LMFDB - Embedded newform 8002.2.a.d.1.52

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, 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("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$63.8962916974$
Analytic rank:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.52
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.23690 q^{3} +1.00000 q^{4} +3.11373 q^{5} +1.23690 q^{6} -1.44595 q^{7} +1.00000 q^{8} -1.47009 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.23690 q^{3} +1.00000 q^{4} +3.11373 q^{5} +1.23690 q^{6} -1.44595 q^{7} +1.00000 q^{8} -1.47009 q^{9} +3.11373 q^{10} -5.75385 q^{11} +1.23690 q^{12} -1.35052 q^{13} -1.44595 q^{14} +3.85135 q^{15} +1.00000 q^{16} +1.60295 q^{17} -1.47009 q^{18} +3.29676 q^{19} +3.11373 q^{20} -1.78849 q^{21} -5.75385 q^{22} -3.23867 q^{23} +1.23690 q^{24} +4.69528 q^{25} -1.35052 q^{26} -5.52903 q^{27} -1.44595 q^{28} -10.6095 q^{29} +3.85135 q^{30} -6.42943 q^{31} +1.00000 q^{32} -7.11691 q^{33} +1.60295 q^{34} -4.50228 q^{35} -1.47009 q^{36} -5.72176 q^{37} +3.29676 q^{38} -1.67045 q^{39} +3.11373 q^{40} -1.73494 q^{41} -1.78849 q^{42} -7.66143 q^{43} -5.75385 q^{44} -4.57745 q^{45} -3.23867 q^{46} -6.61213 q^{47} +1.23690 q^{48} -4.90924 q^{49} +4.69528 q^{50} +1.98269 q^{51} -1.35052 q^{52} +4.26979 q^{53} -5.52903 q^{54} -17.9159 q^{55} -1.44595 q^{56} +4.07775 q^{57} -10.6095 q^{58} -0.942132 q^{59} +3.85135 q^{60} -6.65439 q^{61} -6.42943 q^{62} +2.12567 q^{63} +1.00000 q^{64} -4.20514 q^{65} -7.11691 q^{66} +7.01122 q^{67} +1.60295 q^{68} -4.00590 q^{69} -4.50228 q^{70} +15.1291 q^{71} -1.47009 q^{72} -4.23580 q^{73} -5.72176 q^{74} +5.80758 q^{75} +3.29676 q^{76} +8.31976 q^{77} -1.67045 q^{78} +7.88111 q^{79} +3.11373 q^{80} -2.42857 q^{81} -1.73494 q^{82} +4.84349 q^{83} -1.78849 q^{84} +4.99116 q^{85} -7.66143 q^{86} -13.1228 q^{87} -5.75385 q^{88} +4.37685 q^{89} -4.57745 q^{90} +1.95278 q^{91} -3.23867 q^{92} -7.95254 q^{93} -6.61213 q^{94} +10.2652 q^{95} +1.23690 q^{96} +14.7961 q^{97} -4.90924 q^{98} +8.45867 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) $ 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * 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
$3$	1.23690	0.714122	0.357061	−	0.934081i	$-0.383779\pi$
$3$	1.23690	0.714122	0.357061	+	0.934081i	$0.383779\pi$
$4$	1.00000	0.500000
$5$	3.11373	1.39250	0.696250	−	0.717799i	$-0.254850\pi$
$5$	3.11373	1.39250	0.696250	+	0.717799i	$0.254850\pi$
$6$	1.23690	0.504961
$7$	−1.44595	−0.546517	−0.273258	−	0.961941i	$-0.588101\pi$
$7$	−1.44595	−0.546517	−0.273258	+	0.961941i	$0.588101\pi$
$8$	1.00000	0.353553
$9$	−1.47009	−0.490030
$10$	3.11373	0.984646
$11$	−5.75385	−1.73485	−0.867426	−	0.497567i	$-0.834227\pi$
$11$	−5.75385	−1.73485	−0.867426	+	0.497567i	$0.834227\pi$
$12$	1.23690	0.357061
$13$	−1.35052	−0.374567	−0.187283	−	0.982306i	$-0.559968\pi$
$13$	−1.35052	−0.374567	−0.187283	+	0.982306i	$0.559968\pi$
$14$	−1.44595	−0.386446
$15$	3.85135	0.994415
$16$	1.00000	0.250000
$17$	1.60295	0.388774	0.194387	−	0.980925i	$-0.437728\pi$
$17$	1.60295	0.388774	0.194387	+	0.980925i	$0.437728\pi$
$18$	−1.47009	−0.346503
$19$	3.29676	0.756328	0.378164	−	0.925739i	$-0.376555\pi$
$19$	3.29676	0.756328	0.378164	+	0.925739i	$0.376555\pi$
$20$	3.11373	0.696250
$21$	−1.78849	−0.390280
$22$	−5.75385	−1.22672
$23$	−3.23867	−0.675309	−0.337655	−	0.941270i	$-0.609634\pi$
$23$	−3.23867	−0.675309	−0.337655	+	0.941270i	$0.609634\pi$
$24$	1.23690	0.252480
$25$	4.69528	0.939057
$26$	−1.35052	−0.264859
$27$	−5.52903	−1.06406
$28$	−1.44595	−0.273258
$29$	−10.6095	−1.97013	−0.985065	−	0.172180i	$-0.944919\pi$
$29$	−10.6095	−1.97013	−0.985065	+	0.172180i	$0.944919\pi$
$30$	3.85135	0.703158
$31$	−6.42943	−1.15476	−0.577380	−	0.816475i	$-0.695925\pi$
$31$	−6.42943	−1.15476	−0.577380	+	0.816475i	$0.695925\pi$
$32$	1.00000	0.176777
$33$	−7.11691	−1.23890
$34$	1.60295	0.274904
$35$	−4.50228	−0.761025
$36$	−1.47009	−0.245015
$37$	−5.72176	−0.940652	−0.470326	−	0.882493i	$-0.655864\pi$
$37$	−5.72176	−0.940652	−0.470326	+	0.882493i	$0.655864\pi$
$38$	3.29676	0.534805
$39$	−1.67045	−0.267486
$40$	3.11373	0.492323
$41$	−1.73494	−0.270951	−0.135476	−	0.990781i	$-0.543256\pi$
$41$	−1.73494	−0.270951	−0.135476	+	0.990781i	$0.543256\pi$
$42$	−1.78849	−0.275969
$43$	−7.66143	−1.16836	−0.584179	−	0.811625i	$-0.698583\pi$
$43$	−7.66143	−1.16836	−0.584179	+	0.811625i	$0.698583\pi$
$44$	−5.75385	−0.867426
$45$	−4.57745	−0.682366
$46$	−3.23867	−0.477516
$47$	−6.61213	−0.964479	−0.482239	−	0.876040i	$-0.660176\pi$
$47$	−6.61213	−0.964479	−0.482239	+	0.876040i	$0.660176\pi$
$48$	1.23690	0.178531
$49$	−4.90924	−0.701319
$50$	4.69528	0.664013
$51$	1.98269	0.277632
$52$	−1.35052	−0.187283
$53$	4.26979	0.586501	0.293250	−	0.956036i	$-0.405263\pi$
$53$	4.26979	0.586501	0.293250	+	0.956036i	$0.405263\pi$
$54$	−5.52903	−0.752406
$55$	−17.9159	−2.41578
$56$	−1.44595	−0.193223
$57$	4.07775	0.540111
$58$	−10.6095	−1.39309
$59$	−0.942132	−0.122655	−0.0613275	−	0.998118i	$-0.519533\pi$
$59$	−0.942132	−0.122655	−0.0613275	+	0.998118i	$0.519533\pi$
$60$	3.85135	0.497208
$61$	−6.65439	−0.852007	−0.426003	−	0.904722i	$-0.640079\pi$
$61$	−6.65439	−0.852007	−0.426003	+	0.904722i	$0.640079\pi$
$62$	−6.42943	−0.816539
$63$	2.12567	0.267809
$64$	1.00000	0.125000
$65$	−4.20514	−0.521584
$66$	−7.11691	−0.876031
$67$	7.01122	0.856557	0.428278	−	0.903647i	$-0.359120\pi$
$67$	7.01122	0.856557	0.428278	+	0.903647i	$0.359120\pi$
$68$	1.60295	0.194387
$69$	−4.00590	−0.482253
$70$	−4.50228	−0.538126
$71$	15.1291	1.79549	0.897744	−	0.440517i	$-0.145205\pi$
