LMFDB - Embedded newform 8026.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0879326623$
Analytic rank:	$0$
Dimension:	$96$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.28199 q^{3} +1.00000 q^{4} +4.44756 q^{5} -3.28199 q^{6} -4.87209 q^{7} +1.00000 q^{8} +7.77147 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.28199 q^{3} +1.00000 q^{4} +4.44756 q^{5} -3.28199 q^{6} -4.87209 q^{7} +1.00000 q^{8} +7.77147 q^{9} +4.44756 q^{10} +3.92354 q^{11} -3.28199 q^{12} +5.40636 q^{13} -4.87209 q^{14} -14.5969 q^{15} +1.00000 q^{16} -5.94729 q^{17} +7.77147 q^{18} -4.10542 q^{19} +4.44756 q^{20} +15.9902 q^{21} +3.92354 q^{22} -0.861265 q^{23} -3.28199 q^{24} +14.7808 q^{25} +5.40636 q^{26} -15.6599 q^{27} -4.87209 q^{28} -4.76258 q^{29} -14.5969 q^{30} -0.962863 q^{31} +1.00000 q^{32} -12.8770 q^{33} -5.94729 q^{34} -21.6689 q^{35} +7.77147 q^{36} +8.86854 q^{37} -4.10542 q^{38} -17.7436 q^{39} +4.44756 q^{40} +5.07334 q^{41} +15.9902 q^{42} +1.73766 q^{43} +3.92354 q^{44} +34.5641 q^{45} -0.861265 q^{46} +9.90456 q^{47} -3.28199 q^{48} +16.7373 q^{49} +14.7808 q^{50} +19.5189 q^{51} +5.40636 q^{52} -5.66588 q^{53} -15.6599 q^{54} +17.4502 q^{55} -4.87209 q^{56} +13.4739 q^{57} -4.76258 q^{58} +11.0651 q^{59} -14.5969 q^{60} -2.21504 q^{61} -0.962863 q^{62} -37.8633 q^{63} +1.00000 q^{64} +24.0451 q^{65} -12.8770 q^{66} -0.292663 q^{67} -5.94729 q^{68} +2.82666 q^{69} -21.6689 q^{70} +3.82127 q^{71} +7.77147 q^{72} -9.70486 q^{73} +8.86854 q^{74} -48.5105 q^{75} -4.10542 q^{76} -19.1158 q^{77} -17.7436 q^{78} -5.00168 q^{79} +4.44756 q^{80} +28.0813 q^{81} +5.07334 q^{82} +5.73133 q^{83} +15.9902 q^{84} -26.4509 q^{85} +1.73766 q^{86} +15.6307 q^{87} +3.92354 q^{88} +1.66689 q^{89} +34.5641 q^{90} -26.3403 q^{91} -0.861265 q^{92} +3.16011 q^{93} +9.90456 q^{94} -18.2591 q^{95} -3.28199 q^{96} +4.00245 q^{97} +16.7373 q^{98} +30.4917 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) $ 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * 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
$3$	−3.28199	−1.89486	−0.947429	−	0.319965i	$-0.896329\pi$
$3$	−3.28199	−1.89486	−0.947429	+	0.319965i	$0.896329\pi$
$4$	1.00000	0.500000
$5$	4.44756	1.98901	0.994505	−	0.104687i	$-0.0333839\pi$
$5$	4.44756	1.98901	0.994505	+	0.104687i	$0.0333839\pi$
$6$	−3.28199	−1.33987
$7$	−4.87209	−1.84148	−0.920739	−	0.390180i	$-0.872413\pi$
$7$	−4.87209	−1.84148	−0.920739	+	0.390180i	$0.872413\pi$
$8$	1.00000	0.353553
$9$	7.77147	2.59049
$10$	4.44756	1.40644
$11$	3.92354	1.18299	0.591496	−	0.806308i	$-0.298538\pi$
$11$	3.92354	1.18299	0.591496	+	0.806308i	$0.298538\pi$
$12$	−3.28199	−0.947429
$13$	5.40636	1.49945	0.749727	−	0.661748i	$-0.230185\pi$
$13$	5.40636	1.49945	0.749727	+	0.661748i	$0.230185\pi$
$14$	−4.87209	−1.30212
$15$	−14.5969	−3.76889
$16$	1.00000	0.250000
$17$	−5.94729	−1.44243	−0.721215	−	0.692712i	$-0.756416\pi$
$17$	−5.94729	−1.44243	−0.721215	+	0.692712i	$0.756416\pi$
$18$	7.77147	1.83175
$19$	−4.10542	−0.941847	−0.470924	−	0.882174i	$-0.656079\pi$
$19$	−4.10542	−0.941847	−0.470924	+	0.882174i	$0.656079\pi$
$20$	4.44756	0.994505
$21$	15.9902	3.48934
$22$	3.92354	0.836501
$23$	−0.861265	−0.179586	−0.0897931	−	0.995960i	$-0.528621\pi$
$23$	−0.861265	−0.179586	−0.0897931	+	0.995960i	$0.528621\pi$
$24$	−3.28199	−0.669934
$25$	14.7808	2.95616
$26$	5.40636	1.06027
$27$	−15.6599	−3.01375
$28$	−4.87209	−0.920739
$29$	−4.76258	−0.884389	−0.442195	−	0.896919i	$-0.645800\pi$
$29$	−4.76258	−0.884389	−0.442195	+	0.896919i	$0.645800\pi$
$30$	−14.5969	−2.66501
$31$	−0.962863	−0.172935	−0.0864676	−	0.996255i	$-0.527558\pi$
$31$	−0.962863	−0.172935	−0.0864676	+	0.996255i	$0.527558\pi$
$32$	1.00000	0.176777
$33$	−12.8770	−2.24160
$34$	−5.94729	−1.01995
$35$	−21.6689	−3.66272
$36$	7.77147	1.29524
$37$	8.86854	1.45798	0.728989	−	0.684525i	$-0.239990\pi$
$37$	8.86854	1.45798	0.728989	+	0.684525i	$0.239990\pi$
$38$	−4.10542	−0.665987
$39$	−17.7436	−2.84125
$40$	4.44756	0.703221
$41$	5.07334	0.792322	0.396161	−	0.918181i	$-0.370342\pi$
$41$	5.07334	0.792322	0.396161	+	0.918181i	$0.370342\pi$
$42$	15.9902	2.46734
$43$	1.73766	0.264991	0.132496	−	0.991184i	$-0.457701\pi$
$43$	1.73766	0.264991	0.132496	+	0.991184i	$0.457701\pi$
$44$	3.92354	0.591496
$45$	34.5641	5.15251
$46$	−0.861265	−0.126987
$47$	9.90456	1.44473	0.722365	−	0.691512i	$-0.243055\pi$
$47$	9.90456	1.44473	0.722365	+	0.691512i	$0.243055\pi$
$48$	−3.28199	−0.473715
$49$	16.7373	2.39104
$50$	14.7808	2.09032
$51$	19.5189	2.73320
$52$	5.40636	0.749727
$53$	−5.66588	−0.778269	−0.389134	−	0.921181i	$-0.627226\pi$
$53$	−5.66588	−0.778269	−0.389134	+	0.921181i	$0.627226\pi$
$54$	−15.6599	−2.13104
$55$	17.4502	2.35298
$56$	−4.87209	−0.651061
$57$	13.4739	1.78467
$58$	−4.76258	−0.625358
$59$	11.0651	1.44055	0.720276	−	0.693687i	$-0.244015\pi$
$59$	11.0651	1.44055	0.720276	+	0.693687i	$0.244015\pi$
$60$	−14.5969	−1.88445
$61$	−2.21504	−0.283607	−0.141803	−	0.989895i	$-0.545290\pi$
$61$	−2.21504	−0.283607	−0.141803	+	0.989895i	$0.545290\pi$
$62$	−0.962863	−0.122284
$63$	−37.8633	−4.77033
$64$	1.00000	0.125000
$65$	24.0451	2.98243
$66$	−12.8770	−1.58505
$67$	−0.292663	−0.0357544	−0.0178772	−	0.999840i	$-0.505691\pi$
$67$	−0.292663	−0.0357544	−0.0178772	+	0.999840i	$0.505691\pi$
$68$	−5.94729	−0.721215
$69$	2.82666	0.340290
$70$	−21.6689	−2.58993
$71$	3.82127	0.453501	0.226751	−	0.973953i	$-0.427190\pi$
$71$	3.82127	0.453501	0.226751	+	0.973953i	$0.427190\pi$
$72$	7.77147	0.915876
