LMFDB - Embedded newform 802.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [802,2,Mod(1,802)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(802, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("802.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 802 = 2 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	802.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:	$6.40400224211$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 21x^{8} - 21x^{7} + 124x^{6} + 231x^{5} - 34x^{4} - 255x^{3} - 64x^{2} + 70x + 21 $ x^10 - 21x^8 - 21x^7 + 124x^6 + 231x^5 - 34x^4 - 255x^3 - 64x^2 + 70x + 21
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.58946$ of defining polynomial
Character	$\chi$	$=$	802.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.58946 q^{3} +1.00000 q^{4} +3.26712 q^{5} -2.58946 q^{6} +3.10643 q^{7} +1.00000 q^{8} +3.70532 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.58946 q^{3} +1.00000 q^{4} +3.26712 q^{5} -2.58946 q^{6} +3.10643 q^{7} +1.00000 q^{8} +3.70532 q^{9} +3.26712 q^{10} -0.908032 q^{11} -2.58946 q^{12} +0.423684 q^{13} +3.10643 q^{14} -8.46007 q^{15} +1.00000 q^{16} +0.726609 q^{17} +3.70532 q^{18} -2.96013 q^{19} +3.26712 q^{20} -8.04399 q^{21} -0.908032 q^{22} -2.84646 q^{23} -2.58946 q^{24} +5.67404 q^{25} +0.423684 q^{26} -1.82640 q^{27} +3.10643 q^{28} +4.85092 q^{29} -8.46007 q^{30} -1.79479 q^{31} +1.00000 q^{32} +2.35131 q^{33} +0.726609 q^{34} +10.1491 q^{35} +3.70532 q^{36} +7.30263 q^{37} -2.96013 q^{38} -1.09711 q^{39} +3.26712 q^{40} +6.85438 q^{41} -8.04399 q^{42} +1.66134 q^{43} -0.908032 q^{44} +12.1057 q^{45} -2.84646 q^{46} +0.534686 q^{47} -2.58946 q^{48} +2.64992 q^{49} +5.67404 q^{50} -1.88153 q^{51} +0.423684 q^{52} -10.1364 q^{53} -1.82640 q^{54} -2.96664 q^{55} +3.10643 q^{56} +7.66516 q^{57} +4.85092 q^{58} +13.5309 q^{59} -8.46007 q^{60} +3.71925 q^{61} -1.79479 q^{62} +11.5103 q^{63} +1.00000 q^{64} +1.38423 q^{65} +2.35131 q^{66} +1.58178 q^{67} +0.726609 q^{68} +7.37080 q^{69} +10.1491 q^{70} -11.8676 q^{71} +3.70532 q^{72} -13.5488 q^{73} +7.30263 q^{74} -14.6927 q^{75} -2.96013 q^{76} -2.82074 q^{77} -1.09711 q^{78} -12.1840 q^{79} +3.26712 q^{80} -6.38657 q^{81} +6.85438 q^{82} -1.17195 q^{83} -8.04399 q^{84} +2.37391 q^{85} +1.66134 q^{86} -12.5613 q^{87} -0.908032 q^{88} +11.0725 q^{89} +12.1057 q^{90} +1.31615 q^{91} -2.84646 q^{92} +4.64753 q^{93} +0.534686 q^{94} -9.67110 q^{95} -2.58946 q^{96} -6.65358 q^{97} +2.64992 q^{98} -3.36455 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 10 q^{3} + 10 q^{4} + 9 q^{5} + 10 q^{6} + q^{7} + 10 q^{8} + 22 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 + 10 * q^3 + 10 * q^4 + 9 * q^5 + 10 * q^6 + q^7 + 10 * q^8 + 22 * q^9	\( 10 q + 10 q^{2} + 10 q^{3} + 10 q^{4} + 9 q^{5} + 10 q^{6} + q^{7} + 10 q^{8} + 22 q^{9} + 9 q^{10} + 3 q^{11} + 10 q^{12} + 10 q^{13} + q^{14} - 7 q^{15} + 10 q^{16} + 22 q^{18} - 4 q^{19} + 9 q^{20} - 5 q^{21} + 3 q^{22} + 17 q^{23} + 10 q^{24} + 9 q^{25} + 10 q^{26} + 13 q^{27} + q^{28} - 4 q^{29} - 7 q^{30} - 9 q^{31} + 10 q^{32} - 3 q^{33} - 8 q^{35} + 22 q^{36} + 4 q^{37} - 4 q^{38} - 26 q^{39} + 9 q^{40} + 10 q^{41} - 5 q^{42} - 14 q^{43} + 3 q^{44} + 28 q^{45} + 17 q^{46} + 21 q^{47} + 10 q^{48} + 25 q^{49} + 9 q^{50} + 2 q^{51} + 10 q^{52} - 16 q^{53} + 13 q^{54} - 47 q^{55} + q^{56} + 9 q^{57} - 4 q^{58} + 10 q^{59} - 7 q^{60} + 20 q^{61} - 9 q^{62} - 53 q^{63} + 10 q^{64} - 16 q^{65} - 3 q^{66} - 27 q^{67} - 26 q^{69} - 8 q^{70} - 2 q^{71} + 22 q^{72} - 16 q^{73} + 4 q^{74} - 10 q^{75} - 4 q^{76} + 2 q^{77} - 26 q^{78} - 12 q^{79} + 9 q^{80} + 18 q^{81} + 10 q^{82} - q^{83} - 5 q^{84} - 19 q^{85} - 14 q^{86} - 13 q^{87} + 3 q^{88} - 5 q^{89} + 28 q^{90} - 27 q^{91} + 17 q^{92} - 55 q^{93} + 21 q^{94} - 27 q^{95} + 10 q^{96} - 15 q^{97} + 25 q^{98} - 31 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 10 * q^3 + 10 * q^4 + 9 * q^5 + 10 * q^6 + q^7 + 10 * q^8 + 22 * q^9 + 9 * q^10 + 3 * q^11 + 10 * q^12 + 10 * q^13 + q^14 - 7 * q^15 + 10 * q^16 + 22 * q^18 - 4 * q^19 + 9 * q^20 - 5 * q^21 + 3 * q^22 + 17 * q^23 + 10 * q^24 + 9 * q^25 + 10 * q^26 + 13 * q^27 + q^28 - 4 * q^29 - 7 * q^30 - 9 * q^31 + 10 * q^32 - 3 * q^33 - 8 * q^35 + 22 * q^36 + 4 * q^37 - 4 * q^38 - 26 * q^39 + 9 * q^40 + 10 * q^41 - 5 * q^42 - 14 * q^43 + 3 * q^44 + 28 * q^45 + 17 * q^46 + 21 * q^47 + 10 * q^48 + 25 * q^49 + 9 * q^50 + 2 * q^51 + 10 * q^52 - 16 * q^53 + 13 * q^54 - 47 * q^55 + q^56 + 9 * q^57 - 4 * q^58 + 10 * q^59 - 7 * q^60 + 20 * q^61 - 9 * q^62 - 53 * q^63 + 10 * q^64 - 16 * q^65 - 3 * q^66 - 27 * q^67 - 26 * q^69 - 8 * q^70 - 2 * q^71 + 22 * q^72 - 16 * q^73 + 4 * q^74 - 10 * q^75 - 4 * q^76 + 2 * q^77 - 26 * q^78 - 12 * q^79 + 9 * q^80 + 18 * q^81 + 10 * q^82 - q^83 - 5 * q^84 - 19 * q^85 - 14 * q^86 - 13 * q^87 + 3 * q^88 - 5 * q^89 + 28 * q^90 - 27 * q^91 + 17 * q^92 - 55 * q^93 + 21 * q^94 - 27 * q^95 + 10 * q^96 - 15 * q^97 + 25 * q^98 - 31 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.58946	−1.49503	−0.747514	−	0.664247i	$-0.768753\pi$
$3$	−2.58946	−1.49503	−0.747514	+	0.664247i	$0.768753\pi$
$4$	1.00000	0.500000
$5$	3.26712	1.46110	0.730549	−	0.682860i	$-0.239264\pi$
$5$	3.26712	1.46110	0.730549	+	0.682860i	$0.239264\pi$
$6$	−2.58946	−1.05714
$7$	3.10643	1.17412	0.587061	−	0.809543i	$-0.300285\pi$
$7$	3.10643	1.17412	0.587061	+	0.809543i	$0.300285\pi$
$8$	1.00000	0.353553
$9$	3.70532	1.23511
$10$	3.26712	1.03315
$11$	−0.908032	−0.273782	−0.136891	−	0.990586i	$-0.543711\pi$
$11$	−0.908032	−0.273782	−0.136891	+	0.990586i	$0.543711\pi$
$12$	−2.58946	−0.747514
$13$	0.423684	0.117509	0.0587544	−	0.998272i	$-0.481287\pi$
$13$	0.423684	0.117509	0.0587544	+	0.998272i	$0.481287\pi$
$14$	3.10643	0.830229
$15$	−8.46007	−2.18438
$16$	1.00000	0.250000
$17$	0.726609	0.176228	0.0881142	−	0.996110i	$-0.471916\pi$
$17$	0.726609	0.176228	0.0881142	+	0.996110i	$0.471916\pi$
$18$	3.70532	0.873352
$19$	−2.96013	−0.679101	−0.339551	−	0.940588i	$-0.610275\pi$
$19$	−2.96013	−0.679101	−0.339551	+	0.940588i	$0.610275\pi$
$20$	3.26712	0.730549
$21$	−8.04399	−1.75534
$22$	−0.908032	−0.193593
$23$	−2.84646	−0.593528	−0.296764	−	0.954951i	$-0.595907\pi$
$23$	−2.84646	−0.593528	−0.296764	+	0.954951i	$0.595907\pi$
