.130373
$273$	5.68875	0.344299
$274$	−1.29590	−0.0782880
$275$	−15.9065	−0.959200
$276$	5.50618	0.331433
$277$	18.3243	1.10100	0.550502	−	0.834834i	$-0.314436\pi$
$277$	18.3243	1.10100	0.550502	+	0.834834i	$0.314436\pi$
$278$	−9.63992	−0.578164
$279$	0.936220	0.0560500
$280$	−0.329540	−0.0196938
$281$	−24.5244	−1.46301	−0.731503	−	0.681838i	$-0.761181\pi$
$281$	−24.5244	−1.46301	−0.731503	+	0.681838i	$0.761181\pi$
$282$	−4.07250	−0.242514
$283$	8.45490	0.502591	0.251296	−	0.967910i	$-0.419143\pi$
$283$	8.45490	0.502591	0.251296	+	0.967910i	$0.419143\pi$
$284$	6.95851	0.412911
$285$	0	0
$286$	−11.7184	−0.692923
$287$	−0.542326	−0.0320125
$288$	0.507804	0.0299226
$289$	−12.3768	−0.728046
$290$	−2.39711	−0.140763
$291$	−18.8756	−1.10651
$292$	13.9789	0.818051
$293$	17.0364	0.995278	0.497639	−	0.867384i	$-0.334200\pi$
$293$	17.0364	0.995278	0.497639	+	0.867384i	$0.334200\pi$
$294$	−1.57867	−0.0920699
$295$	−3.12271	−0.181811
$296$	−8.60440	−0.500121
$297$	−18.0081	−1.04494
$298$	10.2034	0.591066
$299$	12.5685	0.726858
$300$	−7.72191	−0.445825
$301$	−5.42210	−0.312525
$302$	−6.67071	−0.383856
$303$	−22.7520	−1.30707
$304$	0	0
$305$	1.04586	0.0598858
$306$	−1.09186	−0.0624176
$307$	21.8506	1.24708	0.623540	−	0.781792i	$-0.285694\pi$
$307$	21.8506	1.24708	0.623540	+	0.781792i	$0.285694\pi$
$308$	3.25194	0.185296
$309$	7.12919	0.405565
$310$	0.607563	0.0345072
$311$	−6.93231	−0.393095	−0.196548	−	0.980494i	$-0.562973\pi$
$311$	−6.93231	−0.393095	−0.196548	+	0.980494i	$0.562973\pi$
$312$	−5.68875	−0.322062
$313$	−31.0443	−1.75473	−0.877365	−	0.479823i	$-0.840701\pi$
$313$	−31.0443	−1.75473	−0.877365	+	0.479823i	$0.840701\pi$
$314$	14.4348	0.814600
$315$	−0.167342	−0.00942865
$316$	3.46990	0.195197
$317$	31.0129	1.74186	0.870930	−	0.491406i	$-0.163517\pi$
$317$	31.0129	1.74186	0.870930	+	0.491406i	$0.163517\pi$
$318$	−20.6248	−1.15658
$319$	23.6549	1.32442
$320$	0.329540	0.0184219
$321$	6.97025	0.389041
$322$	−3.48786	−0.194371
$323$	0	0
$324$	−7.21872	−0.401040
$325$	−17.6262	−0.977727
$326$	−19.3303	−1.07061
$327$	19.5912	1.08340
$328$	0.542326	0.0299449
$329$	2.57970	0.142224
$330$	−1.69177	−0.0931290
$331$	19.0103	1.04490	0.522451	−	0.852669i	$-0.325018\pi$
$331$	19.0103	1.04490	0.522451	+	0.852669i	$0.325018\pi$
$332$	−5.46502	−0.299932
$333$	−4.36935	−0.239439
$334$	−15.5520	−0.850969
$335$	0.123640	0.00675515
$336$	1.57867	0.0861235
$337$	−4.79618	−0.261265	−0.130632	−	0.991431i	$-0.541701\pi$
$337$	−4.79618	−0.261265	−0.130632	+	0.991431i	$0.541701\pi$
$338$	0.0147006	0.000799605 0
$339$	4.20060	0.228145
$340$	−0.708567	−0.0384274
$341$	−5.99548	−0.324674
$342$	0	0
$343$	1.00000	0.0539949
$344$	5.42210	0.292340
$345$	1.81451	0.0976899
$346$	12.9845	0.698051
$347$	−2.98419	−0.160200	−0.0800999	−	0.996787i	$-0.525524\pi$
$347$	−2.98419	−0.160200	−0.0800999	+	0.996787i	$0.525524\pi$
$348$	11.4834	0.615574
$349$	20.1084	1.07638	0.538188	−	0.842825i	$-0.319109\pi$
$349$	20.1084	1.07638	0.538188	+	0.842825i	$0.319109\pi$
$350$	4.89140	0.261456
$351$	−19.9550	−1.06512
$352$	−3.25194	−0.173329
$353$	−25.3624	−1.34990	−0.674951	−	0.737862i	$-0.735835\pi$
$353$	−25.3624	−1.34990	−0.674951	+	0.737862i	$0.735835\pi$
$354$	14.9594	0.795084
$355$	2.29311	0.121706
$356$	0.179118	0.00949325
$357$	−3.39440	−0.179651
$358$	−22.3945	−1.18359
$359$	−30.2965	−1.59899	−0.799495	−	0.600673i	$-0.794899\pi$
$359$	−30.2965	−1.59899	−0.799495	+	0.600673i	$0.794899\pi$
$360$	0.167342	0.00881969
$361$	0	0
$362$	−20.7177	−1.08890
$363$	−0.670797	−0.0352077
$364$	3.60351	0.188875
$365$	4.60660	0.241120
$366$	−5.01021	−0.261888
$367$	12.7503	0.665561	0.332780	−	0.943004i	$-0.392013\pi$
$367$	12.7503	0.665561	0.332780	+	0.943004i	$0.392013\pi$
$368$	3.48786	0.181817
$369$	0.275395	0.0143365
$370$	−2.83550	−0.147411
$371$	13.0647	0.678283
$372$	−2.91054	−0.150904
$373$	−5.23786	−0.271206	−0.135603	−	0.990763i	$-0.543297\pi$
$373$	−5.23786	−0.271206	−0.135603	+	0.990763i	$0.543297\pi$
$374$	6.99220	0.361558
$375$	−5.14586	−0.265731
$376$	−2.57970	−0.133038
