LMFDB - Embedded newform 8026.2.a.b.1.5

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			1.5
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)

$f(q)$	$=$	$q-1.00000 q^{2} -3.01169 q^{3} +1.00000 q^{4} +2.74703 q^{5} +3.01169 q^{6} -2.66211 q^{7} -1.00000 q^{8} +6.07025 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.01169 q^{3} +1.00000 q^{4} +2.74703 q^{5} +3.01169 q^{6} -2.66211 q^{7} -1.00000 q^{8} +6.07025 q^{9} -2.74703 q^{10} +0.0649906 q^{11} -3.01169 q^{12} +2.20169 q^{13} +2.66211 q^{14} -8.27318 q^{15} +1.00000 q^{16} +5.48409 q^{17} -6.07025 q^{18} -0.873682 q^{19} +2.74703 q^{20} +8.01745 q^{21} -0.0649906 q^{22} +4.00223 q^{23} +3.01169 q^{24} +2.54615 q^{25} -2.20169 q^{26} -9.24662 q^{27} -2.66211 q^{28} -9.55873 q^{29} +8.27318 q^{30} +0.674543 q^{31} -1.00000 q^{32} -0.195731 q^{33} -5.48409 q^{34} -7.31289 q^{35} +6.07025 q^{36} +4.71224 q^{37} +0.873682 q^{38} -6.63079 q^{39} -2.74703 q^{40} -1.87337 q^{41} -8.01745 q^{42} -7.06122 q^{43} +0.0649906 q^{44} +16.6751 q^{45} -4.00223 q^{46} -11.5645 q^{47} -3.01169 q^{48} +0.0868436 q^{49} -2.54615 q^{50} -16.5163 q^{51} +2.20169 q^{52} +2.81039 q^{53} +9.24662 q^{54} +0.178531 q^{55} +2.66211 q^{56} +2.63126 q^{57} +9.55873 q^{58} +13.7162 q^{59} -8.27318 q^{60} -1.69076 q^{61} -0.674543 q^{62} -16.1597 q^{63} +1.00000 q^{64} +6.04809 q^{65} +0.195731 q^{66} +4.20994 q^{67} +5.48409 q^{68} -12.0535 q^{69} +7.31289 q^{70} -8.14094 q^{71} -6.07025 q^{72} +6.46563 q^{73} -4.71224 q^{74} -7.66822 q^{75} -0.873682 q^{76} -0.173012 q^{77} +6.63079 q^{78} -10.5182 q^{79} +2.74703 q^{80} +9.63718 q^{81} +1.87337 q^{82} -7.11724 q^{83} +8.01745 q^{84} +15.0649 q^{85} +7.06122 q^{86} +28.7879 q^{87} -0.0649906 q^{88} -1.13575 q^{89} -16.6751 q^{90} -5.86114 q^{91} +4.00223 q^{92} -2.03151 q^{93} +11.5645 q^{94} -2.40003 q^{95} +3.01169 q^{96} +1.33627 q^{97} -0.0868436 q^{98} +0.394509 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−3.01169	−1.73880	−0.869399	−	0.494111i	$-0.835494\pi$
$3$	−3.01169	−1.73880	−0.869399	+	0.494111i	$0.835494\pi$
$4$	1.00000	0.500000
$5$	2.74703	1.22851	0.614254	−	0.789109i	$-0.289457\pi$
$5$	2.74703	1.22851	0.614254	+	0.789109i	$0.289457\pi$
$6$	3.01169	1.22952
$7$	−2.66211	−1.00618	−0.503092	−	0.864233i	$-0.667804\pi$
$7$	−2.66211	−1.00618	−0.503092	+	0.864233i	$0.667804\pi$
$8$	−1.00000	−0.353553
$9$	6.07025	2.02342
$10$	−2.74703	−0.868686
$11$	0.0649906	0.0195954	0.00979770	−	0.999952i	$-0.496881\pi$
$11$	0.0649906	0.0195954	0.00979770	+	0.999952i	$0.496881\pi$
$12$	−3.01169	−0.869399
$13$	2.20169	0.610638	0.305319	−	0.952250i	$-0.401237\pi$
$13$	2.20169	0.610638	0.305319	+	0.952250i	$0.401237\pi$
$14$	2.66211	0.711480
$15$	−8.27318	−2.13613
$16$	1.00000	0.250000
$17$	5.48409	1.33009	0.665043	−	0.746805i	$-0.268413\pi$
$17$	5.48409	1.33009	0.665043	+	0.746805i	$0.268413\pi$
$18$	−6.07025	−1.43077
$19$	−0.873682	−0.200436	−0.100218	−	0.994965i	$-0.531954\pi$
$19$	−0.873682	−0.200436	−0.100218	+	0.994965i	$0.531954\pi$
$20$	2.74703	0.614254
$21$	8.01745	1.74955
$22$	−0.0649906	−0.0138560
$23$	4.00223	0.834523	0.417261	−	0.908787i	$-0.362990\pi$
$23$	4.00223	0.834523	0.417261	+	0.908787i	$0.362990\pi$
$24$	3.01169	0.614758
$25$	2.54615	0.509231
$26$	−2.20169	−0.431786
$27$	−9.24662	−1.77951
$28$	−2.66211	−0.503092
$29$	−9.55873	−1.77501	−0.887506	−	0.460796i	$-0.847564\pi$
$29$	−9.55873	−1.77501	−0.887506	+	0.460796i	$0.847564\pi$
$30$	8.27318	1.51047
$31$	0.674543	0.121151	0.0605757	−	0.998164i	$-0.480706\pi$
$31$	0.674543	0.121151	0.0605757	+	0.998164i	$0.480706\pi$
$32$	−1.00000	−0.176777
$33$	−0.195731	−0.0340724
$34$	−5.48409	−0.940513
$35$	−7.31289	−1.23610
$36$	6.07025	1.01171
$37$	4.71224	0.774688	0.387344	−	0.921935i	$-0.373393\pi$
$37$	4.71224	0.774688	0.387344	+	0.921935i	$0.373393\pi$
$38$	0.873682	0.141730
$39$	−6.63079	−1.06178
$40$	−2.74703	−0.434343
$41$	−1.87337	−0.292572	−0.146286	−	0.989242i	$-0.546732\pi$
$41$	−1.87337	−0.292572	−0.146286	+	0.989242i	$0.546732\pi$
$42$	−8.01745	−1.23712
$43$	−7.06122	−1.07683	−0.538413	−	0.842681i	$-0.680976\pi$
$43$	−7.06122	−1.07683	−0.538413	+	0.842681i	$0.680976\pi$
$44$	0.0649906	0.00979770
$45$	16.6751	2.48578
$46$	−4.00223	−0.590097
$47$	−11.5645	−1.68685	−0.843425	−	0.537248i	$-0.819464\pi$
$47$	−11.5645	−1.68685	−0.843425	+	0.537248i	$0.819464\pi$
$48$	−3.01169	−0.434699
$49$	0.0868436	0.0124062
$50$	−2.54615	−0.360081
$51$	−16.5163	−2.31275
$52$	2.20169	0.305319
$53$	2.81039	0.386036	0.193018	−	0.981195i	$-0.438172\pi$
$53$	2.81039	0.386036	0.193018	+	0.981195i	$0.438172\pi$
$54$	9.24662	1.25831
$55$	0.178531	0.0240731
$56$	2.66211	0.355740
$57$	2.63126	0.348518
$58$	9.55873	1.25512
$59$	13.7162	1.78570	0.892852	−	0.450351i	$-0.148701\pi$
$59$	13.7162	1.78570	0.892852	+	0.450351i	$0.148701\pi$
$60$	−8.27318	−1.06806
$61$	−1.69076	−0.216480	−0.108240	−	0.994125i	$-0.534522\pi$
$61$	−1.69076	−0.216480	−0.108240	+	0.994125i	$0.534522\pi$
$62$	−0.674543	−0.0856670
$63$	−16.1597	−2.03593
$64$	1.00000	0.125000
$65$	6.04809	0.750173
$66$	0.195731	0.0240928
$67$	4.20994	0.514326	0.257163	−	0.966368i	$-0.417212\pi$
$67$	4.20994	0.514326	0.257163	+	0.966368i	$0.417212\pi$
$68$	5.48409	0.665043
$69$	−12.0535	−1.45107
$70$	7.31289	0.874058
$71$	−8.14094	−0.966152	−0.483076	−	0.875578i	$-0.660481\pi$
$71$	−8.14094	−0.966152	−0.483076	+	0.875578i	$0.660481\pi$
$72$	−6.07025	−0.715386
$73$	6.46563	0.756744	0.378372	−	0.925654i	$-0.376484\pi$
$73$	6.46563	0.756744	0.378372	+	0.925654i	$0.376484\pi$
$74$	−4.71224	−0.547787
$75$	−7.66822	−0.885449
