LMFDB - Embedded newform 8007.2.a.e.1.29

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:	$1$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.29
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)

$f(q)$	$=$	$q+0.751824 q^{2} +1.00000 q^{3} -1.43476 q^{4} +3.06060 q^{5} +0.751824 q^{6} -2.02078 q^{7} -2.58233 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.751824 q^{2} +1.00000 q^{3} -1.43476 q^{4} +3.06060 q^{5} +0.751824 q^{6} -2.02078 q^{7} -2.58233 q^{8} +1.00000 q^{9} +2.30103 q^{10} -2.87419 q^{11} -1.43476 q^{12} -0.853656 q^{13} -1.51927 q^{14} +3.06060 q^{15} +0.928063 q^{16} -1.00000 q^{17} +0.751824 q^{18} +1.01630 q^{19} -4.39123 q^{20} -2.02078 q^{21} -2.16088 q^{22} +2.89886 q^{23} -2.58233 q^{24} +4.36726 q^{25} -0.641799 q^{26} +1.00000 q^{27} +2.89933 q^{28} -7.11490 q^{29} +2.30103 q^{30} +1.50911 q^{31} +5.86241 q^{32} -2.87419 q^{33} -0.751824 q^{34} -6.18478 q^{35} -1.43476 q^{36} +8.80348 q^{37} +0.764077 q^{38} -0.853656 q^{39} -7.90349 q^{40} +4.79907 q^{41} -1.51927 q^{42} -0.143371 q^{43} +4.12378 q^{44} +3.06060 q^{45} +2.17943 q^{46} -6.98716 q^{47} +0.928063 q^{48} -2.91646 q^{49} +3.28341 q^{50} -1.00000 q^{51} +1.22479 q^{52} -7.81555 q^{53} +0.751824 q^{54} -8.79674 q^{55} +5.21832 q^{56} +1.01630 q^{57} -5.34915 q^{58} -9.82923 q^{59} -4.39123 q^{60} -8.44330 q^{61} +1.13459 q^{62} -2.02078 q^{63} +2.55137 q^{64} -2.61270 q^{65} -2.16088 q^{66} -0.210466 q^{67} +1.43476 q^{68} +2.89886 q^{69} -4.64987 q^{70} -4.66633 q^{71} -2.58233 q^{72} +4.89518 q^{73} +6.61866 q^{74} +4.36726 q^{75} -1.45815 q^{76} +5.80809 q^{77} -0.641799 q^{78} +14.7425 q^{79} +2.84043 q^{80} +1.00000 q^{81} +3.60806 q^{82} +2.85980 q^{83} +2.89933 q^{84} -3.06060 q^{85} -0.107790 q^{86} -7.11490 q^{87} +7.42212 q^{88} -14.3348 q^{89} +2.30103 q^{90} +1.72505 q^{91} -4.15917 q^{92} +1.50911 q^{93} -5.25311 q^{94} +3.11048 q^{95} +5.86241 q^{96} +11.0575 q^{97} -2.19267 q^{98} -2.87419 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * 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 $

$2$	0.751824	0.531620	0.265810	−	0.964026i	$-0.414361\pi$
$2$	0.751824	0.531620	0.265810	+	0.964026i	$0.414361\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.43476	−0.717381
$5$	3.06060	1.36874	0.684370	−	0.729135i	$-0.260077\pi$
$5$	3.06060	1.36874	0.684370	+	0.729135i	$0.260077\pi$
$6$	0.751824	0.306931
$7$	−2.02078	−0.763782	−0.381891	−	0.924207i	$-0.624727\pi$
$7$	−2.02078	−0.763782	−0.381891	+	0.924207i	$0.624727\pi$
$8$	−2.58233	−0.912993
$9$	1.00000	0.333333
$10$	2.30103	0.727649
$11$	−2.87419	−0.866601	−0.433300	−	0.901250i	$-0.642651\pi$
$11$	−2.87419	−0.866601	−0.433300	+	0.901250i	$0.642651\pi$
$12$	−1.43476	−0.414180
$13$	−0.853656	−0.236762	−0.118381	−	0.992968i	$-0.537770\pi$
$13$	−0.853656	−0.236762	−0.118381	+	0.992968i	$0.537770\pi$
$14$	−1.51927	−0.406041
$15$	3.06060	0.790243
$16$	0.928063	0.232016
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.751824	0.177207
$19$	1.01630	0.233155	0.116577	−	0.993182i	$-0.462808\pi$
$19$	1.01630	0.233155	0.116577	+	0.993182i	$0.462808\pi$
$20$	−4.39123	−0.981908
$21$	−2.02078	−0.440970
$22$	−2.16088	−0.460702
$23$	2.89886	0.604454	0.302227	−	0.953236i	$-0.402270\pi$
$23$	2.89886	0.604454	0.302227	+	0.953236i	$0.402270\pi$
$24$	−2.58233	−0.527117
$25$	4.36726	0.873452
$26$	−0.641799	−0.125867
$27$	1.00000	0.192450
$28$	2.89933	0.547922
$29$	−7.11490	−1.32120	−0.660602	−	0.750737i	$-0.729699\pi$
$29$	−7.11490	−1.32120	−0.660602	+	0.750737i	$0.729699\pi$
$30$	2.30103	0.420109
$31$	1.50911	0.271045	0.135522	−	0.990774i	$-0.456729\pi$
$31$	1.50911	0.271045	0.135522	+	0.990774i	$0.456729\pi$
$32$	5.86241	1.03634
$33$	−2.87419	−0.500332
$34$	−0.751824	−0.128937
$35$	−6.18478	−1.04542
$36$	−1.43476	−0.239127
$37$	8.80348	1.44728	0.723642	−	0.690176i	$-0.242467\pi$
$37$	8.80348	1.44728	0.723642	+	0.690176i	$0.242467\pi$
$38$	0.764077	0.123950
$39$	−0.853656	−0.136694
$40$	−7.90349	−1.24965
$41$	4.79907	0.749489	0.374745	−	0.927128i	$-0.377730\pi$
$41$	4.79907	0.749489	0.374745	+	0.927128i	$0.377730\pi$
$42$	−1.51927	−0.234428
$43$	−0.143371	−0.0218639	−0.0109319	−	0.999940i	$-0.503480\pi$
$43$	−0.143371	−0.0218639	−0.0109319	+	0.999940i	$0.503480\pi$
$44$	4.12378	0.621683
$45$	3.06060	0.456247
$46$	2.17943	0.321339
$47$	−6.98716	−1.01918	−0.509591	−	0.860417i	$-0.670203\pi$
$47$	−6.98716	−1.01918	−0.509591	+	0.860417i	$0.670203\pi$
$48$	0.928063	0.133954
$49$	−2.91646	−0.416638
$50$	3.28341	0.464344
$51$	−1.00000	−0.140028
$52$	1.22479	0.169848
$53$	−7.81555	−1.07355	−0.536774	−	0.843726i	$-0.680357\pi$
$53$	−7.81555	−1.07355	−0.536774	+	0.843726i	$0.680357\pi$
$54$	0.751824	0.102310
$55$	−8.79674	−1.18615
$56$	5.21832	0.697327
$57$	1.01630	0.134612
$58$	−5.34915	−0.702377
$59$	−9.82923	−1.27966	−0.639829	−	0.768518i	$-0.720995\pi$
$59$	−9.82923	−1.27966	−0.639829	+	0.768518i	$0.720995\pi$
$60$	−4.39123	−0.566905
$61$	−8.44330	−1.08105	−0.540527	−	0.841327i	$-0.681775\pi$
$61$	−8.44330	−1.08105	−0.540527	+	0.841327i	$0.681775\pi$
$62$	1.13459	0.144093
$63$	−2.02078	−0.254594
$64$	2.55137	0.318921
$65$	−2.61270	−0.324065
$66$	−2.16088	−0.265986
$67$	−0.210466	−0.0257125	−0.0128563	−	0.999917i	$-0.504092\pi$
$67$	−0.210466	−0.0257125	−0.0128563	+	0.999917i	$0.504092\pi$
$68$	1.43476	0.173990
$69$	2.89886	0.348982
$70$	−4.64987	−0.555765
$71$	−4.66633	−0.553792	−0.276896	−	0.960900i	$-0.589306\pi$
$71$	−4.66633	−0.553792	−0.276896	+	0.960900i	$0.589306\pi$
$72$	−2.58233	−0.304331
$73$	4.89518	0.572938	0.286469	−	0.958090i	$-0.407518\pi$
