LMFDB - Embedded newform 8026.2.a.c.1.9

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:	$0$
Dimension:	$86$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.64301 q^{3} +1.00000 q^{4} -0.786430 q^{5} +2.64301 q^{6} -4.08167 q^{7} -1.00000 q^{8} +3.98548 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.64301 q^{3} +1.00000 q^{4} -0.786430 q^{5} +2.64301 q^{6} -4.08167 q^{7} -1.00000 q^{8} +3.98548 q^{9} +0.786430 q^{10} +2.82596 q^{11} -2.64301 q^{12} -4.08175 q^{13} +4.08167 q^{14} +2.07854 q^{15} +1.00000 q^{16} -2.00425 q^{17} -3.98548 q^{18} -1.19350 q^{19} -0.786430 q^{20} +10.7879 q^{21} -2.82596 q^{22} +1.16417 q^{23} +2.64301 q^{24} -4.38153 q^{25} +4.08175 q^{26} -2.60463 q^{27} -4.08167 q^{28} -6.12838 q^{29} -2.07854 q^{30} +2.96112 q^{31} -1.00000 q^{32} -7.46902 q^{33} +2.00425 q^{34} +3.20994 q^{35} +3.98548 q^{36} +0.348305 q^{37} +1.19350 q^{38} +10.7881 q^{39} +0.786430 q^{40} +9.36395 q^{41} -10.7879 q^{42} -9.34806 q^{43} +2.82596 q^{44} -3.13430 q^{45} -1.16417 q^{46} -10.1362 q^{47} -2.64301 q^{48} +9.65999 q^{49} +4.38153 q^{50} +5.29724 q^{51} -4.08175 q^{52} -3.33421 q^{53} +2.60463 q^{54} -2.22242 q^{55} +4.08167 q^{56} +3.15443 q^{57} +6.12838 q^{58} -4.54320 q^{59} +2.07854 q^{60} +0.634755 q^{61} -2.96112 q^{62} -16.2674 q^{63} +1.00000 q^{64} +3.21001 q^{65} +7.46902 q^{66} +2.04198 q^{67} -2.00425 q^{68} -3.07691 q^{69} -3.20994 q^{70} -11.5374 q^{71} -3.98548 q^{72} -3.97603 q^{73} -0.348305 q^{74} +11.5804 q^{75} -1.19350 q^{76} -11.5346 q^{77} -10.7881 q^{78} +5.49412 q^{79} -0.786430 q^{80} -5.07238 q^{81} -9.36395 q^{82} -7.05482 q^{83} +10.7879 q^{84} +1.57620 q^{85} +9.34806 q^{86} +16.1974 q^{87} -2.82596 q^{88} -13.2871 q^{89} +3.13430 q^{90} +16.6603 q^{91} +1.16417 q^{92} -7.82625 q^{93} +10.1362 q^{94} +0.938606 q^{95} +2.64301 q^{96} +8.62490 q^{97} -9.65999 q^{98} +11.2628 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) $ 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * 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
$3$	−2.64301	−1.52594	−0.762970	−	0.646434i	$-0.776260\pi$
$3$	−2.64301	−1.52594	−0.762970	+	0.646434i	$0.776260\pi$
$4$	1.00000	0.500000
$5$	−0.786430	−0.351702	−0.175851	−	0.984417i	$-0.556268\pi$
$5$	−0.786430	−0.351702	−0.175851	+	0.984417i	$0.556268\pi$
$6$	2.64301	1.07900
$7$	−4.08167	−1.54272	−0.771362	−	0.636396i	$-0.780424\pi$
$7$	−4.08167	−1.54272	−0.771362	+	0.636396i	$0.780424\pi$
$8$	−1.00000	−0.353553
$9$	3.98548	1.32849
$10$	0.786430	0.248691
$11$	2.82596	0.852058	0.426029	−	0.904709i	$-0.359912\pi$
$11$	2.82596	0.852058	0.426029	+	0.904709i	$0.359912\pi$
$12$	−2.64301	−0.762970
$13$	−4.08175	−1.13207	−0.566037	−	0.824380i	$-0.691524\pi$
$13$	−4.08175	−1.13207	−0.566037	+	0.824380i	$0.691524\pi$
$14$	4.08167	1.09087
$15$	2.07854	0.536676
$16$	1.00000	0.250000
$17$	−2.00425	−0.486102	−0.243051	−	0.970014i	$-0.578148\pi$
$17$	−2.00425	−0.486102	−0.243051	+	0.970014i	$0.578148\pi$
$18$	−3.98548	−0.939387
$19$	−1.19350	−0.273808	−0.136904	−	0.990584i	$-0.543715\pi$
$19$	−1.19350	−0.273808	−0.136904	+	0.990584i	$0.543715\pi$
$20$	−0.786430	−0.175851
$21$	10.7879	2.35411
$22$	−2.82596	−0.602496
$23$	1.16417	0.242746	0.121373	−	0.992607i	$-0.461270\pi$
$23$	1.16417	0.242746	0.121373	+	0.992607i	$0.461270\pi$
$24$	2.64301	0.539501
$25$	−4.38153	−0.876306
$26$	4.08175	0.800498
$27$	−2.60463	−0.501262
$28$	−4.08167	−0.771362
$29$	−6.12838	−1.13801	−0.569006	−	0.822333i	$-0.692672\pi$
$29$	−6.12838	−1.13801	−0.569006	+	0.822333i	$0.692672\pi$
$30$	−2.07854	−0.379487
$31$	2.96112	0.531832	0.265916	−	0.963996i	$-0.414326\pi$
$31$	2.96112	0.531832	0.265916	+	0.963996i	$0.414326\pi$
$32$	−1.00000	−0.176777
$33$	−7.46902	−1.30019
$34$	2.00425	0.343726
$35$	3.20994	0.542579
$36$	3.98548	0.664247
$37$	0.348305	0.0572611	0.0286305	−	0.999590i	$-0.490885\pi$
$37$	0.348305	0.0572611	0.0286305	+	0.999590i	$0.490885\pi$
$38$	1.19350	0.193612
$39$	10.7881	1.72748
$40$	0.786430	0.124345
$41$	9.36395	1.46240	0.731202	−	0.682161i	$-0.238960\pi$
$41$	9.36395	1.46240	0.731202	+	0.682161i	$0.238960\pi$
$42$	−10.7879	−1.66460
$43$	−9.34806	−1.42557	−0.712783	−	0.701385i	$-0.752566\pi$
$43$	−9.34806	−1.42557	−0.712783	+	0.701385i	$0.752566\pi$
$44$	2.82596	0.426029
$45$	−3.13430	−0.467234
$46$	−1.16417	−0.171647
$47$	−10.1362	−1.47851	−0.739255	−	0.673426i	$-0.764822\pi$
$47$	−10.1362	−1.47851	−0.739255	+	0.673426i	$0.764822\pi$
$48$	−2.64301	−0.381485
$49$	9.65999	1.38000
$50$	4.38153	0.619642
$51$	5.29724	0.741762
$52$	−4.08175	−0.566037
$53$	−3.33421	−0.457989	−0.228994	−	0.973428i	$-0.573544\pi$
$53$	−3.33421	−0.457989	−0.228994	+	0.973428i	$0.573544\pi$
$54$	2.60463	0.354446
$55$	−2.22242	−0.299671
$56$	4.08167	0.545435
$57$	3.15443	0.417815
$58$	6.12838	0.804696
$59$	−4.54320	−0.591474	−0.295737	−	0.955269i	$-0.595565\pi$
$59$	−4.54320	−0.591474	−0.295737	+	0.955269i	$0.595565\pi$
$60$	2.07854	0.268338
$61$	0.634755	0.0812721	0.0406360	−	0.999174i	$-0.487062\pi$
$61$	0.634755	0.0812721	0.0406360	+	0.999174i	$0.487062\pi$
$62$	−2.96112	−0.376062
$63$	−16.2674	−2.04950
$64$	1.00000	0.125000
$65$	3.21001	0.398153
$66$	7.46902	0.919373
$67$	2.04198	0.249468	0.124734	−	0.992190i	$-0.460192\pi$
$67$	2.04198	0.249468	0.124734	+	0.992190i	$0.460192\pi$
$68$	−2.00425	−0.243051
$69$	−3.07691	−0.370416
$70$	−3.20994	−0.383661
$71$	−11.5374	−1.36923	−0.684616	−	0.728904i	$-0.740030\pi$
$71$	−11.5374	−1.36923	−0.684616	+	0.728904i	$0.740030\pi$
$72$	−3.98548	−0.469693