$24$	−2.58946	−0.528572
$25$	5.67404	1.13481
$26$	0.423684	0.0830913
$27$	−1.82640	−0.351490
$28$	3.10643	0.587061
$29$	4.85092	0.900794	0.450397	−	0.892828i	$-0.351283\pi$
$29$	4.85092	0.900794	0.450397	+	0.892828i	$0.351283\pi$
$30$	−8.46007	−1.54459
$31$	−1.79479	−0.322353	−0.161177	−	0.986926i	$-0.551529\pi$
$31$	−1.79479	−0.322353	−0.161177	+	0.986926i	$0.551529\pi$
$32$	1.00000	0.176777
$33$	2.35131	0.409311
$34$	0.726609	0.124612
$35$	10.1491	1.71551
$36$	3.70532	0.617553
$37$	7.30263	1.20055	0.600273	−	0.799795i	$-0.295059\pi$
$37$	7.30263	1.20055	0.600273	+	0.799795i	$0.295059\pi$
$38$	−2.96013	−0.480197
$39$	−1.09711	−0.175679
$40$	3.26712	0.516576
$41$	6.85438	1.07047	0.535237	−	0.844702i	$-0.320222\pi$
$41$	6.85438	1.07047	0.535237	+	0.844702i	$0.320222\pi$
$42$	−8.04399	−1.24121
$43$	1.66134	0.253352	0.126676	−	0.991944i	$-0.459569\pi$
$43$	1.66134	0.253352	0.126676	+	0.991944i	$0.459569\pi$
$44$	−0.908032	−0.136891
$45$	12.1057	1.80461
$46$	−2.84646	−0.419687
$47$	0.534686	0.0779920	0.0389960	−	0.999239i	$-0.487584\pi$
$47$	0.534686	0.0779920	0.0389960	+	0.999239i	$0.487584\pi$
$48$	−2.58946	−0.373757
$49$	2.64992	0.378560
$50$	5.67404	0.802431
$51$	−1.88153	−0.263466
$52$	0.423684	0.0587544
$53$	−10.1364	−1.39234	−0.696168	−	0.717878i	$-0.745113\pi$
$53$	−10.1364	−1.39234	−0.696168	+	0.717878i	$0.745113\pi$
$54$	−1.82640	−0.248541
$55$	−2.96664	−0.400022
$56$	3.10643	0.415114
$57$	7.66516	1.01527
$58$	4.85092	0.636957
$59$	13.5309	1.76157	0.880783	−	0.473519i	$-0.157017\pi$
$59$	13.5309	1.76157	0.880783	+	0.473519i	$0.157017\pi$
$60$	−8.46007	−1.09219
$61$	3.71925	0.476202	0.238101	−	0.971240i	$-0.423475\pi$
$61$	3.71925	0.476202	0.238101	+	0.971240i	$0.423475\pi$
$62$	−1.79479	−0.227938
$63$	11.5103	1.45016
$64$	1.00000	0.125000
$65$	1.38423	0.171692
$66$	2.35131	0.289427
$67$	1.58178	0.193245	0.0966225	−	0.995321i	$-0.469196\pi$
$67$	1.58178	0.193245	0.0966225	+	0.995321i	$0.469196\pi$
$68$	0.726609	0.0881142
$69$	7.37080	0.887340
$70$	10.1491	1.21305
$71$	−11.8676	−1.40842	−0.704212	−	0.709990i	$-0.748700\pi$
$71$	−11.8676	−1.40842	−0.704212	+	0.709990i	$0.748700\pi$
$72$	3.70532	0.436676
$73$	−13.5488	−1.58577	−0.792883	−	0.609374i	$-0.791421\pi$
$73$	−13.5488	−1.58577	−0.792883	+	0.609374i	$0.791421\pi$
$74$	7.30263	0.848914
$75$	−14.6927	−1.69657
$76$	−2.96013	−0.339551
$77$	−2.82074	−0.321453
$78$	−1.09711	−0.124224
$79$	−12.1840	−1.37080	−0.685402	−	0.728165i	$-0.740374\pi$
$79$	−12.1840	−1.37080	−0.685402	+	0.728165i	$0.740374\pi$
$80$	3.26712	0.365275
$81$	−6.38657	−0.709619
$82$	6.85438	0.756940
$83$	−1.17195	−0.128638	−0.0643190	−	0.997929i	$-0.520488\pi$
$83$	−1.17195	−0.128638	−0.0643190	+	0.997929i	$0.520488\pi$
$84$	−8.04399	−0.877671
$85$	2.37391	0.257487
$86$	1.66134	0.179147
$87$	−12.5613	−1.34671
$88$	−0.908032	−0.0967965
$89$	11.0725	1.17369	0.586843	−	0.809701i	$-0.300370\pi$
$89$	11.0725	1.17369	0.586843	+	0.809701i	$0.300370\pi$
$90$	12.1057	1.27605
$91$	1.31615	0.137970
$92$	−2.84646	−0.296764
$93$	4.64753	0.481927
$94$	0.534686	0.0551487
$95$	−9.67110	−0.992234
$96$	−2.58946	−0.264286
$97$	−6.65358	−0.675569	−0.337784	−	0.941224i	$-0.609677\pi$
$97$	−6.65358	−0.675569	−0.337784	+	0.941224i	$0.609677\pi$
$98$	2.64992	0.267683
$99$	−3.36455	−0.338150
$100$	5.67404	0.567404
$101$	−0.886172	−0.0881774	−0.0440887	−	0.999028i	$-0.514038\pi$
$101$	−0.886172	−0.0881774	−0.0440887	+	0.999028i	$0.514038\pi$
$102$	−1.88153	−0.186299
$103$	8.36526	0.824253	0.412127	−	0.911127i	$-0.364786\pi$
$103$	8.36526	0.824253	0.412127	+	0.911127i	$0.364786\pi$
$104$	0.423684	0.0415457
$105$	−26.2806	−2.56473
$106$	−10.1364	−0.984531
$107$	−3.42709	−0.331309	−0.165654	−	0.986184i	$-0.552974\pi$
$107$	−3.42709	−0.331309	−0.165654	+	0.986184i	$0.552974\pi$
$108$	−1.82640	−0.175745
$109$	17.0958	1.63748	0.818740	−	0.574164i	$-0.194673\pi$
$109$	17.0958	1.63748	0.818740	+	0.574164i	$0.194673\pi$
$110$	−2.96664	−0.282858
$111$	−18.9099	−1.79485
$112$	3.10643	0.293530
$113$	−0.961140	−0.0904165	−0.0452082	−	0.998978i	$-0.514395\pi$
$113$	−0.961140	−0.0904165	−0.0452082	+	0.998978i	$0.514395\pi$
$114$	7.66516	0.717908
$115$	−9.29971	−0.867202
$116$	4.85092	0.450397
$117$	1.56989	0.145136
$118$	13.5309	1.24562
$119$	2.25716	0.206914
$120$	−8.46007	−0.772296
$121$	−10.1755	−0.925043
$122$	3.71925	0.336725
$123$	−17.7492	−1.60039
$124$	−1.79479	−0.161177
$125$	2.20217	0.196968
$126$	11.5103	1.02542
$127$	11.3719	1.00909	0.504546	−	0.863385i	$-0.331660\pi$
$127$	11.3719	1.00909	0.504546	+	0.863385i	$0.331660\pi$
$128$	1.00000	0.0883883
$129$	−4.30197	−0.378768
$130$	1.38423	0.121405
$131$	3.82347	0.334058	0.167029	−	0.985952i	$-0.446583\pi$
$131$	3.82347	0.334058	0.167029	+	0.985952i	$0.446583\pi$
$132$	2.35131	0.204656
$133$	−9.19545	−0.797347
$134$	1.58178	0.136645
$135$	−5.96705	−0.513562
$136$	0.726609	0.0623062
$137$	−0.465272	−0.0397508	−0.0198754	−	0.999802i	$-0.506327\pi$
$137$	−0.465272	−0.0397508	−0.0198754	+	0.999802i	$0.506327\pi$
$138$	7.37080	0.627444
$139$	−17.7866	−1.50864	−0.754318	−	0.656509i	$-0.772032\pi$
$139$	−17.7866	−1.50864	−0.754318	+	0.656509i	$0.772032\pi$
$140$	10.1491	0.857753
$141$	−1.38455	−0.116600
$142$	−11.8676	−0.995906
$143$	−0.384719	−0.0321718
$144$	3.70532	0.308777
$145$	15.8485	1.31615
$146$	−13.5488	−1.12131
$147$	−6.86188	−0.565958
$148$	7.30263	0.600273
$149$	−3.78033	−0.309696	−0.154848	−	0.987938i	$-0.549489\pi$
$149$	−3.78033	−0.309696	−0.154848	+	0.987938i	$0.549489\pi$
$150$	−14.6927	−1.19966
$151$	−14.2575	−1.16026	−0.580130	−	0.814524i	$-0.696998\pi$
$151$	−14.2575	−1.16026	−0.580130	+	0.814524i	$0.696998\pi$
$152$	−2.96013	−0.240099
$153$	2.69232	0.217661
$154$	−2.82074	−0.227302
$155$	−5.86377	−0.470990
$156$	−1.09711	−0.0878395
$157$	3.66891	0.292811	0.146405	−	0.989225i	$-0.453230\pi$
$157$	3.66891	0.292811	0.146405	+	0.989225i	$0.453230\pi$
$158$	−12.1840	−0.969305
$159$	26.2477	2.08158
$160$	3.26712	0.258288
$161$	−8.84233	−0.696873
$162$	−6.38657	−0.501776
$163$	13.0154	1.01944	0.509722	−	0.860339i	$-0.329748\pi$
$163$	13.0154	1.01944	0.509722	+	0.860339i	$0.329748\pi$
$164$	6.85438	0.535237
$165$	7.68202	0.598044
$166$	−1.17195	−0.0909608
