LMFDB - Embedded newform 8026.2.a.b.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0879326623$
Analytic rank:	$1$
Dimension:	$81$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.45434 q^{3} +1.00000 q^{4} -0.137052 q^{5} +2.45434 q^{6} +1.42878 q^{7} -1.00000 q^{8} +3.02378 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.45434 q^{3} +1.00000 q^{4} -0.137052 q^{5} +2.45434 q^{6} +1.42878 q^{7} -1.00000 q^{8} +3.02378 q^{9} +0.137052 q^{10} +5.99295 q^{11} -2.45434 q^{12} +0.00977416 q^{13} -1.42878 q^{14} +0.336373 q^{15} +1.00000 q^{16} +4.90318 q^{17} -3.02378 q^{18} -4.84695 q^{19} -0.137052 q^{20} -3.50671 q^{21} -5.99295 q^{22} +1.82484 q^{23} +2.45434 q^{24} -4.98122 q^{25} -0.00977416 q^{26} -0.0583726 q^{27} +1.42878 q^{28} +9.26593 q^{29} -0.336373 q^{30} -4.94749 q^{31} -1.00000 q^{32} -14.7087 q^{33} -4.90318 q^{34} -0.195818 q^{35} +3.02378 q^{36} -8.39758 q^{37} +4.84695 q^{38} -0.0239891 q^{39} +0.137052 q^{40} +9.26345 q^{41} +3.50671 q^{42} -0.700127 q^{43} +5.99295 q^{44} -0.414417 q^{45} -1.82484 q^{46} -4.55239 q^{47} -2.45434 q^{48} -4.95859 q^{49} +4.98122 q^{50} -12.0341 q^{51} +0.00977416 q^{52} -5.19938 q^{53} +0.0583726 q^{54} -0.821347 q^{55} -1.42878 q^{56} +11.8961 q^{57} -9.26593 q^{58} -5.69783 q^{59} +0.336373 q^{60} -11.0441 q^{61} +4.94749 q^{62} +4.32032 q^{63} +1.00000 q^{64} -0.00133957 q^{65} +14.7087 q^{66} +4.91331 q^{67} +4.90318 q^{68} -4.47877 q^{69} +0.195818 q^{70} -15.3451 q^{71} -3.02378 q^{72} +6.97316 q^{73} +8.39758 q^{74} +12.2256 q^{75} -4.84695 q^{76} +8.56260 q^{77} +0.0239891 q^{78} -0.741388 q^{79} -0.137052 q^{80} -8.92808 q^{81} -9.26345 q^{82} -16.0427 q^{83} -3.50671 q^{84} -0.671993 q^{85} +0.700127 q^{86} -22.7417 q^{87} -5.99295 q^{88} -12.7080 q^{89} +0.414417 q^{90} +0.0139651 q^{91} +1.82484 q^{92} +12.1428 q^{93} +4.55239 q^{94} +0.664286 q^{95} +2.45434 q^{96} -12.1654 q^{97} +4.95859 q^{98} +18.1214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9}+O(q^{10}) $ 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9} + 26 q^{10} - 41 q^{11} - 10 q^{12} + 33 q^{13} - 3 q^{14} - 7 q^{15} + 81 q^{16} - 9 q^{17} - 59 q^{18} - 32 q^{19} - 26 q^{20} - 23 q^{21} + 41 q^{22} - 28 q^{23} + 10 q^{24} + 81 q^{25} - 33 q^{26} - 37 q^{27} + 3 q^{28} - 35 q^{29} + 7 q^{30} - 29 q^{31} - 81 q^{32} - 7 q^{33} + 9 q^{34} - 67 q^{35} + 59 q^{36} + 13 q^{37} + 32 q^{38} - 42 q^{39} + 26 q^{40} - 66 q^{41} + 23 q^{42} - 22 q^{43} - 41 q^{44} - 65 q^{45} + 28 q^{46} - 71 q^{47} - 10 q^{48} + 64 q^{49} - 81 q^{50} - 43 q^{51} + 33 q^{52} - 37 q^{53} + 37 q^{54} + 12 q^{55} - 3 q^{56} - q^{57} + 35 q^{58} - 162 q^{59} - 7 q^{60} + 19 q^{61} + 29 q^{62} - 16 q^{63} + 81 q^{64} - 45 q^{65} + 7 q^{66} - 43 q^{67} - 9 q^{68} - 21 q^{69} + 67 q^{70} - 99 q^{71} - 59 q^{72} + 53 q^{73} - 13 q^{74} - 61 q^{75} - 32 q^{76} - 31 q^{77} + 42 q^{78} + 4 q^{79} - 26 q^{80} + q^{81} + 66 q^{82} - 112 q^{83} - 23 q^{84} + 17 q^{85} + 22 q^{86} - 15 q^{87} + 41 q^{88} - 111 q^{89} + 65 q^{90} - 49 q^{91} - 28 q^{92} - 19 q^{93} + 71 q^{94} - 53 q^{95} + 10 q^{96} + 50 q^{97} - 64 q^{98} - 97 q^{99}+O(q^{100}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9 + 26 * q^10 - 41 * q^11 - 10 * q^12 + 33 * q^13 - 3 * q^14 - 7 * q^15 + 81 * q^16 - 9 * q^17 - 59 * q^18 - 32 * q^19 - 26 * q^20 - 23 * q^21 + 41 * q^22 - 28 * q^23 + 10 * q^24 + 81 * q^25 - 33 * q^26 - 37 * q^27 + 3 * q^28 - 35 * q^29 + 7 * q^30 - 29 * q^31 - 81 * q^32 - 7 * q^33 + 9 * q^34 - 67 * q^35 + 59 * q^36 + 13 * q^37 + 32 * q^38 - 42 * q^39 + 26 * q^40 - 66 * q^41 + 23 * q^42 - 22 * q^43 - 41 * q^44 - 65 * q^45 + 28 * q^46 - 71 * q^47 - 10 * q^48 + 64 * q^49 - 81 * q^50 - 43 * q^51 + 33 * q^52 - 37 * q^53 + 37 * q^54 + 12 * q^55 - 3 * q^56 - q^57 + 35 * q^58 - 162 * q^59 - 7 * q^60 + 19 * q^61 + 29 * q^62 - 16 * q^63 + 81 * q^64 - 45 * q^65 + 7 * q^66 - 43 * q^67 - 9 * q^68 - 21 * q^69 + 67 * q^70 - 99 * q^71 - 59 * q^72 + 53 * q^73 - 13 * q^74 - 61 * q^75 - 32 * q^76 - 31 * q^77 + 42 * q^78 + 4 * q^79 - 26 * q^80 + q^81 + 66 * q^82 - 112 * q^83 - 23 * q^84 + 17 * q^85 + 22 * q^86 - 15 * q^87 + 41 * q^88 - 111 * q^89 + 65 * q^90 - 49 * q^91 - 28 * q^92 - 19 * q^93 + 71 * q^94 - 53 * q^95 + 10 * q^96 + 50 * q^97 - 64 * q^98 - 97 * 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
$3$	−2.45434	−1.41701	−0.708507	−	0.705704i	$-0.750631\pi$
$3$	−2.45434	−1.41701	−0.708507	+	0.705704i	$0.750631\pi$
$4$	1.00000	0.500000
$5$	−0.137052	−0.0612917	−0.0306458	−	0.999530i	$-0.509756\pi$
$5$	−0.137052	−0.0612917	−0.0306458	+	0.999530i	$0.509756\pi$
$6$	2.45434	1.00198
$7$	1.42878	0.540028	0.270014	−	0.962856i	$-0.412972\pi$
$7$	1.42878	0.540028	0.270014	+	0.962856i	$0.412972\pi$
$8$	−1.00000	−0.353553
$9$	3.02378	1.00793
$10$	0.137052	0.0433397
$11$	5.99295	1.80694	0.903471	−	0.428650i	$-0.141011\pi$
$11$	5.99295	1.80694	0.903471	+	0.428650i	$0.141011\pi$
$12$	−2.45434	−0.708507
$13$	0.00977416	0.00271087	0.00135543	−	0.999999i	$-0.499569\pi$
$13$	0.00977416	0.00271087	0.00135543	+	0.999999i	$0.499569\pi$
$14$	−1.42878	−0.381858
$15$	0.336373	0.0868511
$16$	1.00000	0.250000
$17$	4.90318	1.18920	0.594598	−	0.804023i	$-0.297311\pi$
$17$	4.90318	1.18920	0.594598	+	0.804023i	$0.297311\pi$
$18$	−3.02378	−0.712713
$19$	−4.84695	−1.11197	−0.555984	−	0.831193i	$-0.687658\pi$
$19$	−4.84695	−1.11197	−0.555984	+	0.831193i	$0.687658\pi$
$20$	−0.137052	−0.0306458
$21$	−3.50671	−0.765227
$22$	−5.99295	−1.27770
$23$	1.82484	0.380504	0.190252	−	0.981735i	$-0.439069\pi$
$23$	1.82484	0.380504	0.190252	+	0.981735i	$0.439069\pi$
$24$	2.45434	0.500990
$25$	−4.98122	−0.996243
$26$	−0.00977416	−0.00191687
$27$	−0.0583726	−0.0112338
$28$	1.42878	0.270014
$29$	9.26593	1.72064	0.860320	−	0.509755i	$-0.170264\pi$
$29$	9.26593	1.72064	0.860320	+	0.509755i	$0.170264\pi$
$30$	−0.336373	−0.0614130
$31$	−4.94749	−0.888595	−0.444298	−	0.895879i	$-0.646547\pi$
$31$	−4.94749	−0.888595	−0.444298	+	0.895879i	$0.646547\pi$
$32$	−1.00000	−0.176777
$33$	−14.7087	−2.56046
$34$	−4.90318	−0.840889
$35$	−0.195818	−0.0330992
$36$	3.02378	0.503964
$37$	−8.39758	−1.38055	−0.690277	−	0.723545i	$-0.742511\pi$
$37$	−8.39758	−1.38055	−0.690277	+	0.723545i	$0.742511\pi$
