LMFDB - Embedded newform 8007.2.a.j.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.62615 q^{2} -1.00000 q^{3} +0.644366 q^{4} +0.536374 q^{5} +1.62615 q^{6} +4.53678 q^{7} +2.20447 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.62615 q^{2} -1.00000 q^{3} +0.644366 q^{4} +0.536374 q^{5} +1.62615 q^{6} +4.53678 q^{7} +2.20447 q^{8} +1.00000 q^{9} -0.872225 q^{10} +2.87790 q^{11} -0.644366 q^{12} +1.05243 q^{13} -7.37748 q^{14} -0.536374 q^{15} -4.87352 q^{16} +1.00000 q^{17} -1.62615 q^{18} +6.13593 q^{19} +0.345621 q^{20} -4.53678 q^{21} -4.67990 q^{22} +2.66713 q^{23} -2.20447 q^{24} -4.71230 q^{25} -1.71140 q^{26} -1.00000 q^{27} +2.92334 q^{28} +4.14006 q^{29} +0.872225 q^{30} -2.93407 q^{31} +3.51615 q^{32} -2.87790 q^{33} -1.62615 q^{34} +2.43341 q^{35} +0.644366 q^{36} -5.20943 q^{37} -9.97794 q^{38} -1.05243 q^{39} +1.18242 q^{40} +0.258454 q^{41} +7.37748 q^{42} +0.594529 q^{43} +1.85442 q^{44} +0.536374 q^{45} -4.33715 q^{46} +4.62488 q^{47} +4.87352 q^{48} +13.5823 q^{49} +7.66291 q^{50} -1.00000 q^{51} +0.678147 q^{52} -4.78052 q^{53} +1.62615 q^{54} +1.54363 q^{55} +10.0012 q^{56} -6.13593 q^{57} -6.73235 q^{58} -2.88225 q^{59} -0.345621 q^{60} +10.4506 q^{61} +4.77124 q^{62} +4.53678 q^{63} +4.02926 q^{64} +0.564494 q^{65} +4.67990 q^{66} +16.2149 q^{67} +0.644366 q^{68} -2.66713 q^{69} -3.95709 q^{70} +9.88860 q^{71} +2.20447 q^{72} +2.83517 q^{73} +8.47132 q^{74} +4.71230 q^{75} +3.95378 q^{76} +13.0564 q^{77} +1.71140 q^{78} -4.89662 q^{79} -2.61403 q^{80} +1.00000 q^{81} -0.420286 q^{82} +2.12890 q^{83} -2.92334 q^{84} +0.536374 q^{85} -0.966794 q^{86} -4.14006 q^{87} +6.34423 q^{88} -10.2701 q^{89} -0.872225 q^{90} +4.77462 q^{91} +1.71860 q^{92} +2.93407 q^{93} -7.52076 q^{94} +3.29115 q^{95} -3.51615 q^{96} +11.9098 q^{97} -22.0869 q^{98} +2.87790 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * 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 $

$2$	−1.62615	−1.14986	−0.574931	−	0.818202i	$-0.694971\pi$
$2$	−1.62615	−1.14986	−0.574931	+	0.818202i	$0.694971\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.644366	0.322183
$5$	0.536374	0.239874	0.119937	−	0.992782i	$-0.461731\pi$
$5$	0.536374	0.239874	0.119937	+	0.992782i	$0.461731\pi$
$6$	1.62615	0.663873
$7$	4.53678	1.71474	0.857370	−	0.514701i	$-0.172097\pi$
$7$	4.53678	1.71474	0.857370	+	0.514701i	$0.172097\pi$
$8$	2.20447	0.779396
$9$	1.00000	0.333333
$10$	−0.872225	−0.275822
$11$	2.87790	0.867719	0.433860	−	0.900981i	$-0.357151\pi$
$11$	2.87790	0.867719	0.433860	+	0.900981i	$0.357151\pi$
$12$	−0.644366	−0.186012
$13$	1.05243	0.291890	0.145945	−	0.989293i	$-0.453378\pi$
$13$	1.05243	0.291890	0.145945	+	0.989293i	$0.453378\pi$
$14$	−7.37748	−1.97171
$15$	−0.536374	−0.138491
$16$	−4.87352	−1.21838
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.62615	−0.383287
$19$	6.13593	1.40768	0.703839	−	0.710359i	$-0.251467\pi$
$19$	6.13593	1.40768	0.703839	+	0.710359i	$0.251467\pi$
$20$	0.345621	0.0772832
$21$	−4.53678	−0.990006
$22$	−4.67990	−0.997757
$23$	2.66713	0.556134	0.278067	−	0.960562i	$-0.410306\pi$
$23$	2.66713	0.556134	0.278067	+	0.960562i	$0.410306\pi$
$24$	−2.20447	−0.449985
$25$	−4.71230	−0.942461
$26$	−1.71140	−0.335634
$27$	−1.00000	−0.192450
$28$	2.92334	0.552460
$29$	4.14006	0.768789	0.384395	−	0.923169i	$-0.374410\pi$
$29$	4.14006	0.768789	0.384395	+	0.923169i	$0.374410\pi$
$30$	0.872225	0.159246
$31$	−2.93407	−0.526974	−0.263487	−	0.964663i	$-0.584873\pi$
$31$	−2.93407	−0.526974	−0.263487	+	0.964663i	$0.584873\pi$
$32$	3.51615	0.621574
$33$	−2.87790	−0.500978
$34$	−1.62615	−0.278883
$35$	2.43341	0.411321
$36$	0.644366	0.107394
$37$	−5.20943	−0.856425	−0.428212	−	0.903678i	$-0.640857\pi$
$37$	−5.20943	−0.856425	−0.428212	+	0.903678i	$0.640857\pi$
$38$	−9.97794	−1.61864
$39$	−1.05243	−0.168523
$40$	1.18242	0.186957
$41$	0.258454	0.0403638	0.0201819	−	0.999796i	$-0.493575\pi$
$41$	0.258454	0.0403638	0.0201819	+	0.999796i	$0.493575\pi$
$42$	7.37748	1.13837
$43$	0.594529	0.0906649	0.0453324	−	0.998972i	$-0.485565\pi$
$43$	0.594529	0.0906649	0.0453324	+	0.998972i	$0.485565\pi$
$44$	1.85442	0.279564
$45$	0.536374	0.0799579
$46$	−4.33715	−0.639477
$47$	4.62488	0.674609	0.337304	−	0.941396i	$-0.390485\pi$
$47$	4.62488	0.674609	0.337304	+	0.941396i	$0.390485\pi$
$48$	4.87352	0.703433
$49$	13.5823	1.94033
$50$	7.66291	1.08370
$51$	−1.00000	−0.140028
$52$	0.678147	0.0940421
$53$	−4.78052	−0.656654	−0.328327	−	0.944564i	$-0.606485\pi$
$53$	−4.78052	−0.656654	−0.328327	+	0.944564i	$0.606485\pi$
$54$	1.62615	0.221291
$55$	1.54363	0.208143
$56$	10.0012	1.33646
$57$	−6.13593	−0.812724
$58$	−6.73235	−0.884001
$59$	−2.88225	−0.375237	−0.187618	−	0.982242i	$-0.560077\pi$
$59$	−2.88225	−0.375237	−0.187618	+	0.982242i	$0.560077\pi$
$60$	−0.345621	−0.0446195
$61$	10.4506	1.33806	0.669029	−	0.743237i	$-0.266710\pi$
$61$	10.4506	1.33806	0.669029	+	0.743237i	$0.266710\pi$
$62$	4.77124	0.605948
$63$	4.53678	0.571580
$64$	4.02926	0.503657
$65$	0.564494	0.0700168
$66$	4.67990	0.576055
$67$	16.2149	1.98096	0.990481	−	0.137648i	$-0.0439542\pi$
$67$	16.2149	1.98096	0.990481	+	0.137648i	$0.0439542\pi$
$68$	0.644366	0.0781408
$69$	−2.66713	−0.321084
$70$	−3.95709	−0.472962
$71$	9.88860	1.17356	0.586780	−	0.809746i	$-0.300395\pi$
$71$	9.88860	1.17356	0.586780	+	0.809746i	$0.300395\pi$
$72$	2.20447	0.259799
$73$	2.83517	0.331831	0.165916	−	0.986140i	$-0.446942\pi$
$73$	2.83517	0.331831	0.165916	+	0.986140i	$0.446942\pi$
$74$	8.47132	0.984770
$75$	4.71230	0.544130
$76$	3.95378	0.453530