$167$	−11.1426	−0.862237	−0.431119	−	0.902295i	$-0.641881\pi$
$167$	−11.1426	−0.862237	−0.431119	+	0.902295i	$0.641881\pi$
$168$	−8.04399	−0.620607
$169$	−12.8205	−0.986192
$170$	2.37391	0.182071
$171$	−10.9682	−0.838762
$172$	1.66134	0.126676
$173$	−4.20986	−0.320070	−0.160035	−	0.987111i	$-0.551161\pi$
$173$	−4.20986	−0.320070	−0.160035	+	0.987111i	$0.551161\pi$
$174$	−12.5613	−0.952268
$175$	17.6260	1.33240
$176$	−0.908032	−0.0684455
$177$	−35.0376	−2.63359
$178$	11.0725	0.829922
$179$	−18.5913	−1.38958	−0.694789	−	0.719214i	$-0.744502\pi$
$179$	−18.5913	−1.38958	−0.694789	+	0.719214i	$0.744502\pi$
$180$	12.1057	0.902306
$181$	−18.4792	−1.37355	−0.686775	−	0.726870i	$-0.740974\pi$
$181$	−18.4792	−1.37355	−0.686775	+	0.726870i	$0.740974\pi$
$182$	1.31615	0.0975593
$183$	−9.63087	−0.711934
$184$	−2.84646	−0.209844
$185$	23.8585	1.75411
$186$	4.64753	0.340774
$187$	−0.659784	−0.0482482
$188$	0.534686	0.0389960
$189$	−5.67358	−0.412692
$190$	−9.67110	−0.701615
$191$	−11.6877	−0.845692	−0.422846	−	0.906202i	$-0.638969\pi$
$191$	−11.6877	−0.845692	−0.422846	+	0.906202i	$0.638969\pi$
$192$	−2.58946	−0.186878
$193$	0.758955	0.0546308	0.0273154	−	0.999627i	$-0.491304\pi$
$193$	0.758955	0.0546308	0.0273154	+	0.999627i	$0.491304\pi$
$194$	−6.65358	−0.477699
$195$	−3.58440	−0.256684
$196$	2.64992	0.189280
$197$	4.97164	0.354215	0.177107	−	0.984192i	$-0.443326\pi$
$197$	4.97164	0.354215	0.177107	+	0.984192i	$0.443326\pi$
$198$	−3.36455	−0.239108
$199$	−26.2501	−1.86082	−0.930410	−	0.366520i	$-0.880549\pi$
$199$	−26.2501	−1.86082	−0.930410	+	0.366520i	$0.880549\pi$
$200$	5.67404	0.401215
$201$	−4.09596	−0.288906
$202$	−0.886172	−0.0623508
$203$	15.0691	1.05764
$204$	−1.88153	−0.131733
$205$	22.3940	1.56407
$206$	8.36526	0.582835
$207$	−10.5470	−0.733070
$208$	0.423684	0.0293772
$209$	2.68790	0.185926
$210$	−26.2806	−1.81354
$211$	−16.7850	−1.15553	−0.577765	−	0.816203i	$-0.696075\pi$
$211$	−16.7850	−1.15553	−0.577765	+	0.816203i	$0.696075\pi$
$212$	−10.1364	−0.696168
$213$	30.7307	2.10563
$214$	−3.42709	−0.234271
$215$	5.42778	0.370172
$216$	−1.82640	−0.124271
$217$	−5.57538	−0.378482
$218$	17.0958	1.15787
$219$	35.0841	2.37076
$220$	−2.96664	−0.200011
$221$	0.307853	0.0207084
$222$	−18.9099	−1.26915
$223$	16.2892	1.09080	0.545401	−	0.838175i	$-0.316377\pi$
$223$	16.2892	1.09080	0.545401	+	0.838175i	$0.316377\pi$
$224$	3.10643	0.207557
$225$	21.0241	1.40161
$226$	−0.961140	−0.0639341
$227$	2.96072	0.196510	0.0982551	−	0.995161i	$-0.468674\pi$
$227$	2.96072	0.196510	0.0982551	+	0.995161i	$0.468674\pi$
$228$	7.66516	0.507637
$229$	6.29273	0.415835	0.207918	−	0.978146i	$-0.433331\pi$
$229$	6.29273	0.415835	0.207918	+	0.978146i	$0.433331\pi$
$230$	−9.29971	−0.613205
$231$	7.30420	0.480581
$232$	4.85092	0.318479
$233$	10.9177	0.715244	0.357622	−	0.933866i	$-0.383588\pi$
$233$	10.9177	0.715244	0.357622	+	0.933866i	$0.383588\pi$
$234$	1.56989	0.102627
$235$	1.74688	0.113954
$236$	13.5309	0.880783
$237$	31.5500	2.04939
$238$	2.25716	0.146310
$239$	−7.47240	−0.483350	−0.241675	−	0.970357i	$-0.577697\pi$
$239$	−7.47240	−0.483350	−0.241675	+	0.970357i	$0.577697\pi$
$240$	−8.46007	−0.546095
$241$	16.3012	1.05005	0.525027	−	0.851086i	$-0.324055\pi$
$241$	16.3012	1.05005	0.525027	+	0.851086i	$0.324055\pi$
$242$	−10.1755	−0.654105
$243$	22.0170	1.41239
$244$	3.71925	0.238101
$245$	8.65760	0.553114
$246$	−17.7492	−1.13165
$247$	−1.25416	−0.0798004
$248$	−1.79479	−0.113969
$249$	3.03472	0.192317
$250$	2.20217	0.139278
$251$	−26.3779	−1.66496	−0.832478	−	0.554059i	$-0.813078\pi$
$251$	−26.3779	−1.66496	−0.832478	+	0.554059i	$0.813078\pi$
$252$	11.5103	0.725082
$253$	2.58467	0.162497
$254$	11.3719	0.713536
$255$	−6.14716	−0.384950
$256$	1.00000	0.0625000
$257$	14.2107	0.886440	0.443220	−	0.896413i	$-0.353836\pi$
$257$	14.2107	0.886440	0.443220	+	0.896413i	$0.353836\pi$
$258$	−4.30197	−0.267829
$259$	22.6851	1.40959
$260$	1.38423	0.0858460
$261$	17.9742	1.11258
$262$	3.82347	0.236215
$263$	14.5159	0.895087	0.447543	−	0.894262i	$-0.352299\pi$
$263$	14.5159	0.895087	0.447543	+	0.894262i	$0.352299\pi$
$264$	2.35131	0.144713
$265$	−33.1167	−2.03434
$266$	−9.19545	−0.563810
$267$	−28.6719	−1.75469
$268$	1.58178	0.0966225
$269$	4.58958	0.279832	0.139916	−	0.990163i	$-0.455317\pi$
$269$	4.58958	0.279832	0.139916	+	0.990163i	$0.455317\pi$
$270$	−5.96705	−0.363143
$271$	20.0282	1.21663	0.608313	−	0.793697i	$-0.291847\pi$
$271$	20.0282	1.21663	0.608313	+	0.793697i	$0.291847\pi$
$272$	0.726609	0.0440571
$273$	−3.40811	−0.206268
$274$	−0.465272	−0.0281081
$275$	−5.15221	−0.310690
$276$	7.37080	0.443670
$277$	−3.94100	−0.236792	−0.118396	−	0.992966i	$-0.537775\pi$
$277$	−3.94100	−0.236792	−0.118396	+	0.992966i	$0.537775\pi$
$278$	−17.7866	−1.06677
$279$	−6.65026	−0.398140
$280$	10.1491	0.606523
$281$	−27.9837	−1.66937	−0.834684	−	0.550729i	$-0.814350\pi$
$281$	−27.9837	−1.66937	−0.834684	+	0.550729i	$0.814350\pi$
$282$	−1.38455	−0.0824488
$283$	−16.3706	−0.973130	−0.486565	−	0.873644i	$-0.661750\pi$
$283$	−16.3706	−0.973130	−0.486565	+	0.873644i	$0.661750\pi$
$284$	−11.8676	−0.704212
$285$	25.0429	1.48342
$286$	−0.384719	−0.0227489
$287$	21.2927	1.25687
$288$	3.70532	0.218338
$289$	−16.4720	−0.968944
$290$	15.8485	0.930657
$291$	17.2292	1.00999
$292$	−13.5488	−0.792883
$293$	26.4450	1.54494	0.772468	−	0.635054i	$-0.219022\pi$
$293$	26.4450	1.54494	0.772468	+	0.635054i	$0.219022\pi$
$294$	−6.86188	−0.400193
$295$	44.2069	2.57382
$296$	7.30263	0.424457
$297$	1.65843	0.0962316
$298$	−3.78033	−0.218988
$299$	−1.20600	−0.0697448
$300$	−14.6927	−0.848285
$301$	5.16083	0.297466
$302$	−14.2575	−0.820428
$303$	2.29471	0.131828
$304$	−2.96013	−0.169775
$305$	12.1512	0.695778
$306$	2.69232	0.153909
$307$	21.3964	1.22116	0.610578	−	0.791956i	$-0.290937\pi$
$307$	21.3964	1.22116	0.610578	+	0.791956i	$0.290937\pi$
$308$	−2.82074	−0.160727
$309$	−21.6615	−1.23228
$310$	−5.86377	−0.333040
$311$	19.8494	1.12556	0.562778	−	0.826608i	$-0.309733\pi$
$311$	19.8494	1.12556	0.562778	+	0.826608i	$0.309733\pi$
$312$	−1.09711	−0.0621119
$313$	−5.98475	−0.338278	−0.169139	−	0.985592i	$-0.554099\pi$
$313$	−5.98475	−0.338278	−0.169139	+	0.985592i	$0.554099\pi$
$314$	3.66891	0.207049
$315$	37.6055	2.11883
$316$	−12.1840	−0.685402