$76$	−0.873682	−0.100218
$77$	−0.173012	−0.0197166
$78$	6.63079	0.750789
$79$	−10.5182	−1.18339	−0.591696	−	0.806161i	$-0.701541\pi$
$79$	−10.5182	−1.18339	−0.591696	+	0.806161i	$0.701541\pi$
$80$	2.74703	0.307127
$81$	9.63718	1.07080
$82$	1.87337	0.206880
$83$	−7.11724	−0.781218	−0.390609	−	0.920557i	$-0.627736\pi$
$83$	−7.11724	−0.781218	−0.390609	+	0.920557i	$0.627736\pi$
$84$	8.01745	0.874775
$85$	15.0649	1.63402
$86$	7.06122	0.761431
$87$	28.7879	3.08639
$88$	−0.0649906	−0.00692802
$89$	−1.13575	−0.120389	−0.0601944	−	0.998187i	$-0.519172\pi$
$89$	−1.13575	−0.120389	−0.0601944	+	0.998187i	$0.519172\pi$
$90$	−16.6751	−1.75771
$91$	−5.86114	−0.614414
$92$	4.00223	0.417261
$93$	−2.03151	−0.210658
$94$	11.5645	1.19278
$95$	−2.40003	−0.246238
$96$	3.01169	0.307379
$97$	1.33627	0.135677	0.0678387	−	0.997696i	$-0.478390\pi$
$97$	1.33627	0.135677	0.0678387	+	0.997696i	$0.478390\pi$
$98$	−0.0868436	−0.00877253
$99$	0.394509	0.0396496
$100$	2.54615	0.254615
$101$	10.8014	1.07478	0.537392	−	0.843333i	$-0.319410\pi$
$101$	10.8014	1.07478	0.537392	+	0.843333i	$0.319410\pi$
$102$	16.5163	1.63536
$103$	−2.52341	−0.248639	−0.124320	−	0.992242i	$-0.539675\pi$
$103$	−2.52341	−0.248639	−0.124320	+	0.992242i	$0.539675\pi$
$104$	−2.20169	−0.215893
$105$	22.0241	2.14934
$106$	−2.81039	−0.272969
$107$	−17.8835	−1.72886	−0.864431	−	0.502752i	$-0.832321\pi$
$107$	−17.8835	−1.72886	−0.864431	+	0.502752i	$0.832321\pi$
$108$	−9.24662	−0.889757
$109$	−10.9162	−1.04558	−0.522792	−	0.852460i	$-0.675110\pi$
$109$	−10.9162	−1.04558	−0.522792	+	0.852460i	$0.675110\pi$
$110$	−0.178531	−0.0170222
$111$	−14.1918	−1.34703
$112$	−2.66211	−0.251546
$113$	−0.810229	−0.0762199	−0.0381099	−	0.999274i	$-0.512134\pi$
$113$	−0.810229	−0.0762199	−0.0381099	+	0.999274i	$0.512134\pi$
$114$	−2.63126	−0.246440
$115$	10.9942	1.02522
$116$	−9.55873	−0.887506
$117$	13.3648	1.23557
$118$	−13.7162	−1.26268
$119$	−14.5993	−1.33831
$120$	8.27318	0.755235
$121$	−10.9958	−0.999616
$122$	1.69076	0.153075
$123$	5.64201	0.508723
$124$	0.674543	0.0605757
$125$	−6.74078	−0.602914
$126$	16.1597	1.43962
$127$	−0.430484	−0.0381992	−0.0190996	−	0.999818i	$-0.506080\pi$
$127$	−0.430484	−0.0381992	−0.0190996	+	0.999818i	$0.506080\pi$
$128$	−1.00000	−0.0883883
$129$	21.2662	1.87238
$130$	−6.04809	−0.530453
$131$	−0.401883	−0.0351126	−0.0175563	−	0.999846i	$-0.505589\pi$
$131$	−0.401883	−0.0351126	−0.0175563	+	0.999846i	$0.505589\pi$
$132$	−0.195731	−0.0170362
$133$	2.32584	0.201676
$134$	−4.20994	−0.363683
$135$	−25.4007	−2.18615
$136$	−5.48409	−0.470256
$137$	13.6246	1.16403	0.582014	−	0.813178i	$-0.302265\pi$
$137$	13.6246	1.16403	0.582014	+	0.813178i	$0.302265\pi$
$138$	12.0535	1.02606
$139$	0.742615	0.0629878	0.0314939	−	0.999504i	$-0.489974\pi$
$139$	0.742615	0.0629878	0.0314939	+	0.999504i	$0.489974\pi$
$140$	−7.31289	−0.618052
$141$	34.8285	2.93309
$142$	8.14094	0.683173
$143$	0.143089	0.0119657
$144$	6.07025	0.505854
$145$	−26.2581	−2.18062
$146$	−6.46563	−0.535099
$147$	−0.261546	−0.0215719
$148$	4.71224	0.387344
$149$	−8.24650	−0.675580	−0.337790	−	0.941222i	$-0.609679\pi$
$149$	−8.24650	−0.675580	−0.337790	+	0.941222i	$0.609679\pi$
$150$	7.66822	0.626107
$151$	7.12433	0.579770	0.289885	−	0.957062i	$-0.406383\pi$
$151$	7.12433	0.579770	0.289885	+	0.957062i	$0.406383\pi$
$152$	0.873682	0.0708650
$153$	33.2898	2.69132
$154$	0.173012	0.0139417
$155$	1.85299	0.148835
$156$	−6.63079	−0.530888
$157$	−6.66264	−0.531737	−0.265868	−	0.964009i	$-0.585659\pi$
$157$	−6.66264	−0.531737	−0.265868	+	0.964009i	$0.585659\pi$
$158$	10.5182	0.836785
$159$	−8.46400	−0.671239
$160$	−2.74703	−0.217172
$161$	−10.6544	−0.839683
$162$	−9.63718	−0.757168
$163$	−22.9165	−1.79496	−0.897479	−	0.441057i	$-0.854603\pi$
$163$	−22.9165	−1.79496	−0.897479	+	0.441057i	$0.854603\pi$
$164$	−1.87337	−0.146286
$165$	−0.537679	−0.0418582
$166$	7.11724	0.552405
$167$	20.9118	1.61821	0.809103	−	0.587666i	$-0.199953\pi$
$167$	20.9118	1.61821	0.809103	+	0.587666i	$0.199953\pi$
$168$	−8.01745	−0.618559
$169$	−8.15258	−0.627121
$170$	−15.0649	−1.15543
$171$	−5.30347	−0.405566
$172$	−7.06122	−0.538413
$173$	20.1507	1.53203	0.766016	−	0.642821i	$-0.222236\pi$
$173$	20.1507	1.53203	0.766016	+	0.642821i	$0.222236\pi$
$174$	−28.7879	−2.18240
$175$	−6.77815	−0.512380
$176$	0.0649906	0.00489885
$177$	−41.3090	−3.10498
$178$	1.13575	0.0851278
$179$	10.5909	0.791603	0.395801	−	0.918336i	$-0.370467\pi$
$179$	10.5909	0.791603	0.395801	+	0.918336i	$0.370467\pi$
$180$	16.6751	1.24289
$181$	−14.9826	−1.11365	−0.556823	−	0.830631i	$-0.687980\pi$
$181$	−14.9826	−1.11365	−0.556823	+	0.830631i	$0.687980\pi$
$182$	5.86114	0.434456
$183$	5.09205	0.376415
$184$	−4.00223	−0.295048
$185$	12.9447	0.951710
$186$	2.03151	0.148958
$187$	0.356414	0.0260636
$188$	−11.5645	−0.843425
$189$	24.6156	1.79052
$190$	2.40003	0.174116
$191$	21.8984	1.58451	0.792255	−	0.610190i	$-0.208907\pi$
$191$	21.8984	1.58451	0.792255	+	0.610190i	$0.208907\pi$
$192$	−3.01169	−0.217350
$193$	−8.22404	−0.591980	−0.295990	−	0.955191i	$-0.595649\pi$
$193$	−8.22404	−0.591980	−0.295990	+	0.955191i	$0.595649\pi$
$194$	−1.33627	−0.0959384
$195$	−18.2149	−1.30440
$196$	0.0868436	0.00620312
$197$	−2.69101	−0.191726	−0.0958631	−	0.995395i	$-0.530561\pi$
$197$	−2.69101	−0.191726	−0.0958631	+	0.995395i	$0.530561\pi$
$198$	−0.394509	−0.0280365
$199$	0.529682	0.0375482	0.0187741	−	0.999824i	$-0.494024\pi$
$199$	0.529682	0.0375482	0.0187741	+	0.999824i	$0.494024\pi$
$200$	−2.54615	−0.180040
$201$	−12.6790	−0.894308
$202$	−10.8014	−0.759987
$203$	25.4464	1.78599