$73$	−3.97603	−0.465359	−0.232680	−	0.972553i	$-0.574749\pi$
$73$	−3.97603	−0.465359	−0.232680	+	0.972553i	$0.574749\pi$
$74$	−0.348305	−0.0404897
$75$	11.5804	1.33719
$76$	−1.19350	−0.136904
$77$	−11.5346	−1.31449
$78$	−10.7881	−1.22151
$79$	5.49412	0.618137	0.309068	−	0.951040i	$-0.399983\pi$
$79$	5.49412	0.618137	0.309068	+	0.951040i	$0.399983\pi$
$80$	−0.786430	−0.0879255
$81$	−5.07238	−0.563598
$82$	−9.36395	−1.03408
$83$	−7.05482	−0.774367	−0.387184	−	0.922003i	$-0.626552\pi$
$83$	−7.05482	−0.774367	−0.387184	+	0.922003i	$0.626552\pi$
$84$	10.7879	1.17705
$85$	1.57620	0.170963
$86$	9.34806	1.00803
$87$	16.1974	1.73654
$88$	−2.82596	−0.301248
$89$	−13.2871	−1.40843	−0.704215	−	0.709987i	$-0.748701\pi$
$89$	−13.2871	−1.40843	−0.704215	+	0.709987i	$0.748701\pi$
$90$	3.13430	0.330384
$91$	16.6603	1.74648
$92$	1.16417	0.121373
$93$	−7.82625	−0.811544
$94$	10.1362	1.04546
$95$	0.938606	0.0962989
$96$	2.64301	0.269751
$97$	8.62490	0.875726	0.437863	−	0.899042i	$-0.355735\pi$
$97$	8.62490	0.875726	0.437863	+	0.899042i	$0.355735\pi$
$98$	−9.65999	−0.975806
$99$	11.2628	1.13195
$100$	−4.38153	−0.438153
$101$	−14.9799	−1.49056	−0.745278	−	0.666754i	$-0.767683\pi$
$101$	−14.9799	−1.49056	−0.745278	+	0.666754i	$0.767683\pi$
$102$	−5.29724	−0.524505
$103$	−1.48388	−0.146211	−0.0731055	−	0.997324i	$-0.523291\pi$
$103$	−1.48388	−0.146211	−0.0731055	+	0.997324i	$0.523291\pi$
$104$	4.08175	0.400249
$105$	−8.48390	−0.827944
$106$	3.33421	0.323847
$107$	12.7515	1.23274	0.616368	−	0.787458i	$-0.288603\pi$
$107$	12.7515	1.23274	0.616368	+	0.787458i	$0.288603\pi$
$108$	−2.60463	−0.250631
$109$	9.25672	0.886633	0.443317	−	0.896365i	$-0.353802\pi$
$109$	9.25672	0.886633	0.443317	+	0.896365i	$0.353802\pi$
$110$	2.22242	0.211899
$111$	−0.920573	−0.0873770
$112$	−4.08167	−0.385681
$113$	−4.75945	−0.447731	−0.223866	−	0.974620i	$-0.571868\pi$
$113$	−4.75945	−0.447731	−0.223866	+	0.974620i	$0.571868\pi$
$114$	−3.15443	−0.295440
$115$	−0.915537	−0.0853743
$116$	−6.12838	−0.569006
$117$	−16.2677	−1.50395
$118$	4.54320	0.418235
$119$	8.18067	0.749921
$120$	−2.07854	−0.189744
$121$	−3.01396	−0.273997
$122$	−0.634755	−0.0574680
$123$	−24.7490	−2.23154
$124$	2.96112	0.265916
$125$	7.37791	0.659900
$126$	16.2674	1.44922
$127$	−19.4269	−1.72386	−0.861929	−	0.507029i	$-0.830744\pi$
$127$	−19.4269	−1.72386	−0.861929	+	0.507029i	$0.830744\pi$
$128$	−1.00000	−0.0883883
$129$	24.7070	2.17533
$130$	−3.21001	−0.281537
$131$	−9.57566	−0.836629	−0.418314	−	0.908302i	$-0.637379\pi$
$131$	−9.57566	−0.836629	−0.418314	+	0.908302i	$0.637379\pi$
$132$	−7.46902	−0.650095
$133$	4.87148	0.422411
$134$	−2.04198	−0.176400
$135$	2.04836	0.176295
$136$	2.00425	0.171863
$137$	−14.8457	−1.26836	−0.634178	−	0.773187i	$-0.718661\pi$
$137$	−14.8457	−1.26836	−0.634178	+	0.773187i	$0.718661\pi$
$138$	3.07691	0.261924
$139$	12.8901	1.09333	0.546664	−	0.837352i	$-0.315898\pi$
$139$	12.8901	1.09333	0.546664	+	0.837352i	$0.315898\pi$
$140$	3.20994	0.271290
$141$	26.7899	2.25612
$142$	11.5374	0.968194
$143$	−11.5349	−0.964593
$144$	3.98548	0.332123
$145$	4.81954	0.400241
$146$	3.97603	0.329059
$147$	−25.5314	−2.10580
$148$	0.348305	0.0286305
$149$	−20.4834	−1.67807	−0.839033	−	0.544081i	$-0.816879\pi$
$149$	−20.4834	−1.67807	−0.839033	+	0.544081i	$0.816879\pi$
$150$	−11.5804	−0.945536
$151$	−22.0899	−1.79765	−0.898825	−	0.438308i	$-0.855578\pi$
$151$	−22.0899	−1.79765	−0.898825	+	0.438308i	$0.855578\pi$
$152$	1.19350	0.0968058
$153$	−7.98789	−0.645783
$154$	11.5346	0.929486
$155$	−2.32871	−0.187046
$156$	10.7881	0.863739
$157$	−16.6063	−1.32533	−0.662664	−	0.748917i	$-0.730574\pi$
$157$	−16.6063	−1.32533	−0.662664	+	0.748917i	$0.730574\pi$
$158$	−5.49412	−0.437089
$159$	8.81233	0.698863
$160$	0.786430	0.0621727
$161$	−4.75175	−0.374490
$162$	5.07238	0.398524
$163$	14.0847	1.10320	0.551600	−	0.834109i	$-0.314018\pi$
$163$	14.0847	1.10320	0.551600	+	0.834109i	$0.314018\pi$
$164$	9.36395	0.731202
$165$	5.87386	0.457279
$166$	7.05482	0.547560
$167$	−16.0187	−1.23956	−0.619780	−	0.784775i	$-0.712778\pi$
$167$	−16.0187	−1.23956	−0.619780	+	0.784775i	$0.712778\pi$
$168$	−10.7879	−0.832302
$169$	3.66070	0.281593
$170$	−1.57620	−0.120889
$171$	−4.75668	−0.363753
$172$	−9.34806	−0.712783
$173$	−0.652072	−0.0495761	−0.0247881	−	0.999693i	$-0.507891\pi$
$173$	−0.652072	−0.0495761	−0.0247881	+	0.999693i	$0.507891\pi$
$174$	−16.1974	−1.22792
$175$	17.8839	1.35190
$176$	2.82596	0.213015
$177$	12.0077	0.902554
$178$	13.2871	0.995910
$179$	24.1100	1.80206	0.901032	−	0.433752i	$-0.142811\pi$
$179$	24.1100	1.80206	0.901032	+	0.433752i	$0.142811\pi$
$180$	−3.13430	−0.233617
$181$	−10.6181	−0.789239	−0.394620	−	0.918845i	$-0.629124\pi$
$181$	−10.6181	−0.789239	−0.394620	+	0.918845i	$0.629124\pi$
$182$	−16.6603	−1.23495
$183$	−1.67766	−0.124016
$184$	−1.16417	−0.0858237
$185$	−0.273918	−0.0201388
$186$	7.82625	0.573848
$187$	−5.66392	−0.414187
$188$	−10.1362	−0.739255
$189$	10.6312	0.773309
$190$	−0.938606	−0.0680936
$191$	−25.4784	−1.84356	−0.921778	−	0.387719i	$-0.873263\pi$
$191$	−25.4784	−1.84356	−0.921778	+	0.387719i	$0.873263\pi$
$192$	−2.64301	−0.190743
$193$	−11.2426	−0.809264	−0.404632	−	0.914480i	$-0.632600\pi$
$193$	−11.2426	−0.809264	−0.404632	+	0.914480i	$0.632600\pi$
$194$	−8.62490	−0.619232
$195$	−8.48408	−0.607557
$196$	9.65999	0.689999
$197$	−23.8797	−1.70136	−0.850680	−	0.525684i	$-0.823809\pi$
$197$	−23.8797	−1.70136	−0.850680	+	0.525684i	$0.823809\pi$
$198$	−11.2628	−0.800412
$199$	5.85674	0.415173	0.207587	−	0.978217i	$-0.433439\pi$