$317$	25.0057	1.40446	0.702231	−	0.711949i	$-0.252187\pi$
$317$	25.0057	1.40446	0.702231	+	0.711949i	$0.252187\pi$
$318$	26.2477	1.47190
$319$	−4.40479	−0.246621
$320$	3.26712	0.182637
$321$	8.87431	0.495316
$322$	−8.84233	−0.492764
$323$	−2.15086	−0.119677
$324$	−6.38657	−0.354809
$325$	2.40400	0.133350
$326$	13.0154	0.720856
$327$	−44.2689	−2.44808
$328$	6.85438	0.378470
$329$	1.66097	0.0915721
$330$	7.68202	0.422881
$331$	−8.25673	−0.453831	−0.226916	−	0.973914i	$-0.572864\pi$
$331$	−8.25673	−0.453831	−0.226916	+	0.973914i	$0.572864\pi$
$332$	−1.17195	−0.0643190
$333$	27.0586	1.48280
$334$	−11.1426	−0.609694
$335$	5.16785	0.282350
$336$	−8.04399	−0.438836
$337$	−33.9817	−1.85110	−0.925550	−	0.378627i	$-0.876396\pi$
$337$	−33.9817	−1.85110	−0.925550	+	0.378627i	$0.876396\pi$
$338$	−12.8205	−0.697343
$339$	2.48884	0.135175
$340$	2.37391	0.128744
$341$	1.62972	0.0882544
$342$	−10.9682	−0.593094
$343$	−13.5132	−0.729645
$344$	1.66134	0.0895733
$345$	24.0813	1.29649
$346$	−4.20986	−0.226323
$347$	1.17557	0.0631081	0.0315540	−	0.999502i	$-0.489954\pi$
$347$	1.17557	0.0631081	0.0315540	+	0.999502i	$0.489954\pi$
$348$	−12.5613	−0.673355
$349$	−32.4569	−1.73738	−0.868688	−	0.495360i	$-0.835036\pi$
$349$	−32.4569	−1.73738	−0.868688	+	0.495360i	$0.835036\pi$
$350$	17.6260	0.942151
$351$	−0.773816	−0.0413032
$352$	−0.908032	−0.0483983
$353$	−13.1837	−0.701700	−0.350850	−	0.936432i	$-0.614107\pi$
$353$	−13.1837	−0.701700	−0.350850	+	0.936432i	$0.614107\pi$
$354$	−35.0376	−1.86223
$355$	−38.7728	−2.05785
$356$	11.0725	0.586843
$357$	−5.84483	−0.309341
$358$	−18.5913	−0.982580
$359$	4.36093	0.230161	0.115080	−	0.993356i	$-0.463287\pi$
$359$	4.36093	0.230161	0.115080	+	0.993356i	$0.463287\pi$
$360$	12.1057	0.638027
$361$	−10.2376	−0.538822
$362$	−18.4792	−0.971247
$363$	26.3490	1.38297
$364$	1.31615	0.0689848
$365$	−44.2655	−2.31696
$366$	−9.63087	−0.503414
$367$	2.43669	0.127194	0.0635970	−	0.997976i	$-0.479743\pi$
$367$	2.43669	0.127194	0.0635970	+	0.997976i	$0.479743\pi$
$368$	−2.84646	−0.148382
$369$	25.3977	1.32215
$370$	23.8585	1.24035
$371$	−31.4879	−1.63477
$372$	4.64753	0.240963
$373$	10.5200	0.544705	0.272352	−	0.962198i	$-0.412198\pi$
$373$	10.5200	0.544705	0.272352	+	0.962198i	$0.412198\pi$
$374$	−0.659784	−0.0341166
$375$	−5.70245	−0.294473
$376$	0.534686	0.0275743
$377$	2.05526	0.105851
$378$	−5.67358	−0.291817
$379$	4.56086	0.234276	0.117138	−	0.993116i	$-0.462628\pi$
$379$	4.56086	0.234276	0.117138	+	0.993116i	$0.462628\pi$
$380$	−9.67110	−0.496117
$381$	−29.4471	−1.50862
$382$	−11.6877	−0.597994
$383$	35.0887	1.79295	0.896476	−	0.443093i	$-0.146119\pi$
$383$	35.0887	1.79295	0.896476	+	0.443093i	$0.146119\pi$
$384$	−2.58946	−0.132143
$385$	−9.21568	−0.469675
$386$	0.758955	0.0386298
$387$	6.15579	0.312916
$388$	−6.65358	−0.337784
$389$	23.2111	1.17685	0.588425	−	0.808552i	$-0.299748\pi$
$389$	23.2111	1.17685	0.588425	+	0.808552i	$0.299748\pi$
$390$	−3.58440	−0.181503
$391$	−2.06826	−0.104596
$392$	2.64992	0.133841
$393$	−9.90074	−0.499426
$394$	4.97164	0.250468
$395$	−39.8065	−2.00288
$396$	−3.36455	−0.169075
$397$	−32.2274	−1.61744	−0.808722	−	0.588190i	$-0.799841\pi$
$397$	−32.2274	−1.61744	−0.808722	+	0.588190i	$0.799841\pi$
$398$	−26.2501	−1.31580
$399$	23.8113	1.19206
$400$	5.67404	0.283702
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−4.09596	−0.204288
$403$	−0.760423	−0.0378794
$404$	−0.886172	−0.0440887
$405$	−20.8657	−1.03682
$406$	15.0691	0.747865
$407$	−6.63102	−0.328687
$408$	−1.88153	−0.0931494
$409$	−11.6103	−0.574092	−0.287046	−	0.957917i	$-0.592673\pi$
$409$	−11.6103	−0.574092	−0.287046	+	0.957917i	$0.592673\pi$
$410$	22.3940	1.10596
$411$	1.20480	0.0594286
$412$	8.36526	0.412127
$413$	42.0327	2.06829
$414$	−10.5470	−0.518359
$415$	−3.82889	−0.187953
$416$	0.423684	0.0207728
$417$	46.0576	2.25545
$418$	2.68790	0.131469
$419$	27.7858	1.35742	0.678712	−	0.734404i	$-0.262538\pi$
$419$	27.7858	1.35742	0.678712	+	0.734404i	$0.262538\pi$
$420$	−26.2806	−1.28236
$421$	−33.2355	−1.61980	−0.809900	−	0.586568i	$-0.800479\pi$
$421$	−33.2355	−1.61980	−0.809900	+	0.586568i	$0.800479\pi$
$422$	−16.7850	−0.817083
$423$	1.98118	0.0963284
$424$	−10.1364	−0.492265
$425$	4.12281	0.199986
$426$	30.7307	1.48891
$427$	11.5536	0.559118
$428$	−3.42709	−0.165654
$429$	0.996215	0.0480977
$430$	5.42778	0.261751
$431$	12.8516	0.619040	0.309520	−	0.950893i	$-0.399832\pi$
$431$	12.8516	0.619040	0.309520	+	0.950893i	$0.399832\pi$
$432$	−1.82640	−0.0878726
$433$	−29.0094	−1.39410	−0.697052	−	0.717020i	$-0.745505\pi$
$433$	−29.0094	−1.39410	−0.697052	+	0.717020i	$0.745505\pi$
$434$	−5.57538	−0.267627
$435$	−41.0392	−1.96768
$436$	17.0958	0.818740
$437$	8.42590	0.403065
$438$	35.0841	1.67638
$439$	−11.3573	−0.542055	−0.271028	−	0.962572i	$-0.587363\pi$
$439$	−11.3573	−0.542055	−0.271028	+	0.962572i	$0.587363\pi$
$440$	−2.96664	−0.141429
$441$	9.81881	0.467562
$442$	0.307853	0.0146431
$443$	−11.1541	−0.529948	−0.264974	−	0.964256i	$-0.585363\pi$
$443$	−11.1541	−0.529948	−0.264974	+	0.964256i	$0.585363\pi$
$444$	−18.9099	−0.897424
$445$	36.1753	1.71487
$446$	16.2892	0.771314
$447$	9.78901	0.463004
$448$	3.10643	0.146765
$449$	−33.0440	−1.55944	−0.779720	−	0.626128i	$-0.784639\pi$
$449$	−33.0440	−1.55944	−0.779720	+	0.626128i	$0.784639\pi$
$450$	21.0241	0.991087
$451$	−6.22399	−0.293076
$452$	−0.961140	−0.0452082
$453$	36.9193	1.73462
$454$	2.96072	0.138954
$455$	4.30000	0.201587
$456$	7.66516	0.358954
$457$	−41.0129	−1.91850	−0.959250	−	0.282557i	$-0.908817\pi$
$457$	−41.0129	−1.91850	−0.959250	+	0.282557i	$0.908817\pi$
$458$	6.29273	0.294040
$459$	−1.32708	−0.0619426
$460$	−9.29971	−0.433601
$461$	25.2081	1.17406	0.587029	−	0.809566i	$-0.300297\pi$
$461$	25.2081	1.17406	0.587029	+	0.809566i	$0.300297\pi$
$462$	7.30420	0.339822
$463$	4.23683	0.196902	0.0984512	−	0.995142i	$-0.468611\pi$
$463$	4.23683	0.196902	0.0984512	+	0.995142i	$0.468611\pi$
$464$	4.85092	0.225198
$465$	15.1840	0.704142
$466$	10.9177	0.505754
$467$	34.6643	1.60407	0.802036	−	0.597276i	$-0.203750\pi$
$467$	34.6643	1.60407	0.802036	+	0.597276i	$0.203750\pi$
$468$	1.56989	0.0725680
$469$	4.91369	0.226893
$470$	1.74688	0.0805777
$471$	−9.50051	−0.437760
$472$	13.5309	0.622808