$204$	−16.5163	−1.15638
$205$	−5.14621	−0.359427
$206$	2.52341	0.175814
$207$	24.2945	1.68859
$208$	2.20169	0.152660
$209$	−0.0567811	−0.00392763
$210$	−22.0241	−1.51981
$211$	19.5618	1.34669	0.673344	−	0.739329i	$-0.264857\pi$
$211$	19.5618	1.34669	0.673344	+	0.739329i	$0.264857\pi$
$212$	2.81039	0.193018
$213$	24.5180	1.67994
$214$	17.8835	1.22249
$215$	−19.3974	−1.32289
$216$	9.24662	0.629153
$217$	−1.79571	−0.121901
$218$	10.9162	0.739340
$219$	−19.4724	−1.31583
$220$	0.178531	0.0120365
$221$	12.0742	0.812201
$222$	14.1918	0.952491
$223$	−19.1705	−1.28375	−0.641875	−	0.766810i	$-0.721843\pi$
$223$	−19.1705	−1.28375	−0.641875	+	0.766810i	$0.721843\pi$
$224$	2.66211	0.177870
$225$	15.4558	1.03039
$226$	0.810229	0.0538956
$227$	21.5432	1.42987	0.714937	−	0.699189i	$-0.246455\pi$
$227$	21.5432	1.42987	0.714937	+	0.699189i	$0.246455\pi$
$228$	2.63126	0.174259
$229$	−3.43036	−0.226684	−0.113342	−	0.993556i	$-0.536156\pi$
$229$	−3.43036	−0.226684	−0.113342	+	0.993556i	$0.536156\pi$
$230$	−10.9942	−0.724938
$231$	0.521058	0.0342831
$232$	9.55873	0.627561
$233$	15.7993	1.03505	0.517523	−	0.855669i	$-0.326854\pi$
$233$	15.7993	1.03505	0.517523	+	0.855669i	$0.326854\pi$
$234$	−13.3648	−0.873683
$235$	−31.7679	−2.07231
$236$	13.7162	0.892852
$237$	31.6776	2.05768
$238$	14.5993	0.946329
$239$	−12.2853	−0.794669	−0.397335	−	0.917674i	$-0.630065\pi$
$239$	−12.2853	−0.794669	−0.397335	+	0.917674i	$0.630065\pi$
$240$	−8.27318	−0.534031
$241$	1.49893	0.0965548	0.0482774	−	0.998834i	$-0.484627\pi$
$241$	1.49893	0.0965548	0.0482774	+	0.998834i	$0.484627\pi$
$242$	10.9958	0.706835
$243$	−1.28427	−0.0823860
$244$	−1.69076	−0.108240
$245$	0.238562	0.0152412
$246$	−5.64201	−0.359722
$247$	−1.92357	−0.122394
$248$	−0.674543	−0.0428335
$249$	21.4349	1.35838
$250$	6.74078	0.426324
$251$	−26.5077	−1.67315	−0.836574	−	0.547854i	$-0.815445\pi$
$251$	−26.5077	−1.67315	−0.836574	+	0.547854i	$0.815445\pi$
$252$	−16.1597	−1.01796
$253$	0.260107	0.0163528
$254$	0.430484	0.0270109
$255$	−45.3708	−2.84123
$256$	1.00000	0.0625000
$257$	7.17237	0.447400	0.223700	−	0.974658i	$-0.428186\pi$
$257$	7.17237	0.447400	0.223700	+	0.974658i	$0.428186\pi$
$258$	−21.2662	−1.32397
$259$	−12.5445	−0.779479
$260$	6.04809	0.375087
$261$	−58.0239	−3.59159
$262$	0.401883	0.0248284
$263$	24.1079	1.48656	0.743280	−	0.668981i	$-0.233269\pi$
$263$	24.1079	1.48656	0.743280	+	0.668981i	$0.233269\pi$
$264$	0.195731	0.0120464
$265$	7.72020	0.474248
$266$	−2.32584	−0.142606
$267$	3.42051	0.209332
$268$	4.20994	0.257163
$269$	5.82777	0.355326	0.177663	−	0.984091i	$-0.443146\pi$
$269$	5.82777	0.355326	0.177663	+	0.984091i	$0.443146\pi$
$270$	25.4007	1.54584
$271$	12.1095	0.735597	0.367799	−	0.929905i	$-0.380112\pi$
$271$	12.1095	0.735597	0.367799	+	0.929905i	$0.380112\pi$
$272$	5.48409	0.332522
$273$	17.6519	1.06834
$274$	−13.6246	−0.823093
$275$	0.165476	0.00997858
$276$	−12.0535	−0.725533
$277$	1.37935	0.0828770	0.0414385	−	0.999141i	$-0.486806\pi$
$277$	1.37935	0.0828770	0.0414385	+	0.999141i	$0.486806\pi$
$278$	−0.742615	−0.0445391
$279$	4.09464	0.245140
$280$	7.31289	0.437029
$281$	−20.7904	−1.24025	−0.620125	−	0.784503i	$-0.712918\pi$
$281$	−20.7904	−1.24025	−0.620125	+	0.784503i	$0.712918\pi$
$282$	−34.8285	−2.07401
$283$	−9.84266	−0.585085	−0.292543	−	0.956252i	$-0.594501\pi$
$283$	−9.84266	−0.585085	−0.292543	+	0.956252i	$0.594501\pi$
$284$	−8.14094	−0.483076
$285$	7.22813	0.428157
$286$	−0.143089	−0.00846102
$287$	4.98713	0.294381
$288$	−6.07025	−0.357693
$289$	13.0752	0.769129
$290$	26.2581	1.54193
$291$	−4.02442	−0.235915
$292$	6.46563	0.378372
$293$	0.197306	0.0115267	0.00576336	−	0.999983i	$-0.498165\pi$
$293$	0.197306	0.0115267	0.00576336	+	0.999983i	$0.498165\pi$
$294$	0.261546	0.0152537
$295$	37.6789	2.19375
$296$	−4.71224	−0.273894
$297$	−0.600943	−0.0348703
$298$	8.24650	0.477707
$299$	8.81166	0.509591
$300$	−7.66822	−0.442725
$301$	18.7978	1.08348
$302$	−7.12433	−0.409959
$303$	−32.5305	−1.86883
$304$	−0.873682	−0.0501091
$305$	−4.64457	−0.265947
$306$	−33.2898	−1.90305
$307$	23.7898	1.35776	0.678879	−	0.734251i	$-0.262466\pi$
$307$	23.7898	1.35776	0.678879	+	0.734251i	$0.262466\pi$
$308$	−0.173012	−0.00985828
$309$	7.59972	0.432333
$310$	−1.85299	−0.105243
$311$	−11.5630	−0.655675	−0.327838	−	0.944734i	$-0.606320\pi$
$311$	−11.5630	−0.655675	−0.327838	+	0.944734i	$0.606320\pi$
$312$	6.63079	0.375394
$313$	30.8392	1.74314	0.871568	−	0.490274i	$-0.163103\pi$
$313$	30.8392	1.74314	0.871568	+	0.490274i	$0.163103\pi$
$314$	6.66264	0.375995
$315$	−44.3911	−2.50115
$316$	−10.5182	−0.591696
$317$	−4.23652	−0.237947	−0.118973	−	0.992897i	$-0.537960\pi$
$317$	−4.23652	−0.237947	−0.118973	+	0.992897i	$0.537960\pi$
$318$	8.46400	0.474637
$319$	−0.621227	−0.0347820
$320$	2.74703	0.153563
$321$	53.8594	3.00614
$322$	10.6544	0.593746
$323$	−4.79135	−0.266598
$324$	9.63718	0.535399
$325$	5.60583	0.310956
$326$	22.9165	1.26923
$327$	32.8762	1.81806
$328$	1.87337	0.103440
$329$	30.7859	1.69728
$330$	0.537679	0.0295982
$331$	−2.07600	−0.114107	−0.0570535	−	0.998371i	$-0.518171\pi$
$331$	−2.07600	−0.114107	−0.0570535	+	0.998371i	$0.518171\pi$
$332$	−7.11724	−0.390609
$333$	28.6045	1.56752
$334$	−20.9118	−1.14425
$335$	11.5648	0.631853
$336$	8.01745	0.437388
$337$	10.9770	0.597955	0.298977	−	0.954260i	$-0.403355\pi$
$337$	10.9770	0.597955	0.298977	+	0.954260i	$0.403355\pi$
$338$	8.15258	0.443442
$339$	2.44015	0.132531
$340$	15.0649	0.817010
$341$	0.0438389	0.00237401
$342$	5.30347	0.286779
$343$	18.4036	0.993701
$344$	7.06122	0.380715