$73$	−9.70486	−1.13587	−0.567934	−	0.823074i	$-0.692257\pi$
$73$	−9.70486	−1.13587	−0.567934	+	0.823074i	$0.692257\pi$
$74$	8.86854	1.03095
$75$	−48.5105	−5.60151
$76$	−4.10542	−0.470924
$77$	−19.1158	−2.17845
$78$	−17.7436	−2.00907
$79$	−5.00168	−0.562733	−0.281366	−	0.959600i	$-0.590788\pi$
$79$	−5.00168	−0.562733	−0.281366	+	0.959600i	$0.590788\pi$
$80$	4.44756	0.497253
$81$	28.0813	3.12015
$82$	5.07334	0.560256
$83$	5.73133	0.629095	0.314548	−	0.949242i	$-0.398147\pi$
$83$	5.73133	0.629095	0.314548	+	0.949242i	$0.398147\pi$
$84$	15.9902	1.74467
$85$	−26.4509	−2.86901
$86$	1.73766	0.187377
$87$	15.6307	1.67579
$88$	3.92354	0.418251
$89$	1.66689	0.176690	0.0883452	−	0.996090i	$-0.471842\pi$
$89$	1.66689	0.176690	0.0883452	+	0.996090i	$0.471842\pi$
$90$	34.5641	3.64338
$91$	−26.3403	−2.76121
$92$	−0.861265	−0.0897931
$93$	3.16011	0.327688
$94$	9.90456	1.02158
$95$	−18.2591	−1.87334
$96$	−3.28199	−0.334967
$97$	4.00245	0.406387	0.203193	−	0.979139i	$-0.434868\pi$
$97$	4.00245	0.406387	0.203193	+	0.979139i	$0.434868\pi$
$98$	16.7373	1.69072
$99$	30.4917	3.06453
$100$	14.7808	1.47808
$101$	6.40952	0.637771	0.318885	−	0.947793i	$-0.396692\pi$
$101$	6.40952	0.637771	0.318885	+	0.947793i	$0.396692\pi$
$102$	19.5189	1.93266
$103$	−8.56592	−0.844025	−0.422013	−	0.906590i	$-0.638676\pi$
$103$	−8.56592	−0.844025	−0.422013	+	0.906590i	$0.638676\pi$
$104$	5.40636	0.530137
$105$	71.1172	6.94033
$106$	−5.66588	−0.550319
$107$	8.84887	0.855453	0.427726	−	0.903908i	$-0.359315\pi$
$107$	8.84887	0.855453	0.427726	+	0.903908i	$0.359315\pi$
$108$	−15.6599	−1.50688
$109$	−9.38966	−0.899366	−0.449683	−	0.893188i	$-0.648463\pi$
$109$	−9.38966	−0.899366	−0.449683	+	0.893188i	$0.648463\pi$
$110$	17.4502	1.66381
$111$	−29.1065	−2.76266
$112$	−4.87209	−0.460369
$113$	−18.4574	−1.73633	−0.868163	−	0.496279i	$-0.834699\pi$
$113$	−18.4574	−1.73633	−0.868163	+	0.496279i	$0.834699\pi$
$114$	13.4739	1.26195
$115$	−3.83053	−0.357199
$116$	−4.76258	−0.442195
$117$	42.0153	3.88432
$118$	11.0651	1.01862
$119$	28.9757	2.65620
$120$	−14.5969	−1.33251
$121$	4.39415	0.399468
$122$	−2.21504	−0.200540
$123$	−16.6506	−1.50134
$124$	−0.962863	−0.0864676
$125$	43.5008	3.89083
$126$	−37.8633	−3.37313
$127$	0.748632	0.0664304	0.0332152	−	0.999448i	$-0.489425\pi$
$127$	0.748632	0.0664304	0.0332152	+	0.999448i	$0.489425\pi$
$128$	1.00000	0.0883883
$129$	−5.70300	−0.502121
$130$	24.0451	2.10890
$131$	−6.87248	−0.600452	−0.300226	−	0.953868i	$-0.597062\pi$
$131$	−6.87248	−0.600452	−0.300226	+	0.953868i	$0.597062\pi$
$132$	−12.8770	−1.12080
$133$	20.0020	1.73439
$134$	−0.292663	−0.0252822
$135$	−69.6485	−5.99439
$136$	−5.94729	−0.509976
$137$	−11.8602	−1.01329	−0.506643	−	0.862156i	$-0.669114\pi$
$137$	−11.8602	−1.01329	−0.506643	+	0.862156i	$0.669114\pi$
$138$	2.82666	0.240622
$139$	13.7863	1.16934	0.584668	−	0.811273i	$-0.301225\pi$
$139$	13.7863	1.16934	0.584668	+	0.811273i	$0.301225\pi$
$140$	−21.6689	−1.83136
$141$	−32.5067	−2.73756
$142$	3.82127	0.320674
$143$	21.2120	1.77384
$144$	7.77147	0.647622
$145$	−21.1819	−1.75906
$146$	−9.70486	−0.803180
$147$	−54.9316	−4.53068
$148$	8.86854	0.728989
$149$	−5.16578	−0.423197	−0.211598	−	0.977357i	$-0.567867\pi$
$149$	−5.16578	−0.423197	−0.211598	+	0.977357i	$0.567867\pi$
$150$	−48.5105	−3.96087
$151$	7.18552	0.584749	0.292374	−	0.956304i	$-0.405555\pi$
$151$	7.18552	0.584749	0.292374	+	0.956304i	$0.405555\pi$
$152$	−4.10542	−0.332993
$153$	−46.2192	−3.73660
$154$	−19.1158	−1.54040
$155$	−4.28239	−0.343970
$156$	−17.7436	−1.42063
$157$	−21.8727	−1.74563	−0.872816	−	0.488049i	$-0.837709\pi$
$157$	−21.8727	−1.74563	−0.872816	+	0.488049i	$0.837709\pi$
$158$	−5.00168	−0.397912
$159$	18.5954	1.47471
$160$	4.44756	0.351611
$161$	4.19616	0.330704
$162$	28.0813	2.20628
$163$	2.11442	0.165614	0.0828071	−	0.996566i	$-0.473611\pi$
$163$	2.11442	0.165614	0.0828071	+	0.996566i	$0.473611\pi$
$164$	5.07334	0.396161
$165$	−57.2714	−4.45857
$166$	5.73133	0.444838
$167$	11.9610	0.925570	0.462785	−	0.886470i	$-0.346850\pi$
$167$	11.9610	0.925570	0.462785	+	0.886470i	$0.346850\pi$
$168$	15.9902	1.23367
$169$	16.2287	1.24836
$170$	−26.4509	−2.02869
$171$	−31.9051	−2.43985
$172$	1.73766	0.132496
$173$	2.54029	0.193135	0.0965675	−	0.995326i	$-0.469214\pi$
$173$	2.54029	0.193135	0.0965675	+	0.995326i	$0.469214\pi$
$174$	15.6307	1.18496
$175$	−72.0135	−5.44371
$176$	3.92354	0.295748
$177$	−36.3155	−2.72964
$178$	1.66689	0.124939
$179$	7.28832	0.544755	0.272377	−	0.962191i	$-0.412190\pi$
$179$	7.28832	0.544755	0.272377	+	0.962191i	$0.412190\pi$
$180$	34.5641	2.57626
$181$	23.3062	1.73234	0.866168	−	0.499752i	$-0.166576\pi$
$181$	23.3062	1.73234	0.866168	+	0.499752i	$0.166576\pi$
$182$	−26.3403	−1.95247
$183$	7.26974	0.537394
$184$	−0.861265	−0.0634933
$185$	39.4434	2.89993
$186$	3.16011	0.231710
$187$	−23.3344	−1.70638
$188$	9.90456	0.722365
$189$	76.2965	5.54976
$190$	−18.2591	−1.32465
$191$	7.61725	0.551165	0.275583	−	0.961277i	$-0.411129\pi$
$191$	7.61725	0.551165	0.275583	+	0.961277i	$0.411129\pi$
$192$	−3.28199	−0.236857
$193$	−20.1813	−1.45268	−0.726342	−	0.687334i	$-0.758781\pi$
$193$	−20.1813	−1.45268	−0.726342	+	0.687334i	$0.758781\pi$
$194$	4.00245	0.287359
$195$	−78.9158	−5.65128
$196$	16.7373	1.19552
$197$	−1.60892	−0.114631	−0.0573154	−	0.998356i	$-0.518254\pi$
$197$	−1.60892	−0.114631	−0.0573154	+	0.998356i	$0.518254\pi$
$198$	30.4917	2.16695
$199$	6.55624	0.464760	0.232380	−	0.972625i	$-0.425349\pi$
$199$	6.55624	0.464760	0.232380	+	0.972625i	$0.425349\pi$
