LMFDB - Embedded newform 8026.2.a.c.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0879326623$
Analytic rank:	$0$
Dimension:	$86$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.61892 q^{3} +1.00000 q^{4} +3.93925 q^{5} +2.61892 q^{6} +4.49129 q^{7} -1.00000 q^{8} +3.85875 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.61892 q^{3} +1.00000 q^{4} +3.93925 q^{5} +2.61892 q^{6} +4.49129 q^{7} -1.00000 q^{8} +3.85875 q^{9} -3.93925 q^{10} +5.80663 q^{11} -2.61892 q^{12} +1.31735 q^{13} -4.49129 q^{14} -10.3166 q^{15} +1.00000 q^{16} +3.74127 q^{17} -3.85875 q^{18} -0.785058 q^{19} +3.93925 q^{20} -11.7623 q^{21} -5.80663 q^{22} -2.51635 q^{23} +2.61892 q^{24} +10.5177 q^{25} -1.31735 q^{26} -2.24900 q^{27} +4.49129 q^{28} -8.02017 q^{29} +10.3166 q^{30} -6.32906 q^{31} -1.00000 q^{32} -15.2071 q^{33} -3.74127 q^{34} +17.6923 q^{35} +3.85875 q^{36} -0.903346 q^{37} +0.785058 q^{38} -3.45003 q^{39} -3.93925 q^{40} -3.99569 q^{41} +11.7623 q^{42} -1.69467 q^{43} +5.80663 q^{44} +15.2006 q^{45} +2.51635 q^{46} +0.775534 q^{47} -2.61892 q^{48} +13.1717 q^{49} -10.5177 q^{50} -9.79810 q^{51} +1.31735 q^{52} -2.69823 q^{53} +2.24900 q^{54} +22.8738 q^{55} -4.49129 q^{56} +2.05600 q^{57} +8.02017 q^{58} -5.88473 q^{59} -10.3166 q^{60} -8.50789 q^{61} +6.32906 q^{62} +17.3308 q^{63} +1.00000 q^{64} +5.18936 q^{65} +15.2071 q^{66} +4.96827 q^{67} +3.74127 q^{68} +6.59012 q^{69} -17.6923 q^{70} +9.60610 q^{71} -3.85875 q^{72} +2.19639 q^{73} +0.903346 q^{74} -27.5449 q^{75} -0.785058 q^{76} +26.0793 q^{77} +3.45003 q^{78} +5.64803 q^{79} +3.93925 q^{80} -5.68630 q^{81} +3.99569 q^{82} +13.3294 q^{83} -11.7623 q^{84} +14.7378 q^{85} +1.69467 q^{86} +21.0042 q^{87} -5.80663 q^{88} +4.02482 q^{89} -15.2006 q^{90} +5.91660 q^{91} -2.51635 q^{92} +16.5753 q^{93} -0.775534 q^{94} -3.09254 q^{95} +2.61892 q^{96} -9.30063 q^{97} -13.1717 q^{98} +22.4063 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) $ 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.61892	−1.51203	−0.756017	−	0.654551i	$-0.772858\pi$
$3$	−2.61892	−1.51203	−0.756017	+	0.654551i	$0.772858\pi$
$4$	1.00000	0.500000
$5$	3.93925	1.76168	0.880842	−	0.473410i	$-0.156977\pi$
$5$	3.93925	1.76168	0.880842	+	0.473410i	$0.156977\pi$
$6$	2.61892	1.06917
$7$	4.49129	1.69755	0.848774	−	0.528756i	$-0.177341\pi$
$7$	4.49129	1.69755	0.848774	+	0.528756i	$0.177341\pi$
$8$	−1.00000	−0.353553
$9$	3.85875	1.28625
$10$	−3.93925	−1.24570
$11$	5.80663	1.75077	0.875383	−	0.483430i	$-0.160609\pi$
$11$	5.80663	1.75077	0.875383	+	0.483430i	$0.160609\pi$
$12$	−2.61892	−0.756017
$13$	1.31735	0.365367	0.182684	−	0.983172i	$-0.441522\pi$
$13$	1.31735	0.365367	0.182684	+	0.983172i	$0.441522\pi$
$14$	−4.49129	−1.20035
$15$	−10.3166	−2.66373
$16$	1.00000	0.250000
$17$	3.74127	0.907392	0.453696	−	0.891157i	$-0.350105\pi$
$17$	3.74127	0.907392	0.453696	+	0.891157i	$0.350105\pi$
$18$	−3.85875	−0.909516
$19$	−0.785058	−0.180105	−0.0900523	−	0.995937i	$-0.528703\pi$
$19$	−0.785058	−0.180105	−0.0900523	+	0.995937i	$0.528703\pi$
$20$	3.93925	0.880842
$21$	−11.7623	−2.56675
$22$	−5.80663	−1.23798
$23$	−2.51635	−0.524695	−0.262347	−	0.964973i	$-0.584497\pi$
$23$	−2.51635	−0.524695	−0.262347	+	0.964973i	$0.584497\pi$
$24$	2.61892	0.534585
$25$	10.5177	2.10353
$26$	−1.31735	−0.258353
$27$	−2.24900	−0.432820
$28$	4.49129	0.848774
$29$	−8.02017	−1.48931	−0.744655	−	0.667450i	$-0.767386\pi$
$29$	−8.02017	−1.48931	−0.744655	+	0.667450i	$0.767386\pi$
$30$	10.3166	1.88354
$31$	−6.32906	−1.13673	−0.568366	−	0.822776i	$-0.692424\pi$
$31$	−6.32906	−1.13673	−0.568366	+	0.822776i	$0.692424\pi$
$32$	−1.00000	−0.176777
$33$	−15.2071	−2.64722
$34$	−3.74127	−0.641623
$35$	17.6923	2.99054
$36$	3.85875	0.643125
$37$	−0.903346	−0.148509	−0.0742546	−	0.997239i	$-0.523658\pi$
$37$	−0.903346	−0.148509	−0.0742546	+	0.997239i	$0.523658\pi$
$38$	0.785058	0.127353
$39$	−3.45003	−0.552448
$40$	−3.93925	−0.622850
$41$	−3.99569	−0.624022	−0.312011	−	0.950078i	$-0.601003\pi$
$41$	−3.99569	−0.624022	−0.312011	+	0.950078i	$0.601003\pi$
$42$	11.7623	1.81497
$43$	−1.69467	−0.258434	−0.129217	−	0.991616i	$-0.541246\pi$
$43$	−1.69467	−0.258434	−0.129217	+	0.991616i	$0.541246\pi$
$44$	5.80663	0.875383
$45$	15.2006	2.26597
$46$	2.51635	0.371015
$47$	0.775534	0.113123	0.0565616	−	0.998399i	$-0.481986\pi$
$47$	0.775534	0.113123	0.0565616	+	0.998399i	$0.481986\pi$
$48$	−2.61892	−0.378009
$49$	13.1717	1.88167
$50$	−10.5177	−1.48742
$51$	−9.79810	−1.37201
$52$	1.31735	0.182684
$53$	−2.69823	−0.370631	−0.185315	−	0.982679i	$-0.559331\pi$
$53$	−2.69823	−0.370631	−0.185315	+	0.982679i	$0.559331\pi$
$54$	2.24900	0.306050
$55$	22.8738	3.08430
$56$	−4.49129	−0.600174
$57$	2.05600	0.272324
$58$	8.02017	1.05310
$59$	−5.88473	−0.766126	−0.383063	−	0.923722i	$-0.625131\pi$
$59$	−5.88473	−0.766126	−0.383063	+	0.923722i	$0.625131\pi$
$60$	−10.3166	−1.33186
$61$	−8.50789	−1.08932	−0.544662	−	0.838656i	$-0.683342\pi$
$61$	−8.50789	−1.08932	−0.544662	+	0.838656i	$0.683342\pi$
$62$	6.32906	0.803791
$63$	17.3308	2.18347
$64$	1.00000	0.125000
$65$	5.18936	0.643661
$66$	15.2071	1.87187
$67$	4.96827	0.606971	0.303486	−	0.952836i	$-0.401850\pi$
$67$	4.96827	0.606971	0.303486	+	0.952836i	$0.401850\pi$
$68$	3.74127	0.453696
$69$	6.59012	0.793357
$70$	−17.6923	−2.11463
$71$	9.60610	1.14003	0.570017	−	0.821633i	$-0.306937\pi$
$71$	9.60610	1.14003	0.570017	+	0.821633i	$0.306937\pi$
$72$	−3.85875	−0.454758
$73$	2.19639	0.257068	0.128534	−	0.991705i	$-0.458973\pi$