$71$	15.1291	1.79549	0.897744	+	0.440517i	$0.145205\pi$
$72$	−1.47009	−0.173252
$73$	−4.23580	−0.495763	−0.247882	−	0.968790i	$-0.579734\pi$
$73$	−4.23580	−0.495763	−0.247882	+	0.968790i	$0.579734\pi$
$74$	−5.72176	−0.665142
$75$	5.80758	0.670601
$76$	3.29676	0.378164
$77$	8.31976	0.948125
$78$	−1.67045	−0.189141
$79$	7.88111	0.886695	0.443347	−	0.896350i	$-0.353791\pi$
$79$	7.88111	0.886695	0.443347	+	0.896350i	$0.353791\pi$
$80$	3.11373	0.348125
$81$	−2.42857	−0.269841
$82$	−1.73494	−0.191592
$83$	4.84349	0.531642	0.265821	−	0.964022i	$-0.414357\pi$
$83$	4.84349	0.531642	0.265821	+	0.964022i	$0.414357\pi$
$84$	−1.78849	−0.195140
$85$	4.99116	0.541367
$86$	−7.66143	−0.826154
$87$	−13.1228	−1.40691
$88$	−5.75385	−0.613362
$89$	4.37685	0.463946	0.231973	−	0.972722i	$-0.425482\pi$
$89$	4.37685	0.463946	0.231973	+	0.972722i	$0.425482\pi$
$90$	−4.57745	−0.482506
$91$	1.95278	0.204707
$92$	−3.23867	−0.337655
$93$	−7.95254	−0.824640
$94$	−6.61213	−0.681989
$95$	10.2652	1.05319
$96$	1.23690	0.126240
$97$	14.7961	1.50232	0.751159	−	0.660121i	$-0.229495\pi$
$97$	14.7961	1.50232	0.751159	+	0.660121i	$0.229495\pi$
$98$	−4.90924	−0.495908
$99$	8.45867	0.850128
$100$	4.69528	0.469528
$101$	0.982355	0.0977480	0.0488740	−	0.998805i	$-0.484437\pi$
$101$	0.982355	0.0977480	0.0488740	+	0.998805i	$0.484437\pi$
$102$	1.98269	0.196315
$103$	0.920325	0.0906823	0.0453412	−	0.998972i	$-0.485563\pi$
$103$	0.920325	0.0906823	0.0453412	+	0.998972i	$0.485563\pi$
$104$	−1.35052	−0.132429
$105$	−5.56885	−0.543465
$106$	4.26979	0.414719
$107$	11.4347	1.10543	0.552716	−	0.833369i	$-0.313591\pi$
$107$	11.4347	1.10543	0.552716	+	0.833369i	$0.313591\pi$
$108$	−5.52903	−0.532032
$109$	−1.03975	−0.0995904	−0.0497952	−	0.998759i	$-0.515857\pi$
$109$	−1.03975	−0.0995904	−0.0497952	+	0.998759i	$0.515857\pi$
$110$	−17.9159	−1.70821
$111$	−7.07723	−0.671741
$112$	−1.44595	−0.136629
$113$	−9.57852	−0.901072	−0.450536	−	0.892758i	$-0.648767\pi$
$113$	−9.57852	−0.901072	−0.450536	+	0.892758i	$0.648767\pi$
$114$	4.07775	0.381916
$115$	−10.0843	−0.940368
$116$	−10.6095	−0.985065
$117$	1.98538	0.183549
$118$	−0.942132	−0.0867302
$119$	−2.31779	−0.212471
$120$	3.85135	0.351579
$121$	22.1068	2.00971
$122$	−6.65439	−0.602460
$123$	−2.14594	−0.193492
$124$	−6.42943	−0.577380
$125$	−0.948801	−0.0848633
$126$	2.12567	0.189370
$127$	21.4592	1.90419	0.952097	−	0.305798i	$-0.0989231\pi$
$127$	21.4592	1.90419	0.952097	+	0.305798i	$0.0989231\pi$
$128$	1.00000	0.0883883
$129$	−9.47640	−0.834350
$130$	−4.20514	−0.368816
$131$	5.50808	0.481243	0.240622	−	0.970619i	$-0.422649\pi$
$131$	5.50808	0.481243	0.240622	+	0.970619i	$0.422649\pi$
$132$	−7.11691	−0.619448
$133$	−4.76694	−0.413346
$134$	7.01122	0.605677
$135$	−17.2159	−1.48171
$136$	1.60295	0.137452
$137$	−14.8931	−1.27241	−0.636203	−	0.771522i	$-0.719496\pi$
$137$	−14.8931	−1.27241	−0.636203	+	0.771522i	$0.719496\pi$
$138$	−4.00590	−0.341004
$139$	−10.8511	−0.920382	−0.460191	−	0.887820i	$-0.652219\pi$
$139$	−10.8511	−0.920382	−0.460191	+	0.887820i	$0.652219\pi$
$140$	−4.50228	−0.380512
$141$	−8.17852	−0.688756
$142$	15.1291	1.26960
$143$	7.77068	0.649817
$144$	−1.47009	−0.122507
$145$	−33.0350	−2.74341
$146$	−4.23580	−0.350557
$147$	−6.07221	−0.500828
$148$	−5.72176	−0.470326
$149$	14.5632	1.19306	0.596530	−	0.802591i	$-0.296546\pi$
$149$	14.5632	1.19306	0.596530	+	0.802591i	$0.296546\pi$
$150$	5.80758	0.474187
$151$	17.5736	1.43012	0.715058	−	0.699065i	$-0.246400\pi$
$151$	17.5736	1.43012	0.715058	+	0.699065i	$0.246400\pi$
$152$	3.29676	0.267402
$153$	−2.35649	−0.190511
$154$	8.31976	0.670426
$155$	−20.0195	−1.60800
$156$	−1.67045	−0.133743
$157$	5.58047	0.445370	0.222685	−	0.974890i	$-0.428518\pi$
$157$	5.58047	0.445370	0.222685	+	0.974890i	$0.428518\pi$
$158$	7.88111	0.626988
$159$	5.28129	0.418833
$160$	3.11373	0.246162
$161$	4.68295	0.369068
$162$	−2.42857	−0.190807
$163$	8.85302	0.693422	0.346711	−	0.937972i	$-0.387298\pi$
$163$	8.85302	0.693422	0.346711	+	0.937972i	$0.387298\pi$
$164$	−1.73494	−0.135476
$165$	−22.1601	−1.72516
$166$	4.84349	0.375928
$167$	6.94161	0.537158	0.268579	−	0.963258i	$-0.413446\pi$
$167$	6.94161	0.537158	0.268579	+	0.963258i	$0.413446\pi$
$168$	−1.78849	−0.137985
$169$	−11.1761	−0.859700
$170$	4.99116	0.382805
$171$	−4.84653	−0.370623
$172$	−7.66143	−0.584179
$173$	−22.0057	−1.67306	−0.836531	−	0.547920i	$-0.815420\pi$
$173$	−22.0057	−1.67306	−0.836531	+	0.547920i	$0.815420\pi$
$174$	−13.1228	−0.994838
$175$	−6.78913	−0.513210
$176$	−5.75385	−0.433713
$177$	−1.16532	−0.0875907
$178$	4.37685	0.328059
$179$	8.33385	0.622901	0.311451	−	0.950262i	$-0.399185\pi$
$179$	8.33385	0.622901	0.311451	+	0.950262i	$0.399185\pi$
$180$	−4.57745	−0.341183
$181$	−15.8835	−1.18061	−0.590305	−	0.807180i	$-0.700993\pi$
$181$	−15.8835	−1.18061	−0.590305	+	0.807180i	$0.700993\pi$
$182$	1.95278	0.144750
$183$	−8.23078	−0.608437
$184$	−3.23867	−0.238758
$185$	−17.8160	−1.30986
$186$	−7.95254	−0.583108
$187$	−9.22316	−0.674464
$188$	−6.61213	−0.482239
$189$	7.99469	0.581528
$190$	10.2652	0.744716
$191$	10.0754	0.729032	0.364516	−	0.931197i	$-0.381234\pi$
$191$	10.0754	0.729032	0.364516	+	0.931197i	$0.381234\pi$
$192$	1.23690	0.0892653
$193$	−4.21717	−0.303559	−0.151779	−	0.988414i	$-0.548500\pi$
$193$	−4.21717	−0.303559	−0.151779	+	0.988414i	$0.548500\pi$
$194$	14.7961	1.06230
$195$	−5.20133	−0.372475
$196$	−4.90924	−0.350660
$197$	16.6626	1.18716	0.593582	−	0.804773i	$-0.297713\pi$
$197$	16.6626	1.18716	0.593582	+	0.804773i	$0.297713\pi$
$198$	8.45867	0.601132