$200$	14.7808	1.04516
$201$	0.960516	0.0677496
$202$	6.40952	0.450972
$203$	23.2037	1.62858
$204$	19.5189	1.36660
$205$	22.5640	1.57594
$206$	−8.56592	−0.596816
$207$	−6.69329	−0.465216
$208$	5.40636	0.374863
$209$	−16.1078	−1.11420
$210$	71.1172	4.90756
$211$	−7.60808	−0.523762	−0.261881	−	0.965100i	$-0.584343\pi$
$211$	−7.60808	−0.523762	−0.261881	+	0.965100i	$0.584343\pi$
$212$	−5.66588	−0.389134
$213$	−12.5414	−0.859321
$214$	8.84887	0.604896
$215$	7.72837	0.527070
$216$	−15.6599	−1.06552
$217$	4.69116	0.318456
$218$	−9.38966	−0.635948
$219$	31.8513	2.15231
$220$	17.4502	1.17649
$221$	−32.1532	−2.16286
$222$	−29.1065	−1.95350
$223$	21.3847	1.43202	0.716011	−	0.698089i	$-0.245966\pi$
$223$	21.3847	1.43202	0.716011	+	0.698089i	$0.245966\pi$
$224$	−4.87209	−0.325530
$225$	114.869	7.65791
$226$	−18.4574	−1.22777
$227$	11.5884	0.769151	0.384575	−	0.923094i	$-0.374348\pi$
$227$	11.5884	0.769151	0.384575	+	0.923094i	$0.374348\pi$
$228$	13.4739	0.892334
$229$	25.0691	1.65661	0.828305	−	0.560277i	$-0.189305\pi$
$229$	25.0691	1.65661	0.828305	+	0.560277i	$0.189305\pi$
$230$	−3.83053	−0.252578
$231$	62.7380	4.12786
$232$	−4.76258	−0.312679
$233$	−6.24819	−0.409332	−0.204666	−	0.978832i	$-0.565611\pi$
$233$	−6.24819	−0.409332	−0.204666	+	0.978832i	$0.565611\pi$
$234$	42.0153	2.74663
$235$	44.0512	2.87358
$236$	11.0651	0.720276
$237$	16.4155	1.06630
$238$	28.9757	1.87822
$239$	−4.60645	−0.297966	−0.148983	−	0.988840i	$-0.547600\pi$
$239$	−4.60645	−0.297966	−0.148983	+	0.988840i	$0.547600\pi$
$240$	−14.5969	−0.942223
$241$	−17.1239	−1.10305	−0.551524	−	0.834159i	$-0.685954\pi$
$241$	−17.1239	−1.10305	−0.551524	+	0.834159i	$0.685954\pi$
$242$	4.39415	0.282467
$243$	−45.1829	−2.89848
$244$	−2.21504	−0.141803
$245$	74.4401	4.75580
$246$	−16.6506	−1.06161
$247$	−22.1953	−1.41226
$248$	−0.962863	−0.0611419
$249$	−18.8102	−1.19205
$250$	43.5008	2.75123
$251$	20.8538	1.31628	0.658141	−	0.752895i	$-0.271343\pi$
$251$	20.8538	1.31628	0.658141	+	0.752895i	$0.271343\pi$
$252$	−37.8633	−2.38516
$253$	−3.37921	−0.212449
$254$	0.748632	0.0469734
$255$	86.8117	5.43636
$256$	1.00000	0.0625000
$257$	26.0310	1.62377	0.811884	−	0.583818i	$-0.198442\pi$
$257$	26.0310	1.62377	0.811884	+	0.583818i	$0.198442\pi$
$258$	−5.70300	−0.355053
$259$	−43.2083	−2.68483
$260$	24.0451	1.49121
$261$	−37.0122	−2.29100
$262$	−6.87248	−0.424584
$263$	−6.41116	−0.395329	−0.197665	−	0.980270i	$-0.563336\pi$
$263$	−6.41116	−0.395329	−0.197665	+	0.980270i	$0.563336\pi$
$264$	−12.8770	−0.792526
$265$	−25.1994	−1.54799
$266$	20.0020	1.22640
$267$	−5.47073	−0.334803
$268$	−0.292663	−0.0178772
$269$	13.2634	0.808683	0.404341	−	0.914608i	$-0.367501\pi$
$269$	13.2634	0.808683	0.404341	+	0.914608i	$0.367501\pi$
$270$	−69.6485	−4.23867
$271$	−4.70399	−0.285747	−0.142874	−	0.989741i	$-0.545634\pi$
$271$	−4.70399	−0.285747	−0.142874	+	0.989741i	$0.545634\pi$
$272$	−5.94729	−0.360607
$273$	86.4485	5.23210
$274$	−11.8602	−0.716502
$275$	57.9931	3.49711
$276$	2.82666	0.170145
$277$	3.57064	0.214539	0.107270	−	0.994230i	$-0.465789\pi$
$277$	3.57064	0.214539	0.107270	+	0.994230i	$0.465789\pi$
$278$	13.7863	0.826845
$279$	−7.48286	−0.447987
$280$	−21.6689	−1.29497
$281$	−4.05182	−0.241712	−0.120856	−	0.992670i	$-0.538564\pi$
$281$	−4.05182	−0.241712	−0.120856	+	0.992670i	$0.538564\pi$
$282$	−32.5067	−1.93575
$283$	29.1608	1.73343	0.866713	−	0.498806i	$-0.166228\pi$
$283$	29.1608	1.73343	0.866713	+	0.498806i	$0.166228\pi$
$284$	3.82127	0.226751
$285$	59.9262	3.54972
$286$	21.2120	1.25429
$287$	−24.7178	−1.45904
$288$	7.77147	0.457938
$289$	18.3702	1.08060
$290$	−21.1819	−1.24384
$291$	−13.1360	−0.770046
$292$	−9.70486	−0.567934
$293$	−1.06895	−0.0624487	−0.0312243	−	0.999512i	$-0.509941\pi$
$293$	−1.06895	−0.0624487	−0.0312243	+	0.999512i	$0.509941\pi$
$294$	−54.9316	−3.20367
$295$	49.2127	2.86527
$296$	8.86854	0.515473
$297$	−61.4423	−3.56524
$298$	−5.16578	−0.299245
$299$	−4.65630	−0.269281
$300$	−48.5105	−2.80076
$301$	−8.46606	−0.487975
$302$	7.18552	0.413480
$303$	−21.0360	−1.20849
$304$	−4.10542	−0.235462
$305$	−9.85152	−0.564097
$306$	−46.2192	−2.64217
$307$	−1.33686	−0.0762984	−0.0381492	−	0.999272i	$-0.512146\pi$
$307$	−1.33686	−0.0762984	−0.0381492	+	0.999272i	$0.512146\pi$
$308$	−19.1158	−1.08923
$309$	28.1133	1.59931
$310$	−4.28239	−0.243224
$311$	−2.77131	−0.157146	−0.0785732	−	0.996908i	$-0.525036\pi$
$311$	−2.77131	−0.157146	−0.0785732	+	0.996908i	$0.525036\pi$
$312$	−17.7436	−1.00453
$313$	−0.140885	−0.00796329	−0.00398165	−	0.999992i	$-0.501267\pi$
$313$	−0.140885	−0.00796329	−0.00398165	+	0.999992i	$0.501267\pi$
$314$	−21.8727	−1.23435
$315$	−168.399	−9.48823
$316$	−5.00168	−0.281366
$317$	−7.18419	−0.403505	−0.201752	−	0.979437i	$-0.564664\pi$
$317$	−7.18419	−0.403505	−0.201752	+	0.979437i	$0.564664\pi$
$318$	18.5954	1.04278
$319$	−18.6862	−1.04622
$320$	4.44756	0.248626
$321$	−29.0419	−1.62096
$322$	4.19616	0.233843
$323$	24.4161	1.35855
$324$	28.0813	1.56007
$325$	79.9103	4.43263
$326$	2.11442	0.117107
$327$	30.8168	1.70417
$328$	5.07334	0.280128
$329$	−48.2559	−2.66044
$330$	−57.2714	−3.15268
$331$	34.4539	1.89376	0.946879	−	0.321589i	$-0.104217\pi$
$331$	34.4539	1.89376	0.946879	+	0.321589i	$0.104217\pi$
$332$	5.73133	0.314548
$333$	68.9216	3.77688
$334$	11.9610	0.654477
$335$	−1.30164	−0.0711159
$336$	15.9902	0.872335
$337$	27.3821	1.49160	0.745800	−	0.666170i	$-0.232067\pi$
$337$	27.3821	1.49160	0.745800	+	0.666170i	$0.232067\pi$
$338$	16.2287	0.882724
$339$	60.5770	3.29009