$345$	−33.1112	−1.78265
$346$	−20.1507	−1.08331
$347$	−20.9780	−1.12616	−0.563080	−	0.826402i	$-0.690384\pi$
$347$	−20.9780	−1.12616	−0.563080	+	0.826402i	$0.690384\pi$
$348$	28.7879	1.54319
$349$	−26.6011	−1.42393	−0.711963	−	0.702217i	$-0.752193\pi$
$349$	−26.6011	−1.42393	−0.711963	+	0.702217i	$0.752193\pi$
$350$	6.77815	0.362307
$351$	−20.3582	−1.08664
$352$	−0.0649906	−0.00346401
$353$	−27.4978	−1.46356	−0.731779	−	0.681542i	$-0.761310\pi$
$353$	−27.4978	−1.46356	−0.731779	+	0.681542i	$0.761310\pi$
$354$	41.3090	2.19555
$355$	−22.3634	−1.18693
$356$	−1.13575	−0.0601944
$357$	43.9684	2.32705
$358$	−10.5909	−0.559748
$359$	28.2444	1.49068	0.745342	−	0.666683i	$-0.232286\pi$
$359$	28.2444	1.49068	0.745342	+	0.666683i	$0.232286\pi$
$360$	−16.6751	−0.878857
$361$	−18.2367	−0.959825
$362$	14.9826	0.787467
$363$	33.1158	1.73813
$364$	−5.86114	−0.307207
$365$	17.7612	0.929666
$366$	−5.09205	−0.266166
$367$	0.342723	0.0178900	0.00894500	−	0.999960i	$-0.497153\pi$
$367$	0.342723	0.0178900	0.00894500	+	0.999960i	$0.497153\pi$
$368$	4.00223	0.208631
$369$	−11.3718	−0.591995
$370$	−12.9447	−0.672961
$371$	−7.48156	−0.388423
$372$	−2.03151	−0.105329
$373$	25.7521	1.33339	0.666696	−	0.745330i	$-0.267708\pi$
$373$	25.7521	1.33339	0.666696	+	0.745330i	$0.267708\pi$
$374$	−0.356414	−0.0184297
$375$	20.3011	1.04834
$376$	11.5645	0.596391
$377$	−21.0453	−1.08389
$378$	−24.6156	−1.26609
$379$	11.0076	0.565423	0.282712	−	0.959205i	$-0.408766\pi$
$379$	11.0076	0.565423	0.282712	+	0.959205i	$0.408766\pi$
$380$	−2.40003	−0.123119
$381$	1.29648	0.0664207
$382$	−21.8984	−1.12042
$383$	−22.0743	−1.12794	−0.563971	−	0.825795i	$-0.690727\pi$
$383$	−22.0743	−1.12794	−0.563971	+	0.825795i	$0.690727\pi$
$384$	3.01169	0.153689
$385$	−0.475269	−0.0242220
$386$	8.22404	0.418593
$387$	−42.8634	−2.17887
$388$	1.33627	0.0678387
$389$	−28.9017	−1.46538	−0.732688	−	0.680564i	$-0.761735\pi$
$389$	−28.9017	−1.46538	−0.732688	+	0.680564i	$0.761735\pi$
$390$	18.2149	0.922350
$391$	21.9486	1.10999
$392$	−0.0868436	−0.00438627
$393$	1.21034	0.0610538
$394$	2.69101	0.135571
$395$	−28.8938	−1.45381
$396$	0.394509	0.0198248
$397$	10.2341	0.513635	0.256818	−	0.966460i	$-0.417326\pi$
$397$	10.2341	0.513635	0.256818	+	0.966460i	$0.417326\pi$
$398$	−0.529682	−0.0265506
$399$	−7.00470	−0.350674
$400$	2.54615	0.127308
$401$	−3.99611	−0.199556	−0.0997781	−	0.995010i	$-0.531813\pi$
$401$	−3.99611	−0.199556	−0.0997781	+	0.995010i	$0.531813\pi$
$402$	12.6790	0.632371
$403$	1.48513	0.0739797
$404$	10.8014	0.537392
$405$	26.4736	1.31548
$406$	−25.4464	−1.26288
$407$	0.306251	0.0151803
$408$	16.5163	0.817681
$409$	19.3955	0.959044	0.479522	−	0.877530i	$-0.340810\pi$
$409$	19.3955	0.959044	0.479522	+	0.877530i	$0.340810\pi$
$410$	5.14621	0.254153
$411$	−41.0330	−2.02401
$412$	−2.52341	−0.124320
$413$	−36.5142	−1.79675
$414$	−24.2945	−1.19401
$415$	−19.5512	−0.959733
$416$	−2.20169	−0.107947
$417$	−2.23652	−0.109523
$418$	0.0567811	0.00277725
$419$	−20.4663	−0.999845	−0.499922	−	0.866070i	$-0.666638\pi$
$419$	−20.4663	−0.999845	−0.499922	+	0.866070i	$0.666638\pi$
$420$	22.0241	1.07467
$421$	−10.5729	−0.515293	−0.257646	−	0.966239i	$-0.582947\pi$
$421$	−10.5729	−0.515293	−0.257646	+	0.966239i	$0.582947\pi$
$422$	−19.5618	−0.952253
$423$	−70.1991	−3.41320
$424$	−2.81039	−0.136484
$425$	13.9633	0.677321
$426$	−24.5180	−1.18790
$427$	4.50100	0.217819
$428$	−17.8835	−0.864431
$429$	−0.430939	−0.0208059
$430$	19.3974	0.935424
$431$	−29.6678	−1.42905	−0.714523	−	0.699612i	$-0.753356\pi$
$431$	−29.6678	−1.42905	−0.714523	+	0.699612i	$0.753356\pi$
$432$	−9.24662	−0.444878
$433$	15.6734	0.753213	0.376607	−	0.926373i	$-0.377091\pi$
$433$	15.6734	0.753213	0.376607	+	0.926373i	$0.377091\pi$
$434$	1.79571	0.0861968
$435$	79.0811	3.79165
$436$	−10.9162	−0.522792
$437$	−3.49668	−0.167269
$438$	19.4724	0.930429
$439$	−5.69008	−0.271573	−0.135786	−	0.990738i	$-0.543356\pi$
$439$	−5.69008	−0.271573	−0.135786	+	0.990738i	$0.543356\pi$
$440$	−0.178531	−0.00851112
$441$	0.527162	0.0251030
$442$	−12.0742	−0.574313
$443$	−6.16187	−0.292759	−0.146380	−	0.989228i	$-0.546762\pi$
$443$	−6.16187	−0.292759	−0.146380	+	0.989228i	$0.546762\pi$
$444$	−14.1918	−0.673513
$445$	−3.11992	−0.147899
$446$	19.1705	0.907748
$447$	24.8359	1.17470
$448$	−2.66211	−0.125773
$449$	12.7168	0.600145	0.300072	−	0.953916i	$-0.402989\pi$
$449$	12.7168	0.600145	0.300072	+	0.953916i	$0.402989\pi$
$450$	−15.4558	−0.728593
$451$	−0.121752	−0.00573306
$452$	−0.810229	−0.0381099
$453$	−21.4562	−1.00810
$454$	−21.5432	−1.01107
$455$	−16.1007	−0.754812
$456$	−2.63126	−0.123220
$457$	−24.8365	−1.16180	−0.580900	−	0.813975i	$-0.697299\pi$
$457$	−24.8365	−1.16180	−0.580900	+	0.813975i	$0.697299\pi$
$458$	3.43036	0.160290
$459$	−50.7093	−2.36691
$460$	10.9942	0.512609
$461$	−11.1272	−0.518244	−0.259122	−	0.965845i	$-0.583433\pi$
$461$	−11.1272	−0.518244	−0.259122	+	0.965845i	$0.583433\pi$
$462$	−0.521058	−0.0242418
$463$	−6.84005	−0.317884	−0.158942	−	0.987288i	$-0.550808\pi$
$463$	−6.84005	−0.317884	−0.158942	+	0.987288i	$0.550808\pi$
$464$	−9.55873	−0.443753
$465$	−5.58061	−0.258795
$466$	−15.7993	−0.731889
$467$	14.6518	0.678006	0.339003	−	0.940785i	$-0.389910\pi$
$467$	14.6518	0.678006	0.339003	+	0.940785i	$0.389910\pi$
$468$	13.3648	0.617787
$469$	−11.2073	−0.517506
$470$	31.7679	1.46534
$471$	20.0658	0.924582
$472$	−13.7162	−0.631341
$473$	−0.458913	−0.0211008
$474$	−31.6776	−1.45500
$475$	−2.22453	−0.102068
$476$	−14.5993	−0.669156
$477$	17.0597	0.781112
$478$	12.2853	0.561916
$479$	4.40030	0.201055	0.100527	−	0.994934i	$-0.467947\pi$