$38$	4.84695	0.786280
$39$	−0.0239891	−0.00384133
$40$	0.137052	0.0216699
$41$	9.26345	1.44671	0.723354	−	0.690477i	$-0.242599\pi$
$41$	9.26345	1.44671	0.723354	+	0.690477i	$0.242599\pi$
$42$	3.50671	0.541097
$43$	−0.700127	−0.106768	−0.0533842	−	0.998574i	$-0.517001\pi$
$43$	−0.700127	−0.106768	−0.0533842	+	0.998574i	$0.517001\pi$
$44$	5.99295	0.903471
$45$	−0.414417	−0.0617776
$46$	−1.82484	−0.269057
$47$	−4.55239	−0.664034	−0.332017	−	0.943273i	$-0.607729\pi$
$47$	−4.55239	−0.664034	−0.332017	+	0.943273i	$0.607729\pi$
$48$	−2.45434	−0.354253
$49$	−4.95859	−0.708370
$50$	4.98122	0.704450
$51$	−12.0341	−1.68511
$52$	0.00977416	0.00135543
$53$	−5.19938	−0.714190	−0.357095	−	0.934068i	$-0.616233\pi$
$53$	−5.19938	−0.714190	−0.357095	+	0.934068i	$0.616233\pi$
$54$	0.0583726	0.00794351
$55$	−0.821347	−0.110750
$56$	−1.42878	−0.190929
$57$	11.8961	1.57567
$58$	−9.26593	−1.21668
$59$	−5.69783	−0.741794	−0.370897	−	0.928674i	$-0.620950\pi$
$59$	−5.69783	−0.741794	−0.370897	+	0.928674i	$0.620950\pi$
$60$	0.336373	0.0434256
$61$	−11.0441	−1.41405	−0.707027	−	0.707187i	$-0.749964\pi$
$61$	−11.0441	−1.41405	−0.707027	+	0.707187i	$0.749964\pi$
$62$	4.94749	0.628332
$63$	4.32032	0.544309
$64$	1.00000	0.125000
$65$	−0.00133957	−0.000166153 0
$66$	14.7087	1.81052
$67$	4.91331	0.600256	0.300128	−	0.953899i	$-0.402971\pi$
$67$	4.91331	0.600256	0.300128	+	0.953899i	$0.402971\pi$
$68$	4.90318	0.594598
$69$	−4.47877	−0.539180
$70$	0.195818	0.0234047
$71$	−15.3451	−1.82113	−0.910566	−	0.413364i	$-0.864354\pi$
$71$	−15.3451	−1.82113	−0.910566	+	0.413364i	$0.864354\pi$
$72$	−3.02378	−0.356356
$73$	6.97316	0.816146	0.408073	−	0.912949i	$-0.366201\pi$
$73$	6.97316	0.816146	0.408073	+	0.912949i	$0.366201\pi$
$74$	8.39758	0.976199
$75$	12.2256	1.41169
$76$	−4.84695	−0.555984
$77$	8.56260	0.975799
$78$	0.0239891	0.00271623
$79$	−0.741388	−0.0834126	−0.0417063	−	0.999130i	$-0.513279\pi$
$79$	−0.741388	−0.0834126	−0.0417063	+	0.999130i	$0.513279\pi$
$80$	−0.137052	−0.0153229
$81$	−8.92808	−0.992009
$82$	−9.26345	−1.02298
$83$	−16.0427	−1.76091	−0.880455	−	0.474129i	$-0.842763\pi$
$83$	−16.0427	−1.76091	−0.880455	+	0.474129i	$0.842763\pi$
$84$	−3.50671	−0.382614
$85$	−0.671993	−0.0728878
$86$	0.700127	0.0754966
$87$	−22.7417	−2.43817
$88$	−5.99295	−0.638850
$89$	−12.7080	−1.34704	−0.673522	−	0.739167i	$-0.735220\pi$
$89$	−12.7080	−1.34704	−0.673522	+	0.739167i	$0.735220\pi$
$90$	0.414417	0.0436833
$91$	0.0139651	0.00146394
$92$	1.82484	0.190252
$93$	12.1428	1.25915
$94$	4.55239	0.469543
$95$	0.664286	0.0681543
$96$	2.45434	0.250495
$97$	−12.1654	−1.23521	−0.617604	−	0.786489i	$-0.711897\pi$
$97$	−12.1654	−1.23521	−0.617604	+	0.786489i	$0.711897\pi$
$98$	4.95859	0.500893
$99$	18.1214	1.82127
$100$	−4.98122	−0.498122
$101$	−10.5306	−1.04784	−0.523918	−	0.851769i	$-0.675530\pi$
$101$	−10.5306	−1.04784	−0.523918	+	0.851769i	$0.675530\pi$
$102$	12.0341	1.19155
$103$	10.2439	1.00936	0.504682	−	0.863305i	$-0.331610\pi$
$103$	10.2439	1.00936	0.504682	+	0.863305i	$0.331610\pi$
$104$	−0.00977416	−0.000958436 0
$105$	0.480603	0.0469021
$106$	5.19938	0.505009
$107$	17.7284	1.71387	0.856933	−	0.515428i	$-0.172367\pi$
$107$	17.7284	1.71387	0.856933	+	0.515428i	$0.172367\pi$
$108$	−0.0583726	−0.00561691
$109$	−11.8292	−1.13303	−0.566514	−	0.824052i	$-0.691708\pi$
$109$	−11.8292	−1.13303	−0.566514	+	0.824052i	$0.691708\pi$
$110$	0.821347	0.0783124
$111$	20.6105	1.95626
$112$	1.42878	0.135007
$113$	5.06230	0.476221	0.238110	−	0.971238i	$-0.423472\pi$
$113$	5.06230	0.476221	0.238110	+	0.971238i	$0.423472\pi$
$114$	−11.8961	−1.11417
$115$	−0.250098	−0.0233218
$116$	9.26593	0.860320
$117$	0.0295550	0.00273236
$118$	5.69783	0.524528
$119$	7.00557	0.642200
$120$	−0.336373	−0.0307065
$121$	24.9154	2.26504
$122$	11.0441	0.999887
$123$	−22.7357	−2.05001
$124$	−4.94749	−0.444298
$125$	1.36795	0.122353
$126$	−4.32032	−0.384885
$127$	−9.89192	−0.877766	−0.438883	−	0.898544i	$-0.644626\pi$
$127$	−9.89192	−0.877766	−0.438883	+	0.898544i	$0.644626\pi$
$128$	−1.00000	−0.0883883
$129$	1.71835	0.151292
$130$	0.00133957	0.000117488 0
$131$	−0.477737	−0.0417401	−0.0208700	−	0.999782i	$-0.506644\pi$
$131$	−0.477737	−0.0417401	−0.0208700	+	0.999782i	$0.506644\pi$
$132$	−14.7087	−1.28023
$133$	−6.92523	−0.600494
$134$	−4.91331	−0.424445
$135$	0.00800010	0.000688539 0
$136$	−4.90318	−0.420445
$137$	13.3288	1.13875	0.569377	−	0.822076i	$-0.307184\pi$
$137$	13.3288	1.13875	0.569377	+	0.822076i	$0.307184\pi$
$138$	4.47877	0.381258
$139$	−23.4731	−1.99096	−0.995480	−	0.0949676i	$-0.969725\pi$
$139$	−23.4731	−1.99096	−0.995480	+	0.0949676i	$0.969725\pi$
$140$	−0.195818	−0.0165496
$141$	11.1731	0.940945
$142$	15.3451	1.28773
$143$	0.0585761	0.00489838
$144$	3.02378	0.251982
$145$	−1.26992	−0.105461
$146$	−6.97316	−0.577103
$147$	12.1701	1.00377
$148$	−8.39758	−0.690277
$149$	5.11508	0.419044	0.209522	−	0.977804i	$-0.432809\pi$
$149$	5.11508	0.419044	0.209522	+	0.977804i	$0.432809\pi$
$150$	−12.2256	−0.998216
$151$	20.4990	1.66819	0.834094	−	0.551623i	$-0.185991\pi$
$151$	20.4990	1.66819	0.834094	+	0.551623i	$0.185991\pi$
$152$	4.84695	0.393140
$153$	14.8262	1.19862
$154$	−8.56260	−0.689994
$155$	0.678065	0.0544635
$156$	−0.0239891	−0.00192067
$157$	−10.2882	−0.821086	−0.410543	−	0.911841i	$-0.634661\pi$
$157$	−10.2882	−0.821086	−0.410543	+	0.911841i	$0.634661\pi$
$158$	0.741388	0.0589816
$159$	12.7611	1.01202
$160$	0.137052	0.0108349
$161$	2.60729	0.205483
$162$	8.92808	0.701457
$163$	−2.16669	−0.169708	−0.0848541	−	0.996393i	$-0.527042\pi$
$163$	−2.16669	−0.169708	−0.0848541	+	0.996393i	$0.527042\pi$
$164$	9.26345	0.723354
$165$	2.01587	0.156935
$166$	16.0427	1.24515
$167$	−4.48301	−0.346906	−0.173453	−	0.984842i	$-0.555492\pi$
$167$	−4.48301	−0.346906	−0.173453	+	0.984842i	$0.555492\pi$
$168$	3.50671	0.270549
$169$	−12.9999	−0.999993
$170$	0.671993	0.0515395
$171$	−14.6561	−1.12078
$172$	−0.700127	−0.0533842
$173$	22.5659	1.71565	0.857827	−	0.513939i	$-0.171814\pi$
$173$	22.5659	1.71565	0.857827	+	0.513939i	$0.171814\pi$
$174$	22.7417	1.72405
$175$	−7.11706	−0.537999
$176$	5.99295	0.451735
$177$	13.9844	1.05113
$178$	12.7080	0.952505