$377$	26.2123	1.35000
$378$	5.53766	0.284827
$379$	−25.2856	−1.29884	−0.649418	−	0.760432i	$-0.724987\pi$
$379$	−25.2856	−1.29884	−0.649418	+	0.760432i	$0.724987\pi$
$380$	0	0
$381$	2.71380	0.139032
$382$	14.0674	0.719749
$383$	−26.6421	−1.36135	−0.680673	−	0.732588i	$-0.738312\pi$
$383$	−26.6421	−1.36135	−0.680673	+	0.732588i	$0.738312\pi$
$384$	−1.57867	−0.0805611
$385$	1.07164	0.0546161
$386$	15.0982	0.768479
$387$	2.75336	0.139961
$388$	−11.9566	−0.607006
$389$	14.4792	0.734123	0.367062	−	0.930197i	$-0.380364\pi$
$389$	14.4792	0.734123	0.367062	+	0.930197i	$0.380364\pi$
$390$	−1.87467	−0.0949278
$391$	−7.49948	−0.379265
$392$	−1.00000	−0.0505076
$393$	−15.4684	−0.780276
$394$	−23.9075	−1.20444
$395$	1.14347	0.0575344
$396$	−1.65134	−0.0829832
$397$	−31.0558	−1.55865	−0.779324	−	0.626621i	$-0.784437\pi$
$397$	−31.0558	−1.55865	−0.779324	+	0.626621i	$0.784437\pi$
$398$	−19.5919	−0.982054
$399$	0	0
$400$	−4.89140	−0.244570
$401$	−5.75381	−0.287331	−0.143666	−	0.989626i	$-0.545889\pi$
$401$	−5.75381	−0.287331	−0.143666	+	0.989626i	$0.545889\pi$
$402$	−0.592298	−0.0295411
$403$	−6.64367	−0.330945
$404$	−14.4122	−0.717032
$405$	−2.37886	−0.118207
$406$	−7.27409	−0.361007
$407$	27.9810	1.38696
$408$	3.39440	0.168048
$409$	2.53464	0.125330	0.0626649	−	0.998035i	$-0.480040\pi$
$409$	2.53464	0.125330	0.0626649	+	0.998035i	$0.480040\pi$
$410$	0.178718	0.00882627
$411$	2.04579	0.100912
$412$	4.51595	0.222485
$413$	−9.47596	−0.466282
$414$	1.77115	0.0870472
$415$	−1.80094	−0.0884049
$416$	−3.60351	−0.176677
$417$	15.2182	0.745240
$418$	0	0
$419$	10.2109	0.498834	0.249417	−	0.968396i	$-0.419761\pi$
$419$	10.2109	0.498834	0.249417	+	0.968396i	$0.419761\pi$
$420$	0.520235	0.0253849
$421$	25.0336	1.22006	0.610032	−	0.792377i	$-0.291157\pi$
$421$	25.0336	1.22006	0.610032	+	0.792377i	$0.291157\pi$
$422$	1.27051	0.0618477
$423$	−1.30998	−0.0636935
$424$	−13.0647	−0.634476
$425$	10.5173	0.510165
$426$	−10.9852	−0.532234
$427$	3.17369	0.153586
$428$	4.41527	0.213420
$429$	18.4995	0.893162
$430$	1.78680	0.0861672
$431$	5.03621	0.242586	0.121293	−	0.992617i	$-0.461296\pi$
$431$	5.03621	0.242586	0.121293	+	0.992617i	$0.461296\pi$
$432$	−5.53766	−0.266431
$433$	22.8793	1.09951	0.549754	−	0.835326i	$-0.314721\pi$
$433$	22.8793	1.09951	0.549754	+	0.835326i	$0.314721\pi$
$434$	1.84367	0.0884988
$435$	3.78424	0.181440
$436$	12.4100	0.594330
$437$	0	0
$438$	−22.0680	−1.05445
$439$	39.2842	1.87493	0.937467	−	0.348073i	$-0.113164\pi$
$439$	39.2842	1.87493	0.937467	+	0.348073i	$0.113164\pi$
$440$	−1.07164	−0.0510886
$441$	−0.507804	−0.0241811
$442$	7.74815	0.368542
$443$	22.2515	1.05720	0.528600	−	0.848871i	$-0.322717\pi$
$443$	22.2515	1.05720	0.528600	+	0.848871i	$0.322717\pi$
$444$	13.5835	0.644645
$445$	0.0590267	0.00279814
$446$	−15.3761	−0.728081
$447$	−16.1078	−0.761871
$448$	1.00000	0.0472456
$449$	4.10639	0.193793	0.0968963	−	0.995294i	$-0.469108\pi$
$449$	4.10639	0.193793	0.0968963	+	0.995294i	$0.469108\pi$
$450$	−2.48387	−0.117091
$451$	−1.76361	−0.0830451
$452$	2.66085	0.125156
$453$	10.5308	0.494782
$454$	24.6193	1.15544
$455$	1.18750	0.0556710
$456$	0	0
$457$	27.1225	1.26874	0.634368	−	0.773031i	$-0.281261\pi$
$457$	27.1225	1.26874	0.634368	+	0.773031i	$0.281261\pi$
$458$	−8.99878	−0.420485
$459$	11.9069	0.555766
$460$	1.14939	0.0535906
$461$	34.2020	1.59294	0.796472	−	0.604676i	$-0.206697\pi$
$461$	34.2020	1.59294	0.796472	+	0.604676i	$0.206697\pi$
$462$	−5.13373	−0.238843
$463$	12.1690	0.565542	0.282771	−	0.959187i	$-0.408746\pi$
$463$	12.1690	0.565542	0.282771	+	0.959187i	$0.408746\pi$
$464$	7.27409	0.337691
$465$	−0.959140	−0.0444791
$466$	8.54664	0.395915
$467$	−19.7876	−0.915661	−0.457831	−	0.889039i	$-0.651373\pi$
$467$	−19.7876	−0.915661	−0.457831	+	0.889039i	$0.651373\pi$
$468$	−1.82988	−0.0845861
$469$	0.375188	0.0173246
$470$	−0.850116	−0.0392129
$471$	−22.7877	−1.05000
$472$	9.47596	0.436166
$473$	−17.6323	−0.810735
$474$	−5.47783	−0.251605
$475$	0	0
$476$	−2.15017	−0.0985527
$477$	−6.63428	−0.303763
$478$	2.44971	0.112047
