LMFDB - Embedded newform 8026.2.a.b.1.2

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			1.2
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)

$f(q)$	$=$	$q-1.00000 q^{2} -3.25240 q^{3} +1.00000 q^{4} -3.99675 q^{5} +3.25240 q^{6} +3.80728 q^{7} -1.00000 q^{8} +7.57814 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.25240 q^{3} +1.00000 q^{4} -3.99675 q^{5} +3.25240 q^{6} +3.80728 q^{7} -1.00000 q^{8} +7.57814 q^{9} +3.99675 q^{10} +2.88637 q^{11} -3.25240 q^{12} +4.13982 q^{13} -3.80728 q^{14} +12.9990 q^{15} +1.00000 q^{16} +6.32016 q^{17} -7.57814 q^{18} +2.13804 q^{19} -3.99675 q^{20} -12.3828 q^{21} -2.88637 q^{22} -4.59837 q^{23} +3.25240 q^{24} +10.9740 q^{25} -4.13982 q^{26} -14.8900 q^{27} +3.80728 q^{28} -0.802524 q^{29} -12.9990 q^{30} +1.62651 q^{31} -1.00000 q^{32} -9.38766 q^{33} -6.32016 q^{34} -15.2167 q^{35} +7.57814 q^{36} +5.94031 q^{37} -2.13804 q^{38} -13.4644 q^{39} +3.99675 q^{40} -3.62788 q^{41} +12.3828 q^{42} -7.55916 q^{43} +2.88637 q^{44} -30.2879 q^{45} +4.59837 q^{46} -5.60393 q^{47} -3.25240 q^{48} +7.49536 q^{49} -10.9740 q^{50} -20.5557 q^{51} +4.13982 q^{52} +10.7997 q^{53} +14.8900 q^{54} -11.5361 q^{55} -3.80728 q^{56} -6.95376 q^{57} +0.802524 q^{58} -6.39923 q^{59} +12.9990 q^{60} -10.8698 q^{61} -1.62651 q^{62} +28.8521 q^{63} +1.00000 q^{64} -16.5458 q^{65} +9.38766 q^{66} -10.6271 q^{67} +6.32016 q^{68} +14.9558 q^{69} +15.2167 q^{70} +9.79640 q^{71} -7.57814 q^{72} +0.131361 q^{73} -5.94031 q^{74} -35.6919 q^{75} +2.13804 q^{76} +10.9892 q^{77} +13.4644 q^{78} -7.22795 q^{79} -3.99675 q^{80} +25.6938 q^{81} +3.62788 q^{82} -16.9820 q^{83} -12.3828 q^{84} -25.2601 q^{85} +7.55916 q^{86} +2.61013 q^{87} -2.88637 q^{88} -11.3007 q^{89} +30.2879 q^{90} +15.7615 q^{91} -4.59837 q^{92} -5.29007 q^{93} +5.60393 q^{94} -8.54520 q^{95} +3.25240 q^{96} -9.78252 q^{97} -7.49536 q^{98} +21.8733 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−3.25240	−1.87778	−0.938888	−	0.344222i	$-0.888143\pi$
$3$	−3.25240	−1.87778	−0.938888	+	0.344222i	$0.888143\pi$
$4$	1.00000	0.500000
$5$	−3.99675	−1.78740	−0.893700	−	0.448665i	$-0.851900\pi$
$5$	−3.99675	−1.78740	−0.893700	+	0.448665i	$0.851900\pi$
$6$	3.25240	1.32779
$7$	3.80728	1.43902	0.719508	−	0.694484i	$-0.244367\pi$
$7$	3.80728	1.43902	0.719508	+	0.694484i	$0.244367\pi$
$8$	−1.00000	−0.353553
$9$	7.57814	2.52605
$10$	3.99675	1.26388
$11$	2.88637	0.870275	0.435137	−	0.900364i	$-0.356700\pi$
$11$	2.88637	0.870275	0.435137	+	0.900364i	$0.356700\pi$
$12$	−3.25240	−0.938888
$13$	4.13982	1.14818	0.574090	−	0.818792i	$-0.305356\pi$
$13$	4.13982	1.14818	0.574090	+	0.818792i	$0.305356\pi$
$14$	−3.80728	−1.01754
$15$	12.9990	3.35634
$16$	1.00000	0.250000
$17$	6.32016	1.53286	0.766432	−	0.642325i	$-0.222030\pi$
$17$	6.32016	1.53286	0.766432	+	0.642325i	$0.222030\pi$
$18$	−7.57814	−1.78618
$19$	2.13804	0.490499	0.245250	−	0.969460i	$-0.421130\pi$
$19$	2.13804	0.490499	0.245250	+	0.969460i	$0.421130\pi$
$20$	−3.99675	−0.893700
$21$	−12.3828	−2.70215
$22$	−2.88637	−0.615377
$23$	−4.59837	−0.958827	−0.479413	−	0.877589i	$-0.659151\pi$
$23$	−4.59837	−0.958827	−0.479413	+	0.877589i	$0.659151\pi$
$24$	3.25240	0.663894
$25$	10.9740	2.19480
$26$	−4.13982	−0.811886
$27$	−14.8900	−2.86557
$28$	3.80728	0.719508
$29$	−0.802524	−0.149025	−0.0745125	−	0.997220i	$-0.523740\pi$
$29$	−0.802524	−0.149025	−0.0745125	+	0.997220i	$0.523740\pi$
$30$	−12.9990	−2.37329
$31$	1.62651	0.292130	0.146065	−	0.989275i	$-0.453339\pi$
$31$	1.62651	0.292130	0.146065	+	0.989275i	$0.453339\pi$
$32$	−1.00000	−0.176777
$33$	−9.38766	−1.63418
$34$	−6.32016	−1.08390
$35$	−15.2167	−2.57210
$36$	7.57814	1.26302
$37$	5.94031	0.976581	0.488290	−	0.872681i	$-0.337621\pi$
$37$	5.94031	0.976581	0.488290	+	0.872681i	$0.337621\pi$
$38$	−2.13804	−0.346835
$39$	−13.4644	−2.15603
$40$	3.99675	0.631942
$41$	−3.62788	−0.566579	−0.283290	−	0.959034i	$-0.591426\pi$
$41$	−3.62788	−0.566579	−0.283290	+	0.959034i	$0.591426\pi$
$42$	12.3828	1.91071
$43$	−7.55916	−1.15276	−0.576381	−	0.817181i	$-0.695536\pi$
$43$	−7.55916	−1.15276	−0.576381	+	0.817181i	$0.695536\pi$
$44$	2.88637	0.435137
$45$	−30.2879	−4.51506
$46$	4.59837	0.677993
$47$	−5.60393	−0.817418	−0.408709	−	0.912665i	$-0.634021\pi$
$47$	−5.60393	−0.817418	−0.408709	+	0.912665i	$0.634021\pi$
$48$	−3.25240	−0.469444
$49$	7.49536	1.07077
$50$	−10.9740	−1.55196
$51$	−20.5557	−2.87838
$52$	4.13982	0.574090
$53$	10.7997	1.48346	0.741728	−	0.670701i	$-0.234006\pi$
$53$	10.7997	1.48346	0.741728	+	0.670701i	$0.234006\pi$
$54$	14.8900	2.02627
$55$	−11.5361	−1.55553
$56$	−3.80728	−0.508769
$57$	−6.95376	−0.921048
$58$	0.802524	0.105377
$59$	−6.39923	−0.833109	−0.416554	−	0.909111i	$-0.636762\pi$
$59$	−6.39923	−0.833109	−0.416554	+	0.909111i	$0.636762\pi$
$60$	12.9990	1.67817
$61$	−10.8698	−1.39173	−0.695867	−	0.718171i	$-0.744980\pi$
$61$	−10.8698	−1.39173	−0.695867	+	0.718171i	$0.744980\pi$
$62$	−1.62651	−0.206567
$63$	28.8521	3.63502
$64$	1.00000	0.125000
$65$	−16.5458	−2.05226
$66$	9.38766	1.15554
$67$	−10.6271	−1.29831	−0.649154	−	0.760657i	$-0.724877\pi$
$67$	−10.6271	−1.29831	−0.649154	+	0.760657i	$0.724877\pi$
$68$	6.32016	0.766432
$69$	14.9558	1.80046
$70$	15.2167	1.81875
$71$	9.79640	1.16262	0.581310	−	0.813682i	$-0.302541\pi$
$71$	9.79640	1.16262	0.581310	+	0.813682i	$0.302541\pi$
$72$	−7.57814	−0.893092
$73$	0.131361	0.0153746	0.00768732	−	0.999970i	$-0.497553\pi$
$73$	0.131361	0.0153746	0.00768732	+	0.999970i	$0.497553\pi$
$74$	−5.94031	−0.690547