$179$	−17.0091	−1.27132	−0.635661	−	0.771968i	$-0.719272\pi$
$179$	−17.0091	−1.27132	−0.635661	+	0.771968i	$0.719272\pi$
$180$	−0.414417	−0.0308888
$181$	13.3169	0.989839	0.494919	−	0.868939i	$-0.335198\pi$
$181$	13.3169	0.989839	0.494919	+	0.868939i	$0.335198\pi$
$182$	−0.0139651	−0.00103516
$183$	27.1060	2.00373
$184$	−1.82484	−0.134529
$185$	1.15091	0.0846165
$186$	−12.1428	−0.890355
$187$	29.3845	2.14881
$188$	−4.55239	−0.332017
$189$	−0.0834016	−0.00606658
$190$	−0.664286	−0.0481924
$191$	8.84916	0.640303	0.320151	−	0.947366i	$-0.396266\pi$
$191$	8.84916	0.640303	0.320151	+	0.947366i	$0.396266\pi$
$192$	−2.45434	−0.177127
$193$	−0.409805	−0.0294984	−0.0147492	−	0.999891i	$-0.504695\pi$
$193$	−0.409805	−0.0294984	−0.0147492	+	0.999891i	$0.504695\pi$
$194$	12.1654	0.873424
$195$	0.00328776	0.000235442 0
$196$	−4.95859	−0.354185
$197$	−9.43960	−0.672544	−0.336272	−	0.941765i	$-0.609166\pi$
$197$	−9.43960	−0.672544	−0.336272	+	0.941765i	$0.609166\pi$
$198$	−18.1214	−1.28783
$199$	−14.7052	−1.04242	−0.521212	−	0.853427i	$-0.674520\pi$
$199$	−14.7052	−1.04242	−0.521212	+	0.853427i	$0.674520\pi$
$200$	4.98122	0.352225
$201$	−12.0589	−0.850571
$202$	10.5306	0.740932
$203$	13.2390	0.929194
$204$	−12.0341	−0.842554
$205$	−1.26958	−0.0886711
$206$	−10.2439	−0.713728
$207$	5.51791	0.383521
$208$	0.00977416	0.000677716 0
$209$	−29.0475	−2.00926
$210$	−0.480603	−0.0331648
$211$	0.793503	0.0546270	0.0273135	−	0.999627i	$-0.491305\pi$
$211$	0.793503	0.0546270	0.0273135	+	0.999627i	$0.491305\pi$
$212$	−5.19938	−0.357095
$213$	37.6622	2.58057
$214$	−17.7284	−1.21189
$215$	0.0959540	0.00654401
$216$	0.0583726	0.00397175
$217$	−7.06888	−0.479867
$218$	11.8292	0.801171
$219$	−17.1145	−1.15649
$220$	−0.821347	−0.0553752
$221$	0.0479245	0.00322375
$222$	−20.6105	−1.38329
$223$	5.34875	0.358179	0.179089	−	0.983833i	$-0.442685\pi$
$223$	5.34875	0.358179	0.179089	+	0.983833i	$0.442685\pi$
$224$	−1.42878	−0.0954644
$225$	−15.0621	−1.00414
$226$	−5.06230	−0.336739
$227$	−1.54953	−0.102846	−0.0514229	−	0.998677i	$-0.516376\pi$
$227$	−1.54953	−0.102846	−0.0514229	+	0.998677i	$0.516376\pi$
$228$	11.8961	0.787836
$229$	16.3209	1.07852	0.539258	−	0.842140i	$-0.318705\pi$
$229$	16.3209	1.07852	0.539258	+	0.842140i	$0.318705\pi$
$230$	0.250098	0.0164910
$231$	−21.0155	−1.38272
$232$	−9.26593	−0.608338
$233$	14.3662	0.941163	0.470581	−	0.882357i	$-0.344044\pi$
$233$	14.3662	0.941163	0.470581	+	0.882357i	$0.344044\pi$
$234$	−0.0295550	−0.00193207
$235$	0.623915	0.0406997
$236$	−5.69783	−0.370897
$237$	1.81962	0.118197
$238$	−7.00557	−0.454104
$239$	−3.02501	−0.195672	−0.0978358	−	0.995203i	$-0.531192\pi$
$239$	−3.02501	−0.195672	−0.0978358	+	0.995203i	$0.531192\pi$
$240$	0.336373	0.0217128
$241$	−13.9546	−0.898897	−0.449448	−	0.893306i	$-0.648379\pi$
$241$	−13.9546	−0.898897	−0.449448	+	0.893306i	$0.648379\pi$
$242$	−24.9154	−1.60162
$243$	22.0877	1.41692
$244$	−11.0441	−0.707027
$245$	0.679586	0.0434171
$246$	22.7357	1.44957
$247$	−0.0473749	−0.00301439
$248$	4.94749	0.314166
$249$	39.3741	2.49523
$250$	−1.36795	−0.0865167
$251$	−10.3014	−0.650216	−0.325108	−	0.945677i	$-0.605401\pi$
$251$	−10.3014	−0.650216	−0.325108	+	0.945677i	$0.605401\pi$
$252$	4.32032	0.272155
$253$	10.9361	0.687549
$254$	9.89192	0.620674
$255$	1.64930	0.103283
$256$	1.00000	0.0625000
$257$	−19.4002	−1.21015	−0.605076	−	0.796168i	$-0.706857\pi$
$257$	−19.4002	−1.21015	−0.605076	+	0.796168i	$0.706857\pi$
$258$	−1.71835	−0.106980
$259$	−11.9983	−0.745538
$260$	−0.00133957	−8.30767e−5 0
$261$	28.0182	1.73428
$262$	0.477737	0.0295147
$263$	10.1706	0.627145	0.313572	−	0.949564i	$-0.398474\pi$
$263$	10.1706	0.627145	0.313572	+	0.949564i	$0.398474\pi$
$264$	14.7087	0.905260
$265$	0.712588	0.0437739
$266$	6.92523	0.424613
$267$	31.1897	1.90878
$268$	4.91331	0.300128
$269$	15.4943	0.944704	0.472352	−	0.881410i	$-0.343405\pi$
$269$	15.4943	0.944704	0.472352	+	0.881410i	$0.343405\pi$
$270$	−0.00800010	−0.000486871 0
$271$	3.04090	0.184722	0.0923609	−	0.995726i	$-0.470559\pi$
$271$	3.04090	0.184722	0.0923609	+	0.995726i	$0.470559\pi$
$272$	4.90318	0.297299
$273$	−0.0342752	−0.00207443
$274$	−13.3288	−0.805221
$275$	−29.8522	−1.80015
$276$	−4.47877	−0.269590
$277$	5.84665	0.351291	0.175646	−	0.984453i	$-0.443799\pi$
$277$	5.84665	0.351291	0.175646	+	0.984453i	$0.443799\pi$
$278$	23.4731	1.40782
$279$	−14.9601	−0.895640
$280$	0.195818	0.0117023
$281$	−14.2179	−0.848168	−0.424084	−	0.905623i	$-0.639404\pi$
$281$	−14.2179	−0.848168	−0.424084	+	0.905623i	$0.639404\pi$
$282$	−11.1731	−0.665349
$283$	4.49920	0.267450	0.133725	−	0.991019i	$-0.457306\pi$
$283$	4.49920	0.267450	0.133725	+	0.991019i	$0.457306\pi$
$284$	−15.3451	−0.910566
$285$	−1.63038	−0.0965756
$286$	−0.0585761	−0.00346367
$287$	13.2354	0.781263
$288$	−3.02378	−0.178178
$289$	7.04121	0.414189
$290$	1.26992	0.0745721
$291$	29.8580	1.75031
$292$	6.97316	0.408073
$293$	8.04758	0.470145	0.235072	−	0.971978i	$-0.424467\pi$
$293$	8.04758	0.470145	0.235072	+	0.971978i	$0.424467\pi$
$294$	−12.1701	−0.709772
$295$	0.780901	0.0454658
$296$	8.39758	0.488100
$297$	−0.349824	−0.0202988
$298$	−5.11508	−0.296309
$299$	0.0178362	0.00103150
$300$	12.2256	0.705845
$301$	−1.00033	−0.0576579
$302$	−20.4990	−1.17959
$303$	25.8457	1.48480
$304$	−4.84695	−0.277992
$305$	1.51362	0.0866697
$306$	−14.8262	−0.847555
$307$	−7.31022	−0.417216	−0.208608	−	0.977999i	$-0.566893\pi$
$307$	−7.31022	−0.417216	−0.208608	+	0.977999i	$0.566893\pi$
$308$	8.56260	0.487900
$309$	−25.1421	−1.43028
$310$	−0.678065	−0.0385115
$311$	−26.0829	−1.47903	−0.739514	−	0.673141i	$-0.764945\pi$
$311$	−26.0829	−1.47903	−0.739514	+	0.673141i	$0.764945\pi$
$312$	0.0239891	0.00135812
$313$	27.2000	1.53743	0.768717	−	0.639589i	$-0.220895\pi$
$313$	27.2000	1.53743	0.768717	+	0.639589i	$0.220895\pi$
$314$	10.2882	0.580596
$315$	−0.592110	−0.0333616
$316$	−0.741388	−0.0417063
$317$	−12.2350	−0.687187	−0.343594	−	0.939118i	$-0.611644\pi$
$317$	−12.2350	−0.687187	−0.343594	+	0.939118i	$0.611644\pi$
$318$	−12.7611	−0.715604
$319$	55.5302	3.10910
$320$	−0.137052	−0.00766146
$321$	−43.5114	−2.42857
$322$	−2.60729	−0.145299
$323$	−23.7655	−1.32235
$324$	−8.92808	−0.496005
$325$	−0.0486872	−0.00270068