$479$	4.40030	0.201055	0.100527	+	0.994934i	$0.467947\pi$
$480$	8.27318	0.377617
$481$	10.3749	0.473054
$482$	−1.49893	−0.0682746
$483$	32.0877	1.46004
$484$	−10.9958	−0.499808
$485$	3.67076	0.166681
$486$	1.28427	0.0582557
$487$	−29.4774	−1.33575	−0.667875	−	0.744274i	$-0.732796\pi$
$487$	−29.4774	−1.33575	−0.667875	+	0.744274i	$0.732796\pi$
$488$	1.69076	0.0765373
$489$	69.0172	3.12107
$490$	−0.238562	−0.0107771
$491$	−11.1023	−0.501038	−0.250519	−	0.968112i	$-0.580601\pi$
$491$	−11.1023	−0.501038	−0.250519	+	0.968112i	$0.580601\pi$
$492$	5.64201	0.254362
$493$	−52.4209	−2.36092
$494$	1.92357	0.0865457
$495$	1.08373	0.0487099
$496$	0.674543	0.0302879
$497$	21.6721	0.972127
$498$	−21.4349	−0.960520
$499$	−36.4064	−1.62977	−0.814887	−	0.579620i	$-0.803201\pi$
$499$	−36.4064	−1.62977	−0.814887	+	0.579620i	$0.803201\pi$
$500$	−6.74078	−0.301457
$501$	−62.9799	−2.81373
$502$	26.5077	1.18309
$503$	−24.6410	−1.09869	−0.549343	−	0.835597i	$-0.685122\pi$
$503$	−24.6410	−1.09869	−0.549343	+	0.835597i	$0.685122\pi$
$504$	16.1597	0.719810
$505$	29.6718	1.32038
$506$	−0.260107	−0.0115632
$507$	24.5530	1.09044
$508$	−0.430484	−0.0190996
$509$	−25.3071	−1.12172	−0.560859	−	0.827912i	$-0.689529\pi$
$509$	−25.3071	−1.12172	−0.560859	+	0.827912i	$0.689529\pi$
$510$	45.3708	2.00905
$511$	−17.2122	−0.761424
$512$	−1.00000	−0.0441942
$513$	8.07861	0.356679
$514$	−7.17237	−0.316360
$515$	−6.93188	−0.305455
$516$	21.2662	0.936191
$517$	−0.751580	−0.0330545
$518$	12.5445	0.551175
$519$	−60.6877	−2.66389
$520$	−6.04809	−0.265226
$521$	−3.59864	−0.157659	−0.0788296	−	0.996888i	$-0.525118\pi$
$521$	−3.59864	−0.157659	−0.0788296	+	0.996888i	$0.525118\pi$
$522$	58.0239	2.53964
$523$	−0.159499	−0.00697442	−0.00348721	−	0.999994i	$-0.501110\pi$
$523$	−0.159499	−0.00697442	−0.00348721	+	0.999994i	$0.501110\pi$
$524$	−0.401883	−0.0175563
$525$	20.4137	0.890925
$526$	−24.1079	−1.05116
$527$	3.69925	0.161142
$528$	−0.195731	−0.00851810
$529$	−6.98216	−0.303572
$530$	−7.72020	−0.335344
$531$	83.2610	3.61322
$532$	2.32584	0.100838
$533$	−4.12458	−0.178656
$534$	−3.42051	−0.148020
$535$	−49.1264	−2.12392
$536$	−4.20994	−0.181842
$537$	−31.8965	−1.37644
$538$	−5.82777	−0.251253
$539$	0.00564402	0.000243105 0
$540$	−25.4007	−1.09307
$541$	−32.3538	−1.39100	−0.695499	−	0.718527i	$-0.744817\pi$
$541$	−32.3538	−1.39100	−0.695499	+	0.718527i	$0.744817\pi$
$542$	−12.1095	−0.520146
$543$	45.1228	1.93640
$544$	−5.48409	−0.235128
$545$	−29.9872	−1.28451
$546$	−17.6519	−0.755432
$547$	30.9058	1.32144	0.660718	−	0.750634i	$-0.270252\pi$
$547$	30.9058	1.32144	0.660718	+	0.750634i	$0.270252\pi$
$548$	13.6246	0.582014
$549$	−10.2634	−0.438029
$550$	−0.165476	−0.00705592
$551$	8.35129	0.355777
$552$	12.0535	0.513029
$553$	28.0007	1.19071
$554$	−1.37935	−0.0586029
$555$	−38.9852	−1.65483
$556$	0.742615	0.0314939
$557$	16.4832	0.698417	0.349209	−	0.937045i	$-0.386450\pi$
$557$	16.4832	0.698417	0.349209	+	0.937045i	$0.386450\pi$
$558$	−4.09464	−0.173340
$559$	−15.5466	−0.657551
$560$	−7.31289	−0.309026
$561$	−1.07341	−0.0453192
$562$	20.7904	0.876989
$563$	−28.9389	−1.21963	−0.609815	−	0.792544i	$-0.708756\pi$
$563$	−28.9389	−1.21963	−0.609815	+	0.792544i	$0.708756\pi$
$564$	34.8285	1.46654
$565$	−2.22572	−0.0936367
$566$	9.84266	0.413718
$567$	−25.6552	−1.07742
$568$	8.14094	0.341586
$569$	19.1359	0.802217	0.401109	−	0.916031i	$-0.368625\pi$
$569$	19.1359	0.802217	0.401109	+	0.916031i	$0.368625\pi$
$570$	−7.22813	−0.302753
$571$	−14.3827	−0.601898	−0.300949	−	0.953640i	$-0.597303\pi$
$571$	−14.3827	−0.601898	−0.300949	+	0.953640i	$0.597303\pi$
$572$	0.143089	0.00598285
$573$	−65.9510	−2.75514
$574$	−4.98713	−0.208159
$575$	10.1903	0.424965
$576$	6.07025	0.252927
$577$	−33.5823	−1.39805	−0.699024	−	0.715098i	$-0.746382\pi$
$577$	−33.5823	−1.39805	−0.699024	+	0.715098i	$0.746382\pi$
$578$	−13.0752	−0.543856
$579$	24.7682	1.02933
$580$	−26.2581	−1.09031
$581$	18.9469	0.786049
$582$	4.02442	0.166817
$583$	0.182649	0.00756453
$584$	−6.46563	−0.267550
$585$	36.7134	1.51791
$586$	−0.197306	−0.00815063
$587$	6.27514	0.259003	0.129501	−	0.991579i	$-0.458662\pi$
$587$	6.27514	0.259003	0.129501	+	0.991579i	$0.458662\pi$
$588$	−0.261546	−0.0107860
$589$	−0.589336	−0.0242832
$590$	−37.6789	−1.55122
$591$	8.10447	0.333373
$592$	4.71224	0.193672
$593$	−12.6963	−0.521374	−0.260687	−	0.965423i	$-0.583949\pi$
$593$	−12.6963	−0.521374	−0.260687	+	0.965423i	$0.583949\pi$
$594$	0.600943	0.0246570
$595$	−40.1045	−1.64413
$596$	−8.24650	−0.337790
$597$	−1.59524	−0.0652886
$598$	−8.81166	−0.360335
$599$	−24.8060	−1.01355	−0.506773	−	0.862079i	$-0.669162\pi$
$599$	−24.8060	−1.01355	−0.506773	+	0.862079i	$0.669162\pi$
$600$	7.66822	0.313054
$601$	25.7322	1.04964	0.524819	−	0.851214i	$-0.324133\pi$
$601$	25.7322	1.04964	0.524819	+	0.851214i	$0.324133\pi$
$602$	−18.7978	−0.766139
$603$	25.5554	1.04069
$604$	7.12433	0.289885
$605$	−30.2057	−1.22804
$606$	32.5305	1.32146
$607$	32.9608	1.33784	0.668918	−	0.743336i	$-0.266758\pi$
$607$	32.9608	1.33784	0.668918	+	0.743336i	$0.266758\pi$
$608$	0.873682	0.0354325
$609$	−76.6366	−3.10547
$610$	4.64457	0.188053
$611$	−25.4613	−1.03005
$612$	33.2898	1.34566
$613$	4.29391	0.173429	0.0867147	−	0.996233i	$-0.472363\pi$
$613$	4.29391	0.173429	0.0867147	+	0.996233i	$0.472363\pi$
$614$	−23.7898	−0.960079
$615$	15.4988	0.624970
$616$	0.173012	0.00697086
$617$	−36.4450	−1.46722	−0.733611	−	0.679570i	$-0.762166\pi$
$617$	−36.4450	−1.46722	−0.733611	+	0.679570i	$0.762166\pi$
$618$	−7.59972	−0.305706
$619$	−13.7383	−0.552190	−0.276095	−	0.961130i	$-0.589040\pi$