$199$	−2.32840	−0.165056	−0.0825280	−	0.996589i	$-0.526299\pi$
$199$	−2.32840	−0.165056	−0.0825280	+	0.996589i	$0.526299\pi$
$200$	4.69528	0.332007
$201$	8.67215	0.611686
$202$	0.982355	0.0691182
$203$	15.3407	1.07671
$204$	1.98269	0.138816
$205$	−5.40211	−0.377300
$206$	0.920325	0.0641221
$207$	4.76113	0.330921
$208$	−1.35052	−0.0936416
$209$	−18.9691	−1.31212
$210$	−5.56885	−0.384287
$211$	−12.0848	−0.831950	−0.415975	−	0.909376i	$-0.636560\pi$
$211$	−12.0848	−0.831950	−0.415975	+	0.909376i	$0.636560\pi$
$212$	4.26979	0.293250
$213$	18.7131	1.28220
$214$	11.4347	0.781659
$215$	−23.8556	−1.62694
$216$	−5.52903	−0.376203
$217$	9.29662	0.631096
$218$	−1.03975	−0.0704211
$219$	−5.23924	−0.354035
$220$	−17.9159	−1.20789
$221$	−2.16482	−0.145622
$222$	−7.07723	−0.474992
$223$	24.0351	1.60951	0.804755	−	0.593607i	$-0.202297\pi$
$223$	24.0351	1.60951	0.804755	+	0.593607i	$0.202297\pi$
$224$	−1.44595	−0.0966114
$225$	−6.90249	−0.460166
$226$	−9.57852	−0.637154
$227$	−23.2415	−1.54259	−0.771297	−	0.636476i	$-0.780392\pi$
$227$	−23.2415	−1.54259	−0.771297	+	0.636476i	$0.780392\pi$
$228$	4.07775	0.270055
$229$	10.0899	0.666758	0.333379	−	0.942793i	$-0.391811\pi$
$229$	10.0899	0.666758	0.333379	+	0.942793i	$0.391811\pi$
$230$	−10.0843	−0.664941
$231$	10.2907	0.677077
$232$	−10.6095	−0.696546
$233$	8.00760	0.524596	0.262298	−	0.964987i	$-0.415520\pi$
$233$	8.00760	0.524596	0.262298	+	0.964987i	$0.415520\pi$
$234$	1.98538	0.129789
$235$	−20.5884	−1.34304
$236$	−0.942132	−0.0613275
$237$	9.74812	0.633208
$238$	−2.31779	−0.150240
$239$	−10.1271	−0.655069	−0.327535	−	0.944839i	$-0.606218\pi$
$239$	−10.1271	−0.655069	−0.327535	+	0.944839i	$0.606218\pi$
$240$	3.85135	0.248604
$241$	16.5848	1.06832	0.534159	−	0.845384i	$-0.320628\pi$
$241$	16.5848	1.06832	0.534159	+	0.845384i	$0.320628\pi$
$242$	22.1068	1.42108
$243$	13.5832	0.871363
$244$	−6.65439	−0.426003
$245$	−15.2860	−0.976587
$246$	−2.14594	−0.136820
$247$	−4.45234	−0.283295
$248$	−6.42943	−0.408269
$249$	5.99089	0.379657
$250$	−0.948801	−0.0600074
$251$	−19.5402	−1.23337	−0.616683	−	0.787212i	$-0.711524\pi$
$251$	−19.5402	−1.23337	−0.616683	+	0.787212i	$0.711524\pi$
$252$	2.12567	0.133905
$253$	18.6348	1.17156
$254$	21.4592	1.34647
$255$	6.17355	0.386602
$256$	1.00000	0.0625000
$257$	−17.5935	−1.09745	−0.548727	−	0.836002i	$-0.684887\pi$
$257$	−17.5935	−1.09745	−0.548727	+	0.836002i	$0.684887\pi$
$258$	−9.47640	−0.589975
$259$	8.27337	0.514082
$260$	−4.20514	−0.260792
$261$	15.5969	0.965422
$262$	5.50808	0.340290
$263$	−26.8730	−1.65706	−0.828531	−	0.559943i	$-0.810823\pi$
$263$	−26.8730	−1.65706	−0.828531	+	0.559943i	$0.810823\pi$
$264$	−7.11691	−0.438016
$265$	13.2950	0.816703
$266$	−4.76694	−0.292280
$267$	5.41371	0.331314
$268$	7.01122	0.428278
$269$	5.45724	0.332734	0.166367	−	0.986064i	$-0.446796\pi$
$269$	5.45724	0.332734	0.166367	+	0.986064i	$0.446796\pi$
$270$	−17.2159	−1.04773
$271$	−13.9437	−0.847021	−0.423510	−	0.905891i	$-0.639202\pi$
$271$	−13.9437	−0.847021	−0.423510	+	0.905891i	$0.639202\pi$
$272$	1.60295	0.0971934
$273$	2.41538	0.146186
$274$	−14.8931	−0.899727
$275$	−27.0160	−1.62912
$276$	−4.00590	−0.241127
$277$	−28.2105	−1.69501	−0.847503	−	0.530791i	$-0.821895\pi$
$277$	−28.2105	−1.69501	−0.847503	+	0.530791i	$0.821895\pi$
$278$	−10.8511	−0.650808
$279$	9.45184	0.565867
$280$	−4.50228	−0.269063
$281$	−9.12171	−0.544155	−0.272078	−	0.962275i	$-0.587711\pi$
$281$	−9.12171	−0.544155	−0.272078	+	0.962275i	$0.587711\pi$
$282$	−8.17852	−0.487024
$283$	14.6806	0.872669	0.436335	−	0.899785i	$-0.356276\pi$
$283$	14.6806	0.872669	0.436335	+	0.899785i	$0.356276\pi$
$284$	15.1291	0.897744
$285$	12.6970	0.752104
$286$	7.77068	0.459490
$287$	2.50863	0.148080
$288$	−1.47009	−0.0866258
$289$	−14.4305	−0.848855
$290$	−33.0350	−1.93988
$291$	18.3013	1.07284
$292$	−4.23580	−0.247882
$293$	0.120411	0.00703448	0.00351724	−	0.999994i	$-0.498880\pi$
$293$	0.120411	0.00703448	0.00351724	+	0.999994i	$0.498880\pi$
$294$	−6.07221	−0.354139
$295$	−2.93354	−0.170797
$296$	−5.72176	−0.332571
$297$	31.8132	1.84599
$298$	14.5632	0.843621
$299$	4.37388	0.252948
$300$	5.80758	0.335301
$301$	11.0780	0.638527
$302$	17.5736	1.01124
$303$	1.21507	0.0698040
$304$	3.29676	0.189082
$305$	−20.7199	−1.18642
$306$	−2.35649	−0.134711
$307$	−10.3894	−0.592956	−0.296478	−	0.955040i	$-0.595812\pi$
$307$	−10.3894	−0.592956	−0.296478	+	0.955040i	$0.595812\pi$
$308$	8.31976	0.474063
$309$	1.13835	0.0647583
$310$	−20.0195	−1.13703
$311$	−15.1215	−0.857462	−0.428731	−	0.903432i	$-0.641039\pi$
$311$	−15.1215	−0.857462	−0.428731	+	0.903432i	$0.641039\pi$
$312$	−1.67045	−0.0945707
$313$	−18.4000	−1.04003	−0.520015	−	0.854157i	$-0.674074\pi$
$313$	−18.4000	−1.04003	−0.520015	+	0.854157i	$0.674074\pi$
$314$	5.58047	0.314924
$315$	6.61876	0.372925
$316$	7.88111	0.443347
$317$	−29.1815	−1.63900	−0.819499	−	0.573080i	$-0.805748\pi$
$317$	−29.1815	−1.63900	−0.819499	+	0.573080i	$0.805748\pi$
$318$	5.28129	0.296160
$319$	61.0454	3.41788
$320$	3.11373	0.174063
$321$	14.1435	0.789414
$322$	4.68295	0.260970
$323$	5.28456	0.294041
$324$	−2.42857	−0.134921
$325$	−6.34107	−0.351739
$326$	8.85302	0.490323
$327$	−1.28607	−0.0711197
$328$	−1.73494	−0.0957958
$329$	9.56080	0.527104
$330$	−22.1601	−1.21987
$331$	4.59533	0.252582	0.126291	−	0.991993i	$-0.459693\pi$
$331$	4.59533	0.252582	0.126291	+	0.991993i	$0.459693\pi$
$332$	4.84349	0.265821
$333$	8.41150	0.460947
$334$	6.94161	0.379828
$335$	21.8310	1.19276
$336$	−1.78849	−0.0975699
$337$	−16.1631	−0.880462	−0.440231	−	0.897884i	$-0.645103\pi$