$326$	2.16669	0.120002
$327$	29.0328	1.60552
$328$	−9.26345	−0.511489
$329$	−6.50436	−0.358597
$330$	−2.01587	−0.110970
$331$	7.14191	0.392555	0.196277	−	0.980548i	$-0.437115\pi$
$331$	7.14191	0.392555	0.196277	+	0.980548i	$0.437115\pi$
$332$	−16.0427	−0.880455
$333$	−25.3925	−1.39150
$334$	4.48301	0.245299
$335$	−0.673380	−0.0367907
$336$	−3.50671	−0.191307
$337$	11.5483	0.629075	0.314537	−	0.949245i	$-0.398151\pi$
$337$	11.5483	0.629075	0.314537	+	0.949245i	$0.398151\pi$
$338$	12.9999	0.707102
$339$	−12.4246	−0.674811
$340$	−0.671993	−0.0364439
$341$	−29.6500	−1.60564
$342$	14.6561	0.792513
$343$	−17.0862	−0.922568
$344$	0.700127	0.0377483
$345$	0.613825	0.0330472
$346$	−22.5659	−1.21315
$347$	11.2020	0.601357	0.300678	−	0.953726i	$-0.402787\pi$
$347$	11.2020	0.601357	0.300678	+	0.953726i	$0.402787\pi$
$348$	−22.7417	−1.21908
$349$	−30.6352	−1.63986	−0.819932	−	0.572460i	$-0.805989\pi$
$349$	−30.6352	−1.63986	−0.819932	+	0.572460i	$0.805989\pi$
$350$	7.11706	0.380423
$351$	−0.000570544 0	−3.04534e−5 0
$352$	−5.99295	−0.319425
$353$	−7.09554	−0.377658	−0.188829	−	0.982010i	$-0.560469\pi$
$353$	−7.09554	−0.377658	−0.188829	+	0.982010i	$0.560469\pi$
$354$	−13.9844	−0.743263
$355$	2.10309	0.111620
$356$	−12.7080	−0.673522
$357$	−17.1941	−0.910006
$358$	17.0091	0.898960
$359$	−25.8061	−1.36199	−0.680997	−	0.732286i	$-0.738453\pi$
$359$	−25.8061	−1.36199	−0.680997	+	0.732286i	$0.738453\pi$
$360$	0.414417	0.0218417
$361$	4.49295	0.236471
$362$	−13.3169	−0.699922
$363$	−61.1509	−3.20959
$364$	0.0139651	0.000731972 0
$365$	−0.955687	−0.0500230
$366$	−27.1060	−1.41685
$367$	−12.9688	−0.676968	−0.338484	−	0.940972i	$-0.609914\pi$
$367$	−12.9688	−0.676968	−0.338484	+	0.940972i	$0.609914\pi$
$368$	1.82484	0.0951261
$369$	28.0107	1.45818
$370$	−1.15091	−0.0598329
$371$	−7.42878	−0.385683
$372$	12.1428	0.629576
$373$	−30.5186	−1.58019	−0.790097	−	0.612981i	$-0.789970\pi$
$373$	−30.5186	−1.58019	−0.790097	+	0.612981i	$0.789970\pi$
$374$	−29.3845	−1.51944
$375$	−3.35741	−0.173376
$376$	4.55239	0.234771
$377$	0.0905667	0.00466442
$378$	0.0834016	0.00428972
$379$	−4.04948	−0.208008	−0.104004	−	0.994577i	$-0.533165\pi$
$379$	−4.04948	−0.208008	−0.104004	+	0.994577i	$0.533165\pi$
$380$	0.664286	0.0340772
$381$	24.2781	1.24381
$382$	−8.84916	−0.452762
$383$	26.7076	1.36469	0.682346	−	0.731029i	$-0.260960\pi$
$383$	26.7076	1.36469	0.682346	+	0.731029i	$0.260960\pi$
$384$	2.45434	0.125247
$385$	−1.17352	−0.0598084
$386$	0.409805	0.0208585
$387$	−2.11703	−0.107615
$388$	−12.1654	−0.617604
$389$	−8.35311	−0.423519	−0.211760	−	0.977322i	$-0.567919\pi$
$389$	−8.35311	−0.423519	−0.211760	+	0.977322i	$0.567919\pi$
$390$	−0.00328776	−0.000166482 0
$391$	8.94750	0.452495
$392$	4.95859	0.250446
$393$	1.17253	0.0591462
$394$	9.43960	0.475560
$395$	0.101609	0.00511250
$396$	18.1214	0.910633
$397$	28.4938	1.43006	0.715032	−	0.699091i	$-0.246412\pi$
$397$	28.4938	1.43006	0.715032	+	0.699091i	$0.246412\pi$
$398$	14.7052	0.737105
$399$	16.9969	0.850908
$400$	−4.98122	−0.249061
$401$	22.8453	1.14084	0.570419	−	0.821354i	$-0.306781\pi$
$401$	22.8453	1.14084	0.570419	+	0.821354i	$0.306781\pi$
$402$	12.0589	0.601444
$403$	−0.0483576	−0.00240886
$404$	−10.5306	−0.523918
$405$	1.22361	0.0608019
$406$	−13.2390	−0.657039
$407$	−50.3263	−2.49458
$408$	12.0341	0.595776
$409$	20.7883	1.02791	0.513957	−	0.857816i	$-0.328179\pi$
$409$	20.7883	1.02791	0.513957	+	0.857816i	$0.328179\pi$
$410$	1.26958	0.0627000
$411$	−32.7133	−1.61363
$412$	10.2439	0.504682
$413$	−8.14095	−0.400590
$414$	−5.51791	−0.271190
$415$	2.19868	0.107929
$416$	−0.00977416	−0.000479218 0
$417$	57.6109	2.82122
$418$	29.0475	1.42076
$419$	−22.2246	−1.08574	−0.542871	−	0.839816i	$-0.682663\pi$
$419$	−22.2246	−1.08574	−0.542871	+	0.839816i	$0.682663\pi$
$420$	0.480603	0.0234510
$421$	23.4087	1.14087	0.570434	−	0.821343i	$-0.306775\pi$
$421$	23.4087	1.14087	0.570434	+	0.821343i	$0.306775\pi$
$422$	−0.793503	−0.0386271
$423$	−13.7654	−0.669298
$424$	5.19938	0.252504
$425$	−24.4238	−1.18473
$426$	−37.6622	−1.82474
$427$	−15.7796	−0.763629
$428$	17.7284	0.856933
$429$	−0.143766	−0.00694107
$430$	−0.0959540	−0.00462731
$431$	−17.9526	−0.864748	−0.432374	−	0.901694i	$-0.642324\pi$
$431$	−17.9526	−0.864748	−0.432374	+	0.901694i	$0.642324\pi$
$432$	−0.0583726	−0.00280845
$433$	−29.0315	−1.39517	−0.697583	−	0.716504i	$-0.745741\pi$
$433$	−29.0315	−1.39517	−0.697583	+	0.716504i	$0.745741\pi$
$434$	7.06888	0.339317
$435$	3.11681	0.149439
$436$	−11.8292	−0.566514
$437$	−8.84489	−0.423109
$438$	17.1145	0.817762
$439$	27.0239	1.28978	0.644889	−	0.764276i	$-0.276903\pi$
$439$	27.0239	1.28978	0.644889	+	0.764276i	$0.276903\pi$
$440$	0.821347	0.0391562
$441$	−14.9937	−0.713985
$442$	−0.0479245	−0.00227954
$443$	−6.58663	−0.312940	−0.156470	−	0.987683i	$-0.550011\pi$
$443$	−6.58663	−0.312940	−0.156470	+	0.987683i	$0.550011\pi$
$444$	20.6105	0.978132
$445$	1.74166	0.0825626
$446$	−5.34875	−0.253271
$447$	−12.5541	−0.593790
$448$	1.42878	0.0675035
$449$	−2.05847	−0.0971451	−0.0485725	−	0.998820i	$-0.515467\pi$
$449$	−2.05847	−0.0971451	−0.0485725	+	0.998820i	$0.515467\pi$
$450$	15.0621	0.710035
$451$	55.5154	2.61412
$452$	5.06230	0.238110
$453$	−50.3116	−2.36384
$454$	1.54953	0.0727229
$455$	−0.00191395	−8.97275e−5 0
$456$	−11.8961	−0.557085
$457$	2.08943	0.0977392	0.0488696	−	0.998805i	$-0.484438\pi$
$457$	2.08943	0.0977392	0.0488696	+	0.998805i	$0.484438\pi$
$458$	−16.3209	−0.762627
$459$	−0.286212	−0.0133592
$460$	−0.250098	−0.0116609
$461$	24.9368	1.16142	0.580711	−	0.814110i	$-0.302775\pi$
$461$	24.9368	1.16142	0.580711	+	0.814110i	$0.302775\pi$
$462$	21.0155	0.977731
$463$	−28.5744	−1.32797	−0.663983	−	0.747748i	$-0.731135\pi$
$463$	−28.5744	−1.32797	−0.663983	+	0.747748i	$0.731135\pi$
$464$	9.26593	0.430160
$465$	−1.66420	−0.0771755
$466$	−14.3662	−0.665503
$467$	−23.2494	−1.07585	−0.537927	−	0.842991i	$-0.680793\pi$
$467$	−23.2494	−1.07585	−0.537927	+	0.842991i	$0.680793\pi$
$468$	0.0295550	0.00136618
$469$	7.02003	0.324155
$470$	−0.623915	−0.0287791
$471$	25.2507	1.16349
$472$	5.69783	0.262264
$473$	−4.19582	−0.192924
$474$	−1.81962	−0.0835778
$475$	24.1437	1.10779
$476$	7.00557	0.321100
$477$	−15.7218	−0.719852