$473$	−1.50855	−0.0693631
$474$	31.5500	1.44914
$475$	−16.7959	−0.770650
$476$	2.25716	0.103457
$477$	−37.5585	−1.71968
$478$	−7.47240	−0.341780
$479$	35.9768	1.64382	0.821911	−	0.569616i	$-0.192908\pi$
$479$	35.9768	1.64382	0.821911	+	0.569616i	$0.192908\pi$
$480$	−8.46007	−0.386148
$481$	3.09401	0.141075
$482$	16.3012	0.742500
$483$	22.8969	1.04184
$484$	−10.1755	−0.462522
$485$	−21.7380	−0.987072
$486$	22.0170	0.998710
$487$	−14.8441	−0.672652	−0.336326	−	0.941746i	$-0.609184\pi$
$487$	−14.8441	−0.672652	−0.336326	+	0.941746i	$0.609184\pi$
$488$	3.71925	0.168363
$489$	−33.7029	−1.52410
$490$	8.65760	0.391111
$491$	−6.52389	−0.294419	−0.147209	−	0.989105i	$-0.547029\pi$
$491$	−6.52389	−0.294419	−0.147209	+	0.989105i	$0.547029\pi$
$492$	−17.7492	−0.800194
$493$	3.52472	0.158745
$494$	−1.25416	−0.0564274
$495$	−10.9924	−0.494070
$496$	−1.79479	−0.0805883
$497$	−36.8659	−1.65366
$498$	3.03472	0.135989
$499$	39.9862	1.79003	0.895014	−	0.446037i	$-0.147165\pi$
$499$	39.9862	1.79003	0.895014	+	0.446037i	$0.147165\pi$
$500$	2.20217	0.0984842
$501$	28.8533	1.28907
$502$	−26.3779	−1.17730
$503$	−13.3161	−0.593738	−0.296869	−	0.954918i	$-0.595942\pi$
$503$	−13.3161	−0.593738	−0.296869	+	0.954918i	$0.595942\pi$
$504$	11.5103	0.512711
$505$	−2.89522	−0.128836
$506$	2.58467	0.114903
$507$	33.1982	1.47438
$508$	11.3719	0.504546
$509$	−9.88372	−0.438088	−0.219044	−	0.975715i	$-0.570294\pi$
$509$	−9.88372	−0.438088	−0.219044	+	0.975715i	$0.570294\pi$
$510$	−6.14716	−0.272201
$511$	−42.0884	−1.86188
$512$	1.00000	0.0441942
$513$	5.40638	0.238697
$514$	14.2107	0.626808
$515$	27.3303	1.20432
$516$	−4.30197	−0.189384
$517$	−0.485512	−0.0213528
$518$	22.6851	0.996727
$519$	10.9013	0.478513
$520$	1.38423	0.0607023
$521$	18.6009	0.814921	0.407460	−	0.913223i	$-0.366414\pi$
$521$	18.6009	0.814921	0.407460	+	0.913223i	$0.366414\pi$
$522$	17.9742	0.786710
$523$	29.2740	1.28006	0.640031	−	0.768349i	$-0.278921\pi$
$523$	29.2740	1.28006	0.640031	+	0.768349i	$0.278921\pi$
$524$	3.82347	0.167029
$525$	−45.6420	−1.99198
$526$	14.5159	0.632922
$527$	−1.30411	−0.0568078
$528$	2.35131	0.102328
$529$	−14.8977	−0.647725
$530$	−33.1167	−1.43850
$531$	50.1361	2.17572
$532$	−9.19545	−0.398674
$533$	2.90409	0.125790
$534$	−28.6719	−1.24076
$535$	−11.1967	−0.484075
$536$	1.58178	0.0683224
$537$	48.1414	2.07746
$538$	4.58958	0.197871
$539$	−2.40621	−0.103643
$540$	−5.96705	−0.256781
$541$	−6.31742	−0.271607	−0.135804	−	0.990736i	$-0.543362\pi$
$541$	−6.31742	−0.271607	−0.135804	+	0.990736i	$0.543362\pi$
$542$	20.0282	0.860284
$543$	47.8513	2.05350
$544$	0.726609	0.0311531
$545$	55.8539	2.39252
$546$	−3.40811	−0.145854
$547$	42.6105	1.82189	0.910947	−	0.412523i	$-0.135352\pi$
$547$	42.6105	1.82189	0.910947	+	0.412523i	$0.135352\pi$
$548$	−0.465272	−0.0198754
$549$	13.7810	0.588160
$550$	−5.15221	−0.219691
$551$	−14.3594	−0.611730
$552$	7.37080	0.313722
$553$	−37.8487	−1.60949
$554$	−3.94100	−0.167437
$555$	−61.7808	−2.62245
$556$	−17.7866	−0.754318
$557$	−21.0265	−0.890921	−0.445461	−	0.895302i	$-0.646960\pi$
$557$	−21.0265	−0.890921	−0.445461	+	0.895302i	$0.646960\pi$
$558$	−6.65026	−0.281528
$559$	0.703883	0.0297711
$560$	10.1491	0.428877
$561$	1.70849	0.0721323
$562$	−27.9837	−1.18042
$563$	3.91936	0.165181	0.0825906	−	0.996584i	$-0.473681\pi$
$563$	3.91936	0.165181	0.0825906	+	0.996584i	$0.473681\pi$
$564$	−1.38455	−0.0583001
$565$	−3.14016	−0.132107
$566$	−16.3706	−0.688107
$567$	−19.8394	−0.833178
$568$	−11.8676	−0.497953
$569$	−21.0763	−0.883563	−0.441782	−	0.897123i	$-0.645653\pi$
$569$	−21.0763	−0.883563	−0.441782	+	0.897123i	$0.645653\pi$
$570$	25.0429	1.04893
$571$	−3.99041	−0.166993	−0.0834967	−	0.996508i	$-0.526609\pi$
$571$	−3.99041	−0.166993	−0.0834967	+	0.996508i	$0.526609\pi$
$572$	−0.384719	−0.0160859
$573$	30.2648	1.26433
$574$	21.2927	0.888739
$575$	−16.1509	−0.673540
$576$	3.70532	0.154388
$577$	19.9849	0.831982	0.415991	−	0.909369i	$-0.363435\pi$
$577$	19.9849	0.831982	0.415991	+	0.909369i	$0.363435\pi$
$578$	−16.4720	−0.685147
$579$	−1.96529	−0.0816745
$580$	15.8485	0.658074
$581$	−3.64058	−0.151037
$582$	17.2292	0.714173
$583$	9.20414	0.381197
$584$	−13.5488	−0.560653
$585$	5.12900	0.212058
$586$	26.4450	1.09243
$587$	−22.9351	−0.946632	−0.473316	−	0.880893i	$-0.656943\pi$
$587$	−22.9351	−0.946632	−0.473316	+	0.880893i	$0.656943\pi$
$588$	−6.86188	−0.282979
$589$	5.31281	0.218910
$590$	44.2069	1.81997
$591$	−12.8739	−0.529561
$592$	7.30263	0.300136
$593$	2.21705	0.0910432	0.0455216	−	0.998963i	$-0.485505\pi$
$593$	2.21705	0.0910432	0.0455216	+	0.998963i	$0.485505\pi$
$594$	1.65843	0.0680461
$595$	7.37440	0.302321
$596$	−3.78033	−0.154848
$597$	67.9737	2.78198
$598$	−1.20600	−0.0493170
$599$	30.3915	1.24176	0.620881	−	0.783905i	$-0.286775\pi$
$599$	30.3915	1.24176	0.620881	+	0.783905i	$0.286775\pi$
$600$	−14.6927	−0.599828
$601$	39.0523	1.59297	0.796487	−	0.604655i	$-0.206689\pi$
$601$	39.0523	1.59297	0.796487	+	0.604655i	$0.206689\pi$
$602$	5.16083	0.210340
$603$	5.86099	0.238678
$604$	−14.2575	−0.580130
$605$	−33.2445	−1.35158
$606$	2.29471	0.0932162
$607$	26.7410	1.08538	0.542692	−	0.839931i	$-0.317405\pi$
$607$	26.7410	1.08538	0.542692	+	0.839931i	$0.317405\pi$
$608$	−2.96013	−0.120049
$609$	−39.0208	−1.58120
$610$	12.1512	0.491989
$611$	0.226538	0.00916475
$612$	2.69232	0.108830
$613$	18.2637	0.737662	0.368831	−	0.929496i	$-0.379758\pi$
$613$	18.2637	0.737662	0.368831	+	0.929496i	$0.379758\pi$
$614$	21.3964	0.863488
$615$	−57.9886	−2.33832
$616$	−2.82074	−0.113651
$617$	−0.364818	−0.0146870	−0.00734352	−	0.999973i	$-0.502338\pi$
$617$	−0.364818	−0.0146870	−0.00734352	+	0.999973i	$0.502338\pi$
$618$	−21.6615	−0.871355
$619$	3.61279	0.145210	0.0726052	−	0.997361i	$-0.476869\pi$
$619$	3.61279	0.145210	0.0726052	+	0.997361i	$0.476869\pi$
$620$	−5.86377	−0.235495
$621$	5.19876	0.208619
$622$	19.8494	0.795888
$623$	34.3961	1.37805
$624$	−1.09711	−0.0439197
$625$	−21.1755	−0.847018
$626$	−5.98475	−0.239199
$627$	−6.96021	−0.277964
$628$	3.66891	0.146405
$629$	5.30615	0.211570
$630$	37.6055	1.49824
$631$	−31.7836	−1.26529	−0.632643	−	0.774444i	$-0.718030\pi$
$631$	−31.7836	−1.26529	−0.632643	+	0.774444i	$0.718030\pi$
$632$	−12.1840	−0.484653
$633$	43.4642	1.72755
$634$	25.0057	0.993105