$340$	−26.4509	−1.43450
$341$	−3.77783	−0.204581
$342$	−31.9051	−1.72523
$343$	−47.4409	−2.56157
$344$	1.73766	0.0936886
$345$	12.5718	0.676841
$346$	2.54029	0.136567
$347$	−26.4352	−1.41911	−0.709557	−	0.704648i	$-0.751105\pi$
$347$	−26.4352	−1.41911	−0.709557	+	0.704648i	$0.751105\pi$
$348$	15.6307	0.837896
$349$	32.4982	1.73959	0.869794	−	0.493416i	$-0.164252\pi$
$349$	32.4982	1.73959	0.869794	+	0.493416i	$0.164252\pi$
$350$	−72.0135	−3.84928
$351$	−84.6631	−4.51898
$352$	3.92354	0.209125
$353$	20.4342	1.08760	0.543802	−	0.839214i	$-0.316984\pi$
$353$	20.4342	1.08760	0.543802	+	0.839214i	$0.316984\pi$
$354$	−36.3155	−1.93015
$355$	16.9953	0.902019
$356$	1.66689	0.0883452
$357$	−95.0981	−5.03312
$358$	7.28832	0.385200
$359$	−21.8952	−1.15559	−0.577793	−	0.816183i	$-0.696086\pi$
$359$	−21.8952	−1.15559	−0.577793	+	0.816183i	$0.696086\pi$
$360$	34.5641	1.82169
$361$	−2.14555	−0.112924
$362$	23.3062	1.22495
$363$	−14.4216	−0.756936
$364$	−26.3403	−1.38060
$365$	−43.1630	−2.25925
$366$	7.26974	0.379995
$367$	−15.4356	−0.805733	−0.402866	−	0.915259i	$-0.631986\pi$
$367$	−15.4356	−0.805733	−0.402866	+	0.915259i	$0.631986\pi$
$368$	−0.861265	−0.0448965
$369$	39.4273	2.05250
$370$	39.4434	2.05056
$371$	27.6047	1.43316
$372$	3.16011	0.163844
$373$	−29.8221	−1.54413	−0.772066	−	0.635542i	$-0.780777\pi$
$373$	−29.8221	−1.54413	−0.772066	+	0.635542i	$0.780777\pi$
$374$	−23.3344	−1.20659
$375$	−142.769	−7.37257
$376$	9.90456	0.510789
$377$	−25.7482	−1.32610
$378$	76.2965	3.92427
$379$	33.3505	1.71310	0.856550	−	0.516063i	$-0.172603\pi$
$379$	33.3505	1.71310	0.856550	+	0.516063i	$0.172603\pi$
$380$	−18.2591	−0.936672
$381$	−2.45701	−0.125876
$382$	7.61725	0.389733
$383$	−5.51962	−0.282039	−0.141020	−	0.990007i	$-0.545038\pi$
$383$	−5.51962	−0.282039	−0.141020	+	0.990007i	$0.545038\pi$
$384$	−3.28199	−0.167483
$385$	−85.0189	−4.33296
$386$	−20.1813	−1.02720
$387$	13.5042	0.686457
$388$	4.00245	0.203193
$389$	35.7109	1.81062	0.905308	−	0.424756i	$-0.139640\pi$
$389$	35.7109	1.81062	0.905308	+	0.424756i	$0.139640\pi$
$390$	−78.9158	−3.99606
$391$	5.12219	0.259040
$392$	16.7373	0.845360
$393$	22.5554	1.13777
$394$	−1.60892	−0.0810562
$395$	−22.2453	−1.11928
$396$	30.4917	1.53226
$397$	−8.46884	−0.425039	−0.212519	−	0.977157i	$-0.568167\pi$
$397$	−8.46884	−0.425039	−0.212519	+	0.977157i	$0.568167\pi$
$398$	6.55624	0.328635
$399$	−65.6463	−3.28642
$400$	14.7808	0.739041
$401$	−12.6315	−0.630785	−0.315392	−	0.948961i	$-0.602136\pi$
$401$	−12.6315	−0.630785	−0.315392	+	0.948961i	$0.602136\pi$
$402$	0.960516	0.0479062
$403$	−5.20558	−0.259308
$404$	6.40952	0.318885
$405$	124.893	6.20600
$406$	23.2037	1.15158
$407$	34.7960	1.72478
$408$	19.5189	0.966332
$409$	23.9948	1.18647	0.593234	−	0.805030i	$-0.297851\pi$
$409$	23.9948	1.18647	0.593234	+	0.805030i	$0.297851\pi$
$410$	22.5640	1.11436
$411$	38.9251	1.92003
$412$	−8.56592	−0.422013
$413$	−53.9102	−2.65275
$414$	−6.69329	−0.328957
$415$	25.4905	1.25128
$416$	5.40636	0.265068
$417$	−45.2464	−2.21573
$418$	−16.1078	−0.787856
$419$	7.76941	0.379560	0.189780	−	0.981827i	$-0.439222\pi$
$419$	7.76941	0.379560	0.189780	+	0.981827i	$0.439222\pi$
$420$	71.1172	3.47017
$421$	0.339761	0.0165589	0.00827947	−	0.999966i	$-0.497365\pi$
$421$	0.339761	0.0165589	0.00827947	+	0.999966i	$0.497365\pi$
$422$	−7.60808	−0.370356
$423$	76.9730	3.74256
$424$	−5.66588	−0.275160
$425$	−87.9058	−4.26406
$426$	−12.5414	−0.607632
$427$	10.7919	0.522255
$428$	8.84887	0.427726
$429$	−69.6178	−3.36118
$430$	7.72837	0.372695
$431$	−35.7250	−1.72081	−0.860407	−	0.509608i	$-0.829790\pi$
$431$	−35.7250	−1.72081	−0.860407	+	0.509608i	$0.829790\pi$
$432$	−15.6599	−0.753438
$433$	−24.7023	−1.18712	−0.593559	−	0.804790i	$-0.702278\pi$
$433$	−24.7023	−1.18712	−0.593559	+	0.804790i	$0.702278\pi$
$434$	4.69116	0.225183
$435$	69.5187	3.33317
$436$	−9.38966	−0.449683
$437$	3.53585	0.169143
$438$	31.8513	1.52191
$439$	−1.38286	−0.0660001	−0.0330001	−	0.999455i	$-0.510506\pi$
$439$	−1.38286	−0.0660001	−0.0330001	+	0.999455i	$0.510506\pi$
$440$	17.4502	0.831905
$441$	130.073	6.19396
$442$	−32.1532	−1.52937
$443$	20.4034	0.969393	0.484697	−	0.874682i	$-0.338930\pi$
$443$	20.4034	0.969393	0.484697	+	0.874682i	$0.338930\pi$
$444$	−29.1065	−1.38133
$445$	7.41362	0.351439
$446$	21.3847	1.01259
$447$	16.9540	0.801898
$448$	−4.87209	−0.230185
$449$	−1.86879	−0.0881937	−0.0440969	−	0.999027i	$-0.514041\pi$
$449$	−1.86879	−0.0881937	−0.0440969	+	0.999027i	$0.514041\pi$
$450$	114.869	5.41496
$451$	19.9054	0.937310
$452$	−18.4574	−0.868163
$453$	−23.5828	−1.10802
$454$	11.5884	0.543872
$455$	−117.150	−5.49207
$456$	13.4739	0.630975
$457$	5.07315	0.237312	0.118656	−	0.992935i	$-0.462141\pi$
$457$	5.07315	0.237312	0.118656	+	0.992935i	$0.462141\pi$
$458$	25.0691	1.17140
$459$	93.1340	4.34712
$460$	−3.83053	−0.178599
$461$	−4.47987	−0.208648	−0.104324	−	0.994543i	$-0.533268\pi$
$461$	−4.47987	−0.208648	−0.104324	+	0.994543i	$0.533268\pi$
$462$	62.7380	2.91884
$463$	10.4890	0.487465	0.243733	−	0.969842i	$-0.421628\pi$
$463$	10.4890	0.487465	0.243733	+	0.969842i	$0.421628\pi$
$464$	−4.76258	−0.221097
$465$	14.0548	0.651775
$466$	−6.24819	−0.289442
$467$	−22.1661	−1.02573	−0.512863	−	0.858470i	$-0.671415\pi$
$467$	−22.1661	−1.02573	−0.512863	+	0.858470i	$0.671415\pi$
$468$	42.0153	1.94216
$469$	1.42588	0.0658410
$470$	44.0512	2.03193
$471$	71.7861	3.30773
$472$	11.0651	0.509312
$473$	6.81779	0.313482
$474$	16.4155	0.753987
$475$	−60.6814	−2.78425
$476$	28.9757	1.32810