$77$	13.0564	1.48791
$78$	1.71140	0.193778
$79$	−4.89662	−0.550913	−0.275456	−	0.961314i	$-0.588829\pi$
$79$	−4.89662	−0.550913	−0.275456	+	0.961314i	$0.588829\pi$
$80$	−2.61403	−0.292258
$81$	1.00000	0.111111
$82$	−0.420286	−0.0464128
$83$	2.12890	0.233678	0.116839	−	0.993151i	$-0.462724\pi$
$83$	2.12890	0.233678	0.116839	+	0.993151i	$0.462724\pi$
$84$	−2.92334	−0.318963
$85$	0.536374	0.0581779
$86$	−0.966794	−0.104252
$87$	−4.14006	−0.443861
$88$	6.34423	0.676297
$89$	−10.2701	−1.08863	−0.544313	−	0.838882i	$-0.683210\pi$
$89$	−10.2701	−1.08863	−0.544313	+	0.838882i	$0.683210\pi$
$90$	−0.872225	−0.0919406
$91$	4.77462	0.500516
$92$	1.71860	0.179177
$93$	2.93407	0.304249
$94$	−7.52076	−0.775707
$95$	3.29115	0.337665
$96$	−3.51615	−0.358866
$97$	11.9098	1.20925	0.604627	−	0.796508i	$-0.293322\pi$
$97$	11.9098	1.20925	0.604627	+	0.796508i	$0.293322\pi$
$98$	−22.0869	−2.23112
$99$	2.87790	0.289240
$100$	−3.03645	−0.303645
$101$	−13.8417	−1.37730	−0.688651	−	0.725093i	$-0.741797\pi$
$101$	−13.8417	−1.37730	−0.688651	+	0.725093i	$0.741797\pi$
$102$	1.62615	0.161013
$103$	15.2504	1.50267	0.751333	−	0.659923i	$-0.229411\pi$
$103$	15.2504	1.50267	0.751333	+	0.659923i	$0.229411\pi$
$104$	2.32004	0.227498
$105$	−2.43341	−0.237476
$106$	7.77384	0.755062
$107$	−13.9722	−1.35074	−0.675372	−	0.737477i	$-0.736017\pi$
$107$	−13.9722	−1.35074	−0.675372	+	0.737477i	$0.736017\pi$
$108$	−0.644366	−0.0620041
$109$	−6.26962	−0.600520	−0.300260	−	0.953857i	$-0.597074\pi$
$109$	−6.26962	−0.600520	−0.300260	+	0.953857i	$0.597074\pi$
$110$	−2.51017	−0.239336
$111$	5.20943	0.494457
$112$	−22.1101	−2.08921
$113$	−3.82481	−0.359808	−0.179904	−	0.983684i	$-0.557579\pi$
$113$	−3.82481	−0.359808	−0.179904	+	0.983684i	$0.557579\pi$
$114$	9.97794	0.934520
$115$	1.43058	0.133402
$116$	2.66771	0.247691
$117$	1.05243	0.0972968
$118$	4.68697	0.431470
$119$	4.53678	0.415886
$120$	−1.18242	−0.107939
$121$	−2.71770	−0.247064
$122$	−16.9942	−1.53858
$123$	−0.258454	−0.0233040
$124$	−1.89061	−0.169782
$125$	−5.20943	−0.465945
$126$	−7.37748	−0.657238
$127$	11.5276	1.02291	0.511455	−	0.859310i	$-0.329107\pi$
$127$	11.5276	1.02291	0.511455	+	0.859310i	$0.329107\pi$
$128$	−13.5845	−1.20071
$129$	−0.594529	−0.0523454
$130$	−0.917952	−0.0805097
$131$	8.80112	0.768958	0.384479	−	0.923134i	$-0.374381\pi$
$131$	8.80112	0.768958	0.384479	+	0.923134i	$0.374381\pi$
$132$	−1.85442	−0.161406
$133$	27.8373	2.41380
$134$	−26.3678	−2.27783
$135$	−0.536374	−0.0461637
$136$	2.20447	0.189031
$137$	−15.2872	−1.30607	−0.653037	−	0.757326i	$-0.726505\pi$
$137$	−15.2872	−1.30607	−0.653037	+	0.757326i	$0.726505\pi$
$138$	4.33715	0.369203
$139$	13.7436	1.16572	0.582858	−	0.812574i	$-0.301934\pi$
$139$	13.7436	1.16572	0.582858	+	0.812574i	$0.301934\pi$
$140$	1.56800	0.132521
$141$	−4.62488	−0.389486
$142$	−16.0803	−1.34943
$143$	3.02878	0.253279
$144$	−4.87352	−0.406127
$145$	2.22062	0.184412
$146$	−4.61041	−0.381560
$147$	−13.5823	−1.12025
$148$	−3.35678	−0.275925
$149$	2.98768	0.244761	0.122380	−	0.992483i	$-0.460947\pi$
$149$	2.98768	0.244761	0.122380	+	0.992483i	$0.460947\pi$
$150$	−7.66291	−0.625674
$151$	23.0024	1.87191	0.935955	−	0.352118i	$-0.114539\pi$
$151$	23.0024	1.87191	0.935955	+	0.352118i	$0.114539\pi$
$152$	13.5264	1.09714
$153$	1.00000	0.0808452
$154$	−21.2316	−1.71089
$155$	−1.57376	−0.126407
$156$	−0.678147	−0.0542952
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	7.96264	0.633474
$159$	4.78052	0.379120
$160$	1.88597	0.149099
$161$	12.1001	0.953625
$162$	−1.62615	−0.127762
$163$	14.6184	1.14500	0.572502	−	0.819903i	$-0.305973\pi$
$163$	14.6184	1.14500	0.572502	+	0.819903i	$0.305973\pi$
$164$	0.166539	0.0130045
$165$	−1.54363	−0.120171
$166$	−3.46192	−0.268697
$167$	−0.252002	−0.0195005	−0.00975025	−	0.999952i	$-0.503104\pi$
$167$	−0.252002	−0.0195005	−0.00975025	+	0.999952i	$0.503104\pi$
$168$	−10.0012	−0.771607
$169$	−11.8924	−0.914800
$170$	−0.872225	−0.0668966
$171$	6.13593	0.469226
$172$	0.383094	0.0292107
$173$	15.8601	1.20582	0.602909	−	0.797810i	$-0.294008\pi$
$173$	15.8601	1.20582	0.602909	+	0.797810i	$0.294008\pi$
$174$	6.73235	0.510378
$175$	−21.3787	−1.61607
$176$	−14.0255	−1.05721
$177$	2.88225	0.216643
$178$	16.7007	1.25177
$179$	20.2145	1.51091	0.755453	−	0.655203i	$-0.227417\pi$
$179$	20.2145	1.51091	0.755453	+	0.655203i	$0.227417\pi$
$180$	0.345621	0.0257611
$181$	0.965690	0.0717791	0.0358896	−	0.999356i	$-0.488574\pi$
$181$	0.965690	0.0717791	0.0358896	+	0.999356i	$0.488574\pi$
$182$	−7.76425	−0.575525
$183$	−10.4506	−0.772528
$184$	5.87959	0.433449
$185$	−2.79420	−0.205434
$186$	−4.77124	−0.349844
$187$	2.87790	0.210453
$188$	2.98012	0.217347
$189$	−4.53678	−0.330002
$190$	−5.35191	−0.388268
$191$	−17.6222	−1.27510	−0.637550	−	0.770409i	$-0.720052\pi$
$191$	−17.6222	−1.27510	−0.637550	+	0.770409i	$0.720052\pi$
$192$	−4.02926	−0.290786
$193$	−14.3544	−1.03325	−0.516625	−	0.856212i	$-0.672812\pi$
$193$	−14.3544	−1.03325	−0.516625	+	0.856212i	$0.672812\pi$
$194$	−19.3671	−1.39048
$195$	−0.564494	−0.0404242
$196$	8.75199	0.625142
$197$	6.30328	0.449090	0.224545	−	0.974464i	$-0.427910\pi$
$197$	6.30328	0.449090	0.224545	+	0.974464i	$0.427910\pi$
$198$	−4.67990	−0.332586
$199$	−22.9260	−1.62518	−0.812592	−	0.582833i	$-0.801944\pi$
$199$	−22.9260	−1.62518	−0.812592	+	0.582833i	$0.801944\pi$
$200$	−10.3881	−0.734550
$201$	−16.2149	−1.14371
$202$	22.5087	1.58371
$203$	18.7825	1.31827
$204$	−0.644366	−0.0451146
$205$	0.138628	0.00968221
$206$	−24.7994	−1.72786
$207$	2.66713	0.185378