$479$	−8.03308	−0.367041	−0.183520	−	0.983016i	$-0.558749\pi$
$479$	−8.03308	−0.367041	−0.183520	+	0.983016i	$0.558749\pi$
$480$	−0.520235	−0.0237454
$481$	31.0061	1.41375
$482$	−23.6441	−1.07696
$483$	5.50618	0.250540
$484$	−0.424913	−0.0193142
$485$	−3.94020	−0.178915
$486$	−5.21701	−0.236648
$487$	−36.7402	−1.66486	−0.832428	−	0.554134i	$-0.813050\pi$
$487$	−36.7402	−1.66486	−0.832428	+	0.554134i	$0.813050\pi$
$488$	−3.17369	−0.143666
$489$	30.5161	1.37999
$490$	−0.329540	−0.0148871
$491$	21.1225	0.953245	0.476622	−	0.879108i	$-0.341861\pi$
$491$	21.1225	0.953245	0.476622	+	0.879108i	$0.341861\pi$
$492$	−0.856153	−0.0385984
$493$	−15.6405	−0.704413
$494$	0	0
$495$	−0.544185	−0.0244593
$496$	−1.84367	−0.0827830
$497$	6.95851	0.312132
$498$	8.62745	0.386605
$499$	0.685934	0.0307066	0.0153533	−	0.999882i	$-0.495113\pi$
$499$	0.685934	0.0307066	0.0153533	+	0.999882i	$0.495113\pi$
$500$	−3.25962	−0.145775
$501$	24.5515	1.09688
$502$	10.5052	0.468870
$503$	−12.0679	−0.538081	−0.269040	−	0.963129i	$-0.586706\pi$
$503$	−12.0679	−0.538081	−0.269040	+	0.963129i	$0.586706\pi$
$504$	0.507804	0.0226194
$505$	−4.74939	−0.211345
$506$	−11.3423	−0.504227
$507$	−0.0232073	−0.00103067
$508$	1.71904	0.0762701
$509$	−28.3925	−1.25848	−0.629238	−	0.777213i	$-0.716633\pi$
$509$	−28.3925	−1.25848	−0.629238	+	0.777213i	$0.716633\pi$
$510$	1.11859	0.0495321
$511$	13.9789	0.618388
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	20.2657	0.893883
$515$	1.48819	0.0655774
$516$	−8.55970	−0.376820
$517$	8.38902	0.368949
$518$	−8.60440	−0.378056
$519$	−20.4982	−0.899772
$520$	−1.18750	−0.0520755
$521$	−23.3223	−1.02177	−0.510883	−	0.859650i	$-0.670682\pi$
$521$	−23.3223	−1.02177	−0.510883	+	0.859650i	$0.670682\pi$
$522$	3.69381	0.161674
$523$	−24.6270	−1.07686	−0.538431	−	0.842669i	$-0.680983\pi$
$523$	−24.6270	−1.07686	−0.538431	+	0.842669i	$0.680983\pi$
$524$	−9.79836	−0.428043
$525$	−7.72191	−0.337012
$526$	12.1640	0.530378
$527$	3.96419	0.172683
$528$	5.13373	0.223417
$529$	−10.8348	−0.471079
$530$	−4.30533	−0.187012
$531$	4.81193	0.208820
$532$	0	0
$533$	−1.95428	−0.0846492
$534$	−0.282769	−0.0122366
$535$	1.45501	0.0629056
$536$	−0.375188	−0.0162056
$537$	35.3535	1.52562
$538$	−9.58961	−0.413437
$539$	3.25194	0.140071
$540$	−1.82488	−0.0785305
$541$	2.10786	0.0906241	0.0453120	−	0.998973i	$-0.485572\pi$
$541$	2.10786	0.0906241	0.0453120	+	0.998973i	$0.485572\pi$
$542$	23.1109	0.992697
$543$	32.7064	1.40357
$544$	2.15017	0.0921876
$545$	4.08959	0.175179
$546$	−5.68875	−0.243456
$547$	−16.3284	−0.698153	−0.349076	−	0.937094i	$-0.613505\pi$
$547$	−16.3284	−0.698153	−0.349076	+	0.937094i	$0.613505\pi$
$548$	1.29590	0.0553580
$549$	−1.61161	−0.0687820
$550$	15.9065	0.678257
$551$	0	0
$552$	−5.50618	−0.234359
$553$	3.46990	0.147555
$554$	−18.3243	−0.778527
$555$	4.47631	0.190009
$556$	9.63992	0.408824
$557$	−16.4612	−0.697481	−0.348741	−	0.937219i	$-0.613391\pi$
$557$	−16.4612	−0.697481	−0.348741	+	0.937219i	$0.613391\pi$
$558$	−0.936220	−0.0396334
$559$	−19.5386	−0.826395
$560$	0.329540	0.0139256
$561$	−11.0384	−0.466041
$562$	24.5244	1.03450
$563$	24.1047	1.01589	0.507946	−	0.861389i	$-0.330405\pi$
$563$	24.1047	1.01589	0.507946	+	0.861389i	$0.330405\pi$
$564$	4.07250	0.171483
$565$	0.876858	0.0368897
$566$	−8.45490	−0.355386
$567$	−7.21872	−0.303158
$568$	−6.95851	−0.291972
$569$	6.90463	0.289457	0.144729	−	0.989471i	$-0.453769\pi$
$569$	6.90463	0.289457	0.144729	+	0.989471i	$0.453769\pi$
$570$	0	0
$571$	−27.2226	−1.13923	−0.569615	−	0.821911i	$-0.692908\pi$
$571$	−27.2226	−1.13923	−0.569615	+	0.821911i	$0.692908\pi$
$572$	11.7184	0.489971
$573$	−22.2077	−0.927741
$574$	0.542326	0.0226362
$575$	−17.0605	−0.711473
$576$	−0.507804	−0.0211585
$577$	−18.7327	−0.779854	−0.389927	−	0.920846i	$-0.627500\pi$
$577$	−18.7327	−0.779854	−0.389927	+	0.920846i	$0.627500\pi$
$578$	12.3768	0.514806
$579$	−23.8351	−0.990552
$580$	2.39711	0.0995344
$581$	−5.46502	−0.226727
$582$	18.8756	0.782418
$583$	42.4854	1.75957
$584$	−13.9789	−0.578449
$585$	−0.603018	−0.0249317