$199$	5.85674	0.415173	0.207587	+	0.978217i	$0.433439\pi$
$200$	4.38153	0.309821
$201$	−5.39697	−0.380673
$202$	14.9799	1.05398
$203$	25.0140	1.75564
$204$	5.29724	0.370881
$205$	−7.36409	−0.514330
$206$	1.48388	0.103387
$207$	4.63977	0.322487
$208$	−4.08175	−0.283019
$209$	−3.37279	−0.233301
$210$	8.48390	0.585445
$211$	−23.3983	−1.61080	−0.805402	−	0.592729i	$-0.798050\pi$
$211$	−23.3983	−1.61080	−0.805402	+	0.592729i	$0.798050\pi$
$212$	−3.33421	−0.228994
$213$	30.4933	2.08937
$214$	−12.7515	−0.871676
$215$	7.35159	0.501374
$216$	2.60463	0.177223
$217$	−12.0863	−0.820471
$218$	−9.25672	−0.626944
$219$	10.5087	0.710110
$220$	−2.22242	−0.149835
$221$	8.18085	0.550303
$222$	0.920573	0.0617848
$223$	14.8097	0.991730	0.495865	−	0.868400i	$-0.334851\pi$
$223$	14.8097	0.991730	0.495865	+	0.868400i	$0.334851\pi$
$224$	4.08167	0.272718
$225$	−17.4625	−1.16417
$226$	4.75945	0.316594
$227$	−2.57869	−0.171153	−0.0855767	−	0.996332i	$-0.527273\pi$
$227$	−2.57869	−0.171153	−0.0855767	+	0.996332i	$0.527273\pi$
$228$	3.15443	0.208908
$229$	−23.6386	−1.56208	−0.781042	−	0.624479i	$-0.785311\pi$
$229$	−23.6386	−1.56208	−0.781042	+	0.624479i	$0.785311\pi$
$230$	0.915537	0.0603687
$231$	30.4861	2.00583
$232$	6.12838	0.402348
$233$	4.11548	0.269614	0.134807	−	0.990872i	$-0.456958\pi$
$233$	4.11548	0.269614	0.134807	+	0.990872i	$0.456958\pi$
$234$	16.2677	1.06346
$235$	7.97137	0.519995
$236$	−4.54320	−0.295737
$237$	−14.5210	−0.943239
$238$	−8.18067	−0.530274
$239$	−2.13346	−0.138002	−0.0690012	−	0.997617i	$-0.521981\pi$
$239$	−2.13346	−0.138002	−0.0690012	+	0.997617i	$0.521981\pi$
$240$	2.07854	0.134169
$241$	−3.13407	−0.201883	−0.100942	−	0.994892i	$-0.532186\pi$
$241$	−3.13407	−0.201883	−0.100942	+	0.994892i	$0.532186\pi$
$242$	3.01396	0.193745
$243$	21.2202	1.36128
$244$	0.634755	0.0406360
$245$	−7.59690	−0.485348
$246$	24.7490	1.57794
$247$	4.87158	0.309971
$248$	−2.96112	−0.188031
$249$	18.6459	1.18164
$250$	−7.37791	−0.466620
$251$	24.0059	1.51524	0.757620	−	0.652696i	$-0.226362\pi$
$251$	24.0059	1.51524	0.757620	+	0.652696i	$0.226362\pi$
$252$	−16.2674	−1.02475
$253$	3.28989	0.206834
$254$	19.4269	1.21895
$255$	−4.16591	−0.260879
$256$	1.00000	0.0625000
$257$	25.5765	1.59542	0.797708	−	0.603043i	$-0.206045\pi$
$257$	25.5765	1.59542	0.797708	+	0.603043i	$0.206045\pi$
$258$	−24.7070	−1.53819
$259$	−1.42167	−0.0883380
$260$	3.21001	0.199076
$261$	−24.4245	−1.51184
$262$	9.57566	0.591586
$263$	−17.4498	−1.07600	−0.538000	−	0.842945i	$-0.680820\pi$
$263$	−17.4498	−1.07600	−0.538000	+	0.842945i	$0.680820\pi$
$264$	7.46902	0.459687
$265$	2.62212	0.161076
$266$	−4.87148	−0.298689
$267$	35.1179	2.14918
$268$	2.04198	0.124734
$269$	20.1864	1.23079	0.615395	−	0.788219i	$-0.288997\pi$
$269$	20.1864	1.23079	0.615395	+	0.788219i	$0.288997\pi$
$270$	−2.04836	−0.124659
$271$	24.1182	1.46508	0.732538	−	0.680726i	$-0.238335\pi$
$271$	24.1182	1.46508	0.732538	+	0.680726i	$0.238335\pi$
$272$	−2.00425	−0.121525
$273$	−44.0334	−2.66502
$274$	14.8457	0.896863
$275$	−12.3820	−0.746664
$276$	−3.07691	−0.185208
$277$	5.03516	0.302534	0.151267	−	0.988493i	$-0.451665\pi$
$277$	5.03516	0.302534	0.151267	+	0.988493i	$0.451665\pi$
$278$	−12.8901	−0.773100
$279$	11.8015	0.706536
$280$	−3.20994	−0.191831
$281$	18.9374	1.12971	0.564856	−	0.825189i	$-0.308932\pi$
$281$	18.9374	1.12971	0.564856	+	0.825189i	$0.308932\pi$
$282$	−26.7899	−1.59532
$283$	5.42126	0.322260	0.161130	−	0.986933i	$-0.448486\pi$
$283$	5.42126	0.322260	0.161130	+	0.986933i	$0.448486\pi$
$284$	−11.5374	−0.684616
$285$	−2.48074	−0.146946
$286$	11.5349	0.682071
$287$	−38.2205	−2.25609
$288$	−3.98548	−0.234847
$289$	−12.9830	−0.763705
$290$	−4.81954	−0.283013
$291$	−22.7957	−1.33631
$292$	−3.97603	−0.232680
$293$	10.2937	0.601364	0.300682	−	0.953724i	$-0.402786\pi$
$293$	10.2937	0.601364	0.300682	+	0.953724i	$0.402786\pi$
$294$	25.5314	1.48902
$295$	3.57291	0.208023
$296$	−0.348305	−0.0202448
$297$	−7.36058	−0.427104
$298$	20.4834	1.18657
$299$	−4.75185	−0.274807
$300$	11.5804	0.668595
$301$	38.1557	2.19926
$302$	22.0899	1.27113
$303$	39.5920	2.27450
$304$	−1.19350	−0.0684521
$305$	−0.499190	−0.0285835
$306$	7.98789	0.456638
$307$	−16.7362	−0.955188	−0.477594	−	0.878581i	$-0.658491\pi$
$307$	−16.7362	−0.955188	−0.477594	+	0.878581i	$0.658491\pi$
$308$	−11.5346	−0.657246
$309$	3.92190	0.223109
$310$	2.32871	0.132262
$311$	19.5561	1.10893	0.554463	−	0.832208i	$-0.312924\pi$
$311$	19.5561	1.10893	0.554463	+	0.832208i	$0.312924\pi$
$312$	−10.7881	−0.610756
$313$	−27.3689	−1.54698	−0.773491	−	0.633807i	$-0.781491\pi$
$313$	−27.3689	−1.54698	−0.773491	+	0.633807i	$0.781491\pi$
$314$	16.6063	0.937148
$315$	12.7932	0.720813
$316$	5.49412	0.309068
$317$	−14.1582	−0.795202	−0.397601	−	0.917558i	$-0.630157\pi$
$317$	−14.1582	−0.795202	−0.397601	+	0.917558i	$0.630157\pi$
$318$	−8.81233	−0.494171
$319$	−17.3185	−0.969653
$320$	−0.786430	−0.0439628
$321$	−33.7024	−1.88108
$322$	4.75175	0.264805
$323$	2.39208	0.133099
$324$	−5.07238	−0.281799
$325$	17.8843	0.992043
$326$	−14.0847	−0.780080
$327$	−24.4656	−1.35295
$328$	−9.36395	−0.517038
$329$	41.3724	2.28093
$330$	−5.87386	−0.323345
$331$	−20.8203	−1.14439	−0.572195	−	0.820118i	$-0.693908\pi$
$331$	−20.8203	−1.14439	−0.572195	+	0.820118i	$0.693908\pi$
$332$	−7.05482	−0.387184
$333$	1.38816	0.0760710
$334$	16.0187	0.876502
$335$	−1.60588	−0.0877383
$336$	10.7879	0.588526
$337$	−22.2572	−1.21243	−0.606213	−	0.795302i	$-0.707312\pi$
$337$	−22.2572	−1.21243	−0.606213	+	0.795302i	$0.707312\pi$
$338$	−3.66070	−0.199116