$337$	−16.1631	−0.880462	−0.440231	+	0.897884i	$0.645103\pi$
$338$	−11.1761	−0.607900
$339$	−11.8476	−0.643475
$340$	4.99116	0.270684
$341$	36.9940	2.00334
$342$	−4.84653	−0.262070
$343$	17.2201	0.929800
$344$	−7.66143	−0.413077
$345$	−12.4733	−0.671538
$346$	−22.0057	−1.18303
$347$	−10.4944	−0.563367	−0.281683	−	0.959507i	$-0.590893\pi$
$347$	−10.4944	−0.563367	−0.281683	+	0.959507i	$0.590893\pi$
$348$	−13.1228	−0.703457
$349$	−13.9727	−0.747939	−0.373969	−	0.927441i	$-0.622004\pi$
$349$	−13.9727	−0.747939	−0.373969	+	0.927441i	$0.622004\pi$
$350$	−6.78913	−0.362895
$351$	7.46706	0.398562
$352$	−5.75385	−0.306681
$353$	14.5296	0.773333	0.386666	−	0.922220i	$-0.373627\pi$
$353$	14.5296	0.773333	0.386666	+	0.922220i	$0.373627\pi$
$354$	−1.16532	−0.0619360
$355$	47.1077	2.50022
$356$	4.37685	0.231973
$357$	−2.86686	−0.151730
$358$	8.33385	0.440458
$359$	−8.79213	−0.464031	−0.232015	−	0.972712i	$-0.574532\pi$
$359$	−8.79213	−0.464031	−0.232015	+	0.972712i	$0.574532\pi$
$360$	−4.57745	−0.241253
$361$	−8.13138	−0.427967
$362$	−15.8835	−0.834818
$363$	27.3438	1.43518
$364$	1.95278	0.102353
$365$	−13.1891	−0.690350
$366$	−8.23078	−0.430230
$367$	9.86155	0.514769	0.257384	−	0.966309i	$-0.417139\pi$
$367$	9.86155	0.514769	0.257384	+	0.966309i	$0.417139\pi$
$368$	−3.23867	−0.168827
$369$	2.55051	0.132774
$370$	−17.8160	−0.926210
$371$	−6.17389	−0.320533
$372$	−7.95254	−0.412320
$373$	−16.1035	−0.833809	−0.416904	−	0.908950i	$-0.636885\pi$
$373$	−16.1035	−0.833809	−0.416904	+	0.908950i	$0.636885\pi$
$374$	−9.22316	−0.476918
$375$	−1.17357	−0.0606028
$376$	−6.61213	−0.340995
$377$	14.3283	0.737945
$378$	7.99469	0.411203
$379$	1.56085	0.0801757	0.0400878	−	0.999196i	$-0.487236\pi$
$379$	1.56085	0.0801757	0.0400878	+	0.999196i	$0.487236\pi$
$380$	10.2652	0.526594
$381$	26.5428	1.35983
$382$	10.0754	0.515503
$383$	1.18739	0.0606729	0.0303364	−	0.999540i	$-0.490342\pi$
$383$	1.18739	0.0606729	0.0303364	+	0.999540i	$0.490342\pi$
$384$	1.23690	0.0631201
$385$	25.9055	1.32026
$386$	−4.21717	−0.214648
$387$	11.2630	0.572530
$388$	14.7961	0.751159
$389$	−14.9570	−0.758349	−0.379175	−	0.925325i	$-0.623792\pi$
$389$	−14.9570	−0.758349	−0.379175	+	0.925325i	$0.623792\pi$
$390$	−5.20133	−0.263379
$391$	−5.19144	−0.262542
$392$	−4.90924	−0.247954
$393$	6.81292	0.343667
$394$	16.6626	0.839452
$395$	24.5396	1.23472
$396$	8.45867	0.425064
$397$	23.1990	1.16432	0.582161	−	0.813073i	$-0.302207\pi$
$397$	23.1990	1.16432	0.582161	+	0.813073i	$0.302207\pi$
$398$	−2.32840	−0.116712
$399$	−5.89621	−0.295180
$400$	4.69528	0.234764
$401$	13.0232	0.650346	0.325173	−	0.945655i	$-0.394577\pi$
$401$	13.0232	0.650346	0.325173	+	0.945655i	$0.394577\pi$
$402$	8.67215	0.432527
$403$	8.68307	0.432535
$404$	0.982355	0.0488740
$405$	−7.56191	−0.375754
$406$	15.3407	0.761349
$407$	32.9222	1.63189
$408$	1.98269	0.0981577
$409$	−21.8291	−1.07938	−0.539689	−	0.841865i	$-0.681458\pi$
$409$	−21.8291	−1.07938	−0.539689	+	0.841865i	$0.681458\pi$
$410$	−5.40211	−0.266791
$411$	−18.4212	−0.908653
$412$	0.920325	0.0453412
$413$	1.36227	0.0670331
$414$	4.76113	0.233997
$415$	15.0813	0.740311
$416$	−1.35052	−0.0662146
$417$	−13.4217	−0.657265
$418$	−18.9691	−0.927807
$419$	−5.18471	−0.253290	−0.126645	−	0.991948i	$-0.540421\pi$
$419$	−5.18471	−0.253290	−0.126645	+	0.991948i	$0.540421\pi$
$420$	−5.56885	−0.271732
$421$	−13.9954	−0.682094	−0.341047	−	0.940046i	$-0.610781\pi$
$421$	−13.9954	−0.682094	−0.341047	+	0.940046i	$0.610781\pi$
$422$	−12.0848	−0.588277
$423$	9.72042	0.472623
$424$	4.26979	0.207359
$425$	7.52633	0.365081
$426$	18.7131	0.906651
$427$	9.62189	0.465636
$428$	11.4347	0.552716
$429$	9.61152	0.464049
$430$	−23.8556	−1.15042
$431$	−5.74412	−0.276684	−0.138342	−	0.990384i	$-0.544177\pi$
$431$	−5.74412	−0.276684	−0.138342	+	0.990384i	$0.544177\pi$
$432$	−5.52903	−0.266016
$433$	39.8676	1.91591	0.957957	−	0.286913i	$-0.0926290\pi$
$433$	39.8676	1.91591	0.957957	+	0.286913i	$0.0926290\pi$
$434$	9.29662	0.446252
$435$	−40.8609	−1.95913
$436$	−1.03975	−0.0497952
$437$	−10.6771	−0.510755
$438$	−5.23924	−0.250341
$439$	29.7274	1.41881	0.709405	−	0.704801i	$-0.248964\pi$
$439$	29.7274	1.41881	0.709405	+	0.704801i	$0.248964\pi$
$440$	−17.9159	−0.854107
$441$	7.21701	0.343667
$442$	−2.16482	−0.102970
$443$	29.7160	1.41185	0.705926	−	0.708286i	$-0.250531\pi$
$443$	29.7160	1.41185	0.705926	+	0.708286i	$0.250531\pi$
$444$	−7.07723	−0.335870
$445$	13.6283	0.646044
$446$	24.0351	1.13810
$447$	18.0131	0.851991
$448$	−1.44595	−0.0683146
$449$	5.95467	0.281018	0.140509	−	0.990079i	$-0.455126\pi$
$449$	5.95467	0.281018	0.140509	+	0.990079i	$0.455126\pi$
$450$	−6.90249	−0.325386
$451$	9.98256	0.470060
$452$	−9.57852	−0.450536
$453$	21.7367	1.02128
$454$	−23.2415	−1.09078
$455$	6.08042	0.285054
$456$	4.07775	0.190958
$457$	−20.0720	−0.938927	−0.469463	−	0.882952i	$-0.655553\pi$
$457$	−20.0720	−0.938927	−0.469463	+	0.882952i	$0.655553\pi$
$458$	10.0899	0.471469
$459$	−8.86279	−0.413680
$460$	−10.0843	−0.470184
$461$	−6.66445	−0.310394	−0.155197	−	0.987884i	$-0.549601\pi$
$461$	−6.66445	−0.310394	−0.155197	+	0.987884i	$0.549601\pi$
$462$	10.2907	0.478766
$463$	−3.35943	−0.156126	−0.0780630	−	0.996948i	$-0.524874\pi$
$463$	−3.35943	−0.156126	−0.0780630	+	0.996948i	$0.524874\pi$
$464$	−10.6095	−0.492533
$465$	−24.7620	−1.14831
$466$	8.00760	0.370945
$467$	−10.9065	−0.504695	−0.252347	−	0.967637i	$-0.581203\pi$
$467$	−10.9065	−0.504695	−0.252347	+	0.967637i	$0.581203\pi$
$468$	1.98538	0.0917743
$469$	−10.1379	−0.468123
$470$	−20.5884	−0.949670
$471$	6.90246	0.318049
$472$	−0.942132	−0.0433651