$586$	−17.0364	−0.703768
$587$	13.5578	0.559589	0.279795	−	0.960060i	$-0.409734\pi$
$587$	13.5578	0.559589	0.279795	+	0.960060i	$0.409734\pi$
$588$	1.57867	0.0651032
$589$	0	0
$590$	3.12271	0.128560
$591$	37.7421	1.55250
$592$	8.60440	0.353639
$593$	11.4793	0.471397	0.235698	−	0.971826i	$-0.424262\pi$
$593$	11.4793	0.471397	0.235698	+	0.971826i	$0.424262\pi$
$594$	18.0081	0.738882
$595$	−0.708567	−0.0290484
$596$	−10.2034	−0.417947
$597$	30.9292	1.26585
$598$	−12.5685	−0.513966
$599$	−44.1593	−1.80430	−0.902149	−	0.431424i	$-0.858011\pi$
$599$	−44.1593	−1.80430	−0.902149	+	0.431424i	$0.858011\pi$
$600$	7.72191	0.315246
$601$	−11.6639	−0.475781	−0.237891	−	0.971292i	$-0.576456\pi$
$601$	−11.6639	−0.475781	−0.237891	+	0.971292i	$0.576456\pi$
$602$	5.42210	0.220988
$603$	−0.190522	−0.00775865
$604$	6.67071	0.271427
$605$	−0.140026	−0.00569287
$606$	22.7520	0.924238
$607$	−35.4486	−1.43881	−0.719407	−	0.694589i	$-0.755586\pi$
$607$	−35.4486	−1.43881	−0.719407	+	0.694589i	$0.755586\pi$
$608$	0	0
$609$	11.4834	0.465330
$610$	−1.04586	−0.0423456
$611$	9.29599	0.376075
$612$	1.09186	0.0441359
$613$	−33.4320	−1.35031	−0.675154	−	0.737677i	$-0.735923\pi$
$613$	−33.4320	−1.35031	−0.675154	+	0.737677i	$0.735923\pi$
$614$	−21.8506	−0.881819
$615$	−0.282137	−0.0113769
$616$	−3.25194	−0.131024
$617$	40.5839	1.63385	0.816924	−	0.576746i	$-0.195678\pi$
$617$	40.5839	1.63385	0.816924	+	0.576746i	$0.195678\pi$
$618$	−7.12919	−0.286778
$619$	44.7296	1.79784	0.898918	−	0.438117i	$-0.144355\pi$
$619$	44.7296	1.79784	0.898918	+	0.438117i	$0.144355\pi$
$620$	−0.607563	−0.0244003
$621$	−19.3146	−0.775068
$622$	6.93231	0.277960
$623$	0.179118	0.00717622
$624$	5.68875	0.227732
$625$	23.3828	0.935314
$626$	31.0443	1.24078
$627$	0	0
$628$	−14.4348	−0.576009
$629$	−18.5009	−0.737679
$630$	0.167342	0.00666706
$631$	5.40969	0.215356	0.107678	−	0.994186i	$-0.465658\pi$
$631$	5.40969	0.215356	0.107678	+	0.994186i	$0.465658\pi$
$632$	−3.46990	−0.138025
$633$	−2.00572	−0.0797203
$634$	−31.0129	−1.23168
$635$	0.566494	0.0224806
$636$	20.6248	0.817825
$637$	3.60351	0.142776
$638$	−23.6549	−0.936505
$639$	−3.53355	−0.139785
$640$	−0.329540	−0.0130262
$641$	−26.6258	−1.05166	−0.525829	−	0.850591i	$-0.676245\pi$
$641$	−26.6258	−1.05166	−0.525829	+	0.850591i	$0.676245\pi$
$642$	−6.97025	−0.275094
$643$	49.1958	1.94009	0.970046	−	0.242922i	$-0.0781059\pi$
$643$	49.1958	1.94009	0.970046	+	0.242922i	$0.0781059\pi$
$644$	3.48786	0.137441
$645$	−2.82077	−0.111068
$646$	0	0
$647$	1.92878	0.0758283	0.0379141	−	0.999281i	$-0.487929\pi$
$647$	1.92878	0.0758283	0.0379141	+	0.999281i	$0.487929\pi$
$648$	7.21872	0.283578
$649$	−30.8152	−1.20960
$650$	17.6262	0.691358
$651$	−2.91054	−0.114073
$652$	19.3303	0.757032
$653$	17.9611	0.702872	0.351436	−	0.936212i	$-0.385693\pi$
$653$	17.9611	0.702872	0.351436	+	0.936212i	$0.385693\pi$
$654$	−19.5912	−0.766078
$655$	−3.22895	−0.126166
$656$	−0.542326	−0.0211743
$657$	−7.09851	−0.276939
$658$	−2.57970	−0.100567
$659$	−24.3370	−0.948036	−0.474018	−	0.880515i	$-0.657197\pi$
$659$	−24.3370	−0.948036	−0.474018	+	0.880515i	$0.657197\pi$
$660$	1.69177	0.0658521
$661$	9.64706	0.375227	0.187614	−	0.982243i	$-0.439925\pi$
$661$	9.64706	0.375227	0.187614	+	0.982243i	$0.439925\pi$
$662$	−19.0103	−0.738858
$663$	−12.2318	−0.475042
$664$	5.46502	0.212084
$665$	0	0
$666$	4.36935	0.169309
$667$	25.3710	0.982369
$668$	15.5520	0.601726
$669$	24.2738	0.938481
$670$	−0.123640	−0.00477661
$671$	10.3206	0.398424
$672$	−1.57867	−0.0608985
$673$	15.7750	0.608081	0.304041	−	0.952659i	$-0.401664\pi$
$673$	15.7750	0.608081	0.304041	+	0.952659i	$0.401664\pi$
$674$	4.79618	0.184742
$675$	27.0869	1.04258
$676$	−0.0147006	−0.000565406 0
$677$	28.9103	1.11111	0.555556	−	0.831479i	$-0.312505\pi$
$677$	28.9103	1.11111	0.555556	+	0.831479i	$0.312505\pi$
$678$	−4.20060	−0.161323
$679$	−11.9566	−0.458854
$680$	0.708567	0.0271723
$681$	−38.8658	−1.48934
$682$	5.99548	0.229579
$683$	25.8139	0.987741	0.493871	−	0.869535i	$-0.335582\pi$
$683$	25.8139	0.987741	0.493871	+	0.869535i	$0.335582\pi$