$477$	−44.0322	−2.01610
$478$	−4.60645	−0.210694
$479$	−24.9780	−1.14128	−0.570638	−	0.821202i	$-0.693304\pi$
$479$	−24.9780	−1.14128	−0.570638	+	0.821202i	$0.693304\pi$
$480$	−14.5969	−0.666253
$481$	47.9465	2.18617
$482$	−17.1239	−0.779973
$483$	−13.7718	−0.626637
$484$	4.39415	0.199734
$485$	17.8011	0.808308
$486$	−45.1829	−2.04954
$487$	25.7055	1.16483	0.582413	−	0.812893i	$-0.302109\pi$
$487$	25.7055	1.16483	0.582413	+	0.812893i	$0.302109\pi$
$488$	−2.21504	−0.100270
$489$	−6.93951	−0.313816
$490$	74.4401	3.36286
$491$	−17.9511	−0.810121	−0.405061	−	0.914290i	$-0.632750\pi$
$491$	−17.9511	−0.810121	−0.405061	+	0.914290i	$0.632750\pi$
$492$	−16.6506	−0.750669
$493$	28.3244	1.27567
$494$	−22.1953	−0.998616
$495$	135.614	6.09538
$496$	−0.962863	−0.0432338
$497$	−18.6176	−0.835112
$498$	−18.8102	−0.842904
$499$	41.9214	1.87666	0.938329	−	0.345744i	$-0.112374\pi$
$499$	41.9214	1.87666	0.938329	+	0.345744i	$0.112374\pi$
$500$	43.5008	1.94541
$501$	−39.2559	−1.75383
$502$	20.8538	0.930752
$503$	38.6605	1.72379	0.861893	−	0.507089i	$-0.169279\pi$
$503$	38.6605	1.72379	0.861893	+	0.507089i	$0.169279\pi$
$504$	−37.8633	−1.68657
$505$	28.5067	1.26853
$506$	−3.37921	−0.150224
$507$	−53.2624	−2.36547
$508$	0.748632	0.0332152
$509$	16.7234	0.741251	0.370626	−	0.928782i	$-0.379143\pi$
$509$	16.7234	0.741251	0.370626	+	0.928782i	$0.379143\pi$
$510$	86.8117	3.84409
$511$	47.2830	2.09168
$512$	1.00000	0.0441942
$513$	64.2905	2.83849
$514$	26.0310	1.14818
$515$	−38.0975	−1.67878
$516$	−5.70300	−0.251060
$517$	38.8609	1.70910
$518$	−43.2083	−1.89846
$519$	−8.33722	−0.365964
$520$	24.0451	1.05445
$521$	14.1607	0.620393	0.310197	−	0.950672i	$-0.399605\pi$
$521$	14.1607	0.620393	0.310197	+	0.950672i	$0.399605\pi$
$522$	−37.0122	−1.61998
$523$	−30.6006	−1.33807	−0.669034	−	0.743231i	$-0.733292\pi$
$523$	−30.6006	−1.33807	−0.669034	+	0.743231i	$0.733292\pi$
$524$	−6.87248	−0.300226
$525$	236.348	10.3151
$526$	−6.41116	−0.279540
$527$	5.72642	0.249447
$528$	−12.8770	−0.560400
$529$	−22.2582	−0.967749
$530$	−25.1994	−1.09459
$531$	85.9920	3.73174
$532$	20.0020	0.867195
$533$	27.4283	1.18805
$534$	−5.47073	−0.236742
$535$	39.3559	1.70150
$536$	−0.292663	−0.0126411
$537$	−23.9202	−1.03223
$538$	13.2634	0.571825
$539$	65.6693	2.82858
$540$	−69.6485	−2.99719
$541$	−3.00981	−0.129402	−0.0647008	−	0.997905i	$-0.520609\pi$
$541$	−3.00981	−0.129402	−0.0647008	+	0.997905i	$0.520609\pi$
$542$	−4.70399	−0.202054
$543$	−76.4908	−3.28253
$544$	−5.94729	−0.254988
$545$	−41.7611	−1.78885
$546$	86.4485	3.69965
$547$	−3.93505	−0.168251	−0.0841253	−	0.996455i	$-0.526810\pi$
$547$	−3.93505	−0.168251	−0.0841253	+	0.996455i	$0.526810\pi$
$548$	−11.8602	−0.506643
$549$	−17.2141	−0.734680
$550$	57.9931	2.47283
$551$	19.5524	0.832959
$552$	2.82666	0.120311
$553$	24.3686	1.03626
$554$	3.57064	0.151702
$555$	−129.453	−5.49497
$556$	13.7863	0.584668
$557$	−5.16817	−0.218983	−0.109491	−	0.993988i	$-0.534922\pi$
$557$	−5.16817	−0.218983	−0.109491	+	0.993988i	$0.534922\pi$
$558$	−7.48286	−0.316775
$559$	9.39443	0.397342
$560$	−21.6689	−0.915679
$561$	76.5833	3.23335
$562$	−4.05182	−0.170916
$563$	9.92609	0.418335	0.209167	−	0.977880i	$-0.432925\pi$
$563$	9.92609	0.418335	0.209167	+	0.977880i	$0.432925\pi$
$564$	−32.5067	−1.36878
$565$	−82.0905	−3.45357
$566$	29.1608	1.22572
$567$	−136.815	−5.74568
$568$	3.82127	0.160337
$569$	16.3245	0.684358	0.342179	−	0.939635i	$-0.388835\pi$
$569$	16.3245	0.684358	0.342179	+	0.939635i	$0.388835\pi$
$570$	59.9262	2.51003
$571$	−20.9095	−0.875036	−0.437518	−	0.899210i	$-0.644142\pi$
$571$	−20.9095	−0.875036	−0.437518	+	0.899210i	$0.644142\pi$
$572$	21.2120	0.886920
$573$	−24.9998	−1.04438
$574$	−24.7178	−1.03170
$575$	−12.7302	−0.530886
$576$	7.77147	0.323811
$577$	−32.4136	−1.34940	−0.674698	−	0.738094i	$-0.735726\pi$
$577$	−32.4136	−1.34940	−0.674698	+	0.738094i	$0.735726\pi$
$578$	18.3702	0.764101
$579$	66.2349	2.75263
$580$	−21.1819	−0.879530
$581$	−27.9236	−1.15846
$582$	−13.1360	−0.544505
$583$	−22.2303	−0.920685
$584$	−9.70486	−0.401590
$585$	186.866	7.72595
$586$	−1.06895	−0.0441579
$587$	42.4142	1.75062	0.875310	−	0.483562i	$-0.160657\pi$
$587$	42.4142	1.75062	0.875310	+	0.483562i	$0.160657\pi$
$588$	−54.9316	−2.26534
$589$	3.95295	0.162879
$590$	49.2127	2.02606
$591$	5.28046	0.217209
$592$	8.86854	0.364495
$593$	−6.86111	−0.281752	−0.140876	−	0.990027i	$-0.544992\pi$
$593$	−6.86111	−0.281752	−0.140876	+	0.990027i	$0.544992\pi$
$594$	−61.4423	−2.52101
$595$	128.871	5.28321
$596$	−5.16578	−0.211598
$597$	−21.5175	−0.880654
$598$	−4.65630	−0.190410
$599$	−14.7400	−0.602260	−0.301130	−	0.953583i	$-0.597364\pi$
$599$	−14.7400	−0.602260	−0.301130	+	0.953583i	$0.597364\pi$
$600$	−48.5105	−1.98043
$601$	−19.3661	−0.789961	−0.394980	−	0.918690i	$-0.629249\pi$
$601$	−19.3661	−0.789961	−0.394980	+	0.918690i	$0.629249\pi$
$602$	−8.46606	−0.345051
$603$	−2.27442	−0.0926215
$604$	7.18552	0.292374
$605$	19.5433	0.794547
$606$	−21.0360	−0.854528
$607$	13.9007	0.564214	0.282107	−	0.959383i	$-0.408967\pi$
$607$	13.9007	0.564214	0.282107	+	0.959383i	$0.408967\pi$
$608$	−4.10542	−0.166497
$609$	−76.1544	−3.08593
$610$	−9.85152	−0.398876
$611$	53.5476	2.16630
$612$	−46.2192	−1.86830
$613$	−5.40493	−0.218303	−0.109151	−	0.994025i	$-0.534813\pi$
$613$	−5.40493	−0.218303	−0.109151	+	0.994025i	$0.534813\pi$
$614$	−1.33686	−0.0539511
$615$	−74.0548	−2.98618
$616$	−19.1158	−0.770199
$617$	−14.6055	−0.587994	−0.293997	−	0.955806i	$-0.594986\pi$