$73$	2.19639	0.257068	0.128534	+	0.991705i	$0.458973\pi$
$74$	0.903346	0.105012
$75$	−27.5449	−3.18062
$76$	−0.785058	−0.0900523
$77$	26.0793	2.97201
$78$	3.45003	0.390640
$79$	5.64803	0.635453	0.317727	−	0.948182i	$-0.397081\pi$
$79$	5.64803	0.635453	0.317727	+	0.948182i	$0.397081\pi$
$80$	3.93925	0.440421
$81$	−5.68630	−0.631811
$82$	3.99569	0.441250
$83$	13.3294	1.46309	0.731545	−	0.681794i	$-0.238800\pi$
$83$	13.3294	1.46309	0.731545	+	0.681794i	$0.238800\pi$
$84$	−11.7623	−1.28338
$85$	14.7378	1.59854
$86$	1.69467	0.182740
$87$	21.0042	2.25189
$88$	−5.80663	−0.618989
$89$	4.02482	0.426630	0.213315	−	0.976983i	$-0.431574\pi$
$89$	4.02482	0.426630	0.213315	+	0.976983i	$0.431574\pi$
$90$	−15.2006	−1.60228
$91$	5.91660	0.620228
$92$	−2.51635	−0.262347
$93$	16.5753	1.71878
$94$	−0.775534	−0.0799902
$95$	−3.09254	−0.317288
$96$	2.61892	0.267293
$97$	−9.30063	−0.944336	−0.472168	−	0.881509i	$-0.656528\pi$
$97$	−9.30063	−0.944336	−0.472168	+	0.881509i	$0.656528\pi$
$98$	−13.1717	−1.33054
$99$	22.4063	2.25192
$100$	10.5177	1.05177
$101$	−10.4995	−1.04474	−0.522370	−	0.852719i	$-0.674952\pi$
$101$	−10.4995	−1.04474	−0.522370	+	0.852719i	$0.674952\pi$
$102$	9.79810	0.970156
$103$	−14.2734	−1.40640	−0.703202	−	0.710990i	$-0.748247\pi$
$103$	−14.2734	−1.40640	−0.703202	+	0.710990i	$0.748247\pi$
$104$	−1.31735	−0.129177
$105$	−46.3347	−4.52181
$106$	2.69823	0.262076
$107$	11.8800	1.14849	0.574244	−	0.818684i	$-0.305296\pi$
$107$	11.8800	1.14849	0.574244	+	0.818684i	$0.305296\pi$
$108$	−2.24900	−0.216410
$109$	17.8709	1.71172	0.855860	−	0.517207i	$-0.173028\pi$
$109$	17.8709	1.71172	0.855860	+	0.517207i	$0.173028\pi$
$110$	−22.8738	−2.18093
$111$	2.36579	0.224551
$112$	4.49129	0.424387
$113$	5.44622	0.512338	0.256169	−	0.966632i	$-0.417540\pi$
$113$	5.44622	0.512338	0.256169	+	0.966632i	$0.417540\pi$
$114$	−2.05600	−0.192562
$115$	−9.91251	−0.924347
$116$	−8.02017	−0.744655
$117$	5.08332	0.469953
$118$	5.88473	0.541733
$119$	16.8031	1.54034
$120$	10.3166	0.941770
$121$	22.7170	2.06518
$122$	8.50789	0.770268
$123$	10.4644	0.943544
$124$	−6.32906	−0.568366
$125$	21.7354	1.94408
$126$	−17.3308	−1.54395
$127$	8.57632	0.761026	0.380513	−	0.924776i	$-0.375747\pi$
$127$	8.57632	0.761026	0.380513	+	0.924776i	$0.375747\pi$
$128$	−1.00000	−0.0883883
$129$	4.43819	0.390761
$130$	−5.18936	−0.455137
$131$	16.6809	1.45741	0.728707	−	0.684825i	$-0.240122\pi$
$131$	16.6809	1.45741	0.728707	+	0.684825i	$0.240122\pi$
$132$	−15.2071	−1.32361
$133$	−3.52592	−0.305736
$134$	−4.96827	−0.429193
$135$	−8.85935	−0.762492
$136$	−3.74127	−0.320811
$137$	0.305861	0.0261315	0.0130658	−	0.999915i	$-0.495841\pi$
$137$	0.305861	0.0261315	0.0130658	+	0.999915i	$0.495841\pi$
$138$	−6.59012	−0.560988
$139$	20.0524	1.70082	0.850409	−	0.526122i	$-0.176354\pi$
$139$	20.0524	1.70082	0.850409	+	0.526122i	$0.176354\pi$
$140$	17.6923	1.49527
$141$	−2.03106	−0.171046
$142$	−9.60610	−0.806126
$143$	7.64936	0.639672
$144$	3.85875	0.321562
$145$	−31.5934	−2.62369
$146$	−2.19639	−0.181775
$147$	−34.4956	−2.84515
$148$	−0.903346	−0.0742546
$149$	−15.6107	−1.27888	−0.639441	−	0.768840i	$-0.720834\pi$
$149$	−15.6107	−1.27888	−0.639441	+	0.768840i	$0.720834\pi$
$150$	27.5449	2.24903
$151$	−1.76779	−0.143861	−0.0719304	−	0.997410i	$-0.522916\pi$
$151$	−1.76779	−0.143861	−0.0719304	+	0.997410i	$0.522916\pi$
$152$	0.785058	0.0636766
$153$	14.4366	1.16713
$154$	−26.0793	−2.10153
$155$	−24.9317	−2.00256
$156$	−3.45003	−0.276224
$157$	4.59100	0.366401	0.183201	−	0.983076i	$-0.441354\pi$
$157$	4.59100	0.366401	0.183201	+	0.983076i	$0.441354\pi$
$158$	−5.64803	−0.449333
$159$	7.06646	0.560407
$160$	−3.93925	−0.311425
$161$	−11.3016	−0.890694
$162$	5.68630	0.446758
$163$	−21.6568	−1.69629	−0.848145	−	0.529765i	$-0.822280\pi$
$163$	−21.6568	−1.69629	−0.848145	+	0.529765i	$0.822280\pi$
$164$	−3.99569	−0.312011
$165$	−59.9046	−4.66356
$166$	−13.3294	−1.03456
$167$	8.64005	0.668587	0.334294	−	0.942469i	$-0.391502\pi$
$167$	8.64005	0.668587	0.334294	+	0.942469i	$0.391502\pi$
$168$	11.7623	0.907484
$169$	−11.2646	−0.866507
$170$	−14.7378	−1.13034
$171$	−3.02934	−0.231660
$172$	−1.69467	−0.129217
$173$	15.8586	1.20571	0.602854	−	0.797851i	$-0.294030\pi$
$173$	15.8586	1.20571	0.602854	+	0.797851i	$0.294030\pi$
$174$	−21.0042	−1.59232
$175$	47.2379	3.57085
$176$	5.80663	0.437691
$177$	15.4116	1.15841
$178$	−4.02482	−0.301673
$179$	−4.08226	−0.305122	−0.152561	−	0.988294i	$-0.548752\pi$
$179$	−4.08226	−0.305122	−0.152561	+	0.988294i	$0.548752\pi$
$180$	15.2006	1.13298
$181$	18.5624	1.37973	0.689867	−	0.723936i	$-0.257669\pi$
$181$	18.5624	1.37973	0.689867	+	0.723936i	$0.257669\pi$
$182$	−5.91660	−0.438567
$183$	22.2815	1.64709
$184$	2.51635	0.185508
$185$	−3.55850	−0.261626
$186$	−16.5753	−1.21536
$187$	21.7242	1.58863
$188$	0.775534	0.0565616
$189$	−10.1009	−0.734732
$190$	3.09254	0.224356
$191$	−0.173461	−0.0125512	−0.00627560	−	0.999980i	$-0.501998\pi$
$191$	−0.173461	−0.0125512	−0.00627560	+	0.999980i	$0.501998\pi$
$192$	−2.61892	−0.189004
$193$	7.10113	0.511151	0.255575	−	0.966789i	$-0.417735\pi$
$193$	7.10113	0.511151	0.255575	+	0.966789i	$0.417735\pi$
$194$	9.30063	0.667746
$195$	−13.5905	−0.973239
$196$	13.1717	0.940834
$197$	3.58474	0.255402	0.127701	−	0.991813i	$-0.459240\pi$
$197$	3.58474	0.255402	0.127701	+	0.991813i	$0.459240\pi$
$198$	−22.4063	−1.59235
$199$	24.5937	1.74340	0.871702	−	0.490036i	$-0.163016\pi$
$199$	24.5937	1.74340	0.871702	+	0.490036i	$0.163016\pi$
$200$	−10.5177	−0.743711
$201$	−13.0115	−0.917761