$684$	0	0
$685$	0.427051	0.0163168
$686$	−1.00000	−0.0381802
$687$	14.2061	0.541997
$688$	−5.42210	−0.206716
$689$	47.0786	1.79355
$690$	−1.81451	−0.0690772
$691$	−34.1466	−1.29900	−0.649498	−	0.760363i	$-0.725021\pi$
$691$	−34.1466	−1.29900	−0.649498	+	0.760363i	$0.725021\pi$
$692$	−12.9845	−0.493597
$693$	−1.65134	−0.0627294
$694$	2.98419	0.113278
$695$	3.17674	0.120501
$696$	−11.4834	−0.435276
$697$	1.16609	0.0441688
$698$	−20.1084	−0.761113
$699$	−13.4923	−0.510326
$700$	−4.89140	−0.184878
$701$	24.7906	0.936329	0.468165	−	0.883641i	$-0.344915\pi$
$701$	24.7906	0.936329	0.468165	+	0.883641i	$0.344915\pi$
$702$	19.9550	0.753154
$703$	0	0
$704$	3.25194	0.122562
$705$	1.34205	0.0505446
$706$	25.3624	0.954525
$707$	−14.4122	−0.542025
$708$	−14.9594	−0.562209
$709$	2.17814	0.0818018	0.0409009	−	0.999163i	$-0.486977\pi$
$709$	2.17814	0.0818018	0.0409009	+	0.999163i	$0.486977\pi$
$710$	−2.29311	−0.0860589
$711$	−1.76203	−0.0660813
$712$	−0.179118	−0.00671274
$713$	−6.43045	−0.240822
$714$	3.39440	0.127032
$715$	3.86168	0.144419
$716$	22.3945	0.836923
$717$	−3.86728	−0.144426
$718$	30.2965	1.13066
$719$	32.5589	1.21424	0.607122	−	0.794609i	$-0.292324\pi$
$719$	32.5589	1.21424	0.607122	+	0.794609i	$0.292324\pi$
$720$	−0.167342	−0.00623646
$721$	4.51595	0.168183
$722$	0	0
$723$	37.3262	1.38818
$724$	20.7177	0.769967
$725$	−35.5805	−1.32143
$726$	0.670797	0.0248956
$727$	9.19706	0.341100	0.170550	−	0.985349i	$-0.445446\pi$
$727$	9.19706	0.341100	0.170550	+	0.985349i	$0.445446\pi$
$728$	−3.60351	−0.133555
$729$	29.8921	1.10711
$730$	−4.60660	−0.170498
$731$	11.6584	0.431202
$732$	5.01021	0.185183
$733$	−38.5617	−1.42431	−0.712154	−	0.702023i	$-0.752280\pi$
$733$	−38.5617	−1.42431	−0.712154	+	0.702023i	$0.752280\pi$
$734$	−12.7503	−0.470623
$735$	0.520235	0.0191892
$736$	−3.48786	−0.128564
$737$	1.22009	0.0449425
$738$	−0.275395	−0.0101374
$739$	25.3696	0.933236	0.466618	−	0.884459i	$-0.345472\pi$
$739$	25.3696	0.933236	0.466618	+	0.884459i	$0.345472\pi$
$740$	2.83550	0.104235
$741$	0	0
$742$	−13.0647	−0.479618
$743$	−19.5869	−0.718572	−0.359286	−	0.933227i	$-0.616980\pi$
$743$	−19.5869	−0.718572	−0.359286	+	0.933227i	$0.616980\pi$
$744$	2.91054	0.106706
$745$	−3.36243	−0.123190
$746$	5.23786	0.191772
$747$	2.77516	0.101538
$748$	−6.99220	−0.255660
$749$	4.41527	0.161330
$750$	5.14586	0.187900
$751$	−23.7965	−0.868347	−0.434173	−	0.900829i	$-0.642959\pi$
$751$	−23.7965	−0.868347	−0.434173	+	0.900829i	$0.642959\pi$
$752$	2.57970	0.0940720
$753$	−16.5842	−0.604363
$754$	−26.2123	−0.954594
$755$	2.19827	0.0800032
$756$	−5.53766	−0.201403
$757$	21.8202	0.793070	0.396535	−	0.918020i	$-0.370213\pi$
$757$	21.8202	0.793070	0.396535	+	0.918020i	$0.370213\pi$
$758$	25.2856	0.918415
$759$	17.9057	0.649937
$760$	0	0
$761$	−14.3446	−0.519990	−0.259995	−	0.965610i	$-0.583721\pi$
$761$	−14.3446	−0.519990	−0.259995	+	0.965610i	$0.583721\pi$
$762$	−2.71380	−0.0983105
$763$	12.4100	0.449271
$764$	−14.0674	−0.508939
$765$	0.359813	0.0130091
$766$	26.6421	0.962616
$767$	−34.1467	−1.23297
$768$	1.57867	0.0569653
$769$	30.3984	1.09619	0.548097	−	0.836415i	$-0.315352\pi$
$769$	30.3984	1.09619	0.548097	+	0.836415i	$0.315352\pi$
$770$	−1.07164	−0.0386194
$771$	−31.9929	−1.15220
$772$	−15.0982	−0.543397
$773$	37.3600	1.34375	0.671873	−	0.740667i	$-0.265490\pi$
$773$	37.3600	1.34375	0.671873	+	0.740667i	$0.265490\pi$
$774$	−2.75336	−0.0989675
$775$	9.01811	0.323940
$776$	11.9566	0.429218
$777$	13.5835	0.487305
$778$	−14.4792	−0.519104
$779$	0	0
$780$	1.87467	0.0671241
$781$	22.6286	0.809716
$782$	7.49948	0.268181
$783$	−40.2814	−1.43954
$784$	1.00000	0.0357143
$785$	−4.75683	−0.169779
$786$	15.4684	0.551738
$787$	33.6001	1.19771	0.598857	−	0.800856i	$-0.295622\pi$
$787$	33.6001	1.19771	0.598857	+	0.800856i	$0.295622\pi$
$788$	23.9075	0.851670
$789$	−19.2030	−0.683645
$790$	−1.14347	−0.0406830
$791$	2.66085	0.0946089
$792$	1.65134	0.0586780
$793$	11.4364	0.406120
$794$	31.0558	1.10213
$795$	6.79669	0.241054
$796$	19.5919	0.694417