$473$	44.0827	2.02693
$474$	9.74812	0.447746
$475$	15.4792	0.710235
$476$	−2.31779	−0.106236
$477$	−6.27697	−0.287403
$478$	−10.1271	−0.463204
$479$	17.6883	0.808201	0.404100	−	0.914715i	$-0.367585\pi$
$479$	17.6883	0.808201	0.404100	+	0.914715i	$0.367585\pi$
$480$	3.85135	0.175789
$481$	7.72735	0.352337
$482$	16.5848	0.755415
$483$	5.79231	0.263559
$484$	22.1068	1.00485
$485$	46.0711	2.09198
$486$	13.5832	0.616147
$487$	−8.73973	−0.396035	−0.198017	−	0.980198i	$-0.563450\pi$
$487$	−8.73973	−0.396035	−0.198017	+	0.980198i	$0.563450\pi$
$488$	−6.65439	−0.301230
$489$	10.9503	0.495188
$490$	−15.2860	−0.690552
$491$	2.99176	0.135016	0.0675080	−	0.997719i	$-0.478495\pi$
$491$	2.99176	0.135016	0.0675080	+	0.997719i	$0.478495\pi$
$492$	−2.14594	−0.0967462
$493$	−17.0065	−0.765935
$494$	−4.45234	−0.200320
$495$	26.3380	1.18380
$496$	−6.42943	−0.288690
$497$	−21.8758	−0.981264
$498$	5.99089	0.268458
$499$	7.36726	0.329804	0.164902	−	0.986310i	$-0.447269\pi$
$499$	7.36726	0.329804	0.164902	+	0.986310i	$0.447269\pi$
$500$	−0.948801	−0.0424316
$501$	8.58605	0.383597
$502$	−19.5402	−0.872121
$503$	9.35195	0.416983	0.208491	−	0.978024i	$-0.433145\pi$
$503$	9.35195	0.416983	0.208491	+	0.978024i	$0.433145\pi$
$504$	2.12567	0.0946849
$505$	3.05878	0.136114
$506$	18.6348	0.828419
$507$	−13.8237	−0.613931
$508$	21.4592	0.952097
$509$	−33.8979	−1.50250	−0.751248	−	0.660020i	$-0.770548\pi$
$509$	−33.8979	−1.50250	−0.751248	+	0.660020i	$0.770548\pi$
$510$	6.17355	0.273369
$511$	6.12475	0.270943
$512$	1.00000	0.0441942
$513$	−18.2279	−0.804781
$514$	−17.5935	−0.776017
$515$	2.86564	0.126275
$516$	−9.47640	−0.417175
$517$	38.0452	1.67323
$518$	8.27337	0.363511
$519$	−27.2187	−1.19477
$520$	−4.20514	−0.184408
$521$	−4.65001	−0.203721	−0.101860	−	0.994799i	$-0.532479\pi$
$521$	−4.65001	−0.203721	−0.101860	+	0.994799i	$0.532479\pi$
$522$	15.5969	0.682657
$523$	−25.8627	−1.13090	−0.565448	−	0.824784i	$-0.691297\pi$
$523$	−25.8627	−1.13090	−0.565448	+	0.824784i	$0.691297\pi$
$524$	5.50808	0.240622
$525$	−8.39745	−0.366495
$526$	−26.8730	−1.17172
$527$	−10.3061	−0.448940
$528$	−7.11691	−0.309724
$529$	−12.5110	−0.543958
$530$	13.2950	0.577496
$531$	1.38502	0.0601046
$532$	−4.76694	−0.206673
$533$	2.34306	0.101489
$534$	5.41371	0.234274
$535$	35.6045	1.53932
$536$	7.01122	0.302838
$537$	10.3081	0.444828
$538$	5.45724	0.235279
$539$	28.2470	1.21668
$540$	−17.2159	−0.740854
$541$	−16.5269	−0.710548	−0.355274	−	0.934762i	$-0.615612\pi$
$541$	−16.5269	−0.710548	−0.355274	+	0.934762i	$0.615612\pi$
$542$	−13.9437	−0.598934
$543$	−19.6462	−0.843100
$544$	1.60295	0.0687261
$545$	−3.23751	−0.138680
$546$	2.41538	0.103369
$547$	0.244974	0.0104743	0.00523717	−	0.999986i	$-0.498333\pi$
$547$	0.244974	0.0104743	0.00523717	+	0.999986i	$0.498333\pi$
$548$	−14.8931	−0.636203
$549$	9.78254	0.417509
$550$	−27.0160	−1.15196
$551$	−34.9769	−1.49007
$552$	−4.00590	−0.170502
$553$	−11.3957	−0.484594
$554$	−28.2105	−1.19855
$555$	−22.0365	−0.935399
$556$	−10.8511	−0.460191
$557$	22.1815	0.939861	0.469931	−	0.882703i	$-0.344279\pi$
$557$	22.1815	0.939861	0.469931	+	0.882703i	$0.344279\pi$
$558$	9.45184	0.400128
$559$	10.3469	0.437628
$560$	−4.50228	−0.190256
$561$	−11.4081	−0.481650
$562$	−9.12171	−0.384776
$563$	−24.9619	−1.05202	−0.526010	−	0.850478i	$-0.676312\pi$
$563$	−24.9619	−1.05202	−0.526010	+	0.850478i	$0.676312\pi$
$564$	−8.17852	−0.344378
$565$	−29.8249	−1.25474
$566$	14.6806	0.617070
$567$	3.51159	0.147473
$568$	15.1291	0.634801
$569$	−7.67053	−0.321565	−0.160783	−	0.986990i	$-0.551402\pi$
$569$	−7.67053	−0.321565	−0.160783	+	0.986990i	$0.551402\pi$
$570$	12.6970	0.531818
$571$	−34.2401	−1.43290	−0.716452	−	0.697637i	$-0.754235\pi$
$571$	−34.2401	−1.43290	−0.716452	+	0.697637i	$0.754235\pi$
$572$	7.77068	0.324909
$573$	12.4622	0.520618
$574$	2.50863	0.104708
$575$	−15.2065	−0.634154
$576$	−1.47009	−0.0612537
$577$	−14.9566	−0.622649	−0.311325	−	0.950304i	$-0.600773\pi$
$577$	−14.9566	−0.622649	−0.311325	+	0.950304i	$0.600773\pi$
$578$	−14.4305	−0.600231
$579$	−5.21620	−0.216778
$580$	−33.0350	−1.37170
$581$	−7.00343	−0.290551
$582$	18.3013	0.758612
$583$	−24.5677	−1.01749
$584$	−4.23580	−0.175279
$585$	6.18194	0.255592
$586$	0.120411	0.00497413
$587$	33.5232	1.38365	0.691826	−	0.722064i	$-0.256806\pi$
$587$	33.5232	1.38365	0.691826	+	0.722064i	$0.256806\pi$
$588$	−6.07221	−0.250414
$589$	−21.1963	−0.873378
$590$	−2.93354	−0.120772
$591$	20.6100	0.847781
$592$	−5.72176	−0.235163
$593$	11.7729	0.483453	0.241727	−	0.970344i	$-0.422286\pi$
$593$	11.7729	0.483453	0.241727	+	0.970344i	$0.422286\pi$
$594$	31.8132	1.30531
$595$	−7.21696	−0.295866
$596$	14.5632	0.596530
$597$	−2.87999	−0.117870
$598$	4.37388	0.178861
$599$	10.1614	0.415185	0.207592	−	0.978215i	$-0.433437\pi$
$599$	10.1614	0.415185	0.207592	+	0.978215i	$0.433437\pi$
$600$	5.80758	0.237093
$601$	15.2061	0.620270	0.310135	−	0.950692i	$-0.399626\pi$
$601$	15.2061	0.620270	0.310135	+	0.950692i	$0.399626\pi$
$602$	11.0780	0.451507
$603$	−10.3071	−0.419738
$604$	17.5736	0.715058
$605$	68.8345	2.79852
$606$	1.21507	0.0493589
$607$	−13.0191	−0.528430	−0.264215	−	0.964464i	$-0.585113\pi$
$607$	−13.0191	−0.528430	−0.264215	+	0.964464i	$0.585113\pi$
$608$	3.29676	0.133701
$609$	18.9749	0.768902
$610$	−20.7199	−0.838925
$611$	8.92981	0.361261
$612$	−2.35649	−0.0952553
$613$	7.25869	0.293176	0.146588	−	0.989198i	$-0.453171\pi$
$613$	7.25869	0.293176	0.146588	+	0.989198i	$0.453171\pi$
$614$	−10.3894	−0.419283
$615$	−6.68185	−0.269438
$616$	8.31976	0.335213
$617$	25.6151	1.03123	0.515613	−	0.856821i	$-0.327564\pi$