$202$	10.4995	0.738743
$203$	−36.0209	−2.52817
$204$	−9.79810	−0.686004
$205$	−15.7400	−1.09933
$206$	14.2734	0.994478
$207$	−9.70995	−0.674889
$208$	1.31735	0.0913418
$209$	−4.55854	−0.315321
$210$	46.3347	3.19740
$211$	5.34388	0.367888	0.183944	−	0.982937i	$-0.441114\pi$
$211$	5.34388	0.367888	0.183944	+	0.982937i	$0.441114\pi$
$212$	−2.69823	−0.185315
$213$	−25.1576	−1.72377
$214$	−11.8800	−0.812103
$215$	−6.67570	−0.455279
$216$	2.24900	0.153025
$217$	−28.4256	−1.92966
$218$	−17.8709	−1.21037
$219$	−5.75218	−0.388696
$220$	22.8738	1.54215
$221$	4.92856	0.331531
$222$	−2.36579	−0.158782
$223$	−24.5402	−1.64333	−0.821665	−	0.569970i	$-0.806955\pi$
$223$	−24.5402	−1.64333	−0.821665	+	0.569970i	$0.806955\pi$
$224$	−4.49129	−0.300087
$225$	40.5850	2.70567
$226$	−5.44622	−0.362277
$227$	−12.4526	−0.826509	−0.413254	−	0.910616i	$-0.635608\pi$
$227$	−12.4526	−0.826509	−0.413254	+	0.910616i	$0.635608\pi$
$228$	2.05600	0.136162
$229$	17.7035	1.16988	0.584940	−	0.811077i	$-0.301118\pi$
$229$	17.7035	1.16988	0.584940	+	0.811077i	$0.301118\pi$
$230$	9.91251	0.653612
$231$	−68.2995	−4.49378
$232$	8.02017	0.526550
$233$	−14.9519	−0.979529	−0.489764	−	0.871855i	$-0.662917\pi$
$233$	−14.9519	−0.979529	−0.489764	+	0.871855i	$0.662917\pi$
$234$	−5.08332	−0.332307
$235$	3.05502	0.199287
$236$	−5.88473	−0.383063
$237$	−14.7918	−0.960827
$238$	−16.8031	−1.08919
$239$	4.23479	0.273926	0.136963	−	0.990576i	$-0.456266\pi$
$239$	4.23479	0.273926	0.136963	+	0.990576i	$0.456266\pi$
$240$	−10.3166	−0.665932
$241$	−1.51363	−0.0975013	−0.0487506	−	0.998811i	$-0.515524\pi$
$241$	−1.51363	−0.0975013	−0.0487506	+	0.998811i	$0.515524\pi$
$242$	−22.7170	−1.46030
$243$	21.6390	1.38814
$244$	−8.50789	−0.544662
$245$	51.8865	3.31491
$246$	−10.4644	−0.667186
$247$	−1.03420	−0.0658043
$248$	6.32906	0.401896
$249$	−34.9086	−2.21224
$250$	−21.7354	−1.37467
$251$	7.20428	0.454730	0.227365	−	0.973810i	$-0.426989\pi$
$251$	7.20428	0.454730	0.227365	+	0.973810i	$0.426989\pi$
$252$	17.3308	1.09174
$253$	−14.6115	−0.918618
$254$	−8.57632	−0.538126
$255$	−38.5971	−2.41705
$256$	1.00000	0.0625000
$257$	16.4328	1.02505	0.512525	−	0.858673i	$-0.328710\pi$
$257$	16.4328	1.02505	0.512525	+	0.858673i	$0.328710\pi$
$258$	−4.43819	−0.276310
$259$	−4.05719	−0.252101
$260$	5.18936	0.321831
$261$	−30.9478	−1.91562
$262$	−16.6809	−1.03055
$263$	−28.2197	−1.74010	−0.870050	−	0.492964i	$-0.835913\pi$
$263$	−28.2197	−1.74010	−0.870050	+	0.492964i	$0.835913\pi$
$264$	15.2071	0.935933
$265$	−10.6290	−0.652935
$266$	3.52592	0.216188
$267$	−10.5407	−0.645079
$268$	4.96827	0.303486
$269$	13.8702	0.845682	0.422841	−	0.906204i	$-0.361033\pi$
$269$	13.8702	0.845682	0.422841	+	0.906204i	$0.361033\pi$
$270$	8.85935	0.539163
$271$	−2.69146	−0.163494	−0.0817472	−	0.996653i	$-0.526050\pi$
$271$	−2.69146	−0.163494	−0.0817472	+	0.996653i	$0.526050\pi$
$272$	3.74127	0.226848
$273$	−15.4951	−0.937806
$274$	−0.305861	−0.0184778
$275$	61.0722	3.68279
$276$	6.59012	0.396678
$277$	−13.5538	−0.814370	−0.407185	−	0.913346i	$-0.633490\pi$
$277$	−13.5538	−0.814370	−0.407185	+	0.913346i	$0.633490\pi$
$278$	−20.0524	−1.20266
$279$	−24.4222	−1.46212
$280$	−17.6923	−1.05732
$281$	5.75940	0.343577	0.171789	−	0.985134i	$-0.445045\pi$
$281$	5.75940	0.343577	0.171789	+	0.985134i	$0.445045\pi$
$282$	2.03106	0.120948
$283$	−0.495341	−0.0294450	−0.0147225	−	0.999892i	$-0.504686\pi$
$283$	−0.495341	−0.0294450	−0.0147225	+	0.999892i	$0.504686\pi$
$284$	9.60610	0.570017
$285$	8.09911	0.479750
$286$	−7.64936	−0.452316
$287$	−17.9458	−1.05931
$288$	−3.85875	−0.227379
$289$	−3.00289	−0.176640
$290$	31.5934	1.85523
$291$	24.3576	1.42787
$292$	2.19639	0.128534
$293$	−31.2968	−1.82838	−0.914190	−	0.405286i	$-0.867172\pi$
$293$	−31.2968	−1.82838	−0.914190	+	0.405286i	$0.867172\pi$
$294$	34.4956	2.01182
$295$	−23.1814	−1.34967
$296$	0.903346	0.0525059
$297$	−13.0591	−0.757766
$298$	15.6107	0.904306
$299$	−3.31491	−0.191706
$300$	−27.5449	−1.59031
$301$	−7.61123	−0.438704
$302$	1.76779	0.101725
$303$	27.4974	1.57968
$304$	−0.785058	−0.0450262
$305$	−33.5147	−1.91904
$306$	−14.4366	−0.825287
$307$	25.7558	1.46996	0.734982	−	0.678087i	$-0.237191\pi$
$307$	25.7558	1.46996	0.734982	+	0.678087i	$0.237191\pi$
$308$	26.0793	1.48600
$309$	37.3810	2.12653
$310$	24.9317	1.41603
$311$	−0.562789	−0.0319128	−0.0159564	−	0.999873i	$-0.505079\pi$
$311$	−0.562789	−0.0319128	−0.0159564	+	0.999873i	$0.505079\pi$
$312$	3.45003	0.195320
$313$	−11.9982	−0.678177	−0.339089	−	0.940754i	$-0.610119\pi$
$313$	−11.9982	−0.678177	−0.339089	+	0.940754i	$0.610119\pi$
$314$	−4.59100	−0.259085
$315$	68.2701	3.84659
$316$	5.64803	0.317727
$317$	−22.5185	−1.26477	−0.632383	−	0.774656i	$-0.717923\pi$
$317$	−22.5185	−1.26477	−0.632383	+	0.774656i	$0.717923\pi$
$318$	−7.06646	−0.396267
$319$	−46.5702	−2.60743
$320$	3.93925	0.220211
$321$	−31.1129	−1.73655
$322$	11.3016	0.629816
$323$	−2.93711	−0.163425
$324$	−5.68630	−0.315906
$325$	13.8554	0.768562
$326$	21.6568	1.19946
$327$	−46.8025	−2.58818
$328$	3.99569	0.220625
$329$	3.48315	0.192032
$330$	59.9046	3.29764
$331$	17.0821	0.938919	0.469459	−	0.882954i	$-0.344449\pi$
$331$	17.0821	0.938919	0.469459	+	0.882954i	$0.344449\pi$
$332$	13.3294	0.731545
$333$	−3.48578	−0.191020
$334$	−8.64005	−0.472763
$335$	19.5712	1.06929
$336$	−11.7623	−0.641688
$337$	15.5298	0.845961	0.422981	−	0.906139i	$-0.360984\pi$
$337$	15.5298	0.845961	0.422981	+	0.906139i	$0.360984\pi$
$338$	11.2646	0.612713
$339$	−14.2632	−0.774672
$340$	14.7378	0.799269
$341$	−36.7505	−1.99015