$75$	−35.6919	−4.12135
$76$	2.13804	0.245250
$77$	10.9892	1.25234
$78$	13.4644	1.52454
$79$	−7.22795	−0.813208	−0.406604	−	0.913605i	$-0.633287\pi$
$79$	−7.22795	−0.813208	−0.406604	+	0.913605i	$0.633287\pi$
$80$	−3.99675	−0.446850
$81$	25.6938	2.85486
$82$	3.62788	0.400632
$83$	−16.9820	−1.86402	−0.932008	−	0.362437i	$-0.881945\pi$
$83$	−16.9820	−1.86402	−0.932008	+	0.362437i	$0.881945\pi$
$84$	−12.3828	−1.35108
$85$	−25.2601	−2.73984
$86$	7.55916	0.815126
$87$	2.61013	0.279836
$88$	−2.88637	−0.307689
$89$	−11.3007	−1.19787	−0.598934	−	0.800798i	$-0.704409\pi$
$89$	−11.3007	−1.19787	−0.598934	+	0.800798i	$0.704409\pi$
$90$	30.2879	3.19263
$91$	15.7615	1.65225
$92$	−4.59837	−0.479413
$93$	−5.29007	−0.548555
$94$	5.60393	0.578002
$95$	−8.54520	−0.876719
$96$	3.25240	0.331947
$97$	−9.78252	−0.993265	−0.496632	−	0.867961i	$-0.665430\pi$
$97$	−9.78252	−0.993265	−0.496632	+	0.867961i	$0.665430\pi$
$98$	−7.49536	−0.757146
$99$	21.8733	2.19835
$100$	10.9740	1.09740
$101$	−4.36156	−0.433992	−0.216996	−	0.976173i	$-0.569626\pi$
$101$	−4.36156	−0.433992	−0.216996	+	0.976173i	$0.569626\pi$
$102$	20.5557	2.03532
$103$	10.9210	1.07608	0.538039	−	0.842920i	$-0.319165\pi$
$103$	10.9210	1.07608	0.538039	+	0.842920i	$0.319165\pi$
$104$	−4.13982	−0.405943
$105$	49.4910	4.82982
$106$	−10.7997	−1.04896
$107$	−1.32947	−0.128524	−0.0642622	−	0.997933i	$-0.520469\pi$
$107$	−1.32947	−0.128524	−0.0642622	+	0.997933i	$0.520469\pi$
$108$	−14.8900	−1.43279
$109$	−3.56068	−0.341051	−0.170526	−	0.985353i	$-0.554547\pi$
$109$	−3.56068	−0.341051	−0.170526	+	0.985353i	$0.554547\pi$
$110$	11.5361	1.09993
$111$	−19.3203	−1.83380
$112$	3.80728	0.359754
$113$	1.00789	0.0948139	0.0474070	−	0.998876i	$-0.484904\pi$
$113$	1.00789	0.0948139	0.0474070	+	0.998876i	$0.484904\pi$
$114$	6.95376	0.651279
$115$	18.3785	1.71381
$116$	−0.802524	−0.0745125
$117$	31.3721	2.90036
$118$	6.39923	0.589097
$119$	24.0626	2.20582
$120$	−12.9990	−1.18665
$121$	−2.66884	−0.242622
$122$	10.8698	0.984104
$123$	11.7993	1.06391
$124$	1.62651	0.146065
$125$	−23.8766	−2.13559
$126$	−28.8521	−2.57035
$127$	1.15529	0.102516	0.0512578	−	0.998685i	$-0.483677\pi$
$127$	1.15529	0.102516	0.0512578	+	0.998685i	$0.483677\pi$
$128$	−1.00000	−0.0883883
$129$	24.5855	2.16463
$130$	16.5458	1.45117
$131$	−9.78537	−0.854952	−0.427476	−	0.904027i	$-0.640597\pi$
$131$	−9.78537	−0.854952	−0.427476	+	0.904027i	$0.640597\pi$
$132$	−9.38766	−0.817091
$133$	8.14010	0.705836
$134$	10.6271	0.918043
$135$	59.5114	5.12193
$136$	−6.32016	−0.541949
$137$	−7.12944	−0.609110	−0.304555	−	0.952495i	$-0.598508\pi$
$137$	−7.12944	−0.609110	−0.304555	+	0.952495i	$0.598508\pi$
$138$	−14.9558	−1.27312
$139$	13.2644	1.12507	0.562534	−	0.826774i	$-0.309826\pi$
$139$	13.2644	1.12507	0.562534	+	0.826774i	$0.309826\pi$
$140$	−15.2167	−1.28605
$141$	18.2263	1.53493
$142$	−9.79640	−0.822096
$143$	11.9491	0.999232
$144$	7.57814	0.631511
$145$	3.20749	0.266367
$146$	−0.131361	−0.0108715
$147$	−24.3779	−2.01066
$148$	5.94031	0.488290
$149$	−3.44506	−0.282230	−0.141115	−	0.989993i	$-0.545069\pi$
$149$	−3.44506	−0.282230	−0.141115	+	0.989993i	$0.545069\pi$
$150$	35.6919	2.91423
$151$	−5.48792	−0.446601	−0.223300	−	0.974750i	$-0.571683\pi$
$151$	−5.48792	−0.446601	−0.223300	+	0.974750i	$0.571683\pi$
$152$	−2.13804	−0.173418
$153$	47.8950	3.87209
$154$	−10.9892	−0.885537
$155$	−6.50076	−0.522153
$156$	−13.4644	−1.07801
$157$	13.2053	1.05390	0.526950	−	0.849897i	$-0.323336\pi$
$157$	13.2053	1.05390	0.526950	+	0.849897i	$0.323336\pi$
$158$	7.22795	0.575025
$159$	−35.1251	−2.78560
$160$	3.99675	0.315971
$161$	−17.5073	−1.37977
$162$	−25.6938	−2.01869
$163$	17.0589	1.33615	0.668077	−	0.744092i	$-0.267118\pi$
$163$	17.0589	1.33615	0.668077	+	0.744092i	$0.267118\pi$
$164$	−3.62788	−0.283290
$165$	37.5201	2.92094
$166$	16.9820	1.31806
$167$	−15.8541	−1.22683	−0.613414	−	0.789762i	$-0.710204\pi$
$167$	−15.8541	−1.22683	−0.613414	+	0.789762i	$0.710204\pi$
$168$	12.3828	0.955354
$169$	4.13813	0.318318
$170$	25.2601	1.93736
$171$	16.2023	1.23902
$172$	−7.55916	−0.576381
$173$	−10.1804	−0.774005	−0.387003	−	0.922079i	$-0.626490\pi$
$173$	−10.1804	−0.774005	−0.387003	+	0.922079i	$0.626490\pi$
$174$	−2.61013	−0.197874
$175$	41.7811	3.15835
$176$	2.88637	0.217569
$177$	20.8129	1.56439
$178$	11.3007	0.847021
$179$	−6.71823	−0.502144	−0.251072	−	0.967968i	$-0.580783\pi$
$179$	−6.71823	−0.502144	−0.251072	+	0.967968i	$0.580783\pi$
$180$	−30.2879	−2.25753
$181$	−19.4108	−1.44279	−0.721397	−	0.692522i	$-0.756500\pi$
$181$	−19.4108	−1.44279	−0.721397	+	0.692522i	$0.756500\pi$
$182$	−15.7615	−1.16832
$183$	35.3529	2.61336
$184$	4.59837	0.338997
$185$	−23.7419	−1.74554
$186$	5.29007	0.387887
$187$	18.2424	1.33401
$188$	−5.60393	−0.408709
$189$	−56.6902	−4.12360
$190$	8.54520	0.619934
$191$	18.9172	1.36880	0.684401	−	0.729106i	$-0.260064\pi$
$191$	18.9172	1.36880	0.684401	+	0.729106i	$0.260064\pi$
$192$	−3.25240	−0.234722
$193$	−0.352483	−0.0253722	−0.0126861	−	0.999920i	$-0.504038\pi$
$193$	−0.352483	−0.0253722	−0.0126861	+	0.999920i	$0.504038\pi$
$194$	9.78252	0.702344
$195$	53.8137	3.85368
$196$	7.49536	0.535383
$197$	−27.1253	−1.93260	−0.966299	−	0.257424i	$-0.917126\pi$
$197$	−27.1253	−1.93260	−0.966299	+	0.257424i	$0.917126\pi$
$198$	−21.8733	−1.55447
$199$	−15.8773	−1.12551	−0.562756	−	0.826623i	$-0.690259\pi$
$199$	−15.8773	−1.12551	−0.562756	+	0.826623i	$0.690259\pi$
$200$	−10.9740	−0.775979
$201$	34.5637	2.43793
$202$	4.36156	0.306878