$339$	12.5792	0.683211
$340$	1.57620	0.0854815
$341$	8.36799	0.453152
$342$	4.75668	0.257212
$343$	−10.8572	−0.586233
$344$	9.34806	0.504014
$345$	2.41977	0.130276
$346$	0.652072	0.0350556
$347$	−30.3067	−1.62695	−0.813474	−	0.581601i	$-0.802426\pi$
$347$	−30.3067	−1.62695	−0.813474	+	0.581601i	$0.802426\pi$
$348$	16.1974	0.868269
$349$	−20.3891	−1.09140	−0.545701	−	0.837980i	$-0.683737\pi$
$349$	−20.3891	−1.09140	−0.545701	+	0.837980i	$0.683737\pi$
$350$	−17.8839	−0.955936
$351$	10.6315	0.567466
$352$	−2.82596	−0.150624
$353$	18.9632	1.00931	0.504655	−	0.863321i	$-0.331620\pi$
$353$	18.9632	1.00931	0.504655	+	0.863321i	$0.331620\pi$
$354$	−12.0077	−0.638202
$355$	9.07332	0.481562
$356$	−13.2871	−0.704215
$357$	−21.6216	−1.14433
$358$	−24.1100	−1.27425
$359$	13.9995	0.738866	0.369433	−	0.929257i	$-0.379552\pi$
$359$	13.9995	0.738866	0.369433	+	0.929257i	$0.379552\pi$
$360$	3.13430	0.165192
$361$	−17.5756	−0.925029
$362$	10.6181	0.558076
$363$	7.96592	0.418103
$364$	16.6603	0.873239
$365$	3.12687	0.163668
$366$	1.67766	0.0876928
$367$	1.27736	0.0666778	0.0333389	−	0.999444i	$-0.489386\pi$
$367$	1.27736	0.0666778	0.0333389	+	0.999444i	$0.489386\pi$
$368$	1.16417	0.0606865
$369$	37.3198	1.94279
$370$	0.273918	0.0142403
$371$	13.6091	0.706550
$372$	−7.82625	−0.405772
$373$	6.74287	0.349132	0.174566	−	0.984645i	$-0.444148\pi$
$373$	6.74287	0.349132	0.174566	+	0.984645i	$0.444148\pi$
$374$	5.66392	0.292874
$375$	−19.4999	−1.00697
$376$	10.1362	0.522732
$377$	25.0145	1.28831
$378$	−10.6312	−0.546812
$379$	24.4335	1.25507	0.627533	−	0.778590i	$-0.284065\pi$
$379$	24.4335	1.25507	0.627533	+	0.778590i	$0.284065\pi$
$380$	0.938606	0.0481495
$381$	51.3454	2.63050
$382$	25.4784	1.30359
$383$	−25.1112	−1.28312	−0.641561	−	0.767072i	$-0.721713\pi$
$383$	−25.1112	−1.28312	−0.641561	+	0.767072i	$0.721713\pi$
$384$	2.64301	0.134875
$385$	9.07116	0.462309
$386$	11.2426	0.572236
$387$	−37.2565	−1.89386
$388$	8.62490	0.437863
$389$	−13.7810	−0.698723	−0.349361	−	0.936988i	$-0.613601\pi$
$389$	−13.7810	−0.698723	−0.349361	+	0.936988i	$0.613601\pi$
$390$	8.48408	0.429608
$391$	−2.33328	−0.117999
$392$	−9.65999	−0.487903
$393$	25.3085	1.27665
$394$	23.8797	1.20304
$395$	−4.32074	−0.217400
$396$	11.2628	0.565977
$397$	−16.3493	−0.820549	−0.410275	−	0.911962i	$-0.634567\pi$
$397$	−16.3493	−0.820549	−0.410275	+	0.911962i	$0.634567\pi$
$398$	−5.85674	−0.293572
$399$	−12.8753	−0.644574
$400$	−4.38153	−0.219076
$401$	26.3350	1.31511	0.657553	−	0.753409i	$-0.271592\pi$
$401$	26.3350	1.31511	0.657553	+	0.753409i	$0.271592\pi$
$402$	5.39697	0.269176
$403$	−12.0865	−0.602074
$404$	−14.9799	−0.745278
$405$	3.98907	0.198219
$406$	−25.0140	−1.24142
$407$	0.984296	0.0487898
$408$	−5.29724	−0.262253
$409$	−38.6354	−1.91040	−0.955199	−	0.295964i	$-0.904359\pi$
$409$	−38.6354	−1.91040	−0.955199	+	0.295964i	$0.904359\pi$
$410$	7.36409	0.363686
$411$	39.2373	1.93544
$412$	−1.48388	−0.0731055
$413$	18.5438	0.912481
$414$	−4.63977	−0.228032
$415$	5.54812	0.272346
$416$	4.08175	0.200124
$417$	−34.0687	−1.66835
$418$	3.37279	0.164968
$419$	3.15225	0.153998	0.0769989	−	0.997031i	$-0.475466\pi$
$419$	3.15225	0.153998	0.0769989	+	0.997031i	$0.475466\pi$
$420$	−8.48390	−0.413972
$421$	−33.5542	−1.63533	−0.817665	−	0.575694i	$-0.804732\pi$
$421$	−33.5542	−1.63533	−0.817665	+	0.575694i	$0.804732\pi$
$422$	23.3983	1.13901
$423$	−40.3974	−1.96419
$424$	3.33421	0.161923
$425$	8.78167	0.425974
$426$	−30.4933	−1.47741
$427$	−2.59086	−0.125380
$428$	12.7515	0.616368
$429$	30.4867	1.47191
$430$	−7.35159	−0.354525
$431$	5.01479	0.241554	0.120777	−	0.992680i	$-0.461461\pi$
$431$	5.01479	0.241554	0.120777	+	0.992680i	$0.461461\pi$
$432$	−2.60463	−0.125315
$433$	−0.0725544	−0.00348674	−0.00174337	−	0.999998i	$-0.500555\pi$
$433$	−0.0725544	−0.00348674	−0.00174337	+	0.999998i	$0.500555\pi$
$434$	12.0863	0.580160
$435$	−12.7381	−0.610744
$436$	9.25672	0.443317
$437$	−1.38944	−0.0664659
$438$	−10.5087	−0.502124
$439$	−13.8168	−0.659439	−0.329720	−	0.944079i	$-0.606954\pi$
$439$	−13.8168	−0.659439	−0.329720	+	0.944079i	$0.606954\pi$
$440$	2.22242	0.105950
$441$	38.4997	1.83332
$442$	−8.18085	−0.389123
$443$	29.6007	1.40637	0.703186	−	0.711006i	$-0.251760\pi$
$443$	29.6007	1.40637	0.703186	+	0.711006i	$0.251760\pi$
$444$	−0.920573	−0.0436885
$445$	10.4494	0.495347
$446$	−14.8097	−0.701259
$447$	54.1378	2.56063
$448$	−4.08167	−0.192841
$449$	2.43872	0.115090	0.0575452	−	0.998343i	$-0.481673\pi$
$449$	2.43872	0.115090	0.0575452	+	0.998343i	$0.481673\pi$
$450$	17.4625	0.823190
$451$	26.4621	1.24605
$452$	−4.75945	−0.223866
$453$	58.3837	2.74311
$454$	2.57869	0.121024
$455$	−13.1022	−0.614240
$456$	−3.15443	−0.147720
$457$	26.5304	1.24104	0.620519	−	0.784191i	$-0.286922\pi$
$457$	26.5304	1.24104	0.620519	+	0.784191i	$0.286922\pi$
$458$	23.6386	1.10456
$459$	5.22033	0.243664
$460$	−0.915537	−0.0426871
$461$	−40.6064	−1.89123	−0.945615	−	0.325288i	$-0.894539\pi$
$461$	−40.6064	−1.89123	−0.945615	+	0.325288i	$0.894539\pi$
$462$	−30.4861	−1.41834
$463$	15.4346	0.717309	0.358655	−	0.933470i	$-0.383236\pi$
$463$	15.4346	0.717309	0.358655	+	0.933470i	$0.383236\pi$
$464$	−6.12838	−0.284503
$465$	6.15479	0.285422
$466$	−4.11548	−0.190646
$467$	34.0254	1.57451	0.787254	−	0.616628i	$-0.211502\pi$
$467$	34.0254	1.57451	0.787254	+	0.616628i	$0.211502\pi$
$468$	−16.2677	−0.751977
$469$	−8.33469	−0.384860
$470$	−7.97137	−0.367692
$471$	43.8906	2.02237
$472$	4.54320	0.209118
$473$	−26.4172	−1.21467
$474$	14.5210	0.666971
$475$	5.22937	0.239940