$208$	−5.12902	−0.355634
$209$	17.6586	1.22147
$210$	3.95709	0.273065
$211$	−28.1637	−1.93887	−0.969433	−	0.245357i	$-0.921095\pi$
$211$	−28.1637	−1.93887	−0.969433	+	0.245357i	$0.921095\pi$
$212$	−3.08040	−0.211563
$213$	−9.88860	−0.677556
$214$	22.7209	1.55317
$215$	0.318890	0.0217481
$216$	−2.20447	−0.149995
$217$	−13.3112	−0.903624
$218$	10.1953	0.690516
$219$	−2.83517	−0.191583
$220$	0.994662	0.0670601
$221$	1.05243	0.0707938
$222$	−8.47132	−0.568558
$223$	−12.3845	−0.829328	−0.414664	−	0.909975i	$-0.636101\pi$
$223$	−12.3845	−0.829328	−0.414664	+	0.909975i	$0.636101\pi$
$224$	15.9520	1.06584
$225$	−4.71230	−0.314154
$226$	6.21971	0.413729
$227$	−11.2981	−0.749878	−0.374939	−	0.927049i	$-0.622336\pi$
$227$	−11.2981	−0.749878	−0.374939	+	0.927049i	$0.622336\pi$
$228$	−3.95378	−0.261846
$229$	7.65246	0.505689	0.252844	−	0.967507i	$-0.418634\pi$
$229$	7.65246	0.505689	0.252844	+	0.967507i	$0.418634\pi$
$230$	−2.32633	−0.153394
$231$	−13.0564	−0.859047
$232$	9.12661	0.599191
$233$	−3.81049	−0.249634	−0.124817	−	0.992180i	$-0.539834\pi$
$233$	−3.81049	−0.249634	−0.124817	+	0.992180i	$0.539834\pi$
$234$	−1.71140	−0.111878
$235$	2.48067	0.161821
$236$	−1.85722	−0.120895
$237$	4.89662	0.318070
$238$	−7.37748	−0.478211
$239$	−12.0878	−0.781897	−0.390948	−	0.920413i	$-0.627853\pi$
$239$	−12.0878	−0.781897	−0.390948	+	0.920413i	$0.627853\pi$
$240$	2.61403	0.168735
$241$	−6.32255	−0.407271	−0.203636	−	0.979047i	$-0.565276\pi$
$241$	−6.32255	−0.407271	−0.203636	+	0.979047i	$0.565276\pi$
$242$	4.41939	0.284089
$243$	−1.00000	−0.0641500
$244$	6.73398	0.431099
$245$	7.28521	0.465435
$246$	0.420286	0.0267964
$247$	6.45761	0.410888
$248$	−6.46805	−0.410722
$249$	−2.12890	−0.134914
$250$	8.47131	0.535773
$251$	0.350954	0.0221520	0.0110760	−	0.999939i	$-0.496474\pi$
$251$	0.350954	0.0221520	0.0110760	+	0.999939i	$0.496474\pi$
$252$	2.92334	0.184153
$253$	7.67572	0.482568
$254$	−18.7456	−1.17620
$255$	−0.536374	−0.0335890
$256$	14.0319	0.876994
$257$	−20.1141	−1.25469	−0.627343	−	0.778743i	$-0.715858\pi$
$257$	−20.1141	−1.25469	−0.627343	+	0.778743i	$0.715858\pi$
$258$	0.966794	0.0601900
$259$	−23.6340	−1.46855
$260$	0.363740	0.0225582
$261$	4.14006	0.256263
$262$	−14.3119	−0.884195
$263$	−15.3035	−0.943653	−0.471826	−	0.881691i	$-0.656405\pi$
$263$	−15.3035	−0.943653	−0.471826	+	0.881691i	$0.656405\pi$
$264$	−6.34423	−0.390460
$265$	−2.56414	−0.157514
$266$	−45.2677	−2.77554
$267$	10.2701	0.628519
$268$	10.4483	0.638232
$269$	20.3913	1.24328	0.621641	−	0.783302i	$-0.286466\pi$
$269$	20.3913	1.24328	0.621641	+	0.783302i	$0.286466\pi$
$270$	0.872225	0.0530819
$271$	25.8269	1.56887	0.784435	−	0.620211i	$-0.212953\pi$
$271$	25.8269	1.56887	0.784435	+	0.620211i	$0.212953\pi$
$272$	−4.87352	−0.295501
$273$	−4.77462	−0.288973
$274$	24.8593	1.50180
$275$	−13.5615	−0.817791
$276$	−1.71860	−0.103448
$277$	−20.2293	−1.21546	−0.607731	−	0.794143i	$-0.707920\pi$
$277$	−20.2293	−1.21546	−0.607731	+	0.794143i	$0.707920\pi$
$278$	−22.3491	−1.34041
$279$	−2.93407	−0.175658
$280$	5.36436	0.320582
$281$	5.07183	0.302560	0.151280	−	0.988491i	$-0.451661\pi$
$281$	5.07183	0.302560	0.151280	+	0.988491i	$0.451661\pi$
$282$	7.52076	0.447855
$283$	11.7889	0.700778	0.350389	−	0.936604i	$-0.386049\pi$
$283$	11.7889	0.700778	0.350389	+	0.936604i	$0.386049\pi$
$284$	6.37187	0.378101
$285$	−3.29115	−0.194951
$286$	−4.92524	−0.291236
$287$	1.17255	0.0692134
$288$	3.51615	0.207191
$289$	1.00000	0.0588235
$290$	−3.61106	−0.212049
$291$	−11.9098	−0.698164
$292$	1.82688	0.106910
$293$	−13.3955	−0.782574	−0.391287	−	0.920269i	$-0.627970\pi$
$293$	−13.3955	−0.782574	−0.391287	+	0.920269i	$0.627970\pi$
$294$	22.0869	1.28814
$295$	−1.54596	−0.0900094
$296$	−11.4840	−0.667494
$297$	−2.87790	−0.166993
$298$	−4.85843	−0.281441
$299$	2.80695	0.162330
$300$	3.03645	0.175309
$301$	2.69725	0.155467
$302$	−37.4054	−2.15244
$303$	13.8417	0.795186
$304$	−29.9036	−1.71509
$305$	5.60541	0.320965
$306$	−1.62615	−0.0929608
$307$	−5.92232	−0.338005	−0.169002	−	0.985616i	$-0.554055\pi$
$307$	−5.92232	−0.338005	−0.169002	+	0.985616i	$0.554055\pi$
$308$	8.41308	0.479380
$309$	−15.2504	−0.867565
$310$	2.55917	0.145351
$311$	13.1833	0.747554	0.373777	−	0.927519i	$-0.378063\pi$
$311$	13.1833	0.747554	0.373777	+	0.927519i	$0.378063\pi$
$312$	−2.32004	−0.131346
$313$	15.1808	0.858069	0.429035	−	0.903288i	$-0.358854\pi$
$313$	15.1808	0.858069	0.429035	+	0.903288i	$0.358854\pi$
$314$	1.62615	0.0917690
$315$	2.43341	0.137107
$316$	−3.15521	−0.177495
$317$	−18.2857	−1.02702	−0.513512	−	0.858082i	$-0.671656\pi$
$317$	−18.2857	−1.02702	−0.513512	+	0.858082i	$0.671656\pi$
$318$	−7.77384	−0.435935
$319$	11.9147	0.667093
$320$	2.16119	0.120814
$321$	13.9722	0.779852
$322$	−19.6767	−1.09654
$323$	6.13593	0.341412
$324$	0.644366	0.0357981
$325$	−4.95935	−0.275095
$326$	−23.7718	−1.31660
$327$	6.26962	0.346711
$328$	0.569754	0.0314594
$329$	20.9821	1.15678
$330$	2.51017	0.138181
$331$	5.35412	0.294289	0.147145	−	0.989115i	$-0.452992\pi$
$331$	5.35412	0.294289	0.147145	+	0.989115i	$0.452992\pi$
$332$	1.37179	0.0752869
$333$	−5.20943	−0.285475
$334$	0.409793	0.0224229
$335$	8.69724	0.475181
$336$	22.1101	1.20620
$337$	28.5799	1.55685	0.778423	−	0.627740i	$-0.216020\pi$
$337$	28.5799	1.55685	0.778423	+	0.627740i	$0.216020\pi$
$338$	19.3388	1.05189
$339$	3.82481	0.207735
$340$	0.345621	0.0187439
$341$	−8.44395	−0.457266
$342$	−9.97794	−0.539545
$343$	29.8626	1.61243
$344$	1.31062	0.0706639
$345$	−1.43058	−0.0770197
$346$	−25.7909	−1.38652