$478$	3.02501	0.138361
$479$	−22.6187	−1.03348	−0.516738	−	0.856144i	$-0.672854\pi$
$479$	−22.6187	−1.03348	−0.516738	+	0.856144i	$0.672854\pi$
$480$	−0.336373	−0.0153533
$481$	−0.0820794	−0.00374250
$482$	13.9546	0.635616
$483$	−6.39917	−0.291172
$484$	24.9154	1.13252
$485$	1.66730	0.0757080
$486$	−22.0877	−1.00192
$487$	42.3068	1.91710	0.958552	−	0.284916i	$-0.0919657\pi$
$487$	42.3068	1.91710	0.958552	+	0.284916i	$0.0919657\pi$
$488$	11.0441	0.499943
$489$	5.31779	0.240479
$490$	−0.679586	−0.0307006
$491$	−18.1085	−0.817226	−0.408613	−	0.912708i	$-0.633987\pi$
$491$	−18.1085	−0.817226	−0.408613	+	0.912708i	$0.633987\pi$
$492$	−22.7357	−1.02500
$493$	45.4325	2.04618
$494$	0.0473749	0.00213150
$495$	−2.48358	−0.111628
$496$	−4.94749	−0.222149
$497$	−21.9248	−0.983462
$498$	−39.3741	−1.76440
$499$	−5.03264	−0.225292	−0.112646	−	0.993635i	$-0.535933\pi$
$499$	−5.03264	−0.225292	−0.112646	+	0.993635i	$0.535933\pi$
$500$	1.36795	0.0611765
$501$	11.0028	0.491570
$502$	10.3014	0.459772
$503$	−26.9491	−1.20160	−0.600800	−	0.799400i	$-0.705151\pi$
$503$	−26.9491	−1.20160	−0.600800	+	0.799400i	$0.705151\pi$
$504$	−4.32032	−0.192442
$505$	1.44325	0.0642236
$506$	−10.9361	−0.486171
$507$	31.9062	1.41700
$508$	−9.89192	−0.438883
$509$	7.20158	0.319204	0.159602	−	0.987181i	$-0.448979\pi$
$509$	7.20158	0.319204	0.159602	+	0.987181i	$0.448979\pi$
$510$	−1.64930	−0.0730322
$511$	9.96311	0.440742
$512$	−1.00000	−0.0441942
$513$	0.282929	0.0124916
$514$	19.4002	0.855706
$515$	−1.40395	−0.0618656
$516$	1.71835	0.0756461
$517$	−27.2822	−1.19987
$518$	11.9983	0.527175
$519$	−55.3844	−2.43110
$520$	0.00133957	5.87441e−5 0
$521$	33.1858	1.45390	0.726949	−	0.686692i	$-0.240938\pi$
$521$	33.1858	1.45390	0.726949	+	0.686692i	$0.240938\pi$
$522$	−28.0182	−1.22632
$523$	−0.527926	−0.0230846	−0.0115423	−	0.999933i	$-0.503674\pi$
$523$	−0.527926	−0.0230846	−0.0115423	+	0.999933i	$0.503674\pi$
$524$	−0.477737	−0.0208700
$525$	17.4677	0.762353
$526$	−10.1706	−0.443458
$527$	−24.2585	−1.05671
$528$	−14.7087	−0.640115
$529$	−19.6700	−0.855216
$530$	−0.712588	−0.0309528
$531$	−17.2290	−0.747675
$532$	−6.92523	−0.300247
$533$	0.0905425	0.00392183
$534$	−31.1897	−1.34971
$535$	−2.42971	−0.105046
$536$	−4.91331	−0.212222
$537$	41.7462	1.80148
$538$	−15.4943	−0.668006
$539$	−29.7166	−1.27998
$540$	0.00800010	0.000344270 0
$541$	0.976162	0.0419685	0.0209842	−	0.999780i	$-0.493320\pi$
$541$	0.976162	0.0419685	0.0209842	+	0.999780i	$0.493320\pi$
$542$	−3.04090	−0.130618
$543$	−32.6842	−1.40262
$544$	−4.90318	−0.210222
$545$	1.62121	0.0694451
$546$	0.0342752	0.00146684
$547$	14.3144	0.612038	0.306019	−	0.952025i	$-0.401003\pi$
$547$	14.3144	0.612038	0.306019	+	0.952025i	$0.401003\pi$
$548$	13.3288	0.569377
$549$	−33.3950	−1.42526
$550$	29.8522	1.27290
$551$	−44.9115	−1.91329
$552$	4.47877	0.190629
$553$	−1.05928	−0.0450452
$554$	−5.84665	−0.248400
$555$	−2.82472	−0.119903
$556$	−23.4731	−0.995480
$557$	−39.1941	−1.66071	−0.830355	−	0.557235i	$-0.811862\pi$
$557$	−39.1941	−1.66071	−0.830355	+	0.557235i	$0.811862\pi$
$558$	14.9601	0.633313
$559$	−0.00684315	−0.000289435 0
$560$	−0.195818	−0.00827481
$561$	−72.1196	−3.04489
$562$	14.2179	0.599745
$563$	−26.7561	−1.12763	−0.563817	−	0.825900i	$-0.690668\pi$
$563$	−26.7561	−1.12763	−0.563817	+	0.825900i	$0.690668\pi$
$564$	11.1731	0.470473
$565$	−0.693799	−0.0291884
$566$	−4.49920	−0.189115
$567$	−12.7563	−0.535713
$568$	15.3451	0.643867
$569$	−13.7662	−0.577110	−0.288555	−	0.957463i	$-0.593175\pi$
$569$	−13.7662	−0.577110	−0.288555	+	0.957463i	$0.593175\pi$
$570$	1.63038	0.0682893
$571$	8.24697	0.345125	0.172563	−	0.984999i	$-0.444795\pi$
$571$	8.24697	0.345125	0.172563	+	0.984999i	$0.444795\pi$
$572$	0.0585761	0.00244919
$573$	−21.7188	−0.907318
$574$	−13.2354	−0.552436
$575$	−9.08990	−0.379075
$576$	3.02378	0.125991
$577$	−38.4509	−1.60073	−0.800365	−	0.599512i	$-0.795361\pi$
$577$	−38.4509	−1.60073	−0.800365	+	0.599512i	$0.795361\pi$
$578$	−7.04121	−0.292876
$579$	1.00580	0.0417997
$580$	−1.26992	−0.0527304
$581$	−22.9214	−0.950941
$582$	−29.8580	−1.23765
$583$	−31.1596	−1.29050
$584$	−6.97316	−0.288551
$585$	−0.00405058	−0.000167471 0
$586$	−8.04758	−0.332442
$587$	−19.7961	−0.817074	−0.408537	−	0.912742i	$-0.633961\pi$
$587$	−19.7961	−0.817074	−0.408537	+	0.912742i	$0.633961\pi$
$588$	12.1701	0.501885
$589$	23.9803	0.988089
$590$	−0.780901	−0.0321492
$591$	23.1680	0.953004
$592$	−8.39758	−0.345139
$593$	8.03835	0.330096	0.165048	−	0.986286i	$-0.447222\pi$
$593$	8.03835	0.330096	0.165048	+	0.986286i	$0.447222\pi$
$594$	0.349824	0.0143535
$595$	−0.960130	−0.0393615
$596$	5.11508	0.209522
$597$	36.0916	1.47713
$598$	−0.0178362	−0.000729378 0
$599$	30.7079	1.25469	0.627344	−	0.778742i	$-0.284142\pi$
$599$	30.7079	1.25469	0.627344	+	0.778742i	$0.284142\pi$
$600$	−12.2256	−0.499108
$601$	0.909361	0.0370936	0.0185468	−	0.999828i	$-0.494096\pi$
$601$	0.909361	0.0370936	0.0185468	+	0.999828i	$0.494096\pi$
$602$	1.00033	0.0407703
$603$	14.8568	0.605015
$604$	20.4990	0.834094
$605$	−3.41472	−0.138828
$606$	−25.8457	−1.04991
$607$	−20.4440	−0.829797	−0.414898	−	0.909868i	$-0.636183\pi$
$607$	−20.4440	−0.829797	−0.414898	+	0.909868i	$0.636183\pi$
$608$	4.84695	0.196570
$609$	−32.4929	−1.31668
$610$	−1.51362	−0.0612847
$611$	−0.0444958	−0.00180011
$612$	14.8262	0.599312
$613$	34.8601	1.40799	0.703994	−	0.710206i	$-0.251398\pi$
$613$	34.8601	1.40799	0.703994	+	0.710206i	$0.251398\pi$
$614$	7.31022	0.295016
$615$	3.11597	0.125648
$616$	−8.56260	−0.344997
$617$	12.5665	0.505910	0.252955	−	0.967478i	$-0.418598\pi$
$617$	12.5665	0.505910	0.252955	+	0.967478i	$0.418598\pi$
$618$	25.1421	1.01136
$619$	−48.8725	−1.96435	−0.982175	−	0.187966i	$-0.939810\pi$
$619$	−48.8725	−1.96435	−0.982175	+	0.187966i	$0.939810\pi$
$620$	0.678065	0.0272317
$621$	−0.106520	−0.00427452
$622$	26.0829	1.04583
$623$	−18.1569	−0.727442
$624$	−0.0239891	−0.000960333 0
$625$	24.7186	0.988744
$626$	−27.2000	−1.08713
$627$	71.2925	2.84715
$628$	−10.2882	−0.410543
$629$	−41.1749	−1.64175
$630$	0.592110	0.0235902
$631$	19.1865	0.763801	0.381901	−	0.924203i	$-0.375270\pi$
$631$	19.1865	0.763801	0.381901	+	0.924203i	$0.375270\pi$