$203$	−3.05543	−0.214449
$204$	−20.5557	−1.43919
$205$	14.4997	1.01270
$206$	−10.9210	−0.760902
$207$	−34.8471	−2.42204
$208$	4.13982	0.287045
$209$	6.17117	0.426869
$210$	−49.4910	−3.41520
$211$	−9.82939	−0.676683	−0.338341	−	0.941023i	$-0.609866\pi$
$211$	−9.82939	−0.676683	−0.338341	+	0.941023i	$0.609866\pi$
$212$	10.7997	0.741728
$213$	−31.8619	−2.18314
$214$	1.32947	0.0908805
$215$	30.2121	2.06045
$216$	14.8900	1.01313
$217$	6.19258	0.420380
$218$	3.56068	0.241160
$219$	−0.427239	−0.0288702
$220$	−11.5361	−0.777765
$221$	26.1643	1.76000
$222$	19.3203	1.29669
$223$	5.06035	0.338866	0.169433	−	0.985542i	$-0.445806\pi$
$223$	5.06035	0.338866	0.169433	+	0.985542i	$0.445806\pi$
$224$	−3.80728	−0.254384
$225$	83.1625	5.54417
$226$	−1.00789	−0.0670436
$227$	−7.25409	−0.481471	−0.240736	−	0.970591i	$-0.577389\pi$
$227$	−7.25409	−0.481471	−0.240736	+	0.970591i	$0.577389\pi$
$228$	−6.95376	−0.460524
$229$	−21.1404	−1.39700	−0.698500	−	0.715610i	$-0.746149\pi$
$229$	−21.1404	−1.39700	−0.698500	+	0.715610i	$0.746149\pi$
$230$	−18.3785	−1.21185
$231$	−35.7414	−2.35161
$232$	0.802524	0.0526883
$233$	11.0948	0.726847	0.363423	−	0.931624i	$-0.381608\pi$
$233$	11.0948	0.726847	0.363423	+	0.931624i	$0.381608\pi$
$234$	−31.3721	−2.05086
$235$	22.3975	1.46105
$236$	−6.39923	−0.416554
$237$	23.5082	1.52702
$238$	−24.0626	−1.55975
$239$	−28.5271	−1.84527	−0.922634	−	0.385678i	$-0.873968\pi$
$239$	−28.5271	−1.84527	−0.922634	+	0.385678i	$0.873968\pi$
$240$	12.9990	0.839085
$241$	3.97261	0.255898	0.127949	−	0.991781i	$-0.459161\pi$
$241$	3.97261	0.255898	0.127949	+	0.991781i	$0.459161\pi$
$242$	2.66884	0.171560
$243$	−38.8966	−2.49522
$244$	−10.8698	−0.695867
$245$	−29.9571	−1.91389
$246$	−11.7993	−0.752297
$247$	8.85109	0.563181
$248$	−1.62651	−0.103284
$249$	55.2323	3.50021
$250$	23.8766	1.51009
$251$	−17.8593	−1.12727	−0.563633	−	0.826025i	$-0.690597\pi$
$251$	−17.8593	−1.12727	−0.563633	+	0.826025i	$0.690597\pi$
$252$	28.8521	1.81751
$253$	−13.2726	−0.834443
$254$	−1.15529	−0.0724895
$255$	82.1561	5.14481
$256$	1.00000	0.0625000
$257$	15.0330	0.937731	0.468865	−	0.883270i	$-0.344663\pi$
$257$	15.0330	0.937731	0.468865	+	0.883270i	$0.344663\pi$
$258$	−24.5855	−1.53062
$259$	22.6164	1.40532
$260$	−16.5458	−1.02613
$261$	−6.08164	−0.376444
$262$	9.78537	0.604542
$263$	−21.8751	−1.34888	−0.674440	−	0.738330i	$-0.735615\pi$
$263$	−21.8751	−1.34888	−0.674440	+	0.738330i	$0.735615\pi$
$264$	9.38766	0.577770
$265$	−43.1638	−2.65153
$266$	−8.14010	−0.499101
$267$	36.7544	2.24933
$268$	−10.6271	−0.649154
$269$	−28.8825	−1.76100	−0.880499	−	0.474049i	$-0.842792\pi$
$269$	−28.8825	−1.76100	−0.880499	+	0.474049i	$0.842792\pi$
$270$	−59.5114	−3.62175
$271$	−12.9886	−0.789004	−0.394502	−	0.918895i	$-0.629083\pi$
$271$	−12.9886	−0.789004	−0.394502	+	0.918895i	$0.629083\pi$
$272$	6.32016	0.383216
$273$	−51.2626	−3.10256
$274$	7.12944	0.430705
$275$	31.6751	1.91008
$276$	14.9558	0.900231
$277$	16.8340	1.01146	0.505729	−	0.862692i	$-0.331224\pi$
$277$	16.8340	1.01146	0.505729	+	0.862692i	$0.331224\pi$
$278$	−13.2644	−0.795544
$279$	12.3259	0.737934
$280$	15.2167	0.909374
$281$	13.4772	0.803981	0.401990	−	0.915644i	$-0.368319\pi$
$281$	13.4772	0.803981	0.401990	+	0.915644i	$0.368319\pi$
$282$	−18.2263	−1.08536
$283$	19.9476	1.18576	0.592882	−	0.805290i	$-0.297990\pi$
$283$	19.9476	1.18576	0.592882	+	0.805290i	$0.297990\pi$
$284$	9.79640	0.581310
$285$	27.7924	1.64628
$286$	−11.9491	−0.706564
$287$	−13.8123	−0.815316
$288$	−7.57814	−0.446546
$289$	22.9444	1.34967
$290$	−3.20749	−0.188350
$291$	31.8167	1.86513
$292$	0.131361	0.00768732
$293$	−18.5408	−1.08317	−0.541584	−	0.840647i	$-0.682175\pi$
$293$	−18.5408	−1.08317	−0.541584	+	0.840647i	$0.682175\pi$
$294$	24.3779	1.42175
$295$	25.5761	1.48910
$296$	−5.94031	−0.345273
$297$	−42.9780	−2.49384
$298$	3.44506	0.199567
$299$	−19.0364	−1.10091
$300$	−35.6919	−2.06067
$301$	−28.7798	−1.65884
$302$	5.48792	0.315794
$303$	14.1856	0.814939
$304$	2.13804	0.122625
$305$	43.4438	2.48758
$306$	−47.8950	−2.73798
$307$	−6.12886	−0.349792	−0.174896	−	0.984587i	$-0.555959\pi$
$307$	−6.12886	−0.349792	−0.174896	+	0.984587i	$0.555959\pi$
$308$	10.9892	0.626169
$309$	−35.5195	−2.02063
$310$	6.50076	0.369218
$311$	23.9942	1.36058	0.680292	−	0.732941i	$-0.261853\pi$
$311$	23.9942	1.36058	0.680292	+	0.732941i	$0.261853\pi$
$312$	13.4644	0.762270
$313$	18.6482	1.05406	0.527031	−	0.849846i	$-0.323305\pi$
$313$	18.6482	1.05406	0.527031	+	0.849846i	$0.323305\pi$
$314$	−13.2053	−0.745219
$315$	−115.314	−6.49724
$316$	−7.22795	−0.406604
$317$	17.1682	0.964260	0.482130	−	0.876100i	$-0.339863\pi$
$317$	17.1682	0.964260	0.482130	+	0.876100i	$0.339863\pi$
$318$	35.1251	1.96972
$319$	−2.31639	−0.129693
$320$	−3.99675	−0.223425
$321$	4.32397	0.241340
$322$	17.5073	0.975643
$323$	13.5127	0.751869
$324$	25.6938	1.42743
$325$	45.4304	2.52003
$326$	−17.0589	−0.944804
$327$	11.5808	0.640418
$328$	3.62788	0.200316
$329$	−21.3357	−1.17628
$330$	−37.5201	−2.06541
$331$	−16.7347	−0.919823	−0.459912	−	0.887965i	$-0.652119\pi$
$331$	−16.7347	−0.919823	−0.459912	+	0.887965i	$0.652119\pi$
$332$	−16.9820	−0.932008
$333$	45.0165	2.46689
$334$	15.8541	0.867498
$335$	42.4739	2.32060
$336$	−12.3828	−0.675538
$337$	−16.8740	−0.919185	−0.459593	−	0.888130i	$-0.652005\pi$
$337$	−16.8740	−0.919185	−0.459593	+	0.888130i	$0.652005\pi$
$338$	−4.13813	−0.225085
$339$	−3.27805	−0.178039
$340$	−25.2601	−1.36992
$341$	4.69472	0.254233
$342$	−16.2023	−0.876122
$343$	1.88598	0.101833