$619$	−13.7383	−0.552190	−0.276095	+	0.961130i	$0.589040\pi$
$620$	1.85299	0.0744177
$621$	−37.0071	−1.48504
$622$	11.5630	0.463632
$623$	3.02348	0.121133
$624$	−6.63079	−0.265444
$625$	−31.2479	−1.24991
$626$	−30.8392	−1.23258
$627$	0.171007	0.00682935
$628$	−6.66264	−0.265868
$629$	25.8423	1.03040
$630$	44.3911	1.76858
$631$	−41.1376	−1.63766	−0.818831	−	0.574034i	$-0.805378\pi$
$631$	−41.1376	−1.63766	−0.818831	+	0.574034i	$0.805378\pi$
$632$	10.5182	0.418392
$633$	−58.9139	−2.34162
$634$	4.23652	0.168254
$635$	−1.18255	−0.0469280
$636$	−8.46400	−0.335619
$637$	0.191202	0.00757572
$638$	0.621227	0.0245946
$639$	−49.4176	−1.95493
$640$	−2.74703	−0.108586
$641$	−1.01204	−0.0399734	−0.0199867	−	0.999800i	$-0.506362\pi$
$641$	−1.01204	−0.0399734	−0.0199867	+	0.999800i	$0.506362\pi$
$642$	−53.8594	−2.12566
$643$	−29.1068	−1.14786	−0.573931	−	0.818904i	$-0.694582\pi$
$643$	−29.1068	−1.14786	−0.573931	+	0.818904i	$0.694582\pi$
$644$	−10.6544	−0.419842
$645$	58.4187	2.30024
$646$	4.79135	0.188513
$647$	46.3274	1.82132	0.910658	−	0.413160i	$-0.135575\pi$
$647$	46.3274	1.82132	0.910658	+	0.413160i	$0.135575\pi$
$648$	−9.63718	−0.378584
$649$	0.891427	0.0349916
$650$	−5.60583	−0.219879
$651$	5.40811	0.211961
$652$	−22.9165	−0.897479
$653$	19.5661	0.765679	0.382839	−	0.923815i	$-0.374946\pi$
$653$	19.5661	0.765679	0.382839	+	0.923815i	$0.374946\pi$
$654$	−32.8762	−1.28556
$655$	−1.10398	−0.0431362
$656$	−1.87337	−0.0731430
$657$	39.2480	1.53121
$658$	−30.7859	−1.20016
$659$	−38.8709	−1.51420	−0.757098	−	0.653302i	$-0.773383\pi$
$659$	−38.8709	−1.51420	−0.757098	+	0.653302i	$0.773383\pi$
$660$	−0.537679	−0.0209291
$661$	−2.27857	−0.0886262	−0.0443131	−	0.999018i	$-0.514110\pi$
$661$	−2.27857	−0.0886262	−0.0443131	+	0.999018i	$0.514110\pi$
$662$	2.07600	0.0806858
$663$	−36.3638	−1.41225
$664$	7.11724	0.276202
$665$	6.38914	0.247760
$666$	−28.6045	−1.10840
$667$	−38.2562	−1.48129
$668$	20.9118	0.809103
$669$	57.7354	2.23218
$670$	−11.5648	−0.446787
$671$	−0.109884	−0.00424201
$672$	−8.01745	−0.309280
$673$	27.1857	1.04793	0.523966	−	0.851739i	$-0.324452\pi$
$673$	27.1857	1.04793	0.523966	+	0.851739i	$0.324452\pi$
$674$	−10.9770	−0.422818
$675$	−23.5433	−0.906183
$676$	−8.15258	−0.313561
$677$	21.8831	0.841037	0.420519	−	0.907284i	$-0.361848\pi$
$677$	21.8831	0.841037	0.420519	+	0.907284i	$0.361848\pi$
$678$	−2.44015	−0.0937135
$679$	−3.55729	−0.136516
$680$	−15.0649	−0.577714
$681$	−64.8814	−2.48626
$682$	−0.0438389	−0.00167868
$683$	−22.3081	−0.853596	−0.426798	−	0.904347i	$-0.640358\pi$
$683$	−22.3081	−0.853596	−0.426798	+	0.904347i	$0.640358\pi$
$684$	−5.30347	−0.202783
$685$	37.4272	1.43002
$686$	−18.4036	−0.702653
$687$	10.3312	0.394158
$688$	−7.06122	−0.269206
$689$	6.18759	0.235728
$690$	33.1112	1.26052
$691$	39.1659	1.48994	0.744971	−	0.667097i	$-0.232463\pi$
$691$	39.1659	1.48994	0.744971	+	0.667097i	$0.232463\pi$
$692$	20.1507	0.766016
$693$	−1.05023	−0.0398948
$694$	20.9780	0.796316
$695$	2.03998	0.0773810
$696$	−28.7879	−1.09120
$697$	−10.2737	−0.389146
$698$	26.6011	1.00687
$699$	−47.5825	−1.79974
$700$	−6.77815	−0.256190
$701$	−10.0287	−0.378780	−0.189390	−	0.981902i	$-0.560651\pi$
$701$	−10.0287	−0.378780	−0.189390	+	0.981902i	$0.560651\pi$
$702$	20.3582	0.768370
$703$	−4.11700	−0.155276
$704$	0.0649906	0.00244942
$705$	95.6748	3.60332
$706$	27.4978	1.03489
$707$	−28.7546	−1.08143
$708$	−41.3090	−1.55249
$709$	29.4061	1.10437	0.552184	−	0.833722i	$-0.313794\pi$
$709$	29.4061	1.10437	0.552184	+	0.833722i	$0.313794\pi$
$710$	22.3634	0.839283
$711$	−63.8482	−2.39450
$712$	1.13575	0.0425639
$713$	2.69967	0.101104
$714$	−43.9684	−1.64547
$715$	0.393069	0.0146999
$716$	10.5909	0.395801
$717$	36.9994	1.38177
$718$	−28.2444	−1.05407
$719$	−27.7970	−1.03665	−0.518326	−	0.855183i	$-0.673445\pi$
$719$	−27.7970	−1.03665	−0.518326	+	0.855183i	$0.673445\pi$
$720$	16.6751	0.621446
$721$	6.71760	0.250177
$722$	18.2367	0.678699
$723$	−4.51432	−0.167889
$724$	−14.9826	−0.556823
$725$	−24.3380	−0.903891
$726$	−33.1158	−1.22904
$727$	−16.5293	−0.613039	−0.306519	−	0.951864i	$-0.599164\pi$
$727$	−16.5293	−0.613039	−0.306519	+	0.951864i	$0.599164\pi$
$728$	5.86114	0.217228
$729$	−25.0437	−0.927545
$730$	−17.7612	−0.657373
$731$	−38.7243	−1.43227
$732$	5.09205	0.188208
$733$	−15.5813	−0.575508	−0.287754	−	0.957704i	$-0.592909\pi$
$733$	−15.5813	−0.575508	−0.287754	+	0.957704i	$0.592909\pi$
$734$	−0.342723	−0.0126501
$735$	−0.718473	−0.0265013
$736$	−4.00223	−0.147524
$737$	0.273606	0.0100784
$738$	11.3718	0.418604
$739$	18.6723	0.686873	0.343437	−	0.939176i	$-0.388409\pi$
$739$	18.6723	0.686873	0.343437	+	0.939176i	$0.388409\pi$
$740$	12.9447	0.475855
$741$	5.79320	0.212819
$742$	7.48156	0.274657
$743$	13.2794	0.487174	0.243587	−	0.969879i	$-0.421676\pi$
$743$	13.2794	0.487174	0.243587	+	0.969879i	$0.421676\pi$
$744$	2.03151	0.0744788
$745$	−22.6534	−0.829955
$746$	−25.7521	−0.942850
$747$	−43.2034	−1.58073
$748$	0.356414	0.0130318
$749$	47.6079	1.73955
$750$	−20.3011	−0.741292
$751$	−21.7948	−0.795305	−0.397653	−	0.917536i	$-0.630175\pi$
$751$	−21.7948	−0.795305	−0.397653	+	0.917536i	$0.630175\pi$
$752$	−11.5645	−0.421712
$753$	79.8327	2.90927
$754$	21.0453	0.766426
$755$	19.5707	0.712252
$756$	24.6156	0.895259
$757$	−9.47739	−0.344462	−0.172231	−	0.985057i	$-0.555098\pi$
$757$	−9.47739	−0.344462	−0.172231	+	0.985057i	$0.555098\pi$
$758$	−11.0076	−0.399815
$759$	−0.783361	−0.0284342
$760$	2.40003	0.0870582
$761$	−44.6175	−1.61738	−0.808692	−	0.588232i	$-0.799824\pi$