$617$	−14.6055	−0.587994	−0.293997	+	0.955806i	$0.594986\pi$
$618$	28.1133	1.13088
$619$	−29.5641	−1.18828	−0.594141	−	0.804361i	$-0.702508\pi$
$619$	−29.5641	−1.18828	−0.594141	+	0.804361i	$0.702508\pi$
$620$	−4.28239	−0.171985
$621$	13.4873	0.541228
$622$	−2.77131	−0.111119
$623$	−8.12126	−0.325371
$624$	−17.7436	−0.710313
$625$	119.568	4.78274
$626$	−0.140885	−0.00563090
$627$	52.8655	2.11125
$628$	−21.8727	−0.872816
$629$	−52.7437	−2.10303
$630$	−168.399	−6.70919
$631$	47.1471	1.87690	0.938449	−	0.345418i	$-0.112263\pi$
$631$	47.1471	1.87690	0.938449	+	0.345418i	$0.112263\pi$
$632$	−5.00168	−0.198956
$633$	24.9697	0.992455
$634$	−7.18419	−0.285321
$635$	3.32959	0.132131
$636$	18.5954	0.737355
$637$	90.4876	3.58525
$638$	−18.6862	−0.739792
$639$	29.6969	1.17479
$640$	4.44756	0.175805
$641$	−39.6265	−1.56515	−0.782576	−	0.622556i	$-0.786094\pi$
$641$	−39.6265	−1.56515	−0.782576	+	0.622556i	$0.786094\pi$
$642$	−29.0419	−1.14619
$643$	33.8869	1.33637	0.668185	−	0.743995i	$-0.267071\pi$
$643$	33.8869	1.33637	0.668185	+	0.743995i	$0.267071\pi$
$644$	4.19616	0.165352
$645$	−25.3644	−0.998724
$646$	24.4161	0.960638
$647$	16.4059	0.644983	0.322492	−	0.946572i	$-0.395480\pi$
$647$	16.4059	0.644983	0.322492	+	0.946572i	$0.395480\pi$
$648$	28.0813	1.10314
$649$	43.4143	1.70416
$650$	79.9103	3.13434
$651$	−15.3963	−0.603430
$652$	2.11442	0.0828071
$653$	3.76575	0.147365	0.0736826	−	0.997282i	$-0.476525\pi$
$653$	3.76575	0.147365	0.0736826	+	0.997282i	$0.476525\pi$
$654$	30.8168	1.20503
$655$	−30.5658	−1.19430
$656$	5.07334	0.198081
$657$	−75.4210	−2.94246
$658$	−48.2559	−1.88121
$659$	25.0977	0.977667	0.488834	−	0.872377i	$-0.337422\pi$
$659$	25.0977	0.977667	0.488834	+	0.872377i	$0.337422\pi$
$660$	−57.2714	−2.22928
$661$	−40.8504	−1.58890	−0.794449	−	0.607331i	$-0.792240\pi$
$661$	−40.8504	−1.58890	−0.794449	+	0.607331i	$0.792240\pi$
$662$	34.4539	1.33909
$663$	105.526	4.09830
$664$	5.73133	0.222419
$665$	88.9600	3.44972
$666$	68.9216	2.67066
$667$	4.10184	0.158824
$668$	11.9610	0.462785
$669$	−70.1843	−2.71348
$670$	−1.30164	−0.0502866
$671$	−8.69079	−0.335504
$672$	15.9902	0.616834
$673$	1.09857	0.0423466	0.0211733	−	0.999776i	$-0.493260\pi$
$673$	1.09857	0.0423466	0.0211733	+	0.999776i	$0.493260\pi$
$674$	27.3821	1.05472
$675$	−231.466	−8.90914
$676$	16.2287	0.624180
$677$	29.7317	1.14268	0.571342	−	0.820712i	$-0.306423\pi$
$677$	29.7317	1.14268	0.571342	+	0.820712i	$0.306423\pi$
$678$	60.5770	2.32645
$679$	−19.5003	−0.748352
$680$	−26.4509	−1.01435
$681$	−38.0331	−1.45743
$682$	−3.77783	−0.144661
$683$	−2.69505	−0.103123	−0.0515616	−	0.998670i	$-0.516420\pi$
$683$	−2.69505	−0.103123	−0.0515616	+	0.998670i	$0.516420\pi$
$684$	−31.9051	−1.21992
$685$	−52.7490	−2.01544
$686$	−47.4409	−1.81130
$687$	−82.2765	−3.13904
$688$	1.73766	0.0662478
$689$	−30.6318	−1.16698
$690$	12.5718	0.478599
$691$	28.5333	1.08546	0.542730	−	0.839907i	$-0.317391\pi$
$691$	28.5333	1.08546	0.542730	+	0.839907i	$0.317391\pi$
$692$	2.54029	0.0965675
$693$	−148.558	−5.64326
$694$	−26.4352	−1.00347
$695$	61.3153	2.32582
$696$	15.6307	0.592482
$697$	−30.1726	−1.14287
$698$	32.4982	1.23007
$699$	20.5065	0.775627
$700$	−72.0135	−2.72185
$701$	2.07992	0.0785574	0.0392787	−	0.999228i	$-0.487494\pi$
$701$	2.07992	0.0785574	0.0392787	+	0.999228i	$0.487494\pi$
$702$	−84.6631	−3.19540
$703$	−36.4090	−1.37319
$704$	3.92354	0.147874
$705$	−144.576	−5.44503
$706$	20.4342	0.769052
$707$	−31.2277	−1.17444
$708$	−36.3155	−1.36482
$709$	34.2300	1.28553	0.642767	−	0.766062i	$-0.277786\pi$
$709$	34.2300	1.28553	0.642767	+	0.766062i	$0.277786\pi$
$710$	16.9953	0.637824
$711$	−38.8704	−1.45775
$712$	1.66689	0.0624695
$713$	0.829280	0.0310568
$714$	−95.0981	−3.55896
$715$	94.3419	3.52819
$716$	7.28832	0.272377
$717$	15.1183	0.564604
$718$	−21.8952	−0.817123
$719$	−22.2743	−0.830690	−0.415345	−	0.909664i	$-0.636339\pi$
$719$	−22.2743	−0.830690	−0.415345	+	0.909664i	$0.636339\pi$
$720$	34.5641	1.28813
$721$	41.7339	1.55425
$722$	−2.14555	−0.0798493
$723$	56.2006	2.09012
$724$	23.3062	0.866168
$725$	−70.3948	−2.61440
$726$	−14.4216	−0.535235
$727$	−17.8068	−0.660419	−0.330210	−	0.943908i	$-0.607119\pi$
$727$	−17.8068	−0.660419	−0.330210	+	0.943908i	$0.607119\pi$
$728$	−26.3403	−0.976235
$729$	64.0459	2.37207
$730$	−43.1630	−1.59753
$731$	−10.3344	−0.382231
$732$	7.26974	0.268697
$733$	28.5186	1.05336	0.526679	−	0.850064i	$-0.323437\pi$
$733$	28.5186	1.05336	0.526679	+	0.850064i	$0.323437\pi$
$734$	−15.4356	−0.569739
$735$	−244.312	−9.01157
$736$	−0.861265	−0.0317466
$737$	−1.14827	−0.0422972
$738$	39.4273	1.45134
$739$	−12.9432	−0.476125	−0.238063	−	0.971250i	$-0.576512\pi$
$739$	−12.9432	−0.476125	−0.238063	+	0.971250i	$0.576512\pi$
$740$	39.4434	1.44997
$741$	72.8449	2.67603
$742$	27.6047	1.01340
$743$	−27.3553	−1.00357	−0.501785	−	0.864993i	$-0.667323\pi$
$743$	−27.3553	−1.00357	−0.501785	+	0.864993i	$0.667323\pi$
$744$	3.16011	0.115855
$745$	−22.9751	−0.841743
$746$	−29.8221	−1.09187
$747$	44.5409	1.62966
$748$	−23.3344	−0.853191
$749$	−43.1125	−1.57530
$750$	−142.769	−5.21319
$751$	−19.2639	−0.702949	−0.351474	−	0.936198i	$-0.614320\pi$
$751$	−19.2639	−0.702949	−0.351474	+	0.936198i	$0.614320\pi$
$752$	9.90456	0.361182
$753$	−68.4421	−2.49417
$754$	−25.7482	−0.937694
$755$	31.9580	1.16307
$756$	76.2965	2.77488
$757$	43.6556	1.58669	0.793344	−	0.608773i	$-0.208338\pi$
$757$	43.6556	1.58669	0.793344	+	0.608773i	$0.208338\pi$
$758$	33.3505	1.21135
$759$	11.0905	0.402560
$760$	−18.2591	−0.662327