$344$	7.55916	0.407563
$345$	−59.7745	−3.21815
$346$	10.1804	0.547304
$347$	−31.9689	−1.71618	−0.858090	−	0.513499i	$-0.828349\pi$
$347$	−31.9689	−1.71618	−0.858090	+	0.513499i	$0.828349\pi$
$348$	2.61013	0.139918
$349$	−20.6616	−1.10599	−0.552996	−	0.833184i	$-0.686515\pi$
$349$	−20.6616	−1.10599	−0.552996	+	0.833184i	$0.686515\pi$
$350$	−41.7811	−2.23329
$351$	−61.6418	−3.29019
$352$	−2.88637	−0.153844
$353$	−2.47786	−0.131883	−0.0659415	−	0.997823i	$-0.521005\pi$
$353$	−2.47786	−0.131883	−0.0659415	+	0.997823i	$0.521005\pi$
$354$	−20.8129	−1.10619
$355$	−39.1538	−2.07807
$356$	−11.3007	−0.598934
$357$	−78.2613	−4.14203
$358$	6.71823	0.355069
$359$	−23.5077	−1.24069	−0.620346	−	0.784329i	$-0.713008\pi$
$359$	−23.5077	−1.24069	−0.620346	+	0.784329i	$0.713008\pi$
$360$	30.2879	1.59631
$361$	−14.4288	−0.759410
$362$	19.4108	1.02021
$363$	8.68015	0.455590
$364$	15.7615	0.826125
$365$	−0.525017	−0.0274807
$366$	−35.3529	−1.84793
$367$	−4.78477	−0.249763	−0.124882	−	0.992172i	$-0.539855\pi$
$367$	−4.78477	−0.249763	−0.124882	+	0.992172i	$0.539855\pi$
$368$	−4.59837	−0.239707
$369$	−27.4925	−1.43120
$370$	23.7419	1.23428
$371$	41.1175	2.13472
$372$	−5.29007	−0.274278
$373$	13.1465	0.680701	0.340351	−	0.940299i	$-0.389454\pi$
$373$	13.1465	0.680701	0.340351	+	0.940299i	$0.389454\pi$
$374$	−18.2424	−0.943290
$375$	77.6563	4.01016
$376$	5.60393	0.289001
$377$	−3.32231	−0.171108
$378$	56.6902	2.91583
$379$	−11.9473	−0.613693	−0.306847	−	0.951759i	$-0.599274\pi$
$379$	−11.9473	−0.613693	−0.306847	+	0.951759i	$0.599274\pi$
$380$	−8.54520	−0.438359
$381$	−3.75748	−0.192501
$382$	−18.9172	−0.967889
$383$	−11.3980	−0.582409	−0.291205	−	0.956661i	$-0.594056\pi$
$383$	−11.3980	−0.582409	−0.291205	+	0.956661i	$0.594056\pi$
$384$	3.25240	0.165974
$385$	−43.9212	−2.23843
$386$	0.352483	0.0179409
$387$	−57.2844	−2.91193
$388$	−9.78252	−0.496632
$389$	−27.9873	−1.41901	−0.709507	−	0.704699i	$-0.751082\pi$
$389$	−27.9873	−1.41901	−0.709507	+	0.704699i	$0.751082\pi$
$390$	−53.8137	−2.72496
$391$	−29.0625	−1.46975
$392$	−7.49536	−0.378573
$393$	31.8260	1.60541
$394$	27.1253	1.36655
$395$	28.8883	1.45353
$396$	21.8733	1.09918
$397$	11.5882	0.581593	0.290796	−	0.956785i	$-0.406080\pi$
$397$	11.5882	0.581593	0.290796	+	0.956785i	$0.406080\pi$
$398$	15.8773	0.795858
$399$	−26.4749	−1.32540
$400$	10.9740	0.548700
$401$	−12.7038	−0.634398	−0.317199	−	0.948359i	$-0.602742\pi$
$401$	−12.7038	−0.634398	−0.317199	+	0.948359i	$0.602742\pi$
$402$	−34.5637	−1.72388
$403$	6.73347	0.335418
$404$	−4.36156	−0.216996
$405$	−102.691	−5.10278
$406$	3.05543	0.151639
$407$	17.1460	0.849894
$408$	20.5557	1.01766
$409$	37.7945	1.86882	0.934408	−	0.356206i	$-0.115930\pi$
$409$	37.7945	1.86882	0.934408	+	0.356206i	$0.115930\pi$
$410$	−14.4997	−0.716090
$411$	23.1878	1.14377
$412$	10.9210	0.538039
$413$	−24.3636	−1.19886
$414$	34.8471	1.71264
$415$	67.8728	3.33174
$416$	−4.13982	−0.202971
$417$	−43.1411	−2.11263
$418$	−6.17117	−0.301842
$419$	−17.8891	−0.873940	−0.436970	−	0.899476i	$-0.643948\pi$
$419$	−17.8891	−0.873940	−0.436970	+	0.899476i	$0.643948\pi$
$420$	49.4910	2.41491
$421$	−9.19648	−0.448209	−0.224105	−	0.974565i	$-0.571946\pi$
$421$	−9.19648	−0.448209	−0.224105	+	0.974565i	$0.571946\pi$
$422$	9.82939	0.478487
$423$	−42.4674	−2.06483
$424$	−10.7997	−0.524481
$425$	69.3575	3.36433
$426$	31.8619	1.54371
$427$	−41.3843	−2.00273
$428$	−1.32947	−0.0642622
$429$	−38.8632	−1.87633
$430$	−30.2121	−1.45696
$431$	13.2698	0.639184	0.319592	−	0.947555i	$-0.396454\pi$
$431$	13.2698	0.639184	0.319592	+	0.947555i	$0.396454\pi$
$432$	−14.8900	−0.716393
$433$	27.1957	1.30694	0.653471	−	0.756952i	$-0.273312\pi$
$433$	27.1957	1.30694	0.653471	+	0.756952i	$0.273312\pi$
$434$	−6.19258	−0.297253
$435$	−10.4321	−0.500179
$436$	−3.56068	−0.170526
$437$	−9.83149	−0.470304
$438$	0.427239	0.0204143
$439$	−16.4466	−0.784951	−0.392476	−	0.919762i	$-0.628381\pi$
$439$	−16.4466	−0.784951	−0.392476	+	0.919762i	$0.628381\pi$
$440$	11.5361	0.549963
$441$	56.8009	2.70480
$442$	−26.1643	−1.24451
$443$	3.16232	0.150246	0.0751231	−	0.997174i	$-0.476065\pi$
$443$	3.16232	0.150246	0.0751231	+	0.997174i	$0.476065\pi$
$444$	−19.3203	−0.916900
$445$	45.1659	2.14107
$446$	−5.06035	−0.239615
$447$	11.2047	0.529965
$448$	3.80728	0.179877
$449$	37.5895	1.77396	0.886979	−	0.461810i	$-0.152800\pi$
$449$	37.5895	1.77396	0.886979	+	0.461810i	$0.152800\pi$
$450$	−83.1625	−3.92032
$451$	−10.4714	−0.493079
$452$	1.00789	0.0474070
$453$	17.8489	0.838616
$454$	7.25409	0.340452
$455$	−62.9946	−2.95323
$456$	6.95376	0.325640
$457$	−38.9083	−1.82005	−0.910026	−	0.414551i	$-0.863939\pi$
$457$	−38.9083	−1.82005	−0.910026	+	0.414551i	$0.863939\pi$
$458$	21.1404	0.987828
$459$	−94.1069	−4.39253
$460$	18.3785	0.856904
$461$	−20.0051	−0.931732	−0.465866	−	0.884855i	$-0.654257\pi$
$461$	−20.0051	−0.931732	−0.465866	+	0.884855i	$0.654257\pi$
$462$	35.7414	1.66284
$463$	−30.9562	−1.43866	−0.719329	−	0.694669i	$-0.755551\pi$
$463$	−30.9562	−1.43866	−0.719329	+	0.694669i	$0.755551\pi$
$464$	−0.802524	−0.0372563
$465$	21.1431	0.980488
$466$	−11.0948	−0.513958
$467$	−2.16050	−0.0999758	−0.0499879	−	0.998750i	$-0.515918\pi$
$467$	−2.16050	−0.0999758	−0.0499879	+	0.998750i	$0.515918\pi$
$468$	31.3721	1.45018
$469$	−40.4604	−1.86829
$470$	−22.3975	−1.03312
$471$	−42.9490	−1.97899
$472$	6.39923	0.294548
$473$	−21.8186	−1.00322
$474$	−23.5082	−1.07977
$475$	23.4628	1.07655
$476$	24.0626	1.10291
$477$	81.8418	3.74728
$478$	28.5271	1.30480