$632$	0.741388	0.0294908
$633$	−1.94753	−0.0774072
$634$	12.2350	0.485915
$635$	1.35571	0.0537997
$636$	12.7611	0.506009
$637$	−0.0484660	−0.00192029
$638$	−55.5302	−2.19846
$639$	−46.4003	−1.83557
$640$	0.137052	0.00541747
$641$	−14.4187	−0.569503	−0.284752	−	0.958601i	$-0.591911\pi$
$641$	−14.4187	−0.569503	−0.284752	+	0.958601i	$0.591911\pi$
$642$	43.5114	1.71726
$643$	−34.9972	−1.38016	−0.690078	−	0.723735i	$-0.742424\pi$
$643$	−34.9972	−1.38016	−0.690078	+	0.723735i	$0.742424\pi$
$644$	2.60729	0.102742
$645$	−0.235504	−0.00927295
$646$	23.7655	0.935041
$647$	21.1774	0.832568	0.416284	−	0.909235i	$-0.363332\pi$
$647$	21.1774	0.832568	0.416284	+	0.909235i	$0.363332\pi$
$648$	8.92808	0.350728
$649$	−34.1468	−1.34038
$650$	0.0486872	0.00190967
$651$	17.3494	0.679977
$652$	−2.16669	−0.0848541
$653$	25.1885	0.985702	0.492851	−	0.870114i	$-0.335955\pi$
$653$	25.1885	0.985702	0.492851	+	0.870114i	$0.335955\pi$
$654$	−29.0328	−1.13527
$655$	0.0654749	0.00255832
$656$	9.26345	0.361677
$657$	21.0853	0.822617
$658$	6.50436	0.253566
$659$	39.5449	1.54045	0.770225	−	0.637773i	$-0.220144\pi$
$659$	39.5449	1.54045	0.770225	+	0.637773i	$0.220144\pi$
$660$	2.01587	0.0784675
$661$	39.1443	1.52254	0.761268	−	0.648437i	$-0.224577\pi$
$661$	39.1443	1.52254	0.761268	+	0.648437i	$0.224577\pi$
$662$	−7.14191	−0.277578
$663$	−0.117623	−0.00456810
$664$	16.0427	0.622576
$665$	0.949119	0.0368053
$666$	25.3925	0.983938
$667$	16.9088	0.654711
$668$	−4.48301	−0.173453
$669$	−13.1277	−0.507544
$670$	0.673380	0.0260149
$671$	−66.1868	−2.55511
$672$	3.50671	0.135274
$673$	11.6357	0.448523	0.224262	−	0.974529i	$-0.428003\pi$
$673$	11.6357	0.448523	0.224262	+	0.974529i	$0.428003\pi$
$674$	−11.5483	−0.444823
$675$	0.290767	0.0111916
$676$	−12.9999	−0.499996
$677$	6.58000	0.252890	0.126445	−	0.991974i	$-0.459643\pi$
$677$	6.58000	0.252890	0.126445	+	0.991974i	$0.459643\pi$
$678$	12.4246	0.477164
$679$	−17.3817	−0.667048
$680$	0.671993	0.0257697
$681$	3.80307	0.145734
$682$	29.6500	1.13536
$683$	4.44863	0.170222	0.0851111	−	0.996371i	$-0.472875\pi$
$683$	4.44863	0.170222	0.0851111	+	0.996371i	$0.472875\pi$
$684$	−14.6561	−0.560391
$685$	−1.82674	−0.0697961
$686$	17.0862	0.652354
$687$	−40.0571	−1.52827
$688$	−0.700127	−0.0266921
$689$	−0.0508196	−0.00193607
$690$	−0.613825	−0.0233679
$691$	−25.3568	−0.964620	−0.482310	−	0.876001i	$-0.660202\pi$
$691$	−25.3568	−0.964620	−0.482310	+	0.876001i	$0.660202\pi$
$692$	22.5659	0.857827
$693$	25.8915	0.983535
$694$	−11.2020	−0.425223
$695$	3.21704	0.122029
$696$	22.7417	0.862023
$697$	45.4204	1.72042
$698$	30.6352	1.15956
$699$	−35.2596	−1.33364
$700$	−7.11706	−0.269000
$701$	3.90649	0.147546	0.0737730	−	0.997275i	$-0.476496\pi$
$701$	3.90649	0.147546	0.0737730	+	0.997275i	$0.476496\pi$
$702$	0.000570544 0	2.15338e−5 0
$703$	40.7027	1.53513
$704$	5.99295	0.225868
$705$	−1.53130	−0.0576721
$706$	7.09554	0.267044
$707$	−15.0459	−0.565861
$708$	13.9844	0.525566
$709$	−0.183682	−0.00689831	−0.00344915	−	0.999994i	$-0.501098\pi$
$709$	−0.183682	−0.00689831	−0.00344915	+	0.999994i	$0.501098\pi$
$710$	−2.10309	−0.0789274
$711$	−2.24180	−0.0840739
$712$	12.7080	0.476252
$713$	−9.02836	−0.338115
$714$	17.1941	0.643471
$715$	−0.00802798	−0.000300230 0
$716$	−17.0091	−0.635661
$717$	7.42440	0.277269
$718$	25.8061	0.963075
$719$	−40.1896	−1.49882	−0.749409	−	0.662107i	$-0.769662\pi$
$719$	−40.1896	−1.49882	−0.749409	+	0.662107i	$0.769662\pi$
$720$	−0.414417	−0.0154444
$721$	14.6363	0.545085
$722$	−4.49295	−0.167210
$723$	34.2494	1.27375
$724$	13.3169	0.494919
$725$	−46.1556	−1.71418
$726$	61.1509	2.26952
$727$	7.11827	0.264002	0.132001	−	0.991250i	$-0.457860\pi$
$727$	7.11827	0.264002	0.132001	+	0.991250i	$0.457860\pi$
$728$	−0.0139651	−0.000517582 0
$729$	−27.4264	−1.01579
$730$	0.955687	0.0353716
$731$	−3.43285	−0.126969
$732$	27.1060	1.00187
$733$	−39.0184	−1.44118	−0.720589	−	0.693363i	$-0.756128\pi$
$733$	−39.0184	−1.44118	−0.720589	+	0.693363i	$0.756128\pi$
$734$	12.9688	0.478689
$735$	−1.66793	−0.0615227
$736$	−1.82484	−0.0672643
$737$	29.4452	1.08463
$738$	−28.0107	−1.03109
$739$	−17.6882	−0.650669	−0.325335	−	0.945599i	$-0.605477\pi$
$739$	−17.6882	−0.650669	−0.325335	+	0.945599i	$0.605477\pi$
$740$	1.15091	0.0423082
$741$	0.116274	0.00427144
$742$	7.42878	0.272719
$743$	−51.0836	−1.87408	−0.937039	−	0.349226i	$-0.886445\pi$
$743$	−51.0836	−1.87408	−0.937039	+	0.349226i	$0.886445\pi$
$744$	−12.1428	−0.445177
$745$	−0.701033	−0.0256839
$746$	30.5186	1.11737
$747$	−48.5095	−1.77487
$748$	29.3845	1.07440
$749$	25.3299	0.925536
$750$	3.35741	0.122595
$751$	22.4849	0.820486	0.410243	−	0.911976i	$-0.365444\pi$
$751$	22.4849	0.820486	0.410243	+	0.911976i	$0.365444\pi$
$752$	−4.55239	−0.166008
$753$	25.2830	0.921365
$754$	−0.0905667	−0.00329824
$755$	−2.80944	−0.102246
$756$	−0.0834016	−0.00303329
$757$	27.8522	1.01230	0.506152	−	0.862444i	$-0.331067\pi$
$757$	27.8522	1.01230	0.506152	+	0.862444i	$0.331067\pi$
$758$	4.04948	0.147084
$759$	−26.8410	−0.974267
$760$	−0.664286	−0.0240962
$761$	47.0399	1.70520	0.852598	−	0.522567i	$-0.175025\pi$
$761$	47.0399	1.70520	0.852598	+	0.522567i	$0.175025\pi$
$762$	−24.2781	−0.879504
$763$	−16.9013	−0.611867
$764$	8.84916	0.320151
$765$	−2.03196	−0.0734657
$766$	−26.7076	−0.964983
$767$	−0.0556915	−0.00201090
$768$	−2.45434	−0.0885634
$769$	−27.4460	−0.989727	−0.494863	−	0.868971i	$-0.664782\pi$
$769$	−27.4460	−0.989727	−0.494863	+	0.868971i	$0.664782\pi$
$770$	1.17352	0.0422909
$771$	47.6147	1.71480
$772$	−0.409805	−0.0147492
$773$	20.9286	0.752748	0.376374	−	0.926468i	$-0.377171\pi$
$773$	20.9286	0.752748	0.376374	+	0.926468i	$0.377171\pi$
$774$	2.11703	0.0760951
$775$	24.6445	0.885257
$776$	12.1654	0.436712
$777$	29.4479	1.05644
$778$	8.35311	0.299473
$779$	−44.8995	−1.60869
$780$	0.00328776	0.000117721 0
$781$	−91.9625	−3.29068
$782$	−8.94750	−0.319962
$783$	−0.540876	−0.0193293
$784$	−4.95859	−0.177092
$785$	1.41002	0.0503257
$786$	−1.17253	−0.0418227
$787$	−41.5818	−1.48223	−0.741115	−	0.671378i	$-0.765703\pi$
$787$	−41.5818	−1.48223	−0.741115	+	0.671378i	$0.765703\pi$
$788$	−9.43960	−0.336272
$789$	−24.9620	−0.888672
$790$	−0.101609	−0.00361508
$791$	7.23291	0.257173