$761$	−24.2854	−0.880346	−0.440173	−	0.897913i	$-0.645083\pi$
$761$	−24.2854	−0.880346	−0.440173	+	0.897913i	$0.645083\pi$
$762$	−2.45701	−0.0890079
$763$	45.7473	1.65616
$764$	7.61725	0.275583
$765$	−205.563	−7.43213
$766$	−5.51962	−0.199432
$767$	59.8218	2.16004
$768$	−3.28199	−0.118429
$769$	20.6434	0.744421	0.372211	−	0.928148i	$-0.378600\pi$
$769$	20.6434	0.744421	0.372211	+	0.928148i	$0.378600\pi$
$770$	−85.0189	−3.06387
$771$	−85.4335	−3.07681
$772$	−20.1813	−0.726342
$773$	35.8789	1.29047	0.645237	−	0.763983i	$-0.276759\pi$
$773$	35.8789	1.29047	0.645237	+	0.763983i	$0.276759\pi$
$774$	13.5042	0.485398
$775$	−14.2319	−0.511225
$776$	4.00245	0.143679
$777$	141.809	5.08738
$778$	35.7109	1.28030
$779$	−20.8282	−0.746246
$780$	−78.9158	−2.82564
$781$	14.9929	0.536488
$782$	5.12219	0.183169
$783$	74.5816	2.66533
$784$	16.7373	0.597760
$785$	−97.2803	−3.47208
$786$	22.5554	0.804526
$787$	−14.4187	−0.513970	−0.256985	−	0.966415i	$-0.582729\pi$
$787$	−14.4187	−0.513970	−0.256985	+	0.966415i	$0.582729\pi$
$788$	−1.60892	−0.0573154
$789$	21.0414	0.749093
$790$	−22.2453	−0.791451
$791$	89.9262	3.19741
$792$	30.4917	1.08347
$793$	−11.9753	−0.425255
$794$	−8.46884	−0.300548
$795$	82.7041	2.93321
$796$	6.55624	0.232380
$797$	19.7010	0.697845	0.348922	−	0.937152i	$-0.386548\pi$
$797$	19.7010	0.697845	0.348922	+	0.937152i	$0.386548\pi$
$798$	−65.6463	−2.32385
$799$	−58.9053	−2.08392
$800$	14.7808	0.522581
$801$	12.9542	0.457715
$802$	−12.6315	−0.446032
$803$	−38.0774	−1.34372
$804$	0.960516	0.0338748
$805$	18.6627	0.657773
$806$	−5.20558	−0.183359
$807$	−43.5303	−1.53234
$808$	6.40952	0.225486
$809$	41.7890	1.46922	0.734611	−	0.678488i	$-0.237365\pi$
$809$	41.7890	1.46922	0.734611	+	0.678488i	$0.237365\pi$
$810$	124.893	4.38831
$811$	15.2620	0.535920	0.267960	−	0.963430i	$-0.413650\pi$
$811$	15.2620	0.535920	0.267960	+	0.963430i	$0.413650\pi$
$812$	23.2037	0.814291
$813$	15.4385	0.541451
$814$	34.7960	1.21960
$815$	9.40402	0.329409
$816$	19.5189	0.683300
$817$	−7.13383	−0.249581
$818$	23.9948	0.838960
$819$	−204.702	−7.15288
$820$	22.5640	0.787969
$821$	34.9055	1.21821	0.609106	−	0.793089i	$-0.291528\pi$
$821$	34.9055	1.21821	0.609106	+	0.793089i	$0.291528\pi$
$822$	38.9251	1.35767
$823$	37.8551	1.31954	0.659772	−	0.751466i	$-0.270653\pi$
$823$	37.8551	1.31954	0.659772	+	0.751466i	$0.270653\pi$
$824$	−8.56592	−0.298408
$825$	−190.333	−6.62654
$826$	−53.9102	−1.87577
$827$	−25.9796	−0.903399	−0.451699	−	0.892170i	$-0.649182\pi$
$827$	−25.9796	−0.903399	−0.451699	+	0.892170i	$0.649182\pi$
$828$	−6.69329	−0.232608
$829$	24.7398	0.859250	0.429625	−	0.903008i	$-0.358646\pi$
$829$	24.7398	0.859250	0.429625	+	0.903008i	$0.358646\pi$
$830$	25.4905	0.884787
$831$	−11.7188	−0.406521
$832$	5.40636	0.187432
$833$	−99.5414	−3.44890
$834$	−45.2464	−1.56675
$835$	53.1973	1.84097
$836$	−16.1078	−0.557099
$837$	15.0784	0.521184
$838$	7.76941	0.268390
$839$	12.2789	0.423914	0.211957	−	0.977279i	$-0.432016\pi$
$839$	12.2789	0.423914	0.211957	+	0.977279i	$0.432016\pi$
$840$	71.1172	2.45378
$841$	−6.31782	−0.217856
$842$	0.339761	0.0117089
$843$	13.2980	0.458009
$844$	−7.60808	−0.261881
$845$	72.1781	2.48300
$846$	76.9730	2.64639
$847$	−21.4087	−0.735612
$848$	−5.66588	−0.194567
$849$	−95.7053	−3.28460
$850$	−87.9058	−3.01514
$851$	−7.63816	−0.261833
$852$	−12.5414	−0.429660
$853$	−30.6734	−1.05024	−0.525119	−	0.851029i	$-0.675979\pi$
$853$	−30.6734	−1.05024	−0.525119	+	0.851029i	$0.675979\pi$
$854$	10.7919	0.369290
$855$	−141.900	−4.85288
$856$	8.84887	0.302448
$857$	48.3962	1.65318	0.826591	−	0.562803i	$-0.190277\pi$
$857$	48.3962	1.65318	0.826591	+	0.562803i	$0.190277\pi$
$858$	−69.6178	−2.37671
$859$	18.2383	0.622284	0.311142	−	0.950363i	$-0.399289\pi$
$859$	18.2383	0.622284	0.311142	+	0.950363i	$0.399289\pi$
$860$	7.72837	0.263535
$861$	81.1235	2.76468
$862$	−35.7250	−1.21680
$863$	−1.06285	−0.0361797	−0.0180899	−	0.999836i	$-0.505758\pi$
$863$	−1.06285	−0.0361797	−0.0180899	+	0.999836i	$0.505758\pi$
$864$	−15.6599	−0.532761
$865$	11.2981	0.384148
$866$	−24.7023	−0.839420
$867$	−60.2909	−2.04759
$868$	4.69116	0.159228
$869$	−19.6243	−0.665708
$870$	69.5187	2.35691
$871$	−1.58224	−0.0536121
$872$	−9.38966	−0.317974
$873$	31.1049	1.05274
$874$	3.53585	0.119602
$875$	−211.940	−7.16487
$876$	31.8513	1.07616
$877$	23.9807	0.809772	0.404886	−	0.914367i	$-0.367311\pi$
$877$	23.9807	0.809772	0.404886	+	0.914367i	$0.367311\pi$
$878$	−1.38286	−0.0466691
$879$	3.50828	0.118331
$880$	17.4502	0.588246
$881$	5.45035	0.183627	0.0918134	−	0.995776i	$-0.470734\pi$
$881$	5.45035	0.183627	0.0918134	+	0.995776i	$0.470734\pi$
$882$	130.073	4.37979
$883$	−21.1542	−0.711897	−0.355948	−	0.934506i	$-0.615842\pi$
$883$	−21.1542	−0.711897	−0.355948	+	0.934506i	$0.615842\pi$
$884$	−32.1532	−1.08143
$885$	−161.516	−5.42929
$886$	20.4034	0.685465
$887$	−20.8287	−0.699360	−0.349680	−	0.936869i	$-0.613710\pi$
$887$	−20.8287	−0.699360	−0.349680	+	0.936869i	$0.613710\pi$
$888$	−29.1065	−0.976749
$889$	−3.64741	−0.122330
$890$	7.41362	0.248505
$891$	110.178	3.69111
$892$	21.3847	0.716011
$893$	−40.6624	−1.36071
$894$	16.9540	0.567028
$895$	32.4153	1.08352
$896$	−4.87209	−0.162765
$897$	15.2819	0.510249
$898$	−1.86879	−0.0623624
$899$	4.58571	0.152942
$900$	114.869	3.82895
$901$	33.6966	1.12260
$902$	19.9054	0.662778
$903$	27.7855	0.924644
$904$	−18.4574	−0.613884
$905$	103.656	3.44564
$906$	−23.5828	−0.783486
$907$	−32.1832	−1.06863	−0.534313	−	0.845287i	$-0.679430\pi$
$907$	−32.1832	−1.06863	−0.534313	+	0.845287i	$0.679430\pi$