$479$	34.8382	1.59180	0.795899	−	0.605429i	$-0.206998\pi$
$479$	34.8382	1.59180	0.795899	+	0.605429i	$0.206998\pi$
$480$	−12.9990	−0.593323
$481$	24.5918	1.12129
$482$	−3.97261	−0.180947
$483$	56.9408	2.59089
$484$	−2.66884	−0.121311
$485$	39.0983	1.77536
$486$	38.8966	1.76439
$487$	−15.8138	−0.716592	−0.358296	−	0.933608i	$-0.616642\pi$
$487$	−15.8138	−0.716592	−0.358296	+	0.933608i	$0.616642\pi$
$488$	10.8698	0.492052
$489$	−55.4824	−2.50900
$490$	29.9571	1.35332
$491$	18.6864	0.843304	0.421652	−	0.906758i	$-0.361450\pi$
$491$	18.6864	0.843304	0.421652	+	0.906758i	$0.361450\pi$
$492$	11.7993	0.531955
$493$	−5.07208	−0.228435
$494$	−8.85109	−0.398229
$495$	−87.4223	−3.92934
$496$	1.62651	0.0730325
$497$	37.2976	1.67303
$498$	−55.2323	−2.47502
$499$	21.3817	0.957177	0.478589	−	0.878039i	$-0.341149\pi$
$499$	21.3817	0.957177	0.478589	+	0.878039i	$0.341149\pi$
$500$	−23.8766	−1.06779
$501$	51.5640	2.30371
$502$	17.8593	0.797098
$503$	35.7621	1.59455	0.797277	−	0.603613i	$-0.206273\pi$
$503$	35.7621	1.59455	0.797277	+	0.603613i	$0.206273\pi$
$504$	−28.8521	−1.28517
$505$	17.4321	0.775717
$506$	13.2726	0.590040
$507$	−13.4589	−0.597730
$508$	1.15529	0.0512578
$509$	16.5306	0.732704	0.366352	−	0.930476i	$-0.380607\pi$
$509$	16.5306	0.732704	0.366352	+	0.930476i	$0.380607\pi$
$510$	−82.1561	−3.63793
$511$	0.500128	0.0221244
$512$	−1.00000	−0.0441942
$513$	−31.8353	−1.40556
$514$	−15.0330	−0.663076
$515$	−43.6485	−1.92338
$516$	24.5855	1.08231
$517$	−16.1751	−0.711378
$518$	−22.6164	−0.993708
$519$	33.1109	1.45341
$520$	16.5458	0.725583
$521$	17.5213	0.767623	0.383812	−	0.923411i	$-0.374611\pi$
$521$	17.5213	0.767623	0.383812	+	0.923411i	$0.374611\pi$
$522$	6.08164	0.266186
$523$	−41.4250	−1.81139	−0.905695	−	0.423929i	$-0.860651\pi$
$523$	−41.4250	−1.81139	−0.905695	+	0.423929i	$0.860651\pi$
$524$	−9.78537	−0.427476
$525$	−135.889	−5.93068
$526$	21.8751	0.953802
$527$	10.2798	0.447796
$528$	−9.38766	−0.408545
$529$	−1.85497	−0.0806509
$530$	43.1638	1.87492
$531$	−48.4942	−2.10447
$532$	8.14010	0.352918
$533$	−15.0188	−0.650535
$534$	−36.7544	−1.59052
$535$	5.31355	0.229725
$536$	10.6271	0.459021
$537$	21.8504	0.942914
$538$	28.8825	1.24521
$539$	21.6344	0.931860
$540$	59.5114	2.56096
$541$	36.8939	1.58619	0.793095	−	0.609098i	$-0.208468\pi$
$541$	36.8939	1.58619	0.793095	+	0.609098i	$0.208468\pi$
$542$	12.9886	0.557910
$543$	63.1318	2.70925
$544$	−6.32016	−0.270975
$545$	14.2311	0.609595
$546$	51.2626	2.19384
$547$	5.22081	0.223226	0.111613	−	0.993752i	$-0.464398\pi$
$547$	5.22081	0.223226	0.111613	+	0.993752i	$0.464398\pi$
$548$	−7.12944	−0.304555
$549$	−82.3727	−3.51558
$550$	−31.6751	−1.35063
$551$	−1.71583	−0.0730967
$552$	−14.9558	−0.636560
$553$	−27.5188	−1.17022
$554$	−16.8340	−0.715209
$555$	77.2184	3.27774
$556$	13.2644	0.562534
$557$	−32.7374	−1.38713	−0.693564	−	0.720395i	$-0.743961\pi$
$557$	−32.7374	−1.38713	−0.693564	+	0.720395i	$0.743961\pi$
$558$	−12.3259	−0.521798
$559$	−31.2936	−1.32358
$560$	−15.2167	−0.643024
$561$	−59.3315	−2.50498
$562$	−13.4772	−0.568500
$563$	45.5557	1.91994	0.959971	−	0.280098i	$-0.0903670\pi$
$563$	45.5557	1.91994	0.959971	+	0.280098i	$0.0903670\pi$
$564$	18.2263	0.767464
$565$	−4.02827	−0.169470
$566$	−19.9476	−0.838461
$567$	97.8232	4.10819
$568$	−9.79640	−0.411048
$569$	−13.8992	−0.582685	−0.291343	−	0.956619i	$-0.594102\pi$
$569$	−13.8992	−0.582685	−0.291343	+	0.956619i	$0.594102\pi$
$570$	−27.7924	−1.16410
$571$	43.3005	1.81207	0.906034	−	0.423205i	$-0.139095\pi$
$571$	43.3005	1.81207	0.906034	+	0.423205i	$0.139095\pi$
$572$	11.9491	0.499616
$573$	−61.5265	−2.57030
$574$	13.8123	0.576516
$575$	−50.4626	−2.10443
$576$	7.57814	0.315756
$577$	10.8510	0.451732	0.225866	−	0.974158i	$-0.427479\pi$
$577$	10.8510	0.451732	0.225866	+	0.974158i	$0.427479\pi$
$578$	−22.9444	−0.954363
$579$	1.14642	0.0476434
$580$	3.20749	0.133184
$581$	−64.6552	−2.68235
$582$	−31.8167	−1.31885
$583$	31.1720	1.29101
$584$	−0.131361	−0.00543576
$585$	−125.387	−5.18410
$586$	18.5408	0.765915
$587$	−21.1403	−0.872553	−0.436277	−	0.899813i	$-0.643703\pi$
$587$	−21.1403	−0.872553	−0.436277	+	0.899813i	$0.643703\pi$
$588$	−24.3779	−1.00533
$589$	3.47754	0.143290
$590$	−25.5761	−1.05295
$591$	88.2224	3.62899
$592$	5.94031	0.244145
$593$	−25.8973	−1.06347	−0.531737	−	0.846910i	$-0.678461\pi$
$593$	−25.8973	−1.06347	−0.531737	+	0.846910i	$0.678461\pi$
$594$	42.9780	1.76341
$595$	−96.1722	−3.94268
$596$	−3.44506	−0.141115
$597$	51.6394	2.11346
$598$	19.0364	0.778458
$599$	−32.3833	−1.32315	−0.661573	−	0.749881i	$-0.730111\pi$
$599$	−32.3833	−1.32315	−0.661573	+	0.749881i	$0.730111\pi$
$600$	35.6919	1.45712
$601$	−17.3430	−0.707436	−0.353718	−	0.935352i	$-0.615083\pi$
$601$	−17.3430	−0.707436	−0.353718	+	0.935352i	$0.615083\pi$
$602$	28.7798	1.17298
$603$	−80.5337	−3.27959
$604$	−5.48792	−0.223300
$605$	10.6667	0.433663
$606$	−14.1856	−0.576249
$607$	8.20015	0.332834	0.166417	−	0.986055i	$-0.446780\pi$
$607$	8.20015	0.332834	0.166417	+	0.986055i	$0.446780\pi$
$608$	−2.13804	−0.0867088
$609$	9.93751	0.402688
$610$	−43.4438	−1.75899
$611$	−23.1993	−0.938543
$612$	47.8950	1.93604
$613$	−20.0397	−0.809395	−0.404697	−	0.914451i	$-0.632623\pi$
$613$	−20.0397	−0.809395	−0.404697	+	0.914451i	$0.632623\pi$
$614$	6.12886	0.247341
$615$	−47.1589	−1.90163
$616$	−10.9892	−0.442769
$617$	43.0172	1.73181	0.865904	−	0.500210i	$-0.166744\pi$
$617$	43.0172	1.73181	0.865904	+	0.500210i	$0.166744\pi$
$618$	35.5195	1.42880