$617$	25.6151	1.03123	0.515613	+	0.856821i	$0.327564\pi$
$618$	1.13835	0.0457910
$619$	−45.1686	−1.81548	−0.907740	−	0.419533i	$-0.862194\pi$
$619$	−45.1686	−1.81548	−0.907740	+	0.419533i	$0.862194\pi$
$620$	−20.0195	−0.804002
$621$	17.9067	0.718572
$622$	−15.1215	−0.606317
$623$	−6.32870	−0.253554
$624$	−1.67045	−0.0668716
$625$	−26.4307	−1.05723
$626$	−18.4000	−0.735413
$627$	−23.4627	−0.937012
$628$	5.58047	0.222685
$629$	−9.17173	−0.365701
$630$	6.61876	0.263698
$631$	−20.5391	−0.817648	−0.408824	−	0.912613i	$-0.634061\pi$
$631$	−20.5391	−0.817648	−0.408824	+	0.912613i	$0.634061\pi$
$632$	7.88111	0.313494
$633$	−14.9476	−0.594114
$634$	−29.1815	−1.15895
$635$	66.8179	2.65159
$636$	5.28129	0.209417
$637$	6.63002	0.262691
$638$	61.0454	2.41681
$639$	−22.2411	−0.879842
$640$	3.11373	0.123081
$641$	11.1736	0.441329	0.220665	−	0.975350i	$-0.429177\pi$
$641$	11.1736	0.441329	0.220665	+	0.975350i	$0.429177\pi$
$642$	14.1435	0.558200
$643$	−7.04434	−0.277802	−0.138901	−	0.990306i	$-0.544357\pi$
$643$	−7.04434	−0.277802	−0.138901	+	0.990306i	$0.544357\pi$
$644$	4.68295	0.184534
$645$	−29.5069	−1.16183
$646$	5.28456	0.207918
$647$	−11.9451	−0.469610	−0.234805	−	0.972042i	$-0.575445\pi$
$647$	−11.9451	−0.469610	−0.234805	+	0.972042i	$0.575445\pi$
$648$	−2.42857	−0.0954033
$649$	5.42088	0.212788
$650$	−6.34107	−0.248717
$651$	11.4990	0.450680
$652$	8.85302	0.346711
$653$	−17.6007	−0.688768	−0.344384	−	0.938829i	$-0.611912\pi$
$653$	−17.6007	−0.688768	−0.344384	+	0.938829i	$0.611912\pi$
$654$	−1.28607	−0.0502892
$655$	17.1507	0.670132
$656$	−1.73494	−0.0677379
$657$	6.22700	0.242939
$658$	9.56080	0.372719
$659$	39.3704	1.53365	0.766827	−	0.641854i	$-0.221834\pi$
$659$	39.3704	1.53365	0.766827	+	0.641854i	$0.221834\pi$
$660$	−22.1601	−0.862581
$661$	2.80914	0.109263	0.0546315	−	0.998507i	$-0.482602\pi$
$661$	2.80914	0.109263	0.0546315	+	0.998507i	$0.482602\pi$
$662$	4.59533	0.178602
$663$	−2.67766	−0.103992
$664$	4.84349	0.187964
$665$	−14.8429	−0.575585
$666$	8.41150	0.325939
$667$	34.3606	1.33045
$668$	6.94161	0.268579
$669$	29.7289	1.14939
$670$	21.8310	0.843405
$671$	38.2883	1.47810
$672$	−1.78849	−0.0689924
$673$	10.3561	0.399198	0.199599	−	0.979878i	$-0.436036\pi$
$673$	10.3561	0.399198	0.199599	+	0.979878i	$0.436036\pi$
$674$	−16.1631	−0.622581
$675$	−25.9604	−0.999216
$676$	−11.1761	−0.429850
$677$	−47.1861	−1.81351	−0.906754	−	0.421661i	$-0.861447\pi$
$677$	−47.1861	−1.81351	−0.906754	+	0.421661i	$0.861447\pi$
$678$	−11.8476	−0.455006
$679$	−21.3944	−0.821042
$680$	4.99116	0.191402
$681$	−28.7473	−1.10160
$682$	36.9940	1.41657
$683$	9.04704	0.346175	0.173088	−	0.984906i	$-0.444626\pi$
$683$	9.04704	0.346175	0.173088	+	0.984906i	$0.444626\pi$
$684$	−4.84653	−0.185312
$685$	−46.3731	−1.77183
$686$	17.2201	0.657468
$687$	12.4801	0.476146
$688$	−7.66143	−0.292089
$689$	−5.76643	−0.219684
$690$	−12.4733	−0.474849
$691$	−48.1700	−1.83247	−0.916236	−	0.400638i	$-0.868788\pi$
$691$	−48.1700	−1.83247	−0.916236	+	0.400638i	$0.868788\pi$
$692$	−22.0057	−0.836531
$693$	−12.2308	−0.464609
$694$	−10.4944	−0.398360
$695$	−33.7875	−1.28163
$696$	−13.1228	−0.497419
$697$	−2.78102	−0.105339
$698$	−13.9727	−0.528873
$699$	9.90457	0.374625
$700$	−6.78913	−0.256605
$701$	−51.9136	−1.96075	−0.980375	−	0.197143i	$-0.936834\pi$
$701$	−51.9136	−1.96075	−0.980375	+	0.197143i	$0.936834\pi$
$702$	7.46706	0.281826
$703$	−18.8633	−0.711442
$704$	−5.75385	−0.216856
$705$	−25.4657	−0.959092
$706$	14.5296	0.546829
$707$	−1.42043	−0.0534209
$708$	−1.16532	−0.0437954
$709$	1.14113	0.0428561	0.0214281	−	0.999770i	$-0.493179\pi$
$709$	1.14113	0.0428561	0.0214281	+	0.999770i	$0.493179\pi$
$710$	47.1077	1.76792
$711$	−11.5859	−0.434507
$712$	4.37685	0.164030
$713$	20.8228	0.779820
$714$	−2.86686	−0.107290
$715$	24.1958	0.904870
$716$	8.33385	0.311451
$717$	−12.5262	−0.467799
$718$	−8.79213	−0.328119
$719$	33.7975	1.26043	0.630217	−	0.776419i	$-0.282966\pi$
$719$	33.7975	1.26043	0.630217	+	0.776419i	$0.282966\pi$
$720$	−4.57745	−0.170592
$721$	−1.33074	−0.0495594
$722$	−8.13138	−0.302619
$723$	20.5136	0.762910
$724$	−15.8835	−0.590305
$725$	−49.8145	−1.85006
$726$	27.3438	1.01482
$727$	21.6058	0.801317	0.400658	−	0.916228i	$-0.368781\pi$
$727$	21.6058	0.801317	0.400658	+	0.916228i	$0.368781\pi$
$728$	1.95278	0.0723748
$729$	24.0867	0.892101
$730$	−13.1891	−0.488151
$731$	−12.2809	−0.454227
$732$	−8.23078	−0.304218
$733$	33.6668	1.24351	0.621755	−	0.783212i	$-0.286420\pi$
$733$	33.6668	1.24351	0.621755	+	0.783212i	$0.286420\pi$
$734$	9.86155	0.363996
$735$	−18.9072	−0.697403
$736$	−3.23867	−0.119379
$737$	−40.3415	−1.48600
$738$	2.55051	0.0938856
$739$	−4.61286	−0.169687	−0.0848435	−	0.996394i	$-0.527039\pi$
$739$	−4.61286	−0.169687	−0.0848435	+	0.996394i	$0.527039\pi$
$740$	−17.8160	−0.654929
$741$	−5.50707	−0.202307
$742$	−6.17389	−0.226651
$743$	−41.8251	−1.53441	−0.767207	−	0.641399i	$-0.778354\pi$
$743$	−41.8251	−1.53441	−0.767207	+	0.641399i	$0.778354\pi$
$744$	−7.95254	−0.291554
$745$	45.3457	1.66134
$746$	−16.1035	−0.589592
$747$	−7.12036	−0.260520
$748$	−9.22316	−0.337232
$749$	−16.5340	−0.604138
$750$	−1.17357	−0.0428526
$751$	−8.84778	−0.322860	−0.161430	−	0.986884i	$-0.551611\pi$
$751$	−8.84778	−0.322860	−0.161430	+	0.986884i	$0.551611\pi$
$752$	−6.61213	−0.241120
$753$	−24.1692	−0.880774
$754$	14.3283	0.521806
$755$	54.7192	1.99144
$756$	7.99469	0.290764
$757$	−21.0920	−0.766600	−0.383300	−	0.923624i	$-0.625212\pi$
$757$	−21.0920	−0.766600	−0.383300	+	0.923624i	$0.625212\pi$
$758$	1.56085	0.0566927
$759$	23.0493	0.836637