$761$	−44.6175	−1.61738	−0.808692	+	0.588232i	$0.799824\pi$
$762$	−1.29648	−0.0469665
$763$	29.0602	1.05205
$764$	21.8984	0.792255
$765$	91.4479	3.30630
$766$	22.0743	0.797575
$767$	30.1989	1.09042
$768$	−3.01169	−0.108675
$769$	−32.2867	−1.16429	−0.582144	−	0.813086i	$-0.697786\pi$
$769$	−32.2867	−1.16429	−0.582144	+	0.813086i	$0.697786\pi$
$770$	0.475269	0.0171275
$771$	−21.6009	−0.777938
$772$	−8.22404	−0.295990
$773$	−6.74954	−0.242764	−0.121382	−	0.992606i	$-0.538733\pi$
$773$	−6.74954	−0.242764	−0.121382	+	0.992606i	$0.538733\pi$
$774$	42.8634	1.54069
$775$	1.71749	0.0616941
$776$	−1.33627	−0.0479692
$777$	37.7802	1.35536
$778$	28.9017	1.03618
$779$	1.63673	0.0586421
$780$	−18.2149	−0.652200
$781$	−0.529085	−0.0189321
$782$	−21.9486	−0.784879
$783$	88.3860	3.15866
$784$	0.0868436	0.00310156
$785$	−18.3024	−0.653242
$786$	−1.21034	−0.0431715
$787$	−47.0432	−1.67691	−0.838454	−	0.544972i	$-0.816540\pi$
$787$	−47.0432	−1.67691	−0.838454	+	0.544972i	$0.816540\pi$
$788$	−2.69101	−0.0958631
$789$	−72.6055	−2.58483
$790$	28.8938	1.02800
$791$	2.15692	0.0766912
$792$	−0.394509	−0.0140183
$793$	−3.72253	−0.132191
$794$	−10.2341	−0.363195
$795$	−23.2508	−0.824622
$796$	0.529682	0.0187741
$797$	−15.4652	−0.547804	−0.273902	−	0.961758i	$-0.588314\pi$
$797$	−15.4652	−0.547804	−0.273902	+	0.961758i	$0.588314\pi$
$798$	7.00470	0.247964
$799$	−63.4205	−2.24365
$800$	−2.54615	−0.0900202
$801$	−6.89426	−0.243597
$802$	3.99611	0.141108
$803$	0.420205	0.0148287
$804$	−12.6790	−0.447154
$805$	−29.2679	−1.03156
$806$	−1.48513	−0.0523115
$807$	−17.5514	−0.617839
$808$	−10.8014	−0.379993
$809$	−37.7229	−1.32626	−0.663132	−	0.748502i	$-0.730773\pi$
$809$	−37.7229	−1.32626	−0.663132	+	0.748502i	$0.730773\pi$
$810$	−26.4736	−0.930187
$811$	13.9226	0.488890	0.244445	−	0.969663i	$-0.421394\pi$
$811$	13.9226	0.488890	0.244445	+	0.969663i	$0.421394\pi$
$812$	25.4464	0.892994
$813$	−36.4699	−1.27905
$814$	−0.306251	−0.0107341
$815$	−62.9522	−2.20512
$816$	−16.5163	−0.578188
$817$	6.16926	0.215835
$818$	−19.3955	−0.678147
$819$	−35.5786	−1.24322
$820$	−5.14621	−0.179713
$821$	3.70668	0.129364	0.0646820	−	0.997906i	$-0.479397\pi$
$821$	3.70668	0.129364	0.0646820	+	0.997906i	$0.479397\pi$
$822$	41.0330	1.43119
$823$	16.5539	0.577032	0.288516	−	0.957475i	$-0.406838\pi$
$823$	16.5539	0.577032	0.288516	+	0.957475i	$0.406838\pi$
$824$	2.52341	0.0879072
$825$	−0.498362	−0.0173507
$826$	36.5142	1.27049
$827$	48.4052	1.68321	0.841606	−	0.540091i	$-0.181610\pi$
$827$	48.4052	1.68321	0.841606	+	0.540091i	$0.181610\pi$
$828$	24.2945	0.844293
$829$	25.9967	0.902902	0.451451	−	0.892296i	$-0.350906\pi$
$829$	25.9967	0.902902	0.451451	+	0.892296i	$0.350906\pi$
$830$	19.5512	0.678633
$831$	−4.15416	−0.144106
$832$	2.20169	0.0763298
$833$	0.476258	0.0165014
$834$	2.23652	0.0774444
$835$	57.4454	1.98798
$836$	−0.0567811	−0.00196382
$837$	−6.23724	−0.215591
$838$	20.4663	0.706997
$839$	37.4872	1.29420	0.647102	−	0.762404i	$-0.275981\pi$
$839$	37.4872	1.29420	0.647102	+	0.762404i	$0.275981\pi$
$840$	−22.0241	−0.759905
$841$	62.3693	2.15067
$842$	10.5729	0.364367
$843$	62.6141	2.15654
$844$	19.5618	0.673344
$845$	−22.3953	−0.770423
$846$	70.1991	2.41350
$847$	29.2720	1.00580
$848$	2.81039	0.0965090
$849$	29.6430	1.01734
$850$	−13.9633	−0.478938
$851$	18.8595	0.646495
$852$	24.5180	0.839972
$853$	35.8122	1.22619	0.613093	−	0.790011i	$-0.289925\pi$
$853$	35.8122	1.22619	0.613093	+	0.790011i	$0.289925\pi$
$854$	−4.50100	−0.154021
$855$	−14.5688	−0.498241
$856$	17.8835	0.611245
$857$	−3.84778	−0.131438	−0.0657188	−	0.997838i	$-0.520934\pi$
$857$	−3.84778	−0.131438	−0.0657188	+	0.997838i	$0.520934\pi$
$858$	0.430939	0.0147120
$859$	−3.92013	−0.133753	−0.0668766	−	0.997761i	$-0.521303\pi$
$859$	−3.92013	−0.133753	−0.0668766	+	0.997761i	$0.521303\pi$
$860$	−19.3974	−0.661444
$861$	−15.0197	−0.511869
$862$	29.6678	1.01049
$863$	9.60234	0.326867	0.163434	−	0.986554i	$-0.447743\pi$
$863$	9.60234	0.326867	0.163434	+	0.986554i	$0.447743\pi$
$864$	9.24662	0.314577
$865$	55.3546	1.88211
$866$	−15.6734	−0.532602
$867$	−39.3784	−1.33736
$868$	−1.79571	−0.0609503
$869$	−0.683585	−0.0231890
$870$	−79.0811	−2.68110
$871$	9.26896	0.314067
$872$	10.9162	0.369670
$873$	8.11147	0.274532
$874$	3.49668	0.118277
$875$	17.9447	0.606642
$876$	−19.4724	−0.657913
$877$	53.2901	1.79948	0.899739	−	0.436428i	$-0.143757\pi$
$877$	53.2901	1.79948	0.899739	+	0.436428i	$0.143757\pi$
$878$	5.69008	0.192031
$879$	−0.594223	−0.0200426
$880$	0.178531	0.00601827
$881$	−19.2357	−0.648067	−0.324034	−	0.946046i	$-0.605039\pi$
$881$	−19.2357	−0.648067	−0.324034	+	0.946046i	$0.605039\pi$
$882$	−0.527162	−0.0177505
$883$	12.3793	0.416598	0.208299	−	0.978065i	$-0.433207\pi$
$883$	12.3793	0.416598	0.208299	+	0.978065i	$0.433207\pi$
$884$	12.0742	0.406101
$885$	−113.477	−3.81449
$886$	6.16187	0.207012
$887$	−47.3738	−1.59066	−0.795329	−	0.606179i	$-0.792702\pi$
$887$	−47.3738	−1.59066	−0.795329	+	0.606179i	$0.792702\pi$
$888$	14.1918	0.476245
$889$	1.14600	0.0384355
$890$	3.11992	0.104580
$891$	0.626325	0.0209827
$892$	−19.1705	−0.641875
$893$	10.1037	0.338106
$894$	−24.8359	−0.830636
$895$	29.0936	0.972490
$896$	2.66211	0.0889349
$897$	−26.5379	−0.886076
$898$	−12.7168	−0.424367
$899$	−6.44777	−0.215045
$900$	15.4558	0.515193
$901$	15.4124	0.513461
$902$	0.121752	0.00405389
$903$	−56.6129	−1.88396
$904$	0.810229	0.0269478
$905$	−41.1575	−1.36812
$906$	21.4562	0.712836
$907$	−45.1659	−1.49971	−0.749855	−	0.661602i	$-0.769877\pi$
$907$	−45.1659	−1.49971	−0.749855	+	0.661602i	$0.769877\pi$
$908$	21.5432	0.714937