$635$	37.1533	1.47438
$636$	26.2477	1.04079
$637$	1.12273	0.0444842
$638$	−4.40479	−0.174387
$639$	−43.9732	−1.73955
$640$	3.26712	0.129144
$641$	23.6694	0.934886	0.467443	−	0.884023i	$-0.345175\pi$
$641$	23.6694	0.934886	0.467443	+	0.884023i	$0.345175\pi$
$642$	8.87431	0.350241
$643$	−33.8865	−1.33635	−0.668176	−	0.744004i	$-0.732925\pi$
$643$	−33.8865	−1.33635	−0.668176	+	0.744004i	$0.732925\pi$
$644$	−8.84233	−0.348437
$645$	−14.0550	−0.553417
$646$	−2.15086	−0.0846244
$647$	−15.0135	−0.590240	−0.295120	−	0.955460i	$-0.595360\pi$
$647$	−15.0135	−0.590240	−0.295120	+	0.955460i	$0.595360\pi$
$648$	−6.38657	−0.250888
$649$	−12.2864	−0.482285
$650$	2.40400	0.0942927
$651$	14.4372	0.565840
$652$	13.0154	0.509722
$653$	−9.58847	−0.375226	−0.187613	−	0.982243i	$-0.560075\pi$
$653$	−9.58847	−0.375226	−0.187613	+	0.982243i	$0.560075\pi$
$654$	−44.2689	−1.73105
$655$	12.4917	0.488092
$656$	6.85438	0.267619
$657$	−50.2026	−1.95859
$658$	1.66097	0.0647512
$659$	−13.2867	−0.517576	−0.258788	−	0.965934i	$-0.583323\pi$
$659$	−13.2867	−0.517576	−0.258788	+	0.965934i	$0.583323\pi$
$660$	7.68202	0.299022
$661$	25.3682	0.986709	0.493354	−	0.869828i	$-0.335771\pi$
$661$	25.3682	0.986709	0.493354	+	0.869828i	$0.335771\pi$
$662$	−8.25673	−0.320907
$663$	−0.797173	−0.0309596
$664$	−1.17195	−0.0454804
$665$	−30.0426	−1.16500
$666$	27.0586	1.04850
$667$	−13.8079	−0.534646
$668$	−11.1426	−0.431119
$669$	−42.1802	−1.63078
$670$	5.16785	0.199651
$671$	−3.37720	−0.130375
$672$	−8.04399	−0.310304
$673$	20.6006	0.794095	0.397047	−	0.917798i	$-0.370035\pi$
$673$	20.6006	0.794095	0.397047	+	0.917798i	$0.370035\pi$
$674$	−33.9817	−1.30892
$675$	−10.3631	−0.398874
$676$	−12.8205	−0.493096
$677$	10.3211	0.396671	0.198336	−	0.980134i	$-0.436446\pi$
$677$	10.3211	0.396671	0.198336	+	0.980134i	$0.436446\pi$
$678$	2.48884	0.0955832
$679$	−20.6689	−0.793199
$680$	2.37391	0.0910354
$681$	−7.66669	−0.293788
$682$	1.62972	0.0624053
$683$	25.8486	0.989067	0.494534	−	0.869158i	$-0.335339\pi$
$683$	25.8486	0.989067	0.494534	+	0.869158i	$0.335339\pi$
$684$	−10.9682	−0.419381
$685$	−1.52010	−0.0580799
$686$	−13.5132	−0.515937
$687$	−16.2948	−0.621685
$688$	1.66134	0.0633379
$689$	−4.29462	−0.163612
$690$	24.0813	0.916758
$691$	32.9564	1.25372	0.626859	−	0.779132i	$-0.284340\pi$
$691$	32.9564	1.25372	0.626859	+	0.779132i	$0.284340\pi$
$692$	−4.20986	−0.160035
$693$	−10.4517	−0.397029
$694$	1.17557	0.0446241
$695$	−58.1108	−2.20427
$696$	−12.5613	−0.476134
$697$	4.98045	0.188648
$698$	−32.4569	−1.22851
$699$	−28.2711	−1.06931
$700$	17.6260	0.666201
$701$	−2.95833	−0.111734	−0.0558672	−	0.998438i	$-0.517792\pi$
$701$	−2.95833	−0.111734	−0.0558672	+	0.998438i	$0.517792\pi$
$702$	−0.773816	−0.0292058
$703$	−21.6168	−0.815292
$704$	−0.908032	−0.0342227
$705$	−4.52349	−0.170364
$706$	−13.1837	−0.496176
$707$	−2.75283	−0.103531
$708$	−35.0376	−1.31680
$709$	−31.7189	−1.19123	−0.595615	−	0.803270i	$-0.703092\pi$
$709$	−31.7189	−1.19123	−0.595615	+	0.803270i	$0.703092\pi$
$710$	−38.7728	−1.45512
$711$	−45.1455	−1.69309
$712$	11.0725	0.414961
$713$	5.10878	0.191325
$714$	−5.84483	−0.218737
$715$	−1.25692	−0.0470062
$716$	−18.5913	−0.694789
$717$	19.3495	0.722621
$718$	4.36093	0.162748
$719$	45.0592	1.68042	0.840212	−	0.542258i	$-0.182431\pi$
$719$	45.0592	1.68042	0.840212	+	0.542258i	$0.182431\pi$
$720$	12.1057	0.451153
$721$	25.9861	0.967773
$722$	−10.2376	−0.381004
$723$	−42.2114	−1.56986
$724$	−18.4792	−0.686775
$725$	27.5243	1.02223
$726$	26.3490	0.977904
$727$	−2.33285	−0.0865205	−0.0432603	−	0.999064i	$-0.513774\pi$
$727$	−2.33285	−0.0865205	−0.0432603	+	0.999064i	$0.513774\pi$
$728$	1.31615	0.0487796
$729$	−37.8524	−1.40194
$730$	−44.2655	−1.63834
$731$	1.20714	0.0446478
$732$	−9.63087	−0.355967
$733$	10.6982	0.395148	0.197574	−	0.980288i	$-0.436694\pi$
$733$	10.6982	0.395148	0.197574	+	0.980288i	$0.436694\pi$
$734$	2.43669	0.0899397
$735$	−22.4185	−0.826920
$736$	−2.84646	−0.104922
$737$	−1.43630	−0.0529070
$738$	25.3977	0.934901
$739$	−16.0049	−0.588749	−0.294375	−	0.955690i	$-0.595111\pi$
$739$	−16.0049	−0.588749	−0.294375	+	0.955690i	$0.595111\pi$
$740$	23.8585	0.877057
$741$	3.24761	0.119304
$742$	−31.4879	−1.15596
$743$	2.89904	0.106356	0.0531778	−	0.998585i	$-0.483065\pi$
$743$	2.89904	0.106356	0.0531778	+	0.998585i	$0.483065\pi$
$744$	4.64753	0.170387
$745$	−12.3508	−0.452497
$746$	10.5200	0.385164
$747$	−4.34244	−0.158882
$748$	−0.659784	−0.0241241
$749$	−10.6460	−0.388997
$750$	−5.70245	−0.208224
$751$	−45.3074	−1.65329	−0.826645	−	0.562724i	$-0.809753\pi$
$751$	−45.3074	−1.65329	−0.826645	+	0.562724i	$0.809753\pi$
$752$	0.534686	0.0194980
$753$	68.3045	2.48915
$754$	2.05526	0.0748481
$755$	−46.5810	−1.69526
$756$	−5.67358	−0.206346
$757$	18.1828	0.660866	0.330433	−	0.943829i	$-0.392805\pi$
$757$	18.1828	0.660866	0.330433	+	0.943829i	$0.392805\pi$
$758$	4.56086	0.165658
$759$	−6.69292	−0.242938
$760$	−9.67110	−0.350808
$761$	10.2043	0.369905	0.184952	−	0.982747i	$-0.440787\pi$
$761$	10.2043	0.369905	0.184952	+	0.982747i	$0.440787\pi$
$762$	−29.4471	−1.06676
$763$	53.1069	1.92260
$764$	−11.6877	−0.422846
$765$	8.79611	0.318024
$766$	35.0887	1.26781
$767$	5.73281	0.207000
$768$	−2.58946	−0.0934392
$769$	19.8330	0.715195	0.357598	−	0.933876i	$-0.383596\pi$
$769$	19.8330	0.715195	0.357598	+	0.933876i	$0.383596\pi$
$770$	−9.21568	−0.332110
$771$	−36.7981	−1.32525
$772$	0.758955	0.0273154
$773$	−8.68929	−0.312532	−0.156266	−	0.987715i	$-0.549946\pi$
$773$	−8.68929	−0.312532	−0.156266	+	0.987715i	$0.549946\pi$
$774$	6.15579	0.221265
$775$	−10.1837	−0.365809
$776$	−6.65358	−0.238850
$777$	−58.7423	−2.10737
$778$	23.2111	0.832159
$779$	−20.2899	−0.726960
$780$	−3.58440	−0.128342
$781$	10.7762	0.385601
$782$	−2.06826	−0.0739609
$783$	−8.85971	−0.316620
$784$	2.64992	0.0946401
$785$	11.9868	0.427825
$786$	−9.90074	−0.353148
$787$	−25.8774	−0.922429	−0.461215	−	0.887289i	$-0.652586\pi$
$787$	−25.8774	−0.922429	−0.461215	+	0.887289i	$0.652586\pi$
$788$	4.97164	0.177107
$789$	−37.5883	−1.33818
$790$	−39.8065	−1.41625
$791$	−2.98572	−0.106160
$792$	−3.36455	−0.119554
$793$	1.57579	0.0559579
$794$	−32.2274	−1.14371
$795$	85.7544	3.04140
$796$	−26.2501	−0.930410
$797$	38.7236	1.37166	0.685830	−	0.727762i	$-0.259439\pi$