$619$	−23.1271	−0.929558	−0.464779	−	0.885427i	$-0.653866\pi$
$619$	−23.1271	−0.929558	−0.464779	+	0.885427i	$0.653866\pi$
$620$	−6.50076	−0.261077
$621$	68.4696	2.74759
$622$	−23.9942	−0.962078
$623$	−43.0248	−1.72375
$624$	−13.4644	−0.539007
$625$	40.5587	1.62235
$626$	−18.6482	−0.745334
$627$	−20.0712	−0.801565
$628$	13.2053	0.526950
$629$	37.5437	1.49697
$630$	115.314	4.59424
$631$	1.48555	0.0591388	0.0295694	−	0.999563i	$-0.490586\pi$
$631$	1.48555	0.0591388	0.0295694	+	0.999563i	$0.490586\pi$
$632$	7.22795	0.287512
$633$	31.9691	1.27066
$634$	−17.1682	−0.681835
$635$	−4.61741	−0.183237
$636$	−35.1251	−1.39280
$637$	31.0295	1.22943
$638$	2.31639	0.0917066
$639$	74.2385	2.93683
$640$	3.99675	0.157985
$641$	27.6095	1.09051	0.545254	−	0.838271i	$-0.316433\pi$
$641$	27.6095	1.09051	0.545254	+	0.838271i	$0.316433\pi$
$642$	−4.32397	−0.170653
$643$	−1.82136	−0.0718275	−0.0359137	−	0.999355i	$-0.511434\pi$
$643$	−1.82136	−0.0718275	−0.0359137	+	0.999355i	$0.511434\pi$
$644$	−17.5073	−0.689883
$645$	−98.2619	−3.86906
$646$	−13.5127	−0.531652
$647$	−22.6928	−0.892147	−0.446073	−	0.894996i	$-0.647178\pi$
$647$	−22.6928	−0.892147	−0.446073	+	0.894996i	$0.647178\pi$
$648$	−25.6938	−1.00935
$649$	−18.4706	−0.725033
$650$	−45.4304	−1.78193
$651$	−20.1408	−0.789379
$652$	17.0589	0.668077
$653$	−25.3684	−0.992743	−0.496372	−	0.868110i	$-0.665335\pi$
$653$	−25.3684	−0.992743	−0.496372	+	0.868110i	$0.665335\pi$
$654$	−11.5808	−0.452844
$655$	39.1097	1.52814
$656$	−3.62788	−0.141645
$657$	0.995472	0.0388371
$658$	21.3357	0.831753
$659$	−11.5244	−0.448927	−0.224463	−	0.974483i	$-0.572063\pi$
$659$	−11.5244	−0.448927	−0.224463	+	0.974483i	$0.572063\pi$
$660$	37.5201	1.46047
$661$	−34.7707	−1.35242	−0.676211	−	0.736708i	$-0.736379\pi$
$661$	−34.7707	−1.35242	−0.676211	+	0.736708i	$0.736379\pi$
$662$	16.7347	0.650413
$663$	−85.0970	−3.30490
$664$	16.9820	0.659029
$665$	−32.5339	−1.26161
$666$	−45.0165	−1.74435
$667$	3.69031	0.142889
$668$	−15.8541	−0.613414
$669$	−16.4583	−0.636315
$670$	−42.4739	−1.64091
$671$	−31.3743	−1.21119
$672$	12.3828	0.477677
$673$	19.4281	0.748900	0.374450	−	0.927247i	$-0.377832\pi$
$673$	19.4281	0.748900	0.374450	+	0.927247i	$0.377832\pi$
$674$	16.8740	0.649962
$675$	−163.402	−6.28936
$676$	4.13813	0.159159
$677$	−17.1201	−0.657977	−0.328989	−	0.944334i	$-0.606708\pi$
$677$	−17.1201	−0.657977	−0.328989	+	0.944334i	$0.606708\pi$
$678$	3.27805	0.125893
$679$	−37.2448	−1.42932
$680$	25.2601	0.968681
$681$	23.5933	0.904095
$682$	−4.69472	−0.179770
$683$	24.5272	0.938509	0.469254	−	0.883063i	$-0.344523\pi$
$683$	24.5272	0.938509	0.469254	+	0.883063i	$0.344523\pi$
$684$	16.2023	0.619512
$685$	28.4946	1.08872
$686$	−1.88598	−0.0720070
$687$	68.7573	2.62325
$688$	−7.55916	−0.288190
$689$	44.7089	1.70327
$690$	59.7745	2.27557
$691$	−47.1430	−1.79340	−0.896701	−	0.442636i	$-0.854043\pi$
$691$	−47.1430	−1.79340	−0.896701	+	0.442636i	$0.854043\pi$
$692$	−10.1804	−0.387003
$693$	83.2779	3.16347
$694$	31.9689	1.21352
$695$	−53.0143	−2.01095
$696$	−2.61013	−0.0989369
$697$	−22.9288	−0.868489
$698$	20.6616	0.782054
$699$	−36.0849	−1.36486
$700$	41.7811	1.57918
$701$	52.2553	1.97366	0.986828	−	0.161770i	$-0.0517203\pi$
$701$	52.2553	1.97366	0.986828	+	0.161770i	$0.0517203\pi$
$702$	61.6418	2.32652
$703$	12.7006	0.479012
$704$	2.88637	0.108784
$705$	−72.8458	−2.74353
$706$	2.47786	0.0932554
$707$	−16.6057	−0.624521
$708$	20.8129	0.782196
$709$	40.3693	1.51610	0.758051	−	0.652195i	$-0.226152\pi$
$709$	40.3693	1.51610	0.758051	+	0.652195i	$0.226152\pi$
$710$	39.1538	1.46941
$711$	−54.7744	−2.05420
$712$	11.3007	0.423511
$713$	−7.47930	−0.280102
$714$	78.2613	2.92886
$715$	−47.7575	−1.78603
$716$	−6.71823	−0.251072
$717$	92.7818	3.46500
$718$	23.5077	0.877301
$719$	20.5800	0.767504	0.383752	−	0.923436i	$-0.374632\pi$
$719$	20.5800	0.767504	0.383752	+	0.923436i	$0.374632\pi$
$720$	−30.2879	−1.12876
$721$	41.5793	1.54849
$722$	14.4288	0.536984
$723$	−12.9205	−0.480520
$724$	−19.4108	−0.721397
$725$	−8.80691	−0.327080
$726$	−8.68015	−0.322151
$727$	7.38576	0.273923	0.136961	−	0.990576i	$-0.456266\pi$
$727$	7.38576	0.273923	0.136961	+	0.990576i	$0.456266\pi$
$728$	−15.7615	−0.584158
$729$	49.4263	1.83060
$730$	0.525017	0.0194318
$731$	−47.7751	−1.76703
$732$	35.3529	1.30668
$733$	48.3502	1.78586	0.892928	−	0.450199i	$-0.148647\pi$
$733$	48.3502	1.78586	0.892928	+	0.450199i	$0.148647\pi$
$734$	4.78477	0.176609
$735$	97.4325	3.59385
$736$	4.59837	0.169498
$737$	−30.6738	−1.12988
$738$	27.4925	1.01201
$739$	6.57177	0.241747	0.120873	−	0.992668i	$-0.461431\pi$
$739$	6.57177	0.241747	0.120873	+	0.992668i	$0.461431\pi$
$740$	−23.7419	−0.872771
$741$	−28.7873	−1.05753
$742$	−41.1175	−1.50947
$743$	28.2541	1.03654	0.518271	−	0.855217i	$-0.326576\pi$
$743$	28.2541	1.03654	0.518271	+	0.855217i	$0.326576\pi$
$744$	5.29007	0.193943
$745$	13.7690	0.504458
$746$	−13.1465	−0.481328
$747$	−128.692	−4.70859
$748$	18.2424	0.667006
$749$	−5.06165	−0.184949
$750$	−77.6563	−2.83561
$751$	−7.46474	−0.272392	−0.136196	−	0.990682i	$-0.543488\pi$
$751$	−7.46474	−0.272392	−0.136196	+	0.990682i	$0.543488\pi$
$752$	−5.60393	−0.204354
$753$	58.0856	2.11676
$754$	3.32231	0.120991
$755$	21.9338	0.798254
$756$	−56.6902	−2.06180
$757$	−12.6208	−0.458711	−0.229355	−	0.973343i	$-0.573662\pi$
$757$	−12.6208	−0.458711	−0.229355	+	0.973343i	$0.573662\pi$
$758$	11.9473	0.433946
$759$	43.1679	1.56690
$760$	8.54520	0.309967
$761$	14.7379	0.534248	0.267124	−	0.963662i	$-0.413927\pi$