$342$	3.02934	0.163808
$343$	27.7188	1.49667
$344$	1.69467	0.0913702
$345$	25.9601	1.39764
$346$	−15.8586	−0.852565
$347$	−4.31902	−0.231857	−0.115929	−	0.993258i	$-0.536984\pi$
$347$	−4.31902	−0.231857	−0.115929	+	0.993258i	$0.536984\pi$
$348$	21.0042	1.12594
$349$	−13.6162	−0.728857	−0.364428	−	0.931231i	$-0.618736\pi$
$349$	−13.6162	−0.728857	−0.364428	+	0.931231i	$0.618736\pi$
$350$	−47.2379	−2.52497
$351$	−2.96271	−0.158138
$352$	−5.80663	−0.309495
$353$	26.2903	1.39929	0.699646	−	0.714490i	$-0.253341\pi$
$353$	26.2903	1.39929	0.699646	+	0.714490i	$0.253341\pi$
$354$	−15.4116	−0.819119
$355$	37.8408	2.00838
$356$	4.02482	0.213315
$357$	−44.0061	−2.32905
$358$	4.08226	0.215754
$359$	36.3495	1.91845	0.959226	−	0.282640i	$-0.0912101\pi$
$359$	36.3495	1.91845	0.959226	+	0.282640i	$0.0912101\pi$
$360$	−15.2006	−0.801140
$361$	−18.3837	−0.967562
$362$	−18.5624	−0.975619
$363$	−59.4940	−3.12262
$364$	5.91660	0.310114
$365$	8.65214	0.452873
$366$	−22.2815	−1.16467
$367$	22.7602	1.18807	0.594036	−	0.804439i	$-0.297534\pi$
$367$	22.7602	1.18807	0.594036	+	0.804439i	$0.297534\pi$
$368$	−2.51635	−0.131174
$369$	−15.4184	−0.802649
$370$	3.55850	0.184998
$371$	−12.1185	−0.629163
$372$	16.5753	0.859390
$373$	3.41185	0.176659	0.0883293	−	0.996091i	$-0.471847\pi$
$373$	3.41185	0.176659	0.0883293	+	0.996091i	$0.471847\pi$
$374$	−21.7242	−1.12333
$375$	−56.9234	−2.93951
$376$	−0.775534	−0.0399951
$377$	−10.5654	−0.544144
$378$	10.1009	0.519534
$379$	21.7039	1.11485	0.557426	−	0.830227i	$-0.311789\pi$
$379$	21.7039	1.11485	0.557426	+	0.830227i	$0.311789\pi$
$380$	−3.09254	−0.158644
$381$	−22.4607	−1.15070
$382$	0.173461	0.00887505
$383$	−33.1799	−1.69541	−0.847707	−	0.530464i	$-0.822018\pi$
$383$	−33.1799	−1.69541	−0.847707	+	0.530464i	$0.822018\pi$
$384$	2.61892	0.133646
$385$	102.733	5.23574
$386$	−7.10113	−0.361438
$387$	−6.53929	−0.332411
$388$	−9.30063	−0.472168
$389$	−27.9554	−1.41739	−0.708697	−	0.705513i	$-0.750717\pi$
$389$	−27.9554	−1.41739	−0.708697	+	0.705513i	$0.750717\pi$
$390$	13.5905	0.688184
$391$	−9.41434	−0.476104
$392$	−13.1717	−0.665270
$393$	−43.6859	−2.20366
$394$	−3.58474	−0.180596
$395$	22.2490	1.11947
$396$	22.4063	1.12596
$397$	−3.70520	−0.185959	−0.0929793	−	0.995668i	$-0.529639\pi$
$397$	−3.70520	−0.185959	−0.0929793	+	0.995668i	$0.529639\pi$
$398$	−24.5937	−1.23277
$399$	9.23411	0.462284
$400$	10.5177	0.525883
$401$	−6.45469	−0.322332	−0.161166	−	0.986927i	$-0.551525\pi$
$401$	−6.45469	−0.322332	−0.161166	+	0.986927i	$0.551525\pi$
$402$	13.0115	0.648955
$403$	−8.33758	−0.415324
$404$	−10.4995	−0.522370
$405$	−22.3997	−1.11305
$406$	36.0209	1.78769
$407$	−5.24540	−0.260005
$408$	9.79810	0.485078
$409$	17.4727	0.863972	0.431986	−	0.901880i	$-0.357813\pi$
$409$	17.4727	0.863972	0.431986	+	0.901880i	$0.357813\pi$
$410$	15.7400	0.777344
$411$	−0.801027	−0.0395117
$412$	−14.2734	−0.703202
$413$	−26.4300	−1.30054
$414$	9.70995	0.477218
$415$	52.5077	2.57750
$416$	−1.31735	−0.0645884
$417$	−52.5155	−2.57170
$418$	4.55854	0.222966
$419$	28.0410	1.36989	0.684945	−	0.728595i	$-0.259826\pi$
$419$	28.0410	1.36989	0.684945	+	0.728595i	$0.259826\pi$
$420$	−46.3347	−2.26090
$421$	−22.2883	−1.08626	−0.543132	−	0.839647i	$-0.682762\pi$
$421$	−22.2883	−1.08626	−0.543132	+	0.839647i	$0.682762\pi$
$422$	−5.34388	−0.260136
$423$	2.99259	0.145505
$424$	2.69823	0.131038
$425$	39.3494	1.90873
$426$	25.1576	1.21889
$427$	−38.2114	−1.84918
$428$	11.8800	0.574244
$429$	−20.0331	−0.967206
$430$	6.67570	0.321931
$431$	16.6018	0.799683	0.399841	−	0.916584i	$-0.369065\pi$
$431$	16.6018	0.799683	0.399841	+	0.916584i	$0.369065\pi$
$432$	−2.24900	−0.108205
$433$	−0.467978	−0.0224896	−0.0112448	−	0.999937i	$-0.503579\pi$
$433$	−0.467978	−0.0224896	−0.0112448	+	0.999937i	$0.503579\pi$
$434$	28.4256	1.36447
$435$	82.7408	3.96712
$436$	17.8709	0.855860
$437$	1.97548	0.0944999
$438$	5.75218	0.274850
$439$	−10.4103	−0.496856	−0.248428	−	0.968650i	$-0.579914\pi$
$439$	−10.4103	−0.496856	−0.248428	+	0.968650i	$0.579914\pi$
$440$	−22.8738	−1.09046
$441$	50.8262	2.42029
$442$	−4.92856	−0.234428
$443$	36.1159	1.71592	0.857958	−	0.513719i	$-0.171733\pi$
$443$	36.1159	1.71592	0.857958	+	0.513719i	$0.171733\pi$
$444$	2.36579	0.112275
$445$	15.8548	0.751587
$446$	24.5402	1.16201
$447$	40.8833	1.93371
$448$	4.49129	0.212193
$449$	−10.9373	−0.516164	−0.258082	−	0.966123i	$-0.583090\pi$
$449$	−10.9373	−0.516164	−0.258082	+	0.966123i	$0.583090\pi$
$450$	−40.5850	−1.91320
$451$	−23.2015	−1.09252
$452$	5.44622	0.256169
$453$	4.62970	0.217522
$454$	12.4526	0.584430
$455$	23.3069	1.09265
$456$	−2.05600	−0.0962812
$457$	4.38538	0.205139	0.102570	−	0.994726i	$-0.467294\pi$
$457$	4.38538	0.205139	0.102570	+	0.994726i	$0.467294\pi$
$458$	−17.7035	−0.827230
$459$	−8.41411	−0.392737
$460$	−9.91251	−0.462173
$461$	−17.5097	−0.815506	−0.407753	−	0.913092i	$-0.633688\pi$
$461$	−17.5097	−0.815506	−0.407753	+	0.913092i	$0.633688\pi$
$462$	68.2995	3.17758
$463$	16.3906	0.761736	0.380868	−	0.924630i	$-0.375625\pi$
$463$	16.3906	0.761736	0.380868	+	0.924630i	$0.375625\pi$
$464$	−8.02017	−0.372327
$465$	65.2942	3.02795
$466$	14.9519	0.692631
$467$	−16.3675	−0.757398	−0.378699	−	0.925520i	$-0.623628\pi$
$467$	−16.3675	−0.757398	−0.378699	+	0.925520i	$0.623628\pi$
$468$	5.08332	0.234977
$469$	22.3139	1.03036
$470$	−3.05502	−0.140917
$471$	−12.0235	−0.554012
$472$	5.88473	0.270867
$473$	−9.84030	−0.452457
$474$	14.7918	0.679408
$475$	−8.25697	−0.378856
$476$	16.8031	0.770170
$477$	−10.4118	−0.476724