$347$	−31.9705	−1.71627	−0.858134	−	0.513425i	$-0.828376\pi$
$347$	−31.9705	−1.71627	−0.858134	+	0.513425i	$0.828376\pi$
$348$	−2.66771	−0.143004
$349$	−1.57124	−0.0841065	−0.0420533	−	0.999115i	$-0.513390\pi$
$349$	−1.57124	−0.0841065	−0.0420533	+	0.999115i	$0.513390\pi$
$350$	34.7649	1.85826
$351$	−1.05243	−0.0561743
$352$	10.1191	0.539351
$353$	−10.1771	−0.541674	−0.270837	−	0.962625i	$-0.587300\pi$
$353$	−10.1771	−0.541674	−0.270837	+	0.962625i	$0.587300\pi$
$354$	−4.68697	−0.249110
$355$	5.30399	0.281506
$356$	−6.61769	−0.350737
$357$	−4.53678	−0.240112
$358$	−32.8719	−1.73733
$359$	23.4680	1.23859	0.619297	−	0.785157i	$-0.287418\pi$
$359$	23.4680	1.23859	0.619297	+	0.785157i	$0.287418\pi$
$360$	1.18242	0.0623189
$361$	18.6496	0.981559
$362$	−1.57036	−0.0825361
$363$	2.71770	0.142642
$364$	3.07660	0.161258
$365$	1.52071	0.0795976
$366$	16.9942	0.888300
$367$	−24.7603	−1.29248	−0.646239	−	0.763135i	$-0.723659\pi$
$367$	−24.7603	−1.29248	−0.646239	+	0.763135i	$0.723659\pi$
$368$	−12.9983	−0.677583
$369$	0.258454	0.0134546
$370$	4.54379	0.236221
$371$	−21.6881	−1.12599
$372$	1.89061	0.0980237
$373$	2.41072	0.124822	0.0624111	−	0.998051i	$-0.480121\pi$
$373$	2.41072	0.124822	0.0624111	+	0.998051i	$0.480121\pi$
$374$	−4.67990	−0.241992
$375$	5.20943	0.269014
$376$	10.1954	0.525788
$377$	4.35710	0.224402
$378$	7.37748	0.379457
$379$	6.38995	0.328230	0.164115	−	0.986441i	$-0.447523\pi$
$379$	6.38995	0.328230	0.164115	+	0.986441i	$0.447523\pi$
$380$	2.12071	0.108790
$381$	−11.5276	−0.590577
$382$	28.6564	1.46619
$383$	−14.6608	−0.749132	−0.374566	−	0.927200i	$-0.622208\pi$
$383$	−14.6608	−0.749132	−0.374566	+	0.927200i	$0.622208\pi$
$384$	13.5845	0.693230
$385$	7.00310	0.356911
$386$	23.3423	1.18809
$387$	0.594529	0.0302216
$388$	7.67425	0.389601
$389$	20.7383	1.05147	0.525736	−	0.850648i	$-0.323790\pi$
$389$	20.7383	1.05147	0.525736	+	0.850648i	$0.323790\pi$
$390$	0.917952	0.0464823
$391$	2.66713	0.134882
$392$	29.9418	1.51229
$393$	−8.80112	−0.443958
$394$	−10.2501	−0.516392
$395$	−2.62642	−0.132149
$396$	1.85442	0.0931881
$397$	−31.1806	−1.56491	−0.782455	−	0.622707i	$-0.786033\pi$
$397$	−31.1806	−1.56491	−0.782455	+	0.622707i	$0.786033\pi$
$398$	37.2812	1.86874
$399$	−27.8373	−1.39361
$400$	22.9655	1.14828
$401$	−39.3277	−1.96393	−0.981965	−	0.189064i	$-0.939455\pi$
$401$	−39.3277	−1.96393	−0.981965	+	0.189064i	$0.939455\pi$
$402$	26.3678	1.31511
$403$	−3.08789	−0.153819
$404$	−8.91912	−0.443743
$405$	0.536374	0.0266526
$406$	−30.5432	−1.51583
$407$	−14.9922	−0.743136
$408$	−2.20447	−0.109137
$409$	10.1598	0.502368	0.251184	−	0.967939i	$-0.419180\pi$
$409$	10.1598	0.502368	0.251184	+	0.967939i	$0.419180\pi$
$410$	−0.225430	−0.0111332
$411$	15.2872	0.754062
$412$	9.82683	0.484133
$413$	−13.0761	−0.643433
$414$	−4.33715	−0.213159
$415$	1.14189	0.0560531
$416$	3.70049	0.181431
$417$	−13.7436	−0.673026
$418$	−28.7155	−1.40452
$419$	3.04043	0.148535	0.0742674	−	0.997238i	$-0.476338\pi$
$419$	3.04043	0.148535	0.0742674	+	0.997238i	$0.476338\pi$
$420$	−1.56800	−0.0765108
$421$	−27.7553	−1.35271	−0.676355	−	0.736575i	$-0.736442\pi$
$421$	−27.7553	−1.35271	−0.676355	+	0.736575i	$0.736442\pi$
$422$	45.7983	2.22943
$423$	4.62488	0.224870
$424$	−10.5385	−0.511794
$425$	−4.71230	−0.228580
$426$	16.0803	0.779095
$427$	47.4118	2.29442
$428$	−9.00320	−0.435186
$429$	−3.02878	−0.146231
$430$	−0.518563	−0.0250073
$431$	−27.5938	−1.32915	−0.664573	−	0.747223i	$-0.731387\pi$
$431$	−27.5938	−1.32915	−0.664573	+	0.747223i	$0.731387\pi$
$432$	4.87352	0.234478
$433$	−13.3618	−0.642126	−0.321063	−	0.947058i	$-0.604040\pi$
$433$	−13.3618	−0.642126	−0.321063	+	0.947058i	$0.604040\pi$
$434$	21.6460	1.03904
$435$	−2.22062	−0.106470
$436$	−4.03993	−0.193477
$437$	16.3653	0.782858
$438$	4.61041	0.220294
$439$	−4.65570	−0.222205	−0.111102	−	0.993809i	$-0.535438\pi$
$439$	−4.65570	−0.222205	−0.111102	+	0.993809i	$0.535438\pi$
$440$	3.40288	0.162226
$441$	13.5823	0.646778
$442$	−1.71140	−0.0814031
$443$	−16.4031	−0.779337	−0.389668	−	0.920955i	$-0.627410\pi$
$443$	−16.4031	−0.779337	−0.389668	+	0.920955i	$0.627410\pi$
$444$	3.35678	0.159306
$445$	−5.50860	−0.261133
$446$	20.1391	0.953613
$447$	−2.98768	−0.141313
$448$	18.2798	0.863641
$449$	−2.98737	−0.140983	−0.0704915	−	0.997512i	$-0.522457\pi$
$449$	−2.98737	−0.140983	−0.0704915	+	0.997512i	$0.522457\pi$
$450$	7.66291	0.361233
$451$	0.743805	0.0350244
$452$	−2.46458	−0.115924
$453$	−23.0024	−1.08075
$454$	18.3723	0.862256
$455$	2.56098	0.120061
$456$	−13.5264	−0.633434
$457$	37.8455	1.77034	0.885168	−	0.465272i	$-0.154043\pi$
$457$	37.8455	1.77034	0.885168	+	0.465272i	$0.154043\pi$
$458$	−12.4441	−0.581472
$459$	−1.00000	−0.0466760
$460$	0.921814	0.0429798
$461$	−5.61583	−0.261556	−0.130778	−	0.991412i	$-0.541747\pi$
$461$	−5.61583	−0.261556	−0.130778	+	0.991412i	$0.541747\pi$
$462$	21.2316	0.987785
$463$	16.2899	0.757056	0.378528	−	0.925590i	$-0.376430\pi$
$463$	16.2899	0.757056	0.378528	+	0.925590i	$0.376430\pi$
$464$	−20.1767	−0.936678
$465$	1.57376	0.0729813
$466$	6.19643	0.287044
$467$	25.0009	1.15691	0.578453	−	0.815716i	$-0.303657\pi$
$467$	25.0009	1.15691	0.578453	+	0.815716i	$0.303657\pi$
$468$	0.678147	0.0313474
$469$	73.5633	3.39684
$470$	−4.03394	−0.186072
$471$	1.00000	0.0460776
$472$	−6.35382	−0.292458
$473$	1.71100	0.0786716
$474$	−7.96264	−0.365736
$475$	−28.9144	−1.32668
$476$	2.92334	0.133991
$477$	−4.78052	−0.218885
$478$	19.6566	0.899073
$479$	18.2803	0.835247	0.417624	−	0.908620i	$-0.362863\pi$