$73$	4.89518	0.572938	0.286469	+	0.958090i	$0.407518\pi$
$74$	6.61866	0.769404
$75$	4.36726	0.504287
$76$	−1.45815	−0.167261
$77$	5.80809	0.661894
$78$	−0.641799	−0.0726694
$79$	14.7425	1.65866	0.829329	−	0.558760i	$-0.188723\pi$
$79$	14.7425	1.65866	0.829329	+	0.558760i	$0.188723\pi$
$80$	2.84043	0.317569
$81$	1.00000	0.111111
$82$	3.60806	0.398443
$83$	2.85980	0.313904	0.156952	−	0.987606i	$-0.449833\pi$
$83$	2.85980	0.313904	0.156952	+	0.987606i	$0.449833\pi$
$84$	2.89933	0.316343
$85$	−3.06060	−0.331968
$86$	−0.107790	−0.0116233
$87$	−7.11490	−0.762797
$88$	7.42212	0.791200
$89$	−14.3348	−1.51949	−0.759745	−	0.650221i	$-0.774676\pi$
$89$	−14.3348	−1.51949	−0.759745	+	0.650221i	$0.774676\pi$
$90$	2.30103	0.242550
$91$	1.72505	0.180834
$92$	−4.15917	−0.433623
$93$	1.50911	0.156488
$94$	−5.25311	−0.541817
$95$	3.11048	0.319129
$96$	5.86241	0.598330
$97$	11.0575	1.12272	0.561359	−	0.827572i	$-0.310279\pi$
$97$	11.0575	1.12272	0.561359	+	0.827572i	$0.310279\pi$
$98$	−2.19267	−0.221493
$99$	−2.87419	−0.288867
$100$	−6.26597	−0.626597
$101$	−8.86946	−0.882545	−0.441272	−	0.897373i	$-0.645473\pi$
$101$	−8.86946	−0.882545	−0.441272	+	0.897373i	$0.645473\pi$
$102$	−0.751824	−0.0744416
$103$	−16.5490	−1.63062	−0.815309	−	0.579026i	$-0.803433\pi$
$103$	−16.5490	−1.63062	−0.815309	+	0.579026i	$0.803433\pi$
$104$	2.20442	0.216162
$105$	−6.18478	−0.603573
$106$	−5.87591	−0.570719
$107$	−7.01251	−0.677925	−0.338963	−	0.940800i	$-0.610076\pi$
$107$	−7.01251	−0.677925	−0.338963	+	0.940800i	$0.610076\pi$
$108$	−1.43476	−0.138060
$109$	−12.8152	−1.22747	−0.613736	−	0.789511i	$-0.710334\pi$
$109$	−12.8152	−1.22747	−0.613736	+	0.789511i	$0.710334\pi$
$110$	−6.61359	−0.630581
$111$	8.80348	0.835589
$112$	−1.87541	−0.177209
$113$	−1.53869	−0.144748	−0.0723741	−	0.997378i	$-0.523058\pi$
$113$	−1.53869	−0.144748	−0.0723741	+	0.997378i	$0.523058\pi$
$114$	0.764077	0.0715624
$115$	8.87224	0.827341
$116$	10.2082	0.947806
$117$	−0.853656	−0.0789205
$118$	−7.38985	−0.680291
$119$	2.02078	0.185244
$120$	−7.90349	−0.721486
$121$	−2.73904	−0.249003
$122$	−6.34787	−0.574709
$123$	4.79907	0.432718
$124$	−2.16522	−0.194442
$125$	−1.93657	−0.173212
$126$	−1.51927	−0.135347
$127$	8.04162	0.713579	0.356789	−	0.934185i	$-0.383871\pi$
$127$	8.04162	0.713579	0.356789	+	0.934185i	$0.383871\pi$
$128$	−9.80664	−0.866792
$129$	−0.143371	−0.0126231
$130$	−1.96429	−0.172279
$131$	−18.0424	−1.57638	−0.788188	−	0.615435i	$-0.788981\pi$
$131$	−18.0424	−1.57638	−0.788188	+	0.615435i	$0.788981\pi$
$132$	4.12378	0.358929
$133$	−2.05371	−0.178079
$134$	−0.158233	−0.0136693
$135$	3.06060	0.263414
$136$	2.58233	0.221433
$137$	−17.1264	−1.46321	−0.731604	−	0.681730i	$-0.761228\pi$
$137$	−17.1264	−1.46321	−0.731604	+	0.681730i	$0.761228\pi$
$138$	2.17943	0.185525
$139$	7.56541	0.641690	0.320845	−	0.947132i	$-0.396033\pi$
$139$	7.56541	0.641690	0.320845	+	0.947132i	$0.396033\pi$
$140$	8.87369	0.749963
$141$	−6.98716	−0.588425
$142$	−3.50826	−0.294407
$143$	2.45357	0.205178
$144$	0.928063	0.0773386
$145$	−21.7758	−1.80838
$146$	3.68032	0.304585
$147$	−2.91646	−0.240546
$148$	−12.6309	−1.03825
$149$	−18.9859	−1.55538	−0.777691	−	0.628646i	$-0.783609\pi$
$149$	−18.9859	−1.55538	−0.777691	+	0.628646i	$0.783609\pi$
$150$	3.28341	0.268089
$151$	−14.7577	−1.20096	−0.600482	−	0.799638i	$-0.705025\pi$
$151$	−14.7577	−1.20096	−0.600482	+	0.799638i	$0.705025\pi$
$152$	−2.62442	−0.212869
$153$	−1.00000	−0.0808452
$154$	4.36666	0.351876
$155$	4.61879	0.370990
$156$	1.22479	0.0980619
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	11.0837	0.881775
$159$	−7.81555	−0.619813
$160$	17.9425	1.41848
$161$	−5.85794	−0.461671
$162$	0.751824	0.0590688
$163$	−11.2197	−0.878793	−0.439396	−	0.898293i	$-0.644808\pi$
$163$	−11.2197	−0.878793	−0.439396	+	0.898293i	$0.644808\pi$
$164$	−6.88552	−0.537669
$165$	−8.79674	−0.684825
$166$	2.15007	0.166877
$167$	10.9725	0.849075	0.424538	−	0.905410i	$-0.360437\pi$
$167$	10.9725	0.849075	0.424538	+	0.905410i	$0.360437\pi$
$168$	5.21832	0.402602
$169$	−12.2713	−0.943944
$170$	−2.30103	−0.176481
$171$	1.01630	0.0777183
$172$	0.205703	0.0156847
$173$	−2.30294	−0.175089	−0.0875447	−	0.996161i	$-0.527902\pi$
$173$	−2.30294	−0.175089	−0.0875447	+	0.996161i	$0.527902\pi$
$174$	−5.34915	−0.405518
$175$	−8.82525	−0.667126
$176$	−2.66743	−0.201065
$177$	−9.82923	−0.738811
$178$	−10.7773	−0.807790
$179$	25.8243	1.93020	0.965101	−	0.261879i	$-0.0843420\pi$
$179$	25.8243	1.93020	0.965101	+	0.261879i	$0.0843420\pi$
$180$	−4.39123	−0.327303
$181$	−15.4193	−1.14611	−0.573053	−	0.819518i	$-0.694241\pi$
$181$	−15.4193	−1.14611	−0.573053	+	0.819518i	$0.694241\pi$
$182$	1.29693	0.0961349
$183$	−8.44330	−0.624146
$184$	−7.48582	−0.551862
$185$	26.9439	1.98096
$186$	1.13459	0.0831919
$187$	2.87419	0.210182
$188$	10.0249	0.731141
$189$	−2.02078	−0.146990
$190$	2.33853	0.169655
$191$	−15.4712	−1.11945	−0.559727	−	0.828677i	$-0.689094\pi$
$191$	−15.4712	−1.11945	−0.559727	+	0.828677i	$0.689094\pi$
$192$	2.55137	0.184129
$193$	1.92958	0.138894	0.0694471	−	0.997586i	$-0.477877\pi$
$193$	1.92958	0.138894	0.0694471	+	0.997586i	$0.477877\pi$
$194$	8.31329	0.596859
$195$	−2.61270	−0.187099
$196$	4.18443	0.298888
$197$	25.7976	1.83800	0.919002	−	0.394252i	$-0.128996\pi$
$197$	25.7976	1.83800	0.919002	+	0.394252i	$0.128996\pi$
$198$	−2.16088	−0.153567
$199$	13.7262	0.973028	0.486514	−	0.873673i	$-0.338268\pi$
$199$	13.7262	0.973028	0.486514	+	0.873673i	$0.338268\pi$
$200$	−11.2777	−0.797455
$201$	−0.210466	−0.0148451
$202$	−6.66827	−0.469178