$797$	5.90573	0.209192	0.104596	−	0.994515i	$-0.466645\pi$
$797$	5.90573	0.209192	0.104596	+	0.994515i	$0.466645\pi$
$798$	0	0
$799$	−5.54679	−0.196231
$800$	4.89140	0.172937
$801$	−0.0909569	−0.00321381
$802$	5.75381	0.203174
$803$	45.4583	1.60419
$804$	0.592298	0.0208887
$805$	1.14939	0.0405107
$806$	6.64367	0.234013
$807$	15.1388	0.532912
$808$	14.4122	0.507018
$809$	31.9444	1.12310	0.561552	−	0.827441i	$-0.310204\pi$
$809$	31.9444	1.12310	0.561552	+	0.827441i	$0.310204\pi$
$810$	2.37886	0.0835847
$811$	−38.8625	−1.36465	−0.682323	−	0.731051i	$-0.739030\pi$
$811$	−38.8625	−1.36465	−0.682323	+	0.731051i	$0.739030\pi$
$812$	7.27409	0.255270
$813$	−36.4844	−1.27956
$814$	−27.9810	−0.980732
$815$	6.37011	0.223135
$816$	−3.39440	−0.118828
$817$	0	0
$818$	−2.53464	−0.0886216
$819$	−1.82988	−0.0639411
$820$	−0.178718	−0.00624111
$821$	−28.4360	−0.992423	−0.496212	−	0.868202i	$-0.665276\pi$
$821$	−28.4360	−0.992423	−0.496212	+	0.868202i	$0.665276\pi$
$822$	−2.04579	−0.0713553
$823$	−22.1420	−0.771823	−0.385912	−	0.922536i	$-0.626113\pi$
$823$	−22.1420	−0.771823	−0.385912	+	0.922536i	$0.626113\pi$
$824$	−4.51595	−0.157320
$825$	−25.1111	−0.874258
$826$	9.47596	0.329711
$827$	−48.5386	−1.68785	−0.843927	−	0.536458i	$-0.819762\pi$
$827$	−48.5386	−1.68785	−0.843927	+	0.536458i	$0.819762\pi$
$828$	−1.77115	−0.0615517
$829$	8.86977	0.308060	0.154030	−	0.988066i	$-0.450775\pi$
$829$	8.86977	0.308060	0.154030	+	0.988066i	$0.450775\pi$
$830$	1.80094	0.0625117
$831$	28.9281	1.00350
$832$	3.60351	0.124929
$833$	−2.15017	−0.0744989
$834$	−15.2182	−0.526964
$835$	5.12502	0.177359
$836$	0	0
$837$	10.2096	0.352895
$838$	−10.2109	−0.352729
$839$	−51.1873	−1.76718	−0.883590	−	0.468261i	$-0.844881\pi$
$839$	−51.1873	−1.76718	−0.883590	+	0.468261i	$0.844881\pi$
$840$	−0.520235	−0.0179498
$841$	23.9123	0.824563
$842$	−25.0336	−0.862716
$843$	−38.7160	−1.33345
$844$	−1.27051	−0.0437329
$845$	−0.00484443	−0.000166653 0
$846$	1.30998	0.0450381
$847$	−0.424913	−0.0146002
$848$	13.0647	0.448642
$849$	13.3475	0.458084
$850$	−10.5173	−0.360741
$851$	30.0110	1.02876
$852$	10.9852	0.376346
$853$	21.9185	0.750477	0.375238	−	0.926928i	$-0.377561\pi$
$853$	21.9185	0.750477	0.375238	+	0.926928i	$0.377561\pi$
$854$	−3.17369	−0.108602
$855$	0	0
$856$	−4.41527	−0.150911
$857$	−49.9562	−1.70647	−0.853236	−	0.521524i	$-0.825364\pi$
$857$	−49.9562	−1.70647	−0.853236	+	0.521524i	$0.825364\pi$
$858$	−18.4995	−0.631561
$859$	−52.3034	−1.78457	−0.892285	−	0.451472i	$-0.850899\pi$
$859$	−52.3034	−1.78457	−0.892285	+	0.451472i	$0.850899\pi$
$860$	−1.78680	−0.0609294
$861$	−0.856153	−0.0291776
$862$	−5.03621	−0.171534
$863$	−15.9430	−0.542706	−0.271353	−	0.962480i	$-0.587471\pi$
$863$	−15.9430	−0.542706	−0.271353	+	0.962480i	$0.587471\pi$
$864$	5.53766	0.188395
$865$	−4.27892	−0.145488
$866$	−22.8793	−0.777470
$867$	−19.5388	−0.663574
$868$	−1.84367	−0.0625781
$869$	11.2839	0.382780
$870$	−3.78424	−0.128298
$871$	1.35199	0.0458106
$872$	−12.4100	−0.420255
$873$	6.07163	0.205493
$874$	0	0
$875$	−3.25962	−0.110195
$876$	22.0680	0.745608
$877$	−10.9771	−0.370670	−0.185335	−	0.982675i	$-0.559337\pi$
$877$	−10.9771	−0.370670	−0.185335	+	0.982675i	$0.559337\pi$
$878$	−39.2842	−1.32578
$879$	26.8949	0.907142
$880$	1.07164	0.0361251
$881$	−29.6197	−0.997913	−0.498956	−	0.866627i	$-0.666283\pi$
$881$	−29.6197	−0.997913	−0.498956	+	0.866627i	$0.666283\pi$
$882$	0.507804	0.0170986
$883$	−42.1602	−1.41880	−0.709402	−	0.704805i	$-0.751035\pi$
$883$	−42.1602	−1.41880	−0.709402	+	0.704805i	$0.751035\pi$
$884$	−7.74815	−0.260599
$885$	−4.92973	−0.165711
$886$	−22.2515	−0.747554
$887$	−54.7348	−1.83782	−0.918908	−	0.394472i	$-0.870928\pi$
$887$	−54.7348	−1.83782	−0.918908	+	0.394472i	$0.870928\pi$
$888$	−13.5835	−0.455833
$889$	1.71904	0.0576548
$890$	−0.0590267	−0.00197858
$891$	−23.4748	−0.786436
$892$	15.3761	0.514831
$893$	0	0
$894$	16.1078	0.538724
$895$	7.37990	0.246683
$896$	−1.00000	−0.0334077
$897$	19.8416	0.662491
$898$	−4.10639	−0.137032
$899$	−13.4110	−0.447281
$900$	2.48387	0.0827957