$479$	18.2803	0.835247	0.417624	+	0.908620i	$0.362863\pi$
$480$	−1.88597	−0.0860825
$481$	−5.48254	−0.249982
$482$	10.2814	0.468306
$483$	−12.1001	−0.550576
$484$	−1.75119	−0.0795996
$485$	6.38809	0.290068
$486$	1.62615	0.0737637
$487$	11.9082	0.539611	0.269805	−	0.962915i	$-0.413041\pi$
$487$	11.9082	0.539611	0.269805	+	0.962915i	$0.413041\pi$
$488$	23.0379	1.04288
$489$	−14.6184	−0.661068
$490$	−11.8468	−0.535186
$491$	10.9479	0.494070	0.247035	−	0.969007i	$-0.420544\pi$
$491$	10.9479	0.494070	0.247035	+	0.969007i	$0.420544\pi$
$492$	−0.166539	−0.00750816
$493$	4.14006	0.186459
$494$	−10.5010	−0.472464
$495$	1.54363	0.0693810
$496$	14.2993	0.642056
$497$	44.8623	2.01235
$498$	3.46192	0.155132
$499$	1.98410	0.0888206	0.0444103	−	0.999013i	$-0.485859\pi$
$499$	1.98410	0.0888206	0.0444103	+	0.999013i	$0.485859\pi$
$500$	−3.35677	−0.150120
$501$	0.252002	0.0112586
$502$	−0.570703	−0.0254717
$503$	38.8310	1.73139	0.865695	−	0.500571i	$-0.166877\pi$
$503$	38.8310	1.73139	0.865695	+	0.500571i	$0.166877\pi$
$504$	10.0012	0.445487
$505$	−7.42433	−0.330379
$506$	−12.4819	−0.554887
$507$	11.8924	0.528160
$508$	7.42799	0.329564
$509$	1.53769	0.0681567	0.0340784	−	0.999419i	$-0.489150\pi$
$509$	1.53769	0.0681567	0.0340784	+	0.999419i	$0.489150\pi$
$510$	0.872225	0.0386228
$511$	12.8625	0.569004
$512$	4.35098	0.192288
$513$	−6.13593	−0.270908
$514$	32.7086	1.44272
$515$	8.17992	0.360450
$516$	−0.383094	−0.0168648
$517$	13.3099	0.585371
$518$	38.4325	1.68863
$519$	−15.8601	−0.696180
$520$	1.24441	0.0545709
$521$	0.0367612	0.00161054	0.000805269	−	1.00000i	$-0.499744\pi$
$521$	0.0367612	0.00161054	0.000805269		1.00000i	$0.499744\pi$
$522$	−6.73235	−0.294667
$523$	−17.1989	−0.752054	−0.376027	−	0.926609i	$-0.622710\pi$
$523$	−17.1989	−0.752054	−0.376027	+	0.926609i	$0.622710\pi$
$524$	5.67114	0.247745
$525$	21.3787	0.933041
$526$	24.8858	1.08507
$527$	−2.93407	−0.127810
$528$	14.0255	0.610382
$529$	−15.8864	−0.690715
$530$	4.16968	0.181119
$531$	−2.88225	−0.125079
$532$	17.9374	0.777686
$533$	0.272004	0.0117818
$534$	−16.7007	−0.722710
$535$	−7.49432	−0.324008
$536$	35.7451	1.54395
$537$	−20.2145	−0.872322
$538$	−33.1594	−1.42960
$539$	39.0886	1.68366
$540$	−0.345621	−0.0148732
$541$	25.0584	1.07734	0.538672	−	0.842515i	$-0.318926\pi$
$541$	25.0584	1.07734	0.538672	+	0.842515i	$0.318926\pi$
$542$	−41.9984	−1.80398
$543$	−0.965690	−0.0414417
$544$	3.51615	0.150754
$545$	−3.36286	−0.144049
$546$	7.76425	0.332279
$547$	43.4640	1.85839	0.929193	−	0.369595i	$-0.120504\pi$
$547$	43.4640	1.85839	0.929193	+	0.369595i	$0.120504\pi$
$548$	−9.85055	−0.420794
$549$	10.4506	0.446019
$550$	22.0531	0.940347
$551$	25.4031	1.08221
$552$	−5.87959	−0.250252
$553$	−22.2149	−0.944672
$554$	32.8959	1.39761
$555$	2.79420	0.118607
$556$	8.85590	0.375574
$557$	−42.2867	−1.79174	−0.895872	−	0.444312i	$-0.853448\pi$
$557$	−42.2867	−1.79174	−0.895872	+	0.444312i	$0.853448\pi$
$558$	4.77124	0.201983
$559$	0.625698	0.0264642
$560$	−11.8593	−0.501146
$561$	−2.87790	−0.121505
$562$	−8.24756	−0.347902
$563$	7.91695	0.333660	0.166830	−	0.985986i	$-0.446647\pi$
$563$	7.91695	0.333660	0.166830	+	0.985986i	$0.446647\pi$
$564$	−2.98012	−0.125486
$565$	−2.05153	−0.0863084
$566$	−19.1705	−0.805798
$567$	4.53678	0.190527
$568$	21.7991	0.914669
$569$	−29.0022	−1.21584	−0.607918	−	0.794000i	$-0.707995\pi$
$569$	−29.0022	−1.21584	−0.607918	+	0.794000i	$0.707995\pi$
$570$	5.35191	0.224167
$571$	35.6894	1.49356	0.746778	−	0.665073i	$-0.231600\pi$
$571$	35.6894	1.49356	0.746778	+	0.665073i	$0.231600\pi$
$572$	1.95164	0.0816021
$573$	17.6222	0.736180
$574$	−1.90674	−0.0795858
$575$	−12.5683	−0.524134
$576$	4.02926	0.167886
$577$	23.5907	0.982093	0.491046	−	0.871133i	$-0.336615\pi$
$577$	23.5907	0.982093	0.491046	+	0.871133i	$0.336615\pi$
$578$	−1.62615	−0.0676389
$579$	14.3544	0.596547
$580$	1.43089	0.0594145
$581$	9.65836	0.400696
$582$	19.3671	0.802792
$583$	−13.7578	−0.569791
$584$	6.25003	0.258628
$585$	0.564494	0.0233389
$586$	21.7831	0.899852
$587$	−34.7455	−1.43410	−0.717049	−	0.697022i	$-0.754508\pi$
$587$	−34.7455	−1.43410	−0.717049	+	0.697022i	$0.754508\pi$
$588$	−8.75199	−0.360926
$589$	−18.0032	−0.741811
$590$	2.51397	0.103498
$591$	−6.30328	−0.259282
$592$	25.3883	1.04345
$593$	−25.9954	−1.06751	−0.533753	−	0.845641i	$-0.679219\pi$
$593$	−25.9954	−1.06751	−0.533753	+	0.845641i	$0.679219\pi$
$594$	4.67990	0.192018
$595$	2.43341	0.0997600
$596$	1.92516	0.0788577
$597$	22.9260	0.938300
$598$	−4.56453	−0.186657
$599$	36.7339	1.50091	0.750453	−	0.660924i	$-0.229836\pi$
$599$	36.7339	1.50091	0.750453	+	0.660924i	$0.229836\pi$
$600$	10.3881	0.424093
$601$	1.49323	0.0609103	0.0304552	−	0.999536i	$-0.490304\pi$
$601$	1.49323	0.0609103	0.0304552	+	0.999536i	$0.490304\pi$
$602$	−4.38613	−0.178765
$603$	16.2149	0.660321
$604$	14.8220	0.603097
$605$	−1.45770	−0.0592640
$606$	−22.5087	−0.914354
$607$	−12.0497	−0.489082	−0.244541	−	0.969639i	$-0.578637\pi$
$607$	−12.0497	−0.489082	−0.244541	+	0.969639i	$0.578637\pi$
$608$	21.5749	0.874976
$609$	−18.7825	−0.761106
$610$	−9.11524	−0.369065
$611$	4.86735	0.196912
$612$	0.644366	0.0260469
$613$	−28.2428	−1.14072	−0.570359	−	0.821396i	$-0.693196\pi$
$613$	−28.2428	−1.14072	−0.570359	+	0.821396i	$0.693196\pi$
$614$	9.63058	0.388659
$615$	−0.138628	−0.00559003
$616$	28.7823	1.15967
$617$	−42.3589	−1.70530	−0.852652	−	0.522479i	$-0.825007\pi$
$617$	−42.3589	−1.70530	−0.852652	+	0.522479i	$0.825007\pi$
$618$	24.7994	0.997580
$619$	−32.6557	−1.31254	−0.656271	−	0.754525i	$-0.727867\pi$