$761$	14.7379	0.534248	0.267124	+	0.963662i	$0.413927\pi$
$762$	3.75748	0.136119
$763$	−13.5565	−0.490778
$764$	18.9172	0.684401
$765$	−191.424	−6.92097
$766$	11.3980	0.411826
$767$	−26.4917	−0.956559
$768$	−3.25240	−0.117361
$769$	−20.4704	−0.738183	−0.369091	−	0.929393i	$-0.620331\pi$
$769$	−20.4704	−0.738183	−0.369091	+	0.929393i	$0.620331\pi$
$770$	43.9212	1.58281
$771$	−48.8933	−1.76085
$772$	−0.352483	−0.0126861
$773$	18.4233	0.662639	0.331319	−	0.943519i	$-0.392506\pi$
$773$	18.4233	0.662639	0.331319	+	0.943519i	$0.392506\pi$
$774$	57.2844	2.05904
$775$	17.8493	0.641167
$776$	9.78252	0.351172
$777$	−73.5577	−2.63887
$778$	27.9873	1.00339
$779$	−7.75653	−0.277907
$780$	53.8137	1.92684
$781$	28.2761	1.01180
$782$	29.0625	1.03927
$783$	11.9496	0.427042
$784$	7.49536	0.267691
$785$	−52.7783	−1.88374
$786$	−31.8260	−1.13520
$787$	−46.2297	−1.64791	−0.823956	−	0.566654i	$-0.808238\pi$
$787$	−46.2297	−1.64791	−0.823956	+	0.566654i	$0.808238\pi$
$788$	−27.1253	−0.966299
$789$	71.1468	2.53289
$790$	−28.8883	−1.02780
$791$	3.83730	0.136439
$792$	−21.8733	−0.777235
$793$	−44.9990	−1.59796
$794$	−11.5882	−0.411248
$795$	140.386	4.97898
$796$	−15.8773	−0.562756
$797$	29.3986	1.04135	0.520676	−	0.853754i	$-0.325680\pi$
$797$	29.3986	1.04135	0.520676	+	0.853754i	$0.325680\pi$
$798$	26.4749	0.937201
$799$	−35.4178	−1.25299
$800$	−10.9740	−0.387990
$801$	−85.6380	−3.02587
$802$	12.7038	0.448587
$803$	0.379157	0.0133802
$804$	34.5637	1.21897
$805$	69.9722	2.46620
$806$	−6.73347	−0.237176
$807$	93.9376	3.30676
$808$	4.36156	0.153439
$809$	−9.88336	−0.347480	−0.173740	−	0.984792i	$-0.555585\pi$
$809$	−9.88336	−0.347480	−0.173740	+	0.984792i	$0.555585\pi$
$810$	102.691	3.60821
$811$	−13.5904	−0.477224	−0.238612	−	0.971115i	$-0.576692\pi$
$811$	−13.5904	−0.477224	−0.238612	+	0.971115i	$0.576692\pi$
$812$	−3.05543	−0.107225
$813$	42.2443	1.48157
$814$	−17.1460	−0.600966
$815$	−68.1801	−2.38824
$816$	−20.5557	−0.719594
$817$	−16.1618	−0.565429
$818$	−37.7945	−1.32145
$819$	119.442	4.17366
$820$	14.4997	0.506352
$821$	−22.4927	−0.785002	−0.392501	−	0.919752i	$-0.628390\pi$
$821$	−22.4927	−0.785002	−0.392501	+	0.919752i	$0.628390\pi$
$822$	−23.1878	−0.808769
$823$	27.2718	0.950634	0.475317	−	0.879815i	$-0.342333\pi$
$823$	27.2718	0.950634	0.475317	+	0.879815i	$0.342333\pi$
$824$	−10.9210	−0.380451
$825$	−103.020	−3.58670
$826$	24.3636	0.847720
$827$	2.23107	0.0775818	0.0387909	−	0.999247i	$-0.487649\pi$
$827$	2.23107	0.0775818	0.0387909	+	0.999247i	$0.487649\pi$
$828$	−34.8471	−1.21102
$829$	−26.9319	−0.935385	−0.467692	−	0.883891i	$-0.654914\pi$
$829$	−26.9319	−0.935385	−0.467692	+	0.883891i	$0.654914\pi$
$830$	−67.8728	−2.35590
$831$	−54.7510	−1.89929
$832$	4.13982	0.143523
$833$	47.3719	1.64134
$834$	43.1411	1.49385
$835$	63.3649	2.19283
$836$	6.17117	0.213435
$837$	−24.2187	−0.837120
$838$	17.8891	0.617969
$839$	26.3137	0.908451	0.454226	−	0.890887i	$-0.349916\pi$
$839$	26.3137	0.908451	0.454226	+	0.890887i	$0.349916\pi$
$840$	−49.4910	−1.70760
$841$	−28.3560	−0.977792
$842$	9.19648	0.316932
$843$	−43.8332	−1.50970
$844$	−9.82939	−0.338341
$845$	−16.5391	−0.568961
$846$	42.4674	1.46006
$847$	−10.1610	−0.349137
$848$	10.7997	0.370864
$849$	−64.8777	−2.22660
$850$	−69.3575	−2.37894
$851$	−27.3158	−0.936372
$852$	−31.8619	−1.09157
$853$	−0.578265	−0.0197994	−0.00989971	−	0.999951i	$-0.503151\pi$
$853$	−0.578265	−0.0197994	−0.00989971	+	0.999951i	$0.503151\pi$
$854$	41.3843	1.41614
$855$	−64.7567	−2.21463
$856$	1.32947	0.0454403
$857$	−27.3155	−0.933081	−0.466540	−	0.884500i	$-0.654500\pi$
$857$	−27.3155	−0.933081	−0.466540	+	0.884500i	$0.654500\pi$
$858$	38.8632	1.32677
$859$	−27.2749	−0.930607	−0.465304	−	0.885151i	$-0.654055\pi$
$859$	−27.2749	−0.930607	−0.465304	+	0.885151i	$0.654055\pi$
$860$	30.2121	1.03022
$861$	44.9233	1.53098
$862$	−13.2698	−0.451971
$863$	17.5318	0.596790	0.298395	−	0.954442i	$-0.403549\pi$
$863$	17.5318	0.596790	0.298395	+	0.954442i	$0.403549\pi$
$864$	14.8900	0.506567
$865$	40.6887	1.38346
$866$	−27.1957	−0.924147
$867$	−74.6246	−2.53438
$868$	6.19258	0.210190
$869$	−20.8626	−0.707714
$870$	10.4321	0.353680
$871$	−43.9944	−1.49069
$872$	3.56068	0.120580
$873$	−74.1333	−2.50903
$874$	9.83149	0.332555
$875$	−90.9048	−3.07314
$876$	−0.427239	−0.0144351
$877$	57.8476	1.95338	0.976688	−	0.214663i	$-0.0688654\pi$
$877$	57.8476	1.95338	0.976688	+	0.214663i	$0.0688654\pi$
$878$	16.4466	0.555044
$879$	60.3023	2.03395
$880$	−11.5361	−0.388882
$881$	48.9678	1.64977	0.824883	−	0.565304i	$-0.191241\pi$
$881$	48.9678	1.64977	0.824883	+	0.565304i	$0.191241\pi$
$882$	−56.8009	−1.91258
$883$	50.8665	1.71179	0.855897	−	0.517147i	$-0.173006\pi$
$883$	50.8665	1.71179	0.855897	+	0.517147i	$0.173006\pi$
$884$	26.1643	0.880002
$885$	−83.1839	−2.79620
$886$	−3.16232	−0.106240
$887$	27.4697	0.922341	0.461171	−	0.887311i	$-0.347430\pi$
$887$	27.4697	0.922341	0.461171	+	0.887311i	$0.347430\pi$
$888$	19.3203	0.648347
$889$	4.39852	0.147522
$890$	−45.1659	−1.51397
$891$	74.1618	2.48451
$892$	5.06035	0.169433
$893$	−11.9814	−0.400943
$894$	−11.2047	−0.374742
$895$	26.8511	0.897533
$896$	−3.80728	−0.127192
$897$	61.9142	2.06726
$898$	−37.5895	−1.25438
$899$	−1.30532	−0.0435347
$900$	83.1625	2.77208
$901$	68.2560	2.27394
$902$	10.4714	0.348660
$903$	93.6037	3.11494
$904$	−1.00789	−0.0335218
$905$	77.5802	2.57885
$906$	−17.8489	−0.592991
$907$	−34.4824	−1.14497	−0.572485	−	0.819915i	$-0.694021\pi$
$907$	−34.4824	−1.14497	−0.572485	+	0.819915i	$0.694021\pi$
$908$	−7.25409	−0.240736