$901$	−28.0912	−0.935853
$902$	1.76361	0.0587217
$903$	−8.55970	−0.284849
$904$	−2.66085	−0.0884985
$905$	6.82732	0.226948
$906$	−10.5308	−0.349864
$907$	55.3212	1.83691	0.918456	−	0.395524i	$-0.129437\pi$
$907$	55.3212	1.83691	0.918456	+	0.395524i	$0.129437\pi$
$908$	−24.6193	−0.817021
$909$	7.31855	0.242741
$910$	−1.18750	−0.0393653
$911$	−41.0882	−1.36131	−0.680656	−	0.732603i	$-0.738305\pi$
$911$	−41.0882	−1.36131	−0.680656	+	0.732603i	$0.738305\pi$
$912$	0	0
$913$	−17.7719	−0.588164
$914$	−27.1225	−0.897131
$915$	1.65107	0.0545826
$916$	8.99878	0.297328
$917$	−9.79836	−0.323570
$918$	−11.9069	−0.392986
$919$	−53.0705	−1.75063	−0.875317	−	0.483550i	$-0.839347\pi$
$919$	−53.0705	−1.75063	−0.875317	+	0.483550i	$0.839347\pi$
$920$	−1.14939	−0.0378943
$921$	34.4949	1.13664
$922$	−34.2020	−1.12638
$923$	25.0751	0.825356
$924$	5.13373	0.168887
$925$	−42.0876	−1.38383
$926$	−12.1690	−0.399899
$927$	−2.29321	−0.0753190
$928$	−7.27409	−0.238784
$929$	−57.7910	−1.89606	−0.948031	−	0.318178i	$-0.896929\pi$
$929$	−57.7910	−1.89606	−0.948031	+	0.318178i	$0.896929\pi$
$930$	0.959140	0.0314514
$931$	0	0
$932$	−8.54664	−0.279954
$933$	−10.9438	−0.358285
$934$	19.7876	0.647470
$935$	−2.30421	−0.0753559
$936$	1.82988	0.0598114
$937$	19.0171	0.621262	0.310631	−	0.950531i	$-0.399460\pi$
$937$	19.0171	0.621262	0.310631	+	0.950531i	$0.399460\pi$
$938$	−0.375188	−0.0122503
$939$	−49.0088	−1.59934
$940$	0.850116	0.0277277
$941$	−9.36519	−0.305297	−0.152648	−	0.988281i	$-0.548780\pi$
$941$	−9.36519	−0.305297	−0.152648	+	0.988281i	$0.548780\pi$
$942$	22.7877	0.742463
$943$	−1.89156	−0.0615976
$944$	−9.47596	−0.308416
$945$	−1.82488	−0.0593635
$946$	17.6323	0.573276
$947$	−15.5914	−0.506651	−0.253326	−	0.967381i	$-0.581524\pi$
$947$	−15.5914	−0.506651	−0.253326	+	0.967381i	$0.581524\pi$
$948$	5.47783	0.177912
$949$	50.3730	1.63518
$950$	0	0
$951$	48.9592	1.58761
$952$	2.15017	0.0696873
$953$	0.480389	0.0155613	0.00778067	−	0.999970i	$-0.497523\pi$
$953$	0.480389	0.0155613	0.00778067	+	0.999970i	$0.497523\pi$
$954$	6.63428	0.214793
$955$	−4.63577	−0.150010
$956$	−2.44971	−0.0792293
$957$	37.3432	1.20713
$958$	8.03308	0.259537
$959$	1.29590	0.0418467
$960$	0.520235	0.0167905
$961$	−27.6009	−0.890352
$962$	−31.0061	−0.999676
$963$	−2.24209	−0.0722503
$964$	23.6441	0.761526
$965$	−4.97547	−0.160166
$966$	−5.50618	−0.177158
$967$	27.4013	0.881165	0.440583	−	0.897712i	$-0.354772\pi$
$967$	27.4013	0.881165	0.440583	+	0.897712i	$0.354772\pi$
$968$	0.424913	0.0136572
$969$	0	0
$970$	3.94020	0.126512
$971$	24.4195	0.783661	0.391830	−	0.920038i	$-0.371842\pi$
$971$	24.4195	0.783661	0.391830	+	0.920038i	$0.371842\pi$
$972$	5.21701	0.167336
$973$	9.63992	0.309042
$974$	36.7402	1.17723
$975$	−27.8260	−0.891145
$976$	3.17369	0.101587
$977$	−14.2851	−0.457021	−0.228511	−	0.973541i	$-0.573386\pi$
$977$	−14.2851	−0.457021	−0.228511	+	0.973541i	$0.573386\pi$
$978$	−30.5161	−0.975798
$979$	0.582481	0.0186162
$980$	0.329540	0.0105268
$981$	−6.30183	−0.201202
$982$	−21.1225	−0.674046
$983$	−17.1528	−0.547089	−0.273545	−	0.961859i	$-0.588196\pi$
$983$	−17.1528	−0.547089	−0.273545	+	0.961859i	$0.588196\pi$
$984$	0.856153	0.0272932
$985$	7.87850	0.251030
$986$	15.6405	0.498095
$987$	4.07250	0.129629
$988$	0	0
$989$	−18.9115	−0.601352
$990$	0.544185	0.0172953
$991$	50.6738	1.60971	0.804854	−	0.593473i	$-0.202244\pi$
$991$	50.6738	1.60971	0.804854	+	0.593473i	$0.202244\pi$
$992$	1.84367	0.0585364
$993$	30.0110	0.952371
$994$	−6.95851	−0.220710
$995$	6.45633	0.204679
$996$	−8.62745	−0.273371
$997$	26.5976	0.842355	0.421178	−	0.906978i	$-0.361617\pi$
$997$	26.5976	0.842355	0.421178	+	0.906978i	$0.361617\pi$
$998$	−0.685934	−0.0217129
$999$	−47.6483	−1.50752

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.bg.1.6	✓	8
19.18	odd	2		5054.2.a.bh.1.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5054.2.a.bg.1.6	✓	8	1.1	even	1	trivial