$478$	−4.23479	−0.193695
$479$	37.5219	1.71442	0.857210	−	0.514968i	$-0.172196\pi$
$479$	37.5219	1.71442	0.857210	+	0.514968i	$0.172196\pi$
$480$	10.3166	0.470885
$481$	−1.19002	−0.0542603
$482$	1.51363	0.0689438
$483$	29.5981	1.34676
$484$	22.7170	1.03259
$485$	−36.6375	−1.66362
$486$	−21.6390	−0.981564
$487$	0.368631	0.0167043	0.00835214	−	0.999965i	$-0.497341\pi$
$487$	0.368631	0.0167043	0.00835214	+	0.999965i	$0.497341\pi$
$488$	8.50789	0.385134
$489$	56.7174	2.56485
$490$	−51.8865	−2.34399
$491$	6.63968	0.299645	0.149822	−	0.988713i	$-0.452130\pi$
$491$	6.63968	0.299645	0.149822	+	0.988713i	$0.452130\pi$
$492$	10.4644	0.471772
$493$	−30.0057	−1.35139
$494$	1.03420	0.0465307
$495$	88.2641	3.96718
$496$	−6.32906	−0.284183
$497$	43.1438	1.93526
$498$	34.9086	1.56429
$499$	−21.8303	−0.977260	−0.488630	−	0.872491i	$-0.662503\pi$
$499$	−21.8303	−0.977260	−0.488630	+	0.872491i	$0.662503\pi$
$500$	21.7354	0.972038
$501$	−22.6276	−1.01093
$502$	−7.20428	−0.321543
$503$	−15.2880	−0.681657	−0.340829	−	0.940125i	$-0.610708\pi$
$503$	−15.2880	−0.681657	−0.340829	+	0.940125i	$0.610708\pi$
$504$	−17.3308	−0.771973
$505$	−41.3601	−1.84050
$506$	14.6115	0.649561
$507$	29.5011	1.31019
$508$	8.57632	0.380513
$509$	34.8476	1.54459	0.772296	−	0.635263i	$-0.219108\pi$
$509$	34.8476	1.54459	0.772296	+	0.635263i	$0.219108\pi$
$510$	38.5971	1.70911
$511$	9.86464	0.436386
$512$	−1.00000	−0.0441942
$513$	1.76559	0.0779528
$514$	−16.4328	−0.724819
$515$	−56.2266	−2.47764
$516$	4.43819	0.195381
$517$	4.50324	0.198052
$518$	4.05719	0.178263
$519$	−41.5325	−1.82307
$520$	−5.18936	−0.227569
$521$	24.4079	1.06933	0.534665	−	0.845064i	$-0.320438\pi$
$521$	24.4079	1.06933	0.534665	+	0.845064i	$0.320438\pi$
$522$	30.9478	1.35455
$523$	4.66973	0.204193	0.102097	−	0.994774i	$-0.467445\pi$
$523$	4.66973	0.204193	0.102097	+	0.994774i	$0.467445\pi$
$524$	16.6809	0.728707
$525$	−123.712	−5.39925
$526$	28.2197	1.23044
$527$	−23.6787	−1.03146
$528$	−15.2071	−0.661805
$529$	−16.6680	−0.724695
$530$	10.6290	0.461695
$531$	−22.7077	−0.985430
$532$	−3.52592	−0.152868
$533$	−5.26372	−0.227997
$534$	10.5407	0.456140
$535$	46.7984	2.02327
$536$	−4.96827	−0.214597
$537$	10.6911	0.461356
$538$	−13.8702	−0.597988
$539$	76.4831	3.29436
$540$	−8.85935	−0.381246
$541$	20.9264	0.899695	0.449847	−	0.893105i	$-0.351478\pi$
$541$	20.9264	0.899695	0.449847	+	0.893105i	$0.351478\pi$
$542$	2.69146	0.115608
$543$	−48.6135	−2.08621
$544$	−3.74127	−0.160406
$545$	70.3978	3.01551
$546$	15.4951	0.663129
$547$	19.7536	0.844601	0.422300	−	0.906456i	$-0.361223\pi$
$547$	19.7536	0.844601	0.422300	+	0.906456i	$0.361223\pi$
$548$	0.305861	0.0130658
$549$	−32.8298	−1.40114
$550$	−61.0722	−2.60413
$551$	6.29630	0.268231
$552$	−6.59012	−0.280494
$553$	25.3669	1.07871
$554$	13.5538	0.575846
$555$	9.31944	0.395588
$556$	20.0524	0.850409
$557$	0.641436	0.0271785	0.0135893	−	0.999908i	$-0.495674\pi$
$557$	0.641436	0.0271785	0.0135893	+	0.999908i	$0.495674\pi$
$558$	24.4222	1.03388
$559$	−2.23247	−0.0944233
$560$	17.6923	0.747636
$561$	−56.8939	−2.40206
$562$	−5.75940	−0.242946
$563$	25.5551	1.07702	0.538510	−	0.842619i	$-0.318988\pi$
$563$	25.5551	1.07702	0.538510	+	0.842619i	$0.318988\pi$
$564$	−2.03106	−0.0855231
$565$	21.4540	0.902577
$566$	0.495341	0.0208208
$567$	−25.5388	−1.07253
$568$	−9.60610	−0.403063
$569$	13.2757	0.556548	0.278274	−	0.960502i	$-0.410238\pi$
$569$	13.2757	0.556548	0.278274	+	0.960502i	$0.410238\pi$
$570$	−8.09911	−0.339234
$571$	16.9557	0.709573	0.354786	−	0.934947i	$-0.384554\pi$
$571$	16.9557	0.709573	0.354786	+	0.934947i	$0.384554\pi$
$572$	7.64936	0.319836
$573$	0.454281	0.0189779
$574$	17.9458	0.749044
$575$	−26.4661	−1.10371
$576$	3.85875	0.160781
$577$	−42.8275	−1.78293	−0.891467	−	0.453086i	$-0.850323\pi$
$577$	−42.8275	−1.78293	−0.891467	+	0.453086i	$0.850323\pi$
$578$	3.00289	0.124904
$579$	−18.5973	−0.772878
$580$	−31.5934	−1.31185
$581$	59.8661	2.48366
$582$	−24.3576	−1.00966
$583$	−15.6676	−0.648888
$584$	−2.19639	−0.0908874
$585$	20.0245	0.827909
$586$	31.2968	1.29286
$587$	−43.4651	−1.79400	−0.896998	−	0.442035i	$-0.854257\pi$
$587$	−43.4651	−1.79400	−0.896998	+	0.442035i	$0.854257\pi$
$588$	−34.4956	−1.42257
$589$	4.96868	0.204731
$590$	23.1814	0.954363
$591$	−9.38815	−0.386177
$592$	−0.903346	−0.0371273
$593$	39.8746	1.63745	0.818727	−	0.574184i	$-0.194680\pi$
$593$	39.8746	1.63745	0.818727	+	0.574184i	$0.194680\pi$
$594$	13.0591	0.535821
$595$	66.1917	2.71359
$596$	−15.6107	−0.639441
$597$	−64.4091	−2.63609
$598$	3.31491	0.135557
$599$	31.3258	1.27994	0.639969	−	0.768400i	$-0.278947\pi$
$599$	31.3258	1.27994	0.639969	+	0.768400i	$0.278947\pi$
$600$	27.5449	1.12452
$601$	−36.7477	−1.49897	−0.749486	−	0.662021i	$-0.769699\pi$
$601$	−36.7477	−1.49897	−0.749486	+	0.662021i	$0.769699\pi$
$602$	7.61123	0.310211
$603$	19.1713	0.780716
$604$	−1.76779	−0.0719304
$605$	89.4878	3.63820
$606$	−27.4974	−1.11700
$607$	−27.3214	−1.10894	−0.554471	−	0.832203i	$-0.687079\pi$
$607$	−27.3214	−1.10894	−0.554471	+	0.832203i	$0.687079\pi$
$608$	0.785058	0.0318383
$609$	94.3360	3.82269
$610$	33.5147	1.35697
$611$	1.02165	0.0413315
$612$	14.4366	0.583566
$613$	−22.8699	−0.923707	−0.461853	−	0.886956i	$-0.652815\pi$
$613$	−22.8699	−0.923707	−0.461853	+	0.886956i	$0.652815\pi$
$614$	−25.7558	−1.03942
$615$	41.2219	1.66223
$616$	−26.0793	−1.05076
$617$	14.1183	0.568381	0.284190	−	0.958768i	$-0.408275\pi$
$617$	14.1183	0.568381	0.284190	+	0.958768i	$0.408275\pi$
$618$	−37.3810	−1.50369