$476$	8.18067	0.374960
$477$	−13.2884	−0.608435
$478$	2.13346	0.0975824
$479$	15.4725	0.706957	0.353479	−	0.935443i	$-0.384999\pi$
$479$	15.4725	0.706957	0.353479	+	0.935443i	$0.384999\pi$
$480$	−2.07854	−0.0948719
$481$	−1.42170	−0.0648238
$482$	3.13407	0.142753
$483$	12.5589	0.571450
$484$	−3.01396	−0.136998
$485$	−6.78288	−0.307995
$486$	−21.2202	−0.962570
$487$	15.7989	0.715917	0.357959	−	0.933737i	$-0.383473\pi$
$487$	15.7989	0.715917	0.357959	+	0.933737i	$0.383473\pi$
$488$	−0.634755	−0.0287340
$489$	−37.2260	−1.68342
$490$	7.59690	0.343193
$491$	−36.0897	−1.62871	−0.814354	−	0.580369i	$-0.802908\pi$
$491$	−36.0897	−1.62871	−0.814354	+	0.580369i	$0.802908\pi$
$492$	−24.7490	−1.11577
$493$	12.2828	0.553190
$494$	−4.87158	−0.219183
$495$	−8.85740	−0.398111
$496$	2.96112	0.132958
$497$	47.0916	2.11235
$498$	−18.6459	−0.835544
$499$	16.3836	0.733431	0.366716	−	0.930333i	$-0.380482\pi$
$499$	16.3836	0.733431	0.366716	+	0.930333i	$0.380482\pi$
$500$	7.37791	0.329950
$501$	42.3374	1.89150
$502$	−24.0059	−1.07144
$503$	38.2665	1.70622	0.853110	−	0.521731i	$-0.174713\pi$
$503$	38.2665	1.70622	0.853110	+	0.521731i	$0.174713\pi$
$504$	16.2674	0.724608
$505$	11.7806	0.524232
$506$	−3.28989	−0.146254
$507$	−9.67526	−0.429693
$508$	−19.4269	−0.861929
$509$	13.7264	0.608410	0.304205	−	0.952607i	$-0.401609\pi$
$509$	13.7264	0.608410	0.304205	+	0.952607i	$0.401609\pi$
$510$	4.16591	0.184469
$511$	16.2288	0.717921
$512$	−1.00000	−0.0441942
$513$	3.10864	0.137250
$514$	−25.5765	−1.12813
$515$	1.16697	0.0514227
$516$	24.7070	1.08766
$517$	−28.6443	−1.25978
$518$	1.42167	0.0624644
$519$	1.72343	0.0756502
$520$	−3.21001	−0.140768
$521$	−25.1960	−1.10386	−0.551929	−	0.833891i	$-0.686108\pi$
$521$	−25.1960	−1.10386	−0.551929	+	0.833891i	$0.686108\pi$
$522$	24.4245	1.06903
$523$	27.2543	1.19175	0.595873	−	0.803078i	$-0.296806\pi$
$523$	27.2543	1.19175	0.595873	+	0.803078i	$0.296806\pi$
$524$	−9.57566	−0.418314
$525$	−47.2673	−2.06292
$526$	17.4498	0.760847
$527$	−5.93481	−0.258525
$528$	−7.46902	−0.325048
$529$	−21.6447	−0.941074
$530$	−2.62212	−0.113898
$531$	−18.1068	−0.785769
$532$	4.87148	0.211205
$533$	−38.2213	−1.65555
$534$	−35.1179	−1.51970
$535$	−10.0282	−0.433556
$536$	−2.04198	−0.0882002
$537$	−63.7228	−2.74984
$538$	−20.1864	−0.870300
$539$	27.2987	1.17584
$540$	2.04836	0.0881474
$541$	−30.9969	−1.33266	−0.666330	−	0.745657i	$-0.732136\pi$
$541$	−30.9969	−1.33266	−0.666330	+	0.745657i	$0.732136\pi$
$542$	−24.1182	−1.03597
$543$	28.0638	1.20433
$544$	2.00425	0.0859314
$545$	−7.27976	−0.311831
$546$	44.0334	1.88446
$547$	−15.7377	−0.672897	−0.336449	−	0.941702i	$-0.609226\pi$
$547$	−15.7377	−0.672897	−0.336449	+	0.941702i	$0.609226\pi$
$548$	−14.8457	−0.634178
$549$	2.52980	0.107969
$550$	12.3820	0.527971
$551$	7.31424	0.311597
$552$	3.07691	0.130962
$553$	−22.4251	−0.953614
$554$	−5.03516	−0.213924
$555$	0.723966	0.0307307
$556$	12.8901	0.546664
$557$	19.7163	0.835406	0.417703	−	0.908584i	$-0.362835\pi$
$557$	19.7163	0.835406	0.417703	+	0.908584i	$0.362835\pi$
$558$	−11.8015	−0.499596
$559$	38.1565	1.61385
$560$	3.20994	0.135645
$561$	14.9698	0.632025
$562$	−18.9374	−0.798827
$563$	11.4627	0.483097	0.241548	−	0.970389i	$-0.422345\pi$
$563$	11.4627	0.483097	0.241548	+	0.970389i	$0.422345\pi$
$564$	26.7899	1.12806
$565$	3.74297	0.157468
$566$	−5.42126	−0.227873
$567$	20.7038	0.869477
$568$	11.5374	0.484097
$569$	14.6486	0.614103	0.307051	−	0.951693i	$-0.400658\pi$
$569$	14.6486	0.614103	0.307051	+	0.951693i	$0.400658\pi$
$570$	2.48074	0.103907
$571$	−6.70722	−0.280688	−0.140344	−	0.990103i	$-0.544821\pi$
$571$	−6.70722	−0.280688	−0.140344	+	0.990103i	$0.544821\pi$
$572$	−11.5349	−0.482297
$573$	67.3397	2.81316
$574$	38.2205	1.59529
$575$	−5.10084	−0.212720
$576$	3.98548	0.166062
$577$	−29.3489	−1.22181	−0.610904	−	0.791704i	$-0.709194\pi$
$577$	−29.3489	−1.22181	−0.610904	+	0.791704i	$0.709194\pi$
$578$	12.9830	0.540021
$579$	29.7144	1.23489
$580$	4.81954	0.200121
$581$	28.7954	1.19464
$582$	22.7957	0.944911
$583$	−9.42233	−0.390233
$584$	3.97603	0.164529
$585$	12.7934	0.528944
$586$	−10.2937	−0.425229
$587$	2.91010	0.120113	0.0600564	−	0.998195i	$-0.480872\pi$
$587$	2.91010	0.120113	0.0600564	+	0.998195i	$0.480872\pi$
$588$	−25.5314	−1.05290
$589$	−3.53410	−0.145620
$590$	−3.57291	−0.147094
$591$	63.1142	2.59617
$592$	0.348305	0.0143153
$593$	−19.8473	−0.815031	−0.407516	−	0.913198i	$-0.633605\pi$
$593$	−19.8473	−0.815031	−0.407516	+	0.913198i	$0.633605\pi$
$594$	7.36058	0.302008
$595$	−6.43352	−0.263749
$596$	−20.4834	−0.839033
$597$	−15.4794	−0.633530
$598$	4.75185	0.194318
$599$	15.8227	0.646500	0.323250	−	0.946314i	$-0.395225\pi$
$599$	15.8227	0.646500	0.323250	+	0.946314i	$0.395225\pi$
$600$	−11.5804	−0.472768
$601$	17.7817	0.725329	0.362665	−	0.931920i	$-0.381867\pi$
$601$	17.7817	0.725329	0.362665	+	0.931920i	$0.381867\pi$
$602$	−38.1557	−1.55511
$603$	8.13828	0.331416
$604$	−22.0899	−0.898825
$605$	2.37027	0.0963652
$606$	−39.5920	−1.60831
$607$	13.6685	0.554789	0.277394	−	0.960756i	$-0.410529\pi$
$607$	13.6685	0.554789	0.277394	+	0.960756i	$0.410529\pi$
$608$	1.19350	0.0484029
$609$	−66.1122	−2.67900
$610$	0.499190	0.0202116
$611$	41.3733	1.67378
$612$	−7.98789	−0.322892
$613$	27.7508	1.12084	0.560422	−	0.828207i	$-0.310639\pi$
$613$	27.7508	1.12084	0.560422	+	0.828207i	$0.310639\pi$
$614$	16.7362	0.675420
$615$	19.4633	0.784837
$616$	11.5346	0.464743
$617$	−6.13529	−0.246998	−0.123499	−	0.992345i	$-0.539412\pi$
$617$	−6.13529	−0.246998	−0.123499	+	0.992345i	$0.539412\pi$