$203$	14.3776	1.00911
$204$	1.43476	0.100453
$205$	14.6880	1.02586
$206$	−12.4419	−0.866868
$207$	2.89886	0.201485
$208$	−0.792246	−0.0549324
$209$	−2.92103	−0.202052
$210$	−4.64987	−0.320871
$211$	−15.1204	−1.04093	−0.520466	−	0.853882i	$-0.674242\pi$
$211$	−15.1204	−1.04093	−0.520466	+	0.853882i	$0.674242\pi$
$212$	11.2134	0.770143
$213$	−4.66633	−0.319732
$214$	−5.27217	−0.360398
$215$	−0.438801	−0.0299260
$216$	−2.58233	−0.175706
$217$	−3.04958	−0.207019
$218$	−9.63476	−0.652549
$219$	4.89518	0.330786
$220$	12.6212	0.850922
$221$	0.853656	0.0574231
$222$	6.61866	0.444216
$223$	4.57697	0.306496	0.153248	−	0.988188i	$-0.451027\pi$
$223$	4.57697	0.306496	0.153248	+	0.988188i	$0.451027\pi$
$224$	−11.8466	−0.791535
$225$	4.36726	0.291151
$226$	−1.15683	−0.0769510
$227$	−12.2361	−0.812137	−0.406069	−	0.913843i	$-0.633101\pi$
$227$	−12.2361	−0.812137	−0.406069	+	0.913843i	$0.633101\pi$
$228$	−1.45815	−0.0965681
$229$	−18.7988	−1.24226	−0.621129	−	0.783708i	$-0.713326\pi$
$229$	−18.7988	−1.24226	−0.621129	+	0.783708i	$0.713326\pi$
$230$	6.67036	0.439830
$231$	5.80809	0.382144
$232$	18.3730	1.20625
$233$	−0.383971	−0.0251548	−0.0125774	−	0.999921i	$-0.504004\pi$
$233$	−0.383971	−0.0251548	−0.0125774	+	0.999921i	$0.504004\pi$
$234$	−0.641799	−0.0419557
$235$	−21.3849	−1.39500
$236$	14.1026	0.918001
$237$	14.7425	0.957627
$238$	1.51927	0.0984795
$239$	3.09443	0.200162	0.100081	−	0.994979i	$-0.468090\pi$
$239$	3.09443	0.200162	0.100081	+	0.994979i	$0.468090\pi$
$240$	2.84043	0.183349
$241$	−15.0686	−0.970654	−0.485327	−	0.874333i	$-0.661300\pi$
$241$	−15.0686	−0.970654	−0.485327	+	0.874333i	$0.661300\pi$
$242$	−2.05927	−0.132375
$243$	1.00000	0.0641500
$244$	12.1141	0.775527
$245$	−8.92612	−0.570269
$246$	3.60806	0.230041
$247$	−0.867569	−0.0552021
$248$	−3.89703	−0.247462
$249$	2.85980	0.181233
$250$	−1.45596	−0.0920829
$251$	26.3654	1.66417	0.832083	−	0.554651i	$-0.187148\pi$
$251$	26.3654	1.66417	0.832083	+	0.554651i	$0.187148\pi$
$252$	2.89933	0.182641
$253$	−8.33187	−0.523820
$254$	6.04588	0.379352
$255$	−3.06060	−0.191662
$256$	−12.4756	−0.779725
$257$	−11.1381	−0.694776	−0.347388	−	0.937721i	$-0.612931\pi$
$257$	−11.1381	−0.694776	−0.347388	+	0.937721i	$0.612931\pi$
$258$	−0.107790	−0.00671070
$259$	−17.7899	−1.10541
$260$	3.74860	0.232478
$261$	−7.11490	−0.440401
$262$	−13.5647	−0.838032
$263$	9.87268	0.608776	0.304388	−	0.952548i	$-0.401548\pi$
$263$	9.87268	0.608776	0.304388	+	0.952548i	$0.401548\pi$
$264$	7.42212	0.456800
$265$	−23.9203	−1.46941
$266$	−1.54403	−0.0946705
$267$	−14.3348	−0.877278
$268$	0.301969	0.0184457
$269$	21.1237	1.28794	0.643968	−	0.765053i	$-0.277287\pi$
$269$	21.1237	1.28794	0.643968	+	0.765053i	$0.277287\pi$
$270$	2.30103	0.140036
$271$	19.6114	1.19131	0.595653	−	0.803242i	$-0.296893\pi$
$271$	19.6114	1.19131	0.595653	+	0.803242i	$0.296893\pi$
$272$	−0.928063	−0.0562721
$273$	1.72505	0.104405
$274$	−12.8760	−0.777869
$275$	−12.5523	−0.756934
$276$	−4.15917	−0.250353
$277$	5.34480	0.321138	0.160569	−	0.987025i	$-0.448667\pi$
$277$	5.34480	0.321138	0.160569	+	0.987025i	$0.448667\pi$
$278$	5.68785	0.341135
$279$	1.50911	0.0903482
$280$	15.9712	0.954460
$281$	11.3948	0.679759	0.339879	−	0.940469i	$-0.389614\pi$
$281$	11.3948	0.679759	0.339879	+	0.940469i	$0.389614\pi$
$282$	−5.25311	−0.312818
$283$	17.5218	1.04156	0.520781	−	0.853690i	$-0.325641\pi$
$283$	17.5218	1.04156	0.520781	+	0.853690i	$0.325641\pi$
$284$	6.69507	0.397280
$285$	3.11048	0.184249
$286$	1.84465	0.109076
$287$	−9.69785	−0.572446
$288$	5.86241	0.345446
$289$	1.00000	0.0588235
$290$	−16.3716	−0.961373
$291$	11.0575	0.648202
$292$	−7.02342	−0.411015
$293$	−23.2569	−1.35868	−0.679342	−	0.733822i	$-0.737735\pi$
$293$	−23.2569	−1.35868	−0.679342	+	0.733822i	$0.737735\pi$
$294$	−2.19267	−0.127879
$295$	−30.0833	−1.75152
$296$	−22.7335	−1.32136
$297$	−2.87419	−0.166777
$298$	−14.2740	−0.826872
$299$	−2.47463	−0.143111
$300$	−6.26597	−0.361766
$301$	0.289721	0.0166992
$302$	−11.0952	−0.638456
$303$	−8.86946	−0.509537
$304$	0.943189	0.0540956
$305$	−25.8415	−1.47968
$306$	−0.751824	−0.0429789
$307$	−14.5309	−0.829320	−0.414660	−	0.909976i	$-0.636099\pi$
$307$	−14.5309	−0.829320	−0.414660	+	0.909976i	$0.636099\pi$
$308$	−8.33323	−0.474830
$309$	−16.5490	−0.941438
$310$	3.47251	0.197225
$311$	8.72286	0.494628	0.247314	−	0.968935i	$-0.420452\pi$
$311$	8.72286	0.494628	0.247314	+	0.968935i	$0.420452\pi$
$312$	2.20442	0.124801
$313$	−2.16307	−0.122264	−0.0611319	−	0.998130i	$-0.519471\pi$
$313$	−2.16307	−0.122264	−0.0611319	+	0.998130i	$0.519471\pi$
$314$	0.751824	0.0424279
$315$	−6.18478	−0.348473
$316$	−21.1519	−1.18989
$317$	23.8411	1.33905	0.669525	−	0.742790i	$-0.266498\pi$
$317$	23.8411	1.33905	0.669525	+	0.742790i	$0.266498\pi$
$318$	−5.87591	−0.329505
$319$	20.4496	1.14496
$320$	7.80872	0.436521
$321$	−7.01251	−0.391400
$322$	−4.40414	−0.245433
$323$	−1.01630	−0.0565484
$324$	−1.43476	−0.0797090
$325$	−3.72813	−0.206800
$326$	−8.43521	−0.467183
$327$	−12.8152	−0.708682
$328$	−12.3928	−0.684279
$329$	14.1195	0.778432
$330$	−6.61359	−0.364066
$331$	14.2207	0.781638	0.390819	−	0.920468i	$-0.372192\pi$
$331$	14.2207	0.781638	0.390819	+	0.920468i	$0.372192\pi$
$332$	−4.10313	−0.225189
$333$	8.80348	0.482428
$334$	8.24936	0.451385
$335$	−0.644152	−0.0351938
$336$	−1.87541	−0.102312
$337$	−12.6902	−0.691277	−0.345639	−	0.938368i	$-0.612338\pi$
$337$	−12.6902	−0.691277	−0.345639	+	0.938368i	$0.612338\pi$
$338$	−9.22583	−0.501819
$339$	−1.53869	−0.0835704
$340$	4.39123	0.238148
$341$	−4.33748	−0.234887
$342$	0.764077	0.0413166