$619$	−32.6557	−1.31254	−0.656271	+	0.754525i	$0.727867\pi$
$620$	−1.01408	−0.0407263
$621$	−2.66713	−0.107028
$622$	−21.4380	−0.859584
$623$	−46.5930	−1.86671
$624$	5.12902	0.205325
$625$	20.7673	0.830693
$626$	−24.6863	−0.986662
$627$	−17.6586	−0.705216
$628$	−0.644366	−0.0257130
$629$	−5.20943	−0.207714
$630$	−3.95709	−0.157654
$631$	36.0897	1.43671	0.718355	−	0.695677i	$-0.244896\pi$
$631$	36.0897	1.43671	0.718355	+	0.695677i	$0.244896\pi$
$632$	−10.7944	−0.429379
$633$	28.1637	1.11940
$634$	29.7352	1.18094
$635$	6.18311	0.245369
$636$	3.08040	0.122146
$637$	14.2944	0.566365
$638$	−19.3750	−0.767065
$639$	9.88860	0.391187
$640$	−7.28636	−0.288019
$641$	45.2127	1.78579	0.892897	−	0.450262i	$-0.148669\pi$
$641$	45.2127	1.78579	0.892897	+	0.450262i	$0.148669\pi$
$642$	−22.7209	−0.896722
$643$	18.8719	0.744234	0.372117	−	0.928186i	$-0.378632\pi$
$643$	18.8719	0.744234	0.372117	+	0.928186i	$0.378632\pi$
$644$	7.79692	0.307242
$645$	−0.318890	−0.0125563
$646$	−9.97794	−0.392577
$647$	47.7355	1.87668	0.938338	−	0.345718i	$-0.112365\pi$
$647$	47.7355	1.87668	0.938338	+	0.345718i	$0.112365\pi$
$648$	2.20447	0.0865996
$649$	−8.29482	−0.325600
$650$	8.06465	0.316322
$651$	13.3112	0.521708
$652$	9.41961	0.368901
$653$	45.2808	1.77198	0.885988	−	0.463708i	$-0.153481\pi$
$653$	45.2808	1.77198	0.885988	+	0.463708i	$0.153481\pi$
$654$	−10.1953	−0.398669
$655$	4.72069	0.184453
$656$	−1.25958	−0.0491785
$657$	2.83517	0.110610
$658$	−34.1200	−1.33014
$659$	−1.61714	−0.0629950	−0.0314975	−	0.999504i	$-0.510028\pi$
$659$	−1.61714	−0.0629950	−0.0314975	+	0.999504i	$0.510028\pi$
$660$	−0.994662	−0.0387172
$661$	−50.1186	−1.94939	−0.974695	−	0.223540i	$-0.928239\pi$
$661$	−50.1186	−1.94939	−0.974695	+	0.223540i	$0.928239\pi$
$662$	−8.70661	−0.338392
$663$	−1.05243	−0.0408728
$664$	4.69310	0.182128
$665$	14.9312	0.579008
$666$	8.47132	0.328257
$667$	11.0420	0.427550
$668$	−0.162381	−0.00628272
$669$	12.3845	0.478813
$670$	−14.1430	−0.546392
$671$	30.0757	1.16106
$672$	−15.9520	−0.615362
$673$	33.3422	1.28525	0.642623	−	0.766182i	$-0.277846\pi$
$673$	33.3422	1.28525	0.642623	+	0.766182i	$0.277846\pi$
$674$	−46.4752	−1.79016
$675$	4.71230	0.181377
$676$	−7.66305	−0.294733
$677$	−33.5004	−1.28753	−0.643763	−	0.765225i	$-0.722628\pi$
$677$	−33.5004	−1.28753	−0.643763	+	0.765225i	$0.722628\pi$
$678$	−6.21971	−0.238867
$679$	54.0320	2.07356
$680$	1.18242	0.0453437
$681$	11.2981	0.432942
$682$	13.7311	0.525793
$683$	−29.2586	−1.11955	−0.559775	−	0.828644i	$-0.689113\pi$
$683$	−29.2586	−1.11955	−0.559775	+	0.828644i	$0.689113\pi$
$684$	3.95378	0.151177
$685$	−8.19966	−0.313293
$686$	−48.5610	−1.85407
$687$	−7.65246	−0.291960
$688$	−2.89745	−0.110464
$689$	−5.03114	−0.191671
$690$	2.32633	0.0885620
$691$	25.4297	0.967392	0.483696	−	0.875236i	$-0.339294\pi$
$691$	25.4297	0.967392	0.483696	+	0.875236i	$0.339294\pi$
$692$	10.2197	0.388494
$693$	13.0564	0.495971
$694$	51.9889	1.97347
$695$	7.37170	0.279625
$696$	−9.12661	−0.345943
$697$	0.258454	0.00978965
$698$	2.55507	0.0967109
$699$	3.81049	0.144126
$700$	−13.7757	−0.520671
$701$	−28.3858	−1.07212	−0.536058	−	0.844181i	$-0.680087\pi$
$701$	−28.3858	−1.07212	−0.536058	+	0.844181i	$0.680087\pi$
$702$	1.71140	0.0645927
$703$	−31.9647	−1.20557
$704$	11.5958	0.437033
$705$	−2.48067	−0.0934273
$706$	16.5495	0.622850
$707$	−62.7967	−2.36171
$708$	1.85722	0.0697986
$709$	−9.70194	−0.364364	−0.182182	−	0.983265i	$-0.558316\pi$
$709$	−9.70194	−0.364364	−0.182182	+	0.983265i	$0.558316\pi$
$710$	−8.62508	−0.323693
$711$	−4.89662	−0.183638
$712$	−22.6400	−0.848471
$713$	−7.82553	−0.293068
$714$	7.37748	0.276095
$715$	1.62456	0.0607550
$716$	13.0256	0.486788
$717$	12.0878	0.451428
$718$	−38.1625	−1.42421
$719$	9.74472	0.363417	0.181708	−	0.983352i	$-0.441837\pi$
$719$	9.74472	0.363417	0.181708	+	0.983352i	$0.441837\pi$
$720$	−2.61403	−0.0974192
$721$	69.1876	2.57668
$722$	−30.3271	−1.12866
$723$	6.32255	0.235138
$724$	0.622257	0.0231260
$725$	−19.5092	−0.724553
$726$	−4.41939	−0.164019
$727$	15.3997	0.571144	0.285572	−	0.958357i	$-0.407816\pi$
$727$	15.3997	0.571144	0.285572	+	0.958357i	$0.407816\pi$
$728$	10.5255	0.390101
$729$	1.00000	0.0370370
$730$	−2.47290	−0.0915263
$731$	0.594529	0.0219895
$732$	−6.73398	−0.248895
$733$	27.3353	1.00965	0.504827	−	0.863221i	$-0.331556\pi$
$733$	27.3353	1.00965	0.504827	+	0.863221i	$0.331556\pi$
$734$	40.2640	1.48617
$735$	−7.28521	−0.268719
$736$	9.37802	0.345678
$737$	46.6648	1.71892
$738$	−0.420286	−0.0154709
$739$	−45.5885	−1.67700	−0.838499	−	0.544903i	$-0.816567\pi$
$739$	−45.5885	−1.67700	−0.838499	+	0.544903i	$0.816567\pi$
$740$	−1.80049	−0.0661872
$741$	−6.45761	−0.237226
$742$	35.2682	1.29473
$743$	40.5650	1.48819	0.744093	−	0.668076i	$-0.232882\pi$
$743$	40.5650	1.48819	0.744093	+	0.668076i	$0.232882\pi$
$744$	6.46805	0.237130
$745$	1.60252	0.0587117
$746$	−3.92019	−0.143528
$747$	2.12890	0.0778926
$748$	1.85442	0.0678043
$749$	−63.3887	−2.31617
$750$	−8.47131	−0.309329
$751$	−20.1819	−0.736450	−0.368225	−	0.929737i	$-0.620034\pi$
$751$	−20.1819	−0.736450	−0.368225	+	0.929737i	$0.620034\pi$
$752$	−22.5395	−0.821931
$753$	−0.350954	−0.0127895
$754$	−7.08531	−0.258032
$755$	12.3379	0.449022
$756$	−2.92334	−0.106321
$757$	14.4041	0.523526	0.261763	−	0.965132i	$-0.415696\pi$
$757$	14.4041	0.523526	0.261763	+	0.965132i	$0.415696\pi$
$758$	−10.3910	−0.377419
$759$	−7.67572	−0.278611
$760$	7.25523	0.263175
$761$	0.929157	0.0336819	0.0168410	−	0.999858i	$-0.494639\pi$
$761$	0.929157	0.0336819	0.0168410	+	0.999858i	$0.494639\pi$