$909$	−33.0525	−1.09628
$910$	62.9946	2.08825
$911$	31.5533	1.04541	0.522704	−	0.852514i	$-0.324923\pi$
$911$	31.5533	1.04541	0.522704	+	0.852514i	$0.324923\pi$
$912$	−6.95376	−0.230262
$913$	−49.0164	−1.62221
$914$	38.9083	1.28697
$915$	−141.297	−4.67113
$916$	−21.1404	−0.698500
$917$	−37.2556	−1.23029
$918$	94.1069	3.10599
$919$	46.3691	1.52958	0.764788	−	0.644282i	$-0.222844\pi$
$919$	46.3691	1.52958	0.764788	+	0.644282i	$0.222844\pi$
$920$	−18.3785	−0.605923
$921$	19.9335	0.656832
$922$	20.0051	0.658834
$923$	40.5554	1.33490
$924$	−35.7414	−1.17581
$925$	65.1890	2.14340
$926$	30.9562	1.01729
$927$	82.7608	2.71822
$928$	0.802524	0.0263442
$929$	−31.8782	−1.04589	−0.522944	−	0.852367i	$-0.675166\pi$
$929$	−31.8782	−1.04589	−0.522944	+	0.852367i	$0.675166\pi$
$930$	−21.1431	−0.693309
$931$	16.0254	0.525210
$932$	11.0948	0.363423
$933$	−78.0387	−2.55487
$934$	2.16050	0.0706936
$935$	−72.9101	−2.38442
$936$	−31.3721	−1.02543
$937$	48.7701	1.59325	0.796625	−	0.604474i	$-0.206616\pi$
$937$	48.7701	1.59325	0.796625	+	0.604474i	$0.206616\pi$
$938$	40.4604	1.32108
$939$	−60.6517	−1.97929
$940$	22.3975	0.730527
$941$	−7.37241	−0.240334	−0.120167	−	0.992754i	$-0.538343\pi$
$941$	−7.37241	−0.240334	−0.120167	+	0.992754i	$0.538343\pi$
$942$	42.9490	1.39936
$943$	16.6823	0.543251
$944$	−6.39923	−0.208277
$945$	226.576	7.37053
$946$	21.8186	0.709383
$947$	−59.9483	−1.94806	−0.974030	−	0.226420i	$-0.927298\pi$
$947$	−59.9483	−1.94806	−0.974030	+	0.226420i	$0.927298\pi$
$948$	23.5082	0.763511
$949$	0.543811	0.0176529
$950$	−23.4628	−0.761234
$951$	−55.8378	−1.81066
$952$	−24.0626	−0.779874
$953$	31.5647	1.02248	0.511240	−	0.859438i	$-0.329186\pi$
$953$	31.5647	1.02248	0.511240	+	0.859438i	$0.329186\pi$
$954$	−81.8418	−2.64973
$955$	−75.6074	−2.44660
$956$	−28.5271	−0.922634
$957$	7.53383	0.243534
$958$	−34.8382	−1.12557
$959$	−27.1438	−0.876518
$960$	12.9990	0.419542
$961$	−28.3545	−0.914660
$962$	−24.5918	−0.792872
$963$	−10.0749	−0.324659
$964$	3.97261	0.127949
$965$	1.40878	0.0453504
$966$	−56.9408	−1.83204
$967$	4.25132	0.136713	0.0683567	−	0.997661i	$-0.478224\pi$
$967$	4.25132	0.136713	0.0683567	+	0.997661i	$0.478224\pi$
$968$	2.66884	0.0857798
$969$	−43.9489	−1.41184
$970$	−39.0983	−1.25537
$971$	46.6697	1.49770	0.748851	−	0.662738i	$-0.230606\pi$
$971$	46.6697	1.49770	0.748851	+	0.662738i	$0.230606\pi$
$972$	−38.8966	−1.24761
$973$	50.5011	1.61899
$974$	15.8138	0.506707
$975$	−147.758	−4.73205
$976$	−10.8698	−0.347933
$977$	−56.0288	−1.79252	−0.896260	−	0.443528i	$-0.853727\pi$
$977$	−56.0288	−1.79252	−0.896260	+	0.443528i	$0.853727\pi$
$978$	55.4824	1.77413
$979$	−32.6180	−1.04247
$980$	−29.9571	−0.956944
$981$	−26.9833	−0.861511
$982$	−18.6864	−0.596306
$983$	−52.1331	−1.66279	−0.831394	−	0.555683i	$-0.812457\pi$
$983$	−52.1331	−1.66279	−0.831394	+	0.555683i	$0.812457\pi$
$984$	−11.7993	−0.376149
$985$	108.413	3.45433
$986$	5.07208	0.161528
$987$	69.3924	2.20879
$988$	8.85109	0.281591
$989$	34.7599	1.10530
$990$	87.4223	2.77846
$991$	−10.1941	−0.323825	−0.161913	−	0.986805i	$-0.551766\pi$
$991$	−10.1941	−0.323825	−0.161913	+	0.986805i	$0.551766\pi$
$992$	−1.62651	−0.0516418
$993$	54.4281	1.72722
$994$	−37.2976	−1.18301
$995$	63.4576	2.01174
$996$	55.2323	1.75010
$997$	22.5804	0.715129	0.357565	−	0.933888i	$-0.383607\pi$
$997$	22.5804	0.715129	0.357565	+	0.933888i	$0.383607\pi$
$998$	−21.3817	−0.676826
$999$	−88.4509	−2.79846

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.b.1.2	✓	81

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.b.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.25240 q^{3} +1.00000 q^{4} -3.99675 q^{5} +3.25240 q^{6} +3.80728 q^{7} -1.00000 q^{8} +7.57814 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.25240 q^{3} +1.00000 q^{4} -3.99675 q^{5} +3.25240 q^{6} +3.80728 q^{7} -1.00000 q^{8} +7.57814 q^{9} +3.99675 q^{10} +2.88637 q^{11} -3.25240 q^{12} +4.13982 q^{13} -3.80728 q^{14} +12.9990 q^{15} +1.00000 q^{16} +6.32016 q^{17} -7.57814 q^{18} +2.13804 q^{19} -3.99675 q^{20} -12.3828 q^{21} -2.88637 q^{22} -4.59837 q^{23} +3.25240 q^{24} +10.9740 q^{25} -4.13982 q^{26} -14.8900 q^{27} +3.80728 q^{28} -0.802524 q^{29} -12.9990 q^{30} +1.62651 q^{31} -1.00000 q^{32} -9.38766 q^{33} -6.32016 q^{34} -15.2167 q^{35} +7.57814 q^{36} +5.94031 q^{37} -2.13804 q^{38} -13.4644 q^{39} +3.99675 q^{40} -3.62788 q^{41} +12.3828 q^{42} -7.55916 q^{43} +2.88637 q^{44} -30.2879 q^{45} +4.59837 q^{46} -5.60393 q^{47} -3.25240 q^{48} +7.49536 q^{49} -10.9740 q^{50} -20.5557 q^{51} +4.13982 q^{52} +10.7997 q^{53} +14.8900 q^{54} -11.5361 q^{55} -3.80728 q^{56} -6.95376 q^{57} +0.802524 q^{58} -6.39923 q^{59} +12.9990 q^{60} -10.8698 q^{61} -1.62651 q^{62} +28.8521 q^{63} +1.00000 q^{64} -16.5458 q^{65} +9.38766 q^{66} -10.6271 q^{67} +6.32016 q^{68} +14.9558 q^{69} +15.2167 q^{70} +9.79640 q^{71} -7.57814 q^{72} +0.131361 q^{73} -5.94031 q^{74} -35.6919 q^{75} +2.13804 q^{76} +10.9892 q^{77} +13.4644 q^{78} -7.22795 q^{79} -3.99675 q^{80} +25.6938 q^{81} +3.62788 q^{82} -16.9820 q^{83} -12.3828 q^{84} -25.2601 q^{85} +7.55916 q^{86} +2.61013 q^{87} -2.88637 q^{88} -11.3007 q^{89} +30.2879 q^{90} +15.7615 q^{91} -4.59837 q^{92} -5.29007 q^{93} +5.60393 q^{94} -8.54520 q^{95} +3.25240 q^{96} -9.78252 q^{97} -7.49536 q^{98} +21.8733 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9}+O(q^{10}) \) 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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