$908$	11.5884	0.384575
$909$	49.8113	1.65214
$910$	−117.150	−3.88348
$911$	−10.7111	−0.354874	−0.177437	−	0.984132i	$-0.556781\pi$
$911$	−10.7111	−0.354874	−0.177437	+	0.984132i	$0.556781\pi$
$912$	13.4739	0.446167
$913$	22.4871	0.744214
$914$	5.07315	0.167805
$915$	32.3326	1.06888
$916$	25.0691	0.828305
$917$	33.4834	1.10572
$918$	93.1340	3.07388
$919$	−34.9845	−1.15403	−0.577016	−	0.816733i	$-0.695783\pi$
$919$	−34.9845	−1.15403	−0.577016	+	0.816733i	$0.695783\pi$
$920$	−3.83053	−0.126289
$921$	4.38755	0.144575
$922$	−4.47987	−0.147537
$923$	20.6591	0.680004
$924$	62.7380	2.06393
$925$	131.084	4.31002
$926$	10.4890	0.344690
$927$	−66.5698	−2.18644
$928$	−4.76258	−0.156339
$929$	36.0696	1.18341	0.591703	−	0.806156i	$-0.298456\pi$
$929$	36.0696	1.18341	0.591703	+	0.806156i	$0.298456\pi$
$930$	14.0548	0.460874
$931$	−68.7135	−2.25199
$932$	−6.24819	−0.204666
$933$	9.09541	0.297770
$934$	−22.1661	−0.725298
$935$	−103.781	−3.39401
$936$	42.0153	1.37331
$937$	37.3896	1.22146	0.610732	−	0.791837i	$-0.290875\pi$
$937$	37.3896	1.22146	0.610732	+	0.791837i	$0.290875\pi$
$938$	1.42588	0.0465566
$939$	0.462384	0.0150893
$940$	44.0512	1.43679
$941$	32.9911	1.07548	0.537740	−	0.843111i	$-0.319278\pi$
$941$	32.9911	1.07548	0.537740	+	0.843111i	$0.319278\pi$
$942$	71.7861	2.33892
$943$	−4.36949	−0.142290
$944$	11.0651	0.360138
$945$	339.334	11.0385
$946$	6.81779	0.221665
$947$	16.2907	0.529377	0.264689	−	0.964334i	$-0.414731\pi$
$947$	16.2907	0.529377	0.264689	+	0.964334i	$0.414731\pi$
$948$	16.4155	0.533150
$949$	−52.4680	−1.70318
$950$	−60.6814	−1.96876
$951$	23.5785	0.764584
$952$	28.9757	0.939109
$953$	21.0413	0.681596	0.340798	−	0.940137i	$-0.389303\pi$
$953$	21.0413	0.681596	0.340798	+	0.940137i	$0.389303\pi$
$954$	−44.0322	−1.42560
$955$	33.8782	1.09627
$956$	−4.60645	−0.148983
$957$	61.3278	1.98245
$958$	−24.9780	−0.807004
$959$	57.7840	1.86594
$960$	−14.5969	−0.471112
$961$	−30.0729	−0.970093
$962$	47.9465	1.54586
$963$	68.7687	2.21604
$964$	−17.1239	−0.551524
$965$	−89.7577	−2.88940
$966$	−13.7718	−0.443099
$967$	−10.4829	−0.337108	−0.168554	−	0.985692i	$-0.553910\pi$
$967$	−10.4829	−0.337108	−0.168554	+	0.985692i	$0.553910\pi$
$968$	4.39415	0.141233
$969$	−80.1334	−2.57426
$970$	17.8011	0.571560
$971$	−16.7479	−0.537465	−0.268733	−	0.963215i	$-0.586605\pi$
$971$	−16.7479	−0.537465	−0.268733	+	0.963215i	$0.586605\pi$
$972$	−45.1829	−1.44924
$973$	−67.1679	−2.15331
$974$	25.7055	0.823656
$975$	−262.265	−8.39920
$976$	−2.21504	−0.0709016
$977$	−31.8022	−1.01744	−0.508721	−	0.860932i	$-0.669881\pi$
$977$	−31.8022	−1.01744	−0.508721	+	0.860932i	$0.669881\pi$
$978$	−6.93951	−0.221901
$979$	6.54012	0.209023
$980$	74.4401	2.37790
$981$	−72.9714	−2.32980
$982$	−17.9511	−0.572842
$983$	−38.1170	−1.21574	−0.607872	−	0.794035i	$-0.707976\pi$
$983$	−38.1170	−1.21574	−0.607872	+	0.794035i	$0.707976\pi$
$984$	−16.6506	−0.530803
$985$	−7.15577	−0.228002
$986$	28.3244	0.902034
$987$	158.376	5.04115
$988$	−22.1953	−0.706128
$989$	−1.49659	−0.0475887
$990$	135.614	4.31008
$991$	−41.1150	−1.30606	−0.653031	−	0.757331i	$-0.726503\pi$
$991$	−41.1150	−1.30606	−0.653031	+	0.757331i	$0.726503\pi$
$992$	−0.962863	−0.0305709
$993$	−113.077	−3.58841
$994$	−18.6176	−0.590514
$995$	29.1593	0.924412
$996$	−18.8102	−0.596023
$997$	−26.8487	−0.850306	−0.425153	−	0.905121i	$-0.639780\pi$
$997$	−26.8487	−0.850306	−0.425153	+	0.905121i	$0.639780\pi$
$998$	41.9214	1.32700
$999$	−138.881	−4.39399

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.d.1.3	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.d.1.3	✓	96	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.28199 q^{3} +1.00000 q^{4} +4.44756 q^{5} -3.28199 q^{6} -4.87209 q^{7} +1.00000 q^{8} +7.77147 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.28199 q^{3} +1.00000 q^{4} +4.44756 q^{5} -3.28199 q^{6} -4.87209 q^{7} +1.00000 q^{8} +7.77147 q^{9} +4.44756 q^{10} +3.92354 q^{11} -3.28199 q^{12} +5.40636 q^{13} -4.87209 q^{14} -14.5969 q^{15} +1.00000 q^{16} -5.94729 q^{17} +7.77147 q^{18} -4.10542 q^{19} +4.44756 q^{20} +15.9902 q^{21} +3.92354 q^{22} -0.861265 q^{23} -3.28199 q^{24} +14.7808 q^{25} +5.40636 q^{26} -15.6599 q^{27} -4.87209 q^{28} -4.76258 q^{29} -14.5969 q^{30} -0.962863 q^{31} +1.00000 q^{32} -12.8770 q^{33} -5.94729 q^{34} -21.6689 q^{35} +7.77147 q^{36} +8.86854 q^{37} -4.10542 q^{38} -17.7436 q^{39} +4.44756 q^{40} +5.07334 q^{41} +15.9902 q^{42} +1.73766 q^{43} +3.92354 q^{44} +34.5641 q^{45} -0.861265 q^{46} +9.90456 q^{47} -3.28199 q^{48} +16.7373 q^{49} +14.7808 q^{50} +19.5189 q^{51} +5.40636 q^{52} -5.66588 q^{53} -15.6599 q^{54} +17.4502 q^{55} -4.87209 q^{56} +13.4739 q^{57} -4.76258 q^{58} +11.0651 q^{59} -14.5969 q^{60} -2.21504 q^{61} -0.962863 q^{62} -37.8633 q^{63} +1.00000 q^{64} +24.0451 q^{65} -12.8770 q^{66} -0.292663 q^{67} -5.94729 q^{68} +2.82666 q^{69} -21.6689 q^{70} +3.82127 q^{71} +7.77147 q^{72} -9.70486 q^{73} +8.86854 q^{74} -48.5105 q^{75} -4.10542 q^{76} -19.1158 q^{77} -17.7436 q^{78} -5.00168 q^{79} +4.44756 q^{80} +28.0813 q^{81} +5.07334 q^{82} +5.73133 q^{83} +15.9902 q^{84} -26.4509 q^{85} +1.73766 q^{86} +15.6307 q^{87} +3.92354 q^{88} +1.66689 q^{89} +34.5641 q^{90} -26.3403 q^{91} -0.861265 q^{92} +3.16011 q^{93} +9.90456 q^{94} -18.2591 q^{95} -3.28199 q^{96} +4.00245 q^{97} +16.7373 q^{98} +30.4917 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * q^99

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