$797$	38.7236	1.37166	0.685830	+	0.727762i	$0.259439\pi$
$798$	23.8113	0.842911
$799$	0.388508	0.0137444
$800$	5.67404	0.200608
$801$	41.0273	1.44963
$802$	−1.00000	−0.0353112
$803$	12.3027	0.434154
$804$	−4.09596	−0.144453
$805$	−28.8889	−1.01820
$806$	−0.760423	−0.0267847
$807$	−11.8846	−0.418356
$808$	−0.886172	−0.0311754
$809$	−13.2713	−0.466593	−0.233296	−	0.972406i	$-0.574951\pi$
$809$	−13.2713	−0.466593	−0.233296	+	0.972406i	$0.574951\pi$
$810$	−20.8657	−0.733144
$811$	41.5169	1.45785	0.728927	−	0.684591i	$-0.240019\pi$
$811$	41.5169	1.45785	0.728927	+	0.684591i	$0.240019\pi$
$812$	15.0691	0.528820
$813$	−51.8623	−1.81889
$814$	−6.63102	−0.232417
$815$	42.5228	1.48951
$816$	−1.88153	−0.0658666
$817$	−4.91778	−0.172051
$818$	−11.6103	−0.405944
$819$	4.87674	0.170407
$820$	22.3940	0.782034
$821$	25.2256	0.880381	0.440190	−	0.897904i	$-0.354911\pi$
$821$	25.2256	0.880381	0.440190	+	0.897904i	$0.354911\pi$
$822$	1.20480	0.0420224
$823$	−21.4453	−0.747537	−0.373768	−	0.927522i	$-0.621935\pi$
$823$	−21.4453	−0.747537	−0.373768	+	0.927522i	$0.621935\pi$
$824$	8.36526	0.291418
$825$	13.3415	0.464490
$826$	42.0327	1.46250
$827$	4.37169	0.152018	0.0760092	−	0.997107i	$-0.475782\pi$
$827$	4.37169	0.152018	0.0760092	+	0.997107i	$0.475782\pi$
$828$	−10.5470	−0.366535
$829$	−34.7973	−1.20856	−0.604280	−	0.796772i	$-0.706539\pi$
$829$	−34.7973	−1.20856	−0.604280	+	0.796772i	$0.706539\pi$
$830$	−3.82889	−0.132903
$831$	10.2051	0.354010
$832$	0.423684	0.0146886
$833$	1.92546	0.0667131
$834$	46.0576	1.59485
$835$	−36.4040	−1.25981
$836$	2.68790	0.0929628
$837$	3.27799	0.113304
$838$	27.7858	0.959844
$839$	14.1245	0.487631	0.243816	−	0.969822i	$-0.421601\pi$
$839$	14.1245	0.487631	0.243816	+	0.969822i	$0.421601\pi$
$840$	−26.2806	−0.906769
$841$	−5.46856	−0.188571
$842$	−33.2355	−1.14537
$843$	72.4628	2.49575
$844$	−16.7850	−0.577765
$845$	−41.8860	−1.44092
$846$	1.98118	0.0681145
$847$	−31.6094	−1.08611
$848$	−10.1364	−0.348084
$849$	42.3910	1.45486
$850$	4.12281	0.141411
$851$	−20.7866	−0.712557
$852$	30.7307	1.05282
$853$	51.1554	1.75153	0.875764	−	0.482739i	$-0.160358\pi$
$853$	51.1554	1.75153	0.875764	+	0.482739i	$0.160358\pi$
$854$	11.5536	0.395356
$855$	−35.8345	−1.22551
$856$	−3.42709	−0.117135
$857$	56.2545	1.92162	0.960809	−	0.277210i	$-0.0894099\pi$
$857$	56.2545	1.92162	0.960809	+	0.277210i	$0.0894099\pi$
$858$	0.996215	0.0340102
$859$	20.2235	0.690016	0.345008	−	0.938600i	$-0.387876\pi$
$859$	20.2235	0.690016	0.345008	+	0.938600i	$0.387876\pi$
$860$	5.42778	0.185086
$861$	−55.1366	−1.87905
$862$	12.8516	0.437727
$863$	44.5654	1.51702	0.758512	−	0.651659i	$-0.225927\pi$
$863$	44.5654	1.51702	0.758512	+	0.651659i	$0.225927\pi$
$864$	−1.82640	−0.0621353
$865$	−13.7541	−0.467653
$866$	−29.0094	−0.985781
$867$	42.6537	1.44860
$868$	−5.57538	−0.189241
$869$	11.0634	0.375301
$870$	−41.0392	−1.39136
$871$	0.670174	0.0227080
$872$	17.0958	0.578937
$873$	−24.6536	−0.834399
$874$	8.42590	0.285010
$875$	6.84091	0.231265
$876$	35.0841	1.18538
$877$	−25.9045	−0.874733	−0.437366	−	0.899283i	$-0.644089\pi$
$877$	−25.9045	−0.874733	−0.437366	+	0.899283i	$0.644089\pi$
$878$	−11.3573	−0.383291
$879$	−68.4784	−2.30972
$880$	−2.96664	−0.100006
$881$	13.3504	0.449785	0.224893	−	0.974384i	$-0.427797\pi$
$881$	13.3504	0.449785	0.224893	+	0.974384i	$0.427797\pi$
$882$	9.81881	0.330616
$883$	−5.48598	−0.184618	−0.0923090	−	0.995730i	$-0.529425\pi$
$883$	−5.48598	−0.184618	−0.0923090	+	0.995730i	$0.529425\pi$
$884$	0.307853	0.0103542
$885$	−114.472	−3.84793
$886$	−11.1541	−0.374730
$887$	29.3224	0.984549	0.492275	−	0.870440i	$-0.336166\pi$
$887$	29.3224	0.984549	0.492275	+	0.870440i	$0.336166\pi$
$888$	−18.9099	−0.634574
$889$	35.3260	1.18480
$890$	36.1753	1.21260
$891$	5.79921	0.194281
$892$	16.2892	0.545401
$893$	−1.58274	−0.0529645
$894$	9.78901	0.327394
$895$	−60.7399	−2.03031
$896$	3.10643	0.103779
$897$	3.12289	0.104270
$898$	−33.0440	−1.10269
$899$	−8.70637	−0.290374
$900$	21.0241	0.700805
$901$	−7.36517	−0.245369
$902$	−6.22399	−0.207236
$903$	−13.3638	−0.444719
$904$	−0.961140	−0.0319671
$905$	−60.3738	−2.00689
$906$	36.9193	1.22656
$907$	29.0379	0.964189	0.482094	−	0.876119i	$-0.339876\pi$
$907$	29.0379	0.964189	0.482094	+	0.876119i	$0.339876\pi$
$908$	2.96072	0.0982551
$909$	−3.28355	−0.108908
$910$	4.30000	0.142544
$911$	9.19288	0.304574	0.152287	−	0.988336i	$-0.451336\pi$
$911$	9.19288	0.304574	0.152287	+	0.988336i	$0.451336\pi$
$912$	7.66516	0.253819
$913$	1.06417	0.0352187
$914$	−41.0129	−1.35658
$915$	−31.4652	−1.04021
$916$	6.29273	0.207918
$917$	11.8774	0.392225
$918$	−1.32708	−0.0438000
$919$	50.8567	1.67761	0.838804	−	0.544433i	$-0.183255\pi$
$919$	50.8567	1.67761	0.838804	+	0.544433i	$0.183255\pi$
$920$	−9.29971	−0.306602
$921$	−55.4051	−1.82566
$922$	25.2081	0.830184
$923$	−5.02811	−0.165502
$924$	7.30420	0.240291
$925$	41.4354	1.36239
$926$	4.23683	0.139231
$927$	30.9960	1.01804
$928$	4.85092	0.159239
$929$	16.7134	0.548349	0.274174	−	0.961680i	$-0.411595\pi$
$929$	16.7134	0.548349	0.274174	+	0.961680i	$0.411595\pi$
$930$	15.1840	0.497904
$931$	−7.84412	−0.257081
$932$	10.9177	0.357622
$933$	−51.3993	−1.68274
$934$	34.6643	1.13425
$935$	−2.15559	−0.0704953
$936$	1.56989	0.0513133
$937$	−24.4568	−0.798968	−0.399484	−	0.916740i	$-0.630811\pi$
$937$	−24.4568	−0.798968	−0.399484	+	0.916740i	$0.630811\pi$
$938$	4.91369	0.160438
$939$	15.4973	0.505735
$940$	1.74688	0.0569770
$941$	−14.8832	−0.485180	−0.242590	−	0.970129i	$-0.577997\pi$
$941$	−14.8832	−0.485180	−0.242590	+	0.970129i	$0.577997\pi$
$942$	−9.50051	−0.309543
$943$	−19.5107	−0.635356
$944$	13.5309	0.440392
$945$	−18.5362	−0.602984
$946$	−1.50855	−0.0490471
$947$	25.2384	0.820136	0.410068	−	0.912055i	$-0.365505\pi$
$947$	25.2384	0.820136	0.410068	+	0.912055i	$0.365505\pi$
$948$	31.5500	1.02469
$949$	−5.74041	−0.186342
$950$	−16.7959	−0.544932
$951$	−64.7514	−2.09971
$952$	2.25716	0.0731550
$953$	−19.3195	−0.625819	−0.312909	−	0.949783i	$-0.601304\pi$
$953$	−19.3195	−0.625819	−0.312909	+	0.949783i	$0.601304\pi$
$954$	−37.5585	−1.21600
$955$	−38.1850	−1.23564
$956$	−7.47240	−0.241675
$957$	11.4060	0.368705
$958$	35.9768	1.16236
$959$	−1.44533	−0.0466723
$960$	−8.46007	−0.273048