$619$	17.1045	0.687487	0.343743	−	0.939064i	$-0.388305\pi$
$619$	17.1045	0.687487	0.343743	+	0.939064i	$0.388305\pi$
$620$	−24.9317	−1.00128
$621$	5.65926	0.227098
$622$	0.562789	0.0225658
$623$	18.0766	0.724225
$624$	−3.45003	−0.138112
$625$	33.0329	1.32132
$626$	11.9982	0.479544
$627$	11.9385	0.476776
$628$	4.59100	0.183201
$629$	−3.37966	−0.134756
$630$	−68.2701	−2.71995
$631$	−9.67213	−0.385042	−0.192521	−	0.981293i	$-0.561666\pi$
$631$	−9.67213	−0.385042	−0.192521	+	0.981293i	$0.561666\pi$
$632$	−5.64803	−0.224667
$633$	−13.9952	−0.556259
$634$	22.5185	0.894324
$635$	33.7843	1.34069
$636$	7.06646	0.280203
$637$	17.3517	0.687499
$638$	46.5702	1.84373
$639$	37.0675	1.46637
$640$	−3.93925	−0.155712
$641$	6.46957	0.255533	0.127766	−	0.991804i	$-0.459219\pi$
$641$	6.46957	0.255533	0.127766	+	0.991804i	$0.459219\pi$
$642$	31.1129	1.22793
$643$	−3.96516	−0.156371	−0.0781853	−	0.996939i	$-0.524913\pi$
$643$	−3.96516	−0.156371	−0.0781853	+	0.996939i	$0.524913\pi$
$644$	−11.3016	−0.445347
$645$	17.4831	0.688398
$646$	2.93711	0.115559
$647$	−21.7916	−0.856715	−0.428357	−	0.903609i	$-0.640908\pi$
$647$	−21.7916	−0.856715	−0.428357	+	0.903609i	$0.640908\pi$
$648$	5.68630	0.223379
$649$	−34.1705	−1.34131
$650$	−13.8554	−0.543455
$651$	74.4445	2.91771
$652$	−21.6568	−0.848145
$653$	1.90959	0.0747281	0.0373640	−	0.999302i	$-0.488104\pi$
$653$	1.90959	0.0747281	0.0373640	+	0.999302i	$0.488104\pi$
$654$	46.8025	1.83012
$655$	65.7101	2.56750
$656$	−3.99569	−0.156006
$657$	8.47533	0.330654
$658$	−3.48315	−0.135787
$659$	−13.7157	−0.534289	−0.267145	−	0.963656i	$-0.586080\pi$
$659$	−13.7157	−0.534289	−0.267145	+	0.963656i	$0.586080\pi$
$660$	−59.9046	−2.33178
$661$	−8.02743	−0.312231	−0.156115	−	0.987739i	$-0.549897\pi$
$661$	−8.02743	−0.312231	−0.156115	+	0.987739i	$0.549897\pi$
$662$	−17.0821	−0.663916
$663$	−12.9075	−0.501286
$664$	−13.3294	−0.517280
$665$	−13.8895	−0.538611
$666$	3.48578	0.135071
$667$	20.1815	0.781433
$668$	8.64005	0.334294
$669$	64.2687	2.48477
$670$	−19.5712	−0.756103
$671$	−49.4022	−1.90715
$672$	11.7623	0.453742
$673$	21.5201	0.829539	0.414769	−	0.909927i	$-0.363862\pi$
$673$	21.5201	0.829539	0.414769	+	0.909927i	$0.363862\pi$
$674$	−15.5298	−0.598185
$675$	−23.6542	−0.910450
$676$	−11.2646	−0.433253
$677$	−2.39900	−0.0922011	−0.0461005	−	0.998937i	$-0.514679\pi$
$677$	−2.39900	−0.0922011	−0.0461005	+	0.998937i	$0.514679\pi$
$678$	14.2632	0.547776
$679$	−41.7718	−1.60306
$680$	−14.7378	−0.565169
$681$	32.6124	1.24971
$682$	36.7505	1.40725
$683$	−2.36206	−0.0903816	−0.0451908	−	0.998978i	$-0.514390\pi$
$683$	−2.36206	−0.0903816	−0.0451908	+	0.998978i	$0.514390\pi$
$684$	−3.02934	−0.115830
$685$	1.20486	0.0460355
$686$	−27.7188	−1.05831
$687$	−46.3640	−1.76890
$688$	−1.69467	−0.0646085
$689$	−3.55452	−0.135416
$690$	−25.9601	−0.988284
$691$	20.8899	0.794690	0.397345	−	0.917669i	$-0.369932\pi$
$691$	20.8899	0.794690	0.397345	+	0.917669i	$0.369932\pi$
$692$	15.8586	0.602854
$693$	100.633	3.82274
$694$	4.31902	0.163948
$695$	78.9912	2.99631
$696$	−21.0042	−0.796162
$697$	−14.9490	−0.566233
$698$	13.6162	0.515380
$699$	39.1577	1.48108
$700$	47.2379	1.78542
$701$	−31.2848	−1.18161	−0.590805	−	0.806815i	$-0.701190\pi$
$701$	−31.2848	−1.18161	−0.590805	+	0.806815i	$0.701190\pi$
$702$	2.96271	0.111820
$703$	0.709179	0.0267472
$704$	5.80663	0.218846
$705$	−8.00085	−0.301330
$706$	−26.2903	−0.989449
$707$	−47.1563	−1.77350
$708$	15.4116	0.579205
$709$	−15.3499	−0.576478	−0.288239	−	0.957558i	$-0.593070\pi$
$709$	−15.3499	−0.576478	−0.288239	+	0.957558i	$0.593070\pi$
$710$	−37.8408	−1.42014
$711$	21.7943	0.817351
$712$	−4.02482	−0.150836
$713$	15.9261	0.596438
$714$	44.0061	1.64689
$715$	30.1327	1.12690
$716$	−4.08226	−0.152561
$717$	−11.0906	−0.414186
$718$	−36.3495	−1.35655
$719$	25.4130	0.947744	0.473872	−	0.880594i	$-0.342856\pi$
$719$	25.4130	0.947744	0.473872	+	0.880594i	$0.342856\pi$
$720$	15.2006	0.566492
$721$	−64.1062	−2.38744
$722$	18.3837	0.684170
$723$	3.96407	0.147425
$724$	18.5624	0.689867
$725$	−84.3535	−3.13281
$726$	59.4940	2.20803
$727$	−36.1460	−1.34058	−0.670290	−	0.742099i	$-0.733830\pi$
$727$	−36.1460	−1.34058	−0.670290	+	0.742099i	$0.733830\pi$
$728$	−5.91660	−0.219284
$729$	−39.6119	−1.46711
$730$	−8.65214	−0.320230
$731$	−6.34020	−0.234501
$732$	22.2815	0.823547
$733$	−19.7336	−0.728877	−0.364439	−	0.931227i	$-0.618739\pi$
$733$	−19.7336	−0.728877	−0.364439	+	0.931227i	$0.618739\pi$
$734$	−22.7602	−0.840094
$735$	−135.887	−5.01225
$736$	2.51635	0.0927538
$737$	28.8489	1.06266
$738$	15.4184	0.567558
$739$	−31.4767	−1.15789	−0.578944	−	0.815367i	$-0.696535\pi$
$739$	−31.4767	−1.15789	−0.578944	+	0.815367i	$0.696535\pi$
$740$	−3.55850	−0.130813
$741$	2.70848	0.0994984
$742$	12.1185	0.444886
$743$	−0.336155	−0.0123323	−0.00616617	−	0.999981i	$-0.501963\pi$
$743$	−0.336155	−0.0123323	−0.00616617	+	0.999981i	$0.501963\pi$
$744$	−16.5753	−0.607680
$745$	−61.4946	−2.25299
$746$	−3.41185	−0.124917
$747$	51.4347	1.88190
$748$	21.7242	0.794315
$749$	53.3567	1.94961
$750$	56.9234	2.07855
$751$	33.8598	1.23556	0.617781	−	0.786351i	$-0.288032\pi$
$751$	33.8598	1.23556	0.617781	+	0.786351i	$0.288032\pi$
$752$	0.775534	0.0282808
$753$	−18.8675	−0.687568
$754$	10.5654	0.384768
$755$	−6.96376	−0.253437
$756$	−10.1009	−0.367366
$757$	−47.9539	−1.74291	−0.871457	−	0.490473i	$-0.836824\pi$
$757$	−47.9539	−1.74291	−0.871457	+	0.490473i	$0.836824\pi$
$758$	−21.7039	−0.788320
$759$	38.2664	1.38898
$760$	3.09254	0.112178