$909$	65.5674	2.17473
$910$	16.1007	0.533733
$911$	3.20744	0.106267	0.0531337	−	0.998587i	$-0.483079\pi$
$911$	3.20744	0.106267	0.0531337	+	0.998587i	$0.483079\pi$
$912$	2.63126	0.0871296
$913$	−0.462553	−0.0153083
$914$	24.8365	0.821517
$915$	13.9880	0.462429
$916$	−3.43036	−0.113342
$917$	1.06986	0.0353298
$918$	50.7093	1.67366
$919$	35.3879	1.16734	0.583670	−	0.811991i	$-0.301616\pi$
$919$	35.3879	1.16734	0.583670	+	0.811991i	$0.301616\pi$
$920$	−10.9942	−0.362469
$921$	−71.6475	−2.36086
$922$	11.1272	0.366454
$923$	−17.9238	−0.589969
$924$	0.521058	0.0171416
$925$	11.9981	0.394495
$926$	6.84005	0.224778
$927$	−15.3177	−0.503100
$928$	9.55873	0.313781
$929$	−34.5356	−1.13308	−0.566539	−	0.824035i	$-0.691718\pi$
$929$	−34.5356	−1.13308	−0.566539	+	0.824035i	$0.691718\pi$
$930$	5.58061	0.182996
$931$	−0.0758737	−0.00248666
$932$	15.7993	0.517523
$933$	34.8240	1.14009
$934$	−14.6518	−0.479423
$935$	0.979078	0.0320193
$936$	−13.3648	−0.436842
$937$	−24.3739	−0.796260	−0.398130	−	0.917329i	$-0.630341\pi$
$937$	−24.3739	−0.796260	−0.398130	+	0.917329i	$0.630341\pi$
$938$	11.2073	0.365932
$939$	−92.8781	−3.03096
$940$	−31.7679	−1.03615
$941$	49.6213	1.61761	0.808804	−	0.588078i	$-0.200115\pi$
$941$	49.6213	1.61761	0.808804	+	0.588078i	$0.200115\pi$
$942$	−20.0658	−0.653778
$943$	−7.49767	−0.244158
$944$	13.7162	0.446426
$945$	67.6196	2.19967
$946$	0.458913	0.0149205
$947$	−6.51271	−0.211635	−0.105817	−	0.994386i	$-0.533746\pi$
$947$	−6.51271	−0.211635	−0.105817	+	0.994386i	$0.533746\pi$
$948$	31.6776	1.02884
$949$	14.2353	0.462097
$950$	2.22453	0.0721733
$951$	12.7591	0.413741
$952$	14.5993	0.473165
$953$	−41.7870	−1.35361	−0.676807	−	0.736160i	$-0.736637\pi$
$953$	−41.7870	−1.35361	−0.676807	+	0.736160i	$0.736637\pi$
$954$	−17.0597	−0.552330
$955$	60.1554	1.94658
$956$	−12.2853	−0.397335
$957$	1.87094	0.0604789
$958$	−4.40030	−0.142167
$959$	−36.2702	−1.17123
$960$	−8.27318	−0.267016
$961$	−30.5450	−0.985322
$962$	−10.3749	−0.334500
$963$	−108.557	−3.49821
$964$	1.49893	0.0482774
$965$	−22.5917	−0.727252
$966$	−32.0877	−1.03240
$967$	−29.8292	−0.959241	−0.479621	−	0.877476i	$-0.659226\pi$
$967$	−29.8292	−0.959241	−0.479621	+	0.877476i	$0.659226\pi$
$968$	10.9958	0.353418
$969$	14.4300	0.463559
$970$	−3.67076	−0.117861
$971$	−8.43053	−0.270549	−0.135274	−	0.990808i	$-0.543192\pi$
$971$	−8.43053	−0.270549	−0.135274	+	0.990808i	$0.543192\pi$
$972$	−1.28427	−0.0411930
$973$	−1.97692	−0.0633773
$974$	29.4774	0.944518
$975$	−16.8830	−0.540689
$976$	−1.69076	−0.0541200
$977$	41.7960	1.33717	0.668586	−	0.743634i	$-0.266900\pi$
$977$	41.7960	1.33717	0.668586	+	0.743634i	$0.266900\pi$
$978$	−69.0172	−2.20693
$979$	−0.0738128	−0.00235907
$980$	0.238562	0.00762058
$981$	−66.2642	−2.11565
$982$	11.1023	0.354288
$983$	31.4363	1.00266	0.501331	−	0.865255i	$-0.332844\pi$
$983$	31.4363	1.00266	0.501331	+	0.865255i	$0.332844\pi$
$984$	−5.64201	−0.179861
$985$	−7.39227	−0.235537
$986$	52.4209	1.66942
$987$	−92.7174	−2.95123
$988$	−1.92357	−0.0611971
$989$	−28.2606	−0.898635
$990$	−1.08373	−0.0344431
$991$	−8.57665	−0.272446	−0.136223	−	0.990678i	$-0.543496\pi$
$991$	−8.57665	−0.272446	−0.136223	+	0.990678i	$0.543496\pi$
$992$	−0.674543	−0.0214168
$993$	6.25224	0.198409
$994$	−21.6721	−0.687398
$995$	1.45505	0.0461282
$996$	21.4349	0.679190
$997$	35.1452	1.11306	0.556530	−	0.830828i	$-0.312133\pi$
$997$	35.1452	1.11306	0.556530	+	0.830828i	$0.312133\pi$
$998$	36.4064	1.15242
$999$	−43.5723	−1.37857

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.b.1.5	✓	81

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.b.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.01169 q^{3} +1.00000 q^{4} +2.74703 q^{5} +3.01169 q^{6} -2.66211 q^{7} -1.00000 q^{8} +6.07025 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.01169 q^{3} +1.00000 q^{4} +2.74703 q^{5} +3.01169 q^{6} -2.66211 q^{7} -1.00000 q^{8} +6.07025 q^{9} -2.74703 q^{10} +0.0649906 q^{11} -3.01169 q^{12} +2.20169 q^{13} +2.66211 q^{14} -8.27318 q^{15} +1.00000 q^{16} +5.48409 q^{17} -6.07025 q^{18} -0.873682 q^{19} +2.74703 q^{20} +8.01745 q^{21} -0.0649906 q^{22} +4.00223 q^{23} +3.01169 q^{24} +2.54615 q^{25} -2.20169 q^{26} -9.24662 q^{27} -2.66211 q^{28} -9.55873 q^{29} +8.27318 q^{30} +0.674543 q^{31} -1.00000 q^{32} -0.195731 q^{33} -5.48409 q^{34} -7.31289 q^{35} +6.07025 q^{36} +4.71224 q^{37} +0.873682 q^{38} -6.63079 q^{39} -2.74703 q^{40} -1.87337 q^{41} -8.01745 q^{42} -7.06122 q^{43} +0.0649906 q^{44} +16.6751 q^{45} -4.00223 q^{46} -11.5645 q^{47} -3.01169 q^{48} +0.0868436 q^{49} -2.54615 q^{50} -16.5163 q^{51} +2.20169 q^{52} +2.81039 q^{53} +9.24662 q^{54} +0.178531 q^{55} +2.66211 q^{56} +2.63126 q^{57} +9.55873 q^{58} +13.7162 q^{59} -8.27318 q^{60} -1.69076 q^{61} -0.674543 q^{62} -16.1597 q^{63} +1.00000 q^{64} +6.04809 q^{65} +0.195731 q^{66} +4.20994 q^{67} +5.48409 q^{68} -12.0535 q^{69} +7.31289 q^{70} -8.14094 q^{71} -6.07025 q^{72} +6.46563 q^{73} -4.71224 q^{74} -7.66822 q^{75} -0.873682 q^{76} -0.173012 q^{77} +6.63079 q^{78} -10.5182 q^{79} +2.74703 q^{80} +9.63718 q^{81} +1.87337 q^{82} -7.11724 q^{83} +8.01745 q^{84} +15.0649 q^{85} +7.06122 q^{86} +28.7879 q^{87} -0.0649906 q^{88} -1.13575 q^{89} -16.6751 q^{90} -5.86114 q^{91} +4.00223 q^{92} -2.03151 q^{93} +11.5645 q^{94} -2.40003 q^{95} +3.01169 q^{96} +1.33627 q^{97} -0.0868436 q^{98} +0.394509 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9}+O(q^{10}) \) 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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