$343$	20.0390	1.08200
$344$	0.370232	0.0199616
$345$	8.87224	0.477665
$346$	−1.73141	−0.0930809
$347$	20.6787	1.11009	0.555046	−	0.831819i	$-0.312701\pi$
$347$	20.6787	1.11009	0.555046	+	0.831819i	$0.312701\pi$
$348$	10.2082	0.547216
$349$	32.4140	1.73508	0.867540	−	0.497367i	$-0.165700\pi$
$349$	32.4140	1.73508	0.867540	+	0.497367i	$0.165700\pi$
$350$	−6.63503	−0.354657
$351$	−0.853656	−0.0455648
$352$	−16.8497	−0.898090
$353$	1.31973	0.0702419	0.0351210	−	0.999383i	$-0.488818\pi$
$353$	1.31973	0.0702419	0.0351210	+	0.999383i	$0.488818\pi$
$354$	−7.38985	−0.392766
$355$	−14.2818	−0.757997
$356$	20.5671	1.09005
$357$	2.02078	0.106951
$358$	19.4153	1.02613
$359$	15.0592	0.794793	0.397397	−	0.917647i	$-0.369914\pi$
$359$	15.0592	0.794793	0.397397	+	0.917647i	$0.369914\pi$
$360$	−7.90349	−0.416550
$361$	−17.9671	−0.945639
$362$	−11.5926	−0.609292
$363$	−2.73904	−0.143762
$364$	−2.47503	−0.129727
$365$	14.9822	0.784204
$366$	−6.34787	−0.331808
$367$	−28.1666	−1.47028	−0.735142	−	0.677913i	$-0.762885\pi$
$367$	−28.1666	−1.47028	−0.735142	+	0.677913i	$0.762885\pi$
$368$	2.69032	0.140243
$369$	4.79907	0.249830
$370$	20.2571	1.05311
$371$	15.7935	0.819957
$372$	−2.16522	−0.112261
$373$	7.41684	0.384029	0.192015	−	0.981392i	$-0.438498\pi$
$373$	7.41684	0.384029	0.192015	+	0.981392i	$0.438498\pi$
$374$	2.16088	0.111737
$375$	−1.93657	−0.100004
$376$	18.0432	0.930506
$377$	6.07367	0.312810
$378$	−1.51927	−0.0781427
$379$	13.0462	0.670136	0.335068	−	0.942194i	$-0.391241\pi$
$379$	13.0462	0.670136	0.335068	+	0.942194i	$0.391241\pi$
$380$	−4.46280	−0.228937
$381$	8.04162	0.411985
$382$	−11.6316	−0.595124
$383$	25.6727	1.31181	0.655907	−	0.754842i	$-0.272286\pi$
$383$	25.6727	1.31181	0.655907	+	0.754842i	$0.272286\pi$
$384$	−9.80664	−0.500443
$385$	17.7762	0.905961
$386$	1.45070	0.0738388
$387$	−0.143371	−0.00728796
$388$	−15.8649	−0.805417
$389$	−25.2878	−1.28214	−0.641070	−	0.767482i	$-0.721509\pi$
$389$	−25.2878	−1.28214	−0.641070	+	0.767482i	$0.721509\pi$
$390$	−1.96429	−0.0994655
$391$	−2.89886	−0.146602
$392$	7.53128	0.380387
$393$	−18.0424	−0.910121
$394$	19.3953	0.977119
$395$	45.1208	2.27027
$396$	4.12378	0.207228
$397$	8.37457	0.420308	0.210154	−	0.977668i	$-0.432604\pi$
$397$	8.37457	0.420308	0.210154	+	0.977668i	$0.432604\pi$
$398$	10.3197	0.517281
$399$	−2.05371	−0.102814
$400$	4.05309	0.202654
$401$	−21.8688	−1.09207	−0.546037	−	0.837761i	$-0.683864\pi$
$401$	−21.8688	−1.09207	−0.546037	+	0.837761i	$0.683864\pi$
$402$	−0.158233	−0.00789196
$403$	−1.28826	−0.0641729
$404$	12.7256	0.633120
$405$	3.06060	0.152082
$406$	10.8094	0.536463
$407$	−25.3029	−1.25422
$408$	2.58233	0.127845
$409$	−16.1805	−0.800076	−0.400038	−	0.916499i	$-0.631003\pi$
$409$	−16.1805	−0.800076	−0.400038	+	0.916499i	$0.631003\pi$
$410$	11.0428	0.545365
$411$	−17.1264	−0.844783
$412$	23.7438	1.16977
$413$	19.8627	0.977379
$414$	2.17943	0.107113
$415$	8.75270	0.429653
$416$	−5.00448	−0.245365
$417$	7.56541	0.370480
$418$	−2.19610	−0.107415
$419$	−26.4661	−1.29295	−0.646476	−	0.762934i	$-0.723758\pi$
$419$	−26.4661	−1.29295	−0.646476	+	0.762934i	$0.723758\pi$
$420$	8.87369	0.432992
$421$	−17.0950	−0.833160	−0.416580	−	0.909099i	$-0.636771\pi$
$421$	−17.0950	−0.833160	−0.416580	+	0.909099i	$0.636771\pi$
$422$	−11.3679	−0.553380
$423$	−6.98716	−0.339727
$424$	20.1824	0.980142
$425$	−4.36726	−0.211843
$426$	−3.50826	−0.169976
$427$	17.0620	0.825689
$428$	10.0613	0.486330
$429$	2.45357	0.118459
$430$	−0.329901	−0.0159092
$431$	−0.112786	−0.00543270	−0.00271635	−	0.999996i	$-0.500865\pi$
$431$	−0.112786	−0.00543270	−0.00271635	+	0.999996i	$0.500865\pi$
$432$	0.928063	0.0446514
$433$	19.1178	0.918744	0.459372	−	0.888244i	$-0.348075\pi$
$433$	19.1178	0.918744	0.459372	+	0.888244i	$0.348075\pi$
$434$	−2.29275	−0.110055
$435$	−21.7758	−1.04407
$436$	18.3867	0.880565
$437$	2.94611	0.140931
$438$	3.68032	0.175852
$439$	10.6889	0.510155	0.255078	−	0.966921i	$-0.417899\pi$
$439$	10.6889	0.510155	0.255078	+	0.966921i	$0.417899\pi$
$440$	22.7161	1.08295
$441$	−2.91646	−0.138879
$442$	0.641799	0.0305272
$443$	−18.4793	−0.877979	−0.438990	−	0.898492i	$-0.644664\pi$
$443$	−18.4793	−0.877979	−0.438990	+	0.898492i	$0.644664\pi$
$444$	−12.6309	−0.599436
$445$	−43.8732	−2.07979
$446$	3.44107	0.162939
$447$	−18.9859	−0.898001
$448$	−5.15575	−0.243586
$449$	1.83557	0.0866259	0.0433130	−	0.999062i	$-0.486209\pi$
$449$	1.83557	0.0866259	0.0433130	+	0.999062i	$0.486209\pi$
$450$	3.28341	0.154781
$451$	−13.7934	−0.649508
$452$	2.20766	0.103840
$453$	−14.7577	−0.693377
$454$	−9.19937	−0.431748
$455$	5.27968	0.247515
$456$	−2.62442	−0.122900
$457$	10.1289	0.473811	0.236905	−	0.971533i	$-0.423867\pi$
$457$	10.1289	0.473811	0.236905	+	0.971533i	$0.423867\pi$
$458$	−14.1334	−0.660409
$459$	−1.00000	−0.0466760
$460$	−12.7295	−0.593518
$461$	26.6053	1.23913	0.619565	−	0.784945i	$-0.287309\pi$
$461$	26.6053	1.23913	0.619565	+	0.784945i	$0.287309\pi$
$462$	4.36666	0.203155
$463$	−21.5160	−0.999932	−0.499966	−	0.866045i	$-0.666654\pi$
$463$	−21.5160	−0.999932	−0.499966	+	0.866045i	$0.666654\pi$
$464$	−6.60307	−0.306540
$465$	4.61879	0.214191
$466$	−0.288678	−0.0133728
$467$	40.6119	1.87930	0.939648	−	0.342142i	$-0.111152\pi$
$467$	40.6119	1.87930	0.939648	+	0.342142i	$0.111152\pi$
$468$	1.22479	0.0566160
$469$	0.425305	0.0196388
$470$	−16.0777	−0.741607
$471$	1.00000	0.0460776
$472$	25.3824	1.16832
$473$	0.412076	0.0189473
$474$	11.0837	0.509093
$475$	4.43844	0.203650
$476$	−2.89933	−0.132891
$477$	−7.81555	−0.357849
$478$	2.32646	0.106410