$761$	−8.78050	−0.318293	−0.159146	−	0.987255i	$-0.550874\pi$
$761$	−8.78050	−0.318293	−0.159146	+	0.987255i	$0.550874\pi$
$762$	22.4607	0.813666
$763$	80.2633	2.90573
$764$	−0.173461	−0.00627560
$765$	56.8694	2.05612
$766$	33.1799	1.19884
$767$	−7.75224	−0.279917
$768$	−2.61892	−0.0945022
$769$	−49.1059	−1.77080	−0.885402	−	0.464825i	$-0.846117\pi$
$769$	−49.1059	−1.77080	−0.885402	+	0.464825i	$0.846117\pi$
$770$	−102.733	−3.70223
$771$	−43.0362	−1.54991
$772$	7.10113	0.255575
$773$	−31.9935	−1.15073	−0.575364	−	0.817898i	$-0.695139\pi$
$773$	−31.9935	−1.15073	−0.575364	+	0.817898i	$0.695139\pi$
$774$	6.53929	0.235050
$775$	−66.5669	−2.39115
$776$	9.30063	0.333873
$777$	10.6255	0.381186
$778$	27.9554	1.00225
$779$	3.13685	0.112389
$780$	−13.5905	−0.486619
$781$	55.7791	1.99593
$782$	9.41434	0.336656
$783$	18.0373	0.644602
$784$	13.1717	0.470417
$785$	18.0851	0.645484
$786$	43.6859	1.55822
$787$	50.1550	1.78783	0.893916	−	0.448234i	$-0.147947\pi$
$787$	50.1550	1.78783	0.893916	+	0.448234i	$0.147947\pi$
$788$	3.58474	0.127701
$789$	73.9051	2.63109
$790$	−22.2490	−0.791583
$791$	24.4606	0.869718
$792$	−22.4063	−0.796175
$793$	−11.2079	−0.398003
$794$	3.70520	0.131493
$795$	27.8365	0.987260
$796$	24.5937	0.871702
$797$	1.72404	0.0610688	0.0305344	−	0.999534i	$-0.490279\pi$
$797$	1.72404	0.0610688	0.0305344	+	0.999534i	$0.490279\pi$
$798$	−9.23411	−0.326884
$799$	2.90148	0.102647
$800$	−10.5177	−0.371856
$801$	15.5308	0.548753
$802$	6.45469	0.227923
$803$	12.7536	0.450067
$804$	−13.0115	−0.458881
$805$	−44.5200	−1.56912
$806$	8.33758	0.293679
$807$	−36.3250	−1.27870
$808$	10.4995	0.369371
$809$	−39.7731	−1.39835	−0.699174	−	0.714951i	$-0.746449\pi$
$809$	−39.7731	−1.39835	−0.699174	+	0.714951i	$0.746449\pi$
$810$	22.3997	0.787047
$811$	44.5173	1.56322	0.781608	−	0.623770i	$-0.214400\pi$
$811$	44.5173	1.56322	0.781608	+	0.623770i	$0.214400\pi$
$812$	−36.0209	−1.26409
$813$	7.04871	0.247209
$814$	5.24540	0.183851
$815$	−85.3114	−2.98833
$816$	−9.79810	−0.343002
$817$	1.33041	0.0465452
$818$	−17.4727	−0.610920
$819$	22.8307	0.797768
$820$	−15.7400	−0.549665
$821$	40.7223	1.42122	0.710609	−	0.703587i	$-0.248420\pi$
$821$	40.7223	1.42122	0.710609	+	0.703587i	$0.248420\pi$
$822$	0.801027	0.0279390
$823$	−52.3799	−1.82585	−0.912924	−	0.408130i	$-0.866181\pi$
$823$	−52.3799	−1.82585	−0.912924	+	0.408130i	$0.866181\pi$
$824$	14.2734	0.497239
$825$	−159.943	−5.56851
$826$	26.4300	0.919618
$827$	−16.3342	−0.567996	−0.283998	−	0.958825i	$-0.591661\pi$
$827$	−16.3342	−0.567996	−0.283998	+	0.958825i	$0.591661\pi$
$828$	−9.70995	−0.337444
$829$	−53.4146	−1.85517	−0.927584	−	0.373615i	$-0.878118\pi$
$829$	−53.4146	−1.85517	−0.927584	+	0.373615i	$0.878118\pi$
$830$	−52.5077	−1.82257
$831$	35.4964	1.23136
$832$	1.31735	0.0456709
$833$	49.2788	1.70741
$834$	52.5155	1.81846
$835$	34.0353	1.17784
$836$	−4.55854	−0.157660
$837$	14.2340	0.492000
$838$	−28.0410	−0.968659
$839$	−37.4908	−1.29433	−0.647163	−	0.762352i	$-0.724045\pi$
$839$	−37.4908	−1.29433	−0.647163	+	0.762352i	$0.724045\pi$
$840$	46.3347	1.59870
$841$	35.3232	1.21804
$842$	22.2883	0.768105
$843$	−15.0834	−0.519501
$844$	5.34388	0.183944
$845$	−44.3740	−1.52651
$846$	−2.99259	−0.102887
$847$	102.029	3.50574
$848$	−2.69823	−0.0926577
$849$	1.29726	0.0445219
$850$	−39.3494	−1.34967
$851$	2.27313	0.0779220
$852$	−25.1576	−0.861886
$853$	−49.9306	−1.70959	−0.854795	−	0.518966i	$-0.826317\pi$
$853$	−49.9306	−1.70959	−0.854795	+	0.518966i	$0.826317\pi$
$854$	38.2114	1.30757
$855$	−11.9333	−0.408111
$856$	−11.8800	−0.406052
$857$	3.51508	0.120073	0.0600364	−	0.998196i	$-0.480878\pi$
$857$	3.51508	0.120073	0.0600364	+	0.998196i	$0.480878\pi$
$858$	20.0331	0.683918
$859$	6.19496	0.211369	0.105685	−	0.994400i	$-0.466297\pi$
$859$	6.19496	0.211369	0.105685	+	0.994400i	$0.466297\pi$
$860$	−6.67570	−0.227640
$861$	46.9987	1.60171
$862$	−16.6018	−0.565461
$863$	37.3932	1.27288	0.636439	−	0.771327i	$-0.280407\pi$
$863$	37.3932	1.27288	0.636439	+	0.771327i	$0.280407\pi$
$864$	2.24900	0.0765124
$865$	62.4710	2.12408
$866$	0.467978	0.0159025
$867$	7.86433	0.267086
$868$	−28.4256	−0.964829
$869$	32.7960	1.11253
$870$	−82.7408	−2.80517
$871$	6.54495	0.221767
$872$	−17.8709	−0.605185
$873$	−35.8888	−1.21465
$874$	−1.97548	−0.0668216
$875$	97.6201	3.30016
$876$	−5.75218	−0.194348
$877$	−6.59902	−0.222833	−0.111417	−	0.993774i	$-0.535539\pi$
$877$	−6.59902	−0.222833	−0.111417	+	0.993774i	$0.535539\pi$
$878$	10.4103	0.351330
$879$	81.9639	2.76457
$880$	22.8738	0.771074
$881$	12.1538	0.409473	0.204736	−	0.978817i	$-0.434366\pi$
$881$	12.1538	0.409473	0.204736	+	0.978817i	$0.434366\pi$
$882$	−50.8262	−1.71141
$883$	−33.4057	−1.12419	−0.562096	−	0.827072i	$-0.690005\pi$
$883$	−33.4057	−1.12419	−0.562096	+	0.827072i	$0.690005\pi$
$884$	4.92856	0.165765
$885$	60.7103	2.04075
$886$	−36.1159	−1.21334
$887$	−46.5167	−1.56188	−0.780940	−	0.624606i	$-0.785259\pi$
$887$	−46.5167	−1.56188	−0.780940	+	0.624606i	$0.785259\pi$
$888$	−2.36579	−0.0793908
$889$	38.5187	1.29188
$890$	−15.8548	−0.531453
$891$	−33.0183	−1.10615
$892$	−24.5402	−0.821665
$893$	−0.608839	−0.0203740
$894$	−40.8833	−1.36734
$895$	−16.0810	−0.537529
$896$	−4.49129	−0.150043
$897$	8.68149	0.289866
$898$	10.9373	0.364983
$899$	50.7601	1.69295
$900$	40.5850	1.35283
$901$	−10.0948	−0.336307
$902$	23.2015	0.772526
$903$	19.9332	0.663336
$904$	−5.44622	−0.181139
$905$	73.1219	2.43066
$906$	−4.62970	−0.153812
$907$	−48.8661	−1.62257	−0.811285	−	0.584650i	$-0.801232\pi$
$907$	−48.8661	−1.62257	−0.811285	+	0.584650i	$0.801232\pi$