$792$	−18.1214	−0.643915
$793$	−0.107947	−0.00383331
$794$	−28.4938	−1.01121
$795$	−1.74893	−0.0620282
$796$	−14.7052	−0.521212
$797$	40.5482	1.43629	0.718146	−	0.695893i	$-0.244991\pi$
$797$	40.5482	1.43629	0.718146	+	0.695893i	$0.244991\pi$
$798$	−16.9969	−0.601683
$799$	−22.3212	−0.789667
$800$	4.98122	0.176113
$801$	−38.4262	−1.35772
$802$	−22.8453	−0.806694
$803$	41.7898	1.47473
$804$	−12.0589	−0.425285
$805$	−0.357335	−0.0125944
$806$	0.0483576	0.00170332
$807$	−38.0283	−1.33866
$808$	10.5306	0.370466
$809$	−34.7274	−1.22095	−0.610475	−	0.792036i	$-0.709021\pi$
$809$	−34.7274	−1.22095	−0.610475	+	0.792036i	$0.709021\pi$
$810$	−1.22361	−0.0429934
$811$	−32.9574	−1.15729	−0.578645	−	0.815580i	$-0.696418\pi$
$811$	−32.9574	−1.15729	−0.578645	+	0.815580i	$0.696418\pi$
$812$	13.2390	0.464597
$813$	−7.46341	−0.261753
$814$	50.3263	1.76393
$815$	0.296950	0.0104017
$816$	−12.0341	−0.421277
$817$	3.39348	0.118723
$818$	−20.7883	−0.726846
$819$	0.0422275	0.00147555
$820$	−1.26958	−0.0443356
$821$	−42.3604	−1.47839	−0.739193	−	0.673493i	$-0.764793\pi$
$821$	−42.3604	−1.47839	−0.739193	+	0.673493i	$0.764793\pi$
$822$	32.7133	1.14101
$823$	−31.7638	−1.10722	−0.553609	−	0.832777i	$-0.686750\pi$
$823$	−31.7638	−1.10722	−0.553609	+	0.832777i	$0.686750\pi$
$824$	−10.2439	−0.356864
$825$	73.2674	2.55084
$826$	8.14095	0.283260
$827$	−33.1505	−1.15276	−0.576379	−	0.817183i	$-0.695535\pi$
$827$	−33.1505	−1.15276	−0.576379	+	0.817183i	$0.695535\pi$
$828$	5.51791	0.191761
$829$	−14.1542	−0.491597	−0.245798	−	0.969321i	$-0.579050\pi$
$829$	−14.1542	−0.491597	−0.245798	+	0.969321i	$0.579050\pi$
$830$	−2.19868	−0.0763174
$831$	−14.3497	−0.497785
$832$	0.00977416	0.000338858 0
$833$	−24.3129	−0.842391
$834$	−57.6109	−1.99490
$835$	0.614407	0.0212624
$836$	−29.0475	−1.00463
$837$	0.288798	0.00998232
$838$	22.2246	0.767736
$839$	26.5293	0.915892	0.457946	−	0.888980i	$-0.348585\pi$
$839$	26.5293	0.915892	0.457946	+	0.888980i	$0.348585\pi$
$840$	−0.480603	−0.0165824
$841$	56.8574	1.96060
$842$	−23.4087	−0.806716
$843$	34.8955	1.20187
$844$	0.793503	0.0273135
$845$	1.78167	0.0612912
$846$	13.7654	0.473265
$847$	35.5987	1.22318
$848$	−5.19938	−0.178548
$849$	−11.0426	−0.378980
$850$	24.4238	0.837730
$851$	−15.3242	−0.525307
$852$	37.6622	1.29028
$853$	−57.4083	−1.96562	−0.982812	−	0.184609i	$-0.940898\pi$
$853$	−57.4083	−1.96562	−0.982812	+	0.184609i	$0.940898\pi$
$854$	15.7796	0.539967
$855$	2.00866	0.0686946
$856$	−17.7284	−0.605943
$857$	−12.7008	−0.433850	−0.216925	−	0.976188i	$-0.569603\pi$
$857$	−12.7008	−0.433850	−0.216925	+	0.976188i	$0.569603\pi$
$858$	0.143766	0.00490807
$859$	53.7430	1.83369	0.916843	−	0.399247i	$-0.130729\pi$
$859$	53.7430	1.83369	0.916843	+	0.399247i	$0.130729\pi$
$860$	0.0959540	0.00327200
$861$	−32.4843	−1.10706
$862$	17.9526	0.611469
$863$	−24.4868	−0.833542	−0.416771	−	0.909012i	$-0.636838\pi$
$863$	−24.4868	−0.833542	−0.416771	+	0.909012i	$0.636838\pi$
$864$	0.0583726	0.00198588
$865$	−3.09271	−0.105155
$866$	29.0315	0.986531
$867$	−17.2815	−0.586911
$868$	−7.06888	−0.239933
$869$	−4.44310	−0.150722
$870$	−3.11681	−0.105670
$871$	0.0480235	0.00162721
$872$	11.8292	0.400586
$873$	−36.7855	−1.24500
$874$	8.84489	0.299183
$875$	1.95450	0.0660741
$876$	−17.1145	−0.578245
$877$	−17.9628	−0.606561	−0.303281	−	0.952901i	$-0.598082\pi$
$877$	−17.9628	−0.606561	−0.303281	+	0.952901i	$0.598082\pi$
$878$	−27.0239	−0.912011
$879$	−19.7515	−0.666201
$880$	−0.821347	−0.0276876
$881$	31.4868	1.06082	0.530409	−	0.847742i	$-0.322038\pi$
$881$	31.4868	1.06082	0.530409	+	0.847742i	$0.322038\pi$
$882$	14.9937	0.504864
$883$	−12.7298	−0.428393	−0.214197	−	0.976791i	$-0.568713\pi$
$883$	−12.7298	−0.428393	−0.214197	+	0.976791i	$0.568713\pi$
$884$	0.0479245	0.00161188
$885$	−1.91660	−0.0644257
$886$	6.58663	0.221282
$887$	46.4623	1.56005	0.780025	−	0.625748i	$-0.215206\pi$
$887$	46.4623	1.56005	0.780025	+	0.625748i	$0.215206\pi$
$888$	−20.6105	−0.691644
$889$	−14.1334	−0.474018
$890$	−1.74166	−0.0583806
$891$	−53.5055	−1.79250
$892$	5.34875	0.179089
$893$	22.0652	0.738384
$894$	12.5541	0.419873
$895$	2.33114	0.0779214
$896$	−1.42878	−0.0477322
$897$	−0.0437762	−0.00146164
$898$	2.05847	0.0686919
$899$	−45.8431	−1.52895
$900$	−15.0621	−0.502071
$901$	−25.4935	−0.849313
$902$	−55.5154	−1.84846
$903$	2.45514	0.0817020
$904$	−5.06230	−0.168369
$905$	−1.82511	−0.0606689
$906$	50.3116	1.67149
$907$	−35.1612	−1.16751	−0.583755	−	0.811930i	$-0.698417\pi$
$907$	−35.1612	−1.16751	−0.583755	+	0.811930i	$0.698417\pi$
$908$	−1.54953	−0.0514229
$909$	−31.8423	−1.05614
$910$	0.00191395	6.34470e−5 0
$911$	20.6740	0.684959	0.342479	−	0.939525i	$-0.388733\pi$
$911$	20.6740	0.684959	0.342479	+	0.939525i	$0.388733\pi$
$912$	11.8961	0.393918
$913$	−96.1428	−3.18186
$914$	−2.08943	−0.0691121
$915$	−3.71494	−0.122812
$916$	16.3209	0.539258
$917$	−0.682581	−0.0225408
$918$	0.286212	0.00944639
$919$	−32.2394	−1.06348	−0.531740	−	0.846908i	$-0.678462\pi$
$919$	−32.2394	−1.06348	−0.531740	+	0.846908i	$0.678462\pi$
$920$	0.250098	0.00824548
$921$	17.9418	0.591201
$922$	−24.9368	−0.821249
$923$	−0.149986	−0.00493684
$924$	−21.0155	−0.691361
$925$	41.8302	1.37537
$926$	28.5744	0.939014
$927$	30.9754	1.01737
$928$	−9.26593	−0.304169
$929$	−1.83554	−0.0602222	−0.0301111	−	0.999547i	$-0.509586\pi$
$929$	−1.83554	−0.0602222	−0.0301111	+	0.999547i	$0.509586\pi$
$930$	1.66420	0.0545713
$931$	24.0340	0.787684
$932$	14.3662	0.470581
$933$	64.0164	2.09580
$934$	23.2494	0.760744
$935$	−4.02722	−0.131704
$936$	−0.0295550	−0.000966034 0
$937$	52.1879	1.70491	0.852453	−	0.522805i	$-0.175114\pi$
$937$	52.1879	1.70491	0.852453	+	0.522805i	$0.175114\pi$
$938$	−7.02003	−0.229212
$939$	−66.7580	−2.17857
$940$	0.623915	0.0203499
$941$	13.5294	0.441045	0.220523	−	0.975382i	$-0.429224\pi$
$941$	13.5294	0.441045	0.220523	+	0.975382i	$0.429224\pi$
$942$	−25.2507	−0.822712
$943$	16.9043	0.550479
$944$	−5.69783	−0.185449
$945$	0.0114304	0.000371831 0
$946$	4.19582	0.136418
$947$	−0.139357	−0.00452850	−0.00226425	−	0.999997i	$-0.500721\pi$
$947$	−0.139357	−0.00452850	−0.00226425	+	0.999997i	$0.500721\pi$
$948$	1.81962	0.0590984
$949$	0.0681568	0.00221246
$950$	−24.1437	−0.783326