$479$	−31.9712	−1.46080	−0.730401	−	0.683019i	$-0.760667\pi$
$479$	−31.9712	−1.46080	−0.730401	+	0.683019i	$0.760667\pi$
$480$	17.9425	0.818958
$481$	−7.51514	−0.342661
$482$	−11.3289	−0.516019
$483$	−5.85794	−0.266546
$484$	3.92986	0.178630
$485$	33.8425	1.53671
$486$	0.751824	0.0341034
$487$	10.0548	0.455625	0.227812	−	0.973705i	$-0.426843\pi$
$487$	10.0548	0.455625	0.227812	+	0.973705i	$0.426843\pi$
$488$	21.8034	0.986994
$489$	−11.2197	−0.507371
$490$	−6.71087	−0.303166
$491$	−41.8781	−1.88993	−0.944966	−	0.327168i	$-0.893906\pi$
$491$	−41.8781	−1.88993	−0.944966	+	0.327168i	$0.893906\pi$
$492$	−6.88552	−0.310423
$493$	7.11490	0.320439
$494$	−0.652259	−0.0293465
$495$	−8.79674	−0.395384
$496$	1.40055	0.0628866
$497$	9.42961	0.422976
$498$	2.15007	0.0963468
$499$	−0.922947	−0.0413168	−0.0206584	−	0.999787i	$-0.506576\pi$
$499$	−0.922947	−0.0413168	−0.0206584	+	0.999787i	$0.506576\pi$
$500$	2.77852	0.124259
$501$	10.9725	0.490214
$502$	19.8221	0.884703
$503$	4.32910	0.193025	0.0965126	−	0.995332i	$-0.469231\pi$
$503$	4.32910	0.193025	0.0965126	+	0.995332i	$0.469231\pi$
$504$	5.21832	0.232442
$505$	−27.1459	−1.20797
$506$	−6.26409	−0.278473
$507$	−12.2713	−0.544986
$508$	−11.5378	−0.511908
$509$	−10.0863	−0.447069	−0.223535	−	0.974696i	$-0.571760\pi$
$509$	−10.0863	−0.447069	−0.223535	+	0.974696i	$0.571760\pi$
$510$	−2.30103	−0.101891
$511$	−9.89207	−0.437600
$512$	10.2338	0.452275
$513$	1.01630	0.0448707
$514$	−8.37389	−0.369357
$515$	−50.6497	−2.23189
$516$	0.205703	0.00905559
$517$	20.0824	0.883224
$518$	−13.3748	−0.587657
$519$	−2.30294	−0.101088
$520$	6.74686	0.295869
$521$	−26.0480	−1.14118	−0.570591	−	0.821235i	$-0.693286\pi$
$521$	−26.0480	−1.14118	−0.570591	+	0.821235i	$0.693286\pi$
$522$	−5.34915	−0.234126
$523$	14.5362	0.635625	0.317812	−	0.948154i	$-0.397052\pi$
$523$	14.5362	0.635625	0.317812	+	0.948154i	$0.397052\pi$
$524$	25.8866	1.13086
$525$	−8.82525	−0.385166
$526$	7.42252	0.323637
$527$	−1.50911	−0.0657380
$528$	−2.66743	−0.116085
$529$	−14.5966	−0.634636
$530$	−17.9838	−0.781167
$531$	−9.82923	−0.426552
$532$	2.94659	0.127751
$533$	−4.09676	−0.177450
$534$	−10.7773	−0.466378
$535$	−21.4625	−0.927904
$536$	0.543494	0.0234754
$537$	25.8243	1.11440
$538$	15.8813	0.684692
$539$	8.38247	0.361058
$540$	−4.39123	−0.188968
$541$	34.6129	1.48813	0.744063	−	0.668110i	$-0.232896\pi$
$541$	34.6129	1.48813	0.744063	+	0.668110i	$0.232896\pi$
$542$	14.7443	0.633321
$543$	−15.4193	−0.661704
$544$	−5.86241	−0.251349
$545$	−39.2221	−1.68009
$546$	1.29693	0.0555035
$547$	−2.33926	−0.100020	−0.0500098	−	0.998749i	$-0.515925\pi$
$547$	−2.33926	−0.100020	−0.0500098	+	0.998749i	$0.515925\pi$
$548$	24.5723	1.04968
$549$	−8.44330	−0.360351
$550$	−9.43713	−0.402401
$551$	−7.23086	−0.308045
$552$	−7.48582	−0.318618
$553$	−29.7913	−1.26685
$554$	4.01835	0.170723
$555$	26.9439	1.14371
$556$	−10.8546	−0.460336
$557$	−15.0977	−0.639711	−0.319855	−	0.947466i	$-0.603634\pi$
$557$	−15.0977	−0.639711	−0.319855	+	0.947466i	$0.603634\pi$
$558$	1.13459	0.0480309
$559$	0.122390	0.00517653
$560$	−5.73987	−0.242554
$561$	2.87419	0.121348
$562$	8.56690	0.361373
$563$	20.9076	0.881150	0.440575	−	0.897716i	$-0.354775\pi$
$563$	20.9076	0.881150	0.440575	+	0.897716i	$0.354775\pi$
$564$	10.0249	0.422125
$565$	−4.70933	−0.198123
$566$	13.1733	0.553715
$567$	−2.02078	−0.0848646
$568$	12.0500	0.505608
$569$	32.0864	1.34513	0.672566	−	0.740037i	$-0.265192\pi$
$569$	32.0864	1.34513	0.672566	+	0.740037i	$0.265192\pi$
$570$	2.33853	0.0979504
$571$	−15.3995	−0.644449	−0.322225	−	0.946663i	$-0.604431\pi$
$571$	−15.3995	−0.644449	−0.322225	+	0.946663i	$0.604431\pi$
$572$	−3.52028	−0.147191
$573$	−15.4712	−0.646317
$574$	−7.29107	−0.304324
$575$	12.6601	0.527961
$576$	2.55137	0.106307
$577$	38.3801	1.59778	0.798892	−	0.601474i	$-0.205420\pi$
$577$	38.3801	1.59778	0.798892	+	0.601474i	$0.205420\pi$
$578$	0.751824	0.0312717
$579$	1.92958	0.0801906
$580$	31.2431	1.29730
$581$	−5.77902	−0.239754
$582$	8.31329	0.344597
$583$	22.4634	0.930338
$584$	−12.6410	−0.523088
$585$	−2.61270	−0.108022
$586$	−17.4851	−0.722303
$587$	−26.6605	−1.10040	−0.550198	−	0.835034i	$-0.685448\pi$
$587$	−26.6605	−1.10040	−0.550198	+	0.835034i	$0.685448\pi$
$588$	4.18443	0.172563
$589$	1.53371	0.0631954
$590$	−22.6174	−0.931142
$591$	25.7976	1.06117
$592$	8.17018	0.335792
$593$	−8.89584	−0.365308	−0.182654	−	0.983177i	$-0.558469\pi$
$593$	−8.89584	−0.365308	−0.182654	+	0.983177i	$0.558469\pi$
$594$	−2.16088	−0.0886621
$595$	6.18478	0.253551
$596$	27.2402	1.11580
$597$	13.7262	0.561778
$598$	−1.86048	−0.0760808
$599$	−17.6084	−0.719461	−0.359731	−	0.933056i	$-0.617131\pi$
$599$	−17.6084	−0.719461	−0.359731	+	0.933056i	$0.617131\pi$
$600$	−11.2777	−0.460411
$601$	30.6700	1.25106	0.625528	−	0.780202i	$-0.284884\pi$
$601$	30.6700	1.25106	0.625528	+	0.780202i	$0.284884\pi$
$602$	0.217819	0.00887764
$603$	−0.210466	−0.00857084
$604$	21.1738	0.861549
$605$	−8.38309	−0.340821
$606$	−6.66827	−0.270880
$607$	18.0284	0.731749	0.365874	−	0.930664i	$-0.380770\pi$
$607$	18.0284	0.731749	0.365874	+	0.930664i	$0.380770\pi$
$608$	5.95796	0.241627
$609$	14.3776	0.582610
$610$	−19.4283	−0.786628
$611$	5.96463	0.241303
$612$	1.43476	0.0579968
$613$	16.7268	0.675588	0.337794	−	0.941220i	$-0.390319\pi$
$613$	16.7268	0.675588	0.337794	+	0.941220i	$0.390319\pi$
$614$	−10.9246	−0.440883
$615$	14.6880	0.592279
$616$	−14.9984	−0.604304
$617$	43.9538	1.76951	0.884757	−	0.466052i	$-0.154324\pi$
$617$	43.9538	1.76951	0.884757	+	0.466052i	$0.154324\pi$
$618$	−12.4419	−0.500487