$908$	−12.4526	−0.413254
$909$	−40.5150	−1.34380
$910$	−23.3069	−0.772617
$911$	3.68425	0.122065	0.0610324	−	0.998136i	$-0.480561\pi$
$911$	3.68425	0.122065	0.0610324	+	0.998136i	$0.480561\pi$
$912$	2.05600	0.0680811
$913$	77.3988	2.56153
$914$	−4.38538	−0.145056
$915$	87.7723	2.90166
$916$	17.7035	0.584940
$917$	74.9186	2.47403
$918$	8.41411	0.277707
$919$	−11.2758	−0.371955	−0.185977	−	0.982554i	$-0.559545\pi$
$919$	−11.2758	−0.371955	−0.185977	+	0.982554i	$0.559545\pi$
$920$	9.91251	0.326806
$921$	−67.4525	−2.22264
$922$	17.5097	0.576650
$923$	12.6546	0.416531
$924$	−68.2995	−2.24689
$925$	−9.50109	−0.312394
$926$	−16.3906	−0.538628
$927$	−55.0777	−1.80899
$928$	8.02017	0.263275
$929$	25.6730	0.842305	0.421152	−	0.906990i	$-0.361626\pi$
$929$	25.6730	0.842305	0.421152	+	0.906990i	$0.361626\pi$
$930$	−65.2942	−2.14108
$931$	−10.3405	−0.338897
$932$	−14.9519	−0.489764
$933$	1.47390	0.0482533
$934$	16.3675	0.535561
$935$	85.5769	2.79867
$936$	−5.08332	−0.166154
$937$	−23.0281	−0.752295	−0.376148	−	0.926560i	$-0.622751\pi$
$937$	−23.0281	−0.752295	−0.376148	+	0.926560i	$0.622751\pi$
$938$	−22.3139	−0.728576
$939$	31.4223	1.02543
$940$	3.05502	0.0996437
$941$	15.1953	0.495354	0.247677	−	0.968843i	$-0.420333\pi$
$941$	15.1953	0.495354	0.247677	+	0.968843i	$0.420333\pi$
$942$	12.0235	0.391745
$943$	10.0546	0.327421
$944$	−5.88473	−0.191532
$945$	−39.7899	−1.29437
$946$	9.84030	0.319936
$947$	−17.2013	−0.558968	−0.279484	−	0.960150i	$-0.590163\pi$
$947$	−17.2013	−0.558968	−0.279484	+	0.960150i	$0.590163\pi$
$948$	−14.7918	−0.480414
$949$	2.89342	0.0939243
$950$	8.25697	0.267892
$951$	58.9742	1.91237
$952$	−16.8031	−0.544593
$953$	37.7876	1.22406	0.612030	−	0.790835i	$-0.290353\pi$
$953$	37.7876	1.22406	0.612030	+	0.790835i	$0.290353\pi$
$954$	10.4118	0.337095
$955$	−0.683306	−0.0221113
$956$	4.23479	0.136963
$957$	121.964	3.94253
$958$	−37.5219	−1.21228
$959$	1.37371	0.0443595
$960$	−10.3166	−0.332966
$961$	9.05697	0.292160
$962$	1.19002	0.0383678
$963$	45.8421	1.47724
$964$	−1.51363	−0.0487506
$965$	27.9731	0.900486
$966$	−29.5981	−0.952304
$967$	36.9990	1.18981	0.594904	−	0.803797i	$-0.297190\pi$
$967$	36.9990	1.18981	0.594904	+	0.803797i	$0.297190\pi$
$968$	−22.7170	−0.730151
$969$	7.69207	0.247105
$970$	36.6375	1.17636
$971$	10.9705	0.352062	0.176031	−	0.984385i	$-0.443674\pi$
$971$	10.9705	0.352062	0.176031	+	0.984385i	$0.443674\pi$
$972$	21.6390	0.694070
$973$	90.0609	2.88722
$974$	−0.368631	−0.0118117
$975$	−36.2863	−1.16209
$976$	−8.50789	−0.272331
$977$	38.0702	1.21797	0.608987	−	0.793180i	$-0.291576\pi$
$977$	38.0702	1.21797	0.608987	+	0.793180i	$0.291576\pi$
$978$	−56.7174	−1.81362
$979$	23.3706	0.746929
$980$	51.8865	1.65745
$981$	68.9593	2.20170
$982$	−6.63968	−0.211881
$983$	−26.8617	−0.856754	−0.428377	−	0.903600i	$-0.640914\pi$
$983$	−26.8617	−0.856754	−0.428377	+	0.903600i	$0.640914\pi$
$984$	−10.4644	−0.333593
$985$	14.1212	0.449938
$986$	30.0057	0.955575
$987$	−9.12208	−0.290359
$988$	−1.03420	−0.0329021
$989$	4.26437	0.135599
$990$	−88.2641	−2.80522
$991$	18.9557	0.602147	0.301074	−	0.953601i	$-0.402655\pi$
$991$	18.9557	0.602147	0.301074	+	0.953601i	$0.402655\pi$
$992$	6.32906	0.200948
$993$	−44.7368	−1.41968
$994$	−43.1438	−1.36844
$995$	96.8808	3.07133
$996$	−34.9086	−1.10612
$997$	−27.8092	−0.880725	−0.440363	−	0.897820i	$-0.645150\pi$
$997$	−27.8092	−0.880725	−0.440363	+	0.897820i	$0.645150\pi$
$998$	21.8303	0.691027
$999$	2.03162	0.0642777

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.c.1.11	✓	86

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.c.1.11	✓	86	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.61892 q^{3} +1.00000 q^{4} +3.93925 q^{5} +2.61892 q^{6} +4.49129 q^{7} -1.00000 q^{8} +3.85875 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.61892 q^{3} +1.00000 q^{4} +3.93925 q^{5} +2.61892 q^{6} +4.49129 q^{7} -1.00000 q^{8} +3.85875 q^{9} -3.93925 q^{10} +5.80663 q^{11} -2.61892 q^{12} +1.31735 q^{13} -4.49129 q^{14} -10.3166 q^{15} +1.00000 q^{16} +3.74127 q^{17} -3.85875 q^{18} -0.785058 q^{19} +3.93925 q^{20} -11.7623 q^{21} -5.80663 q^{22} -2.51635 q^{23} +2.61892 q^{24} +10.5177 q^{25} -1.31735 q^{26} -2.24900 q^{27} +4.49129 q^{28} -8.02017 q^{29} +10.3166 q^{30} -6.32906 q^{31} -1.00000 q^{32} -15.2071 q^{33} -3.74127 q^{34} +17.6923 q^{35} +3.85875 q^{36} -0.903346 q^{37} +0.785058 q^{38} -3.45003 q^{39} -3.93925 q^{40} -3.99569 q^{41} +11.7623 q^{42} -1.69467 q^{43} +5.80663 q^{44} +15.2006 q^{45} +2.51635 q^{46} +0.775534 q^{47} -2.61892 q^{48} +13.1717 q^{49} -10.5177 q^{50} -9.79810 q^{51} +1.31735 q^{52} -2.69823 q^{53} +2.24900 q^{54} +22.8738 q^{55} -4.49129 q^{56} +2.05600 q^{57} +8.02017 q^{58} -5.88473 q^{59} -10.3166 q^{60} -8.50789 q^{61} +6.32906 q^{62} +17.3308 q^{63} +1.00000 q^{64} +5.18936 q^{65} +15.2071 q^{66} +4.96827 q^{67} +3.74127 q^{68} +6.59012 q^{69} -17.6923 q^{70} +9.60610 q^{71} -3.85875 q^{72} +2.19639 q^{73} +0.903346 q^{74} -27.5449 q^{75} -0.785058 q^{76} +26.0793 q^{77} +3.45003 q^{78} +5.64803 q^{79} +3.93925 q^{80} -5.68630 q^{81} +3.99569 q^{82} +13.3294 q^{83} -11.7623 q^{84} +14.7378 q^{85} +1.69467 q^{86} +21.0042 q^{87} -5.80663 q^{88} +4.02482 q^{89} -15.2006 q^{90} +5.91660 q^{91} -2.51635 q^{92} +16.5753 q^{93} -0.775534 q^{94} -3.09254 q^{95} +2.61892 q^{96} -9.30063 q^{97} -13.1717 q^{98} +22.4063 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * q^99

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