$961$	−27.7787	−0.896088
$962$	3.09401	0.0997549
$963$	−12.6984	−0.409202
$964$	16.3012	0.525027
$965$	2.47959	0.0798210
$966$	22.8969	0.736695
$967$	3.53561	0.113697	0.0568487	−	0.998383i	$-0.481895\pi$
$967$	3.53561	0.113697	0.0568487	+	0.998383i	$0.481895\pi$
$968$	−10.1755	−0.327052
$969$	5.56957	0.178920
$970$	−21.7380	−0.697965
$971$	−32.8805	−1.05519	−0.527593	−	0.849497i	$-0.676905\pi$
$971$	−32.8805	−1.05519	−0.527593	+	0.849497i	$0.676905\pi$
$972$	22.0170	0.706195
$973$	−55.2528	−1.77132
$974$	−14.8441	−0.475637
$975$	−6.22508	−0.199362
$976$	3.71925	0.119050
$977$	43.1481	1.38043	0.690215	−	0.723604i	$-0.257516\pi$
$977$	43.1481	1.38043	0.690215	+	0.723604i	$0.257516\pi$
$978$	−33.7029	−1.07770
$979$	−10.0542	−0.321334
$980$	8.65760	0.276557
$981$	63.3454	2.02246
$982$	−6.52389	−0.208186
$983$	−17.0097	−0.542526	−0.271263	−	0.962505i	$-0.587441\pi$
$983$	−17.0097	−0.542526	−0.271263	+	0.962505i	$0.587441\pi$
$984$	−17.7492	−0.565823
$985$	16.2429	0.517543
$986$	3.52472	0.112250
$987$	−4.30101	−0.136903
$988$	−1.25416	−0.0399002
$989$	−4.72893	−0.150371
$990$	−10.9924	−0.349360
$991$	−20.5226	−0.651921	−0.325960	−	0.945383i	$-0.605688\pi$
$991$	−20.5226	−0.651921	−0.325960	+	0.945383i	$0.605688\pi$
$992$	−1.79479	−0.0569845
$993$	21.3805	0.678490
$994$	−36.8659	−1.16931
$995$	−85.7621	−2.71884
$996$	3.03472	0.0961586
$997$	−54.7250	−1.73316	−0.866580	−	0.499039i	$-0.833687\pi$
$997$	−54.7250	−1.73316	−0.866580	+	0.499039i	$0.833687\pi$
$998$	39.9862	1.26574
$999$	−13.3375	−0.421980

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	802.2.a.f.1.1	✓	10
3.2	odd	2		7218.2.a.v.1.2		10
4.3	odd	2		6416.2.a.i.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
802.2.a.f.1.1	✓	10	1.1	even	1	trivial
6416.2.a.i.1.10		10	4.3	odd	2
7218.2.a.v.1.2		10	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 802 = 2 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	802.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.58946 q^{3} +1.00000 q^{4} +3.26712 q^{5} -2.58946 q^{6} +3.10643 q^{7} +1.00000 q^{8} +3.70532 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.58946 q^{3} +1.00000 q^{4} +3.26712 q^{5} -2.58946 q^{6} +3.10643 q^{7} +1.00000 q^{8} +3.70532 q^{9} +3.26712 q^{10} -0.908032 q^{11} -2.58946 q^{12} +0.423684 q^{13} +3.10643 q^{14} -8.46007 q^{15} +1.00000 q^{16} +0.726609 q^{17} +3.70532 q^{18} -2.96013 q^{19} +3.26712 q^{20} -8.04399 q^{21} -0.908032 q^{22} -2.84646 q^{23} -2.58946 q^{24} +5.67404 q^{25} +0.423684 q^{26} -1.82640 q^{27} +3.10643 q^{28} +4.85092 q^{29} -8.46007 q^{30} -1.79479 q^{31} +1.00000 q^{32} +2.35131 q^{33} +0.726609 q^{34} +10.1491 q^{35} +3.70532 q^{36} +7.30263 q^{37} -2.96013 q^{38} -1.09711 q^{39} +3.26712 q^{40} +6.85438 q^{41} -8.04399 q^{42} +1.66134 q^{43} -0.908032 q^{44} +12.1057 q^{45} -2.84646 q^{46} +0.534686 q^{47} -2.58946 q^{48} +2.64992 q^{49} +5.67404 q^{50} -1.88153 q^{51} +0.423684 q^{52} -10.1364 q^{53} -1.82640 q^{54} -2.96664 q^{55} +3.10643 q^{56} +7.66516 q^{57} +4.85092 q^{58} +13.5309 q^{59} -8.46007 q^{60} +3.71925 q^{61} -1.79479 q^{62} +11.5103 q^{63} +1.00000 q^{64} +1.38423 q^{65} +2.35131 q^{66} +1.58178 q^{67} +0.726609 q^{68} +7.37080 q^{69} +10.1491 q^{70} -11.8676 q^{71} +3.70532 q^{72} -13.5488 q^{73} +7.30263 q^{74} -14.6927 q^{75} -2.96013 q^{76} -2.82074 q^{77} -1.09711 q^{78} -12.1840 q^{79} +3.26712 q^{80} -6.38657 q^{81} +6.85438 q^{82} -1.17195 q^{83} -8.04399 q^{84} +2.37391 q^{85} +1.66134 q^{86} -12.5613 q^{87} -0.908032 q^{88} +11.0725 q^{89} +12.1057 q^{90} +1.31615 q^{91} -2.84646 q^{92} +4.64753 q^{93} +0.534686 q^{94} -9.67110 q^{95} -2.58946 q^{96} -6.65358 q^{97} +2.64992 q^{98} -3.36455 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 10 q^{3} + 10 q^{4} + 9 q^{5} + 10 q^{6} + q^{7} + 10 q^{8} + 22 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 + 10 * q^3 + 10 * q^4 + 9 * q^5 + 10 * q^6 + q^7 + 10 * q^8 + 22 * q^9	\( 10 q + 10 q^{2} + 10 q^{3} + 10 q^{4} + 9 q^{5} + 10 q^{6} + q^{7} + 10 q^{8} + 22 q^{9} + 9 q^{10} + 3 q^{11} + 10 q^{12} + 10 q^{13} + q^{14} - 7 q^{15} + 10 q^{16} + 22 q^{18} - 4 q^{19} + 9 q^{20} - 5 q^{21} + 3 q^{22} + 17 q^{23} + 10 q^{24} + 9 q^{25} + 10 q^{26} + 13 q^{27} + q^{28} - 4 q^{29} - 7 q^{30} - 9 q^{31} + 10 q^{32} - 3 q^{33} - 8 q^{35} + 22 q^{36} + 4 q^{37} - 4 q^{38} - 26 q^{39} + 9 q^{40} + 10 q^{41} - 5 q^{42} - 14 q^{43} + 3 q^{44} + 28 q^{45} + 17 q^{46} + 21 q^{47} + 10 q^{48} + 25 q^{49} + 9 q^{50} + 2 q^{51} + 10 q^{52} - 16 q^{53} + 13 q^{54} - 47 q^{55} + q^{56} + 9 q^{57} - 4 q^{58} + 10 q^{59} - 7 q^{60} + 20 q^{61} - 9 q^{62} - 53 q^{63} + 10 q^{64} - 16 q^{65} - 3 q^{66} - 27 q^{67} - 26 q^{69} - 8 q^{70} - 2 q^{71} + 22 q^{72} - 16 q^{73} + 4 q^{74} - 10 q^{75} - 4 q^{76} + 2 q^{77} - 26 q^{78} - 12 q^{79} + 9 q^{80} + 18 q^{81} + 10 q^{82} - q^{83} - 5 q^{84} - 19 q^{85} - 14 q^{86} - 13 q^{87} + 3 q^{88} - 5 q^{89} + 28 q^{90} - 27 q^{91} + 17 q^{92} - 55 q^{93} + 21 q^{94} - 27 q^{95} + 10 q^{96} - 15 q^{97} + 25 q^{98} - 31 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 10 * q^3 + 10 * q^4 + 9 * q^5 + 10 * q^6 + q^7 + 10 * q^8 + 22 * q^9 + 9 * q^10 + 3 * q^11 + 10 * q^12 + 10 * q^13 + q^14 - 7 * q^15 + 10 * q^16 + 22 * q^18 - 4 * q^19 + 9 * q^20 - 5 * q^21 + 3 * q^22 + 17 * q^23 + 10 * q^24 + 9 * q^25 + 10 * q^26 + 13 * q^27 + q^28 - 4 * q^29 - 7 * q^30 - 9 * q^31 + 10 * q^32 - 3 * q^33 - 8 * q^35 + 22 * q^36 + 4 * q^37 - 4 * q^38 - 26 * q^39 + 9 * q^40 + 10 * q^41 - 5 * q^42 - 14 * q^43 + 3 * q^44 + 28 * q^45 + 17 * q^46 + 21 * q^47 + 10 * q^48 + 25 * q^49 + 9 * q^50 + 2 * q^51 + 10 * q^52 - 16 * q^53 + 13 * q^54 - 47 * q^55 + q^56 + 9 * q^57 - 4 * q^58 + 10 * q^59 - 7 * q^60 + 20 * q^61 - 9 * q^62 - 53 * q^63 + 10 * q^64 - 16 * q^65 - 3 * q^66 - 27 * q^67 - 26 * q^69 - 8 * q^70 - 2 * q^71 + 22 * q^72 - 16 * q^73 + 4 * q^74 - 10 * q^75 - 4 * q^76 + 2 * q^77 - 26 * q^78 - 12 * q^79 + 9 * q^80 + 18 * q^81 + 10 * q^82 - q^83 - 5 * q^84 - 19 * q^85 - 14 * q^86 - 13 * q^87 + 3 * q^88 - 5 * q^89 + 28 * q^90 - 27 * q^91 + 17 * q^92 - 55 * q^93 + 21 * q^94 - 27 * q^95 + 10 * q^96 - 15 * q^97 + 25 * q^98 - 31 * q^99

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