$619$	−6.86592	−0.275965	−0.137982	−	0.990435i	$-0.544062\pi$
$619$	−6.86592	−0.275965	−0.137982	+	0.990435i	$0.544062\pi$
$620$	−6.62686	−0.266141
$621$	2.89886	0.116327
$622$	6.55805	0.262954
$623$	28.9675	1.16056
$624$	−0.792246	−0.0317152
$625$	−27.7633	−1.11053
$626$	−1.62624	−0.0649978
$627$	−2.92103	−0.116655
$628$	−1.43476	−0.0572532
$629$	−8.80348	−0.351018
$630$	−4.64987	−0.185255
$631$	−3.02352	−0.120364	−0.0601822	−	0.998187i	$-0.519168\pi$
$631$	−3.02352	−0.120364	−0.0601822	+	0.998187i	$0.519168\pi$
$632$	−38.0700	−1.51434
$633$	−15.1204	−0.600982
$634$	17.9243	0.711865
$635$	24.6122	0.976704
$636$	11.2134	0.444642
$637$	2.48966	0.0986437
$638$	15.3745	0.608681
$639$	−4.66633	−0.184597
$640$	−30.0142	−1.18641
$641$	−23.6079	−0.932455	−0.466228	−	0.884665i	$-0.654387\pi$
$641$	−23.6079	−0.932455	−0.466228	+	0.884665i	$0.654387\pi$
$642$	−5.27217	−0.208076
$643$	10.5165	0.414729	0.207365	−	0.978264i	$-0.433511\pi$
$643$	10.5165	0.414729	0.207365	+	0.978264i	$0.433511\pi$
$644$	8.40475	0.331194
$645$	−0.438801	−0.0172778
$646$	−0.764077	−0.0300622
$647$	−12.8500	−0.505185	−0.252592	−	0.967573i	$-0.581283\pi$
$647$	−12.8500	−0.505185	−0.252592	+	0.967573i	$0.581283\pi$
$648$	−2.58233	−0.101444
$649$	28.2511	1.10895
$650$	−2.80290	−0.109939
$651$	−3.04958	−0.119522
$652$	16.0976	0.630429
$653$	36.2697	1.41934	0.709671	−	0.704534i	$-0.248844\pi$
$653$	36.2697	1.41934	0.709671	+	0.704534i	$0.248844\pi$
$654$	−9.63476	−0.376749
$655$	−55.2207	−2.15765
$656$	4.45384	0.173893
$657$	4.89518	0.190979
$658$	10.6154	0.413830
$659$	27.0551	1.05392	0.526959	−	0.849891i	$-0.323332\pi$
$659$	27.0551	1.05392	0.526959	+	0.849891i	$0.323332\pi$
$660$	12.6212	0.491280
$661$	−32.8042	−1.27593	−0.637967	−	0.770063i	$-0.720224\pi$
$661$	−32.8042	−1.27593	−0.637967	+	0.770063i	$0.720224\pi$
$662$	10.6914	0.415534
$663$	0.853656	0.0331532
$664$	−7.38496	−0.286592
$665$	−6.28559	−0.243745
$666$	6.61866	0.256468
$667$	−20.6251	−0.798606
$668$	−15.7429	−0.609110
$669$	4.57697	0.176956
$670$	−0.484289	−0.0187097
$671$	24.2676	0.936842
$672$	−11.8466	−0.456993
$673$	13.7099	0.528478	0.264239	−	0.964457i	$-0.414879\pi$
$673$	13.7099	0.528478	0.264239	+	0.964457i	$0.414879\pi$
$674$	−9.54076	−0.367497
$675$	4.36726	0.168096
$676$	17.6063	0.677167
$677$	39.3539	1.51249	0.756247	−	0.654286i	$-0.227031\pi$
$677$	39.3539	1.51249	0.756247	+	0.654286i	$0.227031\pi$
$678$	−1.15683	−0.0444277
$679$	−22.3447	−0.857512
$680$	7.90349	0.303085
$681$	−12.2361	−0.468888
$682$	−3.26102	−0.124871
$683$	−9.69517	−0.370975	−0.185488	−	0.982647i	$-0.559386\pi$
$683$	−9.69517	−0.370975	−0.185488	+	0.982647i	$0.559386\pi$
$684$	−1.45815	−0.0557536
$685$	−52.4170	−2.00275
$686$	15.0658	0.575213
$687$	−18.7988	−0.717218
$688$	−0.133057	−0.00507277
$689$	6.67179	0.254175
$690$	6.67036	0.253936
$691$	−3.36504	−0.128012	−0.0640060	−	0.997950i	$-0.520388\pi$
$691$	−3.36504	−0.128012	−0.0640060	+	0.997950i	$0.520388\pi$
$692$	3.30417	0.125606
$693$	5.80809	0.220631
$694$	15.5468	0.590147
$695$	23.1547	0.878307
$696$	18.3730	0.696428
$697$	−4.79907	−0.181778
$698$	24.3696	0.922403
$699$	−0.383971	−0.0145231
$700$	12.6621	0.478583
$701$	−38.0574	−1.43741	−0.718704	−	0.695316i	$-0.755264\pi$
$701$	−38.0574	−1.43741	−0.718704	+	0.695316i	$0.755264\pi$
$702$	−0.641799	−0.0242231
$703$	8.94697	0.337441
$704$	−7.33312	−0.276377
$705$	−21.3849	−0.805401
$706$	0.992201	0.0373420
$707$	17.9232	0.674071
$708$	14.1026	0.530008
$709$	−48.8365	−1.83409	−0.917046	−	0.398782i	$-0.869433\pi$
$709$	−48.8365	−1.83409	−0.917046	+	0.398782i	$0.869433\pi$
$710$	−10.7374	−0.402966
$711$	14.7425	0.552886
$712$	37.0173	1.38728
$713$	4.37470	0.163834
$714$	1.51927	0.0568571
$715$	7.50938	0.280835
$716$	−37.0518	−1.38469
$717$	3.09443	0.115564
$718$	11.3218	0.422528
$719$	44.2936	1.65187	0.825936	−	0.563764i	$-0.190647\pi$
$719$	44.2936	1.65187	0.825936	+	0.563764i	$0.190647\pi$
$720$	2.84043	0.105856
$721$	33.4418	1.24544
$722$	−13.5081	−0.502720
$723$	−15.0686	−0.560408
$724$	22.1230	0.822194
$725$	−31.0726	−1.15401
$726$	−2.05927	−0.0764268
$727$	−47.8295	−1.77390	−0.886950	−	0.461866i	$-0.847180\pi$
$727$	−47.8295	−1.77390	−0.886950	+	0.461866i	$0.847180\pi$
$728$	−4.45465	−0.165100
$729$	1.00000	0.0370370
$730$	11.2640	0.416898
$731$	0.143371	0.00530277
$732$	12.1141	0.447751
$733$	−33.2681	−1.22878	−0.614392	−	0.789001i	$-0.710599\pi$
$733$	−33.2681	−1.22878	−0.614392	+	0.789001i	$0.710599\pi$
$734$	−21.1763	−0.781632
$735$	−8.92612	−0.329245
$736$	16.9943	0.626418
$737$	0.604919	0.0222825
$738$	3.60806	0.132814
$739$	6.69262	0.246192	0.123096	−	0.992395i	$-0.460718\pi$
$739$	6.69262	0.246192	0.123096	+	0.992395i	$0.460718\pi$
$740$	−38.6581	−1.42110
$741$	−0.867569	−0.0318710
$742$	11.8739	0.435905
$743$	−43.5418	−1.59739	−0.798697	−	0.601733i	$-0.794477\pi$
$743$	−43.5418	−1.59739	−0.798697	+	0.601733i	$0.794477\pi$
$744$	−3.89703	−0.142872
$745$	−58.1081	−2.12892
$746$	5.57615	0.204157
$747$	2.85980	0.104635
$748$	−4.12378	−0.150780
$749$	14.1707	0.517787
$750$	−1.45596	−0.0531641
$751$	1.41177	0.0515162	0.0257581	−	0.999668i	$-0.491800\pi$
$751$	1.41177	0.0515162	0.0257581	+	0.999668i	$0.491800\pi$
$752$	−6.48452	−0.236466
$753$	26.3654	0.960807
$754$	4.56633	0.166296
$755$	−45.1674	−1.64381
$756$	2.89933	0.105448
$757$	−2.95780	−0.107503	−0.0537516	−	0.998554i	$-0.517118\pi$
$757$	−2.95780	−0.107503	−0.0537516	+	0.998554i	$0.517118\pi$
$758$	9.80841	0.356257
$759$	−8.33187	−0.302428
$760$	−8.03230	−0.291362
$761$	17.3738	0.629798	0.314899	−	0.949125i	$-0.398029\pi$