$760$	10.2652	0.372358
$761$	44.1148	1.59916	0.799580	−	0.600559i	$-0.205055\pi$
$761$	44.1148	1.59916	0.799580	+	0.600559i	$0.205055\pi$
$762$	26.5428	0.961542
$763$	1.50343	0.0544278
$764$	10.0754	0.364516
$765$	−7.33745	−0.265286
$766$	1.18739	0.0429022
$767$	1.27237	0.0459425
$768$	1.23690	0.0446326
$769$	12.7616	0.460196	0.230098	−	0.973167i	$-0.426095\pi$
$769$	12.7616	0.460196	0.230098	+	0.973167i	$0.426095\pi$
$770$	25.9055	0.933568
$771$	−21.7614	−0.783716
$772$	−4.21717	−0.151779
$773$	−39.2689	−1.41241	−0.706203	−	0.708010i	$-0.749593\pi$
$773$	−39.2689	−1.41241	−0.706203	+	0.708010i	$0.749593\pi$
$774$	11.2630	0.404840
$775$	−30.1880	−1.08439
$776$	14.7961	0.531150
$777$	10.2333	0.367117
$778$	−14.9570	−0.536234
$779$	−5.71967	−0.204928
$780$	−5.20133	−0.186237
$781$	−87.0503	−3.11490
$782$	−5.19144	−0.185646
$783$	58.6602	2.09634
$784$	−4.90924	−0.175330
$785$	17.3761	0.620178
$786$	6.81292	0.243009
$787$	15.8434	0.564757	0.282379	−	0.959303i	$-0.408877\pi$
$787$	15.8434	0.564757	0.282379	+	0.959303i	$0.408877\pi$
$788$	16.6626	0.593582
$789$	−33.2391	−1.18334
$790$	24.5396	0.873081
$791$	13.8500	0.492451
$792$	8.45867	0.300566
$793$	8.98687	0.319133
$794$	23.1990	0.823300
$795$	16.4445	0.583225
$796$	−2.32840	−0.0825280
$797$	−44.4866	−1.57580	−0.787898	−	0.615806i	$-0.788831\pi$
$797$	−44.4866	−1.57580	−0.787898	+	0.615806i	$0.788831\pi$
$798$	−5.89621	−0.208724
$799$	−10.5989	−0.374964
$800$	4.69528	0.166003
$801$	−6.43437	−0.227347
$802$	13.0232	0.459864
$803$	24.3722	0.860075
$804$	8.67215	0.305843
$805$	14.5814	0.513927
$806$	8.68307	0.305848
$807$	6.75004	0.237613
$808$	0.982355	0.0345591
$809$	−30.6398	−1.07724	−0.538619	−	0.842550i	$-0.681054\pi$
$809$	−30.6398	−1.07724	−0.538619	+	0.842550i	$0.681054\pi$
$810$	−7.56191	−0.265698
$811$	30.4946	1.07081	0.535405	−	0.844595i	$-0.320159\pi$
$811$	30.4946	1.07081	0.535405	+	0.844595i	$0.320159\pi$
$812$	15.3407	0.538355
$813$	−17.2469	−0.604876
$814$	32.9222	1.15392
$815$	27.5659	0.965590
$816$	1.98269	0.0694080
$817$	−25.2579	−0.883662
$818$	−21.8291	−0.763235
$819$	−2.87076	−0.100312
$820$	−5.40211	−0.188650
$821$	8.26988	0.288621	0.144310	−	0.989532i	$-0.453904\pi$
$821$	8.26988	0.288621	0.144310	+	0.989532i	$0.453904\pi$
$822$	−18.4212	−0.642515
$823$	−3.20143	−0.111595	−0.0557975	−	0.998442i	$-0.517770\pi$
$823$	−3.20143	−0.111595	−0.0557975	+	0.998442i	$0.517770\pi$
$824$	0.920325	0.0320610
$825$	−33.4159	−1.16339
$826$	1.36227	0.0473995
$827$	−15.0610	−0.523724	−0.261862	−	0.965105i	$-0.584336\pi$
$827$	−15.0610	−0.523724	−0.261862	+	0.965105i	$0.584336\pi$
$828$	4.76113	0.165461
$829$	21.8422	0.758611	0.379305	−	0.925272i	$-0.376163\pi$
$829$	21.8422	0.758611	0.379305	+	0.925272i	$0.376163\pi$
$830$	15.0813	0.523479
$831$	−34.8935	−1.21044
$832$	−1.35052	−0.0468208
$833$	−7.86928	−0.272655
$834$	−13.4217	−0.464756
$835$	21.6143	0.747993
$836$	−18.9691	−0.656059
$837$	35.5486	1.22874
$838$	−5.18471	−0.179103
$839$	0.354427	0.0122362	0.00611810	−	0.999981i	$-0.498053\pi$
$839$	0.354427	0.0122362	0.00611810	+	0.999981i	$0.498053\pi$
$840$	−5.56885	−0.192144
$841$	83.5611	2.88142
$842$	−13.9954	−0.482313
$843$	−11.2826	−0.388593
$844$	−12.0848	−0.415975
$845$	−34.7993	−1.19713
$846$	9.72042	0.334195
$847$	−31.9653	−1.09834
$848$	4.26979	0.146625
$849$	18.1583	0.623192
$850$	7.52633	0.258151
$851$	18.5309	0.635231
$852$	18.7131	0.641099
$853$	14.8434	0.508229	0.254115	−	0.967174i	$-0.418216\pi$
$853$	14.8434	0.508229	0.254115	+	0.967174i	$0.418216\pi$
$854$	9.62189	0.329254
$855$	−15.0908	−0.516093
$856$	11.4347	0.390830
$857$	−33.3708	−1.13992	−0.569962	−	0.821671i	$-0.693042\pi$
$857$	−33.3708	−1.13992	−0.569962	+	0.821671i	$0.693042\pi$
$858$	9.61152	0.328132
$859$	5.82160	0.198630	0.0993152	−	0.995056i	$-0.468335\pi$
$859$	5.82160	0.198630	0.0993152	+	0.995056i	$0.468335\pi$
$860$	−23.8556	−0.813469
$861$	3.10291	0.105747
$862$	−5.74412	−0.195645
$863$	−3.59793	−0.122475	−0.0612375	−	0.998123i	$-0.519505\pi$
$863$	−3.59793	−0.122475	−0.0612375	+	0.998123i	$0.519505\pi$
$864$	−5.52903	−0.188102
$865$	−68.5197	−2.32974
$866$	39.8676	1.35476
$867$	−17.8491	−0.606186
$868$	9.29662	0.315548
$869$	−45.3468	−1.53828
$870$	−40.8609	−1.38531
$871$	−9.46878	−0.320837
$872$	−1.03975	−0.0352105
$873$	−21.7516	−0.736181
$874$	−10.6771	−0.361159
$875$	1.37192	0.0463792
$876$	−5.23924	−0.177018
$877$	0.545668	0.0184259	0.00921294	−	0.999958i	$-0.497067\pi$
$877$	0.545668	0.0184259	0.00921294	+	0.999958i	$0.497067\pi$
$878$	29.7274	1.00325
$879$	0.148936	0.00502347
$880$	−17.9159	−0.603945
$881$	16.6145	0.559757	0.279879	−	0.960035i	$-0.409706\pi$
$881$	16.6145	0.559757	0.279879	+	0.960035i	$0.409706\pi$
$882$	7.21701	0.243009
$883$	−42.0514	−1.41514	−0.707570	−	0.706643i	$-0.750209\pi$
$883$	−42.0514	−1.41514	−0.707570	+	0.706643i	$0.750209\pi$
$884$	−2.16482	−0.0728108
$885$	−3.62848	−0.121970
$886$	29.7160	0.998330
$887$	35.2980	1.18519	0.592596	−	0.805500i	$-0.298103\pi$
$887$	35.2980	1.18519	0.592596	+	0.805500i	$0.298103\pi$
$888$	−7.07723	−0.237496
$889$	−31.0288	−1.04067
$890$	13.6283	0.456822
$891$	13.9736	0.468135
$892$	24.0351	0.804755
$893$	−21.7986	−0.729463
$894$	18.0131	0.602448
$895$	25.9493	0.867390
$896$	−1.44595	−0.0483057
$897$	5.41004	0.180636
$898$	5.95467	0.198710
$899$	68.2129	2.27503
$900$	−6.90249	−0.230083
$901$	6.84428	0.228016
$902$	9.98256	0.332383
$903$	13.7024	0.455986
$904$	−9.57852	−0.318577
$905$	−49.4568	−1.64400
$906$	21.7367	0.722152
$907$	−33.9039	−1.12576	−0.562880	−	0.826538i	$-0.690307\pi$