$618$	−3.92190	−0.157762
$619$	17.7134	0.711963	0.355981	−	0.934493i	$-0.384147\pi$
$619$	17.7134	0.711963	0.355981	+	0.934493i	$0.384147\pi$
$620$	−2.32871	−0.0935232
$621$	−3.03223	−0.121679
$622$	−19.5561	−0.784129
$623$	54.2335	2.17282
$624$	10.7881	0.431869
$625$	16.1054	0.644217
$626$	27.3689	1.09388
$627$	8.91430	0.356003
$628$	−16.6063	−0.662664
$629$	−0.698091	−0.0278347
$630$	−12.7932	−0.509692
$631$	33.5967	1.33746	0.668731	−	0.743505i	$-0.266838\pi$
$631$	33.5967	1.33746	0.668731	+	0.743505i	$0.266838\pi$
$632$	−5.49412	−0.218544
$633$	61.8418	2.45799
$634$	14.1582	0.562292
$635$	15.2779	0.606284
$636$	8.81233	0.349432
$637$	−39.4297	−1.56226
$638$	17.3185	0.685648
$639$	−45.9819	−1.81902
$640$	0.786430	0.0310864
$641$	−8.02237	−0.316865	−0.158432	−	0.987370i	$-0.550644\pi$
$641$	−8.02237	−0.316865	−0.158432	+	0.987370i	$0.550644\pi$
$642$	33.7024	1.33013
$643$	3.08523	0.121669	0.0608347	−	0.998148i	$-0.480624\pi$
$643$	3.08523	0.121669	0.0608347	+	0.998148i	$0.480624\pi$
$644$	−4.75175	−0.187245
$645$	−19.4303	−0.765067
$646$	−2.39208	−0.0941150
$647$	3.74448	0.147211	0.0736053	−	0.997287i	$-0.476549\pi$
$647$	3.74448	0.147211	0.0736053	+	0.997287i	$0.476549\pi$
$648$	5.07238	0.199262
$649$	−12.8389	−0.503970
$650$	−17.8843	−0.701481
$651$	31.9441	1.25199
$652$	14.0847	0.551600
$653$	21.2284	0.830732	0.415366	−	0.909654i	$-0.363653\pi$
$653$	21.2284	0.830732	0.415366	+	0.909654i	$0.363653\pi$
$654$	24.4656	0.956680
$655$	7.53058	0.294244
$656$	9.36395	0.365601
$657$	−15.8464	−0.618227
$658$	−41.3724	−1.61286
$659$	29.3226	1.14225	0.571123	−	0.820865i	$-0.306508\pi$
$659$	29.3226	1.14225	0.571123	+	0.820865i	$0.306508\pi$
$660$	5.87386	0.228640
$661$	46.1090	1.79343	0.896716	−	0.442606i	$-0.145946\pi$
$661$	46.1090	1.79343	0.896716	+	0.442606i	$0.145946\pi$
$662$	20.8203	0.809206
$663$	−21.6220	−0.839730
$664$	7.05482	0.273780
$665$	−3.83107	−0.148563
$666$	−1.38816	−0.0537903
$667$	−7.13447	−0.276248
$668$	−16.0187	−0.619780
$669$	−39.1421	−1.51332
$670$	1.60588	0.0620404
$671$	1.79379	0.0692485
$672$	−10.7879	−0.416151
$673$	−21.2025	−0.817297	−0.408648	−	0.912692i	$-0.634000\pi$
$673$	−21.2025	−0.817297	−0.408648	+	0.912692i	$0.634000\pi$
$674$	22.2572	0.857315
$675$	11.4123	0.439258
$676$	3.66070	0.140796
$677$	38.1097	1.46467	0.732337	−	0.680942i	$-0.238430\pi$
$677$	38.1097	1.46467	0.732337	+	0.680942i	$0.238430\pi$
$678$	−12.5792	−0.483103
$679$	−35.2040	−1.35100
$680$	−1.57620	−0.0604445
$681$	6.81548	0.261170
$682$	−8.36799	−0.320427
$683$	43.1458	1.65093	0.825464	−	0.564454i	$-0.190913\pi$
$683$	43.1458	1.65093	0.825464	+	0.564454i	$0.190913\pi$
$684$	−4.75668	−0.181876
$685$	11.6751	0.446083
$686$	10.8572	0.414530
$687$	62.4770	2.38365
$688$	−9.34806	−0.356392
$689$	13.6094	0.518477
$690$	−2.41977	−0.0921191
$691$	−32.3357	−1.23011	−0.615053	−	0.788486i	$-0.710865\pi$
$691$	−32.3357	−1.23011	−0.615053	+	0.788486i	$0.710865\pi$
$692$	−0.652072	−0.0247881
$693$	−45.9710	−1.74629
$694$	30.3067	1.15043
$695$	−10.1372	−0.384526
$696$	−16.1974	−0.613959
$697$	−18.7677	−0.710877
$698$	20.3891	0.771738
$699$	−10.8773	−0.411415
$700$	17.8839	0.675949
$701$	−19.9637	−0.754018	−0.377009	−	0.926210i	$-0.623047\pi$
$701$	−19.9637	−0.754018	−0.377009	+	0.926210i	$0.623047\pi$
$702$	−10.6315	−0.401259
$703$	−0.415703	−0.0156786
$704$	2.82596	0.106507
$705$	−21.0684	−0.793481
$706$	−18.9632	−0.713691
$707$	61.1430	2.29952
$708$	12.0077	0.451277
$709$	10.8199	0.406352	0.203176	−	0.979142i	$-0.434874\pi$
$709$	10.8199	0.406352	0.203176	+	0.979142i	$0.434874\pi$
$710$	−9.07332	−0.340516
$711$	21.8967	0.821190
$712$	13.2871	0.497955
$713$	3.44724	0.129100
$714$	21.6216	0.809167
$715$	9.07135	0.339249
$716$	24.1100	0.901032
$717$	5.63876	0.210583
$718$	−13.9995	−0.522457
$719$	−30.6045	−1.14136	−0.570678	−	0.821174i	$-0.693319\pi$
$719$	−30.6045	−1.14136	−0.570678	+	0.821174i	$0.693319\pi$
$720$	−3.13430	−0.116808
$721$	6.05670	0.225563
$722$	17.5756	0.654094
$723$	8.28338	0.308062
$724$	−10.6181	−0.394620
$725$	26.8517	0.997246
$726$	−7.96592	−0.295643
$727$	41.3099	1.53210	0.766050	−	0.642781i	$-0.222219\pi$
$727$	41.3099	1.53210	0.766050	+	0.642781i	$0.222219\pi$
$728$	−16.6603	−0.617474
$729$	−40.8681	−1.51363
$730$	−3.12687	−0.115731
$731$	18.7358	0.692970
$732$	−1.67766	−0.0620082
$733$	6.99679	0.258432	0.129216	−	0.991616i	$-0.458754\pi$
$733$	6.99679	0.258432	0.129216	+	0.991616i	$0.458754\pi$
$734$	−1.27736	−0.0471483
$735$	20.0787	0.740613
$736$	−1.16417	−0.0429118
$737$	5.77055	0.212561
$738$	−37.3198	−1.37376
$739$	9.57290	0.352145	0.176072	−	0.984377i	$-0.443661\pi$
$739$	9.57290	0.352145	0.176072	+	0.984377i	$0.443661\pi$
$740$	−0.273918	−0.0100694
$741$	−12.8756	−0.472998
$742$	−13.6091	−0.499606
$743$	19.2225	0.705206	0.352603	−	0.935773i	$-0.385297\pi$
$743$	19.2225	0.705206	0.352603	+	0.935773i	$0.385297\pi$
$744$	7.82625	0.286924
$745$	16.1088	0.590179
$746$	−6.74287	−0.246874
$747$	−28.1169	−1.02874
$748$	−5.66392	−0.207093
$749$	−52.0475	−1.90177
$750$	19.4999	0.712034
$751$	7.91648	0.288876	0.144438	−	0.989514i	$-0.453863\pi$
$751$	7.91648	0.288876	0.144438	+	0.989514i	$0.453863\pi$
$752$	−10.1362	−0.369627
$753$	−63.4478	−2.31217
$754$	−25.0145	−0.910976
$755$	17.3721	0.632237
$756$	10.6312	0.386654
$757$	−29.2262	−1.06225	−0.531123	−	0.847295i	$-0.678230\pi$
$757$	−29.2262	−1.06225	−0.531123	+	0.847295i	$0.678230\pi$
$758$	−24.4335	−0.887466
$759$	−8.69520	−0.315616
$760$	−0.938606	−0.0340468