$951$	30.0289	0.973754
$952$	−7.00557	−0.227052
$953$	−20.7179	−0.671118	−0.335559	−	0.942019i	$-0.608925\pi$
$953$	−20.7179	−0.671118	−0.335559	+	0.942019i	$0.608925\pi$
$954$	15.7218	0.509012
$955$	−1.21280	−0.0392452
$956$	−3.02501	−0.0978358
$957$	−136.290	−4.40563
$958$	22.6187	0.730777
$959$	19.0439	0.614959
$960$	0.336373	0.0108564
$961$	−6.52234	−0.210398
$962$	0.0820794	0.00264634
$963$	53.6067	1.72745
$964$	−13.9546	−0.449448
$965$	0.0561648	0.00180801
$966$	6.39917	0.205890
$967$	−10.2093	−0.328310	−0.164155	−	0.986435i	$-0.552490\pi$
$967$	−10.2093	−0.328310	−0.164155	+	0.986435i	$0.552490\pi$
$968$	−24.9154	−0.800812
$969$	58.3286	1.87378
$970$	−1.66730	−0.0535336
$971$	38.6267	1.23959	0.619795	−	0.784764i	$-0.287216\pi$
$971$	38.6267	1.23959	0.619795	+	0.784764i	$0.287216\pi$
$972$	22.0877	0.708462
$973$	−33.5379	−1.07517
$974$	−42.3068	−1.35560
$975$	0.119495	0.00382690
$976$	−11.0441	−0.353513
$977$	32.6530	1.04466	0.522330	−	0.852743i	$-0.325063\pi$
$977$	32.6530	1.04466	0.522330	+	0.852743i	$0.325063\pi$
$978$	−5.31779	−0.170044
$979$	−76.1583	−2.43403
$980$	0.679586	0.0217086
$981$	−35.7688	−1.14201
$982$	18.1085	0.577866
$983$	40.4091	1.28885	0.644424	−	0.764668i	$-0.277097\pi$
$983$	40.4091	1.28885	0.644424	+	0.764668i	$0.277097\pi$
$984$	22.7357	0.724786
$985$	1.29372	0.0412213
$986$	−45.4325	−1.44687
$987$	15.9639	0.508137
$988$	−0.0473749	−0.00150720
$989$	−1.27762	−0.0406258
$990$	2.48358	0.0789332
$991$	−19.4543	−0.617987	−0.308994	−	0.951064i	$-0.599992\pi$
$991$	−19.4543	−0.617987	−0.308994	+	0.951064i	$0.599992\pi$
$992$	4.94749	0.157083
$993$	−17.5287	−0.556256
$994$	21.9248	0.695413
$995$	2.01538	0.0638919
$996$	39.3741	1.24762
$997$	31.6557	1.00255	0.501273	−	0.865289i	$-0.332865\pi$
$997$	31.6557	1.00255	0.501273	+	0.865289i	$0.332865\pi$
$998$	5.03264	0.159306
$999$	0.490189	0.0155089

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.b.1.13	✓	81

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.b.1.13	✓	81	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.45434 q^{3} +1.00000 q^{4} -0.137052 q^{5} +2.45434 q^{6} +1.42878 q^{7} -1.00000 q^{8} +3.02378 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.45434 q^{3} +1.00000 q^{4} -0.137052 q^{5} +2.45434 q^{6} +1.42878 q^{7} -1.00000 q^{8} +3.02378 q^{9} +0.137052 q^{10} +5.99295 q^{11} -2.45434 q^{12} +0.00977416 q^{13} -1.42878 q^{14} +0.336373 q^{15} +1.00000 q^{16} +4.90318 q^{17} -3.02378 q^{18} -4.84695 q^{19} -0.137052 q^{20} -3.50671 q^{21} -5.99295 q^{22} +1.82484 q^{23} +2.45434 q^{24} -4.98122 q^{25} -0.00977416 q^{26} -0.0583726 q^{27} +1.42878 q^{28} +9.26593 q^{29} -0.336373 q^{30} -4.94749 q^{31} -1.00000 q^{32} -14.7087 q^{33} -4.90318 q^{34} -0.195818 q^{35} +3.02378 q^{36} -8.39758 q^{37} +4.84695 q^{38} -0.0239891 q^{39} +0.137052 q^{40} +9.26345 q^{41} +3.50671 q^{42} -0.700127 q^{43} +5.99295 q^{44} -0.414417 q^{45} -1.82484 q^{46} -4.55239 q^{47} -2.45434 q^{48} -4.95859 q^{49} +4.98122 q^{50} -12.0341 q^{51} +0.00977416 q^{52} -5.19938 q^{53} +0.0583726 q^{54} -0.821347 q^{55} -1.42878 q^{56} +11.8961 q^{57} -9.26593 q^{58} -5.69783 q^{59} +0.336373 q^{60} -11.0441 q^{61} +4.94749 q^{62} +4.32032 q^{63} +1.00000 q^{64} -0.00133957 q^{65} +14.7087 q^{66} +4.91331 q^{67} +4.90318 q^{68} -4.47877 q^{69} +0.195818 q^{70} -15.3451 q^{71} -3.02378 q^{72} +6.97316 q^{73} +8.39758 q^{74} +12.2256 q^{75} -4.84695 q^{76} +8.56260 q^{77} +0.0239891 q^{78} -0.741388 q^{79} -0.137052 q^{80} -8.92808 q^{81} -9.26345 q^{82} -16.0427 q^{83} -3.50671 q^{84} -0.671993 q^{85} +0.700127 q^{86} -22.7417 q^{87} -5.99295 q^{88} -12.7080 q^{89} +0.414417 q^{90} +0.0139651 q^{91} +1.82484 q^{92} +12.1428 q^{93} +4.55239 q^{94} +0.664286 q^{95} +2.45434 q^{96} -12.1654 q^{97} +4.95859 q^{98} +18.1214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9}+O(q^{10}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9} + 26 q^{10} - 41 q^{11} - 10 q^{12} + 33 q^{13} - 3 q^{14} - 7 q^{15} + 81 q^{16} - 9 q^{17} - 59 q^{18} - 32 q^{19} - 26 q^{20} - 23 q^{21} + 41 q^{22} - 28 q^{23} + 10 q^{24} + 81 q^{25} - 33 q^{26} - 37 q^{27} + 3 q^{28} - 35 q^{29} + 7 q^{30} - 29 q^{31} - 81 q^{32} - 7 q^{33} + 9 q^{34} - 67 q^{35} + 59 q^{36} + 13 q^{37} + 32 q^{38} - 42 q^{39} + 26 q^{40} - 66 q^{41} + 23 q^{42} - 22 q^{43} - 41 q^{44} - 65 q^{45} + 28 q^{46} - 71 q^{47} - 10 q^{48} + 64 q^{49} - 81 q^{50} - 43 q^{51} + 33 q^{52} - 37 q^{53} + 37 q^{54} + 12 q^{55} - 3 q^{56} - q^{57} + 35 q^{58} - 162 q^{59} - 7 q^{60} + 19 q^{61} + 29 q^{62} - 16 q^{63} + 81 q^{64} - 45 q^{65} + 7 q^{66} - 43 q^{67} - 9 q^{68} - 21 q^{69} + 67 q^{70} - 99 q^{71} - 59 q^{72} + 53 q^{73} - 13 q^{74} - 61 q^{75} - 32 q^{76} - 31 q^{77} + 42 q^{78} + 4 q^{79} - 26 q^{80} + q^{81} + 66 q^{82} - 112 q^{83} - 23 q^{84} + 17 q^{85} + 22 q^{86} - 15 q^{87} + 41 q^{88} - 111 q^{89} + 65 q^{90} - 49 q^{91} - 28 q^{92} - 19 q^{93} + 71 q^{94} - 53 q^{95} + 10 q^{96} + 50 q^{97} - 64 q^{98} - 97 q^{99}+O(q^{100}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9 + 26 * q^10 - 41 * q^11 - 10 * q^12 + 33 * q^13 - 3 * q^14 - 7 * q^15 + 81 * q^16 - 9 * q^17 - 59 * q^18 - 32 * q^19 - 26 * q^20 - 23 * q^21 + 41 * q^22 - 28 * q^23 + 10 * q^24 + 81 * q^25 - 33 * q^26 - 37 * q^27 + 3 * q^28 - 35 * q^29 + 7 * q^30 - 29 * q^31 - 81 * q^32 - 7 * q^33 + 9 * q^34 - 67 * q^35 + 59 * q^36 + 13 * q^37 + 32 * q^38 - 42 * q^39 + 26 * q^40 - 66 * q^41 + 23 * q^42 - 22 * q^43 - 41 * q^44 - 65 * q^45 + 28 * q^46 - 71 * q^47 - 10 * q^48 + 64 * q^49 - 81 * q^50 - 43 * q^51 + 33 * q^52 - 37 * q^53 + 37 * q^54 + 12 * q^55 - 3 * q^56 - q^57 + 35 * q^58 - 162 * q^59 - 7 * q^60 + 19 * q^61 + 29 * q^62 - 16 * q^63 + 81 * q^64 - 45 * q^65 + 7 * q^66 - 43 * q^67 - 9 * q^68 - 21 * q^69 + 67 * q^70 - 99 * q^71 - 59 * q^72 + 53 * q^73 - 13 * q^74 - 61 * q^75 - 32 * q^76 - 31 * q^77 + 42 * q^78 + 4 * q^79 - 26 * q^80 + q^81 + 66 * q^82 - 112 * q^83 - 23 * q^84 + 17 * q^85 + 22 * q^86 - 15 * q^87 + 41 * q^88 - 111 * q^89 + 65 * q^90 - 49 * q^91 - 28 * q^92 - 19 * q^93 + 71 * q^94 - 53 * q^95 + 10 * q^96 + 50 * q^97 - 64 * q^98 - 97 * q^99

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