$907$	−33.9039	−1.12576	−0.562880	+	0.826538i	$0.690307\pi$
$908$	−23.2415	−0.771297
$909$	−1.44415	−0.0478994
$910$	6.08042	0.201564
$911$	−33.1978	−1.09989	−0.549947	−	0.835200i	$-0.685352\pi$
$911$	−33.1978	−1.09989	−0.549947	+	0.835200i	$0.685352\pi$
$912$	4.07775	0.135028
$913$	−27.8687	−0.922319
$914$	−20.0720	−0.663922
$915$	−25.6284	−0.847248
$916$	10.0899	0.333379
$917$	−7.96440	−0.263008
$918$	−8.86279	−0.292516
$919$	−14.3034	−0.471824	−0.235912	−	0.971774i	$-0.575808\pi$
$919$	−14.3034	−0.471824	−0.235912	+	0.971774i	$0.575808\pi$
$920$	−10.0843	−0.332470
$921$	−12.8506	−0.423443
$922$	−6.66445	−0.219482
$923$	−20.4321	−0.672530
$924$	10.2907	0.338539
$925$	−26.8653	−0.883326
$926$	−3.35943	−0.110398
$927$	−1.35296	−0.0444370
$928$	−10.6095	−0.348273
$929$	20.3614	0.668035	0.334017	−	0.942567i	$-0.391596\pi$
$929$	20.3614	0.668035	0.334017	+	0.942567i	$0.391596\pi$
$930$	−24.7620	−0.811979
$931$	−16.1846	−0.530428
$932$	8.00760	0.262298
$933$	−18.7037	−0.612332
$934$	−10.9065	−0.356873
$935$	−28.7184	−0.939192
$936$	1.98538	0.0648943
$937$	45.7113	1.49332	0.746661	−	0.665205i	$-0.231656\pi$
$937$	45.7113	1.49332	0.746661	+	0.665205i	$0.231656\pi$
$938$	−10.1379	−0.331013
$939$	−22.7589	−0.742709
$940$	−20.5884	−0.671518
$941$	36.0230	1.17432	0.587159	−	0.809472i	$-0.300246\pi$
$941$	36.0230	1.17432	0.587159	+	0.809472i	$0.300246\pi$
$942$	6.90246	0.224894
$943$	5.61888	0.182976
$944$	−0.942132	−0.0306638
$945$	24.8933	0.809778
$946$	44.0827	1.43325
$947$	51.3391	1.66830	0.834149	−	0.551540i	$-0.185960\pi$
$947$	51.3391	1.66830	0.834149	+	0.551540i	$0.185960\pi$
$948$	9.74812	0.316604
$949$	5.72053	0.185696
$950$	15.4792	0.502212
$951$	−36.0945	−1.17044
$952$	−2.31779	−0.0751200
$953$	51.7586	1.67662	0.838312	−	0.545191i	$-0.183543\pi$
$953$	51.7586	1.67662	0.838312	+	0.545191i	$0.183543\pi$
$954$	−6.27697	−0.203224
$955$	31.3721	1.01518
$956$	−10.1271	−0.327535
$957$	75.5067	2.44079
$958$	17.6883	0.571484
$959$	21.5347	0.695391
$960$	3.85135	0.124302
$961$	10.3376	0.333471
$962$	7.72735	0.249140
$963$	−16.8100	−0.541695
$964$	16.5848	0.534159
$965$	−13.1311	−0.422705
$966$	5.79231	0.186365
$967$	40.6134	1.30604	0.653020	−	0.757341i	$-0.273502\pi$
$967$	40.6134	1.30604	0.653020	+	0.757341i	$0.273502\pi$
$968$	22.1068	0.710539
$969$	6.53645	0.209981
$970$	46.0711	1.47925
$971$	−35.4107	−1.13638	−0.568191	−	0.822897i	$-0.692357\pi$
$971$	−35.4107	−1.13638	−0.568191	+	0.822897i	$0.692357\pi$
$972$	13.5832	0.435682
$973$	15.6902	0.503004
$974$	−8.73973	−0.280039
$975$	−7.84324	−0.251185
$976$	−6.65439	−0.213002
$977$	1.18443	0.0378934	0.0189467	−	0.999820i	$-0.493969\pi$
$977$	1.18443	0.0378934	0.0189467	+	0.999820i	$0.493969\pi$
$978$	10.9503	0.350151
$979$	−25.1838	−0.804877
$980$	−15.2860	−0.488294
$981$	1.52853	0.0488023
$982$	2.99176	0.0954708
$983$	28.0517	0.894710	0.447355	−	0.894357i	$-0.352366\pi$
$983$	28.0517	0.894710	0.447355	+	0.894357i	$0.352366\pi$
$984$	−2.14594	−0.0684099
$985$	51.8829	1.65313
$986$	−17.0065	−0.541598
$987$	11.8257	0.376416
$988$	−4.45234	−0.141648
$989$	24.8128	0.789003
$990$	26.3380	0.837076
$991$	42.2125	1.34092	0.670462	−	0.741944i	$-0.266096\pi$
$991$	42.2125	1.34092	0.670462	+	0.741944i	$0.266096\pi$
$992$	−6.42943	−0.204135
$993$	5.68394	0.180374
$994$	−21.8758	−0.693859
$995$	−7.25000	−0.229841
$996$	5.99089	0.189829
$997$	34.3532	1.08798	0.543989	−	0.839092i	$-0.316913\pi$
$997$	34.3532	1.08798	0.543989	+	0.839092i	$0.316913\pi$
$998$	7.36726	0.233206
$999$	31.6358	1.00091

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.d.1.52	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.d.1.52	✓	69	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:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.23690 q^{3} +1.00000 q^{4} +3.11373 q^{5} +1.23690 q^{6} -1.44595 q^{7} +1.00000 q^{8} -1.47009 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.23690 q^{3} +1.00000 q^{4} +3.11373 q^{5} +1.23690 q^{6} -1.44595 q^{7} +1.00000 q^{8} -1.47009 q^{9} +3.11373 q^{10} -5.75385 q^{11} +1.23690 q^{12} -1.35052 q^{13} -1.44595 q^{14} +3.85135 q^{15} +1.00000 q^{16} +1.60295 q^{17} -1.47009 q^{18} +3.29676 q^{19} +3.11373 q^{20} -1.78849 q^{21} -5.75385 q^{22} -3.23867 q^{23} +1.23690 q^{24} +4.69528 q^{25} -1.35052 q^{26} -5.52903 q^{27} -1.44595 q^{28} -10.6095 q^{29} +3.85135 q^{30} -6.42943 q^{31} +1.00000 q^{32} -7.11691 q^{33} +1.60295 q^{34} -4.50228 q^{35} -1.47009 q^{36} -5.72176 q^{37} +3.29676 q^{38} -1.67045 q^{39} +3.11373 q^{40} -1.73494 q^{41} -1.78849 q^{42} -7.66143 q^{43} -5.75385 q^{44} -4.57745 q^{45} -3.23867 q^{46} -6.61213 q^{47} +1.23690 q^{48} -4.90924 q^{49} +4.69528 q^{50} +1.98269 q^{51} -1.35052 q^{52} +4.26979 q^{53} -5.52903 q^{54} -17.9159 q^{55} -1.44595 q^{56} +4.07775 q^{57} -10.6095 q^{58} -0.942132 q^{59} +3.85135 q^{60} -6.65439 q^{61} -6.42943 q^{62} +2.12567 q^{63} +1.00000 q^{64} -4.20514 q^{65} -7.11691 q^{66} +7.01122 q^{67} +1.60295 q^{68} -4.00590 q^{69} -4.50228 q^{70} +15.1291 q^{71} -1.47009 q^{72} -4.23580 q^{73} -5.72176 q^{74} +5.80758 q^{75} +3.29676 q^{76} +8.31976 q^{77} -1.67045 q^{78} +7.88111 q^{79} +3.11373 q^{80} -2.42857 q^{81} -1.73494 q^{82} +4.84349 q^{83} -1.78849 q^{84} +4.99116 q^{85} -7.66143 q^{86} -13.1228 q^{87} -5.75385 q^{88} +4.37685 q^{89} -4.57745 q^{90} +1.95278 q^{91} -3.23867 q^{92} -7.95254 q^{93} -6.61213 q^{94} +10.2652 q^{95} +1.23690 q^{96} +14.7961 q^{97} -4.90924 q^{98} +8.45867 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

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