$761$	−18.5196	−0.671334	−0.335667	−	0.941981i	$-0.608962\pi$
$761$	−18.5196	−0.671334	−0.335667	+	0.941981i	$0.608962\pi$
$762$	−51.3454	−1.86005
$763$	−37.7828	−1.36783
$764$	−25.4784	−0.921778
$765$	6.28192	0.227123
$766$	25.1112	0.907304
$767$	18.5442	0.669593
$768$	−2.64301	−0.0953713
$769$	7.80339	0.281397	0.140699	−	0.990052i	$-0.455065\pi$
$769$	7.80339	0.281397	0.140699	+	0.990052i	$0.455065\pi$
$770$	−9.07116	−0.326902
$771$	−67.5988	−2.43451
$772$	−11.2426	−0.404632
$773$	5.34754	0.192338	0.0961688	−	0.995365i	$-0.469341\pi$
$773$	5.34754	0.192338	0.0961688	+	0.995365i	$0.469341\pi$
$774$	37.2565	1.33916
$775$	−12.9742	−0.466048
$776$	−8.62490	−0.309616
$777$	3.75747	0.134799
$778$	13.7810	0.494071
$779$	−11.1759	−0.400418
$780$	−8.48408	−0.303779
$781$	−32.6041	−1.16667
$782$	2.33328	0.0834381
$783$	15.9622	0.570442
$784$	9.65999	0.345000
$785$	13.0597	0.466120
$786$	−25.3085	−0.902725
$787$	27.1473	0.967698	0.483849	−	0.875151i	$-0.339238\pi$
$787$	27.1473	0.967698	0.483849	+	0.875151i	$0.339238\pi$
$788$	−23.8797	−0.850680
$789$	46.1199	1.64191
$790$	4.32074	0.153725
$791$	19.4265	0.690726
$792$	−11.2628	−0.400206
$793$	−2.59091	−0.0920060
$794$	16.3493	0.580216
$795$	−6.93028	−0.245792
$796$	5.85674	0.207587
$797$	−52.3030	−1.85267	−0.926334	−	0.376703i	$-0.877058\pi$
$797$	−52.3030	−1.85267	−0.926334	+	0.376703i	$0.877058\pi$
$798$	12.8753	0.455782
$799$	20.3154	0.718706
$800$	4.38153	0.154910
$801$	−52.9555	−1.87109
$802$	−26.3350	−0.929920
$803$	−11.2361	−0.396513
$804$	−5.39697	−0.190336
$805$	3.73692	0.131709
$806$	12.0865	0.425730
$807$	−53.3529	−1.87811
$808$	14.9799	0.526991
$809$	25.5222	0.897314	0.448657	−	0.893704i	$-0.351902\pi$
$809$	25.5222	0.897314	0.448657	+	0.893704i	$0.351902\pi$
$810$	−3.98907	−0.140162
$811$	50.7046	1.78048	0.890239	−	0.455494i	$-0.150537\pi$
$811$	50.7046	1.78048	0.890239	+	0.455494i	$0.150537\pi$
$812$	25.0140	0.877819
$813$	−63.7446	−2.23562
$814$	−0.984296	−0.0344996
$815$	−11.0766	−0.387998
$816$	5.29724	0.185441
$817$	11.1569	0.390332
$818$	38.6354	1.35086
$819$	66.3995	2.32019
$820$	−7.36409	−0.257165
$821$	29.8439	1.04156	0.520780	−	0.853691i	$-0.325641\pi$
$821$	29.8439	1.04156	0.520780	+	0.853691i	$0.325641\pi$
$822$	−39.2373	−1.36856
$823$	−8.57343	−0.298851	−0.149425	−	0.988773i	$-0.547742\pi$
$823$	−8.57343	−0.298851	−0.149425	+	0.988773i	$0.547742\pi$
$824$	1.48388	0.0516934
$825$	32.7257	1.13936
$826$	−18.5438	−0.645222
$827$	−29.9486	−1.04141	−0.520707	−	0.853735i	$-0.674332\pi$
$827$	−29.9486	−1.04141	−0.520707	+	0.853735i	$0.674332\pi$
$828$	4.63977	0.161243
$829$	−17.6045	−0.611429	−0.305715	−	0.952123i	$-0.598895\pi$
$829$	−17.6045	−0.611429	−0.305715	+	0.952123i	$0.598895\pi$
$830$	−5.54812	−0.192578
$831$	−13.3080	−0.461648
$832$	−4.08175	−0.141509
$833$	−19.3610	−0.670820
$834$	34.0687	1.17970
$835$	12.5975	0.435956
$836$	−3.37279	−0.116650
$837$	−7.71262	−0.266587
$838$	−3.15225	−0.108893
$839$	44.0988	1.52246	0.761230	−	0.648482i	$-0.224596\pi$
$839$	44.0988	1.52246	0.761230	+	0.648482i	$0.224596\pi$
$840$	8.48390	0.292722
$841$	8.55706	0.295071
$842$	33.5542	1.15635
$843$	−50.0517	−1.72387
$844$	−23.3983	−0.805402
$845$	−2.87888	−0.0990366
$846$	40.3974	1.38889
$847$	12.3020	0.422701
$848$	−3.33421	−0.114497
$849$	−14.3284	−0.491750
$850$	−8.78167	−0.301209
$851$	0.405486	0.0138999
$852$	30.4933	1.04468
$853$	−4.60720	−0.157748	−0.0788738	−	0.996885i	$-0.525132\pi$
$853$	−4.60720	−0.157748	−0.0788738	+	0.996885i	$0.525132\pi$
$854$	2.59086	0.0886573
$855$	3.74080	0.127933
$856$	−12.7515	−0.435838
$857$	−46.9959	−1.60535	−0.802675	−	0.596416i	$-0.796591\pi$
$857$	−46.9959	−1.60535	−0.802675	+	0.596416i	$0.796591\pi$
$858$	−30.4867	−1.04080
$859$	47.8418	1.63234	0.816170	−	0.577812i	$-0.196093\pi$
$859$	47.8418	1.63234	0.816170	+	0.577812i	$0.196093\pi$
$860$	7.35159	0.250687
$861$	101.017	3.44265
$862$	−5.01479	−0.170804
$863$	−24.9151	−0.848121	−0.424060	−	0.905634i	$-0.639396\pi$
$863$	−24.9151	−0.848121	−0.424060	+	0.905634i	$0.639396\pi$
$864$	2.60463	0.0886114
$865$	0.512809	0.0174360
$866$	0.0725544	0.00246550
$867$	34.3141	1.16537
$868$	−12.0863	−0.410235
$869$	15.5261	0.526688
$870$	12.7381	0.431861
$871$	−8.33487	−0.282416
$872$	−9.25672	−0.313472
$873$	34.3744	1.16340
$874$	1.38944	0.0469985
$875$	−30.1142	−1.01804
$876$	10.5087	0.355055
$877$	18.9294	0.639201	0.319600	−	0.947552i	$-0.396451\pi$
$877$	18.9294	0.639201	0.319600	+	0.947552i	$0.396451\pi$
$878$	13.8168	0.466294
$879$	−27.2063	−0.917646
$880$	−2.22242	−0.0749177
$881$	9.48389	0.319520	0.159760	−	0.987156i	$-0.448928\pi$
$881$	9.48389	0.319520	0.159760	+	0.987156i	$0.448928\pi$
$882$	−38.4997	−1.29635
$883$	−27.5124	−0.925866	−0.462933	−	0.886393i	$-0.653203\pi$
$883$	−27.5124	−0.925866	−0.462933	+	0.886393i	$0.653203\pi$
$884$	8.18085	0.275152
$885$	−9.44321	−0.317430
$886$	−29.6007	−0.994456
$887$	−28.7157	−0.964178	−0.482089	−	0.876122i	$-0.660122\pi$
$887$	−28.7157	−0.964178	−0.482089	+	0.876122i	$0.660122\pi$
$888$	0.920573	0.0308924
$889$	79.2941	2.65944
$890$	−10.4494	−0.350264
$891$	−14.3343	−0.480219
$892$	14.8097	0.495865
$893$	12.0975	0.404828
$894$	−54.1378	−1.81064
$895$	−18.9608	−0.633790
$896$	4.08167	0.136359
$897$	12.5592	0.419338
$898$	−2.43872	−0.0813813
$899$	−18.1469	−0.605231
$900$	−17.4625	−0.582083
$901$	6.68258	0.222629
$902$	−26.4621	−0.881092
$903$	−100.846	−3.35593
$904$	4.75945	0.158297
$905$	8.35041	0.277577
$906$	−58.3837	−1.93967
$907$	−52.2680	−1.73553	−0.867765	−	0.496975i	$-0.834444\pi$