$762$	18.7456	0.679082
$763$	−28.4438	−1.02974
$764$	−11.3552	−0.410815
$765$	0.536374	0.0193926
$766$	23.8407	0.861398
$767$	−3.03335	−0.109528
$768$	−14.0319	−0.506333
$769$	14.8258	0.534631	0.267316	−	0.963609i	$-0.413863\pi$
$769$	14.8258	0.534631	0.267316	+	0.963609i	$0.413863\pi$
$770$	−11.3881	−0.410399
$771$	20.1141	0.724393
$772$	−9.24945	−0.332895
$773$	−10.7624	−0.387097	−0.193549	−	0.981091i	$-0.562000\pi$
$773$	−10.7624	−0.387097	−0.193549	+	0.981091i	$0.562000\pi$
$774$	−0.966794	−0.0347507
$775$	13.8262	0.496653
$776$	26.2547	0.942489
$777$	23.6340	0.847865
$778$	−33.7236	−1.20905
$779$	1.58586	0.0568192
$780$	−0.363740	−0.0130240
$781$	28.4584	1.01832
$782$	−4.33715	−0.155096
$783$	−4.14006	−0.147954
$784$	−66.1938	−2.36407
$785$	−0.536374	−0.0191440
$786$	14.3119	0.510490
$787$	21.4583	0.764904	0.382452	−	0.923975i	$-0.375080\pi$
$787$	21.4583	0.764904	0.382452	+	0.923975i	$0.375080\pi$
$788$	4.06162	0.144689
$789$	15.3035	0.544818
$790$	4.27095	0.151954
$791$	−17.3523	−0.616977
$792$	6.34423	0.225432
$793$	10.9984	0.390566
$794$	50.7044	1.79943
$795$	2.56414	0.0909408
$796$	−14.7727	−0.523606
$797$	1.32287	0.0468583	0.0234292	−	0.999725i	$-0.492542\pi$
$797$	1.32287	0.0468583	0.0234292	+	0.999725i	$0.492542\pi$
$798$	45.2677	1.60246
$799$	4.62488	0.163617
$800$	−16.5692	−0.585809
$801$	−10.2701	−0.362875
$802$	63.9527	2.25825
$803$	8.15933	0.287936
$804$	−10.4483	−0.368483
$805$	6.49020	0.228750
$806$	5.02138	0.176870
$807$	−20.3913	−0.717809
$808$	−30.5136	−1.07346
$809$	32.0313	1.12616	0.563080	−	0.826402i	$-0.309616\pi$
$809$	32.0313	1.12616	0.563080	+	0.826402i	$0.309616\pi$
$810$	−0.872225	−0.0306469
$811$	45.0726	1.58271	0.791357	−	0.611354i	$-0.209375\pi$
$811$	45.0726	1.58271	0.791357	+	0.611354i	$0.209375\pi$
$812$	12.1028	0.424725
$813$	−25.8269	−0.905788
$814$	24.3796	0.854504
$815$	7.84095	0.274656
$816$	4.87352	0.170607
$817$	3.64799	0.127627
$818$	−16.5213	−0.577654
$819$	4.77462	0.166839
$820$	0.0893272	0.00311944
$821$	−3.23973	−0.113067	−0.0565337	−	0.998401i	$-0.518005\pi$
$821$	−3.23973	−0.113067	−0.0565337	+	0.998401i	$0.518005\pi$
$822$	−24.8593	−0.867067
$823$	−29.2894	−1.02097	−0.510483	−	0.859888i	$-0.670533\pi$
$823$	−29.2894	−1.02097	−0.510483	+	0.859888i	$0.670533\pi$
$824$	33.6190	1.17117
$825$	13.5615	0.472152
$826$	21.2637	0.739860
$827$	35.2182	1.22466	0.612328	−	0.790604i	$-0.290233\pi$
$827$	35.2182	1.22466	0.612328	+	0.790604i	$0.290233\pi$
$828$	1.71860	0.0597256
$829$	−0.0569368	−0.00197750	−0.000988748	−	1.00000i	$-0.500315\pi$
$829$	−0.0569368	−0.00197750	−0.000988748		1.00000i	$0.500315\pi$
$830$	−1.85688	−0.0644534
$831$	20.2293	0.701748
$832$	4.24049	0.147013
$833$	13.5823	0.470600
$834$	22.3491	0.773888
$835$	−0.135167	−0.00467766
$836$	11.3786	0.393537
$837$	2.93407	0.101416
$838$	−4.94420	−0.170795
$839$	−43.2435	−1.49293	−0.746466	−	0.665423i	$-0.768251\pi$
$839$	−43.2435	−1.49293	−0.746466	+	0.665423i	$0.768251\pi$
$840$	−5.36436	−0.185088
$841$	−11.8599	−0.408963
$842$	45.1343	1.55543
$843$	−5.07183	−0.174683
$844$	−18.1477	−0.624669
$845$	−6.37877	−0.219436
$846$	−7.52076	−0.258569
$847$	−12.3296	−0.423650
$848$	23.2980	0.800055
$849$	−11.7889	−0.404594
$850$	7.66291	0.262836
$851$	−13.8942	−0.476287
$852$	−6.37187	−0.218297
$853$	32.4019	1.10942	0.554711	−	0.832043i	$-0.312829\pi$
$853$	32.4019	1.10942	0.554711	+	0.832043i	$0.312829\pi$
$854$	−77.0988	−2.63827
$855$	3.29115	0.112555
$856$	−30.8012	−1.05276
$857$	38.6500	1.32026	0.660130	−	0.751152i	$-0.270501\pi$
$857$	38.6500	1.32026	0.660130	+	0.751152i	$0.270501\pi$
$858$	4.92524	0.168145
$859$	−52.1116	−1.77802	−0.889012	−	0.457883i	$-0.848608\pi$
$859$	−52.1116	−1.77802	−0.889012	+	0.457883i	$0.848608\pi$
$860$	0.205482	0.00700687
$861$	−1.17255	−0.0399604
$862$	44.8717	1.52833
$863$	−29.6109	−1.00797	−0.503983	−	0.863714i	$-0.668133\pi$
$863$	−29.6109	−1.00797	−0.503983	+	0.863714i	$0.668133\pi$
$864$	−3.51615	−0.119622
$865$	8.50693	0.289244
$866$	21.7282	0.738356
$867$	−1.00000	−0.0339618
$868$	−8.57729	−0.291132
$869$	−14.0920	−0.478037
$870$	3.61106	0.122426
$871$	17.0650	0.578224
$872$	−13.8212	−0.468043
$873$	11.9098	0.403085
$874$	−26.6124	−0.900179
$875$	−23.6340	−0.798975
$876$	−1.82688	−0.0617247
$877$	−15.6832	−0.529583	−0.264792	−	0.964306i	$-0.585303\pi$
$877$	−15.6832	−0.529583	−0.264792	+	0.964306i	$0.585303\pi$
$878$	7.57088	0.255505
$879$	13.3955	0.451819
$880$	−7.52292	−0.253598
$881$	−49.5529	−1.66948	−0.834740	−	0.550644i	$-0.814382\pi$
$881$	−49.5529	−1.66948	−0.834740	+	0.550644i	$0.814382\pi$
$882$	−22.0869	−0.743705
$883$	13.7529	0.462821	0.231410	−	0.972856i	$-0.425666\pi$
$883$	13.7529	0.462821	0.231410	+	0.972856i	$0.425666\pi$
$884$	0.678147	0.0228086
$885$	1.54596	0.0519670
$886$	26.6740	0.896130
$887$	20.0163	0.672082	0.336041	−	0.941847i	$-0.390912\pi$
$887$	20.0163	0.672082	0.336041	+	0.941847i	$0.390912\pi$
$888$	11.4840	0.385378
$889$	52.2982	1.75402
$890$	8.95782	0.300267
$891$	2.87790	0.0964132
$892$	−7.98015	−0.267195
$893$	28.3780	0.949632
$894$	4.85843	0.162490
$895$	10.8426	0.362426
$896$	−61.6297	−2.05891
$897$	−2.80695	−0.0937214
$898$	4.85792	0.162111
$899$	−12.1472	−0.405132
$900$	−3.03645	−0.101215
$901$	−4.78052	−0.159262
$902$	−1.20954	−0.0402733
$903$	−2.69725	−0.0897587
$904$	−8.43166	−0.280433
$905$	0.517971	0.0172179
$906$	37.4054	1.24271
$907$	−45.4528	−1.50924	−0.754618	−	0.656164i	$-0.772178\pi$
$907$	−45.4528	−1.50924	−0.754618	+	0.656164i	$0.772178\pi$
$908$	−7.28007	−0.241598