5054.2.a.bh.1.3	yes	8	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:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.57867 q^{3} +1.00000 q^{4} +0.329540 q^{5} -1.57867 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.507804 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.57867 q^{3} +1.00000 q^{4} +0.329540 q^{5} -1.57867 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.507804 q^{9} -0.329540 q^{10} +3.25194 q^{11} +1.57867 q^{12} +3.60351 q^{13} -1.00000 q^{14} +0.520235 q^{15} +1.00000 q^{16} -2.15017 q^{17} +0.507804 q^{18} +0.329540 q^{20} +1.57867 q^{21} -3.25194 q^{22} +3.48786 q^{23} -1.57867 q^{24} -4.89140 q^{25} -3.60351 q^{26} -5.53766 q^{27} +1.00000 q^{28} +7.27409 q^{29} -0.520235 q^{30} -1.84367 q^{31} -1.00000 q^{32} +5.13373 q^{33} +2.15017 q^{34} +0.329540 q^{35} -0.507804 q^{36} +8.60440 q^{37} +5.68875 q^{39} -0.329540 q^{40} -0.542326 q^{41} -1.57867 q^{42} -5.42210 q^{43} +3.25194 q^{44} -0.167342 q^{45} -3.48786 q^{46} +2.57970 q^{47} +1.57867 q^{48} +1.00000 q^{49} +4.89140 q^{50} -3.39440 q^{51} +3.60351 q^{52} +13.0647 q^{53} +5.53766 q^{54} +1.07164 q^{55} -1.00000 q^{56} -7.27409 q^{58} -9.47596 q^{59} +0.520235 q^{60} +3.17369 q^{61} +1.84367 q^{62} -0.507804 q^{63} +1.00000 q^{64} +1.18750 q^{65} -5.13373 q^{66} +0.375188 q^{67} -2.15017 q^{68} +5.50618 q^{69} -0.329540 q^{70} +6.95851 q^{71} +0.507804 q^{72} +13.9789 q^{73} -8.60440 q^{74} -7.72191 q^{75} +3.25194 q^{77} -5.68875 q^{78} +3.46990 q^{79} +0.329540 q^{80} -7.21872 q^{81} +0.542326 q^{82} -5.46502 q^{83} +1.57867 q^{84} -0.708567 q^{85} +5.42210 q^{86} +11.4834 q^{87} -3.25194 q^{88} +0.179118 q^{89} +0.167342 q^{90} +3.60351 q^{91} +3.48786 q^{92} -2.91054 q^{93} -2.57970 q^{94} -1.57867 q^{96} -11.9566 q^{97} -1.00000 q^{98} -1.65134 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 4 q^{3} + 8 q^{4} - 2 q^{5} - 4 q^{6} + 8 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 4 * q^3 + 8 * q^4 - 2 * q^5 - 4 * q^6 + 8 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} + 4 q^{3} + 8 q^{4} - 2 q^{5} - 4 q^{6} + 8 q^{7} - 8 q^{8} + 8 q^{9} + 2 q^{10} - 12 q^{11} + 4 q^{12} + 10 q^{13} - 8 q^{14} + 24 q^{15} + 8 q^{16} - 6 q^{17} - 8 q^{18} - 2 q^{20} + 4 q^{21} + 12 q^{22} - 20 q^{23} - 4 q^{24} + 8 q^{25} - 10 q^{26} + 22 q^{27} + 8 q^{28} + 8 q^{29} - 24 q^{30} + 18 q^{31} - 8 q^{32} - 16 q^{33} + 6 q^{34} - 2 q^{35} + 8 q^{36} + 36 q^{37} + 2 q^{40} + 4 q^{41} - 4 q^{42} - 16 q^{43} - 12 q^{44} + 8 q^{45} + 20 q^{46} - 10 q^{47} + 4 q^{48} + 8 q^{49} - 8 q^{50} + 12 q^{51} + 10 q^{52} + 32 q^{53} - 22 q^{54} - 22 q^{55} - 8 q^{56} - 8 q^{58} - 2 q^{59} + 24 q^{60} + 2 q^{61} - 18 q^{62} + 8 q^{63} + 8 q^{64} + 16 q^{66} + 44 q^{67} - 6 q^{68} + 2 q^{70} + 8 q^{71} - 8 q^{72} + 30 q^{73} - 36 q^{74} - 16 q^{75} - 12 q^{77} + 60 q^{79} - 2 q^{80} + 12 q^{81} - 4 q^{82} - 28 q^{83} + 4 q^{84} - 16 q^{85} + 16 q^{86} + 24 q^{87} + 12 q^{88} - 22 q^{89} - 8 q^{90} + 10 q^{91} - 20 q^{92} - 16 q^{93} + 10 q^{94} - 4 q^{96} - 6 q^{97} - 8 q^{98} - 52 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 4 * q^3 + 8 * q^4 - 2 * q^5 - 4 * q^6 + 8 * q^7 - 8 * q^8 + 8 * q^9 + 2 * q^10 - 12 * q^11 + 4 * q^12 + 10 * q^13 - 8 * q^14 + 24 * q^15 + 8 * q^16 - 6 * q^17 - 8 * q^18 - 2 * q^20 + 4 * q^21 + 12 * q^22 - 20 * q^23 - 4 * q^24 + 8 * q^25 - 10 * q^26 + 22 * q^27 + 8 * q^28 + 8 * q^29 - 24 * q^30 + 18 * q^31 - 8 * q^32 - 16 * q^33 + 6 * q^34 - 2 * q^35 + 8 * q^36 + 36 * q^37 + 2 * q^40 + 4 * q^41 - 4 * q^42 - 16 * q^43 - 12 * q^44 + 8 * q^45 + 20 * q^46 - 10 * q^47 + 4 * q^48 + 8 * q^49 - 8 * q^50 + 12 * q^51 + 10 * q^52 + 32 * q^53 - 22 * q^54 - 22 * q^55 - 8 * q^56 - 8 * q^58 - 2 * q^59 + 24 * q^60 + 2 * q^61 - 18 * q^62 + 8 * q^63 + 8 * q^64 + 16 * q^66 + 44 * q^67 - 6 * q^68 + 2 * q^70 + 8 * q^71 - 8 * q^72 + 30 * q^73 - 36 * q^74 - 16 * q^75 - 12 * q^77 + 60 * q^79 - 2 * q^80 + 12 * q^81 - 4 * q^82 - 28 * q^83 + 4 * q^84 - 16 * q^85 + 16 * q^86 + 24 * q^87 + 12 * q^88 - 22 * q^89 - 8 * q^90 + 10 * q^91 - 20 * q^92 - 16 * q^93 + 10 * q^94 - 4 * q^96 - 6 * q^97 - 8 * q^98 - 52 * q^99

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