$907$	−52.2680	−1.73553	−0.867765	+	0.496975i	$0.834444\pi$
$908$	−2.57869	−0.0855767
$909$	−59.7021	−1.98019
$910$	13.1022	0.434333
$911$	0.561874	0.0186157	0.00930785	−	0.999957i	$-0.497037\pi$
$911$	0.561874	0.0186157	0.00930785	+	0.999957i	$0.497037\pi$
$912$	3.15443	0.104454
$913$	−19.9366	−0.659806
$914$	−26.5304	−0.877547
$915$	1.31936	0.0436168
$916$	−23.6386	−0.781042
$917$	39.0846	1.29069
$918$	−5.22033	−0.172297
$919$	12.8113	0.422607	0.211303	−	0.977421i	$-0.432229\pi$
$919$	12.8113	0.422607	0.211303	+	0.977421i	$0.432229\pi$
$920$	0.915537	0.0301844
$921$	44.2340	1.45756
$922$	40.6064	1.33730
$923$	47.0926	1.55007
$924$	30.4861	1.00292
$925$	−1.52611	−0.0501782
$926$	−15.4346	−0.507214
$927$	−5.91397	−0.194240
$928$	6.12838	0.201174
$929$	−36.1276	−1.18531	−0.592653	−	0.805458i	$-0.701920\pi$
$929$	−36.1276	−1.18531	−0.592653	+	0.805458i	$0.701920\pi$
$930$	−6.15479	−0.201824
$931$	−11.5292	−0.377855
$932$	4.11548	0.134807
$933$	−51.6870	−1.69216
$934$	−34.0254	−1.11335
$935$	4.45428	0.145670
$936$	16.2677	0.531728
$937$	24.2885	0.793471	0.396736	−	0.917933i	$-0.370143\pi$
$937$	24.2885	0.793471	0.396736	+	0.917933i	$0.370143\pi$
$938$	8.33469	0.272137
$939$	72.3362	2.36060
$940$	7.97137	0.259997
$941$	8.37572	0.273041	0.136520	−	0.990637i	$-0.456408\pi$
$941$	8.37572	0.273041	0.136520	+	0.990637i	$0.456408\pi$
$942$	−43.8906	−1.43003
$943$	10.9012	0.354993
$944$	−4.54320	−0.147868
$945$	−8.36072	−0.271974
$946$	26.4172	0.858898
$947$	6.33539	0.205873	0.102936	−	0.994688i	$-0.467176\pi$
$947$	6.33539	0.205873	0.102936	+	0.994688i	$0.467176\pi$
$948$	−14.5210	−0.471620
$949$	16.2292	0.526821
$950$	−5.22937	−0.169663
$951$	37.4201	1.21343
$952$	−8.18067	−0.265137
$953$	42.9484	1.39124	0.695618	−	0.718412i	$-0.255131\pi$
$953$	42.9484	1.39124	0.695618	+	0.718412i	$0.255131\pi$
$954$	13.2884	0.430229
$955$	20.0370	0.648382
$956$	−2.13346	−0.0690012
$957$	45.7730	1.47963
$958$	−15.4725	−0.499894
$959$	60.5953	1.95672
$960$	2.07854	0.0670845
$961$	−22.2318	−0.717154
$962$	1.42170	0.0458373
$963$	50.8210	1.63768
$964$	−3.13407	−0.100942
$965$	8.84155	0.284620
$966$	−12.5589	−0.404076
$967$	51.0674	1.64222	0.821109	−	0.570772i	$-0.193356\pi$
$967$	51.0674	1.64222	0.821109	+	0.570772i	$0.193356\pi$
$968$	3.01396	0.0968725
$969$	−6.32227	−0.203101
$970$	6.78288	0.217785
$971$	16.2105	0.520219	0.260110	−	0.965579i	$-0.416241\pi$
$971$	16.2105	0.520219	0.260110	+	0.965579i	$0.416241\pi$
$972$	21.2202	0.680639
$973$	−52.6133	−1.68670
$974$	−15.7989	−0.506230
$975$	−47.2684	−1.51380
$976$	0.634755	0.0203180
$977$	−50.0269	−1.60050	−0.800252	−	0.599664i	$-0.795301\pi$
$977$	−50.0269	−1.60050	−0.800252	+	0.599664i	$0.795301\pi$
$978$	37.2260	1.19036
$979$	−37.5488	−1.20006
$980$	−7.59690	−0.242674
$981$	36.8925	1.17789
$982$	36.0897	1.15167
$983$	−15.7631	−0.502766	−0.251383	−	0.967888i	$-0.580885\pi$
$983$	−15.7631	−0.502766	−0.251383	+	0.967888i	$0.580885\pi$
$984$	24.7490	0.788968
$985$	18.7797	0.598372
$986$	−12.2828	−0.391164
$987$	−109.347	−3.48057
$988$	4.87158	0.154986
$989$	−10.8827	−0.346050
$990$	8.85740	0.281507
$991$	−25.5487	−0.811581	−0.405791	−	0.913966i	$-0.633004\pi$
$991$	−25.5487	−0.811581	−0.405791	+	0.913966i	$0.633004\pi$
$992$	−2.96112	−0.0940155
$993$	55.0283	1.74627
$994$	−47.0916	−1.49366
$995$	−4.60592	−0.146017
$996$	18.6459	0.590819
$997$	41.8007	1.32384	0.661920	−	0.749574i	$-0.269742\pi$
$997$	41.8007	1.32384	0.661920	+	0.749574i	$0.269742\pi$
$998$	−16.3836	−0.518614
$999$	−0.907208	−0.0287028

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.c.1.9	✓	86

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.c.1.9	✓	86	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.64301 q^{3} +1.00000 q^{4} -0.786430 q^{5} +2.64301 q^{6} -4.08167 q^{7} -1.00000 q^{8} +3.98548 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.64301 q^{3} +1.00000 q^{4} -0.786430 q^{5} +2.64301 q^{6} -4.08167 q^{7} -1.00000 q^{8} +3.98548 q^{9} +0.786430 q^{10} +2.82596 q^{11} -2.64301 q^{12} -4.08175 q^{13} +4.08167 q^{14} +2.07854 q^{15} +1.00000 q^{16} -2.00425 q^{17} -3.98548 q^{18} -1.19350 q^{19} -0.786430 q^{20} +10.7879 q^{21} -2.82596 q^{22} +1.16417 q^{23} +2.64301 q^{24} -4.38153 q^{25} +4.08175 q^{26} -2.60463 q^{27} -4.08167 q^{28} -6.12838 q^{29} -2.07854 q^{30} +2.96112 q^{31} -1.00000 q^{32} -7.46902 q^{33} +2.00425 q^{34} +3.20994 q^{35} +3.98548 q^{36} +0.348305 q^{37} +1.19350 q^{38} +10.7881 q^{39} +0.786430 q^{40} +9.36395 q^{41} -10.7879 q^{42} -9.34806 q^{43} +2.82596 q^{44} -3.13430 q^{45} -1.16417 q^{46} -10.1362 q^{47} -2.64301 q^{48} +9.65999 q^{49} +4.38153 q^{50} +5.29724 q^{51} -4.08175 q^{52} -3.33421 q^{53} +2.60463 q^{54} -2.22242 q^{55} +4.08167 q^{56} +3.15443 q^{57} +6.12838 q^{58} -4.54320 q^{59} +2.07854 q^{60} +0.634755 q^{61} -2.96112 q^{62} -16.2674 q^{63} +1.00000 q^{64} +3.21001 q^{65} +7.46902 q^{66} +2.04198 q^{67} -2.00425 q^{68} -3.07691 q^{69} -3.20994 q^{70} -11.5374 q^{71} -3.98548 q^{72} -3.97603 q^{73} -0.348305 q^{74} +11.5804 q^{75} -1.19350 q^{76} -11.5346 q^{77} -10.7881 q^{78} +5.49412 q^{79} -0.786430 q^{80} -5.07238 q^{81} -9.36395 q^{82} -7.05482 q^{83} +10.7879 q^{84} +1.57620 q^{85} +9.34806 q^{86} +16.1974 q^{87} -2.82596 q^{88} -13.2871 q^{89} +3.13430 q^{90} +16.6603 q^{91} +1.16417 q^{92} -7.82625 q^{93} +10.1362 q^{94} +0.938606 q^{95} +2.64301 q^{96} +8.62490 q^{97} -9.65999 q^{98} +11.2628 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * q^99

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