$909$	−13.8417	−0.459101
$910$	−4.16454	−0.138053
$911$	−35.1316	−1.16396	−0.581980	−	0.813203i	$-0.697722\pi$
$911$	−35.1316	−1.16396	−0.581980	+	0.813203i	$0.697722\pi$
$912$	29.9036	0.990207
$913$	6.12677	0.202767
$914$	−61.5424	−2.03564
$915$	−5.60541	−0.185309
$916$	4.93098	0.162924
$917$	39.9287	1.31856
$918$	1.62615	0.0536710
$919$	−3.92819	−0.129579	−0.0647896	−	0.997899i	$-0.520638\pi$
$919$	−3.92819	−0.129579	−0.0647896	+	0.997899i	$0.520638\pi$
$920$	3.15366	0.103973
$921$	5.92232	0.195147
$922$	9.13219	0.300753
$923$	10.4070	0.342551
$924$	−8.41308	−0.276770
$925$	24.5484	0.807147
$926$	−26.4898	−0.870510
$927$	15.2504	0.500889
$928$	14.5571	0.477859
$929$	4.22701	0.138684	0.0693419	−	0.997593i	$-0.477910\pi$
$929$	4.22701	0.138684	0.0693419	+	0.997593i	$0.477910\pi$
$930$	−2.55917	−0.0839184
$931$	83.3402	2.73137
$932$	−2.45535	−0.0804276
$933$	−13.1833	−0.431600
$934$	−40.6553	−1.33028
$935$	1.54363	0.0504821
$936$	2.32004	0.0758328
$937$	50.7125	1.65671	0.828353	−	0.560206i	$-0.189278\pi$
$937$	50.7125	1.65671	0.828353	+	0.560206i	$0.189278\pi$
$938$	−119.625	−3.90589
$939$	−15.1808	−0.495407
$940$	1.59846	0.0521359
$941$	30.3991	0.990984	0.495492	−	0.868613i	$-0.334988\pi$
$941$	30.3991	0.990984	0.495492	+	0.868613i	$0.334988\pi$
$942$	−1.62615	−0.0529828
$943$	0.689330	0.0224477
$944$	14.0467	0.457181
$945$	−2.43341	−0.0791588
$946$	−2.78234	−0.0904615
$947$	16.9509	0.550830	0.275415	−	0.961325i	$-0.411185\pi$
$947$	16.9509	0.550830	0.275415	+	0.961325i	$0.411185\pi$
$948$	3.15521	0.102477
$949$	2.98380	0.0968584
$950$	47.0191	1.52550
$951$	18.2857	0.592953
$952$	10.0012	0.324140
$953$	−4.80852	−0.155763	−0.0778815	−	0.996963i	$-0.524816\pi$
$953$	−4.80852	−0.155763	−0.0778815	+	0.996963i	$0.524816\pi$
$954$	7.77384	0.251687
$955$	−9.45211	−0.305863
$956$	−7.78898	−0.251914
$957$	−11.9147	−0.385146
$958$	−29.7265	−0.960419
$959$	−69.3546	−2.23958
$960$	−2.16119	−0.0697520
$961$	−22.3912	−0.722298
$962$	8.91543	0.287445
$963$	−13.9722	−0.450248
$964$	−4.07404	−0.131216
$965$	−7.69930	−0.247849
$966$	19.6767	0.633086
$967$	−8.11932	−0.261100	−0.130550	−	0.991442i	$-0.541674\pi$
$967$	−8.11932	−0.261100	−0.130550	+	0.991442i	$0.541674\pi$
$968$	−5.99107	−0.192560
$969$	−6.13593	−0.197114
$970$	−10.3880	−0.333539
$971$	7.69890	0.247069	0.123535	−	0.992340i	$-0.460577\pi$
$971$	7.69890	0.247069	0.123535	+	0.992340i	$0.460577\pi$
$972$	−0.644366	−0.0206680
$973$	62.3516	1.99890
$974$	−19.3645	−0.620478
$975$	4.95935	0.158826
$976$	−50.9311	−1.63026
$977$	−47.4683	−1.51865	−0.759323	−	0.650713i	$-0.774470\pi$
$977$	−47.4683	−1.51865	−0.759323	+	0.650713i	$0.774470\pi$
$978$	23.7718	0.760137
$979$	−29.5563	−0.944622
$980$	4.69434	0.149955
$981$	−6.26962	−0.200173
$982$	−17.8029	−0.568112
$983$	−17.1451	−0.546845	−0.273423	−	0.961894i	$-0.588156\pi$
$983$	−17.1451	−0.546845	−0.273423	+	0.961894i	$0.588156\pi$
$984$	−0.569754	−0.0181631
$985$	3.38092	0.107725
$986$	−6.73235	−0.214402
$987$	−20.9821	−0.667866
$988$	4.16106	0.132381
$989$	1.58568	0.0504218
$990$	−2.51017	−0.0797786
$991$	54.3776	1.72736	0.863681	−	0.504039i	$-0.168153\pi$
$991$	54.3776	1.72736	0.863681	+	0.504039i	$0.168153\pi$
$992$	−10.3166	−0.327553
$993$	−5.35412	−0.169908
$994$	−72.9529	−2.31393
$995$	−12.2969	−0.389839
$996$	−1.37179	−0.0434669
$997$	−30.7869	−0.975031	−0.487516	−	0.873114i	$-0.662097\pi$
$997$	−30.7869	−0.975031	−0.487516	+	0.873114i	$0.662097\pi$
$998$	−3.22645	−0.102131
$999$	5.20943	0.164819

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.16	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.16	✓	64	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-1.62615 q^{2} -1.00000 q^{3} +0.644366 q^{4} +0.536374 q^{5} +1.62615 q^{6} +4.53678 q^{7} +2.20447 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.62615 q^{2} -1.00000 q^{3} +0.644366 q^{4} +0.536374 q^{5} +1.62615 q^{6} +4.53678 q^{7} +2.20447 q^{8} +1.00000 q^{9} -0.872225 q^{10} +2.87790 q^{11} -0.644366 q^{12} +1.05243 q^{13} -7.37748 q^{14} -0.536374 q^{15} -4.87352 q^{16} +1.00000 q^{17} -1.62615 q^{18} +6.13593 q^{19} +0.345621 q^{20} -4.53678 q^{21} -4.67990 q^{22} +2.66713 q^{23} -2.20447 q^{24} -4.71230 q^{25} -1.71140 q^{26} -1.00000 q^{27} +2.92334 q^{28} +4.14006 q^{29} +0.872225 q^{30} -2.93407 q^{31} +3.51615 q^{32} -2.87790 q^{33} -1.62615 q^{34} +2.43341 q^{35} +0.644366 q^{36} -5.20943 q^{37} -9.97794 q^{38} -1.05243 q^{39} +1.18242 q^{40} +0.258454 q^{41} +7.37748 q^{42} +0.594529 q^{43} +1.85442 q^{44} +0.536374 q^{45} -4.33715 q^{46} +4.62488 q^{47} +4.87352 q^{48} +13.5823 q^{49} +7.66291 q^{50} -1.00000 q^{51} +0.678147 q^{52} -4.78052 q^{53} +1.62615 q^{54} +1.54363 q^{55} +10.0012 q^{56} -6.13593 q^{57} -6.73235 q^{58} -2.88225 q^{59} -0.345621 q^{60} +10.4506 q^{61} +4.77124 q^{62} +4.53678 q^{63} +4.02926 q^{64} +0.564494 q^{65} +4.67990 q^{66} +16.2149 q^{67} +0.644366 q^{68} -2.66713 q^{69} -3.95709 q^{70} +9.88860 q^{71} +2.20447 q^{72} +2.83517 q^{73} +8.47132 q^{74} +4.71230 q^{75} +3.95378 q^{76} +13.0564 q^{77} +1.71140 q^{78} -4.89662 q^{79} -2.61403 q^{80} +1.00000 q^{81} -0.420286 q^{82} +2.12890 q^{83} -2.92334 q^{84} +0.536374 q^{85} -0.966794 q^{86} -4.14006 q^{87} +6.34423 q^{88} -10.2701 q^{89} -0.872225 q^{90} +4.77462 q^{91} +1.71860 q^{92} +2.93407 q^{93} -7.52076 q^{94} +3.29115 q^{95} -3.51615 q^{96} +11.9098 q^{97} -22.0869 q^{98} +2.87790 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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