$761$	17.3738	0.629798	0.314899	+	0.949125i	$0.398029\pi$
$762$	6.04588	0.219019
$763$	25.8966	0.937521
$764$	22.1974	0.803075
$765$	−3.06060	−0.110656
$766$	19.3013	0.697386
$767$	8.39078	0.302974
$768$	−12.4756	−0.450175
$769$	−12.3801	−0.446438	−0.223219	−	0.974768i	$-0.571656\pi$
$769$	−12.3801	−0.446438	−0.223219	+	0.974768i	$0.571656\pi$
$770$	13.3646	0.481626
$771$	−11.1381	−0.401129
$772$	−2.76848	−0.0996400
$773$	7.23875	0.260360	0.130180	−	0.991490i	$-0.458445\pi$
$773$	7.23875	0.260360	0.130180	+	0.991490i	$0.458445\pi$
$774$	−0.107790	−0.00387442
$775$	6.59068	0.236744
$776$	−28.5542	−1.02503
$777$	−17.7899	−0.638208
$778$	−19.0119	−0.681611
$779$	4.87729	0.174747
$780$	3.74860	0.134221
$781$	13.4119	0.479916
$782$	−2.17943	−0.0779363
$783$	−7.11490	−0.254266
$784$	−2.70666	−0.0966665
$785$	3.06060	0.109237
$786$	−13.5647	−0.483838
$787$	5.70181	0.203248	0.101624	−	0.994823i	$-0.467596\pi$
$787$	5.70181	0.203248	0.101624	+	0.994823i	$0.467596\pi$
$788$	−37.0134	−1.31855
$789$	9.87268	0.351477
$790$	33.9229	1.20692
$791$	3.10936	0.110556
$792$	7.42212	0.263733
$793$	7.20767	0.255952
$794$	6.29620	0.223444
$795$	−23.9203	−0.848364
$796$	−19.6939	−0.698031
$797$	−30.4071	−1.07708	−0.538538	−	0.842602i	$-0.681023\pi$
$797$	−30.4071	−1.07708	−0.538538	+	0.842602i	$0.681023\pi$
$798$	−1.54403	−0.0546580
$799$	6.98716	0.247188
$800$	25.6026	0.905190
$801$	−14.3348	−0.506497
$802$	−16.4415	−0.580568
$803$	−14.0697	−0.496508
$804$	0.301969	0.0106496
$805$	−17.9288	−0.631908
$806$	−0.968546	−0.0341156
$807$	21.1237	0.743590
$808$	22.9039	0.805757
$809$	4.41526	0.155232	0.0776161	−	0.996983i	$-0.475269\pi$
$809$	4.41526	0.155232	0.0776161	+	0.996983i	$0.475269\pi$
$810$	2.30103	0.0808499
$811$	52.0026	1.82606	0.913030	−	0.407893i	$-0.133736\pi$
$811$	52.0026	1.82606	0.913030	+	0.407893i	$0.133736\pi$
$812$	−20.6284	−0.723917
$813$	19.6114	0.687801
$814$	−19.0233	−0.666766
$815$	−34.3389	−1.20284
$816$	−0.928063	−0.0324887
$817$	−0.145708	−0.00509767
$818$	−12.1649	−0.425336
$819$	1.72505	0.0602780
$820$	−21.0738	−0.735930
$821$	−53.0794	−1.85249	−0.926243	−	0.376928i	$-0.876980\pi$
$821$	−53.0794	−1.85249	−0.926243	+	0.376928i	$0.876980\pi$
$822$	−12.8760	−0.449103
$823$	21.6924	0.756150	0.378075	−	0.925775i	$-0.376586\pi$
$823$	21.6924	0.756150	0.378075	+	0.925775i	$0.376586\pi$
$824$	42.7350	1.48874
$825$	−12.5523	−0.437016
$826$	14.9332	0.519594
$827$	−29.6985	−1.03272	−0.516359	−	0.856372i	$-0.672713\pi$
$827$	−29.6985	−1.03272	−0.516359	+	0.856372i	$0.672713\pi$
$828$	−4.15917	−0.144541
$829$	43.3733	1.50642	0.753209	−	0.657781i	$-0.228505\pi$
$829$	43.3733	1.50642	0.753209	+	0.657781i	$0.228505\pi$
$830$	6.58049	0.228412
$831$	5.34480	0.185409
$832$	−2.17799	−0.0755083
$833$	2.91646	0.101049
$834$	5.68785	0.196954
$835$	33.5823	1.16216
$836$	4.19099	0.144948
$837$	1.50911	0.0521626
$838$	−19.8978	−0.687359
$839$	−13.8906	−0.479557	−0.239779	−	0.970828i	$-0.577075\pi$
$839$	−13.8906	−0.479557	−0.239779	+	0.970828i	$0.577075\pi$
$840$	15.9712	0.551058
$841$	21.6218	0.745578
$842$	−12.8524	−0.442924
$843$	11.3948	0.392459
$844$	21.6942	0.746745
$845$	−37.5574	−1.29201
$846$	−5.25311	−0.180606
$847$	5.53498	0.190184
$848$	−7.25332	−0.249080
$849$	17.5218	0.601346
$850$	−3.28341	−0.112620
$851$	25.5200	0.874816
$852$	6.69507	0.229369
$853$	21.0813	0.721810	0.360905	−	0.932603i	$-0.382468\pi$
$853$	21.0813	0.721810	0.360905	+	0.932603i	$0.382468\pi$
$854$	12.8276	0.438952
$855$	3.11048	0.106376
$856$	18.1087	0.618941
$857$	−25.1539	−0.859242	−0.429621	−	0.903009i	$-0.641353\pi$
$857$	−25.1539	−0.859242	−0.429621	+	0.903009i	$0.641353\pi$
$858$	1.84465	0.0629753
$859$	26.6151	0.908096	0.454048	−	0.890977i	$-0.349980\pi$
$859$	26.6151	0.908096	0.454048	+	0.890977i	$0.349980\pi$
$860$	0.629575	0.0214683
$861$	−9.69785	−0.330502
$862$	−0.0847950	−0.00288813
$863$	1.47149	0.0500901	0.0250450	−	0.999686i	$-0.492027\pi$
$863$	1.47149	0.0500901	0.0250450	+	0.999686i	$0.492027\pi$
$864$	5.86241	0.199443
$865$	−7.04838	−0.239652
$866$	14.3732	0.488422
$867$	1.00000	0.0339618
$868$	4.37542	0.148511
$869$	−42.3727	−1.43739
$870$	−16.3716	−0.555049
$871$	0.179666	0.00608774
$872$	33.0931	1.12067
$873$	11.0575	0.374240
$874$	2.21495	0.0749219
$875$	3.91337	0.132296
$876$	−7.02342	−0.237299
$877$	−49.4100	−1.66846	−0.834228	−	0.551420i	$-0.814086\pi$
$877$	−49.4100	−1.66846	−0.834228	+	0.551420i	$0.814086\pi$
$878$	8.03619	0.271208
$879$	−23.2569	−0.784436
$880$	−8.16392	−0.275206
$881$	−40.5718	−1.36690	−0.683449	−	0.729998i	$-0.739521\pi$
$881$	−40.5718	−1.36690	−0.683449	+	0.729998i	$0.739521\pi$
$882$	−2.19267	−0.0738309
$883$	48.6389	1.63683	0.818415	−	0.574627i	$-0.194853\pi$
$883$	48.6389	1.63683	0.818415	+	0.574627i	$0.194853\pi$
$884$	−1.22479	−0.0411942
$885$	−30.0833	−1.01124
$886$	−13.8932	−0.466751
$887$	−5.97463	−0.200609	−0.100304	−	0.994957i	$-0.531982\pi$
$887$	−5.97463	−0.200609	−0.100304	+	0.994957i	$0.531982\pi$
$888$	−22.7335	−0.762887
$889$	−16.2503	−0.545018
$890$	−32.9849	−1.10566
$891$	−2.87419	−0.0962890
$892$	−6.56685	−0.219875
$893$	−7.10104	−0.237627
$894$	−14.2740	−0.477395
$895$	79.0379	2.64195
$896$	19.8170	0.662040
$897$	−2.47463	−0.0826254
$898$	1.38003	0.0460520
$899$	−10.7372	−0.358105
$900$	−6.26597	−0.208866
$901$	7.81555	0.260374
$902$	−10.3702	−0.345291
$903$	0.289721	0.00964131
$904$	3.97342	0.132154
$905$	−47.1922	−1.56872
$906$	−11.0952	−0.368613
$907$	−31.7784	−1.05519	−0.527593	−	0.849497i	$-0.676905\pi$
$907$	−31.7784	−1.05519	−0.527593	+	0.849497i	$0.676905\pi$
$908$	17.5559	0.582612
$909$	−8.86946	−0.294182
$910$	3.96938	0.131584
$911$	−9.13900	−0.302788	−0.151394	−	0.988473i	$-0.548376\pi$
$911$	−9.13900	−0.302788	−0.151394	+	0.988473i	$0.548376\pi$
$912$	0.943189	0.0312321
$913$	−8.21961	−0.272029
$914$	7.61516	0.251887
$915$	−25.8415	−0.854295
$916$	26.9718	0.891172
$917$	36.4597	1.20401
$918$	−0.751824	−0.0248139
$919$	−16.2553	−0.536212	−0.268106	−	0.963389i	$-0.586398\pi$
$919$	−16.2553	−0.536212	−0.268106	+	0.963389i	$0.586398\pi$
$920$	−22.9111	−0.755356
$921$	−14.5309	−0.478808
$922$	20.0025	0.658746
$923$	3.98344	0.131117
$924$	−8.33323	−0.274143
$925$	38.4471	1.26413
$926$	−16.1762	−0.531583
$927$	−16.5490	−0.543539
$928$	−41.7104	−1.36921
$929$	24.6580	0.809003	0.404501	−	0.914537i	$-0.367445\pi$
$929$	24.6580	0.809003	0.404501	+	0.914537i	$0.367445\pi$
$930$	3.47251	0.113868
$931$	−2.96400	−0.0971411
$932$	0.550907	0.0180455
$933$	8.72286	0.285573
$934$	30.5330	0.999071
$935$	8.79674	0.287684
$936$	2.20442	0.0720539
$937$	−12.1762	−0.397781	−0.198890	−	0.980022i	$-0.563734\pi$
$937$	−12.1762	−0.397781	−0.198890	+	0.980022i	$0.563734\pi$
$938$	0.319754	0.0104403
$939$	−2.16307	−0.0705890
$940$	30.6822	1.00074
$941$	19.3439	0.630592	0.315296	−	0.948993i	$-0.397896\pi$
$941$	19.3439	0.630592	0.315296	+	0.948993i	$0.397896\pi$
$942$	0.751824	0.0244957
$943$	13.9118	0.453032
$944$	−9.12215	−0.296901
$945$	−6.18478	−0.201191
$946$	0.309808	0.0100727
$947$	42.2358	1.37248	0.686239	−	0.727376i	$-0.259260\pi$
$947$	42.2358	1.37248	0.686239	+	0.727376i	$0.259260\pi$
$948$	−21.1519	−0.686983
$949$	−4.17880	−0.135650
$950$	3.33692	0.108264
$951$	23.8411	0.773101
$952$	−5.21832	−0.169127
$953$	−9.78065	−0.316826	−0.158413	−	0.987373i	$-0.550638\pi$
$953$	−9.78065	−0.316826	−0.158413	+	0.987373i	$0.550638\pi$
$954$	−5.87591	−0.190240
$955$	−47.3510	−1.53224
$956$	−4.43977	−0.143592
$957$	20.4496	0.661040
$958$	−24.0367	−0.776591
$959$	34.6086	1.11757
$960$	7.80872	0.252025
$961$	−28.7226	−0.926535
$962$	−5.65006	−0.182165
$963$	−7.01251	−0.225975
$964$	21.6199	0.696329
$965$	5.90566	0.190110
$966$	−4.40414	−0.141701
$967$	−46.3642	−1.49097	−0.745487	−	0.666520i	$-0.767783\pi$
$967$	−46.3642	−1.49097	−0.745487	+	0.666520i	$0.767783\pi$
$968$	7.07311	0.227338
$969$	−1.01630	−0.0326482
$970$	25.4436	0.816946
$971$	−13.1383	−0.421630	−0.210815	−	0.977526i	$-0.567612\pi$
$971$	−13.1383	−0.421630	−0.210815	+	0.977526i	$0.567612\pi$
$972$	−1.43476	−0.0460200
$973$	−15.2880	−0.490111
$974$	7.55941	0.242219
$975$	−3.72813	−0.119396
$976$	−7.83591	−0.250821
$977$	−35.9138	−1.14898	−0.574492	−	0.818510i	$-0.694801\pi$
$977$	−35.9138	−1.14898	−0.574492	+	0.818510i	$0.694801\pi$
$978$	−8.43521	−0.269728
$979$	41.2010	1.31679
$980$	12.8069	0.409100
$981$	−12.8152	−0.409158
$982$	−31.4849	−1.00472
$983$	0.197517	0.00629982	0.00314991	−	0.999995i	$-0.498997\pi$
$983$	0.197517	0.00629982	0.00314991	+	0.999995i	$0.498997\pi$
$984$	−12.3928	−0.395068
$985$	78.9562	2.51575
$986$	5.34915	0.170352
$987$	14.1195	0.449428
$988$	1.24475	0.0396009
$989$	−0.415613	−0.0132157
$990$	−6.61359	−0.210194
$991$	9.28548	0.294963	0.147481	−	0.989065i	$-0.452883\pi$
$991$	9.28548	0.294963	0.147481	+	0.989065i	$0.452883\pi$
$992$	8.84704	0.280894
$993$	14.2207	0.451279
$994$	7.08941	0.224862
$995$	42.0105	1.33182
$996$	−4.10313	−0.130013
$997$	−47.3535	−1.49970	−0.749850	−	0.661608i	$-0.769874\pi$
$997$	−47.3535	−1.49970	−0.749850	+	0.661608i	$0.769874\pi$
$998$	−0.693894	−0.0219648
$999$	8.80348	0.278530

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.e.1.29	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.e.1.29	✓	46	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)

\(f(q)\)	\(=\)	\(q+0.751824 q^{2} +1.00000 q^{3} -1.43476 q^{4} +3.06060 q^{5} +0.751824 q^{6} -2.02078 q^{7} -2.58233 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.751824 q^{2} +1.00000 q^{3} -1.43476 q^{4} +3.06060 q^{5} +0.751824 q^{6} -2.02078 q^{7} -2.58233 q^{8} +1.00000 q^{9} +2.30103 q^{10} -2.87419 q^{11} -1.43476 q^{12} -0.853656 q^{13} -1.51927 q^{14} +3.06060 q^{15} +0.928063 q^{16} -1.00000 q^{17} +0.751824 q^{18} +1.01630 q^{19} -4.39123 q^{20} -2.02078 q^{21} -2.16088 q^{22} +2.89886 q^{23} -2.58233 q^{24} +4.36726 q^{25} -0.641799 q^{26} +1.00000 q^{27} +2.89933 q^{28} -7.11490 q^{29} +2.30103 q^{30} +1.50911 q^{31} +5.86241 q^{32} -2.87419 q^{33} -0.751824 q^{34} -6.18478 q^{35} -1.43476 q^{36} +8.80348 q^{37} +0.764077 q^{38} -0.853656 q^{39} -7.90349 q^{40} +4.79907 q^{41} -1.51927 q^{42} -0.143371 q^{43} +4.12378 q^{44} +3.06060 q^{45} +2.17943 q^{46} -6.98716 q^{47} +0.928063 q^{48} -2.91646 q^{49} +3.28341 q^{50} -1.00000 q^{51} +1.22479 q^{52} -7.81555 q^{53} +0.751824 q^{54} -8.79674 q^{55} +5.21832 q^{56} +1.01630 q^{57} -5.34915 q^{58} -9.82923 q^{59} -4.39123 q^{60} -8.44330 q^{61} +1.13459 q^{62} -2.02078 q^{63} +2.55137 q^{64} -2.61270 q^{65} -2.16088 q^{66} -0.210466 q^{67} +1.43476 q^{68} +2.89886 q^{69} -4.64987 q^{70} -4.66633 q^{71} -2.58233 q^{72} +4.89518 q^{73} +6.61866 q^{74} +4.36726 q^{75} -1.45815 q^{76} +5.80809 q^{77} -0.641799 q^{78} +14.7425 q^{79} +2.84043 q^{80} +1.00000 q^{81} +3.60806 q^{82} +2.85980 q^{83} +2.89933 q^{84} -3.06060 q^{85} -0.107790 q^{86} -7.11490 q^{87} +7.42212 q^{88} -14.3348 q^{89} +2.30103 q^{90} +1.72505 q^{91} -4.15917 q^{92} +1.50911 q^{93} -5.25311 q^{94} +3.11048 q^{95} +5.86241 q^{96} +11.0575 q^{97} -2.19267 q^{98} -2.87419 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * q^99

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